LMFDB - Embedded newform 471.2.e.c.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.3
Character	$\chi$	$=$	471.301
Dual form			471.2.e.c.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03783 q^{2} +(-0.500000 + 0.866025i) q^{3} +2.15276 q^{4} +(-0.0788428 + 0.136560i) q^{5} +(1.01892 - 1.76481i) q^{6} -4.73558 q^{7} -0.311299 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-2.03783 q^{2} +(-0.500000 + 0.866025i) q^{3} +2.15276 q^{4} +(-0.0788428 + 0.136560i) q^{5} +(1.01892 - 1.76481i) q^{6} -4.73558 q^{7} -0.311299 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.160668 - 0.278286i) q^{10} +(2.02603 - 3.50919i) q^{11} +(-1.07638 + 1.86434i) q^{12} +(1.05044 + 1.81942i) q^{13} +9.65032 q^{14} +(-0.0788428 - 0.136560i) q^{15} -3.67114 q^{16} +(1.09464 - 1.89598i) q^{17} +(1.01892 + 1.76481i) q^{18} +(-0.198166 + 0.343234i) q^{19} +(-0.169730 + 0.293980i) q^{20} +(2.36779 - 4.10114i) q^{21} +(-4.12871 + 7.15113i) q^{22} +2.82866 q^{23} +(0.155650 - 0.269593i) q^{24} +(2.48757 + 4.30859i) q^{25} +(-2.14062 - 3.70766i) q^{26} +1.00000 q^{27} -10.1946 q^{28} -2.76446 q^{29} +(0.160668 + 0.278286i) q^{30} +(-1.77863 - 3.08067i) q^{31} +8.10377 q^{32} +(2.02603 + 3.50919i) q^{33} +(-2.23070 + 3.86369i) q^{34} +(0.373367 - 0.646690i) q^{35} +(-1.07638 - 1.86434i) q^{36} +(-0.209147 - 0.362253i) q^{37} +(0.403830 - 0.699454i) q^{38} -2.10088 q^{39} +(0.0245437 - 0.0425110i) q^{40} +9.59869 q^{41} +(-4.82516 + 8.35743i) q^{42} +(6.00950 + 10.4088i) q^{43} +(4.36156 - 7.55444i) q^{44} +0.157686 q^{45} -5.76434 q^{46} +(0.483864 + 0.838078i) q^{47} +(1.83557 - 3.17930i) q^{48} +15.4257 q^{49} +(-5.06925 - 8.78019i) q^{50} +(1.09464 + 1.89598i) q^{51} +(2.26134 + 3.91676i) q^{52} +(6.91968 + 11.9852i) q^{53} -2.03783 q^{54} +(0.319476 + 0.553348i) q^{55} +1.47418 q^{56} +(-0.198166 - 0.343234i) q^{57} +5.63350 q^{58} +9.38272 q^{59} +(-0.169730 - 0.293980i) q^{60} +(7.13557 - 12.3592i) q^{61} +(3.62454 + 6.27789i) q^{62} +(2.36779 + 4.10114i) q^{63} -9.17184 q^{64} -0.331278 q^{65} +(-4.12871 - 7.15113i) q^{66} +6.81775 q^{67} +(2.35651 - 4.08159i) q^{68} +(-1.41433 + 2.44970i) q^{69} +(-0.760859 + 1.31785i) q^{70} +(-3.75903 - 6.51083i) q^{71} +(0.155650 + 0.269593i) q^{72} +(-1.51790 + 2.62907i) q^{73} +(0.426206 + 0.738210i) q^{74} -4.97514 q^{75} +(-0.426605 + 0.738901i) q^{76} +(-9.59443 + 16.6180i) q^{77} +4.28124 q^{78} -5.64926 q^{79} +(0.289443 - 0.501330i) q^{80} +(-0.500000 + 0.866025i) q^{81} -19.5605 q^{82} +(-7.27997 - 12.6093i) q^{83} +(5.09729 - 8.82876i) q^{84} +(0.172610 + 0.298969i) q^{85} +(-12.2464 - 21.2113i) q^{86} +(1.38223 - 2.39409i) q^{87} +(-0.630702 + 1.09241i) q^{88} +(-2.47878 + 4.29337i) q^{89} -0.321337 q^{90} +(-4.97444 - 8.61599i) q^{91} +6.08944 q^{92} +3.55725 q^{93} +(-0.986034 - 1.70786i) q^{94} +(-0.0312480 - 0.0541231i) q^{95} +(-4.05189 + 7.01807i) q^{96} +(2.81804 + 4.88099i) q^{97} -31.4351 q^{98} -4.05206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.03783			−1.44096			−0.720482	−	0.693473i	$-0.756080\pi$
$2$	−2.03783			−1.44096			−0.720482	+	0.693473i	$0.756080\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	2.15276			1.07638
$5$	−0.0788428	+	0.136560i	−0.0352596	+	0.0610714i	−0.883117	−	0.469153i	$-0.844559\pi$
$5$	−0.0788428	+	0.136560i	−0.0352596	+	0.0610714i	0.847857	+	0.530225i	$0.177892\pi$
$6$	1.01892	−	1.76481i	0.415971	−	0.720482i
$7$	−4.73558			−1.78988			−0.894941	−	0.446184i	$-0.852783\pi$
$7$	−4.73558			−1.78988			−0.894941	+	0.446184i	$0.852783\pi$
$8$	−0.311299			−0.110061
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.160668	−	0.278286i	0.0508078	−	0.0880017i
$11$	2.02603	−	3.50919i	0.610871	−	1.05806i	−0.380223	−	0.924895i	$-0.624153\pi$
$11$	2.02603	−	3.50919i	0.610871	−	1.05806i	0.991094	−	0.133165i	$-0.0425139\pi$
$12$	−1.07638	+	1.86434i	−0.310724	+	0.538190i
$13$	1.05044	+	1.81942i	0.291340	+	0.504615i	0.974127	−	0.226002i	$-0.0725657\pi$
$13$	1.05044	+	1.81942i	0.291340	+	0.504615i	−0.682787	+	0.730617i	$0.739232\pi$
$14$	9.65032			2.57916
$15$	−0.0788428	−	0.136560i	−0.0203571	−	0.0352596i
$16$	−3.67114			−0.917786
$17$	1.09464	−	1.89598i	0.265490	−	0.459842i	−0.702202	−	0.711978i	$-0.747800\pi$
$17$	1.09464	−	1.89598i	0.265490	−	0.459842i	0.967692	+	0.252136i	$0.0811329\pi$
$18$	1.01892	+	1.76481i	0.240161	+	0.415971i
$19$	−0.198166	+	0.343234i	−0.0454625	+	0.0787434i	−0.887861	−	0.460111i	$-0.847809\pi$
$19$	−0.198166	+	0.343234i	−0.0454625	+	0.0787434i	0.842399	+	0.538855i	$0.181143\pi$
$20$	−0.169730	+	0.293980i	−0.0379527	+	0.0657360i
$21$	2.36779	−	4.10114i	0.516694	−	0.894941i
$22$	−4.12871	+	7.15113i	−0.880244	+	1.52463i
$23$	2.82866			0.589817			0.294909	−	0.955525i	$-0.404711\pi$
$23$	2.82866			0.589817			0.294909	+	0.955525i	$0.404711\pi$
$24$	0.155650	−	0.269593i	0.0317719	−	0.0550305i
$25$	2.48757	+	4.30859i	0.497514	+	0.861719i
$26$	−2.14062	−	3.70766i	−0.419810	−	0.727132i
$27$	1.00000			0.192450
$28$	−10.1946			−1.92659
$29$	−2.76446			−0.513346			−0.256673	−	0.966498i	$-0.582626\pi$
$29$	−2.76446			−0.513346			−0.256673	+	0.966498i	$0.582626\pi$
$30$	0.160668	+	0.278286i	0.0293339	+	0.0508078i
$31$	−1.77863	−	3.08067i	−0.319451	−	0.553305i	0.660923	−	0.750454i	$-0.270165\pi$
$31$	−1.77863	−	3.08067i	−0.319451	−	0.553305i	−0.980374	+	0.197149i	$0.936832\pi$
$32$	8.10377			1.43256
$33$	2.02603	+	3.50919i	0.352686	+	0.610871i
$34$	−2.23070	+	3.86369i	−0.382562	+	0.662617i
$35$	0.373367	−	0.646690i	0.0631105	−	0.109311i
$36$	−1.07638	−	1.86434i	−0.179397	−	0.310724i
$37$	−0.209147	−	0.362253i	−0.0343835	−	0.0595540i	0.848322	−	0.529481i	$-0.177613\pi$
$37$	−0.209147	−	0.362253i	−0.0343835	−	0.0595540i	−0.882705	+	0.469927i	$0.844280\pi$
$38$	0.403830	−	0.699454i	0.0655099	−	0.113466i
$39$	−2.10088			−0.336410
$40$	0.0245437	−	0.0425110i	0.00388070	−	0.00672157i
$41$	9.59869			1.49906			0.749532	−	0.661968i	$-0.230279\pi$
$41$	9.59869			1.49906			0.749532	+	0.661968i	$0.230279\pi$
$42$	−4.82516	+	8.35743i	−0.744539	+	1.28958i
$43$	6.00950	+	10.4088i	0.916441	+	1.58732i	0.804778	+	0.593575i	$0.202284\pi$
$43$	6.00950	+	10.4088i	0.916441	+	1.58732i	0.111662	+	0.993746i	$0.464383\pi$
$44$	4.36156	−	7.55444i	0.657529	−	1.13887i
$45$	0.157686			0.0235064
$46$	−5.76434			−0.849906
$47$	0.483864	+	0.838078i	0.0705789	+	0.122246i	0.899155	−	0.437630i	$-0.144182\pi$
$47$	0.483864	+	0.838078i	0.0705789	+	0.122246i	−0.828576	+	0.559876i	$0.810849\pi$
$48$	1.83557	−	3.17930i	0.264942	−	0.458893i
$49$	15.4257			2.20368
$50$	−5.06925	−	8.78019i	−0.716900	−	1.24171i
$51$	1.09464	+	1.89598i	0.153281	+	0.265490i
$52$	2.26134	+	3.91676i	0.313592	+	0.543157i
$53$	6.91968	+	11.9852i	0.950491	+	1.64630i	0.744364	+	0.667774i	$0.232753\pi$
$53$	6.91968	+	11.9852i	0.950491	+	1.64630i	0.206127	+	0.978525i	$0.433914\pi$
$54$	−2.03783			−0.277314
$55$	0.319476	+	0.553348i	0.0430781	+	0.0746134i
$56$	1.47418			0.196996
$57$	−0.198166	−	0.343234i	−0.0262478	−	0.0454625i
$58$	5.63350			0.739714
$59$	9.38272			1.22153			0.610763	−	0.791813i	$-0.290863\pi$
$59$	9.38272			1.22153			0.610763	+	0.791813i	$0.290863\pi$
$60$	−0.169730	−	0.293980i	−0.0219120	−	0.0379527i
$61$	7.13557	−	12.3592i	0.913616	−	1.58243i	0.104701	−	0.994504i	$-0.466611\pi$
$61$	7.13557	−	12.3592i	0.913616	−	1.58243i	0.808915	−	0.587926i	$-0.200055\pi$
$62$	3.62454	+	6.27789i	0.460317	+	0.797293i
$63$	2.36779	+	4.10114i	0.298314	+	0.516694i
$64$	−9.17184			−1.14648
$65$	−0.331278			−0.0410900
$66$	−4.12871	−	7.15113i	−0.508209	−	0.880244i
$67$	6.81775			0.832921			0.416460	−	0.909154i	$-0.363270\pi$
$67$	6.81775			0.832921			0.416460	+	0.909154i	$0.363270\pi$
$68$	2.35651	−	4.08159i	0.285768	−	0.494965i
$69$	−1.41433	+	2.44970i	−0.170266	+	0.294909i
$70$	−0.760859	+	1.31785i	−0.0909400	+	0.157513i
$71$	−3.75903	−	6.51083i	−0.446115	−	0.772693i	0.552014	−	0.833835i	$-0.313859\pi$
$71$	−3.75903	−	6.51083i	−0.446115	−	0.772693i	−0.998129	+	0.0611412i	$0.980526\pi$
$72$	0.155650	+	0.269593i	0.0183435	+	0.0317719i
$73$	−1.51790	+	2.62907i	−0.177656	+	0.307710i	−0.941077	−	0.338192i	$-0.890185\pi$
$73$	−1.51790	+	2.62907i	−0.177656	+	0.307710i	0.763421	+	0.645901i	$0.223518\pi$
$74$	0.426206	+	0.738210i	0.0495454	+	0.0858152i
$75$	−4.97514			−0.574479
$76$	−0.426605	+	0.738901i	−0.0489349	+	0.0847578i
$77$	−9.59443	+	16.6180i	−1.09339	+	1.89380i
$78$	4.28124			0.484755
$79$	−5.64926			−0.635591			−0.317796	−	0.948159i	$-0.602943\pi$
$79$	−5.64926			−0.635591			−0.317796	+	0.948159i	$0.602943\pi$
$80$	0.289443	−	0.501330i	0.0323607	−	0.0560505i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−19.5605			−2.16010
$83$	−7.27997	−	12.6093i	−0.799080	−	1.38405i	−0.920216	−	0.391412i	$-0.871987\pi$
$83$	−7.27997	−	12.6093i	−0.799080	−	1.38405i	0.121135	−	0.992636i	$-0.461347\pi$
$84$	5.09729	−	8.82876i	0.556160	−	0.963297i
$85$	0.172610	+	0.298969i	0.0187221	+	0.0324277i
$86$	−12.2464	−	21.2113i	−1.32056	−	2.28727i
$87$	1.38223	−	2.39409i	0.148190	−	0.256673i
$88$	−0.630702	+	1.09241i	−0.0672330	+	0.116451i
$89$	−2.47878	+	4.29337i	−0.262750	+	0.455096i	−0.966972	−	0.254884i	$-0.917963\pi$
$89$	−2.47878	+	4.29337i	−0.262750	+	0.455096i	0.704222	+	0.709980i	$0.251296\pi$
$90$	−0.321337			−0.0338719
$91$	−4.97444	−	8.61599i	−0.521464	−	0.903201i
$92$	6.08944			0.634868
$93$	3.55725			0.368870
$94$	−0.986034	−	1.70786i	−0.101702	−	0.176152i
$95$	−0.0312480	−	0.0541231i	−0.00320598	−	0.00555291i
$96$	−4.05189	+	7.01807i	−0.413544	+	0.716279i
$97$	2.81804	+	4.88099i	0.286129	+	0.495590i	0.972882	−	0.231301i	$-0.0742981\pi$
$97$	2.81804	+	4.88099i	0.286129	+	0.495590i	−0.686753	+	0.726890i	$0.740965\pi$
$98$	−31.4351			−3.17542
$99$	−4.05206			−0.407247
$100$	5.35514	+	9.27537i	0.535514	+	0.927537i
$101$	10.5905			1.05380			0.526898	−	0.849929i	$-0.323355\pi$
$101$	10.5905			1.05380			0.526898	+	0.849929i	$0.323355\pi$
$102$	−2.23070	−	3.86369i	−0.220872	−	0.382562i
$103$	−7.95977			−0.784300			−0.392150	−	0.919901i	$-0.628269\pi$
$103$	−7.95977			−0.784300			−0.392150	+	0.919901i	$0.628269\pi$
$104$	−0.327001	−	0.566383i	−0.0320651	−	0.0555384i
$105$	0.373367	+	0.646690i	0.0364369	+	0.0631105i
$106$	−14.1011	−	24.4239i	−1.36962	−	2.37226i
$107$	−1.76968	−	3.06518i	−0.171081	−	0.296322i	0.767717	−	0.640789i	$-0.221393\pi$
$107$	−1.76968	−	3.06518i	−0.171081	−	0.296322i	−0.938798	+	0.344468i	$0.888059\pi$
$108$	2.15276			0.207149
$109$	2.71248	−	4.69816i	0.259809	−	0.450002i	−0.706382	−	0.707831i	$-0.749674\pi$
$109$	2.71248	−	4.69816i	0.259809	−	0.450002i	0.966191	+	0.257829i	$0.0830071\pi$
$110$	−0.651038	−	1.12763i	−0.0620740	−	0.107515i
$111$	0.418293			0.0397026
$112$	17.3850			1.64273
$113$	1.49220	−	2.58456i	0.140374	−	0.243135i	−0.787263	−	0.616617i	$-0.788503\pi$
$113$	1.49220	−	2.58456i	0.140374	−	0.243135i	0.927638	+	0.373482i	$0.121836\pi$
$114$	0.403830	+	0.699454i	0.0378221	+	0.0655099i
$115$	−0.223020	+	0.386282i	−0.0207967	+	0.0360210i
$116$	−5.95121			−0.552556
$117$	1.05044	−	1.81942i	0.0971132	−	0.168205i
$118$	−19.1204			−1.76018
$119$	−5.18378	+	8.97856i	−0.475196	+	0.823064i
$120$	0.0245437	+	0.0425110i	0.00224052	+	0.00388070i
$121$	−2.70959	−	4.69315i	−0.246326	−	0.426650i
$122$	−14.5411	+	25.1859i	−1.31649	+	2.28023i
$123$	−4.79935	+	8.31271i	−0.432742	+	0.749532i
$124$	−3.82896	−	6.63195i	−0.343850	−	0.595566i
$125$	−1.57294			−0.140688
$126$	−4.82516	−	8.35743i	−0.429860	−	0.744539i
$127$	−8.77849	−	15.2048i	−0.778965	−	1.34921i	−0.932539	−	0.361070i	$-0.882412\pi$
$127$	−8.77849	−	15.2048i	−0.778965	−	1.34921i	0.153574	−	0.988137i	$-0.450922\pi$
$128$	2.48313			0.219480
$129$	−12.0190			−1.05821
$130$	0.675090			0.0592093
$131$	2.31322	+	4.00662i	0.202107	+	0.350060i	0.949207	−	0.314652i	$-0.101888\pi$
$131$	2.31322	+	4.00662i	0.202107	+	0.350060i	−0.747100	+	0.664712i	$0.768554\pi$
$132$	4.36156	+	7.55444i	0.379625	+	0.657529i
$133$	0.938434	−	1.62541i	0.0813725	−	0.140941i
$134$	−13.8934			−1.20021
$135$	−0.0788428	+	0.136560i	−0.00678571	+	0.0117532i
$136$	−0.340762	+	0.590217i	−0.0292201	+	0.0506107i
$137$	−1.70601	+	2.95490i	−0.145754	+	0.252454i	−0.929654	−	0.368433i	$-0.879894\pi$
$137$	−1.70601	+	2.95490i	−0.145754	+	0.252454i	0.783900	+	0.620887i	$0.213228\pi$
$138$	2.88217	−	4.99207i	0.245347	−	0.424953i
$139$	7.41740	+	12.8473i	0.629136	+	1.08969i	0.987726	+	0.156200i	$0.0499243\pi$
$139$	7.41740	+	12.8473i	0.629136	+	1.08969i	−0.358590	+	0.933495i	$0.616742\pi$
$140$	0.803769	−	1.39217i	0.0679309	−	0.117660i
$141$	−0.967729			−0.0814975
$142$	7.66027	+	13.2680i	0.642836	+	1.11342i
$143$	8.51289			0.711883
$144$	1.83557	+	3.17930i	0.152964	+	0.264942i
$145$	0.217957	−	0.377513i	0.0181004	−	0.0313508i
$146$	3.09322	−	5.35761i	0.255996	−	0.443399i
$147$	−7.71287	+	13.3591i	−0.636147	+	1.10184i
$148$	−0.450243	−	0.779843i	−0.0370097	−	0.0641027i
$149$	1.78424			0.146171			0.0730853	−	0.997326i	$-0.476715\pi$
$149$	1.78424			0.146171			0.0730853	+	0.997326i	$0.476715\pi$
$150$	10.1385			0.827804
$151$	−0.673926	+	1.16727i	−0.0548433	+	0.0949914i	−0.892144	−	0.451752i	$-0.850799\pi$
$151$	−0.673926	+	1.16727i	−0.0548433	+	0.0949914i	0.837300	+	0.546743i	$0.184133\pi$
$152$	0.0616891	−	0.106849i	0.00500365	−	0.00866657i
$153$	−2.18929			−0.176993
$154$	19.5518	−	33.8648i	1.57553	−	2.72890i
$155$	0.560928			0.0450548
$156$	−4.52269			−0.362105
$157$	11.6325	+	4.65664i	0.928377	+	0.371640i
$157$	11.6325	+	4.65664i	0.928377	+	0.371640i
$158$	11.5122			0.915864
$159$	−13.8394			−1.09753
$160$	−0.638924	+	1.10665i	−0.0505114	+	0.0874883i
$161$	−13.3954			−1.05570
$162$	1.01892	−	1.76481i	0.0800536	−	0.138657i
$163$	0.909515	−	1.57533i	0.0712387	−	0.123389i	−0.828206	−	0.560424i	$-0.810638\pi$
$163$	0.909515	−	1.57533i	0.0712387	−	0.123389i	0.899444	+	0.437035i	$0.143971\pi$
$164$	20.6637			1.61356
$165$	−0.638951			−0.0497423
$166$	14.8354	+	25.6956i	1.15145	+	1.99436i
$167$	10.6356	−	18.4215i	0.823011	−	1.42550i	−0.0804189	−	0.996761i	$-0.525626\pi$
$167$	10.6356	−	18.4215i	0.823011	−	1.42550i	0.903430	−	0.428736i	$-0.141041\pi$
$168$	−0.737092	+	1.27668i	−0.0568679	+	0.0984981i
$169$	4.29315	−	7.43596i	0.330242	−	0.571997i
$170$	−0.351749	−	0.609248i	−0.0269779	−	0.0467272i
$171$	0.396333			0.0303083
$172$	12.9370	+	22.4076i	0.986438	+	1.70856i
$173$	−19.8384			−1.50829			−0.754143	−	0.656710i	$-0.771947\pi$
$173$	−19.8384			−1.50829			−0.754143	+	0.656710i	$0.771947\pi$
$174$	−2.81675	+	4.87875i	−0.213537	+	0.369857i
$175$	−11.7801	−	20.4037i	−0.890491	−	1.54237i
$176$	−7.43785	+	12.8827i	−0.560649	+	0.971072i
$177$	−4.69136	+	8.12567i	−0.352624	+	0.610763i
$178$	5.05133	−	8.74916i	0.378613	−	0.655778i
$179$	9.31169	−	16.1283i	0.695988	−	1.20549i	−0.273858	−	0.961770i	$-0.588300\pi$
$179$	9.31169	−	16.1283i	0.695988	−	1.20549i	0.969846	−	0.243717i	$-0.0783668\pi$
$180$	0.339459			0.0253018
$181$	−2.06812	+	3.58209i	−0.153722	+	0.266254i	−0.932593	−	0.360930i	$-0.882459\pi$
$181$	−2.06812	+	3.58209i	−0.153722	+	0.266254i	0.778871	+	0.627184i	$0.215793\pi$
$182$	10.1371	+	17.5579i	0.751411	+	1.30148i
$183$	7.13557	+	12.3592i	0.527476	+	0.913616i
$184$	−0.880562			−0.0649159
$185$	0.0659588			0.00484939
$186$	−7.24909			−0.531529
$187$	−4.43556	−	7.68262i	−0.324360	−	0.561809i
$188$	1.04164	+	1.80418i	0.0759697	+	0.131583i
$189$	−4.73558			−0.344463
$190$	0.0636782	+	0.110294i	0.00461970	+	0.00800155i
$191$	8.03720	−	13.9208i	0.581551	−	1.00728i	−0.413744	−	0.910393i	$-0.635779\pi$
$191$	8.03720	−	13.9208i	0.581551	−	1.00728i	0.995296	−	0.0968836i	$-0.0308874\pi$
$192$	4.58592	−	7.94305i	0.330960	−	0.573240i
$193$	3.71854	+	6.44071i	0.267667	+	0.463612i	0.968259	−	0.249950i	$-0.0804141\pi$
$193$	3.71854	+	6.44071i	0.267667	+	0.463612i	−0.700592	+	0.713562i	$0.747081\pi$
$194$	−5.74270	−	9.94665i	−0.412302	−	0.714128i
$195$	0.165639	−	0.286896i	0.0118617	−	0.0205450i
$196$	33.2079			2.37199
$197$	12.0128	−	20.8067i	0.855875	−	1.48242i	−0.0199560	−	0.999801i	$-0.506353\pi$
$197$	12.0128	−	20.8067i	0.855875	−	1.48242i	0.875831	−	0.482618i	$-0.160314\pi$
$198$	8.25742			0.586829
$199$	−1.43647	+	2.48804i	−0.101829	+	0.176372i	−0.912438	−	0.409215i	$-0.865803\pi$
$199$	−1.43647	+	2.48804i	−0.101829	+	0.176372i	0.810610	+	0.585587i	$0.199136\pi$
$200$	−0.774378	−	1.34126i	−0.0547568	−	0.0948416i
$201$	−3.40887	+	5.90434i	−0.240443	+	0.416460i
$202$	−21.5817			−1.51848
$203$	13.0913			0.918830
$204$	2.35651	+	4.08159i	0.164988	+	0.285768i
$205$	−0.756788	+	1.31079i	−0.0528563	+	0.0915499i
$206$	16.2207			1.13015
$207$	−1.41433	−	2.44970i	−0.0983029	−	0.170266i
$208$	−3.85632	−	6.67934i	−0.267387	−	0.463129i
$209$	0.802982	+	1.39081i	0.0555434	+	0.0962040i
$210$	−0.760859	−	1.31785i	−0.0525042	−	0.0909400i
$211$	−19.3176			−1.32988			−0.664940	−	0.746896i	$-0.731543\pi$
$211$	−19.3176			−1.32988			−0.664940	+	0.746896i	$0.731543\pi$
$212$	14.8964	+	25.8013i	1.02309	+	1.77204i
$213$	7.51806			0.515129
$214$	3.60631	+	6.24631i	0.246522	+	0.426989i
$215$	−1.89522			−0.129253
$216$	−0.311299			−0.0211812
$217$	8.42283	+	14.5888i	0.571779	+	0.990351i
$218$	−5.52759	+	9.57406i	−0.374375	+	0.648437i
$219$	−1.51790	−	2.62907i	−0.102570	−	0.177656i
$220$	0.687755	+	1.19123i	0.0463684	+	0.0803124i
$221$	4.59943			0.309391
$222$	−0.852412			−0.0572101
$223$	7.24236	+	12.5441i	0.484984	+	0.840017i	0.999851	−	0.0172530i	$-0.00549206\pi$
$223$	7.24236	+	12.5441i	0.484984	+	0.840017i	−0.514867	+	0.857270i	$0.672159\pi$
$224$	−38.3761			−2.56411
$225$	2.48757	−	4.30859i	0.165838	−	0.287240i
$226$	−3.04085	+	5.26691i	−0.202274	+	0.350349i
$227$	−3.70682	+	6.42040i	−0.246030	+	0.426137i	−0.962421	−	0.271562i	$-0.912460\pi$
$227$	−3.70682	+	6.42040i	−0.246030	+	0.426137i	0.716390	+	0.697700i	$0.245793\pi$
$228$	−0.426605	−	0.738901i	−0.0282526	−	0.0489349i
$229$	9.65510	+	16.7231i	0.638027	+	1.10510i	0.985865	+	0.167541i	$0.0535825\pi$
$229$	9.65510	+	16.7231i	0.638027	+	1.10510i	−0.347838	+	0.937555i	$0.613084\pi$
$230$	0.454477	−	0.787177i	0.0299673	−	0.0519049i
$231$	−9.59443	−	16.6180i	−0.631267	−	1.09339i
$232$	0.860573			0.0564994
$233$	0.961804	−	1.66589i	0.0630099	−	0.109136i	−0.832800	−	0.553575i	$-0.813263\pi$
$233$	0.961804	−	1.66589i	0.0630099	−	0.109136i	0.895809	+	0.444438i	$0.146597\pi$
$234$	−2.14062	+	3.70766i	−0.139937	+	0.242377i
$235$	−0.152597			−0.00995432
$236$	20.1987			1.31483
$237$	2.82463	−	4.89240i	0.183479	−	0.317796i
$238$	10.5637	−	18.2968i	0.684741	−	1.18601i
$239$	−2.12092			−0.137191			−0.0685953	−	0.997645i	$-0.521852\pi$
$239$	−2.12092			−0.137191			−0.0685953	+	0.997645i	$0.521852\pi$
$240$	0.289443	+	0.501330i	0.0186835	+	0.0323607i
$241$	−7.04829	+	12.2080i	−0.454020	+	0.786386i	−0.998631	−	0.0523026i	$-0.983344\pi$
$241$	−7.04829	+	12.2080i	−0.454020	+	0.786386i	0.544611	+	0.838689i	$0.316677\pi$
$242$	5.52169	+	9.56385i	0.354948	+	0.614788i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	15.3612	−	26.6063i	0.983398	−	1.70330i
$245$	−1.21621	+	2.10654i	−0.0777007	+	0.134582i
$246$	9.78026	−	16.9399i	0.623567	−	1.08005i
$247$	−0.832648			−0.0529801
$248$	0.553685	+	0.959011i	0.0351591	+	0.0608973i
$249$	14.5599			0.922699
$250$	3.20538			0.202726
$251$	12.0775	+	20.9188i	0.762323	+	1.32038i	0.941650	+	0.336593i	$0.109275\pi$
$251$	12.0775	+	20.9188i	0.762323	+	1.32038i	−0.179327	+	0.983789i	$0.557392\pi$
$252$	5.09729	+	8.82876i	0.321099	+	0.556160i
$253$	5.73096	−	9.92631i	0.360302	−	0.624062i
$254$	17.8891	+	30.9848i	1.12246	+	1.94416i
$255$	−0.345219			−0.0216185
$256$	13.2835			0.830218
$257$	7.51499	+	13.0163i	0.468772	+	0.811937i	0.999363	−	0.0356908i	$-0.0113631\pi$
$257$	7.51499	+	13.0163i	0.468772	+	0.811937i	−0.530591	+	0.847628i	$0.678030\pi$
$258$	24.4927			1.52485
$259$	0.990431	+	1.71548i	0.0615424	+	0.106595i
$260$	−0.713163			−0.0442285
$261$	1.38223	+	2.39409i	0.0855577	+	0.148190i
$262$	−4.71396	−	8.16482i	−0.291230	−	0.504424i
$263$	−7.85443	−	13.6043i	−0.484325	−	0.838875i	0.515513	−	0.856882i	$-0.327601\pi$
$263$	−7.85443	−	13.6043i	−0.484325	−	0.838875i	−0.999838	+	0.0180065i	$0.994268\pi$
$264$	−0.630702	−	1.09241i	−0.0388170	−	0.0672330i
$265$	−2.18227			−0.134056
$266$	−1.91237	+	3.31232i	−0.117255	+	0.203092i
$267$	−2.47878	−	4.29337i	−0.151699	−	0.262750i
$268$	14.6770			0.896539
$269$	−3.52113			−0.214687			−0.107343	−	0.994222i	$-0.534234\pi$
$269$	−3.52113			−0.214687			−0.107343	+	0.994222i	$0.534234\pi$
$270$	0.160668	−	0.278286i	0.00977797	−	0.0169359i
$271$	11.7940	+	20.4278i	0.716436	+	1.24090i	0.962403	+	0.271625i	$0.0875611\pi$
$271$	11.7940	+	20.4278i	0.716436	+	1.24090i	−0.245967	+	0.969278i	$0.579106\pi$
$272$	−4.01860	+	6.96041i	−0.243663	+	0.422037i
$273$	9.94889			0.602134
$274$	3.47656	−	6.02158i	0.210027	−	0.363777i
$275$	20.1595			1.21567
$276$	−3.04472	+	5.27361i	−0.183270	+	0.317434i
$277$	−1.88259	−	3.26074i	−0.113114	−	0.195919i	0.803910	−	0.594751i	$-0.202749\pi$
$277$	−1.88259	−	3.26074i	−0.113114	−	0.195919i	−0.917024	+	0.398831i	$0.869416\pi$
$278$	−15.1154	−	26.1807i	−0.906562	−	1.57021i
$279$	−1.77863	+	3.08067i	−0.106484	+	0.184435i
$280$	−0.116229	+	0.201314i	−0.00694600	+	0.0120308i
$281$	−9.74057	−	16.8712i	−0.581074	−	1.00645i	−0.995352	−	0.0962992i	$-0.969299\pi$
$281$	−9.74057	−	16.8712i	−0.581074	−	1.00645i	0.414279	−	0.910150i	$-0.364034\pi$
$282$	1.97207			0.117435
$283$	−6.99825	−	12.1213i	−0.416003	−	0.720538i	0.579530	−	0.814951i	$-0.303236\pi$
$283$	−6.99825	−	12.1213i	−0.416003	−	0.720538i	−0.995533	+	0.0944124i	$0.969903\pi$
$284$	−8.09229	−	14.0163i	−0.480189	−	0.831712i
$285$	0.0624960			0.00370194
$286$	−17.3478			−1.02580
$287$	−45.4554			−2.68315
$288$	−4.05189	−	7.01807i	−0.238760	−	0.413544i
$289$	6.10351	+	10.5716i	0.359030	+	0.621858i
$290$	−0.444161	+	0.769309i	−0.0260820	+	0.0451754i
$291$	−5.63609			−0.330393
$292$	−3.26766	+	5.65976i	−0.191226	+	0.331212i
$293$	−9.42380	+	16.3225i	−0.550544	+	0.953571i	0.447691	+	0.894188i	$0.352246\pi$
$293$	−9.42380	+	16.3225i	−0.550544	+	0.953571i	−0.998235	+	0.0593823i	$0.981087\pi$
$294$	15.7175	−	27.2236i	0.916666	−	1.58771i
$295$	−0.739760	+	1.28130i	−0.0430705	+	0.0746003i
$296$	0.0651072	+	0.112769i	0.00378428	+	0.00655457i
$297$	2.02603	−	3.50919i	0.117562	−	0.203624i
$298$	−3.63598			−0.210627
$299$	2.97134	+	5.14652i	0.171837	+	0.297631i
$300$	−10.7103			−0.618358
$301$	−28.4585	−	49.2916i	−1.64032	−	2.84112i
$302$	1.37335	−	2.37871i	0.0790273	−	0.136879i
$303$	−5.29526	+	9.17166i	−0.304205	+	0.526898i
$304$	0.727498	−	1.26006i	0.0417248	−	0.0722696i
$305$	1.12518	+	1.94886i	0.0644274	+	0.111592i
$306$	4.46140			0.255041
$307$	29.2301			1.66825			0.834126	−	0.551575i	$-0.185973\pi$
$307$	29.2301			1.66825			0.834126	+	0.551575i	$0.185973\pi$
$308$	−20.6545	+	35.7747i	−1.17690	+	2.03845i
$309$	3.97989	−	6.89337i	0.226408	−	0.392150i
$310$	−1.14308			−0.0649224
$311$	−5.61095	+	9.71845i	−0.318168	+	0.551083i	−0.980106	−	0.198476i	$-0.936401\pi$
$311$	−5.61095	+	9.71845i	−0.318168	+	0.551083i	0.661938	+	0.749559i	$0.269734\pi$
$312$	0.654003			0.0370256
$313$	−9.11855			−0.515411			−0.257705	−	0.966224i	$-0.582966\pi$
$313$	−9.11855			−0.515411			−0.257705	+	0.966224i	$0.582966\pi$
$314$	−23.7051	−	9.48945i	−1.33776	−	0.535520i
$315$	−0.746733			−0.0420737
$316$	−12.1615			−0.684137
$317$	−4.12850	+	7.15077i	−0.231880	+	0.401627i	−0.958361	−	0.285559i	$-0.907821\pi$
$317$	−4.12850	+	7.15077i	−0.231880	+	0.401627i	0.726482	+	0.687186i	$0.241154\pi$
$318$	28.2023			1.58151
$319$	−5.60087	+	9.70099i	−0.313588	+	0.543151i
$320$	0.723134	−	1.25250i	0.0404244	−	0.0700171i
$321$	3.53936			0.197548
$322$	27.2975			1.52123
$323$	0.433843	+	0.751439i	0.0241397	+	0.0418112i
$324$	−1.07638	+	1.86434i	−0.0597989	+	0.103575i
$325$	−5.22608	+	9.05184i	−0.289891	+	0.502106i
$326$	−1.85344	+	3.21025i	−0.102652	+	0.177799i
$327$	2.71248	+	4.69816i	0.150001	+	0.259809i
$328$	−2.98807			−0.164988
$329$	−2.29138	−	3.96879i	−0.126328	−	0.218806i
$330$	1.30208			0.0716769
$331$	11.5344	−	19.9781i	0.633985	−	1.09810i	−0.352744	−	0.935720i	$-0.614751\pi$
$331$	11.5344	−	19.9781i	0.633985	−	1.09810i	0.986729	−	0.162375i	$-0.0519155\pi$
$332$	−15.6720	−	27.1447i	−0.860114	−	1.48976i
$333$	−0.209147	+	0.362253i	−0.0114612	+	0.0198513i
$334$	−21.6737	+	37.5399i	−1.18593	+	2.05409i
$335$	−0.537530	+	0.931030i	−0.0293684	+	0.0508676i
$336$	−8.69250	+	15.0559i	−0.474215	+	0.821364i
$337$	−6.58166			−0.358526			−0.179263	−	0.983801i	$-0.557371\pi$
$337$	−6.58166			−0.358526			−0.179263	+	0.983801i	$0.557371\pi$
$338$	−8.74872	+	15.1532i	−0.475868	+	0.824227i
$339$	1.49220	+	2.58456i	0.0810451	+	0.140374i
$340$	0.371587	+	0.643608i	0.0201521	+	0.0349045i
$341$	−14.4142			−0.780573
$342$	−0.807660			−0.0436732
$343$	−39.9008			−2.15444
$344$	−1.87075	−	3.24024i	−0.100864	−	0.174702i
$345$	−0.223020	−	0.386282i	−0.0120070	−	0.0207967i
$346$	40.4273			2.17339
$347$	6.02641	+	10.4380i	0.323514	+	0.560343i	0.981211	−	0.192940i	$-0.0618023\pi$
$347$	6.02641	+	10.4380i	0.323514	+	0.560343i	−0.657696	+	0.753283i	$0.728469\pi$
$348$	2.97560	−	5.15390i	0.159509	−	0.276278i
$349$	15.3881	−	26.6530i	0.823708	−	1.42670i	−0.0791939	−	0.996859i	$-0.525235\pi$
$349$	15.3881	−	26.6530i	0.823708	−	1.42670i	0.902902	−	0.429846i	$-0.141432\pi$
$350$	24.0058	+	41.5793i	1.28317	+	2.22251i
$351$	1.05044	+	1.81942i	0.0560683	+	0.0971132i
$352$	16.4185	−	28.4377i	0.875108	−	1.51573i
$353$	22.5448			1.19994			0.599969	−	0.800023i	$-0.295180\pi$
$353$	22.5448			1.19994			0.599969	+	0.800023i	$0.295180\pi$
$354$	9.56021	−	16.5588i	0.508119	−	0.880088i
$355$	1.18549			0.0629193
$356$	−5.33621	+	9.24259i	−0.282819	+	0.489856i
$357$	−5.18378	−	8.97856i	−0.274355	−	0.475196i
$358$	−18.9757	+	32.8668i	−1.00289	+	1.73706i
$359$	1.48218			0.0782263			0.0391131	−	0.999235i	$-0.487547\pi$
$359$	1.48218			0.0782263			0.0391131	+	0.999235i	$0.487547\pi$
$360$	−0.0490874			−0.00258714
$361$	9.42146	+	16.3184i	0.495866	+	0.858866i
$362$	4.21448	−	7.29969i	0.221508	−	0.383663i
$363$	5.41918			0.284433
$364$	−10.7088	−	18.5482i	−0.561293	−	0.972188i
$365$	−0.239350	−	0.414567i	−0.0125282	−	0.0216994i
$366$	−14.5411	−	25.1859i	−0.760075	−	1.31649i
$367$	13.0269	+	22.5632i	0.679996	+	1.17779i	0.974981	+	0.222286i	$0.0713520\pi$
$367$	13.0269	+	22.5632i	0.679996	+	1.17779i	−0.294985	+	0.955502i	$0.595315\pi$
$368$	−10.3844			−0.541326
$369$	−4.79935	−	8.31271i	−0.249844	−	0.432742i
$370$	−0.134413			−0.00698780
$371$	−32.7687	−	56.7571i	−1.70127	−	2.94668i
$372$	7.65791			0.397044
$373$	−18.3305			−0.949118			−0.474559	−	0.880224i	$-0.657392\pi$
$373$	−18.3305			−0.949118			−0.474559	+	0.880224i	$0.657392\pi$
$374$	9.03893	+	15.6559i	0.467392	+	0.809547i
$375$	0.786468	−	1.36220i	0.0406130	−	0.0703438i
$376$	−0.150627	−	0.260893i	−0.00776798	−	0.0134545i
$377$	−2.90389	−	5.02969i	−0.149558	−	0.259042i
$378$	9.65032			0.496359
$379$	−38.7673			−1.99134			−0.995672	−	0.0929336i	$-0.970376\pi$
$379$	−38.7673			−1.99134			−0.995672	+	0.0929336i	$0.970376\pi$
$380$	−0.0672694	−	0.116514i	−0.00345085	−	0.00597705i
$381$	17.5570			0.899471
$382$	−16.3785	+	28.3683i	−0.837995	+	1.45145i
$383$	−3.81135	+	6.60145i	−0.194751	+	0.337318i	−0.946819	−	0.321767i	$-0.895723\pi$
$383$	−3.81135	+	6.60145i	−0.194751	+	0.337318i	0.752068	+	0.659086i	$0.229057\pi$
$384$	−1.24157	+	2.15045i	−0.0633584	+	0.109740i
$385$	−1.51290	−	2.62043i	−0.0771047	−	0.133549i
$386$	−7.57777	−	13.1251i	−0.385698	−	0.668049i
$387$	6.00950	−	10.4088i	0.305480	−	0.529107i
$388$	6.06657	+	10.5076i	0.307983	+	0.533443i
$389$	9.09708			0.461240			0.230620	−	0.973044i	$-0.425925\pi$
$389$	9.09708			0.461240			0.230620	+	0.973044i	$0.425925\pi$
$390$	−0.337545	+	0.584645i	−0.0170923	+	0.0296047i
$391$	3.09638	−	5.36309i	0.156591	−	0.271223i
$392$	−4.80203			−0.242539
$393$	−4.62645			−0.233373
$394$	−24.4800	+	42.4006i	−1.23329	+	2.13611i
$395$	0.445403	−	0.771461i	0.0224107	−	0.0388164i
$396$	−8.72311			−0.438353
$397$	−7.94354	−	13.7586i	−0.398675	−	0.690525i	0.594888	−	0.803809i	$-0.297196\pi$
$397$	−7.94354	−	13.7586i	−0.398675	−	0.690525i	−0.993563	+	0.113284i	$0.963863\pi$
$398$	2.92728	−	5.07020i	0.146731	−	0.254146i
$399$	0.938434	+	1.62541i	0.0469804	+	0.0813725i
$400$	−9.13222	−	15.8175i	−0.456611	−	0.790873i
$401$	12.2205	−	21.1666i	0.610265	−	1.05701i	−0.380931	−	0.924603i	$-0.624396\pi$
$401$	12.2205	−	21.1666i	0.610265	−	1.05701i	0.991196	−	0.132406i	$-0.0422702\pi$
$402$	6.94671	−	12.0321i	0.346471	−	0.600105i
$403$	3.73668	−	6.47212i	0.186137	−	0.322399i
$404$	22.7988			1.13428
$405$	−0.0788428	−	0.136560i	−0.00391773	−	0.00678571i
$406$	−26.6779			−1.32400
$407$	−1.69495			−0.0840155
$408$	−0.340762	−	0.590217i	−0.0168702	−	0.0292201i
$409$	−2.98984	−	5.17856i	−0.147838	−	0.256063i	0.782590	−	0.622537i	$-0.213898\pi$
$409$	−2.98984	−	5.17856i	−0.147838	−	0.256063i	−0.930428	+	0.366474i	$0.880565\pi$
$410$	1.54221	−	2.67118i	0.0761641	−	0.131920i
$411$	−1.70601	−	2.95490i	−0.0841513	−	0.145754i
$412$	−17.1355			−0.844205
$413$	−44.4327			−2.18639
$414$	2.88217	+	4.99207i	0.141651	+	0.245347i
$415$	2.29589			0.112701
$416$	8.51253	+	14.7441i	0.417361	+	0.722890i
$417$	−14.8348			−0.726463
$418$	−1.63634	−	2.83423i	−0.0800361	−	0.138627i
$419$	16.8679	+	29.2160i	0.824049	+	1.42729i	0.902644	+	0.430388i	$0.141623\pi$
$419$	16.8679	+	29.2160i	0.824049	+	1.42729i	−0.0785954	+	0.996907i	$0.525044\pi$
$420$	0.803769	+	1.39217i	0.0392199	+	0.0679309i
$421$	12.3902	+	21.4605i	0.603862	+	1.04592i	0.992230	+	0.124415i	$0.0397054\pi$
$421$	12.3902	+	21.4605i	0.603862	+	1.04592i	−0.388369	+	0.921504i	$0.626961\pi$
$422$	39.3661			1.91631
$423$	0.483864	−	0.838078i	0.0235263	−	0.0407487i
$424$	−2.15409	−	3.73100i	−0.104612	−	0.181193i
$425$	10.8920			0.528340
$426$	−15.3205			−0.742283
$427$	−33.7911	+	58.5279i	−1.63526	+	2.83236i
$428$	−3.80970	−	6.59859i	−0.184149	−	0.318955i
$429$	−4.25644	+	7.37238i	−0.205503	+	0.355942i
$430$	3.86215			0.186249
$431$	1.72116	−	2.98114i	0.0829055	−	0.143597i	−0.821591	−	0.570077i	$-0.806913\pi$
$431$	1.72116	−	2.98114i	0.0829055	−	0.143597i	0.904497	+	0.426480i	$0.140247\pi$
$432$	−3.67114			−0.176628
$433$	16.2139	−	28.0834i	0.779192	−	1.34960i	−0.153216	−	0.988193i	$-0.548963\pi$
$433$	16.2139	−	28.0834i	0.779192	−	1.34960i	0.932408	−	0.361407i	$-0.117704\pi$
$434$	−17.1643	−	29.7295i	−0.823914	−	1.42706i
$435$	0.217957	+	0.377513i	0.0104503	+	0.0181004i
$436$	5.83933	−	10.1140i	0.279653	−	0.484373i
$437$	−0.560546	+	0.970895i	−0.0268146	+	0.0464442i
$438$	3.09322	+	5.35761i	0.147800	+	0.255996i
$439$	−12.8591			−0.613730			−0.306865	−	0.951753i	$-0.599280\pi$
$439$	−12.8591			−0.613730			−0.306865	+	0.951753i	$0.599280\pi$
$440$	−0.0994526	−	0.172257i	−0.00474122	−	0.00821203i
$441$	−7.71287	−	13.3591i	−0.367280	−	0.636147i
$442$	−9.37287			−0.445822
$443$	−22.4392			−1.06612			−0.533059	−	0.846078i	$-0.678958\pi$
$443$	−22.4392			−1.06612			−0.533059	+	0.846078i	$0.678958\pi$
$444$	0.900485			0.0427351
$445$	−0.390868	−	0.677002i	−0.0185289	−	0.0320930i
$446$	−14.7587	−	25.5628i	−0.698845	−	1.21044i
$447$	−0.892120	+	1.54520i	−0.0421958	+	0.0730853i
$448$	43.4340			2.05207
$449$	0.638502	−	1.10592i	0.0301328	−	0.0521915i	−0.850566	−	0.525869i	$-0.823740\pi$
$449$	0.638502	−	1.10592i	0.0301328	−	0.0521915i	0.880699	+	0.473677i	$0.157074\pi$
$450$	−5.06925	+	8.78019i	−0.238967	+	0.413902i
$451$	19.4472	−	33.6836i	0.915734	−	1.58610i
$452$	3.21234	−	5.56394i	0.151096	−	0.261706i
$453$	−0.673926	−	1.16727i	−0.0316638	−	0.0548433i
$454$	7.55388	−	13.0837i	0.354521	−	0.614049i
$455$	1.56880			0.0735463
$456$	0.0616891	+	0.106849i	0.00288886	+	0.00500365i
$457$	37.0729			1.73420			0.867099	−	0.498136i	$-0.165982\pi$
$457$	37.0729			1.73420			0.867099	+	0.498136i	$0.165982\pi$
$458$	−19.6755	−	34.0789i	−0.919374	−	1.59240i
$459$	1.09464	−	1.89598i	0.0510936	−	0.0884967i
$460$	−0.480108	+	0.831572i	−0.0223852	+	0.0387722i
$461$	−6.43918	+	11.1530i	−0.299902	+	0.519446i	−0.976113	−	0.217262i	$-0.930287\pi$
$461$	−6.43918	+	11.1530i	−0.299902	+	0.519446i	0.676211	+	0.736708i	$0.263621\pi$
$462$	19.5518	+	33.8648i	0.909634	+	1.57553i
$463$	−34.4322			−1.60020			−0.800099	−	0.599868i	$-0.795220\pi$
$463$	−34.4322			−1.60020			−0.800099	+	0.599868i	$0.795220\pi$
$464$	10.1487			0.471142
$465$	−0.280464	+	0.485778i	−0.0130062	+	0.0225274i
$466$	−1.96000	+	3.39481i	−0.0907951	+	0.157262i
$467$	−32.1227			−1.48646			−0.743230	−	0.669037i	$-0.766707\pi$
$467$	−32.1227			−1.48646			−0.743230	+	0.669037i	$0.766707\pi$
$468$	2.26134	−	3.91676i	0.104531	−	0.181052i
$469$	−32.2860			−1.49083
$470$	0.310967			0.0143438
$471$	−9.84903	+	7.74575i	−0.453819	+	0.356905i
$472$	−2.92084			−0.134442
$473$	48.7017			2.23931
$474$	−5.75612	+	9.96989i	−0.264387	+	0.457932i
$475$	−1.97181			−0.0904728
$476$	−11.1594	+	19.3287i	−0.511492	+	0.885929i
$477$	6.91968	−	11.9852i	0.316830	−	0.548766i
$478$	4.32207			0.197687
$479$	14.3570			0.655989			0.327994	−	0.944680i	$-0.393627\pi$
$479$	14.3570			0.655989			0.327994	+	0.944680i	$0.393627\pi$
$480$	−0.638924	−	1.10665i	−0.0291628	−	0.0505114i
$481$	0.439392	−	0.761049i	0.0200345	−	0.0347009i
$482$	14.3632	−	24.8778i	0.654227	−	1.13315i
$483$	6.69769	−	11.6007i	0.304755	−	0.527852i
$484$	−5.83310	−	10.1032i	−0.265141	−	0.459238i
$485$	−0.888730			−0.0403551
$486$	1.01892	+	1.76481i	0.0462190	+	0.0800536i
$487$	30.8375			1.39738			0.698691	−	0.715424i	$-0.253766\pi$
$487$	30.8375			1.39738			0.698691	+	0.715424i	$0.253766\pi$
$488$	−2.22130	+	3.84740i	−0.100553	+	0.174164i
$489$	0.909515	+	1.57533i	0.0411297	+	0.0712387i
$490$	2.47843	−	4.29277i	0.111964	−	0.193927i
$491$	8.26862	−	14.3217i	0.373158	−	0.646328i	−0.616892	−	0.787048i	$-0.711608\pi$
$491$	8.26862	−	14.3217i	0.373158	−	0.646328i	0.990049	+	0.140720i	$0.0449418\pi$
$492$	−10.3318	+	17.8953i	−0.465795	+	0.806781i
$493$	−3.02609	+	5.24135i	−0.136288	+	0.236058i
$494$	1.69680			0.0763425
$495$	0.319476	−	0.553348i	0.0143594	−	0.0248711i
$496$	6.52959	+	11.3096i	0.293187	+	0.507816i
$497$	17.8012	+	30.8326i	0.798493	+	1.38303i
$498$	−29.6707			−1.32958
$499$	−25.6000			−1.14601			−0.573006	−	0.819551i	$-0.694223\pi$
$499$	−25.6000			−1.14601			−0.573006	+	0.819551i	$0.694223\pi$
$500$	−3.38615			−0.151433
$501$	10.6356	+	18.4215i	0.475166	+	0.823011i
$502$	−24.6119	−	42.6290i	−1.09848	−	1.90262i
$503$	13.7059			0.611117			0.305559	−	0.952173i	$-0.401157\pi$
$503$	13.7059			0.611117			0.305559	+	0.952173i	$0.401157\pi$
$504$	−0.737092	−	1.27668i	−0.0328327	−	0.0568679i
$505$	−0.834986	+	1.44624i	−0.0371564	+	0.0643567i
$506$	−11.6787	+	20.2282i	−0.519183	+	0.899251i
$507$	4.29315	+	7.43596i	0.190666	+	0.330242i
$508$	−18.8980	−	32.7323i	−0.838462	−	1.45226i
$509$	12.7284	−	22.0463i	0.564178	−	0.977185i	−0.432948	−	0.901419i	$-0.642527\pi$
$509$	12.7284	−	22.0463i	0.564178	−	0.977185i	0.997126	−	0.0757657i	$-0.0241401\pi$
$510$	0.703499			0.0311514
$511$	7.18812	−	12.4502i	0.317984	−	0.550764i
$512$	−32.0358			−1.41579
$513$	−0.198166	+	0.343234i	−0.00874926	+	0.0151542i
$514$	−15.3143	−	26.5251i	−0.675485	−	1.16997i
$515$	0.627571	−	1.08698i	0.0276541	−	0.0478983i
$516$	−25.8740			−1.13904
$517$	3.92129			0.172458
$518$	−2.01833	−	3.49585i	−0.0886804	−	0.153599i
$519$	9.91920	−	17.1806i	0.435405	−	0.754143i
$520$	0.103127			0.00452241
$521$	14.4541	+	25.0353i	0.633247	+	1.09682i	0.986884	+	0.161433i	$0.0516115\pi$
$521$	14.4541	+	25.0353i	0.633247	+	1.09682i	−0.353637	+	0.935383i	$0.615055\pi$
$522$	−2.81675	−	4.87875i	−0.123286	−	0.213537i
$523$	5.40126	+	9.35525i	0.236181	+	0.409077i	0.959615	−	0.281316i	$-0.0907710\pi$
$523$	5.40126	+	9.35525i	0.236181	+	0.409077i	−0.723435	+	0.690393i	$0.757438\pi$
$524$	4.97982	+	8.62530i	0.217544	+	0.376798i
$525$	23.5602			1.02825
$526$	16.0060	+	27.7232i	0.697895	+	1.20879i
$527$	−7.78785			−0.339244
$528$	−7.43785	−	12.8827i	−0.323691	−	0.560649i
$529$	−14.9987			−0.652115
$530$	4.44710			0.193170
$531$	−4.69136	−	8.12567i	−0.203588	−	0.352624i
$532$	2.02022	−	3.49913i	0.0875877	−	0.151706i
$533$	10.0828	+	17.4640i	0.436737	+	0.756450i
$534$	5.05133	+	8.74916i	0.218593	+	0.378613i
$535$	0.558106			0.0241290
$536$	−2.12236			−0.0916721
$537$	9.31169	+	16.1283i	0.401829	+	0.695988i
$538$	7.17547			0.309356
$539$	31.2530	−	54.1318i	1.34616	−	2.33162i
$540$	−0.169730	+	0.293980i	−0.00730400	+	0.0126509i
$541$	−20.5645	+	35.6187i	−0.884137	+	1.53137i	−0.0374365	+	0.999299i	$0.511919\pi$
$541$	−20.5645	+	35.6187i	−0.884137	+	1.53137i	−0.846700	+	0.532070i	$0.821414\pi$
$542$	−24.0342	−	41.6285i	−1.03236	−	1.78810i
$543$	−2.06812	−	3.58209i	−0.0887515	−	0.153722i
$544$	8.87075	−	15.3646i	0.380330	−	0.658751i
$545$	0.427720	+	0.740832i	0.0183215	+	0.0317338i
$546$	−20.2742			−0.867654
$547$	−7.66136	+	13.2699i	−0.327576	+	0.567378i	−0.982030	−	0.188723i	$-0.939565\pi$
$547$	−7.66136	+	13.2699i	−0.327576	+	0.567378i	0.654454	+	0.756102i	$0.272898\pi$
$548$	−3.67263	+	6.36118i	−0.156887	+	0.271736i
$549$	−14.2711			−0.609077
$550$	−41.0818			−1.75173
$551$	0.547822	−	0.948856i	0.0233380	−	0.0404226i
$552$	0.440281	−	0.762589i	0.0187396	−	0.0324579i
$553$	26.7525			1.13763
$554$	3.83640	+	6.64485i	0.162993	+	0.282313i
$555$	−0.0329794	+	0.0571220i	−0.00139990	+	0.00242469i
$556$	15.9679	+	27.6572i	0.677189	+	1.17293i
$557$	−21.0811	−	36.5136i	−0.893235	−	1.54713i	−0.835973	−	0.548770i	$-0.815096\pi$
$557$	−21.0811	−	36.5136i	−0.893235	−	1.54713i	−0.0572621	−	0.998359i	$-0.518237\pi$
$558$	3.62454	−	6.27789i	0.153439	−	0.265764i
$559$	−12.6252	+	21.8676i	−0.533991	+	0.924899i
$560$	−1.37068	+	2.37409i	−0.0579219	+	0.100324i
$561$	8.87112			0.374539
$562$	19.8497	+	34.3806i	0.837307	+	1.45026i
$563$	10.6976			0.450848			0.225424	−	0.974261i	$-0.427623\pi$
$563$	10.6976			0.450848			0.225424	+	0.974261i	$0.427623\pi$
$564$	−2.08329			−0.0877222
$565$	0.235298	+	0.407548i	0.00989907	+	0.0171457i
$566$	14.2613	+	24.7012i	0.599446	+	1.03827i
$567$	2.36779	−	4.10114i	0.0994379	−	0.172231i
$568$	1.17018	+	2.02682i	0.0490998	+	0.0850434i
$569$	0.904748			0.0379290			0.0189645	−	0.999820i	$-0.493963\pi$
$569$	0.904748			0.0379290			0.0189645	+	0.999820i	$0.493963\pi$
$570$	−0.127356			−0.00533437
$571$	−5.61063	−	9.71790i	−0.234798	−	0.406681i	0.724416	−	0.689363i	$-0.242109\pi$
$571$	−5.61063	−	9.71790i	−0.234798	−	0.406681i	−0.959214	+	0.282681i	$0.908776\pi$
$572$	18.3262			0.766257
$573$	8.03720	+	13.9208i	0.335759	+	0.581551i
$574$	92.6305			3.86632
$575$	7.03649	+	12.1876i	0.293442	+	0.508257i
$576$	4.58592	+	7.94305i	0.191080	+	0.330960i
$577$	14.1168	+	24.4510i	0.587691	+	1.01791i	0.994534	+	0.104412i	$0.0332961\pi$
$577$	14.1168	+	24.4510i	0.587691	+	1.01791i	−0.406844	+	0.913498i	$0.633371\pi$
$578$	−12.4379	−	21.5431i	−0.517350	−	0.896076i
$579$	−7.43709			−0.309075
$580$	0.469210	−	0.812695i	0.0194829	−	0.0337453i
$581$	34.4749	+	59.7123i	1.43026	+	2.47728i
$582$	11.4854			0.476085
$583$	56.0779			2.32251
$584$	0.472520	−	0.818429i	0.0195530	−	0.0338668i
$585$	0.165639	+	0.286896i	0.00684834	+	0.0118617i
$586$	19.2041	−	33.2625i	0.793315	−	1.37406i
$587$	−16.6769			−0.688329			−0.344165	−	0.938909i	$-0.611838\pi$
$587$	−16.6769			−0.688329			−0.344165	+	0.938909i	$0.611838\pi$
$588$	−16.6040	+	28.7589i	−0.684736	+	1.18600i
$589$	1.40986			0.0580921
$590$	1.50751	−	2.61108i	0.0620631	−	0.107496i
$591$	12.0128	+	20.8067i	0.494140	+	0.855875i
$592$	0.767807	+	1.32988i	0.0315567	+	0.0546578i
$593$	4.62125	−	8.00425i	0.189772	−	0.328695i	−0.755402	−	0.655262i	$-0.772558\pi$
$593$	4.62125	−	8.00425i	0.189772	−	0.328695i	0.945174	+	0.326567i	$0.105892\pi$
$594$	−4.12871	+	7.15113i	−0.169403	+	0.293415i
$595$	−0.817407	−	1.41579i	−0.0335104	−	0.0580417i
$596$	3.84104			0.157335
$597$	−1.43647	−	2.48804i	−0.0587907	−	0.101829i
$598$	−6.05510	−	10.4877i	−0.247611	−	0.428875i
$599$	33.7678			1.37971			0.689857	−	0.723946i	$-0.257674\pi$
$599$	33.7678			1.37971			0.689857	+	0.723946i	$0.257674\pi$
$600$	1.54876			0.0632277
$601$	−6.49856			−0.265082			−0.132541	−	0.991178i	$-0.542314\pi$
$601$	−6.49856			−0.265082			−0.132541	+	0.991178i	$0.542314\pi$
$602$	57.9936	+	100.448i	2.36364	+	4.09395i
$603$	−3.40887	−	5.90434i	−0.138820	−	0.240443i
$604$	−1.45080	+	2.51286i	−0.0590323	+	0.102247i
$605$	0.854527			0.0347415
$606$	10.7908	−	18.6903i	0.438348	−	0.759241i
$607$	−9.06082	+	15.6938i	−0.367767	+	0.636992i	−0.989216	−	0.146463i	$-0.953211\pi$
$607$	−9.06082	+	15.6938i	−0.367767	+	0.636992i	0.621449	+	0.783455i	$0.286544\pi$
$608$	−1.60590	+	2.78149i	−0.0651277	+	0.112804i
$609$	−6.54565	+	11.3374i	−0.265243	+	0.459415i
$610$	−2.29292	−	3.97146i	−0.0928377	−	0.160800i
$611$	−1.01654	+	1.76070i	−0.0411248	+	0.0712303i
$612$	−4.71301			−0.190512
$613$	8.38026	+	14.5150i	0.338475	+	0.586257i	0.984146	−	0.177359i	$-0.0567554\pi$
$613$	8.38026	+	14.5150i	0.338475	+	0.586257i	−0.645671	+	0.763616i	$0.723422\pi$
$614$	−59.5661			−2.40389
$615$	−0.756788	−	1.31079i	−0.0305166	−	0.0528563i
$616$	2.98674	−	5.17319i	0.120339	−	0.208434i
$617$	11.4705	−	19.8675i	0.461784	−	0.799834i	−0.537266	−	0.843413i	$-0.680543\pi$
$617$	11.4705	−	19.8675i	0.461784	−	0.799834i	0.999050	+	0.0435793i	$0.0138761\pi$
$618$	−8.11034	+	14.0475i	−0.326246	+	0.565074i
$619$	−2.97794	−	5.15794i	−0.119693	−	0.207315i	0.799953	−	0.600063i	$-0.204858\pi$
$619$	−2.97794	−	5.15794i	−0.119693	−	0.207315i	−0.919646	+	0.392748i	$0.871524\pi$
$620$	1.20754			0.0484961
$621$	2.82866			0.113510
$622$	11.4342	−	19.8046i	0.458469	−	0.794091i
$623$	11.7385	−	20.3316i	0.470291	−	0.814568i
$624$	7.71263			0.308752
$625$	−12.3138	+	21.3282i	−0.492553	+	0.853127i
$626$	18.5821			0.742689
$627$	−1.60596			−0.0641360
$628$	25.0420	+	10.0246i	0.999286	+	0.400026i
$629$	−0.915764			−0.0365139
$630$	1.52172			0.0606267
$631$	−16.1264	+	27.9318i	−0.641984	+	1.11195i	0.343006	+	0.939333i	$0.388555\pi$
$631$	−16.1264	+	27.9318i	−0.641984	+	1.11195i	−0.984989	+	0.172615i	$0.944778\pi$
$632$	1.75861			0.0699538
$633$	9.65882	−	16.7296i	0.383903	−	0.664940i
$634$	8.41319	−	14.5721i	0.334131	−	0.578731i
$635$	2.76848			0.109864
$636$	−29.7928			−1.18136
$637$	16.2038	+	28.0658i	0.642019	+	1.11201i
$638$	11.4136	−	19.7690i	0.451870	−	0.782662i
$639$	−3.75903	+	6.51083i	−0.148705	+	0.257564i
$640$	−0.195777	+	0.339096i	−0.00773877	+	0.0134039i
$641$	4.61290	+	7.98978i	0.182199	+	0.315577i	0.942629	−	0.333842i	$-0.108345\pi$
$641$	4.61290	+	7.98978i	0.182199	+	0.315577i	−0.760430	+	0.649419i	$0.775012\pi$
$642$	−7.21262			−0.284659
$643$	−8.40414	−	14.5564i	−0.331427	−	0.574049i	0.651365	−	0.758765i	$-0.274197\pi$
$643$	−8.40414	−	14.5564i	−0.331427	−	0.574049i	−0.982792	+	0.184716i	$0.940863\pi$
$644$	−28.8370			−1.13634
$645$	0.947612	−	1.64131i	0.0373122	−	0.0646266i
$646$	−0.884100	−	1.53131i	−0.0347844	−	0.0602484i
$647$	−22.4105	+	38.8161i	−0.881048	+	1.52602i	−0.0308705	+	0.999523i	$0.509828\pi$
$647$	−22.4105	+	38.8161i	−0.881048	+	1.52602i	−0.850177	+	0.526496i	$0.823505\pi$
$648$	0.155650	−	0.269593i	0.00611450	−	0.0105906i
$649$	19.0097	−	32.9257i	0.746195	−	1.29245i
$650$	10.6499	−	18.4461i	0.417722	−	0.723516i
$651$	−16.8457			−0.660234
$652$	1.95797	−	3.39130i	0.0766799	−	0.132813i
$653$	−12.5689	−	21.7700i	−0.491860	−	0.851927i	0.508096	−	0.861300i	$-0.330350\pi$
$653$	−12.5689	−	21.7700i	−0.491860	−	0.851927i	−0.999956	+	0.00937375i	$0.997016\pi$
$654$	−5.52759	−	9.57406i	−0.216146	−	0.374375i
$655$	−0.729524			−0.0285049
$656$	−35.2382			−1.37582
$657$	3.03579			0.118437
$658$	4.66945	+	8.08772i	0.182034	+	0.315292i
$659$	−4.54441	−	7.87115i	−0.177025	−	0.306616i	0.763835	−	0.645411i	$-0.223314\pi$
$659$	−4.54441	−	7.87115i	−0.177025	−	0.306616i	−0.940860	+	0.338795i	$0.889981\pi$
$660$	−1.37551			−0.0535416
$661$	−0.829859	−	1.43736i	−0.0322778	−	0.0559068i	0.849435	−	0.527693i	$-0.176943\pi$
$661$	−0.829859	−	1.43736i	−0.0322778	−	0.0559068i	−0.881713	+	0.471786i	$0.843609\pi$
$662$	−23.5051	+	40.7120i	−0.913551	+	1.58232i
$663$	−2.29971	+	3.98322i	−0.0893135	+	0.154696i
$664$	2.26625	+	3.92526i	0.0879476	+	0.152330i
$665$	0.147977	+	0.256304i	0.00573832	+	0.00993906i
$666$	0.426206	−	0.738210i	0.0165151	−	0.0286051i
$667$	−7.81972			−0.302781
$668$	22.8960	−	39.6570i	0.885873	−	1.53438i
$669$	−14.4847			−0.560011
$670$	1.09540	−	1.89728i	0.0423189	−	0.0732984i
$671$	−28.9137	−	50.0801i	−1.11620	−	1.93332i
$672$	19.1880	−	33.2347i	0.740195	−	1.28206i
$673$	−47.6688			−1.83750			−0.918749	−	0.394841i	$-0.870800\pi$
$673$	−47.6688			−1.83750			−0.918749	+	0.394841i	$0.870800\pi$
$674$	13.4123			0.516624
$675$	2.48757	+	4.30859i	0.0957465	+	0.165838i
$676$	9.24213	−	16.0078i	0.355466	−	0.615686i
$677$	−41.6886			−1.60222			−0.801111	−	0.598516i	$-0.795757\pi$
$677$	−41.6886			−1.60222			−0.801111	+	0.598516i	$0.795757\pi$
$678$	−3.04085	−	5.26691i	−0.116783	−	0.202274i
$679$	−13.3451	−	23.1144i	−0.512137	−	0.887047i
$680$	−0.0537333	−	0.0930687i	−0.00206058	−	0.00356902i
$681$	−3.70682	−	6.42040i	−0.142046	−	0.246030i
$682$	29.3737			1.12478
$683$	−9.44683	−	16.3624i	−0.361473	−	0.626090i	0.626730	−	0.779236i	$-0.284393\pi$
$683$	−9.44683	−	16.3624i	−0.361473	−	0.626090i	−0.988204	+	0.153146i	$0.951059\pi$
$684$	0.853210			0.0326233
$685$	−0.269013	−	0.465945i	−0.0102785	−	0.0178028i
$686$	81.3112			3.10447
$687$	−19.3102			−0.736730
$688$	−22.0617	−	38.2121i	−0.841096	−	1.45682i
$689$	−14.5374	+	25.1795i	−0.553832	+	0.959264i
$690$	0.454477	+	0.787177i	0.0173016	+	0.0299673i
$691$	−5.43540	−	9.41439i	−0.206772	−	0.358140i	0.743924	−	0.668265i	$-0.232963\pi$
$691$	−5.43540	−	9.41439i	−0.206772	−	0.358140i	−0.950696	+	0.310124i	$0.899629\pi$
$692$	−42.7073			−1.62349
$693$	19.1889			0.728925
$694$	−12.2808	−	21.2710i	−0.466173	−	0.807435i
$695$	−2.33923			−0.0887322
$696$	−0.430287	+	0.745278i	−0.0163100	+	0.0282497i
$697$	10.5071	−	18.1989i	0.397987	−	0.689333i
$698$	−31.3585	+	54.3144i	−1.18694	+	2.05583i
$699$	0.961804	+	1.66589i	0.0363788	+	0.0630099i
$700$	−25.3597	−	43.9243i	−0.958506	−	1.66018i
$701$	−0.571357	+	0.989619i	−0.0215798	+	0.0373774i	−0.876614	−	0.481195i	$-0.840203\pi$
$701$	−0.571357	+	0.989619i	−0.0215798	+	0.0373774i	0.855034	+	0.518572i	$0.173536\pi$
$702$	−2.14062	−	3.70766i	−0.0807925	−	0.139937i
$703$	0.165783			0.00625264
$704$	−18.5824	+	32.1857i	−0.700352	+	1.21304i
$705$	0.0762984	−	0.132153i	0.00287357	−	0.00497716i
$706$	−45.9425			−1.72907
$707$	−50.1523			−1.88617
$708$	−10.0994	+	17.4926i	−0.379558	+	0.657413i
$709$	6.58317	−	11.4024i	0.247236	−	0.428225i	−0.715522	−	0.698590i	$-0.753811\pi$
$709$	6.58317	−	11.4024i	0.247236	−	0.428225i	0.962758	+	0.270365i	$0.0871444\pi$
$710$	−2.41583			−0.0906645
$711$	2.82463	+	4.89240i	0.105932	+	0.183479i
$712$	0.771642	−	1.33652i	0.0289185	−	0.0500883i
$713$	−5.03114	−	8.71419i	−0.188418	−	0.326349i
$714$	10.5637	+	18.2968i	0.395335	+	0.684741i
$715$	−0.671180	+	1.16252i	−0.0251007	+	0.0434757i
$716$	20.0458	−	34.7204i	0.749148	−	1.29756i
$717$	1.06046	−	1.83677i	0.0396035	−	0.0685953i
$718$	−3.02043			−0.112721
$719$	17.1537	+	29.7111i	0.639725	+	1.10804i	0.985493	+	0.169716i	$0.0542850\pi$
$719$	17.1537	+	29.7111i	0.639725	+	1.10804i	−0.345768	+	0.938320i	$0.612382\pi$
$720$	−0.578887			−0.0215738
$721$	37.6942			1.40380
$722$	−19.1994	−	33.2543i	−0.714526	−	1.23760i
$723$	−7.04829	−	12.2080i	−0.262129	−	0.454020i
$724$	−4.45216	+	7.71137i	−0.165463	+	0.286591i
$725$	−6.87677	−	11.9109i	−0.255397	−	0.442360i
$726$	−11.0434			−0.409858
$727$	6.88081			0.255195			0.127598	−	0.991826i	$-0.459273\pi$
$727$	6.88081			0.255195			0.127598	+	0.991826i	$0.459273\pi$
$728$	1.54854	+	2.68215i	0.0573928	+	0.0994072i
$729$	1.00000			0.0370370
$730$	0.487756	+	0.844818i	0.0180526	+	0.0312681i
$731$	26.3131			0.973224
$732$	15.3612	+	26.6063i	0.567765	+	0.983398i
$733$	−21.6382	−	37.4784i	−0.799225	−	1.38430i	−0.920122	−	0.391633i	$-0.871910\pi$
$733$	−21.6382	−	37.4784i	−0.799225	−	1.38430i	0.120897	−	0.992665i	$-0.461423\pi$
$734$	−26.5465	−	45.9800i	−0.979851	−	1.69715i
$735$	−1.21621	−	2.10654i	−0.0448605	−	0.0777007i
$736$	22.9229			0.844948
$737$	13.8130	−	23.9248i	0.508807	−	0.881280i
$738$	9.78026	+	16.9399i	0.360016	+	0.623567i
$739$	−19.5619			−0.719595			−0.359797	−	0.933030i	$-0.617154\pi$
$739$	−19.5619			−0.719595			−0.359797	+	0.933030i	$0.617154\pi$
$740$	0.141994			0.00521979
$741$	0.416324	−	0.721094i	0.0152940	−	0.0264901i
$742$	66.7772	+	115.661i	2.45147	+	4.24607i
$743$	−17.1215	+	29.6553i	−0.628126	+	1.08795i	0.359802	+	0.933029i	$0.382844\pi$
$743$	−17.1215	+	29.6553i	−0.628126	+	1.08795i	−0.987927	+	0.154917i	$0.950489\pi$
$744$	−1.10737			−0.0405982
$745$	−0.140674	+	0.243655i	−0.00515391	+	0.00892684i
$746$	37.3545			1.36765
$747$	−7.27997	+	12.6093i	−0.266360	+	0.461349i
$748$	−9.54870	−	16.5388i	−0.349135	−	0.604720i
$749$	8.38047	+	14.5154i	0.306216	+	0.530381i
$750$	−1.60269	+	2.77594i	−0.0585219	+	0.101363i
$751$	3.21952	−	5.57637i	0.117482	−	0.203485i	−0.801287	−	0.598280i	$-0.795851\pi$
$751$	3.21952	−	5.57637i	0.117482	−	0.203485i	0.918769	+	0.394795i	$0.129184\pi$
$752$	−1.77634	−	3.07670i	−0.0647763	−	0.112196i
$753$	−24.1549			−0.880255
$754$	5.91765	+	10.2497i	0.215508	+	0.373271i
$755$	−0.106268	−	0.184062i	−0.00386750	−	0.00669871i
$756$	−10.1946			−0.370773
$757$	34.6706			1.26012			0.630062	−	0.776545i	$-0.283029\pi$
$757$	34.6706			1.26012			0.630062	+	0.776545i	$0.283029\pi$
$758$	79.0013			2.86946
$759$	5.73096	+	9.92631i	0.208021	+	0.360302i
$760$	0.00972748	+	0.0168485i	0.000352853	+	0.000611159i
$761$	18.4729	−	31.9960i	0.669642	−	1.15985i	−0.308362	−	0.951269i	$-0.599781\pi$
$761$	18.4729	−	31.9960i	0.669642	−	1.15985i	0.978004	−	0.208585i	$-0.0668860\pi$
$762$	−35.7782			−1.29611
$763$	−12.8452	+	22.2485i	−0.465027	+	0.805450i
$764$	17.3022	−	29.9682i	0.625970	−	1.08421i
$765$	0.172610	−	0.298969i	0.00624071	−	0.0108092i
$766$	7.76689	−	13.4527i	0.280629	−	0.486064i
$767$	9.85598	+	17.0711i	0.355879	+	0.616400i
$768$	−6.64174	+	11.5038i	−0.239663	+	0.415109i
$769$	−25.0707			−0.904074			−0.452037	−	0.891999i	$-0.649302\pi$
$769$	−25.0707			−0.904074			−0.452037	+	0.891999i	$0.649302\pi$
$770$	3.08304	+	5.33999i	0.111105	+	0.192440i
$771$	−15.0300			−0.541292
$772$	8.00513	+	13.8653i	0.288111	+	0.499023i
$773$	7.28686	−	12.6212i	0.262090	−	0.453954i	−0.704707	−	0.709499i	$-0.748922\pi$
$773$	7.28686	−	12.6212i	0.262090	−	0.453954i	0.966797	+	0.255545i	$0.0822549\pi$
$774$	−12.2464	+	21.2113i	−0.440186	+	0.762425i
$775$	8.84891	−	15.3268i	0.317862	−	0.550553i
$776$	−0.877255	−	1.51945i	−0.0314916	−	0.0545451i
$777$	−1.98086			−0.0710630
$778$	−18.5383			−0.664631
$779$	−1.90214	+	3.29460i	−0.0681512	+	0.118041i
$780$	0.356582	−	0.617617i	0.0127677	−	0.0221142i
$781$	−30.4636			−1.09007
$782$	−6.30990	+	10.9291i	−0.225642	+	0.390823i
$783$	−2.76446			−0.0987936
$784$	−56.6301			−2.02250
$785$	−1.55305	+	1.22139i	−0.0554307	+	0.0435934i
$786$	9.42793			0.336283
$787$	48.1159			1.71515			0.857573	−	0.514362i	$-0.171971\pi$
$787$	48.1159			1.71515			0.857573	+	0.514362i	$0.171971\pi$
$788$	25.8606	−	44.7919i	0.921247	−	1.59565i
$789$	15.7089			0.559250
$790$	−0.907657	+	1.57211i	−0.0322930	+	0.0559331i
$791$	−7.06643	+	12.2394i	−0.251253	+	0.435183i
$792$	1.26140			0.0448220
$793$	29.9819			1.06469
$794$	16.1876	+	28.0377i	0.574476	+	0.995022i
$795$	1.09113	−	1.88990i	0.0386985	−	0.0670278i
$796$	−3.09237	+	5.35615i	−0.109606	+	0.189844i
$797$	−9.76957	+	16.9214i	−0.346056	+	0.599386i	−0.985545	−	0.169414i	$-0.945813\pi$
$797$	−9.76957	+	16.9214i	−0.346056	+	0.599386i	0.639489	+	0.768800i	$0.279146\pi$
$798$	−1.91237	−	3.31232i	−0.0676972	−	0.117255i
$799$	2.11864			0.0749520
$800$	20.1587	+	34.9159i	0.712717	+	1.23446i
$801$	4.95755			0.175167
$802$	−24.9034	+	43.1340i	−0.879370	+	1.52311i
$803$	6.15060	+	10.6532i	0.217050	+	0.375942i
$804$	−7.33849	+	12.7106i	−0.258809	+	0.448270i
$805$	1.05613	−	1.82927i	0.0372237	−	0.0644733i
$806$	−7.61473	+	13.1891i	−0.268217	+	0.464566i
$807$	1.76056	−	3.04939i	0.0619748	−	0.107343i
$808$	−3.29682			−0.115982
$809$	7.76102	−	13.4425i	0.272863	−	0.472612i	−0.696731	−	0.717333i	$-0.745363\pi$
$809$	7.76102	−	13.4425i	0.272863	−	0.472612i	0.969594	+	0.244720i	$0.0786961\pi$
$810$	0.160668	+	0.278286i	0.00564531	+	0.00977797i
$811$	−10.5304	−	18.2392i	−0.369772	−	0.640464i	0.619758	−	0.784793i	$-0.287231\pi$
$811$	−10.5304	−	18.2392i	−0.369772	−	0.640464i	−0.989530	+	0.144329i	$0.953898\pi$
$812$	28.1824			0.989010
$813$	−23.5880			−0.827269
$814$	3.45402			0.121063
$815$	0.143417	+	0.248406i	0.00502369	+	0.00870129i
$816$	−4.01860	−	6.96041i	−0.140679	−	0.243663i
$817$	−4.76353			−0.166655
$818$	6.09280	+	10.5530i	0.213030	+	0.368978i
$819$	−4.97444	+	8.61599i	−0.173821	+	0.301067i
$820$	−1.62918	+	2.82183i	−0.0568935	+	0.0985425i
$821$	1.34179	+	2.32405i	0.0468288	+	0.0811099i	0.888490	−	0.458897i	$-0.151755\pi$
$821$	1.34179	+	2.32405i	0.0468288	+	0.0811099i	−0.841661	+	0.540006i	$0.818422\pi$
$822$	3.47656	+	6.02158i	0.121259	+	0.210027i
$823$	27.0656	−	46.8789i	0.943446	−	1.63410i	0.184614	−	0.982811i	$-0.440896\pi$
$823$	27.0656	−	46.8789i	0.943446	−	1.63410i	0.758832	−	0.651286i	$-0.225770\pi$
$824$	2.47787			0.0863208
$825$	−10.0798	+	17.4587i	−0.350933	+	0.607833i
$826$	90.5463			3.15051
$827$	−1.23174	+	2.13344i	−0.0428319	+	0.0741870i	−0.886647	−	0.462448i	$-0.846971\pi$
$827$	−1.23174	+	2.13344i	−0.0428319	+	0.0741870i	0.843815	+	0.536635i	$0.180305\pi$
$828$	−3.04472	−	5.27361i	−0.105811	−	0.183270i
$829$	−11.8118	+	20.4587i	−0.410242	+	0.710559i	−0.994916	−	0.100709i	$-0.967889\pi$
$829$	−11.8118	+	20.4587i	−0.410242	+	0.710559i	0.584674	+	0.811268i	$0.301222\pi$
$830$	−4.67864			−0.162398
$831$	3.76518			0.130613
$832$	−9.63447	−	16.6874i	−0.334015	−	0.578531i
$833$	16.8857	−	29.2469i	0.585055	−	1.01334i
$834$	30.2308			1.04681
$835$	1.67709	+	2.90480i	0.0580380	+	0.100525i
$836$	1.72863	+	2.99407i	0.0597858	+	0.103552i
$837$	−1.77863	−	3.08067i	−0.0614783	−	0.106484i
$838$	−34.3739	−	59.5373i	−1.18743	−	2.05668i
$839$	23.4123			0.808282			0.404141	−	0.914697i	$-0.367571\pi$
$839$	23.4123			0.808282			0.404141	+	0.914697i	$0.367571\pi$
$840$	−0.116229	−	0.201314i	−0.00401028	−	0.00694600i
$841$	−21.3578			−0.736475
$842$	−25.2492	−	43.7328i	−0.870143	−	1.50713i
$843$	19.4811			0.670966
$844$	−41.5862			−1.43146
$845$	0.676968	+	1.17254i	0.0232884	+	0.0403367i
$846$	−0.986034	+	1.70786i	−0.0339006	+	0.0587175i
$847$	12.8315	+	22.2248i	0.440895	+	0.763653i
$848$	−25.4031	−	43.9995i	−0.872348	−	1.51095i
$849$	13.9965			0.480359
$850$	−22.1961			−0.761319
$851$	−0.591606	−	1.02469i	−0.0202800	−	0.0351260i
$852$	16.1846			0.554474
$853$	−7.80061	+	13.5110i	−0.267088	+	0.462610i	−0.968108	−	0.250531i	$-0.919395\pi$
$853$	−7.80061	+	13.5110i	−0.267088	+	0.462610i	0.701021	+	0.713141i	$0.252728\pi$
$854$	68.8605	−	119.270i	2.35636	−	4.08133i
$855$	−0.0312480	+	0.0541231i	−0.00106866	+	0.00185097i
$856$	0.550900	+	0.954188i	0.0188294	+	0.0326135i
$857$	8.17759	+	14.1640i	0.279341	+	0.483833i	0.971221	−	0.238180i	$-0.0765507\pi$
$857$	8.17759	+	14.1640i	0.279341	+	0.483833i	−0.691880	+	0.722012i	$0.743217\pi$
$858$	8.67392	−	15.0237i	0.296123	−	0.512900i
$859$	9.56258	+	16.5629i	0.326271	+	0.565118i	0.981769	−	0.190079i	$-0.0608744\pi$
$859$	9.56258	+	16.5629i	0.326271	+	0.565118i	−0.655498	+	0.755197i	$0.727541\pi$
$860$	−4.07996			−0.139126
$861$	22.7277	−	39.3655i	0.774558	−	1.34157i
$862$	−3.50744	+	6.07507i	−0.119464	+	0.206918i
$863$	14.0692			0.478921			0.239460	−	0.970906i	$-0.423029\pi$
$863$	14.0692			0.478921			0.239460	+	0.970906i	$0.423029\pi$
$864$	8.10377			0.275696
$865$	1.56412	−	2.70913i	0.0531815	−	0.0921131i
$866$	−33.0413	+	57.2292i	−1.12279	+	1.94473i
$867$	−12.2070			−0.414572
$868$	18.1323	+	31.4061i	0.615452	+	1.06599i
$869$	−11.4456	+	19.8243i	−0.388264	+	0.672493i
$870$	−0.444161	−	0.769309i	−0.0150585	−	0.0260820i
$871$	7.16164	+	12.4043i	0.242663	+	0.420304i
$872$	−0.844395	+	1.46253i	−0.0285948	+	0.0495277i
$873$	2.81804	−	4.88099i	0.0953763	−	0.165197i
$874$	1.14230	−	1.97852i	0.0386389	−	0.0669245i
$875$	7.44877			0.251814
$876$	−3.26766	−	5.65976i	−0.110404	−	0.191226i
$877$	−31.2206			−1.05424			−0.527122	−	0.849790i	$-0.676729\pi$
$877$	−31.2206			−1.05424			−0.527122	+	0.849790i	$0.676729\pi$
$878$	26.2046			0.884364
$879$	−9.42380	−	16.3225i	−0.317857	−	0.550544i
$880$	−1.17284	−	2.03142i	−0.0395365	−	0.0684792i
$881$	−18.8699	+	32.6836i	−0.635742	+	1.10114i	0.350616	+	0.936519i	$0.385972\pi$
$881$	−18.8699	+	32.6836i	−0.635742	+	1.10114i	−0.986357	+	0.164618i	$0.947361\pi$
$882$	15.7175	+	27.2236i	0.529237	+	0.916666i
$883$	−41.4378			−1.39449			−0.697247	−	0.716831i	$-0.745592\pi$
$883$	−41.4378			−1.39449			−0.697247	+	0.716831i	$0.745592\pi$
$884$	9.90147			0.333022
$885$	−0.739760	−	1.28130i	−0.0248668	−	0.0430705i
$886$	45.7273			1.53624
$887$	14.7827	+	25.6044i	0.496355	+	0.859712i	0.999991	−	0.00420415i	$-0.00133823\pi$
$887$	14.7827	+	25.6044i	0.496355	+	0.859712i	−0.503636	+	0.863916i	$0.668005\pi$
$888$	−0.130214			−0.00436971
$889$	41.5713	+	72.0035i	1.39426	+	2.41492i
$890$	0.796522	+	1.37962i	0.0266995	+	0.0462449i
$891$	2.02603	+	3.50919i	0.0678745	+	0.117562i
$892$	15.5911	+	27.0045i	0.522027	+	0.904178i
$893$	−0.383543			−0.0128348
$894$	1.81799	−	3.14885i	0.0608027	−	0.105313i
$895$	1.46832	+	2.54320i	0.0490805	+	0.0850099i
$896$	−11.7591			−0.392843
$897$	−5.94268			−0.198420
$898$	−1.30116	+	2.25368i	−0.0434203	+	0.0752061i
$899$	4.91693	+	8.51638i	0.163989	+	0.284037i
$900$	5.35514	−	9.27537i	0.178505	−	0.309179i
$901$	30.2983			1.00938
$902$	−39.6302	+	68.6415i	−1.31954	+	2.28551i
$903$	56.9170			1.89408
$904$	−0.464520	+	0.804573i	−0.0154497	+	0.0267597i
$905$	−0.326113	−	0.564843i	−0.0108403	−	0.0187760i
$906$	1.37335	+	2.37871i	0.0456264	+	0.0790273i
$907$	−2.24921	+	3.89575i	−0.0746839	+	0.129356i	−0.900949	−	0.433925i	$-0.857128\pi$
$907$	−2.24921	+	3.89575i	−0.0746839	+	0.129356i	0.826265	+	0.563282i	$0.190461\pi$
$908$	−7.97990	+	13.8216i	−0.264822	+	0.458686i
$909$	−5.29526	−	9.17166i	−0.175633	−	0.304205i
$910$	−3.19694			−0.105978
$911$	3.87177	+	6.70611i	0.128278	+	0.222183i	0.923009	−	0.384777i	$-0.125722\pi$
$911$	3.87177	+	6.70611i	0.128278	+	0.222183i	−0.794732	+	0.606961i	$0.792388\pi$
$912$	0.727498	+	1.26006i	0.0240899	+	0.0417248i
$913$	−58.9977			−1.95254
$914$	−75.5484			−2.49892
$915$	−2.25035			−0.0743944
$916$	20.7851	+	36.0009i	0.686759	+	1.18950i
$917$	−10.9545	−	18.9737i	−0.361748	−	0.626566i
$918$	−2.23070	+	3.86369i	−0.0736241	+	0.127521i
$919$	10.1641			0.335282			0.167641	−	0.985848i	$-0.446385\pi$
$919$	10.1641			0.335282			0.167641	+	0.985848i	$0.446385\pi$
$920$	0.0694260	−	0.120249i	0.00228891	−	0.00396450i
$921$	−14.6151	+	25.3140i	−0.481583	+	0.834126i
$922$	13.1220	−	22.7279i	0.432149	−	0.748504i
$923$	7.89727	−	13.6785i	0.259942	−	0.450232i
$924$	−20.6545	−	35.7747i	−0.679483	−	1.17690i
$925$	1.04053	−	1.80226i	0.0342125	−	0.0592578i
$926$	70.1670			2.30583
$927$	3.97989	+	6.89337i	0.130717	+	0.226408i
$928$	−22.4025			−0.735399
$929$	−12.5972	−	21.8190i	−0.413302	−	0.715860i	0.581947	−	0.813227i	$-0.302291\pi$
$929$	−12.5972	−	21.8190i	−0.413302	−	0.715860i	−0.995249	+	0.0973672i	$0.968958\pi$
$930$	0.571538	−	0.989933i	0.0187415	−	0.0324612i
$931$	−3.05686	+	5.29465i	−0.100185	+	0.173525i
$932$	2.07053	−	3.58627i	0.0678226	−	0.117472i
$933$	−5.61095	−	9.71845i	−0.183694	−	0.318168i
$934$	65.4606			2.14194
$935$	1.39885			0.0457472
$936$	−0.327001	+	0.566383i	−0.0106884	+	0.0185128i
$937$	13.7448	−	23.8067i	0.449024	−	0.777732i	−0.549299	−	0.835626i	$-0.685105\pi$
$937$	13.7448	−	23.8067i	0.449024	−	0.777732i	0.998323	+	0.0578942i	$0.0184386\pi$
$938$	65.7935			2.14823
$939$	4.55928	−	7.89690i	0.148786	−	0.257705i
$940$	−0.328505			−0.0107146
$941$	−43.8518			−1.42953			−0.714765	−	0.699365i	$-0.753466\pi$
$941$	−43.8518			−1.42953			−0.714765	+	0.699365i	$0.753466\pi$
$942$	20.0707	−	15.7845i	0.653938	−	0.514288i
$943$	27.1515			0.884174
$944$	−34.4453			−1.12110
$945$	0.373367	−	0.646690i	0.0121456	−	0.0210368i
$946$	−99.2459			−3.22676
$947$	29.9643	−	51.8997i	0.973709	−	1.68651i	0.289579	−	0.957154i	$-0.406485\pi$
$947$	29.9643	−	51.8997i	0.973709	−	1.68651i	0.684130	−	0.729360i	$-0.260182\pi$
$948$	6.08075	−	10.5322i	0.197493	−	0.342069i
$949$	−6.37783			−0.207033
$950$	4.01822			0.130368
$951$	−4.12850	−	7.15077i	−0.133876	−	0.231880i
$952$	1.61371	−	2.79502i	0.0523005	−	0.0905872i
$953$	19.5054	−	33.7844i	0.631843	−	1.09438i	−0.355331	−	0.934740i	$-0.615632\pi$
$953$	19.5054	−	33.7844i	0.631843	−	1.09438i	0.987175	−	0.159644i	$-0.0510347\pi$
$954$	−14.1011	+	24.4239i	−0.456542	+	0.790753i
$955$	1.26735	+	2.19512i	0.0410105	+	0.0710323i
$956$	−4.56582			−0.147669
$957$	−5.60087	−	9.70099i	−0.181050	−	0.313588i
$958$	−29.2572			−0.945257
$959$	8.07895	−	13.9932i	0.260883	−	0.451863i
$960$	0.723134	+	1.25250i	0.0233390	+	0.0404244i
$961$	9.17297	−	15.8881i	0.295902	−	0.512518i
$962$	−0.895407	+	1.55089i	−0.0288691	+	0.0500027i
$963$	−1.76968	+	3.06518i	−0.0570271	+	0.0987739i
$964$	−15.1733	+	26.2809i	−0.488698	+	0.846450i
$965$	−1.17272			−0.0377512
$966$	−13.6488	+	23.6404i	−0.439142	+	0.760616i
$967$	18.5789	+	32.1795i	0.597456	+	1.03482i	0.993195	+	0.116461i	$0.0371549\pi$
$967$	18.5789	+	32.1795i	0.597456	+	1.03482i	−0.395740	+	0.918363i	$0.629512\pi$
$968$	0.843494	+	1.46097i	0.0271109	+	0.0469575i
$969$	−0.867687			−0.0278741
$970$	1.81108			0.0581503
$971$	−3.27042			−0.104953			−0.0524764	−	0.998622i	$-0.516711\pi$
$971$	−3.27042			−0.104953			−0.0524764	+	0.998622i	$0.516711\pi$
$972$	−1.07638	−	1.86434i	−0.0345249	−	0.0597989i
$973$	−35.1257	−	60.8395i	−1.12608	−	1.95043i
$974$	−62.8417			−2.01358
$975$	−5.22608	−	9.05184i	−0.167369	−	0.289891i
$976$	−26.1957	+	45.3723i	−0.838504	+	1.45233i
$977$	−6.02967	+	10.4437i	−0.192906	+	0.334124i	−0.946212	−	0.323547i	$-0.895125\pi$
$977$	−6.02967	+	10.4437i	−0.192906	+	0.334124i	0.753306	+	0.657670i	$0.228458\pi$
$978$	−1.85344	−	3.21025i	−0.0592664	−	0.102652i
$979$	10.0442	+	17.3970i	0.321013	+	0.556010i
$980$	−2.61821	+	4.53487i	−0.0836355	+	0.144861i
$981$	−5.42497			−0.173206
$982$	−16.8501	+	29.1852i	−0.537707	+	0.931336i
$983$	−19.1944			−0.612206			−0.306103	−	0.951998i	$-0.599025\pi$
$983$	−19.1944			−0.612206			−0.306103	+	0.951998i	$0.599025\pi$
$984$	1.49403	−	2.58774i	0.0476281	−	0.0824942i
$985$	1.89424	+	3.28092i	0.0603556	+	0.104539i
$986$	6.16667	−	10.6810i	0.196387	−	0.340152i
$987$	4.58276			0.145871
$988$	−1.79249			−0.0570267
$989$	16.9989	+	29.4429i	0.540533	+	0.936230i
$990$	−0.651038	+	1.12763i	−0.0206913	+	0.0358385i
$991$	−43.2900			−1.37515			−0.687576	−	0.726112i	$-0.741325\pi$
$991$	−43.2900			−1.37515			−0.687576	+	0.726112i	$0.741325\pi$
$992$	−14.4136	−	24.9651i	−0.457632	−	0.792642i
$993$	11.5344	+	19.9781i	0.366032	+	0.633985i
$994$	−36.2759	−	62.8316i	−1.15060	−	1.99290i
$995$	−0.226510	−	0.392328i	−0.00718086	−	0.0124376i
$996$	31.3441			0.993174
$997$	−5.79095	−	10.0302i	−0.183401	−	0.317660i	0.759635	−	0.650349i	$-0.225377\pi$
$997$	−5.79095	−	10.0302i	−0.183401	−	0.317660i	−0.943037	+	0.332689i	$0.892044\pi$
$998$	52.1685			1.65136
$999$	−0.209147	−	0.362253i	−0.00661711	−	0.0114612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.301.3	yes	28
157.12	even	3	inner	471.2.e.c.169.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.3	✓	28	157.12	even	3	inner
471.2.e.c.301.3	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.03783 q^{2} +(-0.500000 + 0.866025i) q^{3} +2.15276 q^{4} +(-0.0788428 + 0.136560i) q^{5} +(1.01892 - 1.76481i) q^{6} -4.73558 q^{7} -0.311299 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-2.03783 q^{2} +(-0.500000 + 0.866025i) q^{3} +2.15276 q^{4} +(-0.0788428 + 0.136560i) q^{5} +(1.01892 - 1.76481i) q^{6} -4.73558 q^{7} -0.311299 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.160668 - 0.278286i) q^{10} +(2.02603 - 3.50919i) q^{11} +(-1.07638 + 1.86434i) q^{12} +(1.05044 + 1.81942i) q^{13} +9.65032 q^{14} +(-0.0788428 - 0.136560i) q^{15} -3.67114 q^{16} +(1.09464 - 1.89598i) q^{17} +(1.01892 + 1.76481i) q^{18} +(-0.198166 + 0.343234i) q^{19} +(-0.169730 + 0.293980i) q^{20} +(2.36779 - 4.10114i) q^{21} +(-4.12871 + 7.15113i) q^{22} +2.82866 q^{23} +(0.155650 - 0.269593i) q^{24} +(2.48757 + 4.30859i) q^{25} +(-2.14062 - 3.70766i) q^{26} +1.00000 q^{27} -10.1946 q^{28} -2.76446 q^{29} +(0.160668 + 0.278286i) q^{30} +(-1.77863 - 3.08067i) q^{31} +8.10377 q^{32} +(2.02603 + 3.50919i) q^{33} +(-2.23070 + 3.86369i) q^{34} +(0.373367 - 0.646690i) q^{35} +(-1.07638 - 1.86434i) q^{36} +(-0.209147 - 0.362253i) q^{37} +(0.403830 - 0.699454i) q^{38} -2.10088 q^{39} +(0.0245437 - 0.0425110i) q^{40} +9.59869 q^{41} +(-4.82516 + 8.35743i) q^{42} +(6.00950 + 10.4088i) q^{43} +(4.36156 - 7.55444i) q^{44} +0.157686 q^{45} -5.76434 q^{46} +(0.483864 + 0.838078i) q^{47} +(1.83557 - 3.17930i) q^{48} +15.4257 q^{49} +(-5.06925 - 8.78019i) q^{50} +(1.09464 + 1.89598i) q^{51} +(2.26134 + 3.91676i) q^{52} +(6.91968 + 11.9852i) q^{53} -2.03783 q^{54} +(0.319476 + 0.553348i) q^{55} +1.47418 q^{56} +(-0.198166 - 0.343234i) q^{57} +5.63350 q^{58} +9.38272 q^{59} +(-0.169730 - 0.293980i) q^{60} +(7.13557 - 12.3592i) q^{61} +(3.62454 + 6.27789i) q^{62} +(2.36779 + 4.10114i) q^{63} -9.17184 q^{64} -0.331278 q^{65} +(-4.12871 - 7.15113i) q^{66} +6.81775 q^{67} +(2.35651 - 4.08159i) q^{68} +(-1.41433 + 2.44970i) q^{69} +(-0.760859 + 1.31785i) q^{70} +(-3.75903 - 6.51083i) q^{71} +(0.155650 + 0.269593i) q^{72} +(-1.51790 + 2.62907i) q^{73} +(0.426206 + 0.738210i) q^{74} -4.97514 q^{75} +(-0.426605 + 0.738901i) q^{76} +(-9.59443 + 16.6180i) q^{77} +4.28124 q^{78} -5.64926 q^{79} +(0.289443 - 0.501330i) q^{80} +(-0.500000 + 0.866025i) q^{81} -19.5605 q^{82} +(-7.27997 - 12.6093i) q^{83} +(5.09729 - 8.82876i) q^{84} +(0.172610 + 0.298969i) q^{85} +(-12.2464 - 21.2113i) q^{86} +(1.38223 - 2.39409i) q^{87} +(-0.630702 + 1.09241i) q^{88} +(-2.47878 + 4.29337i) q^{89} -0.321337 q^{90} +(-4.97444 - 8.61599i) q^{91} +6.08944 q^{92} +3.55725 q^{93} +(-0.986034 - 1.70786i) q^{94} +(-0.0312480 - 0.0541231i) q^{95} +(-4.05189 + 7.01807i) q^{96} +(2.81804 + 4.88099i) q^{97} -31.4351 q^{98} -4.05206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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