LMFDB - Embedded newform 429.2.s.b.166.11

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			166.11
Character	$\chi$	$=$	429.166
Dual form			429.2.s.b.199.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56752 - 0.905006i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.638073 - 1.10517i) q^{4} +2.99723i q^{5} +(-1.56752 - 0.905006i) q^{6} +(3.93315 + 2.27081i) q^{7} +1.31019i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.56752 - 0.905006i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.638073 - 1.10517i) q^{4} +2.99723i q^{5} +(-1.56752 - 0.905006i) q^{6} +(3.93315 + 2.27081i) q^{7} +1.31019i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.71252 + 4.69821i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.27615 q^{12} +(-3.60367 + 0.116400i) q^{13} +8.22038 q^{14} +(2.59568 - 1.49862i) q^{15} +(2.46187 + 4.26409i) q^{16} +(2.79588 - 4.84260i) q^{17} +1.81001i q^{18} +(-0.372032 - 0.214793i) q^{19} +(3.31247 + 1.91245i) q^{20} -4.54162i q^{21} +(-0.905006 + 1.56752i) q^{22} +(-3.86033 - 6.68629i) q^{23} +(1.13465 - 0.655093i) q^{24} -3.98341 q^{25} +(-5.54347 + 3.44381i) q^{26} +1.00000 q^{27} +(5.01928 - 2.89788i) q^{28} +(-2.28470 - 3.95722i) q^{29} +(2.71252 - 4.69821i) q^{30} +0.104718i q^{31} +(5.44874 + 3.14583i) q^{32} +(0.866025 + 0.500000i) q^{33} -10.1211i q^{34} +(-6.80614 + 11.7886i) q^{35} +(0.638073 + 1.10517i) q^{36} +(7.18252 - 4.14683i) q^{37} -0.777556 q^{38} +(1.90264 + 3.06267i) q^{39} -3.92693 q^{40} +(9.17604 - 5.29779i) q^{41} +(-4.11019 - 7.11906i) q^{42} +(1.14419 - 1.98180i) q^{43} +1.27615i q^{44} +(-2.59568 - 1.49862i) q^{45} +(-12.1023 - 6.98725i) q^{46} +9.86720i q^{47} +(2.46187 - 4.26409i) q^{48} +(6.81313 + 11.8007i) q^{49} +(-6.24406 + 3.60501i) q^{50} -5.59175 q^{51} +(-2.17076 + 4.05696i) q^{52} -10.6258 q^{53} +(1.56752 - 0.905006i) q^{54} +(-1.49862 - 2.59568i) q^{55} +(-2.97518 + 5.15316i) q^{56} +0.429586i q^{57} +(-7.16262 - 4.13534i) q^{58} +(-7.64844 - 4.41583i) q^{59} -3.82491i q^{60} +(2.73074 - 4.72978i) q^{61} +(0.0947707 + 0.164148i) q^{62} +(-3.93315 + 2.27081i) q^{63} +1.54051 q^{64} +(-0.348879 - 10.8010i) q^{65} +1.81001 q^{66} +(5.85524 - 3.38052i) q^{67} +(-3.56795 - 6.17986i) q^{68} +(-3.86033 + 6.68629i) q^{69} +24.6384i q^{70} +(2.16985 + 1.25276i) q^{71} +(-1.13465 - 0.655093i) q^{72} +13.2630i q^{73} +(7.50581 - 13.0004i) q^{74} +(1.99171 + 3.44973i) q^{75} +(-0.474768 + 0.274107i) q^{76} -4.54162 q^{77} +(5.75416 + 3.07889i) q^{78} +7.11430 q^{79} +(-12.7805 + 7.37881i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.58907 - 16.6088i) q^{82} -0.999903i q^{83} +(-5.01928 - 2.89788i) q^{84} +(14.5144 + 8.37990i) q^{85} -4.14200i q^{86} +(-2.28470 + 3.95722i) q^{87} +(-0.655093 - 1.13465i) q^{88} +(-6.28593 + 3.62919i) q^{89} -5.42503 q^{90} +(-14.4381 - 7.72542i) q^{91} -9.85270 q^{92} +(0.0906887 - 0.0523592i) q^{93} +(8.92988 + 15.4670i) q^{94} +(0.643785 - 1.11507i) q^{95} -6.29167i q^{96} +(8.20323 + 4.73614i) q^{97} +(21.3594 + 12.3319i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	1.56752	−	0.905006i	1.10840	−	0.639936i	0.169987	−	0.985446i	$-0.445627\pi$
$2$	1.56752	−	0.905006i	1.10840	−	0.639936i	0.938415	+	0.345510i	$0.112294\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.638073	−	1.10517i	0.319036	−	0.552587i
$5$			2.99723i			1.34040i	0.742179	+	0.670202i	$0.233792\pi$
$5$			2.99723i			1.34040i	−0.742179	+	0.670202i	$0.766208\pi$
$6$	−1.56752	−	0.905006i	−0.639936	−	0.369467i
$7$	3.93315	+	2.27081i	1.48659	+	0.858285i	0.999883	−	0.0152795i	$-0.00486380\pi$
$7$	3.93315	+	2.27081i	1.48659	+	0.858285i	0.486709	+	0.873564i	$0.338197\pi$
$8$			1.31019i			0.463220i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.71252	+	4.69821i	0.857773	+	1.48571i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.27615			−0.368392
$13$	−3.60367	+	0.116400i	−0.999479	+	0.0322837i
$13$	−3.60367	+	0.116400i	−0.999479	+	0.0322837i
$14$	8.22038			2.19699
$15$	2.59568	−	1.49862i	0.670202	−	0.386941i
$16$	2.46187	+	4.26409i	0.615468	+	1.06602i
$17$	2.79588	−	4.84260i	0.678100	−	1.17450i	−0.297453	−	0.954737i	$-0.596137\pi$
$17$	2.79588	−	4.84260i	0.678100	−	1.17450i	0.975552	−	0.219767i	$-0.0705296\pi$
$18$			1.81001i			0.426624i
$19$	−0.372032	−	0.214793i	−0.0853501	−	0.0492769i	0.456718	−	0.889612i	$-0.349025\pi$
$19$	−0.372032	−	0.214793i	−0.0853501	−	0.0492769i	−0.542068	+	0.840335i	$0.682358\pi$
$20$	3.31247	+	1.91245i	0.740690	+	0.427638i
$21$		−	4.54162i		−	0.991062i
$22$	−0.905006	+	1.56752i	−0.192948	+	0.334196i
$23$	−3.86033	−	6.68629i	−0.804935	−	1.39419i	−0.916335	−	0.400413i	$-0.868867\pi$
$23$	−3.86033	−	6.68629i	−0.804935	−	1.39419i	0.111400	−	0.993776i	$-0.464467\pi$
$24$	1.13465	−	0.655093i	0.231610	−	0.133720i
$25$	−3.98341			−0.796682
$26$	−5.54347	+	3.44381i	−1.08716	+	0.675386i
$27$	1.00000			0.192450
$28$	5.01928	−	2.89788i	0.948554	−	0.547648i
$29$	−2.28470	−	3.95722i	−0.424259	−	0.734837i	0.572092	−	0.820189i	$-0.306132\pi$
$29$	−2.28470	−	3.95722i	−0.424259	−	0.734837i	−0.996351	+	0.0853519i	$0.972799\pi$
$30$	2.71252	−	4.69821i	0.495235	−	0.857773i
$31$			0.104718i			0.0188080i	0.999956	+	0.00940398i	$0.00299342\pi$
$31$			0.104718i			0.0188080i	−0.999956	+	0.00940398i	$0.997007\pi$
$32$	5.44874	+	3.14583i	0.963211	+	0.556110i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$		−	10.1211i		−	1.73576i
$35$	−6.80614	+	11.7886i	−1.15045	+	1.99263i
$36$	0.638073	+	1.10517i	0.106345	+	0.184196i
$37$	7.18252	−	4.14683i	1.18080	−	0.681734i	0.224599	−	0.974451i	$-0.427893\pi$
$37$	7.18252	−	4.14683i	1.18080	−	0.681734i	0.956199	+	0.292717i	$0.0945594\pi$
$38$	−0.777556			−0.126136
$39$	1.90264	+	3.06267i	0.304666	+	0.490420i
$40$	−3.92693			−0.620902
$41$	9.17604	−	5.29779i	1.43306	−	0.827376i	0.435704	−	0.900090i	$-0.356499\pi$
$41$	9.17604	−	5.29779i	1.43306	−	0.827376i	0.997353	+	0.0727138i	$0.0231660\pi$
$42$	−4.11019	−	7.11906i	−0.634216	−	1.09849i
$43$	1.14419	−	1.98180i	0.174488	−	0.302221i	−0.765496	−	0.643440i	$-0.777506\pi$
$43$	1.14419	−	1.98180i	0.174488	−	0.302221i	0.939984	+	0.341219i	$0.110840\pi$
$44$			1.27615i			0.192386i
$45$	−2.59568	−	1.49862i	−0.386941	−	0.223401i
$46$	−12.1023	−	6.98725i	−1.78438	−	1.03021i
$47$			9.86720i			1.43928i	0.694348	+	0.719639i	$0.255693\pi$
$47$			9.86720i			1.43928i	−0.694348	+	0.719639i	$0.744307\pi$
$48$	2.46187	−	4.26409i	0.355341	−	0.615468i
$49$	6.81313	+	11.8007i	0.973305	+	1.68581i
$50$	−6.24406	+	3.60501i	−0.883044	+	0.509826i
$51$	−5.59175			−0.783002
$52$	−2.17076	+	4.05696i	−0.301031	+	0.562599i
$53$	−10.6258			−1.45956			−0.729780	−	0.683682i	$-0.760378\pi$
$53$	−10.6258			−1.45956			−0.729780	+	0.683682i	$0.760378\pi$
$54$	1.56752	−	0.905006i	0.213312	−	0.123156i
$55$	−1.49862	−	2.59568i	−0.202073	−	0.350002i
$56$	−2.97518	+	5.15316i	−0.397575	+	0.688620i
$57$			0.429586i			0.0569001i
$58$	−7.16262	−	4.13534i	−0.940498	−	0.542997i
$59$	−7.64844	−	4.41583i	−0.995742	−	0.574892i	−0.0887561	−	0.996053i	$-0.528289\pi$
$59$	−7.64844	−	4.41583i	−0.995742	−	0.574892i	−0.906986	+	0.421162i	$0.861623\pi$
$60$		−	3.82491i		−	0.493793i
$61$	2.73074	−	4.72978i	0.349636	−	0.605587i	−0.636549	−	0.771236i	$-0.719639\pi$
$61$	2.73074	−	4.72978i	0.349636	−	0.605587i	0.986185	+	0.165649i	$0.0529720\pi$
$62$	0.0947707	+	0.164148i	0.0120359	+	0.0208468i
$63$	−3.93315	+	2.27081i	−0.495531	+	0.286095i
$64$	1.54051			0.192564
$65$	−0.348879	−	10.8010i	−0.0432731	−	1.33971i
$66$	1.81001			0.222797
$67$	5.85524	−	3.38052i	0.715331	−	0.412997i	−0.0977006	−	0.995216i	$-0.531149\pi$
$67$	5.85524	−	3.38052i	0.715331	−	0.412997i	0.813032	+	0.582219i	$0.197815\pi$
$68$	−3.56795	−	6.17986i	−0.432677	−	0.749419i
$69$	−3.86033	+	6.68629i	−0.464730	+	0.804935i
$70$			24.6384i			2.94485i
$71$	2.16985	+	1.25276i	0.257513	+	0.148675i	0.623200	−	0.782063i	$-0.285832\pi$
$71$	2.16985	+	1.25276i	0.257513	+	0.148675i	−0.365686	+	0.930738i	$0.619166\pi$
$72$	−1.13465	−	0.655093i	−0.133720	−	0.0772034i
$73$			13.2630i			1.55232i	0.630536	+	0.776160i	$0.282835\pi$
$73$			13.2630i			1.55232i	−0.630536	+	0.776160i	$0.717165\pi$
$74$	7.50581	−	13.0004i	0.872533	−	1.51127i
$75$	1.99171	+	3.44973i	0.229982	+	0.398341i
$76$	−0.474768	+	0.274107i	−0.0544596	+	0.0314423i
$77$	−4.54162			−0.517565
$78$	5.75416	+	3.07889i	0.651530	+	0.348615i
$79$	7.11430			0.800421			0.400210	−	0.916423i	$-0.368937\pi$
$79$	7.11430			0.800421			0.400210	+	0.916423i	$0.368937\pi$
$80$	−12.7805	+	7.37881i	−1.42890	+	0.824975i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.58907	−	16.6088i	1.05894	−	1.83413i
$83$		−	0.999903i		−	0.109754i	−0.998493	−	0.0548768i	$-0.982523\pi$
$83$		−	0.999903i		−	0.109754i	0.998493	−	0.0548768i	$-0.0174766\pi$
$84$	−5.01928	−	2.89788i	−0.547648	−	0.316185i
$85$	14.5144	+	8.37990i	1.57431	+	0.908927i
$86$		−	4.14200i		−	0.446644i
$87$	−2.28470	+	3.95722i	−0.244946	+	0.424259i
$88$	−0.655093	−	1.13465i	−0.0698331	−	0.120954i
$89$	−6.28593	+	3.62919i	−0.666308	+	0.384693i	−0.794676	−	0.607034i	$-0.792359\pi$
$89$	−6.28593	+	3.62919i	−0.666308	+	0.384693i	0.128368	+	0.991727i	$0.459026\pi$
$90$	−5.42503			−0.571849
$91$	−14.4381	−	7.72542i	−1.51353	−	0.809845i
$92$	−9.85270			−1.02721
$93$	0.0906887	−	0.0523592i	0.00940398	−	0.00542939i
$94$	8.92988	+	15.4670i	0.921047	+	1.59530i
$95$	0.643785	−	1.11507i	0.0660509	−	0.114404i
$96$		−	6.29167i		−	0.642141i
$97$	8.20323	+	4.73614i	0.832912	+	0.480882i	0.854849	−	0.518878i	$-0.173650\pi$
$97$	8.20323	+	4.73614i	0.832912	+	0.480882i	−0.0219369	+	0.999759i	$0.506983\pi$
$98$	21.3594	+	12.3319i	2.15763	+	1.24571i
$99$		−	1.00000i		−	0.100504i
$100$	−2.54171	+	4.40236i	−0.254171	+	0.440236i
$101$	1.32130	+	2.28855i	0.131474	+	0.227720i	0.924245	−	0.381800i	$-0.124696\pi$
$101$	1.32130	+	2.28855i	0.131474	+	0.227720i	−0.792771	+	0.609520i	$0.791362\pi$
$102$	−8.76517	+	5.06057i	−0.867881	+	0.501071i
$103$	−14.4302			−1.42185			−0.710927	−	0.703265i	$-0.751725\pi$
$103$	−14.4302			−1.42185			−0.710927	+	0.703265i	$0.751725\pi$
$104$	−0.152506	−	4.72148i	−0.0149544	−	0.462979i
$105$	13.6123			1.32842
$106$	−16.6561	+	9.61638i	−1.61778	+	0.934025i
$107$	−6.79256	−	11.7651i	−0.656661	−	1.13737i	−0.981475	−	0.191592i	$-0.938635\pi$
$107$	−6.79256	−	11.7651i	−0.656661	−	1.13737i	0.324813	−	0.945778i	$-0.394699\pi$
$108$	0.638073	−	1.10517i	0.0613986	−	0.106345i
$109$		−	0.777084i		−	0.0744312i	−0.999307	−	0.0372156i	$-0.988151\pi$
$109$		−	0.777084i		−	0.0744312i	0.999307	−	0.0372156i	$-0.0118488\pi$
$110$	−4.69821	−	2.71252i	−0.447957	−	0.258628i
$111$	−7.18252	−	4.14683i	−0.681734	−	0.393599i
$112$			22.3617i			2.11299i
$113$	5.44080	−	9.42375i	0.511828	−	0.886512i	−0.488078	−	0.872800i	$-0.662302\pi$
$113$	5.44080	−	9.42375i	0.511828	−	0.886512i	0.999906	−	0.0137118i	$-0.00436474\pi$
$114$	0.388778	+	0.673384i	0.0364124	+	0.0630681i
$115$	20.0404	−	11.5703i	1.86878	−	1.07894i
$116$	−5.83123			−0.541416
$117$	1.70103	−	3.17907i	0.157260	−	0.293905i
$118$	−15.9854			−1.47158
$119$	21.9932	−	12.6978i	2.01612	−	1.16400i
$120$	1.96347	+	3.40082i	0.179239	+	0.310451i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	9.88536i		−	0.894978i
$123$	−9.17604	−	5.29779i	−0.827376	−	0.477686i
$124$	0.115732	+	0.0668179i	0.0103930	+	0.00600043i
$125$			3.04696i			0.272528i
$126$	−4.11019	+	7.11906i	−0.366165	+	0.634216i
$127$	−3.87815	−	6.71715i	−0.344130	−	0.596051i	0.641065	−	0.767486i	$-0.278493\pi$
$127$	−3.87815	−	6.71715i	−0.344130	−	0.596051i	−0.985195	+	0.171436i	$0.945159\pi$
$128$	−8.48271	+	4.89749i	−0.749773	+	0.432881i
$129$	−2.28838			−0.201481
$130$	−10.3219	−	16.6151i	−0.905290	−	1.45724i
$131$	4.07520			0.356052			0.178026	−	0.984026i	$-0.443029\pi$
$131$	4.07520			0.356052			0.178026	+	0.984026i	$0.443029\pi$
$132$	1.10517	−	0.638073i	0.0961931	−	0.0555371i
$133$	−0.975507	−	1.68963i	−0.0845872	−	0.146509i
$134$	6.11879	−	10.5981i	0.528583	−	0.915533i
$135$			2.99723i			0.257961i
$136$	6.34470	+	3.66312i	0.544054	+	0.314110i
$137$	−3.20153	−	1.84840i	−0.273525	−	0.157920i	0.356964	−	0.934118i	$-0.383812\pi$
$137$	−3.20153	−	1.84840i	−0.273525	−	0.157920i	−0.630488	+	0.776199i	$0.717145\pi$
$138$			13.9745i			1.18959i
$139$	−0.283460	+	0.490967i	−0.0240428	+	0.0416433i	−0.877796	−	0.479034i	$-0.840987\pi$
$139$	−0.283460	+	0.490967i	−0.0240428	+	0.0416433i	0.853754	+	0.520677i	$0.174320\pi$
$140$	8.68563	+	15.0440i	0.734070	+	1.27145i
$141$	8.54524	−	4.93360i	0.719639	−	0.415484i
$142$	4.53503			0.380571
$143$	3.06267	−	1.90264i	0.256113	−	0.159107i
$144$	−4.92374			−0.410312
$145$	11.8607	−	6.84779i	0.984979	−	0.568678i
$146$	12.0031	+	20.7900i	0.993385	+	1.72059i
$147$	6.81313	−	11.8007i	0.561938	−	0.973305i
$148$		−	10.5839i		−	0.869992i
$149$	0.134256	+	0.0775127i	0.0109987	+	0.00635009i	0.505489	−	0.862833i	$-0.331312\pi$
$149$	0.134256	+	0.0775127i	0.0109987	+	0.00635009i	−0.494491	+	0.869183i	$0.664645\pi$
$150$	6.24406	+	3.60501i	0.509826	+	0.294348i
$151$			11.5828i			0.942594i	0.881975	+	0.471297i	$0.156214\pi$
$151$			11.5828i			0.942594i	−0.881975	+	0.471297i	$0.843786\pi$
$152$	0.281419	−	0.487431i	0.0228261	−	0.0395359i
$153$	2.79588	+	4.84260i	0.226033	+	0.391501i
$154$	−7.11906	+	4.11019i	−0.573670	+	0.331209i
$155$	−0.313865			−0.0252103
$156$	4.59881	−	0.148544i	0.368200	−	0.0118930i
$157$	−10.1019			−0.806219			−0.403110	−	0.915152i	$-0.632071\pi$
$157$	−10.1019			−0.806219			−0.403110	+	0.915152i	$0.632071\pi$
$158$	11.1518	−	6.43848i	0.887188	−	0.512218i
$159$	5.31288	+	9.20218i	0.421339	+	0.729780i
$160$	−9.42880	+	16.3312i	−0.745412	+	1.29109i
$161$		−	35.0643i		−	2.76345i
$162$	−1.56752	−	0.905006i	−0.123156	−	0.0711040i
$163$	−9.57883	−	5.53034i	−0.750272	−	0.433170i	0.0755202	−	0.997144i	$-0.475938\pi$
$163$	−9.57883	−	5.53034i	−0.750272	−	0.433170i	−0.825792	+	0.563975i	$0.809272\pi$
$164$		−	13.5215i		−	1.05585i
$165$	−1.49862	+	2.59568i	−0.116667	+	0.202073i
$166$	−0.904919	−	1.56737i	−0.0702353	−	0.121651i
$167$	−20.5465	+	11.8625i	−1.58993	+	0.917949i	−0.596618	+	0.802525i	$0.703489\pi$
$167$	−20.5465	+	11.8625i	−1.58993	+	0.917949i	−0.993316	+	0.115424i	$0.963177\pi$
$168$	5.95036			0.459080
$169$	12.9729	−	0.838938i	0.997916	−	0.0645337i
$170$	30.3354			2.32662
$171$	0.372032	−	0.214793i	0.0284500	−	0.0164256i
$172$	−1.46016	−	2.52906i	−0.111336	−	0.192839i
$173$	−6.68274	+	11.5749i	−0.508080	+	0.880020i	0.491877	+	0.870665i	$0.336311\pi$
$173$	−6.68274	+	11.5749i	−0.508080	+	0.880020i	−0.999956	+	0.00935478i	$0.997022\pi$
$174$			8.27068i			0.626999i
$175$	−15.6674	−	9.04556i	−1.18434	−	0.683780i
$176$	−4.26409	−	2.46187i	−0.321418	−	0.185571i
$177$			8.83165i			0.663828i
$178$	−6.56887	+	11.3776i	−0.492358	+	0.852789i
$179$	−8.57924	−	14.8597i	−0.641243	−	1.11067i	−0.985156	−	0.171664i	$-0.945086\pi$
$179$	−8.57924	−	14.8597i	−0.641243	−	1.11067i	0.343913	−	0.939002i	$-0.388248\pi$
$180$	−3.31247	+	1.91245i	−0.246897	+	0.142546i
$181$	−7.27163			−0.540496			−0.270248	−	0.962791i	$-0.587106\pi$
$181$	−7.27163			−0.540496			−0.270248	+	0.962791i	$0.587106\pi$
$182$	−29.6236	+	0.956855i	−2.19584	+	0.0709268i
$183$	−5.46149			−0.403725
$184$	8.76028	−	5.05775i	0.645817	−	0.372862i
$185$	12.4290	+	21.5277i	0.913799	+	1.58275i
$186$	0.0947707	−	0.164148i	0.00694893	−	0.0120359i
$187$			5.59175i			0.408909i
$188$	10.9050	+	6.29599i	0.795327	+	0.459182i
$189$	3.93315	+	2.27081i	0.286095	+	0.165177i
$190$		−	2.33052i		−	0.169074i
$191$	5.95829	−	10.3201i	0.431126	−	0.746733i	−0.565844	−	0.824512i	$-0.691450\pi$
$191$	5.95829	−	10.3201i	0.431126	−	0.746733i	0.996971	+	0.0777794i	$0.0247830\pi$
$192$	−0.770256	−	1.33412i	−0.0555884	−	0.0962820i
$193$	6.46938	−	3.73510i	0.465676	−	0.268858i	−0.248752	−	0.968567i	$-0.580020\pi$
$193$	6.46938	−	3.73510i	0.465676	−	0.268858i	0.714428	+	0.699709i	$0.246687\pi$
$194$	17.1449			1.23093
$195$	−9.17954	+	5.70266i	−0.657361	+	0.408376i
$196$	17.3891			1.24208
$197$	2.88252	−	1.66422i	0.205371	−	0.118571i	−0.393787	−	0.919202i	$-0.628835\pi$
$197$	2.88252	−	1.66422i	0.205371	−	0.118571i	0.599158	+	0.800631i	$0.295502\pi$
$198$	−0.905006	−	1.56752i	−0.0643160	−	0.111399i
$199$	0.951549	−	1.64813i	0.0674535	−	0.116833i	−0.830326	−	0.557278i	$-0.811846\pi$
$199$	0.951549	−	1.64813i	0.0674535	−	0.116833i	0.897780	+	0.440445i	$0.145179\pi$
$200$		−	5.21900i		−	0.369039i
$201$	−5.85524	−	3.38052i	−0.412997	−	0.238444i
$202$	4.14231	+	2.39156i	0.291452	+	0.168270i
$203$		−	20.7525i		−	1.45654i
$204$	−3.56795	+	6.17986i	−0.249806	+	0.432677i
$205$	15.8787	+	27.5027i	1.10902	+	1.92088i
$206$	−22.6197	+	13.0595i	−1.57599	+	0.909896i
$207$	7.72067			0.536623
$208$	−9.36812	−	15.0798i	−0.649562	−	1.04560i
$209$	0.429586			0.0297151
$210$	21.3375	−	12.3192i	1.47243	−	0.850106i
$211$	0.555345	+	0.961886i	0.0382316	+	0.0662190i	0.884508	−	0.466525i	$-0.154494\pi$
$211$	0.555345	+	0.961886i	0.0382316	+	0.0662190i	−0.846276	+	0.532744i	$0.821161\pi$
$212$	−6.78001	+	11.7433i	−0.465653	+	0.806535i
$213$		−	2.50552i		−	0.171676i
$214$	−21.2949	−	12.2946i	−1.45569	−	0.840442i
$215$	5.93991	+	3.42941i	0.405099	+	0.233884i
$216$			1.31019i			0.0891468i
$217$	−0.237795	+	0.411873i	−0.0161426	+	0.0279598i
$218$	−0.703266	−	1.21809i	−0.0476312	−	0.0824996i
$219$	11.4861	−	6.63151i	0.776160	−	0.448116i
$220$	−3.82491			−0.257875
$221$	−9.51174	+	17.7766i	−0.639829	+	1.19578i
$222$	−15.0116			−1.00751
$223$	18.8287	−	10.8708i	1.26087	−	0.727961i	0.287624	−	0.957743i	$-0.407135\pi$
$223$	18.8287	−	10.8708i	1.26087	−	0.727961i	0.973242	+	0.229782i	$0.0738013\pi$
$224$	14.2872	+	24.7461i	0.954601	+	1.65342i
$225$	1.99171	−	3.44973i	0.132780	−	0.229982i
$226$		−	19.6958i		−	1.31015i
$227$	−23.8743	−	13.7838i	−1.58459	−	0.914866i	−0.994176	−	0.107769i	$-0.965629\pi$
$227$	−23.8743	−	13.7838i	−1.58459	−	0.914866i	−0.590419	−	0.807097i	$-0.701037\pi$
$228$	0.474768	+	0.274107i	0.0314423	+	0.0181532i
$229$			17.5599i			1.16039i	0.814476	+	0.580197i	$0.197024\pi$
$229$			17.5599i			1.16039i	−0.814476	+	0.580197i	$0.802976\pi$
$230$	20.9424	−	36.2734i	1.38090	−	2.39179i
$231$	2.27081	+	3.93315i	0.149408	+	0.258783i
$232$	5.18469	−	2.99338i	0.340392	−	0.196525i
$233$	5.10960			0.334741			0.167371	−	0.985894i	$-0.446472\pi$
$233$	5.10960			0.334741			0.167371	+	0.985894i	$0.446472\pi$
$234$	−0.210686	−	6.52269i	−0.0137730	−	0.426402i
$235$	−29.5743			−1.92921
$236$	−9.76052	+	5.63524i	−0.635356	+	0.366823i
$237$	−3.55715	−	6.16116i	−0.231062	−	0.400210i
$238$	22.9832	−	39.8080i	1.48978	−	2.58037i
$239$			11.8494i			0.766475i	0.923650	+	0.383238i	$0.125191\pi$
$239$			11.8494i			0.766475i	−0.923650	+	0.383238i	$0.874809\pi$
$240$	12.7805	+	7.37881i	0.824975	+	0.476300i
$241$	0.544166	+	0.314174i	0.0350528	+	0.0202378i	0.517424	−	0.855729i	$-0.326891\pi$
$241$	0.544166	+	0.314174i	0.0350528	+	0.0202378i	−0.482371	+	0.875967i	$0.660224\pi$
$242$		−	1.81001i		−	0.116352i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.48483	−	6.03590i	−0.223093	−	0.386409i
$245$	−35.3694	+	20.4206i	−2.25967	+	1.30462i
$246$	−19.1781			−1.22275
$247$	1.36568	+	0.730739i	0.0868965	+	0.0464958i
$248$	−0.137200			−0.00871223
$249$	−0.865941	+	0.499952i	−0.0548768	+	0.0316831i
$250$	2.75752	+	4.77616i	0.174401	+	0.302071i
$251$	−6.40387	+	11.0918i	−0.404209	+	0.700110i	−0.994229	−	0.107278i	$-0.965786\pi$
$251$	−6.40387	+	11.0918i	−0.404209	+	0.700110i	0.590020	+	0.807388i	$0.299120\pi$
$252$			5.79576i			0.365099i
$253$	6.68629	+	3.86033i	0.420364	+	0.242697i
$254$	−12.1581	−	7.01950i	−0.762869	−	0.440442i
$255$		−	16.7598i		−	1.04954i
$256$	−10.4050	+	18.0221i	−0.650315	+	1.12638i
$257$	6.57801	+	11.3934i	0.410325	+	0.710703i	0.994925	−	0.100618i	$-0.0320820\pi$
$257$	6.57801	+	11.3934i	0.410325	+	0.710703i	−0.584600	+	0.811321i	$0.698749\pi$
$258$	−3.58708	+	2.07100i	−0.223322	+	0.128935i
$259$	37.6666			2.34049
$260$	−12.1597	−	6.50628i	−0.754110	−	0.403503i
$261$	4.56940			0.282839
$262$	6.38795	−	3.68808i	0.394649	−	0.227851i
$263$	4.35205	+	7.53797i	0.268359	+	0.464811i	0.968438	−	0.249254i	$-0.0801854\pi$
$263$	4.35205	+	7.53797i	0.268359	+	0.464811i	−0.700079	+	0.714065i	$0.746852\pi$
$264$	−0.655093	+	1.13465i	−0.0403182	+	0.0698331i
$265$		−	31.8479i		−	1.95640i
$266$	−3.05825	−	1.76568i	−0.187513	−	0.108261i
$267$	6.28593	+	3.62919i	0.384693	+	0.222103i
$268$		−	8.62808i		−	0.527044i
$269$	−5.05893	+	8.76232i	−0.308448	+	0.534248i	−0.978023	−	0.208497i	$-0.933143\pi$
$269$	−5.05893	+	8.76232i	−0.308448	+	0.534248i	0.669575	+	0.742745i	$0.266476\pi$
$270$	2.71252	+	4.69821i	0.165078	+	0.285924i
$271$	−25.0413	+	14.4576i	−1.52115	+	0.878238i	−0.521464	+	0.853273i	$0.674614\pi$
$271$	−25.0413	+	14.4576i	−1.52115	+	0.878238i	−0.999688	+	0.0249643i	$0.992053\pi$
$272$	27.5324			1.66939
$273$	0.528646	+	16.3665i	0.0319951	+	0.990545i
$274$	−6.69126			−0.404234
$275$	3.44973	−	1.99171i	0.208027	−	0.120104i
$276$	4.92635	+	8.53269i	0.296531	+	0.513607i
$277$	−4.64518	+	8.04569i	−0.279102	+	0.483418i	−0.971162	−	0.238422i	$-0.923370\pi$
$277$	−4.64518	+	8.04569i	−0.279102	+	0.483418i	0.692060	+	0.721840i	$0.256703\pi$
$278$			1.02613i			0.0615433i
$279$	−0.0906887	−	0.0523592i	−0.00542939	−	0.00313466i
$280$	−15.4452	−	8.91730i	−0.923029	−	0.532911i
$281$		−	1.40995i		−	0.0841105i	−0.999115	−	0.0420553i	$-0.986609\pi$
$281$		−	1.40995i		−	0.0841105i	0.999115	−	0.0420553i	$-0.0133906\pi$
$282$	8.92988	−	15.4670i	0.531766	−	0.921047i
$283$	−1.60603	−	2.78172i	−0.0954684	−	0.165356i	0.814336	−	0.580394i	$-0.197102\pi$
$283$	−1.60603	−	2.78172i	−0.0954684	−	0.165356i	−0.909804	+	0.415038i	$0.863768\pi$
$284$	2.76904	−	1.59871i	0.164312	−	0.0948658i
$285$	−1.28757			−0.0762691
$286$	3.07889	−	5.75416i	0.182058	−	0.340251i
$287$	48.1211			2.84050
$288$	−5.44874	+	3.14583i	−0.321070	+	0.185370i
$289$	−7.13385	−	12.3562i	−0.419638	−	0.726835i
$290$	12.3946	−	21.4680i	0.727835	−	1.26065i
$291$		−	9.47227i		−	0.555274i
$292$	14.6580	+	8.46278i	0.857792	+	0.495247i
$293$	18.8255	+	10.8689i	1.09980	+	0.634969i	0.936168	−	0.351553i	$-0.114346\pi$
$293$	18.8255	+	10.8689i	1.09980	+	0.634969i	0.163630	+	0.986522i	$0.447680\pi$
$294$		−	24.6637i		−	1.43842i
$295$	13.2353	−	22.9242i	0.770587	−	1.33470i
$296$	5.43311	+	9.41043i	0.315793	+	0.546970i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	0.280598			0.0162546
$299$	14.6897	+	23.6459i	0.849525	+	1.36748i
$300$	5.08341			0.293491
$301$	9.00057	−	5.19648i	0.518784	−	0.299520i
$302$	10.4825	+	18.1562i	0.603200	+	1.04477i
$303$	1.32130	−	2.28855i	0.0759065	−	0.131474i
$304$		−	2.11517i		−	0.121313i
$305$	14.1763	+	8.18467i	0.811731	+	0.468653i
$306$	8.76517	+	5.06057i	0.501071	+	0.289294i
$307$		−	15.2363i		−	0.869579i	−0.900532	−	0.434789i	$-0.856823\pi$
$307$		−	15.2363i		−	0.869579i	0.900532	−	0.434789i	$-0.143177\pi$
$308$	−2.89788	+	5.01928i	−0.165122	+	0.286000i
$309$	7.21512	+	12.4970i	0.410454	+	0.710927i
$310$	−0.491989	+	0.284050i	−0.0279431	+	0.0161330i
$311$	7.66303			0.434530			0.217265	−	0.976113i	$-0.430286\pi$
$311$	7.66303			0.434530			0.217265	+	0.976113i	$0.430286\pi$
$312$	−4.01267	+	2.49281i	−0.227172	+	0.141128i
$313$	13.9879			0.790642			0.395321	−	0.918543i	$-0.370633\pi$
$313$	13.9879			0.790642			0.395321	+	0.918543i	$0.370633\pi$
$314$	−15.8349	+	9.14228i	−0.893615	+	0.515929i
$315$	−6.80614	−	11.7886i	−0.383483	−	0.664211i
$316$	4.53944	−	7.86254i	0.255363	−	0.442302i
$317$			2.11260i			0.118655i	0.998239	+	0.0593277i	$0.0188957\pi$
$317$			2.11260i			0.118655i	−0.998239	+	0.0593277i	$0.981104\pi$
$318$	16.6561	+	9.61638i	0.934025	+	0.539260i
$319$	3.95722	+	2.28470i	0.221562	+	0.127919i
$320$			4.61728i			0.258114i
$321$	−6.79256	+	11.7651i	−0.379124	+	0.656661i
$322$	−31.7334	−	54.9639i	−1.76843	−	3.06302i
$323$	−2.08031	+	1.20107i	−0.115752	+	0.0668293i
$324$	−1.27615			−0.0708970
$325$	14.3549	−	0.463670i	0.796267	−	0.0257198i
$326$	−20.0200			−1.10880
$327$	−0.672975	+	0.388542i	−0.0372156	+	0.0214864i
$328$	6.94109	+	12.0223i	0.383257	+	0.663821i
$329$	−22.4065	+	38.8092i	−1.23531	+	2.13962i
$330$			5.42503i			0.298638i
$331$	13.2106	+	7.62716i	0.726122	+	0.419227i	0.817002	−	0.576635i	$-0.195635\pi$
$331$	13.2106	+	7.62716i	0.726122	+	0.419227i	−0.0908798	+	0.995862i	$0.528968\pi$
$332$	−1.10507	−	0.638011i	−0.0606485	−	0.0350154i
$333$			8.29366i			0.454490i
$334$	−21.4713	+	37.1894i	−1.17486	+	2.03491i
$335$	10.1322	+	17.5495i	0.553582	+	0.958833i
$336$	19.3658	−	11.1809i	1.05649	−	0.609967i
$337$	19.7832			1.07766			0.538831	−	0.842414i	$-0.318866\pi$
$337$	19.7832			1.07766			0.538831	+	0.842414i	$0.318866\pi$
$338$	19.5760	−	13.0556i	1.06479	−	0.710131i
$339$	−10.8816			−0.591008
$340$	18.5225	−	10.6940i	1.00452	−	0.579962i
$341$	−0.0523592	−	0.0906887i	−0.00283541	−	0.00491107i
$342$	0.388778	−	0.673384i	0.0210227	−	0.0364124i
$343$			30.0940i			1.62492i
$344$	2.59652	+	1.49910i	0.139995	+	0.0808262i
$345$	−20.0404	−	11.5703i	−1.07894	−	0.622925i
$346$			24.1917i			1.30055i
$347$	−2.61739	+	4.53346i	−0.140509	+	0.243369i	−0.927688	−	0.373355i	$-0.878207\pi$
$347$	−2.61739	+	4.53346i	−0.140509	+	0.243369i	0.787179	+	0.616724i	$0.211541\pi$
$348$	2.91561	+	5.04999i	0.156293	+	0.270708i
$349$	−18.1416	+	10.4741i	−0.971099	+	0.560664i	−0.899571	−	0.436774i	$-0.856121\pi$
$349$	−18.1416	+	10.4741i	−0.971099	+	0.560664i	−0.0715281	+	0.997439i	$0.522788\pi$
$350$	−32.7452			−1.75030
$351$	−3.60367	+	0.116400i	−0.192350	+	0.00621299i
$352$	−6.29167			−0.335347
$353$	12.3660	−	7.13949i	0.658173	−	0.379996i	−0.133407	−	0.991061i	$-0.542592\pi$
$353$	12.3660	−	7.13949i	0.658173	−	0.379996i	0.791581	+	0.611065i	$0.209259\pi$
$354$	7.99270	+	13.8438i	0.424807	+	0.735788i
$355$	−3.75482	+	6.50354i	−0.199285	+	0.345172i
$356$			9.26274i			0.490924i
$357$	−21.9932	−	12.6978i	−1.16400	−	0.672039i
$358$	−26.8962	−	15.5285i	−1.42151	−	0.820709i
$359$		−	17.5026i		−	0.923751i	−0.886945	−	0.461875i	$-0.847177\pi$
$359$		−	17.5026i		−	0.923751i	0.886945	−	0.461875i	$-0.152823\pi$
$360$	1.96347	−	3.40082i	0.103484	−	0.179239i
$361$	−9.40773	−	16.2947i	−0.495144	−	0.857614i
$362$	−11.3984	+	6.58087i	−0.599087	+	0.345883i
$363$	−1.00000			−0.0524864
$364$	−17.7505	+	11.0273i	−0.930380	+	0.577986i
$365$	−39.7524			−2.08073
$366$	−8.56097	+	4.94268i	−0.447489	+	0.258358i
$367$	−4.59106	−	7.95195i	−0.239651	−	0.415088i	0.720963	−	0.692974i	$-0.243700\pi$
$367$	−4.59106	−	7.95195i	−0.239651	−	0.415088i	−0.960614	+	0.277885i	$0.910366\pi$
$368$	19.0073	−	32.9216i	0.990824	−	1.71616i
$369$			10.5956i			0.551584i
$370$	38.9654	+	22.4967i	2.02571	+	1.16955i
$371$	−41.7927	−	24.1291i	−2.16977	−	1.25272i
$372$		−	0.133636i		−	0.00692870i
$373$	−6.21197	+	10.7594i	−0.321643	+	0.557103i	−0.980827	−	0.194879i	$-0.937569\pi$
$373$	−6.21197	+	10.7594i	−0.321643	+	0.557103i	0.659184	+	0.751982i	$0.270902\pi$
$374$	5.06057	+	8.76517i	0.261676	+	0.453236i
$375$	2.63874	−	1.52348i	0.136264	−	0.0786721i
$376$	−12.9279			−0.666703
$377$	8.69394	+	13.9946i	0.447761	+	0.720758i
$378$	8.22038			0.422811
$379$	−26.1130	+	15.0764i	−1.34134	+	0.774420i	−0.987003	−	0.160700i	$-0.948625\pi$
$379$	−26.1130	+	15.0764i	−1.34134	+	0.774420i	−0.354332	+	0.935120i	$0.615292\pi$
$380$	−0.821564	−	1.42299i	−0.0421453	−	0.0729978i
$381$	−3.87815	+	6.71715i	−0.198684	+	0.344130i
$382$		−	21.5691i		−	1.10357i
$383$	−7.73350	−	4.46494i	−0.395163	−	0.228148i	0.289232	−	0.957259i	$-0.406600\pi$
$383$	−7.73350	−	4.46494i	−0.395163	−	0.228148i	−0.684395	+	0.729112i	$0.739934\pi$
$384$	8.48271	+	4.89749i	0.432881	+	0.249924i
$385$		−	13.6123i		−	0.693746i
$386$	6.76058	−	11.7097i	0.344104	−	0.596006i
$387$	1.14419	+	1.98180i	0.0581625	+	0.100740i
$388$	10.4685	−	6.04400i	0.531458	−	0.306838i
$389$	2.58520			0.131075			0.0655373	−	0.997850i	$-0.479124\pi$
$389$	2.58520			0.131075			0.0655373	+	0.997850i	$0.479124\pi$
$390$	−9.22814	+	17.2466i	−0.467285	+	0.873314i
$391$	−43.1721			−2.18331
$392$	−15.4611	+	8.92647i	−0.780903	+	0.450855i
$393$	−2.03760	−	3.52923i	−0.102783	−	0.178026i
$394$	3.01226	−	5.21739i	0.151756	−	0.262848i
$395$			21.3232i			1.07289i
$396$	−1.10517	−	0.638073i	−0.0555371	−	0.0320644i
$397$	16.0578	+	9.27097i	0.805917	+	0.465297i	0.845536	−	0.533918i	$-0.179281\pi$
$397$	16.0578	+	9.27097i	0.805917	+	0.465297i	−0.0396188	+	0.999215i	$0.512614\pi$
$398$		−	3.44463i		−	0.172664i
$399$	−0.975507	+	1.68963i	−0.0488365	+	0.0845872i
$400$	−9.80665	−	16.9856i	−0.490332	−	0.849280i
$401$	18.3275	−	10.5814i	0.915234	−	0.528411i	0.0331226	−	0.999451i	$-0.489455\pi$
$401$	18.3275	−	10.5814i	0.915234	−	0.528411i	0.882111	+	0.471041i	$0.156121\pi$
$402$	−12.2376			−0.610355
$403$	−0.0121893	−	0.377370i	−0.000607190	−	0.0187982i
$404$	3.37234			0.167780
$405$	2.59568	−	1.49862i	0.128980	−	0.0744669i
$406$	−18.7811	−	32.5299i	−0.932091	−	1.61443i
$407$	−4.14683	+	7.18252i	−0.205551	+	0.356024i
$408$		−	7.32623i		−	0.362702i
$409$	−14.8574	−	8.57790i	−0.734649	−	0.424150i	0.0854716	−	0.996341i	$-0.472760\pi$
$409$	−14.8574	−	8.57790i	−0.734649	−	0.424150i	−0.820120	+	0.572191i	$0.806094\pi$
$410$	49.7803	+	28.7407i	2.45848	+	1.41940i
$411$			3.69680i			0.182350i
$412$	−9.20755	+	15.9479i	−0.453624	+	0.785699i
$413$	−20.0550	−	34.7363i	−0.986841	−	1.70926i
$414$	12.1023	−	6.98725i	0.594794	−	0.343405i
$415$	2.99694			0.147114
$416$	−20.0017	−	10.7023i	−0.980662	−	0.524724i
$417$	0.566920			0.0277622
$418$	0.673384	−	0.388778i	0.0329363	−	0.0190158i
$419$	7.86209	+	13.6175i	0.384088	+	0.665260i	0.991642	−	0.129018i	$-0.0411826\pi$
$419$	7.86209	+	13.6175i	0.384088	+	0.665260i	−0.607554	+	0.794278i	$0.707849\pi$
$420$	8.68563	−	15.0440i	0.423815	−	0.734070i
$421$		−	14.8298i		−	0.722758i	−0.932419	−	0.361379i	$-0.882306\pi$
$421$		−	14.8298i		−	0.722758i	0.932419	−	0.361379i	$-0.117694\pi$
$422$	1.74103	+	1.00518i	0.0847518	+	0.0489315i
$423$	−8.54524	−	4.93360i	−0.415484	−	0.239880i
$424$		−	13.9217i		−	0.676098i
$425$	−11.1371	+	19.2901i	−0.540230	+	0.935706i
$426$	−2.26751	−	3.92745i	−0.109861	−	0.190286i
$427$	21.4809	−	12.4020i	1.03953	−	0.600174i
$428$	−17.3366			−0.837996
$429$	−3.17907	−	1.70103i	−0.153487	−	0.0821265i
$430$	12.4146			0.598683
$431$	−33.6629	+	19.4353i	−1.62148	+	0.936164i	−0.634961	+	0.772545i	$0.718984\pi$
$431$	−33.6629	+	19.4353i	−1.62148	+	0.936164i	−0.986523	+	0.163620i	$0.947683\pi$
$432$	2.46187	+	4.26409i	0.118447	+	0.205156i
$433$	15.9488	−	27.6242i	0.766451	−	1.32753i	−0.173024	−	0.984918i	$-0.555354\pi$
$433$	15.9488	−	27.6242i	0.766451	−	1.32753i	0.939476	−	0.342615i	$-0.111313\pi$
$434$			0.860824i			0.0413209i
$435$	−11.8607	−	6.84779i	−0.568678	−	0.328326i
$436$	−0.858814	−	0.495836i	−0.0411297	−	0.0237463i
$437$			3.31669i			0.158659i
$438$	12.0031	−	20.7900i	0.573531	−	0.993385i
$439$	11.0450	+	19.1304i	0.527147	+	0.913045i	0.999499	+	0.0316356i	$0.0100716\pi$
$439$	11.0450	+	19.1304i	0.527147	+	0.913045i	−0.472352	+	0.881410i	$0.656595\pi$
$440$	3.40082	−	1.96347i	0.162128	−	0.0936045i
$441$	−13.6263			−0.648870
$442$	1.17810	+	36.4733i	0.0560367	+	1.73486i
$443$	39.1634			1.86071			0.930355	−	0.366660i	$-0.119499\pi$
$443$	39.1634			1.86071			0.930355	+	0.366660i	$0.119499\pi$
$444$	−9.16594	+	5.29196i	−0.434996	+	0.251145i
$445$	−10.8775	−	18.8404i	−0.515644	−	0.893121i
$446$	19.6763	−	34.0803i	0.931698	−	1.61375i
$447$		−	0.155025i		−	0.00733245i
$448$	6.05907	+	3.49821i	0.286264	+	0.165275i
$449$	−26.3060	−	15.1878i	−1.24146	−	0.716755i	−0.272065	−	0.962279i	$-0.587707\pi$
$449$	−26.3060	−	15.1878i	−1.24146	−	0.716755i	−0.969391	+	0.245524i	$0.921040\pi$
$450$		−	7.21002i		−	0.339884i
$451$	−5.29779	+	9.17604i	−0.249463	+	0.432083i
$452$	−6.94326	−	12.0261i	−0.326583	−	0.565659i
$453$	10.0310	−	5.79139i	0.471297	−	0.272103i
$454$	−49.8979			−2.34182
$455$	23.1549	−	43.2744i	1.08552	−	2.02874i
$456$	−0.562837			−0.0263573
$457$	−26.3026	+	15.1858i	−1.23039	+	0.710364i	−0.967110	−	0.254357i	$-0.918136\pi$
$457$	−26.3026	+	15.1858i	−1.23039	+	0.710364i	−0.263276	+	0.964721i	$0.584803\pi$
$458$	15.8919	+	27.5255i	0.742578	+	1.28618i
$459$	2.79588	−	4.84260i	0.130500	−	0.226033i
$460$		−	29.5308i		−	1.37688i
$461$	0.517649	+	0.298865i	0.0241093	+	0.0139195i	0.512006	−	0.858982i	$-0.328902\pi$
$461$	0.517649	+	0.298865i	0.0241093	+	0.0139195i	−0.487897	+	0.872901i	$0.662236\pi$
$462$	7.11906	+	4.11019i	0.331209	+	0.191223i
$463$		−	37.7369i		−	1.75378i	−0.480687	−	0.876892i	$-0.659613\pi$
$463$		−	37.7369i		−	1.75378i	0.480687	−	0.876892i	$-0.340387\pi$
$464$	11.2493	−	19.4843i	0.522235	−	0.904538i
$465$	0.156933	+	0.271815i	0.00727758	+	0.0126051i
$466$	8.00939	−	4.62422i	0.371028	−	0.214213i
$467$	8.43576			0.390360			0.195180	−	0.980767i	$-0.437471\pi$
$467$	8.43576			0.390360			0.195180	+	0.980767i	$0.437471\pi$
$468$	−2.42805	−	3.90842i	−0.112237	−	0.180667i
$469$	30.7061			1.41787
$470$	−46.3582	+	26.7649i	−2.13835	+	1.23457i
$471$	5.05095	+	8.74850i	0.232735	+	0.403110i
$472$	5.78555	−	10.0209i	0.266302	−	0.461248i
$473$			2.28838i			0.105220i
$474$	−11.1518	−	6.43848i	−0.512218	−	0.295729i
$475$	1.48196	+	0.855609i	0.0679969	+	0.0392580i
$476$		−	32.4085i		−	1.48544i
$477$	5.31288	−	9.20218i	0.243260	−	0.421339i
$478$	10.7238	+	18.5742i	0.490495	+	0.849563i
$479$	−13.9427	+	8.04984i	−0.637060	+	0.367807i	−0.783481	−	0.621416i	$-0.786558\pi$
$479$	−13.9427	+	8.04984i	−0.637060	+	0.367807i	0.146421	+	0.989222i	$0.453224\pi$
$480$	18.8576			0.860728
$481$	−25.4007	+	15.7799i	−1.15817	+	0.719499i
$482$	1.13732			0.0518035
$483$	−30.3666	+	17.5321i	−1.38173	+	0.797740i
$484$	−0.638073	−	1.10517i	−0.0290033	−	0.0502352i
$485$	−14.1953	+	24.5870i	−0.644576	+	1.11644i
$486$			1.81001i			0.0821038i
$487$	−27.0055	−	15.5917i	−1.22374	−	0.706525i	−0.258025	−	0.966138i	$-0.583072\pi$
$487$	−27.0055	−	15.5917i	−1.22374	−	0.706525i	−0.965713	+	0.259613i	$0.916405\pi$
$488$	6.19689	+	3.57778i	0.280520	+	0.161958i
$489$			11.0607i			0.500181i
$490$	−36.9615	+	64.0191i	−1.66975	+	2.89209i
$491$	−3.02452	−	5.23862i	−0.136495	−	0.236416i	0.789673	−	0.613528i	$-0.210250\pi$
$491$	−3.02452	−	5.23862i	−0.136495	−	0.236416i	−0.926167	+	0.377112i	$0.876917\pi$
$492$	−11.7100	+	6.76076i	−0.527926	+	0.304798i
$493$	−25.5510			−1.15076
$494$	2.80206	−	0.0905078i	0.126071	−	0.00407214i
$495$	2.99723			0.134716
$496$	−0.446528	+	0.257803i	−0.0200497	+	0.0115757i
$497$	5.68956	+	9.85461i	0.255212	+	0.442039i
$498$	−0.904919	+	1.56737i	−0.0405504	+	0.0702353i
$499$		−	9.70687i		−	0.434539i	−0.976112	−	0.217270i	$-0.930285\pi$
$499$		−	9.70687i		−	0.434539i	0.976112	−	0.217270i	$-0.0697151\pi$
$500$	3.36742	+	1.94418i	0.150596	+	0.0869464i
$501$	20.5465	+	11.8625i	0.917949	+	0.529978i
$502$			23.1822i			1.03467i
$503$	3.33594	−	5.77801i	0.148742	−	0.257629i	−0.782021	−	0.623252i	$-0.785811\pi$
$503$	3.33594	−	5.77801i	0.148742	−	0.257629i	0.930763	+	0.365624i	$0.119144\pi$
$504$	−2.97518	−	5.15316i	−0.132525	−	0.229540i
$505$	−6.85933	+	3.96024i	−0.305236	+	0.176228i
$506$	13.9745			0.621243
$507$	−7.21299	−	10.8154i	−0.320340	−	0.480329i
$508$	−9.89817			−0.439160
$509$	30.3509	−	17.5231i	1.34528	−	0.776698i	0.357704	−	0.933835i	$-0.383560\pi$
$509$	30.3509	−	17.5231i	1.34528	−	0.776698i	0.987577	+	0.157137i	$0.0502264\pi$
$510$	−15.1677	−	26.2713i	−0.671638	−	1.16331i
$511$	−30.1178	+	52.1655i	−1.33233	+	2.30767i
$512$			18.0765i			0.798877i
$513$	−0.372032	−	0.214793i	−0.0164256	−	0.00948334i
$514$	20.6223	+	11.9063i	0.909609	+	0.525163i
$515$		−	43.2508i		−	1.90586i
$516$	−1.46016	+	2.52906i	−0.0642798	+	0.111336i
$517$	−4.93360	−	8.54524i	−0.216979	−	0.375819i
$518$	59.0430	−	34.0885i	2.59420	−	1.49776i
$519$	13.3655			0.586680
$520$	14.1514	−	0.457096i	0.620579	−	0.0200450i
$521$	−25.2873			−1.10786			−0.553928	−	0.832564i	$-0.686872\pi$
$521$	−25.2873			−1.10786			−0.553928	+	0.832564i	$0.686872\pi$
$522$	7.16262	−	4.13534i	0.313499	−	0.180999i
$523$	12.7624	+	22.1051i	0.558059	+	0.966587i	0.997658	+	0.0683932i	$0.0217872\pi$
$523$	12.7624	+	22.1051i	0.558059	+	0.966587i	−0.439599	+	0.898194i	$0.644879\pi$
$524$	2.60028	−	4.50381i	0.113594	−	0.196750i
$525$			18.0911i			0.789561i
$526$	13.6438	+	7.87727i	0.594899	+	0.343465i
$527$	0.507109	+	0.292779i	0.0220900	+	0.0127537i
$528$			4.92374i			0.214278i
$529$	−18.3043	+	31.7041i	−0.795841	+	1.37844i
$530$	−28.8225	−	49.9221i	−1.25197	−	2.16848i
$531$	7.64844	−	4.41583i	0.331914	−	0.191631i
$532$	−2.48978			−0.107946
$533$	−32.4508	+	20.1596i	−1.40560	+	0.873209i
$534$	13.1377			0.568526
$535$	35.2626	−	20.3589i	1.52454	−	0.880191i
$536$	4.42911	+	7.67145i	0.191309	+	0.331356i
$537$	−8.57924	+	14.8597i	−0.370222	+	0.641243i
$538$			18.3134i			0.789549i
$539$	−11.8007	−	6.81313i	−0.508292	−	0.293462i
$540$	3.31247	+	1.91245i	0.142546	+	0.0822989i
$541$			25.0265i			1.07597i	0.842953	+	0.537987i	$0.180815\pi$
$541$			25.0265i			1.07597i	−0.842953	+	0.537987i	$0.819185\pi$
$542$	−26.1685	+	45.3251i	−1.12403	+	1.94688i
$543$	3.63582	+	6.29742i	0.156028	+	0.270248i
$544$	30.4680	−	17.5907i	1.30631	−	0.754196i
$545$	2.32910			0.0997678
$546$	15.6404	+	25.1763i	0.669349	+	1.07745i
$547$	−30.3554			−1.29790			−0.648951	−	0.760830i	$-0.724792\pi$
$547$	−30.3554			−1.29790			−0.648951	+	0.760830i	$0.724792\pi$
$548$	−4.08561	+	2.35883i	−0.174529	+	0.100764i
$549$	2.73074	+	4.72978i	0.116545	+	0.201862i
$550$	3.60501	−	6.24406i	0.153718	−	0.266248i
$551$			1.96295i			0.0836246i
$552$	−8.76028	−	5.05775i	−0.372862	−	0.215272i
$553$	27.9816	+	16.1552i	1.18990	+	0.686989i
$554$			16.8157i			0.714429i
$555$	12.4290	−	21.5277i	0.527582	−	0.913799i
$556$	0.361736	+	0.626545i	0.0153410	+	0.0265714i
$557$	−2.71656	+	1.56840i	−0.115104	+	0.0664554i	−0.556447	−	0.830883i	$-0.687836\pi$
$557$	−2.71656	+	1.56840i	−0.115104	+	0.0664554i	0.441343	+	0.897339i	$0.354502\pi$
$558$	−0.189541			−0.00802393
$559$	−3.89261	+	7.27494i	−0.164640	+	0.307697i
$560$	−67.0234			−2.83225
$561$	4.84260	−	2.79588i	0.204455	−	0.118042i
$562$	−1.27601	−	2.21012i	−0.0538254	−	0.0932282i
$563$	−2.07613	+	3.59597i	−0.0874985	+	0.151552i	−0.906453	−	0.422306i	$-0.861221\pi$
$563$	−2.07613	+	3.59597i	−0.0874985	+	0.151552i	0.818955	+	0.573858i	$0.194554\pi$
$564$		−	12.5920i		−	0.530218i
$565$	28.2452	+	16.3074i	1.18828	+	0.686056i
$566$	−5.03495	−	2.90693i	−0.211635	−	0.122187i
$567$		−	4.54162i		−	0.190730i
$568$	−1.64135	+	2.84290i	−0.0688695	+	0.119285i
$569$	6.27920	+	10.8759i	0.263238	+	0.455941i	0.967100	−	0.254395i	$-0.0818763\pi$
$569$	6.27920	+	10.8759i	0.263238	+	0.455941i	−0.703863	+	0.710336i	$0.748543\pi$
$570$	−2.01829	+	1.16526i	−0.0845368	+	0.0488073i
$571$	11.4736			0.480154			0.240077	−	0.970754i	$-0.422827\pi$
$571$	11.4736			0.480154			0.240077	+	0.970754i	$0.422827\pi$
$572$	−0.148544	−	4.59881i	−0.00621093	−	0.192286i
$573$	−11.9166			−0.497822
$574$	75.4306	−	43.5499i	3.14841	−	1.81774i
$575$	15.3773	+	26.6343i	0.641277	+	1.11073i
$576$	−0.770256	+	1.33412i	−0.0320940	+	0.0555884i
$577$		−	31.6119i		−	1.31602i	−0.753009	−	0.658010i	$-0.771398\pi$
$577$		−	31.6119i		−	1.31602i	0.753009	−	0.658010i	$-0.228602\pi$
$578$	−22.3649	−	12.9124i	−0.930256	−	0.537083i
$579$	−6.46938	−	3.73510i	−0.268858	−	0.155225i
$580$		−	17.4775i		−	0.725716i
$581$	2.27059	−	3.93277i	0.0941998	−	0.163159i
$582$	−8.57247	−	14.8479i	−0.355340	−	0.615467i
$583$	9.20218	−	5.31288i	0.381115	−	0.220037i
$584$	−17.3770			−0.719066
$585$	9.52842	+	5.09839i	0.393952	+	0.210792i
$586$	39.3457			1.62536
$587$	25.8323	−	14.9143i	1.06621	−	0.615579i	0.139069	−	0.990283i	$-0.455589\pi$
$587$	25.8323	−	14.9143i	1.06621	−	0.615579i	0.927145	+	0.374704i	$0.122256\pi$
$588$	−8.69455	−	15.0594i	−0.358557	−	0.621039i
$589$	0.0224928	−	0.0389586i	0.000926798	−	0.00160526i
$590$		−	47.9120i		−	1.97251i
$591$	−2.88252	−	1.66422i	−0.118571	−	0.0684569i
$592$	35.3649	+	20.4179i	1.45349	+	0.839171i
$593$			5.64786i			0.231930i	0.993253	+	0.115965i	$0.0369960\pi$
$593$			5.64786i			0.231930i	−0.993253	+	0.115965i	$0.963004\pi$
$594$	−0.905006	+	1.56752i	−0.0371329	+	0.0643160i
$595$	38.0583	+	65.9188i	1.56024	+	2.70241i
$596$	0.171330	−	0.0989175i	0.00701796	−	0.00405182i
$597$	−1.90310			−0.0778886
$598$	44.4260	+	23.7711i	1.81671	+	0.972071i
$599$	10.6802			0.436382			0.218191	−	0.975906i	$-0.429984\pi$
$599$	10.6802			0.436382			0.218191	+	0.975906i	$0.429984\pi$
$600$	−4.51979	+	2.60950i	−0.184520	+	0.106532i
$601$	4.11581	+	7.12879i	0.167887	+	0.290790i	0.937677	−	0.347508i	$-0.112972\pi$
$601$	4.11581	+	7.12879i	0.167887	+	0.290790i	−0.769789	+	0.638298i	$0.779639\pi$
$602$	9.40569	−	16.2911i	0.383347	−	0.663977i
$603$			6.76105i			0.275331i
$604$	12.8010	+	7.39067i	0.520866	+	0.300722i
$605$	2.59568	+	1.49862i	0.105529	+	0.0609274i
$606$		−	4.78313i		−	0.194301i
$607$	6.42540	−	11.1291i	0.260799	−	0.451717i	−0.705656	−	0.708555i	$-0.749347\pi$
$607$	6.42540	−	11.1291i	0.260799	−	0.451717i	0.966454	+	0.256838i	$0.0826808\pi$
$608$	−1.35141	−	2.34070i	−0.0548068	−	0.0949281i
$609$	−17.9722	+	10.3762i	−0.728269	+	0.420466i
$610$	29.6287			1.19963
$611$	−1.14855	−	35.5581i	−0.0464652	−	1.43853i
$612$	7.13589			0.288451
$613$	26.3443	−	15.2099i	1.06404	−	0.614321i	0.137490	−	0.990503i	$-0.456097\pi$
$613$	26.3443	−	15.2099i	1.06404	−	0.614321i	0.926546	+	0.376182i	$0.122763\pi$
$614$	−13.7889	−	23.8831i	−0.556475	−	0.963843i
$615$	15.8787	−	27.5027i	0.640292	−	1.10902i
$616$		−	5.95036i		−	0.239747i
$617$	11.1619	+	6.44431i	0.449360	+	0.259438i	0.707560	−	0.706653i	$-0.249796\pi$
$617$	11.1619	+	6.44431i	0.449360	+	0.259438i	−0.258200	+	0.966092i	$0.583129\pi$
$618$	22.6197	+	13.0595i	0.909896	+	0.525329i
$619$			24.0307i			0.965876i	0.875655	+	0.482938i	$0.160430\pi$
$619$			24.0307i			0.965876i	−0.875655	+	0.482938i	$0.839570\pi$
$620$	−0.200269	+	0.346876i	−0.00804299	+	0.0139309i
$621$	−3.86033	−	6.68629i	−0.154910	−	0.268312i
$622$	12.0119	−	6.93509i	0.481634	−	0.278072i
$623$	−32.9647			−1.32070
$624$	−8.37544	+	15.6529i	−0.335286	+	0.626619i
$625$	−29.0495			−1.16198
$626$	21.9262	−	12.6591i	0.876349	−	0.505960i
$627$	−0.214793	−	0.372032i	−0.00857801	−	0.0148575i
$628$	−6.44575	+	11.1644i	−0.257213	+	0.445507i
$629$		−	46.3761i		−	1.84914i
$630$	−21.3375	−	12.3192i	−0.850106	−	0.490809i
$631$	−8.00573	−	4.62211i	−0.318703	−	0.184003i	0.332111	−	0.943240i	$-0.392239\pi$
$631$	−8.00573	−	4.62211i	−0.318703	−	0.184003i	−0.650814	+	0.759237i	$0.725572\pi$
$632$			9.32104i			0.370771i
$633$	0.555345	−	0.961886i	0.0220730	−	0.0382316i
$634$	1.91192	+	3.31153i	0.0759318	+	0.131518i
$635$	20.1329	−	11.6237i	0.798948	−	0.461273i
$636$	13.5600			0.537690
$637$	−25.9259	−	41.7328i	−1.02722	−	1.65351i
$638$	8.27068			0.327439
$639$	−2.16985	+	1.25276i	−0.0858378	+	0.0495585i
$640$	−14.6789	−	25.4247i	−0.580236	−	1.00500i
$641$	7.78729	−	13.4880i	0.307579	−	0.532743i	−0.670253	−	0.742133i	$-0.733814\pi$
$641$	7.78729	−	13.4880i	0.307579	−	0.532743i	0.977832	+	0.209390i	$0.0671477\pi$
$642$			24.5892i			0.970459i
$643$	−7.35665	−	4.24736i	−0.290118	−	0.167500i	0.347877	−	0.937540i	$-0.386903\pi$
$643$	−7.35665	−	4.24736i	−0.290118	−	0.167500i	−0.637995	+	0.770041i	$0.720236\pi$
$644$	−38.7522	−	22.3736i	−1.52705	−	0.881643i
$645$		−	6.85882i		−	0.270066i
$646$	−2.17395	+	3.76539i	−0.0855330	+	0.148147i
$647$	−10.7440	−	18.6092i	−0.422391	−	0.731603i	0.573781	−	0.819008i	$-0.305476\pi$
$647$	−10.7440	−	18.6092i	−0.422391	−	0.731603i	−0.996173	+	0.0874051i	$0.972143\pi$
$648$	1.13465	−	0.655093i	0.0445734	−	0.0257345i
$649$	8.83165			0.346673
$650$	22.0819	−	13.7181i	0.866125	−	0.538068i
$651$	0.475590			0.0186399
$652$	−12.2240	+	7.05752i	−0.478728	+	0.276394i
$653$	18.2448	+	31.6010i	0.713976	+	1.23664i	0.963353	+	0.268236i	$0.0864407\pi$
$653$	18.2448	+	31.6010i	0.713976	+	1.23664i	−0.249377	+	0.968406i	$0.580226\pi$
$654$	−0.703266	+	1.21809i	−0.0274999	+	0.0476312i
$655$			12.2143i			0.477254i
$656$	45.1805	+	26.0850i	1.76400	+	1.01845i
$657$	−11.4861	−	6.63151i	−0.448116	−	0.258720i
$658$			81.1121i			3.16208i
$659$	9.50284	−	16.4594i	0.370178	−	0.641167i	−0.619415	−	0.785064i	$-0.712630\pi$
$659$	9.50284	−	16.4594i	0.370178	−	0.641167i	0.989593	+	0.143897i	$0.0459633\pi$
$660$	1.91245	+	3.31247i	0.0744422	+	0.128938i
$661$	23.8108	−	13.7472i	0.926135	−	0.534704i	0.0405476	−	0.999178i	$-0.487090\pi$
$661$	23.8108	−	13.7472i	0.926135	−	0.534704i	0.885587	+	0.464474i	$0.153756\pi$
$662$	27.6105			1.07311
$663$	20.1508	−	0.650882i	0.782594	−	0.0252782i
$664$	1.31006			0.0508401
$665$	5.06421	−	2.92382i	0.196382	−	0.113381i
$666$	7.50581	+	13.0004i	0.290844	+	0.503757i
$667$	−17.6394	+	30.5524i	−0.683001	+	1.18299i
$668$			30.2766i			1.17144i
$669$	−18.8287	−	10.8708i	−0.727961	−	0.420289i
$670$	31.7649	+	18.3394i	1.22718	+	0.708515i
$671$			5.46149i			0.210838i
$672$	14.2872	−	24.7461i	0.551139	−	0.954601i
$673$	−13.6365	−	23.6190i	−0.525647	−	0.910447i	−0.999554	−	0.0298719i	$-0.990490\pi$
$673$	−13.6365	−	23.6190i	−0.525647	−	0.910447i	0.473907	−	0.880575i	$-0.342843\pi$
$674$	31.0106	−	17.9040i	1.19448	−	0.689635i
$675$	−3.98341			−0.153322
$676$	7.35049	−	14.8726i	0.282711	−	0.572024i
$677$	37.4349			1.43874			0.719370	−	0.694627i	$-0.244431\pi$
$677$	37.4349			1.43874			0.719370	+	0.694627i	$0.244431\pi$
$678$	−17.0571	+	9.84792i	−0.655074	+	0.378207i
$679$	21.5097	+	37.2559i	0.825467	+	1.42975i
$680$	−10.9792	+	19.0166i	−0.421034	+	0.729252i
$681$			27.5677i			1.05640i
$682$	−0.164148	−	0.0947707i	−0.00628554	−	0.00362896i
$683$	−7.94679	−	4.58808i	−0.304076	−	0.175558i	0.340197	−	0.940354i	$-0.389506\pi$
$683$	−7.94679	−	4.58808i	−0.304076	−	0.175558i	−0.644272	+	0.764796i	$0.722840\pi$
$684$		−	0.548215i		−	0.0209615i
$685$	5.54009	−	9.59572i	0.211676	−	0.366634i
$686$	27.2352	+	47.1728i	1.03985	+	1.80107i
$687$	15.2074	−	8.77997i	0.580197	−	0.334977i
$688$	11.2674			0.429566
$689$	38.2917	−	1.23684i	1.45880	−	0.0471199i
$690$	−41.8849			−1.59453
$691$	−22.9322	+	13.2399i	−0.872382	+	0.503670i	−0.868139	−	0.496321i	$-0.834684\pi$
$691$	−22.9322	+	13.2399i	−0.872382	+	0.503670i	−0.00424315	+	0.999991i	$0.501351\pi$
$692$	8.52816	+	14.7712i	0.324192	+	0.561517i
$693$	2.27081	−	3.93315i	0.0862608	−	0.149408i
$694$			9.47503i			0.359667i
$695$	−1.47154	−	0.849595i	−0.0558188	−	0.0322270i
$696$	−5.18469	−	2.99338i	−0.196525	−	0.113464i
$697$		−	59.2479i		−	2.24417i
$698$	−18.9582	+	32.8366i	−0.717579	+	1.24288i
$699$	−2.55480	−	4.42505i	−0.0966315	−	0.167371i
$700$	−19.9938	+	11.5435i	−0.755696	+	0.436301i
$701$	17.2177			0.650304			0.325152	−	0.945662i	$-0.394584\pi$
$701$	17.2177			0.650304			0.325152	+	0.945662i	$0.394584\pi$
$702$	−5.54347	+	3.44381i	−0.209225	+	0.129978i
$703$	−3.56284			−0.134375
$704$	−1.33412	+	0.770256i	−0.0502816	+	0.0290301i
$705$	14.7872	+	25.6121i	0.556916	+	0.964607i
$706$	12.9226	−	22.3825i	0.486347	−	0.842378i
$707$			12.0016i			0.451368i
$708$	9.76052	+	5.63524i	0.366823	+	0.211785i
$709$	40.8461	+	23.5825i	1.53401	+	0.885660i	0.999171	+	0.0407037i	$0.0129600\pi$
$709$	40.8461	+	23.5825i	1.53401	+	0.885660i	0.534836	+	0.844956i	$0.320373\pi$
$710$			13.5925i			0.510119i
$711$	−3.55715	+	6.16116i	−0.133403	+	0.231062i
$712$	−4.75490	−	8.23574i	−0.178198	−	0.308647i
$713$	0.700177	−	0.404248i	0.0262219	−	0.0151392i
$714$	−45.9663			−1.72025
$715$	5.70266	+	9.17954i	0.213267	+	0.343295i
$716$	−21.8967			−0.818319
$717$	10.2619	−	5.92471i	0.383238	−	0.221262i
$718$	−15.8399	−	27.4356i	−0.591142	−	1.02389i
$719$	6.09048	−	10.5490i	0.227137	−	0.393412i	−0.729822	−	0.683638i	$-0.760397\pi$
$719$	6.09048	−	10.5490i	0.227137	−	0.393412i	0.956958	+	0.290225i	$0.0937303\pi$
$720$		−	14.7576i		−	0.549984i
$721$	−56.7564	−	32.7683i	−2.11372	−	1.22036i
$722$	−29.4935	−	17.0281i	−1.09764	−	0.633721i
$723$		−	0.628349i		−	0.0233685i
$724$	−4.63983	+	8.03643i	−0.172438	+	0.298671i
$725$	9.10091	+	15.7632i	0.337999	+	0.585432i
$726$	−1.56752	+	0.905006i	−0.0581760	+	0.0335879i
$727$	20.6572			0.766131			0.383066	−	0.923721i	$-0.374868\pi$
$727$	20.6572			0.766131			0.383066	+	0.923721i	$0.374868\pi$
$728$	10.1217	−	18.9166i	0.375136	−	0.701096i
$729$	1.00000			0.0370370
$730$	−62.3125	+	35.9762i	−2.30629	+	1.33154i
$731$	−6.39804	−	11.0817i	−0.236640	−	0.409873i
$732$	−3.48483	+	6.03590i	−0.128803	+	0.223093i
$733$		−	12.2521i		−	0.452542i	−0.974064	−	0.226271i	$-0.927346\pi$
$733$		−	12.2521i		−	0.452542i	0.974064	−	0.226271i	$-0.0726535\pi$
$734$	−14.3931	−	8.30987i	−0.531260	−	0.306723i
$735$	35.3694	+	20.4206i	1.30462	+	0.753223i
$736$		−	48.5759i		−	1.79053i
$737$	−3.38052	+	5.85524i	−0.124523	+	0.215681i
$738$	9.58907	+	16.6088i	0.352979	+	0.611377i
$739$	−39.8325	+	22.9973i	−1.46526	+	0.845970i	−0.999247	−	0.0388063i	$-0.987644\pi$
$739$	−39.8325	+	22.9973i	−1.46526	+	0.845970i	−0.466016	+	0.884776i	$0.654311\pi$
$740$	31.7225			1.16614
$741$	−0.0500040	−	1.54809i	−0.00183694	−	0.0568704i
$742$	−87.3478			−3.20664
$743$	−3.93396	+	2.27127i	−0.144323	+	0.0833248i	−0.570423	−	0.821351i	$-0.693221\pi$
$743$	−3.93396	+	2.27127i	−0.144323	+	0.0833248i	0.426100	+	0.904676i	$0.359887\pi$
$744$	0.0686002	+	0.118819i	0.00251500	+	0.00435612i
$745$	−0.232324	+	0.402396i	−0.00851168	+	0.0147427i
$746$			22.4875i			0.823325i
$747$	0.865941	+	0.499952i	0.0316831	+	0.0182923i
$748$	6.17986	+	3.56795i	0.225958	+	0.130457i
$749$		−	61.6984i		−	2.25441i
$750$	2.75752	−	4.77616i	0.100690	−	0.174401i
$751$	−1.17328	−	2.03218i	−0.0428136	−	0.0741554i	0.843825	−	0.536619i	$-0.180299\pi$
$751$	−1.17328	−	2.03218i	−0.0428136	−	0.0741554i	−0.886638	+	0.462464i	$0.846965\pi$
$752$	−42.0746	+	24.2918i	−1.53430	+	0.885830i
$753$	12.8077			0.466740
$754$	26.2931	+	14.0687i	0.957538	+	0.512351i
$755$	−34.7163			−1.26346
$756$	5.01928	−	2.89788i	0.182549	−	0.105395i
$757$	−18.1966	−	31.5175i	−0.661368	−	1.14552i	−0.980257	−	0.197730i	$-0.936643\pi$
$757$	−18.1966	−	31.5175i	−0.661368	−	1.14552i	0.318889	−	0.947792i	$-0.396690\pi$
$758$	−27.2884	+	47.2649i	−0.991159	+	1.71674i
$759$		−	7.72067i		−	0.280242i
$760$	1.46095	+	0.843477i	0.0529941	+	0.0305961i
$761$	27.6938	+	15.9890i	1.00390	+	0.579602i	0.909400	−	0.415923i	$-0.136541\pi$
$761$	27.6938	+	15.9890i	1.00390	+	0.579602i	0.0945002	+	0.995525i	$0.469875\pi$
$762$			14.0390i			0.508579i
$763$	1.76461	−	3.05639i	0.0638831	−	0.110649i
$764$	−7.60364	−	13.1699i	−0.275090	−	0.476470i
$765$	−14.5144	+	8.37990i	−0.524769	+	0.302976i
$766$	−16.1632			−0.584000
$767$	28.0765	+	15.0229i	1.01378	+	0.542446i
$768$	20.8101			0.750919
$769$	−21.8299	+	12.6035i	−0.787205	+	0.454493i	−0.838978	−	0.544166i	$-0.816846\pi$
$769$	−21.8299	+	12.6035i	−0.787205	+	0.454493i	0.0517727	+	0.998659i	$0.483513\pi$
$770$	−12.3192	−	21.3375i	−0.443953	−	0.768950i
$771$	6.57801	−	11.3934i	0.236901	−	0.410325i
$772$		−	9.53307i		−	0.343103i
$773$	16.0958	+	9.29291i	0.578925	+	0.334243i	0.760706	−	0.649096i	$-0.224853\pi$
$773$	16.0958	+	9.29291i	0.578925	+	0.334243i	−0.181781	+	0.983339i	$0.558186\pi$
$774$	3.58708	+	2.07100i	0.128935	+	0.0744406i
$775$		−	0.417136i		−	0.0149840i
$776$	−6.20521	+	10.7477i	−0.222754	+	0.385822i
$777$	−18.8333	−	32.6202i	−0.675641	−	1.17024i
$778$	4.05234	−	2.33962i	0.145283	−	0.0838794i
$779$	−4.55172			−0.163082
$780$	0.445221	+	13.7837i	0.0159415	+	0.493536i
$781$	−2.50552			−0.0896546
$782$	−67.6729	+	39.0710i	−2.41998	+	1.39718i
$783$	−2.28470	−	3.95722i	−0.0816486	−	0.141420i
$784$	−33.5461	+	58.1036i	−1.19808	+	2.07513i
$785$		−	30.2778i		−	1.08066i
$786$	−6.38795	−	3.68808i	−0.227851	−	0.131550i
$787$	−2.62987	−	1.51836i	−0.0937449	−	0.0541236i	0.452395	−	0.891818i	$-0.350570\pi$
$787$	−2.62987	−	1.51836i	−0.0937449	−	0.0541236i	−0.546140	+	0.837694i	$0.683903\pi$
$788$		−	4.24758i		−	0.151314i
$789$	4.35205	−	7.53797i	0.154937	−	0.268359i
$790$	19.2976	+	33.4245i	0.686579	+	1.18919i
$791$	42.7990	−	24.7100i	1.52176	−	0.878588i
$792$	1.31019			0.0465554
$793$	−9.29015	+	17.3625i	−0.329903	+	0.616559i
$794$	33.5611			1.19104
$795$	−27.5811	+	15.9239i	−0.978200	+	0.564764i
$796$	−1.21432	−	2.10326i	−0.0430403	−	0.0745479i
$797$	−1.23924	+	2.14643i	−0.0438963	+	0.0760306i	−0.887139	−	0.461503i	$-0.847310\pi$
$797$	−1.23924	+	2.14643i	−0.0438963	+	0.0760306i	0.843242	+	0.537533i	$0.180644\pi$
$798$			3.53136i			0.125009i
$799$	47.7829	+	27.5875i	1.69044	+	0.975975i
$800$	−21.7046	−	12.5311i	−0.767373	−	0.443043i
$801$		−	7.25837i		−	0.256462i
$802$	19.1525	−	33.1731i	0.676298	−	1.17138i
$803$	−6.63151	−	11.4861i	−0.234021	−	0.405336i
$804$	−7.47214	+	4.31404i	−0.263522	+	0.152145i
$805$	105.096			3.70414
$806$	−0.360630	−	0.580503i	−0.0127026	−	0.0204474i
$807$	10.1179			0.356165
$808$	−2.99843	+	1.73114i	−0.105484	+	0.0609014i
$809$	−12.2470	−	21.2124i	−0.430581	−	0.745788i	0.566342	−	0.824170i	$-0.308358\pi$
$809$	−12.2470	−	21.2124i	−0.430581	−	0.745788i	−0.996923	+	0.0783818i	$0.975025\pi$
$810$	2.71252	−	4.69821i	0.0953081	−	0.165078i
$811$			31.4384i			1.10395i	0.833860	+	0.551976i	$0.186126\pi$
$811$			31.4384i			1.10395i	−0.833860	+	0.551976i	$0.813874\pi$
$812$	−22.9351	−	13.2416i	−0.804865	−	0.464689i
$813$	25.0413	+	14.4576i	0.878238	+	0.507051i
$814$			15.0116i			0.526157i
$815$	16.5757	−	28.7100i	0.580622	−	1.00567i
$816$	−13.7662	−	23.8437i	−0.481913	−	0.834697i
$817$	−0.851353	+	0.491529i	−0.0297851	+	0.0171964i
$818$	−31.0522			−1.08571
$819$	13.9095	−	8.64107i	0.486036	−	0.301943i
$820$	40.5271			1.41527
$821$	−10.3660	+	5.98484i	−0.361777	+	0.208872i	−0.669860	−	0.742487i	$-0.733646\pi$
$821$	−10.3660	+	5.98484i	−0.361777	+	0.208872i	0.308083	+	0.951360i	$0.400313\pi$
$822$	3.34563	+	5.79480i	0.116692	+	0.202117i
$823$	2.46818	−	4.27501i	0.0860352	−	0.149017i	−0.819797	−	0.572655i	$-0.805914\pi$
$823$	2.46818	−	4.27501i	0.0860352	−	0.149017i	0.905832	+	0.423637i	$0.139247\pi$
$824$		−	18.9063i		−	0.658632i
$825$	−3.44973	−	1.99171i	−0.120104	−	0.0693423i
$826$	−62.8731	−	36.2998i	−2.18763	−	1.26303i
$827$			48.5995i			1.68997i	0.534791	+	0.844984i	$0.320390\pi$
$827$			48.5995i			1.68997i	−0.534791	+	0.844984i	$0.679610\pi$
$828$	4.92635	−	8.53269i	0.171202	−	0.296531i
$829$	12.7311	+	22.0509i	0.442169	+	0.765860i	0.997850	−	0.0655359i	$-0.0208757\pi$
$829$	12.7311	+	22.0509i	0.442169	+	0.765860i	−0.555681	+	0.831396i	$0.687542\pi$
$830$	4.69776	−	2.71225i	0.163062	−	0.0941437i
$831$	9.29036			0.322279
$832$	−5.55150	+	0.179316i	−0.192464	+	0.00621667i
$833$	76.1947			2.63999
$834$	0.888656	−	0.513066i	0.0307716	−	0.0177660i
$835$	−35.5547	−	61.5826i	−1.23042	−	2.13115i
$836$	0.274107	−	0.474768i	0.00948020	−	0.0164202i
$837$			0.104718i			0.00361959i
$838$	24.6479	+	14.2305i	0.851448	+	0.491584i
$839$	−16.4242	−	9.48249i	−0.567025	−	0.327372i	0.188935	−	0.981990i	$-0.439496\pi$
$839$	−16.4242	−	9.48249i	−0.567025	−	0.327372i	−0.755960	+	0.654618i	$0.772830\pi$
$840$			17.8346i			0.615352i
$841$	4.06027	−	7.03260i	0.140009	−	0.242503i
$842$	−13.4210	−	23.2459i	−0.462519	−	0.801106i
$843$	−1.22105	+	0.704975i	−0.0420553	+	0.0242806i
$844$	1.41740			0.0487890
$845$	2.51449	+	38.8828i	0.0865012	+	1.33761i
$846$	−17.8598			−0.614031
$847$	3.93315	−	2.27081i	0.135145	−	0.0780259i
$848$	−26.1593	−	45.3092i	−0.898312	−	1.55592i
$849$	−1.60603	+	2.78172i	−0.0551187	+	0.0954684i
$850$			40.3167i			1.38285i
$851$	−55.4538	−	32.0163i	−1.90093	−	1.09750i
$852$	−2.76904	−	1.59871i	−0.0948658	−	0.0547708i
$853$		−	9.05734i		−	0.310117i	−0.987905	−	0.155059i	$-0.950443\pi$
$853$		−	9.05734i		−	0.310117i	0.987905	−	0.155059i	$-0.0495567\pi$
$854$	22.4477	−	38.8806i	0.768146	−	1.33047i
$855$	0.643785	+	1.11507i	0.0220170	+	0.0381345i
$856$	15.4144	−	8.89951i	0.526853	−	0.304179i
$857$	32.6253			1.11446			0.557230	−	0.830358i	$-0.311864\pi$
$857$	32.6253			1.11446			0.557230	+	0.830358i	$0.311864\pi$
$858$	−6.52269	+	0.210686i	−0.222681	+	0.00719271i
$859$	−30.6821			−1.04686			−0.523429	−	0.852069i	$-0.675348\pi$
$859$	−30.6821			−1.04686			−0.523429	+	0.852069i	$0.675348\pi$
$860$	7.58020	−	4.37643i	0.258483	−	0.149235i
$861$	−24.0605	−	41.6741i	−0.819981	−	1.42025i
$862$	−35.1781	+	60.9302i	−1.19817	+	2.07529i
$863$			26.7121i			0.909290i	0.890673	+	0.454645i	$0.150234\pi$
$863$			26.7121i			0.909290i	−0.890673	+	0.454645i	$0.849766\pi$
$864$	5.44874	+	3.14583i	0.185370	+	0.107023i
$865$	−34.6925	−	20.0297i	−1.17958	−	0.681032i
$866$		−	57.7351i		−	1.96192i
$867$	−7.13385	+	12.3562i	−0.242278	+	0.419638i
$868$	0.303461	+	0.525610i	0.0103001	+	0.0178404i
$869$	−6.16116	+	3.55715i	−0.209003	+	0.120668i
$870$	−24.7892			−0.840431
$871$	−20.7069	+	12.8639i	−0.701625	+	0.435875i
$872$	1.01812			0.0344780
$873$	−8.20323	+	4.73614i	−0.277637	+	0.160294i
$874$	3.00163	+	5.19897i	0.101532	+	0.175858i
$875$	−6.91905	+	11.9841i	−0.233907	+	0.405138i
$876$		−	16.9256i		−	0.571862i
$877$	−10.5702	−	6.10270i	−0.356930	−	0.206073i	0.310803	−	0.950474i	$-0.399402\pi$
$877$	−10.5702	−	6.10270i	−0.356930	−	0.206073i	−0.667733	+	0.744401i	$0.732735\pi$
$878$	34.6263	+	19.9915i	1.16858	+	0.674681i
$879$		−	21.7378i		−	0.733199i
$880$	7.37881	−	12.7805i	0.248739	−	0.430829i
$881$	16.7383	+	28.9916i	0.563929	+	0.976753i	0.997148	+	0.0754650i	$0.0240441\pi$
$881$	16.7383	+	28.9916i	0.563929	+	0.976753i	−0.433220	+	0.901288i	$0.642623\pi$
$882$	−21.3594	+	12.3319i	−0.719209	+	0.415235i
$883$	13.2020			0.444284			0.222142	−	0.975014i	$-0.428695\pi$
$883$	13.2020			0.444284			0.222142	+	0.975014i	$0.428695\pi$
$884$	13.5770	+	21.8549i	0.456646	+	0.735060i
$885$	−26.4705			−0.889797
$886$	61.3893	−	35.4431i	2.06241	−	1.19074i
$887$	−0.232915	−	0.403420i	−0.00782051	−	0.0135455i	0.862089	−	0.506757i	$-0.169156\pi$
$887$	−0.232915	−	0.403420i	−0.00782051	−	0.0135455i	−0.869909	+	0.493212i	$0.835823\pi$
$888$	5.43311	−	9.41043i	0.182323	−	0.315793i
$889$		−	35.2261i		−	1.18145i
$890$	−34.1014	−	19.6884i	−1.14308	−	0.659958i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$		−	27.7454i		−	0.928985i
$893$	2.11941	−	3.67092i	0.0709232	−	0.122843i
$894$	−0.140299	−	0.243005i	−0.00469230	−	0.00812730i
$895$	44.5380	−	25.7140i	1.48874	−	0.859524i
$896$	−44.4851			−1.48614
$897$	13.1331	−	24.5446i	0.438501	−	0.819519i
$898$	−54.9801			−1.83471
$899$	0.414393	−	0.239250i	0.0138208	−	0.00797944i
$900$	−2.54171	−	4.40236i	−0.0847236	−	0.146745i
$901$	−29.7083	+	51.4563i	−0.989727	+	1.71426i
$902$			19.1781i			0.638562i
$903$	−9.00057	−	5.19648i	−0.299520	−	0.172928i
$904$	12.3469	+	7.12846i	0.410650	+	0.237089i
$905$		−	21.7948i		−	0.724483i
$906$	10.4825	−	18.1562i	0.348258	−	0.603200i
$907$	−29.5526	−	51.1866i	−0.981277	−	1.69962i	−0.657435	−	0.753511i	$-0.728359\pi$
$907$	−29.5526	−	51.1866i	−0.981277	−	1.69962i	−0.323842	−	0.946111i	$-0.604975\pi$
$908$	−30.4671	+	17.5902i	−1.01109	+	0.583751i
$909$	−2.64259			−0.0876493
$910$	−2.86792	−	88.7887i	−0.0950706	−	2.94332i
$911$	−19.9000			−0.659318			−0.329659	−	0.944100i	$-0.606934\pi$
$911$	−19.9000			−0.659318			−0.329659	+	0.944100i	$0.606934\pi$
$912$	−1.83179	+	1.05759i	−0.0606567	+	0.0350202i
$913$	0.499952	+	0.865941i	0.0165460	+	0.0286585i
$914$	−27.4866	+	47.6081i	−0.909175	+	1.57474i
$915$		−	16.3693i		−	0.541154i
$916$	19.4068	+	11.2045i	0.641219	+	0.370208i
$917$	16.0284	+	9.25400i	0.529304	+	0.305594i
$918$		−	10.1211i		−	0.334048i
$919$	−0.513086	+	0.888691i	−0.0169251	+	0.0293152i	−0.874364	−	0.485271i	$-0.838721\pi$
$919$	−0.513086	+	0.888691i	−0.0169251	+	0.0293152i	0.857439	+	0.514586i	$0.172054\pi$
$920$	15.1593	+	26.2566i	0.499786	+	0.865655i
$921$	−13.1950	+	7.61813i	−0.434789	+	0.251026i
$922$	1.08190			0.0356304
$923$	−7.96523	−	4.26197i	−0.262179	−	0.140284i
$924$	5.79576			0.190667
$925$	−28.6109	+	16.5185i	−0.940721	+	0.543126i
$926$	−34.1522	−	59.1533i	−1.12231	−	1.94390i
$927$	7.21512	−	12.4970i	0.236976	−	0.410454i
$928$		−	28.7492i		−	0.943738i
$929$	22.9386	+	13.2436i	0.752592	+	0.434509i	0.826630	−	0.562746i	$-0.190255\pi$
$929$	22.9386	+	13.2436i	0.752592	+	0.434509i	−0.0740375	+	0.997255i	$0.523588\pi$
$930$	0.491989	+	0.284050i	0.0161330	+	0.00931437i
$931$		−	5.85365i		−	0.191846i
$932$	3.26030	−	5.64701i	0.106795	−	0.184974i
$933$	−3.83151	−	6.63638i	−0.125438	−	0.217265i
$934$	13.2232	−	7.63442i	0.432676	−	0.249806i
$935$	−16.7598			−0.548104
$936$	4.16517	+	2.22866i	0.136143	+	0.0728462i
$937$	5.64595			0.184445			0.0922225	−	0.995738i	$-0.470603\pi$
$937$	5.64595			0.184445			0.0922225	+	0.995738i	$0.470603\pi$
$938$	48.1323	−	27.7892i	1.57158	−	0.907349i
$939$	−6.99394	−	12.1139i	−0.228239	−	0.395321i
$940$	−18.8706	+	32.6848i	−0.615490	+	1.06606i
$941$			46.4041i			1.51273i	0.654149	+	0.756366i	$0.273027\pi$
$941$			46.4041i			1.51273i	−0.654149	+	0.756366i	$0.726973\pi$
$942$	15.8349	+	9.14228i	0.515929	+	0.297872i
$943$	−70.8452	−	40.9025i	−2.30704	−	1.33197i
$944$		−	43.4848i		−	1.41531i
$945$	−6.80614	+	11.7886i	−0.221404	+	0.383483i
$946$	2.07100	+	3.58708i	0.0673341	+	0.116626i
$947$	−31.7980	+	18.3586i	−1.03330	+	0.596574i	−0.917927	−	0.396749i	$-0.870138\pi$
$947$	−31.7980	+	18.3586i	−1.03330	+	0.596574i	−0.115369	+	0.993323i	$0.536805\pi$
$948$	−9.07888			−0.294868
$949$	−1.54382	−	47.7956i	−0.0501146	−	1.55151i
$950$	3.09733			0.100491
$951$	1.82956	−	1.05630i	0.0593277	−	0.0342528i
$952$	16.6365	+	28.8152i	0.539191	+	0.933906i
$953$	−7.18183	+	12.4393i	−0.232642	+	0.402948i	−0.958585	−	0.284807i	$-0.908070\pi$
$953$	−7.18183	+	12.4393i	−0.232642	+	0.402948i	0.725943	+	0.687755i	$0.241404\pi$
$954$		−	19.2328i		−	0.622683i
$955$	30.9316	+	17.8584i	1.00092	+	0.577883i
$956$	13.0957	+	7.56080i	0.423545	+	0.244534i
$957$		−	4.56940i		−	0.147708i
$958$	−14.5703	+	25.2365i	−0.470745	+	0.815355i
$959$	−8.39473	−	14.5401i	−0.271080	−	0.469524i
$960$	3.99868	−	2.30864i	0.129057	−	0.0745110i
$961$	30.9890			0.999646
$962$	−25.5352	+	47.7230i	−0.823289	+	1.53865i
$963$	13.5851			0.437774
$964$	0.694435	−	0.400932i	0.0223663	−	0.0129132i
$965$	11.1950	+	19.3903i	0.360379	+	0.624194i
$966$	−31.7334	+	54.9639i	−1.02101	+	1.76843i
$967$			44.4755i			1.43023i	0.699005	+	0.715117i	$0.253627\pi$
$967$			44.4755i			1.43023i	−0.699005	+	0.715117i	$0.746373\pi$
$968$	1.13465	+	0.655093i	0.0364691	+	0.0210555i
$969$	2.08031	+	1.20107i	0.0668293	+	0.0385839i
$970$			51.3874i			1.64995i
$971$	−13.4138	+	23.2334i	−0.430469	+	0.745594i	−0.996914	−	0.0785058i	$-0.974985\pi$
$971$	−13.4138	+	23.2334i	−0.430469	+	0.745594i	0.566445	+	0.824100i	$0.308318\pi$
$972$	0.638073	+	1.10517i	0.0204662	+	0.0354485i
$973$	−2.22978	+	1.28737i	−0.0714835	+	0.0412710i
$974$	−56.4422			−1.80852
$975$	−7.57900	−	12.1999i	−0.242722	−	0.390709i
$976$	26.8910			0.860758
$977$	−6.90775	+	3.98819i	−0.220999	+	0.127594i	−0.606413	−	0.795150i	$-0.707392\pi$
$977$	−6.90775	+	3.98819i	−0.220999	+	0.127594i	0.385414	+	0.922744i	$0.374059\pi$
$978$	10.0100	+	17.3378i	0.320084	+	0.554402i
$979$	3.62919	−	6.28593i	0.115989	−	0.200899i
$980$			52.1192i			1.66489i
$981$	0.672975	+	0.388542i	0.0214864	+	0.0124052i
$982$	−9.48198	−	5.47442i	−0.302582	−	0.174696i
$983$		−	2.96567i		−	0.0945900i	−0.998881	−	0.0472950i	$-0.984940\pi$
$983$		−	2.96567i		−	0.0945900i	0.998881	−	0.0472950i	$-0.0150601\pi$
$984$	6.94109	−	12.0223i	0.221274	−	0.383257i
$985$	4.98806	+	8.63957i	0.158933	+	0.275280i
$986$	−40.0516	+	23.1238i	−1.27550	+	0.736412i
$987$	44.8130			1.42641
$988$	1.67900	−	1.04306i	0.0534161	−	0.0331840i
$989$	−17.6678			−0.561805
$990$	4.69821	−	2.71252i	0.149319	−	0.0862094i
$991$	11.1802	+	19.3646i	0.355150	+	0.615138i	0.987144	−	0.159835i	$-0.0510964\pi$
$991$	11.1802	+	19.3646i	0.355150	+	0.615138i	−0.631993	+	0.774974i	$0.717763\pi$
$992$	−0.329426	+	0.570583i	−0.0104593	+	0.0181160i
$993$		−	15.2543i		−	0.484081i
$994$	17.8370	+	10.2982i	0.565754	+	0.326638i
$995$	4.93983	+	2.85201i	0.156603	+	0.0904149i
$996$			1.27602i			0.0404323i
$997$	25.6216	−	44.3780i	0.811445	−	1.40546i	−0.100407	−	0.994946i	$-0.532015\pi$
$997$	25.6216	−	44.3780i	0.811445	−	1.40546i	0.911853	−	0.410518i	$-0.134652\pi$
$998$	−8.78478	−	15.2157i	−0.278077	−	0.481644i
$999$	7.18252	−	4.14683i	0.227245	−	0.131200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.b.166.11	✓	28
13.2	odd	12		5577.2.a.bg.1.10		14
13.4	even	6	inner	429.2.s.b.199.11	yes	28
13.11	odd	12		5577.2.a.bf.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.11	✓	28	1.1	even	1	trivial
429.2.s.b.199.11	yes	28	13.4	even	6	inner
5577.2.a.bf.1.5		14	13.11	odd	12
5577.2.a.bg.1.10		14	13.2	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)

\(f(q)\)	\(=\)	\(q+(1.56752 - 0.905006i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.638073 - 1.10517i) q^{4} +2.99723i q^{5} +(-1.56752 - 0.905006i) q^{6} +(3.93315 + 2.27081i) q^{7} +1.31019i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.56752 - 0.905006i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.638073 - 1.10517i) q^{4} +2.99723i q^{5} +(-1.56752 - 0.905006i) q^{6} +(3.93315 + 2.27081i) q^{7} +1.31019i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.71252 + 4.69821i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.27615 q^{12} +(-3.60367 + 0.116400i) q^{13} +8.22038 q^{14} +(2.59568 - 1.49862i) q^{15} +(2.46187 + 4.26409i) q^{16} +(2.79588 - 4.84260i) q^{17} +1.81001i q^{18} +(-0.372032 - 0.214793i) q^{19} +(3.31247 + 1.91245i) q^{20} -4.54162i q^{21} +(-0.905006 + 1.56752i) q^{22} +(-3.86033 - 6.68629i) q^{23} +(1.13465 - 0.655093i) q^{24} -3.98341 q^{25} +(-5.54347 + 3.44381i) q^{26} +1.00000 q^{27} +(5.01928 - 2.89788i) q^{28} +(-2.28470 - 3.95722i) q^{29} +(2.71252 - 4.69821i) q^{30} +0.104718i q^{31} +(5.44874 + 3.14583i) q^{32} +(0.866025 + 0.500000i) q^{33} -10.1211i q^{34} +(-6.80614 + 11.7886i) q^{35} +(0.638073 + 1.10517i) q^{36} +(7.18252 - 4.14683i) q^{37} -0.777556 q^{38} +(1.90264 + 3.06267i) q^{39} -3.92693 q^{40} +(9.17604 - 5.29779i) q^{41} +(-4.11019 - 7.11906i) q^{42} +(1.14419 - 1.98180i) q^{43} +1.27615i q^{44} +(-2.59568 - 1.49862i) q^{45} +(-12.1023 - 6.98725i) q^{46} +9.86720i q^{47} +(2.46187 - 4.26409i) q^{48} +(6.81313 + 11.8007i) q^{49} +(-6.24406 + 3.60501i) q^{50} -5.59175 q^{51} +(-2.17076 + 4.05696i) q^{52} -10.6258 q^{53} +(1.56752 - 0.905006i) q^{54} +(-1.49862 - 2.59568i) q^{55} +(-2.97518 + 5.15316i) q^{56} +0.429586i q^{57} +(-7.16262 - 4.13534i) q^{58} +(-7.64844 - 4.41583i) q^{59} -3.82491i q^{60} +(2.73074 - 4.72978i) q^{61} +(0.0947707 + 0.164148i) q^{62} +(-3.93315 + 2.27081i) q^{63} +1.54051 q^{64} +(-0.348879 - 10.8010i) q^{65} +1.81001 q^{66} +(5.85524 - 3.38052i) q^{67} +(-3.56795 - 6.17986i) q^{68} +(-3.86033 + 6.68629i) q^{69} +24.6384i q^{70} +(2.16985 + 1.25276i) q^{71} +(-1.13465 - 0.655093i) q^{72} +13.2630i q^{73} +(7.50581 - 13.0004i) q^{74} +(1.99171 + 3.44973i) q^{75} +(-0.474768 + 0.274107i) q^{76} -4.54162 q^{77} +(5.75416 + 3.07889i) q^{78} +7.11430 q^{79} +(-12.7805 + 7.37881i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.58907 - 16.6088i) q^{82} -0.999903i q^{83} +(-5.01928 - 2.89788i) q^{84} +(14.5144 + 8.37990i) q^{85} -4.14200i q^{86} +(-2.28470 + 3.95722i) q^{87} +(-0.655093 - 1.13465i) q^{88} +(-6.28593 + 3.62919i) q^{89} -5.42503 q^{90} +(-14.4381 - 7.72542i) q^{91} -9.85270 q^{92} +(0.0906887 - 0.0523592i) q^{93} +(8.92988 + 15.4670i) q^{94} +(0.643785 - 1.11507i) q^{95} -6.29167i q^{96} +(8.20323 + 4.73614i) q^{97} +(21.3594 + 12.3319i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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