LMFDB - Embedded newform 349.2.e.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	349.227
Dual form			349.2.e.a.123.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39209 - 1.38107i) q^{2} +(-0.0982202 - 0.170122i) q^{3} +(2.81473 + 4.87525i) q^{4} +(1.45632 + 2.52242i) q^{5} +0.542597i q^{6} +(-2.31421 - 1.33611i) q^{7} -10.0251i q^{8} +(1.48071 - 2.56466i) q^{9} +O(q^{10})$	\(q+(-2.39209 - 1.38107i) q^{2} +(-0.0982202 - 0.170122i) q^{3} +(2.81473 + 4.87525i) q^{4} +(1.45632 + 2.52242i) q^{5} +0.542597i q^{6} +(-2.31421 - 1.33611i) q^{7} -10.0251i q^{8} +(1.48071 - 2.56466i) q^{9} -8.04515i q^{10} +5.35089i q^{11} +(0.552926 - 0.957695i) q^{12} +(-0.294235 - 0.169876i) q^{13} +(3.69053 + 6.39218i) q^{14} +(0.286081 - 0.495506i) q^{15} +(-8.21590 + 14.2304i) q^{16} +0.0351415 q^{17} +(-7.08396 + 4.08992i) q^{18} +(0.808261 + 1.39995i) q^{19} +(-8.19829 + 14.1999i) q^{20} +0.524931i q^{21} +(7.38997 - 12.7998i) q^{22} +(-3.85967 + 6.68514i) q^{23} +(-1.70549 + 0.984664i) q^{24} +(-1.74175 + 3.01680i) q^{25} +(0.469224 + 0.812719i) q^{26} -1.17106 q^{27} -15.0431i q^{28} +(3.63841 + 6.30191i) q^{29} +(-1.36866 + 0.790196i) q^{30} +4.03069 q^{31} +(21.9424 - 12.6685i) q^{32} +(0.910306 - 0.525565i) q^{33} +(-0.0840616 - 0.0485330i) q^{34} -7.78322i q^{35} +16.6711 q^{36} -1.44509 q^{37} -4.46507i q^{38} +0.0667412i q^{39} +(25.2875 - 14.5997i) q^{40} +2.80612 q^{41} +(0.724968 - 1.25568i) q^{42} +(-3.09513 + 1.78697i) q^{43} +(-26.0869 + 15.0613i) q^{44} +8.62554 q^{45} +(18.4653 - 10.6610i) q^{46} +10.5226i q^{47} +3.22787 q^{48} +(0.0703696 + 0.121884i) q^{49} +(8.33284 - 4.81097i) q^{50} +(-0.00345160 - 0.00597836i) q^{51} -1.91262i q^{52} +0.107518i q^{53} +(2.80128 + 1.61732i) q^{54} +(-13.4972 + 7.79262i) q^{55} +(-13.3946 + 23.2001i) q^{56} +(0.158775 - 0.275006i) q^{57} -20.0996i q^{58} +(-8.10140 + 4.67734i) q^{59} +3.22095 q^{60} -9.48691i q^{61} +(-9.64178 - 5.56668i) q^{62} +(-6.85332 + 3.95677i) q^{63} -37.1206 q^{64} -0.989580i q^{65} -2.90338 q^{66} +14.1458 q^{67} +(0.0989137 + 0.171323i) q^{68} +1.51639 q^{69} +(-10.7492 + 18.6181i) q^{70} +(8.80233 + 5.08203i) q^{71} +(-25.7109 - 14.8442i) q^{72} +(7.39161 + 12.8026i) q^{73} +(3.45679 + 1.99578i) q^{74} +0.684300 q^{75} +(-4.55006 + 7.88094i) q^{76} +(7.14937 - 12.3831i) q^{77} +(0.0921745 - 0.159651i) q^{78} +2.08282i q^{79} -47.8600 q^{80} +(-4.32709 - 7.49475i) q^{81} +(-6.71248 - 3.87545i) q^{82} +(3.57122 - 6.18553i) q^{83} +(-2.55917 + 1.47754i) q^{84} +(0.0511773 + 0.0886418i) q^{85} +9.87176 q^{86} +(0.714730 - 1.23795i) q^{87} +53.6430 q^{88} +(-7.24874 + 4.18506i) q^{89} +(-20.6331 - 11.9125i) q^{90} +(0.453947 + 0.786259i) q^{91} -43.4556 q^{92} +(-0.395895 - 0.685711i) q^{93} +(14.5325 - 25.1710i) q^{94} +(-2.35418 + 4.07755i) q^{95} +(-4.31037 - 2.48860i) q^{96} +(-5.65666 - 3.26587i) q^{97} -0.388742i q^{98} +(13.7232 + 7.92309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.39209	−	1.38107i	−1.69146	−	0.976566i	−0.953340	−	0.301899i	$-0.902380\pi$
$2$	−2.39209	−	1.38107i	−1.69146	−	0.976566i	−0.738122	−	0.674667i	$-0.764287\pi$
$3$	−0.0982202	−	0.170122i	−0.0567075	−	0.0982202i	0.836278	−	0.548306i	$-0.184727\pi$
$3$	−0.0982202	−	0.170122i	−0.0567075	−	0.0982202i	−0.892986	+	0.450085i	$0.851394\pi$
$4$	2.81473	+	4.87525i	1.40736	+	2.43762i
$5$	1.45632	+	2.52242i	0.651287	+	1.12806i	0.982811	+	0.184615i	$0.0591040\pi$
$5$	1.45632	+	2.52242i	0.651287	+	1.12806i	−0.331524	+	0.943447i	$0.607563\pi$
$6$			0.542597i			0.221514i
$7$	−2.31421	−	1.33611i	−0.874688	−	0.505001i	−0.00578476	−	0.999983i	$-0.501841\pi$
$7$	−2.31421	−	1.33611i	−0.874688	−	0.505001i	−0.868903	+	0.494982i	$0.835175\pi$
$8$		−	10.0251i		−	3.54440i
$9$	1.48071	−	2.56466i	0.493569	−	0.854886i
$10$		−	8.04515i		−	2.54410i
$11$			5.35089i			1.61335i	0.590993	+	0.806677i	$0.298736\pi$
$11$			5.35089i			1.61335i	−0.590993	+	0.806677i	$0.701264\pi$
$12$	0.552926	−	0.957695i	0.159616	−	0.276463i
$13$	−0.294235	−	0.169876i	−0.0816060	−	0.0471153i	0.458642	−	0.888621i	$-0.348336\pi$
$13$	−0.294235	−	0.169876i	−0.0816060	−	0.0471153i	−0.540248	+	0.841506i	$0.681669\pi$
$14$	3.69053	+	6.39218i	0.986334	+	1.70838i
$15$	0.286081	−	0.495506i	0.0738657	−	0.127939i
$16$	−8.21590	+	14.2304i	−2.05398	+	3.55759i
$17$	0.0351415			0.00852307			0.00426153	−	0.999991i	$-0.498644\pi$
$17$	0.0351415			0.00852307			0.00426153	+	0.999991i	$0.498644\pi$
$18$	−7.08396	+	4.08992i	−1.66970	+	0.964005i
$19$	0.808261	+	1.39995i	0.185428	+	0.321170i	0.943721	−	0.330744i	$-0.107300\pi$
$19$	0.808261	+	1.39995i	0.185428	+	0.321170i	−0.758293	+	0.651914i	$0.773966\pi$
$20$	−8.19829	+	14.1999i	−1.83319	+	3.17519i
$21$			0.524931i			0.114549i
$22$	7.38997	−	12.7998i	1.57555	−	2.72893i
$23$	−3.85967	+	6.68514i	−0.804796	+	1.39395i	0.111632	+	0.993750i	$0.464392\pi$
$23$	−3.85967	+	6.68514i	−0.804796	+	1.39395i	−0.916429	+	0.400198i	$0.868941\pi$
$24$	−1.70549	+	0.984664i	−0.348131	+	0.200994i
$25$	−1.74175	+	3.01680i	−0.348350	+	0.603360i
$26$	0.469224	+	0.812719i	0.0920223	+	0.159387i
$27$	−1.17106			−0.225371
$28$		−	15.0431i		−	2.84288i
$29$	3.63841	+	6.30191i	0.675635	+	1.17023i	0.976283	+	0.216499i	$0.0694639\pi$
$29$	3.63841	+	6.30191i	0.675635	+	1.17023i	−0.300648	+	0.953735i	$0.597203\pi$
$30$	−1.36866	+	0.790196i	−0.249882	+	0.144269i
$31$	4.03069			0.723934			0.361967	−	0.932191i	$-0.382105\pi$
$31$	4.03069			0.723934			0.361967	+	0.932191i	$0.382105\pi$
$32$	21.9424	−	12.6685i	3.87891	−	2.23949i
$33$	0.910306	−	0.525565i	0.158464	−	0.0914892i
$34$	−0.0840616	−	0.0485330i	−0.0144164	−	0.00832334i
$35$		−	7.78322i		−	1.31560i
$36$	16.6711			2.77852
$37$	−1.44509			−0.237572			−0.118786	−	0.992920i	$-0.537900\pi$
$37$	−1.44509			−0.237572			−0.118786	+	0.992920i	$0.537900\pi$
$38$		−	4.46507i		−	0.724330i
$39$			0.0667412i			0.0106871i
$40$	25.2875	−	14.5997i	3.99830	−	2.30842i
$41$	2.80612			0.438242			0.219121	−	0.975698i	$-0.429681\pi$
$41$	2.80612			0.438242			0.219121	+	0.975698i	$0.429681\pi$
$42$	0.724968	−	1.25568i	0.111865	−	0.193756i
$43$	−3.09513	+	1.78697i	−0.472002	+	0.272511i	−0.717078	−	0.696993i	$-0.754521\pi$
$43$	−3.09513	+	1.78697i	−0.472002	+	0.272511i	0.245075	+	0.969504i	$0.421187\pi$
$44$	−26.0869	+	15.0613i	−3.93275	+	2.27057i
$45$	8.62554			1.28582
$46$	18.4653	−	10.6610i	2.72256	−	1.57187i
$47$			10.5226i			1.53488i	0.641120	+	0.767441i	$0.278470\pi$
$47$			10.5226i			1.53488i	−0.641120	+	0.767441i	$0.721530\pi$
$48$	3.22787			0.465903
$49$	0.0703696	+	0.121884i	0.0100528	+	0.0174120i
$50$	8.33284	−	4.81097i	1.17844	−	0.680373i
$51$	−0.00345160	−	0.00597836i	−0.000483321	−	0.000837137i
$52$		−	1.91262i		−	0.265233i
$53$			0.107518i			0.0147687i	0.999973	+	0.00738437i	$0.00235054\pi$
$53$			0.107518i			0.0147687i	−0.999973	+	0.00738437i	$0.997649\pi$
$54$	2.80128	+	1.61732i	0.381206	+	0.220090i
$55$	−13.4972	+	7.79262i	−1.81996	+	1.05076i
$56$	−13.3946	+	23.2001i	−1.78993	+	3.10024i
$57$	0.158775	−	0.275006i	0.0210303	−	0.0364255i
$58$		−	20.0996i		−	2.63921i
$59$	−8.10140	+	4.67734i	−1.05471	+	0.608938i	−0.923965	−	0.382477i	$-0.875071\pi$
$59$	−8.10140	+	4.67734i	−1.05471	+	0.608938i	−0.130747	+	0.991416i	$0.541738\pi$
$60$	3.22095			0.415823
$61$		−	9.48691i		−	1.21467i	−0.794444	−	0.607337i	$-0.792238\pi$
$61$		−	9.48691i		−	1.21467i	0.794444	−	0.607337i	$-0.207762\pi$
$62$	−9.64178	−	5.56668i	−1.22451	−	0.706969i
$63$	−6.85332	+	3.95677i	−0.863437	+	0.498506i
$64$	−37.1206			−4.64008
$65$		−	0.989580i		−	0.122742i
$66$	−2.90338			−0.357381
$67$	14.1458			1.72818			0.864090	−	0.503337i	$-0.167894\pi$
$67$	14.1458			1.72818			0.864090	+	0.503337i	$0.167894\pi$
$68$	0.0989137	+	0.171323i	0.0119950	+	0.0207760i
$69$	1.51639			0.182552
$70$	−10.7492	+	18.6181i	−1.28477	+	2.22529i
$71$	8.80233	+	5.08203i	1.04464	+	0.603126i	0.921145	−	0.389219i	$-0.127255\pi$
$71$	8.80233	+	5.08203i	1.04464	+	0.603126i	0.123499	+	0.992345i	$0.460588\pi$
$72$	−25.7109	−	14.8442i	−3.03006	−	1.74940i
$73$	7.39161	+	12.8026i	0.865122	+	1.49844i	0.866926	+	0.498438i	$0.166093\pi$
$73$	7.39161	+	12.8026i	0.865122	+	1.49844i	−0.00180318	+	0.999998i	$0.500574\pi$
$74$	3.45679	+	1.99578i	0.401843	+	0.232004i
$75$	0.684300			0.0790161
$76$	−4.55006	+	7.88094i	−0.521928	+	0.904006i
$77$	7.14937	−	12.3831i	0.814746	−	1.41118i
$78$	0.0921745	−	0.159651i	0.0104367	−	0.0180769i
$79$			2.08282i			0.234336i	0.993112	+	0.117168i	$0.0373816\pi$
$79$			2.08282i			0.234336i	−0.993112	+	0.117168i	$0.962618\pi$
$80$	−47.8600			−5.35091
$81$	−4.32709	−	7.49475i	−0.480788	−	0.832750i
$82$	−6.71248	−	3.87545i	−0.741270	−	0.427972i
$83$	3.57122	−	6.18553i	0.391992	−	0.678951i	−0.600720	−	0.799460i	$-0.705119\pi$
$83$	3.57122	−	6.18553i	0.391992	−	0.678951i	0.992712	+	0.120509i	$0.0384526\pi$
$84$	−2.55917	+	1.47754i	−0.279228	+	0.161212i
$85$	0.0511773	+	0.0886418i	0.00555096	+	0.00961455i
$86$	9.87176			1.06450
$87$	0.714730	−	1.23795i	0.0766271	−	0.132722i
$88$	53.6430			5.71837
$89$	−7.24874	+	4.18506i	−0.768365	+	0.443616i	−0.832291	−	0.554339i	$-0.812971\pi$
$89$	−7.24874	+	4.18506i	−0.768365	+	0.443616i	0.0639259	+	0.997955i	$0.479638\pi$
$90$	−20.6331	−	11.9125i	−2.17491	−	1.25569i
$91$	0.453947	+	0.786259i	0.0475865	+	0.0824223i
$92$	−43.4556			−4.53056
$93$	−0.395895	−	0.685711i	−0.0410524	−	0.0711049i
$94$	14.5325	−	25.1710i	1.49891	−	2.59619i
$95$	−2.35418	+	4.07755i	−0.241533	+	0.418348i
$96$	−4.31037	−	2.48860i	−0.439926	−	0.253991i
$97$	−5.65666	−	3.26587i	−0.574347	−	0.331599i	0.184537	−	0.982826i	$-0.440922\pi$
$97$	−5.65666	−	3.26587i	−0.574347	−	0.331599i	−0.758884	+	0.651226i	$0.774255\pi$
$98$		−	0.388742i		−	0.0392689i
$99$	13.7232	+	7.92309i	1.37923	+	0.796301i
$100$	−19.6102			−1.96102
$101$		−	16.8964i		−	1.68125i	−0.541616	−	0.840626i	$-0.682187\pi$
$101$		−	16.8964i		−	1.68125i	0.541616	−	0.840626i	$-0.317813\pi$
$102$			0.0190677i			0.00188798i
$103$			11.8362i			1.16626i	0.812380	+	0.583129i	$0.198172\pi$
$103$			11.8362i			1.16626i	−0.812380	+	0.583129i	$0.801828\pi$
$104$	−1.70302	+	2.94972i	−0.166995	+	0.289244i
$105$	−1.32410	+	0.764469i	−0.129219	+	0.0746045i
$106$	0.148490	−	0.257193i	0.0144227	−	0.0249808i
$107$	0.133523	+	0.0770895i	0.0129081	+	0.00745252i	0.506440	−	0.862275i	$-0.330961\pi$
$107$	0.133523	+	0.0770895i	0.0129081	+	0.00745252i	−0.493532	+	0.869728i	$0.664294\pi$
$108$	−3.29622	−	5.70922i	−0.317179	−	0.549370i
$109$	−0.821524	−	1.42292i	−0.0786877	−	0.136291i	0.823996	−	0.566595i	$-0.191740\pi$
$109$	−0.821524	−	1.42292i	−0.0786877	−	0.136291i	−0.902684	+	0.430304i	$0.858406\pi$
$110$	43.0487			4.10453
$111$	0.141937	+	0.245842i	0.0134721	+	0.0233343i
$112$	38.0266	−	21.9547i	3.59318	−	2.07452i
$113$	−5.52494	−	3.18982i	−0.519742	−	0.300073i	0.217087	−	0.976152i	$-0.430344\pi$
$113$	−5.52494	−	3.18982i	−0.519742	−	0.300073i	−0.736829	+	0.676079i	$0.763678\pi$
$114$	−0.759608	+	0.438560i	−0.0711438	+	0.0410749i
$115$	−22.4837			−2.09661
$116$	−20.4822	+	35.4763i	−1.90173	+	3.29389i
$117$	−0.871350	+	0.503074i	−0.0805563	+	0.0465092i
$118$	25.8390			2.37867
$119$	−0.0813247	−	0.0469528i	−0.00745502	−	0.00430416i
$120$	−4.96748	−	2.86798i	−0.453467	−	0.261809i
$121$	−17.6320			−1.60291
$122$	−13.1021	+	22.6935i	−1.18621	+	2.05458i
$123$	−0.275617	−	0.477383i	−0.0248516	−	0.0430442i
$124$	11.3453	+	19.6506i	1.01884	+	1.76468i
$125$	4.41703			0.395071
$126$	21.8583			1.94729
$127$		−	3.59361i		−	0.318881i	−0.987208	−	0.159441i	$-0.949031\pi$
$127$		−	3.59361i		−	0.318881i	0.987208	−	0.159441i	$-0.0509691\pi$
$128$	44.9110	+	25.9294i	3.96961	+	2.29186i
$129$	0.608008	+	0.351034i	0.0535321	+	0.0309068i
$130$	−1.36668	+	2.36716i	−0.119866	+	0.207614i
$131$		−	7.57106i		−	0.661486i	−0.943721	−	0.330743i	$-0.892701\pi$
$131$		−	7.57106i		−	0.661486i	0.943721	−	0.330743i	$-0.107299\pi$
$132$	5.12452	+	2.95864i	0.446032	+	0.257517i
$133$		−	4.31969i		−	0.374565i
$134$	−33.8379	−	19.5363i	−2.92315	−	1.68768i
$135$	−1.70544	−	2.95391i	−0.146781	−	0.254233i
$136$		−	0.352296i		−	0.0302091i
$137$	7.44782	−	4.30000i	0.636310	−	0.367374i	−0.146882	−	0.989154i	$-0.546924\pi$
$137$	7.44782	−	4.30000i	0.636310	−	0.367374i	0.783192	+	0.621780i	$0.213590\pi$
$138$	−3.62734	−	2.09424i	−0.308779	−	0.178274i
$139$	−20.3259			−1.72402			−0.862011	−	0.506890i	$-0.830795\pi$
$139$	−20.3259			−1.72402			−0.862011	+	0.506890i	$0.830795\pi$
$140$	37.9451	−	21.9076i	3.20695	−	1.85153i
$141$	1.79013	−	1.03353i	0.150756	−	0.0870392i
$142$	−14.0373	−	24.3133i	−1.17798	−	2.04033i
$143$	0.908990	−	1.57442i	0.0760136	−	0.131659i
$144$	24.3307	+	42.1420i	2.02756	+	3.51183i
$145$	−10.5974	+	18.3552i	−0.880065	+	1.52432i
$146$		−	40.8334i		−	3.37940i
$147$	0.0138234	−	0.0239429i	0.00114014	−	0.00197478i
$148$	−4.06753	−	7.04518i	−0.334349	−	0.579110i
$149$	11.3275	+	6.53996i	0.927988	+	0.535774i	0.886175	−	0.463351i	$-0.153353\pi$
$149$	11.3275	+	6.53996i	0.927988	+	0.535774i	0.0418135	+	0.999125i	$0.486686\pi$
$150$	−1.63691	−	0.945068i	−0.133653	−	0.0771645i
$151$	−5.33900	−	9.24742i	−0.434482	−	0.752545i	0.562771	−	0.826613i	$-0.309735\pi$
$151$	−5.33900	−	9.24742i	−0.434482	−	0.752545i	−0.997253	+	0.0740680i	$0.976402\pi$
$152$	14.0346	−	8.10287i	1.13836	−	0.657230i
$153$	0.0520342	−	0.0901259i	0.00420672	−	0.00728625i
$154$	−34.2038	+	19.7476i	−2.75622	+	1.59131i
$155$	5.86999	+	10.1671i	0.471489	+	0.816643i
$156$	−0.325380	+	0.187858i	−0.0260512	+	0.0150407i
$157$	0.679906	+	1.17763i	0.0542624	+	0.0939853i	0.891881	−	0.452271i	$-0.149386\pi$
$157$	0.679906	+	1.17763i	0.0542624	+	0.0939853i	−0.837618	+	0.546256i	$0.816053\pi$
$158$	2.87653	−	4.98229i	0.228844	−	0.396370i
$159$	0.0182912	−	0.0105605i	0.00145059	−	0.000837498i
$160$	63.9104	+	36.8987i	5.05256	+	2.91710i
$161$	17.8641	−	10.3139i	1.40789	−	0.812846i
$162$			23.9041i			1.87809i
$163$		−	19.3336i		−	1.51433i	−0.653226	−	0.757163i	$-0.726585\pi$
$163$		−	19.3336i		−	1.51433i	0.653226	−	0.757163i	$-0.273415\pi$
$164$	7.89845	+	13.6805i	0.616765	+	1.06827i
$165$	2.65140	+	1.53079i	0.206411	+	0.119171i
$166$	−17.0853	+	9.86423i	−1.32608	+	0.765613i
$167$		−	20.3762i		−	1.57676i	−0.615192	−	0.788378i	$-0.710921\pi$
$167$		−	20.3762i		−	1.57676i	0.615192	−	0.788378i	$-0.289079\pi$
$168$	5.26247			0.406009
$169$	−6.44228	−	11.1584i	−0.495560	−	0.858336i
$170$		−	0.282719i		−	0.0216835i
$171$	4.78718			0.366085
$172$	−17.4239	−	10.0597i	−1.32856	−	0.767043i
$173$	5.42400	+	3.13155i	0.412379	+	0.238087i	0.691812	−	0.722078i	$-0.256813\pi$
$173$	5.42400	+	3.13155i	0.412379	+	0.238087i	−0.279432	+	0.960165i	$0.590146\pi$
$174$	−3.41940	+	1.97419i	−0.259224	+	0.149663i
$175$	8.06154	−	4.65433i	0.609395	−	0.351834i
$176$	−76.1451	−	43.9624i	−5.73965	−	3.31379i
$177$	1.59144	+	0.918819i	0.119620	+	0.0690627i
$178$	23.1195			1.73288
$179$		−	21.1663i		−	1.58204i	−0.611788	−	0.791022i	$-0.709549\pi$
$179$		−	21.1663i		−	1.58204i	0.611788	−	0.791022i	$-0.290451\pi$
$180$	24.2785	+	42.0516i	1.80961	+	3.13434i
$181$	14.3589			1.06728			0.533642	−	0.845710i	$-0.320823\pi$
$181$	14.3589			1.06728			0.533642	+	0.845710i	$0.320823\pi$
$182$		−	2.50773i		−	0.185886i
$183$	−1.61394	+	0.931806i	−0.119306	+	0.0688811i
$184$	67.0190	+	38.6934i	4.94071	+	2.85252i
$185$	−2.10452	−	3.64513i	−0.154727	−	0.267995i
$186$			2.18704i			0.160362i
$187$			0.188038i			0.0137507i
$188$	−51.3004	+	29.6183i	−3.74146	+	2.16013i
$189$	2.71008	+	1.56467i	0.197129	+	0.113813i
$190$	11.2628	−	6.50258i	0.817089	−	0.471747i
$191$	−12.3588	+	21.4061i	−0.894253	+	1.54889i	−0.0595272	+	0.998227i	$0.518959\pi$
$191$	−12.3588	+	21.4061i	−0.894253	+	1.54889i	−0.834726	+	0.550665i	$0.814374\pi$
$192$	3.64599	+	6.31505i	0.263127	+	0.455749i
$193$	1.94519	−	1.12306i	0.140018	−	0.0808393i	−0.428355	−	0.903611i	$-0.640907\pi$
$193$	1.94519	−	1.12306i	0.140018	−	0.0808393i	0.568372	+	0.822771i	$0.307573\pi$
$194$	9.02082	+	15.6245i	0.647657	+	1.12178i
$195$	−0.168350	+	0.0971967i	−0.0120558	+	0.00696040i
$196$	−0.396142	+	0.686138i	−0.0282959	+	0.0490099i
$197$	−6.70596	+	3.87169i	−0.477780	+	0.275846i	−0.719491	−	0.694502i	$-0.755625\pi$
$197$	−6.70596	+	3.87169i	−0.477780	+	0.275846i	0.241711	+	0.970348i	$0.422291\pi$
$198$	−21.8847	−	37.9055i	−1.55528	−	2.69382i
$199$	4.34931	+	2.51108i	0.308315	+	0.178005i	0.646172	−	0.763192i	$-0.276369\pi$
$199$	4.34931	+	2.51108i	0.308315	+	0.178005i	−0.337857	+	0.941197i	$0.609702\pi$
$200$	30.2436	+	17.4612i	2.13855	+	1.23469i
$201$	−1.38940	−	2.40651i	−0.0980007	−	0.169742i
$202$	−23.3351	+	40.4176i	−1.64185	+	2.84377i
$203$		−	19.4452i		−	1.36479i
$204$	0.0194306	−	0.0336549i	0.00136042	−	0.00235631i
$205$	4.08661	+	7.07822i	0.285421	+	0.494364i
$206$	16.3467	−	28.3133i	1.13893	−	1.97268i
$207$	11.4301	+	19.7974i	0.794444	+	1.37602i
$208$	4.83481	−	2.79138i	0.335234	−	0.193547i
$209$	−7.49097	+	4.32491i	−0.518161	+	0.299161i
$210$	4.22315			0.291425
$211$	11.7601	+	6.78971i	0.809600	+	0.467423i	0.846817	−	0.531885i	$-0.178516\pi$
$211$	11.7601	+	6.78971i	0.809600	+	0.467423i	−0.0372172	+	0.999307i	$0.511849\pi$
$212$	−0.524177	+	0.302634i	−0.0360006	+	0.0207850i
$213$		−	1.99663i		−	0.136807i
$214$	−0.212932	−	0.368810i	−0.0145558	−	0.0252113i
$215$	−9.01501	−	5.20482i	−0.614818	−	0.354965i
$216$			11.7400i			0.798804i
$217$	−9.32786	−	5.38544i	−0.633216	−	0.365588i
$218$			4.53834i			0.307375i
$219$	1.45201	−	2.51496i	0.0981178	−	0.169945i
$220$	−75.9819	−	43.8682i	−5.12270	−	2.95759i
$221$	−0.0103398	−	0.00596971i	−0.000695534	−	0.000401566i
$222$		−	0.784102i		−	0.0526255i
$223$	−2.47102			−0.165472			−0.0827360	−	0.996571i	$-0.526366\pi$
$223$	−2.47102			−0.165472			−0.0827360	+	0.996571i	$0.526366\pi$
$224$	−67.7057			−4.52378
$225$	5.15804	+	8.93398i	0.343869	+	0.595599i
$226$	8.81076	+	15.2607i	0.586083	+	1.01513i
$227$	6.13283	−	10.6224i	0.407050	−	0.705032i	−0.587508	−	0.809219i	$-0.699891\pi$
$227$	6.13283	−	10.6224i	0.407050	−	0.705032i	0.994558	+	0.104187i	$0.0332241\pi$
$228$	1.78763			0.118389
$229$	−2.79397	−	1.61310i	−0.184631	−	0.106597i	0.404836	−	0.914389i	$-0.367329\pi$
$229$	−2.79397	−	1.61310i	−0.184631	−	0.106597i	−0.589467	+	0.807793i	$0.700662\pi$
$230$	53.7829	+	31.0516i	3.54634	+	2.04748i
$231$	−2.80885			−0.184809
$232$	63.1770	−	36.4753i	4.14778	−	2.39472i
$233$	−4.34800	+	7.53096i	−0.284847	+	0.493370i	−0.972572	−	0.232602i	$-0.925276\pi$
$233$	−4.34800	+	7.53096i	−0.284847	+	0.493370i	0.687725	+	0.725971i	$0.258610\pi$
$234$	2.77913			0.181677
$235$	−26.5425	+	15.3243i	−1.73144	+	0.999649i
$236$	−45.6064	−	26.3309i	−2.96872	−	1.71399i
$237$	0.354335	−	0.204575i	0.0230165	−	0.0132886i
$238$	0.129691	+	0.224631i	0.00840659	+	0.0145606i
$239$	7.24990			0.468957			0.234478	−	0.972121i	$-0.424662\pi$
$239$	7.24990			0.468957			0.234478	+	0.972121i	$0.424662\pi$
$240$	4.70082	+	8.14206i	0.303437	+	0.525568i
$241$	7.76119	+	13.4428i	0.499942	+	0.865926i	1.00000		6.65409e-5i	$-2.11806e-5\pi$
$241$	7.76119	+	13.4428i	0.499942	+	0.865926i	−0.500058	+	0.865992i	$0.666688\pi$
$242$	42.1774	+	24.3511i	2.71126	+	1.56535i
$243$	−2.60661	+	4.51478i	−0.167214	+	0.289623i
$244$	46.2510	−	26.7030i	2.96092	−	1.70949i
$245$	−0.204962	+	0.355004i	−0.0130945	+	0.0226804i
$246$			1.52259i			0.0970769i
$247$		−	0.549218i		−	0.0349459i
$248$		−	40.4080i		−	2.56591i
$249$	−1.40306			−0.0889155
$250$	−10.5659	−	6.10024i	−0.668248	−	0.385813i
$251$		−	20.6764i		−	1.30508i	−0.757753	−	0.652542i	$-0.773703\pi$
$251$		−	20.6764i		−	1.30508i	0.757753	−	0.652542i	$-0.226297\pi$
$252$	−38.5804	−	22.2744i	−2.43034	−	1.40316i
$253$	−35.7714	−	20.6527i	−2.24893	−	1.29842i
$254$	−4.96304	+	8.59624i	−0.311409	+	0.539376i
$255$	0.0100533	−	0.0174128i	0.000629562	−	0.00109043i
$256$	−34.5001	−	59.7559i	−2.15626	−	3.73475i
$257$	23.9827			1.49600			0.748001	−	0.663698i	$-0.231014\pi$
$257$	23.9827			1.49600			0.748001	+	0.663698i	$0.231014\pi$
$258$	−0.969606	−	1.67941i	−0.0603650	−	0.104555i
$259$	3.34424	+	1.93080i	0.207801	+	0.119974i
$260$	4.82445	−	2.78539i	0.299199	−	0.172743i
$261$	21.5496			1.33389
$262$	−10.4562	+	18.1106i	−0.645985	+	1.11888i
$263$	−17.8223			−1.09897			−0.549484	−	0.835504i	$-0.685176\pi$
$263$	−17.8223			−1.09897			−0.549484	+	0.835504i	$0.685176\pi$
$264$	−5.26883	−	9.12588i	−0.324274	−	0.561659i
$265$	−0.271206	+	0.156581i	−0.0166601	+	0.00961870i
$266$	−5.96581	+	10.3331i	−0.365787	+	0.633563i
$267$	1.42395	+	0.822116i	0.0871441	+	0.0503127i
$268$	39.8165	+	68.9641i	2.43218	+	4.21265i
$269$	−8.13958			−0.496279			−0.248140	−	0.968724i	$-0.579819\pi$
$269$	−8.13958			−0.496279			−0.248140	+	0.968724i	$0.579819\pi$
$270$			9.42137i			0.573366i
$271$	11.0480	−	19.1357i	0.671120	−	1.16241i	−0.306467	−	0.951881i	$-0.599147\pi$
$271$	11.0480	−	19.1357i	0.671120	−	1.16241i	0.977587	−	0.210532i	$-0.0675197\pi$
$272$	−0.288719	+	0.500076i	−0.0175062	+	0.0303216i
$273$	0.0891735	−	0.154453i	0.00539702	−	0.00934792i
$274$	−23.7545			−1.43506
$275$	−16.1426	−	9.31991i	−0.973433	−	0.562012i
$276$	4.26822	+	7.39277i	0.256917	+	0.444993i
$277$	−0.868236	−	0.501277i	−0.0521673	−	0.0301188i	0.473690	−	0.880692i	$-0.342922\pi$
$277$	−0.868236	−	0.501277i	−0.0521673	−	0.0301188i	−0.525857	+	0.850573i	$0.676255\pi$
$278$	48.6214	+	28.0716i	2.91612	+	1.68362i
$279$	5.96827	−	10.3373i	0.357311	−	0.618881i
$280$	−78.0273			−4.66302
$281$	0.394144	+	0.682677i	0.0235126	+	0.0407251i	0.877542	−	0.479499i	$-0.159182\pi$
$281$	0.394144	+	0.682677i	0.0235126	+	0.0407251i	−0.854030	+	0.520224i	$0.825848\pi$
$282$	−5.70954			−0.339998
$283$	−2.05156			−0.121952			−0.0609762	−	0.998139i	$-0.519421\pi$
$283$	−2.05156			−0.121952			−0.0609762	+	0.998139i	$0.519421\pi$
$284$			57.2180i			3.39527i
$285$	0.924911			0.0547870
$286$	−4.34877	+	2.51076i	−0.257148	+	0.148465i
$287$	−6.49394	−	3.74928i	−0.383325	−	0.221313i
$288$		−	75.0330i		−	4.42136i
$289$	−16.9988			−0.999927
$290$	50.6998	−	29.2715i	2.97719	−	1.71888i
$291$			1.28310i			0.0752166i
$292$	−41.6107	+	72.0718i	−2.43508	+	4.21769i
$293$	−5.78761	+	10.0244i	−0.338116	+	0.585634i	−0.984078	−	0.177735i	$-0.943123\pi$
$293$	−5.78761	+	10.0244i	−0.338116	+	0.585634i	0.645962	+	0.763369i	$0.276456\pi$
$294$	−0.0661338	+	0.0381823i	−0.00385700	+	0.00222684i
$295$	−23.5965	−	13.6234i	−1.37384	−	0.793187i
$296$			14.4871i			0.842048i
$297$		−	6.26622i		−	0.363603i
$298$	−18.0643	−	31.2883i	−1.04644	−	1.81248i
$299$	2.27130	−	1.31133i	0.131352	−	0.0758364i
$300$	1.92612	+	3.33613i	0.111204	+	0.192612i
$301$	9.55035			0.550473
$302$			29.4942i			1.69720i
$303$	−2.87445	+	1.65957i	−0.165133	+	0.0953395i
$304$	−26.5624			−1.52346
$305$	23.9300	−	13.8160i	1.37023	−	0.791102i
$306$	−0.248941	+	0.143726i	−0.0142310	+	0.00821627i
$307$	7.76635	−	13.4517i	0.443249	−	0.767730i	−0.554679	−	0.832064i	$-0.687159\pi$
$307$	7.76635	−	13.4517i	0.443249	−	0.767730i	0.997928	+	0.0643343i	$0.0204924\pi$
$308$	80.4940			4.58657
$309$	2.01361	−	1.16256i	0.114550	−	0.0661355i
$310$		−	32.4275i		−	1.84176i
$311$			1.80144i			0.102150i	0.998695	+	0.0510751i	$0.0162648\pi$
$311$			1.80144i			0.102150i	−0.998695	+	0.0510751i	$0.983735\pi$
$312$	0.669085			0.0378795
$313$	34.1766			1.93178			0.965889	−	0.258956i	$-0.0833786\pi$
$313$	34.1766			1.93178			0.965889	+	0.258956i	$0.0833786\pi$
$314$		−	3.75600i		−	0.211963i
$315$	−19.9613	−	11.5247i	−1.12469	−	0.649341i
$316$	−10.1543	+	5.86257i	−0.571222	+	0.329795i
$317$	−5.48213	+	3.16511i	−0.307907	+	0.177770i	−0.645990	−	0.763346i	$-0.723555\pi$
$317$	−5.48213	+	3.16511i	−0.307907	+	0.177770i	0.338083	+	0.941116i	$0.390222\pi$
$318$	−0.0583390			−0.00327149
$319$	−33.7208	+	19.4687i	−1.88800	+	1.09004i
$320$	−54.0596	−	93.6340i	−3.02202	−	5.23430i
$321$		−	0.0302870i		−	0.00169045i
$322$	−56.9768			−3.17519
$323$	0.0284035	+	0.0491963i	0.00158041	+	0.00273735i
$324$	24.3592	−	42.1913i	1.35329	−	2.34396i
$325$	1.02497	−	0.591764i	0.0568549	−	0.0328252i
$326$	−26.7011	+	46.2477i	−1.47884	+	2.56143i
$327$	−0.161381	+	0.279519i	−0.00892436	+	0.0154574i
$328$		−	28.1315i		−	1.55330i
$329$	14.0594	−	24.3515i	0.775117	−	1.34254i
$330$	−4.22825	−	7.32355i	−0.232758	−	0.403148i
$331$	13.9623	−	8.06114i	0.767438	−	0.443080i	−0.0645220	−	0.997916i	$-0.520552\pi$
$331$	13.9623	−	8.06114i	0.767438	−	0.443080i	0.831960	+	0.554836i	$0.187219\pi$
$332$	40.2080			2.20670
$333$	−2.13975	+	3.70616i	−0.117258	+	0.203097i
$334$	−28.1410	+	48.7416i	−1.53981	+	2.66702i
$335$	20.6008	+	35.6816i	1.12554	+	1.94950i
$336$	−7.46996	−	4.31278i	−0.407520	−	0.235282i
$337$	−2.95327	+	5.11522i	−0.160875	+	0.278644i	−0.935183	−	0.354166i	$-0.884765\pi$
$337$	−2.95327	+	5.11522i	−0.160875	+	0.278644i	0.774308	+	0.632809i	$0.218098\pi$
$338$			35.5891i			1.93579i
$339$			1.25322i			0.0680656i
$340$	−0.288100	+	0.499004i	−0.0156244	+	0.0270623i
$341$			21.5678i			1.16796i
$342$	−11.4514	−	6.61145i	−0.619219	−	0.357506i
$343$			18.3294i			0.989696i
$344$	17.9145	+	31.0289i	0.965886	+	1.67296i
$345$	2.20835	+	3.82498i	0.118894	+	0.205930i
$346$	−8.64980	−	14.9819i	−0.465016	−	0.805431i
$347$	−4.39995	−	2.54031i	−0.236202	−	0.136371i	0.377228	−	0.926120i	$-0.376877\pi$
$347$	−4.39995	−	2.54031i	−0.236202	−	0.136371i	−0.613430	+	0.789749i	$0.710211\pi$
$348$	8.04707			0.431368
$349$	16.0822	+	9.50595i	0.860860	+	0.508842i
$349$	16.0822	+	9.50595i	0.860860	+	0.508842i
$350$	−25.7119			−1.37436
$351$	0.344567	+	0.198936i	0.0183916	+	0.0106184i
$352$	67.7875	+	117.411i	3.61309	+	6.25805i
$353$	8.22288	+	14.2424i	0.437660	+	0.758049i	0.997509	−	0.0705461i	$-0.0224742\pi$
$353$	8.22288	+	14.2424i	0.437660	+	0.758049i	−0.559849	+	0.828595i	$0.689141\pi$
$354$	−2.53791	−	4.39579i	−0.134889	−	0.233634i
$355$			29.6043i			1.57123i
$356$	−40.8064	−	23.5596i	−2.16274	−	1.24866i
$357$			0.0184469i			0.000976312i
$358$	−29.2322	+	50.6317i	−1.54497	+	2.67597i
$359$		−	11.6802i		−	0.616456i	−0.951313	−	0.308228i	$-0.900264\pi$
$359$		−	11.6802i		−	0.616456i	0.951313	−	0.308228i	$-0.0997359\pi$
$360$		−	86.4716i		−	4.55745i
$361$	8.19343	−	14.1914i	0.431233	−	0.746918i
$362$	−34.3476	−	19.8306i	−1.80527	−	1.04227i
$363$	1.73182	+	2.99960i	0.0908970	+	0.157438i
$364$	−2.55547	+	4.42620i	−0.133943	+	0.231996i
$365$	−21.5291	+	37.2895i	−1.12689	+	1.95182i
$366$	5.14757			0.269068
$367$	−1.51426	+	0.874258i	−0.0790437	+	0.0456359i	−0.539001	−	0.842305i	$-0.681198\pi$
$367$	−1.51426	+	0.874258i	−0.0790437	+	0.0456359i	0.459957	+	0.887941i	$0.347865\pi$
$368$	−63.4213	−	109.849i	−3.30606	−	5.72627i
$369$	4.15503	−	7.19673i	0.216302	−	0.374647i
$370$			11.6260i			0.604406i
$371$	0.143656	−	0.248819i	0.00745824	−	0.0129180i
$372$	2.22867	−	3.86018i	0.115551	−	0.200141i
$373$	9.97244	−	5.75759i	0.516354	−	0.298117i	−0.219088	−	0.975705i	$-0.570308\pi$
$373$	9.97244	−	5.75759i	0.516354	−	0.298117i	0.735441	+	0.677588i	$0.236975\pi$
$374$	0.259695	−	0.449804i	0.0134285	−	0.0232588i
$375$	−0.433842	−	0.751436i	−0.0224035	−	0.0388040i
$376$	105.490			5.44023
$377$		−	2.47232i		−	0.127331i
$378$	−4.32183	−	7.48564i	−0.222291	−	0.385020i
$379$	14.5004	−	8.37181i	0.744835	−	0.430031i	−0.0789894	−	0.996875i	$-0.525169\pi$
$379$	14.5004	−	8.37181i	0.744835	−	0.430031i	0.823825	+	0.566845i	$0.191836\pi$
$380$	−26.5054			−1.35970
$381$	−0.611354	+	0.352965i	−0.0313206	+	0.0180830i
$382$	59.1268	−	34.1369i	3.02519	−	1.74659i
$383$	−10.6927	−	6.17345i	−0.546373	−	0.315449i	0.201285	−	0.979533i	$-0.435488\pi$
$383$	−10.6927	−	6.17345i	−0.546373	−	0.315449i	−0.747658	+	0.664084i	$0.768822\pi$
$384$		−	10.1872i		−	0.519861i
$385$	41.6471			2.12253
$386$	−6.20409			−0.315780
$387$			10.5839i			0.538011i
$388$		−	36.7701i		−	1.86672i
$389$	3.18983	−	1.84165i	0.161731	−	0.0933754i	−0.416950	−	0.908929i	$-0.636901\pi$
$389$	3.18983	−	1.84165i	0.161731	−	0.0933754i	0.578681	+	0.815554i	$0.303568\pi$
$390$	0.536943			0.0271892
$391$	−0.135634	+	0.234926i	−0.00685933	+	0.0118807i
$392$	1.22189	−	0.705460i	0.0617149	−	0.0356311i
$393$	−1.28801	+	0.743631i	−0.0649713	+	0.0375112i
$394$	21.3883			1.07753
$395$	−5.25376	+	3.03326i	−0.264345	+	0.152620i
$396$			89.2053i			4.48274i
$397$	14.2477			0.715073			0.357536	−	0.933899i	$-0.383617\pi$
$397$	14.2477			0.715073			0.357536	+	0.933899i	$0.383617\pi$
$398$	−6.93596	−	12.0134i	−0.347668	−	0.602179i
$399$	−0.734877	+	0.424281i	−0.0367898	+	0.0212406i
$400$	−28.6201	−	49.5714i	−1.43100	−	2.47857i
$401$			19.4375i			0.970663i	0.874330	+	0.485332i	$0.161301\pi$
$401$			19.4375i			0.970663i	−0.874330	+	0.485332i	$0.838699\pi$
$402$			7.67545i			0.382817i
$403$	−1.18597	−	0.684720i	−0.0590774	−	0.0341083i
$404$	82.3740	−	47.5587i	4.09826	−	2.36613i
$405$	12.6033	−	21.8295i	0.626262	−	1.08472i
$406$	−26.8553	+	46.5147i	−1.33280	+	2.30849i
$407$		−	7.73252i		−	0.383287i
$408$	−0.0599334	+	0.0346026i	−0.00296715	+	0.00171308i
$409$	−23.1487			−1.14463			−0.572314	−	0.820034i	$-0.693954\pi$
$409$	−23.1487			−1.14463			−0.572314	+	0.820034i	$0.693954\pi$
$410$		−	22.5756i		−	1.11493i
$411$	−1.46305	−	0.844694i	−0.0721671	−	0.0416657i
$412$	−57.7045	+	33.3157i	−2.84290	+	1.64135i
$413$	24.9977			1.23006
$414$		−	63.1430i		−	3.10331i
$415$	20.8034			1.02120
$416$	−8.60829			−0.422056
$417$	1.99642	+	3.45789i	0.0977649	+	0.169334i
$418$	23.8921			1.16860
$419$	3.01164	−	5.21632i	0.147128	−	0.254834i	−0.783037	−	0.621976i	$-0.786330\pi$
$419$	3.01164	−	5.21632i	0.147128	−	0.254834i	0.930165	+	0.367142i	$0.119664\pi$
$420$	−7.45395	−	4.30354i	−0.363716	−	0.209991i
$421$	15.0567	+	8.69300i	0.733819	+	0.423671i	0.819818	−	0.572625i	$-0.194075\pi$
$421$	15.0567	+	8.69300i	0.733819	+	0.423671i	−0.0859986	+	0.996295i	$0.527408\pi$
$422$	−18.7542	−	32.4832i	−0.912938	−	1.58126i
$423$	26.9869	+	15.5809i	1.31215	+	0.757569i
$424$	1.07788			0.0523463
$425$	−0.0612077	+	0.106015i	−0.00296901	+	0.00514247i
$426$	−2.75749	+	4.77612i	−0.133601	+	0.231404i
$427$	−12.6755	+	21.9547i	−0.613412	+	1.06246i
$428$			0.867943i			0.0419536i
$429$	−0.357125			−0.0172422
$430$	14.3765	+	24.9008i	0.693294	+	1.20082i
$431$	4.56967	+	2.63830i	0.220113	+	0.127082i	0.606003	−	0.795463i	$-0.292772\pi$
$431$	4.56967	+	2.63830i	0.220113	+	0.127082i	−0.385889	+	0.922545i	$0.626105\pi$
$432$	9.62133	−	16.6646i	0.462907	−	0.801778i
$433$	16.3268	−	9.42626i	0.784614	−	0.452997i	−0.0534488	−	0.998571i	$-0.517021\pi$
$433$	16.3268	−	9.42626i	0.784614	−	0.452997i	0.838063	+	0.545573i	$0.183688\pi$
$434$	14.8754	+	25.7649i	0.714041	+	1.23676i
$435$	4.16351			0.199625
$436$	4.62473	−	8.01027i	0.221484	−	0.383622i
$437$	−12.4785			−0.596926
$438$	−6.94668	+	4.01067i	−0.331925	+	0.191637i
$439$	19.9462	+	11.5159i	0.951981	+	0.549626i	0.893696	−	0.448674i	$-0.148103\pi$
$439$	19.9462	+	11.5159i	0.951981	+	0.549626i	0.0582850	+	0.998300i	$0.481437\pi$
$440$	78.1216	+	135.311i	3.72430	+	6.45068i
$441$	0.416787			0.0198470
$442$	0.0164892	+	0.0285602i	0.000784312	+	0.00135847i
$443$	−4.19028	+	7.25778i	−0.199086	+	0.344827i	−0.948232	−	0.317577i	$-0.897131\pi$
$443$	−4.19028	+	7.25778i	−0.199086	+	0.344827i	0.749146	+	0.662405i	$0.230464\pi$
$444$	−0.799028	+	1.38396i	−0.0379202	+	0.0656797i
$445$	−21.1130	−	12.1896i	−1.00085	−	0.577843i
$446$	5.91091	+	3.41266i	0.279890	+	0.161594i
$447$		−	2.56942i		−	0.121530i
$448$	85.9048	+	49.5972i	4.05862	+	2.34325i
$449$	−4.01620			−0.189536			−0.0947681	−	0.995499i	$-0.530211\pi$
$449$	−4.01620			−0.189536			−0.0947681	+	0.995499i	$0.530211\pi$
$450$		−	28.4945i		−	1.34324i
$451$			15.0152i			0.707040i
$452$		−	35.9139i		−	1.68925i
$453$	−1.04880	+	1.81657i	−0.0492767	+	0.0853498i
$454$	−29.3405	+	16.9398i	−1.37702	+	0.795023i
$455$	−1.32219	+	2.29009i	−0.0619850	+	0.107361i
$456$	−2.75696	−	1.59173i	−0.129106	−	0.0745396i
$457$	1.66443	+	2.88288i	0.0778589	+	0.134855i	0.902326	−	0.431054i	$-0.141858\pi$
$457$	1.66443	+	2.88288i	0.0778589	+	0.134855i	−0.824467	+	0.565910i	$0.808525\pi$
$458$	4.45562	+	7.71736i	0.208198	+	0.360609i
$459$	−0.0411529			−0.00192085
$460$	−63.2854	−	109.613i	−2.95070	−	5.11075i
$461$	−1.69157	+	0.976631i	−0.0787845	+	0.0454862i	−0.538875	−	0.842386i	$-0.681150\pi$
$461$	−1.69157	+	0.976631i	−0.0787845	+	0.0454862i	0.460090	+	0.887872i	$0.347817\pi$
$462$	6.71902	+	3.87923i	0.312597	+	0.180478i
$463$	−1.72203	+	0.994212i	−0.0800293	+	0.0462050i	−0.539481	−	0.841998i	$-0.681379\pi$
$463$	−1.72203	+	0.994212i	−0.0800293	+	0.0462050i	0.459451	+	0.888203i	$0.348046\pi$
$464$	−119.571			−5.55095
$465$	1.15310	−	1.99723i	0.0534739	−	0.0926194i
$466$	20.8016	−	12.0098i	0.963617	−	0.556344i
$467$	−7.84717			−0.363123			−0.181562	−	0.983380i	$-0.558115\pi$
$467$	−7.84717			−0.363123			−0.181562	+	0.983380i	$0.558115\pi$
$468$	−4.90522	−	2.83203i	−0.226744	−	0.130911i
$469$	−32.7362	−	18.9003i	−1.51162	−	0.872734i
$470$	84.6560			3.90489
$471$	0.133561	−	0.231335i	0.00615417	−	0.0106593i
$472$	46.8907	+	81.2171i	2.15832	+	3.73832i
$473$	−9.56189	−	16.5617i	−0.439656	−	0.761507i
$474$	−1.13013			−0.0519087
$475$	−5.63115			−0.258375
$476$		−	0.528637i		−	0.0242301i
$477$	0.275747	+	0.159203i	0.0126256	+	0.00728939i
$478$	−17.3424	−	10.0126i	−0.793223	−	0.457967i
$479$	−2.26532	+	3.92365i	−0.103505	+	0.179276i	−0.913126	−	0.407676i	$-0.866339\pi$
$479$	−2.26532	+	3.92365i	−0.103505	+	0.179276i	0.809621	+	0.586952i	$0.199672\pi$
$480$		−	14.4968i		−	0.661685i
$481$	0.425196	+	0.245487i	0.0193873	+	0.0111932i
$482$		−	42.8751i		−	1.95291i
$483$	−3.50924	−	2.02606i	−0.159676	−	0.0921889i
$484$	−49.6293	−	85.9605i	−2.25588	−	3.90729i
$485$		−	19.0247i		−	0.863865i
$486$	12.4705	−	7.19983i	0.565672	−	0.326591i
$487$	0.703125	+	0.405949i	0.0318616	+	0.0183953i	0.515846	−	0.856681i	$-0.327478\pi$
$487$	0.703125	+	0.405949i	0.0318616	+	0.0183953i	−0.483985	+	0.875077i	$0.660811\pi$
$488$	−95.1069			−4.30529
$489$	−3.28908	+	1.89895i	−0.148737	+	0.0858736i
$490$	0.980573	−	0.566134i	0.0442978	−	0.0255753i
$491$	−2.93041	−	5.07562i	−0.132247	−	0.229059i	0.792295	−	0.610138i	$-0.208886\pi$
$491$	−2.93041	−	5.07562i	−0.132247	−	0.229059i	−0.924543	+	0.381079i	$0.875553\pi$
$492$	1.55157	−	2.68741i	0.0699504	−	0.121158i
$493$	0.127859	+	0.221458i	0.00575848	+	0.00997399i
$494$	−0.758510	+	1.31378i	−0.0341270	+	0.0591097i
$495$			46.1543i			2.07448i
$496$	−33.1158	+	57.3582i	−1.48694	+	2.57546i
$497$	−13.5803	−	23.5217i	−0.609159	−	1.05509i
$498$	3.35625	+	1.93773i	0.150397	+	0.0868319i
$499$	7.27105	+	4.19794i	0.325497	+	0.187926i	0.653840	−	0.756633i	$-0.273157\pi$
$499$	7.27105	+	4.19794i	0.325497	+	0.187926i	−0.328343	+	0.944558i	$0.606490\pi$
$500$	12.4327	+	21.5341i	0.556008	+	0.963035i
$501$	−3.46644	+	2.00135i	−0.154869	+	0.0894138i
$502$	−28.5556	+	49.4598i	−1.27450	+	2.20750i
$503$	12.0625	−	6.96431i	0.537842	−	0.310523i	−0.206362	−	0.978476i	$-0.566162\pi$
$503$	12.0625	−	6.96431i	0.537842	−	0.310523i	0.744204	+	0.667953i	$0.232829\pi$
$504$	39.6669	+	68.7050i	1.76690	+	3.06036i
$505$	42.6198	−	24.6066i	1.89656	−	1.09498i
$506$	57.0456	+	98.8060i	2.53599	+	4.39246i
$507$	−1.26552	+	2.19195i	−0.0562039	+	0.0973481i
$508$	17.5197	−	10.1150i	0.777313	−	0.448782i
$509$	24.0920	+	13.9095i	1.06786	+	0.616528i	0.927595	−	0.373587i	$-0.121872\pi$
$509$	24.0920	+	13.9095i	1.06786	+	0.616528i	0.140262	+	0.990114i	$0.455206\pi$
$510$	−0.0480968	+	0.0277687i	−0.00212976	+	0.00122962i
$511$		−	39.5040i		−	1.74755i
$512$			86.8711i			3.83920i
$513$	−0.946523	−	1.63943i	−0.0417900	−	0.0723824i
$514$	−57.3688	−	33.1219i	−2.53043	−	1.46094i
$515$	−29.8560	+	17.2374i	−1.31561	+	0.759568i
$516$			3.95225i			0.173988i
$517$	−56.3054			−2.47631
$518$	−5.33315	−	9.23728i	−0.234325	−	0.405863i
$519$		−	1.23033i		−	0.0540053i
$520$	−9.92061			−0.435047
$521$	−26.4320	−	15.2605i	−1.15801	−	0.668576i	−0.207181	−	0.978303i	$-0.566429\pi$
$521$	−26.4320	−	15.2605i	−1.15801	−	0.668576i	−0.950826	+	0.309727i	$0.899762\pi$
$522$	−51.5486	−	29.7616i	−2.25622	−	1.30263i
$523$	−24.8019	+	14.3194i	−1.08451	+	0.626144i	−0.932110	−	0.362175i	$-0.882034\pi$
$523$	−24.8019	+	14.3194i	−1.08451	+	0.626144i	−0.152403	+	0.988318i	$0.548701\pi$
$524$	36.9108	−	21.3104i	1.61245	−	0.930951i
$525$	−1.58361	−	0.914298i	−0.0691145	−	0.0399033i
$526$	42.6324	+	24.6139i	1.85886	+	1.07321i
$527$	0.141645			0.00617014
$528$			17.2720i			0.751666i
$529$	−18.2941	−	31.6862i	−0.795394	−	1.37766i
$530$	0.864999			0.0375732
$531$			27.7031i			1.20221i
$532$	21.0596	−	12.1588i	0.913048	−	0.527149i
$533$	−0.825657	−	0.476694i	−0.0357632	−	0.0206479i
$534$	−2.27080	−	3.93315i	−0.0982673	−	0.170204i
$535$			0.449069i			0.0194149i
$536$		−	141.812i		−	6.12536i
$537$	−3.60086	+	2.07896i	−0.155389	+	0.0897137i
$538$	19.4706	+	11.2414i	0.839437	+	0.484649i
$539$	−0.652186	+	0.376540i	−0.0280917	+	0.0162187i
$540$	9.60071	−	16.6289i	0.413149	−	0.715595i
$541$	11.5271	+	19.9655i	0.495589	+	0.858385i	0.999987	−	0.00508632i	$-0.00161903\pi$
$541$	11.5271	+	19.9655i	0.495589	+	0.858385i	−0.504398	+	0.863471i	$0.668286\pi$
$542$	−52.8557	+	30.5163i	−2.27035	+	1.31079i
$543$	−1.41033	−	2.44276i	−0.0605230	−	0.104829i
$544$	0.771089	−	0.445188i	0.0330602	−	0.0190873i
$545$	2.39281	−	4.14446i	0.102497	−	0.177529i
$546$	−0.426622	+	0.246310i	−0.0182577	+	0.0105411i
$547$	−2.21491	−	3.83634i	−0.0947028	−	0.164030i	0.814782	−	0.579768i	$-0.196857\pi$
$547$	−2.21491	−	3.83634i	−0.0947028	−	0.164030i	−0.909485	+	0.415738i	$0.863523\pi$
$548$	41.9271	+	24.2066i	1.79104	+	1.03406i
$549$	−24.3307	−	14.0473i	−1.03841	−	0.599525i
$550$	25.7429	+	44.5881i	1.09768	+	1.90124i
$551$	−5.88156	+	10.1872i	−0.250563	+	0.433988i
$552$		−	15.2019i		−	0.647036i
$553$	2.78287	−	4.82008i	0.118340	−	0.204971i
$554$	1.38460	+	2.39820i	0.0588260	+	0.101890i
$555$	−0.413412	+	0.716051i	−0.0175484	+	0.0303947i
$556$	−57.2119	−	99.0938i	−2.42632	−	4.20252i
$557$	−17.4902	+	10.0980i	−0.741084	+	0.427865i	−0.822463	−	0.568818i	$-0.807401\pi$
$557$	−17.4902	+	10.0980i	−0.741084	+	0.427865i	0.0813791	+	0.996683i	$0.474068\pi$
$558$	−28.5533	+	16.4852i	−1.20876	+	0.697876i
$559$	1.21426			0.0513577
$560$	110.758	+	63.9462i	4.68038	+	2.70222i
$561$	0.0319895	−	0.0184692i	0.00135060	−	0.000779768i
$562$		−	2.17736i		−	0.0918466i
$563$	−18.9314	−	32.7901i	−0.797861	−	1.38194i	−0.921006	−	0.389548i	$-0.872631\pi$
$563$	−18.9314	−	32.7901i	−0.797861	−	1.38194i	0.123145	−	0.992389i	$-0.460702\pi$
$564$	10.0775	+	5.81823i	0.424338	+	0.244991i
$565$		−	18.5816i		−	0.781736i
$566$	4.90751	+	2.83335i	0.206278	+	0.119095i
$567$			23.1259i			0.971195i
$568$	50.9477	−	88.2440i	2.13772	−	3.70263i
$569$	−35.2539	−	20.3539i	−1.47792	−	0.853279i	−0.478234	−	0.878233i	$-0.658723\pi$
$569$	−35.2539	−	20.3539i	−1.47792	−	0.853279i	−0.999689	+	0.0249538i	$0.992056\pi$
$570$	−2.21247	−	1.27737i	−0.0926701	−	0.0535031i
$571$			10.0552i			0.420797i	0.977616	+	0.210398i	$0.0674761\pi$
$571$			10.0552i			0.420797i	−0.977616	+	0.210398i	$0.932524\pi$
$572$	10.2342			0.427915
$573$	4.85555			0.202843
$574$	10.3561	+	17.9372i	0.432253	+	0.748685i
$575$	−13.4451	−	23.2877i	−0.560701	−	0.971163i
$576$	−54.9647	+	95.2017i	−2.29020	+	3.96674i
$577$	24.9219			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$577$	24.9219			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$578$	40.6626	+	23.4765i	1.69134	+	0.976495i
$579$	−0.382114	−	0.220614i	−0.0158801	−	0.00916838i
$580$	−119.315			−4.95428
$581$	−16.5291	+	9.54307i	−0.685742	+	0.395913i
$582$	1.77205	−	3.06929i	0.0734540	−	0.127226i
$583$	−0.575318			−0.0238272
$584$	128.347	−	74.1014i	5.31105	−	3.06634i
$585$	−2.53793	−	1.46528i	−0.104931	−	0.0605817i
$586$	27.6890	−	15.9862i	1.14382	−	0.660385i
$587$	13.8072	+	23.9148i	0.569886	+	0.987071i	0.996577	+	0.0826735i	$0.0263459\pi$
$587$	13.8072	+	23.9148i	0.569886	+	0.987071i	−0.426691	+	0.904397i	$0.640321\pi$
$588$	0.155637			0.00641835
$589$	3.25785	+	5.64276i	0.134237	+	0.232506i
$590$	37.6299	+	65.1769i	1.54920	+	2.68329i
$591$	1.31732	+	0.760556i	0.0541874	+	0.0312851i
$592$	11.8727	−	20.5642i	0.487966	−	0.845182i
$593$	−28.9737	+	16.7280i	−1.18981	+	0.686936i	−0.958263	−	0.285888i	$-0.907711\pi$
$593$	−28.9737	+	16.7280i	−1.18981	+	0.686936i	−0.231545	+	0.972824i	$0.574378\pi$
$594$	−8.65411	+	14.9894i	−0.355083	+	0.615021i
$595$		−	0.273514i		−	0.0112130i
$596$			73.6327i			3.01611i
$597$		−	0.986554i		−	0.0403770i
$598$	−7.24419			−0.296237
$599$	1.21040	+	0.698827i	0.0494558	+	0.0285533i	0.524524	−	0.851396i	$-0.324243\pi$
$599$	1.21040	+	0.698827i	0.0494558	+	0.0285533i	−0.475068	+	0.879949i	$0.657577\pi$
$600$		−	6.86015i		−	0.280065i
$601$	6.41172	+	3.70181i	0.261539	+	0.151000i	0.625037	−	0.780595i	$-0.285084\pi$
$601$	6.41172	+	3.70181i	0.261539	+	0.151000i	−0.363497	+	0.931595i	$0.618417\pi$
$602$	−22.8453	−	13.1897i	−0.931105	−	0.537573i
$603$	20.9457	−	36.2791i	0.852976	−	1.47740i
$604$	30.0556	−	52.0579i	1.22295	−	2.11821i
$605$	−25.6779	−	44.4754i	−1.04396	−	1.80818i
$606$	9.16792			0.372421
$607$	−2.21700	−	3.83995i	−0.0899852	−	0.155859i	0.817519	−	0.575901i	$-0.195349\pi$
$607$	−2.21700	−	3.83995i	−0.0899852	−	0.155859i	−0.907505	+	0.420042i	$0.862015\pi$
$608$	35.4704	+	20.4788i	1.43851	+	0.830526i
$609$	−3.30807	+	1.90991i	−0.134050	+	0.0773936i
$610$	−76.3236			−3.09025
$611$	1.78755	−	3.09612i	0.0723163	−	0.125256i
$612$	0.585848			0.0236815
$613$	15.9766	+	27.6724i	0.645291	+	1.11768i	0.984234	+	0.176870i	$0.0565971\pi$
$613$	15.9766	+	27.6724i	0.645291	+	1.11768i	−0.338944	+	0.940807i	$0.610070\pi$
$614$	−37.1556	+	21.4518i	−1.49948	+	0.865724i
$615$	0.802776	−	1.39045i	0.0323710	−	0.0560683i
$616$	−124.141	−	71.6729i	−5.00179	−	2.88778i
$617$	−2.74924	−	4.76183i	−0.110680	−	0.191704i	0.805364	−	0.592780i	$-0.201970\pi$
$617$	−2.74924	−	4.76183i	−0.110680	−	0.191704i	−0.916045	+	0.401076i	$0.868636\pi$
$618$	−6.42230			−0.258343
$619$			22.1024i			0.888372i	0.895935	+	0.444186i	$0.146507\pi$
$619$			22.1024i			0.888372i	−0.895935	+	0.444186i	$0.853493\pi$
$620$	−33.0448	+	57.2353i	−1.32711	+	2.29862i
$621$	4.51991	−	7.82871i	0.181378	−	0.314155i
$622$	2.48792	−	4.30920i	0.0997563	−	0.172783i
$623$	22.3668			0.896107
$624$	−0.949752	−	0.548339i	−0.0380205	−	0.0219511i
$625$	15.1414	+	26.2256i	0.605655	+	1.04902i
$626$	−81.7536	−	47.2004i	−3.26753	−	1.88651i
$627$	1.47153	+	0.849588i	0.0587672	+	0.0339293i
$628$	−3.82750	+	6.62942i	−0.152734	+	0.264543i
$629$	−0.0507827			−0.00202484
$630$	31.8328	+	55.1360i	1.26825	+	2.19667i
$631$	3.43953			0.136925			0.0684627	−	0.997654i	$-0.478191\pi$
$631$	3.43953			0.136925			0.0684627	+	0.997654i	$0.478191\pi$
$632$	20.8804			0.830579
$633$		−	2.66754i		−	0.106025i
$634$	17.4850			0.694417
$635$	9.06461	−	5.23346i	0.359718	−	0.207683i
$636$	0.102970	+	0.0594495i	0.00408301	+	0.00235733i
$637$		−	0.0478166i		−	0.00189456i
$638$	107.551			4.25798
$639$	26.0673	−	15.0500i	1.03121	−	0.595368i
$640$			151.046i			5.97062i
$641$	−9.48636	+	16.4309i	−0.374689	+	0.648980i	−0.990280	−	0.139085i	$-0.955584\pi$
$641$	−9.48636	+	16.4309i	−0.374689	+	0.648980i	0.615592	+	0.788065i	$0.288917\pi$
$642$	−0.0418285	+	0.0724491i	−0.00165084	+	0.00285934i
$643$	−0.726100	+	0.419214i	−0.0286346	+	0.0165322i	−0.514249	−	0.857641i	$-0.671929\pi$
$643$	−0.726100	+	0.419214i	−0.0286346	+	0.0165322i	0.485614	+	0.874173i	$0.338596\pi$
$644$	100.565	+	58.0614i	3.96283	+	2.28794i
$645$			2.04487i			0.0805168i
$646$		−	0.156909i		−	0.00617351i
$647$	15.8390	+	27.4340i	0.622697	+	1.07854i	0.988981	+	0.148040i	$0.0472964\pi$
$647$	15.8390	+	27.4340i	0.622697	+	1.07854i	−0.366284	+	0.930503i	$0.619370\pi$
$648$	−75.1354	+	43.3794i	−2.95160	+	1.70410i
$649$	−25.0279	−	43.3497i	−0.982433	−	1.70162i
$650$	−3.26908			−0.128224
$651$			2.11584i			0.0829262i
$652$	94.2562	−	54.4188i	3.69136	−	2.13121i
$653$	37.2415			1.45737			0.728686	−	0.684848i	$-0.240131\pi$
$653$	37.2415			1.45737			0.728686	+	0.684848i	$0.240131\pi$
$654$	0.772073	−	0.445757i	0.0301904	−	0.0174305i
$655$	19.0974	−	11.0259i	0.746198	−	0.430817i
$656$	−23.0548	+	39.9321i	−0.900139	+	1.55909i
$657$	43.7792			1.70799
$658$	−67.2624	+	38.8340i	−2.62216	+	1.51391i
$659$		−	34.2785i		−	1.33530i	−0.744475	−	0.667651i	$-0.767300\pi$
$659$		−	34.2785i		−	1.33530i	0.744475	−	0.667651i	$-0.232700\pi$
$660$			17.2350i			0.670870i
$661$	27.4661			1.06831			0.534153	−	0.845388i	$-0.320630\pi$
$661$	27.4661			1.06831			0.534153	+	0.845388i	$0.320630\pi$
$662$	−44.5321			−1.73079
$663$			0.00234539i			9.10873e-5i
$664$	−62.0104	−	35.8017i	−2.40647	−	1.38938i
$665$	10.8961	−	6.29087i	0.422533	−	0.243949i
$666$	10.2370	−	5.91031i	0.396674	−	0.229020i
$667$	−56.1722			−2.17499
$668$	99.3388	−	57.3533i	3.84354	−	2.21907i
$669$	0.242704	+	0.420377i	0.00938350	+	0.0162527i
$670$		−	113.805i		−	4.39666i
$671$	50.7634			1.95970
$672$	6.65007	+	11.5183i	0.256532	+	0.444326i
$673$	13.7683	−	23.8473i	0.530728	−	0.919248i	−0.468629	−	0.883395i	$-0.655252\pi$
$673$	13.7683	−	23.8473i	0.530728	−	0.919248i	0.999357	−	0.0358527i	$-0.0114147\pi$
$674$	14.1290	−	8.15737i	0.544228	−	0.314210i
$675$	2.03970	−	3.53286i	0.0785079	−	0.135980i
$676$	36.2665	−	62.8154i	1.39487	−	2.41598i
$677$			23.9968i			0.922273i	0.887329	+	0.461136i	$0.152558\pi$
$677$			23.9968i			0.922273i	−0.887329	+	0.461136i	$0.847442\pi$
$678$	1.73079	−	2.99781i	0.0664705	−	0.115130i
$679$	8.72712	+	15.1158i	0.334916	+	0.580092i
$680$	0.888640	−	0.513057i	0.0340778	−	0.0196748i
$681$	−2.40947			−0.0923311
$682$	29.7867	−	51.5921i	1.14059	−	1.97556i
$683$	6.26767	−	10.8559i	0.239826	−	0.415391i	−0.720838	−	0.693103i	$-0.756243\pi$
$683$	6.26767	−	10.8559i	0.239826	−	0.415391i	0.960664	+	0.277713i	$0.0895763\pi$
$684$	13.4746	+	23.3387i	0.515215	+	0.892378i
$685$	21.6929	+	12.5244i	0.828841	+	0.478532i
$686$	25.3143	−	43.8456i	0.966504	−	1.67403i
$687$			0.633757i			0.0241793i
$688$		−	58.7264i		−	2.23892i
$689$	0.0182648	−	0.0316356i	0.000695833	−	0.00120522i
$690$		−	12.1996i		−	0.464430i
$691$	−16.7691	−	9.68164i	−0.637926	−	0.368307i	0.145889	−	0.989301i	$-0.453396\pi$
$691$	−16.7691	−	9.68164i	−0.637926	−	0.368307i	−0.783815	+	0.620994i	$0.786729\pi$
$692$			35.2578i			1.34030i
$693$	−21.1722	−	36.6714i	−0.804266	−	1.39303i
$694$	7.01671	+	12.1533i	0.266351	+	0.461333i
$695$	−29.6011	−	51.2706i	−1.12283	−	1.94480i
$696$	−12.4105	−	7.16522i	−0.470420	−	0.271597i
$697$	0.0986112			0.00373517
$698$	−25.3416	−	44.9497i	−0.959195	−	1.70137i
$699$	1.70825			0.0646118
$700$	45.3820	+	26.2013i	1.71528	+	0.990317i
$701$	2.47099	+	4.27987i	0.0933279	+	0.161649i	0.908910	−	0.416993i	$-0.136916\pi$
$701$	2.47099	+	4.27987i	0.0933279	+	0.161649i	−0.815582	+	0.578642i	$0.803583\pi$
$702$	−0.549490	−	0.951745i	−0.0207392	−	0.0359213i
$703$	−1.16801	−	2.02305i	−0.0440523	−	0.0763009i
$704$		−	198.628i		−	7.48609i
$705$	5.21402	+	3.01032i	0.196371	+	0.113375i
$706$		−	45.4256i		−	1.70961i
$707$	−22.5754	+	39.1017i	−0.849035	+	1.47057i
$708$			10.3449i			0.388785i
$709$		−	3.49149i		−	0.131126i	−0.997848	−	0.0655629i	$-0.979116\pi$
$709$		−	3.49149i		−	0.131126i	0.997848	−	0.0655629i	$-0.0208843\pi$
$710$	40.8857	−	70.8160i	1.53441	−	2.65768i
$711$	5.34172	+	3.08405i	0.200330	+	0.115661i
$712$	41.9556	+	72.6692i	1.57235	+	2.72339i
$713$	−15.5571	+	26.9457i	−0.582619	+	1.00913i
$714$	0.0254765	−	0.0441265i	0.000953433	−	0.00165139i
$715$	5.29513			0.198027
$716$	103.191	−	59.5773i	3.85643	−	2.22651i
$717$	−0.712086	−	1.23337i	−0.0265934	−	0.0460610i
$718$	−16.1312	+	27.9400i	−0.602010	+	1.04271i
$719$			22.2679i			0.830453i	0.909718	+	0.415227i	$0.136298\pi$
$719$			22.2679i			0.830453i	−0.909718	+	0.415227i	$0.863702\pi$
$720$	−70.8666	+	122.745i	−2.64104	+	4.57442i
$721$	15.8145	−	27.3915i	0.588962	−	1.02011i
$722$	−39.1988	+	22.6314i	−1.45883	+	0.842255i
$723$	1.52461	−	2.64071i	0.0567009	−	0.0982089i
$724$	40.4162	+	70.0029i	1.50206	+	2.60164i
$725$	−25.3488			−0.941430
$726$		−	9.56708i		−	0.355068i
$727$	−11.2124	−	19.4205i	−0.415846	−	0.720266i	0.579671	−	0.814851i	$-0.303181\pi$
$727$	−11.2124	−	19.4205i	−0.415846	−	0.720266i	−0.995517	+	0.0945843i	$0.969848\pi$
$728$	7.88230	−	4.55085i	0.292137	−	0.168666i
$729$	−24.9385			−0.923647
$730$	102.999	−	59.4666i	3.81217	−	2.20096i
$731$	−0.108767	+	0.0627969i	−0.00402291	+	0.00232263i
$732$	−9.08557	−	5.24556i	−0.335812	−	0.193881i
$733$			9.26501i			0.342211i	0.985253	+	0.171106i	$0.0547339\pi$
$733$			9.26501i			0.342211i	−0.985253	+	0.171106i	$0.945266\pi$
$734$	4.82966			0.178266
$735$	0.0805255			0.00297023
$736$			195.584i			7.20932i
$737$			75.6925i			2.78817i
$738$	−19.8784	+	11.4768i	−0.731735	+	0.422467i
$739$	−43.6677			−1.60634			−0.803171	−	0.595748i	$-0.796856\pi$
$739$	−43.6677			−1.60634			−0.803171	+	0.595748i	$0.796856\pi$
$740$	11.8473	−	20.5201i	0.435515	−	0.754334i
$741$	−0.0934343	+	0.0539443i	−0.00343239	+	0.00198169i
$742$	−0.687275	+	0.396798i	−0.0252307	+	0.0145669i
$743$	−23.6138			−0.866306			−0.433153	−	0.901320i	$-0.642599\pi$
$743$	−23.6138			−0.866306			−0.433153	+	0.901320i	$0.642599\pi$
$744$	−6.87430	+	3.96888i	−0.252024	+	0.145506i
$745$			38.0972i			1.39577i
$746$	−31.8066			−1.16452
$747$	−10.5759	−	18.3179i	−0.386950	−	0.670217i
$748$	−0.916733	+	0.529276i	−0.0335191	+	0.0193522i
$749$	−0.206000	−	0.356802i	−0.00752707	−	0.0130373i
$750$			2.39667i			0.0875139i
$751$		−	11.1479i		−	0.406794i	−0.979096	−	0.203397i	$-0.934802\pi$
$751$		−	11.1479i		−	0.406794i	0.979096	−	0.203397i	$-0.0651982\pi$
$752$	−149.741	−	86.4528i	−5.46048	−	3.15261i
$753$	−3.51752	+	2.03084i	−0.128186	+	0.0740079i
$754$	−3.41445	+	5.91401i	−0.124347	+	0.215375i
$755$	15.5506	−	26.9345i	0.565945	−	0.980245i
$756$			17.6164i			0.640703i
$757$	−11.8133	+	6.82039i	−0.429360	+	0.247891i	−0.699074	−	0.715049i	$-0.746404\pi$
$757$	−11.8133	+	6.82039i	−0.429360	+	0.247891i	0.269714	+	0.962941i	$0.413071\pi$
$758$	−46.2483			−1.67981
$759$			8.11403i			0.294521i
$760$	40.8778	+	23.6008i	1.48279	+	0.856090i
$761$	−19.7291	+	11.3906i	−0.715181	+	0.412910i	−0.812976	−	0.582297i	$-0.802154\pi$
$761$	−19.7291	+	11.3906i	−0.715181	+	0.412910i	0.0977954	+	0.995207i	$0.468821\pi$
$762$	1.94988			0.0706368
$763$			4.39058i			0.158950i
$764$	−139.147			−5.03415
$765$	0.303114			0.0109591
$766$	17.0520	+	29.5349i	0.616113	+	1.06714i
$767$	3.17828			0.114761
$768$	−6.77722	+	11.7385i	−0.244552	+	0.423576i
$769$	7.59111	+	4.38273i	0.273743	+	0.158045i	0.630587	−	0.776118i	$-0.282814\pi$
$769$	7.59111	+	4.38273i	0.273743	+	0.158045i	−0.356845	+	0.934164i	$0.616147\pi$
$770$	−99.6236	−	57.5177i	−3.59019	−	2.07279i
$771$	−2.35559	−	4.08000i	−0.0848345	−	0.146938i
$772$	10.9503	+	6.32219i	0.394112	+	0.227540i
$773$	−32.5081			−1.16924			−0.584618	−	0.811309i	$-0.698756\pi$
$773$	−32.5081			−1.16924			−0.584618	+	0.811309i	$0.698756\pi$
$774$	14.6172	−	25.3177i	0.525403	−	0.910025i
$775$	−7.02046	+	12.1598i	−0.252182	+	0.436792i
$776$	−32.7406	+	56.7084i	−1.17532	+	2.03571i
$777$		−	0.758573i		−	0.0272137i
$778$	−10.1738			−0.364749
$779$	2.26808	+	3.92842i	0.0812622	+	0.140750i
$780$	−0.947716	−	0.547164i	−0.0339337	−	0.0195916i
$781$	−27.1934	+	47.1003i	−0.973055	+	1.68538i
$782$	0.648899	−	0.374642i	0.0232046	−	0.0133972i
$783$	−4.26080	−	7.37992i	−0.152269	−	0.263737i
$784$	−2.31260			−0.0825929
$785$	−1.98033	+	3.43002i	−0.0706809	+	0.122423i
$786$	4.10803			0.146529
$787$	11.2738	−	6.50894i	0.401868	−	0.232019i	−0.285422	−	0.958402i	$-0.592134\pi$
$787$	11.2738	−	6.50894i	0.401868	−	0.232019i	0.687290	+	0.726383i	$0.258800\pi$
$788$	−37.7509	−	21.7955i	−1.34482	−	0.776432i
$789$	1.75051	+	3.03197i	0.0623197	+	0.107941i
$790$	16.7566			0.596173
$791$	8.52390	+	14.7638i	0.303075	+	0.524941i
$792$	79.4296	−	137.576i	2.82241	−	4.88855i
$793$	−1.61160	+	2.79138i	−0.0572297	+	0.0991247i
$794$	−34.0818	−	19.6771i	−1.20952	−	0.698316i
$795$	0.0532759	+	0.0307588i	0.00188950	+	0.00109090i
$796$			28.2720i			1.00207i
$797$	−8.79652	−	5.07867i	−0.311589	−	0.179896i	0.336049	−	0.941845i	$-0.390909\pi$
$797$	−8.79652	−	5.07867i	−0.311589	−	0.179896i	−0.647637	+	0.761949i	$0.724243\pi$
$798$	2.34385			0.0829715
$799$			0.369781i			0.0130819i
$800$			88.2611i			3.12050i
$801$			24.7874i			0.875819i
$802$	26.8446	−	46.4963i	0.947917	−	1.64184i
$803$	−68.5055	+	39.5517i	−2.41751	+	1.39575i
$804$	7.82156	−	13.5473i	0.275845	−	0.477778i
$805$	52.0319	+	30.0406i	1.83388	+	1.05879i
$806$	1.89130	+	3.27582i	0.0666181	+	0.115386i
$807$	0.799472	+	1.38473i	0.0281427	+	0.0487446i
$808$	−169.387			−5.95903
$809$	2.63704	+	4.56748i	0.0927132	+	0.160584i	0.908652	−	0.417554i	$-0.137113\pi$
$809$	2.63704	+	4.56748i	0.0927132	+	0.160584i	−0.815939	+	0.578138i	$0.803779\pi$
$810$	−60.2964	+	34.8121i	−2.11860	+	1.22317i
$811$	39.8352	+	22.9989i	1.39880	+	0.807599i	0.994267	−	0.106923i	$-0.0341000\pi$
$811$	39.8352	+	22.9989i	1.39880	+	0.807599i	0.404535	+	0.914522i	$0.367433\pi$
$812$	94.8002	−	54.7329i	3.32684	−	1.92075i
$813$	−4.34056			−0.152230
$814$	−10.6792	+	18.4969i	−0.374305	+	0.648315i
$815$	48.7676	−	28.1560i	1.70825	−	0.986261i
$816$	0.113432			0.00397092
$817$	−5.00334	−	2.88868i	−0.175045	−	0.101062i
$818$	55.3737	+	31.9700i	1.93610	+	1.11781i
$819$	2.68865			0.0939489
$820$	−23.0054	+	39.8465i	−0.803383	+	1.39150i
$821$	−4.24804	−	7.35782i	−0.148257	−	0.256790i	0.782326	−	0.622869i	$-0.214033\pi$
$821$	−4.24804	−	7.35782i	−0.148257	−	0.256790i	−0.930584	+	0.366080i	$0.880700\pi$
$822$	2.33317	+	4.04117i	0.0813786	+	0.140952i
$823$	−16.7106			−0.582494			−0.291247	−	0.956648i	$-0.594070\pi$
$823$	−16.7106			−0.582494			−0.291247	+	0.956648i	$0.594070\pi$
$824$	118.659			4.13368
$825$			3.66161i			0.127481i
$826$	−59.7968	−	34.5237i	−2.08060	−	1.20123i
$827$	−27.5675	−	15.9161i	−0.958616	−	0.553457i	−0.0628692	−	0.998022i	$-0.520025\pi$
$827$	−27.5675	−	15.9161i	−0.958616	−	0.553457i	−0.895747	+	0.444565i	$0.853358\pi$
$828$	−64.3450	+	111.449i	−2.23614	+	3.87311i
$829$			14.0087i			0.486544i	0.969958	+	0.243272i	$0.0782207\pi$
$829$			14.0087i			0.486544i	−0.969958	+	0.243272i	$0.921779\pi$
$830$	−49.7635	−	28.7310i	−1.72732	−	0.997267i
$831$			0.196942i			0.00683184i
$832$	10.9222	+	6.30592i	0.378658	+	0.218618i
$833$	0.00247289	+	0.00428318i	8.56807e−5	+	0.000148403i
$834$		−	11.0288i		−	0.381895i
$835$	51.3973	−	29.6743i	1.77868	−	1.02692i
$836$	−42.1700	−	24.3469i	−1.45848	−	0.842055i
$837$	−4.72019			−0.163154
$838$	−14.4082	+	8.31860i	−0.497724	+	0.287361i
$839$	45.0091	−	25.9860i	1.55389	−	0.897137i	0.556068	−	0.831137i	$-0.312309\pi$
$839$	45.0091	−	25.9860i	1.55389	−	0.897137i	0.997820	−	0.0660008i	$-0.0210240\pi$
$840$	7.66386	+	13.2742i	0.264428	+	0.458003i
$841$	−11.9760	+	20.7431i	−0.412966	+	0.715278i
$842$	−24.0113	−	41.5888i	−0.827485	−	1.43325i
$843$	0.0774257	−	0.134105i	0.00266668	−	0.00461883i
$844$			76.4446i			2.63133i
$845$	18.7641	−	32.5003i	0.645504	−	1.11805i
$846$	−43.0367	−	74.5418i	−1.47963	−	2.56280i
$847$	40.8041	+	23.5583i	1.40205	+	0.809472i
$848$	−1.53002	−	0.883358i	−0.0525412	−	0.0303347i
$849$	0.201504	+	0.349016i	0.00691561	+	0.0119782i
$850$	0.292828	−	0.169065i	0.0100439	−	0.00579887i
$851$	5.57757	−	9.66064i	0.191197	−	0.331162i
$852$	9.73407	−	5.61997i	0.333484	−	0.192537i
$853$	−23.9265	−	41.4418i	−0.819226	−	1.41894i	−0.906253	−	0.422735i	$-0.861070\pi$
$853$	−23.9265	−	41.4418i	−0.819226	−	1.41894i	0.0870269	−	0.996206i	$-0.472263\pi$
$854$	60.6420	−	35.0117i	2.07513	−	1.19808i
$855$	6.97168	+	12.0753i	0.238427	+	0.412967i
$856$	0.772828	−	1.33858i	0.0264147	−	0.0457516i
$857$	−10.1054	+	5.83434i	−0.345193	+	0.199297i	−0.662566	−	0.749004i	$-0.730533\pi$
$857$	−10.1054	+	5.83434i	−0.345193	+	0.199297i	0.317373	+	0.948301i	$0.397199\pi$
$858$	0.854274	+	0.493215i	0.0291644	+	0.0168381i
$859$	−19.0618	+	11.0053i	−0.650379	+	0.375496i	−0.788601	−	0.614905i	$-0.789194\pi$
$859$	−19.0618	+	11.0053i	−0.650379	+	0.375496i	0.138223	+	0.990401i	$0.455861\pi$
$860$		−	58.6005i		−	1.99826i
$861$			1.47302i			0.0502004i
$862$	−7.28737	−	12.6221i	−0.248209	−	0.429910i
$863$	23.5372	+	13.5892i	0.801215	+	0.462582i	0.843896	−	0.536507i	$-0.180257\pi$
$863$	23.5372	+	13.5892i	0.801215	+	0.462582i	−0.0426810	+	0.999089i	$0.513590\pi$
$864$	−25.6959	+	14.8355i	−0.874193	+	0.504715i
$865$			18.2422i			0.620253i
$866$	−52.0734			−1.76953
$867$	1.66962	+	2.89187i	0.0567033	+	0.0982131i
$868$		−	60.6342i		−	2.05806i
$869$	−11.1449			−0.378067
$870$	−9.95948	−	5.75011i	−0.337658	−	0.194947i
$871$	−4.16218	−	2.40303i	−0.141030	−	0.0814237i
$872$	−14.2649	+	8.23584i	−0.483070	+	0.278901i
$873$	−16.7517	+	9.67159i	−0.566959	+	0.327334i
$874$	29.8496	+	17.2337i	1.00968	+	0.582938i
$875$	−10.2219	−	5.90163i	−0.345564	−	0.199512i
$876$	16.3480			0.552349
$877$			13.6733i			0.461715i	0.972988	+	0.230857i	$0.0741531\pi$
$877$			13.6733i			0.461715i	−0.972988	+	0.230857i	$0.925847\pi$
$878$	−31.8087	−	55.0943i	−1.07349	−	1.85934i
$879$	2.27384			0.0766948
$880$		−	256.094i		−	8.63292i
$881$	46.5031	−	26.8486i	1.56673	−	0.904552i	0.570184	−	0.821517i	$-0.306872\pi$
$881$	46.5031	−	26.8486i	1.56673	−	0.904552i	0.996547	−	0.0830348i	$-0.0264613\pi$
$882$	−0.996991	−	0.575613i	−0.0335704	−	0.0193819i
$883$	−16.1093	−	27.9022i	−0.542122	−	0.938983i	−0.998782	−	0.0493417i	$-0.984288\pi$
$883$	−16.1093	−	27.9022i	−0.542122	−	0.938983i	0.456660	−	0.889641i	$-0.349046\pi$
$884$		−	0.0672124i		−	0.00226060i
$885$			5.35239i			0.179919i
$886$	20.0470	−	11.5742i	0.673493	−	0.388842i
$887$	−23.5093	−	13.5731i	−0.789364	−	0.455739i	0.0503748	−	0.998730i	$-0.483958\pi$
$887$	−23.5093	−	13.5731i	−0.789364	−	0.455739i	−0.839739	+	0.542991i	$0.817292\pi$
$888$	2.46459	−	1.42293i	0.0827061	−	0.0477504i
$889$	−4.80145	+	8.31636i	−0.161036	+	0.278922i
$890$	33.6695	+	58.3172i	1.12860	+	1.95480i
$891$	40.1036	−	23.1538i	1.34352	−	0.775682i
$892$	−6.95525	−	12.0469i	−0.232879	−	0.403358i
$893$	−14.7311	+	8.50502i	−0.492958	+	0.284610i
$894$	−3.54856	+	6.14629i	−0.118682	+	0.205563i
$895$	53.3904	−	30.8250i	1.78464	−	1.03036i
$896$	−69.2889	−	120.012i	−2.31478	−	4.00932i
$897$	−0.446174	−	0.257599i	−0.0148973	−	0.00860098i
$898$	9.60711	+	5.54667i	0.320593	+	0.185095i
$899$	14.6653	+	25.4010i	0.489115	+	0.847172i
$900$	−29.0369	+	50.2934i	−0.967897	+	1.67645i
$901$			0.00377835i			0.000125875i
$902$	20.7371	−	35.9178i	0.690471	−	1.19593i
$903$	−0.938038	−	1.62473i	−0.0312159	−	0.0540676i
$904$	−31.9782	+	55.3879i	−1.06358	+	1.84217i
$905$	20.9111	+	36.2191i	0.695109	+	1.20396i
$906$	5.01762	−	2.89693i	0.166699	−	0.0962440i
$907$	0.0668842	−	0.0386156i	0.00222085	−	0.00128221i	−0.498889	−	0.866666i	$-0.666259\pi$
$907$	0.0668842	−	0.0386156i	0.00222085	−	0.00128221i	0.501110	+	0.865384i	$0.332925\pi$
$908$	69.0489			2.29147
$909$	−43.3334	−	25.0186i	−1.43728	−	0.829813i
$910$	6.32557	−	3.65207i	0.209691	−	0.121065i
$911$			46.1768i			1.52991i	0.644086	+	0.764953i	$0.277238\pi$
$911$			46.1768i			1.52991i	−0.644086	+	0.764953i	$0.722762\pi$
$912$	2.60896	+	4.51885i	0.0863913	+	0.149634i
$913$	33.0981	+	19.1092i	1.09539	+	0.632422i
$914$		−	9.19481i		−	0.304137i
$915$	−4.70082	−	2.71402i	−0.155404	−	0.0897227i
$916$		−	18.1618i		−	0.600081i
$917$	−10.1157	+	17.5210i	−0.334051	+	0.578594i
$918$	0.0984413	+	0.0568351i	0.00324905	+	0.00187584i
$919$	−2.17021	−	1.25297i	−0.0715887	−	0.0413318i	0.463778	−	0.885951i	$-0.346493\pi$
$919$	−2.17021	−	1.25297i	−0.0715887	−	0.0413318i	−0.535367	+	0.844619i	$0.679827\pi$
$920$			225.400i			7.43123i
$921$	−3.05125			−0.100542
$922$	5.39519			0.177681
$923$	−1.72663	−	2.99062i	−0.0568328	−	0.0984374i
$924$	−7.90614	−	13.6938i	−0.260093	−	0.450494i
$925$	2.51699	−	4.35955i	0.0827580	−	0.143341i
$926$	5.49232			0.180489
$927$	30.3558	+	17.5260i	0.997017	+	0.575628i
$928$	159.671	+	92.1860i	5.24145	+	3.02615i
$929$	38.8829			1.27571			0.637853	−	0.770158i	$-0.279823\pi$
$929$	38.8829			1.27571			0.637853	+	0.770158i	$0.279823\pi$
$930$	−5.51665	+	3.18504i	−0.180898	+	0.104442i
$931$	−0.113754	+	0.197028i	−0.00372814	+	0.00645732i
$932$	−48.9537			−1.60353
$933$	0.306465	−	0.176938i	0.0100332	−	0.00579267i
$934$	18.7711	+	10.8375i	0.614210	+	0.354614i
$935$	−0.474312	+	0.273844i	−0.0155117	+	0.00895567i
$936$	5.04335	+	8.73535i	0.164847	+	0.285524i
$937$	37.4228			1.22255			0.611275	−	0.791418i	$-0.290657\pi$
$937$	37.4228			1.22255			0.611275	+	0.791418i	$0.290657\pi$
$938$	52.2053	+	90.4223i	1.70456	+	2.95239i
$939$	−3.35684	−	5.81421i	−0.109546	−	0.189740i
$940$	−149.420	−	86.2675i	−4.87353	−	2.81374i
$941$	11.3515	−	19.6614i	0.370049	−	0.640944i	−0.619524	−	0.784978i	$-0.712674\pi$
$941$	11.3515	−	19.6614i	0.370049	−	0.640944i	0.989573	+	0.144034i	$0.0460076\pi$
$942$	−0.638980	+	0.368915i	−0.0208191	+	0.0120199i
$943$	−10.8307	+	18.7593i	−0.352696	+	0.610887i
$944$		−	153.714i		−	5.00298i
$945$			9.11463i			0.296499i
$946$			52.8227i			1.71741i
$947$	−27.7140			−0.900583			−0.450291	−	0.892882i	$-0.648680\pi$
$947$	−27.7140			−0.900583			−0.450291	+	0.892882i	$0.648680\pi$
$948$	1.99471	+	1.15165i	0.0647851	+	0.0374037i
$949$		−	5.02264i		−	0.163042i
$950$	13.4702	+	7.77703i	0.437031	+	0.252320i
$951$	1.07691	+	0.621755i	0.0349212	+	0.0201618i
$952$	−0.470706	+	0.815286i	−0.0152557	+	0.0264236i
$953$	−0.870655	+	1.50802i	−0.0282033	+	0.0488495i	−0.879783	−	0.475376i	$-0.842312\pi$
$953$	−0.870655	+	1.50802i	−0.0282033	+	0.0488495i	0.851579	+	0.524226i	$0.175645\pi$
$954$	−0.439741	−	0.761654i	−0.0142371	−	0.0246595i
$955$	−71.9937			−2.32966
$956$	20.4065	+	35.3450i	0.659992	+	1.14314i
$957$	6.62413	+	3.82444i	0.214128	+	0.123627i
$958$	10.8377	−	6.25714i	0.350150	−	0.202159i
$959$	−22.9811			−0.742097
$960$	−10.6195	+	18.3935i	−0.342742	+	0.593647i
$961$	−14.7535			−0.475920
$962$	−0.678071	−	1.17445i	−0.0218619	−	0.0378659i
$963$	0.395416	−	0.228294i	0.0127421	−	0.00735666i
$964$	−43.6912	+	75.6755i	−1.40720	+	2.43734i
$965$	5.66565	+	3.27106i	0.182384	+	0.105299i
$966$	5.59627	+	9.69303i	0.180057	+	0.311868i
$967$	−22.0124			−0.707871			−0.353936	−	0.935270i	$-0.615157\pi$
$967$	−22.0124			−0.707871			−0.353936	+	0.935270i	$0.615157\pi$
$968$			176.762i			5.68135i
$969$	0.00557959	−	0.00966414i	0.000179242	−	0.000310457i
$970$	−26.2744	+	45.5087i	−0.843621	+	1.46120i
$971$	29.1127	−	50.4246i	0.934270	−	1.61820i	0.158340	−	0.987385i	$-0.449386\pi$
$971$	29.1127	−	50.4246i	0.934270	−	1.61820i	0.775930	−	0.630819i	$-0.217281\pi$
$972$	−29.3476			−0.941323
$973$	47.0384	+	27.1576i	1.50798	+	0.870633i
$974$	−1.12129	−	1.94213i	−0.0359285	−	0.0622299i
$975$	−0.201345	−	0.116246i	−0.00644819	−	0.00372287i
$976$	135.002	+	77.9435i	4.32131	+	2.49491i
$977$	−25.3588	+	43.9227i	−0.811299	+	1.40521i	0.100655	+	0.994921i	$0.467906\pi$
$977$	−25.3588	+	43.9227i	−0.811299	+	1.40521i	−0.911955	+	0.410290i	$0.865427\pi$
$978$	10.4904			0.335445
$979$	−22.3938	−	38.7872i	−0.715709	−	1.23965i
$980$	−2.30764			−0.0737149
$981$	−4.86574			−0.155351
$982$			16.1884i			0.516594i
$983$	45.3668			1.44698			0.723488	−	0.690337i	$-0.242538\pi$
$983$	45.3668			1.44698			0.723488	+	0.690337i	$0.242538\pi$
$984$	−4.78580	+	2.76308i	−0.152566	+	0.0880839i
$985$	−19.5321	−	11.2769i	−0.622344	−	0.359310i
$986$		−	0.706331i		−	0.0224942i
$987$	−5.52365			−0.175820
$988$	2.67757	−	1.54590i	0.0851849	−	0.0491816i
$989$		−	27.5885i		−	0.877263i
$990$	63.7425	−	110.405i	2.02587	−	3.50891i
$991$	24.3542	−	42.1827i	0.773637	−	1.33998i	−0.161920	−	0.986804i	$-0.551769\pi$
$991$	24.3542	−	42.1827i	0.773637	−	1.33998i	0.935557	−	0.353175i	$-0.114898\pi$
$992$	88.4431	−	51.0627i	2.80807	−	1.62124i
$993$	−2.74276	−	1.58353i	−0.0870389	−	0.0502519i
$994$			75.0214i			2.37953i
$995$			14.6277i			0.463731i
$996$	−3.94924	−	6.84028i	−0.125136	−	0.216743i
$997$	−3.43742	+	1.98459i	−0.108864	+	0.0628527i	−0.553443	−	0.832887i	$-0.686687\pi$
$997$	−3.43742	+	1.98459i	−0.108864	+	0.0628527i	0.444579	+	0.895739i	$0.353353\pi$
$998$	−11.5953	−	20.0837i	−0.367044	−	0.635738i
$999$	1.69229			0.0535417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.227.1	yes	58
349.123	even	6	inner	349.2.e.a.123.1	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.1	✓	58	349.123	even	6	inner
349.2.e.a.227.1	yes	58	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39209 - 1.38107i) q^{2} +(-0.0982202 - 0.170122i) q^{3} +(2.81473 + 4.87525i) q^{4} +(1.45632 + 2.52242i) q^{5} +0.542597i q^{6} +(-2.31421 - 1.33611i) q^{7} -10.0251i q^{8} +(1.48071 - 2.56466i) q^{9} +O(q^{10})\)	\(q+(-2.39209 - 1.38107i) q^{2} +(-0.0982202 - 0.170122i) q^{3} +(2.81473 + 4.87525i) q^{4} +(1.45632 + 2.52242i) q^{5} +0.542597i q^{6} +(-2.31421 - 1.33611i) q^{7} -10.0251i q^{8} +(1.48071 - 2.56466i) q^{9} -8.04515i q^{10} +5.35089i q^{11} +(0.552926 - 0.957695i) q^{12} +(-0.294235 - 0.169876i) q^{13} +(3.69053 + 6.39218i) q^{14} +(0.286081 - 0.495506i) q^{15} +(-8.21590 + 14.2304i) q^{16} +0.0351415 q^{17} +(-7.08396 + 4.08992i) q^{18} +(0.808261 + 1.39995i) q^{19} +(-8.19829 + 14.1999i) q^{20} +0.524931i q^{21} +(7.38997 - 12.7998i) q^{22} +(-3.85967 + 6.68514i) q^{23} +(-1.70549 + 0.984664i) q^{24} +(-1.74175 + 3.01680i) q^{25} +(0.469224 + 0.812719i) q^{26} -1.17106 q^{27} -15.0431i q^{28} +(3.63841 + 6.30191i) q^{29} +(-1.36866 + 0.790196i) q^{30} +4.03069 q^{31} +(21.9424 - 12.6685i) q^{32} +(0.910306 - 0.525565i) q^{33} +(-0.0840616 - 0.0485330i) q^{34} -7.78322i q^{35} +16.6711 q^{36} -1.44509 q^{37} -4.46507i q^{38} +0.0667412i q^{39} +(25.2875 - 14.5997i) q^{40} +2.80612 q^{41} +(0.724968 - 1.25568i) q^{42} +(-3.09513 + 1.78697i) q^{43} +(-26.0869 + 15.0613i) q^{44} +8.62554 q^{45} +(18.4653 - 10.6610i) q^{46} +10.5226i q^{47} +3.22787 q^{48} +(0.0703696 + 0.121884i) q^{49} +(8.33284 - 4.81097i) q^{50} +(-0.00345160 - 0.00597836i) q^{51} -1.91262i q^{52} +0.107518i q^{53} +(2.80128 + 1.61732i) q^{54} +(-13.4972 + 7.79262i) q^{55} +(-13.3946 + 23.2001i) q^{56} +(0.158775 - 0.275006i) q^{57} -20.0996i q^{58} +(-8.10140 + 4.67734i) q^{59} +3.22095 q^{60} -9.48691i q^{61} +(-9.64178 - 5.56668i) q^{62} +(-6.85332 + 3.95677i) q^{63} -37.1206 q^{64} -0.989580i q^{65} -2.90338 q^{66} +14.1458 q^{67} +(0.0989137 + 0.171323i) q^{68} +1.51639 q^{69} +(-10.7492 + 18.6181i) q^{70} +(8.80233 + 5.08203i) q^{71} +(-25.7109 - 14.8442i) q^{72} +(7.39161 + 12.8026i) q^{73} +(3.45679 + 1.99578i) q^{74} +0.684300 q^{75} +(-4.55006 + 7.88094i) q^{76} +(7.14937 - 12.3831i) q^{77} +(0.0921745 - 0.159651i) q^{78} +2.08282i q^{79} -47.8600 q^{80} +(-4.32709 - 7.49475i) q^{81} +(-6.71248 - 3.87545i) q^{82} +(3.57122 - 6.18553i) q^{83} +(-2.55917 + 1.47754i) q^{84} +(0.0511773 + 0.0886418i) q^{85} +9.87176 q^{86} +(0.714730 - 1.23795i) q^{87} +53.6430 q^{88} +(-7.24874 + 4.18506i) q^{89} +(-20.6331 - 11.9125i) q^{90} +(0.453947 + 0.786259i) q^{91} -43.4556 q^{92} +(-0.395895 - 0.685711i) q^{93} +(14.5325 - 25.1710i) q^{94} +(-2.35418 + 4.07755i) q^{95} +(-4.31037 - 2.48860i) q^{96} +(-5.65666 - 3.26587i) q^{97} -0.388742i q^{98} +(13.7232 + 7.92309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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