LMFDB - Embedded newform 273.2.r.b.68.22

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			68.22
Character	$\chi$	$=$	273.68
Dual form			273.2.r.b.269.11

$q$-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} +(-0.0656379 + 1.73081i) q^{3} +0.887893 q^{4} +(0.000964697 - 0.00167090i) q^{5} +(-1.82525 - 0.0692194i) q^{6} +(-2.64511 + 0.0584461i) q^{7} +3.04547i q^{8} +(-2.99138 - 0.227213i) q^{9} +(0.00176208 + 0.00101734i) q^{10} +(2.16237 + 1.24844i) q^{11} +(-0.0582795 + 1.53677i) q^{12} +(0.922193 + 3.48562i) q^{13} +(-0.0616352 - 2.78943i) q^{14} +(0.00282869 + 0.00177938i) q^{15} -1.43586 q^{16} -4.17524 q^{17} +(0.239611 - 3.15461i) q^{18} +(4.64914 - 2.68418i) q^{19} +(0.000856548 - 0.00148358i) q^{20} +(0.0724603 - 4.58200i) q^{21} +(-1.31657 + 2.28036i) q^{22} -4.87067i q^{23} +(-5.27112 - 0.199898i) 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} +(-0.00187647 + 0.00298304i) q^{30} +(-6.57778 + 3.79768i) q^{31} +4.57673i q^{32} +(-2.30275 + 3.66070i) q^{33} -4.40306i q^{34} +(-0.00245407 + 0.00447610i) q^{35} +(-2.65603 - 0.201741i) q^{36} +3.65572 q^{37} +(2.83065 + 4.90282i) q^{38} +(-6.09347 + 1.36735i) q^{39} +(0.00508869 + 0.00293796i) q^{40} +(-1.83038 - 3.17031i) q^{41} +(4.83202 + 0.0764141i) 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} +(0.0942468 - 2.48519i) q^{48} +(6.99317 - 0.309192i) q^{49} +(-4.56640 + 2.63641i) q^{50} +(0.274054 - 7.22653i) 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} +(0.00251158 + 0.00157990i) q^{60} +(6.56379 - 3.78960i) q^{61} +(-4.00490 - 6.93670i) q^{62} +(7.92580 + 0.426168i) q^{63} -7.69818 q^{64} +(0.00671378 + 0.00182167i) q^{65} +(-3.86044 - 2.42840i) q^{66} +(-7.12713 + 12.3445i) q^{67} -3.70716 q^{68} +(8.43019 + 0.319701i) q^{69} +(-0.00472034 - 0.00258797i) q^{70} +(-1.24050 - 0.716205i) q^{71} +(0.691971 - 9.11017i) 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} +(-1.44196 - 6.42596i) q^{78} +(3.64483 - 6.31302i) q^{79} +(-0.00138517 + 0.00239918i) q^{80} +(8.89675 + 1.35936i) q^{81} +(3.34329 - 1.93025i) q^{82} -10.4089 q^{83} +(0.0643370 - 4.06833i) 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} +(-7.92144 - 0.300407i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.05456i			0.745690i	0.927894	+	0.372845i	$0.121618\pi$
$2$			1.05456i			0.745690i	−0.927894	+	0.372845i	$0.878382\pi$
$3$	−0.0656379	+	1.73081i	−0.0378961	+	0.999282i
$3$	−0.0656379	+	1.73081i	−0.0378961	+	0.999282i
$4$	0.887893			0.443947
$5$	0.000964697	−	0.00167090i	0.000431425	−	0.000747251i	−0.865810	−	0.500374i	$-0.833196\pi$
$5$	0.000964697	−	0.00167090i	0.000431425	−	0.000747251i	0.866241	+	0.499626i	$0.166529\pi$
$6$	−1.82525	−	0.0692194i	−0.745154	−	0.0282587i
$7$	−2.64511	+	0.0584461i	−0.999756	+	0.0220905i
$7$	−2.64511	+	0.0584461i	−0.999756	+	0.0220905i
$8$			3.04547i			1.07674i
$9$	−2.99138	−	0.227213i	−0.997128	−	0.0757377i
$10$	0.00176208	+	0.00101734i	0.000557217	+	0.000321710i
$11$	2.16237	+	1.24844i	0.651979	+	0.376420i	0.789214	−	0.614118i	$-0.210488\pi$
$11$	2.16237	+	1.24844i	0.651979	+	0.376420i	−0.137235	+	0.990539i	$0.543822\pi$
$12$	−0.0582795	+	1.53677i	−0.0168238	+	0.443628i
$13$	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
$15$	0.00282869	+	0.00177938i	0.000730365	+	0.000459433i
$16$	−1.43586			−0.358965
$17$	−4.17524			−1.01264			−0.506322	−	0.862345i	$-0.668995\pi$
$17$	−4.17524			−1.01264			−0.506322	+	0.862345i	$0.668995\pi$
$18$	0.239611	−	3.15461i	0.0564768	−	0.743548i
$19$	4.64914	−	2.68418i	1.06659	−	0.615794i	0.139340	−	0.990245i	$-0.455502\pi$
$19$	4.64914	−	2.68418i	1.06659	−	0.615794i	0.927247	+	0.374450i	$0.122169\pi$
$20$	0.000856548	−	0.00148358i	0.000191530	−	0.000331740i
$21$	0.0724603	−	4.58200i	0.0158121	−	0.999875i
$22$	−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	$-0.169542\pi$
$24$	−5.27112	−	0.199898i	−1.07596	−	0.0408041i
$25$	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	$-0.365256\pi$
$29$	7.57023	−	4.37067i	1.40576	−	0.811614i	0.994975	+	0.100120i	$0.0319227\pi$
$30$	−0.00187647	+	0.00298304i	−0.000342595	+	0.000544626i
$31$	−6.57778	+	3.79768i	−1.18140	+	0.682084i	−0.956339	−	0.292260i	$-0.905593\pi$
$31$	−6.57778	+	3.79768i	−1.18140	+	0.682084i	−0.225065	+	0.974344i	$0.572260\pi$
$32$			4.57673i			0.809060i
$33$	−2.30275	+	3.66070i	−0.400857	+	0.637246i
$34$		−	4.40306i		−	0.755118i
$35$	−0.00245407	+	0.00447610i	−0.000414813	+	0.000756599i
$36$	−2.65603	−	0.201741i	−0.442672	−	0.0336235i
$37$	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
$39$	−6.09347	+	1.36735i	−0.975736	+	0.218951i
$40$	0.00508869	+	0.00293796i	0.000804592	+	0.000464531i
$41$	−1.83038	−	3.17031i	−0.285857	−	0.495119i	0.686960	−	0.726696i	$-0.258945\pi$
$41$	−1.83038	−	3.17031i	−0.285857	−	0.495119i	−0.972817	+	0.231577i	$0.925612\pi$
$42$	4.83202	+	0.0764141i	0.745597	+	0.0117910i
$43$	1.32938	−	2.30256i	0.202729	−	0.351137i	−0.746678	−	0.665186i	$-0.768352\pi$
$43$	1.32938	−	2.30256i	0.202729	−	0.351137i	0.949407	+	0.314049i	$0.101686\pi$
$44$	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	$-0.917509\pi$
$47$	−1.79190	+	3.10366i	−0.261375	+	0.452715i	0.705232	+	0.708976i	$0.250843\pi$
$48$	0.0942468	−	2.48519i	0.0136033	−	0.358707i
$49$	6.99317	−	0.309192i	0.999024	−	0.0441703i
$50$	−4.56640	+	2.63641i	−0.645786	+	0.372845i
$51$	0.274054	−	7.22653i	0.0383752	−	1.01192i
$52$	0.818809	+	3.09486i	0.113548	+	0.429180i
$53$	12.3735	−	7.14382i	1.69962	−	0.981279i	0.753516	−	0.657429i	$-0.228356\pi$
$53$	12.3735	−	7.14382i	1.69962	−	0.981279i	0.946108	−	0.323850i	$-0.104977\pi$
$54$	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	$-0.389394\pi$
$59$	5.23130			0.681057			0.340529	+	0.940234i	$0.389394\pi$
$60$	0.00251158	+	0.00157990i	0.000324243	+	0.000203964i
$61$	6.56379	−	3.78960i	0.840407	−	0.485209i	−0.0169958	−	0.999856i	$-0.505410\pi$
$61$	6.56379	−	3.78960i	0.840407	−	0.485209i	0.857402	+	0.514647i	$0.172077\pi$
$62$	−4.00490	−	6.93670i	−0.508623	−	0.880961i
$63$	7.92580	+	0.426168i	0.998558	+	0.0536921i
$64$	−7.69818			−0.962273
$65$	0.00671378	+	0.00182167i	0.000832741	+	0.000225951i
$66$	−3.86044	−	2.42840i	−0.475188	−	0.298915i
$67$	−7.12713	+	12.3445i	−0.870717	+	1.50813i	−0.00946155	+	0.999955i	$0.503012\pi$
$67$	−7.12713	+	12.3445i	−0.870717	+	1.50813i	−0.861256	+	0.508172i	$0.830322\pi$
$68$	−3.70716			−0.449560
$69$	8.43019	+	0.319701i	1.01488	+	0.0384875i
$70$	−0.00472034	−	0.00258797i	−0.000564188	−	0.000309322i
$71$	−1.24050	−	0.716205i	−0.147221	−	0.0849979i	0.424580	−	0.905390i	$-0.360422\pi$
$71$	−1.24050	−	0.716205i	−0.147221	−	0.0849979i	−0.571801	+	0.820392i	$0.693755\pi$
$72$	0.691971	−	9.11017i	0.0815495	−	1.07364i
$73$	1.61067	−	0.929921i	0.188515	−	0.108839i	−0.402772	−	0.915300i	$-0.631953\pi$
$73$	1.61067	−	0.929921i	0.188515	−	0.108839i	0.591287	+	0.806461i	$0.298620\pi$
$74$			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
$78$	−1.44196	−	6.42596i	−0.163270	−	0.727596i
$79$	3.64483	−	6.31302i	0.410075	−	0.710271i	−0.584823	−	0.811161i	$-0.698836\pi$
$79$	3.64483	−	6.31302i	0.410075	−	0.710271i	0.994898	+	0.100891i	$0.0321692\pi$
$80$	−0.00138517	+	0.00239918i	−0.000154867	+	0.000268237i
$81$	8.89675	+	1.35936i	0.988528	+	0.151040i
$82$	3.34329	−	1.93025i	0.369205	−	0.213161i
$83$	−10.4089			−1.14253			−0.571263	−	0.820767i	$-0.693546\pi$
$83$	−10.4089			−1.14253			−0.571263	+	0.820767i	$0.693546\pi$
$84$	0.0643370	−	4.06833i	0.00701975	−	0.443891i
$85$	−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	$-0.407541\pi$
$89$	5.40380			0.572801			0.286401	+	0.958110i	$0.407541\pi$
$90$	−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
$96$	−7.92144	−	0.300407i	−0.808479	−	0.0306602i
$97$	2.07015	+	1.19520i	0.210192	+	0.121354i	0.601401	−	0.798948i	$-0.294610\pi$
$97$	2.07015	+	1.19520i	0.210192	+	0.121354i	−0.391209	+	0.920302i	$0.627943\pi$
$98$	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	−0.0691187	+	0.997608i	$0.522019\pi$
$101$	−9.02995	+	15.6403i	−0.898514	+	1.55627i	−0.829395	+	0.558663i	$0.811315\pi$
$102$	7.62084	+	0.289007i	0.754576	+	0.0286160i
$103$	−8.45144	−	4.87944i	−0.832745	−	0.480786i	0.0220466	−	0.999757i	$-0.492982\pi$
$103$	−8.45144	−	4.87944i	−0.832745	−	0.480786i	−0.854792	+	0.518971i	$0.826315\pi$
$104$	−10.6154	+	2.80851i	−1.04092	+	0.275397i
$105$	−0.00758618	−	0.00454132i	−0.000740336	−	0.000443187i
$106$	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	0.633780	−	0.773514i	$-0.281503\pi$
$109$	−3.68535	−	6.38321i	−0.352993	−	0.611401i	−0.986772	+	0.162113i	$0.948169\pi$
$110$	0.00254017	+	0.00439971i	0.000242196	+	0.000419496i
$111$	−0.239954	+	6.32734i	−0.0227754	+	0.600564i
$112$	3.79800	−	0.0839203i	0.358877	−	0.00792972i
$113$	−0.390686	−	0.225562i	−0.0367526	−	0.0212191i	0.481511	−	0.876440i	$-0.340088\pi$
$113$	−0.390686	−	0.225562i	−0.0367526	−	0.0212191i	−0.518264	+	0.855221i	$0.673421\pi$
$114$	−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
$117$	−1.96665	−	10.6364i	−0.181817	−	0.983332i
$118$			5.51674i			0.507857i
$119$	11.0439	−	0.244026i	1.01240	−	0.0223698i
$120$	−0.00541904	+	0.00861469i	−0.000494689	+	0.000786410i
$121$	−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
$126$	−0.449422	+	8.35827i	−0.0400377	+	0.744614i
$127$	−4.71924	−	8.17397i	−0.418765	−	0.725322i	0.577051	−	0.816708i	$-0.304204\pi$
$127$	−4.71924	−	8.17397i	−0.418765	−	0.725322i	−0.995816	+	0.0913863i	$0.970870\pi$
$128$			1.03524i			0.0915032i
$129$	3.89803	+	2.45204i	0.343202	+	0.215890i
$130$	−0.00192107	+	0.00708011i	−0.000168489	+	0.000620967i
$131$	3.11100	−	5.38841i	0.271809	−	0.470788i	−0.697516	−	0.716569i	$-0.745711\pi$
$131$	3.11100	−	5.38841i	0.271809	−	0.470788i	0.969325	+	0.245782i	$0.0790446\pi$
$132$	−2.04460	+	3.25031i	−0.177959	+	0.282903i
$133$	−12.1406	+	7.37168i	−1.05272	+	0.639205i
$134$	−13.0181	−	7.51602i	−1.12459	−	0.649285i
$135$	−0.00805740	−	0.00596552i	−0.000693471	−	0.000513430i
$136$		−	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	$-0.0847062\pi$
$138$	−0.337145	+	8.89018i	−0.0286997	+	0.756783i
$139$	−10.6666	−	6.15838i	−0.904731	−	0.522347i	−0.0259992	−	0.999662i	$-0.508277\pi$
$139$	−10.6666	−	6.15838i	−0.904731	−	0.522347i	−0.878732	+	0.477315i	$0.841610\pi$
$140$	−0.00217895	+	0.00397430i	−0.000184155	+	0.000335890i
$141$	−5.25421	−	3.30515i	−0.442485	−	0.278343i
$142$	0.755285	−	1.30819i	0.0633821	−	0.109781i
$143$	−2.35748	+	8.68851i	−0.197143	+	0.726570i
$144$	4.29520	+	0.326246i	0.357934	+	0.0271872i
$145$		−	0.0168655i		−	0.00140060i
$146$	0.980661	+	1.69856i	0.0811601	+	0.140573i
$147$	0.0761349	+	12.1241i	0.00627950	+	0.999980i
$148$	3.24589			0.266810
$149$	−6.20222	+	3.58086i	−0.508106	+	0.293355i	−0.732055	−	0.681246i	$-0.761438\pi$
$149$	−6.20222	+	3.58086i	−0.508106	+	0.293355i	0.223949	+	0.974601i	$0.428105\pi$
$150$	−4.26339	−	8.07660i	−0.348104	−	0.659451i
$151$	−8.14880	−	14.1141i	−0.663140	−	1.14859i	−0.979786	−	0.200049i	$-0.935890\pi$
$151$	−8.14880	−	14.1141i	−0.663140	−	1.14859i	0.316646	−	0.948544i	$-0.397443\pi$
$152$	8.17460	+	14.1588i	0.663048	+	1.14843i
$153$	12.4897	+	0.948668i	1.00974	+	0.0766953i
$154$	3.34918	−	6.10874i	0.269884	−	0.492256i
$155$			0.0146545i			0.00117707i
$156$	−5.41035	+	1.21406i	−0.433175	+	0.0972026i
$157$	4.07713	−	2.35393i	0.325391	−	0.187864i	−0.328402	−	0.944538i	$-0.606510\pi$
$157$	4.07713	−	2.35393i	0.325391	−	0.187864i	0.653793	+	0.756674i	$0.273177\pi$
$158$	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
$162$	−1.43354	+	9.38220i	−0.112629	+	0.737135i
$163$	2.10316	+	3.64278i	0.164732	+	0.285324i	0.936560	−	0.350507i	$-0.113991\pi$
$163$	2.10316	+	3.64278i	0.164732	+	0.285324i	−0.771828	+	0.635831i	$0.780657\pi$
$164$	−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	−0.997408	−	0.0719525i	$-0.977077\pi$
$167$	−7.24993	−	12.5573i	−0.561017	−	0.971709i	0.436391	−	0.899757i	$-0.356256\pi$
$168$	13.9544	+	0.220676i	1.07660	+	0.0170255i
$169$	−11.2991	+	6.42883i	−0.869163	+	0.494526i
$170$	−0.00735708	−	0.00424761i	−0.000564263	−	0.000325777i
$171$	−14.5173	+	6.97308i	−1.11016	+	0.533245i
$172$	1.18035	−	2.04443i	0.0900009	−	0.155886i
$173$	−7.84836	−	13.5938i	−0.596700	−	1.03351i	−0.993305	−	0.115525i	$-0.963145\pi$
$173$	−7.84836	−	13.5938i	−0.596700	−	1.03351i	0.396605	−	0.917989i	$-0.370188\pi$
$174$	−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
$177$	−0.343371	+	9.05437i	−0.0258094	+	0.680568i
$178$			5.69865i			0.427132i
$179$	5.59852	+	3.23231i	0.418453	+	0.241594i	0.694415	−	0.719575i	$-0.255663\pi$
$179$	5.59852	+	3.23231i	0.418453	+	0.241594i	−0.275962	+	0.961168i	$0.588996\pi$
$180$	−0.00289935	+	0.00424335i	−0.000216105	+	0.000316281i
$181$		−	0.939369i		−	0.0698227i	−0.999390	−	0.0349114i	$-0.988885\pi$
$181$		−	0.939369i		−	0.0698227i	0.999390	−	0.0349114i	$-0.0111149\pi$
$182$	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
$189$	−1.25785	+	13.6901i	−0.0914949	+	0.995806i
$190$	0.0109229			0.000792428
$191$	−4.65873	+	2.68972i	−0.337094	+	0.194621i	−0.658986	−	0.752155i	$-0.729014\pi$
$191$	−4.65873	+	2.68972i	−0.337094	+	0.194621i	0.321892	+	0.946776i	$0.395681\pi$
$192$	0.505292	−	13.3241i	0.0364663	−	0.961581i
$193$	−10.5713	+	18.3100i	−0.760938	+	1.31798i	0.181430	+	0.983404i	$0.441927\pi$
$193$	−10.5713	+	18.3100i	−0.760938	+	1.31798i	−0.942368	+	0.334579i	$0.891406\pi$
$194$	−1.26042	+	2.18311i	−0.0904928	+	0.156738i
$195$	−0.00359364	+	0.0115007i	−0.000257346	+	0.000823581i
$196$	6.20919	−	0.274530i	0.443513	−	0.0196093i
$197$	22.4348	−	12.9527i	1.59841	−	0.922843i	0.606616	−	0.794995i	$-0.292526\pi$
$197$	22.4348	−	12.9527i	1.59841	−	0.922843i	0.991794	−	0.127848i	$-0.0408069\pi$
$198$	4.45648	−	6.52228i	0.316708	−	0.463519i
$199$		−	2.76818i		−	0.196231i	−0.995175	−	0.0981157i	$-0.968718\pi$
$199$		−	2.76818i		−	0.196231i	0.995175	−	0.0981157i	$-0.0312815\pi$
$200$	−13.1873	+	7.61367i	−0.932480	+	0.538368i
$201$	−20.8982	−	13.1460i	−1.47405	−	0.927244i
$202$	−16.4937	−	9.52267i	−1.16050	−	0.670012i
$203$	−19.7686	+	12.0033i	−1.38748	+	0.842470i
$204$	0.243331	−	6.41639i	0.0170365	−	0.449237i
$205$	−0.00706304			−0.000493304
$206$	5.14569	−	8.91259i	0.358517	−	0.620969i
$207$	−1.10668	+	14.5701i	−0.0769196	+	1.01269i
$208$	−1.32414	−	5.00486i	−0.0918125	−	0.347025i
$209$	13.4042			0.927189
$210$	0.00478911	−	0.00800012i	0.000330480	−	0.000552061i
$211$	−3.90647	−	6.76621i	−0.268933	−	0.465805i	0.699654	−	0.714482i	$-0.253338\pi$
$211$	−3.90647	−	6.76621i	−0.268933	−	0.465805i	−0.968586	+	0.248677i	$0.920004\pi$
$212$	10.9863	−	6.34295i	0.754543	−	0.435636i
$213$	1.32104	−	2.10006i	0.0905160	−	0.143894i
$214$	−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
$222$	−6.67259	−	0.253047i	−0.447835	−	0.0169834i
$223$	6.48830	−	3.74602i	0.434489	−	0.250852i	−0.266768	−	0.963761i	$-0.585956\pi$
$223$	6.48830	−	3.74602i	0.434489	−	0.250852i	0.701257	+	0.712909i	$0.252623\pi$
$224$	−0.267492	−	12.1059i	−0.0178726	−	0.808863i
$225$	−6.49459	−	13.5211i	−0.432973	−	0.901406i
$226$	0.237870	−	0.412003i	0.0158229	−	0.0274061i
$227$	8.54135			0.566909			0.283455	−	0.958986i	$-0.408519\pi$
$227$	8.54135			0.566909			0.283455	+	0.958986i	$0.408519\pi$
$228$	3.85403	+	7.30111i	0.255239	+	0.483528i
$229$	8.92049	+	5.15025i	0.589482	+	0.340338i	0.764893	−	0.644158i	$-0.222792\pi$
$229$	8.92049	+	5.15025i	0.589482	+	0.340338i	−0.175410	+	0.984495i	$0.556125\pi$
$230$	0.00495511	−	0.00858250i	0.000326730	−	0.000565913i
$231$	5.87706	−	9.81752i	0.386682	−	0.645945i
$232$	13.3108	+	23.0549i	0.873894	+	1.51363i
$233$	−1.09700	−	0.633351i	−0.0718666	−	0.0414922i	0.463636	−	0.886026i	$-0.346544\pi$
$233$	−1.09700	−	0.633351i	−0.0718666	−	0.0414922i	−0.535503	+	0.844534i	$0.679878\pi$
$234$	11.2167	−	2.07396i	0.733261	−	0.135579i
$235$	0.00345727	+	0.00598818i	0.000225528	+	0.000390626i
$236$	4.64484			0.302353
$237$	10.6874	+	6.72286i	0.694220	+	0.436697i
$238$	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	$0.791441\pi$
$240$	−0.00406160	−	0.00255494i	−0.000262175	−	0.000164920i
$241$			1.22332i			0.0788012i	0.999223	+	0.0394006i	$0.0125448\pi$
$241$			1.22332i			0.0788012i	−0.999223	+	0.0394006i	$0.987455\pi$
$242$	4.35228	−	2.51279i	0.279775	−	0.161528i
$243$	−2.93676	+	15.3093i	−0.188393	+	0.982094i
$244$	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
$249$	0.683219	−	18.0158i	0.0432972	−	1.14171i
$250$			0.0203467i			0.00128684i
$251$	−4.42278	+	7.66048i	−0.279163	+	0.483525i	−0.971177	−	0.238359i	$-0.923390\pi$
$251$	−4.42278	+	7.66048i	−0.279163	+	0.483525i	0.692014	+	0.721884i	$0.256724\pi$
$252$	7.03727	+	0.378392i	0.443306	+	0.0238364i
$253$	6.08077	−	10.5322i	0.382294	−	0.662153i
$254$	8.61998	−	4.97674i	0.540865	−	0.312269i
$255$	−0.0118105	−	0.00742932i	−0.000739599	−	0.000465242i
$256$	−16.4881			−1.03051
$257$	−10.9439			−0.682659			−0.341329	−	0.939944i	$-0.610877\pi$
$257$	−10.9439			−0.682659			−0.341329	+	0.939944i	$0.610877\pi$
$258$	−2.58584	+	4.11072i	−0.160987	+	0.255922i
$259$	−9.66976	+	0.213662i	−0.600849	+	0.0132763i
$260$	0.00596112	+	0.00161745i	0.000369693	+	0.000100310i
$261$	−23.6385	+	11.3543i	−1.46319	+	0.702814i
$262$	5.68243	+	3.28075i	0.351062	+	0.202686i
$263$	−11.0111	−	6.35726i	−0.678973	−	0.392005i	0.120495	−	0.992714i	$-0.461552\pi$
$263$	−11.0111	−	6.35726i	−0.678973	−	0.392005i	−0.799468	+	0.600709i	$0.794885\pi$
$264$	−11.1485	−	7.01295i	−0.686146	−	0.431618i
$265$		−	0.0275665i		−	0.00169339i
$266$	−7.77391	−	12.8030i	−0.476649	−	0.785005i
$267$	−0.354694	+	9.35293i	−0.0217069	+	0.572390i
$268$	−6.32813	+	10.9606i	−0.386552	+	0.669528i
$269$	23.1586			1.41201			0.706003	−	0.708208i	$-0.250496\pi$
$269$	23.1586			1.41201			0.706003	+	0.708208i	$0.250496\pi$
$270$	0.00629102	−	0.00849705i	0.000382860	−	0.000517114i
$271$		−	26.3454i		−	1.60037i	−0.599753	−	0.800185i	$-0.704735\pi$
$271$		−	26.3454i		−	1.60037i	0.599753	−	0.800185i	$-0.295265\pi$
$272$	5.99505			0.363503
$273$	16.0380	−	3.97292i	0.970661	−	0.240452i
$274$	6.49218			0.392207
$275$			12.4844i			0.752840i
$276$	7.48511	+	0.283860i	0.450551	+	0.0170864i
$277$	−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
$279$	20.5395	−	9.86577i	1.22967	−	0.590648i
$280$	−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	$0.870245\pi$
$282$	3.48549	−	5.54091i	0.207558	−	0.329956i
$283$	14.1843	+	8.18929i	0.843167	+	0.486803i	0.858339	−	0.513082i	$-0.171496\pi$
$283$	14.1843	+	8.18929i	0.843167	+	0.486803i	−0.0151725	+	0.999885i	$0.504830\pi$
$284$	−1.10144	−	0.635914i	−0.0653582	−	0.0377346i
$285$	0.0179272		0.000679857i	0.00106191		4.02713e-5i
$286$	−9.16259	−	2.48612i	−0.541796	−	0.147007i
$287$	5.02684	+	8.27882i	0.296725	+	0.488683i
$288$	1.03989	−	13.6908i	0.0612763	−	0.806736i
$289$	0.432600			0.0254470
$290$	0.0177858			0.00104442
$291$	−2.20454	+	3.50458i	−0.129233	+	0.205442i
$292$	1.43010	−	0.825670i	0.0836905	−	0.0483187i
$293$	9.96323	−	17.2568i	0.582058	−	1.00815i	−0.413177	−	0.910651i	$-0.635581\pi$
$293$	9.96323	−	17.2568i	0.582058	−	1.00815i	0.995235	−	0.0975037i	$-0.0310858\pi$
$294$	−12.7857	+	0.0802891i	−0.745675	+	0.00468256i
$295$	0.00504662	−	0.00874100i	0.000293825	−	0.000508920i
$296$			11.1334i			0.647114i
$297$	7.72016	−	10.4273i	0.447969	−	0.605055i
$298$	−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
$303$	−26.4777	−	16.6557i	−1.52110	−	0.956845i
$304$	−6.67551	+	3.85411i	−0.382867	+	0.221048i
$305$		−	0.0146233i		−	0.000837326i
$306$	−1.00043	+	13.1712i	−0.0571909	+	0.752949i
$307$			4.93316i			0.281551i	0.990042	+	0.140775i	$0.0449595\pi$
$307$			4.93316i			0.281551i	−0.990042	+	0.140775i	$0.955040\pi$
$308$	−5.14327	−	2.81985i	−0.293065	−	0.160676i
$309$	9.00010	−	14.3075i	0.511998	−	0.813927i
$310$	−0.0154541			−0.000877732
$311$	−6.69213	−	11.5911i	−0.379476	−	0.657272i	0.611510	−	0.791237i	$-0.290562\pi$
$311$	−6.69213	−	11.5911i	−0.379476	−	0.657272i	−0.990986	+	0.133965i	$0.957229\pi$
$312$	−4.16422	−	18.5575i	−0.235753	−	1.05061i
$313$	23.9599	+	13.8332i	1.35429	+	0.781901i	0.988847	−	0.148932i	$-0.0475835\pi$
$313$	23.9599	+	13.8332i	1.35429	+	0.781901i	0.365445	+	0.930833i	$0.380917\pi$
$314$	2.48238	+	4.29960i	0.140089	+	0.242641i
$315$	0.00835808	−	0.0128321i	0.000470925	−	0.000723009i
$316$	3.23622	−	5.60529i	0.182051	−	0.315322i
$317$	−12.8384	−	7.41223i	−0.721075	−	0.416313i	0.0940735	−	0.995565i	$-0.470011\pi$
$317$	−12.8384	−	7.41223i	−0.721075	−	0.416313i	−0.815148	+	0.579253i	$0.803344\pi$
$318$	−23.0791	+	12.1828i	−1.29421	+	0.683175i
$319$	21.8262			1.22203
$320$	−0.00742641	+	0.0128629i	−0.000415149	+	0.000719059i
$321$	−9.45492	−	0.358562i	−0.527722	−	0.0200130i
$322$	−13.5864	+	0.300205i	−0.757142	+	0.0167298i
$323$	−19.4113	+	11.2071i	−1.08007	+	0.623580i
$324$	7.89936	+	1.20697i	0.438854	+	0.0670538i
$325$	−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	0.775099	−	0.631840i	$-0.217700\pi$
$331$	−2.90440	−	5.03057i	−0.159640	−	0.276505i	−0.934739	+	0.355335i	$0.884367\pi$
$332$	−9.24200			−0.507221
$333$	−10.9356	−	0.830626i	−0.599270	−	0.0455180i
$334$	13.2424	−	7.64552i	0.724594	−	0.418344i
$335$	0.0137510	+	0.0238175i	0.000751299	+	0.00130129i
$336$	−0.104043	+	6.57911i	−0.00567600	+	0.358920i
$337$	−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
$339$	0.416049	−	0.661396i	0.0225967	−	0.0359221i
$340$	−0.00357629	+	0.00619432i	−0.000193952	+	0.000335934i
$341$	−18.9648			−1.02700
$342$	−7.35356	−	15.3094i	−0.397635	−	0.827837i
$343$	−18.4796	+	1.22657i	−0.997804	+	0.0662285i
$344$	7.01238	+	4.04860i	0.378082	+	0.218286i
$345$	0.00866677	−	0.0137776i	0.000466603	−	0.000741763i
$346$	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	−0.998687	−	0.0512262i	$-0.983687\pi$
$349$	−27.1567	+	15.6790i	−1.45367	+	0.839275i	−0.454980	+	0.890501i	$0.650354\pi$
$350$	11.9245	−	7.24047i	0.637392	−	0.387019i
$351$	18.5386	−	2.70575i	0.989516	−	0.144422i
$352$	−5.71380	+	9.89659i	−0.304547	+	0.527490i
$353$	−0.797729	+	1.38171i	−0.0424588	+	0.0735408i	−0.886474	−	0.462779i	$-0.846852\pi$
$353$	−0.797729	+	1.38171i	−0.0424588	+	0.0735408i	0.844015	+	0.536320i	$0.180186\pi$
$354$	−9.54841	−	0.362107i	−0.507493	−	0.0192458i
$355$	−0.00239342	+	0.00138184i	−0.000127030	+	7.33406e-5i
$356$	4.79800			0.254293
$357$	−0.302539	+	19.1309i	−0.0160121	+	1.01252i
$358$	−3.40868	+	5.90400i	−0.180154	+	0.312036i
$359$	−11.1728	−	6.45064i	−0.589680	−	0.340452i	0.175291	−	0.984517i	$-0.443913\pi$
$359$	−11.1728	−	6.45064i	−0.589680	−	0.340452i	−0.764971	+	0.644065i	$0.777247\pi$
$360$	−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	0.765965	−	0.642883i	$-0.222262\pi$
$367$	11.3448	+	6.54993i	0.592194	+	0.341903i	−0.173770	+	0.984786i	$0.555595\pi$
$368$			6.99360i			0.364567i
$369$	4.75503	+	9.89949i	0.247537	+	0.515347i
$370$	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	0.775578	−	0.631252i	$-0.217459\pi$
$373$	−3.06870	−	5.31515i	−0.158891	−	0.275208i	−0.934469	+	0.356044i	$0.884125\pi$
$374$	5.49697	−	9.52103i	0.284242	−	0.492321i
$375$	−0.00126641	+	0.0333941i	−6.53973e−5	+	0.00172446i
$376$	−9.45210	−	5.45717i	−0.487455	−	0.281432i
$377$	22.2157	+	22.3564i	1.14417	+	1.15141i
$378$	−14.4371	−	1.32648i	−0.742562	−	0.0682268i
$379$	6.45103	+	11.1735i	0.331367	+	0.573945i	0.982780	−	0.184779i	$-0.0591568\pi$
$379$	6.45103	+	11.1735i	0.331367	+	0.573945i	−0.651413	+	0.758723i	$0.725823\pi$
$380$		−	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	$-0.0908089\pi$
$383$	4.61988	+	8.00187i	0.236065	+	0.408876i	−0.723517	+	0.690307i	$0.757476\pi$
$384$	−1.79180	−	0.0679510i	−0.0914375	−	0.00346761i
$385$	−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	$-0.774832\pi$
$389$	−11.3864	+	6.57391i	−0.577311	+	0.333311i	0.182753	+	0.983159i	$0.441499\pi$
$390$	−0.0121282	−	0.00378973i	−0.000614136	−	0.000191900i
$391$			20.3362i			1.02845i
$392$	0.941635	+	21.2975i	0.0475598	+	1.07569i
$393$	9.12210	+	5.73823i	0.460149	+	0.289455i
$394$	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	−0.0391097	−	0.999235i	$-0.512452\pi$
$397$	16.0733	−	9.27995i	0.806698	−	0.465747i	0.845808	+	0.533487i	$0.179119\pi$
$398$	2.91923			0.146328
$399$	−11.9621	−	21.4969i	−0.598852	−	1.07619i
$400$	−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	$0.900192\pi$
$402$	13.8633	−	22.0385i	0.691436	−	1.09918i
$403$	−19.3033	−	19.4255i	−0.961565	−	0.967651i
$404$	−8.01763	+	13.8869i	−0.398892	+	0.690901i
$405$	0.0108540	−	0.0135542i	0.000539341	−	0.000673515i
$406$	−12.6583	−	20.8473i	−0.628221	−	1.03463i
$407$	7.90501	+	4.56396i	0.391837	+	0.226227i
$408$	22.0082	+	0.834623i	1.08957	+	0.0413200i
$409$		−	5.77235i		−	0.285424i	−0.989764	−	0.142712i	$-0.954418\pi$
$409$		−	5.77235i		−	0.285424i	0.989764	−	0.142712i	$-0.0455823\pi$
$410$		−	0.00744843i		−	0.000367852i
$411$	10.6553	+	0.404084i	0.525587	+	0.0199320i
$412$	−7.50398	−	4.33242i	−0.369694	−	0.213443i
$413$	−13.8373	+	0.305749i	−0.680891	+	0.0150449i
$414$	−15.3651	−	1.16707i	−0.755152	−	0.0573582i
$415$	−0.0100414	+	0.0173923i	−0.000492915	+	0.000853753i
$416$	−15.9528	+	4.22063i	−0.782149	+	0.206934i
$417$	11.3591	−	18.0576i	0.556257	−	0.884287i
$418$			14.1356i			0.691396i
$419$	17.6169	+	30.5134i	0.860644	+	1.49068i	0.871309	+	0.490736i	$0.163272\pi$
$419$	17.6169	+	30.5134i	0.860644	+	1.49068i	−0.0106648	+	0.999943i	$0.503395\pi$
$420$	−0.00673572	−	0.00403221i	−0.000328670	−	0.000196751i
$421$	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
$426$	2.21465	+	1.39312i	0.107300	+	0.0674968i
$427$	−17.1404	+	10.4075i	−0.829483	+	0.503656i
$428$			4.85032i			0.234449i
$429$	−14.8834	−	4.65064i	−0.718577	−	0.224535i
$430$	0.00468495	−	0.00270486i	0.000225928	−	0.000130440i
$431$	−27.1302	−	15.6636i	−1.30681	−	0.754490i	−0.325252	−	0.945627i	$-0.605449\pi$
$431$	−27.1302	−	15.6636i	−1.30681	−	0.754490i	−0.981563	+	0.191138i	$0.938782\pi$
$432$	−0.846597	+	7.41275i	−0.0407319	+	0.356646i
$433$	3.41909	+	1.97401i	0.164311	+	0.0948649i	0.579900	−	0.814687i	$-0.303091\pi$
$433$	3.41909	+	1.97401i	0.164311	+	0.0948649i	−0.415590	+	0.909552i	$0.636425\pi$
$434$	10.9988	+	18.1142i	0.527960	+	0.869511i
$435$	0.0291909	+	0.00110702i	0.00139960	+	5.30774e-5i
$436$	−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	$0.263566\pi$
$439$			30.8667i			1.47319i	−0.676337	+	0.736593i	$0.736434\pi$
$440$	0.00733575	+	0.0127059i	0.000349718	+	0.000605729i
$441$	−20.9895	−	0.664027i	−0.999500	−	0.0316203i
$442$	15.3474	−	4.06047i	0.730001	−	0.193137i
$443$	16.2769	+	9.39748i	0.773340	+	0.446488i	0.834065	−	0.551667i	$-0.186008\pi$
$443$	16.2769	+	9.39748i	0.773340	+	0.446488i	−0.0607250	+	0.998155i	$0.519341\pi$
$444$	−0.213053	+	5.61800i	−0.0101111	+	0.266619i
$445$	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	$-0.376469\pi$
$449$	−4.95835	−	2.86270i	−0.233999	−	0.135099i	−0.612415	+	0.790536i	$0.709802\pi$
$450$	14.2589	−	6.84897i	0.672169	−	0.322863i
$451$		−	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	$-0.977234\pi$
$461$	−9.37925	+	16.2453i	−0.436835	+	0.756621i	0.560608	+	0.828081i	$0.310567\pi$
$462$	10.3532	+	6.19774i	0.481675	+	0.288345i
$463$	−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
$465$	−0.0253640		0.000961888i	−0.00117623		4.46065e-5i
$466$	0.667909	−	1.15685i	0.0309403	−	0.0535902i
$467$	3.57259	−	6.18791i	0.165320	−	0.286342i	−0.771449	−	0.636291i	$-0.780468\pi$
$467$	3.57259	−	6.18791i	0.165320	−	0.286342i	0.936769	+	0.349949i	$0.113801\pi$
$468$	−1.74618	−	9.44396i	−0.0807172	−	0.436547i
$469$	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
$474$	−7.08969	+	11.2705i	−0.325640	+	0.517673i
$475$	23.2457	+	13.4209i	1.06659	+	0.615794i
$476$	9.80584	−	0.216669i	0.449450	−	0.00993102i
$477$	−38.6369	+	18.5585i	−1.76906	+	0.849735i
$478$	−19.8679			−0.908735
$479$	4.61963	−	8.00143i	0.211076	−	0.365595i	−0.740975	−	0.671532i	$-0.765637\pi$
$479$	4.61963	−	8.00143i	0.211076	−	0.365595i	0.952052	+	0.305938i	$0.0989699\pi$
$480$	−0.00814374	+	0.0129462i	−0.000371709	+	0.000590909i
$481$	3.37128	+	12.7424i	0.153717	+	0.581005i
$482$	−1.29007			−0.0587612
$483$	−22.3174	−	0.352931i	−1.01548	−	0.0160589i
$484$	−2.11565	−	3.66441i	−0.0961658	−	0.166564i
$485$	0.00399414	−	0.00230602i	0.000181364	−	0.000104711i
$486$	−16.1447	−	3.09700i	−0.732337	−	0.140483i
$487$	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	$-0.763086\pi$
$491$	−11.4486	+	6.60986i	−0.516668	+	0.298299i	0.218902	+	0.975747i	$0.429752\pi$
$492$	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
$495$	−0.0130275	+	0.00625752i	−0.000585544	+	0.000281255i
$496$	9.44476	−	5.45294i	0.424082	−	0.244844i
$497$	3.32312	+	1.82194i	0.149062	+	0.0817250i
$498$	18.9988	+	0.720498i	0.851358	+	0.0322863i
$499$	3.18217	−	5.51168i	0.142454	−	0.246737i	−0.785966	−	0.618269i	$-0.787834\pi$
$499$	3.18217	−	5.51168i	0.142454	−	0.246737i	0.928420	+	0.371532i	$0.121168\pi$
$500$	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	−0.135369	−	0.990795i	$-0.543222\pi$
$503$	17.7261	−	30.7026i	0.790370	−	1.36896i	0.925738	−	0.378165i	$-0.123445\pi$
$504$	−1.29788	+	24.1378i	−0.0578122	+	1.07518i
$505$	0.0174223	+	0.0301764i	0.000775283	+	0.00134283i
$506$	11.1069	+	6.41256i	0.493761	+	0.285073i
$507$	−10.3854	−	19.9786i	−0.461233	−	0.887279i
$508$	−4.19018	−	7.25761i	−0.185909	−	0.322004i
$509$	15.6499			0.693670			0.346835	−	0.937926i	$-0.387256\pi$
$509$	15.6499			0.693670			0.346835	+	0.937926i	$0.387256\pi$
$510$	0.00783470	−	0.0124549i	0.000346926	−	0.000551512i
$511$	−4.20604	+	2.55388i	−0.186064	+	0.112977i
$512$		−	15.3173i		−	0.676934i
$513$	−11.1162	−	25.5843i	−0.490791	−	1.12957i
$514$		−	11.5410i		−	0.509052i
$515$	−0.0163062	+	0.00941436i	−0.000718535	+	0.000414846i
$516$	3.46103	+	2.17715i	0.152364	+	0.0958438i
$517$	−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	−0.892136	−	0.451767i	$-0.850794\pi$
$521$	−19.1120	−	33.1029i	−0.837310	−	1.45026i	0.0548261	−	0.998496i	$-0.482540\pi$
$522$	−11.9739	−	24.9284i	−0.524081	−	1.09108i
$523$		−	30.7021i		−	1.34251i	−0.741228	−	0.671254i	$-0.765756\pi$
$523$		−	30.7021i		−	1.34251i	0.741228	−	0.671254i	$-0.234244\pi$
$524$	2.76224	−	4.78434i	0.120669	−	0.209005i
$525$	20.0218	−	11.1412i	0.873823	−	0.486243i
$526$	6.70414	−	11.6119i	0.292314	−	0.506303i
$527$	27.4638	−	15.8562i	1.19634	−	0.690708i
$528$	3.30642	−	5.25624i	0.143894	−	0.228749i
$529$	−0.723461			−0.0314548
$530$	0.0290706			0.00126275
$531$	−15.6488	−	1.18862i	−0.679101	−	0.0515817i
$532$	−10.7796	+	6.54526i	−0.467353	+	0.283773i
$533$	9.36253	−	9.30364i	0.405536	−	0.402985i
$534$	−9.86327	−	0.374048i	−0.426825	−	0.0161866i
$535$	0.00912769	+	0.00526987i	0.000394624	+	0.000227836i
$536$	−37.5950	−	21.7055i	−1.62385	−	0.937533i
$537$	−5.96197	+	9.47779i	−0.257278	+	0.408997i
$538$			24.4223i			1.05292i
$539$	15.5078	+	8.06199i	0.667969	+	0.347255i
$540$	−0.00715411	−	0.00529674i	−0.000307864	−	0.000227936i
$541$	4.56917	−	7.91403i	0.196444	−	0.340251i	−0.750929	−	0.660383i	$-0.770394\pi$
$541$	4.56917	−	7.91403i	0.196444	−	0.340251i	0.947373	+	0.320132i	$0.103727\pi$
$542$	27.7829			1.19338
$543$	1.62587	+	0.0616582i	0.0697726	+	0.00264601i
$544$		−	19.1090i		−	0.819289i
$545$	−0.0142210			−0.000609160
$546$	4.18970	+	16.9131i	0.179303	+	0.723812i
$547$	−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
$549$	−20.4958	+	9.84478i	−0.874741	+	0.420165i
$550$	−13.1656			−0.561385
$551$	23.4634	−	40.6398i	0.999574	−	1.73131i
$552$	−0.973639	+	25.6739i	−0.0414408	+	1.09275i
$553$	−9.27198	+	16.9116i	−0.394285	+	0.719156i
$554$		−	4.64484i		−	0.197340i
$555$	0.0103409	+	0.00650490i	0.000438946	+	0.000276118i
$556$	−9.47083	−	5.46798i	−0.401653	−	0.231894i
$557$	−3.92620	−	2.26679i	−0.166358	−	0.0960470i	0.414509	−	0.910045i	$-0.363953\pi$
$557$	−3.92620	−	2.26679i	−0.166358	−	0.0960470i	−0.580868	+	0.813998i	$0.697287\pi$
$558$	10.4041	+	21.6603i	0.440440	+	0.916953i
$559$	9.25180	+	2.51032i	0.391310	+	0.106175i
$560$	0.00352369	−	0.00642705i	0.000148903	−	0.000271592i
$561$	9.61452	−	15.2843i	0.405925	−	0.645303i
$562$	−14.0164			−0.591246
$563$	12.1324			0.511321			0.255661	−	0.966767i	$-0.417707\pi$
$563$	12.1324			0.511321			0.255661	+	0.966767i	$0.417707\pi$
$564$	−4.66518	−	2.93462i	−0.196440	−	0.123570i
$565$	−0.000753786	0	0.000435199i	−3.17120e−5	0	1.83090e-5i
$566$	−8.63613	+	14.9582i	−0.363004	+	0.628741i
$567$	−23.6123	−	3.07568i	−0.991623	−	0.129166i
$568$	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	$-0.275803\pi$
$570$	−0.000716954		0.0189054i	−3.00299e−5		0.000791858i
$571$	7.04698	+	12.2057i	0.294907	+	0.510794i	0.974963	−	0.222366i	$-0.0713780\pi$
$571$	7.04698	+	12.2057i	0.294907	+	0.510794i	−0.680056	+	0.733160i	$0.738045\pi$
$572$	−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
$576$	23.0282	+	1.74913i	0.959509	+	0.0728803i
$577$	11.4758	−	6.62558i	0.477745	−	0.275826i	−0.241731	−	0.970343i	$-0.577715\pi$
$577$	11.4758	−	6.62558i	0.477745	−	0.275826i	0.719476	+	0.694517i	$0.244382\pi$
$578$			0.456204i			0.0189756i
$579$	−30.9972	−	19.4987i	−1.28820	−	0.810337i
$580$		−	0.0149748i		−	0.000621793i
$581$	27.5327	−	0.608360i	1.14225	−	0.0252390i
$582$	−3.69581	−	2.32483i	−0.153196	−	0.0963675i
$583$	35.6746			1.47749
$584$	2.83205	+	4.90525i	0.117191	+	0.202981i
$585$	−0.0196696	−	0.00697478i	−0.000813237	−	0.000288372i
$586$	18.1984	+	10.5069i	0.751771	+	0.434035i
$587$	−15.6011	−	27.0220i	−0.643928	−	1.11532i	−0.984548	−	0.175115i	$-0.943970\pi$
$587$	−15.6011	−	27.0220i	−0.643928	−	1.11532i	0.340620	−	0.940201i	$-0.389363\pi$
$588$	0.0675996	+	10.7649i	0.00278776	+	0.443938i
$589$	−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	$-0.905623\pi$
$593$	−5.48292	+	9.49670i	−0.225157	+	0.389983i	0.731210	+	0.682153i	$0.238956\pi$
$594$	10.9963	+	8.14141i	0.451184	+	0.334046i
$595$	0.0102463	−	0.0186888i	0.000420058	−	0.000766165i
$596$	−5.50691	+	3.17942i	−0.225572	+	0.130234i
$597$	4.79119	+	0.181698i	0.196090	+	0.00743640i
$598$	4.73679	+	17.9037i	0.193702	+	0.732136i
$599$	12.1466	−	7.01285i	0.496297	−	0.286537i	−0.230886	−	0.972981i	$-0.574162\pi$
$599$	12.1466	−	7.01285i	0.496297	−	0.286537i	0.727183	+	0.686444i	$0.240829\pi$
$600$	−12.3122	−	23.3243i	−0.502644	−	0.952213i
$601$	−3.15684	+	1.82260i	−0.128770	+	0.0743455i	−0.563001	−	0.826456i	$-0.690353\pi$
$601$	−3.15684	+	1.82260i	−0.128770	+	0.0743455i	0.434231	+	0.900801i	$0.357020\pi$
$602$	−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
$606$	17.5645	−	27.9224i	0.713509	−	1.13427i
$607$	14.9262	−	8.61762i	0.605834	−	0.349778i	−0.165499	−	0.986210i	$-0.552924\pi$
$607$	14.9262	−	8.61762i	0.605834	−	0.349778i	0.771333	+	0.636432i	$0.219590\pi$
$608$	12.2848	+	21.2779i	0.498214	+	0.862933i
$609$	−19.4779	−	35.0035i	−0.789284	−	1.41841i
$610$	0.0154212			0.000624386
$611$	−12.4707	−	3.38370i	−0.504509	−	0.136890i
$612$	11.0896	+	0.842316i	0.448269	+	0.0340486i
$613$	15.2562	−	26.4245i	0.616193	−	1.06728i	−0.373982	−	0.927436i	$-0.622008\pi$
$613$	15.2562	−	26.4245i	0.616193	−	1.06728i	0.990174	−	0.139841i	$-0.0446590\pi$
$614$	−5.20234			−0.209949
$615$	0.000463603	−	0.0122248i	1.86943e−5	−	0.000492950i
$616$	9.67207	−	17.6414i	0.389699	−	0.710791i
$617$	5.82452	+	3.36279i	0.234486	+	0.135381i	0.612640	−	0.790362i	$-0.290108\pi$
$617$	5.82452	+	3.36279i	0.234486	+	0.135381i	−0.378154	+	0.925743i	$0.623441\pi$
$618$	15.0882	+	9.49119i	0.606937	+	0.381792i
$619$	8.43263	−	4.86858i	0.338936	−	0.195685i	−0.320865	−	0.947125i	$-0.603974\pi$
$619$	8.43263	−	4.86858i	0.338936	−	0.195685i	0.659801	+	0.751440i	$0.270640\pi$
$620$			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
$624$	8.74936	−	1.96332i	0.350255	−	0.0785957i
$625$	−12.5000	+	21.6506i	−0.499999	+	0.866023i
$626$	−14.5880	+	25.2672i	−0.583056	+	1.00988i
$627$	−0.879825	+	23.2001i	−0.0351368	+	0.926523i
$628$	3.62006	−	2.09004i	0.144456	−	0.0834018i
$629$	−15.2635			−0.608595
$630$	0.0135323	+	0.00881414i	0.000539140	+	0.000351164i
$631$	−1.16211	+	2.01284i	−0.0462630	+	0.0801299i	−0.888230	−	0.459400i	$-0.848065\pi$
$631$	−1.16211	+	2.01284i	−0.0462630	+	0.0801299i	0.841967	+	0.539530i	$0.181398\pi$
$632$	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	$0.930052\pi$
$642$	0.378127	−	9.97082i	0.0149235	−	0.393517i
$643$	−2.75926	−	1.59306i	−0.108815	−	0.0628241i	0.444605	−	0.895727i	$-0.353344\pi$
$643$	−2.75926	−	1.59306i	−0.108815	−	0.0628241i	−0.553420	+	0.832903i	$0.686677\pi$
$644$	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	−0.143416	−	0.989662i	$-0.545809\pi$
$647$	19.9767	−	34.6006i	0.785365	−	1.36029i	0.928781	−	0.370629i	$-0.120858\pi$
$648$	−4.13990	+	27.0948i	−0.162631	+	1.06438i
$649$	11.3120	+	6.53099i	0.444035	+	0.256364i
$650$	−13.4006	−	13.4854i	−0.525616	−	0.528943i
$651$	16.9244	+	30.4146i	0.663318	+	1.19204i
$652$	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
$657$	−5.02942	+	2.41578i	−0.196216	+	0.0942487i
$658$	8.76789	+	4.80709i	0.341808	+	0.187400i
$659$	−43.5079	−	25.1193i	−1.69483	−	0.978510i	−0.950514	−	0.310681i	$-0.899443\pi$
$659$	−43.5079	−	25.1193i	−1.69483	−	0.978510i	−0.744315	−	0.667829i	$-0.767224\pi$
$660$	0.00345854	+	0.00655189i	0.000134623	+	0.000255032i
$661$	43.6126	+	25.1798i	1.69633	+	0.979379i	0.949183	+	0.314725i	$0.101912\pi$
$661$	43.6126	+	25.1798i	1.69633	+	0.979379i	0.747151	+	0.664654i	$0.231421\pi$
$662$	5.30506	−	3.06288i	0.206187	−	0.119042i
$663$	25.4417	−	5.70901i	0.988073	−	0.221719i
$664$		−	31.7000i		−	1.23020i
$665$	0.000605367		0.0273972i	2.34751e−5		0.00106242i
$666$	0.875949	−	11.5323i	0.0339423	−	0.446869i
$667$	−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
$672$	20.9706	+	0.331632i	0.808959	+	0.0127930i
$673$	18.1511	+	31.4387i	0.699674	+	1.21187i	0.968579	+	0.248704i	$0.0800048\pi$
$673$	18.1511	+	31.4387i	0.699674	+	1.21187i	−0.268905	+	0.963167i	$0.586662\pi$
$674$		−	10.0766i		−	0.388135i
$675$	23.8287	−	10.3534i	0.917167	−	0.398502i
$676$	−10.0324	+	5.70812i	−0.385862	+	0.219543i
$677$	−18.7369	+	32.4533i	−0.720119	+	1.24728i	0.240833	+	0.970567i	$0.422579\pi$
$677$	−18.7369	+	32.4533i	−0.720119	+	1.24728i	−0.960952	+	0.276716i	$0.910754\pi$
$678$	0.697485	+	0.438750i	0.0267867	+	0.0168501i
$679$	−5.54562	−	3.04044i	−0.212822	−	0.116682i
$680$	−0.0212465	−	0.0122667i	−0.000814765	−	0.000470405i
$681$	−0.560637	+	14.7834i	−0.0214836	+	0.566502i
$682$		−	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	$-0.257379\pi$
$684$	−12.8898	+	6.19135i	−0.492853	+	0.236732i
$685$	−0.0102865	−	0.00593893i	−0.000393028	−	0.000226915i
$686$	−1.29350	−	19.4879i	−0.0493859	−	0.744053i
$687$	−9.49960	+	15.1016i	−0.362432	+	0.576162i
$688$	−1.90881	+	3.30615i	−0.0727726	+	0.126046i
$689$	36.3114	+	36.5412i	1.38335	+	1.39211i
$690$	0.0145294	+	0.00913967i	0.000553125	+	0.000347941i
$691$			12.9636i			0.493158i	0.969123	+	0.246579i	$0.0793065\pi$
$691$			12.9636i			0.493158i	−0.969123	+	0.246579i	$0.920694\pi$
$692$	−6.96851	−	12.0698i	−0.264903	−	0.458825i
$693$	16.6065	+	10.8165i	0.630828	+	0.410883i
$694$	−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
$699$	1.16821	−	1.85712i	0.0441858	−	0.0702425i
$700$	−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	$0.770879\pi$
$702$	2.85339	+	19.5501i	0.107694	+	0.737872i
$703$	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
$708$	−0.304877	+	8.03931i	−0.0114580	+	0.302136i
$709$	−18.2820	−	31.6653i	−0.686595	−	1.18922i	−0.972933	−	0.231088i	$-0.925771\pi$
$709$	−18.2820	−	31.6653i	−0.686595	−	1.18922i	0.286338	−	0.958129i	$-0.407562\pi$
$710$	−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
$714$	−20.1748	−	0.319047i	−0.755024	−	0.0119400i
$715$	0.0122434	+	0.0123209i	0.000457877	+	0.000460776i
$716$	4.97089	+	2.86994i	0.185771	+	0.107255i
$717$	−32.6082	−	1.23661i	−1.21777	−	0.0461820i
$718$	6.80262	−	11.7825i	0.253871	−	0.439718i
$719$	19.8403	+	34.3644i	0.739919	+	1.28158i	0.952531	+	0.304441i	$0.0984696\pi$
$719$	19.8403	+	34.3644i	0.739919	+	1.28158i	−0.212612	+	0.977137i	$0.568197\pi$
$720$	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
$723$	−2.11734	−	0.0802964i	−0.0787446	−	0.00298625i
$724$		−	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	$-0.906404\pi$
$727$		−	15.6289i		−	0.579644i	0.957081	−	0.289822i	$-0.0935961\pi$
$728$	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	−0.0391289	−	0.999234i	$-0.512458\pi$
$733$	−25.0179	−	14.4441i	−0.924055	−	0.533504i	−0.884927	+	0.465730i	$0.845792\pi$
$734$	−6.90732	+	11.9638i	−0.254954	+	0.441593i
$735$	0.0203317	+	0.0115689i	0.000749945	+	0.000426725i
$736$	22.2918			0.821686
$737$	−30.8230	+	17.7957i	−1.13538	+	0.655511i
$738$	−10.4397	+	5.01448i	−0.384289	+	0.184586i
$739$	−7.56592	+	13.1046i	−0.278317	+	0.482059i	−0.970967	−	0.239215i	$-0.923110\pi$
$739$	−7.56592	+	13.1046i	−0.278317	+	0.482059i	0.692650	+	0.721274i	$0.256443\pi$
$740$	0.00313130	−	0.00542356i	0.000115109	−	0.000199374i
$741$	−24.6592	+	22.7130i	−0.905878	+	0.834383i
$742$	−20.6899	−	34.0746i	−0.759549	−	1.25092i
$743$	−30.5018	+	17.6102i	−1.11900	+	0.646056i	−0.941146	−	0.338001i	$-0.890249\pi$
$743$	−30.5018	+	17.6102i	−1.11900	+	0.646056i	−0.177856	+	0.984057i	$0.556916\pi$
$744$	35.4314	−	18.7032i	1.29898	−	0.685691i
$745$			0.0138178i			0.000506244i
$746$	5.60517	−	3.23614i	0.205220	−	0.118484i
$747$	31.1370	+	2.36504i	1.13924	+	0.0865323i
$748$	−8.01626	−	4.62819i	−0.293103	−	0.169223i
$749$	−0.319275	−	14.4495i	−0.0116660	−	0.527973i
$750$	−0.0352162	−	0.00133551i	−0.00128591	−	4.87661e-5i
$751$	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
$753$	−12.9685	−	8.15780i	−0.472599	−	0.297287i
$754$	−23.5762	+	23.4279i	−0.858595	+	0.853195i
$755$	−0.0314445			−0.00114438
$756$	−1.11683	+	12.1553i	−0.0406189	+	0.442085i
$757$	−7.44232	−	12.8905i	−0.270496	−	0.468513i	0.698493	−	0.715617i	$-0.253854\pi$
$757$	−7.44232	−	12.8905i	−0.270496	−	0.468513i	−0.968989	+	0.247104i	$0.920521\pi$
$758$	−11.7832	+	6.80303i	−0.427985	+	0.247097i
$759$	17.8301	+	11.2159i	0.647190	+	0.407113i
$760$	0.0315441			0.00114422
$761$	−4.20006	−	7.27471i	−0.152252	−	0.263708i	0.779803	−	0.626025i	$-0.215319\pi$
$761$	−4.20006	−	7.27471i	−0.152252	−	0.263708i	−0.932055	+	0.362317i	$0.881986\pi$
$762$	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
$768$	1.08224	−	28.5377i	0.0390521	−	1.02977i
$769$	−40.4429	+	23.3497i	−1.45841	+	0.842013i	−0.998933	−	0.0461769i	$-0.985296\pi$
$769$	−40.4429	+	23.3497i	−1.45841	+	0.842013i	−0.459476	+	0.888190i	$0.651963\pi$
$770$	−0.00697617	−	0.0114892i	−0.000251404	−	0.000414043i
$771$	0.718332	−	18.9417i	0.0258701	−	0.682168i
$772$	−9.38617	+	16.2573i	−0.337816	+	0.585114i
$773$	−34.7010			−1.24811			−0.624055	−	0.781381i	$-0.714516\pi$
$773$	−34.7010			−1.24811			−0.624055	+	0.781381i	$0.714516\pi$
$774$	−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
$777$	0.264894	−	16.7505i	0.00950303	−	0.600921i
$778$	−6.93262	−	12.0076i	−0.248546	−	0.430495i
$779$	−17.0194	−	9.82614i	−0.609783	−	0.352058i
$780$	−0.00319077	+	0.0102114i	−0.000114248	+	0.000365626i
$781$	−1.78829	−	3.09740i	−0.0639899	−	0.110834i
$782$	−21.4459			−0.766902
$783$	−18.1005	−	41.6590i	−0.646860	−	1.48877i
$784$	−10.0412	+	0.443956i	−0.358614	+	0.0158556i
$785$		−	0.00908333i		−	0.000324198i
$786$	−6.05133	+	9.61985i	−0.215844	+	0.343129i
$787$		−	23.0530i		−	0.821750i	−0.911692	−	0.410875i	$-0.865223\pi$
$787$		−	23.0530i		−	0.821750i	0.911692	−	0.410875i	$-0.134777\pi$
$788$	19.9197	−	11.5006i	0.709609	−	0.409693i
$789$	11.7259	−	18.6408i	0.417454	−	0.663630i
$790$	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
$795$	0.0477122	+	0.00180941i	0.00169218	+	6.41730e-5i
$796$		−	2.45785i		−	0.0871163i
$797$	−18.0616	+	31.2836i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$797$	−18.0616	+	31.2836i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$798$	22.6699	−	12.6148i	0.802504	−	0.446558i
$799$	7.48159	−	12.9585i	0.264680	−	0.458439i
$800$	−19.8178	+	11.4418i	−0.700666	+	0.404530i
$801$	−16.1648	−	1.22781i	−0.571156	−	0.0433827i
$802$	−13.0272			−0.460007
$803$	4.64382			0.163877
$804$	−18.5554	−	11.6722i	−0.654398	−	0.411647i
$805$	0.0218016	+	0.0119530i	0.000768406	+	0.000421286i
$806$	20.4854	−	20.3566i	0.721568	−	0.717029i
$807$	−1.52008	+	40.0831i	−0.0535095	+	1.41099i
$808$	−47.6322	−	27.5004i	−1.67569	−	0.967462i
$809$	25.7675	+	14.8769i	0.905938	+	0.523044i	0.879122	−	0.476597i	$-0.158130\pi$
$809$	25.7675	+	14.8769i	0.905938	+	0.523044i	0.0268161	+	0.999640i	$0.491463\pi$
$810$	0.0142938	+	0.0114463i	0.000502234	+	0.000402181i
$811$			17.0021i			0.597025i	0.954406	+	0.298512i	$0.0964904\pi$
$811$			17.0021i			0.597025i	−0.954406	+	0.298512i	$0.903510\pi$
$812$	−17.5524	+	10.6577i	−0.615969	+	0.374012i
$813$	45.5988	+	1.72926i	1.59922	+	0.0606477i
$814$	−4.81299	+	8.33634i	−0.168695	+	0.292189i
$815$	0.00811564			0.000284279
$816$	−0.393502	+	10.3763i	−0.0137753	+	0.363242i
$817$		−	14.2732i		−	0.499358i
$818$	6.08732			0.212838
$819$	5.82366	+	28.0194i	0.203495	+	0.979076i
$820$	−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	$-0.170906\pi$
$822$	−0.426133	+	11.2367i	−0.0148631	+	0.391925i
$823$	−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
$825$	−21.6081	−	0.819452i	−0.752299	−	0.0285297i
$826$	−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	$0.914839\pi$
$828$	−0.982614	+	12.9367i	−0.0341482	+	0.449580i
$829$	−3.44342	−	1.98806i	−0.119595	−	0.0690483i	0.439009	−	0.898483i	$-0.355330\pi$
$829$	−3.44342	−	1.98806i	−0.119595	−	0.0690483i	−0.558604	+	0.829434i	$0.688663\pi$
$830$	−0.0183413	−	0.0105893i	−0.000636635	−	0.000367562i
$831$	0.289103	−	7.62335i	0.0100289	−	0.264451i
$832$	−7.09921	−	26.8329i	−0.246121	−	0.930265i
$833$	−29.1981	+	1.29095i	−1.01166	+	0.0447288i
$834$	19.0430	+	11.9789i	0.659404	+	0.414796i
$835$	−0.0279759			−0.000968148
$836$	11.9015			0.411623
$837$	15.7276	+	36.1976i	0.543624	+	1.25117i
$838$	−32.1784	+	18.5782i	−1.11158	+	0.641773i
$839$	17.0612	−	29.5509i	0.589019	−	1.02021i	−0.405342	−	0.914165i	$-0.632848\pi$
$839$	17.0612	−	29.5509i	0.589019	−	1.02021i	0.994361	−	0.106046i	$-0.0338190\pi$
$840$	0.0138304	−	0.0231035i	0.000477196	−	0.000797146i
$841$	23.7056	−	41.0593i	0.817434	−	1.41584i
$842$			28.5049i			0.982345i
$843$	−23.0044	−	0.872404i	−0.792315	−	0.0300472i
$844$	−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
$849$	−15.1051	+	24.0127i	−0.518406	+	0.824113i
$850$	19.0658	−	11.0076i	0.653951	−	0.377559i
$851$		−	17.8058i		−	0.610375i
$852$	1.17294	−	1.86463i	0.0401843	−	0.0638812i
$853$		−	56.0005i		−	1.91742i	−0.284387	−	0.958710i	$-0.591790\pi$
$853$		−	56.0005i		−	1.91742i	0.284387	−	0.958710i	$-0.408210\pi$
$854$	−10.9754	−	18.0757i	−0.375571	−	0.618537i
$855$	−0.00235340	+	0.0309838i	−8.04847e−5	+	0.00105962i
$856$	−16.6366			−0.568626
$857$	−7.20743	−	12.4836i	−0.246201	−	0.426433i	0.716268	−	0.697826i	$-0.245849\pi$
$857$	−7.20743	−	12.4836i	−0.246201	−	0.426433i	−0.962469	+	0.271393i	$0.912516\pi$
$858$	4.90440	−	15.6955i	0.167434	−	0.535835i
$859$	2.32454	+	1.34207i	0.0793121	+	0.0457909i	0.539132	−	0.842222i	$-0.318753\pi$
$859$	2.32454	+	1.34207i	0.0793121	+	0.0457909i	−0.459819	+	0.888012i	$0.652086\pi$
$860$	−0.00227736	−	0.00394451i	−7.76574e−5	−	0.000134507i
$861$	−14.6590	+	8.15708i	−0.499577	+	0.277992i
$862$	16.5183	−	28.6105i	0.562615	−	0.974479i
$863$	−25.8619	−	14.9314i	−0.880349	−	0.508270i	−0.00957560	−	0.999954i	$-0.503048\pi$
$863$	−25.8619	−	14.9314i	−0.880349	−	0.508270i	−0.870773	+	0.491684i	$0.836381\pi$
$864$	23.6278	+	2.69849i	0.803835	+	0.0918044i
$865$	−0.0302851			−0.00102973
$866$	−2.08172	+	3.60565i	−0.0707398	+	0.122525i
$867$	−0.0283949	+	0.748746i	−0.000964343	+	0.0254288i
$868$	15.2513	−	9.26048i	0.517663	−	0.314321i
$869$	15.7629	−	9.10072i	0.534720	−	0.308721i
$870$	−0.00116742	+	0.0307837i	−3.95792e−5	+	0.00104367i
$871$	−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	0.946851	−	0.321671i	$-0.104245\pi$
$877$	5.77032	+	9.99449i	0.194850	+	0.337490i	−0.752001	+	0.659162i	$0.770911\pi$
$878$	−32.5509			−1.09854
$879$	29.2143	+	18.3771i	0.985373	+	0.619845i
$880$	−0.00599049	+	0.00345861i	−0.000201939	+	0.000116590i
$881$	−3.76362	−	6.51878i	−0.126800	−	0.219623i	0.795635	−	0.605776i	$-0.207137\pi$
$881$	−3.76362	−	6.51878i	−0.126800	−	0.219623i	−0.922435	+	0.386153i	$0.873804\pi$
$882$	0.700259	−	22.1348i	0.0235790	−	0.745317i
$883$	−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
$885$	0.0147977	+	0.00930846i	0.000497420	+	0.000312900i
$886$	−9.91025	+	17.1651i	−0.332941	+	0.576672i
$887$	−28.6232			−0.961074			−0.480537	−	0.876974i	$-0.659558\pi$
$887$	−28.6232			−0.961074			−0.480537	+	0.876974i	$0.659558\pi$
$888$	−19.2697	−	0.730771i	−0.646649	−	0.0245231i
$889$	12.9606	+	21.3452i	0.434686	+	0.715894i
$890$	0.00952190	+	0.00549747i	0.000319175	+	0.000184276i
$891$	17.5410	+	14.0465i	0.587644	+	0.470577i
$892$	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
$897$	6.65991	+	29.6793i	0.222368	+	0.990963i
$898$	3.01891	−	5.22890i	0.100742	−	0.174491i
$899$	−33.1969	+	57.4987i	−1.10718	+	1.91769i
$900$	−5.76651	−	12.0053i	−0.192217	−	0.400176i
$901$	−51.6621	+	29.8271i	−1.72111	+	0.993686i
$902$	9.63925			0.320952
$903$	−10.4540	−	6.25808i	−0.347888	−	0.208256i
$904$	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	−0.505252	−	0.862972i	$-0.668600\pi$
$907$	14.8995	−	25.8067i	0.494730	−	0.856898i	0.999982	+	0.00607461i	$0.00193362\pi$
$908$	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
$915$	0.0253101		0.000959841i	0.000836725		3.17314e-5i
$916$	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	0.913160	+	0.407601i	$0.133634\pi$
$919$	24.5422	+	42.5083i	0.809573	+	1.40222i	−0.103588	+	0.994620i	$0.533032\pi$
$920$	0.0143098	−	0.0247853i	0.000471781	−	0.000817148i
$921$	−8.53835	−	0.323803i	−0.281348	−	0.0106697i
$922$	−17.1318	−	9.89103i	−0.564205	−	0.325744i
$923$	1.35244	−	4.98441i	0.0445160	−	0.164064i
$924$	5.21820	−	8.71691i	0.171666	−	0.286765i
$925$	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	$-0.277443\pi$
$929$	−10.3944	−	18.0037i	−0.341031	−	0.590682i	−0.984624	+	0.174685i	$0.944109\pi$
$930$	0.00101437	−	0.0267480i	3.32626e−5	−	0.000877102i
$931$	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
$936$	32.3927	−	5.98939i	1.05879	−	0.195769i
$937$		−	10.5891i		−	0.345930i	−0.984928	−	0.172965i	$-0.944665\pi$
$937$		−	10.5891i		−	0.345930i	0.984928	−	0.172965i	$-0.0553347\pi$
$938$	34.8736	+	19.1198i	1.13866	+	0.624284i
$939$	−25.5153	+	40.5619i	−0.832662	+	1.32369i
$940$	0.00306969	+	0.00531686i	0.000100122	+	0.000173417i
$941$	21.4748	+	37.1955i	0.700059	+	1.21254i	0.968445	+	0.249227i	$0.0801764\pi$
$941$	21.4748	+	37.1955i	0.700059	+	1.21254i	−0.268386	+	0.963311i	$0.586490\pi$
$942$	−7.60472	+	4.01430i	−0.247775	+	0.130793i
$943$	−15.4415	+	8.91517i	−0.502846	+	0.290318i
$944$	−7.51141			−0.244475
$945$	0.0216613	+	0.0153085i	0.000704643	+	0.000497986i
$946$	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	$0.706364\pi$
$948$	9.48926	+	5.96918i	0.308197	+	0.193870i
$949$	4.72670	+	4.75662i	0.153435	+	0.154406i
$950$	−14.1532	+	24.5141i	−0.459191	+	0.795342i
$951$	13.6718	−	21.7342i	0.443339	−	0.704780i
$952$	0.743175	+	33.6340i	0.0240864	+	1.09008i
$953$	28.5078	+	16.4590i	0.923458	+	0.533159i	0.884737	−	0.466091i	$-0.154338\pi$
$953$	28.5078	+	16.4590i	0.923458	+	0.533159i	0.0387215	+	0.999250i	$0.487671\pi$
$954$	−19.5711	−	40.7451i	−0.633639	−	1.31917i
$955$			0.0103791i			0.000335858i
$956$			16.7278i			0.541015i
$957$	−1.43262	+	37.7769i	−0.0463102	+	1.22115i
$958$	8.43802	+	4.87169i	0.272620	+	0.157397i
$959$	0.359809	+	16.2840i	0.0116189	+	0.525837i
$960$	−0.0217758	−	0.0136980i	−0.000702810	−	0.000442100i
$961$	13.3448	−	23.1139i	0.430478	−	0.745609i
$962$	−13.4377	+	3.55523i	−0.433250	+	0.114625i
$963$	1.24120	−	16.3411i	0.0399972	−	0.526585i
$964$			1.08618i			0.0349835i
$965$	0.0203962	+	0.0353272i	0.000656576	+	0.00113722i
$966$	0.372188	−	23.5352i	0.0119750	−	0.757232i
$967$	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	0.997921	+	0.0644528i	$0.0205302\pi$
$971$	17.2874	+	29.9426i	0.554778	+	0.960904i	−0.443143	+	0.896451i	$0.646136\pi$
$972$	−2.60753	+	13.5930i	−0.0836365	+	0.435997i
$973$	28.5743	+	15.6661i	0.916050	+	0.502233i
$974$			1.37257i			0.0439798i
$975$	−21.1545	−	22.9671i	−0.677485	−	0.735536i
$976$	−9.42467	+	5.44133i	−0.301676	+	0.174173i
$977$	−50.1256	−	28.9400i	−1.60366	−	0.925874i	−0.990747	−	0.135724i	$-0.956664\pi$
$977$	−50.1256	−	28.9400i	−1.60366	−	0.925874i	−0.612914	−	0.790150i	$-0.710003\pi$
$978$	−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
$981$	9.57395	+	19.9320i	0.305673	+	0.636380i
$982$	−6.97052	−	12.0733i	−0.222438	−	0.385274i
$983$	−1.73371	−	3.00288i	−0.0552969	−	0.0957770i	0.837052	−	0.547123i	$-0.184277\pi$
$983$	−1.73371	−	3.00288i	−0.0552969	−	0.0957770i	−0.892349	+	0.451347i	$0.850944\pi$
$984$	9.01440	+	17.0770i	0.287369	+	0.544394i
$985$		−	0.0499818i		−	0.00159255i
$986$	−19.2443	−	33.3322i	−0.612864	−	1.06151i
$987$	14.0911	+	8.43537i	0.448525	+	0.268501i
$988$	12.1139	+	12.1906i	0.385396	+	0.387835i
$989$	−11.2150	−	6.47499i	−0.356617	−	0.205893i
$990$	−0.00659896	−	0.0137384i	−0.000209729	−	0.000436634i
$991$	−4.47519	+	7.75126i	−0.142159	+	0.246227i	−0.928309	−	0.371809i	$-0.878738\pi$
$991$	−4.47519	+	7.75126i	−0.142159	+	0.246227i	0.786150	+	0.618035i	$0.212071\pi$
$992$	−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
$996$	0.606625	−	15.9961i	0.0192217	−	0.506856i
$997$		−	3.25743i		−	0.103164i	−0.998669	−	0.0515818i	$-0.983574\pi$
$997$		−	3.25743i		−	0.103164i	0.998669	−	0.0515818i	$-0.0164263\pi$
$998$	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.68.22	yes	64
3.2	odd	2	inner	273.2.r.b.68.11	✓	64
7.3	odd	6		273.2.bf.b.185.11	yes	64
13.9	even	3		273.2.bf.b.152.22	yes	64
21.17	even	6		273.2.bf.b.185.22	yes	64
39.35	odd	6		273.2.bf.b.152.11	yes	64
91.87	odd	6	inner	273.2.r.b.269.22	yes	64
273.269	even	6	inner	273.2.r.b.269.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.11	✓	64	3.2	odd	2	inner
273.2.r.b.68.22	yes	64	1.1	even	1	trivial
273.2.r.b.269.11	yes	64	273.269	even	6	inner
273.2.r.b.269.22	yes	64	91.87	odd	6	inner
273.2.bf.b.152.11	yes	64	39.35	odd	6
273.2.bf.b.152.22	yes	64	13.9	even	3
273.2.bf.b.185.11	yes	64	7.3	odd	6
273.2.bf.b.185.22	yes	64	21.17	even	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} +(-0.0656379 + 1.73081i) q^{3} +0.887893 q^{4} +(0.000964697 - 0.00167090i) q^{5} +(-1.82525 - 0.0692194i) q^{6} +(-2.64511 + 0.0584461i) q^{7} +3.04547i q^{8} +(-2.99138 - 0.227213i) q^{9} +(0.00176208 + 0.00101734i) q^{10} +(2.16237 + 1.24844i) q^{11} +(-0.0582795 + 1.53677i) q^{12} +(0.922193 + 3.48562i) q^{13} +(-0.0616352 - 2.78943i) q^{14} +(0.00282869 + 0.00177938i) q^{15} -1.43586 q^{16} -4.17524 q^{17} +(0.239611 - 3.15461i) q^{18} +(4.64914 - 2.68418i) q^{19} +(0.000856548 - 0.00148358i) q^{20} +(0.0724603 - 4.58200i) q^{21} +(-1.31657 + 2.28036i) q^{22} -4.87067i q^{23} +(-5.27112 - 0.199898i) 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} +(-0.00187647 + 0.00298304i) q^{30} +(-6.57778 + 3.79768i) q^{31} +4.57673i q^{32} +(-2.30275 + 3.66070i) q^{33} -4.40306i q^{34} +(-0.00245407 + 0.00447610i) q^{35} +(-2.65603 - 0.201741i) q^{36} +3.65572 q^{37} +(2.83065 + 4.90282i) q^{38} +(-6.09347 + 1.36735i) q^{39} +(0.00508869 + 0.00293796i) q^{40} +(-1.83038 - 3.17031i) q^{41} +(4.83202 + 0.0764141i) 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} +(0.0942468 - 2.48519i) q^{48} +(6.99317 - 0.309192i) q^{49} +(-4.56640 + 2.63641i) q^{50} +(0.274054 - 7.22653i) 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} +(0.00251158 + 0.00157990i) q^{60} +(6.56379 - 3.78960i) q^{61} +(-4.00490 - 6.93670i) q^{62} +(7.92580 + 0.426168i) q^{63} -7.69818 q^{64} +(0.00671378 + 0.00182167i) q^{65} +(-3.86044 - 2.42840i) q^{66} +(-7.12713 + 12.3445i) q^{67} -3.70716 q^{68} +(8.43019 + 0.319701i) q^{69} +(-0.00472034 - 0.00258797i) q^{70} +(-1.24050 - 0.716205i) q^{71} +(0.691971 - 9.11017i) 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} +(-1.44196 - 6.42596i) q^{78} +(3.64483 - 6.31302i) q^{79} +(-0.00138517 + 0.00239918i) q^{80} +(8.89675 + 1.35936i) q^{81} +(3.34329 - 1.93025i) q^{82} -10.4089 q^{83} +(0.0643370 - 4.06833i) 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} +(-7.92144 - 0.300407i) 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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