LMFDB - Embedded newform 126.2.t.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(47,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("126.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.6
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	126.47
Dual form			126.2.t.a.59.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.206076 - 1.71975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.42985 q^{5} +(-1.03834 - 1.38631i) q^{6} +(-2.43739 + 1.02913i) q^{7} -1.00000i q^{8} +(-2.91507 + 0.708796i) q^{9} +(1.23829 - 0.714925i) q^{10} +3.41945i q^{11} +(-1.59238 - 0.681407i) q^{12} +(5.48813 - 3.16857i) q^{13} +(-1.59628 + 2.10995i) q^{14} +(-0.294657 - 2.45898i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.14201 + 1.97802i) q^{17} +(-2.17012 + 2.07137i) q^{18} +(-1.87673 - 1.08353i) q^{19} +(0.714925 - 1.23829i) q^{20} +(2.27213 + 3.97962i) q^{21} +(1.70972 + 2.96133i) q^{22} +8.05411i q^{23} +(-1.71975 + 0.206076i) q^{24} -2.95553 q^{25} +(3.16857 - 5.48813i) q^{26} +(1.81967 + 4.86711i) q^{27} +(-0.327442 + 2.62541i) q^{28} +(-0.298879 - 0.172558i) q^{29} +(-1.48467 - 1.98221i) q^{30} +(-3.76052 - 2.17114i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.88058 - 0.704664i) q^{33} +(1.97802 + 1.14201i) q^{34} +(-3.48511 + 1.47150i) q^{35} +(-0.843698 + 2.87892i) q^{36} +(1.07786 - 1.86690i) q^{37} -2.16707 q^{38} +(-6.58012 - 8.78524i) q^{39} -1.42985i q^{40} +(-0.202180 - 0.350186i) q^{41} +(3.95754 + 2.31039i) q^{42} +(2.90883 - 5.03824i) q^{43} +(2.96133 + 1.70972i) q^{44} +(-4.16811 + 1.01347i) q^{45} +(4.02706 + 6.97507i) q^{46} +(-2.75915 - 4.77898i) q^{47} +(-1.38631 + 1.03834i) q^{48} +(4.88178 - 5.01680i) q^{49} +(-2.55956 + 1.47776i) q^{50} +(3.16635 - 2.37159i) q^{51} -6.33715i q^{52} +(-8.56310 + 4.94391i) q^{53} +(4.00944 + 3.30521i) q^{54} +4.88930i q^{55} +(1.02913 + 2.43739i) q^{56} +(-1.47666 + 3.45080i) q^{57} -0.345115 q^{58} +(5.51480 - 9.55191i) q^{59} +(-2.27687 - 0.974311i) q^{60} +(-9.94175 + 5.73987i) q^{61} -4.34228 q^{62} +(6.37572 - 4.72760i) q^{63} -1.00000 q^{64} +(7.84721 - 4.53059i) q^{65} +(4.74040 - 3.55055i) q^{66} +(-2.12683 + 3.68377i) q^{67} +2.28402 q^{68} +(13.8510 - 1.65976i) q^{69} +(-2.28244 + 3.01691i) q^{70} -3.55393i q^{71} +(0.708796 + 2.91507i) q^{72} +(-0.201057 + 0.116080i) q^{73} -2.15571i q^{74} +(0.609062 + 5.08276i) q^{75} +(-1.87673 + 1.08353i) q^{76} +(-3.51906 - 8.33454i) q^{77} +(-10.0912 - 4.31818i) q^{78} +(-7.28100 - 12.6111i) q^{79} +(-0.714925 - 1.23829i) q^{80} +(7.99522 - 4.13237i) q^{81} +(-0.350186 - 0.202180i) q^{82} +(-0.811624 + 1.40577i) q^{83} +(4.58252 + 0.0220855i) q^{84} +(1.63290 + 2.82827i) q^{85} -5.81766i q^{86} +(-0.235164 + 0.549556i) q^{87} +3.41945 q^{88} +(2.02974 - 3.51562i) q^{89} +(-3.10295 + 2.96175i) q^{90} +(-10.1159 + 13.3711i) q^{91} +(6.97507 + 4.02706i) q^{92} +(-2.95886 + 6.91457i) q^{93} +(-4.77898 - 2.75915i) q^{94} +(-2.68345 - 1.54929i) q^{95} +(-0.681407 + 1.59238i) q^{96} +(9.18719 + 5.30423i) q^{97} +(1.71934 - 6.78556i) q^{98} +(-2.42369 - 9.96791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.206076	−	1.71975i	−0.118978	−	0.992897i
$3$	−0.206076	−	1.71975i	−0.118978	−	0.992897i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.42985			0.639449			0.319724	−	0.947511i	$-0.396410\pi$
$5$	1.42985			0.639449			0.319724	+	0.947511i	$0.396410\pi$
$6$	−1.03834	−	1.38631i	−0.423901	−	0.565958i
$7$	−2.43739	+	1.02913i	−0.921248	+	0.388975i
$7$	−2.43739	+	1.02913i	−0.921248	+	0.388975i
$8$		−	1.00000i		−	0.353553i
$9$	−2.91507	+	0.708796i	−0.971689	+	0.236265i
$10$	1.23829	−	0.714925i	0.391581	−	0.226079i
$11$			3.41945i			1.03100i	0.856889	+	0.515501i	$0.172394\pi$
$11$			3.41945i			1.03100i	−0.856889	+	0.515501i	$0.827606\pi$
$12$	−1.59238	−	0.681407i	−0.459681	−	0.196705i
$13$	5.48813	−	3.16857i	1.52213	−	0.878804i	0.522476	−	0.852654i	$-0.325009\pi$
$13$	5.48813	−	3.16857i	1.52213	−	0.878804i	0.999658	−	0.0261501i	$-0.00832479\pi$
$14$	−1.59628	+	2.10995i	−0.426623	+	0.563908i
$15$	−0.294657	−	2.45898i	−0.0760802	−	0.634907i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	0.970632	−	0.240569i	$-0.0773339\pi$
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	−0.693655	+	0.720308i	$0.744001\pi$
$18$	−2.17012	+	2.07137i	−0.511503	+	0.488226i
$19$	−1.87673	−	1.08353i	−0.430553	−	0.248580i	0.269029	−	0.963132i	$-0.413297\pi$
$19$	−1.87673	−	1.08353i	−0.430553	−	0.248580i	−0.699582	+	0.714552i	$0.746630\pi$
$20$	0.714925	−	1.23829i	0.159862	−	0.276889i
$21$	2.27213	+	3.97962i	0.495820	+	0.868425i
$22$	1.70972	+	2.96133i	0.364514	+	0.631357i
$23$			8.05411i			1.67940i	0.543052	+	0.839699i	$0.317269\pi$
$23$			8.05411i			1.67940i	−0.543052	+	0.839699i	$0.682731\pi$
$24$	−1.71975	+	0.206076i	−0.351042	+	0.0420650i
$25$	−2.95553			−0.591106
$26$	3.16857	−	5.48813i	0.621408	−	1.07631i
$27$	1.81967	+	4.86711i	0.350196	+	0.936676i
$28$	−0.327442	+	2.62541i	−0.0618808	+	0.496156i
$29$	−0.298879	−	0.172558i	−0.0555003	−	0.0320431i	0.471993	−	0.881602i	$-0.343535\pi$
$29$	−0.298879	−	0.172558i	−0.0555003	−	0.0320431i	−0.527493	+	0.849559i	$0.676868\pi$
$30$	−1.48467	−	1.98221i	−0.271063	−	0.361901i
$31$	−3.76052	−	2.17114i	−0.675410	−	0.389948i	0.122713	−	0.992442i	$-0.460840\pi$
$31$	−3.76052	−	2.17114i	−0.675410	−	0.389948i	−0.798123	+	0.602494i	$0.794174\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.88058	−	0.704664i	1.02368	−	0.122666i
$34$	1.97802	+	1.14201i	0.339227	+	0.195853i
$35$	−3.48511	+	1.47150i	−0.589091	+	0.248730i
$36$	−0.843698	+	2.87892i	−0.140616	+	0.479820i
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	−0.763721	−	0.645546i	$-0.776630\pi$
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	0.940920	+	0.338629i	$0.109963\pi$
$38$	−2.16707			−0.351545
$39$	−6.58012	−	8.78524i	−1.05366	−	1.40676i
$40$		−	1.42985i		−	0.226079i
$41$	−0.202180	−	0.350186i	−0.0315752	−	0.0546898i	0.849806	−	0.527096i	$-0.176719\pi$
$41$	−0.202180	−	0.350186i	−0.0315752	−	0.0546898i	−0.881381	+	0.472406i	$0.843386\pi$
$42$	3.95754	+	2.31039i	0.610661	+	0.356501i
$43$	2.90883	−	5.03824i	0.443592	−	0.768325i	−0.554361	−	0.832277i	$-0.687037\pi$
$43$	2.90883	−	5.03824i	0.443592	−	0.768325i	0.997953	+	0.0639521i	$0.0203705\pi$
$44$	2.96133	+	1.70972i	0.446437	+	0.257750i
$45$	−4.16811	+	1.01347i	−0.621345	+	0.151080i
$46$	4.02706	+	6.97507i	0.593757	+	1.02842i
$47$	−2.75915	−	4.77898i	−0.402463	−	0.697086i	0.591560	−	0.806261i	$-0.298512\pi$
$47$	−2.75915	−	4.77898i	−0.402463	−	0.697086i	−0.994023	+	0.109175i	$0.965179\pi$
$48$	−1.38631	+	1.03834i	−0.200096	+	0.149872i
$49$	4.88178	−	5.01680i	0.697396	−	0.716686i
$50$	−2.55956	+	1.47776i	−0.361977	+	0.208987i
$51$	3.16635	−	2.37159i	0.443378	−	0.332089i
$52$		−	6.33715i		−	0.878804i
$53$	−8.56310	+	4.94391i	−1.17623	+	0.679098i	−0.955140	−	0.296155i	$-0.904296\pi$
$53$	−8.56310	+	4.94391i	−1.17623	+	0.679098i	−0.221093	+	0.975253i	$0.570962\pi$
$54$	4.00944	+	3.30521i	0.545616	+	0.449782i
$55$			4.88930i			0.659273i
$56$	1.02913	+	2.43739i	0.137524	+	0.325710i
$57$	−1.47666	+	3.45080i	−0.195588	+	0.457070i
$58$	−0.345115			−0.0453158
$59$	5.51480	−	9.55191i	0.717966	−	1.24355i	−0.243839	−	0.969816i	$-0.578407\pi$
$59$	5.51480	−	9.55191i	0.717966	−	1.24355i	0.961805	−	0.273737i	$-0.0882598\pi$
$60$	−2.27687	−	0.974311i	−0.293943	−	0.125783i
$61$	−9.94175	+	5.73987i	−1.27291	+	0.734915i	−0.975535	−	0.219845i	$-0.929445\pi$
$61$	−9.94175	+	5.73987i	−1.27291	+	0.734915i	−0.297376	+	0.954760i	$0.596112\pi$
$62$	−4.34228			−0.551470
$63$	6.37572	−	4.72760i	0.803265	−	0.595622i
$64$	−1.00000			−0.125000
$65$	7.84721	−	4.53059i	0.973326	−	0.561950i
$66$	4.74040	−	3.55055i	0.583503	−	0.437042i
$67$	−2.12683	+	3.68377i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$67$	−2.12683	+	3.68377i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$68$	2.28402			0.276978
$69$	13.8510	−	1.65976i	1.66747	−	0.199811i
$70$	−2.28244	+	3.01691i	−0.272804	+	0.360590i
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$	0.708796	+	2.91507i	0.0835324	+	0.343544i
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	−0.511720	−	0.859152i	$-0.670991\pi$
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	0.488188	+	0.872739i	$0.337658\pi$
$74$		−	2.15571i		−	0.250597i
$75$	0.609062	+	5.08276i	0.0703284	+	0.586907i
$76$	−1.87673	+	1.08353i	−0.215276	+	0.124290i
$77$	−3.51906	−	8.33454i	−0.401034	−	0.949808i
$78$	−10.0912	−	4.31818i	−1.14260	−	0.488937i
$79$	−7.28100	−	12.6111i	−0.819177	−	1.41886i	−0.906290	−	0.422657i	$-0.861097\pi$
$79$	−7.28100	−	12.6111i	−0.819177	−	1.41886i	0.0871130	−	0.996198i	$-0.472236\pi$
$80$	−0.714925	−	1.23829i	−0.0799311	−	0.138445i
$81$	7.99522	−	4.13237i	0.888357	−	0.459153i
$82$	−0.350186	−	0.202180i	−0.0386716	−	0.0223270i
$83$	−0.811624	+	1.40577i	−0.0890873	+	0.154304i	−0.907126	−	0.420860i	$-0.861728\pi$
$83$	−0.811624	+	1.40577i	−0.0890873	+	0.154304i	0.818038	+	0.575164i	$0.195062\pi$
$84$	4.58252	+	0.0220855i	0.499994	+	0.00240972i
$85$	1.63290	+	2.82827i	0.177113	+	0.306769i
$86$		−	5.81766i		−	0.627334i
$87$	−0.235164	+	0.549556i	−0.0252122	+	0.0589185i
$88$	3.41945			0.364514
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	−0.738167	−	0.674618i	$-0.764309\pi$
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	0.953320	+	0.301963i	$0.0976419\pi$
$90$	−3.10295	+	2.96175i	−0.327080	+	0.312196i
$91$	−10.1159	+	13.3711i	−1.06043	+	1.40167i
$92$	6.97507	+	4.02706i	0.727201	+	0.419850i
$93$	−2.95886	+	6.91457i	−0.306820	+	0.717008i
$94$	−4.77898	−	2.75915i	−0.492914	−	0.284584i
$95$	−2.68345	−	1.54929i	−0.275316	−	0.158954i
$96$	−0.681407	+	1.59238i	−0.0695458	+	0.162522i
$97$	9.18719	+	5.30423i	0.932818	+	0.538563i	0.887702	−	0.460419i	$-0.152301\pi$
$97$	9.18719	+	5.30423i	0.932818	+	0.538563i	0.0451164	+	0.998982i	$0.485634\pi$
$98$	1.71934	−	6.78556i	0.173680	−	0.685445i
$99$	−2.42369	−	9.96791i	−0.243590	−	1.00181i
$100$	−1.47776	+	2.55956i	−0.147776	+	0.255956i
$101$	−8.04886			−0.800892			−0.400446	−	0.916320i	$-0.631145\pi$
$101$	−8.04886			−0.800892			−0.400446	+	0.916320i	$0.631145\pi$
$102$	1.55635	−	3.63703i	0.154101	−	0.360120i
$103$		−	2.81391i		−	0.277263i	−0.990344	−	0.138631i	$-0.955730\pi$
$103$		−	2.81391i		−	0.277263i	0.990344	−	0.138631i	$-0.0442703\pi$
$104$	−3.16857	−	5.48813i	−0.310704	−	0.538156i
$105$	3.24881	+	5.69027i	0.317052	+	0.555313i
$106$	−4.94391	+	8.56310i	−0.480195	+	0.831722i
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.984460	−	0.175607i	$-0.0561888\pi$
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.340150	+	0.940371i	$0.389522\pi$
$108$	5.12488	+	0.857672i	0.493142	+	0.0825296i
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	0.999922	−	0.0124977i	$-0.00397826\pi$
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	−0.510784	+	0.859709i	$0.670645\pi$
$110$	2.44465	+	4.23425i	0.233088	+	0.403720i
$111$	−3.43272	−	1.46892i	−0.325819	−	0.139424i
$112$	2.10995	+	1.59628i	0.199372	+	0.150834i
$113$	7.28808	−	4.20778i	0.685605	−	0.395834i	−0.116359	−	0.993207i	$-0.537122\pi$
$113$	7.28808	−	4.20778i	0.685605	−	0.395834i	0.801963	+	0.597373i	$0.203789\pi$
$114$	0.446579	+	3.72681i	0.0418260	+	0.349048i
$115$			11.5162i			1.07389i
$116$	−0.298879	+	0.172558i	−0.0277502	+	0.0160216i
$117$	−13.7524	+	13.1266i	−1.27141	+	1.21355i
$118$		−	11.0296i		−	1.01536i
$119$	−4.81916	−	3.64593i	−0.441772	−	0.334222i
$120$	−2.45898	+	0.294657i	−0.224473	+	0.0268984i
$121$	−0.692610			−0.0629646
$122$	−5.73987	+	9.94175i	−0.519664	+	0.900084i
$123$	−0.560567	+	0.419863i	−0.0505446	+	0.0378578i
$124$	−3.76052	+	2.17114i	−0.337705	+	0.194974i
$125$	−11.3752			−1.01743
$126$	3.15773	−	7.28208i	0.281313	−	0.648739i
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−9.26394	−	3.96420i	−0.815645	−	0.349028i
$130$	4.53059	−	7.84721i	0.397359	−	0.688246i
$131$	4.45667			0.389381			0.194690	−	0.980865i	$-0.437630\pi$
$131$	4.45667			0.389381			0.194690	+	0.980865i	$0.437630\pi$
$132$	2.33004	−	5.44507i	0.202804	−	0.473932i
$133$	5.68944	+	0.709590i	0.493337	+	0.0615292i
$134$			4.25366i			0.367460i
$135$	2.60186	+	6.95924i	0.223933	+	0.598956i
$136$	1.97802	−	1.14201i	0.169613	−	0.0979264i
$137$			9.65668i			0.825026i	0.910952	+	0.412513i	$0.135349\pi$
$137$			9.65668i			0.825026i	−0.910952	+	0.412513i	$0.864651\pi$
$138$	11.1655	−	8.36291i	0.950469	−	0.711898i
$139$	−16.0680	+	9.27686i	−1.36287	+	0.786853i	−0.990005	−	0.141033i	$-0.954958\pi$
$139$	−16.0680	+	9.27686i	−1.36287	+	0.786853i	−0.372864	+	0.927886i	$0.621624\pi$
$140$	−0.468194	+	3.75394i	−0.0395696	+	0.317266i
$141$	−7.65005	+	5.72987i	−0.644251	+	0.482542i
$142$	−1.77696	−	3.07779i	−0.149119	−	0.258282i
$143$	10.8348	+	18.7664i	0.906049	+	1.56932i
$144$	2.07137	+	2.17012i	0.172614	+	0.180844i
$145$	−0.427352	−	0.246732i	−0.0354896	−	0.0204899i
$146$	−0.116080	+	0.201057i	−0.00960689	+	0.0166396i
$147$	−9.63364	−	7.36158i	−0.794570	−	0.607173i
$148$	−1.07786	−	1.86690i	−0.0885993	−	0.153458i
$149$			6.50694i			0.533069i	0.963825	+	0.266535i	$0.0858786\pi$
$149$			6.50694i			0.533069i	−0.963825	+	0.266535i	$0.914121\pi$
$150$	3.06884	+	4.09727i	0.250570	+	0.334541i
$151$	5.75901			0.468661			0.234331	−	0.972157i	$-0.424710\pi$
$151$	5.75901			0.468661			0.234331	+	0.972157i	$0.424710\pi$
$152$	−1.08353	+	1.87673i	−0.0878862	+	0.152223i
$153$	−4.73104	−	4.95660i	−0.382482	−	0.400717i
$154$	−7.21486	−	5.45839i	−0.581390	−	0.439850i
$155$	−5.37699	−	3.10441i	−0.431890	−	0.249352i
$156$	−10.8983	+	1.30593i	−0.872562	+	0.104558i
$157$	6.89669	+	3.98180i	0.550415	+	0.317783i	0.749290	−	0.662243i	$-0.230395\pi$
$157$	6.89669	+	3.98180i	0.550415	+	0.317783i	−0.198874	+	0.980025i	$0.563728\pi$
$158$	−12.6111	−	7.28100i	−1.00328	−	0.579245i
$159$	10.2669	+	13.7076i	0.814220	+	1.08708i
$160$	−1.23829	−	0.714925i	−0.0978952	−	0.0565198i
$161$	−8.28874	−	19.6310i	−0.653245	−	1.54714i
$162$	4.85787	−	7.57635i	0.381671	−	0.595254i
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	−0.552237	−	0.833687i	$-0.686226\pi$
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	0.998113	+	0.0614080i	$0.0195591\pi$
$164$	−0.404360			−0.0315752
$165$	8.40836	−	1.00756i	0.654590	−	0.0784388i
$166$			1.62325i			0.125988i
$167$	5.66418	+	9.81065i	0.438308	+	0.759171i	0.997559	−	0.0698271i	$-0.0222447\pi$
$167$	5.66418	+	9.81065i	0.438308	+	0.759171i	−0.559252	+	0.828998i	$0.688911\pi$
$168$	3.97962	−	2.27213i	0.307035	−	0.175299i
$169$	13.5797	−	23.5208i	1.04459	−	1.80929i
$170$	2.82827	+	1.63290i	0.216918	+	0.125238i
$171$	6.23881	+	1.82835i	0.477094	+	0.139817i
$172$	−2.90883	−	5.03824i	−0.221796	−	0.384162i
$173$	−10.8457	−	18.7853i	−0.824584	−	1.42822i	−0.902237	−	0.431241i	$-0.858076\pi$
$173$	−10.8457	−	18.7853i	−0.824584	−	1.42822i	0.0776528	−	0.996980i	$-0.475257\pi$
$174$	0.0711198	+	0.593511i	0.00539158	+	0.0449940i
$175$	7.20378	−	3.04163i	0.544555	−	0.229925i
$176$	2.96133	−	1.70972i	0.223218	−	0.128875i
$177$	−17.5633	−	7.51565i	−1.32014	−	0.564911i
$178$		−	4.05949i		−	0.304271i
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.358155	−	0.933662i	$-0.383406\pi$
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.987653	+	0.156660i	$0.0500726\pi$
$180$	−1.20636	+	4.11642i	−0.0899169	+	0.306820i
$181$		−	21.5301i		−	1.60032i	−0.599788	−	0.800159i	$-0.704748\pi$
$181$		−	21.5301i		−	1.60032i	0.599788	−	0.800159i	$-0.295252\pi$
$182$	−2.07505	+	16.6376i	−0.153813	+	1.23326i
$183$	11.9199	+	15.9145i	0.881143	+	1.17643i
$184$	8.05411			0.593757
$185$	1.54117	−	2.66939i	0.113309	−	0.196258i
$186$	0.894838	+	7.46763i	0.0656127	+	0.547553i
$187$	−6.76372	+	3.90503i	−0.494612	+	0.285564i
$188$	−5.51829			−0.402463
$189$	−9.44416	−	9.99038i	−0.686962	−	0.726694i
$190$	−3.09858			−0.224795
$191$	−6.38207	+	3.68469i	−0.461791	+	0.266615i	−0.712797	−	0.701371i	$-0.752572\pi$
$191$	−6.38207	+	3.68469i	−0.461791	+	0.266615i	0.251006	+	0.967985i	$0.419239\pi$
$192$	0.206076	+	1.71975i	0.0148722	+	0.124112i
$193$	1.41279	−	2.44703i	0.101695	−	0.176141i	−0.810688	−	0.585478i	$-0.800907\pi$
$193$	1.41279	−	2.44703i	0.101695	−	0.176141i	0.912383	+	0.409337i	$0.134240\pi$
$194$	10.6085			0.761643
$195$	−9.40859	−	12.5616i	−0.673763	−	0.899553i
$196$	−1.90379	−	6.73614i	−0.135985	−	0.481153i
$197$			26.0883i			1.85871i	0.369183	+	0.929357i	$0.379637\pi$
$197$			26.0883i			1.85871i	−0.369183	+	0.929357i	$0.620363\pi$
$198$	−7.08293	−	7.42062i	−0.503362	−	0.527360i
$199$	13.3511	−	7.70826i	0.946434	−	0.546424i	0.0544625	−	0.998516i	$-0.482655\pi$
$199$	13.3511	−	7.70826i	0.946434	−	0.546424i	0.891971	+	0.452092i	$0.149322\pi$
$200$			2.95553i			0.208987i
$201$	6.77345	+	2.89847i	0.477762	+	0.204442i
$202$	−6.97052	+	4.02443i	−0.490444	+	0.283158i
$203$	0.906069	+	0.113005i	0.0635936	+	0.00793142i
$204$	−0.470680	−	3.92793i	−0.0329542	−	0.275010i
$205$	−0.289087	−	0.500713i	−0.0201907	−	0.0349713i
$206$	−1.40695	−	2.43692i	−0.0980272	−	0.169788i
$207$	−5.70872	−	23.4783i	−0.396784	−	1.63185i
$208$	−5.48813	−	3.16857i	−0.380533	−	0.219701i
$209$	3.70508	−	6.41739i	0.256286	−	0.443900i
$210$	5.65869	+	3.30351i	0.390487	+	0.227964i
$211$	4.42465	+	7.66371i	0.304605	+	0.527592i	0.977173	−	0.212443i	$-0.0681421\pi$
$211$	4.42465	+	7.66371i	0.304605	+	0.527592i	−0.672568	+	0.740035i	$0.734809\pi$
$212$			9.88782i			0.679098i
$213$	−6.11186	+	0.732377i	−0.418778	+	0.0501817i
$214$	15.8216			1.08154
$215$	4.15919	−	7.20393i	0.283655	−	0.491304i
$216$	4.86711	−	1.81967i	0.331165	−	0.123813i
$217$	11.4003	+	1.42185i	0.773901	+	0.0965212i
$218$	8.84514	+	5.10675i	0.599069	+	0.345873i
$219$	0.241062	+	0.321846i	0.0162895	+	0.0217484i
$220$	4.23425	+	2.44465i	0.285473	+	0.164818i
$221$	12.5350	+	7.23707i	0.843194	+	0.486818i
$222$	−3.70728	+	0.444240i	−0.248817	+	0.0298154i
$223$	6.88961	+	3.97772i	0.461363	+	0.266368i	0.712617	−	0.701553i	$-0.247510\pi$
$223$	6.88961	+	3.97772i	0.461363	+	0.266368i	−0.251254	+	0.967921i	$0.580843\pi$
$224$	2.62541	+	0.327442i	0.175418	+	0.0218782i
$225$	8.61556	−	2.09487i	0.574370	−	0.139658i
$226$	4.20778	−	7.28808i	0.279897	−	0.484796i
$227$	9.23968			0.613259			0.306630	−	0.951829i	$-0.400799\pi$
$227$	9.23968			0.613259			0.306630	+	0.951829i	$0.400799\pi$
$228$	2.25015	+	3.00422i	0.149020	+	0.198959i
$229$		−	8.44454i		−	0.558031i	−0.960287	−	0.279016i	$-0.909992\pi$
$229$		−	8.44454i		−	0.558031i	0.960287	−	0.279016i	$-0.0900081\pi$
$230$	5.75809	+	9.97330i	0.379677	+	0.657620i
$231$	−13.6081	+	7.76944i	−0.895348	+	0.511192i
$232$	−0.172558	+	0.298879i	−0.0113290	+	0.0196223i
$233$	−14.4176	−	8.32399i	−0.944526	−	0.545323i	−0.0531500	−	0.998587i	$-0.516926\pi$
$233$	−14.4176	−	8.32399i	−0.944526	−	0.545323i	−0.891376	+	0.453264i	$0.850259\pi$
$234$	−5.34664	+	18.2441i	−0.349521	+	1.19266i
$235$	−3.94517	−	6.83323i	−0.257354	−	0.445751i
$236$	−5.51480	−	9.55191i	−0.358983	−	0.621776i
$237$	−20.1874	+	15.1203i	−1.31131	+	0.982170i
$238$	−5.99648	−	0.747884i	−0.388694	−	0.0484781i
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.529242	+	0.848471i	$0.677524\pi$
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.999418	+	0.0341012i	$0.989143\pi$
$240$	−1.98221	+	1.48467i	−0.127951	+	0.0958352i
$241$			25.2900i			1.62907i	0.580111	+	0.814537i	$0.303009\pi$
$241$			25.2900i			1.62907i	−0.580111	+	0.814537i	$0.696991\pi$
$242$	−0.599818	+	0.346305i	−0.0385578	+	0.0222613i
$243$	−8.75426	−	12.8982i	−0.561586	−	0.827418i
$244$			11.4797i			0.734915i
$245$	6.98021	−	7.17327i	0.445949	−	0.458284i
$246$	−0.275534	+	0.643896i	−0.0175674	+	0.0410533i
$247$	−13.7330			−0.873811
$248$	−2.17114	+	3.76052i	−0.137868	+	0.238794i
$249$	2.58483	+	1.10609i	0.163807	+	0.0700958i
$250$	−9.85123	+	5.68761i	−0.623046	+	0.359716i
$251$	8.19337			0.517161			0.258581	−	0.965990i	$-0.416745\pi$
$251$	8.19337			0.517161			0.258581	+	0.965990i	$0.416745\pi$
$252$	−0.906364	−	7.88533i	−0.0570956	−	0.496729i
$253$	−27.5406			−1.73146
$254$	5.00366	−	2.88886i	0.313958	−	0.181264i
$255$	4.52741	−	3.39101i	0.283517	−	0.212354i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.63445			−0.413846			−0.206923	−	0.978357i	$-0.566345\pi$
$257$	−6.63445			−0.413846			−0.206923	+	0.978357i	$0.566345\pi$
$258$	−10.0049	+	1.19888i	−0.622878	+	0.0746388i
$259$	−0.705872	+	5.65963i	−0.0438607	+	0.351672i
$260$		−	9.06117i		−	0.561950i
$261$	0.993559	+	0.291173i	0.0614997	+	0.0180231i
$262$	3.85959	−	2.22833i	0.238446	−	0.137667i
$263$			6.04590i			0.372806i	0.982473	+	0.186403i	$0.0596830\pi$
$263$			6.04590i			0.372806i	−0.982473	+	0.186403i	$0.940317\pi$
$264$	−0.704664	−	5.88058i	−0.0433691	−	0.361925i
$265$	−12.2440	+	7.06905i	−0.752140	+	0.434248i
$266$	5.28199	−	2.23020i	0.323860	−	0.136742i
$267$	−6.46426	−	2.76616i	−0.395606	−	0.169286i
$268$	2.12683	+	3.68377i	0.129917	+	0.225022i
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	0.743116	−	0.669163i	$-0.233347\pi$
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	−0.951070	+	0.308976i	$0.900014\pi$
$270$	5.73290	+	4.72595i	0.348893	+	0.287612i
$271$	−4.39780	−	2.53907i	−0.267148	−	0.154238i	0.360443	−	0.932781i	$-0.382625\pi$
$271$	−4.39780	−	2.53907i	−0.267148	−	0.154238i	−0.627591	+	0.778543i	$0.715959\pi$
$272$	1.14201	−	1.97802i	0.0692444	−	0.119935i
$273$	25.0795	+	14.6413i	1.51788	+	0.886130i
$274$	4.82834	+	8.36293i	0.291691	+	0.505223i
$275$		−	10.1063i		−	0.609431i
$276$	5.48813	−	12.8252i	0.330347	−	0.771988i
$277$	−1.97913			−0.118915			−0.0594573	−	0.998231i	$-0.518937\pi$
$277$	−1.97913			−0.118915			−0.0594573	+	0.998231i	$0.518937\pi$
$278$	−9.27686	+	16.0680i	−0.556389	+	0.963694i
$279$	12.5011	+	3.66357i	0.748420	+	0.219332i
$280$	1.47150	+	3.48511i	0.0879392	+	0.208275i
$281$	−15.2703	−	8.81631i	−0.910950	−	0.525937i	−0.0302131	−	0.999543i	$-0.509619\pi$
$281$	−15.2703	−	8.81631i	−0.910950	−	0.525937i	−0.880737	+	0.473606i	$0.842952\pi$
$282$	−3.76021	+	8.78724i	−0.223917	+	0.523272i
$283$	4.46337	+	2.57693i	0.265320	+	0.153182i	0.626759	−	0.779213i	$-0.284381\pi$
$283$	4.46337	+	2.57693i	0.265320	+	0.153182i	−0.361439	+	0.932396i	$0.617714\pi$
$284$	−3.07779	−	1.77696i	−0.182633	−	0.105443i
$285$	−2.11140	+	4.93413i	−0.125068	+	0.292273i
$286$	18.7664	+	10.8348i	1.10968	+	0.640673i
$287$	0.853179	+	0.645471i	0.0503616	+	0.0381009i
$288$	2.87892	+	0.843698i	0.169642	+	0.0497154i
$289$	5.89164	−	10.2046i	0.346567	−	0.600271i
$290$	−0.493463			−0.0289772
$291$	7.22868	−	16.8927i	0.423753	−	0.990269i
$292$			0.232161i			0.0135862i
$293$	−1.03248	−	1.78831i	−0.0603183	−	0.104474i	0.834289	−	0.551327i	$-0.185878\pi$
$293$	−1.03248	−	1.78831i	−0.0603183	−	0.104474i	−0.894608	+	0.446852i	$0.852545\pi$
$294$	−12.0238	−	1.55850i	−0.701241	−	0.0908933i
$295$	7.88534	−	13.6578i	0.459102	−	0.795188i
$296$	−1.86690	−	1.07786i	−0.108511	−	0.0626491i
$297$	−16.6428	+	6.22228i	−0.965715	+	0.361053i
$298$	3.25347	+	5.63517i	0.188468	+	0.326437i
$299$	25.5201	+	44.2020i	1.47586	+	2.55627i
$300$	4.70633	+	2.01392i	0.271720	+	0.116274i
$301$	−1.90495	+	15.2737i	−0.109799	+	0.880364i
$302$	4.98745	−	2.87950i	0.286995	−	0.165697i
$303$	1.65867	+	13.8420i	0.0952883	+	0.795203i
$304$			2.16707i			0.124290i
$305$	−14.2152	+	8.20716i	−0.813961	+	0.469941i
$306$	−6.57550	−	1.92702i	−0.375896	−	0.110160i
$307$			1.09119i			0.0622772i	0.999515	+	0.0311386i	$0.00991333\pi$
$307$			1.09119i			0.0622772i	−0.999515	+	0.0311386i	$0.990087\pi$
$308$	−8.97745	−	1.11967i	−0.511538	−	0.0637992i
$309$	−4.83921	+	0.579878i	−0.275293	+	0.0329881i
$310$	−6.20881			−0.352637
$311$	7.61100	−	13.1826i	0.431580	−	0.747519i	−0.565429	−	0.824797i	$-0.691289\pi$
$311$	7.61100	−	13.1826i	0.431580	−	0.747519i	0.997010	+	0.0772777i	$0.0246228\pi$
$312$	−8.78524	+	6.58012i	−0.497366	+	0.372526i
$313$	10.0202	−	5.78518i	0.566377	−	0.326998i	−0.189324	−	0.981915i	$-0.560630\pi$
$313$	10.0202	−	5.78518i	0.566377	−	0.326998i	0.755701	+	0.654917i	$0.227296\pi$
$314$	7.96361			0.449412
$315$	9.11632	−	6.75976i	0.513647	−	0.380870i
$316$	−14.5620			−0.819177
$317$	14.8613	−	8.58020i	0.834696	−	0.481912i	−0.0207618	−	0.999784i	$-0.506609\pi$
$317$	14.8613	−	8.58020i	0.834696	−	0.481912i	0.855458	+	0.517872i	$0.173276\pi$
$318$	15.7452	+	6.73763i	0.882947	+	0.377828i
$319$	0.590051	−	1.02200i	0.0330365	−	0.0572210i
$320$	−1.42985			−0.0799311
$321$	10.7809	−	25.1940i	0.601733	−	1.40619i
$322$	−16.9938	−	12.8566i	−0.947027	−	0.716471i
$323$		−	4.94962i		−	0.275404i
$324$	0.418868	−	8.99025i	0.0232704	−	0.499458i
$325$	−16.2203	+	9.36481i	−0.899742	+	0.519466i
$326$		−	11.3851i		−	0.630563i
$327$	14.1590	−	10.6051i	0.782997	−	0.586463i
$328$	−0.350186	+	0.202180i	−0.0193358	+	0.0111635i
$329$	11.6433	+	8.80874i	0.641918	+	0.485641i
$330$	6.77807	−	5.07676i	0.373120	−	0.279466i
$331$	13.2466	+	22.9437i	0.728096	+	1.26110i	0.957687	+	0.287812i	$0.0929280\pi$
$331$	13.2466	+	22.9437i	0.728096	+	1.26110i	−0.229591	+	0.973287i	$0.573739\pi$
$332$	0.811624	+	1.40577i	0.0445436	+	0.0771519i
$333$	−1.81877	+	6.20612i	−0.0996680	+	0.340093i
$334$	9.81065	+	5.66418i	0.536815	+	0.309930i
$335$	−3.04105	+	5.26725i	−0.166150	+	0.287780i
$336$	2.31039	−	3.95754i	0.126042	−	0.215901i
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	0.955236	−	0.295846i	$-0.0956015\pi$
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	−0.733828	+	0.679335i	$0.762268\pi$
$338$		−	27.1594i		−	1.47728i
$339$	−8.73821	−	11.6665i	−0.474594	−	0.633640i
$340$	3.26580			0.177113
$341$	7.42410	−	12.8589i	0.402037	−	0.696349i
$342$	6.31714	−	1.53601i	0.341592	−	0.0830578i
$343$	−6.73586	+	17.2519i	−0.363702	+	0.931515i
$344$	−5.03824	−	2.90883i	−0.271644	−	0.156834i
$345$	19.8049	−	2.37320i	1.06626	−	0.127769i
$346$	−18.7853	−	10.8457i	−1.00991	−	0.583069i
$347$	−22.1851	−	12.8086i	−1.19096	−	0.687599i	−0.232433	−	0.972612i	$-0.574669\pi$
$347$	−22.1851	−	12.8086i	−1.19096	−	0.687599i	−0.958524	+	0.285013i	$0.908002\pi$
$348$	0.358347	+	0.478436i	0.0192094	+	0.0256469i
$349$	−9.11932	−	5.26504i	−0.488146	−	0.281831i	0.235659	−	0.971836i	$-0.424275\pi$
$349$	−9.11932	−	5.26504i	−0.488146	−	0.281831i	−0.723805	+	0.690005i	$0.757609\pi$
$350$	4.71785	−	6.23602i	0.252179	−	0.333329i
$351$	25.4084	+	20.9456i	1.35620	+	1.11799i
$352$	1.70972	−	2.96133i	0.0911285	−	0.157839i
$353$	12.8437			0.683602			0.341801	−	0.939772i	$-0.388963\pi$
$353$	12.8437			0.683602			0.341801	+	0.939772i	$0.388963\pi$
$354$	−18.9681	+	2.27293i	−1.00814	+	0.120805i
$355$		−	5.08158i		−	0.269702i
$356$	−2.02974	−	3.51562i	−0.107576	−	0.186327i
$357$	−5.27696	+	9.03908i	−0.279286	+	0.478399i
$358$	10.3956	−	18.0057i	0.549424	−	0.951630i
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.366718	−	0.930332i	$-0.619518\pi$
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.989050	+	0.147579i	$0.952852\pi$
$360$	1.01347	+	4.16811i	0.0534147	+	0.219679i
$361$	−7.15191	−	12.3875i	−0.376416	−	0.651972i
$362$	−10.7650	−	18.6456i	−0.565798	−	0.979991i
$363$	0.142730	+	1.19112i	0.00749139	+	0.0625173i
$364$	6.52176	+	15.4461i	0.341833	+	0.809597i
$365$	−0.287482	+	0.165978i	−0.0150475	+	0.00868767i
$366$	18.2802	+	7.82238i	0.955519	+	0.408883i
$367$		−	23.9979i		−	1.25268i	−0.779550	−	0.626340i	$-0.784552\pi$
$367$		−	23.9979i		−	1.25268i	0.779550	−	0.626340i	$-0.215448\pi$
$368$	6.97507	−	4.02706i	0.363600	−	0.209925i
$369$	0.837578	+	0.877510i	0.0436026	+	0.0456814i
$370$		−	3.08235i		−	0.160244i
$371$	15.7837	−	20.8628i	0.819450	−	1.08314i
$372$	4.50877	+	6.01974i	0.233769	+	0.312109i
$373$	−11.8390			−0.612998			−0.306499	−	0.951871i	$-0.599158\pi$
$373$	−11.8390			−0.612998			−0.306499	+	0.951871i	$0.599158\pi$
$374$	−3.90503	+	6.76372i	−0.201925	+	0.349744i
$375$	2.34415	+	19.5625i	0.121052	+	1.01020i
$376$	−4.77898	+	2.75915i	−0.246457	+	0.142292i
$377$	−2.18705			−0.112639
$378$	−13.1741	−	3.92985i	−0.677601	−	0.202129i
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$	−2.68345	+	1.54929i	−0.137658	+	0.0794769i
$381$	−1.19065	−	9.93624i	−0.0609988	−	0.509049i
$382$	−3.68469	+	6.38207i	−0.188525	+	0.326535i
$383$	−17.5521			−0.896868			−0.448434	−	0.893816i	$-0.648018\pi$
$383$	−17.5521			−0.896868			−0.448434	+	0.893816i	$0.648018\pi$
$384$	1.03834	+	1.38631i	0.0529876	+	0.0707447i
$385$	−5.03173	−	11.9171i	−0.256441	−	0.607354i
$386$		−	2.82559i		−	0.143819i
$387$	−4.90834	+	16.7486i	−0.249505	+	0.851378i
$388$	9.18719	−	5.30423i	0.466409	−	0.269281i
$389$			21.8410i			1.10738i	0.832722	+	0.553691i	$0.186781\pi$
$389$			21.8410i			1.10738i	−0.832722	+	0.553691i	$0.813219\pi$
$390$	−14.4289	−	6.17435i	−0.730634	−	0.312650i
$391$	−15.9312	+	9.19786i	−0.805674	+	0.465156i
$392$	−5.01680	−	4.88178i	−0.253387	−	0.246567i
$393$	−0.918411	−	7.66435i	−0.0463277	−	0.386615i
$394$	13.0441	+	22.5931i	0.657154	+	1.13822i
$395$	−10.4107	−	18.0319i	−0.523821	−	0.907285i
$396$	−9.84431	−	2.88498i	−0.494695	−	0.144976i
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.950757	+	0.309937i	$0.100308\pi$
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.743792	+	0.668411i	$0.233025\pi$
$398$	7.70826	−	13.3511i	0.386380	−	0.669230i
$399$	0.0478607	−	9.93063i	0.00239603	−	0.497153i
$400$	1.47776	+	2.55956i	0.0738882	+	0.127978i
$401$			23.1979i			1.15845i	0.815169	+	0.579223i	$0.196644\pi$
$401$			23.1979i			1.15845i	−0.815169	+	0.579223i	$0.803356\pi$
$402$	7.31522	−	0.876575i	0.364850	−	0.0437196i
$403$	−27.5177			−1.37075
$404$	−4.02443	+	6.97052i	−0.200223	+	0.346796i
$405$	11.4320	−	5.90868i	0.568059	−	0.293605i
$406$	0.841182	−	0.355169i	0.0417471	−	0.0176267i
$407$	6.38377	+	3.68567i	0.316432	+	0.182692i
$408$	−2.37159	−	3.16635i	−0.117411	−	0.156758i
$409$	−21.3205	−	12.3094i	−1.05423	−	0.608659i	−0.130398	−	0.991462i	$-0.541626\pi$
$409$	−21.3205	−	12.3094i	−1.05423	−	0.608659i	−0.923830	+	0.382803i	$0.874959\pi$
$410$	−0.500713	−	0.289087i	−0.0247285	−	0.0142770i
$411$	16.6071	−	1.99001i	0.819166	−	0.0981597i
$412$	−2.43692	−	1.40695i	−0.120058	−	0.0693157i
$413$	−3.61156	+	28.9572i	−0.177713	+	1.42489i
$414$	−16.6830	−	17.4784i	−0.819926	−	0.859017i
$415$	−1.16050	+	2.01005i	−0.0569667	+	0.0986693i
$416$	−6.33715			−0.310704
$417$	19.2651	+	25.7212i	0.943415	+	1.25957i
$418$		−	7.41017i		−	0.362443i
$419$	−8.53996	−	14.7916i	−0.417204	−	0.722619i	0.578453	−	0.815716i	$-0.303657\pi$
$419$	−8.53996	−	14.7916i	−0.417204	−	0.722619i	−0.995657	+	0.0930969i	$0.970323\pi$
$420$	6.55232	+	0.0315789i	0.319721	+	0.00154089i
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	−0.987716	−	0.156258i	$-0.950057\pi$
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	0.629182	+	0.777258i	$0.283390\pi$
$422$	7.66371	+	4.42465i	0.373064	+	0.215388i
$423$	11.4304	+	11.9754i	0.555766	+	0.582263i
$424$	4.94391	+	8.56310i	0.240097	+	0.415861i
$425$	−3.37524	−	5.84608i	−0.163723	−	0.283577i
$426$	−4.92684	+	3.69019i	−0.238706	+	0.178790i
$427$	18.3249	−	24.2217i	0.886803	−	1.17217i
$428$	13.7019	−	7.91078i	0.662305	−	0.382382i
$429$	30.0406	−	22.5004i	1.45038	−	1.08633i
$430$		−	8.31838i		−	0.401148i
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	−0.285973	−	0.958238i	$-0.592317\pi$
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	0.686871	+	0.726779i	$0.258984\pi$
$432$	3.30521	−	4.00944i	0.159022	−	0.192904i
$433$		−	9.04314i		−	0.434585i	−0.976106	−	0.217293i	$-0.930277\pi$
$433$		−	9.04314i		−	0.434585i	0.976106	−	0.217293i	$-0.0697226\pi$
$434$	10.5838	−	4.46878i	0.508041	−	0.214508i
$435$	−0.336249	+	0.785782i	−0.0161219	+	0.0376754i
$436$	10.2135			0.489138
$437$	8.72690	−	15.1154i	0.417464	−	0.723069i
$438$	0.369689	+	0.158196i	0.0176644	+	0.00755890i
$439$	0.791370	−	0.456897i	0.0377700	−	0.0218065i	−0.480996	−	0.876723i	$-0.659725\pi$
$439$	0.791370	−	0.456897i	0.0377700	−	0.0218065i	0.518766	+	0.854916i	$0.326392\pi$
$440$	4.88930			0.233088
$441$	−10.6748	+	18.0845i	−0.508324	+	0.861166i
$442$	14.4741			0.688465
$443$	−25.4279	+	14.6808i	−1.20812	+	0.697507i	−0.962348	−	0.271821i	$-0.912374\pi$
$443$	−25.4279	+	14.6808i	−1.20812	+	0.697507i	−0.245770	+	0.969328i	$0.579041\pi$
$444$	−2.98848	+	2.23836i	−0.141827	+	0.106228i
$445$	2.90223	−	5.02681i	0.137579	−	0.238294i
$446$	7.95544			0.376701
$447$	11.1903	−	1.34092i	0.529283	−	0.0634234i
$448$	2.43739	−	1.02913i	0.115156	−	0.0486219i
$449$			3.36736i			0.158915i	0.996838	+	0.0794577i	$0.0253189\pi$
$449$			3.36736i			0.158915i	−0.996838	+	0.0794577i	$0.974681\pi$
$450$	6.41386	−	6.12199i	0.302352	−	0.288593i
$451$	1.19744	−	0.691343i	0.0563853	−	0.0325541i
$452$		−	8.41555i		−	0.395834i
$453$	−1.18679	−	9.90404i	−0.0557603	−	0.465332i
$454$	8.00180	−	4.61984i	0.375543	−	0.216820i
$455$	−14.4642	+	19.1186i	−0.678090	+	0.896295i
$456$	3.45080	+	1.47666i	0.161599	+	0.0691507i
$457$	7.55693	+	13.0890i	0.353498	+	0.612277i	0.986860	−	0.161579i	$-0.0516588\pi$
$457$	7.55693	+	13.0890i	0.353498	+	0.612277i	−0.633362	+	0.773856i	$0.718325\pi$
$458$	−4.22227	−	7.31319i	−0.197294	−	0.341723i
$459$	−7.54914	+	9.15763i	−0.352364	+	0.427441i
$460$	9.97330	+	5.75809i	0.465008	+	0.268472i
$461$	−5.19445	+	8.99706i	−0.241930	+	0.419035i	−0.961264	−	0.275629i	$-0.911114\pi$
$461$	−5.19445	+	8.99706i	−0.241930	+	0.419035i	0.719334	+	0.694664i	$0.244447\pi$
$462$	−7.90025	+	13.5326i	−0.367553	+	0.629593i
$463$	−2.65722	−	4.60244i	−0.123492	−	0.213894i	0.797651	−	0.603120i	$-0.206076\pi$
$463$	−2.65722	−	4.60244i	−0.123492	−	0.213894i	−0.921142	+	0.389226i	$0.872743\pi$
$464$			0.345115i			0.0160216i
$465$	−4.23073	+	9.88681i	−0.196195	+	0.458490i
$466$	−16.6480			−0.771203
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	−0.998459	−	0.0554907i	$-0.982328\pi$
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	0.547286	+	0.836946i	$0.315661\pi$
$468$	4.49174	+	18.4732i	0.207631	+	0.853924i
$469$	1.39283	−	11.1676i	0.0643148	−	0.515672i
$470$	−6.83323	−	3.94517i	−0.315193	−	0.181977i
$471$	5.42646	−	12.6811i	0.250038	−	0.584315i
$472$	−9.55191	−	5.51480i	−0.439662	−	0.253839i
$473$	17.2280	+	9.94659i	0.792144	+	0.457345i
$474$	−9.92265	+	23.1883i	−0.455763	+	1.06507i
$475$	5.54674	+	3.20241i	0.254502	+	0.146937i
$476$	−5.56705	+	2.35055i	−0.255165	+	0.107737i
$477$	21.4578	−	20.4813i	0.982484	−	0.937775i
$478$	−13.6442	+	23.6325i	−0.624073	+	1.08093i
$479$	−27.8024			−1.27033			−0.635163	−	0.772378i	$-0.719067\pi$
$479$	−27.8024			−1.27033			−0.635163	+	0.772378i	$0.719067\pi$
$480$	−0.974311	+	2.27687i	−0.0444710	+	0.103924i
$481$		−	13.6611i		−	0.622891i
$482$	12.6450	+	21.9018i	0.575965	+	0.997600i
$483$	−32.0523	+	18.3000i	−1.45843	+	0.832680i
$484$	−0.346305	+	0.599818i	−0.0157411	+	0.0272645i
$485$	13.1363	+	7.58425i	0.596489	+	0.344383i
$486$	−14.0305	−	6.79302i	−0.636436	−	0.308138i
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	0.938210	−	0.346067i	$-0.112483\pi$
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	−0.768808	+	0.639480i	$0.779150\pi$
$488$	5.73987	+	9.94175i	0.259832	+	0.450042i
$489$	−18.1295	−	7.75790i	−0.819843	−	0.350824i
$490$	2.45840	−	9.70234i	0.111059	−	0.438307i
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	−0.00130103	−	0.999999i	$-0.500414\pi$
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	0.865374	+	0.501126i	$0.167081\pi$
$492$	0.0833287	+	0.695397i	0.00375675	+	0.0313509i
$493$		−	0.788249i		−	0.0355009i
$494$	−11.8931	+	6.86651i	−0.535098	+	0.308939i
$495$	−3.46551	−	14.2526i	−0.155763	−	0.640608i
$496$			4.34228i			0.194974i
$497$	3.65746	+	8.66232i	0.164059	+	0.388558i
$498$	2.79158	−	0.334512i	0.125094	−	0.0149898i
$499$	32.9042			1.47300			0.736498	−	0.676439i	$-0.236478\pi$
$499$	32.9042			1.47300			0.736498	+	0.676439i	$0.236478\pi$
$500$	−5.68761	+	9.85123i	−0.254358	+	0.440560i
$501$	15.7046	−	11.7627i	0.701630	−	0.525519i
$502$	7.09567	−	4.09669i	0.316695	−	0.182844i
$503$	25.6142			1.14208			0.571039	−	0.820923i	$-0.306540\pi$
$503$	25.6142			1.14208			0.571039	+	0.820923i	$0.306540\pi$
$504$	−4.72760	−	6.37572i	−0.210584	−	0.283997i
$505$	−11.5087			−0.512129
$506$	−23.8509	+	13.7703i	−1.06030	+	0.612165i
$507$	−43.2482	−	18.5066i	−1.92072	−	0.821909i
$508$	2.88886	−	5.00366i	0.128173	−	0.222002i
$509$	−21.4717			−0.951715			−0.475857	−	0.879522i	$-0.657862\pi$
$509$	−21.4717			−0.951715			−0.475857	+	0.879522i	$0.657862\pi$
$510$	2.22534	−	5.20041i	0.0985398	−	0.230278i
$511$	0.370594	−	0.489848i	0.0163941	−	0.0216696i
$512$			1.00000i			0.0441942i
$513$	1.85863	−	11.1060i	0.0820607	−	0.490340i
$514$	−5.74560	+	3.31723i	−0.253428	+	0.146317i
$515$		−	4.02347i		−	0.177295i
$516$	−8.06507	+	6.04071i	−0.355045	+	0.265928i
$517$	16.3415	−	9.43475i	0.718697	−	0.414940i
$518$	2.21851	+	5.25432i	0.0974759	+	0.230862i
$519$	−30.0710	+	22.5231i	−1.31997	+	0.988654i
$520$	−4.53059	−	7.84721i	−0.198679	−	0.344123i
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	0.928079	−	0.372382i	$-0.121459\pi$
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	−0.786532	+	0.617549i	$0.788126\pi$
$522$	1.00603	−	0.244616i	0.0440329	−	0.0107066i
$523$	11.7830	+	6.80291i	0.515234	+	0.297470i	0.734982	−	0.678086i	$-0.237190\pi$
$523$	11.7830	+	6.80291i	0.515234	+	0.297470i	−0.219749	+	0.975557i	$0.570524\pi$
$524$	2.22833	−	3.85959i	0.0973452	−	0.168607i
$525$	−6.71536	−	11.7619i	−0.293082	−	0.513331i
$526$	3.02295	+	5.23590i	0.131807	+	0.228296i
$527$		−	9.91784i		−	0.432028i
$528$	−3.55055	−	4.74040i	−0.154518	−	0.206300i
$529$	−41.8687			−1.82038
$530$	−7.06905	+	12.2440i	−0.307060	+	0.531843i
$531$	−9.30564	+	31.7533i	−0.403830	+	1.37798i
$532$	3.45924	−	4.57241i	0.149977	−	0.198239i
$533$	−2.21918	−	1.28124i	−0.0961233	−	0.0554968i
$534$	−6.98129	+	0.836561i	−0.302110	+	0.0362015i
$535$	19.5916	+	11.3112i	0.847020	+	0.489027i
$536$	3.68377	+	2.12683i	0.159115	+	0.0918650i
$537$	−21.5883	−	28.8230i	−0.931604	−	1.24380i
$538$	−5.90750	−	3.41069i	−0.254690	−	0.147045i
$539$	17.1547	+	16.6930i	0.738904	+	0.719017i
$540$	7.32781	+	1.22634i	0.315339	+	0.0527734i
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	0.343184	+	0.939268i	$0.388494\pi$
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	−0.985022	+	0.172428i	$0.944839\pi$
$542$	−5.07815			−0.218125
$543$	−37.0263	+	4.43682i	−1.58895	+	0.190402i
$544$		−	2.28402i		−	0.0979264i
$545$	7.30188	+	12.6472i	0.312778	+	0.541748i
$546$	29.0401	+	0.139959i	1.24280	+	0.00598969i
$547$	−9.07207	+	15.7133i	−0.387894	+	0.671852i	−0.992166	−	0.124926i	$-0.960131\pi$
$547$	−9.07207	+	15.7133i	−0.387894	+	0.671852i	0.604272	+	0.796778i	$0.293464\pi$
$548$	8.36293	+	4.82834i	0.357247	+	0.206256i
$549$	24.9125	−	23.7788i	1.06324	−	1.01485i
$550$	−5.05313	−	8.75228i	−0.215466	−	0.373199i
$551$	0.373944	+	0.647690i	0.0159305	+	0.0275925i
$552$	−1.65976	−	13.8510i	−0.0706439	−	0.589540i
$553$	30.7251	+	23.2450i	1.30656	+	0.988479i
$554$	−1.71398	+	0.989567i	−0.0728201	+	0.0420427i
$555$	−4.90828	−	2.10033i	−0.208345	−	0.0891542i
$556$			18.5537i			0.786853i
$557$	32.5079	−	18.7684i	1.37740	−	0.795245i	0.385558	−	0.922684i	$-0.374009\pi$
$557$	32.5079	−	18.7684i	1.37740	−	0.795245i	0.991846	+	0.127439i	$0.0406757\pi$
$558$	12.6580	−	3.07779i	0.535857	−	0.130293i
$559$		−	36.8674i		−	1.55932i
$560$	3.01691	+	2.28244i	0.127488	+	0.0964507i
$561$	8.10951	+	10.8272i	0.342384	+	0.457123i
$562$	−17.6326			−0.743787
$563$	3.55341	−	6.15468i	0.149758	−	0.259389i	−0.781380	−	0.624056i	$-0.785484\pi$
$563$	3.55341	−	6.15468i	0.149758	−	0.259389i	0.931138	+	0.364667i	$0.118817\pi$
$564$	1.13719	+	9.49008i	0.0478841	+	0.399604i
$565$	10.4209	−	6.01649i	0.438409	−	0.253116i
$566$	5.15385			0.216633
$567$	−15.2347	+	18.3004i	−0.639799	+	0.768543i
$568$	−3.55393			−0.149119
$569$	35.6499	−	20.5825i	1.49452	−	0.862862i	0.494541	−	0.869154i	$-0.335336\pi$
$569$	35.6499	−	20.5825i	1.49452	−	0.862862i	0.999980	+	0.00629202i	$0.00200283\pi$
$570$	0.638542	+	5.32878i	0.0267456	+	0.223198i
$571$	−2.21293	+	3.83290i	−0.0926080	+	0.160402i	−0.908608	−	0.417650i	$-0.862854\pi$
$571$	−2.21293	+	3.83290i	−0.0926080	+	0.160402i	0.816000	+	0.578052i	$0.196187\pi$
$572$	21.6695			0.906049
$573$	7.65193	+	10.2162i	0.319664	+	0.426789i
$574$	1.06161	+	0.132405i	0.0443108	+	0.00552646i
$575$		−	23.8042i		−	0.992702i
$576$	2.91507	−	0.708796i	0.121461	−	0.0295332i
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	−0.449739	−	0.893160i	$-0.648483\pi$
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	0.548629	+	0.836066i	$0.315150\pi$
$578$		−	11.7833i		−	0.490119i
$579$	−4.49942	−	1.92538i	−0.186989	−	0.0800159i
$580$	−0.427352	+	0.246732i	−0.0177448	+	0.0102450i
$581$	0.531520	−	4.26169i	0.0220512	−	0.176805i
$582$	−2.18614	−	18.2439i	−0.0906186	−	0.756233i
$583$	−16.9054	−	29.2811i	−0.700151	−	1.21270i
$584$	0.116080	+	0.201057i	0.00480344	+	0.00831981i
$585$	−19.6639	+	18.7690i	−0.813001	+	0.776004i
$586$	−1.78831	−	1.03248i	−0.0738745	−	0.0426515i
$587$	−9.90248	+	17.1516i	−0.408719	+	0.707922i	−0.994747	−	0.102369i	$-0.967358\pi$
$587$	−9.90248	+	17.1516i	−0.408719	+	0.707922i	0.586027	+	0.810291i	$0.300691\pi$
$588$	−11.1921	+	4.66219i	−0.461556	+	0.192265i
$589$	4.70501	+	8.14931i	0.193866	+	0.335786i
$590$		−	15.7707i		−	0.649268i
$591$	44.8653	−	5.37616i	1.84551	−	0.221146i
$592$	−2.15571			−0.0885993
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	−0.874816	−	0.484456i	$-0.839018\pi$
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	0.856959	+	0.515385i	$0.172351\pi$
$594$	−11.3020	+	13.7101i	−0.463726	+	0.562531i
$595$	−6.89068	−	5.21313i	−0.282490	−	0.213717i
$596$	5.63517	+	3.25347i	0.230826	+	0.133267i
$597$	−16.0076	−	21.3720i	−0.655147	−	0.874699i
$598$	44.2020	+	25.5201i	1.80756	+	1.04359i
$599$	2.33277	+	1.34682i	0.0953143	+	0.0550297i	0.546899	−	0.837198i	$-0.315808\pi$
$599$	2.33277	+	1.34682i	0.0953143	+	0.0550297i	−0.451585	+	0.892228i	$0.649141\pi$
$600$	5.08276	−	0.609062i	0.207503	−	0.0248648i
$601$	−0.115325	−	0.0665827i	−0.00470419	−	0.00271596i	0.497646	−	0.867380i	$-0.334198\pi$
$601$	−0.115325	−	0.0665827i	−0.00470419	−	0.00271596i	−0.502350	+	0.864664i	$0.667531\pi$
$602$	5.98714	+	14.1799i	0.244018	+	0.577931i
$603$	3.58880	−	12.2459i	0.146147	−	0.498693i
$604$	2.87950	−	4.98745i	0.117165	−	0.202936i
$605$	−0.990329			−0.0402626
$606$	8.35746	+	11.1582i	0.339499	+	0.453271i
$607$		−	44.3243i		−	1.79907i	−0.436851	−	0.899534i	$-0.643906\pi$
$607$		−	44.3243i		−	1.79907i	0.436851	−	0.899534i	$-0.356094\pi$
$608$	1.08353	+	1.87673i	0.0439431	+	0.0761117i
$609$	0.00762203	−	1.58150i	0.000308860	−	0.0640855i
$610$	−8.20716	+	14.2152i	−0.332298	+	0.575557i
$611$	−30.2851	−	17.4851i	−1.22520	−	0.707372i
$612$	−6.65806	+	1.61890i	−0.269136	+	0.0654402i
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	0.924926	−	0.380147i	$-0.124127\pi$
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	−0.791680	+	0.610936i	$0.790793\pi$
$614$	0.545593	+	0.944994i	0.0220183	+	0.0381369i
$615$	−0.801527	+	0.600342i	−0.0323207	+	0.0242081i
$616$	−8.33454	+	3.51906i	−0.335808	+	0.141787i
$617$	−7.99450	+	4.61563i	−0.321846	+	0.185818i	−0.652215	−	0.758034i	$-0.726160\pi$
$617$	−7.99450	+	4.61563i	−0.321846	+	0.185818i	0.330369	+	0.943852i	$0.392827\pi$
$618$	−3.90094	+	2.92180i	−0.156919	+	0.117532i
$619$			6.53894i			0.262822i	0.991328	+	0.131411i	$0.0419508\pi$
$619$			6.53894i			0.262822i	−0.991328	+	0.131411i	$0.958049\pi$
$620$	−5.37699	+	3.10441i	−0.215945	+	0.124676i
$621$	−39.2003	+	14.6559i	−1.57305	+	0.588119i
$622$		−	15.2220i		−	0.610347i
$623$	−1.32925	+	10.6578i	−0.0532552	+	0.426996i
$624$	−4.31818	+	10.0912i	−0.172866	+	0.403970i
$625$	−1.48722			−0.0594888
$626$	5.78518	−	10.0202i	0.231222	−	0.400489i
$627$	−11.7998	−	5.04934i	−0.471240	−	0.201651i
$628$	6.89669	−	3.98180i	0.275208	−	0.158891i
$629$	4.92368			0.196320
$630$	4.51509	−	10.4123i	0.179885	−	0.414836i
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$	−12.6111	+	7.28100i	−0.501641	+	0.289623i
$633$	12.2678	−	9.18858i	0.487603	−	0.365213i
$634$	8.58020	−	14.8613i	0.340763	−	0.590219i
$635$	8.26129			0.327839
$636$	17.0046	−	2.03764i	0.674274	−	0.0807976i
$637$	10.8957	−	43.0011i	0.431704	−	1.70377i
$638$		−	1.18010i		−	0.0467207i
$639$	2.51901	+	10.3599i	0.0996504	+	0.409832i
$640$	−1.23829	+	0.714925i	−0.0489476	+	0.0282599i
$641$		−	15.2351i		−	0.601752i	−0.953663	−	0.300876i	$-0.902721\pi$
$641$		−	15.2351i		−	0.601752i	0.953663	−	0.300876i	$-0.0972790\pi$
$642$	−3.26044	−	27.2091i	−0.128679	−	1.07386i
$643$	16.5813	−	9.57324i	0.653904	−	0.377532i	−0.136046	−	0.990702i	$-0.543440\pi$
$643$	16.5813	−	9.57324i	0.653904	−	0.377532i	0.789950	+	0.613171i	$0.210106\pi$
$644$	−21.1454	−	2.63726i	−0.833244	−	0.103923i
$645$	−13.2461	−	5.66821i	−0.521563	−	0.223185i
$646$	−2.47481	−	4.28649i	−0.0973700	−	0.168650i
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	0.849996	−	0.526789i	$-0.176604\pi$
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	−0.881211	+	0.472723i	$0.843271\pi$
$648$	−4.13237	−	7.99522i	−0.162335	−	0.314082i
$649$	32.6622	+	18.8576i	1.28211	+	0.740224i
$650$	−9.36481	+	16.2203i	−0.367318	+	0.636213i
$651$	0.0959013	−	19.8986i	0.00375867	−	0.779887i
$652$	−5.69256	−	9.85980i	−0.222938	−	0.386140i
$653$			17.9639i			0.702983i	0.936191	+	0.351492i	$0.114325\pi$
$653$			17.9639i			0.702983i	−0.936191	+	0.351492i	$0.885675\pi$
$654$	6.95955	−	16.2638i	0.272140	−	0.635965i
$655$	6.37237			0.248989
$656$	−0.202180	+	0.350186i	−0.00789380	+	0.0136725i
$657$	0.503818	−	0.480891i	0.0196558	−	0.0187613i
$658$	14.4878	+	1.80692i	0.564793	+	0.0704412i
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	0.683574	−	0.729881i	$-0.260424\pi$
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	−0.290308	+	0.956933i	$0.593758\pi$
$660$	3.33160	−	7.78563i	0.129682	−	0.303055i
$661$	−15.7786	−	9.10975i	−0.613715	−	0.354328i	0.160703	−	0.987003i	$-0.448624\pi$
$661$	−15.7786	−	9.10975i	−0.613715	−	0.354328i	−0.774418	+	0.632674i	$0.781957\pi$
$662$	22.9437	+	13.2466i	0.891732	+	0.514842i
$663$	9.86279	−	23.0484i	0.383039	−	0.895125i
$664$	1.40577	+	0.811624i	0.0545546	+	0.0314971i
$665$	8.13505	+	1.01461i	0.315464	+	0.0393448i
$666$	1.52796	+	6.28404i	0.0592073	+	0.243502i
$667$	1.38980	−	2.40720i	0.0538132	−	0.0932072i
$668$	11.3284			0.438308
$669$	5.42090	−	12.6681i	0.209584	−	0.489777i
$670$			6.08209i			0.234972i
$671$	−19.6272	−	33.9953i	−0.757699	−	1.31237i
$672$	0.0220855	−	4.58252i	0.000851965	−	0.176775i
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	−0.815807	−	0.578324i	$-0.803707\pi$
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	0.908747	+	0.417348i	$0.137040\pi$
$674$	7.03993	+	4.06451i	0.271168	+	0.156559i
$675$	−5.37810	−	14.3849i	−0.207003	−	0.553675i
$676$	−13.5797	−	23.5208i	−0.522297	−	0.904645i
$677$	11.5645	+	20.0303i	0.444460	+	0.769827i	0.998014	−	0.0629856i	$-0.0200622\pi$
$677$	11.5645	+	20.0303i	0.444460	+	0.769827i	−0.553554	+	0.832813i	$0.686729\pi$
$678$	−13.4008	−	5.73442i	−0.514654	−	0.220229i
$679$	−27.8516	−	3.47366i	−1.06884	−	0.133307i
$680$	2.82827	−	1.63290i	0.108459	−	0.0626189i
$681$	−1.90407	−	15.8899i	−0.0729642	−	0.608903i
$682$		−	14.8482i		−	0.568567i
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	−0.364220	−	0.931313i	$-0.618664\pi$
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	0.624431	+	0.781080i	$0.285331\pi$
$684$	4.70280	−	4.48879i	0.179816	−	0.171633i
$685$			13.8076i			0.527562i
$686$	2.79253	+	18.3085i	0.106619	+	0.699022i
$687$	−14.5225	+	1.74021i	−0.554067	+	0.0663933i
$688$	−5.81766			−0.221796
$689$	−31.3303	+	54.2656i	−1.19359	+	2.06736i
$690$	15.9650	−	11.9577i	0.607776	−	0.455222i
$691$	−14.8676	+	8.58379i	−0.565589	+	0.326543i	−0.755386	−	0.655281i	$-0.772550\pi$
$691$	−14.8676	+	8.58379i	−0.565589	+	0.326543i	0.189797	+	0.981823i	$0.439217\pi$
$692$	−21.6914			−0.824584
$693$	16.1658	+	21.8014i	0.614087	+	0.828168i
$694$	−25.6171			−0.972412
$695$	−22.9748	+	13.2645i	−0.871485	+	0.503152i
$696$	0.549556	+	0.235164i	0.0208309	+	0.00891387i
$697$	0.461782	−	0.799830i	0.0174912	−	0.0302957i
$698$	−10.5301			−0.398570
$699$	−11.3441	+	26.5100i	−0.429071	+	1.00270i
$700$	0.967765	−	7.75947i	0.0365781	−	0.293281i
$701$		−	34.9404i		−	1.31968i	−0.751406	−	0.659840i	$-0.770624\pi$
$701$		−	34.9404i		−	1.31968i	0.751406	−	0.659840i	$-0.229376\pi$
$702$	32.4771	+	5.43520i	1.22577	+	0.205138i
$703$	−4.04570	+	2.33579i	−0.152587	+	0.0880959i
$704$		−	3.41945i		−	0.128875i
$705$	−10.9384	+	8.19286i	−0.411965	+	0.308561i
$706$	11.1230	−	6.42186i	0.418619	−	0.241690i
$707$	19.6183	−	8.28334i	0.737820	−	0.311527i
$708$	−15.2904	+	11.4525i	−0.574649	+	0.430410i
$709$	12.1668	+	21.0735i	0.456933	+	0.791432i	0.998797	−	0.0490345i	$-0.0156144\pi$
$709$	12.1668	+	21.0735i	0.456933	+	0.791432i	−0.541864	+	0.840466i	$0.682281\pi$
$710$	−2.54079	−	4.40078i	−0.0953542	−	0.165158i
$711$	30.1633	+	31.6013i	1.13121	+	1.18514i
$712$	−3.51562	−	2.02974i	−0.131753	−	0.0760678i
$713$	17.4866	−	30.2877i	0.654879	−	1.13428i
$714$	−0.0504436	+	10.4666i	−0.00188780	+	0.391701i
$715$	15.4921	+	26.8331i	0.579372	+	1.00350i
$716$		−	20.7912i		−	0.777002i
$717$	28.3347	+	37.8302i	1.05818	+	1.41280i
$718$	−29.6621			−1.10698
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	−0.981920	−	0.189297i	$-0.939379\pi$
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	0.654896	+	0.755719i	$0.272712\pi$
$720$	2.96175	+	3.10295i	0.110378	+	0.115640i
$721$	2.89588	+	6.85860i	0.107848	+	0.255428i
$722$	−12.3875	−	7.15191i	−0.461014	−	0.266167i
$723$	43.4925	−	5.21166i	1.61750	−	0.193824i
$724$	−18.6456	−	10.7650i	−0.692958	−	0.400079i
$725$	0.883344	+	0.509999i	0.0328066	+	0.0189409i
$726$	0.719166	+	0.960171i	0.0266907	+	0.0356353i
$727$	33.8627	+	19.5507i	1.25590	+	0.725094i	0.972275	−	0.233841i	$-0.0751296\pi$
$727$	33.8627	+	19.5507i	1.25590	+	0.725094i	0.283625	+	0.958935i	$0.408463\pi$
$728$	13.3711	+	10.1159i	0.495565	+	0.374919i
$729$	−20.3776	+	17.7131i	−0.754725	+	0.656041i
$730$	−0.165978	+	0.287482i	−0.00614311	+	0.0106402i
$731$	13.2876			0.491461
$732$	19.7423	−	2.36570i	0.729695	−	0.0874386i
$733$			23.4489i			0.866105i	0.901369	+	0.433053i	$0.142564\pi$
$733$			23.4489i			0.866105i	−0.901369	+	0.433053i	$0.857436\pi$
$734$	−11.9989	−	20.7828i	−0.442889	−	0.767107i
$735$	−13.7747	−	10.5260i	−0.508086	−	0.388256i
$736$	4.02706	−	6.97507i	0.148439	−	0.257104i
$737$	−12.5965	−	7.27257i	−0.463997	−	0.267889i
$738$	1.16412	+	0.341157i	0.0428518	+	0.0125582i
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	0.999954	−	0.00957820i	$-0.00304888\pi$
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	−0.508272	+	0.861197i	$0.669716\pi$
$740$	−1.54117	−	2.66939i	−0.0566547	−	0.0981288i
$741$	2.83004	+	23.6173i	0.103964	+	0.867605i
$742$	3.23769	−	25.9596i	0.118859	−	0.953006i
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	−0.689458	−	0.724326i	$-0.742151\pi$
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	0.282555	+	0.959251i	$0.408818\pi$
$744$	6.91457	+	2.95886i	0.253501	+	0.108477i
$745$			9.30395i			0.340870i
$746$	−10.2528	+	5.91948i	−0.375383	+	0.216727i
$747$	1.36953	−	4.67320i	0.0501085	−	0.170983i
$748$			7.81007i			0.285564i
$749$	−41.5381	−	5.18065i	−1.51777	−	0.189297i
$750$	11.8113	+	15.7695i	0.431289	+	0.575822i
$751$	−10.2483			−0.373967			−0.186984	−	0.982363i	$-0.559871\pi$
$751$	−10.2483			−0.373967			−0.186984	+	0.982363i	$0.559871\pi$
$752$	−2.75915	+	4.77898i	−0.100616	+	0.174272i
$753$	−1.68845	−	14.0905i	−0.0615307	−	0.513488i
$754$	−1.89404	+	1.09352i	−0.0689768	+	0.0398238i
$755$	8.23452			0.299685
$756$	−13.3740	+	3.18369i	−0.486408	+	0.115790i
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$	−11.3778	+	6.56897i	−0.413260	+	0.238596i
$759$	5.67544	+	47.3629i	0.206006	+	1.71916i
$760$	−1.54929	+	2.68345i	−0.0561987	+	0.0973390i
$761$	−16.2999			−0.590870			−0.295435	−	0.955363i	$-0.595465\pi$
$761$	−16.2999			−0.590870			−0.295435	+	0.955363i	$0.595465\pi$
$762$	−5.99925	−	8.00971i	−0.217330	−	0.290161i
$763$	−21.5500	−	16.3036i	−0.780161	−	0.590229i
$764$			7.36938i			0.266615i
$765$	−6.76468	−	7.08719i	−0.244577	−	0.256238i
$766$	−15.2005	+	8.77603i	−0.549217	+	0.317091i
$767$		−	69.8962i		−	2.52380i
$768$	1.59238	+	0.681407i	0.0574602	+	0.0245882i
$769$	−41.4043	+	23.9048i	−1.49308	+	0.862029i	−0.999968	−	0.00793771i	$-0.997473\pi$
$769$	−41.4043	+	23.9048i	−1.49308	+	0.862029i	−0.493110	+	0.869967i	$0.664140\pi$
$770$	−10.3162	−	7.80468i	−0.371769	−	0.281261i
$771$	1.36720	+	11.4096i	0.0492384	+	0.410906i
$772$	−1.41279	−	2.44703i	−0.0508476	−	0.0880706i
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	0.956306	−	0.292367i	$-0.0944429\pi$
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	−0.731350	+	0.682002i	$0.761110\pi$
$774$	4.12353	+	16.9589i	0.148217	+	0.609574i
$775$	11.1143	+	6.41686i	0.399239	+	0.230501i
$776$	5.30423	−	9.18719i	0.190411	−	0.329801i
$777$	9.87860	+	0.0476099i	0.354393	+	0.00170800i
$778$	10.9205	+	18.9148i	0.391518	+	0.678130i
$779$			0.876275i			0.0313958i
$780$	−15.5829	+	1.86729i	−0.557959	+	0.0668596i
$781$	12.1525			0.434849
$782$	−9.19786	+	15.9312i	−0.328915	+	0.569697i
$783$	0.295996	−	1.76867i	0.0105780	−	0.0632073i
$784$	−6.78556	−	1.71934i	−0.242342	−	0.0614051i
$785$	9.86123	+	5.69338i	0.351962	+	0.203206i
$786$	−4.62754	−	6.17831i	−0.165059	−	0.220373i
$787$	0.226048	+	0.130509i	0.00805773	+	0.00465213i	0.504023	−	0.863690i	$-0.331853\pi$
$787$	0.226048	+	0.130509i	0.00805773	+	0.00465213i	−0.495966	+	0.868342i	$0.665186\pi$
$788$	22.5931	+	13.0441i	0.804846	+	0.464678i
$789$	10.3974	−	1.24591i	0.370158	−	0.0443556i
$790$	−18.0319	−	10.4107i	−0.641548	−	0.370398i
$791$	−13.4336	+	17.7564i	−0.477643	+	0.631345i
$792$	−9.96791	+	2.42369i	−0.354194	+	0.0861221i
$793$	−36.3744	+	63.0024i	−1.29169	+	2.23728i
$794$	38.9869			1.38359
$795$	14.6802	+	19.5998i	0.520652	+	0.695132i
$796$		−	15.4165i		−	0.546424i
$797$	−1.85220	−	3.20810i	−0.0656083	−	0.113637i	0.831355	−	0.555741i	$-0.187565\pi$
$797$	−1.85220	−	3.20810i	−0.0656083	−	0.113637i	−0.896964	+	0.442104i	$0.854232\pi$
$798$	−4.92387	−	8.62411i	−0.174303	−	0.305290i
$799$	6.30194	−	10.9153i	0.222946	−	0.386155i
$800$	2.55956	+	1.47776i	0.0904942	+	0.0522468i
$801$	−3.42498	+	11.6869i	−0.121016	+	0.412937i
$802$	11.5989	+	20.0899i	0.409573	+	0.709400i
$803$	−0.396931	−	0.687504i	−0.0140074	−	0.0242615i
$804$	5.89688	−	4.41674i	0.207967	−	0.155767i
$805$	−11.8517	−	28.0695i	−0.417716	−	0.989318i
$806$	−23.8310	+	13.7588i	−0.839411	+	0.484634i
$807$	−9.45654	+	7.08292i	−0.332886	+	0.249331i
$808$			8.04886i			0.283158i
$809$	−5.94276	+	3.43105i	−0.208936	+	0.120629i	−0.600817	−	0.799387i	$-0.705158\pi$
$809$	−5.94276	+	3.43105i	−0.208936	+	0.120629i	0.391881	+	0.920016i	$0.371825\pi$
$810$	6.94603	−	10.8330i	0.244059	−	0.380634i
$811$			23.1945i			0.814470i	0.913323	+	0.407235i	$0.133507\pi$
$811$			23.1945i			0.814470i	−0.913323	+	0.407235i	$0.866493\pi$
$812$	0.550900	−	0.728176i	0.0193328	−	0.0255540i
$813$	−3.46029	+	8.08635i	−0.121358	+	0.283601i
$814$	7.37134			0.258365
$815$	8.13951	−	14.0980i	0.285114	−	0.493833i
$816$	−3.63703	−	1.55635i	−0.127321	−	0.0544830i
$817$	−10.9182	+	6.30363i	−0.381980	+	0.220536i
$818$	−24.6187			−0.860774
$819$	20.0110	−	46.1476i	0.699242	−	1.61253i
$820$	−0.578174			−0.0201907
$821$	−3.28550	+	1.89688i	−0.114665	+	0.0662017i	−0.556236	−	0.831025i	$-0.687755\pi$
$821$	−3.28550	+	1.89688i	−0.114665	+	0.0662017i	0.441571	+	0.897226i	$0.354421\pi$
$822$	13.3871	−	10.0269i	0.466930	−	0.349729i
$823$	7.45395	−	12.9106i	0.259828	−	0.450036i	−0.706368	−	0.707845i	$-0.749667\pi$
$823$	7.45395	−	12.9106i	0.259828	−	0.450036i	0.966196	+	0.257810i	$0.0830007\pi$
$824$	−2.81391			−0.0980272
$825$	−17.3802	+	2.08265i	−0.605102	+	0.0725087i
$826$	11.3509	+	26.8835i	0.394949	+	0.935395i
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$	−23.1871	−	6.79524i	−0.805809	−	0.236151i
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	−0.272137	−	0.962259i	$-0.587730\pi$
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	0.697272	+	0.716807i	$0.254397\pi$
$830$			2.32100i			0.0805631i
$831$	0.407851	+	3.40361i	0.0141482	+	0.118070i
$832$	−5.48813	+	3.16857i	−0.190267	+	0.109851i
$833$	15.4983	+	3.92700i	0.536985	+	0.136063i
$834$	29.5446	+	12.6426i	1.02305	+	0.437779i
$835$	8.09893	+	14.0278i	0.280275	+	0.485451i
$836$	−3.70508	−	6.41739i	−0.128143	−	0.221950i
$837$	3.72425	−	22.2537i	0.128729	−	0.769199i
$838$	−14.7916	−	8.53996i	−0.510969	−	0.295008i
$839$	−8.92488	+	15.4583i	−0.308121	+	0.533681i	−0.977951	−	0.208833i	$-0.933034\pi$
$839$	−8.92488	+	15.4583i	−0.308121	+	0.533681i	0.669830	+	0.742514i	$0.266367\pi$
$840$	5.69027	−	3.24881i	0.196333	−	0.112095i
$841$	−14.4404	−	25.0116i	−0.497946	−	0.862469i
$842$			14.7130i			0.507045i
$843$	−12.0150	+	28.0779i	−0.413819	+	0.967054i
$844$	8.84930			0.304605
$845$	19.4170	−	33.6312i	0.667964	−	1.15695i
$846$	15.8867	+	4.65577i	0.546197	+	0.160069i
$847$	1.68816	−	0.712787i	0.0580060	−	0.0244917i
$848$	8.56310	+	4.94391i	0.294058	+	0.169775i
$849$	3.51187	−	8.20691i	0.120527	−	0.281660i
$850$	−5.84608	−	3.37524i	−0.200519	−	0.115770i
$851$	15.0362	+	8.68118i	0.515436	+	0.297587i
$852$	−2.42167	+	5.65921i	−0.0829651	+	0.193881i
$853$	−35.2392	−	20.3454i	−1.20657	−	0.696612i	−0.244559	−	0.969634i	$-0.578643\pi$
$853$	−35.2392	−	20.3454i	−1.20657	−	0.696612i	−0.962008	+	0.273022i	$0.911977\pi$
$854$	3.75896	−	30.1391i	0.128629	−	1.03134i
$855$	8.92057	+	2.61427i	0.305077	+	0.0894060i
$856$	7.91078	−	13.7019i	0.270385	−	0.468320i
$857$	5.45792			0.186439			0.0932194	−	0.995646i	$-0.470284\pi$
$857$	5.45792			0.186439			0.0932194	+	0.995646i	$0.470284\pi$
$858$	14.7658	−	34.5062i	0.504095	−	1.17802i
$859$			44.8973i			1.53188i	0.642914	+	0.765938i	$0.277725\pi$
$859$			44.8973i			1.53188i	−0.642914	+	0.765938i	$0.722275\pi$
$860$	−4.15919	−	7.20393i	−0.141827	−	0.245652i
$861$	0.934228	−	1.60027i	0.0318384	−	0.0545370i
$862$	4.80521	−	8.32286i	0.163666	−	0.283478i
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	0.126363	−	0.991984i	$-0.459670\pi$
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	−0.795902	+	0.605426i	$0.793003\pi$
$864$	0.857672	−	5.12488i	0.0291786	−	0.174352i
$865$	−15.5077	−	26.8602i	−0.527279	−	0.913274i
$866$	−4.52157	−	7.83159i	−0.153649	−	0.266128i
$867$	−18.7635	−	8.02921i	−0.637241	−	0.272686i
$868$	6.93149	−	9.16200i	0.235270	−	0.310978i
$869$	43.1229	−	24.8970i	1.46284	−	0.844573i
$870$	0.101691	+	0.848632i	0.00344764	+	0.0287713i
$871$			26.9560i			0.913371i
$872$	8.84514	−	5.10675i	0.299534	−	0.172936i
$873$	−30.5409	−	8.95033i	−1.03365	−	0.302923i
$874$		−	17.4538i		−	0.590384i
$875$	27.7259	−	11.7066i	0.937306	−	0.395755i
$876$	0.399258	−	0.0478427i	0.0134897	−	0.00161645i
$877$	−30.4891			−1.02954			−0.514771	−	0.857327i	$-0.672123\pi$
$877$	−30.4891			−1.02954			−0.514771	+	0.857327i	$0.672123\pi$
$878$	0.456897	−	0.791370i	0.0154195	−	0.0267074i
$879$	−2.86268	+	2.14414i	−0.0965557	+	0.0723200i
$880$	4.23425	−	2.44465i	0.142737	−	0.0824091i
$881$	−29.3810			−0.989871			−0.494935	−	0.868930i	$-0.664808\pi$
$881$	−29.3810			−0.989871			−0.494935	+	0.868930i	$0.664808\pi$
$882$	−0.202414	+	20.9990i	−0.00681564	+	0.707074i
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$	12.5350	−	7.23707i	0.421597	−	0.243409i
$885$	−25.1130	−	10.7463i	−0.844163	−	0.361231i
$886$	−14.6808	+	25.4279i	−0.493212	+	0.854268i
$887$	−32.7073			−1.09821			−0.549103	−	0.835755i	$-0.685030\pi$
$887$	−32.7073			−1.09821			−0.549103	+	0.835755i	$0.685030\pi$
$888$	−1.46892	+	3.43272i	−0.0492937	+	0.115195i
$889$	−14.0826	+	5.94605i	−0.472315	+	0.199424i
$890$		−	5.80446i		−	0.194566i
$891$	14.1304	+	27.3392i	0.473387	+	0.915898i
$892$	6.88961	−	3.97772i	0.230681	−	0.133184i
$893$			11.9585i			0.400176i
$894$	9.02062	−	6.75642i	0.301695	−	0.225968i
$895$	25.7454	−	14.8641i	0.860575	−	0.496853i
$896$	1.59628	−	2.10995i	0.0533279	−	0.0704885i
$897$	70.7573	−	52.9970i	2.36252	−	1.76952i
$898$	1.68368	+	2.91622i	0.0561851	+	0.0973154i
$899$	0.749293	+	1.29781i	0.0249903	+	0.0432845i
$900$	2.49357	−	8.50872i	0.0831190	−	0.283624i
$901$	−19.5583	−	11.2920i	−0.651580	−	0.376190i
$902$	0.691343	−	1.19744i	0.0230192	−	0.0398704i
$903$	26.6596	+	0.128486i	0.887174	+	0.00427574i
$904$	−4.20778	−	7.28808i	−0.139949	−	0.242398i
$905$		−	30.7848i		−	1.02332i
$906$	−5.97981	−	7.98375i	−0.198666	−	0.265242i
$907$	56.6934			1.88248			0.941238	−	0.337745i	$-0.109664\pi$
$907$	56.6934			1.88248			0.941238	+	0.337745i	$0.109664\pi$
$908$	4.61984	−	8.00180i	0.153315	−	0.265549i
$909$	23.4630	−	5.70500i	0.778218	−	0.189223i
$910$	−2.96701	+	23.7893i	−0.0983555	+	0.788608i
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	0.510265	−	0.860017i	$-0.329547\pi$
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	−0.489664	+	0.871911i	$0.662881\pi$
$912$	3.72681	−	0.446579i	0.123407	−	0.0147877i
$913$	−4.80697	−	2.77530i	−0.159087	−	0.0918492i
$914$	13.0890	+	7.55693i	0.432945	+	0.249961i
$915$	17.0437	+	22.7553i	0.563446	+	0.752267i
$916$	−7.31319	−	4.22227i	−0.241635	−	0.139508i
$917$	−10.8627	+	4.58650i	−0.358717	+	0.151460i
$918$	−1.95894	+	11.7053i	−0.0646546	+	0.386333i
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	−0.362550	−	0.931964i	$-0.618094\pi$
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	0.988380	−	0.152004i	$-0.0485727\pi$
$920$	11.5162			0.379677
$921$	1.87656	−	0.224867i	0.0618349	−	0.00740961i
$922$			10.3889i			0.342140i
$923$	−11.2609	−	19.5044i	−0.370656	−	0.641996i
$924$	−0.0755201	+	15.6697i	−0.00248443	+	0.515495i
$925$	−3.18563	+	5.51768i	−0.104743	+	0.181420i
$926$	−4.60244	−	2.65722i	−0.151246	−	0.0873217i
$927$	1.99449	+	8.20273i	0.0655076	+	0.269413i
$928$	0.172558	+	0.298879i	0.00566448	+	0.00981117i
$929$	21.4350	+	37.1265i	0.703259	+	1.21808i	0.967316	+	0.253574i	$0.0816060\pi$
$929$	21.4350	+	37.1265i	0.703259	+	1.21808i	−0.264057	+	0.964507i	$0.585061\pi$
$930$	1.27948	+	10.6776i	0.0419559	+	0.350132i
$931$	−14.5977	+	4.12564i	−0.478419	+	0.135212i
$932$	−14.4176	+	8.32399i	−0.472263	+	0.272661i
$933$	−24.2393	−	10.3724i	−0.793558	−	0.339577i
$934$			19.4999i			0.638055i
$935$	−9.67111	+	5.58362i	−0.316279	+	0.182604i
$936$	13.1266	+	13.7524i	0.429055	+	0.449511i
$937$		−	8.64637i		−	0.282464i	−0.989976	−	0.141232i	$-0.954894\pi$
$937$		−	8.64637i		−	0.282464i	0.989976	−	0.141232i	$-0.0451064\pi$
$938$	−4.37757	−	10.3678i	−0.142933	−	0.338522i
$939$	−12.0140	−	16.0401i	−0.392061	−	0.523448i
$940$	−7.89034			−0.257354
$941$	5.04603	−	8.73997i	0.164496	−	0.284915i	−0.771980	−	0.635646i	$-0.780734\pi$
$941$	5.04603	−	8.73997i	0.164496	−	0.284915i	0.936476	+	0.350731i	$0.114067\pi$
$942$	−1.64110	−	13.6954i	−0.0534701	−	0.446220i
$943$	2.82044	−	1.62838i	0.0918460	−	0.0530273i
$944$	−11.0296			−0.358983
$945$	−13.5037	−	14.2848i	−0.439277	−	0.464683i
$946$	19.8932			0.646783
$947$	50.4627	−	29.1346i	1.63982	−	0.946749i	0.658922	−	0.752212i	$-0.271013\pi$
$947$	50.4627	−	29.1346i	1.63982	−	0.946749i	0.980895	−	0.194537i	$-0.0623205\pi$
$948$	3.00087	+	25.0430i	0.0974638	+	0.813358i
$949$	−0.735619	+	1.27413i	−0.0238792	+	0.0413600i
$950$	6.40483			0.207800
$951$	−17.8183	−	23.7896i	−0.577799	−	0.771430i
$952$	−3.64593	+	4.81916i	−0.118165	+	0.156190i
$953$			46.9356i			1.52039i	0.649694	+	0.760196i	$0.274897\pi$
$953$			46.9356i			1.52039i	−0.649694	+	0.760196i	$0.725103\pi$
$954$	8.34233	−	28.4662i	0.270093	−	0.921628i
$955$	−9.12541	+	5.26856i	−0.295291	+	0.170487i
$956$			27.2885i			0.882572i
$957$	−1.87918	−	0.804131i	−0.0607451	−	0.0259939i
$958$	−24.0776	+	13.9012i	−0.777912	+	0.449128i
$959$	−9.93800	−	23.5371i	−0.320915	−	0.760054i
$960$	0.294657	+	2.45898i	0.00951002	+	0.0793633i
$961$	−6.07230	−	10.5175i	−0.195881	−	0.339275i
$962$	−6.83054	−	11.8308i	−0.220225	−	0.381441i
$963$	−45.5490	−	13.3486i	−1.46780	−	0.430153i
$964$	21.9018	+	12.6450i	0.705410	+	0.407269i
$965$	2.02008	−	3.49889i	0.0650288	−	0.112633i
$966$	−18.6081	+	31.8745i	−0.598707	+	1.02554i
$967$	6.43145	+	11.1396i	0.206822	+	0.358226i	0.950712	−	0.310077i	$-0.100355\pi$
$967$	6.43145	+	11.1396i	0.206822	+	0.358226i	−0.743890	+	0.668302i	$0.767021\pi$
$968$			0.692610i			0.0222613i
$969$	−8.51209	+	1.01999i	−0.273448	+	0.0327670i
$970$	15.1685			0.487031
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	0.440134	+	0.897932i	$0.354931\pi$
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	−0.997699	+	0.0677990i	$0.978402\pi$
$972$	−15.5473	+	1.13232i	−0.498679	+	0.0363193i
$973$	29.6169	−	39.1474i	0.949474	−	1.25501i
$974$	6.47506	+	3.73838i	0.207474	+	0.119785i
$975$	19.4477	+	25.9650i	0.622826	+	0.831546i
$976$	9.94175	+	5.73987i	0.318228	+	0.183729i
$977$	−17.6381	−	10.1834i	−0.564293	−	0.325795i	0.190574	−	0.981673i	$-0.438965\pi$
$977$	−17.6381	−	10.1834i	−0.564293	−	0.325795i	−0.754867	+	0.655878i	$0.772299\pi$
$978$	−19.5795	+	2.34619i	−0.626084	+	0.0750230i
$979$	12.0215	+	6.94060i	0.384208	+	0.221822i
$980$	−2.72213	−	9.63167i	−0.0869553	−	0.307673i
$981$	−21.1559	−	22.1645i	−0.675456	−	0.707659i
$982$	11.0543	−	19.1466i	0.352756	−	0.610992i
$983$	−29.3364			−0.935686			−0.467843	−	0.883811i	$-0.654969\pi$
$983$	−29.3364			−0.935686			−0.467843	+	0.883811i	$0.654969\pi$
$984$	0.419863	+	0.560567i	0.0133847	+	0.0178702i
$985$			37.3023i			1.18855i
$986$	−0.394124	−	0.682643i	−0.0125515	−	0.0217398i
$987$	12.7494	−	21.8389i	0.405818	−	0.695139i
$988$	−6.86651	+	11.8931i	−0.218453	+	0.378371i
$989$	40.5786	+	23.4280i	1.29032	+	0.744968i
$990$	−10.1275	−	10.6104i	−0.321874	−	0.337220i
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	0.528933	−	0.848664i	$-0.322592\pi$
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	−0.999431	+	0.0337371i	$0.989259\pi$
$992$	2.17114	+	3.76052i	0.0689338	+	0.119397i
$993$	36.7276	−	27.5089i	1.16551	−	0.872967i
$994$	7.49861	+	5.67306i	0.237842	+	0.179938i
$995$	19.0901	−	11.0217i	0.605196	−	0.349410i
$996$	2.25032	−	1.68548i	0.0713041	−	0.0534066i
$997$		−	27.0213i		−	0.855772i	−0.903833	−	0.427886i	$-0.859258\pi$
$997$		−	27.0213i		−	0.855772i	0.903833	−	0.427886i	$-0.140742\pi$
$998$	28.4959	−	16.4521i	0.902022	−	0.520783i
$999$	11.0478	+	1.84890i	0.349536	+	0.0584965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.t.a.47.6	yes	16
3.2	odd	2		378.2.t.a.89.2		16
4.3	odd	2		1008.2.df.c.929.6		16
7.2	even	3		882.2.m.a.587.4		16
7.3	odd	6		126.2.l.a.101.7	yes	16
7.4	even	3		882.2.l.b.227.6		16
7.5	odd	6		882.2.m.b.587.1		16
7.6	odd	2		882.2.t.a.803.7		16
9.2	odd	6		1134.2.k.a.971.7		16
9.4	even	3		378.2.l.a.341.6		16
9.5	odd	6		126.2.l.a.5.3	✓	16
9.7	even	3		1134.2.k.b.971.2		16
12.11	even	2		3024.2.df.c.1601.3		16
21.2	odd	6		2646.2.m.a.1763.7		16
21.5	even	6		2646.2.m.b.1763.6		16
21.11	odd	6		2646.2.l.a.521.3		16
21.17	even	6		378.2.l.a.143.2		16
21.20	even	2		2646.2.t.b.1979.3		16
28.3	even	6		1008.2.ca.c.353.3		16
36.23	even	6		1008.2.ca.c.257.3		16
36.31	odd	6		3024.2.ca.c.2609.3		16
63.4	even	3		2646.2.t.b.2285.3		16
63.5	even	6		882.2.m.a.293.4		16
63.13	odd	6		2646.2.l.a.1097.7		16
63.23	odd	6		882.2.m.b.293.1		16
63.31	odd	6		378.2.t.a.17.2		16
63.32	odd	6		882.2.t.a.815.7		16
63.38	even	6		1134.2.k.b.647.2		16
63.40	odd	6		2646.2.m.a.881.7		16
63.41	even	6		882.2.l.b.509.2		16
63.52	odd	6		1134.2.k.a.647.7		16
63.58	even	3		2646.2.m.b.881.6		16
63.59	even	6	inner	126.2.t.a.59.6	yes	16
84.59	odd	6		3024.2.ca.c.2033.3		16
252.31	even	6		3024.2.df.c.17.3		16
252.59	odd	6		1008.2.df.c.689.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	9.5	odd	6
126.2.l.a.101.7	yes	16	7.3	odd	6
126.2.t.a.47.6	yes	16	1.1	even	1	trivial
126.2.t.a.59.6	yes	16	63.59	even	6	inner
378.2.l.a.143.2		16	21.17	even	6
378.2.l.a.341.6		16	9.4	even	3
378.2.t.a.17.2		16	63.31	odd	6
378.2.t.a.89.2		16	3.2	odd	2
882.2.l.b.227.6		16	7.4	even	3
882.2.l.b.509.2		16	63.41	even	6
882.2.m.a.293.4		16	63.5	even	6
882.2.m.a.587.4		16	7.2	even	3
882.2.m.b.293.1		16	63.23	odd	6
882.2.m.b.587.1		16	7.5	odd	6
882.2.t.a.803.7		16	7.6	odd	2
882.2.t.a.815.7		16	63.32	odd	6
1008.2.ca.c.257.3		16	36.23	even	6
1008.2.ca.c.353.3		16	28.3	even	6
1008.2.df.c.689.6		16	252.59	odd	6
1008.2.df.c.929.6		16	4.3	odd	2
1134.2.k.a.647.7		16	63.52	odd	6
1134.2.k.a.971.7		16	9.2	odd	6
1134.2.k.b.647.2		16	63.38	even	6
1134.2.k.b.971.2		16	9.7	even	3
2646.2.l.a.521.3		16	21.11	odd	6
2646.2.l.a.1097.7		16	63.13	odd	6
2646.2.m.a.881.7		16	63.40	odd	6
2646.2.m.a.1763.7		16	21.2	odd	6
2646.2.m.b.881.6		16	63.58	even	3
2646.2.m.b.1763.6		16	21.5	even	6
2646.2.t.b.1979.3		16	21.20	even	2
2646.2.t.b.2285.3		16	63.4	even	3
3024.2.ca.c.2033.3		16	84.59	odd	6
3024.2.ca.c.2609.3		16	36.31	odd	6
3024.2.df.c.17.3		16	252.31	even	6
3024.2.df.c.1601.3		16	12.11	even	2

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.206076 - 1.71975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.42985 q^{5} +(-1.03834 - 1.38631i) q^{6} +(-2.43739 + 1.02913i) q^{7} -1.00000i q^{8} +(-2.91507 + 0.708796i) q^{9} +(1.23829 - 0.714925i) q^{10} +3.41945i q^{11} +(-1.59238 - 0.681407i) q^{12} +(5.48813 - 3.16857i) q^{13} +(-1.59628 + 2.10995i) q^{14} +(-0.294657 - 2.45898i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.14201 + 1.97802i) q^{17} +(-2.17012 + 2.07137i) q^{18} +(-1.87673 - 1.08353i) q^{19} +(0.714925 - 1.23829i) q^{20} +(2.27213 + 3.97962i) q^{21} +(1.70972 + 2.96133i) q^{22} +8.05411i q^{23} +(-1.71975 + 0.206076i) q^{24} -2.95553 q^{25} +(3.16857 - 5.48813i) q^{26} +(1.81967 + 4.86711i) q^{27} +(-0.327442 + 2.62541i) q^{28} +(-0.298879 - 0.172558i) q^{29} +(-1.48467 - 1.98221i) q^{30} +(-3.76052 - 2.17114i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.88058 - 0.704664i) q^{33} +(1.97802 + 1.14201i) q^{34} +(-3.48511 + 1.47150i) q^{35} +(-0.843698 + 2.87892i) q^{36} +(1.07786 - 1.86690i) q^{37} -2.16707 q^{38} +(-6.58012 - 8.78524i) q^{39} -1.42985i q^{40} +(-0.202180 - 0.350186i) q^{41} +(3.95754 + 2.31039i) q^{42} +(2.90883 - 5.03824i) q^{43} +(2.96133 + 1.70972i) q^{44} +(-4.16811 + 1.01347i) q^{45} +(4.02706 + 6.97507i) q^{46} +(-2.75915 - 4.77898i) q^{47} +(-1.38631 + 1.03834i) q^{48} +(4.88178 - 5.01680i) q^{49} +(-2.55956 + 1.47776i) q^{50} +(3.16635 - 2.37159i) q^{51} -6.33715i q^{52} +(-8.56310 + 4.94391i) q^{53} +(4.00944 + 3.30521i) q^{54} +4.88930i q^{55} +(1.02913 + 2.43739i) q^{56} +(-1.47666 + 3.45080i) q^{57} -0.345115 q^{58} +(5.51480 - 9.55191i) q^{59} +(-2.27687 - 0.974311i) q^{60} +(-9.94175 + 5.73987i) q^{61} -4.34228 q^{62} +(6.37572 - 4.72760i) q^{63} -1.00000 q^{64} +(7.84721 - 4.53059i) q^{65} +(4.74040 - 3.55055i) q^{66} +(-2.12683 + 3.68377i) q^{67} +2.28402 q^{68} +(13.8510 - 1.65976i) q^{69} +(-2.28244 + 3.01691i) q^{70} -3.55393i q^{71} +(0.708796 + 2.91507i) q^{72} +(-0.201057 + 0.116080i) q^{73} -2.15571i q^{74} +(0.609062 + 5.08276i) q^{75} +(-1.87673 + 1.08353i) q^{76} +(-3.51906 - 8.33454i) q^{77} +(-10.0912 - 4.31818i) q^{78} +(-7.28100 - 12.6111i) q^{79} +(-0.714925 - 1.23829i) q^{80} +(7.99522 - 4.13237i) q^{81} +(-0.350186 - 0.202180i) q^{82} +(-0.811624 + 1.40577i) q^{83} +(4.58252 + 0.0220855i) q^{84} +(1.63290 + 2.82827i) q^{85} -5.81766i q^{86} +(-0.235164 + 0.549556i) q^{87} +3.41945 q^{88} +(2.02974 - 3.51562i) q^{89} +(-3.10295 + 2.96175i) q^{90} +(-10.1159 + 13.3711i) q^{91} +(6.97507 + 4.02706i) q^{92} +(-2.95886 + 6.91457i) q^{93} +(-4.77898 - 2.75915i) q^{94} +(-2.68345 - 1.54929i) q^{95} +(-0.681407 + 1.59238i) q^{96} +(9.18719 + 5.30423i) q^{97} +(1.71934 - 6.78556i) q^{98} +(-2.42369 - 9.96791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

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