LMFDB - Embedded newform 847.2.f.x.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$-1.38112 + 1.00344i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.x.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38112 + 1.00344i) q^{2} +(0.708129 + 2.17940i) q^{3} +(0.282562 - 0.869638i) q^{4} +(-3.28976 - 2.39015i) q^{5} +(-3.16491 - 2.29944i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +(-1.82128 + 1.32323i) q^{9} +O(q^{10})$	\(q+(-1.38112 + 1.00344i) q^{2} +(0.708129 + 2.17940i) q^{3} +(0.282562 - 0.869638i) q^{4} +(-3.28976 - 2.39015i) q^{5} +(-3.16491 - 2.29944i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +(-1.82128 + 1.32323i) q^{9} +6.94194 q^{10} +2.09538 q^{12} +(2.65189 - 1.92671i) q^{13} +(-0.527541 - 1.62360i) q^{14} +(2.87952 - 8.86224i) q^{15} +(4.03916 + 2.93462i) q^{16} +(-1.06862 - 0.776394i) q^{17} +(1.18761 - 3.65509i) q^{18} +(-0.668017 - 2.05594i) q^{19} +(-3.00813 + 2.18553i) q^{20} -2.29155 q^{21} -1.86611 q^{23} +(3.43586 - 2.49630i) q^{24} +(3.56462 + 10.9708i) q^{25} +(-1.72924 + 5.32205i) q^{26} +(1.38817 + 1.00856i) q^{27} +(0.739758 + 0.537466i) q^{28} +(0.0754316 - 0.232155i) q^{29} +(4.91579 + 15.1292i) q^{30} +(5.55785 - 4.03801i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(3.28976 - 2.39015i) q^{35} +(0.636110 + 1.95775i) q^{36} +(0.0789907 - 0.243108i) q^{37} +(2.98563 + 2.16919i) q^{38} +(6.07696 + 4.41517i) q^{39} +(-2.32882 + 7.16738i) q^{40} +(1.77139 + 5.45177i) q^{41} +(3.16491 - 2.29944i) q^{42} +8.01781 q^{43} +9.15429 q^{45} +(2.57733 - 1.87254i) q^{46} +(-1.25698 - 3.86859i) q^{47} +(-3.53546 + 10.8810i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-15.9317 - 11.5751i) q^{50} +(0.935354 - 2.87873i) q^{51} +(-0.926218 - 2.85060i) q^{52} +(4.04982 - 2.94237i) q^{53} -2.92926 q^{54} +1.85331 q^{56} +(4.00768 - 2.91175i) q^{57} +(0.128774 + 0.396325i) q^{58} +(-0.303947 + 0.935452i) q^{59} +(-6.89329 - 5.00827i) q^{60} +(1.49402 + 1.08547i) q^{61} +(-3.62414 + 11.1540i) q^{62} +(-0.695665 - 2.14104i) q^{63} +(-1.42591 + 1.03598i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(-0.977133 + 0.709928i) q^{68} +(-1.32145 - 4.06700i) q^{69} +(-2.14518 + 6.60218i) q^{70} +(-5.23953 - 3.80674i) q^{71} +(3.37538 + 2.45236i) q^{72} +(2.98252 - 9.17926i) q^{73} +(0.134850 + 0.415025i) q^{74} +(-21.3855 + 15.5375i) q^{75} -1.97668 q^{76} -12.8234 q^{78} +(-4.47750 + 3.25310i) q^{79} +(-6.27368 - 19.3084i) q^{80} +(-3.30205 + 10.1627i) q^{81} +(-7.91704 - 5.75206i) q^{82} +(1.67485 + 1.21685i) q^{83} +(-0.647507 + 1.99282i) q^{84} +(1.65979 + 5.10831i) q^{85} +(-11.0736 + 8.04542i) q^{86} +0.559372 q^{87} +16.6306 q^{89} +(-12.6432 + 9.18581i) q^{90} +(1.01293 + 3.11749i) q^{91} +(-0.527294 + 1.62284i) q^{92} +(12.7361 + 9.25333i) q^{93} +(5.61795 + 4.08168i) q^{94} +(-2.71640 + 8.36023i) q^{95} +(-3.41082 - 10.4974i) q^{96} +(2.09179 - 1.51977i) q^{97} +1.70716 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.38112	+	1.00344i	−0.976600	+	0.709541i	−0.956946	−	0.290266i	$-0.906256\pi$
$2$	−1.38112	+	1.00344i	−0.976600	+	0.709541i	−0.0196536	+	0.999807i	$0.506256\pi$
$3$	0.708129	+	2.17940i	0.408839	+	1.25828i	0.917647	+	0.397396i	$0.130086\pi$
$3$	0.708129	+	2.17940i	0.408839	+	1.25828i	−0.508809	+	0.860880i	$0.669914\pi$
$4$	0.282562	−	0.869638i	0.141281	−	0.434819i
$5$	−3.28976	−	2.39015i	−1.47123	−	1.06891i	−0.980256	−	0.197732i	$-0.936642\pi$
$5$	−3.28976	−	2.39015i	−1.47123	−	1.06891i	−0.490971	−	0.871176i	$-0.663358\pi$
$6$	−3.16491	−	2.29944i	−1.29207	−	0.938744i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.572703	−	1.76260i	−0.202481	−	0.623173i
$9$	−1.82128	+	1.32323i	−0.607092	+	0.441078i
$10$	6.94194			2.19523
$11$		0			0
$11$		0			0
$12$	2.09538			0.604883
$13$	2.65189	−	1.92671i	0.735503	−	0.534374i	−0.155796	−	0.987789i	$-0.549794\pi$
$13$	2.65189	−	1.92671i	0.735503	−	0.534374i	0.891300	+	0.453415i	$0.149794\pi$
$14$	−0.527541	−	1.62360i	−0.140991	−	0.433927i
$15$	2.87952	−	8.86224i	0.743488	−	2.28822i
$16$	4.03916	+	2.93462i	1.00979	+	0.733655i
$17$	−1.06862	−	0.776394i	−0.259177	−	0.188303i	0.450607	−	0.892722i	$-0.351208\pi$
$17$	−1.06862	−	0.776394i	−0.259177	−	0.188303i	−0.709784	+	0.704419i	$0.751208\pi$
$18$	1.18761	−	3.65509i	0.279923	−	0.861513i
$19$	−0.668017	−	2.05594i	−0.153254	−	0.471666i	0.844726	−	0.535199i	$-0.179763\pi$
$19$	−0.668017	−	2.05594i	−0.153254	−	0.471666i	−0.997980	+	0.0635328i	$0.979763\pi$
$20$	−3.00813	+	2.18553i	−0.672638	+	0.488700i
$21$	−2.29155			−0.500058
$22$		0			0
$23$	−1.86611			−0.389112			−0.194556	−	0.980891i	$-0.562327\pi$
$23$	−1.86611			−0.389112			−0.194556	+	0.980891i	$0.562327\pi$
$24$	3.43586	−	2.49630i	0.701341	−	0.509554i
$25$	3.56462	+	10.9708i	0.712925	+	2.19416i
$26$	−1.72924	+	5.32205i	−0.339132	+	1.04374i
$27$	1.38817	+	1.00856i	0.267153	+	0.194098i
$28$	0.739758	+	0.537466i	0.139801	+	0.101571i
$29$	0.0754316	−	0.232155i	0.0140073	−	0.0431100i	−0.943809	−	0.330493i	$-0.892785\pi$
$29$	0.0754316	−	0.232155i	0.0140073	−	0.0431100i	0.957816	+	0.287383i	$0.0927851\pi$
$30$	4.91579	+	15.1292i	0.897496	+	2.76221i
$31$	5.55785	−	4.03801i	0.998219	−	0.725249i	0.0365136	−	0.999333i	$-0.488375\pi$
$31$	5.55785	−	4.03801i	0.998219	−	0.725249i	0.961706	+	0.274084i	$0.0883748\pi$
$32$	−4.81667			−0.851475
$33$		0			0
$34$	2.25495			0.386721
$35$	3.28976	−	2.39015i	0.556071	−	0.404009i
$36$	0.636110	+	1.95775i	0.106018	+	0.326291i
$37$	0.0789907	−	0.243108i	0.0129860	−	0.0399668i	−0.944354	−	0.328932i	$-0.893311\pi$
$37$	0.0789907	−	0.243108i	0.0129860	−	0.0399668i	0.957340	+	0.288965i	$0.0933112\pi$
$38$	2.98563	+	2.16919i	0.484334	+	0.351889i
$39$	6.07696	+	4.41517i	0.973092	+	0.706993i
$40$	−2.32882	+	7.16738i	−0.368219	+	1.13326i
$41$	1.77139	+	5.45177i	0.276644	+	0.851423i	0.988780	+	0.149381i	$0.0477282\pi$
$41$	1.77139	+	5.45177i	0.276644	+	0.851423i	−0.712136	+	0.702042i	$0.752272\pi$
$42$	3.16491	−	2.29944i	0.488357	−	0.354812i
$43$	8.01781			1.22270			0.611352	−	0.791358i	$-0.290626\pi$
$43$	8.01781			1.22270			0.611352	+	0.791358i	$0.290626\pi$
$44$		0			0
$45$	9.15429			1.36464
$46$	2.57733	−	1.87254i	0.380006	−	0.276091i
$47$	−1.25698	−	3.86859i	−0.183350	−	0.564292i	0.816566	−	0.577251i	$-0.195875\pi$
$47$	−1.25698	−	3.86859i	−0.183350	−	0.564292i	−0.999916	+	0.0129595i	$0.995875\pi$
$48$	−3.53546	+	10.8810i	−0.510299	+	1.57054i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−15.9317	−	11.5751i	−2.25309	−	1.63696i
$51$	0.935354	−	2.87873i	0.130976	−	0.403102i
$52$	−0.926218	−	2.85060i	−0.128443	−	0.395308i
$53$	4.04982	−	2.94237i	0.556285	−	0.404165i	−0.273812	−	0.961783i	$-0.588285\pi$
$53$	4.04982	−	2.94237i	0.556285	−	0.404165i	0.830098	+	0.557618i	$0.188285\pi$
$54$	−2.92926			−0.398622
$55$		0			0
$56$	1.85331			0.247658
$57$	4.00768	−	2.91175i	0.530830	−	0.385670i
$58$	0.128774	+	0.396325i	0.0169088	+	0.0520400i
$59$	−0.303947	+	0.935452i	−0.0395705	+	0.121785i	−0.968890	−	0.247490i	$-0.920394\pi$
$59$	−0.303947	+	0.935452i	−0.0395705	+	0.121785i	0.929320	+	0.369276i	$0.120394\pi$
$60$	−6.89329	−	5.00827i	−0.889920	−	0.646565i
$61$	1.49402	+	1.08547i	0.191290	+	0.138980i	0.679308	−	0.733853i	$-0.262280\pi$
$61$	1.49402	+	1.08547i	0.191290	+	0.138980i	−0.488018	+	0.872833i	$0.662280\pi$
$62$	−3.62414	+	11.1540i	−0.460267	+	1.41656i
$63$	−0.695665	−	2.14104i	−0.0876456	−	0.269745i
$64$	−1.42591	+	1.03598i	−0.178239	+	0.129498i
$65$	−13.3292			−1.65329
$66$		0			0
$67$	−3.00700			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$67$	−3.00700			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$68$	−0.977133	+	0.709928i	−0.118495	+	0.0860915i
$69$	−1.32145	−	4.06700i	−0.159084	−	0.489610i
$70$	−2.14518	+	6.60218i	−0.256398	+	0.789111i
$71$	−5.23953	−	3.80674i	−0.621818	−	0.451777i	0.231738	−	0.972778i	$-0.425559\pi$
$71$	−5.23953	−	3.80674i	−0.621818	−	0.451777i	−0.853556	+	0.521001i	$0.825559\pi$
$72$	3.37538	+	2.45236i	0.397792	+	0.289013i
$73$	2.98252	−	9.17926i	0.349078	−	1.07435i	−0.610287	−	0.792181i	$-0.708946\pi$
$73$	2.98252	−	9.17926i	0.349078	−	1.07435i	0.959364	−	0.282170i	$-0.0910542\pi$
$74$	0.134850	+	0.415025i	0.0156760	+	0.0482456i
$75$	−21.3855	+	15.5375i	−2.46938	+	1.79411i
$76$	−1.97668			−0.226741
$77$		0			0
$78$	−12.8234			−1.45196
$79$	−4.47750	+	3.25310i	−0.503759	+	0.366002i	−0.810451	−	0.585807i	$-0.800778\pi$
$79$	−4.47750	+	3.25310i	−0.503759	+	0.366002i	0.306692	+	0.951809i	$0.400778\pi$
$80$	−6.27368	−	19.3084i	−0.701419	−	2.15874i
$81$	−3.30205	+	10.1627i	−0.366895	+	1.12919i
$82$	−7.91704	−	5.75206i	−0.874290	−	0.635209i
$83$	1.67485	+	1.21685i	0.183839	+	0.133567i	0.675898	−	0.736995i	$-0.263756\pi$
$83$	1.67485	+	1.21685i	0.183839	+	0.133567i	−0.492060	+	0.870561i	$0.663756\pi$
$84$	−0.647507	+	1.99282i	−0.0706488	+	0.217435i
$85$	1.65979	+	5.10831i	0.180029	+	0.554074i
$86$	−11.0736	+	8.04542i	−1.19409	+	0.867559i
$87$	0.559372			0.0599710
$88$		0			0
$89$	16.6306			1.76284			0.881421	−	0.472331i	$-0.156587\pi$
$89$	16.6306			1.76284			0.881421	+	0.472331i	$0.156587\pi$
$90$	−12.6432	+	9.18581i	−1.33271	+	0.968269i
$91$	1.01293	+	3.11749i	0.106184	+	0.326802i
$92$	−0.527294	+	1.62284i	−0.0549742	+	0.169193i
$93$	12.7361	+	9.25333i	1.32067	+	0.959525i
$94$	5.61795	+	4.08168i	0.579448	+	0.420993i
$95$	−2.71640	+	8.36023i	−0.278697	+	0.857741i
$96$	−3.41082	−	10.4974i	−0.348116	−	1.07139i
$97$	2.09179	−	1.51977i	0.212389	−	0.154310i	−0.476505	−	0.879172i	$-0.658097\pi$
$97$	2.09179	−	1.51977i	0.212389	−	0.154310i	0.688894	+	0.724862i	$0.258097\pi$
$98$	1.70716			0.172449
$99$		0			0
$100$	10.5478			1.05478
$101$	8.55018	−	6.21207i	0.850775	−	0.618124i	−0.0745850	−	0.997215i	$-0.523763\pi$
$101$	8.55018	−	6.21207i	0.850775	−	0.618124i	0.925359	+	0.379091i	$0.123763\pi$
$102$	1.59680	+	4.91444i	0.158107	+	0.486602i
$103$	4.27954	−	13.1711i	0.421676	−	1.29778i	−0.484466	−	0.874810i	$-0.660986\pi$
$103$	4.27954	−	13.1711i	0.421676	−	1.29778i	0.906142	−	0.422974i	$-0.139014\pi$
$104$	−4.91477	−	3.57079i	−0.481933	−	0.350145i
$105$	7.53867	+	5.47716i	0.735699	+	0.534516i
$106$	−2.64079	+	8.12752i	−0.256496	+	0.789415i
$107$	−3.84066	−	11.8203i	−0.371291	−	1.14272i	−0.945947	−	0.324321i	$-0.894864\pi$
$107$	−3.84066	−	11.8203i	−0.371291	−	1.14272i	0.574656	−	0.818395i	$-0.305136\pi$
$108$	1.26933	−	0.922221i	0.122141	−	0.0887408i
$109$	7.36748			0.705676			0.352838	−	0.935684i	$-0.385217\pi$
$109$	7.36748			0.705676			0.352838	+	0.935684i	$0.385217\pi$
$110$		0			0
$111$	0.585766			0.0555984
$112$	−4.03916	+	2.93462i	−0.381664	+	0.277295i
$113$	3.52535	+	10.8499i	0.331637	+	1.02067i	0.968355	+	0.249577i	$0.0802916\pi$
$113$	3.52535	+	10.8499i	0.331637	+	1.02067i	−0.636718	+	0.771097i	$0.719708\pi$
$114$	−2.61331	+	8.04295i	−0.244759	+	0.753291i
$115$	6.13907	+	4.46030i	0.572471	+	0.415925i
$116$	−0.180576	−	0.131196i	−0.0167661	−	0.0121813i
$117$	−2.28034	+	7.01815i	−0.210817	+	0.648828i
$118$	−0.518885	−	1.59696i	−0.0477673	−	0.147013i
$119$	1.06862	−	0.776394i	0.0979598	−	0.0711720i
$120$	−17.2697			−1.57650
$121$		0			0
$122$	−3.15263			−0.285425
$123$	−10.6272	+	7.72111i	−0.958222	+	0.696189i
$124$	−1.94117	−	5.97431i	−0.174322	−	0.536509i
$125$	8.21219	−	25.2745i	0.734521	−	2.26062i
$126$	3.10921	+	2.25897i	0.276990	+	0.201245i
$127$	−7.07765	−	5.14221i	−0.628040	−	0.456297i	0.227681	−	0.973736i	$-0.426886\pi$
$127$	−7.07765	−	5.14221i	−0.628040	−	0.456297i	−0.855720	+	0.517438i	$0.826886\pi$
$128$	3.90667	−	12.0235i	0.345304	−	1.06274i
$129$	5.67765	+	17.4740i	0.499889	+	1.53850i
$130$	18.4093	−	13.3751i	1.61460	−	1.17308i
$131$	12.5516			1.09664			0.548319	−	0.836269i	$-0.315268\pi$
$131$	12.5516			1.09664			0.548319	+	0.836269i	$0.315268\pi$
$132$		0			0
$133$	2.16175			0.187447
$134$	4.15303	−	3.01735i	0.358767	−	0.260660i
$135$	−2.15612	−	6.63587i	−0.185570	−	0.571124i
$136$	−0.756473	+	2.32818i	−0.0648670	+	0.199640i
$137$	5.11961	+	3.71962i	0.437398	+	0.317788i	0.784600	−	0.620002i	$-0.212868\pi$
$137$	5.11961	+	3.71962i	0.437398	+	0.317788i	−0.347202	+	0.937790i	$0.612868\pi$
$138$	5.90609	+	4.29102i	0.502760	+	0.365276i
$139$	−4.46311	+	13.7361i	−0.378556	+	1.16508i	0.562491	+	0.826803i	$0.309843\pi$
$139$	−4.46311	+	13.7361i	−0.378556	+	1.16508i	−0.941048	+	0.338274i	$0.890157\pi$
$140$	−1.14900	−	3.53627i	−0.0971085	−	0.298869i
$141$	7.54109	−	5.47892i	0.635075	−	0.461409i
$142$	11.0563			0.927822
$143$		0			0
$144$	−11.2396			−0.936633
$145$	−0.803037	+	0.583440i	−0.0666886	+	0.0484521i
$146$	5.09164	+	15.6704i	0.421387	+	1.29690i
$147$	0.708129	−	2.17940i	0.0584055	−	0.179754i
$148$	−0.189096	−	0.137387i	−0.0155436	−	0.0112931i
$149$	19.4643	+	14.1417i	1.59458	+	1.15853i	0.897009	+	0.442012i	$0.145735\pi$
$149$	19.4643	+	14.1417i	1.59458	+	1.15853i	0.697570	+	0.716517i	$0.254265\pi$
$150$	13.9450	−	42.9182i	1.13860	−	3.50426i
$151$	0.409195	+	1.25937i	0.0332998	+	0.102486i	0.966325	−	0.257325i	$-0.0828411\pi$
$151$	0.409195	+	1.25937i	0.0332998	+	0.102486i	−0.933025	+	0.359811i	$0.882841\pi$
$152$	−3.24123	+	2.35489i	−0.262898	+	0.191007i
$153$	2.97359			0.240401
$154$		0			0
$155$	−27.9355			−2.24383
$156$	5.55672	−	4.03719i	0.444894	−	0.323234i
$157$	4.51600	+	13.8988i	0.360416	+	1.10925i	0.952802	+	0.303592i	$0.0981859\pi$
$157$	4.51600	+	13.8988i	0.360416	+	1.10925i	−0.592386	+	0.805654i	$0.701814\pi$
$158$	2.91968	−	8.98584i	0.232277	−	0.714875i
$159$	9.28038	+	6.74259i	0.735982	+	0.534722i
$160$	15.8457	+	11.5126i	1.25271	+	0.910149i
$161$	0.576661	−	1.77478i	0.0454472	−	0.139872i
$162$	−5.63713	−	17.3493i	−0.442895	−	1.36309i
$163$	16.9258	−	12.2973i	1.32573	−	0.963202i	0.325892	−	0.945407i	$-0.394335\pi$
$163$	16.9258	−	12.2973i	1.32573	−	0.963202i	0.999842	−	0.0177952i	$-0.00566470\pi$
$164$	5.24159			0.409300
$165$		0			0
$166$	−3.53421			−0.274308
$167$	3.97498	−	2.88799i	0.307593	−	0.223480i	−0.423270	−	0.906004i	$-0.639118\pi$
$167$	3.97498	−	2.88799i	0.307593	−	0.223480i	0.730863	+	0.682524i	$0.239118\pi$
$168$	1.31238	+	4.03909i	0.101252	+	0.311623i
$169$	−0.696904	+	2.14485i	−0.0536080	+	0.164989i
$170$	−7.41826	−	5.38968i	−0.568955	−	0.413370i
$171$	3.93714	+	2.86050i	0.301080	+	0.218748i
$172$	2.26553	−	6.97259i	0.172745	−	0.531655i
$173$	−6.07460	−	18.6957i	−0.461844	−	1.42141i	−0.862909	−	0.505359i	$-0.831360\pi$
$173$	−6.07460	−	18.6957i	−0.461844	−	1.42141i	0.401066	−	0.916049i	$-0.368640\pi$
$174$	−0.772561	+	0.561298i	−0.0585677	+	0.0425519i
$175$	−11.5354			−0.871992
$176$		0			0
$177$	−2.25395			−0.169418
$178$	−22.9689	+	16.6879i	−1.72159	+	1.25081i
$179$	−7.83631	−	24.1177i	−0.585714	−	1.80264i	−0.596386	−	0.802698i	$-0.703397\pi$
$179$	−7.83631	−	24.1177i	−0.585714	−	1.80264i	0.0106719	−	0.999943i	$-0.496603\pi$
$180$	2.58666	−	7.96092i	0.192798	−	0.593372i
$181$	1.59836	+	1.16128i	0.118805	+	0.0863172i	0.645601	−	0.763675i	$-0.276607\pi$
$181$	1.59836	+	1.16128i	0.118805	+	0.0863172i	−0.526796	+	0.849992i	$0.676607\pi$
$182$	−4.52720	−	3.28921i	−0.335579	−	0.243812i
$183$	−1.30771	+	4.02471i	−0.0966686	+	0.297515i
$184$	1.06873	+	3.28921i	0.0787878	+	0.242484i
$185$	−0.840927	+	0.610969i	−0.0618262	+	0.0449194i
$186$	−26.8753			−1.97059
$187$		0			0
$188$	−3.71945			−0.271269
$189$	−1.38817	+	1.00856i	−0.100974	+	0.0733622i
$190$	−4.63733	−	14.2722i	−0.336427	−	1.03542i
$191$	0.300672	−	0.925373i	0.0217559	−	0.0669577i	−0.939589	−	0.342304i	$-0.888793\pi$
$191$	0.300672	−	0.925373i	0.0217559	−	0.0669577i	0.961345	+	0.275347i	$0.0887926\pi$
$192$	−3.26755	−	2.37401i	−0.235815	−	0.171330i
$193$	−18.7147	−	13.5970i	−1.34711	−	0.978735i	−0.999150	−	0.0412267i	$-0.986873\pi$
$193$	−18.7147	−	13.5970i	−1.34711	−	0.978735i	−0.347963	−	0.937508i	$-0.613127\pi$
$194$	−1.36401	+	4.19798i	−0.0979299	+	0.301397i
$195$	−9.43883	−	29.0497i	−0.675928	−	2.08029i
$196$	−0.739758	+	0.537466i	−0.0528399	+	0.0383904i
$197$	9.91237			0.706227			0.353114	−	0.935580i	$-0.385123\pi$
$197$	9.91237			0.706227			0.353114	+	0.935580i	$0.385123\pi$
$198$		0			0
$199$	10.3847			0.736154			0.368077	−	0.929795i	$-0.380016\pi$
$199$	10.3847			0.736154			0.368077	+	0.929795i	$0.380016\pi$
$200$	17.2956	−	12.5660i	1.22299	−	0.888551i
$201$	−2.12934	−	6.55345i	−0.150192	−	0.462245i
$202$	−5.57537	+	17.1592i	−0.392282	+	1.20732i
$203$	0.197482	+	0.143479i	0.0138606	+	0.0100703i
$204$	−2.23915	−	1.62684i	−0.156772	−	0.113902i
$205$	7.20312	−	22.1689i	0.503087	−	1.54834i
$206$	7.30586	+	22.4851i	0.509023	+	1.56661i
$207$	3.39871	−	2.46931i	0.236226	−	0.171629i
$208$	16.3656			1.13475
$209$		0			0
$210$	−15.9078			−1.09774
$211$	−10.5104	+	7.63627i	−0.723567	+	0.525702i	−0.887522	−	0.460766i	$-0.847575\pi$
$211$	−10.5104	+	7.63627i	−0.723567	+	0.525702i	0.163955	+	0.986468i	$0.447575\pi$
$212$	−1.41447	−	4.35328i	−0.0971459	−	0.298984i
$213$	4.58614	−	14.1147i	0.314237	−	0.967122i
$214$	17.1655	+	12.4714i	1.17341	+	0.852530i
$215$	−26.3767	−	19.1638i	−1.79888	−	1.30696i
$216$	0.982684	−	3.02439i	0.0668632	−	0.205784i
$217$	2.12291	+	6.53364i	0.144112	+	0.443533i
$218$	−10.1754	+	7.39284i	−0.689163	+	0.500706i
$219$	22.1173			1.49455
$220$		0			0
$221$	−4.32975			−0.291250
$222$	−0.809013	+	0.587782i	−0.0542974	+	0.0394494i
$223$	−4.43522	−	13.6502i	−0.297004	−	0.914086i	−0.982541	−	0.186047i	$-0.940432\pi$
$223$	−4.43522	−	13.6502i	−0.297004	−	0.914086i	0.685536	−	0.728038i	$-0.259568\pi$
$224$	1.48843	−	4.58093i	0.0994501	−	0.306076i
$225$	−21.0091	−	15.2640i	−1.40061	−	1.01760i
$226$	−15.7562	−	11.4476i	−1.04809	−	0.761480i
$227$	−1.96992	+	6.06279i	−0.130748	+	0.402401i	−0.994904	−	0.100822i	$-0.967853\pi$
$227$	−1.96992	+	6.06279i	−0.130748	+	0.402401i	0.864156	+	0.503223i	$0.167853\pi$
$228$	−1.39975	−	4.30798i	−0.0927005	−	0.285303i
$229$	6.47405	−	4.70368i	0.427817	−	0.310828i	−0.352958	−	0.935639i	$-0.614824\pi$
$229$	6.47405	−	4.70368i	0.427817	−	0.310828i	0.780776	+	0.624812i	$0.214824\pi$
$230$	−12.9545			−0.854191
$231$		0			0
$232$	−0.452395			−0.0297012
$233$	−8.73915	+	6.34937i	−0.572521	+	0.415961i	−0.836020	−	0.548699i	$-0.815123\pi$
$233$	−8.73915	+	6.34937i	−0.572521	+	0.415961i	0.263499	+	0.964660i	$0.415123\pi$
$234$	−3.89290	−	11.9811i	−0.254487	−	0.783229i
$235$	−5.11135	+	15.7311i	−0.333428	+	1.02619i
$236$	0.727620	+	0.528647i	0.0473641	+	0.0344120i
$237$	−10.2604	−	7.45465i	−0.666487	−	0.484231i
$238$	−0.696819	+	2.14459i	−0.0451681	+	0.139013i
$239$	−7.77433	−	23.9269i	−0.502880	−	1.54770i	−0.804306	−	0.594215i	$-0.797463\pi$
$239$	−7.77433	−	23.9269i	−0.502880	−	1.54770i	0.301427	−	0.953489i	$-0.402537\pi$
$240$	37.6381	−	27.3457i	2.42953	−	1.76516i
$241$	18.2462			1.17534			0.587669	−	0.809101i	$-0.300046\pi$
$241$	18.2462			1.17534			0.587669	+	0.809101i	$0.300046\pi$
$242$		0			0
$243$	−19.3392			−1.24061
$244$	1.36612	−	0.992543i	0.0874568	−	0.0635411i
$245$	1.25658	+	3.86735i	0.0802798	+	0.247076i
$246$	6.92975	−	21.3276i	0.441825	−	1.35980i
$247$	−5.73273	−	4.16507i	−0.364765	−	0.265017i
$248$	−10.3004	−	7.48368i	−0.654076	−	0.475214i
$249$	−1.46599	+	4.51185i	−0.0929032	+	0.285927i
$250$	14.0195	+	43.1476i	0.886672	+	2.72890i
$251$	−12.4009	+	9.00981i	−0.782740	+	0.568694i	−0.905800	−	0.423705i	$-0.860729\pi$
$251$	−12.4009	+	9.00981i	−0.782740	+	0.568694i	0.123060	+	0.992399i	$0.460729\pi$
$252$	−2.05850			−0.129673
$253$		0			0
$254$	14.9350			0.937105
$255$	−9.95769	+	7.23468i	−0.623574	+	0.453053i
$256$	5.58000	+	17.1735i	0.348750	+	1.07334i
$257$	0.828102	−	2.54864i	0.0516556	−	0.158980i	−0.921901	−	0.387426i	$-0.873364\pi$
$257$	0.828102	−	2.54864i	0.0516556	−	0.158980i	0.973557	+	0.228446i	$0.0733644\pi$
$258$	−25.3757	−	18.4365i	−1.57982	−	1.14781i
$259$	0.206800	+	0.150249i	0.0128500	+	0.00933604i
$260$	−3.76634	+	11.5916i	−0.233579	+	0.718881i
$261$	0.169813	+	0.522631i	0.0105112	+	0.0323500i
$262$	−17.3353	+	12.5948i	−1.07098	+	0.778110i
$263$	9.97733			0.615229			0.307614	−	0.951511i	$-0.400469\pi$
$263$	9.97733			0.615229			0.307614	+	0.951511i	$0.400469\pi$
$264$		0			0
$265$	−20.3556			−1.25044
$266$	−2.98563	+	2.16919i	−0.183061	+	0.133002i
$267$	11.7766	+	36.2447i	0.720718	+	2.21814i
$268$	−0.849665	+	2.61500i	−0.0519016	+	0.159737i
$269$	17.4565	+	12.6829i	1.06434	+	0.773288i	0.974886	−	0.222703i	$-0.0714879\pi$
$269$	17.4565	+	12.6829i	1.06434	+	0.773288i	0.0894538	+	0.995991i	$0.471488\pi$
$270$	9.63658	+	7.00138i	0.586463	+	0.426091i
$271$	4.63100	−	14.2528i	0.281313	−	0.865793i	−0.706166	−	0.708046i	$-0.749577\pi$
$271$	4.63100	−	14.2528i	0.281313	−	0.865793i	0.987480	−	0.157747i	$-0.0504232\pi$
$272$	−2.03788	−	6.27196i	−0.123565	−	0.380293i
$273$	−6.07696	+	4.41517i	−0.367794	+	0.267218i
$274$	−10.8032			−0.652647
$275$		0			0
$276$	−3.91021			−0.235367
$277$	4.21207	−	3.06025i	0.253079	−	0.183872i	−0.454012	−	0.890996i	$-0.650008\pi$
$277$	4.21207	−	3.06025i	0.253079	−	0.183872i	0.707090	+	0.707123i	$0.250008\pi$
$278$	−7.61924	−	23.4496i	−0.456972	−	1.40641i
$279$	−4.77914	+	14.7087i	−0.286119	+	0.880585i
$280$	−6.09694	−	4.42968i	−0.364362	−	0.264724i
$281$	12.2647	+	8.91086i	0.731654	+	0.531577i	0.890086	−	0.455792i	$-0.150644\pi$
$281$	12.2647	+	8.91086i	0.731654	+	0.531577i	−0.158433	+	0.987370i	$0.550644\pi$
$282$	−4.91737	+	15.1341i	−0.292825	+	0.901223i
$283$	1.75076	+	5.38829i	0.104072	+	0.320301i	0.989512	−	0.144454i	$-0.0461425\pi$
$283$	1.75076	+	5.38829i	0.104072	+	0.320301i	−0.885439	+	0.464755i	$0.846143\pi$
$284$	−4.79098	+	3.48085i	−0.284292	+	0.206551i
$285$	−20.1438			−1.19322
$286$		0			0
$287$	−5.73233			−0.338369
$288$	8.77248	−	6.37358i	0.516923	−	0.375567i
$289$	−4.71414	−	14.5086i	−0.277302	−	0.853449i
$290$	0.523642	−	1.61160i	0.0307493	−	0.0946366i
$291$	4.79344	+	3.48264i	0.280997	+	0.204156i
$292$	−7.13988	−	5.18743i	−0.417830	−	0.303571i
$293$	8.32502	−	25.6218i	0.486353	−	1.49684i	−0.343659	−	0.939095i	$-0.611666\pi$
$293$	8.32502	−	25.6218i	0.486353	−	1.49684i	0.830012	−	0.557746i	$-0.188334\pi$
$294$	1.20889	+	3.72058i	0.0705038	+	0.216988i
$295$	3.23579	−	2.35094i	0.188395	−	0.136877i
$296$	−0.473741			−0.0275356
$297$		0			0
$298$	−41.0729			−2.37929
$299$	−4.94874	+	3.59547i	−0.286193	+	0.207931i
$300$	7.46923	+	22.9879i	0.431236	+	1.32721i
$301$	−2.47764	+	7.62539i	−0.142809	+	0.439520i
$302$	−1.82885	−	1.32874i	−0.105239	−	0.0764604i
$303$	19.5932	+	14.2353i	1.12560	+	0.817796i
$304$	3.33519	−	10.2647i	0.191286	−	0.588718i
$305$	−2.32053	−	7.14187i	−0.132873	−	0.408942i
$306$	−4.10689	+	2.98383i	−0.234775	+	0.170574i
$307$	−24.6157			−1.40489			−0.702447	−	0.711736i	$-0.747909\pi$
$307$	−24.6157			−1.40489			−0.702447	+	0.711736i	$0.747909\pi$
$308$		0			0
$309$	31.7355			1.80537
$310$	38.5823	−	28.0316i	2.19132	−	1.59209i
$311$	−3.15602	−	9.71323i	−0.178962	−	0.550787i	0.820831	−	0.571172i	$-0.193511\pi$
$311$	−3.15602	−	9.71323i	−0.178962	−	0.550787i	−0.999792	+	0.0203847i	$0.993511\pi$
$312$	4.30188	−	13.2398i	0.243546	−	0.749557i
$313$	−18.1222	−	13.1665i	−1.02433	−	0.744217i	−0.0571612	−	0.998365i	$-0.518205\pi$
$313$	−18.1222	−	13.1665i	−1.02433	−	0.744217i	−0.967165	+	0.254148i	$0.918205\pi$
$314$	−20.1838	−	14.6644i	−1.13904	−	0.827559i
$315$	−2.82883	+	8.70625i	−0.159387	+	0.490542i
$316$	1.56384	+	4.81301i	0.0879730	+	0.270753i
$317$	−18.8982	+	13.7304i	−1.06143	+	0.771174i	−0.974352	−	0.225028i	$-0.927753\pi$
$317$	−18.8982	+	13.7304i	−1.06143	+	0.771174i	−0.0870776	+	0.996202i	$0.527753\pi$
$318$	−19.5831			−1.09817
$319$		0			0
$320$	7.16707			0.400651
$321$	23.0415	−	16.7407i	1.28605	−	0.934373i
$322$	0.984452	+	3.02983i	0.0548614	+	0.168846i
$323$	−0.882371	+	2.71566i	−0.0490964	+	0.151103i
$324$	7.90481	+	5.74318i	0.439156	+	0.319066i
$325$	30.5906	+	22.2254i	1.69686	+	1.23284i
$326$	−11.0369	+	33.9682i	−0.611280	+	1.88133i
$327$	5.21713	+	16.0567i	0.288508	+	0.887935i
$328$	8.59480	−	6.24449i	0.474569	−	0.344794i
$329$	4.06768			0.224258
$330$		0			0
$331$	15.6444			0.859892			0.429946	−	0.902855i	$-0.358533\pi$
$331$	15.6444			0.859892			0.429946	+	0.902855i	$0.358533\pi$
$332$	1.53147	−	1.11268i	0.0840502	−	0.0610660i
$333$	0.177826	+	0.547291i	0.00974478	+	0.0299913i
$334$	−2.59199	+	7.97734i	−0.141828	+	0.436500i
$335$	9.89232	+	7.18719i	0.540475	+	0.392678i
$336$	−9.25594	−	6.72484i	−0.504953	−	0.366870i
$337$	−10.0712	+	30.9959i	−0.548611	+	1.68845i	0.163634	+	0.986521i	$0.447678\pi$
$337$	−10.0712	+	30.9959i	−0.548611	+	1.68845i	−0.712245	+	0.701931i	$0.752322\pi$
$338$	−1.18973	−	3.66160i	−0.0647126	−	0.199165i
$339$	−21.1499	+	15.3663i	−1.14870	+	0.834582i
$340$	4.91137			0.266356
$341$		0			0
$342$	−8.30801			−0.449245
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−4.59183	−	14.1322i	−0.247575	−	0.761957i
$345$	−5.37350	+	16.5379i	−0.289300	+	0.890373i
$346$	27.1498	+	19.7255i	1.45958	+	1.06045i
$347$	4.65414	+	3.38143i	0.249848	+	0.181525i	0.705659	−	0.708551i	$-0.250651\pi$
$347$	4.65414	+	3.38143i	0.249848	+	0.181525i	−0.455812	+	0.890076i	$0.650651\pi$
$348$	0.158058	−	0.486451i	0.00847278	−	0.0260765i
$349$	0.0568404	+	0.174937i	0.00304260	+	0.00936415i	0.952566	−	0.304331i	$-0.0984329\pi$
$349$	0.0568404	+	0.174937i	0.00304260	+	0.00936415i	−0.949524	+	0.313695i	$0.898433\pi$
$350$	15.9317	−	11.5751i	0.851587	−	0.618714i
$351$	5.62449			0.300213
$352$		0			0
$353$	19.0211			1.01239			0.506195	−	0.862419i	$-0.331052\pi$
$353$	19.0211			1.01239			0.506195	+	0.862419i	$0.331052\pi$
$354$	3.11298	−	2.26171i	0.165453	−	0.120209i
$355$	8.13812	+	25.0466i	0.431927	+	1.32933i
$356$	4.69919	−	14.4626i	0.249057	−	0.766517i
$357$	2.44879	+	1.77915i	0.129604	+	0.0941626i
$358$	35.0236	+	25.4462i	1.85106	+	1.34487i
$359$	0.222161	−	0.683741i	0.0117252	−	0.0360865i	−0.945023	−	0.327005i	$-0.893961\pi$
$359$	0.222161	−	0.683741i	0.0117252	−	0.0360865i	0.956748	+	0.290918i	$0.0939607\pi$
$360$	−5.24269	−	16.1354i	−0.276314	−	0.850408i
$361$	11.5907	−	8.42111i	0.610035	−	0.443216i
$362$	−3.37281			−0.177271
$363$		0			0
$364$	2.99730			0.157101
$365$	−31.7516	+	23.0689i	−1.66196	+	1.20748i
$366$	−2.23247	−	6.87083i	−0.116693	−	0.359144i
$367$	−2.43906	+	7.50664i	−0.127318	+	0.391843i	−0.994316	−	0.106467i	$-0.966046\pi$
$367$	−2.43906	+	7.50664i	−0.127318	+	0.391843i	0.866999	+	0.498311i	$0.166046\pi$
$368$	−7.53753	−	5.47633i	−0.392921	−	0.285474i
$369$	−10.4401	−	7.58521i	−0.543492	−	0.394870i
$370$	0.548349	−	1.68764i	0.0285073	−	0.0877364i
$371$	1.54689	+	4.76085i	0.0803107	+	0.247171i
$372$	11.6458	−	8.46116i	0.603806	−	0.438691i
$373$	−15.6686			−0.811292			−0.405646	−	0.914030i	$-0.632953\pi$
$373$	−15.6686			−0.811292			−0.405646	+	0.914030i	$0.632953\pi$
$374$		0			0
$375$	60.8985			3.14479
$376$	−6.09890	+	4.43111i	−0.314527	+	0.228517i
$377$	−0.247259	−	0.760984i	−0.0127345	−	0.0391927i
$378$	0.905192	−	2.78589i	0.0465580	−	0.143291i
$379$	10.7716	+	7.82600i	0.553298	+	0.401995i	0.829000	−	0.559248i	$-0.188910\pi$
$379$	10.7716	+	7.82600i	0.553298	+	0.401995i	−0.275702	+	0.961243i	$0.588910\pi$
$380$	6.50282	+	4.72457i	0.333587	+	0.242365i
$381$	6.19503	−	19.0664i	0.317381	−	0.976799i
$382$	0.513295	+	1.57976i	0.0262625	+	0.0808275i
$383$	−9.58558	+	6.96433i	−0.489800	+	0.355861i	−0.805107	−	0.593129i	$-0.797892\pi$
$383$	−9.58558	+	6.96433i	−0.489800	+	0.355861i	0.315307	+	0.948990i	$0.397892\pi$
$384$	28.9704			1.47839
$385$		0			0
$386$	39.4911			2.01004
$387$	−14.6026	+	10.6094i	−0.742294	+	0.539308i
$388$	−0.730591	−	2.24853i	−0.0370901	−	0.114152i
$389$	−1.86947	+	5.75362i	−0.0947857	+	0.291720i	−0.987198	−	0.159501i	$-0.949011\pi$
$389$	−1.86947	+	5.75362i	−0.0947857	+	0.291720i	0.892412	+	0.451221i	$0.149011\pi$
$390$	42.1859	+	30.6498i	2.13617	+	1.55201i
$391$	1.99416	+	1.44884i	0.100849	+	0.0732710i
$392$	−0.572703	+	1.76260i	−0.0289259	+	0.0890247i
$393$	8.88816	+	27.3549i	0.448348	+	1.37987i
$394$	−13.6902	+	9.94650i	−0.689701	+	0.501097i
$395$	22.5053			1.13237
$396$		0			0
$397$	−11.5763			−0.580996			−0.290498	−	0.956876i	$-0.593821\pi$
$397$	−11.5763			−0.580996			−0.290498	+	0.956876i	$0.593821\pi$
$398$	−14.3426	+	10.4205i	−0.718927	+	0.522331i
$399$	1.53080	+	4.71131i	0.0766357	+	0.235860i
$400$	−17.7970	+	54.7735i	−0.889850	+	2.73868i
$401$	−27.3386	−	19.8627i	−1.36522	−	0.991894i	−0.998093	−	0.0617249i	$-0.980340\pi$
$401$	−27.3386	−	19.8627i	−1.36522	−	0.991894i	−0.367132	−	0.930169i	$-0.619660\pi$
$402$	9.51689	+	6.91443i	0.474659	+	0.344860i
$403$	6.95873	−	21.4168i	0.346639	−	1.06685i
$404$	−2.98629	−	9.19086i	−0.148573	−	0.457262i
$405$	35.1533	−	25.5404i	1.74678	−	1.26911i
$406$	−0.416720			−0.0206815
$407$		0			0
$408$	−5.60972			−0.277722
$409$	14.6044	−	10.6107i	0.722139	−	0.524665i	−0.164928	−	0.986306i	$-0.552739\pi$
$409$	14.6044	−	10.6107i	0.722139	−	0.524665i	0.887067	+	0.461641i	$0.152739\pi$
$410$	12.2969	+	37.8458i	0.607299	+	1.86907i
$411$	−4.48118	+	13.7916i	−0.221040	+	0.680291i
$412$	−10.2448	−	7.44330i	−0.504726	−	0.366705i
$413$	−0.795743	−	0.578141i	−0.0391559	−	0.0284485i
$414$	−2.21622	+	6.82082i	−0.108921	+	0.335225i
$415$	−2.60140	−	8.00629i	−0.127698	−	0.393013i
$416$	−12.7733	+	9.28034i	−0.626262	+	0.455006i
$417$	−33.0968			−1.62076
$418$		0			0
$419$	2.58559			0.126314			0.0631571	−	0.998004i	$-0.479883\pi$
$419$	2.58559			0.126314			0.0631571	+	0.998004i	$0.479883\pi$
$420$	6.89329	−	5.00827i	0.336358	−	0.244379i
$421$	4.32462	+	13.3098i	0.210769	+	0.648681i	0.999427	+	0.0338486i	$0.0107764\pi$
$421$	4.32462	+	13.3098i	0.210769	+	0.648681i	−0.788658	+	0.614833i	$0.789224\pi$
$422$	6.85360	−	21.0932i	0.333628	−	1.02680i
$423$	7.40836	+	5.38249i	0.360207	+	0.261706i
$424$	−7.50556	−	5.45311i	−0.364502	−	0.264826i
$425$	4.70845	−	14.4911i	0.228393	−	0.702922i
$426$	7.82927	+	24.0960i	0.379329	+	1.16746i
$427$	−1.49402	+	1.08547i	−0.0723007	+	0.0525295i
$428$	−11.3646			−0.549331
$429$		0			0
$430$	55.6592			2.68412
$431$	−27.2381	+	19.7897i	−1.31201	+	0.953234i	−0.312019	+	0.950076i	$0.601005\pi$
$431$	−27.2381	+	19.7897i	−1.31201	+	0.953234i	−0.999995	+	0.00315862i	$0.998995\pi$
$432$	2.64728	+	8.14749i	0.127367	+	0.391996i
$433$	2.32471	−	7.15472i	0.111718	−	0.343834i	−0.879530	−	0.475843i	$-0.842143\pi$
$433$	2.32471	−	7.15472i	0.111718	−	0.343834i	0.991248	+	0.132009i	$0.0421429\pi$
$434$	−9.48813	−	6.89353i	−0.455445	−	0.330900i
$435$	−1.84020	−	1.33699i	−0.0882309	−	0.0641035i
$436$	2.08177	−	6.40704i	0.0996988	−	0.306841i
$437$	1.24660	+	3.83663i	0.0596327	+	0.183531i
$438$	−30.5466	+	22.1934i	−1.45957	+	1.06044i
$439$	22.0123			1.05059			0.525294	−	0.850921i	$-0.323955\pi$
$439$	22.0123			1.05059			0.525294	+	0.850921i	$0.323955\pi$
$440$		0			0
$441$	2.25122			0.107201
$442$	5.97990	−	4.34465i	0.284435	−	0.206654i
$443$	7.32039	+	22.5299i	0.347802	+	1.07043i	0.960066	+	0.279772i	$0.0902589\pi$
$443$	7.32039	+	22.5299i	0.347802	+	1.07043i	−0.612264	+	0.790653i	$0.709741\pi$
$444$	0.165515	−	0.509404i	0.00785501	−	0.0241752i
$445$	−54.7108	−	39.7497i	−2.59354	−	1.88432i
$446$	19.8228	+	14.4021i	0.938636	+	0.681959i
$447$	−17.0370	+	52.4346i	−0.805824	+	2.48007i
$448$	−0.544649	−	1.67626i	−0.0257323	−	0.0791958i
$449$	−1.84062	+	1.33729i	−0.0868643	+	0.0631106i	−0.630370	−	0.776295i	$-0.717097\pi$
$449$	−1.84062	+	1.33729i	−0.0868643	+	0.0631106i	0.543505	+	0.839406i	$0.317097\pi$
$450$	44.3326			2.08986
$451$		0			0
$452$	10.4316			0.490663
$453$	−2.45491	+	1.78360i	−0.115342	+	0.0838006i
$454$	−3.36297	−	10.3501i	−0.157832	−	0.485756i
$455$	4.11896	−	12.6769i	0.193100	−	0.594300i
$456$	−7.42745	−	5.39636i	−0.347822	−	0.252708i
$457$	−22.0970	−	16.0544i	−1.03365	−	0.750993i	−0.0646170	−	0.997910i	$-0.520583\pi$
$457$	−22.0970	−	16.0544i	−1.03365	−	0.750993i	−0.969037	+	0.246917i	$0.920583\pi$
$458$	−4.22158	+	12.9927i	−0.197261	+	0.607108i
$459$	−0.700375	−	2.15553i	−0.0326907	−	0.100612i
$460$	5.61351	−	4.07846i	0.261731	−	0.190159i
$461$	8.21908			0.382801			0.191400	−	0.981512i	$-0.438697\pi$
$461$	8.21908			0.382801			0.191400	+	0.981512i	$0.438697\pi$
$462$		0			0
$463$	−27.9839			−1.30052			−0.650261	−	0.759711i	$-0.725340\pi$
$463$	−27.9839			−1.30052			−0.650261	+	0.759711i	$0.725340\pi$
$464$	0.985965	−	0.716345i	0.0457723	−	0.0332555i
$465$	−19.7819	−	60.8825i	−0.917365	−	2.82336i
$466$	5.69860	−	17.5385i	0.263982	−	0.812454i
$467$	−21.5801	−	15.6789i	−0.998610	−	0.725533i	−0.0368204	−	0.999322i	$-0.511723\pi$
$467$	−21.5801	−	15.6789i	−0.998610	−	0.725533i	−0.961790	+	0.273789i	$0.911723\pi$
$468$	5.45891	+	3.96613i	0.252338	+	0.183335i
$469$	0.929214	−	2.85983i	0.0429071	−	0.132055i
$470$	−8.72589	−	26.8555i	−0.402495	−	1.23875i
$471$	−27.0931	+	19.6843i	−1.24839	+	0.907005i
$472$	1.82290			0.0839057
$473$		0			0
$474$	21.6512			0.994474
$475$	20.1741	−	14.6573i	0.925651	−	0.672525i
$476$	−0.373231	−	1.14869i	−0.0171070	−	0.0526500i
$477$	−3.48240	+	10.7177i	−0.159448	+	0.490730i
$478$	34.7466	+	25.2449i	1.58927	+	1.15467i
$479$	−18.7886	−	13.6507i	−0.858473	−	0.623717i	0.0689958	−	0.997617i	$-0.478020\pi$
$479$	−18.7886	−	13.6507i	−0.858473	−	0.623717i	−0.927469	+	0.373900i	$0.878020\pi$
$480$	−13.8697	+	42.6865i	−0.633061	+	1.94836i
$481$	−0.258925	−	0.796890i	−0.0118060	−	0.0363351i
$482$	−25.2001	+	18.3090i	−1.14783	+	0.833951i
$483$	4.27630			0.194578
$484$		0			0
$485$	−10.5140			−0.477415
$486$	26.7097	−	19.4058i	1.21158	−	0.880263i
$487$	−5.80706	−	17.8723i	−0.263143	−	0.809870i	−0.992115	−	0.125327i	$-0.960002\pi$
$487$	−5.80706	−	17.8723i	−0.263143	−	0.809870i	0.728973	−	0.684543i	$-0.239998\pi$
$488$	1.05762	−	3.25501i	0.0478761	−	0.147347i
$489$	38.7865	+	28.1800i	1.75398	+	1.27434i
$490$	−5.61615	−	4.08037i	−0.253712	−	0.184332i
$491$	−2.28850	+	7.04327i	−0.103278	+	0.317858i	−0.989323	−	0.145743i	$-0.953443\pi$
$491$	−2.28850	+	7.04327i	−0.103278	+	0.317858i	0.886044	+	0.463601i	$0.153443\pi$
$492$	3.71172	+	11.4235i	0.167337	+	0.515012i
$493$	−0.260851	+	0.189519i	−0.0117481	+	0.00853552i
$494$	12.0970			0.544269
$495$		0			0
$496$	34.2991			1.54007
$497$	5.23953	−	3.80674i	0.235025	−	0.170756i
$498$	−2.50267	−	7.70244i	−0.112148	−	0.345155i
$499$	7.31454	−	22.5118i	0.327444	−	1.00777i	−0.642882	−	0.765965i	$-0.722261\pi$
$499$	7.31454	−	22.5118i	0.327444	−	1.00777i	0.970325	−	0.241803i	$-0.0777386\pi$
$500$	−19.6592	−	14.2833i	−0.879188	−	0.638767i
$501$	9.10889	+	6.61799i	0.406955	+	0.295670i
$502$	8.08636	−	24.8873i	0.360912	−	1.11077i
$503$	2.59491	+	7.98632i	0.115701	+	0.356092i	0.992093	−	0.125507i	$-0.0400559\pi$
$503$	2.59491	+	7.98632i	0.115701	+	0.356092i	−0.876391	+	0.481600i	$0.840056\pi$
$504$	−3.37538	+	2.45236i	−0.150351	+	0.109237i
$505$	−42.9758			−1.91240
$506$		0			0
$507$	−5.16798			−0.229518
$508$	−6.47174	+	4.70199i	−0.287137	+	0.208617i
$509$	4.42094	+	13.6062i	0.195955	+	0.603086i	0.999964	+	0.00846991i	$0.00269609\pi$
$509$	4.42094	+	13.6062i	0.195955	+	0.603086i	−0.804009	+	0.594616i	$0.797304\pi$
$510$	6.49317	−	19.9839i	0.287523	−	0.884904i
$511$	7.80834	+	5.67309i	0.345421	+	0.250963i
$512$	−4.48369	−	3.25759i	−0.198153	−	0.143967i
$513$	1.14623	−	3.52773i	0.0506073	−	0.155753i
$514$	1.41370	+	4.35093i	0.0623557	+	0.191911i
$515$	−45.5595	+	33.1009i	−2.00759	+	1.45860i
$516$	16.8003			0.739594
$517$		0			0
$518$	−0.436383			−0.0191736
$519$	36.4438	−	26.4780i	1.59970	−	1.16225i
$520$	7.63370	+	23.4941i	0.334760	+	1.03028i
$521$	−10.3114	+	31.7352i	−0.451750	+	1.39034i	0.423158	+	0.906056i	$0.360921\pi$
$521$	−10.3114	+	31.7352i	−0.451750	+	1.39034i	−0.874909	+	0.484288i	$0.839079\pi$
$522$	−0.758963	−	0.551419i	−0.0332189	−	0.0241349i
$523$	10.8261	+	7.86559i	0.473390	+	0.343938i	0.798761	−	0.601648i	$-0.205489\pi$
$523$	10.8261	+	7.86559i	0.473390	+	0.343938i	−0.325371	+	0.945587i	$0.605489\pi$
$524$	3.54661	−	10.9153i	0.154934	−	0.476839i
$525$	−8.16853	−	25.1401i	−0.356504	−	1.09721i
$526$	−13.7799	+	10.0117i	−0.600832	+	0.436530i
$527$	−9.07430			−0.395283
$528$		0			0
$529$	−19.5176			−0.848592
$530$	28.1136	−	20.4257i	1.22118	−	0.887237i
$531$	−0.684251	−	2.10591i	−0.0296940	−	0.0913886i
$532$	0.610829	−	1.87994i	0.0264828	−	0.0815056i
$533$	15.2015	+	11.0446i	0.658451	+	0.478393i
$534$	−52.6345	−	38.2412i	−2.27772	−	1.65486i
$535$	−15.6176	+	48.0659i	−0.675206	+	2.07807i
$536$	1.72212	+	5.30014i	0.0743842	+	0.228931i
$537$	47.0129	−	34.1569i	2.02876	−	1.47398i
$538$	−36.8360			−1.58811
$539$		0			0
$540$	−6.38004			−0.274553
$541$	−27.5583	+	20.0223i	−1.18482	+	0.860825i	−0.992708	−	0.120547i	$-0.961535\pi$
$541$	−27.5583	+	20.0223i	−1.18482	+	0.860825i	−0.192117	+	0.981372i	$0.561535\pi$
$542$	7.90586	+	24.3317i	0.339586	+	1.04514i
$543$	−1.39904	+	4.30581i	−0.0600386	+	0.184780i
$544$	5.14717	+	3.73964i	0.220683	+	0.160336i
$545$	−24.2373	−	17.6094i	−1.03821	−	0.754304i
$546$	3.96264	−	12.1958i	0.169585	−	0.521930i
$547$	4.87054	+	14.9900i	0.208249	+	0.640925i	0.999564	+	0.0295167i	$0.00939681\pi$
$547$	4.87054	+	14.9900i	0.208249	+	0.640925i	−0.791315	+	0.611409i	$0.790603\pi$
$548$	4.68133	−	3.40118i	0.199976	−	0.145291i
$549$	−4.15735			−0.177431
$550$		0			0
$551$	−0.527686			−0.0224802
$552$	−6.41170	+	4.65837i	−0.272900	+	0.198274i
$553$	−1.71025	−	5.26362i	−0.0727274	−	0.223832i
$554$	−2.74659	+	8.45314i	−0.116691	+	0.359139i
$555$	−1.92703	−	1.40007i	−0.0817979	−	0.0594296i
$556$	10.6843	+	7.76258i	0.453114	+	0.329207i
$557$	−4.97593	+	15.3143i	−0.210837	+	0.648889i	0.788586	+	0.614924i	$0.210813\pi$
$557$	−4.97593	+	15.3143i	−0.210837	+	0.648889i	−0.999423	+	0.0339647i	$0.989187\pi$
$558$	−8.15875	−	25.1100i	−0.345387	−	1.06299i
$559$	21.2624	−	15.4480i	0.899303	−	0.653382i
$560$	20.3020			0.857918
$561$		0			0
$562$	−25.8806			−1.09171
$563$	−13.9397	+	10.1278i	−0.587490	+	0.426836i	−0.841416	−	0.540387i	$-0.818278\pi$
$563$	−13.9397	+	10.1278i	−0.587490	+	0.426836i	0.253927	+	0.967223i	$0.418278\pi$
$564$	−2.63385	−	8.10616i	−0.110905	−	0.341331i
$565$	14.3354	−	44.1198i	0.603094	−	1.85613i
$566$	−7.82486	−	5.68509i	−0.328903	−	0.238962i
$567$	−8.64489	−	6.28088i	−0.363051	−	0.263772i
$568$	−3.70907	+	11.4153i	−0.155629	+	0.478977i
$569$	11.0054	+	33.8712i	0.461371	+	1.41995i	0.863490	+	0.504366i	$0.168274\pi$
$569$	11.0054	+	33.8712i	0.461371	+	1.41995i	−0.402119	+	0.915587i	$0.631726\pi$
$570$	27.8210	−	20.2132i	1.16530	−	0.846637i
$571$	−26.6026			−1.11329			−0.556643	−	0.830752i	$-0.687911\pi$
$571$	−26.6026			−1.11329			−0.556643	+	0.830752i	$0.687911\pi$
$572$		0			0
$573$	2.22967			0.0931459
$574$	7.91704	−	5.75206i	0.330451	−	0.240087i
$575$	−6.65200	−	20.4727i	−0.277407	−	0.853772i
$576$	1.22613	−	3.77363i	0.0510886	−	0.157234i
$577$	−23.3584	−	16.9708i	−0.972421	−	0.706505i	−0.0164191	−	0.999865i	$-0.505227\pi$
$577$	−23.3584	−	16.9708i	−0.972421	−	0.706505i	−0.956002	+	0.293360i	$0.905227\pi$
$578$	21.0694	+	15.3078i	0.876370	+	0.636720i
$579$	16.3809	−	50.4152i	0.680767	−	2.09518i
$580$	0.280474	+	0.863209i	0.0116460	+	0.0358428i
$581$	−1.67485	+	1.21685i	−0.0694844	+	0.0504834i
$582$	−10.1150			−0.419278
$583$		0			0
$584$	−17.8874			−0.740188
$585$	24.2762	−	17.6377i	1.00370	−	0.729229i
$586$	14.2121	+	43.7404i	0.587098	+	1.80690i
$587$	0.752191	−	2.31500i	0.0310462	−	0.0955505i	−0.934333	−	0.356402i	$-0.884003\pi$
$587$	0.752191	−	2.31500i	0.0310462	−	0.0955505i	0.965379	+	0.260852i	$0.0840033\pi$
$588$	−1.69520	−	1.23163i	−0.0699087	−	0.0507916i
$589$	−12.0147	−	8.72917i	−0.495056	−	0.359679i
$590$	−2.10998	+	6.49385i	−0.0868665	+	0.267348i
$591$	7.01924	+	21.6030i	0.288733	+	0.888629i
$592$	1.03249	−	0.750145i	0.0424349	−	0.0308308i
$593$	−15.6870			−0.644187			−0.322093	−	0.946708i	$-0.604387\pi$
$593$	−15.6870			−0.644187			−0.322093	+	0.946708i	$0.604387\pi$
$594$		0			0
$595$	−5.37119			−0.220197
$596$	17.7980	−	12.9310i	0.729034	−	0.529675i
$597$	7.35373	+	22.6324i	0.300968	+	0.926284i
$598$	3.22696	−	9.93155i	0.131960	−	0.406131i
$599$	10.6967	+	7.77160i	0.437055	+	0.317539i	0.784464	−	0.620175i	$-0.212938\pi$
$599$	10.6967	+	7.77160i	0.437055	+	0.317539i	−0.347409	+	0.937714i	$0.612938\pi$
$600$	39.6339	+	28.7957i	1.61805	+	1.17558i
$601$	3.47035	−	10.6806i	0.141559	−	0.435673i	−0.854994	−	0.518638i	$-0.826439\pi$
$601$	3.47035	−	10.6806i	0.141559	−	0.435673i	0.996552	+	0.0829656i	$0.0264391\pi$
$602$	−4.22973	−	13.0178i	−0.172391	−	0.530564i
$603$	5.47658	−	3.97897i	0.223023	−	0.162036i
$604$	1.21082			0.0492676
$605$		0			0
$606$	−41.3449			−1.67952
$607$	15.6526	−	11.3723i	0.635319	−	0.461587i	−0.222920	−	0.974837i	$-0.571559\pi$
$607$	15.6526	−	11.3723i	0.635319	−	0.461587i	0.858239	+	0.513250i	$0.171559\pi$
$608$	3.21762	+	9.90280i	0.130492	+	0.401612i
$609$	−0.172856	+	0.531995i	−0.00700446	+	0.0215575i
$610$	10.3714	+	7.53526i	0.419925	+	0.305094i
$611$	−10.7870	−	7.83725i	−0.436397	−	0.317061i
$612$	0.840226	−	2.58595i	0.0339641	−	0.104531i
$613$	−6.50631	−	20.0244i	−0.262787	−	0.808776i	−0.992195	−	0.124697i	$-0.960204\pi$
$613$	−6.50631	−	20.0244i	−0.262787	−	0.808776i	0.729408	−	0.684079i	$-0.239796\pi$
$614$	33.9973	−	24.7005i	1.37202	−	0.996830i
$615$	53.4156			2.15392
$616$		0			0
$617$	−24.1496			−0.972228			−0.486114	−	0.873895i	$-0.661586\pi$
$617$	−24.1496			−0.972228			−0.486114	+	0.873895i	$0.661586\pi$
$618$	−43.8305	+	31.8447i	−1.76312	+	1.28098i
$619$	0.811091	+	2.49628i	0.0326005	+	0.100334i	0.966033	−	0.258420i	$-0.0832018\pi$
$619$	0.811091	+	2.49628i	0.0326005	+	0.100334i	−0.933432	+	0.358754i	$0.883202\pi$
$620$	−7.89352	+	24.2937i	−0.317011	+	0.975660i
$621$	−2.59048	−	1.88209i	−0.103952	−	0.0755258i
$622$	14.1055	+	10.2483i	0.565580	+	0.410918i
$623$	−5.13915	+	15.8167i	−0.205896	+	0.633681i
$624$	11.5889	+	35.6671i	0.463929	+	1.42783i
$625$	−40.7646	+	29.6172i	−1.63058	+	1.18469i
$626$	38.2408			1.52841
$627$		0			0
$628$	13.3630			0.533241
$629$	−0.273159	+	0.198461i	−0.0108916	+	0.00791318i
$630$	−4.82927	−	14.8630i	−0.192403	−	0.592154i
$631$	−7.76175	+	23.8882i	−0.308991	+	0.950975i	0.669167	+	0.743112i	$0.266651\pi$
$631$	−7.76175	+	23.8882i	−0.308991	+	0.950975i	−0.978158	+	0.207863i	$0.933349\pi$
$632$	8.29819	+	6.02899i	0.330084	+	0.239820i
$633$	−24.0852	−	17.4989i	−0.957300	−	0.695519i
$634$	12.3231	−	37.9266i	0.489412	−	1.50626i
$635$	10.9931	+	33.8333i	0.436248	+	1.34263i
$636$	8.48590	−	6.16537i	0.336488	−	0.244473i
$637$	−3.27792			−0.129876
$638$		0			0
$639$	14.5798			0.576770
$640$	−41.5900	+	30.2169i	−1.64399	+	1.19443i
$641$	6.38380	+	19.6473i	0.252145	+	0.776022i	0.994379	+	0.105881i	$0.0337664\pi$
$641$	6.38380	+	19.6473i	0.252145	+	0.776022i	−0.742234	+	0.670141i	$0.766234\pi$
$642$	−15.0249	+	46.2417i	−0.592984	+	1.82502i
$643$	−13.3190	−	9.67683i	−0.525251	−	0.381617i	0.293328	−	0.956012i	$-0.405237\pi$
$643$	−13.3190	−	9.67683i	−0.525251	−	0.381617i	−0.818578	+	0.574395i	$0.805237\pi$
$644$	−1.38047	−	1.00297i	−0.0543983	−	0.0395226i
$645$	23.0874	−	71.0557i	0.909066	−	2.79782i
$646$	−1.50635	−	4.63606i	−0.0592664	−	0.182403i
$647$	28.2819	−	20.5480i	1.11188	−	0.807825i	0.128918	−	0.991655i	$-0.458850\pi$
$647$	28.2819	−	20.5480i	1.11188	−	0.807825i	0.982958	+	0.183830i	$0.0588495\pi$
$648$	19.8038			0.777967
$649$		0			0
$650$	−64.5511			−2.53190
$651$	−12.7361	+	9.25333i	−0.499168	+	0.362666i
$652$	−5.91163	−	18.1941i	−0.231517	−	0.712537i
$653$	0.746736	−	2.29822i	0.0292221	−	0.0899362i	−0.935382	−	0.353639i	$-0.884944\pi$
$653$	0.746736	−	2.29822i	0.0292221	−	0.0899362i	0.964604	+	0.263703i	$0.0849440\pi$
$654$	−23.3174	−	16.9411i	−0.911783	−	0.662449i
$655$	−41.2918	−	30.0002i	−1.61340	−	1.17221i
$656$	−8.84395	+	27.2189i	−0.345298	+	1.06272i
$657$	6.71431	+	20.6645i	0.261950	+	0.806200i
$658$	−5.61795	+	4.08168i	−0.219011	+	0.159121i
$659$	−16.9733			−0.661186			−0.330593	−	0.943773i	$-0.607249\pi$
$659$	−16.9733			−0.661186			−0.330593	+	0.943773i	$0.607249\pi$
$660$		0			0
$661$	7.96946			0.309976			0.154988	−	0.987916i	$-0.450466\pi$
$661$	7.96946			0.309976			0.154988	+	0.987916i	$0.450466\pi$
$662$	−21.6068	+	15.6982i	−0.839770	+	0.610129i
$663$	−3.06602	−	9.43624i	−0.119074	−	0.366473i
$664$	1.18563	−	3.64898i	0.0460112	−	0.141608i
$665$	−7.11164	−	5.16691i	−0.275777	−	0.200364i
$666$	−0.794773	−	0.577437i	−0.0307968	−	0.0223752i
$667$	−0.140764	+	0.433227i	−0.00545040	+	0.0167746i
$668$	−1.38833	−	4.27283i	−0.0537160	−	0.165321i
$669$	26.6085	−	19.3322i	1.02875	−	0.747427i
$670$	−20.8744			−0.806449
$671$		0			0
$672$	11.0377			0.425787
$673$	12.9645	−	9.41925i	0.499744	−	0.363085i	−0.309175	−	0.951005i	$-0.600053\pi$
$673$	12.9645	−	9.41925i	0.499744	−	0.363085i	0.808919	+	0.587920i	$0.200053\pi$
$674$	−17.1931	−	52.9148i	−0.662253	−	2.03820i
$675$	−6.11643	+	18.8244i	−0.235422	+	0.724553i
$676$	1.66832	+	1.21211i	0.0641663	+	0.0466196i
$677$	12.3266	+	8.95583i	0.473751	+	0.344200i	0.798901	−	0.601462i	$-0.205415\pi$
$677$	12.3266	+	8.95583i	0.473751	+	0.344200i	−0.325150	+	0.945662i	$0.605415\pi$
$678$	13.7913	−	42.4454i	0.529653	−	1.63010i
$679$	0.798992	+	2.45904i	0.0306625	+	0.0943694i
$680$	8.05333	−	5.85109i	0.308831	−	0.224379i
$681$	−14.6082			−0.559787
$682$		0			0
$683$	14.3742			0.550013			0.275007	−	0.961442i	$-0.411320\pi$
$683$	14.3742			0.550013			0.275007	+	0.961442i	$0.411320\pi$
$684$	3.60008	−	2.61561i	0.137653	−	0.100010i
$685$	−7.95186	−	24.4733i	−0.303825	−	0.935077i
$686$	−0.527541	+	1.62360i	−0.0201416	+	0.0619895i
$687$	14.8356	+	10.7787i	0.566015	+	0.411234i
$688$	32.3852	+	23.5292i	1.23467	+	0.897043i
$689$	5.07059	−	15.6057i	0.193174	−	0.594529i
$690$	−9.17342	−	28.2329i	−0.349226	−	1.07481i
$691$	36.2422	−	26.3315i	1.37872	−	1.00170i	0.381720	−	0.924278i	$-0.375332\pi$
$691$	36.2422	−	26.3315i	1.37872	−	1.00170i	0.996999	−	0.0774200i	$-0.0246682\pi$
$692$	−17.9750			−0.683305
$693$		0			0
$694$	−9.82101			−0.372800
$695$	47.5138	−	34.5208i	1.80230	−	1.30945i
$696$	−0.320354	−	0.985949i	−0.0121430	−	0.0373723i
$697$	2.33979	−	7.20114i	0.0886259	−	0.272763i
$698$	−0.254043	−	0.184573i	−0.00961565	−	0.00698618i
$699$	−20.0262	−	14.5499i	−0.757462	−	0.550328i
$700$	−3.25946	+	10.0316i	−0.123196	+	0.379158i
$701$	0.0742660	+	0.228567i	0.00280499	+	0.00863287i	0.952449	−	0.304697i	$-0.0985553\pi$
$701$	0.0742660	+	0.228567i	0.00280499	+	0.00863287i	−0.949644	+	0.313330i	$0.898555\pi$
$702$	−7.76809	+	5.64385i	−0.293188	+	0.213013i
$703$	−0.552584			−0.0208411
$704$		0			0
$705$	−37.9039			−1.42754
$706$	−26.2704	+	19.0866i	−0.988699	+	0.718332i
$707$	3.26588	+	10.0513i	0.122826	+	0.378019i
$708$	−0.636883	+	1.96012i	−0.0239355	+	0.0736660i
$709$	−8.69968	−	6.32068i	−0.326723	−	0.237378i	0.412316	−	0.911041i	$-0.364720\pi$
$709$	−8.69968	−	6.32068i	−0.326723	−	0.237378i	−0.739039	+	0.673663i	$0.764720\pi$
$710$	−36.3725	−	26.4262i	−1.36504	−	0.991757i
$711$	3.85016	−	11.8496i	0.144392	−	0.444394i
$712$	−9.52441	−	29.3131i	−0.356942	−	1.09856i
$713$	−10.3716	+	7.53539i	−0.388419	+	0.282203i
$714$	−5.16735			−0.193383
$715$		0			0
$716$	−23.1879			−0.866573
$717$	46.6411	−	33.8867i	1.74184	−	1.26552i
$718$	0.379264	+	1.16725i	0.0141540	+	0.0435615i
$719$	−7.96486	+	24.5133i	−0.297039	+	0.914193i	0.685489	+	0.728083i	$0.259588\pi$
$719$	−7.96486	+	24.5133i	−0.297039	+	0.914193i	−0.982529	+	0.186111i	$0.940412\pi$
$720$	36.9756	+	26.8644i	1.37800	+	1.00118i
$721$	11.2040	+	8.14017i	0.417258	+	0.303156i
$722$	−7.55800	+	23.2611i	−0.281280	+	0.865690i
$723$	12.9206	+	39.7656i	0.480524	+	1.47890i
$724$	1.46153	−	1.06186i	0.0543174	−	0.0394639i
$725$	2.81580			0.104576
$726$		0			0
$727$	−5.47160			−0.202930			−0.101465	−	0.994839i	$-0.532353\pi$
$727$	−5.47160			−0.202930			−0.101465	+	0.994839i	$0.532353\pi$
$728$	4.91477	−	3.57079i	0.182154	−	0.132342i
$729$	−3.78848	−	11.6597i	−0.140314	−	0.431842i
$730$	20.7045	−	63.7218i	0.766307	−	2.35845i
$731$	−8.56796	−	6.22498i	−0.316897	−	0.230239i
$732$	3.13053	+	2.27447i	0.115708	+	0.0840667i
$733$	6.13595	−	18.8845i	0.226636	−	0.697515i	−0.771485	−	0.636248i	$-0.780486\pi$
$733$	6.13595	−	18.8845i	0.226636	−	0.697515i	0.998121	−	0.0612676i	$-0.0195143\pi$
$734$	−4.16386	−	12.8150i	−0.153691	−	0.473011i
$735$	−7.53867	+	5.47716i	−0.278068	+	0.202028i
$736$	8.98845			0.331319
$737$		0			0
$738$	22.0304			0.810951
$739$	1.45685	−	1.05847i	0.0535912	−	0.0389363i	−0.560667	−	0.828041i	$-0.689455\pi$
$739$	1.45685	−	1.05847i	0.0535912	−	0.0389363i	0.614258	+	0.789105i	$0.289455\pi$
$740$	0.293708	+	0.903939i	0.0107969	+	0.0332295i
$741$	5.01783	−	15.4433i	0.184335	−	0.567324i
$742$	−6.91368	−	5.02309i	−0.253809	−	0.184403i
$743$	38.8797	+	28.2477i	1.42636	+	1.03631i	0.990681	+	0.136205i	$0.0434906\pi$
$743$	38.8797	+	28.2477i	1.42636	+	1.03631i	0.435676	+	0.900104i	$0.356509\pi$
$744$	9.01590	−	27.7481i	0.330539	−	1.01729i
$745$	−30.2323	−	93.0454i	−1.10762	−	3.40892i
$746$	21.6403	−	15.7226i	0.792307	−	0.575645i
$747$	−4.66054			−0.170520
$748$		0			0
$749$	12.4286			0.454133
$750$	−84.1082	+	61.1082i	−3.07120	+	2.23136i
$751$	−7.73980	−	23.8207i	−0.282429	−	0.869228i	−0.987157	−	0.159751i	$-0.948931\pi$
$751$	−7.73980	−	23.8207i	−0.282429	−	0.869228i	0.704728	−	0.709478i	$-0.251069\pi$
$752$	6.27569	−	19.3146i	0.228851	−	0.704331i
$753$	−28.4174	−	20.6465i	−1.03559	−	0.752399i
$754$	1.10510	+	0.802901i	0.0402453	+	0.0292399i
$755$	1.66394	−	5.12107i	0.0605569	−	0.186375i
$756$	0.484840	+	1.49219i	0.0176335	+	0.0542703i
$757$	−8.61495	+	6.25913i	−0.313116	+	0.227492i	−0.733232	−	0.679978i	$-0.761989\pi$
$757$	−8.61495	+	6.25913i	−0.313116	+	0.227492i	0.420116	+	0.907470i	$0.361989\pi$
$758$	−22.7298			−0.825583
$759$		0			0
$760$	16.2914			0.590952
$761$	−24.1216	+	17.5254i	−0.874408	+	0.635295i	−0.931766	−	0.363059i	$-0.881732\pi$
$761$	−24.1216	+	17.5254i	−0.874408	+	0.635295i	0.0573579	+	0.998354i	$0.481732\pi$
$762$	10.5759	+	32.5493i	0.383125	+	1.17914i
$763$	−2.27668	+	7.00689i	−0.0824212	+	0.253666i
$764$	−0.719781	−	0.522952i	−0.0260408	−	0.0189197i
$765$	−9.78242	−	7.10734i	−0.353684	−	0.256967i
$766$	6.25053	−	19.2372i	0.225841	−	0.695067i
$767$	0.996314	+	3.06634i	0.0359748	+	0.110719i
$768$	−33.4765	+	24.3221i	−1.20798	+	0.877648i
$769$	28.3115			1.02094			0.510470	−	0.859896i	$-0.329471\pi$
$769$	28.3115			1.02094			0.510470	+	0.859896i	$0.329471\pi$
$770$		0			0
$771$	6.14090			0.221159
$772$	−17.1126	+	12.4330i	−0.615894	+	0.447473i
$773$	4.09645	+	12.6076i	0.147339	+	0.453463i	0.997304	−	0.0733754i	$-0.0233771\pi$
$773$	4.09645	+	12.6076i	0.147339	+	0.453463i	−0.849965	+	0.526839i	$0.823377\pi$
$774$	9.52204	−	29.3058i	0.342263	−	1.05338i
$775$	64.1118	+	46.5800i	2.30296	+	1.67320i
$776$	−3.87672	−	2.81660i	−0.139166	−	0.101110i
$777$	−0.181012	+	0.557096i	−0.00649375	+	0.0199857i
$778$	−3.19147	−	9.82235i	−0.114420	−	0.352148i
$779$	10.0252	−	7.28374i	0.359191	−	0.260967i
$780$	−27.9298			−1.00005
$781$		0			0
$782$	−4.20800			−0.150478
$783$	0.338854	−	0.246192i	0.0121097	−	0.00879818i
$784$	−1.54282	−	4.74831i	−0.0551007	−	0.169583i
$785$	18.3637	−	56.5177i	0.655429	−	2.01720i
$786$	−39.7247	−	28.8617i	−1.41693	−	1.02946i
$787$	42.6167	+	30.9628i	1.51912	+	1.10370i	0.961922	+	0.273325i	$0.0881235\pi$
$787$	42.6167	+	30.9628i	1.51912	+	1.10370i	0.557198	+	0.830380i	$0.311876\pi$
$788$	2.80086	−	8.62017i	0.0997767	−	0.307081i
$789$	7.06524	+	21.7446i	0.251529	+	0.774127i
$790$	−31.0826	+	22.5828i	−1.10587	+	0.803460i
$791$	−11.4083			−0.405632
$792$		0			0
$793$	6.05337			0.214961
$794$	15.9882	−	11.6161i	0.567401	−	0.412241i
$795$	−14.4144	−	44.3630i	−0.511227	−	1.57339i
$796$	2.93433	−	9.03095i	0.104005	−	0.320094i
$797$	5.93398	+	4.31129i	0.210192	+	0.152714i	0.687901	−	0.725805i	$-0.258532\pi$
$797$	5.93398	+	4.31129i	0.210192	+	0.152714i	−0.477708	+	0.878518i	$0.658532\pi$
$798$	−6.84174	−	4.97082i	−0.242195	−	0.175965i
$799$	−1.66032	+	5.10995i	−0.0587380	+	0.180777i
$800$	−17.1696	−	52.8426i	−0.607038	−	1.86827i
$801$	−30.2889	+	22.0062i	−1.07021	+	0.777551i
$802$	57.6890			2.03707
$803$		0			0
$804$	−6.30080			−0.222212
$805$	−6.13907	+	4.46030i	−0.216374	+	0.157205i
$806$	11.8797	+	36.5618i	0.418443	+	1.28784i
$807$	−15.2796	+	47.0257i	−0.537867	+	1.65538i
$808$	−15.8461	−	11.5129i	−0.557464	−	0.405021i
$809$	7.01263	+	5.09497i	0.246551	+	0.179130i	0.704197	−	0.710005i	$-0.251307\pi$
$809$	7.01263	+	5.09497i	0.246551	+	0.179130i	−0.457646	+	0.889135i	$0.651307\pi$
$810$	−22.9227	+	70.5487i	−0.805420	+	2.47883i
$811$	−6.16449	−	18.9723i	−0.216464	−	0.666209i	−0.999046	−	0.0436614i	$-0.986098\pi$
$811$	−6.16449	−	18.9723i	−0.216464	−	0.666209i	0.782582	−	0.622548i	$-0.213902\pi$
$812$	0.180576	−	0.131196i	0.00633698	−	0.00460409i
$813$	34.3418			1.20442
$814$		0			0
$815$	−85.0745			−2.98003
$816$	12.2260	−	8.88271i	0.427996	−	0.310957i
$817$	−5.35603	−	16.4842i	−0.187384	−	0.576708i
$818$	−9.52316	+	29.3093i	−0.332969	+	1.02477i
$819$	−5.97000	−	4.33746i	−0.208609	−	0.151563i
$820$	−17.2436	−	12.5282i	−0.602172	−	0.437504i
$821$	−16.5524	+	50.9432i	−0.577684	+	1.77793i	0.0491669	+	0.998791i	$0.484343\pi$
$821$	−16.5524	+	50.9432i	−0.577684	+	1.77793i	−0.626851	+	0.779139i	$0.715657\pi$
$822$	−7.65008	−	23.5445i	−0.266827	−	0.821209i
$823$	6.83491	−	4.96585i	0.238250	−	0.173099i	−0.462253	−	0.886748i	$-0.652959\pi$
$823$	6.83491	−	4.96585i	0.238250	−	0.173099i	0.700503	+	0.713649i	$0.252959\pi$
$824$	−25.6662			−0.894125
$825$		0			0
$826$	1.67915			0.0584250
$827$	−2.57477	+	1.87068i	−0.0895337	+	0.0650500i	−0.631652	−	0.775252i	$-0.717623\pi$
$827$	−2.57477	+	1.87068i	−0.0895337	+	0.0650500i	0.542118	+	0.840302i	$0.317623\pi$
$828$	−1.18705	−	3.65338i	−0.0412530	−	0.126964i
$829$	17.7712	−	54.6943i	0.617221	−	1.89961i	0.259837	−	0.965652i	$-0.416331\pi$
$829$	17.7712	−	54.6943i	0.617221	−	1.89961i	0.357384	−	0.933958i	$-0.383669\pi$
$830$	11.6267	+	8.44729i	0.403569	+	0.293210i
$831$	9.65218	+	7.01272i	0.334830	+	0.243269i
$832$	−1.78532	+	5.49464i	−0.0618948	+	0.190492i
$833$	0.408175	+	1.25623i	0.0141424	+	0.0435259i
$834$	45.7106	−	33.2107i	1.58283	−	1.14999i
$835$	−19.9795			−0.691419
$836$		0			0
$837$	11.7878			0.407447
$838$	−3.57101	+	2.59449i	−0.123358	+	0.0896251i
$839$	3.88108	+	11.9447i	0.133990	+	0.412378i	0.995432	−	0.0954784i	$-0.0304381\pi$
$839$	3.88108	+	11.9447i	0.133990	+	0.412378i	−0.861442	+	0.507856i	$0.830438\pi$
$840$	5.33662	−	16.4244i	0.184131	−	0.566697i
$841$	23.4133	+	17.0107i	0.807355	+	0.586578i
$842$	−19.3285	−	14.0430i	−0.666103	−	0.483952i
$843$	−10.7353	+	33.0398i	−0.369743	+	1.13795i
$844$	3.67094	+	11.2980i	0.126359	+	0.388892i
$845$	7.41917	−	5.39034i	0.255227	−	0.185433i
$846$	−15.6329			−0.537469
$847$		0			0
$848$	24.9926			0.858248
$849$	−10.5035	+	7.63122i	−0.360478	+	0.261903i
$850$	8.03806	+	24.7386i	0.275703	+	0.848528i
$851$	−0.147406	+	0.453668i	−0.00505300	+	0.0155515i
$852$	−10.9788	−	7.97656i	−0.376127	−	0.273272i
$853$	26.9658	+	19.5918i	0.923290	+	0.670810i	0.944341	−	0.328969i	$-0.106701\pi$
$853$	26.9658	+	19.5918i	0.923290	+	0.670810i	−0.0210505	+	0.999778i	$0.506701\pi$
$854$	0.974215	−	2.99833i	0.0333370	−	0.102601i
$855$	−6.11522	−	18.8207i	−0.209136	−	0.643655i
$856$	−18.6350	+	13.5391i	−0.636930	+	0.462757i
$857$	−54.0291			−1.84560			−0.922800	−	0.385279i	$-0.874105\pi$
$857$	−54.0291			−1.84560			−0.922800	+	0.385279i	$0.874105\pi$
$858$		0			0
$859$	−12.8624			−0.438860			−0.219430	−	0.975628i	$-0.570420\pi$
$859$	−12.8624			−0.438860			−0.219430	+	0.975628i	$0.570420\pi$
$860$	−24.1186	+	17.5232i	−0.822438	+	0.597536i
$861$	−4.05923	−	12.4930i	−0.138338	−	0.425761i
$862$	17.7613	−	54.6638i	0.604954	−	1.86186i
$863$	26.8813	+	19.5304i	0.915049	+	0.664822i	0.942287	−	0.334807i	$-0.108671\pi$
$863$	26.8813	+	19.5304i	0.915049	+	0.664822i	−0.0272379	+	0.999629i	$0.508671\pi$
$864$	−6.68635	−	4.85791i	−0.227474	−	0.165270i
$865$	−24.7016	+	76.0237i	−0.839879	+	2.58488i
$866$	3.96865	+	12.2143i	0.134860	+	0.415057i
$867$	28.2818	−	20.5480i	0.960502	−	0.697845i
$868$	6.28176			0.213217
$869$		0			0
$870$	3.88313			0.131650
$871$	−7.97425	+	5.79363i	−0.270197	+	0.196310i
$872$	−4.21938	−	12.9859i	−0.142886	−	0.439758i
$873$	−1.79871	+	5.53585i	−0.0608770	+	0.187360i
$874$	−5.57153	−	4.04796i	−0.188460	−	0.136924i
$875$	21.4998	+	15.6205i	0.726826	+	0.528070i
$876$	6.24951	−	19.2340i	0.211151	−	0.649857i
$877$	−8.55077	−	26.3166i	−0.288739	−	0.888647i	−0.985253	−	0.171104i	$-0.945267\pi$
$877$	−8.55077	−	26.3166i	−0.288739	−	0.888647i	0.696514	−	0.717543i	$-0.254733\pi$
$878$	−30.4016	+	22.0880i	−1.02600	+	0.745435i
$879$	61.7352			2.08228
$880$		0			0
$881$	48.9636			1.64963			0.824813	−	0.565406i	$-0.191280\pi$
$881$	48.9636			1.64963			0.824813	+	0.565406i	$0.191280\pi$
$882$	−3.10921	+	2.25897i	−0.104692	+	0.0760635i
$883$	6.58897	+	20.2788i	0.221736	+	0.682435i	0.998607	+	0.0527736i	$0.0168062\pi$
$883$	6.58897	+	20.2788i	0.221736	+	0.682435i	−0.776870	+	0.629661i	$0.783194\pi$
$884$	−1.22342	+	3.76531i	−0.0411482	+	0.126641i
$885$	7.41498	+	5.38730i	0.249252	+	0.181092i
$886$	−32.7178	−	23.7708i	−1.09917	−	0.798597i
$887$	13.9825	−	43.0337i	0.469487	−	1.44493i	−0.383765	−	0.923431i	$-0.625373\pi$
$887$	13.9825	−	43.0337i	0.469487	−	1.44493i	0.853251	−	0.521500i	$-0.174627\pi$
$888$	−0.335470	−	1.03247i	−0.0112576	−	0.0346474i
$889$	7.07765	−	5.14221i	0.237377	−	0.172464i
$890$	115.449			3.86985
$891$		0			0
$892$	−13.1240			−0.439423
$893$	−7.11392	+	5.16857i	−0.238058	+	0.172959i
$894$	−29.0849	−	89.5142i	−0.972745	−	2.99380i
$895$	−31.8654	+	98.0715i	−1.06514	+	3.27817i
$896$	10.2278	+	7.43092i	0.341687	+	0.248250i
$897$	−11.3403	−	8.23921i	−0.378642	−	0.275099i
$898$	1.20023	−	3.69392i	0.0400521	−	0.123268i
$899$	−0.518206	−	1.59487i	−0.0172831	−	0.0531920i
$900$	−19.2105	+	13.9573i	−0.640351	+	0.465242i
$901$	−6.61213			−0.220282
$902$		0			0
$903$	−18.3732			−0.611423
$904$	17.1051	−	12.4276i	0.568906	−	0.413335i
$905$	−2.48260	−	7.64067i	−0.0825245	−	0.253984i
$906$	1.60079	−	4.92672i	0.0531826	−	0.163679i
$907$	36.4596	+	26.4894i	1.21062	+	0.879568i	0.995287	−	0.0969727i	$-0.0309160\pi$
$907$	36.4596	+	26.4894i	1.21062	+	0.879568i	0.215334	+	0.976540i	$0.430916\pi$
$908$	4.71581	+	3.42623i	0.156499	+	0.113704i
$909$	−7.35221	+	22.6278i	−0.243857	+	0.750516i
$910$	7.03172	+	21.6414i	0.233099	+	0.717406i
$911$	7.45484	−	5.41626i	0.246990	−	0.179449i	−0.457402	−	0.889260i	$-0.651220\pi$
$911$	7.45484	−	5.41626i	0.246990	−	0.179449i	0.704392	+	0.709812i	$0.251220\pi$
$912$	24.7325			0.818975
$913$		0			0
$914$	46.6283			1.54233
$915$	13.9217	−	10.1147i	0.460238	−	0.334383i
$916$	−2.26117	−	6.95916i	−0.0747111	−	0.229937i
$917$	−3.87866	+	11.9373i	−0.128085	+	0.394204i
$918$	3.13025	+	2.27426i	0.103314	+	0.0750619i
$919$	40.2198	+	29.2214i	1.32673	+	0.963924i	0.999822	+	0.0188673i	$0.00600600\pi$
$919$	40.2198	+	29.2214i	1.32673	+	0.963924i	0.326906	+	0.945057i	$0.393994\pi$
$920$	4.34585	−	13.3751i	0.143278	−	0.440966i
$921$	−17.4311	−	53.6475i	−0.574375	−	1.76774i
$922$	−11.3515	+	8.24738i	−0.373843	+	0.271613i
$923$	−21.2292			−0.698767
$924$		0			0
$925$	2.94866			0.0969514
$926$	38.6491	−	28.0802i	1.27009	−	0.922773i
$927$	9.63419	+	29.6510i	0.316428	+	0.973866i
$928$	−0.363329	+	1.11821i	−0.0119269	+	0.0367071i
$929$	−40.0548	−	29.1015i	−1.31416	−	0.954790i	−0.999985	−	0.00542290i	$-0.998274\pi$
$929$	−40.0548	−	29.1015i	−1.31416	−	0.954790i	−0.314170	−	0.949367i	$-0.601726\pi$
$930$	88.4133	+	64.2360i	2.89919	+	2.10638i
$931$	−0.668017	+	2.05594i	−0.0218934	+	0.0673808i
$932$	3.05229	+	9.39399i	0.0999812	+	0.307710i
$933$	18.9341	−	13.7564i	0.619875	−	0.450366i
$934$	45.5377			1.49004
$935$		0			0
$936$	13.6761			0.447019
$937$	5.65333	−	4.10739i	0.184686	−	0.134182i	−0.491601	−	0.870821i	$-0.663588\pi$
$937$	5.65333	−	4.10739i	0.184686	−	0.134182i	0.676287	+	0.736638i	$0.263588\pi$
$938$	1.58632	+	4.88218i	0.0517951	+	0.159409i
$939$	15.8623	−	48.8191i	0.517646	−	1.59315i
$940$	12.2361	+	8.89005i	0.399098	+	0.289961i
$941$	37.8815	+	27.5225i	1.23490	+	0.897208i	0.997248	−	0.0741421i	$-0.0236219\pi$
$941$	37.8815	+	27.5225i	1.23490	+	0.897208i	0.237653	+	0.971350i	$0.423622\pi$
$942$	17.6668	−	54.3728i	0.575615	−	1.77156i
$943$	−3.30561	−	10.1736i	−0.107645	−	0.331299i
$944$	−3.97288	+	2.88647i	−0.129306	+	0.0939465i
$945$	6.97736			0.226974
$946$		0			0
$947$	15.1286			0.491614			0.245807	−	0.969319i	$-0.420947\pi$
$947$	15.1286			0.491614			0.245807	+	0.969319i	$0.420947\pi$
$948$	−9.38206	+	6.81647i	−0.304715	+	0.221389i
$949$	−9.77647	−	30.0889i	−0.317358	−	0.976726i
$950$	−13.1551	+	40.4871i	−0.426806	+	1.31357i
$951$	−43.3063	−	31.4639i	−1.40430	−	1.02029i
$952$	−1.98047	−	1.43890i	−0.0641875	−	0.0466349i
$953$	17.3752	−	53.4753i	0.562838	−	1.73224i	−0.111453	−	0.993770i	$-0.535550\pi$
$953$	17.3752	−	53.4753i	0.562838	−	1.73224i	0.674291	−	0.738466i	$-0.264450\pi$
$954$	−5.94500	−	18.2968i	−0.192477	−	0.592382i
$955$	−3.20092	+	2.32561i	−0.103579	+	0.0752549i
$956$	−23.0045			−0.744019
$957$		0			0
$958$	39.6470			1.28094
$959$	−5.11961	+	3.71962i	−0.165321	+	0.120113i
$960$	5.07521	+	15.6199i	0.163802	+	0.504130i
$961$	5.00461	−	15.4026i	0.161439	−	0.496858i
$962$	1.15724	+	0.840785i	0.0373110	+	0.0271080i
$963$	22.6360	+	16.4460i	0.729435	+	0.529965i
$964$	5.15568	−	15.8675i	0.166053	−	0.511059i
$965$	29.0679	+	89.4619i	0.935730	+	2.87988i
$966$	−5.90609	+	4.29102i	−0.190025	+	0.138061i
$967$	−46.3761			−1.49136			−0.745678	−	0.666307i	$-0.767874\pi$
$967$	−46.3761			−1.49136			−0.745678	+	0.666307i	$0.767874\pi$
$968$		0			0
$969$	−6.54333			−0.210202
$970$	14.5211	−	10.5502i	0.466243	−	0.338746i
$971$	4.80211	+	14.7794i	0.154107	+	0.474293i	0.998069	−	0.0621097i	$-0.0197828\pi$
$971$	4.80211	+	14.7794i	0.154107	+	0.474293i	−0.843962	+	0.536403i	$0.819783\pi$
$972$	−5.46453	+	16.8181i	−0.175275	+	0.539440i
$973$	−11.6846	−	8.48935i	−0.374591	−	0.272156i
$974$	25.9541	+	18.8567i	0.831622	+	0.604208i
$975$	−26.7758	+	82.4074i	−0.857512	+	2.63915i
$976$	2.84914	+	8.76876i	0.0911988	+	0.280681i
$977$	−26.5590	+	19.2962i	−0.849697	+	0.617341i	−0.925062	−	0.379815i	$-0.875988\pi$
$977$	−26.5590	+	19.2962i	−0.849697	+	0.617341i	0.0753657	+	0.997156i	$0.475988\pi$
$978$	−81.8458			−2.61714
$979$		0			0
$980$	3.71825			0.118775
$981$	−13.4182	+	9.74890i	−0.428410	+	0.311258i
$982$	−3.90683	−	12.0240i	−0.124672	−	0.383701i
$983$	7.51478	−	23.1281i	0.239684	−	0.737673i	−0.756781	−	0.653668i	$-0.773229\pi$
$983$	7.51478	−	23.1281i	0.239684	−	0.737673i	0.996465	−	0.0840042i	$-0.0267709\pi$
$984$	19.6955	+	14.3096i	0.627868	+	0.456173i
$985$	−32.6093	−	23.6921i	−1.03902	−	0.754892i
$986$	0.170095	−	0.523498i	0.00541692	−	0.0166716i
$987$	2.88044	+	8.86509i	0.0916854	+	0.282179i
$988$	−5.24195	+	3.80850i	−0.166769	+	0.121165i
$989$	−14.9622			−0.475769
$990$		0			0
$991$	−47.7104			−1.51557			−0.757786	−	0.652503i	$-0.773719\pi$
$991$	−47.7104			−1.51557			−0.757786	+	0.652503i	$0.773719\pi$
$992$	−26.7703	+	19.4498i	−0.849959	+	0.617531i
$993$	11.0782	+	34.0953i	0.351557	+	1.08198i
$994$	−3.41658	+	10.5151i	−0.108367	+	0.333520i
$995$	−34.1633	−	24.8211i	−1.08305	−	0.786881i
$996$	3.50944	+	2.54976i	0.111201	+	0.0807922i
$997$	−6.13241	+	18.8736i	−0.194215	+	0.597733i	0.805770	+	0.592229i	$0.201752\pi$
$997$	−6.13241	+	18.8736i	−0.194215	+	0.597733i	−0.999985	+	0.00550400i	$0.998248\pi$
$998$	12.4871	+	38.4313i	0.395272	+	1.21652i
$999$	0.354843	−	0.257808i	0.0112267	−	0.00815669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.729.1		16
11.2	odd	10		847.2.a.p.1.2		8
11.3	even	5		847.2.f.v.148.4		16
11.4	even	5	inner	847.2.f.x.323.1		16
11.5	even	5		847.2.f.v.372.4		16
11.6	odd	10		847.2.f.w.372.1		16
11.7	odd	10		77.2.f.b.15.4	✓	16
11.8	odd	10		847.2.f.w.148.1		16
11.9	even	5		847.2.a.o.1.7		8
11.10	odd	2		77.2.f.b.36.4	yes	16
33.2	even	10		7623.2.a.ct.1.7		8
33.20	odd	10		7623.2.a.cw.1.2		8
33.29	even	10		693.2.m.i.631.1		16
33.32	even	2		693.2.m.i.190.1		16
77.10	even	6		539.2.q.f.520.4		32
77.13	even	10		5929.2.a.bt.1.2		8
77.18	odd	30		539.2.q.g.422.1		32
77.20	odd	10		5929.2.a.bs.1.7		8
77.32	odd	6		539.2.q.g.520.4		32
77.40	even	30		539.2.q.f.312.4		32
77.51	odd	30		539.2.q.g.312.4		32
77.54	even	6		539.2.q.f.410.1		32
77.62	even	10		539.2.f.e.246.4		16
77.65	odd	6		539.2.q.g.410.1		32
77.73	even	30		539.2.q.f.422.1		32
77.76	even	2		539.2.f.e.344.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.4	✓	16	11.7	odd	10
77.2.f.b.36.4	yes	16	11.10	odd	2
539.2.f.e.246.4		16	77.62	even	10
539.2.f.e.344.4		16	77.76	even	2
539.2.q.f.312.4		32	77.40	even	30
539.2.q.f.410.1		32	77.54	even	6
539.2.q.f.422.1		32	77.73	even	30
539.2.q.f.520.4		32	77.10	even	6
539.2.q.g.312.4		32	77.51	odd	30
539.2.q.g.410.1		32	77.65	odd	6
539.2.q.g.422.1		32	77.18	odd	30
539.2.q.g.520.4		32	77.32	odd	6
693.2.m.i.190.1		16	33.32	even	2
693.2.m.i.631.1		16	33.29	even	10
847.2.a.o.1.7		8	11.9	even	5
847.2.a.p.1.2		8	11.2	odd	10
847.2.f.v.148.4		16	11.3	even	5
847.2.f.v.372.4		16	11.5	even	5
847.2.f.w.148.1		16	11.8	odd	10
847.2.f.w.372.1		16	11.6	odd	10
847.2.f.x.323.1		16	11.4	even	5	inner
847.2.f.x.729.1		16	1.1	even	1	trivial
5929.2.a.bs.1.7		8	77.20	odd	10
5929.2.a.bt.1.2		8	77.13	even	10
7623.2.a.ct.1.7		8	33.2	even	10
7623.2.a.cw.1.2		8	33.20	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38112 + 1.00344i) q^{2} +(0.708129 + 2.17940i) q^{3} +(0.282562 - 0.869638i) q^{4} +(-3.28976 - 2.39015i) q^{5} +(-3.16491 - 2.29944i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +(-1.82128 + 1.32323i) q^{9} +O(q^{10})\)	\(q+(-1.38112 + 1.00344i) q^{2} +(0.708129 + 2.17940i) q^{3} +(0.282562 - 0.869638i) q^{4} +(-3.28976 - 2.39015i) q^{5} +(-3.16491 - 2.29944i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +(-1.82128 + 1.32323i) q^{9} +6.94194 q^{10} +2.09538 q^{12} +(2.65189 - 1.92671i) q^{13} +(-0.527541 - 1.62360i) q^{14} +(2.87952 - 8.86224i) q^{15} +(4.03916 + 2.93462i) q^{16} +(-1.06862 - 0.776394i) q^{17} +(1.18761 - 3.65509i) q^{18} +(-0.668017 - 2.05594i) q^{19} +(-3.00813 + 2.18553i) q^{20} -2.29155 q^{21} -1.86611 q^{23} +(3.43586 - 2.49630i) q^{24} +(3.56462 + 10.9708i) q^{25} +(-1.72924 + 5.32205i) q^{26} +(1.38817 + 1.00856i) q^{27} +(0.739758 + 0.537466i) q^{28} +(0.0754316 - 0.232155i) q^{29} +(4.91579 + 15.1292i) q^{30} +(5.55785 - 4.03801i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(3.28976 - 2.39015i) q^{35} +(0.636110 + 1.95775i) q^{36} +(0.0789907 - 0.243108i) q^{37} +(2.98563 + 2.16919i) q^{38} +(6.07696 + 4.41517i) q^{39} +(-2.32882 + 7.16738i) q^{40} +(1.77139 + 5.45177i) q^{41} +(3.16491 - 2.29944i) q^{42} +8.01781 q^{43} +9.15429 q^{45} +(2.57733 - 1.87254i) q^{46} +(-1.25698 - 3.86859i) q^{47} +(-3.53546 + 10.8810i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-15.9317 - 11.5751i) q^{50} +(0.935354 - 2.87873i) q^{51} +(-0.926218 - 2.85060i) q^{52} +(4.04982 - 2.94237i) q^{53} -2.92926 q^{54} +1.85331 q^{56} +(4.00768 - 2.91175i) q^{57} +(0.128774 + 0.396325i) q^{58} +(-0.303947 + 0.935452i) q^{59} +(-6.89329 - 5.00827i) q^{60} +(1.49402 + 1.08547i) q^{61} +(-3.62414 + 11.1540i) q^{62} +(-0.695665 - 2.14104i) q^{63} +(-1.42591 + 1.03598i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(-0.977133 + 0.709928i) q^{68} +(-1.32145 - 4.06700i) q^{69} +(-2.14518 + 6.60218i) q^{70} +(-5.23953 - 3.80674i) q^{71} +(3.37538 + 2.45236i) q^{72} +(2.98252 - 9.17926i) q^{73} +(0.134850 + 0.415025i) q^{74} +(-21.3855 + 15.5375i) q^{75} -1.97668 q^{76} -12.8234 q^{78} +(-4.47750 + 3.25310i) q^{79} +(-6.27368 - 19.3084i) q^{80} +(-3.30205 + 10.1627i) q^{81} +(-7.91704 - 5.75206i) q^{82} +(1.67485 + 1.21685i) q^{83} +(-0.647507 + 1.99282i) q^{84} +(1.65979 + 5.10831i) q^{85} +(-11.0736 + 8.04542i) q^{86} +0.559372 q^{87} +16.6306 q^{89} +(-12.6432 + 9.18581i) q^{90} +(1.01293 + 3.11749i) q^{91} +(-0.527294 + 1.62284i) q^{92} +(12.7361 + 9.25333i) q^{93} +(5.61795 + 4.08168i) q^{94} +(-2.71640 + 8.36023i) q^{95} +(-3.41082 - 10.4974i) q^{96} +(2.09179 - 1.51977i) q^{97} +1.70716 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

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