LMFDB - Embedded newform 252.2.ba.a.155.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.19
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0439092 + 1.41353i) q^{2} +(-1.25879 - 1.18972i) q^{3} +(-1.99614 + 0.124134i) q^{4} +(-0.245511 + 0.141746i) q^{5} +(1.62644 - 1.83159i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.263117 - 2.81616i) q^{8} +(0.169128 + 2.99523i) q^{9} +O(q^{10})$	\(q+(0.0439092 + 1.41353i) q^{2} +(-1.25879 - 1.18972i) q^{3} +(-1.99614 + 0.124134i) q^{4} +(-0.245511 + 0.141746i) q^{5} +(1.62644 - 1.83159i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.263117 - 2.81616i) q^{8} +(0.169128 + 2.99523i) q^{9} +(-0.211142 - 0.340813i) q^{10} +(2.59732 - 4.49870i) q^{11} +(2.66042 + 2.21859i) q^{12} +(-3.18766 - 5.52119i) q^{13} +(0.668739 - 1.24611i) q^{14} +(0.477686 + 0.113661i) q^{15} +(3.96918 - 0.495579i) q^{16} -4.61251i q^{17} +(-4.22642 + 0.370586i) q^{18} +1.33072i q^{19} +(0.472479 - 0.313421i) q^{20} +(0.495288 + 1.65973i) q^{21} +(6.47310 + 3.47387i) q^{22} +(-1.74930 - 3.02987i) q^{23} +(-3.01924 + 3.85801i) q^{24} +(-2.45982 + 4.26053i) q^{25} +(7.66440 - 4.74829i) q^{26} +(3.35059 - 3.97159i) q^{27} +(1.79078 + 0.890569i) q^{28} +(2.94700 + 1.70145i) q^{29} +(-0.139688 + 0.680214i) q^{30} +(-6.40568 + 3.69832i) q^{31} +(0.874801 + 5.58880i) q^{32} +(-8.62169 + 2.57285i) q^{33} +(6.51993 - 0.202532i) q^{34} +0.283491 q^{35} +(-0.709414 - 5.95791i) q^{36} -4.23573 q^{37} +(-1.88102 + 0.0584309i) q^{38} +(-2.55606 + 10.7425i) q^{39} +(0.463777 + 0.654103i) q^{40} +(-3.44487 + 1.98890i) q^{41} +(-2.32433 + 0.772982i) q^{42} +(7.21047 + 4.16297i) q^{43} +(-4.62619 + 9.30247i) q^{44} +(-0.466084 - 0.711388i) q^{45} +(4.20601 - 2.60573i) q^{46} +(4.56827 - 7.91247i) q^{47} +(-5.58599 - 4.09839i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.13040 - 3.28995i) q^{50} +(-5.48760 + 5.80620i) q^{51} +(7.04839 + 10.6254i) q^{52} -1.30189i q^{53} +(5.76109 + 4.56177i) q^{54} +1.47264i q^{55} +(-1.18022 + 2.57043i) q^{56} +(1.58319 - 1.67510i) q^{57} +(-2.27565 + 4.24038i) q^{58} +(-2.57739 - 4.46416i) q^{59} +(-0.967638 - 0.167586i) q^{60} +(5.25592 - 9.10352i) q^{61} +(-5.50896 - 8.89224i) q^{62} +(1.35115 - 2.67851i) q^{63} +(-7.86154 + 1.48196i) q^{64} +(1.56521 + 0.903674i) q^{65} +(-4.01537 - 12.0741i) q^{66} +(-4.13135 + 2.38524i) q^{67} +(0.572570 + 9.20723i) q^{68} +(-1.40270 + 5.89516i) q^{69} +(0.0124479 + 0.400724i) q^{70} +4.38110 q^{71} +(8.39055 - 1.26439i) q^{72} +9.30211 q^{73} +(-0.185988 - 5.98734i) q^{74} +(8.16524 - 2.43663i) q^{75} +(-0.165188 - 2.65631i) q^{76} +(-4.49870 + 2.59732i) q^{77} +(-15.2970 - 3.14138i) q^{78} +(-12.5954 - 7.27197i) q^{79} +(-0.904231 + 0.684285i) q^{80} +(-8.94279 + 1.01315i) q^{81} +(-2.96263 - 4.78210i) q^{82} +(-0.436034 + 0.755232i) q^{83} +(-1.19469 - 3.25157i) q^{84} +(0.653803 + 1.13242i) q^{85} +(-5.56788 + 10.3750i) q^{86} +(-1.68541 - 5.64788i) q^{87} +(-13.3525 - 6.13080i) q^{88} +4.68117i q^{89} +(0.985104 - 0.690060i) q^{90} +6.37532i q^{91} +(3.86796 + 5.83091i) q^{92} +(12.4634 + 2.96555i) q^{93} +(11.3851 + 6.10996i) q^{94} +(-0.188624 - 0.326706i) q^{95} +(5.54792 - 8.07592i) q^{96} +(-2.07255 + 3.58977i) q^{97} +(-1.20220 + 0.744792i) q^{98} +(13.9139 + 7.01873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.0439092	+	1.41353i	0.0310485	+	0.999518i
$2$	0.0439092	+	1.41353i	0.0310485	+	0.999518i
$3$	−1.25879	−	1.18972i	−0.726765	−	0.686886i
$3$	−1.25879	−	1.18972i	−0.726765	−	0.686886i
$4$	−1.99614	+	0.124134i	−0.998072	+	0.0620671i
$5$	−0.245511	+	0.141746i	−0.109796	+	0.0633906i	−0.553892	−	0.832588i	$-0.686858\pi$
$5$	−0.245511	+	0.141746i	−0.109796	+	0.0633906i	0.444097	+	0.895979i	$0.353525\pi$
$6$	1.62644	−	1.83159i	0.663990	−	0.747742i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−0.263117	−	2.81616i	−0.0930258	−	0.995664i
$9$	0.169128	+	2.99523i	0.0563760	+	0.998410i
$10$	−0.211142	−	0.340813i	−0.0667691	−	0.107775i
$11$	2.59732	−	4.49870i	0.783123	−	1.35641i	−0.146991	−	0.989138i	$-0.546959\pi$
$11$	2.59732	−	4.49870i	0.783123	−	1.35641i	0.930114	−	0.367271i	$-0.119708\pi$
$12$	2.66042	+	2.21859i	0.767997	+	0.640453i
$13$	−3.18766	−	5.52119i	−0.884097	−	1.53130i	−0.846745	−	0.531999i	$-0.821441\pi$
$13$	−3.18766	−	5.52119i	−0.884097	−	1.53130i	−0.0373526	−	0.999302i	$-0.511892\pi$
$14$	0.668739	−	1.24611i	0.178728	−	0.333037i
$15$	0.477686	+	0.113661i	0.123338	+	0.0293470i
$16$	3.96918	−	0.495579i	0.992295	−	0.123895i
$17$		−	4.61251i		−	1.11870i	−0.828932	−	0.559349i	$-0.811051\pi$
$17$		−	4.61251i		−	1.11870i	0.828932	−	0.559349i	$-0.188949\pi$
$18$	−4.22642	+	0.370586i	−0.996178	+	0.0873479i
$19$			1.33072i			0.305288i	0.988281	+	0.152644i	$0.0487788\pi$
$19$			1.33072i			0.305288i	−0.988281	+	0.152644i	$0.951221\pi$
$20$	0.472479	−	0.313421i	0.105650	−	0.0700831i
$21$	0.495288	+	1.65973i	0.108081	+	0.362182i
$22$	6.47310	+	3.47387i	1.38007	+	0.740631i
$23$	−1.74930	−	3.02987i	−0.364754	−	0.631772i	0.623983	−	0.781438i	$-0.285513\pi$
$23$	−1.74930	−	3.02987i	−0.364754	−	0.631772i	−0.988737	+	0.149666i	$0.952180\pi$
$24$	−3.01924	+	3.85801i	−0.616299	+	0.787512i
$25$	−2.45982	+	4.26053i	−0.491963	+	0.852105i
$26$	7.66440	−	4.74829i	1.50311	−	0.931216i
$27$	3.35059	−	3.97159i	0.644821	−	0.764333i
$28$	1.79078	+	0.890569i	0.338425	+	0.168302i
$29$	2.94700	+	1.70145i	0.547244	+	0.315951i	0.748009	−	0.663688i	$-0.231010\pi$
$29$	2.94700	+	1.70145i	0.547244	+	0.315951i	−0.200766	+	0.979639i	$0.564343\pi$
$30$	−0.139688	+	0.680214i	−0.0255034	+	0.124190i
$31$	−6.40568	+	3.69832i	−1.15049	+	0.664238i	−0.949008	−	0.315253i	$-0.897911\pi$
$31$	−6.40568	+	3.69832i	−1.15049	+	0.664238i	−0.201487	+	0.979491i	$0.564577\pi$
$32$	0.874801	+	5.58880i	0.154644	+	0.987970i
$33$	−8.62169	+	2.57285i	−1.50084	+	0.447875i
$34$	6.51993	−	0.202532i	1.11816	−	0.0347339i
$35$	0.283491			0.0479188
$36$	−0.709414	−	5.95791i	−0.118236	−	0.992986i
$37$	−4.23573			−0.696350			−0.348175	−	0.937430i	$-0.613198\pi$
$37$	−4.23573			−0.696350			−0.348175	+	0.937430i	$0.613198\pi$
$38$	−1.88102	+	0.0584309i	−0.305141	+	0.00947875i
$39$	−2.55606	+	10.7425i	−0.409298	+	1.72017i
$40$	0.463777	+	0.654103i	0.0733296	+	0.103423i
$41$	−3.44487	+	1.98890i	−0.537999	+	0.310614i	−0.744267	−	0.667882i	$-0.767201\pi$
$41$	−3.44487	+	1.98890i	−0.537999	+	0.310614i	0.206269	+	0.978495i	$0.433868\pi$
$42$	−2.32433	+	0.772982i	−0.358652	+	0.119274i
$43$	7.21047	+	4.16297i	1.09959	+	0.634846i	0.936112	−	0.351701i	$-0.114397\pi$
$43$	7.21047	+	4.16297i	1.09959	+	0.634846i	0.163474	+	0.986548i	$0.447730\pi$
$44$	−4.62619	+	9.30247i	−0.697425	+	1.40240i
$45$	−0.466084	−	0.711388i	−0.0694796	−	0.106047i
$46$	4.20601	−	2.60573i	0.620142	−	0.384193i
$47$	4.56827	−	7.91247i	0.666350	−	1.15415i	−0.312567	−	0.949896i	$-0.601189\pi$
$47$	4.56827	−	7.91247i	0.666350	−	1.15415i	0.978917	−	0.204257i	$-0.0654778\pi$
$48$	−5.58599	−	4.09839i	−0.806268	−	0.591551i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−6.13040	−	3.28995i	−0.866969	−	0.465269i
$51$	−5.48760	+	5.80620i	−0.768417	+	0.813031i
$52$	7.04839	+	10.6254i	0.977436	+	1.47348i
$53$		−	1.30189i		−	0.178828i	−0.995995	−	0.0894140i	$-0.971501\pi$
$53$		−	1.30189i		−	0.178828i	0.995995	−	0.0894140i	$-0.0284994\pi$
$54$	5.76109	+	4.56177i	0.783986	+	0.620779i
$55$			1.47264i			0.198571i
$56$	−1.18022	+	2.57043i	−0.157713	+	0.343488i
$57$	1.58319	−	1.67510i	0.209698	−	0.221873i
$58$	−2.27565	+	4.24038i	−0.298808	+	0.556790i
$59$	−2.57739	−	4.46416i	−0.335547	−	0.581185i	0.648043	−	0.761604i	$-0.275588\pi$
$59$	−2.57739	−	4.46416i	−0.335547	−	0.581185i	−0.983590	+	0.180419i	$0.942254\pi$
$60$	−0.967638	−	0.167586i	−0.124922	−	0.0216352i
$61$	5.25592	−	9.10352i	0.672951	−	1.16559i	−0.304112	−	0.952636i	$-0.598360\pi$
$61$	5.25592	−	9.10352i	0.672951	−	1.16559i	0.977063	−	0.212950i	$-0.0683071\pi$
$62$	−5.50896	−	8.89224i	−0.699639	−	1.12932i
$63$	1.35115	−	2.67851i	0.170228	−	0.337460i
$64$	−7.86154	+	1.48196i	−0.982692	+	0.185245i
$65$	1.56521	+	0.903674i	0.194140	+	0.112087i
$66$	−4.01537	−	12.0741i	−0.494258	−	1.48621i
$67$	−4.13135	+	2.38524i	−0.504725	+	0.291403i	−0.730663	−	0.682739i	$-0.760789\pi$
$67$	−4.13135	+	2.38524i	−0.504725	+	0.291403i	0.225938	+	0.974142i	$0.427455\pi$
$68$	0.572570	+	9.20723i	0.0694343	+	1.11654i
$69$	−1.40270	+	5.89516i	−0.168865	+	0.709694i
$70$	0.0124479	+	0.400724i	0.00148781	+	0.0478957i
$71$	4.38110			0.519941			0.259971	−	0.965617i	$-0.416287\pi$
$71$	4.38110			0.519941			0.259971	+	0.965617i	$0.416287\pi$
$72$	8.39055	−	1.26439i	0.988836	−	0.149009i
$73$	9.30211			1.08873			0.544365	−	0.838849i	$-0.316771\pi$
$73$	9.30211			1.08873			0.544365	+	0.838849i	$0.316771\pi$
$74$	−0.185988	−	5.98734i	−0.0216206	−	0.696014i
$75$	8.16524	−	2.43663i	0.942841	−	0.281358i
$76$	−0.165188	−	2.65631i	−0.0189484	−	0.304700i
$77$	−4.49870	+	2.59732i	−0.512674	+	0.295993i
$78$	−15.2970	−	3.14138i	−1.73205	−	0.355692i
$79$	−12.5954	−	7.27197i	−1.41710	−	0.818161i	−0.421054	−	0.907036i	$-0.638340\pi$
$79$	−12.5954	−	7.27197i	−1.41710	−	0.818161i	−0.996043	+	0.0888748i	$0.971673\pi$
$80$	−0.904231	+	0.684285i	−0.101096	+	0.0765053i
$81$	−8.94279	+	1.01315i	−0.993644	+	0.112573i
$82$	−2.96263	−	4.78210i	−0.327168	−	0.528095i
$83$	−0.436034	+	0.755232i	−0.0478609	+	0.0828975i	−0.888963	−	0.457978i	$-0.848574\pi$
$83$	−0.436034	+	0.755232i	−0.0478609	+	0.0828975i	0.841103	+	0.540876i	$0.181907\pi$
$84$	−1.19469	−	3.25157i	−0.130352	−	0.354775i
$85$	0.653803	+	1.13242i	0.0709149	+	0.122828i
$86$	−5.56788	+	10.3750i	−0.600400	+	1.11877i
$87$	−1.68541	−	5.64788i	−0.180695	−	0.605516i
$88$	−13.3525	−	6.13080i	−1.42338	−	0.653546i
$89$			4.68117i			0.496203i	0.968734	+	0.248102i	$0.0798067\pi$
$89$			4.68117i			0.496203i	−0.968734	+	0.248102i	$0.920193\pi$
$90$	0.985104	−	0.690060i	0.103839	−	0.0727388i
$91$			6.37532i			0.668315i
$92$	3.86796	+	5.83091i	0.403262	+	0.607914i
$93$	12.4634	+	2.96555i	1.29240	+	0.307513i
$94$	11.3851	+	6.10996i	1.17429	+	0.630194i
$95$	−0.188624	−	0.326706i	−0.0193524	−	0.0335194i
$96$	5.54792	−	8.07592i	0.566232	−	0.824246i
$97$	−2.07255	+	3.58977i	−0.210436	+	0.364486i	−0.951851	−	0.306561i	$-0.900822\pi$
$97$	−2.07255	+	3.58977i	−0.210436	+	0.364486i	0.741415	+	0.671047i	$0.234155\pi$
$98$	−1.20220	+	0.744792i	−0.121441	+	0.0752354i
$99$	13.9139	+	7.01873i	1.39840	+	0.705408i
$100$	4.38127	−	8.80997i	0.438127	−	0.880997i
$101$	8.09946	+	4.67622i	0.805926	+	0.465302i	0.845539	−	0.533913i	$-0.179279\pi$
$101$	8.09946	+	4.67622i	0.805926	+	0.465302i	−0.0396131	+	0.999215i	$0.512613\pi$
$102$	−8.44821	−	7.50195i	−0.836497	−	0.742804i
$103$	−0.693427	+	0.400350i	−0.0683254	+	0.0394477i	−0.533774	−	0.845627i	$-0.679227\pi$
$103$	−0.693427	+	0.400350i	−0.0683254	+	0.0394477i	0.465448	+	0.885075i	$0.345893\pi$
$104$	−14.7098	+	10.4297i	−1.44242	+	1.02271i
$105$	−0.356858	−	0.337276i	−0.0348257	−	0.0329147i
$106$	1.84026	−	0.0571649i	0.178742	−	0.00555234i
$107$	2.74697			0.265560			0.132780	−	0.991146i	$-0.457610\pi$
$107$	2.74697			0.265560			0.132780	+	0.991146i	$0.457610\pi$
$108$	−6.19525	+	8.34379i	−0.596138	+	0.802882i
$109$	11.8507			1.13509			0.567545	−	0.823342i	$-0.307893\pi$
$109$	11.8507			1.13509			0.567545	+	0.823342i	$0.307893\pi$
$110$	−2.08162	+	0.0646624i	−0.198475	+	0.00616532i
$111$	5.33191	+	5.03934i	0.506083	+	0.478313i
$112$	−3.68520	−	1.55541i	−0.348219	−	0.146972i
$113$	12.8174	−	7.40012i	1.20576	−	0.696144i	0.243928	−	0.969793i	$-0.421564\pi$
$113$	12.8174	−	7.40012i	1.20576	−	0.696144i	0.961830	+	0.273649i	$0.0882307\pi$
$114$	2.43733	+	2.16433i	0.228277	+	0.202708i
$115$	0.858942	+	0.495911i	0.0800968	+	0.0462439i
$116$	−6.09384	−	3.03051i	−0.565799	−	0.281376i
$117$	15.9981	−	10.4816i	1.47902	−	0.969020i
$118$	6.19707	−	3.83923i	0.570486	−	0.353430i
$119$	−2.30625	+	3.99455i	−0.211414	+	0.366180i
$120$	0.194400	−	1.37515i	0.0177462	−	0.125533i
$121$	−7.99219	−	13.8429i	−0.726563	−	1.25844i
$122$	13.0989	+	7.02968i	1.18592	+	0.636437i
$123$	6.70262	+	1.59482i	0.604355	+	0.143800i
$124$	12.3276	−	8.17755i	1.10705	−	0.734365i
$125$		−	2.81213i		−	0.251525i
$126$	3.84548	+	1.79228i	0.342583	+	0.159669i
$127$			3.96302i			0.351661i	0.984420	+	0.175830i	$0.0562611\pi$
$127$			3.96302i			0.351661i	−0.984420	+	0.175830i	$0.943739\pi$
$128$	−2.43999	−	11.0475i	−0.215667	−	0.976467i
$129$	−4.12373	−	13.8188i	−0.363074	−	1.21667i
$130$	−1.20864	+	2.25215i	−0.106005	+	0.197527i
$131$	3.50647	+	6.07338i	0.306362	+	0.530634i	0.977564	−	0.210641i	$-0.0675550\pi$
$131$	3.50647	+	6.07338i	0.306362	+	0.530634i	−0.671202	+	0.741275i	$0.734222\pi$
$132$	16.8908	−	6.20602i	1.47015	−	0.540164i
$133$	0.665361	−	1.15244i	0.0576941	−	0.0999291i
$134$	−3.55301	−	5.73507i	−0.306934	−	0.495434i
$135$	−0.259650	+	1.45000i	−0.0223471	+	0.124796i
$136$	−12.9896	+	1.21363i	−1.11385	+	0.104068i
$137$	15.0483	+	8.68816i	1.28567	+	0.742280i	0.977878	−	0.209175i	$-0.0670780\pi$
$137$	15.0483	+	8.68816i	1.28567	+	0.742280i	0.307788	+	0.951455i	$0.400411\pi$
$138$	−8.39459	−	1.72390i	−0.714595	−	0.146748i
$139$	5.01147	−	2.89337i	0.425067	−	0.245413i	−0.272176	−	0.962248i	$-0.587743\pi$
$139$	5.01147	−	2.89337i	0.425067	−	0.245413i	0.697243	+	0.716835i	$0.254410\pi$
$140$	−0.565890	+	0.0351910i	−0.0478264	+	0.00297418i
$141$	−15.1641	+	4.52521i	−1.27705	+	0.381092i
$142$	0.192371	+	6.19283i	0.0161434	+	0.519690i
$143$	−33.1175			−2.76943
$144$	2.15567	+	11.8048i	0.179639	+	0.983733i
$145$	−0.964693			−0.0801134
$146$	0.408448	+	13.1488i	0.0338034	+	1.08820i
$147$	0.400931	−	1.68501i	0.0330683	−	0.138977i
$148$	8.45513	−	0.525799i	0.695007	−	0.0432204i
$149$	6.33260	−	3.65613i	0.518786	−	0.299521i	−0.217652	−	0.976027i	$-0.569840\pi$
$149$	6.33260	−	3.65613i	0.518786	−	0.299521i	0.736438	+	0.676505i	$0.236506\pi$
$150$	3.80279	+	11.4348i	0.310496	+	0.933651i
$151$	−7.67503	−	4.43118i	−0.624585	−	0.360605i	0.154067	−	0.988060i	$-0.450763\pi$
$151$	−7.67503	−	4.43118i	−0.624585	−	0.360605i	−0.778652	+	0.627456i	$0.784096\pi$
$152$	3.74753	−	0.350135i	0.303965	−	0.0283997i
$153$	13.8155	−	0.780104i	1.11692	−	0.0630677i
$154$	−3.86893	−	6.24501i	−0.311768	−	0.503237i
$155$	1.04844	−	1.81596i	0.0842129	−	0.145861i
$156$	3.76876	−	21.7608i	0.301743	−	1.74226i
$157$	−2.30277	−	3.98852i	−0.183781	−	0.318318i	0.759384	−	0.650643i	$-0.225500\pi$
$157$	−2.30277	−	3.98852i	−0.183781	−	0.318318i	−0.943165	+	0.332324i	$0.892167\pi$
$158$	9.72611	−	18.1233i	0.773768	−	1.44182i
$159$	−1.54888	+	1.63881i	−0.122834	+	0.129966i
$160$	−1.00696	−	1.24811i	−0.0796073	−	0.0986719i
$161$			3.49859i			0.275728i
$162$	−1.82480	−	12.5964i	−0.143369	−	0.989669i
$163$		−	6.44257i		−	0.504621i	−0.967646	−	0.252310i	$-0.918810\pi$
$163$		−	6.44257i		−	0.504621i	0.967646	−	0.252310i	$-0.0811904\pi$
$164$	6.62957	−	4.39775i	0.517682	−	0.343407i
$165$	1.75203	−	1.85375i	0.136395	−	0.144314i
$166$	−1.08669	−	0.583186i	−0.0843435	−	0.0452640i
$167$	8.09211	+	14.0159i	0.626186	+	1.08459i	0.988310	+	0.152456i	$0.0487184\pi$
$167$	8.09211	+	14.0159i	0.626186	+	1.08459i	−0.362124	+	0.932130i	$0.617948\pi$
$168$	4.54374	−	1.83151i	0.350557	−	0.141304i
$169$	−13.8223	+	23.9410i	−1.06326	+	1.84161i
$170$	−1.57200	+	0.973896i	−0.120567	+	0.0746944i
$171$	−3.98581	+	0.225062i	−0.304803	+	0.0172109i
$172$	−14.9099	−	7.41481i	−1.13687	−	0.565374i
$173$	−18.1511	−	10.4796i	−1.38000	−	0.796746i	−0.387845	−	0.921725i	$-0.626780\pi$
$173$	−18.1511	−	10.4796i	−1.38000	−	0.796746i	−0.992159	+	0.124979i	$0.960114\pi$
$174$	7.90945	−	2.63038i	0.599614	−	0.199409i
$175$	4.26053	−	2.45982i	0.322066	−	0.185945i
$176$	8.07979	−	19.1433i	0.609037	−	1.44298i
$177$	−2.06671	+	8.68583i	−0.155343	+	0.652867i
$178$	−6.61698	+	0.205547i	−0.495964	+	0.0154064i
$179$	16.0586			1.20028			0.600139	−	0.799895i	$-0.295112\pi$
$179$	16.0586			1.20028			0.600139	+	0.799895i	$0.295112\pi$
$180$	1.01868	+	1.36218i	0.0759277	+	0.101531i
$181$	−4.86853			−0.361875			−0.180937	−	0.983495i	$-0.557913\pi$
$181$	−4.86853			−0.361875			−0.180937	+	0.983495i	$0.557913\pi$
$182$	−9.01171	+	0.279935i	−0.667993	+	0.0207502i
$183$	−17.4468	+	5.20638i	−1.28970	+	0.384867i
$184$	−8.07234	+	5.72351i	−0.595101	+	0.421943i
$185$	1.03992	−	0.600397i	0.0764562	−	0.0441420i
$186$	−3.64463	+	17.7476i	−0.267238	+	1.30132i
$187$	−20.7503	−	11.9802i	−1.51741	−	0.876078i
$188$	−8.13671	+	16.3615i	−0.593431	+	1.19329i
$189$	−4.88749	+	1.76421i	−0.355513	+	0.128327i
$190$	0.453528	−	0.280971i	0.0329023	−	0.0203838i
$191$	−5.03046	+	8.71301i	−0.363991	+	0.630452i	−0.988614	−	0.150475i	$-0.951920\pi$
$191$	−5.03046	+	8.71301i	−0.363991	+	0.630452i	0.624622	+	0.780927i	$0.285253\pi$
$192$	11.6592	+	7.48756i	0.841429	+	0.540368i
$193$	−3.43621	−	5.95168i	−0.247343	−	0.428411i	0.715444	−	0.698670i	$-0.246224\pi$
$193$	−3.43621	−	5.95168i	−0.247343	−	0.428411i	−0.962788	+	0.270258i	$0.912891\pi$
$194$	−5.16525	−	2.77199i	−0.370844	−	0.199018i
$195$	−0.895157	−	2.99970i	−0.0641035	−	0.214813i
$196$	−1.10558	−	1.66664i	−0.0789697	−	0.119046i
$197$		−	8.23175i		−	0.586488i	−0.956038	−	0.293244i	$-0.905265\pi$
$197$		−	8.23175i		−	0.586488i	0.956038	−	0.293244i	$-0.0947348\pi$
$198$	−9.31024	+	19.9759i	−0.661650	+	1.41963i
$199$			1.63284i			0.115749i	0.998324	+	0.0578745i	$0.0184323\pi$
$199$			1.63284i			0.115749i	−0.998324	+	0.0578745i	$0.981568\pi$
$200$	12.6456	+	5.80623i	0.894176	+	0.410562i
$201$	8.03829	+	1.91263i	0.566978	+	0.134907i
$202$	−6.25435	+	11.6542i	−0.440054	+	0.819984i
$203$	−1.70145	−	2.94700i	−0.119418	−	0.206839i
$204$	10.2333	−	12.2712i	0.716473	−	0.859157i
$205$	0.563835	−	0.976592i	0.0393800	−	0.0682081i
$206$	−0.596356	−	0.962602i	−0.0415501	−	0.0670677i
$207$	8.77930	−	5.75198i	0.610204	−	0.399790i
$208$	−15.3886	−	20.3349i	−1.06701	−	1.40997i
$209$	5.98651	+	3.45631i	0.414096	+	0.239078i
$210$	0.461081	−	0.519239i	0.0318176	−	0.0358309i
$211$	21.5474	−	12.4404i	1.48338	−	0.856432i	0.483562	−	0.875310i	$-0.339343\pi$
$211$	21.5474	−	12.4404i	1.48338	−	0.856432i	0.999822	+	0.0188780i	$0.00600940\pi$
$212$	0.161609	+	2.59875i	0.0110993	+	0.178483i
$213$	−5.51491	−	5.21229i	−0.377875	−	0.357140i
$214$	0.120617	+	3.88293i	0.00824524	+	0.265432i
$215$	−2.36033			−0.160973
$216$	−12.0662	−	8.39081i	−0.821004	−	0.570922i
$217$	7.39664			0.502117
$218$	0.520355	+	16.7513i	0.0352429	+	1.13454i
$219$	−11.7094	−	11.0669i	−0.791251	−	0.747833i
$220$	−0.182805	−	2.93960i	−0.0123247	−	0.198188i
$221$	−25.4665	+	14.7031i	−1.71306	+	0.989038i
$222$	−6.88914	+	7.75810i	−0.462369	+	0.520690i
$223$	6.90473	+	3.98645i	0.462375	+	0.266952i	0.713042	−	0.701121i	$-0.247317\pi$
$223$	6.90473	+	3.98645i	0.462375	+	0.266952i	−0.250667	+	0.968073i	$0.580650\pi$
$224$	2.03680	−	5.27745i	0.136090	−	0.352614i
$225$	−13.1773	−	6.64714i	−0.878485	−	0.443143i
$226$	11.0231	+	17.7928i	0.733246	+	1.18356i
$227$	7.24105	−	12.5419i	0.480605	−	0.832433i	−0.519147	−	0.854685i	$-0.673750\pi$
$227$	7.24105	−	12.5419i	0.480605	−	0.832433i	0.999752	+	0.0222523i	$0.00708370\pi$
$228$	−2.95233	+	3.54028i	−0.195523	+	0.234461i
$229$	2.08709	+	3.61495i	0.137919	+	0.238882i	0.926709	−	0.375781i	$-0.122625\pi$
$229$	2.08709	+	3.61495i	0.137919	+	0.238882i	−0.788790	+	0.614663i	$0.789292\pi$
$230$	−0.663270	+	1.23592i	−0.0437347	+	0.0814940i
$231$	8.75303	+	2.08270i	0.575907	+	0.137031i
$232$	4.01615	−	8.74690i	0.263673	−	0.574262i
$233$		−	23.4451i		−	1.53594i	−0.640485	−	0.767971i	$-0.721266\pi$
$233$		−	23.4451i		−	1.53594i	0.640485	−	0.767971i	$-0.278734\pi$
$234$	15.5185	+	22.1536i	1.01447	+	1.44822i
$235$			2.59013i			0.168961i
$236$	5.69899	+	8.59117i	0.370973	+	0.559238i
$237$	7.20344	+	24.1390i	0.467914	+	1.56799i
$238$	−5.74769	−	3.08457i	−0.372567	−	0.199943i
$239$	−5.76854	−	9.99141i	−0.373136	−	0.646290i	0.616910	−	0.787034i	$-0.288384\pi$
$239$	−5.76854	−	9.99141i	−0.373136	−	0.646290i	−0.990046	+	0.140743i	$0.955051\pi$
$240$	1.95235	+	0.214408i	0.126024	+	0.0138400i
$241$	−7.67674	+	13.2965i	−0.494502	+	0.856503i	−0.999980	−	0.00633693i	$-0.997983\pi$
$241$	−7.67674	+	13.2965i	−0.494502	+	0.856503i	0.505478	+	0.862840i	$0.331316\pi$
$242$	19.2164	−	11.9050i	1.23528	−	0.765285i
$243$	12.4625	+	9.36407i	0.799470	+	0.600706i
$244$	−9.36151	+	18.8244i	−0.599309	+	1.20511i
$245$	−0.245511	−	0.141746i	−0.0156851	−	0.00905580i
$246$	−1.96003	+	9.54439i	−0.124967	+	0.608528i
$247$	7.34716	−	4.24188i	0.467488	−	0.269905i
$248$	12.1005	+	17.0663i	0.768383	+	1.08371i
$249$	1.44739	−	0.431924i	0.0917248	−	0.0273721i
$250$	3.97504	−	0.123478i	0.251403	−	0.00780947i
$251$	−4.45639			−0.281285			−0.140643	−	0.990060i	$-0.544917\pi$
$251$	−4.45639			−0.281285			−0.140643	+	0.990060i	$0.544917\pi$
$252$	−2.36459	+	5.51441i	−0.148955	+	0.347375i
$253$	−18.1740			−1.14259
$254$	−5.60185	+	0.174013i	−0.351491	+	0.0109185i
$255$	0.524260	−	2.20333i	0.0328305	−	0.137978i
$256$	15.5088	−	3.93409i	0.969300	−	0.245881i
$257$	−11.8898	+	6.86460i	−0.741667	+	0.428202i	−0.822675	−	0.568512i	$-0.807519\pi$
$257$	−11.8898	+	6.86460i	−0.741667	+	0.428202i	0.0810078	+	0.996713i	$0.474186\pi$
$258$	19.3522	−	6.43580i	1.20481	−	0.400675i
$259$	3.66825	+	2.11786i	0.227934	+	0.131598i
$260$	−3.23656	−	1.60957i	−0.200723	−	0.0998211i
$261$	−4.59781	+	9.11469i	−0.284597	+	0.564185i
$262$	−8.43095	+	5.22318i	−0.520866	+	0.322689i
$263$	−7.31057	+	12.6623i	−0.450789	+	0.780790i	−0.998435	−	0.0559204i	$-0.982191\pi$
$263$	−7.31057	+	12.6623i	−0.450789	+	0.780790i	0.547646	+	0.836710i	$0.315524\pi$
$264$	9.51406	+	23.6031i	0.585550	+	1.45267i
$265$	0.184537	+	0.319627i	0.0113360	+	0.0196346i
$266$	1.65822	+	0.889906i	0.101672	+	0.0545636i
$267$	5.56929	−	5.89263i	0.340835	−	0.360623i
$268$	7.95069	−	5.27412i	0.485666	−	0.322168i
$269$			11.3921i			0.694587i	0.937756	+	0.347294i	$0.112899\pi$
$269$			11.3921i			0.694587i	−0.937756	+	0.347294i	$0.887101\pi$
$270$	−2.06102	−	0.303354i	−0.125430	−	0.0184616i
$271$			13.6043i			0.826405i	0.910639	+	0.413202i	$0.135590\pi$
$271$			13.6043i			0.826405i	−0.910639	+	0.413202i	$0.864410\pi$
$272$	−2.28586	−	18.3079i	−0.138601	−	1.11008i
$273$	7.58485	−	8.02521i	0.459056	−	0.485708i
$274$	−11.6202	+	21.6528i	−0.702004	+	1.30809i
$275$	12.7779	+	22.1319i	0.770535	+	1.33461i
$276$	2.06819	−	11.9417i	0.124490	−	0.718806i
$277$	−10.6989	+	18.5310i	−0.642834	+	1.11342i	0.341963	+	0.939713i	$0.388908\pi$
$277$	−10.6989	+	18.5310i	−0.642834	+	1.11342i	−0.984797	+	0.173708i	$0.944425\pi$
$278$	4.30992	+	6.95683i	0.258492	+	0.417243i
$279$	−12.1607	−	18.5610i	−0.728042	−	1.11122i
$280$	−0.0745913	−	0.798358i	−0.00445769	−	0.0477110i
$281$	2.80552	+	1.61977i	0.167363	+	0.0966273i	0.581342	−	0.813659i	$-0.302528\pi$
$281$	2.80552	+	1.61977i	0.167363	+	0.0966273i	−0.413979	+	0.910287i	$0.635861\pi$
$282$	−7.06238	−	21.2363i	−0.420559	−	1.26460i
$283$	10.3911	−	5.99933i	0.617689	−	0.356623i	−0.158280	−	0.987394i	$-0.550595\pi$
$283$	10.3911	−	5.99933i	0.617689	−	0.356623i	0.775969	+	0.630771i	$0.217261\pi$
$284$	−8.74531	+	0.543844i	−0.518939	+	0.0322712i
$285$	−0.151251	+	0.635666i	−0.00895931	+	0.0376536i
$286$	−1.45417	−	46.8127i	−0.0859866	−	2.76809i
$287$	3.97779			0.234802
$288$	−16.5918	+	3.56545i	−0.977681	+	0.210096i
$289$	−4.27523			−0.251484
$290$	−0.0423589	−	1.36362i	−0.00248740	−	0.0800747i
$291$	6.87974	−	2.05302i	0.403297	−	0.120350i
$292$	−18.5683	+	1.15471i	−1.08663	+	0.0675742i
$293$	−1.52900	+	0.882771i	−0.0893253	+	0.0515720i	−0.543997	−	0.839087i	$-0.683090\pi$
$293$	−1.52900	+	0.882771i	−0.0893253	+	0.0515720i	0.454672	+	0.890659i	$0.349756\pi$
$294$	2.39942	+	0.492742i	0.139937	+	0.0287373i
$295$	1.26555	+	0.730667i	0.0736833	+	0.0425411i
$296$	1.11449	+	11.9285i	0.0647785	+	0.693330i
$297$	−9.16443	−	25.3888i	−0.531774	−	1.47321i
$298$	5.44611	+	8.79079i	0.315485	+	0.509237i
$299$	−11.1523	+	19.3164i	−0.644955	+	1.11710i
$300$	−15.9965	+	5.87746i	−0.923560	+	0.339335i
$301$	−4.16297	−	7.21047i	−0.239949	−	0.415604i
$302$	5.92661	−	11.0435i	0.341038	−	0.635481i
$303$	−4.63215	−	15.5225i	−0.266110	−	0.891744i
$304$	0.659478	+	5.28187i	0.0378236	+	0.302936i
$305$			2.98002i			0.170635i
$306$	1.70933	+	19.4944i	0.0977159	+	1.11442i
$307$		−	9.54105i		−	0.544537i	−0.962221	−	0.272268i	$-0.912226\pi$
$307$		−	9.54105i		−	0.544537i	0.962221	−	0.272268i	$-0.0877738\pi$
$308$	8.65763	−	5.74308i	0.493314	−	0.327242i
$309$	1.34919	+	0.321026i	0.0767526	+	0.0182625i
$310$	2.61295	+	1.40227i	0.148405	+	0.0796436i
$311$	−2.05899	−	3.56627i	−0.116755	−	0.202225i	0.801725	−	0.597693i	$-0.203916\pi$
$311$	−2.05899	−	3.56627i	−0.116755	−	0.202225i	−0.918480	+	0.395468i	$0.870582\pi$
$312$	30.9251	+	4.37177i	1.75079	+	0.247503i
$313$	12.3611	−	21.4100i	0.698690	−	1.21017i	−0.270231	−	0.962796i	$-0.587100\pi$
$313$	12.3611	−	21.4100i	0.698690	−	1.21017i	0.968921	−	0.247371i	$-0.0795667\pi$
$314$	5.53678	−	3.43017i	0.312459	−	0.193576i
$315$	0.0479463	+	0.849122i	0.00270147	+	0.0478426i
$316$	26.0450	+	12.9524i	1.46515	+	0.728629i
$317$	−11.8984	−	6.86952i	−0.668279	−	0.385831i	0.127145	−	0.991884i	$-0.459419\pi$
$317$	−11.8984	−	6.86952i	−0.668279	−	0.385831i	−0.795424	+	0.606053i	$0.792752\pi$
$318$	−2.38452	−	2.11744i	−0.133717	−	0.118740i
$319$	15.3086	−	8.83843i	0.857118	−	0.494857i
$320$	1.72003	−	1.47818i	0.0961527	−	0.0826326i
$321$	−3.45787	−	3.26813i	−0.193000	−	0.182409i
$322$	−4.94537	+	0.153620i	−0.275595	+	0.00856094i
$323$	6.13796			0.341525
$324$	17.7253	−	3.13251i	0.984741	−	0.174028i
$325$	31.3642			1.73977
$326$	9.10677	−	0.282888i	0.504378	−	0.0156677i
$327$	−14.9176	−	14.0990i	−0.824944	−	0.779677i
$328$	6.50746	+	9.17800i	0.359314	+	0.506771i
$329$	−7.91247	+	4.56827i	−0.436229	+	0.251857i
$330$	2.69726	+	2.39515i	0.148479	+	0.131849i
$331$	−4.77302	−	2.75570i	−0.262349	−	0.151467i	0.363057	−	0.931767i	$-0.381733\pi$
$331$	−4.77302	−	2.75570i	−0.262349	−	0.151467i	−0.625405	+	0.780300i	$0.715066\pi$
$332$	0.776636	−	1.56168i	0.0426234	−	0.0857083i
$333$	−0.716380	−	12.6870i	−0.0392574	−	0.695242i
$334$	−19.4567	+	12.0539i	−1.06462	+	0.659559i
$335$	0.676195	−	1.17120i	0.0369445	−	0.0639897i
$336$	2.78841	+	6.34230i	0.152120	+	0.346001i
$337$	16.7448	+	29.0028i	0.912145	+	1.57988i	0.811028	+	0.585008i	$0.198908\pi$
$337$	16.7448	+	29.0028i	0.912145	+	1.57988i	0.101118	+	0.994874i	$0.467758\pi$
$338$	−34.4483	−	18.4871i	−1.87374	−	1.00556i
$339$	−24.9385	−	5.93388i	−1.35447	−	0.322284i
$340$	−1.44566	−	2.17932i	−0.0784018	−	0.118190i
$341$			38.4230i			2.08072i
$342$	−0.493146	−	5.62419i	−0.0266663	−	0.304121i
$343$		−	1.00000i		−	0.0539949i
$344$	9.82639	−	21.4012i	0.529803	−	1.15387i
$345$	−0.491237	−	1.64615i	−0.0264473	−	0.0886258i
$346$	14.0162	−	26.1173i	0.753515	−	1.40408i
$347$	−6.90711	−	11.9635i	−0.370793	−	0.642232i	0.618895	−	0.785474i	$-0.287581\pi$
$347$	−6.90711	−	11.9635i	−0.370793	−	0.642232i	−0.989688	+	0.143242i	$0.954247\pi$
$348$	4.06542	+	11.0648i	0.217930	+	0.593134i
$349$	4.66788	−	8.08500i	0.249866	−	0.432780i	−0.713623	−	0.700530i	$-0.752947\pi$
$349$	4.66788	−	8.08500i	0.249866	−	0.432780i	0.963488	+	0.267750i	$0.0862802\pi$
$350$	3.66410	+	5.91438i	0.195855	+	0.316137i
$351$	−32.6084	−	5.83915i	−1.74051	−	0.311671i
$352$	27.4145	+	10.5805i	1.46120	+	0.563941i
$353$	−27.3592	−	15.7958i	−1.45618	−	0.840727i	−0.457362	−	0.889281i	$-0.651206\pi$
$353$	−27.3592	−	15.7958i	−1.45618	−	0.840727i	−0.998821	+	0.0485532i	$0.984539\pi$
$354$	−12.3685	−	2.53997i	−0.657376	−	0.134998i
$355$	−1.07561	+	0.621002i	−0.0570873	+	0.0329594i
$356$	−0.581093	−	9.34429i	−0.0307979	−	0.495247i
$357$	7.65550	−	2.28452i	0.405172	−	0.120910i
$358$	0.705122	+	22.6994i	0.0372669	+	1.19970i
$359$	27.3029			1.44099			0.720495	−	0.693460i	$-0.243915\pi$
$359$	27.3029			1.44099			0.720495	+	0.693460i	$0.243915\pi$
$360$	−1.88075	+	1.49975i	−0.0991242	+	0.0790435i
$361$	17.2292			0.906799
$362$	−0.213773	−	6.88182i	−0.0112357	−	0.361700i
$363$	−6.40864	+	26.9338i	−0.336366	+	1.41366i
$364$	−0.791395	−	12.7260i	−0.0414803	−	0.667026i
$365$	−2.28377	+	1.31853i	−0.119538	+	0.0690152i
$366$	−8.12546	−	24.4330i	−0.424725	−	1.27713i
$367$	−2.54676	−	1.47038i	−0.132940	−	0.0767530i	0.432055	−	0.901847i	$-0.357789\pi$
$367$	−2.54676	−	1.47038i	−0.132940	−	0.0767530i	−0.564995	+	0.825094i	$0.691122\pi$
$368$	−8.44482	−	11.1592i	−0.440216	−	0.581713i
$369$	−6.53983	−	9.98180i	−0.340450	−	0.519632i
$370$	0.894341	+	1.44359i	0.0464946	+	0.0750488i
$371$	−0.650944	+	1.12747i	−0.0337953	+	0.0585352i
$372$	−25.2469	−	4.37252i	−1.30899	−	0.226705i
$373$	−8.33048	−	14.4288i	−0.431336	−	0.747095i	0.565653	−	0.824643i	$-0.308624\pi$
$373$	−8.33048	−	14.4288i	−0.431336	−	0.747095i	−0.996989	+	0.0775481i	$0.975291\pi$
$374$	16.0232	−	29.8572i	0.828542	−	1.54388i
$375$	−3.34565	+	3.53990i	−0.172769	+	0.182799i
$376$	−23.4848	−	10.7831i	−1.21114	−	0.556095i
$377$		−	21.6946i		−	1.11733i
$378$	−2.70837	−	6.83116i	−0.139303	−	0.351357i
$379$			1.47107i			0.0755636i	0.999286	+	0.0377818i	$0.0120292\pi$
$379$			1.47107i			0.0755636i	−0.999286	+	0.0377818i	$0.987971\pi$
$380$	0.417076	+	0.628738i	0.0213956	+	0.0322536i
$381$	4.71489	−	4.98863i	0.241551	−	0.255575i
$382$	−12.5370	−	6.72813i	−0.641449	−	0.344241i
$383$	−10.5727	−	18.3125i	−0.540241	−	0.935725i	−0.998890	−	0.0471073i	$-0.985000\pi$
$383$	−10.5727	−	18.3125i	−0.540241	−	0.935725i	0.458649	−	0.888618i	$-0.348334\pi$
$384$	−10.0720	+	16.8094i	−0.513982	+	0.857801i
$385$	0.736319	−	1.27534i	0.0375263	−	0.0649975i
$386$	8.26201	−	5.11852i	0.420525	−	0.260526i
$387$	−11.2495	+	22.3011i	−0.571846	+	1.13363i
$388$	3.69150	−	7.42296i	0.187408	−	0.376844i
$389$	−23.8066	−	13.7447i	−1.20704	−	0.696886i	−0.244931	−	0.969541i	$-0.578765\pi$
$389$	−23.8066	−	13.7447i	−1.20704	−	0.696886i	−0.962112	+	0.272654i	$0.912098\pi$
$390$	4.20087	−	1.39705i	0.212719	−	0.0707422i
$391$	−13.9753	+	8.06864i	−0.706761	+	0.408049i
$392$	2.30731	−	1.63595i	0.116537	−	0.0826278i
$393$	2.81171	−	11.8169i	0.141832	−	0.596082i
$394$	11.6358	−	0.361450i	0.586205	−	0.0182096i
$395$	4.12308			0.207455
$396$	−28.6454	−	12.2832i	−1.43949	−	0.617254i
$397$	18.3231			0.919611			0.459805	−	0.888020i	$-0.347919\pi$
$397$	18.3231			0.919611			0.459805	+	0.888020i	$0.347919\pi$
$398$	−2.30807	+	0.0716968i	−0.115693	+	0.00359384i
$399$	−2.20863	+	0.659090i	−0.110570	+	0.0329958i
$400$	−7.65203	+	18.1298i	−0.382601	+	0.906492i
$401$	32.3553	−	18.6804i	1.61575	−	0.932853i	0.627746	−	0.778419i	$-0.283978\pi$
$401$	32.3553	−	18.6804i	1.61575	−	0.932853i	0.988003	−	0.154434i	$-0.0493555\pi$
$402$	−2.35061	+	11.4464i	−0.117238	+	0.570893i
$403$	40.8382	+	23.5780i	2.03430	+	1.17450i
$404$	−16.7482	−	8.32900i	−0.833252	−	0.414383i
$405$	2.05194	−	1.51634i	0.101962	−	0.0753477i
$406$	4.09096	−	2.53445i	0.203031	−	0.125783i
$407$	−11.0016	+	19.0553i	−0.545327	+	0.944534i
$408$	17.7951	+	13.9263i	0.880988	+	0.689453i
$409$	6.75304	+	11.6966i	0.333916	+	0.578360i	0.983276	−	0.182121i	$-0.0582964\pi$
$409$	6.75304	+	11.6966i	0.333916	+	0.578360i	−0.649360	+	0.760481i	$0.724963\pi$
$410$	1.40520	+	0.754118i	0.0693979	+	0.0372432i
$411$	−8.60628	−	28.8399i	−0.424516	−	1.42257i
$412$	1.33448	−	0.885235i	0.0657453	−	0.0436124i
$413$			5.15477i			0.253650i
$414$	8.51610	+	12.1573i	0.418543	+	0.597496i
$415$		−	0.247224i		−	0.0121357i
$416$	28.0683	−	22.6451i	1.37616	−	1.11027i
$417$	−9.75072	−	2.32009i	−0.477495	−	0.113615i
$418$	−4.62275	+	8.61389i	−0.226106	+	0.421319i
$419$	5.98133	+	10.3600i	0.292207	+	0.506118i	0.974331	−	0.225119i	$-0.0722770\pi$
$419$	5.98133	+	10.3600i	0.292207	+	0.506118i	−0.682124	+	0.731236i	$0.738944\pi$
$420$	0.754206	+	0.628953i	0.0368015	+	0.0306898i
$421$	8.47295	−	14.6756i	0.412946	−	0.715244i	−0.582264	−	0.813000i	$-0.697833\pi$
$421$	8.47295	−	14.6756i	0.412946	−	0.715244i	0.995210	+	0.0977555i	$0.0311663\pi$
$422$	18.5310	+	29.9117i	0.902076	+	1.45608i
$423$	24.4723	+	12.3448i	1.18988	+	0.600224i
$424$	−3.66633	+	0.342548i	−0.178053	+	0.0166356i
$425$	19.6517	+	11.3459i	0.953248	+	0.550358i
$426$	7.12558	−	8.02436i	0.345235	−	0.388782i
$427$	−9.10352	+	5.25592i	−0.440550	+	0.254352i
$428$	−5.48335	+	0.340993i	−0.265048	+	0.0164825i
$429$	41.6882	+	39.4006i	2.01272	+	1.90228i
$430$	−0.103640	−	3.33640i	−0.00499798	−	0.160896i
$431$	−9.32329			−0.449087			−0.224544	−	0.974464i	$-0.572089\pi$
$431$	−9.32329			−0.449087			−0.224544	+	0.974464i	$0.572089\pi$
$432$	11.3309	−	17.4245i	0.545156	−	0.838335i
$433$	3.56552			0.171348			0.0856739	−	0.996323i	$-0.472696\pi$
$433$	3.56552			0.171348			0.0856739	+	0.996323i	$0.472696\pi$
$434$	0.324781	+	10.4554i	0.0155900	+	0.501875i
$435$	1.21435	+	1.14772i	0.0582236	+	0.0550287i
$436$	−23.6557	+	1.47108i	−1.13290	+	0.0704517i
$437$	4.03191	−	2.32783i	0.192873	−	0.111355i
$438$	15.1293	−	17.0376i	0.722905	−	0.814088i
$439$	28.3901	+	16.3910i	1.35499	+	0.782301i	0.988943	−	0.148297i	$-0.0473792\pi$
$439$	28.3901	+	16.3910i	1.35499	+	0.782301i	0.366042	+	0.930598i	$0.380713\pi$
$440$	4.14719	−	0.387476i	0.197709	−	0.0184722i
$441$	−2.50938	+	1.64408i	−0.119494	+	0.0782897i
$442$	−21.9015	−	35.3521i	−1.04175	−	1.68153i
$443$	13.4406	−	23.2798i	0.638583	−	1.10606i	−0.347161	−	0.937805i	$-0.612854\pi$
$443$	13.4406	−	23.2798i	0.638583	−	1.10606i	0.985744	−	0.168252i	$-0.0538123\pi$
$444$	−11.2688	−	9.39737i	−0.534795	−	0.445979i
$445$	−0.663536	−	1.14928i	−0.0314546	−	0.0544810i
$446$	−5.33179	+	9.93510i	−0.252468	+	0.470441i
$447$	−12.3212	−	2.93171i	−0.582773	−	0.138665i
$448$	7.54927	+	2.64736i	0.356670	+	0.125076i
$449$		−	1.04740i		−	0.0494297i	−0.999695	−	0.0247148i	$-0.992132\pi$
$449$		−	1.04740i		−	0.0494297i	0.999695	−	0.0247148i	$-0.00786778\pi$
$450$	8.81734	−	18.9184i	0.415653	−	0.891820i
$451$			20.6632i			0.972994i
$452$	−24.6667	+	16.3628i	−1.16023	+	0.769640i
$453$	4.38942	+	14.7091i	0.206233	+	0.691094i
$454$	18.0463	+	9.68475i	0.846953	+	0.454528i
$455$	−0.903674	−	1.56521i	−0.0423649	−	0.0733781i
$456$	−5.13393	−	4.01776i	−0.240418	−	0.188149i
$457$	−21.1466	+	36.6270i	−0.989198	+	1.71334i	−0.367649	+	0.929964i	$0.619837\pi$
$457$	−21.1466	+	36.6270i	−0.989198	+	1.71334i	−0.621548	+	0.783376i	$0.713496\pi$
$458$	−5.01820	+	3.10890i	−0.234485	+	0.145269i
$459$	−18.3190	−	15.4546i	−0.855058	−	0.721360i
$460$	−1.77613	−	0.883285i	−0.0828126	−	0.0411834i
$461$	−16.9776	−	9.80201i	−0.790725	−	0.456525i	0.0494928	−	0.998774i	$-0.484240\pi$
$461$	−16.9776	−	9.80201i	−0.790725	−	0.456525i	−0.840218	+	0.542249i	$0.817573\pi$
$462$	−2.55962	+	12.4641i	−0.119084	+	0.579884i
$463$	−7.09420	+	4.09584i	−0.329696	+	0.190350i	−0.655706	−	0.755016i	$-0.727629\pi$
$463$	−7.09420	+	4.09584i	−0.329696	+	0.190350i	0.326010	+	0.945366i	$0.394296\pi$
$464$	12.5404	+	5.29289i	0.582172	+	0.245716i
$465$	−3.48025	+	1.03856i	−0.161393	+	0.0481621i
$466$	33.1404	−	1.02946i	1.53520	−	0.0476887i
$467$	−32.5920			−1.50818			−0.754088	−	0.656773i	$-0.771921\pi$
$467$	−32.5920			−1.50818			−0.754088	+	0.656773i	$0.771921\pi$
$468$	−30.6334	+	22.9086i	−1.41603	+	1.05895i
$469$	4.77048			0.220280
$470$	−3.66123	+	0.113731i	−0.168880	+	0.00524600i
$471$	−1.84651	+	7.76038i	−0.0850825	+	0.357579i
$472$	−11.8937	+	8.43293i	−0.547450	+	0.388157i
$473$	37.4558	−	21.6251i	1.72222	−	0.994325i
$474$	−33.8049	+	11.2422i	−1.55271	+	0.516372i
$475$	−5.66957	−	3.27333i	−0.260138	−	0.150191i
$476$	4.10776	−	8.25998i	0.188279	−	0.378596i
$477$	3.89945	−	0.220185i	0.178544	−	0.0100816i
$478$	13.8699	−	8.59273i	0.634393	−	0.393022i
$479$	4.82415	−	8.35568i	0.220421	−	0.381781i	−0.734515	−	0.678593i	$-0.762590\pi$
$479$	4.82415	−	8.35568i	0.220421	−	0.381781i	0.954936	+	0.296812i	$0.0959235\pi$
$480$	−0.217347	+	2.76912i	−0.00992049	+	0.126393i
$481$	13.5021	+	23.3862i	0.615641	+	1.06632i
$482$	−19.1321	−	10.2675i	−0.871443	−	0.467670i
$483$	4.16235	−	4.40401i	0.189393	−	0.200389i
$484$	17.6719	+	26.6403i	0.803270	+	1.21092i
$485$		−	1.17510i		−	0.0533586i
$486$	−12.6892	+	18.0273i	−0.575594	+	0.817736i
$487$			4.57534i			0.207328i	0.994612	+	0.103664i	$0.0330567\pi$
$487$			4.57534i			0.207328i	−0.994612	+	0.103664i	$0.966943\pi$
$488$	−27.0199	−	12.4062i	−1.22313	−	0.561604i
$489$	−7.66486	+	8.10987i	−0.346617	+	0.366741i
$490$	0.189582	−	0.353261i	0.00856444	−	0.0159587i
$491$	−1.30164	−	2.25451i	−0.0587422	−	0.101744i	0.835159	−	0.550009i	$-0.185376\pi$
$491$	−1.30164	−	2.25451i	−0.0587422	−	0.101744i	−0.893901	+	0.448264i	$0.852042\pi$
$492$	−13.5774	−	2.35147i	−0.612115	−	0.106013i
$493$	7.84795	−	13.5930i	0.353454	−	0.612200i
$494$	6.31865	+	10.1992i	0.284289	+	0.458883i
$495$	−4.41089	+	0.249064i	−0.198255	+	0.0111946i
$496$	−23.5925	+	17.8538i	−1.05933	+	0.801661i
$497$	−3.79415	−	2.19055i	−0.170191	−	0.0982596i
$498$	0.674092	+	2.02697i	0.0302068	+	0.0908307i
$499$	32.4773	−	18.7508i	1.45388	−	0.839399i	0.455183	−	0.890398i	$-0.349574\pi$
$499$	32.4773	−	18.7508i	1.45388	−	0.839399i	0.998699	+	0.0509989i	$0.0162405\pi$
$500$	0.349082	+	5.61342i	0.0156114	+	0.251040i
$501$	6.48876	−	27.2705i	0.289896	−	1.21836i
$502$	−0.195677	−	6.29926i	−0.00873348	−	0.281150i
$503$	43.0405			1.91908			0.959541	−	0.281568i	$-0.0908544\pi$
$503$	43.0405			1.91908			0.959541	+	0.281568i	$0.0908544\pi$
$504$	−7.89862	−	3.10028i	−0.351833	−	0.138098i
$505$	−2.65134			−0.117983
$506$	−0.798005	−	25.6895i	−0.0354756	−	1.14204i
$507$	45.8826	−	13.6921i	2.03772	−	0.608086i
$508$	−0.491946	−	7.91075i	−0.0218266	−	0.350983i
$509$	−20.8692	+	12.0489i	−0.925012	+	0.534056i	−0.885231	−	0.465152i	$-0.846000\pi$
$509$	−20.8692	+	12.0489i	−0.925012	+	0.534056i	−0.0397817	+	0.999208i	$0.512666\pi$
$510$	3.13749	+	0.644312i	0.138931	+	0.0285306i
$511$	−8.05586	−	4.65105i	−0.356370	−	0.205750i
$512$	6.24194	+	21.7494i	0.275857	+	0.961199i
$513$	5.28508	+	4.45870i	0.233342	+	0.196856i
$514$	−10.2254	−	16.5052i	−0.451023	−	0.728015i
$515$	0.113496	−	0.196581i	0.00500123	−	0.00866238i
$516$	9.94694	+	27.0723i	0.437890	+	1.19179i
$517$	−23.7306	−	41.1025i	−1.04367	−	1.80769i
$518$	−2.83260	+	5.27818i	−0.124457	+	0.231910i
$519$	10.3808	+	34.7864i	0.455666	+	1.52695i
$520$	2.13306	−	4.64565i	0.0935409	−	0.203725i
$521$			38.4077i			1.68267i	0.540512	+	0.841336i	$0.318231\pi$
$521$			38.4077i			1.68267i	−0.540512	+	0.841336i	$0.681769\pi$
$522$	−13.0858	−	6.09893i	−0.572750	−	0.266943i
$523$			14.2799i			0.624419i	0.950013	+	0.312209i	$0.101069\pi$
$523$			14.2799i			0.624419i	−0.950013	+	0.312209i	$0.898931\pi$
$524$	−7.75333	−	11.6881i	−0.338706	−	0.510596i
$525$	−8.28962	−	1.97243i	−0.361789	−	0.0860841i
$526$	−18.2195	−	9.77773i	−0.794410	−	0.426329i
$527$	17.0585	+	29.5463i	0.743082	+	1.28706i
$528$	−32.9460	+	14.4848i	−1.43379	+	0.630371i
$529$	5.37992	−	9.31830i	0.233910	−	0.405144i
$530$	−0.443701	+	0.274883i	−0.0192731	+	0.0119402i
$531$	12.9353	−	8.47487i	0.561343	−	0.367778i
$532$	−1.18510	+	2.38303i	−0.0513805	+	0.103317i
$533$	21.9621	+	12.6799i	0.951286	+	0.549225i
$534$	8.57397	+	7.61362i	0.371032	+	0.329474i
$535$	−0.674411	+	0.389372i	−0.0291573	+	0.0168340i
$536$	7.80425	+	11.0070i	0.337092	+	0.475429i
$537$	−20.2145	−	19.1053i	−0.872321	−	0.824455i
$538$	−16.1031	+	0.500217i	−0.694252	+	0.0215659i
$539$	5.19465			0.223749
$540$	0.338303	−	2.92664i	0.0145583	−	0.125943i
$541$	−24.7195			−1.06277			−0.531387	−	0.847129i	$-0.678329\pi$
$541$	−24.7195			−1.06277			−0.531387	+	0.847129i	$0.678329\pi$
$542$	−19.2302	+	0.597356i	−0.826006	+	0.0256586i
$543$	6.12847	+	5.79219i	0.262998	+	0.248567i
$544$	25.7784	−	4.03503i	1.10524	−	0.173000i
$545$	−2.90947	+	1.67978i	−0.124628	+	0.0719541i
$546$	11.6769	+	10.3690i	0.499727	+	0.443754i
$547$	−30.7804	−	17.7711i	−1.31608	−	0.759836i	−0.332980	−	0.942934i	$-0.608054\pi$
$547$	−30.7804	−	17.7711i	−1.31608	−	0.759836i	−0.983095	+	0.183097i	$0.941388\pi$
$548$	−31.1171	−	15.4748i	−1.32926	−	0.661051i
$549$	28.1560	+	14.2030i	1.20167	+	0.606170i
$550$	−30.7231	+	19.0337i	−1.31004	+	0.811601i
$551$	−2.26415	+	3.92163i	−0.0964562	+	0.167067i
$552$	16.9708	+	2.39910i	0.722325	+	0.102113i
$553$	7.27197	+	12.5954i	0.309236	+	0.535612i
$554$	−26.6640	−	14.3095i	−1.13284	−	0.607954i
$555$	−2.02335	−	0.481435i	−0.0858863	−	0.0204358i
$556$	−9.64445	+	6.39768i	−0.409016	+	0.271322i
$557$			1.00910i			0.0427571i	0.999771	+	0.0213786i	$0.00680553\pi$
$557$			1.00910i			0.0427571i	−0.999771	+	0.0213786i	$0.993194\pi$
$558$	25.7026	−	18.0045i	1.08808	−	0.762193i
$559$		−	53.0804i		−	2.24506i
$560$	1.12523	−	0.140493i	0.0475496	−	0.00593689i
$561$	11.8673	+	39.7676i	0.501037	+	1.67899i
$562$	−2.16641	+	4.03682i	−0.0913843	+	0.170283i
$563$	18.8215	+	32.5998i	0.793231	+	1.37392i	0.923957	+	0.382497i	$0.124936\pi$
$563$	18.8215	+	32.5998i	0.793231	+	1.37392i	−0.130726	+	0.991419i	$0.541731\pi$
$564$	29.7081	−	10.9154i	1.25094	−	0.459620i
$565$	−2.09787	+	3.63362i	−0.0882580	+	0.152867i
$566$	8.93651	+	14.4248i	0.375629	+	0.606319i
$567$	8.25126	+	3.59398i	0.346520	+	0.150933i
$568$	−1.15274	−	12.3379i	−0.0483679	−	0.517686i
$569$	−3.77832	−	2.18142i	−0.158396	−	0.0914498i	0.418707	−	0.908121i	$-0.362483\pi$
$569$	−3.77832	−	2.18142i	−0.158396	−	0.0914498i	−0.577103	+	0.816672i	$0.695817\pi$
$570$	−0.905176	−	0.185886i	−0.0379136	−	0.00778590i
$571$	−19.7051	+	11.3768i	−0.824634	+	0.476103i	−0.852012	−	0.523523i	$-0.824618\pi$
$571$	−19.7051	+	11.3768i	−0.824634	+	0.476103i	0.0273779	+	0.999625i	$0.491284\pi$
$572$	66.1074	−	4.11102i	2.76409	−	0.171890i
$573$	16.6984	−	4.98305i	0.697585	−	0.208170i
$574$	0.174662	+	5.62274i	0.00729025	+	0.234689i
$575$	17.2118			0.717781
$576$	−5.76841	−	23.2965i	−0.240350	−	0.970686i
$577$	−22.8243			−0.950190			−0.475095	−	0.879935i	$-0.657586\pi$
$577$	−22.8243			−0.950190			−0.475095	+	0.879935i	$0.657586\pi$
$578$	−0.187722	−	6.04318i	−0.00780821	−	0.251363i
$579$	−2.75536	+	11.5801i	−0.114509	+	0.481251i
$580$	1.92567	−	0.119751i	0.0799589	−	0.00497240i
$581$	0.755232	−	0.436034i	0.0313323	−	0.0180897i
$582$	3.20409	+	9.63458i	0.132814	+	0.399366i
$583$	−5.85680	−	3.38142i	−0.242564	−	0.140044i
$584$	−2.44754	−	26.1962i	−0.101280	−	1.08401i
$585$	−2.44199	+	4.84100i	−0.100964	+	0.200151i
$586$	−1.31496	−	2.12253i	−0.0543206	−	0.0876810i
$587$	−11.3398	+	19.6411i	−0.468044	+	0.810675i	−0.999333	−	0.0365151i	$-0.988374\pi$
$587$	−11.3398	+	19.6411i	−0.468044	+	0.810675i	0.531290	+	0.847190i	$0.321708\pi$
$588$	−0.591149	+	3.41329i	−0.0243786	+	0.140762i
$589$	−4.92143	−	8.52417i	−0.202784	−	0.351232i
$590$	−0.977251	+	1.82098i	−0.0402328	+	0.0749686i
$591$	−9.79348	+	10.3621i	−0.402850	+	0.426239i
$592$	−16.8124	+	2.09914i	−0.690984	+	0.0862741i
$593$		−	30.6072i		−	1.25689i	−0.777855	−	0.628444i	$-0.783692\pi$
$593$		−	30.6072i		−	1.25689i	0.777855	−	0.628444i	$-0.216308\pi$
$594$	35.4855	−	14.0690i	1.45599	−	0.577259i
$595$		−	1.30761i		−	0.0536066i
$596$	−12.1869	+	8.08424i	−0.499196	+	0.331144i
$597$	1.94263	−	2.05541i	0.0795064	−	0.0841224i
$598$	−27.7940	−	14.9160i	−1.13658	−	0.609960i
$599$	−15.6111	−	27.0393i	−0.637854	−	1.10480i	−0.985903	−	0.167319i	$-0.946489\pi$
$599$	−15.6111	−	27.0393i	−0.637854	−	1.10480i	0.348049	−	0.937476i	$-0.386844\pi$
$600$	−9.01037	−	22.3535i	−0.367847	−	0.912579i
$601$	−17.4406	+	30.2081i	−0.711418	+	1.23221i	0.252906	+	0.967491i	$0.418614\pi$
$601$	−17.4406	+	30.2081i	−0.711418	+	1.23221i	−0.964325	+	0.264722i	$0.914720\pi$
$602$	10.0094	−	6.20109i	0.407954	−	0.252738i
$603$	−7.84306	−	11.9709i	−0.319394	−	0.487494i
$604$	15.8705	+	7.89255i	0.645763	+	0.321143i
$605$	3.92434	+	2.26572i	0.159547	+	0.0921145i
$606$	21.7381	−	7.22927i	0.883052	−	0.293669i
$607$	−15.9076	+	9.18428i	−0.645671	+	0.372779i	−0.786796	−	0.617213i	$-0.788262\pi$
$607$	−15.9076	+	9.18428i	−0.645671	+	0.372779i	0.141124	+	0.989992i	$0.454928\pi$
$608$	−7.43714	+	1.16412i	−0.301616	+	0.0472111i
$609$	−1.36433	+	5.73391i	−0.0552854	+	0.232350i
$610$	−4.21235	+	0.130850i	−0.170553	+	0.00529797i
$611$	−58.2483			−2.35647
$612$	−27.4809	+	3.27218i	−1.11085	+	0.132270i
$613$	10.2078			0.412290			0.206145	−	0.978521i	$-0.433908\pi$
$613$	10.2078			0.412290			0.206145	+	0.978521i	$0.433908\pi$
$614$	13.4866	−	0.418940i	0.544274	−	0.0169070i
$615$	−1.87162	+	0.558521i	−0.0754712	+	0.0225218i
$616$	8.49817	+	11.9857i	0.342401	+	0.482916i
$617$	25.4669	−	14.7033i	1.02526	−	0.591933i	0.109636	−	0.993972i	$-0.465031\pi$
$617$	25.4669	−	14.7033i	1.02526	−	0.591933i	0.915623	+	0.402038i	$0.131698\pi$
$618$	−0.394539	+	1.92122i	−0.0158707	+	0.0772826i
$619$	8.53412	+	4.92718i	0.343015	+	0.198040i	0.661605	−	0.749853i	$-0.269876\pi$
$619$	8.53412	+	4.92718i	0.343015	+	0.198040i	−0.318589	+	0.947893i	$0.603209\pi$
$620$	−1.86742	+	3.75506i	−0.0749974	+	0.150807i
$621$	−17.8946	−	3.20436i	−0.718085	−	0.128586i
$622$	4.95063	−	3.06704i	0.198502	−	0.122977i
$623$	2.34059	−	4.05401i	0.0937736	−	0.162421i
$624$	−4.82174	+	43.9055i	−0.193024	+	1.75763i
$625$	−11.9005	−	20.6122i	−0.476019	−	0.824489i
$626$	30.8065	+	16.5327i	1.23128	+	0.660779i
$627$	−3.42374	−	11.4731i	−0.136731	−	0.458190i
$628$	5.09178	+	7.67580i	0.203184	+	0.306298i
$629$			19.5373i			0.779005i
$630$	−1.19816	+	0.105058i	−0.0477357	+	0.00418561i
$631$			10.1932i			0.405784i	0.979201	+	0.202892i	$0.0650340\pi$
$631$			10.1932i			0.405784i	−0.979201	+	0.202892i	$0.934966\pi$
$632$	−17.1650	+	37.3841i	−0.682787	+	1.48706i
$633$	−41.9243	−	9.97549i	−1.66634	−	0.396490i
$634$	9.18784	−	17.1204i	0.364896	−	0.679936i
$635$	−0.561741	−	0.972964i	−0.0222920	−	0.0386109i
$636$	2.88836	−	3.46357i	0.114531	−	0.137339i
$637$	3.18766	−	5.52119i	0.126300	−	0.218757i
$638$	13.1656	+	21.2511i	0.521231	+	0.841340i
$639$	0.740967	+	13.1224i	0.0293122	+	0.519114i
$640$	2.16497	+	2.36641i	0.0855781	+	0.0935407i
$641$	2.82315	+	1.62995i	0.111508	+	0.0643791i	0.554717	−	0.832039i	$-0.312827\pi$
$641$	2.82315	+	1.62995i	0.111508	+	0.0643791i	−0.443209	+	0.896418i	$0.646160\pi$
$642$	4.46777	−	5.03132i	0.176329	−	0.198570i
$643$	−42.4702	+	24.5202i	−1.67486	+	0.966981i	−0.710006	+	0.704196i	$0.751308\pi$
$643$	−42.4702	+	24.5202i	−1.67486	+	0.966981i	−0.964854	+	0.262786i	$0.915359\pi$
$644$	−0.434295	−	6.98370i	−0.0171136	−	0.275196i
$645$	2.97117	+	2.80813i	0.116990	+	0.110570i
$646$	0.269513	+	8.67620i	0.0106039	+	0.341361i
$647$	10.7149			0.421244			0.210622	−	0.977568i	$-0.432451\pi$
$647$	10.7149			0.421244			0.210622	+	0.977568i	$0.432451\pi$
$648$	5.20620	+	24.9178i	0.204519	+	0.978863i
$649$	−26.7772			−1.05110
$650$	1.37718	+	44.3343i	0.0540174	+	1.73893i
$651$	−9.31085	−	8.79994i	−0.364921	−	0.344897i
$652$	0.799743	+	12.8603i	0.0313203	+	0.503648i
$653$	7.26100	−	4.19214i	0.284145	−	0.164051i	−0.351154	−	0.936318i	$-0.614210\pi$
$653$	7.26100	−	4.19214i	0.284145	−	0.164051i	0.635298	+	0.772267i	$0.280877\pi$
$654$	19.2744	−	21.7056i	0.753688	−	0.848754i
$655$	−1.72175	−	0.994054i	−0.0672744	−	0.0388409i
$656$	−12.6877	+	9.60150i	−0.495370	+	0.374876i
$657$	1.57325	+	27.8619i	0.0613782	+	1.08700i
$658$	−6.80482	−	10.9839i	−0.265280	−	0.428199i
$659$	2.48938	−	4.31172i	0.0969723	−	0.167961i	−0.813458	−	0.581624i	$-0.802418\pi$
$659$	2.48938	−	4.31172i	0.0969723	−	0.167961i	0.910430	+	0.413663i	$0.135751\pi$
$660$	−3.26719	+	3.91784i	−0.127175	+	0.152502i
$661$	3.70211	+	6.41225i	0.143996	+	0.249408i	0.928998	−	0.370085i	$-0.120672\pi$
$661$	3.70211	+	6.41225i	0.143996	+	0.249408i	−0.785002	+	0.619493i	$0.787338\pi$
$662$	3.68569	−	6.86781i	0.143249	−	0.266925i
$663$	49.5497	+	11.7899i	1.92435	+	0.457880i
$664$	2.24158	+	1.02923i	0.0869903	+	0.0399417i
$665$			0.377248i			0.0146291i
$666$	17.9020	−	1.56970i	0.693688	−	0.0608247i
$667$		−	11.9054i		−	0.460977i
$668$	−17.8929	−	26.9733i	−0.692296	−	1.04363i
$669$	−3.94888	−	13.2328i	−0.152672	−	0.511611i
$670$	1.68522	+	0.904396i	0.0651059	+	0.0349399i
$671$	−27.3027	−	47.2896i	−1.05401	−	1.82559i
$672$	−8.84260	+	4.21999i	−0.341111	+	0.162790i
$673$	23.0671	−	39.9534i	0.889172	−	1.54009i	0.0483153	−	0.998832i	$-0.484615\pi$
$673$	23.0671	−	39.9534i	0.889172	−	1.54009i	0.840856	−	0.541258i	$-0.182052\pi$
$674$	−40.2611	+	24.9427i	−1.55080	+	0.960759i
$675$	8.67924	+	24.0447i	0.334064	+	0.925480i
$676$	24.6195	−	49.5055i	0.946903	−	1.90406i
$677$	−13.4541	−	7.76771i	−0.517082	−	0.298537i	0.218658	−	0.975802i	$-0.429832\pi$
$677$	−13.4541	−	7.76771i	−0.517082	−	0.298537i	−0.735740	+	0.677264i	$0.763165\pi$
$678$	7.29269	−	35.5119i	0.280074	−	1.36383i
$679$	3.58977	−	2.07255i	0.137763	−	0.0795373i
$680$	3.01705	−	2.13918i	0.115699	−	0.0820336i
$681$	−24.0363	+	7.17280i	−0.921073	+	0.274862i
$682$	−54.3121	+	1.68712i	−2.07972	+	0.0646033i
$683$	−33.9411			−1.29872			−0.649360	−	0.760481i	$-0.724963\pi$
$683$	−33.9411			−1.29872			−0.649360	+	0.760481i	$0.724963\pi$
$684$	7.92832	−	0.944032i	0.303147	−	0.0360960i
$685$	−4.92604			−0.188214
$686$	1.41353	−	0.0439092i	0.0539689	−	0.00167646i
$687$	1.67356	−	7.03353i	0.0638503	−	0.268346i
$688$	30.6827	+	12.9502i	1.16977	+	0.493722i
$689$	−7.18796	+	4.14997i	−0.273840	+	0.158101i
$690$	2.30532	−	0.766660i	0.0877619	−	0.0291862i
$691$	−4.36811	−	2.52193i	−0.166171	−	0.0959387i	0.414608	−	0.910000i	$-0.363919\pi$
$691$	−4.36811	−	2.52193i	−0.166171	−	0.0959387i	−0.580779	+	0.814061i	$0.697252\pi$
$692$	37.5331	+	18.6655i	1.42680	+	0.709557i
$693$	−8.54044	−	13.0353i	−0.324424	−	0.495172i
$694$	16.6075	−	10.2887i	0.630410	−	0.390555i
$695$	−0.820247	+	1.42071i	−0.0311137	+	0.0538906i
$696$	−15.4619	+	6.23245i	−0.586081	+	0.236240i
$697$	9.17381	+	15.8895i	0.347483	+	0.601858i
$698$	11.6334	+	6.24319i	0.440330	+	0.236308i
$699$	−27.8932	+	29.5126i	−1.05502	+	1.11627i
$700$	−8.19928	+	5.43902i	−0.309904	+	0.205576i
$701$		−	42.4401i		−	1.60294i	−0.598035	−	0.801470i	$-0.704052\pi$
$701$		−	42.4401i		−	1.60294i	0.598035	−	0.801470i	$-0.295948\pi$
$702$	6.82201	−	46.3495i	0.257480	−	1.74935i
$703$		−	5.63657i		−	0.212587i
$704$	−13.7521	+	39.2158i	−0.518301	+	1.47800i
$705$	3.08153	−	3.26044i	0.116057	−	0.122795i
$706$	21.1266	−	39.3667i	0.795110	−	1.48158i
$707$	−4.67622	−	8.09946i	−0.175867	−	0.304611i
$708$	3.04724	−	17.5947i	0.114522	−	0.661250i
$709$	14.3922	−	24.9280i	0.540509	−	0.936189i	−0.458366	−	0.888764i	$-0.651565\pi$
$709$	14.3922	−	24.9280i	0.540509	−	0.936189i	0.998875	−	0.0474254i	$-0.0151016\pi$
$710$	−0.925036	−	1.49314i	−0.0347160	−	0.0560365i
$711$	19.6510	−	38.9561i	0.736970	−	1.46097i
$712$	13.1829	−	1.23169i	0.494052	−	0.0461597i
$713$	22.4109	+	12.9389i	0.839294	+	0.484566i
$714$	3.56539	+	10.7210i	0.133431	+	0.401223i
$715$	8.13071	−	4.69427i	0.304071	−	0.175556i
$716$	−32.0554	+	1.99343i	−1.19796	+	0.0744978i
$717$	−4.62558	+	19.4401i	−0.172745	+	0.726003i
$718$	1.19885	+	38.5935i	0.0447406	+	1.44029i
$719$	28.0366			1.04559			0.522794	−	0.852459i	$-0.324890\pi$
$719$	28.0366			1.04559			0.522794	+	0.852459i	$0.324890\pi$
$720$	−2.20252	−	2.59265i	−0.0820831	−	0.0966222i
$721$	0.800701			0.0298196
$722$	0.756520	+	24.3540i	0.0281548	+	0.906362i
$723$	25.4826	−	7.60438i	0.947706	−	0.282810i
$724$	9.71828	−	0.604350i	0.361177	−	0.0224605i
$725$	−14.4981	+	8.37051i	−0.538447	+	0.310873i
$726$	−38.3532	−	7.87617i	−1.42342	−	0.292312i
$727$	24.4114	+	14.0939i	0.905368	+	0.522714i	0.878938	−	0.476936i	$-0.158253\pi$
$727$	24.4114	+	14.0939i	0.905368	+	0.522714i	0.0264300	+	0.999651i	$0.491586\pi$
$728$	17.9539	−	1.67745i	0.665417	−	0.0621705i
$729$	−4.54710	−	26.6144i	−0.168411	−	0.985717i
$730$	−1.96407	−	3.17028i	−0.0726934	−	0.117337i
$731$	19.2017	−	33.2583i	0.710201	−	1.23010i
$732$	34.1800	−	12.5584i	1.26333	−	0.464173i
$733$	8.90422	+	15.4226i	0.328885	+	0.569645i	0.982291	−	0.187363i	$-0.0599939\pi$
$733$	8.90422	+	15.4226i	0.328885	+	0.569645i	−0.653406	+	0.757008i	$0.726661\pi$
$734$	1.96660	−	3.66450i	0.0725884	−	0.135259i
$735$	0.140410	+	0.470518i	0.00517909	+	0.0173553i
$736$	15.4031	−	12.4270i	0.567764	−	0.458066i
$737$			24.7809i			0.912818i
$738$	13.8224	−	9.68255i	0.508811	−	0.356419i
$739$		−	1.70322i		−	0.0626540i	−0.999509	−	0.0313270i	$-0.990027\pi$
$739$		−	1.70322i		−	0.0626540i	0.999509	−	0.0313270i	$-0.00997332\pi$
$740$	−2.00129	+	1.32757i	−0.0735691	+	0.0488023i
$741$	−14.2952	−	3.40141i	−0.525148	−	0.124954i
$742$	−1.62229	−	0.870623i	−0.0595563	−	0.0319616i
$743$	−9.45709	−	16.3802i	−0.346947	−	0.600929i	0.638759	−	0.769407i	$-0.279448\pi$
$743$	−9.45709	−	16.3802i	−0.346947	−	0.600929i	−0.985705	+	0.168478i	$0.946115\pi$
$744$	5.07213	−	35.8793i	0.185953	−	1.31540i
$745$	−1.03648	+	1.79524i	−0.0379737	+	0.0657724i
$746$	20.0298	−	12.4090i	0.733343	−	0.454324i
$747$	−2.33584	−	1.17829i	−0.0854639	−	0.0431114i
$748$	42.9077	+	21.3383i	1.56886	+	0.780207i
$749$	−2.37895	−	1.37349i	−0.0869249	−	0.0501861i
$750$	−5.15066	−	4.57375i	−0.188076	−	0.167010i
$751$	9.95504	−	5.74755i	0.363265	−	0.209731i	−0.307247	−	0.951630i	$-0.599408\pi$
$751$	9.95504	−	5.74755i	0.363265	−	0.209731i	0.670512	+	0.741899i	$0.266075\pi$
$752$	14.2110	−	33.6700i	0.518223	−	1.22782i
$753$	5.60969	+	5.30187i	0.204428	+	0.193211i
$754$	30.6659	−	0.952591i	1.11679	−	0.0346913i
$755$	2.51241			0.0914358
$756$	9.53714	−	4.12831i	0.346862	−	0.150145i
$757$	−40.9948			−1.48998			−0.744990	−	0.667075i	$-0.767546\pi$
$757$	−40.9948			−1.48998			−0.744990	+	0.667075i	$0.767546\pi$
$758$	−2.07940	+	0.0645933i	−0.0755271	+	0.00234614i
$759$	22.8773	+	21.6219i	0.830393	+	0.784827i
$760$	−0.870428	+	0.617158i	−0.0315737	+	0.0223867i
$761$	−2.97912	+	1.72000i	−0.107993	+	0.0623499i	−0.553024	−	0.833165i	$-0.686526\pi$
$761$	−2.97912	+	1.72000i	−0.107993	+	0.0623499i	0.445031	+	0.895515i	$0.353193\pi$
$762$	7.25861	+	6.44559i	0.262952	+	0.233499i
$763$	−10.2630	−	5.92534i	−0.371545	−	0.214512i
$764$	8.95994	−	18.0169i	0.324159	−	0.651828i
$765$	−3.28128	+	2.14981i	−0.118635	+	0.0777267i
$766$	25.4211	−	15.7490i	0.918500	−	0.569033i
$767$	−16.4317	+	28.4605i	−0.593313	+	1.02765i
$768$	−24.2029	−	13.4989i	−0.873346	−	0.487101i
$769$	4.31091	+	7.46671i	0.155455	+	0.269257i	0.933225	−	0.359293i	$-0.116982\pi$
$769$	4.31091	+	7.46671i	0.155455	+	0.269257i	−0.777769	+	0.628550i	$0.783649\pi$
$770$	1.83507	+	0.984811i	0.0661313	+	0.0354901i
$771$	23.1338	+	5.50446i	0.833144	+	0.198238i
$772$	7.59797	+	11.4539i	0.273457	+	0.412234i
$773$			25.5952i			0.920595i	0.887765	+	0.460298i	$0.152257\pi$
$773$			25.5952i			0.920595i	−0.887765	+	0.460298i	$0.847743\pi$
$774$	−32.0172	−	14.9224i	−1.15084	−	0.536373i
$775$		−	36.3888i		−	1.30712i
$776$	10.6547	+	4.89212i	0.382481	+	0.175617i
$777$	−2.09790	−	7.03015i	−0.0752619	−	0.252205i
$778$	18.3833	−	34.2549i	0.659074	−	1.22810i
$779$	−2.64667	−	4.58416i	−0.0948267	−	0.164245i
$780$	2.15923	+	5.87672i	0.0773128	+	0.210420i
$781$	11.3791	−	19.7093i	0.407178	−	0.705252i
$782$	−12.0189	−	19.4002i	−0.429796	−	0.693751i
$783$	16.6316	−	6.00341i	0.594366	−	0.214544i
$784$	2.41377	+	3.18962i	0.0862062	+	0.113915i
$785$	1.13071	+	0.652816i	0.0403568	+	0.0233000i
$786$	16.8270	+	3.45557i	0.600198	+	0.123256i
$787$	−43.8437	+	25.3132i	−1.56286	+	0.902318i	−0.565894	+	0.824478i	$0.691469\pi$
$787$	−43.8437	+	25.3132i	−1.56286	+	0.902318i	−0.996966	+	0.0778398i	$0.975198\pi$
$788$	1.02184	+	16.4318i	0.0364016	+	0.585357i
$789$	24.2671	−	7.24167i	0.863931	−	0.257810i
$790$	0.181041	+	5.82811i	0.00644117	+	0.207355i
$791$	−14.8002			−0.526236
$792$	16.1049	−	41.0306i	0.572262	−	1.45796i
$793$	−67.0163			−2.37982
$794$	0.804554	+	25.9003i	0.0285525	+	0.919167i
$795$	0.147973	−	0.621893i	0.00524807	−	0.0220563i
$796$	−0.202691	−	3.25939i	−0.00718421	−	0.115526i
$797$	40.3787	−	23.3127i	1.43029	−	0.825777i	0.433145	−	0.901324i	$-0.357404\pi$
$797$	40.3787	−	23.3127i	1.43029	−	0.825777i	0.997142	+	0.0755475i	$0.0240705\pi$
$798$	−1.02862	−	3.09303i	−0.0364129	−	0.109492i
$799$	−36.4963	−	21.0712i	−1.29115	−	0.745445i
$800$	−25.9631	−	10.0203i	−0.917934	−	0.354272i
$801$	−14.0212	+	0.791717i	−0.495414	+	0.0279739i
$802$	27.8260	+	44.9151i	0.982570	+	1.58601i
$803$	24.1606	−	41.8474i	0.852609	−	1.47676i
$804$	−16.2830	−	2.82006i	−0.574258	−	0.0994560i
$805$	−0.495911	−	0.858942i	−0.0174786	−	0.0302737i
$806$	−31.5350	+	58.7614i	−1.11077	+	2.06978i
$807$	13.5534	−	14.3403i	0.477102	−	0.504802i
$808$	11.0379	−	24.0398i	0.388312	−	0.845716i
$809$			33.8386i			1.18970i	0.803837	+	0.594850i	$0.202789\pi$
$809$			33.8386i			1.18970i	−0.803837	+	0.594850i	$0.797211\pi$
$810$	2.23350	+	2.83390i	0.0784771	+	0.0995732i
$811$		−	50.8671i		−	1.78618i	−0.449874	−	0.893092i	$-0.648531\pi$
$811$		−	50.8671i		−	1.78618i	0.449874	−	0.893092i	$-0.351469\pi$
$812$	3.76216	+	5.67142i	0.132026	+	0.199028i
$813$	16.1854	−	17.1251i	0.567646	−	0.600602i
$814$	−27.4183	−	14.7144i	−0.961011	−	0.515738i
$815$	0.913206	+	1.58172i	0.0319882	+	0.0554052i
$816$	−18.9038	+	25.7654i	−0.661767	+	0.901970i
$817$	−5.53975	+	9.59512i	−0.193811	+	0.335691i
$818$	−16.2370	+	10.0592i	−0.567713	+	0.351712i
$819$	−19.0955	+	1.07824i	−0.667252	+	0.0376769i
$820$	−1.00427	+	2.01941i	−0.0350706	+	0.0705208i
$821$	25.7593	+	14.8722i	0.899007	+	0.519042i	0.876878	−	0.480713i	$-0.159622\pi$
$821$	25.7593	+	14.8722i	0.899007	+	0.519042i	0.0221288	+	0.999755i	$0.492956\pi$
$822$	40.3883	−	13.4316i	1.40870	−	0.468480i
$823$	−30.0725	+	17.3624i	−1.04826	+	0.605215i	−0.922162	−	0.386803i	$-0.873579\pi$
$823$	−30.0725	+	17.3624i	−1.04826	+	0.605215i	−0.126100	+	0.992018i	$0.540246\pi$
$824$	1.30990	+	1.84746i	0.0456327	+	0.0643595i
$825$	10.2461	−	43.0617i	0.356724	−	1.49922i
$826$	−7.28643	+	0.226342i	−0.253527	+	0.00787545i
$827$	2.44585			0.0850504			0.0425252	−	0.999095i	$-0.486460\pi$
$827$	2.44585			0.0850504			0.0425252	+	0.999095i	$0.486460\pi$
$828$	−16.8107	+	12.5716i	−0.584213	+	0.436893i
$829$	49.9650			1.73536			0.867679	−	0.497126i	$-0.165611\pi$
$829$	49.9650			1.73536			0.867679	+	0.497126i	$0.165611\pi$
$830$	0.349458	−	0.0108554i	0.0121299	−	0.000376796i
$831$	35.5144	−	10.5981i	1.23198	−	0.367642i
$832$	33.2421	+	38.6810i	1.15246	+	1.34102i
$833$	3.99455	−	2.30625i	0.138403	−	0.0799070i
$834$	2.85137	−	13.8848i	0.0987349	−	0.480792i
$835$	−3.97340	−	2.29404i	−0.137505	−	0.0793887i
$836$	−12.3790	−	6.15617i	−0.428136	−	0.212916i
$837$	−6.77458	+	37.8323i	−0.234164	+	1.30768i
$838$	−14.3815	+	8.90970i	−0.496801	+	0.307781i
$839$	−0.959068	+	1.66115i	−0.0331107	+	0.0573494i	−0.882106	−	0.471051i	$-0.843875\pi$
$839$	−0.959068	+	1.66115i	−0.0331107	+	0.0573494i	0.848995	+	0.528401i	$0.177208\pi$
$840$	−0.855928	+	1.09371i	−0.0295323	+	0.0377366i
$841$	−8.71014	−	15.0864i	−0.300350	−	0.520221i
$842$	21.1164	+	11.3324i	0.727721	+	0.390540i
$843$	−1.60450	−	5.37674i	−0.0552620	−	0.185185i
$844$	−41.4674	+	27.5076i	−1.42737	+	0.946850i
$845$		−	7.83703i		−	0.269602i
$846$	−16.3752	+	35.1344i	−0.562991	+	1.20795i
$847$			15.9844i			0.549230i
$848$	−0.645188	−	5.16743i	−0.0221559	−	0.177450i
$849$	−20.2178	−	4.81064i	−0.693874	−	0.165101i
$850$	−15.1749	+	28.2765i	−0.520496	+	0.969876i
$851$	7.40955	+	12.8337i	0.253996	+	0.439934i
$852$	11.6556	+	9.71989i	0.399313	+	0.332998i
$853$	−7.25573	+	12.5673i	−0.248431	+	0.430296i	−0.963091	−	0.269177i	$-0.913248\pi$
$853$	−7.25573	+	12.5673i	−0.248431	+	0.430296i	0.714659	+	0.699473i	$0.246582\pi$
$854$	−7.82914	−	12.6373i	−0.267908	−	0.432440i
$855$	0.946659	−	0.620227i	0.0323750	−	0.0212113i
$856$	−0.722774	−	7.73592i	−0.0247039	−	0.264408i
$857$	−2.41215	−	1.39265i	−0.0823974	−	0.0475722i	0.458235	−	0.888831i	$-0.348482\pi$
$857$	−2.41215	−	1.39265i	−0.0823974	−	0.0475722i	−0.540633	+	0.841259i	$0.681815\pi$
$858$	−53.8635	+	60.6576i	−1.83887	+	2.07082i
$859$	11.8920	−	6.86584i	0.405749	−	0.234259i	−0.283212	−	0.959057i	$-0.591400\pi$
$859$	11.8920	−	6.86584i	0.405749	−	0.234259i	0.688962	+	0.724798i	$0.258067\pi$
$860$	4.71156	−	0.292998i	0.160663	−	0.00999114i
$861$	−5.00723	−	4.73247i	−0.170646	−	0.161282i
$862$	−0.409378	−	13.1788i	−0.0139435	−	0.448871i
$863$	44.6593			1.52022			0.760111	−	0.649793i	$-0.225145\pi$
$863$	44.6593			1.52022			0.760111	+	0.649793i	$0.225145\pi$
$864$	25.1276	+	15.2514i	0.854857	+	0.518864i
$865$	5.94173			0.202025
$866$	0.156559	+	5.03997i	0.00532009	+	0.171265i
$867$	5.38164	+	5.08634i	0.182770	+	0.172741i
$868$	−14.7648	+	0.918176i	−0.501149	+	0.0311649i
$869$	−65.4288	+	37.7754i	−2.21952	+	1.28144i
$870$	−1.56901	+	1.76692i	−0.0531944	+	0.0599041i
$871$	26.3387	+	15.2066i	0.892452	+	0.515258i
$872$	−3.11811	−	33.3735i	−0.105593	−	1.13017i
$873$	−11.1027	−	5.60064i	−0.375769	−	0.189553i
$874$	3.46749	+	5.59702i	0.117290	+	0.189322i
$875$	−1.40607	+	2.43538i	−0.0475337	+	0.0823308i
$876$	24.7475	+	20.6376i	0.836141	+	0.697280i
$877$	22.5032	+	38.9767i	0.759880	+	1.31615i	0.942912	+	0.333043i	$0.108075\pi$
$877$	22.5032	+	38.9767i	0.759880	+	1.31615i	−0.183032	+	0.983107i	$0.558591\pi$
$878$	−21.9226	+	40.8500i	−0.739854	+	1.37862i
$879$	2.97495	+	0.707861i	0.100343	+	0.0238755i
$880$	0.729809	+	5.84517i	0.0246019	+	0.197041i
$881$		−	31.1837i		−	1.05061i	−0.850915	−	0.525304i	$-0.823952\pi$
$881$		−	31.1837i		−	1.05061i	0.850915	−	0.525304i	$-0.176048\pi$
$882$	−2.43415	−	3.47490i	−0.0819621	−	0.117006i
$883$		−	2.34237i		−	0.0788270i	−0.999223	−	0.0394135i	$-0.987451\pi$
$883$		−	2.34237i		−	0.0788270i	0.999223	−	0.0394135i	$-0.0125490\pi$
$884$	49.0097	−	32.5108i	1.64837	−	1.09346i
$885$	−0.723781	−	2.42541i	−0.0243296	−	0.0815294i
$886$	33.4969	+	17.9765i	1.12535	+	0.603933i
$887$	5.70759	+	9.88583i	0.191642	+	0.331934i	0.945795	−	0.324766i	$-0.105285\pi$
$887$	5.70759	+	9.88583i	0.191642	+	0.331934i	−0.754153	+	0.656699i	$0.771952\pi$
$888$	12.7887	−	16.3415i	0.429160	−	0.548384i
$889$	1.98151	−	3.43207i	0.0664577	−	0.115108i
$890$	1.59541	−	0.988393i	0.0534781	−	0.0331310i
$891$	−18.6695	+	42.8624i	−0.625450	+	1.43594i
$892$	−14.2777	−	7.10042i	−0.478053	−	0.237739i
$893$	10.5293	+	6.07909i	0.352349	+	0.203429i
$894$	3.60305	−	17.5451i	0.120504	−	0.586797i
$895$	−3.94257	+	2.27624i	−0.131786	+	0.0760864i
$896$	−3.41064	+	10.7874i	−0.113941	+	0.360381i
$897$	37.0196	−	11.0472i	1.23605	−	0.368856i
$898$	1.48053	−	0.0459904i	0.0494058	−	0.00153472i
$899$	−25.1700			−0.839467
$900$	27.1289	+	11.6329i	0.904296	+	0.387763i
$901$	−6.00497			−0.200054
$902$	−29.2082	+	0.907307i	−0.972525	+	0.0302100i
$903$	−3.33813	+	14.0293i	−0.111086	+	0.466865i
$904$	−24.2124	−	34.1487i	−0.805292	−	1.13577i
$905$	1.19528	−	0.690093i	0.0397323	−	0.0229395i
$906$	−20.5990	+	6.85045i	−0.684357	+	0.227591i
$907$	−32.9493	−	19.0233i	−1.09406	−	0.631659i	−0.159409	−	0.987213i	$-0.550959\pi$
$907$	−32.9493	−	19.0233i	−1.09406	−	0.631659i	−0.934656	+	0.355554i	$0.884292\pi$
$908$	−12.8973	+	25.9342i	−0.428012	+	0.860657i
$909$	−12.6365	+	25.0506i	−0.419127	+	0.830876i
$910$	2.17279	−	1.34610i	0.0720274	−	0.0446227i
$911$	−1.90901	+	3.30650i	−0.0632483	+	0.109549i	−0.895916	−	0.444224i	$-0.853479\pi$
$911$	−1.90901	+	3.30650i	−0.0632483	+	0.109549i	0.832667	+	0.553774i	$0.186813\pi$
$912$	5.45381	−	7.43339i	0.180594	−	0.246144i
$913$	2.26504	+	3.92317i	0.0749619	+	0.129838i
$914$	−52.7020	−	28.2832i	−1.74323	−	0.935524i
$915$	3.54539	−	3.75123i	0.117207	−	0.124012i
$916$	−4.61487	−	6.95687i	−0.152480	−	0.229862i
$917$		−	7.01294i		−	0.231588i
$918$	21.0412	−	26.5731i	0.694464	−	0.877043i
$919$			30.5003i			1.00611i	0.864254	+	0.503056i	$0.167791\pi$
$919$			30.5003i			1.00611i	−0.864254	+	0.503056i	$0.832209\pi$
$920$	1.17056	−	2.54940i	0.0385923	−	0.0840513i
$921$	−11.3512	+	12.0102i	−0.374034	+	0.395750i
$922$	13.1100	−	24.4288i	0.431754	−	0.804518i
$923$	−13.9655	−	24.1889i	−0.459679	−	0.796187i
$924$	−17.7308	−	3.07081i	−0.583302	−	0.101022i
$925$	10.4191	−	18.0464i	0.342578	−	0.593363i
$926$	−6.10110	−	9.84804i	−0.200495	−	0.323627i
$927$	−1.31642	−	2.00926i	−0.0432369	−	0.0659928i
$928$	−6.93103	+	17.9586i	−0.227522	+	0.589520i
$929$	8.88101	+	5.12745i	0.291376	+	0.168226i	0.638562	−	0.769570i	$-0.279529\pi$
$929$	8.88101	+	5.12745i	0.291376	+	0.168226i	−0.347186	+	0.937796i	$0.612863\pi$
$930$	−1.62085	−	4.87385i	−0.0531499	−	0.159820i
$931$	−1.15244	+	0.665361i	−0.0377696	+	0.0218063i
$932$	2.91034	+	46.7999i	0.0953314	+	1.53298i
$933$	−1.65103	+	6.93883i	−0.0540522	+	0.227167i
$934$	−1.43109	−	46.0698i	−0.0468266	−	1.50745i
$935$	6.79256			0.222140
$936$	−33.7271	−	42.2954i	−1.10241	−	1.38247i
$937$	18.1122			0.591700			0.295850	−	0.955234i	$-0.404397\pi$
$937$	18.1122			0.591700			0.295850	+	0.955234i	$0.404397\pi$
$938$	0.209468	+	6.74322i	0.00683937	+	0.220174i
$939$	−41.0320	+	12.2446i	−1.33903	+	0.399587i
$940$	−0.321524	−	5.17027i	−0.0104869	−	0.168636i
$941$	−17.9634	+	10.3712i	−0.585589	+	0.338090i	−0.763351	−	0.645983i	$-0.776448\pi$
$941$	−17.9634	+	10.3712i	−0.585589	+	0.338090i	0.177762	+	0.984073i	$0.443114\pi$
$942$	−11.0506	−	2.26934i	−0.360049	−	0.0739392i
$943$	12.0522	+	6.95834i	0.392474	+	0.226595i
$944$	−12.4425	−	16.4418i	−0.404968	−	0.535134i
$945$	0.949863	−	1.12591i	0.0308991	−	0.0366259i
$946$	32.2125	+	51.9955i	1.04732	+	1.69052i
$947$	−4.30839	+	7.46235i	−0.140004	+	0.242494i	−0.927498	−	0.373829i	$-0.878045\pi$
$947$	−4.30839	+	7.46235i	−0.140004	+	0.242494i	0.787494	+	0.616322i	$0.211378\pi$
$948$	−17.3756	−	47.2907i	−0.564332	−	1.53593i
$949$	−29.6519	−	51.3587i	−0.962543	−	1.66717i
$950$	4.37801	−	8.15785i	0.142041	−	0.264676i
$951$	6.80478	+	22.8031i	0.220660	+	0.739440i
$952$	11.8561	+	5.44375i	0.384259	+	0.176433i
$953$			17.7222i			0.574080i	0.957919	+	0.287040i	$0.0926712\pi$
$953$			17.7222i			0.574080i	−0.957919	+	0.287040i	$0.907329\pi$
$954$	0.482461	+	5.50233i	0.0156203	+	0.178144i
$955$		−	2.85219i		−	0.0922945i
$956$	12.7551	+	19.2282i	0.412530	+	0.621885i
$957$	−29.7857	−	7.08721i	−0.962834	−	0.229097i
$958$	12.0228	+	6.45220i	0.388440	+	0.208461i
$959$	−8.68816	−	15.0483i	−0.280555	−	0.485936i
$960$	−3.92378	−	0.185637i	−0.126640	−	0.00599141i
$961$	11.8552	−	20.5337i	0.382425	−	0.662379i
$962$	−32.4643	+	20.1125i	−1.04669	+	0.648452i
$963$	0.464590	+	8.22781i	0.0149712	+	0.265137i
$964$	13.6733	−	27.4947i	0.440388	−	0.885544i
$965$	1.68725	+	0.974135i	0.0543145	+	0.0313585i
$966$	6.40797	+	5.69024i	0.206173	+	0.183080i
$967$	1.58259	−	0.913707i	0.0508925	−	0.0293828i	−0.474338	−	0.880343i	$-0.657312\pi$
$967$	1.58259	−	0.913707i	0.0508925	−	0.0293828i	0.525230	+	0.850960i	$0.323979\pi$
$968$	−36.8809	+	26.1496i	−1.18540	+	0.840480i
$969$	−7.72643	−	7.30246i	−0.248209	−	0.234589i
$970$	1.66104	−	0.0515978i	0.0533329	−	0.00165671i
$971$	18.1975			0.583987			0.291994	−	0.956420i	$-0.405681\pi$
$971$	18.1975			0.583987			0.291994	+	0.956420i	$0.405681\pi$
$972$	−26.0394	−	17.1450i	−0.835213	−	0.549927i
$973$	−5.78675			−0.185515
$974$	−6.46738	+	0.200899i	−0.207228	+	0.00643723i
$975$	−39.4811	−	37.3147i	−1.26441	−	1.19503i
$976$	16.3502	−	38.7382i	0.523357	−	1.23998i
$977$	−27.3325	+	15.7804i	−0.874443	+	0.504860i	−0.868822	−	0.495124i	$-0.835123\pi$
$977$	−27.3325	+	15.7804i	−0.874443	+	0.504860i	−0.00562116	+	0.999984i	$0.501789\pi$
$978$	−11.8001	−	10.4784i	−0.377326	−	0.335063i
$979$	21.0592	+	12.1585i	0.673054	+	0.388588i
$980$	0.507670	+	0.252469i	0.0162169	+	0.00806481i
$981$	2.00428	+	35.4955i	0.0639918	+	1.13328i
$982$	3.12966	−	1.93890i	0.0998716	−	0.0618729i
$983$	−0.804596	+	1.39360i	−0.0256626	+	0.0444490i	−0.878572	−	0.477611i	$-0.841503\pi$
$983$	−0.804596	+	1.39360i	−0.0256626	+	0.0444490i	0.852909	+	0.522060i	$0.174836\pi$
$984$	2.72771	−	19.2953i	0.0869561	−	0.615111i
$985$	1.16681	+	2.02098i	0.0371778	+	0.0643939i
$986$	19.5588	+	10.4965i	0.622879	+	0.334276i
$987$	15.3951	+	3.66312i	0.490033	+	0.116599i
$988$	−14.1394	+	9.37944i	−0.449835	+	0.298400i
$989$		−	29.1290i		−	0.926250i
$990$	−0.545739	−	6.22400i	−0.0173447	−	0.197812i
$991$		−	4.17469i		−	0.132613i	−0.997799	−	0.0663067i	$-0.978878\pi$
$991$		−	4.17469i		−	0.132613i	0.997799	−	0.0663067i	$-0.0211216\pi$
$992$	−26.2729	−	32.5648i	−0.834165	−	1.03393i
$993$	2.72973	+	9.14742i	0.0866254	+	0.290285i
$994$	2.92981	−	5.45933i	0.0929281	−	0.173159i
$995$	−0.231448	−	0.400880i	−0.00733740	−	0.0127088i
$996$	−2.83559	+	1.04185i	−0.0898490	+	0.0330124i
$997$	−9.82251	+	17.0131i	−0.311082	+	0.538810i	−0.978597	−	0.205786i	$-0.934025\pi$
$997$	−9.82251	+	17.0131i	−0.311082	+	0.538810i	0.667515	+	0.744597i	$0.267358\pi$
$998$	27.9308	+	45.0843i	0.884135	+	1.42712i
$999$	−14.1922	+	16.8226i	−0.449021	+	0.532243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.19	✓	72
3.2	odd	2		756.2.ba.a.575.18		72
4.3	odd	2	inner	252.2.ba.a.155.31	yes	72
9.4	even	3		756.2.ba.a.71.6		72
9.5	odd	6	inner	252.2.ba.a.239.31	yes	72
12.11	even	2		756.2.ba.a.575.6		72
36.23	even	6	inner	252.2.ba.a.239.19	yes	72
36.31	odd	6		756.2.ba.a.71.18		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.19	✓	72	1.1	even	1	trivial
252.2.ba.a.155.31	yes	72	4.3	odd	2	inner
252.2.ba.a.239.19	yes	72	36.23	even	6	inner
252.2.ba.a.239.31	yes	72	9.5	odd	6	inner
756.2.ba.a.71.6		72	9.4	even	3
756.2.ba.a.71.18		72	36.31	odd	6
756.2.ba.a.575.6		72	12.11	even	2
756.2.ba.a.575.18		72	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0439092 + 1.41353i) q^{2} +(-1.25879 - 1.18972i) q^{3} +(-1.99614 + 0.124134i) q^{4} +(-0.245511 + 0.141746i) q^{5} +(1.62644 - 1.83159i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.263117 - 2.81616i) q^{8} +(0.169128 + 2.99523i) q^{9} +O(q^{10})\)	\(q+(0.0439092 + 1.41353i) q^{2} +(-1.25879 - 1.18972i) q^{3} +(-1.99614 + 0.124134i) q^{4} +(-0.245511 + 0.141746i) q^{5} +(1.62644 - 1.83159i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.263117 - 2.81616i) q^{8} +(0.169128 + 2.99523i) q^{9} +(-0.211142 - 0.340813i) q^{10} +(2.59732 - 4.49870i) q^{11} +(2.66042 + 2.21859i) q^{12} +(-3.18766 - 5.52119i) q^{13} +(0.668739 - 1.24611i) q^{14} +(0.477686 + 0.113661i) q^{15} +(3.96918 - 0.495579i) q^{16} -4.61251i q^{17} +(-4.22642 + 0.370586i) q^{18} +1.33072i q^{19} +(0.472479 - 0.313421i) q^{20} +(0.495288 + 1.65973i) q^{21} +(6.47310 + 3.47387i) q^{22} +(-1.74930 - 3.02987i) q^{23} +(-3.01924 + 3.85801i) q^{24} +(-2.45982 + 4.26053i) q^{25} +(7.66440 - 4.74829i) q^{26} +(3.35059 - 3.97159i) q^{27} +(1.79078 + 0.890569i) q^{28} +(2.94700 + 1.70145i) q^{29} +(-0.139688 + 0.680214i) q^{30} +(-6.40568 + 3.69832i) q^{31} +(0.874801 + 5.58880i) q^{32} +(-8.62169 + 2.57285i) q^{33} +(6.51993 - 0.202532i) q^{34} +0.283491 q^{35} +(-0.709414 - 5.95791i) q^{36} -4.23573 q^{37} +(-1.88102 + 0.0584309i) q^{38} +(-2.55606 + 10.7425i) q^{39} +(0.463777 + 0.654103i) q^{40} +(-3.44487 + 1.98890i) q^{41} +(-2.32433 + 0.772982i) q^{42} +(7.21047 + 4.16297i) q^{43} +(-4.62619 + 9.30247i) q^{44} +(-0.466084 - 0.711388i) q^{45} +(4.20601 - 2.60573i) q^{46} +(4.56827 - 7.91247i) q^{47} +(-5.58599 - 4.09839i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.13040 - 3.28995i) q^{50} +(-5.48760 + 5.80620i) q^{51} +(7.04839 + 10.6254i) q^{52} -1.30189i q^{53} +(5.76109 + 4.56177i) q^{54} +1.47264i q^{55} +(-1.18022 + 2.57043i) q^{56} +(1.58319 - 1.67510i) q^{57} +(-2.27565 + 4.24038i) q^{58} +(-2.57739 - 4.46416i) q^{59} +(-0.967638 - 0.167586i) q^{60} +(5.25592 - 9.10352i) q^{61} +(-5.50896 - 8.89224i) q^{62} +(1.35115 - 2.67851i) q^{63} +(-7.86154 + 1.48196i) q^{64} +(1.56521 + 0.903674i) q^{65} +(-4.01537 - 12.0741i) q^{66} +(-4.13135 + 2.38524i) q^{67} +(0.572570 + 9.20723i) q^{68} +(-1.40270 + 5.89516i) q^{69} +(0.0124479 + 0.400724i) q^{70} +4.38110 q^{71} +(8.39055 - 1.26439i) q^{72} +9.30211 q^{73} +(-0.185988 - 5.98734i) q^{74} +(8.16524 - 2.43663i) q^{75} +(-0.165188 - 2.65631i) q^{76} +(-4.49870 + 2.59732i) q^{77} +(-15.2970 - 3.14138i) q^{78} +(-12.5954 - 7.27197i) q^{79} +(-0.904231 + 0.684285i) q^{80} +(-8.94279 + 1.01315i) q^{81} +(-2.96263 - 4.78210i) q^{82} +(-0.436034 + 0.755232i) q^{83} +(-1.19469 - 3.25157i) q^{84} +(0.653803 + 1.13242i) q^{85} +(-5.56788 + 10.3750i) q^{86} +(-1.68541 - 5.64788i) q^{87} +(-13.3525 - 6.13080i) q^{88} +4.68117i q^{89} +(0.985104 - 0.690060i) q^{90} +6.37532i q^{91} +(3.86796 + 5.83091i) q^{92} +(12.4634 + 2.96555i) q^{93} +(11.3851 + 6.10996i) q^{94} +(-0.188624 - 0.326706i) q^{95} +(5.54792 - 8.07592i) q^{96} +(-2.07255 + 3.58977i) q^{97} +(-1.20220 + 0.744792i) q^{98} +(13.9139 + 7.01873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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