LMFDB - Embedded newform 930.2.j.e.683.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.e.497.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} +(1.67303 + 1.48356i) q^{5} -1.73205 q^{6} +(2.00000 - 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(-0.133975 - 2.23205i) q^{10} -2.31079i q^{11} +(1.22474 + 1.22474i) q^{12} +(3.36603 + 3.36603i) q^{13} -2.82843 q^{14} +(3.86603 - 0.232051i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(-2.12132 + 2.12132i) q^{18} +3.00000i q^{19} +(-1.48356 + 1.67303i) q^{20} -4.89898i q^{21} +(-1.63397 + 1.63397i) q^{22} +(2.44949 - 2.44949i) q^{23} -1.73205i q^{24} +(0.598076 + 4.96410i) q^{25} -4.76028i q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.00000 + 2.00000i) q^{28} -4.62158 q^{29} +(-2.89778 - 2.56961i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.83013 - 2.83013i) q^{33} +1.00000i q^{34} +(6.31319 - 0.378937i) q^{35} +3.00000 q^{36} +(-0.464102 + 0.464102i) q^{37} +(2.12132 - 2.12132i) q^{38} +8.24504 q^{39} +(2.23205 - 0.133975i) q^{40} -5.65685i q^{41} +(-3.46410 + 3.46410i) q^{42} +(3.46410 + 3.46410i) q^{43} +2.31079 q^{44} +(4.45069 - 5.01910i) q^{45} -3.46410 q^{46} +(0.189469 + 0.189469i) q^{47} +(-1.22474 + 1.22474i) q^{48} -1.00000i q^{49} +(3.08725 - 3.93305i) q^{50} -1.73205 q^{51} +(-3.36603 + 3.36603i) q^{52} +(-4.89898 + 4.89898i) q^{53} +5.19615i q^{54} +(3.42820 - 3.86603i) q^{55} -2.82843i q^{56} +(3.67423 + 3.67423i) q^{57} +(3.26795 + 3.26795i) q^{58} +9.52056 q^{59} +(0.232051 + 3.86603i) q^{60} +10.1244 q^{61} +(0.707107 + 0.707107i) q^{62} +(-6.00000 - 6.00000i) q^{63} -1.00000i q^{64} +(0.637756 + 10.6252i) q^{65} +4.00240i q^{66} +(0.169873 - 0.169873i) q^{67} +(0.707107 - 0.707107i) q^{68} -6.00000i q^{69} +(-4.73205 - 4.19615i) q^{70} -15.3161i q^{71} +(-2.12132 - 2.12132i) q^{72} +(-9.46410 - 9.46410i) q^{73} +0.656339 q^{74} +(6.81225 + 5.34727i) q^{75} -3.00000 q^{76} +(-4.62158 - 4.62158i) q^{77} +(-5.83013 - 5.83013i) q^{78} +3.73205i q^{79} +(-1.67303 - 1.48356i) q^{80} -9.00000 q^{81} +(-4.00000 + 4.00000i) q^{82} +(-4.43211 + 4.43211i) q^{83} +4.89898 q^{84} +(-0.133975 - 2.23205i) q^{85} -4.89898i q^{86} +(-5.66025 + 5.66025i) q^{87} +(-1.63397 - 1.63397i) q^{88} -9.89949 q^{89} +(-6.69615 + 0.401924i) q^{90} +13.4641 q^{91} +(2.44949 + 2.44949i) q^{92} +(-1.22474 + 1.22474i) q^{93} -0.267949i q^{94} +(-4.45069 + 5.01910i) q^{95} +1.73205 q^{96} +(-8.36603 + 8.36603i) q^{97} +(-0.707107 + 0.707107i) q^{98} -6.93237 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} - 8 q^{10} + 20 q^{13} + 24 q^{15} - 8 q^{16} - 20 q^{22} - 16 q^{25} + 16 q^{28} - 8 q^{31} + 12 q^{33} + 24 q^{36} + 24 q^{37} + 4 q^{40} - 20 q^{52} - 28 q^{55} + 40 q^{58} - 12 q^{60}+ \cdots - 60 q^{97}+O(q^{100}) $ 8 * q + 16 * q^7 - 8 * q^10 + 20 * q^13 + 24 * q^15 - 8 * q^16 - 20 * q^22 - 16 * q^25 + 16 * q^28 - 8 * q^31 + 12 * q^33 + 24 * q^36 + 24 * q^37 + 4 * q^40 - 20 * q^52 - 28 * q^55 + 40 * q^58 - 12 * q^60 - 16 * q^61 - 48 * q^63 + 36 * q^67 - 24 * q^70 - 48 * q^73 - 24 * q^76 - 12 * q^78 - 72 * q^81 - 32 * q^82 - 8 * q^85 + 24 * q^87 - 20 * q^88 - 12 * q^90 + 80 * q^91 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$4$			1.00000i			0.500000i
$5$	1.67303	+	1.48356i	0.748203	+	0.663470i
$5$	1.67303	+	1.48356i	0.748203	+	0.663470i
$6$	−1.73205			−0.707107
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	−0.219650	−	0.975579i	$-0.570491\pi$
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	0.975579	+	0.219650i	$0.0704915\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	3.00000i		−	1.00000i
$10$	−0.133975	−	2.23205i	−0.0423665	−	0.705836i
$11$		−	2.31079i		−	0.696729i	−0.937359	−	0.348365i	$-0.886737\pi$
$11$		−	2.31079i		−	0.696729i	0.937359	−	0.348365i	$-0.113263\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	3.36603	+	3.36603i	0.933567	+	0.933567i	0.997927	−	0.0643593i	$-0.0205004\pi$
$13$	3.36603	+	3.36603i	0.933567	+	0.933567i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	−2.82843			−0.755929
$15$	3.86603	−	0.232051i	0.998203	−	0.0599153i
$16$	−1.00000			−0.250000
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i	0.616139	−	0.787638i	$-0.288696\pi$
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i	−0.787638	+	0.616139i	$0.788696\pi$
$18$	−2.12132	+	2.12132i	−0.500000	+	0.500000i
$19$			3.00000i			0.688247i	0.938924	+	0.344124i	$0.111824\pi$
$19$			3.00000i			0.688247i	−0.938924	+	0.344124i	$0.888176\pi$
$20$	−1.48356	+	1.67303i	−0.331735	+	0.374101i
$21$		−	4.89898i		−	1.06904i
$22$	−1.63397	+	1.63397i	−0.348365	+	0.348365i
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	−0.404004	−	0.914757i	$-0.632382\pi$
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	0.914757	+	0.404004i	$0.132382\pi$
$24$		−	1.73205i		−	0.353553i
$25$	0.598076	+	4.96410i	0.119615	+	0.992820i
$26$		−	4.76028i		−	0.933567i
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$	2.00000	+	2.00000i	0.377964	+	0.377964i
$29$	−4.62158			−0.858206			−0.429103	−	0.903256i	$-0.641170\pi$
$29$	−4.62158			−0.858206			−0.429103	+	0.903256i	$0.641170\pi$
$30$	−2.89778	−	2.56961i	−0.529059	−	0.469144i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.83013	−	2.83013i	−0.492662	−	0.492662i
$34$			1.00000i			0.171499i
$35$	6.31319	−	0.378937i	1.06712	−	0.0640521i
$36$	3.00000			0.500000
$37$	−0.464102	+	0.464102i	−0.0762978	+	0.0762978i	−0.744226	−	0.667928i	$-0.767181\pi$
$37$	−0.464102	+	0.464102i	−0.0762978	+	0.0762978i	0.667928	+	0.744226i	$0.267181\pi$
$38$	2.12132	−	2.12132i	0.344124	−	0.344124i
$39$	8.24504			1.32026
$40$	2.23205	−	0.133975i	0.352918	−	0.0211832i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	−3.46410	+	3.46410i	−0.534522	+	0.534522i
$43$	3.46410	+	3.46410i	0.528271	+	0.528271i	0.920056	−	0.391786i	$-0.128143\pi$
$43$	3.46410	+	3.46410i	0.528271	+	0.528271i	−0.391786	+	0.920056i	$0.628143\pi$
$44$	2.31079			0.348365
$45$	4.45069	−	5.01910i	0.663470	−	0.748203i
$46$	−3.46410			−0.510754
$47$	0.189469	+	0.189469i	0.0276368	+	0.0276368i	0.720790	−	0.693153i	$-0.243779\pi$
$47$	0.189469	+	0.189469i	0.0276368	+	0.0276368i	−0.693153	+	0.720790i	$0.743779\pi$
$48$	−1.22474	+	1.22474i	−0.176777	+	0.176777i
$49$		−	1.00000i		−	0.142857i
$50$	3.08725	−	3.93305i	0.436603	−	0.556218i
$51$	−1.73205			−0.242536
$52$	−3.36603	+	3.36603i	−0.466784	+	0.466784i
$53$	−4.89898	+	4.89898i	−0.672927	+	0.672927i	−0.958390	−	0.285463i	$-0.907853\pi$
$53$	−4.89898	+	4.89898i	−0.672927	+	0.672927i	0.285463	+	0.958390i	$0.407853\pi$
$54$			5.19615i			0.707107i
$55$	3.42820	−	3.86603i	0.462259	−	0.521295i
$56$		−	2.82843i		−	0.377964i
$57$	3.67423	+	3.67423i	0.486664	+	0.486664i
$58$	3.26795	+	3.26795i	0.429103	+	0.429103i
$59$	9.52056			1.23947			0.619736	−	0.784811i	$-0.287240\pi$
$59$	9.52056			1.23947			0.619736	+	0.784811i	$0.287240\pi$
$60$	0.232051	+	3.86603i	0.0299576	+	0.499102i
$61$	10.1244			1.29629			0.648145	−	0.761517i	$-0.275545\pi$
$61$	10.1244			1.29629			0.648145	+	0.761517i	$0.275545\pi$
$62$	0.707107	+	0.707107i	0.0898027	+	0.0898027i
$63$	−6.00000	−	6.00000i	−0.755929	−	0.755929i
$64$		−	1.00000i		−	0.125000i
$65$	0.637756	+	10.6252i	0.0791039	+	1.31789i
$66$			4.00240i			0.492662i
$67$	0.169873	−	0.169873i	0.0207533	−	0.0207533i	−0.696654	−	0.717407i	$-0.745329\pi$
$67$	0.169873	−	0.169873i	0.0207533	−	0.0207533i	0.717407	+	0.696654i	$0.245329\pi$
$68$	0.707107	−	0.707107i	0.0857493	−	0.0857493i
$69$		−	6.00000i		−	0.722315i
$70$	−4.73205	−	4.19615i	−0.565588	−	0.501536i
$71$		−	15.3161i		−	1.81769i	−0.417136	−	0.908844i	$-0.636966\pi$
$71$		−	15.3161i		−	1.81769i	0.417136	−	0.908844i	$-0.363034\pi$
$72$	−2.12132	−	2.12132i	−0.250000	−	0.250000i
$73$	−9.46410	−	9.46410i	−1.10769	−	1.10769i	−0.993454	−	0.114236i	$-0.963558\pi$
$73$	−9.46410	−	9.46410i	−1.10769	−	1.10769i	−0.114236	−	0.993454i	$-0.536442\pi$
$74$	0.656339			0.0762978
$75$	6.81225	+	5.34727i	0.786611	+	0.617449i
$76$	−3.00000			−0.344124
$77$	−4.62158	−	4.62158i	−0.526678	−	0.526678i
$78$	−5.83013	−	5.83013i	−0.660132	−	0.660132i
$79$			3.73205i			0.419889i	0.977713	+	0.209944i	$0.0673283\pi$
$79$			3.73205i			0.419889i	−0.977713	+	0.209944i	$0.932672\pi$
$80$	−1.67303	−	1.48356i	−0.187051	−	0.165867i
$81$	−9.00000			−1.00000
$82$	−4.00000	+	4.00000i	−0.441726	+	0.441726i
$83$	−4.43211	+	4.43211i	−0.486487	+	0.486487i	−0.907196	−	0.420709i	$-0.861781\pi$
$83$	−4.43211	+	4.43211i	−0.486487	+	0.486487i	0.420709	+	0.907196i	$0.361781\pi$
$84$	4.89898			0.534522
$85$	−0.133975	−	2.23205i	−0.0145316	−	0.242100i
$86$		−	4.89898i		−	0.528271i
$87$	−5.66025	+	5.66025i	−0.606843	+	0.606843i
$88$	−1.63397	−	1.63397i	−0.174182	−	0.174182i
$89$	−9.89949			−1.04934			−0.524672	−	0.851304i	$-0.675812\pi$
$89$	−9.89949			−1.04934			−0.524672	+	0.851304i	$0.675812\pi$
$90$	−6.69615	+	0.401924i	−0.705836	+	0.0423665i
$91$	13.4641			1.41142
$92$	2.44949	+	2.44949i	0.255377	+	0.255377i
$93$	−1.22474	+	1.22474i	−0.127000	+	0.127000i
$94$		−	0.267949i		−	0.0276368i
$95$	−4.45069	+	5.01910i	−0.456631	+	0.514949i
$96$	1.73205			0.176777
$97$	−8.36603	+	8.36603i	−0.849441	+	0.849441i	−0.990063	−	0.140622i	$-0.955090\pi$
$97$	−8.36603	+	8.36603i	−0.849441	+	0.849441i	0.140622	+	0.990063i	$0.455090\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−6.93237			−0.696729
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	1.22474	+	1.22474i	0.121268	+	0.121268i
$103$	−5.46410	−	5.46410i	−0.538394	−	0.538394i	0.384663	−	0.923057i	$-0.374318\pi$
$103$	−5.46410	−	5.46410i	−0.538394	−	0.538394i	−0.923057	+	0.384663i	$0.874318\pi$
$104$	4.76028			0.466784
$105$	7.26795	−	8.19615i	0.709279	−	0.799863i
$106$	6.92820			0.672927
$107$	−12.2474	−	12.2474i	−1.18401	−	1.18401i	−0.978697	−	0.205308i	$-0.934180\pi$
$107$	−12.2474	−	12.2474i	−1.18401	−	1.18401i	−0.205308	−	0.978697i	$-0.565820\pi$
$108$	3.67423	−	3.67423i	0.353553	−	0.353553i
$109$		−	1.07180i		−	0.102660i	−0.998682	−	0.0513298i	$-0.983654\pi$
$109$		−	1.07180i		−	0.102660i	0.998682	−	0.0513298i	$-0.0163460\pi$
$110$	−5.15780	+	0.309587i	−0.491777	+	0.0295180i
$111$			1.13681i			0.107901i
$112$	−2.00000	+	2.00000i	−0.188982	+	0.188982i
$113$	−10.1769	+	10.1769i	−0.957362	+	0.957362i	−0.999127	−	0.0417656i	$-0.986702\pi$
$113$	−10.1769	+	10.1769i	−0.957362	+	0.957362i	0.0417656	+	0.999127i	$0.486702\pi$
$114$		−	5.19615i		−	0.486664i
$115$	7.73205	−	0.464102i	0.721017	−	0.0432777i
$116$		−	4.62158i		−	0.429103i
$117$	10.0981	−	10.0981i	0.933567	−	0.933567i
$118$	−6.73205	−	6.73205i	−0.619736	−	0.619736i
$119$	−2.82843			−0.259281
$120$	2.56961	−	2.89778i	0.234572	−	0.264530i
$121$	5.66025			0.514569
$122$	−7.15900	−	7.15900i	−0.648145	−	0.648145i
$123$	−6.92820	−	6.92820i	−0.624695	−	0.624695i
$124$		−	1.00000i		−	0.0898027i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$			8.48528i			0.755929i
$127$	3.73205	−	3.73205i	0.331166	−	0.331166i	−0.521863	−	0.853029i	$-0.674763\pi$
$127$	3.73205	−	3.73205i	0.331166	−	0.331166i	0.853029	+	0.521863i	$0.174763\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	8.48528			0.747087
$130$	7.06218	−	7.96410i	0.619394	−	0.698498i
$131$			12.3490i			1.07894i	0.842006	+	0.539468i	$0.181375\pi$
$131$			12.3490i			1.07894i	−0.842006	+	0.539468i	$0.818625\pi$
$132$	2.83013	−	2.83013i	0.246331	−	0.246331i
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	−0.240237			−0.0207533
$135$	−0.696152	−	11.5981i	−0.0599153	−	0.998203i
$136$	−1.00000			−0.0857493
$137$	14.7985	+	14.7985i	1.26432	+	1.26432i	0.948979	+	0.315340i	$0.102119\pi$
$137$	14.7985	+	14.7985i	1.26432	+	1.26432i	0.315340	+	0.948979i	$0.397881\pi$
$138$	−4.24264	+	4.24264i	−0.361158	+	0.361158i
$139$			22.7846i			1.93257i	0.257484	+	0.966283i	$0.417107\pi$
$139$			22.7846i			1.93257i	−0.257484	+	0.966283i	$0.582893\pi$
$140$	0.378937	+	6.31319i	0.0320261	+	0.533562i
$141$	0.464102			0.0390844
$142$	−10.8301	+	10.8301i	−0.908844	+	0.908844i
$143$	7.77817	−	7.77817i	0.650444	−	0.650444i
$144$			3.00000i			0.250000i
$145$	−7.73205	−	6.85641i	−0.642112	−	0.569394i
$146$			13.3843i			1.10769i
$147$	−1.22474	−	1.22474i	−0.101015	−	0.101015i
$148$	−0.464102	−	0.464102i	−0.0381489	−	0.0381489i
$149$	−5.03768			−0.412703			−0.206351	−	0.978478i	$-0.566159\pi$
$149$	−5.03768			−0.412703			−0.206351	+	0.978478i	$0.566159\pi$
$150$	−1.03590	−	8.59808i	−0.0845807	−	0.702030i
$151$	14.3205			1.16539			0.582693	−	0.812692i	$-0.301999\pi$
$151$	14.3205			1.16539			0.582693	+	0.812692i	$0.301999\pi$
$152$	2.12132	+	2.12132i	0.172062	+	0.172062i
$153$	−2.12132	+	2.12132i	−0.171499	+	0.171499i
$154$			6.53590i			0.526678i
$155$	−1.67303	−	1.48356i	−0.134381	−	0.119163i
$156$			8.24504i			0.660132i
$157$	4.73205	−	4.73205i	0.377659	−	0.377659i	−0.492598	−	0.870257i	$-0.663953\pi$
$157$	4.73205	−	4.73205i	0.377659	−	0.377659i	0.870257	+	0.492598i	$0.163953\pi$
$158$	2.63896	−	2.63896i	0.209944	−	0.209944i
$159$			12.0000i			0.951662i
$160$	0.133975	+	2.23205i	0.0105916	+	0.176459i
$161$		−	9.79796i		−	0.772187i
$162$	6.36396	+	6.36396i	0.500000	+	0.500000i
$163$	3.36603	+	3.36603i	0.263647	+	0.263647i	0.826534	−	0.562887i	$-0.190309\pi$
$163$	3.36603	+	3.36603i	0.263647	+	0.263647i	−0.562887	+	0.826534i	$0.690309\pi$
$164$	5.65685			0.441726
$165$	−0.536220	−	8.93357i	−0.0417447	−	0.695477i
$166$	6.26795			0.486487
$167$	1.13681	+	1.13681i	0.0879692	+	0.0879692i	0.749722	−	0.661753i	$-0.230187\pi$
$167$	1.13681	+	1.13681i	0.0879692	+	0.0879692i	−0.661753	+	0.749722i	$0.730187\pi$
$168$	−3.46410	−	3.46410i	−0.267261	−	0.267261i
$169$			9.66025i			0.743096i
$170$	−1.48356	+	1.67303i	−0.113784	+	0.128316i
$171$	9.00000			0.688247
$172$	−3.46410	+	3.46410i	−0.264135	+	0.264135i
$173$	−13.1948	+	13.1948i	−1.00318	+	1.00318i	−0.00318655	+	0.999995i	$0.501014\pi$
$173$	−13.1948	+	13.1948i	−1.00318	+	1.00318i	−0.999995	+	0.00318655i	$0.998986\pi$
$174$	8.00481			0.606843
$175$	11.1244	+	8.73205i	0.840922	+	0.660081i
$176$			2.31079i			0.174182i
$177$	11.6603	−	11.6603i	0.876438	−	0.876438i
$178$	7.00000	+	7.00000i	0.524672	+	0.524672i
$179$	4.76028			0.355800			0.177900	−	0.984049i	$-0.443070\pi$
$179$	4.76028			0.355800			0.177900	+	0.984049i	$0.443070\pi$
$180$	5.01910	+	4.45069i	0.374101	+	0.331735i
$181$	−12.9282			−0.960946			−0.480473	−	0.877010i	$-0.659535\pi$
$181$	−12.9282			−0.960946			−0.480473	+	0.877010i	$0.659535\pi$
$182$	−9.52056	−	9.52056i	−0.705711	−	0.705711i
$183$	12.3998	−	12.3998i	0.916616	−	0.916616i
$184$		−	3.46410i		−	0.255377i
$185$	−1.46498	+	0.0879327i	−0.107708	+	0.00646494i
$186$	1.73205			0.127000
$187$	−1.63397	+	1.63397i	−0.119488	+	0.119488i
$188$	−0.189469	+	0.189469i	−0.0138184	+	0.0138184i
$189$	−14.6969			−1.06904
$190$	6.69615	−	0.401924i	0.485790	−	0.0291586i
$191$			4.52004i			0.327059i	0.986538	+	0.163529i	$0.0522879\pi$
$191$			4.52004i			0.327059i	−0.986538	+	0.163529i	$0.947712\pi$
$192$	−1.22474	−	1.22474i	−0.0883883	−	0.0883883i
$193$	−12.3660	−	12.3660i	−0.890126	−	0.890126i	0.104409	−	0.994534i	$-0.466705\pi$
$193$	−12.3660	−	12.3660i	−0.890126	−	0.890126i	−0.994534	+	0.104409i	$0.966705\pi$
$194$	11.8313			0.849441
$195$	13.7942	+	12.2321i	0.987825	+	0.875955i
$196$	1.00000			0.0714286
$197$	13.2827	+	13.2827i	0.946355	+	0.946355i	0.998633	−	0.0522776i	$-0.0166481\pi$
$197$	13.2827	+	13.2827i	0.946355	+	0.946355i	−0.0522776	+	0.998633i	$0.516648\pi$
$198$	4.90192	+	4.90192i	0.348365	+	0.348365i
$199$		−	3.39230i		−	0.240474i	−0.992745	−	0.120237i	$-0.961635\pi$
$199$		−	3.39230i		−	0.240474i	0.992745	−	0.120237i	$-0.0383655\pi$
$200$	3.93305	+	3.08725i	0.278109	+	0.218301i
$201$		−	0.416102i		−	0.0293496i
$202$	−7.00000	+	7.00000i	−0.492518	+	0.492518i
$203$	−9.24316	+	9.24316i	−0.648742	+	0.648742i
$204$		−	1.73205i		−	0.121268i
$205$	8.39230	−	9.46410i	0.586144	−	0.661002i
$206$			7.72741i			0.538394i
$207$	−7.34847	−	7.34847i	−0.510754	−	0.510754i
$208$	−3.36603	−	3.36603i	−0.233392	−	0.233392i
$209$	6.93237			0.479522
$210$	−10.9348	+	0.656339i	−0.754571	+	0.0452917i
$211$	5.60770			0.386050			0.193025	−	0.981194i	$-0.438170\pi$
$211$	5.60770			0.386050			0.193025	+	0.981194i	$0.438170\pi$
$212$	−4.89898	−	4.89898i	−0.336463	−	0.336463i
$213$	−18.7583	−	18.7583i	−1.28530	−	1.28530i
$214$			17.3205i			1.18401i
$215$	0.656339	+	10.9348i	0.0447619	+	0.745745i
$216$	−5.19615			−0.353553
$217$	−2.00000	+	2.00000i	−0.135769	+	0.135769i
$218$	−0.757875	+	0.757875i	−0.0513298	+	0.0513298i
$219$	−23.1822			−1.56651
$220$	3.86603	+	3.42820i	0.260647	+	0.231129i
$221$		−	4.76028i		−	0.320211i
$222$	0.803848	−	0.803848i	0.0539507	−	0.0539507i
$223$	−1.09808	−	1.09808i	−0.0735326	−	0.0735326i	0.669384	−	0.742917i	$-0.266558\pi$
$223$	−1.09808	−	1.09808i	−0.0735326	−	0.0735326i	−0.742917	+	0.669384i	$0.766558\pi$
$224$	2.82843			0.188982
$225$	14.8923	−	1.79423i	0.992820	−	0.119615i
$226$	14.3923			0.957362
$227$	12.6264	+	12.6264i	0.838043	+	0.838043i	0.988601	−	0.150558i	$-0.0481072\pi$
$227$	12.6264	+	12.6264i	0.838043	+	0.838043i	−0.150558	+	0.988601i	$0.548107\pi$
$228$	−3.67423	+	3.67423i	−0.243332	+	0.243332i
$229$			24.3205i			1.60714i	0.595207	+	0.803572i	$0.297070\pi$
$229$			24.3205i			1.60714i	−0.595207	+	0.803572i	$0.702930\pi$
$230$	−5.79555	−	5.13922i	−0.382148	−	0.338870i
$231$	−11.3205			−0.744835
$232$	−3.26795	+	3.26795i	−0.214551	+	0.214551i
$233$	11.5911	−	11.5911i	0.759359	−	0.759359i	−0.216847	−	0.976206i	$-0.569577\pi$
$233$	11.5911	−	11.5911i	0.759359	−	0.759359i	0.976206	+	0.216847i	$0.0695772\pi$
$234$	−14.2808			−0.933567
$235$	0.0358984	+	0.598076i	0.00234175	+	0.0390142i
$236$			9.52056i			0.619736i
$237$	4.57081	+	4.57081i	0.296906	+	0.296906i
$238$	2.00000	+	2.00000i	0.129641	+	0.129641i
$239$	2.55103			0.165012			0.0825061	−	0.996591i	$-0.473708\pi$
$239$	2.55103			0.165012			0.0825061	+	0.996591i	$0.473708\pi$
$240$	−3.86603	+	0.232051i	−0.249551	+	0.0149788i
$241$	−16.3923			−1.05592			−0.527961	−	0.849269i	$-0.677043\pi$
$241$	−16.3923			−1.05592			−0.527961	+	0.849269i	$0.677043\pi$
$242$	−4.00240	−	4.00240i	−0.257284	−	0.257284i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$			10.1244i			0.648145i
$245$	1.48356	−	1.67303i	0.0947814	−	0.106886i
$246$			9.79796i			0.624695i
$247$	−10.0981	+	10.0981i	−0.642525	+	0.642525i
$248$	−0.707107	+	0.707107i	−0.0449013	+	0.0449013i
$249$			10.8564i			0.687997i
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$			6.03579i			0.380976i	0.981690	+	0.190488i	$0.0610070\pi$
$251$			6.03579i			0.380976i	−0.981690	+	0.190488i	$0.938993\pi$
$252$	6.00000	−	6.00000i	0.377964	−	0.377964i
$253$	−5.66025	−	5.66025i	−0.355857	−	0.355857i
$254$	−5.27792			−0.331166
$255$	−2.89778	−	2.56961i	−0.181466	−	0.160915i
$256$	1.00000			0.0625000
$257$	15.4548	+	15.4548i	0.964045	+	0.964045i	0.999376	−	0.0353309i	$-0.0112485\pi$
$257$	15.4548	+	15.4548i	0.964045	+	0.964045i	−0.0353309	+	0.999376i	$0.511249\pi$
$258$	−6.00000	−	6.00000i	−0.373544	−	0.373544i
$259$			1.85641i			0.115351i
$260$	−10.6252	+	0.637756i	−0.658946	+	0.0395520i
$261$			13.8647i			0.858206i
$262$	8.73205	−	8.73205i	0.539468	−	0.539468i
$263$	−15.7322	+	15.7322i	−0.970090	+	0.970090i	−0.999566	−	0.0294756i	$-0.990616\pi$
$263$	−15.7322	+	15.7322i	−0.970090	+	0.970090i	0.0294756	+	0.999566i	$0.490616\pi$
$264$	−4.00240			−0.246331
$265$	−15.4641	+	0.928203i	−0.949952	+	0.0570191i
$266$		−	8.48528i		−	0.520266i
$267$	−12.1244	+	12.1244i	−0.741999	+	0.741999i
$268$	0.169873	+	0.169873i	0.0103766	+	0.0103766i
$269$	9.24316			0.563565			0.281783	−	0.959478i	$-0.409074\pi$
$269$	9.24316			0.563565			0.281783	+	0.959478i	$0.409074\pi$
$270$	−7.70882	+	8.69333i	−0.469144	+	0.529059i
$271$	−25.5885			−1.55439			−0.777194	−	0.629261i	$-0.783358\pi$
$271$	−25.5885			−1.55439			−0.777194	+	0.629261i	$0.783358\pi$
$272$	0.707107	+	0.707107i	0.0428746	+	0.0428746i
$273$	16.4901	−	16.4901i	0.998026	−	0.998026i
$274$		−	20.9282i		−	1.26432i
$275$	11.4710	−	1.38203i	0.691727	−	0.0833394i
$276$	6.00000			0.361158
$277$	14.7583	−	14.7583i	0.886742	−	0.886742i	−0.107467	−	0.994209i	$-0.534274\pi$
$277$	14.7583	−	14.7583i	0.886742	−	0.886742i	0.994209	+	0.107467i	$0.0342739\pi$
$278$	16.1112	−	16.1112i	0.966283	−	0.966283i
$279$			3.00000i			0.179605i
$280$	4.19615	−	4.73205i	0.250768	−	0.282794i
$281$			10.0010i			0.596611i	0.954470	+	0.298306i	$0.0964215\pi$
$281$			10.0010i			0.596611i	−0.954470	+	0.298306i	$0.903578\pi$
$282$	−0.328169	−	0.328169i	−0.0195422	−	0.0195422i
$283$	4.90192	+	4.90192i	0.291389	+	0.291389i	0.837629	−	0.546240i	$-0.183941\pi$
$283$	4.90192	+	4.90192i	0.291389	+	0.291389i	−0.546240	+	0.837629i	$0.683941\pi$
$284$	15.3161			0.908844
$285$	0.696152	+	11.5981i	0.0412365	+	0.687011i
$286$	−11.0000			−0.650444
$287$	−11.3137	−	11.3137i	−0.667827	−	0.667827i
$288$	2.12132	−	2.12132i	0.125000	−	0.125000i
$289$		−	16.0000i		−	0.941176i
$290$	0.619174	+	10.3156i	0.0363592	+	0.605753i
$291$			20.4925i			1.20129i
$292$	9.46410	−	9.46410i	0.553845	−	0.553845i
$293$	−18.2832	+	18.2832i	−1.06812	+	1.06812i	−0.0706146	+	0.997504i	$0.522496\pi$
$293$	−18.2832	+	18.2832i	−1.06812	+	1.06812i	−0.997504	+	0.0706146i	$0.977504\pi$
$294$			1.73205i			0.101015i
$295$	15.9282	+	14.1244i	0.927376	+	0.822352i
$296$			0.656339i			0.0381489i
$297$	−8.49038	+	8.49038i	−0.492662	+	0.492662i
$298$	3.56218	+	3.56218i	0.206351	+	0.206351i
$299$	16.4901			0.953646
$300$	−5.34727	+	6.81225i	−0.308725	+	0.393305i
$301$	13.8564			0.798670
$302$	−10.1261	−	10.1261i	−0.582693	−	0.582693i
$303$	−12.1244	−	12.1244i	−0.696526	−	0.696526i
$304$		−	3.00000i		−	0.172062i
$305$	16.9384	+	15.0201i	0.969889	+	0.860050i
$306$	3.00000			0.171499
$307$	−19.5885	+	19.5885i	−1.11797	+	1.11797i	−0.125934	+	0.992039i	$0.540193\pi$
$307$	−19.5885	+	19.5885i	−1.11797	+	1.11797i	−0.992039	+	0.125934i	$0.959807\pi$
$308$	4.62158	−	4.62158i	0.263339	−	0.263339i
$309$	−13.3843			−0.761404
$310$	0.133975	+	2.23205i	0.00760925	+	0.126772i
$311$		−	9.65926i		−	0.547726i	−0.961769	−	0.273863i	$-0.911698\pi$
$311$		−	9.65926i		−	0.547726i	0.961769	−	0.273863i	$-0.0883015\pi$
$312$	5.83013	−	5.83013i	0.330066	−	0.330066i
$313$	−11.8564	−	11.8564i	−0.670164	−	0.670164i	0.287590	−	0.957754i	$-0.407146\pi$
$313$	−11.8564	−	11.8564i	−0.670164	−	0.670164i	−0.957754	+	0.287590i	$0.907146\pi$
$314$	−6.69213			−0.377659
$315$	−1.13681	−	18.9396i	−0.0640521	−	1.06712i
$316$	−3.73205			−0.209944
$317$	−4.57081	−	4.57081i	−0.256722	−	0.256722i	0.566997	−	0.823720i	$-0.308105\pi$
$317$	−4.57081	−	4.57081i	−0.256722	−	0.256722i	−0.823720	+	0.566997i	$0.808105\pi$
$318$	8.48528	−	8.48528i	0.475831	−	0.475831i
$319$			10.6795i			0.597937i
$320$	1.48356	−	1.67303i	0.0829337	−	0.0935254i
$321$	−30.0000			−1.67444
$322$	−6.92820	+	6.92820i	−0.386094	+	0.386094i
$323$	2.12132	−	2.12132i	0.118033	−	0.118033i
$324$		−	9.00000i		−	0.500000i
$325$	−14.6962	+	18.7224i	−0.815196	+	1.03853i
$326$		−	4.76028i		−	0.263647i
$327$	−1.31268	−	1.31268i	−0.0725912	−	0.0725912i
$328$	−4.00000	−	4.00000i	−0.220863	−	0.220863i
$329$	0.757875			0.0417830
$330$	−5.93782	+	6.69615i	−0.326866	+	0.368611i
$331$	18.3923			1.01093			0.505466	−	0.862846i	$-0.331321\pi$
$331$	18.3923			1.01093			0.505466	+	0.862846i	$0.331321\pi$
$332$	−4.43211	−	4.43211i	−0.243244	−	0.243244i
$333$	1.39230	+	1.39230i	0.0762978	+	0.0762978i
$334$		−	1.60770i		−	0.0879692i
$335$	0.536220	−	0.0321856i	0.0292969	−	0.00175849i
$336$			4.89898i			0.267261i
$337$	7.85641	−	7.85641i	0.427966	−	0.427966i	−0.459969	−	0.887935i	$-0.652140\pi$
$337$	7.85641	−	7.85641i	0.427966	−	0.427966i	0.887935	+	0.459969i	$0.152140\pi$
$338$	6.83083	−	6.83083i	0.371548	−	0.371548i
$339$			24.9282i			1.35391i
$340$	2.23205	−	0.133975i	0.121050	−	0.00726579i
$341$			2.31079i			0.125136i
$342$	−6.36396	−	6.36396i	−0.344124	−	0.344124i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	4.89898			0.264135
$345$	8.90138	−	10.0382i	0.479234	−	0.540438i
$346$	18.6603			1.00318
$347$	−13.6753	−	13.6753i	−0.734127	−	0.734127i	0.237308	−	0.971435i	$-0.423735\pi$
$347$	−13.6753	−	13.6753i	−0.734127	−	0.734127i	−0.971435	+	0.237308i	$0.923735\pi$
$348$	−5.66025	−	5.66025i	−0.303421	−	0.303421i
$349$		−	22.2487i		−	1.19095i	−0.803375	−	0.595473i	$-0.796965\pi$
$349$		−	22.2487i		−	1.19095i	0.803375	−	0.595473i	$-0.203035\pi$
$350$	−1.69161	−	14.0406i	−0.0904206	−	0.750502i
$351$		−	24.7351i		−	1.32026i
$352$	1.63397	−	1.63397i	0.0870911	−	0.0870911i
$353$	−6.50266	+	6.50266i	−0.346102	+	0.346102i	−0.858655	−	0.512554i	$-0.828700\pi$
$353$	−6.50266	+	6.50266i	−0.346102	+	0.346102i	0.512554	+	0.858655i	$0.328700\pi$
$354$	−16.4901			−0.876438
$355$	22.7224	−	25.6244i	1.20598	−	1.36000i
$356$		−	9.89949i		−	0.524672i
$357$	−3.46410	+	3.46410i	−0.183340	+	0.183340i
$358$	−3.36603	−	3.36603i	−0.177900	−	0.177900i
$359$	8.14351			0.429798			0.214899	−	0.976636i	$-0.431058\pi$
$359$	8.14351			0.429798			0.214899	+	0.976636i	$0.431058\pi$
$360$	−0.401924	−	6.69615i	−0.0211832	−	0.352918i
$361$	10.0000			0.526316
$362$	9.14162	+	9.14162i	0.480473	+	0.480473i
$363$	6.93237	−	6.93237i	0.363855	−	0.363855i
$364$			13.4641i			0.705711i
$365$	−1.79315	−	29.8744i	−0.0938578	−	1.56369i
$366$	−17.5359			−0.916616
$367$	−24.8827	+	24.8827i	−1.29887	+	1.29887i	−0.369724	+	0.929142i	$0.620548\pi$
$367$	−24.8827	+	24.8827i	−1.29887	+	1.29887i	−0.929142	+	0.369724i	$0.879452\pi$
$368$	−2.44949	+	2.44949i	−0.127688	+	0.127688i
$369$	−16.9706			−0.883452
$370$	1.09808	+	0.973721i	0.0570863	+	0.0506213i
$371$			19.5959i			1.01737i
$372$	−1.22474	−	1.22474i	−0.0635001	−	0.0635001i
$373$	−17.8564	−	17.8564i	−0.924570	−	0.924570i	0.0727785	−	0.997348i	$-0.476813\pi$
$373$	−17.8564	−	17.8564i	−0.924570	−	0.924570i	−0.997348	+	0.0727785i	$0.976813\pi$
$374$	2.31079			0.119488
$375$	3.46410	+	19.0526i	0.178885	+	0.983870i
$376$	0.267949			0.0138184
$377$	−15.5563	−	15.5563i	−0.801193	−	0.801193i
$378$	10.3923	+	10.3923i	0.534522	+	0.534522i
$379$		−	18.8038i		−	0.965889i	−0.875651	−	0.482944i	$-0.839567\pi$
$379$		−	18.8038i		−	0.965889i	0.875651	−	0.482944i	$-0.160433\pi$
$380$	−5.01910	−	4.45069i	−0.257474	−	0.228316i
$381$		−	9.14162i		−	0.468339i
$382$	3.19615	−	3.19615i	0.163529	−	0.163529i
$383$	3.86370	−	3.86370i	0.197426	−	0.197426i	−0.601470	−	0.798896i	$-0.705418\pi$
$383$	3.86370	−	3.86370i	0.197426	−	0.197426i	0.798896	+	0.601470i	$0.205418\pi$
$384$			1.73205i			0.0883883i
$385$	−0.875644	−	14.5885i	−0.0446270	−	0.743497i
$386$			17.4882i			0.890126i
$387$	10.3923	−	10.3923i	0.528271	−	0.528271i
$388$	−8.36603	−	8.36603i	−0.424721	−	0.424721i
$389$	−5.93426			−0.300879			−0.150439	−	0.988619i	$-0.548069\pi$
$389$	−5.93426			−0.300879			−0.150439	+	0.988619i	$0.548069\pi$
$390$	−1.10463	−	18.4034i	−0.0559349	−	0.931890i
$391$	−3.46410			−0.175187
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	15.1244	+	15.1244i	0.762923	+	0.762923i
$394$		−	18.7846i		−	0.946355i
$395$	−5.53674	+	6.24384i	−0.278583	+	0.314162i
$396$		−	6.93237i		−	0.348365i
$397$	−27.5167	+	27.5167i	−1.38102	+	1.38102i	−0.538212	+	0.842809i	$0.680900\pi$
$397$	−27.5167	+	27.5167i	−1.38102	+	1.38102i	−0.842809	+	0.538212i	$0.819100\pi$
$398$	−2.39872	+	2.39872i	−0.120237	+	0.120237i
$399$	14.6969			0.735767
$400$	−0.598076	−	4.96410i	−0.0299038	−	0.248205i
$401$			13.5230i			0.675304i	0.941271	+	0.337652i	$0.109633\pi$
$401$			13.5230i			0.675304i	−0.941271	+	0.337652i	$0.890367\pi$
$402$	−0.294229	+	0.294229i	−0.0146748	+	0.0146748i
$403$	−3.36603	−	3.36603i	−0.167674	−	0.167674i
$404$	9.89949			0.492518
$405$	−15.0573	−	13.3521i	−0.748203	−	0.663470i
$406$	13.0718			0.648742
$407$	1.07244	+	1.07244i	0.0531589	+	0.0531589i
$408$	−1.22474	+	1.22474i	−0.0606339	+	0.0606339i
$409$		−	29.1769i		−	1.44271i	−0.692568	−	0.721353i	$-0.743521\pi$
$409$		−	29.1769i		−	1.44271i	0.692568	−	0.721353i	$-0.256479\pi$
$410$	−12.6264	+	0.757875i	−0.623573	+	0.0374288i
$411$	36.2487			1.78802
$412$	5.46410	−	5.46410i	0.269197	−	0.269197i
$413$	19.0411	−	19.0411i	0.936952	−	0.936952i
$414$			10.3923i			0.510754i
$415$	−13.9904	+	0.839746i	−0.686761	+	0.0412215i
$416$			4.76028i			0.233392i
$417$	27.9053	+	27.9053i	1.36653	+	1.36653i
$418$	−4.90192	−	4.90192i	−0.239761	−	0.239761i
$419$	31.9449			1.56061			0.780305	−	0.625399i	$-0.215064\pi$
$419$	31.9449			1.56061			0.780305	+	0.625399i	$0.215064\pi$
$420$	8.19615	+	7.26795i	0.399931	+	0.354640i
$421$	4.92820			0.240186			0.120093	−	0.992763i	$-0.461681\pi$
$421$	4.92820			0.240186			0.120093	+	0.992763i	$0.461681\pi$
$422$	−3.96524	−	3.96524i	−0.193025	−	0.193025i
$423$	0.568406	−	0.568406i	0.0276368	−	0.0276368i
$424$			6.92820i			0.336463i
$425$	3.08725	−	3.93305i	0.149753	−	0.190781i
$426$			26.5283i			1.28530i
$427$	20.2487	−	20.2487i	0.979904	−	0.979904i
$428$	12.2474	−	12.2474i	0.592003	−	0.592003i
$429$		−	19.0526i		−	0.919866i
$430$	7.26795	−	8.19615i	0.350492	−	0.395254i
$431$		−	29.0149i		−	1.39760i	−0.715317	−	0.698800i	$-0.753718\pi$
$431$		−	29.0149i		−	1.39760i	0.715317	−	0.698800i	$-0.246282\pi$
$432$	3.67423	+	3.67423i	0.176777	+	0.176777i
$433$	22.3923	+	22.3923i	1.07611	+	1.07611i	0.996855	+	0.0792508i	$0.0252528\pi$
$433$	22.3923	+	22.3923i	1.07611	+	1.07611i	0.0792508	+	0.996855i	$0.474747\pi$
$434$	2.82843			0.135769
$435$	−17.8671	+	1.07244i	−0.856664	+	0.0514196i
$436$	1.07180			0.0513298
$437$	7.34847	+	7.34847i	0.351525	+	0.351525i
$438$	16.3923	+	16.3923i	0.783255	+	0.783255i
$439$		−	10.0000i		−	0.477274i	−0.971109	−	0.238637i	$-0.923299\pi$
$439$		−	10.0000i		−	0.477274i	0.971109	−	0.238637i	$-0.0767006\pi$
$440$	−0.309587	−	5.15780i	−0.0147590	−	0.245888i
$441$	−3.00000			−0.142857
$442$	−3.36603	+	3.36603i	−0.160106	+	0.160106i
$443$	−23.2838	+	23.2838i	−1.10624	+	1.10624i	−0.112605	+	0.993640i	$0.535919\pi$
$443$	−23.2838	+	23.2838i	−1.10624	+	1.10624i	−0.993640	+	0.112605i	$0.964081\pi$
$444$	−1.13681			−0.0539507
$445$	−16.5622	−	14.6865i	−0.785123	−	0.696208i
$446$			1.55291i			0.0735326i
$447$	−6.16987	+	6.16987i	−0.291825	+	0.291825i
$448$	−2.00000	−	2.00000i	−0.0944911	−	0.0944911i
$449$	14.9372			0.704929			0.352464	−	0.935825i	$-0.385344\pi$
$449$	14.9372			0.704929			0.352464	+	0.935825i	$0.385344\pi$
$450$	−11.7992	−	9.26174i	−0.556218	−	0.436603i
$451$	−13.0718			−0.615527
$452$	−10.1769	−	10.1769i	−0.478681	−	0.478681i
$453$	17.5390	−	17.5390i	0.824053	−	0.824053i
$454$		−	17.8564i		−	0.838043i
$455$	22.5259	+	19.9749i	1.05603	+	0.936436i
$456$	5.19615			0.243332
$457$	8.19615	−	8.19615i	0.383400	−	0.383400i	−0.488926	−	0.872325i	$-0.662611\pi$
$457$	8.19615	−	8.19615i	0.383400	−	0.383400i	0.872325	+	0.488926i	$0.162611\pi$
$458$	17.1972	−	17.1972i	0.803572	−	0.803572i
$459$			5.19615i			0.242536i
$460$	0.464102	+	7.73205i	0.0216388	+	0.360509i
$461$		−	27.2490i		−	1.26911i	−0.772877	−	0.634556i	$-0.781183\pi$
$461$		−	27.2490i		−	1.26911i	0.772877	−	0.634556i	$-0.218817\pi$
$462$	8.00481	+	8.00481i	0.372417	+	0.372417i
$463$	23.9019	+	23.9019i	1.11082	+	1.11082i	0.993040	+	0.117776i	$0.0375766\pi$
$463$	23.9019	+	23.9019i	1.11082	+	1.11082i	0.117776	+	0.993040i	$0.462423\pi$
$464$	4.62158			0.214551
$465$	−3.86603	+	0.232051i	−0.179283	+	0.0107611i
$466$	−16.3923			−0.759359
$467$	6.21166	+	6.21166i	0.287441	+	0.287441i	0.836068	−	0.548626i	$-0.184849\pi$
$467$	6.21166	+	6.21166i	0.287441	+	0.287441i	−0.548626	+	0.836068i	$0.684849\pi$
$468$	10.0981	+	10.0981i	0.466784	+	0.466784i
$469$		−	0.679492i		−	0.0313760i
$470$	0.397520	−	0.448288i	0.0183362	−	0.0206780i
$471$		−	11.5911i		−	0.534090i
$472$	6.73205	−	6.73205i	0.309868	−	0.309868i
$473$	8.00481	−	8.00481i	0.368061	−	0.368061i
$474$		−	6.46410i		−	0.296906i
$475$	−14.8923	+	1.79423i	−0.683306	+	0.0823249i
$476$		−	2.82843i		−	0.129641i
$477$	14.6969	+	14.6969i	0.672927	+	0.672927i
$478$	−1.80385	−	1.80385i	−0.0825061	−	0.0825061i
$479$	−25.2899			−1.15553			−0.577763	−	0.816204i	$-0.696074\pi$
$479$	−25.2899			−1.15553			−0.577763	+	0.816204i	$0.696074\pi$
$480$	2.89778	+	2.56961i	0.132265	+	0.117286i
$481$	−3.12436			−0.142458
$482$	11.5911	+	11.5911i	0.527961	+	0.527961i
$483$	−12.0000	−	12.0000i	−0.546019	−	0.546019i
$484$			5.66025i			0.257284i
$485$	−26.4082	+	1.58510i	−1.19913	+	0.0719757i
$486$	15.5885			0.707107
$487$	−9.16987	+	9.16987i	−0.415527	+	0.415527i	−0.883659	−	0.468132i	$-0.844927\pi$
$487$	−9.16987	+	9.16987i	−0.415527	+	0.415527i	0.468132	+	0.883659i	$0.344927\pi$
$488$	7.15900	−	7.15900i	0.324073	−	0.324073i
$489$	8.24504			0.372854
$490$	−2.23205	+	0.133975i	−0.100834	+	0.00605236i
$491$			16.5916i			0.748770i	0.927273	+	0.374385i	$0.122146\pi$
$491$			16.5916i			0.748770i	−0.927273	+	0.374385i	$0.877854\pi$
$492$	6.92820	−	6.92820i	0.312348	−	0.312348i
$493$	3.26795	+	3.26795i	0.147181	+	0.147181i
$494$	14.2808			0.642525
$495$	−11.5981	−	10.2846i	−0.521295	−	0.462259i
$496$	1.00000			0.0449013
$497$	−30.6322	−	30.6322i	−1.37404	−	1.37404i
$498$	7.67664	−	7.67664i	0.343998	−	0.343998i
$499$			2.14359i			0.0959604i	0.998848	+	0.0479802i	$0.0152784\pi$
$499$			2.14359i			0.0959604i	−0.998848	+	0.0479802i	$0.984722\pi$
$500$	−9.19239	−	6.36396i	−0.411096	−	0.284605i
$501$	2.78461			0.124407
$502$	4.26795	−	4.26795i	0.190488	−	0.190488i
$503$	−12.8159	+	12.8159i	−0.571431	+	0.571431i	−0.932528	−	0.361097i	$-0.882402\pi$
$503$	−12.8159	+	12.8159i	−0.571431	+	0.571431i	0.361097	+	0.932528i	$0.382402\pi$
$504$	−8.48528			−0.377964
$505$	14.6865	−	16.5622i	0.653542	−	0.737007i
$506$			8.00481i			0.355857i
$507$	11.8313	+	11.8313i	0.525449	+	0.525449i
$508$	3.73205	+	3.73205i	0.165583	+	0.165583i
$509$	−28.6360			−1.26927			−0.634634	−	0.772813i	$-0.718849\pi$
$509$	−28.6360			−1.26927			−0.634634	+	0.772813i	$0.718849\pi$
$510$	0.232051	+	3.86603i	0.0102754	+	0.171190i
$511$	−37.8564			−1.67467
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.0227	−	11.0227i	0.486664	−	0.486664i
$514$		−	21.8564i		−	0.964045i
$515$	−1.03528	−	17.2480i	−0.0456197	−	0.760036i
$516$			8.48528i			0.373544i
$517$	0.437822	−	0.437822i	0.0192554	−	0.0192554i
$518$	1.31268	−	1.31268i	0.0576757	−	0.0576757i
$519$			32.3205i			1.41871i
$520$	7.96410	+	7.06218i	0.349249	+	0.309697i
$521$		−	15.9353i		−	0.698138i	−0.937097	−	0.349069i	$-0.886498\pi$
$521$		−	15.9353i		−	0.698138i	0.937097	−	0.349069i	$-0.113502\pi$
$522$	9.80385	−	9.80385i	0.429103	−	0.429103i
$523$	−29.3205	−	29.3205i	−1.28210	−	1.28210i	−0.939473	−	0.342624i	$-0.888684\pi$
$523$	−29.3205	−	29.3205i	−1.28210	−	1.28210i	−0.342624	−	0.939473i	$-0.611316\pi$
$524$	−12.3490			−0.539468
$525$	24.3190	−	2.92996i	1.06137	−	0.127874i
$526$	22.2487			0.970090
$527$	0.707107	+	0.707107i	0.0308021	+	0.0308021i
$528$	2.83013	+	2.83013i	0.123165	+	0.123165i
$529$			11.0000i			0.478261i
$530$	11.5911	+	10.2784i	0.503486	+	0.446467i
$531$		−	28.5617i		−	1.23947i
$532$	−6.00000	+	6.00000i	−0.260133	+	0.260133i
$533$	19.0411	−	19.0411i	0.824762	−	0.824762i
$534$	17.1464			0.741999
$535$	−2.32051	−	38.6603i	−0.100324	−	1.67143i
$536$		−	0.240237i		−	0.0103766i
$537$	5.83013	−	5.83013i	0.251589	−	0.251589i
$538$	−6.53590	−	6.53590i	−0.281783	−	0.281783i
$539$	−2.31079			−0.0995327
$540$	11.5981	−	0.696152i	0.499102	−	0.0299576i
$541$	−29.7128			−1.27745			−0.638727	−	0.769434i	$-0.720539\pi$
$541$	−29.7128			−1.27745			−0.638727	+	0.769434i	$0.720539\pi$
$542$	18.0938	+	18.0938i	0.777194	+	0.777194i
$543$	−15.8338	+	15.8338i	−0.679491	+	0.679491i
$544$		−	1.00000i		−	0.0428746i
$545$	1.59008	−	1.79315i	0.0681115	−	0.0768101i
$546$	−23.3205			−0.998026
$547$	20.2679	−	20.2679i	0.866595	−	0.866595i	−0.125499	−	0.992094i	$-0.540053\pi$
$547$	20.2679	−	20.2679i	0.866595	−	0.866595i	0.992094	+	0.125499i	$0.0400531\pi$
$548$	−14.7985	+	14.7985i	−0.632159	+	0.632159i
$549$		−	30.3731i		−	1.29629i
$550$	−9.08846	−	7.13397i	−0.387533	−	0.304194i
$551$		−	13.8647i		−	0.590658i
$552$	−4.24264	−	4.24264i	−0.180579	−	0.180579i
$553$	7.46410	+	7.46410i	0.317406	+	0.317406i
$554$	−20.8714			−0.886742
$555$	−1.68653	+	1.90192i	−0.0715894	+	0.0807322i
$556$	−22.7846			−0.966283
$557$	−12.9038	−	12.9038i	−0.546751	−	0.546751i	0.378749	−	0.925500i	$-0.376355\pi$
$557$	−12.9038	−	12.9038i	−0.546751	−	0.546751i	−0.925500	+	0.378749i	$0.876355\pi$
$558$	2.12132	−	2.12132i	0.0898027	−	0.0898027i
$559$			23.3205i			0.986352i
$560$	−6.31319	+	0.378937i	−0.266781	+	0.0160130i
$561$			4.00240i			0.168982i
$562$	7.07180	−	7.07180i	0.298306	−	0.298306i
$563$	9.62209	−	9.62209i	0.405523	−	0.405523i	−0.474651	−	0.880174i	$-0.657426\pi$
$563$	9.62209	−	9.62209i	0.405523	−	0.405523i	0.880174	+	0.474651i	$0.157426\pi$
$564$			0.464102i			0.0195422i
$565$	−32.1244	+	1.92820i	−1.35148	+	0.0811201i
$566$		−	6.93237i		−	0.291389i
$567$	−18.0000	+	18.0000i	−0.755929	+	0.755929i
$568$	−10.8301	−	10.8301i	−0.454422	−	0.454422i
$569$	−23.0807			−0.967593			−0.483796	−	0.875181i	$-0.660742\pi$
$569$	−23.0807			−0.967593			−0.483796	+	0.875181i	$0.660742\pi$
$570$	7.70882	−	8.69333i	0.322887	−	0.364124i
$571$	9.85641			0.412478			0.206239	−	0.978502i	$-0.433878\pi$
$571$	9.85641			0.412478			0.206239	+	0.978502i	$0.433878\pi$
$572$	7.77817	+	7.77817i	0.325222	+	0.325222i
$573$	5.53590	+	5.53590i	0.231265	+	0.231265i
$574$			16.0000i			0.667827i
$575$	13.6245	+	10.6945i	0.568181	+	0.445993i
$576$	−3.00000			−0.125000
$577$	−6.83013	+	6.83013i	−0.284342	+	0.284342i	−0.834838	−	0.550496i	$-0.814439\pi$
$577$	−6.83013	+	6.83013i	−0.284342	+	0.284342i	0.550496	+	0.834838i	$0.314439\pi$
$578$	−11.3137	+	11.3137i	−0.470588	+	0.470588i
$579$	−30.2905			−1.25883
$580$	6.85641	−	7.73205i	0.284697	−	0.321056i
$581$			17.7284i			0.735500i
$582$	14.4904	−	14.4904i	0.600646	−	0.600646i
$583$	11.3205	+	11.3205i	0.468848	+	0.468848i
$584$	−13.3843			−0.553845
$585$	31.8756	−	1.91327i	1.31789	−	0.0791039i
$586$	25.8564			1.06812
$587$	−13.9898	−	13.9898i	−0.577422	−	0.577422i	0.356770	−	0.934192i	$-0.383878\pi$
$587$	−13.9898	−	13.9898i	−0.577422	−	0.577422i	−0.934192	+	0.356770i	$0.883878\pi$
$588$	1.22474	−	1.22474i	0.0505076	−	0.0505076i
$589$		−	3.00000i		−	0.123613i
$590$	−1.27551	−	21.2504i	−0.0525120	−	0.874864i
$591$	32.5359			1.33835
$592$	0.464102	−	0.464102i	0.0190745	−	0.0190745i
$593$	28.0812	−	28.0812i	1.15316	−	1.15316i	0.167241	−	0.985916i	$-0.446514\pi$
$593$	28.0812	−	28.0812i	1.15316	−	1.15316i	0.985916	−	0.167241i	$-0.0534856\pi$
$594$	12.0072			0.492662
$595$	−4.73205	−	4.19615i	−0.193995	−	0.172025i
$596$		−	5.03768i		−	0.206351i
$597$	−4.15471	−	4.15471i	−0.170041	−	0.170041i
$598$	−11.6603	−	11.6603i	−0.476823	−	0.476823i
$599$	15.4920			0.632985			0.316493	−	0.948595i	$-0.397495\pi$
$599$	15.4920			0.632985			0.316493	+	0.948595i	$0.397495\pi$
$600$	8.59808	−	1.03590i	0.351015	−	0.0422904i
$601$	35.4641			1.44661			0.723305	−	0.690528i	$-0.242622\pi$
$601$	35.4641			1.44661			0.723305	+	0.690528i	$0.242622\pi$
$602$	−9.79796	−	9.79796i	−0.399335	−	0.399335i
$603$	−0.509619	−	0.509619i	−0.0207533	−	0.0207533i
$604$			14.3205i			0.582693i
$605$	9.46979	+	8.39735i	0.385002	+	0.341401i
$606$			17.1464i			0.696526i
$607$	0.535898	−	0.535898i	0.0217514	−	0.0217514i	−0.696147	−	0.717899i	$-0.745104\pi$
$607$	0.535898	−	0.535898i	0.0217514	−	0.0217514i	0.717899	+	0.696147i	$0.245104\pi$
$608$	−2.12132	+	2.12132i	−0.0860309	+	0.0860309i
$609$			22.6410i			0.917460i
$610$	−1.35641	−	22.5981i	−0.0549193	−	0.914969i
$611$			1.27551i			0.0516017i
$612$	−2.12132	−	2.12132i	−0.0857493	−	0.0857493i
$613$	16.5622	+	16.5622i	0.668940	+	0.668940i	0.957471	−	0.288531i	$-0.0931667\pi$
$613$	16.5622	+	16.5622i	0.668940	+	0.668940i	−0.288531	+	0.957471i	$0.593167\pi$
$614$	27.7023			1.11797
$615$	−1.31268	−	21.8695i	−0.0529323	−	0.881865i
$616$	−6.53590			−0.263339
$617$	−28.1827	−	28.1827i	−1.13459	−	1.13459i	−0.989404	−	0.145190i	$-0.953621\pi$
$617$	−28.1827	−	28.1827i	−1.13459	−	1.13459i	−0.145190	−	0.989404i	$-0.546379\pi$
$618$	9.46410	+	9.46410i	0.380702	+	0.380702i
$619$		−	4.67949i		−	0.188085i	−0.995568	−	0.0940423i	$-0.970021\pi$
$619$		−	4.67949i		−	0.188085i	0.995568	−	0.0940423i	$-0.0299789\pi$
$620$	1.48356	−	1.67303i	0.0595814	−	0.0671906i
$621$	−18.0000			−0.722315
$622$	−6.83013	+	6.83013i	−0.273863	+	0.273863i
$623$	−19.7990	+	19.7990i	−0.793230	+	0.793230i
$624$	−8.24504			−0.330066
$625$	−24.2846	+	5.93782i	−0.971384	+	0.237513i
$626$			16.7675i			0.670164i
$627$	8.49038	−	8.49038i	0.339073	−	0.339073i
$628$	4.73205	+	4.73205i	0.188829	+	0.188829i
$629$	0.656339			0.0261699
$630$	−12.5885	+	14.1962i	−0.501536	+	0.565588i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	2.63896	+	2.63896i	0.104972	+	0.104972i
$633$	6.86800	−	6.86800i	0.272978	−	0.272978i
$634$			6.46410i			0.256722i
$635$	11.7806	−	0.707107i	0.467498	−	0.0280607i
$636$	−12.0000			−0.475831
$637$	3.36603	−	3.36603i	0.133367	−	0.133367i
$638$	7.55154	−	7.55154i	0.298968	−	0.298968i
$639$	−45.9483			−1.81769
$640$	−2.23205	+	0.133975i	−0.0882296	+	0.00529581i
$641$		−	17.9687i		−	0.709720i	−0.934919	−	0.354860i	$-0.884529\pi$
$641$		−	17.9687i		−	0.709720i	0.934919	−	0.354860i	$-0.115471\pi$
$642$	21.2132	+	21.2132i	0.837218	+	0.837218i
$643$	11.6603	+	11.6603i	0.459836	+	0.459836i	0.898601	−	0.438766i	$-0.144584\pi$
$643$	11.6603	+	11.6603i	0.459836	+	0.459836i	−0.438766	+	0.898601i	$0.644584\pi$
$644$	9.79796			0.386094
$645$	14.1962	+	12.5885i	0.558973	+	0.495670i
$646$	−3.00000			−0.118033
$647$	13.7632	+	13.7632i	0.541087	+	0.541087i	0.923848	−	0.382760i	$-0.125027\pi$
$647$	13.7632	+	13.7632i	0.541087	+	0.541087i	−0.382760	+	0.923848i	$0.625027\pi$
$648$	−6.36396	+	6.36396i	−0.250000	+	0.250000i
$649$		−	22.0000i		−	0.863576i
$650$	23.6305	−	2.84701i	0.926865	−	0.111669i
$651$			4.89898i			0.192006i
$652$	−3.36603	+	3.36603i	−0.131824	+	0.131824i
$653$	−2.29719	+	2.29719i	−0.0898958	+	0.0898958i	−0.750625	−	0.660729i	$-0.770247\pi$
$653$	−2.29719	+	2.29719i	−0.0898958	+	0.0898958i	0.660729	+	0.750625i	$0.270247\pi$
$654$			1.85641i			0.0725912i
$655$	−18.3205	+	20.6603i	−0.715841	+	0.807263i
$656$			5.65685i			0.220863i
$657$	−28.3923	+	28.3923i	−1.10769	+	1.10769i
$658$	−0.535898	−	0.535898i	−0.0208915	−	0.0208915i
$659$	−11.3137			−0.440720			−0.220360	−	0.975419i	$-0.570723\pi$
$659$	−11.3137			−0.440720			−0.220360	+	0.975419i	$0.570723\pi$
$660$	8.93357	−	0.536220i	0.347739	−	0.0208724i
$661$	35.1769			1.36822			0.684112	−	0.729377i	$-0.260190\pi$
$661$	35.1769			1.36822			0.684112	+	0.729377i	$0.260190\pi$
$662$	−13.0053	−	13.0053i	−0.505466	−	0.505466i
$663$	−5.83013	−	5.83013i	−0.226423	−	0.226423i
$664$			6.26795i			0.243244i
$665$	1.13681	+	18.9396i	0.0440837	+	0.734445i
$666$		−	1.96902i		−	0.0762978i
$667$	−11.3205	+	11.3205i	−0.438332	+	0.438332i
$668$	−1.13681	+	1.13681i	−0.0439846	+	0.0439846i
$669$	−2.68973			−0.103991
$670$	−0.401924	−	0.356406i	−0.0155277	−	0.0137692i
$671$		−	23.3953i		−	0.903164i
$672$	3.46410	−	3.46410i	0.133631	−	0.133631i
$673$	−15.8038	−	15.8038i	−0.609194	−	0.609194i	0.333542	−	0.942735i	$-0.391756\pi$
$673$	−15.8038	−	15.8038i	−0.609194	−	0.609194i	−0.942735	+	0.333542i	$0.891756\pi$
$674$	−11.1106			−0.427966
$675$	16.0418	−	20.4367i	0.617449	−	0.786611i
$676$	−9.66025			−0.371548
$677$	23.6627	+	23.6627i	0.909431	+	0.909431i	0.996226	−	0.0867950i	$-0.0276625\pi$
$677$	23.6627	+	23.6627i	0.909431	+	0.909431i	−0.0867950	+	0.996226i	$0.527663\pi$
$678$	17.6269	−	17.6269i	0.676957	−	0.676957i
$679$			33.4641i			1.28423i
$680$	−1.67303	−	1.48356i	−0.0641579	−	0.0568921i
$681$	30.9282			1.18517
$682$	1.63397	−	1.63397i	0.0625681	−	0.0625681i
$683$	31.6675	−	31.6675i	1.21172	−	1.21172i	0.241264	−	0.970460i	$-0.422438\pi$
$683$	31.6675	−	31.6675i	1.21172	−	1.21172i	0.970460	−	0.241264i	$-0.0775619\pi$
$684$			9.00000i			0.344124i
$685$	2.80385	+	46.7128i	0.107130	+	1.78480i
$686$		−	16.9706i		−	0.647939i
$687$	29.7864	+	29.7864i	1.13642	+	1.13642i
$688$	−3.46410	−	3.46410i	−0.132068	−	0.132068i
$689$	−32.9802			−1.25644
$690$	−13.3923	+	0.803848i	−0.509836	+	0.0306020i
$691$	−28.3731			−1.07936			−0.539681	−	0.841869i	$-0.681455\pi$
$691$	−28.3731			−1.07936			−0.539681	+	0.841869i	$0.681455\pi$
$692$	−13.1948	−	13.1948i	−0.501591	−	0.501591i
$693$	−13.8647	+	13.8647i	−0.526678	+	0.526678i
$694$			19.3397i			0.734127i
$695$	−33.8024	+	38.1194i	−1.28220	+	1.44595i
$696$			8.00481i			0.303421i
$697$	−4.00000	+	4.00000i	−0.151511	+	0.151511i
$698$	−15.7322	+	15.7322i	−0.595473	+	0.595473i
$699$		−	28.3923i		−	1.07390i
$700$	−8.73205	+	11.1244i	−0.330040	+	0.420461i
$701$		−	4.20548i		−	0.158839i	−0.996841	−	0.0794193i	$-0.974693\pi$
$701$		−	4.20548i		−	0.158839i	0.996841	−	0.0794193i	$-0.0253066\pi$
$702$	−17.4904	+	17.4904i	−0.660132	+	0.660132i
$703$	−1.39230	−	1.39230i	−0.0525118	−	0.0525118i
$704$	−2.31079			−0.0870911
$705$	0.776457	+	0.688524i	0.0292431	+	0.0259313i
$706$	9.19615			0.346102
$707$	−19.7990	−	19.7990i	−0.744618	−	0.744618i
$708$	11.6603	+	11.6603i	0.438219	+	0.438219i
$709$			15.1962i			0.570703i	0.958423	+	0.285352i	$0.0921104\pi$
$709$			15.1962i			0.570703i	−0.958423	+	0.285352i	$0.907890\pi$
$710$	−34.1863	+	2.05197i	−1.28299	+	0.0770091i
$711$	11.1962			0.419889
$712$	−7.00000	+	7.00000i	−0.262336	+	0.262336i
$713$	−2.44949	+	2.44949i	−0.0917341	+	0.0917341i
$714$	4.89898			0.183340
$715$	24.5526	−	1.47372i	0.918214	−	0.0551140i
$716$			4.76028i			0.177900i
$717$	3.12436	−	3.12436i	0.116681	−	0.116681i
$718$	−5.75833	−	5.75833i	−0.214899	−	0.214899i
$719$	40.4302			1.50779			0.753896	−	0.656994i	$-0.228172\pi$
$719$	40.4302			1.50779			0.753896	+	0.656994i	$0.228172\pi$
$720$	−4.45069	+	5.01910i	−0.165867	+	0.187051i
$721$	−21.8564			−0.813975
$722$	−7.07107	−	7.07107i	−0.263158	−	0.263158i
$723$	−20.0764	+	20.0764i	−0.746649	+	0.746649i
$724$		−	12.9282i		−	0.480473i
$725$	−2.76406	−	22.9420i	−0.102654	−	0.852044i
$726$	−9.80385			−0.363855
$727$	−14.5359	+	14.5359i	−0.539107	+	0.539107i	−0.923267	−	0.384160i	$-0.874491\pi$
$727$	−14.5359	+	14.5359i	−0.539107	+	0.539107i	0.384160	+	0.923267i	$0.374491\pi$
$728$	9.52056	−	9.52056i	0.352855	−	0.352855i
$729$			27.0000i			1.00000i
$730$	−19.8564	+	22.3923i	−0.734919	+	0.828776i
$731$		−	4.89898i		−	0.181195i
$732$	12.3998	+	12.3998i	0.458308	+	0.458308i
$733$	1.41154	+	1.41154i	0.0521365	+	0.0521365i	0.732694	−	0.680558i	$-0.238263\pi$
$733$	1.41154	+	1.41154i	0.0521365	+	0.0521365i	−0.680558	+	0.732694i	$0.738263\pi$
$734$	35.1894			1.29887
$735$	−0.232051	−	3.86603i	−0.00855932	−	0.142600i
$736$	3.46410			0.127688
$737$	−0.392541	−	0.392541i	−0.0144594	−	0.0144594i
$738$	12.0000	+	12.0000i	0.441726	+	0.441726i
$739$		−	16.9282i		−	0.622714i	−0.950293	−	0.311357i	$-0.899217\pi$
$739$		−	16.9282i		−	0.622714i	0.950293	−	0.311357i	$-0.100783\pi$
$740$	−0.0879327	−	1.46498i	−0.00323247	−	0.0538538i
$741$			24.7351i			0.908668i
$742$	13.8564	−	13.8564i	0.508685	−	0.508685i
$743$	−24.6980	+	24.6980i	−0.906081	+	0.906081i	−0.995953	−	0.0898726i	$-0.971354\pi$
$743$	−24.6980	+	24.6980i	−0.906081	+	0.906081i	0.0898726	+	0.995953i	$0.471354\pi$
$744$			1.73205i			0.0635001i
$745$	−8.42820	−	7.47372i	−0.308785	−	0.273816i
$746$			25.2528i			0.924570i
$747$	13.2963	+	13.2963i	0.486487	+	0.486487i
$748$	−1.63397	−	1.63397i	−0.0597440	−	0.0597440i
$749$	−48.9898			−1.79005
$750$	11.0227	−	15.9217i	0.402492	−	0.581378i
$751$	−10.3923			−0.379221			−0.189610	−	0.981859i	$-0.560722\pi$
$751$	−10.3923			−0.379221			−0.189610	+	0.981859i	$0.560722\pi$
$752$	−0.189469	−	0.189469i	−0.00690921	−	0.00690921i
$753$	7.39230	+	7.39230i	0.269391	+	0.269391i
$754$			22.0000i			0.801193i
$755$	23.9587	+	21.2454i	0.871946	+	0.773199i
$756$		−	14.6969i		−	0.534522i
$757$	13.3923	−	13.3923i	0.486752	−	0.486752i	−0.420528	−	0.907280i	$-0.638155\pi$
$757$	13.3923	−	13.3923i	0.486752	−	0.486752i	0.907280	+	0.420528i	$0.138155\pi$
$758$	−13.2963	+	13.2963i	−0.482944	+	0.482944i
$759$	−13.8647			−0.503258
$760$	0.401924	+	6.69615i	0.0145793	+	0.242895i
$761$			5.21355i			0.188991i	0.995525	+	0.0944954i	$0.0301238\pi$
$761$			5.21355i			0.188991i	−0.995525	+	0.0944954i	$0.969876\pi$
$762$	−6.46410	+	6.46410i	−0.234170	+	0.234170i
$763$	−2.14359	−	2.14359i	−0.0776033	−	0.0776033i
$764$	−4.52004			−0.163529
$765$	−6.69615	+	0.401924i	−0.242100	+	0.0145316i
$766$	−5.46410			−0.197426
$767$	32.0464	+	32.0464i	1.15713	+	1.15713i
$768$	1.22474	−	1.22474i	0.0441942	−	0.0441942i
$769$		−	50.6410i		−	1.82616i	−0.407779	−	0.913081i	$-0.633696\pi$
$769$		−	50.6410i		−	1.82616i	0.407779	−	0.913081i	$-0.366304\pi$
$770$	−9.69642	+	10.9348i	−0.349435	+	0.394062i
$771$	37.8564			1.36337
$772$	12.3660	−	12.3660i	0.445063	−	0.445063i
$773$	−7.72741	+	7.72741i	−0.277935	+	0.277935i	−0.832284	−	0.554349i	$-0.812967\pi$
$773$	−7.72741	+	7.72741i	−0.277935	+	0.277935i	0.554349	+	0.832284i	$0.312967\pi$
$774$	−14.6969			−0.528271
$775$	−0.598076	−	4.96410i	−0.0214835	−	0.178316i
$776$			11.8313i			0.424721i
$777$	2.27362	+	2.27362i	0.0815658	+	0.0815658i
$778$	4.19615	+	4.19615i	0.150439	+	0.150439i
$779$	16.9706			0.608034
$780$	−12.2321	+	13.7942i	−0.437978	+	0.493913i
$781$	−35.3923			−1.26644
$782$	2.44949	+	2.44949i	0.0875936	+	0.0875936i
$783$	16.9808	+	16.9808i	0.606843	+	0.606843i
$784$			1.00000i			0.0357143i
$785$	14.9372	−	0.896575i	0.533131	−	0.0320002i
$786$		−	21.3891i		−	0.762923i
$787$	19.1244	−	19.1244i	0.681710	−	0.681710i	−0.278676	−	0.960385i	$-0.589895\pi$
$787$	19.1244	−	19.1244i	0.681710	−	0.681710i	0.960385	+	0.278676i	$0.0898954\pi$
$788$	−13.2827	+	13.2827i	−0.473177	+	0.473177i
$789$			38.5359i			1.37191i
$790$	8.33013	−	0.500000i	0.296373	−	0.0177892i
$791$			40.7076i			1.44740i
$792$	−4.90192	+	4.90192i	−0.174182	+	0.174182i
$793$	34.0788	+	34.0788i	1.21018	+	1.21018i
$794$	38.9144			1.38102
$795$	−17.8028	+	20.0764i	−0.631399	+	0.712036i
$796$	3.39230			0.120237
$797$	−18.1817	−	18.1817i	−0.644029	−	0.644029i	0.307514	−	0.951543i	$-0.400503\pi$
$797$	−18.1817	−	18.1817i	−0.644029	−	0.644029i	−0.951543	+	0.307514i	$0.900503\pi$
$798$	−10.3923	−	10.3923i	−0.367884	−	0.367884i
$799$		−	0.267949i		−	0.00947936i
$800$	−3.08725	+	3.93305i	−0.109151	+	0.139054i
$801$			29.6985i			1.04934i
$802$	9.56218	−	9.56218i	0.337652	−	0.337652i
$803$	−21.8695	+	21.8695i	−0.771759	+	0.771759i
$804$	0.416102			0.0146748
$805$	14.5359	−	16.3923i	0.512323	−	0.577753i
$806$			4.76028i			0.167674i
$807$	11.3205	−	11.3205i	0.398501	−	0.398501i
$808$	−7.00000	−	7.00000i	−0.246259	−	0.246259i
$809$	−35.1894			−1.23719			−0.618597	−	0.785708i	$-0.712299\pi$
$809$	−35.1894			−1.23719			−0.618597	+	0.785708i	$0.712299\pi$
$810$	1.20577	+	20.0885i	0.0423665	+	0.705836i
$811$	38.3923			1.34814			0.674068	−	0.738669i	$-0.264545\pi$
$811$	38.3923			1.34814			0.674068	+	0.738669i	$0.264545\pi$
$812$	−9.24316	−	9.24316i	−0.324371	−	0.324371i
$813$	−31.3393	+	31.3393i	−1.09912	+	1.09912i
$814$		−	1.51666i		−	0.0531589i
$815$	0.637756	+	10.6252i	0.0223396	+	0.372184i
$816$	1.73205			0.0606339
$817$	−10.3923	+	10.3923i	−0.363581	+	0.363581i
$818$	−20.6312	+	20.6312i	−0.721353	+	0.721353i
$819$		−	40.3923i		−	1.41142i
$820$	9.46410	+	8.39230i	0.330501	+	0.293072i
$821$		−	41.6685i		−	1.45424i	−0.686509	−	0.727121i	$-0.740858\pi$
$821$		−	41.6685i		−	1.45424i	0.686509	−	0.727121i	$-0.259142\pi$
$822$	−25.6317	−	25.6317i	−0.894009	−	0.894009i
$823$	2.56218	+	2.56218i	0.0893119	+	0.0893119i	0.750351	−	0.661039i	$-0.229884\pi$
$823$	2.56218	+	2.56218i	0.0893119	+	0.0893119i	−0.661039	+	0.750351i	$0.729884\pi$
$824$	−7.72741			−0.269197
$825$	12.3564	−	15.7417i	0.430195	−	0.548055i
$826$	−26.9282			−0.936952
$827$	16.2635	+	16.2635i	0.565536	+	0.565536i	0.930875	−	0.365339i	$-0.119047\pi$
$827$	16.2635	+	16.2635i	0.565536	+	0.565536i	−0.365339	+	0.930875i	$0.619047\pi$
$828$	7.34847	−	7.34847i	0.255377	−	0.255377i
$829$		−	37.0718i		−	1.28756i	−0.765212	−	0.643778i	$-0.777366\pi$
$829$		−	37.0718i		−	1.28756i	0.765212	−	0.643778i	$-0.222634\pi$
$830$	10.4865	+	9.29890i	0.363991	+	0.322770i
$831$		−	36.1504i		−	1.25404i
$832$	3.36603	−	3.36603i	0.116696	−	0.116696i
$833$	−0.707107	+	0.707107i	−0.0244998	+	0.0244998i
$834$		−	39.4641i		−	1.36653i
$835$	0.215390	+	3.58846i	0.00745389	+	0.124184i
$836$			6.93237i			0.239761i
$837$	3.67423	+	3.67423i	0.127000	+	0.127000i
$838$	−22.5885	−	22.5885i	−0.780305	−	0.780305i
$839$	48.2591			1.66609			0.833045	−	0.553205i	$-0.186595\pi$
$839$	48.2591			1.66609			0.833045	+	0.553205i	$0.186595\pi$
$840$	−0.656339	−	10.9348i	−0.0226458	−	0.377285i
$841$	−7.64102			−0.263483
$842$	−3.48477	−	3.48477i	−0.120093	−	0.120093i
$843$	12.2487	+	12.2487i	0.421868	+	0.421868i
$844$			5.60770i			0.193025i
$845$	−14.3316	+	16.1619i	−0.493022	+	0.555987i
$846$	−0.803848			−0.0276368
$847$	11.3205	−	11.3205i	0.388977	−	0.388977i
$848$	4.89898	−	4.89898i	0.168232	−	0.168232i
$849$	12.0072			0.412086
$850$	−4.96410	+	0.598076i	−0.170267	+	0.0205138i
$851$			2.27362i			0.0779388i
$852$	18.7583	−	18.7583i	0.642650	−	0.642650i
$853$	−12.1962	−	12.1962i	−0.417588	−	0.417588i	0.466783	−	0.884372i	$-0.345413\pi$
$853$	−12.1962	−	12.1962i	−0.417588	−	0.417588i	−0.884372	+	0.466783i	$0.845413\pi$
$854$	−28.6360			−0.979904
$855$	15.0573	+	13.3521i	0.514949	+	0.456631i
$856$	−17.3205			−0.592003
$857$	21.8695	+	21.8695i	0.747049	+	0.747049i	0.973924	−	0.226875i	$-0.0728508\pi$
$857$	21.8695	+	21.8695i	0.747049	+	0.747049i	−0.226875	+	0.973924i	$0.572851\pi$
$858$	−13.4722	+	13.4722i	−0.459933	+	0.459933i
$859$		−	24.6410i		−	0.840741i	−0.907353	−	0.420370i	$-0.861900\pi$
$859$		−	24.6410i		−	0.840741i	0.907353	−	0.420370i	$-0.138100\pi$
$860$	−10.9348	+	0.656339i	−0.372873	+	0.0223810i
$861$	−27.7128			−0.944450
$862$	−20.5167	+	20.5167i	−0.698800	+	0.698800i
$863$	−20.5569	+	20.5569i	−0.699764	+	0.699764i	−0.964359	−	0.264596i	$-0.914762\pi$
$863$	−20.5569	+	20.5569i	−0.699764	+	0.699764i	0.264596	+	0.964359i	$0.414762\pi$
$864$		−	5.19615i		−	0.176777i
$865$	−41.6506	+	2.50000i	−1.41616	+	0.0850026i
$866$		−	31.6675i		−	1.07611i
$867$	−19.5959	−	19.5959i	−0.665512	−	0.665512i
$868$	−2.00000	−	2.00000i	−0.0678844	−	0.0678844i
$869$	8.62398			0.292549
$870$	13.3923	+	11.8756i	0.454042	+	0.402622i
$871$	1.14359			0.0387492
$872$	−0.757875	−	0.757875i	−0.0256649	−	0.0256649i
$873$	25.0981	+	25.0981i	0.849441	+	0.849441i
$874$		−	10.3923i		−	0.351525i
$875$	5.65685	+	31.1127i	0.191237	+	1.05180i
$876$		−	23.1822i		−	0.783255i
$877$	14.7321	−	14.7321i	0.497466	−	0.497466i	−0.413182	−	0.910648i	$-0.635583\pi$
$877$	14.7321	−	14.7321i	0.497466	−	0.497466i	0.910648	+	0.413182i	$0.135583\pi$
$878$	−7.07107	+	7.07107i	−0.238637	+	0.238637i
$879$			44.7846i			1.51055i
$880$	−3.42820	+	3.86603i	−0.115565	+	0.130324i
$881$			45.7725i			1.54211i	0.636766	+	0.771057i	$0.280272\pi$
$881$			45.7725i			1.54211i	−0.636766	+	0.771057i	$0.719728\pi$
$882$	2.12132	+	2.12132i	0.0714286	+	0.0714286i
$883$	4.73205	+	4.73205i	0.159246	+	0.159246i	0.782233	−	0.622986i	$-0.214081\pi$
$883$	4.73205	+	4.73205i	0.159246	+	0.159246i	−0.622986	+	0.782233i	$0.714081\pi$
$884$	4.76028			0.160106
$885$	36.8067	−	2.20925i	1.23724	−	0.0742632i
$886$	32.9282			1.10624
$887$	−13.2084	−	13.2084i	−0.443495	−	0.443495i	0.449690	−	0.893185i	$-0.351534\pi$
$887$	−13.2084	−	13.2084i	−0.443495	−	0.443495i	−0.893185	+	0.449690i	$0.851534\pi$
$888$	0.803848	+	0.803848i	0.0269754	+	0.0269754i
$889$		−	14.9282i		−	0.500676i
$890$	1.32628	+	22.0962i	0.0444570	+	0.740665i
$891$			20.7971i			0.696729i
$892$	1.09808	−	1.09808i	0.0367663	−	0.0367663i
$893$	−0.568406	+	0.568406i	−0.0190210	+	0.0190210i
$894$	8.72552			0.291825
$895$	7.96410	+	7.06218i	0.266211	+	0.236063i
$896$			2.82843i			0.0944911i
$897$	20.1962	−	20.1962i	0.674330	−	0.674330i
$898$	−10.5622	−	10.5622i	−0.352464	−	0.352464i
$899$	4.62158			0.154138
$900$	1.79423	+	14.8923i	0.0598076	+	0.496410i
$901$	6.92820			0.230812
$902$	9.24316	+	9.24316i	0.307763	+	0.307763i
$903$	16.9706	−	16.9706i	0.564745	−	0.564745i
$904$			14.3923i			0.478681i
$905$	−21.6293	−	19.1798i	−0.718982	−	0.637559i
$906$	−24.8038			−0.824053
$907$	39.7583	−	39.7583i	1.32015	−	1.32015i	0.406505	−	0.913648i	$-0.366747\pi$
$907$	39.7583	−	39.7583i	1.32015	−	1.32015i	0.913648	−	0.406505i	$-0.133253\pi$
$908$	−12.6264	+	12.6264i	−0.419021	+	0.419021i
$909$	−29.6985			−0.985037
$910$	−1.80385	−	30.0526i	−0.0597970	−	0.996233i
$911$		−	23.7370i		−	0.786443i	−0.919444	−	0.393221i	$-0.871361\pi$
$911$		−	23.7370i		−	0.786443i	0.919444	−	0.393221i	$-0.128639\pi$
$912$	−3.67423	−	3.67423i	−0.121666	−	0.121666i
$913$	10.2417	+	10.2417i	0.338950	+	0.338950i
$914$	−11.5911			−0.383400
$915$	39.1410	−	2.34936i	1.29396	−	0.0776676i
$916$	−24.3205			−0.803572
$917$	24.6980	+	24.6980i	0.815599	+	0.815599i
$918$	3.67423	−	3.67423i	0.121268	−	0.121268i
$919$		−	11.4641i		−	0.378166i	−0.981961	−	0.189083i	$-0.939449\pi$
$919$		−	11.4641i		−	0.378166i	0.981961	−	0.189083i	$-0.0605515\pi$
$920$	5.13922	−	5.79555i	0.169435	−	0.191074i
$921$			47.9817i			1.58105i
$922$	−19.2679	+	19.2679i	−0.634556	+	0.634556i
$923$	51.5544	−	51.5544i	1.69693	−	1.69693i
$924$		−	11.3205i		−	0.372417i
$925$	−2.58142	−	2.02628i	−0.0848764	−	0.0666237i
$926$		−	33.8024i		−	1.11082i
$927$	−16.3923	+	16.3923i	−0.538394	+	0.538394i
$928$	−3.26795	−	3.26795i	−0.107276	−	0.107276i
$929$	3.48477			0.114331			0.0571657	−	0.998365i	$-0.481794\pi$
$929$	3.48477			0.114331			0.0571657	+	0.998365i	$0.481794\pi$
$930$	2.89778	+	2.56961i	0.0950219	+	0.0842608i
$931$	3.00000			0.0983210
$932$	11.5911	+	11.5911i	0.379679	+	0.379679i
$933$	−11.8301	−	11.8301i	−0.387301	−	0.387301i
$934$		−	8.78461i		−	0.287441i
$935$	−5.15780	+	0.309587i	−0.168678	+	0.0101246i
$936$		−	14.2808i		−	0.466784i
$937$	22.3468	−	22.3468i	0.730038	−	0.730038i	−0.240589	−	0.970627i	$-0.577341\pi$
$937$	22.3468	−	22.3468i	0.730038	−	0.730038i	0.970627	+	0.240589i	$0.0773407\pi$
$938$	−0.480473	+	0.480473i	−0.0156880	+	0.0156880i
$939$	−29.0421			−0.947755
$940$	−0.598076	+	0.0358984i	−0.0195071	+	0.00117088i
$941$		−	13.8647i		−	0.451977i	−0.974130	−	0.225989i	$-0.927439\pi$
$941$		−	13.8647i		−	0.451977i	0.974130	−	0.225989i	$-0.0725612\pi$
$942$	−8.19615	+	8.19615i	−0.267045	+	0.267045i
$943$	−13.8564	−	13.8564i	−0.451227	−	0.451227i
$944$	−9.52056			−0.309868
$945$	−24.5885	−	21.8038i	−0.799863	−	0.709279i
$946$	−11.3205			−0.368061
$947$	9.95026	+	9.95026i	0.323340	+	0.323340i	0.850047	−	0.526707i	$-0.176573\pi$
$947$	9.95026	+	9.95026i	0.323340	+	0.323340i	−0.526707	+	0.850047i	$0.676573\pi$
$948$	−4.57081	+	4.57081i	−0.148453	+	0.148453i
$949$		−	63.7128i		−	2.06821i
$950$	11.7992	+	9.26174i	0.382815	+	0.300490i
$951$	−11.1962			−0.363060
$952$	−2.00000	+	2.00000i	−0.0648204	+	0.0648204i
$953$	−40.2407	+	40.2407i	−1.30352	+	1.30352i	−0.377525	+	0.925999i	$0.623225\pi$
$953$	−40.2407	+	40.2407i	−1.30352	+	1.30352i	−0.925999	+	0.377525i	$0.876775\pi$
$954$		−	20.7846i		−	0.672927i
$955$	−6.70577	+	7.56218i	−0.216994	+	0.244706i
$956$			2.55103i			0.0825061i
$957$	13.0797	+	13.0797i	0.422805	+	0.422805i
$958$	17.8827	+	17.8827i	0.577763	+	0.577763i
$959$	59.1939			1.91147
$960$	−0.232051	−	3.86603i	−0.00748941	−	0.124775i
$961$	1.00000			0.0322581
$962$	2.20925	+	2.20925i	0.0712292	+	0.0712292i
$963$	−36.7423	+	36.7423i	−1.18401	+	1.18401i
$964$		−	16.3923i		−	0.527961i
$965$	−2.34297	−	39.0346i	−0.0754230	−	1.25657i
$966$			16.9706i			0.546019i
$967$	39.4186	−	39.4186i	1.26762	−	1.26762i	0.320300	−	0.947316i	$-0.396216\pi$
$967$	39.4186	−	39.4186i	1.26762	−	1.26762i	0.947316	−	0.320300i	$-0.103784\pi$
$968$	4.00240	−	4.00240i	0.128642	−	0.128642i
$969$		−	5.19615i		−	0.166924i
$970$	19.7942	+	17.5526i	0.635554	+	0.563579i
$971$		−	53.0566i		−	1.70267i	−0.524625	−	0.851333i	$-0.675795\pi$
$971$		−	53.0566i		−	1.70267i	0.524625	−	0.851333i	$-0.324205\pi$
$972$	−11.0227	−	11.0227i	−0.353553	−	0.353553i
$973$	45.5692	+	45.5692i	1.46088	+	1.46088i
$974$	12.9682			0.415527
$975$	4.93117	+	40.9292i	0.157924	+	1.31078i
$976$	−10.1244			−0.324073
$977$	1.61729	+	1.61729i	0.0517415	+	0.0517415i	0.732504	−	0.680763i	$-0.238351\pi$
$977$	1.61729	+	1.61729i	0.0517415	+	0.0517415i	−0.680763	+	0.732504i	$0.738351\pi$
$978$	−5.83013	−	5.83013i	−0.186427	−	0.186427i
$979$			22.8756i			0.731109i
$980$	1.67303	+	1.48356i	0.0534431	+	0.0473907i
$981$	−3.21539			−0.102660
$982$	11.7321	−	11.7321i	0.374385	−	0.374385i
$983$	−15.3533	+	15.3533i	−0.489693	+	0.489693i	−0.908209	−	0.418516i	$-0.862550\pi$
$983$	−15.3533	+	15.3533i	−0.489693	+	0.489693i	0.418516	+	0.908209i	$0.362550\pi$
$984$	−9.79796			−0.312348
$985$	2.51666	+	41.9282i	0.0801875	+	1.33594i
$986$		−	4.62158i		−	0.147181i
$987$	0.928203	−	0.928203i	0.0295450	−	0.0295450i
$988$	−10.0981	−	10.0981i	−0.321263	−	0.321263i
$989$	16.9706			0.539633
$990$	0.928761	+	15.4734i	0.0295180	+	0.491777i
$991$	−16.5359			−0.525280			−0.262640	−	0.964894i	$-0.584593\pi$
$991$	−16.5359			−0.525280			−0.262640	+	0.964894i	$0.584593\pi$
$992$	−0.707107	−	0.707107i	−0.0224507	−	0.0224507i
$993$	22.5259	−	22.5259i	0.714837	−	0.714837i
$994$			43.3205i			1.37404i
$995$	5.03270	−	5.67544i	0.159547	−	0.179923i
$996$	−10.8564			−0.343998
$997$	−4.73205	+	4.73205i	−0.149866	+	0.149866i	−0.778058	−	0.628192i	$-0.783795\pi$
$997$	−4.73205	+	4.73205i	−0.149866	+	0.149866i	0.628192	+	0.778058i	$0.283795\pi$
$998$	1.51575	−	1.51575i	0.0479802	−	0.0479802i
$999$	3.41044			0.107901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.e.683.2	yes	8
3.2	odd	2	inner	930.2.j.e.683.3	yes	8
5.2	odd	4	inner	930.2.j.e.497.3	yes	8
15.2	even	4	inner	930.2.j.e.497.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.e.497.2	✓	8	15.2	even	4	inner
930.2.j.e.497.3	yes	8	5.2	odd	4	inner
930.2.j.e.683.2	yes	8	1.1	even	1	trivial
930.2.j.e.683.3	yes	8	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} +(1.67303 + 1.48356i) q^{5} -1.73205 q^{6} +(2.00000 - 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(-0.133975 - 2.23205i) q^{10} -2.31079i q^{11} +(1.22474 + 1.22474i) q^{12} +(3.36603 + 3.36603i) q^{13} -2.82843 q^{14} +(3.86603 - 0.232051i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(-2.12132 + 2.12132i) q^{18} +3.00000i q^{19} +(-1.48356 + 1.67303i) q^{20} -4.89898i q^{21} +(-1.63397 + 1.63397i) q^{22} +(2.44949 - 2.44949i) q^{23} -1.73205i q^{24} +(0.598076 + 4.96410i) q^{25} -4.76028i q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.00000 + 2.00000i) q^{28} -4.62158 q^{29} +(-2.89778 - 2.56961i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.83013 - 2.83013i) q^{33} +1.00000i q^{34} +(6.31319 - 0.378937i) q^{35} +3.00000 q^{36} +(-0.464102 + 0.464102i) q^{37} +(2.12132 - 2.12132i) q^{38} +8.24504 q^{39} +(2.23205 - 0.133975i) q^{40} -5.65685i q^{41} +(-3.46410 + 3.46410i) q^{42} +(3.46410 + 3.46410i) q^{43} +2.31079 q^{44} +(4.45069 - 5.01910i) q^{45} -3.46410 q^{46} +(0.189469 + 0.189469i) q^{47} +(-1.22474 + 1.22474i) q^{48} -1.00000i q^{49} +(3.08725 - 3.93305i) q^{50} -1.73205 q^{51} +(-3.36603 + 3.36603i) q^{52} +(-4.89898 + 4.89898i) q^{53} +5.19615i q^{54} +(3.42820 - 3.86603i) q^{55} -2.82843i q^{56} +(3.67423 + 3.67423i) q^{57} +(3.26795 + 3.26795i) q^{58} +9.52056 q^{59} +(0.232051 + 3.86603i) q^{60} +10.1244 q^{61} +(0.707107 + 0.707107i) q^{62} +(-6.00000 - 6.00000i) q^{63} -1.00000i q^{64} +(0.637756 + 10.6252i) q^{65} +4.00240i q^{66} +(0.169873 - 0.169873i) q^{67} +(0.707107 - 0.707107i) q^{68} -6.00000i q^{69} +(-4.73205 - 4.19615i) q^{70} -15.3161i q^{71} +(-2.12132 - 2.12132i) q^{72} +(-9.46410 - 9.46410i) q^{73} +0.656339 q^{74} +(6.81225 + 5.34727i) q^{75} -3.00000 q^{76} +(-4.62158 - 4.62158i) q^{77} +(-5.83013 - 5.83013i) q^{78} +3.73205i q^{79} +(-1.67303 - 1.48356i) q^{80} -9.00000 q^{81} +(-4.00000 + 4.00000i) q^{82} +(-4.43211 + 4.43211i) q^{83} +4.89898 q^{84} +(-0.133975 - 2.23205i) q^{85} -4.89898i q^{86} +(-5.66025 + 5.66025i) q^{87} +(-1.63397 - 1.63397i) q^{88} -9.89949 q^{89} +(-6.69615 + 0.401924i) q^{90} +13.4641 q^{91} +(2.44949 + 2.44949i) q^{92} +(-1.22474 + 1.22474i) q^{93} -0.267949i q^{94} +(-4.45069 + 5.01910i) q^{95} +1.73205 q^{96} +(-8.36603 + 8.36603i) q^{97} +(-0.707107 + 0.707107i) q^{98} -6.93237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} - 8 q^{10} + 20 q^{13} + 24 q^{15} - 8 q^{16} - 20 q^{22} - 16 q^{25} + 16 q^{28} - 8 q^{31} + 12 q^{33} + 24 q^{36} + 24 q^{37} + 4 q^{40} - 20 q^{52} - 28 q^{55} + 40 q^{58} - 12 q^{60}+ \cdots - 60 q^{97}+O(q^{100}) \) 8 * q + 16 * q^7 - 8 * q^10 + 20 * q^13 + 24 * q^15 - 8 * q^16 - 20 * q^22 - 16 * q^25 + 16 * q^28 - 8 * q^31 + 12 * q^33 + 24 * q^36 + 24 * q^37 + 4 * q^40 - 20 * q^52 - 28 * q^55 + 40 * q^58 - 12 * q^60 - 16 * q^61 - 48 * q^63 + 36 * q^67 - 24 * q^70 - 48 * q^73 - 24 * q^76 - 12 * q^78 - 72 * q^81 - 32 * q^82 - 8 * q^85 + 24 * q^87 - 20 * q^88 - 12 * q^90 + 80 * q^91 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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