LMFDB - Embedded newform 399.2.j.c.172.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(58,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
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			172.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	399.172
Dual form			399.2.j.c.58.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(-0.914214 - 1.58346i) q^{5} +0.414214 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.378680 + 0.655892i) q^{10} +(-0.914214 + 1.58346i) q^{11} +(0.914214 + 1.58346i) q^{12} -2.82843 q^{13} +(0.207107 + 1.07616i) q^{14} +1.82843 q^{15} +(-1.50000 - 2.59808i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(-0.207107 + 0.358719i) q^{18} +(0.500000 + 0.866025i) q^{19} -3.34315 q^{20} +(2.00000 - 1.73205i) q^{21} +0.757359 q^{22} +(-1.91421 - 3.31552i) q^{23} +(0.792893 - 1.37333i) q^{24} +(0.828427 - 1.43488i) q^{25} +(0.585786 + 1.01461i) q^{26} +1.00000 q^{27} +(-3.65685 + 3.16693i) q^{28} +0.828427 q^{29} +(-0.378680 - 0.655892i) q^{30} +(4.41421 - 7.64564i) q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.914214 - 1.58346i) q^{33} +3.17157 q^{34} +(0.914214 + 4.75039i) q^{35} -1.82843 q^{36} +(-3.41421 - 5.91359i) q^{37} +(0.207107 - 0.358719i) q^{38} +(1.41421 - 2.44949i) q^{39} +(1.44975 + 2.51104i) q^{40} -3.65685 q^{41} +(-1.03553 - 0.358719i) q^{42} -1.34315 q^{43} +(1.67157 + 2.89525i) q^{44} +(-0.914214 + 1.58346i) q^{45} +(-0.792893 + 1.37333i) q^{46} +(-5.91421 - 10.2437i) q^{47} +3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -0.686292 q^{50} +(-3.82843 - 6.63103i) q^{51} +(-2.58579 + 4.47871i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-0.207107 - 0.358719i) q^{54} +3.34315 q^{55} +(3.96447 + 1.37333i) q^{56} -1.00000 q^{57} +(-0.171573 - 0.297173i) q^{58} +(-2.58579 + 4.47871i) q^{59} +(1.67157 - 2.89525i) q^{60} +(1.67157 + 2.89525i) q^{61} -3.65685 q^{62} +(0.500000 + 2.59808i) q^{63} -4.17157 q^{64} +(2.58579 + 4.47871i) q^{65} +(-0.378680 + 0.655892i) q^{66} +(6.00000 - 10.3923i) q^{67} +(7.00000 + 12.1244i) q^{68} +3.82843 q^{69} +(1.51472 - 1.31178i) q^{70} +15.6569 q^{71} +(0.792893 + 1.37333i) q^{72} +(-6.15685 + 10.6640i) q^{73} +(-1.41421 + 2.44949i) q^{74} +(0.828427 + 1.43488i) q^{75} +1.82843 q^{76} +(3.65685 - 3.16693i) q^{77} -1.17157 q^{78} +(-6.82843 - 11.8272i) q^{79} +(-2.74264 + 4.75039i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.757359 + 1.31178i) q^{82} +9.82843 q^{83} +(-0.914214 - 4.75039i) q^{84} +14.0000 q^{85} +(0.278175 + 0.481813i) q^{86} +(-0.414214 + 0.717439i) q^{87} +(1.44975 - 2.51104i) q^{88} +(-2.58579 - 4.47871i) q^{89} +0.757359 q^{90} +(7.07107 + 2.44949i) q^{91} -7.00000 q^{92} +(4.41421 + 7.64564i) q^{93} +(-2.44975 + 4.24309i) q^{94} +(0.914214 - 1.58346i) q^{95} +(-2.20711 - 3.82282i) q^{96} +11.1716 q^{97} +(0.414214 - 2.86976i) q^{98} +1.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{7} - 12 q^{8} - 2 q^{9} - 10 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 4 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} - 36 q^{20} + 8 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 10 * q^7 - 12 * q^8 - 2 * q^9 - 10 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 4 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 - 36 * q^20 + 8 * q^21 + 20 * q^22 - 2 * q^23 + 6 * q^24 - 8 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 - 10 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 - 14 * q^40 + 8 * q^41 + 10 * q^42 - 28 * q^43 + 18 * q^44 + 2 * q^45 - 6 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 - 48 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^53 + 2 * q^54 + 36 * q^55 + 30 * q^56 - 4 * q^57 - 12 * q^58 - 16 * q^59 + 18 * q^60 + 18 * q^61 + 8 * q^62 + 2 * q^63 - 28 * q^64 + 16 * q^65 - 10 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 40 * q^70 + 40 * q^71 + 6 * q^72 - 2 * q^73 - 8 * q^75 - 4 * q^76 - 8 * q^77 - 16 * q^78 - 16 * q^79 + 6 * q^80 - 2 * q^81 + 20 * q^82 + 28 * q^83 + 2 * q^84 + 56 * q^85 - 30 * q^86 + 4 * q^87 - 14 * q^88 - 16 * q^89 + 20 * q^90 - 28 * q^92 + 12 * q^93 + 10 * q^94 - 2 * q^95 - 6 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	0.783465	−	0.621436i	$-0.213450\pi$
$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	−0.929912	+	0.367783i	$0.880117\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	0.585912	−	0.810374i	$-0.300736\pi$
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	−0.994761	+	0.102228i	$0.967403\pi$
$6$	0.414214			0.169102
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	−1.58579			−0.560660
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.378680	+	0.655892i	−0.119749	+	0.207411i
$11$	−0.914214	+	1.58346i	−0.275646	+	0.477432i	−0.970298	−	0.241913i	$-0.922225\pi$
$11$	−0.914214	+	1.58346i	−0.275646	+	0.477432i	0.694652	+	0.719346i	$0.255558\pi$
$12$	0.914214	+	1.58346i	0.263911	+	0.457107i
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$	0.207107	+	1.07616i	0.0553516	+	0.287615i
$15$	1.82843			0.472098
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.142747	+	0.989759i	$0.545593\pi$
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.785783	+	0.618502i	$0.787740\pi$
$18$	−0.207107	+	0.358719i	−0.0488155	+	0.0845510i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$	−3.34315			−0.747550
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	0.757359			0.161470
$23$	−1.91421	−	3.31552i	−0.399141	−	0.691333i	0.594479	−	0.804111i	$-0.297358\pi$
$23$	−1.91421	−	3.31552i	−0.399141	−	0.691333i	−0.993620	+	0.112778i	$0.964025\pi$
$24$	0.792893	−	1.37333i	0.161849	−	0.280330i
$25$	0.828427	−	1.43488i	0.165685	−	0.286976i
$26$	0.585786	+	1.01461i	0.114882	+	0.198982i
$27$	1.00000			0.192450
$28$	−3.65685	+	3.16693i	−0.691080	+	0.598493i
$29$	0.828427			0.153835			0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427			0.153835			0.0769175	+	0.997037i	$0.475492\pi$
$30$	−0.378680	−	0.655892i	−0.0691371	−	0.119749i
$31$	4.41421	−	7.64564i	0.792816	−	1.37320i	−0.131401	−	0.991329i	$-0.541947\pi$
$31$	4.41421	−	7.64564i	0.792816	−	1.37320i	0.924217	−	0.381869i	$-0.124719\pi$
$32$	−2.20711	+	3.82282i	−0.390165	+	0.675786i
$33$	−0.914214	−	1.58346i	−0.159144	−	0.275646i
$34$	3.17157			0.543920
$35$	0.914214	+	4.75039i	0.154530	+	0.802963i
$36$	−1.82843			−0.304738
$37$	−3.41421	−	5.91359i	−0.561293	−	0.972188i	−0.997384	−	0.0722857i	$-0.976971\pi$
$37$	−3.41421	−	5.91359i	−0.561293	−	0.972188i	0.436091	−	0.899903i	$-0.356363\pi$
$38$	0.207107	−	0.358719i	0.0335972	−	0.0581920i
$39$	1.41421	−	2.44949i	0.226455	−	0.392232i
$40$	1.44975	+	2.51104i	0.229225	+	0.397030i
$41$	−3.65685			−0.571105			−0.285552	−	0.958363i	$-0.592177\pi$
$41$	−3.65685			−0.571105			−0.285552	+	0.958363i	$0.592177\pi$
$42$	−1.03553	−	0.358719i	−0.159786	−	0.0553516i
$43$	−1.34315			−0.204828			−0.102414	−	0.994742i	$-0.532657\pi$
$43$	−1.34315			−0.204828			−0.102414	+	0.994742i	$0.532657\pi$
$44$	1.67157	+	2.89525i	0.251999	+	0.436475i
$45$	−0.914214	+	1.58346i	−0.136283	+	0.236049i
$46$	−0.792893	+	1.37333i	−0.116906	+	0.202487i
$47$	−5.91421	−	10.2437i	−0.862677	−	1.49420i	−0.869336	−	0.494222i	$-0.835453\pi$
$47$	−5.91421	−	10.2437i	−0.862677	−	1.49420i	0.00665898	−	0.999978i	$-0.497880\pi$
$48$	3.00000			0.433013
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−0.686292			−0.0970563
$51$	−3.82843	−	6.63103i	−0.536087	−	0.928530i
$52$	−2.58579	+	4.47871i	−0.358584	+	0.621086i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	−0.207107	−	0.358719i	−0.0281837	−	0.0488155i
$55$	3.34315			0.450790
$56$	3.96447	+	1.37333i	0.529774	+	0.183519i
$57$	−1.00000			−0.132453
$58$	−0.171573	−	0.297173i	−0.0225286	−	0.0390207i
$59$	−2.58579	+	4.47871i	−0.336641	+	0.583079i	−0.983799	−	0.179277i	$-0.942624\pi$
$59$	−2.58579	+	4.47871i	−0.336641	+	0.583079i	0.647158	+	0.762356i	$0.275957\pi$
$60$	1.67157	−	2.89525i	0.215799	−	0.373775i
$61$	1.67157	+	2.89525i	0.214023	+	0.370699i	0.952970	−	0.303065i	$-0.0980099\pi$
$61$	1.67157	+	2.89525i	0.214023	+	0.370699i	−0.738947	+	0.673764i	$0.764677\pi$
$62$	−3.65685			−0.464421
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$	−4.17157			−0.521447
$65$	2.58579	+	4.47871i	0.320727	+	0.555516i
$66$	−0.378680	+	0.655892i	−0.0466122	+	0.0807348i
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	7.00000	+	12.1244i	0.848875	+	1.47029i
$69$	3.82843			0.460888
$70$	1.51472	−	1.31178i	0.181044	−	0.156788i
$71$	15.6569			1.85813			0.929063	−	0.369921i	$-0.120615\pi$
$71$	15.6569			1.85813			0.929063	+	0.369921i	$0.120615\pi$
$72$	0.792893	+	1.37333i	0.0934434	+	0.161849i
$73$	−6.15685	+	10.6640i	−0.720605	+	1.24812i	0.240152	+	0.970735i	$0.422803\pi$
$73$	−6.15685	+	10.6640i	−0.720605	+	1.24812i	−0.960757	+	0.277390i	$0.910531\pi$
$74$	−1.41421	+	2.44949i	−0.164399	+	0.284747i
$75$	0.828427	+	1.43488i	0.0956585	+	0.165685i
$76$	1.82843			0.209735
$77$	3.65685	−	3.16693i	0.416737	−	0.360905i
$78$	−1.17157			−0.132655
$79$	−6.82843	−	11.8272i	−0.768258	−	1.33066i	−0.938507	−	0.345261i	$-0.887790\pi$
$79$	−6.82843	−	11.8272i	−0.768258	−	1.33066i	0.170249	−	0.985401i	$-0.445543\pi$
$80$	−2.74264	+	4.75039i	−0.306637	+	0.531110i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.757359	+	1.31178i	0.0836363	+	0.144862i
$83$	9.82843			1.07881			0.539405	−	0.842046i	$-0.318649\pi$
$83$	9.82843			1.07881			0.539405	+	0.842046i	$0.318649\pi$
$84$	−0.914214	−	4.75039i	−0.0997489	−	0.518310i
$85$	14.0000			1.51851
$86$	0.278175	+	0.481813i	0.0299963	+	0.0519552i
$87$	−0.414214	+	0.717439i	−0.0444084	+	0.0769175i
$88$	1.44975	−	2.51104i	0.154544	−	0.267677i
$89$	−2.58579	−	4.47871i	−0.274093	−	0.474743i	0.695813	−	0.718223i	$-0.255044\pi$
$89$	−2.58579	−	4.47871i	−0.274093	−	0.474743i	−0.969906	+	0.243480i	$0.921711\pi$
$90$	0.757359			0.0798327
$91$	7.07107	+	2.44949i	0.741249	+	0.256776i
$92$	−7.00000			−0.729800
$93$	4.41421	+	7.64564i	0.457733	+	0.792816i
$94$	−2.44975	+	4.24309i	−0.252672	+	0.437641i
$95$	0.914214	−	1.58346i	0.0937963	−	0.162460i
$96$	−2.20711	−	3.82282i	−0.225262	−	0.390165i
$97$	11.1716			1.13430			0.567151	−	0.823614i	$-0.308046\pi$
$97$	11.1716			1.13430			0.567151	+	0.823614i	$0.308046\pi$
$98$	0.414214	−	2.86976i	0.0418419	−	0.289889i
$99$	1.82843			0.183764
$100$	−1.51472	−	2.62357i	−0.151472	−	0.262357i
$101$	−6.74264	+	11.6786i	−0.670918	+	1.16206i	0.306726	+	0.951798i	$0.400766\pi$
$101$	−6.74264	+	11.6786i	−0.670918	+	1.16206i	−0.977644	+	0.210266i	$0.932567\pi$
$102$	−1.58579	+	2.74666i	−0.157016	+	0.271960i
$103$	3.82843	+	6.63103i	0.377226	+	0.653375i	0.990658	−	0.136373i	$-0.0435446\pi$
$103$	3.82843	+	6.63103i	0.377226	+	0.653375i	−0.613431	+	0.789748i	$0.710211\pi$
$104$	4.48528			0.439818
$105$	−4.57107	−	1.58346i	−0.446091	−	0.154530i
$106$	−0.828427			−0.0804640
$107$	−1.41421	−	2.44949i	−0.136717	−	0.236801i	0.789535	−	0.613706i	$-0.210322\pi$
$107$	−1.41421	−	2.44949i	−0.136717	−	0.236801i	−0.926252	+	0.376905i	$0.876988\pi$
$108$	0.914214	−	1.58346i	0.0879702	−	0.152369i
$109$	5.07107	−	8.78335i	0.485720	−	0.841292i	−0.514145	−	0.857703i	$-0.671891\pi$
$109$	5.07107	−	8.78335i	0.485720	−	0.841292i	0.999865	+	0.0164111i	$0.00522406\pi$
$110$	−0.692388	−	1.19925i	−0.0660166	−	0.114344i
$111$	6.82843			0.648126
$112$	1.50000	+	7.79423i	0.141737	+	0.736485i
$113$	−7.17157			−0.674645			−0.337322	−	0.941389i	$-0.609521\pi$
$113$	−7.17157			−0.674645			−0.337322	+	0.941389i	$0.609521\pi$
$114$	0.207107	+	0.358719i	0.0193973	+	0.0335972i
$115$	−3.50000	+	6.06218i	−0.326377	+	0.565301i
$116$	0.757359	−	1.31178i	0.0703190	−	0.121796i
$117$	1.41421	+	2.44949i	0.130744	+	0.226455i
$118$	2.14214			0.197200
$119$	15.3137	−	13.2621i	1.40381	−	1.21573i
$120$	−2.89949			−0.264686
$121$	3.82843	+	6.63103i	0.348039	+	0.602821i
$122$	0.692388	−	1.19925i	0.0626859	−	0.108575i
$123$	1.82843	−	3.16693i	0.164864	−	0.285552i
$124$	−8.07107	−	13.9795i	−0.724803	−	1.25540i
$125$	−12.1716			−1.08866
$126$	0.828427	−	0.717439i	0.0738022	−	0.0639145i
$127$	−16.9706			−1.50589			−0.752947	−	0.658081i	$-0.771368\pi$
$127$	−16.9706			−1.50589			−0.752947	+	0.658081i	$0.771368\pi$
$128$	5.27817	+	9.14207i	0.466529	+	0.808052i
$129$	0.671573	−	1.16320i	0.0591287	−	0.102414i
$130$	1.07107	−	1.85514i	0.0939389	−	0.162707i
$131$	−10.8284	−	18.7554i	−0.946084	−	1.63867i	−0.753566	−	0.657372i	$-0.771668\pi$
$131$	−10.8284	−	18.7554i	−0.946084	−	1.63867i	−0.192518	−	0.981293i	$-0.561665\pi$
$132$	−3.34315			−0.290983
$133$	−0.500000	−	2.59808i	−0.0433555	−	0.225282i
$134$	−4.97056			−0.429391
$135$	−0.914214	−	1.58346i	−0.0786830	−	0.136283i
$136$	6.07107	−	10.5154i	0.520590	−	0.901688i
$137$	4.08579	−	7.07679i	0.349072	−	0.604611i	−0.637013	−	0.770853i	$-0.719830\pi$
$137$	4.08579	−	7.07679i	0.349072	−	0.604611i	0.986085	+	0.166242i	$0.0531634\pi$
$138$	−0.792893	−	1.37333i	−0.0674956	−	0.116906i
$139$	4.65685			0.394989			0.197495	−	0.980304i	$-0.436720\pi$
$139$	4.65685			0.394989			0.197495	+	0.980304i	$0.436720\pi$
$140$	8.35786	+	2.89525i	0.706368	+	0.244693i
$141$	11.8284			0.996133
$142$	−3.24264	−	5.61642i	−0.272116	−	0.471319i
$143$	2.58579	−	4.47871i	0.216234	−	0.374529i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−0.757359	−	1.31178i	−0.0628953	−	0.108938i
$146$	5.10051			0.422121
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	−12.4853			−1.02628
$149$	0.914214	+	1.58346i	0.0748953	+	0.129722i	0.901041	−	0.433734i	$-0.142804\pi$
$149$	0.914214	+	1.58346i	0.0748953	+	0.129722i	−0.826145	+	0.563457i	$0.809471\pi$
$150$	0.343146	−	0.594346i	0.0280177	−	0.0485281i
$151$	−6.65685	+	11.5300i	−0.541727	+	0.938299i	0.457078	+	0.889427i	$0.348896\pi$
$151$	−6.65685	+	11.5300i	−0.541727	+	0.938299i	−0.998805	+	0.0488722i	$0.984437\pi$
$152$	−0.792893	−	1.37333i	−0.0643121	−	0.111392i
$153$	7.65685			0.619020
$154$	−1.89340	−	0.655892i	−0.152574	−	0.0528533i
$155$	−16.1421			−1.29657
$156$	−2.58579	−	4.47871i	−0.207029	−	0.358584i
$157$	0.328427	−	0.568852i	0.0262113	−	0.0453994i	−0.852622	−	0.522528i	$-0.824989\pi$
$157$	0.328427	−	0.568852i	0.0262113	−	0.0453994i	0.878834	+	0.477129i	$0.158322\pi$
$158$	−2.82843	+	4.89898i	−0.225018	+	0.389742i
$159$	1.00000	+	1.73205i	0.0793052	+	0.137361i
$160$	8.07107			0.638074
$161$	1.91421	+	9.94655i	0.150861	+	0.783898i
$162$	0.414214			0.0325437
$163$	5.98528	+	10.3668i	0.468803	+	0.811991i	0.999364	−	0.0356556i	$-0.0113519\pi$
$163$	5.98528	+	10.3668i	0.468803	+	0.811991i	−0.530561	+	0.847647i	$0.678019\pi$
$164$	−3.34315	+	5.79050i	−0.261056	+	0.452162i
$165$	−1.67157	+	2.89525i	−0.130132	+	0.225395i
$166$	−2.03553	−	3.52565i	−0.157988	−	0.273643i
$167$	3.17157			0.245424			0.122712	−	0.992442i	$-0.460841\pi$
$167$	3.17157			0.245424			0.122712	+	0.992442i	$0.460841\pi$
$168$	−3.17157	+	2.74666i	−0.244692	+	0.211910i
$169$	−5.00000			−0.384615
$170$	−2.89949	−	5.02207i	−0.222381	−	0.385175i
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	−1.22792	+	2.12682i	−0.0936282	+	0.162169i
$173$	1.41421	+	2.44949i	0.107521	+	0.186231i	0.914765	−	0.403986i	$-0.132375\pi$
$173$	1.41421	+	2.44949i	0.107521	+	0.186231i	−0.807245	+	0.590217i	$0.799042\pi$
$174$	0.343146			0.0260138
$175$	−3.31371	+	2.86976i	−0.250493	+	0.216933i
$176$	5.48528			0.413469
$177$	−2.58579	−	4.47871i	−0.194360	−	0.336641i
$178$	−1.07107	+	1.85514i	−0.0802799	+	0.139049i
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	−0.961388	−	0.275197i	$-0.911257\pi$
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	0.719022	+	0.694988i	$0.244590\pi$
$180$	1.67157	+	2.89525i	0.124592	+	0.215799i
$181$	−0.343146			−0.0255058			−0.0127529	−	0.999919i	$-0.504059\pi$
$181$	−0.343146			−0.0255058			−0.0127529	+	0.999919i	$0.504059\pi$
$182$	−0.585786	−	3.04384i	−0.0434214	−	0.225624i
$183$	−3.34315			−0.247132
$184$	3.03553	+	5.25770i	0.223783	+	0.387603i
$185$	−6.24264	+	10.8126i	−0.458968	+	0.794956i
$186$	1.82843	−	3.16693i	0.134067	−	0.232210i
$187$	−7.00000	−	12.1244i	−0.511891	−	0.886621i
$188$	−21.6274			−1.57734
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$	−0.757359			−0.0549446
$191$	−3.08579	−	5.34474i	−0.223280	−	0.386732i	0.732522	−	0.680743i	$-0.238343\pi$
$191$	−3.08579	−	5.34474i	−0.223280	−	0.386732i	−0.955802	+	0.294011i	$0.905010\pi$
$192$	2.08579	−	3.61269i	0.150529	−	0.260723i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−2.31371	−	4.00746i	−0.166115	−	0.287719i
$195$	−5.17157			−0.370344
$196$	11.8848	−	4.75039i	0.848913	−	0.339314i
$197$	−0.514719			−0.0366722			−0.0183361	−	0.999832i	$-0.505837\pi$
$197$	−0.514719			−0.0366722			−0.0183361	+	0.999832i	$0.505837\pi$
$198$	−0.378680	−	0.655892i	−0.0269116	−	0.0466122i
$199$	−7.32843	+	12.6932i	−0.519498	+	0.899798i	0.480245	+	0.877135i	$0.340548\pi$
$199$	−7.32843	+	12.6932i	−0.519498	+	0.899798i	−0.999743	+	0.0226631i	$0.992785\pi$
$200$	−1.31371	+	2.27541i	−0.0928932	+	0.160896i
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$	5.58579			0.393015
$203$	−2.07107	−	0.717439i	−0.145360	−	0.0503543i
$204$	−14.0000			−0.980196
$205$	3.34315	+	5.79050i	0.233495	+	0.404426i
$206$	1.58579	−	2.74666i	0.110487	−	0.191369i
$207$	−1.91421	+	3.31552i	−0.133047	+	0.230444i
$208$	4.24264	+	7.34847i	0.294174	+	0.509525i
$209$	−1.82843			−0.126475
$210$	0.378680	+	1.96768i	0.0261314	+	0.135783i
$211$	−0.485281			−0.0334081			−0.0167041	−	0.999860i	$-0.505317\pi$
$211$	−0.485281			−0.0334081			−0.0167041	+	0.999860i	$0.505317\pi$
$212$	−1.82843	−	3.16693i	−0.125577	−	0.217506i
$213$	−7.82843	+	13.5592i	−0.536395	+	0.929063i
$214$	−0.585786	+	1.01461i	−0.0400435	+	0.0693574i
$215$	1.22792	+	2.12682i	0.0837436	+	0.145048i
$216$	−1.58579			−0.107899
$217$	−17.6569	+	15.2913i	−1.19863	+	1.03804i
$218$	−4.20101			−0.284528
$219$	−6.15685	−	10.6640i	−0.416042	−	0.720605i
$220$	3.05635	−	5.29375i	0.206059	−	0.356905i
$221$	10.8284	−	18.7554i	0.728399	−	1.26162i
$222$	−1.41421	−	2.44949i	−0.0949158	−	0.164399i
$223$	−17.7990			−1.19191			−0.595954	−	0.803018i	$-0.703226\pi$
$223$	−17.7990			−1.19191			−0.595954	+	0.803018i	$0.703226\pi$
$224$	8.82843	−	7.64564i	0.589874	−	0.510846i
$225$	−1.65685			−0.110457
$226$	1.48528	+	2.57258i	0.0987994	+	0.171126i
$227$	8.82843	−	15.2913i	0.585963	−	1.01492i	−0.408791	−	0.912628i	$-0.634050\pi$
$227$	8.82843	−	15.2913i	0.585963	−	1.01492i	0.994755	−	0.102290i	$-0.0326171\pi$
$228$	−0.914214	+	1.58346i	−0.0605453	+	0.104867i
$229$	2.17157	+	3.76127i	0.143502	+	0.248552i	0.928813	−	0.370549i	$-0.120830\pi$
$229$	2.17157	+	3.76127i	0.143502	+	0.248552i	−0.785311	+	0.619101i	$0.787497\pi$
$230$	2.89949			0.191187
$231$	0.914214	+	4.75039i	0.0601508	+	0.312553i
$232$	−1.31371			−0.0862492
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	0.585786	−	1.01461i	0.0382941	−	0.0663273i
$235$	−10.8137	+	18.7299i	−0.705409	+	1.22180i
$236$	4.72792	+	8.18900i	0.307762	+	0.533059i
$237$	13.6569			0.887108
$238$	−7.92893	−	2.74666i	−0.513956	−	0.178040i
$239$	13.6569			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$239$	13.6569			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$240$	−2.74264	−	4.75039i	−0.177037	−	0.306637i
$241$	9.89949	−	17.1464i	0.637683	−	1.10450i	−0.348257	−	0.937399i	$-0.613227\pi$
$241$	9.89949	−	17.1464i	0.637683	−	1.10450i	0.985940	−	0.167100i	$-0.0534402\pi$
$242$	1.58579	−	2.74666i	0.101938	−	0.176562i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.11270			0.391325
$245$	1.82843	−	12.6677i	0.116814	−	0.809311i
$246$	−1.51472			−0.0965749
$247$	−1.41421	−	2.44949i	−0.0899843	−	0.155857i
$248$	−7.00000	+	12.1244i	−0.444500	+	0.769897i
$249$	−4.91421	+	8.51167i	−0.311426	+	0.539405i
$250$	2.52082	+	4.36618i	0.159430	+	0.276141i
$251$	3.48528			0.219989			0.109995	−	0.993932i	$-0.464917\pi$
$251$	3.48528			0.219989			0.109995	+	0.993932i	$0.464917\pi$
$252$	4.57107	+	1.58346i	0.287950	+	0.0997489i
$253$	7.00000			0.440086
$254$	3.51472	+	6.08767i	0.220533	+	0.381974i
$255$	−7.00000	+	12.1244i	−0.438357	+	0.759257i
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	−0.912222	−	0.409695i	$-0.865635\pi$
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	0.101305	−	0.994855i	$-0.467698\pi$
$258$	−0.556349			−0.0346368
$259$	3.41421	+	17.7408i	0.212149	+	1.10236i
$260$	9.45584			0.586427
$261$	−0.414214	−	0.717439i	−0.0256392	−	0.0444084i
$262$	−4.48528	+	7.76874i	−0.277102	+	0.479954i
$263$	5.65685	−	9.79796i	0.348817	−	0.604168i	−0.637223	−	0.770680i	$-0.719917\pi$
$263$	5.65685	−	9.79796i	0.348817	−	0.604168i	0.986040	+	0.166511i	$0.0532503\pi$
$264$	1.44975	+	2.51104i	0.0892258	+	0.154544i
$265$	−3.65685			−0.224639
$266$	−0.828427	+	0.717439i	−0.0507941	+	0.0439890i
$267$	5.17157			0.316495
$268$	−10.9706	−	19.0016i	−0.670134	−	1.16071i
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	−0.717933	−	0.696112i	$-0.754912\pi$
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	0.961817	+	0.273692i	$0.0882449\pi$
$270$	−0.378680	+	0.655892i	−0.0230457	+	0.0399163i
$271$	−12.8137	−	22.1940i	−0.778377	−	1.34819i	−0.932877	−	0.360196i	$-0.882710\pi$
$271$	−12.8137	−	22.1940i	−0.778377	−	1.34819i	0.154499	−	0.987993i	$-0.450624\pi$
$272$	22.9706			1.39279
$273$	−5.65685	+	4.89898i	−0.342368	+	0.296500i
$274$	−3.38478			−0.204482
$275$	1.51472	+	2.62357i	0.0913410	+	0.158207i
$276$	3.50000	−	6.06218i	0.210675	−	0.364900i
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	−0.964466	−	1.67050i	−0.0578448	−	0.100190i
$279$	−8.82843			−0.528544
$280$	−1.44975	−	7.53311i	−0.0866390	−	0.450189i
$281$	−26.9706			−1.60893			−0.804464	−	0.594001i	$-0.797548\pi$
$281$	−26.9706			−1.60893			−0.804464	+	0.594001i	$0.797548\pi$
$282$	−2.44975	−	4.24309i	−0.145880	−	0.252672i
$283$	6.81371	−	11.8017i	0.405033	−	0.701538i	−0.589292	−	0.807920i	$-0.700593\pi$
$283$	6.81371	−	11.8017i	0.405033	−	0.701538i	0.994325	+	0.106382i	$0.0339267\pi$
$284$	14.3137	−	24.7921i	0.849362	−	1.47114i
$285$	0.914214	+	1.58346i	0.0541533	+	0.0937963i
$286$	−2.14214			−0.126667
$287$	9.14214	+	3.16693i	0.539643	+	0.186938i
$288$	4.41421			0.260110
$289$	−20.8137	−	36.0504i	−1.22434	−	2.12061i
$290$	−0.313708	+	0.543359i	−0.0184216	+	0.0319071i
$291$	−5.58579	+	9.67487i	−0.327445	+	0.567151i
$292$	11.2574	+	19.4983i	0.658787	+	1.14105i
$293$	4.82843			0.282080			0.141040	−	0.990004i	$-0.454955\pi$
$293$	4.82843			0.282080			0.141040	+	0.990004i	$0.454955\pi$
$294$	2.27817	+	1.79360i	0.132866	+	0.104605i
$295$	9.45584			0.550541
$296$	5.41421	+	9.37769i	0.314695	+	0.545067i
$297$	−0.914214	+	1.58346i	−0.0530481	+	0.0918819i
$298$	0.378680	−	0.655892i	0.0219363	−	0.0379948i
$299$	5.41421	+	9.37769i	0.313112	+	0.542326i
$300$	3.02944			0.174905
$301$	3.35786	+	1.16320i	0.193544	+	0.0670456i
$302$	5.51472			0.317336
$303$	−6.74264	−	11.6786i	−0.387355	−	0.670918i
$304$	1.50000	−	2.59808i	0.0860309	−	0.149010i
$305$	3.05635	−	5.29375i	0.175006	−	0.303119i
$306$	−1.58579	−	2.74666i	−0.0906534	−	0.157016i
$307$	−14.4853			−0.826719			−0.413359	−	0.910568i	$-0.635645\pi$
$307$	−14.4853			−0.826719			−0.413359	+	0.910568i	$0.635645\pi$
$308$	−1.67157	−	8.68575i	−0.0952467	−	0.494916i
$309$	−7.65685			−0.435583
$310$	3.34315	+	5.79050i	0.189878	+	0.328878i
$311$	11.3137	−	19.5959i	0.641542	−	1.11118i	−0.343547	−	0.939135i	$-0.611629\pi$
$311$	11.3137	−	19.5959i	0.641542	−	1.11118i	0.985089	−	0.172047i	$-0.0550381\pi$
$312$	−2.24264	+	3.88437i	−0.126965	+	0.219909i
$313$	12.6421	+	21.8968i	0.714576	+	1.23768i	0.963123	+	0.269062i	$0.0867136\pi$
$313$	12.6421	+	21.8968i	0.714576	+	1.23768i	−0.248547	+	0.968620i	$0.579953\pi$
$314$	−0.272078			−0.0153542
$315$	3.65685	−	3.16693i	0.206040	−	0.178436i
$316$	−24.9706			−1.40470
$317$	4.89949	+	8.48617i	0.275183	+	0.476631i	0.970181	−	0.242380i	$-0.0779282\pi$
$317$	4.89949	+	8.48617i	0.275183	+	0.476631i	−0.694998	+	0.719011i	$0.744595\pi$
$318$	0.414214	−	0.717439i	0.0232279	−	0.0402320i
$319$	−0.757359	+	1.31178i	−0.0424040	+	0.0734458i
$320$	3.81371	+	6.60554i	0.213193	+	0.369261i
$321$	2.82843			0.157867
$322$	3.17157	−	2.74666i	0.176745	−	0.153066i
$323$	−7.65685			−0.426039
$324$	0.914214	+	1.58346i	0.0507896	+	0.0879702i
$325$	−2.34315	+	4.05845i	−0.129974	+	0.225122i
$326$	2.47918	−	4.29407i	0.137309	−	0.237827i
$327$	5.07107	+	8.78335i	0.280431	+	0.485720i
$328$	5.79899			0.320196
$329$	5.91421	+	30.7312i	0.326061	+	1.69426i
$330$	1.38478			0.0762294
$331$	11.2426	+	19.4728i	0.617951	+	1.07032i	0.989859	+	0.142053i	$0.0453705\pi$
$331$	11.2426	+	19.4728i	0.617951	+	1.07032i	−0.371908	+	0.928270i	$0.621296\pi$
$332$	8.98528	−	15.5630i	0.493131	−	0.854129i
$333$	−3.41421	+	5.91359i	−0.187098	+	0.324063i
$334$	−0.656854	−	1.13770i	−0.0359415	−	0.0622524i
$335$	−21.9411			−1.19877
$336$	−7.50000	−	2.59808i	−0.409159	−	0.141737i
$337$	10.4853			0.571170			0.285585	−	0.958353i	$-0.407812\pi$
$337$	10.4853			0.571170			0.285585	+	0.958353i	$0.407812\pi$
$338$	1.03553	+	1.79360i	0.0563256	+	0.0975588i
$339$	3.58579	−	6.21076i	0.194753	−	0.337322i
$340$	12.7990	−	22.1685i	0.694123	−	1.20226i
$341$	8.07107	+	13.9795i	0.437073	+	0.757032i
$342$	−0.414214			−0.0223981
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	2.12994			0.114839
$345$	−3.50000	−	6.06218i	−0.188434	−	0.326377i
$346$	0.585786	−	1.01461i	0.0314921	−	0.0545459i
$347$	15.2279	−	26.3755i	0.817478	−	1.41591i	−0.0900574	−	0.995937i	$-0.528705\pi$
$347$	15.2279	−	26.3755i	0.817478	−	1.41591i	0.907535	−	0.419976i	$-0.137962\pi$
$348$	0.757359	+	1.31178i	0.0405987	+	0.0703190i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	1.71573	+	0.594346i	0.0917096	+	0.0317691i
$351$	−2.82843			−0.150970
$352$	−4.03553	−	6.98975i	−0.215095	−	0.372555i
$353$	−10.6569	+	18.4582i	−0.567207	+	0.982432i	0.429633	+	0.903003i	$0.358643\pi$
$353$	−10.6569	+	18.4582i	−0.567207	+	0.982432i	−0.996841	+	0.0794282i	$0.974691\pi$
$354$	−1.07107	+	1.85514i	−0.0569266	+	0.0985998i
$355$	−14.3137	−	24.7921i	−0.759693	−	1.31583i
$356$	−9.45584			−0.501159
$357$	3.82843	+	19.8931i	0.202622	+	1.05285i
$358$	2.68629			0.141975
$359$	5.91421	+	10.2437i	0.312140	+	0.540643i	0.978825	−	0.204697i	$-0.0656208\pi$
$359$	5.91421	+	10.2437i	0.312140	+	0.540643i	−0.666685	+	0.745339i	$0.732287\pi$
$360$	1.44975	−	2.51104i	0.0764084	−	0.132343i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	0.0710678	+	0.123093i	0.00373524	+	0.00646963i
$363$	−7.65685			−0.401881
$364$	10.3431	−	8.95743i	0.542128	−	0.469497i
$365$	22.5147			1.17847
$366$	0.692388	+	1.19925i	0.0361917	+	0.0626859i
$367$	−9.17157	+	15.8856i	−0.478752	+	0.829223i	−0.999703	−	0.0243635i	$-0.992244\pi$
$367$	−9.17157	+	15.8856i	−0.478752	+	0.829223i	0.520951	+	0.853587i	$0.325577\pi$
$368$	−5.74264	+	9.94655i	−0.299356	+	0.518500i
$369$	1.82843	+	3.16693i	0.0951841	+	0.164864i
$370$	5.17157			0.268857
$371$	−4.00000	+	3.46410i	−0.207670	+	0.179847i
$372$	16.1421			0.836931
$373$	18.1421	+	31.4231i	0.939364	+	1.62703i	0.766661	+	0.642053i	$0.221917\pi$
$373$	18.1421	+	31.4231i	0.939364	+	1.62703i	0.172704	+	0.984974i	$0.444750\pi$
$374$	−2.89949	+	5.02207i	−0.149929	+	0.259685i
$375$	6.08579	−	10.5409i	0.314269	−	0.544329i
$376$	9.37868	+	16.2443i	0.483668	+	0.837738i
$377$	−2.34315			−0.120678
$378$	0.207107	+	1.07616i	0.0106524	+	0.0553516i
$379$	0.485281			0.0249272			0.0124636	−	0.999922i	$-0.496033\pi$
$379$	0.485281			0.0249272			0.0124636	+	0.999922i	$0.496033\pi$
$380$	−1.67157	−	2.89525i	−0.0857499	−	0.148523i
$381$	8.48528	−	14.6969i	0.434714	−	0.752947i
$382$	−1.27817	+	2.21386i	−0.0653971	+	0.113271i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	−10.5563			−0.538701
$385$	−8.35786	−	2.89525i	−0.425956	−	0.147556i
$386$	1.65685			0.0843317
$387$	0.671573	+	1.16320i	0.0341380	+	0.0591287i
$388$	10.2132	−	17.6898i	0.518497	−	0.898063i
$389$	−7.82843	+	13.5592i	−0.396917	+	0.687480i	−0.993344	−	0.115187i	$-0.963253\pi$
$389$	−7.82843	+	13.5592i	−0.396917	+	0.687480i	0.596427	+	0.802667i	$0.296587\pi$
$390$	1.07107	+	1.85514i	0.0542356	+	0.0939389i
$391$	29.3137			1.48246
$392$	−8.72183	−	6.86666i	−0.440519	−	0.346819i
$393$	21.6569			1.09244
$394$	0.106602	+	0.184640i	0.00537052	+	0.00930201i
$395$	−12.4853	+	21.6251i	−0.628203	+	1.08808i
$396$	1.67157	−	2.89525i	0.0839997	−	0.145492i
$397$	8.65685	+	14.9941i	0.434475	+	0.752533i	0.997253	−	0.0740755i	$-0.0236006\pi$
$397$	8.65685	+	14.9941i	0.434475	+	0.752533i	−0.562778	+	0.826608i	$0.690267\pi$
$398$	6.07107			0.304315
$399$	2.50000	+	0.866025i	0.125157	+	0.0433555i
$400$	−4.97056			−0.248528
$401$	11.6569	+	20.1903i	0.582116	+	1.00825i	0.995228	+	0.0975738i	$0.0311082\pi$
$401$	11.6569	+	20.1903i	0.582116	+	1.00825i	−0.413113	+	0.910680i	$0.635558\pi$
$402$	2.48528	−	4.30463i	0.123955	−	0.214696i
$403$	−12.4853	+	21.6251i	−0.621936	+	1.07723i
$404$	12.3284	+	21.3535i	0.613362	+	1.06237i
$405$	1.82843			0.0908553
$406$	0.171573	+	0.891519i	0.00851502	+	0.0442453i
$407$	12.4853			0.618872
$408$	6.07107	+	10.5154i	0.300563	+	0.520590i
$409$	8.65685	−	14.9941i	0.428054	−	0.741411i	−0.568646	−	0.822582i	$-0.692533\pi$
$409$	8.65685	−	14.9941i	0.428054	−	0.741411i	0.996700	+	0.0811711i	$0.0258660\pi$
$410$	1.38478	−	2.39850i	0.0683892	−	0.118454i
$411$	4.08579	+	7.07679i	0.201537	+	0.349072i
$412$	14.0000			0.689730
$413$	10.3431	−	8.95743i	0.508953	−	0.440766i
$414$	1.58579			0.0779372
$415$	−8.98528	−	15.5630i	−0.441070	−	0.763956i
$416$	6.24264	−	10.8126i	0.306071	−	0.530130i
$417$	−2.32843	+	4.03295i	−0.114024	+	0.197495i
$418$	0.378680	+	0.655892i	0.0185218	+	0.0320807i
$419$	−15.8284			−0.773269			−0.386635	−	0.922233i	$-0.626363\pi$
$419$	−15.8284			−0.773269			−0.386635	+	0.922233i	$0.626363\pi$
$420$	−6.68629	+	5.79050i	−0.326258	+	0.282547i
$421$	24.8284			1.21006			0.605032	−	0.796201i	$-0.293160\pi$
$421$	24.8284			1.21006			0.605032	+	0.796201i	$0.293160\pi$
$422$	0.100505	+	0.174080i	0.00489251	+	0.00847408i
$423$	−5.91421	+	10.2437i	−0.287559	+	0.498067i
$424$	−1.58579	+	2.74666i	−0.0770126	+	0.133390i
$425$	6.34315	+	10.9867i	0.307688	+	0.532931i
$426$	6.48528			0.314213
$427$	−1.67157	−	8.68575i	−0.0808931	−	0.420333i
$428$	−5.17157			−0.249977
$429$	2.58579	+	4.47871i	0.124843	+	0.216234i
$430$	0.508622	−	0.880959i	0.0245279	−	0.0424836i
$431$	14.4142	−	24.9662i	0.694308	−	1.20258i	−0.276105	−	0.961127i	$-0.589044\pi$
$431$	14.4142	−	24.9662i	0.694308	−	1.20258i	0.970413	−	0.241450i	$-0.0776229\pi$
$432$	−1.50000	−	2.59808i	−0.0721688	−	0.125000i
$433$	−8.48528			−0.407777			−0.203888	−	0.978994i	$-0.565358\pi$
$433$	−8.48528			−0.407777			−0.203888	+	0.978994i	$0.565358\pi$
$434$	9.14214	+	3.16693i	0.438837	+	0.152017i
$435$	1.51472			0.0726252
$436$	−9.27208	−	16.0597i	−0.444052	−	0.769121i
$437$	1.91421	−	3.31552i	0.0915693	−	0.158603i
$438$	−2.55025	+	4.41717i	−0.121856	+	0.211060i
$439$	−9.89949	−	17.1464i	−0.472477	−	0.818354i	0.527027	−	0.849849i	$-0.323307\pi$
$439$	−9.89949	−	17.1464i	−0.472477	−	0.818354i	−0.999504	+	0.0314943i	$0.989973\pi$
$440$	−5.30152			−0.252740
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	−8.97056			−0.426686
$443$	11.1716	+	19.3497i	0.530777	+	0.919334i	0.999355	+	0.0359111i	$0.0114333\pi$
$443$	11.1716	+	19.3497i	0.530777	+	0.919334i	−0.468578	+	0.883422i	$0.655233\pi$
$444$	6.24264	−	10.8126i	0.296263	−	0.513142i
$445$	−4.72792	+	8.18900i	−0.224125	+	0.388196i
$446$	3.68629	+	6.38484i	0.174551	+	0.302331i
$447$	−1.82843			−0.0864816
$448$	10.4289	+	3.61269i	0.492721	+	0.170683i
$449$	−2.14214			−0.101094			−0.0505468	−	0.998722i	$-0.516096\pi$
$449$	−2.14214			−0.101094			−0.0505468	+	0.998722i	$0.516096\pi$
$450$	0.343146	+	0.594346i	0.0161760	+	0.0280177i
$451$	3.34315	−	5.79050i	0.157423	−	0.272664i
$452$	−6.55635	+	11.3559i	−0.308385	+	0.534138i
$453$	−6.65685	−	11.5300i	−0.312766	−	0.541727i
$454$	−7.31371			−0.343249
$455$	−2.58579	−	13.4361i	−0.121224	−	0.629896i
$456$	1.58579			0.0742613
$457$	1.67157	+	2.89525i	0.0781929	+	0.135434i	0.902470	−	0.430752i	$-0.141752\pi$
$457$	1.67157	+	2.89525i	0.0781929	+	0.135434i	−0.824277	+	0.566186i	$0.808418\pi$
$458$	0.899495	−	1.55797i	0.0420306	−	0.0727992i
$459$	−3.82843	+	6.63103i	−0.178696	+	0.309510i
$460$	6.39949	+	11.0843i	0.298378	+	0.516806i
$461$	−28.4558			−1.32532			−0.662660	−	0.748920i	$-0.730573\pi$
$461$	−28.4558			−1.32532			−0.662660	+	0.748920i	$0.730573\pi$
$462$	1.51472	−	1.31178i	0.0704711	−	0.0610298i
$463$	−9.34315			−0.434213			−0.217106	−	0.976148i	$-0.569662\pi$
$463$	−9.34315			−0.434213			−0.217106	+	0.976148i	$0.569662\pi$
$464$	−1.24264	−	2.15232i	−0.0576881	−	0.0999188i
$465$	8.07107	−	13.9795i	0.374287	−	0.648284i
$466$	−1.24264	+	2.15232i	−0.0575642	+	0.0997042i
$467$	−4.25736	−	7.37396i	−0.197007	−	0.341226i	0.750550	−	0.660814i	$-0.229789\pi$
$467$	−4.25736	−	7.37396i	−0.197007	−	0.341226i	−0.947557	+	0.319588i	$0.896456\pi$
$468$	5.17157			0.239056
$469$	−24.0000	+	20.7846i	−1.10822	+	0.959744i
$470$	8.95837			0.413219
$471$	0.328427	+	0.568852i	0.0151331	+	0.0262113i
$472$	4.10051	−	7.10228i	0.188741	−	0.326909i
$473$	1.22792	−	2.12682i	0.0564599	−	0.0977914i
$474$	−2.82843	−	4.89898i	−0.129914	−	0.225018i
$475$	1.65685			0.0760217
$476$	−7.00000	−	36.3731i	−0.320844	−	1.66716i
$477$	−2.00000			−0.0915737
$478$	−2.82843	−	4.89898i	−0.129369	−	0.224074i
$479$	−8.91421	+	15.4399i	−0.407301	+	0.705466i	−0.994586	−	0.103914i	$-0.966863\pi$
$479$	−8.91421	+	15.4399i	−0.407301	+	0.705466i	0.587285	+	0.809380i	$0.300197\pi$
$480$	−4.03553	+	6.98975i	−0.184196	+	0.319037i
$481$	9.65685	+	16.7262i	0.440315	+	0.762647i
$482$	−8.20101			−0.373546
$483$	−9.57107	−	3.31552i	−0.435499	−	0.150861i
$484$	14.0000			0.636364
$485$	−10.2132	−	17.6898i	−0.463758	−	0.803252i
$486$	−0.207107	+	0.358719i	−0.00939455	+	0.0162718i
$487$	5.82843	−	10.0951i	0.264111	−	0.457454i	−0.703219	−	0.710973i	$-0.748255\pi$
$487$	5.82843	−	10.0951i	0.264111	−	0.457454i	0.967330	+	0.253519i	$0.0815881\pi$
$488$	−2.65076	−	4.59125i	−0.119994	−	0.207836i
$489$	−11.9706			−0.541328
$490$	−4.92284	+	1.96768i	−0.222391	+	0.0888906i
$491$	−25.4853			−1.15013			−0.575067	−	0.818106i	$-0.695024\pi$
$491$	−25.4853			−1.15013			−0.575067	+	0.818106i	$0.695024\pi$
$492$	−3.34315	−	5.79050i	−0.150721	−	0.261056i
$493$	−3.17157	+	5.49333i	−0.142840	+	0.247407i
$494$	−0.585786	+	1.01461i	−0.0263558	+	0.0456495i
$495$	−1.67157	−	2.89525i	−0.0751316	−	0.130132i
$496$	−26.4853			−1.18922
$497$	−39.1421	−	13.5592i	−1.75576	−	0.608215i
$498$	4.07107			0.182429
$499$	6.98528	+	12.0989i	0.312704	+	0.541619i	0.978947	−	0.204116i	$-0.0654318\pi$
$499$	6.98528	+	12.0989i	0.312704	+	0.541619i	−0.666243	+	0.745735i	$0.732098\pi$
$500$	−11.1274	+	19.2733i	−0.497633	+	0.861926i
$501$	−1.58579	+	2.74666i	−0.0708477	+	0.122712i
$502$	−0.721825	−	1.25024i	−0.0322166	−	0.0558009i
$503$	−42.1127			−1.87771			−0.938856	−	0.344309i	$-0.888113\pi$
$503$	−42.1127			−1.87771			−0.938856	+	0.344309i	$0.888113\pi$
$504$	−0.792893	−	4.11999i	−0.0353183	−	0.183519i
$505$	24.6569			1.09722
$506$	−1.44975	−	2.51104i	−0.0644491	−	0.111629i
$507$	2.50000	−	4.33013i	0.111029	−	0.192308i
$508$	−15.5147	+	26.8723i	−0.688354	+	1.19226i
$509$	−3.24264	−	5.61642i	−0.143728	−	0.248943i	0.785170	−	0.619280i	$-0.212576\pi$
$509$	−3.24264	−	5.61642i	−0.143728	−	0.248943i	−0.928897	+	0.370337i	$0.879242\pi$
$510$	5.79899			0.256784
$511$	24.6274	−	21.3280i	1.08945	−	0.943494i
$512$	22.7574			1.00574
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−5.38478	+	9.32671i	−0.237512	+	0.411383i
$515$	7.00000	−	12.1244i	0.308457	−	0.534263i
$516$	−1.22792	−	2.12682i	−0.0540563	−	0.0936282i
$517$	21.6274			0.951173
$518$	5.65685	−	4.89898i	0.248548	−	0.215249i
$519$	−2.82843			−0.124154
$520$	−4.10051	−	7.10228i	−0.179819	−	0.311456i
$521$	3.51472	−	6.08767i	0.153983	−	0.266706i	−0.778705	−	0.627390i	$-0.784123\pi$
$521$	3.51472	−	6.08767i	0.153983	−	0.266706i	0.932688	+	0.360684i	$0.117457\pi$
$522$	−0.171573	+	0.297173i	−0.00750954	+	0.0130069i
$523$	−0.899495	−	1.55797i	−0.0393322	−	0.0681253i	0.845689	−	0.533676i	$-0.179190\pi$
$523$	−0.899495	−	1.55797i	−0.0393322	−	0.0681253i	−0.885021	+	0.465550i	$0.845856\pi$
$524$	−39.5980			−1.72985
$525$	−0.828427	−	4.30463i	−0.0361555	−	0.187870i
$526$	−4.68629			−0.204332
$527$	33.7990	+	58.5416i	1.47231	+	2.55011i
$528$	−2.74264	+	4.75039i	−0.119358	+	0.206734i
$529$	4.17157	−	7.22538i	0.181373	−	0.314147i
$530$	0.757359	+	1.31178i	0.0328976	+	0.0569803i
$531$	5.17157			0.224427
$532$	−4.57107	−	1.58346i	−0.198181	−	0.0686519i
$533$	10.3431			0.448011
$534$	−1.07107	−	1.85514i	−0.0463496	−	0.0802799i
$535$	−2.58579	+	4.47871i	−0.111793	+	0.193632i
$536$	−9.51472	+	16.4800i	−0.410973	+	0.711827i
$537$	−3.24264	−	5.61642i	−0.139930	−	0.242366i
$538$	−3.31371			−0.142864
$539$	−11.8848	+	4.75039i	−0.511914	+	0.204614i
$540$	−3.34315			−0.143866
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	0.505556	−	0.862794i	$-0.331288\pi$
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	−0.999979	+	0.00642713i	$0.997954\pi$
$542$	−5.30761	+	9.19305i	−0.227981	+	0.394875i
$543$	0.171573	−	0.297173i	0.00736290	−	0.0127529i
$544$	−16.8995	−	29.2708i	−0.724560	−	1.25497i
$545$	−18.5442			−0.794344
$546$	2.92893	+	1.01461i	0.125347	+	0.0434214i
$547$	33.7990			1.44514			0.722570	−	0.691298i	$-0.242961\pi$
$547$	33.7990			1.44514			0.722570	+	0.691298i	$0.242961\pi$
$548$	−7.47056	−	12.9394i	−0.319127	−	0.552744i
$549$	1.67157	−	2.89525i	0.0713410	−	0.123566i
$550$	0.627417	−	1.08672i	0.0267532	−	0.0463378i
$551$	0.414214	+	0.717439i	0.0176461	+	0.0305639i
$552$	−6.07107			−0.258402
$553$	6.82843	+	35.4815i	0.290374	+	1.50883i
$554$	5.38478			0.228777
$555$	−6.24264	−	10.8126i	−0.264985	−	0.458968i
$556$	4.25736	−	7.37396i	0.180552	−	0.312726i
$557$	18.2279	−	31.5717i	0.772342	−	1.33774i	−0.163935	−	0.986471i	$-0.552419\pi$
$557$	18.2279	−	31.5717i	0.772342	−	1.33774i	0.936276	−	0.351264i	$-0.114248\pi$
$558$	1.82843	+	3.16693i	0.0774035	+	0.134067i
$559$	3.79899			0.160680
$560$	10.9706	−	9.50079i	0.463591	−	0.401481i
$561$	14.0000			0.591080
$562$	5.58579	+	9.67487i	0.235622	+	0.408110i
$563$	8.24264	−	14.2767i	0.347386	−	0.601690i	−0.638398	−	0.769706i	$-0.720403\pi$
$563$	8.24264	−	14.2767i	0.347386	−	0.601690i	0.985784	+	0.168016i	$0.0537361\pi$
$564$	10.8137	−	18.7299i	0.455339	−	0.788671i
$565$	6.55635	+	11.3559i	0.275828	+	0.477748i
$566$	−5.64466			−0.237263
$567$	2.00000	−	1.73205i	0.0839921	−	0.0727393i
$568$	−24.8284			−1.04178
$569$	3.10051	+	5.37023i	0.129980	+	0.225132i	0.923669	−	0.383192i	$-0.125175\pi$
$569$	3.10051	+	5.37023i	0.129980	+	0.225132i	−0.793689	+	0.608324i	$0.791842\pi$
$570$	0.378680	−	0.655892i	0.0158611	−	0.0274723i
$571$	14.6421	−	25.3609i	0.612754	−	1.06132i	−0.378020	−	0.925798i	$-0.623395\pi$
$571$	14.6421	−	25.3609i	0.612754	−	1.06132i	0.990774	−	0.135524i	$-0.0432718\pi$
$572$	−4.72792	−	8.18900i	−0.197684	−	0.342399i
$573$	6.17157			0.257821
$574$	−0.757359	−	3.93535i	−0.0316116	−	0.164259i
$575$	−6.34315			−0.264527
$576$	2.08579	+	3.61269i	0.0869078	+	0.150529i
$577$	2.15685	−	3.73578i	0.0897910	−	0.155523i	−0.817632	−	0.575742i	$-0.804713\pi$
$577$	2.15685	−	3.73578i	0.0897910	−	0.155523i	0.907423	+	0.420219i	$0.138047\pi$
$578$	−8.62132	+	14.9326i	−0.358600	+	0.621113i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	−2.76955			−0.114999
$581$	−24.5711	−	8.51167i	−1.01938	−	0.353123i
$582$	4.62742			0.191813
$583$	1.82843	+	3.16693i	0.0757257	+	0.131161i
$584$	9.76346	−	16.9108i	0.404015	−	0.699774i
$585$	2.58579	−	4.47871i	0.106909	−	0.185172i
$586$	−1.00000	−	1.73205i	−0.0413096	−	0.0715504i
$587$	18.6274			0.768836			0.384418	−	0.923159i	$-0.374402\pi$
$587$	18.6274			0.768836			0.384418	+	0.923159i	$0.374402\pi$
$588$	−1.82843	+	12.6677i	−0.0754031	+	0.522408i
$589$	8.82843			0.363769
$590$	−1.95837	−	3.39200i	−0.0806248	−	0.139646i
$591$	0.257359	−	0.445759i	0.0105863	−	0.0183361i
$592$	−10.2426	+	17.7408i	−0.420970	+	0.729141i
$593$	−5.25736	−	9.10601i	−0.215894	−	0.373939i	0.737655	−	0.675178i	$-0.235933\pi$
$593$	−5.25736	−	9.10601i	−0.215894	−	0.373939i	−0.953549	+	0.301239i	$0.902600\pi$
$594$	0.757359			0.0310748
$595$	−35.0000	−	12.1244i	−1.43486	−	0.497050i
$596$	3.34315			0.136941
$597$	−7.32843	−	12.6932i	−0.299933	−	0.519498i
$598$	2.24264	−	3.88437i	0.0917084	−	0.158844i
$599$	−16.5563	+	28.6764i	−0.676474	+	1.17169i	0.299562	+	0.954077i	$0.403160\pi$
$599$	−16.5563	+	28.6764i	−0.676474	+	1.17169i	−0.976036	+	0.217611i	$0.930174\pi$
$600$	−1.31371	−	2.27541i	−0.0536319	−	0.0928932i
$601$	−31.3137			−1.27731			−0.638656	−	0.769492i	$-0.720509\pi$
$601$	−31.3137			−1.27731			−0.638656	+	0.769492i	$0.720509\pi$
$602$	−0.278175	−	1.44544i	−0.0113376	−	0.0589116i
$603$	−12.0000			−0.488678
$604$	12.1716	+	21.0818i	0.495254	+	0.857806i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$	−2.79289	+	4.83743i	−0.113454	+	0.196507i
$607$	−21.0711	−	36.4962i	−0.855248	−	1.48133i	−0.876415	−	0.481557i	$-0.840071\pi$
$607$	−21.0711	−	36.4962i	−0.855248	−	1.48133i	0.0211663	−	0.999776i	$-0.493262\pi$
$608$	−4.41421			−0.179020
$609$	1.65685	−	1.43488i	0.0671391	−	0.0581442i
$610$	−2.53196			−0.102516
$611$	16.7279	+	28.9736i	0.676739	+	1.17215i
$612$	7.00000	−	12.1244i	0.282958	−	0.490098i
$613$	−4.31371	+	7.47156i	−0.174229	+	0.301774i	−0.939894	−	0.341466i	$-0.889077\pi$
$613$	−4.31371	+	7.47156i	−0.174229	+	0.301774i	0.765665	+	0.643239i	$0.222410\pi$
$614$	3.00000	+	5.19615i	0.121070	+	0.209700i
$615$	−6.68629			−0.269617
$616$	−5.79899	+	5.02207i	−0.233648	+	0.202345i
$617$	−37.8284			−1.52292			−0.761458	−	0.648215i	$-0.775516\pi$
$617$	−37.8284			−1.52292			−0.761458	+	0.648215i	$0.775516\pi$
$618$	1.58579	+	2.74666i	0.0637897	+	0.110487i
$619$	−10.3284	+	17.8894i	−0.415135	+	0.719034i	−0.995443	−	0.0953630i	$-0.969599\pi$
$619$	−10.3284	+	17.8894i	−0.415135	+	0.719034i	0.580308	+	0.814397i	$0.302932\pi$
$620$	−14.7574	+	25.5605i	−0.592670	+	1.02653i
$621$	−1.91421	−	3.31552i	−0.0768147	−	0.133047i
$622$	−9.37258			−0.375806
$623$	2.58579	+	13.4361i	0.103597	+	0.538308i
$624$	−8.48528			−0.339683
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$	5.23654	−	9.06996i	0.209294	−	0.362509i
$627$	0.914214	−	1.58346i	0.0365102	−	0.0632375i
$628$	−0.600505	−	1.04011i	−0.0239628	−	0.0415047i
$629$	52.2843			2.08471
$630$	−1.89340	−	0.655892i	−0.0754348	−	0.0261314i
$631$	−5.34315			−0.212707			−0.106354	−	0.994328i	$-0.533918\pi$
$631$	−5.34315			−0.212707			−0.106354	+	0.994328i	$0.533918\pi$
$632$	10.8284	+	18.7554i	0.430732	+	0.746049i
$633$	0.242641	−	0.420266i	0.00964410	−	0.0167041i
$634$	2.02944	−	3.51509i	0.0805992	−	0.139602i
$635$	15.5147	+	26.8723i	0.615683	+	1.06639i
$636$	3.65685			0.145004
$637$	−15.5563	−	12.2474i	−0.616365	−	0.485262i
$638$	0.627417			0.0248397
$639$	−7.82843	−	13.5592i	−0.309688	−	0.536395i
$640$	9.65076	−	16.7156i	0.381480	−	0.660742i
$641$	5.41421	−	9.37769i	0.213849	−	0.370397i	−0.739067	−	0.673632i	$-0.764733\pi$
$641$	5.41421	−	9.37769i	0.213849	−	0.370397i	0.952916	+	0.303235i	$0.0980668\pi$
$642$	−0.585786	−	1.01461i	−0.0231191	−	0.0400435i
$643$	46.6274			1.83881			0.919403	−	0.393317i	$-0.128673\pi$
$643$	46.6274			1.83881			0.919403	+	0.393317i	$0.128673\pi$
$644$	17.5000	+	6.06218i	0.689597	+	0.238883i
$645$	−2.45584			−0.0966988
$646$	1.58579	+	2.74666i	0.0623919	+	0.108066i
$647$	−17.5711	+	30.4340i	−0.690790	+	1.19648i	0.280789	+	0.959769i	$0.409404\pi$
$647$	−17.5711	+	30.4340i	−0.690790	+	1.19648i	−0.971579	+	0.236714i	$0.923930\pi$
$648$	0.792893	−	1.37333i	0.0311478	−	0.0539496i
$649$	−4.72792	−	8.18900i	−0.185587	−	0.321446i
$650$	1.94113			0.0761372
$651$	−4.41421	−	22.9369i	−0.173007	−	0.898969i
$652$	21.8873			0.857173
$653$	13.9706	+	24.1977i	0.546710	+	0.946930i	0.998497	+	0.0548042i	$0.0174535\pi$
$653$	13.9706	+	24.1977i	0.546710	+	0.946930i	−0.451787	+	0.892126i	$0.649213\pi$
$654$	2.10051	−	3.63818i	0.0821362	−	0.142264i
$655$	−19.7990	+	34.2929i	−0.773611	+	1.33993i
$656$	5.48528	+	9.50079i	0.214164	+	0.370943i
$657$	12.3137			0.480404
$658$	9.79899	−	8.48617i	0.382004	−	0.330826i
$659$	−38.4853			−1.49917			−0.749587	−	0.661906i	$-0.769748\pi$
$659$	−38.4853			−1.49917			−0.749587	+	0.661906i	$0.769748\pi$
$660$	3.05635	+	5.29375i	0.118968	+	0.206059i
$661$	22.1421	−	38.3513i	0.861229	−	1.49169i	−0.00951390	−	0.999955i	$-0.503028\pi$
$661$	22.1421	−	38.3513i	0.861229	−	1.49169i	0.870743	−	0.491738i	$-0.163638\pi$
$662$	4.65685	−	8.06591i	0.180994	−	0.313490i
$663$	10.8284	+	18.7554i	0.420541	+	0.728399i
$664$	−15.5858			−0.604846
$665$	−3.65685	+	3.16693i	−0.141807	+	0.122808i
$666$	2.82843			0.109599
$667$	−1.58579	−	2.74666i	−0.0614019	−	0.106351i
$668$	2.89949	−	5.02207i	0.112185	−	0.194310i
$669$	8.89949	−	15.4144i	0.344074	−	0.595954i
$670$	4.54416	+	7.87071i	0.175556	+	0.304072i
$671$	−6.11270			−0.235978
$672$	2.20711	+	11.4685i	0.0851410	+	0.442406i
$673$	−2.82843			−0.109028			−0.0545139	−	0.998513i	$-0.517361\pi$
$673$	−2.82843			−0.109028			−0.0545139	+	0.998513i	$0.517361\pi$
$674$	−2.17157	−	3.76127i	−0.0836459	−	0.144879i
$675$	0.828427	−	1.43488i	0.0318862	−	0.0552285i
$676$	−4.57107	+	7.91732i	−0.175810	+	0.304512i
$677$	8.00000	+	13.8564i	0.307465	+	0.532545i	0.977807	−	0.209507i	$-0.0671860\pi$
$677$	8.00000	+	13.8564i	0.307465	+	0.532545i	−0.670342	+	0.742052i	$0.733853\pi$
$678$	−2.97056			−0.114084
$679$	−27.9289	−	9.67487i	−1.07181	−	0.371287i
$680$	−22.2010			−0.851370
$681$	8.82843	+	15.2913i	0.338306	+	0.585963i
$682$	3.34315	−	5.79050i	0.128016	−	0.221730i
$683$	−19.4853	+	33.7495i	−0.745584	+	1.29139i	0.204338	+	0.978900i	$0.434496\pi$
$683$	−19.4853	+	33.7495i	−0.745584	+	1.29139i	−0.949922	+	0.312488i	$0.898838\pi$
$684$	−0.914214	−	1.58346i	−0.0349558	−	0.0605453i
$685$	−14.9411			−0.570871
$686$	−3.52082	+	6.81567i	−0.134425	+	0.260223i
$687$	−4.34315			−0.165701
$688$	2.01472	+	3.48960i	0.0768104	+	0.133040i
$689$	−2.82843	+	4.89898i	−0.107754	+	0.186636i
$690$	−1.44975	+	2.51104i	−0.0551909	+	0.0955935i
$691$	−6.00000	−	10.3923i	−0.228251	−	0.395342i	0.729039	−	0.684472i	$-0.239967\pi$
$691$	−6.00000	−	10.3923i	−0.228251	−	0.395342i	−0.957290	+	0.289130i	$0.906634\pi$
$692$	5.17157			0.196594
$693$	−4.57107	−	1.58346i	−0.173641	−	0.0601508i
$694$	−12.6152			−0.478867
$695$	−4.25736	−	7.37396i	−0.161491	−	0.279710i
$696$	0.656854	−	1.13770i	0.0248980	−	0.0431246i
$697$	14.0000	−	24.2487i	0.530288	−	0.918485i
$698$	−2.89949	−	5.02207i	−0.109748	−	0.190088i
$699$	6.00000			0.226941
$700$	1.51472	+	7.87071i	0.0572510	+	0.297485i
$701$	−48.4558			−1.83015			−0.915076	−	0.403281i	$-0.867870\pi$
$701$	−48.4558			−1.83015			−0.915076	+	0.403281i	$0.867870\pi$
$702$	0.585786	+	1.01461i	0.0221091	+	0.0382941i
$703$	3.41421	−	5.91359i	0.128770	−	0.223035i
$704$	3.81371	−	6.60554i	0.143735	−	0.248956i
$705$	−10.8137	−	18.7299i	−0.407268	−	0.705409i
$706$	8.82843			0.332262
$707$	26.9706	−	23.3572i	1.01433	−	0.878438i
$708$	−9.45584			−0.355372
$709$	−8.98528	−	15.5630i	−0.337449	−	0.584479i	0.646503	−	0.762912i	$-0.276231\pi$
$709$	−8.98528	−	15.5630i	−0.337449	−	0.584479i	−0.983952	+	0.178432i	$0.942897\pi$
$710$	−5.92893	+	10.2692i	−0.222509	+	0.385397i
$711$	−6.82843	+	11.8272i	−0.256086	+	0.443554i
$712$	4.10051	+	7.10228i	0.153673	+	0.266169i
$713$	−33.7990			−1.26578
$714$	6.34315	−	5.49333i	0.237386	−	0.205583i
$715$	−9.45584			−0.353629
$716$	5.92893	+	10.2692i	0.221575	+	0.383778i
$717$	−6.82843	+	11.8272i	−0.255012	+	0.441694i
$718$	2.44975	−	4.24309i	0.0914238	−	0.158351i
$719$	−16.4853	−	28.5533i	−0.614797	−	1.06486i	−0.990420	−	0.138087i	$-0.955905\pi$
$719$	−16.4853	−	28.5533i	−0.614797	−	1.06486i	0.375623	−	0.926773i	$-0.377429\pi$
$720$	5.48528			0.204424
$721$	−3.82843	−	19.8931i	−0.142578	−	0.740857i
$722$	0.414214			0.0154154
$723$	9.89949	+	17.1464i	0.368166	+	0.637683i
$724$	−0.313708	+	0.543359i	−0.0116589	+	0.0201938i
$725$	0.686292	−	1.18869i	0.0254882	−	0.0441469i
$726$	1.58579	+	2.74666i	0.0588541	+	0.101938i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	−11.2132	−	3.88437i	−0.415589	−	0.143964i
$729$	1.00000			0.0370370
$730$	−4.66295	−	8.07647i	−0.172584	−	0.298923i
$731$	5.14214	−	8.90644i	0.190189	−	0.329417i
$732$	−3.05635	+	5.29375i	−0.112966	+	0.195663i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	7.59798			0.280447
$735$	10.0563	+	7.91732i	0.370934	+	0.292035i
$736$	16.8995			0.622924
$737$	10.9706	+	19.0016i	0.404106	+	0.699932i
$738$	0.757359	−	1.31178i	0.0278788	−	0.0482875i
$739$	4.00000	−	6.92820i	0.147142	−	0.254858i	−0.783028	−	0.621987i	$-0.786326\pi$
$739$	4.00000	−	6.92820i	0.147142	−	0.254858i	0.930170	+	0.367129i	$0.119659\pi$
$740$	11.4142	+	19.7700i	0.419595	+	0.726760i
$741$	2.82843			0.103905
$742$	2.07107	+	0.717439i	0.0760313	+	0.0263380i
$743$	38.8284			1.42448			0.712238	−	0.701938i	$-0.247681\pi$
$743$	38.8284			1.42448			0.712238	+	0.701938i	$0.247681\pi$
$744$	−7.00000	−	12.1244i	−0.256632	−	0.444500i
$745$	1.67157	−	2.89525i	0.0612417	−	0.106074i
$746$	7.51472	−	13.0159i	0.275133	−	0.476545i
$747$	−4.91421	−	8.51167i	−0.179802	−	0.311426i
$748$	−25.5980			−0.935955
$749$	1.41421	+	7.34847i	0.0516742	+	0.268507i
$750$	−5.04163			−0.184094
$751$	5.31371	+	9.20361i	0.193900	+	0.335845i	0.946539	−	0.322588i	$-0.104553\pi$
$751$	5.31371	+	9.20361i	0.193900	+	0.335845i	−0.752639	+	0.658433i	$0.771220\pi$
$752$	−17.7426	+	30.7312i	−0.647008	+	1.12065i
$753$	−1.74264	+	3.01834i	−0.0635054	+	0.109995i
$754$	0.485281	+	0.840532i	0.0176729	+	0.0306104i
$755$	24.3431			0.885938
$756$	−3.65685	+	3.16693i	−0.132999	+	0.115180i
$757$	20.6569			0.750786			0.375393	−	0.926866i	$-0.377508\pi$
$757$	20.6569			0.750786			0.375393	+	0.926866i	$0.377508\pi$
$758$	−0.100505	−	0.174080i	−0.00365051	−	0.00632287i
$759$	−3.50000	+	6.06218i	−0.127042	+	0.220043i
$760$	−1.44975	+	2.51104i	−0.0525879	+	0.0910849i
$761$	−10.3995	−	18.0125i	−0.376981	−	0.652951i	0.613640	−	0.789586i	$-0.289705\pi$
$761$	−10.3995	−	18.0125i	−0.376981	−	0.652951i	−0.990621	+	0.136635i	$0.956371\pi$
$762$	−7.02944			−0.254650
$763$	−20.2843	+	17.5667i	−0.734340	+	0.635957i
$764$	−11.2843			−0.408251
$765$	−7.00000	−	12.1244i	−0.253086	−	0.438357i
$766$	−3.31371	+	5.73951i	−0.119729	+	0.207377i
$767$	7.31371	−	12.6677i	0.264083	−	0.457405i
$768$	−1.98528	−	3.43861i	−0.0716377	−	0.124080i
$769$	−8.31371			−0.299800			−0.149900	−	0.988701i	$-0.547895\pi$
$769$	−8.31371			−0.299800			−0.149900	+	0.988701i	$0.547895\pi$
$770$	0.692388	+	3.59775i	0.0249519	+	0.129654i
$771$	26.0000			0.936367
$772$	3.65685	+	6.33386i	0.131613	+	0.227961i
$773$	1.41421	−	2.44949i	0.0508657	−	0.0881020i	−0.839471	−	0.543404i	$-0.817135\pi$
$773$	1.41421	−	2.44949i	0.0508657	−	0.0881020i	0.890337	+	0.455302i	$0.150469\pi$
$774$	0.278175	−	0.481813i	0.00999878	−	0.0173184i
$775$	−7.31371	−	12.6677i	−0.262716	−	0.455038i
$776$	−17.7157			−0.635958
$777$	−17.0711	−	5.91359i	−0.612421	−	0.212149i
$778$	6.48528			0.232509
$779$	−1.82843	−	3.16693i	−0.0655102	−	0.113467i
$780$	−4.72792	+	8.18900i	−0.169287	+	0.293213i
$781$	−14.3137	+	24.7921i	−0.512185	+	0.887130i
$782$	−6.07107	−	10.5154i	−0.217101	−	0.376030i
$783$	0.828427			0.0296056
$784$	3.00000	−	20.7846i	0.107143	−	0.742307i
$785$	−1.20101			−0.0428659
$786$	−4.48528	−	7.76874i	−0.159985	−	0.277102i
$787$	20.1421	−	34.8872i	0.717990	−	1.24359i	−0.243806	−	0.969824i	$-0.578396\pi$
$787$	20.1421	−	34.8872i	0.717990	−	1.24359i	0.961795	−	0.273770i	$-0.0882708\pi$
$788$	−0.470563	+	0.815039i	−0.0167631	+	0.0290345i
$789$	5.65685	+	9.79796i	0.201389	+	0.348817i
$790$	10.3431			0.367993
$791$	17.9289	+	6.21076i	0.637479	+	0.220829i
$792$	−2.89949			−0.103029
$793$	−4.72792	−	8.18900i	−0.167893	−	0.290800i
$794$	3.58579	−	6.21076i	0.127255	−	0.220412i
$795$	1.82843	−	3.16693i	0.0648476	−	0.112319i
$796$	13.3995	+	23.2086i	0.474933	+	0.822607i
$797$	24.4853			0.867313			0.433657	−	0.901078i	$-0.357223\pi$
$797$	24.4853			0.867313			0.433657	+	0.901078i	$0.357223\pi$
$798$	−0.207107	−	1.07616i	−0.00733150	−	0.0380956i
$799$	90.5685			3.20408
$800$	3.65685	+	6.33386i	0.129289	+	0.223936i
$801$	−2.58579	+	4.47871i	−0.0913643	+	0.158248i
$802$	4.82843	−	8.36308i	0.170498	−	0.295311i
$803$	−11.2574	−	19.4983i	−0.397264	−	0.688081i
$804$	21.9411			0.773804
$805$	14.0000	−	12.1244i	0.493435	−	0.427327i
$806$	10.3431			0.364322
$807$	4.00000	+	6.92820i	0.140807	+	0.243884i
$808$	10.6924	−	18.5198i	0.376157	−	0.651523i
$809$	−7.39949	+	12.8163i	−0.260152	+	0.450597i	−0.966282	−	0.257485i	$-0.917106\pi$
$809$	−7.39949	+	12.8163i	−0.260152	+	0.450597i	0.706130	+	0.708082i	$0.250439\pi$
$810$	−0.378680	−	0.655892i	−0.0133054	−	0.0230457i
$811$	16.1421			0.566827			0.283414	−	0.958998i	$-0.408533\pi$
$811$	16.1421			0.566827			0.283414	+	0.958998i	$0.408533\pi$
$812$	−3.02944	+	2.62357i	−0.106312	+	0.0920692i
$813$	25.6274			0.898793
$814$	−2.58579	−	4.47871i	−0.0906318	−	0.156979i
$815$	10.9437	−	18.9550i	0.383339	−	0.663963i
$816$	−11.4853	+	19.8931i	−0.402065	+	0.696397i
$817$	−0.671573	−	1.16320i	−0.0234954	−	0.0406952i
$818$	−7.17157			−0.250748
$819$	−1.41421	−	7.34847i	−0.0494166	−	0.256776i
$820$	12.2254			0.426929
$821$	−17.5711	−	30.4340i	−0.613234	−	1.06215i	−0.990692	−	0.136126i	$-0.956535\pi$
$821$	−17.5711	−	30.4340i	−0.613234	−	1.06215i	0.377457	−	0.926027i	$-0.376799\pi$
$822$	1.69239	−	2.93130i	0.0590288	−	0.102241i
$823$	0.985281	−	1.70656i	0.0343447	−	0.0594869i	−0.848342	−	0.529448i	$-0.822399\pi$
$823$	0.985281	−	1.70656i	0.0343447	−	0.0594869i	0.882687	+	0.469962i	$0.155732\pi$
$824$	−6.07107	−	10.5154i	−0.211496	−	0.366321i
$825$	−3.02944			−0.105471
$826$	−5.35534	−	1.85514i	−0.186336	−	0.0645487i
$827$	47.1127			1.63827			0.819135	−	0.573601i	$-0.194454\pi$
$827$	47.1127			1.63827			0.819135	+	0.573601i	$0.194454\pi$
$828$	3.50000	+	6.06218i	0.121633	+	0.210675i
$829$	4.92893	−	8.53716i	0.171189	−	0.296508i	−0.767647	−	0.640873i	$-0.778572\pi$
$829$	4.92893	−	8.53716i	0.171189	−	0.296508i	0.938836	+	0.344365i	$0.111906\pi$
$830$	−3.72183	+	6.44639i	−0.129186	+	0.223757i
$831$	−6.50000	−	11.2583i	−0.225483	−	0.390547i
$832$	11.7990			0.409056
$833$	−49.7696	+	19.8931i	−1.72441	+	0.689255i
$834$	1.92893			0.0667935
$835$	−2.89949	−	5.02207i	−0.100341	−	0.173796i
$836$	−1.67157	+	2.89525i	−0.0578126	+	0.100134i
$837$	4.41421	−	7.64564i	0.152578	−	0.264272i
$838$	3.27817	+	5.67796i	0.113243	+	0.196142i
$839$	45.2548			1.56237			0.781185	−	0.624299i	$-0.214615\pi$
$839$	45.2548			1.56237			0.781185	+	0.624299i	$0.214615\pi$
$840$	7.24874	+	2.51104i	0.250105	+	0.0866390i
$841$	−28.3137			−0.976335
$842$	−5.14214	−	8.90644i	−0.177210	−	0.306936i
$843$	13.4853	−	23.3572i	0.464458	−	0.804464i
$844$	−0.443651	+	0.768426i	−0.0152711	+	0.0264503i
$845$	4.57107	+	7.91732i	0.157250	+	0.272364i
$846$	4.89949			0.168448
$847$	−3.82843	−	19.8931i	−0.131546	−	0.683535i
$848$	−6.00000			−0.206041
$849$	6.81371	+	11.8017i	0.233846	+	0.405033i
$850$	2.62742	−	4.55082i	0.0901197	−	0.156092i
$851$	−13.0711	+	22.6398i	−0.448070	+	0.776081i
$852$	14.3137	+	24.7921i	0.490380	+	0.849362i
$853$	−51.6274			−1.76769			−0.883845	−	0.467781i	$-0.845054\pi$
$853$	−51.6274			−1.76769			−0.883845	+	0.467781i	$0.845054\pi$
$854$	−2.76955	+	2.39850i	−0.0947721	+	0.0820751i
$855$	−1.82843			−0.0625309
$856$	2.24264	+	3.88437i	0.0766519	+	0.132765i
$857$	10.5858	−	18.3351i	0.361604	−	0.626316i	−0.626621	−	0.779324i	$-0.715563\pi$
$857$	10.5858	−	18.3351i	0.361604	−	0.626316i	0.988225	+	0.153008i	$0.0488961\pi$
$858$	1.07107	−	1.85514i	0.0365657	−	0.0633336i
$859$	18.4706	+	31.9920i	0.630207	+	1.09155i	0.987509	+	0.157562i	$0.0503635\pi$
$859$	18.4706	+	31.9920i	0.630207	+	1.09155i	−0.357302	+	0.933989i	$0.616303\pi$
$860$	4.49033			0.153119
$861$	−7.31371	+	6.33386i	−0.249251	+	0.215857i
$862$	−11.9411			−0.406716
$863$	−6.41421	−	11.1097i	−0.218342	−	0.378180i	0.735959	−	0.677026i	$-0.236732\pi$
$863$	−6.41421	−	11.1097i	−0.218342	−	0.378180i	−0.954301	+	0.298846i	$0.903398\pi$
$864$	−2.20711	+	3.82282i	−0.0750873	+	0.130055i
$865$	2.58579	−	4.47871i	0.0879194	−	0.152281i
$866$	1.75736	+	3.04384i	0.0597175	+	0.103434i
$867$	41.6274			1.41374
$868$	8.07107	+	41.9385i	0.273950	+	1.42349i
$869$	24.9706			0.847068
$870$	−0.313708	−	0.543359i	−0.0106357	−	0.0184216i
$871$	−16.9706	+	29.3939i	−0.575026	+	0.995974i
$872$	−8.04163	+	13.9285i	−0.272324	+	0.471679i
$873$	−5.58579	−	9.67487i	−0.189050	−	0.327445i
$874$	−1.58579			−0.0536400
$875$	30.4289	+	10.5409i	1.02869	+	0.356347i
$876$	−22.5147			−0.760702
$877$	−5.17157	−	8.95743i	−0.174632	−	0.302471i	0.765402	−	0.643552i	$-0.222540\pi$
$877$	−5.17157	−	8.95743i	−0.174632	−	0.302471i	−0.940034	+	0.341082i	$0.889207\pi$
$878$	−4.10051	+	7.10228i	−0.138385	+	0.239690i
$879$	−2.41421	+	4.18154i	−0.0814294	+	0.141040i
$880$	−5.01472	−	8.68575i	−0.169046	−	0.292796i
$881$	40.6274			1.36877			0.684386	−	0.729120i	$-0.260070\pi$
$881$	40.6274			1.36877			0.684386	+	0.729120i	$0.260070\pi$
$882$	−2.69239	+	1.07616i	−0.0906574	+	0.0362361i
$883$	−11.0294			−0.371170			−0.185585	−	0.982628i	$-0.559418\pi$
$883$	−11.0294			−0.371170			−0.185585	+	0.982628i	$0.559418\pi$
$884$	−19.7990	−	34.2929i	−0.665912	−	1.15339i
$885$	−4.72792	+	8.18900i	−0.158927	+	0.275270i
$886$	4.62742	−	8.01492i	0.155461	−	0.269267i
$887$	−17.7279	−	30.7057i	−0.595245	−	1.03100i	−0.993512	−	0.113726i	$-0.963722\pi$
$887$	−17.7279	−	30.7057i	−0.595245	−	1.03100i	0.398267	−	0.917270i	$-0.369612\pi$
$888$	−10.8284			−0.363378
$889$	42.4264	+	14.6969i	1.42294	+	0.492919i
$890$	3.91674			0.131289
$891$	−0.914214	−	1.58346i	−0.0306273	−	0.0530481i
$892$	−16.2721	+	28.1841i	−0.544829	+	0.943672i
$893$	5.91421	−	10.2437i	0.197912	−	0.342793i
$894$	0.378680	+	0.655892i	0.0126649	+	0.0219363i
$895$	11.8579			0.396365
$896$	−5.27817	−	27.4262i	−0.176331	−	0.916245i
$897$	−10.8284			−0.361551
$898$	0.443651	+	0.768426i	0.0148048	+	0.0256427i
$899$	3.65685	−	6.33386i	0.121963	−	0.211246i
$900$	−1.51472	+	2.62357i	−0.0504906	+	0.0874523i
$901$	7.65685	+	13.2621i	0.255087	+	0.441823i
$902$	−2.76955			−0.0922160
$903$	−2.68629	+	2.32640i	−0.0893942	+	0.0774176i
$904$	11.3726			0.378246
$905$	0.313708	+	0.543359i	0.0104280	+	0.0180619i
$906$	−2.75736	+	4.77589i	−0.0916071	+	0.158668i
$907$	4.17157	−	7.22538i	0.138515	−	0.239915i	−0.788420	−	0.615138i	$-0.789100\pi$
$907$	4.17157	−	7.22538i	0.138515	−	0.239915i	0.926935	+	0.375223i	$0.122434\pi$
$908$	−16.1421	−	27.9590i	−0.535696	−	0.927852i
$909$	13.4853			0.447279
$910$	−4.28427	+	3.71029i	−0.142022	+	0.122995i
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$	1.50000	+	2.59808i	0.0496700	+	0.0860309i
$913$	−8.98528	+	15.5630i	−0.297369	+	0.515059i
$914$	0.692388	−	1.19925i	0.0229022	−	0.0396677i
$915$	3.05635	+	5.29375i	0.101040	+	0.175006i
$916$	7.94113			0.262382
$917$	10.8284	+	56.2662i	0.357586	+	1.85807i
$918$	3.17157			0.104678
$919$	27.3284	+	47.3342i	0.901482	+	1.56141i	0.825572	+	0.564297i	$0.190853\pi$
$919$	27.3284	+	47.3342i	0.901482	+	1.56141i	0.0759100	+	0.997115i	$0.475814\pi$
$920$	5.55025	−	9.61332i	0.182986	−	0.316942i
$921$	7.24264	−	12.5446i	0.238653	−	0.413359i
$922$	5.89340	+	10.2077i	0.194089	+	0.336172i
$923$	−44.2843			−1.45763
$924$	8.35786	+	2.89525i	0.274954	+	0.0952467i
$925$	−11.3137			−0.371992
$926$	1.93503	+	3.35157i	0.0635890	+	0.110139i
$927$	3.82843	−	6.63103i	0.125742	−	0.217792i
$928$	−1.82843	+	3.16693i	−0.0600211	+	0.103960i
$929$	17.2279	+	29.8396i	0.565230	+	0.979007i	0.997028	+	0.0770366i	$0.0245458\pi$
$929$	17.2279	+	29.8396i	0.565230	+	0.979007i	−0.431798	+	0.901970i	$0.642121\pi$
$930$	−6.68629			−0.219252
$931$	−1.00000	+	6.92820i	−0.0327737	+	0.227063i
$932$	−10.9706			−0.359353
$933$	11.3137	+	19.5959i	0.370394	+	0.641542i
$934$	−1.76346	+	3.05440i	−0.0577020	+	0.0999429i
$935$	−12.7990	+	22.1685i	−0.418572	+	0.724987i
$936$	−2.24264	−	3.88437i	−0.0733030	−	0.126965i
$937$	−27.0000			−0.882052			−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000			−0.882052			−0.441026	+	0.897494i	$0.645385\pi$
$938$	12.4264	+	4.30463i	0.405737	+	0.140551i
$939$	−25.2843			−0.825121
$940$	19.7721	+	34.2462i	0.644894	+	1.11699i
$941$	3.97056	−	6.87722i	0.129437	−	0.224191i	−0.794022	−	0.607889i	$-0.792016\pi$
$941$	3.97056	−	6.87722i	0.129437	−	0.224191i	0.923458	+	0.383698i	$0.125350\pi$
$942$	0.136039	−	0.235626i	0.00443239	−	0.00767712i
$943$	7.00000	+	12.1244i	0.227951	+	0.394823i
$944$	15.5147			0.504961
$945$	0.914214	+	4.75039i	0.0297394	+	0.154530i
$946$	−1.01724			−0.0330735
$947$	19.6569	+	34.0467i	0.638762	+	1.10637i	0.985705	+	0.168482i	$0.0538865\pi$
$947$	19.6569	+	34.0467i	0.638762	+	1.10637i	−0.346943	+	0.937886i	$0.612780\pi$
$948$	12.4853	−	21.6251i	0.405503	−	0.702352i
$949$	17.4142	−	30.1623i	0.565289	−	0.979110i
$950$	−0.343146	−	0.594346i	−0.0111331	−	0.0192831i
$951$	−9.79899			−0.317754
$952$	−24.2843	+	21.0308i	−0.787058	+	0.681612i
$953$	18.6274			0.603401			0.301701	−	0.953403i	$-0.402446\pi$
$953$	18.6274			0.603401			0.301701	+	0.953403i	$0.402446\pi$
$954$	0.414214	+	0.717439i	0.0134107	+	0.0232279i
$955$	−5.64214	+	9.77247i	−0.182575	+	0.316230i
$956$	12.4853	−	21.6251i	0.403803	−	0.699407i
$957$	−0.757359	−	1.31178i	−0.0244819	−	0.0424040i
$958$	7.38478			0.238591
$959$	−16.3431	+	14.1536i	−0.527748	+	0.457043i
$960$	−7.62742			−0.246174
$961$	−23.4706	−	40.6522i	−0.757115	−	1.31136i
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$	−1.41421	+	2.44949i	−0.0455724	+	0.0789337i
$964$	−18.1005	−	31.3510i	−0.582978	−	1.00975i
$965$	7.31371			0.235437
$966$	0.792893	+	4.11999i	0.0255109	+	0.132559i
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	−6.07107	−	10.5154i	−0.195132	−	0.337978i
$969$	3.82843	−	6.63103i	0.122987	−	0.213019i
$970$	−4.23045	+	7.32735i	−0.135831	+	0.235267i
$971$	0.100505	+	0.174080i	0.00322536	+	0.00558649i	0.867634	−	0.497204i	$-0.165640\pi$
$971$	0.100505	+	0.174080i	0.00322536	+	0.00558649i	−0.864408	+	0.502791i	$0.832307\pi$
$972$	−1.82843			−0.0586468
$973$	−11.6421	−	4.03295i	−0.373230	−	0.129291i
$974$	−4.82843			−0.154713
$975$	−2.34315	−	4.05845i	−0.0750407	−	0.129974i
$976$	5.01472	−	8.68575i	0.160517	−	0.278024i
$977$	19.5563	−	33.8726i	0.625663	−	1.08368i	−0.362749	−	0.931887i	$-0.618162\pi$
$977$	19.5563	−	33.8726i	0.625663	−	1.08368i	0.988412	−	0.151793i	$-0.0485048\pi$
$978$	2.47918	+	4.29407i	0.0792756	+	0.137309i
$979$	9.45584			0.302210
$980$	−18.3873	−	14.4762i	−0.587361	−	0.462427i
$981$	−10.1421			−0.323813
$982$	5.27817	+	9.14207i	0.168433	+	0.291735i
$983$	23.7279	−	41.0980i	0.756803	−	1.31082i	−0.187670	−	0.982232i	$-0.560093\pi$
$983$	23.7279	−	41.0980i	0.756803	−	1.31082i	0.944473	−	0.328589i	$-0.106573\pi$
$984$	−2.89949	+	5.02207i	−0.0924325	+	0.160098i
$985$	0.470563	+	0.815039i	0.0149934	+	0.0259693i
$986$	2.62742			0.0836740
$987$	−29.5711	−	10.2437i	−0.941257	−	0.326061i
$988$	−5.17157			−0.164530
$989$	2.57107	+	4.45322i	0.0817552	+	0.141604i
$990$	−0.692388	+	1.19925i	−0.0220055	+	0.0381147i
$991$	18.6274	−	32.2636i	0.591719	−	1.02489i	−0.402281	−	0.915516i	$-0.631783\pi$
$991$	18.6274	−	32.2636i	0.591719	−	1.02489i	0.994001	−	0.109372i	$-0.0348840\pi$
$992$	19.4853	+	33.7495i	0.618658	+	1.07155i
$993$	−22.4853			−0.713549
$994$	3.24264	+	16.8493i	0.102850	+	0.534426i
$995$	26.7990			0.849585
$996$	8.98528	+	15.5630i	0.284710	+	0.493131i
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	−0.524537	−	0.851388i	$-0.675762\pi$
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	0.999592	+	0.0285686i	$0.00909491\pi$
$998$	2.89340	−	5.01151i	0.0915889	−	0.158637i
$999$	−3.41421	−	5.91359i	−0.108021	−	0.187098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.c.172.1	yes	4
3.2	odd	2		1197.2.j.d.172.2		4
7.2	even	3	inner	399.2.j.c.58.1	✓	4
7.3	odd	6		2793.2.a.n.1.2		2
7.4	even	3		2793.2.a.o.1.2		2
21.2	odd	6		1197.2.j.d.856.2		4
21.11	odd	6		8379.2.a.bm.1.1		2
21.17	even	6		8379.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.c.58.1	✓	4	7.2	even	3	inner
399.2.j.c.172.1	yes	4	1.1	even	1	trivial
1197.2.j.d.172.2		4	3.2	odd	2
1197.2.j.d.856.2		4	21.2	odd	6
2793.2.a.n.1.2		2	7.3	odd	6
2793.2.a.o.1.2		2	7.4	even	3
8379.2.a.bh.1.1		2	21.17	even	6
8379.2.a.bm.1.1		2	21.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(-0.914214 - 1.58346i) q^{5} +0.414214 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.378680 + 0.655892i) q^{10} +(-0.914214 + 1.58346i) q^{11} +(0.914214 + 1.58346i) q^{12} -2.82843 q^{13} +(0.207107 + 1.07616i) q^{14} +1.82843 q^{15} +(-1.50000 - 2.59808i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(-0.207107 + 0.358719i) q^{18} +(0.500000 + 0.866025i) q^{19} -3.34315 q^{20} +(2.00000 - 1.73205i) q^{21} +0.757359 q^{22} +(-1.91421 - 3.31552i) q^{23} +(0.792893 - 1.37333i) q^{24} +(0.828427 - 1.43488i) q^{25} +(0.585786 + 1.01461i) q^{26} +1.00000 q^{27} +(-3.65685 + 3.16693i) q^{28} +0.828427 q^{29} +(-0.378680 - 0.655892i) q^{30} +(4.41421 - 7.64564i) q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.914214 - 1.58346i) q^{33} +3.17157 q^{34} +(0.914214 + 4.75039i) q^{35} -1.82843 q^{36} +(-3.41421 - 5.91359i) q^{37} +(0.207107 - 0.358719i) q^{38} +(1.41421 - 2.44949i) q^{39} +(1.44975 + 2.51104i) q^{40} -3.65685 q^{41} +(-1.03553 - 0.358719i) q^{42} -1.34315 q^{43} +(1.67157 + 2.89525i) q^{44} +(-0.914214 + 1.58346i) q^{45} +(-0.792893 + 1.37333i) q^{46} +(-5.91421 - 10.2437i) q^{47} +3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -0.686292 q^{50} +(-3.82843 - 6.63103i) q^{51} +(-2.58579 + 4.47871i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-0.207107 - 0.358719i) q^{54} +3.34315 q^{55} +(3.96447 + 1.37333i) q^{56} -1.00000 q^{57} +(-0.171573 - 0.297173i) q^{58} +(-2.58579 + 4.47871i) q^{59} +(1.67157 - 2.89525i) q^{60} +(1.67157 + 2.89525i) q^{61} -3.65685 q^{62} +(0.500000 + 2.59808i) q^{63} -4.17157 q^{64} +(2.58579 + 4.47871i) q^{65} +(-0.378680 + 0.655892i) q^{66} +(6.00000 - 10.3923i) q^{67} +(7.00000 + 12.1244i) q^{68} +3.82843 q^{69} +(1.51472 - 1.31178i) q^{70} +15.6569 q^{71} +(0.792893 + 1.37333i) q^{72} +(-6.15685 + 10.6640i) q^{73} +(-1.41421 + 2.44949i) q^{74} +(0.828427 + 1.43488i) q^{75} +1.82843 q^{76} +(3.65685 - 3.16693i) q^{77} -1.17157 q^{78} +(-6.82843 - 11.8272i) q^{79} +(-2.74264 + 4.75039i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.757359 + 1.31178i) q^{82} +9.82843 q^{83} +(-0.914214 - 4.75039i) q^{84} +14.0000 q^{85} +(0.278175 + 0.481813i) q^{86} +(-0.414214 + 0.717439i) q^{87} +(1.44975 - 2.51104i) q^{88} +(-2.58579 - 4.47871i) q^{89} +0.757359 q^{90} +(7.07107 + 2.44949i) q^{91} -7.00000 q^{92} +(4.41421 + 7.64564i) q^{93} +(-2.44975 + 4.24309i) q^{94} +(0.914214 - 1.58346i) q^{95} +(-2.20711 - 3.82282i) q^{96} +11.1716 q^{97} +(0.414214 - 2.86976i) q^{98} +1.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{7} - 12 q^{8} - 2 q^{9} - 10 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 4 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} - 36 q^{20} + 8 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 10 * q^7 - 12 * q^8 - 2 * q^9 - 10 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 4 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 - 36 * q^20 + 8 * q^21 + 20 * q^22 - 2 * q^23 + 6 * q^24 - 8 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 - 10 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 - 14 * q^40 + 8 * q^41 + 10 * q^42 - 28 * q^43 + 18 * q^44 + 2 * q^45 - 6 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 - 48 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^53 + 2 * q^54 + 36 * q^55 + 30 * q^56 - 4 * q^57 - 12 * q^58 - 16 * q^59 + 18 * q^60 + 18 * q^61 + 8 * q^62 + 2 * q^63 - 28 * q^64 + 16 * q^65 - 10 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 40 * q^70 + 40 * q^71 + 6 * q^72 - 2 * q^73 - 8 * q^75 - 4 * q^76 - 8 * q^77 - 16 * q^78 - 16 * q^79 + 6 * q^80 - 2 * q^81 + 20 * q^82 + 28 * q^83 + 2 * q^84 + 56 * q^85 - 30 * q^86 + 4 * q^87 - 14 * q^88 - 16 * q^89 + 20 * q^90 - 28 * q^92 + 12 * q^93 + 10 * q^94 - 2 * q^95 - 6 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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