LMFDB - Embedded newform 1218.2.i.i.1045.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$1218 = 2 \cdot 3 \cdot 7 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [12,6,6,-6,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 2 x^{11} + 20 x^{10} - 32 x^{9} + 283 x^{8} - 404 x^{7} + 1490 x^{6} - 50 x^{5} + 2281 x^{4} + \cdots + 529$ x^12 - 2x^11 + 20x^10 - 32x^9 + 283x^8 - 404x^7 + 1490x^6 - 50x^5 + 2281x^4 - 8x^3 + 2451x^2 + 920*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1045.5
Root			$1.51719 + 2.62785i$ of defining polynomial
Character	$\chi$	$=$	1218.1045
Dual form			1218.2.i.i.697.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.454851 - 0.787826i) q^{5} +1.00000 q^{6} +(-2.61863 + 0.377887i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.454851 - 0.787826i) q^{10} +(-2.66608 - 4.61779i) q^{11} +(0.500000 - 0.866025i) q^{12} -0.690111 q^{13} +(-0.982053 + 2.45674i) q^{14} +0.909703 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.14263 - 1.97909i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.59109 + 6.21996i) q^{19} -0.909703 q^{20} +(-1.63657 - 2.07885i) q^{21} -5.33216 q^{22} +(-1.67609 + 2.90308i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.08622 + 3.61344i) q^{25} +(-0.345055 + 0.597653i) q^{26} -1.00000 q^{27} +(1.63657 + 2.07885i) q^{28} +1.00000 q^{29} +(0.454851 - 0.787826i) q^{30} +(-5.52389 - 9.56767i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.66608 - 4.61779i) q^{33} -2.28525 q^{34} +(-0.893377 + 2.23490i) q^{35} +1.00000 q^{36} +(-3.57953 + 6.19993i) q^{37} +(3.59109 + 6.21996i) q^{38} +(-0.345055 - 0.597653i) q^{39} +(-0.454851 + 0.787826i) q^{40} -6.46476 q^{41} +(-2.61863 + 0.377887i) q^{42} -1.72449 q^{43} +(-2.66608 + 4.61779i) q^{44} +(0.454851 + 0.787826i) q^{45} +(1.67609 + 2.90308i) q^{46} +(-2.27357 + 3.93794i) q^{47} -1.00000 q^{48} +(6.71440 - 1.97909i) q^{49} +4.17244 q^{50} +(1.14263 - 1.97909i) q^{51} +(0.345055 + 0.597653i) q^{52} +(-4.77512 - 8.27076i) q^{53} +(-0.500000 + 0.866025i) q^{54} -4.85068 q^{55} +(2.61863 - 0.377887i) q^{56} -7.18219 q^{57} +(0.500000 - 0.866025i) q^{58} +(-6.98891 - 12.1051i) q^{59} +(-0.454851 - 0.787826i) q^{60} +(4.93846 - 8.55366i) q^{61} -11.0478 q^{62} +(0.982053 - 2.45674i) q^{63} +1.00000 q^{64} +(-0.313898 + 0.543687i) q^{65} +(-2.66608 - 4.61779i) q^{66} +(-2.91683 - 5.05210i) q^{67} +(-1.14263 + 1.97909i) q^{68} -3.35218 q^{69} +(1.48879 + 1.89114i) q^{70} +14.0262 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.19772 + 3.80656i) q^{73} +(3.57953 + 6.19993i) q^{74} +(-2.08622 + 3.61344i) q^{75} +7.18219 q^{76} +(8.72647 + 11.0848i) q^{77} -0.690111 q^{78} +(-6.18160 + 10.7068i) q^{79} +(0.454851 + 0.787826i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.23238 + 5.59864i) q^{82} -3.37316 q^{83} +(-0.982053 + 2.45674i) q^{84} -2.07890 q^{85} +(-0.862247 + 1.49346i) q^{86} +(0.500000 + 0.866025i) q^{87} +(2.66608 + 4.61779i) q^{88} +(5.65618 - 9.79679i) q^{89} +0.909703 q^{90} +(1.80714 - 0.260784i) q^{91} +3.35218 q^{92} +(5.52389 - 9.56767i) q^{93} +(2.27357 + 3.93794i) q^{94} +(3.26683 + 5.65831i) q^{95} +(-0.500000 + 0.866025i) q^{96} -9.51276 q^{97} +(1.64326 - 6.80439i) q^{98} +5.33216 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} - q^{5} + 12 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9} + q^{10} - 3 q^{11} + 6 q^{12} - 14 q^{13} + 2 q^{14} - 2 q^{15} - 6 q^{16} - 8 q^{17} + 6 q^{18} + 10 q^{19} + 2 q^{20}+ \cdots + 6 q^{99}+O(q^{100})$ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 - q^5 + 12 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9 + q^10 - 3 * q^11 + 6 * q^12 - 14 * q^13 + 2 * q^14 - 2 * q^15 - 6 * q^16 - 8 * q^17 + 6 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^21 - 6 * q^22 - 6 * q^24 - 9 * q^25 - 7 * q^26 - 12 * q^27 + 4 * q^28 + 12 * q^29 - q^30 - 8 * q^31 + 6 * q^32 + 3 * q^33 - 16 * q^34 + 22 * q^35 + 12 * q^36 - 17 * q^37 - 10 * q^38 - 7 * q^39 + q^40 + 2 * q^41 - 2 * q^42 + 6 * q^43 - 3 * q^44 - q^45 + 5 * q^47 - 12 * q^48 + 16 * q^49 - 18 * q^50 + 8 * q^51 + 7 * q^52 + 11 * q^53 - 6 * q^54 - 72 * q^55 + 2 * q^56 + 20 * q^57 + 6 * q^58 - 14 * q^59 + q^60 + 3 * q^61 - 16 * q^62 - 2 * q^63 + 12 * q^64 - 15 * q^65 - 3 * q^66 + 21 * q^67 - 8 * q^68 + 14 * q^70 + 42 * q^71 + 6 * q^72 + 6 * q^73 + 17 * q^74 + 9 * q^75 - 20 * q^76 + 41 * q^77 - 14 * q^78 - 17 * q^79 - q^80 - 6 * q^81 + q^82 - 52 * q^83 + 2 * q^84 + 44 * q^85 + 3 * q^86 + 6 * q^87 + 3 * q^88 - 36 * q^89 - 2 * q^90 + 57 * q^91 + 8 * q^93 - 5 * q^94 - 3 * q^95 - 6 * q^96 - 82 * q^97 - 4 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$ .

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.454851	−	0.787826i	0.203416	−	0.352326i	−0.746211	−	0.665709i	$-0.768129\pi$
$5$	0.454851	−	0.787826i	0.203416	−	0.352326i	0.949627	+	0.313383i	$0.101462\pi$
$6$	1.00000			0.408248
$7$	−2.61863	+	0.377887i	−0.989748	+	0.142828i
$7$	−2.61863	+	0.377887i	−0.989748	+	0.142828i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.454851	−	0.787826i	−0.143837	−	0.249132i
$11$	−2.66608	−	4.61779i	−0.803854	−	1.39232i	−0.917062	−	0.398744i	$-0.869446\pi$
$11$	−2.66608	−	4.61779i	−0.803854	−	1.39232i	0.113208	−	0.993571i	$-0.463887\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.690111			−0.191402			−0.0957011	−	0.995410i	$-0.530509\pi$
$13$	−0.690111			−0.191402			−0.0957011	+	0.995410i	$0.530509\pi$
$14$	−0.982053	+	2.45674i	−0.262465	+	0.656591i
$15$	0.909703			0.234884
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.14263	−	1.97909i	−0.277128	−	0.479999i	0.693542	−	0.720416i	$-0.256049\pi$
$17$	−1.14263	−	1.97909i	−0.277128	−	0.479999i	−0.970670	+	0.240417i	$0.922716\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.59109	+	6.21996i	−0.823854	+	1.42696i	0.0789387	+	0.996879i	$0.474847\pi$
$19$	−3.59109	+	6.21996i	−0.823854	+	1.42696i	−0.902792	+	0.430077i	$0.858486\pi$
$20$	−0.909703			−0.203416
$21$	−1.63657	−	2.07885i	−0.357129	−	0.453643i
$22$	−5.33216			−1.13682
$23$	−1.67609	+	2.90308i	−0.349489	+	0.605333i	−0.986159	−	0.165804i	$-0.946978\pi$
$23$	−1.67609	+	2.90308i	−0.349489	+	0.605333i	0.636669	+	0.771137i	$0.280312\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.08622	+	3.61344i	0.417244	+	0.722688i
$26$	−0.345055	+	0.597653i	−0.0676709	+	0.117209i
$27$	−1.00000			−0.192450
$28$	1.63657	+	2.07885i	0.309283	+	0.392866i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	0.454851	−	0.787826i	0.0830441	−	0.143837i
$31$	−5.52389	−	9.56767i	−0.992121	−	1.71840i	−0.604561	−	0.796559i	$-0.706651\pi$
$31$	−5.52389	−	9.56767i	−0.992121	−	1.71840i	−0.387560	−	0.921844i	$-0.626682\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.66608	−	4.61779i	0.464105	−	0.803854i
$34$	−2.28525			−0.391918
$35$	−0.893377	+	2.23490i	−0.151008	+	0.377768i
$36$	1.00000			0.166667
$37$	−3.57953	+	6.19993i	−0.588471	+	1.01926i	0.405961	+	0.913890i	$0.366937\pi$
$37$	−3.57953	+	6.19993i	−0.588471	+	1.01926i	−0.994433	+	0.105372i	$0.966397\pi$
$38$	3.59109	+	6.21996i	0.582552	+	1.00901i
$39$	−0.345055	−	0.597653i	−0.0552531	−	0.0957011i
$40$	−0.454851	+	0.787826i	−0.0719183	+	0.124566i
$41$	−6.46476			−1.00963			−0.504813	−	0.863229i	$-0.668438\pi$
$41$	−6.46476			−1.00963			−0.504813	+	0.863229i	$0.668438\pi$
$42$	−2.61863	+	0.377887i	−0.404063	+	0.0583092i
$43$	−1.72449			−0.262983			−0.131491	−	0.991317i	$-0.541977\pi$
$43$	−1.72449			−0.262983			−0.131491	+	0.991317i	$0.541977\pi$
$44$	−2.66608	+	4.61779i	−0.401927	+	0.696158i
$45$	0.454851	+	0.787826i	0.0678053	+	0.117442i
$46$	1.67609	+	2.90308i	0.247126	+	0.428035i
$47$	−2.27357	+	3.93794i	−0.331634	+	0.574408i	−0.982832	−	0.184500i	$-0.940933\pi$
$47$	−2.27357	+	3.93794i	−0.331634	+	0.574408i	0.651198	+	0.758908i	$0.274267\pi$
$48$	−1.00000			−0.144338
$49$	6.71440	−	1.97909i	0.959200	−	0.282727i
$50$	4.17244			0.590072
$51$	1.14263	−	1.97909i	0.160000	−	0.277128i
$52$	0.345055	+	0.597653i	0.0478506	+	0.0828796i
$53$	−4.77512	−	8.27076i	−0.655914	−	1.13608i	−0.981664	−	0.190620i	$-0.938950\pi$
$53$	−4.77512	−	8.27076i	−0.655914	−	1.13608i	0.325750	−	0.945456i	$-0.394383\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−4.85068			−0.654066
$56$	2.61863	−	0.377887i	0.349929	−	0.0504972i
$57$	−7.18219			−0.951304
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	−6.98891	−	12.1051i	−0.909878	−	1.57595i	−0.814232	−	0.580539i	$-0.802842\pi$
$59$	−6.98891	−	12.1051i	−0.909878	−	1.57595i	−0.0956459	−	0.995415i	$-0.530492\pi$
$60$	−0.454851	−	0.787826i	−0.0587211	−	0.101708i
$61$	4.93846	−	8.55366i	0.632305	−	1.09518i	−0.354775	−	0.934952i	$-0.615442\pi$
$61$	4.93846	−	8.55366i	0.632305	−	1.09518i	0.987079	−	0.160232i	$-0.0512242\pi$
$62$	−11.0478			−1.40307
$63$	0.982053	−	2.45674i	0.123727	−	0.309520i
$64$	1.00000			0.125000
$65$	−0.313898	+	0.543687i	−0.0389342	+	0.0674361i
$66$	−2.66608	−	4.61779i	−0.328172	−	0.568411i
$67$	−2.91683	−	5.05210i	−0.356348	−	0.617212i	0.631000	−	0.775783i	$-0.282645\pi$
$67$	−2.91683	−	5.05210i	−0.356348	−	0.617212i	−0.987348	+	0.158571i	$0.949311\pi$
$68$	−1.14263	+	1.97909i	−0.138564	+	0.240000i
$69$	−3.35218			−0.403556
$70$	1.48879	+	1.89114i	0.177945	+	0.226034i
$71$	14.0262			1.66461			0.832304	−	0.554320i	$-0.187022\pi$
$71$	14.0262			1.66461			0.832304	+	0.554320i	$0.187022\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.19772	+	3.80656i	0.257223	+	0.445524i	0.965497	−	0.260414i	$-0.0838590\pi$
$73$	2.19772	+	3.80656i	0.257223	+	0.445524i	−0.708274	+	0.705938i	$0.750526\pi$
$74$	3.57953	+	6.19993i	0.416112	+	0.720727i
$75$	−2.08622	+	3.61344i	−0.240896	+	0.417244i
$76$	7.18219			0.823854
$77$	8.72647	+	11.0848i	0.994474	+	1.26323i
$78$	−0.690111			−0.0781397
$79$	−6.18160	+	10.7068i	−0.695484	+	1.20461i	0.274533	+	0.961578i	$0.411477\pi$
$79$	−6.18160	+	10.7068i	−0.695484	+	1.20461i	−0.970017	+	0.243036i	$0.921857\pi$
$80$	0.454851	+	0.787826i	0.0508539	+	0.0880816i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.23238	+	5.59864i	−0.356956	+	0.618267i
$83$	−3.37316			−0.370253			−0.185126	−	0.982715i	$-0.559269\pi$
$83$	−3.37316			−0.370253			−0.185126	+	0.982715i	$0.559269\pi$
$84$	−0.982053	+	2.45674i	−0.107151	+	0.268052i
$85$	−2.07890			−0.225489
$86$	−0.862247	+	1.49346i	−0.0929785	+	0.161043i
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	2.66608	+	4.61779i	0.284205	+	0.492258i
$89$	5.65618	−	9.79679i	0.599554	−	1.03846i	−0.393333	−	0.919396i	$-0.628678\pi$
$89$	5.65618	−	9.79679i	0.599554	−	1.03846i	0.992887	−	0.119062i	$-0.0379887\pi$
$90$	0.909703			0.0958911
$91$	1.80714	−	0.260784i	0.189440	−	0.0273376i
$92$	3.35218			0.349489
$93$	5.52389	−	9.56767i	0.572801	−	0.992121i
$94$	2.27357	+	3.93794i	0.234501	+	0.406167i
$95$	3.26683	+	5.65831i	0.335170	+	0.580531i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−9.51276			−0.965874			−0.482937	−	0.875655i	$-0.660430\pi$
$97$	−9.51276			−0.965874			−0.482937	+	0.875655i	$0.660430\pi$
$98$	1.64326	−	6.80439i	0.165994	−	0.687347i
$99$	5.33216			0.535903
$100$	2.08622	−	3.61344i	0.208622	−	0.361344i
$101$	7.06589	+	12.2385i	0.703082	+	1.21777i	0.967379	+	0.253332i	$0.0815266\pi$
$101$	7.06589	+	12.2385i	0.703082	+	1.21777i	−0.264297	+	0.964441i	$0.585140\pi$
$102$	−1.14263	−	1.97909i	−0.113137	−	0.195959i
$103$	6.94241	−	12.0246i	0.684056	−	1.18482i	−0.289676	−	0.957125i	$-0.593548\pi$
$103$	6.94241	−	12.0246i	0.684056	−	1.18482i	0.973732	−	0.227695i	$-0.0731191\pi$
$104$	0.690111			0.0676709
$105$	−2.38217	+	0.343765i	−0.232476	+	0.0335480i
$106$	−9.55025			−0.927602
$107$	−0.285680	+	0.494812i	−0.0276177	+	0.0478353i	−0.879504	−	0.475892i	$-0.842125\pi$
$107$	−0.285680	+	0.494812i	−0.0276177	+	0.0478353i	0.851886	+	0.523727i	$0.175459\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.75638	−	4.77419i	−0.264013	−	0.457284i	0.703291	−	0.710902i	$-0.251713\pi$
$109$	−2.75638	−	4.77419i	−0.264013	−	0.457284i	−0.967305	+	0.253617i	$0.918380\pi$
$110$	−2.42534	+	4.20082i	−0.231247	+	0.400532i
$111$	−7.15906			−0.679508
$112$	0.982053	−	2.45674i	0.0927953	−	0.232140i
$113$	9.22473			0.867789			0.433895	−	0.900964i	$-0.357139\pi$
$113$	9.22473			0.867789			0.433895	+	0.900964i	$0.357139\pi$
$114$	−3.59109	+	6.21996i	−0.336337	+	0.582552i
$115$	1.52475	+	2.64094i	0.142183	+	0.246269i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	0.345055	−	0.597653i	0.0319004	−	0.0552531i
$118$	−13.9778			−1.28676
$119$	3.73998	+	4.75071i	0.342844	+	0.435497i
$120$	−0.909703			−0.0830441
$121$	−8.71598	+	15.0965i	−0.792362	+	1.37241i
$122$	−4.93846	−	8.55366i	−0.447107	−	0.774412i
$123$	−3.23238	−	5.59864i	−0.291454	−	0.504813i
$124$	−5.52389	+	9.56767i	−0.496060	+	0.859202i
$125$	8.34420			0.746328
$126$	−1.63657	−	2.07885i	−0.145797	−	0.185199i
$127$	−5.87845			−0.521628			−0.260814	−	0.965389i	$-0.583991\pi$
$127$	−5.87845			−0.521628			−0.260814	+	0.965389i	$0.583991\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.862247	−	1.49346i	−0.0759166	−	0.131491i
$130$	0.313898	+	0.543687i	0.0275307	+	0.0476845i
$131$	−3.65285	+	6.32691i	−0.319151	+	0.552785i	−0.980311	−	0.197459i	$-0.936731\pi$
$131$	−3.65285	+	6.32691i	−0.319151	+	0.552785i	0.661160	+	0.750245i	$0.270064\pi$
$132$	−5.33216			−0.464105
$133$	7.05329	−	17.6448i	0.611598	−	1.53000i
$134$	−5.83366			−0.503952
$135$	−0.454851	+	0.787826i	−0.0391474	+	0.0678053i
$136$	1.14263	+	1.97909i	0.0979795	+	0.169705i
$137$	3.70609	+	6.41914i	0.316633	+	0.548424i	0.979783	−	0.200062i	$-0.0641143\pi$
$137$	3.70609	+	6.41914i	0.316633	+	0.548424i	−0.663150	+	0.748486i	$0.730781\pi$
$138$	−1.67609	+	2.90308i	−0.142678	+	0.247126i
$139$	−4.96095			−0.420782			−0.210391	−	0.977617i	$-0.567474\pi$
$139$	−4.96095			−0.420782			−0.210391	+	0.977617i	$0.567474\pi$
$140$	2.38217	−	0.343765i	0.201330	−	0.0290534i
$141$	−4.54714			−0.382938
$142$	7.01311	−	12.1471i	0.588528	−	1.01936i
$143$	1.83989	+	3.18679i	0.153859	+	0.266492i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.454851	−	0.787826i	0.0377734	−	0.0654254i
$146$	4.39544			0.363769
$147$	5.07114	+	4.82530i	0.418261	+	0.397984i
$148$	7.15906			0.588471
$149$	5.00475	−	8.66849i	0.410005	−	0.710150i	−0.584884	−	0.811117i	$-0.698860\pi$
$149$	5.00475	−	8.66849i	0.410005	−	0.710150i	0.994890	+	0.100967i	$0.0321935\pi$
$150$	2.08622	+	3.61344i	0.170339	+	0.295036i
$151$	−2.44903	−	4.24184i	−0.199299	−	0.345196i	0.749002	−	0.662567i	$-0.230533\pi$
$151$	−2.44903	−	4.24184i	−0.199299	−	0.345196i	−0.948301	+	0.317371i	$0.897200\pi$
$152$	3.59109	−	6.21996i	0.291276	−	0.504505i
$153$	2.28525			0.184752
$154$	13.9629	−	2.01495i	1.12517	−	0.162370i
$155$	−10.0502			−0.807252
$156$	−0.345055	+	0.597653i	−0.0276265	+	0.0478506i
$157$	7.08812	+	12.2770i	0.565693	+	0.979810i	0.996985	+	0.0775969i	$0.0247247\pi$
$157$	7.08812	+	12.2770i	0.565693	+	0.979810i	−0.431292	+	0.902213i	$0.641942\pi$
$158$	6.18160	+	10.7068i	0.491782	+	0.851791i
$159$	4.77512	−	8.27076i	0.378692	−	0.655914i
$160$	0.909703			0.0719183
$161$	3.29202	−	8.23544i	0.259448	−	0.649044i
$162$	−1.00000			−0.0785674
$163$	6.06544	−	10.5057i	0.475082	−	0.822867i	−0.524510	−	0.851404i	$-0.675752\pi$
$163$	6.06544	−	10.5057i	0.475082	−	0.822867i	0.999593	+	0.0285373i	$0.00908495\pi$
$164$	3.23238	+	5.59864i	0.252406	+	0.437181i
$165$	−2.42534	−	4.20082i	−0.188813	−	0.327033i
$166$	−1.68658	+	2.92124i	−0.130904	+	0.226732i
$167$	1.23390			0.0954824			0.0477412	−	0.998860i	$-0.484798\pi$
$167$	1.23390			0.0954824			0.0477412	+	0.998860i	$0.484798\pi$
$168$	1.63657	+	2.07885i	0.126264	+	0.160387i
$169$	−12.5237			−0.963365
$170$	−1.03945	+	1.80038i	−0.0797223	+	0.138083i
$171$	−3.59109	−	6.21996i	−0.274618	−	0.475652i
$172$	0.862247	+	1.49346i	0.0657457	+	0.113875i
$173$	−9.97752	+	17.2816i	−0.758577	+	1.31389i	0.184999	+	0.982739i	$0.440772\pi$
$173$	−9.97752	+	17.2816i	−0.758577	+	1.31389i	−0.943576	+	0.331155i	$0.892562\pi$
$174$	1.00000			0.0758098
$175$	−6.82850	−	8.67389i	−0.516186	−	0.655685i
$176$	5.33216			0.401927
$177$	6.98891	−	12.1051i	0.525318	−	0.909878i
$178$	−5.65618	−	9.79679i	−0.423949	−	0.734301i
$179$	5.81029	+	10.0637i	0.434281	+	0.752197i	0.997237	−	0.0742899i	$-0.0236690\pi$
$179$	5.81029	+	10.0637i	0.434281	+	0.752197i	−0.562955	+	0.826487i	$0.690336\pi$
$180$	0.454851	−	0.787826i	0.0339026	−	0.0587211i
$181$	−8.34117			−0.619994			−0.309997	−	0.950738i	$-0.600328\pi$
$181$	−8.34117			−0.619994			−0.309997	+	0.950738i	$0.600328\pi$
$182$	0.677726	−	1.69542i	0.0502364	−	0.125673i
$183$	9.87691			0.730123
$184$	1.67609	−	2.90308i	0.123563	−	0.214018i
$185$	3.25631	+	5.64010i	0.239409	+	0.414668i
$186$	−5.52389	−	9.56767i	−0.405032	−	0.701535i
$187$	−6.09267	+	10.5528i	−0.445541	+	0.771699i
$188$	4.54714			0.331634
$189$	2.61863	−	0.377887i	0.190477	−	0.0274872i
$190$	6.53366			0.474001
$191$	5.22252	−	9.04566i	0.377888	−	0.654521i	−0.612867	−	0.790186i	$-0.709984\pi$
$191$	5.22252	−	9.04566i	0.377888	−	0.654521i	0.990755	+	0.135665i	$0.0433171\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−4.90192	−	8.49037i	−0.352848	−	0.611150i	0.633900	−	0.773415i	$-0.281453\pi$
$193$	−4.90192	−	8.49037i	−0.352848	−	0.611150i	−0.986747	+	0.162265i	$0.948120\pi$
$194$	−4.75638	+	8.23829i	−0.341488	+	0.591475i
$195$	−0.627796			−0.0449574
$196$	−5.07114	−	4.82530i	−0.362224	−	0.344664i
$197$	19.4696			1.38715			0.693577	−	0.720382i	$-0.256034\pi$
$197$	19.4696			1.38715			0.693577	+	0.720382i	$0.256034\pi$
$198$	2.66608	−	4.61779i	0.189470	−	0.328172i
$199$	−5.42059	−	9.38874i	−0.384256	−	0.665550i	0.607410	−	0.794389i	$-0.292209\pi$
$199$	−5.42059	−	9.38874i	−0.384256	−	0.665550i	−0.991666	+	0.128838i	$0.958875\pi$
$200$	−2.08622	−	3.61344i	−0.147518	−	0.255509i
$201$	2.91683	−	5.05210i	0.205737	−	0.356348i
$202$	14.1318			0.994308
$203$	−2.61863	+	0.377887i	−0.183792	+	0.0265225i
$204$	−2.28525			−0.160000
$205$	−2.94050	+	5.09310i	−0.205374	+	0.355718i
$206$	−6.94241	−	12.0246i	−0.483701	−	0.837794i
$207$	−1.67609	−	2.90308i	−0.116496	−	0.201778i
$208$	0.345055	−	0.597653i	0.0239253	−	0.0414398i
$209$	38.2966			2.64903
$210$	−0.893377	+	2.23490i	−0.0616489	+	0.154223i
$211$	14.5804			1.00375			0.501877	−	0.864939i	$-0.332643\pi$
$211$	14.5804			1.00375			0.501877	+	0.864939i	$0.332643\pi$
$212$	−4.77512	+	8.27076i	−0.327957	+	0.568038i
$213$	7.01311	+	12.1471i	0.480531	+	0.832304i
$214$	0.285680	+	0.494812i	0.0195287	+	0.0338246i
$215$	−0.784389	+	1.35860i	−0.0534949	+	0.0926558i
$216$	1.00000			0.0680414
$217$	18.0805	+	22.9667i	1.22738	+	1.55908i
$218$	−5.51276			−0.373371
$219$	−2.19772	+	3.80656i	−0.148508	+	0.257223i
$220$	2.42534	+	4.20082i	0.163517	+	0.283219i
$221$	0.788539	+	1.36579i	0.0530429	+	0.0918730i
$222$	−3.57953	+	6.19993i	−0.240242	+	0.416112i
$223$	−25.8081			−1.72824			−0.864120	−	0.503286i	$-0.832124\pi$
$223$	−25.8081			−1.72824			−0.864120	+	0.503286i	$0.832124\pi$
$224$	−1.63657	−	2.07885i	−0.109348	−	0.138899i
$225$	−4.17244			−0.278163
$226$	4.61236	−	7.98885i	0.306810	−	0.531410i
$227$	2.36664	+	4.09915i	0.157080	+	0.272070i	0.933814	−	0.357758i	$-0.116459\pi$
$227$	2.36664	+	4.09915i	0.157080	+	0.272070i	−0.776735	+	0.629828i	$0.783125\pi$
$228$	3.59109	+	6.21996i	0.237826	+	0.411927i
$229$	−8.18249	+	14.1725i	−0.540714	+	0.936544i	0.458149	+	0.888875i	$0.348513\pi$
$229$	−8.18249	+	14.1725i	−0.540714	+	0.936544i	−0.998863	+	0.0476691i	$0.984821\pi$
$230$	3.04949			0.201078
$231$	−5.23647	+	13.0997i	−0.344534	+	0.861900i
$232$	−1.00000			−0.0656532
$233$	10.1343	−	17.5531i	0.663921	−	1.14994i	−0.315656	−	0.948874i	$-0.602225\pi$
$233$	10.1343	−	17.5531i	0.663921	−	1.14994i	0.979577	−	0.201071i	$-0.0644420\pi$
$234$	−0.345055	−	0.597653i	−0.0225570	−	0.0390698i
$235$	2.06827	+	3.58236i	0.134919	+	0.233687i
$236$	−6.98891	+	12.1051i	−0.454939	+	0.787977i
$237$	−12.3632			−0.803076
$238$	5.98423	−	0.863567i	0.387900	−	0.0559768i
$239$	25.1911			1.62948			0.814738	−	0.579829i	$-0.196881\pi$
$239$	25.1911			1.62948			0.814738	+	0.579829i	$0.196881\pi$
$240$	−0.454851	+	0.787826i	−0.0293605	+	0.0508539i
$241$	6.15610	+	10.6627i	0.396549	+	0.686843i	0.993298	−	0.115585i	$-0.0368743\pi$
$241$	6.15610	+	10.6627i	0.396549	+	0.686843i	−0.596748	+	0.802428i	$0.703541\pi$
$242$	8.71598	+	15.0965i	0.560285	+	0.970441i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−9.87691			−0.632305
$245$	1.49488	−	6.18997i	0.0955043	−	0.395463i
$246$	−6.46476			−0.412178
$247$	2.47825	−	4.29246i	0.157687	−	0.273123i
$248$	5.52389	+	9.56767i	0.350768	+	0.607547i
$249$	−1.68658	−	2.92124i	−0.106883	−	0.185126i
$250$	4.17210	−	7.22629i	0.263867	−	0.457030i
$251$	−22.6769			−1.43135			−0.715676	−	0.698432i	$-0.753881\pi$
$251$	−22.6769			−1.43135			−0.715676	+	0.698432i	$0.753881\pi$
$252$	−2.61863	+	0.377887i	−0.164958	+	0.0238046i
$253$	17.8744			1.12375
$254$	−2.93923	+	5.09089i	−0.184423	+	0.319431i
$255$	−1.03945	−	1.80038i	−0.0650930	−	0.112744i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.75123	+	6.49732i	−0.233995	+	0.405292i	−0.958980	−	0.283473i	$-0.908513\pi$
$257$	−3.75123	+	6.49732i	−0.233995	+	0.405292i	0.724985	+	0.688765i	$0.241847\pi$
$258$	−1.72449			−0.107362
$259$	7.03058	−	17.5880i	0.436859	−	1.09286i
$260$	0.627796			0.0389342
$261$	−0.500000	+	0.866025i	−0.0309492	+	0.0536056i
$262$	3.65285	+	6.32691i	0.225674	+	0.390878i
$263$	8.91184	+	15.4358i	0.549528	+	0.951810i	0.998307	+	0.0581674i	$0.0185257\pi$
$263$	8.91184	+	15.4358i	0.549528	+	0.951810i	−0.448779	+	0.893643i	$0.648141\pi$
$264$	−2.66608	+	4.61779i	−0.164086	+	0.284205i
$265$	−8.68789			−0.533693
$266$	−11.7542	−	14.9307i	−0.720695	−	0.915461i
$267$	11.3124			0.692305
$268$	−2.91683	+	5.05210i	−0.178174	+	0.308606i
$269$	−3.63368	−	6.29371i	−0.221549	−	0.383734i	0.733729	−	0.679442i	$-0.237778\pi$
$269$	−3.63368	−	6.29371i	−0.221549	−	0.383734i	−0.955279	+	0.295707i	$0.904445\pi$
$270$	0.454851	+	0.787826i	0.0276814	+	0.0479456i
$271$	15.1075	−	26.1670i	0.917716	−	1.58953i	0.114841	−	0.993384i	$-0.463364\pi$
$271$	15.1075	−	26.1670i	0.917716	−	1.58953i	0.802875	−	0.596148i	$-0.203303\pi$
$272$	2.28525			0.138564
$273$	1.12942	+	1.43464i	0.0683554	+	0.0868283i
$274$	7.41219			0.447787
$275$	11.1241	−	19.2675i	0.670807	−	1.16187i
$276$	1.67609	+	2.90308i	0.100889	+	0.174745i
$277$	6.35055	+	10.9995i	0.381568	+	0.660894i	0.991287	−	0.131723i	$-0.0420510\pi$
$277$	6.35055	+	10.9995i	0.381568	+	0.660894i	−0.609719	+	0.792618i	$0.708718\pi$
$278$	−2.48047	+	4.29631i	−0.148769	+	0.257675i
$279$	11.0478			0.661414
$280$	0.893377	−	2.23490i	0.0533895	−	0.133561i
$281$	−1.37338			−0.0819292			−0.0409646	−	0.999161i	$-0.513043\pi$
$281$	−1.37338			−0.0819292			−0.0409646	+	0.999161i	$0.513043\pi$
$282$	−2.27357	+	3.93794i	−0.135389	+	0.234501i
$283$	−3.04005	−	5.26553i	−0.180713	−	0.313003i	0.761411	−	0.648270i	$-0.224507\pi$
$283$	−3.04005	−	5.26553i	−0.180713	−	0.313003i	−0.942123	+	0.335266i	$0.891174\pi$
$284$	−7.01311	−	12.1471i	−0.416152	−	0.720796i
$285$	−3.26683	+	5.65831i	−0.193510	+	0.335170i
$286$	3.67978			0.217590
$287$	16.9288	−	2.44295i	0.999274	−	0.144203i
$288$	−1.00000			−0.0589256
$289$	5.88881	−	10.1997i	0.346400	−	0.599983i
$290$	−0.454851	−	0.787826i	−0.0267098	−	0.0462627i
$291$	−4.75638	−	8.23829i	−0.278824	−	0.482937i
$292$	2.19772	−	3.80656i	0.128612	−	0.222762i
$293$	−13.9106			−0.812665			−0.406332	−	0.913725i	$-0.633193\pi$
$293$	−13.9106			−0.812665			−0.406332	+	0.913725i	$0.633193\pi$
$294$	6.71440	−	1.97909i	0.391592	−	0.115423i
$295$	−12.7157			−0.740334
$296$	3.57953	−	6.19993i	0.208056	−	0.360364i
$297$	2.66608	+	4.61779i	0.154702	+	0.267951i
$298$	−5.00475	−	8.66849i	−0.289918	−	0.502152i
$299$	1.15669	−	2.00344i	0.0668931	−	0.115862i
$300$	4.17244			0.240896
$301$	4.51581	−	0.651664i	0.260287	−	0.0375613i
$302$	−4.89806			−0.281852
$303$	−7.06589	+	12.2385i	−0.405924	+	0.703082i
$304$	−3.59109	−	6.21996i	−0.205963	−	0.356739i
$305$	−4.49253	−	7.78129i	−0.257241	−	0.445555i
$306$	1.14263	−	1.97909i	0.0653196	−	0.113137i
$307$	−16.3783			−0.934758			−0.467379	−	0.884057i	$-0.654802\pi$
$307$	−16.3783			−0.934758			−0.467379	+	0.884057i	$0.654802\pi$
$308$	5.23647	−	13.0997i	0.298376	−	0.746427i
$309$	13.8848			0.789880
$310$	−5.02510	+	8.70373i	−0.285407	+	0.494339i
$311$	−12.6798	−	21.9621i	−0.719006	−	1.24536i	−0.961394	−	0.275176i	$-0.911264\pi$
$311$	−12.6798	−	21.9621i	−0.719006	−	1.24536i	0.242387	−	0.970180i	$-0.422070\pi$
$312$	0.345055	+	0.597653i	0.0195349	+	0.0338355i
$313$	−3.23058	+	5.59553i	−0.182603	+	0.316278i	−0.942766	−	0.333454i	$-0.891786\pi$
$313$	−3.23058	+	5.59553i	−0.182603	+	0.316278i	0.760163	+	0.649732i	$0.225119\pi$
$314$	14.1762			0.800011
$315$	−1.48879	−	1.89114i	−0.0838841	−	0.106554i
$316$	12.3632			0.695484
$317$	4.22018	−	7.30957i	0.237029	−	0.410546i	−0.722831	−	0.691024i	$-0.757160\pi$
$317$	4.22018	−	7.30957i	0.237029	−	0.410546i	0.959860	+	0.280478i	$0.0904930\pi$
$318$	−4.77512	−	8.27076i	−0.267776	−	0.463801i
$319$	−2.66608	−	4.61779i	−0.149272	−	0.258547i
$320$	0.454851	−	0.787826i	0.0254270	−	0.0440408i
$321$	−0.571360			−0.0318902
$322$	−5.48609	−	6.96870i	−0.305728	−	0.388350i
$323$	16.4131			0.913251
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.43972	−	2.49367i	−0.0798615	−	0.138324i
$326$	−6.06544	−	10.5057i	−0.335934	−	0.581855i
$327$	2.75638	−	4.77419i	0.152428	−	0.264013i
$328$	6.46476			0.356956
$329$	4.46554	−	11.1711i	0.246193	−	0.615885i
$330$	−4.85068			−0.267021
$331$	−9.30548	+	16.1176i	−0.511476	+	0.885902i	0.488436	+	0.872600i	$0.337568\pi$
$331$	−9.30548	+	16.1176i	−0.511476	+	0.885902i	−0.999912	+	0.0133020i	$0.995766\pi$
$332$	1.68658	+	2.92124i	0.0925631	+	0.160324i
$333$	−3.57953	−	6.19993i	−0.196157	−	0.339754i
$334$	0.616952	−	1.06859i	0.0337581	−	0.0584708i
$335$	−5.30690			−0.289947
$336$	2.61863	−	0.377887i	0.142858	−	0.0206154i
$337$	17.5904			0.958209			0.479104	−	0.877758i	$-0.340962\pi$
$337$	17.5904			0.958209			0.479104	+	0.877758i	$0.340962\pi$
$338$	−6.26187	+	10.8459i	−0.340601	+	0.589938i
$339$	4.61236	+	7.98885i	0.250509	+	0.433895i
$340$	1.03945	+	1.80038i	0.0563722	+	0.0976394i
$341$	−29.4543	+	51.0164i	−1.59504	+	2.76269i
$342$	−7.18219			−0.388368
$343$	−16.8346	+	7.71978i	−0.908985	+	0.416829i
$344$	1.72449			0.0929785
$345$	−1.52475	+	2.64094i	−0.0820895	+	0.142183i
$346$	9.97752	+	17.2816i	0.536395	+	0.929063i
$347$	−18.1083	−	31.3646i	−0.972107	−	1.68374i	−0.689170	−	0.724600i	$-0.742025\pi$
$347$	−18.1083	−	31.3646i	−0.972107	−	1.68374i	−0.282937	−	0.959138i	$-0.591309\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	4.02980			0.215710			0.107855	−	0.994167i	$-0.465602\pi$
$349$	4.02980			0.215710			0.107855	+	0.994167i	$0.465602\pi$
$350$	−10.9261	+	1.57671i	−0.584023	+	0.0842787i
$351$	0.690111			0.0368354
$352$	2.66608	−	4.61779i	0.142103	−	0.246129i
$353$	−2.18843	−	3.79048i	−0.116479	−	0.201747i	0.801891	−	0.597470i	$-0.203827\pi$
$353$	−2.18843	−	3.79048i	−0.116479	−	0.201747i	−0.918370	+	0.395723i	$0.870494\pi$
$354$	−6.98891	−	12.1051i	−0.371456	−	0.643381i
$355$	6.37985	−	11.0502i	0.338607	−	0.586485i
$356$	−11.3124			−0.599554
$357$	−2.24424	+	5.61428i	−0.118778	+	0.297139i
$358$	11.6206			0.614167
$359$	−7.37875	+	12.7804i	−0.389436	+	0.674522i	−0.992374	−	0.123266i	$-0.960663\pi$
$359$	−7.37875	+	12.7804i	−0.389436	+	0.674522i	0.602938	+	0.797788i	$0.293997\pi$
$360$	−0.454851	−	0.787826i	−0.0239728	−	0.0415221i
$361$	−16.2919	−	28.2184i	−0.857469	−	1.48518i
$362$	−4.17058	+	7.22366i	−0.219201	+	0.379667i
$363$	−17.4320			−0.914941
$364$	−1.12942	−	1.43464i	−0.0591975	−	0.0751955i
$365$	3.99854			0.209293
$366$	4.93846	−	8.55366i	0.258137	−	0.447107i
$367$	−2.45183	−	4.24670i	−0.127985	−	0.221676i	0.794911	−	0.606726i	$-0.207517\pi$
$367$	−2.45183	−	4.24670i	−0.127985	−	0.221676i	−0.922896	+	0.385050i	$0.874184\pi$
$368$	−1.67609	−	2.90308i	−0.0873723	−	0.151333i
$369$	3.23238	−	5.59864i	0.168271	−	0.291454i
$370$	6.51262			0.338575
$371$	15.6297	+	19.8536i	0.811452	+	1.03075i
$372$	−11.0478			−0.572801
$373$	7.41897	−	12.8500i	0.384140	−	0.665350i	−0.607510	−	0.794312i	$-0.707831\pi$
$373$	7.41897	−	12.8500i	0.384140	−	0.665350i	0.991649	+	0.128963i	$0.0411647\pi$
$374$	6.09267	+	10.5528i	0.315045	+	0.545673i
$375$	4.17210	+	7.22629i	0.215446	+	0.373164i
$376$	2.27357	−	3.93794i	0.117250	−	0.203084i
$377$	−0.690111			−0.0355425
$378$	0.982053	−	2.45674i	0.0505114	−	0.126361i
$379$	−11.5100			−0.591228			−0.295614	−	0.955307i	$-0.595524\pi$
$379$	−11.5100			−0.591228			−0.295614	+	0.955307i	$0.595524\pi$
$380$	3.26683	−	5.65831i	0.167585	−	0.290265i
$381$	−2.93923	−	5.09089i	−0.150581	−	0.260814i
$382$	−5.22252	−	9.04566i	−0.267207	−	0.462816i
$383$	−3.06830	+	5.31445i	−0.156783	+	0.271556i	−0.933707	−	0.358039i	$-0.883446\pi$
$383$	−3.06830	+	5.31445i	−0.156783	+	0.271556i	0.776924	+	0.629594i	$0.216779\pi$
$384$	1.00000			0.0510310
$385$	12.7021	−	1.83301i	0.647360	−	0.0934188i
$386$	−9.80383			−0.499002
$387$	0.862247	−	1.49346i	0.0438305	−	0.0759166i
$388$	4.75638	+	8.23829i	0.241469	+	0.418236i
$389$	−14.8658	−	25.7483i	−0.753725	−	1.30549i	−0.946006	−	0.324150i	$-0.894922\pi$
$389$	−14.8658	−	25.7483i	−0.753725	−	1.30549i	0.192281	−	0.981340i	$-0.438412\pi$
$390$	−0.313898	+	0.543687i	−0.0158948	+	0.0275307i
$391$	7.66059			0.387413
$392$	−6.71440	+	1.97909i	−0.339129	+	0.0999591i
$393$	−7.30569			−0.368523
$394$	9.73482	−	16.8612i	0.490433	−	0.849455i
$395$	5.62342	+	9.74005i	0.282945	+	0.490075i
$396$	−2.66608	−	4.61779i	−0.133976	−	0.232053i
$397$	17.2610	−	29.8969i	0.866303	−	1.50048i	0.000555583	−	1.00000i	$-0.499823\pi$
$397$	17.2610	−	29.8969i	0.866303	−	1.50048i	0.865747	−	0.500481i	$-0.166844\pi$
$398$	−10.8412			−0.543420
$399$	18.8075	−	2.71405i	0.941551	−	0.135873i
$400$	−4.17244			−0.208622
$401$	−2.29712	+	3.97873i	−0.114713	+	0.198688i	−0.917665	−	0.397355i	$-0.869928\pi$
$401$	−2.29712	+	3.97873i	−0.114713	+	0.198688i	0.802952	+	0.596044i	$0.203261\pi$
$402$	−2.91683	−	5.05210i	−0.145478	−	0.251976i
$403$	3.81210	+	6.60275i	0.189894	+	0.328906i
$404$	7.06589	−	12.2385i	0.351541	−	0.608887i
$405$	−0.909703			−0.0452035
$406$	−0.982053	+	2.45674i	−0.0487385	+	0.121926i
$407$	38.1733			1.89218
$408$	−1.14263	+	1.97909i	−0.0565685	+	0.0979795i
$409$	−8.23684	−	14.2666i	−0.407286	−	0.705439i	0.587299	−	0.809370i	$-0.300191\pi$
$409$	−8.23684	−	14.2666i	−0.407286	−	0.705439i	−0.994585	+	0.103931i	$0.966858\pi$
$410$	2.94050	+	5.09310i	0.145221	+	0.251530i
$411$	−3.70609	+	6.41914i	−0.182808	+	0.316633i
$412$	−13.8848			−0.684056
$413$	22.8757	+	29.0578i	1.12564	+	1.42984i
$414$	−3.35218			−0.164751
$415$	−1.53429	+	2.65746i	−0.0753152	+	0.130450i
$416$	−0.345055	−	0.597653i	−0.0169177	−	0.0293024i
$417$	−2.48047	−	4.29631i	−0.121469	−	0.210391i
$418$	19.1483	−	33.1658i	0.936574	−	1.62219i
$419$	−2.07350			−0.101297			−0.0506485	−	0.998717i	$-0.516129\pi$
$419$	−2.07350			−0.101297			−0.0506485	+	0.998717i	$0.516129\pi$
$420$	1.48879	+	1.89114i	0.0726457	+	0.0922781i
$421$	−27.4605			−1.33834			−0.669170	−	0.743109i	$-0.733350\pi$
$421$	−27.4605			−1.33834			−0.669170	+	0.743109i	$0.733350\pi$
$422$	7.29019	−	12.6270i	0.354881	−	0.614672i
$423$	−2.27357	−	3.93794i	−0.110545	−	0.191469i
$424$	4.77512	+	8.27076i	0.231900	+	0.401663i
$425$	4.76754	−	8.25763i	0.231260	−	0.400554i
$426$	14.0262			0.679573
$427$	−9.69966	+	24.2650i	−0.469399	+	1.17427i
$428$	0.571360			0.0276177
$429$	−1.83989	+	3.18679i	−0.0888308	+	0.153859i
$430$	0.784389	+	1.35860i	0.0378266	+	0.0655176i
$431$	−4.53528	−	7.85533i	−0.218457	−	0.378378i	0.735880	−	0.677112i	$-0.236769\pi$
$431$	−4.53528	−	7.85533i	−0.218457	−	0.378378i	−0.954336	+	0.298734i	$0.903436\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−21.0209			−1.01020			−0.505101	−	0.863060i	$-0.668545\pi$
$433$	−21.0209			−1.01020			−0.505101	+	0.863060i	$0.668545\pi$
$434$	28.9300	−	4.17481i	1.38869	−	0.200397i
$435$	0.909703			0.0436169
$436$	−2.75638	+	4.77419i	−0.132007	+	0.228642i
$437$	−12.0380	−	20.8504i	−0.575856	−	0.997412i
$438$	2.19772	+	3.80656i	0.105011	+	0.181884i
$439$	−18.7383	+	32.4557i	−0.894332	+	1.54903i	−0.0597019	+	0.998216i	$0.519015\pi$
$439$	−18.7383	+	32.4557i	−0.894332	+	1.54903i	−0.834630	+	0.550812i	$0.814318\pi$
$440$	4.85068			0.231247
$441$	−1.64326	+	6.80439i	−0.0782505	+	0.324018i
$442$	1.57708			0.0750140
$443$	−16.9173	+	29.3017i	−0.803767	+	1.39216i	0.113354	+	0.993555i	$0.463841\pi$
$443$	−16.9173	+	29.3017i	−0.803767	+	1.39216i	−0.917121	+	0.398610i	$0.869493\pi$
$444$	3.57953	+	6.19993i	0.169877	+	0.294236i
$445$	−5.14545	−	8.91217i	−0.243918	−	0.422478i
$446$	−12.9041	+	22.3505i	−0.611025	+	1.05833i
$447$	10.0095			0.473433
$448$	−2.61863	+	0.377887i	−0.123718	+	0.0178535i
$449$	−29.7587			−1.40440			−0.702200	−	0.711980i	$-0.747799\pi$
$449$	−29.7587			−1.40440			−0.702200	+	0.711980i	$0.747799\pi$
$450$	−2.08622	+	3.61344i	−0.0983454	+	0.170339i
$451$	17.2356	+	29.8529i	0.811591	+	1.40572i
$452$	−4.61236	−	7.98885i	−0.216947	−	0.375764i
$453$	2.44903	−	4.24184i	0.115065	−	0.199299i
$454$	4.73329			0.222144
$455$	0.616529	−	1.54233i	0.0289033	−	0.0723056i
$456$	7.18219			0.336337
$457$	17.2349	−	29.8517i	0.806213	−	1.39640i	−0.109256	−	0.994014i	$-0.534847\pi$
$457$	17.2349	−	29.8517i	0.806213	−	1.39640i	0.915469	−	0.402389i	$-0.131820\pi$
$458$	8.18249	+	14.1725i	0.382343	+	0.662237i
$459$	1.14263	+	1.97909i	0.0533333	+	0.0923759i
$460$	1.52475	−	2.64094i	0.0710916	−	0.123134i
$461$	28.4680			1.32589			0.662944	−	0.748669i	$-0.269307\pi$
$461$	28.4680			1.32589			0.662944	+	0.748669i	$0.269307\pi$
$462$	8.72647	+	11.0848i	0.405992	+	0.515711i
$463$	−15.9129			−0.739533			−0.369767	−	0.929125i	$-0.620562\pi$
$463$	−15.9129			−0.739533			−0.369767	+	0.929125i	$0.620562\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	−5.02510	−	8.70373i	−0.233034	−	0.403626i
$466$	−10.1343	−	17.5531i	−0.469463	−	0.813133i
$467$	−17.5350	+	30.3714i	−0.811421	+	1.40542i	0.100448	+	0.994942i	$0.467972\pi$
$467$	−17.5350	+	30.3714i	−0.811421	+	1.40542i	−0.911869	+	0.410481i	$0.865361\pi$
$468$	−0.690111			−0.0319004
$469$	9.54721	+	12.1273i	0.440849	+	0.559988i
$470$	4.13655			0.190805
$471$	−7.08812	+	12.2770i	−0.326603	+	0.565693i
$472$	6.98891	+	12.1051i	0.321690	+	0.557184i
$473$	4.59764	+	7.96335i	0.211400	+	0.366155i
$474$	−6.18160	+	10.7068i	−0.283930	+	0.491782i
$475$	−29.9673			−1.37499
$476$	2.24424	−	5.61428i	0.102865	−	0.257330i
$477$	9.55025			0.437276
$478$	12.5955	−	21.8161i	0.576107	−	0.997846i
$479$	5.37819	+	9.31530i	0.245736	+	0.425627i	0.962338	−	0.271855i	$-0.0876371\pi$
$479$	5.37819	+	9.31530i	0.245736	+	0.425627i	−0.716602	+	0.697482i	$0.754304\pi$
$480$	0.454851	+	0.787826i	0.0207610	+	0.0359592i
$481$	2.47027	−	4.27864i	0.112635	−	0.195089i
$482$	12.3122			0.560805
$483$	8.77812	−	1.26675i	0.399418	−	0.0576389i
$484$	17.4320			0.792362
$485$	−4.32689	+	7.49440i	−0.196474	+	0.340303i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	19.3383	+	33.4949i	0.876303	+	1.51780i	0.855368	+	0.518020i	$0.173331\pi$
$487$	19.3383	+	33.4949i	0.876303	+	1.51780i	0.0209344	+	0.999781i	$0.493336\pi$
$488$	−4.93846	+	8.55366i	−0.223553	+	0.387206i
$489$	12.1309			0.548578
$490$	−4.61323	−	4.38959i	−0.208405	−	0.198301i
$491$	10.6180			0.479184			0.239592	−	0.970874i	$-0.422986\pi$
$491$	10.6180			0.479184			0.239592	+	0.970874i	$0.422986\pi$
$492$	−3.23238	+	5.59864i	−0.145727	+	0.252406i
$493$	−1.14263	−	1.97909i	−0.0514613	−	0.0891337i
$494$	−2.47825	−	4.29246i	−0.111502	−	0.193127i
$495$	2.42534	−	4.20082i	0.109011	−	0.188813i
$496$	11.0478			0.496060
$497$	−36.7294	+	5.30033i	−1.64754	+	0.237752i
$498$	−3.37316			−0.151155
$499$	4.87704	−	8.44727i	0.218326	−	0.378152i	−0.735970	−	0.677014i	$-0.763274\pi$
$499$	4.87704	−	8.44727i	0.218326	−	0.378152i	0.954296	+	0.298862i	$0.0966070\pi$
$500$	−4.17210	−	7.22629i	−0.186582	−	0.323169i
$501$	0.616952	+	1.06859i	0.0275634	+	0.0477412i
$502$	−11.3384	+	19.6388i	−0.506059	+	0.876521i
$503$	9.30877			0.415057			0.207529	−	0.978229i	$-0.433458\pi$
$503$	9.30877			0.415057			0.207529	+	0.978229i	$0.433458\pi$
$504$	−0.982053	+	2.45674i	−0.0437441	+	0.109432i
$505$	12.8557			0.572072
$506$	8.93720	−	15.4797i	0.397307	−	0.688156i
$507$	−6.26187	−	10.8459i	−0.278100	−	0.481683i
$508$	2.93923	+	5.09089i	0.130407	+	0.225872i
$509$	19.7520	−	34.2115i	0.875494	−	1.51640i	0.0192584	−	0.999815i	$-0.493869\pi$
$509$	19.7520	−	34.2115i	0.875494	−	1.51640i	0.856236	−	0.516586i	$-0.172797\pi$
$510$	−2.07890			−0.0920553
$511$	−7.19345	−	9.13746i	−0.318219	−	0.404218i
$512$	−1.00000			−0.0441942
$513$	3.59109	−	6.21996i	0.158551	−	0.274618i
$514$	3.75123	+	6.49732i	0.165460	+	0.286584i
$515$	−6.31553	−	10.9388i	−0.278296	−	0.482022i
$516$	−0.862247	+	1.49346i	−0.0379583	+	0.0657457i
$517$	24.2461			1.06634
$518$	−11.7163	−	14.8826i	−0.514786	−	0.653906i
$519$	−19.9550			−0.875929
$520$	0.313898	−	0.543687i	0.0137653	−	0.0238423i
$521$	−21.5508	−	37.3271i	−0.944158	−	1.63533i	−0.757428	−	0.652919i	$-0.773544\pi$
$521$	−21.5508	−	37.3271i	−0.944158	−	1.63533i	−0.186730	−	0.982411i	$-0.559789\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	−9.54857	+	16.5386i	−0.417530	+	0.723183i	−0.995690	−	0.0927404i	$-0.970437\pi$
$523$	−9.54857	+	16.5386i	−0.417530	+	0.723183i	0.578161	+	0.815923i	$0.303771\pi$
$524$	7.30569			0.319151
$525$	4.09756	−	10.2506i	0.178832	−	0.447373i
$526$	17.8237			0.777150
$527$	−12.6235	+	21.8646i	−0.549888	+	0.952435i
$528$	2.66608	+	4.61779i	0.116026	+	0.200963i
$529$	5.88143	+	10.1869i	0.255714	+	0.442910i
$530$	−4.34394	+	7.52393i	−0.188689	+	0.326819i
$531$	13.9778			0.606585
$532$	−18.8075	+	2.71405i	−0.815407	+	0.117669i
$533$	4.46140			0.193245
$534$	5.65618	−	9.79679i	0.244767	−	0.423949i
$535$	0.259884	+	0.450132i	0.0112358	+	0.0194609i
$536$	2.91683	+	5.05210i	0.125988	+	0.218217i
$537$	−5.81029	+	10.0637i	−0.250732	+	0.434281i
$538$	−7.26735			−0.313318
$539$	−27.0402	−	25.7293i	−1.16470	−	1.10824i
$540$	0.909703			0.0391474
$541$	−16.7890	+	29.0794i	−0.721815	+	1.25022i	0.238457	+	0.971153i	$0.423358\pi$
$541$	−16.7890	+	29.0794i	−0.721815	+	1.25022i	−0.960272	+	0.279067i	$0.909975\pi$
$542$	−15.1075	−	26.1670i	−0.648923	−	1.12397i
$543$	−4.17058	−	7.22366i	−0.178977	−	0.309997i
$544$	1.14263	−	1.97909i	0.0489897	−	0.0848527i
$545$	−5.01497			−0.214818
$546$	1.80714	−	0.260784i	0.0773385	−	0.0111605i
$547$	−29.8057			−1.27440			−0.637200	−	0.770699i	$-0.719907\pi$
$547$	−29.8057			−1.27440			−0.637200	+	0.770699i	$0.719907\pi$
$548$	3.70609	−	6.41914i	0.158317	−	0.274212i
$549$	4.93846	+	8.55366i	0.210768	+	0.365061i
$550$	−11.1241	−	19.2675i	−0.474332	−	0.821567i
$551$	−3.59109	+	6.21996i	−0.152986	+	0.264979i
$552$	3.35218			0.142678
$553$	12.1413	−	30.3732i	0.516302	−	1.29160i
$554$	12.7011			0.539618
$555$	−3.25631	+	5.64010i	−0.138223	+	0.239409i
$556$	2.48047	+	4.29631i	0.105195	+	0.182204i
$557$	11.4307	+	19.7986i	0.484335	+	0.838893i	0.999838	−	0.0179945i	$-0.00572814\pi$
$557$	11.4307	+	19.7986i	0.484335	+	0.838893i	−0.515503	+	0.856888i	$0.672395\pi$
$558$	5.52389	−	9.56767i	0.233845	−	0.405032i
$559$	1.19009			0.0503355
$560$	−1.48879	−	1.89114i	−0.0629131	−	0.0799152i
$561$	−12.1853			−0.514466
$562$	−0.686691	+	1.18938i	−0.0289663	+	0.0501712i
$563$	−3.47237	−	6.01433i	−0.146343	−	0.253474i	0.783530	−	0.621354i	$-0.213417\pi$
$563$	−3.47237	−	6.01433i	−0.146343	−	0.253474i	−0.929873	+	0.367880i	$0.880084\pi$
$564$	2.27357	+	3.93794i	0.0957346	+	0.165817i
$565$	4.19588	−	7.26748i	0.176522	−	0.305745i
$566$	−6.08011			−0.255566
$567$	1.63657	+	2.07885i	0.0687296	+	0.0873036i
$568$	−14.0262			−0.588528
$569$	−15.6428	+	27.0941i	−0.655779	+	1.13584i	0.325918	+	0.945398i	$0.394327\pi$
$569$	−15.6428	+	27.0941i	−0.655779	+	1.13584i	−0.981698	+	0.190445i	$0.939007\pi$
$570$	3.26683	+	5.65831i	0.136832	+	0.237001i
$571$	−14.7756	−	25.5921i	−0.618339	−	1.07099i	−0.989789	−	0.142541i	$-0.954473\pi$
$571$	−14.7756	−	25.5921i	−0.618339	−	1.07099i	0.371450	−	0.928453i	$-0.378861\pi$
$572$	1.83989	−	3.18679i	0.0769297	−	0.133246i
$573$	10.4450			0.436348
$574$	6.34873	−	15.8822i	0.264991	−	0.662911i
$575$	−13.9868			−0.583289
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	19.2405	+	33.3256i	0.800994	+	1.38736i	0.918963	+	0.394344i	$0.129028\pi$
$577$	19.2405	+	33.3256i	0.800994	+	1.38736i	−0.117969	+	0.993017i	$0.537638\pi$
$578$	−5.88881	−	10.1997i	−0.244942	−	0.424252i
$579$	4.90192	−	8.49037i	0.203717	−	0.352848i
$580$	−0.909703			−0.0377734
$581$	8.83305	−	1.27467i	0.366457	−	0.0528824i
$582$	−9.51276			−0.394316
$583$	−25.4617	+	44.1010i	−1.05452	+	1.82648i
$584$	−2.19772	−	3.80656i	−0.0909422	−	0.157517i
$585$	−0.313898	−	0.543687i	−0.0129781	−	0.0224787i
$586$	−6.95529	+	12.0469i	−0.287320	+	0.497654i
$587$	−2.86159			−0.118110			−0.0590552	−	0.998255i	$-0.518809\pi$
$587$	−2.86159			−0.118110			−0.0590552	+	0.998255i	$0.518809\pi$
$588$	1.64326	−	6.80439i	0.0677669	−	0.280608i
$589$	79.3473			3.26945
$590$	−6.35783	+	11.0121i	−0.261748	+	0.453360i
$591$	9.73482	+	16.8612i	0.400437	+	0.693577i
$592$	−3.57953	−	6.19993i	−0.147118	−	0.254816i
$593$	−16.7879	+	29.0774i	−0.689395	+	1.19407i	0.282639	+	0.959226i	$0.408790\pi$
$593$	−16.7879	+	29.0774i	−0.689395	+	1.19407i	−0.972034	+	0.234841i	$0.924543\pi$
$594$	5.33216			0.218781
$595$	5.44387	−	0.785590i	0.223177	−	0.0322060i
$596$	−10.0095			−0.410005
$597$	5.42059	−	9.38874i	0.221850	−	0.384256i
$598$	−1.15669	−	2.00344i	−0.0473005	−	0.0819269i
$599$	21.1201	+	36.5810i	0.862943	+	1.49466i	0.869075	+	0.494680i	$0.164715\pi$
$599$	21.1201	+	36.5810i	0.862943	+	1.49466i	−0.00613259	+	0.999981i	$0.501952\pi$
$600$	2.08622	−	3.61344i	0.0851696	−	0.147518i
$601$	−22.0015			−0.897459			−0.448730	−	0.893668i	$-0.648123\pi$
$601$	−22.0015			−0.897459			−0.448730	+	0.893668i	$0.648123\pi$
$602$	1.69355	−	4.23663i	0.0690238	−	0.172672i
$603$	5.83366			0.237565
$604$	−2.44903	+	4.24184i	−0.0996496	+	0.172598i
$605$	7.92896	+	13.7334i	0.322358	+	0.558340i
$606$	7.06589	+	12.2385i	0.287032	+	0.497154i
$607$	−11.8310	+	20.4918i	−0.480204	+	0.831737i	−0.999742	−	0.0227098i	$-0.992771\pi$
$607$	−11.8310	+	20.4918i	−0.480204	+	0.831737i	0.519538	+	0.854447i	$0.326104\pi$
$608$	−7.18219			−0.291276
$609$	−1.63657	−	2.07885i	−0.0663173	−	0.0842394i
$610$	−8.98506			−0.363794
$611$	1.56902	−	2.71761i	0.0634756	−	0.109943i
$612$	−1.14263	−	1.97909i	−0.0461880	−	0.0799999i
$613$	1.87428	+	3.24634i	0.0757014	+	0.131119i	0.901391	−	0.433006i	$-0.142547\pi$
$613$	1.87428	+	3.24634i	0.0757014	+	0.131119i	−0.825690	+	0.564125i	$0.809214\pi$
$614$	−8.18914	+	14.1840i	−0.330487	+	0.572420i
$615$	−5.88101			−0.237145
$616$	−8.72647	−	11.0848i	−0.351600	−	0.446619i
$617$	−23.1670			−0.932670			−0.466335	−	0.884608i	$-0.654426\pi$
$617$	−23.1670			−0.932670			−0.466335	+	0.884608i	$0.654426\pi$
$618$	6.94241	−	12.0246i	0.279265	−	0.483701i
$619$	−0.920536	−	1.59441i	−0.0369995	−	0.0640849i	0.846933	−	0.531700i	$-0.178447\pi$
$619$	−0.920536	−	1.59441i	−0.0369995	−	0.0640849i	−0.883932	+	0.467615i	$0.845113\pi$
$620$	5.02510	+	8.70373i	0.201813	+	0.349550i
$621$	1.67609	−	2.90308i	0.0672593	−	0.116496i
$622$	−25.3596			−1.01683
$623$	−11.1093	+	27.7915i	−0.445087	+	1.11344i
$624$	0.690111			0.0276265
$625$	−6.63573	+	11.4934i	−0.265429	+	0.459737i
$626$	3.23058	+	5.59553i	0.129120	+	0.223642i
$627$	19.1483	+	33.1658i	0.764710	+	1.32452i
$628$	7.08812	−	12.2770i	0.282847	−	0.489905i
$629$	16.3603			0.652327
$630$	−2.38217	+	0.343765i	−0.0949080	+	0.0136959i
$631$	−22.5906			−0.899319			−0.449659	−	0.893200i	$-0.648455\pi$
$631$	−22.5906			−0.899319			−0.449659	+	0.893200i	$0.648455\pi$
$632$	6.18160	−	10.7068i	0.245891	−	0.425895i
$633$	7.29019	+	12.6270i	0.289759	+	0.501877i
$634$	−4.22018	−	7.30957i	−0.167605	−	0.290300i
$635$	−2.67382	+	4.63120i	−0.106107	+	0.183783i
$636$	−9.55025			−0.378692
$637$	−4.63368	+	1.36579i	−0.183593	+	0.0541146i
$638$	−5.33216			−0.211102
$639$	−7.01311	+	12.1471i	−0.277435	+	0.480531i
$640$	−0.454851	−	0.787826i	−0.0179796	−	0.0311415i
$641$	−14.7698	−	25.5820i	−0.583370	−	1.01043i	−0.995076	−	0.0991103i	$-0.968400\pi$
$641$	−14.7698	−	25.5820i	−0.583370	−	1.01043i	0.411706	−	0.911317i	$-0.364933\pi$
$642$	−0.285680	+	0.494812i	−0.0112749	+	0.0195287i
$643$	−0.357542			−0.0141001			−0.00705004	−	0.999975i	$-0.502244\pi$
$643$	−0.357542			−0.0141001			−0.00705004	+	0.999975i	$0.502244\pi$
$644$	−8.77812	+	1.26675i	−0.345906	+	0.0499168i
$645$	−1.56878			−0.0617705
$646$	8.20656	−	14.2142i	0.322883	−	0.559250i
$647$	8.54939	+	14.8080i	0.336111	+	0.582162i	0.983698	−	0.179830i	$-0.0575548\pi$
$647$	8.54939	+	14.8080i	0.336111	+	0.582162i	−0.647586	+	0.761992i	$0.724221\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−37.2660	+	64.5466i	−1.46282	+	2.53367i
$650$	−2.87945			−0.112941
$651$	−10.8495	+	27.1415i	−0.425226	+	1.06376i
$652$	−12.1309			−0.475082
$653$	1.01852	−	1.76414i	0.0398579	−	0.0690360i	−0.845408	−	0.534121i	$-0.820643\pi$
$653$	1.01852	−	1.76414i	0.0398579	−	0.0690360i	0.885266	+	0.465085i	$0.153976\pi$
$654$	−2.75638	−	4.77419i	−0.107783	−	0.186686i
$655$	3.32300	+	5.75561i	0.129841	+	0.224890i
$656$	3.23238	−	5.59864i	0.126203	−	0.218590i
$657$	−4.39544			−0.171482
$658$	−7.44173	−	9.45284i	−0.290109	−	0.368510i
$659$	3.07552			0.119805			0.0599026	−	0.998204i	$-0.480921\pi$
$659$	3.07552			0.119805			0.0599026	+	0.998204i	$0.480921\pi$
$660$	−2.42534	+	4.20082i	−0.0944063	+	0.163517i
$661$	0.949879	+	1.64524i	0.0369460	+	0.0639924i	0.883907	−	0.467662i	$-0.154904\pi$
$661$	0.949879	+	1.64524i	0.0369460	+	0.0639924i	−0.846961	+	0.531655i	$0.821570\pi$
$662$	9.30548	+	16.1176i	0.361668	+	0.626427i
$663$	−0.788539	+	1.36579i	−0.0306243	+	0.0530429i
$664$	3.37316			0.130904
$665$	−10.6928	−	13.5825i	−0.414649	−	0.526707i
$666$	−7.15906			−0.277408
$667$	−1.67609	+	2.90308i	−0.0648985	+	0.112408i
$668$	−0.616952	−	1.06859i	−0.0238706	−	0.0413451i
$669$	−12.9041	−	22.3505i	−0.498900	−	0.864120i
$670$	−2.65345	+	4.59591i	−0.102512	+	0.177555i
$671$	−52.6653			−2.03312
$672$	0.982053	−	2.45674i	0.0378835	−	0.0947708i
$673$	39.0024			1.50343			0.751716	−	0.659487i	$-0.229226\pi$
$673$	39.0024			1.50343			0.751716	+	0.659487i	$0.229226\pi$
$674$	8.79519	−	15.2337i	0.338778	−	0.586781i
$675$	−2.08622	−	3.61344i	−0.0802987	−	0.139081i
$676$	6.26187	+	10.8459i	0.240841	+	0.417149i
$677$	7.42747	−	12.8648i	0.285461	−	0.494433i	−0.687260	−	0.726412i	$-0.741187\pi$
$677$	7.42747	−	12.8648i	0.285461	−	0.494433i	0.972721	+	0.231979i	$0.0745199\pi$
$678$	9.22473			0.354273
$679$	24.9104	−	3.59475i	0.955972	−	0.137954i
$680$	2.07890			0.0797223
$681$	−2.36664	+	4.09915i	−0.0906899	+	0.157080i
$682$	29.4543	+	51.0164i	1.12786	+	1.95352i
$683$	−8.84493	−	15.3199i	−0.338442	−	0.586198i	0.645698	−	0.763593i	$-0.276567\pi$
$683$	−8.84493	−	15.3199i	−0.338442	−	0.586198i	−0.984140	+	0.177394i	$0.943233\pi$
$684$	−3.59109	+	6.21996i	−0.137309	+	0.237826i
$685$	6.74289			0.257633
$686$	−1.73180	+	18.4391i	−0.0661203	+	0.704009i
$687$	−16.3650			−0.624363
$688$	0.862247	−	1.49346i	0.0328729	−	0.0569375i
$689$	3.29536	+	5.70774i	0.125543	+	0.217447i
$690$	1.52475	+	2.64094i	0.0580461	+	0.100539i
$691$	0.0308831	−	0.0534912i	0.00117485	−	0.00203490i	−0.865437	−	0.501017i	$-0.832959\pi$
$691$	0.0308831	−	0.0534912i	0.00117485	−	0.00203490i	0.866612	+	0.498982i	$0.166293\pi$
$692$	19.9550			0.758577
$693$	−13.9629	+	2.01495i	−0.530408	+	0.0765418i
$694$	−36.2167			−1.37477
$695$	−2.25649	+	3.90836i	−0.0855937	+	0.148253i
$696$	−0.500000	−	0.866025i	−0.0189525	−	0.0328266i
$697$	7.38680	+	12.7943i	0.279795	+	0.484619i
$698$	2.01490	−	3.48991i	0.0762651	−	0.132095i
$699$	20.2686			0.766629
$700$	−4.09756	+	10.2506i	−0.154873	+	0.387436i
$701$	−36.6942			−1.38592			−0.692961	−	0.720975i	$-0.743694\pi$
$701$	−36.6942			−1.38592			−0.692961	+	0.720975i	$0.743694\pi$
$702$	0.345055	−	0.597653i	0.0130233	−	0.0225570i
$703$	−25.7089	−	44.5291i	−0.969629	−	1.67945i
$704$	−2.66608	−	4.61779i	−0.100482	−	0.174039i
$705$	−2.06827	+	3.58236i	−0.0778957	+	0.134919i
$706$	−4.37687			−0.164726
$707$	−23.1277	−	29.3779i	−0.869805	−	1.10487i
$708$	−13.9778			−0.525318
$709$	−21.4677	+	37.1831i	−0.806235	+	1.39644i	0.109219	+	0.994018i	$0.465165\pi$
$709$	−21.4677	+	37.1831i	−0.806235	+	1.39644i	−0.915454	+	0.402423i	$0.868168\pi$
$710$	−6.37985	−	11.0502i	−0.239432	−	0.414708i
$711$	−6.18160	−	10.7068i	−0.231828	−	0.401538i
$712$	−5.65618	+	9.79679i	−0.211974	+	0.367150i
$713$	37.0342			1.38694
$714$	3.73998	+	4.75071i	0.139965	+	0.177791i
$715$	3.34751			0.125190
$716$	5.81029	−	10.0637i	0.217141	−	0.376099i
$717$	12.5955	+	21.8161i	0.470389	+	0.814738i
$718$	7.37875	+	12.7804i	0.275373	+	0.476959i
$719$	−6.61971	+	11.4657i	−0.246874	+	0.427598i	−0.962657	−	0.270725i	$-0.912737\pi$
$719$	−6.61971	+	11.4657i	−0.246874	+	0.427598i	0.715783	+	0.698323i	$0.246070\pi$
$720$	−0.909703			−0.0339026
$721$	−13.6356	+	34.1114i	−0.507818	+	1.27038i
$722$	−32.5838			−1.21264
$723$	−6.15610	+	10.6627i	−0.228948	+	0.396549i
$724$	4.17058	+	7.22366i	0.154999	+	0.268465i
$725$	2.08622	+	3.61344i	0.0774803	+	0.134200i
$726$	−8.71598	+	15.0965i	−0.323480	+	0.560285i
$727$	39.8095			1.47645			0.738226	−	0.674553i	$-0.235664\pi$
$727$	39.8095			1.47645			0.738226	+	0.674553i	$0.235664\pi$
$728$	−1.80714	+	0.260784i	−0.0669771	+	0.00966529i
$729$	1.00000			0.0370370
$730$	1.99927	−	3.46284i	0.0739963	−	0.128165i
$731$	1.97045	+	3.41293i	0.0728799	+	0.126232i
$732$	−4.93846	−	8.55366i	−0.182531	−	0.316152i
$733$	13.2619	−	22.9702i	0.489838	−	0.848424i	−0.510094	−	0.860119i	$-0.670389\pi$
$733$	13.2619	−	22.9702i	0.489838	−	0.848424i	0.999932	+	0.0116946i	$0.00372260\pi$
$734$	−4.90366			−0.180997
$735$	6.10811	−	1.80038i	0.225301	−	0.0664081i
$736$	−3.35218			−0.123563
$737$	−15.5530	+	26.9386i	−0.572903	+	0.992297i
$738$	−3.23238	−	5.59864i	−0.118985	−	0.206089i
$739$	−19.8469	−	34.3758i	−0.730079	−	1.26453i	−0.956849	−	0.290585i	$-0.906150\pi$
$739$	−19.8469	−	34.3758i	−0.730079	−	1.26453i	0.226770	−	0.973948i	$-0.427183\pi$
$740$	3.25631	−	5.64010i	0.119704	−	0.207334i
$741$	4.95651			0.182082
$742$	25.0085	−	3.60891i	0.918092	−	0.132487i
$743$	20.9414			0.768265			0.384133	−	0.923278i	$-0.374501\pi$
$743$	20.9414			0.768265			0.384133	+	0.923278i	$0.374501\pi$
$744$	−5.52389	+	9.56767i	−0.202516	+	0.350768i
$745$	−4.55284	−	7.88575i	−0.166803	−	0.288911i
$746$	−7.41897	−	12.8500i	−0.271628	−	0.470473i
$747$	1.68658	−	2.92124i	0.0617088	−	0.106883i
$748$	12.1853			0.445541
$749$	0.561106	−	1.40368i	0.0205024	−	0.0512894i
$750$	8.34420			0.304687
$751$	9.89195	−	17.1334i	0.360963	−	0.625205i	−0.627157	−	0.778893i	$-0.715782\pi$
$751$	9.89195	−	17.1334i	0.360963	−	0.625205i	0.988120	+	0.153687i	$0.0491149\pi$
$752$	−2.27357	−	3.93794i	−0.0829086	−	0.143602i
$753$	−11.3384	−	19.6388i	−0.413196	−	0.715676i
$754$	−0.345055	+	0.597653i	−0.0125662	+	0.0217653i
$755$	−4.45578			−0.162162
$756$	−1.63657	−	2.07885i	−0.0595216	−	0.0756072i
$757$	30.0117			1.09079			0.545397	−	0.838178i	$-0.316379\pi$
$757$	30.0117			1.09079			0.545397	+	0.838178i	$0.316379\pi$
$758$	−5.75499	+	9.96794i	−0.209031	+	0.362052i
$759$	8.93720	+	15.4797i	0.324400	+	0.561877i
$760$	−3.26683	−	5.65831i	−0.118500	−	0.205249i
$761$	−2.54680	+	4.41118i	−0.0923213	+	0.159905i	−0.908487	−	0.417912i	$-0.862762\pi$
$761$	−2.54680	+	4.41118i	−0.0923213	+	0.159905i	0.816166	+	0.577817i	$0.196095\pi$
$762$	−5.87845			−0.212954
$763$	9.02203	+	11.4602i	0.326619	+	0.414888i
$764$	−10.4450			−0.377888
$765$	1.03945	−	1.80038i	0.0375814	−	0.0650930i
$766$	3.06830	+	5.31445i	0.110862	+	0.192019i
$767$	4.82312	+	8.35389i	0.174153	+	0.301641i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	11.2209			0.404634			0.202317	−	0.979320i	$-0.435153\pi$
$769$	11.2209			0.404634			0.202317	+	0.979320i	$0.435153\pi$
$770$	4.76363	−	11.9169i	0.171669	−	0.429454i
$771$	−7.50246			−0.270194
$772$	−4.90192	+	8.49037i	−0.176424	+	0.305575i
$773$	−14.4890	−	25.0956i	−0.521131	−	0.902626i	−0.999698	−	0.0245748i	$-0.992177\pi$
$773$	−14.4890	−	25.0956i	−0.521131	−	0.902626i	0.478567	−	0.878051i	$-0.341157\pi$
$774$	−0.862247	−	1.49346i	−0.0309928	−	0.0536812i
$775$	23.0481	−	39.9205i	0.827913	−	1.43399i
$776$	9.51276			0.341488
$777$	18.7469	−	2.70532i	0.672542	−	0.0970527i
$778$	−29.7316			−1.06593
$779$	23.2155	−	40.2105i	0.831783	−	1.44069i
$780$	0.313898	+	0.543687i	0.0112393	+	0.0194671i
$781$	−37.3951	−	64.7702i	−1.33810	−	2.31766i
$782$	3.83030	−	6.63427i	0.136971	−	0.237241i
$783$	−1.00000			−0.0357371
$784$	−1.64326	+	6.80439i	−0.0586879	+	0.243014i
$785$	12.8962			0.460284
$786$	−3.65285	+	6.32691i	−0.130293	+	0.225674i
$787$	−13.2498	−	22.9492i	−0.472303	−	0.818052i	0.527195	−	0.849744i	$-0.323244\pi$
$787$	−13.2498	−	22.9492i	−0.472303	−	0.818052i	−0.999498	+	0.0316920i	$0.989910\pi$
$788$	−9.73482	−	16.8612i	−0.346789	−	0.600656i
$789$	−8.91184	+	15.4358i	−0.317270	+	0.549528i
$790$	11.2468			0.400145
$791$	−24.1561	+	3.48590i	−0.858892	+	0.123944i
$792$	−5.33216			−0.189470
$793$	−3.40808	+	5.90297i	−0.121025	+	0.209621i
$794$	−17.2610	−	29.8969i	−0.612569	−	1.06100i
$795$	−4.34394	−	7.52393i	−0.154064	−	0.266846i
$796$	−5.42059	+	9.38874i	−0.192128	+	0.332775i
$797$	−27.8665			−0.987081			−0.493540	−	0.869723i	$-0.664297\pi$
$797$	−27.8665			−0.987081			−0.493540	+	0.869723i	$0.664297\pi$
$798$	7.05329	−	17.6448i	0.249684	−	0.624618i
$799$	10.3914			0.367620
$800$	−2.08622	+	3.61344i	−0.0737590	+	0.127754i
$801$	5.65618	+	9.79679i	0.199851	+	0.346153i
$802$	2.29712	+	3.97873i	0.0811142	+	0.140494i
$803$	11.7186	−	20.2972i	0.413540	−	0.716272i
$804$	−5.83366			−0.205737
$805$	−4.99071	−	6.33944i	−0.175900	−	0.223436i
$806$	7.62420			0.268551
$807$	3.63368	−	6.29371i	0.127911	−	0.221549i
$808$	−7.06589	−	12.2385i	−0.248577	−	0.430548i
$809$	−6.99574	−	12.1170i	−0.245957	−	0.426010i	0.716443	−	0.697646i	$-0.245769\pi$
$809$	−6.99574	−	12.1170i	−0.245957	−	0.426010i	−0.962400	+	0.271635i	$0.912436\pi$
$810$	−0.454851	+	0.787826i	−0.0159819	+	0.0276814i
$811$	−31.6615			−1.11179			−0.555893	−	0.831254i	$-0.687624\pi$
$811$	−31.6615			−1.11179			−0.555893	+	0.831254i	$0.687624\pi$
$812$	1.63657	+	2.07885i	0.0574324	+	0.0729534i
$813$	30.2150			1.05969
$814$	19.0866	−	33.0590i	0.668987	−	1.15872i
$815$	−5.51775	−	9.55703i	−0.193278	−	0.334768i
$816$	1.14263	+	1.97909i	0.0400000	+	0.0692819i
$817$	6.19282	−	10.7263i	0.216659	−	0.375265i
$818$	−16.4737			−0.575989
$819$	−0.677726	+	1.69542i	−0.0236816	+	0.0592429i
$820$	5.88101			0.205374
$821$	17.4728	−	30.2637i	0.609804	−	1.05621i	−0.381469	−	0.924382i	$-0.624582\pi$
$821$	17.4728	−	30.2637i	0.609804	−	1.05621i	0.991272	−	0.131829i	$-0.0420850\pi$
$822$	3.70609	+	6.41914i	0.129265	+	0.223893i
$823$	13.4712	+	23.3328i	0.469576	+	0.813329i	0.999395	−	0.0347816i	$-0.0110736\pi$
$823$	13.4712	+	23.3328i	0.469576	+	0.813329i	−0.529819	+	0.848111i	$0.677740\pi$
$824$	−6.94241	+	12.0246i	−0.241850	+	0.418897i
$825$	22.2481			0.774581
$826$	36.6027	−	5.28203i	1.27357	−	0.183785i
$827$	−26.4345			−0.919219			−0.459609	−	0.888121i	$-0.652011\pi$
$827$	−26.4345			−0.919219			−0.459609	+	0.888121i	$0.652011\pi$
$828$	−1.67609	+	2.90308i	−0.0582482	+	0.100889i
$829$	19.8936	+	34.4568i	0.690935	+	1.19673i	0.971532	+	0.236909i	$0.0761342\pi$
$829$	19.8936	+	34.4568i	0.690935	+	1.19673i	−0.280597	+	0.959826i	$0.590532\pi$
$830$	1.53429	+	2.65746i	0.0532559	+	0.0922419i
$831$	−6.35055	+	10.9995i	−0.220298	+	0.381568i
$832$	−0.690111			−0.0239253
$833$	−11.5888	−	11.0270i	−0.401530	−	0.382064i
$834$	−4.96095			−0.171784
$835$	0.561243	−	0.972102i	0.0194226	−	0.0336410i
$836$	−19.1483	−	33.1658i	−0.662258	−	1.14706i
$837$	5.52389	+	9.56767i	0.190934	+	0.330707i
$838$	−1.03675	+	1.79570i	−0.0358139	+	0.0620315i
$839$	−15.2408			−0.526172			−0.263086	−	0.964772i	$-0.584740\pi$
$839$	−15.2408			−0.526172			−0.263086	+	0.964772i	$0.584740\pi$
$840$	2.38217	−	0.343765i	0.0821927	−	0.0118610i
$841$	1.00000			0.0344828
$842$	−13.7302	+	23.7814i	−0.473175	+	0.819563i
$843$	−0.686691	−	1.18938i	−0.0236509	−	0.0409646i
$844$	−7.29019	−	12.6270i	−0.250939	−	0.434638i
$845$	−5.69644	+	9.86653i	−0.195964	+	0.339419i
$846$	−4.54714			−0.156334
$847$	17.1191	−	42.8258i	0.588220	−	1.47151i
$848$	9.55025			0.327957
$849$	3.04005	−	5.26553i	0.104334	−	0.180713i
$850$	−4.76754	−	8.25763i	−0.163525	−	0.283234i
$851$	−11.9992	−	20.7833i	−0.411329	−	0.712443i
$852$	7.01311	−	12.1471i	0.240265	−	0.416152i
$853$	44.1547			1.51183			0.755913	−	0.654672i	$-0.227193\pi$
$853$	44.1547			1.51183			0.755913	+	0.654672i	$0.227193\pi$
$854$	16.1643	+	20.5327i	0.553130	+	0.702613i
$855$	−6.53366			−0.223446
$856$	0.285680	−	0.494812i	0.00976433	−	0.0169123i
$857$	−15.0516	−	26.0701i	−0.514151	−	0.890536i	−0.999865	−	0.0164183i	$-0.994774\pi$
$857$	−15.0516	−	26.0701i	−0.514151	−	0.890536i	0.485714	−	0.874118i	$-0.338560\pi$
$858$	1.83989	+	3.18679i	0.0628129	+	0.108795i
$859$	−16.9706	+	29.3940i	−0.579031	+	1.00291i	0.416560	+	0.909108i	$0.363236\pi$
$859$	−16.9706	+	29.3940i	−0.579031	+	1.00291i	−0.995591	+	0.0938024i	$0.970098\pi$
$860$	1.56878			0.0534949
$861$	10.5800	+	13.4393i	0.360567	+	0.458009i
$862$	−9.07055			−0.308944
$863$	18.4437	−	31.9454i	0.627831	−	1.08744i	−0.360155	−	0.932892i	$-0.617276\pi$
$863$	18.4437	−	31.9454i	0.627831	−	1.08744i	0.987986	−	0.154543i	$-0.0493905\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	9.07658	+	15.7211i	0.308613	+	0.534533i
$866$	−10.5105	+	18.2047i	−0.357160	+	0.618620i
$867$	11.7776			0.399989
$868$	10.8495	−	27.1415i	0.368257	−	0.921244i
$869$	65.9226			2.23627
$870$	0.454851	−	0.787826i	0.0154209	−	0.0267098i
$871$	2.01294	+	3.48651i	0.0682058	+	0.118136i
$872$	2.75638	+	4.77419i	0.0933428	+	0.161674i
$873$	4.75638	−	8.23829i	0.160979	−	0.278824i
$874$	−24.0760			−0.814383
$875$	−21.8503	+	3.15316i	−0.738676	+	0.106596i
$876$	4.39544			0.148508
$877$	−8.40593	+	14.5595i	−0.283848	+	0.491639i	−0.972329	−	0.233615i	$-0.924944\pi$
$877$	−8.40593	+	14.5595i	−0.283848	+	0.491639i	0.688481	+	0.725254i	$0.258278\pi$
$878$	18.7383	+	32.4557i	0.632388	+	1.09533i
$879$	−6.95529	−	12.0469i	−0.234596	−	0.406332i
$880$	2.42534	−	4.20082i	0.0817583	−	0.141609i
$881$	0.521378			0.0175657			0.00878284	−	0.999961i	$-0.497204\pi$
$881$	0.521378			0.0175657			0.00878284	+	0.999961i	$0.497204\pi$
$882$	5.07114	+	4.82530i	0.170754	+	0.162476i
$883$	−42.8627			−1.44245			−0.721223	−	0.692703i	$-0.756420\pi$
$883$	−42.8627			−1.44245			−0.721223	+	0.692703i	$0.756420\pi$
$884$	0.788539	−	1.36579i	0.0265214	−	0.0459365i
$885$	−6.35783	−	11.0121i	−0.213716	−	0.370167i
$886$	16.9173	+	29.3017i	0.568349	+	0.984409i
$887$	9.90548	−	17.1568i	0.332593	−	0.576069i	−0.650426	−	0.759570i	$-0.725410\pi$
$887$	9.90548	−	17.1568i	0.332593	−	0.576069i	0.983020	+	0.183501i	$0.0587430\pi$
$888$	7.15906			0.240242
$889$	15.3935	−	2.22139i	0.516280	−	0.0745030i
$890$	−10.2909			−0.344951
$891$	−2.66608	+	4.61779i	−0.0893171	+	0.154702i
$892$	12.9041	+	22.3505i	0.432060	+	0.748350i
$893$	−16.3292	−	28.2830i	−0.546436	−	0.946455i
$894$	5.00475	−	8.66849i	0.167384	−	0.289918i
$895$	10.5713			0.353359
$896$	−0.982053	+	2.45674i	−0.0328081	+	0.0820739i
$897$	2.31338			0.0772414
$898$	−14.8793	+	25.7718i	−0.496530	+	0.860016i
$899$	−5.52389	−	9.56767i	−0.184232	−	0.319100i
$900$	2.08622	+	3.61344i	0.0695407	+	0.120448i
$901$	−10.9124	+	18.9008i	−0.363544	+	0.629676i
$902$	34.4711			1.14776
$903$	2.82226	+	3.58497i	0.0939189	+	0.119300i
$904$	−9.22473			−0.306810
$905$	−3.79399	+	6.57139i	−0.126117	+	0.218440i
$906$	−2.44903	−	4.24184i	−0.0813635	−	0.140926i
$907$	1.54123	+	2.66949i	0.0511758	+	0.0886391i	0.890479	−	0.455025i	$-0.150370\pi$
$907$	1.54123	+	2.66949i	0.0511758	+	0.0886391i	−0.839303	+	0.543664i	$0.817036\pi$
$908$	2.36664	−	4.09915i	0.0785398	−	0.136035i
$909$	−14.1318			−0.468721
$910$	−1.02743	−	1.30510i	−0.0340591	−	0.0432635i
$911$	7.67638			0.254330			0.127165	−	0.991882i	$-0.459412\pi$
$911$	7.67638			0.254330			0.127165	+	0.991882i	$0.459412\pi$
$912$	3.59109	−	6.21996i	0.118913	−	0.205963i
$913$	8.99312	+	15.5765i	0.297629	+	0.515508i
$914$	−17.2349	−	29.8517i	−0.570079	−	0.987405i
$915$	4.49253	−	7.78129i	0.148518	−	0.257241i
$916$	16.3650			0.540714
$917$	7.17458	−	17.9482i	0.236925	−	0.592701i
$918$	2.28525			0.0754246
$919$	−1.33690	+	2.31557i	−0.0441002	+	0.0763837i	−0.887233	−	0.461322i	$-0.847375\pi$
$919$	−1.33690	+	2.31557i	−0.0441002	+	0.0763837i	0.843133	+	0.537705i	$0.180709\pi$
$920$	−1.52475	−	2.64094i	−0.0502694	−	0.0870691i
$921$	−8.18914	−	14.1840i	−0.269841	−	0.467379i
$922$	14.2340	−	24.6540i	0.468772	−	0.811937i
$923$	−9.67965			−0.318610
$924$	13.9629	−	2.01495i	0.459347	−	0.0662871i
$925$	−29.8708			−0.982145
$926$	−7.95643	+	13.7809i	−0.261465	+	0.452870i
$927$	6.94241	+	12.0246i	0.228019	+	0.394940i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−3.50326	+	6.06782i	−0.114938	+	0.199079i	−0.917755	−	0.397147i	$-0.870000\pi$
$929$	−3.50326	+	6.06782i	−0.114938	+	0.199079i	0.802817	+	0.596226i	$0.203334\pi$
$930$	−10.0502			−0.329559
$931$	−11.8022	+	48.8704i	−0.386802	+	1.60166i
$932$	−20.2686			−0.663921
$933$	12.6798	−	21.9621i	0.415119	−	0.719006i
$934$	17.5350	+	30.3714i	0.573761	+	0.993784i
$935$	5.54252	+	9.59993i	0.181260	+	0.313951i
$936$	−0.345055	+	0.597653i	−0.0112785	+	0.0195349i
$937$	−16.9909			−0.555067			−0.277534	−	0.960716i	$-0.589517\pi$
$937$	−16.9909			−0.555067			−0.277534	+	0.960716i	$0.589517\pi$
$938$	15.2762	−	2.20446i	0.498785	−	0.0719783i
$939$	−6.46116			−0.210852
$940$	2.06827	−	3.58236i	0.0674596	−	0.116844i
$941$	−11.4374	−	19.8101i	−0.372848	−	0.645791i	0.617155	−	0.786842i	$-0.288285\pi$
$941$	−11.4374	−	19.8101i	−0.372848	−	0.645791i	−0.990002	+	0.141051i	$0.954952\pi$
$942$	7.08812	+	12.2770i	0.230943	+	0.400006i
$943$	10.8355	−	18.7677i	0.352853	−	0.611160i
$944$	13.9778			0.454939
$945$	0.893377	−	2.23490i	0.0290615	−	0.0727014i
$946$	9.19528			0.298964
$947$	13.2074	−	22.8759i	0.429183	−	0.743366i	−0.567618	−	0.823292i	$-0.692135\pi$
$947$	13.2074	−	22.8759i	0.429183	−	0.743366i	0.996801	+	0.0799258i	$0.0254683\pi$
$948$	6.18160	+	10.7068i	0.200769	+	0.347742i
$949$	−1.51667	−	2.62695i	−0.0492331	−	0.0852743i
$950$	−14.9836	+	25.9524i	−0.486133	+	0.842007i
$951$	8.44036			0.273698
$952$	−3.73998	−	4.75071i	−0.121214	−	0.153971i
$953$	51.0421			1.65342			0.826708	−	0.562632i	$-0.190211\pi$
$953$	51.0421			1.65342			0.826708	+	0.562632i	$0.190211\pi$
$954$	4.77512	−	8.27076i	0.154600	−	0.267776i
$955$	−4.75094	−	8.22887i	−0.153737	−	0.266280i
$956$	−12.5955	−	21.8161i	−0.407369	−	0.705584i
$957$	2.66608	−	4.61779i	0.0861822	−	0.149272i
$958$	10.7564			0.347523
$959$	−12.1306	−	15.4089i	−0.391717	−	0.497578i
$960$	0.909703			0.0293605
$961$	−45.5268	+	78.8548i	−1.46861	+	2.54370i
$962$	−2.47027	−	4.27864i	−0.0796448	−	0.137949i
$963$	−0.285680	−	0.494812i	−0.00920590	−	0.0159451i
$964$	6.15610	−	10.6627i	0.198275	−	0.343422i
$965$	−8.91857			−0.287099
$966$	3.29202	−	8.23544i	0.105919	−	0.264971i
$967$	23.2470			0.747573			0.373787	−	0.927515i	$-0.378059\pi$
$967$	23.2470			0.747573			0.373787	+	0.927515i	$0.378059\pi$
$968$	8.71598	−	15.0965i	0.280142	−	0.485221i
$969$	8.20656	+	14.2142i	0.263633	+	0.456625i
$970$	4.32689	+	7.49440i	0.138928	+	0.240631i
$971$	12.2505	−	21.2185i	0.393137	−	0.680933i	−0.599725	−	0.800206i	$-0.704723\pi$
$971$	12.2505	−	21.2185i	0.393137	−	0.680933i	0.992861	+	0.119273i	$0.0380565\pi$
$972$	−1.00000			−0.0320750
$973$	12.9909	−	1.87468i	0.416468	−	0.0600994i
$974$	38.6766			1.23928
$975$	1.43972	−	2.49367i	0.0461080	−	0.0798615i
$976$	4.93846	+	8.55366i	0.158076	+	0.273796i
$977$	−2.13089	−	3.69081i	−0.0681732	−	0.118080i	0.829924	−	0.557877i	$-0.188384\pi$
$977$	−2.13089	−	3.69081i	−0.0681732	−	0.118080i	−0.898097	+	0.439797i	$0.855050\pi$
$978$	6.06544	−	10.5057i	0.193952	−	0.335934i
$979$	−60.3194			−1.92782
$980$	−6.10811	+	1.80038i	−0.195116	+	0.0575111i
$981$	5.51276			0.176009
$982$	5.30901	−	9.19547i	0.169417	−	0.293439i
$983$	−6.83499	−	11.8386i	−0.218002	−	0.377591i	0.736195	−	0.676770i	$-0.236621\pi$
$983$	−6.83499	−	11.8386i	−0.218002	−	0.377591i	−0.954197	+	0.299179i	$0.903287\pi$
$984$	3.23238	+	5.59864i	0.103044	+	0.178478i
$985$	8.85580	−	15.3387i	0.282169	−	0.488731i
$986$	−2.28525			−0.0727773
$987$	11.9073	−	1.71830i	0.379012	−	0.0546942i
$988$	−4.95651			−0.157687
$989$	2.89041	−	5.00634i	0.0919097	−	0.159192i
$990$	−2.42534	−	4.20082i	−0.0770824	−	0.133511i
$991$	16.6117	+	28.7723i	0.527688	+	0.913983i	0.999479	+	0.0322724i	$0.0102744\pi$
$991$	16.6117	+	28.7723i	0.527688	+	0.913983i	−0.471791	+	0.881711i	$0.656392\pi$
$992$	5.52389	−	9.56767i	0.175384	−	0.303774i
$993$	−18.6110			−0.590601
$994$	−13.7745	+	34.4588i	−0.436901	+	1.09297i
$995$	−9.86226			−0.312655
$996$	−1.68658	+	2.92124i	−0.0534414	+	0.0925631i
$997$	5.16287	+	8.94235i	0.163510	+	0.283207i	0.936125	−	0.351667i	$-0.114385\pi$
$997$	5.16287	+	8.94235i	0.163510	+	0.283207i	−0.772615	+	0.634874i	$0.781052\pi$
$998$	−4.87704	−	8.44727i	−0.154380	−	0.267394i
$999$	3.57953	−	6.19993i	0.113251	−	0.196157i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.i.1045.5	yes	12
7.2	even	3		8526.2.a.ci.1.2		6
7.4	even	3	inner	1218.2.i.i.697.5	✓	12
7.5	odd	6		8526.2.a.cj.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.i.697.5	✓	12	7.4	even	3	inner
1218.2.i.i.1045.5	yes	12	1.1	even	1	trivial
8526.2.a.ci.1.2		6	7.2	even	3
8526.2.a.cj.1.5		6	7.5	odd	6

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Classical	Maass
Hilbert	Bianchi

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

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1218.2.i.i.1045.5

Level	$1218$
Weight	$2$
Character	1218.1045
Analytic conductor	$9.726$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$