LMFDB - Embedded newform 414.2.e.c.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.1481180578947.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 6x^{8} - 11x^{7} + 22x^{6} - 45x^{5} + 66x^{4} - 99x^{3} + 162x^{2} - 162x + 243 $ x^10 - 2x^9 + 6x^8 - 11x^7 + 22x^6 - 45x^5 + 66x^4 - 99x^3 + 162x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$-0.643944 - 1.60790i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.c.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.07051 + 1.36162i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08471 - 1.87878i) q^{5} +(-1.71445 + 0.246277i) q^{6} +(1.41120 - 2.44426i) q^{7} +1.00000 q^{8} +(-0.708023 + 2.91525i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.07051 + 1.36162i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08471 - 1.87878i) q^{5} +(-1.71445 + 0.246277i) q^{6} +(1.41120 - 2.44426i) q^{7} +1.00000 q^{8} +(-0.708023 + 2.91525i) q^{9} +2.16943 q^{10} +(2.01128 - 3.48364i) q^{11} +(0.643944 - 1.60790i) q^{12} +(3.22866 + 5.59220i) q^{13} +(1.41120 + 2.44426i) q^{14} +(1.39699 - 3.48822i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.41605 q^{17} +(-2.17067 - 2.07079i) q^{18} +4.95772 q^{19} +(-1.08471 + 1.87878i) q^{20} +(4.83886 - 0.695091i) q^{21} +(2.01128 + 3.48364i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.07051 + 1.36162i) q^{24} +(0.146790 - 0.254247i) q^{25} -6.45732 q^{26} +(-4.72741 + 2.15675i) q^{27} -2.82239 q^{28} +(0.341850 - 0.592102i) q^{29} +(2.32239 + 2.95394i) q^{30} +(1.11269 + 1.92723i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.89648 - 0.990665i) q^{33} +(-0.708023 + 1.22633i) q^{34} -6.12298 q^{35} +(2.87870 - 0.844461i) q^{36} -6.39817 q^{37} +(-2.47886 + 4.29351i) q^{38} +(-4.15815 + 10.3827i) q^{39} +(-1.08471 - 1.87878i) q^{40} +(-3.85138 - 6.67079i) q^{41} +(-1.81746 + 4.53812i) q^{42} +(1.14595 - 1.98484i) q^{43} -4.02256 q^{44} +(6.24512 - 1.83200i) q^{45} +1.00000 q^{46} +(-0.787888 + 1.36466i) q^{47} +(-1.71445 + 0.246277i) q^{48} +(-0.482949 - 0.836491i) q^{49} +(0.146790 + 0.254247i) q^{50} +(1.51589 + 1.92812i) q^{51} +(3.22866 - 5.59220i) q^{52} -5.20602 q^{53} +(0.495910 - 5.17243i) q^{54} -8.72665 q^{55} +(1.41120 - 2.44426i) q^{56} +(5.30728 + 6.75053i) q^{57} +(0.341850 + 0.592102i) q^{58} +(6.09768 + 10.5615i) q^{59} +(-3.71938 + 0.534281i) q^{60} +(4.69131 - 8.12558i) q^{61} -2.22537 q^{62} +(6.12649 + 5.84459i) q^{63} +1.00000 q^{64} +(7.00434 - 12.1319i) q^{65} +(-2.59030 + 6.46786i) q^{66} +(4.17428 + 7.23006i) q^{67} +(-0.708023 - 1.22633i) q^{68} +(0.643944 - 1.60790i) q^{69} +(3.06149 - 5.30265i) q^{70} -12.7185 q^{71} +(-0.708023 + 2.91525i) q^{72} -0.0997459 q^{73} +(3.19908 - 5.54098i) q^{74} +(0.503328 - 0.0723019i) q^{75} +(-2.47886 - 4.29351i) q^{76} +(-5.67662 - 9.83219i) q^{77} +(-6.91261 - 8.79242i) q^{78} +(3.08471 - 5.34288i) q^{79} +2.16943 q^{80} +(-7.99741 - 4.12813i) q^{81} +7.70276 q^{82} +(-1.53684 + 2.66189i) q^{83} +(-3.02140 - 3.84303i) q^{84} +(-1.53600 - 2.66044i) q^{85} +(1.14595 + 1.98484i) q^{86} +(1.17217 - 0.168380i) q^{87} +(2.01128 - 3.48364i) q^{88} +7.82691 q^{89} +(-1.53600 + 6.32443i) q^{90} +18.2251 q^{91} +(-0.500000 + 0.866025i) q^{92} +(-1.43302 + 3.57817i) q^{93} +(-0.787888 - 1.36466i) q^{94} +(-5.37771 - 9.31446i) q^{95} +(0.643944 - 1.60790i) q^{96} +(-6.48054 + 11.2246i) q^{97} +0.965897 q^{98} +(8.73166 + 8.32988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.07051	+	1.36162i	0.618058	+	0.786132i
$3$	1.07051	+	1.36162i	0.618058	+	0.786132i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.08471	−	1.87878i	−0.485099	−	0.840216i	0.514754	−	0.857338i	$-0.327883\pi$
$5$	−1.08471	−	1.87878i	−0.485099	−	0.840216i	−0.999853	+	0.0171216i	$0.994550\pi$
$6$	−1.71445	+	0.246277i	−0.699922	+	0.100542i
$7$	1.41120	−	2.44426i	0.533382	−	0.923845i	−0.465858	−	0.884860i	$-0.654254\pi$
$7$	1.41120	−	2.44426i	0.533382	−	0.923845i	0.999240	−	0.0389851i	$-0.0124125\pi$
$8$	1.00000			0.353553
$9$	−0.708023	+	2.91525i	−0.236008	+	0.971751i
$10$	2.16943			0.686034
$11$	2.01128	−	3.48364i	0.606423	−	1.05036i	−0.385401	−	0.922749i	$-0.625937\pi$
$11$	2.01128	−	3.48364i	0.606423	−	1.05036i	0.991825	−	0.127607i	$-0.0407297\pi$
$12$	0.643944	−	1.60790i	0.185891	−	0.464160i
$13$	3.22866	+	5.59220i	0.895469	+	1.55100i	0.833223	+	0.552936i	$0.186493\pi$
$13$	3.22866	+	5.59220i	0.895469	+	1.55100i	0.0622452	+	0.998061i	$0.480174\pi$
$14$	1.41120	+	2.44426i	0.377158	+	0.653257i
$15$	1.39699	−	3.48822i	0.360701	−	0.900655i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41605			0.343441			0.171721	−	0.985146i	$-0.445067\pi$
$17$	1.41605			0.343441			0.171721	+	0.985146i	$0.445067\pi$
$18$	−2.17067	−	2.07079i	−0.511632	−	0.488090i
$19$	4.95772			1.13738			0.568689	−	0.822552i	$-0.307451\pi$
$19$	4.95772			1.13738			0.568689	+	0.822552i	$0.307451\pi$
$20$	−1.08471	+	1.87878i	−0.242549	+	0.420108i
$21$	4.83886	−	0.695091i	1.05593	−	0.151681i
$22$	2.01128	+	3.48364i	0.428806	+	0.742714i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	1.07051	+	1.36162i	0.218517	+	0.277940i
$25$	0.146790	−	0.254247i	0.0293579	−	0.0508494i
$26$	−6.45732			−1.26638
$27$	−4.72741	+	2.15675i	−0.909791	+	0.415066i
$28$	−2.82239			−0.533382
$29$	0.341850	−	0.592102i	0.0634800	−	0.109951i	−0.832539	−	0.553967i	$-0.813113\pi$
$29$	0.341850	−	0.592102i	0.0634800	−	0.109951i	0.896019	+	0.444016i	$0.146447\pi$
$30$	2.32239	+	2.95394i	0.424009	+	0.539313i
$31$	1.11269	+	1.92723i	0.199844	+	0.346141i	0.948478	−	0.316843i	$-0.102623\pi$
$31$	1.11269	+	1.92723i	0.199844	+	0.346141i	−0.748633	+	0.662984i	$0.769290\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	6.89648	−	0.990665i	1.20052	−	0.172453i
$34$	−0.708023	+	1.22633i	−0.121425	+	0.210314i
$35$	−6.12298			−1.03497
$36$	2.87870	−	0.844461i	0.479783	−	0.140744i
$37$	−6.39817			−1.05185			−0.525926	−	0.850530i	$-0.676281\pi$
$37$	−6.39817			−1.05185			−0.525926	+	0.850530i	$0.676281\pi$
$38$	−2.47886	+	4.29351i	−0.402124	+	0.696499i
$39$	−4.15815	+	10.3827i	−0.665837	+	1.66256i
$40$	−1.08471	−	1.87878i	−0.171508	−	0.297061i
$41$	−3.85138	−	6.67079i	−0.601485	−	1.04180i	−0.992596	−	0.121459i	$-0.961243\pi$
$41$	−3.85138	−	6.67079i	−0.601485	−	1.04180i	0.391112	−	0.920343i	$-0.372091\pi$
$42$	−1.81746	+	4.53812i	−0.280441	+	0.700247i
$43$	1.14595	−	1.98484i	0.174755	−	0.302685i	−0.765321	−	0.643648i	$-0.777420\pi$
$43$	1.14595	−	1.98484i	0.174755	−	0.302685i	0.940077	+	0.340963i	$0.110753\pi$
$44$	−4.02256			−0.606423
$45$	6.24512	−	1.83200i	0.930968	−	0.273098i
$46$	1.00000			0.147442
$47$	−0.787888	+	1.36466i	−0.114925	+	0.199056i	−0.917750	−	0.397159i	$-0.869996\pi$
$47$	−0.787888	+	1.36466i	−0.114925	+	0.199056i	0.802825	+	0.596215i	$0.203330\pi$
$48$	−1.71445	+	0.246277i	−0.247460	+	0.0355471i
$49$	−0.482949	−	0.836491i	−0.0689926	−	0.119499i
$50$	0.146790	+	0.254247i	0.0207592	+	0.0359560i
$51$	1.51589	+	1.92812i	0.212267	+	0.269990i
$52$	3.22866	−	5.59220i	0.447734	−	0.775499i
$53$	−5.20602			−0.715102			−0.357551	−	0.933894i	$-0.616388\pi$
$53$	−5.20602			−0.715102			−0.357551	+	0.933894i	$0.616388\pi$
$54$	0.495910	−	5.17243i	0.0674849	−	0.703879i
$55$	−8.72665			−1.17670
$56$	1.41120	−	2.44426i	0.188579	−	0.326628i
$57$	5.30728	+	6.75053i	0.702966	+	0.894130i
$58$	0.341850	+	0.592102i	0.0448872	+	0.0777468i
$59$	6.09768	+	10.5615i	0.793850	+	1.37499i	0.923567	+	0.383437i	$0.125260\pi$
$59$	6.09768	+	10.5615i	0.793850	+	1.37499i	−0.129717	+	0.991551i	$0.541407\pi$
$60$	−3.71938	+	0.534281i	−0.480170	+	0.0689754i
$61$	4.69131	−	8.12558i	0.600660	−	1.04037i	−0.392061	−	0.919939i	$-0.628238\pi$
$61$	4.69131	−	8.12558i	0.600660	−	1.04037i	0.992721	−	0.120435i	$-0.0384290\pi$
$62$	−2.22537			−0.282623
$63$	6.12649	+	5.84459i	0.771865	+	0.736349i
$64$	1.00000			0.125000
$65$	7.00434	−	12.1319i	0.868782	−	1.50477i
$66$	−2.59030	+	6.46786i	−0.318844	+	0.796139i
$67$	4.17428	+	7.23006i	0.509969	+	0.883293i	0.999933	+	0.0115499i	$0.00367654\pi$
$67$	4.17428	+	7.23006i	0.509969	+	0.883293i	−0.489964	+	0.871743i	$0.662990\pi$
$68$	−0.708023	−	1.22633i	−0.0858603	−	0.148714i
$69$	0.643944	−	1.60790i	0.0775217	−	0.193568i
$70$	3.06149	−	5.30265i	0.365918	−	0.633788i
$71$	−12.7185			−1.50941			−0.754703	−	0.656067i	$-0.772219\pi$
$71$	−12.7185			−1.50941			−0.754703	+	0.656067i	$0.772219\pi$
$72$	−0.708023	+	2.91525i	−0.0834413	+	0.343566i
$73$	−0.0997459			−0.0116744			−0.00583719	−	0.999983i	$-0.501858\pi$
$73$	−0.0997459			−0.0116744			−0.00583719	+	0.999983i	$0.501858\pi$
$74$	3.19908	−	5.54098i	0.371886	−	0.644125i
$75$	0.503328	−	0.0723019i	0.0581193	−	0.00834871i
$76$	−2.47886	−	4.29351i	−0.284345	−	0.492499i
$77$	−5.67662	−	9.83219i	−0.646911	−	1.12048i
$78$	−6.91261	−	8.79242i	−0.782699	−	0.995545i
$79$	3.08471	−	5.34288i	0.347057	−	0.601121i	−0.638668	−	0.769483i	$-0.720514\pi$
$79$	3.08471	−	5.34288i	0.347057	−	0.601121i	0.985725	+	0.168361i	$0.0538475\pi$
$80$	2.16943			0.242549
$81$	−7.99741	−	4.12813i	−0.888601	−	0.458681i
$82$	7.70276			0.850628
$83$	−1.53684	+	2.66189i	−0.168691	+	0.292181i	−0.937960	−	0.346744i	$-0.887287\pi$
$83$	−1.53684	+	2.66189i	−0.168691	+	0.292181i	0.769269	+	0.638925i	$0.220621\pi$
$84$	−3.02140	−	3.84303i	−0.329661	−	0.419309i
$85$	−1.53600	−	2.66044i	−0.166603	−	0.288565i
$86$	1.14595	+	1.98484i	0.123571	+	0.214031i
$87$	1.17217	−	0.168380i	0.125670	−	0.0180522i
$88$	2.01128	−	3.48364i	0.214403	−	0.371357i
$89$	7.82691			0.829651			0.414825	−	0.909901i	$-0.363843\pi$
$89$	7.82691			0.829651			0.414825	+	0.909901i	$0.363843\pi$
$90$	−1.53600	+	6.32443i	−0.161909	+	0.666654i
$91$	18.2251			1.91051
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$	−1.43302	+	3.57817i	−0.148597	+	0.371039i
$94$	−0.787888	−	1.36466i	−0.0812644	−	0.140754i
$95$	−5.37771	−	9.31446i	−0.551741	−	0.955644i
$96$	0.643944	−	1.60790i	0.0657222	−	0.164105i
$97$	−6.48054	+	11.2246i	−0.657999	+	1.13969i	0.323134	+	0.946353i	$0.395264\pi$
$97$	−6.48054	+	11.2246i	−0.657999	+	1.13969i	−0.981133	+	0.193335i	$0.938070\pi$
$98$	0.965897			0.0975703
$99$	8.73166	+	8.32988i	0.877564	+	0.837185i
$100$	−0.293579			−0.0293579
$101$	4.57702	−	7.92763i	0.455430	−	0.788829i	−0.543282	−	0.839550i	$-0.682819\pi$
$101$	4.57702	−	7.92763i	0.455430	−	0.788829i	0.998713	+	0.0507213i	$0.0161520\pi$
$102$	−2.42774	+	0.348740i	−0.240382	+	0.0345304i
$103$	−2.72423	−	4.71851i	−0.268427	−	0.464928i	0.700029	−	0.714114i	$-0.253170\pi$
$103$	−2.72423	−	4.71851i	−0.268427	−	0.464928i	−0.968456	+	0.249186i	$0.919837\pi$
$104$	3.22866	+	5.59220i	0.316596	+	0.548360i
$105$	−6.55470	−	8.33717i	−0.639673	−	0.813625i
$106$	2.60301	−	4.50854i	0.252827	−	0.437909i
$107$	−20.4092			−1.97303			−0.986515	−	0.163671i	$-0.947666\pi$
$107$	−20.4092			−1.97303			−0.986515	+	0.163671i	$0.947666\pi$
$108$	4.23150	+	3.01569i	0.407177	+	0.290185i
$109$	−17.8299			−1.70780			−0.853898	−	0.520441i	$-0.825768\pi$
$109$	−17.8299			−1.70780			−0.853898	+	0.520441i	$0.825768\pi$
$110$	4.36333	−	7.55750i	0.416027	−	0.720580i
$111$	−6.84929	−	8.71188i	−0.650106	−	0.826895i
$112$	1.41120	+	2.44426i	0.133345	+	0.230961i
$113$	1.69550	+	2.93669i	0.159499	+	0.276261i	0.934688	−	0.355469i	$-0.115679\pi$
$113$	1.69550	+	2.93669i	0.159499	+	0.276261i	−0.775189	+	0.631729i	$0.782345\pi$
$114$	−8.49977	+	1.22097i	−0.796077	+	0.114355i
$115$	−1.08471	+	1.87878i	−0.101150	+	0.175197i
$116$	−0.683701			−0.0634800
$117$	−18.5886	+	5.45295i	−1.71852	+	0.504126i
$118$	−12.1954			−1.12267
$119$	1.99832	−	3.46119i	0.183185	−	0.317286i
$120$	1.39699	−	3.48822i	0.127527	−	0.318429i
$121$	−2.59049	−	4.48685i	−0.235499	−	0.407896i
$122$	4.69131	+	8.12558i	0.424731	+	0.735656i
$123$	4.96015	−	12.3853i	0.447241	−	1.11674i
$124$	1.11269	−	1.92723i	0.0999222	−	0.173070i
$125$	−11.4840			−1.02716
$126$	−8.12481	+	2.38340i	−0.723815	+	0.212330i
$127$	−1.63273			−0.144881			−0.0724407	−	0.997373i	$-0.523079\pi$
$127$	−1.63273			−0.144881			−0.0724407	+	0.997373i	$0.523079\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.92934	−	0.564441i	0.345959	−	0.0496963i
$130$	7.00434	+	12.1319i	0.614322	+	1.06404i
$131$	5.96457	+	10.3309i	0.521127	+	0.902619i	0.999698	+	0.0245698i	$0.00782159\pi$
$131$	5.96457	+	10.3309i	0.521127	+	0.902619i	−0.478571	+	0.878049i	$0.658845\pi$
$132$	−4.30618	−	5.47720i	−0.374805	−	0.476729i
$133$	6.99631	−	12.1180i	0.606657	−	1.05076i
$134$	−8.34856			−0.721205
$135$	9.17995	+	6.54232i	0.790084	+	0.563073i
$136$	1.41605			0.121425
$137$	−6.75615	+	11.7020i	−0.577217	+	0.999768i	0.418580	+	0.908180i	$0.362528\pi$
$137$	−6.75615	+	11.7020i	−0.577217	+	0.999768i	−0.995797	+	0.0915886i	$0.970806\pi$
$138$	1.07051	+	1.36162i	0.0911277	+	0.115909i
$139$	−10.6039	−	18.3665i	−0.899413	−	1.55783i	−0.828246	−	0.560364i	$-0.810661\pi$
$139$	−10.6039	−	18.3665i	−0.899413	−	1.55783i	−0.0711666	−	0.997464i	$-0.522672\pi$
$140$	3.06149	+	5.30265i	0.258743	+	0.448156i
$141$	−2.70159	+	0.388078i	−0.227515	+	0.0326820i
$142$	6.35924	−	11.0145i	0.533655	−	0.924318i
$143$	25.9749			2.17213
$144$	−2.17067	−	2.07079i	−0.180889	−	0.172566i
$145$	−1.48324			−0.123176
$146$	0.0498729	−	0.0863825i	0.00412751	−	0.00714906i
$147$	0.621984	−	1.55306i	0.0513003	−	0.128095i
$148$	3.19908	+	5.54098i	0.262963	+	0.455465i
$149$	−2.84134	−	4.92135i	−0.232772	−	0.403173i	0.725851	−	0.687852i	$-0.241446\pi$
$149$	−2.84134	−	4.92135i	−0.232772	−	0.403173i	−0.958623	+	0.284679i	$0.908113\pi$
$150$	−0.189049	+	0.472046i	−0.0154358	+	0.0385424i
$151$	−7.91670	+	13.7121i	−0.644252	+	1.11588i	0.340222	+	0.940345i	$0.389498\pi$
$151$	−7.91670	+	13.7121i	−0.644252	+	1.11588i	−0.984474	+	0.175532i	$0.943835\pi$
$152$	4.95772			0.402124
$153$	−1.00259	+	4.12813i	−0.0810547	+	0.333740i
$154$	11.3532			0.914870
$155$	2.41389	−	4.18099i	0.193889	−	0.335825i
$156$	11.0708	−	1.59029i	0.886370	−	0.127325i
$157$	−7.92682	−	13.7297i	−0.632629	−	1.09575i	−0.987012	−	0.160645i	$-0.948642\pi$
$157$	−7.92682	−	13.7297i	−0.632629	−	1.09575i	0.354383	−	0.935100i	$-0.384691\pi$
$158$	3.08471	+	5.34288i	0.245407	+	0.425057i
$159$	−5.57309	−	7.08862i	−0.441975	−	0.562164i
$160$	−1.08471	+	1.87878i	−0.0857542	+	0.148531i
$161$	−2.82239			−0.222436
$162$	7.57377	−	4.86189i	0.595052	−	0.381986i
$163$	11.5815			0.907130			0.453565	−	0.891223i	$-0.350152\pi$
$163$	11.5815			0.907130			0.453565	+	0.891223i	$0.350152\pi$
$164$	−3.85138	+	6.67079i	−0.300742	+	0.520901i
$165$	−9.34196	−	11.8824i	−0.727270	−	0.925043i
$166$	−1.53684	−	2.66189i	−0.119282	−	0.206603i
$167$	10.0870	+	17.4711i	0.780553	+	1.35196i	0.931620	+	0.363434i	$0.118396\pi$
$167$	10.0870	+	17.4711i	0.780553	+	1.35196i	−0.151067	+	0.988524i	$0.548271\pi$
$168$	4.83886	−	0.695091i	0.373326	−	0.0536274i
$169$	−14.3485	+	24.8523i	−1.10373	+	1.91171i
$170$	3.07201			0.235612
$171$	−3.51018	+	14.4530i	−0.268430	+	1.10525i
$172$	−2.29189			−0.174755
$173$	−3.40426	+	5.89635i	−0.258821	+	0.448291i	−0.965926	−	0.258817i	$-0.916667\pi$
$173$	−3.40426	+	5.89635i	−0.258821	+	0.448291i	0.707105	+	0.707108i	$0.250001\pi$
$174$	−0.440265	+	1.09932i	−0.0333764	+	0.0833393i
$175$	−0.414298	−	0.717585i	−0.0313180	−	0.0542444i
$176$	2.01128	+	3.48364i	0.151606	+	0.262589i
$177$	−7.85312	+	19.6089i	−0.590277	+	1.47389i
$178$	−3.91346	+	6.77830i	−0.293326	+	0.508055i
$179$	8.15856			0.609799			0.304900	−	0.952384i	$-0.401377\pi$
$179$	8.15856			0.609799			0.304900	+	0.952384i	$0.401377\pi$
$180$	−4.70912	−	4.49244i	−0.350997	−	0.334846i
$181$	16.3437			1.21482			0.607410	−	0.794388i	$-0.292208\pi$
$181$	16.3437			1.21482			0.607410	+	0.794388i	$0.292208\pi$
$182$	−9.11254	+	15.7834i	−0.675466	+	1.16994i
$183$	16.0861	−	2.31073i	1.18912	−	0.170814i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	6.94018	+	12.0208i	0.510252	+	0.883783i
$186$	−2.38228	−	3.03011i	−0.174677	−	0.222179i
$187$	2.84806	−	4.93299i	0.208271	−	0.360736i
$188$	1.57578			0.114925
$189$	−1.39965	+	14.5986i	−0.101810	+	1.06189i
$190$	10.7554			0.780280
$191$	7.54338	−	13.0655i	0.545820	−	0.945387i	−0.452735	−	0.891645i	$-0.649552\pi$
$191$	7.54338	−	13.0655i	0.545820	−	0.945387i	0.998555	−	0.0537422i	$-0.0171149\pi$
$192$	1.07051	+	1.36162i	0.0772573	+	0.0982665i
$193$	−4.75406	−	8.23428i	−0.342205	−	0.592716i	0.642637	−	0.766171i	$-0.277840\pi$
$193$	−4.75406	−	8.23428i	−0.342205	−	0.592716i	−0.984842	+	0.173455i	$0.944507\pi$
$194$	−6.48054	−	11.2246i	−0.465276	−	0.805881i
$195$	24.0172	−	3.45002i	1.71991	−	0.247061i
$196$	−0.482949	+	0.836491i	−0.0344963	+	0.0597494i
$197$	20.1318			1.43433			0.717167	−	0.696902i	$-0.245439\pi$
$197$	20.1318			1.43433			0.717167	+	0.696902i	$0.245439\pi$
$198$	−11.5797	+	3.39689i	−0.822935	+	0.241407i
$199$	−15.7175			−1.11418			−0.557091	−	0.830452i	$-0.688082\pi$
$199$	−15.7175			−1.11418			−0.557091	+	0.830452i	$0.688082\pi$
$200$	0.146790	−	0.254247i	0.0103796	−	0.0179780i
$201$	−5.37600	+	13.4236i	−0.379194	+	0.946830i
$202$	4.57702	+	7.92763i	0.322038	+	0.557786i
$203$	−0.964836	−	1.67114i	−0.0677182	−	0.117291i
$204$	0.911854	−	2.27686i	0.0638425	−	0.159412i
$205$	−8.35529	+	14.4718i	−0.583559	+	1.01075i
$206$	5.44846			0.379612
$207$	2.87870	−	0.844461i	0.200083	−	0.0586941i
$208$	−6.45732			−0.447734
$209$	9.97135	−	17.2709i	0.689733	−	1.19465i
$210$	10.4976	−	1.50795i	0.724400	−	0.104058i
$211$	12.3293	+	21.3550i	0.848786	+	1.47014i	0.882292	+	0.470702i	$0.155999\pi$
$211$	12.3293	+	21.3550i	0.848786	+	1.47014i	−0.0335058	+	0.999439i	$0.510667\pi$
$212$	2.60301	+	4.50854i	0.178775	+	0.309648i
$213$	−13.6152	−	17.3177i	−0.932901	−	1.18659i
$214$	10.2046	−	17.6749i	0.697571	−	1.20823i
$215$	−4.97210			−0.339094
$216$	−4.72741	+	2.15675i	−0.321660	+	0.146748i
$217$	6.28088			0.426374
$218$	8.91495	−	15.4412i	0.603797	−	1.04581i
$219$	−0.106779	−	0.135816i	−0.00721545	−	0.00917760i
$220$	4.36333	+	7.55750i	0.294175	+	0.509527i
$221$	4.57193	+	7.91881i	0.307541	+	0.532677i
$222$	10.9694	−	1.57572i	0.736215	−	0.105756i
$223$	−11.3305	+	19.6250i	−0.758746	+	1.31419i	0.184744	+	0.982787i	$0.440854\pi$
$223$	−11.3305	+	19.6250i	−0.758746	+	1.31419i	−0.943490	+	0.331400i	$0.892479\pi$
$224$	−2.82239			−0.188579
$225$	0.637265	+	0.607942i	0.0424843	+	0.0405295i
$226$	−3.39100			−0.225566
$227$	1.15380	−	1.99845i	0.0765806	−	0.132642i	−0.825192	−	0.564852i	$-0.808933\pi$
$227$	1.15380	−	1.99845i	0.0765806	−	0.132642i	0.901773	+	0.432211i	$0.142266\pi$
$228$	3.19249	−	7.97150i	0.211428	−	0.527926i
$229$	−12.4381	−	21.5434i	−0.821933	−	1.42363i	−0.904241	−	0.427022i	$-0.859563\pi$
$229$	−12.4381	−	21.5434i	−0.821933	−	1.42363i	0.0823085	−	0.996607i	$-0.473771\pi$
$230$	−1.08471	−	1.87878i	−0.0715239	−	0.123883i
$231$	7.31085	−	18.2548i	0.481018	−	1.20108i
$232$	0.341850	−	0.592102i	0.0224436	−	0.0388734i
$233$	29.4308			1.92807			0.964037	−	0.265768i	$-0.0856256\pi$
$233$	29.4308			1.92807			0.964037	+	0.265768i	$0.0856256\pi$
$234$	4.57193	−	18.8247i	0.298876	−	1.23061i
$235$	3.41853			0.223000
$236$	6.09768	−	10.5615i	0.396925	−	0.687494i
$237$	10.5772	−	1.51939i	0.687062	−	0.0986950i
$238$	1.99832	+	3.46119i	0.129532	+	0.224355i
$239$	2.00326	+	3.46975i	0.129580	+	0.224440i	0.923514	−	0.383565i	$-0.125304\pi$
$239$	2.00326	+	3.46975i	0.129580	+	0.224440i	−0.793934	+	0.608004i	$0.791970\pi$
$240$	2.32239	+	2.95394i	0.149910	+	0.190676i
$241$	−12.8861	+	22.3195i	−0.830069	+	1.43772i	0.0679133	+	0.997691i	$0.478366\pi$
$241$	−12.8861	+	22.3195i	−0.830069	+	1.43772i	−0.897983	+	0.440031i	$0.854967\pi$
$242$	5.18097			0.333046
$243$	−2.94035	−	15.3086i	−0.188623	−	0.982050i
$244$	−9.38262			−0.600660
$245$	−1.04772	+	1.81471i	−0.0669365	+	0.115937i
$246$	8.24587	+	10.4882i	0.525738	+	0.668706i
$247$	16.0068	+	27.7245i	1.01849	+	1.76407i
$248$	1.11269	+	1.92723i	0.0706557	+	0.122379i
$249$	−5.26969	+	0.756980i	−0.333953	+	0.0479716i
$250$	5.74202	−	9.94547i	0.363157	−	0.629007i
$251$	−16.7532			−1.05745			−0.528726	−	0.848793i	$-0.677330\pi$
$251$	−16.7532			−1.05745			−0.528726	+	0.848793i	$0.677330\pi$
$252$	1.99832	−	8.22799i	0.125882	−	0.518315i
$253$	−4.02256			−0.252896
$254$	0.816366	−	1.41399i	0.0512233	−	0.0887214i
$255$	1.97820	−	4.93948i	0.123880	−	0.309322i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.1162	−	17.5218i	−0.631033	−	1.09298i	−0.987341	−	0.158612i	$-0.949298\pi$
$257$	−10.1162	−	17.5218i	−0.631033	−	1.09298i	0.356308	−	0.934369i	$-0.384035\pi$
$258$	−1.47585	+	3.68513i	−0.0918825	+	0.229426i
$259$	−9.02907	+	15.6388i	−0.561039	+	0.971748i
$260$	−14.0087			−0.868782
$261$	1.48409	+	1.41580i	0.0918629	+	0.0876360i
$262$	−11.9291			−0.736985
$263$	−11.0018	+	19.0557i	−0.678402	+	1.17503i	0.297060	+	0.954859i	$0.403994\pi$
$263$	−11.0018	+	19.0557i	−0.678402	+	1.17503i	−0.975462	+	0.220168i	$0.929339\pi$
$264$	6.89648	−	0.990665i	0.424449	−	0.0609712i
$265$	5.64704	+	9.78097i	0.346895	+	0.600840i
$266$	6.99631	+	12.1180i	0.428971	+	0.743000i
$267$	8.37878	+	10.6573i	0.512773	+	0.652215i
$268$	4.17428	−	7.23006i	0.254985	−	0.441646i
$269$	−21.2060			−1.29295			−0.646477	−	0.762934i	$-0.723758\pi$
$269$	−21.2060			−1.29295			−0.646477	+	0.762934i	$0.723758\pi$
$270$	−10.2558	+	4.67891i	−0.624147	+	0.284749i
$271$	−25.2462			−1.53359			−0.766797	−	0.641889i	$-0.778151\pi$
$271$	−25.2462			−1.53359			−0.766797	+	0.641889i	$0.778151\pi$
$272$	−0.708023	+	1.22633i	−0.0429302	+	0.0743572i
$273$	19.5101	+	24.8156i	1.18081	+	1.50191i
$274$	−6.75615	−	11.7020i	−0.408154	−	0.706943i
$275$	−0.590470	−	1.02272i	−0.0356067	−	0.0616726i
$276$	−1.71445	+	0.246277i	−0.103198	+	0.0148241i
$277$	2.45672	−	4.25516i	0.147610	−	0.255668i	−0.782734	−	0.622357i	$-0.786175\pi$
$277$	2.45672	−	4.25516i	0.147610	−	0.255668i	0.930344	+	0.366689i	$0.119509\pi$
$278$	21.2078			1.27196
$279$	−6.40617	+	1.87924i	−0.383527	+	0.112507i
$280$	−6.12298			−0.365918
$281$	0.212449	−	0.367973i	0.0126737	−	0.0219514i	−0.859619	−	0.510936i	$-0.829299\pi$
$281$	0.212449	−	0.367973i	0.0126737	−	0.0219514i	0.872293	+	0.488984i	$0.162632\pi$
$282$	1.01471	−	2.53369i	0.0604252	−	0.150879i
$283$	5.94195	+	10.2918i	0.353212	+	0.611781i	0.986810	−	0.161881i	$-0.0517561\pi$
$283$	5.94195	+	10.2918i	0.353212	+	0.611781i	−0.633598	+	0.773662i	$0.718423\pi$
$284$	6.35924	+	11.0145i	0.377351	+	0.653592i
$285$	6.92588	−	17.2936i	0.410254	−	1.02439i
$286$	−12.9875	+	22.4949i	−0.767965	+	1.33015i
$287$	−21.7402			−1.28328
$288$	2.87870	−	0.844461i	0.169629	−	0.0497604i
$289$	−14.9948			−0.882048
$290$	0.741620	−	1.28452i	0.0435494	−	0.0754298i
$291$	−22.2212	+	3.19202i	−1.30263	+	0.187120i
$292$	0.0498729	+	0.0863825i	0.00291859	+	0.00505515i
$293$	5.26625	+	9.12141i	0.307657	+	0.532878i	0.977849	−	0.209309i	$-0.0671216\pi$
$293$	5.26625	+	9.12141i	0.307657	+	0.532878i	−0.670192	+	0.742188i	$0.733788\pi$
$294$	1.03400	+	1.31519i	0.0603042	+	0.0767032i
$295$	13.2285	−	22.9124i	0.770191	−	1.33401i
$296$	−6.39817			−0.371886
$297$	−1.99483	+	20.8064i	−0.115752	+	1.20731i
$298$	5.68269			0.329189
$299$	3.22866	−	5.59220i	0.186718	−	0.323405i
$300$	−0.314279	−	0.399744i	−0.0181449	−	0.0230792i
$301$	−3.23431	−	5.60199i	−0.186423	−	0.322894i
$302$	−7.91670	−	13.7121i	−0.455555	−	0.789044i
$303$	15.6942	−	2.25443i	0.901606	−	0.129514i
$304$	−2.47886	+	4.29351i	−0.142172	+	0.246250i
$305$	−20.3549			−1.16552
$306$	−3.07377	−	2.93234i	−0.175716	−	0.167630i
$307$	16.9536			0.967592			0.483796	−	0.875181i	$-0.339258\pi$
$307$	16.9536			0.967592			0.483796	+	0.875181i	$0.339258\pi$
$308$	−5.67662	+	9.83219i	−0.323455	+	0.560241i
$309$	3.50850	−	8.76057i	0.199592	−	0.498372i
$310$	2.41389	+	4.18099i	0.137100	+	0.237464i
$311$	2.62383	+	4.54460i	0.148784	+	0.257701i	0.930778	−	0.365584i	$-0.119131\pi$
$311$	2.62383	+	4.54460i	0.148784	+	0.257701i	−0.781995	+	0.623285i	$0.785798\pi$
$312$	−4.15815	+	10.3827i	−0.235409	+	0.587805i
$313$	5.08898	−	8.81437i	0.287646	−	0.498217i	−0.685601	−	0.727977i	$-0.740461\pi$
$313$	5.08898	−	8.81437i	0.287646	−	0.498217i	0.973247	+	0.229760i	$0.0737940\pi$
$314$	15.8536			0.894673
$315$	4.33521	−	17.8500i	0.244261	−	1.00574i
$316$	−6.16943			−0.347057
$317$	2.06189	−	3.57130i	0.115807	−	0.200584i	−0.802295	−	0.596928i	$-0.796388\pi$
$317$	2.06189	−	3.57130i	0.115807	−	0.200584i	0.918102	+	0.396344i	$0.129721\pi$
$318$	8.92547	−	1.28212i	0.500516	−	0.0718980i
$319$	−1.37511	−	2.38177i	−0.0769916	−	0.133353i
$320$	−1.08471	−	1.87878i	−0.0606374	−	0.105027i
$321$	−21.8482	−	27.7896i	−1.21945	−	1.55106i
$322$	1.41120	−	2.44426i	0.0786429	−	0.136213i
$323$	7.02035			0.390623
$324$	0.423638	+	8.99002i	0.0235354	+	0.499446i
$325$	1.89574			0.105156
$326$	−5.79073	+	10.0298i	−0.320719	+	0.555502i
$327$	−19.0871	−	24.2776i	−1.05552	−	1.34255i
$328$	−3.85138	−	6.67079i	−0.212657	−	0.368333i
$329$	2.22373	+	3.85161i	0.122598	+	0.212346i
$330$	14.9614	−	2.14918i	0.823600	−	0.118308i
$331$	10.4130	−	18.0358i	0.572348	−	0.991335i	−0.423977	−	0.905673i	$-0.639366\pi$
$331$	10.4130	−	18.0358i	0.572348	−	0.991335i	0.996324	−	0.0856619i	$-0.0273005\pi$
$332$	3.07369			0.168691
$333$	4.53005	−	18.6523i	0.248245	−	1.02214i
$334$	−20.1739			−1.10387
$335$	9.05580	−	15.6851i	0.494771	−	0.856969i
$336$	−1.81746	+	4.53812i	−0.0991507	+	0.247575i
$337$	−7.47686	−	12.9503i	−0.407290	−	0.705447i	0.587295	−	0.809373i	$-0.300193\pi$
$337$	−7.47686	−	12.9503i	−0.407290	−	0.705447i	−0.994585	+	0.103926i	$0.966860\pi$
$338$	−14.3485	−	24.8523i	−0.780454	−	1.35179i
$339$	−2.18361	+	5.45238i	−0.118598	+	0.296133i
$340$	−1.53600	+	2.66044i	−0.0833015	+	0.144282i
$341$	8.95169			0.484761
$342$	−10.7616	−	10.2664i	−0.581920	−	0.555144i
$343$	17.0306			0.919566
$344$	1.14595	−	1.98484i	0.0617853	−	0.107015i
$345$	−3.71938	+	0.534281i	−0.200245	+	0.0287647i
$346$	−3.40426	−	5.89635i	−0.183014	−	0.316990i
$347$	7.87386	+	13.6379i	0.422691	+	0.732122i	0.996202	−	0.0870760i	$-0.0277523\pi$
$347$	7.87386	+	13.6379i	0.422691	+	0.732122i	−0.573511	+	0.819198i	$0.694419\pi$
$348$	−0.731908	−	0.930941i	−0.0392344	−	0.0499037i
$349$	5.16200	−	8.94084i	0.276315	−	0.478592i	−0.694151	−	0.719830i	$-0.744220\pi$
$349$	5.16200	−	8.94084i	0.276315	−	0.478592i	0.970466	+	0.241237i	$0.0775532\pi$
$350$	0.828596			0.0442903
$351$	−27.3242	−	19.4733i	−1.45846	−	1.03941i
$352$	−4.02256			−0.214403
$353$	8.41830	−	14.5809i	0.448061	−	0.776065i	−0.550199	−	0.835034i	$-0.685448\pi$
$353$	8.41830	−	14.5809i	0.448061	−	0.776065i	0.998260	+	0.0589691i	$0.0187814\pi$
$354$	−13.0552	−	16.6054i	−0.693878	−	0.882569i
$355$	13.7959	+	23.8952i	0.732211	+	1.26823i
$356$	−3.91346	−	6.77830i	−0.207413	−	0.359249i
$357$	6.85204	−	0.984280i	0.362648	−	0.0520936i
$358$	−4.07928	+	7.06552i	−0.215597	+	0.373424i
$359$	−8.82553			−0.465794			−0.232897	−	0.972501i	$-0.574820\pi$
$359$	−8.82553			−0.465794			−0.232897	+	0.972501i	$0.574820\pi$
$360$	6.24512	−	1.83200i	0.329147	−	0.0965548i
$361$	5.57897			0.293630
$362$	−8.17187	+	14.1541i	−0.429504	+	0.743923i
$363$	3.33626	−	8.33048i	0.175108	−	0.437237i
$364$	−9.11254	−	15.7834i	−0.477627	−	0.827274i
$365$	0.108196	+	0.187401i	0.00566323	+	0.00980900i
$366$	−6.04188	+	15.0863i	−0.315814	+	0.788573i
$367$	−0.214118	+	0.370863i	−0.0111769	+	0.0193589i	−0.871560	−	0.490289i	$-0.836891\pi$
$367$	−0.214118	+	0.370863i	−0.0111769	+	0.0193589i	0.860383	+	0.509648i	$0.170224\pi$
$368$	1.00000			0.0521286
$369$	22.1739	−	6.50468i	1.15433	−	0.338620i
$370$	−13.8804			−0.721606
$371$	−7.34671	+	12.7249i	−0.381422	+	0.660643i
$372$	3.81530	−	0.548059i	0.197814	−	0.0284155i
$373$	−6.35650	−	11.0098i	−0.329127	−	0.570064i	0.653212	−	0.757175i	$-0.273421\pi$
$373$	−6.35650	−	11.0098i	−0.329127	−	0.570064i	−0.982339	+	0.187111i	$0.940088\pi$
$374$	2.84806	+	4.93299i	0.147270	+	0.255079i
$375$	−12.2938	−	15.6369i	−0.634847	−	0.807487i
$376$	−0.787888	+	1.36466i	−0.0406322	+	0.0703771i
$377$	4.41487			0.227378
$378$	−11.9430	−	8.51145i	−0.614280	−	0.437782i
$379$	6.99928			0.359529			0.179765	−	0.983710i	$-0.442466\pi$
$379$	6.99928			0.359529			0.179765	+	0.983710i	$0.442466\pi$
$380$	−5.37771	+	9.31446i	−0.275871	+	0.477822i
$381$	−1.74785	−	2.22316i	−0.0895452	−	0.113896i
$382$	7.54338	+	13.0655i	0.385953	+	0.668490i
$383$	−0.00995434	−	0.0172414i	−0.000508643	−	0.000880995i	0.865771	−	0.500440i	$-0.166829\pi$
$383$	−0.00995434	−	0.0172414i	−0.000508643	−	0.000880995i	−0.866280	+	0.499559i	$0.833495\pi$
$384$	−1.71445	+	0.246277i	−0.0874903	+	0.0125678i
$385$	−12.3150	+	21.3302i	−0.627631	+	1.08709i
$386$	9.50812			0.483951
$387$	4.97495	+	4.74604i	0.252891	+	0.241255i
$388$	12.9611			0.657999
$389$	−5.70357	+	9.87886i	−0.289182	+	0.500878i	−0.973615	−	0.228198i	$-0.926717\pi$
$389$	−5.70357	+	9.87886i	−0.289182	+	0.500878i	0.684433	+	0.729076i	$0.260050\pi$
$390$	−9.02081	+	22.5245i	−0.456786	+	1.14057i
$391$	−0.708023	−	1.22633i	−0.0358062	−	0.0620182i
$392$	−0.482949	−	0.836491i	−0.0243926	−	0.0422492i
$393$	−7.68170	+	19.1808i	−0.387491	+	0.967546i
$394$	−10.0659	+	17.4347i	−0.507113	+	0.878346i
$395$	−13.3841			−0.673429
$396$	2.84806	−	11.7268i	0.143120	−	0.589293i
$397$	−9.29494			−0.466499			−0.233250	−	0.972417i	$-0.574936\pi$
$397$	−9.29494			−0.466499			−0.233250	+	0.972417i	$0.574936\pi$
$398$	7.85873	−	13.6117i	0.393923	−	0.682294i
$399$	23.9897	−	3.44606i	1.20099	−	0.172519i
$400$	0.146790	+	0.254247i	0.00733949	+	0.0127124i
$401$	3.92390	+	6.79640i	0.195950	+	0.339396i	0.947212	−	0.320609i	$-0.103888\pi$
$401$	3.92390	+	6.79640i	0.195950	+	0.339396i	−0.751261	+	0.660005i	$0.770554\pi$
$402$	−8.93720	−	11.3676i	−0.445747	−	0.566963i
$403$	−7.18497	+	12.4447i	−0.357909	+	0.619916i
$404$	−9.15404			−0.455430
$405$	0.919053	+	19.5032i	0.0456681	+	0.969123i
$406$	1.92967			0.0957680
$407$	−12.8685	+	22.2889i	−0.637868	+	1.10482i
$408$	1.51589	+	1.92812i	0.0750477	+	0.0954560i
$409$	−16.1629	−	27.9949i	−0.799203	−	1.38426i	−0.920136	−	0.391600i	$-0.871922\pi$
$409$	−16.1629	−	27.9949i	−0.799203	−	1.38426i	0.120932	−	0.992661i	$-0.461412\pi$
$410$	−8.35529	−	14.4718i	−0.412639	−	0.714711i
$411$	−23.1662	+	3.32777i	−1.14270	+	0.164147i
$412$	−2.72423	+	4.71851i	−0.134213	+	0.232464i
$413$	34.4201			1.69370
$414$	−0.708023	+	2.91525i	−0.0347974	+	0.143277i
$415$	6.66815			0.327327
$416$	3.22866	−	5.59220i	0.158298	−	0.274180i
$417$	13.6567	−	34.1000i	0.668770	−	1.66989i
$418$	9.97135	+	17.2709i	0.487715	+	0.844747i
$419$	13.1380	+	22.7557i	0.641833	+	1.11169i	0.985023	+	0.172421i	$0.0551590\pi$
$419$	13.1380	+	22.7557i	0.641833	+	1.11169i	−0.343191	+	0.939266i	$0.611508\pi$
$420$	−3.94285	+	9.84512i	−0.192392	+	0.480393i
$421$	12.5632	−	21.7600i	0.612291	−	1.06052i	−0.378562	−	0.925576i	$-0.623581\pi$
$421$	12.5632	−	21.7600i	0.612291	−	1.06052i	0.990853	−	0.134943i	$-0.0430852\pi$
$422$	−24.6587			−1.20037
$423$	−3.42049	−	3.26310i	−0.166310	−	0.158658i
$424$	−5.20602			−0.252827
$425$	0.207861	−	0.360026i	0.0100827	−	0.0174638i
$426$	21.8052	−	3.13227i	1.05647	−	0.151759i
$427$	−13.2407	−	22.9336i	−0.640763	−	1.10983i
$428$	10.2046	+	17.6749i	0.493257	+	0.854347i
$429$	27.8064	+	35.3680i	1.34251	+	1.70758i
$430$	2.48605	−	4.30597i	0.119888	−	0.207652i
$431$	25.9871			1.25176			0.625878	−	0.779921i	$-0.284741\pi$
$431$	25.9871			1.25176			0.625878	+	0.779921i	$0.284741\pi$
$432$	0.495910	−	5.17243i	0.0238595	−	0.248859i
$433$	31.5776			1.51752			0.758762	−	0.651368i	$-0.225804\pi$
$433$	31.5776			1.51752			0.758762	+	0.651368i	$0.225804\pi$
$434$	−3.14044	+	5.43940i	−0.150746	+	0.261099i
$435$	−1.58782	−	2.01961i	−0.0761302	−	0.0968329i
$436$	8.91495	+	15.4412i	0.426949	+	0.739497i
$437$	−2.47886	−	4.29351i	−0.118580	−	0.205386i
$438$	0.171010	−	0.0245651i	0.00817115	−	0.00117377i
$439$	4.69806	−	8.13728i	0.224226	−	0.388371i	−0.731861	−	0.681454i	$-0.761348\pi$
$439$	4.69806	−	8.13728i	0.224226	−	0.388371i	0.956087	+	0.293083i	$0.0946813\pi$
$440$	−8.72665			−0.416027
$441$	2.78052	−	0.815663i	0.132406	−	0.0388411i
$442$	−9.14385			−0.434929
$443$	8.51929	−	14.7558i	0.404764	−	0.701071i	−0.589530	−	0.807746i	$-0.700687\pi$
$443$	8.51929	−	14.7558i	0.404764	−	0.701071i	0.994294	+	0.106675i	$0.0340205\pi$
$444$	−4.12006	+	10.2876i	−0.195529	+	0.488228i
$445$	−8.48996	−	14.7050i	−0.402463	−	0.697086i
$446$	−11.3305	−	19.6250i	−0.536515	−	0.929270i
$447$	3.65933	−	9.13719i	0.173081	−	0.432174i
$448$	1.41120	−	2.44426i	0.0666727	−	0.115481i
$449$	−33.3327			−1.57307			−0.786533	−	0.617548i	$-0.788126\pi$
$449$	−33.3327			−1.57307			−0.786533	+	0.617548i	$0.788126\pi$
$450$	−0.845126	+	0.247916i	−0.0398396	+	0.0116869i
$451$	−30.9848			−1.45902
$452$	1.69550	−	2.93669i	0.0797496	−	0.138130i
$453$	−27.1456	+	3.89941i	−1.27541	+	0.183210i
$454$	1.15380	+	1.99845i	0.0541507	+	0.0937917i
$455$	−19.7690	−	34.2409i	−0.926785	−	1.60524i
$456$	5.30728	+	6.75053i	0.248536	+	0.316123i
$457$	−13.0221	+	22.5550i	−0.609150	+	1.05508i	0.382231	+	0.924067i	$0.375156\pi$
$457$	−13.0221	+	22.5550i	−0.609150	+	1.05508i	−0.991381	+	0.131012i	$0.958178\pi$
$458$	24.8762			1.16239
$459$	−6.69423	+	3.05405i	−0.312460	+	0.142551i
$460$	2.16943			0.101150
$461$	7.85044	−	13.5974i	0.365631	−	0.633292i	−0.623246	−	0.782026i	$-0.714186\pi$
$461$	7.85044	−	13.5974i	0.365631	−	0.633292i	0.988877	+	0.148734i	$0.0475198\pi$
$462$	12.1537	+	15.4588i	0.565443	+	0.719209i
$463$	20.8073	+	36.0394i	0.966999	+	1.67489i	0.704144	+	0.710057i	$0.251331\pi$
$463$	20.8073	+	36.0394i	0.966999	+	1.67489i	0.262855	+	0.964835i	$0.415336\pi$
$464$	0.341850	+	0.592102i	0.0158700	+	0.0274877i
$465$	8.27702	−	1.18897i	0.383837	−	0.0551374i
$466$	−14.7154	+	25.4878i	−0.681677	+	1.18070i
$467$	0.842074			0.0389666			0.0194833	−	0.999810i	$-0.493798\pi$
$467$	0.842074			0.0389666			0.0194833	+	0.999810i	$0.493798\pi$
$468$	14.0167	+	13.3718i	0.647923	+	0.618110i
$469$	23.5629			1.08803
$470$	−1.70927	+	2.96054i	−0.0788426	+	0.136559i
$471$	10.2089	−	25.4910i	0.470399	−	1.17456i
$472$	6.09768	+	10.5615i	0.280668	+	0.486132i
$473$	−4.60964	−	7.98413i	−0.211951	−	0.367111i
$474$	−3.97277	+	9.91981i	−0.182475	+	0.455632i
$475$	0.727742	−	1.26049i	0.0333911	−	0.0578351i
$476$	−3.99663			−0.183185
$477$	3.68598	−	15.1769i	0.168769	−	0.694901i
$478$	−4.00653			−0.183254
$479$	−8.63031	+	14.9481i	−0.394329	+	0.682998i	−0.993015	−	0.117986i	$-0.962356\pi$
$479$	−8.63031	+	14.9481i	−0.394329	+	0.682998i	0.598686	+	0.800984i	$0.295690\pi$
$480$	−3.71938	+	0.534281i	−0.169766	+	0.0243865i
$481$	−20.6575	−	35.7798i	−0.941901	−	1.63142i
$482$	−12.8861	−	22.3195i	−0.586948	−	1.01662i
$483$	−3.02140	−	3.84303i	−0.137478	−	0.174864i
$484$	−2.59049	+	4.48685i	−0.117749	+	0.203948i
$485$	28.1181			1.27678
$486$	14.7278	+	5.10790i	0.668068	+	0.231699i
$487$	12.7447			0.577518			0.288759	−	0.957402i	$-0.406757\pi$
$487$	12.7447			0.577518			0.288759	+	0.957402i	$0.406757\pi$
$488$	4.69131	−	8.12558i	0.212366	−	0.367828i
$489$	12.3981	+	15.7696i	0.560659	+	0.713124i
$490$	−1.04772	−	1.81471i	−0.0473313	−	0.0819802i
$491$	−0.838245	−	1.45188i	−0.0378295	−	0.0655226i	0.846491	−	0.532403i	$-0.178711\pi$
$491$	−0.838245	−	1.45188i	−0.0378295	−	0.0655226i	−0.884320	+	0.466881i	$0.845378\pi$
$492$	−13.2060	+	1.89701i	−0.595373	+	0.0855240i
$493$	0.484076	−	0.838444i	0.0218017	−	0.0377616i
$494$	−32.0136			−1.44036
$495$	6.17867	−	25.4404i	0.277710	−	1.14346i
$496$	−2.22537			−0.0999222
$497$	−17.9483	+	31.0873i	−0.805089	+	1.39446i
$498$	1.97928	−	4.94218i	0.0886938	−	0.221464i
$499$	−11.9303	−	20.6640i	−0.534075	−	0.925046i	−0.999207	−	0.0398043i	$-0.987327\pi$
$499$	−11.9303	−	20.6640i	−0.534075	−	0.925046i	0.465132	−	0.885241i	$-0.346007\pi$
$500$	5.74202	+	9.94547i	0.256791	+	0.444775i
$501$	−12.9909	+	32.4376i	−0.580390	+	1.44921i
$502$	8.37659	−	14.5087i	0.373865	−	0.647554i
$503$	−30.8241			−1.37438			−0.687189	−	0.726479i	$-0.741156\pi$
$503$	−30.8241			−1.37438			−0.687189	+	0.726479i	$0.741156\pi$
$504$	6.12649	+	5.84459i	0.272896	+	0.260339i
$505$	−19.8590			−0.883715
$506$	2.01128	−	3.48364i	0.0894123	−	0.154867i
$507$	−49.1995	+	7.06740i	−2.18503	+	0.313874i
$508$	0.816366	+	1.41399i	0.0362204	+	0.0627355i
$509$	7.26292	+	12.5798i	0.321923	+	0.557588i	0.980885	−	0.194589i	$-0.0623373\pi$
$509$	7.26292	+	12.5798i	0.321923	+	0.557588i	−0.658961	+	0.752177i	$0.729004\pi$
$510$	3.28861	+	4.18291i	0.145622	+	0.185222i
$511$	−0.140761	+	0.243805i	−0.00622690	+	0.0107853i
$512$	1.00000			0.0441942
$513$	−23.4372	+	10.6925i	−1.03478	+	0.472087i
$514$	20.2325			0.892415
$515$	−5.91003	+	10.2365i	−0.260427	+	0.451073i
$516$	−2.45349	−	3.12069i	−0.108009	−	0.137381i
$517$	3.16932	+	5.48943i	0.139387	+	0.241425i
$518$	−9.02907	−	15.6388i	−0.396715	−	0.687130i
$519$	−11.6729	+	1.67678i	−0.512383	+	0.0736026i
$520$	7.00434	−	12.1319i	0.307161	−	0.532018i
$521$	17.4637			0.765098			0.382549	−	0.923935i	$-0.375046\pi$
$521$	17.4637			0.765098			0.382549	+	0.923935i	$0.375046\pi$
$522$	−1.96817	+	0.577359i	−0.0861443	+	0.0252703i
$523$	37.0807			1.62143			0.810714	−	0.585442i	$-0.199079\pi$
$523$	37.0807			1.62143			0.810714	+	0.585442i	$0.199079\pi$
$524$	5.96457	−	10.3309i	0.260564	−	0.451309i
$525$	0.533569	−	1.33230i	0.0232869	−	0.0581463i
$526$	−11.0018	−	19.0557i	−0.479703	−	0.830870i
$527$	1.57561	+	2.72904i	0.0686348	+	0.118879i
$528$	−2.59030	+	6.46786i	−0.112728	+	0.281478i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−11.2941			−0.490584
$531$	−35.1067	+	10.2985i	−1.52350	+	0.446917i
$532$	−13.9926			−0.606657
$533$	24.8696	−	43.0754i	1.07722	−	1.86580i
$534$	−13.4189	+	1.92759i	−0.580691	+	0.0834150i
$535$	22.1381	+	38.3444i	0.957115	+	1.65777i
$536$	4.17428	+	7.23006i	0.180301	+	0.312291i
$537$	8.73381	+	11.1089i	0.376892	+	0.479383i
$538$	10.6030	−	18.3650i	0.457128	−	0.791769i
$539$	−3.88538			−0.167355
$540$	1.07584	−	11.2212i	0.0462969	−	0.482885i
$541$	18.7452			0.805918			0.402959	−	0.915218i	$-0.367982\pi$
$541$	18.7452			0.805918			0.402959	+	0.915218i	$0.367982\pi$
$542$	12.6231	−	21.8638i	0.542208	−	0.939131i
$543$	17.4961	+	22.2540i	0.750830	+	0.955010i
$544$	−0.708023	−	1.22633i	−0.0303562	−	0.0525785i
$545$	19.3404	+	33.4985i	0.828450	+	1.43492i
$546$	−31.2460	+	4.48842i	−1.33721	+	0.192087i
$547$	12.2794	−	21.2686i	0.525031	−	0.909381i	−0.474544	−	0.880232i	$-0.657387\pi$
$547$	12.2794	−	21.2686i	0.525031	−	0.909381i	0.999575	−	0.0291488i	$-0.00927967\pi$
$548$	13.5123			0.577217
$549$	20.3666	+	19.4295i	0.869225	+	0.829229i
$550$	1.18094			0.0503555
$551$	1.69480	−	2.93548i	0.0722008	−	0.125055i
$552$	0.643944	−	1.60790i	0.0274081	−	0.0684367i
$553$	−8.70627	−	15.0797i	−0.370228	−	0.641254i
$554$	2.45672	+	4.25516i	0.104376	+	0.180784i
$555$	−8.93818	+	22.3182i	−0.379405	+	0.947356i
$556$	−10.6039	+	18.3665i	−0.449706	+	0.778914i
$557$	25.4438			1.07809			0.539044	−	0.842278i	$-0.318786\pi$
$557$	25.4438			1.07809			0.539044	+	0.842278i	$0.318786\pi$
$558$	1.57561	−	6.48753i	0.0667011	−	0.274639i
$559$	14.7995			0.625952
$560$	3.06149	−	5.30265i	0.129372	−	0.224078i
$561$	9.76573	−	1.40283i	0.412310	−	0.0592273i
$562$	0.212449	+	0.367973i	0.00896163	+	0.0155220i
$563$	−3.62764	−	6.28325i	−0.152887	−	0.264808i	0.779401	−	0.626526i	$-0.215524\pi$
$563$	−3.62764	−	6.28325i	−0.152887	−	0.264808i	−0.932288	+	0.361718i	$0.882190\pi$
$564$	1.68688	+	2.14561i	0.0710305	+	0.0903464i
$565$	3.67827	−	6.37094i	0.154746	−	0.268028i
$566$	−11.8839			−0.499517
$567$	−21.3761	+	13.7222i	−0.897714	+	0.576277i
$568$	−12.7185			−0.533655
$569$	0.880459	−	1.52500i	0.0369107	−	0.0639313i	−0.846980	−	0.531625i	$-0.821582\pi$
$569$	0.880459	−	1.52500i	0.0369107	−	0.0639313i	0.883891	+	0.467694i	$0.154915\pi$
$570$	11.5138	+	14.6448i	0.482259	+	0.613403i
$571$	−8.22147	−	14.2400i	−0.344058	−	0.595926i	0.641124	−	0.767437i	$-0.278468\pi$
$571$	−8.22147	−	14.2400i	−0.344058	−	0.595926i	−0.985182	+	0.171511i	$0.945135\pi$
$572$	−12.9875	−	22.4949i	−0.543033	−	0.940561i
$573$	25.8655	−	3.71552i	1.08055	−	0.155218i
$574$	10.8701	−	18.8276i	0.453709	−	0.785848i
$575$	−0.293579			−0.0122431
$576$	−0.708023	+	2.91525i	−0.0295009	+	0.121469i
$577$	−6.03325			−0.251167			−0.125584	−	0.992083i	$-0.540080\pi$
$577$	−6.03325			−0.251167			−0.125584	+	0.992083i	$0.540080\pi$
$578$	7.49741	−	12.9859i	0.311851	−	0.540142i
$579$	6.12270	−	15.2881i	0.254451	−	0.635352i
$580$	0.741620	+	1.28452i	0.0307941	+	0.0533369i
$581$	4.33758	+	7.51291i	0.179953	+	0.311688i
$582$	8.34621	−	20.8401i	0.345962	−	0.863850i
$583$	−10.4708	+	18.1359i	−0.433654	+	0.751112i
$584$	−0.0997459			−0.00412751
$585$	30.4083	+	29.0091i	1.25723	+	1.19938i
$586$	−10.5325			−0.435093
$587$	−1.30892	+	2.26712i	−0.0540251	+	0.0935742i	−0.891773	−	0.452483i	$-0.850538\pi$
$587$	−1.30892	+	2.26712i	−0.0540251	+	0.0935742i	0.837748	+	0.546057i	$0.183872\pi$
$588$	−1.65598	+	0.237878i	−0.0682917	+	0.00980994i
$589$	5.51639	+	9.55466i	0.227299	+	0.393693i
$590$	13.2285	+	22.9124i	0.544608	+	0.943288i
$591$	21.5513	+	27.4119i	0.886502	+	1.12758i
$592$	3.19908	−	5.54098i	0.131482	−	0.227733i
$593$	−0.114495			−0.00470173			−0.00235087	−	0.999997i	$-0.500748\pi$
$593$	−0.114495			−0.00470173			−0.00235087	+	0.999997i	$0.500748\pi$
$594$	−17.0215	−	12.1308i	−0.698399	−	0.497732i
$595$	−8.67041			−0.355452
$596$	−2.84134	+	4.92135i	−0.116386	+	0.201587i
$597$	−16.8257	−	21.4012i	−0.688629	−	0.875894i
$598$	3.22866	+	5.59220i	0.132030	+	0.228682i
$599$	−6.68037	−	11.5707i	−0.272953	−	0.472768i	0.696664	−	0.717398i	$-0.254667\pi$
$599$	−6.68037	−	11.5707i	−0.272953	−	0.472768i	−0.969617	+	0.244630i	$0.921334\pi$
$600$	0.503328	−	0.0723019i	0.0205483	−	0.00295171i
$601$	−9.09836	+	15.7588i	−0.371130	+	0.642816i	−0.989740	−	0.142883i	$-0.954363\pi$
$601$	−9.09836	+	15.7588i	−0.371130	+	0.642816i	0.618610	+	0.785698i	$0.287696\pi$
$602$	6.46862			0.263641
$603$	−24.0329	+	7.05003i	−0.978697	+	0.287100i
$604$	15.8334			0.644252
$605$	−5.61988	+	9.73391i	−0.228480	+	0.395740i
$606$	−5.89469	+	14.7188i	−0.239455	+	0.597909i
$607$	2.74361	+	4.75207i	0.111360	+	0.192881i	0.916319	−	0.400450i	$-0.131146\pi$
$607$	2.74361	+	4.75207i	0.111360	+	0.192881i	−0.804959	+	0.593330i	$0.797813\pi$
$608$	−2.47886	−	4.29351i	−0.100531	−	0.174125i
$609$	1.24260	−	3.10272i	0.0503527	−	0.125728i
$610$	10.1775	−	17.6279i	0.412073	−	0.713732i
$611$	−10.1753			−0.411648
$612$	4.07636	−	1.19580i	0.164777	−	0.0483372i
$613$	8.44305			0.341011			0.170506	−	0.985357i	$-0.445460\pi$
$613$	8.44305			0.341011			0.170506	+	0.985357i	$0.445460\pi$
$614$	−8.47679	+	14.6822i	−0.342095	+	0.592527i
$615$	−28.6495	+	4.11544i	−1.15526	+	0.165950i
$616$	−5.67662	−	9.83219i	−0.228717	−	0.396150i
$617$	8.68294	+	15.0393i	0.349562	+	0.605459i	0.986172	−	0.165727i	$-0.0529970\pi$
$617$	8.68294	+	15.0393i	0.349562	+	0.605459i	−0.636610	+	0.771186i	$0.719664\pi$
$618$	5.83263	+	7.41874i	0.234623	+	0.298426i
$619$	13.0426	−	22.5904i	0.524225	−	0.907985i	−0.475377	−	0.879782i	$-0.657688\pi$
$619$	13.0426	−	22.5904i	0.524225	−	0.907985i	0.999602	−	0.0282024i	$-0.00897830\pi$
$620$	−4.82779			−0.193889
$621$	4.23150	+	3.01569i	0.169804	+	0.121015i
$622$	−5.24766			−0.210412
$623$	11.0453	−	19.1310i	0.442521	−	0.766469i
$624$	−6.91261	−	8.79242i	−0.276726	−	0.351978i
$625$	11.7230	+	20.3048i	0.468918	+	0.812190i
$626$	5.08898	+	8.81437i	0.203396	+	0.352293i
$627$	34.1908	−	4.91144i	1.36545	−	0.196144i
$628$	−7.92682	+	13.7297i	−0.316315	+	0.547873i
$629$	−9.06009			−0.361250
$630$	13.2910	+	12.6794i	0.529525	+	0.505160i
$631$	22.4588			0.894072			0.447036	−	0.894516i	$-0.352480\pi$
$631$	22.4588			0.894072			0.447036	+	0.894516i	$0.352480\pi$
$632$	3.08471	−	5.34288i	0.122703	−	0.212528i
$633$	−15.8788	+	39.6486i	−0.631126	+	1.57589i
$634$	2.06189	+	3.57130i	0.0818881	+	0.141834i
$635$	1.77105	+	3.06754i	0.0702819	+	0.121732i
$636$	−3.35238	+	8.37075i	−0.132931	+	0.331922i
$637$	3.11855	−	5.40149i	0.123562	−	0.214015i
$638$	2.75023			0.108882
$639$	9.00497	−	37.0776i	0.356231	−	1.46677i
$640$	2.16943			0.0857542
$641$	−14.9471	+	25.8891i	−0.590375	+	1.02256i	0.403807	+	0.914844i	$0.367687\pi$
$641$	−14.9471	+	25.8891i	−0.590375	+	1.02256i	−0.994182	+	0.107715i	$0.965647\pi$
$642$	34.9906	−	5.02632i	1.38097	−	0.198373i
$643$	−16.7219	−	28.9632i	−0.659447	−	1.14220i	−0.980759	−	0.195223i	$-0.937457\pi$
$643$	−16.7219	−	28.9632i	−0.659447	−	1.14220i	0.321312	−	0.946973i	$-0.395876\pi$
$644$	1.41120	+	2.44426i	0.0556089	+	0.0963175i
$645$	−5.32268	−	6.77012i	−0.209580	−	0.266573i
$646$	−3.51018	+	6.07980i	−0.138106	+	0.239207i
$647$	−32.0815			−1.26125			−0.630627	−	0.776086i	$-0.717202\pi$
$647$	−32.0815			−1.26125			−0.630627	+	0.776086i	$0.717202\pi$
$648$	−7.99741	−	4.12813i	−0.314168	−	0.162168i
$649$	49.0565			1.92564
$650$	−0.947868	+	1.64175i	−0.0371784	+	0.0643949i
$651$	6.72373	+	8.55217i	0.263524	+	0.335186i
$652$	−5.79073	−	10.0298i	−0.226783	−	0.392799i
$653$	−12.8433	−	22.2453i	−0.502597	−	0.870524i	−0.999995	−	0.00300167i	$-0.999045\pi$
$653$	−12.8433	−	22.2453i	−0.502597	−	0.870524i	0.497398	−	0.867522i	$-0.334289\pi$
$654$	30.5685	−	4.39110i	1.19532	−	0.171706i
$655$	12.9397	−	22.4122i	0.505596	−	0.875719i
$656$	7.70276			0.300742
$657$	0.0706223	−	0.290785i	0.00275524	−	0.0113446i
$658$	−4.44746			−0.173380
$659$	−8.12448	+	14.0720i	−0.316485	+	0.548167i	−0.979752	−	0.200215i	$-0.935836\pi$
$659$	−8.12448	+	14.0720i	−0.316485	+	0.548167i	0.663267	+	0.748383i	$0.269169\pi$
$660$	−5.61947	+	14.0316i	−0.218738	+	0.546178i
$661$	0.540173	+	0.935606i	0.0210103	+	0.0363909i	0.876339	−	0.481694i	$-0.159978\pi$
$661$	0.540173	+	0.935606i	0.0210103	+	0.0363909i	−0.855329	+	0.518085i	$0.826645\pi$
$662$	10.4130	+	18.0358i	0.404711	+	0.700980i
$663$	−5.88813	+	14.7024i	−0.228676	+	0.570993i
$664$	−1.53684	+	2.66189i	−0.0596411	+	0.103301i
$665$	−30.3560			−1.17716
$666$	13.8883	+	13.2493i	0.538162	+	0.513399i
$667$	−0.683701			−0.0264730
$668$	10.0870	−	17.4711i	0.390277	−	0.675979i
$669$	−38.8512	+	5.58089i	−1.50207	+	0.215770i
$670$	9.05580	+	15.6851i	0.349856	+	0.605968i
$671$	−18.8711	−	32.6856i	−0.728509	−	1.26181i
$672$	−3.02140	−	3.84303i	−0.116553	−	0.148248i
$673$	16.0426	−	27.7866i	0.618398	−	1.07110i	−0.371380	−	0.928481i	$-0.621115\pi$
$673$	16.0426	−	27.7866i	0.618398	−	1.07110i	0.989778	−	0.142616i	$-0.0455513\pi$
$674$	14.9537			0.575995
$675$	−0.145589	+	1.51852i	−0.00560373	+	0.0584479i
$676$	28.6969			1.10373
$677$	3.10249	−	5.37367i	0.119238	−	0.206527i	−0.800228	−	0.599696i	$-0.795288\pi$
$677$	3.10249	−	5.37367i	0.119238	−	0.206527i	0.919466	+	0.393169i	$0.128621\pi$
$678$	−3.63009	−	4.61726i	−0.139413	−	0.177325i
$679$	18.2906	+	31.6803i	0.701930	+	1.21578i
$680$	−1.53600	−	2.66044i	−0.0589031	−	0.102023i
$681$	3.95628	−	0.568311i	0.151605	−	0.0217777i
$682$	−4.47585	+	7.75239i	−0.171389	+	0.296855i
$683$	23.9060			0.914738			0.457369	−	0.889277i	$-0.348792\pi$
$683$	23.9060			0.914738			0.457369	+	0.889277i	$0.348792\pi$
$684$	14.2718	−	4.18660i	0.545694	−	0.160079i
$685$	29.3140			1.12003
$686$	−8.51530	+	14.7489i	−0.325116	+	0.563117i
$687$	16.0189	−	39.9984i	0.611158	−	1.52603i
$688$	1.14595	+	1.98484i	0.0436888	+	0.0756713i
$689$	−16.8085	−	29.1131i	−0.640351	−	1.10912i
$690$	1.39699	−	3.48822i	0.0531825	−	0.132794i
$691$	19.5685	−	33.8936i	0.744421	−	1.28937i	−0.206044	−	0.978543i	$-0.566059\pi$
$691$	19.5685	−	33.8936i	0.744421	−	1.28937i	0.950465	−	0.310832i	$-0.100608\pi$
$692$	6.80852			0.258821
$693$	32.6825	−	9.58737i	1.24151	−	0.364194i
$694$	−15.7477			−0.597775
$695$	−23.0045	+	39.8449i	−0.872609	+	1.51140i
$696$	1.17217	−	0.168380i	0.0444311	−	0.00638243i
$697$	−5.45373	−	9.44613i	−0.206575	−	0.357798i
$698$	5.16200	+	8.94084i	0.195384	+	0.338416i
$699$	31.5059	+	40.0735i	1.19166	+	1.51572i
$700$	−0.414298	+	0.717585i	−0.0156590	+	0.0271222i
$701$	−33.1200			−1.25093			−0.625463	−	0.780254i	$-0.715090\pi$
$701$	−33.1200			−1.25093			−0.625463	+	0.780254i	$0.715090\pi$
$702$	30.5264	−	13.9268i	1.15215	−	0.525633i
$703$	−31.7203			−1.19635
$704$	2.01128	−	3.48364i	0.0758029	−	0.131295i
$705$	3.65957	+	4.65475i	0.137827	+	0.175308i
$706$	8.41830	+	14.5809i	0.316827	+	0.548761i
$707$	−12.9181	−	22.3749i	−0.485837	−	0.841494i
$708$	20.9084	−	3.00344i	0.785784	−	0.112876i
$709$	22.3177	−	38.6554i	0.838159	−	1.45173i	−0.0532738	−	0.998580i	$-0.516966\pi$
$709$	22.3177	−	38.6554i	0.838159	−	1.45173i	0.891432	−	0.453154i	$-0.149701\pi$
$710$	−27.5918			−1.03550
$711$	13.3918	+	12.7756i	0.502232	+	0.479123i
$712$	7.82691			0.293326
$713$	1.11269	−	1.92723i	0.0416704	−	0.0721753i
$714$	−2.57361	+	6.42618i	−0.0963149	+	0.240494i
$715$	−28.1754	−	48.8012i	−1.05370	−	1.82506i
$716$	−4.07928	−	7.06552i	−0.152450	−	0.264051i
$717$	−2.57998	+	6.44209i	−0.0963511	+	0.240584i
$718$	4.41277	−	7.64314i	0.164683	−	0.285239i
$719$	46.1369			1.72062			0.860308	−	0.509774i	$-0.170271\pi$
$719$	46.1369			1.72062			0.860308	+	0.509774i	$0.170271\pi$
$720$	−1.53600	+	6.32443i	−0.0572435	+	0.235698i
$721$	−15.3777			−0.572695
$722$	−2.78948	+	4.83153i	−0.103814	+	0.179811i
$723$	−44.1854	+	6.34713i	−1.64327	+	0.236052i
$724$	−8.17187	−	14.1541i	−0.303705	−	0.526033i
$725$	−0.100360	−	0.173829i	−0.00372729	−	0.00645585i
$726$	5.54628	+	7.05452i	0.205842	+	0.261818i
$727$	13.7399	−	23.7982i	0.509584	−	0.882625i	−0.490355	−	0.871523i	$-0.663133\pi$
$727$	13.7399	−	23.7982i	0.509584	−	0.882625i	0.999938	−	0.0111019i	$-0.00353391\pi$
$728$	18.2251			0.675466
$729$	17.6969	−	20.3917i	0.655440	−	0.755247i
$730$	−0.216392			−0.00800901
$731$	1.62271	−	2.81062i	0.0600182	−	0.103955i
$732$	−10.0442	−	12.7756i	−0.371243	−	0.472198i
$733$	5.91630	+	10.2473i	0.218524	+	0.378494i	0.954357	−	0.298669i	$-0.0965426\pi$
$733$	5.91630	+	10.2473i	0.218524	+	0.378494i	−0.735833	+	0.677163i	$0.763209\pi$
$734$	−0.214118	−	0.370863i	−0.00790323	−	0.0136888i
$735$	−3.59254	+	0.516060i	−0.132513	+	0.0190352i
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	33.5825			1.23703
$738$	−5.45373	+	22.4555i	−0.200754	+	0.826598i
$739$	4.39270			0.161588			0.0807941	−	0.996731i	$-0.474254\pi$
$739$	4.39270			0.161588			0.0807941	+	0.996731i	$0.474254\pi$
$740$	6.94018	−	12.0208i	0.255126	−	0.441892i
$741$	−20.6149	+	51.4745i	−0.757308	+	1.89096i
$742$	−7.34671	−	12.7249i	−0.269706	−	0.467145i
$743$	13.8796	+	24.0402i	0.509195	+	0.881951i	0.999943	+	0.0106499i	$0.00339004\pi$
$743$	13.8796	+	24.0402i	0.509195	+	0.881951i	−0.490749	+	0.871301i	$0.663277\pi$
$744$	−1.43302	+	3.57817i	−0.0525369	+	0.131182i
$745$	−6.16410	+	10.6765i	−0.225835	+	0.391158i
$746$	12.7130			0.465456
$747$	−6.67197	−	6.36497i	−0.244115	−	0.232882i
$748$	−5.69612			−0.208271
$749$	−28.8014	+	49.8854i	−1.05238	+	1.82277i
$750$	19.6888	−	2.82826i	0.718935	−	0.103273i
$751$	−6.10609	−	10.5761i	−0.222814	−	0.385926i	0.732847	−	0.680393i	$-0.238191\pi$
$751$	−6.10609	−	10.5761i	−0.222814	−	0.385926i	−0.955661	+	0.294468i	$0.904858\pi$
$752$	−0.787888	−	1.36466i	−0.0287313	−	0.0497641i
$753$	−17.9344	−	22.8115i	−0.653567	−	0.831296i
$754$	−2.20744	+	3.82339i	−0.0803901	+	0.139240i
$755$	34.3494			1.25010
$756$	13.3426	−	6.08718i	0.485266	−	0.221389i
$757$	−12.1313			−0.440921			−0.220460	−	0.975396i	$-0.570756\pi$
$757$	−12.1313			−0.440921			−0.220460	+	0.975396i	$0.570756\pi$
$758$	−3.49964	+	6.06156i	−0.127113	+	0.220166i
$759$	−4.30618	−	5.47720i	−0.156305	−	0.198810i
$760$	−5.37771	−	9.31446i	−0.195070	−	0.337871i
$761$	18.3079	+	31.7103i	0.663663	+	1.14950i	0.979646	+	0.200733i	$0.0643322\pi$
$761$	18.3079	+	31.7103i	0.663663	+	1.14950i	−0.315984	+	0.948765i	$0.602334\pi$
$762$	2.79924	−	0.402105i	0.101406	−	0.0145667i
$763$	−25.1615	+	43.5810i	−0.910907	+	1.57774i
$764$	−15.0868			−0.545820
$765$	8.84338	−	2.59419i	0.319733	−	0.0937932i
$766$	0.0199087			0.000719330
$767$	−39.3746	+	68.1989i	−1.42174	+	2.46252i
$768$	0.643944	−	1.60790i	0.0232363	−	0.0580200i
$769$	13.9356	+	24.1371i	0.502530	+	0.870407i	0.999996	+	0.00292339i	$0.000930545\pi$
$769$	13.9356	+	24.1371i	0.502530	+	0.870407i	−0.497466	+	0.867483i	$0.665736\pi$
$770$	−12.3150	−	21.3302i	−0.443802	−	0.768688i
$771$	13.0286	−	32.5317i	0.469212	−	1.17160i
$772$	−4.75406	+	8.23428i	−0.171102	+	0.296358i
$773$	12.6974			0.456694			0.228347	−	0.973580i	$-0.426668\pi$
$773$	12.6974			0.456694			0.228347	+	0.973580i	$0.426668\pi$
$774$	−6.59766	+	1.93542i	−0.237148	+	0.0695671i
$775$	0.653324			0.0234681
$776$	−6.48054	+	11.2246i	−0.232638	+	0.402941i
$777$	−30.9598	+	4.44731i	−1.11068	+	0.159546i
$778$	−5.70357	−	9.87886i	−0.204483	−	0.354174i
$779$	−19.0941	−	33.0719i	−0.684116	−	1.18492i
$780$	−14.9964	−	19.0745i	−0.536958	−	0.682977i
$781$	−25.5804	+	44.3066i	−0.915339	+	1.58541i
$782$	1.41605			0.0506377
$783$	−0.339054	+	3.53640i	−0.0121168	+	0.126381i
$784$	0.965897			0.0344963
$785$	−17.1967	+	29.7855i	−0.613775	+	1.06309i
$786$	−12.7703	−	16.2430i	−0.455500	−	0.579368i
$787$	−4.83150	−	8.36840i	−0.172224	−	0.298301i	0.766973	−	0.641679i	$-0.221762\pi$
$787$	−4.83150	−	8.36840i	−0.172224	−	0.298301i	−0.939197	+	0.343378i	$0.888429\pi$
$788$	−10.0659	−	17.4347i	−0.358583	−	0.621085i
$789$	−37.7242	+	5.41900i	−1.34302	+	0.192922i
$790$	6.69207	−	11.5910i	0.238093	−	0.412389i
$791$	9.57073			0.340296
$792$	8.73166	+	8.32988i	0.310266	+	0.295989i
$793$	60.5865			2.15149
$794$	4.64747	−	8.04965i	0.164932	−	0.285671i
$795$	−7.27276	+	18.1597i	−0.257938	+	0.644060i
$796$	7.85873	+	13.6117i	0.278545	+	0.482455i
$797$	−23.2943	−	40.3469i	−0.825126	−	1.42916i	−0.901823	−	0.432105i	$-0.857771\pi$
$797$	−23.2943	−	40.3469i	−0.825126	−	1.42916i	0.0766973	−	0.997054i	$-0.475563\pi$
$798$	−9.01046	+	22.4987i	−0.318967	+	0.796446i
$799$	−1.11568	+	1.93242i	−0.0394701	+	0.0683642i
$800$	−0.293579			−0.0103796
$801$	−5.54163	+	22.8174i	−0.195804	+	0.806214i
$802$	−7.84780			−0.277116
$803$	−0.200617	+	0.347479i	−0.00707961	+	0.0122623i
$804$	14.3132	−	2.05606i	0.504788	−	0.0725116i
$805$	3.06149	+	5.30265i	0.107903	+	0.186894i
$806$	−7.18497	−	12.4447i	−0.253080	−	0.438347i
$807$	−22.7012	−	28.8746i	−0.799121	−	1.01643i
$808$	4.57702	−	7.92763i	0.161019	−	0.278893i
$809$	−25.5913			−0.899741			−0.449870	−	0.893094i	$-0.648530\pi$
$809$	−25.5913			−0.899741			−0.449870	+	0.893094i	$0.648530\pi$
$810$	−17.3498	−	8.95568i	−0.609610	−	0.314671i
$811$	−22.9169			−0.804722			−0.402361	−	0.915481i	$-0.631810\pi$
$811$	−22.9169			−0.804722			−0.402361	+	0.915481i	$0.631810\pi$
$812$	−0.964836	+	1.67114i	−0.0338591	+	0.0586457i
$813$	−27.0262	−	34.3757i	−0.947851	−	1.20561i
$814$	−12.8685	−	22.2889i	−0.451041	−	0.781225i
$815$	−12.5626	−	21.7590i	−0.440048	−	0.762185i
$816$	−2.42774	+	0.348740i	−0.0849880	+	0.0122083i
$817$	5.68128	−	9.84027i	0.198763	−	0.344267i
$818$	32.3258			1.13024
$819$	−12.9038	+	53.1307i	−0.450894	+	1.85654i
$820$	16.7106			0.583559
$821$	6.48263	−	11.2282i	0.226245	−	0.391868i	−0.730447	−	0.682969i	$-0.760688\pi$
$821$	6.48263	−	11.2282i	0.226245	−	0.391868i	0.956692	+	0.291101i	$0.0940216\pi$
$822$	8.70116	−	21.7264i	0.303488	−	0.757795i
$823$	9.69827	+	16.7979i	0.338060	+	0.585538i	0.984068	−	0.177793i	$-0.0568959\pi$
$823$	9.69827	+	16.7979i	0.338060	+	0.585538i	−0.646008	+	0.763331i	$0.723563\pi$
$824$	−2.72423	−	4.71851i	−0.0949031	−	0.164377i
$825$	0.760459	−	1.89883i	0.0264758	−	0.0661088i
$826$	−17.2100	+	29.8087i	−0.598814	+	1.03718i
$827$	6.16626			0.214422			0.107211	−	0.994236i	$-0.465808\pi$
$827$	6.16626			0.214422			0.107211	+	0.994236i	$0.465808\pi$
$828$	−2.17067	−	2.07079i	−0.0754361	−	0.0719650i
$829$	−35.7526			−1.24174			−0.620869	−	0.783914i	$-0.713220\pi$
$829$	−35.7526			−1.24174			−0.620869	+	0.783914i	$0.713220\pi$
$830$	−3.33407	+	5.77479i	−0.115727	+	0.200446i
$831$	8.42385	−	1.21007i	0.292220	−	0.0419767i
$832$	3.22866	+	5.59220i	0.111934	+	0.193875i
$833$	−0.683877	−	1.18451i	−0.0236949	−	0.0410408i
$834$	22.7032	+	28.8770i	0.786147	+	0.999930i
$835$	21.8830	−	37.9024i	0.757291	−	1.31167i
$836$	−19.9427			−0.689733
$837$	−9.41668	−	6.71103i	−0.325488	−	0.231967i
$838$	−26.2760			−0.907688
$839$	−0.141635	+	0.245318i	−0.00488977	+	0.00846933i	−0.868460	−	0.495759i	$-0.834890\pi$
$839$	−0.141635	+	0.245318i	−0.00488977	+	0.00846933i	0.863570	+	0.504229i	$0.168223\pi$
$840$	−6.55470	−	8.33717i	−0.226159	−	0.287660i
$841$	14.2663	+	24.7099i	0.491941	+	0.852066i
$842$	12.5632	+	21.7600i	0.432955	+	0.749900i
$843$	0.728468	−	0.104643i	0.0250898	−	0.00360409i
$844$	12.3293	−	21.3550i	0.424393	−	0.735070i
$845$	62.2560			2.14167
$846$	4.53618	−	1.33068i	0.155957	−	0.0457498i
$847$	−14.6227			−0.502443
$848$	2.60301	−	4.50854i	0.0893877	−	0.154824i
$849$	−7.65256	+	19.1081i	−0.262635	+	0.655788i
$850$	0.207861	+	0.360026i	0.00712957	+	0.0123488i
$851$	3.19908	+	5.54098i	0.109663	+	0.189942i
$852$	−8.18998	+	20.4500i	−0.280584	+	0.700606i
$853$	−6.21187	+	10.7593i	−0.212690	+	0.368391i	−0.952556	−	0.304365i	$-0.901556\pi$
$853$	−6.21187	+	10.7593i	−0.212690	+	0.368391i	0.739865	+	0.672755i	$0.234889\pi$
$854$	26.4814			0.906176
$855$	30.9616	−	9.08253i	1.05886	−	0.310616i
$856$	−20.4092			−0.697571
$857$	11.1302	−	19.2780i	0.380200	−	0.658525i	−0.610891	−	0.791715i	$-0.709189\pi$
$857$	11.1302	−	19.2780i	0.380200	−	0.658525i	0.991091	+	0.133190i	$0.0425219\pi$
$858$	−44.5328	+	6.39703i	−1.52032	+	0.218391i
$859$	11.7292	+	20.3155i	0.400194	+	0.693157i	0.993749	−	0.111637i	$-0.0356093\pi$
$859$	11.7292	+	20.3155i	0.400194	+	0.693157i	−0.593555	+	0.804794i	$0.702276\pi$
$860$	2.48605	+	4.30597i	0.0847736	+	0.146832i
$861$	−23.2731	−	29.6019i	−0.793145	−	1.00883i
$862$	−12.9936	+	22.5055i	−0.442563	+	0.766541i
$863$	−37.8216			−1.28746			−0.643731	−	0.765252i	$-0.722614\pi$
$863$	−37.8216			−1.28746			−0.643731	+	0.765252i	$0.722614\pi$
$864$	4.23150	+	3.01569i	0.143959	+	0.102596i
$865$	14.7706			0.502215
$866$	−15.7888	+	27.3470i	−0.536526	+	0.929290i
$867$	−16.0521	−	20.4173i	−0.545157	−	0.693406i
$868$	−3.14044	−	5.43940i	−0.106593	−	0.184625i
$869$	−12.4084	−	21.4921i	−0.420928	−	0.729068i
$870$	2.54294	−	0.365288i	0.0862139	−	0.0123844i
$871$	−26.9546	+	46.6868i	−0.913323	+	1.58192i
$872$	−17.8299			−0.603797
$873$	−28.1343	−	26.8397i	−0.952201	−	0.908387i
$874$	4.95772			0.167697
$875$	−16.2062	+	28.0700i	−0.547871	+	0.948940i
$876$	−0.0642308	+	0.160381i	−0.00217016	+	0.00541878i
$877$	21.4394	+	37.1342i	0.723959	+	1.25393i	0.959401	+	0.282045i	$0.0910127\pi$
$877$	21.4394	+	37.1342i	0.723959	+	1.25393i	−0.235443	+	0.971888i	$0.575654\pi$
$878$	4.69806	+	8.13728i	0.158552	+	0.274620i
$879$	−6.78234	+	16.9352i	−0.228763	+	0.571209i
$880$	4.36333	−	7.55750i	0.147088	−	0.254763i
$881$	−24.8744			−0.838040			−0.419020	−	0.907977i	$-0.637626\pi$
$881$	−24.8744			−0.838040			−0.419020	+	0.907977i	$0.637626\pi$
$882$	−0.683877	+	2.81583i	−0.0230273	+	0.0948141i
$883$	−36.9929			−1.24491			−0.622455	−	0.782656i	$-0.713865\pi$
$883$	−36.9929			−1.24491			−0.622455	+	0.782656i	$0.713865\pi$
$884$	4.57193	−	7.91881i	0.153770	−	0.266338i
$885$	45.3592	−	6.51574i	1.52473	−	0.219024i
$886$	8.51929	+	14.7558i	0.286211	+	0.495732i
$887$	−27.7113	−	47.9973i	−0.930453	−	1.61159i	−0.782547	−	0.622591i	$-0.786080\pi$
$887$	−27.7113	−	47.9973i	−0.930453	−	1.61159i	−0.147906	−	0.989001i	$-0.547253\pi$
$888$	−6.84929	−	8.71188i	−0.229847	−	0.292351i
$889$	−2.30410	+	3.99083i	−0.0772772	+	0.133848i
$890$	16.9799			0.569168
$891$	−30.4659	+	19.5572i	−1.02065	+	0.655192i
$892$	22.6610			0.758746
$893$	−3.90613	+	6.76561i	−0.130714	+	0.226402i
$894$	6.08337	+	7.73767i	0.203458	+	0.258786i
$895$	−8.84970	−	15.3281i	−0.295813	−	0.512363i
$896$	1.41120	+	2.44426i	0.0471448	+	0.0816571i
$897$	11.0708	−	1.59029i	0.369642	−	0.0530982i
$898$	16.6663	−	28.8669i	0.556163	−	0.963302i
$899$	1.52149			0.0507445
$900$	0.207861	−	0.855858i	0.00692869	−	0.0285286i
$901$	−7.37196			−0.245596
$902$	15.4924	−	26.8336i	0.515841	−	0.893462i
$903$	4.16543	−	10.4009i	0.138617	−	0.346120i
$904$	1.69550	+	2.93669i	0.0563915	+	0.0976729i
$905$	−17.7283	−	30.7063i	−0.589308	−	1.02071i
$906$	10.1958	−	25.4585i	0.338734	−	0.845802i
$907$	−9.41990	+	16.3158i	−0.312783	+	0.541756i	−0.978964	−	0.204035i	$-0.934595\pi$
$907$	−9.41990	+	16.3158i	−0.312783	+	0.541756i	0.666181	+	0.745790i	$0.267928\pi$
$908$	−2.30761			−0.0765806
$909$	19.8704	+	18.9561i	0.659060	+	0.628735i
$910$	39.5380			1.31067
$911$	9.25039	−	16.0221i	0.306479	−	0.530837i	−0.671111	−	0.741357i	$-0.734182\pi$
$911$	9.25039	−	16.0221i	0.306479	−	0.530837i	0.977590	+	0.210520i	$0.0675157\pi$
$912$	−8.49977	+	1.22097i	−0.281456	+	0.0404305i
$913$	6.18205	+	10.7076i	0.204596	+	0.354370i
$914$	−13.0221	−	22.5550i	−0.430734	−	0.746053i
$915$	−21.7901	−	27.7157i	−0.720359	−	0.916252i
$916$	−12.4381	+	21.5434i	−0.410966	+	0.711815i
$917$	33.6687			1.11184
$918$	0.702231	−	7.32440i	0.0231771	−	0.241741i
$919$	−19.2244			−0.634153			−0.317077	−	0.948400i	$-0.602701\pi$
$919$	−19.2244			−0.634153			−0.317077	+	0.948400i	$0.602701\pi$
$920$	−1.08471	+	1.87878i	−0.0357620	+	0.0619416i
$921$	18.1490	+	23.0843i	0.598028	+	0.760655i
$922$	7.85044	+	13.5974i	0.258540	+	0.447805i
$923$	−41.0636	−	71.1242i	−1.35162	−	2.34108i
$924$	−19.4646	+	2.79604i	−0.640338	+	0.0919831i
$925$	−0.939185	+	1.62672i	−0.0308802	+	0.0534861i
$926$	−41.6147			−1.36754
$927$	15.6845	−	4.60102i	0.515145	−	0.151117i
$928$	−0.683701			−0.0224436
$929$	23.9097	−	41.4128i	0.784452	−	1.35871i	−0.144874	−	0.989450i	$-0.546278\pi$
$929$	23.9097	−	41.4128i	0.784452	−	1.35871i	0.929326	−	0.369261i	$-0.120389\pi$
$930$	−3.10883	+	7.76259i	−0.101942	+	0.254545i
$931$	−2.39432	−	4.14709i	−0.0784707	−	0.135915i
$932$	−14.7154	−	25.4878i	−0.482018	−	0.834880i
$933$	−3.37920	+	8.43770i	−0.110630	+	0.276238i
$934$	−0.421037	+	0.729258i	−0.0137768	+	0.0238620i
$935$	−12.3573			−0.404128
$936$	−18.5886	+	5.45295i	−0.607589	+	0.178235i
$937$	−19.0752			−0.623160			−0.311580	−	0.950220i	$-0.600858\pi$
$937$	−19.0752			−0.623160			−0.311580	+	0.950220i	$0.600858\pi$
$938$	−11.7814	+	20.4061i	−0.384678	+	0.666282i
$939$	17.4496	−	2.50660i	0.569447	−	0.0817998i
$940$	−1.70927	−	2.96054i	−0.0557501	−	0.0965620i
$941$	−19.7521	−	34.2117i	−0.643901	−	1.11527i	−0.984554	−	0.175080i	$-0.943981\pi$
$941$	−19.7521	−	34.2117i	−0.643901	−	1.11527i	0.340653	−	0.940189i	$-0.389352\pi$
$942$	16.9715	+	21.5866i	0.552960	+	0.703331i
$943$	−3.85138	+	6.67079i	−0.125418	+	0.217231i
$944$	−12.1954			−0.396925
$945$	28.9459	−	13.2057i	0.941609	−	0.429582i
$946$	9.21928			0.299745
$947$	−0.918510	+	1.59091i	−0.0298475	+	0.0516975i	−0.880563	−	0.473928i	$-0.842836\pi$
$947$	−0.918510	+	1.59091i	−0.0298475	+	0.0516975i	0.850716	+	0.525626i	$0.176169\pi$
$948$	−6.60443	−	8.40042i	−0.214502	−	0.272833i
$949$	−0.322045	−	0.557799i	−0.0104540	−	0.0181069i
$950$	0.727742	+	1.26049i	0.0236111	+	0.0408956i
$951$	7.07003	−	1.01559i	0.229261	−	0.0329329i
$952$	1.99832	−	3.46119i	0.0647658	−	0.112178i
$953$	−14.1476			−0.458284			−0.229142	−	0.973393i	$-0.573592\pi$
$953$	−14.1476			−0.458284			−0.229142	+	0.973393i	$0.573592\pi$
$954$	11.3006	+	10.7806i	0.365869	+	0.349034i
$955$	−32.7296			−1.05911
$956$	2.00326	−	3.46975i	0.0647902	−	0.112220i
$957$	1.77099	−	4.42208i	0.0572480	−	0.142946i
$958$	−8.63031	−	14.9481i	−0.278833	−	0.482953i
$959$	19.0685	+	33.0276i	0.615754	+	1.06652i
$960$	1.39699	−	3.48822i	0.0450877	−	0.112582i
$961$	13.0239	−	22.5580i	0.420124	−	0.727677i
$962$	41.3150			1.33205
$963$	14.4502	−	59.4979i	0.465650	−	1.91729i
$964$	25.7723			0.830069
$965$	−10.3136	+	17.8637i	−0.332006	+	0.575052i
$966$	4.83886	−	0.695091i	0.155688	−	0.0223642i
$967$	4.21027	+	7.29240i	0.135393	+	0.234508i	0.925748	−	0.378142i	$-0.123437\pi$
$967$	4.21027	+	7.29240i	0.135393	+	0.234508i	−0.790354	+	0.612650i	$0.790104\pi$
$968$	−2.59049	−	4.48685i	−0.0832614	−	0.144213i
$969$	7.51535	+	9.55906i	0.241428	+	0.307081i
$970$	−14.0591	+	24.3510i	−0.451410	+	0.781864i
$971$	31.4248			1.00847			0.504235	−	0.863567i	$-0.331775\pi$
$971$	31.4248			1.00847			0.504235	+	0.863567i	$0.331775\pi$
$972$	−11.7875	+	10.2007i	−0.378084	+	0.327189i
$973$	−59.8568			−1.91892
$974$	−6.37235	+	11.0372i	−0.204183	+	0.353656i
$975$	2.02940	+	2.58127i	0.0649928	+	0.0826669i
$976$	4.69131	+	8.12558i	0.150165	+	0.260094i
$977$	22.2807	+	38.5914i	0.712824	+	1.23465i	0.963793	+	0.266652i	$0.0859175\pi$
$977$	22.2807	+	38.5914i	0.712824	+	1.23465i	−0.250969	+	0.967995i	$0.580749\pi$
$978$	−19.8559	+	2.85225i	−0.634921	+	0.0912049i
$979$	15.7421	−	27.2661i	0.503120	−	0.871429i
$980$	2.09544			0.0669365
$981$	12.6240	−	51.9787i	0.403053	−	1.65955i
$982$	1.67649			0.0534990
$983$	−0.510467	+	0.884155i	−0.0162814	+	0.0282002i	−0.874051	−	0.485834i	$-0.838516\pi$
$983$	−0.510467	+	0.884155i	−0.0162814	+	0.0282002i	0.857770	+	0.514034i	$0.171849\pi$
$984$	4.96015	−	12.3853i	0.158124	−	0.394827i
$985$	−21.8373	−	37.8233i	−0.695794	−	1.20515i
$986$	0.484076	+	0.838444i	0.0154161	+	0.0267015i
$987$	−2.86391	+	7.15106i	−0.0911593	+	0.227621i
$988$	16.0068	−	27.7245i	0.509243	−	0.882035i
$989$	−2.29189			−0.0728780
$990$	18.9427	+	18.0711i	0.602039	+	0.574337i
$991$	21.2518			0.675085			0.337542	−	0.941310i	$-0.390404\pi$
$991$	21.2518			0.675085			0.337542	+	0.941310i	$0.390404\pi$
$992$	1.11269	−	1.92723i	0.0353278	−	0.0611896i
$993$	35.7050	−	5.12895i	1.13306	−	0.162762i
$994$	−17.9483	−	31.0873i	−0.569284	−	0.986029i
$995$	17.0490	+	29.5297i	0.540488	+	0.936153i
$996$	3.29041	+	4.18520i	0.104261	+	0.132613i
$997$	−15.9347	+	27.5998i	−0.504658	+	0.874094i	0.495327	+	0.868706i	$0.335048\pi$
$997$	−15.9347	+	27.5998i	−0.504658	+	0.874094i	−0.999985	+	0.00538718i	$0.998285\pi$
$998$	23.8607			0.755297
$999$	30.2468	−	13.7992i	0.956966	−	0.436588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.c.277.4	yes	10
3.2	odd	2		1242.2.e.c.829.5		10
9.2	odd	6		3726.2.a.s.1.1		5
9.4	even	3	inner	414.2.e.c.139.4	✓	10
9.5	odd	6		1242.2.e.c.415.5		10
9.7	even	3		3726.2.a.t.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.c.139.4	✓	10	9.4	even	3	inner
414.2.e.c.277.4	yes	10	1.1	even	1	trivial
1242.2.e.c.415.5		10	9.5	odd	6
1242.2.e.c.829.5		10	3.2	odd	2
3726.2.a.s.1.1		5	9.2	odd	6
3726.2.a.t.1.5		5	9.7	even	3

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.07051 + 1.36162i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08471 - 1.87878i) q^{5} +(-1.71445 + 0.246277i) q^{6} +(1.41120 - 2.44426i) q^{7} +1.00000 q^{8} +(-0.708023 + 2.91525i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.07051 + 1.36162i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08471 - 1.87878i) q^{5} +(-1.71445 + 0.246277i) q^{6} +(1.41120 - 2.44426i) q^{7} +1.00000 q^{8} +(-0.708023 + 2.91525i) q^{9} +2.16943 q^{10} +(2.01128 - 3.48364i) q^{11} +(0.643944 - 1.60790i) q^{12} +(3.22866 + 5.59220i) q^{13} +(1.41120 + 2.44426i) q^{14} +(1.39699 - 3.48822i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.41605 q^{17} +(-2.17067 - 2.07079i) q^{18} +4.95772 q^{19} +(-1.08471 + 1.87878i) q^{20} +(4.83886 - 0.695091i) q^{21} +(2.01128 + 3.48364i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.07051 + 1.36162i) q^{24} +(0.146790 - 0.254247i) q^{25} -6.45732 q^{26} +(-4.72741 + 2.15675i) q^{27} -2.82239 q^{28} +(0.341850 - 0.592102i) q^{29} +(2.32239 + 2.95394i) q^{30} +(1.11269 + 1.92723i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.89648 - 0.990665i) q^{33} +(-0.708023 + 1.22633i) q^{34} -6.12298 q^{35} +(2.87870 - 0.844461i) q^{36} -6.39817 q^{37} +(-2.47886 + 4.29351i) q^{38} +(-4.15815 + 10.3827i) q^{39} +(-1.08471 - 1.87878i) q^{40} +(-3.85138 - 6.67079i) q^{41} +(-1.81746 + 4.53812i) q^{42} +(1.14595 - 1.98484i) q^{43} -4.02256 q^{44} +(6.24512 - 1.83200i) q^{45} +1.00000 q^{46} +(-0.787888 + 1.36466i) q^{47} +(-1.71445 + 0.246277i) q^{48} +(-0.482949 - 0.836491i) q^{49} +(0.146790 + 0.254247i) q^{50} +(1.51589 + 1.92812i) q^{51} +(3.22866 - 5.59220i) q^{52} -5.20602 q^{53} +(0.495910 - 5.17243i) q^{54} -8.72665 q^{55} +(1.41120 - 2.44426i) q^{56} +(5.30728 + 6.75053i) q^{57} +(0.341850 + 0.592102i) q^{58} +(6.09768 + 10.5615i) q^{59} +(-3.71938 + 0.534281i) q^{60} +(4.69131 - 8.12558i) q^{61} -2.22537 q^{62} +(6.12649 + 5.84459i) q^{63} +1.00000 q^{64} +(7.00434 - 12.1319i) q^{65} +(-2.59030 + 6.46786i) q^{66} +(4.17428 + 7.23006i) q^{67} +(-0.708023 - 1.22633i) q^{68} +(0.643944 - 1.60790i) q^{69} +(3.06149 - 5.30265i) q^{70} -12.7185 q^{71} +(-0.708023 + 2.91525i) q^{72} -0.0997459 q^{73} +(3.19908 - 5.54098i) q^{74} +(0.503328 - 0.0723019i) q^{75} +(-2.47886 - 4.29351i) q^{76} +(-5.67662 - 9.83219i) q^{77} +(-6.91261 - 8.79242i) q^{78} +(3.08471 - 5.34288i) q^{79} +2.16943 q^{80} +(-7.99741 - 4.12813i) q^{81} +7.70276 q^{82} +(-1.53684 + 2.66189i) q^{83} +(-3.02140 - 3.84303i) q^{84} +(-1.53600 - 2.66044i) q^{85} +(1.14595 + 1.98484i) q^{86} +(1.17217 - 0.168380i) q^{87} +(2.01128 - 3.48364i) q^{88} +7.82691 q^{89} +(-1.53600 + 6.32443i) q^{90} +18.2251 q^{91} +(-0.500000 + 0.866025i) q^{92} +(-1.43302 + 3.57817i) q^{93} +(-0.787888 - 1.36466i) q^{94} +(-5.37771 - 9.31446i) q^{95} +(0.643944 - 1.60790i) q^{96} +(-6.48054 + 11.2246i) q^{97} +0.965897 q^{98} +(8.73166 + 8.32988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

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