LMFDB - Embedded newform 1110.2.bb.e.1009.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.13
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.19729 + 0.414645i) q^{5} -1.00000 q^{6} +(3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.19729 + 0.414645i) q^{5} -1.00000 q^{6} +(3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.11023 - 0.739551i) q^{10} -4.18276 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.82427 + 2.78529i) q^{13} +4.57922 q^{14} +(1.69558 - 1.45774i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.24768 + 1.87505i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.75460 + 4.77111i) q^{19} +(-1.45774 - 1.69558i) q^{20} +(-2.28961 + 3.96572i) q^{21} +(-3.62238 - 2.09138i) q^{22} +8.23560i q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.65614 - 1.82219i) q^{25} -5.57058 q^{26} +1.00000i q^{27} +(3.96572 + 2.28961i) q^{28} -6.64680 q^{29} +(2.19729 - 0.414645i) q^{30} -10.0797 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.62238 - 2.09138i) q^{33} +(1.87505 + 3.24768i) q^{34} +(-7.76446 + 6.67530i) q^{35} +1.00000 q^{36} +(4.03282 + 4.55372i) q^{37} +5.50921i q^{38} +(2.78529 - 4.82427i) q^{39} +(-0.414645 - 2.19729i) q^{40} +(-1.72520 - 2.98814i) q^{41} +(-3.96572 + 2.28961i) q^{42} -5.52664i q^{43} +(-2.09138 - 3.62238i) q^{44} +(-0.739551 + 2.11023i) q^{45} +(-4.11780 + 7.13224i) q^{46} +9.71453i q^{47} -1.00000i q^{48} +(6.98464 - 12.0977i) q^{49} +(4.94343 + 0.750010i) q^{50} -3.75010 q^{51} +(-4.82427 - 2.78529i) q^{52} +(-7.22208 - 4.16967i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(9.19073 - 1.73436i) q^{55} +(2.28961 + 3.96572i) q^{56} +(-4.77111 - 2.75460i) q^{57} +(-5.75630 - 3.32340i) q^{58} +(-3.16809 + 5.48730i) q^{59} +(2.11023 + 0.739551i) q^{60} +(0.298205 + 0.516507i) q^{61} +(-8.72928 - 5.03985i) q^{62} -4.57922i q^{63} -1.00000 q^{64} +(9.44539 - 8.12044i) q^{65} +4.18276 q^{66} +(7.24674 - 4.18391i) q^{67} +3.75010i q^{68} +(-4.11780 - 7.13224i) q^{69} +(-10.0619 + 1.89875i) q^{70} +(0.302090 + 0.523236i) q^{71} +(0.866025 + 0.500000i) q^{72} +5.58023i q^{73} +(1.21566 + 5.96005i) q^{74} +(-3.12124 + 3.90613i) q^{75} +(-2.75460 + 4.77111i) q^{76} +(-16.5877 + 9.57690i) q^{77} +(4.82427 - 2.78529i) q^{78} +(-1.36388 - 2.36231i) q^{79} +(0.739551 - 2.11023i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.45041i q^{82} +(-2.45612 - 1.41804i) q^{83} -4.57922 q^{84} +(-7.91357 - 2.77339i) q^{85} +(2.76332 - 4.78621i) q^{86} +(5.75630 - 3.32340i) q^{87} -4.18276i q^{88} +(-2.97261 + 5.14872i) q^{89} +(-1.69558 + 1.45774i) q^{90} +(-12.7545 + 22.0914i) q^{91} +(-7.13224 + 4.11780i) q^{92} +(8.72928 - 5.03985i) q^{93} +(-4.85726 + 8.41303i) q^{94} +(-8.03097 - 9.34132i) q^{95} +(0.500000 - 0.866025i) q^{96} +5.22592i q^{97} +(12.0977 - 6.98464i) q^{98} +(-2.09138 + 3.62238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.19729	+	0.414645i	−0.982657	+	0.185435i
$5$	−2.19729	+	0.414645i	−0.982657	+	0.185435i
$6$	−1.00000			−0.408248
$7$	3.96572	−	2.28961i	1.49890	−	0.865392i	0.498903	−	0.866658i	$-0.333736\pi$
$7$	3.96572	−	2.28961i	1.49890	−	0.865392i	0.999999	+	0.00126619i	$0.000403042\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.11023	−	0.739551i	−0.667313	−	0.233866i
$11$	−4.18276			−1.26115			−0.630575	−	0.776128i	$-0.717181\pi$
$11$	−4.18276			−1.26115			−0.630575	+	0.776128i	$0.717181\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−4.82427	+	2.78529i	−1.33801	+	0.772501i	−0.986512	−	0.163688i	$-0.947661\pi$
$13$	−4.82427	+	2.78529i	−1.33801	+	0.772501i	−0.351499	+	0.936188i	$0.614328\pi$
$14$	4.57922			1.22385
$15$	1.69558	−	1.45774i	0.437798	−	0.376386i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.24768	+	1.87505i	0.787679	+	0.454767i	0.839145	−	0.543908i	$-0.183056\pi$
$17$	3.24768	+	1.87505i	0.787679	+	0.454767i	−0.0514658	+	0.998675i	$0.516389\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.75460	+	4.77111i	0.631949	+	1.09457i	0.987153	+	0.159779i	$0.0510782\pi$
$19$	2.75460	+	4.77111i	0.631949	+	1.09457i	−0.355203	+	0.934789i	$0.615588\pi$
$20$	−1.45774	−	1.69558i	−0.325960	−	0.379144i
$21$	−2.28961	+	3.96572i	−0.499634	+	0.865392i
$22$	−3.62238	−	2.09138i	−0.772293	−	0.445884i
$23$			8.23560i			1.71724i	0.512611	+	0.858621i	$0.328678\pi$
$23$			8.23560i			1.71724i	−0.512611	+	0.858621i	$0.671322\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.65614	−	1.82219i	0.931228	−	0.364437i
$26$	−5.57058			−1.09248
$27$			1.00000i			0.192450i
$28$	3.96572	+	2.28961i	0.749451	+	0.432696i
$29$	−6.64680			−1.23428			−0.617140	−	0.786853i	$-0.711709\pi$
$29$	−6.64680			−1.23428			−0.617140	+	0.786853i	$0.711709\pi$
$30$	2.19729	−	0.414645i	0.401168	−	0.0757034i
$31$	−10.0797			−1.81037			−0.905184	−	0.425020i	$-0.860267\pi$
$31$	−10.0797			−1.81037			−0.905184	+	0.425020i	$0.860267\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.62238	−	2.09138i	0.630575	−	0.364063i
$34$	1.87505	+	3.24768i	0.321569	+	0.556973i
$35$	−7.76446	+	6.67530i	−1.31243	+	1.12833i
$36$	1.00000			0.166667
$37$	4.03282	+	4.55372i	0.662991	+	0.748628i
$37$	4.03282	+	4.55372i	0.662991	+	0.748628i
$38$			5.50921i			0.893711i
$39$	2.78529	−	4.82427i	0.446004	−	0.772501i
$40$	−0.414645	−	2.19729i	−0.0655611	−	0.347422i
$41$	−1.72520	−	2.98814i	−0.269432	−	0.466669i	0.699284	−	0.714844i	$-0.253502\pi$
$41$	−1.72520	−	2.98814i	−0.269432	−	0.466669i	−0.968715	+	0.248175i	$0.920169\pi$
$42$	−3.96572	+	2.28961i	−0.611924	+	0.353295i
$43$		−	5.52664i		−	0.842805i	−0.906874	−	0.421403i	$-0.861538\pi$
$43$		−	5.52664i		−	0.842805i	0.906874	−	0.421403i	$-0.138462\pi$
$44$	−2.09138	−	3.62238i	−0.315287	−	0.546094i
$45$	−0.739551	+	2.11023i	−0.110246	+	0.314574i
$46$	−4.11780	+	7.13224i	−0.607137	+	1.05159i
$47$			9.71453i			1.41701i	0.705706	+	0.708505i	$0.250630\pi$
$47$			9.71453i			1.41701i	−0.705706	+	0.708505i	$0.749370\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.98464	−	12.0977i	0.997805	−	1.72825i
$50$	4.94343	+	0.750010i	0.699106	+	0.106067i
$51$	−3.75010			−0.525119
$52$	−4.82427	−	2.78529i	−0.669005	−	0.386250i
$53$	−7.22208	−	4.16967i	−0.992029	−	0.572748i	−0.0861487	−	0.996282i	$-0.527456\pi$
$53$	−7.22208	−	4.16967i	−0.992029	−	0.572748i	−0.905880	+	0.423534i	$0.860789\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	9.19073	−	1.73436i	1.23928	−	0.233861i
$56$	2.28961	+	3.96572i	0.305962	+	0.529942i
$57$	−4.77111	−	2.75460i	−0.631949	−	0.364856i
$58$	−5.75630	−	3.32340i	−0.755839	−	0.436384i
$59$	−3.16809	+	5.48730i	−0.412450	+	0.714385i	−0.995157	−	0.0982975i	$-0.968660\pi$
$59$	−3.16809	+	5.48730i	−0.412450	+	0.714385i	0.582707	+	0.812683i	$0.301994\pi$
$60$	2.11023	+	0.739551i	0.272429	+	0.0954756i
$61$	0.298205	+	0.516507i	0.0381813	+	0.0661319i	0.884485	−	0.466569i	$-0.154510\pi$
$61$	0.298205	+	0.516507i	0.0381813	+	0.0661319i	−0.846303	+	0.532701i	$0.821177\pi$
$62$	−8.72928	−	5.03985i	−1.10862	−	0.640062i
$63$		−	4.57922i		−	0.576928i
$64$	−1.00000			−0.125000
$65$	9.44539	−	8.12044i	1.17156	−	1.00722i
$66$	4.18276			0.514862
$67$	7.24674	−	4.18391i	0.885330	−	0.511145i	0.0129178	−	0.999917i	$-0.495888\pi$
$67$	7.24674	−	4.18391i	0.885330	−	0.511145i	0.872412	+	0.488771i	$0.162555\pi$
$68$			3.75010i			0.454767i
$69$	−4.11780	−	7.13224i	−0.495725	−	0.858621i
$70$	−10.0619	+	1.89875i	−1.20262	+	0.226944i
$71$	0.302090	+	0.523236i	0.0358515	+	0.0620966i	0.883394	−	0.468630i	$-0.155252\pi$
$71$	0.302090	+	0.523236i	0.0358515	+	0.0620966i	−0.847543	+	0.530727i	$0.821919\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			5.58023i			0.653117i	0.945177	+	0.326558i	$0.105889\pi$
$73$			5.58023i			0.653117i	−0.945177	+	0.326558i	$0.894111\pi$
$74$	1.21566	+	5.96005i	0.141317	+	0.692842i
$75$	−3.12124	+	3.90613i	−0.360410	+	0.451041i
$76$	−2.75460	+	4.77111i	−0.315975	+	0.547284i
$77$	−16.5877	+	9.57690i	−1.89034	+	1.09139i
$78$	4.82427	−	2.78529i	0.546241	−	0.315372i
$79$	−1.36388	−	2.36231i	−0.153449	−	0.265781i	0.779044	−	0.626969i	$-0.215705\pi$
$79$	−1.36388	−	2.36231i	−0.153449	−	0.265781i	−0.932493	+	0.361188i	$0.882371\pi$
$80$	0.739551	−	2.11023i	0.0826843	−	0.235931i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	3.45041i		−	0.381034i
$83$	−2.45612	−	1.41804i	−0.269595	−	0.155651i	0.359109	−	0.933296i	$-0.383081\pi$
$83$	−2.45612	−	1.41804i	−0.269595	−	0.155651i	−0.628703	+	0.777645i	$0.716414\pi$
$84$	−4.57922			−0.499634
$85$	−7.91357	−	2.77339i	−0.858347	−	0.300816i
$86$	2.76332	−	4.78621i	0.297977	−	0.516111i
$87$	5.75630	−	3.32340i	0.617140	−	0.356306i
$88$		−	4.18276i		−	0.445884i
$89$	−2.97261	+	5.14872i	−0.315097	+	0.545763i	−0.979458	−	0.201648i	$-0.935370\pi$
$89$	−2.97261	+	5.14872i	−0.315097	+	0.545763i	0.664361	+	0.747411i	$0.268704\pi$
$90$	−1.69558	+	1.45774i	−0.178730	+	0.153659i
$91$	−12.7545	+	22.0914i	−1.33703	+	2.31581i
$92$	−7.13224	+	4.11780i	−0.743588	+	0.429311i
$93$	8.72928	−	5.03985i	0.905184	−	0.522608i
$94$	−4.85726	+	8.41303i	−0.500989	+	0.867738i
$95$	−8.03097	−	9.34132i	−0.823960	−	0.958399i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			5.22592i			0.530612i	0.964164	+	0.265306i	$0.0854729\pi$
$97$			5.22592i			0.530612i	−0.964164	+	0.265306i	$0.914527\pi$
$98$	12.0977	−	6.98464i	1.22206	−	0.705555i
$99$	−2.09138	+	3.62238i	−0.210192	+	0.364063i
$100$	3.90613	+	3.12124i	0.390613	+	0.312124i
$101$	12.5383			1.24761			0.623803	−	0.781582i	$-0.285587\pi$
$101$	12.5383			1.24761			0.623803	+	0.781582i	$0.285587\pi$
$102$	−3.24768	−	1.87505i	−0.321569	−	0.185658i
$103$			2.86952i			0.282743i	0.989957	+	0.141371i	$0.0451511\pi$
$103$			2.86952i			0.282743i	−0.989957	+	0.141371i	$0.954849\pi$
$104$	−2.78529	−	4.82427i	−0.273120	−	0.473058i
$105$	3.38657	−	9.66321i	0.330495	−	0.943032i
$106$	−4.16967	−	7.22208i	−0.404994	−	0.701470i
$107$	0.698094	−	0.403045i	0.0674873	−	0.0389638i	−0.465877	−	0.884850i	$-0.654261\pi$
$107$	0.698094	−	0.403045i	0.0674873	−	0.0389638i	0.533364	+	0.845886i	$0.320928\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−6.60168	+	11.4344i	−0.632326	+	1.09522i	0.354749	+	0.934962i	$0.384566\pi$
$109$	−6.60168	+	11.4344i	−0.632326	+	1.09522i	−0.987075	+	0.160259i	$0.948767\pi$
$110$	8.82658	+	3.09336i	0.841582	+	0.294941i
$111$	−5.76938	−	1.92723i	−0.547606	−	0.182925i
$112$			4.57922i			0.432696i
$113$	8.27478	+	4.77745i	0.778426	+	0.449424i	0.835872	−	0.548924i	$-0.184962\pi$
$113$	8.27478	+	4.77745i	0.778426	+	0.449424i	−0.0574462	+	0.998349i	$0.518296\pi$
$114$	−2.75460	−	4.77111i	−0.257992	−	0.446856i
$115$	−3.41485	−	18.0960i	−0.318436	−	1.68746i
$116$	−3.32340	−	5.75630i	−0.308570	−	0.534459i
$117$			5.57058i			0.515001i
$118$	−5.48730	+	3.16809i	−0.505147	+	0.291647i
$119$	17.1725			1.57421
$120$	1.45774	+	1.69558i	0.133073	+	0.154785i
$121$	6.49549			0.590499
$122$			0.596411i			0.0539965i
$123$	2.98814	+	1.72520i	0.269432	+	0.155556i
$124$	−5.03985	−	8.72928i	−0.452592	−	0.783912i
$125$	−9.47532	+	5.93451i	−0.847498	+	0.530799i
$126$	2.28961	−	3.96572i	0.203975	−	0.353295i
$127$	−3.47606	−	2.00690i	−0.308450	−	0.178084i	0.337783	−	0.941224i	$-0.390323\pi$
$127$	−3.47606	−	2.00690i	−0.308450	−	0.178084i	−0.646233	+	0.763140i	$0.723656\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.76332	+	4.78621i	0.243297	+	0.421403i
$130$	12.2402	−	2.30981i	1.07353	−	0.202584i
$131$	10.1142	−	17.5184i	0.883684	−	1.53059i	0.0364701	−	0.999335i	$-0.488389\pi$
$131$	10.1142	−	17.5184i	0.883684	−	1.53059i	0.847214	−	0.531251i	$-0.178278\pi$
$132$	3.62238	+	2.09138i	0.315287	+	0.182031i
$133$	21.8480	+	12.6139i	1.89446	+	1.09377i
$134$	8.36781			0.722869
$135$	−0.414645	−	2.19729i	−0.0356869	−	0.189112i
$136$	−1.87505	+	3.24768i	−0.160784	+	0.278487i
$137$		−	6.90574i		−	0.589997i	−0.955498	−	0.294999i	$-0.904681\pi$
$137$		−	6.90574i		−	0.589997i	0.955498	−	0.294999i	$-0.0953192\pi$
$138$		−	8.23560i		−	0.701061i
$139$	7.39989	−	12.8170i	0.627651	−	1.08712i	−0.360371	−	0.932809i	$-0.617350\pi$
$139$	7.39989	−	12.8170i	0.627651	−	1.08712i	0.988022	−	0.154314i	$-0.0493167\pi$
$140$	−9.66321	−	3.38657i	−0.816690	−	0.286217i
$141$	−4.85726	−	8.41303i	−0.409055	−	0.708505i
$142$			0.604180i			0.0507017i
$143$	20.1788	−	11.6502i	1.68743	−	0.974239i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	14.6049	−	2.75606i	1.21287	−	0.228878i
$146$	−2.79012	+	4.83262i	−0.230912	+	0.399951i
$147$			13.9693i			1.15217i
$148$	−1.92723	+	5.76938i	−0.158418	+	0.474240i
$149$	10.4295			0.854414			0.427207	−	0.904154i	$-0.359498\pi$
$149$	10.4295			0.854414			0.427207	+	0.904154i	$0.359498\pi$
$150$	−4.65614	+	1.82219i	−0.380172	+	0.148781i
$151$	−0.371586	−	0.643606i	−0.0302393	−	0.0523759i	0.850510	−	0.525959i	$-0.176294\pi$
$151$	−0.371586	−	0.643606i	−0.0302393	−	0.0523759i	−0.880749	+	0.473583i	$0.842960\pi$
$152$	−4.77111	+	2.75460i	−0.386988	+	0.223428i
$153$	3.24768	−	1.87505i	0.262560	−	0.151589i
$154$	−19.1538			−1.54346
$155$	22.1480	−	4.17949i	1.77897	−	0.335705i
$156$	5.57058			0.446004
$157$	19.1303	+	11.0449i	1.52676	+	0.881477i	0.999495	+	0.0317784i	$0.0101171\pi$
$157$	19.1303	+	11.0449i	1.52676	+	0.881477i	0.527268	+	0.849699i	$0.323216\pi$
$158$		−	2.72776i		−	0.217009i
$159$	8.33934			0.661353
$160$	1.69558	−	1.45774i	0.134048	−	0.115244i
$161$	18.8563	+	32.6601i	1.48609	+	2.57398i
$162$		−	1.00000i		−	0.0785674i
$163$	−3.40441	−	1.96554i	−0.266654	−	0.153953i	0.360712	−	0.932677i	$-0.382534\pi$
$163$	−3.40441	−	1.96554i	−0.266654	−	0.153953i	−0.627366	+	0.778725i	$0.715867\pi$
$164$	1.72520	−	2.98814i	0.134716	−	0.233335i
$165$	−7.09222	+	6.09736i	−0.552129	+	0.474679i
$166$	−1.41804	−	2.45612i	−0.110062	−	0.190632i
$167$	1.04771	−	0.604896i	0.0810743	−	0.0468083i	−0.458915	−	0.888480i	$-0.651762\pi$
$167$	1.04771	−	0.604896i	0.0810743	−	0.0468083i	0.539989	+	0.841672i	$0.318428\pi$
$168$	−3.96572	−	2.28961i	−0.305962	−	0.176647i
$169$	9.01570	−	15.6156i	0.693515	−	1.20120i
$170$	−5.46666	−	6.35861i	−0.419274	−	0.487683i
$171$	5.50921			0.421300
$172$	4.78621	−	2.76332i	0.364945	−	0.210701i
$173$	−7.10450	−	4.10179i	−0.540145	−	0.311853i	0.204993	−	0.978764i	$-0.434283\pi$
$173$	−7.10450	−	4.10179i	−0.540145	−	0.311853i	−0.745138	+	0.666910i	$0.767616\pi$
$174$	6.64680			0.503893
$175$	14.2929	−	17.8870i	1.08044	−	1.35213i
$176$	2.09138	−	3.62238i	0.157644	−	0.273047i
$177$		−	6.33618i		−	0.476257i
$178$	−5.14872	+	2.97261i	−0.385913	+	0.222807i
$179$	−9.96177			−0.744578			−0.372289	−	0.928117i	$-0.621427\pi$
$179$	−9.96177			−0.744578			−0.372289	+	0.928117i	$0.621427\pi$
$180$	−2.19729	+	0.414645i	−0.163776	+	0.0309058i
$181$	8.90549	+	15.4248i	0.661940	+	1.14651i	0.980105	+	0.198478i	$0.0635998\pi$
$181$	8.90549	+	15.4248i	0.661940	+	1.14651i	−0.318166	+	0.948035i	$0.603067\pi$
$182$	−22.0914	+	12.7545i	−1.63752	+	0.945424i
$183$	−0.516507	−	0.298205i	−0.0381813	−	0.0220440i
$184$	−8.23560			−0.607137
$185$	−10.7494	−	8.33365i	−0.790314	−	0.612702i
$186$	10.0797			0.739080
$187$	−13.5843	−	7.84289i	−0.993381	−	0.573529i
$188$	−8.41303	+	4.85726i	−0.613583	+	0.354252i
$189$	2.28961	+	3.96572i	0.166545	+	0.288464i
$190$	−2.28436	−	12.1053i	−0.165725	−	0.878211i
$191$	−1.93822			−0.140245			−0.0701224	−	0.997538i	$-0.522339\pi$
$191$	−1.93822			−0.140245			−0.0701224	+	0.997538i	$0.522339\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	20.5829i		−	1.48159i	−0.671731	−	0.740795i	$-0.734449\pi$
$193$		−	20.5829i		−	1.48159i	0.671731	−	0.740795i	$-0.265551\pi$
$194$	−2.61296	+	4.52578i	−0.187600	+	0.324932i
$195$	−4.11973	+	11.7552i	−0.295020	+	0.841808i
$196$	13.9693			0.997805
$197$	−4.92564	−	2.84382i	−0.350937	−	0.202614i	0.314161	−	0.949370i	$-0.398277\pi$
$197$	−4.92564	−	2.84382i	−0.350937	−	0.202614i	−0.665098	+	0.746756i	$0.731610\pi$
$198$	−3.62238	+	2.09138i	−0.257431	+	0.148628i
$199$	17.8092			1.26246			0.631231	−	0.775594i	$-0.282550\pi$
$199$	17.8092			1.26246			0.631231	+	0.775594i	$0.282550\pi$
$200$	1.82219	+	4.65614i	0.128848	+	0.329239i
$201$	−4.18391	+	7.24674i	−0.295110	+	0.511145i
$202$	10.8585	+	6.26914i	0.763999	+	0.441095i
$203$	−26.3594	+	15.2186i	−1.85007	+	1.06814i
$204$	−1.87505	−	3.24768i	−0.131280	−	0.227383i
$205$	5.02978	+	5.85046i	0.351295	+	0.408614i
$206$	−1.43476	+	2.48508i	−0.0999646	+	0.173144i
$207$	7.13224	+	4.11780i	0.495725	+	0.286207i
$208$		−	5.57058i		−	0.386250i
$209$	−11.5218	−	19.9564i	−0.796983	−	1.38041i
$210$	7.76446	−	6.67530i	0.535798	−	0.460639i
$211$	1.70560			0.117418			0.0587090	−	0.998275i	$-0.481302\pi$
$211$	1.70560			0.117418			0.0587090	+	0.998275i	$0.481302\pi$
$212$		−	8.33934i		−	0.572748i
$213$	−0.523236	−	0.302090i	−0.0358515	−	0.0206989i
$214$	0.806090			0.0551032
$215$	2.29159	+	12.1436i	0.156285	+	0.828188i
$216$	−1.00000			−0.0680414
$217$	−39.9733	+	23.0786i	−2.71356	+	1.56668i
$218$	−11.4344	+	6.60168i	−0.774438	+	0.447122i
$219$	−2.79012	−	4.83262i	−0.188539	−	0.326558i
$220$	6.09736	+	7.09222i	0.411084	+	0.478158i
$221$	−20.8903			−1.40523
$222$	−4.03282	−	4.55372i	−0.270665	−	0.305626i
$223$			2.08896i			0.139887i	0.997551	+	0.0699437i	$0.0222820\pi$
$223$			2.08896i			0.139887i	−0.997551	+	0.0699437i	$0.977718\pi$
$224$	−2.28961	+	3.96572i	−0.152981	+	0.264971i
$225$	0.750010	−	4.94343i	0.0500007	−	0.329562i
$226$	4.77745	+	8.27478i	0.317791	+	0.550430i
$227$	−14.5152	+	8.38038i	−0.963411	+	0.556225i	−0.897221	−	0.441582i	$-0.854418\pi$
$227$	−14.5152	+	8.38038i	−0.963411	+	0.556225i	−0.0661896	+	0.997807i	$0.521084\pi$
$228$		−	5.50921i		−	0.364856i
$229$	8.31975	+	14.4102i	0.549784	+	0.952255i	0.998289	+	0.0584740i	$0.0186235\pi$
$229$	8.31975	+	14.4102i	0.549784	+	0.952255i	−0.448504	+	0.893781i	$0.648043\pi$
$230$	6.09065	−	17.3790i	0.401605	−	1.14594i
$231$	9.57690	−	16.5877i	0.630113	−	1.09139i
$232$		−	6.64680i		−	0.436384i
$233$			23.8625i			1.56329i	0.623727	+	0.781643i	$0.285618\pi$
$233$			23.8625i			1.56329i	−0.623727	+	0.781643i	$0.714382\pi$
$234$	−2.78529	+	4.82427i	−0.182080	+	0.315372i
$235$	−4.02808	−	21.3456i	−0.262763	−	1.39243i
$236$	−6.33618			−0.412450
$237$	2.36231	+	1.36388i	0.153449	+	0.0885937i
$238$	14.8719	+	8.58627i	0.964000	+	0.556566i
$239$	3.83371	−	6.64017i	0.247982	−	0.429517i	−0.714984	−	0.699141i	$-0.753566\pi$
$239$	3.83371	−	6.64017i	0.247982	−	0.429517i	0.962966	+	0.269624i	$0.0868993\pi$
$240$	0.414645	+	2.19729i	0.0267652	+	0.141834i
$241$	−0.838677	−	1.45263i	−0.0540239	−	0.0935722i	0.837749	−	0.546056i	$-0.183871\pi$
$241$	−0.838677	−	1.45263i	−0.0540239	−	0.0935722i	−0.891773	+	0.452484i	$0.850538\pi$
$242$	5.62526	+	3.24774i	0.361605	+	0.208773i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−0.298205	+	0.516507i	−0.0190906	+	0.0330660i
$245$	−10.3310	+	29.4784i	−0.660023	+	1.88330i
$246$	1.72520	+	2.98814i	0.109995	+	0.190517i
$247$	−26.5779	−	15.3447i	−1.69111	−	0.976363i
$248$		−	10.0797i		−	0.640062i
$249$	2.83609			0.179730
$250$	−11.1731	+	0.401778i	−0.706650	+	0.0254107i
$251$	−6.71568			−0.423890			−0.211945	−	0.977282i	$-0.567980\pi$
$251$	−6.71568			−0.423890			−0.211945	+	0.977282i	$0.567980\pi$
$252$	3.96572	−	2.28961i	0.249817	−	0.144232i
$253$		−	34.4476i		−	2.16570i
$254$	−2.00690	−	3.47606i	−0.125924	−	0.218107i
$255$	8.24005	−	1.55496i	0.516012	−	0.0973753i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.7106	+	13.1120i	1.41665	+	0.817904i	0.996003	−	0.0893200i	$-0.0284694\pi$
$257$	22.7106	+	13.1120i	1.41665	+	0.817904i	0.420648	+	0.907224i	$0.361803\pi$
$258$			5.52664i			0.344074i
$259$	26.4193	+	8.82523i	1.64161	+	0.548373i
$260$	11.7552	+	4.11973i	0.729027	+	0.255495i
$261$	−3.32340	+	5.75630i	−0.205713	+	0.356306i
$262$	17.5184	−	10.1142i	1.08229	−	0.624859i
$263$	19.3473	−	11.1702i	1.19301	−	0.688783i	0.234019	−	0.972232i	$-0.424812\pi$
$263$	19.3473	−	11.1702i	1.19301	−	0.688783i	0.958987	+	0.283449i	$0.0914788\pi$
$264$	2.09138	+	3.62238i	0.128716	+	0.222942i
$265$	17.5979	+	6.16736i	1.08103	+	0.378858i
$266$	12.6139	+	21.8480i	0.773410	+	1.33959i
$267$		−	5.94523i		−	0.363842i
$268$	7.24674	+	4.18391i	0.442665	+	0.255573i
$269$	15.5342			0.947135			0.473568	−	0.880757i	$-0.342966\pi$
$269$	15.5342			0.947135			0.473568	+	0.880757i	$0.342966\pi$
$270$	0.739551	−	2.11023i	0.0450076	−	0.128424i
$271$	12.4256	−	21.5218i	0.754803	−	1.30736i	−0.190670	−	0.981654i	$-0.561066\pi$
$271$	12.4256	−	21.5218i	0.754803	−	1.30736i	0.945472	−	0.325702i	$-0.105601\pi$
$272$	−3.24768	+	1.87505i	−0.196920	+	0.113692i
$273$		−	25.5089i		−	1.54387i
$274$	3.45287	−	5.98054i	0.208595	−	0.361298i
$275$	−19.4755	+	7.62177i	−1.17442	+	0.459610i
$276$	4.11780	−	7.13224i	0.247863	−	0.429311i
$277$	−16.5182	+	9.53678i	−0.992482	+	0.573010i	−0.906015	−	0.423245i	$-0.860891\pi$
$277$	−16.5182	+	9.53678i	−0.992482	+	0.573010i	−0.0864665	+	0.996255i	$0.527558\pi$
$278$	12.8170	−	7.39989i	0.768712	−	0.443816i
$279$	−5.03985	+	8.72928i	−0.301728	+	0.522608i
$280$	−6.67530	−	7.76446i	−0.398925	−	0.464015i
$281$	4.22604	−	7.31971i	0.252104	−	0.436657i	−0.712001	−	0.702179i	$-0.752211\pi$
$281$	4.22604	−	7.31971i	0.252104	−	0.436657i	0.964105	+	0.265521i	$0.0855441\pi$
$282$		−	9.71453i		−	0.578492i
$283$	−13.3709	+	7.71970i	−0.794819	+	0.458889i	−0.841656	−	0.540014i	$-0.818419\pi$
$283$	−13.3709	+	7.71970i	−0.794819	+	0.458889i	0.0468376	+	0.998903i	$0.485086\pi$
$284$	−0.302090	+	0.523236i	−0.0179258	+	0.0310483i
$285$	11.6257	+	4.07434i	0.688646	+	0.241343i
$286$	23.3004			1.37778
$287$	−13.6834	−	7.90009i	−0.807703	−	0.466328i
$288$			1.00000i			0.0589256i
$289$	−1.46837	−	2.54329i	−0.0863745	−	0.149605i
$290$	14.0263	+	4.91565i	0.823651	+	0.288657i
$291$	−2.61296	−	4.52578i	−0.153174	−	0.265306i
$292$	−4.83262	+	2.79012i	−0.282808	+	0.163279i
$293$	0.158974	−	0.0917835i	0.00928734	−	0.00536205i	−0.495349	−	0.868694i	$-0.664960\pi$
$293$	0.158974	−	0.0917835i	0.00928734	−	0.00536205i	0.504636	+	0.863332i	$0.331627\pi$
$294$	−6.98464	+	12.0977i	−0.407352	+	0.705555i
$295$	4.68593	−	13.3708i	0.272825	−	0.778478i
$296$	−4.55372	+	4.03282i	−0.264680	+	0.234403i
$297$		−	4.18276i		−	0.242708i
$298$	9.03217	+	5.21473i	0.523220	+	0.302081i
$299$	−22.9386	−	39.7308i	−1.32657	−	2.29769i
$300$	−4.94343	−	0.750010i	−0.285409	−	0.0433019i
$301$	−12.6539	−	21.9171i	−0.729357	−	1.26328i
$302$		−	0.743173i		−	0.0427648i
$303$	−10.8585	+	6.26914i	−0.623803	+	0.360153i
$304$	−5.50921			−0.315975
$305$	−0.869409	−	1.01126i	−0.0497822	−	0.0579048i
$306$	3.75010			0.214379
$307$			3.29796i			0.188224i	0.995562	+	0.0941122i	$0.0300013\pi$
$307$			3.29796i			0.188224i	−0.995562	+	0.0941122i	$0.969999\pi$
$308$	−16.5877	−	9.57690i	−0.945170	−	0.545694i
$309$	−1.43476	−	2.48508i	−0.0816208	−	0.141371i
$310$	21.2705	+	7.45445i	1.20808	+	0.423384i
$311$	5.30350	−	9.18593i	0.300734	−	0.520886i	−0.675568	−	0.737297i	$-0.736102\pi$
$311$	5.30350	−	9.18593i	0.300734	−	0.520886i	0.976302	+	0.216411i	$0.0694351\pi$
$312$	4.82427	+	2.78529i	0.273120	+	0.157686i
$313$	−25.2054	−	14.5523i	−1.42469	−	0.822546i	−0.427996	−	0.903781i	$-0.640780\pi$
$313$	−25.2054	−	14.5523i	−1.42469	−	0.822546i	−0.996695	+	0.0812347i	$0.974114\pi$
$314$	11.0449	+	19.1303i	0.623299	+	1.07958i
$315$	1.89875	+	10.0619i	0.106982	+	0.566922i
$316$	1.36388	−	2.36231i	0.0767244	−	0.132890i
$317$	4.10591	+	2.37055i	0.230611	+	0.133143i	0.610854	−	0.791743i	$-0.290826\pi$
$317$	4.10591	+	2.37055i	0.230611	+	0.133143i	−0.380243	+	0.924887i	$0.624160\pi$
$318$	7.22208	+	4.16967i	0.404994	+	0.233823i
$319$	27.8020			1.55661
$320$	2.19729	−	0.414645i	0.122832	−	0.0231793i
$321$	−0.403045	+	0.698094i	−0.0224958	+	0.0389638i
$322$			37.7127i			2.10164i
$323$			20.6601i			1.14956i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−17.3871	+	21.7594i	−0.964465	+	1.20700i
$326$	−1.96554	−	3.40441i	−0.108861	−	0.188553i
$327$		−	13.2034i		−	0.730147i
$328$	2.98814	−	1.72520i	0.164992	−	0.0952584i
$329$	22.2425	+	38.5251i	1.22627	+	2.12396i
$330$	−9.19073	+	1.73436i	−0.505933	+	0.0954733i
$331$	−0.885114	+	1.53306i	−0.0486502	+	0.0842647i	−0.889325	−	0.457276i	$-0.848825\pi$
$331$	−0.885114	+	1.53306i	−0.0486502	+	0.0842647i	0.840675	+	0.541540i	$0.182159\pi$
$332$		−	2.83609i		−	0.155651i
$333$	5.96005	−	1.21566i	0.326609	−	0.0666177i
$334$	1.20979			0.0661969
$335$	−14.1883	+	12.1981i	−0.775191	+	0.666451i
$336$	−2.28961	−	3.96572i	−0.124909	−	0.216348i
$337$	9.05634	−	5.22868i	0.493330	−	0.284824i	−0.232625	−	0.972567i	$-0.574731\pi$
$337$	9.05634	−	5.22868i	0.493330	−	0.284824i	0.725955	+	0.687742i	$0.241398\pi$
$338$	15.6156	−	9.01570i	0.849379	−	0.490389i
$339$	−9.55489			−0.518951
$340$	−1.55496	−	8.24005i	−0.0843295	−	0.446879i
$341$	42.1610			2.28315
$342$	4.77111	+	2.75460i	0.257992	+	0.148952i
$343$		−	31.9139i		−	1.72319i
$344$	5.52664			0.297977
$345$	12.0053	+	13.9642i	0.646346	+	0.751805i
$346$	−4.10179	−	7.10450i	−0.220513	−	0.381940i
$347$			4.86908i			0.261386i	0.991423	+	0.130693i	$0.0417202\pi$
$347$			4.86908i			0.261386i	−0.991423	+	0.130693i	$0.958280\pi$
$348$	5.75630	+	3.32340i	0.308570	+	0.178153i
$349$	4.84694	−	8.39515i	0.259451	−	0.449382i	−0.706644	−	0.707569i	$-0.749792\pi$
$349$	4.84694	−	8.39515i	0.259451	−	0.449382i	0.966095	+	0.258187i	$0.0831252\pi$
$350$	21.3215	−	8.34420i	1.13968	−	0.446016i
$351$	−2.78529	−	4.82427i	−0.148668	−	0.257500i
$352$	3.62238	−	2.09138i	0.193073	−	0.111471i
$353$	−12.6257	−	7.28943i	−0.671997	−	0.387977i	0.124836	−	0.992177i	$-0.460159\pi$
$353$	−12.6257	−	7.28943i	−0.671997	−	0.387977i	−0.796833	+	0.604200i	$0.793493\pi$
$354$	3.16809	−	5.48730i	0.168382	−	0.291647i
$355$	−0.880736	−	1.02444i	−0.0467446	−	0.0543716i
$356$	−5.94523			−0.315097
$357$	−14.8719	+	8.58627i	−0.787103	+	0.454434i
$358$	−8.62715	−	4.98089i	−0.455959	−	0.263248i
$359$	−8.82695			−0.465869			−0.232934	−	0.972492i	$-0.574833\pi$
$359$	−8.82695			−0.465869			−0.232934	+	0.972492i	$0.574833\pi$
$360$	−2.11023	−	0.739551i	−0.111219	−	0.0389777i
$361$	−5.67568	+	9.83056i	−0.298720	+	0.517398i
$362$			17.8110i			0.936124i
$363$	−5.62526	+	3.24774i	−0.295249	+	0.170462i
$364$	−25.5089			−1.33703
$365$	−2.31381	−	12.2614i	−0.121111	−	0.641790i
$366$	−0.298205	−	0.516507i	−0.0155874	−	0.0269982i
$367$	−23.2192	+	13.4056i	−1.21203	+	0.699769i	−0.963202	−	0.268778i	$-0.913380\pi$
$367$	−23.2192	+	13.4056i	−1.21203	+	0.699769i	−0.248833	+	0.968546i	$0.580047\pi$
$368$	−7.13224	−	4.11780i	−0.371794	−	0.214655i
$369$	−3.45041			−0.179621
$370$	−5.14245	−	12.5919i	−0.267343	−	0.654620i
$371$	−38.1877			−1.98261
$372$	8.72928	+	5.03985i	0.452592	+	0.261304i
$373$	8.49823	−	4.90645i	0.440021	−	0.254046i	−0.263585	−	0.964636i	$-0.584905\pi$
$373$	8.49823	−	4.90645i	0.440021	−	0.254046i	0.703607	+	0.710590i	$0.251572\pi$
$374$	−7.84289	−	13.5843i	−0.405546	−	0.702427i
$375$	5.23861	−	9.87709i	0.270521	−	0.510051i
$376$	−9.71453			−0.500989
$377$	32.0659	−	18.5133i	1.65148	−	0.953483i
$378$			4.57922i			0.235530i
$379$	−2.82111	+	4.88631i	−0.144911	+	0.250993i	−0.929340	−	0.369226i	$-0.879623\pi$
$379$	−2.82111	+	4.88631i	−0.144911	+	0.250993i	0.784429	+	0.620219i	$0.212956\pi$
$380$	4.07434	−	11.6257i	0.209009	−	0.596385i
$381$	4.01381			0.205633
$382$	−1.67855	−	0.969111i	−0.0858821	−	0.0495840i
$383$	−12.2337	+	7.06310i	−0.625110	+	0.360908i	−0.778856	−	0.627203i	$-0.784200\pi$
$383$	−12.2337	+	7.06310i	−0.625110	+	0.360908i	0.153746	+	0.988110i	$0.450866\pi$
$384$	1.00000			0.0510310
$385$	32.4769	−	27.9212i	1.65517	−	1.42299i
$386$	10.2914	−	17.8253i	0.523821	−	0.907285i
$387$	−4.78621	−	2.76332i	−0.243297	−	0.140468i
$388$	−4.52578	+	2.61296i	−0.229762	+	0.132653i
$389$	3.92142	+	6.79209i	0.198824	+	0.344373i	0.948147	−	0.317831i	$-0.102955\pi$
$389$	3.92142	+	6.79209i	0.198824	+	0.344373i	−0.749324	+	0.662204i	$0.769621\pi$
$390$	−9.44539	+	8.12044i	−0.478286	+	0.411194i
$391$	−15.4422	+	26.7466i	−0.780945	+	1.35264i
$392$	12.0977	+	6.98464i	0.611028	+	0.352777i
$393$			20.2285i			1.02039i
$394$	−2.84382	−	4.92564i	−0.143269	−	0.248150i
$395$	3.97636	+	4.62515i	0.200072	+	0.232717i
$396$	−4.18276			−0.210192
$397$			25.5763i			1.28364i	0.766856	+	0.641819i	$0.221820\pi$
$397$			25.5763i			1.28364i	−0.766856	+	0.641819i	$0.778180\pi$
$398$	15.4232	+	8.90462i	0.773098	+	0.446348i
$399$	−25.2279			−1.26297
$400$	−0.750010	+	4.94343i	−0.0375005	+	0.247171i
$401$	−3.60169			−0.179860			−0.0899298	−	0.995948i	$-0.528664\pi$
$401$	−3.60169			−0.179860			−0.0899298	+	0.995948i	$0.528664\pi$
$402$	−7.24674	+	4.18391i	−0.361434	+	0.208674i
$403$	48.6272	−	28.0749i	2.42229	−	1.39851i
$404$	6.26914	+	10.8585i	0.311901	+	0.540229i
$405$	1.45774	+	1.69558i	0.0724355	+	0.0842542i
$406$	−30.4372			−1.51057
$407$	−16.8683	−	19.0471i	−0.836131	−	0.944132i
$408$		−	3.75010i		−	0.185658i
$409$	−13.3199	+	23.0708i	−0.658628	+	1.14078i	0.322343	+	0.946623i	$0.395530\pi$
$409$	−13.3199	+	23.0708i	−0.658628	+	1.14078i	−0.980971	+	0.194155i	$0.937804\pi$
$410$	1.43069	+	7.58154i	0.0706569	+	0.374425i
$411$	3.45287	+	5.98054i	0.170317	+	0.294999i
$412$	−2.48508	+	1.43476i	−0.122431	+	0.0706857i
$413$			29.0148i			1.42772i
$414$	4.11780	+	7.13224i	0.202379	+	0.350531i
$415$	5.98479	+	2.09743i	0.293782	+	0.102959i
$416$	2.78529	−	4.82427i	0.136560	−	0.236529i
$417$			14.7998i			0.724749i
$418$		−	23.0437i		−	1.12710i
$419$	−6.51205	+	11.2792i	−0.318134	+	0.551025i	−0.980099	−	0.198510i	$-0.936390\pi$
$419$	−6.51205	+	11.2792i	−0.318134	+	0.551025i	0.661964	+	0.749535i	$0.269723\pi$
$420$	10.0619	−	1.89875i	0.490969	−	0.0926495i
$421$	4.51198			0.219900			0.109950	−	0.993937i	$-0.464931\pi$
$421$	4.51198			0.219900			0.109950	+	0.993937i	$0.464931\pi$
$422$	1.47709	+	0.852798i	0.0719036	+	0.0415135i
$423$	8.41303	+	4.85726i	0.409055	+	0.236168i
$424$	4.16967	−	7.22208i	0.202497	−	0.350735i
$425$	18.5384	+	2.81261i	0.899243	+	0.136432i
$426$	−0.302090	−	0.523236i	−0.0146363	−	0.0253508i
$427$	2.36520	+	1.36555i	0.114460	+	0.0660835i
$428$	0.698094	+	0.403045i	0.0337437	+	0.0194819i
$429$	−11.6502	+	20.1788i	−0.562477	+	0.974239i
$430$	−4.08723	+	11.6625i	−0.197104	+	0.562415i
$431$	−4.15984	−	7.20505i	−0.200372	−	0.347055i	0.748276	−	0.663387i	$-0.230882\pi$
$431$	−4.15984	−	7.20505i	−0.200372	−	0.347055i	−0.948648	+	0.316332i	$0.897549\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			22.0718i			1.06070i	0.847777	+	0.530352i	$0.177940\pi$
$433$			22.0718i			1.06070i	−0.847777	+	0.530352i	$0.822060\pi$
$434$	−46.1572			−2.21562
$435$	−11.2702	+	9.68928i	−0.540365	+	0.464566i
$436$	−13.2034			−0.632326
$437$	−39.2930	+	22.6858i	−1.87964	+	1.08521i
$438$		−	5.58023i		−	0.266634i
$439$	2.71505	+	4.70261i	0.129582	+	0.224443i	0.923515	−	0.383563i	$-0.125303\pi$
$439$	2.71505	+	4.70261i	0.129582	+	0.224443i	−0.793932	+	0.608006i	$0.791970\pi$
$440$	1.73436	+	9.19073i	0.0826823	+	0.438151i
$441$	−6.98464	−	12.0977i	−0.332602	−	0.576083i
$442$	−18.0915	−	10.4451i	−0.860524	−	0.496824i
$443$		−	13.5696i		−	0.644713i	−0.946618	−	0.322357i	$-0.895525\pi$
$443$		−	13.5696i		−	0.644713i	0.946618	−	0.322357i	$-0.104475\pi$
$444$	−1.21566	−	5.96005i	−0.0576926	−	0.282851i
$445$	4.39680	−	12.5458i	0.208428	−	0.594728i
$446$	−1.04448	+	1.80910i	−0.0494577	+	0.0856632i
$447$	−9.03217	+	5.21473i	−0.427207	+	0.246648i
$448$	−3.96572	+	2.28961i	−0.187363	+	0.108174i
$449$	13.0248	+	22.5597i	0.614679	+	1.06466i	0.990441	+	0.137939i	$0.0440480\pi$
$449$	13.0248	+	22.5597i	0.614679	+	1.06466i	−0.375761	+	0.926717i	$0.622619\pi$
$450$	3.12124	−	3.90613i	0.147137	−	0.184137i
$451$	7.21611	+	12.4987i	0.339794	+	0.588540i
$452$			9.55489i			0.449424i
$453$	0.643606	+	0.371586i	0.0302393	+	0.0174586i
$454$	−16.7608			−0.786621
$455$	18.8652	−	53.8297i	0.884412	−	2.52357i
$456$	2.75460	−	4.77111i	0.128996	−	0.223428i
$457$	4.31378	−	2.49056i	0.201790	−	0.116504i	−0.395700	−	0.918380i	$-0.629498\pi$
$457$	4.31378	−	2.49056i	0.201790	−	0.116504i	0.597490	+	0.801876i	$0.296165\pi$
$458$			16.6395i			0.777513i
$459$	−1.87505	+	3.24768i	−0.0875199	+	0.151589i
$460$	13.9642	−	12.0053i	0.651082	−	0.559752i
$461$	−12.3801	+	21.4429i	−0.576598	+	0.998697i	0.419268	+	0.907863i	$0.362287\pi$
$461$	−12.3801	+	21.4429i	−0.576598	+	0.998697i	−0.995866	+	0.0908345i	$0.971047\pi$
$462$	16.5877	−	9.57690i	0.771728	−	0.445557i
$463$	11.2827	−	6.51406i	0.524350	−	0.302734i	−0.214362	−	0.976754i	$-0.568767\pi$
$463$	11.2827	−	6.51406i	0.524350	−	0.302734i	0.738713	+	0.674020i	$0.235434\pi$
$464$	3.32340	−	5.75630i	0.154285	−	0.267230i
$465$	−17.0910	+	14.6935i	−0.792575	+	0.681397i
$466$	−11.9313	+	20.6655i	−0.552705	+	0.957313i
$467$		−	38.2527i		−	1.77012i	−0.465473	−	0.885062i	$-0.654116\pi$
$467$		−	38.2527i		−	1.77012i	0.465473	−	0.885062i	$-0.345884\pi$
$468$	−4.82427	+	2.78529i	−0.223002	+	0.128750i
$469$	19.1590	−	33.1844i	0.884682	−	1.53231i
$470$	7.18439	−	20.4999i	0.331391	−	0.945589i
$471$	−22.0898			−1.01784
$472$	−5.48730	−	3.16809i	−0.252573	−	0.145823i
$473$			23.1166i			1.06290i
$474$	1.36388	+	2.36231i	0.0626452	+	0.108505i
$475$	21.5197	+	17.1956i	0.987390	+	0.788987i
$476$	8.58627	+	14.8719i	0.393551	+	0.681651i
$477$	−7.22208	+	4.16967i	−0.330676	+	0.190916i
$478$	6.64017	−	3.83371i	0.303715	−	0.175350i
$479$	3.32298	−	5.75557i	0.151831	−	0.262979i	−0.780070	−	0.625693i	$-0.784816\pi$
$479$	3.32298	−	5.75557i	0.151831	−	0.262979i	0.931901	+	0.362714i	$0.118150\pi$
$480$	−0.739551	+	2.11023i	−0.0337557	+	0.0963183i
$481$	−32.1388	−	10.7358i	−1.46540	−	0.489511i
$482$		−	1.67735i		−	0.0764014i
$483$	−32.6601	−	18.8563i	−1.48609	−	0.857993i
$484$	3.24774	+	5.62526i	0.147625	+	0.255694i
$485$	−2.16690	−	11.4828i	−0.0983938	−	0.521409i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$			15.4029i			0.697971i	0.937128	+	0.348985i	$0.113474\pi$
$487$			15.4029i			0.697971i	−0.937128	+	0.348985i	$0.886526\pi$
$488$	−0.516507	+	0.298205i	−0.0233812	+	0.0134991i
$489$	3.93107			0.177769
$490$	−23.6861	+	20.3635i	−1.07003	+	0.919930i
$491$	10.0817			0.454981			0.227491	−	0.973780i	$-0.426948\pi$
$491$	10.0817			0.454981			0.227491	+	0.973780i	$0.426948\pi$
$492$			3.45041i			0.155556i
$493$	−21.5867	−	12.4631i	−0.972217	−	0.561310i
$494$	−15.3447	−	26.5779i	−0.690393	−	1.19580i
$495$	3.09336	−	8.82658i	0.139036	−	0.396725i
$496$	5.03985	−	8.72928i	0.226296	−	0.391956i
$497$	2.39601	+	1.38334i	0.107476	+	0.0620512i
$498$	2.45612	+	1.41804i	0.110062	+	0.0635441i
$499$	−17.0377	−	29.5101i	−0.762711	−	1.32106i	−0.941448	−	0.337158i	$-0.890534\pi$
$499$	−17.0377	−	29.5101i	−0.762711	−	1.32106i	0.178737	−	0.983897i	$-0.442799\pi$
$500$	−9.87709	−	5.23861i	−0.441717	−	0.234278i
$501$	−0.604896	+	1.04771i	−0.0270248	+	0.0468083i
$502$	−5.81595	−	3.35784i	−0.259579	−	0.149868i
$503$	11.5209	+	6.65159i	0.513691	+	0.296580i	0.734350	−	0.678771i	$-0.237487\pi$
$503$	11.5209	+	6.65159i	0.513691	+	0.296580i	−0.220658	+	0.975351i	$0.570821\pi$
$504$	4.57922			0.203975
$505$	−27.5502	+	5.19893i	−1.22597	+	0.231349i
$506$	17.2238	−	29.8325i	0.765691	−	1.32621i
$507$			18.0314i			0.800802i
$508$		−	4.01381i		−	0.178084i
$509$	16.8275	−	29.1462i	0.745868	−	1.29188i	−0.203920	−	0.978988i	$-0.565368\pi$
$509$	16.8275	−	29.1462i	0.745868	−	1.29188i	0.949788	−	0.312894i	$-0.101298\pi$
$510$	7.91357	+	2.77339i	0.350419	+	0.122808i
$511$	12.7766	+	22.1297i	0.565202	+	0.978959i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.77111	+	2.75460i	−0.210650	+	0.121619i
$514$	13.1120	+	22.7106i	0.578345	+	1.00172i
$515$	−1.18983	−	6.30517i	−0.0524303	−	0.277839i
$516$	−2.76332	+	4.78621i	−0.121648	+	0.210701i
$517$		−	40.6335i		−	1.78706i
$518$	18.4672	+	20.8525i	0.811400	+	0.916207i
$519$	8.20357			0.360097
$520$	8.12044	+	9.44539i	0.356105	+	0.414208i
$521$	−0.796349	−	1.37932i	−0.0348887	−	0.0604290i	0.848054	−	0.529910i	$-0.177774\pi$
$521$	−0.796349	−	1.37932i	−0.0348887	−	0.0604290i	−0.882943	+	0.469481i	$0.844441\pi$
$522$	−5.75630	+	3.32340i	−0.251946	+	0.145461i
$523$	−0.698071	+	0.403031i	−0.0305245	+	0.0176233i	−0.515185	−	0.857079i	$-0.672277\pi$
$523$	−0.698071	+	0.403031i	−0.0305245	+	0.0176233i	0.484660	+	0.874703i	$0.338943\pi$
$524$	20.2285			0.883684
$525$	−3.43446	+	22.6371i	−0.149892	+	0.987962i
$526$	22.3404			0.974086
$527$	−32.7357	−	18.9000i	−1.42599	−	0.823295i
$528$			4.18276i			0.182031i
$529$	−44.8252			−1.94892
$530$	12.1566	+	14.1400i	0.528047	+	0.614204i
$531$	3.16809	+	5.48730i	0.137483	+	0.238128i
$532$			25.2279i			1.09377i
$533$	16.6457	+	9.61039i	0.721005	+	0.416272i
$534$	2.97261	−	5.14872i	0.128638	−	0.222807i
$535$	−1.36679	+	1.17507i	−0.0590916	+	0.0508025i
$536$	4.18391	+	7.24674i	0.180717	+	0.313011i
$537$	8.62715	−	4.98089i	0.372289	−	0.214941i
$538$	13.4530	+	7.76709i	0.580000	+	0.334863i
$539$	−29.2151	+	50.6020i	−1.25838	+	2.17958i
$540$	1.69558	−	1.45774i	0.0729663	−	0.0627310i
$541$	0.492550			0.0211764			0.0105882	−	0.999944i	$-0.496630\pi$
$541$	0.492550			0.0211764			0.0105882	+	0.999944i	$0.496630\pi$
$542$	21.5218	−	12.4256i	0.924441	−	0.533726i
$543$	−15.4248	−	8.90549i	−0.661940	−	0.382171i
$544$	−3.75010			−0.160784
$545$	9.76455	−	27.8621i	0.418267	−	1.19348i
$546$	12.7545	−	22.0914i	0.545841	−	0.945424i
$547$		−	31.4095i		−	1.34297i	−0.741016	−	0.671487i	$-0.765656\pi$
$547$		−	31.4095i		−	1.34297i	0.741016	−	0.671487i	$-0.234344\pi$
$548$	5.98054	−	3.45287i	0.255476	−	0.147499i
$549$	0.596411			0.0254542
$550$	−20.6772	−	3.13711i	−0.881678	−	0.133767i
$551$	−18.3093	−	31.7126i	−0.780003	−	1.35100i
$552$	7.13224	−	4.11780i	0.303568	−	0.175265i
$553$	−10.8176	−	6.24552i	−0.460009	−	0.265586i
$554$	−19.0736			−0.810358
$555$	13.4761	+	1.84244i	0.572029	+	0.0782073i
$556$	14.7998			0.627651
$557$	21.5188	+	12.4239i	0.911780	+	0.526416i	0.881003	−	0.473110i	$-0.156869\pi$
$557$	21.5188	+	12.4239i	0.911780	+	0.526416i	0.0307766	+	0.999526i	$0.490202\pi$
$558$	−8.72928	+	5.03985i	−0.369540	+	0.213354i
$559$	15.3933	+	26.6620i	0.651068	+	1.12768i
$560$	−1.89875	−	10.0619i	−0.0802368	−	0.425191i
$561$	15.6858			0.662254
$562$	7.31971	−	4.22604i	0.308763	−	0.178265i
$563$		−	11.5541i		−	0.486946i	−0.969908	−	0.243473i	$-0.921713\pi$
$563$		−	11.5541i		−	0.486946i	0.969908	−	0.243473i	$-0.0782867\pi$
$564$	4.85726	−	8.41303i	0.204528	−	0.354252i
$565$	−20.1630	−	7.06633i	−0.848264	−	0.297283i
$566$	−15.4394			−0.648967
$567$	−3.96572	−	2.28961i	−0.166545	−	0.0961546i
$568$	−0.523236	+	0.302090i	−0.0219545	+	0.0126754i
$569$	−22.5180			−0.944006			−0.472003	−	0.881597i	$-0.656469\pi$
$569$	−22.5180			−0.944006			−0.472003	+	0.881597i	$0.656469\pi$
$570$	8.03097	+	9.34132i	0.336380	+	0.391265i
$571$	−16.9488	+	29.3563i	−0.709287	+	1.22852i	0.255835	+	0.966720i	$0.417650\pi$
$571$	−16.9488	+	29.3563i	−0.709287	+	1.22852i	−0.965122	+	0.261801i	$0.915684\pi$
$572$	20.1788	+	11.6502i	0.843716	+	0.487120i
$573$	1.67855	−	0.969111i	0.0701224	−	0.0404852i
$574$	−7.90009	−	13.6834i	−0.329743	−	0.571132i
$575$	15.0068	+	38.3461i	0.625827	+	1.59914i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	12.9296	+	7.46489i	0.538265	+	0.310767i	0.744375	−	0.667761i	$-0.232747\pi$
$577$	12.9296	+	7.46489i	0.538265	+	0.310767i	−0.206111	+	0.978529i	$0.566081\pi$
$578$		−	2.93673i		−	0.122152i
$579$	10.2914	+	17.8253i	0.427698	+	0.740795i
$580$	9.68928	+	11.2702i	0.402326	+	0.467970i
$581$	−12.9871			−0.538795
$582$		−	5.22592i		−	0.216621i
$583$	30.2082	+	17.4407i	1.25110	+	0.722321i
$584$	−5.58023			−0.230912
$585$	−2.30981	−	12.2402i	−0.0954990	−	0.506069i
$586$	0.183567			0.00758309
$587$	26.2694	−	15.1666i	1.08425	−	0.625994i	0.152213	−	0.988348i	$-0.451360\pi$
$587$	26.2694	−	15.1666i	1.08425	−	0.625994i	0.932041	+	0.362354i	$0.118027\pi$
$588$	−12.0977	+	6.98464i	−0.498903	+	0.288042i
$589$	−27.7656	−	48.0914i	−1.14406	−	1.98157i
$590$	10.7435	−	9.23648i	0.442304	−	0.380260i
$591$	5.68764			0.233958
$592$	−5.96005	+	1.21566i	−0.244956	+	0.0499632i
$593$		−	15.8854i		−	0.652336i	−0.945312	−	0.326168i	$-0.894242\pi$
$593$		−	15.8854i		−	0.652336i	0.945312	−	0.326168i	$-0.105758\pi$
$594$	2.09138	−	3.62238i	0.0858104	−	0.148628i
$595$	−37.7330	+	7.12050i	−1.54690	+	0.291912i
$596$	5.21473	+	9.03217i	0.213603	+	0.369972i
$597$	−15.4232	+	8.90462i	−0.631231	+	0.364442i
$598$		−	45.8771i		−	1.87605i
$599$	−9.92060	−	17.1830i	−0.405345	−	0.702078i	0.589017	−	0.808121i	$-0.299515\pi$
$599$	−9.92060	−	17.1830i	−0.405345	−	0.702078i	−0.994362	+	0.106043i	$0.966182\pi$
$600$	−3.90613	−	3.12124i	−0.159467	−	0.127424i
$601$	−11.9182	+	20.6430i	−0.486154	+	0.842044i	−0.999873	−	0.0159146i	$-0.994934\pi$
$601$	−11.9182	+	20.6430i	−0.486154	+	0.842044i	0.513719	+	0.857958i	$0.328267\pi$
$602$		−	25.3077i		−	1.03147i
$603$		−	8.36781i		−	0.340764i
$604$	0.371586	−	0.643606i	0.0151196	−	0.0261880i
$605$	−14.2725	+	2.69332i	−0.580258	+	0.109499i
$606$	−12.5383			−0.509333
$607$	32.1539	+	18.5641i	1.30509	+	0.753492i	0.981272	−	0.192628i	$-0.0617011\pi$
$607$	32.1539	+	18.5641i	1.30509	+	0.753492i	0.323815	+	0.946120i	$0.395034\pi$
$608$	−4.77111	−	2.75460i	−0.193494	−	0.111714i
$609$	15.2186	−	26.3594i	0.616688	−	1.06814i
$610$	−0.247298	−	1.31049i	−0.0100128	−	0.0530600i
$611$	−27.0578	−	46.8655i	−1.09464	−	1.89597i
$612$	3.24768	+	1.87505i	0.131280	+	0.0757944i
$613$	7.82729	+	4.51909i	0.316141	+	0.182524i	0.649671	−	0.760215i	$-0.274906\pi$
$613$	7.82729	+	4.51909i	0.316141	+	0.182524i	−0.333530	+	0.942740i	$0.608240\pi$
$614$	−1.64898	+	2.85612i	−0.0665474	+	0.115263i
$615$	−7.28115	−	2.55175i	−0.293604	−	0.102897i
$616$	−9.57690	−	16.5877i	−0.385864	−	0.668336i
$617$	22.6729	+	13.0902i	0.912778	+	0.526993i	0.881324	−	0.472512i	$-0.156653\pi$
$617$	22.6729	+	13.0902i	0.912778	+	0.526993i	0.0314542	+	0.999505i	$0.489986\pi$
$618$		−	2.86952i		−	0.115429i
$619$	−11.4692			−0.460986			−0.230493	−	0.973074i	$-0.574034\pi$
$619$	−11.4692			−0.460986			−0.230493	+	0.973074i	$0.574034\pi$
$620$	14.6935	+	17.0910i	0.590107	+	0.686390i
$621$	−8.23560			−0.330483
$622$	9.18593	−	5.30350i	0.368322	−	0.212651i
$623$			27.2245i			1.09073i
$624$	2.78529	+	4.82427i	0.111501	+	0.193125i
$625$	18.3593	−	16.9687i	0.734371	−	0.678748i
$626$	−14.5523	−	25.2054i	−0.581628	−	1.00741i
$627$	19.9564	+	11.5218i	0.796983	+	0.460138i
$628$			22.0898i			0.881477i
$629$	4.55884	+	22.3508i	0.181773	+	0.891184i
$630$	−3.38657	+	9.66321i	−0.134924	+	0.384991i
$631$	15.7822	−	27.3356i	0.628280	−	1.08821i	−0.359617	−	0.933100i	$-0.617092\pi$
$631$	15.7822	−	27.3356i	0.628280	−	1.08821i	0.987897	−	0.155113i	$-0.0495742\pi$
$632$	2.36231	−	1.36388i	0.0939678	−	0.0542523i
$633$	−1.47709	+	0.852798i	−0.0587090	+	0.0338957i
$634$	2.37055	+	4.10591i	0.0941465	+	0.163066i
$635$	8.47005	+	2.96841i	0.336124	+	0.117798i
$636$	4.16967	+	7.22208i	0.165338	+	0.286374i
$637$			77.8170i			3.08322i
$638$	24.0772	+	13.9010i	0.953227	+	0.550346i
$639$	0.604180			0.0239010
$640$	2.11023	+	0.739551i	0.0834141	+	0.0292333i
$641$	6.05099	−	10.4806i	0.239000	−	0.413960i	−0.721428	−	0.692490i	$-0.756514\pi$
$641$	6.05099	−	10.4806i	0.239000	−	0.413960i	0.960428	+	0.278530i	$0.0898471\pi$
$642$	−0.698094	+	0.403045i	−0.0275516	+	0.0159069i
$643$			20.6467i			0.814227i	0.913378	+	0.407113i	$0.133465\pi$
$643$			20.6467i			0.814227i	−0.913378	+	0.407113i	$0.866535\pi$
$644$	−18.8563	+	32.6601i	−0.743044	+	1.28699i
$645$	−8.05639	−	9.37089i	−0.317220	−	0.368978i
$646$	−10.3300	+	17.8922i	−0.406430	+	0.703958i
$647$	−43.8191	+	25.2990i	−1.72271	+	0.994605i	−0.809486	+	0.587139i	$0.800254\pi$
$647$	−43.8191	+	25.2990i	−1.72271	+	0.994605i	−0.913220	+	0.407467i	$0.866412\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	13.2514	−	22.9520i	0.520162	−	0.900947i
$650$	−25.9374	+	10.1506i	−1.01735	+	0.398141i
$651$	23.0786	−	39.9733i	0.904521	−	1.56668i
$652$		−	3.93107i		−	0.153953i
$653$	13.1566	−	7.59596i	0.514857	−	0.297253i	−0.219971	−	0.975506i	$-0.570596\pi$
$653$	13.1566	−	7.59596i	0.514857	−	0.297253i	0.734828	+	0.678254i	$0.237263\pi$
$654$	6.60168	−	11.4344i	0.258146	−	0.447122i
$655$	−14.9600	+	42.6867i	−0.584534	+	1.66791i
$656$	3.45041			0.134716
$657$	4.83262	+	2.79012i	0.188539	+	0.108853i
$658$			44.4850i			1.73421i
$659$	−1.74703	−	3.02595i	−0.0680547	−	0.117874i	0.829990	−	0.557778i	$-0.188346\pi$
$659$	−1.74703	−	3.02595i	−0.0680547	−	0.117874i	−0.898045	+	0.439904i	$0.855013\pi$
$660$	−8.82658	−	3.09336i	−0.343574	−	0.120409i
$661$	22.2105	+	38.4698i	0.863890	+	1.49630i	0.868145	+	0.496311i	$0.165312\pi$
$661$	22.2105	+	38.4698i	0.863890	+	1.49630i	−0.00425497	+	0.999991i	$0.501354\pi$
$662$	−1.53306	+	0.885114i	−0.0595841	+	0.0344009i
$663$	18.0915	−	10.4451i	0.702615	−	0.405655i
$664$	1.41804	−	2.45612i	0.0550308	−	0.0953161i
$665$	−53.2366	−	18.6573i	−2.06443	−	0.723499i
$666$	5.76938	+	1.92723i	0.223559	+	0.0746788i
$667$		−	54.7404i		−	2.11956i
$668$	1.04771	+	0.604896i	0.0405371	+	0.0234041i
$669$	−1.04448	−	1.80910i	−0.0403820	−	0.0699437i
$670$	−18.3865	+	3.46967i	−0.710332	+	0.134045i
$671$	−1.24732	−	2.16042i	−0.0481523	−	0.0834023i
$672$		−	4.57922i		−	0.176647i
$673$	−24.1922	+	13.9674i	−0.932540	+	0.538402i	−0.887614	−	0.460588i	$-0.847639\pi$
$673$	−24.1922	+	13.9674i	−0.932540	+	0.538402i	−0.0449260	+	0.998990i	$0.514305\pi$
$674$	10.4574			0.402802
$675$	1.82219	+	4.65614i	0.0701360	+	0.179215i
$676$	18.0314			0.693515
$677$		−	23.3818i		−	0.898637i	−0.893372	−	0.449318i	$-0.851667\pi$
$677$		−	23.3818i		−	0.898637i	0.893372	−	0.449318i	$-0.148333\pi$
$678$	−8.27478	−	4.77745i	−0.317791	−	0.183477i
$679$	11.9653	+	20.7245i	0.459187	+	0.795335i
$680$	2.77339	−	7.91357i	0.106355	−	0.303472i
$681$	8.38038	−	14.5152i	0.321137	−	0.556225i
$682$	36.5125	+	21.0805i	1.39814	+	0.807214i
$683$	15.2247	+	8.78999i	0.582557	+	0.336339i	0.762149	−	0.647402i	$-0.224144\pi$
$683$	15.2247	+	8.78999i	0.582557	+	0.336339i	−0.179592	+	0.983741i	$0.557478\pi$
$684$	2.75460	+	4.77111i	0.105325	+	0.182428i
$685$	2.86343	+	15.1739i	0.109406	+	0.579764i
$686$	15.9569	−	27.6382i	0.609238	−	1.05523i
$687$	−14.4102	−	8.31975i	−0.549784	−	0.317418i
$688$	4.78621	+	2.76332i	0.182473	+	0.105351i
$689$	46.4550			1.76979
$690$	3.41485	+	18.0960i	0.130001	+	0.688902i
$691$	−3.01129	+	5.21571i	−0.114555	+	0.198415i	−0.917602	−	0.397501i	$-0.869877\pi$
$691$	−3.01129	+	5.21571i	−0.114555	+	0.198415i	0.803047	+	0.595916i	$0.203211\pi$
$692$		−	8.20357i		−	0.311853i
$693$			19.1538i			0.727592i
$694$	−2.43454	+	4.21674i	−0.0924138	+	0.160065i
$695$	−10.9452	+	31.2309i	−0.415175	+	1.18466i
$696$	3.32340	+	5.75630i	0.125973	+	0.218192i
$697$		−	12.9394i		−	0.490114i
$698$	8.39515	−	4.84694i	0.317761	−	0.183459i
$699$	−11.9313	−	20.6655i	−0.451282	−	0.781643i
$700$	22.6371	+	3.43446i	0.855600	+	0.129811i
$701$	12.0939	−	20.9473i	0.456781	−	0.791167i	−0.542008	−	0.840373i	$-0.682336\pi$
$701$	12.0939	−	20.9473i	0.456781	−	0.791167i	0.998789	+	0.0492061i	$0.0156691\pi$
$702$		−	5.57058i		−	0.210248i
$703$	−10.6175	+	31.7847i	−0.400448	+	1.19878i
$704$	4.18276			0.157644
$705$	14.1612	+	16.4718i	0.533342	+	0.620364i
$706$	−7.28943	−	12.6257i	−0.274341	−	0.475173i
$707$	49.7233	−	28.7078i	1.87004	−	1.07967i
$708$	5.48730	−	3.16809i	0.206225	−	0.119064i
$709$	39.9123			1.49894			0.749468	−	0.662040i	$-0.230309\pi$
$709$	39.9123			1.49894			0.749468	+	0.662040i	$0.230309\pi$
$710$	−0.250520	−	1.32756i	−0.00940185	−	0.0498224i
$711$	−2.72776			−0.102299
$712$	−5.14872	−	2.97261i	−0.192956	−	0.111403i
$713$		−	83.0124i		−	3.10884i
$714$	−17.1725			−0.642667
$715$	−39.5078	+	33.9659i	−1.47751	+	1.27025i
$716$	−4.98089	−	8.62715i	−0.186144	−	0.322412i
$717$			7.66741i			0.286345i
$718$	−7.64436	−	4.41348i	−0.285285	−	0.164709i
$719$	−21.1418	+	36.6186i	−0.788455	+	1.36564i	0.138458	+	0.990368i	$0.455785\pi$
$719$	−21.1418	+	36.6186i	−0.788455	+	1.36564i	−0.926913	+	0.375276i	$0.877548\pi$
$720$	−1.45774	−	1.69558i	−0.0543266	−	0.0631907i
$721$	6.57009	+	11.3797i	0.244683	+	0.423804i
$722$	−9.83056	+	5.67568i	−0.365856	+	0.211227i
$723$	1.45263	+	0.838677i	0.0540239	+	0.0311907i
$724$	−8.90549	+	15.4248i	−0.330970	+	0.573256i
$725$	−30.9484	+	12.1117i	−1.14940	+	0.449818i
$726$	−6.49549			−0.241070
$727$	−4.93626	+	2.84995i	−0.183076	+	0.105699i	−0.588737	−	0.808325i	$-0.700375\pi$
$727$	−4.93626	+	2.84995i	−0.183076	+	0.105699i	0.405661	+	0.914024i	$0.367041\pi$
$728$	−22.0914	−	12.7545i	−0.818761	−	0.472712i
$729$	−1.00000			−0.0370370
$730$	4.12687	−	11.7756i	0.152742	−	0.435833i
$731$	10.3627	−	17.9488i	0.383280	−	0.663860i
$732$		−	0.596411i		−	0.0220440i
$733$	−8.02569	+	4.63363i	−0.296436	+	0.171147i	−0.640841	−	0.767674i	$-0.721414\pi$
$733$	−8.02569	+	4.63363i	−0.296436	+	0.171147i	0.344405	+	0.938821i	$0.388081\pi$
$734$	−26.8113			−0.989622
$735$	−5.79228	−	30.6945i	−0.213652	−	1.13218i
$736$	−4.11780	−	7.13224i	−0.151784	−	0.262898i
$737$	−30.3114	+	17.5003i	−1.11653	+	0.644631i
$738$	−2.98814	−	1.72520i	−0.109995	−	0.0635056i
$739$	23.2319			0.854599			0.427299	−	0.904110i	$-0.359465\pi$
$739$	23.2319			0.854599			0.427299	+	0.904110i	$0.359465\pi$
$740$	1.84244	−	13.4761i	0.0677295	−	0.495391i
$741$	30.6895			1.12741
$742$	−33.0715	−	19.0938i	−1.21409	−	0.700957i
$743$	−41.6189	+	24.0287i	−1.52685	+	0.881527i	−0.527358	+	0.849643i	$0.676817\pi$
$743$	−41.6189	+	24.0287i	−1.52685	+	0.881527i	−0.999492	+	0.0318840i	$0.989849\pi$
$744$	5.03985	+	8.72928i	0.184770	+	0.320031i
$745$	−22.9165	+	4.32452i	−0.839596	+	0.158438i
$746$	9.81291			0.359276
$747$	−2.45612	+	1.41804i	−0.0898649	+	0.0518835i
$748$		−	15.6858i		−	0.573529i
$749$	1.84563	−	3.19673i	0.0674379	−	0.116806i
$750$	9.47532	−	5.93451i	0.345990	−	0.216698i
$751$	−20.1739			−0.736155			−0.368077	−	0.929795i	$-0.619984\pi$
$751$	−20.1739			−0.736155			−0.368077	+	0.929795i	$0.619984\pi$
$752$	−8.41303	−	4.85726i	−0.306792	−	0.177126i
$753$	5.81595	−	3.35784i	0.211945	−	0.122366i
$754$	37.0266			1.34843
$755$	1.08335	+	1.26011i	0.0394271	+	0.0458602i
$756$	−2.28961	+	3.96572i	−0.0832723	+	0.144232i
$757$	−37.0425	−	21.3865i	−1.34633	−	0.777305i	−0.358604	−	0.933490i	$-0.616747\pi$
$757$	−37.0425	−	21.3865i	−1.34633	−	0.777305i	−0.987728	+	0.156185i	$0.950080\pi$
$758$	−4.88631	+	2.82111i	−0.177479	+	0.102467i
$759$	17.2238	+	29.8325i	0.625184	+	1.08285i
$760$	9.34132	−	8.03097i	0.338845	−	0.291314i
$761$	6.54203	−	11.3311i	0.237148	−	0.410753i	−0.722747	−	0.691113i	$-0.757121\pi$
$761$	6.54203	−	11.3311i	0.237148	−	0.410753i	0.959895	+	0.280360i	$0.0904539\pi$
$762$	3.47606	+	2.00690i	0.125924	+	0.0727024i
$763$			60.4611i			2.18884i
$764$	−0.969111	−	1.67855i	−0.0350612	−	0.0607278i
$765$	−6.35861	+	5.46666i	−0.229896	+	0.197647i
$766$	−14.1262			−0.510400
$767$		−	35.2962i		−	1.27447i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−17.2721			−0.622848			−0.311424	−	0.950271i	$-0.600806\pi$
$769$	−17.2721			−0.622848			−0.311424	+	0.950271i	$0.600806\pi$
$770$	42.0864	−	7.94202i	1.51669	−	0.286210i
$771$	−26.2240			−0.944434
$772$	17.8253	−	10.2914i	0.641547	−	0.370397i
$773$	−27.7646	+	16.0299i	−0.998624	+	0.576556i	−0.907841	−	0.419315i	$-0.862270\pi$
$773$	−27.7646	+	16.0299i	−0.998624	+	0.576556i	−0.0907834	+	0.995871i	$0.528937\pi$
$774$	−2.76332	−	4.78621i	−0.0993255	−	0.172037i
$775$	−46.9325	+	18.3671i	−1.68587	+	0.659766i
$776$	−5.22592			−0.187600
$777$	−27.2924	+	5.56677i	−0.979109	+	0.199707i
$778$			7.84283i			0.281179i
$779$	9.50450	−	16.4623i	0.340534	−	0.589822i
$780$	−12.2402	+	2.30981i	−0.438268	+	0.0827045i
$781$	−1.26357	−	2.18857i	−0.0452141	−	0.0783132i
$782$	−26.7466	+	15.4422i	−0.956458	+	0.552211i
$783$		−	6.64680i		−	0.237537i
$784$	6.98464	+	12.0977i	0.249451	+	0.432062i
$785$	−46.6144	−	16.3365i	−1.66374	−	0.583074i
$786$	−10.1142	+	17.5184i	−0.360763	+	0.624859i
$787$			28.1927i			1.00496i	0.864589	+	0.502481i	$0.167579\pi$
$787$			28.1927i			1.00496i	−0.864589	+	0.502481i	$0.832421\pi$
$788$		−	5.68764i		−	0.202614i
$789$	−11.1702	+	19.3473i	−0.397669	+	0.688783i
$790$	1.13105	+	5.99368i	0.0402410	+	0.213246i
$791$	43.7540			1.55571
$792$	−3.62238	−	2.09138i	−0.128716	−	0.0743140i
$793$	−2.87724	−	1.66118i	−0.102174	−	0.0589901i
$794$	−12.7881	+	22.1497i	−0.453834	+	0.786064i
$795$	−18.3239	+	3.45786i	−0.649882	+	0.122638i
$796$	8.90462	+	15.4232i	0.315616	+	0.546662i
$797$	40.6011	+	23.4411i	1.43816	+	0.830325i	0.997722	−	0.0674559i	$-0.0214882\pi$
$797$	40.6011	+	23.4411i	1.43816	+	0.830325i	0.440443	+	0.897781i	$0.354822\pi$
$798$	−21.8480	−	12.6139i	−0.773410	−	0.446529i
$799$	−18.2152	+	31.5497i	−0.644409	+	1.11615i
$800$	−3.12124	+	3.90613i	−0.110353	+	0.138103i
$801$	2.97261	+	5.14872i	0.105032	+	0.181921i
$802$	−3.11915	−	1.80084i	−0.110141	−	0.0635900i
$803$		−	23.3408i		−	0.823678i
$804$	−8.36781			−0.295110
$805$	−54.9751	−	63.9450i	−1.93762	−	2.25376i
$806$	56.1498			1.97779
$807$	−13.4530	+	7.76709i	−0.473568	+	0.273414i
$808$			12.5383i			0.441095i
$809$	−19.1934	−	33.2440i	−0.674806	−	1.16880i	−0.976526	−	0.215401i	$-0.930894\pi$
$809$	−19.1934	−	33.2440i	−0.674806	−	1.16880i	0.301720	−	0.953397i	$-0.402439\pi$
$810$	0.414645	+	2.19729i	0.0145691	+	0.0772048i
$811$	3.35066	+	5.80350i	0.117657	+	0.203789i	0.918839	−	0.394633i	$-0.129128\pi$
$811$	3.35066	+	5.80350i	0.117657	+	0.203789i	−0.801181	+	0.598421i	$0.795795\pi$
$812$	−26.3594	−	15.2186i	−0.925033	−	0.534068i
$813$			24.8512i			0.871571i
$814$	−5.08481	−	24.9295i	−0.178222	−	0.873777i
$815$	8.29546	+	2.90723i	0.290577	+	0.101836i
$816$	1.87505	−	3.24768i	0.0656399	−	0.113692i
$817$	26.3682	−	15.2237i	0.922508	−	0.532610i
$818$	−23.0708	+	13.3199i	−0.806652	+	0.465721i
$819$	12.7545	+	22.0914i	0.445677	+	0.771936i
$820$	−2.55175	+	7.28115i	−0.0891110	+	0.254269i
$821$	4.27815	+	7.40998i	0.149309	+	0.258610i	0.930972	−	0.365090i	$-0.118962\pi$
$821$	4.27815	+	7.40998i	0.149309	+	0.258610i	−0.781664	+	0.623700i	$0.785629\pi$
$822$			6.90574i			0.240865i
$823$	−46.7365	−	26.9833i	−1.62913	−	0.940580i	−0.984352	−	0.176211i	$-0.943616\pi$
$823$	−46.7365	−	26.9833i	−1.62913	−	0.940580i	−0.644779	−	0.764369i	$-0.723051\pi$
$824$	−2.86952			−0.0999646
$825$	13.0554	−	16.3384i	0.454531	−	0.568830i
$826$	−14.5074	+	25.1275i	−0.504777	+	0.874299i
$827$	47.8927	−	27.6509i	1.66539	−	0.961514i	0.695319	−	0.718702i	$-0.255263\pi$
$827$	47.8927	−	27.6509i	1.66539	−	0.961514i	0.970073	−	0.242813i	$-0.0780700\pi$
$828$			8.23560i			0.286207i
$829$	9.85669	−	17.0723i	0.342337	−	0.592945i	−0.642529	−	0.766261i	$-0.722115\pi$
$829$	9.85669	−	17.0723i	0.342337	−	0.592945i	0.984866	+	0.173316i	$0.0554482\pi$
$830$	4.13427	+	4.80882i	0.143503	+	0.166917i
$831$	9.53678	−	16.5182i	0.330827	−	0.573010i
$832$	4.82427	−	2.78529i	0.167251	−	0.0965626i
$833$	45.3678	−	26.1931i	1.57190	−	0.907537i
$834$	−7.39989	+	12.8170i	−0.256237	+	0.443816i
$835$	−2.05130	+	1.76356i	−0.0709883	+	0.0610304i
$836$	11.5218	−	19.9564i	0.398491	−	0.690207i
$837$		−	10.0797i		−	0.348405i
$838$	−11.2792	+	6.51205i	−0.389633	+	0.224955i
$839$	−3.39845	+	5.88629i	−0.117328	+	0.203217i	−0.918708	−	0.394938i	$-0.870766\pi$
$839$	−3.39845	+	5.88629i	−0.117328	+	0.203217i	0.801380	+	0.598155i	$0.204099\pi$
$840$	9.66321	+	3.38657i	0.333412	+	0.116848i
$841$	15.1800			0.523448
$842$	3.90749	+	2.25599i	0.134661	+	0.0777465i
$843$			8.45207i			0.291105i
$844$	0.852798	+	1.47709i	0.0293545	+	0.0508435i
$845$	−13.3351	+	38.0504i	−0.458742	+	1.30897i
$846$	4.85726	+	8.41303i	0.166996	+	0.289246i
$847$	25.7593	−	14.8721i	0.885100	−	0.511013i
$848$	7.22208	−	4.16967i	0.248007	−	0.143187i
$849$	7.71970	−	13.3709i	0.264940	−	0.458889i
$850$	14.6484	+	11.7050i	0.502435	+	0.401477i
$851$	−37.5027	+	33.2127i	−1.28557	+	1.13852i
$852$		−	0.604180i		−	0.0206989i
$853$	15.6208	+	9.01868i	0.534846	+	0.308794i	0.742988	−	0.669305i	$-0.233408\pi$
$853$	15.6208	+	9.01868i	0.534846	+	0.308794i	−0.208141	+	0.978099i	$0.566741\pi$
$854$	1.36555	+	2.36520i	0.0467281	+	0.0809355i
$855$	−12.1053	+	2.28436i	−0.413993	+	0.0781236i
$856$	0.403045	+	0.698094i	0.0137758	+	0.0238604i
$857$			37.8423i			1.29267i	0.763055	+	0.646334i	$0.223699\pi$
$857$			37.8423i			1.29267i	−0.763055	+	0.646334i	$0.776301\pi$
$858$	−20.1788	+	11.6502i	−0.688891	+	0.397732i
$859$	−12.4759			−0.425672			−0.212836	−	0.977088i	$-0.568270\pi$
$859$	−12.4759			−0.425672			−0.212836	+	0.977088i	$0.568270\pi$
$860$	−9.37089	+	8.05639i	−0.319545	+	0.274721i
$861$	15.8002			0.538469
$862$		−	8.31967i		−	0.283369i
$863$	−3.18094	−	1.83652i	−0.108281	−	0.0625158i	0.444882	−	0.895589i	$-0.353246\pi$
$863$	−3.18094	−	1.83652i	−0.108281	−	0.0625158i	−0.553162	+	0.833074i	$0.686579\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	17.3114	+	6.06696i	0.588606	+	0.206283i
$866$	−11.0359	+	19.1148i	−0.375016	+	0.649546i
$867$	2.54329	+	1.46837i	0.0863745	+	0.0498684i
$868$	−39.9733	−	23.0786i	−1.35678	−	0.783339i
$869$	5.70479	+	9.88099i	0.193522	+	0.335190i
$870$	−14.6049	+	2.75606i	−0.495154	+	0.0934392i
$871$	−23.3068	+	40.3686i	−0.789721	+	1.36784i
$872$	−11.4344	−	6.60168i	−0.387219	−	0.223561i
$873$	4.52578	+	2.61296i	0.153174	+	0.0884353i
$874$	−45.3716			−1.53472
$875$	−23.9888	+	45.2294i	−0.810968	+	1.52903i
$876$	2.79012	−	4.83262i	0.0942693	−	0.163279i
$877$		−	10.9592i		−	0.370066i	−0.982732	−	0.185033i	$-0.940761\pi$
$877$		−	10.9592i		−	0.370066i	0.982732	−	0.185033i	$-0.0592392\pi$
$878$			5.43011i			0.183257i
$879$	−0.0917835	+	0.158974i	−0.00309578	+	0.00536205i
$880$	−3.09336	+	8.82658i	−0.104277	+	0.297544i
$881$	−4.86470	−	8.42591i	−0.163896	−	0.283876i	0.772367	−	0.635177i	$-0.219073\pi$
$881$	−4.86470	−	8.42591i	−0.163896	−	0.283876i	−0.936263	+	0.351301i	$0.885739\pi$
$882$		−	13.9693i		−	0.470370i
$883$	40.7970	−	23.5542i	1.37293	−	0.792660i	0.381632	−	0.924314i	$-0.375362\pi$
$883$	40.7970	−	23.5542i	1.37293	−	0.792660i	0.991296	+	0.131654i	$0.0420287\pi$
$884$	−10.4451	−	18.0915i	−0.351308	−	0.608483i
$885$	2.62726	+	13.9224i	0.0883145	+	0.467997i
$886$	6.78482	−	11.7517i	0.227941	−	0.394805i
$887$			4.68737i			0.157387i	0.996899	+	0.0786933i	$0.0250748\pi$
$887$			4.68737i			0.157387i	−0.996899	+	0.0786933i	$0.974925\pi$
$888$	1.92723	−	5.76938i	0.0646737	−	0.193608i
$889$	−18.3801			−0.616449
$890$	10.0806	−	8.66658i	0.337904	−	0.290504i
$891$	2.09138	+	3.62238i	0.0700639	+	0.121354i
$892$	−1.80910	+	1.04448i	−0.0605730	+	0.0349718i
$893$	−46.3491	+	26.7597i	−1.55101	+	0.895478i
$894$	−10.4295			−0.348813
$895$	21.8889	−	4.13059i	0.731664	−	0.138071i
$896$	−4.57922			−0.152981
$897$	39.7308	+	22.9386i	1.32657	+	0.765896i
$898$			26.0496i			0.869288i
$899$	66.9978			2.23450
$900$	4.65614	−	1.82219i	0.155205	−	0.0607395i
$901$	−15.6367	−	27.0835i	−0.520933	−	0.902283i
$902$			14.4322i			0.480541i
$903$	21.9171	+	12.6539i	0.729357	+	0.421094i
$904$	−4.77745	+	8.27478i	−0.158896	+	0.275215i
$905$	−25.9637	−	30.2000i	−0.863063	−	1.00388i
$906$	0.371586	+	0.643606i	0.0123451	+	0.0213824i
$907$	21.3093	−	12.3029i	0.707565	−	0.408513i	−0.102594	−	0.994723i	$-0.532714\pi$
$907$	21.3093	−	12.3029i	0.707565	−	0.408513i	0.810159	+	0.586211i	$0.199381\pi$
$908$	−14.5152	−	8.38038i	−0.481705	−	0.278113i
$909$	6.26914	−	10.8585i	0.207934	−	0.360153i
$910$	43.2525	−	37.1853i	1.43381	−	1.23268i
$911$	−13.3266			−0.441530			−0.220765	−	0.975327i	$-0.570855\pi$
$911$	−13.3266			−0.441530			−0.220765	+	0.975327i	$0.570855\pi$
$912$	4.77111	−	2.75460i	0.157987	−	0.0912140i
$913$	10.2734	+	5.93134i	0.339999	+	0.196299i
$914$	4.98113			0.164761
$915$	1.25856	+	0.441076i	0.0416068	+	0.0145815i
$916$	−8.31975	+	14.4102i	−0.274892	+	0.476127i
$917$		−	92.6306i		−	3.05893i
$918$	−3.24768	+	1.87505i	−0.107190	+	0.0618859i
$919$	−43.7496			−1.44317			−0.721583	−	0.692328i	$-0.756585\pi$
$919$	−43.7496			−1.44317			−0.721583	+	0.692328i	$0.756585\pi$
$920$	18.0960	−	3.41485i	0.596607	−	0.112584i
$921$	−1.64898	−	2.85612i	−0.0543357	−	0.0941122i
$922$	−21.4429	+	12.3801i	−0.706185	+	0.407716i
$923$	−2.91473	−	1.68282i	−0.0959394	−	0.0553907i
$924$	19.1538			0.630113
$925$	27.0751	+	13.8542i	0.890223	+	0.455524i
$926$	13.0281			0.428130
$927$	2.48508	+	1.43476i	0.0816208	+	0.0471238i
$928$	5.75630	−	3.32340i	0.188960	−	0.109096i
$929$	16.9938	+	29.4340i	0.557547	+	0.965700i	0.997700	+	0.0677771i	$0.0215907\pi$
$929$	16.9938	+	29.4340i	0.557547	+	0.965700i	−0.440154	+	0.897923i	$0.645076\pi$
$930$	−22.1480	+	4.17949i	−0.726261	+	0.137051i
$931$	76.9596			2.52225
$932$	−20.6655	+	11.9313i	−0.676922	+	0.390821i
$933$			10.6070i			0.347258i
$934$	19.1263	−	33.1278i	0.625833	−	1.08397i
$935$	33.1006	+	11.6004i	1.08250	+	0.379375i
$936$	−5.57058			−0.182080
$937$	10.7600	+	6.21227i	0.351513	+	0.202946i	0.665351	−	0.746530i	$-0.268282\pi$
$937$	10.7600	+	6.21227i	0.351513	+	0.202946i	−0.313838	+	0.949476i	$0.601615\pi$
$938$	33.1844	−	19.1590i	1.08351	−	0.625565i
$939$	29.1046			0.949794
$940$	16.4718	−	14.1612i	0.537251	−	0.461888i
$941$	−11.0826	+	19.1956i	−0.361282	+	0.625759i	−0.988172	−	0.153349i	$-0.950994\pi$
$941$	−11.0826	+	19.1956i	−0.361282	+	0.625759i	0.626890	+	0.779108i	$0.284327\pi$
$942$	−19.1303	−	11.0449i	−0.623299	−	0.359862i
$943$	24.6091	−	14.2081i	0.801384	−	0.462679i
$944$	−3.16809	−	5.48730i	−0.103113	−	0.178596i
$945$	−6.67530	−	7.76446i	−0.217147	−	0.252578i
$946$	−11.5583	+	20.0196i	−0.375793	+	0.650893i
$947$	34.6632	+	20.0128i	1.12640	+	0.650329i	0.943028	−	0.332713i	$-0.107964\pi$
$947$	34.6632	+	20.0128i	1.12640	+	0.650329i	0.183376	+	0.983043i	$0.441298\pi$
$948$			2.72776i			0.0885937i
$949$	−15.5426	−	26.9205i	−0.504533	−	0.873878i
$950$	10.0388	+	25.6516i	0.325702	+	0.832249i
$951$	−4.74110			−0.153741
$952$			17.1725i			0.556566i
$953$	44.8481	+	25.8930i	1.45277	+	0.838758i	0.998638	−	0.0521754i	$-0.0166155\pi$
$953$	44.8481	+	25.8930i	1.45277	+	0.838758i	0.454134	+	0.890934i	$0.349949\pi$
$954$	−8.33934			−0.269996
$955$	4.25883	−	0.803673i	0.137813	−	0.0260063i
$956$	7.66741			0.247982
$957$	−24.0772	+	13.9010i	−0.778306	+	0.449355i
$958$	5.75557	−	3.32298i	0.185954	−	0.107361i
$959$	−15.8115	−	27.3862i	−0.510578	−	0.884348i
$960$	−1.69558	+	1.45774i	−0.0547247	+	0.0470482i
$961$	70.6004			2.27743
$962$	−22.4651	−	25.3669i	−0.724305	−	0.817862i
$963$		−	0.806090i		−	0.0259759i
$964$	0.838677	−	1.45263i	0.0270120	−	0.0467861i
$965$	8.53459	+	45.2265i	0.274738	+	1.45589i
$966$	−18.8563	−	32.6601i	−0.606693	−	1.05082i
$967$	−20.5417	+	11.8597i	−0.660576	+	0.381383i	−0.792496	−	0.609877i	$-0.791219\pi$
$967$	−20.5417	+	11.8597i	−0.660576	+	0.381383i	0.131921	+	0.991260i	$0.457886\pi$
$968$			6.49549i			0.208773i
$969$	−10.3300	−	17.8922i	−0.331849	−	0.574779i
$970$	3.86483	−	11.0279i	0.124092	−	0.354084i
$971$	−4.98194	+	8.62897i	−0.159878	+	0.276917i	−0.934825	−	0.355110i	$-0.884443\pi$
$971$	−4.98194	+	8.62897i	−0.159878	+	0.276917i	0.774946	+	0.632027i	$0.217777\pi$
$972$			1.00000i			0.0320750i
$973$		−	67.7715i		−	2.17265i
$974$	−7.70143	+	13.3393i	−0.246770	+	0.427418i
$975$	4.17799	−	27.5378i	0.133803	−	0.881915i
$976$	−0.596411			−0.0190906
$977$	20.1943	+	11.6592i	0.646073	+	0.373011i	0.786950	−	0.617016i	$-0.211659\pi$
$977$	20.1943	+	11.6592i	0.646073	+	0.373011i	−0.140877	+	0.990027i	$0.544992\pi$
$978$	3.40441	+	1.96554i	0.108861	+	0.0628509i
$979$	12.4337	−	21.5359i	0.397384	−	0.688289i
$980$	−30.6945	+	5.79228i	−0.980500	+	0.185028i
$981$	6.60168	+	11.4344i	0.210775	+	0.365074i
$982$	8.73102	+	5.04086i	0.278618	+	0.160860i
$983$	43.2837	+	24.9899i	1.38054	+	0.797052i	0.992223	−	0.124475i	$-0.0397247\pi$
$983$	43.2837	+	24.9899i	1.38054	+	0.797052i	0.388313	+	0.921528i	$0.373058\pi$
$984$	−1.72520	+	2.98814i	−0.0549975	+	0.0952584i
$985$	12.0022	+	4.20629i	0.382422	+	0.134024i
$986$	−12.4631	−	21.5867i	−0.396906	−	0.687461i
$987$	−38.5251	−	22.2425i	−1.22627	−	0.707986i
$988$		−	30.6895i		−	0.976363i
$989$	45.5153			1.44730
$990$	7.09222	−	6.09736i	0.225406	−	0.193787i
$991$	23.7445			0.754270			0.377135	−	0.926158i	$-0.376909\pi$
$991$	23.7445			0.754270			0.377135	+	0.926158i	$0.376909\pi$
$992$	8.72928	−	5.03985i	0.277155	−	0.160015i
$993$		−	1.77023i		−	0.0561765i
$994$	1.38334	+	2.39601i	0.0438768	+	0.0759969i
$995$	−39.1320	+	7.38450i	−1.24057	+	0.234104i
$996$	1.41804	+	2.45612i	0.0449324	+	0.0778253i
$997$	11.4563	+	6.61428i	0.362824	+	0.209476i	0.670319	−	0.742073i	$-0.266157\pi$
$997$	11.4563	+	6.61428i	0.362824	+	0.209476i	−0.307495	+	0.951550i	$0.599491\pi$
$998$		−	34.0754i		−	1.07864i
$999$	−4.55372	+	4.03282i	−0.144073	+	0.127593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.13	yes	40
5.4	even	2	inner	1110.2.bb.e.1009.8	✓	40
37.26	even	3	inner	1110.2.bb.e.1099.8	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.8	✓	40	5.4	even	2	inner
1110.2.bb.e.1009.13	yes	40	1.1	even	1	trivial
1110.2.bb.e.1099.8	yes	40	37.26	even	3	inner
1110.2.bb.e.1099.13	yes	40	185.174	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.19729 + 0.414645i) q^{5} -1.00000 q^{6} +(3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.19729 + 0.414645i) q^{5} -1.00000 q^{6} +(3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.11023 - 0.739551i) q^{10} -4.18276 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.82427 + 2.78529i) q^{13} +4.57922 q^{14} +(1.69558 - 1.45774i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.24768 + 1.87505i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.75460 + 4.77111i) q^{19} +(-1.45774 - 1.69558i) q^{20} +(-2.28961 + 3.96572i) q^{21} +(-3.62238 - 2.09138i) q^{22} +8.23560i q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.65614 - 1.82219i) q^{25} -5.57058 q^{26} +1.00000i q^{27} +(3.96572 + 2.28961i) q^{28} -6.64680 q^{29} +(2.19729 - 0.414645i) q^{30} -10.0797 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.62238 - 2.09138i) q^{33} +(1.87505 + 3.24768i) q^{34} +(-7.76446 + 6.67530i) q^{35} +1.00000 q^{36} +(4.03282 + 4.55372i) q^{37} +5.50921i q^{38} +(2.78529 - 4.82427i) q^{39} +(-0.414645 - 2.19729i) q^{40} +(-1.72520 - 2.98814i) q^{41} +(-3.96572 + 2.28961i) q^{42} -5.52664i q^{43} +(-2.09138 - 3.62238i) q^{44} +(-0.739551 + 2.11023i) q^{45} +(-4.11780 + 7.13224i) q^{46} +9.71453i q^{47} -1.00000i q^{48} +(6.98464 - 12.0977i) q^{49} +(4.94343 + 0.750010i) q^{50} -3.75010 q^{51} +(-4.82427 - 2.78529i) q^{52} +(-7.22208 - 4.16967i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(9.19073 - 1.73436i) q^{55} +(2.28961 + 3.96572i) q^{56} +(-4.77111 - 2.75460i) q^{57} +(-5.75630 - 3.32340i) q^{58} +(-3.16809 + 5.48730i) q^{59} +(2.11023 + 0.739551i) q^{60} +(0.298205 + 0.516507i) q^{61} +(-8.72928 - 5.03985i) q^{62} -4.57922i q^{63} -1.00000 q^{64} +(9.44539 - 8.12044i) q^{65} +4.18276 q^{66} +(7.24674 - 4.18391i) q^{67} +3.75010i q^{68} +(-4.11780 - 7.13224i) q^{69} +(-10.0619 + 1.89875i) q^{70} +(0.302090 + 0.523236i) q^{71} +(0.866025 + 0.500000i) q^{72} +5.58023i q^{73} +(1.21566 + 5.96005i) q^{74} +(-3.12124 + 3.90613i) q^{75} +(-2.75460 + 4.77111i) q^{76} +(-16.5877 + 9.57690i) q^{77} +(4.82427 - 2.78529i) q^{78} +(-1.36388 - 2.36231i) q^{79} +(0.739551 - 2.11023i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.45041i q^{82} +(-2.45612 - 1.41804i) q^{83} -4.57922 q^{84} +(-7.91357 - 2.77339i) q^{85} +(2.76332 - 4.78621i) q^{86} +(5.75630 - 3.32340i) q^{87} -4.18276i q^{88} +(-2.97261 + 5.14872i) q^{89} +(-1.69558 + 1.45774i) q^{90} +(-12.7545 + 22.0914i) q^{91} +(-7.13224 + 4.11780i) q^{92} +(8.72928 - 5.03985i) q^{93} +(-4.85726 + 8.41303i) q^{94} +(-8.03097 - 9.34132i) q^{95} +(0.500000 - 0.866025i) q^{96} +5.22592i q^{97} +(12.0977 - 6.98464i) q^{98} +(-2.09138 + 3.62238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

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