LMFDB - Embedded newform 1110.2.bb.e.1009.17

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			1009.17
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98769 - 1.02425i) q^{5} -1.00000 q^{6} +(0.304101 - 0.175573i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98769 - 1.02425i) q^{5} -1.00000 q^{6} +(0.304101 - 0.175573i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23352 + 0.106818i) q^{10} -1.03694 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.89463 + 1.09386i) q^{13} +0.351145 q^{14} +(-1.20927 + 1.88087i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.45383 + 2.57142i) q^{17} +(0.866025 - 0.500000i) q^{18} +(4.10098 + 7.10310i) q^{19} +(1.88087 + 1.20927i) q^{20} +(-0.175573 + 0.304101i) q^{21} +(-0.898016 - 0.518470i) q^{22} -4.23909i q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.90182 - 4.07178i) q^{25} -2.18772 q^{26} +1.00000i q^{27} +(0.304101 + 0.175573i) q^{28} +3.20052 q^{29} +(-1.98769 + 1.02425i) q^{30} +0.148735 q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.898016 - 0.518470i) q^{33} +(2.57142 + 4.45383i) q^{34} +(0.424628 - 0.660459i) q^{35} +1.00000 q^{36} +(5.69935 - 2.12543i) q^{37} +8.20196i q^{38} +(1.09386 - 1.89463i) q^{39} +(1.02425 + 1.98769i) q^{40} +(5.56385 + 9.63687i) q^{41} +(-0.304101 + 0.175573i) q^{42} -6.34319i q^{43} +(-0.518470 - 0.898016i) q^{44} +(0.106818 - 2.23352i) q^{45} +(2.11955 - 3.67116i) q^{46} -8.96463i q^{47} -1.00000i q^{48} +(-3.43835 + 5.95539i) q^{49} +(4.54894 - 2.07536i) q^{50} -5.14284 q^{51} +(-1.89463 - 1.09386i) q^{52} +(3.86558 + 2.23180i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.06111 + 1.06209i) q^{55} +(0.175573 + 0.304101i) q^{56} +(-7.10310 - 4.10098i) q^{57} +(2.77173 + 1.60026i) q^{58} +(-5.49650 + 9.52022i) q^{59} +(-2.23352 - 0.106818i) q^{60} +(1.15060 + 1.99289i) q^{61} +(0.128809 + 0.0743676i) q^{62} -0.351145i q^{63} -1.00000 q^{64} +(-2.64554 + 4.11483i) q^{65} +1.03694 q^{66} +(-12.4250 + 7.17356i) q^{67} +5.14284i q^{68} +(2.11955 + 3.67116i) q^{69} +(0.697968 - 0.359661i) q^{70} +(-5.35314 - 9.27190i) q^{71} +(0.866025 + 0.500000i) q^{72} -8.52271i q^{73} +(5.99849 + 1.00900i) q^{74} +(-0.477161 + 4.97718i) q^{75} +(-4.10098 + 7.10310i) q^{76} +(-0.315334 + 0.182058i) q^{77} +(1.89463 - 1.09386i) q^{78} +(4.72489 + 8.18375i) q^{79} +(-0.106818 + 2.23352i) q^{80} +(-0.500000 - 0.866025i) q^{81} +11.1277i q^{82} +(3.80546 + 2.19708i) q^{83} -0.351145 q^{84} +(11.4866 + 0.549350i) q^{85} +(3.17160 - 5.49337i) q^{86} +(-2.77173 + 1.60026i) q^{87} -1.03694i q^{88} +(2.10936 - 3.65351i) q^{89} +(1.20927 - 1.88087i) q^{90} +(-0.384105 + 0.665289i) q^{91} +(3.67116 - 2.11955i) q^{92} +(-0.128809 + 0.0743676i) q^{93} +(4.48232 - 7.76360i) q^{94} +(15.4268 + 9.91834i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.4855i q^{97} +(-5.95539 + 3.43835i) q^{98} +(-0.518470 + 0.898016i) 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
$5$	1.98769	−	1.02425i	0.888922	−	0.458059i
$5$	1.98769	−	1.02425i	0.888922	−	0.458059i
$6$	−1.00000			−0.408248
$7$	0.304101	−	0.175573i	0.114939	−	0.0663602i	−0.441428	−	0.897297i	$-0.645528\pi$
$7$	0.304101	−	0.175573i	0.114939	−	0.0663602i	0.556368	+	0.830936i	$0.312195\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.23352	+	0.106818i	0.706299	+	0.0337789i
$11$	−1.03694			−0.312649			−0.156325	−	0.987706i	$-0.549965\pi$
$11$	−1.03694			−0.312649			−0.156325	+	0.987706i	$0.549965\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.89463	+	1.09386i	−0.525475	+	0.303383i	−0.739172	−	0.673517i	$-0.764783\pi$
$13$	−1.89463	+	1.09386i	−0.525475	+	0.303383i	0.213697	+	0.976900i	$0.431449\pi$
$14$	0.351145			0.0938475
$15$	−1.20927	+	1.88087i	−0.312231	+	0.485639i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.45383	+	2.57142i	1.08021	+	0.623661i	0.930954	−	0.365137i	$-0.118978\pi$
$17$	4.45383	+	2.57142i	1.08021	+	0.623661i	0.149259	+	0.988798i	$0.452311\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	4.10098	+	7.10310i	0.940829	+	1.62956i	0.763895	+	0.645341i	$0.223285\pi$
$19$	4.10098	+	7.10310i	0.940829	+	1.62956i	0.176935	+	0.984223i	$0.443382\pi$
$20$	1.88087	+	1.20927i	0.420576	+	0.270400i
$21$	−0.175573	+	0.304101i	−0.0383131	+	0.0663602i
$22$	−0.898016	−	0.518470i	−0.191458	−	0.110538i
$23$		−	4.23909i		−	0.883912i	−0.897037	−	0.441956i	$-0.854285\pi$
$23$		−	4.23909i		−	0.883912i	0.897037	−	0.441956i	$-0.145715\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.90182	−	4.07178i	0.580365	−	0.814357i
$26$	−2.18772			−0.429048
$27$			1.00000i			0.192450i
$28$	0.304101	+	0.175573i	0.0574696	+	0.0331801i
$29$	3.20052			0.594322			0.297161	−	0.954827i	$-0.403960\pi$
$29$	3.20052			0.594322			0.297161	+	0.954827i	$0.403960\pi$
$30$	−1.98769	+	1.02425i	−0.362901	+	0.187002i
$31$	0.148735			0.0267136			0.0133568	−	0.999911i	$-0.495748\pi$
$31$	0.148735			0.0267136			0.0133568	+	0.999911i	$0.495748\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.898016	−	0.518470i	0.156325	−	0.0902540i
$34$	2.57142	+	4.45383i	0.440995	+	0.763826i
$35$	0.424628	−	0.660459i	0.0717752	−	0.111638i
$36$	1.00000			0.166667
$37$	5.69935	−	2.12543i	0.936967	−	0.349419i
$37$	5.69935	−	2.12543i	0.936967	−	0.349419i
$38$			8.20196i			1.33053i
$39$	1.09386	−	1.89463i	0.175158	−	0.303383i
$40$	1.02425	+	1.98769i	0.161948	+	0.314281i
$41$	5.56385	+	9.63687i	0.868927	+	1.50503i	0.863094	+	0.505043i	$0.168523\pi$
$41$	5.56385	+	9.63687i	0.868927	+	1.50503i	0.00583262	+	0.999983i	$0.498143\pi$
$42$	−0.304101	+	0.175573i	−0.0469238	+	0.0270915i
$43$		−	6.34319i		−	0.967328i	−0.875254	−	0.483664i	$-0.839306\pi$
$43$		−	6.34319i		−	0.967328i	0.875254	−	0.483664i	$-0.160694\pi$
$44$	−0.518470	−	0.898016i	−0.0781623	−	0.135381i
$45$	0.106818	−	2.23352i	0.0159235	−	0.332953i
$46$	2.11955	−	3.67116i	0.312510	−	0.541283i
$47$		−	8.96463i		−	1.30763i	−0.756656	−	0.653813i	$-0.773168\pi$
$47$		−	8.96463i		−	1.30763i	0.756656	−	0.653813i	$-0.226832\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.43835	+	5.95539i	−0.491193	+	0.850771i
$50$	4.54894	−	2.07536i	0.643318	−	0.293500i
$51$	−5.14284			−0.720142
$52$	−1.89463	−	1.09386i	−0.262737	−	0.151691i
$53$	3.86558	+	2.23180i	0.530979	+	0.306561i	0.741415	−	0.671047i	$-0.234155\pi$
$53$	3.86558	+	2.23180i	0.530979	+	0.306561i	−0.210436	+	0.977608i	$0.567488\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.06111	+	1.06209i	−0.277921	+	0.143212i
$56$	0.175573	+	0.304101i	0.0234619	+	0.0406372i
$57$	−7.10310	−	4.10098i	−0.940829	−	0.543188i
$58$	2.77173	+	1.60026i	0.363946	+	0.210125i
$59$	−5.49650	+	9.52022i	−0.715584	+	1.23943i	0.247150	+	0.968977i	$0.420506\pi$
$59$	−5.49650	+	9.52022i	−0.715584	+	1.23943i	−0.962734	+	0.270450i	$0.912828\pi$
$60$	−2.23352	−	0.106818i	−0.288346	−	0.0137902i
$61$	1.15060	+	1.99289i	0.147319	+	0.255164i	0.930236	−	0.366963i	$-0.119602\pi$
$61$	1.15060	+	1.99289i	0.147319	+	0.255164i	−0.782917	+	0.622126i	$0.786269\pi$
$62$	0.128809	+	0.0743676i	0.0163587	+	0.00944470i
$63$		−	0.351145i		−	0.0442402i
$64$	−1.00000			−0.125000
$65$	−2.64554	+	4.11483i	−0.328139	+	0.510382i
$66$	1.03694			0.127638
$67$	−12.4250	+	7.17356i	−1.51795	+	0.876390i	−0.518175	+	0.855274i	$0.673389\pi$
$67$	−12.4250	+	7.17356i	−1.51795	+	0.876390i	−0.999777	+	0.0211159i	$0.993278\pi$
$68$			5.14284i			0.623661i
$69$	2.11955	+	3.67116i	0.255163	+	0.441956i
$70$	0.697968	−	0.359661i	0.0834231	−	0.0429877i
$71$	−5.35314	−	9.27190i	−0.635300	−	1.10037i	−0.986451	−	0.164054i	$-0.947543\pi$
$71$	−5.35314	−	9.27190i	−0.635300	−	1.10037i	0.351151	−	0.936319i	$-0.385790\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	8.52271i		−	0.997507i	−0.866744	−	0.498754i	$-0.833791\pi$
$73$		−	8.52271i		−	0.997507i	0.866744	−	0.498754i	$-0.166209\pi$
$74$	5.99849	+	1.00900i	0.697311	+	0.117293i
$75$	−0.477161	+	4.97718i	−0.0550978	+	0.574715i
$76$	−4.10098	+	7.10310i	−0.470415	+	0.814782i
$77$	−0.315334	+	0.182058i	−0.0359357	+	0.0207475i
$78$	1.89463	−	1.09386i	0.214524	−	0.123856i
$79$	4.72489	+	8.18375i	0.531592	+	0.920744i	0.999320	+	0.0368718i	$0.0117393\pi$
$79$	4.72489	+	8.18375i	0.531592	+	0.920744i	−0.467728	+	0.883872i	$0.654927\pi$
$80$	−0.106818	+	2.23352i	−0.0119427	+	0.249715i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			11.1277i			1.22885i
$83$	3.80546	+	2.19708i	0.417704	+	0.241161i	0.694094	−	0.719884i	$-0.255805\pi$
$83$	3.80546	+	2.19708i	0.417704	+	0.241161i	−0.276391	+	0.961045i	$0.589138\pi$
$84$	−0.351145			−0.0383131
$85$	11.4866	+	0.549350i	1.24590	+	0.0595854i
$86$	3.17160	−	5.49337i	0.342002	−	0.592365i
$87$	−2.77173	+	1.60026i	−0.297161	+	0.171566i
$88$		−	1.03694i		−	0.110538i
$89$	2.10936	−	3.65351i	0.223591	−	0.387272i	−0.732305	−	0.680977i	$-0.761555\pi$
$89$	2.10936	−	3.65351i	0.223591	−	0.387272i	0.955896	+	0.293706i	$0.0948885\pi$
$90$	1.20927	−	1.88087i	0.127468	−	0.198261i
$91$	−0.384105	+	0.665289i	−0.0402651	+	0.0697412i
$92$	3.67116	−	2.11955i	0.382745	−	0.220978i
$93$	−0.128809	+	0.0743676i	−0.0133568	+	0.00771156i
$94$	4.48232	−	7.76360i	0.462316	−	0.800754i
$95$	15.4268	+	9.91834i	1.58276	+	1.01760i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	15.4855i		−	1.57231i	−0.618027	−	0.786157i	$-0.712068\pi$
$97$		−	15.4855i		−	1.57231i	0.618027	−	0.786157i	$-0.287932\pi$
$98$	−5.95539	+	3.43835i	−0.601586	+	0.347326i
$99$	−0.518470	+	0.898016i	−0.0521082	+	0.0902540i
$100$	4.97718	+	0.477161i	0.497718	+	0.0477161i
$101$	−5.93705			−0.590759			−0.295379	−	0.955380i	$-0.595446\pi$
$101$	−5.93705			−0.590759			−0.295379	+	0.955380i	$0.595446\pi$
$102$	−4.45383	−	2.57142i	−0.440995	−	0.254609i
$103$			13.0217i			1.28307i	0.767095	+	0.641534i	$0.221702\pi$
$103$			13.0217i			1.28307i	−0.767095	+	0.641534i	$0.778298\pi$
$104$	−1.09386	−	1.89463i	−0.107262	−	0.185783i
$105$	−0.0375088	+	0.784288i	−0.00366048	+	0.0765387i
$106$	2.23180	+	3.86558i	0.216771	+	0.375459i
$107$	−1.36568	+	0.788474i	−0.132025	+	0.0762247i	−0.564558	−	0.825394i	$-0.690953\pi$
$107$	−1.36568	+	0.788474i	−0.132025	+	0.0762247i	0.432533	+	0.901618i	$0.357620\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	5.10648	−	8.84469i	0.489112	−	0.847167i	−0.510809	−	0.859694i	$-0.670654\pi$
$109$	5.10648	−	8.84469i	0.489112	−	0.847167i	0.999922	+	0.0125267i	$0.00398747\pi$
$110$	−2.31602	−	0.110764i	−0.220824	−	0.0105610i
$111$	−3.87306	+	4.69035i	−0.367615	+	0.445188i
$112$			0.351145i			0.0331801i
$113$	−2.52503	−	1.45783i	−0.237535	−	0.137141i	0.376508	−	0.926413i	$-0.377125\pi$
$113$	−2.52503	−	1.45783i	−0.237535	−	0.137141i	−0.614043	+	0.789272i	$0.710458\pi$
$114$	−4.10098	−	7.10310i	−0.384092	−	0.665267i
$115$	−4.34189	−	8.42600i	−0.404883	−	0.785729i
$116$	1.60026	+	2.77173i	0.148580	+	0.257349i
$117$			2.18772i			0.202255i
$118$	−9.52022	+	5.49650i	−0.876407	+	0.505994i
$119$	1.80588			0.165545
$120$	−1.88087	−	1.20927i	−0.171699	−	0.110390i
$121$	−9.92476			−0.902251
$122$			2.30120i			0.208340i
$123$	−9.63687	−	5.56385i	−0.868927	−	0.501675i
$124$	0.0743676	+	0.128809i	0.00667841	+	0.0115673i
$125$	1.59740	−	11.0656i	0.142876	−	0.989741i
$126$	0.175573	−	0.304101i	0.0156413	−	0.0270915i
$127$	−12.4109	−	7.16541i	−1.10129	−	0.635828i	−0.164727	−	0.986339i	$-0.552674\pi$
$127$	−12.4109	−	7.16541i	−1.10129	−	0.635828i	−0.936558	+	0.350511i	$0.886008\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.17160	+	5.49337i	0.279244	+	0.483664i
$130$	−4.34852	+	2.24078i	−0.381390	+	0.196529i
$131$	−4.64477	+	8.04498i	−0.405816	+	0.702893i	−0.994416	−	0.105531i	$-0.966346\pi$
$131$	−4.64477	+	8.04498i	−0.405816	+	0.702893i	0.588600	+	0.808424i	$0.299679\pi$
$132$	0.898016	+	0.518470i	0.0781623	+	0.0451270i
$133$	2.49422	+	1.44004i	0.216276	+	0.124867i
$134$	−14.3471			−1.23940
$135$	1.02425	+	1.98769i	0.0881534	+	0.171073i
$136$	−2.57142	+	4.45383i	−0.220498	+	0.381913i
$137$			3.80455i			0.325045i	0.986705	+	0.162522i	$0.0519630\pi$
$137$			3.80455i			0.325045i	−0.986705	+	0.162522i	$0.948037\pi$
$138$			4.23909i			0.360855i
$139$	7.47368	−	12.9448i	0.633909	−	1.09796i	−0.352836	−	0.935685i	$-0.614783\pi$
$139$	7.47368	−	12.9448i	0.633909	−	1.09796i	0.986745	−	0.162278i	$-0.0518841\pi$
$140$	0.784288	+	0.0375088i	0.0662845	+	0.00317007i
$141$	4.48232	+	7.76360i	0.377479	+	0.653813i
$142$		−	10.7063i		−	0.898450i
$143$	1.96461	−	1.13427i	0.164289	−	0.0948524i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	6.36164	−	3.27813i	0.528306	−	0.272234i
$146$	4.26135	−	7.38088i	0.352672	−	0.610846i
$147$		−	6.87670i		−	0.567180i
$148$	4.69035	+	3.87306i	0.385544	+	0.318364i
$149$	21.2248			1.73880			0.869401	−	0.494107i	$-0.164505\pi$
$149$	21.2248			1.73880			0.869401	+	0.494107i	$0.164505\pi$
$150$	−2.90182	+	4.07178i	−0.236933	+	0.332460i
$151$	−10.9668	−	18.9951i	−0.892469	−	1.54580i	−0.836906	−	0.547346i	$-0.815638\pi$
$151$	−10.9668	−	18.9951i	−0.892469	−	1.54580i	−0.0555624	−	0.998455i	$-0.517695\pi$
$152$	−7.10310	+	4.10098i	−0.576138	+	0.332633i
$153$	4.45383	−	2.57142i	0.360071	−	0.207887i
$154$	−0.364117			−0.0293414
$155$	0.295640	−	0.152342i	0.0237463	−	0.0122364i
$156$	2.18772			0.175158
$157$	−17.8306	−	10.2945i	−1.42304	−	0.821590i	−0.426478	−	0.904498i	$-0.640246\pi$
$157$	−17.8306	−	10.2945i	−1.42304	−	0.821590i	−0.996557	+	0.0829079i	$0.973579\pi$
$158$			9.44979i			0.751785i
$159$	−4.46359			−0.353986
$160$	−1.20927	+	1.88087i	−0.0956008	+	0.148696i
$161$	−0.744269	−	1.28911i	−0.0586566	−	0.101596i
$162$		−	1.00000i		−	0.0785674i
$163$	−4.52748	−	2.61394i	−0.354620	−	0.204740i	0.312098	−	0.950050i	$-0.398968\pi$
$163$	−4.52748	−	2.61394i	−0.354620	−	0.204740i	−0.666718	+	0.745310i	$0.732301\pi$
$164$	−5.56385	+	9.63687i	−0.434463	+	0.752513i
$165$	1.25394	−	1.95035i	0.0976187	−	0.151835i
$166$	2.19708	+	3.80546i	0.170527	+	0.295361i
$167$	−6.62307	+	3.82383i	−0.512509	+	0.295897i	−0.733864	−	0.679296i	$-0.762285\pi$
$167$	−6.62307	+	3.82383i	−0.512509	+	0.295897i	0.221356	+	0.975193i	$0.428952\pi$
$168$	−0.304101	−	0.175573i	−0.0234619	−	0.0135457i
$169$	−4.10693	+	7.11341i	−0.315918	+	0.547185i
$170$	9.67302	+	6.21906i	0.741887	+	0.476980i
$171$	8.20196			0.627219
$172$	5.49337	−	3.17160i	0.418865	−	0.241832i
$173$	8.50015	+	4.90756i	0.646254	+	0.373115i	0.787020	−	0.616928i	$-0.211623\pi$
$173$	8.50015	+	4.90756i	0.646254	+	0.373115i	−0.140765	+	0.990043i	$0.544956\pi$
$174$	−3.20052			−0.242631
$175$	0.167553	−	1.74771i	0.0126658	−	0.132115i
$176$	0.518470	−	0.898016i	0.0390811	−	0.0676905i
$177$		−	10.9930i		−	0.826285i
$178$	3.65351	−	2.10936i	0.273842	−	0.158103i
$179$	5.67181			0.423931			0.211966	−	0.977277i	$-0.432014\pi$
$179$	5.67181			0.423931			0.211966	+	0.977277i	$0.432014\pi$
$180$	1.98769	−	1.02425i	0.148154	−	0.0763431i
$181$	−8.40034	−	14.5498i	−0.624392	−	1.08148i	−0.988658	−	0.150184i	$-0.952013\pi$
$181$	−8.40034	−	14.5498i	−0.624392	−	1.08148i	0.364266	−	0.931295i	$-0.381320\pi$
$182$	−0.665289	+	0.384105i	−0.0493145	+	0.0284717i
$183$	−1.99289	−	1.15060i	−0.147319	−	0.0850546i
$184$	4.23909			0.312510
$185$	9.15156	−	10.0623i	0.672836	−	0.739792i
$186$	−0.148735			−0.0109058
$187$	−4.61835	−	2.66641i	−0.337728	−	0.194987i
$188$	7.76360	−	4.48232i	0.566219	−	0.326906i
$189$	0.175573	+	0.304101i	0.0127710	+	0.0221201i
$190$	8.40086	+	16.3029i	0.609462	+	1.18274i
$191$	−2.86947			−0.207628			−0.103814	−	0.994597i	$-0.533105\pi$
$191$	−2.86947			−0.207628			−0.103814	+	0.994597i	$0.533105\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	13.0276i		−	0.937746i	−0.883266	−	0.468873i	$-0.844660\pi$
$193$		−	13.0276i		−	0.937746i	0.883266	−	0.468873i	$-0.155340\pi$
$194$	7.74275	−	13.4108i	0.555897	−	0.962842i
$195$	0.233689	−	4.88632i	0.0167348	−	0.349916i
$196$	−6.87670			−0.491193
$197$	−1.19533	−	0.690124i	−0.0851637	−	0.0491693i	0.456813	−	0.889563i	$-0.348991\pi$
$197$	−1.19533	−	0.690124i	−0.0851637	−	0.0491693i	−0.541977	+	0.840393i	$0.682324\pi$
$198$	−0.898016	+	0.518470i	−0.0638192	+	0.0368461i
$199$	−4.07318			−0.288740			−0.144370	−	0.989524i	$-0.546116\pi$
$199$	−4.07318			−0.288740			−0.144370	+	0.989524i	$0.546116\pi$
$200$	4.07178	+	2.90182i	0.287919	+	0.205190i
$201$	7.17356	−	12.4250i	0.505984	−	0.876390i
$202$	−5.14164	−	2.96853i	−0.361764	−	0.208865i
$203$	0.973281	−	0.561924i	0.0683109	−	0.0394393i
$204$	−2.57142	−	4.45383i	−0.180035	−	0.311831i
$205$	20.9298	+	13.4563i	1.46180	+	0.939831i
$206$	−6.51086	+	11.2771i	−0.453633	+	0.785716i
$207$	−3.67116	−	2.11955i	−0.255163	−	0.147319i
$208$		−	2.18772i		−	0.151691i
$209$	−4.25247	−	7.36549i	−0.294149	−	0.509482i
$210$	−0.424628	+	0.660459i	−0.0293021	+	0.0455760i
$211$	−26.2931			−1.81009			−0.905046	−	0.425315i	$-0.860163\pi$
$211$	−26.2931			−1.81009			−0.905046	+	0.425315i	$0.860163\pi$
$212$			4.46359i			0.306561i
$213$	9.27190	+	5.35314i	0.635300	+	0.366791i
$214$	−1.57695			−0.107798
$215$	−6.49702	−	12.6083i	−0.443093	−	0.859879i
$216$	−1.00000			−0.0680414
$217$	0.0452305	−	0.0261138i	0.00307045	−	0.00177272i
$218$	8.84469	−	5.10648i	0.599038	−	0.345855i
$219$	4.26135	+	7.38088i	0.287956	+	0.498754i
$220$	−1.95035	−	1.25394i	−0.131493	−	0.0845403i
$221$	−11.2511			−0.756832
$222$	−5.69935	+	2.12543i	−0.382515	+	0.142650i
$223$		−	7.74058i		−	0.518348i	−0.965831	−	0.259174i	$-0.916550\pi$
$223$		−	7.74058i		−	0.518348i	0.965831	−	0.259174i	$-0.0834503\pi$
$224$	−0.175573	+	0.304101i	−0.0117309	+	0.0203186i
$225$	−2.07536	−	4.54894i	−0.138357	−	0.303263i
$226$	−1.45783	−	2.52503i	−0.0969732	−	0.167962i
$227$	7.11370	−	4.10709i	0.472153	−	0.272597i	−0.244988	−	0.969526i	$-0.578784\pi$
$227$	7.11370	−	4.10709i	0.472153	−	0.272597i	0.717140	+	0.696929i	$0.245451\pi$
$228$		−	8.20196i		−	0.543188i
$229$	−7.53968	−	13.0591i	−0.498236	−	0.862970i	0.501762	−	0.865006i	$-0.332685\pi$
$229$	−7.53968	−	13.0591i	−0.498236	−	0.862970i	−0.999998	+	0.00203575i	$0.999352\pi$
$230$	0.452813	−	9.46807i	0.0298576	−	0.624306i
$231$	0.182058	−	0.315334i	0.0119786	−	0.0207475i
$232$			3.20052i			0.210125i
$233$			5.64661i			0.369922i	0.982746	+	0.184961i	$0.0592159\pi$
$233$			5.64661i			0.369922i	−0.982746	+	0.184961i	$0.940784\pi$
$234$	−1.09386	+	1.89463i	−0.0715080	+	0.123856i
$235$	−9.18202	−	17.8189i	−0.598969	−	1.16238i
$236$	−10.9930			−0.715584
$237$	−8.18375	−	4.72489i	−0.531592	−	0.306915i
$238$	1.56394	+	0.902942i	0.101375	+	0.0585291i
$239$	−5.72492	+	9.91584i	−0.370314	+	0.641403i	−0.989614	−	0.143752i	$-0.954083\pi$
$239$	−5.72492	+	9.91584i	−0.370314	+	0.641403i	0.619300	+	0.785155i	$0.287417\pi$
$240$	−1.02425	−	1.98769i	−0.0661151	−	0.128305i
$241$	−2.07844	−	3.59997i	−0.133884	−	0.231894i	0.791286	−	0.611446i	$-0.209412\pi$
$241$	−2.07844	−	3.59997i	−0.133884	−	0.231894i	−0.925171	+	0.379551i	$0.876078\pi$
$242$	−8.59509	−	4.96238i	−0.552513	−	0.318994i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.15060	+	1.99289i	−0.0736595	+	0.127582i
$245$	−0.734558	+	15.3592i	−0.0469292	+	0.981264i
$246$	−5.56385	−	9.63687i	−0.354738	−	0.614424i
$247$	−15.5396	−	8.97181i	−0.988763	−	0.570863i
$248$			0.148735i			0.00944470i
$249$	−4.39417			−0.278469
$250$	6.91621	−	8.78442i	0.437419	−	0.555576i
$251$	24.8423			1.56803			0.784016	−	0.620740i	$-0.213168\pi$
$251$	24.8423			1.56803			0.784016	+	0.620740i	$0.213168\pi$
$252$	0.304101	−	0.175573i	0.0191565	−	0.0110600i
$253$			4.39568i			0.276354i
$254$	−7.16541	−	12.4109i	−0.449598	−	0.778727i
$255$	−10.2224	+	5.26756i	−0.640150	+	0.329867i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.62690	+	2.09399i	0.226240	+	0.130620i	0.608836	−	0.793296i	$-0.291637\pi$
$257$	3.62690	+	2.09399i	0.226240	+	0.130620i	−0.382596	+	0.923916i	$0.624970\pi$
$258$			6.34319i			0.394910i
$259$	1.36001	−	1.64699i	0.0845068	−	0.102339i
$260$	−4.88632	−	0.233689i	−0.303036	−	0.0144928i
$261$	1.60026	−	2.77173i	0.0990536	−	0.171566i
$262$	−8.04498	+	4.64477i	−0.497021	+	0.286955i
$263$	5.44423	−	3.14323i	0.335706	−	0.193820i	−0.322666	−	0.946513i	$-0.604579\pi$
$263$	5.44423	−	3.14323i	0.335706	−	0.193820i	0.658371	+	0.752693i	$0.271246\pi$
$264$	0.518470	+	0.898016i	0.0319096	+	0.0552691i
$265$	9.96950	+	0.476794i	0.612421	+	0.0292892i
$266$	1.44004	+	2.49422i	0.0882945	+	0.152931i
$267$			4.21871i			0.258181i
$268$	−12.4250	−	7.17356i	−0.758976	−	0.438195i
$269$	−25.1995			−1.53644			−0.768220	−	0.640186i	$-0.778857\pi$
$269$	−25.1995			−1.53644			−0.768220	+	0.640186i	$0.778857\pi$
$270$	−0.106818	+	2.23352i	−0.00650076	+	0.135927i
$271$	9.81317	−	16.9969i	0.596108	−	1.03249i	−0.397282	−	0.917697i	$-0.630047\pi$
$271$	9.81317	−	16.9969i	0.596108	−	1.03249i	0.993390	−	0.114792i	$-0.0366201\pi$
$272$	−4.45383	+	2.57142i	−0.270053	+	0.155915i
$273$		−	0.768209i		−	0.0464941i
$274$	−1.90228	+	3.29484i	−0.114921	+	0.199049i
$275$	−3.00902	+	4.22219i	−0.181451	+	0.254608i
$276$	−2.11955	+	3.67116i	−0.127582	+	0.220978i
$277$	8.48886	−	4.90105i	0.510046	−	0.294475i	−0.222807	−	0.974863i	$-0.571522\pi$
$277$	8.48886	−	4.90105i	0.510046	−	0.294475i	0.732853	+	0.680387i	$0.238188\pi$
$278$	12.9448	−	7.47368i	0.776377	−	0.448242i
$279$	0.0743676	−	0.128809i	0.00445227	−	0.00771156i
$280$	0.660459	+	0.424628i	0.0394700	+	0.0253764i
$281$	6.23548	−	10.8002i	0.371978	−	0.644285i	−0.617892	−	0.786263i	$-0.712013\pi$
$281$	6.23548	−	10.8002i	0.371978	−	0.644285i	0.989870	+	0.141979i	$0.0453464\pi$
$282$			8.96463i			0.533836i
$283$	5.25871	−	3.03612i	0.312598	−	0.180479i	−0.335490	−	0.942044i	$-0.608902\pi$
$283$	5.25871	−	3.03612i	0.312598	−	0.180479i	0.648088	+	0.761565i	$0.275569\pi$
$284$	5.35314	−	9.27190i	0.317650	−	0.550186i
$285$	−18.3192	−	0.876120i	−1.08514	−	0.0518969i
$286$	2.26854			0.134142
$287$	3.38394	+	1.95372i	0.199748	+	0.115324i
$288$			1.00000i			0.0589256i
$289$	4.72441	+	8.18292i	0.277906	+	0.481348i
$290$	7.14841	+	0.341875i	0.419769	+	0.0200756i
$291$	7.74275	+	13.4108i	0.453888	+	0.786157i
$292$	7.38088	−	4.26135i	0.431933	−	0.249377i
$293$	11.4814	−	6.62880i	0.670751	−	0.387258i	−0.125610	−	0.992080i	$-0.540089\pi$
$293$	11.4814	−	6.62880i	0.670751	−	0.387258i	0.796361	+	0.604821i	$0.206755\pi$
$294$	3.43835	−	5.95539i	0.200529	−	0.347326i
$295$	−1.17426	+	24.5530i	−0.0683678	+	1.42953i
$296$	2.12543	+	5.69935i	0.123538	+	0.331268i
$297$		−	1.03694i		−	0.0601694i
$298$	18.3812	+	10.6124i	1.06479	+	0.614759i
$299$	4.63698	+	8.03149i	0.268164	+	0.464473i
$300$	−4.54894	+	2.07536i	−0.262633	+	0.119821i
$301$	−1.11369	−	1.92897i	−0.0641921	−	0.111184i
$302$		−	21.9337i		−	1.26214i
$303$	5.14164	−	2.96853i	0.295379	−	0.170537i
$304$	−8.20196			−0.470415
$305$	4.32825	+	2.78275i	0.247835	+	0.159340i
$306$	5.14284			0.293997
$307$			24.4956i			1.39804i	0.715104	+	0.699018i	$0.246379\pi$
$307$			24.4956i			1.39804i	−0.715104	+	0.699018i	$0.753621\pi$
$308$	−0.315334	−	0.182058i	−0.0179678	−	0.0103737i
$309$	−6.51086	−	11.2771i	−0.370390	−	0.641534i
$310$	0.332202	+	0.0158877i	0.0188678	+	0.000902359i
$311$	12.5340	−	21.7096i	0.710740	−	1.23104i	−0.253840	−	0.967246i	$-0.581694\pi$
$311$	12.5340	−	21.7096i	0.710740	−	1.23104i	0.964580	−	0.263791i	$-0.0849730\pi$
$312$	1.89463	+	1.09386i	0.107262	+	0.0619278i
$313$	27.0113	+	15.5950i	1.52677	+	0.881482i	0.999495	+	0.0317875i	$0.0101200\pi$
$313$	27.0113	+	15.5950i	1.52677	+	0.881482i	0.527276	+	0.849694i	$0.323213\pi$
$314$	−10.2945	−	17.8306i	−0.580952	−	1.00624i
$315$	−0.359661	−	0.697968i	−0.0202646	−	0.0393260i
$316$	−4.72489	+	8.18375i	−0.265796	+	0.460372i
$317$	3.95290	+	2.28221i	0.222017	+	0.128182i	0.606884	−	0.794790i	$-0.292419\pi$
$317$	3.95290	+	2.28221i	0.222017	+	0.128182i	−0.384867	+	0.922972i	$0.625753\pi$
$318$	−3.86558	−	2.23180i	−0.216771	−	0.125153i
$319$	−3.31875			−0.185814
$320$	−1.98769	+	1.02425i	−0.111115	+	0.0572573i
$321$	0.788474	−	1.36568i	0.0440083	−	0.0762247i
$322$		−	1.48854i		−	0.0829529i
$323$			42.1814i			2.34703i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−1.04390	+	10.8887i	−0.0579050	+	0.603996i
$326$	−2.61394	−	4.52748i	−0.144773	−	0.250754i
$327$			10.2130i			0.564778i
$328$	−9.63687	+	5.56385i	−0.532107	+	0.307212i
$329$	−1.57394	−	2.72615i	−0.0867743	−	0.150298i
$330$	2.06111	−	1.06209i	0.113461	−	0.0584659i
$331$	−6.08628	+	10.5418i	−0.334532	+	0.579427i	−0.983395	−	0.181479i	$-0.941912\pi$
$331$	−6.08628	+	10.5418i	−0.334532	+	0.579427i	0.648863	+	0.760906i	$0.275245\pi$
$332$			4.39417i			0.241161i
$333$	1.00900	−	5.99849i	0.0552926	−	0.328715i
$334$	−7.64767			−0.418462
$335$	−17.3495	+	26.9851i	−0.947903	+	1.47435i
$336$	−0.175573	−	0.304101i	−0.00957827	−	0.0165901i
$337$	−25.8863	+	14.9455i	−1.41012	+	0.814131i	−0.995399	−	0.0958189i	$-0.969453\pi$
$337$	−25.8863	+	14.9455i	−1.41012	+	0.814131i	−0.414718	+	0.909950i	$0.636120\pi$
$338$	−7.11341	+	4.10693i	−0.386919	+	0.223388i
$339$	2.91565			0.158356
$340$	5.26756	+	10.2224i	0.285673	+	0.554386i
$341$	−0.154229			−0.00835200
$342$	7.10310	+	4.10098i	0.384092	+	0.221756i
$343$			4.87274i			0.263103i
$344$	6.34319			0.342002
$345$	7.97319	+	5.12618i	0.429262	+	0.275985i
$346$	4.90756	+	8.50015i	0.263832	+	0.456971i
$347$			9.15356i			0.491389i	0.969347	+	0.245695i	$0.0790160\pi$
$347$			9.15356i			0.491389i	−0.969347	+	0.245695i	$0.920984\pi$
$348$	−2.77173	−	1.60026i	−0.148580	−	0.0857830i
$349$	7.08124	−	12.2651i	0.379050	−	0.656534i	−0.611874	−	0.790955i	$-0.709584\pi$
$349$	7.08124	−	12.2651i	0.379050	−	0.656534i	0.990924	+	0.134421i	$0.0429175\pi$
$350$	1.01896	−	1.42979i	0.0544658	−	0.0764254i
$351$	−1.09386	−	1.89463i	−0.0583861	−	0.101128i
$352$	0.898016	−	0.518470i	0.0478644	−	0.0276345i
$353$	−22.9078	−	13.2258i	−1.21926	−	0.703939i	−0.254499	−	0.967073i	$-0.581910\pi$
$353$	−22.9078	−	13.2258i	−1.21926	−	0.703939i	−0.964759	+	0.263134i	$0.915244\pi$
$354$	5.49650	−	9.52022i	0.292136	−	0.505994i
$355$	−20.1371	−	12.9467i	−1.06877	−	0.687141i
$356$	4.21871			0.223591
$357$	−1.56394	+	0.902942i	−0.0827726	+	0.0477888i
$358$	4.91193	+	2.83591i	0.259604	+	0.149882i
$359$	−5.09170			−0.268729			−0.134365	−	0.990932i	$-0.542899\pi$
$359$	−5.09170			−0.268729			−0.134365	+	0.990932i	$0.542899\pi$
$360$	2.23352	+	0.106818i	0.117717	+	0.00562982i
$361$	−24.1361	+	41.8049i	−1.27032	+	2.20026i
$362$		−	16.8007i		−	0.883024i
$363$	8.59509	−	4.96238i	0.451125	−	0.260457i
$364$	−0.768209			−0.0402651
$365$	−8.72938	−	16.9405i	−0.456917	−	0.886706i
$366$	−1.15060	−	1.99289i	−0.0601427	−	0.104170i
$367$	8.68282	−	5.01303i	0.453239	−	0.261678i	−0.255958	−	0.966688i	$-0.582391\pi$
$367$	8.68282	−	5.01303i	0.453239	−	0.261678i	0.709197	+	0.705010i	$0.249058\pi$
$368$	3.67116	+	2.11955i	0.191372	+	0.110489i
$369$	11.1277			0.579285
$370$	12.9566	−	4.13839i	0.673582	−	0.215145i
$371$	1.56737			0.0813738
$372$	−0.128809	−	0.0743676i	−0.00667841	−	0.00385578i
$373$	26.2347	−	15.1466i	1.35838	−	0.784262i	0.368976	−	0.929439i	$-0.379708\pi$
$373$	26.2347	−	15.1466i	1.35838	−	0.784262i	0.989406	+	0.145176i	$0.0463750\pi$
$374$	−2.66641	−	4.61835i	−0.137877	−	0.238809i
$375$	4.14943	+	10.3818i	0.214276	+	0.536115i
$376$	8.96463			0.462316
$377$	−6.06379	+	3.50093i	−0.312301	+	0.180307i
$378$			0.351145i			0.0180610i
$379$	0.592452	−	1.02616i	0.0304322	−	0.0527101i	−0.850408	−	0.526123i	$-0.823645\pi$
$379$	0.592452	−	1.02616i	0.0304322	−	0.0527101i	0.880840	+	0.473413i	$0.156978\pi$
$380$	−0.876120	+	18.3192i	−0.0449440	+	0.939755i
$381$	14.3308			0.734191
$382$	−2.48504	−	1.43474i	−0.127146	−	0.0734075i
$383$	−27.4338	+	15.8389i	−1.40180	+	0.809332i	−0.994578	−	0.103996i	$-0.966837\pi$
$383$	−27.4338	+	15.8389i	−1.40180	+	0.809332i	−0.407226	+	0.913327i	$0.633504\pi$
$384$	1.00000			0.0510310
$385$	−0.440313	+	0.684857i	−0.0224405	+	0.0349035i
$386$	6.51379	−	11.2822i	0.331543	−	0.574250i
$387$	−5.49337	−	3.17160i	−0.279244	−	0.161221i
$388$	13.4108	−	7.74275i	0.680832	−	0.393078i
$389$	8.19649	+	14.1967i	0.415578	+	0.719803i	0.995489	−	0.0948773i	$-0.0302459\pi$
$389$	8.19649	+	14.1967i	0.415578	+	0.719803i	−0.579911	+	0.814680i	$0.696913\pi$
$390$	2.64554	−	4.11483i	0.133962	−	0.208362i
$391$	10.9005	−	18.8802i	0.551261	−	0.954813i
$392$	−5.95539	−	3.43835i	−0.300793	−	0.173663i
$393$		−	9.28954i		−	0.468595i
$394$	−0.690124	−	1.19533i	−0.0347679	−	0.0602198i
$395$	17.7738	+	11.4273i	0.894299	+	0.574970i
$396$	−1.03694			−0.0521082
$397$		−	4.91832i		−	0.246843i	−0.992354	−	0.123422i	$-0.960613\pi$
$397$		−	4.91832i		−	0.246843i	0.992354	−	0.123422i	$-0.0393868\pi$
$398$	−3.52748	−	2.03659i	−0.176816	−	0.102085i
$399$	−2.88008			−0.144184
$400$	2.07536	+	4.54894i	0.103768	+	0.227447i
$401$	30.0213			1.49919			0.749596	−	0.661896i	$-0.230248\pi$
$401$	30.0213			1.49919			0.749596	+	0.661896i	$0.230248\pi$
$402$	12.4250	−	7.17356i	0.619701	−	0.357785i
$403$	−0.281798	+	0.162696i	−0.0140373	+	0.00810446i
$404$	−2.96853	−	5.14164i	−0.147690	−	0.255806i
$405$	−1.88087	−	1.20927i	−0.0934613	−	0.0600889i
$406$	1.12385			0.0557756
$407$	−5.90988	+	2.20394i	−0.292942	+	0.109245i
$408$		−	5.14284i		−	0.254609i
$409$	−14.8741	+	25.7626i	−0.735475	+	1.27388i	0.219040	+	0.975716i	$0.429707\pi$
$409$	−14.8741	+	25.7626i	−0.735475	+	1.27388i	−0.954515	+	0.298164i	$0.903626\pi$
$410$	11.3975	+	22.1184i	0.562885	+	1.09235i
$411$	−1.90228	−	3.29484i	−0.0938324	−	0.162522i
$412$	−11.2771	+	6.51086i	−0.555585	+	0.320767i
$413$			3.86014i			0.189945i
$414$	−2.11955	−	3.67116i	−0.104170	−	0.180428i
$415$	9.81444	+	0.469378i	0.481772	+	0.0230409i
$416$	1.09386	−	1.89463i	0.0536310	−	0.0928916i
$417$			14.9474i			0.731976i
$418$		−	8.50494i		−	0.415990i
$419$	12.3182	−	21.3357i	0.601782	−	1.04232i	−0.390769	−	0.920489i	$-0.627791\pi$
$419$	12.3182	−	21.3357i	0.601782	−	1.04232i	0.992551	−	0.121829i	$-0.0388758\pi$
$420$	−0.697968	+	0.359661i	−0.0340574	+	0.0175496i
$421$	−39.3615			−1.91836			−0.959182	−	0.282790i	$-0.908740\pi$
$421$	−39.3615			−1.91836			−0.959182	+	0.282790i	$0.908740\pi$
$422$	−22.7705	−	13.1465i	−1.10845	−	0.639964i
$423$	−7.76360	−	4.48232i	−0.377479	−	0.217938i
$424$	−2.23180	+	3.86558i	−0.108386	+	0.187729i
$425$	23.3945	−	10.6732i	1.13480	−	0.517728i
$426$	5.35314	+	9.27190i	0.259360	+	0.449225i
$427$	0.699795	+	0.404027i	0.0338655	+	0.0195522i
$428$	−1.36568	−	0.788474i	−0.0660125	−	0.0381123i
$429$	−1.13427	+	1.96461i	−0.0547630	+	0.0948524i
$430$	0.677570	−	14.1676i	0.0326753	−	0.683223i
$431$	5.50220	+	9.53008i	0.265032	+	0.459048i	0.967572	−	0.252596i	$-0.0812843\pi$
$431$	5.50220	+	9.53008i	0.265032	+	0.459048i	−0.702540	+	0.711644i	$0.747951\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	16.8494i		−	0.809731i	−0.914376	−	0.404865i	$-0.867318\pi$
$433$		−	16.8494i		−	0.809731i	0.914376	−	0.404865i	$-0.132682\pi$
$434$	0.0522277			0.00250701
$435$	−3.87028	+	6.01977i	−0.185566	+	0.288626i
$436$	10.2130			0.489112
$437$	30.1107	−	17.3844i	1.44039	−	0.831610i
$438$			8.52271i			0.407231i
$439$	1.92873	+	3.34066i	0.0920534	+	0.159441i	0.908375	−	0.418156i	$-0.137324\pi$
$439$	1.92873	+	3.34066i	0.0920534	+	0.159441i	−0.816322	+	0.577598i	$0.803990\pi$
$440$	−1.06209	−	2.06111i	−0.0506330	−	0.0982598i
$441$	3.43835	+	5.95539i	0.163731	+	0.283590i
$442$	−9.74376	−	5.62556i	−0.463463	−	0.267581i
$443$			18.7295i			0.889866i	0.895564	+	0.444933i	$0.146772\pi$
$443$			18.7295i			0.889866i	−0.895564	+	0.444933i	$0.853228\pi$
$444$	−5.99849	−	1.00900i	−0.284676	−	0.0478848i
$445$	0.450636	−	9.42256i	0.0213622	−	0.446672i
$446$	3.87029	−	6.70354i	0.183264	−	0.317422i
$447$	−18.3812	+	10.6124i	−0.869401	+	0.501949i
$448$	−0.304101	+	0.175573i	−0.0143674	+	0.00829503i
$449$	13.7190	+	23.7620i	0.647439	+	1.12140i	0.983732	+	0.179640i	$0.0574933\pi$
$449$	13.7190	+	23.7620i	0.647439	+	1.12140i	−0.336293	+	0.941757i	$0.609173\pi$
$450$	0.477161	−	4.97718i	0.0224936	−	0.234626i
$451$	−5.76937	−	9.99285i	−0.271669	−	0.470545i
$452$		−	2.91565i		−	0.137141i
$453$	18.9951	+	10.9668i	0.892469	+	0.515267i
$454$	8.21419			0.385511
$455$	−0.0820589	+	1.71581i	−0.00384698	+	0.0804383i
$456$	4.10098	−	7.10310i	0.192046	−	0.332633i
$457$	−8.23909	+	4.75684i	−0.385408	+	0.222516i	−0.680169	−	0.733056i	$-0.738094\pi$
$457$	−8.23909	+	4.75684i	−0.385408	+	0.222516i	0.294760	+	0.955571i	$0.404760\pi$
$458$		−	15.0794i		−	0.704612i
$459$	−2.57142	+	4.45383i	−0.120024	+	0.207887i
$460$	5.12618	−	7.97319i	0.239010	−	0.371752i
$461$	−12.8493	+	22.2556i	−0.598451	+	1.03655i	0.394599	+	0.918854i	$0.370884\pi$
$461$	−12.8493	+	22.2556i	−0.598451	+	1.03655i	−0.993050	+	0.117694i	$0.962450\pi$
$462$	0.315334	−	0.182058i	0.0146707	−	0.00847012i
$463$	−22.2273	+	12.8330i	−1.03299	+	0.596398i	−0.917840	−	0.396950i	$-0.870069\pi$
$463$	−22.2273	+	12.8330i	−1.03299	+	0.596398i	−0.115151	+	0.993348i	$0.536735\pi$
$464$	−1.60026	+	2.77173i	−0.0742902	+	0.128674i
$465$	−0.179860	+	0.279752i	−0.00834082	+	0.0129732i
$466$	−2.82331	+	4.89011i	−0.130787	+	0.226530i
$467$		−	38.2172i		−	1.76848i	−0.467031	−	0.884241i	$-0.654676\pi$
$467$		−	38.2172i		−	1.76848i	0.467031	−	0.884241i	$-0.345324\pi$
$468$	−1.89463	+	1.09386i	−0.0875791	+	0.0505638i
$469$	−2.51896	+	4.36297i	−0.116315	+	0.201463i
$470$	0.957588	−	20.0226i	0.0441702	−	0.923575i
$471$	20.5890			0.948690
$472$	−9.52022	−	5.49650i	−0.438204	−	0.252997i
$473$			6.57751i			0.302434i
$474$	−4.72489	−	8.18375i	−0.217022	−	0.375892i
$475$	40.8226	+	3.91365i	1.87307	+	0.179571i
$476$	0.902942	+	1.56394i	0.0413863	+	0.0716832i
$477$	3.86558	−	2.23180i	0.176993	−	0.102187i
$478$	−9.91584	+	5.72492i	−0.453540	+	0.261852i
$479$	−6.20726	+	10.7513i	−0.283617	+	0.491239i	−0.972273	−	0.233850i	$-0.924868\pi$
$479$	−6.20726	+	10.7513i	−0.283617	+	0.491239i	0.688656	+	0.725088i	$0.258201\pi$
$480$	0.106818	−	2.23352i	0.00487557	−	0.101946i
$481$	−8.47319	+	10.2612i	−0.386344	+	0.467870i
$482$		−	4.15689i		−	0.189341i
$483$	1.28911	+	0.744269i	0.0586566	+	0.0338654i
$484$	−4.96238	−	8.59509i	−0.225563	−	0.390686i
$485$	−15.8610	−	30.7804i	−0.720212	−	1.39766i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$			12.0323i			0.545236i	0.962122	+	0.272618i	$0.0878895\pi$
$487$			12.0323i			0.545236i	−0.962122	+	0.272618i	$0.912110\pi$
$488$	−1.99289	+	1.15060i	−0.0902141	+	0.0520851i
$489$	5.22788			0.236413
$490$	−8.31575	+	12.9342i	−0.375667	+	0.584307i
$491$	5.77157			0.260467			0.130234	−	0.991483i	$-0.458427\pi$
$491$	5.77157			0.260467			0.130234	+	0.991483i	$0.458427\pi$
$492$		−	11.1277i		−	0.501675i
$493$	14.2546	+	8.22989i	0.641994	+	0.370655i
$494$	−8.97181	−	15.5396i	−0.403661	−	0.699161i
$495$	−0.110764	+	2.31602i	−0.00497848	+	0.104097i
$496$	−0.0743676	+	0.128809i	−0.00333920	+	0.00578367i
$497$	−3.25579	−	1.87973i	−0.146042	−	0.0843174i
$498$	−3.80546	−	2.19708i	−0.170527	−	0.0984537i
$499$	2.36226	+	4.09155i	0.105749	+	0.183163i	0.914044	−	0.405615i	$-0.132943\pi$
$499$	2.36226	+	4.09155i	0.105749	+	0.183163i	−0.808295	+	0.588778i	$0.799609\pi$
$500$	10.3818	−	4.14943i	0.464289	−	0.185568i
$501$	3.82383	−	6.62307i	0.170836	−	0.295897i
$502$	21.5141	+	12.4212i	0.960220	+	0.554383i
$503$	−34.0945	−	19.6845i	−1.52020	−	0.877686i	−0.999716	−	0.0238131i	$-0.992419\pi$
$503$	−34.0945	−	19.6845i	−1.52020	−	0.877686i	−0.520481	−	0.853873i	$-0.674247\pi$
$504$	0.351145			0.0156413
$505$	−11.8010	+	6.08103i	−0.525138	+	0.270602i
$506$	−2.19784	+	3.80677i	−0.0977060	+	0.169232i
$507$		−	8.21386i		−	0.364790i
$508$		−	14.3308i		−	0.635828i
$509$	−3.14558	+	5.44830i	−0.139425	+	0.241492i	−0.927279	−	0.374370i	$-0.877859\pi$
$509$	−3.14558	+	5.44830i	−0.139425	+	0.241492i	0.787854	+	0.615862i	$0.211192\pi$
$510$	−11.4866	−	0.549350i	−0.508636	−	0.0243256i
$511$	−1.49635	−	2.59176i	−0.0661948	−	0.114653i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.10310	+	4.10098i	−0.313610	+	0.181063i
$514$	2.09399	+	3.62690i	0.0923621	+	0.159976i
$515$	13.3375	+	25.8831i	0.587720	+	1.14055i
$516$	−3.17160	+	5.49337i	−0.139622	+	0.241832i
$517$			9.29578i			0.408828i
$518$	2.00130	−	0.746335i	0.0879320	−	0.0327921i
$519$	−9.81513			−0.430836
$520$	−4.11483	−	2.64554i	−0.180447	−	0.116015i
$521$	5.15531	+	8.92926i	0.225858	+	0.391198i	0.956577	−	0.291481i	$-0.0941480\pi$
$521$	5.15531	+	8.92926i	0.225858	+	0.391198i	−0.730718	+	0.682679i	$0.760815\pi$
$522$	2.77173	−	1.60026i	0.121315	−	0.0700415i
$523$	−11.9515	+	6.90023i	−0.522605	+	0.301726i	−0.738000	−	0.674801i	$-0.764229\pi$
$523$	−11.9515	+	6.90023i	−0.522605	+	0.301726i	0.215395	+	0.976527i	$0.430896\pi$
$524$	−9.28954			−0.405816
$525$	0.728752	+	1.59734i	0.0318053	+	0.0697137i
$526$	6.28646			0.274103
$527$	0.662442	+	0.382461i	0.0288564	+	0.0166603i
$528$			1.03694i			0.0451270i
$529$	5.03010			0.218700
$530$	8.39544	+	5.39766i	0.364675	+	0.234460i
$531$	5.49650	+	9.52022i	0.238528	+	0.413142i
$532$			2.88008i			0.124867i
$533$	−21.0828	−	12.1722i	−0.913198	−	0.527235i
$534$	−2.10936	+	3.65351i	−0.0912808	+	0.158103i
$535$	−1.90695	+	2.96604i	−0.0824446	+	0.128233i
$536$	−7.17356	−	12.4250i	−0.309851	−	0.536677i
$537$	−4.91193	+	2.83591i	−0.211966	+	0.122378i
$538$	−21.8234	−	12.5997i	−0.940873	−	0.543214i
$539$	3.56536	−	6.17539i	0.153571	−	0.265993i
$540$	−1.20927	+	1.88087i	−0.0520385	+	0.0809398i
$541$	−31.7423			−1.36471			−0.682354	−	0.731022i	$-0.739044\pi$
$541$	−31.7423			−1.36471			−0.682354	+	0.731022i	$0.739044\pi$
$542$	16.9969	−	9.81317i	0.730080	−	0.421512i
$543$	14.5498	+	8.40034i	0.624392	+	0.360493i
$544$	−5.14284			−0.220498
$545$	1.09093	−	22.8108i	0.0467304	−	0.977108i
$546$	0.384105	−	0.665289i	0.0164382	−	0.0284717i
$547$		−	35.1291i		−	1.50201i	−0.660295	−	0.751007i	$-0.729569\pi$
$547$		−	35.1291i		−	1.50201i	0.660295	−	0.751007i	$-0.270431\pi$
$548$	−3.29484	+	1.90228i	−0.140749	+	0.0812612i
$549$	2.30120			0.0982126
$550$	−4.71698	+	2.15202i	−0.201133	+	0.0917624i
$551$	13.1253	+	22.7336i	0.559155	+	0.968485i
$552$	−3.67116	+	2.11955i	−0.156255	+	0.0902139i
$553$	2.87369	+	1.65912i	0.122202	+	0.0705531i
$554$	9.80209			0.416451
$555$	−2.89436	+	13.2899i	−0.122859	+	0.564127i
$556$	14.9474			0.633909
$557$	19.8368	+	11.4528i	0.840514	+	0.485271i	0.857439	−	0.514586i	$-0.172054\pi$
$557$	19.8368	+	11.4528i	0.840514	+	0.485271i	−0.0169250	+	0.999857i	$0.505388\pi$
$558$	0.128809	−	0.0743676i	0.00545290	−	0.00314823i
$559$	6.93858	+	12.0180i	0.293471	+	0.508306i
$560$	0.359661	+	0.697968i	0.0151984	+	0.0294945i
$561$	5.33282			0.225152
$562$	10.8002	−	6.23548i	0.455578	−	0.263028i
$563$		−	4.77144i		−	0.201092i	−0.994932	−	0.100546i	$-0.967941\pi$
$563$		−	4.77144i		−	0.201092i	0.994932	−	0.100546i	$-0.0320590\pi$
$564$	−4.48232	+	7.76360i	−0.188740	+	0.326906i
$565$	−6.51215	−	0.311445i	−0.273968	−	0.0131026i
$566$	6.07224			0.255235
$567$	−0.304101	−	0.175573i	−0.0127710	−	0.00737336i
$568$	9.27190	−	5.35314i	0.389040	−	0.224613i
$569$	−8.99096			−0.376920			−0.188460	−	0.982081i	$-0.560350\pi$
$569$	−8.99096			−0.376920			−0.188460	+	0.982081i	$0.560350\pi$
$570$	−15.4268	−	9.91834i	−0.646159	−	0.415434i
$571$	5.84667	−	10.1267i	0.244676	−	0.423791i	−0.717365	−	0.696698i	$-0.754652\pi$
$571$	5.84667	−	10.1267i	0.244676	−	0.423791i	0.962040	+	0.272907i	$0.0879852\pi$
$572$	1.96461	+	1.13427i	0.0821446	+	0.0474262i
$573$	2.48504	−	1.43474i	0.103814	−	0.0599370i
$574$	1.95372	+	3.38394i	0.0815467	+	0.141243i
$575$	−17.2607	−	12.3011i	−0.719819	−	0.512991i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−20.6234	−	11.9069i	−0.858564	−	0.495692i	0.00496739	−	0.999988i	$-0.498419\pi$
$577$	−20.6234	−	11.9069i	−0.858564	−	0.495692i	−0.863531	+	0.504296i	$0.831752\pi$
$578$			9.44882i			0.393019i
$579$	6.51379	+	11.2822i	0.270704	+	0.468873i
$580$	6.01977	+	3.87028i	0.249957	+	0.160705i
$581$	1.54299			0.0640141
$582$			15.4855i			0.641895i
$583$	−4.00838	−	2.31424i	−0.166010	−	0.0958459i
$584$	8.52271			0.352672
$585$	2.24078	+	4.34852i	0.0926447	+	0.179789i
$586$	13.2576			0.547666
$587$	−35.3186	+	20.3912i	−1.45776	+	0.841636i	−0.998901	−	0.0468745i	$-0.985074\pi$
$587$	−35.3186	+	20.3912i	−1.45776	+	0.841636i	−0.458856	+	0.888511i	$0.651741\pi$
$588$	5.95539	−	3.43835i	0.245596	−	0.141795i
$589$	0.609960	+	1.05648i	0.0251330	+	0.0435316i
$590$	−13.2935	+	20.6764i	−0.547283	+	0.851235i
$591$	1.38025			0.0567758
$592$	−1.00900	+	5.99849i	−0.0414694	+	0.246537i
$593$		−	19.9212i		−	0.818066i	−0.912519	−	0.409033i	$-0.865866\pi$
$593$		−	19.9212i		−	0.818066i	0.912519	−	0.409033i	$-0.134134\pi$
$594$	0.518470	−	0.898016i	0.0212731	−	0.0368461i
$595$	3.58954	−	1.84968i	0.147157	−	0.0758294i
$596$	10.6124	+	18.3812i	0.434701	+	0.752923i
$597$	3.52748	−	2.03659i	0.144370	−	0.0833521i
$598$			9.27397i			0.379241i
$599$	2.95130	+	5.11181i	0.120587	+	0.208863i	0.919999	−	0.391920i	$-0.128189\pi$
$599$	2.95130	+	5.11181i	0.120587	+	0.208863i	−0.799412	+	0.600783i	$0.794856\pi$
$600$	−4.97718	−	0.477161i	−0.203193	−	0.0194800i
$601$	8.64560	−	14.9746i	0.352661	−	0.610827i	−0.634054	−	0.773289i	$-0.718610\pi$
$601$	8.64560	−	14.9746i	0.352661	−	0.610827i	0.986715	+	0.162462i	$0.0519435\pi$
$602$		−	2.22738i		−	0.0907813i
$603$			14.3471i			0.584260i
$604$	10.9668	−	18.9951i	0.446234	−	0.772901i
$605$	−19.7273	+	10.1654i	−0.802030	+	0.413284i
$606$	5.93705			0.241176
$607$	35.1499	+	20.2938i	1.42669	+	0.823700i	0.996858	−	0.0792093i	$-0.0252395\pi$
$607$	35.1499	+	20.2938i	1.42669	+	0.823700i	0.429832	+	0.902909i	$0.358573\pi$
$608$	−7.10310	−	4.10098i	−0.288069	−	0.166317i
$609$	−0.561924	+	0.973281i	−0.0227703	+	0.0394393i
$610$	2.35700	+	4.57406i	0.0954321	+	0.185198i
$611$	9.80607	+	16.9846i	0.396711	+	0.687124i
$612$	4.45383	+	2.57142i	0.180035	+	0.103944i
$613$	31.0066	+	17.9017i	1.25235	+	0.723042i	0.971575	−	0.236733i	$-0.0760766\pi$
$613$	31.0066	+	17.9017i	1.25235	+	0.723042i	0.280771	+	0.959775i	$0.409410\pi$
$614$	−12.2478	+	21.2138i	−0.494280	+	0.856118i
$615$	−24.8539	−	1.18864i	−1.00220	−	0.0479307i
$616$	−0.182058	−	0.315334i	−0.00733534	−	0.0127052i
$617$	−29.3879	−	16.9671i	−1.18311	−	0.683070i	−0.226379	−	0.974039i	$-0.572689\pi$
$617$	−29.3879	−	16.9671i	−1.18311	−	0.683070i	−0.956732	+	0.290970i	$0.906022\pi$
$618$		−	13.0217i		−	0.523810i
$619$	16.2711			0.653992			0.326996	−	0.945026i	$-0.393964\pi$
$619$	16.2711			0.653992			0.326996	+	0.945026i	$0.393964\pi$
$620$	0.279752	+	0.179860i	0.0112351	+	0.00722336i
$621$	4.23909			0.170109
$622$	21.7096	−	12.5340i	0.870475	−	0.502569i
$623$		−	1.48138i		−	0.0593503i
$624$	1.09386	+	1.89463i	0.0437895	+	0.0758457i
$625$	−8.15884	−	23.6312i	−0.326354	−	0.945248i
$626$	15.5950	+	27.0113i	0.623302	+	1.07959i
$627$	7.36549	+	4.25247i	0.294149	+	0.169827i
$628$		−	20.5890i		−	0.821590i
$629$	30.8493	+	5.18910i	1.23004	+	0.206903i
$630$	0.0375088	−	0.784288i	0.00149439	−	0.0312468i
$631$	21.2168	−	36.7486i	0.844628	−	1.46294i	−0.0413166	−	0.999146i	$-0.513155\pi$
$631$	21.2168	−	36.7486i	0.844628	−	1.46294i	0.885944	−	0.463792i	$-0.153511\pi$
$632$	−8.18375	+	4.72489i	−0.325532	+	0.187946i
$633$	22.7705	−	13.1465i	0.905046	−	0.522528i
$634$	2.28221	+	3.95290i	0.0906381	+	0.156990i
$635$	−32.0081	−	1.53080i	−1.27020	−	0.0607478i
$636$	−2.23180	−	3.86558i	−0.0884964	−	0.153280i
$637$		−	15.0443i		−	0.596078i
$638$	−2.87412	−	1.65937i	−0.113787	−	0.0656952i
$639$	−10.7063			−0.423534
$640$	−2.23352	−	0.106818i	−0.0882874	−	0.00422237i
$641$	−6.92226	+	11.9897i	−0.273413	+	0.473565i	−0.969733	−	0.244166i	$-0.921486\pi$
$641$	−6.92226	+	11.9897i	−0.273413	+	0.473565i	0.696321	+	0.717731i	$0.254819\pi$
$642$	1.36568	−	0.788474i	0.0538990	−	0.0311186i
$643$			10.3728i			0.409062i	0.978860	+	0.204531i	$0.0655669\pi$
$643$			10.3728i			0.409062i	−0.978860	+	0.204531i	$0.934433\pi$
$644$	0.744269	−	1.28911i	0.0293283	−	0.0507981i
$645$	11.9307	+	7.67060i	0.469772	+	0.302030i
$646$	−21.0907	+	36.5301i	−0.829802	+	1.43726i
$647$	−1.70856	+	0.986437i	−0.0671704	+	0.0387808i	−0.533209	−	0.845984i	$-0.679014\pi$
$647$	−1.70856	+	0.986437i	−0.0671704	+	0.0387808i	0.466039	+	0.884764i	$0.345681\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	5.69954	−	9.87190i	0.223727	−	0.387506i
$650$	−6.34839	+	8.90794i	−0.249004	+	0.349398i
$651$	−0.0261138	+	0.0452305i	−0.00102348	+	0.00177272i
$652$		−	5.22788i		−	0.204740i
$653$	−20.5764	+	11.8798i	−0.805218	+	0.464893i	−0.845293	−	0.534304i	$-0.820574\pi$
$653$	−20.5764	+	11.8798i	−0.805218	+	0.464893i	0.0400743	+	0.999197i	$0.487241\pi$
$654$	−5.10648	+	8.84469i	−0.199679	+	0.345855i
$655$	−0.992294	+	20.7483i	−0.0387721	+	0.810705i
$656$	−11.1277			−0.434463
$657$	−7.38088	−	4.26135i	−0.287956	−	0.166251i
$658$		−	3.14789i		−	0.122717i
$659$	0.0838988	+	0.145317i	0.00326824	+	0.00566075i	0.867655	−	0.497167i	$-0.165626\pi$
$659$	0.0838988	+	0.145317i	0.00326824	+	0.00566075i	−0.864387	+	0.502828i	$0.832293\pi$
$660$	2.31602	+	0.110764i	0.0901510	+	0.00431149i
$661$	11.8069	+	20.4502i	0.459237	+	0.795421i	0.998921	−	0.0464464i	$-0.0147897\pi$
$661$	11.8069	+	20.4502i	0.459237	+	0.795421i	−0.539684	+	0.841868i	$0.681456\pi$
$662$	−10.5418	+	6.08628i	−0.409717	+	0.236550i
$663$	9.74376	−	5.62556i	0.378416	−	0.218479i
$664$	−2.19708	+	3.80546i	−0.0852634	+	0.147681i
$665$	6.43270	+	0.307645i	0.249449	+	0.0119300i
$666$	3.87306	−	4.69035i	0.150078	−	0.181747i
$667$		−	13.5673i		−	0.525328i
$668$	−6.62307	−	3.82383i	−0.256254	−	0.147949i
$669$	3.87029	+	6.70354i	0.149634	+	0.259174i
$670$	−28.5176	+	14.6950i	−1.10173	+	0.567719i
$671$	−1.19310	−	2.06651i	−0.0460591	−	0.0797768i
$672$		−	0.351145i		−	0.0135457i
$673$	0.949348	−	0.548106i	0.0365947	−	0.0211279i	−0.481591	−	0.876396i	$-0.659941\pi$
$673$	0.949348	−	0.548106i	0.0365947	−	0.0211279i	0.518186	+	0.855268i	$0.326608\pi$
$674$	−29.8909			−1.15136
$675$	4.07178	+	2.90182i	0.156723	+	0.111691i
$676$	−8.21386			−0.315918
$677$			36.6324i			1.40790i	0.710251	+	0.703948i	$0.248581\pi$
$677$			36.6324i			1.40790i	−0.710251	+	0.703948i	$0.751419\pi$
$678$	2.52503	+	1.45783i	0.0969732	+	0.0559875i
$679$	−2.71883	−	4.70915i	−0.104339	−	0.180721i
$680$	−0.549350	+	11.4866i	−0.0210666	+	0.440492i
$681$	−4.10709	+	7.11370i	−0.157384	+	0.272597i
$682$	−0.133567	−	0.0771147i	−0.00511453	−	0.00295288i
$683$	−0.469910	−	0.271303i	−0.0179806	−	0.0103811i	0.490983	−	0.871169i	$-0.336638\pi$
$683$	−0.469910	−	0.271303i	−0.0179806	−	0.0103811i	−0.508963	+	0.860788i	$0.669971\pi$
$684$	4.10098	+	7.10310i	0.156805	+	0.271594i
$685$	3.89681	+	7.56227i	0.148890	+	0.288940i
$686$	−2.43637	+	4.21991i	−0.0930210	+	0.161117i
$687$	13.0591	+	7.53968i	0.498236	+	0.287657i
$688$	5.49337	+	3.17160i	0.209433	+	0.120916i
$689$	−9.76511			−0.372021
$690$	4.34189	+	8.42600i	0.165293	+	0.320772i
$691$	−14.8083	+	25.6487i	−0.563334	+	0.975723i	0.433869	+	0.900976i	$0.357148\pi$
$691$	−14.8083	+	25.6487i	−0.563334	+	0.975723i	−0.997203	+	0.0747469i	$0.976185\pi$
$692$			9.81513i			0.373115i
$693$			0.364117i			0.0138316i
$694$	−4.57678	+	7.92722i	−0.173732	+	0.300913i
$695$	1.59665	−	33.3852i	0.0605645	−	1.26637i
$696$	−1.60026	−	2.77173i	−0.0606577	−	0.105062i
$697$			57.2280i			2.16766i
$698$	12.2651	−	7.08124i	0.464240	−	0.268029i
$699$	−2.82331	−	4.89011i	−0.106787	−	0.184961i
$700$	1.59734	−	0.728752i	0.0603738	−	0.0275442i
$701$	21.2332	−	36.7770i	0.801968	−	1.38905i	−0.116351	−	0.993208i	$-0.537120\pi$
$701$	21.2332	−	36.7770i	0.801968	−	1.38905i	0.918319	−	0.395841i	$-0.129547\pi$
$702$		−	2.18772i		−	0.0825704i
$703$	38.4701	+	31.7667i	1.45093	+	1.19810i
$704$	1.03694			0.0390811
$705$	16.8613	+	10.8406i	0.635034	+	0.408281i
$706$	−13.2258	−	22.9078i	−0.497760	−	0.862145i
$707$	−1.80546	+	1.04238i	−0.0679014	+	0.0392029i
$708$	9.52022	−	5.49650i	0.357792	−	0.206571i
$709$	−3.69702			−0.138844			−0.0694222	−	0.997587i	$-0.522116\pi$
$709$	−3.69702			−0.138844			−0.0694222	+	0.997587i	$0.522116\pi$
$710$	−10.9659	−	21.2807i	−0.411543	−	0.798652i
$711$	9.44979			0.354395
$712$	3.65351	+	2.10936i	0.136921	+	0.0790515i
$713$		−	0.630502i		−	0.0236125i
$714$	−1.80588			−0.0675835
$715$	2.74326	−	4.26683i	0.102592	−	0.159570i
$716$	2.83591	+	4.91193i	0.105983	+	0.183568i
$717$		−	11.4498i		−	0.427602i
$718$	−4.40954	−	2.54585i	−0.164562	−	0.0950102i
$719$	2.14283	−	3.71149i	0.0799140	−	0.138415i	−0.823299	−	0.567608i	$-0.807869\pi$
$719$	2.14283	−	3.71149i	0.0799140	−	0.138415i	0.903213	+	0.429193i	$0.141202\pi$
$720$	1.88087	+	1.20927i	0.0700959	+	0.0450666i
$721$	2.28626	+	3.95992i	0.0851447	+	0.147475i
$722$	−41.8049	+	24.1361i	−1.55582	+	0.898251i
$723$	3.59997	+	2.07844i	0.133884	+	0.0772981i
$724$	8.40034	−	14.5498i	0.312196	−	0.540740i
$725$	9.28735	−	13.0318i	0.344923	−	0.483990i
$726$	9.92476			0.368342
$727$	15.0030	−	8.66199i	0.556431	−	0.321255i	−0.195281	−	0.980747i	$-0.562562\pi$
$727$	15.0030	−	8.66199i	0.556431	−	0.321255i	0.751712	+	0.659492i	$0.229229\pi$
$728$	−0.665289	−	0.384105i	−0.0246572	−	0.0142359i
$729$	−1.00000			−0.0370370
$730$	0.910382	−	19.0356i	0.0336948	−	0.704539i
$731$	16.3110	−	28.2515i	0.603285	−	1.04492i
$732$		−	2.30120i		−	0.0850546i
$733$	−26.4474	+	15.2694i	−0.976856	+	0.563988i	−0.901320	−	0.433155i	$-0.857400\pi$
$733$	−26.4474	+	15.2694i	−0.976856	+	0.563988i	−0.0755367	+	0.997143i	$0.524067\pi$
$734$	10.0261			0.370068
$735$	−7.04346	−	13.6687i	−0.259802	−	0.504179i
$736$	2.11955	+	3.67116i	0.0781275	+	0.135321i
$737$	12.8840	−	7.43855i	0.474586	−	0.274003i
$738$	9.63687	+	5.56385i	0.354738	+	0.204808i
$739$	−3.59115			−0.132103			−0.0660513	−	0.997816i	$-0.521040\pi$
$739$	−3.59115			−0.132103			−0.0660513	+	0.997816i	$0.521040\pi$
$740$	13.2899	+	2.89436i	0.488548	+	0.106399i
$741$	17.9436			0.659176
$742$	1.35738	+	0.783685i	0.0498310	+	0.0287700i
$743$	−16.3085	+	9.41573i	−0.598301	+	0.345429i	−0.768373	−	0.640002i	$-0.778933\pi$
$743$	−16.3085	+	9.41573i	−0.598301	+	0.345429i	0.170072	+	0.985432i	$0.445600\pi$
$744$	−0.0743676	−	0.128809i	−0.00272645	−	0.00472235i
$745$	42.1883	−	21.7395i	1.54566	−	0.796473i
$746$	30.2932			1.10911
$747$	3.80546	−	2.19708i	0.139235	−	0.0803871i
$748$		−	5.33282i		−	0.194987i
$749$	−0.276869	+	0.479551i	−0.0101166	+	0.0175224i
$750$	−1.59740	+	11.0656i	−0.0583288	+	0.404060i
$751$	13.4876			0.492171			0.246086	−	0.969248i	$-0.420856\pi$
$751$	13.4876			0.492171			0.246086	+	0.969248i	$0.420856\pi$
$752$	7.76360	+	4.48232i	0.283109	+	0.163453i
$753$	−21.5141	+	12.4212i	−0.784016	+	0.452652i
$754$	−7.00186			−0.254993
$755$	−41.2544	−	26.5236i	−1.50140	−	0.965294i
$756$	−0.175573	+	0.304101i	−0.00638552	+	0.0110600i
$757$	3.81556	+	2.20291i	0.138679	+	0.0800663i	0.567734	−	0.823212i	$-0.307820\pi$
$757$	3.81556	+	2.20291i	0.138679	+	0.0800663i	−0.429055	+	0.903278i	$0.641153\pi$
$758$	1.02616	−	0.592452i	0.0372717	−	0.0215188i
$759$	−2.19784	−	3.80677i	−0.0797766	−	0.138177i
$760$	−9.91834	+	15.4268i	−0.359776	+	0.559590i
$761$	13.2151	−	22.8892i	0.479046	−	0.829732i	−0.520665	−	0.853761i	$-0.674316\pi$
$761$	13.2151	−	22.8892i	0.479046	−	0.829732i	0.999711	+	0.0240287i	$0.00764929\pi$
$762$	12.4109	+	7.16541i	0.449598	+	0.259576i
$763$		−	3.58624i		−	0.129830i
$764$	−1.43474	−	2.48504i	−0.0519070	−	0.0899055i
$765$	6.21906	−	9.67302i	0.224851	−	0.349729i
$766$	−31.6779			−1.14457
$767$		−	24.0497i		−	0.868383i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	53.8224			1.94089			0.970443	−	0.241331i	$-0.0775841\pi$
$769$	53.8224			1.94089			0.970443	+	0.241331i	$0.0775841\pi$
$770$	−0.723751	+	0.372946i	−0.0260822	+	0.0134401i
$771$	−4.18799			−0.150827
$772$	11.2822	−	6.51379i	0.406056	−	0.234437i
$773$	−5.01032	+	2.89271i	−0.180209	+	0.104043i	−0.587391	−	0.809304i	$-0.699845\pi$
$773$	−5.01032	+	2.89271i	−0.180209	+	0.104043i	0.407182	+	0.913347i	$0.366511\pi$
$774$	−3.17160	−	5.49337i	−0.114001	−	0.197455i
$775$	0.431603	−	0.605618i	0.0155037	−	0.0217544i
$776$	15.4855			0.555897
$777$	−0.354304	+	2.10634i	−0.0127106	+	0.0755646i
$778$			16.3930i			0.587717i
$779$	−45.6344	+	79.0412i	−1.63502	+	2.83194i
$780$	4.34852	−	2.24078i	0.155702	−	0.0802327i
$781$	5.55088	+	9.61441i	0.198626	+	0.344030i
$782$	18.8802	−	10.9005i	0.675154	−	0.389801i
$783$			3.20052i			0.114377i
$784$	−3.43835	−	5.95539i	−0.122798	−	0.212693i
$785$	−45.9858	−	2.19928i	−1.64130	−	0.0784958i
$786$	4.64477	−	8.04498i	0.165674	−	0.286955i
$787$			38.5550i			1.37434i	0.726499	+	0.687168i	$0.241146\pi$
$787$			38.5550i			1.37434i	−0.726499	+	0.687168i	$0.758854\pi$
$788$		−	1.38025i		−	0.0491693i
$789$	−3.14323	+	5.44423i	−0.111902	+	0.193820i
$790$	9.67894	+	18.7832i	0.344361	+	0.668278i
$791$	−1.02382			−0.0364028
$792$	−0.898016	−	0.518470i	−0.0319096	−	0.0184230i
$793$	−4.35990	−	2.51719i	−0.154825	−	0.0893881i
$794$	2.45916	−	4.25939i	0.0872723	−	0.151160i
$795$	−8.87223	+	4.57183i	−0.314666	+	0.162146i
$796$	−2.03659	−	3.52748i	−0.0721850	−	0.125028i
$797$	27.0678	+	15.6276i	0.958790	+	0.553558i	0.895800	−	0.444456i	$-0.146603\pi$
$797$	27.0678	+	15.6276i	0.958790	+	0.553558i	0.0629896	+	0.998014i	$0.479936\pi$
$798$	−2.49422	−	1.44004i	−0.0882945	−	0.0509769i
$799$	23.0518	−	39.9270i	0.815515	−	1.41251i
$800$	−0.477161	+	4.97718i	−0.0168702	+	0.175970i
$801$	−2.10936	−	3.65351i	−0.0745305	−	0.129091i
$802$	25.9992	+	15.0106i	0.918063	+	0.530044i
$803$			8.83753i			0.311870i
$804$	14.3471			0.505984
$805$	−2.79975	−	1.80004i	−0.0986781	−	0.0634429i
$806$	−0.325392			−0.0114614
$807$	21.8234	−	12.5997i	0.768220	−	0.443532i
$808$		−	5.93705i		−	0.208865i
$809$	5.31272	+	9.20190i	0.186785	+	0.323522i	0.944177	−	0.329440i	$-0.106860\pi$
$809$	5.31272	+	9.20190i	0.186785	+	0.323522i	−0.757391	+	0.652961i	$0.773526\pi$
$810$	−1.02425	−	1.98769i	−0.0359885	−	0.0698403i
$811$	10.1316	+	17.5484i	0.355767	+	0.616207i	0.987249	−	0.159184i	$-0.0508862\pi$
$811$	10.1316	+	17.5484i	0.355767	+	0.616207i	−0.631482	+	0.775391i	$0.717553\pi$
$812$	0.973281	+	0.561924i	0.0341555	+	0.0197197i
$813$			19.6263i			0.688326i
$814$	−6.22008	−	1.04627i	−0.218014	−	0.0366716i
$815$	−11.6766	−	0.558434i	−0.409012	−	0.0195611i
$816$	2.57142	−	4.45383i	0.0900177	−	0.155915i
$817$	45.0564	−	26.0133i	1.57632	−	0.910090i
$818$	−25.7626	+	14.8741i	−0.900769	+	0.520059i
$819$	0.384105	+	0.665289i	0.0134217	+	0.0232471i
$820$	−1.18864	+	24.8539i	−0.0415092	+	0.867935i
$821$	5.37951	+	9.31759i	0.187746	+	0.325186i	0.944498	−	0.328516i	$-0.106548\pi$
$821$	5.37951	+	9.31759i	0.187746	+	0.325186i	−0.756752	+	0.653702i	$0.773215\pi$
$822$		−	3.80455i		−	0.132699i
$823$	−34.7362	−	20.0550i	−1.21083	−	0.699072i	−0.247888	−	0.968789i	$-0.579737\pi$
$823$	−34.7362	−	20.0550i	−1.21083	−	0.699072i	−0.962940	+	0.269717i	$0.913070\pi$
$824$	−13.0217			−0.453633
$825$	0.494787	−	5.16104i	0.0172263	−	0.179684i
$826$	−1.93007	+	3.34298i	−0.0671558	+	0.116317i
$827$	27.9009	−	16.1086i	0.970208	−	0.560150i	0.0709082	−	0.997483i	$-0.477410\pi$
$827$	27.9009	−	16.1086i	0.970208	−	0.560150i	0.899300	+	0.437333i	$0.144077\pi$
$828$		−	4.23909i		−	0.147319i
$829$	−1.91397	+	3.31510i	−0.0664750	+	0.115138i	−0.897347	−	0.441325i	$-0.854509\pi$
$829$	−1.91397	+	3.31510i	−0.0664750	+	0.115138i	0.830872	+	0.556463i	$0.187842\pi$
$830$	8.26487	+	5.31371i	0.286878	+	0.184442i
$831$	−4.90105	+	8.48886i	−0.170015	+	0.294475i
$832$	1.89463	−	1.09386i	0.0656843	−	0.0379229i
$833$	−30.6276	+	17.6829i	−1.06119	+	0.612676i
$834$	−7.47368	+	12.9448i	−0.258792	+	0.448242i
$835$	−9.24806	+	14.3843i	−0.320042	+	0.497789i
$836$	4.25247	−	7.36549i	0.147075	−	0.254741i
$837$			0.148735i			0.00514104i
$838$	21.3357	−	12.3182i	0.737030	−	0.425524i
$839$	6.96994	−	12.0723i	0.240629	−	0.416782i	−0.720265	−	0.693699i	$-0.755980\pi$
$839$	6.96994	−	12.0723i	0.240629	−	0.416782i	0.960894	+	0.276918i	$0.0893130\pi$
$840$	−0.784288	−	0.0375088i	−0.0270605	−	0.00129418i
$841$	−18.7567			−0.646782
$842$	−34.0881	−	19.6808i	−1.17475	−	0.678244i
$843$			12.4710i			0.429523i
$844$	−13.1465	−	22.7705i	−0.452523	−	0.783792i
$845$	−0.877391	+	18.3458i	−0.0301832	+	0.631114i
$846$	−4.48232	−	7.76360i	−0.154105	−	0.266918i
$847$	−3.01813	+	1.74252i	−0.103704	+	0.0598736i
$848$	−3.86558	+	2.23180i	−0.132745	+	0.0766402i
$849$	−3.03612	+	5.25871i	−0.104199	+	0.180479i
$850$	25.5968	+	2.45396i	0.877965	+	0.0841703i
$851$	−9.00990	−	24.1600i	−0.308855	−	0.828196i
$852$			10.7063i			0.366791i
$853$	−11.4111	−	6.58817i	−0.390707	−	0.225575i	0.291759	−	0.956492i	$-0.405759\pi$
$853$	−11.4111	−	6.58817i	−0.390707	−	0.225575i	−0.682466	+	0.730917i	$0.739093\pi$
$854$	0.404027	+	0.699795i	0.0138255	+	0.0239465i
$855$	16.3029	−	8.40086i	0.557549	−	0.287303i
$856$	−0.788474	−	1.36568i	−0.0269495	−	0.0466779i
$857$		−	27.9617i		−	0.955154i	−0.878590	−	0.477577i	$-0.841515\pi$
$857$		−	27.9617i		−	0.955154i	0.878590	−	0.477577i	$-0.158485\pi$
$858$	−1.96461	+	1.13427i	−0.0670708	+	0.0387233i
$859$	43.7281			1.49199			0.745993	−	0.665954i	$-0.231975\pi$
$859$	43.7281			1.49199			0.745993	+	0.665954i	$0.231975\pi$
$860$	7.67060	−	11.9307i	0.261565	−	0.406835i
$861$	−3.90744			−0.133165
$862$			11.0044i			0.374811i
$863$	−20.9209	−	12.0787i	−0.712156	−	0.411163i	0.0997031	−	0.995017i	$-0.468211\pi$
$863$	−20.9209	−	12.0787i	−0.712156	−	0.411163i	−0.811859	+	0.583854i	$0.801544\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	21.9222	+	1.04844i	0.745378	+	0.0356479i
$866$	8.42470	−	14.5920i	0.286283	−	0.495857i
$867$	−8.18292	−	4.72441i	−0.277906	−	0.160449i
$868$	0.0452305	+	0.0261138i	0.00153522	+	0.000886362i
$869$	−4.89943	−	8.48606i	−0.166202	−	0.287870i
$870$	−6.36164	+	3.27813i	−0.215680	+	0.111139i
$871$	15.6938	−	27.1824i	0.531764	−	0.921041i
$872$	8.84469	+	5.10648i	0.299519	+	0.172927i
$873$	−13.4108	−	7.74275i	−0.453888	−	0.262052i
$874$	34.7688			1.17607
$875$	−1.45705	−	3.64553i	−0.0492574	−	0.123241i
$876$	−4.26135	+	7.38088i	−0.143978	+	0.249377i
$877$			21.9678i			0.741799i	0.928673	+	0.370899i	$0.120951\pi$
$877$			21.9678i			0.741799i	−0.928673	+	0.370899i	$0.879049\pi$
$878$			3.85747i			0.130183i
$879$	−6.62880	+	11.4814i	−0.223584	+	0.387258i
$880$	0.110764	−	2.31602i	0.00373386	−	0.0780730i
$881$	13.9118	+	24.0960i	0.468702	+	0.811816i	0.999360	−	0.0357702i	$-0.0113884\pi$
$881$	13.9118	+	24.0960i	0.468702	+	0.811816i	−0.530658	+	0.847586i	$0.678055\pi$
$882$			6.87670i			0.231550i
$883$	−8.08341	+	4.66696i	−0.272028	+	0.157056i	−0.629809	−	0.776750i	$-0.716867\pi$
$883$	−8.08341	+	4.66696i	−0.272028	+	0.157056i	0.357781	+	0.933806i	$0.383534\pi$
$884$	−5.62556	−	9.74376i	−0.189208	−	0.327718i
$885$	−11.2596	−	21.8507i	−0.378487	−	0.734503i
$886$	−9.36475	+	16.2202i	−0.314615	+	0.544929i
$887$			5.13029i			0.172258i	0.996284	+	0.0861291i	$0.0274498\pi$
$887$			5.13029i			0.172258i	−0.996284	+	0.0861291i	$0.972550\pi$
$888$	−4.69035	−	3.87306i	−0.157398	−	0.129971i
$889$	−5.03220			−0.168775
$890$	5.10154	−	7.93486i	0.171004	−	0.265977i
$891$	0.518470	+	0.898016i	0.0173694	+	0.0300847i
$892$	6.70354	−	3.87029i	0.224451	−	0.129587i
$893$	63.6767	−	36.7638i	2.13086	−	1.23025i
$894$	−21.2248			−0.709863
$895$	11.2738	−	5.80935i	0.376842	−	0.194185i
$896$	−0.351145			−0.0117309
$897$	−8.03149	−	4.63698i	−0.268164	−	0.154824i
$898$			27.4380i			0.915617i
$899$	0.476030			0.0158765
$900$	2.90182	−	4.07178i	0.0967274	−	0.135726i
$901$	11.4778	+	19.8801i	0.382380	+	0.662301i
$902$		−	11.5387i		−	0.384198i
$903$	1.92897	+	1.11369i	0.0641921	+	0.0370613i
$904$	1.45783	−	2.52503i	0.0484866	−	0.0839812i
$905$	−31.5999	−	20.3165i	−1.05042	−	0.675342i
$906$	10.9668	+	18.9951i	0.364349	+	0.631071i
$907$	2.25302	−	1.30078i	0.0748103	−	0.0431918i	−0.462128	−	0.886813i	$-0.652914\pi$
$907$	2.25302	−	1.30078i	0.0748103	−	0.0431918i	0.536939	+	0.843621i	$0.319581\pi$
$908$	7.11370	+	4.10709i	0.236076	+	0.136299i
$909$	−2.96853	+	5.14164i	−0.0984598	+	0.170537i
$910$	−0.928969	+	1.44490i	−0.0307950	+	0.0478981i
$911$	−53.5330			−1.77363			−0.886814	−	0.462126i	$-0.847087\pi$
$911$	−53.5330			−1.77363			−0.886814	+	0.462126i	$0.847087\pi$
$912$	7.10310	−	4.10098i	0.235207	−	0.135797i
$913$	−3.94603	−	2.27824i	−0.130595	−	0.0753989i
$914$	−9.51368			−0.314685
$915$	−5.13975	−	0.245810i	−0.169915	−	0.00812623i
$916$	7.53968	−	13.0591i	0.249118	−	0.431485i
$917$			3.26198i			0.107720i
$918$	−4.45383	+	2.57142i	−0.146998	+	0.0848695i
$919$	−19.2472			−0.634905			−0.317453	−	0.948274i	$-0.602827\pi$
$919$	−19.2472			−0.634905			−0.317453	+	0.948274i	$0.602827\pi$
$920$	8.42600	−	4.34189i	0.277797	−	0.143148i
$921$	−12.2478	−	21.2138i	−0.403578	−	0.699018i
$922$	−22.2556	+	12.8493i	−0.732950	+	0.423169i
$923$	20.2844	+	11.7112i	0.667668	+	0.385478i
$924$	0.364117			0.0119786
$925$	7.88420	−	29.3741i	0.259231	−	0.965815i
$926$	−25.6659			−0.843434
$927$	11.2771	+	6.51086i	0.370390	+	0.213845i
$928$	−2.77173	+	1.60026i	−0.0909866	+	0.0525311i
$929$	−11.7772	−	20.3986i	−0.386396	−	0.669257i	0.605566	−	0.795795i	$-0.292947\pi$
$929$	−11.7772	−	20.3986i	−0.386396	−	0.669257i	−0.991962	+	0.126538i	$0.959613\pi$
$930$	−0.295640	+	0.152342i	−0.00969440	+	0.00499549i
$931$	−56.4024			−1.84851
$932$	−4.89011	+	2.82331i	−0.160181	+	0.0924805i
$933$			25.0681i			0.820692i
$934$	19.1086	−	33.0971i	0.625253	−	1.08297i
$935$	−11.9109	−	0.569643i	−0.389529	−	0.0186293i
$936$	−2.18772			−0.0715080
$937$	−38.5661	−	22.2662i	−1.25990	−	0.727404i	−0.286845	−	0.957977i	$-0.592606\pi$
$937$	−38.5661	−	22.2662i	−1.25990	−	0.727404i	−0.973055	+	0.230574i	$0.925940\pi$
$938$	−4.36297	+	2.51896i	−0.142456	+	0.0822471i
$939$	−31.1900			−1.01785
$940$	10.8406	−	16.8613i	0.353582	−	0.549956i
$941$	2.75666	−	4.77467i	0.0898645	−	0.155650i	−0.817589	−	0.575802i	$-0.804690\pi$
$941$	2.75666	−	4.77467i	0.0898645	−	0.155650i	0.907454	+	0.420152i	$0.138023\pi$
$942$	17.8306	+	10.2945i	0.580952	+	0.335413i
$943$	40.8516	−	23.5857i	1.33031	−	0.768055i
$944$	−5.49650	−	9.52022i	−0.178896	−	0.309857i
$945$	0.660459	+	0.424628i	0.0214847	+	0.0138131i
$946$	−3.28875	+	5.69629i	−0.106927	+	0.185202i
$947$	15.2638	+	8.81253i	0.496005	+	0.286369i	0.727062	−	0.686571i	$-0.240885\pi$
$947$	15.2638	+	8.81253i	0.496005	+	0.286369i	−0.231057	+	0.972940i	$0.574218\pi$
$948$		−	9.44979i		−	0.306915i
$949$	9.32267	+	16.1473i	0.302627	+	0.524165i
$950$	33.3966	+	23.8006i	1.08353	+	0.772195i
$951$	−4.56442			−0.148011
$952$			1.80588i			0.0585291i
$953$	−13.3304	−	7.69631i	−0.431814	−	0.249308i	0.268305	−	0.963334i	$-0.413536\pi$
$953$	−13.3304	−	7.69631i	−0.431814	−	0.249308i	−0.700119	+	0.714026i	$0.746870\pi$
$954$	4.46359			0.144514
$955$	−5.70363	+	2.93906i	−0.184565	+	0.0951057i
$956$	−11.4498			−0.370314
$957$	2.87412	−	1.65937i	0.0929071	−	0.0536399i
$958$	−10.7513	+	6.20726i	−0.347358	+	0.200547i
$959$	0.667976	+	1.15697i	0.0215701	+	0.0373604i
$960$	1.20927	−	1.88087i	0.0390289	−	0.0607049i
$961$	−30.9779			−0.999286
$962$	−12.4686	+	4.64986i	−0.402004	+	0.149917i
$963$			1.57695i			0.0508164i
$964$	2.07844	−	3.59997i	0.0669421	−	0.115947i
$965$	−13.3435	−	25.8948i	−0.429543	−	0.833583i
$966$	0.744269	+	1.28911i	0.0239465	+	0.0414765i
$967$	22.4827	−	12.9804i	0.722994	−	0.417421i	−0.0928599	−	0.995679i	$-0.529601\pi$
$967$	22.4827	−	12.9804i	0.722994	−	0.417421i	0.815854	+	0.578259i	$0.196268\pi$
$968$		−	9.92476i		−	0.318994i
$969$	−21.0907	−	36.5301i	−0.677530	−	1.17352i
$970$	1.65414	−	34.5871i	0.0531111	−	1.11052i
$971$	21.5442	−	37.3157i	0.691387	−	1.19752i	−0.279996	−	0.960001i	$-0.590333\pi$
$971$	21.5442	−	37.3157i	0.691387	−	1.19752i	0.971383	−	0.237517i	$-0.0763334\pi$
$972$			1.00000i			0.0320750i
$973$		−	5.24870i		−	0.168266i
$974$	−6.01615	+	10.4203i	−0.192770	+	0.333888i
$975$	−4.54031	−	9.95184i	−0.145406	−	0.318714i
$976$	−2.30120			−0.0736595
$977$	8.98984	+	5.19028i	0.287610	+	0.166052i	0.636864	−	0.770976i	$-0.280231\pi$
$977$	8.98984	+	5.19028i	0.287610	+	0.166052i	−0.349253	+	0.937028i	$0.613565\pi$
$978$	4.52748	+	2.61394i	0.144773	+	0.0835846i
$979$	−2.18728	+	3.78847i	−0.0699057	+	0.121080i
$980$	−13.6687	+	7.04346i	−0.436632	+	0.224995i
$981$	−5.10648	−	8.84469i	−0.163037	−	0.282389i
$982$	4.99833	+	2.88579i	0.159503	+	0.0920891i
$983$	−9.34020	−	5.39257i	−0.297906	−	0.171996i	0.343596	−	0.939118i	$-0.388355\pi$
$983$	−9.34020	−	5.39257i	−0.297906	−	0.171996i	−0.641502	+	0.767121i	$0.721688\pi$
$984$	5.56385	−	9.63687i	0.177369	−	0.307212i
$985$	−3.08280	−	0.147436i	−0.0982263	−	0.00469770i
$986$	8.22989	+	14.2546i	0.262093	+	0.453958i
$987$	2.72615	+	1.57394i	0.0867743	+	0.0500992i
$988$		−	17.9436i		−	0.570863i
$989$	−26.8894			−0.855032
$990$	−1.25394	+	1.95035i	−0.0398527	+	0.0619862i
$991$	1.91476			0.0608243			0.0304122	−	0.999537i	$-0.490318\pi$
$991$	1.91476			0.0608243			0.0304122	+	0.999537i	$0.490318\pi$
$992$	−0.128809	+	0.0743676i	−0.00408967	+	0.00236117i
$993$		−	12.1726i		−	0.386285i
$994$	−1.87973	−	3.25579i	−0.0596214	−	0.103267i
$995$	−8.09622	+	4.17196i	−0.256667	+	0.132260i
$996$	−2.19708	−	3.80546i	−0.0696173	−	0.120581i
$997$	42.4017	+	24.4806i	1.34287	+	0.775309i	0.987228	−	0.159311i	$-0.0509274\pi$
$997$	42.4017	+	24.4806i	1.34287	+	0.775309i	0.355647	+	0.934621i	$0.384261\pi$
$998$			4.72452i			0.149552i
$999$	2.12543	+	5.69935i	0.0672457	+	0.180319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.17	yes	40
5.4	even	2	inner	1110.2.bb.e.1009.4	✓	40
37.26	even	3	inner	1110.2.bb.e.1099.4	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.4	✓	40	5.4	even	2	inner
1110.2.bb.e.1009.17	yes	40	1.1	even	1	trivial
1110.2.bb.e.1099.4	yes	40	37.26	even	3	inner
1110.2.bb.e.1099.17	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98769 - 1.02425i) q^{5} -1.00000 q^{6} +(0.304101 - 0.175573i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98769 - 1.02425i) q^{5} -1.00000 q^{6} +(0.304101 - 0.175573i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23352 + 0.106818i) q^{10} -1.03694 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.89463 + 1.09386i) q^{13} +0.351145 q^{14} +(-1.20927 + 1.88087i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.45383 + 2.57142i) q^{17} +(0.866025 - 0.500000i) q^{18} +(4.10098 + 7.10310i) q^{19} +(1.88087 + 1.20927i) q^{20} +(-0.175573 + 0.304101i) q^{21} +(-0.898016 - 0.518470i) q^{22} -4.23909i q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.90182 - 4.07178i) q^{25} -2.18772 q^{26} +1.00000i q^{27} +(0.304101 + 0.175573i) q^{28} +3.20052 q^{29} +(-1.98769 + 1.02425i) q^{30} +0.148735 q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.898016 - 0.518470i) q^{33} +(2.57142 + 4.45383i) q^{34} +(0.424628 - 0.660459i) q^{35} +1.00000 q^{36} +(5.69935 - 2.12543i) q^{37} +8.20196i q^{38} +(1.09386 - 1.89463i) q^{39} +(1.02425 + 1.98769i) q^{40} +(5.56385 + 9.63687i) q^{41} +(-0.304101 + 0.175573i) q^{42} -6.34319i q^{43} +(-0.518470 - 0.898016i) q^{44} +(0.106818 - 2.23352i) q^{45} +(2.11955 - 3.67116i) q^{46} -8.96463i q^{47} -1.00000i q^{48} +(-3.43835 + 5.95539i) q^{49} +(4.54894 - 2.07536i) q^{50} -5.14284 q^{51} +(-1.89463 - 1.09386i) q^{52} +(3.86558 + 2.23180i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.06111 + 1.06209i) q^{55} +(0.175573 + 0.304101i) q^{56} +(-7.10310 - 4.10098i) q^{57} +(2.77173 + 1.60026i) q^{58} +(-5.49650 + 9.52022i) q^{59} +(-2.23352 - 0.106818i) q^{60} +(1.15060 + 1.99289i) q^{61} +(0.128809 + 0.0743676i) q^{62} -0.351145i q^{63} -1.00000 q^{64} +(-2.64554 + 4.11483i) q^{65} +1.03694 q^{66} +(-12.4250 + 7.17356i) q^{67} +5.14284i q^{68} +(2.11955 + 3.67116i) q^{69} +(0.697968 - 0.359661i) q^{70} +(-5.35314 - 9.27190i) q^{71} +(0.866025 + 0.500000i) q^{72} -8.52271i q^{73} +(5.99849 + 1.00900i) q^{74} +(-0.477161 + 4.97718i) q^{75} +(-4.10098 + 7.10310i) q^{76} +(-0.315334 + 0.182058i) q^{77} +(1.89463 - 1.09386i) q^{78} +(4.72489 + 8.18375i) q^{79} +(-0.106818 + 2.23352i) q^{80} +(-0.500000 - 0.866025i) q^{81} +11.1277i q^{82} +(3.80546 + 2.19708i) q^{83} -0.351145 q^{84} +(11.4866 + 0.549350i) q^{85} +(3.17160 - 5.49337i) q^{86} +(-2.77173 + 1.60026i) q^{87} -1.03694i q^{88} +(2.10936 - 3.65351i) q^{89} +(1.20927 - 1.88087i) q^{90} +(-0.384105 + 0.665289i) q^{91} +(3.67116 - 2.11955i) q^{92} +(-0.128809 + 0.0743676i) q^{93} +(4.48232 - 7.76360i) q^{94} +(15.4268 + 9.91834i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.4855i q^{97} +(-5.95539 + 3.43835i) q^{98} +(-0.518470 + 0.898016i) 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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