LMFDB - Embedded newform 930.2.j.e.497.3

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			497.3
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.e.683.3

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−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	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	3.36603	−	3.36603i	0.933567	−	0.933567i	0.997927	+	0.0643593i	$0.0205004\pi$
$14$	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	$-0.711304\pi$
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	0.787638	+	0.616139i	$0.211304\pi$
$18$	2.12132	+	2.12132i	0.500000	+	0.500000i
$19$		−	3.00000i		−	0.688247i	−0.938924	−	0.344124i	$-0.888176\pi$
$19$		−	3.00000i		−	0.688247i	0.938924	−	0.344124i	$-0.111824\pi$
$20$	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	$-0.367618\pi$
$23$	−2.44949	−	2.44949i	−0.510754	−	0.510754i	−0.914757	+	0.404004i	$0.867618\pi$
$24$			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	$-0.358830\pi$
$29$	4.62158			0.858206			0.429103	+	0.903256i	$0.358830\pi$
$30$	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	0.667928	−	0.744226i	$-0.267181\pi$
$37$	−0.464102	−	0.464102i	−0.0762978	−	0.0762978i	−0.744226	+	0.667928i	$0.767181\pi$
$38$	−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	−0.391786	−	0.920056i	$-0.628143\pi$
$43$	3.46410	−	3.46410i	0.528271	−	0.528271i	0.920056	+	0.391786i	$0.128143\pi$
$44$	−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	$-0.756221\pi$
$47$	−0.189469	+	0.189469i	−0.0276368	+	0.0276368i	0.693153	+	0.720790i	$0.256221\pi$
$48$	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	$-0.0921474\pi$
$53$	4.89898	+	4.89898i	0.672927	+	0.672927i	−0.285463	+	0.958390i	$0.592147\pi$
$54$		−	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	$-0.712760\pi$
$59$	−9.52056			−1.23947			−0.619736	+	0.784811i	$0.712760\pi$
$60$	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	0.717407	−	0.696654i	$-0.245329\pi$
$67$	0.169873	+	0.169873i	0.0207533	+	0.0207533i	−0.696654	+	0.717407i	$0.745329\pi$
$68$	−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	−0.114236	+	0.993454i	$0.536442\pi$
$73$	−9.46410	+	9.46410i	−1.10769	+	1.10769i	−0.993454	+	0.114236i	$0.963558\pi$
$74$	−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	$-0.932672\pi$
$79$		−	3.73205i		−	0.419889i	0.977713	−	0.209944i	$-0.0673283\pi$
$80$	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	$-0.138219\pi$
$83$	4.43211	+	4.43211i	0.486487	+	0.486487i	−0.420709	+	0.907196i	$0.638219\pi$
$84$	−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	$-0.324188\pi$
$89$	9.89949			1.04934			0.524672	+	0.851304i	$0.324188\pi$
$90$	−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	0.140622	−	0.990063i	$-0.455090\pi$
$97$	−8.36603	−	8.36603i	−0.849441	−	0.849441i	−0.990063	+	0.140622i	$0.955090\pi$
$98$	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	−0.923057	−	0.384663i	$-0.874318\pi$
$103$	−5.46410	+	5.46410i	−0.538394	+	0.538394i	0.384663	+	0.923057i	$0.374318\pi$
$104$	−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	0.205308	−	0.978697i	$-0.434180\pi$
$107$	12.2474	−	12.2474i	1.18401	−	1.18401i	0.978697	−	0.205308i	$-0.0658197\pi$
$108$	−3.67423	−	3.67423i	−0.353553	−	0.353553i
$109$			1.07180i			0.102660i	0.998682	+	0.0513298i	$0.0163460\pi$
$109$			1.07180i			0.102660i	−0.998682	+	0.0513298i	$0.983654\pi$
$110$	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	$-0.0132983\pi$
$113$	10.1769	+	10.1769i	0.957362	+	0.957362i	−0.0417656	+	0.999127i	$0.513298\pi$
$114$			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	0.853029	−	0.521863i	$-0.174763\pi$
$127$	3.73205	+	3.73205i	0.331166	+	0.331166i	−0.521863	+	0.853029i	$0.674763\pi$
$128$	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	−0.315340	+	0.948979i	$0.602119\pi$
$137$	−14.7985	+	14.7985i	−1.26432	+	1.26432i	−0.948979	+	0.315340i	$0.897881\pi$
$138$	4.24264	+	4.24264i	0.361158	+	0.361158i
$139$		−	22.7846i		−	1.93257i	−0.257484	−	0.966283i	$-0.582893\pi$
$139$		−	22.7846i		−	1.93257i	0.257484	−	0.966283i	$-0.417107\pi$
$140$	−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	$-0.433841\pi$
$149$	5.03768			0.412703			0.206351	+	0.978478i	$0.433841\pi$
$150$	−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	0.870257	−	0.492598i	$-0.163953\pi$
$157$	4.73205	+	4.73205i	0.377659	+	0.377659i	−0.492598	+	0.870257i	$0.663953\pi$
$158$	−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	−0.562887	−	0.826534i	$-0.690309\pi$
$163$	3.36603	−	3.36603i	0.263647	−	0.263647i	0.826534	+	0.562887i	$0.190309\pi$
$164$	−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	$-0.769813\pi$
$167$	−1.13681	+	1.13681i	−0.0879692	+	0.0879692i	0.661753	+	0.749722i	$0.269813\pi$
$168$	−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	0.999995	+	0.00318655i	$0.00101431\pi$
$173$	13.1948	+	13.1948i	1.00318	+	1.00318i	0.00318655	+	0.999995i	$0.498986\pi$
$174$	−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	$-0.556930\pi$
$179$	−4.76028			−0.355800			−0.177900	+	0.984049i	$0.556930\pi$
$180$	−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	−0.994534	−	0.104409i	$-0.966705\pi$
$193$	−12.3660	+	12.3660i	−0.890126	+	0.890126i	0.104409	+	0.994534i	$0.466705\pi$
$194$	−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	$-0.983352\pi$
$197$	−13.2827	+	13.2827i	−0.946355	+	0.946355i	0.0522776	+	0.998633i	$0.483352\pi$
$198$	4.90192	−	4.90192i	0.348365	−	0.348365i
$199$			3.39230i			0.240474i	0.992745	+	0.120237i	$0.0383655\pi$
$199$			3.39230i			0.240474i	−0.992745	+	0.120237i	$0.961635\pi$
$200$	−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	−0.742917	−	0.669384i	$-0.766558\pi$
$223$	−1.09808	+	1.09808i	−0.0735326	+	0.0735326i	0.669384	+	0.742917i	$0.266558\pi$
$224$	−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	$-0.951893\pi$
$227$	−12.6264	+	12.6264i	−0.838043	+	0.838043i	0.150558	+	0.988601i	$0.451893\pi$
$228$	3.67423	+	3.67423i	0.243332	+	0.243332i
$229$		−	24.3205i		−	1.60714i	−0.595207	−	0.803572i	$-0.702930\pi$
$229$		−	24.3205i		−	1.60714i	0.595207	−	0.803572i	$-0.297070\pi$
$230$	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	$-0.430423\pi$
$233$	−11.5911	−	11.5911i	−0.759359	−	0.759359i	−0.976206	+	0.216847i	$0.930423\pi$
$234$	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	$-0.526292\pi$
$239$	−2.55103			−0.165012			−0.0825061	+	0.996591i	$0.526292\pi$
$240$	−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	$-0.988751\pi$
$257$	−15.4548	+	15.4548i	−0.964045	+	0.964045i	0.0353309	+	0.999376i	$0.488751\pi$
$258$	−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	$-0.00938373\pi$
$263$	15.7322	+	15.7322i	0.970090	+	0.970090i	−0.0294756	+	0.999566i	$0.509384\pi$
$264$	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	$-0.590926\pi$
$269$	−9.24316			−0.563565			−0.281783	+	0.959478i	$0.590926\pi$
$270$	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	0.994209	−	0.107467i	$-0.0342739\pi$
$277$	14.7583	+	14.7583i	0.886742	+	0.886742i	−0.107467	+	0.994209i	$0.534274\pi$
$278$	−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	−0.546240	−	0.837629i	$-0.683941\pi$
$283$	4.90192	−	4.90192i	0.291389	−	0.291389i	0.837629	+	0.546240i	$0.183941\pi$
$284$	−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	0.997504	+	0.0706146i	$0.0224961\pi$
$293$	18.2832	+	18.2832i	1.06812	+	1.06812i	0.0706146	+	0.997504i	$0.477504\pi$
$294$		−	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	−0.992039	−	0.125934i	$-0.959807\pi$
$307$	−19.5885	−	19.5885i	−1.11797	−	1.11797i	−0.125934	−	0.992039i	$-0.540193\pi$
$308$	−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	−0.957754	−	0.287590i	$-0.907146\pi$
$313$	−11.8564	+	11.8564i	−0.670164	+	0.670164i	0.287590	+	0.957754i	$0.407146\pi$
$314$	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	$-0.691895\pi$
$317$	4.57081	−	4.57081i	0.256722	−	0.256722i	0.823720	+	0.566997i	$0.191895\pi$
$318$	−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	0.887935	−	0.459969i	$-0.152140\pi$
$337$	7.85641	+	7.85641i	0.427966	+	0.427966i	−0.459969	+	0.887935i	$0.652140\pi$
$338$	−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	$-0.576265\pi$
$347$	13.6753	−	13.6753i	0.734127	−	0.734127i	0.971435	+	0.237308i	$0.0762650\pi$
$348$	−5.66025	+	5.66025i	−0.303421	+	0.303421i
$349$			22.2487i			1.19095i	0.803375	+	0.595473i	$0.203035\pi$
$349$			22.2487i			1.19095i	−0.803375	+	0.595473i	$0.796965\pi$
$350$	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	$-0.171300\pi$
$353$	6.50266	+	6.50266i	0.346102	+	0.346102i	−0.512554	+	0.858655i	$0.671300\pi$
$354$	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	$-0.568942\pi$
$359$	−8.14351			−0.429798			−0.214899	+	0.976636i	$0.568942\pi$
$360$	−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	−0.929142	−	0.369724i	$-0.879452\pi$
$367$	−24.8827	−	24.8827i	−1.29887	−	1.29887i	−0.369724	−	0.929142i	$-0.620548\pi$
$368$	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	−0.997348	−	0.0727785i	$-0.976813\pi$
$373$	−17.8564	+	17.8564i	−0.924570	+	0.924570i	0.0727785	+	0.997348i	$0.476813\pi$
$374$	−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	$0.160433\pi$
$379$			18.8038i			0.965889i	−0.875651	+	0.482944i	$0.839567\pi$
$380$	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	$-0.294582\pi$
$383$	−3.86370	−	3.86370i	−0.197426	−	0.197426i	−0.798896	+	0.601470i	$0.794582\pi$
$384$		−	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	$-0.451931\pi$
$389$	5.93426			0.300879			0.150439	+	0.988619i	$0.451931\pi$
$390$	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	−0.842809	−	0.538212i	$-0.819100\pi$
$397$	−27.5167	−	27.5167i	−1.38102	−	1.38102i	−0.538212	−	0.842809i	$-0.680900\pi$
$398$	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	$0.256479\pi$
$409$			29.1769i			1.44271i	−0.692568	+	0.721353i	$0.743521\pi$
$410$	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	$-0.784936\pi$
$419$	−31.9449			−1.56061			−0.780305	+	0.625399i	$0.784936\pi$
$420$	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	0.0792508	−	0.996855i	$-0.474747\pi$
$433$	22.3923	−	22.3923i	1.07611	−	1.07611i	0.996855	−	0.0792508i	$-0.0252528\pi$
$434$	−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	$0.0767006\pi$
$439$			10.0000i			0.477274i	−0.971109	+	0.238637i	$0.923299\pi$
$440$	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	0.993640	+	0.112605i	$0.0359194\pi$
$443$	23.2838	+	23.2838i	1.10624	+	1.10624i	0.112605	+	0.993640i	$0.464081\pi$
$444$	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	$-0.614656\pi$
$449$	−14.9372			−0.704929			−0.352464	+	0.935825i	$0.614656\pi$
$450$	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	0.872325	−	0.488926i	$-0.162611\pi$
$457$	8.19615	+	8.19615i	0.383400	+	0.383400i	−0.488926	+	0.872325i	$0.662611\pi$
$458$	−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	0.117776	−	0.993040i	$-0.462423\pi$
$463$	23.9019	−	23.9019i	1.11082	−	1.11082i	0.993040	−	0.117776i	$-0.0375766\pi$
$464$	−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	$-0.815151\pi$
$467$	−6.21166	+	6.21166i	−0.287441	+	0.287441i	0.548626	+	0.836068i	$0.315151\pi$
$468$	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	$-0.303926\pi$
$479$	25.2899			1.15553			0.577763	+	0.816204i	$0.303926\pi$
$480$	−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	0.468132	−	0.883659i	$-0.344927\pi$
$487$	−9.16987	−	9.16987i	−0.415527	−	0.415527i	−0.883659	+	0.468132i	$0.844927\pi$
$488$	−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	$-0.984722\pi$
$499$		−	2.14359i		−	0.0959604i	0.998848	−	0.0479802i	$-0.0152784\pi$
$500$	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	$-0.117598\pi$
$503$	12.8159	+	12.8159i	0.571431	+	0.571431i	−0.361097	+	0.932528i	$0.617598\pi$
$504$	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	$-0.281151\pi$
$509$	28.6360			1.26927			0.634634	+	0.772813i	$0.281151\pi$
$510$	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	−0.342624	+	0.939473i	$0.611316\pi$
$523$	−29.3205	+	29.3205i	−1.28210	+	1.28210i	−0.939473	+	0.342624i	$0.888684\pi$
$524$	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	0.992094	−	0.125499i	$-0.0400531\pi$
$547$	20.2679	+	20.2679i	0.866595	+	0.866595i	−0.125499	+	0.992094i	$0.540053\pi$
$548$	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	$-0.623645\pi$
$557$	12.9038	−	12.9038i	0.546751	−	0.546751i	0.925500	+	0.378749i	$0.123645\pi$
$558$	−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	$-0.342574\pi$
$563$	−9.62209	−	9.62209i	−0.405523	−	0.405523i	−0.880174	+	0.474651i	$0.842574\pi$
$564$		−	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	$-0.339258\pi$
$569$	23.0807			0.967593			0.483796	+	0.875181i	$0.339258\pi$
$570$	−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	0.550496	−	0.834838i	$-0.314439\pi$
$577$	−6.83013	−	6.83013i	−0.284342	−	0.284342i	−0.834838	+	0.550496i	$0.814439\pi$
$578$	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	$-0.616122\pi$
$587$	13.9898	−	13.9898i	0.577422	−	0.577422i	0.934192	+	0.356770i	$0.116122\pi$
$588$	−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	−0.985916	−	0.167241i	$-0.946514\pi$
$593$	−28.0812	−	28.0812i	−1.15316	−	1.15316i	−0.167241	−	0.985916i	$-0.553486\pi$
$594$	−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	$-0.602505\pi$
$599$	−15.4920			−0.632985			−0.316493	+	0.948595i	$0.602505\pi$
$600$	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	0.717899	−	0.696147i	$-0.245104\pi$
$607$	0.535898	+	0.535898i	0.0217514	+	0.0217514i	−0.696147	+	0.717899i	$0.745104\pi$
$608$	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	−0.288531	−	0.957471i	$-0.593167\pi$
$613$	16.5622	−	16.5622i	0.668940	−	0.668940i	0.957471	+	0.288531i	$0.0931667\pi$
$614$	−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	0.145190	−	0.989404i	$-0.453621\pi$
$617$	28.1827	−	28.1827i	1.13459	−	1.13459i	0.989404	−	0.145190i	$-0.0463795\pi$
$618$	9.46410	−	9.46410i	0.380702	−	0.380702i
$619$			4.67949i			0.188085i	0.995568	+	0.0940423i	$0.0299789\pi$
$619$			4.67949i			0.188085i	−0.995568	+	0.0940423i	$0.970021\pi$
$620$	−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	−0.438766	−	0.898601i	$-0.644584\pi$
$643$	11.6603	−	11.6603i	0.459836	−	0.459836i	0.898601	+	0.438766i	$0.144584\pi$
$644$	−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	$-0.874973\pi$
$647$	−13.7632	+	13.7632i	−0.541087	+	0.541087i	0.382760	+	0.923848i	$0.374973\pi$
$648$	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	$-0.229753\pi$
$653$	2.29719	+	2.29719i	0.0898958	+	0.0898958i	−0.660729	+	0.750625i	$0.729753\pi$
$654$		−	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	$-0.429277\pi$
$659$	11.3137			0.440720			0.220360	+	0.975419i	$0.429277\pi$
$660$	−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	−0.942735	−	0.333542i	$-0.891756\pi$
$673$	−15.8038	+	15.8038i	−0.609194	+	0.609194i	0.333542	+	0.942735i	$0.391756\pi$
$674$	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	$-0.972337\pi$
$677$	−23.6627	+	23.6627i	−0.909431	+	0.909431i	0.0867950	+	0.996226i	$0.472337\pi$
$678$	−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	−0.970460	−	0.241264i	$-0.922438\pi$
$683$	−31.6675	−	31.6675i	−1.21172	−	1.21172i	−0.241264	−	0.970460i	$-0.577562\pi$
$684$		−	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	$-0.907890\pi$
$709$		−	15.1962i		−	0.570703i	0.958423	−	0.285352i	$-0.0921104\pi$
$710$	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	$-0.771828\pi$
$719$	−40.4302			−1.50779			−0.753896	+	0.656994i	$0.771828\pi$
$720$	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	0.384160	−	0.923267i	$-0.374491\pi$
$727$	−14.5359	−	14.5359i	−0.539107	−	0.539107i	−0.923267	+	0.384160i	$0.874491\pi$
$728$	−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	−0.680558	−	0.732694i	$-0.738263\pi$
$733$	1.41154	−	1.41154i	0.0521365	−	0.0521365i	0.732694	+	0.680558i	$0.238263\pi$
$734$	−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	$0.100783\pi$
$739$			16.9282i			0.622714i	−0.950293	+	0.311357i	$0.899217\pi$
$740$	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	$-0.0286460\pi$
$743$	24.6980	+	24.6980i	0.906081	+	0.906081i	−0.0898726	+	0.995953i	$0.528646\pi$
$744$		−	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	0.907280	−	0.420528i	$-0.138155\pi$
$757$	13.3923	+	13.3923i	0.486752	+	0.486752i	−0.420528	+	0.907280i	$0.638155\pi$
$758$	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	$0.366304\pi$
$769$			50.6410i			1.82616i	−0.407779	+	0.913081i	$0.633696\pi$
$770$	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	$-0.187033\pi$
$773$	7.72741	+	7.72741i	0.277935	+	0.277935i	−0.554349	+	0.832284i	$0.687033\pi$
$774$	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	0.960385	−	0.278676i	$-0.0898954\pi$
$787$	19.1244	+	19.1244i	0.681710	+	0.681710i	−0.278676	+	0.960385i	$0.589895\pi$
$788$	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	$-0.599497\pi$
$797$	18.1817	−	18.1817i	0.644029	−	0.644029i	0.951543	+	0.307514i	$0.0994972\pi$
$798$	−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	$-0.287701\pi$
$809$	35.1894			1.23719			0.618597	+	0.785708i	$0.287701\pi$
$810$	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	−0.661039	−	0.750351i	$-0.729884\pi$
$823$	2.56218	−	2.56218i	0.0893119	−	0.0893119i	0.750351	+	0.661039i	$0.229884\pi$
$824$	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	$-0.880953\pi$
$827$	−16.2635	+	16.2635i	−0.565536	+	0.565536i	0.365339	+	0.930875i	$0.380953\pi$
$828$	−7.34847	−	7.34847i	−0.255377	−	0.255377i
$829$			37.0718i			1.28756i	0.765212	+	0.643778i	$0.222634\pi$
$829$			37.0718i			1.28756i	−0.765212	+	0.643778i	$0.777366\pi$
$830$	−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	$-0.813405\pi$
$839$	−48.2591			−1.66609			−0.833045	+	0.553205i	$0.813405\pi$
$840$	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	−0.884372	−	0.466783i	$-0.845413\pi$
$853$	−12.1962	+	12.1962i	−0.417588	+	0.417588i	0.466783	+	0.884372i	$0.345413\pi$
$854$	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	$-0.927149\pi$
$857$	−21.8695	+	21.8695i	−0.747049	+	0.747049i	0.226875	+	0.973924i	$0.427149\pi$
$858$	13.4722	+	13.4722i	0.459933	+	0.459933i
$859$			24.6410i			0.840741i	0.907353	+	0.420370i	$0.138100\pi$
$859$			24.6410i			0.840741i	−0.907353	+	0.420370i	$0.861900\pi$
$860$	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	$-0.0852385\pi$
$863$	20.5569	+	20.5569i	0.699764	+	0.699764i	−0.264596	+	0.964359i	$0.585238\pi$
$864$			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	0.910648	−	0.413182i	$-0.135583\pi$
$877$	14.7321	+	14.7321i	0.497466	+	0.497466i	−0.413182	+	0.910648i	$0.635583\pi$
$878$	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	−0.622986	−	0.782233i	$-0.714081\pi$
$883$	4.73205	−	4.73205i	0.159246	−	0.159246i	0.782233	+	0.622986i	$0.214081\pi$
$884$	−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	$-0.648466\pi$
$887$	13.2084	−	13.2084i	0.443495	−	0.443495i	0.893185	+	0.449690i	$0.148466\pi$
$888$	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	0.913648	+	0.406505i	$0.133253\pi$
$907$	39.7583	+	39.7583i	1.32015	+	1.32015i	0.406505	+	0.913648i	$0.366747\pi$
$908$	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	$0.0605515\pi$
$919$			11.4641i			0.378166i	−0.981961	+	0.189083i	$0.939449\pi$
$920$	−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	$-0.518206\pi$
$929$	−3.48477			−0.114331			−0.0571657	+	0.998365i	$0.518206\pi$
$930$	−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	0.970627	−	0.240589i	$-0.0773407\pi$
$937$	22.3468	+	22.3468i	0.730038	+	0.730038i	−0.240589	+	0.970627i	$0.577341\pi$
$938$	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	$-0.823427\pi$
$947$	−9.95026	+	9.95026i	−0.323340	+	0.323340i	0.526707	+	0.850047i	$0.323427\pi$
$948$	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	0.925999	+	0.377525i	$0.123225\pi$
$953$	40.2407	+	40.2407i	1.30352	+	1.30352i	0.377525	+	0.925999i	$0.376775\pi$
$954$			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	0.947316	+	0.320300i	$0.103784\pi$
$967$	39.4186	+	39.4186i	1.26762	+	1.26762i	0.320300	+	0.947316i	$0.396216\pi$
$968$	−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	$-0.761649\pi$
$977$	−1.61729	+	1.61729i	−0.0517415	+	0.0517415i	0.680763	+	0.732504i	$0.261649\pi$
$978$	−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	$-0.137450\pi$
$983$	15.3533	+	15.3533i	0.489693	+	0.489693i	−0.418516	+	0.908209i	$0.637450\pi$
$984$	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	0.628192	−	0.778058i	$-0.283795\pi$
$997$	−4.73205	−	4.73205i	−0.149866	−	0.149866i	−0.778058	+	0.628192i	$0.783795\pi$
$998$	−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.497.3	yes	8
3.2	odd	2	inner	930.2.j.e.497.2	✓	8
5.3	odd	4	inner	930.2.j.e.683.2	yes	8
15.8	even	4	inner	930.2.j.e.683.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.e.497.2	✓	8	3.2	odd	2	inner
930.2.j.e.497.3	yes	8	1.1	even	1	trivial
930.2.j.e.683.2	yes	8	5.3	odd	4	inner
930.2.j.e.683.3	yes	8	15.8	even	4	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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