LMFDB - Embedded newform 1155.2.q.j.331.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.3
Root			$-0.544976 - 0.943925i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.544976 + 0.943925i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.406003 + 0.703218i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.08995 q^{6} +(-0.0476864 + 2.64532i) q^{7} -3.06495 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.544976 + 0.943925i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.406003 + 0.703218i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.08995 q^{6} +(-0.0476864 + 2.64532i) q^{7} -3.06495 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.544976 + 0.943925i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.406003 - 0.703218i) q^{12} +4.56615 q^{13} +(-2.47100 - 1.48665i) q^{14} -1.00000 q^{15} +(0.858317 - 1.48665i) q^{16} +(1.81201 + 3.13849i) q^{17} +(-0.544976 - 0.943925i) q^{18} +(2.27682 - 3.94356i) q^{19} +0.812006 q^{20} +(2.31476 - 1.28136i) q^{21} -1.08995 q^{22} +(-1.88549 + 3.26576i) q^{23} +(1.53247 + 2.65432i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.48844 + 4.31010i) q^{26} +1.00000 q^{27} +(-1.87960 + 1.04047i) q^{28} -9.80465 q^{29} +(0.544976 - 0.943925i) q^{30} +(0.282284 + 0.488930i) q^{31} +(-2.12943 - 3.68827i) q^{32} +(0.500000 - 0.866025i) q^{33} -3.95000 q^{34} +(2.26707 + 1.36396i) q^{35} -0.812006 q^{36} +(-3.36053 + 5.82061i) q^{37} +(2.48162 + 4.29829i) q^{38} +(-2.28307 - 3.95440i) q^{39} +(-1.53247 + 2.65432i) q^{40} +3.09471 q^{41} +(-0.0519758 + 2.88327i) q^{42} +8.41992 q^{43} +(-0.406003 + 0.703218i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-2.05509 - 3.55952i) q^{46} +(-4.25895 + 7.37671i) q^{47} -1.71663 q^{48} +(-6.99545 - 0.252292i) q^{49} +1.08995 q^{50} +(1.81201 - 3.13849i) q^{51} +(1.85387 + 3.21100i) q^{52} +(2.12904 + 3.68761i) q^{53} +(-0.544976 + 0.943925i) q^{54} +1.00000 q^{55} +(0.146156 - 8.10778i) q^{56} -4.55363 q^{57} +(5.34330 - 9.25486i) q^{58} +(1.65136 + 2.86024i) q^{59} +(-0.406003 - 0.703218i) q^{60} +(-0.951886 + 1.64872i) q^{61} -0.615352 q^{62} +(-2.26707 - 1.36396i) q^{63} +8.07521 q^{64} +(2.28307 - 3.95440i) q^{65} +(0.544976 + 0.943925i) q^{66} +(7.09400 + 12.2872i) q^{67} +(-1.47136 + 2.54847i) q^{68} +3.77098 q^{69} +(-2.52297 + 1.39662i) q^{70} +6.05493 q^{71} +(1.53247 - 2.65432i) q^{72} +(1.35391 + 2.34504i) q^{73} +(-3.66282 - 6.34419i) q^{74} +(-0.500000 + 0.866025i) q^{75} +3.69758 q^{76} +(-2.31476 + 1.28136i) q^{77} +4.97688 q^{78} +(-7.27575 + 12.6020i) q^{79} +(-0.858317 - 1.48665i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.68654 + 2.92118i) q^{82} -9.16676 q^{83} +(1.84088 + 1.10754i) q^{84} +3.62401 q^{85} +(-4.58865 + 7.94778i) q^{86} +(4.90233 + 8.49108i) q^{87} +(-1.53247 - 2.65432i) q^{88} +(0.560941 - 0.971578i) q^{89} -1.08995 q^{90} +(-0.217743 + 12.0789i) q^{91} -3.06206 q^{92} +(0.282284 - 0.488930i) q^{93} +(-4.64205 - 8.04026i) q^{94} +(-2.27682 - 3.94356i) q^{95} +(-2.12943 + 3.68827i) q^{96} +2.92803 q^{97} +(4.05050 - 6.46569i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.544976	+	0.943925i	−0.385356	+	0.667456i	−0.991819	−	0.127656i	$-0.959255\pi$
$2$	−0.544976	+	0.943925i	−0.385356	+	0.667456i	0.606463	+	0.795112i	$0.292588\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.406003	+	0.703218i	0.203002	+	0.351609i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.08995			0.444971
$7$	−0.0476864	+	2.64532i	−0.0180238	+	0.999838i
$7$	−0.0476864	+	2.64532i	−0.0180238	+	0.999838i
$8$	−3.06495			−1.08362
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.544976	+	0.943925i	0.172336	+	0.298495i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.406003	−	0.703218i	0.117203	−	0.203002i
$13$	4.56615			1.26642			0.633211	−	0.773979i	$-0.281737\pi$
$13$	4.56615			1.26642			0.633211	+	0.773979i	$0.281737\pi$
$14$	−2.47100	−	1.48665i	−0.660402	−	0.397323i
$15$	−1.00000			−0.258199
$16$	0.858317	−	1.48665i	0.214579	−	0.371662i
$17$	1.81201	+	3.13849i	0.439476	+	0.761195i	0.997649	−	0.0685297i	$-0.0218308\pi$
$17$	1.81201	+	3.13849i	0.439476	+	0.761195i	−0.558173	+	0.829725i	$0.688497\pi$
$18$	−0.544976	−	0.943925i	−0.128452	−	0.222485i
$19$	2.27682	−	3.94356i	0.522338	−	0.904715i	−0.477325	−	0.878727i	$-0.658393\pi$
$19$	2.27682	−	3.94356i	0.522338	−	0.904715i	0.999662	−	0.0259882i	$-0.00827325\pi$
$20$	0.812006			0.181570
$21$	2.31476	−	1.28136i	0.505122	−	0.279616i
$22$	−1.08995			−0.232378
$23$	−1.88549	+	3.26576i	−0.393152	+	0.680959i	−0.992863	−	0.119257i	$-0.961949\pi$
$23$	−1.88549	+	3.26576i	−0.393152	+	0.680959i	0.599712	+	0.800216i	$0.295282\pi$
$24$	1.53247	+	2.65432i	0.312815	+	0.541812i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.48844	+	4.31010i	−0.488023	+	0.845281i
$27$	1.00000			0.192450
$28$	−1.87960	+	1.04047i	−0.355211	+	0.196631i
$29$	−9.80465			−1.82068			−0.910339	−	0.413863i	$-0.864179\pi$
$29$	−9.80465			−1.82068			−0.910339	+	0.413863i	$0.864179\pi$
$30$	0.544976	−	0.943925i	0.0994985	−	0.172336i
$31$	0.282284	+	0.488930i	0.0506997	+	0.0878144i	0.890261	−	0.455450i	$-0.150522\pi$
$31$	0.282284	+	0.488930i	0.0506997	+	0.0878144i	−0.839562	+	0.543264i	$0.817188\pi$
$32$	−2.12943	−	3.68827i	−0.376433	−	0.652001i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−3.95000			−0.677419
$35$	2.26707	+	1.36396i	0.383205	+	0.230551i
$36$	−0.812006			−0.135334
$37$	−3.36053	+	5.82061i	−0.552468	+	0.956903i	0.445627	+	0.895219i	$0.352981\pi$
$37$	−3.36053	+	5.82061i	−0.552468	+	0.956903i	−0.998096	+	0.0616846i	$0.980353\pi$
$38$	2.48162	+	4.29829i	0.402572	+	0.697275i
$39$	−2.28307	−	3.95440i	−0.365585	−	0.633211i
$40$	−1.53247	+	2.65432i	−0.242306	+	0.419686i
$41$	3.09471			0.483313			0.241657	−	0.970362i	$-0.422309\pi$
$41$	3.09471			0.483313			0.241657	+	0.970362i	$0.422309\pi$
$42$	−0.0519758	+	2.88327i	−0.00802005	+	0.444898i
$43$	8.41992			1.28403			0.642013	−	0.766694i	$-0.278100\pi$
$43$	8.41992			1.28403			0.642013	+	0.766694i	$0.278100\pi$
$44$	−0.406003	+	0.703218i	−0.0612073	+	0.106014i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−2.05509	−	3.55952i	−0.303007	−	0.524823i
$47$	−4.25895	+	7.37671i	−0.621231	+	1.07600i	0.368025	+	0.929816i	$0.380034\pi$
$47$	−4.25895	+	7.37671i	−0.621231	+	1.07600i	−0.989257	+	0.146189i	$0.953299\pi$
$48$	−1.71663			−0.247775
$49$	−6.99545	−	0.252292i	−0.999350	−	0.0360417i
$50$	1.08995			0.154142
$51$	1.81201	−	3.13849i	0.253732	−	0.439476i
$52$	1.85387	+	3.21100i	0.257086	+	0.445285i
$53$	2.12904	+	3.68761i	0.292446	+	0.506532i	0.974388	−	0.224875i	$-0.0721974\pi$
$53$	2.12904	+	3.68761i	0.292446	+	0.506532i	−0.681941	+	0.731407i	$0.738864\pi$
$54$	−0.544976	+	0.943925i	−0.0741618	+	0.128452i
$55$	1.00000			0.134840
$56$	0.146156	−	8.10778i	0.0195310	−	1.08345i
$57$	−4.55363			−0.603144
$58$	5.34330	−	9.25486i	0.701609	−	1.21522i
$59$	1.65136	+	2.86024i	0.214988	+	0.372371i	0.953269	−	0.302123i	$-0.0976953\pi$
$59$	1.65136	+	2.86024i	0.214988	+	0.372371i	−0.738281	+	0.674494i	$0.764362\pi$
$60$	−0.406003	−	0.703218i	−0.0524148	−	0.0907851i
$61$	−0.951886	+	1.64872i	−0.121877	+	0.211096i	−0.920508	−	0.390724i	$-0.872225\pi$
$61$	−0.951886	+	1.64872i	−0.121877	+	0.211096i	0.798631	+	0.601821i	$0.205558\pi$
$62$	−0.615352			−0.0781497
$63$	−2.26707	−	1.36396i	−0.285624	−	0.171843i
$64$	8.07521			1.00940
$65$	2.28307	−	3.95440i	0.283181	−	0.490483i
$66$	0.544976	+	0.943925i	0.0670819	+	0.116189i
$67$	7.09400	+	12.2872i	0.866670	+	1.50112i	0.865379	+	0.501118i	$0.167078\pi$
$67$	7.09400	+	12.2872i	0.866670	+	1.50112i	0.00129142	+	0.999999i	$0.499589\pi$
$68$	−1.47136	+	2.54847i	−0.178429	+	0.309047i
$69$	3.77098			0.453973
$70$	−2.52297	+	1.39662i	−0.301553	+	0.166928i
$71$	6.05493			0.718588			0.359294	−	0.933224i	$-0.383017\pi$
$71$	6.05493			0.718588			0.359294	+	0.933224i	$0.383017\pi$
$72$	1.53247	−	2.65432i	0.180604	−	0.312815i
$73$	1.35391	+	2.34504i	0.158463	+	0.274466i	0.934315	−	0.356450i	$-0.116013\pi$
$73$	1.35391	+	2.34504i	0.158463	+	0.274466i	−0.775852	+	0.630915i	$0.782679\pi$
$74$	−3.66282	−	6.34419i	−0.425794	−	0.737497i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	3.69758			0.424141
$77$	−2.31476	+	1.28136i	−0.263791	+	0.146025i
$78$	4.97688			0.563521
$79$	−7.27575	+	12.6020i	−0.818585	+	1.41783i	0.0881393	+	0.996108i	$0.471908\pi$
$79$	−7.27575	+	12.6020i	−0.818585	+	1.41783i	−0.906725	+	0.421723i	$0.861425\pi$
$80$	−0.858317	−	1.48665i	−0.0959627	−	0.166212i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.68654	+	2.92118i	−0.186248	+	0.322590i
$83$	−9.16676			−1.00618			−0.503091	−	0.864233i	$-0.667804\pi$
$83$	−9.16676			−1.00618			−0.503091	+	0.864233i	$0.667804\pi$
$84$	1.84088	+	1.10754i	0.200856	+	0.120843i
$85$	3.62401			0.393079
$86$	−4.58865	+	7.94778i	−0.494807	+	0.857031i
$87$	4.90233	+	8.49108i	0.525584	+	0.910339i
$88$	−1.53247	−	2.65432i	−0.163362	−	0.282952i
$89$	0.560941	−	0.971578i	0.0594596	−	0.102987i	−0.834763	−	0.550609i	$-0.814396\pi$
$89$	0.560941	−	0.971578i	0.0594596	−	0.102987i	0.894223	+	0.447622i	$0.147729\pi$
$90$	−1.08995			−0.114891
$91$	−0.217743	+	12.0789i	−0.0228257	+	1.26622i
$92$	−3.06206			−0.319242
$93$	0.282284	−	0.488930i	0.0292715	−	0.0506997i
$94$	−4.64205	−	8.04026i	−0.478790	−	0.829289i
$95$	−2.27682	−	3.94356i	−0.233596	−	0.404601i
$96$	−2.12943	+	3.68827i	−0.217334	+	0.376433i
$97$	2.92803			0.297296			0.148648	−	0.988890i	$-0.452508\pi$
$97$	2.92803			0.297296			0.148648	+	0.988890i	$0.452508\pi$
$98$	4.05050	−	6.46569i	0.409162	−	0.653134i
$99$	−1.00000			−0.100504
$100$	0.406003	−	0.703218i	0.0406003	−	0.0703218i
$101$	−9.38682	−	16.2585i	−0.934024	−	1.61778i	−0.776366	−	0.630283i	$-0.782939\pi$
$101$	−9.38682	−	16.2585i	−0.934024	−	1.61778i	−0.157658	−	0.987494i	$-0.550394\pi$
$102$	1.97500	+	3.42080i	0.195554	+	0.338709i
$103$	−9.65425	+	16.7216i	−0.951261	+	1.64763i	−0.208560	+	0.978010i	$0.566878\pi$
$103$	−9.65425	+	16.7216i	−0.951261	+	1.64763i	−0.742701	+	0.669623i	$0.766456\pi$
$104$	−13.9950			−1.37232
$105$	0.0476864	−	2.64532i	0.00465371	−	0.258157i
$106$	−4.64110			−0.450784
$107$	4.29363	−	7.43678i	0.415080	−	0.718940i	−0.580356	−	0.814363i	$-0.697087\pi$
$107$	4.29363	−	7.43678i	0.415080	−	0.718940i	0.995437	+	0.0954221i	$0.0304201\pi$
$108$	0.406003	+	0.703218i	0.0390677	+	0.0676672i
$109$	−3.32851	−	5.76515i	−0.318814	−	0.552201i	0.661427	−	0.750009i	$-0.269951\pi$
$109$	−3.32851	−	5.76515i	−0.318814	−	0.552201i	−0.980241	+	0.197808i	$0.936618\pi$
$110$	−0.544976	+	0.943925i	−0.0519614	+	0.0899998i
$111$	6.72107			0.637935
$112$	3.89173	+	2.34142i	0.367734	+	0.221243i
$113$	8.03060			0.755456			0.377728	−	0.925917i	$-0.376706\pi$
$113$	8.03060			0.755456			0.377728	+	0.925917i	$0.376706\pi$
$114$	2.48162	−	4.29829i	0.232425	−	0.402572i
$115$	1.88549	+	3.26576i	0.175823	+	0.304534i
$116$	−3.98072	−	6.89481i	−0.369600	−	0.640167i
$117$	−2.28307	+	3.95440i	−0.211070	+	0.365585i
$118$	−3.59980			−0.331388
$119$	−8.38871	+	4.64368i	−0.768992	+	0.425685i
$120$	3.06495			0.279790
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.03751	−	1.79702i	−0.0939317	−	0.162694i
$123$	−1.54736	−	2.68010i	−0.139520	−	0.241657i
$124$	−0.229216	+	0.397014i	−0.0205842	+	0.0356529i
$125$	−1.00000			−0.0894427
$126$	2.52297	−	1.39662i	0.224764	−	0.124421i
$127$	−8.66717			−0.769087			−0.384543	−	0.923107i	$-0.625641\pi$
$127$	−8.66717			−0.769087			−0.384543	+	0.923107i	$0.625641\pi$
$128$	−0.141939	+	0.245846i	−0.0125458	+	0.0217299i
$129$	−4.20996	−	7.29186i	−0.370666	−	0.642013i
$130$	2.48844	+	4.31010i	0.218251	+	0.378021i
$131$	−6.70254	+	11.6091i	−0.585603	+	1.01429i	0.409196	+	0.912446i	$0.365809\pi$
$131$	−6.70254	+	11.6091i	−0.585603	+	1.01429i	−0.994800	+	0.101849i	$0.967524\pi$
$132$	0.812006			0.0706761
$133$	10.3234	+	6.21097i	0.895154	+	0.538559i
$134$	−15.4642			−1.33591
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−5.55371	−	9.61930i	−0.476227	−	0.824849i
$137$	1.53947	+	2.66644i	0.131526	+	0.227810i	0.924265	−	0.381752i	$-0.124679\pi$
$137$	1.53947	+	2.66644i	0.131526	+	0.227810i	−0.792739	+	0.609561i	$0.791346\pi$
$138$	−2.05509	+	3.55952i	−0.174941	+	0.303007i
$139$	19.9958			1.69602			0.848010	−	0.529981i	$-0.177801\pi$
$139$	19.9958			1.69602			0.848010	+	0.529981i	$0.177801\pi$
$140$	−0.0387216	+	2.14802i	−0.00327258	+	0.181541i
$141$	8.51790			0.717336
$142$	−3.29979	+	5.71540i	−0.276912	+	0.479626i
$143$	2.28307	+	3.95440i	0.190920	+	0.330684i
$144$	0.858317	+	1.48665i	0.0715264	+	0.123887i
$145$	−4.90233	+	8.49108i	−0.407116	+	0.705146i
$146$	−2.95139			−0.244259
$147$	3.27924	+	6.18438i	0.270467	+	0.510079i
$148$	−5.45755			−0.448608
$149$	0.250270	−	0.433480i	0.0205029	−	0.0355121i	−0.855592	−	0.517651i	$-0.826807\pi$
$149$	0.250270	−	0.433480i	0.0205029	−	0.0355121i	0.876095	+	0.482139i	$0.160140\pi$
$150$	−0.544976	−	0.943925i	−0.0444971	−	0.0770712i
$151$	−2.98833	−	5.17593i	−0.243187	−	0.421212i	0.718434	−	0.695596i	$-0.244859\pi$
$151$	−2.98833	−	5.17593i	−0.243187	−	0.421212i	−0.961620	+	0.274384i	$0.911526\pi$
$152$	−6.97833	+	12.0868i	−0.566017	+	0.980371i
$153$	−3.62401			−0.292984
$154$	0.0519758	−	2.88327i	0.00418833	−	0.232341i
$155$	0.564568			0.0453472
$156$	1.85387	−	3.21100i	0.148428	−	0.257086i
$157$	−6.50396	−	11.2652i	−0.519073	−	0.899060i	−0.999754	−	0.0221652i	$-0.992944\pi$
$157$	−6.50396	−	11.2652i	−0.519073	−	0.899060i	0.480682	−	0.876895i	$-0.340389\pi$
$158$	−7.93021	−	13.7355i	−0.630893	−	1.09274i
$159$	2.12904	−	3.68761i	0.168844	−	0.292446i
$160$	−4.25885			−0.336692
$161$	−8.54908	−	5.14346i	−0.673762	−	0.405361i
$162$	1.08995			0.0856347
$163$	8.22576	−	14.2474i	0.644291	−	1.11594i	−0.340174	−	0.940363i	$-0.610486\pi$
$163$	8.22576	−	14.2474i	0.644291	−	1.11594i	0.984465	−	0.175582i	$-0.0561808\pi$
$164$	1.25646	+	2.17626i	0.0981133	+	0.169937i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	4.99566	−	8.65274i	0.387738	−	0.671583i
$167$	4.96417			0.384139			0.192070	−	0.981381i	$-0.438480\pi$
$167$	4.96417			0.384139			0.192070	+	0.981381i	$0.438480\pi$
$168$	−7.09462	+	3.92731i	−0.547362	+	0.302999i
$169$	7.84972			0.603824
$170$	−1.97500	+	3.42080i	−0.151475	+	0.262363i
$171$	2.27682	+	3.94356i	0.174113	+	0.301572i
$172$	3.41851	+	5.92104i	0.260659	+	0.451475i
$173$	−1.06328	+	1.84165i	−0.0808397	+	0.140018i	−0.903611	−	0.428354i	$-0.859094\pi$
$173$	−1.06328	+	1.84165i	−0.0808397	+	0.140018i	0.822771	+	0.568373i	$0.192427\pi$
$174$	−10.6866			−0.810148
$175$	2.31476	−	1.28136i	0.174979	−	0.0968619i
$176$	1.71663			0.129396
$177$	1.65136	−	2.86024i	0.124124	−	0.214988i
$178$	0.611398	+	1.05897i	0.0458262	+	0.0793733i
$179$	−1.65217	−	2.86164i	−0.123489	−	0.213889i	0.797652	−	0.603117i	$-0.206075\pi$
$179$	−1.65217	−	2.86164i	−0.123489	−	0.213889i	−0.921141	+	0.389229i	$0.872742\pi$
$180$	−0.406003	+	0.703218i	−0.0302617	+	0.0524148i
$181$	15.8784			1.18023			0.590117	−	0.807317i	$-0.299081\pi$
$181$	15.8784			1.18023			0.590117	+	0.807317i	$0.299081\pi$
$182$	−11.2829	−	6.78826i	−0.836348	−	0.503179i
$183$	1.90377			0.140731
$184$	5.77893	−	10.0094i	0.426028	−	0.737903i
$185$	3.36053	+	5.82061i	0.247071	+	0.427940i
$186$	0.307676	+	0.532910i	0.0225599	+	0.0390749i
$187$	−1.81201	+	3.13849i	−0.132507	+	0.229509i
$188$	−6.91658			−0.504444
$189$	−0.0476864	+	2.64532i	−0.00346867	+	0.192419i
$190$	4.96324			0.360071
$191$	10.9157	−	18.9066i	0.789833	−	1.36803i	−0.136235	−	0.990677i	$-0.543500\pi$
$191$	10.9157	−	18.9066i	0.789833	−	1.36803i	0.926069	−	0.377355i	$-0.123166\pi$
$192$	−4.03760	−	6.99334i	−0.291389	−	0.504701i
$193$	−2.81708	−	4.87933i	−0.202778	−	0.351222i	0.746644	−	0.665223i	$-0.231664\pi$
$193$	−2.81708	−	4.87933i	−0.202778	−	0.351222i	−0.949423	+	0.314001i	$0.898330\pi$
$194$	−1.59571	+	2.76384i	−0.114565	+	0.198432i
$195$	−4.56615			−0.326989
$196$	−2.66276	−	5.02176i	−0.190197	−	0.358697i
$197$	5.85298			0.417008			0.208504	−	0.978022i	$-0.433141\pi$
$197$	5.85298			0.417008			0.208504	+	0.978022i	$0.433141\pi$
$198$	0.544976	−	0.943925i	0.0387297	−	0.0670819i
$199$	2.24182	+	3.88295i	0.158919	+	0.275255i	0.934479	−	0.356018i	$-0.115866\pi$
$199$	2.24182	+	3.88295i	0.158919	+	0.275255i	−0.775560	+	0.631273i	$0.782533\pi$
$200$	1.53247	+	2.65432i	0.108362	+	0.187689i
$201$	7.09400	−	12.2872i	0.500372	−	0.866670i
$202$	20.4624			1.43973
$203$	0.467548	−	25.9365i	0.0328155	−	1.82038i
$204$	2.94272			0.206032
$205$	1.54736	−	2.68010i	0.108072	−	0.187186i
$206$	−10.5227	−	18.2258i	−0.733148	−	1.26985i
$207$	−1.88549	−	3.26576i	−0.131051	−	0.226986i
$208$	3.91920	−	6.78826i	0.271748	−	0.470681i
$209$	4.55363			0.314981
$210$	2.47100	+	1.48665i	0.170515	+	0.102588i
$211$	13.6484			0.939593			0.469797	−	0.882775i	$-0.344327\pi$
$211$	13.6484			0.939593			0.469797	+	0.882775i	$0.344327\pi$
$212$	−1.72879	+	2.99436i	−0.118734	+	0.205653i
$213$	−3.02747	−	5.24372i	−0.207439	−	0.359294i
$214$	4.67984	+	8.10573i	0.319907	+	0.554096i
$215$	4.20996	−	7.29186i	0.287117	−	0.497301i
$216$	−3.06495			−0.208543
$217$	−1.30684	+	0.723417i	−0.0887140	+	0.0491087i
$218$	7.25583			0.491427
$219$	1.35391	−	2.34504i	0.0914886	−	0.158463i
$220$	0.406003	+	0.703218i	0.0273727	+	0.0474109i
$221$	8.27389	+	14.3308i	0.556562	+	0.963994i
$222$	−3.66282	+	6.34419i	−0.245832	+	0.425794i
$223$	−18.9801			−1.27100			−0.635500	−	0.772101i	$-0.719206\pi$
$223$	−18.9801			−1.27100			−0.635500	+	0.772101i	$0.719206\pi$
$224$	9.85822	−	5.45714i	0.658680	−	0.364620i
$225$	1.00000			0.0666667
$226$	−4.37648	+	7.58029i	−0.291119	+	0.504233i
$227$	11.9600	+	20.7154i	0.793814	+	1.37493i	0.923589	+	0.383383i	$0.125241\pi$
$227$	11.9600	+	20.7154i	0.793814	+	1.37493i	−0.129775	+	0.991543i	$0.541425\pi$
$228$	−1.84879	−	3.20220i	−0.122439	−	0.212071i
$229$	5.20026	−	9.00712i	0.343643	−	0.595207i	−0.641463	−	0.767154i	$-0.721672\pi$
$229$	5.20026	−	9.00712i	0.343643	−	0.595207i	0.985106	+	0.171947i	$0.0550057\pi$
$230$	−4.11018			−0.271017
$231$	2.26707	+	1.36396i	0.149162	+	0.0897419i
$232$	30.0508			1.97293
$233$	5.64314	−	9.77420i	0.369694	−	0.640329i	−0.619823	−	0.784741i	$-0.712796\pi$
$233$	5.64314	−	9.77420i	0.369694	−	0.640329i	0.989518	+	0.144412i	$0.0461291\pi$
$234$	−2.48844	−	4.31010i	−0.162674	−	0.281760i
$235$	4.25895	+	7.37671i	0.277823	+	0.481204i
$236$	−1.34091	+	2.32253i	−0.0872860	+	0.151184i
$237$	14.5515			0.945221
$238$	0.188361	−	10.4490i	0.0122096	−	0.677309i
$239$	13.2352			0.856114			0.428057	−	0.903752i	$-0.359198\pi$
$239$	13.2352			0.856114			0.428057	+	0.903752i	$0.359198\pi$
$240$	−0.858317	+	1.48665i	−0.0554041	+	0.0959627i
$241$	−11.6530	−	20.1836i	−0.750638	−	1.30014i	−0.947514	−	0.319714i	$-0.896413\pi$
$241$	−11.6530	−	20.1836i	−0.750638	−	1.30014i	0.196876	−	0.980428i	$-0.436920\pi$
$242$	−0.544976	−	0.943925i	−0.0350324	−	0.0606778i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.54587			−0.0989645
$245$	−3.71622	+	5.93209i	−0.237420	+	0.378988i
$246$	3.37309			0.215060
$247$	10.3963	−	18.0069i	0.661500	−	1.14575i
$248$	−0.865186	−	1.49855i	−0.0549394	−	0.0951578i
$249$	4.58338	+	7.93865i	0.290460	+	0.503091i
$250$	0.544976	−	0.943925i	0.0344673	−	0.0596991i
$251$	22.6632			1.43049			0.715244	−	0.698875i	$-0.246315\pi$
$251$	22.6632			1.43049			0.715244	+	0.698875i	$0.246315\pi$
$252$	0.0387216	−	2.14802i	0.00243923	−	0.135312i
$253$	−3.77098			−0.237079
$254$	4.72340	−	8.18116i	0.296372	−	0.513332i
$255$	−1.81201	−	3.13849i	−0.113472	−	0.196540i
$256$	7.92050	+	13.7187i	0.495031	+	0.857419i
$257$	−7.62914	+	13.2141i	−0.475893	+	0.824271i	−0.999619	−	0.0276164i	$-0.991208\pi$
$257$	−7.62914	+	13.2141i	−0.475893	+	0.824271i	0.523726	+	0.851887i	$0.324542\pi$
$258$	9.17730			0.571354
$259$	−15.2371	−	9.16726i	−0.946790	−	0.569626i
$260$	3.70774			0.229944
$261$	4.90233	−	8.49108i	0.303446	−	0.525584i
$262$	−7.30544	−	12.6534i	−0.451332	−	0.781729i
$263$	−12.7125	−	22.0187i	−0.783886	−	1.35773i	−0.929662	−	0.368412i	$-0.879901\pi$
$263$	−12.7125	−	22.0187i	−0.783886	−	1.35773i	0.145777	−	0.989318i	$-0.453432\pi$
$264$	−1.53247	+	2.65432i	−0.0943173	+	0.163362i
$265$	4.25808			0.261572
$266$	−11.4887	+	6.35971i	−0.704417	+	0.389939i
$267$	−1.12188			−0.0686580
$268$	−5.76037	+	9.97726i	−0.351871	+	0.609458i
$269$	−3.72485	−	6.45162i	−0.227108	−	0.393362i	0.729842	−	0.683616i	$-0.239594\pi$
$269$	−3.72485	−	6.45162i	−0.227108	−	0.393362i	−0.956950	+	0.290254i	$0.906260\pi$
$270$	0.544976	+	0.943925i	0.0331662	+	0.0574455i
$271$	−9.85902	+	17.0763i	−0.598893	+	1.03731i	0.394092	+	0.919071i	$0.371059\pi$
$271$	−9.85902	+	17.0763i	−0.598893	+	1.03731i	−0.992985	+	0.118242i	$0.962274\pi$
$272$	6.22110			0.377210
$273$	10.5695	−	5.85090i	0.639697	−	0.354112i
$274$	−3.35590			−0.202737
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	1.53103	+	2.65182i	0.0921571	+	0.159621i
$277$	−8.01389	−	13.8805i	−0.481508	−	0.833996i	0.518267	−	0.855219i	$-0.326577\pi$
$277$	−8.01389	−	13.8805i	−0.481508	−	0.833996i	−0.999775	+	0.0212226i	$0.993244\pi$
$278$	−10.8972	+	18.8745i	−0.653571	+	1.13202i
$279$	−0.564568			−0.0337998
$280$	−6.94846	−	4.18046i	−0.415250	−	0.249831i
$281$	−24.7348			−1.47555			−0.737777	−	0.675044i	$-0.764125\pi$
$281$	−24.7348			−1.47555			−0.737777	+	0.675044i	$0.764125\pi$
$282$	−4.64205	+	8.04026i	−0.276430	+	0.478790i
$283$	−5.96299	−	10.3282i	−0.354463	−	0.613948i	0.632563	−	0.774509i	$-0.282003\pi$
$283$	−5.96299	−	10.3282i	−0.354463	−	0.613948i	−0.987026	+	0.160561i	$0.948670\pi$
$284$	2.45832	+	4.25794i	0.145875	+	0.252662i
$285$	−2.27682	+	3.94356i	−0.134867	+	0.233596i
$286$	−4.97688			−0.294289
$287$	−0.147576	+	8.18651i	−0.00871112	+	0.483235i
$288$	4.25885			0.250955
$289$	1.93327	−	3.34852i	0.113722	−	0.196972i
$290$	−5.34330	−	9.25486i	−0.313769	−	0.543464i
$291$	−1.46402	−	2.53575i	−0.0858221	−	0.148648i
$292$	−1.09938	+	1.90418i	−0.0643364	+	0.111434i
$293$	21.7379			1.26994			0.634970	−	0.772537i	$-0.281013\pi$
$293$	21.7379			1.26994			0.634970	+	0.772537i	$0.281013\pi$
$294$	−7.62470	−	0.274986i	−0.444682	−	0.0160375i
$295$	3.30272			0.192292
$296$	10.2999	−	17.8399i	0.598668	−	1.03692i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	0.272782	+	0.472472i	0.0158018	+	0.0273696i
$299$	−8.60943	+	14.9120i	−0.497896	+	0.862381i
$300$	−0.812006			−0.0468812
$301$	−0.401515	+	22.2734i	−0.0231430	+	1.28382i
$302$	6.51426			0.374854
$303$	−9.38682	+	16.2585i	−0.539259	+	0.934024i
$304$	−3.90846	−	6.76965i	−0.224166	−	0.388266i
$305$	0.951886	+	1.64872i	0.0545048	+	0.0944052i
$306$	1.97500	−	3.42080i	0.112903	−	0.195554i
$307$	18.2233			1.04006			0.520029	−	0.854149i	$-0.325921\pi$
$307$	18.2233			1.04006			0.520029	+	0.854149i	$0.325921\pi$
$308$	−1.84088	−	1.10754i	−0.104894	−	0.0631081i
$309$	19.3085			1.09842
$310$	−0.307676	+	0.532910i	−0.0174748	+	0.0302673i
$311$	8.72183	+	15.1067i	0.494570	+	0.856620i	0.999980	−	0.00625887i	$-0.00199227\pi$
$311$	8.72183	+	15.1067i	0.494570	+	0.856620i	−0.505411	+	0.862879i	$0.668659\pi$
$312$	6.99751	+	12.1200i	0.396156	+	0.686162i
$313$	6.75003	−	11.6914i	0.381534	−	0.660836i	−0.609748	−	0.792596i	$-0.708729\pi$
$313$	6.75003	−	11.6914i	0.381534	−	0.660836i	0.991282	+	0.131759i	$0.0420625\pi$
$314$	14.1780			0.800111
$315$	−2.31476	+	1.28136i	−0.130422	+	0.0721966i
$316$	−11.8159			−0.664696
$317$	−2.47108	+	4.28003i	−0.138790	+	0.240391i	−0.927039	−	0.374966i	$-0.877654\pi$
$317$	−2.47108	+	4.28003i	−0.138790	+	0.240391i	0.788249	+	0.615356i	$0.210988\pi$
$318$	2.32055	+	4.01931i	0.130130	+	0.225392i
$319$	−4.90233	−	8.49108i	−0.274478	−	0.475409i
$320$	4.03760	−	6.99334i	0.225709	−	0.390939i
$321$	−8.58725			−0.479294
$322$	9.51408	−	5.26664i	0.530199	−	0.293498i
$323$	16.5024			0.918219
$324$	0.406003	−	0.703218i	0.0225557	−	0.0390677i
$325$	−2.28307	−	3.95440i	−0.126642	−	0.219351i
$326$	8.96567	+	15.5290i	0.496563	+	0.860072i
$327$	−3.32851	+	5.76515i	−0.184067	+	0.318814i
$328$	−9.48514			−0.523729
$329$	−19.3107	−	11.6181i	−1.06463	−	0.640524i
$330$	1.08995			0.0599998
$331$	−3.39076	+	5.87297i	−0.186373	+	0.322808i	−0.944038	−	0.329836i	$-0.893007\pi$
$331$	−3.39076	+	5.87297i	−0.186373	+	0.322808i	0.757665	+	0.652643i	$0.226340\pi$
$332$	−3.72173	−	6.44623i	−0.204257	−	0.353783i
$333$	−3.36053	−	5.82061i	−0.184156	−	0.318968i
$334$	−2.70535	+	4.68581i	−0.148030	+	0.256396i
$335$	14.1880			0.775174
$336$	0.0818600	−	4.54105i	0.00446583	−	0.247734i
$337$	20.7851			1.13224			0.566120	−	0.824323i	$-0.308444\pi$
$337$	20.7851			1.13224			0.566120	+	0.824323i	$0.308444\pi$
$338$	−4.27791	+	7.40955i	−0.232687	+	0.403026i
$339$	−4.01530	−	6.95471i	−0.218081	−	0.377728i
$340$	1.47136	+	2.54847i	0.0797957	+	0.138210i
$341$	−0.282284	+	0.488930i	−0.0152865	+	0.0264771i
$342$	−4.96324			−0.268381
$343$	1.00098	−	18.4932i	0.0540479	−	0.998538i
$344$	−25.8066			−1.39140
$345$	1.88549	−	3.26576i	0.101511	−	0.175823i
$346$	−1.15892	−	2.00731i	−0.0623041	−	0.107914i
$347$	10.3345	+	17.9000i	0.554788	+	0.960920i	0.997920	+	0.0644641i	$0.0205338\pi$
$347$	10.3345	+	17.9000i	0.554788	+	0.960920i	−0.443132	+	0.896456i	$0.646133\pi$
$348$	−3.98072	+	6.89481i	−0.213389	+	0.369600i
$349$	28.4125			1.52089			0.760444	−	0.649404i	$-0.224982\pi$
$349$	28.4125			1.52089			0.760444	+	0.649404i	$0.224982\pi$
$350$	−0.0519758	+	2.88327i	−0.00277823	+	0.154117i
$351$	4.56615			0.243723
$352$	2.12943	−	3.68827i	0.113499	−	0.196586i
$353$	8.40945	+	14.5656i	0.447590	+	0.775248i	0.998229	−	0.0594952i	$-0.0189491\pi$
$353$	8.40945	+	14.5656i	0.447590	+	0.775248i	−0.550639	+	0.834744i	$0.685616\pi$
$354$	1.79990	+	3.11752i	0.0956636	+	0.165694i
$355$	3.02747	−	5.24372i	0.160681	−	0.278308i
$356$	0.910974			0.0482816
$357$	8.21590	+	4.94300i	0.434831	+	0.261611i
$358$	3.60156			0.190349
$359$	17.1145	−	29.6431i	0.903266	−	1.56450i	0.0800390	−	0.996792i	$-0.474496\pi$
$359$	17.1145	−	29.6431i	0.903266	−	1.56450i	0.823227	−	0.567712i	$-0.192171\pi$
$360$	−1.53247	−	2.65432i	−0.0807685	−	0.139895i
$361$	−0.867790	−	1.50306i	−0.0456731	−	0.0791082i
$362$	−8.65336	+	14.9881i	−0.454811	+	0.787755i
$363$	1.00000			0.0524864
$364$	−8.58253	+	4.75096i	−0.449847	+	0.249018i
$365$	2.70782			0.141734
$366$	−1.03751	+	1.79702i	−0.0542315	+	0.0939317i
$367$	−8.27428	−	14.3315i	−0.431914	−	0.748096i	0.565124	−	0.825006i	$-0.308828\pi$
$367$	−8.27428	−	14.3315i	−0.431914	−	0.748096i	−0.997038	+	0.0769093i	$0.975495\pi$
$368$	3.23669	+	5.60612i	0.168724	+	0.292239i
$369$	−1.54736	+	2.68010i	−0.0805522	+	0.139520i
$370$	−7.32564			−0.380842
$371$	−9.85643	+	5.45615i	−0.511720	+	0.283269i
$372$	0.458433			0.0237686
$373$	−2.86660	+	4.96510i	−0.148427	+	0.257083i	−0.930646	−	0.365920i	$-0.880754\pi$
$373$	−2.86660	+	4.96510i	−0.148427	+	0.257083i	0.782219	+	0.623003i	$0.214088\pi$
$374$	−1.97500	−	3.42080i	−0.102125	−	0.176885i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	13.0535	−	22.6093i	0.673181	−	1.16598i
$377$	−44.7695			−2.30575
$378$	−2.47100	−	1.48665i	−0.127094	−	0.0764649i
$379$	1.31598			0.0675975			0.0337987	−	0.999429i	$-0.489239\pi$
$379$	1.31598			0.0675975			0.0337987	+	0.999429i	$0.489239\pi$
$380$	1.84879	−	3.20220i	0.0948409	−	0.164269i
$381$	4.33358	+	7.50599i	0.222016	+	0.384543i
$382$	11.8976	+	20.6072i	0.608734	+	1.05436i
$383$	−2.19354	+	3.79932i	−0.112085	+	0.194136i	−0.916611	−	0.399781i	$-0.869086\pi$
$383$	−2.19354	+	3.79932i	−0.112085	+	0.194136i	0.804526	+	0.593917i	$0.202419\pi$
$384$	0.283879			0.0144866
$385$	−0.0476864	+	2.64532i	−0.00243032	+	0.134818i
$386$	6.14097			0.312567
$387$	−4.20996	+	7.29186i	−0.214004	+	0.370666i
$388$	1.18879	+	2.05904i	0.0603516	+	0.104532i
$389$	−15.5050	−	26.8554i	−0.786134	−	1.36162i	−0.928320	−	0.371783i	$-0.878746\pi$
$389$	−15.5050	−	26.8554i	−0.786134	−	1.36162i	0.142186	−	0.989840i	$-0.454587\pi$
$390$	2.48844	−	4.31010i	0.126007	−	0.218251i
$391$	−13.6661			−0.691123
$392$	21.4407	+	0.773261i	1.08292	+	0.0390556i
$393$	13.4051			0.676197
$394$	−3.18973	+	5.52478i	−0.160696	+	0.278334i
$395$	7.27575	+	12.6020i	0.366082	+	0.634073i
$396$	−0.406003	−	0.703218i	−0.0204024	−	0.0353380i
$397$	7.97468	−	13.8126i	0.400238	−	0.693232i	−0.593517	−	0.804822i	$-0.702261\pi$
$397$	7.97468	−	13.8126i	0.400238	−	0.693232i	0.993754	+	0.111590i	$0.0355942\pi$
$398$	−4.88696			−0.244961
$399$	0.217146	−	12.0458i	0.0108709	−	0.603046i
$400$	−1.71663			−0.0858317
$401$	3.07553	−	5.32698i	0.153585	−	0.266017i	−0.778958	−	0.627076i	$-0.784252\pi$
$401$	3.07553	−	5.32698i	0.153585	−	0.266017i	0.932543	+	0.361059i	$0.117585\pi$
$402$	7.73212	+	13.3924i	0.385643	+	0.667953i
$403$	1.28895	+	2.23253i	0.0642072	+	0.111210i
$404$	7.62216	−	13.2020i	0.379217	−	0.656822i
$405$	−1.00000			−0.0496904
$406$	24.2273	+	14.5761i	1.20238	+	0.723398i
$407$	−6.72107			−0.333151
$408$	−5.55371	+	9.61930i	−0.274950	+	0.476227i
$409$	−11.1758	−	19.3570i	−0.552608	−	0.957144i	−0.998085	−	0.0618514i	$-0.980300\pi$
$409$	−11.1758	−	19.3570i	−0.552608	−	0.957144i	0.445478	−	0.895293i	$-0.353034\pi$
$410$	1.68654	+	2.92118i	0.0832924	+	0.144267i
$411$	1.53947	−	2.66644i	0.0759365	−	0.131526i
$412$	−15.6786			−0.772430
$413$	−7.64499	+	4.23198i	−0.376185	+	0.208242i
$414$	4.11018			0.202004
$415$	−4.58338	+	7.93865i	−0.224989	+	0.389693i
$416$	−9.72328	−	16.8412i	−0.476723	−	0.825708i
$417$	−9.99789	−	17.3168i	−0.489599	−	0.848010i
$418$	−2.48162	+	4.29829i	−0.121380	+	0.210236i
$419$	40.1788			1.96286			0.981431	−	0.191816i	$-0.0614378\pi$
$419$	40.1788			1.96286			0.981431	+	0.191816i	$0.0614378\pi$
$420$	1.87960	−	1.04047i	0.0917150	−	0.0507700i
$421$	−3.98451			−0.194193			−0.0970966	−	0.995275i	$-0.530956\pi$
$421$	−3.98451			−0.194193			−0.0970966	+	0.995275i	$0.530956\pi$
$422$	−7.43803	+	12.8831i	−0.362078	+	0.627137i
$423$	−4.25895	−	7.37671i	−0.207077	−	0.358668i
$424$	−6.52540	−	11.3023i	−0.316902	−	0.548890i
$425$	1.81201	−	3.13849i	0.0878952	−	0.152239i
$426$	6.59958			0.319751
$427$	−4.31599	−	2.59667i	−0.208865	−	0.125661i
$428$	6.97290			0.337048
$429$	2.28307	−	3.95440i	0.110228	−	0.190920i
$430$	4.58865	+	7.94778i	0.221284	+	0.383276i
$431$	−12.1571	−	21.0567i	−0.585585	−	1.01426i	−0.994802	−	0.101826i	$-0.967531\pi$
$431$	−12.1571	−	21.0567i	−0.585585	−	1.01426i	0.409217	−	0.912437i	$-0.365802\pi$
$432$	0.858317	−	1.48665i	0.0412958	−	0.0715264i
$433$	−14.7157			−0.707190			−0.353595	−	0.935399i	$-0.615041\pi$
$433$	−14.7157			−0.707190			−0.353595	+	0.935399i	$0.615041\pi$
$434$	0.0293439	−	1.62780i	0.00140855	−	0.0781370i
$435$	9.80465			0.470097
$436$	2.70277	−	4.68134i	0.129439	−	0.224196i
$437$	8.58583	+	14.8711i	0.410716	+	0.711381i
$438$	1.47569	+	2.55598i	0.0705114	+	0.122129i
$439$	11.7212	−	20.3017i	0.559423	−	0.968949i	−0.438122	−	0.898916i	$-0.644356\pi$
$439$	11.7212	−	20.3017i	0.559423	−	0.968949i	0.997545	−	0.0700332i	$-0.0223105\pi$
$440$	−3.06495			−0.146116
$441$	3.71622	−	5.93209i	0.176963	−	0.282481i
$442$	−18.0363			−0.857898
$443$	−12.7064	+	22.0081i	−0.603698	+	1.04564i	0.388558	+	0.921424i	$0.372973\pi$
$443$	−12.7064	+	22.0081i	−0.603698	+	1.04564i	−0.992256	+	0.124211i	$0.960360\pi$
$444$	2.72877	+	4.72638i	0.129502	+	0.224304i
$445$	−0.560941	−	0.971578i	−0.0265911	−	0.0460572i
$446$	10.3437	−	17.9158i	0.489787	−	0.848337i
$447$	−0.500540			−0.0236747
$448$	−0.385078	+	21.3615i	−0.0181932	+	1.00924i
$449$	−10.1008			−0.476687			−0.238344	−	0.971181i	$-0.576604\pi$
$449$	−10.1008			−0.476687			−0.238344	+	0.971181i	$0.576604\pi$
$450$	−0.544976	+	0.943925i	−0.0256904	+	0.0444971i
$451$	1.54736	+	2.68010i	0.0728622	+	0.126201i
$452$	3.26045	+	5.64726i	0.153359	+	0.265625i
$453$	−2.98833	+	5.17593i	−0.140404	+	0.243187i
$454$	−26.0717			−1.22360
$455$	10.3518	+	6.22804i	0.485299	+	0.291975i
$456$	13.9567			0.653580
$457$	19.5100	−	33.7922i	0.912637	−	1.58073i	0.102313	−	0.994752i	$-0.467376\pi$
$457$	19.5100	−	33.7922i	0.912637	−	1.58073i	0.810324	−	0.585982i	$-0.199291\pi$
$458$	5.66803	+	9.81732i	0.264850	+	0.458733i
$459$	1.81201	+	3.13849i	0.0845772	+	0.146492i
$460$	−1.53103	+	2.65182i	−0.0713846	+	0.123642i
$461$	5.24439			0.244256			0.122128	−	0.992514i	$-0.461028\pi$
$461$	5.24439			0.244256			0.122128	+	0.992514i	$0.461028\pi$
$462$	−2.52297	+	1.39662i	−0.117379	+	0.0649768i
$463$	−2.16220			−0.100486			−0.0502429	−	0.998737i	$-0.516000\pi$
$463$	−2.16220			−0.100486			−0.0502429	+	0.998737i	$0.516000\pi$
$464$	−8.41550	+	14.5761i	−0.390680	+	0.676677i
$465$	−0.282284	−	0.488930i	−0.0130906	−	0.0226736i
$466$	6.15074	+	10.6534i	0.284928	+	0.493509i
$467$	−9.24904	+	16.0198i	−0.427994	+	0.741308i	−0.996695	−	0.0812367i	$-0.974113\pi$
$467$	−9.24904	+	16.0198i	−0.427994	+	0.741308i	0.568700	+	0.822545i	$0.307446\pi$
$468$	−3.70774			−0.171390
$469$	−32.8418	+	18.1800i	−1.51649	+	0.839474i
$470$	−9.28409			−0.428243
$471$	−6.50396	+	11.2652i	−0.299687	+	0.519073i
$472$	−5.06133	−	8.76648i	−0.232967	−	0.403510i
$473$	4.20996	+	7.29186i	0.193574	+	0.335280i
$474$	−7.93021	+	13.7355i	−0.364247	+	0.630893i
$475$	−4.55363			−0.208935
$476$	−6.67136	−	4.01375i	−0.305781	−	0.183970i
$477$	−4.25808			−0.194964
$478$	−7.21286	+	12.4930i	−0.329909	+	0.571419i
$479$	5.35944	+	9.28282i	0.244879	+	0.424143i	0.962098	−	0.272705i	$-0.0879184\pi$
$479$	5.35944	+	9.28282i	0.244879	+	0.424143i	−0.717219	+	0.696848i	$0.754585\pi$
$480$	2.12943	+	3.68827i	0.0971946	+	0.168346i
$481$	−15.3447	+	26.5778i	−0.699658	+	1.21184i
$482$	25.4025			1.15705
$483$	−0.179824	+	9.97545i	−0.00818229	+	0.453899i
$484$	−0.812006			−0.0369094
$485$	1.46402	−	2.53575i	0.0664775	−	0.115142i
$486$	−0.544976	−	0.943925i	−0.0247206	−	0.0428173i
$487$	15.6570	+	27.1187i	0.709485	+	1.22886i	0.965048	+	0.262072i	$0.0844056\pi$
$487$	15.6570	+	27.1187i	0.709485	+	1.22886i	−0.255564	+	0.966792i	$0.582261\pi$
$488$	2.91748	−	5.05323i	0.132068	−	0.228749i
$489$	−16.4515			−0.743963
$490$	−3.57421	−	6.74068i	−0.161466	−	0.304513i
$491$	−7.92758			−0.357766			−0.178883	−	0.983870i	$-0.557248\pi$
$491$	−7.92758			−0.357766			−0.178883	+	0.983870i	$0.557248\pi$
$492$	1.25646	−	2.17626i	0.0566457	−	0.0981133i
$493$	−17.7661	−	30.7718i	−0.800144	−	1.38589i
$494$	11.3314	+	19.6266i	0.509826	+	0.883044i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	0.969156			0.0435164
$497$	−0.288738	+	16.0172i	−0.0129517	+	0.718471i
$498$	−9.99132			−0.447722
$499$	6.16578	−	10.6794i	0.276018	−	0.478077i	−0.694373	−	0.719615i	$-0.744318\pi$
$499$	6.16578	−	10.6794i	0.276018	−	0.478077i	0.970391	+	0.241538i	$0.0776517\pi$
$500$	−0.406003	−	0.703218i	−0.0181570	−	0.0314489i
$501$	−2.48209	−	4.29910i	−0.110891	−	0.192070i
$502$	−12.3509	+	21.3924i	−0.551247	+	0.954788i
$503$	43.4277			1.93635			0.968173	−	0.250280i	$-0.0805228\pi$
$503$	43.4277			1.93635			0.968173	+	0.250280i	$0.0805228\pi$
$504$	6.94846	+	4.18046i	0.309509	+	0.186213i
$505$	−18.7736			−0.835416
$506$	2.05509	−	3.55952i	0.0913600	−	0.158240i
$507$	−3.92486	−	6.79806i	−0.174309	−	0.301912i
$508$	−3.51890	−	6.09491i	−0.156126	−	0.270418i
$509$	2.84944	−	4.93537i	0.126299	−	0.218756i	−0.795941	−	0.605374i	$-0.793023\pi$
$509$	2.84944	−	4.93537i	0.126299	−	0.218756i	0.922240	+	0.386618i	$0.126357\pi$
$510$	3.95000			0.174909
$511$	−6.26794	+	3.46970i	−0.277277	+	0.153490i
$512$	−17.8337			−0.788145
$513$	2.27682	−	3.94356i	0.100524	−	0.174113i
$514$	−8.31539	−	14.4027i	−0.366776	−	0.635275i
$515$	9.65425	+	16.7216i	0.425417	+	0.736844i
$516$	3.41851	−	5.92104i	0.150492	−	0.260659i
$517$	−8.51790			−0.374617
$518$	16.9571	−	9.38680i	0.745051	−	0.412432i
$519$	2.12656			0.0933456
$520$	−6.99751	+	12.1200i	−0.306861	+	0.531499i
$521$	7.75717	+	13.4358i	0.339848	+	0.588633i	0.984404	−	0.175924i	$-0.0562911\pi$
$521$	7.75717	+	13.4358i	0.339848	+	0.588633i	−0.644556	+	0.764557i	$0.722958\pi$
$522$	5.34330	+	9.25486i	0.233870	+	0.405074i
$523$	−5.95941	+	10.3220i	−0.260587	+	0.451349i	−0.966398	−	0.257051i	$-0.917249\pi$
$523$	−5.95941	+	10.3220i	−0.260587	+	0.451349i	0.705811	+	0.708400i	$0.250583\pi$
$524$	−10.8850			−0.475514
$525$	−2.26707	−	1.36396i	−0.0989432	−	0.0595280i
$526$	27.7120			1.20830
$527$	−1.02300	+	1.77189i	−0.0445626	+	0.0771847i
$528$	−0.858317	−	1.48665i	−0.0373534	−	0.0646981i
$529$	4.38986	+	7.60346i	0.190863	+	0.330585i
$530$	−2.32055	+	4.01931i	−0.100798	+	0.174588i
$531$	−3.30272			−0.143326
$532$	−0.176324	+	9.78128i	−0.00764462	+	0.424072i
$533$	14.1309			0.612078
$534$	0.611398	−	1.05897i	0.0264578	−	0.0458262i
$535$	−4.29363	−	7.43678i	−0.185630	−	0.321520i
$536$	−21.7428	−	37.6596i	−0.939144	−	1.62665i
$537$	−1.65217	+	2.86164i	−0.0712963	+	0.123489i
$538$	8.11980			0.350069
$539$	−3.27924	−	6.18438i	−0.141247	−	0.266380i
$540$	0.812006			0.0349432
$541$	−16.7163	+	28.9536i	−0.718692	+	1.24481i	0.242827	+	0.970070i	$0.421925\pi$
$541$	−16.7163	+	28.9536i	−0.718692	+	1.24481i	−0.961518	+	0.274741i	$0.911408\pi$
$542$	−10.7459	−	18.6124i	−0.461574	−	0.799470i
$543$	−7.93922	−	13.7511i	−0.340704	−	0.590117i
$544$	7.71707	−	13.3664i	0.330867	−	0.573078i
$545$	−6.65702			−0.285156
$546$	−0.237329	+	13.1654i	−0.0101568	+	0.563429i
$547$	−5.49897			−0.235119			−0.117559	−	0.993066i	$-0.537507\pi$
$547$	−5.49897			−0.235119			−0.117559	+	0.993066i	$0.537507\pi$
$548$	−1.25006	+	2.16517i	−0.0533999	+	0.0924914i
$549$	−0.951886	−	1.64872i	−0.0406255	−	0.0703654i
$550$	0.544976	+	0.943925i	0.0232378	+	0.0402491i
$551$	−22.3234	+	38.6653i	−0.951009	+	1.64720i
$552$	−11.5579			−0.491935
$553$	−32.9893	−	19.8476i	−1.40285	−	0.844007i
$554$	17.4695			0.742208
$555$	3.36053	−	5.82061i	0.142647	−	0.247071i
$556$	8.11835	+	14.0614i	0.344295	+	0.596336i
$557$	−0.0355532	−	0.0615800i	−0.00150644	−	0.00260923i	0.865271	−	0.501304i	$-0.167146\pi$
$557$	−0.0355532	−	0.0615800i	−0.00150644	−	0.00260923i	−0.866778	+	0.498695i	$0.833813\pi$
$558$	0.307676	−	0.532910i	0.0130250	−	0.0225599i
$559$	38.4466			1.62612
$560$	3.97359	−	2.19963i	0.167915	−	0.0929514i
$561$	3.62401			0.153006
$562$	13.4799	−	23.3478i	0.568614	−	0.984868i
$563$	−20.7606	−	35.9583i	−0.874953	−	1.51546i	−0.856813	−	0.515628i	$-0.827559\pi$
$563$	−20.7606	−	35.9583i	−0.874953	−	1.51546i	−0.0181407	−	0.999835i	$-0.505775\pi$
$564$	3.45829	+	5.98994i	0.145620	+	0.252222i
$565$	4.01530	−	6.95471i	0.168925	−	0.292587i
$566$	12.9987			0.546378
$567$	2.31476	−	1.28136i	0.0972107	−	0.0538122i
$568$	−18.5581			−0.778679
$569$	−4.37064	+	7.57016i	−0.183227	+	0.317358i	−0.942978	−	0.332856i	$-0.891988\pi$
$569$	−4.37064	+	7.57016i	−0.183227	+	0.317358i	0.759751	+	0.650214i	$0.225321\pi$
$570$	−2.48162	−	4.29829i	−0.103944	−	0.180036i
$571$	15.8440	+	27.4425i	0.663049	+	1.14843i	0.979810	+	0.199929i	$0.0640713\pi$
$571$	15.8440	+	27.4425i	0.663049	+	1.14843i	−0.316761	+	0.948505i	$0.602595\pi$
$572$	−1.85387	+	3.21100i	−0.0775142	+	0.134259i
$573$	−21.8314			−0.912021
$574$	−7.64703	−	4.60075i	−0.319181	−	0.192032i
$575$	3.77098			0.157261
$576$	−4.03760	+	6.99334i	−0.168234	+	0.291389i
$577$	17.4987	+	30.3087i	0.728482	+	1.26177i	0.957525	+	0.288351i	$0.0931071\pi$
$577$	17.4987	+	30.3087i	0.728482	+	1.26177i	−0.229043	+	0.973416i	$0.573560\pi$
$578$	2.10717	+	3.64972i	0.0876466	+	0.151808i
$579$	−2.81708	+	4.87933i	−0.117074	+	0.202778i
$580$	−7.96144			−0.330581
$581$	0.437130	−	24.2490i	0.0181352	−	1.00602i
$582$	3.19141			0.132288
$583$	−2.12904	+	3.68761i	−0.0881759	+	0.152725i
$584$	−4.14966	−	7.18742i	−0.171714	−	0.297418i
$585$	2.28307	+	3.95440i	0.0943935	+	0.163494i
$586$	−11.8466	+	20.5189i	−0.489379	+	0.847629i
$587$	−14.2265			−0.587190			−0.293595	−	0.955930i	$-0.594852\pi$
$587$	−14.2265			−0.587190			−0.293595	+	0.955930i	$0.594852\pi$
$588$	−3.01759	+	4.81690i	−0.124443	+	0.198645i
$589$	2.57084			0.105929
$590$	−1.79990	+	3.11752i	−0.0741007	+	0.128346i
$591$	−2.92649	−	5.06883i	−0.120380	−	0.208504i
$592$	5.76880	+	9.99186i	0.237096	+	0.410663i
$593$	−1.84828	+	3.20131i	−0.0758996	+	0.131462i	−0.901477	−	0.432827i	$-0.857516\pi$
$593$	−1.84828	+	3.20131i	−0.0758996	+	0.131462i	0.825578	+	0.564289i	$0.190850\pi$
$594$	−1.08995			−0.0447212
$595$	−0.172816	+	9.58668i	−0.00708477	+	0.393015i
$596$	0.406442			0.0166485
$597$	2.24182	−	3.88295i	0.0917518	−	0.158919i
$598$	−9.38385	−	16.2533i	−0.383734	−	0.664647i
$599$	7.46832	+	12.9355i	0.305147	+	0.528531i	0.977294	−	0.211887i	$-0.0679610\pi$
$599$	7.46832	+	12.9355i	0.305147	+	0.528531i	−0.672147	+	0.740418i	$0.734628\pi$
$600$	1.53247	−	2.65432i	0.0625630	−	0.108362i
$601$	−27.2425			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$601$	−27.2425			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$602$	−20.8056	−	12.5175i	−0.847973	−	0.510173i
$603$	−14.1880			−0.577780
$604$	2.42654	−	4.20289i	0.0987345	−	0.171013i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−10.2312	−	17.7209i	−0.415613	−	0.719863i
$607$	7.92559	−	13.7275i	0.321690	−	0.557183i	−0.659147	−	0.752014i	$-0.729083\pi$
$607$	7.92559	−	13.7275i	0.321690	−	0.557183i	0.980837	+	0.194831i	$0.0624159\pi$
$608$	−19.3933			−0.786500
$609$	−22.6954	+	12.5633i	−0.919664	+	0.509091i
$610$	−2.07502			−0.0840151
$611$	−19.4470	+	33.6832i	−0.786741	+	1.36268i
$612$	−1.47136	−	2.54847i	−0.0594762	−	0.103016i
$613$	−10.2997	−	17.8396i	−0.416001	−	0.720535i	0.579532	−	0.814950i	$-0.303235\pi$
$613$	−10.2997	−	17.8396i	−0.416001	−	0.720535i	−0.995533	+	0.0944146i	$0.969902\pi$
$614$	−9.93124	+	17.2014i	−0.400792	+	0.694192i
$615$	−3.09471			−0.124791
$616$	7.09462	−	3.92731i	0.285850	−	0.158236i
$617$	−8.02829			−0.323207			−0.161603	−	0.986856i	$-0.551667\pi$
$617$	−8.02829			−0.323207			−0.161603	+	0.986856i	$0.551667\pi$
$618$	−10.5227	+	18.2258i	−0.423283	+	0.733148i
$619$	14.0340	+	24.3076i	0.564074	+	0.977005i	0.997135	+	0.0756405i	$0.0241001\pi$
$619$	14.0340	+	24.3076i	0.564074	+	0.977005i	−0.433061	+	0.901365i	$0.642567\pi$
$620$	0.229216	+	0.397014i	0.00920555	+	0.0159445i
$621$	−1.88549	+	3.26576i	−0.0756621	+	0.131051i
$622$	−19.0127			−0.762342
$623$	2.54339	+	1.53020i	0.101899	+	0.0613061i
$624$	−7.83840			−0.313787
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.35720	+	12.7430i	0.294053	+	0.509315i
$627$	−2.27682	−	3.94356i	−0.0909273	−	0.157491i
$628$	5.28126	−	9.14741i	0.210745	−	0.365021i
$629$	−24.3572			−0.971186
$630$	0.0519758	−	2.88327i	0.00207077	−	0.114872i
$631$	−44.9940			−1.79118			−0.895592	−	0.444877i	$-0.853248\pi$
$631$	−44.9940			−1.79118			−0.895592	+	0.444877i	$0.853248\pi$
$632$	22.2998	−	38.6244i	0.887038	−	1.53640i
$633$	−6.82419	−	11.8198i	−0.271237	−	0.469797i
$634$	−2.69335	−	4.66503i	−0.106967	−	0.185272i
$635$	−4.33358	+	7.50599i	−0.171973	+	0.297866i
$636$	3.45759			0.137102
$637$	−31.9423	−	1.15200i	−1.26560	−	0.0456440i
$638$	10.6866			0.423086
$639$	−3.02747	+	5.24372i	−0.119765	+	0.207439i
$640$	0.141939	+	0.245846i	0.00561065	+	0.00971792i
$641$	−7.01047	−	12.1425i	−0.276897	−	0.479600i	0.693715	−	0.720250i	$-0.255973\pi$
$641$	−7.01047	−	12.1425i	−0.276897	−	0.479600i	−0.970612	+	0.240650i	$0.922639\pi$
$642$	4.67984	−	8.10573i	0.184699	−	0.319907i
$643$	1.75660			0.0692736			0.0346368	−	0.999400i	$-0.488973\pi$
$643$	1.75660			0.0692736			0.0346368	+	0.999400i	$0.488973\pi$
$644$	0.146018	−	8.10013i	0.00575393	−	0.319190i
$645$	−8.41992			−0.331534
$646$	−8.99342	+	15.5771i	−0.353841	+	0.612871i
$647$	3.01755	+	5.22655i	0.118632	+	0.205477i	0.919226	−	0.393731i	$-0.128816\pi$
$647$	3.01755	+	5.22655i	0.118632	+	0.205477i	−0.800594	+	0.599208i	$0.795482\pi$
$648$	1.53247	+	2.65432i	0.0602013	+	0.104272i
$649$	−1.65136	+	2.86024i	−0.0648215	+	0.112274i
$650$	4.97688			0.195209
$651$	1.27992	+	0.770047i	0.0501639	+	0.0301805i
$652$	13.3587			0.523168
$653$	9.14583	−	15.8410i	0.357904	−	0.619908i	−0.629707	−	0.776833i	$-0.716825\pi$
$653$	9.14583	−	15.8410i	0.357904	−	0.619908i	0.987610	+	0.156925i	$0.0501582\pi$
$654$	−3.62792	−	6.28374i	−0.141863	−	0.245713i
$655$	6.70254	+	11.6091i	0.261890	+	0.453606i
$656$	2.65624	−	4.60075i	0.103709	−	0.179629i
$657$	−2.70782			−0.105642
$658$	21.4904	−	11.8963i	0.837784	−	0.463766i
$659$	−7.53407			−0.293486			−0.146743	−	0.989175i	$-0.546879\pi$
$659$	−7.53407			−0.293486			−0.146743	+	0.989175i	$0.546879\pi$
$660$	0.406003	−	0.703218i	0.0158036	−	0.0273727i
$661$	−3.21551	−	5.56942i	−0.125069	−	0.216625i	0.796691	−	0.604387i	$-0.206582\pi$
$661$	−3.21551	−	5.56942i	−0.125069	−	0.216625i	−0.921760	+	0.387761i	$0.873248\pi$
$662$	−3.69576	−	6.40125i	−0.143640	−	0.248792i
$663$	8.27389	−	14.3308i	0.321331	−	0.556562i
$664$	28.0957			1.09032
$665$	10.5406	−	5.83486i	0.408746	−	0.226266i
$666$	7.32564			0.283863
$667$	18.4866	−	32.0197i	0.715803	−	1.23981i
$668$	2.01547	+	3.49089i	0.0779808	+	0.135067i
$669$	9.49004	+	16.4372i	0.366906	+	0.635500i
$670$	−7.73212	+	13.3924i	−0.298718	+	0.517394i
$671$	−1.90377			−0.0734943
$672$	−9.65513	−	5.80890i	−0.372455	−	0.224083i
$673$	−46.6969			−1.80004			−0.900018	−	0.435854i	$-0.856447\pi$
$673$	−46.6969			−1.80004			−0.900018	+	0.435854i	$0.856447\pi$
$674$	−11.3274	+	19.6196i	−0.436315	+	0.755720i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	3.18701	+	5.52006i	0.122577	+	0.212310i
$677$	8.42812	−	14.5979i	0.323919	−	0.561044i	−0.657374	−	0.753564i	$-0.728333\pi$
$677$	8.42812	−	14.5979i	0.323919	−	0.561044i	0.981293	+	0.192520i	$0.0616661\pi$
$678$	8.75297			0.336156
$679$	−0.139627	+	7.74558i	−0.00535840	+	0.297248i
$680$	−11.1074			−0.425950
$681$	11.9600	−	20.7154i	0.458309	−	0.793814i
$682$	−0.307676	−	0.532910i	−0.0117815	−	0.0204062i
$683$	20.8524	+	36.1174i	0.797895	+	1.38199i	0.920985	+	0.389598i	$0.127386\pi$
$683$	20.8524	+	36.1174i	0.797895	+	1.38199i	−0.123090	+	0.992395i	$0.539280\pi$
$684$	−1.84879	+	3.20220i	−0.0706902	+	0.122439i
$685$	3.07894			0.117640
$686$	16.9107	+	11.0232i	0.645653	+	0.420867i
$687$	−10.4005			−0.396805
$688$	7.22696	−	12.5175i	0.275525	−	0.477224i
$689$	9.72152	+	16.8382i	0.370360	+	0.641483i
$690$	2.05509	+	3.55952i	0.0782360	+	0.135509i
$691$	−7.60601	+	13.1740i	−0.289346	+	0.501162i	−0.973654	−	0.228031i	$-0.926771\pi$
$691$	−7.60601	+	13.1740i	−0.289346	+	0.501162i	0.684308	+	0.729193i	$0.260105\pi$
$692$	−1.72678			−0.0656423
$693$	0.0476864	−	2.64532i	0.00181146	−	0.100487i
$694$	−22.5283			−0.855163
$695$	9.99789	−	17.3168i	0.379241	−	0.656865i
$696$	−15.0254	−	26.0247i	−0.569536	−	0.986465i
$697$	5.60764	+	9.71272i	0.212405	+	0.367895i
$698$	−15.4841	+	26.8193i	−0.586083	+	1.01513i
$699$	−11.2863			−0.426886
$700$	1.84088	+	1.10754i	0.0695786	+	0.0418612i
$701$	−27.3303			−1.03225			−0.516126	−	0.856513i	$-0.672626\pi$
$701$	−27.3303			−1.03225			−0.516126	+	0.856513i	$0.672626\pi$
$702$	−2.48844	+	4.31010i	−0.0939201	+	0.162674i
$703$	15.3026	+	26.5049i	0.577150	+	0.999653i
$704$	4.03760	+	6.99334i	0.152173	+	0.263571i
$705$	4.25895	−	7.37671i	0.160401	−	0.277823i
$706$	−18.3318			−0.689926
$707$	43.4565	−	24.0559i	1.63435	−	0.904714i
$708$	2.68183			0.100789
$709$	−4.68810	+	8.12002i	−0.176065	+	0.304954i	−0.940529	−	0.339712i	$-0.889670\pi$
$709$	−4.68810	+	8.12002i	−0.176065	+	0.304954i	0.764464	+	0.644666i	$0.223004\pi$
$710$	3.29979	+	5.71540i	0.123839	+	0.214495i
$711$	−7.27575	−	12.6020i	−0.272862	−	0.472610i
$712$	−1.71925	+	2.97784i	−0.0644318	+	0.111599i
$713$	−2.12897			−0.0797307
$714$	−9.14329	+	5.06138i	−0.342179	+	0.189417i
$715$	4.56615			0.170764
$716$	1.34157	−	2.32367i	0.0501368	−	0.0868396i
$717$	−6.61760	−	11.4620i	−0.247139	−	0.428057i
$718$	18.6539	+	32.3095i	0.696158	+	1.20578i
$719$	14.0582	−	24.3495i	0.524283	−	0.908085i	−0.475317	−	0.879814i	$-0.657667\pi$
$719$	14.0582	−	24.3495i	0.524283	−	0.908085i	0.999600	−	0.0282704i	$-0.00899996\pi$
$720$	1.71663			0.0639752
$721$	−43.7738	−	26.3360i	−1.63022	−	0.980803i
$722$	1.89170			0.0704017
$723$	−11.6530	+	20.1836i	−0.433381	+	0.750638i
$724$	6.44669	+	11.1660i	0.239590	+	0.414981i
$725$	4.90233	+	8.49108i	0.182068	+	0.315351i
$726$	−0.544976	+	0.943925i	−0.0202259	+	0.0350324i
$727$	27.3955			1.01604			0.508021	−	0.861345i	$-0.330377\pi$
$727$	27.3955			1.01604			0.508021	+	0.861345i	$0.330377\pi$
$728$	0.667372	−	37.0213i	0.0247344	−	1.37210i
$729$	1.00000			0.0370370
$730$	−1.47569	+	2.55598i	−0.0546179	+	0.0946009i
$731$	15.2569	+	26.4258i	0.564298	+	0.977394i
$732$	0.772937	+	1.33877i	0.0285686	+	0.0494823i
$733$	11.8397	−	20.5069i	0.437308	−	0.757439i	−0.560173	−	0.828376i	$-0.689265\pi$
$733$	11.8397	−	20.5069i	0.437308	−	0.757439i	0.997481	+	0.0709363i	$0.0225987\pi$
$734$	18.0371			0.665762
$735$	6.99545	+	0.252292i	0.258031	+	0.00930592i
$736$	16.0600			0.591981
$737$	−7.09400	+	12.2872i	−0.261311	+	0.452604i
$738$	−1.68654	−	2.92118i	−0.0620825	−	0.107530i
$739$	13.9769	+	24.2087i	0.514148	+	0.890530i	0.999865	+	0.0164143i	$0.00522506\pi$
$739$	13.9769	+	24.2087i	0.514148	+	0.890530i	−0.485717	+	0.874116i	$0.661442\pi$
$740$	−2.72877	+	4.72638i	−0.100312	+	0.173745i
$741$	−20.7926			−0.763834
$742$	0.221317	−	12.2772i	0.00812482	−	0.450710i
$743$	20.8443			0.764705			0.382352	−	0.924017i	$-0.375114\pi$
$743$	20.8443			0.764705			0.382352	+	0.924017i	$0.375114\pi$
$744$	−0.865186	+	1.49855i	−0.0317193	+	0.0549394i
$745$	−0.250270	−	0.433480i	−0.00916918	−	0.0158815i
$746$	−3.12446	−	5.41172i	−0.114394	−	0.198137i
$747$	4.58338	−	7.93865i	0.167697	−	0.290460i
$748$	−2.94272			−0.107597
$749$	19.4679	+	11.7127i	0.711342	+	0.427971i
$750$	−1.08995			−0.0397994
$751$	−14.0136	+	24.2722i	−0.511362	+	0.885705i	0.488551	+	0.872535i	$0.337525\pi$
$751$	−14.0136	+	24.2722i	−0.511362	+	0.885705i	−0.999913	+	0.0131697i	$0.995808\pi$
$752$	7.31105	+	12.6631i	0.266607	+	0.461776i
$753$	−11.3316	−	19.6269i	−0.412946	−	0.715244i
$754$	24.3983	−	42.2591i	0.888533	−	1.53898i
$755$	−5.97665			−0.217513
$756$	−1.87960	+	1.04047i	−0.0683603	+	0.0378417i
$757$	−2.91603			−0.105985			−0.0529925	−	0.998595i	$-0.516876\pi$
$757$	−2.91603			−0.105985			−0.0529925	+	0.998595i	$0.516876\pi$
$758$	−0.717178	+	1.24219i	−0.0260491	+	0.0451184i
$759$	1.88549	+	3.26576i	0.0684389	+	0.118540i
$760$	6.97833	+	12.0868i	0.253131	+	0.438435i
$761$	−9.64229	+	16.7009i	−0.349533	+	0.605408i	−0.986166	−	0.165758i	$-0.946993\pi$
$761$	−9.64229	+	16.7009i	−0.349533	+	0.605408i	0.636634	+	0.771166i	$0.280326\pi$
$762$	−9.44679			−0.342221
$763$	15.4094	−	8.53007i	0.557858	−	0.308809i
$764$	17.7273			0.641350
$765$	−1.81201	+	3.13849i	−0.0655132	+	0.113472i
$766$	−2.39085	−	4.14107i	−0.0863849	−	0.149623i
$767$	7.54035	+	13.0603i	0.272266	+	0.471579i
$768$	7.92050	−	13.7187i	0.285806	−	0.495031i
$769$	49.5688			1.78750			0.893748	−	0.448570i	$-0.148066\pi$
$769$	49.5688			1.78750			0.893748	+	0.448570i	$0.148066\pi$
$770$	−2.47100	−	1.48665i	−0.0890486	−	0.0535751i
$771$	15.2583			0.549514
$772$	2.28749	−	3.96205i	0.0823286	−	0.142597i
$773$	−10.1173	−	17.5237i	−0.363895	−	0.630285i	0.624703	−	0.780863i	$-0.285220\pi$
$773$	−10.1173	−	17.5237i	−0.363895	−	0.630285i	−0.988598	+	0.150577i	$0.951887\pi$
$774$	−4.58865	−	7.94778i	−0.164936	−	0.285677i
$775$	0.282284	−	0.488930i	0.0101399	−	0.0175629i
$776$	−8.97427			−0.322157
$777$	−0.320503	+	17.7794i	−0.0114980	+	0.637832i
$778$	33.7993			1.21177
$779$	7.04610	−	12.2042i	0.252453	−	0.437261i
$780$	−1.85387	−	3.21100i	−0.0663792	−	0.114972i
$781$	3.02747	+	5.24372i	0.108331	+	0.187635i
$782$	7.44768	−	12.8998i	0.266328	−	0.461294i
$783$	−9.80465			−0.350390
$784$	−6.37938	+	10.1832i	−0.227835	+	0.363687i
$785$	−13.0079			−0.464273
$786$	−7.30544	+	12.6534i	−0.260576	+	0.451332i
$787$	−23.5695	−	40.8235i	−0.840161	−	1.45520i	−0.889758	−	0.456432i	$-0.849127\pi$
$787$	−23.5695	−	40.8235i	−0.840161	−	1.45520i	0.0495971	−	0.998769i	$-0.484206\pi$
$788$	2.37633	+	4.11592i	0.0846532	+	0.146624i
$789$	−12.7125	+	22.0187i	−0.452577	+	0.783886i
$790$	−15.8604			−0.564288
$791$	−0.382950	+	21.2435i	−0.0136161	+	0.755333i
$792$	3.06495			0.108908
$793$	−4.34645	+	7.52828i	−0.154347	+	0.267337i
$794$	8.69201	+	15.0550i	0.308468	+	0.534282i
$795$	−2.12904	−	3.68761i	−0.0755093	−	0.130786i
$796$	−1.82038	+	3.15298i	−0.0645215	+	0.111755i
$797$	−39.1413			−1.38646			−0.693229	−	0.720718i	$-0.743812\pi$
$797$	−39.1413			−1.38646			−0.693229	+	0.720718i	$0.743812\pi$
$798$	11.2520	+	6.76965i	0.398317	+	0.239643i
$799$	−30.8690			−1.09207
$800$	−2.12943	+	3.68827i	−0.0752866	+	0.130400i
$801$	0.560941	+	0.971578i	0.0198199	+	0.0343290i
$802$	3.35218	+	5.80615i	0.118370	+	0.205022i
$803$	−1.35391	+	2.34504i	−0.0477784	+	0.0827546i
$804$	11.5207			0.406305
$805$	−8.72891	+	4.83199i	−0.307654	+	0.170305i
$806$	−2.80979			−0.0989705
$807$	−3.72485	+	6.45162i	−0.131121	+	0.227108i
$808$	28.7701	+	49.8313i	1.01213	+	1.75306i
$809$	20.9945	+	36.3636i	0.738128	+	1.27848i	0.953337	+	0.301908i	$0.0976234\pi$
$809$	20.9945	+	36.3636i	0.738128	+	1.27848i	−0.215209	+	0.976568i	$0.569043\pi$
$810$	0.544976	−	0.943925i	0.0191485	−	0.0331662i
$811$	−35.5453			−1.24817			−0.624083	−	0.781358i	$-0.714527\pi$
$811$	−35.5453			−1.24817			−0.624083	+	0.781358i	$0.714527\pi$
$812$	18.4288	−	10.2015i	0.646724	−	0.358002i
$813$	19.7180			0.691542
$814$	3.66282	−	6.34419i	0.128382	−	0.222364i
$815$	−8.22576	−	14.2474i	−0.288136	−	0.499066i
$816$	−3.11055	−	5.38763i	−0.108891	−	0.188605i
$817$	19.1706	−	33.2045i	0.670695	−	1.16168i
$818$	24.3621			0.851802
$819$	−10.3518	−	6.22804i	−0.361721	−	0.217625i
$820$	2.51293			0.0877552
$821$	18.3944	−	31.8601i	0.641970	−	1.11192i	−0.343023	−	0.939327i	$-0.611451\pi$
$821$	18.3944	−	31.8601i	0.641970	−	1.11192i	0.984993	−	0.172597i	$-0.0552159\pi$
$822$	1.67795	+	2.90629i	0.0585252	+	0.101369i
$823$	−19.5874	−	33.9264i	−0.682774	−	1.18260i	−0.974131	−	0.225984i	$-0.927440\pi$
$823$	−19.5874	−	33.9264i	−0.682774	−	1.18260i	0.291357	−	0.956614i	$-0.405893\pi$
$824$	29.5898	−	51.2510i	1.03081	−	1.78541i
$825$	−1.00000			−0.0348155
$826$	0.171661	−	9.52263i	0.00597286	−	0.331335i
$827$	2.03711			0.0708372			0.0354186	−	0.999373i	$-0.488724\pi$
$827$	2.03711			0.0708372			0.0354186	+	0.999373i	$0.488724\pi$
$828$	1.53103	−	2.65182i	0.0532069	−	0.0921571i
$829$	−0.790011	−	1.36834i	−0.0274382	−	0.0475244i	0.851980	−	0.523574i	$-0.175402\pi$
$829$	−0.790011	−	1.36834i	−0.0274382	−	0.0475244i	−0.879418	+	0.476050i	$0.842068\pi$
$830$	−4.99566	−	8.65274i	−0.173402	−	0.300341i
$831$	−8.01389	+	13.8805i	−0.277999	+	0.481508i
$832$	36.8726			1.27833
$833$	−11.8840	−	22.4123i	−0.411756	−	0.776540i
$834$	21.7944			0.754679
$835$	2.48209	−	4.29910i	0.0858961	−	0.148776i
$836$	1.84879	+	3.20220i	0.0639417	+	0.110750i
$837$	0.282284	+	0.488930i	0.00975716	+	0.0168999i
$838$	−21.8965	+	37.9258i	−0.756400	+	1.31012i
$839$	−26.0088			−0.897923			−0.448961	−	0.893551i	$-0.648206\pi$
$839$	−26.0088			−0.897923			−0.448961	+	0.893551i	$0.648206\pi$
$840$	−0.146156	+	8.10778i	−0.00504287	+	0.279745i
$841$	67.1312			2.31487
$842$	2.17146	−	3.76108i	0.0748335	−	0.129615i
$843$	12.3674	+	21.4210i	0.425956	+	0.737777i
$844$	5.54128	+	9.59779i	0.190739	+	0.330369i
$845$	3.92486	−	6.79806i	0.135019	−	0.233860i
$846$	9.28409			0.319194
$847$	−2.26707	−	1.36396i	−0.0778975	−	0.0468662i
$848$	7.30957			0.251011
$849$	−5.96299	+	10.3282i	−0.204649	+	0.354463i
$850$	1.97500	+	3.42080i	0.0677419	+	0.117332i
$851$	−12.6725	−	21.9494i	−0.434408	−	0.752416i
$852$	2.45832	−	4.25794i	0.0842207	−	0.145875i
$853$	3.98652			0.136496			0.0682479	−	0.997668i	$-0.478259\pi$
$853$	3.98652			0.136496			0.0682479	+	0.997668i	$0.478259\pi$
$854$	4.80317	−	2.65885i	0.164361	−	0.0909841i
$855$	4.55363			0.155731
$856$	−13.1597	+	22.7934i	−0.449791	+	0.779061i
$857$	23.4318	+	40.5851i	0.800415	+	1.38636i	0.919343	+	0.393457i	$0.128721\pi$
$857$	23.4318	+	40.5851i	0.800415	+	1.38636i	−0.118928	+	0.992903i	$0.537946\pi$
$858$	2.48844	+	4.31010i	0.0849539	+	0.147145i
$859$	−2.94014	+	5.09248i	−0.100316	+	0.173753i	−0.911815	−	0.410601i	$-0.865319\pi$
$859$	−2.94014	+	5.09248i	−0.100316	+	0.173753i	0.811499	+	0.584354i	$0.198652\pi$
$860$	6.83703			0.233141
$861$	7.16352	−	3.96545i	0.244132	−	0.135142i
$862$	26.5012			0.902635
$863$	−23.1233	+	40.0508i	−0.787128	+	1.36335i	0.140592	+	0.990068i	$0.455099\pi$
$863$	−23.1233	+	40.0508i	−0.787128	+	1.36335i	−0.927720	+	0.373278i	$0.878234\pi$
$864$	−2.12943	−	3.68827i	−0.0724446	−	0.125478i
$865$	1.06328	+	1.84165i	0.0361526	+	0.0626181i
$866$	8.01969	−	13.8905i	0.272520	−	0.472019i
$867$	−3.86653			−0.131314
$868$	−1.03930	−	0.625283i	−0.0352761	−	0.0212235i
$869$	−14.5515			−0.493626
$870$	−5.34330	+	9.25486i	−0.181155	+	0.313769i
$871$	32.3923	+	56.1051i	1.09757	+	1.90105i
$872$	10.2017	+	17.6699i	0.345474	+	0.598378i
$873$	−1.46402	+	2.53575i	−0.0495494	+	0.0858221i
$874$	−18.7163			−0.633087
$875$	0.0476864	−	2.64532i	0.00161209	−	0.0894282i
$876$	2.19876			0.0742893
$877$	−15.1394	+	26.2223i	−0.511223	+	0.885464i	0.488693	+	0.872456i	$0.337474\pi$
$877$	−15.1394	+	26.2223i	−0.511223	+	0.885464i	−0.999915	+	0.0130077i	$0.995859\pi$
$878$	12.7755	+	22.1279i	0.431154	+	0.746780i
$879$	−10.8689	−	18.8255i	−0.366600	−	0.634970i
$880$	0.858317	−	1.48665i	0.0289339	−	0.0501149i
$881$	7.13297			0.240316			0.120158	−	0.992755i	$-0.461660\pi$
$881$	7.13297			0.240316			0.120158	+	0.992755i	$0.461660\pi$
$882$	3.57421	+	6.74068i	0.120350	+	0.226970i
$883$	56.5578			1.90332			0.951660	−	0.307152i	$-0.0993760\pi$
$883$	56.5578			1.90332			0.951660	+	0.307152i	$0.0993760\pi$
$884$	−6.71845	+	11.6367i	−0.225966	+	0.391385i
$885$	−1.65136	−	2.86024i	−0.0555098	−	0.0961458i
$886$	−13.8493	−	23.9877i	−0.465277	−	0.805884i
$887$	6.28909	−	10.8930i	0.211167	−	0.365752i	−0.740913	−	0.671601i	$-0.765607\pi$
$887$	6.28909	−	10.8930i	0.211167	−	0.365752i	0.952080	+	0.305849i	$0.0989403\pi$
$888$	−20.5997			−0.691282
$889$	0.413306	−	22.9275i	0.0138618	−	0.768962i
$890$	1.22280			0.0409882
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−7.70597	−	13.3471i	−0.258015	−	0.446895i
$893$	19.3937	+	33.5909i	0.648985	+	1.12408i
$894$	0.272782	−	0.472472i	0.00912320	−	0.0158018i
$895$	−3.30434			−0.110452
$896$	−0.643574	−	0.387199i	−0.0215003	−	0.0129354i
$897$	17.2189			0.574921
$898$	5.50470	−	9.53443i	0.183694	−	0.318168i
$899$	−2.76770	−	4.79379i	−0.0923078	−	0.159882i
$900$	0.406003	+	0.703218i	0.0135334	+	0.0234406i
$901$	−7.71567	+	13.3639i	−0.257046	+	0.445217i
$902$	−3.37309			−0.112312
$903$	19.4901	−	10.7890i	0.648589	−	0.359035i
$904$	−24.6134			−0.818629
$905$	7.93922	−	13.7511i	0.263909	−	0.457103i
$906$	−3.25713	−	5.64152i	−0.108211	−	0.187427i
$907$	−23.2301	−	40.2358i	−0.771344	−	1.33601i	−0.936827	−	0.349794i	$-0.886252\pi$
$907$	−23.2301	−	40.2358i	−0.771344	−	1.33601i	0.165483	−	0.986213i	$-0.447082\pi$
$908$	−9.71161	+	16.8210i	−0.322291	+	0.558225i
$909$	18.7736			0.622682
$910$	−11.5203	+	6.37719i	−0.381893	+	0.211402i
$911$	47.8151			1.58418			0.792092	−	0.610401i	$-0.208992\pi$
$911$	47.8151			1.58418			0.792092	+	0.610401i	$0.208992\pi$
$912$	−3.90846	+	6.76965i	−0.129422	+	0.224166i
$913$	−4.58338	−	7.93865i	−0.151688	−	0.262731i
$914$	21.2649	+	36.8319i	0.703380	+	1.21829i
$915$	0.951886	−	1.64872i	0.0314684	−	0.0545048i
$916$	8.44529			0.279040
$917$	−30.3903	−	18.2840i	−1.00358	−	0.603790i
$918$	−3.95000			−0.130369
$919$	−13.8531	+	23.9942i	−0.456970	+	0.791495i	−0.998799	−	0.0489934i	$-0.984399\pi$
$919$	−13.8531	+	23.9942i	−0.456970	+	0.791495i	0.541829	+	0.840489i	$0.317732\pi$
$920$	−5.77893	−	10.0094i	−0.190526	−	0.330000i
$921$	−9.11164	−	15.7818i	−0.300239	−	0.520029i
$922$	−2.85807	+	4.95031i	−0.0941254	+	0.163030i
$923$	27.6477			0.910036
$924$	−0.0387216	+	2.14802i	−0.00127385	+	0.0706646i
$925$	6.72107			0.220987
$926$	1.17835	−	2.04095i	0.0387228	−	0.0670699i
$927$	−9.65425	−	16.7216i	−0.317087	−	0.549211i
$928$	20.8783	+	36.1622i	0.685363	+	1.18708i
$929$	10.4325	−	18.0697i	0.342281	−	0.592848i	−0.642575	−	0.766223i	$-0.722134\pi$
$929$	10.4325	−	18.0697i	0.342281	−	0.592848i	0.984856	+	0.173375i	$0.0554673\pi$
$930$	0.615352			0.0201782
$931$	−16.9223	+	27.0126i	−0.554606	+	0.885302i
$932$	9.16452			0.300194
$933$	8.72183	−	15.1067i	0.285540	−	0.494570i
$934$	−10.0810	−	17.4608i	−0.329860	−	0.571335i
$935$	1.81201	+	3.13849i	0.0592589	+	0.102639i
$936$	6.99751	−	12.1200i	0.228721	−	0.396156i
$937$	−27.1500			−0.886951			−0.443476	−	0.896286i	$-0.646255\pi$
$937$	−27.1500			−0.886951			−0.443476	+	0.896286i	$0.646255\pi$
$938$	0.737433	−	40.9079i	0.0240781	−	1.33569i
$939$	−13.5001			−0.440558
$940$	−3.45829	+	5.98994i	−0.112797	+	0.195370i
$941$	24.3653	+	42.2019i	0.794286	+	1.37574i	0.923292	+	0.384099i	$0.125488\pi$
$941$	24.3653	+	42.2019i	0.794286	+	1.37574i	−0.129006	+	0.991644i	$0.541179\pi$
$942$	−7.08900	−	12.2785i	−0.230972	−	0.400056i
$943$	−5.83505	+	10.1066i	−0.190015	+	0.329116i
$944$	5.66955			0.184528
$945$	2.26707	+	1.36396i	0.0737479	+	0.0443696i
$946$	−9.17730			−0.298380
$947$	24.5507	−	42.5231i	0.797791	−	1.38181i	−0.123261	−	0.992374i	$-0.539335\pi$
$947$	24.5507	−	42.5231i	0.797791	−	1.38181i	0.921052	−	0.389440i	$-0.127331\pi$
$948$	5.90795	+	10.2329i	0.191881	+	0.332348i
$949$	6.18215	+	10.7078i	0.200681	+	0.347590i
$950$	2.48162	−	4.29829i	0.0805144	−	0.139455i
$951$	4.94215			0.160260
$952$	25.7110	−	14.2326i	0.833298	−	0.461282i
$953$	33.3622			1.08071			0.540353	−	0.841438i	$-0.318291\pi$
$953$	33.3622			1.08071			0.540353	+	0.841438i	$0.318291\pi$
$954$	2.32055	−	4.01931i	0.0751306	−	0.130130i
$955$	−10.9157	−	18.9066i	−0.353224	−	0.611802i
$956$	5.37353	+	9.30724i	0.173793	+	0.301018i
$957$	−4.90233	+	8.49108i	−0.158470	+	0.274478i
$958$	−11.6831			−0.377463
$959$	−7.12701	+	3.94524i	−0.230143	+	0.127399i
$960$	−8.07521			−0.260626
$961$	15.3406	−	26.5708i	0.494859	−	0.857121i
$962$	−16.7250	−	28.9685i	−0.539235	−	0.933982i
$963$	4.29363	+	7.43678i	0.138360	+	0.239647i
$964$	9.46233	−	16.3892i	0.304761	−	0.527862i
$965$	−5.63417			−0.181370
$966$	−9.31808	−	5.60612i	−0.299804	−	0.180374i
$967$	−32.6247			−1.04914			−0.524569	−	0.851368i	$-0.675774\pi$
$967$	−32.6247			−1.04914			−0.524569	+	0.851368i	$0.675774\pi$
$968$	1.53247	−	2.65432i	0.0492556	−	0.0853132i
$969$	−8.25121	−	14.2915i	−0.265067	−	0.459110i
$970$	1.59571	+	2.76384i	0.0512350	+	0.0887416i
$971$	−4.13691	+	7.16535i	−0.132760	+	0.229947i	−0.924739	−	0.380601i	$-0.875717\pi$
$971$	−4.13691	+	7.16535i	−0.132760	+	0.229947i	0.791980	+	0.610548i	$0.209051\pi$
$972$	−0.812006			−0.0260451
$973$	−0.953526	+	52.8953i	−0.0305686	+	1.69574i
$974$	−34.1307			−1.09362
$975$	−2.28307	+	3.95440i	−0.0731169	+	0.126642i
$976$	1.63404	+	2.83024i	0.0523043	+	0.0905938i
$977$	−5.82327	−	10.0862i	−0.186303	−	0.322686i	0.757712	−	0.652589i	$-0.226317\pi$
$977$	−5.82327	−	10.0862i	−0.186303	−	0.322686i	−0.944015	+	0.329903i	$0.892984\pi$
$978$	8.96567	−	15.5290i	0.286691	−	0.496563i
$979$	1.12188			0.0358555
$980$	−5.68035	−	0.204862i	−0.181452	−	0.00654409i
$981$	6.65702			0.212542
$982$	4.32034	−	7.48304i	0.137867	−	0.238793i
$983$	−12.8240	−	22.2119i	−0.409023	−	0.708449i	0.585757	−	0.810487i	$-0.300797\pi$
$983$	−12.8240	−	22.2119i	−0.409023	−	0.708449i	−0.994781	+	0.102037i	$0.967464\pi$
$984$	4.74257	+	8.21437i	0.151188	+	0.261865i
$985$	2.92649	−	5.06883i	0.0932457	−	0.161506i
$986$	38.7283			1.23336
$987$	−0.406188	+	22.5326i	−0.0129291	+	0.717220i
$988$	16.8837			0.537142
$989$	−15.8757	+	27.4975i	−0.504817	+	0.874368i
$990$	−0.544976	−	0.943925i	−0.0173205	−	0.0299999i
$991$	7.51261	+	13.0122i	0.238646	+	0.413347i	0.960326	−	0.278880i	$-0.0899631\pi$
$991$	7.51261	+	13.0122i	0.238646	+	0.413347i	−0.721680	+	0.692227i	$0.756630\pi$
$992$	1.20221	−	2.08228i	0.0381701	−	0.0661125i
$993$	6.78152			0.215205
$994$	−14.9617	−	9.00155i	−0.474557	−	0.285512i
$995$	4.48365			0.142141
$996$	−3.72173	+	6.44623i	−0.117928	+	0.204257i
$997$	−12.3191	−	21.3374i	−0.390151	−	0.675762i	0.602318	−	0.798256i	$-0.294244\pi$
$997$	−12.3191	−	21.3374i	−0.390151	−	0.675762i	−0.992469	+	0.122495i	$0.960911\pi$
$998$	6.72039	+	11.6401i	0.212730	+	0.368460i
$999$	−3.36053	+	5.82061i	−0.106323	+	0.184156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.3	✓	16
7.2	even	3		8085.2.a.cf.1.6		8
7.4	even	3	inner	1155.2.q.j.991.3	yes	16
7.5	odd	6		8085.2.a.ce.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.3	✓	16	1.1	even	1	trivial
1155.2.q.j.991.3	yes	16	7.4	even	3	inner
8085.2.a.ce.1.6		8	7.5	odd	6
8085.2.a.cf.1.6		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544976 + 0.943925i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.406003 + 0.703218i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.08995 q^{6} +(-0.0476864 + 2.64532i) q^{7} -3.06495 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.544976 + 0.943925i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.406003 + 0.703218i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.08995 q^{6} +(-0.0476864 + 2.64532i) q^{7} -3.06495 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.544976 + 0.943925i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.406003 - 0.703218i) q^{12} +4.56615 q^{13} +(-2.47100 - 1.48665i) q^{14} -1.00000 q^{15} +(0.858317 - 1.48665i) q^{16} +(1.81201 + 3.13849i) q^{17} +(-0.544976 - 0.943925i) q^{18} +(2.27682 - 3.94356i) q^{19} +0.812006 q^{20} +(2.31476 - 1.28136i) q^{21} -1.08995 q^{22} +(-1.88549 + 3.26576i) q^{23} +(1.53247 + 2.65432i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.48844 + 4.31010i) q^{26} +1.00000 q^{27} +(-1.87960 + 1.04047i) q^{28} -9.80465 q^{29} +(0.544976 - 0.943925i) q^{30} +(0.282284 + 0.488930i) q^{31} +(-2.12943 - 3.68827i) q^{32} +(0.500000 - 0.866025i) q^{33} -3.95000 q^{34} +(2.26707 + 1.36396i) q^{35} -0.812006 q^{36} +(-3.36053 + 5.82061i) q^{37} +(2.48162 + 4.29829i) q^{38} +(-2.28307 - 3.95440i) q^{39} +(-1.53247 + 2.65432i) q^{40} +3.09471 q^{41} +(-0.0519758 + 2.88327i) q^{42} +8.41992 q^{43} +(-0.406003 + 0.703218i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-2.05509 - 3.55952i) q^{46} +(-4.25895 + 7.37671i) q^{47} -1.71663 q^{48} +(-6.99545 - 0.252292i) q^{49} +1.08995 q^{50} +(1.81201 - 3.13849i) q^{51} +(1.85387 + 3.21100i) q^{52} +(2.12904 + 3.68761i) q^{53} +(-0.544976 + 0.943925i) q^{54} +1.00000 q^{55} +(0.146156 - 8.10778i) q^{56} -4.55363 q^{57} +(5.34330 - 9.25486i) q^{58} +(1.65136 + 2.86024i) q^{59} +(-0.406003 - 0.703218i) q^{60} +(-0.951886 + 1.64872i) q^{61} -0.615352 q^{62} +(-2.26707 - 1.36396i) q^{63} +8.07521 q^{64} +(2.28307 - 3.95440i) q^{65} +(0.544976 + 0.943925i) q^{66} +(7.09400 + 12.2872i) q^{67} +(-1.47136 + 2.54847i) q^{68} +3.77098 q^{69} +(-2.52297 + 1.39662i) q^{70} +6.05493 q^{71} +(1.53247 - 2.65432i) q^{72} +(1.35391 + 2.34504i) q^{73} +(-3.66282 - 6.34419i) q^{74} +(-0.500000 + 0.866025i) q^{75} +3.69758 q^{76} +(-2.31476 + 1.28136i) q^{77} +4.97688 q^{78} +(-7.27575 + 12.6020i) q^{79} +(-0.858317 - 1.48665i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.68654 + 2.92118i) q^{82} -9.16676 q^{83} +(1.84088 + 1.10754i) q^{84} +3.62401 q^{85} +(-4.58865 + 7.94778i) q^{86} +(4.90233 + 8.49108i) q^{87} +(-1.53247 - 2.65432i) q^{88} +(0.560941 - 0.971578i) q^{89} -1.08995 q^{90} +(-0.217743 + 12.0789i) q^{91} -3.06206 q^{92} +(0.282284 - 0.488930i) q^{93} +(-4.64205 - 8.04026i) q^{94} +(-2.27682 - 3.94356i) q^{95} +(-2.12943 + 3.68827i) q^{96} +2.92803 q^{97} +(4.05050 - 6.46569i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Introduction

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