LMFDB - Embedded newform 349.2.e.a.123.13

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			123.13
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} +O(q^{10})$	\(q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} -0.0402489i q^{10} -2.60755i q^{11} +(0.788160 + 1.36513i) q^{12} +(-3.80680 + 2.19786i) q^{13} +(1.12264 - 1.94446i) q^{14} +(0.0319195 + 0.0552861i) q^{15} +(-0.949976 - 1.64541i) q^{16} -5.89706 q^{17} +(-1.09046 - 0.629575i) q^{18} +(-1.73717 + 3.00886i) q^{19} +(-0.0535879 - 0.0928170i) q^{20} +3.56124i q^{21} +(0.796504 + 1.37959i) q^{22} +(-0.241590 - 0.418446i) q^{23} +(-1.85931 - 1.07348i) q^{24} +(2.49783 + 4.32637i) q^{25} +(1.34271 - 2.32565i) q^{26} +4.90410 q^{27} -5.97877i q^{28} +(-1.77131 + 3.06800i) q^{29} +(-0.0337754 - 0.0195003i) q^{30} +2.61433 q^{31} +(4.84287 + 2.79603i) q^{32} +(-2.18817 - 1.26334i) q^{33} +(3.11997 - 1.80132i) q^{34} -0.242133i q^{35} -3.35290 q^{36} -10.1686 q^{37} -2.12254i q^{38} +4.25937i q^{39} +(0.126417 + 0.0729868i) q^{40} +0.703340 q^{41} +(-1.08782 - 1.88415i) q^{42} +(3.36545 + 1.94304i) q^{43} +(3.67360 + 2.12095i) q^{44} -0.135788 q^{45} +(0.255637 + 0.147592i) q^{46} +6.07101i q^{47} -1.84102 q^{48} +(3.25365 - 5.63549i) q^{49} +(-2.64307 - 1.52598i) q^{50} +(-2.85708 + 4.94860i) q^{51} -7.15084i q^{52} -8.09749i q^{53} +(-2.59462 + 1.49801i) q^{54} +(0.148776 + 0.0858958i) q^{55} +(4.07155 + 7.05213i) q^{56} +(1.68329 + 2.91554i) q^{57} -2.16426i q^{58} +(5.72348 + 3.30445i) q^{59} -0.103852 q^{60} -12.7178i q^{61} +(-1.38317 + 0.798574i) q^{62} +(-6.56006 - 3.78745i) q^{63} +0.383599 q^{64} -0.289600i q^{65} +1.54360 q^{66} +0.571467 q^{67} +(4.79660 - 8.30795i) q^{68} -0.468194 q^{69} +(0.0739619 + 0.128106i) q^{70} +(6.44742 - 3.72242i) q^{71} +(3.95484 - 2.28333i) q^{72} +(-0.720077 + 1.24721i) q^{73} +(5.37990 - 3.10609i) q^{74} +4.84071 q^{75} +(-2.82598 - 4.89474i) q^{76} +(4.79168 + 8.29943i) q^{77} +(-1.30107 - 2.25352i) q^{78} +2.78194i q^{79} +0.125173 q^{80} +(-0.715611 + 1.23947i) q^{81} +(-0.372118 + 0.214842i) q^{82} +(6.64377 + 11.5073i) q^{83} +(-5.01718 - 2.89667i) q^{84} +(0.194256 - 0.336461i) q^{85} -2.37409 q^{86} +(1.71637 + 2.97284i) q^{87} -5.77748 q^{88} +(11.2523 + 6.49654i) q^{89} +(0.0718418 - 0.0414779i) q^{90} +(8.07762 - 13.9908i) q^{91} +0.786026 q^{92} +(1.26662 - 2.19385i) q^{93} +(-1.85445 - 3.21201i) q^{94} +(-0.114449 - 0.198231i) q^{95} +(4.69266 - 2.70931i) q^{96} +(2.30308 - 1.32968i) q^{97} +3.97544i q^{98} +(4.65432 - 2.68718i) 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 $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.529073	+	0.305460i	−0.374111	+	0.215993i	−0.675253	−	0.737586i	$-0.735966\pi$
$2$	−0.529073	+	0.305460i	−0.374111	+	0.215993i	0.301142	+	0.953579i	$0.402632\pi$
$3$	0.484492	−	0.839165i	0.279722	−	0.484492i	−0.691594	−	0.722287i	$-0.743091\pi$
$3$	0.484492	−	0.839165i	0.279722	−	0.484492i	0.971315	+	0.237795i	$0.0764245\pi$
$4$	−0.813388	+	1.40883i	−0.406694	+	0.704415i
$5$	−0.0329412	+	0.0570558i	−0.0147317	+	0.0255161i	−0.873297	−	0.487188i	$-0.838023\pi$
$5$	−0.0329412	+	0.0570558i	−0.0147317	+	0.0255161i	0.858566	+	0.512704i	$0.171356\pi$
$6$			0.591972i			0.241672i
$7$	−3.18284	+	1.83761i	−1.20300	+	0.694553i	−0.961221	−	0.275778i	$-0.911064\pi$
$7$	−3.18284	+	1.83761i	−1.20300	+	0.694553i	−0.241780	+	0.970331i	$0.577731\pi$
$8$		−	2.21567i		−	0.783358i
$9$	1.03054	+	1.78494i	0.343512	+	0.594980i
$10$		−	0.0402489i		−	0.0127278i
$11$		−	2.60755i		−	0.786207i	−0.919494	−	0.393103i	$-0.871401\pi$
$11$		−	2.60755i		−	0.786207i	0.919494	−	0.393103i	$-0.128599\pi$
$12$	0.788160	+	1.36513i	0.227522	+	0.394080i
$13$	−3.80680	+	2.19786i	−1.05582	+	0.609575i	−0.924272	−	0.381735i	$-0.875327\pi$
$13$	−3.80680	+	2.19786i	−1.05582	+	0.609575i	−0.131544	+	0.991310i	$0.541993\pi$
$14$	1.12264	−	1.94446i	0.300037	−	0.519680i
$15$	0.0319195	+	0.0552861i	0.00824157	+	0.0142748i
$16$	−0.949976	−	1.64541i	−0.237494	−	0.411352i
$17$	−5.89706			−1.43025			−0.715124	−	0.698998i	$-0.753630\pi$
$17$	−5.89706			−1.43025			−0.715124	+	0.698998i	$0.753630\pi$
$18$	−1.09046	−	0.629575i	−0.257023	−	0.148392i
$19$	−1.73717	+	3.00886i	−0.398533	+	0.690280i	−0.993545	−	0.113437i	$-0.963814\pi$
$19$	−1.73717	+	3.00886i	−0.398533	+	0.690280i	0.595012	+	0.803717i	$0.297147\pi$
$20$	−0.0535879	−	0.0928170i	−0.0119826	−	0.0207545i
$21$			3.56124i			0.777126i
$22$	0.796504	+	1.37959i	0.169815	+	0.294129i
$23$	−0.241590	−	0.418446i	−0.0503750	−	0.0872521i	0.839738	−	0.542991i	$-0.182708\pi$
$23$	−0.241590	−	0.418446i	−0.0503750	−	0.0872521i	−0.890113	+	0.455739i	$0.849375\pi$
$24$	−1.85931	−	1.07348i	−0.379531	−	0.219122i
$25$	2.49783	+	4.32637i	0.499566	+	0.865274i
$26$	1.34271	−	2.32565i	0.263328	−	0.456098i
$27$	4.90410			0.943794
$28$		−	5.97877i		−	1.12988i
$29$	−1.77131	+	3.06800i	−0.328924	+	0.569713i	−0.982299	−	0.187322i	$-0.940019\pi$
$29$	−1.77131	+	3.06800i	−0.328924	+	0.569713i	0.653375	+	0.757035i	$0.273353\pi$
$30$	−0.0337754	−	0.0195003i	−0.00616652	−	0.00356024i
$31$	2.61433			0.469548			0.234774	−	0.972050i	$-0.424565\pi$
$31$	2.61433			0.469548			0.234774	+	0.972050i	$0.424565\pi$
$32$	4.84287	+	2.79603i	0.856106	+	0.494273i
$33$	−2.18817	−	1.26334i	−0.380911	−	0.219919i
$34$	3.11997	−	1.80132i	0.535071	−	0.308923i
$35$		−	0.242133i		−	0.0409279i
$36$	−3.35290			−0.558817
$37$	−10.1686			−1.67170			−0.835850	−	0.548958i	$-0.815025\pi$
$37$	−10.1686			−1.67170			−0.835850	+	0.548958i	$0.815025\pi$
$38$		−	2.12254i		−	0.344322i
$39$			4.25937i			0.682046i
$40$	0.126417	+	0.0729868i	0.0199883	+	0.0115402i
$41$	0.703340			0.109843			0.0549216	−	0.998491i	$-0.482509\pi$
$41$	0.703340			0.109843			0.0549216	+	0.998491i	$0.482509\pi$
$42$	−1.08782	−	1.88415i	−0.167854	−	0.290731i
$43$	3.36545	+	1.94304i	0.513226	+	0.296311i	0.734159	−	0.678978i	$-0.237577\pi$
$43$	3.36545	+	1.94304i	0.513226	+	0.296311i	−0.220933	+	0.975289i	$0.570910\pi$
$44$	3.67360	+	2.12095i	0.553816	+	0.319746i
$45$	−0.135788			−0.0202421
$46$	0.255637	+	0.147592i	0.0376917	+	0.0217613i
$47$			6.07101i			0.885548i	0.896633	+	0.442774i	$0.146006\pi$
$47$			6.07101i			0.885548i	−0.896633	+	0.442774i	$0.853994\pi$
$48$	−1.84102			−0.265729
$49$	3.25365	−	5.63549i	0.464807	−	0.805070i
$50$	−2.64307	−	1.52598i	−0.373786	−	0.215806i
$51$	−2.85708	+	4.94860i	−0.400071	+	0.692943i
$52$		−	7.15084i		−	0.991643i
$53$		−	8.09749i		−	1.11228i	−0.831090	−	0.556138i	$-0.812283\pi$
$53$		−	8.09749i		−	1.11228i	0.831090	−	0.556138i	$-0.187717\pi$
$54$	−2.59462	+	1.49801i	−0.353083	+	0.203853i
$55$	0.148776	+	0.0858958i	0.0200609	+	0.0115822i
$56$	4.07155	+	7.05213i	0.544084	+	0.942381i
$57$	1.68329	+	2.91554i	0.222957	+	0.386172i
$58$		−	2.16426i		−	0.284181i
$59$	5.72348	+	3.30445i	0.745133	+	0.430203i	0.823933	−	0.566688i	$-0.191775\pi$
$59$	5.72348	+	3.30445i	0.745133	+	0.430203i	−0.0787994	+	0.996890i	$0.525109\pi$
$60$	−0.103852			−0.0134072
$61$		−	12.7178i		−	1.62834i	−0.580623	−	0.814172i	$-0.697191\pi$
$61$		−	12.7178i		−	1.62834i	0.580623	−	0.814172i	$-0.302809\pi$
$62$	−1.38317	+	0.798574i	−0.175663	+	0.101419i
$63$	−6.56006	−	3.78745i	−0.826490	−	0.477174i
$64$	0.383599			0.0479499
$65$		−	0.289600i		−	0.0359204i
$66$	1.54360			0.190004
$67$	0.571467			0.0698158			0.0349079	−	0.999391i	$-0.488886\pi$
$67$	0.571467			0.0698158			0.0349079	+	0.999391i	$0.488886\pi$
$68$	4.79660	−	8.30795i	0.581673	−	1.00749i
$69$	−0.468194			−0.0563639
$70$	0.0739619	+	0.128106i	0.00884014	+	0.0153116i
$71$	6.44742	−	3.72242i	0.765167	−	0.441770i	−0.0659805	−	0.997821i	$-0.521018\pi$
$71$	6.44742	−	3.72242i	0.765167	−	0.441770i	0.831148	+	0.556051i	$0.187684\pi$
$72$	3.95484	−	2.28333i	0.466082	−	0.269093i
$73$	−0.720077	+	1.24721i	−0.0842786	+	0.145975i	−0.905084	−	0.425234i	$-0.860192\pi$
$73$	−0.720077	+	1.24721i	−0.0842786	+	0.145975i	0.820805	+	0.571209i	$0.193525\pi$
$74$	5.37990	−	3.10609i	0.625401	−	0.361075i
$75$	4.84071			0.558957
$76$	−2.82598	−	4.89474i	−0.324162	−	0.561466i
$77$	4.79168	+	8.29943i	0.546062	+	0.945808i
$78$	−1.30107	−	2.25352i	−0.147317	−	0.255161i
$79$			2.78194i			0.312992i	0.987679	+	0.156496i	$0.0500199\pi$
$79$			2.78194i			0.312992i	−0.987679	+	0.156496i	$0.949980\pi$
$80$	0.125173			0.0139948
$81$	−0.715611	+	1.23947i	−0.0795123	+	0.137719i
$82$	−0.372118	+	0.214842i	−0.0410935	+	0.0237254i
$83$	6.64377	+	11.5073i	0.729248	+	1.26310i	0.957201	+	0.289423i	$0.0934634\pi$
$83$	6.64377	+	11.5073i	0.729248	+	1.26310i	−0.227953	+	0.973672i	$0.573203\pi$
$84$	−5.01718	−	2.89667i	−0.547419	−	0.316052i
$85$	0.194256	−	0.336461i	0.0210700	−	0.0364944i
$86$	−2.37409			−0.256005
$87$	1.71637	+	2.97284i	0.184014	+	0.318722i
$88$	−5.77748			−0.615882
$89$	11.2523	+	6.49654i	1.19274	+	0.688631i	0.958928	−	0.283649i	$-0.0915452\pi$
$89$	11.2523	+	6.49654i	1.19274	+	0.688631i	0.233816	+	0.972281i	$0.424879\pi$
$90$	0.0718418	−	0.0414779i	0.00757279	−	0.00437215i
$91$	8.07762	−	13.9908i	0.846765	−	1.46664i
$92$	0.786026			0.0819489
$93$	1.26662	−	2.19385i	0.131343	−	0.227492i
$94$	−1.85445	−	3.21201i	−0.191272	−	0.331293i
$95$	−0.114449	−	0.198231i	−0.0117422	−	0.0203380i
$96$	4.69266	−	2.70931i	0.478943	−	0.276518i
$97$	2.30308	−	1.32968i	0.233842	−	0.135009i	−0.378501	−	0.925601i	$-0.623560\pi$
$97$	2.30308	−	1.32968i	0.233842	−	0.135009i	0.612343	+	0.790592i	$0.290227\pi$
$98$			3.97544i			0.401580i
$99$	4.65432	−	2.68718i	0.467777	−	0.270071i
$100$	−8.12682			−0.812682
$101$		−	4.77597i		−	0.475227i	−0.971360	−	0.237613i	$-0.923635\pi$
$101$		−	4.77597i		−	0.475227i	0.971360	−	0.237613i	$-0.0763652\pi$
$102$		−	3.49090i		−	0.345650i
$103$		−	14.0869i		−	1.38802i	−0.719965	−	0.694010i	$-0.755842\pi$
$103$		−	14.0869i		−	1.38802i	0.719965	−	0.694010i	$-0.244158\pi$
$104$	4.86973	+	8.43461i	0.477516	+	0.827082i
$105$	−0.203189	−	0.117311i	−0.0198292	−	0.0114484i
$106$	2.47346	+	4.28416i	0.240244	+	0.416115i
$107$	−6.30756	+	3.64167i	−0.609774	+	0.352053i	−0.772877	−	0.634556i	$-0.781183\pi$
$107$	−6.30756	+	3.64167i	−0.609774	+	0.352053i	0.163103	+	0.986609i	$0.447850\pi$
$108$	−3.98893	+	6.90903i	−0.383835	+	0.664822i
$109$	−4.14488	+	7.17914i	−0.397007	+	0.687637i	−0.993355	−	0.115089i	$-0.963285\pi$
$109$	−4.14488	+	7.17914i	−0.397007	+	0.687637i	0.596348	+	0.802726i	$0.296618\pi$
$110$	−0.104951			−0.0100067
$111$	−4.92658	+	8.53309i	−0.467610	+	0.809925i
$112$	6.04725	+	3.49138i	0.571411	+	0.329904i
$113$	−6.90896	+	3.98889i	−0.649941	+	0.375243i	−0.788433	−	0.615120i	$-0.789108\pi$
$113$	−6.90896	+	3.98889i	−0.649941	+	0.375243i	0.138493	+	0.990363i	$0.455774\pi$
$114$	−1.78116	−	1.02835i	−0.166821	−	0.0963142i
$115$	0.0318330			0.00296845
$116$	−2.88152	−	4.99094i	−0.267543	−	0.463398i
$117$	−7.84608	−	4.52993i	−0.725370	−	0.418793i
$118$	−4.03751			−0.371683
$119$	18.7694	−	10.8365i	1.72059	−	0.993382i
$120$	0.122496	−	0.0707230i	0.0111823	−	0.00645610i
$121$	4.20067			0.381879
$122$	3.88478	+	6.72863i	0.351711	+	0.609181i
$123$	0.340762	−	0.590218i	0.0307255	−	0.0532181i
$124$	−2.12647	+	3.68315i	−0.190962	+	0.330756i
$125$	−0.658537			−0.0589014
$126$	4.62766			0.412265
$127$			16.2872i			1.44526i	0.691237	+	0.722628i	$0.257066\pi$
$127$			16.2872i			1.44526i	−0.691237	+	0.722628i	$0.742934\pi$
$128$	−9.88869	+	5.70924i	−0.874045	+	0.504630i
$129$	3.26107	−	1.88278i	0.287121	−	0.165769i
$130$	0.0884612	+	0.153219i	0.00775856	+	0.0134382i
$131$		−	12.8306i		−	1.12102i	−0.828149	−	0.560508i	$-0.810606\pi$
$131$		−	12.8306i		−	1.12102i	0.828149	−	0.560508i	$-0.189394\pi$
$132$	3.55966	−	2.05517i	0.309828	−	0.178880i
$133$		−	12.7690i		−	1.10721i
$134$	−0.302347	+	0.174560i	−0.0261188	+	0.0150797i
$135$	−0.161547	+	0.279807i	−0.0139037	+	0.0240819i
$136$			13.0660i			1.12040i
$137$	7.14959	+	4.12782i	0.610831	+	0.352663i	0.773290	−	0.634052i	$-0.218609\pi$
$137$	7.14959	+	4.12782i	0.610831	+	0.352663i	−0.162460	+	0.986715i	$0.551943\pi$
$138$	0.247708	−	0.143015i	0.0210863	−	0.0121742i
$139$	−10.6756			−0.905493			−0.452747	−	0.891639i	$-0.649556\pi$
$139$	−10.6756			−0.905493			−0.452747	+	0.891639i	$0.649556\pi$
$140$	0.341124	+	0.196948i	0.0288302	+	0.0166451i
$141$	5.09458	+	2.94136i	0.429041	+	0.247707i
$142$	−2.27410	+	3.93886i	−0.190838	+	0.330542i
$143$	5.73103	+	9.92643i	0.479252	+	0.830090i
$144$	1.95797	−	3.39130i	0.163164	−	0.282608i
$145$	−0.116698	−	0.202127i	−0.00969124	−	0.0167857i
$146$		−	0.879820i		−	0.0728144i
$147$	−3.15273	−	5.46070i	−0.260033	−	0.450391i
$148$	8.27098	−	14.3258i	0.679870	−	1.17757i
$149$	−18.7146	+	10.8049i	−1.53316	+	0.885170i	−0.533946	+	0.845519i	$0.679291\pi$
$149$	−18.7146	+	10.8049i	−1.53316	+	0.885170i	−0.999214	+	0.0396514i	$0.987375\pi$
$150$	−2.56109	+	1.47865i	−0.209112	+	0.120731i
$151$	1.40691	−	2.43685i	0.114493	−	0.198308i	−0.803084	−	0.595866i	$-0.796809\pi$
$151$	1.40691	−	2.43685i	0.114493	−	0.198308i	0.917577	+	0.397558i	$0.130142\pi$
$152$	6.66665	+	3.84899i	0.540737	+	0.312194i
$153$	−6.07713	−	10.5259i	−0.491307	−	0.850968i
$154$	−5.07029	−	2.92733i	−0.408576	−	0.235891i
$155$	−0.0861191	+	0.149163i	−0.00691725	+	0.0119810i
$156$	−6.00073	−	3.46452i	−0.480443	−	0.277384i
$157$	3.97829	−	6.89061i	0.317502	−	0.549930i	−0.662464	−	0.749094i	$-0.730489\pi$
$157$	3.97829	−	6.89061i	0.317502	−	0.549930i	0.979966	+	0.199163i	$0.0638225\pi$
$158$	−0.849771	−	1.47185i	−0.0676042	−	0.117094i
$159$	−6.79513	−	3.92317i	−0.538889	−	0.311128i
$160$	−0.319060	+	0.184209i	−0.0252239	+	0.0145630i
$161$	1.53789	+	0.887898i	0.121202	+	0.0699762i
$162$		−	0.874362i		−	0.0686964i
$163$			20.9215i			1.63870i	0.573293	+	0.819351i	$0.305666\pi$
$163$			20.9215i			1.63870i	−0.573293	+	0.819351i	$0.694334\pi$
$164$	−0.572088	+	0.990886i	−0.0446726	+	0.0773752i
$165$	0.144162	−	0.0832317i	0.0112230	−	0.00647958i
$166$	−7.03007	−	4.05881i	−0.545639	−	0.315025i
$167$			13.1321i			1.01619i	0.861300	+	0.508096i	$0.169650\pi$
$167$			13.1321i			1.01619i	−0.861300	+	0.508096i	$0.830350\pi$
$168$	7.89053			0.608768
$169$	3.16114	−	5.47525i	0.243164	−	0.421173i
$170$			0.237350i			0.0182039i
$171$	−7.16084			−0.547604
$172$	−5.47483	+	3.16090i	−0.417452	+	0.241016i
$173$	−20.6719	+	11.9349i	−1.57165	+	0.907395i	−0.575687	+	0.817670i	$0.695265\pi$
$173$	−20.6719	+	11.9349i	−1.57165	+	0.907395i	−0.995967	+	0.0897243i	$0.971401\pi$
$174$	−1.81617	−	1.04857i	−0.137683	−	0.0794916i
$175$	−15.9004	−	9.18009i	−1.20196	−	0.693950i
$176$	−4.29049	+	2.47711i	−0.323408	+	0.186720i
$177$	5.54596	−	3.20196i	0.416860	−	0.240674i
$178$	−7.93773			−0.594958
$179$		−	14.9034i		−	1.11393i	−0.830535	−	0.556966i	$-0.811965\pi$
$179$		−	14.9034i		−	1.11393i	0.830535	−	0.556966i	$-0.188035\pi$
$180$	0.110448	−	0.191302i	0.00823234	−	0.0142588i
$181$	−10.6366			−0.790615			−0.395307	−	0.918549i	$-0.629362\pi$
$181$	−10.6366			−0.790615			−0.395307	+	0.918549i	$0.629362\pi$
$182$			9.86957i			0.731581i
$183$	−10.6723	−	6.16166i	−0.788920	−	0.455483i
$184$	−0.927139	+	0.535284i	−0.0683496	+	0.0394617i
$185$	0.334964	−	0.580174i	0.0246270	−	0.0426553i
$186$			1.54761i			0.113476i
$187$			15.3769i			1.12447i
$188$	−8.55302	−	4.93809i	−0.623793	−	0.360147i
$189$	−15.6090	+	9.01183i	−1.13538	+	0.655514i
$190$	0.121103	+	0.0699190i	0.00878575	+	0.00507246i
$191$	5.70685	+	9.88456i	0.412933	+	0.715222i	0.995209	−	0.0977697i	$-0.0311709\pi$
$191$	5.70685	+	9.88456i	0.412933	+	0.715222i	−0.582276	+	0.812991i	$0.697838\pi$
$192$	0.185851	−	0.321903i	0.0134126	−	0.0232313i
$193$	−6.52322	−	3.76618i	−0.469552	−	0.271096i	0.246500	−	0.969143i	$-0.420719\pi$
$193$	−6.52322	−	3.76618i	−0.469552	−	0.271096i	−0.716052	+	0.698047i	$0.754053\pi$
$194$	−0.812330	+	1.40700i	−0.0583219	+	0.101017i
$195$	−0.243022	−	0.140309i	−0.0174032	−	0.0100477i
$196$	5.29296	+	9.16768i	0.378069	+	0.654834i
$197$	−1.18484	−	0.684070i	−0.0844166	−	0.0487380i	0.457197	−	0.889365i	$-0.348853\pi$
$197$	−1.18484	−	0.684070i	−0.0844166	−	0.0487380i	−0.541614	+	0.840627i	$0.682187\pi$
$198$	−1.64165	+	2.84342i	−0.116667	+	0.202073i
$199$	−17.4193	+	10.0570i	−1.23482	+	0.712923i	−0.968031	−	0.250833i	$-0.919296\pi$
$199$	−17.4193	+	10.0570i	−1.23482	+	0.712923i	−0.266788	+	0.963755i	$0.585962\pi$
$200$	9.58581	−	5.53437i	0.677819	−	0.391339i
$201$	0.276871	−	0.479555i	0.0195290	−	0.0338252i
$202$	1.45887	+	2.52684i	0.102646	+	0.177788i
$203$		−	13.0199i		−	0.913820i
$204$	−4.64783	−	8.05027i	−0.325413	−	0.563632i
$205$	−0.0231688	+	0.0401296i	−0.00161818	+	0.00280277i
$206$	4.30298	+	7.45298i	0.299803	+	0.519274i
$207$	0.497934	−	0.862447i	0.0346088	−	0.0599442i
$208$	7.23274	+	4.17582i	0.501500	+	0.289541i
$209$	7.84577	+	4.52975i	0.542703	+	0.313330i
$210$	0.143336			0.00989111
$211$	14.8483	−	8.57265i	1.02220	−	0.590166i	0.107458	−	0.994210i	$-0.465729\pi$
$211$	14.8483	−	8.57265i	1.02220	−	0.590166i	0.914740	+	0.404044i	$0.132396\pi$
$212$	11.4080	+	6.58640i	0.783504	+	0.452356i
$213$		−	7.21392i		−	0.494290i
$214$	2.22477	−	3.85342i	0.152082	−	0.263414i
$215$	−0.221724	+	0.128012i	−0.0151214	+	0.00873036i
$216$		−	10.8659i		−	0.739329i
$217$	−8.32100	+	4.80413i	−0.564866	+	0.326126i
$218$		−	5.06438i		−	0.343003i
$219$	0.697743	+	1.20853i	0.0471491	+	0.0816646i
$220$	−0.242025	+	0.139733i	−0.0163173	+	0.00942082i
$221$	22.4489	−	12.9609i	1.51008	−	0.871843i
$222$		−	6.01950i		−	0.404002i
$223$	−22.6112			−1.51416			−0.757078	−	0.653324i	$-0.773374\pi$
$223$	−22.6112			−1.51416			−0.757078	+	0.653324i	$0.773374\pi$
$224$	−20.5521			−1.37320
$225$	−5.14820	+	8.91695i	−0.343214	+	0.594463i
$226$	2.43690	−	4.22083i	0.162100	−	0.280765i
$227$	−14.8239	−	25.6757i	−0.983895	−	1.70416i	−0.646749	−	0.762703i	$-0.723872\pi$
$227$	−14.8239	−	25.6757i	−0.983895	−	1.70416i	−0.337146	−	0.941453i	$-0.609461\pi$
$228$	−5.47666			−0.362701
$229$	2.89333	−	1.67047i	0.191197	−	0.110388i	−0.401346	−	0.915927i	$-0.631457\pi$
$229$	2.89333	−	1.67047i	0.191197	−	0.110388i	0.592543	+	0.805539i	$0.298124\pi$
$230$	−0.0168420	+	0.00972372i	−0.00111053	+	0.000641163i
$231$	9.28611			0.610981
$232$	6.79768	+	3.92464i	0.446289	+	0.257665i
$233$	9.37841	+	16.2439i	0.614400	+	1.06417i	0.990489	+	0.137589i	$0.0439352\pi$
$233$	9.37841	+	16.2439i	0.614400	+	1.06417i	−0.376089	+	0.926583i	$0.622731\pi$
$234$	5.53486			0.361825
$235$	−0.346386	−	0.199986i	−0.0225957	−	0.0130457i
$236$	−9.31082	+	5.37560i	−0.606083	+	0.349922i
$237$	2.33450	+	1.34783i	0.151642	+	0.0875507i
$238$	−6.62025	+	11.4666i	−0.429127	+	0.743270i
$239$	10.7559			0.695738			0.347869	−	0.937543i	$-0.386905\pi$
$239$	10.7559			0.695738			0.347869	+	0.937543i	$0.386905\pi$
$240$	0.0606455	−	0.105041i	0.00391465	−	0.00678037i
$241$	−7.44705	+	12.8987i	−0.479707	+	0.830877i	−0.999729	−	0.0232760i	$-0.992590\pi$
$241$	−7.44705	+	12.8987i	−0.479707	+	0.830877i	0.520022	+	0.854153i	$0.325924\pi$
$242$	−2.22246	+	1.28314i	−0.142865	+	0.0824831i
$243$	8.04956	+	13.9422i	0.516379	+	0.894395i
$244$	17.9172	+	10.3445i	1.14703	+	0.662238i
$245$	0.214358	+	0.371279i	0.0136948	+	0.0237201i
$246$			0.416357i			0.0265460i
$247$		−	15.2722i		−	0.971745i
$248$		−	5.79250i		−	0.367824i
$249$	12.8754			0.815946
$250$	0.348414	−	0.201157i	0.0220356	−	0.0127223i
$251$			10.0816i			0.636348i	0.948032	+	0.318174i	$0.103070\pi$
$251$			10.0816i			0.636348i	−0.948032	+	0.318174i	$0.896930\pi$
$252$	10.6717	−	6.16134i	0.672257	−	0.388128i
$253$	−1.09112	+	0.629959i	−0.0685982	+	0.0396052i
$254$	−4.97510	−	8.61712i	−0.312165	−	0.540686i
$255$	−0.188231	−	0.326026i	−0.0117875	−	0.0204165i
$256$	3.10429	−	5.37679i	0.194018	−	0.336049i
$257$	5.65623			0.352826			0.176413	−	0.984316i	$-0.443551\pi$
$257$	5.65623			0.352826			0.176413	+	0.984316i	$0.443551\pi$
$258$	−1.15023	+	1.99225i	−0.0716100	+	0.124032i
$259$	32.3649	−	18.6859i	2.01106	−	1.16108i
$260$	0.407997	+	0.235557i	0.0253029	+	0.0146086i
$261$	−7.30159			−0.451957
$262$	3.91924	+	6.78832i	0.242131	+	0.419384i
$263$	17.7953			1.09730			0.548651	−	0.836051i	$-0.315141\pi$
$263$	17.7953			1.09730			0.548651	+	0.836051i	$0.315141\pi$
$264$	−2.79914	+	4.84826i	−0.172275	+	0.298390i
$265$	0.462009	+	0.266741i	0.0283810	+	0.0163858i
$266$	3.90041	+	6.75571i	0.239150	+	0.414219i
$267$	10.9033	−	6.29504i	0.667273	−	0.385250i
$268$	−0.464824	+	0.805099i	−0.0283937	+	0.0491792i
$269$	−4.47779			−0.273016			−0.136508	−	0.990639i	$-0.543588\pi$
$269$	−4.47779			−0.273016			−0.136508	+	0.990639i	$0.543588\pi$
$270$		−	0.197384i		−	0.0120124i
$271$	14.1002	+	24.4222i	0.856524	+	1.48354i	0.875224	+	0.483719i	$0.160714\pi$
$271$	14.1002	+	24.4222i	0.856524	+	1.48354i	−0.0186992	+	0.999825i	$0.505952\pi$
$272$	5.60207	+	9.70307i	0.339675	+	0.588335i
$273$	−7.82708	−	13.5569i	−0.473717	−	0.820501i
$274$	−5.04354			−0.304691
$275$	11.2812	−	6.51322i	0.680284	−	0.392762i
$276$	0.380823	−	0.659605i	0.0229229	−	0.0397036i
$277$	19.7530	−	11.4044i	1.18684	−	0.685225i	0.229257	−	0.973366i	$-0.426371\pi$
$277$	19.7530	−	11.4044i	1.18684	−	0.685225i	0.957588	+	0.288141i	$0.0930372\pi$
$278$	5.64817	−	3.26097i	0.338755	−	0.195580i
$279$	2.69416	+	4.66642i	0.161295	+	0.279371i
$280$	−0.536486			−0.0320612
$281$	−4.38624	+	7.59719i	−0.261661	+	0.453210i	−0.966683	−	0.255975i	$-0.917604\pi$
$281$	−4.38624	+	7.59719i	−0.261661	+	0.453210i	0.705022	+	0.709185i	$0.250937\pi$
$282$	−3.59387			−0.214012
$283$	−5.21469			−0.309981			−0.154991	−	0.987916i	$-0.549535\pi$
$283$	−5.21469			−0.309981			−0.154991	+	0.987916i	$0.549535\pi$
$284$			12.1111i			0.718660i
$285$	−0.221798			−0.0131382
$286$	−6.06426	−	3.50120i	−0.358587	−	0.207030i
$287$	−2.23862	+	1.29247i	−0.132141	+	0.0762919i
$288$			11.5256i			0.679155i
$289$	17.7753			1.04561
$290$	0.123483	+	0.0712932i	0.00725120	+	0.00418648i
$291$		−	2.57688i		−	0.151059i
$292$	−1.17140	−	2.02893i	−0.0685512	−	0.118734i
$293$	−8.25302	−	14.2946i	−0.482146	−	0.835102i	0.517643	−	0.855596i	$-0.326809\pi$
$293$	−8.25302	−	14.2946i	−0.482146	−	0.835102i	−0.999790	+	0.0204942i	$0.993476\pi$
$294$	3.33605	+	1.92607i	0.194562	+	0.112331i
$295$	−0.377076	+	0.217705i	−0.0219542	+	0.0126753i
$296$			22.5302i			1.30954i
$297$		−	12.7877i		−	0.742017i
$298$	6.60092	−	11.4331i	0.382381	−	0.662303i
$299$	1.83937	+	1.06196i	0.106373	+	0.0614147i
$300$	−3.93738	+	6.81974i	−0.227325	+	0.393738i
$301$	−14.2823			−0.823215
$302$			1.71903i			0.0989188i
$303$	−4.00783	−	2.31392i	−0.230244	−	0.132931i
$304$	6.60107			0.378597
$305$	0.725623	+	0.418938i	0.0415490	+	0.0239883i
$306$	6.43048	+	3.71264i	0.367606	+	0.212238i
$307$	−2.01788	−	3.49507i	−0.115167	−	0.199474i	0.802680	−	0.596410i	$-0.203407\pi$
$307$	−2.01788	−	3.49507i	−0.115167	−	0.199474i	−0.917846	+	0.396936i	$0.870074\pi$
$308$	−15.5900			−0.888321
$309$	−11.8212	−	6.82497i	−0.672485	−	0.388259i
$310$		−	0.105224i		−	0.00597631i
$311$		−	14.2661i		−	0.808959i	−0.914547	−	0.404479i	$-0.867453\pi$
$311$		−	14.2661i		−	0.808959i	0.914547	−	0.404479i	$-0.132547\pi$
$312$	9.43737			0.534286
$313$	−10.8738			−0.614626			−0.307313	−	0.951608i	$-0.599430\pi$
$313$	−10.8738			−0.614626			−0.307313	+	0.951608i	$0.599430\pi$
$314$			4.86084i			0.274313i
$315$	0.432192	−	0.249526i	0.0243513	−	0.0140592i
$316$	−3.91927	−	2.26279i	−0.220476	−	0.127292i
$317$	−1.56221	−	0.901942i	−0.0877424	−	0.0506581i	0.455487	−	0.890243i	$-0.349465\pi$
$317$	−1.56221	−	0.901942i	−0.0877424	−	0.0506581i	−0.543229	+	0.839584i	$0.682799\pi$
$318$	4.79349			0.268806
$319$	7.99997	+	4.61878i	0.447912	+	0.258602i
$320$	−0.0126362	+	0.0218865i	−0.000706385	+	0.00122349i
$321$			7.05744i			0.393908i
$322$	−1.08487			−0.0604575
$323$	10.2442	−	17.7434i	0.570001	−	0.987271i
$324$	−1.16414	−	2.01635i	−0.0646743	−	0.112019i
$325$	−19.0175	−	10.9797i	−1.05490	−	0.609046i
$326$	−6.39070	−	11.0690i	−0.353948	−	0.613056i
$327$	4.01632	+	6.95647i	0.222103	+	0.384694i
$328$		−	1.55837i		−	0.0860466i
$329$	−11.1562	−	19.3231i	−0.615060	−	1.06531i
$330$	−0.0508479	+	0.0880712i	−0.00279909	+	0.00484816i
$331$	18.9986	+	10.9689i	1.04426	+	0.602903i	0.921037	−	0.389476i	$-0.127344\pi$
$331$	18.9986	+	10.9689i	1.04426	+	0.602903i	0.123222	+	0.992379i	$0.460677\pi$
$332$	−21.6158			−1.18632
$333$	−10.4790	−	18.1502i	−0.574248	−	0.994627i
$334$	−4.01133	−	6.94783i	−0.219490	−	0.380168i
$335$	−0.0188248	+	0.0326055i	−0.00102851	+	0.00178143i
$336$	5.85969	−	3.38309i	0.319672	−	0.184563i
$337$	−15.1256	−	26.1984i	−0.823946	−	1.42712i	−0.902722	−	0.430224i	$-0.858435\pi$
$337$	−15.1256	−	26.1984i	−0.823946	−	1.42712i	0.0787762	−	0.996892i	$-0.474899\pi$
$338$			3.86241i			0.210087i
$339$			7.73034i			0.419855i
$340$	0.316011	+	0.547347i	0.0171381	+	0.0296841i
$341$		−	6.81701i		−	0.369162i
$342$	3.78861	−	2.18735i	0.204864	−	0.118279i
$343$		−	1.81078i		−	0.0977731i
$344$	4.30515	−	7.45673i	0.232118	−	0.402040i
$345$	0.0154228	−	0.0267132i	0.000830338	−	0.00143819i
$346$	7.29128	−	12.6289i	0.391982	−	0.678932i
$347$	13.6240	−	7.86580i	0.731373	−	0.422258i	−0.0875514	−	0.996160i	$-0.527904\pi$
$347$	13.6240	−	7.86580i	0.731373	−	0.422258i	0.818924	+	0.573902i	$0.194571\pi$
$348$	−5.58430			−0.299350
$349$	−15.0052	+	11.1286i	−0.803208	+	0.595698i
$349$	−15.0052	+	11.1286i	−0.803208	+	0.595698i
$350$	11.2166			0.599553
$351$	−18.6689	+	10.7785i	−0.996472	+	0.575313i
$352$	7.29080	−	12.6280i	0.388601	−	0.673077i
$353$	10.2244	−	17.7092i	0.544189	−	0.942563i	−0.454468	−	0.890763i	$-0.650171\pi$
$353$	10.2244	−	17.7092i	0.544189	−	0.942563i	0.998657	−	0.0518003i	$-0.0164959\pi$
$354$	−1.95614	+	3.38814i	−0.103968	+	0.180078i
$355$			0.490483i			0.0260321i
$356$	−18.3050	+	10.5684i	−0.970164	+	0.560125i
$357$		−	21.0008i		−	1.11148i
$358$	4.55240	+	7.88498i	0.240602	+	0.416734i
$359$		−	1.88289i		−	0.0993753i	−0.998765	−	0.0496877i	$-0.984177\pi$
$359$		−	1.88289i		−	0.0993753i	0.998765	−	0.0496877i	$-0.0158226\pi$
$360$			0.300862i			0.0158568i
$361$	3.46450	+	6.00070i	0.182342	+	0.315826i
$362$	5.62755	−	3.24907i	0.295778	−	0.170767i
$363$	2.03519	−	3.52505i	0.106820	−	0.185017i
$364$	13.1405	+	22.7600i	0.688748	+	1.19295i
$365$	−0.0474404	−	0.0821691i	−0.00248314	−	0.00430093i
$366$	7.52857			0.393525
$367$	−15.7224	−	9.07736i	−0.820705	−	0.473834i	0.0299544	−	0.999551i	$-0.490464\pi$
$367$	−15.7224	−	9.07736i	−0.820705	−	0.473834i	−0.850660	+	0.525717i	$0.823797\pi$
$368$	−0.459010	+	0.795028i	−0.0239275	+	0.0414437i
$369$	0.724816	+	1.25542i	0.0377324	+	0.0653545i
$370$			0.409273i			0.0212771i
$371$	14.8801	+	25.7730i	0.772534	+	1.33807i
$372$	2.06051	+	3.56891i	0.106833	+	0.185039i
$373$	24.3582	+	14.0632i	1.26122	+	0.728165i	0.973310	−	0.229493i	$-0.0737067\pi$
$373$	24.3582	+	14.0632i	1.26122	+	0.728165i	0.287909	+	0.957658i	$0.407040\pi$
$374$	−4.69703	−	8.13550i	−0.242878	−	0.420677i
$375$	−0.319056	+	0.552621i	−0.0164760	+	0.0285372i
$376$	13.4514			0.693701
$377$		−	15.5723i		−	0.802016i
$378$	5.50551	−	9.53583i	0.283173	−	0.490470i
$379$	24.8881	+	14.3691i	1.27841	+	0.738093i	0.976557	−	0.215260i	$-0.0690598\pi$
$379$	24.8881	+	14.3691i	1.27841	+	0.738093i	0.301858	+	0.953353i	$0.402393\pi$
$380$	0.372364			0.0191019
$381$	13.6677	+	7.89102i	0.700215	+	0.404269i
$382$	−6.03868	−	3.48643i	−0.308966	−	0.178381i
$383$	15.6597	−	9.04112i	0.800172	−	0.461980i	−0.0433591	−	0.999060i	$-0.513806\pi$
$383$	15.6597	−	9.04112i	0.800172	−	0.461980i	0.843531	+	0.537080i	$0.180473\pi$
$384$			11.0643i			0.564624i
$385$	−0.631374			−0.0321778
$386$	4.60168			0.234219
$387$			8.00950i			0.407146i
$388$			4.32619i			0.219629i
$389$	−3.45237	−	1.99323i	−0.175042	−	0.101061i	0.409919	−	0.912122i	$-0.365557\pi$
$389$	−3.45237	−	1.99323i	−0.175042	−	0.101061i	−0.584961	+	0.811061i	$0.698890\pi$
$390$	0.171435			0.00868095
$391$	1.42467	+	2.46760i	0.0720487	+	0.124792i
$392$	−12.4864	−	7.20902i	−0.630658	−	0.364111i
$393$	−10.7670	−	6.21632i	−0.543123	−	0.313572i
$394$	0.835825			0.0421082
$395$	−0.158726	−	0.0916402i	−0.00798635	−	0.00461092i
$396$			8.74287i			0.439346i
$397$	−26.6310			−1.33657			−0.668287	−	0.743904i	$-0.732972\pi$
$397$	−26.6310			−1.33657			−0.668287	+	0.743904i	$0.732972\pi$
$398$	6.14404	−	10.6418i	0.307973	−	0.533424i
$399$	−10.7153	−	6.18646i	−0.536434	−	0.309710i
$400$	4.74576	−	8.21990i	0.237288	−	0.410995i
$401$			24.5098i			1.22396i	0.790873	+	0.611981i	$0.209627\pi$
$401$			24.5098i			1.22396i	−0.790873	+	0.611981i	$0.790373\pi$
$402$			0.338292i			0.0168725i
$403$	−9.95223	+	5.74592i	−0.495756	+	0.286225i
$404$	6.72853	+	3.88472i	0.334757	+	0.193272i
$405$	−0.0471461	−	0.0816594i	−0.00234271	−	0.00405769i
$406$	3.97707	+	6.88849i	0.197379	+	0.341870i
$407$			26.5150i			1.31430i
$408$	10.9645	+	6.33035i	0.542823	+	0.313399i
$409$	20.5899			1.01811			0.509053	−	0.860735i	$-0.329996\pi$
$409$	20.5899			1.01811			0.509053	+	0.860735i	$0.329996\pi$
$410$		−	0.0283086i		−	0.00139806i
$411$	6.92784	−	3.99979i	0.341725	−	0.197295i
$412$	19.8460	+	11.4581i	0.977742	+	0.564500i
$413$	−24.2892			−1.19519
$414$			0.608396i			0.0299010i
$415$	−0.875414			−0.0429724
$416$	−24.5811			−1.20519
$417$	−5.17225	+	8.95859i	−0.253286	+	0.438704i
$418$	−5.53464			−0.270708
$419$	−13.3192	−	23.0695i	−0.650686	−	1.12702i	−0.982957	−	0.183837i	$-0.941148\pi$
$419$	−13.3192	−	23.0695i	−0.650686	−	1.12702i	0.332271	−	0.943184i	$-0.392185\pi$
$420$	0.330543	−	0.190839i	0.0161289	−	0.00931200i
$421$	−3.90209	+	2.25287i	−0.190176	+	0.109798i	−0.592065	−	0.805890i	$-0.701687\pi$
$421$	−3.90209	+	2.25287i	−0.190176	+	0.109798i	0.401889	+	0.915688i	$0.368354\pi$
$422$	−5.23721	+	9.07111i	−0.254943	+	0.441575i
$423$	−10.8364	+	6.25639i	−0.526883	+	0.304196i
$424$	−17.9414			−0.871311
$425$	−14.7299	−	25.5129i	−0.714503	−	1.23756i
$426$	2.20357	+	3.81669i	0.106763	+	0.184919i
$427$	23.3704	+	40.4787i	1.13097	+	1.95890i
$428$		−	11.8484i		−	0.572712i
$429$	11.1065			0.536229
$430$	0.0782053	−	0.135456i	0.00377139	−	0.00653225i
$431$	21.6611	−	12.5060i	1.04338	−	0.602395i	0.122590	−	0.992457i	$-0.460880\pi$
$431$	21.6611	−	12.5060i	1.04338	−	0.602395i	0.920788	+	0.390063i	$0.127547\pi$
$432$	−4.65878	−	8.06924i	−0.224145	−	0.388231i
$433$	−31.5227	−	18.1996i	−1.51488	−	0.874618i	−0.999848	−	0.0174483i	$-0.994446\pi$
$433$	−31.5227	−	18.1996i	−1.51488	−	0.874618i	−0.515035	−	0.857169i	$-0.672221\pi$
$434$	2.93494	−	5.08347i	0.140882	−	0.244014i
$435$	−0.226157			−0.0108434
$436$	−6.74279	−	11.6788i	−0.322921	−	0.559315i
$437$	1.67873			0.0803045
$438$	−0.738314	−	0.426266i	−0.0352780	−	0.0203678i
$439$	−25.0422	+	14.4581i	−1.19520	+	0.690048i	−0.959481	−	0.281774i	$-0.909077\pi$
$439$	−25.0422	+	14.4581i	−1.19520	+	0.690048i	−0.235717	+	0.971822i	$0.575744\pi$
$440$	0.190317	−	0.329639i	0.00907301	−	0.0157149i
$441$	13.4120			0.638667
$442$	−7.91807	+	13.7145i	−0.376624	+	0.652332i
$443$	9.11927	+	15.7950i	0.433270	+	0.750445i	0.997153	−	0.0754096i	$-0.0240264\pi$
$443$	9.11927	+	15.7950i	0.433270	+	0.750445i	−0.563883	+	0.825855i	$0.690693\pi$
$444$	−8.01444	−	13.8814i	−0.380349	−	0.658783i
$445$	−0.741330	+	0.428007i	−0.0351424	+	0.0202895i
$446$	11.9630	−	6.90682i	0.566462	−	0.327047i
$447$			20.9395i			0.990405i
$448$	−1.22093	+	0.704907i	−0.0576837	+	0.0333037i
$449$	−28.2792			−1.33458			−0.667288	−	0.744800i	$-0.732545\pi$
$449$	−28.2792			−1.33458			−0.667288	+	0.744800i	$0.732545\pi$
$450$		−	6.29029i		−	0.296527i
$451$		−	1.83400i		−	0.0863595i
$452$		−	12.9781i		−	0.610437i
$453$	−1.36328	−	2.36127i	−0.0640524	−	0.110942i
$454$	15.6858	+	9.05620i	0.736171	+	0.425029i
$455$	0.532172	+	0.921750i	0.0249486	+	0.0432123i
$456$	6.45988	−	3.72961i	0.302511	−	0.174655i
$457$	4.76212	−	8.24824i	0.222763	−	0.385836i	−0.732883	−	0.680355i	$-0.761826\pi$
$457$	4.76212	−	8.24824i	0.222763	−	0.385836i	0.955646	+	0.294518i	$0.0951591\pi$
$458$	−1.02052	+	1.76760i	−0.0476859	+	0.0825943i
$459$	−28.9197			−1.34986
$460$	−0.0258926	+	0.0448473i	−0.00120725	+	0.00209102i
$461$	27.7864	+	16.0425i	1.29414	+	0.747173i	0.979386	−	0.201999i	$-0.0647438\pi$
$461$	27.7864	+	16.0425i	1.29414	+	0.747173i	0.314756	+	0.949172i	$0.398077\pi$
$462$	−4.91303	+	2.83654i	−0.228575	+	0.131968i
$463$	25.1154	+	14.5004i	1.16721	+	0.673889i	0.953021	−	0.302903i	$-0.0979560\pi$
$463$	25.1154	+	14.5004i	1.16721	+	0.673889i	0.214189	+	0.976792i	$0.431289\pi$
$464$	6.73081			0.312470
$465$	0.0834480	+	0.144536i	0.00386981	+	0.00670271i
$466$	−9.92372	−	5.72946i	−0.459707	−	0.265412i
$467$	−9.71497			−0.449555			−0.224778	−	0.974410i	$-0.572166\pi$
$467$	−9.71497			−0.449555			−0.224778	+	0.974410i	$0.572166\pi$
$468$	12.7638	−	7.36919i	0.590007	−	0.340641i
$469$	−1.81889	+	1.05014i	−0.0839884	+	0.0484907i
$470$	0.244351			0.0112711
$471$	−3.85490	−	6.67689i	−0.177625	−	0.307655i
$472$	7.32158	−	12.6814i	0.337003	−	0.583706i
$473$	5.06659	−	8.77559i	0.232962	−	0.403502i
$474$	−1.64683			−0.0756414
$475$	−17.3566			−0.796375
$476$			35.2572i			1.61601i
$477$	14.4535	−	8.34475i	0.661782	−	0.382080i
$478$	−5.69063	+	3.28549i	−0.260283	+	0.150275i
$479$	−7.05043	−	12.2117i	−0.322143	−	0.557967i	0.658787	−	0.752329i	$-0.271070\pi$
$479$	−7.05043	−	12.2117i	−0.322143	−	0.557967i	−0.980930	+	0.194362i	$0.937736\pi$
$480$			0.356991i			0.0162943i
$481$	38.7096	−	22.3490i	1.76501	−	1.01903i
$482$		−	9.09912i		−	0.414453i
$483$	1.49019	−	0.860359i	0.0678058	−	0.0391477i
$484$	−3.41677	+	5.91802i	−0.155308	+	0.269001i
$485$			0.175205i			0.00795566i
$486$	−8.51760	−	4.91764i	−0.386366	−	0.223069i
$487$	1.45510	−	0.840105i	0.0659370	−	0.0380688i	−0.466669	−	0.884432i	$-0.654546\pi$
$487$	1.45510	−	0.840105i	0.0659370	−	0.0380688i	0.532606	+	0.846363i	$0.321213\pi$
$488$	−28.1784			−1.27558
$489$	17.5566	+	10.1363i	0.793938	+	0.458380i
$490$	−0.226822	−	0.130956i	−0.0102468	−	0.00591598i
$491$	−0.172737	+	0.299189i	−0.00779551	+	0.0135022i	−0.869897	−	0.493234i	$-0.835815\pi$
$491$	−0.172737	+	0.299189i	−0.00779551	+	0.0135022i	0.862101	+	0.506736i	$0.169148\pi$
$492$	0.554344	+	0.960152i	0.0249918	+	0.0432870i
$493$	10.4455	−	18.0922i	0.470442	−	0.814830i
$494$	4.66504	+	8.08009i	0.209890	+	0.363540i
$495$			0.354075i			0.0159145i
$496$	−2.48355	−	4.30164i	−0.111515	−	0.193149i
$497$	−13.6807	+	23.6957i	−0.613665	+	1.06290i
$498$	−6.81203	+	3.93293i	−0.305254	+	0.176239i
$499$	−36.1175	+	20.8525i	−1.61684	+	0.933484i	−0.629112	+	0.777315i	$0.716581\pi$
$499$	−36.1175	+	20.8525i	−1.61684	+	0.933484i	−0.987730	+	0.156169i	$0.950086\pi$
$500$	0.535646	−	0.927767i	0.0239548	−	0.0414910i
$501$	11.0200	+	6.36239i	0.492337	+	0.284251i
$502$	−3.07954	−	5.33393i	−0.137447	−	0.238065i
$503$	30.6297	+	17.6841i	1.36571	+	0.788494i	0.990377	−	0.138396i	$-0.0441947\pi$
$503$	30.6297	+	17.6841i	1.36571	+	0.788494i	0.375334	+	0.926890i	$0.377528\pi$
$504$	−8.39175	+	14.5349i	−0.373798	+	0.647438i
$505$	0.272497	+	0.157326i	0.0121259	+	0.00700092i
$506$	0.384855	−	0.666588i	0.0171089	−	0.0296335i
$507$	−3.06309	−	5.30543i	−0.136037	−	0.235622i
$508$	−22.9459	−	13.2478i	−1.01806	−	0.587777i
$509$	26.8662	−	15.5112i	1.19082	−	0.687521i	0.232329	−	0.972637i	$-0.425366\pi$
$509$	26.8662	−	15.5112i	1.19082	−	0.687521i	0.958493	+	0.285116i	$0.0920322\pi$
$510$	0.199176	+	0.114994i	0.00881965	+	0.00509203i
$511$		−	5.29289i		−	0.234144i
$512$		−	19.0440i		−	0.841634i
$513$	−8.51923	+	14.7557i	−0.376133	+	0.651482i
$514$	−2.99256	+	1.72775i	−0.131996	+	0.0762080i
$515$	0.803737	+	0.464038i	0.0354169	+	0.0204480i
$516$			6.12571i			0.269670i
$517$	15.8305			0.696224
$518$	−11.4156	+	19.7724i	−0.501572	+	0.868748i
$519$			23.1295i			1.01527i
$520$	−0.641658			−0.0281386
$521$	−29.2477	+	16.8862i	−1.28137	+	0.739797i	−0.977098	−	0.212789i	$-0.931745\pi$
$521$	−29.2477	+	16.8862i	−1.28137	+	0.739797i	−0.304268	+	0.952586i	$0.598412\pi$
$522$	3.86307	−	2.23034i	0.169082	−	0.0976195i
$523$	13.3663	+	7.71703i	0.584467	+	0.337442i	0.762907	−	0.646509i	$-0.223772\pi$
$523$	13.3663	+	7.71703i	0.584467	+	0.337442i	−0.178440	+	0.983951i	$0.557105\pi$
$524$	18.0761	+	10.4363i	0.789660	+	0.455910i
$525$	−15.4072	+	8.89536i	−0.672426	+	0.388225i
$526$	−9.41499	+	5.43574i	−0.410513	+	0.237010i
$527$	−15.4169			−0.671569
$528$			4.80057i			0.208918i
$529$	11.3833	−	19.7164i	0.494925	−	0.857235i
$530$	−0.325915			−0.0141568
$531$			13.6214i			0.591119i
$532$	17.9893	+	10.3861i	0.779935	+	0.450296i
$533$	−2.67747	+	1.54584i	−0.115974	+	0.0669577i
$534$	−3.84577	+	6.66107i	−0.166423	+	0.288252i
$535$		−	0.479843i		−	0.0207454i
$536$		−	1.26618i		−	0.0546908i
$537$	−12.5064	−	7.22058i	−0.539691	−	0.311591i
$538$	2.36908	−	1.36779i	0.102138	−	0.0589695i
$539$	−14.6948	−	8.48407i	−0.632951	−	0.365435i
$540$	−0.262800	−	0.455183i	−0.0113091	−	0.0195880i
$541$	−14.5392	+	25.1827i	−0.625090	+	1.08269i	0.363434	+	0.931620i	$0.381604\pi$
$541$	−14.5392	+	25.1827i	−0.625090	+	1.08269i	−0.988524	+	0.151067i	$0.951729\pi$
$542$	−14.9200	−	8.61408i	−0.640870	−	0.370007i
$543$	−5.15336	+	8.92589i	−0.221152	+	0.383046i
$544$	−28.5587	−	16.4884i	−1.22444	−	0.706933i
$545$	−0.273074	−	0.472978i	−0.0116972	−	0.0202602i
$546$	8.28219	+	4.78173i	0.354445	+	0.204639i
$547$	12.9096	−	22.3602i	0.551976	−	0.956051i	−0.446155	−	0.894955i	$-0.647207\pi$
$547$	12.9096	−	22.3602i	0.551976	−	0.956051i	0.998132	−	0.0610958i	$-0.0194595\pi$
$548$	−11.6308	+	6.71503i	−0.496842	+	0.286852i
$549$	22.7005	−	13.1061i	0.968832	−	0.559355i
$550$	−3.97906	+	6.89194i	−0.169668	+	0.293873i
$551$	−6.15412	−	10.6592i	−0.262174	−	0.454099i
$552$			1.03736i			0.0441531i
$553$	−5.11213	−	8.85446i	−0.217390	−	0.376530i
$554$	−6.96719	+	12.0675i	−0.296008	+	0.512700i
$555$	−0.324575	−	0.562180i	−0.0137774	−	0.0238632i
$556$	8.68341	−	15.0401i	0.368259	−	0.637843i
$557$	5.98848	+	3.45745i	0.253740	+	0.146497i	0.621476	−	0.783433i	$-0.286533\pi$
$557$	5.98848	+	3.45745i	0.253740	+	0.146497i	−0.367735	+	0.929930i	$0.619867\pi$
$558$	−2.85081	−	1.64592i	−0.120685	−	0.0696773i
$559$	−17.0821			−0.722496
$560$	−0.398407	+	0.230020i	−0.0168358	+	0.00972013i
$561$	12.9038	+	7.44998i	0.544797	+	0.314539i
$562$		−	5.35929i		−	0.226068i
$563$	15.8382	−	27.4326i	0.667502	−	1.15615i	−0.311099	−	0.950378i	$-0.600697\pi$
$563$	15.8382	−	27.4326i	0.667502	−	1.15615i	0.978601	−	0.205769i	$-0.0659696\pi$
$564$	−8.28774	+	4.78493i	−0.348977	+	0.201482i
$565$		−	0.525595i		−	0.0221119i
$566$	2.75895	−	1.59288i	0.115967	−	0.0669538i
$567$		−	5.26006i		−	0.220902i
$568$	−8.24765	−	14.2854i	−0.346064	−	0.599400i
$569$	5.36889	−	3.09973i	0.225076	−	0.129948i	−0.383223	−	0.923656i	$-0.625186\pi$
$569$	5.36889	−	3.09973i	0.225076	−	0.129948i	0.608298	+	0.793709i	$0.291852\pi$
$570$	0.117347	−	0.0677504i	0.00491513	−	0.00283775i
$571$		−	24.2302i		−	1.01400i	−0.861946	−	0.507000i	$-0.830754\pi$
$571$		−	24.2302i		−	1.01400i	0.861946	−	0.507000i	$-0.169246\pi$
$572$	−18.6462			−0.779636
$573$	11.0597			0.462026
$574$	0.789594	−	1.36762i	0.0329570	−	0.0570833i
$575$	1.20690	−	2.09041i	0.0503313	−	0.0871763i
$576$	0.395312	+	0.684701i	0.0164713	+	0.0285292i
$577$	15.1103			0.629050			0.314525	−	0.949249i	$-0.398155\pi$
$577$	15.1103			0.629050			0.314525	+	0.949249i	$0.398155\pi$
$578$	−9.40443	+	5.42965i	−0.391173	+	0.225844i
$579$	−6.32089	+	3.64937i	−0.262687	+	0.151663i
$580$	0.379683			0.0157655
$581$	−42.2921	−	24.4174i	−1.75457	−	1.01300i
$582$	0.787135	+	1.36336i	0.0326278	+	0.0565130i
$583$	−21.1146			−0.874479
$584$	2.76341	+	1.59545i	0.114351	+	0.0660204i
$585$	0.516918	−	0.298443i	0.0213719	−	0.0123391i
$586$	8.73289	+	5.04194i	0.360752	+	0.208281i
$587$	−16.9349	+	29.3321i	−0.698979	+	1.21067i	0.269842	+	0.962904i	$0.413028\pi$
$587$	−16.9349	+	29.3321i	−0.698979	+	1.21067i	−0.968821	+	0.247762i	$0.920305\pi$
$588$	10.2576			0.423016
$589$	−4.54153	+	7.86616i	−0.187130	+	0.324119i
$590$	0.133000	−	0.230364i	0.00547554	−	0.00948392i
$591$	−1.14809	+	0.662853i	−0.0472263	+	0.0272661i
$592$	9.65988	+	16.7314i	0.397019	+	0.687657i
$593$	−35.0640	−	20.2442i	−1.43991	−	0.831331i	−0.442064	−	0.896983i	$-0.645754\pi$
$593$	−35.0640	−	20.2442i	−1.43991	−	0.831331i	−0.997843	+	0.0656525i	$0.979087\pi$
$594$	3.90613	+	6.76562i	0.160271	+	0.277597i
$595$			1.42787i			0.0585370i
$596$		−	35.1542i		−	1.43997i
$597$			19.4902i			0.797679i
$598$	−1.29755			−0.0530606
$599$	19.7990	−	11.4310i	0.808967	−	0.467057i	−0.0376301	−	0.999292i	$-0.511981\pi$
$599$	19.7990	−	11.4310i	0.808967	−	0.467057i	0.846597	+	0.532235i	$0.178648\pi$
$600$		−	10.7254i		−	0.437864i
$601$	−16.0598	+	9.27214i	−0.655094	+	0.378218i	−0.790405	−	0.612585i	$-0.790130\pi$
$601$	−16.0598	+	9.27214i	−0.655094	+	0.378218i	0.135311	+	0.990803i	$0.456797\pi$
$602$	7.55635	−	4.36266i	0.307974	−	0.177809i
$603$	0.588916	+	1.02003i	0.0239825	+	0.0415390i
$604$	2.28874	+	3.96421i	0.0931273	+	0.161301i
$605$	−0.138375	+	0.239672i	−0.00562574	+	0.00974406i
$606$	2.82724			0.114849
$607$	4.19724	−	7.26984i	0.170361	−	0.295074i	−0.768185	−	0.640228i	$-0.778840\pi$
$607$	4.19724	−	7.26984i	0.170361	−	0.295074i	0.938546	+	0.345154i	$0.112173\pi$
$608$	−16.8257	+	9.71435i	−0.682374	+	0.393969i
$609$	−10.9259	−	6.30805i	−0.442738	−	0.255615i
$610$	−0.511876			−0.0207253
$611$	−13.3432	−	23.1111i	−0.539808	−	0.934975i
$612$	19.7723			0.799246
$613$	−18.9341	+	32.7949i	−0.764742	+	1.32457i	0.175641	+	0.984454i	$0.443800\pi$
$613$	−18.9341	+	32.7949i	−0.764742	+	1.32457i	−0.940383	+	0.340118i	$0.889533\pi$
$614$	2.13521	+	1.23277i	0.0861701	+	0.0497504i
$615$	0.0224502	+	0.0388849i	0.000905280	+	0.00156799i
$616$	18.3888	−	10.6168i	0.740906	−	0.427762i
$617$	−3.15799	+	5.46980i	−0.127136	+	0.220206i	−0.922566	−	0.385840i	$-0.873912\pi$
$617$	−3.15799	+	5.46980i	−0.127136	+	0.220206i	0.795430	+	0.606045i	$0.207245\pi$
$618$	8.33903			0.335445
$619$			18.3845i			0.738934i	0.929244	+	0.369467i	$0.120460\pi$
$619$			18.3845i			0.738934i	−0.929244	+	0.369467i	$0.879540\pi$
$620$	−0.140097	−	0.242654i	−0.00562641	−	0.00974523i
$621$	−1.18478	−	2.05210i	−0.0475436	−	0.0823479i
$622$	4.35774	+	7.54783i	0.174729	+	0.302640i
$623$	−47.7525			−1.91316
$624$	7.00840	−	4.04630i	0.280561	−	0.161982i
$625$	−12.4675	+	21.5943i	−0.498698	+	0.863771i
$626$	5.75305	−	3.32153i	0.229938	−	0.132755i
$627$	7.60242	−	4.38926i	0.303611	−	0.175290i
$628$	6.47179	+	11.2095i	0.258253	+	0.447307i
$629$	59.9646			2.39094
$630$	−0.152441	+	0.264035i	−0.00607338	+	0.0105194i
$631$	−6.38203			−0.254065			−0.127032	−	0.991899i	$-0.540545\pi$
$631$	−6.38203			−0.254065			−0.127032	+	0.991899i	$0.540545\pi$
$632$	6.16386			0.245185
$633$		−	16.6135i		−	0.660328i
$634$	1.10203			0.0437672
$635$	−0.929280	−	0.536520i	−0.0368773	−	0.0212911i
$636$	11.0542	−	6.38212i	0.438326	−	0.253067i
$637$			28.6042i			1.13334i
$638$	−5.64342			−0.223425
$639$	13.2886	+	7.67216i	0.525688	+	0.303506i
$640$		−	0.752276i		−	0.0297363i
$641$	3.02171	+	5.23375i	0.119350	+	0.206721i	0.919510	−	0.393066i	$-0.128586\pi$
$641$	3.02171	+	5.23375i	0.119350	+	0.206721i	−0.800160	+	0.599787i	$0.795252\pi$
$642$	−2.15577	−	3.73390i	−0.0850813	−	0.147365i
$643$	5.63940	+	3.25591i	0.222396	+	0.128400i	0.607059	−	0.794657i	$-0.292349\pi$
$643$	5.63940	+	3.25591i	0.222396	+	0.128400i	−0.384663	+	0.923057i	$0.625682\pi$
$644$	−2.50179	+	1.44441i	−0.0985845	+	0.0569178i
$645$			0.248084i			0.00976828i
$646$			12.5168i			0.492465i
$647$	5.33314	−	9.23727i	0.209667	−	0.363155i	−0.741942	−	0.670464i	$-0.766095\pi$
$647$	5.33314	−	9.23727i	0.209667	−	0.363155i	0.951610	+	0.307309i	$0.0994285\pi$
$648$	2.74627	+	1.58556i	0.107884	+	0.0622866i
$649$	8.61653	−	14.9243i	0.338229	−	0.585829i
$650$	13.4155			0.526199
$651$			9.31025i			0.364898i
$652$	−29.4749	−	17.0173i	−1.15433	−	0.666450i
$653$	30.6993			1.20136			0.600678	−	0.799491i	$-0.294898\pi$
$653$	30.6993			1.20136			0.600678	+	0.799491i	$0.294898\pi$
$654$	−4.24985	−	2.45365i	−0.166182	−	0.0959454i
$655$	0.732060	+	0.422655i	0.0286040	+	0.0165145i
$656$	−0.668156	−	1.15728i	−0.0260871	−	0.0451842i
$657$	−2.96826			−0.115803
$658$	11.8049	+	6.81554i	0.460201	+	0.265697i
$659$		−	14.2111i		−	0.553586i	−0.960930	−	0.276793i	$-0.910728\pi$
$659$		−	14.2111i		−	0.553586i	0.960930	−	0.276793i	$-0.0892716\pi$
$660$			0.270799i			0.0105408i
$661$	17.9533			0.698303			0.349152	−	0.937066i	$-0.386470\pi$
$661$	17.9533			0.698303			0.349152	+	0.937066i	$0.386470\pi$
$662$	−13.4022			−0.520891
$663$		−	25.1178i		−	0.975494i
$664$	25.4965	−	14.7204i	0.989456	−	0.571263i
$665$	0.728543	+	0.420625i	0.0282517	+	0.0163111i
$666$	11.0884	+	6.40187i	0.429665	+	0.248067i
$667$	1.71172			0.0662782
$668$	−18.5009	−	10.6815i	−0.715820	−	0.413279i
$669$	−10.9549	+	18.9745i	−0.423542	+	0.733597i
$670$		−	0.0230009i		−	0.000888602i
$671$	−33.1623			−1.28022
$672$	−9.95733	+	17.2466i	−0.384112	+	0.665302i
$673$	4.85546	+	8.40990i	0.187164	+	0.324178i	0.944304	−	0.329076i	$-0.106737\pi$
$673$	4.85546	+	8.40990i	0.187164	+	0.324178i	−0.757140	+	0.653253i	$0.773404\pi$
$674$	16.0051	+	9.24056i	0.616494	+	0.355933i
$675$	12.2496	+	21.2169i	0.471487	+	0.816640i
$676$	5.14246	+	8.90701i	0.197787	+	0.342577i
$677$			36.1255i			1.38842i	0.719775	+	0.694208i	$0.244245\pi$
$677$			36.1255i			1.38842i	−0.719775	+	0.694208i	$0.755755\pi$
$678$	−2.36131	−	4.08991i	−0.0906857	−	0.157072i
$679$	−4.88689	+	8.46433i	−0.187541	+	0.324831i
$680$	−0.745488	−	0.430408i	−0.0285882	−	0.0165054i
$681$	−28.7282			−1.10087
$682$	2.08233	+	3.60669i	0.0797363	+	0.138107i
$683$	−19.3319	−	33.4838i	−0.739714	−	1.28122i	−0.952624	−	0.304150i	$-0.901628\pi$
$683$	−19.3319	−	33.4838i	−0.739714	−	1.28122i	0.212911	−	0.977072i	$-0.431706\pi$
$684$	5.82455	−	10.0884i	0.222707	−	0.385740i
$685$	−0.471031	+	0.271950i	−0.0179972	+	0.0103907i
$686$	0.553122	+	0.958036i	0.0211183	+	0.0365780i
$687$		−	3.23731i		−	0.123511i
$688$		−	7.38338i		−	0.281489i
$689$	17.7971	+	30.8255i	0.678016	+	1.17436i
$690$			0.0188443i			0.000717389i
$691$	41.1334	−	23.7484i	1.56479	−	0.903431i	0.568028	−	0.823009i	$-0.307706\pi$
$691$	41.1334	−	23.7484i	1.56479	−	0.903431i	0.996761	−	0.0804224i	$-0.0256269\pi$
$692$		−	38.8309i		−	1.47613i
$693$	−9.87598	+	17.1057i	−0.375158	+	0.649792i
$694$	−4.80538	+	8.32316i	−0.182410	+	0.315943i
$695$	0.351667	−	0.609105i	0.0133395	−	0.0231047i
$696$	6.58684	−	3.80291i	0.249673	−	0.144149i
$697$	−4.14764			−0.157103
$698$	4.53949	−	10.4713i	0.171822	−	0.396345i
$699$	18.1751			0.687444
$700$	25.8664	−	14.9340i	0.977657	−	0.564451i
$701$	10.2181	−	17.6983i	0.385934	−	0.668457i	−0.605965	−	0.795492i	$-0.707213\pi$
$701$	10.2181	−	17.6983i	0.385934	−	0.668457i	0.991898	+	0.127035i	$0.0405460\pi$
$702$	6.58480	−	11.4052i	0.248527	−	0.430462i
$703$	17.6645	−	30.5958i	0.666228	−	1.15394i
$704$		−	1.00025i		−	0.0376985i
$705$	−0.335643	+	0.193783i	−0.0126410	+	0.00729830i
$706$			12.4926i			0.470164i
$707$	8.77639	+	15.2012i	0.330070	+	0.571698i
$708$			10.4177i			0.391523i
$709$		−	7.43814i		−	0.279345i	−0.990198	−	0.139673i	$-0.955395\pi$
$709$		−	7.43814i		−	0.279345i	0.990198	−	0.139673i	$-0.0446050\pi$
$710$	−0.149823	−	0.259501i	−0.00562276	−	0.00973891i
$711$	−4.96559	+	2.86688i	−0.186224	+	0.107517i
$712$	14.3942	−	24.9315i	0.539445	−	0.934346i
$713$	−0.631596	−	1.09396i	−0.0236535	−	0.0409690i
$714$	6.41492	+	11.1110i	0.240072	+	0.415817i
$715$	−0.755147			−0.0282409
$716$	20.9964	+	12.1222i	0.784671	+	0.453030i
$717$	5.21113	−	9.02593i	0.194613	−	0.337080i
$718$	0.575149	+	0.996187i	0.0214644	+	0.0371774i
$719$			28.0198i			1.04496i	0.852651	+	0.522481i	$0.174993\pi$
$719$			28.0198i			1.04496i	−0.852651	+	0.522481i	$0.825007\pi$
$720$	0.128995	+	0.223427i	0.00480738	+	0.00832662i
$721$	25.8862	+	44.8363i	0.964053	+	1.66979i
$722$	−3.66595	−	2.11654i	−0.136432	−	0.0787693i
$723$	7.21607	+	12.4986i	0.268369	+	0.464828i
$724$	8.65171	−	14.9852i	0.321538	−	0.556921i
$725$	−17.6977			−0.657277
$726$			2.48668i			0.0922892i
$727$	8.65263	−	14.9868i	0.320908	−	0.555829i	−0.659767	−	0.751470i	$-0.729345\pi$
$727$	8.65263	−	14.9868i	0.320908	−	0.555829i	0.980676	+	0.195640i	$0.0626786\pi$
$728$	−30.9991	−	17.8974i	−1.14890	−	0.663320i
$729$	11.3061			0.418745
$730$	0.0501988	+	0.0289823i	0.00185794	+	0.00107268i
$731$	−19.8463	−	11.4582i	−0.734040	−	0.423798i
$732$	17.3615	−	10.0236i	0.641698	−	0.370484i
$733$			5.67833i			0.209734i	0.994486	+	0.104867i	$0.0334416\pi$
$733$			5.67833i			0.209734i	−0.994486	+	0.104867i	$0.966558\pi$
$734$	11.0911			0.409380
$735$	0.415419			0.0153230
$736$		−	2.70197i		−	0.0995961i
$737$		−	1.49013i		−	0.0548896i
$738$	−0.766961	−	0.442805i	−0.0282322	−	0.0162999i
$739$	24.6857			0.908078			0.454039	−	0.890982i	$-0.349983\pi$
$739$	24.6857			0.908078			0.454039	+	0.890982i	$0.349983\pi$
$740$	0.544911	+	0.943814i	0.0200313	+	0.0346953i
$741$	−12.8159	−	7.39924i	−0.470802	−	0.271818i
$742$	−15.7453	−	9.09054i	−0.578027	−	0.333724i
$743$	29.2601			1.07345			0.536724	−	0.843758i	$-0.319662\pi$
$743$	29.2601			1.07345			0.536724	+	0.843758i	$0.319662\pi$
$744$	−4.86086	−	2.80642i	−0.178208	−	0.102888i
$745$		−	1.42370i		−	0.0521604i
$746$	−17.1830			−0.629114
$747$	−13.6933	+	23.7174i	−0.501011	+	0.867776i
$748$	−21.6634	−	12.5074i	−0.792093	−	0.457315i
$749$	13.3840	−	23.1817i	0.489039	−	0.847041i
$750$		−	0.389836i		−	0.0142348i
$751$			16.9243i			0.617578i	0.951131	+	0.308789i	$0.0999237\pi$
$751$			16.9243i			0.617578i	−0.951131	+	0.308789i	$0.900076\pi$
$752$	9.98929	−	5.76732i	0.364272	−	0.210312i
$753$	8.46016	+	4.88448i	0.308306	+	0.178000i
$754$	4.75673	+	8.23889i	0.173230	+	0.300043i
$755$	0.0926908	+	0.160545i	0.00337336	+	0.00584284i
$756$		−	29.3205i		−	1.06638i
$757$	37.1940	+	21.4740i	1.35184	+	0.780485i	0.988507	−	0.151174i	$-0.0483053\pi$
$757$	37.1940	+	21.4740i	1.35184	+	0.780485i	0.363333	+	0.931659i	$0.381639\pi$
$758$	−17.5568			−0.637692
$759$			1.22084i			0.0443137i
$760$	−0.439214	+	0.253581i	−0.0159320	+	0.00919833i
$761$	−5.83662	−	3.36977i	−0.211577	−	0.122154i	0.390467	−	0.920617i	$-0.372314\pi$
$761$	−5.83662	−	3.36977i	−0.211577	−	0.122154i	−0.602044	+	0.798463i	$0.705647\pi$
$762$	−9.64158			−0.349277
$763$		−	30.4667i		−	1.10297i
$764$	−18.5675			−0.671750
$765$	0.800751			0.0289512
$766$	−5.52341	+	9.56682i	−0.199569	+	0.345663i
$767$	−29.0508			−1.04896
$768$	−3.00801	−	5.21002i	−0.108542	−	0.188001i
$769$	−25.8319	+	14.9141i	−0.931522	+	0.537815i	−0.887293	−	0.461207i	$-0.847417\pi$
$769$	−25.8319	+	14.9141i	−0.931522	+	0.537815i	−0.0442296	+	0.999021i	$0.514083\pi$
$770$	0.334043	−	0.192860i	0.0120381	−	0.00695018i
$771$	2.74040	−	4.74651i	0.0986931	−	0.170941i
$772$	10.6118	−	6.12674i	0.381928	−	0.220506i
$773$	−6.68609			−0.240482			−0.120241	−	0.992745i	$-0.538367\pi$
$773$	−6.68609			−0.240482			−0.120241	+	0.992745i	$0.538367\pi$
$774$	−2.44658	−	4.23761i	−0.0879406	−	0.152318i
$775$	6.53015	+	11.3106i	0.234570	+	0.406287i
$776$	−2.94614	−	5.10286i	−0.105760	−	0.183182i
$777$		−	36.2126i		−	1.29912i
$778$	2.43541			0.0873136
$779$	−1.22182	+	2.11625i	−0.0437762	+	0.0758226i
$780$	0.395342	−	0.228251i	0.0141555	−	0.00817269i
$781$	−9.70640	−	16.8120i	−0.347322	−	0.601580i
$782$	−1.50751	−	0.870361i	−0.0539084	−	0.0311240i
$783$	−8.68667	+	15.0458i	−0.310436	+	0.537691i
$784$	−12.3636			−0.441556
$785$	0.262099	+	0.453969i	0.00935473	+	0.0162029i
$786$	7.59536			0.270918
$787$	−18.3482	−	10.5933i	−0.654042	−	0.377611i	0.135961	−	0.990714i	$-0.456588\pi$
$787$	−18.3482	−	10.5933i	−0.654042	−	0.377611i	−0.790003	+	0.613103i	$0.789921\pi$
$788$	1.92748	−	1.11283i	0.0686635	−	0.0396429i
$789$	8.62166	−	14.9332i	0.306939	−	0.531634i
$790$	0.111970			0.00398371
$791$	14.6601	−	25.3920i	0.521253	−	0.902836i
$792$	−5.95390	−	10.3125i	−0.211563	−	0.366437i
$793$	27.9518	+	48.4140i	0.992599	+	1.71923i
$794$	14.0898	−	8.13473i	0.500027	−	0.288691i
$795$	0.447679	−	0.258468i	0.0158775	−	0.00916690i
$796$		−	32.7210i		−	1.15977i
$797$	−1.08770	+	0.627981i	−0.0385281	+	0.0222442i	−0.519140	−	0.854689i	$-0.673748\pi$
$797$	−1.08770	+	0.627981i	−0.0385281	+	0.0222442i	0.480612	+	0.876933i	$0.340414\pi$
$798$	7.55887			0.267581
$799$		−	35.8011i		−	1.26655i
$800$			27.9360i			0.987688i
$801$			26.7796i			0.946212i
$802$	−7.48677	−	12.9675i	−0.264367	−	0.457897i
$803$	3.25217	+	1.87764i	0.114766	+	0.0662605i
$804$	0.450407	+	0.780128i	0.0158846	+	0.0275130i
$805$	−0.101319	+	0.0584968i	−0.00357104	+	0.00206174i
$806$	3.51030	−	6.08002i	0.123645	−	0.214160i
$807$	−2.16945	+	3.75760i	−0.0763684	+	0.132274i
$808$	−10.5820			−0.372273
$809$	−4.04643	+	7.00863i	−0.142265	+	0.246410i	−0.928349	−	0.371709i	$-0.878772\pi$
$809$	−4.04643	+	7.00863i	−0.142265	+	0.246410i	0.786084	+	0.618119i	$0.212105\pi$
$810$	0.0498874	+	0.0288025i	0.00175287	+	0.00101202i
$811$	−10.3681	+	5.98601i	−0.364072	+	0.210197i	−0.670866	−	0.741579i	$-0.734077\pi$
$811$	−10.3681	+	5.98601i	−0.364072	+	0.210197i	0.306793	+	0.951776i	$0.400744\pi$
$812$	18.3429	+	10.5903i	0.643708	+	0.371645i
$813$	27.3257			0.958353
$814$	−8.09929	−	14.0284i	−0.283880	−	0.491695i
$815$	−1.19369	−	0.689180i	−0.0418133	−	0.0241409i
$816$	10.8566			0.380058
$817$	−11.6927	+	6.75078i	−0.409076	+	0.236180i
$818$	−10.8936	+	6.28941i	−0.380885	+	0.219904i
$819$	33.2971			1.16349
$820$	−0.0376905	−	0.0652818i	−0.00131621	−	0.00227974i
$821$	−3.19083	+	5.52668i	−0.111361	+	0.192883i	−0.916319	−	0.400449i	$-0.868854\pi$
$821$	−3.19083	+	5.52668i	−0.111361	+	0.192883i	0.804958	+	0.593331i	$0.202188\pi$
$822$	−2.44355	+	4.23236i	−0.0852287	+	0.147620i
$823$	−33.0111			−1.15069			−0.575347	−	0.817909i	$-0.695133\pi$
$823$	−33.0111			−1.15069			−0.575347	+	0.817909i	$0.695133\pi$
$824$	−31.2119			−1.08732
$825$		−	12.6224i		−	0.439456i
$826$	12.8508	−	7.41939i	0.447135	−	0.258154i
$827$	32.9396	−	19.0177i	1.14542	−	0.661309i	0.197654	−	0.980272i	$-0.436668\pi$
$827$	32.9396	−	19.0177i	1.14542	−	0.661309i	0.947767	+	0.318962i	$0.103334\pi$
$828$	0.810027	+	1.40301i	0.0281504	+	0.0487579i
$829$		−	34.0552i		−	1.18279i	−0.806384	−	0.591393i	$-0.798578\pi$
$829$		−	34.0552i		−	1.18279i	0.806384	−	0.591393i	$-0.201422\pi$
$830$	0.463158	−	0.267404i	0.0160764	−	0.00928173i
$831$		−	22.1014i		−	0.766689i
$832$	−1.46028	+	0.843095i	−0.0506262	+	0.0292291i
$833$	−19.1870	+	33.2328i	−0.664789	+	1.15145i
$834$		−	6.31966i		−	0.218832i
$835$	−0.749262	−	0.432586i	−0.0259293	−	0.0149703i
$836$	−12.7633	+	7.36890i	−0.441428	+	0.254859i
$837$	12.8209			0.443156
$838$	14.0937	+	8.13697i	0.486857	+	0.281087i
$839$	−24.9244	−	14.3901i	−0.860485	−	0.496801i	0.00368984	−	0.999993i	$-0.498825\pi$
$839$	−24.9244	−	14.3901i	−0.860485	−	0.496801i	−0.864175	+	0.503192i	$0.832159\pi$
$840$	−0.259923	+	0.450200i	−0.00896821	+	0.0155334i
$841$	8.22493	+	14.2460i	0.283618	+	0.491241i
$842$	1.37633	−	2.38387i	0.0474313	−	0.0821535i
$843$	4.25019	+	7.36155i	0.146384	+	0.253545i
$844$			27.8916i			0.960068i
$845$	0.208263	+	0.360722i	0.00716447	+	0.0124092i
$846$	3.82216	−	6.62017i	0.131408	−	0.227606i
$847$	−13.3700	+	7.71920i	−0.459400	+	0.265235i
$848$	−13.3237	+	7.69243i	−0.457537	+	0.264159i
$849$	−2.52648	+	4.37599i	−0.0867084	+	0.150183i
$850$	15.5863	+	8.99877i	0.534607	+	0.308655i
$851$	2.45662	+	4.25499i	0.0842119	+	0.145859i
$852$	10.1632	+	5.86772i	0.348185	+	0.201025i
$853$	−14.1032	+	24.4275i	−0.482884	+	0.836380i	−0.999807	−	0.0196519i	$-0.993744\pi$
$853$	−14.1032	+	24.4275i	−0.482884	+	0.836380i	0.516922	+	0.856032i	$0.327078\pi$
$854$	−24.7292	−	14.2774i	−0.846217	−	0.488564i
$855$	0.235887	−	0.408568i	0.00806715	−	0.0139727i
$856$	8.06874	+	13.9755i	0.275784	+	0.477672i
$857$	27.4094	+	15.8248i	0.936288	+	0.540566i	0.888795	−	0.458305i	$-0.151543\pi$
$857$	27.4094	+	15.8248i	0.936288	+	0.540566i	0.0474933	+	0.998872i	$0.484877\pi$
$858$	−5.87617	+	3.39261i	−0.200609	+	0.115822i
$859$	9.12093	+	5.26597i	0.311202	+	0.179673i	0.647464	−	0.762096i	$-0.275830\pi$
$859$	9.12093	+	5.26597i	0.311202	+	0.179673i	−0.336262	+	0.941768i	$0.609163\pi$
$860$		−	0.416494i		−	0.0142023i
$861$			2.50476i			0.0853620i
$862$	−7.64019	+	13.2332i	−0.260226	+	0.450725i
$863$	12.4957	−	7.21437i	0.425357	−	0.245580i	−0.272010	−	0.962295i	$-0.587688\pi$
$863$	12.4957	−	7.21437i	0.425357	−	0.245580i	0.697367	+	0.716715i	$0.254355\pi$
$864$	23.7499	+	13.7120i	0.807988	+	0.466492i
$865$		−	1.57260i		−	0.0534700i
$866$	22.2370			0.755645
$867$	8.61200	−	14.9164i	0.292479	−	0.506588i
$868$		−	15.6305i		−	0.530534i
$869$	7.25405			0.246077
$870$	0.119653	−	0.0690819i	0.00405663	−	0.00234210i
$871$	−2.17546	+	1.25600i	−0.0737126	+	0.0425580i
$872$	15.9066	+	9.18369i	0.538666	+	0.310999i
$873$	4.74680	+	2.74057i	0.160655	+	0.0927542i
$874$	−0.888169	+	0.512785i	−0.0300428	+	0.0173452i
$875$	2.09602	−	1.21014i	0.0708584	−	0.0409101i
$876$	−2.27014			−0.0767010
$877$		−	45.0171i		−	1.52012i	−0.649853	−	0.760060i	$-0.725169\pi$
$877$		−	45.0171i		−	1.52012i	0.649853	−	0.760060i	$-0.274831\pi$
$878$	8.83276	−	15.2988i	0.298091	−	0.516309i
$879$	−15.9941			−0.539467
$880$		−	0.326396i		−	0.0110028i
$881$	34.2226	+	19.7584i	1.15299	+	0.665679i	0.949614	−	0.313422i	$-0.101475\pi$
$881$	34.2226	+	19.7584i	1.15299	+	0.665679i	0.203376	+	0.979101i	$0.434809\pi$
$882$	−7.09592	+	4.09683i	−0.238932	+	0.137948i
$883$	14.2338	−	24.6536i	0.479004	−	0.829660i	−0.520706	−	0.853736i	$-0.674331\pi$
$883$	14.2338	−	24.6536i	0.479004	−	0.829660i	0.999710	+	0.0240762i	$0.00766444\pi$
$884$			42.1689i			1.41829i
$885$			0.421905i			0.0141822i
$886$	−9.64951	−	5.57115i	−0.324182	−	0.187166i
$887$	−24.8701	+	14.3588i	−0.835057	+	0.482120i	−0.855581	−	0.517669i	$-0.826800\pi$
$887$	−24.8701	+	14.3588i	−0.835057	+	0.482120i	0.0205242	+	0.999789i	$0.493466\pi$
$888$	18.9065	+	10.9157i	0.634461	+	0.366306i
$889$	−29.9296	−	51.8396i	−1.00381	−	1.73864i
$890$	0.261478	−	0.452894i	0.00876477	−	0.0151810i
$891$	3.23199	+	1.86599i	0.108276	+	0.0625131i
$892$	18.3917	−	31.8553i	0.615798	−	1.06659i
$893$	−18.2668	−	10.5464i	−0.611276	−	0.352920i
$894$	−6.39619	−	11.0785i	−0.213920	−	0.370521i
$895$	0.850325	+	0.490935i	0.0284232	+	0.0164102i
$896$	20.9828	−	36.3432i	0.700985	−	1.21414i
$897$	1.78232	−	1.02902i	0.0595099	−	0.0343580i
$898$	14.9617	−	8.63816i	0.499279	−	0.288259i
$899$	−4.63079	+	8.02076i	−0.154445	+	0.267507i
$900$	−8.37497	−	14.5059i	−0.279166	−	0.483529i
$901$			47.7514i			1.59083i
$902$	0.560213	+	0.970317i	0.0186530	+	0.0323080i
$903$	−6.91964	+	11.9852i	−0.230271	+	0.398841i
$904$	8.83808	+	15.3080i	0.293950	+	0.509136i
$905$	0.350383	−	0.606881i	0.0116471	−	0.0201734i
$906$	1.44255	+	0.832854i	0.0479254	+	0.0276697i
$907$	35.5314	+	20.5141i	1.17980	+	0.681159i	0.955969	−	0.293468i	$-0.0948096\pi$
$907$	35.5314	+	20.5141i	1.17980	+	0.681159i	0.223833	+	0.974627i	$0.428143\pi$
$908$	48.2302			1.60058
$909$	8.52482	−	4.92181i	0.282750	−	0.163246i
$910$	−0.563116	−	0.325115i	−0.0186671	−	0.0107775i
$911$			5.53633i			0.183427i	0.995785	+	0.0917135i	$0.0292344\pi$
$911$			5.53633i			0.183427i	−0.995785	+	0.0917135i	$0.970766\pi$
$912$	3.19816	−	5.53938i	0.105902	−	0.183427i
$913$	30.0060	−	17.3240i	0.993054	−	0.573340i
$914$			5.81856i			0.192461i
$915$	0.703117	−	0.405945i	0.0232443	−	0.0134201i
$916$			5.43495i			0.179576i
$917$	23.5777	+	40.8378i	0.778604	+	1.34858i
$918$	15.3006	−	8.83383i	0.504997	−	0.291560i
$919$	−24.5474	+	14.1724i	−0.809744	+	0.467506i	−0.846867	−	0.531805i	$-0.821514\pi$
$919$	−24.5474	+	14.1724i	−0.809744	+	0.467506i	0.0371230	+	0.999311i	$0.488181\pi$
$920$		−	0.0705315i		−	0.00232536i
$921$	−3.91059			−0.128858
$922$	−19.6014			−0.645537
$923$	−16.3627	+	28.3410i	−0.538584	+	0.932855i
$924$	−7.55321	+	13.0826i	−0.248483	+	0.430384i
$925$	−25.3993	−	43.9929i	−0.835124	−	1.44648i
$926$	−17.7171			−0.582221
$927$	25.1442	−	14.5170i	0.825844	−	0.476801i
$928$	−17.1564	+	9.90527i	−0.563188	+	0.325157i
$929$	−12.2803			−0.402902			−0.201451	−	0.979499i	$-0.564566\pi$
$929$	−12.2803			−0.402902			−0.201451	+	0.979499i	$0.564566\pi$
$930$	−0.0883002	−	0.0509801i	−0.00289548	−	0.00167170i
$931$	11.3043	+	19.5796i	0.370482	+	0.641694i
$932$	−30.5131			−0.999491
$933$	−11.9716	−	6.91183i	−0.391934	−	0.226283i
$934$	5.13993	−	2.96754i	0.168184	−	0.0971008i
$935$	−0.877341	−	0.506533i	−0.0286921	−	0.0165654i
$936$	−10.0368	+	17.3843i	−0.328065	+	0.568225i
$937$	−21.7065			−0.709121			−0.354561	−	0.935033i	$-0.615370\pi$
$937$	−21.7065			−0.709121			−0.354561	+	0.935033i	$0.615370\pi$
$938$	0.641549	−	1.11120i	0.0209473	−	0.0362818i
$939$	−5.26829	+	9.12494i	−0.171924	+	0.297781i
$940$	0.563493	−	0.325333i	0.0183791	−	0.0106112i
$941$	22.3654	+	38.7380i	0.729090	+	1.26282i	0.957268	+	0.289202i	$0.0933900\pi$
$941$	22.3654	+	38.7380i	0.729090	+	1.26282i	−0.228178	+	0.973620i	$0.573277\pi$
$942$	4.07905	+	2.35504i	0.132903	+	0.0767313i
$943$	−0.169920	−	0.294310i	−0.00553335	−	0.00958405i
$944$		−	12.5566i		−	0.408683i
$945$		−	1.18744i		−	0.0386275i
$946$			6.19057i			0.201273i
$947$	26.0635			0.846951			0.423476	−	0.905907i	$-0.360810\pi$
$947$	26.0635			0.846951			0.423476	+	0.905907i	$0.360810\pi$
$948$	−3.79771	+	2.19261i	−0.123344	+	0.0712127i
$949$		−	6.33050i		−	0.205497i
$950$	9.18290	−	5.30175i	0.297932	−	0.172011i
$951$	−1.51375	+	0.873967i	−0.0490869	+	0.0283403i
$952$	−24.0102	−	41.5868i	−0.778174	−	1.34784i
$953$	30.4249	+	52.6974i	0.985558	+	1.70704i	0.639432	+	0.768848i	$0.279170\pi$
$953$	30.4249	+	52.6974i	0.985558	+	1.70704i	0.346126	+	0.938188i	$0.387497\pi$
$954$	−5.09798	+	8.82996i	−0.165053	+	0.285880i
$955$	−0.751962			−0.0243329
$956$	−8.74868	+	15.1532i	−0.282953	+	0.490088i
$957$	7.75184	−	4.47553i	0.250581	−	0.144673i
$958$	7.46039	+	4.30726i	0.241034	+	0.139161i
$959$	−30.3413			−0.979773
$960$	0.0122443	+	0.0212077i	0.000395182	+	0.000684476i
$961$	−24.1653			−0.779525
$962$	−13.6535	+	23.6485i	−0.440205	+	0.762458i
$963$	−13.0003	−	7.50574i	−0.418929	−	0.241869i
$964$	−12.1147	−	20.9833i	−0.390188	−	0.675825i
$965$	0.429765	−	0.248125i	0.0138346	−	0.00798742i
$966$	−0.525611	+	0.910385i	−0.0169113	+	0.0292912i
$967$	−38.7856			−1.24726			−0.623631	−	0.781719i	$-0.714343\pi$
$967$	−38.7856			−1.24726			−0.623631	+	0.781719i	$0.714343\pi$
$968$		−	9.30730i		−	0.299148i
$969$	−9.92644	−	17.1931i	−0.318883	−	0.552322i
$970$	−0.0535182	−	0.0926963i	−0.00171837	−	0.00297630i
$971$	−7.81721	−	13.5398i	−0.250866	−	0.434513i	0.712898	−	0.701267i	$-0.247382\pi$
$971$	−7.81721	−	13.5398i	−0.250866	−	0.434513i	−0.963765	+	0.266754i	$0.914049\pi$
$972$	−26.1897			−0.840034
$973$	33.9788	−	19.6176i	1.08931	−	0.628913i
$974$	−0.513237	+	0.888953i	−0.0164452	+	0.0284839i
$975$	−18.4276	+	10.6392i	−0.590156	+	0.340727i
$976$	−20.9259	+	12.0816i	−0.669823	+	0.386722i
$977$	−22.8855	−	39.6388i	−0.732172	−	1.26816i	−0.955953	−	0.293519i	$-0.905173\pi$
$977$	−22.8855	−	39.6388i	−0.732172	−	1.26816i	0.223781	−	0.974639i	$-0.428160\pi$
$978$	−12.3850			−0.396028
$979$	16.9401	−	29.3411i	0.541407	−	0.937744i
$980$	−0.697425			−0.0222784
$981$	−17.0858			−0.545507
$982$		−	0.211057i		−	0.00673510i
$983$	−23.0664			−0.735704			−0.367852	−	0.929884i	$-0.619907\pi$
$983$	−23.0664			−0.735704			−0.367852	+	0.929884i	$0.619907\pi$
$984$	−1.30773	−	0.755018i	−0.0416889	−	0.0240691i
$985$	0.0780603	−	0.0450681i	0.00248721	−	0.00143599i
$986$			12.7628i			0.406449i
$987$	−21.6203			−0.688182
$988$	21.5159	+	12.4222i	0.684511	+	0.395203i
$989$		−	1.87768i		−	0.0597067i
$990$	−0.108156	−	0.187331i	−0.00343742	−	0.00595378i
$991$	12.0487	+	20.8690i	0.382740	+	0.662926i	0.991453	−	0.130465i	$-0.0416471\pi$
$991$	12.0487	+	20.8690i	0.382740	+	0.662926i	−0.608713	+	0.793391i	$0.708314\pi$
$992$	12.6609	+	7.30975i	0.401983	+	0.232085i
$993$	18.4094	−	10.6286i	0.584203	−	0.337290i
$994$		−	16.7157i		−	0.530189i
$995$		−	1.32516i		−	0.0420104i
$996$	−10.4727	+	18.1393i	−0.331840	+	0.574764i
$997$	44.7610	+	25.8428i	1.41760	+	0.818450i	0.996087	−	0.0883747i	$-0.0281673\pi$
$997$	44.7610	+	25.8428i	1.41760	+	0.818450i	0.421509	+	0.906824i	$0.361501\pi$
$998$	12.7392	−	22.0649i	0.403252	−	0.698453i
$999$	−49.8675			−1.57774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.13	✓	58
349.227	even	6	inner	349.2.e.a.227.13	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.13	✓	58	1.1	even	1	trivial
349.2.e.a.227.13	yes	58	349.227	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} +O(q^{10})\)	\(q+(-0.529073 + 0.305460i) q^{2} +(0.484492 - 0.839165i) q^{3} +(-0.813388 + 1.40883i) q^{4} +(-0.0329412 + 0.0570558i) q^{5} +0.591972i q^{6} +(-3.18284 + 1.83761i) q^{7} -2.21567i q^{8} +(1.03054 + 1.78494i) q^{9} -0.0402489i q^{10} -2.60755i q^{11} +(0.788160 + 1.36513i) q^{12} +(-3.80680 + 2.19786i) q^{13} +(1.12264 - 1.94446i) q^{14} +(0.0319195 + 0.0552861i) q^{15} +(-0.949976 - 1.64541i) q^{16} -5.89706 q^{17} +(-1.09046 - 0.629575i) q^{18} +(-1.73717 + 3.00886i) q^{19} +(-0.0535879 - 0.0928170i) q^{20} +3.56124i q^{21} +(0.796504 + 1.37959i) q^{22} +(-0.241590 - 0.418446i) q^{23} +(-1.85931 - 1.07348i) q^{24} +(2.49783 + 4.32637i) q^{25} +(1.34271 - 2.32565i) q^{26} +4.90410 q^{27} -5.97877i q^{28} +(-1.77131 + 3.06800i) q^{29} +(-0.0337754 - 0.0195003i) q^{30} +2.61433 q^{31} +(4.84287 + 2.79603i) q^{32} +(-2.18817 - 1.26334i) q^{33} +(3.11997 - 1.80132i) q^{34} -0.242133i q^{35} -3.35290 q^{36} -10.1686 q^{37} -2.12254i q^{38} +4.25937i q^{39} +(0.126417 + 0.0729868i) q^{40} +0.703340 q^{41} +(-1.08782 - 1.88415i) q^{42} +(3.36545 + 1.94304i) q^{43} +(3.67360 + 2.12095i) q^{44} -0.135788 q^{45} +(0.255637 + 0.147592i) q^{46} +6.07101i q^{47} -1.84102 q^{48} +(3.25365 - 5.63549i) q^{49} +(-2.64307 - 1.52598i) q^{50} +(-2.85708 + 4.94860i) q^{51} -7.15084i q^{52} -8.09749i q^{53} +(-2.59462 + 1.49801i) q^{54} +(0.148776 + 0.0858958i) q^{55} +(4.07155 + 7.05213i) q^{56} +(1.68329 + 2.91554i) q^{57} -2.16426i q^{58} +(5.72348 + 3.30445i) q^{59} -0.103852 q^{60} -12.7178i q^{61} +(-1.38317 + 0.798574i) q^{62} +(-6.56006 - 3.78745i) q^{63} +0.383599 q^{64} -0.289600i q^{65} +1.54360 q^{66} +0.571467 q^{67} +(4.79660 - 8.30795i) q^{68} -0.468194 q^{69} +(0.0739619 + 0.128106i) q^{70} +(6.44742 - 3.72242i) q^{71} +(3.95484 - 2.28333i) q^{72} +(-0.720077 + 1.24721i) q^{73} +(5.37990 - 3.10609i) q^{74} +4.84071 q^{75} +(-2.82598 - 4.89474i) q^{76} +(4.79168 + 8.29943i) q^{77} +(-1.30107 - 2.25352i) q^{78} +2.78194i q^{79} +0.125173 q^{80} +(-0.715611 + 1.23947i) q^{81} +(-0.372118 + 0.214842i) q^{82} +(6.64377 + 11.5073i) q^{83} +(-5.01718 - 2.89667i) q^{84} +(0.194256 - 0.336461i) q^{85} -2.37409 q^{86} +(1.71637 + 2.97284i) q^{87} -5.77748 q^{88} +(11.2523 + 6.49654i) q^{89} +(0.0718418 - 0.0414779i) q^{90} +(8.07762 - 13.9908i) q^{91} +0.786026 q^{92} +(1.26662 - 2.19385i) q^{93} +(-1.85445 - 3.21201i) q^{94} +(-0.114449 - 0.198231i) q^{95} +(4.69266 - 2.70931i) q^{96} +(2.30308 - 1.32968i) q^{97} +3.97544i q^{98} +(4.65432 - 2.68718i) 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

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