LMFDB - Embedded newform 429.2.j.a.122.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.10
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37738 - 1.37738i) q^{2} +(1.00936 + 1.40755i) q^{3} +1.79436i q^{4} +(2.82918 + 2.82918i) q^{5} +(0.548456 - 3.32900i) q^{6} +(-0.289134 - 0.289134i) q^{7} +(-0.283251 + 0.283251i) q^{8} +(-0.962383 + 2.84145i) q^{9} +O(q^{10})$	\(q+(-1.37738 - 1.37738i) q^{2} +(1.00936 + 1.40755i) q^{3} +1.79436i q^{4} +(2.82918 + 2.82918i) q^{5} +(0.548456 - 3.32900i) q^{6} +(-0.289134 - 0.289134i) q^{7} +(-0.283251 + 0.283251i) q^{8} +(-0.962383 + 2.84145i) q^{9} -7.79370i q^{10} +(0.707107 - 0.707107i) q^{11} +(-2.52564 + 1.81115i) q^{12} +(3.17441 - 1.70971i) q^{13} +0.796496i q^{14} +(-1.12654 + 6.83786i) q^{15} +4.36900 q^{16} -4.12916 q^{17} +(5.23932 - 2.58819i) q^{18} +(-4.10478 + 4.10478i) q^{19} +(-5.07655 + 5.07655i) q^{20} +(0.115130 - 0.698811i) q^{21} -1.94791 q^{22} -0.872109 q^{23} +(-0.684591 - 0.112787i) q^{24} +11.0085i q^{25} +(-6.72729 - 2.01746i) q^{26} +(-4.97086 + 1.51344i) q^{27} +(0.518810 - 0.518810i) q^{28} +0.158120i q^{29} +(10.9700 - 7.86666i) q^{30} +(1.76143 - 1.76143i) q^{31} +(-5.45127 - 5.45127i) q^{32} +(1.70901 + 0.281561i) q^{33} +(5.68742 + 5.68742i) q^{34} -1.63602i q^{35} +(-5.09857 - 1.72686i) q^{36} +(6.69080 + 6.69080i) q^{37} +11.3077 q^{38} +(5.61062 + 2.74243i) q^{39} -1.60273 q^{40} +(4.78874 + 4.78874i) q^{41} +(-1.12111 + 0.803952i) q^{42} -4.70673i q^{43} +(1.26880 + 1.26880i) q^{44} +(-10.7617 + 5.31620i) q^{45} +(1.20123 + 1.20123i) q^{46} +(6.11141 - 6.11141i) q^{47} +(4.40990 + 6.14958i) q^{48} -6.83280i q^{49} +(15.1628 - 15.1628i) q^{50} +(-4.16781 - 5.81199i) q^{51} +(3.06782 + 5.69603i) q^{52} -13.4294i q^{53} +(8.93136 + 4.76218i) q^{54} +4.00106 q^{55} +0.163795 q^{56} +(-9.92088 - 1.63447i) q^{57} +(0.217792 - 0.217792i) q^{58} +(-4.64558 + 4.64558i) q^{59} +(-12.2695 - 2.02142i) q^{60} +7.54626 q^{61} -4.85231 q^{62} +(1.09982 - 0.543302i) q^{63} +6.27896i q^{64} +(13.8180 + 4.14392i) q^{65} +(-1.96614 - 2.74178i) q^{66} +(-6.51845 + 6.51845i) q^{67} -7.40918i q^{68} +(-0.880272 - 1.22754i) q^{69} +(-2.25343 + 2.25343i) q^{70} +(-6.54495 - 6.54495i) q^{71} +(-0.532246 - 1.07744i) q^{72} +(4.03257 + 4.03257i) q^{73} -18.4315i q^{74} +(-15.4949 + 11.1115i) q^{75} +(-7.36544 - 7.36544i) q^{76} -0.408898 q^{77} +(-3.95059 - 11.5053i) q^{78} +8.13040 q^{79} +(12.3607 + 12.3607i) q^{80} +(-7.14764 - 5.46912i) q^{81} -13.1918i q^{82} +(7.36350 + 7.36350i) q^{83} +(1.25392 + 0.206584i) q^{84} +(-11.6821 - 11.6821i) q^{85} +(-6.48296 + 6.48296i) q^{86} +(-0.222562 + 0.159601i) q^{87} +0.400577i q^{88} +(-4.20906 + 4.20906i) q^{89} +(22.1454 + 7.50053i) q^{90} +(-1.41217 - 0.423498i) q^{91} -1.56487i q^{92} +(4.25721 + 0.701378i) q^{93} -16.8355 q^{94} -23.2263 q^{95} +(2.17063 - 13.1752i) q^{96} +(7.98446 - 7.98446i) q^{97} +(-9.41137 + 9.41137i) q^{98} +(1.32870 + 2.68971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.37738	−	1.37738i	−0.973955	−	0.973955i	0.0257141	−	0.999669i	$-0.491814\pi$
$2$	−1.37738	−	1.37738i	−0.973955	−	0.973955i	−0.999669	+	0.0257141i	$0.991814\pi$
$3$	1.00936	+	1.40755i	0.582755	+	0.812648i
$3$	1.00936	+	1.40755i	0.582755	+	0.812648i
$4$			1.79436i			0.897178i
$5$	2.82918	+	2.82918i	1.26525	+	1.26525i	0.948516	+	0.316730i	$0.102585\pi$
$5$	2.82918	+	2.82918i	1.26525	+	1.26525i	0.316730	+	0.948516i	$0.397415\pi$
$6$	0.548456	−	3.32900i	0.223906	−	1.35906i
$7$	−0.289134	−	0.289134i	−0.109283	−	0.109283i	0.650351	−	0.759634i	$-0.274622\pi$
$7$	−0.289134	−	0.289134i	−0.109283	−	0.109283i	−0.759634	+	0.650351i	$0.774622\pi$
$8$	−0.283251	+	0.283251i	−0.100144	+	0.100144i
$9$	−0.962383	+	2.84145i	−0.320794	+	0.947149i
$10$		−	7.79370i		−	2.46459i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	−2.52564	+	1.81115i	−0.729090	+	0.522834i
$13$	3.17441	−	1.70971i	0.880424	−	0.474187i
$13$	3.17441	−	1.70971i	0.880424	−	0.474187i
$14$			0.796496i			0.212873i
$15$	−1.12654	+	6.83786i	−0.290872	+	1.76553i
$16$	4.36900			1.09225
$17$	−4.12916			−1.00147			−0.500734	−	0.865601i	$-0.666937\pi$
$17$	−4.12916			−1.00147			−0.500734	+	0.865601i	$0.666937\pi$
$18$	5.23932	−	2.58819i	1.23492	−	0.610041i
$19$	−4.10478	+	4.10478i	−0.941701	+	0.941701i	−0.998392	−	0.0566904i	$-0.981945\pi$
$19$	−4.10478	+	4.10478i	−0.941701	+	0.941701i	0.0566904	+	0.998392i	$0.481945\pi$
$20$	−5.07655	+	5.07655i	−1.13515	+	1.13515i
$21$	0.115130	−	0.698811i	0.0251234	−	0.152493i
$22$	−1.94791			−0.415296
$23$	−0.872109			−0.181847			−0.0909237	−	0.995858i	$-0.528982\pi$
$23$	−0.872109			−0.181847			−0.0909237	+	0.995858i	$0.528982\pi$
$24$	−0.684591	−	0.112787i	−0.139742	−	0.0230225i
$25$			11.0085i			2.20169i
$26$	−6.72729	−	2.01746i	−1.31933	−	0.395657i
$27$	−4.97086	+	1.51344i	−0.956643	+	0.291262i
$28$	0.518810	−	0.518810i	0.0980458	−	0.0980458i
$29$			0.158120i			0.0293622i	0.999892	+	0.0146811i	$0.00467331\pi$
$29$			0.158120i			0.0293622i	−0.999892	+	0.0146811i	$0.995327\pi$
$30$	10.9700	−	7.86666i	2.00284	−	1.43625i
$31$	1.76143	−	1.76143i	0.316362	−	0.316362i	−0.531006	−	0.847368i	$-0.678186\pi$
$31$	1.76143	−	1.76143i	0.316362	−	0.316362i	0.847368	+	0.531006i	$0.178186\pi$
$32$	−5.45127	−	5.45127i	−0.963658	−	0.963658i
$33$	1.70901	+	0.281561i	0.297501	+	0.0490135i
$34$	5.68742	+	5.68742i	0.975385	+	0.975385i
$35$		−	1.63602i		−	0.276538i
$36$	−5.09857	−	1.72686i	−0.849761	−	0.287810i
$37$	6.69080	+	6.69080i	1.09996	+	1.09996i	0.994414	+	0.105546i	$0.0336590\pi$
$37$	6.69080	+	6.69080i	1.09996	+	1.09996i	0.105546	+	0.994414i	$0.466341\pi$
$38$	11.3077			1.83435
$39$	5.61062	+	2.74243i	0.898418	+	0.439141i
$40$	−1.60273			−0.253414
$41$	4.78874	+	4.78874i	0.747876	+	0.747876i	0.974080	−	0.226204i	$-0.0726317\pi$
$41$	4.78874	+	4.78874i	0.747876	+	0.747876i	−0.226204	+	0.974080i	$0.572632\pi$
$42$	−1.12111	+	0.803952i	−0.172990	+	0.124052i
$43$		−	4.70673i		−	0.717770i	−0.933382	−	0.358885i	$-0.883157\pi$
$43$		−	4.70673i		−	0.717770i	0.933382	−	0.358885i	$-0.116843\pi$
$44$	1.26880	+	1.26880i	0.191279	+	0.191279i
$45$	−10.7617	+	5.31620i	−1.60426	+	0.792492i
$46$	1.20123	+	1.20123i	0.177111	+	0.177111i
$47$	6.11141	−	6.11141i	0.891441	−	0.891441i	−0.103217	−	0.994659i	$-0.532914\pi$
$47$	6.11141	−	6.11141i	0.891441	−	0.891441i	0.994659	+	0.103217i	$0.0329137\pi$
$48$	4.40990	+	6.14958i	0.636514	+	0.887615i
$49$		−	6.83280i		−	0.976115i
$50$	15.1628	−	15.1628i	2.14435	−	2.14435i
$51$	−4.16781	−	5.81199i	−0.583610	−	0.813841i
$52$	3.06782	+	5.69603i	0.425430	+	0.789897i
$53$		−	13.4294i		−	1.84467i	−0.386389	−	0.922336i	$-0.626278\pi$
$53$		−	13.4294i		−	1.84467i	0.386389	−	0.922336i	$-0.373722\pi$
$54$	8.93136	+	4.76218i	1.21540	+	0.648051i
$55$	4.00106			0.539503
$56$	0.163795			0.0218880
$57$	−9.92088	−	1.63447i	−1.31405	−	0.216491i
$58$	0.217792	−	0.217792i	0.0285975	−	0.0285975i
$59$	−4.64558	+	4.64558i	−0.604803	+	0.604803i	−0.941583	−	0.336780i	$-0.890662\pi$
$59$	−4.64558	+	4.64558i	−0.604803	+	0.604803i	0.336780	+	0.941583i	$0.390662\pi$
$60$	−12.2695	−	2.02142i	−1.58399	−	0.260964i
$61$	7.54626			0.966199			0.483100	−	0.875565i	$-0.339511\pi$
$61$	7.54626			0.966199			0.483100	+	0.875565i	$0.339511\pi$
$62$	−4.85231			−0.616244
$63$	1.09982	−	0.543302i	0.138564	−	0.0684496i
$64$			6.27896i			0.784870i
$65$	13.8180	+	4.14392i	1.71392	+	0.513990i
$66$	−1.96614	−	2.74178i	−0.242016	−	0.337490i
$67$	−6.51845	+	6.51845i	−0.796355	+	0.796355i	−0.982519	−	0.186163i	$-0.940395\pi$
$67$	−6.51845	+	6.51845i	−0.796355	+	0.796355i	0.186163	+	0.982519i	$0.440395\pi$
$68$		−	7.40918i		−	0.898495i
$69$	−0.880272	−	1.22754i	−0.105972	−	0.147778i
$70$	−2.25343	+	2.25343i	−0.269336	+	0.269336i
$71$	−6.54495	−	6.54495i	−0.776742	−	0.776742i	0.202533	−	0.979275i	$-0.435083\pi$
$71$	−6.54495	−	6.54495i	−0.776742	−	0.776742i	−0.979275	+	0.202533i	$0.935083\pi$
$72$	−0.532246	−	1.07744i	−0.0627258	−	0.126977i
$73$	4.03257	+	4.03257i	0.471977	+	0.471977i	0.902554	−	0.430577i	$-0.141690\pi$
$73$	4.03257	+	4.03257i	0.471977	+	0.471977i	−0.430577	+	0.902554i	$0.641690\pi$
$74$		−	18.4315i		−	2.14262i
$75$	−15.4949	+	11.1115i	−1.78920	+	1.28305i
$76$	−7.36544	−	7.36544i	−0.844874	−	0.844874i
$77$	−0.408898			−0.0465982
$78$	−3.95059	−	11.5053i	−0.447316	−	1.30272i
$79$	8.13040			0.914741			0.457370	−	0.889276i	$-0.348791\pi$
$79$	8.13040			0.914741			0.457370	+	0.889276i	$0.348791\pi$
$80$	12.3607	+	12.3607i	1.38196	+	1.38196i
$81$	−7.14764	−	5.46912i	−0.794182	−	0.607680i
$82$		−	13.1918i		−	1.45679i
$83$	7.36350	+	7.36350i	0.808250	+	0.808250i	0.984369	−	0.176119i	$-0.0563544\pi$
$83$	7.36350	+	7.36350i	0.808250	+	0.808250i	−0.176119	+	0.984369i	$0.556354\pi$
$84$	1.25392	+	0.206584i	0.136813	+	0.0225401i
$85$	−11.6821	−	11.6821i	−1.26710	−	1.26710i
$86$	−6.48296	+	6.48296i	−0.699076	+	0.699076i
$87$	−0.222562	+	0.159601i	−0.0238612	+	0.0171110i
$88$			0.400577i			0.0427016i
$89$	−4.20906	+	4.20906i	−0.446160	+	0.446160i	−0.894076	−	0.447916i	$-0.852166\pi$
$89$	−4.20906	+	4.20906i	−0.446160	+	0.446160i	0.447916	+	0.894076i	$0.352166\pi$
$90$	22.1454	+	7.50053i	2.33433	+	0.790625i
$91$	−1.41217	−	0.423498i	−0.148035	−	0.0443946i
$92$		−	1.56487i		−	0.163149i
$93$	4.25721	+	0.701378i	0.441452	+	0.0727295i
$94$	−16.8355			−1.73645
$95$	−23.2263			−2.38297
$96$	2.17063	−	13.1752i	0.221539	−	1.34469i
$97$	7.98446	−	7.98446i	0.810699	−	0.810699i	−0.174040	−	0.984739i	$-0.555682\pi$
$97$	7.98446	−	7.98446i	0.810699	−	0.810699i	0.984739	+	0.174040i	$0.0556821\pi$
$98$	−9.41137	+	9.41137i	−0.950692	+	0.950692i
$99$	1.32870	+	2.68971i	0.133539	+	0.270326i
$100$	−19.7531			−1.97531
$101$	0.364314			0.0362506			0.0181253	−	0.999836i	$-0.494230\pi$
$101$	0.364314			0.0362506			0.0181253	+	0.999836i	$0.494230\pi$
$102$	−2.26466	+	13.7460i	−0.224235	+	1.36105i
$103$		−	6.78283i		−	0.668332i	−0.942514	−	0.334166i	$-0.891545\pi$
$103$		−	6.78283i		−	0.668332i	0.942514	−	0.334166i	$-0.108455\pi$
$104$	−0.414880	+	1.38343i	−0.0406823	+	0.135656i
$105$	2.30278	−	1.65134i	0.224728	−	0.161154i
$106$	−18.4974	+	18.4974i	−1.79663	+	1.79663i
$107$		−	1.19461i		−	0.115488i	−0.998331	−	0.0577439i	$-0.981609\pi$
$107$		−	1.19461i		−	0.115488i	0.998331	−	0.0577439i	$-0.0183907\pi$
$108$	−2.71566	−	8.91950i	−0.261314	−	0.858279i
$109$	−8.09386	+	8.09386i	−0.775251	+	0.775251i	−0.979019	−	0.203768i	$-0.934681\pi$
$109$	−8.09386	+	8.09386i	−0.775251	+	0.775251i	0.203768	+	0.979019i	$0.434681\pi$
$110$	−5.51098	−	5.51098i	−0.525451	−	0.525451i
$111$	−2.66419	+	16.1710i	−0.252874	+	1.53489i
$112$	−1.26323	−	1.26323i	−0.119364	−	0.119364i
$113$		−	7.03052i		−	0.661375i	−0.943740	−	0.330688i	$-0.892719\pi$
$113$		−	7.03052i		−	0.661375i	0.943740	−	0.330688i	$-0.107281\pi$
$114$	11.4135	+	15.9161i	1.06898	+	1.49068i
$115$	−2.46735	−	2.46735i	−0.230082	−	0.230082i
$116$	−0.283724			−0.0263431
$117$	1.80303	+	10.6653i	0.166691	+	0.986009i
$118$	12.7975			1.17810
$119$	1.19388	+	1.19388i	0.109443	+	0.109443i
$120$	−1.61773	−	2.25592i	−0.147678	−	0.205936i
$121$		−	1.00000i		−	0.0909091i
$122$	−10.3941	−	10.3941i	−0.941035	−	0.941035i
$123$	−1.90682	+	11.5739i	−0.171932	+	1.04359i
$124$	3.16063	+	3.16063i	0.283833	+	0.283833i
$125$	−16.9990	+	16.9990i	−1.52044	+	1.52044i
$126$	−2.26320	−	0.766534i	−0.201622	−	0.0682883i
$127$		−	12.7177i		−	1.12852i	−0.825598	−	0.564258i	$-0.809162\pi$
$127$		−	12.7177i		−	1.12852i	0.825598	−	0.564258i	$-0.190838\pi$
$128$	−2.25403	+	2.25403i	−0.199230	+	0.199230i
$129$	6.62495	−	4.75079i	0.583295	−	0.418284i
$130$	−13.3249	−	24.7404i	−1.16867	−	2.16988i
$131$		−	7.11459i		−	0.621605i	−0.950475	−	0.310802i	$-0.899402\pi$
$131$		−	7.11459i		−	0.621605i	0.950475	−	0.310802i	$-0.100598\pi$
$132$	−0.505221	+	3.06658i	−0.0439738	+	0.266911i
$133$	2.37367			0.205823
$134$	17.9568			1.55123
$135$	−18.3452	−	9.78165i	−1.57891	−	0.841870i
$136$	1.16959	−	1.16959i	0.100291	−	0.100291i
$137$	8.77445	−	8.77445i	0.749652	−	0.749652i	−0.224762	−	0.974414i	$-0.572160\pi$
$137$	8.77445	−	8.77445i	0.749652	−	0.749652i	0.974414	+	0.224762i	$0.0721605\pi$
$138$	−0.478313	+	2.90325i	−0.0407167	+	0.247141i
$139$	−5.58449			−0.473670			−0.236835	−	0.971550i	$-0.576110\pi$
$139$	−5.58449			−0.473670			−0.236835	+	0.971550i	$0.576110\pi$
$140$	2.93561			0.248104
$141$	14.7707	+	2.43349i	1.24392	+	0.204937i
$142$			18.0298i			1.51302i
$143$	1.03571	−	3.45359i	0.0866101	−	0.288804i
$144$	−4.20465	+	12.4143i	−0.350387	+	1.03452i
$145$	−0.447351	+	0.447351i	−0.0371504	+	0.0371504i
$146$		−	11.1088i		−	0.919369i
$147$	9.61750	−	6.89676i	0.793238	−	0.568835i
$148$	−12.0057	+	12.0057i	−0.986860	+	0.986860i
$149$	7.63776	+	7.63776i	0.625709	+	0.625709i	0.946986	−	0.321276i	$-0.104112\pi$
$149$	7.63776	+	7.63776i	0.625709	+	0.625709i	−0.321276	+	0.946986i	$0.604112\pi$
$150$	36.6472	+	6.03766i	2.99223	+	0.492973i
$151$	−5.37147	−	5.37147i	−0.437124	−	0.437124i	0.453919	−	0.891043i	$-0.350026\pi$
$151$	−5.37147	−	5.37147i	−0.437124	−	0.437124i	−0.891043	+	0.453919i	$0.850026\pi$
$152$		−	2.32536i		−	0.188612i
$153$	3.97383	−	11.7328i	0.321265	−	0.948539i
$154$	0.563208	+	0.563208i	0.0453846	+	0.0453846i
$155$	9.96677			0.800550
$156$	−4.92090	+	10.0674i	−0.393987	+	0.806041i
$157$	−4.92303			−0.392900			−0.196450	−	0.980514i	$-0.562941\pi$
$157$	−4.92303			−0.392900			−0.196450	+	0.980514i	$0.562941\pi$
$158$	−11.1987	−	11.1987i	−0.890917	−	0.890917i
$159$	18.9025	−	13.5551i	1.49907	−	1.07499i
$160$		−	30.8452i		−	2.43853i
$161$	0.252157	+	0.252157i	0.0198727	+	0.0198727i
$162$	2.31196	+	17.3781i	0.181645	+	1.36535i
$163$	−16.9761	−	16.9761i	−1.32967	−	1.32967i	−0.905652	−	0.424021i	$-0.860618\pi$
$163$	−16.9761	−	16.9761i	−1.32967	−	1.32967i	−0.424021	−	0.905652i	$-0.639382\pi$
$164$	−8.59270	+	8.59270i	−0.670977	+	0.670977i
$165$	4.03851	+	5.63168i	0.314398	+	0.438426i
$166$		−	20.2847i		−	1.57440i
$167$	16.7718	−	16.7718i	1.29784	−	1.29784i	0.368026	−	0.929816i	$-0.380034\pi$
$167$	16.7718	−	16.7718i	1.29784	−	1.29784i	0.929816	−	0.368026i	$-0.119966\pi$
$168$	0.165328	+	0.230549i	0.0127553	+	0.0177873i
$169$	7.15382	−	10.8546i	0.550294	−	0.834971i
$170$			32.1814i			2.46820i
$171$	−7.71315	−	15.6139i	−0.589839	−	1.19402i
$172$	8.44555			0.643967
$173$	−14.5006			−1.10246			−0.551231	−	0.834353i	$-0.685842\pi$
$173$	−14.5006			−1.10246			−0.551231	+	0.834353i	$0.685842\pi$
$174$	0.526384	+	0.0867221i	0.0399050	+	0.00657439i
$175$	3.18292	−	3.18292i	0.240606	−	0.240606i
$176$	3.08935	−	3.08935i	0.232868	−	0.232868i
$177$	−11.2279	−	1.84981i	−0.843944	−	0.139040i
$178$	11.5950			0.869079
$179$	7.09845			0.530563			0.265282	−	0.964171i	$-0.414535\pi$
$179$	7.09845			0.530563			0.265282	+	0.964171i	$0.414535\pi$
$180$	−9.53915	−	19.3103i	−0.711007	−	1.43931i
$181$			0.533688i			0.0396687i	0.999803	+	0.0198344i	$0.00631389\pi$
$181$			0.533688i			0.0396687i	−0.999803	+	0.0198344i	$0.993686\pi$
$182$	1.36177	+	2.52841i	0.100941	+	0.187418i
$183$	7.61690	+	10.6217i	0.563057	+	0.785180i
$184$	0.247025	−	0.247025i	0.0182110	−	0.0182110i
$185$			37.8589i			2.78344i
$186$	−4.89773	−	6.82986i	−0.359119	−	0.500790i
$187$	−2.91976	+	2.91976i	−0.213514	+	0.213514i
$188$	10.9661	+	10.9661i	0.799781	+	0.799781i
$189$	1.87484	+	0.999659i	0.136374	+	0.0727145i
$190$	31.9914	+	31.9914i	2.32090	+	2.32090i
$191$		−	6.51594i		−	0.471477i	−0.971817	−	0.235738i	$-0.924249\pi$
$191$		−	6.51594i		−	0.471477i	0.971817	−	0.235738i	$-0.0757509\pi$
$192$	−8.83794	+	6.33774i	−0.637823	+	0.457387i
$193$	2.68411	+	2.68411i	0.193206	+	0.193206i	0.797080	−	0.603874i	$-0.206377\pi$
$193$	2.68411	+	2.68411i	0.193206	+	0.193206i	−0.603874	+	0.797080i	$0.706377\pi$
$194$	−21.9953			−1.57917
$195$	8.11461	+	23.6322i	0.581099	+	1.69234i
$196$	12.2605			0.875748
$197$	3.49567	+	3.49567i	0.249056	+	0.249056i	0.820583	−	0.571527i	$-0.193649\pi$
$197$	3.49567	+	3.49567i	0.249056	+	0.249056i	−0.571527	+	0.820583i	$0.693649\pi$
$198$	1.87464	−	5.53488i	0.133225	−	0.393347i
$199$			17.5765i			1.24596i	0.782237	+	0.622981i	$0.214079\pi$
$199$			17.5765i			1.24596i	−0.782237	+	0.622981i	$0.785921\pi$
$200$	−3.11815	−	3.11815i	−0.220487	−	0.220487i
$201$	−15.7545	−	2.59557i	−1.11124	−	0.183077i
$202$	−0.501799	−	0.501799i	−0.0353065	−	0.0353065i
$203$	0.0457181	−	0.0457181i	0.00320878	−	0.00320878i
$204$	10.4288	−	7.47853i	0.730160	−	0.523602i
$205$			27.0964i			1.89249i
$206$	−9.34254	+	9.34254i	−0.650926	+	0.650926i
$207$	0.839303	−	2.47805i	0.0583356	−	0.172236i
$208$	13.8690	−	7.46970i	0.961643	−	0.517931i
$209$			5.80504i			0.401543i
$210$	−5.44633	−	0.897287i	−0.375832	−	0.0619187i
$211$	1.62824			0.112092			0.0560462	−	0.998428i	$-0.482151\pi$
$211$	1.62824			0.112092			0.0560462	+	0.998428i	$0.482151\pi$
$212$	24.0971			1.65500
$213$	2.60612	−	15.8185i	0.178568	−	1.08387i
$214$	−1.64544	+	1.64544i	−0.112480	+	0.112480i
$215$	13.3162	−	13.3162i	0.908155	−	0.908155i
$216$	0.979316	−	1.83668i	0.0666340	−	0.124971i
$217$	−1.01858			−0.0691456
$218$	22.2967			1.51012
$219$	−1.60572	+	9.74636i	−0.108504	+	0.658598i
$220$			7.17932i			0.484030i
$221$	−13.1077	+	7.05964i	−0.881717	+	0.474883i
$222$	25.9433	−	18.6041i	1.74120	−	1.24862i
$223$	−1.51020	+	1.51020i	−0.101130	+	0.101130i	−0.755862	−	0.654731i	$-0.772782\pi$
$223$	−1.51020	+	1.51020i	−0.101130	+	0.101130i	0.654731	+	0.755862i	$0.272782\pi$
$224$			3.15230i			0.210622i
$225$	−31.2800	−	10.5944i	−2.08533	−	0.706290i
$226$	−9.68370	+	9.68370i	−0.644150	+	0.644150i
$227$	−10.8868	−	10.8868i	−0.722583	−	0.722583i	0.246548	−	0.969131i	$-0.420704\pi$
$227$	−10.8868	−	10.8868i	−0.722583	−	0.722583i	−0.969131	+	0.246548i	$0.920704\pi$
$228$	2.93283	−	17.8016i	0.194231	−	1.17894i
$229$	9.34908	+	9.34908i	0.617805	+	0.617805i	0.944968	−	0.327163i	$-0.106093\pi$
$229$	9.34908	+	9.34908i	0.617805	+	0.617805i	−0.327163	+	0.944968i	$0.606093\pi$
$230$			6.79696i			0.448178i
$231$	−0.412725	−	0.575543i	−0.0271553	−	0.0378680i
$232$	−0.0447877	−	0.0447877i	−0.00294046	−	0.00294046i
$233$	−17.9895			−1.17853			−0.589266	−	0.807939i	$-0.700583\pi$
$233$	−17.9895			−1.17853			−0.589266	+	0.807939i	$0.700583\pi$
$234$	12.2067	−	17.1737i	0.797980	−	1.12268i
$235$	34.5805			2.25578
$236$	−8.33582	−	8.33582i	−0.542616	−	0.542616i
$237$	8.20650	+	11.4439i	0.533069	+	0.743363i
$238$		−	3.28886i		−	0.213185i
$239$	0.481114	+	0.481114i	0.0311206	+	0.0311206i	0.722496	−	0.691375i	$-0.242995\pi$
$239$	0.481114	+	0.481114i	0.0311206	+	0.0311206i	−0.691375	+	0.722496i	$0.742995\pi$
$240$	−4.92186	+	29.8746i	−0.317705	+	1.92840i
$241$	8.98594	+	8.98594i	0.578835	+	0.578835i	0.934582	−	0.355747i	$-0.115774\pi$
$241$	8.98594	+	8.98594i	0.578835	+	0.578835i	−0.355747	+	0.934582i	$0.615774\pi$
$242$	−1.37738	+	1.37738i	−0.0885414	+	0.0885414i
$243$	0.483504	−	15.5810i	0.0310168	−	0.999519i
$244$			13.5407i			0.866853i
$245$	19.3312	−	19.3312i	1.23502	−	1.23502i
$246$	18.5681	−	13.3153i	1.18386	−	0.848954i
$247$	−6.01231	+	20.0482i	−0.382554	+	1.27564i
$248$			0.997850i			0.0633636i
$249$	−2.93206	+	17.7969i	−0.185811	+	1.12783i
$250$	46.8282			2.96167
$251$	22.0836			1.39390			0.696952	−	0.717118i	$-0.254539\pi$
$251$	22.0836			1.39390			0.696952	+	0.717118i	$0.254539\pi$
$252$	0.974877	+	1.97346i	0.0614115	+	0.124317i
$253$	−0.616674	+	0.616674i	−0.0387700	+	0.0387700i
$254$	−17.5172	+	17.5172i	−1.09913	+	1.09913i
$255$	4.65167	−	28.2346i	0.291299	−	1.76812i
$256$	18.7672			1.17295
$257$	−1.97585			−0.123250			−0.0616252	−	0.998099i	$-0.519628\pi$
$257$	−1.97585			−0.123250			−0.0616252	+	0.998099i	$0.519628\pi$
$258$	−15.6687	−	2.58144i	−0.975492	−	0.160713i
$259$		−	3.86908i		−	0.240413i
$260$	−7.43567	+	24.7945i	−0.461140	+	1.53769i
$261$	−0.449291	−	0.152172i	−0.0278104	−	0.00941924i
$262$	−9.79950	+	9.79950i	−0.605415	+	0.605415i
$263$		−	9.04737i		−	0.557885i	−0.960308	−	0.278942i	$-0.910016\pi$
$263$		−	9.04737i		−	0.557885i	0.960308	−	0.278942i	$-0.0899838\pi$
$264$	−0.563831	+	0.404326i	−0.0347014	+	0.0248846i
$265$	37.9942	−	37.9942i	2.33396	−	2.33396i
$266$	−3.26944	−	3.26944i	−0.200462	−	0.200462i
$267$	−10.1729	−	1.67600i	−0.622573	−	0.102569i
$268$	−11.6964	−	11.6964i	−0.714472	−	0.714472i
$269$			0.767919i			0.0468209i	0.999726	+	0.0234104i	$0.00745245\pi$
$269$			0.767919i			0.0468209i	−0.999726	+	0.0234104i	$0.992548\pi$
$270$	11.7953	+	38.7414i	0.717841	+	2.35773i
$271$	−15.6183	−	15.6183i	−0.948744	−	0.948744i	0.0500050	−	0.998749i	$-0.484076\pi$
$271$	−15.6183	−	15.6183i	−0.948744	−	0.948744i	−0.998749	+	0.0500050i	$0.984076\pi$
$272$	−18.0403			−1.09385
$273$	−0.829292	−	2.41515i	−0.0501910	−	0.146172i
$274$	−24.1715			−1.46025
$275$	7.78416	+	7.78416i	0.469402	+	0.469402i
$276$	2.20264	−	1.57952i	0.132583	−	0.0950760i
$277$			20.5772i			1.23636i	0.786035	+	0.618181i	$0.212130\pi$
$277$			20.5772i			1.23636i	−0.786035	+	0.618181i	$0.787870\pi$
$278$	7.69196	+	7.69196i	0.461333	+	0.461333i
$279$	3.30983	+	6.70017i	0.198155	+	0.401128i
$280$	0.463405	+	0.463405i	0.0276937	+	0.0276937i
$281$	−8.24413	+	8.24413i	−0.491804	+	0.491804i	−0.908874	−	0.417070i	$-0.863057\pi$
$281$	−8.24413	+	8.24413i	−0.491804	+	0.491804i	0.417070	+	0.908874i	$0.363057\pi$
$282$	−16.9931	−	23.6968i	−1.01192	−	1.41112i
$283$		−	16.1980i		−	0.962873i	−0.876481	−	0.481437i	$-0.840115\pi$
$283$		−	16.1980i		−	0.962873i	0.876481	−	0.481437i	$-0.159885\pi$
$284$	11.7440	−	11.7440i	0.696876	−	0.696876i
$285$	−23.4437	−	32.6921i	−1.38868	−	1.93651i
$286$	−6.18348	+	3.33035i	−0.365637	+	0.196928i
$287$		−	2.76918i		−	0.163459i
$288$	20.7357	−	10.2433i	1.22186	−	0.603592i
$289$	0.0499464			0.00293802
$290$	1.23234			0.0723657
$291$	19.2977	+	3.17931i	1.13125	+	0.186375i
$292$	−7.23587	+	7.23587i	−0.423447	+	0.423447i
$293$	16.0852	−	16.0852i	0.939710	−	0.939710i	−0.0585732	−	0.998283i	$-0.518655\pi$
$293$	16.0852	−	16.0852i	0.939710	−	0.939710i	0.998283	+	0.0585732i	$0.0186551\pi$
$294$	−22.7464	−	3.74749i	−1.32660	−	0.218558i
$295$	−26.2863			−1.53045
$296$	−3.79034			−0.220309
$297$	−2.44477	+	4.58510i	−0.141860	+	0.266054i
$298$		−	21.0402i		−	1.21883i
$299$	−2.76844	+	1.49105i	−0.160103	+	0.0862296i
$300$	−19.9380	−	27.8034i	−1.15112	−	1.60523i
$301$	−1.36088	+	1.36088i	−0.0784397	+	0.0784397i
$302$			14.7971i			0.851479i
$303$	0.367724	+	0.512790i	0.0211252	+	0.0294590i
$304$	−17.9338	+	17.9338i	−1.02857	+	1.02857i
$305$	21.3497	+	21.3497i	1.22248	+	1.22248i
$306$	−21.6340	+	10.6870i	−1.23673	+	0.610937i
$307$	1.96300	+	1.96300i	0.112034	+	0.112034i	0.760902	−	0.648867i	$-0.224757\pi$
$307$	1.96300	+	1.96300i	0.112034	+	0.112034i	−0.648867	+	0.760902i	$0.724757\pi$
$308$		−	0.733708i		−	0.0418069i
$309$	9.54716	−	6.84632i	0.543119	−	0.389474i
$310$	−13.7280	−	13.7280i	−0.779700	−	0.779700i
$311$	−10.5074			−0.595822			−0.297911	−	0.954594i	$-0.596290\pi$
$311$	−10.5074			−0.595822			−0.297911	+	0.954594i	$0.596290\pi$
$312$	−2.36601	+	0.812416i	−0.133949	+	0.0459940i
$313$	5.40289			0.305389			0.152695	−	0.988273i	$-0.451205\pi$
$313$	5.40289			0.305389			0.152695	+	0.988273i	$0.451205\pi$
$314$	6.78088	+	6.78088i	0.382667	+	0.382667i
$315$	4.64867	+	1.57448i	0.261923	+	0.0887119i
$316$			14.5888i			0.820685i
$317$	5.25444	+	5.25444i	0.295119	+	0.295119i	0.839098	−	0.543980i	$-0.183083\pi$
$317$	5.25444	+	5.25444i	0.295119	+	0.295119i	−0.543980	+	0.839098i	$0.683083\pi$
$318$	−44.7066	−	7.36544i	−2.50702	−	0.413033i
$319$	0.111808	+	0.111808i	0.00626005	+	0.00626005i
$320$	−17.7643	+	17.7643i	−0.993054	+	0.993054i
$321$	1.68148	−	1.20580i	0.0938509	−	0.0673010i
$322$		−	0.694632i		−	0.0387103i
$323$	16.9493	−	16.9493i	0.943084	−	0.943084i
$324$	9.81354	−	12.8254i	0.545197	−	0.712523i
$325$	18.8212	+	34.9454i	1.04401	+	1.93842i
$326$			46.7652i			2.59008i
$327$	−19.5621	−	3.22287i	−1.08179	−	0.178225i
$328$	−2.71283			−0.149791
$329$	−3.53404			−0.194838
$330$	2.19440	−	13.3195i	0.120798	−	0.733216i
$331$	−22.2343	+	22.2343i	−1.22211	+	1.22211i	−0.255227	+	0.966881i	$0.582150\pi$
$331$	−22.2343	+	22.2343i	−1.22211	+	1.22211i	−0.966881	+	0.255227i	$0.917850\pi$
$332$	−13.2127	+	13.2127i	−0.725144	+	0.725144i
$333$	−25.4507	+	12.5724i	−1.39469	+	0.688965i
$334$	−46.2023			−2.52808
$335$	−36.8837			−2.01517
$336$	0.503001	−	3.05311i	0.0274410	−	0.166561i
$337$		−	32.9237i		−	1.79347i	−0.442572	−	0.896733i	$-0.645934\pi$
$337$		−	32.9237i		−	1.79347i	0.442572	−	0.896733i	$-0.354066\pi$
$338$	−24.8045	+	5.09742i	−1.34919	+	0.277263i
$339$	9.89579	−	7.09633i	0.537465	−	0.385419i
$340$	20.9619	−	20.9619i	1.13682	−	1.13682i
$341$		−	2.49103i		−	0.134897i
$342$	−10.8823	+	32.1302i	−0.588449	+	1.73740i
$343$	−3.99954	+	3.99954i	−0.215955	+	0.215955i
$344$	1.33319	+	1.33319i	0.0718805	+	0.0718805i
$345$	0.982468	−	5.96336i	0.0528943	−	0.321056i
$346$	19.9729	+	19.9729i	1.07375	+	1.07375i
$347$			18.8464i			1.01173i	0.862614	+	0.505863i	$0.168826\pi$
$347$			18.8464i			1.01173i	−0.862614	+	0.505863i	$0.831174\pi$
$348$	−0.286380	−	0.399356i	−0.0153516	−	0.0214077i
$349$	−2.27768	−	2.27768i	−0.121921	−	0.121921i	0.643513	−	0.765435i	$-0.277476\pi$
$349$	−2.27768	−	2.27768i	−0.121921	−	0.121921i	−0.765435	+	0.643513i	$0.777476\pi$
$350$	−8.76820			−0.468680
$351$	−13.1920	+	13.3030i	−0.704139	+	0.710062i
$352$	−7.70927			−0.410905
$353$	4.66580	+	4.66580i	0.248336	+	0.248336i	0.820287	−	0.571952i	$-0.193814\pi$
$353$	4.66580	+	4.66580i	0.248336	+	0.248336i	−0.571952	+	0.820287i	$0.693814\pi$
$354$	12.9173	+	18.0130i	0.686544	+	0.957383i
$355$		−	37.0336i		−	1.96554i
$356$	−7.55256	−	7.55256i	−0.400285	−	0.400285i
$357$	−0.475389	+	2.88550i	−0.0251602	+	0.152717i
$358$	−9.77727	−	9.77727i	−0.516745	−	0.516745i
$359$	21.6409	−	21.6409i	1.14216	−	1.14216i	0.154108	−	0.988054i	$-0.450750\pi$
$359$	21.6409	−	21.6409i	1.14216	−	1.14216i	0.988054	−	0.154108i	$-0.0492503\pi$
$360$	1.54244	−	4.55408i	0.0812938	−	0.240021i
$361$		−	14.6985i		−	0.773603i
$362$	0.735092	−	0.735092i	0.0386356	−	0.0386356i
$363$	1.40755	−	1.00936i	0.0738771	−	0.0529777i
$364$	0.759906	−	2.53393i	0.0398299	−	0.132814i
$365$			22.8177i			1.19433i
$366$	4.13879	−	25.1215i	0.216338	−	1.31312i
$367$	1.63590			0.0853935			0.0426968	−	0.999088i	$-0.486405\pi$
$367$	1.63590			0.0853935			0.0426968	+	0.999088i	$0.486405\pi$
$368$	−3.81024			−0.198623
$369$	−18.2156	+	8.99835i	−0.948264	+	0.468435i
$370$	52.1461	−	52.1461i	2.71095	−	2.71095i
$371$	−3.88290	+	3.88290i	−0.201590	+	0.201590i
$372$	−1.25852	+	7.63894i	−0.0652513	+	0.396061i
$373$	−26.8491			−1.39019			−0.695097	−	0.718916i	$-0.744639\pi$
$373$	−26.8491			−1.39019			−0.695097	+	0.718916i	$0.744639\pi$
$374$	8.04323			0.415906
$375$	−41.0850	−	6.76879i	−2.12162	−	0.349539i
$376$			3.46212i			0.178545i
$377$	0.270339	+	0.501940i	0.0139232	+	0.0258512i
$378$	−1.20545	−	3.95927i	−0.0620018	−	0.203643i
$379$	−21.3081	+	21.3081i	−1.09452	+	1.09452i	−0.0994838	+	0.995039i	$0.531719\pi$
$379$	−21.3081	+	21.3081i	−1.09452	+	1.09452i	−0.995039	+	0.0994838i	$0.968281\pi$
$380$		−	41.6762i		−	2.13795i
$381$	17.9008	−	12.8368i	0.917087	−	0.657648i
$382$	−8.97493	+	8.97493i	−0.459197	+	0.459197i
$383$	−23.5325	−	23.5325i	−1.20246	−	1.20246i	−0.973417	−	0.229039i	$-0.926442\pi$
$383$	−23.5325	−	23.5325i	−1.20246	−	1.20246i	−0.229039	−	0.973417i	$-0.573558\pi$
$384$	−5.44778	−	0.897525i	−0.278006	−	0.0458016i
$385$	−1.15684	−	1.15684i	−0.0589582	−	0.0589582i
$386$		−	7.39408i		−	0.376349i
$387$	13.3739	+	4.52968i	0.679835	+	0.230257i
$388$	14.3270	+	14.3270i	0.727341	+	0.727341i
$389$	12.8477			0.651405			0.325703	−	0.945472i	$-0.394399\pi$
$389$	12.8477			0.651405			0.325703	+	0.945472i	$0.394399\pi$
$390$	21.3737	−	43.7275i	1.08230	−	2.21423i
$391$	3.60108			0.182114
$392$	1.93540	+	1.93540i	0.0977522	+	0.0977522i
$393$	10.0141	−	7.18118i	0.505146	−	0.362243i
$394$		−	9.62973i		−	0.485139i
$395$	23.0023	+	23.0023i	1.15737	+	1.15737i
$396$	−4.82630	+	2.38416i	−0.242531	+	0.119808i
$397$	−1.33973	−	1.33973i	−0.0672392	−	0.0672392i	0.672688	−	0.739927i	$-0.265140\pi$
$397$	−1.33973	−	1.33973i	−0.0672392	−	0.0672392i	−0.739927	+	0.672688i	$0.765140\pi$
$398$	24.2095	−	24.2095i	1.21351	−	1.21351i
$399$	2.39588	+	3.34105i	0.119944	+	0.167262i
$400$			48.0960i			2.40480i
$401$	16.1850	−	16.1850i	0.808238	−	0.808238i	−0.176129	−	0.984367i	$-0.556358\pi$
$401$	16.1850	−	16.1850i	0.808238	−	0.808238i	0.984367	+	0.176129i	$0.0563576\pi$
$402$	18.1249	+	25.2750i	0.903986	+	1.26060i
$403$	2.57998	−	8.60302i	0.128518	−	0.428547i
$404$			0.653709i			0.0325232i
$405$	−4.74883	−	35.6950i	−0.235971	−	1.77370i
$406$	−0.125942			−0.00625041
$407$	9.46222			0.469025
$408$	2.82678	+	0.465715i	0.139947	+	0.0230563i
$409$	−8.44587	+	8.44587i	−0.417622	+	0.417622i	−0.884383	−	0.466762i	$-0.845421\pi$
$409$	−8.44587	+	8.44587i	−0.417622	+	0.417622i	0.466762	+	0.884383i	$0.345421\pi$
$410$	37.3220	−	37.3220i	1.84320	−	1.84320i
$411$	21.2070	+	3.49388i	1.04607	+	0.172340i
$412$	12.1708			0.599613
$413$	2.68639			0.132189
$414$	−4.56926	+	2.25718i	−0.224567	+	0.110934i
$415$			41.6653i			2.04527i
$416$	−26.6247	−	7.98453i	−1.30538	−	0.391474i
$417$	−5.63676	−	7.86043i	−0.276033	−	0.384927i
$418$	7.99575	−	7.99575i	0.391085	−	0.391085i
$419$			14.3914i			0.703068i	0.936175	+	0.351534i	$0.114340\pi$
$419$			14.3914i			0.703068i	−0.936175	+	0.351534i	$0.885660\pi$
$420$	2.96309	+	4.13201i	0.144584	+	0.201621i
$421$	0.255662	−	0.255662i	0.0124602	−	0.0124602i	−0.700849	−	0.713309i	$-0.747195\pi$
$421$	0.255662	−	0.255662i	0.0124602	−	0.0124602i	0.713309	+	0.700849i	$0.247195\pi$
$422$	−2.24270	−	2.24270i	−0.109173	−	0.109173i
$423$	11.4837	+	23.2468i	0.558358	+	1.13030i
$424$	3.80389	+	3.80389i	0.184733	+	0.184733i
$425$		−	45.4557i		−	2.20492i
$426$	−25.3778	+	18.1985i	−1.22956	+	0.881722i
$427$	−2.18188	−	2.18188i	−0.105589	−	0.105589i
$428$	2.14356			0.103613
$429$	5.90650	−	2.02812i	0.285169	−	0.0979183i
$430$	−36.6829			−1.76901
$431$	5.60612	+	5.60612i	0.270037	+	0.270037i	0.829115	−	0.559078i	$-0.188845\pi$
$431$	5.60612	+	5.60612i	0.270037	+	0.270037i	−0.559078	+	0.829115i	$0.688845\pi$
$432$	−21.7177	+	6.61224i	−1.04489	+	0.318131i
$433$			9.71901i			0.467066i	0.972349	+	0.233533i	$0.0750287\pi$
$433$			9.71901i			0.467066i	−0.972349	+	0.233533i	$0.924971\pi$
$434$	1.40297	+	1.40297i	0.0673447	+	0.0673447i
$435$	−1.08121	−	0.178129i	−0.0518398	−	0.00854065i
$436$	−14.5233	−	14.5233i	−0.695538	−	0.695538i
$437$	3.57982	−	3.57982i	0.171246	−	0.171246i
$438$	15.6361	−	11.2128i	0.747123	−	0.535766i
$439$			7.43286i			0.354751i	0.984143	+	0.177376i	$0.0567607\pi$
$439$			7.43286i			0.354751i	−0.984143	+	0.177376i	$0.943239\pi$
$440$	−1.13330	+	1.13330i	−0.0540281	+	0.0540281i
$441$	19.4150	+	6.57577i	0.924526	+	0.313132i
$442$	27.7781	+	8.33042i	1.32127	+	0.396238i
$443$		−	8.28831i		−	0.393789i	−0.980425	−	0.196895i	$-0.936914\pi$
$443$		−	8.28831i		−	0.393789i	0.980425	−	0.196895i	$-0.0630857\pi$
$444$	−29.0166	−	4.78051i	−1.37707	−	0.226873i
$445$	−23.8164			−1.12900
$446$	4.16024			0.196993
$447$	−3.04126	+	18.4598i	−0.143847	+	0.873117i
$448$	1.81546	−	1.81546i	0.0857726	−	0.0857726i
$449$	−28.5897	+	28.5897i	−1.34923	+	1.34923i	−0.462732	+	0.886498i	$0.653131\pi$
$449$	−28.5897	+	28.5897i	−1.34923	+	1.34923i	−0.886498	+	0.462732i	$0.846869\pi$
$450$	28.4920	+	57.6769i	1.34312	+	2.71891i
$451$	6.77230			0.318895
$452$	12.6152			0.593371
$453$	2.13885	−	12.9824i	0.100492	−	0.609965i
$454$			29.9906i			1.40753i
$455$	−2.79712	−	5.19342i	−0.131131	−	0.243471i
$456$	3.27306	−	2.34713i	0.153275	−	0.109914i
$457$	23.1656	−	23.1656i	1.08364	−	1.08364i	0.0874725	−	0.996167i	$-0.472121\pi$
$457$	23.1656	−	23.1656i	1.08364	−	1.08364i	0.996167	−	0.0874725i	$-0.0278790\pi$
$458$		−	25.7545i		−	1.20343i
$459$	20.5255	−	6.24925i	0.958047	−	0.291690i
$460$	4.42730	−	4.42730i	0.206424	−	0.206424i
$461$	19.6560	+	19.6560i	0.915470	+	0.915470i	0.996696	−	0.0812262i	$-0.0258836\pi$
$461$	19.6560	+	19.6560i	0.915470	+	0.915470i	−0.0812262	+	0.996696i	$0.525884\pi$
$462$	−0.224262	+	1.36122i	−0.0104336	+	0.0633298i
$463$	14.9657	+	14.9657i	0.695515	+	0.695515i	0.963440	−	0.267925i	$-0.0863379\pi$
$463$	14.9657	+	14.9657i	0.695515	+	0.695515i	−0.267925	+	0.963440i	$0.586338\pi$
$464$			0.690828i			0.0320709i
$465$	10.0601	+	14.0287i	0.466524	+	0.650566i
$466$	24.7784	+	24.7784i	1.14784	+	1.14784i
$467$	−16.1626			−0.747917			−0.373959	−	0.927445i	$-0.622000\pi$
$467$	−16.1626			−0.747917			−0.373959	+	0.927445i	$0.622000\pi$
$468$	−19.1374	+	3.23528i	−0.884626	+	0.149551i
$469$	3.76942			0.174055
$470$	−47.6305	−	47.6305i	−2.19703	−	2.19703i
$471$	−4.96911	−	6.92940i	−0.228965	−	0.319290i
$472$		−	2.63173i		−	0.121135i
$473$	−3.32816	−	3.32816i	−0.153029	−	0.153029i
$474$	4.45916	−	27.0661i	0.204816	−	1.24319i
$475$	−45.1873	−	45.1873i	−2.07334	−	2.07334i
$476$	−2.14225	+	2.14225i	−0.0981898	+	0.0981898i
$477$	38.1590	+	12.9242i	1.74718	+	0.591760i
$478$		−	1.32535i		−	0.0606202i
$479$	−27.8311	+	27.8311i	−1.27164	+	1.27164i	−0.326405	+	0.945230i	$0.605837\pi$
$479$	−27.8311	+	27.8311i	−1.27164	+	1.27164i	−0.945230	+	0.326405i	$0.894163\pi$
$480$	43.4161	−	31.1339i	1.98167	−	1.42106i
$481$	32.6787	+	9.80007i	1.49002	+	0.446845i
$482$		−	24.7541i		−	1.12752i
$483$	−0.100406	+	0.609440i	−0.00456861	+	0.0277305i
$484$	1.79436			0.0815616
$485$	45.1789			2.05147
$486$	−22.1269	+	20.7949i	−1.00370	+	0.943278i
$487$	16.1607	−	16.1607i	0.732313	−	0.732313i	−0.238764	−	0.971078i	$-0.576742\pi$
$487$	16.1607	−	16.1607i	0.732313	−	0.732313i	0.971078	+	0.238764i	$0.0767424\pi$
$488$	−2.13748	+	2.13748i	−0.0967593	+	0.0967593i
$489$	6.75968	−	41.0298i	0.305684	−	1.85543i
$490$	−53.2528			−2.40572
$491$	3.19349			0.144120			0.0720602	−	0.997400i	$-0.477043\pi$
$491$	3.19349			0.144120			0.0720602	+	0.997400i	$0.477043\pi$
$492$	−20.7678	−	3.42151i	−0.936284	−	0.154253i
$493$		−	0.652904i		−	0.0294053i
$494$	35.8953	−	19.3328i	1.61501	−	0.869825i
$495$	−3.85055	+	11.3688i	−0.173069	+	0.510989i
$496$	7.69567	−	7.69567i	0.345546	−	0.345546i
$497$			3.78474i			0.169769i
$498$	28.5517	−	20.4746i	1.27943	−	0.917488i
$499$	−3.57634	+	3.57634i	−0.160099	+	0.160099i	−0.782611	−	0.622512i	$-0.786112\pi$
$499$	−3.57634	+	3.57634i	−0.160099	+	0.160099i	0.622512	+	0.782611i	$0.286112\pi$
$500$	−30.5022	−	30.5022i	−1.36410	−	1.36410i
$501$	40.5359	+	6.67832i	1.81101	+	0.298366i
$502$	−30.4175	−	30.4175i	−1.35760	−	1.35760i
$503$			37.2389i			1.66040i	0.557465	+	0.830200i	$0.311774\pi$
$503$			37.2389i			1.66040i	−0.557465	+	0.830200i	$0.688226\pi$
$504$	−0.157633	+	0.465415i	−0.00702155	+	0.0207312i
$505$	1.03071	+	1.03071i	0.0458659	+	0.0458659i
$506$	1.69879			0.0755204
$507$	22.4992	−	0.886889i	0.999224	−	0.0393881i
$508$	22.8201			1.01248
$509$	11.5344	+	11.5344i	0.511255	+	0.511255i	0.914911	−	0.403656i	$-0.132261\pi$
$509$	11.5344	+	11.5344i	0.511255	+	0.511255i	−0.403656	+	0.914911i	$0.632261\pi$
$510$	−45.2969	+	32.4827i	−2.00578	+	1.43836i
$511$		−	2.33191i		−	0.103158i
$512$	−21.3416	−	21.3416i	−0.943173	−	0.943173i
$513$	14.1920	−	26.6167i	0.626590	−	1.17515i
$514$	2.72150	+	2.72150i	0.120040	+	0.120040i
$515$	19.1898	−	19.1898i	0.845604	−	0.845604i
$516$	8.52461	+	11.8875i	0.375275	+	0.523319i
$517$		−	8.64285i		−	0.380112i
$518$	−5.32919	+	5.32919i	−0.234151	+	0.234151i
$519$	−14.6363	−	20.4103i	−0.642464	−	0.895913i
$520$	−5.08773	+	2.74020i	−0.223112	+	0.120166i
$521$			29.7577i			1.30371i	0.758345	+	0.651854i	$0.226008\pi$
$521$			29.7577i			1.30371i	−0.758345	+	0.651854i	$0.773992\pi$
$522$	0.409245	+	0.828444i	0.0179122	+	0.0362600i
$523$	−40.0299			−1.75038			−0.875192	−	0.483775i	$-0.839265\pi$
$523$	−40.0299			−1.75038			−0.875192	+	0.483775i	$0.839265\pi$
$524$	12.7661			0.557690
$525$	7.69284	+	1.26740i	0.335743	+	0.0553139i
$526$	−12.4617	+	12.4617i	−0.543355	+	0.543355i
$527$	−7.27321	+	7.27321i	−0.316826	+	0.316826i
$528$	7.46667	+	1.23014i	0.324945	+	0.0535350i
$529$	−22.2394			−0.966932
$530$	−104.665			−4.54635
$531$	−8.72934	−	17.6710i	−0.378821	−	0.766856i
$532$			4.25920i			0.184660i
$533$	23.3888	+	7.01411i	1.01308	+	0.303815i
$534$	11.7035	+	16.3205i	0.506460	+	0.706256i
$535$	3.37977	−	3.37977i	0.146120	−	0.146120i
$536$		−	3.69271i		−	0.159501i
$537$	7.16490	+	9.99141i	0.309188	+	0.431161i
$538$	1.05772	−	1.05772i	0.0456014	−	0.0456014i
$539$	−4.83152	−	4.83152i	−0.208108	−	0.208108i
$540$	17.5518	−	32.9179i	0.755307	−	1.41656i
$541$	17.4080	+	17.4080i	0.748426	+	0.748426i	0.974184	−	0.225757i	$-0.0724856\pi$
$541$	17.4080	+	17.4080i	0.748426	+	0.748426i	−0.225757	+	0.974184i	$0.572486\pi$
$542$			43.0247i			1.84807i
$543$	−0.751192	+	0.538684i	−0.0322367	+	0.0231171i
$544$	22.5092	+	22.5092i	0.965073	+	0.965073i
$545$	−45.7979			−1.96177
$546$	−2.18434	+	4.46884i	−0.0934810	+	0.191249i
$547$	14.2676			0.610038			0.305019	−	0.952346i	$-0.401337\pi$
$547$	14.2676			0.610038			0.305019	+	0.952346i	$0.401337\pi$
$548$	15.7445	+	15.7445i	0.672571	+	0.672571i
$549$	−7.26239	+	21.4423i	−0.309951	+	0.915135i
$550$		−	21.4435i		−	0.914354i
$551$	−0.649050	−	0.649050i	−0.0276505	−	0.0276505i
$552$	0.597038	+	0.0983625i	0.0254116	+	0.00418658i
$553$	−2.35078	−	2.35078i	−0.0999652	−	0.0999652i
$554$	28.3426	−	28.3426i	1.20416	−	1.20416i
$555$	−53.2882	+	38.2132i	−2.26196	+	1.62206i
$556$		−	10.0206i		−	0.424966i
$557$	−28.6734	+	28.6734i	−1.21493	+	1.21493i	−0.245549	+	0.969384i	$0.578968\pi$
$557$	−28.6734	+	28.6734i	−1.21493	+	1.21493i	−0.969384	+	0.245549i	$0.921032\pi$
$558$	4.66978	−	13.7876i	0.197688	−	0.583675i
$559$	−8.04712	−	14.9411i	−0.340357	−	0.631942i
$560$		−	7.14778i		−	0.302049i
$561$	−7.05678	−	1.16261i	−0.297938	−	0.0490854i
$562$	22.7106			0.957990
$563$	38.4578			1.62080			0.810402	−	0.585874i	$-0.199249\pi$
$563$	38.4578			1.62080			0.810402	+	0.585874i	$0.199249\pi$
$564$	−4.36654	+	26.5039i	−0.183865	+	1.11602i
$565$	19.8906	−	19.8906i	0.836802	−	0.836802i
$566$	−22.3109	+	22.3109i	−0.937795	+	0.937795i
$567$	0.485318	+	3.64794i	0.0203814	+	0.153199i
$568$	3.70772			0.155572
$569$	−2.94686			−0.123539			−0.0617693	−	0.998090i	$-0.519674\pi$
$569$	−2.94686			−0.123539			−0.0617693	+	0.998090i	$0.519674\pi$
$570$	−12.7386	+	77.3204i	−0.533561	+	3.23859i
$571$			25.3575i			1.06118i	0.847629	+	0.530589i	$0.178029\pi$
$571$			25.3575i			1.06118i	−0.847629	+	0.530589i	$0.821971\pi$
$572$	6.19698	+	1.85843i	0.259109	+	0.0777047i
$573$	9.17150	−	6.57693i	0.383145	−	0.274755i
$574$	−3.81421	+	3.81421i	−0.159202	+	0.159202i
$575$		−	9.60058i		−	0.400372i
$576$	−17.8413	−	6.04277i	−0.743389	−	0.251782i
$577$	25.9455	−	25.9455i	1.08013	−	1.08013i	0.0836294	−	0.996497i	$-0.473349\pi$
$577$	25.9455	−	25.9455i	1.08013	−	1.08013i	0.996497	−	0.0836294i	$-0.0266512\pi$
$578$	−0.0687952	−	0.0687952i	−0.00286150	−	0.00286150i
$579$	−1.06878	+	6.48725i	−0.0444169	+	0.269601i
$580$	−0.802706	−	0.802706i	−0.0333305	−	0.0333305i
$581$		−	4.25808i		−	0.176655i
$582$	−22.2012	−	30.9594i	−0.920268	−	1.28331i
$583$	−9.49603	−	9.49603i	−0.393285	−	0.393285i
$584$	−2.28446			−0.0945315
$585$	−25.0730	+	35.2752i	−1.03664	+	1.45845i
$586$	−44.3110			−1.83047
$587$	−0.925234	−	0.925234i	−0.0381885	−	0.0381885i	0.687755	−	0.725943i	$-0.258596\pi$
$587$	−0.925234	−	0.925234i	−0.0381885	−	0.0381885i	−0.725943	+	0.687755i	$0.758596\pi$
$588$	12.3752	+	17.2572i	0.510346	+	0.711675i
$589$			14.4605i			0.595836i
$590$	36.2063	+	36.2063i	1.49059	+	1.49059i
$591$	−1.39193	+	8.44870i	−0.0572564	+	0.347533i
$592$	29.2321	+	29.2321i	1.20143	+	1.20143i
$593$	0.856592	−	0.856592i	0.0351760	−	0.0351760i	−0.689300	−	0.724476i	$-0.742082\pi$
$593$	0.856592	−	0.856592i	0.0351760	−	0.0351760i	0.724476	+	0.689300i	$0.242082\pi$
$594$	9.68280	−	2.94805i	0.397290	−	0.120960i
$595$			6.75540i			0.276944i
$596$	−13.7049	+	13.7049i	−0.561373	+	0.561373i
$597$	−24.7397	+	17.7410i	−1.01253	+	0.726090i
$598$	5.86693	+	1.75945i	0.239917	+	0.0719492i
$599$		−	11.4994i		−	0.469853i	−0.972013	−	0.234927i	$-0.924515\pi$
$599$		−	11.4994i		−	0.469853i	0.972013	−	0.234927i	$-0.0754850\pi$
$600$	1.24161	−	7.53629i	0.0506885	−	0.307668i
$601$	−11.1773			−0.455932			−0.227966	−	0.973669i	$-0.573207\pi$
$601$	−11.1773			−0.455932			−0.227966	+	0.973669i	$0.573207\pi$
$602$	3.74889			0.152794
$603$	−12.2486	−	24.7951i	−0.498801	−	1.00973i
$604$	9.63834	−	9.63834i	0.392178	−	0.392178i
$605$	2.82918	−	2.82918i	0.115022	−	0.115022i
$606$	0.199810	−	1.21280i	0.00811674	−	0.0492668i
$607$	24.8397			1.00821			0.504105	−	0.863642i	$-0.331822\pi$
$607$	24.8397			1.00821			0.504105	+	0.863642i	$0.331822\pi$
$608$	44.7526			1.81496
$609$	0.110496	+	0.0182044i	0.00447754	+	0.000737678i
$610$		−	58.8133i		−	2.38128i
$611$	8.95145	−	29.8489i	0.362137	−	1.20756i
$612$	21.0528	+	7.13047i	0.851008	+	0.288232i
$613$	−26.9823	+	26.9823i	−1.08981	+	1.08981i	−0.0942582	+	0.995548i	$0.530048\pi$
$613$	−26.9823	+	26.9823i	−1.08981	+	1.08981i	−0.995548	+	0.0942582i	$0.969952\pi$
$614$		−	5.40760i		−	0.218233i
$615$	−38.1394	+	27.3500i	−1.53793	+	1.10286i
$616$	0.115821	−	0.115821i	0.00466654	−	0.00466654i
$617$	−5.19846	−	5.19846i	−0.209282	−	0.209282i	0.594680	−	0.803962i	$-0.297279\pi$
$617$	−5.19846	−	5.19846i	−0.209282	−	0.209282i	−0.803962	+	0.594680i	$0.797279\pi$
$618$	−22.5801	−	3.72008i	−0.908304	−	0.149644i
$619$	10.8767	+	10.8767i	0.437173	+	0.437173i	0.891060	−	0.453886i	$-0.149963\pi$
$619$	10.8767	+	10.8767i	0.437173	+	0.437173i	−0.453886	+	0.891060i	$0.649963\pi$
$620$			17.8839i			0.718236i
$621$	4.33514	−	1.31989i	0.173963	−	0.0529653i
$622$	14.4728	+	14.4728i	0.580304	+	0.580304i
$623$	2.43397			0.0975149
$624$	24.5128	+	11.9817i	0.981297	+	0.479651i
$625$	−41.1439			−1.64576
$626$	−7.44183	−	7.44183i	−0.297435	−	0.297435i
$627$	−8.17087	+	5.85938i	−0.326313	+	0.234001i
$628$		−	8.83366i		−	0.352502i
$629$	−27.6274	−	27.6274i	−1.10157	−	1.10157i
$630$	−4.23433	−	8.57165i	−0.168700	−	0.341503i
$631$	2.82182	+	2.82182i	0.112335	+	0.112335i	0.761040	−	0.648705i	$-0.224689\pi$
$631$	2.82182	+	2.82182i	0.112335	+	0.112335i	−0.648705	+	0.761040i	$0.724689\pi$
$632$	−2.30294	+	2.30294i	−0.0916060	+	0.0916060i
$633$	1.64348	+	2.29182i	0.0653224	+	0.0910917i
$634$		−	14.4747i		−	0.574865i
$635$	35.9807	−	35.9807i	1.42785	−	1.42785i
$636$	24.3227	+	33.9179i	0.964458	+	1.34493i
$637$	−11.6821	−	21.6901i	−0.462861	−	0.859395i
$638$		−	0.308005i		−	0.0121940i
$639$	24.8959	−	12.2984i	0.984865	−	0.486516i
$640$	−12.7541			−0.504149
$641$	−15.1201			−0.597207			−0.298603	−	0.954377i	$-0.596521\pi$
$641$	−15.1201			−0.597207			−0.298603	+	0.954377i	$0.596521\pi$
$642$	−3.97688	−	0.655193i	−0.156955	−	0.0258584i
$643$	−5.64139	+	5.64139i	−0.222475	+	0.222475i	−0.809540	−	0.587065i	$-0.800283\pi$
$643$	−5.64139	+	5.64139i	−0.222475	+	0.222475i	0.587065	+	0.809540i	$0.300283\pi$
$644$	−0.452459	+	0.452459i	−0.0178294	+	0.0178294i
$645$	32.1840	+	5.30233i	1.26724	+	0.208779i
$646$	−46.6913			−1.83704
$647$	8.70508			0.342232			0.171116	−	0.985251i	$-0.445263\pi$
$647$	8.70508			0.342232			0.171116	+	0.985251i	$0.445263\pi$
$648$	3.57370	−	0.475442i	0.140388	−	0.0186771i
$649$			6.56984i			0.257889i
$650$	22.2092	−	74.0571i	0.871115	−	2.90476i
$651$	−1.02811	−	1.43370i	−0.0402949	−	0.0561910i
$652$	30.4612	−	30.4612i	1.19295	−	1.19295i
$653$			46.4359i			1.81718i	0.417692	+	0.908589i	$0.362839\pi$
$653$			46.4359i			1.81718i	−0.417692	+	0.908589i	$0.637161\pi$
$654$	22.5054	+	31.3836i	0.880029	+	1.22720i
$655$	20.1284	−	20.1284i	0.786482	−	0.786482i
$656$	20.9220	+	20.9220i	0.816867	+	0.816867i
$657$	−15.3392	+	7.57746i	−0.598440	+	0.295625i
$658$	4.86772	+	4.86772i	0.189763	+	0.189763i
$659$		−	36.7594i		−	1.43194i	−0.698130	−	0.715971i	$-0.745984\pi$
$659$		−	36.7594i		−	1.43194i	0.698130	−	0.715971i	$-0.254016\pi$
$660$	−10.1052	+	7.24652i	−0.393346	+	0.282070i
$661$	−23.6978	−	23.6978i	−0.921737	−	0.921737i	0.0754153	−	0.997152i	$-0.475972\pi$
$661$	−23.6978	−	23.6978i	−0.921737	−	0.921737i	−0.997152	+	0.0754153i	$0.975972\pi$
$662$	61.2502			2.38056
$663$	−23.1671	−	11.3239i	−0.899737	−	0.439785i
$664$	−4.17143			−0.161883
$665$	6.71552	+	6.71552i	0.260417	+	0.260417i
$666$	52.3723	+	17.7382i	2.02938	+	0.687342i
$667$		−	0.137898i		−	0.00533944i
$668$	30.0946	+	30.0946i	1.16439	+	1.16439i
$669$	−3.65001	−	0.601343i	−0.141118	−	0.0232492i
$670$	50.8029	+	50.8029i	1.96269	+	1.96269i
$671$	5.33601	−	5.33601i	0.205994	−	0.205994i
$672$	−4.43702	+	3.18181i	−0.171162	+	0.122741i
$673$			11.7934i			0.454603i	0.973824	+	0.227301i	$0.0729903\pi$
$673$			11.7934i			0.454603i	−0.973824	+	0.227301i	$0.927010\pi$
$674$	−45.3484	+	45.3484i	−1.74676	+	1.74676i
$675$	−16.6607	−	54.7216i	−0.641270	−	2.10623i
$676$	19.4771	+	12.8365i	0.749118	+	0.493711i
$677$		−	18.9690i		−	0.729037i	−0.931196	−	0.364519i	$-0.881234\pi$
$677$		−	18.9690i		−	0.729037i	0.931196	−	0.364519i	$-0.118766\pi$
$678$	−23.4046	−	3.85593i	−0.898849	−	0.148086i
$679$	−4.61716			−0.177190
$680$	6.61793			0.253786
$681$	4.33499	−	26.3124i	0.166117	−	1.00829i
$682$	−3.43110	+	3.43110i	−0.131384	+	0.131384i
$683$	−19.9571	+	19.9571i	−0.763639	+	0.763639i	−0.976978	−	0.213339i	$-0.931566\pi$
$683$	−19.9571	+	19.9571i	−0.763639	+	0.763639i	0.213339	+	0.976978i	$0.431566\pi$
$684$	28.0169	−	13.8401i	1.07125	−	0.529190i
$685$	49.6489			1.89699
$686$	11.0178			0.420661
$687$	−3.72269	+	22.5959i	−0.142029	+	0.862086i
$688$		−	20.5637i		−	0.783984i
$689$	−22.9603	−	42.6305i	−0.874719	−	1.62409i
$690$	−9.56705	+	6.86058i	−0.364211	+	0.261178i
$691$	−8.33936	+	8.33936i	−0.317244	+	0.317244i	−0.847708	−	0.530464i	$-0.822018\pi$
$691$	−8.33936	+	8.33936i	−0.317244	+	0.317244i	0.530464	+	0.847708i	$0.322018\pi$
$692$		−	26.0193i		−	0.989104i
$693$	0.393516	−	1.16186i	0.0149484	−	0.0441354i
$694$	25.9586	−	25.9586i	0.985375	−	0.985375i
$695$	−15.7995	−	15.7995i	−0.599309	−	0.599309i
$696$	0.0178339	−	0.108248i	0.000675993	−	0.00410312i
$697$	−19.7735	−	19.7735i	−0.748973	−	0.748973i
$698$			6.27447i			0.237492i
$699$	−18.1579	−	25.3211i	−0.686795	−	0.957732i
$700$	5.71130	+	5.71130i	0.215867	+	0.215867i
$701$	−1.82829			−0.0690537			−0.0345269	−	0.999404i	$-0.510992\pi$
$701$	−1.82829			−0.0690537			−0.0345269	+	0.999404i	$0.510992\pi$
$702$	36.4938	−	0.152847i	1.37737	−	0.00576884i
$703$	−54.9285			−2.07167
$704$	4.43990	+	4.43990i	0.167335	+	0.167335i
$705$	34.9042	+	48.6737i	1.31457	+	1.83316i
$706$		−	12.8532i		−	0.483736i
$707$	−0.105336	−	0.105336i	−0.00396156	−	0.00396156i
$708$	3.31922	−	20.1469i	0.124744	−	0.757168i
$709$	21.3374	+	21.3374i	0.801344	+	0.801344i	0.983306	−	0.181962i	$-0.0582447\pi$
$709$	21.3374	+	21.3374i	0.801344	+	0.801344i	−0.181962	+	0.983306i	$0.558245\pi$
$710$	−51.0094	+	51.0094i	−1.91435	+	1.91435i
$711$	−7.82455	+	23.1021i	−0.293444	+	0.866396i
$712$		−	2.38444i		−	0.0893606i
$713$	−1.53616	+	1.53616i	−0.0575295	+	0.0575295i
$714$	4.62923	−	3.31964i	0.173244	−	0.124235i
$715$	12.7010	−	6.84063i	0.474991	−	0.255825i
$716$			12.7371i			0.476010i
$717$	−0.191573	+	1.16281i	−0.00715444	+	0.0434258i
$718$	−59.6155			−2.22483
$719$	−35.9222			−1.33967			−0.669836	−	0.742509i	$-0.733636\pi$
$719$	−35.9222			−1.33967			−0.669836	+	0.742509i	$0.733636\pi$
$720$	−47.0179	+	23.2265i	−1.75225	+	0.865600i
$721$	−1.96115	+	1.96115i	−0.0730370	+	0.0730370i
$722$	−20.2454	+	20.2454i	−0.753455	+	0.753455i
$723$	−3.57809	+	21.7182i	−0.133071	+	0.807708i
$724$	−0.957627			−0.0355899
$725$	−1.74066			−0.0646466
$726$	−3.32900	−	0.548456i	−0.123551	−	0.0203551i
$727$			13.4738i			0.499715i	0.968283	+	0.249858i	$0.0803838\pi$
$727$			13.4738i			0.499715i	−0.968283	+	0.249858i	$0.919616\pi$
$728$	0.519953	−	0.280041i	0.0192707	−	0.0103790i
$729$	22.4190	−	15.0462i	0.830332	−	0.557268i
$730$	31.4287	−	31.4287i	1.16323	−	1.16323i
$731$			19.4348i			0.718824i
$732$	−19.0591	+	13.6674i	−0.704446	+	0.505162i
$733$	20.7977	−	20.7977i	0.768181	−	0.768181i	−0.209605	−	0.977786i	$-0.567218\pi$
$733$	20.7977	−	20.7977i	0.768181	−	0.768181i	0.977786	+	0.209605i	$0.0672178\pi$
$734$	−2.25326	−	2.25326i	−0.0831695	−	0.0831695i
$735$	46.7217	+	7.69744i	1.72336	+	0.283924i
$736$	4.75411	+	4.75411i	0.175239	+	0.175239i
$737$			9.21848i			0.339567i
$738$	37.4839	+	12.6956i	1.37980	+	0.467331i
$739$	−34.7723	−	34.7723i	−1.27912	−	1.27912i	−0.941161	−	0.337959i	$-0.890263\pi$
$739$	−34.7723	−	34.7723i	−1.27912	−	1.27912i	−0.337959	−	0.941161i	$-0.609737\pi$
$740$	−67.9323			−2.49724
$741$	−34.2875	+	11.7733i	−1.25958	+	0.432502i
$742$	10.6965			0.392680
$743$	−9.30310	−	9.30310i	−0.341298	−	0.341298i	0.515557	−	0.856855i	$-0.327585\pi$
$743$	−9.30310	−	9.30310i	−0.341298	−	0.341298i	−0.856855	+	0.515557i	$0.827585\pi$
$744$	−1.40452	+	1.00719i	−0.0514923	+	0.0369254i
$745$			43.2171i			1.58335i
$746$	36.9815	+	36.9815i	1.35399	+	1.35399i
$747$	−28.0095	+	13.8365i	−1.02481	+	0.506251i
$748$	−5.23908	−	5.23908i	−0.191560	−	0.191560i
$749$	−0.345404	+	0.345404i	−0.0126208	+	0.0126208i
$750$	47.2665	+	65.9129i	1.72593	+	2.40680i
$751$			19.4516i			0.709800i	0.934904	+	0.354900i	$0.115485\pi$
$751$			19.4516i			0.709800i	−0.934904	+	0.354900i	$0.884515\pi$
$752$	26.7008	−	26.7008i	0.973677	−	0.973677i
$753$	22.2903	+	31.0837i	0.812304	+	1.13275i
$754$	0.319002	−	1.06372i	0.0116174	−	0.0387385i
$755$		−	30.3937i		−	1.10614i
$756$	−1.79374	+	3.36412i	−0.0652378	+	0.122352i
$757$	−9.21177			−0.334807			−0.167404	−	0.985888i	$-0.553538\pi$
$757$	−9.21177			−0.334807			−0.167404	+	0.985888i	$0.553538\pi$
$758$	58.6987			2.13203
$759$	−1.49045	−	0.245552i	−0.0540997	−	0.00891297i
$760$	6.57886	−	6.57886i	0.238640	−	0.238640i
$761$	13.3368	−	13.3368i	0.483457	−	0.483457i	−0.422777	−	0.906234i	$-0.638945\pi$
$761$	13.3368	−	13.3368i	0.483457	−	0.483457i	0.906234	+	0.422777i	$0.138945\pi$
$762$	−42.3374	−	6.97512i	−1.53372	−	0.252682i
$763$	4.68043			0.169443
$764$	11.6919			0.422999
$765$	44.4368	−	21.9514i	1.60661	−	0.793656i
$766$			64.8265i			2.34228i
$767$	−6.80443	+	22.6896i	−0.245694	+	0.819273i
$768$	18.9429	+	26.4158i	0.683543	+	0.953197i
$769$	33.0293	−	33.0293i	1.19107	−	1.19107i	0.214300	−	0.976768i	$-0.431253\pi$
$769$	33.0293	−	33.0293i	1.19107	−	1.19107i	0.976768	−	0.214300i	$-0.0687471\pi$
$770$			3.18683i			0.114845i
$771$	−1.99435	−	2.78111i	−0.0718247	−	0.100159i
$772$	−4.81625	+	4.81625i	−0.173341	+	0.173341i
$773$	0.192208	+	0.192208i	0.00691325	+	0.00691325i	0.710555	−	0.703642i	$-0.248444\pi$
$773$	0.192208	+	0.192208i	0.00691325	+	0.00691325i	−0.703642	+	0.710555i	$0.748444\pi$
$774$	−12.1819	−	24.6601i	−0.437869	−	0.886389i
$775$	19.3906	+	19.3906i	0.696531	+	0.696531i
$776$			4.52321i			0.162374i
$777$	5.44591	−	3.90529i	0.195371	−	0.140102i
$778$	−17.6962	−	17.6962i	−0.634440	−	0.634440i
$779$	−39.3135			−1.40855
$780$	−42.4047	+	14.5605i	−1.51833	+	0.521349i
$781$	−9.25595			−0.331204
$782$	−4.96005	−	4.96005i	−0.177371	−	0.177371i
$783$	−0.239306	−	0.785995i	−0.00855212	−	0.0280892i
$784$		−	29.8525i		−	1.06616i
$785$	−13.9281	−	13.9281i	−0.497116	−	0.497116i
$786$	−23.6845	−	3.90204i	−0.844798	−	0.139181i
$787$	−4.36815	−	4.36815i	−0.155708	−	0.155708i	0.624954	−	0.780662i	$-0.285118\pi$
$787$	−4.36815	−	4.36815i	−0.155708	−	0.155708i	−0.780662	+	0.624954i	$0.785118\pi$
$788$	−6.27247	+	6.27247i	−0.223447	+	0.223447i
$789$	12.7346	−	9.13205i	0.453364	−	0.325110i
$790$		−	63.3659i		−	2.25446i
$791$	−2.03276	+	2.03276i	−0.0722768	+	0.0722768i
$792$	−1.13822	−	0.385508i	−0.0404448	−	0.0136984i
$793$	23.9550	−	12.9019i	0.850665	−	0.458159i
$794$			3.69064i			0.130976i
$795$	91.8284	+	15.1288i	3.25682	+	0.536563i
$796$	−31.5384			−1.11785
$797$	−38.1892			−1.35273			−0.676365	−	0.736567i	$-0.736446\pi$
$797$	−38.1892			−1.35273			−0.676365	+	0.736567i	$0.736446\pi$
$798$	1.30185	−	7.90194i	0.0460850	−	0.279726i
$799$	−25.2350	+	25.2350i	−0.892750	+	0.892750i
$800$	60.0101	−	60.0101i	2.12168	−	2.12168i
$801$	−7.90910	−	16.0106i	−0.279454	−	0.565705i
$802$	−44.5857			−1.57438
$803$	5.70292			0.201252
$804$	4.65737	−	28.2692i	0.164253	−	0.996977i
$805$			1.42679i			0.0502878i
$806$	−15.4032	+	8.29602i	−0.542556	+	0.292215i
$807$	−1.08088	+	0.775108i	−0.0380489	+	0.0272851i
$808$	−0.103192	+	0.103192i	−0.00363029	+	0.00363029i
$809$			12.7906i			0.449693i	0.974394	+	0.224847i	$0.0721881\pi$
$809$			12.7906i			0.449693i	−0.974394	+	0.224847i	$0.927812\pi$
$810$	−42.6247	+	55.7066i	−1.49768	+	1.95733i
$811$	12.2794	−	12.2794i	0.431188	−	0.431188i	−0.457844	−	0.889032i	$-0.651378\pi$
$811$	12.2794	−	12.2794i	0.431188	−	0.431188i	0.889032	+	0.457844i	$0.151378\pi$
$812$	0.0820345	+	0.0820345i	0.00287884	+	0.00287884i
$813$	6.21901	−	37.7480i	0.218110	−	1.32388i
$814$	−13.0331	−	13.0331i	−0.456809	−	0.456809i
$815$		−	96.0569i		−	3.36473i
$816$	−18.2092	−	25.3926i	−0.637448	−	0.888918i
$817$	19.3201	+	19.3201i	0.675925	+	0.675925i
$818$	23.2664			0.813489
$819$	2.56239	−	3.60503i	0.0895372	−	0.125970i
$820$	−48.6205			−1.69790
$821$	−30.8207	−	30.8207i	−1.07565	−	1.07565i	−0.996894	−	0.0787577i	$-0.974905\pi$
$821$	−30.8207	−	30.8207i	−1.07565	−	1.07565i	−0.0787577	−	0.996894i	$-0.525095\pi$
$822$	−24.3978	−	34.0226i	−0.850970	−	1.18667i
$823$			42.2133i			1.47146i	0.677274	+	0.735731i	$0.263161\pi$
$823$			42.2133i			1.47146i	−0.677274	+	0.735731i	$0.736839\pi$
$824$	1.92124	+	1.92124i	0.0669296	+	0.0669296i
$825$	−3.09955	+	18.8136i	−0.107913	+	0.655005i
$826$	−3.70019	−	3.70019i	−0.128746	−	0.128746i
$827$	−9.41747	+	9.41747i	−0.327477	+	0.327477i	−0.851627	−	0.524149i	$-0.824383\pi$
$827$	−9.41747	+	9.41747i	−0.327477	+	0.327477i	0.524149	+	0.851627i	$0.324383\pi$
$828$	4.44651	+	1.50601i	0.154527	+	0.0523374i
$829$		−	0.899846i		−	0.0312530i	−0.999878	−	0.0156265i	$-0.995026\pi$
$829$		−	0.899846i		−	0.0312530i	0.999878	−	0.0156265i	$-0.00497426\pi$
$830$	57.3890	−	57.3890i	1.99200	−	1.99200i
$831$	−28.9634	+	20.7698i	−1.00473	+	0.720496i
$832$	10.7352	+	19.9320i	0.372175	+	0.691019i
$833$			28.2137i			0.977548i
$834$	−3.06284	+	18.5908i	−0.106058	+	0.643746i
$835$	94.9008			3.28418
$836$	−10.4163			−0.360255
$837$	−6.08999	+	11.4216i	−0.210501	+	0.394789i
$838$	19.8225	−	19.8225i	0.684757	−	0.684757i
$839$	−7.61283	+	7.61283i	−0.262824	+	0.262824i	−0.826200	−	0.563376i	$-0.809502\pi$
$839$	−7.61283	+	7.61283i	−0.262824	+	0.262824i	0.563376	+	0.826200i	$0.309502\pi$
$840$	−0.184522	+	1.12001i	−0.00636661	+	0.0386439i
$841$	28.9750			0.999138
$842$	−0.704289			−0.0242714
$843$	−19.9253	−	3.28271i	−0.686264	−	0.113063i
$844$			2.92164i			0.100567i
$845$	50.9490	−	10.4702i	1.75270	−	0.360187i
$846$	16.2022	−	47.8371i	0.557043	−	1.64468i
$847$	−0.289134	+	0.289134i	−0.00993477	+	0.00993477i
$848$		−	58.6731i		−	2.01484i
$849$	22.7995	−	16.3497i	0.782477	−	0.561119i
$850$	−62.6098	+	62.6098i	−2.14750	+	2.14750i
$851$	−5.83510	−	5.83510i	−0.200025	−	0.200025i
$852$	28.3841	+	4.67630i	0.972422	+	0.160207i
$853$	−33.0627	−	33.0627i	−1.13204	−	1.13204i	−0.989837	−	0.142207i	$-0.954580\pi$
$853$	−33.0627	−	33.0627i	−1.13204	−	1.13204i	−0.142207	−	0.989837i	$-0.545420\pi$
$854$			6.01057i			0.205677i
$855$	22.3526	−	65.9963i	0.764442	−	2.25702i
$856$	0.338375	+	0.338375i	0.0115654	+	0.0115654i
$857$	1.11365			0.0380416			0.0190208	−	0.999819i	$-0.493945\pi$
$857$	1.11365			0.0380416			0.0190208	+	0.999819i	$0.493945\pi$
$858$	−10.9290	−	5.34201i	−0.373109	−	0.182373i
$859$	−8.27321			−0.282278			−0.141139	−	0.989990i	$-0.545076\pi$
$859$	−8.27321			−0.282278			−0.141139	+	0.989990i	$0.545076\pi$
$860$	23.8939	+	23.8939i	0.814777	+	0.814777i
$861$	3.89775	−	2.79510i	0.132835	−	0.0952567i
$862$		−	15.4435i		−	0.526008i
$863$	7.87694	+	7.87694i	0.268134	+	0.268134i	0.828348	−	0.560214i	$-0.189281\pi$
$863$	7.87694	+	7.87694i	0.268134	+	0.268134i	−0.560214	+	0.828348i	$0.689281\pi$
$864$	35.3477	+	18.8473i	1.20255	+	0.641200i
$865$	−41.0248	−	41.0248i	−1.39488	−	1.39488i
$866$	13.3868	−	13.3868i	0.454901	−	0.454901i
$867$	0.0504139	+	0.0703020i	0.00171215	+	0.00238758i
$868$		−	1.82769i		−	0.0620359i
$869$	5.74906	−	5.74906i	0.195023	−	0.195023i
$870$	1.24388	+	1.73458i	0.0421715	+	0.0588079i
$871$	−9.54764	+	31.8369i	−0.323509	+	1.07875i
$872$		−	4.58518i		−	0.155274i
$873$	15.0033	+	30.3715i	0.507785	+	1.02792i
$874$	−9.86154			−0.333572
$875$	9.82998			0.332314
$876$	−17.4884	−	2.88123i	−0.590879	−	0.0973478i
$877$	−3.25149	+	3.25149i	−0.109795	+	0.109795i	−0.759870	−	0.650075i	$-0.774737\pi$
$877$	−3.25149	+	3.25149i	−0.109795	+	0.109795i	0.650075	+	0.759870i	$0.274737\pi$
$878$	10.2379	−	10.2379i	0.345512	−	0.345512i
$879$	38.8766	+	6.40494i	1.31127	+	0.216033i
$880$	17.4806			0.589271
$881$	48.8855			1.64699			0.823497	−	0.567321i	$-0.192020\pi$
$881$	48.8855			1.64699			0.823497	+	0.567321i	$0.192020\pi$
$882$	−17.6846	−	35.7993i	−0.595470	−	1.20542i
$883$			16.9409i			0.570106i	0.958512	+	0.285053i	$0.0920112\pi$
$883$			16.9409i			0.570106i	−0.958512	+	0.285053i	$0.907989\pi$
$884$	−12.6675	−	23.5198i	−0.426054	−	0.791057i
$885$	−26.5324	−	36.9993i	−0.891876	−	1.24372i
$886$	−11.4162	+	11.4162i	−0.383533	+	0.383533i
$887$			33.4223i			1.12221i	0.827744	+	0.561106i	$0.189624\pi$
$887$			33.4223i			1.12221i	−0.827744	+	0.561106i	$0.810376\pi$
$888$	−3.82582	−	5.33509i	−0.128386	−	0.179034i
$889$	−3.67714	+	3.67714i	−0.123327	+	0.123327i
$890$	32.8042	+	32.8042i	1.09960	+	1.09960i
$891$	−8.92139	+	1.18689i	−0.298878	+	0.0397624i
$892$	−2.70983	−	2.70983i	−0.0907320	−	0.0907320i
$893$			50.1720i			1.67894i
$894$	29.6151	−	21.2371i	0.990477	−	0.710276i
$895$	20.0828	+	20.0828i	0.671293	+	0.671293i
$896$	1.30343			0.0435446
$897$	−4.89307	−	2.39170i	−0.163375	−	0.0798565i
$898$	78.7578			2.62818
$899$	0.278518	+	0.278518i	0.00928908	+	0.00928908i
$900$	19.0100	−	56.1274i	0.633668	−	1.87091i
$901$			55.4522i			1.84738i
$902$	−9.32804	−	9.32804i	−0.310590	−	0.310590i
$903$	−3.28912	−	0.541885i	−0.109455	−	0.0180328i
$904$	1.99140	+	1.99140i	0.0662329	+	0.0662329i
$905$	−1.50990	+	1.50990i	−0.0501907	+	0.0501907i
$906$	−20.8277	+	14.9356i	−0.691953	+	0.496203i
$907$		−	16.9615i		−	0.563197i	−0.959532	−	0.281599i	$-0.909135\pi$
$907$		−	16.9615i		−	0.563197i	0.959532	−	0.281599i	$-0.0908646\pi$
$908$	19.5348	−	19.5348i	0.648285	−	0.648285i
$909$	−0.350610	+	1.03518i	−0.0116290	+	0.0343347i
$910$	−3.30062	+	11.0060i	−0.109414	+	0.364846i
$911$		−	23.0649i		−	0.764174i	−0.924126	−	0.382087i	$-0.875205\pi$
$911$		−	23.0649i		−	0.764174i	0.924126	−	0.382087i	$-0.124795\pi$
$912$	−43.3443	−	7.14101i	−1.43527	−	0.236462i
$913$	10.4136			0.344639
$914$	−63.8156			−2.11083
$915$	−8.50118	+	51.6002i	−0.281040	+	1.70585i
$916$	−16.7756	+	16.7756i	−0.554281	+	0.554281i
$917$	−2.05707	+	2.05707i	−0.0679305	+	0.0679305i
$918$	−36.8790	−	19.6638i	−1.21719	−	0.649002i
$919$	11.2833			0.372202			0.186101	−	0.982531i	$-0.440415\pi$
$919$	11.2833			0.372202			0.186101	+	0.982531i	$0.440415\pi$
$920$	1.39776			0.0460827
$921$	−0.781642	+	4.74439i	−0.0257560	+	0.156333i
$922$		−	54.1475i		−	1.78325i
$923$	−31.9663	−	9.58644i	−1.05218	−	0.315542i
$924$	1.03273	−	0.740576i	0.0339743	−	0.0243632i
$925$	−73.6554	+	73.6554i	−2.42177	+	2.42177i
$926$		−	41.2269i		−	1.35480i
$927$	19.2731	+	6.52768i	0.633010	+	0.214397i
$928$	0.861958	−	0.861958i	0.0282952	−	0.0282952i
$929$	3.46828	+	3.46828i	0.113791	+	0.113791i	0.761709	−	0.647919i	$-0.224360\pi$
$929$	3.46828	+	3.46828i	0.113791	+	0.113791i	−0.647919	+	0.761709i	$0.724360\pi$
$930$	5.46633	−	33.1794i	0.179248	−	1.08800i
$931$	28.0472	+	28.0472i	0.919209	+	0.919209i
$932$		−	32.2796i		−	1.05735i
$933$	−10.6058	−	14.7897i	−0.347218	−	0.484194i
$934$	22.2621	+	22.2621i	0.728438	+	0.728438i
$935$	−16.5210			−0.540294
$936$	−3.53167	−	2.51025i	−0.115436	−	0.0820500i
$937$	−28.5276			−0.931957			−0.465979	−	0.884796i	$-0.654298\pi$
$937$	−28.5276			−0.931957			−0.465979	+	0.884796i	$0.654298\pi$
$938$	−5.19192	−	5.19192i	−0.169522	−	0.169522i
$939$	5.45346	+	7.60482i	0.177967	+	0.248174i
$940$			62.0498i			2.02384i
$941$	−3.84561	−	3.84561i	−0.125363	−	0.125363i	0.641641	−	0.767005i	$-0.278254\pi$
$941$	−3.84561	−	3.84561i	−0.125363	−	0.125363i	−0.767005	+	0.641641i	$0.778254\pi$
$942$	−2.70006	+	16.3888i	−0.0879728	+	0.533975i
$943$	−4.17630	−	4.17630i	−0.135999	−	0.135999i
$944$	−20.2965	+	20.2965i	−0.660596	+	0.660596i
$945$	2.47603	+	8.13245i	0.0805452	+	0.264549i
$946$			9.16829i			0.298087i
$947$	−25.0112	+	25.0112i	−0.812755	+	0.812755i	−0.985046	−	0.172291i	$-0.944883\pi$
$947$	−25.0112	+	25.0112i	−0.812755	+	0.812755i	0.172291	+	0.985046i	$0.444883\pi$
$948$	−20.5345	+	14.7254i	−0.666928	+	0.478258i
$949$	19.6956	+	5.90655i	0.639345	+	0.191735i
$950$			124.480i			4.03867i
$951$	−2.09225	+	12.6995i	−0.0678459	+	0.411810i
$952$	−0.676335			−0.0219202
$953$	35.0923			1.13675			0.568376	−	0.822769i	$-0.307572\pi$
$953$	35.0923			1.13675			0.568376	+	0.822769i	$0.307572\pi$
$954$	−34.7578	−	70.3610i	−1.12533	−	2.27802i
$955$	18.4347	−	18.4347i	0.596534	−	0.596534i
$956$	−0.863289	+	0.863289i	−0.0279208	+	0.0279208i
$957$	−0.0445206	+	0.270230i	−0.00143915	+	0.00873529i
$958$	76.6680			2.47703
$959$	−5.07399			−0.163848
$960$	−42.9346	−	7.07352i	−1.38571	−	0.228297i
$961$			24.7948i			0.799831i
$962$	−31.5125	−	58.5094i	−1.01600	−	1.88642i
$963$	3.39443	+	1.14968i	0.109384	+	0.0370478i
$964$	−16.1240	+	16.1240i	−0.519318	+	0.519318i
$965$			15.1876i			0.488907i
$966$	0.977727	−	0.701134i	0.0314579	−	0.0225586i
$967$	−20.9978	+	20.9978i	−0.675245	+	0.675245i	−0.958920	−	0.283675i	$-0.908446\pi$
$967$	−20.9978	+	20.9978i	−0.675245	+	0.675245i	0.283675	+	0.958920i	$0.408446\pi$
$968$	0.283251	+	0.283251i	0.00910402	+	0.00910402i
$969$	40.9649	+	6.74900i	1.31598	+	0.216809i
$970$	−62.2285	−	62.2285i	−1.99804	−	1.99804i
$971$		−	50.7468i		−	1.62854i	−0.580485	−	0.814271i	$-0.697137\pi$
$971$		−	50.7468i		−	1.62854i	0.580485	−	0.814271i	$-0.302863\pi$
$972$	27.9578	+	0.867578i	0.896746	+	0.0278276i
$973$	1.61467	+	1.61467i	0.0517638	+	0.0517638i
$974$	−44.5190			−1.42648
$975$	−30.1900	+	61.7643i	−0.966853	+	1.97804i
$976$	32.9696			1.05533
$977$	−36.4852	−	36.4852i	−1.16727	−	1.16727i	−0.982848	−	0.184417i	$-0.940960\pi$
$977$	−36.4852	−	36.4852i	−1.16727	−	1.16727i	−0.184417	−	0.982848i	$-0.559040\pi$
$978$	−65.8243	+	47.2029i	−2.10483	+	1.50938i
$979$			5.95251i			0.190243i
$980$	34.6870	+	34.6870i	1.10804	+	1.10804i
$981$	−15.2089	−	30.7877i	−0.485582	−	0.982974i
$982$	−4.39866	−	4.39866i	−0.140367	−	0.140367i
$983$	9.83629	−	9.83629i	0.313729	−	0.313729i	−0.532623	−	0.846352i	$-0.678794\pi$
$983$	9.83629	−	9.83629i	0.313729	−	0.313729i	0.846352	+	0.532623i	$0.178794\pi$
$984$	−2.73822	−	3.81844i	−0.0872913	−	0.121727i
$985$			19.7797i			0.630234i
$986$	−0.899298	+	0.899298i	−0.0286395	+	0.0286395i
$987$	−3.56712	−	4.97433i	−0.113543	−	0.158335i
$988$	−35.9737	−	10.7882i	−1.14448	−	0.343219i
$989$			4.10478i			0.130525i
$990$	20.9628	−	10.3555i	0.666242	−	0.329119i
$991$	−37.5594			−1.19311			−0.596557	−	0.802570i	$-0.703465\pi$
$991$	−37.5594			−1.19311			−0.596557	+	0.802570i	$0.703465\pi$
$992$	−19.2040			−0.609729
$993$	−53.7383	−	8.85342i	−1.70533	−	0.280955i
$994$	5.21302	−	5.21302i	0.165347	−	0.165347i
$995$	−49.7269	+	49.7269i	−1.57645	+	1.57645i
$996$	−31.9340	−	5.26115i	−1.01187	−	0.166706i
$997$	10.3620			0.328168			0.164084	−	0.986446i	$-0.447533\pi$
$997$	10.3620			0.328168			0.164084	+	0.986446i	$0.447533\pi$
$998$	9.85198			0.311859
$999$	−43.3852	−	23.1329i	−1.37265	−	0.731892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.10	✓	96
3.2	odd	2	inner	429.2.j.a.122.39	yes	96
13.8	odd	4	inner	429.2.j.a.320.39	yes	96
39.8	even	4	inner	429.2.j.a.320.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.10	✓	96	1.1	even	1	trivial
429.2.j.a.122.39	yes	96	3.2	odd	2	inner
429.2.j.a.320.10	yes	96	39.8	even	4	inner
429.2.j.a.320.39	yes	96	13.8	odd	4	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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37738 - 1.37738i) q^{2} +(1.00936 + 1.40755i) q^{3} +1.79436i q^{4} +(2.82918 + 2.82918i) q^{5} +(0.548456 - 3.32900i) q^{6} +(-0.289134 - 0.289134i) q^{7} +(-0.283251 + 0.283251i) q^{8} +(-0.962383 + 2.84145i) q^{9} +O(q^{10})\)	\(q+(-1.37738 - 1.37738i) q^{2} +(1.00936 + 1.40755i) q^{3} +1.79436i q^{4} +(2.82918 + 2.82918i) q^{5} +(0.548456 - 3.32900i) q^{6} +(-0.289134 - 0.289134i) q^{7} +(-0.283251 + 0.283251i) q^{8} +(-0.962383 + 2.84145i) q^{9} -7.79370i q^{10} +(0.707107 - 0.707107i) q^{11} +(-2.52564 + 1.81115i) q^{12} +(3.17441 - 1.70971i) q^{13} +0.796496i q^{14} +(-1.12654 + 6.83786i) q^{15} +4.36900 q^{16} -4.12916 q^{17} +(5.23932 - 2.58819i) q^{18} +(-4.10478 + 4.10478i) q^{19} +(-5.07655 + 5.07655i) q^{20} +(0.115130 - 0.698811i) q^{21} -1.94791 q^{22} -0.872109 q^{23} +(-0.684591 - 0.112787i) q^{24} +11.0085i q^{25} +(-6.72729 - 2.01746i) q^{26} +(-4.97086 + 1.51344i) q^{27} +(0.518810 - 0.518810i) q^{28} +0.158120i q^{29} +(10.9700 - 7.86666i) q^{30} +(1.76143 - 1.76143i) q^{31} +(-5.45127 - 5.45127i) q^{32} +(1.70901 + 0.281561i) q^{33} +(5.68742 + 5.68742i) q^{34} -1.63602i q^{35} +(-5.09857 - 1.72686i) q^{36} +(6.69080 + 6.69080i) q^{37} +11.3077 q^{38} +(5.61062 + 2.74243i) q^{39} -1.60273 q^{40} +(4.78874 + 4.78874i) q^{41} +(-1.12111 + 0.803952i) q^{42} -4.70673i q^{43} +(1.26880 + 1.26880i) q^{44} +(-10.7617 + 5.31620i) q^{45} +(1.20123 + 1.20123i) q^{46} +(6.11141 - 6.11141i) q^{47} +(4.40990 + 6.14958i) q^{48} -6.83280i q^{49} +(15.1628 - 15.1628i) q^{50} +(-4.16781 - 5.81199i) q^{51} +(3.06782 + 5.69603i) q^{52} -13.4294i q^{53} +(8.93136 + 4.76218i) q^{54} +4.00106 q^{55} +0.163795 q^{56} +(-9.92088 - 1.63447i) q^{57} +(0.217792 - 0.217792i) q^{58} +(-4.64558 + 4.64558i) q^{59} +(-12.2695 - 2.02142i) q^{60} +7.54626 q^{61} -4.85231 q^{62} +(1.09982 - 0.543302i) q^{63} +6.27896i q^{64} +(13.8180 + 4.14392i) q^{65} +(-1.96614 - 2.74178i) q^{66} +(-6.51845 + 6.51845i) q^{67} -7.40918i q^{68} +(-0.880272 - 1.22754i) q^{69} +(-2.25343 + 2.25343i) q^{70} +(-6.54495 - 6.54495i) q^{71} +(-0.532246 - 1.07744i) q^{72} +(4.03257 + 4.03257i) q^{73} -18.4315i q^{74} +(-15.4949 + 11.1115i) q^{75} +(-7.36544 - 7.36544i) q^{76} -0.408898 q^{77} +(-3.95059 - 11.5053i) q^{78} +8.13040 q^{79} +(12.3607 + 12.3607i) q^{80} +(-7.14764 - 5.46912i) q^{81} -13.1918i q^{82} +(7.36350 + 7.36350i) q^{83} +(1.25392 + 0.206584i) q^{84} +(-11.6821 - 11.6821i) q^{85} +(-6.48296 + 6.48296i) q^{86} +(-0.222562 + 0.159601i) q^{87} +0.400577i q^{88} +(-4.20906 + 4.20906i) q^{89} +(22.1454 + 7.50053i) q^{90} +(-1.41217 - 0.423498i) q^{91} -1.56487i q^{92} +(4.25721 + 0.701378i) q^{93} -16.8355 q^{94} -23.2263 q^{95} +(2.17063 - 13.1752i) q^{96} +(7.98446 - 7.98446i) q^{97} +(-9.41137 + 9.41137i) q^{98} +(1.32870 + 2.68971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

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Database

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