LMFDB - Embedded newform 765.2.bt.b.752.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(353,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.353"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 9, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$1$
Dimension:	$4$
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:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			752.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	765.752
Dual form			765.2.bt.b.353.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.866025 - 3.23205i) q^{6} +(0.232051 - 0.133975i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-4.09808 - 1.36603i) q^{10} +(-3.36603 - 0.901924i) q^{11} +3.00000 q^{12} +(-0.267949 - 1.00000i) q^{13} +(0.133975 + 0.500000i) q^{14} +(-1.73205 - 3.46410i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-4.00000 + 1.00000i) q^{17} +(4.09808 + 4.09808i) q^{18} +8.46410 q^{19} +(2.13397 - 3.23205i) q^{20} +(-0.232051 + 0.401924i) q^{21} +(3.36603 - 5.83013i) q^{22} +(-5.59808 - 3.23205i) q^{23} +(0.232051 - 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +2.00000 q^{26} +5.19615i q^{27} -0.464102 q^{28} +(-6.09808 - 1.63397i) q^{29} +(7.33013 - 1.50000i) q^{30} +(-1.00000 - 3.73205i) q^{31} +(7.33013 - 1.96410i) q^{32} +(5.83013 - 1.56218i) q^{33} +(0.133975 - 7.96410i) q^{34} +(0.267949 + 0.535898i) q^{35} +(-4.50000 + 2.59808i) q^{36} +1.19615 q^{37} +(-4.23205 + 15.7942i) q^{38} +(1.26795 + 1.26795i) q^{39} +(-0.767949 - 0.866025i) q^{40} +(-1.19615 - 4.46410i) q^{41} +(-0.633975 - 0.633975i) q^{42} +(-2.00000 + 7.46410i) q^{43} +(4.26795 + 4.26795i) q^{44} +(5.59808 + 3.69615i) q^{45} +(8.83013 - 8.83013i) q^{46} +(8.09808 + 2.16987i) q^{47} +(6.69615 + 3.86603i) q^{48} +(-3.46410 + 6.00000i) q^{49} +(3.59808 - 8.96410i) q^{50} +(5.13397 - 4.96410i) q^{51} +(-0.464102 + 1.73205i) q^{52} +(4.00000 - 4.00000i) q^{53} +(-9.69615 - 2.59808i) q^{54} +(2.46410 - 7.39230i) q^{55} +(-0.0358984 + 0.133975i) q^{56} +(-12.6962 + 7.33013i) q^{57} +(6.09808 - 10.5622i) q^{58} +(4.03590 + 2.33013i) q^{59} +(-0.401924 + 6.69615i) q^{60} +(3.29423 - 12.2942i) q^{61} +7.46410 q^{62} -0.803848i q^{63} +5.73205i q^{64} +(2.26795 - 0.464102i) q^{65} +11.6603i q^{66} +(-3.46410 + 0.928203i) q^{67} +(6.86603 + 1.96410i) q^{68} +11.1962 q^{69} +(-1.13397 + 0.232051i) q^{70} +(11.1962 + 11.1962i) q^{71} +(0.401924 + 1.50000i) q^{72} +13.1962i q^{73} +(-0.598076 + 2.23205i) q^{74} +(7.96410 - 3.40192i) q^{75} +(-12.6962 - 7.33013i) q^{76} +(-0.901924 + 0.241670i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(-9.46410 - 2.53590i) q^{79} +(8.92820 - 4.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +8.92820 q^{82} +(-2.36603 - 0.633975i) q^{83} +(0.696152 - 0.401924i) q^{84} +(-1.69615 - 9.06218i) q^{85} +(-12.9282 - 7.46410i) q^{86} +(10.5622 - 2.83013i) q^{87} +(1.56218 - 0.901924i) q^{88} -15.1962 q^{89} +(-9.69615 + 8.59808i) q^{90} +(-0.196152 - 0.196152i) q^{91} +(5.59808 + 9.69615i) q^{92} +(4.73205 + 4.73205i) q^{93} +(-8.09808 + 14.0263i) q^{94} +(-1.13397 + 18.8923i) q^{95} +(-9.29423 + 9.29423i) q^{96} +(-5.19615 - 9.00000i) q^{97} +(-9.46410 - 9.46410i) q^{98} +(-7.39230 + 7.39230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 6 q^{4} - 4 q^{5} - 6 q^{7} + 2 q^{8} + 6 q^{9} - 6 q^{10} - 10 q^{11} + 12 q^{12} - 8 q^{13} + 4 q^{14} - 2 q^{16} - 16 q^{17} + 6 q^{18} + 20 q^{19} + 12 q^{20} + 6 q^{21} + 10 q^{22}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 6 * q^4 - 4 * q^5 - 6 * q^7 + 2 * q^8 + 6 * q^9 - 6 * q^10 - 10 * q^11 + 12 * q^12 - 8 * q^13 + 4 * q^14 - 2 * q^16 - 16 * q^17 + 6 * q^18 + 20 * q^19 + 12 * q^20 + 6 * q^21 + 10 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^25 + 8 * q^26 + 12 * q^28 - 14 * q^29 + 12 * q^30 - 4 * q^31 + 12 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^35 - 18 * q^36 - 16 * q^37 - 10 * q^38 + 12 * q^39 - 10 * q^40 + 16 * q^41 - 6 * q^42 - 8 * q^43 + 24 * q^44 + 12 * q^45 + 18 * q^46 + 22 * q^47 + 6 * q^48 + 4 * q^50 + 24 * q^51 + 12 * q^52 + 16 * q^53 - 18 * q^54 - 4 * q^55 - 14 * q^56 - 30 * q^57 + 14 * q^58 + 30 * q^59 - 12 * q^60 - 18 * q^61 + 16 * q^62 + 16 * q^65 + 24 * q^68 + 24 * q^69 - 8 * q^70 + 24 * q^71 + 12 * q^72 + 8 * q^74 + 18 * q^75 - 30 * q^76 - 14 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 18 * q^81 + 8 * q^82 - 6 * q^83 - 18 * q^84 + 14 * q^85 - 24 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^89 - 18 * q^90 + 20 * q^91 + 12 * q^92 + 12 * q^93 - 22 * q^94 - 8 * q^95 - 6 * q^96 - 24 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	0.528742	+	0.848783i	$0.322664\pi$
$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	−0.882295	+	0.470696i	$0.844003\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$6$	−0.866025	−	3.23205i	−0.353553	−	1.31948i
$7$	0.232051	−	0.133975i	0.0877070	−	0.0506376i	−0.455505	−	0.890233i	$-0.650541\pi$
$7$	0.232051	−	0.133975i	0.0877070	−	0.0506376i	0.543212	+	0.839596i	$0.317208\pi$
$8$	−0.366025	+	0.366025i	−0.129410	+	0.129410i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−4.09808	−	1.36603i	−1.29593	−	0.431975i
$11$	−3.36603	−	0.901924i	−1.01489	−	0.271940i	−0.287222	−	0.957864i	$-0.592732\pi$
$11$	−3.36603	−	0.901924i	−1.01489	−	0.271940i	−0.727673	+	0.685924i	$0.759398\pi$
$12$	3.00000			0.866025
$13$	−0.267949	−	1.00000i	−0.0743157	−	0.277350i	0.918762	−	0.394813i	$-0.129191\pi$
$13$	−0.267949	−	1.00000i	−0.0743157	−	0.277350i	−0.993077	+	0.117463i	$0.962524\pi$
$14$	0.133975	+	0.500000i	0.0358062	+	0.133631i
$15$	−1.73205	−	3.46410i	−0.447214	−	0.894427i
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$18$	4.09808	+	4.09808i	0.965926	+	0.965926i
$19$	8.46410			1.94180			0.970899	−	0.239489i	$-0.0769800\pi$
$19$	8.46410			1.94180			0.970899	+	0.239489i	$0.0769800\pi$
$20$	2.13397	−	3.23205i	0.477171	−	0.722709i
$21$	−0.232051	+	0.401924i	−0.0506376	+	0.0877070i
$22$	3.36603	−	5.83013i	0.717639	−	1.24299i
$23$	−5.59808	−	3.23205i	−1.16728	−	0.673929i	−0.214242	−	0.976781i	$-0.568728\pi$
$23$	−5.59808	−	3.23205i	−1.16728	−	0.673929i	−0.953038	+	0.302851i	$0.902061\pi$
$24$	0.232051	−	0.866025i	0.0473672	−	0.176777i
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	2.00000			0.392232
$27$			5.19615i			1.00000i
$28$	−0.464102			−0.0877070
$29$	−6.09808	−	1.63397i	−1.13238	−	0.303421i	−0.356499	−	0.934296i	$-0.616030\pi$
$29$	−6.09808	−	1.63397i	−1.13238	−	0.303421i	−0.775885	+	0.630874i	$0.782696\pi$
$30$	7.33013	−	1.50000i	1.33829	−	0.273861i
$31$	−1.00000	−	3.73205i	−0.179605	−	0.670296i	−0.995721	−	0.0924079i	$-0.970544\pi$
$31$	−1.00000	−	3.73205i	−0.179605	−	0.670296i	0.816116	−	0.577888i	$-0.196123\pi$
$32$	7.33013	−	1.96410i	1.29580	−	0.347207i
$33$	5.83013	−	1.56218i	1.01489	−	0.271940i
$34$	0.133975	−	7.96410i	0.0229765	−	1.36583i
$35$	0.267949	+	0.535898i	0.0452917	+	0.0905834i
$36$	−4.50000	+	2.59808i	−0.750000	+	0.433013i
$37$	1.19615			0.196646			0.0983231	−	0.995155i	$-0.468652\pi$
$37$	1.19615			0.196646			0.0983231	+	0.995155i	$0.468652\pi$
$38$	−4.23205	+	15.7942i	−0.686529	+	2.56216i
$39$	1.26795	+	1.26795i	0.203034	+	0.203034i
$40$	−0.767949	−	0.866025i	−0.121423	−	0.136931i
$41$	−1.19615	−	4.46410i	−0.186808	−	0.697176i	−0.994236	−	0.107210i	$-0.965808\pi$
$41$	−1.19615	−	4.46410i	−0.186808	−	0.697176i	0.807429	−	0.589965i	$-0.200859\pi$
$42$	−0.633975	−	0.633975i	−0.0978244	−	0.0978244i
$43$	−2.00000	+	7.46410i	−0.304997	+	1.13826i	0.627951	+	0.778253i	$0.283894\pi$
$43$	−2.00000	+	7.46410i	−0.304997	+	1.13826i	−0.932948	+	0.360012i	$0.882773\pi$
$44$	4.26795	+	4.26795i	0.643418	+	0.643418i
$45$	5.59808	+	3.69615i	0.834512	+	0.550990i
$46$	8.83013	−	8.83013i	1.30193	−	1.30193i
$47$	8.09808	+	2.16987i	1.18123	+	0.316509i	0.795413	−	0.606068i	$-0.207254\pi$
$47$	8.09808	+	2.16987i	1.18123	+	0.316509i	0.385813	+	0.922577i	$0.373921\pi$
$48$	6.69615	+	3.86603i	0.966506	+	0.558013i
$49$	−3.46410	+	6.00000i	−0.494872	+	0.857143i
$50$	3.59808	−	8.96410i	0.508845	−	1.26772i
$51$	5.13397	−	4.96410i	0.718900	−	0.695113i
$52$	−0.464102	+	1.73205i	−0.0643593	+	0.240192i
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	−0.376837	−	0.926279i	$-0.622988\pi$
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	0.926279	+	0.376837i	$0.122988\pi$
$54$	−9.69615	−	2.59808i	−1.31948	−	0.353553i
$55$	2.46410	−	7.39230i	0.332259	−	0.996778i
$56$	−0.0358984	+	0.133975i	−0.00479712	+	0.0179031i
$57$	−12.6962	+	7.33013i	−1.68165	+	0.970899i
$58$	6.09808	−	10.5622i	0.800717	−	1.38688i
$59$	4.03590	+	2.33013i	0.525429	+	0.303357i	0.739153	−	0.673537i	$-0.235226\pi$
$59$	4.03590	+	2.33013i	0.525429	+	0.303357i	−0.213724	+	0.976894i	$0.568559\pi$
$60$	−0.401924	+	6.69615i	−0.0518881	+	0.864470i
$61$	3.29423	−	12.2942i	0.421783	−	1.57411i	−0.349067	−	0.937098i	$-0.613501\pi$
$61$	3.29423	−	12.2942i	0.421783	−	1.57411i	0.770850	−	0.637017i	$-0.219832\pi$
$62$	7.46410			0.947942
$63$		−	0.803848i		−	0.101275i
$64$			5.73205i			0.716506i
$65$	2.26795	−	0.464102i	0.281304	−	0.0575647i
$66$			11.6603i			1.43528i
$67$	−3.46410	+	0.928203i	−0.423207	+	0.113398i	−0.464136	−	0.885764i	$-0.653635\pi$
$67$	−3.46410	+	0.928203i	−0.423207	+	0.113398i	0.0409285	+	0.999162i	$0.486968\pi$
$68$	6.86603	+	1.96410i	0.832628	+	0.238182i
$69$	11.1962			1.34786
$70$	−1.13397	+	0.232051i	−0.135536	+	0.0277354i
$71$	11.1962	+	11.1962i	1.32874	+	1.32874i	0.906471	+	0.422268i	$0.138766\pi$
$71$	11.1962	+	11.1962i	1.32874	+	1.32874i	0.422268	+	0.906471i	$0.361234\pi$
$72$	0.401924	+	1.50000i	0.0473672	+	0.176777i
$73$			13.1962i			1.54449i	0.635323	+	0.772246i	$0.280867\pi$
$73$			13.1962i			1.54449i	−0.635323	+	0.772246i	$0.719133\pi$
$74$	−0.598076	+	2.23205i	−0.0695249	+	0.259471i
$75$	7.96410	−	3.40192i	0.919615	−	0.392820i
$76$	−12.6962	−	7.33013i	−1.45635	−	0.840823i
$77$	−0.901924	+	0.241670i	−0.102784	+	0.0275408i
$78$	−3.00000	+	1.73205i	−0.339683	+	0.196116i
$79$	−9.46410	−	2.53590i	−1.06479	−	0.285311i	−0.316442	−	0.948612i	$-0.602488\pi$
$79$	−9.46410	−	2.53590i	−1.06479	−	0.285311i	−0.748353	+	0.663301i	$0.769155\pi$
$80$	8.92820	−	4.46410i	0.998203	−	0.499102i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	8.92820			0.985955
$83$	−2.36603	−	0.633975i	−0.259705	−	0.0695878i	0.126617	−	0.991952i	$-0.459588\pi$
$83$	−2.36603	−	0.633975i	−0.259705	−	0.0695878i	−0.386322	+	0.922364i	$0.626255\pi$
$84$	0.696152	−	0.401924i	0.0759565	−	0.0438535i
$85$	−1.69615	−	9.06218i	−0.183974	−	0.982931i
$86$	−12.9282	−	7.46410i	−1.39408	−	0.804875i
$87$	10.5622	−	2.83013i	1.13238	−	0.303421i
$88$	1.56218	−	0.901924i	0.166529	−	0.0961454i
$89$	−15.1962			−1.61079			−0.805394	−	0.592739i	$-0.798046\pi$
$89$	−15.1962			−1.61079			−0.805394	+	0.592739i	$0.798046\pi$
$90$	−9.69615	+	8.59808i	−1.02206	+	0.906317i
$91$	−0.196152	−	0.196152i	−0.0205624	−	0.0205624i
$92$	5.59808	+	9.69615i	0.583640	+	1.01089i
$93$	4.73205	+	4.73205i	0.490691	+	0.490691i
$94$	−8.09808	+	14.0263i	−0.835253	+	1.44670i
$95$	−1.13397	+	18.8923i	−0.116343	+	1.93831i
$96$	−9.29423	+	9.29423i	−0.948588	+	0.948588i
$97$	−5.19615	−	9.00000i	−0.527589	−	0.913812i	−0.999483	−	0.0321560i	$-0.989763\pi$
$97$	−5.19615	−	9.00000i	−0.527589	−	0.913812i	0.471894	−	0.881656i	$-0.343571\pi$
$98$	−9.46410	−	9.46410i	−0.956019	−	0.956019i
$99$	−7.39230	+	7.39230i	−0.742955	+	0.742955i
$100$	6.92820	+	5.19615i	0.692820	+	0.519615i
$101$	−4.50000	+	2.59808i	−0.447767	+	0.258518i	−0.706887	−	0.707327i	$-0.749901\pi$
$101$	−4.50000	+	2.59808i	−0.447767	+	0.258518i	0.259120	+	0.965845i	$0.416568\pi$
$102$	6.69615	+	12.0622i	0.663018	+	1.19433i
$103$	−1.73205	−	6.46410i	−0.170664	−	0.636927i	−0.997250	−	0.0741158i	$-0.976387\pi$
$103$	−1.73205	−	6.46410i	−0.170664	−	0.636927i	0.826586	−	0.562811i	$-0.190280\pi$
$104$	0.464102	+	0.267949i	0.0455089	+	0.0262746i
$105$	−0.866025	−	0.571797i	−0.0845154	−	0.0558017i
$106$	5.46410	+	9.46410i	0.530720	+	0.919235i
$107$		−	14.3923i		−	1.39136i	−0.718353	−	0.695678i	$-0.755104\pi$
$107$		−	14.3923i		−	1.39136i	0.718353	−	0.695678i	$-0.244896\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	−6.46410	+	6.46410i	−0.619149	+	0.619149i	−0.945313	−	0.326164i	$-0.894244\pi$
$109$	−6.46410	+	6.46410i	−0.619149	+	0.619149i	0.326164	+	0.945313i	$0.394244\pi$
$110$	12.5622	+	8.29423i	1.19776	+	0.790824i
$111$	−1.79423	+	1.03590i	−0.170301	+	0.0983231i
$112$	−1.03590	−	0.598076i	−0.0978832	−	0.0565129i
$113$	−7.79423	−	4.50000i	−0.733219	−	0.423324i	0.0863794	−	0.996262i	$-0.472470\pi$
$113$	−7.79423	−	4.50000i	−0.733219	−	0.423324i	−0.819599	+	0.572938i	$0.805804\pi$
$114$	−7.33013	−	27.3564i	−0.686529	−	2.56216i
$115$	7.96410	−	12.0622i	0.742656	−	1.12480i
$116$	7.73205	+	7.73205i	0.717903	+	0.717903i
$117$	−3.00000	−	0.803848i	−0.277350	−	0.0743157i
$118$	−6.36603	+	6.36603i	−0.586040	+	0.586040i
$119$	−0.794229	+	0.767949i	−0.0728068	+	0.0703978i
$120$	1.90192	+	0.633975i	0.173621	+	0.0578737i
$121$	0.990381	+	0.571797i	0.0900346	+	0.0519815i
$122$	21.2942	+	12.2942i	1.92789	+	1.11307i
$123$	5.66025	+	5.66025i	0.510368	+	0.510368i
$124$	−1.73205	+	6.46410i	−0.155543	+	0.580493i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	1.50000	+	0.401924i	0.133631	+	0.0358062i
$127$	−3.00000	+	3.00000i	−0.266207	+	0.266207i	−0.827570	−	0.561363i	$-0.810277\pi$
$127$	−3.00000	+	3.00000i	−0.266207	+	0.266207i	0.561363	+	0.827570i	$0.310277\pi$
$128$	3.96410	+	1.06218i	0.350380	+	0.0938841i
$129$	−3.46410	−	12.9282i	−0.304997	−	1.13826i
$130$	−0.267949	+	4.46410i	−0.0235007	+	0.391528i
$131$	2.73205	−	0.732051i	0.238700	−	0.0639596i	−0.137486	−	0.990504i	$-0.543902\pi$
$131$	2.73205	−	0.732051i	0.238700	−	0.0639596i	0.376186	+	0.926544i	$0.377235\pi$
$132$	−10.0981	−	2.70577i	−0.878925	−	0.235507i
$133$	1.96410	−	1.13397i	0.170309	−	0.0983281i
$134$		−	6.92820i		−	0.598506i
$135$	−11.5981	−	0.696152i	−0.998203	−	0.0599153i
$136$	1.09808	−	1.83013i	0.0941593	−	0.156932i
$137$	−12.8301	−	3.43782i	−1.09615	−	0.293713i	−0.334955	−	0.942234i	$-0.608721\pi$
$137$	−12.8301	−	3.43782i	−1.09615	−	0.293713i	−0.761197	+	0.648521i	$0.775388\pi$
$138$	−5.59808	+	20.8923i	−0.476540	+	1.77847i
$139$	−8.46410	+	2.26795i	−0.717916	+	0.192365i	−0.599242	−	0.800568i	$-0.704531\pi$
$139$	−8.46410	+	2.26795i	−0.717916	+	0.192365i	−0.118674	+	0.992933i	$0.537864\pi$
$140$	0.0621778	−	1.03590i	0.00525499	−	0.0875494i
$141$	−14.0263	+	3.75833i	−1.18123	+	0.316509i
$142$	−26.4904	+	15.2942i	−2.22302	+	1.28346i
$143$			3.60770i			0.301691i
$144$	−13.3923			−1.11603
$145$	4.46410	−	13.3923i	0.370723	−	1.11217i
$146$	−24.6244	−	6.59808i	−2.03793	−	0.546061i
$147$		−	12.0000i		−	0.989743i
$148$	−1.79423	−	1.03590i	−0.147485	−	0.0851503i
$149$	7.86603	−	13.6244i	0.644410	−	1.11615i	−0.340028	−	0.940415i	$-0.610436\pi$
$149$	7.86603	−	13.6244i	0.644410	−	1.11615i	0.984437	−	0.175735i	$-0.0562303\pi$
$150$	2.36603	+	16.5622i	0.193185	+	1.35230i
$151$	−3.06218	+	1.76795i	−0.249196	+	0.143874i	−0.619396	−	0.785078i	$-0.712623\pi$
$151$	−3.06218	+	1.76795i	−0.249196	+	0.143874i	0.370200	+	0.928952i	$0.379289\pi$
$152$	−3.09808	+	3.09808i	−0.251287	+	0.251287i
$153$	−3.40192	+	11.8923i	−0.275029	+	0.961436i
$154$		−	1.80385i		−	0.145358i
$155$	8.46410	−	1.73205i	0.679853	−	0.139122i
$156$	−0.803848	−	3.00000i	−0.0643593	−	0.240192i
$157$	−18.3923	+	4.92820i	−1.46787	+	0.393313i	−0.902199	−	0.431320i	$-0.858048\pi$
$157$	−18.3923	+	4.92820i	−1.46787	+	0.393313i	−0.565667	+	0.824634i	$0.691381\pi$
$158$	9.46410	−	16.3923i	0.752923	−	1.30410i
$159$	−2.53590	+	9.46410i	−0.201110	+	0.750552i
$160$	3.40192	+	16.6244i	0.268946	+	1.31427i
$161$	−1.73205			−0.136505
$162$	16.7942	−	4.50000i	1.31948	−	0.353553i
$163$	−8.26795			−0.647596			−0.323798	−	0.946126i	$-0.604960\pi$
$163$	−8.26795			−0.647596			−0.323798	+	0.946126i	$0.604960\pi$
$164$	−2.07180	+	7.73205i	−0.161780	+	0.603772i
$165$	2.70577	+	13.2224i	0.210644	+	1.02936i
$166$	2.36603	−	4.09808i	0.183639	−	0.318072i
$167$	8.59808	+	4.96410i	0.665339	+	0.384134i	0.794308	−	0.607515i	$-0.207833\pi$
$167$	8.59808	+	4.96410i	0.665339	+	0.384134i	−0.128969	+	0.991649i	$0.541167\pi$
$168$	−0.0621778	−	0.232051i	−0.00479712	−	0.0179031i
$169$	10.3301	−	5.96410i	0.794625	−	0.458777i
$170$	17.7583	+	1.36603i	1.36200	+	0.104769i
$171$	12.6962	−	21.9904i	0.970899	−	1.68165i
$172$	9.46410	−	9.46410i	0.721631	−	0.721631i
$173$	−6.69615	−	11.5981i	−0.509099	−	0.881785i	−0.999944	−	0.0105387i	$-0.996645\pi$
$173$	−6.69615	−	11.5981i	−0.509099	−	0.881785i	0.490845	−	0.871247i	$-0.336688\pi$
$174$			21.1244i			1.60143i
$175$	−1.23205	+	0.526279i	−0.0931343	+	0.0397830i
$176$	4.02628	+	15.0263i	0.303492	+	1.13265i
$177$	−8.07180			−0.606713
$178$	7.59808	−	28.3564i	0.569500	−	2.12540i
$179$			11.1962i			0.836840i	0.908254	+	0.418420i	$0.137416\pi$
$179$			11.1962i			0.836840i	−0.908254	+	0.418420i	$0.862584\pi$
$180$	−5.19615	−	10.3923i	−0.387298	−	0.774597i
$181$	−10.7321	−	10.7321i	−0.797707	−	0.797707i	0.185026	−	0.982734i	$-0.440763\pi$
$181$	−10.7321	−	10.7321i	−0.797707	−	0.797707i	−0.982734	+	0.185026i	$0.940763\pi$
$182$	0.464102	−	0.267949i	0.0344015	−	0.0198617i
$183$	5.70577	+	21.2942i	0.421783	+	1.57411i
$184$	3.23205	−	0.866025i	0.238270	−	0.0638442i
$185$	−0.160254	+	2.66987i	−0.0117821	+	0.196293i
$186$	−11.1962	+	6.46410i	−0.820942	+	0.473971i
$187$	14.3660	+	0.241670i	1.05055	+	0.0176726i
$188$	−10.2679	−	10.2679i	−0.748867	−	0.748867i
$189$	0.696152	+	1.20577i	0.0506376	+	0.0877070i
$190$	−34.6865	−	11.5622i	−2.51643	−	0.838809i
$191$	−2.30385	+	1.33013i	−0.166701	+	0.0962446i	−0.581029	−	0.813883i	$-0.697350\pi$
$191$	−2.30385	+	1.33013i	−0.166701	+	0.0962446i	0.414329	+	0.910127i	$0.364016\pi$
$192$	−4.96410	−	8.59808i	−0.358253	−	0.620513i
$193$	1.73205	−	3.00000i	0.124676	−	0.215945i	−0.796930	−	0.604071i	$-0.793544\pi$
$193$	1.73205	−	3.00000i	0.124676	−	0.215945i	0.921606	+	0.388126i	$0.126878\pi$
$194$	19.3923	−	5.19615i	1.39229	−	0.373062i
$195$	−3.00000	+	2.66025i	−0.214834	+	0.190505i
$196$	10.3923	−	6.00000i	0.742307	−	0.428571i
$197$	18.8564			1.34346			0.671732	−	0.740795i	$-0.265551\pi$
$197$	18.8564			1.34346			0.671732	+	0.740795i	$0.265551\pi$
$198$	−10.0981	−	17.4904i	−0.717639	−	1.24299i
$199$	2.00000	+	2.00000i	0.141776	+	0.141776i	0.774433	−	0.632656i	$-0.218035\pi$
$199$	2.00000	+	2.00000i	0.141776	+	0.141776i	−0.632656	+	0.774433i	$0.718035\pi$
$200$	2.03590	−	1.59808i	0.143960	−	0.113001i
$201$	4.39230	−	4.39230i	0.309809	−	0.309809i
$202$	−2.59808	−	9.69615i	−0.182800	−	0.682219i
$203$	−1.63397	+	0.437822i	−0.114683	+	0.0307291i
$204$	−12.0000	+	3.00000i	−0.840168	+	0.210042i
$205$	10.1244	−	2.07180i	0.707116	−	0.144701i
$206$	12.9282			0.900751
$207$	−16.7942	+	9.69615i	−1.16728	+	0.673929i
$208$	−3.26795	+	3.26795i	−0.226592	+	0.226592i
$209$	−28.4904	−	7.63397i	−1.97072	−	0.528053i
$210$	1.50000	−	1.33013i	0.103510	−	0.0917875i
$211$	−15.2942	+	4.09808i	−1.05290	+	0.282123i	−0.743449	−	0.668793i	$-0.766811\pi$
$211$	−15.2942	+	4.09808i	−1.05290	+	0.282123i	−0.309449	+	0.950916i	$0.600145\pi$
$212$	−9.46410	+	2.53590i	−0.649997	+	0.174166i
$213$	−26.4904	−	7.09808i	−1.81509	−	0.486352i
$214$	26.8564	+	7.19615i	1.83587	+	0.491919i
$215$	−16.3923	−	5.46410i	−1.11795	−	0.372649i
$216$	−1.90192	−	1.90192i	−0.129410	−	0.129410i
$217$	−0.732051	−	0.732051i	−0.0496948	−	0.0496948i
$218$	−8.83013	−	15.2942i	−0.598052	−	1.03586i
$219$	−11.4282	−	19.7942i	−0.772246	−	1.33757i
$220$	−10.0981	+	8.95448i	−0.680812	+	0.603711i
$221$	2.07180	+	3.73205i	0.139364	+	0.251045i
$222$	−1.03590	−	3.86603i	−0.0695249	−	0.259471i
$223$	−4.73205	+	17.6603i	−0.316882	+	1.18262i	0.605343	+	0.795964i	$0.293036\pi$
$223$	−4.73205	+	17.6603i	−0.316882	+	1.18262i	−0.922225	+	0.386654i	$0.873631\pi$
$224$	1.43782	−	1.43782i	0.0960685	−	0.0960685i
$225$	−9.00000	+	12.0000i	−0.600000	+	0.800000i
$226$	12.2942	−	12.2942i	0.817800	−	0.817800i
$227$	−7.96410	−	13.7942i	−0.528596	−	0.915555i	−0.999444	−	0.0333408i	$-0.989385\pi$
$227$	−7.96410	−	13.7942i	−0.528596	−	0.915555i	0.470848	−	0.882214i	$-0.343948\pi$
$228$	25.3923			1.68165
$229$	−3.96410	+	6.86603i	−0.261955	+	0.453720i	−0.966761	−	0.255680i	$-0.917701\pi$
$229$	−3.96410	+	6.86603i	−0.261955	+	0.453720i	0.704806	+	0.709400i	$0.251034\pi$
$230$	18.5263	+	20.8923i	1.22159	+	1.37760i
$231$	1.14359	−	1.14359i	0.0752429	−	0.0752429i
$232$	2.83013	−	1.63397i	0.185807	−	0.107276i
$233$	1.14359			0.0749193			0.0374597	−	0.999298i	$-0.488073\pi$
$233$	1.14359			0.0749193			0.0374597	+	0.999298i	$0.488073\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	−5.92820	+	17.7846i	−0.386713	+	1.16014i
$236$	−4.03590	−	6.99038i	−0.262715	−	0.455035i
$237$	16.3923	−	4.39230i	1.06479	−	0.285311i
$238$	−1.03590	−	1.86603i	−0.0671473	−	0.120956i
$239$	−3.73205	+	6.46410i	−0.241406	+	0.418128i	−0.961115	−	0.276148i	$-0.910942\pi$
$239$	−3.73205	+	6.46410i	−0.241406	+	0.418128i	0.719709	+	0.694276i	$0.244275\pi$
$240$	−9.52628	+	14.4282i	−0.614919	+	0.931337i
$241$	−1.09808	−	0.294229i	−0.0707333	−	0.0189529i	0.223279	−	0.974755i	$-0.428324\pi$
$241$	−1.09808	−	0.294229i	−0.0707333	−	0.0189529i	−0.294012	+	0.955802i	$0.594991\pi$
$242$	−1.56218	+	1.56218i	−0.100421	+	0.100421i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−15.5885	+	15.5885i	−0.997949	+	0.997949i
$245$	−12.9282	−	8.53590i	−0.825953	−	0.545339i
$246$	−13.3923	+	7.73205i	−0.853862	+	0.492978i
$247$	−2.26795	−	8.46410i	−0.144306	−	0.538558i
$248$	1.73205	+	1.00000i	0.109985	+	0.0635001i
$249$	4.09808	−	1.09808i	0.259705	−	0.0695878i
$250$	19.5263	+	9.23205i	1.23495	+	0.583886i
$251$		−	16.6603i		−	1.05159i	−0.850613	−	0.525793i	$-0.823769\pi$
$251$		−	16.6603i		−	1.05159i	0.850613	−	0.525793i	$-0.176231\pi$
$252$	−0.696152	+	1.20577i	−0.0438535	+	0.0759565i
$253$	15.9282	+	15.9282i	1.00140	+	1.00140i
$254$	−4.09808	−	7.09808i	−0.257136	−	0.445373i
$255$	10.3923	+	12.1244i	0.650791	+	0.759257i
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−13.5622	+	3.63397i	−0.845985	+	0.226681i	−0.655675	−	0.755043i	$-0.727616\pi$
$257$	−13.5622	+	3.63397i	−0.845985	+	0.226681i	−0.190310	+	0.981724i	$0.560949\pi$
$258$	25.8564			1.60975
$259$	0.277568	−	0.160254i	0.0172472	−	0.00995770i
$260$	−3.80385	−	1.26795i	−0.235905	−	0.0786349i
$261$	−13.3923	+	13.3923i	−0.828963	+	0.828963i
$262$			5.46410i			0.337573i
$263$	−2.00000	−	0.535898i	−0.123325	−	0.0330449i	0.196628	−	0.980478i	$-0.437001\pi$
$263$	−2.00000	−	0.535898i	−0.123325	−	0.0330449i	−0.319954	+	0.947433i	$0.603667\pi$
$264$	−1.56218	+	2.70577i	−0.0961454	+	0.166529i
$265$	8.39230	+	9.46410i	0.515535	+	0.581375i
$266$	1.13397	+	4.23205i	0.0695284	+	0.259484i
$267$	22.7942	−	13.1603i	1.39498	−	0.805394i
$268$	6.00000	+	1.60770i	0.366508	+	0.0982056i
$269$	−18.2679	+	18.2679i	−1.11382	+	1.11382i	−0.121187	+	0.992630i	$0.538670\pi$
$269$	−18.2679	+	18.2679i	−1.11382	+	1.11382i	−0.992630	+	0.121187i	$0.961330\pi$
$270$	7.09808	−	21.2942i	0.431975	−	1.29593i
$271$	8.07180			0.490327			0.245163	−	0.969482i	$-0.421158\pi$
$271$	8.07180			0.490327			0.245163	+	0.969482i	$0.421158\pi$
$272$	12.7942	+	13.2321i	0.775764	+	0.802311i
$273$	0.464102	+	0.124356i	0.0280887	+	0.00752635i
$274$	12.8301	−	22.2224i	0.775096	−	1.34251i
$275$	16.1699	+	6.49038i	0.975080	+	0.391385i
$276$	−16.7942	−	9.69615i	−1.01089	−	0.583640i
$277$	−12.8660	−	22.2846i	−0.773045	−	1.33895i	−0.935887	−	0.352300i	$-0.885400\pi$
$277$	−12.8660	−	22.2846i	−0.773045	−	1.33895i	0.162842	−	0.986652i	$-0.447934\pi$
$278$		−	16.9282i		−	1.01529i
$279$	−11.1962	−	3.00000i	−0.670296	−	0.179605i
$280$	−0.294229	−	0.0980762i	−0.0175835	−	0.00586117i
$281$	9.40192	+	16.2846i	0.560872	+	0.971458i	0.997421	+	0.0717778i	$0.0228673\pi$
$281$	9.40192	+	16.2846i	0.560872	+	0.971458i	−0.436549	+	0.899681i	$0.643799\pi$
$282$		−	28.0526i		−	1.67051i
$283$	−8.39230	+	14.5359i	−0.498871	+	0.864069i	−0.999999	−	0.00130347i	$-0.999585\pi$
$283$	−8.39230	+	14.5359i	−0.498871	+	0.864069i	0.501128	+	0.865373i	$0.332918\pi$
$284$	−7.09808	−	26.4904i	−0.421193	−	1.57191i
$285$	−14.6603	−	29.3205i	−0.868399	−	1.73680i
$286$	−6.73205	−	1.80385i	−0.398075	−	0.106664i
$287$	−0.875644	−	0.875644i	−0.0516877	−	0.0516877i
$288$	5.89230	−	21.9904i	0.347207	−	1.29580i
$289$	15.0000	−	8.00000i	0.882353	−	0.470588i
$290$	22.7583	+	15.0263i	1.33642	+	0.882374i
$291$	15.5885	+	9.00000i	0.913812	+	0.527589i
$292$	11.4282	−	19.7942i	0.668785	−	1.15837i
$293$	5.73205	−	1.53590i	0.334870	−	0.0897281i	−0.0874660	−	0.996168i	$-0.527877\pi$
$293$	5.73205	−	1.53590i	0.334870	−	0.0897281i	0.422336	+	0.906439i	$0.361210\pi$
$294$	22.3923	+	6.00000i	1.30595	+	0.349927i
$295$	−5.74167	+	8.69615i	−0.334293	+	0.506310i
$296$	−0.437822	+	0.437822i	−0.0254479	+	0.0254479i
$297$	4.68653	−	17.4904i	0.271940	−	1.01489i
$298$	21.4904	+	21.4904i	1.24490	+	1.24490i
$299$	−1.73205	+	6.46410i	−0.100167	+	0.373829i
$300$	−14.8923	−	1.79423i	−0.859808	−	0.103590i
$301$	0.535898	+	2.00000i	0.0308887	+	0.115278i
$302$	−1.76795	−	6.59808i	−0.101734	−	0.379677i
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$	−18.8923	−	32.7224i	−1.08355	−	1.87676i
$305$	27.0000	+	9.00000i	1.54602	+	0.515339i
$306$	−20.4904	−	12.2942i	−1.17136	−	0.702814i
$307$	3.46410	+	3.46410i	0.197707	+	0.197707i	0.799016	−	0.601309i	$-0.205354\pi$
$307$	3.46410	+	3.46410i	0.197707	+	0.197707i	−0.601309	+	0.799016i	$0.705354\pi$
$308$	1.56218	+	0.418584i	0.0890133	+	0.0238511i
$309$	8.19615	+	8.19615i	0.466263	+	0.466263i
$310$	−1.00000	+	16.6603i	−0.0567962	+	0.946239i
$311$	−6.09808	+	1.63397i	−0.345790	+	0.0926542i	−0.427534	−	0.903999i	$-0.640618\pi$
$311$	−6.09808	+	1.63397i	−0.345790	+	0.0926542i	0.0817441	+	0.996653i	$0.473951\pi$
$312$	−0.928203			−0.0525492
$313$	6.66025	+	11.5359i	0.376460	+	0.652048i	0.990544	−	0.137193i	$-0.0438080\pi$
$313$	6.66025	+	11.5359i	0.376460	+	0.652048i	−0.614085	+	0.789240i	$0.710475\pi$
$314$		−	36.7846i		−	2.07588i
$315$	1.79423	+	0.107695i	0.101093	+	0.00606793i
$316$	12.0000	+	12.0000i	0.675053	+	0.675053i
$317$	6.19615	+	10.7321i	0.348011	+	0.602772i	0.985896	−	0.167359i	$-0.0535240\pi$
$317$	6.19615	+	10.7321i	0.348011	+	0.602772i	−0.637885	+	0.770131i	$0.720191\pi$
$318$	−16.3923	−	9.46410i	−0.919235	−	0.530720i
$319$	19.0526	+	11.0000i	1.06674	+	0.615882i
$320$	−12.7942	−	0.767949i	−0.715219	−	0.0429297i
$321$	12.4641	+	21.5885i	0.695678	+	1.20495i
$322$	0.866025	−	3.23205i	0.0482617	−	0.180115i
$323$	−33.8564	+	8.46410i	−1.88382	+	0.470955i
$324$			15.5885i			0.866025i
$325$	0.732051	+	5.12436i	0.0406069	+	0.284248i
$326$	4.13397	−	15.4282i	0.228960	−	0.854489i
$327$	4.09808	−	15.2942i	0.226624	−	0.845773i
$328$	2.07180	+	1.19615i	0.114396	+	0.0660465i
$329$	2.16987	−	0.581416i	0.119629	−	0.0320545i
$330$	−26.0263	−	1.56218i	−1.43270	−	0.0859951i
$331$	30.6506	−	17.6962i	1.68471	−	0.972669i	0.726257	−	0.687424i	$-0.241258\pi$
$331$	30.6506	−	17.6962i	1.68471	−	0.972669i	0.958455	−	0.285245i	$-0.0920749\pi$
$332$	3.00000	+	3.00000i	0.164646	+	0.164646i
$333$	1.79423	−	3.10770i	0.0983231	−	0.170301i
$334$	−13.5622	+	13.5622i	−0.742089	+	0.742089i
$335$	−1.60770	−	7.85641i	−0.0878378	−	0.429241i
$336$	2.07180			0.113026
$337$	−15.3923	+	26.6603i	−0.838472	+	1.45228i	0.0526994	+	0.998610i	$0.483217\pi$
$337$	−15.3923	+	26.6603i	−0.838472	+	1.45228i	−0.891172	+	0.453666i	$0.850116\pi$
$338$	5.96410	+	22.2583i	0.324404	+	1.21069i
$339$	15.5885			0.846649
$340$	−5.30385	+	15.0622i	−0.287642	+	0.816861i
$341$			13.4641i			0.729122i
$342$	34.6865	+	34.6865i	1.87563	+	1.87563i
$343$			3.73205i			0.201512i
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$	−1.50000	+	24.9904i	−0.0807573	+	1.34544i
$346$	24.9904	−	6.69615i	1.34349	−	0.359987i
$347$	−5.42820	+	9.40192i	−0.291401	+	0.504722i	−0.974141	−	0.225940i	$-0.927455\pi$
$347$	−5.42820	+	9.40192i	−0.291401	+	0.504722i	0.682740	+	0.730661i	$0.260788\pi$
$348$	−18.2942	−	4.90192i	−0.980674	−	0.262771i
$349$	11.1244	+	19.2679i	0.595473	+	1.03139i	0.993480	+	0.114007i	$0.0363687\pi$
$349$	11.1244	+	19.2679i	0.595473	+	1.03139i	−0.398007	+	0.917382i	$0.630298\pi$
$350$	−0.366025	−	2.56218i	−0.0195649	−	0.136954i
$351$	5.19615	−	1.39230i	0.277350	−	0.0743157i
$352$	−26.4449			−1.40952
$353$	0.0262794	−	0.0980762i	0.00139871	−	0.00522007i	−0.965223	−	0.261428i	$-0.915807\pi$
$353$	0.0262794	−	0.0980762i	0.00139871	−	0.00522007i	0.966622	+	0.256208i	$0.0824732\pi$
$354$	4.03590	−	15.0622i	0.214506	−	0.800546i
$355$	−26.4904	+	23.4904i	−1.40596	+	1.24674i
$356$	22.7942	+	13.1603i	1.20809	+	0.697492i
$357$	0.526279	−	1.83975i	0.0278537	−	0.0973697i
$358$	−20.8923	−	5.59808i	−1.10419	−	0.295868i
$359$		−	10.1244i		−	0.534343i	−0.963649	−	0.267172i	$-0.913911\pi$
$359$		−	10.1244i		−	0.534343i	0.963649	−	0.267172i	$-0.0860890\pi$
$360$	−3.40192	+	0.696152i	−0.179297	+	0.0366905i
$361$	52.6410			2.77058
$362$	25.3923	−	14.6603i	1.33459	−	0.770526i
$363$	−1.98076			−0.103963
$364$	0.124356	+	0.464102i	0.00651801	+	0.0243255i
$365$	−29.4545	−	1.76795i	−1.54172	−	0.0925387i
$366$	−42.5885			−2.22613
$367$	6.69615	−	3.86603i	0.349536	−	0.201805i	−0.314945	−	0.949110i	$-0.601986\pi$
$367$	6.69615	−	3.86603i	0.349536	−	0.201805i	0.664481	+	0.747305i	$0.268653\pi$
$368$			28.8564i			1.50424i
$369$	−13.3923	−	3.58846i	−0.697176	−	0.186808i
$370$	−4.90192	−	1.63397i	−0.254839	−	0.0849463i
$371$	0.392305	−	1.46410i	0.0203675	−	0.0760124i
$372$	−3.00000	−	11.1962i	−0.155543	−	0.580493i
$373$	0.169873	+	0.633975i	0.00879569	+	0.0328260i	0.970184	−	0.242369i	$-0.0779244\pi$
$373$	0.169873	+	0.633975i	0.00879569	+	0.0328260i	−0.961389	+	0.275195i	$0.911258\pi$
$374$	−7.63397	+	26.6865i	−0.394743	+	1.37993i
$375$	6.52628	+	18.2321i	0.337016	+	0.941499i
$376$	−3.75833	+	2.16987i	−0.193821	+	0.111903i
$377$			6.53590i			0.336616i
$378$	−2.59808	+	0.696152i	−0.133631	+	0.0358062i
$379$	5.26795	+	5.26795i	0.270596	+	0.270596i	0.829340	−	0.558744i	$-0.188717\pi$
$379$	5.26795	+	5.26795i	0.270596	+	0.270596i	−0.558744	+	0.829340i	$0.688717\pi$
$380$	18.0622	−	27.3564i	0.926570	−	1.40335i
$381$	1.90192	−	7.09808i	0.0974385	−	0.363645i
$382$	−1.33013	−	4.96410i	−0.0680552	−	0.253986i
$383$	−6.85641	−	25.5885i	−0.350346	−	1.30751i	−0.886241	−	0.463224i	$-0.846692\pi$
$383$	−6.85641	−	25.5885i	−0.350346	−	1.30751i	0.535895	−	0.844285i	$-0.319974\pi$
$384$	−6.86603	+	1.83975i	−0.350380	+	0.0938841i
$385$	−0.418584	−	2.04552i	−0.0213330	−	0.104249i
$386$	4.73205	+	4.73205i	0.240855	+	0.240855i
$387$	16.3923	+	16.3923i	0.833268	+	0.833268i
$388$			18.0000i			0.913812i
$389$	−2.66025	+	1.53590i	−0.134880	+	0.0778731i	−0.565922	−	0.824459i	$-0.691480\pi$
$389$	−2.66025	+	1.53590i	−0.134880	+	0.0778731i	0.431042	+	0.902332i	$0.358146\pi$
$390$	−3.46410	−	6.92820i	−0.175412	−	0.350823i
$391$	25.6244	+	7.33013i	1.29588	+	0.370700i
$392$	−0.928203	−	3.46410i	−0.0468813	−	0.174964i
$393$	−3.46410	+	3.46410i	−0.174741	+	0.174741i
$394$	−9.42820	+	35.1865i	−0.474986	+	1.77267i
$395$	6.92820	−	20.7846i	0.348596	−	1.04579i
$396$	17.4904	−	4.68653i	0.878925	−	0.235507i
$397$		−	20.2487i		−	1.01625i	−0.861282	−	0.508127i	$-0.830338\pi$
$397$		−	20.2487i		−	1.01625i	0.861282	−	0.508127i	$-0.169662\pi$
$398$	−4.73205	+	2.73205i	−0.237196	+	0.136945i
$399$	−1.96410	+	3.40192i	−0.0983281	+	0.170309i
$400$	8.76795	+	20.5263i	0.438397	+	1.02631i
$401$	7.32051	+	27.3205i	0.365569	+	1.36432i	0.866648	+	0.498920i	$0.166270\pi$
$401$	7.32051	+	27.3205i	0.365569	+	1.36432i	−0.501079	+	0.865401i	$0.667064\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$	−3.46410	+	2.00000i	−0.172559	+	0.0996271i
$404$	9.00000			0.447767
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$		−	3.26795i		−	0.162186i
$407$	−4.02628	−	1.07884i	−0.199575	−	0.0534760i
$408$	−0.0621778	+	3.69615i	−0.00307826	+	0.182987i
$409$	6.52628	+	3.76795i	0.322704	+	0.186313i	0.652597	−	0.757705i	$-0.273679\pi$
$409$	6.52628	+	3.76795i	0.322704	+	0.186313i	−0.329893	+	0.944018i	$0.607013\pi$
$410$	−1.19615	+	19.9282i	−0.0590738	+	0.984184i
$411$	22.2224	−	5.95448i	1.09615	−	0.293713i
$412$	−3.00000	+	11.1962i	−0.147799	+	0.551595i
$413$	1.24871			0.0614451
$414$	−9.69615	−	36.1865i	−0.476540	−	1.77847i
$415$	1.73205	−	5.19615i	0.0850230	−	0.255069i
$416$	−3.92820	−	6.80385i	−0.192596	−	0.333586i
$417$	10.7321	−	10.7321i	0.525551	−	0.525551i
$418$	28.4904	−	49.3468i	1.39351	−	2.41363i
$419$	2.26795	−	0.607695i	0.110797	−	0.0296879i	−0.202995	−	0.979180i	$-0.565067\pi$
$419$	2.26795	−	0.607695i	0.110797	−	0.0296879i	0.313791	+	0.949492i	$0.398401\pi$
$420$	0.803848	+	1.60770i	0.0392237	+	0.0784475i
$421$	−2.16025	−	3.74167i	−0.105284	−	0.182358i	0.808570	−	0.588400i	$-0.200242\pi$
$421$	−2.16025	−	3.74167i	−0.105284	−	0.182358i	−0.913854	+	0.406042i	$0.866909\pi$
$422$		−	30.5885i		−	1.48902i
$423$	17.7846	−	17.7846i	0.864717	−	0.864717i
$424$			2.92820i			0.142206i
$425$	20.4545	−	2.57180i	0.992188	−	0.124750i
$426$	26.4904	−	45.8827i	1.28346	−	2.22302i
$427$	−0.882686	−	3.29423i	−0.0427162	−	0.159419i
$428$	−12.4641	+	21.5885i	−0.602475	+	1.04352i
$429$	−3.12436	−	5.41154i	−0.150845	−	0.261272i
$430$	18.3923	−	27.8564i	0.886956	−	1.34336i
$431$	−5.92820	+	5.92820i	−0.285552	+	0.285552i	−0.835318	−	0.549767i	$-0.814717\pi$
$431$	−5.92820	+	5.92820i	−0.285552	+	0.285552i	0.549767	+	0.835318i	$0.314717\pi$
$432$	20.0885	−	11.5981i	0.966506	−	0.558013i
$433$	−26.3205	−	26.3205i	−1.26488	−	1.26488i	−0.948697	−	0.316186i	$-0.897598\pi$
$433$	−26.3205	−	26.3205i	−1.26488	−	1.26488i	−0.316186	−	0.948697i	$-0.602402\pi$
$434$	1.73205	−	1.00000i	0.0831411	−	0.0480015i
$435$	4.90192	+	23.9545i	0.235029	+	1.14853i
$436$	15.2942	−	4.09808i	0.732461	−	0.196262i
$437$	−47.3827	−	27.3564i	−2.26662	−	1.30863i
$438$	42.6506	−	11.4282i	2.03793	−	0.546061i
$439$	−7.39230	+	27.5885i	−0.352815	+	1.31673i	0.530396	+	0.847750i	$0.322043\pi$
$439$	−7.39230	+	27.5885i	−0.352815	+	1.31673i	−0.883211	+	0.468975i	$0.844623\pi$
$440$	1.80385	+	3.60770i	0.0859951	+	0.171990i
$441$	10.3923	+	18.0000i	0.494872	+	0.857143i
$442$	−8.00000	+	2.00000i	−0.380521	+	0.0951303i
$443$	−2.26795	+	8.46410i	−0.107754	+	0.402142i	−0.998643	−	0.0520785i	$-0.983415\pi$
$443$	−2.26795	+	8.46410i	−0.107754	+	0.402142i	0.890889	+	0.454220i	$0.150082\pi$
$444$	3.58846			0.170301
$445$	2.03590	−	33.9186i	0.0965108	−	1.60790i
$446$	−30.5885	−	17.6603i	−1.44841	−	0.836237i
$447$			27.2487i			1.28882i
$448$	0.767949	+	1.33013i	0.0362822	+	0.0628426i
$449$	−6.80385	−	6.80385i	−0.321093	−	0.321093i	0.528093	−	0.849186i	$-0.322907\pi$
$449$	−6.80385	−	6.80385i	−0.321093	−	0.321093i	−0.849186	+	0.528093i	$0.822907\pi$
$450$	−17.8923	−	22.7942i	−0.843451	−	1.07453i
$451$			16.1051i			0.758360i
$452$	7.79423	+	13.5000i	0.366610	+	0.634987i
$453$	3.06218	−	5.30385i	0.143874	−	0.249196i
$454$	29.7224	−	7.96410i	1.39494	−	0.373774i
$455$	0.464102	−	0.411543i	0.0217574	−	0.0192934i
$456$	1.96410	−	7.33013i	0.0919775	−	0.343265i
$457$	−18.1244	−	4.85641i	−0.847822	−	0.227173i	−0.191348	−	0.981522i	$-0.561286\pi$
$457$	−18.1244	−	4.85641i	−0.847822	−	0.227173i	−0.656473	+	0.754349i	$0.727953\pi$
$458$	−10.8301	−	10.8301i	−0.506059	−	0.506059i
$459$	−5.19615	−	20.7846i	−0.242536	−	0.970143i
$460$	−22.3923	+	11.1962i	−1.04405	+	0.522023i
$461$	−6.46410	−	11.1962i	−0.301063	−	0.521457i	0.675314	−	0.737530i	$-0.264008\pi$
$461$	−6.46410	−	11.1962i	−0.301063	−	0.521457i	−0.976377	+	0.216074i	$0.930675\pi$
$462$	1.56218	+	2.70577i	0.0726791	+	0.125884i
$463$	3.58846	+	13.3923i	0.166770	+	0.622393i	0.997808	+	0.0661777i	$0.0210804\pi$
$463$	3.58846	+	13.3923i	0.166770	+	0.622393i	−0.831038	+	0.556215i	$0.812253\pi$
$464$	7.29423	+	27.2224i	0.338626	+	1.26377i
$465$	−11.1962	+	9.92820i	−0.519209	+	0.460409i
$466$	−0.571797	+	2.13397i	−0.0264880	+	0.0988545i
$467$	−11.2679	−	11.2679i	−0.521419	−	0.521419i	0.396581	−	0.918000i	$-0.370197\pi$
$467$	−11.2679	−	11.2679i	−0.521419	−	0.521419i	−0.918000	+	0.396581i	$0.870197\pi$
$468$	3.80385	+	3.80385i	0.175833	+	0.175833i
$469$	−0.679492	+	0.679492i	−0.0313760	+	0.0313760i
$470$	−30.2224	−	19.9545i	−1.39406	−	0.920432i
$471$	23.3205	−	23.3205i	1.07455	−	1.07455i
$472$	−2.33013	+	0.624356i	−0.107253	+	0.0287383i
$473$	13.4641	−	23.3205i	0.619080	−	1.07228i
$474$			32.7846i			1.50585i
$475$	−42.0167	−	5.06218i	−1.92786	−	0.232269i
$476$	1.85641	−	0.464102i	0.0850883	−	0.0212721i
$477$	−4.39230	−	16.3923i	−0.201110	−	0.750552i
$478$	−10.1962	−	10.1962i	−0.466361	−	0.466361i
$479$	19.9282	+	5.33975i	0.910543	+	0.243979i	0.683538	−	0.729915i	$-0.260440\pi$
$479$	19.9282	+	5.33975i	0.910543	+	0.243979i	0.227004	+	0.973894i	$0.427107\pi$
$480$	−19.5000	−	21.9904i	−0.890049	−	1.00372i
$481$	−0.320508	−	1.19615i	−0.0146139	−	0.0545399i
$482$	1.09808	−	1.90192i	0.0500160	−	0.0866303i
$483$	2.59808	−	1.50000i	0.118217	−	0.0682524i
$484$	−0.990381	−	1.71539i	−0.0450173	−	0.0779723i
$485$	20.7846	−	10.3923i	0.943781	−	0.471890i
$486$	−21.2942	+	21.2942i	−0.965926	+	0.965926i
$487$			13.5885i			0.615752i	0.951427	+	0.307876i	$0.0996182\pi$
$487$			13.5885i			0.615752i	−0.951427	+	0.307876i	$0.900382\pi$
$488$	3.29423	+	5.70577i	0.149123	+	0.258288i
$489$	12.4019	−	7.16025i	0.560834	−	0.323798i
$490$	22.3923	−	19.8564i	1.01158	−	0.897021i
$491$	12.7224	−	22.0359i	0.574155	−	0.994466i	−0.421978	−	0.906606i	$-0.638664\pi$
$491$	12.7224	−	22.0359i	0.574155	−	0.994466i	0.996133	−	0.0878599i	$-0.0280028\pi$
$492$	−3.58846	−	13.3923i	−0.161780	−	0.603772i
$493$	26.0263	+	0.437822i	1.17216	+	0.0197185i
$494$	16.9282			0.761636
$495$	−15.5096	−	17.4904i	−0.697106	−	0.786134i
$496$	−12.1962	+	12.1962i	−0.547623	+	0.547623i
$497$	4.09808	+	1.09808i	0.183824	+	0.0492554i
$498$			8.19615i			0.367278i
$499$	3.85641	+	14.3923i	0.172636	+	0.644288i	0.996942	+	0.0781431i	$0.0248991\pi$
$499$	3.85641	+	14.3923i	0.172636	+	0.644288i	−0.824306	+	0.566145i	$0.808434\pi$
$500$	−12.5263	+	14.7679i	−0.560192	+	0.660443i
$501$	−17.1962			−0.768267
$502$	31.0885	+	8.33013i	1.38755	+	0.371792i
$503$			16.0718i			0.716606i	0.933605	+	0.358303i	$0.116645\pi$
$503$			16.0718i			0.716606i	−0.933605	+	0.358303i	$0.883355\pi$
$504$	0.294229	+	0.294229i	0.0131060	+	0.0131060i
$505$	−5.19615	−	10.3923i	−0.231226	−	0.462451i
$506$	−37.6865	+	21.7583i	−1.67537	+	0.967276i
$507$	−10.3301	+	17.8923i	−0.458777	+	0.794625i
$508$	7.09808	−	1.90192i	0.314926	−	0.0843842i
$509$	−14.2583	+	24.6962i	−0.631989	+	1.09464i	0.355155	+	0.934807i	$0.384428\pi$
$509$	−14.2583	+	24.6962i	−0.631989	+	1.09464i	−0.987145	+	0.159830i	$0.948905\pi$
$510$	−27.8205	+	13.3301i	−1.23191	+	0.590268i
$511$	1.76795	+	3.06218i	0.0782095	+	0.135463i
$512$	−20.6865	−	20.6865i	−0.914224	−	0.914224i
$513$			43.9808i			1.94180i
$514$		−	27.1244i		−	1.19640i
$515$	14.6603	−	3.00000i	0.646008	−	0.132196i
$516$	−6.00000	+	22.3923i	−0.264135	+	0.985766i
$517$	−25.3013	−	14.6077i	−1.11275	−	0.642446i
$518$	0.160254	+	0.598076i	0.00704116	+	0.0262780i
$519$	20.0885	+	11.5981i	0.881785	+	0.509099i
$520$	−0.660254	+	1.00000i	−0.0289541	+	0.0438529i
$521$	22.3205	−	22.3205i	0.977879	−	0.977879i	−0.0218814	−	0.999761i	$-0.506966\pi$
$521$	22.3205	−	22.3205i	0.977879	−	0.977879i	0.999761	+	0.0218814i	$0.00696561\pi$
$522$	−18.2942	−	31.6865i	−0.800717	−	1.38688i
$523$	29.0000	−	29.0000i	1.26808	−	1.26808i	0.321003	−	0.947078i	$-0.395980\pi$
$523$	29.0000	−	29.0000i	1.26808	−	1.26808i	0.947078	−	0.321003i	$-0.104020\pi$
$524$	−4.73205	−	1.26795i	−0.206721	−	0.0553906i
$525$	1.39230	−	1.85641i	0.0607652	−	0.0810202i
$526$	2.00000	−	3.46410i	0.0872041	−	0.151042i
$527$	7.73205	+	13.9282i	0.336813	+	0.606722i
$528$	−19.0526	−	19.0526i	−0.829156	−	0.829156i
$529$	9.39230	+	16.2679i	0.408361	+	0.707302i
$530$	−21.8564	+	10.9282i	−0.949382	+	0.474691i
$531$	12.1077	−	6.99038i	0.525429	−	0.303357i
$532$	−3.92820			−0.170309
$533$	−4.14359	+	2.39230i	−0.179479	+	0.103622i
$534$	13.1603	+	49.1147i	0.569500	+	2.12540i
$535$	32.1244	+	1.92820i	1.38886	+	0.0833635i
$536$	0.928203	−	1.60770i	0.0400923	−	0.0694419i
$537$	−9.69615	−	16.7942i	−0.418420	−	0.724724i
$538$	−24.9545	−	43.2224i	−1.07586	−	1.86345i
$539$	17.0718	−	17.0718i	0.735334	−	0.735334i
$540$	16.7942	+	11.0885i	0.722709	+	0.477171i
$541$	7.12436	−	7.12436i	0.306300	−	0.306300i	−0.537172	−	0.843472i	$-0.680508\pi$
$541$	7.12436	−	7.12436i	0.306300	−	0.306300i	0.843472	+	0.537172i	$0.180508\pi$
$542$	−4.03590	+	15.0622i	−0.173357	+	0.646976i
$543$	25.3923	+	6.80385i	1.08969	+	0.291981i
$544$	−27.3564	+	15.1865i	−1.17290	+	0.651117i
$545$	−13.5622	−	15.2942i	−0.580940	−	0.655133i
$546$	−0.464102	+	0.803848i	−0.0198617	+	0.0344015i
$547$	−8.52628	−	14.7679i	−0.364557	−	0.631432i	0.624148	−	0.781306i	$-0.285446\pi$
$547$	−8.52628	−	14.7679i	−0.364557	−	0.631432i	−0.988705	+	0.149875i	$0.952113\pi$
$548$	16.2679	+	16.2679i	0.694932	+	0.694932i
$549$	−27.0000	−	27.0000i	−1.15233	−	1.15233i
$550$	−20.1962	+	26.9282i	−0.861167	+	1.14822i
$551$	−51.6147	−	13.8301i	−2.19886	−	0.589183i
$552$	−4.09808	+	4.09808i	−0.174426	+	0.174426i
$553$	−2.53590	+	0.679492i	−0.107837	+	0.0288949i
$554$	48.0167	−	12.8660i	2.04003	−	0.546625i
$555$	−2.07180	−	4.14359i	−0.0879429	−	0.175886i
$556$	14.6603	+	3.92820i	0.621733	+	0.166593i
$557$	2.07180	−	2.07180i	0.0877848	−	0.0877848i	−0.661851	−	0.749636i	$-0.730229\pi$
$557$	2.07180	−	2.07180i	0.0877848	−	0.0877848i	0.749636	+	0.661851i	$0.230229\pi$
$558$	11.1962	−	19.3923i	0.473971	−	0.820942i
$559$	8.00000			0.338364
$560$	1.47372	−	2.23205i	0.0622761	−	0.0943214i
$561$	−21.7583	+	12.0788i	−0.918637	+	0.509969i
$562$	−35.0885	+	9.40192i	−1.48012	+	0.396596i
$563$	4.58846	+	17.1244i	0.193380	+	0.721706i	0.992680	+	0.120773i	$0.0385373\pi$
$563$	4.58846	+	17.1244i	0.193380	+	0.721706i	−0.799300	+	0.600933i	$0.794796\pi$
$564$	24.2942	+	6.50962i	1.02297	+	0.274104i
$565$	11.0885	−	16.7942i	0.466495	−	0.706539i
$566$	−22.9282	−	22.9282i	−0.963744	−	0.963744i
$567$	−2.08846	−	1.20577i	−0.0877070	−	0.0506376i
$568$	−8.19615			−0.343903
$569$	−10.0359	+	5.79423i	−0.420727	+	0.242907i	−0.695388	−	0.718634i	$-0.744768\pi$
$569$	−10.0359	+	5.79423i	−0.420727	+	0.242907i	0.274661	+	0.961541i	$0.411434\pi$
$570$	62.0429	−	12.6962i	2.59869	−	0.531783i
$571$	13.2942	−	3.56218i	0.556346	−	0.149073i	0.0303190	−	0.999540i	$-0.490348\pi$
$571$	13.2942	−	3.56218i	0.556346	−	0.149073i	0.526027	+	0.850468i	$0.323681\pi$
$572$	3.12436	−	5.41154i	0.130636	−	0.226268i
$573$	2.30385	−	3.99038i	0.0962446	−	0.166701i
$574$	2.07180	−	1.19615i	0.0864751	−	0.0499264i
$575$	25.8564	+	19.3923i	1.07829	+	0.808715i
$576$	14.8923	+	8.59808i	0.620513	+	0.358253i
$577$	−31.9282	−	31.9282i	−1.32919	−	1.32919i	−0.906078	−	0.423110i	$-0.860938\pi$
$577$	−31.9282	−	31.9282i	−1.32919	−	1.32919i	−0.423110	−	0.906078i	$-0.639062\pi$
$578$	7.42820	+	31.9904i	0.308973	+	1.33062i
$579$			6.00000i			0.249351i
$580$	−18.2942	+	16.2224i	−0.759626	+	0.673600i
$581$	−0.633975	+	0.169873i	−0.0263017	+	0.00704752i
$582$	−24.5885	+	24.5885i	−1.01922	+	1.01922i
$583$	−17.0718	+	9.85641i	−0.707042	+	0.408211i
$584$	−4.83013	−	4.83013i	−0.199872	−	0.199872i
$585$	2.19615	−	6.58846i	0.0907997	−	0.272399i
$586$			11.4641i			0.473578i
$587$	−2.75833	+	10.2942i	−0.113848	+	0.424888i	−0.999198	−	0.0400374i	$-0.987252\pi$
$587$	−2.75833	+	10.2942i	−0.113848	+	0.424888i	0.885350	+	0.464926i	$0.153919\pi$
$588$	−10.3923	+	18.0000i	−0.428571	+	0.742307i
$589$	−8.46410	−	31.5885i	−0.348757	−	1.30158i
$590$	−13.3564	−	15.0622i	−0.549875	−	0.620100i
$591$	−28.2846	+	16.3301i	−1.16347	+	0.671732i
$592$	−2.66987	−	4.62436i	−0.109731	−	0.190060i
$593$	−7.46410	+	7.46410i	−0.306514	+	0.306514i	−0.843556	−	0.537042i	$-0.819542\pi$
$593$	−7.46410	+	7.46410i	−0.306514	+	0.306514i	0.537042	+	0.843556i	$0.319542\pi$
$594$	30.2942	+	17.4904i	1.24299	+	0.717639i
$595$	−1.60770	−	1.87564i	−0.0659091	−	0.0768939i
$596$	−23.5981	+	13.6244i	−0.966615	+	0.558075i
$597$	−4.73205	−	1.26795i	−0.193670	−	0.0518937i
$598$	−11.1962	−	6.46410i	−0.457845	−	0.264337i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$	−1.66987	+	4.16025i	−0.0681723	+	0.169842i
$601$	−4.53590	+	16.9282i	−0.185023	+	0.690516i	0.809602	+	0.586979i	$0.199683\pi$
$601$	−4.53590	+	16.9282i	−0.185023	+	0.690516i	−0.994626	+	0.103537i	$0.966984\pi$
$602$	−4.00000			−0.163028
$603$	−2.78461	+	10.3923i	−0.113398	+	0.423207i
$604$	6.12436			0.249196
$605$	−1.40897	+	2.13397i	−0.0572826	+	0.0867584i
$606$	12.2942	+	12.2942i	0.499419	+	0.499419i
$607$	−9.59808	+	16.6244i	−0.389574	+	0.674762i	−0.992392	−	0.123117i	$-0.960711\pi$
$607$	−9.59808	+	16.6244i	−0.389574	+	0.674762i	0.602818	+	0.797878i	$0.294044\pi$
$608$	62.0429	−	16.6244i	2.51617	−	0.674207i
$609$	2.07180	−	2.07180i	0.0839534	−	0.0839534i
$610$	−30.2942	+	45.8827i	−1.22658	+	1.85774i
$611$		−	8.67949i		−	0.351135i
$612$	15.4019	−	14.8923i	0.622586	−	0.601986i
$613$	−20.5167	+	20.5167i	−0.828660	+	0.828660i	−0.987331	−	0.158671i	$-0.949279\pi$
$613$	−20.5167	+	20.5167i	−0.828660	+	0.828660i	0.158671	+	0.987331i	$0.449279\pi$
$614$	−8.19615	+	4.73205i	−0.330770	+	0.190970i
$615$	−13.3923	+	11.8756i	−0.540030	+	0.478872i
$616$	0.241670	−	0.418584i	0.00973715	−	0.0168652i
$617$	6.80385	+	3.92820i	0.273913	+	0.158144i	0.630664	−	0.776056i	$-0.282782\pi$
$617$	6.80385	+	3.92820i	0.273913	+	0.158144i	−0.356752	+	0.934199i	$0.616116\pi$
$618$	−19.3923	+	11.1962i	−0.780073	+	0.450375i
$619$	−15.7583	−	4.22243i	−0.633381	−	0.169714i	−0.0721774	−	0.997392i	$-0.522995\pi$
$619$	−15.7583	−	4.22243i	−0.633381	−	0.169714i	−0.561203	+	0.827678i	$0.689661\pi$
$620$	−14.1962	−	4.73205i	−0.570131	−	0.190044i
$621$	16.7942	−	29.0885i	0.673929	−	1.16728i
$622$		−	12.1962i		−	0.489021i
$623$	−3.52628	+	2.03590i	−0.141277	+	0.0815665i
$624$	2.07180	−	7.73205i	0.0829382	−	0.309530i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−24.8564	+	6.66025i	−0.993462	+	0.266197i
$627$	49.3468	−	13.2224i	1.97072	−	0.528053i
$628$	31.8564	+	8.53590i	1.27121	+	0.340619i
$629$	−4.78461	+	1.19615i	−0.190775	+	0.0476937i
$630$	−1.09808	+	3.29423i	−0.0437484	+	0.131245i
$631$		−	9.60770i		−	0.382476i	−0.981544	−	0.191238i	$-0.938750\pi$
$631$		−	9.60770i		−	0.382476i	0.981544	−	0.191238i	$-0.0612503\pi$
$632$	4.39230	−	2.53590i	0.174717	−	0.100873i
$633$	19.3923	−	19.3923i	0.770775	−	0.770775i
$634$	−23.1244	+	6.19615i	−0.918385	+	0.246081i
$635$	−6.29423	−	7.09808i	−0.249779	−	0.281679i
$636$	12.0000	−	12.0000i	0.475831	−	0.475831i
$637$	6.92820	+	1.85641i	0.274505	+	0.0735535i
$638$	−30.0526	+	30.0526i	−1.18979	+	1.18979i
$639$	45.8827	−	12.2942i	1.81509	−	0.486352i
$640$	−2.90192	+	8.70577i	−0.114709	+	0.344126i
$641$	−5.88269	+	21.9545i	−0.232352	+	0.867150i	0.746973	+	0.664855i	$0.231507\pi$
$641$	−5.88269	+	21.9545i	−0.232352	+	0.867150i	−0.979325	+	0.202295i	$0.935160\pi$
$642$	−46.5167	+	12.4641i	−1.83587	+	0.491919i
$643$	−4.62436	−	2.66987i	−0.182367	−	0.105290i	0.406037	−	0.913856i	$-0.366910\pi$
$643$	−4.62436	−	2.66987i	−0.182367	−	0.105290i	−0.588404	+	0.808567i	$0.700244\pi$
$644$	2.59808	+	1.50000i	0.102379	+	0.0591083i
$645$	29.3205	−	6.00000i	1.15449	−	0.236250i
$646$	1.13397	−	67.4090i	0.0446156	−	2.65217i
$647$	6.92820	−	6.92820i	0.272376	−	0.272376i	−0.557680	−	0.830056i	$-0.688308\pi$
$647$	6.92820	−	6.92820i	0.272376	−	0.272376i	0.830056	+	0.557680i	$0.188308\pi$
$648$	4.50000	+	1.20577i	0.176777	+	0.0473672i
$649$	−11.4833	−	11.4833i	−0.450761	−	0.450761i
$650$	−9.92820	−	1.19615i	−0.389416	−	0.0469170i
$651$	1.73205	+	0.464102i	0.0678844	+	0.0181896i
$652$	12.4019	+	7.16025i	0.485697	+	0.280417i
$653$	−22.7942	−	13.1603i	−0.892007	−	0.515001i	−0.0174086	−	0.999848i	$-0.505542\pi$
$653$	−22.7942	−	13.1603i	−0.892007	−	0.515001i	−0.874598	+	0.484848i	$0.838875\pi$
$654$	26.4904	+	15.2942i	1.03586	+	0.598052i
$655$	1.26795	+	6.19615i	0.0495429	+	0.242104i
$656$	−14.5885	+	14.5885i	−0.569584	+	0.569584i
$657$	34.2846	+	19.7942i	1.33757	+	0.772246i
$658$			4.33975i			0.169181i
$659$	−5.86603	−	10.1603i	−0.228508	−	0.395787i	0.728858	−	0.684665i	$-0.240051\pi$
$659$	−5.86603	−	10.1603i	−0.228508	−	0.395787i	−0.957366	+	0.288877i	$0.906718\pi$
$660$	7.39230	−	22.1769i	0.287745	−	0.863235i
$661$	32.7224	+	18.8923i	1.27276	+	0.734825i	0.975506	−	0.219974i	$-0.0705974\pi$
$661$	32.7224	+	18.8923i	1.27276	+	0.734825i	0.297249	+	0.954800i	$0.403931\pi$
$662$	17.6962	+	66.0429i	0.687780	+	2.56683i
$663$	−6.33975	−	3.80385i	−0.246215	−	0.147729i
$664$	1.09808	−	0.633975i	0.0426136	−	0.0246030i
$665$	2.26795	+	4.53590i	0.0879473	+	0.175895i
$666$	4.90192	+	4.90192i	0.189946	+	0.189946i
$667$	28.8564	+	28.8564i	1.11732	+	1.11732i
$668$	−8.59808	−	14.8923i	−0.332670	−	0.576201i
$669$	−8.19615	−	30.5885i	−0.316882	−	1.18262i
$670$	15.4641	+	0.928203i	0.597430	+	0.0358596i
$671$	−22.1769	+	38.4115i	−0.856130	+	1.48286i
$672$	−0.911543	+	3.40192i	−0.0351635	+	0.131232i
$673$	−15.7942	−	27.3564i	−0.608823	−	1.05451i	−0.991435	−	0.130603i	$-0.958309\pi$
$673$	−15.7942	−	27.3564i	−0.608823	−	1.05451i	0.382612	−	0.923909i	$-0.375025\pi$
$674$	−42.0526	−	42.0526i	−1.61980	−	1.61980i
$675$	3.10770	−	25.7942i	0.119615	−	0.992820i
$676$	−20.6603			−0.794625
$677$	−25.6699	+	14.8205i	−0.986573	+	0.569598i	−0.904248	−	0.427007i	$-0.859568\pi$
$677$	−25.6699	+	14.8205i	−0.986573	+	0.569598i	−0.0823251	+	0.996606i	$0.526235\pi$
$678$	−7.79423	+	29.0885i	−0.299336	+	1.11714i
$679$	−2.41154	−	1.39230i	−0.0925465	−	0.0534318i
$680$	3.93782	+	2.69615i	0.151009	+	0.103393i
$681$	23.8923	+	13.7942i	0.915555	+	0.528596i
$682$	−25.1244	−	6.73205i	−0.962061	−	0.257784i
$683$	21.8564			0.836312			0.418156	−	0.908375i	$-0.362677\pi$
$683$	21.8564			0.836312			0.418156	+	0.908375i	$0.362677\pi$
$684$	−38.0885	+	21.9904i	−1.45635	+	0.840823i
$685$	9.39230	−	28.1769i	0.358862	−	1.07658i
$686$	−6.96410	−	1.86603i	−0.265891	−	0.0712452i
$687$		−	13.7321i		−	0.523910i
$688$	33.3205	−	8.92820i	1.27033	−	0.340385i
$689$	−5.07180	−	2.92820i	−0.193220	−	0.111556i
$690$	−45.8827	−	15.2942i	−1.74672	−	0.582241i
$691$	−3.09808	+	11.5622i	−0.117856	+	0.439846i	−0.999485	−	0.0320984i	$-0.989781\pi$
$691$	−3.09808	+	11.5622i	−0.117856	+	0.439846i	0.881628	+	0.471944i	$0.156448\pi$
$692$			23.1962i			0.881785i
$693$	−0.725009	+	2.70577i	−0.0275408	+	0.102784i
$694$	−14.8301	−	14.8301i	−0.562944	−	0.562944i
$695$	−3.92820	−	19.1962i	−0.149005	−	0.728152i
$696$	−2.83013	+	4.90192i	−0.107276	+	0.185807i
$697$	9.24871	+	16.6603i	0.350320	+	0.631052i
$698$	−41.5167	+	11.1244i	−1.57143	+	0.421063i
$699$	−1.71539	+	0.990381i	−0.0648820	+	0.0374597i
$700$	2.30385	+	0.277568i	0.0870773	+	0.0104911i
$701$			25.9808i			0.981280i	0.871362	+	0.490640i	$0.163237\pi$
$701$			25.9808i			0.981280i	−0.871362	+	0.490640i	$0.836763\pi$
$702$			10.3923i			0.392232i
$703$	10.1244			0.381847
$704$	5.16987	−	19.2942i	0.194847	−	0.727179i
$705$	−6.50962	−	31.8109i	−0.245166	−	1.19807i
$706$	0.169873	+	0.0980762i	0.00639325	+	0.00369115i
$707$	−0.696152	+	1.20577i	−0.0261815	+	0.0453477i
$708$	12.1077	+	6.99038i	0.455035	+	0.262715i
$709$	3.58846	−	13.3923i	0.134767	−	0.502959i	−0.865231	−	0.501373i	$-0.832829\pi$
$709$	3.58846	−	13.3923i	0.134767	−	0.502959i	0.999999	−	0.00158583i	$-0.000504785\pi$
$710$	−30.5885	−	61.1769i	−1.14796	−	2.29593i
$711$	−20.7846	+	20.7846i	−0.779484	+	0.779484i
$712$	5.56218	−	5.56218i	0.208451	−	0.208451i
$713$	−6.46410	+	24.1244i	−0.242083	+	0.903464i
$714$	3.16987	+	1.90192i	0.118630	+	0.0711777i
$715$	−8.05256	−	0.483340i	−0.301149	−	0.0180759i
$716$	9.69615	−	16.7942i	0.362362	−	0.627630i
$717$		−	12.9282i		−	0.482813i
$718$	18.8923	+	5.06218i	0.705055	+	0.188919i
$719$	−22.5885	+	22.5885i	−0.842407	+	0.842407i	−0.989172	−	0.146764i	$-0.953114\pi$
$719$	−22.5885	+	22.5885i	−0.842407	+	0.842407i	0.146764	+	0.989172i	$0.453114\pi$
$720$	1.79423	−	29.8923i	0.0668670	−	1.11402i
$721$	−1.26795	−	1.26795i	−0.0472209	−	0.0472209i
$722$	−26.3205	+	98.2295i	−0.979548	+	3.65572i
$723$	1.90192	−	0.509619i	0.0707333	−	0.0189529i
$724$	6.80385	+	25.3923i	0.252863	+	0.943698i
$725$	29.2942	+	11.7583i	1.08796	+	0.436693i
$726$	0.990381	−	3.69615i	0.0367565	−	0.137177i
$727$	−10.5622	+	39.4186i	−0.391729	+	1.46195i	0.435550	+	0.900164i	$0.356554\pi$
$727$	−10.5622	+	39.4186i	−0.391729	+	1.46195i	−0.827280	+	0.561790i	$0.810113\pi$
$728$	0.143594			0.00532193
$729$	−27.0000			−1.00000
$730$	18.0263	−	54.0788i	0.667183	−	2.00155i
$731$	0.535898	−	31.8564i	0.0198209	−	1.17825i
$732$	9.88269	−	36.8827i	0.365275	−	1.36322i
$733$	−4.53590	+	1.21539i	−0.167537	+	0.0448915i	−0.341613	−	0.939841i	$-0.610973\pi$
$733$	−4.53590	+	1.21539i	−0.167537	+	0.0448915i	0.174075	+	0.984732i	$0.444306\pi$
$734$	3.86603	+	14.4282i	0.142698	+	0.532555i
$735$	26.7846	+	1.60770i	0.987965	+	0.0593007i
$736$	−47.3827	−	12.6962i	−1.74655	−	0.467986i
$737$	12.4974			0.460348
$738$	13.3923	−	23.1962i	0.492978	−	0.853862i
$739$	−9.24871			−0.340219			−0.170110	−	0.985425i	$-0.554412\pi$
$739$	−9.24871			−0.340219			−0.170110	+	0.985425i	$0.554412\pi$
$740$	2.55256	−	3.86603i	0.0938339	−	0.142118i
$741$	10.7321	+	10.7321i	0.394252	+	0.394252i
$742$	2.53590	+	1.46410i	0.0930958	+	0.0537489i
$743$	−9.69615	+	16.7942i	−0.355717	+	0.616120i	−0.987240	−	0.159237i	$-0.949097\pi$
$743$	−9.69615	+	16.7942i	−0.355717	+	0.616120i	0.631523	+	0.775357i	$0.282430\pi$
$744$	−3.46410			−0.127000
$745$	29.3564	+	19.3827i	1.07554	+	0.710127i
$746$	−1.26795			−0.0464229
$747$	−5.19615	+	5.19615i	−0.190117	+	0.190117i
$748$	−21.3397	−	12.8038i	−0.780258	−	0.468155i
$749$	−1.92820	−	3.33975i	−0.0704550	−	0.122032i
$750$	−37.2846	+	3.06218i	−1.36144	+	0.111815i
$751$	8.51666	+	31.7846i	0.310777	+	1.15984i	0.927857	+	0.372936i	$0.121649\pi$
$751$	8.51666	+	31.7846i	0.310777	+	1.15984i	−0.617080	+	0.786901i	$0.711684\pi$
$752$	−9.68653	−	36.1506i	−0.353232	−	1.31828i
$753$	14.4282	+	24.9904i	0.525793	+	0.910700i
$754$	−12.1962	−	3.26795i	−0.444158	−	0.119012i
$755$	−3.53590	−	7.07180i	−0.128685	−	0.257369i
$756$		−	2.41154i		−	0.0877070i
$757$	−6.14359	+	6.14359i	−0.223293	+	0.223293i	−0.809883	−	0.586591i	$-0.800470\pi$
$757$	−6.14359	+	6.14359i	−0.223293	+	0.223293i	0.586591	+	0.809883i	$0.300470\pi$
$758$	−12.4641	+	7.19615i	−0.452717	+	0.261376i
$759$	−37.6865	−	10.0981i	−1.36793	−	0.366537i
$760$	−6.50000	−	7.33013i	−0.235780	−	0.265892i
$761$	−2.76795	−	1.59808i	−0.100338	−	0.0579302i	0.448991	−	0.893536i	$-0.351783\pi$
$761$	−2.76795	−	1.59808i	−0.100338	−	0.0579302i	−0.549329	+	0.835606i	$0.685117\pi$
$762$	12.2942	+	7.09808i	0.445373	+	0.257136i
$763$	−0.633975	+	2.36603i	−0.0229514	+	0.0856559i
$764$	4.60770			0.166701
$765$	−26.0885	−	9.18653i	−0.943230	−	0.332140i
$766$	51.1769			1.84910
$767$	1.24871	−	4.66025i	0.0450884	−	0.168272i
$768$		−	33.5885i		−	1.21202i
$769$	4.33013	+	2.50000i	0.156148	+	0.0901523i	0.576038	−	0.817423i	$-0.304598\pi$
$769$	4.33013	+	2.50000i	0.156148	+	0.0901523i	−0.419890	+	0.907575i	$0.637931\pi$
$770$	4.02628	+	0.241670i	0.145097	+	0.00870917i
$771$	17.1962	−	17.1962i	0.619304	−	0.619304i
$772$	−5.19615	+	3.00000i	−0.187014	+	0.107972i
$773$	19.2487	−	19.2487i	0.692328	−	0.692328i	−0.270416	−	0.962744i	$-0.587161\pi$
$773$	19.2487	−	19.2487i	0.692328	−	0.692328i	0.962744	+	0.270416i	$0.0871611\pi$
$774$	−38.7846	+	22.3923i	−1.39408	+	0.804875i
$775$	2.73205	+	19.1244i	0.0981382	+	0.686967i
$776$	5.19615	+	1.39230i	0.186531	+	0.0499808i
$777$	−0.277568	+	0.480762i	−0.00995770	+	0.0172472i
$778$	−1.53590	−	5.73205i	−0.0550646	−	0.205504i
$779$	−10.1244	−	37.7846i	−0.362743	−	1.35377i
$780$	6.80385	−	1.39230i	0.243617	−	0.0498525i
$781$	−27.5885	−	47.7846i	−0.987193	−	1.70987i
$782$	−26.4904	+	44.1506i	−0.947294	+	1.57882i
$783$	8.49038	−	31.6865i	0.303421	−	1.13238i
$784$	30.9282			1.10458
$785$	−8.53590	−	41.7128i	−0.304659	−	1.48879i
$786$	−4.73205	−	8.19615i	−0.168787	−	0.292347i
$787$	12.1962	−	21.1244i	0.434746	−	0.753002i	−0.562529	−	0.826778i	$-0.690172\pi$
$787$	12.1962	−	21.1244i	0.434746	−	0.753002i	0.997275	+	0.0737756i	$0.0235049\pi$
$788$	−28.2846	−	16.3301i	−1.00760	−	0.581737i
$789$	3.46410	−	0.928203i	0.123325	−	0.0330449i
$790$	35.3205	+	23.3205i	1.25665	+	0.829706i
$791$	−2.41154			−0.0857446
$792$		−	5.41154i		−	0.192291i
$793$	−13.1769			−0.467926
$794$	37.7846	+	10.1244i	1.34093	+	0.359300i
$795$	−20.7846	−	6.92820i	−0.737154	−	0.245718i
$796$	−1.26795	−	4.73205i	−0.0449413	−	0.167723i
$797$	−21.8564	+	5.85641i	−0.774194	+	0.207445i	−0.624223	−	0.781246i	$-0.714584\pi$
$797$	−21.8564	+	5.85641i	−0.774194	+	0.207445i	−0.149970	+	0.988691i	$0.547918\pi$
$798$	−5.36603	−	5.36603i	−0.189955	−	0.189955i
$799$	−34.5622	−	0.581416i	−1.22272	−	0.0205690i
$800$	−37.5622	+	5.36603i	−1.32802	+	0.189718i
$801$	−22.7942	+	39.4808i	−0.805394	+	1.39498i
$802$	−54.6410			−1.92944
$803$	11.9019	−	44.4186i	0.420010	−	1.56750i
$804$	−10.3923	+	2.78461i	−0.366508	+	0.0982056i
$805$	0.232051	−	3.86603i	0.00817872	−	0.136259i
$806$	−2.00000	−	7.46410i	−0.0704470	−	0.262912i
$807$	11.5814	−	43.2224i	0.407685	−	1.52150i
$808$	0.696152	−	2.59808i	0.0244906	−	0.0914000i
$809$	8.78461	+	8.78461i	0.308850	+	0.308850i	0.844464	−	0.535613i	$-0.179919\pi$
$809$	8.78461	+	8.78461i	0.308850	+	0.308850i	−0.535613	+	0.844464i	$0.679919\pi$
$810$	7.79423	+	38.0885i	0.273861	+	1.33829i
$811$	−7.60770	+	7.60770i	−0.267142	+	0.267142i	−0.827948	−	0.560805i	$-0.810492\pi$
$811$	−7.60770	+	7.60770i	−0.267142	+	0.267142i	0.560805	+	0.827948i	$0.310492\pi$
$812$	2.83013	+	0.758330i	0.0993180	+	0.0266122i
$813$	−12.1077	+	6.99038i	−0.424635	+	0.245163i
$814$	4.02628	−	6.97372i	0.141121	−	0.244429i
$815$	1.10770	−	18.4545i	0.0388009	−	0.646432i
$816$	−30.6506	−	8.76795i	−1.07299	−	0.306940i
$817$	−16.9282	+	63.1769i	−0.592243	+	2.21028i
$818$	−10.2942	+	10.2942i	−0.359929	+	0.359929i
$819$	−0.803848	+	0.215390i	−0.0280887	+	0.00752635i
$820$	−16.9808	−	5.66025i	−0.592994	−	0.197665i
$821$	−1.39230	+	5.19615i	−0.0485918	+	0.181347i	−0.985956	−	0.167003i	$-0.946591\pi$
$821$	−1.39230	+	5.19615i	−0.0485918	+	0.181347i	0.937365	+	0.348350i	$0.113258\pi$
$822$			44.4449i			1.55019i
$823$	12.7224	−	22.0359i	0.443476	−	0.768123i	−0.554469	−	0.832205i	$-0.687078\pi$
$823$	12.7224	−	22.0359i	0.443476	−	0.768123i	0.997945	+	0.0640815i	$0.0204118\pi$
$824$	3.00000	+	1.73205i	0.104510	+	0.0603388i
$825$	−29.8756	+	4.26795i	−1.04014	+	0.148591i
$826$	−0.624356	+	2.33013i	−0.0217241	+	0.0810755i
$827$	2.07180			0.0720434			0.0360217	−	0.999351i	$-0.488531\pi$
$827$	2.07180			0.0720434			0.0360217	+	0.999351i	$0.488531\pi$
$828$	33.5885			1.16728
$829$			20.3923i			0.708254i	0.935197	+	0.354127i	$0.115222\pi$
$829$			20.3923i			0.708254i	−0.935197	+	0.354127i	$0.884778\pi$
$830$	8.83013	+	5.83013i	0.306498	+	0.202367i
$831$	38.5981	+	22.2846i	1.33895	+	0.773045i
$832$	5.73205	−	1.53590i	0.198723	−	0.0532477i
$833$	7.85641	−	27.4641i	0.272208	−	0.951575i
$834$	14.6603	+	25.3923i	0.507643	+	0.879264i
$835$	−12.2321	+	18.5263i	−0.423308	+	0.641128i
$836$	36.1244	+	36.1244i	1.24939	+	1.24939i
$837$	19.3923	−	5.19615i	0.670296	−	0.179605i
$838$			4.53590i			0.156690i
$839$	−8.22243	+	30.6865i	−0.283870	+	1.05942i	0.665791	+	0.746138i	$0.268094\pi$
$839$	−8.22243	+	30.6865i	−0.283870	+	1.05942i	−0.949661	+	0.313279i	$0.898573\pi$
$840$	0.526279	−	0.107695i	0.0181584	−	0.00371584i
$841$	9.40192	+	5.42820i	0.324204	+	0.187179i
$842$	8.06218	−	2.16025i	0.277841	−	0.0744473i
$843$	−28.2058	−	16.2846i	−0.971458	−	0.560872i
$844$	26.4904	+	7.09808i	0.911837	+	0.244326i
$845$	11.9282	+	23.8564i	0.410343	+	0.820685i
$846$	24.2942	+	42.0788i	0.835253	+	1.44670i
$847$	0.306425			0.0105289
$848$	−24.3923	−	6.53590i	−0.837635	−	0.224444i
$849$		−	29.0718i		−	0.997741i
$850$	−5.42820	+	39.4545i	−0.186186	+	1.35328i
$851$	−6.69615	−	3.86603i	−0.229541	−	0.132526i
$852$	33.5885	+	33.5885i	1.15072	+	1.15072i
$853$	−37.0692	+	21.4019i	−1.26923	+	0.732788i	−0.974842	−	0.222899i	$-0.928448\pi$
$853$	−37.0692	+	21.4019i	−1.26923	+	0.732788i	−0.294384	+	0.955687i	$0.595115\pi$
$854$	6.58846			0.225452
$855$	47.3827	+	31.2846i	1.62045	+	1.06991i
$856$	5.26795	+	5.26795i	0.180055	+	0.180055i
$857$	11.8038	+	20.4449i	0.403212	+	0.698383i	0.994112	−	0.108362i	$-0.0345605\pi$
$857$	11.8038	+	20.4449i	0.403212	+	0.698383i	−0.590900	+	0.806745i	$0.701227\pi$
$858$	11.6603	−	3.12436i	0.398075	−	0.106664i
$859$	19.1962	−	33.2487i	0.654964	−	1.13443i	−0.326938	−	0.945046i	$-0.606017\pi$
$859$	19.1962	−	33.2487i	0.654964	−	1.13443i	0.981903	−	0.189386i	$-0.0606497\pi$
$860$	19.8564	+	22.3923i	0.677098	+	0.763571i
$861$	2.07180	+	0.555136i	0.0706066	+	0.0189190i
$862$	−8.09808	−	14.0263i	−0.275822	−	0.477737i
$863$	22.7846	+	22.7846i	0.775597	+	0.775597i	0.979079	−	0.203482i	$-0.0652257\pi$
$863$	22.7846	+	22.7846i	0.775597	+	0.775597i	−0.203482	+	0.979079i	$0.565226\pi$
$864$	10.2058	+	38.0885i	0.347207	+	1.29580i
$865$	26.7846	−	13.3923i	0.910704	−	0.455352i
$866$	62.2750	−	35.9545i	2.11619	−	1.22178i
$867$	−15.5718	+	24.9904i	−0.528846	+	0.848718i
$868$	0.464102	+	1.73205i	0.0157526	+	0.0587896i
$869$	29.5692	+	17.0718i	1.00307	+	0.579121i
$870$	−47.1506	−	2.83013i	−1.59856	−	0.0959503i
$871$	1.85641	+	3.21539i	0.0629019	+	0.108949i
$872$		−	4.73205i		−	0.160247i
$873$	−31.1769			−1.05518
$874$	74.7391	−	74.7391i	2.52809	−	2.52809i
$875$	−1.00962	−	2.82051i	−0.0341313	−	0.0953506i
$876$			39.5885i			1.33757i
$877$	20.6603	+	11.9282i	0.697647	+	0.402787i	0.806471	−	0.591274i	$-0.201375\pi$
$877$	20.6603	+	11.9282i	0.697647	+	0.402787i	−0.108823	+	0.994061i	$0.534708\pi$
$878$	−47.7846	−	27.5885i	−1.61265	−	0.931065i
$879$	−7.26795	+	7.26795i	−0.245142	+	0.245142i
$880$	−34.0788	+	6.97372i	−1.14880	+	0.235084i
$881$	−36.1769	−	36.1769i	−1.21883	−	1.21883i	−0.968042	−	0.250790i	$-0.919310\pi$
$881$	−36.1769	−	36.1769i	−1.21883	−	1.21883i	−0.250790	−	0.968042i	$-0.580690\pi$
$882$	−38.7846	+	10.3923i	−1.30595	+	0.349927i
$883$	26.7321	−	26.7321i	0.899605	−	0.899605i	−0.0957959	−	0.995401i	$-0.530540\pi$
$883$	26.7321	−	26.7321i	0.899605	−	0.899605i	0.995401	+	0.0957959i	$0.0305396\pi$
$884$	0.124356	−	7.39230i	0.00418253	−	0.248630i
$885$	1.08142	−	18.0167i	0.0363514	−	0.605623i
$886$	−14.6603	−	8.46410i	−0.492521	−	0.284357i
$887$	35.5981	+	20.5526i	1.19527	+	0.690087i	0.959496	−	0.281721i	$-0.0909054\pi$
$887$	35.5981	+	20.5526i	1.19527	+	0.690087i	0.235770	+	0.971809i	$0.424239\pi$
$888$	0.277568	−	1.03590i	0.00931458	−	0.0347625i
$889$	−0.294229	+	1.09808i	−0.00986811	+	0.0368283i
$890$	62.2750	+	20.7583i	2.08746	+	0.695821i
$891$	8.11731	+	30.2942i	0.271940	+	1.01489i
$892$	22.3923	−	22.3923i	0.749750	−	0.749750i
$893$	68.5429	+	18.3660i	2.29370	+	0.614596i
$894$	−50.8468	−	13.6244i	−1.70057	−	0.455667i
$895$	−24.9904	−	1.50000i	−0.835336	−	0.0501395i
$896$	1.06218	−	0.284610i	0.0354849	−	0.00950814i
$897$	−3.00000	−	11.1962i	−0.100167	−	0.373829i
$898$	16.0981	−	9.29423i	0.537200	−	0.310152i
$899$			24.3923i			0.813529i
$900$	23.8923	−	10.2058i	0.796410	−	0.340192i
$901$	−12.0000	+	20.0000i	−0.399778	+	0.666297i
$902$	−30.0526	−	8.05256i	−1.00064	−	0.268121i
$903$	−2.53590	−	2.53590i	−0.0843894	−	0.0843894i
$904$	4.50000	−	1.20577i	0.149668	−	0.0401034i
$905$	25.3923	−	22.5167i	0.844069	−	0.748479i
$906$	8.36603	+	8.36603i	0.277943	+	0.277943i
$907$	−5.32051	+	3.07180i	−0.176665	+	0.101997i	−0.585725	−	0.810510i	$-0.699190\pi$
$907$	−5.32051	+	3.07180i	−0.176665	+	0.101997i	0.409060	+	0.912507i	$0.365857\pi$
$908$			27.5885i			0.915555i
$909$			15.5885i			0.517036i
$910$	0.535898	+	1.07180i	0.0177649	+	0.0355297i
$911$	49.1506	+	13.1699i	1.62843	+	0.436337i	0.953464	−	0.301508i	$-0.0974901\pi$
$911$	49.1506	+	13.1699i	1.62843	+	0.436337i	0.674970	+	0.737846i	$0.264157\pi$
$912$	56.6769	+	32.7224i	1.87676	+	1.08355i
$913$	7.39230	+	4.26795i	0.244650	+	0.141249i
$914$	18.1244	−	31.3923i	0.599500	−	1.03837i
$915$	−48.2942	+	9.88269i	−1.59656	+	0.326712i
$916$	11.8923	−	6.86603i	0.392933	−	0.226860i
$917$	0.535898	−	0.535898i	0.0176969	−	0.0176969i
$918$	41.3827	+	0.696152i	1.36583	+	0.0229765i
$919$			5.24871i			0.173139i	0.996246	+	0.0865695i	$0.0275905\pi$
$919$			5.24871i			0.173139i	−0.996246	+	0.0865695i	$0.972410\pi$
$920$	1.50000	+	7.33013i	0.0494535	+	0.241667i
$921$	−8.19615	−	2.19615i	−0.270072	−	0.0723657i
$922$	24.1244	−	6.46410i	0.794493	−	0.212884i
$923$	8.19615	−	14.1962i	0.269780	−	0.467272i
$924$	−2.70577	+	0.725009i	−0.0890133	+	0.0238511i
$925$	−5.93782	−	0.715390i	−0.195234	−	0.0235219i
$926$	−26.7846			−0.880197
$927$	−19.3923	−	5.19615i	−0.636927	−	0.170664i
$928$	−47.9090			−1.57269
$929$	1.21539	−	4.53590i	0.0398757	−	0.148818i	−0.943118	−	0.332459i	$-0.892122\pi$
$929$	1.21539	−	4.53590i	0.0398757	−	0.148818i	0.982993	+	0.183641i	$0.0587884\pi$
$930$	−12.9282	−	25.8564i	−0.423932	−	0.847865i
$931$	−29.3205	+	50.7846i	−0.960941	+	1.66440i
$932$	−1.71539	−	0.990381i	−0.0561895	−	0.0324410i
$933$	7.73205	−	7.73205i	0.253136	−	0.253136i
$934$	26.6603	−	15.3923i	0.872350	−	0.503652i
$935$	−2.46410	+	32.0333i	−0.0805847	+	1.04760i
$936$	1.39230	−	0.803848i	0.0455089	−	0.0262746i
$937$	3.46410	−	3.46410i	0.113167	−	0.113167i	−0.648256	−	0.761423i	$-0.724501\pi$
$937$	3.46410	−	3.46410i	0.113167	−	0.113167i	0.761423	+	0.648256i	$0.224501\pi$
$938$	−0.928203	−	1.60770i	−0.0303069	−	0.0524931i
$939$	−19.9808	−	11.5359i	−0.652048	−	0.376460i
$940$	24.2942	−	21.5429i	0.792390	−	0.702653i
$941$	−11.5359	−	43.0526i	−0.376060	−	1.40347i	−0.851791	−	0.523882i	$-0.824483\pi$
$941$	−11.5359	−	43.0526i	−0.376060	−	1.40347i	0.475731	−	0.879591i	$-0.342184\pi$
$942$	31.8564	+	55.1769i	1.03794	+	1.79776i
$943$	−7.73205	+	28.8564i	−0.251790	+	0.939694i
$944$		−	20.8038i		−	0.677108i
$945$	−2.78461	+	1.39230i	−0.0905834	+	0.0452917i
$946$	36.7846	+	36.7846i	1.19597	+	1.19597i
$947$	15.4019	−	8.89230i	0.500495	−	0.288961i	−0.228423	−	0.973562i	$-0.573357\pi$
$947$	15.4019	−	8.89230i	0.500495	−	0.288961i	0.728918	+	0.684601i	$0.240024\pi$
$948$	−28.3923	−	7.60770i	−0.922139	−	0.247086i
$949$	13.1962	−	3.53590i	0.428365	−	0.114780i
$950$	30.4545	−	75.8731i	0.988074	−	2.46165i
$951$	−18.5885	−	10.7321i	−0.602772	−	0.348011i
$952$	0.00961894	−	0.571797i	0.000311752	−	0.0185320i
$953$	−12.3205	−	12.3205i	−0.399100	−	0.399100i	0.478815	−	0.877916i	$-0.341066\pi$
$953$	−12.3205	−	12.3205i	−0.399100	−	0.399100i	−0.877916	+	0.478815i	$0.841066\pi$
$954$	32.7846			1.06144
$955$	−2.66025	−	5.32051i	−0.0860838	−	0.172168i
$956$	11.1962	−	6.46410i	0.362109	−	0.209064i
$957$	−38.1051			−1.23176
$958$	−19.9282	+	34.5167i	−0.643851	+	1.11518i
$959$	−3.43782	+	0.921162i	−0.111013	+	0.0297459i
$960$	19.8564	−	9.92820i	0.640863	−	0.320431i
$961$	13.9186	−	8.03590i	0.448987	−	0.259223i
$962$	2.39230			0.0771310
$963$	−37.3923	−	21.5885i	−1.20495	−	0.695678i
$964$	1.39230	+	1.39230i	0.0448431	+	0.0448431i
$965$	6.46410	+	4.26795i	0.208087	+	0.137390i
$966$	1.50000	+	5.59808i	0.0482617	+	0.180115i
$967$	−1.16987	−	4.36603i	−0.0376206	−	0.140402i	0.944561	−	0.328336i	$-0.106488\pi$
$967$	−1.16987	−	4.36603i	−0.0376206	−	0.140402i	−0.982182	+	0.187934i	$0.939821\pi$
$968$	−0.571797	+	0.153212i	−0.0183782	+	0.00492444i
$969$	43.4545	−	42.0167i	1.39596	−	1.34977i
$970$	9.00000	+	43.9808i	0.288973	+	1.41214i
$971$	14.5359			0.466479			0.233240	−	0.972419i	$-0.425067\pi$
$971$	14.5359			0.466479			0.233240	+	0.972419i	$0.425067\pi$
$972$	−13.5000	−	23.3827i	−0.433013	−	0.750000i
$973$	−1.66025	+	1.66025i	−0.0532253	+	0.0532253i
$974$	−25.3564	−	6.79423i	−0.812472	−	0.217701i
$975$	−5.53590	−	7.05256i	−0.177291	−	0.225863i
$976$	−54.8827	+	14.7058i	−1.75675	+	0.470720i
$977$	2.46410	−	0.660254i	0.0788336	−	0.0211234i	−0.219187	−	0.975683i	$-0.570340\pi$
$977$	2.46410	−	0.660254i	0.0788336	−	0.0211234i	0.298020	+	0.954560i	$0.403674\pi$
$978$	7.16025	+	26.7224i	0.228960	+	0.854489i
$979$	51.1506	+	13.7058i	1.63478	+	0.438038i
$980$	12.0000	+	24.0000i	0.383326	+	0.766652i
$981$	7.09808	+	26.4904i	0.226624	+	0.845773i
$982$	34.7583	+	34.7583i	1.10918	+	1.10918i
$983$	14.1603	+	24.5263i	0.451642	+	0.782267i	0.998488	−	0.0549662i	$-0.0175051\pi$
$983$	14.1603	+	24.5263i	0.451642	+	0.782267i	−0.546846	+	0.837233i	$0.684172\pi$
$984$	−4.14359			−0.132093
$985$	−2.52628	+	42.0885i	−0.0804940	+	1.34105i
$986$	−13.8301	+	48.3468i	−0.440441	+	1.53968i
$987$	−2.75129	+	2.75129i	−0.0875745	+	0.0875745i
$988$	−3.92820	+	14.6603i	−0.124973	+	0.466405i
$989$	35.3205	−	35.3205i	1.12313	−	1.12313i
$990$	40.3923	−	20.1962i	1.28375	−	0.641876i
$991$	−27.5885	+	27.5885i	−0.876376	+	0.876376i	−0.993158	−	0.116781i	$-0.962742\pi$
$991$	−27.5885	+	27.5885i	−0.876376	+	0.876376i	0.116781	+	0.993158i	$0.462742\pi$
$992$	−14.6603	−	25.3923i	−0.465464	−	0.806206i
$993$	−30.6506	+	53.0885i	−0.972669	+	1.68471i
$994$	−4.09808	+	7.09808i	−0.129983	+	0.225137i
$995$	−4.73205	+	4.19615i	−0.150016	+	0.133027i
$996$	−7.09808	−	1.90192i	−0.224911	−	0.0602648i
$997$	−9.92820	+	5.73205i	−0.314429	+	0.181536i	−0.648907	−	0.760868i	$-0.724774\pi$
$997$	−9.92820	+	5.73205i	−0.314429	+	0.181536i	0.334477	+	0.942404i	$0.391440\pi$
$998$	−28.7846			−0.911161
$999$			6.21539i			0.196646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bt.b.752.1	yes	4
5.3	odd	4		765.2.bm.b.293.1	yes	4
9.2	odd	6		765.2.bt.a.497.1	yes	4
17.13	even	4		765.2.bm.a.302.1	yes	4
45.38	even	12		765.2.bm.a.38.1	✓	4
85.13	odd	4		765.2.bt.a.608.1	yes	4
153.47	odd	12		765.2.bm.b.47.1	yes	4
765.353	even	12	inner	765.2.bt.b.353.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
765.2.bm.a.38.1	✓	4	45.38	even	12
765.2.bm.a.302.1	yes	4	17.13	even	4
765.2.bm.b.47.1	yes	4	153.47	odd	12
765.2.bm.b.293.1	yes	4	5.3	odd	4
765.2.bt.a.497.1	yes	4	9.2	odd	6
765.2.bt.a.608.1	yes	4	85.13	odd	4
765.2.bt.b.353.1	yes	4	765.353	even	12	inner
765.2.bt.b.752.1	yes	4	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.866025 - 3.23205i) q^{6} +(0.232051 - 0.133975i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-4.09808 - 1.36603i) q^{10} +(-3.36603 - 0.901924i) q^{11} +3.00000 q^{12} +(-0.267949 - 1.00000i) q^{13} +(0.133975 + 0.500000i) q^{14} +(-1.73205 - 3.46410i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-4.00000 + 1.00000i) q^{17} +(4.09808 + 4.09808i) q^{18} +8.46410 q^{19} +(2.13397 - 3.23205i) q^{20} +(-0.232051 + 0.401924i) q^{21} +(3.36603 - 5.83013i) q^{22} +(-5.59808 - 3.23205i) q^{23} +(0.232051 - 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +2.00000 q^{26} +5.19615i q^{27} -0.464102 q^{28} +(-6.09808 - 1.63397i) q^{29} +(7.33013 - 1.50000i) q^{30} +(-1.00000 - 3.73205i) q^{31} +(7.33013 - 1.96410i) q^{32} +(5.83013 - 1.56218i) q^{33} +(0.133975 - 7.96410i) q^{34} +(0.267949 + 0.535898i) q^{35} +(-4.50000 + 2.59808i) q^{36} +1.19615 q^{37} +(-4.23205 + 15.7942i) q^{38} +(1.26795 + 1.26795i) q^{39} +(-0.767949 - 0.866025i) q^{40} +(-1.19615 - 4.46410i) q^{41} +(-0.633975 - 0.633975i) q^{42} +(-2.00000 + 7.46410i) q^{43} +(4.26795 + 4.26795i) q^{44} +(5.59808 + 3.69615i) q^{45} +(8.83013 - 8.83013i) q^{46} +(8.09808 + 2.16987i) q^{47} +(6.69615 + 3.86603i) q^{48} +(-3.46410 + 6.00000i) q^{49} +(3.59808 - 8.96410i) q^{50} +(5.13397 - 4.96410i) q^{51} +(-0.464102 + 1.73205i) q^{52} +(4.00000 - 4.00000i) q^{53} +(-9.69615 - 2.59808i) q^{54} +(2.46410 - 7.39230i) q^{55} +(-0.0358984 + 0.133975i) q^{56} +(-12.6962 + 7.33013i) q^{57} +(6.09808 - 10.5622i) q^{58} +(4.03590 + 2.33013i) q^{59} +(-0.401924 + 6.69615i) q^{60} +(3.29423 - 12.2942i) q^{61} +7.46410 q^{62} -0.803848i q^{63} +5.73205i q^{64} +(2.26795 - 0.464102i) q^{65} +11.6603i q^{66} +(-3.46410 + 0.928203i) q^{67} +(6.86603 + 1.96410i) q^{68} +11.1962 q^{69} +(-1.13397 + 0.232051i) q^{70} +(11.1962 + 11.1962i) q^{71} +(0.401924 + 1.50000i) q^{72} +13.1962i q^{73} +(-0.598076 + 2.23205i) q^{74} +(7.96410 - 3.40192i) q^{75} +(-12.6962 - 7.33013i) q^{76} +(-0.901924 + 0.241670i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(-9.46410 - 2.53590i) q^{79} +(8.92820 - 4.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +8.92820 q^{82} +(-2.36603 - 0.633975i) q^{83} +(0.696152 - 0.401924i) q^{84} +(-1.69615 - 9.06218i) q^{85} +(-12.9282 - 7.46410i) q^{86} +(10.5622 - 2.83013i) q^{87} +(1.56218 - 0.901924i) q^{88} -15.1962 q^{89} +(-9.69615 + 8.59808i) q^{90} +(-0.196152 - 0.196152i) q^{91} +(5.59808 + 9.69615i) q^{92} +(4.73205 + 4.73205i) q^{93} +(-8.09808 + 14.0263i) q^{94} +(-1.13397 + 18.8923i) q^{95} +(-9.29423 + 9.29423i) q^{96} +(-5.19615 - 9.00000i) q^{97} +(-9.46410 - 9.46410i) q^{98} +(-7.39230 + 7.39230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 6 q^{4} - 4 q^{5} - 6 q^{7} + 2 q^{8} + 6 q^{9} - 6 q^{10} - 10 q^{11} + 12 q^{12} - 8 q^{13} + 4 q^{14} - 2 q^{16} - 16 q^{17} + 6 q^{18} + 20 q^{19} + 12 q^{20} + 6 q^{21} + 10 q^{22}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 6 * q^4 - 4 * q^5 - 6 * q^7 + 2 * q^8 + 6 * q^9 - 6 * q^10 - 10 * q^11 + 12 * q^12 - 8 * q^13 + 4 * q^14 - 2 * q^16 - 16 * q^17 + 6 * q^18 + 20 * q^19 + 12 * q^20 + 6 * q^21 + 10 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^25 + 8 * q^26 + 12 * q^28 - 14 * q^29 + 12 * q^30 - 4 * q^31 + 12 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^35 - 18 * q^36 - 16 * q^37 - 10 * q^38 + 12 * q^39 - 10 * q^40 + 16 * q^41 - 6 * q^42 - 8 * q^43 + 24 * q^44 + 12 * q^45 + 18 * q^46 + 22 * q^47 + 6 * q^48 + 4 * q^50 + 24 * q^51 + 12 * q^52 + 16 * q^53 - 18 * q^54 - 4 * q^55 - 14 * q^56 - 30 * q^57 + 14 * q^58 + 30 * q^59 - 12 * q^60 - 18 * q^61 + 16 * q^62 + 16 * q^65 + 24 * q^68 + 24 * q^69 - 8 * q^70 + 24 * q^71 + 12 * q^72 + 8 * q^74 + 18 * q^75 - 30 * q^76 - 14 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 18 * q^81 + 8 * q^82 - 6 * q^83 - 18 * q^84 + 14 * q^85 - 24 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^89 - 18 * q^90 + 20 * q^91 + 12 * q^92 + 12 * q^93 - 22 * q^94 - 8 * q^95 - 6 * q^96 - 24 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more