LMFDB - Embedded newform 210.2.n.b.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(79,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("210.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.7652750400000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} + \cdots + 64 $ x^12 - 6x^11 + 18x^10 - 14x^9 + 21x^8 - 108x^7 + 368x^6 - 216x^5 + 84x^4 - 112x^3 + 288x^2 - 192*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.5
Root			$-1.45845 + 1.45845i$ of defining polynomial
Character	$\chi$	$=$	210.79
Dual form			210.2.n.b.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.806615 + 2.08551i) q^{5} +1.00000 q^{6} +(1.45550 + 2.20942i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.806615 + 2.08551i) q^{5} +1.00000 q^{6} +(1.45550 + 2.20942i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.74131 + 1.40280i) q^{10} +(-3.05362 - 5.28903i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.68842i q^{13} +(0.155792 + 2.64116i) q^{14} +(0.344208 + 2.20942i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.92159 - 3.41883i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.844208 - 1.46221i) q^{19} +(-2.20942 + 0.344208i) q^{20} +(2.36521 + 1.18566i) q^{21} -6.10725i q^{22} +(-2.00189 - 1.15579i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.69874 - 3.36441i) q^{25} +(-0.844208 + 1.46221i) q^{26} -1.00000i q^{27} +(-1.18566 + 2.36521i) q^{28} -8.41883 q^{29} +(-0.806615 + 2.08551i) q^{30} +(0.344208 + 0.596186i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.28903 - 3.05362i) q^{33} +6.83767 q^{34} +(-5.78180 + 1.25332i) q^{35} +1.00000 q^{36} +(2.00189 + 1.15579i) q^{37} +(1.46221 - 0.844208i) q^{38} +(0.844208 + 1.46221i) q^{39} +(-2.08551 - 0.806615i) q^{40} +5.14925 q^{41} +(1.45550 + 2.20942i) q^{42} -2.00000i q^{43} +(3.05362 - 5.28903i) q^{44} +(1.40280 + 1.74131i) q^{45} +(-1.15579 - 2.00189i) q^{46} +(-2.65458 - 1.53263i) q^{47} +1.00000i q^{48} +(-2.76304 + 6.43161i) q^{49} +(-1.52100 - 4.76304i) q^{50} +(3.41883 - 5.92159i) q^{51} +(-1.46221 + 0.844208i) q^{52} +(-9.05935 + 5.23042i) q^{53} +(0.500000 - 0.866025i) q^{54} +(13.4935 - 2.10217i) q^{55} +(-2.20942 + 1.45550i) q^{56} -1.68842i q^{57} +(-7.29092 - 4.20942i) q^{58} +(-3.52100 - 6.09855i) q^{59} +(-1.74131 + 1.40280i) q^{60} +(-4.73042 + 8.19332i) q^{61} +0.688417i q^{62} +(2.64116 - 0.155792i) q^{63} -1.00000 q^{64} +(-3.52122 - 1.36190i) q^{65} +(-3.05362 - 5.28903i) q^{66} +(10.5781 - 6.10725i) q^{67} +(5.92159 + 3.41883i) q^{68} -2.31158 q^{69} +(-5.63384 - 1.80549i) q^{70} +6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(1.15579 + 2.00189i) q^{74} +(-4.88541 - 1.06430i) q^{75} +1.68842 q^{76} +(7.24113 - 14.4449i) q^{77} +1.68842i q^{78} +(3.65579 - 6.33202i) q^{79} +(-1.40280 - 1.74131i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.45938 + 2.57462i) q^{82} +13.5261i q^{83} +(0.155792 + 2.64116i) q^{84} +(2.35358 + 15.1072i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-7.29092 + 4.20942i) q^{87} +(5.28903 - 3.05362i) q^{88} +(-6.10725 + 10.5781i) q^{89} +(0.344208 + 2.20942i) q^{90} +(-3.73042 + 2.45749i) q^{91} -2.31158i q^{92} +(0.596186 + 0.344208i) q^{93} +(-1.53263 - 2.65458i) q^{94} +(2.36851 + 2.94005i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.95800i q^{97} +(-5.60867 + 4.18842i) q^{98} -6.10725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9} - 6 q^{11} + 6 q^{14} - 6 q^{16} + 6 q^{19} + 6 q^{21} + 6 q^{24} - 6 q^{26} - 48 q^{29} - 24 q^{34} - 30 q^{35} + 12 q^{36} + 6 q^{39} - 36 q^{41} + 6 q^{44} - 18 q^{46} + 24 q^{49} - 12 q^{51} + 6 q^{54} + 60 q^{55} - 24 q^{59} - 12 q^{61} - 12 q^{64} - 30 q^{65} - 6 q^{66} - 36 q^{69} - 30 q^{70} + 72 q^{71} + 18 q^{74} + 12 q^{76} + 48 q^{79} - 6 q^{81} + 6 q^{84} + 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 12 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9 - 6 * q^11 + 6 * q^14 - 6 * q^16 + 6 * q^19 + 6 * q^21 + 6 * q^24 - 6 * q^26 - 48 * q^29 - 24 * q^34 - 30 * q^35 + 12 * q^36 + 6 * q^39 - 36 * q^41 + 6 * q^44 - 18 * q^46 + 24 * q^49 - 12 * q^51 + 6 * q^54 + 60 * q^55 - 24 * q^59 - 12 * q^61 - 12 * q^64 - 30 * q^65 - 6 * q^66 - 36 * q^69 - 30 * q^70 + 72 * q^71 + 18 * q^74 + 12 * q^76 + 48 * q^79 - 6 * q^81 + 6 * q^84 + 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.806615	+	2.08551i	−0.360729	+	0.932671i
$5$	−0.806615	+	2.08551i	−0.360729	+	0.932671i
$6$	1.00000			0.408248
$7$	1.45550	+	2.20942i	0.550127	+	0.835081i
$7$	1.45550	+	2.20942i	0.550127	+	0.835081i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.74131	+	1.40280i	−0.550649	+	0.443605i
$11$	−3.05362	−	5.28903i	−0.920703	−	1.59470i	−0.798331	−	0.602219i	$-0.794283\pi$
$11$	−3.05362	−	5.28903i	−0.920703	−	1.59470i	−0.122372	−	0.992484i	$-0.539050\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			1.68842i			0.468283i	0.972203	+	0.234141i	$0.0752278\pi$
$13$			1.68842i			0.468283i	−0.972203	+	0.234141i	$0.924772\pi$
$14$	0.155792	+	2.64116i	0.0416370	+	0.705880i
$15$	0.344208	+	2.20942i	0.0888742	+	0.570469i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.92159	−	3.41883i	1.43620	−	0.829189i	0.438614	−	0.898675i	$-0.355470\pi$
$17$	5.92159	−	3.41883i	1.43620	−	0.829189i	0.997583	+	0.0694868i	$0.0221362\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	0.844208	−	1.46221i	0.193675	−	0.335454i	−0.752791	−	0.658260i	$-0.771293\pi$
$19$	0.844208	−	1.46221i	0.193675	−	0.335454i	0.946465	+	0.322806i	$0.104626\pi$
$20$	−2.20942	+	0.344208i	−0.494041	+	0.0769673i
$21$	2.36521	+	1.18566i	0.516131	+	0.258732i
$22$		−	6.10725i		−	1.30207i
$23$	−2.00189	−	1.15579i	−0.417423	−	0.240999i	0.276551	−	0.960999i	$-0.410808\pi$
$23$	−2.00189	−	1.15579i	−0.417423	−	0.240999i	−0.693974	+	0.720000i	$0.744142\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.69874	−	3.36441i	−0.739749	−	0.672883i
$26$	−0.844208	+	1.46221i	−0.165563	+	0.286763i
$27$		−	1.00000i		−	0.192450i
$28$	−1.18566	+	2.36521i	−0.224069	+	0.446982i
$29$	−8.41883			−1.56334			−0.781669	−	0.623694i	$-0.785631\pi$
$29$	−8.41883			−1.56334			−0.781669	+	0.623694i	$0.785631\pi$
$30$	−0.806615	+	2.08551i	−0.147267	+	0.380761i
$31$	0.344208	+	0.596186i	0.0618217	+	0.107078i	0.895280	−	0.445504i	$-0.146976\pi$
$31$	0.344208	+	0.596186i	0.0618217	+	0.107078i	−0.833458	+	0.552583i	$0.813642\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.28903	−	3.05362i	−0.920703	−	0.531568i
$34$	6.83767			1.17265
$35$	−5.78180	+	1.25332i	−0.977302	+	0.211849i
$36$	1.00000			0.166667
$37$	2.00189	+	1.15579i	0.329109	+	0.190011i	0.655445	−	0.755243i	$-0.272481\pi$
$37$	2.00189	+	1.15579i	0.329109	+	0.190011i	−0.326337	+	0.945254i	$0.605814\pi$
$38$	1.46221	−	0.844208i	0.237202	−	0.136949i
$39$	0.844208	+	1.46221i	0.135182	+	0.234141i
$40$	−2.08551	−	0.806615i	−0.329749	−	0.127537i
$41$	5.14925			0.804178			0.402089	−	0.915601i	$-0.368284\pi$
$41$	5.14925			0.804178			0.402089	+	0.915601i	$0.368284\pi$
$42$	1.45550	+	2.20942i	0.224588	+	0.340920i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	3.05362	−	5.28903i	0.460351	−	0.797352i
$45$	1.40280	+	1.74131i	0.209117	+	0.259579i
$46$	−1.15579	−	2.00189i	−0.170412	−	0.295163i
$47$	−2.65458	−	1.53263i	−0.387211	−	0.223556i	0.293740	−	0.955885i	$-0.405100\pi$
$47$	−2.65458	−	1.53263i	−0.387211	−	0.223556i	−0.680951	+	0.732329i	$0.738433\pi$
$48$			1.00000i			0.144338i
$49$	−2.76304	+	6.43161i	−0.394720	+	0.918801i
$50$	−1.52100	−	4.76304i	−0.215102	−	0.673596i
$51$	3.41883	−	5.92159i	0.478732	−	0.829189i
$52$	−1.46221	+	0.844208i	−0.202772	+	0.117071i
$53$	−9.05935	+	5.23042i	−1.24440	+	0.718453i	−0.969986	−	0.243160i	$-0.921816\pi$
$53$	−9.05935	+	5.23042i	−1.24440	+	0.718453i	−0.274411	+	0.961613i	$0.588483\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	13.4935	−	2.10217i	1.81946	−	0.283456i
$56$	−2.20942	+	1.45550i	−0.295246	+	0.194499i
$57$		−	1.68842i		−	0.223636i
$58$	−7.29092	−	4.20942i	−0.957345	−	0.552723i
$59$	−3.52100	−	6.09855i	−0.458395	−	0.793964i	0.540481	−	0.841356i	$-0.318242\pi$
$59$	−3.52100	−	6.09855i	−0.458395	−	0.793964i	−0.998876	+	0.0473925i	$0.984909\pi$
$60$	−1.74131	+	1.40280i	−0.224802	+	0.181101i
$61$	−4.73042	+	8.19332i	−0.605668	+	1.04905i	0.386278	+	0.922382i	$0.373761\pi$
$61$	−4.73042	+	8.19332i	−0.605668	+	1.04905i	−0.991946	+	0.126665i	$0.959573\pi$
$62$			0.688417i			0.0874290i
$63$	2.64116	−	0.155792i	0.332755	−	0.0196279i
$64$	−1.00000			−0.125000
$65$	−3.52122	−	1.36190i	−0.436753	−	0.168923i
$66$	−3.05362	−	5.28903i	−0.375875	−	0.651035i
$67$	10.5781	−	6.10725i	1.29232	−	0.746119i	0.313252	−	0.949670i	$-0.398582\pi$
$67$	10.5781	−	6.10725i	1.29232	−	0.746119i	0.979064	+	0.203551i	$0.0652482\pi$
$68$	5.92159	+	3.41883i	0.718098	+	0.414594i
$69$	−2.31158			−0.278282
$70$	−5.63384	−	1.80549i	−0.673373	−	0.215798i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$	1.15579	+	2.00189i	0.134358	+	0.232715i
$75$	−4.88541	−	1.06430i	−0.564119	−	0.122894i
$76$	1.68842			0.193675
$77$	7.24113	−	14.4449i	0.825203	−	1.64615i
$78$			1.68842i			0.191176i
$79$	3.65579	−	6.33202i	0.411309	−	0.712408i	−0.583724	−	0.811952i	$-0.698405\pi$
$79$	3.65579	−	6.33202i	0.411309	−	0.712408i	0.995033	+	0.0995443i	$0.0317385\pi$
$80$	−1.40280	−	1.74131i	−0.156838	−	0.194684i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.45938	+	2.57462i	0.492456	+	0.284320i
$83$			13.5261i			1.48468i	0.670023	+	0.742340i	$0.266284\pi$
$83$			13.5261i			1.48468i	−0.670023	+	0.742340i	$0.733716\pi$
$84$	0.155792	+	2.64116i	0.0169983	+	0.288174i
$85$	2.35358	+	15.1072i	0.255282	+	1.63861i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	−7.29092	+	4.20942i	−0.781669	+	0.451297i
$88$	5.28903	−	3.05362i	0.563813	−	0.325517i
$89$	−6.10725	+	10.5781i	−0.647367	+	1.12127i	0.336382	+	0.941726i	$0.390797\pi$
$89$	−6.10725	+	10.5781i	−0.647367	+	1.12127i	−0.983749	+	0.179547i	$0.942537\pi$
$90$	0.344208	+	2.20942i	0.0362828	+	0.232893i
$91$	−3.73042	+	2.45749i	−0.391054	+	0.257615i
$92$		−	2.31158i		−	0.240999i
$93$	0.596186	+	0.344208i	0.0618217	+	0.0356928i
$94$	−1.53263	−	2.65458i	−0.158078	−	0.273800i
$95$	2.36851	+	2.94005i	0.243004	+	0.301643i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			4.95800i			0.503409i	0.967804	+	0.251704i	$0.0809911\pi$
$97$			4.95800i			0.503409i	−0.967804	+	0.251704i	$0.919009\pi$
$98$	−5.60867	+	4.18842i	−0.566561	+	0.423094i
$99$	−6.10725			−0.613802
$100$	1.06430	−	4.88541i	0.106430	−	0.488541i
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	5.92159	−	3.41883i	0.586325	−	0.338515i
$103$	−0.725439	−	0.418833i	−0.0714797	−	0.0412688i	0.463834	−	0.885922i	$-0.346473\pi$
$103$	−0.725439	−	0.418833i	−0.0714797	−	0.0412688i	−0.535314	+	0.844653i	$0.679807\pi$
$104$	−1.68842			−0.165563
$105$	−4.38053	+	3.97630i	−0.427495	+	0.388048i
$106$	−10.4608			−1.01605
$107$	13.4460	+	7.76304i	1.29987	+	0.750482i	0.980382	−	0.197108i	$-0.0631550\pi$
$107$	13.4460	+	7.76304i	1.29987	+	0.750482i	0.319490	+	0.947590i	$0.396488\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−5.83767	−	10.1111i	−0.559147	−	0.968471i	−0.997568	−	0.0697012i	$-0.977795\pi$
$109$	−5.83767	−	10.1111i	−0.559147	−	0.968471i	0.438421	−	0.898770i	$-0.355538\pi$
$110$	12.7368	+	4.92620i	1.21440	+	0.469695i
$111$	2.31158			0.219406
$112$	−2.64116	+	0.155792i	−0.249566	+	0.0147209i
$113$		−	3.37683i		−	0.317666i	−0.987305	−	0.158833i	$-0.949227\pi$
$113$		−	3.37683i		−	0.317666i	0.987305	−	0.158833i	$-0.0507731\pi$
$114$	0.844208	−	1.46221i	0.0790674	−	0.136949i
$115$	4.02517	−	3.24269i	0.375349	−	0.302383i
$116$	−4.20942	−	7.29092i	−0.390834	−	0.676945i
$117$	1.46221	+	0.844208i	0.135182	+	0.0780471i
$118$		−	7.04200i		−	0.648269i
$119$	16.1725	+	8.10715i	1.48253	+	0.743181i
$120$	−2.20942	+	0.344208i	−0.201691	+	0.0314218i
$121$	−13.1492	+	22.7752i	−1.19539	+	2.07047i
$122$	−8.19332	+	4.73042i	−0.741788	+	0.428272i
$123$	4.45938	−	2.57462i	0.402089	−	0.232146i
$124$	−0.344208	+	0.596186i	−0.0309108	+	0.0535391i
$125$	10.0000	−	5.00000i	0.894427	−	0.447214i
$126$	2.36521	+	1.18566i	0.210709	+	0.105627i
$127$			4.94491i			0.438790i	0.975636	+	0.219395i	$0.0704084\pi$
$127$			4.94491i			0.438790i	−0.975636	+	0.219395i	$0.929592\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−1.00000	−	1.73205i	−0.0880451	−	0.152499i
$130$	−2.36851	−	2.94005i	−0.207732	−	0.257860i
$131$	3.36521	−	5.82871i	0.294020	−	0.509257i	−0.680737	−	0.732528i	$-0.738340\pi$
$131$	3.36521	−	5.82871i	0.294020	−	0.509257i	0.974756	+	0.223271i	$0.0716736\pi$
$132$		−	6.10725i		−	0.531568i
$133$	4.45938	−	0.263041i	0.386677	−	0.0228086i
$134$	12.2145			1.05517
$135$	2.08551	+	0.806615i	0.179493	+	0.0694224i
$136$	3.41883	+	5.92159i	0.293162	+	0.507772i
$137$	−16.4997	+	9.52608i	−1.40966	+	0.813868i	−0.995355	−	0.0962697i	$-0.969309\pi$
$137$	−16.4997	+	9.52608i	−1.40966	+	0.813868i	−0.414306	+	0.910138i	$0.635976\pi$
$138$	−2.00189	−	1.15579i	−0.170412	−	0.0983875i
$139$	−13.3768			−1.13461			−0.567304	−	0.823508i	$-0.692014\pi$
$139$	−13.3768			−1.13461			−0.567304	+	0.823508i	$0.692014\pi$
$140$	−3.97630	−	4.38053i	−0.336059	−	0.370222i
$141$	−3.06525			−0.258141
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$	8.93009	−	5.15579i	0.746772	−	0.431149i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	6.79076	−	17.5576i	0.563942	−	1.45808i
$146$	4.00000			0.331042
$147$	0.822941	+	6.95146i	0.0678750	+	0.573347i
$148$			2.31158i			0.190011i
$149$	6.31158	−	10.9320i	0.517065	−	0.895583i	−0.482739	−	0.875765i	$-0.660358\pi$
$149$	6.31158	−	10.9320i	0.517065	−	0.895583i	0.999804	−	0.0198184i	$-0.00630881\pi$
$150$	−3.69874	−	3.36441i	−0.302001	−	0.274703i
$151$	−0.967375	−	1.67554i	−0.0787238	−	0.136354i	0.823976	−	0.566625i	$-0.191751\pi$
$151$	−0.967375	−	1.67554i	−0.0787238	−	0.136354i	−0.902700	+	0.430271i	$0.858418\pi$
$152$	1.46221	+	0.844208i	0.118601	+	0.0684743i
$153$		−	6.83767i		−	0.552792i
$154$	13.4935	−	8.88910i	1.08733	−	0.716304i
$155$	−1.52100	+	0.236959i	−0.122170	+	0.0190330i
$156$	−0.844208	+	1.46221i	−0.0675908	+	0.117071i
$157$	−14.8517	+	8.57462i	−1.18529	+	0.684330i	−0.957233	−	0.289317i	$-0.906572\pi$
$157$	−14.8517	+	8.57462i	−1.18529	+	0.684330i	−0.228060	+	0.973647i	$0.573238\pi$
$158$	6.33202	−	3.65579i	0.503748	−	0.290839i
$159$	−5.23042	+	9.05935i	−0.414799	+	0.718453i
$160$	−0.344208	−	2.20942i	−0.0272121	−	0.174670i
$161$	−0.360125	−	6.10526i	−0.0283818	−	0.481162i
$162$		−	1.00000i		−	0.0785674i
$163$	−0.466934	−	0.269584i	−0.0365731	−	0.0211155i	0.481602	−	0.876390i	$-0.340055\pi$
$163$	−0.466934	−	0.269584i	−0.0365731	−	0.0211155i	−0.518175	+	0.855275i	$0.673388\pi$
$164$	2.57462	+	4.45938i	0.201044	+	0.348219i
$165$	10.6346	−	8.56726i	0.827902	−	0.666960i
$166$	−6.76304	+	11.7139i	−0.524914	+	0.909177i
$167$			3.14925i			0.243696i	0.992549	+	0.121848i	$0.0388821\pi$
$167$			3.14925i			0.243696i	−0.992549	+	0.121848i	$0.961118\pi$
$168$	−1.18566	+	2.36521i	−0.0914757	+	0.182480i
$169$	10.1492			0.780711
$170$	−5.51536	+	14.2601i	−0.423009	+	1.09370i
$171$	−0.844208	−	1.46221i	−0.0645582	−	0.111818i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	9.11585	+	5.26304i	0.693066	+	0.400142i	0.804759	−	0.593601i	$-0.202294\pi$
$173$	9.11585	+	5.26304i	0.693066	+	0.400142i	−0.111694	+	0.993743i	$0.535628\pi$
$174$	−8.41883			−0.638230
$175$	2.04987	−	13.0690i	0.154956	−	0.987921i
$176$	6.10725			0.460351
$177$	−6.09855	−	3.52100i	−0.458395	−	0.264655i
$178$	−10.5781	+	6.10725i	−0.792860	+	0.457758i
$179$	2.46737	+	4.27362i	0.184420	+	0.319425i	0.943381	−	0.331711i	$-0.107626\pi$
$179$	2.46737	+	4.27362i	0.184420	+	0.319425i	−0.758961	+	0.651136i	$0.774293\pi$
$180$	−0.806615	+	2.08551i	−0.0601215	+	0.155445i
$181$	6.13050			0.455677			0.227838	−	0.973699i	$-0.426834\pi$
$181$	6.13050			0.455677			0.227838	+	0.973699i	$0.426834\pi$
$182$	−4.45938	+	0.263041i	−0.330551	+	0.0194979i
$183$			9.46083i			0.699365i
$184$	1.15579	−	2.00189i	0.0852061	−	0.147581i
$185$	−4.02517	+	3.24269i	−0.295937	+	0.238407i
$186$	0.344208	+	0.596186i	0.0252386	+	0.0437145i
$187$	−36.1646	−	20.8797i	−2.64462	−	1.52687i
$188$		−	3.06525i		−	0.223556i
$189$	2.20942	−	1.45550i	0.160711	−	0.105872i
$190$	0.581167	+	3.73042i	0.0421623	+	0.270633i
$191$	7.46083	−	12.9225i	0.539847	−	0.935042i	−0.459065	−	0.888403i	$-0.651815\pi$
$191$	7.46083	−	12.9225i	0.539847	−	0.935042i	0.998912	−	0.0466394i	$-0.0148512\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−4.83343	+	2.79058i	−0.347918	+	0.200871i	−0.663768	−	0.747939i	$-0.731044\pi$
$193$	−4.83343	+	2.79058i	−0.347918	+	0.200871i	0.315850	+	0.948809i	$0.397710\pi$
$194$	−2.47900	+	4.29375i	−0.177982	+	0.308274i
$195$	−3.73042	+	0.581167i	−0.267141	+	0.0416183i
$196$	−6.95146	+	0.822941i	−0.496533	+	0.0587815i
$197$		−	14.5261i		−	1.03494i	−0.855701	−	0.517470i	$-0.826874\pi$
$197$		−	14.5261i		−	1.03494i	0.855701	−	0.517470i	$-0.173126\pi$
$198$	−5.28903	−	3.05362i	−0.375875	−	0.217012i
$199$	−4.31158	−	7.46788i	−0.305640	−	0.529384i	0.671764	−	0.740766i	$-0.265537\pi$
$199$	−4.31158	−	7.46788i	−0.305640	−	0.529384i	−0.977404	+	0.211382i	$0.932204\pi$
$200$	3.36441	−	3.69874i	0.237900	−	0.261541i
$201$	6.10725	−	10.5781i	0.430772	−	0.746119i
$202$			8.00000i			0.562878i
$203$	−12.2536	−	18.6007i	−0.860035	−	1.30551i
$204$	6.83767			0.478732
$205$	−4.15346	+	10.7388i	−0.290090	+	0.750033i
$206$	−0.418833	−	0.725439i	−0.0291815	−	0.0505438i
$207$	−2.00189	+	1.15579i	−0.139141	+	0.0803331i
$208$	−1.46221	−	0.844208i	−0.101386	−	0.0585353i
$209$	−10.3116			−0.713267
$210$	−5.78180	+	1.25332i	−0.398982	+	0.0864872i
$211$	−7.68842			−0.529292			−0.264646	−	0.964346i	$-0.585255\pi$
$211$	−7.68842			−0.529292			−0.264646	+	0.964346i	$0.585255\pi$
$212$	−9.05935	−	5.23042i	−0.622198	−	0.359226i
$213$	5.19615	−	3.00000i	0.356034	−	0.205557i
$214$	7.76304	+	13.4460i	0.530671	+	0.919148i
$215$	4.17103	+	1.61323i	0.284462	+	0.110021i
$216$	1.00000			0.0680414
$217$	−0.816229	+	1.62825i	−0.0554092	+	0.110533i
$218$		−	11.6753i		−	0.790753i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	8.56726	+	10.6346i	0.577604	+	0.716984i
$221$	5.77241	+	9.99812i	0.388295	+	0.672546i
$222$	2.00189	+	1.15579i	0.134358	+	0.0775717i
$223$		−	11.1725i		−	0.748166i	−0.927395	−	0.374083i	$-0.877958\pi$
$223$		−	11.1725i		−	0.748166i	0.927395	−	0.374083i	$-0.122042\pi$
$224$	−2.36521	−	1.18566i	−0.158032	−	0.0792203i
$225$	−4.76304	+	1.52100i	−0.317536	+	0.101400i
$226$	1.68842	−	2.92442i	0.112312	−	0.194530i
$227$	−3.33485	+	1.92538i	−0.221342	+	0.127792i	−0.606571	−	0.795029i	$-0.707456\pi$
$227$	−3.33485	+	1.92538i	−0.221342	+	0.127792i	0.385230	+	0.922821i	$0.374122\pi$
$228$	1.46221	−	0.844208i	0.0968373	−	0.0559091i
$229$	2.83767	−	4.91498i	0.187518	−	0.324791i	−0.756904	−	0.653526i	$-0.773289\pi$
$229$	2.83767	−	4.91498i	0.187518	−	0.324791i	0.944422	+	0.328735i	$0.106622\pi$
$230$	5.10725	−	0.795666i	0.336762	−	0.0524647i
$231$	−0.951458	−	16.1302i	−0.0626013	−	1.06129i
$232$		−	8.41883i		−	0.552723i
$233$	9.92537	+	5.73042i	0.650233	+	0.375412i	0.788545	−	0.614977i	$-0.210835\pi$
$233$	9.92537	+	5.73042i	0.650233	+	0.375412i	−0.138313	+	0.990389i	$0.544168\pi$
$234$	0.844208	+	1.46221i	0.0551876	+	0.0955878i
$235$	5.33754	−	4.29994i	0.348183	−	0.280497i
$236$	3.52100	−	6.09855i	0.229198	−	0.396982i
$237$		−	7.31158i		−	0.474938i
$238$	9.95222	+	15.1072i	0.645107	+	0.979258i
$239$	−15.4608			−1.00008			−0.500039	−	0.866003i	$-0.666681\pi$
$239$	−15.4608			−1.00008			−0.500039	+	0.866003i	$0.666681\pi$
$240$	−2.08551	−	0.806615i	−0.134619	−	0.0520668i
$241$	−2.18842	−	3.79045i	−0.140968	−	0.244164i	0.786893	−	0.617089i	$-0.211688\pi$
$241$	−2.18842	−	3.79045i	−0.140968	−	0.244164i	−0.927862	+	0.372925i	$0.878355\pi$
$242$	−22.7752	+	13.1492i	−1.46404	+	0.845266i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−9.46083			−0.605668
$245$	−11.1845	−	10.9502i	−0.714552	−	0.699582i
$246$	5.14925			0.328304
$247$	2.46882	+	1.42538i	0.157087	+	0.0906945i
$248$	−0.596186	+	0.344208i	−0.0378579	+	0.0218573i
$249$	6.76304	+	11.7139i	0.428590	+	0.742340i
$250$	11.1603	+	0.669873i	0.705836	+	0.0423665i
$251$	−26.5362			−1.67495			−0.837477	−	0.546473i	$-0.815970\pi$
$251$	−26.5362			−1.67495			−0.837477	+	0.546473i	$0.815970\pi$
$252$	1.45550	+	2.20942i	0.0916879	+	0.139180i
$253$			14.1174i			0.887554i
$254$	−2.47246	+	4.28242i	−0.155136	+	0.268703i
$255$	9.59189	+	11.9065i	0.600667	+	0.745612i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	19.4241	+	11.2145i	1.21164	+	0.699541i	0.963117	−	0.269084i	$-0.0867211\pi$
$257$	19.4241	+	11.2145i	1.21164	+	0.699541i	0.248524	+	0.968626i	$0.420054\pi$
$258$		−	2.00000i		−	0.124515i
$259$	0.360125	+	6.10526i	0.0223771	+	0.379363i
$260$	−0.581167	−	3.73042i	−0.0360425	−	0.231351i
$261$	−4.20942	+	7.29092i	−0.260556	+	0.451297i
$262$	5.82871	−	3.36521i	0.360099	−	0.207903i
$263$	−16.9666	+	9.79567i	−1.04620	+	0.604027i	−0.921584	−	0.388178i	$-0.873105\pi$
$263$	−16.9666	+	9.79567i	−1.04620	+	0.604027i	−0.124620	+	0.992204i	$0.539771\pi$
$264$	3.05362	−	5.28903i	0.187938	−	0.325517i
$265$	−3.60071	−	23.1123i	−0.221190	−	1.41978i
$266$	3.99346	+	2.00189i	0.244855	+	0.122744i
$267$			12.2145i			0.747515i
$268$	10.5781	+	6.10725i	0.646158	+	0.373060i
$269$	−3.47900	−	6.02581i	−0.212118	−	0.367400i	0.740259	−	0.672322i	$-0.234703\pi$
$269$	−3.47900	−	6.02581i	−0.212118	−	0.367400i	−0.952377	+	0.304922i	$0.901370\pi$
$270$	1.40280	+	1.74131i	0.0853718	+	0.105973i
$271$	14.1819	−	24.5637i	0.861487	−	1.49214i	−0.00900561	−	0.999959i	$-0.502867\pi$
$271$	14.1819	−	24.5637i	0.861487	−	1.49214i	0.870493	−	0.492181i	$-0.163800\pi$
$272$			6.83767i			0.414594i
$273$	−2.00189	+	3.99346i	−0.121160	+	0.241695i
$274$	−19.0522			−1.15098
$275$	−6.49992	+	29.8364i	−0.391960	+	1.79921i
$276$	−1.15579	−	2.00189i	−0.0695705	−	0.120500i
$277$	−4.37530	+	2.52608i	−0.262886	+	0.151778i	−0.625651	−	0.780103i	$-0.715166\pi$
$277$	−4.37530	+	2.52608i	−0.262886	+	0.151778i	0.362764	+	0.931881i	$0.381833\pi$
$278$	−11.5847	−	6.68842i	−0.694803	−	0.401145i
$279$	0.688417			0.0412144
$280$	−1.25332	−	5.78180i	−0.0749001	−	0.345529i
$281$	7.68842			0.458652			0.229326	−	0.973350i	$-0.426348\pi$
$281$	7.68842			0.458652			0.229326	+	0.973350i	$0.426348\pi$
$282$	−2.65458	−	1.53263i	−0.158078	−	0.0912665i
$283$	15.9600	−	9.21450i	0.948722	−	0.547745i	0.0560386	−	0.998429i	$-0.482153\pi$
$283$	15.9600	−	9.21450i	0.948722	−	0.547745i	0.892684	+	0.450683i	$0.148820\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	3.52122	+	1.36190i	0.208579	+	0.0806721i
$286$	10.3116			0.609737
$287$	7.49473	+	11.3768i	0.442400	+	0.671553i
$288$			1.00000i			0.0589256i
$289$	14.8768	−	25.7674i	0.875108	−	1.51573i
$290$	14.6598	−	11.8100i	0.860851	−	0.693504i
$291$	2.47900	+	4.29375i	0.145322	+	0.251704i
$292$	3.46410	+	2.00000i	0.202721	+	0.117041i
$293$		−	1.83767i		−	0.107358i	−0.998558	−	0.0536788i	$-0.982905\pi$
$293$		−	1.83767i		−	0.107358i	0.998558	−	0.0536788i	$-0.0170947\pi$
$294$	−2.76304	+	6.43161i	−0.161144	+	0.375099i
$295$	15.5587	−	2.42392i	0.905863	−	0.141126i
$296$	−1.15579	+	2.00189i	−0.0671790	+	0.116357i
$297$	−5.28903	+	3.05362i	−0.306901	+	0.177189i
$298$	10.9320	−	6.31158i	0.633273	−	0.365620i
$299$	1.95146	−	3.38002i	0.112856	−	0.195472i
$300$	−1.52100	−	4.76304i	−0.0878149	−	0.274994i
$301$	4.41883	−	2.91100i	0.254697	−	0.167787i
$302$		−	1.93475i		−	0.111332i
$303$	6.92820	+	4.00000i	0.398015	+	0.229794i
$304$	0.844208	+	1.46221i	0.0484187	+	0.0838636i
$305$	−13.2717	−	16.4742i	−0.759933	−	0.943310i
$306$	3.41883	−	5.92159i	0.195442	−	0.338515i
$307$			16.0840i			0.917962i	0.888446	+	0.458981i	$0.151785\pi$
$307$			16.0840i			0.917962i	−0.888446	+	0.458981i	$0.848215\pi$
$308$	16.1302	−	0.951458i	0.919105	−	0.0542143i
$309$	−0.837665			−0.0476531
$310$	−1.43570	−	0.555287i	−0.0815425	−	0.0315382i
$311$	7.68842	+	13.3167i	0.435970	+	0.755122i	0.997374	−	0.0724194i	$-0.0230720\pi$
$311$	7.68842	+	13.3167i	0.435970	+	0.755122i	−0.561404	+	0.827542i	$0.689739\pi$
$312$	−1.46221	+	0.844208i	−0.0827814	+	0.0477939i
$313$	19.4153	+	11.2094i	1.09742	+	0.633594i	0.935541	−	0.353218i	$-0.114912\pi$
$313$	19.4153	+	11.2094i	1.09742	+	0.633594i	0.161875	+	0.986811i	$0.448246\pi$
$314$	−17.1492			−0.967788
$315$	−1.80549	+	5.63384i	−0.101728	+	0.317431i
$316$	7.31158			0.411309
$317$	−8.71676	−	5.03263i	−0.489582	−	0.282660i	0.234819	−	0.972039i	$-0.424550\pi$
$317$	−8.71676	−	5.03263i	−0.489582	−	0.282660i	−0.724401	+	0.689379i	$0.757884\pi$
$318$	−9.05935	+	5.23042i	−0.508023	+	0.293307i
$319$	25.7080	+	44.5275i	1.43937	+	2.49306i
$320$	0.806615	−	2.08551i	0.0450911	−	0.116584i
$321$	15.5261			0.866581
$322$	2.74075	−	5.46737i	0.152736	−	0.304685i
$323$		−	11.5448i		−	0.642371i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	5.68053	−	6.24502i	0.315099	−	0.346412i
$326$	−0.269584	−	0.466934i	−0.0149309	−	0.0258611i
$327$	−10.1111	−	5.83767i	−0.559147	−	0.322824i
$328$			5.14925i			0.284320i
$329$	−0.477540	−	8.09582i	−0.0263276	−	0.446337i
$330$	13.4935	−	2.10217i	0.742790	−	0.115720i
$331$	−11.6399	+	20.1609i	−0.639785	+	1.10814i	0.345694	+	0.938347i	$0.387643\pi$
$331$	−11.6399	+	20.1609i	−0.639785	+	1.10814i	−0.985480	+	0.169794i	$0.945690\pi$
$332$	−11.7139	+	6.76304i	−0.642885	+	0.371170i
$333$	2.00189	−	1.15579i	0.109703	−	0.0633370i
$334$	−1.57462	+	2.72733i	−0.0861596	+	0.149233i
$335$	4.20433	+	26.9869i	0.229707	+	1.47445i
$336$	−2.20942	+	1.45550i	−0.120534	+	0.0794040i
$337$			5.17250i			0.281764i	0.990026	+	0.140882i	$0.0449938\pi$
$337$			5.17250i			0.281764i	−0.990026	+	0.140882i	$0.955006\pi$
$338$	8.78951	+	5.07462i	0.478086	+	0.276023i
$339$	−1.68842	−	2.92442i	−0.0917022	−	0.158833i
$340$	−11.9065	+	9.59189i	−0.645719	+	0.520193i
$341$	2.10217	−	3.64106i	0.113839	−	0.197174i
$342$		−	1.68842i		−	0.0912991i
$343$	−18.2317	+	3.25650i	−0.984420	+	0.175834i
$344$	2.00000			0.107833
$345$	1.86456	−	4.82084i	0.100384	−	0.259545i
$346$	5.26304	+	9.11585i	0.282943	+	0.490071i
$347$	8.37908	−	4.83767i	0.449813	−	0.259699i	−0.257938	−	0.966161i	$-0.583043\pi$
$347$	8.37908	−	4.83767i	0.449813	−	0.259699i	0.707751	+	0.706462i	$0.249710\pi$
$348$	−7.29092	−	4.20942i	−0.390834	−	0.225648i
$349$	−28.2985			−1.51478			−0.757392	−	0.652961i	$-0.773527\pi$
$349$	−28.2985			−1.51478			−0.757392	+	0.652961i	$0.773527\pi$
$350$	8.30973	−	10.2931i	0.444174	−	0.550191i
$351$	1.68842			0.0901210
$352$	5.28903	+	3.05362i	0.281906	+	0.162759i
$353$	15.3073	−	8.83767i	0.814725	−	0.470381i	−0.0338693	−	0.999426i	$-0.510783\pi$
$353$	15.3073	−	8.83767i	0.814725	−	0.470381i	0.848594	+	0.529045i	$0.177450\pi$
$354$	−3.52100	−	6.09855i	−0.187139	−	0.324134i
$355$	−4.83969	+	12.5131i	−0.256864	+	0.664126i
$356$	−12.2145			−0.647367
$357$	18.0594	−	1.06525i	0.955803	−	0.0563790i
$358$			4.93475i			0.260810i
$359$	−2.41883	+	4.18954i	−0.127661	+	0.221116i	−0.922770	−	0.385351i	$-0.874080\pi$
$359$	−2.41883	+	4.18954i	−0.127661	+	0.221116i	0.795109	+	0.606467i	$0.207414\pi$
$360$	−1.74131	+	1.40280i	−0.0917749	+	0.0739341i
$361$	8.07462	+	13.9857i	0.424980	+	0.736087i
$362$	5.30917	+	3.06525i	0.279044	+	0.161106i
$363$			26.2985i			1.38031i
$364$	−3.99346	−	2.00189i	−0.209314	−	0.104928i
$365$	1.37683	+	8.83767i	0.0720668	+	0.462585i
$366$	−4.73042	+	8.19332i	−0.247263	+	0.428272i
$367$	9.22007	−	5.32321i	0.481284	−	0.277869i	−0.239668	−	0.970855i	$-0.577038\pi$
$367$	9.22007	−	5.32321i	0.481284	−	0.277869i	0.720951	+	0.692986i	$0.243705\pi$
$368$	2.00189	−	1.15579i	0.104356	−	0.0602498i
$369$	2.57462	−	4.45938i	0.134030	−	0.232146i
$370$	−5.10725	+	0.795666i	−0.265513	+	0.0413647i
$371$	−24.7420	−	12.4030i	−1.28454	−	0.643932i
$372$			0.688417i			0.0356928i
$373$	−30.0749	−	17.3637i	−1.55722	−	0.899061i	−0.997521	−	0.0703638i	$-0.977584\pi$
$373$	−30.0749	−	17.3637i	−1.55722	−	0.899061i	−0.559698	−	0.828697i	$-0.689083\pi$
$374$	−20.8797	−	36.1646i	−1.07966	−	1.87003i
$375$	6.16025	−	9.33013i	0.318114	−	0.481806i
$376$	1.53263	−	2.65458i	0.0790391	−	0.136900i
$377$		−	14.2145i		−	0.732084i
$378$	2.64116	−	0.155792i	0.135847	−	0.00801305i
$379$	19.4477			0.998964			0.499482	−	0.866324i	$-0.333524\pi$
$379$	19.4477			0.998964			0.499482	+	0.866324i	$0.333524\pi$
$380$	−1.36190	+	3.52122i	−0.0698641	+	0.180635i
$381$	2.47246	+	4.28242i	0.126668	+	0.219395i
$382$	12.9225	−	7.46083i	0.661175	−	0.381729i
$383$	0.736772	+	0.425376i	0.0376473	+	0.0217357i	0.518706	−	0.854953i	$-0.326414\pi$
$383$	0.736772	+	0.425376i	0.0376473	+	0.0217357i	−0.481058	+	0.876689i	$0.659747\pi$
$384$	−1.00000			−0.0510310
$385$	24.2843	+	26.7530i	1.23764	+	1.36346i
$386$	−5.58117			−0.284074
$387$	−1.73205	−	1.00000i	−0.0880451	−	0.0508329i
$388$	−4.29375	+	2.47900i	−0.217982	+	0.125852i
$389$	13.1492	+	22.7752i	0.666693	+	1.15475i	0.978823	+	0.204707i	$0.0656243\pi$
$389$	13.1492	+	22.7752i	0.666693	+	1.15475i	−0.312130	+	0.950039i	$0.601042\pi$
$390$	−3.52122	−	1.36190i	−0.178304	−	0.0689626i
$391$	−15.8058			−0.799335
$392$	−6.43161	−	2.76304i	−0.324845	−	0.139555i
$393$		−	6.73042i		−	0.339505i
$394$	7.26304	−	12.5800i	0.365907	−	0.633769i
$395$	10.2567	+	12.7317i	0.516071	+	0.640602i
$396$	−3.05362	−	5.28903i	−0.153450	−	0.265784i
$397$	−1.47354	−	0.850752i	−0.0739551	−	0.0426980i	0.462566	−	0.886585i	$-0.346929\pi$
$397$	−1.47354	−	0.850752i	−0.0739551	−	0.0426980i	−0.536522	+	0.843887i	$0.680262\pi$
$398$		−	8.62317i		−	0.432240i
$399$	3.73042	−	2.45749i	0.186754	−	0.123028i
$400$	4.76304	−	1.52100i	0.238152	−	0.0760500i
$401$	−1.50937	+	2.61431i	−0.0753745	+	0.130553i	−0.901249	−	0.433301i	$-0.857349\pi$
$401$	−1.50937	+	2.61431i	−0.0753745	+	0.130553i	0.825875	+	0.563854i	$0.190682\pi$
$402$	10.5781	−	6.10725i	0.527586	−	0.304602i
$403$	−1.00661	+	0.581167i	−0.0501429	+	0.0289500i
$404$	−4.00000	+	6.92820i	−0.199007	+	0.344691i
$405$	2.20942	−	0.344208i	0.109787	−	0.0171039i
$406$	−1.31158	−	22.2355i	−0.0650928	−	1.10353i
$407$		−	14.1174i		−	0.699774i
$408$	5.92159	+	3.41883i	0.293162	+	0.169257i
$409$	−2.07462	−	3.59335i	−0.102584	−	0.177680i	0.810165	−	0.586202i	$-0.199378\pi$
$409$	−2.07462	−	3.59335i	−0.102584	−	0.177680i	−0.912748	+	0.408522i	$0.866044\pi$
$410$	−8.96642	+	7.22337i	−0.442820	+	0.356737i
$411$	−9.52608	+	16.4997i	−0.469887	+	0.813868i
$412$		−	0.837665i		−	0.0412688i
$413$	8.34942	−	16.6558i	0.410848	−	0.819578i
$414$	−2.31158			−0.113608
$415$	−28.2088	−	10.9103i	−1.38472	−	0.535568i
$416$	−0.844208	−	1.46221i	−0.0413907	−	0.0716908i
$417$	−11.5847	+	6.68842i	−0.567304	+	0.327533i
$418$	−8.93009	−	5.15579i	−0.436785	−	0.252178i
$419$	−13.8189			−0.675098			−0.337549	−	0.941308i	$-0.609598\pi$
$419$	−13.8189			−0.675098			−0.337549	+	0.941308i	$0.609598\pi$
$420$	−5.63384	−	1.80549i	−0.274903	−	0.0880991i
$421$	25.2667			1.23142			0.615711	−	0.787972i	$-0.288869\pi$
$421$	25.2667			1.23142			0.615711	+	0.787972i	$0.288869\pi$
$422$	−6.65836	−	3.84421i	−0.324124	−	0.187133i
$423$	−2.65458	+	1.53263i	−0.129070	+	0.0745188i
$424$	−5.23042	−	9.05935i	−0.254011	−	0.439961i
$425$	−33.4048	−	7.27730i	−1.62037	−	0.353001i
$426$	6.00000			0.290701
$427$	−24.9876	+	1.47392i	−1.20923	+	0.0713279i
$428$			15.5261i			0.750482i
$429$	5.15579	−	8.93009i	0.248924	−	0.431149i
$430$	2.80560	+	3.48261i	0.135298	+	0.167947i
$431$	−9.77241	−	16.9263i	−0.470721	−	0.815312i	0.528719	−	0.848797i	$-0.322673\pi$
$431$	−9.77241	−	16.9263i	−0.470721	−	0.815312i	−0.999439	+	0.0334851i	$0.989339\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	14.7537i		−	0.709016i	−0.935053	−	0.354508i	$-0.884648\pi$
$433$		−	14.7537i		−	0.709016i	0.935053	−	0.354508i	$-0.115352\pi$
$434$	−1.52100	+	1.00199i	−0.0730103	+	0.0480971i
$435$	−2.89783	−	18.6007i	−0.138940	−	0.891836i
$436$	5.83767	−	10.1111i	0.279573	−	0.484235i
$437$	−3.38002	+	1.95146i	−0.161688	+	0.0933509i
$438$	3.46410	−	2.00000i	0.165521	−	0.0955637i
$439$	−7.96737	+	13.7999i	−0.380262	+	0.658633i	−0.991100	−	0.133123i	$-0.957500\pi$
$439$	−7.96737	+	13.7999i	−0.380262	+	0.658633i	0.610838	+	0.791756i	$0.290833\pi$
$440$	2.10217	+	13.4935i	0.100217	+	0.643275i
$441$	4.18842	+	5.60867i	0.199448	+	0.267079i
$442$			11.5448i			0.549132i
$443$	−18.9006	−	10.9123i	−0.897997	−	0.518459i	−0.0214469	−	0.999770i	$-0.506827\pi$
$443$	−18.9006	−	10.9123i	−0.897997	−	0.518459i	−0.876550	+	0.481311i	$0.840161\pi$
$444$	1.15579	+	2.00189i	0.0548514	+	0.0950055i
$445$	−17.1345	−	21.2692i	−0.812254	−	1.00826i
$446$	5.58625	−	9.67567i	0.264517	−	0.458156i
$447$		−	12.6232i		−	0.597055i
$448$	−1.45550	−	2.20942i	−0.0687659	−	0.104385i
$449$	11.3637			0.536288			0.268144	−	0.963379i	$-0.413590\pi$
$449$	11.3637			0.536288			0.268144	+	0.963379i	$0.413590\pi$
$450$	−4.88541	−	1.06430i	−0.230301	−	0.0501714i
$451$	−15.7239	−	27.2345i	−0.740408	−	1.28242i
$452$	2.92442	−	1.68842i	0.137553	−	0.0794164i
$453$	−1.67554	−	0.967375i	−0.0787238	−	0.0454512i
$454$	−3.85075			−0.180725
$455$	−2.11612	−	9.76209i	−0.0992054	−	0.457654i
$456$	1.68842			0.0790674
$457$	5.55887	+	3.20942i	0.260033	+	0.150130i	0.624350	−	0.781145i	$-0.285364\pi$
$457$	5.55887	+	3.20942i	0.260033	+	0.150130i	−0.364317	+	0.931275i	$0.618697\pi$
$458$	4.91498	−	2.83767i	0.229662	−	0.132595i
$459$	−3.41883	−	5.92159i	−0.159577	−	0.276396i
$460$	4.82084	+	1.86456i	0.224773	+	0.0869354i
$461$	1.50733			0.0702036			0.0351018	−	0.999384i	$-0.488824\pi$
$461$	1.50733			0.0702036			0.0351018	+	0.999384i	$0.488824\pi$
$462$	7.24113	−	14.4449i	0.336888	−	0.672038i
$463$		−	24.1174i		−	1.12083i	−0.828211	−	0.560416i	$-0.810641\pi$
$463$		−	24.1174i		−	1.12083i	0.828211	−	0.560416i	$-0.189359\pi$
$464$	4.20942	−	7.29092i	0.195417	−	0.338473i
$465$	−1.19874	+	0.965712i	−0.0555905	+	0.0447838i
$466$	5.73042	+	9.92537i	0.265456	+	0.459784i
$467$	20.3904	+	11.7724i	0.943556	+	0.544762i	0.891073	−	0.453859i	$-0.149953\pi$
$467$	20.3904	+	11.7724i	0.943556	+	0.544762i	0.0524828	+	0.998622i	$0.483287\pi$
$468$			1.68842i			0.0780471i
$469$	28.8898	+	14.4823i	1.33401	+	0.668728i
$470$	6.77241	−	1.05509i	0.312388	−	0.0486674i
$471$	−8.57462	+	14.8517i	−0.395098	+	0.684330i
$472$	6.09855	−	3.52100i	0.280709	−	0.162067i
$473$	−10.5781	+	6.10725i	−0.486380	+	0.280812i
$474$	3.65579	−	6.33202i	0.167916	−	0.290839i
$475$	−8.04200	+	2.56808i	−0.368992	+	0.117832i
$476$	1.06525	+	18.0594i	0.0488257	+	0.827750i
$477$			10.4608i			0.478969i
$478$	−13.3895	−	7.73042i	−0.612420	−	0.353581i
$479$	14.9869	+	25.9581i	0.684770	+	1.18606i	0.973509	+	0.228648i	$0.0734305\pi$
$479$	14.9869	+	25.9581i	0.684770	+	1.18606i	−0.288740	+	0.957408i	$0.593236\pi$
$480$	−1.40280	−	1.74131i	−0.0640288	−	0.0794794i
$481$	−1.95146	+	3.38002i	−0.0889788	+	0.154116i
$482$		−	4.37683i		−	0.199359i
$483$	−3.36451	−	5.10725i	−0.153090	−	0.232388i
$484$	−26.2985			−1.19539
$485$	−10.3400	−	3.99920i	−0.469515	−	0.181594i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	26.4162	−	15.2514i	1.19703	−	0.691108i	0.237141	−	0.971475i	$-0.423790\pi$
$487$	26.4162	−	15.2514i	1.19703	−	0.691108i	0.959893	+	0.280368i	$0.0904564\pi$
$488$	−8.19332	−	4.73042i	−0.370894	−	0.214136i
$489$	−0.539168			−0.0243820
$490$	−4.21097	−	15.0754i	−0.190232	−	0.681037i
$491$	−3.87966			−0.175087			−0.0875434	−	0.996161i	$-0.527902\pi$
$491$	−3.87966			−0.175087			−0.0875434	+	0.996161i	$0.527902\pi$
$492$	4.45938	+	2.57462i	0.201044	+	0.116073i
$493$	−49.8529	+	28.7826i	−2.24526	+	1.29630i
$494$	1.42538	+	2.46882i	0.0641307	+	0.111078i
$495$	4.92620	−	12.7368i	0.221416	−	0.572475i
$496$	−0.688417			−0.0309108
$497$	8.73300	+	13.2565i	0.391729	+	0.594635i
$498$			13.5261i			0.606118i
$499$	4.68842	−	8.12058i	0.209882	−	0.363527i	−0.741795	−	0.670627i	$-0.766025\pi$
$499$	4.68842	−	8.12058i	0.209882	−	0.363527i	0.951677	+	0.307100i	$0.0993586\pi$
$500$	9.33013	+	6.16025i	0.417256	+	0.275495i
$501$	1.57462	+	2.72733i	0.0703490	+	0.121848i
$502$	−22.9811	−	13.2681i	−1.02570	−	0.592185i
$503$			14.2145i			0.633793i	0.948460	+	0.316897i	$0.102641\pi$
$503$			14.2145i			0.633793i	−0.948460	+	0.316897i	$0.897359\pi$
$504$	0.155792	+	2.64116i	0.00693951	+	0.117647i
$505$	−17.6753	+	2.75367i	−0.786542	+	0.122537i
$506$	−7.05871	+	12.2260i	−0.313798	+	0.543514i
$507$	8.78951	−	5.07462i	0.390356	−	0.225372i
$508$	−4.28242	+	2.47246i	−0.190002	+	0.109698i
$509$	15.9818	−	27.6813i	0.708382	−	1.22695i	−0.257075	−	0.966392i	$-0.582759\pi$
$509$	15.9818	−	27.6813i	0.708382	−	1.22695i	0.965457	−	0.260562i	$-0.0839080\pi$
$510$	2.35358	+	15.1072i	0.104218	+	0.668960i
$511$	9.46083	+	4.74264i	0.418523	+	0.209802i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.46221	−	0.844208i	−0.0645582	−	0.0372727i
$514$	11.2145	+	19.4241i	0.494650	+	0.856760i
$515$	1.45863	−	1.17508i	0.0642750	−	0.0517801i
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$			18.7203i			0.823316i
$518$	−2.74075	+	5.46737i	−0.120422	+	0.240223i
$519$	10.5261			0.462044
$520$	1.36190	−	3.52122i	0.0597234	−	0.154416i
$521$	18.1007	+	31.3513i	0.793006	+	1.37353i	0.924097	+	0.382157i	$0.124819\pi$
$521$	18.1007	+	31.3513i	0.793006	+	1.37353i	−0.131091	+	0.991370i	$0.541848\pi$
$522$	−7.29092	+	4.20942i	−0.319115	+	0.184241i
$523$	32.0154	+	18.4841i	1.39993	+	0.808253i	0.994385	−	0.105821i	$-0.0337470\pi$
$523$	32.0154	+	18.4841i	1.39993	+	0.808253i	0.405549	+	0.914073i	$0.367080\pi$
$524$	6.73042			0.294020
$525$	−4.75925	−	12.3430i	−0.207710	−	0.538693i
$526$	−19.5913			−0.854223
$527$	4.07652	+	2.35358i	0.177576	+	0.102524i
$528$	5.28903	−	3.05362i	0.230176	−	0.132892i
$529$	−8.82829	−	15.2910i	−0.383839	−	0.664828i
$530$	8.43786	−	21.8162i	0.366517	−	0.947636i
$531$	−7.04200			−0.305597
$532$	2.45749	+	3.73042i	0.106546	+	0.161734i
$533$			8.69408i			0.376582i
$534$	−6.10725	+	10.5781i	−0.264287	+	0.457758i
$535$	−27.0357	+	21.7800i	−1.16885	+	0.941632i
$536$	6.10725	+	10.5781i	0.263793	+	0.456903i
$537$	4.27362	+	2.46737i	0.184420	+	0.106475i
$538$		−	6.95800i		−	0.299981i
$539$	42.4543	−	5.02591i	1.82864	−	0.216481i
$540$	0.344208	+	2.20942i	0.0148124	+	0.0950781i
$541$	8.63333	−	14.9534i	0.371176	−	0.642896i	−0.618571	−	0.785729i	$-0.712288\pi$
$541$	8.63333	−	14.9534i	0.371176	−	0.642896i	0.989747	+	0.142834i	$0.0456213\pi$
$542$	24.5637	−	14.1819i	1.05510	−	0.609164i
$543$	5.30917	−	3.06525i	0.227838	−	0.131542i
$544$	−3.41883	+	5.92159i	−0.146581	+	0.253886i
$545$	25.7957	−	4.01875i	1.10496	−	0.172144i
$546$	−3.73042	+	2.45749i	−0.159647	+	0.105171i
$547$		−	39.4347i		−	1.68610i	−0.537832	−	0.843052i	$-0.680756\pi$
$547$		−	39.4347i		−	1.68610i	0.537832	−	0.843052i	$-0.319244\pi$
$548$	−16.4997	−	9.52608i	−0.704830	−	0.406934i
$549$	4.73042	+	8.19332i	0.201889	+	0.349682i
$550$	−20.5473	+	22.5892i	−0.876141	+	0.963205i
$551$	−7.10725	+	12.3101i	−0.302779	+	0.524429i
$552$		−	2.31158i		−	0.0983875i
$553$	19.3111	−	1.13908i	0.821190	−	0.0484387i
$554$	−5.05216			−0.214646
$555$	−1.86456	+	4.82084i	−0.0791461	+	0.204633i
$556$	−6.68842	−	11.5847i	−0.283652	−	0.491300i
$557$	28.4834	−	16.4449i	1.20688	−	0.696793i	0.244805	−	0.969572i	$-0.421276\pi$
$557$	28.4834	−	16.4449i	1.20688	−	0.696793i	0.962077	+	0.272779i	$0.0879428\pi$
$558$	0.596186	+	0.344208i	0.0252386	+	0.0145715i
$559$	3.37683			0.142825
$560$	1.80549	−	5.63384i	0.0762960	−	0.238073i
$561$	−41.7593			−1.76308
$562$	6.65836	+	3.84421i	0.280866	+	0.162158i
$563$	−30.4853	+	17.6007i	−1.28480	+	0.741781i	−0.977722	−	0.209902i	$-0.932685\pi$
$563$	−30.4853	+	17.6007i	−1.28480	+	0.741781i	−0.307081	+	0.951684i	$0.599352\pi$
$564$	−1.53263	−	2.65458i	−0.0645352	−	0.111778i
$565$	7.04244	+	2.72380i	0.296278	+	0.114591i
$566$	18.4290			0.774629
$567$	1.18566	−	2.36521i	0.0497931	−	0.0993294i
$568$			6.00000i			0.251754i
$569$	8.74712	−	15.1505i	0.366699	−	0.635140i	−0.622349	−	0.782740i	$-0.713821\pi$
$569$	8.74712	−	15.1505i	0.366699	−	0.635140i	0.989047	+	0.147600i	$0.0471547\pi$
$570$	2.36851	+	2.94005i	0.0992061	+	0.123145i
$571$	−4.41883	−	7.65364i	−0.184922	−	0.320295i	0.758628	−	0.651524i	$-0.225870\pi$
$571$	−4.41883	−	7.65364i	−0.184922	−	0.320295i	−0.943550	+	0.331229i	$0.892537\pi$
$572$	8.93009	+	5.15579i	0.373386	+	0.215574i
$573$		−	14.9217i		−	0.623361i
$574$	0.802209	+	13.6000i	0.0334836	+	0.567653i
$575$	3.51592	+	11.0102i	0.146624	+	0.459156i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	34.9083	−	20.1543i	1.45325	−	0.839036i	0.454588	−	0.890702i	$-0.349786\pi$
$577$	34.9083	−	20.1543i	1.45325	−	0.839036i	0.998664	+	0.0516659i	$0.0164531\pi$
$578$	25.7674	−	14.8768i	1.07178	−	0.618795i
$579$	−2.79058	+	4.83343i	−0.115973	+	0.200871i
$580$	18.6007	−	2.89783i	0.772352	−	0.120326i
$581$	−29.8847	+	19.6872i	−1.23983	+	0.816763i
$582$			4.95800i			0.205516i
$583$	55.3277	+	31.9435i	2.29144	+	1.32296i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$	−2.94005	+	2.36851i	−0.121556	+	0.0979260i
$586$	0.918833	−	1.59146i	0.0379566	−	0.0657428i
$587$		−	36.1492i		−	1.49204i	−0.665924	−	0.746020i	$-0.731963\pi$
$587$		−	36.1492i		−	1.49204i	0.665924	−	0.746020i	$-0.268037\pi$
$588$	−5.60867	+	4.18842i	−0.231298	+	0.172727i
$589$	1.16233			0.0478932
$590$	14.6862	+	5.68018i	0.604621	+	0.233849i
$591$	−7.26304	−	12.5800i	−0.298762	−	0.517470i
$592$	−2.00189	+	1.15579i	−0.0822772	+	0.0475027i
$593$	3.53685	+	2.04200i	0.145241	+	0.0838548i	0.570859	−	0.821048i	$-0.306610\pi$
$593$	3.53685	+	2.04200i	0.145241	+	0.0838548i	−0.425619	+	0.904903i	$0.639943\pi$
$594$	−6.10725			−0.250583
$595$	−29.9526	+	27.1886i	−1.22794	+	1.11463i
$596$	12.6232			0.517065
$597$	−7.46788	−	4.31158i	−0.305640	−	0.176461i
$598$	3.38002	−	1.95146i	0.138219	−	0.0798011i
$599$	−9.87966	−	17.1121i	−0.403672	−	0.699181i	0.590494	−	0.807042i	$-0.298933\pi$
$599$	−9.87966	−	17.1121i	−0.403672	−	0.699181i	−0.994166	+	0.107862i	$0.965600\pi$
$600$	1.06430	−	4.88541i	0.0434497	−	0.199446i
$601$	3.72025			0.151752			0.0758761	−	0.997117i	$-0.475825\pi$
$601$	3.72025			0.151752			0.0758761	+	0.997117i	$0.475825\pi$
$602$	5.28232	−	0.311583i	0.215291	−	0.0126992i
$603$		−	12.2145i		−	0.497413i
$604$	0.967375	−	1.67554i	0.0393619	−	0.0681768i
$605$	−36.8916	−	45.7937i	−1.49986	−	1.86178i
$606$	4.00000	+	6.92820i	0.162489	+	0.281439i
$607$	9.73708	+	5.62171i	0.395216	+	0.228178i	0.684418	−	0.729090i	$-0.260057\pi$
$607$	9.73708	+	5.62171i	0.395216	+	0.228178i	−0.289202	+	0.957268i	$0.593390\pi$
$608$			1.68842i			0.0684743i
$609$	−19.9123	−	9.98188i	−0.806887	−	0.404486i
$610$	−3.25650	−	20.9029i	−0.131852	−	0.846334i
$611$	2.58771	−	4.48205i	0.104688	−	0.181324i
$612$	5.92159	−	3.41883i	0.239366	−	0.138198i
$613$	−23.3262	+	13.4674i	−0.942135	+	0.543942i	−0.890629	−	0.454731i	$-0.849736\pi$
$613$	−23.3262	+	13.4674i	−0.942135	+	0.543942i	−0.0515063	+	0.998673i	$0.516402\pi$
$614$	−8.04200	+	13.9292i	−0.324549	+	0.562135i
$615$	1.77241	+	11.3768i	0.0714707	+	0.458758i
$616$	14.4449	+	7.24113i	0.582002	+	0.291753i
$617$			33.4608i			1.34708i	0.739150	+	0.673541i	$0.235228\pi$
$617$			33.4608i			1.34708i	−0.739150	+	0.673541i	$0.764772\pi$
$618$	−0.725439	−	0.418833i	−0.0291815	−	0.0168479i
$619$	−17.4355	−	30.1992i	−0.700794	−	1.21381i	−0.968188	−	0.250223i	$-0.919496\pi$
$619$	−17.4355	−	30.1992i	−0.700794	−	1.21381i	0.267395	−	0.963587i	$-0.413837\pi$
$620$	−0.965712	−	1.19874i	−0.0387839	−	0.0481427i
$621$	−1.15579	+	2.00189i	−0.0463803	+	0.0803331i
$622$			15.3768i			0.616555i
$623$	−32.2605	+	1.90292i	−1.29249	+	0.0762387i
$624$	−1.68842			−0.0675908
$625$	2.36143	+	24.8882i	0.0944570	+	0.995529i
$626$	11.2094	+	19.4153i	0.448018	+	0.775991i
$627$	−8.93009	+	5.15579i	−0.356634	+	0.205902i
$628$	−14.8517	−	8.57462i	−0.592647	−	0.342165i
$629$	15.8058			0.630220
$630$	−4.38053	+	3.97630i	−0.174524	+	0.158420i
$631$	−10.4942			−0.417769			−0.208885	−	0.977940i	$-0.566983\pi$
$631$	−10.4942			−0.417769			−0.208885	+	0.977940i	$0.566983\pi$
$632$	6.33202	+	3.65579i	0.251874	+	0.145420i
$633$	−6.65836	+	3.84421i	−0.264646	+	0.152794i
$634$	−5.03263	−	8.71676i	−0.199871	−	0.346187i
$635$	−10.3127	−	3.98864i	−0.409247	−	0.158284i
$636$	−10.4608			−0.414799
$637$	−10.8592	−	4.66517i	−0.430259	−	0.184841i
$638$			51.4159i			2.03558i
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	1.74131	−	1.40280i	0.0688312	−	0.0554506i
$641$	−3.88621	−	6.73111i	−0.153496	−	0.265863i	0.779014	−	0.627006i	$-0.215720\pi$
$641$	−3.88621	−	6.73111i	−0.153496	−	0.265863i	−0.932510	+	0.361143i	$0.882387\pi$
$642$	13.4460	+	7.76304i	0.530671	+	0.306383i
$643$			21.7218i			0.856626i	0.903631	+	0.428313i	$0.140892\pi$
$643$			21.7218i			0.856626i	−0.903631	+	0.428313i	$0.859108\pi$
$644$	5.10725	−	3.36451i	0.201254	−	0.132580i
$645$	4.41883	−	0.688417i	0.173991	−	0.0271064i
$646$	5.77241	−	9.99812i	0.227113	−	0.393371i
$647$	8.27740	−	4.77896i	0.325418	−	0.187880i	−0.328387	−	0.944543i	$-0.606505\pi$
$647$	8.27740	−	4.77896i	0.325418	−	0.187880i	0.653805	+	0.756663i	$0.273172\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−21.5036	+	37.2454i	−0.844091	+	1.46201i
$650$	8.04200	−	2.56808i	0.315433	−	0.100728i
$651$	0.107250	+	1.81822i	0.00420344	+	0.0712616i
$652$		−	0.539168i		−	0.0211155i
$653$	43.5322	+	25.1333i	1.70355	+	0.983543i	0.942110	+	0.335304i	$0.108839\pi$
$653$	43.5322	+	25.1333i	1.70355	+	0.983543i	0.761437	+	0.648239i	$0.224494\pi$
$654$	−5.83767	−	10.1111i	−0.228271	−	0.395377i
$655$	9.44144	+	11.7197i	0.368907	+	0.457927i
$656$	−2.57462	+	4.45938i	−0.100522	+	0.174110i
$657$		−	4.00000i		−	0.156055i
$658$	3.63435	−	7.24995i	0.141682	−	0.282633i
$659$	−11.1623			−0.434823			−0.217411	−	0.976080i	$-0.569761\pi$
$659$	−11.1623			−0.434823			−0.217411	+	0.976080i	$0.569761\pi$
$660$	12.7368	+	4.92620i	0.495778	+	0.191752i
$661$	−7.17250	−	12.4231i	−0.278978	−	0.483204i	0.692153	−	0.721751i	$-0.256662\pi$
$661$	−7.17250	−	12.4231i	−0.278978	−	0.483204i	−0.971131	+	0.238547i	$0.923329\pi$
$662$	−20.1609	+	11.6399i	−0.783574	+	0.452397i
$663$	9.99812	+	5.77241i	0.388295	+	0.224182i
$664$	−13.5261			−0.524914
$665$	−3.04843	+	9.51228i	−0.118213	+	0.368870i
$666$	2.31158			0.0895720
$667$	16.8536	+	9.73042i	0.652573	+	0.376763i
$668$	−2.72733	+	1.57462i	−0.105524	+	0.0609240i
$669$	−5.58625	−	9.67567i	−0.215977	−	0.374083i
$670$	−9.85240	+	25.4735i	−0.380631	+	0.984128i
$671$	57.7797			2.23056
$672$	−2.64116	+	0.155792i	−0.101885	+	0.00600979i
$673$		−	30.8013i		−	1.18730i	−0.804722	−	0.593652i	$-0.797686\pi$
$673$		−	30.8013i		−	1.18730i	0.804722	−	0.593652i	$-0.202314\pi$
$674$	−2.58625	+	4.47952i	−0.0996186	+	0.172545i
$675$	−3.36441	+	3.69874i	−0.129496	+	0.142365i
$676$	5.07462	+	8.78951i	0.195178	+	0.338058i
$677$	12.2649	+	7.08117i	0.471380	+	0.272151i	0.716817	−	0.697261i	$-0.245598\pi$
$677$	12.2649	+	7.08117i	0.471380	+	0.272151i	−0.245437	+	0.969412i	$0.578932\pi$
$678$		−	3.37683i		−	0.129687i
$679$	−10.9543	+	7.21637i	−0.420387	+	0.276939i
$680$	−15.1072	+	2.35358i	−0.579337	+	0.0902558i
$681$	−1.92538	+	3.33485i	−0.0737806	+	0.127792i
$682$	3.64106	−	2.10217i	0.139423	−	0.0804961i
$683$	26.5946	−	15.3544i	1.01761	−	0.587519i	0.104201	−	0.994556i	$-0.466771\pi$
$683$	26.5946	−	15.3544i	1.01761	−	0.587519i	0.913411	+	0.407037i	$0.133438\pi$
$684$	0.844208	−	1.46221i	0.0322791	−	0.0559091i
$685$	−6.55792	−	42.0942i	−0.250565	−	1.60834i
$686$	−17.4174	−	6.29564i	−0.664998	−	0.240369i
$687$		−	5.67533i		−	0.216527i
$688$	1.73205	+	1.00000i	0.0660338	+	0.0381246i
$689$	−8.83112	−	15.2960i	−0.336439	−	0.582729i
$690$	4.02517	−	3.24269i	0.153236	−	0.123447i
$691$	19.6753	−	34.0787i	0.748485	−	1.29641i	−0.200064	−	0.979783i	$-0.564115\pi$
$691$	19.6753	−	34.0787i	0.748485	−	1.29641i	0.948549	−	0.316631i	$-0.102552\pi$
$692$			10.5261i			0.400142i
$693$	−8.88910	−	13.4935i	−0.337669	−	0.512574i
$694$	9.67533			0.367271
$695$	10.7900	−	27.8976i	0.409286	−	1.05822i
$696$	−4.20942	−	7.29092i	−0.159558	−	0.276362i
$697$	30.4917	−	17.6044i	1.15496	−	0.666815i
$698$	−24.5072	−	14.1492i	−0.927612	−	0.535557i
$699$	11.4608			0.433488
$700$	12.3430	−	4.75925i	0.466521	−	0.179883i
$701$	−3.79567			−0.143360			−0.0716802	−	0.997428i	$-0.522836\pi$
$701$	−3.79567			−0.143360			−0.0716802	+	0.997428i	$0.522836\pi$
$702$	1.46221	+	0.844208i	0.0551876	+	0.0318626i
$703$	3.38002	−	1.95146i	0.127480	−	0.0736006i
$704$	3.05362	+	5.28903i	0.115088	+	0.199338i
$705$	2.47248	−	6.39263i	0.0931189	−	0.240760i
$706$	17.6753			0.665220
$707$	−9.48529	+	18.9217i	−0.356731	+	0.711622i
$708$		−	7.04200i		−	0.264655i
$709$	−10.2797	+	17.8050i	−0.386064	+	0.668683i	−0.991916	−	0.126895i	$-0.959499\pi$
$709$	−10.2797	+	17.8050i	−0.386064	+	0.668683i	0.605852	+	0.795577i	$0.292832\pi$
$710$	−10.4478	+	8.41681i	−0.392100	+	0.315877i
$711$	−3.65579	−	6.33202i	−0.137103	−	0.237469i
$712$	−10.5781	−	6.10725i	−0.396430	−	0.228879i
$713$		−	1.59133i		−	0.0595959i
$714$	16.1725	+	8.10715i	0.605241	+	0.303403i
$715$	3.54933	+	22.7826i	0.132738	+	0.852020i
$716$	−2.46737	+	4.27362i	−0.0922101	+	0.159713i
$717$	−13.3895	+	7.73042i	−0.500039	+	0.288698i
$718$	−4.18954	+	2.41883i	−0.156352	+	0.0902700i
$719$	−12.4057	+	21.4874i	−0.462656	+	0.801344i	−0.999092	−	0.0425968i	$-0.986437\pi$
$719$	−12.4057	+	21.4874i	−0.462656	+	0.801344i	0.536436	+	0.843941i	$0.319770\pi$
$720$	−2.20942	+	0.344208i	−0.0823401	+	0.0128279i
$721$	−0.130501	−	2.21241i	−0.00486012	−	0.0823944i
$722$			16.1492i			0.601013i
$723$	−3.79045	−	2.18842i	−0.140968	−	0.0813881i
$724$	3.06525	+	5.30917i	0.113919	+	0.197314i
$725$	31.1391	+	28.3244i	1.15648	+	1.05194i
$726$	−13.1492	+	22.7752i	−0.488014	+	0.845266i
$727$			39.2899i			1.45718i	0.684949	+	0.728591i	$0.259825\pi$
$727$			39.2899i			1.45718i	−0.684949	+	0.728591i	$0.740175\pi$
$728$	−2.45749	−	3.73042i	−0.0910806	−	0.138258i
$729$	−1.00000			−0.0370370
$730$	−3.22646	+	8.34206i	−0.119417	+	0.308753i
$731$	−6.83767	−	11.8432i	−0.252900	−	0.438036i
$732$	−8.19332	+	4.73042i	−0.302834	+	0.174841i
$733$	7.81046	+	4.50937i	0.288486	+	0.166558i	0.637259	−	0.770650i	$-0.280068\pi$
$733$	7.81046	+	4.50937i	0.288486	+	0.166558i	−0.348773	+	0.937207i	$0.613402\pi$
$734$	10.6464			0.392966
$735$	−15.1612	−	3.89089i	−0.559228	−	0.143518i
$736$	2.31158			0.0852061
$737$	−64.6029	−	37.2985i	−2.37968	−	1.37391i
$738$	4.45938	−	2.57462i	0.164152	−	0.0947732i
$739$	−7.03546	−	12.1858i	−0.258803	−	0.448261i	0.707118	−	0.707095i	$-0.249995\pi$
$739$	−7.03546	−	12.1858i	−0.258803	−	0.448261i	−0.965922	+	0.258835i	$0.916662\pi$
$740$	−4.82084	−	1.86456i	−0.177218	−	0.0685425i
$741$	2.85075			0.104725
$742$	−15.2257	−	23.1123i	−0.558954	−	0.848480i
$743$		−	39.1492i		−	1.43625i	−0.695916	−	0.718123i	$-0.745001\pi$
$743$		−	39.1492i		−	1.43625i	0.695916	−	0.718123i	$-0.254999\pi$
$744$	−0.344208	+	0.596186i	−0.0126193	+	0.0218573i
$745$	17.7078	+	21.9808i	0.648763	+	0.805314i
$746$	−17.3637	−	30.0749i	−0.635732	−	1.10112i
$747$	11.7139	+	6.76304i	0.428590	+	0.247447i
$748$		−	41.7593i		−	1.52687i
$749$	2.41883	+	41.0069i	0.0883822	+	1.49836i
$750$	10.0000	−	5.00000i	0.365148	−	0.182574i
$751$	19.6427	−	34.0222i	0.716773	−	1.24149i	−0.245499	−	0.969397i	$-0.578952\pi$
$751$	19.6427	−	34.0222i	0.716773	−	1.24149i	0.962272	−	0.272090i	$-0.0877147\pi$
$752$	2.65458	−	1.53263i	0.0968028	−	0.0558891i
$753$	−22.9811	+	13.2681i	−0.837477	+	0.483517i
$754$	7.10725	−	12.3101i	0.258831	−	0.448308i
$755$	4.27467	−	0.665957i	0.155571	−	0.0242367i
$756$	2.36521	+	1.18566i	0.0860218	+	0.0431221i
$757$			28.9217i			1.05118i	0.850739	+	0.525588i	$0.176155\pi$
$757$			28.9217i			1.05118i	−0.850739	+	0.525588i	$0.823845\pi$
$758$	16.8422	+	9.72387i	0.611738	+	0.353187i
$759$	7.05871	+	12.2260i	0.256215	+	0.443777i
$760$	−2.94005	+	2.36851i	−0.106647	+	0.0859150i
$761$	−7.77896	+	13.4736i	−0.281987	+	0.488416i	−0.971874	−	0.235501i	$-0.924327\pi$
$761$	−7.77896	+	13.4736i	−0.281987	+	0.488416i	0.689887	+	0.723917i	$0.257660\pi$
$762$			4.94491i			0.179135i
$763$	13.8430	−	27.6146i	0.501150	−	0.999715i
$764$	14.9217			0.539847
$765$	14.2601	+	5.51536i	0.515573	+	0.199408i
$766$	0.425376	+	0.736772i	0.0153695	+	0.0266207i
$767$	10.2969	−	5.94491i	0.371799	−	0.214658i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	4.05216			0.146125			0.0730624	−	0.997327i	$-0.476723\pi$
$769$	4.05216			0.146125			0.0730624	+	0.997327i	$0.476723\pi$
$770$	7.65433	+	35.3109i	0.275843	+	1.27252i
$771$	22.4290			0.807761
$772$	−4.83343	−	2.79058i	−0.173959	−	0.100435i
$773$	−18.5743	+	10.7239i	−0.668071	+	0.385711i	−0.795345	−	0.606157i	$-0.792710\pi$
$773$	−18.5743	+	10.7239i	−0.668071	+	0.385711i	0.127274	+	0.991868i	$0.459377\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	0.732680	−	3.36320i	0.0263186	−	0.120810i
$776$	−4.95800			−0.177982
$777$	3.36451	+	5.10725i	0.120701	+	0.183222i
$778$			26.2985i			0.942847i
$779$	4.34704	−	7.52929i	0.155749	−	0.269765i
$780$	−2.36851	−	2.94005i	−0.0848064	−	0.105271i
$781$	−18.3217	−	31.7342i	−0.655604	−	1.13554i
$782$	−13.6883	−	7.90292i	−0.489491	−	0.282608i
$783$			8.41883i			0.300865i
$784$	−4.18842	−	5.60867i	−0.149586	−	0.200310i
$785$	−5.90292	−	37.8898i	−0.210684	−	1.35235i
$786$	3.36521	−	5.82871i	0.120033	−	0.207903i
$787$	3.74527	−	2.16233i	0.133505	−	0.0770789i	−0.431760	−	0.901988i	$-0.642107\pi$
$787$	3.74527	−	2.16233i	0.133505	−	0.0770789i	0.565265	+	0.824910i	$0.308774\pi$
$788$	12.5800	−	7.26304i	0.448142	−	0.258735i
$789$	−9.79567	+	16.9666i	−0.348735	+	0.604027i
$790$	2.51671	+	16.1543i	0.0895405	+	0.574745i
$791$	7.46083	−	4.91498i	0.265277	−	0.174757i
$792$		−	6.10725i		−	0.217012i
$793$	−13.8337	−	7.98691i	−0.491251	−	0.283624i
$794$	−0.850752	−	1.47354i	−0.0301920	−	0.0522941i
$795$	−14.6745	−	18.2155i	−0.520450	−	0.646038i
$796$	4.31158	−	7.46788i	0.152820	−	0.264692i
$797$		−	41.1549i		−	1.45778i	−0.684630	−	0.728891i	$-0.740036\pi$
$797$		−	41.1549i		−	1.45778i	0.684630	−	0.728891i	$-0.259964\pi$
$798$	4.45938	−	0.263041i	0.157860	−	0.00931155i
$799$	−20.9592			−0.741482
$800$	4.88541	+	1.06430i	0.172725	+	0.0376286i
$801$	6.10725	+	10.5781i	0.215789	+	0.373758i
$802$	−2.61431	+	1.50937i	−0.0923146	+	0.0532978i
$803$	−21.1561	−	12.2145i	−0.746584	−	0.431040i
$804$	12.2145			0.430772
$805$	13.0231	+	4.17355i	0.459004	+	0.147098i
$806$	−1.16233			−0.0409415
$807$	−6.02581	−	3.47900i	−0.212118	−	0.122467i
$808$	−6.92820	+	4.00000i	−0.243733	+	0.140720i
$809$	−8.88621	−	15.3914i	−0.312422	−	0.541131i	0.666464	−	0.745537i	$-0.267807\pi$
$809$	−8.88621	−	15.3914i	−0.312422	−	0.541131i	−0.978886	+	0.204406i	$0.934474\pi$
$810$	2.08551	+	0.806615i	0.0732775	+	0.0283416i
$811$	47.1231			1.65472			0.827358	−	0.561676i	$-0.189843\pi$
$811$	47.1231			1.65472			0.827358	+	0.561676i	$0.189843\pi$
$812$	9.98188	−	19.9123i	0.350295	−	0.698784i
$813$		−	28.3637i		−	0.994760i
$814$	7.05871	−	12.2260i	0.247408	−	0.428522i
$815$	0.938857	−	0.756346i	0.0328867	−	0.0264937i
$816$	3.41883	+	5.92159i	0.119683	+	0.207297i
$817$	−2.92442	−	1.68842i	−0.102313	−	0.0590702i
$818$		−	4.14925i		−	0.145075i
$819$	0.263041	+	4.45938i	0.00919140	+	0.155823i
$820$	−11.3768	+	1.77241i	−0.397296	+	0.0618954i
$821$	−2.85583	+	4.94645i	−0.0996693	+	0.172632i	−0.911548	−	0.411194i	$-0.865112\pi$
$821$	−2.85583	+	4.94645i	−0.0996693	+	0.172632i	0.811878	+	0.583826i	$0.198445\pi$
$822$	−16.4997	+	9.52608i	−0.575492	+	0.332260i
$823$	−26.2795	+	15.1725i	−0.916047	+	0.528880i	−0.882372	−	0.470553i	$-0.844055\pi$
$823$	−26.2795	+	15.1725i	−0.916047	+	0.528880i	−0.0336753	+	0.999433i	$0.510721\pi$
$824$	0.418833	−	0.725439i	0.0145907	−	0.0252719i
$825$	9.28912	+	29.0891i	0.323406	+	1.01275i
$826$	15.5587	−	10.2496i	0.541357	−	0.356630i
$827$			27.2014i			0.945886i	0.881093	+	0.472943i	$0.156808\pi$
$827$			27.2014i			0.945886i	−0.881093	+	0.472943i	$0.843192\pi$
$828$	−2.00189	−	1.15579i	−0.0695705	−	0.0401665i
$829$	5.41883	+	9.38569i	0.188204	+	0.325979i	0.944651	−	0.328076i	$-0.106400\pi$
$829$	5.41883	+	9.38569i	0.188204	+	0.325979i	−0.756448	+	0.654054i	$0.773067\pi$
$830$	−18.9744	−	23.5531i	−0.658611	−	0.817538i
$831$	−2.52608	+	4.37530i	−0.0876288	+	0.151778i
$832$		−	1.68842i		−	0.0585353i
$833$	5.62700	+	47.5317i	0.194964	+	1.64688i
$834$	−13.3768			−0.463202
$835$	−6.56780	−	2.54023i	−0.227288	−	0.0879083i
$836$	−5.15579	−	8.93009i	−0.178317	−	0.308854i
$837$	0.596186	−	0.344208i	0.0206072	−	0.0118976i
$838$	−11.9675	−	6.90946i	−0.413412	−	0.238683i
$839$	1.59133			0.0549389			0.0274695	−	0.999623i	$-0.491255\pi$
$839$	1.59133			0.0549389			0.0274695	+	0.999623i	$0.491255\pi$
$840$	−3.97630	−	4.38053i	−0.137196	−	0.151142i
$841$	41.8767			1.44403
$842$	21.8816	+	12.6333i	0.754089	+	0.435373i
$843$	6.65836	−	3.84421i	0.229326	−	0.132402i
$844$	−3.84421	−	6.65836i	−0.132323	−	0.229190i
$845$	−8.18654	+	21.1664i	−0.281625	+	0.728147i
$846$	−3.06525			−0.105385
$847$	−69.4586	+	4.09708i	−2.38662	+	0.140777i
$848$		−	10.4608i		−	0.359226i
$849$	9.21450	−	15.9600i	0.316241	−	0.547745i
$850$	−25.2908	−	23.0047i	−0.867467	−	0.789056i
$851$	−2.67171	−	4.62753i	−0.0915850	−	0.158630i
$852$	5.19615	+	3.00000i	0.178017	+	0.102778i
$853$		−	29.9869i		−	1.02673i	−0.858170	−	0.513366i	$-0.828398\pi$
$853$		−	29.9869i		−	1.02673i	0.858170	−	0.513366i	$-0.171602\pi$
$854$	−22.3768	−	11.2173i	−0.765719	−	0.383849i
$855$	3.73042	−	0.581167i	0.127578	−	0.0198755i
$856$	−7.76304	+	13.4460i	−0.265335	+	0.459574i
$857$	−32.0478	+	18.5028i	−1.09473	+	0.632045i	−0.934833	−	0.355088i	$-0.884451\pi$
$857$	−32.0478	+	18.5028i	−1.09473	+	0.632045i	−0.159901	+	0.987133i	$0.551117\pi$
$858$	8.93009	−	5.15579i	0.304868	−	0.176016i
$859$	13.8797	−	24.0403i	0.473568	−	0.820244i	−0.525974	−	0.850501i	$-0.676299\pi$
$859$	13.8797	−	24.0403i	0.473568	−	0.820244i	0.999542	+	0.0302567i	$0.00963247\pi$
$860$	0.688417	+	4.41883i	0.0234748	+	0.150681i
$861$	12.1790	+	6.10526i	0.415061	+	0.208067i
$862$		−	19.5448i		−	0.665700i
$863$	3.12152	+	1.80221i	0.106258	+	0.0613479i	0.552187	−	0.833720i	$-0.313793\pi$
$863$	3.12152	+	1.80221i	0.106258	+	0.0613479i	−0.445929	+	0.895068i	$0.647127\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−18.3291	+	14.7660i	−0.623209	+	0.502059i
$866$	7.37683	−	12.7771i	0.250675	−	0.434182i
$867$		−	29.7537i		−	1.01049i
$868$	−1.81822	+	0.107250i	−0.0617144	+	0.00364029i
$869$	−44.6537			−1.51477
$870$	6.79076	−	17.5576i	0.230228	−	0.595258i
$871$	10.3116	+	17.8602i	0.349395	+	0.605169i
$872$	10.1111	−	5.83767i	0.342406	−	0.197688i
$873$	4.29375	+	2.47900i	0.145322	+	0.0839015i
$874$	−3.90292			−0.132018
$875$	25.6021	+	14.8167i	0.865508	+	0.500895i
$876$	4.00000			0.135147
$877$	−10.4764	−	6.04854i	−0.353762	−	0.204245i	0.312579	−	0.949892i	$-0.398807\pi$
$877$	−10.4764	−	6.04854i	−0.353762	−	0.204245i	−0.666341	+	0.745647i	$0.732141\pi$
$878$	−13.7999	+	7.96737i	−0.465724	+	0.268886i
$879$	−0.918833	−	1.59146i	−0.0309915	−	0.0536788i
$880$	−4.92620	+	12.7368i	−0.166062	+	0.429356i
$881$	−44.7406			−1.50735			−0.753674	−	0.657248i	$-0.771720\pi$
$881$	−44.7406			−1.50735			−0.753674	+	0.657248i	$0.771720\pi$
$882$	0.822941	+	6.95146i	0.0277099	+	0.234068i
$883$			36.5970i			1.23159i	0.787908	+	0.615793i	$0.211164\pi$
$883$			36.5970i			1.23159i	−0.787908	+	0.615793i	$0.788836\pi$
$884$	−5.77241	+	9.99812i	−0.194147	+	0.336273i
$885$	12.2623	−	9.87853i	0.412192	−	0.332063i
$886$	−10.9123	−	18.9006i	−0.366606	−	0.634979i
$887$	−48.5475	−	28.0289i	−1.63007	−	0.941119i	−0.984071	−	0.177777i	$-0.943109\pi$
$887$	−48.5475	−	28.0289i	−1.63007	−	0.941119i	−0.645995	−	0.763342i	$-0.723557\pi$
$888$			2.31158i			0.0775717i
$889$	−10.9254	+	7.19732i	−0.366425	+	0.241390i
$890$	−4.20433	−	26.9869i	−0.140930	−	0.904603i
$891$	−3.05362	+	5.28903i	−0.102300	+	0.177189i
$892$	9.67567	−	5.58625i	0.323965	−	0.187041i
$893$	−4.48205	+	2.58771i	−0.149986	+	0.0865944i
$894$	6.31158	−	10.9320i	0.211091	−	0.365620i
$895$	−10.9029	+	1.69858i	−0.364444	+	0.0567773i
$896$	−0.155792	−	2.64116i	−0.00520463	−	0.0882350i
$897$		−	3.90292i		−	0.130315i
$898$	9.84129	+	5.68187i	0.328408	+	0.189607i
$899$	−2.89783	−	5.01919i	−0.0966481	−	0.167400i
$900$	−3.69874	−	3.36441i	−0.123291	−	0.112147i
$901$	−35.7638	+	61.9448i	−1.19147	+	2.06368i
$902$		−	31.4477i		−	1.04710i
$903$	2.37132	−	4.73042i	0.0789126	−	0.157418i
$904$	3.37683			0.112312
$905$	−4.94495	+	12.7853i	−0.164376	+	0.424996i
$906$	−0.967375	−	1.67554i	−0.0321389	−	0.0556662i
$907$	−16.1457	+	9.32175i	−0.536111	+	0.309524i	−0.743501	−	0.668735i	$-0.766836\pi$
$907$	−16.1457	+	9.32175i	−0.536111	+	0.309524i	0.207391	+	0.978258i	$0.433503\pi$
$908$	−3.33485	−	1.92538i	−0.110671	−	0.0638958i
$909$	8.00000			0.265343
$910$	3.04843	−	9.51228i	0.101054	−	0.315329i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	1.46221	+	0.844208i	0.0484187	+	0.0279545i
$913$	71.5399	−	41.3036i	2.36763	−	1.36695i
$914$	3.20942	+	5.55887i	0.106158	+	0.183871i
$915$	−19.7307	−	7.63125i	−0.652277	−	0.252281i
$916$	5.67533			0.187518
$917$	17.7761	−	1.04854i	0.587019	−	0.0346259i
$918$		−	6.83767i		−	0.225677i
$919$	−19.4608	+	33.7071i	−0.641954	+	1.11190i	0.343043	+	0.939320i	$0.388542\pi$
$919$	−19.4608	+	33.7071i	−0.641954	+	1.11190i	−0.984996	+	0.172576i	$0.944791\pi$
$920$	3.24269	+	4.02517i	0.106908	+	0.132706i
$921$	8.04200	+	13.9292i	0.264993	+	0.458981i
$922$	1.30539	+	0.753667i	0.0429907	+	0.0248207i
$923$			10.1305i			0.333450i
$924$	13.4935	−	8.88910i	0.443902	−	0.292430i
$925$	−3.51592	−	11.0102i	−0.115603	−	0.362012i
$926$	12.0587	−	20.8863i	0.396274	−	0.686366i
$927$	−0.725439	+	0.418833i	−0.0238266	+	0.0137563i
$928$	7.29092	−	4.20942i	0.239336	−	0.138181i
$929$	6.86746	−	11.8948i	0.225314	−	0.390255i	−0.731100	−	0.682271i	$-0.760993\pi$
$929$	6.86746	−	11.8948i	0.225314	−	0.390255i	0.956414	+	0.292015i	$0.0943259\pi$
$930$	−1.52100	+	0.236959i	−0.0498755	+	0.00777019i
$931$	7.07179	+	9.46977i	0.231769	+	0.310359i
$932$			11.4608i			0.375412i
$933$	13.3167	+	7.68842i	0.435970	+	0.251707i
$934$	11.7724	+	20.3904i	0.385205	+	0.667195i
$935$	72.7158	−	58.5800i	2.37806	−	1.91577i
$936$	−0.844208	+	1.46221i	−0.0275938	+	0.0477939i
$937$			20.7435i			0.677661i	0.940847	+	0.338830i	$0.110031\pi$
$937$			20.7435i			0.677661i	−0.940847	+	0.338830i	$0.889969\pi$
$938$	17.7782	+	26.9869i	0.580479	+	0.881154i
$939$	22.4188			0.731611
$940$	6.39263	+	2.47248i	0.208504	+	0.0806433i
$941$	−6.54425	−	11.3350i	−0.213336	−	0.369510i	0.739420	−	0.673244i	$-0.235100\pi$
$941$	−6.54425	−	11.3350i	−0.213336	−	0.369510i	−0.952757	+	0.303735i	$0.901766\pi$
$942$	−14.8517	+	8.57462i	−0.483894	+	0.279376i
$943$	−10.3082	−	5.95146i	−0.335682	−	0.193806i
$944$	7.04200			0.229198
$945$	1.25332	+	5.78180i	0.0407704	+	0.188082i
$946$	−12.2145			−0.397128
$947$	17.5465	+	10.1305i	0.570186	+	0.329197i	0.757224	−	0.653156i	$-0.226555\pi$
$947$	17.5465	+	10.1305i	0.570186	+	0.329197i	−0.187038	+	0.982353i	$0.559889\pi$
$948$	6.33202	−	3.65579i	0.205654	−	0.118735i
$949$	3.37683	+	5.84885i	0.109617	+	0.189862i
$950$	−8.24862	−	1.79698i	−0.267620	−	0.0583016i
$951$	−10.0653			−0.326388
$952$	−8.10715	+	16.1725i	−0.262754	+	0.524154i
$953$			1.65500i			0.0536107i	0.999641	+	0.0268053i	$0.00853343\pi$
$953$			1.65500i			0.0536107i	−0.999641	+	0.0268053i	$0.991467\pi$
$954$	−5.23042	+	9.05935i	−0.169341	+	0.293307i
$955$	20.9321	+	25.9832i	0.677348	+	0.840796i
$956$	−7.73042	−	13.3895i	−0.250020	−	0.433047i
$957$	44.5275	+	25.7080i	1.43937	+	0.831020i
$958$			29.9738i			0.968410i
$959$	−45.0623	−	22.5894i	−1.45514	−	0.729450i
$960$	−0.344208	−	2.20942i	−0.0111093	−	0.0713086i
$961$	15.2630	−	26.4364i	0.492356	−	0.852786i
$962$	−3.38002	+	1.95146i	−0.108976	+	0.0629175i
$963$	13.4460	−	7.76304i	0.433291	−	0.250161i
$964$	2.18842	−	3.79045i	0.0704842	−	0.122082i
$965$	−1.92108	−	12.3311i	−0.0618419	−	0.396953i
$966$	−0.360125	−	6.10526i	−0.0115868	−	0.196434i
$967$			15.3405i			0.493317i	0.969102	+	0.246659i	$0.0793326\pi$
$967$			15.3405i			0.493317i	−0.969102	+	0.246659i	$0.920667\pi$
$968$	−22.7752	−	13.1492i	−0.732022	−	0.422633i
$969$	−5.77241	−	9.99812i	−0.185437	−	0.321186i
$970$	−6.95509	−	8.63340i	−0.223315	−	0.277202i
$971$	−23.5565	+	40.8010i	−0.755963	+	1.30937i	0.188932	+	0.981990i	$0.439498\pi$
$971$	−23.5565	+	40.8010i	−0.755963	+	1.30937i	−0.944894	+	0.327375i	$0.893836\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−19.4700	−	29.5550i	−0.624179	−	0.947490i
$974$	30.5028			0.977374
$975$	1.79698	−	8.24862i	0.0575493	−	0.264167i
$976$	−4.73042	−	8.19332i	−0.151417	−	0.262262i
$977$	−25.8854	+	14.9449i	−0.828146	+	0.478130i	−0.853217	−	0.521555i	$-0.825352\pi$
$977$	−25.8854	+	14.9449i	−0.828146	+	0.478130i	0.0250716	+	0.999686i	$0.492019\pi$
$978$	−0.466934	−	0.269584i	−0.0149309	−	0.00862035i
$979$	74.5970			2.38413
$980$	3.89089	−	15.1612i	0.124290	−	0.484306i
$981$	−11.6753			−0.372765
$982$	−3.35989	−	1.93983i	−0.107218	−	0.0619025i
$983$	4.45938	−	2.57462i	0.142232	−	0.0821178i	−0.427195	−	0.904159i	$-0.640498\pi$
$983$	4.45938	−	2.57462i	0.142232	−	0.0821178i	0.569427	+	0.822042i	$0.307165\pi$
$984$	2.57462	+	4.45938i	0.0820760	+	0.142160i
$985$	30.2944	+	11.7170i	0.965259	+	0.373333i
$986$	−57.5652			−1.83325
$987$	−4.46147	−	6.77241i	−0.142010	−	0.215568i
$988$			2.85075i			0.0906945i
$989$	−2.31158	+	4.00378i	−0.0735041	+	0.127313i
$990$	10.6346	−	8.56726i	0.337990	−	0.272285i
$991$	−3.40946	−	5.90536i	−0.108305	−	0.187590i	0.806779	−	0.590854i	$-0.201209\pi$
$991$	−3.40946	−	5.90536i	−0.108305	−	0.187590i	−0.915084	+	0.403264i	$0.867876\pi$
$992$	−0.596186	−	0.344208i	−0.0189289	−	0.0109286i
$993$			23.2797i			0.738761i
$994$	0.934749	+	15.8470i	0.0296485	+	0.502635i
$995$	19.0522	−	2.96817i	0.603994	−	0.0940972i
$996$	−6.76304	+	11.7139i	−0.214295	+	0.371170i
$997$	−44.6567	+	25.7826i	−1.41429	+	0.816543i	−0.995789	−	0.0916725i	$-0.970779\pi$
$997$	−44.6567	+	25.7826i	−1.41429	+	0.816543i	−0.418504	+	0.908215i	$0.637445\pi$
$998$	8.12058	−	4.68842i	0.257052	−	0.148409i
$999$	1.15579	−	2.00189i	0.0365676	−	0.0633370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.n.b.79.5	yes	12
3.2	odd	2		630.2.u.f.289.2		12
4.3	odd	2		1680.2.di.c.289.2		12
5.2	odd	4		1050.2.i.u.751.1		6
5.3	odd	4		1050.2.i.v.751.3		6
5.4	even	2	inner	210.2.n.b.79.1	✓	12
7.2	even	3		1470.2.g.i.589.3		6
7.3	odd	6		1470.2.n.j.949.3		12
7.4	even	3	inner	210.2.n.b.109.1	yes	12
7.5	odd	6		1470.2.g.h.589.1		6
7.6	odd	2		1470.2.n.j.79.5		12
15.14	odd	2		630.2.u.f.289.6		12
20.19	odd	2		1680.2.di.c.289.4		12
21.11	odd	6		630.2.u.f.109.6		12
28.11	odd	6		1680.2.di.c.529.4		12
35.2	odd	12		7350.2.a.dq.1.3		3
35.4	even	6	inner	210.2.n.b.109.5	yes	12
35.9	even	6		1470.2.g.i.589.6		6
35.12	even	12		7350.2.a.dp.1.3		3
35.18	odd	12		1050.2.i.v.151.3		6
35.19	odd	6		1470.2.g.h.589.4		6
35.23	odd	12		7350.2.a.dn.1.3		3
35.24	odd	6		1470.2.n.j.949.5		12
35.32	odd	12		1050.2.i.u.151.1		6
35.33	even	12		7350.2.a.do.1.3		3
35.34	odd	2		1470.2.n.j.79.3		12
105.74	odd	6		630.2.u.f.109.2		12
140.39	odd	6		1680.2.di.c.529.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.b.79.1	✓	12	5.4	even	2	inner
210.2.n.b.79.5	yes	12	1.1	even	1	trivial
210.2.n.b.109.1	yes	12	7.4	even	3	inner
210.2.n.b.109.5	yes	12	35.4	even	6	inner
630.2.u.f.109.2		12	105.74	odd	6
630.2.u.f.109.6		12	21.11	odd	6
630.2.u.f.289.2		12	3.2	odd	2
630.2.u.f.289.6		12	15.14	odd	2
1050.2.i.u.151.1		6	35.32	odd	12
1050.2.i.u.751.1		6	5.2	odd	4
1050.2.i.v.151.3		6	35.18	odd	12
1050.2.i.v.751.3		6	5.3	odd	4
1470.2.g.h.589.1		6	7.5	odd	6
1470.2.g.h.589.4		6	35.19	odd	6
1470.2.g.i.589.3		6	7.2	even	3
1470.2.g.i.589.6		6	35.9	even	6
1470.2.n.j.79.3		12	35.34	odd	2
1470.2.n.j.79.5		12	7.6	odd	2
1470.2.n.j.949.3		12	7.3	odd	6
1470.2.n.j.949.5		12	35.24	odd	6
1680.2.di.c.289.2		12	4.3	odd	2
1680.2.di.c.289.4		12	20.19	odd	2
1680.2.di.c.529.2		12	140.39	odd	6
1680.2.di.c.529.4		12	28.11	odd	6
7350.2.a.dn.1.3		3	35.23	odd	12
7350.2.a.do.1.3		3	35.33	even	12
7350.2.a.dp.1.3		3	35.12	even	12
7350.2.a.dq.1.3		3	35.2	odd	12

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.806615 + 2.08551i) q^{5} +1.00000 q^{6} +(1.45550 + 2.20942i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.806615 + 2.08551i) q^{5} +1.00000 q^{6} +(1.45550 + 2.20942i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.74131 + 1.40280i) q^{10} +(-3.05362 - 5.28903i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.68842i q^{13} +(0.155792 + 2.64116i) q^{14} +(0.344208 + 2.20942i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.92159 - 3.41883i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.844208 - 1.46221i) q^{19} +(-2.20942 + 0.344208i) q^{20} +(2.36521 + 1.18566i) q^{21} -6.10725i q^{22} +(-2.00189 - 1.15579i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.69874 - 3.36441i) q^{25} +(-0.844208 + 1.46221i) q^{26} -1.00000i q^{27} +(-1.18566 + 2.36521i) q^{28} -8.41883 q^{29} +(-0.806615 + 2.08551i) q^{30} +(0.344208 + 0.596186i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.28903 - 3.05362i) q^{33} +6.83767 q^{34} +(-5.78180 + 1.25332i) q^{35} +1.00000 q^{36} +(2.00189 + 1.15579i) q^{37} +(1.46221 - 0.844208i) q^{38} +(0.844208 + 1.46221i) q^{39} +(-2.08551 - 0.806615i) q^{40} +5.14925 q^{41} +(1.45550 + 2.20942i) q^{42} -2.00000i q^{43} +(3.05362 - 5.28903i) q^{44} +(1.40280 + 1.74131i) q^{45} +(-1.15579 - 2.00189i) q^{46} +(-2.65458 - 1.53263i) q^{47} +1.00000i q^{48} +(-2.76304 + 6.43161i) q^{49} +(-1.52100 - 4.76304i) q^{50} +(3.41883 - 5.92159i) q^{51} +(-1.46221 + 0.844208i) q^{52} +(-9.05935 + 5.23042i) q^{53} +(0.500000 - 0.866025i) q^{54} +(13.4935 - 2.10217i) q^{55} +(-2.20942 + 1.45550i) q^{56} -1.68842i q^{57} +(-7.29092 - 4.20942i) q^{58} +(-3.52100 - 6.09855i) q^{59} +(-1.74131 + 1.40280i) q^{60} +(-4.73042 + 8.19332i) q^{61} +0.688417i q^{62} +(2.64116 - 0.155792i) q^{63} -1.00000 q^{64} +(-3.52122 - 1.36190i) q^{65} +(-3.05362 - 5.28903i) q^{66} +(10.5781 - 6.10725i) q^{67} +(5.92159 + 3.41883i) q^{68} -2.31158 q^{69} +(-5.63384 - 1.80549i) q^{70} +6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(1.15579 + 2.00189i) q^{74} +(-4.88541 - 1.06430i) q^{75} +1.68842 q^{76} +(7.24113 - 14.4449i) q^{77} +1.68842i q^{78} +(3.65579 - 6.33202i) q^{79} +(-1.40280 - 1.74131i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.45938 + 2.57462i) q^{82} +13.5261i q^{83} +(0.155792 + 2.64116i) q^{84} +(2.35358 + 15.1072i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-7.29092 + 4.20942i) q^{87} +(5.28903 - 3.05362i) q^{88} +(-6.10725 + 10.5781i) q^{89} +(0.344208 + 2.20942i) q^{90} +(-3.73042 + 2.45749i) q^{91} -2.31158i q^{92} +(0.596186 + 0.344208i) q^{93} +(-1.53263 - 2.65458i) q^{94} +(2.36851 + 2.94005i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.95800i q^{97} +(-5.60867 + 4.18842i) q^{98} -6.10725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9} - 6 q^{11} + 6 q^{14} - 6 q^{16} + 6 q^{19} + 6 q^{21} + 6 q^{24} - 6 q^{26} - 48 q^{29} - 24 q^{34} - 30 q^{35} + 12 q^{36} + 6 q^{39} - 36 q^{41} + 6 q^{44} - 18 q^{46} + 24 q^{49} - 12 q^{51} + 6 q^{54} + 60 q^{55} - 24 q^{59} - 12 q^{61} - 12 q^{64} - 30 q^{65} - 6 q^{66} - 36 q^{69} - 30 q^{70} + 72 q^{71} + 18 q^{74} + 12 q^{76} + 48 q^{79} - 6 q^{81} + 6 q^{84} + 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 12 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9 - 6 * q^11 + 6 * q^14 - 6 * q^16 + 6 * q^19 + 6 * q^21 + 6 * q^24 - 6 * q^26 - 48 * q^29 - 24 * q^34 - 30 * q^35 + 12 * q^36 + 6 * q^39 - 36 * q^41 + 6 * q^44 - 18 * q^46 + 24 * q^49 - 12 * q^51 + 6 * q^54 + 60 * q^55 - 24 * q^59 - 12 * q^61 - 12 * q^64 - 30 * q^65 - 6 * q^66 - 36 * q^69 - 30 * q^70 + 72 * q^71 + 18 * q^74 + 12 * q^76 + 48 * q^79 - 6 * q^81 + 6 * q^84 + 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 12 * q^99

Introduction

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