LMFDB - Embedded newform 273.2.r.b.269.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.22
Character	$\chi$	$=$	273.269
Dual form			273.2.r.b.68.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.05456i q^{2} +(1.46610 + 0.922247i) q^{3} +0.887893 q^{4} +(-0.000964697 - 0.00167090i) q^{5} +(-0.972570 + 1.54610i) q^{6} +(-2.64511 - 0.0584461i) q^{7} +3.04547i q^{8} +(1.29892 + 2.70422i) q^{9} +(0.00176208 - 0.00101734i) q^{10} +(-2.16237 + 1.24844i) q^{11} +(1.30174 + 0.818857i) q^{12} +(0.922193 - 3.48562i) q^{13} +(0.0616352 - 2.78943i) q^{14} +(0.000126641 - 0.00333941i) q^{15} -1.43586 q^{16} +4.17524 q^{17} +(-2.85178 + 1.36979i) q^{18} +(4.64914 + 2.68418i) q^{19} +(-0.000856548 - 0.00148358i) q^{20} +(-3.82410 - 2.52513i) q^{21} +(-1.31657 - 2.28036i) q^{22} -4.87067i q^{23} +(-2.80868 + 4.46497i) q^{24} +(2.50000 - 4.33012i) q^{25} +(3.67581 + 0.972512i) q^{26} +(-0.589610 + 5.16259i) q^{27} +(-2.34857 - 0.0518939i) q^{28} +(-7.57023 - 4.37067i) q^{29} +(0.00352162 + 0.000133551i) q^{30} +(-6.57778 - 3.79768i) q^{31} +4.57673i q^{32} +(-4.32163 - 0.163891i) q^{33} +4.40306i q^{34} +(0.00245407 + 0.00447610i) q^{35} +(1.15330 + 2.40106i) q^{36} +3.65572 q^{37} +(-2.83065 + 4.90282i) q^{38} +(4.56664 - 4.25979i) q^{39} +(0.00508869 - 0.00293796i) q^{40} +(1.83038 - 3.17031i) q^{41} +(2.66291 - 4.03276i) q^{42} +(1.32938 + 2.30256i) q^{43} +(-1.91995 + 1.10849i) q^{44} +(0.00326543 - 0.00477912i) q^{45} +5.13644 q^{46} +(1.79190 + 3.10366i) q^{47} +(-2.10512 - 1.32422i) q^{48} +(6.99317 + 0.309192i) q^{49} +(4.56640 + 2.63641i) q^{50} +(6.12133 + 3.85060i) q^{51} +(0.818809 - 3.09486i) q^{52} +(-12.3735 - 7.14382i) q^{53} +(-5.44429 - 0.621782i) q^{54} +(0.00417206 + 0.00240874i) q^{55} +(0.177996 - 8.05559i) q^{56} +(4.34064 + 8.22295i) q^{57} +(4.60916 - 7.98330i) q^{58} -5.23130 q^{59} +(0.000112444 - 0.00296504i) q^{60} +(6.56379 + 3.78960i) q^{61} +(4.00490 - 6.93670i) q^{62} +(-3.27773 - 7.22887i) q^{63} -7.69818 q^{64} +(-0.00671378 + 0.00182167i) q^{65} +(0.172833 - 4.55744i) q^{66} +(-7.12713 - 12.3445i) q^{67} +3.70716 q^{68} +(4.49197 - 7.14091i) q^{69} +(-0.00472034 + 0.00258797i) q^{70} +(1.24050 - 0.716205i) q^{71} +(-8.23562 + 3.95582i) q^{72} +(1.61067 + 0.929921i) q^{73} +3.85519i q^{74} +(7.65870 - 4.04279i) q^{75} +(4.12794 + 2.38327i) q^{76} +(5.79266 - 3.17589i) q^{77} +(4.49223 + 4.81581i) q^{78} +(3.64483 + 6.31302i) q^{79} +(0.00138517 + 0.00239918i) q^{80} +(-5.62562 + 7.02513i) q^{81} +(3.34329 + 1.93025i) q^{82} +10.4089 q^{83} +(-3.39539 - 2.24205i) q^{84} +(-0.00402784 - 0.00697642i) q^{85} +(-2.42820 + 1.40192i) q^{86} +(-7.06790 - 13.3895i) q^{87} +(-3.80210 - 6.58543i) q^{88} -5.40380 q^{89} +(0.00503989 + 0.00344361i) q^{90} +(-2.64302 + 9.16594i) q^{91} -4.32464i q^{92} +(-6.14130 - 11.6341i) q^{93} +(-3.27301 + 1.88967i) q^{94} -0.0103577i q^{95} +(-4.22088 + 6.70997i) q^{96} +(2.07015 - 1.19520i) q^{97} +(-0.326063 + 7.37475i) q^{98} +(-6.18481 - 4.22589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.05456i			0.745690i	0.927894	+	0.372845i	$0.121618\pi$
$2$			1.05456i			0.745690i	−0.927894	+	0.372845i	$0.878382\pi$
$3$	1.46610	+	0.922247i	0.846455	+	0.532460i
$3$	1.46610	+	0.922247i	0.846455	+	0.532460i
$4$	0.887893			0.443947
$5$	−0.000964697	−	0.00167090i	−0.000431425	−	0.000747251i	0.865810	−	0.500374i	$-0.166804\pi$
$5$	−0.000964697	−	0.00167090i	−0.000431425	−	0.000747251i	−0.866241	+	0.499626i	$0.833471\pi$
$6$	−0.972570	+	1.54610i	−0.397050	+	0.631193i
$7$	−2.64511	−	0.0584461i	−0.999756	−	0.0220905i
$7$	−2.64511	−	0.0584461i	−0.999756	−	0.0220905i
$8$			3.04547i			1.07674i
$9$	1.29892	+	2.70422i	0.432973	+	0.901407i
$10$	0.00176208	−	0.00101734i	0.000557217	−	0.000321710i
$11$	−2.16237	+	1.24844i	−0.651979	+	0.376420i	−0.789214	−	0.614118i	$-0.789512\pi$
$11$	−2.16237	+	1.24844i	−0.651979	+	0.376420i	0.137235	+	0.990539i	$0.456178\pi$
$12$	1.30174	+	0.818857i	0.375781	+	0.236384i
$13$	0.922193	−	3.48562i	0.255770	−	0.966738i
$13$	0.922193	−	3.48562i	0.255770	−	0.966738i
$14$	0.0616352	−	2.78943i	0.0164727	−	0.745508i
$15$	0.000126641	−	0.00333941i	3.26987e−5	−	0.000862231i
$16$	−1.43586			−0.358965
$17$	4.17524			1.01264			0.506322	−	0.862345i	$-0.331005\pi$
$17$	4.17524			1.01264			0.506322	+	0.862345i	$0.331005\pi$
$18$	−2.85178	+	1.36979i	−0.672170	+	0.322864i
$19$	4.64914	+	2.68418i	1.06659	+	0.615794i	0.927247	−	0.374450i	$-0.122169\pi$
$19$	4.64914	+	2.68418i	1.06659	+	0.615794i	0.139340	+	0.990245i	$0.455502\pi$
$20$	−0.000856548	−	0.00148358i	−0.000191530	−	0.000331740i
$21$	−3.82410	−	2.52513i	−0.834486	−	0.551029i
$22$	−1.31657	−	2.28036i	−0.280693	−	0.486174i
$23$		−	4.87067i		−	1.01561i	−0.861473	−	0.507803i	$-0.830458\pi$
$23$		−	4.87067i		−	1.01561i	0.861473	−	0.507803i	$-0.169542\pi$
$24$	−2.80868	+	4.46497i	−0.573319	+	0.911409i
$25$	2.50000	−	4.33012i	0.500000	−	0.866025i
$26$	3.67581	+	0.972512i	0.720886	+	0.190725i
$27$	−0.589610	+	5.16259i	−0.113470	+	0.993541i
$28$	−2.34857	−	0.0518939i	−0.443838	−	0.00980702i
$29$	−7.57023	−	4.37067i	−1.40576	−	0.811614i	−0.410781	−	0.911734i	$-0.634744\pi$
$29$	−7.57023	−	4.37067i	−1.40576	−	0.811614i	−0.994975	+	0.100120i	$0.968077\pi$
$30$	0.00352162		0.000133551i	0.000642957		2.43831e-5i
$31$	−6.57778	−	3.79768i	−1.18140	−	0.682084i	−0.225065	−	0.974344i	$-0.572260\pi$
$31$	−6.57778	−	3.79768i	−1.18140	−	0.682084i	−0.956339	+	0.292260i	$0.905593\pi$
$32$			4.57673i			0.809060i
$33$	−4.32163	−	0.163891i	−0.752300	−	0.0285297i
$34$			4.40306i			0.755118i
$35$	0.00245407	+	0.00447610i	0.000414813	+	0.000756599i
$36$	1.15330	+	2.40106i	0.192217	+	0.400177i
$37$	3.65572			0.600996			0.300498	−	0.953782i	$-0.402847\pi$
$37$	3.65572			0.600996			0.300498	+	0.953782i	$0.402847\pi$
$38$	−2.83065	+	4.90282i	−0.459191	+	0.795343i
$39$	4.56664	−	4.25979i	0.731247	−	0.682113i
$40$	0.00508869	−	0.00293796i	0.000804592	−	0.000464531i
$41$	1.83038	−	3.17031i	0.285857	−	0.495119i	−0.686960	−	0.726696i	$-0.741055\pi$
$41$	1.83038	−	3.17031i	0.285857	−	0.495119i	0.972817	+	0.231577i	$0.0743884\pi$
$42$	2.66291	−	4.03276i	0.410896	−	0.622268i
$43$	1.32938	+	2.30256i	0.202729	+	0.351137i	0.949407	−	0.314049i	$-0.101686\pi$
$43$	1.32938	+	2.30256i	0.202729	+	0.351137i	−0.746678	+	0.665186i	$0.768352\pi$
$44$	−1.91995	+	1.10849i	−0.289444	+	0.167110i
$45$	0.00326543	−	0.00477912i	0.000486781	−	0.000712429i
$46$	5.13644			0.757327
$47$	1.79190	+	3.10366i	0.261375	+	0.452715i	0.966608	−	0.256261i	$-0.0824907\pi$
$47$	1.79190	+	3.10366i	0.261375	+	0.452715i	−0.705232	+	0.708976i	$0.749157\pi$
$48$	−2.10512	−	1.32422i	−0.303848	−	0.191134i
$49$	6.99317	+	0.309192i	0.999024	+	0.0441703i
$50$	4.56640	+	2.63641i	0.645786	+	0.372845i
$51$	6.12133	+	3.85060i	0.857158	+	0.539192i
$52$	0.818809	−	3.09486i	0.113548	−	0.429180i
$53$	−12.3735	−	7.14382i	−1.69962	−	0.981279i	−0.946108	−	0.323850i	$-0.895023\pi$
$53$	−12.3735	−	7.14382i	−1.69962	−	0.981279i	−0.753516	−	0.657429i	$-0.771644\pi$
$54$	−5.44429	−	0.621782i	−0.740874	−	0.0846138i
$55$	0.00417206	+	0.00240874i	0.000562561	+	0.000324795i
$56$	0.177996	−	8.05559i	0.0237857	−	1.07647i
$57$	4.34064	+	8.22295i	0.574932	+	1.08916i
$58$	4.60916	−	7.98330i	0.605212	−	1.04826i
$59$	−5.23130			−0.681057			−0.340529	−	0.940234i	$-0.610606\pi$
$59$	−5.23130			−0.681057			−0.340529	+	0.940234i	$0.610606\pi$
$60$	0.000112444	−	0.00296504i	1.45165e−5	−	0.000382785i
$61$	6.56379	+	3.78960i	0.840407	+	0.485209i	0.857402	−	0.514647i	$-0.172077\pi$
$61$	6.56379	+	3.78960i	0.840407	+	0.485209i	−0.0169958	+	0.999856i	$0.505410\pi$
$62$	4.00490	−	6.93670i	0.508623	−	0.880961i
$63$	−3.27773	−	7.22887i	−0.412955	−	0.910751i
$64$	−7.69818			−0.962273
$65$	−0.00671378	+	0.00182167i	−0.000832741	+	0.000225951i
$66$	0.172833	−	4.55744i	0.0212743	−	0.560982i
$67$	−7.12713	−	12.3445i	−0.870717	−	1.50813i	−0.861256	−	0.508172i	$-0.830322\pi$
$67$	−7.12713	−	12.3445i	−0.870717	−	1.50813i	−0.00946155	−	0.999955i	$-0.503012\pi$
$68$	3.70716			0.449560
$69$	4.49197	−	7.14091i	0.540769	−	0.859665i
$70$	−0.00472034	+	0.00258797i	−0.000564188	+	0.000309322i
$71$	1.24050	−	0.716205i	0.147221	−	0.0849979i	−0.424580	−	0.905390i	$-0.639578\pi$
$71$	1.24050	−	0.716205i	0.147221	−	0.0849979i	0.571801	+	0.820392i	$0.306245\pi$
$72$	−8.23562	+	3.95582i	−0.970577	+	0.466198i
$73$	1.61067	+	0.929921i	0.188515	+	0.108839i	0.591287	−	0.806461i	$-0.298620\pi$
$73$	1.61067	+	0.929921i	0.188515	+	0.108839i	−0.402772	+	0.915300i	$0.631953\pi$
$74$			3.85519i			0.448157i
$75$	7.65870	−	4.04279i	0.884351	−	0.466822i
$76$	4.12794	+	2.38327i	0.473508	+	0.273380i
$77$	5.79266	−	3.17589i	0.660135	−	0.361926i
$78$	4.49223	+	4.81581i	0.508644	+	0.545284i
$79$	3.64483	+	6.31302i	0.410075	+	0.710271i	0.994898	−	0.100891i	$-0.0321692\pi$
$79$	3.64483	+	6.31302i	0.410075	+	0.710271i	−0.584823	+	0.811161i	$0.698836\pi$
$80$	0.00138517	+	0.00239918i	0.000154867	+	0.000268237i
$81$	−5.62562	+	7.02513i	−0.625069	+	0.780570i
$82$	3.34329	+	1.93025i	0.369205	+	0.213161i
$83$	10.4089			1.14253			0.571263	−	0.820767i	$-0.306454\pi$
$83$	10.4089			1.14253			0.571263	+	0.820767i	$0.306454\pi$
$84$	−3.39539	−	2.24205i	−0.370467	−	0.244627i
$85$	−0.00402784	−	0.00697642i	−0.000436880	−	0.000756699i
$86$	−2.42820	+	1.40192i	−0.261839	+	0.151173i
$87$	−7.06790	−	13.3895i	−0.757758	−	1.43550i
$88$	−3.80210	−	6.58543i	−0.405305	−	0.702009i
$89$	−5.40380			−0.572801			−0.286401	−	0.958110i	$-0.592459\pi$
$89$	−5.40380			−0.572801			−0.286401	+	0.958110i	$0.592459\pi$
$90$	0.00503989	+	0.00344361i	0.000531251	+	0.000362988i
$91$	−2.64302	+	9.16594i	−0.277064	+	0.960852i
$92$		−	4.32464i		−	0.450875i
$93$	−6.14130	−	11.6341i	−0.636824	−	1.20640i
$94$	−3.27301	+	1.88967i	−0.337585	+	0.194905i
$95$		−	0.0103577i		−	0.00106268i
$96$	−4.22088	+	6.70997i	−0.430792	+	0.684833i
$97$	2.07015	−	1.19520i	0.210192	−	0.121354i	−0.391209	−	0.920302i	$-0.627943\pi$
$97$	2.07015	−	1.19520i	0.210192	−	0.121354i	0.601401	+	0.798948i	$0.294610\pi$
$98$	−0.326063	+	7.37475i	−0.0329373	+	0.744962i
$99$	−6.18481	−	4.22589i	−0.621597	−	0.424718i
$100$	2.21973	−	3.84469i	0.221973	−	0.384469i
$101$	9.02995	+	15.6403i	0.898514	+	1.55627i	0.829395	+	0.558663i	$0.188685\pi$
$101$	9.02995	+	15.6403i	0.898514	+	1.55627i	0.0691187	+	0.997608i	$0.477981\pi$
$102$	−4.06071	+	6.45534i	−0.402070	+	0.639174i
$103$	−8.45144	+	4.87944i	−0.832745	+	0.480786i	−0.854792	−	0.518971i	$-0.826315\pi$
$103$	−8.45144	+	4.87944i	−0.832745	+	0.480786i	0.0220466	+	0.999757i	$0.492982\pi$
$104$	10.6154	+	2.80851i	1.04092	+	0.275397i
$105$	−0.000530155		0.00882568i	−5.17378e−5		0.000861298i
$106$	7.53362	−	13.0486i	0.731730	−	1.26739i
$107$			5.46272i			0.528101i	0.964509	+	0.264051i	$0.0850586\pi$
$107$			5.46272i			0.528101i	−0.964509	+	0.264051i	$0.914941\pi$
$108$	−0.523511	+	4.58383i	−0.0503748	+	0.441079i
$109$	−3.68535	+	6.38321i	−0.352993	+	0.611401i	−0.986772	−	0.162113i	$-0.948169\pi$
$109$	−3.68535	+	6.38321i	−0.352993	+	0.611401i	0.633780	+	0.773514i	$0.281503\pi$
$110$	−0.00254017	+	0.00439971i	−0.000242196	+	0.000419496i
$111$	5.35966	+	3.37147i	0.508716	+	0.320006i
$112$	3.79800	+	0.0839203i	0.358877	+	0.00792972i
$113$	0.390686	−	0.225562i	0.0367526	−	0.0212191i	−0.481511	−	0.876440i	$-0.659912\pi$
$113$	0.390686	−	0.225562i	0.0367526	−	0.0212191i	0.518264	+	0.855221i	$0.326579\pi$
$114$	−8.67164	+	4.57749i	−0.812173	+	0.428721i
$115$	−0.00813843	+	0.00469872i	−0.000758912	+	0.000438158i
$116$	−6.72156	−	3.88069i	−0.624081	−	0.360313i
$117$	10.6237	−	2.03373i	0.982166	−	0.188018i
$118$		−	5.51674i		−	0.507857i
$119$	−11.0439	−	0.244026i	−1.01240	−	0.0223698i
$120$	0.0101701		0.000385682i	0.000928396		3.52078e-5i
$121$	−2.38277	+	4.12708i	−0.216616	+	0.375189i
$122$	−3.99638	+	6.92194i	−0.361815	+	0.626683i
$123$	5.60733	−	2.95994i	0.505596	−	0.266889i
$124$	−5.84037	−	3.37194i	−0.524481	−	0.302809i
$125$	−0.0192939			−0.00172570
$126$	7.62331	−	3.45658i	0.679138	−	0.307936i
$127$	−4.71924	+	8.17397i	−0.418765	+	0.725322i	−0.995816	−	0.0913863i	$-0.970870\pi$
$127$	−4.71924	+	8.17397i	−0.418765	+	0.725322i	0.577051	+	0.816708i	$0.304204\pi$
$128$			1.03524i			0.0915032i
$129$	−0.174516	+	4.60181i	−0.0153653	+	0.405167i
$130$	−0.00192107	−	0.00708011i	−0.000168489	−	0.000620967i
$131$	−3.11100	−	5.38841i	−0.271809	−	0.470788i	0.697516	−	0.716569i	$-0.254289\pi$
$131$	−3.11100	−	5.38841i	−0.271809	−	0.470788i	−0.969325	+	0.245782i	$0.920955\pi$
$132$	−3.83715	−	0.145517i	−0.333981	−	0.0126657i
$133$	−12.1406	−	7.37168i	−1.05272	−	0.639205i
$134$	13.0181	−	7.51602i	1.12459	−	0.649285i
$135$	0.00919499	−	0.00399515i	0.000791379	−	0.000343848i
$136$			12.7156i			1.09035i
$137$		−	6.15626i		−	0.525965i	−0.964801	−	0.262983i	$-0.915294\pi$
$137$		−	6.15626i		−	0.525965i	0.964801	−	0.262983i	$-0.0847062\pi$
$138$	7.53055	+	4.73707i	0.641043	+	0.403246i
$139$	−10.6666	+	6.15838i	−0.904731	+	0.522347i	−0.878732	−	0.477315i	$-0.841610\pi$
$139$	−10.6666	+	6.15838i	−0.904731	+	0.522347i	−0.0259992	+	0.999662i	$0.508277\pi$
$140$	0.00217895	+	0.00397430i	0.000184155	+	0.000335890i
$141$	−0.235233	+	6.20286i	−0.0198102	+	0.522375i
$142$	0.755285	+	1.30819i	0.0633821	+	0.109781i
$143$	2.35748	+	8.68851i	0.197143	+	0.726570i
$144$	−1.86506	−	3.88288i	−0.155422	−	0.323573i
$145$			0.0168655i			0.00140060i
$146$	−0.980661	+	1.69856i	−0.0811601	+	0.140573i
$147$	9.96756	+	6.90274i	0.822110	+	0.569328i
$148$	3.24589			0.266810
$149$	6.20222	+	3.58086i	0.508106	+	0.293355i	0.732055	−	0.681246i	$-0.238562\pi$
$149$	6.20222	+	3.58086i	0.508106	+	0.293355i	−0.223949	+	0.974601i	$0.571895\pi$
$150$	4.26339	+	8.07660i	0.348104	+	0.659451i
$151$	−8.14880	+	14.1141i	−0.663140	+	1.14859i	0.316646	+	0.948544i	$0.397443\pi$
$151$	−8.14880	+	14.1141i	−0.663140	+	1.14859i	−0.979786	+	0.200049i	$0.935890\pi$
$152$	−8.17460	+	14.1588i	−0.663048	+	1.14843i
$153$	5.42330	+	11.2908i	0.438447	+	0.912804i
$154$	3.34918	+	6.10874i	0.269884	+	0.492256i
$155$			0.0146545i			0.00117707i
$156$	4.05469	−	3.78224i	0.324635	−	0.302822i
$157$	4.07713	+	2.35393i	0.325391	+	0.187864i	0.653793	−	0.756674i	$-0.273177\pi$
$157$	4.07713	+	2.35393i	0.325391	+	0.187864i	−0.328402	+	0.944538i	$0.606510\pi$
$158$	−6.65749	+	3.84370i	−0.529642	+	0.305789i
$159$	−11.5524	−	21.8850i	−0.916165	−	1.73559i
$160$	0.00764728	−	0.00441516i	0.000604571	−	0.000349049i
$161$	−0.284672	+	12.8834i	−0.0224353	+	1.01536i
$162$	−7.40845	−	5.93258i	−0.582063	−	0.466107i
$163$	2.10316	−	3.64278i	0.164732	−	0.285324i	−0.771828	−	0.635831i	$-0.780657\pi$
$163$	2.10316	−	3.64278i	0.164732	−	0.285324i	0.936560	+	0.350507i	$0.113991\pi$
$164$	1.62518	−	2.81490i	0.126905	−	0.219806i
$165$	0.00389522	+	0.00737914i	0.000303242	+	0.000574465i
$166$			10.9769i			0.851970i
$167$	7.24993	−	12.5573i	0.561017	−	0.971709i	−0.436391	−	0.899757i	$-0.643744\pi$
$167$	7.24993	−	12.5573i	0.561017	−	0.971709i	0.997408	−	0.0719525i	$-0.0229230\pi$
$168$	7.69021	−	11.6462i	0.593312	−	0.898522i
$169$	−11.2991	−	6.42883i	−0.869163	−	0.494526i
$170$	0.00735708	−	0.00424761i	0.000564263	−	0.000325777i
$171$	−1.21976	+	16.0588i	−0.0932776	+	1.22805i
$172$	1.18035	+	2.04443i	0.0900009	+	0.155886i
$173$	7.84836	−	13.5938i	0.596700	−	1.03351i	−0.396605	−	0.917989i	$-0.629812\pi$
$173$	7.84836	−	13.5938i	0.596700	−	1.03351i	0.993305	−	0.115525i	$-0.0368550\pi$
$174$	14.1201	−	7.45356i	1.07044	−	0.565053i
$175$	−6.86584	+	11.3075i	−0.519009	+	0.854768i
$176$	3.10486	−	1.79259i	0.234037	−	0.135122i
$177$	−7.66963	−	4.82455i	−0.576484	−	0.362636i
$178$		−	5.69865i		−	0.427132i
$179$	−5.59852	+	3.23231i	−0.418453	+	0.241594i	−0.694415	−	0.719575i	$-0.744337\pi$
$179$	−5.59852	+	3.23231i	−0.418453	+	0.241594i	0.275962	+	0.961168i	$0.411004\pi$
$180$	0.00289935	−	0.00424335i	0.000216105	−	0.000316281i
$181$			0.939369i			0.0698227i	0.999390	+	0.0349114i	$0.0111149\pi$
$181$			0.939369i			0.0698227i	−0.999390	+	0.0349114i	$0.988885\pi$
$182$	−9.66608	−	2.78723i	−0.716497	−	0.206604i
$183$	6.12824	+	11.6094i	0.453012	+	0.858190i
$184$	14.8335			1.09354
$185$	−0.00352666	−	0.00610835i	−0.000259285	−	0.000449095i
$186$	12.2690	−	6.47640i	0.899603	−	0.474873i
$187$	−9.02840	+	5.21255i	−0.660222	+	0.381179i
$188$	1.59101	+	2.75572i	0.116037	+	0.200981i
$189$	1.86131	−	13.6211i	0.135391	−	0.990792i
$190$	0.0109229			0.000792428
$191$	4.65873	+	2.68972i	0.337094	+	0.194621i	0.658986	−	0.752155i	$-0.270986\pi$
$191$	4.65873	+	2.68972i	0.337094	+	0.194621i	−0.321892	+	0.946776i	$0.604319\pi$
$192$	−11.2863	−	7.09963i	−0.814521	−	0.512371i
$193$	−10.5713	−	18.3100i	−0.760938	−	1.31798i	−0.942368	−	0.334579i	$-0.891406\pi$
$193$	−10.5713	−	18.3100i	−0.760938	−	1.31798i	0.181430	−	0.983404i	$-0.441927\pi$
$194$	1.26042	+	2.18311i	0.0904928	+	0.156738i
$195$	−0.0115231	−	0.00352100i	−0.000825188	−	0.000252144i
$196$	6.20919	+	0.274530i	0.443513	+	0.0196093i
$197$	−22.4348	−	12.9527i	−1.59841	−	0.922843i	−0.991794	−	0.127848i	$-0.959193\pi$
$197$	−22.4348	−	12.9527i	−1.59841	−	0.922843i	−0.606616	−	0.794995i	$-0.707474\pi$
$198$	4.45648	−	6.52228i	0.316708	−	0.463519i
$199$			2.76818i			0.196231i	0.995175	+	0.0981157i	$0.0312815\pi$
$199$			2.76818i			0.196231i	−0.995175	+	0.0981157i	$0.968718\pi$
$200$	13.1873	+	7.61367i	0.932480	+	0.538368i
$201$	0.935620	−	24.6714i	0.0659935	−	1.74018i
$202$	−16.4937	+	9.52267i	−1.16050	+	0.670012i
$203$	19.7686	+	12.0033i	1.38748	+	0.842470i
$204$	5.43509	+	3.41892i	0.380532	+	0.239372i
$205$	−0.00706304			−0.000493304
$206$	−5.14569	−	8.91259i	−0.358517	−	0.620969i
$207$	13.1714	−	6.32661i	0.915474	−	0.439730i
$208$	−1.32414	+	5.00486i	−0.0918125	+	0.347025i
$209$	−13.4042			−0.927189
$210$	−0.00930725		0.000559083i	−0.000642261		3.85804e-5i
$211$	−3.90647	+	6.76621i	−0.268933	+	0.465805i	−0.968586	−	0.248677i	$-0.920004\pi$
$211$	−3.90647	+	6.76621i	−0.268933	+	0.465805i	0.699654	+	0.714482i	$0.253338\pi$
$212$	−10.9863	−	6.34295i	−0.754543	−	0.435636i
$213$	2.47923	+	0.0940204i	0.169874	+	0.00644217i
$214$	−5.76080			−0.393800
$215$	0.00256490	−	0.00444254i	0.000174925	−	0.000302979i
$216$	−15.7225	−	1.79564i	−1.06978	−	0.122178i
$217$	17.1770	+	10.4297i	1.16605	+	0.708016i
$218$	−6.73151	−	3.88644i	−0.455916	−	0.263223i
$219$	1.50379	+	2.84880i	0.101617	+	0.192504i
$220$	0.00370435	+	0.00213870i	0.000249747	+	0.000144191i
$221$	3.85037	−	14.5533i	0.259004	−	0.978961i
$222$	−3.55544	+	5.65211i	−0.238625	+	0.379345i
$223$	6.48830	+	3.74602i	0.434489	+	0.250852i	0.701257	−	0.712909i	$-0.252623\pi$
$223$	6.48830	+	3.74602i	0.434489	+	0.250852i	−0.266768	+	0.963761i	$0.585956\pi$
$224$	0.267492	−	12.1059i	0.0178726	−	0.808863i
$225$	14.9569	+	1.13606i	0.997127	+	0.0757376i
$226$	0.237870	+	0.412003i	0.0158229	+	0.0274061i
$227$	−8.54135			−0.566909			−0.283455	−	0.958986i	$-0.591481\pi$
$227$	−8.54135			−0.566909			−0.283455	+	0.958986i	$0.591481\pi$
$228$	3.85403	+	7.30111i	0.255239	+	0.483528i
$229$	8.92049	−	5.15025i	0.589482	−	0.340338i	−0.175410	−	0.984495i	$-0.556125\pi$
$229$	8.92049	−	5.15025i	0.589482	−	0.340338i	0.764893	+	0.644158i	$0.222792\pi$
$230$	−0.00495511	−	0.00858250i	−0.000326730	−	0.000565913i
$231$	11.4216	+	0.686090i	0.751486	+	0.0451414i
$232$	13.3108	−	23.0549i	0.873894	−	1.51363i
$233$	1.09700	−	0.633351i	0.0718666	−	0.0414922i	−0.463636	−	0.886026i	$-0.653456\pi$
$233$	1.09700	−	0.633351i	0.0718666	−	0.0414922i	0.535503	+	0.844534i	$0.320122\pi$
$234$	2.14470	+	11.2034i	0.140203	+	0.732391i
$235$	0.00345727	−	0.00598818i	0.000225528	−	0.000390626i
$236$	−4.64484			−0.302353
$237$	−0.478477	+	12.6170i	−0.0310804	+	0.819561i
$238$	0.257341	−	11.6466i	0.0166810	−	0.754934i
$239$			18.8399i			1.21865i	0.792921	+	0.609325i	$0.208559\pi$
$239$			18.8399i			1.21865i	−0.792921	+	0.609325i	$0.791441\pi$
$240$	−0.000181839		0.00479492i	−1.17377e−5		0.000309511i
$241$		−	1.22332i		−	0.0788012i	−0.999223	−	0.0394006i	$-0.987455\pi$
$241$		−	1.22332i		−	0.0788012i	0.999223	−	0.0394006i	$-0.0125448\pi$
$242$	−4.35228	−	2.51279i	−0.279775	−	0.161528i
$243$	−14.7266	+	5.11136i	−0.944715	+	0.327894i
$244$	5.82794	+	3.36476i	0.373096	+	0.215407i
$245$	−0.00622966	−	0.0119832i	−0.000397998	−	0.000765578i
$246$	3.12145	+	5.91329i	0.199016	+	0.377018i
$247$	13.6435	−	13.7298i	0.868113	−	0.873608i
$248$	11.5657	−	20.0324i	0.734425	−	1.27206i
$249$	15.2605	+	9.59959i	0.967097	+	0.608349i
$250$		−	0.0203467i		−	0.00128684i
$251$	4.42278	+	7.66048i	0.279163	+	0.483525i	0.971177	−	0.238359i	$-0.0766096\pi$
$251$	4.42278	+	7.66048i	0.279163	+	0.483525i	−0.692014	+	0.721884i	$0.743276\pi$
$252$	−2.91027	−	6.41846i	−0.183330	−	0.404325i
$253$	6.08077	+	10.5322i	0.382294	+	0.662153i
$254$	−8.61998	−	4.97674i	−0.540865	−	0.312269i
$255$	0.000528758	−	0.0139428i	3.31121e−5	−	0.000873133i
$256$	−16.4881			−1.03051
$257$	10.9439			0.682659			0.341329	−	0.939944i	$-0.389123\pi$
$257$	10.9439			0.682659			0.341329	+	0.939944i	$0.389123\pi$
$258$	−4.85291	−	0.184038i	−0.302129	−	0.0114577i
$259$	−9.66976	−	0.213662i	−0.600849	−	0.0132763i
$260$	−0.00596112	+	0.00161745i	−0.000369693	+	0.000100310i
$261$	1.98615	−	26.1487i	0.122940	−	1.61857i
$262$	5.68243	−	3.28075i	0.351062	−	0.202686i
$263$	11.0111	−	6.35726i	0.678973	−	0.392005i	−0.120495	−	0.992714i	$-0.538448\pi$
$263$	11.0111	−	6.35726i	0.678973	−	0.392005i	0.799468	+	0.600709i	$0.205115\pi$
$264$	0.499124	−	13.1614i	0.0307189	−	0.810028i
$265$			0.0275665i			0.00169339i
$266$	7.77391	−	12.8030i	0.476649	−	0.785005i
$267$	−7.92253	−	4.98364i	−0.484851	−	0.304994i
$268$	−6.32813	−	10.9606i	−0.386552	−	0.669528i
$269$	−23.1586			−1.41201			−0.706003	−	0.708208i	$-0.749504\pi$
$269$	−23.1586			−1.41201			−0.706003	+	0.708208i	$0.749504\pi$
$270$	0.00421315	+	0.00969671i	0.000256404	+	0.000590123i
$271$			26.3454i			1.60037i	0.599753	+	0.800185i	$0.295265\pi$
$271$			26.3454i			1.60037i	−0.599753	+	0.800185i	$0.704735\pi$
$272$	−5.99505			−0.363503
$273$	−12.3282	+	11.0007i	−0.746137	+	0.665793i
$274$	6.49218			0.392207
$275$			12.4844i			0.752840i
$276$	3.98839	−	6.34037i	0.240073	−	0.381645i
$277$	−4.40451			−0.264641			−0.132321	−	0.991207i	$-0.542243\pi$
$277$	−4.40451			−0.264641			−0.132321	+	0.991207i	$0.542243\pi$
$278$	−6.49441	−	11.2486i	−0.389509	−	0.674649i
$279$	1.72577	−	22.7207i	0.103319	−	1.36025i
$280$	−0.0136318	+	0.00747379i	−0.000814658	+	0.000446644i
$281$			13.2912i			0.792885i	0.918060	+	0.396442i	$0.129755\pi$
$281$			13.2912i			0.792885i	−0.918060	+	0.396442i	$0.870245\pi$
$282$	−6.54131	−	0.248068i	−0.389529	−	0.0147722i
$283$	14.1843	−	8.18929i	0.843167	−	0.486803i	−0.0151725	−	0.999885i	$-0.504830\pi$
$283$	14.1843	−	8.18929i	0.843167	−	0.486803i	0.858339	+	0.513082i	$0.171496\pi$
$284$	1.10144	−	0.635914i	0.0653582	−	0.0377346i
$285$	0.00955236	−	0.0151855i	0.000565833	−	0.000899509i
$286$	−9.16259	+	2.48612i	−0.541796	+	0.147007i
$287$	−5.02684	+	8.27882i	−0.296725	+	0.488683i
$288$	−12.3765	+	5.94481i	−0.729292	+	0.350301i
$289$	0.432600			0.0254470
$290$	−0.0177858			−0.00104442
$291$	4.13733	+	0.156901i	0.242534	+	0.00919771i
$292$	1.43010	+	0.825670i	0.0836905	+	0.0483187i
$293$	−9.96323	−	17.2568i	−0.582058	−	1.00815i	−0.995235	−	0.0975037i	$-0.968914\pi$
$293$	−9.96323	−	17.2568i	−0.582058	−	1.00815i	0.413177	−	0.910651i	$-0.364419\pi$
$294$	−7.27938	+	10.5114i	−0.424542	+	0.613039i
$295$	0.00504662	+	0.00874100i	0.000293825	+	0.000508920i
$296$			11.1334i			0.647114i
$297$	−5.17026	−	11.8995i	−0.300009	−	0.690481i
$298$	−3.77624	+	6.54065i	−0.218752	+	0.378889i
$299$	−16.9773	−	4.49170i	−0.981824	−	0.259762i
$300$	6.80011	−	3.58957i	0.392605	−	0.207244i
$301$	−3.38179	−	6.16821i	−0.194923	−	0.355530i
$302$	−14.8843	−	8.59344i	−0.856494	−	0.494497i
$303$	−1.18541	+	31.2582i	−0.0681003	+	1.79574i
$304$	−6.67551	−	3.85411i	−0.382867	−	0.221048i
$305$		−	0.0146233i		−	0.000837326i
$306$	−11.9068	+	5.71922i	−0.680669	+	0.326946i
$307$		−	4.93316i		−	0.281551i	−0.990042	−	0.140775i	$-0.955040\pi$
$307$		−	4.93316i		−	0.281551i	0.990042	−	0.140775i	$-0.0449595\pi$
$308$	5.14327	−	2.81985i	0.293065	−	0.160676i
$309$	−16.8907	−	0.640552i	−0.960880	−	0.0364398i
$310$	−0.0154541			−0.000877732
$311$	6.69213	−	11.5911i	0.379476	−	0.657272i	−0.611510	−	0.791237i	$-0.709438\pi$
$311$	6.69213	−	11.5911i	0.379476	−	0.657272i	0.990986	+	0.133965i	$0.0427710\pi$
$312$	12.9731	+	13.9076i	0.734456	+	0.787360i
$313$	23.9599	−	13.8332i	1.35429	−	0.781901i	0.365445	−	0.930833i	$-0.380917\pi$
$313$	23.9599	−	13.8332i	1.35429	−	0.781901i	0.988847	+	0.148932i	$0.0475835\pi$
$314$	−2.48238	+	4.29960i	−0.140089	+	0.242641i
$315$	−0.00891673	+	0.0124504i	−0.000502401	+	0.000701502i
$316$	3.23622	+	5.60529i	0.182051	+	0.315322i
$317$	12.8384	−	7.41223i	0.721075	−	0.416313i	−0.0940735	−	0.995565i	$-0.529989\pi$
$317$	12.8384	−	7.41223i	0.721075	−	0.416313i	0.815148	+	0.579253i	$0.196656\pi$
$318$	23.0791	−	12.1828i	1.29421	−	0.683175i
$319$	21.8262			1.22203
$320$	0.00742641	+	0.0128629i	0.000415149	+	0.000719059i
$321$	−5.03798	+	8.00892i	−0.281193	+	0.447014i
$322$	−13.5864	−	0.300205i	−0.757142	−	0.0167298i
$323$	19.4113	+	11.2071i	1.08007	+	0.623580i
$324$	−4.99495	+	6.23757i	−0.277497	+	0.346531i
$325$	−12.7877	−	12.7073i	−0.709334	−	0.704872i
$326$	3.84155	+	2.21792i	0.212764	+	0.122839i
$327$	−11.2900	+	5.95965i	−0.624339	+	0.329569i
$328$	9.65508	+	5.57436i	0.533113	+	0.307793i
$329$	−4.55836	−	8.31423i	−0.251311	−	0.458378i
$330$	−0.00778178	+	0.00410776i	−0.000428373	+	0.000226125i
$331$	−2.90440	+	5.03057i	−0.159640	+	0.276505i	−0.934739	−	0.355335i	$-0.884367\pi$
$331$	−2.90440	+	5.03057i	−0.159640	+	0.276505i	0.775099	+	0.631840i	$0.217700\pi$
$332$	9.24200			0.507221
$333$	4.74848	+	9.88586i	0.260215	+	0.541742i
$334$	13.2424	+	7.64552i	0.724594	+	0.418344i
$335$	−0.0137510	+	0.0238175i	−0.000751299	+	0.00130129i
$336$	5.49086	+	3.62573i	0.299551	+	0.197800i
$337$	−9.55520			−0.520505			−0.260252	−	0.965541i	$-0.583806\pi$
$337$	−9.55520			−0.520505			−0.260252	+	0.965541i	$0.583806\pi$
$338$	6.77962	−	11.9157i	0.368763	−	0.648126i
$339$	0.780810	+	0.0296109i	0.0424078	+	0.00160824i
$340$	−0.00357629	−	0.00619432i	−0.000193952	−	0.000335934i
$341$	18.9648			1.02700
$342$	−16.9351	−	1.28632i	−0.915745	−	0.0695562i
$343$	−18.4796	−	1.22657i	−0.997804	−	0.0662285i
$344$	−7.01238	+	4.04860i	−0.378082	+	0.218286i
$345$	−0.0162652		0.000616829i	−0.000875687		3.32089e-5i
$346$	14.3355	+	8.27660i	0.770681	+	0.444953i
$347$			29.1178i			1.56313i	0.623826	+	0.781563i	$0.285577\pi$
$347$			29.1178i			1.56313i	−0.623826	+	0.781563i	$0.714423\pi$
$348$	−6.27554	−	11.8884i	−0.336404	−	0.637287i
$349$	−27.1567	−	15.6790i	−1.45367	−	0.839275i	−0.454980	−	0.890501i	$-0.650354\pi$
$349$	−27.1567	−	15.6790i	−1.45367	−	0.839275i	−0.998687	+	0.0512262i	$0.983687\pi$
$350$	−11.9245	−	7.24047i	−0.637392	−	0.387019i
$351$	17.4511	+	6.81607i	0.931471	+	0.363815i
$352$	−5.71380	−	9.89659i	−0.304547	−	0.527490i
$353$	0.797729	+	1.38171i	0.0424588	+	0.0735408i	0.886474	−	0.462779i	$-0.153148\pi$
$353$	0.797729	+	1.38171i	0.0424588	+	0.0735408i	−0.844015	+	0.536320i	$0.819814\pi$
$354$	5.08780	−	8.08812i	0.270414	−	0.429879i
$355$	−0.00239342	−	0.00138184i	−0.000127030	−	7.33406e-5i
$356$	−4.79800			−0.254293
$357$	−15.9665	−	10.5430i	−0.845037	−	0.557995i
$358$	−3.40868	−	5.90400i	−0.180154	−	0.312036i
$359$	11.1728	−	6.45064i	0.589680	−	0.340452i	−0.175291	−	0.984517i	$-0.556087\pi$
$359$	11.1728	−	6.45064i	0.589680	−	0.340452i	0.764971	+	0.644065i	$0.222753\pi$
$360$	0.0145547	+	0.00994477i	0.000767099	+	0.000524135i
$361$	4.90969	+	8.50384i	0.258405	+	0.447570i
$362$	−0.990625			−0.0520661
$363$	−7.29958	+	3.85323i	−0.383129	+	0.202242i
$364$	−2.34672	+	8.13838i	−0.123002	+	0.426567i
$365$		−	0.00358837i		−	0.000187824i
$366$	−12.2428	+	6.46262i	−0.639944	+	0.337807i
$367$	11.3448	−	6.54993i	0.592194	−	0.341903i	−0.173770	−	0.984786i	$-0.555595\pi$
$367$	11.3448	−	6.54993i	0.592194	−	0.341903i	0.765965	+	0.642883i	$0.222262\pi$
$368$			6.99360i			0.364567i
$369$	10.9507	+	0.831772i	0.570072	+	0.0433003i
$370$	0.00644165	−	0.00371909i	0.000334885	−	0.000193346i
$371$	32.3116	+	19.6193i	1.67753	+	1.01859i
$372$	−5.45282	−	10.3299i	−0.282716	−	0.535579i
$373$	−3.06870	+	5.31515i	−0.158891	+	0.275208i	−0.934469	−	0.356044i	$-0.884125\pi$
$373$	−3.06870	+	5.31515i	−0.158891	+	0.275208i	0.775578	+	0.631252i	$0.217459\pi$
$374$	−5.49697	−	9.52103i	−0.284242	−	0.492321i
$375$	−0.0282869	−	0.0177938i	−0.00146073	−	0.000918867i
$376$	−9.45210	+	5.45717i	−0.487455	+	0.281432i
$377$	−22.2157	+	22.3564i	−1.14417	+	1.15141i
$378$	14.3644	+	1.96288i	0.738824	+	0.100959i
$379$	6.45103	−	11.1735i	0.331367	−	0.573945i	−0.651413	−	0.758723i	$-0.725823\pi$
$379$	6.45103	−	11.1735i	0.331367	−	0.573945i	0.982780	+	0.184779i	$0.0591568\pi$
$380$		−	0.00919653i		−	0.000471772i
$381$	−14.4573	+	7.63157i	−0.740671	+	0.390977i
$382$	−2.83648	+	4.91293i	−0.145127	+	0.251368i
$383$	−4.61988	+	8.00187i	−0.236065	+	0.408876i	−0.959582	−	0.281430i	$-0.909191\pi$
$383$	−4.61988	+	8.00187i	−0.236065	+	0.408876i	0.723517	+	0.690307i	$0.242524\pi$
$384$	−0.954748	+	1.51777i	−0.0487218	+	0.0774534i
$385$	−0.0108948	−	0.00661521i	−0.000555248	−	0.000337143i
$386$	19.3091	−	11.1481i	0.982806	−	0.567423i
$387$	−4.49987	+	6.58579i	−0.228741	+	0.334774i
$388$	1.83807	−	1.06121i	0.0933140	−	0.0538749i
$389$	11.3864	+	6.57391i	0.577311	+	0.333311i	0.760064	−	0.649848i	$-0.225168\pi$
$389$	11.3864	+	6.57391i	0.577311	+	0.333311i	−0.182753	+	0.983159i	$0.558501\pi$
$390$	0.00371312	−	0.0121519i	0.000188021	−	0.000615334i
$391$		−	20.3362i		−	1.02845i
$392$	−0.941635	+	21.2975i	−0.0475598	+	1.07569i
$393$	0.408399	−	10.7691i	0.0206010	−	0.543228i
$394$	13.6595	−	23.6589i	0.688154	−	1.19192i
$395$	0.00703230	−	0.0121803i	0.000353834	−	0.000612858i
$396$	−5.49145	−	3.75214i	−0.275956	−	0.188552i
$397$	16.0733	+	9.27995i	0.806698	+	0.465747i	0.845808	−	0.533487i	$-0.179119\pi$
$397$	16.0733	+	9.27995i	0.806698	+	0.465747i	−0.0391097	+	0.999235i	$0.512452\pi$
$398$	−2.91923			−0.146328
$399$	−11.0009	−	22.0043i	−0.550732	−	1.10159i
$400$	−3.58964	+	6.21745i	−0.179482	+	0.310872i
$401$			12.3532i			0.616888i	0.951243	+	0.308444i	$0.0998082\pi$
$401$			12.3532i			0.616888i	−0.951243	+	0.308444i	$0.900192\pi$
$402$	26.0176	+	0.986671i	1.29764	+	0.0492107i
$403$	−19.3033	+	19.4255i	−0.961565	+	0.967651i
$404$	8.01763	+	13.8869i	0.398892	+	0.690901i
$405$	0.0171653	+	0.00262275i	0.000852952	+	0.000130325i
$406$	−12.6583	+	20.8473i	−0.628221	+	1.03463i
$407$	−7.90501	+	4.56396i	−0.391837	+	0.226227i
$408$	−11.7269	+	18.6423i	−0.580568	+	0.922933i
$409$			5.77235i			0.285424i	0.989764	+	0.142712i	$0.0455823\pi$
$409$			5.77235i			0.285424i	−0.989764	+	0.142712i	$0.954418\pi$
$410$		−	0.00744843i		−	0.000367852i
$411$	5.67760	−	9.02572i	0.280055	−	0.445206i
$412$	−7.50398	+	4.33242i	−0.369694	+	0.213443i
$413$	13.8373	+	0.305749i	0.680891	+	0.0150449i
$414$	6.67182	+	13.8901i	0.327902	+	0.682660i
$415$	−0.0100414	−	0.0173923i	−0.000492915	−	0.000853753i
$416$	15.9528	+	4.22063i	0.782149	+	0.206934i
$417$	−21.3179	−	0.808446i	−1.04394	−	0.0395898i
$418$		−	14.1356i		−	0.691396i
$419$	−17.6169	+	30.5134i	−0.860644	+	1.49068i	0.0106648	+	0.999943i	$0.496605\pi$
$419$	−17.6169	+	30.5134i	−0.860644	+	1.49068i	−0.871309	+	0.490736i	$0.836728\pi$
$420$	−0.000470721		0.00783626i	−2.29688e−5		0.000382371i
$421$	27.0300			1.31736			0.658682	−	0.752421i	$-0.271114\pi$
$421$	27.0300			1.31736			0.658682	+	0.752421i	$0.271114\pi$
$422$	−7.13541	−	4.11963i	−0.347346	−	0.200540i
$423$	−6.06544	+	8.87709i	−0.294912	+	0.431619i
$424$	21.7563	−	37.6830i	1.05658	−	1.83005i
$425$	10.4381	−	18.0793i	0.506321	−	0.876974i
$426$	−0.0991506	+	2.61450i	−0.00480386	+	0.126673i
$427$	−17.1404	−	10.4075i	−0.829483	−	0.503656i
$428$			4.85032i			0.234449i
$429$	−4.55664	+	14.9124i	−0.219997	+	0.719979i
$430$	0.00468495	+	0.00270486i	0.000225928	+	0.000130440i
$431$	27.1302	−	15.6636i	1.30681	−	0.754490i	0.325252	−	0.945627i	$-0.394551\pi$
$431$	27.1302	−	15.6636i	1.30681	−	0.754490i	0.981563	+	0.191138i	$0.0612177\pi$
$432$	0.846597	−	7.41275i	0.0407319	−	0.356646i
$433$	3.41909	−	1.97401i	0.164311	−	0.0948649i	−0.415590	−	0.909552i	$-0.636425\pi$
$433$	3.41909	−	1.97401i	0.164311	−	0.0948649i	0.579900	+	0.814687i	$0.303091\pi$
$434$	−10.9988	+	18.1142i	−0.527960	+	0.869511i
$435$	−0.0155542	+	0.0247266i	−0.000745765	+	0.00118555i
$436$	−3.27220	+	5.66761i	−0.156710	+	0.271429i
$437$	13.0738	−	22.6445i	0.625404	−	1.08323i
$438$	−3.00424	+	1.58585i	−0.143548	+	0.0757746i
$439$		−	30.8667i		−	1.47319i	−0.676337	−	0.736593i	$-0.736434\pi$
$439$		−	30.8667i		−	1.47319i	0.676337	−	0.736593i	$-0.263566\pi$
$440$	−0.00733575	+	0.0127059i	−0.000349718	+	0.000605729i
$441$	8.24744	+	19.3127i	0.392735	+	0.919652i
$442$	15.3474	+	4.06047i	0.730001	+	0.193137i
$443$	−16.2769	+	9.39748i	−0.773340	+	0.446488i	−0.834065	−	0.551667i	$-0.813992\pi$
$443$	−16.2769	+	9.39748i	−0.773340	+	0.446488i	0.0607250	+	0.998155i	$0.480659\pi$
$444$	4.75881	+	2.99351i	0.225843	+	0.142066i
$445$	0.00521303	+	0.00902923i	0.000247121	+	0.000428026i
$446$	−3.95042	+	6.84233i	−0.187058	+	0.323994i
$447$	5.79067	+	10.9699i	0.273889	+	0.518858i
$448$	20.3625	+	0.449928i	0.962038	+	0.0212571i
$449$	4.95835	−	2.86270i	0.233999	−	0.135099i	−0.378417	−	0.925635i	$-0.623531\pi$
$449$	4.95835	−	2.86270i	0.233999	−	0.135099i	0.612415	+	0.790536i	$0.290198\pi$
$450$	−1.19805	+	15.7730i	−0.0564768	+	0.743547i
$451$			9.14050i			0.430409i
$452$	0.346887	−	0.200275i	0.0163162	−	0.00942016i
$453$	−24.9637	+	13.1776i	−1.17290	+	0.619137i
$454$		−	9.00741i		−	0.422739i
$455$	0.0178651	−	0.00442612i	0.000837529	−	0.000207500i
$456$	−25.0428	+	13.2193i	−1.17273	+	0.619051i
$457$	33.8986			1.58571			0.792854	−	0.609412i	$-0.208594\pi$
$457$	33.8986			1.58571			0.792854	+	0.609412i	$0.208594\pi$
$458$	5.43127	+	9.40723i	0.253786	+	0.439571i
$459$	−2.46176	+	21.5550i	−0.114905	+	1.00610i
$460$	−0.00722605	+	0.00417196i	−0.000336917	+	0.000194519i
$461$	9.37925	+	16.2453i	0.436835	+	0.756621i	0.997443	−	0.0714602i	$-0.0227659\pi$
$461$	9.37925	+	16.2453i	0.436835	+	0.756621i	−0.560608	+	0.828081i	$0.689433\pi$
$462$	−0.723527	+	12.0448i	−0.0336615	+	0.560375i
$463$	−20.1902			−0.938317			−0.469158	−	0.883114i	$-0.655443\pi$
$463$	−20.1902			−0.938317			−0.469158	+	0.883114i	$0.655443\pi$
$464$	10.8698	+	6.27567i	0.504617	+	0.291341i
$465$	−0.0135150	+	0.0214849i	−0.000626745	+	0.000996340i
$466$	0.667909	+	1.15685i	0.0309403	+	0.0535902i
$467$	−3.57259	−	6.18791i	−0.165320	−	0.286342i	0.771449	−	0.636291i	$-0.219532\pi$
$467$	−3.57259	−	6.18791i	−0.165320	−	0.286342i	−0.936769	+	0.349949i	$0.886199\pi$
$468$	9.43275	−	1.80573i	0.436029	−	0.0834701i
$469$	18.1305	+	33.0692i	0.837190	+	1.52699i
$470$	0.00631492	+	0.00364592i	0.000291285	+	0.000168174i
$471$	3.80659	+	7.21124i	0.175398	+	0.332276i
$472$		−	15.9318i		−	0.733319i
$473$	−5.74924	−	3.31932i	−0.264350	−	0.152623i
$474$	−13.3054	−	0.504585i	−0.611138	−	0.0231764i
$475$	23.2457	−	13.4209i	1.06659	−	0.615794i
$476$	−9.80584	−	0.216669i	−0.449450	−	0.00993102i
$477$	3.24634	−	42.7398i	0.148640	−	1.95692i
$478$	−19.8679			−0.908735
$479$	−4.61963	−	8.00143i	−0.211076	−	0.365595i	0.740975	−	0.671532i	$-0.234363\pi$
$479$	−4.61963	−	8.00143i	−0.211076	−	0.365595i	−0.952052	+	0.305938i	$0.901030\pi$
$480$	0.0152836		0.000579604i	0.000697597		2.64552e-5i
$481$	3.37128	−	12.7424i	0.153717	−	0.581005i
$482$	1.29007			0.0587612
$483$	−12.2991	+	18.6259i	−0.559628	+	0.847509i
$484$	−2.11565	+	3.66441i	−0.0961658	+	0.166564i
$485$	−0.00399414	−	0.00230602i	−0.000181364	−	0.000104711i
$486$	−5.39026	−	15.5302i	−0.244507	−	0.704464i
$487$	1.30155			0.0589787			0.0294894	−	0.999565i	$-0.490612\pi$
$487$	1.30155			0.0589787			0.0294894	+	0.999565i	$0.490612\pi$
$488$	−11.5411	+	19.9898i	−0.522442	+	0.904896i
$489$	6.44299	−	3.40106i	0.291362	−	0.153801i
$490$	0.0126370	−	0.00656958i	0.000570884	−	0.000296783i
$491$	11.4486	+	6.60986i	0.516668	+	0.298299i	0.735570	−	0.677448i	$-0.236914\pi$
$491$	11.4486	+	6.60986i	0.516668	+	0.298299i	−0.218902	+	0.975747i	$0.570248\pi$
$492$	4.97871	−	2.62811i	0.224458	−	0.118484i
$493$	−31.6075	−	18.2486i	−1.42353	−	0.821876i
$494$	14.4790	+	14.3879i	0.651440	+	0.647343i
$495$	−0.00109459	+	0.0144109i	−4.91984e−5	+	0.000647723i
$496$	9.44476	+	5.45294i	0.424082	+	0.244844i
$497$	−3.32312	+	1.82194i	−0.149062	+	0.0817250i
$498$	−10.1234	+	16.0932i	−0.453640	+	0.721154i
$499$	3.18217	+	5.51168i	0.142454	+	0.246737i	0.928420	−	0.371532i	$-0.121168\pi$
$499$	3.18217	+	5.51168i	0.142454	+	0.246737i	−0.785966	+	0.618269i	$0.787834\pi$
$500$	−0.0171309			−0.000766119
$501$	22.2100	−	11.7240i	0.992272	−	0.523790i
$502$	−8.07847	+	4.66411i	−0.360560	+	0.208169i
$503$	−17.7261	−	30.7026i	−0.790370	−	1.36896i	−0.925738	−	0.378165i	$-0.876555\pi$
$503$	−17.7261	−	30.7026i	−0.790370	−	1.36896i	0.135369	−	0.990795i	$-0.456778\pi$
$504$	22.0153	−	9.98222i	0.980639	−	0.444644i
$505$	0.0174223	−	0.0301764i	0.000775283	−	0.00134283i
$506$	−11.1069	+	6.41256i	−0.493761	+	0.285073i
$507$	−10.6367	−	19.8459i	−0.472393	−	0.881388i
$508$	−4.19018	+	7.25761i	−0.185909	+	0.322004i
$509$	−15.6499			−0.693670			−0.346835	−	0.937926i	$-0.612744\pi$
$509$	−15.6499			−0.693670			−0.346835	+	0.937926i	$0.612744\pi$
$510$	0.0147036		0.000557609i	0.000651086		2.46913e-5i
$511$	−4.20604	−	2.55388i	−0.186064	−	0.112977i
$512$		−	15.3173i		−	0.676934i
$513$	−16.5985	+	22.4190i	−0.732843	+	0.989824i
$514$			11.5410i			0.509052i
$515$	0.0163062	+	0.00941436i	0.000718535	+	0.000414846i
$516$	−0.154952	+	4.08592i	−0.00682136	+	0.179873i
$517$	−7.74949	−	4.47417i	−0.340822	−	0.196774i
$518$	0.225321	−	10.1974i	0.00990002	−	0.448047i
$519$	24.0433	−	12.6917i	1.05538	−	0.557105i
$520$	−0.00554785	−	0.0204466i	−0.000243289	−	0.000896643i
$521$	19.1120	−	33.1029i	0.837310	−	1.45026i	−0.0548261	−	0.998496i	$-0.517460\pi$
$521$	19.1120	−	33.1029i	0.837310	−	1.45026i	0.892136	−	0.451767i	$-0.149206\pi$
$522$	27.5755	+	2.09452i	1.20695	+	0.0916747i
$523$			30.7021i			1.34251i	0.741228	+	0.671254i	$0.234244\pi$
$523$			30.7021i			1.34251i	−0.741228	+	0.671254i	$0.765756\pi$
$524$	−2.76224	−	4.78434i	−0.120669	−	0.209005i
$525$	−20.4944	+	10.2460i	−0.894447	+	0.447172i
$526$	6.70414	+	11.6119i	0.292314	+	0.506303i
$527$	−27.4638	−	15.8562i	−1.19634	−	0.690708i
$528$	6.20525	+	0.235324i	0.270049	+	0.0102411i
$529$	−0.723461			−0.0314548
$530$	−0.0290706			−0.00126275
$531$	−6.79504	−	14.1466i	−0.294879	−	0.613909i
$532$	−10.7796	−	6.54526i	−0.467353	−	0.283773i
$533$	−9.36253	−	9.30364i	−0.405536	−	0.402985i
$534$	5.25557	−	8.35482i	0.227431	−	0.361548i
$535$	0.00912769	−	0.00526987i	0.000394624	−	0.000227836i
$536$	37.5950	−	21.7055i	1.62385	−	0.937533i
$537$	−11.1890	−	0.424324i	−0.482841	−	0.0183109i
$538$		−	24.4223i		−	1.05292i
$539$	−15.5078	+	8.06199i	−0.667969	+	0.347255i
$540$	0.00816417	−	0.00354727i	0.000351330	−	0.000152650i
$541$	4.56917	+	7.91403i	0.196444	+	0.340251i	0.947373	−	0.320132i	$-0.103727\pi$
$541$	4.56917	+	7.91403i	0.196444	+	0.340251i	−0.750929	+	0.660383i	$0.770394\pi$
$542$	−27.7829			−1.19338
$543$	−0.866330	+	1.37721i	−0.0371778	+	0.0591018i
$544$			19.1090i			0.819289i
$545$	0.0142210			0.000609160
$546$	−11.6009	−	13.0009i	−0.496475	−	0.556387i
$547$	−35.4176			−1.51435			−0.757173	−	0.653214i	$-0.773420\pi$
$547$	−35.4176			−1.51435			−0.757173	+	0.653214i	$0.773420\pi$
$548$		−	5.46611i		−	0.233500i
$549$	−1.72209	+	22.6723i	−0.0734972	+	0.967631i
$550$	−13.1656			−0.561385
$551$	−23.4634	−	40.6398i	−0.999574	−	1.73131i
$552$	21.7474	+	13.6801i	0.925632	+	0.582266i
$553$	−9.27198	−	16.9116i	−0.394285	−	0.719156i
$554$		−	4.64484i		−	0.197340i
$555$	0.000462965	−	0.0122079i	1.96518e−5	−	0.000518198i
$556$	−9.47083	+	5.46798i	−0.401653	+	0.231894i
$557$	3.92620	−	2.26679i	0.166358	−	0.0960470i	−0.414509	−	0.910045i	$-0.636047\pi$
$557$	3.92620	−	2.26679i	0.166358	−	0.0960470i	0.580868	+	0.813998i	$0.302713\pi$
$558$	23.9604	+	1.81993i	1.01432	+	0.0770439i
$559$	9.25180	−	2.51032i	0.391310	−	0.106175i
$560$	−0.00352369	−	0.00642705i	−0.000148903	−	0.000271592i
$561$	−18.0438	−	0.684282i	−0.761811	−	0.0288904i
$562$	−14.0164			−0.591246
$563$	−12.1324			−0.511321			−0.255661	−	0.966767i	$-0.582293\pi$
$563$	−12.1324			−0.511321			−0.255661	+	0.966767i	$0.582293\pi$
$564$	−0.208862	+	5.50747i	−0.00879466	+	0.231906i
$565$	−0.000753786	0	0.000435199i	−3.17120e−5	0	1.83090e-5i
$566$	8.63613	+	14.9582i	0.363004	+	0.628741i
$567$	15.2909	−	18.2534i	0.642159	−	0.766571i
$568$	2.18118	+	3.77792i	0.0915204	+	0.158518i
$569$		−	36.3551i		−	1.52408i	−0.647528	−	0.762042i	$-0.724197\pi$
$569$		−	36.3551i		−	1.52408i	0.647528	−	0.762042i	$-0.275803\pi$
$570$	0.0160140	+	0.0100736i	0.000670754	+	0.000421936i
$571$	7.04698	−	12.2057i	0.294907	−	0.510794i	−0.680056	−	0.733160i	$-0.738045\pi$
$571$	7.04698	−	12.2057i	0.294907	−	0.510794i	0.974963	+	0.222366i	$0.0713780\pi$
$572$	2.09319	+	7.71447i	0.0875208	+	0.322558i
$573$	4.34960	+	8.23991i	0.181707	+	0.344227i
$574$	−8.73055	−	5.30112i	−0.364406	−	0.221265i
$575$	−21.0906	−	12.1767i	−0.879540	−	0.507802i
$576$	−9.99932	−	20.8176i	−0.416638	−	0.867399i
$577$	11.4758	+	6.62558i	0.477745	+	0.275826i	0.719476	−	0.694517i	$-0.244382\pi$
$577$	11.4758	+	6.62558i	0.477745	+	0.275826i	−0.241731	+	0.970343i	$0.577715\pi$
$578$			0.456204i			0.0189756i
$579$	1.38775	−	36.5937i	0.0576731	−	1.52078i
$580$			0.0149748i			0.000621793i
$581$	−27.5327	−	0.608360i	−1.14225	−	0.0252390i
$582$	−0.165462	+	4.36308i	−0.00685864	+	0.180856i
$583$	35.6746			1.47749
$584$	−2.83205	+	4.90525i	−0.117191	+	0.202981i
$585$	−0.0136469	−	0.0157893i	−0.000564228	−	0.000652808i
$586$	18.1984	−	10.5069i	0.751771	−	0.434035i
$587$	15.6011	−	27.0220i	0.643928	−	1.11532i	−0.340620	−	0.940201i	$-0.610637\pi$
$587$	15.6011	−	27.0220i	0.643928	−	1.11532i	0.984548	−	0.175115i	$-0.0560296\pi$
$588$	8.85013	+	6.12890i	0.364973	+	0.252751i
$589$	−20.3874	−	35.3120i	−0.840047	−	1.45500i
$590$	−0.00921795	+	0.00532198i	−0.000379497	+	0.000219103i
$591$	−20.9461	−	39.6804i	−0.861606	−	1.63223i
$592$	−5.24909			−0.215736
$593$	5.48292	+	9.49670i	0.225157	+	0.389983i	0.956366	−	0.292170i	$-0.0943773\pi$
$593$	5.48292	+	9.49670i	0.225157	+	0.389983i	−0.731210	+	0.682153i	$0.761044\pi$
$594$	12.5488	−	5.45237i	0.514884	−	0.223713i
$595$	0.0102463	+	0.0186888i	0.000420058	+	0.000766165i
$596$	5.50691	+	3.17942i	0.225572	+	0.130234i
$597$	−2.55295	+	4.05845i	−0.104485	+	0.166101i
$598$	4.73679	−	17.9037i	0.193702	−	0.732136i
$599$	−12.1466	−	7.01285i	−0.496297	−	0.286537i	0.230886	−	0.972981i	$-0.425838\pi$
$599$	−12.1466	−	7.01285i	−0.496297	−	0.286537i	−0.727183	+	0.686444i	$0.759171\pi$
$600$	12.3122	+	23.3243i	0.502644	+	0.952213i
$601$	−3.15684	−	1.82260i	−0.128770	−	0.0743455i	0.434231	−	0.900801i	$-0.357020\pi$
$601$	−3.15684	−	1.82260i	−0.128770	−	0.0743455i	−0.563001	+	0.826456i	$0.690353\pi$
$602$	6.50478	−	3.56631i	0.265115	−	0.145352i
$603$	24.1248	−	35.3079i	0.982439	−	1.43785i
$604$	−7.23527	+	12.5319i	−0.294399	+	0.509914i
$605$	0.00919461			0.000373814
$606$	−32.9638	−	1.25010i	−1.33906	−	0.0507817i
$607$	14.9262	+	8.61762i	0.605834	+	0.349778i	0.771333	−	0.636432i	$-0.219590\pi$
$607$	14.9262	+	8.61762i	0.605834	+	0.349778i	−0.165499	+	0.986210i	$0.552924\pi$
$608$	−12.2848	+	21.2779i	−0.498214	+	0.862933i
$609$	17.9128	+	35.8297i	0.725862	+	1.45189i
$610$	0.0154212			0.000624386
$611$	12.4707	−	3.38370i	0.504509	−	0.136890i
$612$	4.81531	+	10.0250i	0.194647	+	0.405236i
$613$	15.2562	+	26.4245i	0.616193	+	1.06728i	0.990174	+	0.139841i	$0.0446590\pi$
$613$	15.2562	+	26.4245i	0.616193	+	1.06728i	−0.373982	+	0.927436i	$0.622008\pi$
$614$	5.20234			0.209949
$615$	−0.0103551	−	0.00651387i	−0.000417560	−	0.000262665i
$616$	9.67207	+	17.6414i	0.389699	+	0.710791i
$617$	−5.82452	+	3.36279i	−0.234486	+	0.135381i	−0.612640	−	0.790362i	$-0.709892\pi$
$617$	−5.82452	+	3.36279i	−0.234486	+	0.135381i	0.378154	+	0.925743i	$0.376559\pi$
$618$	0.675504	−	17.8124i	0.0271728	−	0.716519i
$619$	8.43263	+	4.86858i	0.338936	+	0.195685i	0.659801	−	0.751440i	$-0.270640\pi$
$619$	8.43263	+	4.86858i	0.338936	+	0.195685i	−0.320865	+	0.947125i	$0.603974\pi$
$620$			0.0130116i			0.000522558i
$621$	25.1453	+	2.87180i	1.00905	+	0.115241i
$622$	12.2236	+	7.05729i	0.490121	+	0.282971i
$623$	14.2936	+	0.315831i	0.572662	+	0.0126535i
$624$	−6.55704	+	6.11646i	−0.262492	+	0.244854i
$625$	−12.5000	−	21.6506i	−0.499999	−	0.866023i
$626$	14.5880	+	25.2672i	0.583056	+	1.00988i
$627$	−19.6520	−	12.3620i	−0.784824	−	0.493691i
$628$	3.62006	+	2.09004i	0.144456	+	0.0834018i
$629$	15.2635			0.608595
$630$	−0.0131298	−	0.00940326i	−0.000523103	−	0.000374635i
$631$	−1.16211	−	2.01284i	−0.0462630	−	0.0801299i	0.841967	−	0.539530i	$-0.181398\pi$
$631$	−1.16211	−	2.01284i	−0.0462630	−	0.0801299i	−0.888230	+	0.459400i	$0.848065\pi$
$632$	−19.2261	+	11.1002i	−0.764774	+	0.441543i
$633$	−11.9674	+	6.31723i	−0.475662	+	0.251087i
$634$	7.81668	+	13.5389i	0.310440	+	0.537698i
$635$	0.0182105			0.000722663
$636$	−10.2573	−	19.4315i	−0.406728	−	0.770510i
$637$	7.52678	−	24.0904i	0.298222	−	0.954497i
$638$			23.0171i			0.911256i
$639$	3.54809	+	2.42430i	0.140360	+	0.0959040i
$640$	0.00172979		0.000998693i	6.83759e−5		3.94768e-5i
$641$			11.0379i			0.435970i	0.975952	+	0.217985i	$0.0699483\pi$
$641$			11.0379i			0.435970i	−0.975952	+	0.217985i	$0.930052\pi$
$642$	−8.44592	−	5.31288i	−0.333334	−	0.209683i
$643$	−2.75926	+	1.59306i	−0.108815	+	0.0628241i	−0.553420	−	0.832903i	$-0.686677\pi$
$643$	−2.75926	+	1.59306i	−0.108815	+	0.0628241i	0.444605	+	0.895727i	$0.353344\pi$
$644$	−0.252758	+	11.4391i	−0.00996007	+	0.450765i
$645$	0.00785754	−	0.00414775i	0.000309390	−	0.000163318i
$646$	−11.8186	+	20.4704i	−0.464997	+	0.805399i
$647$	−19.9767	−	34.6006i	−0.785365	−	1.36029i	−0.928781	−	0.370629i	$-0.879142\pi$
$647$	−19.9767	−	34.6006i	−0.785365	−	1.36029i	0.143416	−	0.989662i	$-0.454191\pi$
$648$	−21.3948	−	17.1326i	−0.840468	−	0.673034i
$649$	11.3120	−	6.53099i	0.444035	−	0.256364i
$650$	13.4006	−	13.4854i	0.525616	−	0.528943i
$651$	15.5644	+	31.1325i	0.610018	+	1.22018i
$652$	1.86738	−	3.23440i	0.0731323	−	0.126669i
$653$			15.8931i			0.621946i	0.950419	+	0.310973i	$0.100655\pi$
$653$			15.8931i			0.621946i	−0.950419	+	0.310973i	$0.899345\pi$
$654$	−6.28483	−	11.9060i	−0.245756	−	0.465563i
$655$	−0.00600235	+	0.0103964i	−0.000234531	+	0.000406220i
$656$	−2.62816	+	4.55211i	−0.102613	+	0.177730i
$657$	−0.422580	+	5.56350i	−0.0164864	+	0.217053i
$658$	8.76789	−	4.80709i	0.341808	−	0.187400i
$659$	43.5079	−	25.1193i	1.69483	−	0.978510i	0.744315	−	0.667829i	$-0.232776\pi$
$659$	43.5079	−	25.1193i	1.69483	−	0.978510i	0.950514	−	0.310681i	$-0.100557\pi$
$660$	0.00345854	+	0.00655189i	0.000134623	+	0.000255032i
$661$	43.6126	−	25.1798i	1.69633	−	0.979379i	0.747151	−	0.664654i	$-0.231421\pi$
$661$	43.6126	−	25.1798i	1.69633	−	0.979379i	0.949183	−	0.314725i	$-0.101912\pi$
$662$	−5.30506	−	3.06288i	−0.206187	−	0.119042i
$663$	19.0668	−	17.7856i	0.740493	−	0.690737i
$664$			31.7000i			1.23020i
$665$	−0.000605367		0.0273972i	−2.34751e−5		0.00106242i
$666$	−10.4253	+	5.00758i	−0.403971	+	0.194040i
$667$	−21.2881	+	36.8721i	−0.824280	+	1.42769i
$668$	6.43717	−	11.1495i	0.249062	−	0.431387i
$669$	6.05776	+	11.4759i	0.234206	+	0.443683i
$670$	−0.0251171	−	0.0145014i	−0.000970358	−	0.000560236i
$671$	−18.9244			−0.730570
$672$	11.5568	−	17.5019i	0.445815	−	0.675150i
$673$	18.1511	−	31.4387i	0.699674	−	1.21187i	−0.268905	−	0.963167i	$-0.586662\pi$
$673$	18.1511	−	31.4387i	0.699674	−	1.21187i	0.968579	−	0.248704i	$-0.0800048\pi$
$674$		−	10.0766i		−	0.388135i
$675$	20.8806	+	15.4596i	0.803696	+	0.595039i
$676$	−10.0324	−	5.70812i	−0.385862	−	0.219543i
$677$	18.7369	+	32.4533i	0.720119	+	1.24728i	0.960952	+	0.276716i	$0.0892460\pi$
$677$	18.7369	+	32.4533i	0.720119	+	1.24728i	−0.240833	+	0.970567i	$0.577421\pi$
$678$	−0.0312266	+	0.823415i	−0.00119925	+	0.0316231i
$679$	−5.54562	+	3.04044i	−0.212822	+	0.116682i
$680$	0.0212465	−	0.0122667i	0.000814765	−	0.000470405i
$681$	−12.5225	−	7.87724i	−0.479864	−	0.301857i
$682$			19.9996i			0.765824i
$683$		−	37.8062i		−	1.44661i	−0.690526	−	0.723307i	$-0.742621\pi$
$683$		−	37.8062i		−	1.44661i	0.690526	−	0.723307i	$-0.257379\pi$
$684$	−1.08302	+	14.2585i	−0.0414103	+	0.545189i
$685$	−0.0102865	+	0.00593893i	−0.000393028	+	0.000226915i
$686$	1.29350	−	19.4879i	0.0493859	−	0.744053i
$687$	17.8282	+	0.676103i	0.680187	+	0.0257949i
$688$	−1.90881	−	3.30615i	−0.0727726	−	0.126046i
$689$	−36.3114	+	36.5412i	−1.38335	+	1.39211i
$690$	0.000650486	−	0.0171527i	2.47636e−5	−	0.000652991i
$691$		−	12.9636i		−	0.493158i	−0.969123	−	0.246579i	$-0.920694\pi$
$691$		−	12.9636i		−	0.493158i	0.969123	−	0.246579i	$-0.0793065\pi$
$692$	6.96851	−	12.0698i	0.264903	−	0.458825i
$693$	16.1125	+	11.5394i	0.612063	+	0.438346i
$694$	−30.7066			−1.16561
$695$	0.0205801	+	0.0118819i	0.000780648	+	0.000450708i
$696$	40.7773	−	21.5251i	1.54566	−	0.815906i
$697$	7.64226	−	13.2368i	0.289471	−	0.501379i
$698$	16.5345	−	28.6385i	0.625839	−	1.08399i
$699$	2.19241	+	0.0831436i	0.0829247	+	0.00314478i
$700$	−6.09613	+	10.0399i	−0.230412	+	0.379471i
$701$			34.9085i			1.31848i	0.751934	+	0.659238i	$0.229121\pi$
$701$			34.9085i			1.31848i	−0.751934	+	0.659238i	$0.770879\pi$
$702$	−7.18798	+	18.4033i	−0.271293	+	0.694589i
$703$	16.9960	+	9.81262i	0.641014	+	0.370090i
$704$	16.6463	−	9.61075i	0.627381	−	0.362219i
$705$	0.0105913	−	0.00559082i	0.000398892	−	0.000210563i
$706$	−1.45710	+	0.841257i	−0.0548387	+	0.0316611i
$707$	−22.9711	−	41.8981i	−0.863915	−	1.57574i
$708$	−6.80981	−	4.28369i	−0.255928	−	0.160991i
$709$	−18.2820	+	31.6653i	−0.686595	+	1.18922i	0.286338	+	0.958129i	$0.407562\pi$
$709$	−18.2820	+	31.6653i	−0.686595	+	1.18922i	−0.972933	+	0.231088i	$0.925771\pi$
$710$	0.00145724	−	0.00252402i	5.46893e−5	−	9.47247e-5i
$711$	−12.3375	+	18.0565i	−0.462691	+	0.677172i
$712$		−	16.4571i		−	0.616756i
$713$	−18.4973	+	32.0382i	−0.692729	+	1.19984i
$714$	11.1183	−	16.8377i	0.416092	−	0.630136i
$715$	0.0122434	−	0.0123209i	0.000457877	−	0.000460776i
$716$	−4.97089	+	2.86994i	−0.185771	+	0.107255i
$717$	−17.3750	+	27.6212i	−0.648882	+	1.03153i
$718$	6.80262	+	11.7825i	0.253871	+	0.439718i
$719$	−19.8403	+	34.3644i	−0.739919	+	1.28158i	0.212612	+	0.977137i	$0.431803\pi$
$719$	−19.8403	+	34.3644i	−0.739919	+	1.28158i	−0.952531	+	0.304441i	$0.901530\pi$
$720$	−0.00468869	+	0.00686214i	−0.000174737	+	0.000255737i
$721$	22.6401	−	12.4127i	0.843163	−	0.462272i
$722$	−8.96785	+	5.17759i	−0.333749	+	0.192690i
$723$	1.12821	−	1.79352i	0.0419584	−	0.0667017i
$724$			0.834059i			0.0309976i
$725$	−37.8511	+	21.8534i	−1.40576	+	0.811613i
$726$	−4.06348	−	7.69788i	−0.150810	−	0.285695i
$727$			15.6289i			0.579644i	0.957081	+	0.289822i	$0.0935961\pi$
$727$			15.6289i			0.579644i	−0.957081	+	0.289822i	$0.906404\pi$
$728$	−27.9146	−	8.04924i	−1.03458	−	0.298325i
$729$	−26.3047	−	6.08783i	−0.974249	−	0.225475i
$730$	0.00378416			0.000140058
$731$	5.55049	+	9.61373i	0.205292	+	0.355577i
$732$	5.44122	+	10.3079i	0.201113	+	0.380991i
$733$	−25.0179	+	14.4441i	−0.924055	+	0.533504i	−0.884927	−	0.465730i	$-0.845792\pi$
$733$	−25.0179	+	14.4441i	−0.924055	+	0.533504i	−0.0391289	+	0.999234i	$0.512458\pi$
$734$	6.90732	+	11.9638i	0.254954	+	0.441593i
$735$	0.00191814	−	0.0233139i	7.07518e−5	−	0.000859945i
$736$	22.2918			0.821686
$737$	30.8230	+	17.7957i	1.13538	+	0.655511i
$738$	−0.877157	+	11.5482i	−0.0322886	+	0.425097i
$739$	−7.56592	−	13.1046i	−0.278317	−	0.482059i	0.692650	−	0.721274i	$-0.256443\pi$
$739$	−7.56592	−	13.1046i	−0.278317	−	0.482059i	−0.970967	+	0.239215i	$0.923110\pi$
$740$	−0.00313130	−	0.00542356i	−0.000115109	−	0.000199374i
$741$	32.6650	−	7.54669i	1.19998	−	0.277235i
$742$	−20.6899	+	34.0746i	−0.759549	+	1.25092i
$743$	30.5018	+	17.6102i	1.11900	+	0.646056i	0.941146	−	0.338001i	$-0.109751\pi$
$743$	30.5018	+	17.6102i	1.11900	+	0.646056i	0.177856	+	0.984057i	$0.443084\pi$
$744$	35.4314	−	18.7032i	1.29898	−	0.685691i
$745$		−	0.0138178i		−	0.000506244i
$746$	−5.60517	−	3.23614i	−0.205220	−	0.118484i
$747$	13.5203	+	28.1480i	0.494683	+	1.02988i
$748$	−8.01626	+	4.62819i	−0.293103	+	0.169223i
$749$	0.319275	−	14.4495i	0.0116660	−	0.527973i
$750$	0.0187647	−	0.0298304i	0.000685189	−	0.00108925i
$751$	1.65351			0.0603375			0.0301687	−	0.999545i	$-0.490396\pi$
$751$	1.65351			0.0603375			0.0301687	+	0.999545i	$0.490396\pi$
$752$	−2.57291	−	4.45641i	−0.0938244	−	0.162509i
$753$	−0.580604	+	15.3100i	−0.0211584	+	0.557926i
$754$	−23.5762	−	23.4279i	−0.858595	−	0.853195i
$755$	0.0314445			0.00114438
$756$	1.65265	−	12.0941i	0.0601062	−	0.439859i
$757$	−7.44232	+	12.8905i	−0.270496	+	0.468513i	−0.968989	−	0.247104i	$-0.920521\pi$
$757$	−7.44232	+	12.8905i	−0.270496	+	0.468513i	0.698493	+	0.715617i	$0.253854\pi$
$758$	11.7832	+	6.80303i	0.427985	+	0.247097i
$759$	−0.798257	+	21.0493i	−0.0289749	+	0.764040i
$760$	0.0315441			0.00114422
$761$	4.20006	−	7.27471i	0.152252	−	0.263708i	−0.779803	−	0.626025i	$-0.784681\pi$
$761$	4.20006	−	7.27471i	0.152252	−	0.263708i	0.932055	+	0.362317i	$0.118014\pi$
$762$	−8.04799	−	15.2462i	−0.291548	−	0.552311i
$763$	10.1212	−	16.6689i	0.366413	−	0.603454i
$764$	4.13646	+	2.38818i	0.149652	+	0.0864015i
$765$	0.0136339	−	0.0199540i	0.000492936	−	0.000721437i
$766$	−8.43849	−	4.87196i	−0.304895	−	0.176031i
$767$	−4.82427	+	18.2343i	−0.174194	+	0.658403i
$768$	−24.1732	−	15.2061i	−0.872277	−	0.548703i
$769$	−40.4429	−	23.3497i	−1.45841	−	0.842013i	−0.459476	−	0.888190i	$-0.651963\pi$
$769$	−40.4429	−	23.3497i	−1.45841	−	0.842013i	−0.998933	+	0.0461769i	$0.985296\pi$
$770$	0.00697617	−	0.0114892i	0.000251404	−	0.000414043i
$771$	16.0448	+	10.0929i	0.577840	+	0.363488i
$772$	−9.38617	−	16.2573i	−0.337816	−	0.585114i
$773$	34.7010			1.24811			0.624055	−	0.781381i	$-0.285484\pi$
$773$	34.7010			1.24811			0.624055	+	0.781381i	$0.285484\pi$
$774$	−6.94514	−	4.74540i	−0.249638	−	0.170570i
$775$	−32.8889	+	18.9884i	−1.18140	+	0.682084i
$776$	3.63995	+	6.30458i	0.130667	+	0.226321i
$777$	−13.9798	−	9.23116i	−0.501523	−	0.331166i
$778$	−6.93262	+	12.0076i	−0.248546	+	0.430495i
$779$	17.0194	−	9.82614i	0.609783	−	0.352058i
$780$	−0.0102313	−	0.00312627i	−0.000366339	−	0.000111939i
$781$	−1.78829	+	3.09740i	−0.0639899	+	0.110834i
$782$	21.4459			0.766902
$783$	27.0275	−	36.5050i	0.965884	−	1.30458i
$784$	−10.0412	−	0.443956i	−0.358614	−	0.0158556i
$785$		−	0.00908333i		−	0.000324198i
$786$	11.3567	+	0.430683i	0.405080	+	0.0153620i
$787$			23.0530i			0.821750i	0.911692	+	0.410875i	$0.134777\pi$
$787$			23.0530i			0.821750i	−0.911692	+	0.410875i	$0.865223\pi$
$788$	−19.9197	−	11.5006i	−0.709609	−	0.409693i
$789$	22.0064	+	0.834554i	0.783448	+	0.0297109i
$790$	0.0128449	+	0.00741602i	0.000457002	+	0.000263850i
$791$	−1.04659	+	0.573803i	−0.0372124	+	0.0204021i
$792$	12.8698	−	18.8357i	0.457310	−	0.669296i
$793$	19.2622	−	19.3841i	0.684021	−	0.688351i
$794$	−9.78631	+	16.9504i	−0.347303	+	0.601547i
$795$	−0.0254231	+	0.0404153i	−0.000901665	+	0.00143338i
$796$			2.45785i			0.0871163i
$797$	18.0616	+	31.2836i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543054\pi$
$797$	18.0616	+	31.2836i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$798$	23.2049	−	11.6011i	0.821446	−	0.410675i
$799$	7.48159	+	12.9585i	0.264680	+	0.458439i
$800$	19.8178	+	11.4418i	0.700666	+	0.404530i
$801$	−7.01910	−	14.6131i	−0.248008	−	0.516327i
$802$	−13.0272			−0.460007
$803$	−4.64382			−0.163877
$804$	0.830730	−	21.9055i	0.0292976	−	0.772549i
$805$	0.0218016	−	0.0119530i	0.000768406	−	0.000421286i
$806$	−20.4854	−	20.3566i	−0.721568	−	0.717029i
$807$	−33.9530	−	21.3580i	−1.19520	−	0.751837i
$808$	−47.6322	+	27.5004i	−1.67569	+	0.967462i
$809$	−25.7675	+	14.8769i	−0.905938	+	0.523044i	−0.879122	−	0.476597i	$-0.841870\pi$
$809$	−25.7675	+	14.8769i	−0.905938	+	0.523044i	−0.0268161	+	0.999640i	$0.508537\pi$
$810$	−0.00276585	+	0.0181019i	−9.71822e−5	+	0.000636038i
$811$		−	17.0021i		−	0.597025i	−0.954406	−	0.298512i	$-0.903510\pi$
$811$		−	17.0021i		−	0.597025i	0.954406	−	0.298512i	$-0.0964904\pi$
$812$	17.5524	+	10.6577i	0.615969	+	0.374012i
$813$	−24.2970	+	38.6251i	−0.852133	+	1.35464i
$814$	−4.81299	−	8.33634i	−0.168695	−	0.292189i
$815$	−0.00811564			−0.000284279
$816$	−8.78936	−	5.52892i	−0.307689	−	0.193551i
$817$			14.2732i			0.499358i
$818$	−6.08732			−0.212838
$819$	−28.2198	+	4.75851i	−0.986079	+	0.166276i
$820$	−0.00627123			−0.000219001
$821$		−	29.3115i		−	1.02298i	−0.859289	−	0.511490i	$-0.829094\pi$
$821$		−	29.3115i		−	1.02298i	0.859289	−	0.511490i	$-0.170906\pi$
$822$	9.51821	+	5.98739i	0.331986	+	0.208834i
$823$	−2.17785			−0.0759149			−0.0379575	−	0.999279i	$-0.512085\pi$
$823$	−2.17785			−0.0759149			−0.0379575	+	0.999279i	$0.512085\pi$
$824$	−14.8602	−	25.7386i	−0.517679	−	0.896647i
$825$	−11.5137	+	18.3035i	−0.400857	+	0.637245i
$826$	−0.322432	+	14.5924i	−0.0112188	+	0.507733i
$827$			15.2048i			0.528724i	0.964424	+	0.264362i	$0.0851613\pi$
$827$			15.2048i			0.528724i	−0.964424	+	0.264362i	$0.914839\pi$
$828$	11.6948	−	5.61736i	0.406422	−	0.195217i
$829$	−3.44342	+	1.98806i	−0.119595	+	0.0690483i	−0.558604	−	0.829434i	$-0.688663\pi$
$829$	−3.44342	+	1.98806i	−0.119595	+	0.0690483i	0.439009	+	0.898483i	$0.355330\pi$
$830$	0.0183413	−	0.0105893i	0.000636635	−	0.000367562i
$831$	−6.45746	−	4.06205i	−0.224007	−	0.140911i
$832$	−7.09921	+	26.8329i	−0.246121	+	0.930265i
$833$	29.1981	+	1.29095i	1.01166	+	0.0447288i
$834$	0.852559	−	22.4811i	0.0295217	−	0.778458i
$835$	−0.0279759			−0.000968148
$836$	−11.9015			−0.411623
$837$	23.4842	−	31.7193i	0.811733	−	1.09638i
$838$	−32.1784	−	18.5782i	−1.11158	−	0.641773i
$839$	−17.0612	−	29.5509i	−0.589019	−	1.02021i	−0.994361	−	0.106046i	$-0.966181\pi$
$839$	−17.0612	−	29.5509i	−0.589019	−	1.02021i	0.405342	−	0.914165i	$-0.367152\pi$
$840$	−0.0268784	−	0.00161457i	−0.000927391	−	5.57080e-5i
$841$	23.7056	+	41.0593i	0.817434	+	1.41584i
$842$			28.5049i			0.982345i
$843$	−12.2577	+	19.4862i	−0.422179	+	0.671141i
$844$	−3.46853	+	6.00767i	−0.119392	+	0.206793i
$845$	0.000158261		0.0250816i	5.44436e−6		0.000862834i
$846$	−9.36146	−	6.39640i	−0.321854	−	0.219913i
$847$	6.54390	−	10.7773i	0.224851	−	0.370313i
$848$	17.7665	+	10.2575i	0.610105	+	0.352244i
$849$	28.3482	+	1.07506i	0.972906	+	0.0368958i
$850$	19.0658	+	11.0076i	0.653951	+	0.377559i
$851$		−	17.8058i		−	0.610375i
$852$	2.20129	+	0.0834801i	0.0754149	+	0.00285998i
$853$			56.0005i			1.91742i	0.284387	+	0.958710i	$0.408210\pi$
$853$			56.0005i			1.91742i	−0.284387	+	0.958710i	$0.591790\pi$
$854$	10.9754	−	18.0757i	0.375571	−	0.618537i
$855$	0.0280095	−	0.0134538i	0.000957904	−	0.000460111i
$856$	−16.6366			−0.568626
$857$	7.20743	−	12.4836i	0.246201	−	0.426433i	−0.716268	−	0.697826i	$-0.754151\pi$
$857$	7.20743	−	12.4836i	0.246201	−	0.426433i	0.962469	+	0.271393i	$0.0874843\pi$
$858$	−15.7261	−	4.80527i	−0.536881	−	0.164049i
$859$	2.32454	−	1.34207i	0.0793121	−	0.0457909i	−0.459819	−	0.888012i	$-0.652086\pi$
$859$	2.32454	−	1.34207i	0.0793121	−	0.0457909i	0.539132	+	0.842222i	$0.318753\pi$
$860$	0.00227736	−	0.00394451i	7.76574e−5	−	0.000134507i
$861$	−15.0050	+	7.50162i	−0.511368	+	0.255655i
$862$	16.5183	+	28.6105i	0.562615	+	0.974479i
$863$	25.8619	−	14.9314i	0.880349	−	0.508270i	0.00957560	−	0.999954i	$-0.496952\pi$
$863$	25.8619	−	14.9314i	0.880349	−	0.508270i	0.870773	+	0.491684i	$0.163619\pi$
$864$	−23.6278	−	2.69849i	−0.803835	−	0.0918044i
$865$	−0.0302851			−0.00102973
$866$	2.08172	+	3.60565i	0.0707398	+	0.122525i
$867$	0.634236	+	0.398964i	0.0215398	+	0.0135495i
$868$	15.2513	+	9.26048i	0.517663	+	0.314321i
$869$	−15.7629	−	9.10072i	−0.534720	−	0.308721i
$870$	−0.0260758	−	0.0164029i	−0.000884051	−	0.000556109i
$871$	−49.6010	+	13.4584i	−1.68067	+	0.456021i
$872$	−19.4399	−	11.2236i	−0.658318	−	0.380080i
$873$	5.92105	+	4.04567i	0.200397	+	0.136925i
$874$	23.8800	+	13.7872i	0.807755	+	0.466357i
$875$	0.0510345	+	0.00112765i	0.00172528	+	3.81217e-5i
$876$	1.33521	+	2.52943i	0.0451125	+	0.0854614i
$877$	5.77032	−	9.99449i	0.194850	−	0.337490i	−0.752001	−	0.659162i	$-0.770911\pi$
$877$	5.77032	−	9.99449i	0.194850	−	0.337490i	0.946851	+	0.321671i	$0.104245\pi$
$878$	32.5509			1.09854
$879$	1.30793	−	34.4889i	0.0441154	−	1.16328i
$880$	−0.00599049	−	0.00345861i	−0.000201939	−	0.000116590i
$881$	3.76362	−	6.51878i	0.126800	−	0.219623i	−0.795635	−	0.605776i	$-0.792863\pi$
$881$	3.76362	−	6.51878i	0.126800	−	0.219623i	0.922435	+	0.386153i	$0.126196\pi$
$882$	−20.3665	+	8.69746i	−0.685775	+	0.292859i
$883$	−38.2310			−1.28658			−0.643289	−	0.765624i	$-0.722430\pi$
$883$	−38.2310			−1.28658			−0.643289	+	0.765624i	$0.722430\pi$
$884$	3.41872	−	12.9218i	0.114984	−	0.434606i
$885$	−0.000662499		0.0174694i	−2.22696e−5		0.000587229i
$886$	−9.91025	−	17.1651i	−0.332941	−	0.576672i
$887$	28.6232			0.961074			0.480537	−	0.876974i	$-0.340442\pi$
$887$	28.6232			0.961074			0.480537	+	0.876974i	$0.340442\pi$
$888$	−10.2677	+	16.3227i	−0.344562	+	0.547753i
$889$	12.9606	−	21.3452i	0.434686	−	0.715894i
$890$	−0.00952190	+	0.00549747i	−0.000319175	+	0.000184276i
$891$	3.39418	−	22.2142i	0.113709	−	0.744203i
$892$	5.76092	+	3.32607i	0.192890	+	0.111365i
$893$			19.2391i			0.643813i
$894$	−11.5685	+	6.10663i	−0.386907	+	0.204236i
$895$	0.0108017	+	0.00623639i	0.000361063	+	0.000208460i
$896$	0.0605058	−	2.73832i	0.00202136	−	0.0914809i
$897$	−20.7481	−	22.2426i	−0.692757	−	0.742659i
$898$	3.01891	+	5.22890i	0.100742	+	0.174491i
$899$	33.1969	+	57.4987i	1.10718	+	1.91769i
$900$	13.2801	+	1.00870i	0.442671	+	0.0336235i
$901$	−51.6621	−	29.8271i	−1.72111	−	0.993686i
$902$	−9.63925			−0.320952
$903$	0.730571	−	12.1621i	0.0243119	−	0.404729i
$904$	0.686944	+	1.18982i	0.0228474	+	0.0395729i
$905$	0.00156959		0.000906206i	5.21751e−5		3.01233e-5i
$906$	−13.8966	−	26.3259i	−0.461684	−	0.874618i
$907$	14.8995	+	25.8067i	0.494730	+	0.856898i	0.999982	−	0.00607461i	$-0.00193362\pi$
$907$	14.8995	+	25.8067i	0.494730	+	0.856898i	−0.505252	+	0.862972i	$0.668600\pi$
$908$	−7.58381			−0.251678
$909$	−30.5657	+	44.7345i	−1.01380	+	1.48375i
$910$	0.00466763	+	0.0188399i	0.000154730	+	0.000624537i
$911$			28.3029i			0.937717i	0.883273	+	0.468859i	$0.155335\pi$
$911$			28.3029i			0.937717i	−0.883273	+	0.468859i	$0.844665\pi$
$912$	−6.23255	−	11.8070i	−0.206380	−	0.390969i
$913$	−22.5079	+	12.9949i	−0.744903	+	0.430070i
$914$			35.7482i			1.18245i
$915$	0.0134863	−	0.0214392i	0.000445842	−	0.000708759i
$916$	7.92044	−	4.57287i	0.261699	−	0.151092i
$917$	7.91400	+	14.4347i	0.261343	+	0.476677i
$918$	−22.7312	−	2.59609i	−0.750241	−	0.0856836i
$919$	24.5422	−	42.5083i	0.809573	−	1.40222i	−0.103588	−	0.994620i	$-0.533032\pi$
$919$	24.5422	−	42.5083i	0.809573	−	1.40222i	0.913160	−	0.407601i	$-0.133634\pi$
$920$	−0.0143098	−	0.0247853i	−0.000471781	−	0.000817148i
$921$	4.54960	−	7.23253i	0.149914	−	0.238320i
$922$	−17.1318	+	9.89103i	−0.564205	+	0.325744i
$923$	−1.35244	−	4.98441i	−0.0445160	−	0.164064i
$924$	10.1412	+	0.609175i	0.333620	+	0.0200404i
$925$	9.13928	−	15.8297i	0.300498	−	0.520477i
$926$		−	21.2918i		−	0.699693i
$927$	−24.1728	−	16.5166i	−0.793940	−	0.542475i
$928$	20.0034	−	34.6469i	0.656644	−	1.13734i
$929$	10.3944	−	18.0037i	0.341031	−	0.590682i	−0.643594	−	0.765367i	$-0.722557\pi$
$929$	10.3944	−	18.0037i	0.341031	−	0.590682i	0.984624	+	0.174685i	$0.0558907\pi$
$930$	−0.0226573	−	0.0142525i	−0.000742961	−	0.000467357i
$931$	31.6823	+	20.2084i	1.03835	+	0.662305i
$932$	0.974015	−	0.562348i	0.0319049	−	0.0184203i
$933$	20.5012	−	10.8220i	0.671180	−	0.354295i
$934$	6.52555	−	3.76753i	0.213522	−	0.123277i
$935$	0.0174193	+	0.0100571i	0.000569673	+	0.000328901i
$936$	6.19366	+	32.3543i	0.202446	+	1.05753i
$937$			10.5891i			0.345930i	0.984928	+	0.172965i	$0.0553347\pi$
$937$			10.5891i			0.345930i	−0.984928	+	0.172965i	$0.944665\pi$
$938$	−34.8736	+	19.1198i	−1.13866	+	0.624284i
$939$	47.8853	+	1.81597i	1.56268	+	0.0592619i
$940$	0.00306969	−	0.00531686i	0.000100122	−	0.000173417i
$941$	−21.4748	+	37.1955i	−0.700059	+	1.21254i	0.268386	+	0.963311i	$0.413510\pi$
$941$	−21.4748	+	37.1955i	−0.700059	+	1.21254i	−0.968445	+	0.249227i	$0.919824\pi$
$942$	−7.60472	+	4.01430i	−0.247775	+	0.130793i
$943$	−15.4415	−	8.91517i	−0.502846	−	0.290318i
$944$	7.51141			0.244475
$945$	−0.0245552	+	0.0100302i	−0.000798781	+	0.000326282i
$946$	3.50044	−	6.06294i	0.113809	−	0.197123i
$947$			49.0592i			1.59421i	0.603842	+	0.797104i	$0.293636\pi$
$947$			49.0592i			1.59421i	−0.603842	+	0.797104i	$0.706364\pi$
$948$	−0.424837	+	11.2025i	−0.0137981	+	0.363841i
$949$	4.72670	−	4.75662i	0.153435	−	0.154406i
$950$	14.1532	+	24.5141i	0.459191	+	0.795342i
$951$	25.6583	+	0.973047i	0.832027	+	0.0315532i
$952$	0.743175	−	33.6340i	0.0240864	−	1.09008i
$953$	−28.5078	+	16.4590i	−0.923458	+	0.533159i	−0.884737	−	0.466091i	$-0.845662\pi$
$953$	−28.5078	+	16.4590i	−0.923458	+	0.533159i	−0.0387215	+	0.999250i	$0.512329\pi$
$954$	45.0719	+	3.42347i	1.45926	+	0.110839i
$955$		−	0.0103791i		−	0.000335858i
$956$			16.7278i			0.541015i
$957$	31.9994	+	20.1291i	1.03439	+	0.650683i
$958$	8.43802	−	4.87169i	0.272620	−	0.157397i
$959$	−0.359809	+	16.2840i	−0.0116189	+	0.525837i
$960$	−0.000974908		0.0257074i	−3.14650e−5		0.000829701i
$961$	13.3448	+	23.1139i	0.430478	+	0.745609i
$962$	13.4377	+	3.55523i	0.433250	+	0.114625i
$963$	−14.7724	+	7.09564i	−0.476034	+	0.228654i
$964$		−	1.08618i		−	0.0349835i
$965$	−0.0203962	+	0.0353272i	−0.000656576	+	0.00113722i
$966$	−19.6422	−	12.9702i	−0.631979	−	0.417309i
$967$	27.5780			0.886848			0.443424	−	0.896312i	$-0.353764\pi$
$967$	27.5780			0.886848			0.443424	+	0.896312i	$0.353764\pi$
$968$	−12.5689	−	7.25666i	−0.403980	−	0.233238i
$969$	18.1232	+	34.3328i	0.582202	+	1.10293i
$970$	0.00243184	−	0.00421207i	7.80818e−5	−	0.000135242i
$971$	−17.2874	+	29.9426i	−0.554778	+	0.960904i	0.443143	+	0.896451i	$0.353864\pi$
$971$	−17.2874	+	29.9426i	−0.554778	+	0.960904i	−0.997921	+	0.0644528i	$0.979470\pi$
$972$	−13.0757	+	4.53834i	−0.419403	+	0.145567i
$973$	28.5743	−	15.6661i	0.916050	−	0.502233i
$974$			1.37257i			0.0439798i
$975$	−7.02885	−	30.4236i	−0.225103	−	0.974334i
$976$	−9.42467	−	5.44133i	−0.301676	−	0.174173i
$977$	50.1256	−	28.9400i	1.60366	−	0.925874i	0.612914	−	0.790150i	$-0.289997\pi$
$977$	50.1256	−	28.9400i	1.60366	−	0.925874i	0.990747	−	0.135724i	$-0.0433361\pi$
$978$	3.58664	+	6.79455i	0.114688	+	0.217266i
$979$	11.6850	−	6.74634i	0.373454	−	0.215614i
$980$	−0.00553127	−	0.0106398i	−0.000176690	−	0.000339876i
$981$	−22.0486	−	1.67472i	−0.703957	−	0.0534697i
$982$	−6.97052	+	12.0733i	−0.222438	+	0.385274i
$983$	1.73371	−	3.00288i	0.0552969	−	0.0957770i	−0.837052	−	0.547123i	$-0.815723\pi$
$983$	1.73371	−	3.00288i	0.0552969	−	0.0957770i	0.892349	+	0.451347i	$0.149056\pi$
$984$	9.01440	+	17.0770i	0.287369	+	0.544394i
$985$			0.0499818i			0.00159255i
$986$	19.2443	−	33.3322i	0.612864	−	1.06151i
$987$	0.984748	−	16.3935i	0.0313449	−	0.521810i
$988$	12.1139	−	12.1906i	0.385396	−	0.387835i
$989$	11.2150	−	6.47499i	0.356617	−	0.205893i
$990$	−0.0151973	−	0.00115432i	−0.000483001	−	3.66867e-5i
$991$	−4.47519	−	7.75126i	−0.142159	−	0.246227i	0.786150	−	0.618035i	$-0.212071\pi$
$991$	−4.47519	−	7.75126i	−0.142159	−	0.246227i	−0.928309	+	0.371809i	$0.878738\pi$
$992$	17.3810	−	30.1048i	0.551847	−	0.955827i
$993$	−8.89757	+	4.69676i	−0.282356	+	0.149047i
$994$	−1.92135	−	3.50445i	−0.0609415	−	0.111154i
$995$	0.00462537	−	0.00267046i	0.000146634	−	8.46592e-5i
$996$	13.5497	+	8.52341i	0.429339	+	0.270075i
$997$			3.25743i			0.103164i	0.998669	+	0.0515818i	$0.0164263\pi$
$997$			3.25743i			0.103164i	−0.998669	+	0.0515818i	$0.983574\pi$
$998$	−5.81243	+	3.35581i	−0.183989	+	0.106226i
$999$	−2.15545	+	18.8730i	−0.0681953	+	0.597114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.r.b.269.22	yes	64
3.2	odd	2	inner	273.2.r.b.269.11	yes	64
7.5	odd	6		273.2.bf.b.152.22	yes	64
13.3	even	3		273.2.bf.b.185.11	yes	64
21.5	even	6		273.2.bf.b.152.11	yes	64
39.29	odd	6		273.2.bf.b.185.22	yes	64
91.68	odd	6	inner	273.2.r.b.68.22	yes	64
273.68	even	6	inner	273.2.r.b.68.11	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.11	✓	64	273.68	even	6	inner
273.2.r.b.68.22	yes	64	91.68	odd	6	inner
273.2.r.b.269.11	yes	64	3.2	odd	2	inner
273.2.r.b.269.22	yes	64	1.1	even	1	trivial
273.2.bf.b.152.11	yes	64	21.5	even	6
273.2.bf.b.152.22	yes	64	7.5	odd	6
273.2.bf.b.185.11	yes	64	13.3	even	3
273.2.bf.b.185.22	yes	64	39.29	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.05456i q^{2} +(1.46610 + 0.922247i) q^{3} +0.887893 q^{4} +(-0.000964697 - 0.00167090i) q^{5} +(-0.972570 + 1.54610i) q^{6} +(-2.64511 - 0.0584461i) q^{7} +3.04547i q^{8} +(1.29892 + 2.70422i) q^{9} +(0.00176208 - 0.00101734i) q^{10} +(-2.16237 + 1.24844i) q^{11} +(1.30174 + 0.818857i) q^{12} +(0.922193 - 3.48562i) q^{13} +(0.0616352 - 2.78943i) q^{14} +(0.000126641 - 0.00333941i) q^{15} -1.43586 q^{16} +4.17524 q^{17} +(-2.85178 + 1.36979i) q^{18} +(4.64914 + 2.68418i) q^{19} +(-0.000856548 - 0.00148358i) q^{20} +(-3.82410 - 2.52513i) q^{21} +(-1.31657 - 2.28036i) q^{22} -4.87067i q^{23} +(-2.80868 + 4.46497i) q^{24} +(2.50000 - 4.33012i) q^{25} +(3.67581 + 0.972512i) q^{26} +(-0.589610 + 5.16259i) q^{27} +(-2.34857 - 0.0518939i) q^{28} +(-7.57023 - 4.37067i) q^{29} +(0.00352162 + 0.000133551i) q^{30} +(-6.57778 - 3.79768i) q^{31} +4.57673i q^{32} +(-4.32163 - 0.163891i) q^{33} +4.40306i q^{34} +(0.00245407 + 0.00447610i) q^{35} +(1.15330 + 2.40106i) q^{36} +3.65572 q^{37} +(-2.83065 + 4.90282i) q^{38} +(4.56664 - 4.25979i) q^{39} +(0.00508869 - 0.00293796i) q^{40} +(1.83038 - 3.17031i) q^{41} +(2.66291 - 4.03276i) q^{42} +(1.32938 + 2.30256i) q^{43} +(-1.91995 + 1.10849i) q^{44} +(0.00326543 - 0.00477912i) q^{45} +5.13644 q^{46} +(1.79190 + 3.10366i) q^{47} +(-2.10512 - 1.32422i) q^{48} +(6.99317 + 0.309192i) q^{49} +(4.56640 + 2.63641i) q^{50} +(6.12133 + 3.85060i) q^{51} +(0.818809 - 3.09486i) q^{52} +(-12.3735 - 7.14382i) q^{53} +(-5.44429 - 0.621782i) q^{54} +(0.00417206 + 0.00240874i) q^{55} +(0.177996 - 8.05559i) q^{56} +(4.34064 + 8.22295i) q^{57} +(4.60916 - 7.98330i) q^{58} -5.23130 q^{59} +(0.000112444 - 0.00296504i) q^{60} +(6.56379 + 3.78960i) q^{61} +(4.00490 - 6.93670i) q^{62} +(-3.27773 - 7.22887i) q^{63} -7.69818 q^{64} +(-0.00671378 + 0.00182167i) q^{65} +(0.172833 - 4.55744i) q^{66} +(-7.12713 - 12.3445i) q^{67} +3.70716 q^{68} +(4.49197 - 7.14091i) q^{69} +(-0.00472034 + 0.00258797i) q^{70} +(1.24050 - 0.716205i) q^{71} +(-8.23562 + 3.95582i) q^{72} +(1.61067 + 0.929921i) q^{73} +3.85519i q^{74} +(7.65870 - 4.04279i) q^{75} +(4.12794 + 2.38327i) q^{76} +(5.79266 - 3.17589i) q^{77} +(4.49223 + 4.81581i) q^{78} +(3.64483 + 6.31302i) q^{79} +(0.00138517 + 0.00239918i) q^{80} +(-5.62562 + 7.02513i) q^{81} +(3.34329 + 1.93025i) q^{82} +10.4089 q^{83} +(-3.39539 - 2.24205i) q^{84} +(-0.00402784 - 0.00697642i) q^{85} +(-2.42820 + 1.40192i) q^{86} +(-7.06790 - 13.3895i) q^{87} +(-3.80210 - 6.58543i) q^{88} -5.40380 q^{89} +(0.00503989 + 0.00344361i) q^{90} +(-2.64302 + 9.16594i) q^{91} -4.32464i q^{92} +(-6.14130 - 11.6341i) q^{93} +(-3.27301 + 1.88967i) q^{94} -0.0103577i q^{95} +(-4.22088 + 6.70997i) q^{96} +(2.07015 - 1.19520i) q^{97} +(-0.326063 + 7.37475i) q^{98} +(-6.18481 - 4.22589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Introduction

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