LMFDB - Embedded newform 666.2.e.e.445.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(223,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("666.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 28 x^{18} + 304 x^{16} + 1654 x^{14} + 4950 x^{12} + 8429 x^{10} + 8179 x^{8} + 4427 x^{6} + \cdots + 9 $ x^20 + 28x^18 + 304x^16 + 1654x^14 + 4950x^12 + 8429x^10 + 8179x^8 + 4427x^6 + 1273x^4 + 177*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.1
Root			$-0.531449i$ of defining polynomial
Character	$\chi$	$=$	666.445
Dual form			666.2.e.e.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.70319 - 0.314889i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.66931 - 2.89132i) q^{5} +(0.578891 + 1.63245i) q^{6} +(-0.0979808 - 0.169708i) q^{7} +1.00000 q^{8} +(2.80169 + 1.07263i) q^{9} -3.33861 q^{10} +(2.54300 + 4.40461i) q^{11} +(1.12430 - 1.31756i) q^{12} +(2.66420 - 4.61453i) q^{13} +(-0.0979808 + 0.169708i) q^{14} +(-3.75359 + 4.39882i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.739743 q^{17} +(-0.471920 - 2.96265i) q^{18} +5.26526 q^{19} +(1.66931 + 2.89132i) q^{20} +(0.113440 + 0.319897i) q^{21} +(2.54300 - 4.40461i) q^{22} +(-1.25431 + 2.17254i) q^{23} +(-1.70319 - 0.314889i) q^{24} +(-3.07317 - 5.32288i) q^{25} -5.32840 q^{26} +(-4.43404 - 2.70911i) q^{27} +0.195962 q^{28} +(3.06675 + 5.31177i) q^{29} +(5.68628 + 1.05129i) q^{30} +(0.799905 - 1.38548i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.94425 - 8.30264i) q^{33} +(-0.369871 - 0.640636i) q^{34} -0.654240 q^{35} +(-2.32977 + 1.89002i) q^{36} -1.00000 q^{37} +(-2.63263 - 4.55985i) q^{38} +(-5.99070 + 7.02048i) q^{39} +(1.66931 - 2.89132i) q^{40} +(2.62937 - 4.55420i) q^{41} +(0.220319 - 0.258191i) q^{42} +(-2.23757 - 3.87559i) q^{43} -5.08601 q^{44} +(7.77820 - 6.31004i) q^{45} +2.50863 q^{46} +(-6.74071 - 11.6752i) q^{47} +(0.578891 + 1.63245i) q^{48} +(3.48080 - 6.02892i) q^{49} +(-3.07317 + 5.32288i) q^{50} +(-1.25992 - 0.232937i) q^{51} +(2.66420 + 4.61453i) q^{52} -9.76490 q^{53} +(-0.129139 + 5.19455i) q^{54} +16.9802 q^{55} +(-0.0979808 - 0.169708i) q^{56} +(-8.96771 - 1.65797i) q^{57} +(3.06675 - 5.31177i) q^{58} +(-0.410647 + 0.711262i) q^{59} +(-1.93269 - 5.45011i) q^{60} +(-3.06305 - 5.30535i) q^{61} -1.59981 q^{62} +(-0.0924781 - 0.580566i) q^{63} +1.00000 q^{64} +(-8.89474 - 15.4061i) q^{65} +(-5.71818 + 6.70111i) q^{66} +(-3.51438 + 6.08709i) q^{67} +(-0.369871 + 0.640636i) q^{68} +(2.82044 - 3.30527i) q^{69} +(0.327120 + 0.566588i) q^{70} +10.4556 q^{71} +(2.80169 + 1.07263i) q^{72} +7.73574 q^{73} +(0.500000 + 0.866025i) q^{74} +(3.55806 + 10.0336i) q^{75} +(-2.63263 + 4.55985i) q^{76} +(0.498331 - 0.863135i) q^{77} +(9.07527 + 1.67786i) q^{78} +(0.463811 + 0.803345i) q^{79} -3.33861 q^{80} +(6.69893 + 6.01035i) q^{81} -5.25874 q^{82} +(4.42971 + 7.67248i) q^{83} +(-0.333759 - 0.0617062i) q^{84} +(1.23486 - 2.13884i) q^{85} +(-2.23757 + 3.87559i) q^{86} +(-3.55063 - 10.0126i) q^{87} +(2.54300 + 4.40461i) q^{88} -10.6441 q^{89} +(-9.35376 - 3.58110i) q^{90} -1.04416 q^{91} +(-1.25431 - 2.17254i) q^{92} +(-1.79866 + 2.10784i) q^{93} +(-6.74071 + 11.6752i) q^{94} +(8.78933 - 15.2236i) q^{95} +(1.12430 - 1.31756i) q^{96} +(-5.20436 - 9.01421i) q^{97} -6.96160 q^{98} +(2.40019 + 15.0681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{2} + 2 q^{3} - 10 q^{4} - q^{5} + 2 q^{6} - q^{7} + 20 q^{8} + 2 q^{9} + 2 q^{10} - 3 q^{11} - 4 q^{12} - 12 q^{13} - q^{14} - 13 q^{15} - 10 q^{16} + 24 q^{17} + 2 q^{18} + 48 q^{19} - q^{20}+ \cdots + 49 q^{99}+O(q^{100}) $ 20 * q - 10 * q^2 + 2 * q^3 - 10 * q^4 - q^5 + 2 * q^6 - q^7 + 20 * q^8 + 2 * q^9 + 2 * q^10 - 3 * q^11 - 4 * q^12 - 12 * q^13 - q^14 - 13 * q^15 - 10 * q^16 + 24 * q^17 + 2 * q^18 + 48 * q^19 - q^20 - 18 * q^21 - 3 * q^22 - 3 * q^23 + 2 * q^24 - 21 * q^25 + 24 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^30 - 11 * q^31 - 10 * q^32 + 19 * q^33 - 12 * q^34 - 14 * q^35 - 4 * q^36 - 20 * q^37 - 24 * q^38 - 18 * q^39 - q^40 + 3 * q^41 + 30 * q^42 - 6 * q^43 + 6 * q^44 + 18 * q^45 + 6 * q^46 - 8 * q^47 + 2 * q^48 - 35 * q^49 - 21 * q^50 + 17 * q^51 - 12 * q^52 - 20 * q^53 - 31 * q^54 + 4 * q^55 - q^56 - 41 * q^57 - 4 * q^58 - 10 * q^59 + 11 * q^60 - 2 * q^61 + 22 * q^62 + 29 * q^63 + 20 * q^64 - 26 * q^65 - 17 * q^66 - 7 * q^67 - 12 * q^68 + 9 * q^69 + 7 * q^70 + 30 * q^71 + 2 * q^72 + 6 * q^73 + 10 * q^74 - 48 * q^75 - 24 * q^76 - 9 * q^77 + 48 * q^78 - 16 * q^79 + 2 * q^80 + 10 * q^81 - 6 * q^82 + 23 * q^83 - 12 * q^84 - 15 * q^85 - 6 * q^86 + 25 * q^87 - 3 * q^88 + 42 * q^89 - 15 * q^90 + 118 * q^91 - 3 * q^92 - 117 * q^93 - 8 * q^94 + 6 * q^95 - 4 * q^96 - 24 * q^97 + 70 * q^98 + 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.70319	−	0.314889i	−0.983335	−	0.181801i
$3$	−1.70319	−	0.314889i	−0.983335	−	0.181801i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.66931	−	2.89132i	0.746536	−	1.29304i	−0.202937	−	0.979192i	$-0.565049\pi$
$5$	1.66931	−	2.89132i	0.746536	−	1.29304i	0.949473	−	0.313847i	$-0.101618\pi$
$6$	0.578891	+	1.63245i	0.236331	+	0.666444i
$7$	−0.0979808	−	0.169708i	−0.0370333	−	0.0641435i	0.846915	−	0.531729i	$-0.178457\pi$
$7$	−0.0979808	−	0.169708i	−0.0370333	−	0.0641435i	−0.883948	+	0.467585i	$0.845124\pi$
$8$	1.00000			0.353553
$9$	2.80169	+	1.07263i	0.933897	+	0.357543i
$10$	−3.33861			−1.05576
$11$	2.54300	+	4.40461i	0.766745	+	1.32804i	0.939319	+	0.343044i	$0.111458\pi$
$11$	2.54300	+	4.40461i	0.766745	+	1.32804i	−0.172575	+	0.984996i	$0.555209\pi$
$12$	1.12430	−	1.31756i	0.324556	−	0.380346i
$13$	2.66420	−	4.61453i	0.738917	−	1.27984i	−0.214067	−	0.976819i	$-0.568671\pi$
$13$	2.66420	−	4.61453i	0.738917	−	1.27984i	0.952984	−	0.303022i	$-0.0979956\pi$
$14$	−0.0979808	+	0.169708i	−0.0261865	+	0.0453563i
$15$	−3.75359	+	4.39882i	−0.969172	+	1.13577i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.739743			0.179414			0.0897070	−	0.995968i	$-0.471407\pi$
$17$	0.739743			0.179414			0.0897070	+	0.995968i	$0.471407\pi$
$18$	−0.471920	−	2.96265i	−0.111233	−	0.698303i
$19$	5.26526			1.20793			0.603966	−	0.797010i	$-0.293586\pi$
$19$	5.26526			1.20793			0.603966	+	0.797010i	$0.293586\pi$
$20$	1.66931	+	2.89132i	0.373268	+	0.646520i
$21$	0.113440	+	0.319897i	0.0247547	+	0.0698073i
$22$	2.54300	−	4.40461i	0.542170	−	0.939066i
$23$	−1.25431	+	2.17254i	−0.261543	+	0.453005i	−0.966652	−	0.256093i	$-0.917565\pi$
$23$	−1.25431	+	2.17254i	−0.261543	+	0.453005i	0.705109	+	0.709099i	$0.250898\pi$
$24$	−1.70319	−	0.314889i	−0.347662	−	0.0642765i
$25$	−3.07317	−	5.32288i	−0.614633	−	1.06458i
$26$	−5.32840			−1.04499
$27$	−4.43404	−	2.70911i	−0.853331	−	0.521369i
$28$	0.195962			0.0370333
$29$	3.06675	+	5.31177i	0.569482	+	0.986372i	0.996617	+	0.0821840i	$0.0261895\pi$
$29$	3.06675	+	5.31177i	0.569482	+	0.986372i	−0.427135	+	0.904188i	$0.640477\pi$
$30$	5.68628	+	1.05129i	1.03817	+	0.191939i
$31$	0.799905	−	1.38548i	0.143667	−	0.248839i	−0.785208	−	0.619232i	$-0.787444\pi$
$31$	0.799905	−	1.38548i	0.143667	−	0.248839i	0.928875	+	0.370394i	$0.120777\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.94425	−	8.30264i	−0.512527	−	1.44530i
$34$	−0.369871	−	0.640636i	−0.0634324	−	0.109868i
$35$	−0.654240			−0.110587
$36$	−2.32977	+	1.89002i	−0.388295	+	0.315003i
$37$	−1.00000			−0.164399
$37$	−1.00000			−0.164399
$38$	−2.63263	−	4.55985i	−0.427069	−	0.739705i
$39$	−5.99070	+	7.02048i	−0.959280	+	1.12418i
$40$	1.66931	−	2.89132i	0.263941	−	0.457158i
$41$	2.62937	−	4.55420i	0.410638	−	0.711247i	−0.584321	−	0.811522i	$-0.698639\pi$
$41$	2.62937	−	4.55420i	0.410638	−	0.711247i	0.994960	+	0.100276i	$0.0319725\pi$
$42$	0.220319	−	0.258191i	0.0339959	−	0.0398397i
$43$	−2.23757	−	3.87559i	−0.341227	−	0.591022i	0.643434	−	0.765501i	$-0.277509\pi$
$43$	−2.23757	−	3.87559i	−0.341227	−	0.591022i	−0.984661	+	0.174480i	$0.944176\pi$
$44$	−5.08601			−0.766745
$45$	7.77820	−	6.31004i	1.15951	−	0.940645i
$46$	2.50863			0.369877
$47$	−6.74071	−	11.6752i	−0.983233	−	1.70301i	−0.649538	−	0.760329i	$-0.725038\pi$
$47$	−6.74071	−	11.6752i	−0.983233	−	1.70301i	−0.333696	−	0.942681i	$-0.608296\pi$
$48$	0.578891	+	1.63245i	0.0835558	+	0.235624i
$49$	3.48080	−	6.02892i	0.497257	−	0.861275i
$50$	−3.07317	+	5.32288i	−0.434611	+	0.752769i
$51$	−1.25992	−	0.232937i	−0.176424	−	0.0326177i
$52$	2.66420	+	4.61453i	0.369458	+	0.639921i
$53$	−9.76490			−1.34131			−0.670656	−	0.741768i	$-0.733987\pi$
$53$	−9.76490			−1.34131			−0.670656	+	0.741768i	$0.733987\pi$
$54$	−0.129139	+	5.19455i	−0.0175736	+	0.706888i
$55$	16.9802			2.28961
$56$	−0.0979808	−	0.169708i	−0.0130932	−	0.0226781i
$57$	−8.96771	−	1.65797i	−1.18780	−	0.219604i
$58$	3.06675	−	5.31177i	0.402685	−	0.697470i
$59$	−0.410647	+	0.711262i	−0.0534617	+	0.0925984i	−0.891518	−	0.452986i	$-0.850359\pi$
$59$	−0.410647	+	0.711262i	−0.0534617	+	0.0925984i	0.838056	+	0.545584i	$0.183692\pi$
$60$	−1.93269	−	5.45011i	−0.249510	−	0.703606i
$61$	−3.06305	−	5.30535i	−0.392183	−	0.679281i	0.600554	−	0.799584i	$-0.294947\pi$
$61$	−3.06305	−	5.30535i	−0.392183	−	0.679281i	−0.992737	+	0.120303i	$0.961613\pi$
$62$	−1.59981			−0.203176
$63$	−0.0924781	−	0.580566i	−0.0116511	−	0.0731444i
$64$	1.00000			0.125000
$65$	−8.89474	−	15.4061i	−1.10326	−	1.91090i
$66$	−5.71818	+	6.70111i	−0.703859	+	0.824850i
$67$	−3.51438	+	6.08709i	−0.429350	+	0.743656i	−0.996816	−	0.0797409i	$-0.974591\pi$
$67$	−3.51438	+	6.08709i	−0.429350	+	0.743656i	0.567465	+	0.823397i	$0.307924\pi$
$68$	−0.369871	+	0.640636i	−0.0448535	+	0.0776885i
$69$	2.82044	−	3.30527i	0.339541	−	0.397907i
$70$	0.327120	+	0.566588i	0.0390983	+	0.0677203i
$71$	10.4556			1.24085			0.620426	−	0.784265i	$-0.286960\pi$
$71$	10.4556			1.24085			0.620426	+	0.784265i	$0.286960\pi$
$72$	2.80169	+	1.07263i	0.330182	+	0.126411i
$73$	7.73574			0.905400			0.452700	−	0.891663i	$-0.350461\pi$
$73$	7.73574			0.905400			0.452700	+	0.891663i	$0.350461\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$	3.55806	+	10.0336i	0.410849	+	1.15858i
$76$	−2.63263	+	4.55985i	−0.301983	+	0.523050i
$77$	0.498331	−	0.863135i	0.0567901	−	0.0983633i
$78$	9.07527	+	1.67786i	1.02757	+	0.189980i
$79$	0.463811	+	0.803345i	0.0521829	+	0.0903834i	0.890937	−	0.454127i	$-0.150049\pi$
$79$	0.463811	+	0.803345i	0.0521829	+	0.0903834i	−0.838754	+	0.544510i	$0.816715\pi$
$80$	−3.33861			−0.373268
$81$	6.69893	+	6.01035i	0.744325	+	0.667817i
$82$	−5.25874			−0.580730
$83$	4.42971	+	7.67248i	0.486224	+	0.842164i	0.999875	−	0.0158350i	$-0.00504065\pi$
$83$	4.42971	+	7.67248i	0.486224	+	0.842164i	−0.513651	+	0.857999i	$0.671707\pi$
$84$	−0.333759	−	0.0617062i	−0.0364161	−	0.00673270i
$85$	1.23486	−	2.13884i	0.133939	−	0.231989i
$86$	−2.23757	+	3.87559i	−0.241284	+	0.417916i
$87$	−3.55063	−	10.0126i	−0.380668	−	1.07347i
$88$	2.54300	+	4.40461i	0.271085	+	0.469533i
$89$	−10.6441			−1.12827			−0.564137	−	0.825682i	$-0.690791\pi$
$89$	−10.6441			−1.12827			−0.564137	+	0.825682i	$0.690791\pi$
$90$	−9.35376	−	3.58110i	−0.985972	−	0.377481i
$91$	−1.04416			−0.109458
$92$	−1.25431	−	2.17254i	−0.130771	−	0.226503i
$93$	−1.79866	+	2.10784i	−0.186512	+	0.218573i
$94$	−6.74071	+	11.6752i	−0.695251	+	1.20421i
$95$	8.78933	−	15.2236i	0.901766	−	1.56190i
$96$	1.12430	−	1.31756i	0.114748	−	0.134473i
$97$	−5.20436	−	9.01421i	−0.528422	−	0.915254i	−0.999451	−	0.0331362i	$-0.989450\pi$
$97$	−5.20436	−	9.01421i	−0.528422	−	0.915254i	0.471029	−	0.882118i	$-0.343883\pi$
$98$	−6.96160			−0.703228
$99$	2.40019	+	15.0681i	0.241228	+	1.51440i
$100$	6.14633			0.614633
$101$	1.45820	+	2.52568i	0.145097	+	0.251315i	0.929409	−	0.369051i	$-0.120317\pi$
$101$	1.45820	+	2.52568i	0.145097	+	0.251315i	−0.784312	+	0.620366i	$0.786984\pi$
$102$	0.428231	+	1.20759i	0.0424011	+	0.119569i
$103$	−6.30671	+	10.9235i	−0.621419	+	1.07633i	0.367803	+	0.929904i	$0.380110\pi$
$103$	−6.30671	+	10.9235i	−0.621419	+	1.07633i	−0.989222	+	0.146425i	$0.953223\pi$
$104$	2.66420	−	4.61453i	0.261246	−	0.452492i
$105$	1.11429	+	0.206013i	0.108744	+	0.0201048i
$106$	4.88245	+	8.45665i	0.474226	+	0.821383i
$107$	3.87889			0.374987			0.187493	−	0.982266i	$-0.439964\pi$
$107$	3.87889			0.374987			0.187493	+	0.982266i	$0.439964\pi$
$108$	4.56318	−	2.48544i	0.439092	−	0.239161i
$109$	0.536436			0.0513812			0.0256906	−	0.999670i	$-0.491822\pi$
$109$	0.536436			0.0513812			0.0256906	+	0.999670i	$0.491822\pi$
$110$	−8.49010	−	14.7053i	−0.809500	−	1.40209i
$111$	1.70319	+	0.314889i	0.161659	+	0.0298880i
$112$	−0.0979808	+	0.169708i	−0.00925832	+	0.0160359i
$113$	−9.51721	+	16.4843i	−0.895304	+	1.55071i	−0.0618751	+	0.998084i	$0.519708\pi$
$113$	−9.51721	+	16.4843i	−0.895304	+	1.55071i	−0.833428	+	0.552627i	$0.813625\pi$
$114$	3.04801	+	8.59525i	0.285472	+	0.805019i
$115$	4.18767	+	7.25326i	0.390502	+	0.676370i
$116$	−6.13351			−0.569482
$117$	12.4140	−	10.0708i	1.14767	−	0.931044i
$118$	0.821294			0.0756063
$119$	−0.0724806	−	0.125540i	−0.00664428	−	0.0115082i
$120$	−3.75359	+	4.39882i	−0.342654	+	0.401555i
$121$	−7.43374	+	12.8756i	−0.675794	+	1.17051i
$122$	−3.06305	+	5.30535i	−0.277315	+	0.480324i
$123$	−5.91237	+	6.92869i	−0.533101	+	0.624739i
$124$	0.799905	+	1.38548i	0.0718336	+	0.124419i
$125$	−3.82717			−0.342312
$126$	−0.456545	+	0.370371i	−0.0406723	+	0.0329953i
$127$	20.0651			1.78049			0.890247	−	0.455479i	$-0.150532\pi$
$127$	20.0651			1.78049			0.890247	+	0.455479i	$0.150532\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.59062	+	7.30544i	0.228092	+	0.643208i
$130$	−8.89474	+	15.4061i	−0.780120	+	1.35121i
$131$	−4.21323	+	7.29753i	−0.368112	+	0.637588i	−0.989270	−	0.146097i	$-0.953329\pi$
$131$	−4.21323	+	7.29753i	−0.368112	+	0.637588i	0.621159	+	0.783685i	$0.286662\pi$
$132$	8.66242	+	1.60153i	0.753967	+	0.139395i
$133$	−0.515894	−	0.893555i	−0.0447337	−	0.0774810i
$134$	7.02877			0.607193
$135$	−15.2347	+	8.29791i	−1.31119	+	0.714170i
$136$	0.739743			0.0634324
$137$	10.4051	+	18.0222i	0.888969	+	1.53974i	0.841096	+	0.540885i	$0.181911\pi$
$137$	10.4051	+	18.0222i	0.888969	+	1.53974i	0.0478724	+	0.998853i	$0.484756\pi$
$138$	−4.27266	−	0.789940i	−0.363713	−	0.0672442i
$139$	0.0612183	−	0.106033i	0.00519246	−	0.00899361i	−0.863417	−	0.504490i	$-0.831681\pi$
$139$	0.0612183	−	0.106033i	0.00519246	−	0.00899361i	0.868610	+	0.495496i	$0.165014\pi$
$140$	0.327120	−	0.566588i	0.0276467	−	0.0478855i
$141$	7.80427	+	22.0077i	0.657238	+	1.85338i
$142$	−5.22780	−	9.05481i	−0.438707	−	0.759863i
$143$	27.1003			2.26624
$144$	−0.471920	−	2.96265i	−0.0393266	−	0.246887i
$145$	20.4774			1.70056
$146$	−3.86787	−	6.69935i	−0.320107	−	0.554442i
$147$	−7.82689	+	9.17231i	−0.645551	+	0.756520i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−3.42057	+	5.92461i	−0.280224	+	0.485363i	−0.971440	−	0.237286i	$-0.923742\pi$
$149$	−3.42057	+	5.92461i	−0.280224	+	0.485363i	0.691216	+	0.722649i	$0.257076\pi$
$150$	6.91030	−	8.09815i	0.564223	−	0.661212i
$151$	−10.9185	−	18.9115i	−0.888538	−	1.53899i	−0.841604	−	0.540095i	$-0.818388\pi$
$151$	−10.9185	−	18.9115i	−0.888538	−	1.53899i	−0.0469340	−	0.998898i	$-0.514945\pi$
$152$	5.26526			0.427069
$153$	2.07253	+	0.793470i	0.167554	+	0.0641483i
$154$	−0.996662			−0.0803133
$155$	−2.67057	−	4.62557i	−0.214506	−	0.371535i
$156$	−3.08457	−	8.69834i	−0.246963	−	0.696425i
$157$	9.93371	−	17.2057i	0.792797	−	1.37316i	−0.131432	−	0.991325i	$-0.541958\pi$
$157$	9.93371	−	17.2057i	0.792797	−	1.37316i	0.924229	−	0.381839i	$-0.124709\pi$
$158$	0.463811	−	0.803345i	0.0368989	−	0.0639107i
$159$	16.6315	+	3.07486i	1.31896	+	0.243853i
$160$	1.66931	+	2.89132i	0.131970	+	0.228579i
$161$	0.491595			0.0387431
$162$	1.85566	−	8.80662i	0.145794	−	0.691913i
$163$	−4.27443			−0.334799			−0.167399	−	0.985889i	$-0.553537\pi$
$163$	−4.27443			−0.334799			−0.167399	+	0.985889i	$0.553537\pi$
$164$	2.62937	+	4.55420i	0.205319	+	0.355623i
$165$	−28.9205	−	5.34689i	−2.25146	−	0.416254i
$166$	4.42971	−	7.67248i	0.343812	−	0.595500i
$167$	−0.307630	+	0.532831i	−0.0238051	+	0.0412317i	−0.877683	−	0.479242i	$-0.840911\pi$
$167$	−0.307630	+	0.532831i	−0.0238051	+	0.0412317i	0.853877	+	0.520474i	$0.174245\pi$
$168$	0.113440	+	0.319897i	0.00875212	+	0.0246806i
$169$	−7.69594	−	13.3298i	−0.591996	−	1.02537i
$170$	−2.46971			−0.189418
$171$	14.7516	+	5.64767i	1.12808	+	0.431888i
$172$	4.47515			0.341227
$173$	−10.4944	−	18.1768i	−0.797873	−	1.38196i	−0.920999	−	0.389566i	$-0.872625\pi$
$173$	−10.4944	−	18.1768i	−0.797873	−	1.38196i	0.123126	−	0.992391i	$-0.460708\pi$
$174$	−6.89588	+	8.08126i	−0.522775	+	0.612638i
$175$	−0.602223	+	1.04308i	−0.0455238	+	0.0788495i
$176$	2.54300	−	4.40461i	0.191686	−	0.332010i
$177$	0.923377	−	1.08210i	0.0694053	−	0.0813359i
$178$	5.32205	+	9.21807i	0.398905	+	0.690923i
$179$	−22.4414			−1.67735			−0.838673	−	0.544635i	$-0.816668\pi$
$179$	−22.4414			−1.67735			−0.838673	+	0.544635i	$0.816668\pi$
$180$	1.57556	+	9.89114i	0.117435	+	0.737242i
$181$	5.60462			0.416588			0.208294	−	0.978066i	$-0.433209\pi$
$181$	5.60462			0.416588			0.208294	+	0.978066i	$0.433209\pi$
$182$	0.522081	+	0.904271i	0.0386992	+	0.0670290i
$183$	3.54634	+	10.0005i	0.262153	+	0.739260i
$184$	−1.25431	+	2.17254i	−0.0924693	+	0.160162i
$185$	−1.66931	+	2.89132i	−0.122730	+	0.212574i
$186$	2.72478	+	0.503763i	0.199790	+	0.0369377i
$187$	1.88117	+	3.25828i	0.137565	+	0.238269i
$188$	13.4814			0.983233
$189$	−0.0253064	+	1.01793i	−0.00184077	+	0.0740436i
$190$	−17.5787			−1.27529
$191$	2.06194	+	3.57138i	0.149197	+	0.258416i	0.930931	−	0.365196i	$-0.118998\pi$
$191$	2.06194	+	3.57138i	0.149197	+	0.258416i	−0.781734	+	0.623612i	$0.785665\pi$
$192$	−1.70319	−	0.314889i	−0.122917	−	0.0227252i
$193$	4.27549	−	7.40537i	0.307757	−	0.533050i	−0.670115	−	0.742258i	$-0.733755\pi$
$193$	4.27549	−	7.40537i	0.307757	−	0.533050i	0.977871	+	0.209207i	$0.0670884\pi$
$194$	−5.20436	+	9.01421i	−0.373651	+	0.647182i
$195$	10.2982	+	29.0404i	0.737467	+	2.07963i
$196$	3.48080	+	6.02892i	0.248629	+	0.430637i
$197$	13.1755			0.938714			0.469357	−	0.883009i	$-0.344486\pi$
$197$	13.1755			0.938714			0.469357	+	0.883009i	$0.344486\pi$
$198$	11.8492	−	9.61265i	0.842088	−	0.683141i
$199$	18.5811			1.31718			0.658589	−	0.752503i	$-0.271154\pi$
$199$	18.5811			1.31718			0.658589	+	0.752503i	$0.271154\pi$
$200$	−3.07317	−	5.32288i	−0.217306	−	0.376385i
$201$	7.90241	−	9.26081i	0.557393	−	0.653207i
$202$	1.45820	−	2.52568i	0.102599	−	0.177706i
$203$	0.600966	−	1.04090i	0.0421796	−	0.0730571i
$204$	0.831689	−	0.974654i	0.0582299	−	0.0682394i
$205$	−8.77844	−	15.2047i	−0.613113	−	1.06194i
$206$	12.6134			0.878819
$207$	−5.84453	+	4.74136i	−0.406223	+	0.329547i
$208$	−5.32840			−0.369458
$209$	13.3896	+	23.1914i	0.926176	+	1.60418i
$210$	−0.378734	−	1.06801i	−0.0261351	−	0.0736999i
$211$	2.40438	−	4.16450i	0.165524	−	0.286696i	−0.771317	−	0.636451i	$-0.780402\pi$
$211$	2.40438	−	4.16450i	0.165524	−	0.286696i	0.936841	+	0.349755i	$0.113735\pi$
$212$	4.88245	−	8.45665i	0.335328	−	0.580805i
$213$	−17.8078	−	3.29236i	−1.22017	−	0.225589i
$214$	−1.93945	−	3.35922i	−0.132578	−	0.229631i
$215$	−14.9408			−1.01895
$216$	−4.43404	−	2.70911i	−0.301698	−	0.184332i
$217$	−0.313501			−0.0212819
$218$	−0.268218	−	0.464567i	−0.0181660	−	0.0314644i
$219$	−13.1754	−	2.43590i	−0.890311	−	0.164603i
$220$	−8.49010	+	14.7053i	−0.572403	+	0.991431i
$221$	1.97082	−	3.41357i	0.132572	−	0.229621i
$222$	−0.578891	−	1.63245i	−0.0388526	−	0.109563i
$223$	−2.64310	−	4.57799i	−0.176995	−	0.306565i	0.763855	−	0.645388i	$-0.223304\pi$
$223$	−2.64310	−	4.57799i	−0.176995	−	0.306565i	−0.940850	+	0.338823i	$0.889971\pi$
$224$	0.195962			0.0130932
$225$	−2.90058	−	18.2094i	−0.193372	−	1.21396i
$226$	19.0344			1.26615
$227$	−3.26088	−	5.64800i	−0.216432	−	0.374871i	0.737283	−	0.675584i	$-0.236109\pi$
$227$	−3.26088	−	5.64800i	−0.216432	−	0.374871i	−0.953715	+	0.300713i	$0.902775\pi$
$228$	5.91970	−	6.93728i	0.392042	−	0.459433i
$229$	−2.96909	+	5.14261i	−0.196203	+	0.339833i	−0.947294	−	0.320365i	$-0.896194\pi$
$229$	−2.96909	+	5.14261i	−0.196203	+	0.339833i	0.751091	+	0.660198i	$0.229528\pi$
$230$	4.18767	−	7.25326i	0.276127	−	0.478266i
$231$	−1.12054	+	1.31316i	−0.0737263	+	0.0863996i
$232$	3.06675	+	5.31177i	0.201342	+	0.348735i
$233$	18.4107			1.20613			0.603063	−	0.797693i	$-0.293947\pi$
$233$	18.4107			1.20613			0.603063	+	0.797693i	$0.293947\pi$
$234$	−14.9285	−	5.71541i	−0.975909	−	0.373628i
$235$	−45.0092			−2.93608
$236$	−0.410647	−	0.711262i	−0.0267309	−	0.0462992i
$237$	−0.536993	−	1.51430i	−0.0348814	−	0.0983641i
$238$	−0.0724806	+	0.125540i	−0.00469822	+	0.00813755i
$239$	−12.0016	+	20.7874i	−0.776320	+	1.34463i	0.157730	+	0.987482i	$0.449582\pi$
$239$	−12.0016	+	20.7874i	−0.776320	+	1.34463i	−0.934050	+	0.357143i	$0.883751\pi$
$240$	5.68628	+	1.05129i	0.367048	+	0.0678607i
$241$	8.62270	+	14.9350i	0.555437	+	0.962045i	0.997869	+	0.0652431i	$0.0207823\pi$
$241$	8.62270	+	14.9350i	0.555437	+	0.962045i	−0.442432	+	0.896802i	$0.645884\pi$
$242$	14.8675			0.955717
$243$	−9.51693	−	12.3462i	−0.610511	−	0.792008i
$244$	6.12609			0.392183
$245$	−11.6210	−	20.1282i	−0.742441	−	1.28595i
$246$	8.95661	+	1.65592i	0.571053	+	0.105578i
$247$	14.0277	−	24.2967i	0.892561	−	1.54596i
$248$	0.799905	−	1.38548i	0.0507940	−	0.0879778i
$249$	−5.12864	−	14.4625i	−0.325014	−	0.916526i
$250$	1.91358	+	3.31442i	0.121026	+	0.209623i
$251$	5.56820			0.351462			0.175731	−	0.984438i	$-0.443771\pi$
$251$	5.56820			0.351462			0.175731	+	0.984438i	$0.443771\pi$
$252$	0.549024	+	0.210194i	0.0345852	+	0.0132410i
$253$	−12.7589			−0.802146
$254$	−10.0326	−	17.3769i	−0.629499	−	1.09032i
$255$	−2.77669	+	3.25399i	−0.173883	+	0.203773i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.40210	−	11.0888i	0.399352	−	0.691699i	−0.594294	−	0.804248i	$-0.702568\pi$
$257$	6.40210	−	11.0888i	0.399352	−	0.691699i	0.993646	+	0.112550i	$0.0359017\pi$
$258$	5.03139	−	5.89627i	0.313240	−	0.367085i
$259$	0.0979808	+	0.169708i	0.00608823	+	0.0105451i
$260$	17.7895			1.10326
$261$	2.89452	+	18.1714i	0.179166	+	1.12478i
$262$	8.42646			0.520588
$263$	−1.62293	−	2.81100i	−0.100074	−	0.173334i	0.811641	−	0.584157i	$-0.198575\pi$
$263$	−1.62293	−	2.81100i	−0.100074	−	0.173334i	−0.911715	+	0.410823i	$0.865241\pi$
$264$	−2.94425	−	8.30264i	−0.181206	−	0.510992i
$265$	−16.3006	+	28.2335i	−1.00134	+	1.73437i
$266$	−0.515894	+	0.893555i	−0.0316315	+	0.0547873i
$267$	18.1289	+	3.35171i	1.10947	+	0.205122i
$268$	−3.51438	−	6.08709i	−0.214675	−	0.371828i
$269$	−20.4388			−1.24618			−0.623089	−	0.782151i	$-0.714122\pi$
$269$	−20.4388			−1.24618			−0.623089	+	0.782151i	$0.714122\pi$
$270$	14.8035	+	9.04467i	0.900915	+	0.550441i
$271$	−18.6519			−1.13303			−0.566513	−	0.824053i	$-0.691708\pi$
$271$	−18.6519			−1.13303			−0.566513	+	0.824053i	$0.691708\pi$
$272$	−0.369871	−	0.640636i	−0.0224267	−	0.0388443i
$273$	1.77840	+	0.328796i	0.107634	+	0.0198996i
$274$	10.4051	−	18.0222i	0.628596	−	1.08876i
$275$	15.6302	−	27.0722i	0.942534	−	1.63252i
$276$	1.45222	+	4.09521i	0.0874136	+	0.246502i
$277$	3.19738	+	5.53802i	0.192112	+	0.332748i	0.945950	−	0.324313i	$-0.105133\pi$
$277$	3.19738	+	5.53802i	0.192112	+	0.332748i	−0.753838	+	0.657060i	$0.771800\pi$
$278$	−0.122437			−0.00734325
$279$	3.72719	−	3.02367i	0.223141	−	0.181022i
$280$	−0.654240			−0.0390983
$281$	10.1430	+	17.5682i	0.605081	+	1.04803i	0.992039	+	0.125934i	$0.0401926\pi$
$281$	10.1430	+	17.5682i	0.605081	+	1.04803i	−0.386958	+	0.922097i	$0.626474\pi$
$282$	15.1571	−	17.7626i	0.902592	−	1.05774i
$283$	−10.8797	+	18.8442i	−0.646730	+	1.12017i	0.337169	+	0.941444i	$0.390531\pi$
$283$	−10.8797	+	18.8442i	−0.646730	+	1.12017i	−0.983899	+	0.178726i	$0.942803\pi$
$284$	−5.22780	+	9.05481i	−0.310213	+	0.537304i
$285$	−19.7636	+	23.1609i	−1.17069	+	1.37193i
$286$	−13.5502	−	23.4696i	−0.801237	−	1.38778i
$287$	−1.03051			−0.0608291
$288$	−2.32977	+	1.89002i	−0.137283	+	0.111370i
$289$	−16.4528			−0.967811
$290$	−10.2387	−	17.7340i	−0.601238	−	1.04137i
$291$	6.02551	+	16.9917i	0.353222	+	0.996070i
$292$	−3.86787	+	6.69935i	−0.226350	+	0.392050i
$293$	−14.9626	+	25.9160i	−0.874125	+	1.51403i	−0.0164337	+	0.999865i	$0.505231\pi$
$293$	−14.9626	+	25.9160i	−0.874125	+	1.51403i	−0.857692	+	0.514164i	$0.828102\pi$
$294$	11.8569	+	2.19213i	0.691509	+	0.127848i
$295$	1.37099	+	2.37463i	0.0798222	+	0.138256i
$296$	−1.00000			−0.0581238
$297$	0.656804	−	26.4195i	0.0381116	−	1.53302i
$298$	6.84115			0.396297
$299$	6.68350	+	11.5762i	0.386517	+	0.669466i
$300$	−10.4684	−	1.93541i	−0.604391	−	0.111741i
$301$	−0.438478	+	0.759467i	−0.0252735	+	0.0437749i
$302$	−10.9185	+	18.9115i	−0.628291	+	1.08823i
$303$	−1.68828	−	4.76088i	−0.0969893	−	0.273505i
$304$	−2.63263	−	4.55985i	−0.150992	−	0.261525i
$305$	−20.4527			−1.17112
$306$	−0.349099	−	2.19160i	−0.0199567	−	0.125285i
$307$	−22.7730			−1.29972			−0.649861	−	0.760053i	$-0.725173\pi$
$307$	−22.7730			−1.29972			−0.649861	+	0.760053i	$0.725173\pi$
$308$	0.498331	+	0.863135i	0.0283950	+	0.0491817i
$309$	14.1812	−	16.6189i	0.806741	−	0.945418i
$310$	−2.67057	+	4.62557i	−0.151678	+	0.262715i
$311$	15.6903	−	27.1764i	0.889716	−	1.54103i	0.0495060	−	0.998774i	$-0.484235\pi$
$311$	15.6903	−	27.1764i	0.889716	−	1.54103i	0.840211	−	0.542260i	$-0.182431\pi$
$312$	−5.99070	+	7.02048i	−0.339157	+	0.397457i
$313$	−2.09361	−	3.62625i	−0.118338	−	0.204967i	0.800771	−	0.598970i	$-0.204423\pi$
$313$	−2.09361	−	3.62625i	−0.118338	−	0.204967i	−0.919109	+	0.394003i	$0.871090\pi$
$314$	−19.8674			−1.12118
$315$	−1.83298	−	0.701758i	−0.103277	−	0.0395396i
$316$	−0.927623			−0.0521829
$317$	4.85876	+	8.41563i	0.272895	+	0.472669i	0.969602	−	0.244688i	$-0.0786854\pi$
$317$	4.85876	+	8.41563i	0.272895	+	0.472669i	−0.696707	+	0.717356i	$0.745352\pi$
$318$	−5.65282	−	15.9407i	−0.316994	−	0.893910i
$319$	−15.5975	+	27.0157i	−0.873294	+	1.51259i
$320$	1.66931	−	2.89132i	0.0933171	−	0.161630i
$321$	−6.60648	−	1.22142i	−0.368738	−	0.0681731i
$322$	−0.245798	−	0.425734i	−0.0136978	−	0.0237252i
$323$	3.89493			0.216720
$324$	−8.55458	+	2.79626i	−0.475255	+	0.155348i
$325$	−32.7502			−1.81665
$326$	2.13721	+	3.70176i	0.118369	+	0.205022i
$327$	−0.913650	−	0.168918i	−0.0505250	−	0.00934118i
$328$	2.62937	−	4.55420i	0.145183	−	0.251464i
$329$	−1.32092	+	2.28790i	−0.0728247	+	0.126136i
$330$	9.82969	+	27.7193i	0.541107	+	1.52590i
$331$	−2.09734	−	3.63269i	−0.115280	−	0.199671i	0.802612	−	0.596502i	$-0.203443\pi$
$331$	−2.09734	−	3.63269i	−0.115280	−	0.199671i	−0.917892	+	0.396831i	$0.870110\pi$
$332$	−8.85942			−0.486224
$333$	−2.80169	−	1.07263i	−0.153532	−	0.0587798i
$334$	0.615260			0.0336655
$335$	11.7332	+	20.3224i	0.641051	+	1.11033i
$336$	0.220319	−	0.258191i	0.0120194	−	0.0140855i
$337$	−8.66486	+	15.0080i	−0.472005	+	0.817537i	−0.999487	−	0.0320297i	$-0.989803\pi$
$337$	−8.66486	+	15.0080i	−0.472005	+	0.817537i	0.527482	+	0.849566i	$0.323136\pi$
$338$	−7.69594	+	13.3298i	−0.418604	+	0.725044i
$339$	21.4003	−	25.0790i	1.16231	−	1.36210i
$340$	1.23486	+	2.13884i	0.0669695	+	0.115995i
$341$	8.13665			0.440624
$342$	−2.48478	−	15.5991i	−0.134361	−	0.843503i
$343$	−2.73594			−0.147727
$344$	−2.23757	−	3.87559i	−0.120642	−	0.208958i
$345$	−4.84841	−	13.6723i	−0.261030	−	0.736092i
$346$	−10.4944	+	18.1768i	−0.564181	+	0.977191i
$347$	0.302214	−	0.523451i	0.0162237	−	0.0281003i	−0.857800	−	0.513984i	$-0.828169\pi$
$347$	0.302214	−	0.523451i	0.0162237	−	0.0281003i	0.874023	+	0.485884i	$0.161502\pi$
$348$	10.4465	+	1.93138i	0.559992	+	0.103533i
$349$	−7.94873	−	13.7676i	−0.425486	−	0.736963i	0.570980	−	0.820964i	$-0.306563\pi$
$349$	−7.94873	−	13.7676i	−0.425486	−	0.736963i	−0.996466	+	0.0840011i	$0.973230\pi$
$350$	1.20445			0.0643803
$351$	−24.3145	+	13.2434i	−1.29781	+	0.706881i
$352$	−5.08601			−0.271085
$353$	2.99221	+	5.18265i	0.159259	+	0.275845i	0.934602	−	0.355696i	$-0.115756\pi$
$353$	2.99221	+	5.18265i	0.159259	+	0.275845i	−0.775343	+	0.631541i	$0.782423\pi$
$354$	−1.39882	−	0.258617i	−0.0743463	−	0.0137453i
$355$	17.4536	−	30.2305i	0.926341	−	1.60447i
$356$	5.32205	−	9.21807i	0.282068	−	0.488557i
$357$	0.0839167	+	0.236641i	0.00444134	+	0.0125244i
$358$	11.2207	+	19.4348i	0.593031	+	1.02716i
$359$	7.52687			0.397253			0.198627	−	0.980075i	$-0.436352\pi$
$359$	7.52687			0.397253			0.198627	+	0.980075i	$0.436352\pi$
$360$	7.77820	−	6.31004i	0.409947	−	0.332568i
$361$	8.72292			0.459101
$362$	−2.80231	−	4.85374i	−0.147286	−	0.255107i
$363$	16.7154	−	19.5888i	0.877333	−	1.02814i
$364$	0.522081	−	0.904271i	0.0273645	−	0.0473967i
$365$	12.9133	−	22.3665i	0.675914	−	1.17072i
$366$	6.88754	−	8.07148i	0.360017	−	0.421903i
$367$	9.26329	+	16.0445i	0.483540	+	0.837516i	0.999821	−	0.0189032i	$-0.00601742\pi$
$367$	9.26329	+	16.0445i	0.483540	+	0.837516i	−0.516281	+	0.856419i	$0.672684\pi$
$368$	2.50863			0.130771
$369$	12.2516	−	9.93911i	0.637795	−	0.517410i
$370$	3.33861			0.173566
$371$	0.956773	+	1.65718i	0.0496732	+	0.0860365i
$372$	−0.926116	−	2.61161i	−0.0480169	−	0.135405i
$373$	14.7051	−	25.4700i	0.761401	−	1.31878i	−0.180728	−	0.983533i	$-0.557845\pi$
$373$	14.7051	−	25.4700i	0.761401	−	1.31878i	0.942129	−	0.335251i	$-0.108821\pi$
$374$	1.88117	−	3.25828i	0.0972729	−	0.168482i
$375$	6.51838	+	1.20513i	0.336608	+	0.0622328i
$376$	−6.74071	−	11.6752i	−0.347625	−	0.602105i
$377$	32.6818			1.68320
$378$	0.894208	−	0.487050i	0.0459931	−	0.0250511i
$379$	10.0742			0.517475			0.258738	−	0.965948i	$-0.416694\pi$
$379$	10.0742			0.517475			0.258738	+	0.965948i	$0.416694\pi$
$380$	8.78933	+	15.2236i	0.450883	+	0.780952i
$381$	−34.1747	−	6.31830i	−1.75082	−	0.323696i
$382$	2.06194	−	3.57138i	0.105498	−	0.182728i
$383$	−7.81101	+	13.5291i	−0.399124	+	0.691303i	−0.993618	−	0.112797i	$-0.964019\pi$
$383$	−7.81101	+	13.5291i	−0.399124	+	0.691303i	0.594494	+	0.804100i	$0.297352\pi$
$384$	0.578891	+	1.63245i	0.0295414	+	0.0833055i
$385$	−1.66373	−	2.88167i	−0.0847918	−	0.146864i
$386$	−8.55099			−0.435234
$387$	−2.11191	−	13.2583i	−0.107354	−	0.673957i
$388$	10.4087			0.528422
$389$	−8.30491	−	14.3845i	−0.421076	−	0.729324i	0.574969	−	0.818175i	$-0.305014\pi$
$389$	−8.30491	−	14.3845i	−0.421076	−	0.729324i	−0.996045	+	0.0888507i	$0.971681\pi$
$390$	20.0006	−	23.4387i	1.01277	−	1.18686i
$391$	−0.927870	+	1.60712i	−0.0469244	+	0.0812755i
$392$	3.48080	−	6.02892i	0.175807	−	0.304507i
$393$	9.47383	−	11.1023i	0.477891	−	0.560039i
$394$	−6.58774	−	11.4103i	−0.331885	−	0.574843i
$395$	3.09697			0.155826
$396$	−14.2494	−	5.45541i	−0.716060	−	0.274144i
$397$	23.9512			1.20207			0.601037	−	0.799221i	$-0.294754\pi$
$397$	23.9512			1.20207			0.601037	+	0.799221i	$0.294754\pi$
$398$	−9.29054	−	16.0917i	−0.465692	−	0.806603i
$399$	0.597293	+	1.68434i	0.0299021	+	0.0843225i
$400$	−3.07317	+	5.32288i	−0.153658	+	0.266144i
$401$	14.1089	−	24.4374i	0.704566	−	1.22034i	−0.262282	−	0.964991i	$-0.584475\pi$
$401$	14.1089	−	24.4374i	0.704566	−	1.22034i	0.966848	−	0.255353i	$-0.0821917\pi$
$402$	−11.9713	−	2.21328i	−0.597074	−	0.110389i
$403$	−4.26222	−	7.38238i	−0.212316	−	0.367742i
$404$	−2.91641			−0.145097
$405$	28.5604	−	9.33564i	1.41918	−	0.463892i
$406$	−1.20193			−0.0596509
$407$	−2.54300	−	4.40461i	−0.126052	−	0.218329i
$408$	−1.25992	−	0.232937i	−0.0623753	−	0.0115321i
$409$	−10.4182	+	18.0448i	−0.515147	+	0.892260i	0.484699	+	0.874681i	$0.338929\pi$
$409$	−10.4182	+	18.0448i	−0.515147	+	0.892260i	−0.999845	+	0.0175790i	$0.994404\pi$
$410$	−8.77844	+	15.2047i	−0.433536	+	0.750907i
$411$	−12.0469	−	33.9716i	−0.594228	−	1.67570i
$412$	−6.30671	−	10.9235i	−0.310709	−	0.538165i
$413$	0.160942			0.00791945
$414$	7.02840	+	2.69083i	0.345427	+	0.132247i
$415$	29.5782			1.45194
$416$	2.66420	+	4.61453i	0.130623	+	0.226246i
$417$	−0.137655	+	0.161317i	−0.00674098	+	0.00789974i
$418$	13.3896	−	23.1914i	0.654905	−	1.13433i
$419$	−11.7384	+	20.3315i	−0.573457	+	0.993257i	0.422750	+	0.906246i	$0.361065\pi$
$419$	−11.7384	+	20.3315i	−0.573457	+	0.993257i	−0.996207	+	0.0870111i	$0.972268\pi$
$420$	−0.735559	+	0.861999i	−0.0358916	+	0.0420613i
$421$	13.3272	+	23.0834i	0.649527	+	1.12501i	0.983236	+	0.182338i	$0.0583665\pi$
$421$	13.3272	+	23.0834i	0.649527	+	1.12501i	−0.333709	+	0.942676i	$0.608300\pi$
$422$	−4.80875			−0.234086
$423$	−6.36214	−	39.9407i	−0.309338	−	1.94198i
$424$	−9.76490			−0.474226
$425$	−2.27335	−	3.93756i	−0.110274	−	0.191000i
$426$	6.05265	+	17.0682i	0.293252	+	0.826958i
$427$	−0.600239	+	1.03965i	−0.0290476	+	0.0503120i
$428$	−1.93945	+	3.35922i	−0.0937467	+	0.162374i
$429$	−46.1569	−	8.53359i	−2.22847	−	0.412006i
$430$	7.47039	+	12.9391i	0.360254	+	0.623979i
$431$	27.9472			1.34617			0.673085	−	0.739565i	$-0.264969\pi$
$431$	27.9472			1.34617			0.673085	+	0.739565i	$0.264969\pi$
$432$	−0.129139	+	5.19455i	−0.00621322	+	0.249923i
$433$	14.4980			0.696730			0.348365	−	0.937359i	$-0.386737\pi$
$433$	14.4980			0.696730			0.348365	+	0.937359i	$0.386737\pi$
$434$	0.156751	+	0.271500i	0.00752427	+	0.0130324i
$435$	−34.8769	−	6.44812i	−1.67222	−	0.309164i
$436$	−0.268218	+	0.464567i	−0.0128453	+	0.0222487i
$437$	−6.60429	+	11.4390i	−0.315926	+	0.547200i
$438$	4.47815	+	12.6282i	0.213974	+	0.603398i
$439$	−5.12412	−	8.87523i	−0.244561	−	0.423592i	0.717447	−	0.696613i	$-0.245310\pi$
$439$	−5.12412	−	8.87523i	−0.244561	−	0.423592i	−0.962008	+	0.273021i	$0.911977\pi$
$440$	16.9802			0.809500
$441$	16.2189	−	13.1576i	0.772330	−	0.626550i
$442$	−3.94165			−0.187485
$443$	−4.06941	−	7.04842i	−0.193343	−	0.334880i	0.753013	−	0.658006i	$-0.228600\pi$
$443$	−4.06941	−	7.04842i	−0.193343	−	0.334880i	−0.946356	+	0.323125i	$0.895266\pi$
$444$	−1.12430	+	1.31756i	−0.0533567	+	0.0625285i
$445$	−17.7683	+	30.7756i	−0.842297	+	1.45890i
$446$	−2.64310	+	4.57799i	−0.125155	+	0.216774i
$447$	7.69147	−	9.01361i	0.363794	−	0.426329i
$448$	−0.0979808	−	0.169708i	−0.00462916	−	0.00801794i
$449$	1.81755			0.0857754			0.0428877	−	0.999080i	$-0.486344\pi$
$449$	1.81755			0.0857754			0.0428877	+	0.999080i	$0.486344\pi$
$450$	−14.3195	+	11.6167i	−0.675030	+	0.547616i
$451$	26.7460			1.25942
$452$	−9.51721	−	16.4843i	−0.447652	−	0.775356i
$453$	12.6413	+	35.6479i	0.593940	+	1.67488i
$454$	−3.26088	+	5.64800i	−0.153041	+	0.265074i
$455$	−1.74303	+	3.01901i	−0.0817144	+	0.141533i
$456$	−8.96771	−	1.65797i	−0.419952	−	0.0776417i
$457$	19.4938	+	33.7642i	0.911880	+	1.57942i	0.811405	+	0.584484i	$0.198703\pi$
$457$	19.4938	+	33.7642i	0.911880	+	1.57942i	0.100475	+	0.994940i	$0.467964\pi$
$458$	5.93818			0.277473
$459$	−3.28005	−	2.00405i	−0.153100	−	0.0935408i
$460$	−8.37534			−0.390502
$461$	7.32636	+	12.6896i	0.341223	+	0.591015i	0.984660	−	0.174484i	$-0.0558257\pi$
$461$	7.32636	+	12.6896i	0.341223	+	0.591015i	−0.643437	+	0.765499i	$0.722492\pi$
$462$	1.69750	+	0.313838i	0.0789749	+	0.0146011i
$463$	−12.6671	+	21.9400i	−0.588689	+	1.01964i	0.405715	+	0.914000i	$0.367023\pi$
$463$	−12.6671	+	21.9400i	−0.588689	+	1.01964i	−0.994404	+	0.105640i	$0.966311\pi$
$464$	3.06675	−	5.31177i	0.142371	−	0.246593i
$465$	3.09194	+	8.71914i	0.143385	+	0.404340i
$466$	−9.20536	−	15.9442i	−0.426430	−	0.738599i
$467$	−6.52767			−0.302065			−0.151032	−	0.988529i	$-0.548260\pi$
$467$	−6.52767			−0.302065			−0.151032	+	0.988529i	$0.548260\pi$
$468$	2.51458	+	15.7862i	0.116236	+	0.729717i
$469$	1.37737			0.0636010
$470$	22.5046	+	38.9791i	1.03806	+	1.79797i
$471$	−22.3369	+	26.1765i	−1.02923	+	1.20615i
$472$	−0.410647	+	0.711262i	−0.0189016	+	0.0327385i
$473$	11.3803	−	19.7113i	0.523267	−	0.906326i
$474$	−1.04292	+	1.22220i	−0.0479030	+	0.0561374i
$475$	−16.1810	−	28.0263i	−0.742436	−	1.28594i
$476$	0.144961			0.00664428
$477$	−27.3582	−	10.4741i	−1.25265	−	0.479578i
$478$	24.0032			1.09788
$479$	−9.70032	−	16.8014i	−0.443219	−	0.767678i	0.554707	−	0.832045i	$-0.312830\pi$
$479$	−9.70032	−	16.8014i	−0.443219	−	0.767678i	−0.997926	+	0.0643680i	$0.979497\pi$
$480$	−1.93269	−	5.45011i	−0.0882150	−	0.248762i
$481$	−2.66420	+	4.61453i	−0.121477	+	0.210405i
$482$	8.62270	−	14.9350i	0.392753	−	0.680269i
$483$	−0.837278	−	0.154798i	−0.0380975	−	0.00704355i
$484$	−7.43374	−	12.8756i	−0.337897	−	0.585255i
$485$	−34.7507			−1.57795
$486$	−5.93364	+	14.4150i	−0.269155	+	0.653877i
$487$	−11.5204			−0.522040			−0.261020	−	0.965333i	$-0.584059\pi$
$487$	−11.5204			−0.522040			−0.261020	+	0.965333i	$0.584059\pi$
$488$	−3.06305	−	5.30535i	−0.138658	−	0.240162i
$489$	7.28015	+	1.34597i	0.329220	+	0.0608669i
$490$	−11.6210	+	20.1282i	−0.524985	+	0.909301i
$491$	15.0479	−	26.0638i	0.679103	−	1.17624i	−0.296148	−	0.955142i	$-0.595702\pi$
$491$	15.0479	−	26.0638i	0.679103	−	1.17624i	0.975251	−	0.221099i	$-0.0709645\pi$
$492$	−3.04424	−	8.58461i	−0.137245	−	0.387024i
$493$	2.26861	+	3.92935i	0.102173	+	0.176969i
$494$	−28.0554			−1.26227
$495$	47.5733	+	18.2135i	2.13826	+	0.818635i
$496$	−1.59981			−0.0718336
$497$	−1.02445	−	1.77440i	−0.0459528	−	0.0795925i
$498$	−9.96060	+	11.6728i	−0.446345	+	0.523071i
$499$	−9.80578	+	16.9841i	−0.438967	+	0.760313i	−0.997610	−	0.0690953i	$-0.977989\pi$
$499$	−9.80578	+	16.9841i	−0.438967	+	0.760313i	0.558643	+	0.829408i	$0.311322\pi$
$500$	1.91358	−	3.31442i	0.0855781	−	0.148226i
$501$	0.691734	−	0.810641i	0.0309044	−	0.0362167i
$502$	−2.78410	−	4.82221i	−0.124261	−	0.215226i
$503$	−19.1959			−0.855903			−0.427951	−	0.903802i	$-0.640765\pi$
$503$	−19.1959			−0.855903			−0.427951	+	0.903802i	$0.640765\pi$
$504$	−0.0924781	−	0.580566i	−0.00411930	−	0.0258604i
$505$	9.73675			0.433280
$506$	6.37945	+	11.0495i	0.283601	+	0.491212i
$507$	8.91023	+	25.1264i	0.395717	+	1.11590i
$508$	−10.0326	+	17.3769i	−0.445123	+	0.770976i
$509$	−14.7027	+	25.4659i	−0.651687	+	1.12876i	0.331026	+	0.943622i	$0.392605\pi$
$509$	−14.7027	+	25.4659i	−0.651687	+	1.12876i	−0.982713	+	0.185134i	$0.940728\pi$
$510$	4.20638	+	0.777686i	0.186262	+	0.0344365i
$511$	−0.757954	−	1.31281i	−0.0335299	−	0.0580755i
$512$	1.00000			0.0441942
$513$	−23.3464	−	14.2642i	−1.03077	−	0.629778i
$514$	−12.8042			−0.564769
$515$	21.0557	+	36.4695i	0.927824	+	1.60704i
$516$	−7.62201	−	1.40918i	−0.335540	−	0.0620355i
$517$	34.2833	−	59.3804i	1.50778	−	2.61155i
$518$	0.0979808	−	0.169708i	0.00430503	−	0.00745653i
$519$	12.1502	+	34.2631i	0.533335	+	1.50398i
$520$	−8.89474	−	15.4061i	−0.390060	−	0.675604i
$521$	−1.28738			−0.0564013			−0.0282006	−	0.999602i	$-0.508978\pi$
$521$	−1.28738			−0.0564013			−0.0282006	+	0.999602i	$0.508978\pi$
$522$	14.2897	−	11.5924i	0.625442	−	0.507388i
$523$	−4.27752			−0.187043			−0.0935215	−	0.995617i	$-0.529812\pi$
$523$	−4.27752			−0.187043			−0.0935215	+	0.995617i	$0.529812\pi$
$524$	−4.21323	−	7.29753i	−0.184056	−	0.318794i
$525$	1.35415	−	1.58693i	0.0591001	−	0.0692592i
$526$	−1.62293	+	2.81100i	−0.0707632	+	0.122565i
$527$	0.591724	−	1.02490i	0.0257759	−	0.0446452i
$528$	−5.71818	+	6.70111i	−0.248852	+	0.291628i
$529$	8.35339	+	14.4685i	0.363191	+	0.629065i
$530$	32.6012			1.41611
$531$	−1.91343	+	1.55226i	−0.0830357	+	0.0673624i
$532$	1.03179			0.0447337
$533$	−14.0103	−	24.2666i	−0.606855	−	1.05110i
$534$	−6.16178	−	17.3759i	−0.266646	−	0.751931i
$535$	6.47506	−	11.2151i	0.279941	−	0.484872i
$536$	−3.51438	+	6.08709i	−0.151798	+	0.262922i
$537$	38.2218	+	7.06654i	1.64939	+	0.304944i
$538$	10.2194	+	17.7005i	0.440590	+	0.763125i
$539$	35.4067			1.52508
$540$	0.431146	−	17.3426i	0.0185536	−	0.746306i
$541$	5.96148			0.256304			0.128152	−	0.991755i	$-0.459095\pi$
$541$	5.96148			0.256304			0.128152	+	0.991755i	$0.459095\pi$
$542$	9.32597	+	16.1531i	0.400585	+	0.693833i
$543$	−9.54571	−	1.76483i	−0.409646	−	0.0757363i
$544$	−0.369871	+	0.640636i	−0.0158581	+	0.0274670i
$545$	0.895476	−	1.55101i	0.0383580	−	0.0664379i
$546$	−0.604457	−	1.70454i	−0.0258684	−	0.0729476i
$547$	−14.4313	−	24.9957i	−0.617036	−	1.06874i	−0.990024	−	0.140901i	$-0.955000\pi$
$547$	−14.4313	−	24.9957i	−0.617036	−	1.06874i	0.372988	−	0.927836i	$-0.378333\pi$
$548$	−20.8102			−0.888969
$549$	−2.89102	−	18.1495i	−0.123386	−	0.774600i
$550$	−31.2603			−1.33294
$551$	16.1472	+	27.9679i	0.687896	+	1.19147i
$552$	2.82044	−	3.30527i	0.120046	−	0.140681i
$553$	0.0908892	−	0.157425i	0.00386500	−	0.00669438i
$554$	3.19738	−	5.53802i	0.135844	−	0.235288i
$555$	3.75359	−	4.39882i	0.159331	−	0.186719i
$556$	0.0612183	+	0.106033i	0.00259623	+	0.00449681i
$557$	27.3289			1.15796			0.578981	−	0.815341i	$-0.303451\pi$
$557$	27.3289			1.15796			0.578981	+	0.815341i	$0.303451\pi$
$558$	−4.48217	−	1.71600i	−0.189745	−	0.0726443i
$559$	−23.8454			−1.00855
$560$	0.327120	+	0.566588i	0.0138233	+	0.0239427i
$561$	−2.17798	−	6.14182i	−0.0919545	−	0.259308i
$562$	10.1430	−	17.5682i	0.427857	−	0.741070i
$563$	−15.5652	+	26.9598i	−0.655996	+	1.13622i	0.325647	+	0.945492i	$0.394418\pi$
$563$	−15.5652	+	26.9598i	−0.655996	+	1.13622i	−0.981643	+	0.190727i	$0.938915\pi$
$564$	−22.9614	−	4.24515i	−0.966848	−	0.178753i
$565$	31.7743	+	55.0347i	1.33675	+	2.31533i
$566$	21.7594			0.914615
$567$	0.363637	−	1.72576i	0.0152713	−	0.0724751i
$568$	10.4556			0.438707
$569$	10.4703	+	18.1352i	0.438939	+	0.760265i	0.997608	−	0.0691256i	$-0.0220209\pi$
$569$	10.4703	+	18.1352i	0.438939	+	0.760265i	−0.558669	+	0.829391i	$0.688688\pi$
$570$	29.9397	+	5.53533i	1.25404	+	0.231849i
$571$	−18.7627	+	32.4979i	−0.785194	+	1.36000i	0.143689	+	0.989623i	$0.454103\pi$
$571$	−18.7627	+	32.4979i	−0.785194	+	1.36000i	−0.928883	+	0.370373i	$0.879230\pi$
$572$	−13.5502	+	23.4696i	−0.566560	+	0.981311i
$573$	−2.38728	−	6.73202i	−0.0997299	−	0.281234i
$574$	0.515255	+	0.892448i	0.0215063	+	0.0372501i
$575$	15.4189			0.643012
$576$	2.80169	+	1.07263i	0.116737	+	0.0446929i
$577$	−17.9434			−0.746993			−0.373496	−	0.927632i	$-0.621841\pi$
$577$	−17.9434			−0.746993			−0.373496	+	0.927632i	$0.621841\pi$
$578$	8.22639	+	14.2485i	0.342173	+	0.592661i
$579$	−9.61383	+	11.2664i	−0.399537	+	0.468217i
$580$	−10.2387	+	17.7340i	−0.425139	+	0.736363i
$581$	0.868053	−	1.50351i	0.0360129	−	0.0623762i
$582$	11.7025	−	13.7141i	0.485083	−	0.568467i
$583$	−24.8322	−	43.0106i	−1.02844	−	1.78132i
$584$	7.73574			0.320107
$585$	−8.39520	−	52.7040i	−0.347099	−	2.17904i
$586$	29.9252			1.23620
$587$	18.9230	+	32.7757i	0.781037	+	1.35280i	0.931338	+	0.364156i	$0.118643\pi$
$587$	18.9230	+	32.7757i	0.781037	+	1.35280i	−0.150301	+	0.988640i	$0.548024\pi$
$588$	−4.03001	−	11.3644i	−0.166195	−	0.468662i
$589$	4.21170	−	7.29489i	0.173540	−	0.300581i
$590$	1.37099	−	2.37463i	0.0564428	−	0.0977619i
$591$	−22.4403	−	4.14882i	−0.923070	−	0.170660i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−14.5823			−0.598823			−0.299412	−	0.954124i	$-0.596790\pi$
$593$	−14.5823			−0.598823			−0.299412	+	0.954124i	$0.596790\pi$
$594$	−23.2084	+	12.6409i	−0.952251	+	0.518664i
$595$	−0.483969			−0.0198408
$596$	−3.42057	−	5.92461i	−0.140112	−	0.242681i
$597$	−31.6470	−	5.85098i	−1.29523	−	0.239465i
$598$	6.68350	−	11.5762i	0.273308	−	0.473384i
$599$	−0.0784702	+	0.135914i	−0.00320620	+	0.00555331i	−0.867624	−	0.497221i	$-0.834354\pi$
$599$	−0.0784702	+	0.135914i	−0.00320620	+	0.00555331i	0.864418	+	0.502774i	$0.167687\pi$
$600$	3.55806	+	10.0336i	0.145257	+	0.409619i
$601$	−18.4878	−	32.0219i	−0.754135	−	1.30620i	−0.945803	−	0.324740i	$-0.894723\pi$
$601$	−18.4878	−	32.0219i	−0.754135	−	1.30620i	0.191668	−	0.981460i	$-0.438610\pi$
$602$	0.876957			0.0357421
$603$	−16.3754	+	13.2845i	−0.666858	+	0.540987i
$604$	21.8371			0.888538
$605$	24.8184	+	42.9867i	1.00901	+	1.74766i
$606$	−3.27890	+	3.84253i	−0.133196	+	0.156092i
$607$	−20.4928	+	35.4945i	−0.831776	+	1.44068i	0.0648528	+	0.997895i	$0.479342\pi$
$607$	−20.4928	+	35.4945i	−0.831776	+	1.44068i	−0.896629	+	0.442783i	$0.853991\pi$
$608$	−2.63263	+	4.55985i	−0.106767	+	0.184926i
$609$	−1.35133	+	1.58362i	−0.0547585	+	0.0641714i
$610$	10.2263	+	17.7125i	0.414052	+	0.717159i
$611$	−71.8344			−2.90611
$612$	−1.72343	+	1.39813i	−0.0696655	+	0.0565160i
$613$	3.72829			0.150584			0.0752921	−	0.997162i	$-0.476011\pi$
$613$	3.72829			0.150584			0.0752921	+	0.997162i	$0.476011\pi$
$614$	11.3865	+	19.7220i	0.459521	+	0.795914i
$615$	10.1635	+	28.6607i	0.409833	+	1.15571i
$616$	0.498331	−	0.863135i	0.0200783	−	0.0347767i
$617$	8.26639	−	14.3178i	0.332792	−	0.576413i	−0.650266	−	0.759707i	$-0.725343\pi$
$617$	8.26639	−	14.3178i	0.332792	−	0.576413i	0.983058	+	0.183294i	$0.0586759\pi$
$618$	−21.4830	−	3.97183i	−0.864174	−	0.159771i
$619$	−12.2709	−	21.2538i	−0.493208	−	0.854261i	0.506762	−	0.862086i	$-0.330842\pi$
$619$	−12.2709	−	21.2538i	−0.493208	−	0.854261i	−0.999969	+	0.00782551i	$0.997509\pi$
$620$	5.34115			0.214506
$621$	11.4473	−	6.23504i	0.459365	−	0.250203i
$622$	−31.3806			−1.25825
$623$	1.04292	+	1.80639i	0.0417836	+	0.0723714i
$624$	9.07527	+	1.67786i	0.363301	+	0.0671680i
$625$	8.97712	−	15.5488i	0.359085	−	0.621953i
$626$	−2.09361	+	3.62625i	−0.0836776	+	0.144934i
$627$	−15.5022	−	43.7155i	−0.619098	−	1.74583i
$628$	9.93371	+	17.2057i	0.396398	+	0.686582i
$629$	−0.739743			−0.0294955
$630$	0.308749	+	1.93828i	0.0123008	+	0.0772231i
$631$	6.74272			0.268423			0.134212	−	0.990953i	$-0.457150\pi$
$631$	6.74272			0.268423			0.134212	+	0.990953i	$0.457150\pi$
$632$	0.463811	+	0.803345i	0.0184494	+	0.0319553i
$633$	−5.40646	+	6.33581i	−0.214887	+	0.251826i
$634$	4.85876	−	8.41563i	0.192966	−	0.334227i
$635$	33.4949	−	58.0148i	1.32920	−	2.30225i
$636$	−10.9786	+	12.8658i	−0.435331	+	0.510163i
$637$	−18.5471	−	32.1245i	−0.734863	−	1.27282i
$638$	31.1951			1.23502
$639$	29.2933	+	11.2150i	1.15883	+	0.443658i
$640$	−3.33861			−0.131970
$641$	−16.7281	−	28.9739i	−0.660719	−	1.14440i	−0.980427	−	0.196883i	$-0.936918\pi$
$641$	−16.7281	−	28.9739i	−0.660719	−	1.14440i	0.319708	−	0.947516i	$-0.396415\pi$
$642$	2.24546	+	6.33209i	0.0886211	+	0.249908i
$643$	−22.4969	+	38.9659i	−0.887193	+	1.53666i	−0.0440138	+	0.999031i	$0.514015\pi$
$643$	−22.4969	+	38.9659i	−0.887193	+	1.53666i	−0.843179	+	0.537633i	$0.819319\pi$
$644$	−0.245798	+	0.425734i	−0.00968578	+	0.0167763i
$645$	25.4469	+	4.70469i	1.00197	+	0.185247i
$646$	−1.94747	−	3.37311i	−0.0766221	−	0.132713i
$647$	4.93692			0.194090			0.0970451	−	0.995280i	$-0.469061\pi$
$647$	4.93692			0.194090			0.0970451	+	0.995280i	$0.469061\pi$
$648$	6.69893	+	6.01035i	0.263159	+	0.236109i
$649$	−4.17711			−0.163966
$650$	16.3751	+	28.3625i	0.642283	+	1.11247i
$651$	0.533951	+	0.0987182i	0.0209272	+	0.00386907i
$652$	2.13721	−	3.70176i	0.0836997	−	0.144972i
$653$	−18.3552	+	31.7921i	−0.718294	+	1.24412i	0.243381	+	0.969931i	$0.421743\pi$
$653$	−18.3552	+	31.7921i	−0.718294	+	1.24412i	−0.961675	+	0.274191i	$0.911590\pi$
$654$	0.310538	+	0.875703i	0.0121430	+	0.0342427i
$655$	14.0663	+	24.3636i	0.549617	+	0.951965i
$656$	−5.25874			−0.205319
$657$	21.6731	+	8.29759i	0.845550	+	0.323720i
$658$	2.64184			0.102990
$659$	21.8125	+	37.7804i	0.849696	+	1.47172i	0.881480	+	0.472222i	$0.156548\pi$
$659$	21.8125	+	37.7804i	0.849696	+	1.47172i	−0.0317839	+	0.999495i	$0.510119\pi$
$660$	19.0908	−	22.3724i	0.743107	−	0.870845i
$661$	6.82943	−	11.8289i	0.265634	−	0.460091i	−0.702096	−	0.712083i	$-0.747752\pi$
$661$	6.82943	−	11.8289i	0.265634	−	0.460091i	0.967730	+	0.251991i	$0.0810854\pi$
$662$	−2.09734	+	3.63269i	−0.0815153	+	0.141189i
$663$	−4.43158	+	5.19335i	−0.172108	+	0.201693i
$664$	4.42971	+	7.67248i	0.171906	+	0.297750i
$665$	−3.44474			−0.133581
$666$	0.471920	+	2.96265i	0.0182865	+	0.114800i
$667$	−15.3867			−0.595776
$668$	−0.307630	−	0.532831i	−0.0119026	−	0.0206158i
$669$	3.06014	+	8.62946i	0.118312	+	0.333634i
$670$	11.7332	−	20.3224i	0.453292	−	0.785124i
$671$	15.5787	−	26.9831i	0.601408	−	1.04167i
$672$	−0.333759	−	0.0617062i	−0.0128750	−	0.00238037i
$673$	16.5290	+	28.6291i	0.637146	+	1.10357i	0.986056	+	0.166413i	$0.0532186\pi$
$673$	16.5290	+	28.6291i	0.637146	+	1.10357i	−0.348910	+	0.937156i	$0.613448\pi$
$674$	17.3297			0.667516
$675$	−0.793734	+	31.9274i	−0.0305508	+	1.22889i
$676$	15.3919			0.591996
$677$	8.55730	+	14.8217i	0.328884	+	0.569643i	0.982291	−	0.187364i	$-0.0599943\pi$
$677$	8.55730	+	14.8217i	0.328884	+	0.569643i	−0.653407	+	0.757007i	$0.726661\pi$
$678$	−32.4192	−	5.99373i	−1.24505	−	0.230188i
$679$	−1.01985	+	1.76644i	−0.0391384	+	0.0677897i
$680$	1.23486	−	2.13884i	0.0473546	−	0.0820206i
$681$	3.77539	+	10.6464i	0.144673	+	0.407972i
$682$	−4.06832	−	7.04654i	−0.155784	−	0.269826i
$683$	−0.957620			−0.0366423			−0.0183212	−	0.999832i	$-0.505832\pi$
$683$	−0.957620			−0.0366423			−0.0183212	+	0.999832i	$0.505832\pi$
$684$	−12.2668	+	9.95143i	−0.469034	+	0.380503i
$685$	69.4773			2.65459
$686$	1.36797	+	2.36939i	0.0522293	+	0.0904638i
$687$	6.67627	−	7.82389i	0.254715	−	0.298500i
$688$	−2.23757	+	3.87559i	−0.0853067	+	0.147755i
$689$	−26.0157	+	45.0605i	−0.991118	+	1.71667i
$690$	−9.41636	+	11.0350i	−0.358475	+	0.420095i
$691$	4.99898	+	8.65848i	0.190170	+	0.329384i	0.945306	−	0.326184i	$-0.105763\pi$
$691$	4.99898	+	8.65848i	0.190170	+	0.329384i	−0.755136	+	0.655568i	$0.772429\pi$
$692$	20.9888			0.797873
$693$	2.32199	−	1.88371i	0.0882052	−	0.0715562i
$694$	−0.604429			−0.0229438
$695$	−0.204384	−	0.354004i	−0.00775273	−	0.0134281i
$696$	−3.55063	−	10.0126i	−0.134586	−	0.379528i
$697$	1.94506	−	3.36894i	0.0736743	−	0.127608i
$698$	−7.94873	+	13.7676i	−0.300864	+	0.521111i
$699$	−31.3569	−	5.79734i	−1.18603	−	0.219276i
$700$	−0.602223	−	1.04308i	−0.0227619	−	0.0394247i
$701$	3.05328			0.115321			0.0576604	−	0.998336i	$-0.481636\pi$
$701$	3.05328			0.115321			0.0576604	+	0.998336i	$0.481636\pi$
$702$	23.6264	+	14.4352i	0.891719	+	0.544823i
$703$	−5.26526			−0.198583
$704$	2.54300	+	4.40461i	0.0958431	+	0.166005i
$705$	76.6591	+	14.1729i	2.88715	+	0.533783i
$706$	2.99221	−	5.18265i	0.112613	−	0.195052i
$707$	0.285752	−	0.494937i	0.0107468	−	0.0186140i
$708$	0.475440	+	1.34072i	0.0178681	+	0.0503873i
$709$	23.9825	+	41.5389i	0.900682	+	1.56003i	0.826611	+	0.562774i	$0.190266\pi$
$709$	23.9825	+	41.5389i	0.900682	+	1.56003i	0.0740716	+	0.997253i	$0.476401\pi$
$710$	−34.9072			−1.31004
$711$	0.437763	+	2.74822i	0.0164174	+	0.103066i
$712$	−10.6441			−0.398905
$713$	2.00667	+	3.47565i	0.0751502	+	0.130164i
$714$	0.162979	−	0.190995i	0.00609934	−	0.00714780i
$715$	45.2387	−	78.3557i	1.69183	−	2.93034i
$716$	11.2207	−	19.4348i	0.419337	−	0.726312i
$717$	26.9867	−	31.6256i	1.00784	−	1.18108i
$718$	−3.76344	−	6.51846i	−0.140450	−	0.243267i
$719$	32.0932			1.19687			0.598437	−	0.801170i	$-0.295789\pi$
$719$	32.0932			1.19687			0.598437	+	0.801170i	$0.295789\pi$
$720$	−9.35376	−	3.58110i	−0.348594	−	0.133460i
$721$	2.47175			0.0920527
$722$	−4.36146	−	7.55427i	−0.162317	−	0.281141i
$723$	−9.98321	−	28.1522i	−0.371280	−	1.04699i
$724$	−2.80231	+	4.85374i	−0.104147	+	0.180388i
$725$	18.8493	−	32.6479i	0.700045	−	1.21251i
$726$	−25.3221	−	4.68161i	−0.939791	−	0.173751i
$727$	−11.8999	−	20.6112i	−0.441343	−	0.764428i	0.556447	−	0.830883i	$-0.312164\pi$
$727$	−11.8999	−	20.6112i	−0.441343	−	0.764428i	−0.997789	+	0.0664551i	$0.978831\pi$
$728$	−1.04416			−0.0386992
$729$	12.3214	+	24.0246i	0.456349	+	0.889801i
$730$	−25.8266			−0.955887
$731$	−1.65523	−	2.86694i	−0.0612208	−	0.106038i
$732$	−10.4339	−	1.92904i	−0.385647	−	0.0712994i
$733$	−3.31608	+	5.74362i	−0.122482	+	0.212145i	−0.920746	−	0.390163i	$-0.872419\pi$
$733$	−3.31608	+	5.74362i	−0.122482	+	0.212145i	0.798264	+	0.602308i	$0.205752\pi$
$734$	9.26329	−	16.0445i	0.341914	−	0.592213i
$735$	13.4546	+	37.9415i	0.496282	+	1.39949i
$736$	−1.25431	−	2.17254i	−0.0462347	−	0.0800808i
$737$	−35.7484			−1.31681
$738$	−14.7333	−	5.64068i	−0.542342	−	0.207636i
$739$	−42.4986			−1.56334			−0.781669	−	0.623694i	$-0.785631\pi$
$739$	−42.4986			−1.56334			−0.781669	+	0.623694i	$0.785631\pi$
$740$	−1.66931	−	2.89132i	−0.0613649	−	0.106287i
$741$	−31.5426	+	36.9646i	−1.15875	+	1.35793i
$742$	0.956773	−	1.65718i	0.0351242	−	0.0608370i
$743$	21.9594	−	38.0348i	0.805612	−	1.39536i	−0.110264	−	0.993902i	$-0.535170\pi$
$743$	21.9594	−	38.0348i	0.805612	−	1.39536i	0.915877	−	0.401459i	$-0.131497\pi$
$744$	−1.79866	+	2.10784i	−0.0659420	+	0.0772773i
$745$	11.4200	+	19.7800i	0.418395	+	0.724682i
$746$	−29.4102			−1.07678
$747$	4.18093	+	26.2474i	0.152972	+	0.960340i
$748$	−3.76234			−0.137565
$749$	−0.380057	−	0.658278i	−0.0138870	−	0.0240530i
$750$	−2.21551	−	6.24765i	−0.0808991	−	0.228132i
$751$	−5.30741	+	9.19270i	−0.193670	+	0.335446i	−0.946464	−	0.322810i	$-0.895372\pi$
$751$	−5.30741	+	9.19270i	−0.193670	+	0.335446i	0.752794	+	0.658257i	$0.228706\pi$
$752$	−6.74071	+	11.6752i	−0.245808	+	0.425753i
$753$	−9.48369	−	1.75337i	−0.345605	−	0.0638963i
$754$	−16.3409	−	28.3033i	−0.595101	−	1.03074i
$755$	−72.9055			−2.65330
$756$	−0.868902	−	0.530882i	−0.0316016	−	0.0193080i
$757$	40.1639			1.45978			0.729892	−	0.683563i	$-0.239570\pi$
$757$	40.1639			1.45978			0.729892	+	0.683563i	$0.239570\pi$
$758$	−5.03708	−	8.72448i	−0.182955	−	0.316888i
$759$	21.7308	+	4.01764i	0.788778	+	0.145831i
$760$	8.78933	−	15.2236i	0.318822	−	0.552216i
$761$	−8.57336	+	14.8495i	−0.310784	+	0.538294i	−0.978532	−	0.206094i	$-0.933925\pi$
$761$	−8.57336	+	14.8495i	−0.310784	+	0.538294i	0.667748	+	0.744387i	$0.267258\pi$
$762$	11.6155	+	32.7553i	0.420786	+	1.18660i
$763$	−0.0525604	−	0.0910373i	−0.00190281	−	0.00329577i
$764$	−4.12388			−0.149197
$765$	5.75387	−	4.66781i	0.208031	−	0.168765i
$766$	15.6220			0.564446
$767$	2.18809	+	3.78989i	0.0790075	+	0.136845i
$768$	1.12430	−	1.31756i	0.0405695	−	0.0475433i
$769$	−5.97356	+	10.3465i	−0.215412	+	0.373105i	−0.953400	−	0.301709i	$-0.902443\pi$
$769$	−5.97356	+	10.3465i	−0.215412	+	0.373105i	0.737988	+	0.674814i	$0.235776\pi$
$770$	−1.66373	+	2.88167i	−0.0599568	+	0.103848i
$771$	−14.3957	+	16.8703i	−0.518449	+	0.607569i
$772$	4.27549	+	7.40537i	0.153878	+	0.266525i
$773$	−50.8932			−1.83050			−0.915250	−	0.402886i	$-0.868007\pi$
$773$	−50.8932			−1.83050			−0.915250	+	0.402886i	$0.868007\pi$
$774$	−10.4261	+	8.45811i	−0.374757	+	0.304021i
$775$	−9.83297			−0.353211
$776$	−5.20436	−	9.01421i	−0.186825	−	0.323591i
$777$	−0.113440	−	0.319897i	−0.00406965	−	0.0114762i
$778$	−8.30491	+	14.3845i	−0.297745	+	0.515710i
$779$	13.8443	−	23.9790i	0.496023	−	0.859138i
$780$	−30.2988	−	5.60172i	−1.08487	−	0.200574i
$781$	26.5886	+	46.0529i	0.951416	+	1.64790i
$782$	1.85574			0.0663611
$783$	0.792078	−	31.8608i	0.0283065	−	1.13861i
$784$	−6.96160			−0.248629
$785$	−33.1648	−	57.4432i	−1.18370	−	2.05023i
$786$	−14.3518	−	2.65340i	−0.511913	−	0.0946437i
$787$	6.00446	−	10.4000i	0.214036	−	0.370721i	−0.738938	−	0.673773i	$-0.764672\pi$
$787$	6.00446	−	10.4000i	0.214036	−	0.370721i	0.952974	+	0.303053i	$0.0980058\pi$
$788$	−6.58774	+	11.4103i	−0.234678	+	0.406475i
$789$	1.87900	+	5.29870i	0.0668942	+	0.188639i
$790$	−1.54849	−	2.68206i	−0.0550927	−	0.0954233i
$791$	3.73001			0.132624
$792$	2.40019	+	15.0681i	0.0852869	+	0.535420i
$793$	−32.6423			−1.15916
$794$	−11.9756	−	20.7423i	−0.424997	−	0.736117i
$795$	36.6534	−	42.9540i	1.29996	−	1.52342i
$796$	−9.29054	+	16.0917i	−0.329294	+	0.570354i
$797$	0.608907	−	1.05466i	0.0215686	−	0.0373579i	−0.855040	−	0.518563i	$-0.826467\pi$
$797$	0.608907	−	1.05466i	0.0215686	−	0.0373579i	0.876608	+	0.481205i	$0.159801\pi$
$798$	1.16003	−	1.35944i	0.0410648	−	0.0481237i
$799$	−4.98639	−	8.63668i	−0.176406	−	0.305544i
$800$	6.14633			0.217306
$801$	−29.8215	−	11.4172i	−1.05369	−	0.403407i
$802$	−28.2179			−0.996407
$803$	19.6720	+	34.0729i	0.694210	+	1.20241i
$804$	4.06889	+	11.4741i	0.143499	+	0.404660i
$805$	0.820623	−	1.42136i	0.0289232	−	0.0500964i
$806$	−4.26222	+	7.38238i	−0.150130	+	0.260033i
$807$	34.8111	+	6.43597i	1.22541	+	0.226557i
$808$	1.45820	+	2.52568i	0.0512994	+	0.0888532i
$809$	−31.5509			−1.10927			−0.554635	−	0.832094i	$-0.687142\pi$
$809$	−31.5509			−1.10927			−0.554635	+	0.832094i	$0.687142\pi$
$810$	−22.3651	−	20.0662i	−0.785830	−	0.705056i
$811$	−11.0562			−0.388235			−0.194118	−	0.980978i	$-0.562184\pi$
$811$	−11.0562			−0.388235			−0.194118	+	0.980978i	$0.562184\pi$
$812$	0.600966	+	1.04090i	0.0210898	+	0.0365286i
$813$	31.7677	+	5.87330i	1.11414	+	0.205986i
$814$	−2.54300	+	4.40461i	−0.0891322	+	0.154382i
$815$	−7.13533	+	12.3587i	−0.249940	+	0.432908i
$816$	0.428231	+	1.20759i	0.0149911	+	0.0422741i
$817$	−11.7814	−	20.4060i	−0.412179	−	0.713915i
$818$	20.8364			0.728527
$819$	−2.92542	−	1.12000i	−0.102222	−	0.0391360i
$820$	17.5569			0.613113
$821$	−9.80855	−	16.9889i	−0.342321	−	0.592917i	0.642542	−	0.766250i	$-0.277880\pi$
$821$	−9.80855	−	16.9889i	−0.342321	−	0.592917i	−0.984863	+	0.173333i	$0.944546\pi$
$822$	−23.3968	+	27.4187i	−0.816058	+	0.956336i
$823$	20.1860	−	34.9631i	0.703638	−	1.21874i	−0.263543	−	0.964648i	$-0.584891\pi$
$823$	20.1860	−	34.9631i	0.703638	−	1.21874i	0.967181	−	0.254089i	$-0.0817757\pi$
$824$	−6.30671	+	10.9235i	−0.219705	+	0.380540i
$825$	−35.1458	+	41.1873i	−1.22362	+	1.43396i
$826$	−0.0804711	−	0.139380i	−0.00279995	−	0.00484965i
$827$	−44.3183			−1.54110			−0.770549	−	0.637381i	$-0.780018\pi$
$827$	−44.3183			−1.54110			−0.770549	+	0.637381i	$0.780018\pi$
$828$	−1.18387	−	7.43219i	−0.0411424	−	0.258286i
$829$	−14.1163			−0.490279			−0.245139	−	0.969488i	$-0.578834\pi$
$829$	−14.1163			−0.490279			−0.245139	+	0.969488i	$0.578834\pi$
$830$	−14.7891	−	25.6154i	−0.513337	−	0.889125i
$831$	−3.70187	−	10.4391i	−0.128416	−	0.362129i
$832$	2.66420	−	4.61453i	0.0923646	−	0.159980i
$833$	2.57490	−	4.45985i	0.0892149	−	0.154525i
$834$	0.208532	+	0.0385539i	0.00722088	+	0.00133501i
$835$	1.02706	+	1.77891i	0.0355428	+	0.0615619i
$836$	−26.7791			−0.926176
$837$	−7.30022	+	3.97623i	−0.252333	+	0.137438i
$838$	23.4768			0.810991
$839$	2.10020	+	3.63766i	0.0725071	+	0.125586i	0.899999	−	0.435891i	$-0.143567\pi$
$839$	2.10020	+	3.63766i	0.0725071	+	0.125586i	−0.827492	+	0.561477i	$0.810233\pi$
$840$	1.11429	+	0.206013i	0.0384467	+	0.00710813i
$841$	−4.30997	+	7.46508i	−0.148620	+	0.257417i
$842$	13.3272	−	23.0834i	0.459285	−	0.795505i
$843$	−11.7434	−	33.1159i	−0.404464	−	1.14057i
$844$	2.40438	+	4.16450i	0.0827621	+	0.143348i
$845$	−51.3876			−1.76779
$846$	−31.4086	+	25.4801i	−1.07985	+	0.876025i
$847$	2.91345			0.100107
$848$	4.88245	+	8.45665i	0.167664	+	0.290403i
$849$	24.4640	−	28.6692i	0.839601	−	0.983926i
$850$	−2.27335	+	3.93756i	−0.0779754	+	0.135057i
$851$	1.25431	−	2.17254i	0.0429974	−	0.0744736i
$852$	11.7552	−	13.7759i	0.402726	−	0.471953i
$853$	7.97683	+	13.8163i	0.273121	+	0.473060i	0.969659	−	0.244460i	$-0.0786106\pi$
$853$	7.97683	+	13.8163i	0.273121	+	0.473060i	−0.696538	+	0.717520i	$0.745277\pi$
$854$	1.20048			0.0410795
$855$	40.9542	−	33.2240i	1.40060	−	1.13624i
$856$	3.87889			0.132578
$857$	0.493347	+	0.854501i	0.0168524	+	0.0291892i	0.874329	−	0.485334i	$-0.161302\pi$
$857$	0.493347	+	0.854501i	0.0168524	+	0.0291892i	−0.857476	+	0.514524i	$0.827969\pi$
$858$	15.6881	+	44.2398i	0.535584	+	1.51032i
$859$	−3.20746	+	5.55549i	−0.109437	+	0.189551i	−0.915542	−	0.402221i	$-0.868238\pi$
$859$	−3.20746	+	5.55549i	−0.109437	+	0.189551i	0.806105	+	0.591772i	$0.201572\pi$
$860$	7.47039	−	12.9391i	0.254738	−	0.441219i
$861$	1.75515	+	0.324497i	0.0598154	+	0.0110588i
$862$	−13.9736	−	24.2030i	−0.475943	−	0.824357i
$863$	−19.6447			−0.668714			−0.334357	−	0.942446i	$-0.608519\pi$
$863$	−19.6447			−0.668714			−0.334357	+	0.942446i	$0.608519\pi$
$864$	4.56318	−	2.48544i	0.155243	−	0.0845562i
$865$	−70.0733			−2.38257
$866$	−7.24901	−	12.5556i	−0.246331	−	0.426658i
$867$	28.0222	+	5.18080i	0.951682	+	0.175949i
$868$	0.156751	−	0.271500i	0.00532046	−	0.00921531i
$869$	−2.35895	+	4.08582i	−0.0800218	+	0.138602i
$870$	11.8542	+	33.4283i	0.401895	+	1.13333i
$871$	18.7261	+	32.4345i	0.634508	+	1.09900i
$872$	0.536436			0.0181660
$873$	−4.91207	−	30.8374i	−0.166249	−	1.04369i
$874$	13.2086			0.446787
$875$	0.374989	+	0.649500i	0.0126769	+	0.0219571i
$876$	8.69725	−	10.1923i	0.293853	−	0.344365i
$877$	12.5106	−	21.6690i	0.422452	−	0.731709i	−0.573726	−	0.819047i	$-0.694503\pi$
$877$	12.5106	−	21.6690i	0.422452	−	0.731709i	0.996179	+	0.0873382i	$0.0278361\pi$
$878$	−5.12412	+	8.87523i	−0.172931	+	0.299525i
$879$	33.6448	−	39.4282i	1.13481	−	1.32988i
$880$	−8.49010	−	14.7053i	−0.286201	−	0.495715i
$881$	20.0574			0.675751			0.337875	−	0.941191i	$-0.390292\pi$
$881$	20.0574			0.675751			0.337875	+	0.941191i	$0.390292\pi$
$882$	−19.5042	−	7.46722i	−0.656742	−	0.251434i
$883$	−10.4184			−0.350608			−0.175304	−	0.984514i	$-0.556091\pi$
$883$	−10.4184			−0.350608			−0.175304	+	0.984514i	$0.556091\pi$
$884$	1.97082	+	3.41357i	0.0662860	+	0.114811i
$885$	−1.58731	−	4.47614i	−0.0533569	−	0.150464i
$886$	−4.06941	+	7.04842i	−0.136714	+	0.236796i
$887$	14.0344	−	24.3083i	0.471229	−	0.816193i	−0.528229	−	0.849102i	$-0.677144\pi$
$887$	14.0344	−	24.3083i	0.471229	−	0.816193i	0.999458	+	0.0329089i	$0.0104771\pi$
$888$	1.70319	+	0.314889i	0.0571552	+	0.0105670i
$889$	−1.96600	−	3.40521i	−0.0659375	−	0.114207i
$890$	35.5365			1.19119
$891$	−9.43788	+	44.7905i	−0.316181	+	1.50054i
$892$	5.28621			0.176995
$893$	−35.4916	−	61.4732i	−1.18768	−	2.05712i
$894$	−11.6518	−	2.15420i	−0.389693	−	0.0720474i
$895$	−37.4615	+	64.8852i	−1.25220	+	2.16887i
$896$	−0.0979808	+	0.169708i	−0.00327331	+	0.00566954i
$897$	−7.73803	−	21.8209i	−0.258365	−	0.728579i
$898$	−0.908774	−	1.57404i	−0.0303262	−	0.0525265i
$899$	9.81245			0.327264
$900$	17.2201	+	6.59275i	0.574004	+	0.219758i
$901$	−7.22352			−0.240650
$902$	−13.3730	−	23.1627i	−0.445272	−	0.771233i
$903$	0.985958	−	1.15544i	0.0328106	−	0.0384507i
$904$	−9.51721	+	16.4843i	−0.316538	+	0.548259i
$905$	9.35582	−	16.2048i	0.310998	−	0.538664i
$906$	24.5513	−	28.7716i	0.815663	−	0.955873i
$907$	3.40817	+	5.90312i	0.113166	+	0.196010i	0.917045	−	0.398783i	$-0.130567\pi$
$907$	3.40817	+	5.90312i	0.113166	+	0.196010i	−0.803879	+	0.594793i	$0.797234\pi$
$908$	6.52175			0.216432
$909$	1.37631	+	8.64029i	0.0456493	+	0.286580i
$910$	3.48605			0.115562
$911$	−23.0830	−	39.9808i	−0.764772	−	1.32462i	−0.940367	−	0.340162i	$-0.889518\pi$
$911$	−23.0830	−	39.9808i	−0.764772	−	1.32462i	0.175595	−	0.984463i	$-0.443815\pi$
$912$	3.04801	+	8.59525i	0.100930	+	0.284617i
$913$	−22.5295	+	39.0223i	−0.745619	+	1.29145i
$914$	19.4938	−	33.7642i	0.644797	−	1.11682i
$915$	34.8347	+	6.44032i	1.15160	+	0.212910i
$916$	−2.96909	−	5.14261i	−0.0981014	−	0.169917i
$917$	1.65126			0.0545295
$918$	−0.0955299	+	3.84263i	−0.00315296	+	0.126826i
$919$	26.8038			0.884175			0.442087	−	0.896972i	$-0.354238\pi$
$919$	26.8038			0.884175			0.442087	+	0.896972i	$0.354238\pi$
$920$	4.18767	+	7.25326i	0.138063	+	0.239133i
$921$	38.7866	+	7.17096i	1.27806	+	0.236291i
$922$	7.32636	−	12.6896i	0.241281	−	0.417911i
$923$	27.8558	−	48.2477i	0.916886	−	1.58809i
$924$	−0.576959	−	1.62700i	−0.0189806	−	0.0535243i
$925$	3.07317	+	5.32288i	0.101045	+	0.175015i
$926$	25.3342			0.832533
$927$	−29.3864	+	23.8396i	−0.965175	+	0.782996i
$928$	−6.13351			−0.201342
$929$	−12.9589	−	22.4454i	−0.425167	−	0.736411i	0.571269	−	0.820763i	$-0.306451\pi$
$929$	−12.9589	−	22.4454i	−0.425167	−	0.736411i	−0.996436	+	0.0843519i	$0.973118\pi$
$930$	6.00503	−	7.03727i	0.196913	−	0.230761i
$931$	18.3273	−	31.7438i	0.600653	−	1.04036i
$932$	−9.20536	+	15.9442i	−0.301532	+	0.522268i
$933$	−35.2811	+	41.3458i	−1.15505	+	1.35360i
$934$	3.26384	+	5.65313i	0.106796	+	0.184976i
$935$	12.5610			0.410788
$936$	12.4140	−	10.0708i	0.405763	−	0.329174i
$937$	8.04348			0.262769			0.131384	−	0.991331i	$-0.458058\pi$
$937$	8.04348			0.262769			0.131384	+	0.991331i	$0.458058\pi$
$938$	−0.688684	−	1.19284i	−0.0224863	−	0.0389475i
$939$	2.42395	+	6.83543i	0.0791026	+	0.223066i
$940$	22.5046	−	38.9791i	0.734020	−	1.27136i
$941$	−28.5150	+	49.3894i	−0.929563	+	1.61005i	−0.145509	+	0.989357i	$0.546482\pi$
$941$	−28.5150	+	49.3894i	−0.929563	+	1.61005i	−0.784054	+	0.620693i	$0.786851\pi$
$942$	33.8379	+	6.25604i	1.10250	+	0.203833i
$943$	6.59611	+	11.4248i	0.214799	+	0.372043i
$944$	0.821294			0.0267309
$945$	2.90093	+	1.77241i	0.0943671	+	0.0576565i
$946$	−22.7606			−0.740012
$947$	5.99114	+	10.3770i	0.194686	+	0.337206i	0.946798	−	0.321830i	$-0.104298\pi$
$947$	5.99114	+	10.3770i	0.194686	+	0.337206i	−0.752112	+	0.659036i	$0.770965\pi$
$948$	1.57991	+	0.292098i	0.0513132	+	0.00948692i
$949$	20.6096	−	35.6968i	0.669015	−	1.15877i
$950$	−16.1810	+	28.0263i	−0.524981	+	0.909294i
$951$	−5.62539	−	15.8634i	−0.182416	−	0.514405i
$952$	−0.0724806	−	0.125540i	−0.00234911	−	0.00406878i
$953$	53.7478			1.74106			0.870532	−	0.492112i	$-0.163775\pi$
$953$	53.7478			1.74106			0.870532	+	0.492112i	$0.163775\pi$
$954$	4.60825	+	28.9300i	0.149198	+	0.936643i
$955$	13.7680			0.445523
$956$	−12.0016	−	20.7874i	−0.388160	−	0.672313i
$957$	35.0725	−	41.1013i	1.13373	−	1.32862i
$958$	−9.70032	+	16.8014i	−0.313403	+	0.542830i
$959$	2.03900	−	3.53166i	0.0658428	−	0.114043i
$960$	−3.75359	+	4.39882i	−0.121146	+	0.141971i
$961$	14.2203	+	24.6303i	0.458719	+	0.794525i
$962$	5.32840			0.171795
$963$	10.8675	+	4.16062i	0.350199	+	0.134074i
$964$	−17.2454			−0.555437
$965$	−14.2742	−	24.7237i	−0.459503	−	0.795883i
$966$	0.284580	+	0.802503i	0.00915621	+	0.0258201i
$967$	27.0378	−	46.8308i	0.869476	−	1.50598i	0.00694344	−	0.999976i	$-0.497790\pi$
$967$	27.0378	−	46.8308i	0.869476	−	1.50598i	0.862533	−	0.506001i	$-0.168877\pi$
$968$	−7.43374	+	12.8756i	−0.238929	+	0.413838i
$969$	−6.63380	−	1.22647i	−0.213108	−	0.0394000i
$970$	17.3753	+	30.0949i	0.557888	+	0.966291i
$971$	−16.9965			−0.545442			−0.272721	−	0.962093i	$-0.587924\pi$
$971$	−16.9965			−0.545442			−0.272721	+	0.962093i	$0.587924\pi$
$972$	15.4506	−	2.06881i	0.495577	−	0.0663572i
$973$	−0.0239929			−0.000769176
$974$	5.76021	+	9.97697i	0.184569	+	0.319683i
$975$	55.7796	+	10.3127i	1.78638	+	0.330270i
$976$	−3.06305	+	5.30535i	−0.0980457	+	0.169820i
$977$	7.19826	−	12.4677i	0.230293	−	0.398879i	−0.727602	−	0.686000i	$-0.759365\pi$
$977$	7.19826	−	12.4677i	0.230293	−	0.398879i	0.957894	+	0.287121i	$0.0926983\pi$
$978$	−2.47443	−	6.97778i	−0.0791235	−	0.223125i
$979$	−27.0680	−	46.8832i	−0.865097	−	1.49839i
$980$	23.2421			0.742441
$981$	1.50293	+	0.575397i	0.0479847	+	0.0183710i
$982$	−30.0958			−0.960397
$983$	23.1355	+	40.0719i	0.737908	+	1.27809i	0.953436	+	0.301597i	$0.0975196\pi$
$983$	23.1355	+	40.0719i	0.737908	+	1.27809i	−0.215527	+	0.976498i	$0.569147\pi$
$984$	−5.91237	+	6.92869i	−0.188480	+	0.220879i
$985$	21.9939	−	38.0946i	0.700784	−	1.21379i
$986$	2.26861	−	3.92935i	0.0722472	−	0.125136i
$987$	2.97021	−	3.48078i	0.0945428	−	0.110794i
$988$	14.0277	+	24.2967i	0.446281	+	0.772981i
$989$	11.2265			0.356981
$990$	−8.01329	−	50.3064i	−0.254679	−	1.59884i
$991$	50.4576			1.60284			0.801419	−	0.598103i	$-0.204079\pi$
$991$	50.4576			1.60284			0.801419	+	0.598103i	$0.204079\pi$
$992$	0.799905	+	1.38548i	0.0253970	+	0.0439889i
$993$	2.42826	+	6.84758i	0.0770585	+	0.217301i
$994$	−1.02445	+	1.77440i	−0.0324935	+	0.0562804i
$995$	31.0175	−	53.7239i	0.983321	−	1.70316i
$996$	15.0892	+	2.78974i	0.478121	+	0.0883962i
$997$	−25.5684	−	44.2858i	−0.809759	−	1.40254i	−0.913031	−	0.407891i	$-0.866264\pi$
$997$	−25.5684	−	44.2858i	−0.809759	−	1.40254i	0.103272	−	0.994653i	$-0.467069\pi$
$998$	19.6116			0.620793
$999$	4.43404	+	2.70911i	0.140287	+	0.0857125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.e.e.445.1	yes	20
3.2	odd	2		1998.2.e.e.1333.2		20
9.2	odd	6		1998.2.e.e.667.2		20
9.4	even	3		5994.2.a.bb.1.2		10
9.5	odd	6		5994.2.a.ba.1.9		10
9.7	even	3	inner	666.2.e.e.223.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.e.e.223.1	✓	20	9.7	even	3	inner
666.2.e.e.445.1	yes	20	1.1	even	1	trivial
1998.2.e.e.667.2		20	9.2	odd	6
1998.2.e.e.1333.2		20	3.2	odd	2
5994.2.a.ba.1.9		10	9.5	odd	6
5994.2.a.bb.1.2		10	9.4	even	3

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.70319 - 0.314889i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.66931 - 2.89132i) q^{5} +(0.578891 + 1.63245i) q^{6} +(-0.0979808 - 0.169708i) q^{7} +1.00000 q^{8} +(2.80169 + 1.07263i) q^{9} -3.33861 q^{10} +(2.54300 + 4.40461i) q^{11} +(1.12430 - 1.31756i) q^{12} +(2.66420 - 4.61453i) q^{13} +(-0.0979808 + 0.169708i) q^{14} +(-3.75359 + 4.39882i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.739743 q^{17} +(-0.471920 - 2.96265i) q^{18} +5.26526 q^{19} +(1.66931 + 2.89132i) q^{20} +(0.113440 + 0.319897i) q^{21} +(2.54300 - 4.40461i) q^{22} +(-1.25431 + 2.17254i) q^{23} +(-1.70319 - 0.314889i) q^{24} +(-3.07317 - 5.32288i) q^{25} -5.32840 q^{26} +(-4.43404 - 2.70911i) q^{27} +0.195962 q^{28} +(3.06675 + 5.31177i) q^{29} +(5.68628 + 1.05129i) q^{30} +(0.799905 - 1.38548i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.94425 - 8.30264i) q^{33} +(-0.369871 - 0.640636i) q^{34} -0.654240 q^{35} +(-2.32977 + 1.89002i) q^{36} -1.00000 q^{37} +(-2.63263 - 4.55985i) q^{38} +(-5.99070 + 7.02048i) q^{39} +(1.66931 - 2.89132i) q^{40} +(2.62937 - 4.55420i) q^{41} +(0.220319 - 0.258191i) q^{42} +(-2.23757 - 3.87559i) q^{43} -5.08601 q^{44} +(7.77820 - 6.31004i) q^{45} +2.50863 q^{46} +(-6.74071 - 11.6752i) q^{47} +(0.578891 + 1.63245i) q^{48} +(3.48080 - 6.02892i) q^{49} +(-3.07317 + 5.32288i) q^{50} +(-1.25992 - 0.232937i) q^{51} +(2.66420 + 4.61453i) q^{52} -9.76490 q^{53} +(-0.129139 + 5.19455i) q^{54} +16.9802 q^{55} +(-0.0979808 - 0.169708i) q^{56} +(-8.96771 - 1.65797i) q^{57} +(3.06675 - 5.31177i) q^{58} +(-0.410647 + 0.711262i) q^{59} +(-1.93269 - 5.45011i) q^{60} +(-3.06305 - 5.30535i) q^{61} -1.59981 q^{62} +(-0.0924781 - 0.580566i) q^{63} +1.00000 q^{64} +(-8.89474 - 15.4061i) q^{65} +(-5.71818 + 6.70111i) q^{66} +(-3.51438 + 6.08709i) q^{67} +(-0.369871 + 0.640636i) q^{68} +(2.82044 - 3.30527i) q^{69} +(0.327120 + 0.566588i) q^{70} +10.4556 q^{71} +(2.80169 + 1.07263i) q^{72} +7.73574 q^{73} +(0.500000 + 0.866025i) q^{74} +(3.55806 + 10.0336i) q^{75} +(-2.63263 + 4.55985i) q^{76} +(0.498331 - 0.863135i) q^{77} +(9.07527 + 1.67786i) q^{78} +(0.463811 + 0.803345i) q^{79} -3.33861 q^{80} +(6.69893 + 6.01035i) q^{81} -5.25874 q^{82} +(4.42971 + 7.67248i) q^{83} +(-0.333759 - 0.0617062i) q^{84} +(1.23486 - 2.13884i) q^{85} +(-2.23757 + 3.87559i) q^{86} +(-3.55063 - 10.0126i) q^{87} +(2.54300 + 4.40461i) q^{88} -10.6441 q^{89} +(-9.35376 - 3.58110i) q^{90} -1.04416 q^{91} +(-1.25431 - 2.17254i) q^{92} +(-1.79866 + 2.10784i) q^{93} +(-6.74071 + 11.6752i) q^{94} +(8.78933 - 15.2236i) q^{95} +(1.12430 - 1.31756i) q^{96} +(-5.20436 - 9.01421i) q^{97} -6.96160 q^{98} +(2.40019 + 15.0681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{2} + 2 q^{3} - 10 q^{4} - q^{5} + 2 q^{6} - q^{7} + 20 q^{8} + 2 q^{9} + 2 q^{10} - 3 q^{11} - 4 q^{12} - 12 q^{13} - q^{14} - 13 q^{15} - 10 q^{16} + 24 q^{17} + 2 q^{18} + 48 q^{19} - q^{20}+ \cdots + 49 q^{99}+O(q^{100}) \) 20 * q - 10 * q^2 + 2 * q^3 - 10 * q^4 - q^5 + 2 * q^6 - q^7 + 20 * q^8 + 2 * q^9 + 2 * q^10 - 3 * q^11 - 4 * q^12 - 12 * q^13 - q^14 - 13 * q^15 - 10 * q^16 + 24 * q^17 + 2 * q^18 + 48 * q^19 - q^20 - 18 * q^21 - 3 * q^22 - 3 * q^23 + 2 * q^24 - 21 * q^25 + 24 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^30 - 11 * q^31 - 10 * q^32 + 19 * q^33 - 12 * q^34 - 14 * q^35 - 4 * q^36 - 20 * q^37 - 24 * q^38 - 18 * q^39 - q^40 + 3 * q^41 + 30 * q^42 - 6 * q^43 + 6 * q^44 + 18 * q^45 + 6 * q^46 - 8 * q^47 + 2 * q^48 - 35 * q^49 - 21 * q^50 + 17 * q^51 - 12 * q^52 - 20 * q^53 - 31 * q^54 + 4 * q^55 - q^56 - 41 * q^57 - 4 * q^58 - 10 * q^59 + 11 * q^60 - 2 * q^61 + 22 * q^62 + 29 * q^63 + 20 * q^64 - 26 * q^65 - 17 * q^66 - 7 * q^67 - 12 * q^68 + 9 * q^69 + 7 * q^70 + 30 * q^71 + 2 * q^72 + 6 * q^73 + 10 * q^74 - 48 * q^75 - 24 * q^76 - 9 * q^77 + 48 * q^78 - 16 * q^79 + 2 * q^80 + 10 * q^81 - 6 * q^82 + 23 * q^83 - 12 * q^84 - 15 * q^85 - 6 * q^86 + 25 * q^87 - 3 * q^88 + 42 * q^89 - 15 * q^90 + 118 * q^91 - 3 * q^92 - 117 * q^93 - 8 * q^94 + 6 * q^95 - 4 * q^96 - 24 * q^97 + 70 * q^98 + 49 * q^99

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