LMFDB - Embedded newform 945.2.cs.b.104.123

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.123
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.123

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27225 + 0.827033i) q^{2} +(-1.72657 + 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(1.87617 - 1.21654i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(1.56879 + 2.13047i) q^{7} +(2.23324 + 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +O(q^{10})$	\(q+(2.27225 + 0.827033i) q^{2} +(-1.72657 + 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(1.87617 - 1.21654i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(1.56879 + 2.13047i) q^{7} +(2.23324 + 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +(5.26926 - 1.21264i) q^{10} +(-2.20675 + 0.389110i) q^{11} +(-5.42865 - 3.86404i) q^{12} +(-2.64817 + 0.963854i) q^{13} +(1.80272 + 6.13841i) q^{14} +(-3.07193 + 2.35866i) q^{15} +(0.539367 + 3.05890i) q^{16} +(6.27053 + 3.62029i) q^{17} +(7.12372 + 1.36994i) q^{18} +(3.30565 - 1.90852i) q^{19} +(8.53757 + 1.05431i) q^{20} +(-3.00183 - 3.46251i) q^{21} +(-5.33610 - 0.940899i) q^{22} +(-1.53289 - 1.28624i) q^{23} +(-4.38819 - 6.37121i) q^{24} +(2.04004 - 4.56489i) q^{25} -6.81445 q^{26} +(-5.04892 + 1.22816i) q^{27} +(-0.645068 + 10.1581i) q^{28} +(0.483105 - 1.32732i) q^{29} +(-8.93089 + 2.81888i) q^{30} +(-4.71738 + 5.62196i) q^{31} +(0.246961 - 1.40059i) q^{32} +(3.75657 - 0.975522i) q^{33} +(11.2541 + 13.4121i) q^{34} +(5.53513 + 2.08862i) q^{35} +(9.90474 + 5.92445i) q^{36} +(8.73664 + 5.04410i) q^{37} +(9.08968 - 1.60276i) q^{38} +(4.43961 - 2.02861i) q^{39} +(8.89565 + 4.54036i) q^{40} +(-4.34880 + 1.58283i) q^{41} +(-3.95731 - 10.3503i) q^{42} +(-2.57232 + 0.453569i) q^{43} +(-7.46566 - 4.31030i) q^{44} +(4.97931 - 4.49516i) q^{45} +(-2.41934 - 4.19042i) q^{46} +(-1.83180 - 2.18305i) q^{47} +(-1.35223 - 5.20719i) q^{48} +(-2.07779 + 6.68452i) q^{49} +(8.41080 - 8.68541i) q^{50} +(-11.3248 - 5.38774i) q^{51} +(-10.1878 - 3.70806i) q^{52} -0.692478 q^{53} +(-12.4882 - 1.38493i) q^{54} +(-3.66687 + 3.41465i) q^{55} +(-4.73736 + 10.8261i) q^{56} +(-5.44480 + 3.75012i) q^{57} +(2.19548 - 2.61647i) q^{58} +(1.80747 - 10.2507i) q^{59} +(-14.8858 - 0.645402i) q^{60} +(0.0628143 + 0.0748592i) q^{61} +(-15.3686 + 8.87309i) q^{62} +(5.65940 + 5.56518i) q^{63} +(4.82558 - 8.35815i) q^{64} +(-3.79584 + 5.02997i) q^{65} +(9.34267 + 0.890173i) q^{66} +(-0.870116 - 2.39062i) q^{67} +(9.52710 + 26.1755i) q^{68} +(2.82366 + 2.00984i) q^{69} +(10.8499 + 9.32361i) q^{70} +(-10.4867 - 6.05448i) q^{71} +(8.45335 + 10.3965i) q^{72} +(0.469002 + 0.812335i) q^{73} +(15.6802 + 18.6870i) q^{74} +(-2.89406 + 8.16238i) q^{75} +(14.4615 + 2.54995i) q^{76} +(-4.29092 - 4.09098i) q^{77} +(11.7656 - 0.937811i) q^{78} +(-14.0479 - 5.11302i) q^{79} +(4.73324 + 5.08286i) q^{80} +(8.54832 - 2.81535i) q^{81} -11.1906 q^{82} +(-0.0128448 + 0.0352908i) q^{83} +(-0.284204 - 17.6274i) q^{84} +(16.1688 - 0.836089i) q^{85} +(-6.22007 - 1.09677i) q^{86} +(-0.651450 + 2.35820i) q^{87} +(-6.43332 - 7.66694i) q^{88} +(-0.138079 - 0.239159i) q^{89} +(15.0319 - 6.09608i) q^{90} +(-6.20788 - 4.12975i) q^{91} +(-1.33679 - 7.58129i) q^{92} +(7.37122 - 10.3559i) q^{93} +(-2.35685 - 6.47540i) q^{94} +(3.88017 - 7.60217i) q^{95} +(-0.233647 + 2.45220i) q^{96} +(-1.49351 - 8.47013i) q^{97} +(-10.2496 + 13.4705i) q^{98} +(-6.35175 + 2.20129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	2.27225	+	0.827033i	1.60673	+	0.584800i	0.980789	−	0.195073i	$-0.0624944\pi$
$2$	2.27225	+	0.827033i	1.60673	+	0.584800i	0.625937	+	0.779873i	$0.284717\pi$
$3$	−1.72657	+	0.137621i	−0.996838	+	0.0794555i
$3$	−1.72657	+	0.137621i	−0.996838	+	0.0794555i
$4$	2.94706	+	2.47288i	1.47353	+	1.23644i
$5$	1.87617	−	1.21654i	0.839049	−	0.544055i
$5$	1.87617	−	1.21654i	0.839049	−	0.544055i
$6$	−4.03703	−	1.11522i	−1.64811	−	0.455288i
$7$	1.56879	+	2.13047i	0.592947	+	0.805241i
$7$	1.56879	+	2.13047i	0.592947	+	0.805241i
$8$	2.23324	+	3.86809i	0.789571	+	1.36758i
$9$	2.96212	−	0.475226i	0.987374	−	0.158409i
$10$	5.26926	−	1.21264i	1.66629	−	0.383471i
$11$	−2.20675	+	0.389110i	−0.665360	+	0.117321i	−0.496120	−	0.868254i	$-0.665242\pi$
$11$	−2.20675	+	0.389110i	−0.665360	+	0.117321i	−0.169240	+	0.985575i	$0.554131\pi$
$12$	−5.42865	−	3.86404i	−1.56712	−	1.11545i
$13$	−2.64817	+	0.963854i	−0.734469	+	0.267325i	−0.682055	−	0.731300i	$-0.738914\pi$
$13$	−2.64817	+	0.963854i	−0.734469	+	0.267325i	−0.0524139	+	0.998625i	$0.516692\pi$
$14$	1.80272	+	6.13841i	0.481798	+	1.64056i
$15$	−3.07193	+	2.35866i	−0.793168	+	0.609002i
$16$	0.539367	+	3.05890i	0.134842	+	0.764725i
$17$	6.27053	+	3.62029i	1.52083	+	0.878049i	0.999698	+	0.0245706i	$0.00782185\pi$
$17$	6.27053	+	3.62029i	1.52083	+	0.878049i	0.521128	+	0.853479i	$0.325511\pi$
$18$	7.12372	+	1.36994i	1.67908	+	0.322897i
$19$	3.30565	−	1.90852i	0.758368	−	0.437844i	−0.0703418	−	0.997523i	$-0.522409\pi$
$19$	3.30565	−	1.90852i	0.758368	−	0.437844i	0.828709	+	0.559679i	$0.189076\pi$
$20$	8.53757	+	1.05431i	1.90906	+	0.235752i
$21$	−3.00183	−	3.46251i	−0.655053	−	0.755583i
$22$	−5.33610	−	0.940899i	−1.13766	−	0.200600i
$23$	−1.53289	−	1.28624i	−0.319629	−	0.268200i	0.468829	−	0.883289i	$-0.344676\pi$
$23$	−1.53289	−	1.28624i	−0.319629	−	0.268200i	−0.788458	+	0.615088i	$0.789120\pi$
$24$	−4.38819	−	6.37121i	−0.895736	−	1.30052i
$25$	2.04004	−	4.56489i	0.408008	−	0.912978i
$26$	−6.81445			−1.33642
$27$	−5.04892	+	1.22816i	−0.971666	+	0.236360i
$28$	−0.645068	+	10.1581i	−0.121906	+	1.91969i
$29$	0.483105	−	1.32732i	0.0897104	−	0.246477i	−0.886721	−	0.462305i	$-0.847023\pi$
$29$	0.483105	−	1.32732i	0.0897104	−	0.246477i	0.976432	+	0.215827i	$0.0692448\pi$
$30$	−8.93089	+	2.81888i	−1.63055	+	0.514654i
$31$	−4.71738	+	5.62196i	−0.847267	+	1.00973i	0.152503	+	0.988303i	$0.451267\pi$
$31$	−4.71738	+	5.62196i	−0.847267	+	1.00973i	−0.999770	+	0.0214306i	$0.993178\pi$
$32$	0.246961	−	1.40059i	0.0436570	−	0.247591i
$33$	3.75657	−	0.975522i	0.653935	−	0.169817i
$34$	11.2541	+	13.4121i	1.93007	+	2.30016i
$35$	5.53513	+	2.08862i	0.935608	+	0.353041i
$36$	9.90474	+	5.92445i	1.65079	+	0.987408i
$37$	8.73664	+	5.04410i	1.43630	+	0.829245i	0.997590	−	0.0693855i	$-0.0221038\pi$
$37$	8.73664	+	5.04410i	1.43630	+	0.829245i	0.438705	+	0.898631i	$0.355437\pi$
$38$	9.08968	−	1.60276i	1.47454	−	0.260001i
$39$	4.43961	−	2.02861i	0.710907	−	0.324837i
$40$	8.89565	+	4.54036i	1.40653	+	0.717894i
$41$	−4.34880	+	1.58283i	−0.679168	+	0.247197i	−0.658490	−	0.752589i	$-0.728805\pi$
$41$	−4.34880	+	1.58283i	−0.679168	+	0.247197i	−0.0206777	+	0.999786i	$0.506582\pi$
$42$	−3.95731	−	10.3503i	−0.610626	−	1.59709i
$43$	−2.57232	+	0.453569i	−0.392274	+	0.0691686i	−0.366307	−	0.930494i	$-0.619378\pi$
$43$	−2.57232	+	0.453569i	−0.392274	+	0.0691686i	−0.0259678	+	0.999663i	$0.508267\pi$
$44$	−7.46566	−	4.31030i	−1.12549	−	0.649802i
$45$	4.97931	−	4.49516i	0.742272	−	0.670098i
$46$	−2.41934	−	4.19042i	−0.356712	−	0.617844i
$47$	−1.83180	−	2.18305i	−0.267195	−	0.318431i	0.615719	−	0.787966i	$-0.288866\pi$
$47$	−1.83180	−	2.18305i	−0.267195	−	0.318431i	−0.882914	+	0.469535i	$0.844421\pi$
$48$	−1.35223	−	5.20719i	−0.195177	−	0.751594i
$49$	−2.07779	+	6.68452i	−0.296828	+	0.954931i
$50$	8.41080	−	8.68541i	1.18947	−	1.22830i
$51$	−11.3248	−	5.38774i	−1.58578	−	0.754435i
$52$	−10.1878	−	3.70806i	−1.41280	−	0.514216i
$53$	−0.692478			−0.0951192			−0.0475596	−	0.998868i	$-0.515144\pi$
$53$	−0.692478			−0.0951192			−0.0475596	+	0.998868i	$0.515144\pi$
$54$	−12.4882	−	1.38493i	−1.69942	−	0.188465i
$55$	−3.66687	+	3.41465i	−0.494441	+	0.460431i
$56$	−4.73736	+	10.8261i	−0.633056	+	1.44670i
$57$	−5.44480	+	3.75012i	−0.721181	+	0.496716i
$58$	2.19548	−	2.61647i	0.288280	−	0.343559i
$59$	1.80747	−	10.2507i	0.235313	−	1.33453i	−0.606640	−	0.794977i	$-0.707483\pi$
$59$	1.80747	−	10.2507i	0.235313	−	1.33453i	0.841953	−	0.539551i	$-0.181406\pi$
$60$	−14.8858	−	0.645402i	−1.92175	−	0.0833211i
$61$	0.0628143	+	0.0748592i	0.00804255	+	0.00958474i	0.770051	−	0.637983i	$-0.220231\pi$
$61$	0.0628143	+	0.0748592i	0.00804255	+	0.00958474i	−0.762008	+	0.647567i	$0.775786\pi$
$62$	−15.3686	+	8.87309i	−1.95182	+	1.12688i
$63$	5.65940	+	5.56518i	0.713017	+	0.701146i
$64$	4.82558	−	8.35815i	0.603197	−	1.04477i
$65$	−3.79584	+	5.02997i	−0.470817	+	0.623891i
$66$	9.34267	+	0.890173i	1.15000	+	0.109573i
$67$	−0.870116	−	2.39062i	−0.106302	−	0.292061i	0.875126	−	0.483896i	$-0.160779\pi$
$67$	−0.870116	−	2.39062i	−0.106302	−	0.292061i	−0.981427	+	0.191834i	$0.938556\pi$
$68$	9.52710	+	26.1755i	1.15533	+	3.17424i
$69$	2.82366	+	2.00984i	0.339928	+	0.241956i
$70$	10.8499	+	9.32361i	1.29681	+	1.11438i
$71$	−10.4867	−	6.05448i	−1.24454	−	0.718534i	−0.274523	−	0.961581i	$-0.588520\pi$
$71$	−10.4867	−	6.05448i	−1.24454	−	0.718534i	−0.970015	+	0.243046i	$0.921853\pi$
$72$	8.45335	+	10.3965i	0.996237	+	1.22523i
$73$	0.469002	+	0.812335i	0.0548925	+	0.0950766i	0.892166	−	0.451708i	$-0.149185\pi$
$73$	0.469002	+	0.812335i	0.0548925	+	0.0950766i	−0.837273	+	0.546784i	$0.815852\pi$
$74$	15.6802	+	18.6870i	1.82279	+	2.17232i
$75$	−2.89406	+	8.16238i	−0.334177	+	0.942510i
$76$	14.4615	+	2.54995i	1.65885	+	0.292499i
$77$	−4.29092	−	4.09098i	−0.488995	−	0.466211i
$78$	11.7656	−	0.937811i	1.33220	−	0.106186i
$79$	−14.0479	−	5.11302i	−1.58051	−	0.575259i	−0.605197	−	0.796076i	$-0.706906\pi$
$79$	−14.0479	−	5.11302i	−1.58051	−	0.575259i	−0.975315	+	0.220816i	$0.929128\pi$
$80$	4.73324	+	5.08286i	0.529192	+	0.568281i
$81$	8.54832	−	2.81535i	0.949813	−	0.312817i
$82$	−11.1906			−1.23580
$83$	−0.0128448	+	0.0352908i	−0.00140990	+	0.00387367i	−0.940396	−	0.340083i	$-0.889545\pi$
$83$	−0.0128448	+	0.0352908i	−0.00140990	+	0.00387367i	0.938986	+	0.343956i	$0.111767\pi$
$84$	−0.284204	−	17.6274i	−0.0310092	−	1.92331i
$85$	16.1688	−	0.836089i	1.75376	−	0.0906866i
$86$	−6.22007	−	1.09677i	−0.670727	−	0.118267i
$87$	−0.651450	+	2.35820i	−0.0698428	+	0.252826i
$88$	−6.43332	−	7.66694i	−0.685794	−	0.817298i
$89$	−0.138079	−	0.239159i	−0.0146363	−	0.0253508i	0.858614	−	0.512622i	$-0.171326\pi$
$89$	−0.138079	−	0.239159i	−0.0146363	−	0.0253508i	−0.873251	+	0.487271i	$0.837992\pi$
$90$	15.0319	−	6.09608i	1.58450	−	0.642583i
$91$	−6.20788	−	4.12975i	−0.650763	−	0.432916i
$92$	−1.33679	−	7.58129i	−0.139370	−	0.790404i
$93$	7.37122	−	10.3559i	0.764359	−	1.07386i
$94$	−2.35685	−	6.47540i	−0.243091	−	0.667887i
$95$	3.88017	−	7.60217i	0.398097	−	0.779966i
$96$	−0.233647	+	2.45220i	−0.0238465	+	0.250277i
$97$	−1.49351	−	8.47013i	−0.151643	−	0.860012i	−0.961791	−	0.273786i	$-0.911724\pi$
$97$	−1.49351	−	8.47013i	−0.151643	−	0.860012i	0.810148	−	0.586226i	$-0.199387\pi$
$98$	−10.2496	+	13.4705i	−1.03536	+	1.36073i
$99$	−6.35175	+	2.20129i	−0.638375	+	0.221238i
$100$	17.3006	−	8.40826i	1.73006	−	0.840826i
$101$	4.97400	−	4.17368i	0.494931	−	0.415296i	−0.360858	−	0.932621i	$-0.617516\pi$
$101$	4.97400	−	4.17368i	0.494931	−	0.415296i	0.855790	+	0.517324i	$0.173072\pi$
$102$	−21.2769	−	21.6083i	−2.10673	−	2.13954i
$103$	0.0111283	−	0.0631117i	0.00109650	−	0.00621858i	−0.984255	−	0.176757i	$-0.943439\pi$
$103$	0.0111283	−	0.0631117i	0.00109650	−	0.00621858i	0.985351	+	0.170538i	$0.0545506\pi$
$104$	−9.64228	−	8.09083i	−0.945503	−	0.793371i
$105$	−9.84425	−	2.84441i	−0.960701	−	0.277586i
$106$	−1.57349	−	0.572702i	−0.152830	−	0.0556258i
$107$	12.2726			1.18644			0.593218	−	0.805042i	$-0.297857\pi$
$107$	12.2726			1.18644			0.593218	+	0.805042i	$0.297857\pi$
$108$	−17.9166	−	8.86591i	−1.72403	−	0.853122i
$109$	−10.4690			−1.00275			−0.501376	−	0.865229i	$-0.667173\pi$
$109$	−10.4690			−1.00275			−0.501376	+	0.865229i	$0.667173\pi$
$110$	−11.1561	+	4.72632i	−1.06369	+	0.450637i
$111$	−15.7786	−	7.50668i	−1.49764	−	0.712502i
$112$	−5.67074	+	5.94788i	−0.535835	+	0.562022i
$113$	2.66088	−	15.0906i	0.250315	−	1.41961i	−0.557504	−	0.830174i	$-0.688241\pi$
$113$	2.66088	−	15.0906i	0.250315	−	1.41961i	0.807819	−	0.589431i	$-0.200648\pi$
$114$	−15.4734	+	4.01821i	−1.44922	+	0.376340i
$115$	−4.44073	−	0.548391i	−0.414100	−	0.0511377i
$116$	4.70605	−	2.71704i	0.436946	−	0.252271i
$117$	−7.38614	+	4.11353i	−0.682849	+	0.380296i
$118$	12.5847	−	21.7973i	1.15852	−	2.00661i
$119$	2.12423	+	19.0386i	0.194728	+	1.74527i
$120$	−15.9839	−	6.61505i	−1.45912	−	0.603868i
$121$	−5.61828	+	2.04489i	−0.510752	+	0.185899i
$122$	0.0808191	+	0.222049i	0.00731701	+	0.0201033i
$123$	7.29069	−	3.33136i	0.657379	−	0.300379i
$124$	−27.8049	+	4.90275i	−2.49695	+	0.440280i
$125$	−1.72593	−	11.0463i	−0.154372	−	0.988013i
$126$	8.25701	+	17.3260i	0.735593	+	1.54352i
$127$	−1.43824	+	0.830369i	−0.127623	+	0.0736834i	−0.562453	−	0.826830i	$-0.690142\pi$
$127$	−1.43824	+	0.830369i	−0.127623	+	0.0736834i	0.434829	+	0.900513i	$0.356809\pi$
$128$	15.6985	−	13.1726i	1.38756	−	1.16430i
$129$	4.37887	−	1.13712i	0.385538	−	0.100118i
$130$	−12.7851	+	8.29008i	−1.12132	+	0.727088i
$131$	15.3991	+	12.9214i	1.34543	+	1.12895i	0.980196	+	0.198030i	$0.0634543\pi$
$131$	15.3991	+	12.9214i	1.34543	+	1.12895i	0.365231	+	0.930917i	$0.380990\pi$
$132$	13.4832	+	6.41462i	1.17356	+	0.558321i
$133$	9.25190	+	4.04852i	0.802242	+	0.351051i
$134$		−	6.15172i		−	0.531427i
$135$	−7.97853	+	8.44648i	−0.686682	+	0.726958i
$136$			32.3400i			2.77313i
$137$	2.36264	+	0.859931i	0.201854	+	0.0734689i	0.440969	−	0.897522i	$-0.354635\pi$
$137$	2.36264	+	0.859931i	0.201854	+	0.0734689i	−0.239115	+	0.970991i	$0.576857\pi$
$138$	4.75386	+	6.90212i	0.404676	+	0.587548i
$139$	5.79195	−	6.90258i	0.491267	−	0.585469i	−0.462272	−	0.886738i	$-0.652966\pi$
$139$	5.79195	−	6.90258i	0.491267	−	0.585469i	0.953539	+	0.301269i	$0.0974102\pi$
$140$	11.1475	+	19.8430i	0.942133	+	1.67704i
$141$	3.46317	+	3.51711i	0.291651	+	0.296194i
$142$	−18.8211	−	22.4301i	−1.57943	−	1.88229i
$143$	5.46880	−	3.15741i	0.457324	−	0.264036i
$144$	3.05134	+	8.80452i	0.254278	+	0.733710i
$145$	−0.708357	−	3.07800i	−0.0588258	−	0.255614i
$146$	0.393863	+	2.23371i	0.0325964	+	0.184863i
$147$	2.66754	−	11.8273i	0.220015	−	0.975497i
$148$	13.2740	+	36.4700i	1.09111	+	2.99781i
$149$	−5.73366	−	15.7531i	−0.469720	−	1.29054i	−0.917975	−	0.396639i	$-0.870177\pi$
$149$	−5.73366	−	15.7531i	−0.469720	−	1.29054i	0.448255	−	0.893906i	$-0.352046\pi$
$150$	−13.3266	+	16.1535i	−1.08811	+	1.31893i
$151$	−3.90149	−	22.1264i	−0.317499	−	1.80062i	−0.557854	−	0.829939i	$-0.688375\pi$
$151$	−3.90149	−	22.1264i	−0.317499	−	1.80062i	0.240355	−	0.970685i	$-0.422736\pi$
$152$	14.7646	+	8.52436i	1.19757	+	0.691417i
$153$	20.2945	+	7.74382i	1.64071	+	0.626051i
$154$	−6.36667	−	12.8445i	−0.513041	−	1.03504i
$155$	−2.01126	+	16.2867i	−0.161548	+	1.30818i
$156$	18.1003	+	5.00019i	1.44919	+	0.400335i
$157$	1.48339	−	8.41274i	0.118388	−	0.671410i	−0.866629	−	0.498952i	$-0.833718\pi$
$157$	1.48339	−	8.41274i	0.118388	−	0.671410i	0.985017	−	0.172457i	$-0.0551707\pi$
$158$	−27.6918	−	23.2361i	−2.20304	−	1.84857i
$159$	1.19562	−	0.0952996i	0.0948185	−	0.00755775i
$160$	−1.24053	−	2.92818i	−0.0980728	−	0.231493i
$161$	0.335526	−	5.28361i	0.0264431	−	0.416407i
$162$	21.7523	+	0.672544i	1.70903	+	0.0528401i
$163$			9.23757i			0.723542i	0.932267	+	0.361771i	$0.117828\pi$
$163$			9.23757i			0.723542i	−0.932267	+	0.361771i	$0.882172\pi$
$164$	−16.7303	−	6.08935i	−1.30642	−	0.475498i
$165$	5.86120	−	6.40028i	0.456294	−	0.498261i
$166$	−0.0583733	+	0.0695666i	−0.00453065	+	0.00539941i
$167$	−18.3577	−	3.23697i	−1.42056	−	0.250484i	−0.589999	−	0.807404i	$-0.700872\pi$
$167$	−18.3577	−	3.23697i	−1.42056	−	0.250484i	−0.830566	+	0.556920i	$0.811983\pi$
$168$	6.68950	−	19.3440i	0.516106	−	1.49242i
$169$	−3.87480	+	3.25135i	−0.298062	+	0.250104i
$170$	37.4311	+	11.4723i	2.87084	+	0.879888i
$171$	8.88475	−	7.22419i	0.679434	−	0.552447i
$172$	−8.70240	−	5.02433i	−0.663552	−	0.383102i
$173$	−6.84061	+	1.20618i	−0.520082	+	0.0917045i	−0.427526	−	0.904003i	$-0.640615\pi$
$173$	−6.84061	+	1.20618i	−0.520082	+	0.0917045i	−0.0925558	+	0.995707i	$0.529504\pi$
$174$	−3.43057	+	4.81967i	−0.260071	+	0.365378i
$175$	12.9258	−	2.81512i	0.977095	−	0.212803i
$176$	−2.38050	−	6.54036i	−0.179437	−	0.492998i
$177$	−1.71003	+	17.9473i	−0.128534	+	1.34901i
$178$	−0.115957	−	0.657626i	−0.00869136	−	0.0492911i
$179$	10.1633	+	5.86778i	0.759640	+	0.438578i	0.829167	−	0.559002i	$-0.188815\pi$
$179$	10.1633	+	5.86778i	0.759640	+	0.438578i	−0.0695264	+	0.997580i	$0.522149\pi$
$180$	25.7903	−	0.934270i	1.92230	−	0.0696363i
$181$	12.2063	−	7.04731i	0.907287	−	0.523823i	0.0277301	−	0.999615i	$-0.491172\pi$
$181$	12.2063	−	7.04731i	0.907287	−	0.523823i	0.879557	+	0.475793i	$0.157839\pi$
$182$	−10.6904	−	14.5180i	−0.792428	−	1.07614i
$183$	−0.118756	−	0.120605i	−0.00877868	−	0.00891541i
$184$	1.55200	−	8.80184i	0.114415	−	0.648880i
$185$	22.5278	−	1.16491i	1.65628	−	0.0856460i
$186$	25.3140	−	17.4351i	1.85611	−	1.27840i
$187$	−15.2462	−	5.54915i	−1.11491	−	0.405794i
$188$		−	10.9634i		−	0.799589i
$189$	−10.5373	−	8.82984i	−0.766473	−	0.642276i
$190$	15.1040	−	14.0650i	1.09576	−	1.02039i
$191$	−8.79796	+	24.1722i	−0.636598	+	1.74904i	0.0255583	+	0.999673i	$0.491864\pi$
$191$	−8.79796	+	24.1722i	−0.636598	+	1.74904i	−0.662156	+	0.749366i	$0.730359\pi$
$192$	−7.18147	+	15.0951i	−0.518278	+	1.08939i
$193$	−10.7678	+	12.8326i	−0.775083	+	0.923708i	−0.998700	−	0.0509692i	$-0.983769\pi$
$193$	−10.7678	+	12.8326i	−0.775083	+	0.923708i	0.223617	+	0.974677i	$0.428213\pi$
$194$	3.61144	−	20.4815i	0.259286	−	1.47048i
$195$	5.86158	−	9.20700i	0.419756	−	0.659327i
$196$	−22.6534	+	14.5616i	−1.61810	+	1.04011i
$197$	8.78625	+	15.2182i	0.625995	+	1.08425i	0.988348	+	0.152214i	$0.0486402\pi$
$197$	8.78625	+	15.2182i	0.625995	+	1.08425i	−0.362353	+	0.932041i	$0.618027\pi$
$198$	−16.2533	−	0.251202i	−1.15507	−	0.0178522i
$199$	−22.6896	−	13.0999i	−1.60843	−	0.928625i	−0.989723	−	0.143001i	$-0.954325\pi$
$199$	−22.6896	−	13.0999i	−1.60843	−	0.928625i	−0.618704	−	0.785624i	$-0.712342\pi$
$200$	22.2133	−	2.30346i	1.57072	−	0.162879i
$201$	1.83132	+	4.00784i	0.129171	+	0.282691i
$202$	14.7539	−	5.37000i	1.03808	−	0.377832i
$203$	3.58571	−	1.05305i	0.251667	−	0.0739095i
$204$	−20.0515	−	43.8828i	−1.40389	−	3.07241i
$205$	−6.23350	+	8.26017i	−0.435367	+	0.576915i
$206$	0.0774817	−	0.134202i	0.00539841	−	0.00935032i
$207$	−5.15185	−	3.08154i	−0.358078	−	0.214182i
$208$	−4.37667	−	7.58061i	−0.303467	−	0.525621i
$209$	−6.55212	+	5.49788i	−0.453219	+	0.380296i
$210$	−20.0162	−	14.6047i	−1.38125	−	1.00782i
$211$	0.656625	−	3.72391i	0.0452039	−	0.256364i	−0.953828	−	0.300353i	$-0.902895\pi$
$211$	0.656625	−	3.72391i	0.0452039	−	0.256364i	0.999032	+	0.0439888i	$0.0140066\pi$
$212$	−2.04078	−	1.71242i	−0.140161	−	0.117609i
$213$	18.9392	+	9.01032i	1.29769	+	0.617377i
$214$	27.8864	+	10.1498i	1.90628	+	0.693828i
$215$	−4.27432	+	3.98031i	−0.291506	+	0.271455i
$216$	−16.0261	−	16.7869i	−1.09044	−	1.14220i
$217$	−19.3780	−	1.23056i	−1.31546	−	0.0835360i
$218$	−23.7883	−	8.65824i	−1.61115	−	0.586410i
$219$	−0.921561	−	1.33801i	−0.0622733	−	0.0904145i
$220$	−19.2505	+	0.995444i	−1.29787	+	0.0671128i
$221$	−20.0948	−	3.54326i	−1.35172	−	0.238345i
$222$	−29.6448	−	30.1065i	−1.98963	−	2.02062i
$223$	−8.83262	+	7.41145i	−0.591476	+	0.496307i	−0.888693	−	0.458503i	$-0.848386\pi$
$223$	−8.83262	+	7.41145i	−0.591476	+	0.496307i	0.297217	+	0.954810i	$0.403941\pi$
$224$	3.37133	−	1.67108i	0.225257	−	0.111654i
$225$	3.87349	−	14.4912i	0.258233	−	0.966083i
$226$	18.5266	−	32.0891i	1.23237	−	2.13453i
$227$	25.7700	−	4.54395i	1.71041	−	0.301592i	0.769102	−	0.639127i	$-0.220704\pi$
$227$	25.7700	−	4.54395i	1.71041	−	0.301592i	0.941313	+	0.337534i	$0.109593\pi$
$228$	−25.3198	−	2.41248i	−1.67684	−	0.159770i
$229$	−0.631040	−	1.73377i	−0.0417003	−	0.114571i	0.917095	−	0.398669i	$-0.130528\pi$
$229$	−0.631040	−	1.73377i	−0.0417003	−	0.114571i	−0.958795	+	0.284099i	$0.908306\pi$
$230$	−9.63693	−	4.91871i	−0.635440	−	0.324330i
$231$	7.97159	+	6.47287i	0.524492	+	0.425883i
$232$	6.21309	−	1.09554i	0.407909	−	0.0719254i
$233$	−2.03500	+	3.52472i	−0.133317	+	0.230912i	−0.924953	−	0.380081i	$-0.875896\pi$
$233$	−2.03500	+	3.52472i	−0.133317	+	0.230912i	0.791636	+	0.610993i	$0.209230\pi$
$234$	−20.1852	+	3.23840i	−1.31955	+	0.211701i
$235$	−6.09254	−	1.86732i	−0.397434	−	0.121810i
$236$	30.6755	−	25.7398i	1.99681	−	1.67552i
$237$	24.9584	+	6.89472i	1.62122	+	0.447860i
$238$	−10.9188	+	45.0174i	−0.707760	+	2.91805i
$239$	−1.54601	+	1.84246i	−0.100003	+	0.119179i	−0.813725	−	0.581250i	$-0.802564\pi$
$239$	−1.54601	+	1.84246i	−0.100003	+	0.119179i	0.713722	+	0.700429i	$0.247008\pi$
$240$	−8.87179	−	8.12455i	−0.572672	−	0.524437i
$241$	2.02357	−	5.55970i	0.130349	−	0.358132i	−0.857299	−	0.514819i	$-0.827859\pi$
$241$	2.02357	−	5.55970i	0.130349	−	0.358132i	0.987648	+	0.156687i	$0.0500814\pi$
$242$	−14.4573			−0.929353
$243$	−14.3719	+	6.03735i	−0.921955	+	0.387296i
$244$			0.375947i			0.0240675i
$245$	4.23372	+	15.0690i	0.270482	+	0.962725i
$246$	19.3214	−	1.54006i	1.23189	−	0.0981909i
$247$	−6.91438	+	8.24023i	−0.439951	+	0.524313i
$248$	−32.2813	−	5.69207i	−2.04987	−	0.361447i
$249$	0.0173208	−	0.0626999i	0.00109766	−	0.00397345i
$250$	5.21391	−	26.5274i	0.329757	−	1.67774i
$251$	−4.80342	−	8.31977i	−0.303189	−	0.525139i	0.673667	−	0.739035i	$-0.264718\pi$
$251$	−4.80342	−	8.31977i	−0.303189	−	0.525139i	−0.976857	+	0.213895i	$0.931385\pi$
$252$	2.91660	+	30.3960i	0.183729	+	1.91477i
$253$	3.88319	+	2.24196i	0.244134	+	0.140951i
$254$	−3.95479	+	0.697337i	−0.248146	+	0.0437548i
$255$	−27.8016	+	3.66874i	−1.74101	+	0.229745i
$256$	28.4268	−	10.3465i	1.77668	−	0.646658i
$257$	−5.68533	−	15.6203i	−0.354641	−	0.974369i	−0.980859	−	0.194721i	$-0.937620\pi$
$257$	−5.68533	−	15.6203i	−0.354641	−	0.974369i	0.626217	−	0.779649i	$-0.284602\pi$
$258$	10.8904	+	1.03764i	0.678004	+	0.0646004i
$259$	2.95966	+	26.5263i	0.183904	+	1.64826i
$260$	−23.6251	+	5.43697i	−1.46517	+	0.337187i
$261$	0.800239	−	4.16127i	0.0495336	−	0.257576i
$262$	24.3043	+	42.0962i	1.50152	+	2.60071i
$263$	−21.4069	+	17.9625i	−1.32000	+	1.10762i	−0.333700	+	0.942679i	$0.608297\pi$
$263$	−21.4069	+	17.9625i	−1.32000	+	1.10762i	−0.986304	+	0.164936i	$0.947258\pi$
$264$	12.1627	+	12.3522i	0.748565	+	0.760224i
$265$	−1.29921	+	0.842431i	−0.0798097	+	0.0517501i
$266$	17.6744	+	16.8509i	1.08369	+	1.03319i
$267$	0.271316	+	0.393924i	0.0166043	+	0.0241077i
$268$	3.34744	−	9.19701i	0.204477	−	0.561797i
$269$	20.5343			1.25200			0.626001	−	0.779823i	$-0.284691\pi$
$269$	20.5343			1.25200			0.626001	+	0.779823i	$0.284691\pi$
$270$	−25.1148	+	12.5940i	−1.52844	+	0.766449i
$271$			6.10187i			0.370662i	0.982676	+	0.185331i	$0.0593358\pi$
$271$			6.10187i			0.370662i	−0.982676	+	0.185331i	$0.940664\pi$
$272$	−7.69200	+	21.1336i	−0.466396	+	1.28141i
$273$	11.2867	+	6.27599i	0.683103	+	0.379840i
$274$	4.65733	+	3.90796i	0.281359	+	0.236089i
$275$	−2.72561	+	10.8674i	−0.164361	+	0.655328i
$276$	3.35141	+	12.9057i	0.201731	+	0.776831i
$277$	9.70821	+	11.5698i	0.583310	+	0.695162i	0.974305	−	0.225231i	$-0.0723137\pi$
$277$	9.70821	+	11.5698i	0.583310	+	0.695162i	−0.390996	+	0.920393i	$0.627869\pi$
$278$	18.8694	−	10.8943i	1.13171	−	0.653395i
$279$	−11.3018	+	18.8947i	−0.676619	+	1.13120i
$280$	4.28231	+	26.0748i	0.255917	+	1.55827i
$281$	24.6540	−	4.34716i	1.47073	−	0.259330i	0.619864	−	0.784710i	$-0.287188\pi$
$281$	24.6540	−	4.34716i	1.47073	−	0.259330i	0.850868	+	0.525380i	$0.176077\pi$
$282$	4.96044	+	10.8559i	0.295390	+	0.646460i
$283$	−15.9029	+	5.78818i	−0.945329	+	0.344072i	−0.768268	−	0.640128i	$-0.778881\pi$
$283$	−15.9029	+	5.78818i	−0.945329	+	0.344072i	−0.177061	+	0.984200i	$0.556659\pi$
$284$	−15.9329	−	43.7752i	−0.945442	−	2.59758i
$285$	−5.65318	+	13.6597i	−0.334865	+	0.809131i
$286$	15.0378	−	2.65157i	0.889203	−	0.156790i
$287$	−10.1945	−	6.78184i	−0.601764	−	0.400319i
$288$	0.0659339	−	4.26607i	0.00388519	−	0.251380i
$289$	17.7130	+	30.6798i	1.04194	+	1.80469i
$290$	0.936042	−	7.57983i	0.0549663	−	0.445103i
$291$	3.74433	+	14.4188i	0.219496	+	0.845244i
$292$	−0.626629	+	3.55379i	−0.0366707	+	0.207970i
$293$	−12.7809	+	15.2316i	−0.746666	+	0.889842i	−0.996927	−	0.0783368i	$-0.975039\pi$
$293$	−12.7809	+	15.2316i	−0.746666	+	0.889842i	0.250261	+	0.968178i	$0.419483\pi$
$294$	15.8429	−	24.6684i	0.923974	−	1.43869i
$295$	−9.07930	−	21.4309i	−0.528617	−	1.24776i
$296$			45.0588i			2.61899i
$297$	10.6638	−	4.67483i	0.618778	−	0.271261i
$298$		−	40.5370i		−	2.34824i
$299$	5.29909	+	1.92871i	0.306454	+	0.111540i
$300$	−28.7136	+	16.8984i	−1.65778	+	0.975630i
$301$	−5.00174	−	4.76868i	−0.288295	−	0.274862i
$302$	9.43412	−	53.5035i	0.542873	−	3.07878i
$303$	−8.01359	+	7.89069i	−0.460369	+	0.453309i
$304$	7.62092	+	9.08226i	0.437090	+	0.520903i
$305$	0.208920	+	0.0640323i	0.0119627	+	0.00366648i
$306$	39.7099	+	34.3801i	2.27006	+	1.96538i
$307$	−15.4872	+	26.8246i	−0.883899	+	1.53096i	−0.0369295	+	0.999318i	$0.511758\pi$
$307$	−15.4872	+	26.8246i	−0.883899	+	1.53096i	−0.846970	+	0.531641i	$0.821576\pi$
$308$	−2.52909	−	22.6673i	−0.144109	−	1.29159i
$309$	−0.0105283	+	0.110499i	−0.000598936	+	0.00628604i
$310$	−18.0397	+	35.3441i	−1.02459	+	2.00741i
$311$	21.1167	−	7.68586i	1.19742	−	0.435825i	0.335097	−	0.942184i	$-0.391231\pi$
$311$	21.1167	−	7.68586i	1.19742	−	0.435825i	0.862323	+	0.506358i	$0.169009\pi$
$312$	17.7616	+	12.6424i	1.00555	+	0.715737i
$313$	2.58539	+	14.6625i	0.146135	+	0.828771i	0.966449	+	0.256858i	$0.0826873\pi$
$313$	2.58539	+	14.6625i	0.146135	+	0.828771i	−0.820314	+	0.571913i	$0.806202\pi$
$314$	10.3283	−	17.8891i	0.582857	−	1.00954i
$315$	17.3883	+	3.55631i	0.979719	+	0.200375i
$316$	−28.7562	−	49.8072i	−1.61766	−	2.80187i
$317$	−12.6104	+	10.5814i	−0.708270	+	0.594309i	−0.924113	−	0.382119i	$-0.875195\pi$
$317$	−12.6104	+	10.5814i	−0.708270	+	0.594309i	0.215843	+	0.976428i	$0.430750\pi$
$318$	2.79556	+	0.772268i	0.156767	+	0.0433067i
$319$	−0.549620	+	3.11705i	−0.0307728	+	0.174521i
$320$	−1.11444	−	21.5519i	−0.0622994	−	1.20479i
$321$	−21.1895	+	1.68896i	−1.18268	+	0.0942688i
$322$	5.13212	−	11.7282i	0.286002	−	0.653588i
$323$	27.6375			1.53779
$324$	32.1545	+	12.8420i	1.78636	+	0.713442i
$325$	−1.00247	+	14.0549i	−0.0556073	+	0.779625i
$326$	−7.63977	+	20.9901i	−0.423128	+	1.16253i
$327$	18.0756	−	1.44076i	0.999582	−	0.0796742i
$328$	−15.8345	−	13.2867i	−0.874312	−	0.733635i
$329$	1.77722	−	7.32734i	0.0979811	−	0.403969i
$330$	18.6114	−	9.69566i	1.02452	−	0.533728i
$331$	2.27096	−	1.90556i	0.124823	−	0.104739i	−0.578239	−	0.815867i	$-0.696260\pi$
$331$	2.27096	−	1.90556i	0.124823	−	0.104739i	0.703062	+	0.711128i	$0.251815\pi$
$332$	−0.125124	+	0.0722406i	−0.00686709	+	0.00396472i
$333$	28.2761	+	10.7894i	1.54952	+	0.591254i
$334$	−39.0364	−	22.5377i	−2.13598	−	1.23321i
$335$	−4.54079	−	3.42668i	−0.248090	−	0.187220i
$336$	8.97241	−	11.0499i	0.489485	−	0.602820i
$337$	−1.39801	−	3.84099i	−0.0761543	−	0.209232i	0.895774	−	0.444510i	$-0.146622\pi$
$337$	−1.39801	−	3.84099i	−0.0761543	−	0.209232i	−0.971928	+	0.235278i	$0.924400\pi$
$338$	−11.4935	+	4.18330i	−0.625164	+	0.227541i
$339$	−2.51743	+	26.4213i	−0.136728	+	1.43501i
$340$	49.7181	+	37.5196i	2.69634	+	2.03478i
$341$	8.22253	−	14.2418i	0.445275	−	0.771239i
$342$	26.1630	−	9.06720i	1.41474	−	0.490298i
$343$	−17.5008	+	6.05993i	−0.944953	+	0.327206i
$344$	−7.49905	−	8.93702i	−0.404322	−	0.481852i
$345$	7.74272	+	0.335699i	0.416854	+	0.0180735i
$346$	−16.5412	−	2.91665i	−0.889258	−	0.156800i
$347$	18.4741	+	15.5016i	0.991743	+	0.832171i	0.985819	−	0.167811i	$-0.0536699\pi$
$347$	18.4741	+	15.5016i	0.991743	+	0.832171i	0.00592403	+	0.999982i	$0.498114\pi$
$348$	−7.75142	+	5.33882i	−0.415520	+	0.286191i
$349$	−6.92074	+	19.0146i	−0.370459	+	1.01783i	0.604726	+	0.796434i	$0.293283\pi$
$349$	−6.92074	+	19.0146i	−0.370459	+	1.01783i	−0.975185	+	0.221393i	$0.928940\pi$
$350$	31.6988	+	4.29335i	1.69437	+	0.229489i
$351$	12.1866	−	8.11880i	0.650474	−	0.433350i
$352$			3.18684i			0.169859i
$353$	−5.81751	+	15.9835i	−0.309635	+	0.850715i	0.683093	+	0.730332i	$0.260634\pi$
$353$	−5.81751	+	15.9835i	−0.309635	+	0.850715i	−0.992728	+	0.120383i	$0.961588\pi$
$354$	−18.7287	+	39.3667i	−0.995417	+	2.09231i
$355$	−27.0403	+	1.39825i	−1.43515	+	0.0742116i
$356$	0.184486	−	1.04627i	0.00977771	−	0.0554522i
$357$	−6.28775	−	32.5793i	−0.332783	−	1.72428i
$358$	18.2407	+	21.7385i	0.964053	+	1.14891i
$359$	22.0215	−	12.7141i	1.16225	−	0.671027i	0.210409	−	0.977613i	$-0.432520\pi$
$359$	22.0215	−	12.7141i	1.16225	−	0.671027i	0.951843	+	0.306587i	$0.0991869\pi$
$360$	28.5077	+	9.22166i	1.50249	+	0.486024i
$361$	−2.21513	+	3.83672i	−0.116586	+	0.201932i
$362$	33.5642	−	5.91827i	1.76409	−	0.311057i
$363$	9.41896	−	4.30384i	0.494367	−	0.225893i
$364$	−8.08264	−	27.5220i	−0.423645	−	1.44254i
$365$	1.86817	+	0.953518i	0.0977844	+	0.0499094i
$366$	−0.170099	−	0.372261i	−0.00889120	−	0.0194584i
$367$	3.94589	+	22.3783i	0.205974	+	1.16814i	0.895900	+	0.444256i	$0.146532\pi$
$367$	3.94589	+	22.3783i	0.205974	+	1.16814i	−0.689926	+	0.723880i	$0.742357\pi$
$368$	3.10771	−	5.38271i	0.162000	−	0.280593i
$369$	−12.1295	+	6.75520i	−0.631434	+	0.351662i
$370$	52.1523	+	15.9843i	2.71127	+	0.830982i
$371$	−1.08635	−	1.47530i	−0.0564007	−	0.0765939i
$372$	47.3325	−	12.2915i	2.45407	−	0.637284i
$373$	−10.0452	−	1.77125i	−0.520122	−	0.0917116i	−0.0925771	−	0.995706i	$-0.529510\pi$
$373$	−10.0452	−	1.77125i	−0.520122	−	0.0917116i	−0.427545	+	0.903994i	$0.640622\pi$
$374$	−30.0538	−	25.2182i	−1.55405	−	1.30400i
$375$	4.50015	+	18.8348i	0.232387	+	0.972623i
$376$	4.35339	−	11.9608i	0.224509	−	0.616833i
$377$			3.98061i			0.205012i
$378$	−16.6408	−	28.7783i	−0.855909	−	1.48020i
$379$	20.7225			1.06444			0.532220	−	0.846606i	$-0.321358\pi$
$379$	20.7225			1.06444			0.532220	+	0.846606i	$0.321358\pi$
$380$	30.2344	−	12.8089i	1.55099	−	0.657083i
$381$	2.36896	−	1.63163i	0.121365	−	0.0835908i
$382$	−39.9824	+	47.6492i	−2.04568	+	2.43794i
$383$	33.2623	+	5.86503i	1.69962	+	0.299689i	0.937562	−	0.347818i	$-0.113077\pi$
$383$	33.2623	+	5.86503i	1.69962	+	0.299689i	0.762060	+	0.647507i	$0.224188\pi$
$384$	−25.2918	+	24.9039i	−1.29067	+	1.27087i
$385$	−13.0274	−	2.45529i	−0.663935	−	0.125133i
$386$	−35.0801	+	20.2535i	−1.78553	+	1.03088i
$387$	−7.40396	+	2.56596i	−0.376364	+	0.130435i
$388$	16.5441	−	28.6553i	0.839902	−	1.45475i
$389$	23.9282	−	4.21918i	1.21321	−	0.213921i	0.469807	−	0.882769i	$-0.344323\pi$
$389$	23.9282	−	4.21918i	1.21321	−	0.213921i	0.743399	+	0.668848i	$0.233212\pi$
$390$	20.9335	−	16.0729i	1.06001	−	0.813884i
$391$	−4.95542	−	13.6149i	−0.250607	−	0.688536i
$392$	−30.4965	+	6.89106i	−1.54031	+	0.348051i
$393$	−28.3660	−	20.1905i	−1.43087	−	1.01848i
$394$	7.37862	+	41.8462i	0.371729	+	2.10818i
$395$	−32.5765	+	7.49700i	−1.63910	+	0.377215i
$396$	−24.1626	−	9.21976i	−1.21421	−	0.463310i
$397$	−11.6362	−	20.1546i	−0.584006	−	1.01153i	−0.994998	−	0.0998899i	$-0.968151\pi$
$397$	−11.6362	−	20.1546i	−0.584006	−	1.01153i	0.410992	−	0.911639i	$-0.365182\pi$
$398$	−40.7226	−	48.5313i	−2.04124	−	2.43265i
$399$	−16.5313	−	5.71681i	−0.827598	−	0.286198i
$400$	15.0639	+	3.77813i	0.753194	+	0.188906i
$401$	−20.6667	+	24.6297i	−1.03205	+	1.22995i	−0.0592613	+	0.998243i	$0.518875\pi$
$401$	−20.6667	+	24.6297i	−1.03205	+	1.22995i	−0.972786	+	0.231704i	$0.925570\pi$
$402$	0.846605	+	10.6214i	0.0422248	+	0.529747i
$403$	7.07367	−	19.4348i	0.352365	−	0.968114i
$404$	24.9797			1.24279
$405$	12.6131	−	15.6815i	0.626751	−	0.779220i
$406$	9.01854	+	0.572705i	0.447583	+	0.0284229i
$407$	−21.2423	−	7.73157i	−1.05294	−	0.383239i
$408$	−4.45066	−	55.8373i	−0.220340	−	2.76436i
$409$	−6.69644	+	7.98051i	−0.331118	+	0.394611i	−0.905758	−	0.423795i	$-0.860698\pi$
$409$	−6.69644	+	7.98051i	−0.331118	+	0.394611i	0.574640	+	0.818406i	$0.305142\pi$
$410$	−20.9955	+	13.6139i	−1.03690	+	0.672342i
$411$	−4.19762	−	1.15959i	−0.207053	−	0.0571982i
$412$	0.188863	−	0.158475i	0.00930464	−	0.00780752i
$413$	24.6743	−	12.2304i	1.21414	−	0.601820i
$414$	−9.15777	−	11.2628i	−0.450080	−	0.553536i
$415$	0.0188338	+	0.0818379i	0.000924514	+	0.00401726i
$416$	0.695966	+	3.94702i	0.0341225	+	0.193519i
$417$	−9.05030	+	12.7149i	−0.443195	+	0.622652i
$418$	−19.4350	+	7.07376i	−0.950597	+	0.345989i
$419$	−10.4036	+	3.78661i	−0.508250	+	0.184988i	−0.583401	−	0.812184i	$-0.698278\pi$
$419$	−10.4036	+	3.78661i	−0.508250	+	0.184988i	0.0751511	+	0.997172i	$0.476056\pi$
$420$	−21.9778	−	32.7263i	−1.07241	−	1.59688i
$421$	−5.19292	−	29.4505i	−0.253088	−	1.43533i	−0.800934	−	0.598752i	$-0.795663\pi$
$421$	−5.19292	−	29.4505i	−0.253088	−	1.43533i	0.547847	−	0.836579i	$-0.315448\pi$
$422$	4.57181	−	7.91861i	0.222552	−	0.385472i
$423$	−6.46345	−	5.59594i	−0.314264	−	0.272084i
$424$	−1.54647	−	2.67857i	−0.0751033	−	0.130083i
$425$	29.3184	−	21.2387i	1.42215	−	1.03023i
$426$	35.5829	+	36.1371i	1.72400	+	1.75085i
$427$	−0.0609426	+	0.251262i	−0.00294922	+	0.0121594i
$428$	36.1681	+	30.3486i	1.74825	+	1.46696i
$429$	−9.00776	+	6.20413i	−0.434899	+	0.299538i
$430$	−13.0042	+	5.50927i	−0.627117	+	0.265681i
$431$			17.0669i			0.822086i	0.911616	+	0.411043i	$0.134835\pi$
$431$			17.0669i			0.822086i	−0.911616	+	0.411043i	$0.865165\pi$
$432$	−6.48005	−	14.7817i	−0.311772	−	0.711186i
$433$	−29.4009			−1.41292			−0.706458	−	0.707755i	$-0.749708\pi$
$433$	−29.4009			−1.41292			−0.706458	+	0.707755i	$0.749708\pi$
$434$	−43.0140	−	18.8224i	−2.06474	−	0.903503i
$435$	1.64663	+	5.21691i	0.0789498	+	0.250132i
$436$	−30.8529	−	25.8887i	−1.47759	−	1.23984i
$437$	−7.52200	−	1.32633i	−0.359826	−	0.0634470i
$438$	−0.987440	−	3.80246i	−0.0471817	−	0.181689i
$439$	17.3607	+	20.6897i	0.828582	+	0.987465i	0.999997	+	0.00226640i	$0.000721417\pi$
$439$	17.3607	+	20.6897i	0.828582	+	0.987465i	−0.171416	+	0.985199i	$0.554834\pi$
$440$	−21.3972	−	6.55806i	−1.02007	−	0.312643i
$441$	−2.97802	+	20.7878i	−0.141810	+	0.989894i
$442$	−42.7302	−	24.6703i	−2.03247	−	1.17344i
$443$	−2.82708	−	16.0332i	−0.134318	−	0.761758i	−0.975332	−	0.220744i	$-0.929152\pi$
$443$	−2.82708	−	16.0332i	−0.134318	−	0.761758i	0.841013	−	0.541014i	$-0.181960\pi$
$444$	−27.9376	−	61.1414i	−1.32586	−	2.90164i
$445$	−0.550007	−	0.280725i	−0.0260728	−	0.0133076i
$446$	−26.1995	+	9.53582i	−1.24058	+	0.451534i
$447$	12.0676	+	26.4098i	0.570776	+	1.24914i
$448$	25.3771	−	2.83144i	1.19895	−	0.133773i
$449$	9.39365	+	5.42343i	0.443314	+	0.255947i	0.705002	−	0.709205i	$-0.250946\pi$
$449$	9.39365	+	5.42343i	0.443314	+	0.255947i	−0.261688	+	0.965152i	$0.584279\pi$
$450$	20.7863	−	29.7243i	0.979875	−	1.40122i
$451$	8.98081	−	5.18507i	0.422890	−	0.244156i
$452$	45.1591	−	37.8930i	2.12410	−	1.78234i
$453$	9.78127	+	37.6660i	0.459564	+	1.76970i
$454$	62.3140	+	10.9876i	2.92454	+	0.515675i
$455$	−16.6711	−	0.195961i	−0.781552	−	0.00918680i
$456$	−26.6654	−	12.6860i	−1.24872	−	0.594078i
$457$	3.26660	−	8.97492i	0.152805	−	0.419829i	−0.839544	−	0.543292i	$-0.817178\pi$
$457$	3.26660	−	8.97492i	0.152805	−	0.419829i	0.992349	+	0.123463i	$0.0393999\pi$
$458$		−	4.46145i		−	0.208470i
$459$	−36.1057	−	10.5773i	−1.68527	−	0.493708i
$460$	−11.7310	−	12.5975i	−0.546961	−	0.587363i
$461$	−8.78579	−	3.19777i	−0.409195	−	0.148935i	0.129217	−	0.991616i	$-0.458754\pi$
$461$	−8.78579	−	3.19777i	−0.409195	−	0.148935i	−0.538412	+	0.842681i	$0.680976\pi$
$462$	12.7602	+	21.3008i	0.593658	+	0.991001i
$463$	−2.45863	+	2.93008i	−0.114262	+	0.136172i	−0.820144	−	0.572157i	$-0.806107\pi$
$463$	−2.45863	+	2.93008i	−0.114262	+	0.136172i	0.705882	+	0.708330i	$0.250551\pi$
$464$	4.32072	+	0.761859i	0.200584	+	0.0353684i
$465$	1.23120	−	28.3969i	0.0570955	−	1.31688i
$466$	−7.53909	+	6.32605i	−0.349242	+	0.293049i
$467$	8.41520	−	4.85852i	0.389409	−	0.224825i	−0.292495	−	0.956267i	$-0.594485\pi$
$467$	8.41520	−	4.85852i	0.389409	−	0.224825i	0.681904	+	0.731442i	$0.261152\pi$
$468$	−31.9397	−	6.14221i	−1.47641	−	0.283924i
$469$	3.72812	−	5.60414i	0.172149	−	0.258775i
$470$	−12.2995	−	9.28175i	−0.567333	−	0.428135i
$471$	−1.40342	+	14.7294i	−0.0646661	+	0.678693i
$472$	43.6872	−	15.9008i	2.01086	−	0.731895i
$473$	5.49997	−	2.00183i	0.252889	−	0.0920440i
$474$	51.0097	+	36.3080i	2.34295	+	1.66768i
$475$	−1.96852	−	18.9834i	−0.0903220	−	0.871017i
$476$	−40.8200	+	61.3610i	−1.87098	+	2.81248i
$477$	−2.05120	+	0.329084i	−0.0939182	+	0.0150677i
$478$	−5.03670	+	2.90794i	−0.230373	+	0.133006i
$479$	22.1281	−	18.5676i	1.01106	−	0.848377i	0.0225793	−	0.999745i	$-0.492812\pi$
$479$	22.1281	−	18.5676i	1.01106	−	0.848377i	0.988478	+	0.151368i	$0.0483677\pi$
$480$	2.54485	+	4.88500i	0.116156	+	0.222969i
$481$	−27.9979	−	4.93678i	−1.27659	−	0.225098i
$482$	9.19611	−	10.9595i	0.418871	−	0.499192i
$483$	0.147826	+	9.16873i	0.00672631	+	0.417192i
$484$	−21.6142	−	7.86692i	−0.982463	−	0.357587i
$485$	−13.1064	−	14.0745i	−0.595130	−	0.639090i
$486$	−37.6496	+	1.83238i	−1.70782	+	0.0831185i
$487$			20.5657i			0.931919i	0.884806	+	0.465959i	$0.154291\pi$
$487$			20.5657i			0.931919i	−0.884806	+	0.465959i	$0.845709\pi$
$488$	−0.149282	+	0.410150i	−0.00675770	+	0.0185666i
$489$	−1.27128	−	15.9493i	−0.0574894	−	0.721254i
$490$	−2.84250	+	37.7421i	−0.128411	+	1.70501i
$491$	−5.15684	−	0.909291i	−0.232725	−	0.0410357i	0.0560692	−	0.998427i	$-0.482143\pi$
$491$	−5.15684	−	0.909291i	−0.232725	−	0.0410357i	−0.288794	+	0.957391i	$0.593254\pi$
$492$	29.7242	+	8.21126i	1.34007	+	0.370192i
$493$	7.83461	−	6.57402i	0.352853	−	0.296079i
$494$	−22.5262	+	13.0055i	−1.01350	+	0.585144i
$495$	−9.23899	+	11.8572i	−0.415262	+	0.532941i
$496$	−19.7414	−	11.3977i	−0.886416	−	0.511773i
$497$	−3.55250	−	31.8397i	−0.159351	−	1.42821i
$498$	0.0912120	−	0.128145i	0.00408731	−	0.00574233i
$499$	−20.9190	+	7.61388i	−0.936462	+	0.340844i	−0.764768	−	0.644306i	$-0.777146\pi$
$499$	−20.9190	+	7.61388i	−0.936462	+	0.340844i	−0.171694	+	0.985150i	$0.554924\pi$
$500$	22.2298	−	36.8222i	0.994147	−	1.64674i
$501$	32.1415	+	3.06245i	1.43598	+	0.136820i
$502$	−4.03387	−	22.8772i	−0.180041	−	1.02106i
$503$	18.7162	+	10.8058i	0.834513	+	0.481806i	0.855395	−	0.517976i	$-0.173314\pi$
$503$	18.7162	+	10.8058i	0.834513	+	0.481806i	−0.0208823	+	0.999782i	$0.506648\pi$
$504$	−8.88779	+	34.3195i	−0.395893	+	1.52871i
$505$	4.25460	−	13.8816i	0.189327	−	0.617724i
$506$	6.96941	+	8.30582i	0.309828	+	0.369239i
$507$	6.24269	−	6.14695i	0.277247	−	0.272996i
$508$	−6.29200	−	1.10945i	−0.279162	−	0.0492238i
$509$	−13.7735	−	11.5574i	−0.610501	−	0.512272i	0.284300	−	0.958735i	$-0.408239\pi$
$509$	−13.7735	−	11.5574i	−0.610501	−	0.512272i	−0.894802	+	0.446464i	$0.852683\pi$
$510$	−66.2065	−	14.6565i	−2.93167	−	0.649003i
$511$	−0.994888	+	2.27358i	−0.0440113	+	0.100577i
$512$	32.1641			1.42146
$513$	−14.3460	+	13.6958i	−0.633391	+	0.604685i
$514$		−	40.1953i		−	1.77294i
$515$	−0.0558996	−	0.131946i	−0.00246323	−	0.00581425i
$516$	15.7168	+	7.47725i	0.691893	+	0.329168i
$517$	4.89177	+	4.10468i	0.215140	+	0.180524i
$518$	−15.2130	+	62.7222i	−0.668421	+	2.75585i
$519$	11.6448	−	3.02398i	0.511151	−	0.132738i
$520$	−27.9334	−	3.44953i	−1.22496	−	0.151272i
$521$	−3.34304	−	5.79031i	−0.146461	−	0.253678i	0.783456	−	0.621447i	$-0.213455\pi$
$521$	−3.34304	−	5.79031i	−0.146461	−	0.253678i	−0.929917	+	0.367769i	$0.880122\pi$
$522$	5.25985	−	8.79364i	0.230217	−	0.384887i
$523$	10.1124	−	17.5152i	0.442185	−	0.765887i	−0.555667	−	0.831405i	$-0.687537\pi$
$523$	10.1124	−	17.5152i	0.442185	−	0.765887i	0.997851	+	0.0655187i	$0.0208702\pi$
$524$	13.4291	+	76.1603i	0.586654	+	3.32708i
$525$	−21.9299	+	6.63937i	−0.957098	+	0.289766i
$526$	−63.4974	+	23.1112i	−2.76862	+	1.00769i
$527$	−49.9336	+	18.1743i	−2.17514	+	0.791687i
$528$	5.01020	+	10.9648i	0.218041	+	0.477182i
$529$	−3.29859	−	18.7072i	−0.143417	−	0.813359i
$530$	−3.64885	+	0.839729i	−0.158496	+	0.0364755i
$531$	0.482561	−	31.2228i	0.0209414	−	1.35495i
$532$	17.2545	+	34.8101i	0.748076	+	1.50921i
$533$	9.99072	−	8.38321i	0.432746	−	0.363117i
$534$	0.290712	+	1.11948i	0.0125803	+	0.0484447i
$535$	23.0255	−	14.9301i	0.995478	−	0.645486i
$536$	7.30397	−	8.70453i	0.315483	−	0.375978i
$537$	−18.3552	−	8.73248i	−0.792086	−	0.376834i
$538$	46.6592	+	16.9826i	2.01162	+	0.732171i
$539$	1.98416	−	15.5596i	0.0854639	−	0.670197i
$540$	−44.4004	+	5.16238i	−1.91069	+	0.222153i
$541$	33.6954			1.44868			0.724339	−	0.689444i	$-0.242145\pi$
$541$	33.6954			1.44868			0.724339	+	0.689444i	$0.242145\pi$
$542$	−5.04645	+	13.8650i	−0.216764	+	0.595553i
$543$	−20.1052	+	13.8476i	−0.862798	+	0.594256i
$544$	6.61910	−	7.88834i	0.283792	−	0.338210i
$545$	−19.6417	+	12.7361i	−0.841359	+	0.545553i
$546$	20.4558	+	23.5951i	0.875428	+	1.00978i
$547$	19.1467	+	22.8181i	0.818653	+	0.975633i	0.999970	−	0.00779188i	$-0.00248026\pi$
$547$	19.1467	+	22.8181i	0.818653	+	0.975633i	−0.181316	+	0.983425i	$0.558036\pi$
$548$	4.83635	+	8.37680i	0.206599	+	0.357839i
$549$	0.221639	+	0.191891i	0.00945930	+	0.00818971i
$550$	−15.1810	+	22.4393i	−0.647318	+	0.956814i
$551$	−0.936238	−	5.30967i	−0.0398851	−	0.226200i
$552$	−1.46833	+	15.4106i	−0.0624962	+	0.655919i
$553$	−11.1451	−	37.9499i	−0.473937	−	1.61379i
$554$	12.4909	+	34.3185i	0.530688	+	1.45805i
$555$	−38.7356	+	5.11161i	−1.64424	+	0.216976i
$556$	34.1385	−	6.01954i	1.44780	−	0.255285i
$557$	20.5290	−	35.5573i	0.869843	−	1.50661i	0.00768705	−	0.999970i	$-0.497553\pi$
$557$	20.5290	−	35.5573i	0.869843	−	1.50661i	0.862156	−	0.506642i	$-0.169114\pi$
$558$	−41.3070	+	33.5867i	−1.74867	+	1.42184i
$559$	6.37475	−	3.68046i	0.269623	−	0.155667i
$560$	−3.40342	+	18.0580i	−0.143821	+	0.763088i
$561$	27.0873	+	7.48284i	1.14363	+	0.315926i
$562$	59.6153	+	10.5118i	2.51472	+	0.443413i
$563$	−11.2510	+	13.4084i	−0.474172	+	0.565096i	−0.949119	−	0.314919i	$-0.898023\pi$
$563$	−11.2510	+	13.4084i	−0.474172	+	0.565096i	0.474947	+	0.880014i	$0.342467\pi$
$564$	1.50880	+	18.9291i	0.0635317	+	0.797061i
$565$	−13.3661	−	31.5497i	−0.562317	−	1.32730i
$566$	−40.9224			−1.72010
$567$	19.4085	+	13.7952i	0.815082	+	0.579345i
$568$		−	54.0845i		−	2.26933i
$569$	9.03351	−	24.8194i	0.378705	−	1.04048i	−0.593189	−	0.805063i	$-0.702131\pi$
$569$	9.03351	−	24.8194i	0.378705	−	1.04048i	0.971894	−	0.235419i	$-0.0756463\pi$
$570$	−24.1425	+	26.3630i	−1.01122	+	1.10422i
$571$	−8.64103	−	7.25069i	−0.361616	−	0.303432i	0.443819	−	0.896117i	$-0.353623\pi$
$571$	−8.64103	−	7.25069i	−0.361616	−	0.303432i	−0.805434	+	0.592685i	$0.798068\pi$
$572$	23.9248	+	4.21859i	1.00035	+	0.176388i
$573$	11.8637	−	42.9459i	0.495615	−	1.79409i
$574$	−17.5557	−	23.8413i	−0.732762	−	0.995115i
$575$	−8.99871	+	4.37347i	−0.375272	+	0.182386i
$576$	10.3219	−	27.0511i	0.430081	−	1.12713i
$577$	14.8893	−	25.7890i	0.619849	−	1.07361i	−0.369664	−	0.929166i	$-0.620527\pi$
$577$	14.8893	−	25.7890i	0.619849	−	1.07361i	0.989513	−	0.144444i	$-0.0461395\pi$
$578$	14.8752	+	84.3615i	0.618727	+	3.50898i
$579$	16.8254	−	23.6382i	0.699239	−	0.982372i
$580$	5.52396	−	10.8227i	0.229370	−	0.449390i
$581$	−0.0953367	+	0.0279984i	−0.00395523	+	0.00116157i
$582$	−3.41673	+	35.8598i	−0.141628	+	1.48644i
$583$	1.52813	−	0.269450i	0.0632885	−	0.0111595i
$584$	−2.09479	+	3.62828i	−0.0866830	+	0.150139i
$585$	−8.85338	+	16.7033i	−0.366042	+	0.690595i
$586$	−41.6384	+	24.0399i	−1.72007	+	0.993081i
$587$	−7.94765	−	9.47164i	−0.328035	−	0.390936i	0.576669	−	0.816978i	$-0.304352\pi$
$587$	−7.94765	−	9.47164i	−0.328035	−	0.390936i	−0.904704	+	0.426041i	$0.859908\pi$
$588$	37.1088	−	28.2592i	1.53034	−	1.16539i
$589$	−4.86441	+	27.5874i	−0.200434	+	1.13672i
$590$	−2.90638	−	56.2054i	−0.119654	−	2.31394i
$591$	−17.2645	−	25.0663i	−0.710165	−	1.03109i
$592$	−10.7172	+	29.4452i	−0.440473	+	1.21019i
$593$			3.36070i			0.138008i	0.997616	+	0.0690038i	$0.0219821\pi$
$593$			3.36070i			0.138008i	−0.997616	+	0.0690038i	$0.978018\pi$
$594$	28.0971	−	1.80308i	1.15284	−	0.0739813i
$595$	27.1468	+	33.1355i	1.11291	+	1.35842i
$596$	22.0581	−	60.6041i	0.903534	−	2.48244i
$597$	40.9782	+	19.4953i	1.67713	+	0.797891i
$598$	10.4458	+	8.76504i	0.427159	+	0.358429i
$599$	−14.8989	−	2.62707i	−0.608752	−	0.107339i	−0.139230	−	0.990260i	$-0.544463\pi$
$599$	−14.8989	−	2.62707i	−0.608752	−	0.107339i	−0.469522	+	0.882921i	$0.655574\pi$
$600$	−38.0360	+	7.03411i	−1.55281	+	0.287166i
$601$	−0.690837	−	0.823307i	−0.0281798	−	0.0335834i	0.751770	−	0.659425i	$-0.229200\pi$
$601$	−0.690837	−	0.823307i	−0.0281798	−	0.0335834i	−0.779950	+	0.625841i	$0.784756\pi$
$602$	−7.42136	−	14.9723i	−0.302472	−	0.610224i
$603$	−3.71347	−	6.66781i	−0.151224	−	0.271534i
$604$	43.2181	−	74.8560i	1.75852	−	3.04585i
$605$	−8.05316	+	10.6714i	−0.327407	+	0.433856i
$606$	−24.7348	+	11.3022i	−1.00478	+	0.459119i
$607$	20.2049	−	7.35397i	0.820090	−	0.298489i	0.102305	−	0.994753i	$-0.467378\pi$
$607$	20.2049	−	7.35397i	0.820090	−	0.298489i	0.717785	+	0.696265i	$0.245156\pi$
$608$	−1.85667	−	5.10117i	−0.0752981	−	0.206880i
$609$	−6.04607	+	2.31163i	−0.244999	+	0.0936722i
$610$	0.421762	+	0.318281i	0.0170767	+	0.0128868i
$611$	6.95505	+	4.01550i	0.281371	+	0.162450i
$612$	40.6597	+	73.0074i	1.64357	+	2.95115i
$613$	16.4661	−	9.50672i	0.665061	−	0.383973i	−0.129142	−	0.991626i	$-0.541222\pi$
$613$	16.4661	−	9.50672i	0.665061	−	0.383973i	0.794203	+	0.607653i	$0.207889\pi$
$614$	−57.3756	+	48.1438i	−2.31549	+	1.94293i
$615$	9.62583	−	15.1197i	0.388151	−	0.609684i
$616$	6.24163	−	25.7338i	0.251482	−	1.03684i
$617$	11.2361	+	9.42825i	0.452350	+	0.379567i	0.840307	−	0.542111i	$-0.182375\pi$
$617$	11.2361	+	9.42825i	0.452350	+	0.379567i	−0.387957	+	0.921678i	$0.626819\pi$
$618$	−0.115309	+	0.242373i	−0.00463841	+	0.00974969i
$619$	4.10716	−	11.2843i	0.165081	−	0.453556i	−0.829377	−	0.558689i	$-0.811305\pi$
$619$	4.10716	−	11.2843i	0.165081	−	0.453556i	0.994458	+	0.105133i	$0.0335268\pi$
$620$	−46.2023	+	43.0243i	−1.85553	+	1.72790i
$621$	9.31914	+	4.61151i	0.373964	+	0.185054i
$622$	54.3390			2.17880
$623$	0.292905	−	0.669363i	0.0117350	−	0.0268174i
$624$	8.59990	+	12.4862i	0.344271	+	0.499847i
$625$	−16.6765	−	18.6251i	−0.667059	−	0.745005i
$626$	−6.25167	+	35.4550i	−0.249867	+	1.41707i
$627$	10.5561	−	10.3942i	0.421570	−	0.415105i
$628$	25.1754	−	21.1246i	1.00461	−	0.842965i
$629$	36.5222	+	63.2584i	1.45624	+	2.52228i
$630$	36.5694	+	22.4615i	1.45696	+	0.894889i
$631$	−6.00126	+	10.3945i	−0.238907	+	0.413798i	−0.960401	−	0.278622i	$-0.910122\pi$
$631$	−6.00126	+	10.3945i	−0.238907	+	0.413798i	0.721494	+	0.692420i	$0.243456\pi$
$632$	−11.5948	−	65.7572i	−0.461215	−	2.61568i
$633$	−0.621225	+	6.51997i	−0.0246915	+	0.259145i
$634$	−37.4052	+	13.6144i	−1.48555	+	0.540695i
$635$	−1.68821	+	3.30760i	−0.0669945	+	0.131258i
$636$	3.75922	+	2.67576i	0.149063	+	0.106101i
$637$	−0.940556	−	19.7044i	−0.0372662	−	0.780717i
$638$	−3.82678	+	6.62817i	−0.151503	+	0.262412i
$639$	−33.9400	−	12.9506i	−1.34265	−	0.512316i
$640$	13.4280	−	43.8119i	0.530788	−	1.73182i
$641$	21.6357	+	25.7844i	0.854558	+	1.01842i	0.999580	+	0.0289939i	$0.00923034\pi$
$641$	21.6357	+	25.7844i	0.854558	+	1.01842i	−0.145022	+	0.989428i	$0.546325\pi$
$642$	−49.5448	−	13.6867i	−1.95538	−	0.540170i
$643$	−4.14026	+	23.4806i	−0.163276	+	0.925983i	0.787549	+	0.616252i	$0.211350\pi$
$643$	−4.14026	+	23.4806i	−0.163276	+	0.925983i	−0.950824	+	0.309730i	$0.899761\pi$
$644$	14.0546	−	14.7414i	0.553827	−	0.580894i
$645$	6.83216	−	7.46054i	0.269016	−	0.293758i
$646$	62.7995	+	22.8571i	2.47081	+	0.899302i
$647$			37.9377i			1.49148i	0.666235	+	0.745742i	$0.267905\pi$
$647$			37.9377i			1.49148i	−0.666235	+	0.745742i	$0.732095\pi$
$648$	29.9805	+	26.7783i	1.17775	+	1.05195i
$649$			23.3240i			0.915549i
$650$	−13.9017	+	31.1072i	−0.545271	+	1.22013i
$651$	33.6269	−	0.542161i	1.31794	−	0.0212490i
$652$	−22.8434	+	27.2237i	−0.894617	+	1.06616i
$653$	−1.60832	+	9.12124i	−0.0629385	+	0.356942i	0.937032	+	0.349244i	$0.113561\pi$
$653$	−1.60832	+	9.12124i	−0.0629385	+	0.356942i	−0.999970	+	0.00769797i	$0.997550\pi$
$654$	42.2639	+	11.6753i	1.65265	+	0.456541i
$655$	44.6108	+	5.50904i	1.74309	+	0.215256i
$656$	−7.18733	−	12.4488i	−0.280618	−	0.486045i
$657$	1.77528	+	2.18335i	0.0692604	+	0.0851807i
$658$	10.0982	−	15.1798i	0.393670	−	0.591768i
$659$	19.5497	−	3.44714i	0.761549	−	0.134282i	0.220631	−	0.975357i	$-0.429188\pi$
$659$	19.5497	−	3.44714i	0.761549	−	0.134282i	0.540918	+	0.841076i	$0.318077\pi$
$660$	33.1005	−	4.36798i	1.28843	−	0.170024i
$661$	−11.1795	−	30.7153i	−0.434831	−	1.19469i	−0.942814	−	0.333320i	$-0.891831\pi$
$661$	−11.1795	−	30.7153i	−0.434831	−	1.19469i	0.507983	−	0.861367i	$-0.330391\pi$
$662$	6.73616	−	2.45176i	0.261808	−	0.0952904i
$663$	35.1829	+	3.35223i	1.36639	+	0.130190i
$664$	−0.165194	+	0.0291281i	−0.00641075	+	0.00113039i
$665$	22.2834	−	3.65964i	0.864112	−	0.141915i
$666$	55.3273	+	47.9014i	2.14389	+	1.85614i
$667$	−2.44780	+	1.41324i	−0.0947794	+	0.0547209i
$668$	−46.0968	−	54.9361i	−1.78354	−	2.12554i
$669$	14.2302	−	14.0120i	0.550171	−	0.541734i
$670$	−7.48384	−	11.5417i	−0.289126	−	0.445894i
$671$	−0.167744	−	0.140754i	−0.00647568	−	0.00543374i
$672$	−5.59088	+	3.34922i	−0.215673	+	0.129199i
$673$	−2.94873	+	8.10156i	−0.113665	+	0.312292i	−0.983461	−	0.181119i	$-0.942028\pi$
$673$	−2.94873	+	8.10156i	−0.113665	+	0.312292i	0.869796	+	0.493411i	$0.164250\pi$
$674$		−	9.88390i		−	0.380714i
$675$	−4.69357	+	25.5533i	−0.180655	+	0.983546i
$676$	−19.4595			−0.748442
$677$	−12.6740	+	34.8215i	−0.487101	+	1.33830i	0.416194	+	0.909276i	$0.363364\pi$
$677$	−12.6740	+	34.8215i	−0.487101	+	1.33830i	−0.903294	+	0.429022i	$0.858858\pi$
$678$	−27.5715	+	57.9538i	−1.05888	+	2.22570i
$679$	15.7023	−	16.4697i	0.602601	−	0.632051i
$680$	39.3430	+	60.6753i	1.50873	+	2.32679i
$681$	−43.8685	+	11.3920i	−1.68104	+	0.436541i
$682$	30.4621	−	25.5608i	1.16646	−	0.978773i
$683$	−11.8779	−	20.5730i	−0.454493	−	0.787206i	0.544165	−	0.838978i	$-0.316846\pi$
$683$	−11.8779	−	20.5730i	−0.454493	−	0.787206i	−0.998659	+	0.0517722i	$0.983513\pi$
$684$	44.0485	+	0.680788i	1.68424	+	0.0260306i
$685$	5.47886	−	1.26088i	0.209337	−	0.0481757i
$686$	−44.7780	−	0.704007i	−1.70963	−	0.0268791i
$687$	1.32814	+	2.90664i	0.0506717	+	0.110895i
$688$	−2.77484	−	7.62382i	−0.105790	−	0.290655i
$689$	1.83380	−	0.667448i	0.0698621	−	0.0254277i
$690$	17.3158	+	7.16628i	0.659201	+	0.272816i
$691$	−38.3598	+	6.76387i	−1.45928	+	0.257310i	−0.846264	−	0.532763i	$-0.821154\pi$
$691$	−38.3598	+	6.76387i	−1.45928	+	0.257310i	−0.613013	+	0.790073i	$0.710042\pi$
$692$	−23.1425	−	13.3613i	−0.879745	−	0.507921i
$693$	−14.6544	−	10.0788i	−0.556673	−	0.382863i
$694$	29.1575	+	50.5024i	1.10681	+	1.91704i
$695$	2.46940	−	19.9966i	0.0936697	−	0.758514i
$696$	−10.5766	+	2.74658i	−0.400905	+	0.104109i
$697$	−32.9996	−	5.81871i	−1.24995	−	0.220399i
$698$	−31.4513	+	37.4823i	−1.19045	+	1.41872i
$699$	3.02850	−	6.36575i	0.114548	−	0.240775i
$700$	45.0545	+	23.6675i	1.70290	+	0.894548i
$701$			7.18864i			0.271511i	0.990742	+	0.135756i	$0.0433462\pi$
$701$			7.18864i			0.271511i	−0.990742	+	0.135756i	$0.956654\pi$
$702$	34.4056	−	8.36925i	1.29856	−	0.315877i
$703$	38.5070			1.45232
$704$	−7.39661	+	20.3220i	−0.278770	+	0.765915i
$705$	10.7762	+	2.38560i	0.405856	+	0.0898468i
$706$	−26.4377	+	31.5072i	−0.994997	+	1.18579i
$707$	16.6950	+	4.04932i	0.627882	+	0.152290i
$708$	−49.4212	+	48.6633i	−1.85736	+	1.82888i
$709$	−2.61921	+	2.19778i	−0.0983664	+	0.0825392i	−0.690645	−	0.723194i	$-0.742673\pi$
$709$	−2.61921	+	2.19778i	−0.0983664	+	0.0825392i	0.592278	+	0.805734i	$0.298229\pi$
$710$	−62.5988	−	19.1860i	−2.34929	−	0.720039i
$711$	−44.0414	−	8.46945i	−1.65168	−	0.317629i
$712$	0.616726	−	1.06820i	0.0231128	−	0.0400325i
$713$	14.4624	−	2.55012i	0.541622	−	0.0955026i
$714$	12.6568	−	79.2286i	0.473668	−	2.96506i
$715$	6.41927	−	12.5769i	0.240067	−	0.470349i
$716$	15.4416	+	42.4253i	0.577078	+	1.58551i
$717$	2.41574	−	3.39391i	0.0902174	−	0.126748i
$718$	60.5535	−	10.6772i	2.25984	−	0.398470i
$719$	17.4574	−	30.2371i	0.651050	−	1.12765i	−0.331818	−	0.943343i	$-0.607662\pi$
$719$	17.4574	−	30.2371i	0.651050	−	1.12765i	0.982868	−	0.184309i	$-0.0590047\pi$
$720$	16.4359	+	12.8067i	0.612531	+	0.477277i
$721$	0.151915	−	0.0753005i	0.00565763	−	0.00280434i
$722$	−8.20643	+	6.88601i	−0.305412	+	0.256271i
$723$	−2.72871	+	9.87773i	−0.101482	+	0.367357i
$724$	53.3999	+	9.41585i	1.98459	+	0.349937i
$725$	−5.07352	−	4.91311i	−0.188426	−	0.182468i
$726$	24.9617	−	1.98963i	0.926415	−	0.0738422i
$727$	41.7271	+	15.1874i	1.54757	+	0.563271i	0.967847	−	0.251540i	$-0.0809371\pi$
$727$	41.7271	+	15.1874i	1.54757	+	0.563271i	0.579727	+	0.814811i	$0.303159\pi$
$728$	2.11055	−	33.2354i	0.0782222	−	1.23179i
$729$	23.9832	−	12.4018i	0.888268	−	0.459326i
$730$	3.45636	+	3.71167i	0.127926	+	0.137375i
$731$	−17.7718	−	6.46841i	−0.657314	−	0.239243i
$732$	−0.0517382	−	0.649101i	−0.00191230	−	0.0239915i
$733$	−13.6247	−	11.4324i	−0.503238	−	0.422267i	0.355504	−	0.934675i	$-0.384309\pi$
$733$	−13.6247	−	11.4324i	−0.503238	−	0.422267i	−0.858742	+	0.512408i	$0.828754\pi$
$734$	−9.54149	+	54.1125i	−0.352183	+	1.99733i
$735$	−9.38364	−	25.4352i	−0.346121	−	0.938190i
$736$	−2.18006	+	1.82929i	−0.0803580	+	0.0674284i
$737$	2.85034	+	4.93694i	0.104994	+	0.181854i
$738$	−33.1480	+	5.31807i	−1.22019	+	0.195761i
$739$	−10.0882	+	17.4732i	−0.371099	+	0.642762i	−0.989735	−	0.142916i	$-0.954352\pi$
$739$	−10.0882	+	17.4732i	−0.371099	+	0.642762i	0.618636	+	0.785678i	$0.287686\pi$
$740$	69.2716	+	52.2755i	2.54648	+	1.92169i
$741$	10.8042	−	15.1789i	0.396901	−	0.557612i
$742$	−1.24835	−	4.25071i	−0.0458282	−	0.156049i
$743$	26.0534	−	9.48266i	0.955807	−	0.347885i	0.183418	−	0.983035i	$-0.441284\pi$
$743$	26.0534	−	9.48266i	0.955807	−	0.347885i	0.772389	+	0.635150i	$0.219062\pi$
$744$	56.5194	+	5.38519i	2.07210	+	0.197431i
$745$	−29.9217	−	22.5803i	−1.09625	−	0.827277i
$746$	−21.3604	−	12.3325i	−0.782061	−	0.451523i
$747$	−0.0212768	+	0.110640i	−0.000778476	+	0.00404810i
$748$	−31.2091	−	54.0557i	−1.14112	−	1.97647i
$749$	19.2531	+	26.1463i	0.703493	+	0.955367i
$750$	−5.35148	+	46.5192i	−0.195408	+	1.69864i
$751$	1.59015	−	9.01816i	0.0580252	−	0.329077i	−0.941953	−	0.335746i	$-0.891012\pi$
$751$	1.59015	−	9.01816i	0.0580252	−	0.329077i	0.999978	+	0.00666864i	$0.00212271\pi$
$752$	5.68973	−	6.78075i	0.207483	−	0.247269i
$753$	9.43845	+	13.7037i	0.343956	+	0.499389i
$754$	−3.29210	+	9.04496i	−0.119891	+	0.329398i
$755$	−34.2377	−	36.7667i	−1.24604	−	1.33808i
$756$	−9.21886	−	52.0795i	−0.335287	−	1.89411i
$757$		−	26.3766i		−	0.958675i	−0.877631	−	0.479338i	$-0.840877\pi$
$757$		−	26.3766i		−	0.958675i	0.877631	−	0.479338i	$-0.159123\pi$
$758$	47.0867	+	17.1381i	1.71026	+	0.622486i
$759$	−7.01315	−	3.33650i	−0.254561	−	0.121107i
$760$	38.0712	−	1.96866i	1.38099	−	0.0714109i
$761$	−2.18242	+	12.3771i	−0.0791128	+	0.448671i	0.919360	+	0.393418i	$0.128708\pi$
$761$	−2.18242	+	12.3771i	−0.0791128	+	0.448671i	−0.998472	+	0.0552527i	$0.982404\pi$
$762$	6.73228	−	1.74827i	0.243885	−	0.0633330i
$763$	−16.4237	−	22.3040i	−0.594579	−	0.807458i
$764$	−85.7031	+	49.4807i	−3.10063	+	1.79015i
$765$	47.4967	−	10.1604i	1.71725	−	0.367352i
$766$	70.7297	+	40.8358i	2.55557	+	1.47546i
$767$	5.09368	+	28.8877i	0.183922	+	1.04307i
$768$	−47.6572	+	21.7762i	−1.71968	+	0.785780i
$769$	14.5182	+	39.8884i	0.523539	+	1.43841i	0.866555	+	0.499082i	$0.166329\pi$
$769$	14.5182	+	39.8884i	0.523539	+	1.43841i	−0.343016	+	0.939330i	$0.611448\pi$
$770$	−27.5708	−	16.3531i	−0.993584	−	0.589325i
$771$	11.9658	+	26.1872i	0.430939	+	0.943110i
$772$	−63.4668	+	11.1909i	−2.28422	+	0.402770i
$773$	−9.29725	−	5.36777i	−0.334399	−	0.193065i	0.323393	−	0.946265i	$-0.395176\pi$
$773$	−9.29725	−	5.36777i	−0.334399	−	0.193065i	−0.657792	+	0.753199i	$0.728510\pi$
$774$	−18.9458	−	0.292816i	−0.680993	−	0.0105250i
$775$	16.0400	+	33.0034i	0.576173	+	1.18552i
$776$	29.4279	−	24.6929i	1.05640	−	0.886424i
$777$	−8.76065	−	45.3923i	−0.314286	−	1.62844i
$778$	57.8603	+	10.2023i	2.07439	+	0.365771i
$779$	−11.3547	+	13.5320i	−0.406825	+	0.484835i
$780$	40.0423	−	12.6386i	1.43374	−	0.452536i
$781$	25.4973	+	9.28026i	0.912365	+	0.332074i
$782$		−	35.0348i		−	1.25284i
$783$	−0.808995	+	7.29487i	−0.0289111	+	0.260697i
$784$	−21.5680	−	2.75036i	−0.770285	−	0.0982271i
$785$	−7.45137	−	17.5884i	−0.265951	−	0.627755i
$786$	−47.7565	−	69.3375i	−1.70342	−	2.47319i
$787$	−10.2350	−	8.58818i	−0.364838	−	0.306135i	0.441878	−	0.897075i	$-0.354313\pi$
$787$	−10.2350	−	8.58818i	−0.364838	−	0.306135i	−0.806716	+	0.590940i	$0.798757\pi$
$788$	−11.7392	+	66.5765i	−0.418193	+	2.37169i
$789$	34.4886	−	33.9596i	1.22782	−	1.20899i
$790$	−80.2223	−	9.90674i	−2.85418	−	0.352466i
$791$	36.3244	−	18.0051i	1.29155	−	0.640187i
$792$	−22.6998	−	19.6531i	−0.806602	−	0.698343i
$793$	−0.238496	−	0.137696i	−0.00846924	−	0.00488972i
$794$	−9.77201	−	55.4199i	−0.346796	−	1.96678i
$795$	2.12724	−	1.63332i	0.0754456	−	0.0579278i
$796$	−34.4734	−	94.7150i	−1.22188	−	3.35708i
$797$	−3.56408	−	9.79224i	−0.126246	−	0.346859i	0.860427	−	0.509574i	$-0.170197\pi$
$797$	−3.56408	−	9.79224i	−0.126246	−	0.346859i	−0.986673	+	0.162715i	$0.947975\pi$
$798$	−32.8352	−	26.6619i	−1.16235	−	0.943822i
$799$	−3.58306	−	20.3205i	−0.126759	−	0.718888i
$800$	−5.88971	−	3.98460i	−0.208233	−	0.140877i
$801$	−0.522660	−	0.642800i	−0.0184673	−	0.0227122i
$802$	−67.3296	+	38.8728i	−2.37749	+	1.37265i
$803$	−1.35106	−	1.61013i	−0.0476778	−	0.0568202i
$804$	−4.51390	+	16.3400i	−0.159193	+	0.576268i
$805$	−5.79825	−	10.3211i	−0.204361	−	0.363773i
$806$	32.1464	−	38.3105i	1.13231	−	1.34943i
$807$	−35.4541	+	2.82596i	−1.24804	+	0.0994784i
$808$	27.2523	+	9.91903i	0.958733	+	0.348950i
$809$		−	11.8876i		−	0.417946i	−0.977921	−	0.208973i	$-0.932988\pi$
$809$		−	11.8876i		−	0.417946i	0.977921	−	0.208973i	$-0.0670121\pi$
$810$	41.6293	−	25.2009i	1.46270	−	0.885469i
$811$			0.481738i			0.0169161i	0.999964	+	0.00845806i	$0.00269232\pi$
$811$			0.481738i			0.0169161i	−0.999964	+	0.00845806i	$0.997308\pi$
$812$	13.1714	+	5.76363i	0.462225	+	0.202264i
$813$	−0.839746	−	10.5353i	−0.0294512	−	0.369490i
$814$	−41.8736	−	35.1362i	−1.46767	−	1.23152i
$815$	11.2379	+	17.3313i	0.393647	+	0.607087i
$816$	10.3724	−	37.5473i	0.363106	−	1.31442i
$817$	−7.63752	+	6.40864i	−0.267203	+	0.224210i
$818$	−21.8162	+	12.5956i	−0.762784	+	0.440393i
$819$	−20.3511	−	9.28268i	−0.711123	−	0.324363i
$820$	−38.7969	+	8.92854i	−1.35485	+	0.311798i
$821$	−23.0072	+	4.05678i	−0.802955	+	0.141583i	−0.560041	−	0.828465i	$-0.689215\pi$
$821$	−23.0072	+	4.05678i	−0.802955	+	0.141583i	−0.242914	+	0.970048i	$0.578103\pi$
$822$	−8.57904	−	6.10644i	−0.299228	−	0.212987i
$823$	0.497129	+	1.36585i	0.0173288	+	0.0476106i	0.948055	−	0.318105i	$-0.103046\pi$
$823$	0.497129	+	1.36585i	0.0173288	+	0.0476106i	−0.930727	+	0.365716i	$0.880824\pi$
$824$	0.268974	−	0.0978985i	0.00937015	−	0.00341046i
$825$	3.21040	−	19.1384i	0.111772	−	0.666315i
$826$	66.1813	−	7.38415i	2.30274	−	0.256928i
$827$	−20.9368	+	36.2636i	−0.728043	+	1.26101i	0.229666	+	0.973270i	$0.426237\pi$
$827$	−20.9368	+	36.2636i	−0.728043	+	1.26101i	−0.957709	+	0.287738i	$0.907097\pi$
$828$	−7.56255	−	21.8214i	−0.262817	−	0.758347i
$829$	−47.0345	+	27.1554i	−1.63358	+	0.943146i	−0.650599	+	0.759421i	$0.725482\pi$
$829$	−47.0345	+	27.1554i	−1.63358	+	0.943146i	−0.982978	+	0.183725i	$0.941184\pi$
$830$	−0.0248875	+	0.201533i	−0.000863857	+	0.00699530i
$831$	−18.3542	−	18.6401i	−0.636700	−	0.646617i
$832$	−4.72290	+	26.7849i	−0.163737	+	0.928600i
$833$	−37.2287	+	34.3932i	−1.28990	+	1.19165i
$834$	−31.0802	+	21.4066i	−1.07622	+	0.741250i
$835$	−38.3802	+	16.2599i	−1.32820	+	0.562697i
$836$	−32.9051			−1.13805
$837$	16.9130	−	34.1785i	0.584599	−	1.18138i
$838$	−26.7713			−0.924799
$839$	−22.9949	−	8.36944i	−0.793871	−	0.288945i	−0.0869266	−	0.996215i	$-0.527705\pi$
$839$	−22.9949	−	8.36944i	−0.793871	−	0.288945i	−0.706944	+	0.707269i	$0.749927\pi$
$840$	−10.9822	−	44.4307i	−0.378921	−	1.53301i
$841$	20.6869	+	17.3584i	0.713341	+	0.598564i
$842$	12.5569	−	71.2138i	0.432740	−	2.45419i
$843$	−41.9686	+	10.8986i	−1.44548	+	0.375367i
$844$	11.1439	−	9.35084i	0.383589	−	0.321869i
$845$	−3.31439	+	10.8140i	−0.114018	+	0.372011i
$846$	−10.0586	−	18.0609i	−0.345821	−	0.620946i
$847$	−13.1705	−	8.76157i	−0.452542	−	0.301051i
$848$	−0.373500	−	2.11822i	−0.0128260	−	0.0727401i
$849$	26.6610	−	12.1823i	0.915002	−	0.418095i
$850$	84.1839	−	24.0126i	2.88748	−	0.823624i
$851$	−6.90433	−	18.9695i	−0.236677	−	0.650266i
$852$	33.5337	+	73.3884i	1.14884	+	2.51425i
$853$	5.44319	+	30.8698i	0.186371	+	1.05696i	0.924181	+	0.381955i	$0.124749\pi$
$853$	5.44319	+	30.8698i	0.186371	+	1.05696i	−0.737810	+	0.675009i	$0.764140\pi$
$854$	−0.346279	+	0.520530i	−0.0118494	+	0.0178122i
$855$	7.88077	−	24.3625i	0.269517	−	0.833180i
$856$	27.4077	+	47.4715i	0.936774	+	1.62254i
$857$	−3.53365	−	4.21124i	−0.120707	−	0.143853i	0.702307	−	0.711875i	$-0.252154\pi$
$857$	−3.53365	−	4.21124i	−0.120707	−	0.143853i	−0.823014	+	0.568021i	$0.807709\pi$
$858$	−25.5989	+	6.64764i	−0.873934	+	0.226947i
$859$	10.8622	+	1.91530i	0.370614	+	0.0653492i	0.355853	−	0.934542i	$-0.384190\pi$
$859$	10.8622	+	1.91530i	0.370614	+	0.0653492i	0.0147606	+	0.999891i	$0.495301\pi$
$860$	−22.4395	+	1.16035i	−0.765181	+	0.0395675i
$861$	18.5349	+	10.3064i	0.631669	+	0.351240i
$862$	−14.1149	+	38.7804i	−0.480756	+	1.32087i
$863$	30.6107			1.04200			0.521001	−	0.853556i	$-0.325559\pi$
$863$	30.6107			1.04200			0.521001	+	0.853556i	$0.325559\pi$
$864$	0.473261	+	7.37476i	0.0161007	+	0.250894i
$865$	−11.3668	+	10.5849i	−0.386482	+	0.359898i
$866$	−66.8062	−	24.3155i	−2.27017	−	0.826274i
$867$	−34.8050	−	50.5333i	−1.18204	−	1.71620i
$868$	−54.0652	−	51.5460i	−1.83509	−	1.74959i
$869$	32.9897	+	5.81698i	1.11910	+	0.197328i
$870$	−0.573002	+	13.2160i	−0.0194266	+	0.448063i
$871$	4.60842	+	5.49210i	0.156150	+	0.186093i
$872$	−23.3799	−	40.4952i	−0.791744	−	1.37134i
$873$	−8.44919	−	24.3798i	−0.285962	−	0.825131i
$874$	−15.9950	−	9.23470i	−0.541038	−	0.312368i
$875$	20.8262	−	21.0064i	0.704054	−	0.710146i
$876$	0.592846	−	6.22212i	0.0200304	−	0.210226i
$877$	−16.7324	−	45.9718i	−0.565012	−	1.55236i	−0.812194	−	0.583388i	$-0.801727\pi$
$877$	−16.7324	−	45.9718i	−0.565012	−	1.55236i	0.247182	−	0.968969i	$-0.420495\pi$
$878$	22.3369	+	61.3701i	0.753834	+	2.07114i
$879$	19.9709	−	28.0575i	0.673602	−	0.946355i
$880$	−12.4229	−	9.37486i	−0.418775	−	0.316026i
$881$	1.20513	−	2.08734i	0.0406018	−	0.0703244i	−0.845010	−	0.534750i	$-0.820406\pi$
$881$	1.20513	−	2.08734i	0.0406018	−	0.0703244i	0.885612	+	0.464425i	$0.153739\pi$
$882$	−23.9590	+	44.7722i	−0.806741	+	1.50756i
$883$	9.55430	−	5.51618i	0.321528	−	0.185634i	−0.330546	−	0.943790i	$-0.607233\pi$
$883$	9.55430	−	5.51618i	0.321528	−	0.185634i	0.652073	+	0.758156i	$0.273899\pi$
$884$	−50.4587	−	60.1343i	−1.69711	−	2.02254i
$885$	18.6254	+	35.7526i	0.626087	+	1.20181i
$886$	6.83610	−	38.7695i	0.229663	−	1.30249i
$887$	18.4652	−	22.0060i	0.620001	−	0.738888i	−0.361070	−	0.932539i	$-0.617588\pi$
$887$	18.4652	−	22.0060i	0.620001	−	0.738888i	0.981071	+	0.193651i	$0.0620328\pi$
$888$	−6.20104	−	77.7975i	−0.208093	−	2.61071i
$889$	−4.02538	−	1.76145i	−0.135007	−	0.0590773i
$890$	−1.01759	−	1.09275i	−0.0341096	−	0.0366291i
$891$	−17.7685	+	9.53902i	−0.595268	+	0.319569i
$892$	−44.3579			−1.48521
$893$	−10.2217	−	3.72038i	−0.342055	−	0.124498i
$894$	5.57874	+	69.9901i	0.186581	+	2.34082i
$895$	26.2065	−	1.35514i	0.875987	−	0.0452972i
$896$	52.6914	+	12.7801i	1.76030	+	0.426953i
$897$	−9.41470	−	2.60080i	−0.314348	−	0.0868381i
$898$	16.8594	+	20.0923i	0.562606	+	0.670487i
$899$	5.18315	+	8.97748i	0.172868	+	0.299416i
$900$	47.2505	−	33.1280i	1.57502	−	1.10427i
$901$	−4.34220	−	2.50697i	−0.144660	−	0.0835193i
$902$	24.6949	−	4.35438i	0.822251	−	0.144985i
$903$	9.29214	+	7.54514i	0.309223	+	0.251087i
$904$	64.3143	−	23.4085i	2.13906	−	0.778554i
$905$	14.3278	−	28.0715i	0.476271	−	0.933128i
$906$	−8.92550	+	93.6762i	−0.296530	+	3.11218i
$907$	−4.90265	+	0.864469i	−0.162790	+	0.0287042i	−0.254449	−	0.967086i	$-0.581894\pi$
$907$	−4.90265	+	0.864469i	−0.162790	+	0.0287042i	0.0916592	+	0.995790i	$0.470783\pi$
$908$	87.1825	+	50.3348i	2.89325	+	1.67042i
$909$	12.7501	−	14.7267i	0.422895	−	0.488454i
$910$	−37.7188	−	14.2328i	−1.25037	−	0.471813i
$911$	−29.2746	−	34.8881i	−0.969911	−	1.15589i	−0.987749	−	0.156053i	$-0.950123\pi$
$911$	−29.2746	−	34.8881i	−0.969911	−	1.15589i	0.0178381	−	0.999841i	$-0.494322\pi$
$912$	−14.4080	−	14.6324i	−0.477097	−	0.484527i
$913$	0.0146133	−	0.0828760i	0.000483629	−	0.00274280i
$914$	14.8451	−	17.6917i	0.491032	−	0.585190i
$915$	−0.369528	−	0.0818047i	−0.0122162	−	0.00270438i
$916$	2.42769	−	6.67001i	0.0802130	−	0.220383i
$917$	−3.37063	+	53.0783i	−0.111308	+	1.75280i
$918$	−73.2935	−	53.8950i	−2.41905	−	1.77880i
$919$	−44.5852			−1.47073			−0.735366	−	0.677671i	$-0.762990\pi$
$919$	−44.5852			−1.47073			−0.735366	+	0.677671i	$0.762990\pi$
$920$	−7.79601	−	18.4018i	−0.257027	−	0.606691i
$921$	23.0481	−	48.4460i	0.759462	−	1.59635i
$922$	−17.3189	−	14.5323i	−0.570367	−	0.478595i
$923$	33.6061	+	5.92565i	1.10616	+	0.195045i
$924$	7.48617	+	38.7887i	0.246277	+	1.27606i
$925$	40.8489	−	29.5917i	1.34310	−	0.972968i
$926$	−8.00990	+	4.62452i	−0.263222	+	0.151971i
$927$	0.00297104	−	0.192233i	9.75818e−5	−	0.00631376i
$928$	−1.73972	−	1.00443i	−0.0571091	−	0.0329719i
$929$	6.05671	+	34.3493i	0.198714	+	1.12696i	0.907029	+	0.421068i	$0.138345\pi$
$929$	6.05671	+	34.3493i	0.198714	+	1.12696i	−0.708315	+	0.705897i	$0.750544\pi$
$930$	26.2828	−	63.5068i	0.861847	−	2.08247i
$931$	5.88906	+	26.0622i	0.193006	+	0.854153i
$932$	−14.7135	+	5.35527i	−0.481956	+	0.175418i
$933$	−35.4019	+	16.1763i	−1.15901	+	0.529589i
$934$	23.1396	−	4.08014i	0.757152	−	0.133506i
$935$	−35.3552	+	8.13649i	−1.15624	+	0.266092i
$936$	−32.4066	−	19.3838i	−1.05924	−	0.633578i
$937$	−11.1273	−	19.2731i	−0.363513	−	0.629623i	0.625023	−	0.780606i	$-0.285089\pi$
$937$	−11.1273	−	19.2731i	−0.363513	−	0.629623i	−0.988536	+	0.150983i	$0.951756\pi$
$938$	13.1060	−	9.65075i	0.427927	−	0.315108i
$939$	−6.48172	−	24.9600i	−0.211523	−	0.814539i
$940$	−13.3375	−	20.5692i	−0.435020	−	0.670895i
$941$	3.11118	+	2.61059i	0.101422	+	0.0851028i	0.692088	−	0.721813i	$-0.256691\pi$
$941$	3.11118	+	2.61059i	0.101422	+	0.0851028i	−0.590667	+	0.806915i	$0.701135\pi$
$942$	−15.3706	+	32.3082i	−0.500801	+	1.05266i
$943$	8.70212	+	3.16731i	0.283380	+	0.103142i
$944$	32.3308			1.05228
$945$	−30.5116	−	3.74724i	−0.992543	−	0.121898i
$946$	14.1529			0.460151
$947$	−12.3683	−	4.50169i	−0.401915	−	0.146285i	0.133150	−	0.991096i	$-0.457491\pi$
$947$	−12.3683	−	4.50169i	−0.401915	−	0.146285i	−0.535065	+	0.844811i	$0.679713\pi$
$948$	56.5042	+	82.0384i	1.83517	+	2.66448i
$949$	−2.02497	−	1.69915i	−0.0657332	−	0.0551567i
$950$	11.2269	−	44.7631i	0.364248	−	1.45231i
$951$	20.3166	−	20.0050i	0.658810	−	0.648706i
$952$	−68.8993	+	50.7346i	−2.23304	+	1.64432i
$953$	23.2846	+	40.3302i	0.754264	+	1.30642i	0.945740	+	0.324926i	$0.105339\pi$
$953$	23.2846	+	40.3302i	0.754264	+	1.30642i	−0.191476	+	0.981497i	$0.561327\pi$
$954$	−4.93302	−	0.948652i	−0.159712	−	0.0307137i
$955$	12.9001	+	56.0543i	0.417437	+	1.81387i
$956$	−9.11238	+	1.60676i	−0.294715	+	0.0519663i
$957$	0.519988	−	5.45746i	0.0168088	−	0.176414i
$958$	65.6366	−	23.8898i	2.12062	−	0.771844i
$959$	1.87443	+	6.38258i	0.0605286	+	0.206104i
$960$	4.89016	+	37.0575i	0.157829	+	1.19603i
$961$	−3.96962	−	22.5128i	−0.128052	−	0.726220i
$962$	−59.5354	−	34.3728i	−1.91950	−	1.10822i
$963$	36.3529	−	5.83225i	1.17145	−	0.187942i
$964$	19.7121	−	11.3808i	0.634883	−	0.366550i
$965$	−4.59085	+	37.1756i	−0.147785	+	1.19672i
$966$	−7.24694	+	20.9559i	−0.233166	+	0.674246i
$967$	1.86066	+	0.328084i	0.0598347	+	0.0105505i	0.203485	−	0.979078i	$-0.434773\pi$
$967$	1.86066	+	0.328084i	0.0598347	+	0.0105505i	−0.143651	+	0.989628i	$0.545884\pi$
$968$	−20.4568	−	17.1653i	−0.657506	−	0.551713i
$969$	−47.7183	+	3.80350i	−1.53293	+	0.122186i
$970$	−18.1409	−	42.8202i	−0.582471	−	1.37487i
$971$	−15.4395			−0.495476			−0.247738	−	0.968827i	$-0.579687\pi$
$971$	−15.4395			−0.495476			−0.247738	+	0.968827i	$0.579687\pi$
$972$	−57.2844	−	17.7475i	−1.83740	−	0.569250i
$973$	23.7921	+	1.51087i	0.762739	+	0.0484363i
$974$	−17.0085	+	46.7304i	−0.544987	+	1.49734i
$975$	−0.203401	−	24.4048i	−0.00651405	−	0.781579i
$976$	−0.195107	+	0.232519i	−0.00624522	+	0.00744276i
$977$	10.5099	−	59.6045i	0.336241	−	1.90692i	−0.0783786	−	0.996924i	$-0.524974\pi$
$977$	10.5099	−	59.6045i	0.336241	−	1.90692i	0.414620	−	0.909995i	$-0.363915\pi$
$978$	10.3020	−	37.2924i	0.329420	−	1.19248i
$979$	0.397764	+	0.474037i	0.0127126	+	0.0151503i
$980$	−24.7869	+	54.8789i	−0.791788	+	1.75304i
$981$	−31.0106	+	4.97516i	−0.990091	+	0.158845i
$982$	−10.9656	−	6.33102i	−0.349928	−	0.202031i
$983$	−18.7429	+	3.30488i	−0.597806	+	0.105409i	−0.464360	−	0.885647i	$-0.653715\pi$
$983$	−18.7429	+	3.30488i	−0.597806	+	0.105409i	−0.133446	+	0.991056i	$0.542604\pi$
$984$	29.1679	+	20.7613i	0.929839	+	0.661846i
$985$	34.9982	+	17.8632i	1.11513	+	0.569167i
$986$	23.2392	−	8.45836i	0.740085	−	0.269369i
$987$	−2.06010	+	12.8958i	−0.0655737	+	0.410477i
$988$	−40.7542	+	7.18607i	−1.29656	+	0.228619i
$989$	4.52647	+	2.61336i	0.143933	+	0.0830999i
$990$	−30.7996	+	19.3016i	−0.978876	+	0.613445i
$991$	0.604174	+	1.04646i	0.0191922	+	0.0332419i	0.875462	−	0.483287i	$-0.160557\pi$
$991$	0.604174	+	1.04646i	0.0191922	+	0.0332419i	−0.856270	+	0.516529i	$0.827224\pi$
$992$	6.70903	+	7.99551i	0.213012	+	0.253858i
$993$	−3.65874	+	3.60263i	−0.116106	+	0.114326i
$994$	18.2603	−	75.2859i	0.579181	−	2.38792i
$995$	−58.5062	+	3.02535i	−1.85477	+	0.0959102i
$996$	0.206095	−	0.141949i	0.00653036	−	0.00449781i
$997$	−8.41912	−	3.06431i	−0.266636	−	0.0970477i	0.205242	−	0.978711i	$-0.434202\pi$
$997$	−8.41912	−	3.06431i	−0.266636	−	0.0970477i	−0.471879	+	0.881664i	$0.656424\pi$
$998$	−53.8301			−1.70396
$999$	−50.3056	−	14.7373i	−1.59160	−	0.466266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.123	yes	816
5.4	even	2	inner	945.2.cs.b.104.14	yes	816
7.6	odd	2	inner	945.2.cs.b.104.124	yes	816
27.20	odd	18	inner	945.2.cs.b.209.13	yes	816
35.34	odd	2	inner	945.2.cs.b.104.13	✓	816
135.74	odd	18	inner	945.2.cs.b.209.124	yes	816
189.20	even	18	inner	945.2.cs.b.209.14	yes	816
945.209	even	18	inner	945.2.cs.b.209.123	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.13	✓	816	35.34	odd	2	inner
945.2.cs.b.104.14	yes	816	5.4	even	2	inner
945.2.cs.b.104.123	yes	816	1.1	even	1	trivial
945.2.cs.b.104.124	yes	816	7.6	odd	2	inner
945.2.cs.b.209.13	yes	816	27.20	odd	18	inner
945.2.cs.b.209.14	yes	816	189.20	even	18	inner
945.2.cs.b.209.123	yes	816	945.209	even	18	inner
945.2.cs.b.209.124	yes	816	135.74	odd	18	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27225 + 0.827033i) q^{2} +(-1.72657 + 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(1.87617 - 1.21654i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(1.56879 + 2.13047i) q^{7} +(2.23324 + 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +O(q^{10})\)	\(q+(2.27225 + 0.827033i) q^{2} +(-1.72657 + 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(1.87617 - 1.21654i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(1.56879 + 2.13047i) q^{7} +(2.23324 + 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +(5.26926 - 1.21264i) q^{10} +(-2.20675 + 0.389110i) q^{11} +(-5.42865 - 3.86404i) q^{12} +(-2.64817 + 0.963854i) q^{13} +(1.80272 + 6.13841i) q^{14} +(-3.07193 + 2.35866i) q^{15} +(0.539367 + 3.05890i) q^{16} +(6.27053 + 3.62029i) q^{17} +(7.12372 + 1.36994i) q^{18} +(3.30565 - 1.90852i) q^{19} +(8.53757 + 1.05431i) q^{20} +(-3.00183 - 3.46251i) q^{21} +(-5.33610 - 0.940899i) q^{22} +(-1.53289 - 1.28624i) q^{23} +(-4.38819 - 6.37121i) q^{24} +(2.04004 - 4.56489i) q^{25} -6.81445 q^{26} +(-5.04892 + 1.22816i) q^{27} +(-0.645068 + 10.1581i) q^{28} +(0.483105 - 1.32732i) q^{29} +(-8.93089 + 2.81888i) q^{30} +(-4.71738 + 5.62196i) q^{31} +(0.246961 - 1.40059i) q^{32} +(3.75657 - 0.975522i) q^{33} +(11.2541 + 13.4121i) q^{34} +(5.53513 + 2.08862i) q^{35} +(9.90474 + 5.92445i) q^{36} +(8.73664 + 5.04410i) q^{37} +(9.08968 - 1.60276i) q^{38} +(4.43961 - 2.02861i) q^{39} +(8.89565 + 4.54036i) q^{40} +(-4.34880 + 1.58283i) q^{41} +(-3.95731 - 10.3503i) q^{42} +(-2.57232 + 0.453569i) q^{43} +(-7.46566 - 4.31030i) q^{44} +(4.97931 - 4.49516i) q^{45} +(-2.41934 - 4.19042i) q^{46} +(-1.83180 - 2.18305i) q^{47} +(-1.35223 - 5.20719i) q^{48} +(-2.07779 + 6.68452i) q^{49} +(8.41080 - 8.68541i) q^{50} +(-11.3248 - 5.38774i) q^{51} +(-10.1878 - 3.70806i) q^{52} -0.692478 q^{53} +(-12.4882 - 1.38493i) q^{54} +(-3.66687 + 3.41465i) q^{55} +(-4.73736 + 10.8261i) q^{56} +(-5.44480 + 3.75012i) q^{57} +(2.19548 - 2.61647i) q^{58} +(1.80747 - 10.2507i) q^{59} +(-14.8858 - 0.645402i) q^{60} +(0.0628143 + 0.0748592i) q^{61} +(-15.3686 + 8.87309i) q^{62} +(5.65940 + 5.56518i) q^{63} +(4.82558 - 8.35815i) q^{64} +(-3.79584 + 5.02997i) q^{65} +(9.34267 + 0.890173i) q^{66} +(-0.870116 - 2.39062i) q^{67} +(9.52710 + 26.1755i) q^{68} +(2.82366 + 2.00984i) q^{69} +(10.8499 + 9.32361i) q^{70} +(-10.4867 - 6.05448i) q^{71} +(8.45335 + 10.3965i) q^{72} +(0.469002 + 0.812335i) q^{73} +(15.6802 + 18.6870i) q^{74} +(-2.89406 + 8.16238i) q^{75} +(14.4615 + 2.54995i) q^{76} +(-4.29092 - 4.09098i) q^{77} +(11.7656 - 0.937811i) q^{78} +(-14.0479 - 5.11302i) q^{79} +(4.73324 + 5.08286i) q^{80} +(8.54832 - 2.81535i) q^{81} -11.1906 q^{82} +(-0.0128448 + 0.0352908i) q^{83} +(-0.284204 - 17.6274i) q^{84} +(16.1688 - 0.836089i) q^{85} +(-6.22007 - 1.09677i) q^{86} +(-0.651450 + 2.35820i) q^{87} +(-6.43332 - 7.66694i) q^{88} +(-0.138079 - 0.239159i) q^{89} +(15.0319 - 6.09608i) q^{90} +(-6.20788 - 4.12975i) q^{91} +(-1.33679 - 7.58129i) q^{92} +(7.37122 - 10.3559i) q^{93} +(-2.35685 - 6.47540i) q^{94} +(3.88017 - 7.60217i) q^{95} +(-0.233647 + 2.45220i) q^{96} +(-1.49351 - 8.47013i) q^{97} +(-10.2496 + 13.4705i) q^{98} +(-6.35175 + 2.20129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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