LMFDB - Embedded newform 74.2.e.b.11.1

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			11.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	74.11
Dual form			74.2.e.b.27.1

$q$-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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$			0.732051i			0.298858i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$			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	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$			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	−0.876046	−	0.482227i	$-0.839828\pi$
$17$	−3.69615	+	2.13397i	−0.896449	+	0.517565i	−0.0204023	+	0.999792i	$0.506495\pi$
$18$	−2.13397	−	1.23205i	−0.502983	−	0.290397i
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.0501517	−	0.998742i	$-0.515970\pi$
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.890011	+	0.455938i	$0.849304\pi$
$20$	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	$-0.957798\pi$
$23$		−	1.26795i		−	0.264386i	0.991224	−	0.132193i	$-0.0422018\pi$
$24$	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	$0.297344\pi$
$29$			8.66025i			1.60817i	−0.594515	+	0.804084i	$0.702656\pi$
$30$	−0.633975	+	1.09808i	−0.115747	+	0.200480i
$31$			4.73205i			0.849901i	0.905216	+	0.424951i	$0.139709\pi$
$31$			4.73205i			0.849901i	−0.905216	+	0.424951i	$0.860291\pi$
$32$	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	−0.670906	−	0.741542i	$-0.734095\pi$
$41$	1.96410	−	3.40192i	0.306741	−	0.531291i	0.977647	+	0.210251i	$0.0674281\pi$
$42$	1.26795	+	0.732051i	0.195649	+	0.112958i
$43$		−	12.9282i		−	1.97153i	−0.168122	−	0.985766i	$-0.553770\pi$
$43$		−	12.9282i		−	1.97153i	0.168122	−	0.985766i	$-0.446230\pi$
$44$	−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	−0.983123	−	0.182946i	$-0.941437\pi$
$53$	−4.73205	−	8.19615i	−0.649997	−	1.12583i	0.333126	−	0.942882i	$-0.391897\pi$
$54$	−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	−0.927373	−	0.374137i	$-0.877939\pi$
$59$	−8.19615	+	4.73205i	−1.06705	+	0.616061i	−0.139675	+	0.990197i	$0.544606\pi$
$60$		−	1.26795i		−	0.163692i
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	0.592944	−	0.805243i	$-0.297965\pi$
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	−0.400889	+	0.916127i	$0.631299\pi$
$62$	−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	−0.871954	−	0.489587i	$-0.837147\pi$
$67$	−0.0980762	+	0.169873i	−0.0119819	+	0.0207533i	0.859972	+	0.510341i	$0.170481\pi$
$68$			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	−0.744753	−	0.667340i	$-0.767433\pi$
$71$	1.73205	−	3.00000i	0.205557	−	0.356034i	0.950310	+	0.311305i	$0.100766\pi$
$72$	−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	0.984001	+	0.178163i	$0.0570155\pi$
$79$	14.4904	+	8.36603i	1.63030	+	0.941251i	0.646294	+	0.763088i	$0.276318\pi$
$80$		−	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	−0.985446	−	0.169991i	$-0.945626\pi$
$83$	−5.83013	−	10.0981i	−0.639940	−	1.10841i	0.345506	−	0.938417i	$-0.387707\pi$
$84$	−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	0.583523	−	0.812096i	$-0.301674\pi$
$89$	14.8923	−	8.59808i	1.57858	−	0.911394i	0.995058	−	0.0992979i	$-0.0316597\pi$
$90$	−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	$-0.930480\pi$
$97$		−	4.26795i		−	0.433345i	0.976244	−	0.216672i	$-0.0695203\pi$
$98$	−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	$0.275714\pi$
$103$			15.4641i			1.52372i	−0.647740	+	0.761862i	$0.724286\pi$
$104$	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	0.497665	+	0.867369i	$0.334191\pi$
$107$	−5.19615	+	9.00000i	−0.502331	+	0.870063i	−0.999996	+	0.00269372i	$0.999143\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	12.6962	−	7.33013i	1.21607	−	0.702099i	0.251996	−	0.967728i	$-0.418913\pi$
$109$	12.6962	−	7.33013i	1.21607	−	0.702099i	0.964075	+	0.265630i	$0.0855798\pi$
$110$	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	−0.634426	−	0.772983i	$-0.718764\pi$
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	0.352210	+	0.935921i	$0.385430\pi$
$114$	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	0.914711	+	0.404108i	$0.132418\pi$
$127$	9.09808	+	15.7583i	0.807324	+	1.39833i	−0.107387	+	0.994217i	$0.534249\pi$
$128$	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	−0.528702	+	0.848808i	$0.677321\pi$
$131$	−17.4904	+	10.0981i	−1.52814	+	0.882273i	−0.999440	+	0.0334654i	$0.989346\pi$
$132$	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	0.549274	−	0.835642i	$-0.314904\pi$
$139$	−5.29423	−	9.16987i	−0.449051	−	0.777778i	−0.998324	+	0.0578639i	$0.981571\pi$
$140$		−	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	−0.711991	−	0.702189i	$-0.752206\pi$
$151$	3.09808	−	5.36603i	0.252118	−	0.436681i	0.964109	+	0.265508i	$0.0855396\pi$
$152$	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	0.845383	−	0.534160i	$-0.179372\pi$
$157$	−0.500000	−	0.866025i	−0.0399043	−	0.0691164i	−0.885288	+	0.465044i	$0.846039\pi$
$158$	−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	−0.468188	−	0.883629i	$-0.655093\pi$
$163$	0.803848	−	0.464102i	0.0629622	−	0.0363512i	0.531151	+	0.847277i	$0.321760\pi$
$164$	−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	−0.0422232	−	0.999108i	$-0.513444\pi$
$167$	−12.0000	−	6.92820i	−0.928588	−	0.536120i	−0.886365	+	0.462988i	$0.846777\pi$
$168$	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	0.525737	−	0.850647i	$-0.323790\pi$
$173$	−6.23205	−	10.7942i	−0.473814	−	0.820670i	−0.999551	+	0.0299775i	$0.990456\pi$
$174$	−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	$0.0302119\pi$
$179$			2.53590i			0.189542i	−0.995499	+	0.0947710i	$0.969788\pi$
$180$	3.69615	+	2.13397i	0.275495	+	0.159057i
$181$	−5.69615	+	9.86603i	−0.423392	+	0.733336i	−0.996269	−	0.0863054i	$-0.972494\pi$
$181$	−5.69615	+	9.86603i	−0.423392	+	0.733336i	0.572877	+	0.819641i	$0.305827\pi$
$182$	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	$0.0958283\pi$
$191$			8.19615i			0.593053i	−0.955025	+	0.296526i	$0.904172\pi$
$192$	−0.366025	+	0.633975i	−0.0264156	+	0.0457532i
$193$		−	0.803848i		−	0.0578622i	−0.999581	−	0.0289311i	$-0.990790\pi$
$193$		−	0.803848i		−	0.0578622i	0.999581	−	0.0289311i	$-0.00921034\pi$
$194$	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	0.874174	−	0.485614i	$-0.161404\pi$
$197$	0.232051	+	0.401924i	0.0165329	+	0.0286359i	−0.857641	+	0.514250i	$0.828070\pi$
$198$	2.70577	+	1.56218i	0.192291	+	0.111019i
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$	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	0.357797	−	0.933799i	$-0.383528\pi$
$227$	−4.09808	−	2.36603i	−0.271999	−	0.157039i	−0.629796	+	0.776761i	$0.716861\pi$
$228$			3.46410i			0.229416i
$229$	−3.30385	+	5.72243i	−0.218324	+	0.378149i	−0.954296	−	0.298864i	$-0.903392\pi$
$229$	−3.30385	+	5.72243i	−0.218324	+	0.378149i	0.735971	+	0.677013i	$0.236726\pi$
$230$			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	−0.899318	−	0.437295i	$-0.855937\pi$
$239$	−15.0000	+	8.66025i	−0.970269	+	0.560185i	−0.0709510	+	0.997480i	$0.522603\pi$
$240$	−1.09808	−	0.633975i	−0.0708805	−	0.0409229i
$241$	−7.39230	−	4.26795i	−0.476180	−	0.274923i	0.242643	−	0.970116i	$-0.421986\pi$
$241$	−7.39230	−	4.26795i	−0.476180	−	0.274923i	−0.718823	+	0.695193i	$0.755319\pi$
$242$	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	$-0.815910\pi$
$251$		−	17.3205i		−	1.09326i	0.837374	−	0.546630i	$-0.184090\pi$
$252$	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	−0.886481	−	0.462764i	$-0.846858\pi$
$257$	−14.8923	+	8.59808i	−0.928956	+	0.536333i	−0.0424751	+	0.999098i	$0.513524\pi$
$258$	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	−0.998266	−	0.0588577i	$-0.981254\pi$
$263$	−7.26795	+	12.5885i	−0.448161	+	0.776238i	0.550105	+	0.835095i	$0.314588\pi$
$264$	−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	−0.863720	−	0.503972i	$-0.831871\pi$
$271$	−14.2942	−	24.7583i	−0.868313	−	1.50396i	−0.00459256	−	0.999989i	$-0.501462\pi$
$272$	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	0.478940	−	0.877847i	$-0.341021\pi$
$277$	−0.696152	−	0.401924i	−0.0418277	−	0.0241493i	−0.520768	+	0.853698i	$0.674354\pi$
$278$	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	−0.589822	−	0.807533i	$-0.700802\pi$
$281$	−3.10770	+	1.79423i	−0.185390	+	0.107035i	0.404433	+	0.914568i	$0.367469\pi$
$282$			0.928203i			0.0552737i
$283$	−17.1962	−	9.92820i	−1.02221	−	0.590170i	−0.107463	−	0.994209i	$-0.534273\pi$
$283$	−17.1962	−	9.92820i	−1.02221	−	0.590170i	−0.914742	+	0.404039i	$0.867606\pi$
$284$	−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	0.430457	+	0.902611i	$0.358352\pi$
$293$	−9.69615	+	16.7942i	−0.566455	+	0.981129i	−0.996913	+	0.0785184i	$0.974981\pi$
$294$	−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	0.0119847	−	0.999928i	$-0.496185\pi$
$311$	15.5885	−	9.00000i	0.883940	−	0.510343i	0.871956	+	0.489585i	$0.162852\pi$
$312$	−1.26795	−	2.19615i	−0.0717835	−	0.124333i
$313$	0.107695	−	0.0621778i	0.00608729	−	0.00351450i	−0.496953	−	0.867777i	$-0.665548\pi$
$313$	0.107695	−	0.0621778i	0.00608729	−	0.00351450i	0.503041	+	0.864263i	$0.332215\pi$
$314$	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	0.990490	−	0.137584i	$-0.0439338\pi$
$317$	6.69615	+	11.5981i	0.376093	+	0.651413i	−0.614397	+	0.788997i	$0.710601\pi$
$318$	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	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−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	0.0823295	+	0.996605i	$0.473764\pi$
$337$	−15.0885	+	26.1340i	−0.821921	+	1.42361i	−0.904250	+	0.427003i	$0.859569\pi$
$338$	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	$0.133062\pi$
$347$			15.1244i			0.811918i	−0.913891	+	0.405959i	$0.866938\pi$
$348$	5.49038	−	3.16987i	0.294315	−	0.169923i
$349$	4.69615	+	8.13397i	0.251379	+	0.435402i	0.963906	−	0.266243i	$-0.0857825\pi$
$349$	4.69615	+	8.13397i	0.251379	+	0.435402i	−0.712527	+	0.701645i	$0.752449\pi$
$350$	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	−0.0757878	−	0.997124i	$-0.524147\pi$
$353$	14.0885	−	8.13397i	0.749853	−	0.432928i	0.825641	+	0.564196i	$0.190814\pi$
$354$	−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	−0.735477	−	0.677550i	$-0.763042\pi$
$367$	4.19615	−	7.26795i	0.219037	−	0.379384i	0.954514	+	0.298166i	$0.0963750\pi$
$368$	−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	−0.942297	−	0.334777i	$-0.891339\pi$
$373$	−3.50000	+	6.06218i	−0.181223	+	0.313888i	0.761074	+	0.648665i	$0.224672\pi$
$374$	−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	0.765651	−	0.643256i	$-0.222417\pi$
$379$	−3.39230	−	5.87564i	−0.174251	−	0.301812i	−0.939902	+	0.341445i	$0.889084\pi$
$380$	−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	0.421392	−	0.906879i	$-0.361542\pi$
$383$	−3.00000	−	1.73205i	−0.153293	−	0.0885037i	−0.574684	+	0.818375i	$0.694875\pi$
$384$		−	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	−0.194168	−	0.980968i	$-0.562201\pi$
$389$	−22.5000	−	12.9904i	−1.14080	−	0.658638i	−0.946627	+	0.322330i	$0.895534\pi$
$390$	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	$-0.916448\pi$
$401$		−	10.3923i		−	0.518967i	0.965748	−	0.259483i	$-0.0835523\pi$
$402$	−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	0.478386	−	0.878149i	$-0.341222\pi$
$409$	29.8923	−	17.2583i	1.47808	−	0.853370i	0.999693	+	0.0247799i	$0.00788850\pi$
$410$	−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	0.933011	+	0.359849i	$0.117172\pi$
$419$	15.9282	+	27.5885i	0.778144	+	1.34778i	−0.154867	+	0.987935i	$0.549495\pi$
$420$	−2.19615	−	1.26795i	−0.107161	−	0.0618696i
$421$		−	12.1244i		−	0.590905i	−0.955357	−	0.295452i	$-0.904530\pi$
$421$		−	12.1244i		−	0.590905i	0.955357	−	0.295452i	$-0.0954704\pi$
$422$	−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	0.507070	−	0.861905i	$-0.330729\pi$
$431$	0.294229	+	0.169873i	0.0141725	+	0.00818249i	−0.492897	+	0.870088i	$0.664062\pi$
$432$	−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	−0.279110	−	0.960259i	$-0.590039\pi$
$439$	−26.1962	−	15.1244i	−1.25027	−	0.721846i	−0.971164	+	0.238413i	$0.923373\pi$
$440$	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	−0.180436	−	0.983587i	$-0.557751\pi$
$449$	−23.7846	−	13.7321i	−1.12247	−	0.648056i	−0.942029	+	0.335531i	$0.891084\pi$
$450$			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	0.189326	−	0.981914i	$-0.439370\pi$
$457$	−12.1077	−	6.99038i	−0.566374	−	0.326996i	−0.755700	+	0.654918i	$0.772703\pi$
$458$		−	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	0.329848	−	0.944034i	$-0.393002\pi$
$461$	28.1769	−	16.2679i	1.31233	−	0.757674i	0.982482	+	0.186360i	$0.0596691\pi$
$462$	−1.60770	−	0.928203i	−0.0747967	−	0.0431839i
$463$	25.9808	+	15.0000i	1.20743	+	0.697109i	0.962197	−	0.272355i	$-0.0878026\pi$
$463$	25.9808	+	15.0000i	1.20743	+	0.697109i	0.245232	+	0.969465i	$0.421136\pi$
$464$	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	$0.0702707\pi$
$467$			9.46410i			0.437946i	−0.975731	+	0.218973i	$0.929729\pi$
$468$	−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	−0.549333	−	0.835604i	$-0.685118\pi$
$479$	−2.19615	+	1.26795i	−0.100345	+	0.0579341i	0.448988	+	0.893538i	$0.351785\pi$
$480$	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	$0.166537\pi$
$487$			22.0526i			0.999297i	−0.866228	+	0.499648i	$0.833463\pi$
$488$	−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	0.677854	−	0.735197i	$-0.262910\pi$
$499$	8.49038	+	4.90192i	0.380082	+	0.219440i	−0.297772	+	0.954637i	$0.596244\pi$
$500$	−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	−0.298627	−	0.954370i	$-0.596529\pi$
$503$	8.49038	−	4.90192i	0.378567	−	0.218566i	0.677195	+	0.735804i	$0.263195\pi$
$504$			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	0.860837	−	0.508881i	$-0.169941\pi$
$509$	−0.232051	−	0.401924i	−0.0102855	−	0.0178150i	−0.871122	+	0.491066i	$0.836607\pi$
$510$		−	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	−0.995390	−	0.0959151i	$-0.969422\pi$
$521$	−9.46410	+	16.3923i	−0.414630	+	0.718160i	0.580760	+	0.814075i	$0.302756\pi$
$522$	10.6699	−	18.4808i	0.467008	−	0.808881i
$523$	33.2942	+	19.2224i	1.45585	+	0.840538i	0.998804	−	0.0489020i	$-0.0155722\pi$
$523$	33.2942	+	19.2224i	1.45585	+	0.840538i	0.457051	+	0.889440i	$0.348906\pi$
$524$			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	$0.134320\pi$
$541$			19.0526i			0.819133i	−0.912280	+	0.409567i	$0.865680\pi$
$542$	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	$-0.825803\pi$
$547$		−	24.3397i		−	1.04069i	0.853955	−	0.520346i	$-0.174197\pi$
$548$	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	0.320124	−	0.947376i	$-0.396275\pi$
$557$	30.6962	−	17.7224i	1.30064	−	0.750924i	0.980513	+	0.196452i	$0.0629420\pi$
$558$	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	$-0.914539\pi$
$563$		−	12.5885i		−	0.530540i	0.964174	−	0.265270i	$-0.0854611\pi$
$564$	−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	$0.217536\pi$
$569$			30.1244i			1.26288i	−0.775425	+	0.631439i	$0.782464\pi$
$570$	5.19615	−	3.00000i	0.217643	−	0.125656i
$571$	17.6865	+	30.6340i	0.740158	+	1.28199i	0.952423	+	0.304780i	$0.0985828\pi$
$571$	17.6865	+	30.6340i	0.740158	+	1.28199i	−0.212264	+	0.977212i	$0.568084\pi$
$572$	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	−0.714607	−	0.699527i	$-0.753394\pi$
$577$	−11.1962	+	6.46410i	−0.466102	+	0.269104i	0.248505	+	0.968631i	$0.420061\pi$
$578$			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	0.332912	−	0.942958i	$-0.391969\pi$
$587$	−7.68653	−	4.43782i	−0.317257	−	0.183169i	−0.650169	+	0.759789i	$0.725302\pi$
$588$	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	0.369693	+	0.929154i	$0.379463\pi$
$599$	−15.1699	+	26.2750i	−0.619824	+	1.07357i	−0.989517	+	0.144413i	$0.953871\pi$
$600$		−	1.46410i		−	0.0597717i
$601$	16.6962	+	28.9186i	0.681050	+	1.17961i	0.974661	+	0.223688i	$0.0718098\pi$
$601$	16.6962	+	28.9186i	0.681050	+	1.17961i	−0.293610	+	0.955925i	$0.594857\pi$
$602$	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	−0.999543	−	0.0302269i	$-0.990377\pi$
$607$	−36.2942	+	20.9545i	−1.47314	+	0.850516i	−0.473594	+	0.880743i	$0.657044\pi$
$608$	−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	0.974285	+	0.225318i	$0.0723421\pi$
$613$	16.8923	+	29.2583i	0.682274	+	1.18173i	−0.292012	+	0.956415i	$0.594325\pi$
$614$	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	−0.739931	−	0.672683i	$-0.765142\pi$
$617$	−23.6603	−	40.9808i	−0.952526	−	1.64982i	−0.212595	−	0.977140i	$-0.568192\pi$
$618$	−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	−0.763287	−	0.646059i	$-0.776416\pi$
$631$	−14.7058	+	8.49038i	−0.585428	+	0.337997i	0.177860	+	0.984056i	$0.443083\pi$
$632$	−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	−0.996577	−	0.0826663i	$-0.973656\pi$
$641$	−14.4282	−	24.9904i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$642$	−6.58846	−	3.80385i	−0.260026	−	0.150126i
$643$			16.7321i			0.659848i	0.944008	+	0.329924i	$0.107023\pi$
$643$			16.7321i			0.659848i	−0.944008	+	0.329924i	$0.892977\pi$
$644$	−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	−0.284746	−	0.958603i	$-0.591909\pi$
$647$	−31.9808	−	18.4641i	−1.25729	−	0.725899i	−0.972548	+	0.232704i	$0.925243\pi$
$648$	−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	0.358631	−	0.933479i	$-0.383243\pi$
$653$	−6.91154	−	3.99038i	−0.270470	−	0.156156i	−0.629101	+	0.777324i	$0.716577\pi$
$654$	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	−0.840272	−	0.542165i	$-0.817605\pi$
$659$	1.26795	−	2.19615i	0.0493923	−	0.0855500i	0.889665	+	0.456615i	$0.150938\pi$
$660$			1.60770i			0.0625794i
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	0.528888	−	0.848692i	$-0.322609\pi$
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	−0.470545	+	0.882376i	$0.655943\pi$
$662$		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	−0.978008	−	0.208569i	$-0.933119\pi$
$673$	−8.00000	+	13.8564i	−0.308377	+	0.534125i	0.669630	+	0.742695i	$0.266453\pi$
$674$		−	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	0.0296318	−	0.999561i	$-0.490567\pi$
$683$	23.7846	−	13.7321i	0.910093	−	0.525442i	0.880461	+	0.474119i	$0.157233\pi$
$684$	−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	0.999595	−	0.0284531i	$-0.00905811\pi$
$691$	12.4904	+	21.6340i	0.475156	+	0.822995i	−0.524439	+	0.851448i	$0.675725\pi$
$692$	−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	−0.580649	−	0.814154i	$-0.697201\pi$
$701$	−4.39230	+	2.53590i	−0.165895	+	0.0957796i	0.414754	+	0.909934i	$0.363868\pi$
$702$	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	$-0.671465\pi$
$709$		−	45.7128i		−	1.71678i	0.512997	−	0.858390i	$-0.328535\pi$
$710$	−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	−0.943093	−	0.332528i	$-0.892098\pi$
$719$	−20.3660	−	35.2750i	−0.759525	−	1.31554i	0.183569	−	0.983007i	$-0.441235\pi$
$720$	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	0.730645	−	0.682758i	$-0.239220\pi$
$727$	13.6077	+	7.85641i	0.504681	+	0.291378i	−0.225963	+	0.974136i	$0.572553\pi$
$728$	−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	−0.109185	+	0.994021i	$0.534824\pi$
$733$	−24.7846	+	42.9282i	−0.915440	+	1.58559i	−0.806255	+	0.591568i	$0.798509\pi$
$734$			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	−0.122528	−	0.992465i	$-0.539100\pi$
$743$	21.7583	−	37.6865i	0.798236	−	1.38258i	0.920764	−	0.390120i	$-0.127566\pi$
$744$	−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	−0.603243	−	0.797557i	$-0.706125\pi$
$757$	−5.89230	+	3.40192i	−0.214159	+	0.123645i	0.389084	+	0.921202i	$0.372792\pi$
$758$	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	−0.994774	−	0.102101i	$-0.967444\pi$
$761$	−16.1603	−	27.9904i	−0.585809	−	1.01465i	0.408965	−	0.912550i	$-0.365890\pi$
$762$	−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	$-0.787088\pi$
$769$		−	34.3923i		−	1.24022i	0.784516	−	0.620109i	$-0.212912\pi$
$770$	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	−0.988120	−	0.153684i	$-0.950886\pi$
$773$	−10.0359	+	17.3827i	−0.360966	+	0.625212i	0.627154	+	0.778895i	$0.284220\pi$
$774$	−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	0.0957752	−	0.995403i	$-0.469467\pi$
$797$	28.3923	−	16.3923i	1.00571	−	0.580645i	0.909932	+	0.414758i	$0.136134\pi$
$798$	−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	0.962578	−	0.271006i	$-0.0873562\pi$
$809$	34.3923	+	19.8564i	1.20917	+	0.698114i	0.246591	+	0.969120i	$0.420689\pi$
$810$	3.86603	−	6.69615i	0.135838	−	0.235279i
$811$	0.196152	−	0.339746i	0.00688784	−	0.0119301i	−0.862561	−	0.505953i	$-0.831141\pi$
$811$	0.196152	−	0.339746i	0.00688784	−	0.0119301i	0.869449	+	0.494023i	$0.164474\pi$
$812$	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	−0.936708	−	0.350110i	$-0.886144\pi$
$821$	−4.73205	+	8.19615i	−0.165150	+	0.286048i	0.771559	+	0.636158i	$0.219477\pi$
$822$			14.1962i			0.495148i
$823$	−17.0981	−	29.6147i	−0.596001	−	1.03230i	−0.993405	−	0.114661i	$-0.963422\pi$
$823$	−17.0981	−	29.6147i	−0.596001	−	1.03230i	0.397403	−	0.917644i	$-0.369911\pi$
$824$	−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	0.0572973	−	0.998357i	$-0.481752\pi$
$827$	−22.3923	−	12.9282i	−0.778657	−	0.449558i	−0.835954	+	0.548799i	$0.815085\pi$
$828$		−	3.12436i		−	0.108579i
$829$	9.00000	−	5.19615i	0.312583	−	0.180470i	−0.335499	−	0.942041i	$-0.608905\pi$
$829$	9.00000	−	5.19615i	0.312583	−	0.180470i	0.648082	+	0.761571i	$0.275572\pi$
$830$	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	0.874688	−	0.484686i	$-0.161066\pi$
$839$	0.509619	+	0.882686i	0.0175940	+	0.0304737i	−0.857094	+	0.515159i	$0.827733\pi$
$840$	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	−0.282395	−	0.959298i	$-0.591129\pi$
$853$	11.8923	−	6.86603i	0.407185	−	0.235088i	0.689579	+	0.724210i	$0.257795\pi$
$854$	−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	$0.0805596\pi$
$857$			14.6603i			0.500785i	−0.968144	+	0.250392i	$0.919440\pi$
$858$	−1.60770	+	2.78461i	−0.0548858	+	0.0950650i
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−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	0.971137	−	0.238524i	$-0.0766636\pi$
$863$	8.19615	+	14.1962i	0.279000	+	0.483243i	−0.692136	+	0.721767i	$0.743330\pi$
$864$	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	0.0643877	+	0.997925i	$0.479491\pi$
$881$	−24.6962	+	42.7750i	−0.832035	+	1.44113i	−0.896422	+	0.443201i	$0.853843\pi$
$882$		−	7.39230i		−	0.248912i
$883$	−19.0981	−	11.0263i	−0.642701	−	0.371064i	0.142953	−	0.989729i	$-0.454340\pi$
$883$	−19.0981	−	11.0263i	−0.642701	−	0.371064i	−0.785654	+	0.618666i	$0.787674\pi$
$884$	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	−0.258760	−	0.965942i	$-0.583314\pi$
$907$	−36.8827	−	21.2942i	−1.22467	−	0.707063i	−0.965910	+	0.258878i	$0.916647\pi$
$908$	−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	$-0.901741\pi$
$911$		−	18.3397i		−	0.607623i	0.952732	−	0.303811i	$-0.0982593\pi$
$912$	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	$-0.983590\pi$
$919$		−	3.12436i		−	0.103063i	0.998671	−	0.0515315i	$-0.0164103\pi$
$920$	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	−0.825755	−	0.564030i	$-0.809250\pi$
$929$	2.30385	−	3.99038i	0.0755868	−	0.130920i	0.901341	+	0.433110i	$0.142584\pi$
$930$	−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	0.807000	−	0.590551i	$-0.201090\pi$
$937$	−3.30385	−	5.72243i	−0.107932	−	0.186944i	−0.914932	+	0.403607i	$0.867756\pi$
$938$	−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	0.945941	−	0.324340i	$-0.105142\pi$
$941$	5.89230	+	10.2058i	0.192084	+	0.332699i	−0.753857	+	0.657039i	$0.771809\pi$
$942$	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	−0.101987	−	0.994786i	$-0.532520\pi$
$947$	21.8038	−	12.5885i	0.708530	−	0.409070i	0.810516	+	0.585716i	$0.199187\pi$
$948$		−	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	0.922609	−	0.385736i	$-0.126053\pi$
$953$	3.92820	+	6.80385i	0.127247	+	0.220398i	−0.795362	+	0.606135i	$0.792719\pi$
$954$			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	0.986328	−	0.164794i	$-0.0526960\pi$
$967$	41.5692	+	24.0000i	1.33678	+	0.771788i	0.350448	+	0.936582i	$0.386029\pi$
$968$		−	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	0.752941	+	0.658088i	$0.228634\pi$
$971$	29.4904	+	51.0788i	0.946391	+	1.63920i	0.193450	+	0.981110i	$0.438032\pi$
$972$	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	−0.547221	−	0.836988i	$-0.684314\pi$
$977$	−3.00000	+	1.73205i	−0.0959785	+	0.0554132i	0.451243	+	0.892401i	$0.350981\pi$
$978$	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	0.650167	−	0.759791i	$-0.274699\pi$
$983$	−10.4378	−	18.0788i	−0.332915	−	0.576625i	−0.983082	+	0.183166i	$0.941365\pi$
$984$	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	$-0.684831\pi$
$991$		−	52.6410i		−	1.67220i	0.548579	−	0.836098i	$-0.315169\pi$
$992$	−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	−0.635700	−	0.771936i	$-0.719288\pi$
$997$	−9.00000	+	5.19615i	−0.285033	+	0.164564i	0.350667	+	0.936500i	$0.385955\pi$
$998$	−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.11.1	✓	4
3.2	odd	2		666.2.s.a.307.2		4
4.3	odd	2		592.2.w.e.529.1		4
37.8	odd	12		2738.2.a.e.1.2		2
37.27	even	6	inner	74.2.e.b.27.1	yes	4
37.29	odd	12		2738.2.a.i.1.2		2
111.101	odd	6		666.2.s.a.397.2		4
148.27	odd	6		592.2.w.e.545.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.b.11.1	✓	4	1.1	even	1	trivial
74.2.e.b.27.1	yes	4	37.27	even	6	inner
592.2.w.e.529.1		4	4.3	odd	2
592.2.w.e.545.1		4	148.27	odd	6
666.2.s.a.307.2		4	3.2	odd	2
666.2.s.a.397.2		4	111.101	odd	6
2738.2.a.e.1.2		2	37.8	odd	12
2738.2.a.i.1.2		2	37.29	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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