LMFDB - Embedded newform 861.2.i.d.247.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 15 x^{14} - 28 x^{13} + 109 x^{12} - 189 x^{11} + 440 x^{10} - 432 x^{9} + 636 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 15x^14 - 28x^13 + 109x^12 - 189x^11 + 440x^10 - 432x^9 + 636x^8 - 311x^7 + 565x^6 - 129x^5 + 284x^4 + 118x^3 + 56x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.4
Root			$-0.0845397 + 0.146427i$ of defining polynomial
Character	$\chi$	$=$	861.247
Dual form			861.2.i.d.739.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813090 + 1.40831i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.322231 - 0.558120i) q^{4} +(0.836813 - 1.44940i) q^{5} -1.62618 q^{6} +(1.95458 - 1.78315i) q^{7} -2.20435 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.813090 + 1.40831i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.322231 - 0.558120i) q^{4} +(0.836813 - 1.44940i) q^{5} -1.62618 q^{6} +(1.95458 - 1.78315i) q^{7} -2.20435 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36081 + 2.35699i) q^{10} +(-1.36252 - 2.35996i) q^{11} +(0.322231 - 0.558120i) q^{12} +2.59232 q^{13} +(0.921986 + 4.20252i) q^{14} +1.67363 q^{15} +(2.43680 - 4.22066i) q^{16} +(1.24728 + 2.16034i) q^{17} +(-0.813090 - 1.40831i) q^{18} +(-0.382700 + 0.662855i) q^{19} -1.07859 q^{20} +(2.52154 + 0.801139i) q^{21} +4.43142 q^{22} +(-0.775573 + 1.34333i) q^{23} +(-1.10217 - 1.90902i) q^{24} +(1.09949 + 1.90437i) q^{25} +(-2.10779 + 3.65079i) q^{26} -1.00000 q^{27} +(-1.62504 - 0.516304i) q^{28} +9.11743 q^{29} +(-1.36081 + 2.35699i) q^{30} +(4.13457 + 7.16129i) q^{31} +(1.75832 + 3.04550i) q^{32} +(1.36252 - 2.35996i) q^{33} -4.05659 q^{34} +(-0.948886 - 4.32513i) q^{35} +0.644462 q^{36} +(1.60751 - 2.78429i) q^{37} +(-0.622339 - 1.07792i) q^{38} +(1.29616 + 2.24501i) q^{39} +(-1.84463 + 3.19499i) q^{40} -1.00000 q^{41} +(-3.17850 + 2.89972i) q^{42} +11.8356 q^{43} +(-0.878094 + 1.52090i) q^{44} +(0.836813 + 1.44940i) q^{45} +(-1.26122 - 2.18450i) q^{46} +(2.90556 - 5.03259i) q^{47} +4.87359 q^{48} +(0.640750 - 6.97061i) q^{49} -3.57593 q^{50} +(-1.24728 + 2.16034i) q^{51} +(-0.835325 - 1.44682i) q^{52} +(2.29593 + 3.97668i) q^{53} +(0.813090 - 1.40831i) q^{54} -4.56071 q^{55} +(-4.30857 + 3.93069i) q^{56} -0.765400 q^{57} +(-7.41329 + 12.8402i) q^{58} +(-2.38652 - 4.13357i) q^{59} +(-0.539294 - 0.934085i) q^{60} +(-0.433698 + 0.751187i) q^{61} -13.4471 q^{62} +(0.566964 + 2.58429i) q^{63} +4.02849 q^{64} +(2.16928 - 3.75731i) q^{65} +(2.21571 + 3.83772i) q^{66} +(-1.94684 - 3.37202i) q^{67} +(0.803821 - 1.39226i) q^{68} -1.55115 q^{69} +(6.86267 + 2.18039i) q^{70} -10.6283 q^{71} +(1.10217 - 1.90902i) q^{72} +(1.11972 + 1.93942i) q^{73} +(2.61410 + 4.52776i) q^{74} +(-1.09949 + 1.90437i) q^{75} +0.493271 q^{76} +(-6.87132 - 2.18314i) q^{77} -4.21557 q^{78} +(-4.05221 + 7.01864i) q^{79} +(-4.07829 - 7.06380i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.813090 - 1.40831i) q^{82} -8.58566 q^{83} +(-0.365387 - 1.66548i) q^{84} +4.17495 q^{85} +(-9.62343 + 16.6683i) q^{86} +(4.55871 + 7.89592i) q^{87} +(3.00348 + 5.20217i) q^{88} +(0.628086 - 1.08788i) q^{89} -2.72162 q^{90} +(5.06688 - 4.62249i) q^{91} +0.999655 q^{92} +(-4.13457 + 7.16129i) q^{93} +(4.72497 + 8.18389i) q^{94} +(0.640496 + 1.10937i) q^{95} +(-1.75832 + 3.04550i) q^{96} -8.55514 q^{97} +(9.29582 + 6.57011i) q^{98} +2.72505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 8 q^{3} - 13 q^{4} + 7 q^{5} - 2 q^{6} + 9 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 + 8 * q^3 - 13 * q^4 + 7 * q^5 - 2 * q^6 + 9 * q^7 + 12 * q^8 - 8 * q^9	\( 16 q - q^{2} + 8 q^{3} - 13 q^{4} + 7 q^{5} - 2 q^{6} + 9 q^{7} + 12 q^{8} - 8 q^{9} + 8 q^{10} - 11 q^{11} + 13 q^{12} - 20 q^{13} + q^{14} + 14 q^{15} + 17 q^{16} + 3 q^{17} - q^{18} + 6 q^{19} - 22 q^{20} - 9 q^{21} + 30 q^{22} - 14 q^{23} + 6 q^{24} - 25 q^{25} + 24 q^{26} - 16 q^{27} + 20 q^{28} + 4 q^{29} - 8 q^{30} + 16 q^{31} - 3 q^{32} + 11 q^{33} + 8 q^{34} + q^{35} + 26 q^{36} + 20 q^{37} + 10 q^{38} - 10 q^{39} - 3 q^{40} - 16 q^{41} - 4 q^{42} + 14 q^{43} + 7 q^{45} + 5 q^{46} + 14 q^{47} + 34 q^{48} + 13 q^{49} - 10 q^{50} - 3 q^{51} + 23 q^{52} - 7 q^{53} + q^{54} - 96 q^{55} + 51 q^{56} + 12 q^{57} + 20 q^{58} + 22 q^{59} - 11 q^{60} + 66 q^{62} - 18 q^{63} - 20 q^{64} + 14 q^{65} + 15 q^{66} - 12 q^{67} - 27 q^{68} - 28 q^{69} + 61 q^{70} - 10 q^{71} - 6 q^{72} + 2 q^{73} - 6 q^{74} + 25 q^{75} - 86 q^{76} - 3 q^{77} + 48 q^{78} + 15 q^{79} - 7 q^{80} - 8 q^{81} + q^{82} - 30 q^{83} + 34 q^{84} - 86 q^{85} - 31 q^{86} + 2 q^{87} - 17 q^{88} + 29 q^{89} - 16 q^{90} - 18 q^{91} + 38 q^{92} - 16 q^{93} + 20 q^{94} - 14 q^{95} + 3 q^{96} - 38 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) \) 16 * q - q^2 + 8 * q^3 - 13 * q^4 + 7 * q^5 - 2 * q^6 + 9 * q^7 + 12 * q^8 - 8 * q^9 + 8 * q^10 - 11 * q^11 + 13 * q^12 - 20 * q^13 + q^14 + 14 * q^15 + 17 * q^16 + 3 * q^17 - q^18 + 6 * q^19 - 22 * q^20 - 9 * q^21 + 30 * q^22 - 14 * q^23 + 6 * q^24 - 25 * q^25 + 24 * q^26 - 16 * q^27 + 20 * q^28 + 4 * q^29 - 8 * q^30 + 16 * q^31 - 3 * q^32 + 11 * q^33 + 8 * q^34 + q^35 + 26 * q^36 + 20 * q^37 + 10 * q^38 - 10 * q^39 - 3 * q^40 - 16 * q^41 - 4 * q^42 + 14 * q^43 + 7 * q^45 + 5 * q^46 + 14 * q^47 + 34 * q^48 + 13 * q^49 - 10 * q^50 - 3 * q^51 + 23 * q^52 - 7 * q^53 + q^54 - 96 * q^55 + 51 * q^56 + 12 * q^57 + 20 * q^58 + 22 * q^59 - 11 * q^60 + 66 * q^62 - 18 * q^63 - 20 * q^64 + 14 * q^65 + 15 * q^66 - 12 * q^67 - 27 * q^68 - 28 * q^69 + 61 * q^70 - 10 * q^71 - 6 * q^72 + 2 * q^73 - 6 * q^74 + 25 * q^75 - 86 * q^76 - 3 * q^77 + 48 * q^78 + 15 * q^79 - 7 * q^80 - 8 * q^81 + q^82 - 30 * q^83 + 34 * q^84 - 86 * q^85 - 31 * q^86 + 2 * q^87 - 17 * q^88 + 29 * q^89 - 16 * q^90 - 18 * q^91 + 38 * q^92 - 16 * q^93 + 20 * q^94 - 14 * q^95 + 3 * q^96 - 38 * q^97 + 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.813090	+	1.40831i	−0.574942	+	0.995828i	0.421106	+	0.907011i	$0.361642\pi$
$2$	−0.813090	+	1.40831i	−0.574942	+	0.995828i	−0.996048	+	0.0888167i	$0.971691\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.322231	−	0.558120i	−0.161115	−	0.279060i
$5$	0.836813	−	1.44940i	0.374234	−	0.648193i	−0.615978	−	0.787763i	$-0.711239\pi$
$5$	0.836813	−	1.44940i	0.374234	−	0.648193i	0.990212	+	0.139571i	$0.0445723\pi$
$6$	−1.62618			−0.663885
$7$	1.95458	−	1.78315i	0.738761	−	0.673967i
$7$	1.95458	−	1.78315i	0.738761	−	0.673967i
$8$	−2.20435			−0.779355
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.36081	+	2.35699i	0.430326	+	0.745346i
$11$	−1.36252	−	2.35996i	−0.410816	−	0.711555i	0.584163	−	0.811636i	$-0.301423\pi$
$11$	−1.36252	−	2.35996i	−0.410816	−	0.711555i	−0.994979	+	0.100082i	$0.968090\pi$
$12$	0.322231	−	0.558120i	0.0930201	−	0.161115i
$13$	2.59232			0.718979			0.359490	−	0.933149i	$-0.382951\pi$
$13$	2.59232			0.718979			0.359490	+	0.933149i	$0.382951\pi$
$14$	0.921986	+	4.20252i	0.246411	+	1.12317i
$15$	1.67363			0.432128
$16$	2.43680	−	4.22066i	0.609199	−	1.05516i
$17$	1.24728	+	2.16034i	0.302509	+	0.523960i	0.976704	−	0.214593i	$-0.0688425\pi$
$17$	1.24728	+	2.16034i	0.302509	+	0.523960i	−0.674195	+	0.738554i	$0.735509\pi$
$18$	−0.813090	−	1.40831i	−0.191647	−	0.331943i
$19$	−0.382700	+	0.662855i	−0.0877974	+	0.152069i	−0.906580	−	0.422034i	$-0.861316\pi$
$19$	−0.382700	+	0.662855i	−0.0877974	+	0.152069i	0.818782	+	0.574104i	$0.194649\pi$
$20$	−1.07859			−0.241180
$21$	2.52154	+	0.801139i	0.550246	+	0.174823i
$22$	4.43142			0.944781
$23$	−0.775573	+	1.34333i	−0.161718	+	0.280104i	−0.935485	−	0.353366i	$-0.885037\pi$
$23$	−0.775573	+	1.34333i	−0.161718	+	0.280104i	0.773767	+	0.633471i	$0.218370\pi$
$24$	−1.10217	−	1.90902i	−0.224980	−	0.389678i
$25$	1.09949	+	1.90437i	0.219898	+	0.380874i
$26$	−2.10779	+	3.65079i	−0.413371	+	0.715979i
$27$	−1.00000			−0.192450
$28$	−1.62504	−	0.516304i	−0.307103	−	0.0975722i
$29$	9.11743			1.69306			0.846532	−	0.532338i	$-0.178687\pi$
$29$	9.11743			1.69306			0.846532	+	0.532338i	$0.178687\pi$
$30$	−1.36081	+	2.35699i	−0.248449	+	0.430326i
$31$	4.13457	+	7.16129i	0.742591	+	1.28621i	0.951312	+	0.308230i	$0.0997367\pi$
$31$	4.13457	+	7.16129i	0.742591	+	1.28621i	−0.208721	+	0.977975i	$0.566930\pi$
$32$	1.75832	+	3.04550i	0.310830	+	0.538374i
$33$	1.36252	−	2.35996i	0.237185	−	0.410816i
$34$	−4.05659			−0.695699
$35$	−0.948886	−	4.32513i	−0.160391	−	0.731081i
$36$	0.644462			0.107410
$37$	1.60751	−	2.78429i	0.264273	−	0.457734i	−0.703100	−	0.711091i	$-0.748201\pi$
$37$	1.60751	−	2.78429i	0.264273	−	0.457734i	0.967373	+	0.253357i	$0.0815346\pi$
$38$	−0.622339	−	1.07792i	−0.100957	−	0.174862i
$39$	1.29616	+	2.24501i	0.207551	+	0.359490i
$40$	−1.84463	+	3.19499i	−0.291661	+	0.505172i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	−3.17850	+	2.89972i	−0.490453	+	0.447437i
$43$	11.8356			1.80492			0.902458	−	0.430778i	$-0.141761\pi$
$43$	11.8356			1.80492			0.902458	+	0.430778i	$0.141761\pi$
$44$	−0.878094	+	1.52090i	−0.132378	+	0.229285i
$45$	0.836813	+	1.44940i	0.124745	+	0.216064i
$46$	−1.26122	−	2.18450i	−0.185957	−	0.322087i
$47$	2.90556	−	5.03259i	0.423820	−	0.734078i	−0.572489	−	0.819912i	$-0.694022\pi$
$47$	2.90556	−	5.03259i	0.423820	−	0.734078i	0.996309	+	0.0858341i	$0.0273555\pi$
$48$	4.87359			0.703443
$49$	0.640750	−	6.97061i	0.0915358	−	0.995802i
$50$	−3.57593			−0.505713
$51$	−1.24728	+	2.16034i	−0.174653	+	0.302509i
$52$	−0.835325	−	1.44682i	−0.115839	−	0.200638i
$53$	2.29593	+	3.97668i	0.315371	+	0.546238i	0.979516	−	0.201365i	$-0.0645378\pi$
$53$	2.29593	+	3.97668i	0.315371	+	0.546238i	−0.664145	+	0.747603i	$0.731204\pi$
$54$	0.813090	−	1.40831i	0.110648	−	0.191647i
$55$	−4.56071			−0.614966
$56$	−4.30857	+	3.93069i	−0.575757	+	0.525260i
$57$	−0.765400			−0.101380
$58$	−7.41329	+	12.8402i	−0.973412	+	1.68600i
$59$	−2.38652	−	4.13357i	−0.310698	−	0.538145i	0.667815	−	0.744327i	$-0.267230\pi$
$59$	−2.38652	−	4.13357i	−0.310698	−	0.538145i	−0.978514	+	0.206182i	$0.933896\pi$
$60$	−0.539294	−	0.934085i	−0.0696226	−	0.120590i
$61$	−0.433698	+	0.751187i	−0.0555293	+	0.0961797i	−0.892454	−	0.451139i	$-0.851018\pi$
$61$	−0.433698	+	0.751187i	−0.0555293	+	0.0961797i	0.836925	+	0.547318i	$0.184351\pi$
$62$	−13.4471			−1.70779
$63$	0.566964	+	2.58429i	0.0714308	+	0.325590i
$64$	4.02849			0.503562
$65$	2.16928	−	3.75731i	0.269067	−	0.466037i
$66$	2.21571	+	3.83772i	0.272735	+	0.472391i
$67$	−1.94684	−	3.37202i	−0.237844	−	0.411958i	0.722251	−	0.691631i	$-0.243107\pi$
$67$	−1.94684	−	3.37202i	−0.237844	−	0.411958i	−0.960095	+	0.279673i	$0.909774\pi$
$68$	0.803821	−	1.39226i	0.0974777	−	0.168836i
$69$	−1.55115			−0.186736
$70$	6.86267	+	2.18039i	0.820247	+	0.260607i
$71$	−10.6283			−1.26135			−0.630675	−	0.776047i	$-0.717222\pi$
$71$	−10.6283			−1.26135			−0.630675	+	0.776047i	$0.717222\pi$
$72$	1.10217	−	1.90902i	0.129893	−	0.224980i
$73$	1.11972	+	1.93942i	0.131054	+	0.226992i	0.924083	−	0.382192i	$-0.124831\pi$
$73$	1.11972	+	1.93942i	0.131054	+	0.226992i	−0.793029	+	0.609183i	$0.791497\pi$
$74$	2.61410	+	4.52776i	0.303883	+	0.526341i
$75$	−1.09949	+	1.90437i	−0.126958	+	0.219898i
$76$	0.493271			0.0565821
$77$	−6.87132	−	2.18314i	−0.783060	−	0.248792i
$78$	−4.21557			−0.477320
$79$	−4.05221	+	7.01864i	−0.455910	+	0.789659i	−0.998740	−	0.0501836i	$-0.984019\pi$
$79$	−4.05221	+	7.01864i	−0.455910	+	0.789659i	0.542830	+	0.839842i	$0.317353\pi$
$80$	−4.07829	−	7.06380i	−0.455966	−	0.789757i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.813090	−	1.40831i	0.0897908	−	0.155522i
$83$	−8.58566			−0.942398			−0.471199	−	0.882027i	$-0.656179\pi$
$83$	−8.58566			−0.942398			−0.471199	+	0.882027i	$0.656179\pi$
$84$	−0.365387	−	1.66548i	−0.0398670	−	0.181718i
$85$	4.17495			0.452836
$86$	−9.62343	+	16.6683i	−1.03772	+	1.79739i
$87$	4.55871	+	7.89592i	0.488745	+	0.846532i
$88$	3.00348	+	5.20217i	0.320172	+	0.554554i
$89$	0.628086	−	1.08788i	0.0665770	−	0.115315i	−0.830815	−	0.556548i	$-0.812126\pi$
$89$	0.628086	−	1.08788i	0.0665770	−	0.115315i	0.897392	+	0.441233i	$0.145459\pi$
$90$	−2.72162			−0.286884
$91$	5.06688	−	4.62249i	0.531154	−	0.484569i
$92$	0.999655			0.104221
$93$	−4.13457	+	7.16129i	−0.428735	+	0.742591i
$94$	4.72497	+	8.18389i	0.487344	+	0.844104i
$95$	0.640496	+	1.10937i	0.0657135	+	0.113819i
$96$	−1.75832	+	3.04550i	−0.179458	+	0.310830i
$97$	−8.55514			−0.868643			−0.434322	−	0.900758i	$-0.643012\pi$
$97$	−8.55514			−0.868643			−0.434322	+	0.900758i	$0.643012\pi$
$98$	9.29582	+	6.57011i	0.939020	+	0.663682i
$99$	2.72505			0.273877
$100$	0.708578	−	1.22729i	0.0708578	−	0.122729i
$101$	0.654143	+	1.13301i	0.0650896	+	0.112739i	0.896734	−	0.442570i	$-0.145933\pi$
$101$	0.654143	+	1.13301i	0.0650896	+	0.112739i	−0.831644	+	0.555309i	$0.812600\pi$
$102$	−2.02829	−	3.51311i	−0.200831	−	0.347850i
$103$	7.90697	−	13.6953i	0.779097	−	1.34944i	−0.153365	−	0.988170i	$-0.549011\pi$
$103$	7.90697	−	13.6953i	0.779097	−	1.34944i	0.932463	−	0.361266i	$-0.117656\pi$
$104$	−5.71437			−0.560340
$105$	3.27123	−	2.98433i	0.319240	−	0.291240i
$106$	−7.46721			−0.725279
$107$	−3.32818	+	5.76458i	−0.321748	+	0.557283i	−0.980849	−	0.194771i	$-0.937604\pi$
$107$	−3.32818	+	5.76458i	−0.321748	+	0.557283i	0.659101	+	0.752054i	$0.270937\pi$
$108$	0.322231	+	0.558120i	0.0310067	+	0.0537052i
$109$	−3.31368	−	5.73947i	−0.317393	−	0.549741i	0.662550	−	0.749018i	$-0.269474\pi$
$109$	−3.31368	−	5.73947i	−0.317393	−	0.549741i	−0.979943	+	0.199276i	$0.936141\pi$
$110$	3.70827	−	6.42291i	0.353569	−	0.612400i
$111$	3.21502			0.305156
$112$	−2.76315	−	12.5948i	−0.261093	−	1.19009i
$113$	−17.6805			−1.66324			−0.831621	−	0.555343i	$-0.812587\pi$
$113$	−17.6805			−1.66324			−0.831621	+	0.555343i	$0.812587\pi$
$114$	0.622339	−	1.07792i	0.0582874	−	0.100957i
$115$	1.29802	+	2.24824i	0.121041	+	0.209649i
$116$	−2.93792	−	5.08862i	−0.272779	−	0.472467i
$117$	−1.29616	+	2.24501i	−0.119830	+	0.207551i
$118$	7.76182			0.714534
$119$	6.29011	+	1.99848i	0.576614	+	0.183201i
$120$	−3.68926			−0.336781
$121$	1.78706	−	3.09528i	0.162460	−	0.281389i
$122$	−0.705271	−	1.22157i	−0.0638523	−	0.110595i
$123$	−0.500000	−	0.866025i	−0.0450835	−	0.0780869i
$124$	2.66457	−	4.61518i	0.239286	−	0.414455i
$125$	12.0484			1.07764
$126$	−4.10048	−	1.30280i	−0.365300	−	0.116062i
$127$	−15.6503			−1.38874			−0.694371	−	0.719617i	$-0.744317\pi$
$127$	−15.6503			−1.38874			−0.694371	+	0.719617i	$0.744317\pi$
$128$	−6.79217	+	11.7644i	−0.600349	+	1.03983i
$129$	5.91781	+	10.2500i	0.521034	+	0.902458i
$130$	3.52765	+	6.11006i	0.309395	+	0.535888i
$131$	4.81405	−	8.33819i	0.420606	−	0.728511i	−0.575393	−	0.817877i	$-0.695151\pi$
$131$	4.81405	−	8.33819i	0.420606	−	0.728511i	0.995999	+	0.0893664i	$0.0284842\pi$
$132$	−1.75619			−0.152857
$133$	0.433954	+	1.97801i	0.0376286	+	0.171516i
$134$	6.33181			0.546985
$135$	−0.836813	+	1.44940i	−0.0720214	+	0.124745i
$136$	−2.74943	−	4.76215i	−0.235762	−	0.408351i
$137$	1.93964	+	3.35956i	0.165715	+	0.287026i	0.936909	−	0.349574i	$-0.113674\pi$
$137$	1.93964	+	3.35956i	0.165715	+	0.287026i	−0.771194	+	0.636600i	$0.780340\pi$
$138$	1.26122	−	2.18450i	0.107362	−	0.185957i
$139$	−12.8314			−1.08834			−0.544171	−	0.838975i	$-0.683156\pi$
$139$	−12.8314			−1.08834			−0.544171	+	0.838975i	$0.683156\pi$
$140$	−2.10819	+	1.92329i	−0.178174	+	0.162547i
$141$	5.81113			0.489385
$142$	8.64179	−	14.9680i	0.725203	−	1.25609i
$143$	−3.53209	−	6.11776i	−0.295368	−	0.511593i
$144$	2.43680	+	4.22066i	0.203066	+	0.351721i
$145$	7.62958	−	13.2148i	0.633602	−	1.09743i
$146$	−3.64174			−0.301393
$147$	6.35710	−	2.93040i	0.524325	−	0.241695i
$148$	−2.07196			−0.170314
$149$	−0.224360	+	0.388602i	−0.0183802	+	0.0318355i	−0.875069	−	0.483998i	$-0.839184\pi$
$149$	−0.224360	+	0.388602i	−0.0183802	+	0.0318355i	0.856689	+	0.515833i	$0.172518\pi$
$150$	−1.78797	−	3.09685i	−0.145987	−	0.252856i
$151$	1.78680	+	3.09482i	0.145408	+	0.251853i	0.929525	−	0.368759i	$-0.120217\pi$
$151$	1.78680	+	3.09482i	0.145408	+	0.251853i	−0.784117	+	0.620613i	$0.786884\pi$
$152$	0.843604	−	1.46116i	0.0684253	−	0.118516i
$153$	−2.49455			−0.201672
$154$	8.66155	−	7.90188i	0.697967	−	0.636752i
$155$	13.8395			1.11161
$156$	0.835325	−	1.44682i	0.0668795	−	0.115839i
$157$	4.45803	+	7.72154i	0.355790	+	0.616246i	0.987253	−	0.159160i	$-0.0508786\pi$
$157$	4.45803	+	7.72154i	0.355790	+	0.616246i	−0.631463	+	0.775406i	$0.717545\pi$
$158$	−6.58963	−	11.4136i	−0.524243	−	0.908015i
$159$	−2.29593	+	3.97668i	−0.182079	+	0.315371i
$160$	5.88554			0.465293
$161$	0.879445	+	4.00861i	0.0693100	+	0.315923i
$162$	1.62618			0.127765
$163$	12.2435	−	21.2063i	0.958984	−	1.66101i	0.234009	−	0.972234i	$-0.424815\pi$
$163$	12.2435	−	21.2063i	0.958984	−	1.66101i	0.724975	−	0.688775i	$-0.241851\pi$
$164$	0.322231	+	0.558120i	0.0251620	+	0.0435819i
$165$	−2.28035	−	3.94969i	−0.177525	−	0.307483i
$166$	6.98091	−	12.0913i	0.541824	−	0.938466i
$167$	−0.708918			−0.0548577			−0.0274289	−	0.999624i	$-0.508732\pi$
$167$	−0.708918			−0.0548577			−0.0274289	+	0.999624i	$0.508732\pi$
$168$	−5.55836	−	1.76599i	−0.428837	−	0.136249i
$169$	−6.27990			−0.483069
$170$	−3.39461	+	5.87963i	−0.260354	+	0.450947i
$171$	−0.382700	−	0.662855i	−0.0292658	−	0.0506898i
$172$	−3.81380	−	6.60570i	−0.290800	−	0.503680i
$173$	1.48939	−	2.57969i	0.113236	−	0.196130i	−0.803837	−	0.594849i	$-0.797212\pi$
$173$	1.48939	−	2.57969i	0.113236	−	0.196130i	0.917073	+	0.398719i	$0.130545\pi$
$174$	−14.8266			−1.12400
$175$	5.54481	+	1.76169i	0.419148	+	0.133171i
$176$	−13.2808			−1.00108
$177$	2.38652	−	4.13357i	0.179382	−	0.310698i
$178$	1.02138	+	1.76908i	0.0765557	+	0.132598i
$179$	10.4198	+	18.0476i	0.778810	+	1.34894i	0.932628	+	0.360839i	$0.117510\pi$
$179$	10.4198	+	18.0476i	0.778810	+	1.34894i	−0.153819	+	0.988099i	$0.549157\pi$
$180$	0.539294	−	0.934085i	0.0401966	−	0.0696226i
$181$	5.73956			0.426618			0.213309	−	0.976985i	$-0.431576\pi$
$181$	5.73956			0.426618			0.213309	+	0.976985i	$0.431576\pi$
$182$	2.39008	+	10.8943i	0.177165	+	0.807536i
$183$	−0.867396			−0.0641198
$184$	1.70963	−	2.96117i	0.126036	−	0.218301i
$185$	−2.69037	−	4.65986i	−0.197800	−	0.342600i
$186$	−6.72356	−	11.6455i	−0.492995	−	0.853893i
$187$	3.39888	−	5.88704i	0.248551	−	0.430503i
$188$	−3.74505			−0.273136
$189$	−1.95458	+	1.78315i	−0.142175	+	0.129705i
$190$	−2.08313			−0.151126
$191$	1.31853	−	2.28376i	0.0954055	−	0.165247i	−0.814372	−	0.580343i	$-0.802919\pi$
$191$	1.31853	−	2.28376i	0.0954055	−	0.165247i	0.909778	+	0.415096i	$0.136252\pi$
$192$	2.01425	+	3.48878i	0.145366	+	0.251781i
$193$	0.355971	+	0.616559i	0.0256233	+	0.0443809i	0.878553	−	0.477645i	$-0.158510\pi$
$193$	0.355971	+	0.616559i	0.0256233	+	0.0443809i	−0.852929	+	0.522026i	$0.825176\pi$
$194$	6.95610	−	12.0483i	0.499419	−	0.865019i
$195$	4.33857			0.310691
$196$	−4.09691	+	1.88853i	−0.292637	+	0.134895i
$197$	−17.2730			−1.23065			−0.615323	−	0.788275i	$-0.710975\pi$
$197$	−17.2730			−1.23065			−0.615323	+	0.788275i	$0.710975\pi$
$198$	−2.21571	+	3.83772i	−0.157464	+	0.272735i
$199$	1.75669	+	3.04268i	0.124529	+	0.215690i	0.921549	−	0.388263i	$-0.126925\pi$
$199$	1.75669	+	3.04268i	0.124529	+	0.215690i	−0.797020	+	0.603953i	$0.793591\pi$
$200$	−2.42365	−	4.19789i	−0.171378	−	0.296836i
$201$	1.94684	−	3.37202i	0.137319	−	0.237844i
$202$	−2.12751			−0.149691
$203$	17.8207	−	16.2577i	1.25077	−	1.14107i
$204$	1.60764			0.112558
$205$	−0.836813	+	1.44940i	−0.0584456	+	0.101231i
$206$	12.8582	+	22.2710i	0.895871	+	1.55169i
$207$	−0.775573	−	1.34333i	−0.0539061	−	0.0933681i
$208$	6.31695	−	10.9413i	0.438001	−	0.758641i
$209$	2.08575			0.144274
$210$	1.54306	+	7.03345i	0.106481	+	0.485354i
$211$	2.04162			0.140551			0.0702756	−	0.997528i	$-0.477612\pi$
$211$	2.04162			0.140551			0.0702756	+	0.997528i	$0.477612\pi$
$212$	1.47964	−	2.56282i	0.101622	−	0.176015i
$213$	−5.31416	−	9.20440i	−0.364121	−	0.630675i
$214$	−5.41222	−	9.37425i	−0.369972	−	0.640810i
$215$	9.90420	−	17.1546i	0.675461	−	1.16993i
$216$	2.20435			0.149987
$217$	20.8510	+	6.62473i	1.41546	+	0.449716i
$218$	10.7773			0.729930
$219$	−1.11972	+	1.93942i	−0.0756639	+	0.131054i
$220$	1.46960	+	2.54542i	0.0990805	+	0.171613i
$221$	3.23333	+	5.60029i	0.217497	+	0.376717i
$222$	−2.61410	+	4.52776i	−0.175447	+	0.303883i
$223$	−16.3846			−1.09719			−0.548597	−	0.836087i	$-0.684838\pi$
$223$	−16.3846			−1.09719			−0.548597	+	0.836087i	$0.684838\pi$
$224$	8.86736	+	2.81732i	0.592476	+	0.188240i
$225$	−2.19898			−0.146598
$226$	14.3758	−	24.8997i	0.956267	−	1.65630i
$227$	−14.9331	−	25.8649i	−0.991146	−	1.71671i	−0.610563	−	0.791967i	$-0.709057\pi$
$227$	−14.9331	−	25.8649i	−0.991146	−	1.71671i	−0.380582	−	0.924747i	$-0.624276\pi$
$228$	0.246635	+	0.427185i	0.0163338	+	0.0282910i
$229$	−12.1875	+	21.1094i	−0.805374	+	1.39495i	0.110664	+	0.993858i	$0.464702\pi$
$229$	−12.1875	+	21.1094i	−0.805374	+	1.39495i	−0.916038	+	0.401091i	$0.868631\pi$
$230$	−4.22163			−0.278366
$231$	−1.54500	−	7.04231i	−0.101654	−	0.463350i
$232$	−20.0980			−1.31950
$233$	−2.41885	+	4.18957i	−0.158464	+	0.274468i	−0.934315	−	0.356448i	$-0.883988\pi$
$233$	−2.41885	+	4.18957i	−0.158464	+	0.274468i	0.775851	+	0.630916i	$0.217321\pi$
$234$	−2.10779	−	3.65079i	−0.137790	−	0.238660i
$235$	−4.86283	−	8.42267i	−0.317216	−	0.549434i
$236$	−1.53802	+	2.66393i	−0.100117	+	0.173407i
$237$	−8.10443			−0.526439
$238$	−7.92892	+	7.23351i	−0.513955	+	0.468879i
$239$	−4.59128			−0.296985			−0.148493	−	0.988914i	$-0.547442\pi$
$239$	−4.59128			−0.296985			−0.148493	+	0.988914i	$0.547442\pi$
$240$	4.07829	−	7.06380i	0.263252	−	0.455966i
$241$	0.161012	+	0.278880i	0.0103717	+	0.0179643i	0.871165	−	0.490991i	$-0.163365\pi$
$241$	0.161012	+	0.278880i	0.0103717	+	0.0179643i	−0.860793	+	0.508955i	$0.830032\pi$
$242$	2.90608	+	5.03348i	0.186810	+	0.323565i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.559004			0.0357866
$245$	−9.56704	−	6.76181i	−0.611216	−	0.431996i
$246$	1.62618			0.103681
$247$	−0.992079	+	1.71833i	−0.0631245	+	0.109335i
$248$	−9.11404	−	15.7860i	−0.578742	−	1.00241i
$249$	−4.29283	−	7.43540i	−0.272047	−	0.471199i
$250$	−9.79643	+	16.9679i	−0.619581	+	1.07315i
$251$	8.39485			0.529878			0.264939	−	0.964265i	$-0.414648\pi$
$251$	8.39485			0.529878			0.264939	+	0.964265i	$0.414648\pi$
$252$	1.25965	−	1.14917i	0.0793506	−	0.0723911i
$253$	4.22695			0.265746
$254$	12.7251	−	22.0406i	0.798445	−	1.38295i
$255$	2.08747	+	3.61561i	0.130723	+	0.226418i
$256$	−7.01680	−	12.1535i	−0.438550	−	0.759591i
$257$	10.7552	−	18.6286i	0.670892	−	1.16202i	−0.306760	−	0.951787i	$-0.599245\pi$
$257$	10.7552	−	18.6286i	0.670892	−	1.16202i	0.977652	−	0.210232i	$-0.0674219\pi$
$258$	−19.2469			−1.19826
$259$	−1.82280	−	8.30855i	−0.113263	−	0.516268i
$260$	−2.79604			−0.173403
$261$	−4.55871	+	7.89592i	−0.282177	+	0.488745i
$262$	7.82852	+	13.5594i	0.483648	+	0.837702i
$263$	−7.72948	−	13.3879i	−0.476620	−	0.825530i	0.523021	−	0.852320i	$-0.324805\pi$
$263$	−7.72948	−	13.3879i	−0.476620	−	0.825530i	−0.999641	+	0.0267895i	$0.991472\pi$
$264$	−3.00348	+	5.20217i	−0.184851	+	0.320172i
$265$	7.68507			0.472090
$266$	−3.13851	−	0.997160i	−0.192434	−	0.0611398i
$267$	1.25617			0.0768765
$268$	−1.25466	+	2.17314i	−0.0766407	+	0.132746i
$269$	10.6969	+	18.5275i	0.652199	+	1.12964i	0.982588	+	0.185797i	$0.0594867\pi$
$269$	10.6969	+	18.5275i	0.652199	+	1.12964i	−0.330389	+	0.943845i	$0.607180\pi$
$270$	−1.36081	−	2.35699i	−0.0828162	−	0.143442i
$271$	−3.70888	+	6.42397i	−0.225298	+	0.390228i	−0.956409	−	0.292031i	$-0.905669\pi$
$271$	−3.70888	+	6.42397i	−0.225298	+	0.390228i	0.731110	+	0.682259i	$0.239002\pi$
$272$	12.1574			0.737152
$273$	6.53664	+	2.07681i	0.395615	+	0.125694i
$274$	−6.30841			−0.381105
$275$	2.99615	−	5.18949i	0.180675	−	0.312938i
$276$	0.499827	+	0.865727i	0.0300861	+	0.0521106i
$277$	11.9868	+	20.7617i	0.720215	+	1.24745i	0.960913	+	0.276849i	$0.0892903\pi$
$277$	11.9868	+	20.7617i	0.720215	+	1.24745i	−0.240698	+	0.970600i	$0.577376\pi$
$278$	10.4330	−	18.0706i	0.625733	−	1.08380i
$279$	−8.26914			−0.495061
$280$	2.09168	+	9.53411i	0.125002	+	0.569772i
$281$	11.7067			0.698366			0.349183	−	0.937055i	$-0.386459\pi$
$281$	11.7067			0.698366			0.349183	+	0.937055i	$0.386459\pi$
$282$	−4.72497	+	8.18389i	−0.281368	+	0.487344i
$283$	−6.75004	−	11.6914i	−0.401248	−	0.694982i	0.592629	−	0.805476i	$-0.298090\pi$
$283$	−6.75004	−	11.6914i	−0.401248	−	0.694982i	−0.993877	+	0.110494i	$0.964757\pi$
$284$	3.42478	+	5.93189i	0.203223	+	0.351993i
$285$	−0.640496	+	1.10937i	−0.0379397	+	0.0657135i
$286$	11.4876			0.679278
$287$	−1.95458	+	1.78315i	−0.115375	+	0.105256i
$288$	−3.51664			−0.207220
$289$	5.38861	−	9.33334i	0.316977	−	0.549020i
$290$	12.4071	+	21.4897i	0.728568	+	1.26192i
$291$	−4.27757	−	7.40897i	−0.250756	−	0.434322i
$292$	0.721619	−	1.24988i	0.0422296	−	0.0731437i
$293$	21.3767			1.24884			0.624419	−	0.781089i	$-0.285336\pi$
$293$	21.3767			1.24884			0.624419	+	0.781089i	$0.285336\pi$
$294$	−1.04198	+	11.3355i	−0.0607693	+	0.661098i
$295$	−7.98828			−0.465096
$296$	−3.54351	+	6.13755i	−0.205963	+	0.356738i
$297$	1.36252	+	2.35996i	0.0790616	+	0.136939i
$298$	−0.364849	−	0.631937i	−0.0211351	−	0.0366071i
$299$	−2.01053	+	3.48234i	−0.116272	+	0.201389i
$300$	1.41716			0.0818195
$301$	23.1336	−	21.1047i	1.33340	−	1.21645i
$302$	−5.81131			−0.334403
$303$	−0.654143	+	1.13301i	−0.0375795	+	0.0650896i
$304$	1.86512	+	3.23049i	0.106972	+	0.185281i
$305$	0.725848	+	1.25721i	0.0415620	+	0.0719874i
$306$	2.02829	−	3.51311i	0.115950	−	0.200831i
$307$	−25.7934			−1.47211			−0.736053	−	0.676924i	$-0.763312\pi$
$307$	−25.7934			−1.47211			−0.736053	+	0.676924i	$0.763312\pi$
$308$	0.995697	+	4.53850i	0.0567351	+	0.258605i
$309$	15.8139			0.899624
$310$	−11.2527	+	19.4903i	−0.639112	+	1.10697i
$311$	2.12085	+	3.67342i	0.120262	+	0.208300i	0.919871	−	0.392221i	$-0.128293\pi$
$311$	2.12085	+	3.67342i	0.120262	+	0.208300i	−0.799609	+	0.600521i	$0.794960\pi$
$312$	−2.85718	−	4.94879i	−0.161756	−	0.280170i
$313$	3.38716	−	5.86673i	0.191453	−	0.331607i	−0.754279	−	0.656554i	$-0.772013\pi$
$313$	3.38716	−	5.86673i	0.191453	−	0.331607i	0.945732	+	0.324947i	$0.105347\pi$
$314$	−14.4991			−0.818233
$315$	4.22012	+	1.34081i	0.237777	+	0.0755459i
$316$	5.22300			0.293816
$317$	−16.8107	+	29.1170i	−0.944182	+	1.63537i	−0.186802	+	0.982398i	$0.559812\pi$
$317$	−16.8107	+	29.1170i	−0.944182	+	1.63537i	−0.757380	+	0.652974i	$0.773521\pi$
$318$	−3.73360	−	6.46679i	−0.209370	−	0.362640i
$319$	−12.4227	−	21.5168i	−0.695538	−	1.20471i
$320$	3.37110	−	5.83891i	0.188450	−	0.326405i
$321$	−6.65637			−0.371522
$322$	−6.36045	−	2.02083i	−0.354454	−	0.112616i
$323$	−1.90933			−0.106238
$324$	−0.322231	+	0.558120i	−0.0179017	+	0.0310067i
$325$	2.85022	+	4.93673i	0.158102	+	0.273840i
$326$	19.9101	+	34.4853i	1.10272	+	1.90997i
$327$	3.31368	−	5.73947i	0.183247	−	0.317393i
$328$	2.20435			0.121715
$329$	−3.29470	−	15.0176i	−0.181643	−	0.827949i
$330$	7.41653			0.408267
$331$	−14.5178	+	25.1455i	−0.797970	+	1.38212i	0.122967	+	0.992411i	$0.460759\pi$
$331$	−14.5178	+	25.1455i	−0.797970	+	1.38212i	−0.920936	+	0.389713i	$0.872574\pi$
$332$	2.76656	+	4.79183i	0.151835	+	0.262986i
$333$	1.60751	+	2.78429i	0.0880910	+	0.152578i
$334$	0.576414	−	0.998379i	0.0315400	−	0.0546289i
$335$	−6.51655			−0.356037
$336$	9.52582	−	8.69035i	0.519676	−	0.474097i
$337$	−14.5845			−0.794471			−0.397235	−	0.917717i	$-0.630030\pi$
$337$	−14.5845			−0.794471			−0.397235	+	0.917717i	$0.630030\pi$
$338$	5.10612	−	8.84406i	0.277736	−	0.481054i
$339$	−8.84026	−	15.3118i	−0.480137	−	0.831621i
$340$	−1.34530	−	2.33012i	−0.0729590	−	0.126369i
$341$	11.2669	−	19.5148i	0.610137	−	1.05679i
$342$	1.24468			0.0673045
$343$	−11.1773	−	14.7672i	−0.603515	−	0.797352i
$344$	−26.0898			−1.40667
$345$	−1.29802	+	2.24824i	−0.0698830	+	0.121041i
$346$	2.42201	+	4.19504i	0.130208	+	0.225527i
$347$	9.97789	+	17.2822i	0.535641	+	0.927758i	0.999132	+	0.0416563i	$0.0132634\pi$
$347$	9.97789	+	17.2822i	0.535641	+	0.927758i	−0.463491	+	0.886102i	$0.653403\pi$
$348$	2.93792	−	5.08862i	0.157489	−	0.272779i
$349$	−28.9751			−1.55100			−0.775500	−	0.631348i	$-0.782502\pi$
$349$	−28.9751			−1.55100			−0.775500	+	0.631348i	$0.782502\pi$
$350$	−6.98943	+	6.37642i	−0.373601	+	0.340834i
$351$	−2.59232			−0.138368
$352$	4.79151	−	8.29913i	0.255388	−	0.442345i
$353$	7.65840	+	13.2647i	0.407615	+	0.706010i	0.994622	−	0.103572i	$-0.0330271\pi$
$353$	7.65840	+	13.2647i	0.407615	+	0.706010i	−0.587007	+	0.809582i	$0.699694\pi$
$354$	3.88091	+	6.72194i	0.206268	+	0.357267i
$355$	−8.89392	+	15.4047i	−0.472040	+	0.817598i
$356$	−0.809555			−0.0429063
$357$	1.41432	+	6.44664i	0.0748538	+	0.341192i
$358$	−33.8888			−1.79108
$359$	10.8387	−	18.7731i	0.572043	−	0.990807i	−0.424313	−	0.905515i	$-0.639485\pi$
$359$	10.8387	−	18.7731i	0.572043	−	0.990807i	0.996356	−	0.0852915i	$-0.0271822\pi$
$360$	−1.84463	−	3.19499i	−0.0972204	−	0.168391i
$361$	9.20708	+	15.9471i	0.484583	+	0.839323i
$362$	−4.66678	+	8.08309i	−0.245280	+	0.424838i
$363$	3.57412			0.187593
$364$	−4.21261	−	1.33842i	−0.220801	−	0.0701524i
$365$	3.74800			0.196179
$366$	0.705271	−	1.22157i	0.0368651	−	0.0638523i
$367$	−7.03443	−	12.1840i	−0.367194	−	0.635999i	0.621932	−	0.783072i	$-0.286348\pi$
$367$	−7.03443	−	12.1840i	−0.367194	−	0.635999i	−0.989126	+	0.147073i	$0.953015\pi$
$368$	3.77983	+	6.54685i	0.197037	+	0.341278i
$369$	0.500000	−	0.866025i	0.0260290	−	0.0450835i
$370$	8.75006			0.454894
$371$	11.5786	+	3.67873i	0.601131	+	0.190990i
$372$	5.32915			0.276304
$373$	−10.5864	+	18.3362i	−0.548143	+	0.949412i	0.450258	+	0.892898i	$0.351332\pi$
$373$	−10.5864	+	18.3362i	−0.548143	+	0.949412i	−0.998402	+	0.0565139i	$0.982001\pi$
$374$	5.52720	+	9.57338i	0.285804	+	0.495028i
$375$	6.02420	+	10.4342i	0.311088	+	0.538821i
$376$	−6.40488	+	11.0936i	−0.330306	+	0.572108i
$377$	23.6352			1.21728
$378$	−0.921986	−	4.20252i	−0.0474219	−	0.216154i
$379$	0.272209			0.0139824			0.00699122	−	0.999976i	$-0.497775\pi$
$379$	0.272209			0.0139824			0.00699122	+	0.999976i	$0.497775\pi$
$380$	0.412776	−	0.714948i	0.0211749	−	0.0366761i
$381$	−7.82516	−	13.5536i	−0.400895	−	0.694371i
$382$	2.14417	+	3.71381i	0.109705	+	0.190015i
$383$	−7.36597	+	12.7582i	−0.376384	+	0.651916i	−0.990533	−	0.137274i	$-0.956166\pi$
$383$	−7.36597	+	12.7582i	−0.376384	+	0.651916i	0.614149	+	0.789190i	$0.289499\pi$
$384$	−13.5843			−0.693223
$385$	−8.91426	+	8.13243i	−0.454313	+	0.414467i
$386$	−1.15774			−0.0589277
$387$	−5.91781	+	10.2500i	−0.300819	+	0.521034i
$388$	2.75673	+	4.77480i	0.139952	+	0.242404i
$389$	−1.64922	−	2.85654i	−0.0836189	−	0.144832i	0.821183	−	0.570665i	$-0.193315\pi$
$389$	−1.64922	−	2.85654i	−0.0836189	−	0.144832i	−0.904802	+	0.425833i	$0.859981\pi$
$390$	−3.52765	+	6.11006i	−0.178629	+	0.309395i
$391$	−3.86941			−0.195685
$392$	−1.41244	+	15.3657i	−0.0713389	+	0.776083i
$393$	9.62811			0.485674
$394$	14.0445	−	24.3257i	0.707550	−	1.22551i
$395$	6.78189	+	11.7466i	0.341234	+	0.591035i
$396$	−0.878094	−	1.52090i	−0.0441259	−	0.0764283i
$397$	−0.928010	+	1.60736i	−0.0465755	+	0.0806711i	−0.888373	−	0.459122i	$-0.848164\pi$
$397$	−0.928010	+	1.60736i	−0.0465755	+	0.0806711i	0.841798	+	0.539793i	$0.181497\pi$
$398$	−5.71340			−0.286387
$399$	−1.49603	+	1.36482i	−0.0748953	+	0.0683266i
$400$	10.7169			0.535846
$401$	−7.95126	+	13.7720i	−0.397067	+	0.687740i	−0.993363	−	0.115025i	$-0.963305\pi$
$401$	−7.95126	+	13.7720i	−0.397067	+	0.687740i	0.596296	+	0.802765i	$0.296639\pi$
$402$	3.16591	+	5.48351i	0.157901	+	0.273493i
$403$	10.7181	+	18.5643i	0.533907	+	0.924755i
$404$	0.421570	−	0.730181i	0.0209739	−	0.0363279i
$405$	−1.67363			−0.0831632
$406$	8.40614	+	38.3162i	0.417190	+	1.90160i
$407$	−8.76108			−0.434271
$408$	2.74943	−	4.76215i	0.136117	−	0.235762i
$409$	2.31225	+	4.00493i	0.114333	+	0.198031i	0.917513	−	0.397706i	$-0.130194\pi$
$409$	2.31225	+	4.00493i	0.114333	+	0.198031i	−0.803180	+	0.595737i	$0.796860\pi$
$410$	−1.36081	−	2.35699i	−0.0672056	−	0.116403i
$411$	−1.93964	+	3.35956i	−0.0956754	+	0.165715i
$412$	−10.1915			−0.502099
$413$	−12.0354	−	3.82387i	−0.592224	−	0.188160i
$414$	2.52244			0.123971
$415$	−7.18459	+	12.4441i	−0.352678	+	0.610856i
$416$	4.55812	+	7.89490i	0.223480	+	0.387079i
$417$	−6.41568	−	11.1123i	−0.314177	−	0.544171i
$418$	−1.69590	+	2.93739i	−0.0829493	+	0.143672i
$419$	28.4534			1.39004			0.695019	−	0.718991i	$-0.255396\pi$
$419$	28.4534			1.39004			0.695019	+	0.718991i	$0.255396\pi$
$420$	−2.71971	−	0.864099i	−0.132708	−	0.0421637i
$421$	−36.4418			−1.77607			−0.888033	−	0.459780i	$-0.847928\pi$
$421$	−36.4418			−1.77607			−0.888033	+	0.459780i	$0.847928\pi$
$422$	−1.66002	+	2.87525i	−0.0808087	+	0.139965i
$423$	2.90556	+	5.03259i	0.141273	+	0.244693i
$424$	−5.06104	−	8.76598i	−0.245786	−	0.425714i
$425$	−2.74273	+	4.75054i	−0.133042	+	0.230435i
$426$	17.2836			0.837392
$427$	0.491783	+	2.24160i	0.0237990	+	0.108479i
$428$	4.28977			0.207354
$429$	3.53209	−	6.11776i	0.170531	−	0.295368i
$430$	16.1060	+	27.8964i	0.776701	+	1.34529i
$431$	3.71500	+	6.43457i	0.178945	+	0.309942i	0.941520	−	0.336958i	$-0.109398\pi$
$431$	3.71500	+	6.43457i	0.178945	+	0.309942i	−0.762574	+	0.646901i	$0.776065\pi$
$432$	−2.43680	+	4.22066i	−0.117240	+	0.203066i
$433$	13.8996			0.667972			0.333986	−	0.942578i	$-0.391606\pi$
$433$	13.8996			0.667972			0.333986	+	0.942578i	$0.391606\pi$
$434$	−26.2834	+	23.9782i	−1.26165	+	1.15099i
$435$	15.2592			0.731621
$436$	−2.13554	+	3.69887i	−0.102274	+	0.177144i
$437$	−0.593623	−	1.02819i	−0.0283969	−	0.0491848i
$438$	−1.82087	−	3.15384i	−0.0870046	−	0.150696i
$439$	4.54972	−	7.88034i	0.217146	−	0.376108i	−0.736788	−	0.676124i	$-0.763659\pi$
$439$	4.54972	−	7.88034i	0.217146	−	0.376108i	0.953934	+	0.300015i	$0.0969918\pi$
$440$	10.0534			0.479277
$441$	5.71635	+	4.04021i	0.272207	+	0.192391i
$442$	−10.5160			−0.500193
$443$	−13.4816	+	23.3508i	−0.640529	+	1.10943i	0.344786	+	0.938681i	$0.387951\pi$
$443$	−13.4816	+	23.3508i	−0.640529	+	1.10943i	−0.985315	+	0.170747i	$0.945382\pi$
$444$	−1.03598	−	1.79437i	−0.0491654	−	0.0851570i
$445$	−1.05118	−	1.82070i	−0.0498308	−	0.0863094i
$446$	13.3221	−	23.0746i	0.630822	−	1.09262i
$447$	−0.448719			−0.0212237
$448$	7.87400	−	7.18341i	0.372012	−	0.339384i
$449$	16.8277			0.794149			0.397074	−	0.917786i	$-0.370025\pi$
$449$	16.8277			0.794149			0.397074	+	0.917786i	$0.370025\pi$
$450$	1.78797	−	3.09685i	0.0842855	−	0.145987i
$451$	1.36252	+	2.35996i	0.0641587	+	0.111126i
$452$	5.69721	+	9.86786i	0.267974	+	0.464145i
$453$	−1.78680	+	3.09482i	−0.0839511	+	0.145408i
$454$	48.5679			2.27940
$455$	−2.45981	−	11.2121i	−0.115318	−	0.525632i
$456$	1.68721			0.0790107
$457$	−11.0603	+	19.1570i	−0.517379	+	0.896127i	0.482417	+	0.875942i	$0.339759\pi$
$457$	−11.0603	+	19.1570i	−0.517379	+	0.896127i	−0.999796	+	0.0201851i	$0.993574\pi$
$458$	−19.8191	−	34.3277i	−0.926086	−	1.60403i
$459$	−1.24728	−	2.16034i	−0.0582178	−	0.100836i
$460$	0.836524	−	1.44890i	0.0390032	−	0.0675554i
$461$	35.2027			1.63955			0.819776	−	0.572684i	$-0.194098\pi$
$461$	35.2027			1.63955			0.819776	+	0.572684i	$0.194098\pi$
$462$	11.1740	+	3.55018i	0.519862	+	0.165169i
$463$	−20.0710			−0.932777			−0.466389	−	0.884580i	$-0.654445\pi$
$463$	−20.0710			−0.932777			−0.466389	+	0.884580i	$0.654445\pi$
$464$	22.2173	−	38.4815i	1.03141	−	1.78646i
$465$	6.91973	+	11.9853i	0.320895	+	0.555806i
$466$	−3.93349	−	6.81300i	−0.182215	−	0.315606i
$467$	−11.4427	+	19.8193i	−0.529505	+	0.917130i	0.469903	+	0.882718i	$0.344289\pi$
$467$	−11.4427	+	19.8193i	−0.529505	+	0.917130i	−0.999408	+	0.0344115i	$0.989044\pi$
$468$	1.67065			0.0772258
$469$	−9.81806	−	3.11937i	−0.453356	−	0.144039i
$470$	15.8157			0.729523
$471$	−4.45803	+	7.72154i	−0.205415	+	0.355790i
$472$	5.26072	+	9.11184i	0.242144	+	0.419406i
$473$	−16.1263	−	27.9316i	−0.741489	−	1.28430i
$474$	6.58963	−	11.4136i	0.302672	−	0.524243i
$475$	−1.68309			−0.0772257
$476$	−0.911476	−	4.15461i	−0.0417774	−	0.190426i
$477$	−4.59187			−0.210247
$478$	3.73312	−	6.46596i	0.170749	−	0.295746i
$479$	−10.2540	−	17.7605i	−0.468518	−	0.811497i	0.530835	−	0.847475i	$-0.321879\pi$
$479$	−10.2540	−	17.7605i	−0.468518	−	0.811497i	−0.999353	+	0.0359786i	$0.988545\pi$
$480$	2.94277	+	5.09703i	0.134319	+	0.232647i
$481$	4.16718	−	7.21776i	0.190007	−	0.329102i
$482$	−0.523668			−0.0238524
$483$	−3.03184	+	2.76593i	−0.137953	+	0.125854i
$484$	−2.30339			−0.104699
$485$	−7.15906	+	12.3999i	−0.325076	+	0.563048i
$486$	0.813090	+	1.40831i	0.0368825	+	0.0638824i
$487$	2.03686	+	3.52794i	0.0922989	+	0.159866i	0.908478	−	0.417933i	$-0.137245\pi$
$487$	2.03686	+	3.52794i	0.0922989	+	0.159866i	−0.816179	+	0.577799i	$0.803912\pi$
$488$	0.956022	−	1.65588i	0.0432771	−	0.0749581i
$489$	24.4870			1.10734
$490$	17.3016	−	7.97543i	0.781607	−	0.360293i
$491$	−6.31242			−0.284876			−0.142438	−	0.989804i	$-0.545494\pi$
$491$	−6.31242			−0.284876			−0.142438	+	0.989804i	$0.545494\pi$
$492$	−0.322231	+	0.558120i	−0.0145273	+	0.0251620i
$493$	11.3719	+	19.6968i	0.512166	+	0.887098i
$494$	−1.61330	−	2.79432i	−0.0725858	−	0.125722i
$495$	2.28035	−	3.94969i	0.102494	−	0.177525i
$496$	40.3004			1.80954
$497$	−20.7739	+	18.9519i	−0.931837	+	0.850109i
$498$	13.9618			0.625644
$499$	−18.7488	+	32.4738i	−0.839310	+	1.45373i	0.0511617	+	0.998690i	$0.483708\pi$
$499$	−18.7488	+	32.4738i	−0.839310	+	1.45373i	−0.890472	+	0.455038i	$0.849626\pi$
$500$	−3.88237	−	6.72445i	−0.173625	−	0.300727i
$501$	−0.354459	−	0.613941i	−0.0158361	−	0.0274289i
$502$	−6.82577	+	11.8226i	−0.304649	+	0.527667i
$503$	−28.7997			−1.28411			−0.642056	−	0.766657i	$-0.721919\pi$
$503$	−28.7997			−1.28411			−0.642056	+	0.766657i	$0.721919\pi$
$504$	−1.24979	−	5.69668i	−0.0556700	−	0.253750i
$505$	2.18958			0.0974351
$506$	−3.43689	+	5.95286i	−0.152788	+	0.264637i
$507$	−3.13995	−	5.43855i	−0.139450	−	0.241535i
$508$	5.04302	+	8.73477i	0.223748	+	0.387543i
$509$	1.38270	−	2.39490i	0.0612869	−	0.106152i	−0.833754	−	0.552136i	$-0.813813\pi$
$509$	1.38270	−	2.39490i	0.0612869	−	0.106152i	0.895041	+	0.445984i	$0.147146\pi$
$510$	−6.78921			−0.300631
$511$	5.64686	+	1.79411i	0.249802	+	0.0793666i
$512$	−4.34752			−0.192135
$513$	0.382700	−	0.662855i	0.0168966	−	0.0292658i
$514$	17.4899	+	30.2934i	0.771447	+	1.33619i
$515$	−13.2333	−	22.9208i	−0.583130	−	1.01001i
$516$	3.81380	−	6.60570i	0.167893	−	0.290800i
$517$	−15.8356			−0.696449
$518$	13.1831	+	4.18852i	0.579234	+	0.184033i
$519$	2.97877			0.130754
$520$	−4.78186	+	8.28242i	−0.209698	+	0.363208i
$521$	−2.02602	−	3.50917i	−0.0887616	−	0.153740i	0.818226	−	0.574896i	$-0.194958\pi$
$521$	−2.02602	−	3.50917i	−0.0887616	−	0.153740i	−0.906988	+	0.421157i	$0.861624\pi$
$522$	−7.41329	−	12.8402i	−0.324471	−	0.562000i
$523$	2.14322	−	3.71217i	0.0937165	−	0.162322i	−0.815356	−	0.578960i	$-0.803459\pi$
$523$	2.14322	−	3.71217i	0.0937165	−	0.162322i	0.909072	+	0.416639i	$0.136792\pi$
$524$	−6.20495			−0.271064
$525$	1.24674	+	5.68279i	0.0544122	+	0.248017i
$526$	25.1391			1.09611
$527$	−10.3139	+	17.8642i	−0.449281	+	0.778177i
$528$	−6.64038	−	11.5015i	−0.288986	−	0.500538i
$529$	10.2970	+	17.8349i	0.447694	+	0.775430i
$530$	−6.24866	+	10.8230i	−0.271424	+	0.470121i
$531$	4.77304			0.207132
$532$	0.964137	−	0.879576i	0.0418006	−	0.0381345i
$533$	−2.59232			−0.112286
$534$	−1.02138	+	1.76908i	−0.0441995	+	0.0765557i
$535$	5.57013	+	9.64775i	0.240818	+	0.417109i
$536$	4.29151	+	7.43311i	0.185365	+	0.321061i
$537$	−10.4198	+	18.0476i	−0.449646	+	0.778810i
$538$	−34.7900			−1.49991
$539$	−17.3234	+	7.98548i	−0.746172	+	0.343959i
$540$	1.07859			0.0464151
$541$	20.7955	−	36.0189i	0.894069	−	1.54857i	0.0591162	−	0.998251i	$-0.481172\pi$
$541$	20.7955	−	36.0189i	0.894069	−	1.54857i	0.834953	−	0.550322i	$-0.185495\pi$
$542$	−6.03131	−	10.4465i	−0.259067	−	0.448717i
$543$	2.86978	+	4.97060i	0.123154	+	0.213309i
$544$	−4.38622	+	7.59716i	−0.188058	+	0.325725i
$545$	−11.0917			−0.475118
$546$	−8.23967	+	7.51700i	−0.352625	+	0.321698i
$547$	−33.4461			−1.43005			−0.715025	−	0.699099i	$-0.753585\pi$
$547$	−33.4461			−1.43005			−0.715025	+	0.699099i	$0.753585\pi$
$548$	1.25002	−	2.16511i	0.0533984	−	0.0924888i
$549$	−0.433698	−	0.751187i	−0.0185098	−	0.0320599i
$550$	4.87229	+	8.43905i	0.207755	+	0.359842i
$551$	−3.48924	+	6.04354i	−0.148646	+	0.257463i
$552$	3.41927			0.145534
$553$	4.59492	+	20.9442i	0.195396	+	0.890638i
$554$	−38.9853			−1.65633
$555$	2.69037	−	4.65986i	0.114200	−	0.197800i
$556$	4.13466	+	7.16144i	0.175349	+	0.303713i
$557$	−10.8877	−	18.8580i	−0.461326	−	0.799039i	0.537702	−	0.843135i	$-0.319293\pi$
$557$	−10.8877	−	18.8580i	−0.461326	−	0.799039i	−0.999027	+	0.0440958i	$0.985959\pi$
$558$	6.72356	−	11.6455i	0.284631	−	0.492995i
$559$	30.6817			1.29770
$560$	−20.5671	−	6.53455i	−0.869120	−	0.276135i
$561$	6.79777			0.287002
$562$	−9.51864	+	16.4868i	−0.401520	+	0.695452i
$563$	−20.5213	−	35.5440i	−0.864871	−	1.49800i	−0.867176	−	0.498003i	$-0.834067\pi$
$563$	−20.5213	−	35.5440i	−0.864871	−	1.49800i	0.00230492	−	0.999997i	$-0.499266\pi$
$564$	−1.87253	−	3.24331i	−0.0788476	−	0.136568i
$565$	−14.7953	+	25.6262i	−0.622442	+	1.07810i
$566$	21.9536			0.922777
$567$	−2.52154	−	0.801139i	−0.105895	−	0.0336447i
$568$	23.4285			0.983040
$569$	−6.47875	+	11.2215i	−0.271603	+	0.470431i	−0.969273	−	0.245989i	$-0.920887\pi$
$569$	−6.47875	+	11.2215i	−0.271603	+	0.470431i	0.697669	+	0.716420i	$0.254220\pi$
$570$	−1.04156	−	1.80404i	−0.0436263	−	0.0755629i
$571$	−18.4234	−	31.9102i	−0.770994	−	1.33540i	−0.937018	−	0.349280i	$-0.886426\pi$
$571$	−18.4234	−	31.9102i	−0.770994	−	1.33540i	0.166024	−	0.986122i	$-0.446907\pi$
$572$	−2.27630	+	3.94266i	−0.0951768	+	0.164851i
$573$	2.63706			0.110165
$574$	−0.921986	−	4.20252i	−0.0384830	−	0.175410i
$575$	−3.41093			−0.142246
$576$	−2.01425	+	3.48878i	−0.0839269	+	0.145366i
$577$	−23.3735	−	40.4841i	−0.973051	−	1.68537i	−0.686222	−	0.727393i	$-0.740732\pi$
$577$	−23.3735	−	40.4841i	−0.973051	−	1.68537i	−0.286830	−	0.957982i	$-0.592601\pi$
$578$	8.76285	+	15.1777i	0.364486	+	0.631309i
$579$	−0.355971	+	0.616559i	−0.0147936	+	0.0256233i
$580$	−9.83395			−0.408333
$581$	−16.7813	+	15.3095i	−0.696207	+	0.635146i
$582$	13.9122			0.576680
$583$	6.25653	−	10.8366i	0.259119	−	0.448807i
$584$	−2.46826	−	4.27515i	−0.102137	−	0.176907i
$585$	2.16928	+	3.75731i	0.0896889	+	0.155346i
$586$	−17.3812	+	30.1051i	−0.718009	+	1.24363i
$587$	23.0958			0.953266			0.476633	−	0.879102i	$-0.341857\pi$
$587$	23.0958			0.953266			0.476633	+	0.879102i	$0.341857\pi$
$588$	−3.68397	−	2.60376i	−0.151924	−	0.107377i
$589$	−6.32920			−0.260790
$590$	6.49519	−	11.2500i	0.267403	−	0.463155i
$591$	−8.63648	−	14.9588i	−0.355257	−	0.615323i
$592$	−7.83435	−	13.5695i	−0.321990	−	0.557703i
$593$	18.9411	−	32.8070i	0.777820	−	1.34722i	−0.155376	−	0.987855i	$-0.549659\pi$
$593$	18.9411	−	32.8070i	0.777820	−	1.34722i	0.933196	−	0.359368i	$-0.117008\pi$
$594$	−4.43142			−0.181823
$595$	8.16026	−	7.44455i	0.334538	−	0.305197i
$596$	0.289182			0.0118454
$597$	−1.75669	+	3.04268i	−0.0718966	+	0.124529i
$598$	−3.26949	−	5.66292i	−0.133699	−	0.231574i
$599$	11.8306	+	20.4911i	0.483384	+	0.837245i	0.999818	−	0.0190819i	$-0.00607433\pi$
$599$	11.8306	+	20.4911i	0.483384	+	0.837245i	−0.516434	+	0.856327i	$0.672741\pi$
$600$	2.42365	−	4.19789i	0.0989453	−	0.171378i
$601$	47.3526			1.93155			0.965776	−	0.259377i	$-0.0835171\pi$
$601$	47.3526			1.93155			0.965776	+	0.259377i	$0.0835171\pi$
$602$	10.9123	+	49.7394i	0.444751	+	2.02723i
$603$	3.89367			0.158563
$604$	1.15152	−	1.99450i	0.0468548	−	0.0811549i
$605$	−2.99087	−	5.18034i	−0.121596	−	0.210611i
$606$	−1.06375	−	1.84248i	−0.0432121	−	0.0748455i
$607$	5.50912	−	9.54207i	0.223608	−	0.387301i	−0.732293	−	0.680990i	$-0.761550\pi$
$607$	5.50912	−	9.54207i	0.223608	−	0.387301i	0.955901	+	0.293689i	$0.0948831\pi$
$608$	−2.69164			−0.109160
$609$	22.9900	+	7.30433i	0.931601	+	0.295986i
$610$	−2.36072			−0.0955828
$611$	7.53214	−	13.0461i	0.304718	−	0.527787i
$612$	0.803821	+	1.39226i	0.0324926	+	0.0562788i
$613$	−14.3265	−	24.8143i	−0.578643	−	1.00224i	−0.995635	−	0.0933291i	$-0.970249\pi$
$613$	−14.3265	−	24.8143i	−0.578643	−	1.00224i	0.416992	−	0.908910i	$-0.363084\pi$
$614$	20.9723	−	36.3251i	0.846375	−	1.46596i
$615$	−1.67363			−0.0674871
$616$	15.1468	+	4.81241i	0.610281	+	0.193897i
$617$	−19.7501			−0.795109			−0.397554	−	0.917579i	$-0.630141\pi$
$617$	−19.7501			−0.795109			−0.397554	+	0.917579i	$0.630141\pi$
$618$	−12.8582	+	22.2710i	−0.517231	+	0.895871i
$619$	11.7919	+	20.4241i	0.473956	+	0.820916i	0.999555	−	0.0298163i	$-0.00949223\pi$
$619$	11.7919	+	20.4241i	0.473956	+	0.820916i	−0.525599	+	0.850732i	$0.676159\pi$
$620$	−4.45950	−	7.72408i	−0.179098	−	0.310207i
$621$	0.775573	−	1.34333i	0.0311227	−	0.0539061i
$622$	−6.89776			−0.276575
$623$	−0.712205	−	3.24631i	−0.0285339	−	0.130061i
$624$	12.6339			0.505760
$625$	4.58482	−	7.94113i	0.183393	−	0.317645i
$626$	5.50813	+	9.54036i	0.220149	+	0.381309i
$627$	1.04287	+	1.80631i	0.0416484	+	0.0721371i
$628$	2.87303	−	4.97624i	0.114646	−	0.198574i
$629$	8.02003			0.319780
$630$	−5.31961	+	4.85305i	−0.211939	+	0.193350i
$631$	−9.59187			−0.381846			−0.190923	−	0.981605i	$-0.561148\pi$
$631$	−9.59187			−0.381846			−0.190923	+	0.981605i	$0.561148\pi$
$632$	8.93250	−	15.4715i	0.355316	−	0.615425i
$633$	1.02081	+	1.76810i	0.0405736	+	0.0702756i
$634$	−27.3372	−	47.3494i	−1.08570	−	1.88049i
$635$	−13.0964	+	22.6836i	−0.519715	+	0.900172i
$636$	2.95929			0.117343
$637$	1.66103	−	18.0700i	0.0658123	−	0.715961i
$638$	40.4031			1.59957
$639$	5.31416	−	9.20440i	0.210225	−	0.364121i
$640$	11.3676	+	19.6892i	0.449342	+	0.778283i
$641$	15.2172	+	26.3569i	0.601042	+	1.04104i	0.992664	+	0.120909i	$0.0385810\pi$
$641$	15.2172	+	26.3569i	0.601042	+	1.04104i	−0.391621	+	0.920127i	$0.628086\pi$
$642$	5.41222	−	9.37425i	0.213603	−	0.369972i
$643$	−30.7646			−1.21324			−0.606619	−	0.794993i	$-0.707474\pi$
$643$	−30.7646			−1.21324			−0.606619	+	0.794993i	$0.707474\pi$
$644$	1.95390	−	1.78254i	0.0769946	−	0.0702417i
$645$	19.8084			0.779955
$646$	1.55246	−	2.68893i	0.0610806	−	0.105795i
$647$	−21.1405	−	36.6165i	−0.831120	−	1.43954i	−0.897151	−	0.441724i	$-0.854367\pi$
$647$	−21.1405	−	36.6165i	−0.831120	−	1.43954i	0.0660315	−	0.997818i	$-0.478966\pi$
$648$	1.10217	+	1.90902i	0.0432975	+	0.0749935i
$649$	−6.50338	+	11.2642i	−0.255280	+	0.442158i
$650$	−9.26994			−0.363597
$651$	4.68831	+	21.3699i	0.183749	+	0.837551i
$652$	−15.7809			−0.618029
$653$	20.5706	−	35.6294i	0.804992	−	1.39429i	−0.111305	−	0.993786i	$-0.535503\pi$
$653$	20.5706	−	35.6294i	0.804992	−	1.39429i	0.916297	−	0.400500i	$-0.131164\pi$
$654$	5.38865	+	9.33341i	0.210713	+	0.364965i
$655$	−8.05693	−	13.9550i	−0.314810	−	0.545267i
$656$	−2.43680	+	4.22066i	−0.0951409	+	0.164789i
$657$	−2.23945			−0.0873691
$658$	23.8284	+	7.57072i	0.928929	+	0.295137i
$659$	8.33455			0.324668			0.162334	−	0.986736i	$-0.448098\pi$
$659$	8.33455			0.324668			0.162334	+	0.986736i	$0.448098\pi$
$660$	−1.46960	+	2.54542i	−0.0572042	+	0.0990805i
$661$	−2.57755	−	4.46444i	−0.100255	−	0.173647i	0.811535	−	0.584304i	$-0.198633\pi$
$661$	−2.57755	−	4.46444i	−0.100255	−	0.173647i	−0.911790	+	0.410658i	$0.865299\pi$
$662$	−23.6085	−	40.8912i	−0.917572	−	1.58928i
$663$	−3.23333	+	5.60029i	−0.125572	+	0.217497i
$664$	18.9258			0.734463
$665$	3.23008	+	1.02625i	0.125257	+	0.0397964i
$666$	−5.22820			−0.202589
$667$	−7.07123	+	12.2477i	−0.273799	+	0.474234i
$668$	0.228435	+	0.395662i	0.00883843	+	0.0153086i
$669$	−8.19230	−	14.1895i	−0.316732	−	0.548597i
$670$	5.29854	−	9.17735i	0.204701	−	0.354552i
$671$	2.36369			0.0912494
$672$	1.99381	+	9.08802i	0.0769129	+	0.350578i
$673$	15.0044			0.578379			0.289189	−	0.957272i	$-0.406614\pi$
$673$	15.0044			0.578379			0.289189	+	0.957272i	$0.406614\pi$
$674$	11.8585	−	20.5396i	0.456774	−	0.791156i
$675$	−1.09949	−	1.90437i	−0.0423193	−	0.0732992i
$676$	2.02358	+	3.50494i	0.0778299	+	0.134805i
$677$	−7.52387	+	13.0317i	−0.289166	+	0.500850i	−0.973611	−	0.228215i	$-0.926711\pi$
$677$	−7.52387	+	13.0317i	−0.289166	+	0.500850i	0.684445	+	0.729064i	$0.260045\pi$
$678$	28.7517			1.10420
$679$	−16.7217	+	15.2551i	−0.641720	+	0.585437i
$680$	−9.20304			−0.352920
$681$	14.9331	−	25.8649i	0.572238	−	0.991146i
$682$	18.3220	+	31.7347i	0.701586	+	1.21518i
$683$	8.21868	+	14.2352i	0.314479	+	0.544694i	0.979327	−	0.202285i	$-0.0648368\pi$
$683$	8.21868	+	14.2352i	0.314479	+	0.544694i	−0.664848	+	0.746979i	$0.731503\pi$
$684$	−0.246635	+	0.427185i	−0.00943034	+	0.0163338i
$685$	6.49247			0.248064
$686$	29.8849	−	3.73404i	1.14101	−	0.142566i
$687$	−24.3750			−0.929966
$688$	28.8410	−	49.9541i	1.09955	−	1.90448i
$689$	5.95179	+	10.3088i	0.226745	+	0.392734i
$690$	−2.11081	−	3.65604i	−0.0803573	−	0.139183i
$691$	0.469621	−	0.813407i	0.0178652	−	0.0309435i	−0.856955	−	0.515392i	$-0.827646\pi$
$691$	0.469621	−	0.813407i	0.0178652	−	0.0309435i	0.874820	+	0.484448i	$0.160980\pi$
$692$	−1.91970			−0.0729762
$693$	5.32632	−	4.85917i	0.202330	−	0.184584i
$694$	−32.4517			−1.23185
$695$	−10.7374	+	18.5978i	−0.407295	+	0.705455i
$696$	−10.0490	−	17.4054i	−0.380906	−	0.659749i
$697$	−1.24728	−	2.16034i	−0.0472439	−	0.0818289i
$698$	23.5593	−	40.8060i	0.891734	−	1.54453i
$699$	−4.83770			−0.182979
$700$	−0.803477	−	3.66234i	−0.0303686	−	0.138423i
$701$	9.38248			0.354371			0.177186	−	0.984177i	$-0.443301\pi$
$701$	9.38248			0.354371			0.177186	+	0.984177i	$0.443301\pi$
$702$	2.10779	−	3.65079i	0.0795533	−	0.137790i
$703$	1.23039	+	2.13109i	0.0464050	+	0.0803758i
$704$	−5.48891	−	9.50708i	−0.206871	−	0.358311i
$705$	4.86283	−	8.42267i	0.183145	−	0.317216i
$706$	−24.9079			−0.937420
$707$	3.29890	+	1.04812i	0.124068	+	0.0394186i
$708$	−3.07604			−0.115605
$709$	−10.7935	+	18.6949i	−0.405358	+	0.702100i	−0.994363	−	0.106029i	$-0.966186\pi$
$709$	−10.7935	+	18.6949i	−0.405358	+	0.702100i	0.589005	+	0.808129i	$0.299520\pi$
$710$	−14.4631	−	25.0509i	−0.542791	−	0.940142i
$711$	−4.05221	−	7.01864i	−0.151970	−	0.263220i
$712$	−1.38452	+	2.39806i	−0.0518871	+	0.0898711i
$713$	−12.8267			−0.480362
$714$	−10.2289	−	3.24989i	−0.382805	−	0.121624i
$715$	−11.8228			−0.442148
$716$	6.71514	−	11.6310i	0.250957	−	0.434670i
$717$	−2.29564	−	3.97617i	−0.0857323	−	0.148493i
$718$	17.6256	+	30.5285i	0.657782	+	1.13931i
$719$	15.6963	−	27.1867i	0.585372	−	1.01389i	−0.409457	−	0.912330i	$-0.634282\pi$
$719$	15.6963	−	27.1867i	0.585372	−	1.01389i	0.994829	−	0.101565i	$-0.0323850\pi$
$720$	8.15657			0.303978
$721$	−8.96595	−	40.8678i	−0.333909	−	1.52200i
$722$	−29.9447			−1.11443
$723$	−0.161012	+	0.278880i	−0.00598809	+	0.0103717i
$724$	−1.84946	−	3.20336i	−0.0687347	−	0.119052i
$725$	10.0245	+	17.3629i	0.372300	+	0.644843i
$726$	−2.90608	+	5.03348i	−0.107855	+	0.186810i
$727$	−19.3083			−0.716103			−0.358052	−	0.933702i	$-0.616559\pi$
$727$	−19.3083			−0.716103			−0.358052	+	0.933702i	$0.616559\pi$
$728$	−11.1692	+	10.1896i	−0.413957	+	0.377651i
$729$	1.00000			0.0370370
$730$	−3.04746	+	5.27835i	−0.112791	+	0.195361i
$731$	14.7623	+	25.5690i	0.546003	+	0.945704i
$732$	0.279502	+	0.484112i	0.0103307	+	0.0178933i
$733$	24.1576	−	41.8422i	0.892281	−	1.54548i	0.0551462	−	0.998478i	$-0.482438\pi$
$733$	24.1576	−	41.8422i	0.892281	−	1.54548i	0.837134	−	0.546997i	$-0.184229\pi$
$734$	22.8785			0.844460
$735$	1.07238	−	11.6662i	0.0395552	−	0.430314i
$736$	−5.45483			−0.201068
$737$	−5.30522	+	9.18891i	−0.195420	+	0.338478i
$738$	0.813090	+	1.40831i	0.0299303	+	0.0518407i
$739$	−2.86551	−	4.96321i	−0.105409	−	0.182575i	0.808496	−	0.588502i	$-0.200282\pi$
$739$	−2.86551	−	4.96321i	−0.105409	−	0.182575i	−0.913905	+	0.405927i	$0.866949\pi$
$740$	−1.73384	+	3.00310i	−0.0637373	+	0.110396i
$741$	−1.98416			−0.0728899
$742$	−14.5952	+	13.3152i	−0.535808	+	0.488815i
$743$	31.0816			1.14027			0.570136	−	0.821550i	$-0.306890\pi$
$743$	31.0816			1.14027			0.570136	+	0.821550i	$0.306890\pi$
$744$	9.11404	−	15.7860i	0.334137	−	0.578742i
$745$	0.375494	+	0.650375i	0.0137570	+	0.0238279i
$746$	−17.2154	−	29.8180i	−0.630301	−	1.09171i
$747$	4.29283	−	7.43540i	0.157066	−	0.272047i
$748$	−4.38090			−0.160182
$749$	3.77392	+	17.2020i	0.137896	+	0.628546i
$750$	−19.5929			−0.715430
$751$	17.3786	−	30.1006i	0.634153	−	1.09839i	−0.352541	−	0.935797i	$-0.614682\pi$
$751$	17.3786	−	30.1006i	0.634153	−	1.09839i	0.986694	−	0.162589i	$-0.0519845\pi$
$752$	−14.1605	−	24.5268i	−0.516382	−	0.894399i
$753$	4.19742	+	7.27015i	0.152963	+	0.264939i
$754$	−19.2176	+	33.2858i	−0.699863	+	1.21220i
$755$	5.98086			0.217666
$756$	1.62504	+	0.516304i	0.0591021	+	0.0187778i
$757$	−4.67741			−0.170003			−0.0850017	−	0.996381i	$-0.527090\pi$
$757$	−4.67741			−0.170003			−0.0850017	+	0.996381i	$0.527090\pi$
$758$	−0.221331	+	0.383356i	−0.00803909	+	0.0139241i
$759$	2.11347	+	3.66064i	0.0767142	+	0.132873i
$760$	−1.41188	−	2.44544i	−0.0512142	−	0.0887056i
$761$	15.8504	−	27.4536i	0.574575	−	0.995194i	−0.421512	−	0.906823i	$-0.638501\pi$
$761$	15.8504	−	27.4536i	0.574575	−	0.995194i	0.996088	−	0.0883709i	$-0.0281661\pi$
$762$	25.4502			0.921965
$763$	−16.7112	−	5.30944i	−0.604986	−	0.192215i
$764$	−1.69948			−0.0614852
$765$	−2.08747	+	3.61561i	−0.0754727	+	0.130723i
$766$	−11.9784	−	20.7472i	−0.432797	−	0.749627i
$767$	−6.18661	−	10.7155i	−0.223386	−	0.386915i
$768$	7.01680	−	12.1535i	0.253197	−	0.438550i
$769$	25.4093			0.916282			0.458141	−	0.888880i	$-0.348516\pi$
$769$	25.4093			0.916282			0.458141	+	0.888880i	$0.348516\pi$
$770$	−4.20491	−	19.1665i	−0.151534	−	0.690712i
$771$	21.5104			0.774679
$772$	0.229410	−	0.397349i	0.00825663	−	0.0143009i
$773$	19.9691	+	34.5875i	0.718239	+	1.24403i	0.961697	+	0.274115i	$0.0883849\pi$
$773$	19.9691	+	34.5875i	0.718239	+	1.24403i	−0.243458	+	0.969911i	$0.578282\pi$
$774$	−9.62343	−	16.6683i	−0.345907	−	0.599128i
$775$	−9.09182	+	15.7475i	−0.326588	+	0.565667i
$776$	18.8585			0.676982
$777$	6.28401	−	5.73287i	0.225438	−	0.205665i
$778$	5.36387			0.192304
$779$	0.382700	−	0.662855i	0.0137116	−	0.0237493i
$780$	−1.39802	−	2.42144i	−0.0500572	−	0.0867016i
$781$	14.4813	+	25.0824i	0.518183	+	0.897520i
$782$	3.14618	−	5.44935i	0.112507	−	0.194868i
$783$	−9.11743			−0.325830
$784$	−27.8592	−	19.6903i	−0.994970	−	0.703227i
$785$	14.9222			0.532595
$786$	−7.82852	+	13.5594i	−0.279234	+	0.483648i
$787$	−25.4043	−	44.0015i	−0.905565	−	1.56849i	−0.820156	−	0.572139i	$-0.806114\pi$
$787$	−25.4043	−	44.0015i	−0.905565	−	1.56849i	−0.0854090	−	0.996346i	$-0.527220\pi$
$788$	5.56588	+	9.64039i	0.198276	+	0.343425i
$789$	7.72948	−	13.3879i	0.275177	−	0.476620i
$790$	−22.0572			−0.784758
$791$	−34.5579	+	31.5270i	−1.22874	+	1.12097i
$792$	−6.00695			−0.213448
$793$	−1.12428	+	1.94731i	−0.0399244	+	0.0691512i
$794$	−1.50911	−	2.61386i	−0.0535563	−	0.0927623i
$795$	3.84254	+	6.65547i	0.136281	+	0.236045i
$796$	1.13212	−	1.96089i	0.0401270	−	0.0695020i
$797$	−47.0831			−1.66777			−0.833884	−	0.551939i	$-0.813888\pi$
$797$	−47.0831			−1.66777			−0.833884	+	0.551939i	$0.813888\pi$
$798$	−0.705688	−	3.21661i	−0.0249811	−	0.113867i
$799$	14.4962			0.512837
$800$	−3.86650	+	6.69698i	−0.136702	+	0.236774i
$801$	0.628086	+	1.08788i	0.0221923	+	0.0384382i
$802$	−12.9302	−	22.3957i	−0.456580	−	0.790820i
$803$	3.05130	−	5.28500i	0.107678	−	0.186504i
$804$	−2.50932			−0.0884970
$805$	6.54602	+	2.07979i	0.230717	+	0.0733029i
$806$	−34.8592			−1.22786
$807$	−10.6969	+	18.5275i	−0.376547	+	0.652199i
$808$	−1.44196	−	2.49755i	−0.0507279	−	0.0878634i
$809$	−8.85077	−	15.3300i	−0.311176	−	0.538973i	0.667441	−	0.744663i	$-0.267390\pi$
$809$	−8.85077	−	15.3300i	−0.311176	−	0.538973i	−0.978617	+	0.205689i	$0.934056\pi$
$810$	1.36081	−	2.35699i	0.0478140	−	0.0828162i
$811$	−23.0207			−0.808365			−0.404183	−	0.914678i	$-0.632444\pi$
$811$	−23.0207			−0.808365			−0.404183	+	0.914678i	$0.632444\pi$
$812$	−14.8162	−	4.70736i	−0.519945	−	0.165196i
$813$	−7.41776			−0.260152
$814$	7.12355	−	12.3383i	0.249680	−	0.432459i
$815$	−20.4910	−	35.4915i	−0.717769	−	1.24321i
$816$	6.07871	+	10.5286i	0.212797	+	0.368576i
$817$	−4.52949	+	7.84531i	−0.158467	+	0.274473i
$818$	−7.52026			−0.262940
$819$	1.46975	+	6.69929i	0.0513573	+	0.234092i
$820$	1.07859			0.0376659
$821$	3.81682	−	6.61092i	0.133208	−	0.230723i	−0.791704	−	0.610905i	$-0.790806\pi$
$821$	3.81682	−	6.61092i	0.133208	−	0.230723i	0.924911	+	0.380183i	$0.124139\pi$
$822$	−3.15421	−	5.46324i	−0.110016	−	0.190553i
$823$	23.0689	+	39.9566i	0.804133	+	1.39280i	0.916875	+	0.399174i	$0.130703\pi$
$823$	23.0689	+	39.9566i	0.804133	+	1.39280i	−0.112742	+	0.993624i	$0.535963\pi$
$824$	−17.4297	+	30.1892i	−0.607193	+	1.05169i
$825$	5.99231			0.208625
$826$	15.1711	−	13.8405i	0.527870	−	0.481572i
$827$	−8.79619			−0.305874			−0.152937	−	0.988236i	$-0.548873\pi$
$827$	−8.79619			−0.305874			−0.152937	+	0.988236i	$0.548873\pi$
$828$	−0.499827	+	0.865727i	−0.0173702	+	0.0300861i
$829$	−9.48869	−	16.4349i	−0.329556	−	0.570808i	0.652868	−	0.757472i	$-0.273566\pi$
$829$	−9.48869	−	16.4349i	−0.329556	−	0.570808i	−0.982424	+	0.186664i	$0.940232\pi$
$830$	−11.6834	−	20.2363i	−0.405538	−	0.702412i
$831$	−11.9868	+	20.7617i	−0.415816	+	0.720215i
$832$	10.4431			0.362050
$833$	15.8581	−	7.31003i	0.549451	−	0.253278i
$834$	20.8661			0.722534
$835$	−0.593232	+	1.02751i	−0.0205296	+	0.0355584i
$836$	−0.672093	−	1.16410i	−0.0232448	−	0.0402612i
$837$	−4.13457	−	7.16129i	−0.142912	−	0.247530i
$838$	−23.1352	+	40.0713i	−0.799191	+	1.38424i
$839$	−25.8131			−0.891167			−0.445584	−	0.895240i	$-0.647004\pi$
$839$	−25.8131			−0.891167			−0.445584	+	0.895240i	$0.647004\pi$
$840$	−7.21094	+	6.57850i	−0.248801	+	0.226980i
$841$	54.1274			1.86646
$842$	29.6305	−	51.3215i	1.02113	−	1.76866i
$843$	5.85337	+	10.1383i	0.201601	+	0.349183i
$844$	−0.657874	−	1.13947i	−0.0226450	−	0.0392222i
$845$	−5.25510	+	9.10210i	−0.180781	+	0.313122i
$846$	−9.44994			−0.324896
$847$	−2.02640	−	9.23657i	−0.0696279	−	0.317372i
$848$	22.3789			0.768495
$849$	6.75004	−	11.6914i	0.231661	−	0.401248i
$850$	−4.46017	−	7.72524i	−0.152983	−	0.264974i
$851$	2.49348	+	4.31884i	0.0854756	+	0.148048i
$852$	−3.42478	+	5.93189i	−0.117331	+	0.203223i
$853$	23.5448			0.806160			0.403080	−	0.915165i	$-0.367940\pi$
$853$	23.5448			0.806160			0.403080	+	0.915165i	$0.367940\pi$
$854$	−3.55674	−	1.13004i	−0.121709	−	0.0386692i
$855$	−1.28099			−0.0438090
$856$	7.33648	−	12.7071i	0.250756	−	0.434321i
$857$	7.70366	+	13.3431i	0.263152	+	0.455793i	0.967078	−	0.254481i	$-0.0819046\pi$
$857$	7.70366	+	13.3431i	0.263152	+	0.455793i	−0.703926	+	0.710273i	$0.748571\pi$
$858$	5.74382	+	9.94858i	0.196091	+	0.339639i
$859$	5.14203	−	8.90625i	0.175444	−	0.303877i	−0.764871	−	0.644183i	$-0.777197\pi$
$859$	5.14203	−	8.90625i	0.175444	−	0.303877i	0.940315	+	0.340306i	$0.110531\pi$
$860$	−12.7658			−0.435309
$861$	−2.52154	−	0.801139i	−0.0859339	−	0.0273027i
$862$	−12.0825			−0.411532
$863$	8.63157	−	14.9503i	0.293822	−	0.508915i	−0.680888	−	0.732387i	$-0.738406\pi$
$863$	8.63157	−	14.9503i	0.293822	−	0.508915i	0.974710	+	0.223473i	$0.0717394\pi$
$864$	−1.75832	−	3.04550i	−0.0598193	−	0.103610i
$865$	−2.49267	−	4.31744i	−0.0847535	−	0.146797i
$866$	−11.3016	+	19.5750i	−0.384045	+	0.665185i
$867$	10.7772			0.366013
$868$	−3.02144	−	13.7721i	−0.102554	−	0.467454i
$869$	22.0849			0.749180
$870$	−12.4071	+	21.4897i	−0.420639	+	0.728568i
$871$	−5.04682	−	8.74134i	−0.171005	−	0.296189i
$872$	7.30452	+	12.6518i	0.247362	+	0.428444i
$873$	4.27757	−	7.40897i	0.144774	−	0.250756i
$874$	1.93068			0.0653061
$875$	23.5495	−	21.4841i	0.796119	−	0.726295i
$876$	1.44324			0.0487625
$877$	−16.0804	+	27.8521i	−0.542997	+	0.940498i	0.455733	+	0.890116i	$0.349377\pi$
$877$	−16.0804	+	27.8521i	−0.542997	+	0.940498i	−0.998730	+	0.0503814i	$0.983956\pi$
$878$	7.39866	+	12.8149i	0.249693	+	0.432480i
$879$	10.6883	+	18.5127i	0.360509	+	0.624419i
$880$	−11.1135	+	19.2492i	−0.374637	+	0.648890i
$881$	8.00714			0.269767			0.134884	−	0.990861i	$-0.456934\pi$
$881$	8.00714			0.269767			0.134884	+	0.990861i	$0.456934\pi$
$882$	−10.3378	+	4.76536i	−0.348092	+	0.160458i
$883$	−11.9191			−0.401108			−0.200554	−	0.979683i	$-0.564274\pi$
$883$	−11.9191			−0.401108			−0.200554	+	0.979683i	$0.564274\pi$
$884$	2.08376	−	3.60918i	0.0700844	−	0.121390i
$885$	−3.99414	−	6.91806i	−0.134262	−	0.232548i
$886$	−21.9235	−	37.9726i	−0.736533	−	1.27571i
$887$	−27.6158	+	47.8319i	−0.927247	+	1.60604i	−0.139340	+	0.990245i	$0.544498\pi$
$887$	−27.6158	+	47.8319i	−0.927247	+	1.60604i	−0.787907	+	0.615794i	$0.788835\pi$
$888$	−7.08703			−0.237825
$889$	−30.5898	+	27.9069i	−1.02595	+	0.935967i
$890$	3.41882			0.114599
$891$	−1.36252	+	2.35996i	−0.0456462	+	0.0790616i
$892$	5.27962	+	9.14457i	0.176775	+	0.306183i
$893$	2.22392	+	3.85194i	0.0744206	+	0.128900i
$894$	0.364849	−	0.631937i	0.0122024	−	0.0211351i
$895$	34.8776			1.16583
$896$	7.70184	+	35.1059i	0.257300	+	1.17280i
$897$	−4.02106			−0.134259
$898$	−13.6824	+	23.6987i	−0.456589	+	0.790836i
$899$	37.6967	+	65.2925i	1.25725	+	2.17763i
$900$	0.708578	+	1.22729i	0.0236193	+	0.0409098i
$901$	−5.72733	+	9.92002i	−0.190805	+	0.330484i
$902$	−4.43142			−0.147550
$903$	29.8440	+	9.48198i	0.993147	+	0.315541i
$904$	38.9740			1.29626
$905$	4.80294	−	8.31893i	0.159655	−	0.276531i
$906$	−2.90565	−	5.03274i	−0.0965339	−	0.167202i
$907$	14.8384	+	25.7009i	0.492703	+	0.853386i	0.999965	−	0.00840589i	$-0.00267571\pi$
$907$	14.8384	+	25.7009i	0.492703	+	0.853386i	−0.507262	+	0.861792i	$0.669342\pi$
$908$	−9.62382	+	16.6690i	−0.319378	+	0.553179i
$909$	−1.30829			−0.0433931
$910$	17.7902	+	5.65227i	0.589740	+	0.187371i
$911$	43.6581			1.44646			0.723228	−	0.690609i	$-0.242657\pi$
$911$	43.6581			1.44646			0.723228	+	0.690609i	$0.242657\pi$
$912$	−1.86512	+	3.23049i	−0.0617604	+	0.106972i
$913$	11.6982	+	20.2618i	0.387152	+	0.670568i
$914$	−17.9860	−	31.1527i	−0.594925	−	1.03044i
$915$	−0.725848	+	1.25721i	−0.0239958	+	0.0415620i
$916$	15.7088			0.519033
$917$	−5.45879	−	24.8818i	−0.180265	−	0.821670i
$918$	4.05659			0.133887
$919$	11.8326	−	20.4946i	0.390321	−	0.676056i	−0.602171	−	0.798367i	$-0.705697\pi$
$919$	11.8326	−	20.4946i	0.390321	−	0.676056i	0.992492	+	0.122311i	$0.0390307\pi$
$920$	−2.86129	−	4.95590i	−0.0943339	−	0.163391i
$921$	−12.8967	−	22.3377i	−0.424960	−	0.736053i
$922$	−28.6229	+	49.5764i	−0.942646	+	1.63271i
$923$	−27.5520			−0.906885
$924$	−3.43261	+	3.13155i	−0.112925	+	0.103020i
$925$	7.06975			0.232452
$926$	16.3195	−	28.2662i	0.536292	−	0.928885i
$927$	7.90697	+	13.6953i	0.259699	+	0.449812i
$928$	16.0314	+	27.7671i	0.526255	+	0.911501i
$929$	−20.5025	+	35.5114i	−0.672665	+	1.16509i	0.304480	+	0.952519i	$0.401517\pi$
$929$	−20.5025	+	35.5114i	−0.672665	+	1.16509i	−0.977145	+	0.212572i	$0.931816\pi$
$930$	−22.5054			−0.737983
$931$	4.37529	+	3.09238i	0.143394	+	0.101349i
$932$	3.11772			0.102124
$933$	−2.12085	+	3.67342i	−0.0694334	+	0.120262i
$934$	−18.6079	−	32.2298i	−0.608869	−	1.05459i
$935$	−5.68846	−	9.85270i	−0.186033	−	0.322218i
$936$	2.85718	−	4.94879i	0.0933900	−	0.161756i
$937$	−17.7022			−0.578305			−0.289153	−	0.957283i	$-0.593373\pi$
$937$	−17.7022			−0.578305			−0.289153	+	0.957283i	$0.593373\pi$
$938$	12.3760	−	11.2906i	0.404091	−	0.368650i
$939$	6.77432			0.221071
$940$	−3.13391	+	5.42809i	−0.102217	+	0.177045i
$941$	−16.5032	−	28.5843i	−0.537988	−	0.931822i	−0.999012	−	0.0444348i	$-0.985851\pi$
$941$	−16.5032	−	28.5843i	−0.537988	−	0.931822i	0.461024	−	0.887387i	$-0.347482\pi$
$942$	−7.24956	−	12.5566i	−0.236204	−	0.409117i
$943$	0.775573	−	1.34333i	0.0252561	−	0.0437449i
$944$	−23.2619			−0.757109
$945$	0.948886	+	4.32513i	0.0308673	+	0.140697i
$946$	52.4486			1.70525
$947$	−24.5189	+	42.4680i	−0.796758	+	1.38003i	0.124959	+	0.992162i	$0.460120\pi$
$947$	−24.5189	+	42.4680i	−0.796758	+	1.38003i	−0.921717	+	0.387863i	$0.873213\pi$
$948$	2.61150	+	4.52325i	0.0848175	+	0.146908i
$949$	2.90268	+	5.02758i	0.0942248	+	0.163202i
$950$	1.36851	−	2.37032i	0.0444003	−	0.0769035i
$951$	−33.6214			−1.09025
$952$	−13.8656	−	4.40535i	−0.449387	−	0.142778i
$953$	−20.5062			−0.664260			−0.332130	−	0.943234i	$-0.607767\pi$
$953$	−20.5062			−0.664260			−0.332130	+	0.943234i	$0.607767\pi$
$954$	3.73360	−	6.46679i	0.120880	−	0.209370i
$955$	−2.20673	−	3.82216i	−0.0714080	−	0.123682i
$956$	1.47945	+	2.56249i	0.0478489	+	0.0828768i
$957$	12.4227	−	21.5168i	0.401569	−	0.695538i
$958$	33.3498			1.07748
$959$	9.78177	+	3.10784i	0.315870	+	0.100358i
$960$	6.74219			0.217603
$961$	−18.6894	+	32.3709i	−0.602883	+	1.04422i
$962$	6.77658	+	11.7374i	0.218486	+	0.378428i
$963$	−3.32818	−	5.76458i	−0.107249	−	0.185761i
$964$	0.103766	−	0.179728i	0.00334207	−	0.00578864i
$965$	1.19152			0.0383565
$966$	−1.43014	−	6.51872i	−0.0460139	−	0.209737i
$967$	−50.9026			−1.63692			−0.818459	−	0.574566i	$-0.805171\pi$
$967$	−50.9026			−1.63692			−0.818459	+	0.574566i	$0.805171\pi$
$968$	−3.93931	+	6.82308i	−0.126614	+	0.219302i
$969$	−0.954664	−	1.65353i	−0.0306682	−	0.0531189i
$970$	−11.6419	−	20.1644i	−0.373799	−	0.647440i
$971$	−2.62716	+	4.55037i	−0.0843095	+	0.146028i	−0.905097	−	0.425206i	$-0.860202\pi$
$971$	−2.62716	+	4.55037i	−0.0843095	+	0.146028i	0.820787	+	0.571234i	$0.193535\pi$
$972$	−0.644462			−0.0206711
$973$	−25.0799	+	22.8802i	−0.804024	+	0.733507i
$974$	−6.62460			−0.212266
$975$	−2.85022	+	4.93673i	−0.0912801	+	0.158102i
$976$	2.11367	+	3.66098i	0.0676569	+	0.117185i
$977$	−3.45847	−	5.99024i	−0.110646	−	0.191645i	0.805385	−	0.592752i	$-0.201959\pi$
$977$	−3.45847	−	5.99024i	−0.110646	−	0.191645i	−0.916031	+	0.401108i	$0.868625\pi$
$978$	−19.9101	+	34.4853i	−0.636656	+	1.10272i
$979$	−3.42313			−0.109404
$980$	−0.691106	+	7.51842i	−0.0220766	+	0.240167i
$981$	6.62737			0.211596
$982$	5.13257	−	8.88987i	0.163787	−	0.283687i
$983$	15.0871	+	26.1317i	0.481205	+	0.833471i	0.999767	−	0.0215685i	$-0.00686598\pi$
$983$	15.0871	+	26.1317i	0.481205	+	0.833471i	−0.518563	+	0.855040i	$0.673533\pi$
$984$	1.10217	+	1.90902i	0.0351360	+	0.0608574i
$985$	−14.4542	+	25.0355i	−0.460550	+	0.797696i
$986$	−36.9856			−1.17786
$987$	11.3583	−	10.3621i	0.361539	−	0.329830i
$988$	1.27871			0.0406813
$989$	−9.17939	+	15.8992i	−0.291888	+	0.505564i
$990$	3.70827	+	6.42291i	0.117856	+	0.204133i
$991$	2.03705	+	3.52827i	0.0647089	+	0.112079i	0.896565	−	0.442913i	$-0.146055\pi$
$991$	2.03705	+	3.52827i	0.0647089	+	0.112079i	−0.831856	+	0.554992i	$0.812721\pi$
$992$	−14.5398	+	25.1837i	−0.461639	+	0.799583i
$993$	−29.0356			−0.921416
$994$	−9.79917	−	44.6658i	−0.310811	−	1.41671i
$995$	5.88009			0.186411
$996$	−2.76656	+	4.79183i	−0.0876619	+	0.151835i
$997$	16.0561	+	27.8101i	0.508503	+	0.880754i	0.999952	+	0.00984680i	$0.00313438\pi$
$997$	16.0561	+	27.8101i	0.508503	+	0.880754i	−0.491448	+	0.870907i	$0.663532\pi$
$998$	−30.4889	−	52.8083i	−0.965109	−	1.67162i
$999$	−1.60751	+	2.78429i	−0.0508594	+	0.0880910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.d.247.4	✓	16
7.2	even	3		6027.2.a.bb.1.5		8
7.4	even	3	inner	861.2.i.d.739.4	yes	16
7.5	odd	6		6027.2.a.bc.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.4	✓	16	1.1	even	1	trivial
861.2.i.d.739.4	yes	16	7.4	even	3	inner
6027.2.a.bb.1.5		8	7.2	even	3
6027.2.a.bc.1.5		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.813090 + 1.40831i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.322231 - 0.558120i) q^{4} +(0.836813 - 1.44940i) q^{5} -1.62618 q^{6} +(1.95458 - 1.78315i) q^{7} -2.20435 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.813090 + 1.40831i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.322231 - 0.558120i) q^{4} +(0.836813 - 1.44940i) q^{5} -1.62618 q^{6} +(1.95458 - 1.78315i) q^{7} -2.20435 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36081 + 2.35699i) q^{10} +(-1.36252 - 2.35996i) q^{11} +(0.322231 - 0.558120i) q^{12} +2.59232 q^{13} +(0.921986 + 4.20252i) q^{14} +1.67363 q^{15} +(2.43680 - 4.22066i) q^{16} +(1.24728 + 2.16034i) q^{17} +(-0.813090 - 1.40831i) q^{18} +(-0.382700 + 0.662855i) q^{19} -1.07859 q^{20} +(2.52154 + 0.801139i) q^{21} +4.43142 q^{22} +(-0.775573 + 1.34333i) q^{23} +(-1.10217 - 1.90902i) q^{24} +(1.09949 + 1.90437i) q^{25} +(-2.10779 + 3.65079i) q^{26} -1.00000 q^{27} +(-1.62504 - 0.516304i) q^{28} +9.11743 q^{29} +(-1.36081 + 2.35699i) q^{30} +(4.13457 + 7.16129i) q^{31} +(1.75832 + 3.04550i) q^{32} +(1.36252 - 2.35996i) q^{33} -4.05659 q^{34} +(-0.948886 - 4.32513i) q^{35} +0.644462 q^{36} +(1.60751 - 2.78429i) q^{37} +(-0.622339 - 1.07792i) q^{38} +(1.29616 + 2.24501i) q^{39} +(-1.84463 + 3.19499i) q^{40} -1.00000 q^{41} +(-3.17850 + 2.89972i) q^{42} +11.8356 q^{43} +(-0.878094 + 1.52090i) q^{44} +(0.836813 + 1.44940i) q^{45} +(-1.26122 - 2.18450i) q^{46} +(2.90556 - 5.03259i) q^{47} +4.87359 q^{48} +(0.640750 - 6.97061i) q^{49} -3.57593 q^{50} +(-1.24728 + 2.16034i) q^{51} +(-0.835325 - 1.44682i) q^{52} +(2.29593 + 3.97668i) q^{53} +(0.813090 - 1.40831i) q^{54} -4.56071 q^{55} +(-4.30857 + 3.93069i) q^{56} -0.765400 q^{57} +(-7.41329 + 12.8402i) q^{58} +(-2.38652 - 4.13357i) q^{59} +(-0.539294 - 0.934085i) q^{60} +(-0.433698 + 0.751187i) q^{61} -13.4471 q^{62} +(0.566964 + 2.58429i) q^{63} +4.02849 q^{64} +(2.16928 - 3.75731i) q^{65} +(2.21571 + 3.83772i) q^{66} +(-1.94684 - 3.37202i) q^{67} +(0.803821 - 1.39226i) q^{68} -1.55115 q^{69} +(6.86267 + 2.18039i) q^{70} -10.6283 q^{71} +(1.10217 - 1.90902i) q^{72} +(1.11972 + 1.93942i) q^{73} +(2.61410 + 4.52776i) q^{74} +(-1.09949 + 1.90437i) q^{75} +0.493271 q^{76} +(-6.87132 - 2.18314i) q^{77} -4.21557 q^{78} +(-4.05221 + 7.01864i) q^{79} +(-4.07829 - 7.06380i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.813090 - 1.40831i) q^{82} -8.58566 q^{83} +(-0.365387 - 1.66548i) q^{84} +4.17495 q^{85} +(-9.62343 + 16.6683i) q^{86} +(4.55871 + 7.89592i) q^{87} +(3.00348 + 5.20217i) q^{88} +(0.628086 - 1.08788i) q^{89} -2.72162 q^{90} +(5.06688 - 4.62249i) q^{91} +0.999655 q^{92} +(-4.13457 + 7.16129i) q^{93} +(4.72497 + 8.18389i) q^{94} +(0.640496 + 1.10937i) q^{95} +(-1.75832 + 3.04550i) q^{96} -8.55514 q^{97} +(9.29582 + 6.57011i) q^{98} +2.72505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 8 q^{3} - 13 q^{4} + 7 q^{5} - 2 q^{6} + 9 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 + 8 * q^3 - 13 * q^4 + 7 * q^5 - 2 * q^6 + 9 * q^7 + 12 * q^8 - 8 * q^9	\( 16 q - q^{2} + 8 q^{3} - 13 q^{4} + 7 q^{5} - 2 q^{6} + 9 q^{7} + 12 q^{8} - 8 q^{9} + 8 q^{10} - 11 q^{11} + 13 q^{12} - 20 q^{13} + q^{14} + 14 q^{15} + 17 q^{16} + 3 q^{17} - q^{18} + 6 q^{19} - 22 q^{20} - 9 q^{21} + 30 q^{22} - 14 q^{23} + 6 q^{24} - 25 q^{25} + 24 q^{26} - 16 q^{27} + 20 q^{28} + 4 q^{29} - 8 q^{30} + 16 q^{31} - 3 q^{32} + 11 q^{33} + 8 q^{34} + q^{35} + 26 q^{36} + 20 q^{37} + 10 q^{38} - 10 q^{39} - 3 q^{40} - 16 q^{41} - 4 q^{42} + 14 q^{43} + 7 q^{45} + 5 q^{46} + 14 q^{47} + 34 q^{48} + 13 q^{49} - 10 q^{50} - 3 q^{51} + 23 q^{52} - 7 q^{53} + q^{54} - 96 q^{55} + 51 q^{56} + 12 q^{57} + 20 q^{58} + 22 q^{59} - 11 q^{60} + 66 q^{62} - 18 q^{63} - 20 q^{64} + 14 q^{65} + 15 q^{66} - 12 q^{67} - 27 q^{68} - 28 q^{69} + 61 q^{70} - 10 q^{71} - 6 q^{72} + 2 q^{73} - 6 q^{74} + 25 q^{75} - 86 q^{76} - 3 q^{77} + 48 q^{78} + 15 q^{79} - 7 q^{80} - 8 q^{81} + q^{82} - 30 q^{83} + 34 q^{84} - 86 q^{85} - 31 q^{86} + 2 q^{87} - 17 q^{88} + 29 q^{89} - 16 q^{90} - 18 q^{91} + 38 q^{92} - 16 q^{93} + 20 q^{94} - 14 q^{95} + 3 q^{96} - 38 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) \) 16 * q - q^2 + 8 * q^3 - 13 * q^4 + 7 * q^5 - 2 * q^6 + 9 * q^7 + 12 * q^8 - 8 * q^9 + 8 * q^10 - 11 * q^11 + 13 * q^12 - 20 * q^13 + q^14 + 14 * q^15 + 17 * q^16 + 3 * q^17 - q^18 + 6 * q^19 - 22 * q^20 - 9 * q^21 + 30 * q^22 - 14 * q^23 + 6 * q^24 - 25 * q^25 + 24 * q^26 - 16 * q^27 + 20 * q^28 + 4 * q^29 - 8 * q^30 + 16 * q^31 - 3 * q^32 + 11 * q^33 + 8 * q^34 + q^35 + 26 * q^36 + 20 * q^37 + 10 * q^38 - 10 * q^39 - 3 * q^40 - 16 * q^41 - 4 * q^42 + 14 * q^43 + 7 * q^45 + 5 * q^46 + 14 * q^47 + 34 * q^48 + 13 * q^49 - 10 * q^50 - 3 * q^51 + 23 * q^52 - 7 * q^53 + q^54 - 96 * q^55 + 51 * q^56 + 12 * q^57 + 20 * q^58 + 22 * q^59 - 11 * q^60 + 66 * q^62 - 18 * q^63 - 20 * q^64 + 14 * q^65 + 15 * q^66 - 12 * q^67 - 27 * q^68 - 28 * q^69 + 61 * q^70 - 10 * q^71 - 6 * q^72 + 2 * q^73 - 6 * q^74 + 25 * q^75 - 86 * q^76 - 3 * q^77 + 48 * q^78 + 15 * q^79 - 7 * q^80 - 8 * q^81 + q^82 - 30 * q^83 + 34 * q^84 - 86 * q^85 - 31 * q^86 + 2 * q^87 - 17 * q^88 + 29 * q^89 - 16 * q^90 - 18 * q^91 + 38 * q^92 - 16 * q^93 + 20 * q^94 - 14 * q^95 + 3 * q^96 - 38 * q^97 + 56 * q^98 + 22 * q^99

Introduction

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