LMFDB - Embedded newform 74.2.e.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("74.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.e (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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	74.27
Dual form			74.2.e.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +1.73205 q^{10} +1.26795 q^{11} +(1.36603 - 2.36603i) q^{12} +(5.19615 - 3.00000i) q^{13} +4.00000i q^{14} +(4.09808 + 2.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(3.86603 - 2.23205i) q^{18} +(4.09808 - 2.36603i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-5.46410 + 9.46410i) q^{21} +(-1.09808 - 0.633975i) q^{22} +4.73205i q^{23} +(-2.36603 + 1.36603i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} -7.73205i q^{29} +(-2.36603 - 4.09808i) q^{30} -4.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.73205 - 3.00000i) q^{33} +(0.866025 + 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} -4.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -4.73205 q^{38} +(-14.1962 - 8.19615i) q^{39} +(0.866025 + 1.50000i) q^{40} +(3.23205 + 5.59808i) q^{41} +(9.46410 - 5.46410i) q^{42} +2.53590i q^{43} +(0.633975 + 1.09808i) q^{44} -7.73205i q^{45} +(2.36603 - 4.09808i) q^{46} -5.66025 q^{47} +2.73205 q^{48} +(-4.50000 + 7.79423i) q^{49} +(1.73205 - 1.00000i) q^{50} +4.73205i q^{51} +(5.19615 + 3.00000i) q^{52} +(4.73205 - 8.19615i) q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.90192 + 1.09808i) q^{55} +(-3.46410 + 2.00000i) q^{56} +(-11.1962 - 6.46410i) q^{57} +(-3.86603 + 6.69615i) q^{58} +(8.19615 + 4.73205i) q^{59} +4.73205i q^{60} +(2.30385 - 1.33013i) q^{61} +(-2.36603 + 4.09808i) q^{62} +17.8564 q^{63} -1.00000 q^{64} +(-5.19615 + 9.00000i) q^{65} +3.46410i q^{66} +(2.09808 + 3.63397i) q^{67} -1.73205i q^{68} +(11.1962 - 6.46410i) q^{69} +(-3.46410 - 6.00000i) q^{70} +(-4.73205 - 8.19615i) q^{71} +(3.86603 + 2.23205i) q^{72} +8.39230 q^{73} +(3.46410 - 5.00000i) q^{74} +5.46410 q^{75} +(4.09808 + 2.36603i) q^{76} +(-2.53590 - 4.39230i) q^{77} +(8.19615 + 14.1962i) q^{78} +(-1.90192 + 1.09808i) q^{79} -1.73205i q^{80} +(1.23205 + 2.13397i) q^{81} -6.46410i q^{82} +(2.83013 - 4.90192i) q^{83} -10.9282 q^{84} +3.00000 q^{85} +(1.26795 - 2.19615i) q^{86} +(-18.2942 + 10.5622i) q^{87} -1.26795i q^{88} +(4.50000 + 2.59808i) q^{89} +(-3.86603 + 6.69615i) q^{90} +(-20.7846 - 12.0000i) q^{91} +(-4.09808 + 2.36603i) q^{92} +(-11.1962 + 6.46410i) q^{93} +(4.90192 + 2.83013i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(-2.36603 - 1.36603i) q^{96} -5.19615i q^{97} +(7.79423 - 4.50000i) q^{98} +(-2.83013 + 4.90192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9 + 12 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^18 + 6 * q^19 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 6 * q^24 - 4 * q^25 - 24 * q^26 + 16 * q^27 + 8 * q^28 - 6 * q^30 + 24 * q^35 - 4 * q^36 - 2 * q^37 - 12 * q^38 - 36 * q^39 + 6 * q^41 + 24 * q^42 + 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 - 18 * q^49 + 12 * q^53 - 18 * q^55 - 24 * q^57 - 12 * q^58 + 12 * q^59 + 30 * q^61 - 6 * q^62 + 16 * q^63 - 4 * q^64 - 2 * q^67 + 24 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 + 8 * q^75 + 6 * q^76 - 24 * q^77 + 12 * q^78 - 18 * q^79 - 2 * q^81 - 6 * q^83 - 16 * q^84 + 12 * q^85 + 12 * q^86 - 42 * q^87 + 18 * q^89 - 12 * q^90 - 6 * q^92 - 24 * q^93 + 30 * q^94 - 6 * q^95 - 6 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	−0.926779	−	0.375608i	$-0.877434\pi$
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	0.138104	−	0.990418i	$-0.455899\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$			2.73205i			1.11536i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.23205	+	3.86603i	−0.744017	+	1.28868i
$10$	1.73205			0.547723
$11$	1.26795			0.382301			0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795			0.382301			0.191151	+	0.981561i	$0.438778\pi$
$12$	1.36603	−	2.36603i	0.394338	−	0.683013i
$13$	5.19615	−	3.00000i	1.44115	−	0.832050i	0.443227	−	0.896410i	$-0.353834\pi$
$13$	5.19615	−	3.00000i	1.44115	−	0.832050i	0.997927	+	0.0643593i	$0.0205004\pi$
$14$			4.00000i			1.06904i
$15$	4.09808	+	2.36603i	1.05812	+	0.610905i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	0.306944	−	0.951727i	$-0.400693\pi$
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	−0.670748	+	0.741685i	$0.734027\pi$
$18$	3.86603	−	2.23205i	0.911231	−	0.526099i
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$	−1.50000	−	0.866025i	−0.335410	−	0.193649i
$21$	−5.46410	+	9.46410i	−1.19236	+	2.06524i
$22$	−1.09808	−	0.633975i	−0.234111	−	0.135164i
$23$			4.73205i			0.986701i	0.869831	+	0.493350i	$0.164228\pi$
$23$			4.73205i			0.986701i	−0.869831	+	0.493350i	$0.835772\pi$
$24$	−2.36603	+	1.36603i	−0.482963	+	0.278839i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−6.00000			−1.17670
$27$	4.00000			0.769800
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$		−	7.73205i		−	1.43581i	−0.696143	−	0.717903i	$-0.745102\pi$
$29$		−	7.73205i		−	1.43581i	0.696143	−	0.717903i	$-0.254898\pi$
$30$	−2.36603	−	4.09808i	−0.431975	−	0.748203i
$31$		−	4.73205i		−	0.849901i	−0.905216	−	0.424951i	$-0.860291\pi$
$31$		−	4.73205i		−	0.849901i	0.905216	−	0.424951i	$-0.139709\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.73205	−	3.00000i	−0.301511	−	0.522233i
$34$	0.866025	+	1.50000i	0.148522	+	0.257248i
$35$	6.00000	+	3.46410i	1.01419	+	0.585540i
$36$	−4.46410			−0.744017
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$38$	−4.73205			−0.767640
$39$	−14.1962	−	8.19615i	−2.27320	−	1.31243i
$40$	0.866025	+	1.50000i	0.136931	+	0.237171i
$41$	3.23205	+	5.59808i	0.504762	+	0.874273i	0.999985	+	0.00550690i	$0.00175291\pi$
$41$	3.23205	+	5.59808i	0.504762	+	0.874273i	−0.495223	+	0.868766i	$0.664914\pi$
$42$	9.46410	−	5.46410i	1.46034	−	0.843129i
$43$			2.53590i			0.386721i	0.981128	+	0.193360i	$0.0619387\pi$
$43$			2.53590i			0.386721i	−0.981128	+	0.193360i	$0.938061\pi$
$44$	0.633975	+	1.09808i	0.0955753	+	0.165541i
$45$		−	7.73205i		−	1.15263i
$46$	2.36603	−	4.09808i	0.348851	−	0.604228i
$47$	−5.66025			−0.825633			−0.412816	−	0.910814i	$-0.635455\pi$
$47$	−5.66025			−0.825633			−0.412816	+	0.910814i	$0.635455\pi$
$48$	2.73205			0.394338
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	1.73205	−	1.00000i	0.244949	−	0.141421i
$51$			4.73205i			0.662620i
$52$	5.19615	+	3.00000i	0.720577	+	0.416025i
$53$	4.73205	−	8.19615i	0.649997	−	1.12583i	−0.333126	−	0.942882i	$-0.608103\pi$
$53$	4.73205	−	8.19615i	0.649997	−	1.12583i	0.983123	−	0.182946i	$-0.0585633\pi$
$54$	−3.46410	−	2.00000i	−0.471405	−	0.272166i
$55$	−1.90192	+	1.09808i	−0.256455	+	0.148065i
$56$	−3.46410	+	2.00000i	−0.462910	+	0.267261i
$57$	−11.1962	−	6.46410i	−1.48297	−	0.856191i
$58$	−3.86603	+	6.69615i	−0.507634	+	0.879248i
$59$	8.19615	+	4.73205i	1.06705	+	0.616061i	0.927373	−	0.374137i	$-0.122061\pi$
$59$	8.19615	+	4.73205i	1.06705	+	0.616061i	0.139675	+	0.990197i	$0.455394\pi$
$60$			4.73205i			0.610905i
$61$	2.30385	−	1.33013i	0.294977	−	0.170305i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	2.30385	−	1.33013i	0.294977	−	0.170305i	0.640184	+	0.768221i	$0.278858\pi$
$62$	−2.36603	+	4.09808i	−0.300486	+	0.520456i
$63$	17.8564			2.24970
$64$	−1.00000			−0.125000
$65$	−5.19615	+	9.00000i	−0.644503	+	1.11631i
$66$			3.46410i			0.426401i
$67$	2.09808	+	3.63397i	0.256321	+	0.443961i	0.965253	−	0.261316i	$-0.0841563\pi$
$67$	2.09808	+	3.63397i	0.256321	+	0.443961i	−0.708933	+	0.705276i	$0.750823\pi$
$68$		−	1.73205i		−	0.210042i
$69$	11.1962	−	6.46410i	1.34786	−	0.778186i
$70$	−3.46410	−	6.00000i	−0.414039	−	0.717137i
$71$	−4.73205	−	8.19615i	−0.561591	−	0.972704i	−0.997358	−	0.0726447i	$-0.976856\pi$
$71$	−4.73205	−	8.19615i	−0.561591	−	0.972704i	0.435767	−	0.900060i	$-0.356477\pi$
$72$	3.86603	+	2.23205i	0.455615	+	0.263050i
$73$	8.39230			0.982245			0.491122	−	0.871091i	$-0.336587\pi$
$73$	8.39230			0.982245			0.491122	+	0.871091i	$0.336587\pi$
$74$	3.46410	−	5.00000i	0.402694	−	0.581238i
$75$	5.46410			0.630940
$76$	4.09808	+	2.36603i	0.470082	+	0.271402i
$77$	−2.53590	−	4.39230i	−0.288992	−	0.500550i
$78$	8.19615	+	14.1962i	0.928032	+	1.60740i
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	−0.603161	−	0.797619i	$-0.706092\pi$
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	0.389178	+	0.921163i	$0.372759\pi$
$80$		−	1.73205i		−	0.193649i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$		−	6.46410i		−	0.713841i
$83$	2.83013	−	4.90192i	0.310647	−	0.538056i	−0.667856	−	0.744291i	$-0.732788\pi$
$83$	2.83013	−	4.90192i	0.310647	−	0.538056i	0.978503	+	0.206235i	$0.0661210\pi$
$84$	−10.9282			−1.19236
$85$	3.00000			0.325396
$86$	1.26795	−	2.19615i	0.136726	−	0.236817i
$87$	−18.2942	+	10.5622i	−1.96135	+	1.13238i
$88$		−	1.26795i		−	0.135164i
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	0.719165	−	0.694839i	$-0.244525\pi$
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	−0.242166	+	0.970235i	$0.577858\pi$
$90$	−3.86603	+	6.69615i	−0.407515	+	0.705836i
$91$	−20.7846	−	12.0000i	−2.17882	−	1.25794i
$92$	−4.09808	+	2.36603i	−0.427254	+	0.246675i
$93$	−11.1962	+	6.46410i	−1.16099	+	0.670296i
$94$	4.90192	+	2.83013i	0.505595	+	0.291905i
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$	−2.36603	−	1.36603i	−0.241481	−	0.139419i
$97$		−	5.19615i		−	0.527589i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$		−	5.19615i		−	0.527589i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$	7.79423	−	4.50000i	0.787336	−	0.454569i
$99$	−2.83013	+	4.90192i	−0.284438	+	0.492662i
$100$	−2.00000			−0.200000
$101$	6.46410			0.643202			0.321601	−	0.946875i	$-0.395779\pi$
$101$	6.46410			0.643202			0.321601	+	0.946875i	$0.395779\pi$
$102$	2.36603	−	4.09808i	0.234271	−	0.405770i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		−	18.9282i		−	1.84720i
$106$	−8.19615	+	4.73205i	−0.796081	+	0.459617i
$107$	−2.19615	−	3.80385i	−0.212310	−	0.367732i	0.740127	−	0.672467i	$-0.234765\pi$
$107$	−2.19615	−	3.80385i	−0.212310	−	0.367732i	−0.952437	+	0.304735i	$0.901432\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	3.69615	+	2.13397i	0.354027	+	0.204398i	0.666458	−	0.745543i	$-0.267810\pi$
$109$	3.69615	+	2.13397i	0.354027	+	0.204398i	−0.312430	+	0.949941i	$0.601143\pi$
$110$	2.19615			0.209395
$111$	15.0263	−	7.09808i	1.42623	−	0.673720i
$112$	4.00000			0.377964
$113$	6.80385	+	3.92820i	0.640052	+	0.369534i	0.784635	−	0.619958i	$-0.212851\pi$
$113$	6.80385	+	3.92820i	0.640052	+	0.369534i	−0.144582	+	0.989493i	$0.546184\pi$
$114$	6.46410	+	11.1962i	0.605419	+	1.04862i
$115$	−4.09808	−	7.09808i	−0.382148	−	0.661899i
$116$	6.69615	−	3.86603i	0.621722	−	0.358951i
$117$			26.7846i			2.47624i
$118$	−4.73205	−	8.19615i	−0.435621	−	0.754517i
$119$			6.92820i			0.635107i
$120$	2.36603	−	4.09808i	0.215988	−	0.374101i
$121$	−9.39230			−0.853846
$122$	−2.66025			−0.240848
$123$	8.83013	−	15.2942i	0.796186	−	1.37903i
$124$	4.09808	−	2.36603i	0.368018	−	0.212475i
$125$		−	12.1244i		−	1.08444i
$126$	−15.4641	−	8.92820i	−1.37765	−	0.795388i
$127$	−10.2942	+	17.8301i	−0.913465	+	1.58217i	−0.104332	+	0.994543i	$0.533270\pi$
$127$	−10.2942	+	17.8301i	−0.913465	+	1.58217i	−0.809133	+	0.587625i	$0.800063\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.00000	−	3.46410i	0.528271	−	0.304997i
$130$	9.00000	−	5.19615i	0.789352	−	0.455733i
$131$	−1.90192	−	1.09808i	−0.166172	−	0.0959394i	0.414608	−	0.910000i	$-0.363919\pi$
$131$	−1.90192	−	1.09808i	−0.166172	−	0.0959394i	−0.580780	+	0.814061i	$0.697252\pi$
$132$	1.73205	−	3.00000i	0.150756	−	0.261116i
$133$	−16.3923	−	9.46410i	−1.42139	−	0.820642i
$134$		−	4.19615i		−	0.362492i
$135$	−6.00000	+	3.46410i	−0.516398	+	0.298142i
$136$	−0.866025	+	1.50000i	−0.0742611	+	0.128624i
$137$	7.39230			0.631567			0.315784	−	0.948831i	$-0.397733\pi$
$137$	7.39230			0.631567			0.315784	+	0.948831i	$0.397733\pi$
$138$	−12.9282			−1.10052
$139$	−6.09808	+	10.5622i	−0.517232	+	0.895872i	0.482568	+	0.875859i	$0.339704\pi$
$139$	−6.09808	+	10.5622i	−0.517232	+	0.895872i	−0.999800	+	0.0200135i	$0.993629\pi$
$140$			6.92820i			0.585540i
$141$	7.73205	+	13.3923i	0.651156	+	1.12784i
$142$			9.46410i			0.794210i
$143$	6.58846	−	3.80385i	0.550954	−	0.318094i
$144$	−2.23205	−	3.86603i	−0.186004	−	0.322169i
$145$	6.69615	+	11.5981i	0.556085	+	0.963168i
$146$	−7.26795	−	4.19615i	−0.601500	−	0.347276i
$147$	24.5885			2.02802
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	−9.92820			−0.813350			−0.406675	−	0.913573i	$-0.633312\pi$
$149$	−9.92820			−0.813350			−0.406675	+	0.913573i	$0.633312\pi$
$150$	−4.73205	−	2.73205i	−0.386370	−	0.223071i
$151$	6.09808	+	10.5622i	0.496254	+	0.859538i	0.999991	−	0.00431966i	$-0.00137499\pi$
$151$	6.09808	+	10.5622i	0.496254	+	0.859538i	−0.503736	+	0.863857i	$0.668042\pi$
$152$	−2.36603	−	4.09808i	−0.191910	−	0.332398i
$153$	6.69615	−	3.86603i	0.541352	−	0.312550i
$154$			5.07180i			0.408697i
$155$	4.09808	+	7.09808i	0.329165	+	0.570131i
$156$		−	16.3923i		−	1.31243i
$157$	−5.69615	+	9.86603i	−0.454602	+	0.787395i	−0.998665	−	0.0516500i	$-0.983552\pi$
$157$	−5.69615	+	9.86603i	−0.454602	+	0.787395i	0.544063	+	0.839045i	$0.316885\pi$
$158$	2.19615			0.174717
$159$	−25.8564			−2.05055
$160$	−0.866025	+	1.50000i	−0.0684653	+	0.118585i
$161$	16.3923	−	9.46410i	1.29189	−	0.745876i
$162$		−	2.46410i		−	0.193598i
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	0.785374	−	0.619022i	$-0.212471\pi$
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	−0.143402	+	0.989665i	$0.545804\pi$
$164$	−3.23205	+	5.59808i	−0.252381	+	0.437136i
$165$	5.19615	+	3.00000i	0.404520	+	0.233550i
$166$	−4.90192	+	2.83013i	−0.380463	+	0.219660i
$167$	−6.00000	+	3.46410i	−0.464294	+	0.268060i	−0.713848	−	0.700301i	$-0.753049\pi$
$167$	−6.00000	+	3.46410i	−0.464294	+	0.268060i	0.249554	+	0.968361i	$0.419716\pi$
$168$	9.46410	+	5.46410i	0.730171	+	0.421565i
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$	−2.59808	−	1.50000i	−0.199263	−	0.115045i
$171$			21.1244i			1.61542i
$172$	−2.19615	+	1.26795i	−0.167455	+	0.0966802i
$173$	−1.96410	+	3.40192i	−0.149328	+	0.258643i	−0.930979	−	0.365072i	$-0.881044\pi$
$173$	−1.96410	+	3.40192i	−0.149328	+	0.258643i	0.781651	+	0.623716i	$0.214378\pi$
$174$	21.1244			1.60143
$175$	8.00000			0.604743
$176$	−0.633975	+	1.09808i	−0.0477876	+	0.0827706i
$177$		−	25.8564i		−	1.94349i
$178$	−2.59808	−	4.50000i	−0.194734	−	0.337289i
$179$			23.3205i			1.74306i	0.490345	+	0.871528i	$0.336871\pi$
$179$			23.3205i			1.74306i	−0.490345	+	0.871528i	$0.663129\pi$
$180$	6.69615	−	3.86603i	0.499102	−	0.288157i
$181$	−2.69615	−	4.66987i	−0.200403	−	0.347109i	0.748255	−	0.663411i	$-0.230892\pi$
$181$	−2.69615	−	4.66987i	−0.200403	−	0.347109i	−0.948658	+	0.316302i	$0.897559\pi$
$182$	12.0000	+	20.7846i	0.889499	+	1.54066i
$183$	−6.29423	−	3.63397i	−0.465283	−	0.268631i
$184$	4.73205			0.348851
$185$	−4.50000	−	9.52628i	−0.330847	−	0.700386i
$186$	12.9282			0.947942
$187$	−1.90192	−	1.09808i	−0.139082	−	0.0802993i
$188$	−2.83013	−	4.90192i	−0.206408	−	0.357510i
$189$	−8.00000	−	13.8564i	−0.581914	−	1.00791i
$190$	7.09808	−	4.09808i	0.514949	−	0.297306i
$191$		−	6.58846i		−	0.476724i	−0.971176	−	0.238362i	$-0.923390\pi$
$191$		−	6.58846i		−	0.476724i	0.971176	−	0.238362i	$-0.0766105\pi$
$192$	1.36603	+	2.36603i	0.0985844	+	0.170753i
$193$			12.1244i			0.872730i	0.899770	+	0.436365i	$0.143734\pi$
$193$			12.1244i			0.872730i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−2.59808	+	4.50000i	−0.186531	+	0.323081i
$195$	28.3923			2.03322
$196$	−9.00000			−0.642857
$197$	4.16025	−	7.20577i	0.296406	−	0.513390i	−0.678905	−	0.734226i	$-0.737545\pi$
$197$	4.16025	−	7.20577i	0.296406	−	0.513390i	0.975311	+	0.220836i	$0.0708786\pi$
$198$	4.90192	−	2.83013i	0.348365	−	0.201128i
$199$		−	18.9282i		−	1.34178i	−0.741555	−	0.670892i	$-0.765911\pi$
$199$		−	18.9282i		−	1.34178i	0.741555	−	0.670892i	$-0.234089\pi$
$200$	1.73205	+	1.00000i	0.122474	+	0.0707107i
$201$	5.73205	−	9.92820i	0.404308	−	0.700281i
$202$	−5.59808	−	3.23205i	−0.393879	−	0.227406i
$203$	−26.7846	+	15.4641i	−1.87991	+	1.08537i
$204$	−4.09808	+	2.36603i	−0.286923	+	0.165655i
$205$	−9.69615	−	5.59808i	−0.677209	−	0.390987i
$206$	−3.46410	+	6.00000i	−0.241355	+	0.418040i
$207$	−18.2942	−	10.5622i	−1.27154	−	0.734122i
$208$			6.00000i			0.416025i
$209$	5.19615	−	3.00000i	0.359425	−	0.207514i
$210$	−9.46410	+	16.3923i	−0.653085	+	1.13118i
$211$	−8.39230			−0.577750			−0.288875	−	0.957367i	$-0.593281\pi$
$211$	−8.39230			−0.577750			−0.288875	+	0.957367i	$0.593281\pi$
$212$	9.46410			0.649997
$213$	−12.9282	+	22.3923i	−0.885826	+	1.53430i
$214$			4.39230i			0.300252i
$215$	−2.19615	−	3.80385i	−0.149776	−	0.259420i
$216$		−	4.00000i		−	0.272166i
$217$	−16.3923	+	9.46410i	−1.11278	+	0.642465i
$218$	−2.13397	−	3.69615i	−0.144531	−	0.250335i
$219$	−11.4641	−	19.8564i	−0.774672	−	1.34177i
$220$	−1.90192	−	1.09808i	−0.128228	−	0.0740323i
$221$	−10.3923			−0.699062
$222$	−16.5622	−	1.36603i	−1.11158	−	0.0916816i
$223$	8.58846			0.575126			0.287563	−	0.957762i	$-0.407155\pi$
$223$	8.58846			0.575126			0.287563	+	0.957762i	$0.407155\pi$
$224$	−3.46410	−	2.00000i	−0.231455	−	0.133631i
$225$	−4.46410	−	7.73205i	−0.297607	−	0.515470i
$226$	−3.92820	−	6.80385i	−0.261300	−	0.452585i
$227$	4.09808	−	2.36603i	0.271999	−	0.157039i	−0.357797	−	0.933799i	$-0.616472\pi$
$227$	4.09808	−	2.36603i	0.271999	−	0.157039i	0.629796	+	0.776761i	$0.283139\pi$
$228$		−	12.9282i		−	0.856191i
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$			8.19615i			0.540438i
$231$	−6.92820	+	12.0000i	−0.455842	+	0.789542i
$232$	−7.73205			−0.507634
$233$	−25.3923			−1.66351			−0.831753	−	0.555146i	$-0.812662\pi$
$233$	−25.3923			−1.66351			−0.831753	+	0.555146i	$0.812662\pi$
$234$	13.3923	−	23.1962i	0.875482	−	1.51638i
$235$	8.49038	−	4.90192i	0.553851	−	0.319766i
$236$			9.46410i			0.616061i
$237$	5.19615	+	3.00000i	0.337526	+	0.194871i
$238$	3.46410	−	6.00000i	0.224544	−	0.388922i
$239$	16.3923	+	9.46410i	1.06033	+	0.612182i	0.925524	−	0.378690i	$-0.123625\pi$
$239$	16.3923	+	9.46410i	1.06033	+	0.612182i	0.134807	+	0.990872i	$0.456959\pi$
$240$	−4.09808	+	2.36603i	−0.264530	+	0.152726i
$241$	15.5885	−	9.00000i	1.00414	−	0.579741i	0.0946700	−	0.995509i	$-0.469820\pi$
$241$	15.5885	−	9.00000i	1.00414	−	0.579741i	0.909471	+	0.415768i	$0.136487\pi$
$242$	8.13397	+	4.69615i	0.522872	+	0.301880i
$243$	9.36603	−	16.2224i	0.600831	−	1.04067i
$244$	2.30385	+	1.33013i	0.147489	+	0.0851527i
$245$		−	15.5885i		−	0.995910i
$246$	−15.2942	+	8.83013i	−0.975124	+	0.562988i
$247$	14.1962	−	24.5885i	0.903280	−	1.56453i
$248$	−4.73205			−0.300486
$249$	−15.4641			−0.979998
$250$	−6.06218	+	10.5000i	−0.383406	+	0.664078i
$251$		−	18.9282i		−	1.19474i	−0.801967	−	0.597369i	$-0.796213\pi$
$251$		−	18.9282i		−	1.19474i	0.801967	−	0.597369i	$-0.203787\pi$
$252$	8.92820	+	15.4641i	0.562424	+	0.974147i
$253$			6.00000i			0.377217i
$254$	17.8301	−	10.2942i	1.11876	−	0.645917i
$255$	−4.09808	−	7.09808i	−0.256631	−	0.444499i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.696152	−	0.401924i	−0.0434248	−	0.0250713i	0.478130	−	0.878289i	$-0.341315\pi$
$257$	−0.696152	−	0.401924i	−0.0434248	−	0.0250713i	−0.521555	+	0.853218i	$0.674648\pi$
$258$	−6.92820			−0.431331
$259$	22.0000	−	10.3923i	1.36701	−	0.645746i
$260$	−10.3923			−0.644503
$261$	29.8923	+	17.2583i	1.85029	+	1.06826i
$262$	1.09808	+	1.90192i	0.0678394	+	0.117501i
$263$	5.66025	+	9.80385i	0.349026	+	0.604531i	0.986077	−	0.166291i	$-0.0531791\pi$
$263$	5.66025	+	9.80385i	0.349026	+	0.604531i	−0.637051	+	0.770822i	$0.719846\pi$
$264$	−3.00000	+	1.73205i	−0.184637	+	0.106600i
$265$			16.3923i			1.00697i
$266$	9.46410	+	16.3923i	0.580281	+	1.00508i
$267$		−	14.1962i		−	0.868790i
$268$	−2.09808	+	3.63397i	−0.128160	+	0.221980i
$269$	−28.3923			−1.73111			−0.865555	−	0.500814i	$-0.833034\pi$
$269$	−28.3923			−1.73111			−0.865555	+	0.500814i	$0.833034\pi$
$270$	6.92820			0.421637
$271$	−8.29423	+	14.3660i	−0.503839	+	0.872674i	0.496152	+	0.868236i	$0.334746\pi$
$271$	−8.29423	+	14.3660i	−0.503839	+	0.872674i	−0.999990	+	0.00443801i	$0.998587\pi$
$272$	1.50000	−	0.866025i	0.0909509	−	0.0525105i
$273$			65.5692i			3.96843i
$274$	−6.40192	−	3.69615i	−0.386754	−	0.223293i
$275$	−1.26795	+	2.19615i	−0.0764602	+	0.132433i
$276$	11.1962	+	6.46410i	0.673929	+	0.389093i
$277$	14.8923	−	8.59808i	0.894792	−	0.516608i	0.0192850	−	0.999814i	$-0.493861\pi$
$277$	14.8923	−	8.59808i	0.894792	−	0.516608i	0.875507	+	0.483206i	$0.160528\pi$
$278$	10.5622	−	6.09808i	0.633477	−	0.365738i
$279$	18.2942	+	10.5622i	1.09525	+	0.632341i
$280$	3.46410	−	6.00000i	0.207020	−	0.358569i
$281$	0.696152	+	0.401924i	0.0415290	+	0.0239768i	0.520621	−	0.853788i	$-0.325701\pi$
$281$	0.696152	+	0.401924i	0.0415290	+	0.0239768i	−0.479092	+	0.877765i	$0.659034\pi$
$282$		−	15.4641i		−	0.920874i
$283$	−8.19615	+	4.73205i	−0.487211	+	0.281291i	−0.723417	−	0.690412i	$-0.757429\pi$
$283$	−8.19615	+	4.73205i	−0.487211	+	0.281291i	0.236206	+	0.971703i	$0.424096\pi$
$284$	4.73205	−	8.19615i	0.280796	−	0.486352i
$285$	22.3923			1.32641
$286$	−7.60770			−0.449852
$287$	12.9282	−	22.3923i	0.763128	−	1.32178i
$288$			4.46410i			0.263050i
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$		−	13.3923i		−	0.786423i
$291$	−12.2942	+	7.09808i	−0.720700	+	0.416097i
$292$	4.19615	+	7.26795i	0.245561	+	0.425325i
$293$	−2.30385	−	3.99038i	−0.134592	−	0.233121i	0.790849	−	0.612011i	$-0.209639\pi$
$293$	−2.30385	−	3.99038i	−0.134592	−	0.233121i	−0.925442	+	0.378890i	$0.876306\pi$
$294$	−21.2942	−	12.2942i	−1.24190	−	0.717014i
$295$	−16.3923			−0.954397
$296$	6.06218	+	0.500000i	0.352357	+	0.0290619i
$297$	5.07180			0.294295
$298$	8.59808	+	4.96410i	0.498073	+	0.287563i
$299$	14.1962	+	24.5885i	0.820985	+	1.42199i
$300$	2.73205	+	4.73205i	0.157735	+	0.273205i
$301$	8.78461	−	5.07180i	0.506336	−	0.292334i
$302$		−	12.1962i		−	0.701810i
$303$	−8.83013	−	15.2942i	−0.507278	−	0.878630i
$304$			4.73205i			0.271402i
$305$	−2.30385	+	3.99038i	−0.131918	+	0.228489i
$306$	−7.73205			−0.442012
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	2.53590	−	4.39230i	0.144496	−	0.250275i
$309$	−16.3923	+	9.46410i	−0.932526	+	0.538394i
$310$		−	8.19615i		−	0.465510i
$311$	3.80385	+	2.19615i	0.215696	+	0.124532i	0.603956	−	0.797018i	$-0.293590\pi$
$311$	3.80385	+	2.19615i	0.215696	+	0.124532i	−0.388260	+	0.921550i	$0.626924\pi$
$312$	−8.19615	+	14.1962i	−0.464016	+	0.803699i
$313$	8.30385	+	4.79423i	0.469361	+	0.270986i	0.715972	−	0.698129i	$-0.245984\pi$
$313$	8.30385	+	4.79423i	0.469361	+	0.270986i	−0.246611	+	0.969115i	$0.579317\pi$
$314$	9.86603	−	5.69615i	0.556772	−	0.321452i
$315$	−26.7846	+	15.4641i	−1.50914	+	0.871303i
$316$	−1.90192	−	1.09808i	−0.106992	−	0.0617716i
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$	22.3923	+	12.9282i	1.25570	+	0.724978i
$319$		−	9.80385i		−	0.548910i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−18.9282			−1.05483
$323$	−8.19615			−0.456046
$324$	−1.23205	+	2.13397i	−0.0684473	+	0.118554i
$325$			12.0000i			0.665640i
$326$	−4.73205	−	8.19615i	−0.262084	−	0.453943i
$327$		−	11.6603i		−	0.644814i
$328$	5.59808	−	3.23205i	0.309102	−	0.178460i
$329$	11.3205	+	19.6077i	0.624120	+	1.08101i
$330$	−3.00000	−	5.19615i	−0.165145	−	0.286039i
$331$	14.7846	+	8.53590i	0.812636	+	0.469175i	0.847870	−	0.530204i	$-0.177885\pi$
$331$	14.7846	+	8.53590i	0.812636	+	0.469175i	−0.0352347	+	0.999379i	$0.511218\pi$
$332$	5.66025			0.310647
$333$	−22.3205	−	15.4641i	−1.22316	−	0.847428i
$334$	6.92820			0.379094
$335$	−6.29423	−	3.63397i	−0.343890	−	0.198545i
$336$	−5.46410	−	9.46410i	−0.298091	−	0.516309i
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	−19.9186	+	11.5000i	−1.08343	+	0.625518i
$339$		−	21.4641i		−	1.16577i
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$		−	6.00000i		−	0.324918i
$342$	10.5622	−	18.2942i	0.571137	−	0.989239i
$343$	8.00000			0.431959
$344$	2.53590			0.136726
$345$	−11.1962	+	19.3923i	−0.602781	+	1.04405i
$346$	3.40192	−	1.96410i	0.182889	−	0.105591i
$347$		−	28.0526i		−	1.50594i	−0.658055	−	0.752970i	$-0.728620\pi$
$347$		−	28.0526i		−	1.50594i	0.658055	−	0.752970i	$-0.271380\pi$
$348$	−18.2942	−	10.5622i	−0.980674	−	0.566192i
$349$	13.6962	−	23.7224i	0.733138	−	1.26983i	−0.222397	−	0.974956i	$-0.571388\pi$
$349$	13.6962	−	23.7224i	0.733138	−	1.26983i	0.955535	−	0.294877i	$-0.0952785\pi$
$350$	−6.92820	−	4.00000i	−0.370328	−	0.213809i
$351$	20.7846	−	12.0000i	1.10940	−	0.640513i
$352$	1.09808	−	0.633975i	0.0585277	−	0.0337910i
$353$	−5.08846	−	2.93782i	−0.270831	−	0.156364i	0.358434	−	0.933555i	$-0.383311\pi$
$353$	−5.08846	−	2.93782i	−0.270831	−	0.156364i	−0.629265	+	0.777191i	$0.716644\pi$
$354$	−12.9282	+	22.3923i	−0.687126	+	1.19014i
$355$	14.1962	+	8.19615i	0.753454	+	0.435007i
$356$			5.19615i			0.275396i
$357$	16.3923	−	9.46410i	0.867573	−	0.500893i
$358$	11.6603	−	20.1962i	0.616264	−	1.06740i
$359$	26.5359			1.40051			0.700256	−	0.713892i	$-0.253069\pi$
$359$	26.5359			1.40051			0.700256	+	0.713892i	$0.253069\pi$
$360$	−7.73205			−0.407515
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$			5.39230i			0.283413i
$363$	12.8301	+	22.2224i	0.673407	+	1.16638i
$364$		−	24.0000i		−	1.25794i
$365$	−12.5885	+	7.26795i	−0.658910	+	0.380422i
$366$	3.63397	+	6.29423i	0.189951	+	0.329005i
$367$	10.1962	+	17.6603i	0.532235	+	0.921858i	0.999292	+	0.0376305i	$0.0119810\pi$
$367$	10.1962	+	17.6603i	0.532235	+	0.921858i	−0.467057	+	0.884227i	$0.654686\pi$
$368$	−4.09808	−	2.36603i	−0.213627	−	0.123338i
$369$	−28.8564			−1.50220
$370$	−0.866025	+	10.5000i	−0.0450225	+	0.545869i
$371$	−37.8564			−1.96541
$372$	−11.1962	−	6.46410i	−0.580493	−	0.335148i
$373$	−10.8923	−	18.8660i	−0.563982	−	0.976846i	−0.997144	−	0.0755294i	$-0.975935\pi$
$373$	−10.8923	−	18.8660i	−0.563982	−	0.976846i	0.433161	−	0.901316i	$-0.357398\pi$
$374$	1.09808	+	1.90192i	0.0567802	+	0.0983461i
$375$	−28.6865	+	16.5622i	−1.48137	+	0.855267i
$376$			5.66025i			0.291905i
$377$	−23.1962	−	40.1769i	−1.19466	−	2.06922i
$378$			16.0000i			0.822951i
$379$	8.39230	−	14.5359i	0.431084	−	0.746659i	−0.565883	−	0.824485i	$-0.691465\pi$
$379$	8.39230	−	14.5359i	0.431084	−	0.746659i	0.996967	+	0.0778265i	$0.0247980\pi$
$380$	−8.19615			−0.420454
$381$	56.2487			2.88171
$382$	−3.29423	+	5.70577i	−0.168547	+	0.291933i
$383$	1.60770	−	0.928203i	0.0821494	−	0.0474290i	−0.458363	−	0.888765i	$-0.651564\pi$
$383$	1.60770	−	0.928203i	0.0821494	−	0.0474290i	0.540512	+	0.841336i	$0.318231\pi$
$384$		−	2.73205i		−	0.139419i
$385$	7.60770	+	4.39230i	0.387724	+	0.223853i
$386$	6.06218	−	10.5000i	0.308557	−	0.534436i
$387$	−9.80385	−	5.66025i	−0.498358	−	0.287727i
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	−9.69615	+	5.59808i	−0.491614	+	0.283834i	−0.725244	−	0.688492i	$-0.758273\pi$
$389$	−9.69615	+	5.59808i	−0.491614	+	0.283834i	0.233630	+	0.972326i	$0.424940\pi$
$390$	−24.5885	−	14.1962i	−1.24508	−	0.718850i
$391$	4.09808	−	7.09808i	0.207249	−	0.358965i
$392$	7.79423	+	4.50000i	0.393668	+	0.227284i
$393$			6.00000i			0.302660i
$394$	−7.20577	+	4.16025i	−0.363022	+	0.209591i
$395$	1.90192	−	3.29423i	0.0956962	−	0.165751i
$396$	−5.66025			−0.284438
$397$	−5.00000			−0.250943			−0.125471	−	0.992097i	$-0.540044\pi$
$397$	−5.00000			−0.250943			−0.125471	+	0.992097i	$0.540044\pi$
$398$	−9.46410	+	16.3923i	−0.474393	+	0.821672i
$399$			51.7128i			2.58888i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$			26.7846i			1.33756i	0.743461	+	0.668780i	$0.233183\pi$
$401$			26.7846i			1.33756i	−0.743461	+	0.668780i	$0.766817\pi$
$402$	−9.92820	+	5.73205i	−0.495174	+	0.285889i
$403$	−14.1962	−	24.5885i	−0.707161	−	1.22484i
$404$	3.23205	+	5.59808i	0.160801	+	0.278515i
$405$	−3.69615	−	2.13397i	−0.183663	−	0.106038i
$406$	30.9282			1.53494
$407$	−0.633975	+	7.68653i	−0.0314250	+	0.381007i
$408$	4.73205			0.234271
$409$	2.08846	+	1.20577i	0.103268	+	0.0596216i	0.550744	−	0.834674i	$-0.314344\pi$
$409$	2.08846	+	1.20577i	0.103268	+	0.0596216i	−0.447477	+	0.894296i	$0.647677\pi$
$410$	5.59808	+	9.69615i	0.276469	+	0.478859i
$411$	−10.0981	−	17.4904i	−0.498101	−	0.862737i
$412$	6.00000	−	3.46410i	0.295599	−	0.170664i
$413$		−	37.8564i		−	1.86279i
$414$	10.5622	+	18.2942i	0.519103	+	0.899112i
$415$			9.80385i			0.481252i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	33.3205			1.63171
$418$	−6.00000			−0.293470
$419$	−18.9282	+	32.7846i	−0.924703	+	1.60163i	−0.132665	+	0.991161i	$0.542354\pi$
$419$	−18.9282	+	32.7846i	−0.924703	+	1.60163i	−0.792038	+	0.610472i	$0.790980\pi$
$420$	16.3923	−	9.46410i	0.799863	−	0.461801i
$421$			20.6603i			1.00692i	0.864019	+	0.503460i	$0.167940\pi$
$421$			20.6603i			1.00692i	−0.864019	+	0.503460i	$0.832060\pi$
$422$	7.26795	+	4.19615i	0.353798	+	0.204266i
$423$	12.6340	−	21.8827i	0.614285	−	1.06397i
$424$	−8.19615	−	4.73205i	−0.398040	−	0.229809i
$425$	3.00000	−	1.73205i	0.145521	−	0.0840168i
$426$	22.3923	−	12.9282i	1.08491	−	0.626373i
$427$	−9.21539	−	5.32051i	−0.445964	−	0.257477i
$428$	2.19615	−	3.80385i	0.106155	−	0.183866i
$429$	−18.0000	−	10.3923i	−0.869048	−	0.501745i
$430$			4.39230i			0.211816i
$431$	13.9019	−	8.02628i	0.669632	−	0.386612i	−0.126305	−	0.991991i	$-0.540312\pi$
$431$	13.9019	−	8.02628i	0.669632	−	0.386612i	0.795937	+	0.605379i	$0.206979\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−33.3923			−1.60473			−0.802366	−	0.596832i	$-0.796426\pi$
$433$	−33.3923			−1.60473			−0.802366	+	0.596832i	$0.796426\pi$
$434$	18.9282			0.908583
$435$	18.2942	−	31.6865i	0.877141	−	1.51925i
$436$			4.26795i			0.204398i
$437$	11.1962	+	19.3923i	0.535585	+	0.927660i
$438$			22.9282i			1.09555i
$439$	−8.19615	+	4.73205i	−0.391181	+	0.225848i	−0.682672	−	0.730725i	$-0.739182\pi$
$439$	−8.19615	+	4.73205i	−0.391181	+	0.225848i	0.291491	+	0.956574i	$0.405849\pi$
$440$	1.09808	+	1.90192i	0.0523487	+	0.0906707i
$441$	−20.0885	−	34.7942i	−0.956593	−	1.65687i
$442$	9.00000	+	5.19615i	0.428086	+	0.247156i
$443$	−2.53590			−0.120484			−0.0602421	−	0.998184i	$-0.519187\pi$
$443$	−2.53590			−0.120484			−0.0602421	+	0.998184i	$0.519187\pi$
$444$	13.6603	+	9.46410i	0.648287	+	0.449146i
$445$	−9.00000			−0.426641
$446$	−7.43782	−	4.29423i	−0.352191	−	0.203338i
$447$	13.5622	+	23.4904i	0.641469	+	1.11106i
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	−21.5885	+	12.4641i	−1.01882	+	0.588217i	−0.913763	−	0.406249i	$-0.866837\pi$
$449$	−21.5885	+	12.4641i	−1.01882	+	0.588217i	−0.105060	+	0.994466i	$0.533503\pi$
$450$			8.92820i			0.420880i
$451$	4.09808	+	7.09808i	0.192971	+	0.334235i
$452$			7.85641i			0.369534i
$453$	16.6603	−	28.8564i	0.782767	−	1.35579i
$454$	−4.73205			−0.222086
$455$	41.5692			1.94880
$456$	−6.46410	+	11.1962i	−0.302709	+	0.524308i
$457$	17.3038	−	9.99038i	0.809440	−	0.467330i	−0.0373215	−	0.999303i	$-0.511883\pi$
$457$	17.3038	−	9.99038i	0.809440	−	0.467330i	0.846761	+	0.531973i	$0.178549\pi$
$458$		−	19.0000i		−	0.887812i
$459$	−6.00000	−	3.46410i	−0.280056	−	0.161690i
$460$	4.09808	−	7.09808i	0.191074	−	0.330950i
$461$	−29.1962	−	16.8564i	−1.35980	−	0.785081i	−0.370204	−	0.928951i	$-0.620712\pi$
$461$	−29.1962	−	16.8564i	−1.35980	−	0.785081i	−0.989597	+	0.143869i	$0.954045\pi$
$462$	12.0000	−	6.92820i	0.558291	−	0.322329i
$463$	−12.5885	+	7.26795i	−0.585035	+	0.337770i	−0.763132	−	0.646243i	$-0.776339\pi$
$463$	−12.5885	+	7.26795i	−0.585035	+	0.337770i	0.178097	+	0.984013i	$0.443006\pi$
$464$	6.69615	+	3.86603i	0.310861	+	0.179476i
$465$	11.1962	−	19.3923i	0.519209	−	0.899297i
$466$	21.9904	+	12.6962i	1.01868	+	0.588138i
$467$			30.2487i			1.39974i	0.714269	+	0.699872i	$0.246760\pi$
$467$			30.2487i			1.39974i	−0.714269	+	0.699872i	$0.753240\pi$
$468$	−23.1962	+	13.3923i	−1.07224	+	0.619060i
$469$	8.39230	−	14.5359i	0.387521	−	0.671205i
$470$	−9.80385			−0.452218
$471$	31.1244			1.43413
$472$	4.73205	−	8.19615i	0.217810	−	0.377258i
$473$			3.21539i			0.147844i
$474$	−3.00000	−	5.19615i	−0.137795	−	0.238667i
$475$			9.46410i			0.434243i
$476$	−6.00000	+	3.46410i	−0.275010	+	0.158777i
$477$	21.1244	+	36.5885i	0.967218	+	1.67527i
$478$	−9.46410	−	16.3923i	−0.432878	−	0.749767i
$479$	−8.19615	−	4.73205i	−0.374492	−	0.216213i	0.300927	−	0.953647i	$-0.402704\pi$
$479$	−8.19615	−	4.73205i	−0.374492	−	0.216213i	−0.675419	+	0.737434i	$0.736037\pi$
$480$	4.73205			0.215988
$481$	15.5885	+	33.0000i	0.710772	+	1.50467i
$482$	−18.0000			−0.819878
$483$	−44.7846	−	25.8564i	−2.03777	−	1.17651i
$484$	−4.69615	−	8.13397i	−0.213461	−	0.369726i
$485$	4.50000	+	7.79423i	0.204334	+	0.353918i
$486$	−16.2224	+	9.36603i	−0.735864	+	0.424852i
$487$			28.0526i			1.27118i	0.772026	+	0.635591i	$0.219244\pi$
$487$			28.0526i			1.27118i	−0.772026	+	0.635591i	$0.780756\pi$
$488$	−1.33013	−	2.30385i	−0.0602120	−	0.104290i
$489$		−	25.8564i		−	1.16927i
$490$	−7.79423	+	13.5000i	−0.352107	+	0.609868i
$491$	28.9808			1.30788			0.653942	−	0.756545i	$-0.273114\pi$
$491$	28.9808			1.30788			0.653942	+	0.756545i	$0.273114\pi$
$492$	17.6603			0.796186
$493$	−6.69615	+	11.5981i	−0.301580	+	0.522351i
$494$	−24.5885	+	14.1962i	−1.10629	+	0.638715i
$495$		−	9.80385i		−	0.440650i
$496$	4.09808	+	2.36603i	0.184009	+	0.106238i
$497$	−18.9282	+	32.7846i	−0.849046	+	1.47059i
$498$	13.3923	+	7.73205i	0.600124	+	0.346481i
$499$	1.90192	−	1.09808i	0.0851418	−	0.0491566i	−0.456825	−	0.889557i	$-0.651013\pi$
$499$	1.90192	−	1.09808i	0.0851418	−	0.0491566i	0.541966	+	0.840400i	$0.317680\pi$
$500$	10.5000	−	6.06218i	0.469574	−	0.271109i
$501$	16.3923	+	9.46410i	0.732354	+	0.422825i
$502$	−9.46410	+	16.3923i	−0.422404	+	0.731624i
$503$	16.0981	+	9.29423i	0.717778	+	0.414409i	0.813934	−	0.580957i	$-0.197322\pi$
$503$	16.0981	+	9.29423i	0.717778	+	0.414409i	−0.0961565	+	0.995366i	$0.530655\pi$
$504$		−	17.8564i		−	0.795388i
$505$	−9.69615	+	5.59808i	−0.431473	+	0.249111i
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	−62.8372			−2.79070
$508$	−20.5885			−0.913465
$509$	18.8205	−	32.5981i	0.834204	−	1.44488i	−0.0604722	−	0.998170i	$-0.519261\pi$
$509$	18.8205	−	32.5981i	0.834204	−	1.44488i	0.894677	−	0.446714i	$-0.147406\pi$
$510$			8.19615i			0.362932i
$511$	−16.7846	−	29.0718i	−0.742507	−	1.28606i
$512$			1.00000i			0.0441942i
$513$	16.3923	−	9.46410i	0.723738	−	0.417850i
$514$	0.401924	+	0.696152i	0.0177281	+	0.0307060i
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$	6.00000	+	3.46410i	0.264135	+	0.152499i
$517$	−7.17691			−0.315640
$518$	−24.2487	−	2.00000i	−1.06543	−	0.0878750i
$519$	10.7321			0.471085
$520$	9.00000	+	5.19615i	0.394676	+	0.227866i
$521$	−16.7321	−	28.9808i	−0.733044	−	1.26967i	−0.955576	−	0.294745i	$-0.904765\pi$
$521$	−16.7321	−	28.9808i	−0.733044	−	1.26967i	0.222532	−	0.974925i	$-0.428568\pi$
$522$	−17.2583	−	29.8923i	−0.755377	−	1.30835i
$523$	16.0981	−	9.29423i	0.703920	−	0.406408i	−0.104886	−	0.994484i	$-0.533448\pi$
$523$	16.0981	−	9.29423i	0.703920	−	0.406408i	0.808806	+	0.588076i	$0.200114\pi$
$524$		−	2.19615i		−	0.0959394i
$525$	−10.9282	−	18.9282i	−0.476946	−	0.826095i
$526$		−	11.3205i		−	0.493598i
$527$	−4.09808	+	7.09808i	−0.178515	+	0.309197i
$528$	3.46410			0.150756
$529$	0.607695			0.0264215
$530$	8.19615	−	14.1962i	0.356018	−	0.616641i
$531$	−36.5885	+	21.1244i	−1.58780	+	0.916719i
$532$		−	18.9282i		−	0.820642i
$533$	33.5885	+	19.3923i	1.45488	+	0.839974i
$534$	−7.09808	+	12.2942i	−0.307164	+	0.532023i
$535$	6.58846	+	3.80385i	0.284844	+	0.164455i
$536$	3.63397	−	2.09808i	0.156964	−	0.0906231i
$537$	55.1769	−	31.8564i	2.38106	−	1.37471i
$538$	24.5885	+	14.1962i	1.06008	+	0.612040i
$539$	−5.70577	+	9.88269i	−0.245765	+	0.425677i
$540$	−6.00000	−	3.46410i	−0.258199	−	0.149071i
$541$		−	27.5885i		−	1.18612i	−0.805158	−	0.593060i	$-0.797920\pi$
$541$		−	27.5885i		−	1.18612i	0.805158	−	0.593060i	$-0.202080\pi$
$542$	14.3660	−	8.29423i	0.617074	−	0.356268i
$543$	−7.36603	+	12.7583i	−0.316106	+	0.547512i
$544$	−1.73205			−0.0742611
$545$	−7.39230			−0.316652
$546$	32.7846	−	56.7846i	1.40305	−	2.43016i
$547$			18.5885i			0.794785i	0.917649	+	0.397393i	$0.130085\pi$
$547$			18.5885i			0.794785i	−0.917649	+	0.397393i	$0.869915\pi$
$548$	3.69615	+	6.40192i	0.157892	+	0.273477i
$549$			11.8756i			0.506840i
$550$	2.19615	−	1.26795i	0.0936443	−	0.0540655i
$551$	−18.2942	−	31.6865i	−0.779360	−	1.34989i
$552$	−6.46410	−	11.1962i	−0.275130	−	0.476540i
$553$	7.60770	+	4.39230i	0.323512	+	0.186780i
$554$	−17.1962			−0.730595
$555$	−16.3923	+	23.6603i	−0.695815	+	1.00432i
$556$	−12.1962			−0.517232
$557$	29.8923	+	17.2583i	1.26658	+	0.731259i	0.974339	−	0.225086i	$-0.0722665\pi$
$557$	29.8923	+	17.2583i	1.26658	+	0.731259i	0.292239	+	0.956345i	$0.405600\pi$
$558$	−10.5622	−	18.2942i	−0.447133	−	0.774456i
$559$	7.60770	+	13.1769i	0.321771	+	0.557324i
$560$	−6.00000	+	3.46410i	−0.253546	+	0.146385i
$561$			6.00000i			0.253320i
$562$	−0.401924	−	0.696152i	−0.0169541	−	0.0293654i
$563$			42.5885i			1.79489i	0.441127	+	0.897445i	$0.354579\pi$
$563$			42.5885i			1.79489i	−0.441127	+	0.897445i	$0.645421\pi$
$564$	−7.73205	+	13.3923i	−0.325578	+	0.563918i
$565$	−13.6077			−0.572480
$566$	9.46410			0.397806
$567$	4.92820	−	8.53590i	0.206965	−	0.358474i
$568$	−8.19615	+	4.73205i	−0.343903	+	0.198552i
$569$			16.5167i			0.692414i	0.938158	+	0.346207i	$0.112531\pi$
$569$			16.5167i			0.692414i	−0.938158	+	0.346207i	$0.887469\pi$
$570$	−19.3923	−	11.1962i	−0.812254	−	0.468955i
$571$	18.4904	−	32.0263i	0.773798	−	1.34026i	−0.161669	−	0.986845i	$-0.551688\pi$
$571$	18.4904	−	32.0263i	0.773798	−	1.34026i	0.935467	−	0.353413i	$-0.114979\pi$
$572$	6.58846	+	3.80385i	0.275477	+	0.159047i
$573$	−15.5885	+	9.00000i	−0.651217	+	0.375980i
$574$	−22.3923	+	12.9282i	−0.934637	+	0.539613i
$575$	−8.19615	−	4.73205i	−0.341803	−	0.197340i
$576$	2.23205	−	3.86603i	0.0930021	−	0.161084i
$577$	−27.5885	−	15.9282i	−1.14852	−	0.663100i	−0.199996	−	0.979797i	$-0.564093\pi$
$577$	−27.5885	−	15.9282i	−1.14852	−	0.663100i	−0.948527	+	0.316697i	$0.897426\pi$
$578$			14.0000i			0.582323i
$579$	28.6865	−	16.5622i	1.19217	−	0.688301i
$580$	−6.69615	+	11.5981i	−0.278043	+	0.481584i
$581$	−22.6410			−0.939308
$582$	14.1962			0.588449
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$		−	8.39230i		−	0.347276i
$585$	−23.1962	−	40.1769i	−0.959043	−	1.66111i
$586$			4.60770i			0.190342i
$587$	13.9019	−	8.02628i	0.573794	−	0.331280i	−0.184869	−	0.982763i	$-0.559186\pi$
$587$	13.9019	−	8.02628i	0.573794	−	0.331280i	0.758663	+	0.651483i	$0.225853\pi$
$588$	12.2942	+	21.2942i	0.507005	+	0.878159i
$589$	−11.1962	−	19.3923i	−0.461329	−	0.799046i
$590$	14.1962	+	8.19615i	0.584446	+	0.337430i
$591$	−22.7321			−0.935072
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	30.4641			1.25101			0.625505	−	0.780220i	$-0.284893\pi$
$593$	30.4641			1.25101			0.625505	+	0.780220i	$0.284893\pi$
$594$	−4.39230	−	2.53590i	−0.180218	−	0.104049i
$595$	−6.00000	−	10.3923i	−0.245976	−	0.426043i
$596$	−4.96410	−	8.59808i	−0.203338	−	0.352191i
$597$	−44.7846	+	25.8564i	−1.83291	+	1.05823i
$598$		−	28.3923i		−	1.16105i
$599$	−0.633975	−	1.09808i	−0.0259035	−	0.0448662i	0.852783	−	0.522265i	$-0.174913\pi$
$599$	−0.633975	−	1.09808i	−0.0259035	−	0.0448662i	−0.878687	+	0.477399i	$0.841580\pi$
$600$		−	5.46410i		−	0.223071i
$601$	−7.89230	+	13.6699i	−0.321934	+	0.557606i	−0.980887	−	0.194578i	$-0.937666\pi$
$601$	−7.89230	+	13.6699i	−0.321934	+	0.557606i	0.658953	+	0.752184i	$0.271000\pi$
$602$	−10.1436			−0.413422
$603$	−18.7321			−0.762828
$604$	−6.09808	+	10.5622i	−0.248127	+	0.429769i
$605$	14.0885	−	8.13397i	0.572777	−	0.330693i
$606$			17.6603i			0.717399i
$607$	−34.6865	−	20.0263i	−1.40788	−	0.812842i	−0.412699	−	0.910867i	$-0.635414\pi$
$607$	−34.6865	−	20.0263i	−1.40788	−	0.812842i	−0.995184	+	0.0980258i	$0.968747\pi$
$608$	2.36603	−	4.09808i	0.0959550	−	0.166199i
$609$	73.1769	+	42.2487i	2.96528	+	1.71200i
$610$	3.99038	−	2.30385i	0.161566	−	0.0932801i
$611$	−29.4115	+	16.9808i	−1.18986	+	0.686968i
$612$	6.69615	+	3.86603i	0.270676	+	0.156275i
$613$	−16.6962	+	28.9186i	−0.674351	+	1.16801i	0.302307	+	0.953211i	$0.402243\pi$
$613$	−16.6962	+	28.9186i	−0.674351	+	1.16801i	−0.976658	+	0.214800i	$0.931090\pi$
$614$	3.46410	+	2.00000i	0.139800	+	0.0807134i
$615$			30.5885i			1.23345i
$616$	−4.39230	+	2.53590i	−0.176971	+	0.102174i
$617$	5.66025	−	9.80385i	0.227873	−	0.394688i	−0.729304	−	0.684189i	$-0.760156\pi$
$617$	5.66025	−	9.80385i	0.227873	−	0.394688i	0.957178	+	0.289501i	$0.0934895\pi$
$618$	18.9282			0.761404
$619$	−41.1769			−1.65504			−0.827520	−	0.561436i	$-0.810249\pi$
$619$	−41.1769			−1.65504			−0.827520	+	0.561436i	$0.810249\pi$
$620$	−4.09808	+	7.09808i	−0.164583	+	0.285066i
$621$			18.9282i			0.759563i
$622$	−2.19615	−	3.80385i	−0.0880577	−	0.152520i
$623$		−	20.7846i		−	0.832718i
$624$	14.1962	−	8.19615i	0.568301	−	0.328109i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−4.79423	−	8.30385i	−0.191616	−	0.331888i
$627$	−14.1962	−	8.19615i	−0.566940	−	0.327323i
$628$	−11.3923			−0.454602
$629$	6.00000	−	8.66025i	0.239236	−	0.345307i
$630$	30.9282			1.23221
$631$	10.6865	+	6.16987i	0.425424	+	0.245619i	0.697395	−	0.716687i	$-0.254342\pi$
$631$	10.6865	+	6.16987i	0.425424	+	0.245619i	−0.271971	+	0.962305i	$0.587676\pi$
$632$	1.09808	+	1.90192i	0.0436791	+	0.0756545i
$633$	11.4641	+	19.8564i	0.455657	+	0.789221i
$634$	7.79423	−	4.50000i	0.309548	−	0.178718i
$635$		−	35.6603i		−	1.41513i
$636$	−12.9282	−	22.3923i	−0.512637	−	0.887913i
$637$			54.0000i			2.13956i
$638$	−4.90192	+	8.49038i	−0.194069	+	0.336137i
$639$	42.2487			1.67133
$640$	−1.73205			−0.0684653
$641$	23.4282	−	40.5788i	0.925358	−	1.60277i	0.134375	−	0.990931i	$-0.457097\pi$
$641$	23.4282	−	40.5788i	0.925358	−	1.60277i	0.790984	−	0.611837i	$-0.209569\pi$
$642$	10.3923	−	6.00000i	0.410152	−	0.236801i
$643$		−	9.12436i		−	0.359829i	−0.983682	−	0.179915i	$-0.942418\pi$
$643$		−	9.12436i		−	0.359829i	0.983682	−	0.179915i	$-0.0575822\pi$
$644$	16.3923	+	9.46410i	0.645947	+	0.372938i
$645$	−6.00000	+	10.3923i	−0.236250	+	0.409197i
$646$	7.09808	+	4.09808i	0.279270	+	0.161237i
$647$	−8.19615	+	4.73205i	−0.322224	+	0.186036i	−0.652383	−	0.757889i	$-0.726231\pi$
$647$	−8.19615	+	4.73205i	−0.322224	+	0.186036i	0.330159	+	0.943925i	$0.392897\pi$
$648$	2.13397	−	1.23205i	0.0838304	−	0.0483995i
$649$	10.3923	+	6.00000i	0.407934	+	0.235521i
$650$	6.00000	−	10.3923i	0.235339	−	0.407620i
$651$	44.7846	+	25.8564i	1.75525	+	1.01339i
$652$			9.46410i			0.370643i
$653$	5.89230	−	3.40192i	0.230584	−	0.133128i	−0.380258	−	0.924881i	$-0.624165\pi$
$653$	5.89230	−	3.40192i	0.230584	−	0.133128i	0.610841	+	0.791753i	$0.290831\pi$
$654$	−5.83013	+	10.0981i	−0.227976	+	0.394866i
$655$	3.80385			0.148629
$656$	−6.46410			−0.252381
$657$	−18.7321	+	32.4449i	−0.730807	+	1.26579i
$658$		−	22.6410i		−	0.882639i
$659$	−7.26795	−	12.5885i	−0.283119	−	0.490377i	0.689032	−	0.724731i	$-0.258036\pi$
$659$	−7.26795	−	12.5885i	−0.283119	−	0.490377i	−0.972151	+	0.234354i	$0.924703\pi$
$660$			6.00000i			0.233550i
$661$	25.2846	−	14.5981i	0.983457	−	0.567799i	0.0801452	−	0.996783i	$-0.474462\pi$
$661$	25.2846	−	14.5981i	0.983457	−	0.567799i	0.903312	+	0.428984i	$0.141128\pi$
$662$	−8.53590	−	14.7846i	−0.331757	−	0.574620i
$663$	14.1962	+	24.5885i	0.551333	+	0.954937i
$664$	−4.90192	−	2.83013i	−0.190232	−	0.109830i
$665$	32.7846			1.27133
$666$	11.5981	+	24.5526i	0.449416	+	0.951392i
$667$	36.5885			1.41671
$668$	−6.00000	−	3.46410i	−0.232147	−	0.134030i
$669$	−11.7321	−	20.3205i	−0.453587	−	0.785636i
$670$	3.63397	+	6.29423i	0.140393	+	0.243167i
$671$	2.92116	−	1.68653i	0.112770	−	0.0651079i
$672$			10.9282i			0.421565i
$673$	6.19615	+	10.7321i	0.238844	+	0.413690i	0.960383	−	0.278684i	$-0.0898982\pi$
$673$	6.19615	+	10.7321i	0.238844	+	0.413690i	−0.721539	+	0.692374i	$0.756565\pi$
$674$		−	7.00000i		−	0.269630i
$675$	−4.00000	+	6.92820i	−0.153960	+	0.266667i
$676$	23.0000			0.884615
$677$	7.14359			0.274551			0.137275	−	0.990533i	$-0.456165\pi$
$677$	7.14359			0.274551			0.137275	+	0.990533i	$0.456165\pi$
$678$	−10.7321	+	18.5885i	−0.412162	+	0.713885i
$679$	−18.0000	+	10.3923i	−0.690777	+	0.398820i
$680$		−	3.00000i		−	0.115045i
$681$	−11.1962	−	6.46410i	−0.429037	−	0.247705i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	26.7846	+	15.4641i	1.02488	+	0.591717i	0.915515	−	0.402284i	$-0.131783\pi$
$683$	26.7846	+	15.4641i	1.02488	+	0.591717i	0.109370	+	0.994001i	$0.465117\pi$
$684$	−18.2942	+	10.5622i	−0.699497	+	0.403855i
$685$	−11.0885	+	6.40192i	−0.423668	+	0.244605i
$686$	−6.92820	−	4.00000i	−0.264520	−	0.152721i
$687$	25.9545	−	44.9545i	0.990225	−	1.71512i
$688$	−2.19615	−	1.26795i	−0.0837275	−	0.0483401i
$689$		−	56.7846i		−	2.16332i
$690$	19.3923	−	11.1962i	0.738252	−	0.426230i
$691$	5.90192	−	10.2224i	0.224520	−	0.388880i	−0.731655	−	0.681675i	$-0.761252\pi$
$691$	5.90192	−	10.2224i	0.224520	−	0.388880i	0.956175	+	0.292795i	$0.0945853\pi$
$692$	−3.92820			−0.149328
$693$	22.6410			0.860061
$694$	−14.0263	+	24.2942i	−0.532430	+	0.922196i
$695$		−	21.1244i		−	0.801292i
$696$	10.5622	+	18.2942i	0.400358	+	0.693441i
$697$		−	11.1962i		−	0.424085i
$698$	−23.7224	+	13.6962i	−0.897907	+	0.518407i
$699$	34.6865	+	60.0788i	1.31197	+	2.27239i
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	22.3923	+	12.9282i	0.845746	+	0.488291i	0.859213	−	0.511618i	$-0.170954\pi$
$701$	22.3923	+	12.9282i	0.845746	+	0.488291i	−0.0134675	+	0.999909i	$0.504287\pi$
$702$	−24.0000			−0.905822
$703$	12.2942	+	26.0263i	0.463686	+	0.981600i
$704$	−1.26795			−0.0477876
$705$	−23.1962	−	13.3923i	−0.873618	−	0.504383i
$706$	2.93782	+	5.08846i	0.110566	+	0.191507i
$707$	−12.9282	−	22.3923i	−0.486215	−	0.842149i
$708$	22.3923	−	12.9282i	0.841554	−	0.485872i
$709$		−	30.0000i		−	1.12667i	−0.826227	−	0.563337i	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	−8.19615	−	14.1962i	−0.307596	−	0.532772i
$711$		−	9.80385i		−	0.367673i
$712$	2.59808	−	4.50000i	0.0973670	−	0.168645i
$713$	22.3923			0.838598
$714$	−18.9282			−0.708370
$715$	−6.58846	+	11.4115i	−0.246394	+	0.426768i
$716$	−20.1962	+	11.6603i	−0.754766	+	0.435764i
$717$		−	51.7128i		−	1.93125i
$718$	−22.9808	−	13.2679i	−0.857634	−	0.495155i
$719$	−13.2224	+	22.9019i	−0.493114	+	0.854098i	−0.999969	−	0.00793367i	$-0.997475\pi$
$719$	−13.2224	+	22.9019i	−0.493114	+	0.854098i	0.506855	+	0.862031i	$0.330808\pi$
$720$	6.69615	+	3.86603i	0.249551	+	0.144078i
$721$	−24.0000	+	13.8564i	−0.893807	+	0.516040i
$722$	−2.93782	+	1.69615i	−0.109334	+	0.0631243i
$723$	−42.5885	−	24.5885i	−1.58388	−	0.914455i
$724$	2.69615	−	4.66987i	0.100202	−	0.173554i
$725$	13.3923	+	7.73205i	0.497378	+	0.287161i
$726$		−	25.6603i		−	0.952341i
$727$	−22.3923	+	12.9282i	−0.830485	+	0.479481i	−0.854019	−	0.520243i	$-0.825842\pi$
$727$	−22.3923	+	12.9282i	−0.830485	+	0.479481i	0.0235340	+	0.999723i	$0.492508\pi$
$728$	−12.0000	+	20.7846i	−0.444750	+	0.770329i
$729$	−43.7846			−1.62165
$730$	14.5359			0.537998
$731$	2.19615	−	3.80385i	0.0812276	−	0.140690i
$732$		−	7.26795i		−	0.268631i
$733$	−18.1962	−	31.5167i	−0.672090	−	1.16409i	−0.977310	−	0.211813i	$-0.932063\pi$
$733$	−18.1962	−	31.5167i	−0.672090	−	1.16409i	0.305220	−	0.952282i	$-0.401270\pi$
$734$		−	20.3923i		−	0.752694i
$735$	−36.8827	+	21.2942i	−1.36044	+	0.785449i
$736$	2.36603	+	4.09808i	0.0872129	+	0.151057i
$737$	2.66025	+	4.60770i	0.0979917	+	0.169727i
$738$	24.9904	+	14.4282i	0.919909	+	0.531110i
$739$	−44.9808			−1.65464			−0.827322	−	0.561728i	$-0.810137\pi$
$739$	−44.9808			−1.65464			−0.827322	+	0.561728i	$0.810137\pi$
$740$	6.00000	−	8.66025i	0.220564	−	0.318357i
$741$	−77.5692			−2.84958
$742$	32.7846	+	18.9282i	1.20356	+	0.694876i
$743$	−11.9545	−	20.7058i	−0.438567	−	0.759621i	0.559012	−	0.829160i	$-0.311181\pi$
$743$	−11.9545	−	20.7058i	−0.438567	−	0.759621i	−0.997579	+	0.0695386i	$0.977847\pi$
$744$	6.46410	+	11.1962i	0.236985	+	0.410471i
$745$	14.8923	−	8.59808i	0.545612	−	0.315009i
$746$			21.7846i			0.797591i
$747$	12.6340	+	21.8827i	0.462253	+	0.800646i
$748$		−	2.19615i		−	0.0802993i
$749$	−8.78461	+	15.2154i	−0.320983	+	0.555958i
$750$	33.1244			1.20953
$751$	−15.6077			−0.569533			−0.284766	−	0.958597i	$-0.591916\pi$
$751$	−15.6077			−0.569533			−0.284766	+	0.958597i	$0.591916\pi$
$752$	2.83013	−	4.90192i	0.103204	−	0.178755i
$753$	−44.7846	+	25.8564i	−1.63204	+	0.942260i
$754$			46.3923i			1.68951i
$755$	−18.2942	−	10.5622i	−0.665795	−	0.384397i
$756$	8.00000	−	13.8564i	0.290957	−	0.503953i
$757$	−6.69615	−	3.86603i	−0.243376	−	0.140513i	0.373352	−	0.927690i	$-0.378209\pi$
$757$	−6.69615	−	3.86603i	−0.243376	−	0.140513i	−0.616727	+	0.787177i	$0.711542\pi$
$758$	−14.5359	+	8.39230i	−0.527968	+	0.304822i
$759$	14.1962	−	8.19615i	0.515288	−	0.297501i
$760$	7.09808	+	4.09808i	0.257474	+	0.148653i
$761$	1.16025	−	2.00962i	0.0420592	−	0.0728486i	−0.844229	−	0.535982i	$-0.819942\pi$
$761$	1.16025	−	2.00962i	0.0420592	−	0.0728486i	0.886289	+	0.463133i	$0.153275\pi$
$762$	−48.7128	−	28.1244i	−1.76468	−	1.01884i
$763$		−	17.0718i		−	0.618041i
$764$	5.70577	−	3.29423i	0.206428	−	0.119181i
$765$	−6.69615	+	11.5981i	−0.242100	+	0.419329i
$766$	−1.85641			−0.0670747
$767$	56.7846			2.05037
$768$	−1.36603	+	2.36603i	−0.0492922	+	0.0853766i
$769$		−	33.7128i		−	1.21572i	−0.794046	−	0.607858i	$-0.792029\pi$
$769$		−	33.7128i		−	1.21572i	0.794046	−	0.607858i	$-0.207971\pi$
$770$	−4.39230	−	7.60770i	−0.158288	−	0.274162i
$771$			2.19615i			0.0790925i
$772$	−10.5000	+	6.06218i	−0.377903	+	0.218183i
$773$	4.03590	+	6.99038i	0.145161	+	0.251427i	0.929433	−	0.368991i	$-0.120297\pi$
$773$	4.03590	+	6.99038i	0.145161	+	0.251427i	−0.784272	+	0.620417i	$0.786963\pi$
$774$	5.66025	+	9.80385i	0.203454	+	0.352392i
$775$	8.19615	+	4.73205i	0.294414	+	0.169980i
$776$	−5.19615			−0.186531
$777$	−54.6410	−	37.8564i	−1.96024	−	1.35809i
$778$	11.1962			0.401402
$779$	26.4904	+	15.2942i	0.949116	+	0.547973i
$780$	14.1962	+	24.5885i	0.508304	+	0.880408i
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	−7.09808	+	4.09808i	−0.253827	+	0.146547i
$783$		−	30.9282i		−	1.10528i
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$		−	19.7321i		−	0.704267i
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	−29.1769			−1.04004			−0.520022	−	0.854153i	$-0.674076\pi$
$787$	−29.1769			−1.04004			−0.520022	+	0.854153i	$0.674076\pi$
$788$	8.32051			0.296406
$789$	15.4641	−	26.7846i	0.550537	−	0.953557i
$790$	−3.29423	+	1.90192i	−0.117203	+	0.0676674i
$791$		−	31.4256i		−	1.11737i
$792$	4.90192	+	2.83013i	0.174182	+	0.100564i
$793$	7.98076	−	13.8231i	0.283405	−	0.490872i
$794$	4.33013	+	2.50000i	0.153670	+	0.0887217i
$795$	38.7846	−	22.3923i	1.37555	−	0.794173i
$796$	16.3923	−	9.46410i	0.581010	−	0.335446i
$797$	18.0000	+	10.3923i	0.637593	+	0.368114i	0.783687	−	0.621156i	$-0.213337\pi$
$797$	18.0000	+	10.3923i	0.637593	+	0.368114i	−0.146094	+	0.989271i	$0.546670\pi$
$798$	25.8564	−	44.7846i	0.915307	−	1.58536i
$799$	8.49038	+	4.90192i	0.300368	+	0.173418i
$800$			2.00000i			0.0707107i
$801$	−20.0885	+	11.5981i	−0.709791	+	0.409798i
$802$	13.3923	−	23.1962i	0.472899	−	0.819085i
$803$	10.6410			0.375513
$804$	11.4641			0.404308
$805$	−16.3923	+	28.3923i	−0.577753	+	1.00070i
$806$			28.3923i			1.00008i
$807$	38.7846	+	67.1769i	1.36528	+	2.36474i
$808$		−	6.46410i		−	0.227406i
$809$	−37.1769	+	21.4641i	−1.30707	+	0.754638i	−0.981606	−	0.190917i	$-0.938854\pi$
$809$	−37.1769	+	21.4641i	−1.30707	+	0.754638i	−0.325464	+	0.945554i	$0.605521\pi$
$810$	2.13397	+	3.69615i	0.0749802	+	0.129870i
$811$	7.80385	+	13.5167i	0.274030	+	0.474634i	0.969890	−	0.243543i	$-0.0783099\pi$
$811$	7.80385	+	13.5167i	0.274030	+	0.474634i	−0.695860	+	0.718178i	$0.744977\pi$
$812$	−26.7846	−	15.4641i	−0.939956	−	0.542684i
$813$	45.3205			1.58946
$814$	4.39230	−	6.33975i	0.153950	−	0.222208i
$815$	−16.3923			−0.574197
$816$	−4.09808	−	2.36603i	−0.143461	−	0.0828275i
$817$	6.00000	+	10.3923i	0.209913	+	0.363581i
$818$	−1.20577	−	2.08846i	−0.0421588	−	0.0730212i
$819$	92.7846	−	53.5692i	3.24216	−	1.87186i
$820$		−	11.1962i		−	0.390987i
$821$	22.7321	+	39.3731i	0.793354	+	1.37413i	0.923879	+	0.382684i	$0.125000\pi$
$821$	22.7321	+	39.3731i	0.793354	+	1.37413i	−0.130525	+	0.991445i	$0.541666\pi$
$822$			20.1962i			0.704422i
$823$	−3.70577	+	6.41858i	−0.129175	+	0.223738i	−0.923357	−	0.383942i	$-0.874566\pi$
$823$	−3.70577	+	6.41858i	−0.129175	+	0.223738i	0.794182	+	0.607680i	$0.207900\pi$
$824$	−6.92820			−0.241355
$825$	6.92820			0.241209
$826$	−18.9282	+	32.7846i	−0.658596	+	1.14072i
$827$	19.6077	−	11.3205i	0.681826	−	0.393653i	−0.118716	−	0.992928i	$-0.537878\pi$
$827$	19.6077	−	11.3205i	0.681826	−	0.393653i	0.800543	+	0.599276i	$0.204545\pi$
$828$		−	21.1244i		−	0.734122i
$829$	−31.9808	−	18.4641i	−1.11074	−	0.641285i	−0.171717	−	0.985146i	$-0.554932\pi$
$829$	−31.9808	−	18.4641i	−1.11074	−	0.641285i	−0.939020	+	0.343861i	$0.888265\pi$
$830$	4.90192	−	8.49038i	0.170148	−	0.294705i
$831$	−40.6865	−	23.4904i	−1.41140	−	0.814872i
$832$	−5.19615	+	3.00000i	−0.180144	+	0.104006i
$833$	13.5000	−	7.79423i	0.467747	−	0.270054i
$834$	−28.8564	−	16.6603i	−0.999216	−	0.576897i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	5.19615	+	3.00000i	0.179713	+	0.103757i
$837$		−	18.9282i		−	0.654254i
$838$	32.7846	−	18.9282i	1.13253	−	0.653864i
$839$	−10.0981	+	17.4904i	−0.348624	+	0.603835i	−0.986005	−	0.166714i	$-0.946684\pi$
$839$	−10.0981	+	17.4904i	−0.348624	+	0.603835i	0.637381	+	0.770549i	$0.280018\pi$
$840$	−18.9282			−0.653085
$841$	−30.7846			−1.06154
$842$	10.3301	−	17.8923i	0.356000	−	0.616610i
$843$		−	2.19615i		−	0.0756395i
$844$	−4.19615	−	7.26795i	−0.144438	−	0.250173i
$845$			39.8372i			1.37044i
$846$	−21.8827	+	12.6340i	−0.752342	+	0.434365i
$847$	18.7846	+	32.5359i	0.645447	+	1.11795i
$848$	4.73205	+	8.19615i	0.162499	+	0.281457i
$849$	22.3923	+	12.9282i	0.768502	+	0.443695i
$850$	−3.46410			−0.118818
$851$	−28.6865	−	2.36603i	−0.983362	−	0.0811063i
$852$	−25.8564			−0.885826
$853$	19.2846	+	11.1340i	0.660292	+	0.381220i	0.792388	−	0.610017i	$-0.208837\pi$
$853$	19.2846	+	11.1340i	0.660292	+	0.381220i	−0.132096	+	0.991237i	$0.542171\pi$
$854$	5.32051	+	9.21539i	0.182064	+	0.315344i
$855$	−18.2942	−	31.6865i	−0.625649	−	1.08366i
$856$	−3.80385	+	2.19615i	−0.130013	+	0.0750629i
$857$			37.0526i			1.26569i	0.774278	+	0.632846i	$0.218113\pi$
$857$			37.0526i			1.26569i	−0.774278	+	0.632846i	$0.781887\pi$
$858$	10.3923	+	18.0000i	0.354787	+	0.614510i
$859$			21.4641i			0.732346i	0.930547	+	0.366173i	$0.119332\pi$
$859$			21.4641i			0.732346i	−0.930547	+	0.366173i	$0.880668\pi$
$860$	2.19615	−	3.80385i	0.0748882	−	0.129710i
$861$	−70.6410			−2.40744
$862$	−16.0526			−0.546752
$863$	8.19615	−	14.1962i	0.279000	−	0.483243i	−0.692136	−	0.721767i	$-0.743330\pi$
$863$	8.19615	−	14.1962i	0.279000	−	0.483243i	0.971137	+	0.238524i	$0.0766636\pi$
$864$	3.46410	−	2.00000i	0.117851	−	0.0680414i
$865$		−	6.80385i		−	0.231338i
$866$	28.9186	+	16.6962i	0.982693	+	0.567358i
$867$	−19.1244	+	33.1244i	−0.649497	+	1.12496i
$868$	−16.3923	−	9.46410i	−0.556391	−	0.321233i
$869$	−2.41154	+	1.39230i	−0.0818060	+	0.0472307i
$870$	−31.6865	+	18.2942i	−1.07427	+	0.620232i
$871$	21.8038	+	12.5885i	0.738795	+	0.426544i
$872$	2.13397	−	3.69615i	0.0722655	−	0.125168i
$873$	20.0885	+	11.5981i	0.679891	+	0.392535i
$874$		−	22.3923i		−	0.757431i
$875$	−42.0000	+	24.2487i	−1.41986	+	0.819756i
$876$	11.4641	−	19.8564i	0.387336	−	0.670886i
$877$	44.1769			1.49175			0.745874	−	0.666087i	$-0.232032\pi$
$877$	44.1769			1.49175			0.745874	+	0.666087i	$0.232032\pi$
$878$	9.46410			0.319398
$879$	−6.29423	+	10.9019i	−0.212299	+	0.367713i
$880$		−	2.19615i		−	0.0740323i
$881$	24.4808	+	42.4019i	0.824778	+	1.42856i	0.902089	+	0.431550i	$0.142033\pi$
$881$	24.4808	+	42.4019i	0.824778	+	1.42856i	−0.0773111	+	0.997007i	$0.524633\pi$
$882$			40.1769i			1.35283i
$883$	30.8827	−	17.8301i	1.03929	−	0.600032i	0.119654	−	0.992816i	$-0.461821\pi$
$883$	30.8827	−	17.8301i	1.03929	−	0.600032i	0.919631	+	0.392784i	$0.128488\pi$
$884$	−5.19615	−	9.00000i	−0.174766	−	0.302703i
$885$	22.3923	+	38.7846i	0.752709	+	1.30373i
$886$	2.19615	+	1.26795i	0.0737812	+	0.0425976i
$887$	27.1244			0.910747			0.455373	−	0.890301i	$-0.349506\pi$
$887$	27.1244			0.910747			0.455373	+	0.890301i	$0.349506\pi$
$888$	−7.09808	−	15.0263i	−0.238196	−	0.504249i
$889$	82.3538			2.76206
$890$	7.79423	+	4.50000i	0.261263	+	0.150840i
$891$	1.56218	+	2.70577i	0.0523349	+	0.0906468i
$892$	4.29423	+	7.43782i	0.143781	+	0.249037i
$893$	−23.1962	+	13.3923i	−0.776230	+	0.448156i
$894$		−	27.1244i		−	0.907174i
$895$	−20.1962	−	34.9808i	−0.675083	−	1.16928i
$896$		−	4.00000i		−	0.133631i
$897$	38.7846	−	67.1769i	1.29498	−	2.24297i
$898$	24.9282			0.831865
$899$	−36.5885			−1.22029
$900$	4.46410	−	7.73205i	0.148803	−	0.257735i
$901$	−14.1962	+	8.19615i	−0.472942	+	0.273053i
$902$		−	8.19615i		−	0.272902i
$903$	−24.0000	−	13.8564i	−0.798670	−	0.461112i
$904$	3.92820	−	6.80385i	0.130650	−	0.226293i
$905$	8.08846	+	4.66987i	0.268869	+	0.155232i
$906$	−28.8564	+	16.6603i	−0.958690	+	0.553500i
$907$	40.0981	−	23.1506i	1.33143	−	0.768704i	0.345915	−	0.938266i	$-0.387568\pi$
$907$	40.0981	−	23.1506i	1.33143	−	0.768704i	0.985520	+	0.169562i	$0.0542352\pi$
$908$	4.09808	+	2.36603i	0.135999	+	0.0785193i
$909$	−14.4282	+	24.9904i	−0.478553	+	0.828879i
$910$	−36.0000	−	20.7846i	−1.19339	−	0.689003i
$911$			2.87564i			0.0952743i	0.998865	+	0.0476372i	$0.0151691\pi$
$911$			2.87564i			0.0952743i	−0.998865	+	0.0476372i	$0.984831\pi$
$912$	11.1962	−	6.46410i	0.370742	−	0.214048i
$913$	3.58846	−	6.21539i	0.118761	−	0.205699i
$914$	−19.9808			−0.660905
$915$	12.5885			0.416162
$916$	−9.50000	+	16.4545i	−0.313889	+	0.543671i
$917$			8.78461i			0.290093i
$918$	3.46410	+	6.00000i	0.114332	+	0.198030i
$919$		−	28.0526i		−	0.925369i	−0.886523	−	0.462684i	$-0.846886\pi$
$919$		−	28.0526i		−	0.925369i	0.886523	−	0.462684i	$-0.153114\pi$
$920$	−7.09808	+	4.09808i	−0.234017	+	0.135110i
$921$	5.46410	+	9.46410i	0.180048	+	0.311853i
$922$	16.8564	+	29.1962i	0.555136	+	0.961524i
$923$	−49.1769	−	28.3923i	−1.61868	−	0.934544i
$924$	−13.8564			−0.455842
$925$	−10.0000	−	6.92820i	−0.328798	−	0.227798i
$926$	14.5359			0.477679
$927$	26.7846	+	15.4641i	0.879722	+	0.507908i
$928$	−3.86603	−	6.69615i	−0.126909	−	0.219812i
$929$	18.6962	+	32.3827i	0.613401	+	1.06244i	0.990663	+	0.136335i	$0.0435323\pi$
$929$	18.6962	+	32.3827i	0.613401	+	1.06244i	−0.377262	+	0.926107i	$0.623134\pi$
$930$	−19.3923	+	11.1962i	−0.635899	+	0.367136i
$931$			42.5885i			1.39578i
$932$	−12.6962	−	21.9904i	−0.415876	−	0.720319i
$933$		−	12.0000i		−	0.392862i
$934$	15.1244	−	26.1962i	0.494884	−	0.857164i
$935$	3.80385			0.124399
$936$	26.7846			0.875482
$937$	−18.0885	+	31.3301i	−0.590924	+	1.02351i	0.403184	+	0.915119i	$0.367903\pi$
$937$	−18.0885	+	31.3301i	−0.590924	+	1.02351i	−0.994108	+	0.108392i	$0.965430\pi$
$938$	−14.5359	+	8.39230i	−0.474614	+	0.274018i
$939$		−	26.1962i		−	0.854879i
$940$	8.49038	+	4.90192i	0.276926	+	0.159883i
$941$	−29.8923	+	51.7750i	−0.974461	+	1.68782i	−0.292760	+	0.956186i	$0.594574\pi$
$941$	−29.8923	+	51.7750i	−0.974461	+	1.68782i	−0.681701	+	0.731630i	$0.738760\pi$
$942$	−26.9545	−	15.5622i	−0.878225	−	0.507043i
$943$	−26.4904	+	15.2942i	−0.862645	+	0.498049i
$944$	−8.19615	+	4.73205i	−0.266762	+	0.154015i
$945$	24.0000	+	13.8564i	0.780720	+	0.450749i
$946$	1.60770	−	2.78461i	0.0522707	−	0.0905355i
$947$	−45.3731	−	26.1962i	−1.47443	−	0.851261i	−0.474842	−	0.880071i	$-0.657495\pi$
$947$	−45.3731	−	26.1962i	−1.47443	−	0.851261i	−0.999585	+	0.0288107i	$0.990828\pi$
$948$			6.00000i			0.194871i
$949$	43.6077	−	25.1769i	1.41557	−	0.817277i
$950$	4.73205	−	8.19615i	0.153528	−	0.265918i
$951$	24.5885			0.797335
$952$	6.92820			0.224544
$953$	−3.92820	+	6.80385i	−0.127247	+	0.220398i	−0.922609	−	0.385736i	$-0.873947\pi$
$953$	−3.92820	+	6.80385i	−0.127247	+	0.220398i	0.795362	+	0.606135i	$0.207281\pi$
$954$		−	42.2487i		−	1.36785i
$955$	5.70577	+	9.88269i	0.184634	+	0.319796i
$956$			18.9282i			0.612182i
$957$	−23.1962	+	13.3923i	−0.749825	+	0.432912i
$958$	4.73205	+	8.19615i	0.152886	+	0.264806i
$959$	−14.7846	−	25.6077i	−0.477420	−	0.826916i
$960$	−4.09808	−	2.36603i	−0.132265	−	0.0763631i
$961$	8.60770			0.277668
$962$	3.00000	−	36.3731i	0.0967239	−	1.17271i
$963$	19.6077			0.631849
$964$	15.5885	+	9.00000i	0.502070	+	0.289870i
$965$	−10.5000	−	18.1865i	−0.338007	−	0.585445i
$966$	25.8564	+	44.7846i	0.831916	+	1.44092i
$967$	−9.21539	+	5.32051i	−0.296347	+	0.171096i	−0.640801	−	0.767707i	$-0.721397\pi$
$967$	−9.21539	+	5.32051i	−0.296347	+	0.171096i	0.344454	+	0.938803i	$0.388064\pi$
$968$			9.39230i			0.301880i
$969$	11.1962	+	19.3923i	0.359672	+	0.622971i
$970$		−	9.00000i		−	0.288973i
$971$	6.29423	−	10.9019i	0.201991	−	0.349859i	−0.747179	−	0.664623i	$-0.768592\pi$
$971$	6.29423	−	10.9019i	0.201991	−	0.349859i	0.949170	+	0.314764i	$0.101925\pi$
$972$	18.7321			0.600831
$973$	48.7846			1.56396
$974$	14.0263	−	24.2942i	0.449431	−	0.778437i
$975$	28.3923	−	16.3923i	0.909281	−	0.524974i
$976$			2.66025i			0.0851527i
$977$	−49.9808	−	28.8564i	−1.59903	−	0.923198i	−0.991675	−	0.128765i	$-0.958899\pi$
$977$	−49.9808	−	28.8564i	−1.59903	−	0.923198i	−0.607351	−	0.794434i	$-0.707768\pi$
$978$	−12.9282	+	22.3923i	−0.413398	+	0.716027i
$979$	5.70577	+	3.29423i	0.182357	+	0.105284i
$980$	13.5000	−	7.79423i	0.431242	−	0.248978i
$981$	−16.5000	+	9.52628i	−0.526804	+	0.304151i
$982$	−25.0981	−	14.4904i	−0.800912	−	0.462407i
$983$	−9.75833	+	16.9019i	−0.311242	+	0.539088i	−0.978632	−	0.205621i	$-0.934078\pi$
$983$	−9.75833	+	16.9019i	−0.311242	+	0.539088i	0.667389	+	0.744709i	$0.267412\pi$
$984$	−15.2942	−	8.83013i	−0.487562	−	0.281494i
$985$			14.4115i			0.459190i
$986$	11.5981	−	6.69615i	0.369358	−	0.213249i
$987$	30.9282	−	53.5692i	0.984456	−	1.70513i
$988$	28.3923			0.903280
$989$	−12.0000			−0.381578
$990$	−4.90192	+	8.49038i	−0.155793	+	0.269842i
$991$			44.1051i			1.40105i	0.713630	+	0.700523i	$0.247050\pi$
$991$			44.1051i			1.40105i	−0.713630	+	0.700523i	$0.752950\pi$
$992$	−2.36603	−	4.09808i	−0.0751214	−	0.130114i
$993$		−	46.6410i		−	1.48011i
$994$	32.7846	−	18.9282i	1.03986	−	0.600366i
$995$	16.3923	+	28.3923i	0.519671	+	0.900097i
$996$	−7.73205	−	13.3923i	−0.244999	−	0.424351i
$997$	−20.4115	−	11.7846i	−0.646440	−	0.373222i	0.140651	−	0.990059i	$-0.455080\pi$
$997$	−20.4115	−	11.7846i	−0.646440	−	0.373222i	−0.787091	+	0.616837i	$0.788414\pi$
$998$	−2.19615			−0.0695180
$999$	−2.00000	+	24.2487i	−0.0632772	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.e.a.27.1	yes	4
3.2	odd	2		666.2.s.e.397.2		4
4.3	odd	2		592.2.w.d.545.2		4
37.11	even	6	inner	74.2.e.a.11.1	✓	4
37.14	odd	12		2738.2.a.f.1.1		2
37.23	odd	12		2738.2.a.j.1.1		2
111.11	odd	6		666.2.s.e.307.2		4
148.11	odd	6		592.2.w.d.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.a.11.1	✓	4	37.11	even	6	inner
74.2.e.a.27.1	yes	4	1.1	even	1	trivial
592.2.w.d.529.2		4	148.11	odd	6
592.2.w.d.545.2		4	4.3	odd	2
666.2.s.e.307.2		4	111.11	odd	6
666.2.s.e.397.2		4	3.2	odd	2
2738.2.a.f.1.1		2	37.14	odd	12
2738.2.a.j.1.1		2	37.23	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +1.73205 q^{10} +1.26795 q^{11} +(1.36603 - 2.36603i) q^{12} +(5.19615 - 3.00000i) q^{13} +4.00000i q^{14} +(4.09808 + 2.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(3.86603 - 2.23205i) q^{18} +(4.09808 - 2.36603i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-5.46410 + 9.46410i) q^{21} +(-1.09808 - 0.633975i) q^{22} +4.73205i q^{23} +(-2.36603 + 1.36603i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} -7.73205i q^{29} +(-2.36603 - 4.09808i) q^{30} -4.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.73205 - 3.00000i) q^{33} +(0.866025 + 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} -4.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -4.73205 q^{38} +(-14.1962 - 8.19615i) q^{39} +(0.866025 + 1.50000i) q^{40} +(3.23205 + 5.59808i) q^{41} +(9.46410 - 5.46410i) q^{42} +2.53590i q^{43} +(0.633975 + 1.09808i) q^{44} -7.73205i q^{45} +(2.36603 - 4.09808i) q^{46} -5.66025 q^{47} +2.73205 q^{48} +(-4.50000 + 7.79423i) q^{49} +(1.73205 - 1.00000i) q^{50} +4.73205i q^{51} +(5.19615 + 3.00000i) q^{52} +(4.73205 - 8.19615i) q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.90192 + 1.09808i) q^{55} +(-3.46410 + 2.00000i) q^{56} +(-11.1962 - 6.46410i) q^{57} +(-3.86603 + 6.69615i) q^{58} +(8.19615 + 4.73205i) q^{59} +4.73205i q^{60} +(2.30385 - 1.33013i) q^{61} +(-2.36603 + 4.09808i) q^{62} +17.8564 q^{63} -1.00000 q^{64} +(-5.19615 + 9.00000i) q^{65} +3.46410i q^{66} +(2.09808 + 3.63397i) q^{67} -1.73205i q^{68} +(11.1962 - 6.46410i) q^{69} +(-3.46410 - 6.00000i) q^{70} +(-4.73205 - 8.19615i) q^{71} +(3.86603 + 2.23205i) q^{72} +8.39230 q^{73} +(3.46410 - 5.00000i) q^{74} +5.46410 q^{75} +(4.09808 + 2.36603i) q^{76} +(-2.53590 - 4.39230i) q^{77} +(8.19615 + 14.1962i) q^{78} +(-1.90192 + 1.09808i) q^{79} -1.73205i q^{80} +(1.23205 + 2.13397i) q^{81} -6.46410i q^{82} +(2.83013 - 4.90192i) q^{83} -10.9282 q^{84} +3.00000 q^{85} +(1.26795 - 2.19615i) q^{86} +(-18.2942 + 10.5622i) q^{87} -1.26795i q^{88} +(4.50000 + 2.59808i) q^{89} +(-3.86603 + 6.69615i) q^{90} +(-20.7846 - 12.0000i) q^{91} +(-4.09808 + 2.36603i) q^{92} +(-11.1962 + 6.46410i) q^{93} +(4.90192 + 2.83013i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(-2.36603 - 1.36603i) q^{96} -5.19615i q^{97} +(7.79423 - 4.50000i) q^{98} +(-2.83013 + 4.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9 + 12 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^18 + 6 * q^19 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 6 * q^24 - 4 * q^25 - 24 * q^26 + 16 * q^27 + 8 * q^28 - 6 * q^30 + 24 * q^35 - 4 * q^36 - 2 * q^37 - 12 * q^38 - 36 * q^39 + 6 * q^41 + 24 * q^42 + 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 - 18 * q^49 + 12 * q^53 - 18 * q^55 - 24 * q^57 - 12 * q^58 + 12 * q^59 + 30 * q^61 - 6 * q^62 + 16 * q^63 - 4 * q^64 - 2 * q^67 + 24 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 + 8 * q^75 + 6 * q^76 - 24 * q^77 + 12 * q^78 - 18 * q^79 - 2 * q^81 - 6 * q^83 - 16 * q^84 + 12 * q^85 + 12 * q^86 - 42 * q^87 + 18 * q^89 - 12 * q^90 - 6 * q^92 - 24 * q^93 + 30 * q^94 - 6 * q^95 - 6 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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