LMFDB - Embedded newform 74.2.e.b.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.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -0.732051i q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -0.732051i q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} -1.73205 q^{10} -1.26795 q^{11} +(-0.366025 + 0.633975i) q^{12} +(-3.00000 + 1.73205i) q^{13} -2.00000i q^{14} +(1.09808 + 0.633975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69615 - 2.13397i) q^{17} +(-2.13397 + 1.23205i) q^{18} +(-4.09808 + 2.36603i) q^{19} +(1.50000 + 0.866025i) q^{20} +(-0.732051 + 1.26795i) q^{21} +(1.09808 + 0.633975i) q^{22} +1.26795i q^{23} +(0.633975 - 0.366025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +3.46410 q^{26} +4.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} -8.66025i q^{29} +(-0.633975 - 1.09808i) q^{30} -4.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.464102 - 0.803848i) q^{33} +(2.13397 + 3.69615i) q^{34} +(3.00000 + 1.73205i) q^{35} +2.46410 q^{36} +(4.69615 - 3.86603i) q^{37} +4.73205 q^{38} +(-2.19615 - 1.26795i) q^{39} +(-0.866025 - 1.50000i) q^{40} +(1.96410 + 3.40192i) q^{41} +(1.26795 - 0.732051i) q^{42} +12.9282i q^{43} +(-0.633975 - 1.09808i) q^{44} -4.26795i q^{45} +(0.633975 - 1.09808i) q^{46} +1.26795 q^{47} -0.732051 q^{48} +(1.50000 - 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} -3.12436i q^{51} +(-3.00000 - 1.73205i) q^{52} +(-4.73205 + 8.19615i) q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.90192 + 1.09808i) q^{55} +(1.73205 - 1.00000i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(-4.33013 + 7.50000i) q^{58} +(-8.19615 - 4.73205i) q^{59} +1.26795i q^{60} +(1.50000 - 0.866025i) q^{61} +(-2.36603 + 4.09808i) q^{62} +4.92820 q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +0.928203i q^{66} +(-0.0980762 - 0.169873i) q^{67} -4.26795i q^{68} +(-0.803848 + 0.464102i) q^{69} +(-1.73205 - 3.00000i) q^{70} +(1.73205 + 3.00000i) q^{71} +(-2.13397 - 1.23205i) q^{72} +4.00000 q^{73} +(-6.00000 + 1.00000i) q^{74} -1.46410 q^{75} +(-4.09808 - 2.36603i) q^{76} +(-1.26795 - 2.19615i) q^{77} +(1.26795 + 2.19615i) q^{78} +(14.4904 - 8.36603i) q^{79} +1.73205i q^{80} +(-2.23205 - 3.86603i) q^{81} -3.92820i q^{82} +(-5.83013 + 10.0981i) q^{83} -1.46410 q^{84} -7.39230 q^{85} +(6.46410 - 11.1962i) q^{86} +(5.49038 - 3.16987i) q^{87} +1.26795i q^{88} +(14.8923 + 8.59808i) q^{89} +(-2.13397 + 3.69615i) q^{90} +(-6.00000 - 3.46410i) q^{91} +(-1.09808 + 0.633975i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-1.09808 - 0.633975i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(0.633975 + 0.366025i) q^{96} +4.26795i q^{97} +(-2.59808 + 1.50000i) q^{98} +(-1.56218 + 2.70577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9 - 12 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 - 6 * q^22 + 6 * q^24 - 4 * q^25 + 16 * q^27 - 4 * q^28 - 6 * q^30 + 12 * q^33 + 12 * q^34 + 12 * q^35 - 4 * q^36 - 2 * q^37 + 12 * q^38 + 12 * q^39 - 6 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 + 6 * q^49 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 12 * q^57 - 12 * q^59 + 6 * q^61 - 6 * q^62 - 8 * q^63 - 4 * q^64 - 12 * q^65 + 10 * q^67 - 24 * q^69 - 12 * q^72 + 16 * q^73 - 24 * q^74 + 8 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 6 * q^79 - 2 * q^81 - 6 * q^83 + 8 * q^84 + 12 * q^85 + 12 * q^86 - 30 * q^87 + 18 * q^89 - 12 * q^90 - 24 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 + 6 * q^96 + 18 * 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
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		−	0.732051i		−	0.298858i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	−1.73205			−0.547723
$11$	−1.26795			−0.382301			−0.191151	−	0.981561i	$-0.561222\pi$
$11$	−1.26795			−0.382301			−0.191151	+	0.981561i	$0.561222\pi$
$12$	−0.366025	+	0.633975i	−0.105662	+	0.183013i
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$		−	2.00000i		−	0.534522i
$15$	1.09808	+	0.633975i	0.283522	+	0.163692i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.69615	−	2.13397i	−0.896449	−	0.517565i	−0.0204023	−	0.999792i	$-0.506495\pi$
$17$	−3.69615	−	2.13397i	−0.896449	−	0.517565i	−0.876046	+	0.482227i	$0.839828\pi$
$18$	−2.13397	+	1.23205i	−0.502983	+	0.290397i
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.890011	−	0.455938i	$-0.849304\pi$
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.0501517	+	0.998742i	$0.515970\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$	−0.732051	+	1.26795i	−0.159747	+	0.276689i
$22$	1.09808	+	0.633975i	0.234111	+	0.135164i
$23$			1.26795i			0.264386i	0.991224	+	0.132193i	$0.0422018\pi$
$23$			1.26795i			0.264386i	−0.991224	+	0.132193i	$0.957798\pi$
$24$	0.633975	−	0.366025i	0.129410	−	0.0747146i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	3.46410			0.679366
$27$	4.00000			0.769800
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$		−	8.66025i		−	1.60817i	−0.594515	−	0.804084i	$-0.702656\pi$
$29$		−	8.66025i		−	1.60817i	0.594515	−	0.804084i	$-0.297344\pi$
$30$	−0.633975	−	1.09808i	−0.115747	−	0.200480i
$31$		−	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
$33$	−0.464102	−	0.803848i	−0.0807897	−	0.139932i
$34$	2.13397	+	3.69615i	0.365974	+	0.633885i
$35$	3.00000	+	1.73205i	0.507093	+	0.292770i
$36$	2.46410			0.410684
$37$	4.69615	−	3.86603i	0.772043	−	0.635571i
$37$	4.69615	−	3.86603i	0.772043	−	0.635571i
$38$	4.73205			0.767640
$39$	−2.19615	−	1.26795i	−0.351666	−	0.203034i
$40$	−0.866025	−	1.50000i	−0.136931	−	0.237171i
$41$	1.96410	+	3.40192i	0.306741	+	0.531291i	0.977647	−	0.210251i	$-0.0674281\pi$
$41$	1.96410	+	3.40192i	0.306741	+	0.531291i	−0.670906	+	0.741542i	$0.734095\pi$
$42$	1.26795	−	0.732051i	0.195649	−	0.112958i
$43$			12.9282i			1.97153i	0.168122	+	0.985766i	$0.446230\pi$
$43$			12.9282i			1.97153i	−0.168122	+	0.985766i	$0.553770\pi$
$44$	−0.633975	−	1.09808i	−0.0955753	−	0.165541i
$45$		−	4.26795i		−	0.636228i
$46$	0.633975	−	1.09808i	0.0934745	−	0.161903i
$47$	1.26795			0.184949			0.0924747	−	0.995715i	$-0.470522\pi$
$47$	1.26795			0.184949			0.0924747	+	0.995715i	$0.470522\pi$
$48$	−0.732051			−0.105662
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	1.73205	−	1.00000i	0.244949	−	0.141421i
$51$		−	3.12436i		−	0.437497i
$52$	−3.00000	−	1.73205i	−0.416025	−	0.240192i
$53$	−4.73205	+	8.19615i	−0.649997	+	1.12583i	0.333126	+	0.942882i	$0.391897\pi$
$53$	−4.73205	+	8.19615i	−0.649997	+	1.12583i	−0.983123	+	0.182946i	$0.941437\pi$
$54$	−3.46410	−	2.00000i	−0.471405	−	0.272166i
$55$	−1.90192	+	1.09808i	−0.256455	+	0.148065i
$56$	1.73205	−	1.00000i	0.231455	−	0.133631i
$57$	−3.00000	−	1.73205i	−0.397360	−	0.229416i
$58$	−4.33013	+	7.50000i	−0.568574	+	0.984798i
$59$	−8.19615	−	4.73205i	−1.06705	−	0.616061i	−0.139675	−	0.990197i	$-0.544606\pi$
$59$	−8.19615	−	4.73205i	−1.06705	−	0.616061i	−0.927373	+	0.374137i	$0.877939\pi$
$60$			1.26795i			0.163692i
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	−0.400889	−	0.916127i	$-0.631299\pi$
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	0.592944	+	0.805243i	$0.297965\pi$
$62$	−2.36603	+	4.09808i	−0.300486	+	0.520456i
$63$	4.92820			0.620895
$64$	−1.00000			−0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$			0.928203i			0.114254i
$67$	−0.0980762	−	0.169873i	−0.0119819	−	0.0207533i	0.859972	−	0.510341i	$-0.170481\pi$
$67$	−0.0980762	−	0.169873i	−0.0119819	−	0.0207533i	−0.871954	+	0.489587i	$0.837147\pi$
$68$		−	4.26795i		−	0.517565i
$69$	−0.803848	+	0.464102i	−0.0967719	+	0.0558713i
$70$	−1.73205	−	3.00000i	−0.207020	−	0.358569i
$71$	1.73205	+	3.00000i	0.205557	+	0.356034i	0.950310	−	0.311305i	$-0.100766\pi$
$71$	1.73205	+	3.00000i	0.205557	+	0.356034i	−0.744753	+	0.667340i	$0.767433\pi$
$72$	−2.13397	−	1.23205i	−0.251491	−	0.145199i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−6.00000	+	1.00000i	−0.697486	+	0.116248i
$75$	−1.46410			−0.169060
$76$	−4.09808	−	2.36603i	−0.470082	−	0.271402i
$77$	−1.26795	−	2.19615i	−0.144496	−	0.250275i
$78$	1.26795	+	2.19615i	0.143567	+	0.248665i
$79$	14.4904	−	8.36603i	1.63030	−	0.941251i	0.646294	−	0.763088i	$-0.276318\pi$
$79$	14.4904	−	8.36603i	1.63030	−	0.941251i	0.984001	−	0.178163i	$-0.0570155\pi$
$80$			1.73205i			0.193649i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$		−	3.92820i		−	0.433797i
$83$	−5.83013	+	10.0981i	−0.639940	+	1.10841i	0.345506	+	0.938417i	$0.387707\pi$
$83$	−5.83013	+	10.0981i	−0.639940	+	1.10841i	−0.985446	+	0.169991i	$0.945626\pi$
$84$	−1.46410			−0.159747
$85$	−7.39230			−0.801808
$86$	6.46410	−	11.1962i	0.697042	−	1.20731i
$87$	5.49038	−	3.16987i	0.588631	−	0.339846i
$88$			1.26795i			0.135164i
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.995058	+	0.0992979i	$0.0316597\pi$
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.583523	+	0.812096i	$0.301674\pi$
$90$	−2.13397	+	3.69615i	−0.224941	+	0.389609i
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$	−1.09808	+	0.633975i	−0.114482	+	0.0660964i
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$	−1.09808	−	0.633975i	−0.113258	−	0.0653895i
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$	0.633975	+	0.366025i	0.0647048	+	0.0373573i
$97$			4.26795i			0.433345i	0.976244	+	0.216672i	$0.0695203\pi$
$97$			4.26795i			0.433345i	−0.976244	+	0.216672i	$0.930480\pi$
$98$	−2.59808	+	1.50000i	−0.262445	+	0.151523i
$99$	−1.56218	+	2.70577i	−0.157005	+	0.271940i
$100$	−2.00000			−0.200000
$101$	5.53590			0.550842			0.275421	−	0.961324i	$-0.411183\pi$
$101$	5.53590			0.550842			0.275421	+	0.961324i	$0.411183\pi$
$102$	−1.56218	+	2.70577i	−0.154679	+	0.267911i
$103$		−	15.4641i		−	1.52372i	−0.647740	−	0.761862i	$-0.724286\pi$
$103$		−	15.4641i		−	1.52372i	0.647740	−	0.761862i	$-0.275714\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$			2.53590i			0.247478i
$106$	8.19615	−	4.73205i	0.796081	−	0.459617i
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	−0.999996	−	0.00269372i	$-0.999143\pi$
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	0.497665	−	0.867369i	$-0.334191\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	12.6962	+	7.33013i	1.21607	+	0.702099i	0.964075	−	0.265630i	$-0.0855798\pi$
$109$	12.6962	+	7.33013i	1.21607	+	0.702099i	0.251996	+	0.967728i	$0.418913\pi$
$110$	2.19615			0.209395
$111$	4.16987	+	1.56218i	0.395787	+	0.148275i
$112$	−2.00000			−0.188982
$113$	−3.00000	−	1.73205i	−0.282216	−	0.162938i	0.352210	−	0.935921i	$-0.385430\pi$
$113$	−3.00000	−	1.73205i	−0.282216	−	0.162938i	−0.634426	+	0.772983i	$0.718764\pi$
$114$	1.73205	+	3.00000i	0.162221	+	0.280976i
$115$	1.09808	+	1.90192i	0.102396	+	0.177355i
$116$	7.50000	−	4.33013i	0.696358	−	0.402042i
$117$			8.53590i			0.789144i
$118$	4.73205	+	8.19615i	0.435621	+	0.754517i
$119$		−	8.53590i		−	0.782485i
$120$	0.633975	−	1.09808i	0.0578737	−	0.100240i
$121$	−9.39230			−0.853846
$122$	−1.73205			−0.156813
$123$	−1.43782	+	2.49038i	−0.129644	+	0.224550i
$124$	4.09808	−	2.36603i	0.368018	−	0.212475i
$125$			12.1244i			1.08444i
$126$	−4.26795	−	2.46410i	−0.380219	−	0.219520i
$127$	9.09808	−	15.7583i	0.807324	−	1.39833i	−0.107387	−	0.994217i	$-0.534249\pi$
$127$	9.09808	−	15.7583i	0.807324	−	1.39833i	0.914711	−	0.404108i	$-0.132418\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−8.19615	+	4.73205i	−0.721631	+	0.416634i
$130$	5.19615	−	3.00000i	0.455733	−	0.263117i
$131$	−17.4904	−	10.0981i	−1.52814	−	0.882273i	−0.999440	−	0.0334654i	$-0.989346\pi$
$131$	−17.4904	−	10.0981i	−1.52814	−	0.882273i	−0.528702	−	0.848808i	$-0.677321\pi$
$132$	0.464102	−	0.803848i	0.0403949	−	0.0699660i
$133$	−8.19615	−	4.73205i	−0.710697	−	0.410321i
$134$			0.196152i			0.0169450i
$135$	6.00000	−	3.46410i	0.516398	−	0.298142i
$136$	−2.13397	+	3.69615i	−0.182987	+	0.316942i
$137$	19.3923			1.65680			0.828398	−	0.560140i	$-0.189253\pi$
$137$	19.3923			1.65680			0.828398	+	0.560140i	$0.189253\pi$
$138$	0.928203			0.0790139
$139$	−5.29423	+	9.16987i	−0.449051	+	0.777778i	−0.998324	−	0.0578639i	$-0.981571\pi$
$139$	−5.29423	+	9.16987i	−0.449051	+	0.777778i	0.549274	+	0.835642i	$0.314904\pi$
$140$			3.46410i			0.292770i
$141$	0.464102	+	0.803848i	0.0390844	+	0.0676962i
$142$		−	3.46410i		−	0.290701i
$143$	3.80385	−	2.19615i	0.318094	−	0.183651i
$144$	1.23205	+	2.13397i	0.102671	+	0.177831i
$145$	−7.50000	−	12.9904i	−0.622841	−	1.07879i
$146$	−3.46410	−	2.00000i	−0.286691	−	0.165521i
$147$	2.19615			0.181136
$148$	5.69615	+	2.13397i	0.468221	+	0.175412i
$149$	−2.07180			−0.169728			−0.0848641	−	0.996393i	$-0.527046\pi$
$149$	−2.07180			−0.169728			−0.0848641	+	0.996393i	$0.527046\pi$
$150$	1.26795	+	0.732051i	0.103528	+	0.0597717i
$151$	3.09808	+	5.36603i	0.252118	+	0.436681i	0.964109	−	0.265508i	$-0.0855396\pi$
$151$	3.09808	+	5.36603i	0.252118	+	0.436681i	−0.711991	+	0.702189i	$0.752206\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$	−9.10770	+	5.25833i	−0.736314	+	0.425111i
$154$			2.53590i			0.204349i
$155$	−4.09808	−	7.09808i	−0.329165	−	0.570131i
$156$		−	2.53590i		−	0.203034i
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	−0.885288	−	0.465044i	$-0.846039\pi$
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	0.845383	+	0.534160i	$0.179372\pi$
$158$	−16.7321			−1.33113
$159$	−6.92820			−0.549442
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$	−2.19615	+	1.26795i	−0.173081	+	0.0999284i
$162$			4.46410i			0.350733i
$163$	0.803848	+	0.464102i	0.0629622	+	0.0363512i	0.531151	−	0.847277i	$-0.321760\pi$
$163$	0.803848	+	0.464102i	0.0629622	+	0.0363512i	−0.468188	+	0.883629i	$0.655093\pi$
$164$	−1.96410	+	3.40192i	−0.153371	+	0.265646i
$165$	−1.39230	−	0.803848i	−0.108391	−	0.0625794i
$166$	10.0981	−	5.83013i	0.783763	−	0.452506i
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.886365	−	0.462988i	$-0.846777\pi$
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.0422232	+	0.999108i	$0.513444\pi$
$168$	1.26795	+	0.732051i	0.0978244	+	0.0564789i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	6.40192	+	3.69615i	0.491005	+	0.283482i
$171$			11.6603i			0.891682i
$172$	−11.1962	+	6.46410i	−0.853699	+	0.492883i
$173$	−6.23205	+	10.7942i	−0.473814	+	0.820670i	−0.999551	−	0.0299775i	$-0.990456\pi$
$173$	−6.23205	+	10.7942i	−0.473814	+	0.820670i	0.525737	+	0.850647i	$0.323790\pi$
$174$	−6.33975			−0.480615
$175$	−4.00000			−0.302372
$176$	0.633975	−	1.09808i	0.0477876	−	0.0827706i
$177$		−	6.92820i		−	0.520756i
$178$	−8.59808	−	14.8923i	−0.644453	−	1.11623i
$179$		−	2.53590i		−	0.189542i	−0.995499	−	0.0947710i	$-0.969788\pi$
$179$		−	2.53590i		−	0.189542i	0.995499	−	0.0947710i	$-0.0302119\pi$
$180$	3.69615	−	2.13397i	0.275495	−	0.159057i
$181$	−5.69615	−	9.86603i	−0.423392	−	0.733336i	0.572877	−	0.819641i	$-0.305827\pi$
$181$	−5.69615	−	9.86603i	−0.423392	−	0.733336i	−0.996269	+	0.0863054i	$0.972494\pi$
$182$	3.46410	+	6.00000i	0.256776	+	0.444750i
$183$	1.09808	+	0.633975i	0.0811721	+	0.0468648i
$184$	1.26795			0.0934745
$185$	3.69615	−	9.86603i	0.271747	−	0.725365i
$186$	−3.46410			−0.254000
$187$	4.68653	+	2.70577i	0.342713	+	0.197866i
$188$	0.633975	+	1.09808i	0.0462373	+	0.0800854i
$189$	4.00000	+	6.92820i	0.290957	+	0.503953i
$190$	7.09808	−	4.09808i	0.514949	−	0.297306i
$191$		−	8.19615i		−	0.593053i	−0.955025	−	0.296526i	$-0.904172\pi$
$191$		−	8.19615i		−	0.593053i	0.955025	−	0.296526i	$-0.0958283\pi$
$192$	−0.366025	−	0.633975i	−0.0264156	−	0.0457532i
$193$			0.803848i			0.0578622i	0.999581	+	0.0289311i	$0.00921034\pi$
$193$			0.803848i			0.0578622i	−0.999581	+	0.0289311i	$0.990790\pi$
$194$	2.13397	−	3.69615i	0.153210	−	0.265368i
$195$	−4.39230			−0.314539
$196$	3.00000			0.214286
$197$	0.232051	−	0.401924i	0.0165329	−	0.0286359i	−0.857641	−	0.514250i	$-0.828070\pi$
$197$	0.232051	−	0.401924i	0.0165329	−	0.0286359i	0.874174	+	0.485614i	$0.161404\pi$
$198$	2.70577	−	1.56218i	0.192291	−	0.111019i
$199$			10.3923i			0.736691i	0.929689	+	0.368345i	$0.120076\pi$
$199$			10.3923i			0.736691i	−0.929689	+	0.368345i	$0.879924\pi$
$200$	1.73205	+	1.00000i	0.122474	+	0.0707107i
$201$	0.0717968	−	0.124356i	0.00506415	−	0.00877137i
$202$	−4.79423	−	2.76795i	−0.337321	−	0.194752i
$203$	15.0000	−	8.66025i	1.05279	−	0.607831i
$204$	2.70577	−	1.56218i	0.189442	−	0.109374i
$205$	5.89230	+	3.40192i	0.411536	+	0.237601i
$206$	−7.73205	+	13.3923i	−0.538718	+	0.933086i
$207$	2.70577	+	1.56218i	0.188064	+	0.108579i
$208$		−	3.46410i		−	0.240192i
$209$	5.19615	−	3.00000i	0.359425	−	0.207514i
$210$	1.26795	−	2.19615i	0.0874968	−	0.151549i
$211$	18.3923			1.26618			0.633089	−	0.774079i	$-0.281787\pi$
$211$	18.3923			1.26618			0.633089	+	0.774079i	$0.281787\pi$
$212$	−9.46410			−0.649997
$213$	−1.26795	+	2.19615i	−0.0868784	+	0.150478i
$214$			10.3923i			0.710403i
$215$	11.1962	+	19.3923i	0.763571	+	1.32254i
$216$		−	4.00000i		−	0.272166i
$217$	8.19615	−	4.73205i	0.556391	−	0.321233i
$218$	−7.33013	−	12.6962i	−0.496459	−	0.859892i
$219$	1.46410	+	2.53590i	0.0989348	+	0.171360i
$220$	−1.90192	−	1.09808i	−0.128228	−	0.0740323i
$221$	14.7846			0.994520
$222$	−2.83013	−	3.43782i	−0.189946	−	0.230732i
$223$	5.80385			0.388654			0.194327	−	0.980937i	$-0.437748\pi$
$223$	5.80385			0.388654			0.194327	+	0.980937i	$0.437748\pi$
$224$	1.73205	+	1.00000i	0.115728	+	0.0668153i
$225$	2.46410	+	4.26795i	0.164273	+	0.284530i
$226$	1.73205	+	3.00000i	0.115214	+	0.199557i
$227$	−4.09808	+	2.36603i	−0.271999	+	0.157039i	−0.629796	−	0.776761i	$-0.716861\pi$
$227$	−4.09808	+	2.36603i	−0.271999	+	0.157039i	0.357797	+	0.933799i	$0.383528\pi$
$228$		−	3.46410i		−	0.229416i
$229$	−3.30385	−	5.72243i	−0.218324	−	0.378149i	0.735971	−	0.677013i	$-0.236726\pi$
$229$	−3.30385	−	5.72243i	−0.218324	−	0.378149i	−0.954296	+	0.298864i	$0.903392\pi$
$230$		−	2.19615i		−	0.144810i
$231$	0.928203	−	1.60770i	0.0610713	−	0.105779i
$232$	−8.66025			−0.568574
$233$	15.0000			0.982683			0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000			0.982683			0.491341	+	0.870967i	$0.336507\pi$
$234$	4.26795	−	7.39230i	0.279005	−	0.483250i
$235$	1.90192	−	1.09808i	0.124068	−	0.0716306i
$236$		−	9.46410i		−	0.616061i
$237$	10.6077	+	6.12436i	0.689044	+	0.397820i
$238$	−4.26795	+	7.39230i	−0.276650	+	0.479172i
$239$	−15.0000	−	8.66025i	−0.970269	−	0.560185i	−0.0709510	−	0.997480i	$-0.522603\pi$
$239$	−15.0000	−	8.66025i	−0.970269	−	0.560185i	−0.899318	+	0.437295i	$0.855937\pi$
$240$	−1.09808	+	0.633975i	−0.0708805	+	0.0409229i
$241$	−7.39230	+	4.26795i	−0.476180	+	0.274923i	−0.718823	−	0.695193i	$-0.755319\pi$
$241$	−7.39230	+	4.26795i	−0.476180	+	0.274923i	0.242643	+	0.970116i	$0.421986\pi$
$242$	8.13397	+	4.69615i	0.522872	+	0.301880i
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$	1.50000	+	0.866025i	0.0960277	+	0.0554416i
$245$		−	5.19615i		−	0.331970i
$246$	2.49038	−	1.43782i	0.158781	−	0.0916722i
$247$	8.19615	−	14.1962i	0.521509	−	0.903280i
$248$	−4.73205			−0.300486
$249$	−8.53590			−0.540941
$250$	6.06218	−	10.5000i	0.383406	−	0.664078i
$251$			17.3205i			1.09326i	0.837374	+	0.546630i	$0.184090\pi$
$251$			17.3205i			1.09326i	−0.837374	+	0.546630i	$0.815910\pi$
$252$	2.46410	+	4.26795i	0.155224	+	0.268856i
$253$		−	1.60770i		−	0.101075i
$254$	−15.7583	+	9.09808i	−0.988766	+	0.570864i
$255$	−2.70577	−	4.68653i	−0.169442	−	0.293482i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.8923	−	8.59808i	−0.928956	−	0.536333i	−0.0424751	−	0.999098i	$-0.513524\pi$
$257$	−14.8923	−	8.59808i	−0.928956	−	0.536333i	−0.886481	+	0.462764i	$0.846858\pi$
$258$	9.46410			0.589209
$259$	11.3923	+	4.26795i	0.707883	+	0.265197i
$260$	−6.00000			−0.372104
$261$	−18.4808	−	10.6699i	−1.14393	−	0.660449i
$262$	10.0981	+	17.4904i	0.623861	+	1.08056i
$263$	−7.26795	−	12.5885i	−0.448161	−	0.776238i	0.550105	−	0.835095i	$-0.314588\pi$
$263$	−7.26795	−	12.5885i	−0.448161	−	0.776238i	−0.998266	+	0.0588577i	$0.981254\pi$
$264$	−0.803848	+	0.464102i	−0.0494734	+	0.0285635i
$265$			16.3923i			1.00697i
$266$	4.73205	+	8.19615i	0.290141	+	0.502538i
$267$			12.5885i			0.770401i
$268$	0.0980762	−	0.169873i	0.00599096	−	0.0103766i
$269$	16.3923			0.999456			0.499728	−	0.866182i	$-0.333433\pi$
$269$	16.3923			0.999456			0.499728	+	0.866182i	$0.333433\pi$
$270$	−6.92820			−0.421637
$271$	−14.2942	+	24.7583i	−0.868313	+	1.50396i	−0.00459256	+	0.999989i	$0.501462\pi$
$271$	−14.2942	+	24.7583i	−0.868313	+	1.50396i	−0.863720	+	0.503972i	$0.831871\pi$
$272$	3.69615	−	2.13397i	0.224112	−	0.129391i
$273$		−	5.07180i		−	0.306959i
$274$	−16.7942	−	9.69615i	−1.01458	−	0.585766i
$275$	1.26795	−	2.19615i	0.0764602	−	0.132433i
$276$	−0.803848	−	0.464102i	−0.0483859	−	0.0279356i
$277$	−0.696152	+	0.401924i	−0.0418277	+	0.0241493i	−0.520768	−	0.853698i	$-0.674354\pi$
$277$	−0.696152	+	0.401924i	−0.0418277	+	0.0241493i	0.478940	+	0.877847i	$0.341021\pi$
$278$	9.16987	−	5.29423i	0.549972	−	0.317527i
$279$	−10.0981	−	5.83013i	−0.604556	−	0.349041i
$280$	1.73205	−	3.00000i	0.103510	−	0.179284i
$281$	−3.10770	−	1.79423i	−0.185390	−	0.107035i	0.404433	−	0.914568i	$-0.367469\pi$
$281$	−3.10770	−	1.79423i	−0.185390	−	0.107035i	−0.589822	+	0.807533i	$0.700802\pi$
$282$		−	0.928203i		−	0.0552737i
$283$	−17.1962	+	9.92820i	−1.02221	+	0.590170i	−0.914742	−	0.404039i	$-0.867606\pi$
$283$	−17.1962	+	9.92820i	−1.02221	+	0.590170i	−0.107463	+	0.994209i	$0.534273\pi$
$284$	−1.73205	+	3.00000i	−0.102778	+	0.178017i
$285$	−6.00000			−0.355409
$286$	−4.39230			−0.259722
$287$	−3.92820	+	6.80385i	−0.231875	+	0.401618i
$288$		−	2.46410i		−	0.145199i
$289$	0.607695	+	1.05256i	0.0357468	+	0.0619152i
$290$			15.0000i			0.880830i
$291$	−2.70577	+	1.56218i	−0.158615	+	0.0915765i
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−9.69615	−	16.7942i	−0.566455	−	0.981129i	−0.996913	−	0.0785184i	$-0.974981\pi$
$293$	−9.69615	−	16.7942i	−0.566455	−	0.981129i	0.430457	−	0.902611i	$-0.358352\pi$
$294$	−1.90192	−	1.09808i	−0.110922	−	0.0640411i
$295$	−16.3923			−0.954397
$296$	−3.86603	−	4.69615i	−0.224708	−	0.272958i
$297$	−5.07180			−0.294295
$298$	1.79423	+	1.03590i	0.103937	+	0.0600080i
$299$	−2.19615	−	3.80385i	−0.127007	−	0.219982i
$300$	−0.732051	−	1.26795i	−0.0422650	−	0.0732051i
$301$	−22.3923	+	12.9282i	−1.29067	+	0.745169i
$302$		−	6.19615i		−	0.356549i
$303$	2.02628	+	3.50962i	0.116407	+	0.201622i
$304$		−	4.73205i		−	0.271402i
$305$	1.50000	−	2.59808i	0.0858898	−	0.148765i
$306$	10.5167			0.601197
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$	1.26795	−	2.19615i	0.0722481	−	0.125137i
$309$	9.80385	−	5.66025i	0.557721	−	0.322001i
$310$			8.19615i			0.465510i
$311$	15.5885	+	9.00000i	0.883940	+	0.510343i	0.871956	−	0.489585i	$-0.162852\pi$
$311$	15.5885	+	9.00000i	0.883940	+	0.510343i	0.0119847	+	0.999928i	$0.496185\pi$
$312$	−1.26795	+	2.19615i	−0.0717835	+	0.124333i
$313$	0.107695	+	0.0621778i	0.00608729	+	0.00351450i	0.503041	−	0.864263i	$-0.332215\pi$
$313$	0.107695	+	0.0621778i	0.00608729	+	0.00351450i	−0.496953	+	0.867777i	$0.665548\pi$
$314$	0.866025	−	0.500000i	0.0488726	−	0.0282166i
$315$	7.39230	−	4.26795i	0.416509	−	0.240472i
$316$	14.4904	+	8.36603i	0.815148	+	0.470626i
$317$	6.69615	−	11.5981i	0.376093	−	0.651413i	−0.614397	−	0.788997i	$-0.710601\pi$
$317$	6.69615	−	11.5981i	0.376093	−	0.651413i	0.990490	+	0.137584i	$0.0439338\pi$
$318$	6.00000	+	3.46410i	0.336463	+	0.194257i
$319$			10.9808i			0.614805i
$320$	−1.50000	+	0.866025i	−0.0838525	+	0.0484123i
$321$	3.80385	−	6.58846i	0.212310	−	0.367732i
$322$	2.53590			0.141320
$323$	20.1962			1.12374
$324$	2.23205	−	3.86603i	0.124003	−	0.214779i
$325$		−	6.92820i		−	0.384308i
$326$	−0.464102	−	0.803848i	−0.0257042	−	0.0445210i
$327$			10.7321i			0.593484i
$328$	3.40192	−	1.96410i	0.187840	−	0.108449i
$329$	1.26795	+	2.19615i	0.0699043	+	0.121078i
$330$	0.803848	+	1.39230i	0.0442504	+	0.0766439i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−11.6603			−0.639940
$333$	−2.46410	−	14.7846i	−0.135032	−	0.810192i
$334$	13.8564			0.758189
$335$	−0.294229	−	0.169873i	−0.0160754	−	0.00928115i
$336$	−0.732051	−	1.26795i	−0.0399366	−	0.0691723i
$337$	−15.0885	−	26.1340i	−0.821921	−	1.42361i	−0.904250	−	0.427003i	$-0.859569\pi$
$337$	−15.0885	−	26.1340i	−0.821921	−	1.42361i	0.0823295	−	0.996605i	$-0.473764\pi$
$338$	0.866025	−	0.500000i	0.0471056	−	0.0271964i
$339$		−	2.53590i		−	0.137731i
$340$	−3.69615	−	6.40192i	−0.200452	−	0.347193i
$341$			6.00000i			0.324918i
$342$	5.83013	−	10.0981i	0.315257	−	0.546041i
$343$	20.0000			1.07990
$344$	12.9282			0.697042
$345$	−0.803848	+	1.39230i	−0.0432777	+	0.0749592i
$346$	10.7942	−	6.23205i	0.580301	−	0.335037i
$347$		−	15.1244i		−	0.811918i	−0.913891	−	0.405959i	$-0.866938\pi$
$347$		−	15.1244i		−	0.811918i	0.913891	−	0.405959i	$-0.133062\pi$
$348$	5.49038	+	3.16987i	0.294315	+	0.169923i
$349$	4.69615	−	8.13397i	0.251379	−	0.435402i	−0.712527	−	0.701645i	$-0.752449\pi$
$349$	4.69615	−	8.13397i	0.251379	−	0.435402i	0.963906	+	0.266243i	$0.0857825\pi$
$350$	3.46410	+	2.00000i	0.185164	+	0.106904i
$351$	−12.0000	+	6.92820i	−0.640513	+	0.369800i
$352$	−1.09808	+	0.633975i	−0.0585277	+	0.0337910i
$353$	14.0885	+	8.13397i	0.749853	+	0.432928i	0.825641	−	0.564196i	$-0.190814\pi$
$353$	14.0885	+	8.13397i	0.749853	+	0.432928i	−0.0757878	+	0.997124i	$0.524147\pi$
$354$	−3.46410	+	6.00000i	−0.184115	+	0.318896i
$355$	5.19615	+	3.00000i	0.275783	+	0.159223i
$356$			17.1962i			0.911394i
$357$	5.41154	−	3.12436i	0.286409	−	0.165358i
$358$	−1.26795	+	2.19615i	−0.0670132	+	0.116070i
$359$	0.679492			0.0358622			0.0179311	−	0.999839i	$-0.494292\pi$
$359$	0.679492			0.0358622			0.0179311	+	0.999839i	$0.494292\pi$
$360$	−4.26795			−0.224941
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$			11.3923i			0.598766i
$363$	−3.43782	−	5.95448i	−0.180439	−	0.312529i
$364$		−	6.92820i		−	0.363137i
$365$	6.00000	−	3.46410i	0.314054	−	0.181319i
$366$	−0.633975	−	1.09808i	−0.0331384	−	0.0573974i
$367$	4.19615	+	7.26795i	0.219037	+	0.379384i	0.954514	−	0.298166i	$-0.0963750\pi$
$367$	4.19615	+	7.26795i	0.219037	+	0.379384i	−0.735477	+	0.677550i	$0.763042\pi$
$368$	−1.09808	−	0.633975i	−0.0572412	−	0.0330482i
$369$	9.67949			0.503894
$370$	−8.13397	+	6.69615i	−0.422865	+	0.348116i
$371$	−18.9282			−0.982703
$372$	3.00000	+	1.73205i	0.155543	+	0.0898027i
$373$	−3.50000	−	6.06218i	−0.181223	−	0.313888i	0.761074	−	0.648665i	$-0.224672\pi$
$373$	−3.50000	−	6.06218i	−0.181223	−	0.313888i	−0.942297	+	0.334777i	$0.891339\pi$
$374$	−2.70577	−	4.68653i	−0.139912	−	0.242335i
$375$	−7.68653	+	4.43782i	−0.396931	+	0.229168i
$376$		−	1.26795i		−	0.0653895i
$377$	15.0000	+	25.9808i	0.772539	+	1.33808i
$378$		−	8.00000i		−	0.411476i
$379$	−3.39230	+	5.87564i	−0.174251	+	0.301812i	−0.939902	−	0.341445i	$-0.889084\pi$
$379$	−3.39230	+	5.87564i	−0.174251	+	0.301812i	0.765651	+	0.643256i	$0.222417\pi$
$380$	−8.19615			−0.420454
$381$	13.3205			0.682430
$382$	−4.09808	+	7.09808i	−0.209676	+	0.363169i
$383$	−3.00000	+	1.73205i	−0.153293	+	0.0885037i	−0.574684	−	0.818375i	$-0.694875\pi$
$383$	−3.00000	+	1.73205i	−0.153293	+	0.0885037i	0.421392	+	0.906879i	$0.361542\pi$
$384$			0.732051i			0.0373573i
$385$	−3.80385	−	2.19615i	−0.193862	−	0.111926i
$386$	0.401924	−	0.696152i	0.0204574	−	0.0354332i
$387$	27.5885	+	15.9282i	1.40240	+	0.809676i
$388$	−3.69615	+	2.13397i	−0.187644	+	0.108336i
$389$	−22.5000	+	12.9904i	−1.14080	+	0.658638i	−0.946627	−	0.322330i	$-0.895534\pi$
$389$	−22.5000	+	12.9904i	−1.14080	+	0.658638i	−0.194168	+	0.980968i	$0.562201\pi$
$390$	3.80385	+	2.19615i	0.192615	+	0.111207i
$391$	2.70577	−	4.68653i	0.136837	−	0.237008i
$392$	−2.59808	−	1.50000i	−0.131223	−	0.0757614i
$393$		−	14.7846i		−	0.745785i
$394$	−0.401924	+	0.232051i	−0.0202486	+	0.0116906i
$395$	14.4904	−	25.0981i	0.729090	−	1.26282i
$396$	−3.12436			−0.157005
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	5.19615	−	9.00000i	0.260460	−	0.451129i
$399$		−	6.92820i		−	0.346844i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$			10.3923i			0.518967i	0.965748	+	0.259483i	$0.0835523\pi$
$401$			10.3923i			0.518967i	−0.965748	+	0.259483i	$0.916448\pi$
$402$	−0.124356	+	0.0717968i	−0.00620230	+	0.00358090i
$403$	8.19615	+	14.1962i	0.408279	+	0.707161i
$404$	2.76795	+	4.79423i	0.137711	+	0.238522i
$405$	−6.69615	−	3.86603i	−0.332734	−	0.192104i
$406$	−17.3205			−0.859602
$407$	−5.95448	+	4.90192i	−0.295153	+	0.242979i
$408$	−3.12436			−0.154679
$409$	29.8923	+	17.2583i	1.47808	+	0.853370i	0.999693	−	0.0247799i	$-0.00788850\pi$
$409$	29.8923	+	17.2583i	1.47808	+	0.853370i	0.478386	+	0.878149i	$0.341222\pi$
$410$	−3.40192	−	5.89230i	−0.168009	−	0.291000i
$411$	7.09808	+	12.2942i	0.350122	+	0.606430i
$412$	13.3923	−	7.73205i	0.659792	−	0.380931i
$413$		−	18.9282i		−	0.931396i
$414$	−1.56218	−	2.70577i	−0.0767769	−	0.132981i
$415$			20.1962i			0.991390i
$416$	−1.73205	+	3.00000i	−0.0849208	+	0.147087i
$417$	−7.75129			−0.379582
$418$	−6.00000			−0.293470
$419$	15.9282	−	27.5885i	0.778144	−	1.34778i	−0.154867	−	0.987935i	$-0.549495\pi$
$419$	15.9282	−	27.5885i	0.778144	−	1.34778i	0.933011	−	0.359849i	$-0.117172\pi$
$420$	−2.19615	+	1.26795i	−0.107161	+	0.0618696i
$421$			12.1244i			0.590905i	0.955357	+	0.295452i	$0.0954704\pi$
$421$			12.1244i			0.590905i	−0.955357	+	0.295452i	$0.904530\pi$
$422$	−15.9282	−	9.19615i	−0.775373	−	0.447662i
$423$	1.56218	−	2.70577i	0.0759557	−	0.131559i
$424$	8.19615	+	4.73205i	0.398040	+	0.229809i
$425$	7.39230	−	4.26795i	0.358579	−	0.207026i
$426$	2.19615	−	1.26795i	0.106404	−	0.0614323i
$427$	3.00000	+	1.73205i	0.145180	+	0.0838198i
$428$	5.19615	−	9.00000i	0.251166	−	0.435031i
$429$	2.78461	+	1.60770i	0.134442	+	0.0776203i
$430$		−	22.3923i		−	1.07985i
$431$	0.294229	−	0.169873i	0.0141725	−	0.00818249i	−0.492897	−	0.870088i	$-0.664062\pi$
$431$	0.294229	−	0.169873i	0.0141725	−	0.00818249i	0.507070	+	0.861905i	$0.330729\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−25.7846			−1.23913			−0.619565	−	0.784946i	$-0.712691\pi$
$433$	−25.7846			−1.23913			−0.619565	+	0.784946i	$0.712691\pi$
$434$	−9.46410			−0.454291
$435$	5.49038	−	9.50962i	0.263244	−	0.455951i
$436$			14.6603i			0.702099i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		−	2.92820i		−	0.139915i
$439$	−26.1962	+	15.1244i	−1.25027	+	0.721846i	−0.971164	−	0.238413i	$-0.923373\pi$
$439$	−26.1962	+	15.1244i	−1.25027	+	0.721846i	−0.279110	+	0.960259i	$0.590039\pi$
$440$	1.09808	+	1.90192i	0.0523487	+	0.0906707i
$441$	−3.69615	−	6.40192i	−0.176007	−	0.304854i
$442$	−12.8038	−	7.39230i	−0.609017	−	0.351616i
$443$	−21.4641			−1.01979			−0.509895	−	0.860237i	$-0.670316\pi$
$443$	−21.4641			−1.01979			−0.509895	+	0.860237i	$0.670316\pi$
$444$	0.732051	+	4.39230i	0.0347416	+	0.208450i
$445$	29.7846			1.41193
$446$	−5.02628	−	2.90192i	−0.238001	−	0.137410i
$447$	−0.758330	−	1.31347i	−0.0358678	−	0.0621248i
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	−23.7846	+	13.7321i	−1.12247	+	0.648056i	−0.942029	−	0.335531i	$-0.891084\pi$
$449$	−23.7846	+	13.7321i	−1.12247	+	0.648056i	−0.180436	+	0.983587i	$0.557751\pi$
$450$		−	4.92820i		−	0.232318i
$451$	−2.49038	−	4.31347i	−0.117267	−	0.203113i
$452$		−	3.46410i		−	0.162938i
$453$	−2.26795	+	3.92820i	−0.106558	+	0.184563i
$454$	4.73205			0.222086
$455$	−12.0000			−0.562569
$456$	−1.73205	+	3.00000i	−0.0811107	+	0.140488i
$457$	−12.1077	+	6.99038i	−0.566374	+	0.326996i	−0.755700	−	0.654918i	$-0.772703\pi$
$457$	−12.1077	+	6.99038i	−0.566374	+	0.326996i	0.189326	+	0.981914i	$0.439370\pi$
$458$			6.60770i			0.308757i
$459$	−14.7846	−	8.53590i	−0.690086	−	0.398422i
$460$	−1.09808	+	1.90192i	−0.0511981	+	0.0886777i
$461$	28.1769	+	16.2679i	1.31233	+	0.757674i	0.982482	−	0.186360i	$-0.0596691\pi$
$461$	28.1769	+	16.2679i	1.31233	+	0.757674i	0.329848	+	0.944034i	$0.393002\pi$
$462$	−1.60770	+	0.928203i	−0.0747967	+	0.0431839i
$463$	25.9808	−	15.0000i	1.20743	−	0.697109i	0.245232	−	0.969465i	$-0.421136\pi$
$463$	25.9808	−	15.0000i	1.20743	−	0.697109i	0.962197	+	0.272355i	$0.0878026\pi$
$464$	7.50000	+	4.33013i	0.348179	+	0.201021i
$465$	3.00000	−	5.19615i	0.139122	−	0.240966i
$466$	−12.9904	−	7.50000i	−0.601768	−	0.347431i
$467$		−	9.46410i		−	0.437946i	−0.975731	−	0.218973i	$-0.929729\pi$
$467$		−	9.46410i		−	0.437946i	0.975731	−	0.218973i	$-0.0702707\pi$
$468$	−7.39230	+	4.26795i	−0.341709	+	0.197286i
$469$	0.196152	−	0.339746i	0.00905748	−	0.0156880i
$470$	−2.19615			−0.101301
$471$	−0.732051			−0.0337311
$472$	−4.73205	+	8.19615i	−0.217810	+	0.377258i
$473$		−	16.3923i		−	0.753719i
$474$	−6.12436	−	10.6077i	−0.281301	−	0.487228i
$475$		−	9.46410i		−	0.434243i
$476$	7.39230	−	4.26795i	0.338826	−	0.195621i
$477$	11.6603	+	20.1962i	0.533886	+	0.924718i
$478$	8.66025	+	15.0000i	0.396111	+	0.686084i
$479$	−2.19615	−	1.26795i	−0.100345	−	0.0579341i	0.448988	−	0.893538i	$-0.351785\pi$
$479$	−2.19615	−	1.26795i	−0.100345	−	0.0579341i	−0.549333	+	0.835604i	$0.685118\pi$
$480$	1.26795			0.0578737
$481$	−7.39230	+	19.7321i	−0.337060	+	0.899704i
$482$	8.53590			0.388800
$483$	−1.60770	−	0.928203i	−0.0731527	−	0.0422347i
$484$	−4.69615	−	8.13397i	−0.213461	−	0.369726i
$485$	3.69615	+	6.40192i	0.167834	+	0.290696i
$486$	−13.2224	+	7.63397i	−0.599782	+	0.346284i
$487$		−	22.0526i		−	0.999297i	−0.866228	−	0.499648i	$-0.833463\pi$
$487$		−	22.0526i		−	0.999297i	0.866228	−	0.499648i	$-0.166537\pi$
$488$	−0.866025	−	1.50000i	−0.0392031	−	0.0679018i
$489$			0.679492i			0.0307277i
$490$	−2.59808	+	4.50000i	−0.117369	+	0.203289i
$491$	15.8038			0.713218			0.356609	−	0.934254i	$-0.383933\pi$
$491$	15.8038			0.713218			0.356609	+	0.934254i	$0.383933\pi$
$492$	−2.87564			−0.129644
$493$	−18.4808	+	32.0096i	−0.832332	+	1.44164i
$494$	−14.1962	+	8.19615i	−0.638715	+	0.368762i
$495$			5.41154i			0.243231i
$496$	4.09808	+	2.36603i	0.184009	+	0.106238i
$497$	−3.46410	+	6.00000i	−0.155386	+	0.269137i
$498$	7.39230	+	4.26795i	0.331257	+	0.191251i
$499$	8.49038	−	4.90192i	0.380082	−	0.219440i	−0.297772	−	0.954637i	$-0.596244\pi$
$499$	8.49038	−	4.90192i	0.380082	−	0.219440i	0.677854	+	0.735197i	$0.262910\pi$
$500$	−10.5000	+	6.06218i	−0.469574	+	0.271109i
$501$	−8.78461	−	5.07180i	−0.392467	−	0.226591i
$502$	8.66025	−	15.0000i	0.386526	−	0.669483i
$503$	8.49038	+	4.90192i	0.378567	+	0.218566i	0.677195	−	0.735804i	$-0.263195\pi$
$503$	8.49038	+	4.90192i	0.378567	+	0.218566i	−0.298627	+	0.954370i	$0.596529\pi$
$504$		−	4.92820i		−	0.219520i
$505$	8.30385	−	4.79423i	0.369516	−	0.213340i
$506$	−0.803848	+	1.39230i	−0.0357354	+	0.0618955i
$507$	−0.732051			−0.0325115
$508$	18.1962			0.807324
$509$	−0.232051	+	0.401924i	−0.0102855	+	0.0178150i	−0.871122	−	0.491066i	$-0.836607\pi$
$509$	−0.232051	+	0.401924i	−0.0102855	+	0.0178150i	0.860837	+	0.508881i	$0.169941\pi$
$510$			5.41154i			0.239627i
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$			1.00000i			0.0441942i
$513$	−16.3923	+	9.46410i	−0.723738	+	0.417850i
$514$	8.59808	+	14.8923i	0.379245	+	0.656871i
$515$	−13.3923	−	23.1962i	−0.590135	−	1.02214i
$516$	−8.19615	−	4.73205i	−0.360815	−	0.208317i
$517$	−1.60770			−0.0707064
$518$	−7.73205	−	9.39230i	−0.339727	−	0.412674i
$519$	−9.12436			−0.400515
$520$	5.19615	+	3.00000i	0.227866	+	0.131559i
$521$	−9.46410	−	16.3923i	−0.414630	−	0.718160i	0.580760	−	0.814075i	$-0.302756\pi$
$521$	−9.46410	−	16.3923i	−0.414630	−	0.718160i	−0.995390	+	0.0959151i	$0.969422\pi$
$522$	10.6699	+	18.4808i	0.467008	+	0.808881i
$523$	33.2942	−	19.2224i	1.45585	−	0.840538i	0.457051	−	0.889440i	$-0.348906\pi$
$523$	33.2942	−	19.2224i	1.45585	−	0.840538i	0.998804	+	0.0489020i	$0.0155722\pi$
$524$		−	20.1962i		−	0.882273i
$525$	−1.46410	−	2.53590i	−0.0638986	−	0.110676i
$526$			14.5359i			0.633795i
$527$	−10.0981	+	17.4904i	−0.439879	+	0.761893i
$528$	0.928203			0.0403949
$529$	21.3923			0.930100
$530$	8.19615	−	14.1962i	0.356018	−	0.616641i
$531$	−20.1962	+	11.6603i	−0.876438	+	0.506012i
$532$		−	9.46410i		−	0.410321i
$533$	−11.7846	−	6.80385i	−0.510448	−	0.294707i
$534$	6.29423	−	10.9019i	0.272378	−	0.471772i
$535$	−15.5885	−	9.00000i	−0.673948	−	0.389104i
$536$	−0.169873	+	0.0980762i	−0.00733740	+	0.00423625i
$537$	1.60770	−	0.928203i	0.0693772	−	0.0400549i
$538$	−14.1962	−	8.19615i	−0.612040	−	0.353361i
$539$	−1.90192	+	3.29423i	−0.0819217	+	0.141892i
$540$	6.00000	+	3.46410i	0.258199	+	0.149071i
$541$		−	19.0526i		−	0.819133i	−0.912280	−	0.409567i	$-0.865680\pi$
$541$		−	19.0526i		−	0.819133i	0.912280	−	0.409567i	$-0.134320\pi$
$542$	24.7583	−	14.2942i	1.06346	−	0.613990i
$543$	4.16987	−	7.22243i	0.178946	−	0.309944i
$544$	−4.26795			−0.182987
$545$	25.3923			1.08769
$546$	−2.53590	+	4.39230i	−0.108526	+	0.187973i
$547$			24.3397i			1.04069i	0.853955	+	0.520346i	$0.174197\pi$
$547$			24.3397i			1.04069i	−0.853955	+	0.520346i	$0.825803\pi$
$548$	9.69615	+	16.7942i	0.414199	+	0.717414i
$549$		−	4.26795i		−	0.182152i
$550$	−2.19615	+	1.26795i	−0.0936443	+	0.0540655i
$551$	20.4904	+	35.4904i	0.872920	+	1.51194i
$552$	0.464102	+	0.803848i	0.0197535	+	0.0342140i
$553$	28.9808	+	16.7321i	1.23239	+	0.711519i
$554$	0.803848			0.0341522
$555$	7.60770	−	1.26795i	0.322929	−	0.0538214i
$556$	−10.5885			−0.449051
$557$	30.6962	+	17.7224i	1.30064	+	0.750924i	0.980513	−	0.196452i	$-0.0629420\pi$
$557$	30.6962	+	17.7224i	1.30064	+	0.750924i	0.320124	+	0.947376i	$0.396275\pi$
$558$	5.83013	+	10.0981i	0.246809	+	0.427486i
$559$	−22.3923	−	38.7846i	−0.947094	−	1.64041i
$560$	−3.00000	+	1.73205i	−0.126773	+	0.0731925i
$561$			3.96152i			0.167256i
$562$	1.79423	+	3.10770i	0.0756850	+	0.131090i
$563$			12.5885i			0.530540i	0.964174	+	0.265270i	$0.0854611\pi$
$563$			12.5885i			0.530540i	−0.964174	+	0.265270i	$0.914539\pi$
$564$	−0.464102	+	0.803848i	−0.0195422	+	0.0338481i
$565$	−6.00000			−0.252422
$566$	19.8564			0.834627
$567$	4.46410	−	7.73205i	0.187475	−	0.324716i
$568$	3.00000	−	1.73205i	0.125877	−	0.0726752i
$569$		−	30.1244i		−	1.26288i	−0.775425	−	0.631439i	$-0.782464\pi$
$569$		−	30.1244i		−	1.26288i	0.775425	−	0.631439i	$-0.217536\pi$
$570$	5.19615	+	3.00000i	0.217643	+	0.125656i
$571$	17.6865	−	30.6340i	0.740158	−	1.28199i	−0.212264	−	0.977212i	$-0.568084\pi$
$571$	17.6865	−	30.6340i	0.740158	−	1.28199i	0.952423	−	0.304780i	$-0.0985828\pi$
$572$	3.80385	+	2.19615i	0.159047	+	0.0918257i
$573$	5.19615	−	3.00000i	0.217072	−	0.125327i
$574$	6.80385	−	3.92820i	0.283987	−	0.163960i
$575$	−2.19615	−	1.26795i	−0.0915859	−	0.0528771i
$576$	−1.23205	+	2.13397i	−0.0513355	+	0.0889156i
$577$	−11.1962	−	6.46410i	−0.466102	−	0.269104i	0.248505	−	0.968631i	$-0.420061\pi$
$577$	−11.1962	−	6.46410i	−0.466102	−	0.269104i	−0.714607	+	0.699527i	$0.753394\pi$
$578$		−	1.21539i		−	0.0505536i
$579$	−0.509619	+	0.294229i	−0.0211790	+	0.0122277i
$580$	7.50000	−	12.9904i	0.311421	−	0.539396i
$581$	−23.3205			−0.967498
$582$	3.12436			0.129509
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$		−	4.00000i		−	0.165521i
$585$	7.39230	+	12.8038i	0.305634	+	0.529374i
$586$			19.3923i			0.801089i
$587$	−7.68653	+	4.43782i	−0.317257	+	0.183169i	−0.650169	−	0.759789i	$-0.725302\pi$
$587$	−7.68653	+	4.43782i	−0.317257	+	0.183169i	0.332912	+	0.942958i	$0.391969\pi$
$588$	1.09808	+	1.90192i	0.0452839	+	0.0784340i
$589$	11.1962	+	19.3923i	0.461329	+	0.799046i
$590$	14.1962	+	8.19615i	0.584446	+	0.337430i
$591$	0.339746			0.0139753
$592$	1.00000	+	6.00000i	0.0410997	+	0.246598i
$593$	−25.6410			−1.05295			−0.526475	−	0.850191i	$-0.676487\pi$
$593$	−25.6410			−1.05295			−0.526475	+	0.850191i	$0.676487\pi$
$594$	4.39230	+	2.53590i	0.180218	+	0.104049i
$595$	−7.39230	−	12.8038i	−0.303055	−	0.524907i
$596$	−1.03590	−	1.79423i	−0.0424321	−	0.0734945i
$597$	−6.58846	+	3.80385i	−0.269648	+	0.155681i
$598$			4.39230i			0.179615i
$599$	−15.1699	−	26.2750i	−0.619824	−	1.07357i	−0.989517	−	0.144413i	$-0.953871\pi$
$599$	−15.1699	−	26.2750i	−0.619824	−	1.07357i	0.369693	−	0.929154i	$-0.379463\pi$
$600$			1.46410i			0.0597717i
$601$	16.6962	−	28.9186i	0.681050	−	1.17961i	−0.293610	−	0.955925i	$-0.594857\pi$
$601$	16.6962	−	28.9186i	0.681050	−	1.17961i	0.974661	−	0.223688i	$-0.0718098\pi$
$602$	25.8564			1.05383
$603$	−0.483340			−0.0196831
$604$	−3.09808	+	5.36603i	−0.126059	+	0.218340i
$605$	−14.0885	+	8.13397i	−0.572777	+	0.330693i
$606$		−	4.05256i		−	0.164624i
$607$	−36.2942	−	20.9545i	−1.47314	−	0.850516i	−0.473594	−	0.880743i	$-0.657044\pi$
$607$	−36.2942	−	20.9545i	−1.47314	−	0.850516i	−0.999543	+	0.0302269i	$0.990377\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$	10.9808	+	6.33975i	0.444963	+	0.256899i
$610$	−2.59808	+	1.50000i	−0.105193	+	0.0607332i
$611$	−3.80385	+	2.19615i	−0.153887	+	0.0888468i
$612$	−9.10770	−	5.25833i	−0.368157	−	0.212555i
$613$	16.8923	−	29.2583i	0.682274	−	1.18173i	−0.292012	−	0.956415i	$-0.594325\pi$
$613$	16.8923	−	29.2583i	0.682274	−	1.18173i	0.974285	−	0.225318i	$-0.0723421\pi$
$614$	19.0526	+	11.0000i	0.768899	+	0.443924i
$615$			4.98076i			0.200844i
$616$	−2.19615	+	1.26795i	−0.0884855	+	0.0510871i
$617$	−23.6603	+	40.9808i	−0.952526	+	1.64982i	−0.212595	+	0.977140i	$0.568192\pi$
$617$	−23.6603	+	40.9808i	−0.952526	+	1.64982i	−0.739931	+	0.672683i	$0.765142\pi$
$618$	−11.3205			−0.455378
$619$	9.60770			0.386166			0.193083	−	0.981182i	$-0.438151\pi$
$619$	9.60770			0.386166			0.193083	+	0.981182i	$0.438151\pi$
$620$	4.09808	−	7.09808i	0.164583	−	0.285066i
$621$			5.07180i			0.203524i
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$			34.3923i			1.37790i
$624$	2.19615	−	1.26795i	0.0879165	−	0.0507586i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−0.0621778	−	0.107695i	−0.00248513	−	0.00430436i
$627$	3.80385	+	2.19615i	0.151911	+	0.0877059i
$628$	−1.00000			−0.0399043
$629$	−25.6077	+	4.26795i	−1.02105	+	0.170174i
$630$	−8.53590			−0.340078
$631$	−14.7058	−	8.49038i	−0.585428	−	0.337997i	0.177860	−	0.984056i	$-0.443083\pi$
$631$	−14.7058	−	8.49038i	−0.585428	−	0.337997i	−0.763287	+	0.646059i	$0.776416\pi$
$632$	−8.36603	−	14.4904i	−0.332783	−	0.576396i
$633$	6.73205	+	11.6603i	0.267575	+	0.463453i
$634$	−11.5981	+	6.69615i	−0.460618	+	0.265938i
$635$		−	31.5167i		−	1.25070i
$636$	−3.46410	−	6.00000i	−0.137361	−	0.237915i
$637$			10.3923i			0.411758i
$638$	5.49038	−	9.50962i	0.217366	−	0.376489i
$639$	8.53590			0.337675
$640$	1.73205			0.0684653
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	0.426698	+	0.904394i	$0.359677\pi$
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	−0.996577	+	0.0826663i	$0.973656\pi$
$642$	−6.58846	+	3.80385i	−0.260026	+	0.150126i
$643$		−	16.7321i		−	0.659848i	−0.944008	−	0.329924i	$-0.892977\pi$
$643$		−	16.7321i		−	0.659848i	0.944008	−	0.329924i	$-0.107023\pi$
$644$	−2.19615	−	1.26795i	−0.0865405	−	0.0499642i
$645$	−8.19615	+	14.1962i	−0.322723	+	0.558973i
$646$	−17.4904	−	10.0981i	−0.688150	−	0.397303i
$647$	−31.9808	+	18.4641i	−1.25729	+	0.725899i	−0.972548	−	0.232704i	$-0.925243\pi$
$647$	−31.9808	+	18.4641i	−1.25729	+	0.725899i	−0.284746	+	0.958603i	$0.591909\pi$
$648$	−3.86603	+	2.23205i	−0.151872	+	0.0876832i
$649$	10.3923	+	6.00000i	0.407934	+	0.235521i
$650$	−3.46410	+	6.00000i	−0.135873	+	0.235339i
$651$	6.00000	+	3.46410i	0.235159	+	0.135769i
$652$			0.928203i			0.0363512i
$653$	−6.91154	+	3.99038i	−0.270470	+	0.156156i	−0.629101	−	0.777324i	$-0.716577\pi$
$653$	−6.91154	+	3.99038i	−0.270470	+	0.156156i	0.358631	+	0.933479i	$0.383243\pi$
$654$	5.36603	−	9.29423i	0.209828	−	0.363433i
$655$	−34.9808			−1.36681
$656$	−3.92820			−0.153371
$657$	4.92820	−	8.53590i	0.192268	−	0.333017i
$658$		−	2.53590i		−	0.0988596i
$659$	1.26795	+	2.19615i	0.0493923	+	0.0855500i	0.889665	−	0.456615i	$-0.150938\pi$
$659$	1.26795	+	2.19615i	0.0493923	+	0.0855500i	−0.840272	+	0.542165i	$0.817605\pi$
$660$		−	1.60770i		−	0.0625794i
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	−0.470545	−	0.882376i	$-0.655943\pi$
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	0.528888	+	0.848692i	$0.322609\pi$
$662$		0			0
$663$	5.41154	+	9.37307i	0.210167	+	0.364020i
$664$	10.0981	+	5.83013i	0.391881	+	0.226253i
$665$	−16.3923			−0.635666
$666$	−5.25833	+	14.0359i	−0.203756	+	0.543880i
$667$	10.9808			0.425177
$668$	−12.0000	−	6.92820i	−0.464294	−	0.268060i
$669$	2.12436	+	3.67949i	0.0821323	+	0.142257i
$670$	0.169873	+	0.294229i	0.00656277	+	0.0113670i
$671$	−1.90192	+	1.09808i	−0.0734230	+	0.0423908i
$672$			1.46410i			0.0564789i
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	0.669630	−	0.742695i	$-0.266453\pi$
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	−0.978008	+	0.208569i	$0.933119\pi$
$674$			30.1769i			1.16237i
$675$	−4.00000	+	6.92820i	−0.153960	+	0.266667i
$676$	−1.00000			−0.0384615
$677$	20.0718			0.771422			0.385711	−	0.922620i	$-0.373956\pi$
$677$	20.0718			0.771422			0.385711	+	0.922620i	$0.373956\pi$
$678$	−1.26795	+	2.19615i	−0.0486953	+	0.0843427i
$679$	−7.39230	+	4.26795i	−0.283691	+	0.163789i
$680$			7.39230i			0.283482i
$681$	−3.00000	−	1.73205i	−0.114960	−	0.0663723i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	23.7846	+	13.7321i	0.910093	+	0.525442i	0.880461	−	0.474119i	$-0.157233\pi$
$683$	23.7846	+	13.7321i	0.910093	+	0.525442i	0.0296318	+	0.999561i	$0.490567\pi$
$684$	−10.0981	+	5.83013i	−0.386110	+	0.222920i
$685$	29.0885	−	16.7942i	1.11141	−	0.641674i
$686$	−17.3205	−	10.0000i	−0.661300	−	0.381802i
$687$	2.41858	−	4.18911i	0.0922747	−	0.159825i
$688$	−11.1962	−	6.46410i	−0.426849	−	0.246442i
$689$		−	32.7846i		−	1.24899i
$690$	1.39230	−	0.803848i	0.0530041	−	0.0306020i
$691$	12.4904	−	21.6340i	0.475156	−	0.822995i	−0.524439	−	0.851448i	$-0.675725\pi$
$691$	12.4904	−	21.6340i	0.475156	−	0.822995i	0.999595	+	0.0284531i	$0.00905811\pi$
$692$	−12.4641			−0.473814
$693$	−6.24871			−0.237369
$694$	−7.56218	+	13.0981i	−0.287056	+	0.497196i
$695$			18.3397i			0.695666i
$696$	−3.16987	−	5.49038i	−0.120154	−	0.208112i
$697$		−	16.7654i		−	0.635034i
$698$	−8.13397	+	4.69615i	−0.307875	+	0.177752i
$699$	5.49038	+	9.50962i	0.207665	+	0.359687i
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	−4.39230	−	2.53590i	−0.165895	−	0.0957796i	0.414754	−	0.909934i	$-0.363868\pi$
$701$	−4.39230	−	2.53590i	−0.165895	−	0.0957796i	−0.580649	+	0.814154i	$0.697201\pi$
$702$	13.8564			0.522976
$703$	−10.0981	+	26.9545i	−0.380856	+	1.01661i
$704$	1.26795			0.0477876
$705$	1.39230	+	0.803848i	0.0524372	+	0.0302747i
$706$	−8.13397	−	14.0885i	−0.306126	−	0.530226i
$707$	5.53590	+	9.58846i	0.208199	+	0.360611i
$708$	6.00000	−	3.46410i	0.225494	−	0.130189i
$709$			45.7128i			1.71678i	0.512997	+	0.858390i	$0.328535\pi$
$709$			45.7128i			1.71678i	−0.512997	+	0.858390i	$0.671465\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$		−	41.2295i		−	1.54623i
$712$	8.59808	−	14.8923i	0.322227	−	0.558113i
$713$	6.00000			0.224702
$714$	−6.24871			−0.233852
$715$	3.80385	−	6.58846i	0.142256	−	0.246394i
$716$	2.19615	−	1.26795i	0.0820741	−	0.0473855i
$717$		−	12.6795i		−	0.473524i
$718$	−0.588457	−	0.339746i	−0.0219610	−	0.0126792i
$719$	−20.3660	+	35.2750i	−0.759525	+	1.31554i	0.183569	+	0.983007i	$0.441235\pi$
$719$	−20.3660	+	35.2750i	−0.759525	+	1.31554i	−0.943093	+	0.332528i	$0.892098\pi$
$720$	3.69615	+	2.13397i	0.137747	+	0.0795285i
$721$	26.7846	−	15.4641i	0.997511	−	0.575913i
$722$	−2.93782	+	1.69615i	−0.109334	+	0.0631243i
$723$	−5.41154	−	3.12436i	−0.201257	−	0.116196i
$724$	5.69615	−	9.86603i	0.211696	−	0.366668i
$725$	15.0000	+	8.66025i	0.557086	+	0.321634i
$726$			6.87564i			0.255179i
$727$	13.6077	−	7.85641i	0.504681	−	0.291378i	−0.225963	−	0.974136i	$-0.572553\pi$
$727$	13.6077	−	7.85641i	0.504681	−	0.291378i	0.730645	+	0.682758i	$0.239220\pi$
$728$	−3.46410	+	6.00000i	−0.128388	+	0.222375i
$729$	−2.21539			−0.0820515
$730$	−6.92820			−0.256424
$731$	27.5885	−	47.7846i	1.02040	−	1.76738i
$732$			1.26795i			0.0468648i
$733$	−24.7846	−	42.9282i	−0.915440	−	1.58559i	−0.806255	−	0.591568i	$-0.798509\pi$
$733$	−24.7846	−	42.9282i	−0.915440	−	1.58559i	−0.109185	−	0.994021i	$-0.534824\pi$
$734$		−	8.39230i		−	0.309766i
$735$	3.29423	−	1.90192i	0.121509	−	0.0701535i
$736$	0.633975	+	1.09808i	0.0233686	+	0.0404756i
$737$	0.124356	+	0.215390i	0.00458070	+	0.00793400i
$738$	−8.38269	−	4.83975i	−0.308571	−	0.178154i
$739$	1.41154			0.0519244			0.0259622	−	0.999663i	$-0.491735\pi$
$739$	1.41154			0.0519244			0.0259622	+	0.999663i	$0.491735\pi$
$740$	10.3923	−	1.73205i	0.382029	−	0.0636715i
$741$	12.0000			0.440831
$742$	16.3923	+	9.46410i	0.601780	+	0.347438i
$743$	21.7583	+	37.6865i	0.798236	+	1.38258i	0.920764	+	0.390120i	$0.127566\pi$
$743$	21.7583	+	37.6865i	0.798236	+	1.38258i	−0.122528	+	0.992465i	$0.539100\pi$
$744$	−1.73205	−	3.00000i	−0.0635001	−	0.109985i
$745$	−3.10770	+	1.79423i	−0.113857	+	0.0657355i
$746$			7.00000i			0.256288i
$747$	14.3660	+	24.8827i	0.525625	+	0.910410i
$748$			5.41154i			0.197866i
$749$	10.3923	−	18.0000i	0.379727	−	0.657706i
$750$	8.87564			0.324093
$751$	50.3923			1.83884			0.919421	−	0.393276i	$-0.128658\pi$
$751$	50.3923			1.83884			0.919421	+	0.393276i	$0.128658\pi$
$752$	−0.633975	+	1.09808i	−0.0231187	+	0.0400427i
$753$	−10.9808	+	6.33975i	−0.400161	+	0.231033i
$754$		−	30.0000i		−	1.09254i
$755$	9.29423	+	5.36603i	0.338252	+	0.195290i
$756$	−4.00000	+	6.92820i	−0.145479	+	0.251976i
$757$	−5.89230	−	3.40192i	−0.214159	−	0.123645i	0.389084	−	0.921202i	$-0.372792\pi$
$757$	−5.89230	−	3.40192i	−0.214159	−	0.123645i	−0.603243	+	0.797557i	$0.706125\pi$
$758$	5.87564	−	3.39230i	0.213413	−	0.123214i
$759$	1.01924	−	0.588457i	0.0369960	−	0.0213596i
$760$	7.09808	+	4.09808i	0.257474	+	0.148653i
$761$	−16.1603	+	27.9904i	−0.585809	+	1.01465i	0.408965	+	0.912550i	$0.365890\pi$
$761$	−16.1603	+	27.9904i	−0.585809	+	1.01465i	−0.994774	+	0.102101i	$0.967444\pi$
$762$	−11.5359	−	6.66025i	−0.417902	−	0.241276i
$763$			29.3205i			1.06147i
$764$	7.09808	−	4.09808i	0.256799	−	0.148263i
$765$	−9.10770	+	15.7750i	−0.329289	+	0.570346i
$766$	3.46410			0.125163
$767$	32.7846			1.18378
$768$	0.366025	−	0.633975i	0.0132078	−	0.0228766i
$769$			34.3923i			1.24022i	0.784516	+	0.620109i	$0.212912\pi$
$769$			34.3923i			1.24022i	−0.784516	+	0.620109i	$0.787088\pi$
$770$	2.19615	+	3.80385i	0.0791438	+	0.137081i
$771$		−	12.5885i		−	0.453362i
$772$	−0.696152	+	0.401924i	−0.0250551	+	0.0144656i
$773$	−10.0359	−	17.3827i	−0.360966	−	0.625212i	0.627154	−	0.778895i	$-0.284220\pi$
$773$	−10.0359	−	17.3827i	−0.360966	−	0.625212i	−0.988120	+	0.153684i	$0.950886\pi$
$774$	−15.9282	−	27.5885i	−0.572527	−	0.991647i
$775$	8.19615	+	4.73205i	0.294414	+	0.169980i
$776$	4.26795			0.153210
$777$	1.46410	+	8.78461i	0.0525244	+	0.315146i
$778$	25.9808			0.931455
$779$	−16.0981	−	9.29423i	−0.576773	−	0.333000i
$780$	−2.19615	−	3.80385i	−0.0786349	−	0.136200i
$781$	−2.19615	−	3.80385i	−0.0785845	−	0.136112i
$782$	−4.68653	+	2.70577i	−0.167590	+	0.0967582i
$783$		−	34.6410i		−	1.23797i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$			1.73205i			0.0618195i
$786$	−7.39230	+	12.8038i	−0.263675	+	0.456698i
$787$	21.1769			0.754875			0.377438	−	0.926035i	$-0.376805\pi$
$787$	21.1769			0.754875			0.377438	+	0.926035i	$0.376805\pi$
$788$	0.464102			0.0165329
$789$	5.32051	−	9.21539i	0.189415	−	0.328077i
$790$	−25.0981	+	14.4904i	−0.892949	+	0.515545i
$791$		−	6.92820i		−	0.246339i
$792$	2.70577	+	1.56218i	0.0961454	+	0.0555096i
$793$	−3.00000	+	5.19615i	−0.106533	+	0.184521i
$794$	19.9186	+	11.5000i	0.706884	+	0.408120i
$795$	−10.3923	+	6.00000i	−0.368577	+	0.212798i
$796$	−9.00000	+	5.19615i	−0.318997	+	0.184173i
$797$	28.3923	+	16.3923i	1.00571	+	0.580645i	0.909932	−	0.414758i	$-0.136134\pi$
$797$	28.3923	+	16.3923i	1.00571	+	0.580645i	0.0957752	+	0.995403i	$0.469467\pi$
$798$	−3.46410	+	6.00000i	−0.122628	+	0.212398i
$799$	−4.68653	−	2.70577i	−0.165798	−	0.0957233i
$800$			2.00000i			0.0707107i
$801$	36.6962	−	21.1865i	1.29659	−	0.748589i
$802$	5.19615	−	9.00000i	0.183483	−	0.317801i
$803$	−5.07180			−0.178980
$804$	0.143594			0.00506415
$805$	−2.19615	+	3.80385i	−0.0774042	+	0.134068i
$806$		−	16.3923i		−	0.577394i
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$		−	5.53590i		−	0.194752i
$809$	34.3923	−	19.8564i	1.20917	−	0.698114i	0.246591	−	0.969120i	$-0.420689\pi$
$809$	34.3923	−	19.8564i	1.20917	−	0.698114i	0.962578	+	0.271006i	$0.0873562\pi$
$810$	3.86603	+	6.69615i	0.135838	+	0.235279i
$811$	0.196152	+	0.339746i	0.00688784	+	0.0119301i	0.869449	−	0.494023i	$-0.164474\pi$
$811$	0.196152	+	0.339746i	0.00688784	+	0.0119301i	−0.862561	+	0.505953i	$0.831141\pi$
$812$	15.0000	+	8.66025i	0.526397	+	0.303915i
$813$	−20.9282			−0.733984
$814$	7.60770	−	1.26795i	0.266650	−	0.0444416i
$815$	1.60770			0.0563151
$816$	2.70577	+	1.56218i	0.0947209	+	0.0546872i
$817$	−30.5885	−	52.9808i	−1.07015	−	1.85356i
$818$	−17.2583	−	29.8923i	−0.603423	−	1.04516i
$819$	−14.7846	+	8.53590i	−0.516616	+	0.298268i
$820$			6.80385i			0.237601i
$821$	−4.73205	−	8.19615i	−0.165150	−	0.286048i	0.771559	−	0.636158i	$-0.219477\pi$
$821$	−4.73205	−	8.19615i	−0.165150	−	0.286048i	−0.936708	+	0.350110i	$0.886144\pi$
$822$		−	14.1962i		−	0.495148i
$823$	−17.0981	+	29.6147i	−0.596001	+	1.03230i	0.397403	+	0.917644i	$0.369911\pi$
$823$	−17.0981	+	29.6147i	−0.596001	+	1.03230i	−0.993405	+	0.114661i	$0.963422\pi$
$824$	−15.4641			−0.538718
$825$	1.85641			0.0646318
$826$	−9.46410	+	16.3923i	−0.329298	+	0.570361i
$827$	−22.3923	+	12.9282i	−0.778657	+	0.449558i	−0.835954	−	0.548799i	$-0.815085\pi$
$827$	−22.3923	+	12.9282i	−0.778657	+	0.449558i	0.0572973	+	0.998357i	$0.481752\pi$
$828$			3.12436i			0.108579i
$829$	9.00000	+	5.19615i	0.312583	+	0.180470i	0.648082	−	0.761571i	$-0.275572\pi$
$829$	9.00000	+	5.19615i	0.312583	+	0.180470i	−0.335499	+	0.942041i	$0.608905\pi$
$830$	10.0981	−	17.4904i	0.350509	−	0.607100i
$831$	−0.509619	−	0.294229i	−0.0176785	−	0.0102067i
$832$	3.00000	−	1.73205i	0.104006	−	0.0600481i
$833$	−11.0885	+	6.40192i	−0.384192	+	0.221814i
$834$	6.71281	+	3.87564i	0.232446	+	0.134203i
$835$	−12.0000	+	20.7846i	−0.415277	+	0.719281i
$836$	5.19615	+	3.00000i	0.179713	+	0.103757i
$837$		−	18.9282i		−	0.654254i
$838$	−27.5885	+	15.9282i	−0.953027	+	0.550231i
$839$	0.509619	−	0.882686i	0.0175940	−	0.0304737i	−0.857094	−	0.515159i	$-0.827733\pi$
$839$	0.509619	−	0.882686i	0.0175940	−	0.0304737i	0.874688	+	0.484686i	$0.161066\pi$
$840$	2.53590			0.0874968
$841$	−46.0000			−1.58621
$842$	6.06218	−	10.5000i	0.208916	−	0.361854i
$843$		−	2.62693i		−	0.0904764i
$844$	9.19615	+	15.9282i	0.316545	+	0.548271i
$845$			1.73205i			0.0595844i
$846$	−2.70577	+	1.56218i	−0.0930263	+	0.0537088i
$847$	−9.39230	−	16.2679i	−0.322723	−	0.558973i
$848$	−4.73205	−	8.19615i	−0.162499	−	0.281457i
$849$	−12.5885	−	7.26795i	−0.432035	−	0.249435i
$850$	−8.53590			−0.292779
$851$	4.90192	+	5.95448i	0.168036	+	0.204117i
$852$	−2.53590			−0.0868784
$853$	11.8923	+	6.86603i	0.407185	+	0.235088i	0.689579	−	0.724210i	$-0.257795\pi$
$853$	11.8923	+	6.86603i	0.407185	+	0.235088i	−0.282395	+	0.959298i	$0.591129\pi$
$854$	−1.73205	−	3.00000i	−0.0592696	−	0.102658i
$855$	10.0981	+	17.4904i	0.345347	+	0.598158i
$856$	−9.00000	+	5.19615i	−0.307614	+	0.177601i
$857$		−	14.6603i		−	0.500785i	−0.968144	−	0.250392i	$-0.919440\pi$
$857$		−	14.6603i		−	0.500785i	0.968144	−	0.250392i	$-0.0805596\pi$
$858$	−1.60770	−	2.78461i	−0.0548858	−	0.0950650i
$859$			30.0000i			1.02359i	0.859109	+	0.511793i	$0.171019\pi$
$859$			30.0000i			1.02359i	−0.859109	+	0.511793i	$0.828981\pi$
$860$	−11.1962	+	19.3923i	−0.381786	+	0.661272i
$861$	−5.75129			−0.196003
$862$	−0.339746			−0.0115718
$863$	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
$865$			21.5885i			0.734030i
$866$	22.3301	+	12.8923i	0.758809	+	0.438098i
$867$	−0.444864	+	0.770527i	−0.0151084	+	0.0261685i
$868$	8.19615	+	4.73205i	0.278196	+	0.160616i
$869$	−18.3731	+	10.6077i	−0.623264	+	0.359841i
$870$	−9.50962	+	5.49038i	−0.322406	+	0.186141i
$871$	0.588457	+	0.339746i	0.0199391	+	0.0115119i
$872$	7.33013	−	12.6962i	0.248229	−	0.429946i
$873$	9.10770	+	5.25833i	0.308249	+	0.177968i
$874$			6.00000i			0.202953i
$875$	−21.0000	+	12.1244i	−0.709930	+	0.409878i
$876$	−1.46410	+	2.53590i	−0.0494674	+	0.0856801i
$877$	−24.1769			−0.816396			−0.408198	−	0.912893i	$-0.633843\pi$
$877$	−24.1769			−0.816396			−0.408198	+	0.912893i	$0.633843\pi$
$878$	30.2487			1.02084
$879$	7.09808	−	12.2942i	0.239412	−	0.414674i
$880$		−	2.19615i		−	0.0740323i
$881$	−24.6962	−	42.7750i	−0.832035	−	1.44113i	−0.896422	−	0.443201i	$-0.853843\pi$
$881$	−24.6962	−	42.7750i	−0.832035	−	1.44113i	0.0643877	−	0.997925i	$-0.479491\pi$
$882$			7.39230i			0.248912i
$883$	−19.0981	+	11.0263i	−0.642701	+	0.371064i	−0.785654	−	0.618666i	$-0.787674\pi$
$883$	−19.0981	+	11.0263i	−0.642701	+	0.371064i	0.142953	+	0.989729i	$0.454340\pi$
$884$	7.39230	+	12.8038i	0.248630	+	0.430640i
$885$	−6.00000	−	10.3923i	−0.201688	−	0.349334i
$886$	18.5885	+	10.7321i	0.624491	+	0.360550i
$887$	−7.94744			−0.266849			−0.133424	−	0.991059i	$-0.542597\pi$
$887$	−7.94744			−0.266849			−0.133424	+	0.991059i	$0.542597\pi$
$888$	1.56218	−	4.16987i	0.0524233	−	0.139932i
$889$	36.3923			1.22056
$890$	−25.7942	−	14.8923i	−0.864625	−	0.499191i
$891$	2.83013	+	4.90192i	0.0948128	+	0.164221i
$892$	2.90192	+	5.02628i	0.0971636	+	0.168292i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$			1.51666i			0.0507247i
$895$	−2.19615	−	3.80385i	−0.0734093	−	0.127149i
$896$			2.00000i			0.0668153i
$897$	1.60770	−	2.78461i	0.0536794	−	0.0929754i
$898$	27.4641			0.916489
$899$	−40.9808			−1.36678
$900$	−2.46410	+	4.26795i	−0.0821367	+	0.142265i
$901$	34.9808	−	20.1962i	1.16538	−	0.672831i
$902$			4.98076i			0.165841i
$903$	−16.3923	−	9.46410i	−0.545502	−	0.314946i
$904$	−1.73205	+	3.00000i	−0.0576072	+	0.0997785i
$905$	−17.0885	−	9.86603i	−0.568040	−	0.327958i
$906$	3.92820	−	2.26795i	0.130506	−	0.0753476i
$907$	−36.8827	+	21.2942i	−1.22467	+	0.707063i	−0.965910	−	0.258878i	$-0.916647\pi$
$907$	−36.8827	+	21.2942i	−1.22467	+	0.707063i	−0.258760	+	0.965942i	$0.583314\pi$
$908$	−4.09808	−	2.36603i	−0.135999	−	0.0785193i
$909$	6.82051	−	11.8135i	0.226222	−	0.391828i
$910$	10.3923	+	6.00000i	0.344502	+	0.198898i
$911$			18.3397i			0.607623i	0.952732	+	0.303811i	$0.0982593\pi$
$911$			18.3397i			0.607623i	−0.952732	+	0.303811i	$0.901741\pi$
$912$	3.00000	−	1.73205i	0.0993399	−	0.0573539i
$913$	7.39230	−	12.8038i	0.244650	−	0.423746i
$914$	13.9808			0.462443
$915$	2.19615			0.0726026
$916$	3.30385	−	5.72243i	0.109162	−	0.189074i
$917$		−	40.3923i		−	1.33387i
$918$	8.53590	+	14.7846i	0.281727	+	0.487965i
$919$			3.12436i			0.103063i	0.998671	+	0.0515315i	$0.0164103\pi$
$919$			3.12436i			0.103063i	−0.998671	+	0.0515315i	$0.983590\pi$
$920$	1.90192	−	1.09808i	0.0627046	−	0.0362025i
$921$	−8.05256	−	13.9474i	−0.265341	−	0.459584i
$922$	−16.2679	−	28.1769i	−0.535756	−	0.927957i
$923$	−10.3923	−	6.00000i	−0.342067	−	0.197492i
$924$	1.85641			0.0610713
$925$	2.00000	+	12.0000i	0.0657596	+	0.394558i
$926$	−30.0000			−0.985861
$927$	−33.0000	−	19.0526i	−1.08386	−	0.625768i
$928$	−4.33013	−	7.50000i	−0.142143	−	0.246200i
$929$	2.30385	+	3.99038i	0.0755868	+	0.130920i	0.901341	−	0.433110i	$-0.142584\pi$
$929$	2.30385	+	3.99038i	0.0755868	+	0.130920i	−0.825755	+	0.564030i	$0.809250\pi$
$930$	−5.19615	+	3.00000i	−0.170389	+	0.0983739i
$931$			14.1962i			0.465260i
$932$	7.50000	+	12.9904i	0.245671	+	0.425514i
$933$			13.1769i			0.431393i
$934$	−4.73205	+	8.19615i	−0.154837	+	0.268186i
$935$	9.37307			0.306532
$936$	8.53590			0.279005
$937$	−3.30385	+	5.72243i	−0.107932	+	0.186944i	−0.914932	−	0.403607i	$-0.867756\pi$
$937$	−3.30385	+	5.72243i	−0.107932	+	0.186944i	0.807000	+	0.590551i	$0.201090\pi$
$938$	−0.339746	+	0.196152i	−0.0110931	+	0.00640460i
$939$			0.0910347i			0.00297080i
$940$	1.90192	+	1.09808i	0.0620339	+	0.0358153i
$941$	5.89230	−	10.2058i	0.192084	−	0.332699i	−0.753857	−	0.657039i	$-0.771809\pi$
$941$	5.89230	−	10.2058i	0.192084	−	0.332699i	0.945941	+	0.324340i	$0.105142\pi$
$942$	0.633975	+	0.366025i	0.0206560	+	0.0119258i
$943$	−4.31347	+	2.49038i	−0.140466	+	0.0810980i
$944$	8.19615	−	4.73205i	0.266762	−	0.154015i
$945$	12.0000	+	6.92820i	0.390360	+	0.225374i
$946$	−8.19615	+	14.1962i	−0.266480	+	0.461557i
$947$	21.8038	+	12.5885i	0.708530	+	0.409070i	0.810516	−	0.585716i	$-0.199187\pi$
$947$	21.8038	+	12.5885i	0.708530	+	0.409070i	−0.101987	+	0.994786i	$0.532520\pi$
$948$			12.2487i			0.397820i
$949$	−12.0000	+	6.92820i	−0.389536	+	0.224899i
$950$	−4.73205	+	8.19615i	−0.153528	+	0.265918i
$951$	9.80385			0.317912
$952$	−8.53590			−0.276650
$953$	3.92820	−	6.80385i	0.127247	−	0.220398i	−0.795362	−	0.606135i	$-0.792719\pi$
$953$	3.92820	−	6.80385i	0.127247	−	0.220398i	0.922609	+	0.385736i	$0.126053\pi$
$954$		−	23.3205i		−	0.755029i
$955$	−7.09808	−	12.2942i	−0.229688	−	0.397832i
$956$		−	17.3205i		−	0.560185i
$957$	−6.96152	+	4.01924i	−0.225034	+	0.129924i
$958$	1.26795	+	2.19615i	0.0409656	+	0.0709545i
$959$	19.3923	+	33.5885i	0.626210	+	1.08463i
$960$	−1.09808	−	0.633975i	−0.0354403	−	0.0204614i
$961$	8.60770			0.277668
$962$	16.2679	−	13.3923i	0.524500	−	0.431785i
$963$	−25.6077			−0.825196
$964$	−7.39230	−	4.26795i	−0.238090	−	0.137461i
$965$	0.696152	+	1.20577i	0.0224099	+	0.0388152i
$966$	0.928203	+	1.60770i	0.0298644	+	0.0517267i
$967$	41.5692	−	24.0000i	1.33678	−	0.771788i	0.350448	−	0.936582i	$-0.386029\pi$
$967$	41.5692	−	24.0000i	1.33678	−	0.771788i	0.986328	+	0.164794i	$0.0526960\pi$
$968$			9.39230i			0.301880i
$969$	7.39230	+	12.8038i	0.237475	+	0.411319i
$970$		−	7.39230i		−	0.237353i
$971$	29.4904	−	51.0788i	0.946391	−	1.63920i	0.193450	−	0.981110i	$-0.438032\pi$
$971$	29.4904	−	51.0788i	0.946391	−	1.63920i	0.752941	−	0.658088i	$-0.228634\pi$
$972$	15.2679			0.489720
$973$	−21.1769			−0.678901
$974$	−11.0263	+	19.0981i	−0.353305	+	0.611942i
$975$	4.39230	−	2.53590i	0.140666	−	0.0812137i
$976$			1.73205i			0.0554416i
$977$	−3.00000	−	1.73205i	−0.0959785	−	0.0554132i	0.451243	−	0.892401i	$-0.350981\pi$
$977$	−3.00000	−	1.73205i	−0.0959785	−	0.0554132i	−0.547221	+	0.836988i	$0.684314\pi$
$978$	0.339746	−	0.588457i	0.0108639	−	0.0188168i
$979$	−18.8827	−	10.9019i	−0.603493	−	0.348427i
$980$	4.50000	−	2.59808i	0.143747	−	0.0829925i
$981$	31.2846	−	18.0622i	0.998841	−	0.576681i
$982$	−13.6865	−	7.90192i	−0.436755	−	0.252161i
$983$	−10.4378	+	18.0788i	−0.332915	+	0.576625i	−0.983082	−	0.183166i	$-0.941365\pi$
$983$	−10.4378	+	18.0788i	−0.332915	+	0.576625i	0.650167	+	0.759791i	$0.274699\pi$
$984$	2.49038	+	1.43782i	0.0793904	+	0.0458361i
$985$		−	0.803848i		−	0.0256127i
$986$	32.0096	−	18.4808i	1.01939	−	0.588547i
$987$	−0.928203	+	1.60770i	−0.0295450	+	0.0511735i
$988$	16.3923			0.521509
$989$	−16.3923			−0.521245
$990$	2.70577	−	4.68653i	0.0859951	−	0.148948i
$991$			52.6410i			1.67220i	0.548579	+	0.836098i	$0.315169\pi$
$991$			52.6410i			1.67220i	−0.548579	+	0.836098i	$0.684831\pi$
$992$	−2.36603	−	4.09808i	−0.0751214	−	0.130114i
$993$		0			0
$994$	6.00000	−	3.46410i	0.190308	−	0.109875i
$995$	9.00000	+	15.5885i	0.285319	+	0.494187i
$996$	−4.26795	−	7.39230i	−0.135235	−	0.234234i
$997$	−9.00000	−	5.19615i	−0.285033	−	0.164564i	0.350667	−	0.936500i	$-0.385955\pi$
$997$	−9.00000	−	5.19615i	−0.285033	−	0.164564i	−0.635700	+	0.771936i	$0.719288\pi$
$998$	−9.80385			−0.310335
$999$	18.7846	−	15.4641i	0.594319	−	0.489263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.e.b.27.1	yes	4
3.2	odd	2		666.2.s.a.397.2		4
4.3	odd	2		592.2.w.e.545.1		4
37.11	even	6	inner	74.2.e.b.11.1	✓	4
37.14	odd	12		2738.2.a.e.1.2		2
37.23	odd	12		2738.2.a.i.1.2		2
111.11	odd	6		666.2.s.a.307.2		4
148.11	odd	6		592.2.w.e.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.b.11.1	✓	4	37.11	even	6	inner
74.2.e.b.27.1	yes	4	1.1	even	1	trivial
592.2.w.e.529.1		4	148.11	odd	6
592.2.w.e.545.1		4	4.3	odd	2
666.2.s.a.307.2		4	111.11	odd	6
666.2.s.a.397.2		4	3.2	odd	2
2738.2.a.e.1.2		2	37.14	odd	12
2738.2.a.i.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -0.732051i q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -0.732051i q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} -1.73205 q^{10} -1.26795 q^{11} +(-0.366025 + 0.633975i) q^{12} +(-3.00000 + 1.73205i) q^{13} -2.00000i q^{14} +(1.09808 + 0.633975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69615 - 2.13397i) q^{17} +(-2.13397 + 1.23205i) q^{18} +(-4.09808 + 2.36603i) q^{19} +(1.50000 + 0.866025i) q^{20} +(-0.732051 + 1.26795i) q^{21} +(1.09808 + 0.633975i) q^{22} +1.26795i q^{23} +(0.633975 - 0.366025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +3.46410 q^{26} +4.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} -8.66025i q^{29} +(-0.633975 - 1.09808i) q^{30} -4.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.464102 - 0.803848i) q^{33} +(2.13397 + 3.69615i) q^{34} +(3.00000 + 1.73205i) q^{35} +2.46410 q^{36} +(4.69615 - 3.86603i) q^{37} +4.73205 q^{38} +(-2.19615 - 1.26795i) q^{39} +(-0.866025 - 1.50000i) q^{40} +(1.96410 + 3.40192i) q^{41} +(1.26795 - 0.732051i) q^{42} +12.9282i q^{43} +(-0.633975 - 1.09808i) q^{44} -4.26795i q^{45} +(0.633975 - 1.09808i) q^{46} +1.26795 q^{47} -0.732051 q^{48} +(1.50000 - 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} -3.12436i q^{51} +(-3.00000 - 1.73205i) q^{52} +(-4.73205 + 8.19615i) q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.90192 + 1.09808i) q^{55} +(1.73205 - 1.00000i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(-4.33013 + 7.50000i) q^{58} +(-8.19615 - 4.73205i) q^{59} +1.26795i q^{60} +(1.50000 - 0.866025i) q^{61} +(-2.36603 + 4.09808i) q^{62} +4.92820 q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +0.928203i q^{66} +(-0.0980762 - 0.169873i) q^{67} -4.26795i q^{68} +(-0.803848 + 0.464102i) q^{69} +(-1.73205 - 3.00000i) q^{70} +(1.73205 + 3.00000i) q^{71} +(-2.13397 - 1.23205i) q^{72} +4.00000 q^{73} +(-6.00000 + 1.00000i) q^{74} -1.46410 q^{75} +(-4.09808 - 2.36603i) q^{76} +(-1.26795 - 2.19615i) q^{77} +(1.26795 + 2.19615i) q^{78} +(14.4904 - 8.36603i) q^{79} +1.73205i q^{80} +(-2.23205 - 3.86603i) q^{81} -3.92820i q^{82} +(-5.83013 + 10.0981i) q^{83} -1.46410 q^{84} -7.39230 q^{85} +(6.46410 - 11.1962i) q^{86} +(5.49038 - 3.16987i) q^{87} +1.26795i q^{88} +(14.8923 + 8.59808i) q^{89} +(-2.13397 + 3.69615i) q^{90} +(-6.00000 - 3.46410i) q^{91} +(-1.09808 + 0.633975i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-1.09808 - 0.633975i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(0.633975 + 0.366025i) q^{96} +4.26795i q^{97} +(-2.59808 + 1.50000i) q^{98} +(-1.56218 + 2.70577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9 - 12 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 - 6 * q^22 + 6 * q^24 - 4 * q^25 + 16 * q^27 - 4 * q^28 - 6 * q^30 + 12 * q^33 + 12 * q^34 + 12 * q^35 - 4 * q^36 - 2 * q^37 + 12 * q^38 + 12 * q^39 - 6 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 + 6 * q^49 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 12 * q^57 - 12 * q^59 + 6 * q^61 - 6 * q^62 - 8 * q^63 - 4 * q^64 - 12 * q^65 + 10 * q^67 - 24 * q^69 - 12 * q^72 + 16 * q^73 - 24 * q^74 + 8 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 6 * q^79 - 2 * q^81 - 6 * q^83 + 8 * q^84 + 12 * q^85 + 12 * q^86 - 30 * q^87 + 18 * q^89 - 12 * q^90 - 24 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 + 6 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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