LMFDB - Embedded newform 1014.2.e.g.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.529
Dual form			1014.2.e.g.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.86603 + 3.23205i) q^{10} +(-0.633975 + 1.09808i) q^{11} +1.00000 q^{12} -2.73205 q^{14} +(-1.86603 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +1.00000 q^{18} +(-2.36603 - 4.09808i) q^{19} +(-1.86603 - 3.23205i) q^{20} -2.73205 q^{21} +(-0.633975 - 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(-0.500000 + 0.866025i) q^{24} +8.92820 q^{25} +1.00000 q^{27} +(1.36603 - 2.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(-1.86603 - 3.23205i) q^{30} +1.46410 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.633975 - 1.09808i) q^{33} -5.73205 q^{34} +(5.09808 + 8.83013i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.76795 + 3.06218i) q^{37} +4.73205 q^{38} +3.73205 q^{40} +(4.69615 - 8.13397i) q^{41} +(1.36603 - 2.36603i) q^{42} +(4.83013 + 8.36603i) q^{43} +1.26795 q^{44} +(-1.86603 - 3.23205i) q^{45} +(-2.09808 - 3.63397i) q^{46} +2.19615 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.232051 + 0.401924i) q^{49} +(-4.46410 + 7.73205i) q^{50} -5.73205 q^{51} -6.46410 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(2.23205 + 3.86603i) q^{58} +(-4.00000 - 6.92820i) q^{59} +3.73205 q^{60} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} +(1.36603 - 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 + 11.3660i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-2.09808 - 3.63397i) q^{69} -10.1962 q^{70} +(-2.36603 - 4.09808i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(-1.76795 - 3.06218i) q^{74} +(-4.46410 + 7.73205i) q^{75} +(-2.36603 + 4.09808i) q^{76} -3.46410 q^{77} -2.53590 q^{79} +(-1.86603 + 3.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.69615 + 8.13397i) q^{82} -0.196152 q^{83} +(1.36603 + 2.36603i) q^{84} +(10.6962 + 18.5263i) q^{85} -9.66025 q^{86} +(2.23205 + 3.86603i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(4.73205 - 8.19615i) q^{89} +3.73205 q^{90} +4.19615 q^{92} +(-0.732051 + 1.26795i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(-8.83013 - 15.2942i) q^{95} +1.00000 q^{96} +(3.00000 + 5.19615i) q^{97} +(-0.232051 - 0.401924i) q^{98} +1.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^31 - 2 * q^32 - 6 * q^33 - 16 * q^34 + 10 * q^35 - 2 * q^36 - 14 * q^37 + 12 * q^38 + 8 * q^40 - 2 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - 4 * q^45 + 2 * q^46 - 12 * q^47 - 2 * q^48 + 6 * q^49 - 4 * q^50 - 16 * q^51 - 12 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 12 * q^57 + 2 * q^58 - 16 * q^59 + 8 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 8 * q^68 + 2 * q^69 - 20 * q^70 - 6 * q^71 - 2 * q^72 - 32 * q^73 - 14 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^79 - 4 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 + 2 * q^84 + 22 * q^85 - 4 * q^86 + 2 * q^87 - 6 * q^88 + 12 * q^89 + 8 * q^90 - 4 * q^92 + 4 * q^93 + 6 * q^94 - 18 * q^95 + 4 * q^96 + 12 * q^97 + 6 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.73205			1.66902			0.834512	−	0.550990i	$-0.185750\pi$
$5$	3.73205			1.66902			0.834512	+	0.550990i	$0.185750\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.36603	+	2.36603i	0.516309	+	0.894274i	0.999821	+	0.0189356i	$0.00602775\pi$
$7$	1.36603	+	2.36603i	0.516309	+	0.894274i	−0.483512	+	0.875338i	$0.660639\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.86603	+	3.23205i	−0.590089	+	1.02206i
$11$	−0.633975	+	1.09808i	−0.191151	+	0.331082i	−0.945632	−	0.325239i	$-0.894555\pi$
$11$	−0.633975	+	1.09808i	−0.191151	+	0.331082i	0.754481	+	0.656322i	$0.227889\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−2.73205			−0.730171
$15$	−1.86603	+	3.23205i	−0.481806	+	0.834512i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	1.00000			0.235702
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	−0.998742	−	0.0501517i	$-0.984030\pi$
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	0.455938	−	0.890011i	$-0.349304\pi$
$20$	−1.86603	−	3.23205i	−0.417256	−	0.722709i
$21$	−2.73205			−0.596182
$22$	−0.633975	−	1.09808i	−0.135164	−	0.234111i
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	8.92820			1.78564
$26$		0			0
$27$	1.00000			0.192450
$28$	1.36603	−	2.36603i	0.258155	−	0.447137i
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	−0.580892	−	0.813980i	$-0.697296\pi$
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	0.995374	+	0.0960774i	$0.0306296\pi$
$30$	−1.86603	−	3.23205i	−0.340688	−	0.590089i
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.633975	−	1.09808i	−0.110361	−	0.191151i
$34$	−5.73205			−0.983039
$35$	5.09808	+	8.83013i	0.861732	+	1.49256i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.76795	+	3.06218i	−0.290649	+	0.503419i	−0.973963	−	0.226705i	$-0.927205\pi$
$37$	−1.76795	+	3.06218i	−0.290649	+	0.503419i	0.683314	+	0.730124i	$0.260538\pi$
$38$	4.73205			0.767640
$39$		0			0
$40$	3.73205			0.590089
$41$	4.69615	−	8.13397i	0.733416	−	1.27031i	−0.221999	−	0.975047i	$-0.571258\pi$
$41$	4.69615	−	8.13397i	0.733416	−	1.27031i	0.955415	−	0.295267i	$-0.0954085\pi$
$42$	1.36603	−	2.36603i	0.210782	−	0.365086i
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	0.954023	+	0.299732i	$0.0968974\pi$
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	−0.217436	+	0.976075i	$0.569769\pi$
$44$	1.26795			0.191151
$45$	−1.86603	−	3.23205i	−0.278171	−	0.481806i
$46$	−2.09808	−	3.63397i	−0.309344	−	0.535800i
$47$	2.19615			0.320342			0.160171	−	0.987089i	$-0.448795\pi$
$47$	2.19615			0.320342			0.160171	+	0.987089i	$0.448795\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.232051	+	0.401924i	−0.0331501	+	0.0574177i
$50$	−4.46410	+	7.73205i	−0.631319	+	1.09348i
$51$	−5.73205			−0.802648
$52$		0			0
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.36603	+	4.09808i	−0.319035	+	0.552584i
$56$	1.36603	+	2.36603i	0.182543	+	0.316173i
$57$	4.73205			0.626775
$58$	2.23205	+	3.86603i	0.293083	+	0.507634i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$	3.73205			0.481806
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$	−0.732051	+	1.26795i	−0.0929705	+	0.161030i
$63$	1.36603	−	2.36603i	0.172103	−	0.298091i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	−6.56218	+	11.3660i	−0.801698	+	1.38858i	0.116800	+	0.993155i	$0.462736\pi$
$67$	−6.56218	+	11.3660i	−0.801698	+	1.38858i	−0.918498	+	0.395426i	$0.870597\pi$
$68$	2.86603	−	4.96410i	0.347557	−	0.601986i
$69$	−2.09808	−	3.63397i	−0.252579	−	0.437479i
$70$	−10.1962			−1.21867
$71$	−2.36603	−	4.09808i	−0.280796	−	0.486352i	0.690785	−	0.723060i	$-0.257265\pi$
$71$	−2.36603	−	4.09808i	−0.280796	−	0.486352i	−0.971581	+	0.236708i	$0.923932\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−6.26795			−0.733608			−0.366804	−	0.930298i	$-0.619548\pi$
$73$	−6.26795			−0.733608			−0.366804	+	0.930298i	$0.619548\pi$
$74$	−1.76795	−	3.06218i	−0.205520	−	0.355971i
$75$	−4.46410	+	7.73205i	−0.515470	+	0.892820i
$76$	−2.36603	+	4.09808i	−0.271402	+	0.470082i
$77$	−3.46410			−0.394771
$78$		0			0
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	−1.86603	+	3.23205i	−0.208628	+	0.361354i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.69615	+	8.13397i	0.518603	+	0.898247i
$83$	−0.196152			−0.0215305			−0.0107653	−	0.999942i	$-0.503427\pi$
$83$	−0.196152			−0.0215305			−0.0107653	+	0.999942i	$0.503427\pi$
$84$	1.36603	+	2.36603i	0.149046	+	0.258155i
$85$	10.6962	+	18.5263i	1.16016	+	2.00946i
$86$	−9.66025			−1.04169
$87$	2.23205	+	3.86603i	0.239301	+	0.414481i
$88$	−0.633975	+	1.09808i	−0.0675819	+	0.117055i
$89$	4.73205	−	8.19615i	0.501596	−	0.868790i	−0.498402	−	0.866946i	$-0.666080\pi$
$89$	4.73205	−	8.19615i	0.501596	−	0.868790i	0.999998	−	0.00184433i	$-0.000587067\pi$
$90$	3.73205			0.393393
$91$		0			0
$92$	4.19615			0.437479
$93$	−0.732051	+	1.26795i	−0.0759101	+	0.131480i
$94$	−1.09808	+	1.90192i	−0.113258	+	0.196168i
$95$	−8.83013	−	15.2942i	−0.905952	−	1.56915i
$96$	1.00000			0.102062
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	0.977173	−	0.212445i	$-0.0681426\pi$
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	−0.672569	+	0.740034i	$0.734809\pi$
$98$	−0.232051	−	0.401924i	−0.0234407	−	0.0406004i
$99$	1.26795			0.127434
$100$	−4.46410	−	7.73205i	−0.446410	−	0.773205i
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	−0.909997	−	0.414615i	$-0.863916\pi$
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	0.814065	+	0.580773i	$0.197250\pi$
$102$	2.86603	−	4.96410i	0.283779	−	0.491519i
$103$	−15.2679			−1.50440			−0.752198	−	0.658937i	$-0.771006\pi$
$103$	−15.2679			−1.50440			−0.752198	+	0.658937i	$0.771006\pi$
$104$		0			0
$105$	−10.1962			−0.995043
$106$	3.23205	−	5.59808i	0.313925	−	0.543733i
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	−0.999966	−	0.00823695i	$-0.997378\pi$
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	0.507116	+	0.861878i	$0.330711\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.46410			0.140236			0.0701178	−	0.997539i	$-0.477662\pi$
$109$	1.46410			0.140236			0.0701178	+	0.997539i	$0.477662\pi$
$110$	−2.36603	−	4.09808i	−0.225592	−	0.390736i
$111$	−1.76795	−	3.06218i	−0.167806	−	0.290649i
$112$	−2.73205			−0.258155
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	0.895812	−	0.444432i	$-0.146595\pi$
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	−0.832796	+	0.553580i	$0.813261\pi$
$114$	−2.36603	+	4.09808i	−0.221599	+	0.383820i
$115$	−7.83013	+	13.5622i	−0.730163	+	1.26468i
$116$	−4.46410			−0.414481
$117$		0			0
$118$	8.00000			0.736460
$119$	−7.83013	+	13.5622i	−0.717787	+	1.24324i
$120$	−1.86603	+	3.23205i	−0.170344	+	0.295045i
$121$	4.69615	+	8.13397i	0.426923	+	0.739452i
$122$	−9.19615			−0.832581
$123$	4.69615	+	8.13397i	0.423438	+	0.733416i
$124$	−0.732051	−	1.26795i	−0.0657401	−	0.113865i
$125$	14.6603			1.31125
$126$	1.36603	+	2.36603i	0.121695	+	0.210782i
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	−0.560173	−	0.828375i	$-0.689266\pi$
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	0.997481	+	0.0709368i	$0.0225989\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−9.66025			−0.850538
$130$		0			0
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$	−0.633975	+	1.09808i	−0.0551804	+	0.0955753i
$133$	6.46410	−	11.1962i	0.560509	−	0.970830i
$134$	−6.56218	−	11.3660i	−0.566886	−	0.981875i
$135$	3.73205			0.321204
$136$	2.86603	+	4.96410i	0.245760	+	0.425668i
$137$	−5.96410	−	10.3301i	−0.509548	−	0.882562i	−0.999939	−	0.0110599i	$-0.996479\pi$
$137$	−5.96410	−	10.3301i	−0.509548	−	0.882562i	0.490391	−	0.871502i	$-0.336854\pi$
$138$	4.19615			0.357200
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	−0.944233	−	0.329279i	$-0.893194\pi$
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	0.186952	−	0.982369i	$-0.440139\pi$
$140$	5.09808	−	8.83013i	0.430866	−	0.746282i
$141$	−1.09808	+	1.90192i	−0.0924747	+	0.160171i
$142$	4.73205			0.397105
$143$		0			0
$144$	1.00000			0.0833333
$145$	8.33013	−	14.4282i	0.691779	−	1.19820i
$146$	3.13397	−	5.42820i	0.259370	−	0.449241i
$147$	−0.232051	−	0.401924i	−0.0191392	−	0.0331501i
$148$	3.53590			0.290649
$149$	−6.59808	−	11.4282i	−0.540535	−	0.936235i	−0.998873	−	0.0474568i	$-0.984888\pi$
$149$	−6.59808	−	11.4282i	−0.540535	−	0.936235i	0.458338	−	0.888778i	$-0.348445\pi$
$150$	−4.46410	−	7.73205i	−0.364492	−	0.631319i
$151$	6.73205			0.547847			0.273923	−	0.961752i	$-0.411679\pi$
$151$	6.73205			0.547847			0.273923	+	0.961752i	$0.411679\pi$
$152$	−2.36603	−	4.09808i	−0.191910	−	0.332398i
$153$	2.86603	−	4.96410i	0.231704	−	0.401324i
$154$	1.73205	−	3.00000i	0.139573	−	0.241747i
$155$	5.46410			0.438887
$156$		0			0
$157$	7.58846			0.605625			0.302812	−	0.953050i	$-0.402074\pi$
$157$	7.58846			0.605625			0.302812	+	0.953050i	$0.402074\pi$
$158$	1.26795	−	2.19615i	0.100873	−	0.174717i
$159$	3.23205	−	5.59808i	0.256318	−	0.443956i
$160$	−1.86603	−	3.23205i	−0.147522	−	0.255516i
$161$	−11.4641			−0.903498
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	6.73205	+	11.6603i	0.527295	+	0.913302i	0.999494	+	0.0318096i	$0.0101270\pi$
$163$	6.73205	+	11.6603i	0.527295	+	0.913302i	−0.472199	+	0.881492i	$0.656540\pi$
$164$	−9.39230			−0.733416
$165$	−2.36603	−	4.09808i	−0.184195	−	0.319035i
$166$	0.0980762	−	0.169873i	0.00761219	−	0.0131847i
$167$	4.73205	−	8.19615i	0.366177	−	0.634237i	−0.622787	−	0.782391i	$-0.714000\pi$
$167$	4.73205	−	8.19615i	0.366177	−	0.634237i	0.988964	+	0.148154i	$0.0473331\pi$
$168$	−2.73205			−0.210782
$169$		0			0
$170$	−21.3923			−1.64071
$171$	−2.36603	+	4.09808i	−0.180934	+	0.313388i
$172$	4.83013	−	8.36603i	0.368294	−	0.637903i
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	0.770383	−	0.637582i	$-0.220065\pi$
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	−0.937353	+	0.348380i	$0.886732\pi$
$174$	−4.46410			−0.338423
$175$	12.1962	+	21.1244i	0.921942	+	1.59685i
$176$	−0.633975	−	1.09808i	−0.0477876	−	0.0827706i
$177$	8.00000			0.601317
$178$	4.73205	+	8.19615i	0.354682	+	0.614328i
$179$	8.02628	−	13.9019i	0.599912	−	1.03908i	−0.392921	−	0.919572i	$-0.628535\pi$
$179$	8.02628	−	13.9019i	0.599912	−	1.03908i	0.992833	−	0.119506i	$-0.0381312\pi$
$180$	−1.86603	+	3.23205i	−0.139085	+	0.240903i
$181$	19.1962			1.42684			0.713419	−	0.700737i	$-0.247145\pi$
$181$	19.1962			1.42684			0.713419	+	0.700737i	$0.247145\pi$
$182$		0			0
$183$	−9.19615			−0.679799
$184$	−2.09808	+	3.63397i	−0.154672	+	0.267900i
$185$	−6.59808	+	11.4282i	−0.485100	+	0.840218i
$186$	−0.732051	−	1.26795i	−0.0536766	−	0.0929705i
$187$	−7.26795			−0.531485
$188$	−1.09808	−	1.90192i	−0.0800854	−	0.138712i
$189$	1.36603	+	2.36603i	0.0993637	+	0.172103i
$190$	17.6603			1.28121
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	0.963706	−	0.266966i	$-0.0860212\pi$
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	−0.713052	+	0.701111i	$0.752688\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	5.86603	−	10.1603i	0.422246	−	0.731351i	−0.573913	−	0.818916i	$-0.694575\pi$
$193$	5.86603	−	10.1603i	0.422246	−	0.731351i	0.996159	+	0.0875652i	$0.0279086\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	0.464102			0.0331501
$197$	8.92820	−	15.4641i	0.636108	−	1.10177i	−0.350171	−	0.936686i	$-0.613877\pi$
$197$	8.92820	−	15.4641i	0.636108	−	1.10177i	0.986279	−	0.165086i	$-0.0527901\pi$
$198$	−0.633975	+	1.09808i	−0.0450546	+	0.0780369i
$199$	7.09808	+	12.2942i	0.503169	+	0.871515i	0.999993	+	0.00366345i	$0.00116611\pi$
$199$	7.09808	+	12.2942i	0.503169	+	0.871515i	−0.496824	+	0.867851i	$0.665501\pi$
$200$	8.92820			0.631319
$201$	−6.56218	−	11.3660i	−0.462860	−	0.801698i
$202$	−0.964102	−	1.66987i	−0.0678340	−	0.117492i
$203$	12.1962			0.856002
$204$	2.86603	+	4.96410i	0.200662	+	0.347557i
$205$	17.5263	−	30.3564i	1.22409	−	2.12018i
$206$	7.63397	−	13.2224i	0.531884	−	0.921250i
$207$	4.19615			0.291653
$208$		0			0
$209$	6.00000			0.415029
$210$	5.09808	−	8.83013i	0.351801	−	0.609337i
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$212$	3.23205	+	5.59808i	0.221978	+	0.384477i
$213$	4.73205			0.324235
$214$	−5.09808	−	8.83013i	−0.348497	−	0.603615i
$215$	18.0263	+	31.2224i	1.22938	+	2.12935i
$216$	1.00000			0.0680414
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−0.732051	+	1.26795i	−0.0495807	+	0.0858764i
$219$	3.13397	−	5.42820i	0.211774	−	0.366804i
$220$	4.73205			0.319035
$221$		0			0
$222$	3.53590			0.237314
$223$	13.4641	−	23.3205i	0.901623	−	1.56166i	0.0762356	−	0.997090i	$-0.475710\pi$
$223$	13.4641	−	23.3205i	0.901623	−	1.56166i	0.825387	−	0.564567i	$-0.190957\pi$
$224$	1.36603	−	2.36603i	0.0912714	−	0.158087i
$225$	−4.46410	−	7.73205i	−0.297607	−	0.515470i
$226$	−1.33975			−0.0891186
$227$	6.09808	+	10.5622i	0.404744	+	0.701036i	0.994292	−	0.106697i	$-0.0340275\pi$
$227$	6.09808	+	10.5622i	0.404744	+	0.701036i	−0.589548	+	0.807733i	$0.700694\pi$
$228$	−2.36603	−	4.09808i	−0.156694	−	0.271402i
$229$	−11.8564			−0.783493			−0.391747	−	0.920073i	$-0.628129\pi$
$229$	−11.8564			−0.783493			−0.391747	+	0.920073i	$0.628129\pi$
$230$	−7.83013	−	13.5622i	−0.516303	−	0.894264i
$231$	1.73205	−	3.00000i	0.113961	−	0.197386i
$232$	2.23205	−	3.86603i	0.146541	−	0.253817i
$233$	−7.85641			−0.514690			−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641			−0.514690			−0.257345	+	0.966320i	$0.582848\pi$
$234$		0			0
$235$	8.19615			0.534658
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$	1.26795	−	2.19615i	0.0823622	−	0.142655i
$238$	−7.83013	−	13.5622i	−0.507552	−	0.879105i
$239$	7.66025			0.495501			0.247750	−	0.968824i	$-0.420309\pi$
$239$	7.66025			0.495501			0.247750	+	0.968824i	$0.420309\pi$
$240$	−1.86603	−	3.23205i	−0.120451	−	0.208628i
$241$	−6.79423	−	11.7679i	−0.437655	−	0.758040i	0.559853	−	0.828592i	$-0.310857\pi$
$241$	−6.79423	−	11.7679i	−0.437655	−	0.758040i	−0.997508	+	0.0705514i	$0.977524\pi$
$242$	−9.39230			−0.603760
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.59808	−	7.96410i	0.294362	−	0.509849i
$245$	−0.866025	+	1.50000i	−0.0553283	+	0.0958315i
$246$	−9.39230			−0.598831
$247$		0			0
$248$	1.46410			0.0929705
$249$	0.0980762	−	0.169873i	0.00621533	−	0.0107653i
$250$	−7.33013	+	12.6962i	−0.463598	+	0.802975i
$251$	−6.73205	−	11.6603i	−0.424923	−	0.735989i	0.571490	−	0.820609i	$-0.306366\pi$
$251$	−6.73205	−	11.6603i	−0.424923	−	0.735989i	−0.996413	+	0.0846203i	$0.973032\pi$
$252$	−2.73205			−0.172103
$253$	−2.66025	−	4.60770i	−0.167249	−	0.289683i
$254$	4.92820	+	8.53590i	0.309223	+	0.535590i
$255$	−21.3923			−1.33964
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	−0.974117	−	0.226044i	$-0.927421\pi$
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	0.682818	+	0.730588i	$0.260754\pi$
$258$	4.83013	−	8.36603i	0.300711	−	0.520846i
$259$	−9.66025			−0.600259
$260$		0			0
$261$	−4.46410			−0.276321
$262$	−3.26795	+	5.66025i	−0.201895	+	0.349692i
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	−0.668414	−	0.743790i	$-0.733026\pi$
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	0.978348	+	0.206969i	$0.0663598\pi$
$264$	−0.633975	−	1.09808i	−0.0390184	−	0.0675819i
$265$	−24.1244			−1.48195
$266$	6.46410	+	11.1962i	0.396339	+	0.686480i
$267$	4.73205	+	8.19615i	0.289597	+	0.501596i
$268$	13.1244			0.801698
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	0.770638	−	0.637273i	$-0.219938\pi$
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	−0.937214	+	0.348755i	$0.886604\pi$
$270$	−1.86603	+	3.23205i	−0.113563	+	0.196696i
$271$	10.9282	−	18.9282i	0.663841	−	1.14981i	−0.315757	−	0.948840i	$-0.602258\pi$
$271$	10.9282	−	18.9282i	0.663841	−	1.14981i	0.979598	−	0.200966i	$-0.0644082\pi$
$272$	−5.73205			−0.347557
$273$		0			0
$274$	11.9282			0.720609
$275$	−5.66025	+	9.80385i	−0.341326	+	0.591194i
$276$	−2.09808	+	3.63397i	−0.126289	+	0.218740i
$277$	2.86603	+	4.96410i	0.172203	+	0.298264i	0.939190	−	0.343399i	$-0.111578\pi$
$277$	2.86603	+	4.96410i	0.172203	+	0.298264i	−0.766987	+	0.641663i	$0.778245\pi$
$278$	17.8564			1.07096
$279$	−0.732051	−	1.26795i	−0.0438267	−	0.0759101i
$280$	5.09808	+	8.83013i	0.304668	+	0.527701i
$281$	12.3205			0.734980			0.367490	−	0.930027i	$-0.380217\pi$
$281$	12.3205			0.734980			0.367490	+	0.930027i	$0.380217\pi$
$282$	−1.09808	−	1.90192i	−0.0653895	−	0.113258i
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	0.178797	+	0.983886i	$0.442780\pi$
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	−0.941469	+	0.337100i	$0.890554\pi$
$284$	−2.36603	+	4.09808i	−0.140398	+	0.243176i
$285$	17.6603			1.04610
$286$		0			0
$287$	25.6603			1.51468
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$	8.33013	+	14.4282i	0.489162	+	0.847253i
$291$	−6.00000			−0.351726
$292$	3.13397	+	5.42820i	0.183402	+	0.317662i
$293$	−15.2583	−	26.4282i	−0.891401	−	1.54395i	−0.838196	−	0.545368i	$-0.816390\pi$
$293$	−15.2583	−	26.4282i	−0.891401	−	1.54395i	−0.0532048	−	0.998584i	$-0.516944\pi$
$294$	0.464102			0.0270670
$295$	−14.9282	−	25.8564i	−0.869154	−	1.50542i
$296$	−1.76795	+	3.06218i	−0.102760	+	0.177985i
$297$	−0.633975	+	1.09808i	−0.0367869	+	0.0637168i
$298$	13.1962			0.764433
$299$		0			0
$300$	8.92820			0.515470
$301$	−13.1962	+	22.8564i	−0.760614	+	1.31742i
$302$	−3.36603	+	5.83013i	−0.193693	+	0.335486i
$303$	−0.964102	−	1.66987i	−0.0553862	−	0.0959317i
$304$	4.73205			0.271402
$305$	17.1603	+	29.7224i	0.982593	+	1.70190i
$306$	2.86603	+	4.96410i	0.163840	+	0.283779i
$307$	−22.5885			−1.28919			−0.644596	−	0.764524i	$-0.722974\pi$
$307$	−22.5885			−1.28919			−0.644596	+	0.764524i	$0.722974\pi$
$308$	1.73205	+	3.00000i	0.0986928	+	0.170941i
$309$	7.63397	−	13.2224i	0.434282	−	0.752198i
$310$	−2.73205	+	4.73205i	−0.155170	+	0.268762i
$311$	−1.66025			−0.0941444			−0.0470722	−	0.998891i	$-0.514989\pi$
$311$	−1.66025			−0.0941444			−0.0470722	+	0.998891i	$0.514989\pi$
$312$		0			0
$313$	6.53590			0.369431			0.184715	−	0.982792i	$-0.440864\pi$
$313$	6.53590			0.369431			0.184715	+	0.982792i	$0.440864\pi$
$314$	−3.79423	+	6.57180i	−0.214121	+	0.370868i
$315$	5.09808	−	8.83013i	0.287244	−	0.497521i
$316$	1.26795	+	2.19615i	0.0713277	+	0.123543i
$317$	20.6603			1.16040			0.580198	−	0.814476i	$-0.302975\pi$
$317$	20.6603			1.16040			0.580198	+	0.814476i	$0.302975\pi$
$318$	3.23205	+	5.59808i	0.181244	+	0.313925i
$319$	2.83013	+	4.90192i	0.158457	+	0.274455i
$320$	3.73205			0.208628
$321$	−5.09808	−	8.83013i	−0.284547	−	0.492850i
$322$	5.73205	−	9.92820i	0.319435	−	0.553277i
$323$	13.5622	−	23.4904i	0.754620	−	1.30704i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−13.4641			−0.745708
$327$	−0.732051	+	1.26795i	−0.0404825	+	0.0701178i
$328$	4.69615	−	8.13397i	0.259302	−	0.449124i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$	4.73205			0.260491
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	0.0980762	+	0.169873i	0.00538263	+	0.00932299i
$333$	3.53590			0.193766
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$	−24.4904	+	42.4186i	−1.33805	+	2.31757i
$336$	1.36603	−	2.36603i	0.0745228	−	0.129077i
$337$	−20.8564			−1.13612			−0.568060	−	0.822987i	$-0.692306\pi$
$337$	−20.8564			−1.13612			−0.568060	+	0.822987i	$0.692306\pi$
$338$		0			0
$339$	−1.33975			−0.0727650
$340$	10.6962	−	18.5263i	0.580080	−	1.00473i
$341$	−0.928203	+	1.60770i	−0.0502650	+	0.0870616i
$342$	−2.36603	−	4.09808i	−0.127940	−	0.221599i
$343$	17.8564			0.964155
$344$	4.83013	+	8.36603i	0.260423	+	0.451066i
$345$	−7.83013	−	13.5622i	−0.421560	−	0.730163i
$346$	4.39230			0.236132
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.840936	−	0.541135i	$-0.817995\pi$
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.0481683	−	0.998839i	$-0.515338\pi$
$348$	2.23205	−	3.86603i	0.119650	−	0.207241i
$349$	−7.66025	+	13.2679i	−0.410044	+	0.710217i	−0.994894	−	0.100924i	$-0.967820\pi$
$349$	−7.66025	+	13.2679i	−0.410044	+	0.710217i	0.584850	+	0.811141i	$0.301153\pi$
$350$	−24.3923			−1.30382
$351$		0			0
$352$	1.26795			0.0675819
$353$	10.8923	−	18.8660i	0.579739	−	1.00414i	−0.415770	−	0.909470i	$-0.636488\pi$
$353$	10.8923	−	18.8660i	0.579739	−	1.00414i	0.995509	−	0.0946674i	$-0.0301788\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$	−8.83013	−	15.2942i	−0.468654	−	0.811733i
$356$	−9.46410			−0.501596
$357$	−7.83013	−	13.5622i	−0.414414	−	0.717787i
$358$	8.02628	+	13.9019i	0.424202	+	0.734740i
$359$	−1.12436			−0.0593412			−0.0296706	−	0.999560i	$-0.509446\pi$
$359$	−1.12436			−0.0593412			−0.0296706	+	0.999560i	$0.509446\pi$
$360$	−1.86603	−	3.23205i	−0.0983482	−	0.170344i
$361$	−1.69615	+	2.93782i	−0.0892712	+	0.154622i
$362$	−9.59808	+	16.6244i	−0.504464	+	0.873757i
$363$	−9.39230			−0.492968
$364$		0			0
$365$	−23.3923			−1.22441
$366$	4.59808	−	7.96410i	0.240345	−	0.416290i
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	−0.680682	−	0.732579i	$-0.738316\pi$
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	0.974773	+	0.223198i	$0.0716498\pi$
$368$	−2.09808	−	3.63397i	−0.109370	−	0.189434i
$369$	−9.39230			−0.488944
$370$	−6.59808	−	11.4282i	−0.343018	−	0.594124i
$371$	−8.83013	−	15.2942i	−0.458437	−	0.794037i
$372$	1.46410			0.0759101
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	0.987205	−	0.159456i	$-0.0509741\pi$
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	−0.631696	+	0.775216i	$0.717641\pi$
$374$	3.63397	−	6.29423i	0.187908	−	0.325467i
$375$	−7.33013	+	12.6962i	−0.378526	+	0.655626i
$376$	2.19615			0.113258
$377$		0			0
$378$	−2.73205			−0.140522
$379$	2.73205	−	4.73205i	0.140336	−	0.243069i	−0.787287	−	0.616587i	$-0.788515\pi$
$379$	2.73205	−	4.73205i	0.140336	−	0.243069i	0.927623	+	0.373517i	$0.121848\pi$
$380$	−8.83013	+	15.2942i	−0.452976	+	0.784577i
$381$	4.92820	+	8.53590i	0.252479	+	0.437307i
$382$	−6.92820			−0.354478
$383$	0.732051	+	1.26795i	0.0374060	+	0.0647892i	0.884122	−	0.467255i	$-0.154757\pi$
$383$	0.732051	+	1.26795i	0.0374060	+	0.0647892i	−0.846716	+	0.532045i	$0.821424\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−12.9282			−0.658882
$386$	5.86603	+	10.1603i	0.298573	+	0.517143i
$387$	4.83013	−	8.36603i	0.245529	−	0.425269i
$388$	3.00000	−	5.19615i	0.152302	−	0.263795i
$389$	11.7846			0.597503			0.298752	−	0.954331i	$-0.403430\pi$
$389$	11.7846			0.597503			0.298752	+	0.954331i	$0.403430\pi$
$390$		0			0
$391$	−24.0526			−1.21639
$392$	−0.232051	+	0.401924i	−0.0117203	+	0.0203002i
$393$	−3.26795	+	5.66025i	−0.164846	+	0.285522i
$394$	8.92820	+	15.4641i	0.449796	+	0.779070i
$395$	−9.46410			−0.476191
$396$	−0.633975	−	1.09808i	−0.0318584	−	0.0551804i
$397$	−10.1962	−	17.6603i	−0.511730	−	0.886343i	−0.999908	−	0.0135983i	$-0.995671\pi$
$397$	−10.1962	−	17.6603i	−0.511730	−	0.886343i	0.488177	−	0.872744i	$-0.337662\pi$
$398$	−14.1962			−0.711589
$399$	6.46410	+	11.1962i	0.323610	+	0.560509i
$400$	−4.46410	+	7.73205i	−0.223205	+	0.386603i
$401$	−4.03590	+	6.99038i	−0.201543	+	0.349083i	−0.949026	−	0.315198i	$-0.897929\pi$
$401$	−4.03590	+	6.99038i	−0.201543	+	0.349083i	0.747483	+	0.664281i	$0.231262\pi$
$402$	13.1244			0.654583
$403$		0			0
$404$	1.92820			0.0959317
$405$	−1.86603	+	3.23205i	−0.0927235	+	0.160602i
$406$	−6.09808	+	10.5622i	−0.302642	+	0.524192i
$407$	−2.24167	−	3.88269i	−0.111115	−	0.192458i
$408$	−5.73205			−0.283779
$409$	−8.86603	−	15.3564i	−0.438397	−	0.759325i	0.559169	−	0.829053i	$-0.311120\pi$
$409$	−8.86603	−	15.3564i	−0.438397	−	0.759325i	−0.997566	+	0.0697281i	$0.977787\pi$
$410$	17.5263	+	30.3564i	0.865561	+	1.49920i
$411$	11.9282			0.588375
$412$	7.63397	+	13.2224i	0.376099	+	0.651422i
$413$	10.9282	−	18.9282i	0.537742	−	0.931396i
$414$	−2.09808	+	3.63397i	−0.103115	+	0.178600i
$415$	−0.732051			−0.0359350
$416$		0			0
$417$	17.8564			0.874432
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	−0.569979	−	0.821659i	$-0.693049\pi$
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	0.996567	+	0.0827863i	$0.0263819\pi$
$420$	5.09808	+	8.83013i	0.248761	+	0.430866i
$421$	−22.7128			−1.10695			−0.553477	−	0.832864i	$-0.686699\pi$
$421$	−22.7128			−1.10695			−0.553477	+	0.832864i	$0.686699\pi$
$422$	−8.19615	−	14.1962i	−0.398982	−	0.691058i
$423$	−1.09808	−	1.90192i	−0.0533903	−	0.0924747i
$424$	−6.46410			−0.313925
$425$	25.5885	+	44.3205i	1.24122	+	2.14986i
$426$	−2.36603	+	4.09808i	−0.114634	+	0.198552i
$427$	−12.5622	+	21.7583i	−0.607926	+	1.05296i
$428$	10.1962			0.492850
$429$		0			0
$430$	−36.0526			−1.73861
$431$	−6.56218	+	11.3660i	−0.316089	+	0.547482i	−0.979668	−	0.200624i	$-0.935703\pi$
$431$	−6.56218	+	11.3660i	−0.316089	+	0.547482i	0.663579	+	0.748106i	$0.269036\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−6.42820	−	11.1340i	−0.308920	−	0.535065i	0.669207	−	0.743076i	$-0.266634\pi$
$433$	−6.42820	−	11.1340i	−0.308920	−	0.535065i	−0.978126	+	0.208012i	$0.933301\pi$
$434$	−4.00000			−0.192006
$435$	8.33013	+	14.4282i	0.399399	+	0.691779i
$436$	−0.732051	−	1.26795i	−0.0350589	−	0.0607238i
$437$	19.8564			0.949861
$438$	3.13397	+	5.42820i	0.149747	+	0.259370i
$439$	0.169873	−	0.294229i	0.00810760	−	0.0140428i	−0.861943	−	0.507005i	$-0.830753\pi$
$439$	0.169873	−	0.294229i	0.00810760	−	0.0140428i	0.870051	+	0.492962i	$0.164086\pi$
$440$	−2.36603	+	4.09808i	−0.112796	+	0.195368i
$441$	0.464102			0.0221001
$442$		0			0
$443$	15.6077			0.741544			0.370772	−	0.928724i	$-0.379093\pi$
$443$	15.6077			0.741544			0.370772	+	0.928724i	$0.379093\pi$
$444$	−1.76795	+	3.06218i	−0.0839032	+	0.145325i
$445$	17.6603	−	30.5885i	0.837176	−	1.45003i
$446$	13.4641	+	23.3205i	0.637544	+	1.10426i
$447$	13.1962			0.624157
$448$	1.36603	+	2.36603i	0.0645386	+	0.111784i
$449$	−5.66025	−	9.80385i	−0.267124	−	0.462672i	0.700994	−	0.713167i	$-0.252740\pi$
$449$	−5.66025	−	9.80385i	−0.267124	−	0.462672i	−0.968118	+	0.250495i	$0.919407\pi$
$450$	8.92820			0.420880
$451$	5.95448	+	10.3135i	0.280386	+	0.485642i
$452$	0.669873	−	1.16025i	0.0315082	−	0.0545738i
$453$	−3.36603	+	5.83013i	−0.158150	+	0.273923i
$454$	−12.1962			−0.572394
$455$		0			0
$456$	4.73205			0.221599
$457$	−0.669873	+	1.16025i	−0.0313353	+	0.0542744i	−0.881268	−	0.472617i	$-0.843309\pi$
$457$	−0.669873	+	1.16025i	−0.0313353	+	0.0542744i	0.849932	+	0.526892i	$0.176643\pi$
$458$	5.92820	−	10.2679i	0.277007	−	0.479790i
$459$	2.86603	+	4.96410i	0.133775	+	0.231704i
$460$	15.6603			0.730163
$461$	−11.1340	−	19.2846i	−0.518561	−	0.898174i	−0.999767	−	0.0215666i	$-0.993135\pi$
$461$	−11.1340	−	19.2846i	−0.518561	−	0.898174i	0.481207	−	0.876607i	$-0.340199\pi$
$462$	1.73205	+	3.00000i	0.0805823	+	0.139573i
$463$	10.0526			0.467182			0.233591	−	0.972335i	$-0.424952\pi$
$463$	10.0526			0.467182			0.233591	+	0.972335i	$0.424952\pi$
$464$	2.23205	+	3.86603i	0.103620	+	0.179476i
$465$	−2.73205	+	4.73205i	−0.126696	+	0.219444i
$466$	3.92820	−	6.80385i	0.181971	−	0.315182i
$467$	18.5885			0.860171			0.430086	−	0.902788i	$-0.358483\pi$
$467$	18.5885			0.860171			0.430086	+	0.902788i	$0.358483\pi$
$468$		0			0
$469$	−35.8564			−1.65570
$470$	−4.09808	+	7.09808i	−0.189030	+	0.327410i
$471$	−3.79423	+	6.57180i	−0.174829	+	0.302812i
$472$	−4.00000	−	6.92820i	−0.184115	−	0.318896i
$473$	−12.2487			−0.563196
$474$	1.26795	+	2.19615i	0.0582388	+	0.100873i
$475$	−21.1244	−	36.5885i	−0.969252	−	1.67879i
$476$	15.6603			0.717787
$477$	3.23205	+	5.59808i	0.147985	+	0.256318i
$478$	−3.83013	+	6.63397i	−0.175186	+	0.303431i
$479$	−16.7321	+	28.9808i	−0.764507	+	1.32416i	0.176000	+	0.984390i	$0.443684\pi$
$479$	−16.7321	+	28.9808i	−0.764507	+	1.32416i	−0.940507	+	0.339775i	$0.889649\pi$
$480$	3.73205			0.170344
$481$		0			0
$482$	13.5885			0.618937
$483$	5.73205	−	9.92820i	0.260817	−	0.451749i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	11.1962	+	19.3923i	0.508391	+	0.880559i
$486$	1.00000			0.0453609
$487$	1.56218	+	2.70577i	0.0707890	+	0.122610i	0.899247	−	0.437441i	$-0.144115\pi$
$487$	1.56218	+	2.70577i	0.0707890	+	0.122610i	−0.828458	+	0.560051i	$0.810782\pi$
$488$	4.59808	+	7.96410i	0.208145	+	0.360518i
$489$	−13.4641			−0.608868
$490$	−0.866025	−	1.50000i	−0.0391230	−	0.0677631i
$491$	−4.36603	+	7.56218i	−0.197036	+	0.341276i	−0.947566	−	0.319560i	$-0.896465\pi$
$491$	−4.36603	+	7.56218i	−0.197036	+	0.341276i	0.750530	+	0.660836i	$0.229798\pi$
$492$	4.69615	−	8.13397i	0.211719	−	0.366708i
$493$	25.5885			1.15245
$494$		0			0
$495$	4.73205			0.212690
$496$	−0.732051	+	1.26795i	−0.0328701	+	0.0569326i
$497$	6.46410	−	11.1962i	0.289955	−	0.502216i
$498$	0.0980762	+	0.169873i	0.00439490	+	0.00761219i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	−7.33013	−	12.6962i	−0.327813	−	0.567789i
$501$	4.73205	+	8.19615i	0.211412	+	0.366177i
$502$	13.4641			0.600932
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.808908	−	0.587935i	$-0.799941\pi$
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.104713	−	0.994502i	$-0.533392\pi$
$504$	1.36603	−	2.36603i	0.0608476	−	0.105391i
$505$	−3.59808	+	6.23205i	−0.160112	+	0.277323i
$506$	5.32051			0.236525
$507$		0			0
$508$	−9.85641			−0.437307
$509$	−6.86603	+	11.8923i	−0.304331	+	0.527117i	−0.977112	−	0.212725i	$-0.931766\pi$
$509$	−6.86603	+	11.8923i	−0.304331	+	0.527117i	0.672781	+	0.739842i	$0.265100\pi$
$510$	10.6962	−	18.5263i	0.473634	−	0.820357i
$511$	−8.56218	−	14.8301i	−0.378768	−	0.656046i
$512$	1.00000			0.0441942
$513$	−2.36603	−	4.09808i	−0.104463	−	0.180934i
$514$	−4.66987	−	8.08846i	−0.205979	−	0.356767i
$515$	−56.9808			−2.51087
$516$	4.83013	+	8.36603i	0.212634	+	0.368294i
$517$	−1.39230	+	2.41154i	−0.0612335	+	0.106060i
$518$	4.83013	−	8.36603i	0.212224	−	0.367582i
$519$	4.39230			0.192801
$520$		0			0
$521$	41.4449			1.81573			0.907866	−	0.419260i	$-0.137710\pi$
$521$	41.4449			1.81573			0.907866	+	0.419260i	$0.137710\pi$
$522$	2.23205	−	3.86603i	0.0976942	−	0.169211i
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	−0.509220	−	0.860636i	$-0.670066\pi$
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	0.999943	+	0.0106796i	$0.00339949\pi$
$524$	−3.26795	−	5.66025i	−0.142761	−	0.247269i
$525$	−24.3923			−1.06457
$526$	5.02628	+	8.70577i	0.219156	+	0.379590i
$527$	4.19615	+	7.26795i	0.182787	+	0.316597i
$528$	1.26795			0.0551804
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$	12.0622	−	20.8923i	0.523948	−	0.907504i
$531$	−4.00000	+	6.92820i	−0.173585	+	0.300658i
$532$	−12.9282			−0.560509
$533$		0			0
$534$	−9.46410			−0.409552
$535$	−19.0263	+	32.9545i	−0.822578	+	1.42475i
$536$	−6.56218	+	11.3660i	−0.283443	+	0.490938i
$537$	8.02628	+	13.9019i	0.346360	+	0.599912i
$538$	5.46410			0.235574
$539$	−0.294229	−	0.509619i	−0.0126733	−	0.0219508i
$540$	−1.86603	−	3.23205i	−0.0803009	−	0.139085i
$541$	5.67949			0.244180			0.122090	−	0.992519i	$-0.461040\pi$
$541$	5.67949			0.244180			0.122090	+	0.992519i	$0.461040\pi$
$542$	10.9282	+	18.9282i	0.469407	+	0.813036i
$543$	−9.59808	+	16.6244i	−0.411893	+	0.713419i
$544$	2.86603	−	4.96410i	0.122880	−	0.212834i
$545$	5.46410			0.234056
$546$		0			0
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	−5.96410	+	10.3301i	−0.254774	+	0.441281i
$549$	4.59808	−	7.96410i	0.196241	−	0.339900i
$550$	−5.66025	−	9.80385i	−0.241354	−	0.418037i
$551$	−21.1244			−0.899928
$552$	−2.09808	−	3.63397i	−0.0893001	−	0.154672i
$553$	−3.46410	−	6.00000i	−0.147309	−	0.255146i
$554$	−5.73205			−0.243532
$555$	−6.59808	−	11.4282i	−0.280073	−	0.485100i
$556$	−8.92820	+	15.4641i	−0.378640	+	0.655824i
$557$	−21.1865	+	36.6962i	−0.897702	+	1.55487i	−0.0672780	+	0.997734i	$0.521431\pi$
$557$	−21.1865	+	36.6962i	−0.897702	+	1.55487i	−0.830424	+	0.557132i	$0.811902\pi$
$558$	1.46410			0.0619804
$559$		0			0
$560$	−10.1962			−0.430866
$561$	3.63397	−	6.29423i	0.153427	−	0.265743i
$562$	−6.16025	+	10.6699i	−0.259855	+	0.450081i
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	−0.954273	−	0.298938i	$-0.903368\pi$
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	0.218248	−	0.975893i	$-0.429966\pi$
$564$	2.19615			0.0924747
$565$	2.50000	+	4.33013i	0.105176	+	0.182170i
$566$	−12.8301	−	22.2224i	−0.539290	−	0.934078i
$567$	−2.73205			−0.114735
$568$	−2.36603	−	4.09808i	−0.0992762	−	0.171951i
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	0.342656	+	0.939461i	$0.388674\pi$
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	−0.984925	+	0.172982i	$0.944660\pi$
$570$	−8.83013	+	15.2942i	−0.369853	+	0.640605i
$571$	14.0526			0.588081			0.294041	−	0.955793i	$-0.405000\pi$
$571$	14.0526			0.588081			0.294041	+	0.955793i	$0.405000\pi$
$572$		0			0
$573$	−6.92820			−0.289430
$574$	−12.8301	+	22.2224i	−0.535519	+	0.927546i
$575$	−18.7321	+	32.4449i	−0.781181	+	1.35304i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.73205			0.155367			0.0776837	−	0.996978i	$-0.475248\pi$
$577$	3.73205			0.155367			0.0776837	+	0.996978i	$0.475248\pi$
$578$	−7.92820	−	13.7321i	−0.329770	−	0.571178i
$579$	5.86603	+	10.1603i	0.243784	+	0.422246i
$580$	−16.6603			−0.691779
$581$	−0.267949	−	0.464102i	−0.0111164	−	0.0192542i
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	4.09808	−	7.09808i	0.169725	−	0.293972i
$584$	−6.26795			−0.259370
$585$		0			0
$586$	30.5167			1.26063
$587$	−8.00000	+	13.8564i	−0.330195	+	0.571915i	−0.982550	−	0.185999i	$-0.940448\pi$
$587$	−8.00000	+	13.8564i	−0.330195	+	0.571915i	0.652355	+	0.757914i	$0.273781\pi$
$588$	−0.232051	+	0.401924i	−0.00956961	+	0.0165751i
$589$	−3.46410	−	6.00000i	−0.142736	−	0.247226i
$590$	29.8564			1.22917
$591$	8.92820	+	15.4641i	0.367257	+	0.636108i
$592$	−1.76795	−	3.06218i	−0.0726623	−	0.125855i
$593$	−9.14359			−0.375482			−0.187741	−	0.982219i	$-0.560117\pi$
$593$	−9.14359			−0.375482			−0.187741	+	0.982219i	$0.560117\pi$
$594$	−0.633975	−	1.09808i	−0.0260123	−	0.0450546i
$595$	−29.2224	+	50.6147i	−1.19800	+	2.07500i
$596$	−6.59808	+	11.4282i	−0.270268	+	0.468117i
$597$	−14.1962			−0.581010
$598$		0			0
$599$	−2.53590			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$599$	−2.53590			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$600$	−4.46410	+	7.73205i	−0.182246	+	0.315660i
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$	−13.1962	−	22.8564i	−0.537835	−	0.931558i
$603$	13.1244			0.534465
$604$	−3.36603	−	5.83013i	−0.136962	−	0.237225i
$605$	17.5263	+	30.3564i	0.712545	+	1.23416i
$606$	1.92820			0.0783279
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	0.899840	+	0.436221i	$0.143683\pi$
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	−0.0721415	+	0.997394i	$0.522983\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$	−6.09808	+	10.5622i	−0.247107	+	0.428001i
$610$	−34.3205			−1.38960
$611$		0			0
$612$	−5.73205			−0.231704
$613$	4.69615	−	8.13397i	0.189676	−	0.328528i	−0.755466	−	0.655187i	$-0.772590\pi$
$613$	4.69615	−	8.13397i	0.189676	−	0.328528i	0.945142	+	0.326659i	$0.105923\pi$
$614$	11.2942	−	19.5622i	0.455798	−	0.789465i
$615$	17.5263	+	30.3564i	0.706728	+	1.22409i
$616$	−3.46410			−0.139573
$617$	6.62436	+	11.4737i	0.266687	+	0.461915i	0.968004	−	0.250934i	$-0.0807378\pi$
$617$	6.62436	+	11.4737i	0.266687	+	0.461915i	−0.701318	+	0.712849i	$0.747404\pi$
$618$	7.63397	+	13.2224i	0.307083	+	0.531884i
$619$	17.4641			0.701942			0.350971	−	0.936386i	$-0.385852\pi$
$619$	17.4641			0.701942			0.350971	+	0.936386i	$0.385852\pi$
$620$	−2.73205	−	4.73205i	−0.109722	−	0.190044i
$621$	−2.09808	+	3.63397i	−0.0841929	+	0.145826i
$622$	0.830127	−	1.43782i	0.0332851	−	0.0576514i
$623$	25.8564			1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$	−3.26795	+	5.66025i	−0.130614	+	0.226229i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	−3.79423	−	6.57180i	−0.151406	−	0.262243i
$629$	−20.2679			−0.808136
$630$	5.09808	+	8.83013i	0.203112	+	0.351801i
$631$	3.85641	+	6.67949i	0.153521	+	0.265906i	0.932520	−	0.361119i	$-0.117605\pi$
$631$	3.85641	+	6.67949i	0.153521	+	0.265906i	−0.778998	+	0.627026i	$0.784272\pi$
$632$	−2.53590			−0.100873
$633$	−8.19615	−	14.1962i	−0.325768	−	0.564246i
$634$	−10.3301	+	17.8923i	−0.410262	+	0.710594i
$635$	18.3923	−	31.8564i	0.729876	−	1.26418i
$636$	−6.46410			−0.256318
$637$		0			0
$638$	−5.66025			−0.224092
$639$	−2.36603	+	4.09808i	−0.0935985	+	0.162117i
$640$	−1.86603	+	3.23205i	−0.0737611	+	0.127758i
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	0.999885	+	0.0151806i	$0.00483233\pi$
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	−0.486796	+	0.873516i	$0.661834\pi$
$642$	10.1962			0.402410
$643$	6.92820	+	12.0000i	0.273222	+	0.473234i	0.969685	−	0.244359i	$-0.0785774\pi$
$643$	6.92820	+	12.0000i	0.273222	+	0.473234i	−0.696463	+	0.717592i	$0.745244\pi$
$644$	5.73205	+	9.92820i	0.225874	+	0.391226i
$645$	−36.0526			−1.41957
$646$	13.5622	+	23.4904i	0.533597	+	0.924217i
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	−0.560140	−	0.828398i	$-0.689253\pi$
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	0.997484	+	0.0708966i	$0.0225860\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	10.1436			0.398171
$650$		0			0
$651$	−4.00000			−0.156772
$652$	6.73205	−	11.6603i	0.263647	−	0.456651i
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	−0.643039	−	0.765833i	$-0.722327\pi$
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	0.984751	+	0.173972i	$0.0556601\pi$
$654$	−0.732051	−	1.26795i	−0.0286255	−	0.0495807i
$655$	24.3923			0.953086
$656$	4.69615	+	8.13397i	0.183354	+	0.317578i
$657$	3.13397	+	5.42820i	0.122268	+	0.211774i
$658$	−6.00000			−0.233904
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	0.948404	−	0.317064i	$-0.102697\pi$
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	−0.748788	+	0.662810i	$0.769364\pi$
$660$	−2.36603	+	4.09808i	−0.0920974	+	0.159517i
$661$	−5.69615	+	9.86603i	−0.221555	+	0.383744i	−0.955280	−	0.295702i	$-0.904446\pi$
$661$	−5.69615	+	9.86603i	−0.221555	+	0.383744i	0.733726	+	0.679446i	$0.237780\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	−0.196152			−0.00761219
$665$	24.1244	−	41.7846i	0.935502	−	1.62034i
$666$	−1.76795	+	3.06218i	−0.0685066	+	0.118657i
$667$	9.36603	+	16.2224i	0.362654	+	0.628135i
$668$	−9.46410			−0.366177
$669$	13.4641	+	23.3205i	0.520552	+	0.901623i
$670$	−24.4904	−	42.4186i	−0.946146	−	1.63877i
$671$	−11.6603			−0.450139
$672$	1.36603	+	2.36603i	0.0526956	+	0.0912714i
$673$	−13.9641	+	24.1865i	−0.538277	+	0.932322i	0.460720	+	0.887545i	$0.347591\pi$
$673$	−13.9641	+	24.1865i	−0.538277	+	0.932322i	−0.998997	+	0.0447770i	$0.985742\pi$
$674$	10.4282	−	18.0622i	0.401679	−	0.695729i
$675$	8.92820			0.343647
$676$		0			0
$677$	−45.4641			−1.74733			−0.873664	−	0.486530i	$-0.838262\pi$
$677$	−45.4641			−1.74733			−0.873664	+	0.486530i	$0.838262\pi$
$678$	0.669873	−	1.16025i	0.0257263	−	0.0445593i
$679$	−8.19615	+	14.1962i	−0.314539	+	0.544798i
$680$	10.6962	+	18.5263i	0.410179	+	0.710450i
$681$	−12.1962			−0.467358
$682$	−0.928203	−	1.60770i	−0.0355427	−	0.0615618i
$683$	5.07180	+	8.78461i	0.194067	+	0.336134i	0.946594	−	0.322427i	$-0.104499\pi$
$683$	5.07180	+	8.78461i	0.194067	+	0.336134i	−0.752527	+	0.658561i	$0.771165\pi$
$684$	4.73205			0.180934
$685$	−22.2583	−	38.5526i	−0.850447	−	1.47302i
$686$	−8.92820	+	15.4641i	−0.340880	+	0.590422i
$687$	5.92820	−	10.2679i	0.226175	−	0.391747i
$688$	−9.66025			−0.368294
$689$		0			0
$690$	15.6603			0.596176
$691$	−21.8301	+	37.8109i	−0.830457	+	1.43839i	0.0672190	+	0.997738i	$0.478587\pi$
$691$	−21.8301	+	37.8109i	−0.830457	+	1.43839i	−0.897676	+	0.440656i	$0.854746\pi$
$692$	−2.19615	+	3.80385i	−0.0834852	+	0.144601i
$693$	1.73205	+	3.00000i	0.0657952	+	0.113961i
$694$	33.1244			1.25738
$695$	−33.3205	−	57.7128i	−1.26392	−	2.18917i
$696$	2.23205	+	3.86603i	0.0846057	+	0.146541i
$697$	53.8372			2.03923
$698$	−7.66025	−	13.2679i	−0.289945	−	0.502199i
$699$	3.92820	−	6.80385i	0.148578	−	0.257345i
$700$	12.1962	−	21.1244i	0.460971	−	0.798426i
$701$	−3.32051			−0.125414			−0.0627069	−	0.998032i	$-0.519973\pi$
$701$	−3.32051			−0.125414			−0.0627069	+	0.998032i	$0.519973\pi$
$702$		0			0
$703$	16.7321			0.631061
$704$	−0.633975	+	1.09808i	−0.0238938	+	0.0413853i
$705$	−4.09808	+	7.09808i	−0.154342	+	0.267329i
$706$	10.8923	+	18.8660i	0.409937	+	0.710032i
$707$	−5.26795			−0.198122
$708$	−4.00000	−	6.92820i	−0.150329	−	0.260378i
$709$	−6.57180	−	11.3827i	−0.246809	−	0.427486i	0.715830	−	0.698275i	$-0.246049\pi$
$709$	−6.57180	−	11.3827i	−0.246809	−	0.427486i	−0.962639	+	0.270789i	$0.912715\pi$
$710$	17.6603			0.662778
$711$	1.26795	+	2.19615i	0.0475518	+	0.0823622i
$712$	4.73205	−	8.19615i	0.177341	−	0.307164i
$713$	−3.07180	+	5.32051i	−0.115040	+	0.199255i
$714$	15.6603			0.586070
$715$		0			0
$716$	−16.0526			−0.599912
$717$	−3.83013	+	6.63397i	−0.143039	+	0.247750i
$718$	0.562178	−	0.973721i	0.0209803	−	0.0363389i
$719$	14.7321	+	25.5167i	0.549413	+	0.951611i	0.998315	+	0.0580299i	$0.0184819\pi$
$719$	14.7321	+	25.5167i	0.549413	+	0.951611i	−0.448902	+	0.893581i	$0.648185\pi$
$720$	3.73205			0.139085
$721$	−20.8564	−	36.1244i	−0.776733	−	1.34534i
$722$	−1.69615	−	2.93782i	−0.0631243	−	0.109334i
$723$	13.5885			0.505360
$724$	−9.59808	−	16.6244i	−0.356710	−	0.617839i
$725$	19.9282	−	34.5167i	0.740115	−	1.28192i
$726$	4.69615	−	8.13397i	0.174291	−	0.301880i
$727$	−30.9808			−1.14901			−0.574506	−	0.818500i	$-0.694806\pi$
$727$	−30.9808			−1.14901			−0.574506	+	0.818500i	$0.694806\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	11.6962	−	20.2583i	0.432894	−	0.749794i
$731$	−27.6865	+	47.9545i	−1.02402	+	1.77366i
$732$	4.59808	+	7.96410i	0.169950	+	0.294362i
$733$	19.0000			0.701781			0.350891	−	0.936416i	$-0.385879\pi$
$733$	19.0000			0.701781			0.350891	+	0.936416i	$0.385879\pi$
$734$	5.63397	+	9.75833i	0.207954	+	0.360187i
$735$	−0.866025	−	1.50000i	−0.0319438	−	0.0553283i
$736$	4.19615			0.154672
$737$	−8.32051	−	14.4115i	−0.306490	−	0.530856i
$738$	4.69615	−	8.13397i	0.172868	−	0.299416i
$739$	−1.46410	+	2.53590i	−0.0538578	+	0.0932845i	−0.891697	−	0.452632i	$-0.850485\pi$
$739$	−1.46410	+	2.53590i	−0.0538578	+	0.0932845i	0.837840	+	0.545917i	$0.183818\pi$
$740$	13.1962			0.485100
$741$		0			0
$742$	17.6603			0.648328
$743$	24.1962	−	41.9090i	0.887671	−	1.53749i	0.0450491	−	0.998985i	$-0.485656\pi$
$743$	24.1962	−	41.9090i	0.887671	−	1.53749i	0.842622	−	0.538506i	$-0.181011\pi$
$744$	−0.732051	+	1.26795i	−0.0268383	+	0.0464853i
$745$	−24.6244	−	42.6506i	−0.902167	−	1.56260i
$746$	−13.7321			−0.502766
$747$	0.0980762	+	0.169873i	0.00358842	+	0.00621533i
$748$	3.63397	+	6.29423i	0.132871	+	0.230140i
$749$	−27.8564			−1.01785
$750$	−7.33013	−	12.6962i	−0.267658	−	0.463598i
$751$	24.9545	−	43.2224i	0.910602	−	1.57721i	0.0973862	−	0.995247i	$-0.468952\pi$
$751$	24.9545	−	43.2224i	0.910602	−	1.57721i	0.813216	−	0.581962i	$-0.197715\pi$
$752$	−1.09808	+	1.90192i	−0.0400427	+	0.0693560i
$753$	13.4641			0.490659
$754$		0			0
$755$	25.1244			0.914369
$756$	1.36603	−	2.36603i	0.0496819	−	0.0860515i
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	−0.991109	−	0.133056i	$-0.957521\pi$
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	0.610784	+	0.791797i	$0.290854\pi$
$758$	2.73205	+	4.73205i	0.0992326	+	0.171876i
$759$	5.32051			0.193122
$760$	−8.83013	−	15.2942i	−0.320302	−	0.554780i
$761$	−5.66025	−	9.80385i	−0.205184	−	0.355389i	0.745007	−	0.667056i	$-0.232446\pi$
$761$	−5.66025	−	9.80385i	−0.205184	−	0.355389i	−0.950191	+	0.311667i	$0.899113\pi$
$762$	−9.85641			−0.357060
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	3.46410	−	6.00000i	0.125327	−	0.217072i
$765$	10.6962	−	18.5263i	0.386720	−	0.669819i
$766$	−1.46410			−0.0529001
$767$		0			0
$768$	1.00000			0.0360844
$769$	21.9282	−	37.9808i	0.790751	−	1.36962i	−0.134751	−	0.990879i	$-0.543023\pi$
$769$	21.9282	−	37.9808i	0.790751	−	1.36962i	0.925502	−	0.378742i	$-0.123643\pi$
$770$	6.46410	−	11.1962i	0.232950	−	0.403481i
$771$	−4.66987	−	8.08846i	−0.168181	−	0.291299i
$772$	−11.7321			−0.422246
$773$	24.4641	+	42.3731i	0.879913	+	1.52405i	0.851436	+	0.524459i	$0.175732\pi$
$773$	24.4641	+	42.3731i	0.879913	+	1.52405i	0.0284768	+	0.999594i	$0.490934\pi$
$774$	4.83013	+	8.36603i	0.173615	+	0.300711i
$775$	13.0718			0.469553
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	4.83013	−	8.36603i	0.173280	−	0.300129i
$778$	−5.89230	+	10.2058i	−0.211249	+	0.365895i
$779$	−44.4449			−1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$	12.0263	−	20.8301i	0.430059	−	0.744884i
$783$	2.23205	−	3.86603i	0.0797670	−	0.138160i
$784$	−0.232051	−	0.401924i	−0.00828753	−	0.0143544i
$785$	28.3205			1.01080
$786$	−3.26795	−	5.66025i	−0.116564	−	0.201895i
$787$	−2.33975	−	4.05256i	−0.0834029	−	0.144458i	0.821307	−	0.570487i	$-0.193246\pi$
$787$	−2.33975	−	4.05256i	−0.0834029	−	0.144458i	−0.904710	+	0.426029i	$0.859912\pi$
$788$	−17.8564			−0.636108
$789$	5.02628	+	8.70577i	0.178940	+	0.309934i
$790$	4.73205	−	8.19615i	0.168359	−	0.291606i
$791$	−1.83013	+	3.16987i	−0.0650718	+	0.112708i
$792$	1.26795			0.0450546
$793$		0			0
$794$	20.3923			0.723696
$795$	12.0622	−	20.8923i	0.427801	−	0.740974i
$796$	7.09808	−	12.2942i	0.251585	−	0.435757i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$	−12.9282			−0.457653
$799$	6.29423	+	10.9019i	0.222674	+	0.385682i
$800$	−4.46410	−	7.73205i	−0.157830	−	0.273369i
$801$	−9.46410			−0.334398
$802$	−4.03590	−	6.99038i	−0.142513	−	0.246839i
$803$	3.97372	−	6.88269i	0.140230	−	0.242885i
$804$	−6.56218	+	11.3660i	−0.231430	+	0.400849i
$805$	−42.7846			−1.50796
$806$		0			0
$807$	5.46410			0.192345
$808$	−0.964102	+	1.66987i	−0.0339170	+	0.0587459i
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.180453	−	0.983584i	$-0.442244\pi$
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.761582	−	0.648069i	$-0.224423\pi$
$810$	−1.86603	−	3.23205i	−0.0655654	−	0.113563i
$811$	17.1769			0.603163			0.301582	−	0.953440i	$-0.402485\pi$
$811$	17.1769			0.603163			0.301582	+	0.953440i	$0.402485\pi$
$812$	−6.09808	−	10.5622i	−0.214001	−	0.370660i
$813$	10.9282	+	18.9282i	0.383269	+	0.663841i
$814$	4.48334			0.157141
$815$	25.1244	+	43.5167i	0.880068	+	1.52432i
$816$	2.86603	−	4.96410i	0.100331	−	0.173778i
$817$	22.8564	−	39.5885i	0.799644	−	1.38502i
$818$	17.7321			0.619987
$819$		0			0
$820$	−35.0526			−1.22409
$821$	0.464102	−	0.803848i	0.0161973	−	0.0280545i	−0.857813	−	0.513962i	$-0.828177\pi$
$821$	0.464102	−	0.803848i	0.0161973	−	0.0280545i	0.874010	+	0.485907i	$0.161511\pi$
$822$	−5.96410	+	10.3301i	−0.208022	+	0.360305i
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	−0.959177	−	0.282806i	$-0.908735\pi$
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	0.234671	−	0.972075i	$-0.424599\pi$
$824$	−15.2679			−0.531884
$825$	−5.66025	−	9.80385i	−0.197065	−	0.341326i
$826$	10.9282	+	18.9282i	0.380241	+	0.658596i
$827$	26.5359			0.922744			0.461372	−	0.887207i	$-0.347357\pi$
$827$	26.5359			0.922744			0.461372	+	0.887207i	$0.347357\pi$
$828$	−2.09808	−	3.63397i	−0.0729132	−	0.126289i
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	−0.741338	−	0.671132i	$-0.765808\pi$
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	0.951886	+	0.306452i	$0.0991418\pi$
$830$	0.366025	−	0.633975i	0.0127049	−	0.0220056i
$831$	−5.73205			−0.198843
$832$		0			0
$833$	−2.66025			−0.0921723
$834$	−8.92820	+	15.4641i	−0.309158	+	0.535478i
$835$	17.6603	−	30.5885i	0.611158	−	1.05856i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	1.46410			0.0506068
$838$	8.73205	+	15.1244i	0.301644	+	0.522462i
$839$	−20.9282	−	36.2487i	−0.722522	−	1.25144i	−0.959986	−	0.280048i	$-0.909650\pi$
$839$	−20.9282	−	36.2487i	−0.722522	−	1.25144i	0.237464	−	0.971396i	$-0.423684\pi$
$840$	−10.1962			−0.351801
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$	11.3564	−	19.6699i	0.391368	−	0.677869i
$843$	−6.16025	+	10.6699i	−0.212170	+	0.367490i
$844$	16.3923			0.564246
$845$		0			0
$846$	2.19615			0.0755053
$847$	−12.8301	+	22.2224i	−0.440848	+	0.763572i
$848$	3.23205	−	5.59808i	0.110989	−	0.192239i
$849$	−12.8301	−	22.2224i	−0.440329	−	0.762672i
$850$	−51.1769			−1.75535
$851$	−7.41858	−	12.8494i	−0.254306	−	0.440471i
$852$	−2.36603	−	4.09808i	−0.0810587	−	0.140398i
$853$	−54.1769			−1.85498			−0.927491	−	0.373845i	$-0.878039\pi$
$853$	−54.1769			−1.85498			−0.927491	+	0.373845i	$0.878039\pi$
$854$	−12.5622	−	21.7583i	−0.429869	−	0.744555i
$855$	−8.83013	+	15.2942i	−0.301984	+	0.523052i
$856$	−5.09808	+	8.83013i	−0.174249	+	0.301808i
$857$	39.4449			1.34741			0.673705	−	0.739000i	$-0.264702\pi$
$857$	39.4449			1.34741			0.673705	+	0.739000i	$0.264702\pi$
$858$		0			0
$859$	−47.1244			−1.60786			−0.803931	−	0.594722i	$-0.797262\pi$
$859$	−47.1244			−1.60786			−0.803931	+	0.594722i	$0.797262\pi$
$860$	18.0263	−	31.2224i	0.614691	−	1.06468i
$861$	−12.8301	+	22.2224i	−0.437250	+	0.757338i
$862$	−6.56218	−	11.3660i	−0.223509	−	0.387128i
$863$	−17.1244			−0.582920			−0.291460	−	0.956583i	$-0.594141\pi$
$863$	−17.1244			−0.582920			−0.291460	+	0.956583i	$0.594141\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−8.19615	−	14.1962i	−0.278678	−	0.482684i
$866$	12.8564			0.436878
$867$	−7.92820	−	13.7321i	−0.269256	−	0.466365i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	1.60770	−	2.78461i	0.0545373	−	0.0944614i
$870$	−16.6603			−0.564836
$871$		0			0
$872$	1.46410			0.0495807
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$	20.0263	+	34.6865i	0.677012	+	1.17262i
$876$	−6.26795			−0.211774
$877$	−11.9641	−	20.7224i	−0.403999	−	0.699747i	0.590205	−	0.807253i	$-0.299047\pi$
$877$	−11.9641	−	20.7224i	−0.403999	−	0.699747i	−0.994204	+	0.107506i	$0.965713\pi$
$878$	0.169873	+	0.294229i	0.00573294	+	0.00992974i
$879$	30.5167			1.02930
$880$	−2.36603	−	4.09808i	−0.0797587	−	0.138146i
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	−0.530440	−	0.847722i	$-0.677973\pi$
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	0.999369	+	0.0355135i	$0.0113067\pi$
$882$	−0.232051	+	0.401924i	−0.00781356	+	0.0135335i
$883$	42.9282			1.44465			0.722325	−	0.691554i	$-0.243074\pi$
$883$	42.9282			1.44465			0.722325	+	0.691554i	$0.243074\pi$
$884$		0			0
$885$	29.8564			1.00361
$886$	−7.80385	+	13.5167i	−0.262175	+	0.454101i
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	0.350852	+	0.936431i	$0.385892\pi$
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	−0.986399	+	0.164369i	$0.947441\pi$
$888$	−1.76795	−	3.06218i	−0.0593285	−	0.102760i
$889$	26.9282			0.903143
$890$	17.6603	+	30.5885i	0.591973	+	1.02533i
$891$	−0.633975	−	1.09808i	−0.0212389	−	0.0367869i
$892$	−26.9282			−0.901623
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$	−6.59808	+	11.4282i	−0.220673	+	0.382216i
$895$	29.9545	−	51.8827i	1.00127	−	1.73425i
$896$	−2.73205			−0.0912714
$897$		0			0
$898$	11.3205			0.377770
$899$	3.26795	−	5.66025i	0.108992	−	0.188780i
$900$	−4.46410	+	7.73205i	−0.148803	+	0.257735i
$901$	−18.5263	−	32.0885i	−0.617200	−	1.06902i
$902$	−11.9090			−0.396525
$903$	−13.1962	−	22.8564i	−0.439140	−	0.760614i
$904$	0.669873	+	1.16025i	0.0222796	+	0.0385895i
$905$	71.6410			2.38143
$906$	−3.36603	−	5.83013i	−0.111829	−	0.193693i
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	0.387985	+	0.921666i	$0.373171\pi$
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	−0.992178	+	0.124828i	$0.960162\pi$
$908$	6.09808	−	10.5622i	0.202372	−	0.350518i
$909$	1.92820			0.0639545
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$	−2.36603	+	4.09808i	−0.0783469	+	0.135701i
$913$	0.124356	−	0.215390i	0.00411557	−	0.00712838i
$914$	−0.669873	−	1.16025i	−0.0221574	−	0.0383778i
$915$	−34.3205			−1.13460
$916$	5.92820	+	10.2679i	0.195873	+	0.339263i
$917$	8.92820	+	15.4641i	0.294835	+	0.510670i
$918$	−5.73205			−0.189186
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	−0.943836	−	0.330415i	$-0.892811\pi$
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	0.185770	−	0.982593i	$-0.440522\pi$
$920$	−7.83013	+	13.5622i	−0.258152	+	0.447132i
$921$	11.2942	−	19.5622i	0.372157	−	0.644596i
$922$	22.2679			0.733356
$923$		0			0
$924$	−3.46410			−0.113961
$925$	−15.7846	+	27.3397i	−0.518995	+	0.898925i
$926$	−5.02628	+	8.70577i	−0.165174	+	0.286089i
$927$	7.63397	+	13.2224i	0.250733	+	0.434282i
$928$	−4.46410			−0.146541
$929$	19.6244	+	33.9904i	0.643854	+	1.11519i	0.984565	+	0.175020i	$0.0559990\pi$
$929$	19.6244	+	33.9904i	0.643854	+	1.11519i	−0.340711	+	0.940168i	$0.610668\pi$
$930$	−2.73205	−	4.73205i	−0.0895875	−	0.155170i
$931$	2.19615			0.0719760
$932$	3.92820	+	6.80385i	0.128673	+	0.222867i
$933$	0.830127	−	1.43782i	0.0271771	−	0.0470722i
$934$	−9.29423	+	16.0981i	−0.304116	+	0.526745i
$935$	−27.1244			−0.887061
$936$		0			0
$937$	−5.24871			−0.171468			−0.0857340	−	0.996318i	$-0.527324\pi$
$937$	−5.24871			−0.171468			−0.0857340	+	0.996318i	$0.527324\pi$
$938$	17.9282	−	31.0526i	0.585377	−	1.01390i
$939$	−3.26795	+	5.66025i	−0.106645	+	0.184715i
$940$	−4.09808	−	7.09808i	−0.133665	−	0.231514i
$941$	12.6410			0.412085			0.206043	−	0.978543i	$-0.433941\pi$
$941$	12.6410			0.412085			0.206043	+	0.978543i	$0.433941\pi$
$942$	−3.79423	−	6.57180i	−0.123623	−	0.214121i
$943$	19.7058	+	34.1314i	0.641708	+	1.11147i
$944$	8.00000			0.260378
$945$	5.09808	+	8.83013i	0.165840	+	0.287244i
$946$	6.12436	−	10.6077i	0.199120	−	0.344886i
$947$	−10.5359	+	18.2487i	−0.342371	+	0.593003i	−0.984872	−	0.173281i	$-0.944563\pi$
$947$	−10.5359	+	18.2487i	−0.342371	+	0.593003i	0.642502	+	0.766284i	$0.277897\pi$
$948$	−2.53590			−0.0823622
$949$		0			0
$950$	42.2487			1.37073
$951$	−10.3301	+	17.8923i	−0.334977	+	0.580198i
$952$	−7.83013	+	13.5622i	−0.253776	+	0.439553i
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$	−6.46410			−0.209283
$955$	12.9282	+	22.3923i	0.418347	+	0.724598i
$956$	−3.83013	−	6.63397i	−0.123875	−	0.214558i
$957$	−5.66025			−0.182970
$958$	−16.7321	−	28.9808i	−0.540588	−	0.936326i
$959$	16.2942	−	28.2224i	0.526168	−	0.911350i
$960$	−1.86603	+	3.23205i	−0.0602257	+	0.104314i
$961$	−28.8564			−0.930852
$962$		0			0
$963$	10.1962			0.328566
$964$	−6.79423	+	11.7679i	−0.218827	+	0.379020i
$965$	21.8923	−	37.9186i	0.704738	−	1.22064i
$966$	5.73205	+	9.92820i	0.184426	+	0.319435i
$967$	−43.1244			−1.38679			−0.693393	−	0.720560i	$-0.743885\pi$
$967$	−43.1244			−1.38679			−0.693393	+	0.720560i	$0.743885\pi$
$968$	4.69615	+	8.13397i	0.150940	+	0.261436i
$969$	13.5622	+	23.4904i	0.435680	+	0.754620i
$970$	−22.3923			−0.718974
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	0.514495	−	0.857493i	$-0.327979\pi$
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	−0.999859	+	0.0168189i	$0.994646\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	24.3923	−	42.2487i	0.781981	−	1.35443i
$974$	−3.12436			−0.100111
$975$		0			0
$976$	−9.19615			−0.294362
$977$	−22.9641	+	39.7750i	−0.734687	+	1.27251i	0.220174	+	0.975461i	$0.429337\pi$
$977$	−22.9641	+	39.7750i	−0.734687	+	1.27251i	−0.954861	+	0.297054i	$0.903996\pi$
$978$	6.73205	−	11.6603i	0.215267	−	0.372854i
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$	1.73205			0.0553283
$981$	−0.732051	−	1.26795i	−0.0233726	−	0.0404825i
$982$	−4.36603	−	7.56218i	−0.139325	−	0.241319i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$	4.69615	+	8.13397i	0.149708	+	0.259302i
$985$	33.3205	−	57.7128i	1.06168	−	1.83888i
$986$	−12.7942	+	22.1603i	−0.407451	+	0.705726i
$987$	−6.00000			−0.190982
$988$		0			0
$989$	−40.5359			−1.28897
$990$	−2.36603	+	4.09808i	−0.0751972	+	0.130245i
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	−0.987756	−	0.156006i	$-0.950138\pi$
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	0.628983	+	0.777419i	$0.283471\pi$
$992$	−0.732051	−	1.26795i	−0.0232426	−	0.0402574i
$993$	20.0000			0.634681
$994$	6.46410	+	11.1962i	0.205029	+	0.355120i
$995$	26.4904	+	45.8827i	0.839802	+	1.45458i
$996$	−0.196152			−0.00621533
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	0.646123	−	0.763234i	$-0.276389\pi$
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	−0.984041	+	0.177942i	$0.943056\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$	−1.76795	+	3.06218i	−0.0559354	+	0.0968830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.g.529.2		4
13.2	odd	12		78.2.i.a.49.1	yes	4
13.3	even	3	inner	1014.2.e.g.991.2		4
13.4	even	6		1014.2.a.i.1.1		2
13.5	odd	4		1014.2.i.a.823.2		4
13.6	odd	12		1014.2.b.e.337.1		4
13.7	odd	12		1014.2.b.e.337.4		4
13.8	odd	4		78.2.i.a.43.1	✓	4
13.9	even	3		1014.2.a.k.1.2		2
13.10	even	6		1014.2.e.i.991.1		4
13.11	odd	12		1014.2.i.a.361.2		4
13.12	even	2		1014.2.e.i.529.1		4
39.2	even	12		234.2.l.c.127.2		4
39.8	even	4		234.2.l.c.199.2		4
39.17	odd	6		3042.2.a.y.1.2		2
39.20	even	12		3042.2.b.i.1351.1		4
39.32	even	12		3042.2.b.i.1351.4		4
39.35	odd	6		3042.2.a.p.1.1		2
52.15	even	12		624.2.bv.e.49.1		4
52.35	odd	6		8112.2.a.bp.1.2		2
52.43	odd	6		8112.2.a.bj.1.1		2
52.47	even	4		624.2.bv.e.433.2		4
65.2	even	12		1950.2.y.b.49.1		4
65.8	even	4		1950.2.y.b.199.1		4
65.28	even	12		1950.2.y.g.49.2		4
65.34	odd	4		1950.2.bc.d.901.2		4
65.47	even	4		1950.2.y.g.199.2		4
65.54	odd	12		1950.2.bc.d.751.2		4
156.47	odd	4		1872.2.by.h.433.1		4
156.119	odd	12		1872.2.by.h.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	13.8	odd	4
78.2.i.a.49.1	yes	4	13.2	odd	12
234.2.l.c.127.2		4	39.2	even	12
234.2.l.c.199.2		4	39.8	even	4
624.2.bv.e.49.1		4	52.15	even	12
624.2.bv.e.433.2		4	52.47	even	4
1014.2.a.i.1.1		2	13.4	even	6
1014.2.a.k.1.2		2	13.9	even	3
1014.2.b.e.337.1		4	13.6	odd	12
1014.2.b.e.337.4		4	13.7	odd	12
1014.2.e.g.529.2		4	1.1	even	1	trivial
1014.2.e.g.991.2		4	13.3	even	3	inner
1014.2.e.i.529.1		4	13.12	even	2
1014.2.e.i.991.1		4	13.10	even	6
1014.2.i.a.361.2		4	13.11	odd	12
1014.2.i.a.823.2		4	13.5	odd	4
1872.2.by.h.433.1		4	156.47	odd	4
1872.2.by.h.1297.2		4	156.119	odd	12
1950.2.y.b.49.1		4	65.2	even	12
1950.2.y.b.199.1		4	65.8	even	4
1950.2.y.g.49.2		4	65.28	even	12
1950.2.y.g.199.2		4	65.47	even	4
1950.2.bc.d.751.2		4	65.54	odd	12
1950.2.bc.d.901.2		4	65.34	odd	4
3042.2.a.p.1.1		2	39.35	odd	6
3042.2.a.y.1.2		2	39.17	odd	6
3042.2.b.i.1351.1		4	39.20	even	12
3042.2.b.i.1351.4		4	39.32	even	12
8112.2.a.bj.1.1		2	52.43	odd	6
8112.2.a.bp.1.2		2	52.35	odd	6

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.86603 + 3.23205i) q^{10} +(-0.633975 + 1.09808i) q^{11} +1.00000 q^{12} -2.73205 q^{14} +(-1.86603 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +1.00000 q^{18} +(-2.36603 - 4.09808i) q^{19} +(-1.86603 - 3.23205i) q^{20} -2.73205 q^{21} +(-0.633975 - 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(-0.500000 + 0.866025i) q^{24} +8.92820 q^{25} +1.00000 q^{27} +(1.36603 - 2.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(-1.86603 - 3.23205i) q^{30} +1.46410 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.633975 - 1.09808i) q^{33} -5.73205 q^{34} +(5.09808 + 8.83013i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.76795 + 3.06218i) q^{37} +4.73205 q^{38} +3.73205 q^{40} +(4.69615 - 8.13397i) q^{41} +(1.36603 - 2.36603i) q^{42} +(4.83013 + 8.36603i) q^{43} +1.26795 q^{44} +(-1.86603 - 3.23205i) q^{45} +(-2.09808 - 3.63397i) q^{46} +2.19615 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.232051 + 0.401924i) q^{49} +(-4.46410 + 7.73205i) q^{50} -5.73205 q^{51} -6.46410 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(2.23205 + 3.86603i) q^{58} +(-4.00000 - 6.92820i) q^{59} +3.73205 q^{60} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} +(1.36603 - 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 + 11.3660i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-2.09808 - 3.63397i) q^{69} -10.1962 q^{70} +(-2.36603 - 4.09808i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(-1.76795 - 3.06218i) q^{74} +(-4.46410 + 7.73205i) q^{75} +(-2.36603 + 4.09808i) q^{76} -3.46410 q^{77} -2.53590 q^{79} +(-1.86603 + 3.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.69615 + 8.13397i) q^{82} -0.196152 q^{83} +(1.36603 + 2.36603i) q^{84} +(10.6962 + 18.5263i) q^{85} -9.66025 q^{86} +(2.23205 + 3.86603i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(4.73205 - 8.19615i) q^{89} +3.73205 q^{90} +4.19615 q^{92} +(-0.732051 + 1.26795i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(-8.83013 - 15.2942i) q^{95} +1.00000 q^{96} +(3.00000 + 5.19615i) q^{97} +(-0.232051 - 0.401924i) q^{98} +1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^31 - 2 * q^32 - 6 * q^33 - 16 * q^34 + 10 * q^35 - 2 * q^36 - 14 * q^37 + 12 * q^38 + 8 * q^40 - 2 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - 4 * q^45 + 2 * q^46 - 12 * q^47 - 2 * q^48 + 6 * q^49 - 4 * q^50 - 16 * q^51 - 12 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 12 * q^57 + 2 * q^58 - 16 * q^59 + 8 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 8 * q^68 + 2 * q^69 - 20 * q^70 - 6 * q^71 - 2 * q^72 - 32 * q^73 - 14 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^79 - 4 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 + 2 * q^84 + 22 * q^85 - 4 * q^86 + 2 * q^87 - 6 * q^88 + 12 * q^89 + 8 * q^90 - 4 * q^92 + 4 * q^93 + 6 * q^94 - 18 * q^95 + 4 * q^96 + 12 * q^97 + 6 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more