LMFDB - Embedded newform 930.2.j.e.497.4

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			497.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.e.683.4

$q$-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} +(-0.448288 - 2.19067i) q^{5} +1.73205 q^{6} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(-1.86603 - 1.23205i) q^{10} -4.76028i q^{11} +(1.22474 - 1.22474i) q^{12} +(1.63397 - 1.63397i) q^{13} +2.82843 q^{14} +(2.13397 - 3.23205i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(2.12132 + 2.12132i) q^{18} -3.00000i q^{19} +(-2.19067 + 0.448288i) q^{20} +4.89898i q^{21} +(-3.36603 - 3.36603i) q^{22} +(2.44949 + 2.44949i) q^{23} -1.73205i q^{24} +(-4.59808 + 1.96410i) q^{25} -2.31079i q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 2.00000i) q^{28} +9.52056 q^{29} +(-0.776457 - 3.79435i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.83013 - 5.83013i) q^{33} -1.00000i q^{34} +(3.48477 - 5.27792i) q^{35} +3.00000 q^{36} +(6.46410 + 6.46410i) q^{37} +(-2.12132 - 2.12132i) q^{38} +4.00240 q^{39} +(-1.23205 + 1.86603i) q^{40} -5.65685i q^{41} +(3.46410 + 3.46410i) q^{42} +(-3.46410 + 3.46410i) q^{43} -4.76028 q^{44} +(6.57201 - 1.34486i) q^{45} +3.46410 q^{46} +(-2.63896 + 2.63896i) q^{47} +(-1.22474 - 1.22474i) q^{48} +1.00000i q^{49} +(-1.86250 + 4.64016i) q^{50} +1.73205 q^{51} +(-1.63397 - 1.63397i) q^{52} +(-4.89898 - 4.89898i) q^{53} +5.19615i q^{54} +(-10.4282 + 2.13397i) q^{55} -2.82843i q^{56} +(3.67423 - 3.67423i) q^{57} +(6.73205 - 6.73205i) q^{58} -4.62158 q^{59} +(-3.23205 - 2.13397i) q^{60} -14.1244 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.00000 + 6.00000i) q^{63} +1.00000i q^{64} +(-4.31199 - 2.84701i) q^{65} -8.24504i q^{66} +(8.83013 + 8.83013i) q^{67} +(-0.707107 - 0.707107i) q^{68} +6.00000i q^{69} +(-1.26795 - 6.19615i) q^{70} -3.06866i q^{71} +(2.12132 - 2.12132i) q^{72} +(-2.53590 + 2.53590i) q^{73} +9.14162 q^{74} +(-8.03699 - 3.22595i) q^{75} -3.00000 q^{76} +(9.52056 - 9.52056i) q^{77} +(2.83013 - 2.83013i) q^{78} -0.267949i q^{79} +(0.448288 + 2.19067i) q^{80} -9.00000 q^{81} +(-4.00000 - 4.00000i) q^{82} +(6.88160 + 6.88160i) q^{83} +4.89898 q^{84} +(-1.86603 - 1.23205i) q^{85} +4.89898i q^{86} +(11.6603 + 11.6603i) q^{87} +(-3.36603 + 3.36603i) q^{88} +9.89949 q^{89} +(3.69615 - 5.59808i) q^{90} +6.53590 q^{91} +(2.44949 - 2.44949i) q^{92} +(-1.22474 - 1.22474i) q^{93} +3.73205i q^{94} +(-6.57201 + 1.34486i) q^{95} -1.73205 q^{96} +(-6.63397 - 6.63397i) q^{97} +(0.707107 + 0.707107i) q^{98} +14.2808 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
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$6$	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
$10$	−1.86603	−	1.23205i	−0.590089	−	0.389609i
$11$		−	4.76028i		−	1.43528i	−0.696415	−	0.717639i	$-0.745223\pi$
$11$		−	4.76028i		−	1.43528i	0.696415	−	0.717639i	$-0.254777\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$	1.63397	−	1.63397i	0.453183	−	0.453183i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	1.63397	−	1.63397i	0.453183	−	0.453183i	0.896410	+	0.443227i	$0.146166\pi$
$14$	2.82843			0.755929
$15$	2.13397	−	3.23205i	0.550990	−	0.834512i
$16$	−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	$-0.111824\pi$
$20$	−2.19067	+	0.448288i	−0.489849	+	0.100240i
$21$			4.89898i			1.06904i
$22$	−3.36603	−	3.36603i	−0.717639	−	0.717639i
$23$	2.44949	+	2.44949i	0.510754	+	0.510754i	0.914757	−	0.404004i	$-0.132382\pi$
$23$	2.44949	+	2.44949i	0.510754	+	0.510754i	−0.404004	+	0.914757i	$0.632382\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−4.59808	+	1.96410i	−0.919615	+	0.392820i
$26$		−	2.31079i		−	0.453183i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$	9.52056			1.76792			0.883962	−	0.467560i	$-0.154867\pi$
$29$	9.52056			1.76792			0.883962	+	0.467560i	$0.154867\pi$
$30$	−0.776457	−	3.79435i	−0.141761	−	0.692751i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.83013	−	5.83013i	1.01489	−	1.01489i
$34$		−	1.00000i		−	0.171499i
$35$	3.48477	−	5.27792i	0.589033	−	0.892131i
$36$	3.00000			0.500000
$37$	6.46410	+	6.46410i	1.06269	+	1.06269i	0.997899	+	0.0647930i	$0.0206387\pi$
$37$	6.46410	+	6.46410i	1.06269	+	1.06269i	0.0647930	+	0.997899i	$0.479361\pi$
$38$	−2.12132	−	2.12132i	−0.344124	−	0.344124i
$39$	4.00240			0.640898
$40$	−1.23205	+	1.86603i	−0.194804	+	0.295045i
$41$		−	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	$-0.871857\pi$
$43$	−3.46410	+	3.46410i	−0.528271	+	0.528271i	0.391786	+	0.920056i	$0.371857\pi$
$44$	−4.76028			−0.717639
$45$	6.57201	−	1.34486i	0.979698	−	0.200480i
$46$	3.46410			0.510754
$47$	−2.63896	+	2.63896i	−0.384932	+	0.384932i	−0.872875	−	0.487944i	$-0.837747\pi$
$47$	−2.63896	+	2.63896i	−0.384932	+	0.384932i	0.487944	+	0.872875i	$0.337747\pi$
$48$	−1.22474	−	1.22474i	−0.176777	−	0.176777i
$49$			1.00000i			0.142857i
$50$	−1.86250	+	4.64016i	−0.263397	+	0.656218i
$51$	1.73205			0.242536
$52$	−1.63397	−	1.63397i	−0.226592	−	0.226592i
$53$	−4.89898	−	4.89898i	−0.672927	−	0.672927i	0.285463	−	0.958390i	$-0.407853\pi$
$53$	−4.89898	−	4.89898i	−0.672927	−	0.672927i	−0.958390	+	0.285463i	$0.907853\pi$
$54$			5.19615i			0.707107i
$55$	−10.4282	+	2.13397i	−1.40614	+	0.287745i
$56$		−	2.82843i		−	0.377964i
$57$	3.67423	−	3.67423i	0.486664	−	0.486664i
$58$	6.73205	−	6.73205i	0.883962	−	0.883962i
$59$	−4.62158			−0.601678			−0.300839	−	0.953675i	$-0.597267\pi$
$59$	−4.62158			−0.601678			−0.300839	+	0.953675i	$0.597267\pi$
$60$	−3.23205	−	2.13397i	−0.417256	−	0.275495i
$61$	−14.1244			−1.80844			−0.904219	−	0.427069i	$-0.859546\pi$
$61$	−14.1244			−1.80844			−0.904219	+	0.427069i	$0.859546\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−6.00000	+	6.00000i	−0.755929	+	0.755929i
$64$			1.00000i			0.125000i
$65$	−4.31199	−	2.84701i	−0.534837	−	0.353128i
$66$		−	8.24504i		−	1.01489i
$67$	8.83013	+	8.83013i	1.07877	+	1.07877i	0.996620	+	0.0821519i	$0.0261793\pi$
$67$	8.83013	+	8.83013i	1.07877	+	1.07877i	0.0821519	+	0.996620i	$0.473821\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$			6.00000i			0.722315i
$70$	−1.26795	−	6.19615i	−0.151549	−	0.740582i
$71$		−	3.06866i		−	0.364183i	−0.983282	−	0.182092i	$-0.941713\pi$
$71$		−	3.06866i		−	0.364183i	0.983282	−	0.182092i	$-0.0582868\pi$
$72$	2.12132	−	2.12132i	0.250000	−	0.250000i
$73$	−2.53590	+	2.53590i	−0.296804	+	0.296804i	−0.839761	−	0.542956i	$-0.817305\pi$
$73$	−2.53590	+	2.53590i	−0.296804	+	0.296804i	0.542956	+	0.839761i	$0.317305\pi$
$74$	9.14162			1.06269
$75$	−8.03699	−	3.22595i	−0.928032	−	0.372500i
$76$	−3.00000			−0.344124
$77$	9.52056	−	9.52056i	1.08497	−	1.08497i
$78$	2.83013	−	2.83013i	0.320449	−	0.320449i
$79$		−	0.267949i		−	0.0301466i	−0.999886	−	0.0150733i	$-0.995202\pi$
$79$		−	0.267949i		−	0.0301466i	0.999886	−	0.0150733i	$-0.00479817\pi$
$80$	0.448288	+	2.19067i	0.0501201	+	0.244924i
$81$	−9.00000			−1.00000
$82$	−4.00000	−	4.00000i	−0.441726	−	0.441726i
$83$	6.88160	+	6.88160i	0.755354	+	0.755354i	0.975473	−	0.220119i	$-0.0706447\pi$
$83$	6.88160	+	6.88160i	0.755354	+	0.755354i	−0.220119	+	0.975473i	$0.570645\pi$
$84$	4.89898			0.534522
$85$	−1.86603	−	1.23205i	−0.202399	−	0.133635i
$86$			4.89898i			0.528271i
$87$	11.6603	+	11.6603i	1.25011	+	1.25011i
$88$	−3.36603	+	3.36603i	−0.358820	+	0.358820i
$89$	9.89949			1.04934			0.524672	−	0.851304i	$-0.324188\pi$
$89$	9.89949			1.04934			0.524672	+	0.851304i	$0.324188\pi$
$90$	3.69615	−	5.59808i	0.389609	−	0.590089i
$91$	6.53590			0.685148
$92$	2.44949	−	2.44949i	0.255377	−	0.255377i
$93$	−1.22474	−	1.22474i	−0.127000	−	0.127000i
$94$			3.73205i			0.384932i
$95$	−6.57201	+	1.34486i	−0.674274	+	0.137980i
$96$	−1.73205			−0.176777
$97$	−6.63397	−	6.63397i	−0.673578	−	0.673578i	0.284961	−	0.958539i	$-0.408019\pi$
$97$	−6.63397	−	6.63397i	−0.673578	−	0.673578i	−0.958539	+	0.284961i	$0.908019\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	14.2808			1.43528
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$		−	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
$103$	1.46410	−	1.46410i	0.144262	−	0.144262i	−0.631287	−	0.775549i	$-0.717473\pi$
$103$	1.46410	−	1.46410i	0.144262	−	0.144262i	0.775549	+	0.631287i	$0.217473\pi$
$104$	−2.31079			−0.226592
$105$	10.7321	−	2.19615i	1.04734	−	0.214323i
$106$	−6.92820			−0.672927
$107$	−12.2474	+	12.2474i	−1.18401	+	1.18401i	−0.205308	+	0.978697i	$0.565820\pi$
$107$	−12.2474	+	12.2474i	−1.18401	+	1.18401i	−0.978697	+	0.205308i	$0.934180\pi$
$108$	3.67423	+	3.67423i	0.353553	+	0.353553i
$109$			14.9282i			1.42986i	0.699195	+	0.714931i	$0.253542\pi$
$109$			14.9282i			1.42986i	−0.699195	+	0.714931i	$0.746458\pi$
$110$	−5.86491	+	8.88280i	−0.559197	+	0.846942i
$111$			15.8338i			1.50287i
$112$	−2.00000	−	2.00000i	−0.188982	−	0.188982i
$113$	−4.52004	−	4.52004i	−0.425210	−	0.425210i	0.461783	−	0.886993i	$-0.347210\pi$
$113$	−4.52004	−	4.52004i	−0.425210	−	0.425210i	−0.886993	+	0.461783i	$0.847210\pi$
$114$		−	5.19615i		−	0.486664i
$115$	4.26795	−	6.46410i	0.397988	−	0.602781i
$116$		−	9.52056i		−	0.883962i
$117$	4.90192	+	4.90192i	0.453183	+	0.453183i
$118$	−3.26795	+	3.26795i	−0.300839	+	0.300839i
$119$	2.82843			0.259281
$120$	−3.79435	+	0.776457i	−0.346375	+	0.0708805i
$121$	−11.6603			−1.06002
$122$	−9.98743	+	9.98743i	−0.904219	+	0.904219i
$123$	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
$127$	0.267949	+	0.267949i	0.0237766	+	0.0237766i	0.718895	−	0.695119i	$-0.244648\pi$
$127$	0.267949	+	0.267949i	0.0237766	+	0.0237766i	−0.695119	+	0.718895i	$0.744648\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.48528			−0.747087
$130$	−5.06218	+	1.03590i	−0.443982	+	0.0908543i
$131$			7.45001i			0.650910i	0.945558	+	0.325455i	$0.105517\pi$
$131$			7.45001i			0.650910i	−0.945558	+	0.325455i	$0.894483\pi$
$132$	−5.83013	−	5.83013i	−0.507447	−	0.507447i
$133$	6.00000	−	6.00000i	0.520266	−	0.520266i
$134$	12.4877			1.07877
$135$	9.69615	+	6.40192i	0.834512	+	0.550990i
$136$	−1.00000			−0.0857493
$137$	−5.00052	+	5.00052i	−0.427223	+	0.427223i	−0.887681	−	0.460458i	$-0.847685\pi$
$137$	−5.00052	+	5.00052i	−0.427223	+	0.427223i	0.460458	+	0.887681i	$0.347685\pi$
$138$	4.24264	+	4.24264i	0.361158	+	0.361158i
$139$			18.7846i			1.59329i	0.604448	+	0.796645i	$0.293394\pi$
$139$			18.7846i			1.59329i	−0.604448	+	0.796645i	$0.706606\pi$
$140$	−5.27792	−	3.48477i	−0.446065	−	0.294516i
$141$	−6.46410			−0.544376
$142$	−2.16987	−	2.16987i	−0.182092	−	0.182092i
$143$	−7.77817	−	7.77817i	−0.650444	−	0.650444i
$144$		−	3.00000i		−	0.250000i
$145$	−4.26795	−	20.8564i	−0.354434	−	1.73203i
$146$			3.58630i			0.296804i
$147$	−1.22474	+	1.22474i	−0.101015	+	0.101015i
$148$	6.46410	−	6.46410i	0.531346	−	0.531346i
$149$	−12.1087			−0.991987			−0.495994	−	0.868326i	$-0.665196\pi$
$149$	−12.1087			−0.991987			−0.495994	+	0.868326i	$0.665196\pi$
$150$	−7.96410	+	3.40192i	−0.650266	+	0.277766i
$151$	−20.3205			−1.65366			−0.826830	−	0.562452i	$-0.809858\pi$
$151$	−20.3205			−1.65366			−0.826830	+	0.562452i	$0.809858\pi$
$152$	−2.12132	+	2.12132i	−0.172062	+	0.172062i
$153$	2.12132	+	2.12132i	0.171499	+	0.171499i
$154$		−	13.4641i		−	1.08497i
$155$	0.448288	+	2.19067i	0.0360073	+	0.175959i
$156$		−	4.00240i		−	0.320449i
$157$	1.26795	+	1.26795i	0.101193	+	0.101193i	0.755891	−	0.654698i	$-0.227204\pi$
$157$	1.26795	+	1.26795i	0.101193	+	0.101193i	−0.654698	+	0.755891i	$0.727204\pi$
$158$	−0.189469	−	0.189469i	−0.0150733	−	0.0150733i
$159$		−	12.0000i		−	0.951662i
$160$	1.86603	+	1.23205i	0.147522	+	0.0974022i
$161$			9.79796i			0.772187i
$162$	−6.36396	+	6.36396i	−0.500000	+	0.500000i
$163$	1.63397	−	1.63397i	0.127983	−	0.127983i	−0.640214	−	0.768197i	$-0.721154\pi$
$163$	1.63397	−	1.63397i	0.127983	−	0.127983i	0.768197	+	0.640214i	$0.221154\pi$
$164$	−5.65685			−0.441726
$165$	−15.3855	−	10.1583i	−1.19776	−	0.790824i
$166$	9.73205			0.755354
$167$	−15.8338	+	15.8338i	−1.22525	+	1.22525i	−0.259513	+	0.965740i	$0.583562\pi$
$167$	−15.8338	+	15.8338i	−1.22525	+	1.22525i	−0.965740	+	0.259513i	$0.916438\pi$
$168$	3.46410	−	3.46410i	0.267261	−	0.267261i
$169$			7.66025i			0.589250i
$170$	−2.19067	+	0.448288i	−0.168017	+	0.0343821i
$171$	9.00000			0.688247
$172$	3.46410	+	3.46410i	0.264135	+	0.264135i
$173$	0.947343	+	0.947343i	0.0720252	+	0.0720252i	0.742202	−	0.670177i	$-0.233782\pi$
$173$	0.947343	+	0.947343i	0.0720252	+	0.0720252i	−0.670177	+	0.742202i	$0.733782\pi$
$174$	16.4901			1.25011
$175$	−13.1244	−	5.26795i	−0.992108	−	0.398220i
$176$			4.76028i			0.358820i
$177$	−5.66025	−	5.66025i	−0.425451	−	0.425451i
$178$	7.00000	−	7.00000i	0.524672	−	0.524672i
$179$	−2.31079			−0.172716			−0.0863582	−	0.996264i	$-0.527523\pi$
$179$	−2.31079			−0.172716			−0.0863582	+	0.996264i	$0.527523\pi$
$180$	−1.34486	−	6.57201i	−0.100240	−	0.489849i
$181$	0.928203			0.0689928			0.0344964	−	0.999405i	$-0.489017\pi$
$181$	0.928203			0.0689928			0.0344964	+	0.999405i	$0.489017\pi$
$182$	4.62158	−	4.62158i	0.342574	−	0.342574i
$183$	−17.2987	−	17.2987i	−1.27876	−	1.27876i
$184$		−	3.46410i		−	0.255377i
$185$	11.2629	−	17.0585i	0.828068	−	1.25417i
$186$	−1.73205			−0.127000
$187$	−3.36603	−	3.36603i	−0.246148	−	0.246148i
$188$	2.63896	+	2.63896i	0.192466	+	0.192466i
$189$	−14.6969			−1.06904
$190$	−3.69615	+	5.59808i	−0.268147	+	0.406127i
$191$		−	10.1769i		−	0.736374i	−0.929752	−	0.368187i	$-0.879979\pi$
$191$		−	10.1769i		−	0.736374i	0.929752	−	0.368187i	$-0.120021\pi$
$192$	−1.22474	+	1.22474i	−0.0883883	+	0.0883883i
$193$	−10.6340	+	10.6340i	−0.765450	+	0.765450i	−0.977302	−	0.211852i	$-0.932051\pi$
$193$	−10.6340	+	10.6340i	−0.765450	+	0.765450i	0.211852	+	0.977302i	$0.432051\pi$
$194$	−9.38186			−0.673578
$195$	−1.79423	−	8.76795i	−0.128487	−	0.627886i
$196$	1.00000			0.0714286
$197$	16.1112	−	16.1112i	1.14787	−	1.14787i	0.160902	−	0.986970i	$-0.448560\pi$
$197$	16.1112	−	16.1112i	1.14787	−	1.14787i	0.986970	−	0.160902i	$-0.0514402\pi$
$198$	10.0981	−	10.0981i	0.717639	−	0.717639i
$199$		−	17.3923i		−	1.23291i	−0.787391	−	0.616454i	$-0.788569\pi$
$199$		−	17.3923i		−	1.23291i	0.787391	−	0.616454i	$-0.211431\pi$
$200$	4.64016	+	1.86250i	0.328109	+	0.131699i
$201$			21.6293i			1.52561i
$202$	−7.00000	−	7.00000i	−0.492518	−	0.492518i
$203$	19.0411	+	19.0411i	1.33642	+	1.33642i
$204$		−	1.73205i		−	0.121268i
$205$	−12.3923	+	2.53590i	−0.865516	+	0.177115i
$206$		−	2.07055i		−	0.144262i
$207$	−7.34847	+	7.34847i	−0.510754	+	0.510754i
$208$	−1.63397	+	1.63397i	−0.113296	+	0.113296i
$209$	−14.2808			−0.987826
$210$	6.03579	−	9.14162i	0.416509	−	0.630832i
$211$	26.3923			1.81692			0.908461	−	0.417971i	$-0.137258\pi$
$211$	26.3923			1.81692			0.908461	+	0.417971i	$0.137258\pi$
$212$	−4.89898	+	4.89898i	−0.336463	+	0.336463i
$213$	3.75833	−	3.75833i	0.257517	−	0.257517i
$214$			17.3205i			1.18401i
$215$	9.14162	+	6.03579i	0.623453	+	0.411638i
$216$	5.19615			0.353553
$217$	−2.00000	−	2.00000i	−0.135769	−	0.135769i
$218$	10.5558	+	10.5558i	0.714931	+	0.714931i
$219$	−6.21166			−0.419745
$220$	2.13397	+	10.4282i	0.143873	+	0.703069i
$221$		−	2.31079i		−	0.155440i
$222$	11.1962	+	11.1962i	0.751437	+	0.751437i
$223$	4.09808	−	4.09808i	0.274427	−	0.274427i	−0.556452	−	0.830880i	$-0.687838\pi$
$223$	4.09808	−	4.09808i	0.274427	−	0.274427i	0.830880	+	0.556452i	$0.187838\pi$
$224$	−2.82843			−0.188982
$225$	−5.89230	−	13.7942i	−0.392820	−	0.919615i
$226$	−6.39230			−0.425210
$227$	6.96953	−	6.96953i	0.462584	−	0.462584i	−0.436918	−	0.899502i	$-0.643930\pi$
$227$	6.96953	−	6.96953i	0.462584	−	0.462584i	0.899502	+	0.436918i	$0.143930\pi$
$228$	−3.67423	−	3.67423i	−0.243332	−	0.243332i
$229$			10.3205i			0.681998i	0.940064	+	0.340999i	$0.110765\pi$
$229$			10.3205i			0.681998i	−0.940064	+	0.340999i	$0.889235\pi$
$230$	−1.55291	−	7.58871i	−0.102396	−	0.500384i
$231$	23.3205			1.53438
$232$	−6.73205	−	6.73205i	−0.441981	−	0.441981i
$233$	3.10583	+	3.10583i	0.203470	+	0.203470i	0.801485	−	0.598015i	$-0.204044\pi$
$233$	3.10583	+	3.10583i	0.203470	+	0.203470i	−0.598015	+	0.801485i	$0.704044\pi$
$234$	6.93237			0.453183
$235$	6.96410	+	4.59808i	0.454288	+	0.299945i
$236$			4.62158i			0.300839i
$237$	0.328169	−	0.328169i	0.0213169	−	0.0213169i
$238$	2.00000	−	2.00000i	0.129641	−	0.129641i
$239$	−17.2480			−1.11568			−0.557839	−	0.829949i	$-0.688369\pi$
$239$	−17.2480			−1.11568			−0.557839	+	0.829949i	$0.688369\pi$
$240$	−2.13397	+	3.23205i	−0.137747	+	0.208628i
$241$	4.39230			0.282933			0.141467	−	0.989943i	$-0.454818\pi$
$241$	4.39230			0.282933			0.141467	+	0.989943i	$0.454818\pi$
$242$	−8.24504	+	8.24504i	−0.530012	+	0.530012i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$			14.1244i			0.904219i
$245$	2.19067	−	0.448288i	0.139957	−	0.0286401i
$246$		−	9.79796i		−	0.624695i
$247$	−4.90192	−	4.90192i	−0.311902	−	0.311902i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$			16.8564i			1.06823i
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$			10.9348i			0.690197i	0.938567	+	0.345098i	$0.112154\pi$
$251$			10.9348i			0.690197i	−0.938567	+	0.345098i	$0.887846\pi$
$252$	6.00000	+	6.00000i	0.377964	+	0.377964i
$253$	11.6603	−	11.6603i	0.733074	−	0.733074i
$254$	0.378937			0.0237766
$255$	−0.776457	−	3.79435i	−0.0486236	−	0.237612i
$256$	1.00000			0.0625000
$257$	4.14110	−	4.14110i	0.258315	−	0.258315i	−0.566053	−	0.824369i	$-0.691530\pi$
$257$	4.14110	−	4.14110i	0.258315	−	0.258315i	0.824369	+	0.566053i	$0.191530\pi$
$258$	−6.00000	+	6.00000i	−0.373544	+	0.373544i
$259$			25.8564i			1.60664i
$260$	−2.84701	+	4.31199i	−0.176564	+	0.267418i
$261$			28.5617i			1.76792i
$262$	5.26795	+	5.26795i	0.325455	+	0.325455i
$263$	−18.5606	−	18.5606i	−1.14450	−	1.14450i	−0.987618	−	0.156881i	$-0.949856\pi$
$263$	−18.5606	−	18.5606i	−1.14450	−	1.14450i	−0.156881	−	0.987618i	$-0.550144\pi$
$264$	−8.24504			−0.507447
$265$	−8.53590	+	12.9282i	−0.524356	+	0.794173i
$266$		−	8.48528i		−	0.520266i
$267$	12.1244	+	12.1244i	0.741999	+	0.741999i
$268$	8.83013	−	8.83013i	0.539386	−	0.539386i
$269$	−19.0411			−1.16096			−0.580479	−	0.814275i	$-0.697135\pi$
$269$	−19.0411			−1.16096			−0.580479	+	0.814275i	$0.697135\pi$
$270$	11.3831	−	2.32937i	0.692751	−	0.141761i
$271$	5.58846			0.339475			0.169737	−	0.985489i	$-0.445708\pi$
$271$	5.58846			0.339475			0.169737	+	0.985489i	$0.445708\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	8.00481	+	8.00481i	0.484473	+	0.484473i
$274$			7.07180i			0.427223i
$275$	9.34967	+	21.8881i	0.563806	+	1.31990i
$276$	6.00000			0.361158
$277$	−7.75833	−	7.75833i	−0.466153	−	0.466153i	0.434513	−	0.900666i	$-0.356921\pi$
$277$	−7.75833	−	7.75833i	−0.466153	−	0.466153i	−0.900666	+	0.434513i	$0.856921\pi$
$278$	13.2827	+	13.2827i	0.796645	+	0.796645i
$279$		−	3.00000i		−	0.179605i
$280$	−6.19615	+	1.26795i	−0.370291	+	0.0757745i
$281$			29.5969i			1.76561i	0.469743	+	0.882803i	$0.344346\pi$
$281$			29.5969i			1.76561i	−0.469743	+	0.882803i	$0.655654\pi$
$282$	−4.57081	+	4.57081i	−0.272188	+	0.272188i
$283$	10.0981	−	10.0981i	0.600268	−	0.600268i	−0.340115	−	0.940384i	$-0.610466\pi$
$283$	10.0981	−	10.0981i	0.600268	−	0.600268i	0.940384	+	0.340115i	$0.110466\pi$
$284$	−3.06866			−0.182092
$285$	−9.69615	−	6.40192i	−0.574351	−	0.379217i
$286$	−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
$290$	−17.7656	−	11.7298i	−1.04323	−	0.688798i
$291$		−	16.2499i		−	0.952583i
$292$	2.53590	+	2.53590i	0.148402	+	0.148402i
$293$	−1.31268	−	1.31268i	−0.0766874	−	0.0766874i	0.667723	−	0.744410i	$-0.267269\pi$
$293$	−1.31268	−	1.31268i	−0.0766874	−	0.0766874i	−0.744410	+	0.667723i	$0.767269\pi$
$294$			1.73205i			0.101015i
$295$	2.07180	+	10.1244i	0.120625	+	0.589463i
$296$		−	9.14162i		−	0.531346i
$297$	17.4904	+	17.4904i	1.01489	+	1.01489i
$298$	−8.56218	+	8.56218i	−0.495994	+	0.495994i
$299$	8.00481			0.462930
$300$	−3.22595	+	8.03699i	−0.186250	+	0.464016i
$301$	−13.8564			−0.798670
$302$	−14.3688	+	14.3688i	−0.826830	+	0.826830i
$303$	12.1244	−	12.1244i	0.696526	−	0.696526i
$304$			3.00000i			0.172062i
$305$	6.33178	+	30.9418i	0.362556	+	1.77172i
$306$	3.00000			0.171499
$307$	11.5885	+	11.5885i	0.661388	+	0.661388i	0.955707	−	0.294319i	$-0.0950928\pi$
$307$	11.5885	+	11.5885i	0.661388	+	0.661388i	−0.294319	+	0.955707i	$0.595093\pi$
$308$	−9.52056	−	9.52056i	−0.542484	−	0.542484i
$309$	3.58630			0.204018
$310$	1.86603	+	1.23205i	0.105983	+	0.0699758i
$311$			2.58819i			0.146763i	0.997304	+	0.0733814i	$0.0233790\pi$
$311$			2.58819i			0.146763i	−0.997304	+	0.0733814i	$0.976621\pi$
$312$	−2.83013	−	2.83013i	−0.160224	−	0.160224i
$313$	15.8564	−	15.8564i	0.896257	−	0.896257i	−0.0988457	−	0.995103i	$-0.531515\pi$
$313$	15.8564	−	15.8564i	0.896257	−	0.896257i	0.995103	+	0.0988457i	$0.0315150\pi$
$314$	1.79315			0.101193
$315$	15.8338	+	10.4543i	0.892131	+	0.589033i
$316$	−0.267949			−0.0150733
$317$	−0.328169	+	0.328169i	−0.0184318	+	0.0184318i	−0.716263	−	0.697831i	$-0.754149\pi$
$317$	−0.328169	+	0.328169i	−0.0184318	+	0.0184318i	0.697831	+	0.716263i	$0.254149\pi$
$318$	−8.48528	−	8.48528i	−0.475831	−	0.475831i
$319$		−	45.3205i		−	2.53746i
$320$	2.19067	−	0.448288i	0.122462	−	0.0250600i
$321$	−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
$325$	−4.30385	+	10.7224i	−0.238735	+	0.594774i
$326$		−	2.31079i		−	0.127983i
$327$	−18.2832	+	18.2832i	−1.01107	+	1.01107i
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$	−10.5558			−0.581962
$330$	−18.0622	+	3.69615i	−0.994290	+	0.203466i
$331$	−2.39230			−0.131493			−0.0657465	−	0.997836i	$-0.520943\pi$
$331$	−2.39230			−0.131493			−0.0657465	+	0.997836i	$0.520943\pi$
$332$	6.88160	−	6.88160i	0.377677	−	0.377677i
$333$	−19.3923	+	19.3923i	−1.06269	+	1.06269i
$334$			22.3923i			1.22525i
$335$	15.3855	−	23.3023i	0.840598	−	1.27314i
$336$		−	4.89898i		−	0.267261i
$337$	−19.8564	−	19.8564i	−1.08165	−	1.08165i	−0.996356	−	0.0852913i	$-0.972818\pi$
$337$	−19.8564	−	19.8564i	−1.08165	−	1.08165i	−0.0852913	−	0.996356i	$-0.527182\pi$
$338$	5.41662	+	5.41662i	0.294625	+	0.294625i
$339$		−	11.0718i		−	0.601337i
$340$	−1.23205	+	1.86603i	−0.0668173	+	0.101199i
$341$			4.76028i			0.257784i
$342$	6.36396	−	6.36396i	0.344124	−	0.344124i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	4.89898			0.264135
$345$	13.1440	−	2.68973i	0.707650	−	0.144810i
$346$	1.33975			0.0720252
$347$	25.9227	−	25.9227i	1.39160	−	1.39160i	0.569868	−	0.821736i	$-0.306994\pi$
$347$	25.9227	−	25.9227i	1.39160	−	1.39160i	0.821736	−	0.569868i	$-0.193006\pi$
$348$	11.6603	−	11.6603i	0.625055	−	0.625055i
$349$		−	26.2487i		−	1.40506i	−0.711653	−	0.702531i	$-0.752053\pi$
$349$		−	26.2487i		−	1.40506i	0.711653	−	0.702531i	$-0.247947\pi$
$350$	−13.0053	+	5.55532i	−0.695164	+	0.296944i
$351$			12.0072i			0.640898i
$352$	3.36603	+	3.36603i	0.179410	+	0.179410i
$353$	−0.845807	−	0.845807i	−0.0450178	−	0.0450178i	0.684240	−	0.729257i	$-0.260134\pi$
$353$	−0.845807	−	0.845807i	−0.0450178	−	0.0450178i	−0.729257	+	0.684240i	$0.760134\pi$
$354$	−8.00481			−0.425451
$355$	−6.72243	+	1.37564i	−0.356790	+	0.0730116i
$356$		−	9.89949i		−	0.524672i
$357$	3.46410	+	3.46410i	0.183340	+	0.183340i
$358$	−1.63397	+	1.63397i	−0.0863582	+	0.0863582i
$359$	23.6999			1.25083			0.625415	−	0.780292i	$-0.284930\pi$
$359$	23.6999			1.25083			0.625415	+	0.780292i	$0.284930\pi$
$360$	−5.59808	−	3.69615i	−0.295045	−	0.194804i
$361$	10.0000			0.526316
$362$	0.656339	−	0.656339i	0.0344964	−	0.0344964i
$363$	−14.2808	−	14.2808i	−0.749550	−	0.749550i
$364$		−	6.53590i		−	0.342574i
$365$	6.69213	+	4.41851i	0.350282	+	0.231275i
$366$	−24.4641			−1.27876
$367$	21.8827	+	21.8827i	1.14227	+	1.14227i	0.988035	+	0.154232i	$0.0492904\pi$
$367$	21.8827	+	21.8827i	1.14227	+	1.14227i	0.154232	+	0.988035i	$0.450710\pi$
$368$	−2.44949	−	2.44949i	−0.127688	−	0.127688i
$369$	16.9706			0.883452
$370$	−4.09808	−	20.0263i	−0.213049	−	1.04112i
$371$		−	19.5959i		−	1.01737i
$372$	−1.22474	+	1.22474i	−0.0635001	+	0.0635001i
$373$	9.85641	−	9.85641i	0.510345	−	0.510345i	−0.404287	−	0.914632i	$-0.632480\pi$
$373$	9.85641	−	9.85641i	0.510345	−	0.510345i	0.914632	+	0.404287i	$0.132480\pi$
$374$	−4.76028			−0.246148
$375$	−3.46410	+	19.0526i	−0.178885	+	0.983870i
$376$	3.73205			0.192466
$377$	15.5563	−	15.5563i	0.801193	−	0.801193i
$378$	−10.3923	+	10.3923i	−0.534522	+	0.534522i
$379$			29.1962i			1.49971i	0.661605	+	0.749853i	$0.269876\pi$
$379$			29.1962i			1.49971i	−0.661605	+	0.749853i	$0.730124\pi$
$380$	1.34486	+	6.57201i	0.0689900	+	0.337137i
$381$			0.656339i			0.0336253i
$382$	−7.19615	−	7.19615i	−0.368187	−	0.368187i
$383$	1.03528	+	1.03528i	0.0529001	+	0.0529001i	0.733062	−	0.680162i	$-0.238091\pi$
$383$	1.03528	+	1.03528i	0.0529001	+	0.0529001i	−0.680162	+	0.733062i	$0.738091\pi$
$384$			1.73205i			0.0883883i
$385$	−25.1244	−	16.5885i	−1.28046	−	0.845426i
$386$			15.0387i			0.765450i
$387$	−10.3923	−	10.3923i	−0.528271	−	0.528271i
$388$	−6.63397	+	6.63397i	−0.336789	+	0.336789i
$389$	−8.76268			−0.444286			−0.222143	−	0.975014i	$-0.571305\pi$
$389$	−8.76268			−0.444286			−0.222143	+	0.975014i	$0.571305\pi$
$390$	−7.46859	−	4.93117i	−0.378187	−	0.249699i
$391$	3.46410			0.175187
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	−9.12436	+	9.12436i	−0.460263	+	0.460263i
$394$		−	22.7846i		−	1.14787i
$395$	−0.586988	+	0.120118i	−0.0295346	+	0.00604381i
$396$		−	14.2808i		−	0.717639i
$397$	17.5167	+	17.5167i	0.879136	+	0.879136i	0.993445	−	0.114309i	$-0.0364655\pi$
$397$	17.5167	+	17.5167i	0.879136	+	0.879136i	−0.114309	+	0.993445i	$0.536465\pi$
$398$	−12.2982	−	12.2982i	−0.616454	−	0.616454i
$399$	14.6969			0.735767
$400$	4.59808	−	1.96410i	0.229904	−	0.0982051i
$401$		−	3.62347i		−	0.180947i	−0.995899	−	0.0904736i	$-0.971162\pi$
$401$		−	3.62347i		−	0.180947i	0.995899	−	0.0904736i	$-0.0288381\pi$
$402$	15.2942	+	15.2942i	0.762807	+	0.762807i
$403$	−1.63397	+	1.63397i	−0.0813941	+	0.0813941i
$404$	−9.89949			−0.492518
$405$	4.03459	+	19.7160i	0.200480	+	0.979698i
$406$	26.9282			1.33642
$407$	30.7709	−	30.7709i	1.52526	−	1.52526i
$408$	−1.22474	−	1.22474i	−0.0606339	−	0.0606339i
$409$		−	33.1769i		−	1.64049i	−0.572010	−	0.820246i	$-0.693836\pi$
$409$		−	33.1769i		−	1.64049i	0.572010	−	0.820246i	$-0.306164\pi$
$410$	−6.96953	+	10.5558i	−0.344201	+	0.521315i
$411$	−12.2487			−0.604184
$412$	−1.46410	−	1.46410i	−0.0721311	−	0.0721311i
$413$	−9.24316	−	9.24316i	−0.454826	−	0.454826i
$414$			10.3923i			0.510754i
$415$	11.9904	−	18.1603i	0.588585	−	0.891452i
$416$			2.31079i			0.113296i
$417$	−23.0064	+	23.0064i	−1.12663	+	1.12663i
$418$	−10.0981	+	10.0981i	−0.493913	+	0.493913i
$419$	12.1459			0.593367			0.296683	−	0.954976i	$-0.404119\pi$
$419$	12.1459			0.593367			0.296683	+	0.954976i	$0.404119\pi$
$420$	−2.19615	−	10.7321i	−0.107161	−	0.523670i
$421$	−8.92820			−0.435134			−0.217567	−	0.976045i	$-0.569812\pi$
$421$	−8.92820			−0.435134			−0.217567	+	0.976045i	$0.569812\pi$
$422$	18.6622	−	18.6622i	0.908461	−	0.908461i
$423$	−7.91688	−	7.91688i	−0.384932	−	0.384932i
$424$			6.92820i			0.336463i
$425$	−1.86250	+	4.64016i	−0.0903446	+	0.225081i
$426$		−	5.31508i		−	0.257517i
$427$	−28.2487	−	28.2487i	−1.36705	−	1.36705i
$428$	12.2474	+	12.2474i	0.592003	+	0.592003i
$429$		−	19.0526i		−	0.919866i
$430$	10.7321	−	2.19615i	0.517545	−	0.105908i
$431$			34.6718i			1.67008i	0.550188	+	0.835041i	$0.314556\pi$
$431$			34.6718i			1.67008i	−0.550188	+	0.835041i	$0.685444\pi$
$432$	3.67423	−	3.67423i	0.176777	−	0.176777i
$433$	1.60770	−	1.60770i	0.0772609	−	0.0772609i	−0.667420	−	0.744681i	$-0.732602\pi$
$433$	1.60770	−	1.60770i	0.0772609	−	0.0772609i	0.744681	+	0.667420i	$0.232602\pi$
$434$	−2.82843			−0.135769
$435$	20.3166	−	30.7709i	0.974108	−	1.47535i
$436$	14.9282			0.714931
$437$	7.34847	−	7.34847i	0.351525	−	0.351525i
$438$	−4.39230	+	4.39230i	−0.209872	+	0.209872i
$439$			10.0000i			0.477274i	0.971109	+	0.238637i	$0.0767006\pi$
$439$			10.0000i			0.477274i	−0.971109	+	0.238637i	$0.923299\pi$
$440$	8.88280	+	5.86491i	0.423471	+	0.279598i
$441$	−3.00000			−0.142857
$442$	−1.63397	−	1.63397i	−0.0777202	−	0.0777202i
$443$	13.4858	+	13.4858i	0.640730	+	0.640730i	0.950735	−	0.310005i	$-0.100331\pi$
$443$	13.4858	+	13.4858i	0.640730	+	0.640730i	−0.310005	+	0.950735i	$0.600331\pi$
$444$	15.8338			0.751437
$445$	−4.43782	−	21.6865i	−0.210373	−	1.02804i
$446$		−	5.79555i		−	0.274427i
$447$	−14.8301	−	14.8301i	−0.701441	−	0.701441i
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	2.20925			0.104261			0.0521305	−	0.998640i	$-0.483399\pi$
$449$	2.20925			0.104261			0.0521305	+	0.998640i	$0.483399\pi$
$450$	−13.9205	−	5.58750i	−0.656218	−	0.263397i
$451$	−26.9282			−1.26800
$452$	−4.52004	+	4.52004i	−0.212605	+	0.212605i
$453$	−24.8874	−	24.8874i	−1.16931	−	1.16931i
$454$		−	9.85641i		−	0.462584i
$455$	−2.92996	−	14.3180i	−0.137359	−	0.671238i
$456$	−5.19615			−0.243332
$457$	−2.19615	−	2.19615i	−0.102732	−	0.102732i	0.653873	−	0.756604i	$-0.273143\pi$
$457$	−2.19615	−	2.19615i	−0.102732	−	0.102732i	−0.756604	+	0.653873i	$0.773143\pi$
$458$	7.29770	+	7.29770i	0.340999	+	0.340999i
$459$			5.19615i			0.242536i
$460$	−6.46410	−	4.26795i	−0.301390	−	0.198994i
$461$		−	32.1480i		−	1.49728i	−0.662976	−	0.748640i	$-0.730707\pi$
$461$		−	32.1480i		−	1.49728i	0.662976	−	0.748640i	$-0.269293\pi$
$462$	16.4901	−	16.4901i	0.767188	−	0.767188i
$463$	29.0981	−	29.0981i	1.35230	−	1.35230i	0.469222	−	0.883080i	$-0.344534\pi$
$463$	29.0981	−	29.0981i	1.35230	−	1.35230i	0.883080	−	0.469222i	$-0.155466\pi$
$464$	−9.52056			−0.441981
$465$	−2.13397	+	3.23205i	−0.0989607	+	0.149883i
$466$	4.39230			0.203470
$467$	23.1822	−	23.1822i	1.07275	−	1.07275i	0.0756075	−	0.997138i	$-0.475910\pi$
$467$	23.1822	−	23.1822i	1.07275	−	1.07275i	0.997138	−	0.0756075i	$-0.0240896\pi$
$468$	4.90192	−	4.90192i	0.226592	−	0.226592i
$469$			35.3205i			1.63095i
$470$	8.17569	−	1.67303i	0.377117	−	0.0771712i
$471$			3.10583i			0.143109i
$472$	3.26795	+	3.26795i	0.150420	+	0.150420i
$473$	16.4901	+	16.4901i	0.758215	+	0.758215i
$474$		−	0.464102i		−	0.0213169i
$475$	5.89230	+	13.7942i	0.270357	+	0.632923i
$476$		−	2.82843i		−	0.129641i
$477$	14.6969	−	14.6969i	0.672927	−	0.672927i
$478$	−12.1962	+	12.1962i	−0.557839	+	0.557839i
$479$	−40.8463			−1.86631			−0.933157	−	0.359468i	$-0.882958\pi$
$479$	−40.8463			−1.86631			−0.933157	+	0.359468i	$0.882958\pi$
$480$	0.776457	+	3.79435i	0.0354403	+	0.173188i
$481$	21.1244			0.963188
$482$	3.10583	−	3.10583i	0.141467	−	0.141467i
$483$	−12.0000	+	12.0000i	−0.546019	+	0.546019i
$484$			11.6603i			0.530012i
$485$	−11.5589	+	17.5068i	−0.524864	+	0.794942i
$486$	−15.5885			−0.707107
$487$	−17.8301	−	17.8301i	−0.807960	−	0.807960i	0.176365	−	0.984325i	$-0.443566\pi$
$487$	−17.8301	−	17.8301i	−0.807960	−	0.807960i	−0.984325	+	0.176365i	$0.943566\pi$
$488$	9.98743	+	9.98743i	0.452110	+	0.452110i
$489$	4.00240			0.180995
$490$	1.23205	−	1.86603i	0.0556584	−	0.0842984i
$491$			11.6926i			0.527682i	0.964566	+	0.263841i	$0.0849894\pi$
$491$			11.6926i			0.527682i	−0.964566	+	0.263841i	$0.915011\pi$
$492$	−6.92820	−	6.92820i	−0.312348	−	0.312348i
$493$	6.73205	−	6.73205i	0.303196	−	0.303196i
$494$	−6.93237			−0.311902
$495$	−6.40192	−	31.2846i	−0.287745	−	1.40614i
$496$	1.00000			0.0449013
$497$	6.13733	−	6.13733i	0.275297	−	0.275297i
$498$	11.9193	+	11.9193i	0.534116	+	0.534116i
$499$		−	29.8564i		−	1.33656i	−0.743911	−	0.668278i	$-0.767032\pi$
$499$		−	29.8564i		−	1.33656i	0.743911	−	0.668278i	$-0.232968\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$	−38.7846			−1.73277
$502$	7.73205	+	7.73205i	0.345098	+	0.345098i
$503$	−4.33057	−	4.33057i	−0.193091	−	0.193091i	0.603939	−	0.797030i	$-0.293597\pi$
$503$	−4.33057	−	4.33057i	−0.193091	−	0.193091i	−0.797030	+	0.603939i	$0.793597\pi$
$504$	8.48528			0.377964
$505$	−21.6865	+	4.43782i	−0.965038	+	0.197480i
$506$		−	16.4901i		−	0.733074i
$507$	−9.38186	+	9.38186i	−0.416663	+	0.416663i
$508$	0.267949	−	0.267949i	0.0118883	−	0.0118883i
$509$	−39.9497			−1.77074			−0.885370	−	0.464887i	$-0.846095\pi$
$509$	−39.9497			−1.77074			−0.885370	+	0.464887i	$0.846095\pi$
$510$	−3.23205	−	2.13397i	−0.143118	−	0.0944940i
$511$	−10.1436			−0.448726
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	11.0227	+	11.0227i	0.486664	+	0.486664i
$514$		−	5.85641i		−	0.258315i
$515$	−3.86370	−	2.55103i	−0.170255	−	0.112412i
$516$			8.48528i			0.373544i
$517$	12.5622	+	12.5622i	0.552484	+	0.552484i
$518$	18.2832	+	18.2832i	0.803319	+	0.803319i
$519$			2.32051i			0.101859i
$520$	1.03590	+	5.06218i	0.0454271	+	0.221991i
$521$		−	20.8343i		−	0.912766i	−0.889783	−	0.456383i	$-0.849145\pi$
$521$		−	20.8343i		−	0.912766i	0.889783	−	0.456383i	$-0.150855\pi$
$522$	20.1962	+	20.1962i	0.883962	+	0.883962i
$523$	5.32051	−	5.32051i	0.232650	−	0.232650i	−0.581148	−	0.813798i	$-0.697396\pi$
$523$	5.32051	−	5.32051i	0.232650	−	0.232650i	0.813798	+	0.581148i	$0.197396\pi$
$524$	7.45001			0.325455
$525$	−9.62209	−	22.5259i	−0.419943	−	0.983110i
$526$	−26.2487			−1.14450
$527$	−0.707107	+	0.707107i	−0.0308021	+	0.0308021i
$528$	−5.83013	+	5.83013i	−0.253724	+	0.253724i
$529$		−	11.0000i		−	0.478261i
$530$	3.10583	+	15.1774i	0.134909	+	0.659265i
$531$		−	13.8647i		−	0.601678i
$532$	−6.00000	−	6.00000i	−0.260133	−	0.260133i
$533$	−9.24316	−	9.24316i	−0.400366	−	0.400366i
$534$	17.1464			0.741999
$535$	32.3205	+	21.3397i	1.39734	+	0.922598i
$536$		−	12.4877i		−	0.539386i
$537$	−2.83013	−	2.83013i	−0.122129	−	0.122129i
$538$	−13.4641	+	13.4641i	−0.580479	+	0.580479i
$539$	4.76028			0.205040
$540$	6.40192	−	9.69615i	0.275495	−	0.417256i
$541$	25.7128			1.10548			0.552740	−	0.833354i	$-0.313582\pi$
$541$	25.7128			1.10548			0.552740	+	0.833354i	$0.313582\pi$
$542$	3.95164	−	3.95164i	0.169737	−	0.169737i
$543$	1.13681	+	1.13681i	0.0487853	+	0.0487853i
$544$			1.00000i			0.0428746i
$545$	32.7028	−	6.69213i	1.40083	−	0.286659i
$546$	11.3205			0.484473
$547$	23.7321	+	23.7321i	1.01471	+	1.01471i	0.999890	+	0.0148190i	$0.00471722\pi$
$547$	23.7321	+	23.7321i	1.01471	+	1.01471i	0.0148190	+	0.999890i	$0.495283\pi$
$548$	5.00052	+	5.00052i	0.213611	+	0.213611i
$549$		−	42.3731i		−	1.80844i
$550$	22.0885	+	8.86603i	0.941855	+	0.378049i
$551$		−	28.5617i		−	1.21677i
$552$	4.24264	−	4.24264i	0.180579	−	0.180579i
$553$	0.535898	−	0.535898i	0.0227887	−	0.0227887i
$554$	−10.9719			−0.466153
$555$	34.6865	−	7.09808i	1.47236	−	0.301297i
$556$	18.7846			0.796645
$557$	−21.3891	+	21.3891i	−0.906284	+	0.906284i	−0.995970	−	0.0896861i	$-0.971414\pi$
$557$	−21.3891	+	21.3891i	−0.906284	+	0.906284i	0.0896861	+	0.995970i	$0.471414\pi$
$558$	−2.12132	−	2.12132i	−0.0898027	−	0.0898027i
$559$			11.3205i			0.478806i
$560$	−3.48477	+	5.27792i	−0.147258	+	0.223033i
$561$		−	8.24504i		−	0.348106i
$562$	20.9282	+	20.9282i	0.882803	+	0.882803i
$563$	−24.3190	−	24.3190i	−1.02492	−	1.02492i	−0.999681	−	0.0252437i	$-0.991964\pi$
$563$	−24.3190	−	24.3190i	−1.02492	−	1.02492i	−0.0252437	−	0.999681i	$-0.508036\pi$
$564$			6.46410i			0.272188i
$565$	−7.87564	+	11.9282i	−0.331331	+	0.501823i
$566$		−	14.2808i		−	0.600268i
$567$	−18.0000	−	18.0000i	−0.755929	−	0.755929i
$568$	−2.16987	+	2.16987i	−0.0910458	+	0.0910458i
$569$	−25.9091			−1.08617			−0.543083	−	0.839679i	$-0.682743\pi$
$569$	−25.9091			−1.08617			−0.543083	+	0.839679i	$0.682743\pi$
$570$	−11.3831	+	2.32937i	−0.476784	+	0.0975666i
$571$	−17.8564			−0.747267			−0.373634	−	0.927576i	$-0.621888\pi$
$571$	−17.8564			−0.747267			−0.373634	+	0.927576i	$0.621888\pi$
$572$	−7.77817	+	7.77817i	−0.325222	+	0.325222i
$573$	12.4641	−	12.4641i	0.520695	−	0.520695i
$574$		−	16.0000i		−	0.667827i
$575$	−16.0740	−	6.45189i	−0.670332	−	0.269063i
$576$	−3.00000			−0.125000
$577$	1.83013	+	1.83013i	0.0761892	+	0.0761892i	0.744174	−	0.667985i	$-0.232843\pi$
$577$	1.83013	+	1.83013i	0.0761892	+	0.0761892i	−0.667985	+	0.744174i	$0.732843\pi$
$578$	11.3137	+	11.3137i	0.470588	+	0.470588i
$579$	−26.0478			−1.08251
$580$	−20.8564	+	4.26795i	−0.866015	+	0.177217i
$581$			27.5264i			1.14199i
$582$	−11.4904	−	11.4904i	−0.476292	−	0.476292i
$583$	−23.3205	+	23.3205i	−0.965837	+	0.965837i
$584$	3.58630			0.148402
$585$	8.54103	−	12.9360i	0.353128	−	0.534837i
$586$	−1.85641			−0.0766874
$587$	−15.4040	+	15.4040i	−0.635793	+	0.635793i	−0.949515	−	0.313722i	$-0.898424\pi$
$587$	−15.4040	+	15.4040i	−0.635793	+	0.635793i	0.313722	+	0.949515i	$0.398424\pi$
$588$	1.22474	+	1.22474i	0.0505076	+	0.0505076i
$589$			3.00000i			0.123613i
$590$	8.62398	+	5.69402i	0.355044	+	0.234419i
$591$	39.4641			1.62334
$592$	−6.46410	−	6.46410i	−0.265673	−	0.265673i
$593$	11.1106	+	11.1106i	0.456259	+	0.456259i	0.897425	−	0.441166i	$-0.145435\pi$
$593$	11.1106	+	11.1106i	0.456259	+	0.456259i	−0.441166	+	0.897425i	$0.645435\pi$
$594$	24.7351			1.01489
$595$	−1.26795	−	6.19615i	−0.0519808	−	0.254017i
$596$			12.1087i			0.495994i
$597$	21.3011	−	21.3011i	0.871797	−	0.871797i
$598$	5.66025	−	5.66025i	0.231465	−	0.231465i
$599$	31.0483			1.26860			0.634300	−	0.773087i	$-0.281288\pi$
$599$	31.0483			1.26860			0.634300	+	0.773087i	$0.281288\pi$
$600$	3.40192	+	7.96410i	0.138883	+	0.325133i
$601$	28.5359			1.16400			0.582002	−	0.813188i	$-0.302270\pi$
$601$	28.5359			1.16400			0.582002	+	0.813188i	$0.302270\pi$
$602$	−9.79796	+	9.79796i	−0.399335	+	0.399335i
$603$	−26.4904	+	26.4904i	−1.07877	+	1.07877i
$604$			20.3205i			0.826830i
$605$	5.22715	+	25.5438i	0.212514	+	1.03850i
$606$		−	17.1464i		−	0.696526i
$607$	7.46410	+	7.46410i	0.302959	+	0.302959i	0.842170	−	0.539212i	$-0.181278\pi$
$607$	7.46410	+	7.46410i	0.302959	+	0.302959i	−0.539212	+	0.842170i	$0.681278\pi$
$608$	2.12132	+	2.12132i	0.0860309	+	0.0860309i
$609$			46.6410i			1.88999i
$610$	26.3564	+	17.4019i	1.06714	+	0.704583i
$611$			8.62398i			0.348889i
$612$	2.12132	−	2.12132i	0.0857493	−	0.0857493i
$613$	4.43782	−	4.43782i	0.179242	−	0.179242i	−0.611783	−	0.791025i	$-0.709548\pi$
$613$	4.43782	−	4.43782i	0.179242	−	0.179242i	0.791025	+	0.611783i	$0.209548\pi$
$614$	16.3886			0.661388
$615$	−18.2832	−	12.0716i	−0.737251	−	0.486773i
$616$	−13.4641			−0.542484
$617$	8.58682	−	8.58682i	0.345692	−	0.345692i	−0.512810	−	0.858502i	$-0.671395\pi$
$617$	8.58682	−	8.58682i	0.345692	−	0.345692i	0.858502	+	0.512810i	$0.171395\pi$
$618$	2.53590	−	2.53590i	0.102009	−	0.102009i
$619$			39.3205i			1.58042i	0.612833	+	0.790212i	$0.290030\pi$
$619$			39.3205i			1.58042i	−0.612833	+	0.790212i	$0.709970\pi$
$620$	2.19067	−	0.448288i	0.0879795	−	0.0180037i
$621$	−18.0000			−0.722315
$622$	1.83013	+	1.83013i	0.0733814	+	0.0733814i
$623$	19.7990	+	19.7990i	0.793230	+	0.793230i
$624$	−4.00240			−0.160224
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$		−	22.4243i		−	0.896257i
$627$	−17.4904	−	17.4904i	−0.698499	−	0.698499i
$628$	1.26795	−	1.26795i	0.0505967	−	0.0505967i
$629$	9.14162			0.364500
$630$	18.5885	−	3.80385i	0.740582	−	0.151549i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−0.189469	+	0.189469i	−0.00753666	+	0.00753666i
$633$	32.3238	+	32.3238i	1.28476	+	1.28476i
$634$			0.464102i			0.0184318i
$635$	0.466870	−	0.707107i	0.0185272	−	0.0280607i
$636$	−12.0000			−0.475831
$637$	1.63397	+	1.63397i	0.0647404	+	0.0647404i
$638$	−32.0464	−	32.0464i	−1.26873	−	1.26873i
$639$	9.20599			0.364183
$640$	1.23205	−	1.86603i	0.0487011	−	0.0737611i
$641$		−	40.0141i		−	1.58046i	−0.612810	−	0.790231i	$-0.709961\pi$
$641$		−	40.0141i		−	1.58046i	0.612810	−	0.790231i	$-0.290039\pi$
$642$	−21.2132	+	21.2132i	−0.837218	+	0.837218i
$643$	−5.66025	+	5.66025i	−0.223219	+	0.223219i	−0.809852	−	0.586634i	$-0.800453\pi$
$643$	−5.66025	+	5.66025i	−0.223219	+	0.223219i	0.586634	+	0.809852i	$0.300453\pi$
$644$	9.79796			0.386094
$645$	3.80385	+	18.5885i	0.149776	+	0.731920i
$646$	−3.00000			−0.118033
$647$	−8.86422	+	8.86422i	−0.348488	+	0.348488i	−0.859546	−	0.511058i	$-0.829254\pi$
$647$	−8.86422	+	8.86422i	−0.348488	+	0.348488i	0.511058	+	0.859546i	$0.329254\pi$
$648$	6.36396	+	6.36396i	0.250000	+	0.250000i
$649$			22.0000i			0.863576i
$650$	4.53862	+	10.6252i	0.178019	+	0.416754i
$651$		−	4.89898i		−	0.192006i
$652$	−1.63397	−	1.63397i	−0.0639914	−	0.0639914i
$653$	−31.9957	−	31.9957i	−1.25209	−	1.25209i	−0.954783	−	0.297305i	$-0.903912\pi$
$653$	−31.9957	−	31.9957i	−1.25209	−	1.25209i	−0.297305	−	0.954783i	$-0.596088\pi$
$654$			25.8564i			1.01107i
$655$	16.3205	−	3.33975i	0.637695	−	0.130495i
$656$			5.65685i			0.220863i
$657$	−7.60770	−	7.60770i	−0.296804	−	0.296804i
$658$	−7.46410	+	7.46410i	−0.290981	+	0.290981i
$659$	11.3137			0.440720			0.220360	−	0.975419i	$-0.429277\pi$
$659$	11.3137			0.440720			0.220360	+	0.975419i	$0.429277\pi$
$660$	−10.1583	+	15.3855i	−0.395412	+	0.598878i
$661$	−27.1769			−1.05706			−0.528530	−	0.848915i	$-0.677256\pi$
$661$	−27.1769			−1.05706			−0.528530	+	0.848915i	$0.677256\pi$
$662$	−1.69161	+	1.69161i	−0.0657465	+	0.0657465i
$663$	2.83013	−	2.83013i	0.109913	−	0.109913i
$664$		−	9.73205i		−	0.377677i
$665$	−15.8338	−	10.4543i	−0.614007	−	0.405400i
$666$			27.4249i			1.06269i
$667$	23.3205	+	23.3205i	0.902974	+	0.902974i
$668$	15.8338	+	15.8338i	0.612626	+	0.612626i
$669$	10.0382			0.388099
$670$	−5.59808	−	27.3564i	−0.216273	−	1.05687i
$671$			67.2359i			2.59561i
$672$	−3.46410	−	3.46410i	−0.133631	−	0.133631i
$673$	−26.1962	+	26.1962i	−1.00979	+	1.00979i	−0.00983584	+	0.999952i	$0.503131\pi$
$673$	−26.1962	+	26.1962i	−1.00979	+	1.00979i	−0.999952	+	0.00983584i	$0.996869\pi$
$674$	−28.0812			−1.08165
$675$	9.67784	−	24.1110i	0.372500	−	0.928032i
$676$	7.66025			0.294625
$677$	−18.7637	+	18.7637i	−0.721148	+	0.721148i	−0.968839	−	0.247691i	$-0.920328\pi$
$677$	−18.7637	+	18.7637i	−0.721148	+	0.721148i	0.247691	+	0.968839i	$0.420328\pi$
$678$	−7.82894	−	7.82894i	−0.300669	−	0.300669i
$679$		−	26.5359i		−	1.01835i
$680$	0.448288	+	2.19067i	0.0171910	+	0.0840084i
$681$	17.0718			0.654193
$682$	3.36603	+	3.36603i	0.128892	+	0.128892i
$683$	−2.27362	−	2.27362i	−0.0869978	−	0.0869978i	0.662269	−	0.749266i	$-0.269594\pi$
$683$	−2.27362	−	2.27362i	−0.0869978	−	0.0869978i	−0.749266	+	0.662269i	$0.769594\pi$
$684$		−	9.00000i		−	0.344124i
$685$	13.1962	+	8.71281i	0.504199	+	0.332899i
$686$		−	16.9706i		−	0.647939i
$687$	−12.6400	+	12.6400i	−0.482246	+	0.482246i
$688$	3.46410	−	3.46410i	0.132068	−	0.132068i
$689$	−16.0096			−0.609918
$690$	7.39230	−	11.1962i	0.281420	−	0.426230i
$691$	44.3731			1.68803			0.844016	−	0.536319i	$-0.180186\pi$
$691$	44.3731			1.68803			0.844016	+	0.536319i	$0.180186\pi$
$692$	0.947343	−	0.947343i	0.0360126	−	0.0360126i
$693$	28.5617	+	28.5617i	1.08497	+	1.08497i
$694$		−	36.6603i		−	1.39160i
$695$	41.1509	−	8.42091i	1.56094	−	0.319423i
$696$		−	16.4901i		−	0.625055i
$697$	−4.00000	−	4.00000i	−0.151511	−	0.151511i
$698$	−18.5606	−	18.5606i	−0.702531	−	0.702531i
$699$			7.60770i			0.287749i
$700$	−5.26795	+	13.1244i	−0.199110	+	0.496054i
$701$		−	31.1499i		−	1.17651i	−0.808674	−	0.588257i	$-0.799814\pi$
$701$		−	31.1499i		−	1.17651i	0.808674	−	0.588257i	$-0.200186\pi$
$702$	8.49038	+	8.49038i	0.320449	+	0.320449i
$703$	19.3923	−	19.3923i	0.731395	−	0.731395i
$704$	4.76028			0.179410
$705$	2.89778	+	14.1607i	0.109137	+	0.533323i
$706$	−1.19615			−0.0450178
$707$	19.7990	−	19.7990i	0.744618	−	0.744618i
$708$	−5.66025	+	5.66025i	−0.212725	+	0.212725i
$709$		−	4.80385i		−	0.180412i	−0.995923	−	0.0902061i	$-0.971247\pi$
$709$		−	4.80385i		−	0.180412i	0.995923	−	0.0902061i	$-0.0287526\pi$
$710$	−3.78075	+	5.72620i	−0.141889	+	0.214901i
$711$	0.803848			0.0301466
$712$	−7.00000	−	7.00000i	−0.262336	−	0.262336i
$713$	−2.44949	−	2.44949i	−0.0917341	−	0.0917341i
$714$	4.89898			0.183340
$715$	−13.5526	+	20.5263i	−0.506837	+	0.767639i
$716$			2.31079i			0.0863582i
$717$	−21.1244	−	21.1244i	−0.788904	−	0.788904i
$718$	16.7583	−	16.7583i	0.625415	−	0.625415i
$719$	3.66063			0.136519			0.0682593	−	0.997668i	$-0.478255\pi$
$719$	3.66063			0.136519			0.0682593	+	0.997668i	$0.478255\pi$
$720$	−6.57201	+	1.34486i	−0.244924	+	0.0501201i
$721$	5.85641			0.218104
$722$	7.07107	−	7.07107i	0.263158	−	0.263158i
$723$	5.37945	+	5.37945i	0.200064	+	0.200064i
$724$		−	0.928203i		−	0.0344964i
$725$	−43.7762	+	18.6993i	−1.62581	+	0.694476i
$726$	−20.1962			−0.749550
$727$	−21.4641	−	21.4641i	−0.796059	−	0.796059i	0.186412	−	0.982472i	$-0.440314\pi$
$727$	−21.4641	−	21.4641i	−0.796059	−	0.796059i	−0.982472	+	0.186412i	$0.940314\pi$
$728$	−4.62158	−	4.62158i	−0.171287	−	0.171287i
$729$		−	27.0000i		−	1.00000i
$730$	7.85641	−	1.60770i	0.290779	−	0.0595035i
$731$			4.89898i			0.181195i
$732$	−17.2987	+	17.2987i	−0.639380	+	0.639380i
$733$	32.5885	−	32.5885i	1.20368	−	1.20368i	0.230644	−	0.973038i	$-0.425917\pi$
$733$	32.5885	−	32.5885i	1.20368	−	1.20368i	0.973038	−	0.230644i	$-0.0740832\pi$
$734$	30.9468			1.14227
$735$	3.23205	+	2.13397i	0.119216	+	0.0787128i
$736$	−3.46410			−0.127688
$737$	42.0339	−	42.0339i	1.54834	−	1.54834i
$738$	12.0000	−	12.0000i	0.441726	−	0.441726i
$739$			3.07180i			0.112998i	0.998403	+	0.0564989i	$0.0179938\pi$
$739$			3.07180i			0.112998i	−0.998403	+	0.0564989i	$0.982006\pi$
$740$	−17.0585	−	11.2629i	−0.627083	−	0.414034i
$741$		−	12.0072i		−	0.441096i
$742$	−13.8564	−	13.8564i	−0.508685	−	0.508685i
$743$	14.9000	+	14.9000i	0.546628	+	0.546628i	0.925464	−	0.378836i	$-0.123675\pi$
$743$	14.9000	+	14.9000i	0.546628	+	0.546628i	−0.378836	+	0.925464i	$0.623675\pi$
$744$			1.73205i			0.0635001i
$745$	5.42820	+	26.5263i	0.198874	+	0.971848i
$746$		−	13.9391i		−	0.510345i
$747$	−20.6448	+	20.6448i	−0.755354	+	0.755354i
$748$	−3.36603	+	3.36603i	−0.123074	+	0.123074i
$749$	−48.9898			−1.79005
$750$	11.0227	+	15.9217i	0.402492	+	0.581378i
$751$	10.3923			0.379221			0.189610	−	0.981859i	$-0.439278\pi$
$751$	10.3923			0.379221			0.189610	+	0.981859i	$0.439278\pi$
$752$	2.63896	−	2.63896i	0.0962329	−	0.0962329i
$753$	−13.3923	+	13.3923i	−0.488043	+	0.488043i
$754$		−	22.0000i		−	0.801193i
$755$	9.10943	+	44.5155i	0.331526	+	1.62009i
$756$			14.6969i			0.534522i
$757$	−7.39230	−	7.39230i	−0.268678	−	0.268678i	0.559889	−	0.828567i	$-0.310844\pi$
$757$	−7.39230	−	7.39230i	−0.268678	−	0.268678i	−0.828567	+	0.559889i	$0.810844\pi$
$758$	20.6448	+	20.6448i	0.749853	+	0.749853i
$759$	28.5617			1.03672
$760$	5.59808	+	3.69615i	0.203064	+	0.134074i
$761$		−	46.2257i		−	1.67568i	−0.545915	−	0.837841i	$-0.683818\pi$
$761$		−	46.2257i		−	1.67568i	0.545915	−	0.837841i	$-0.316182\pi$
$762$	0.464102	+	0.464102i	0.0168126	+	0.0168126i
$763$	−29.8564	+	29.8564i	−1.08087	+	1.08087i
$764$	−10.1769			−0.368187
$765$	3.69615	−	5.59808i	0.133635	−	0.202399i
$766$	1.46410			0.0529001
$767$	−7.55154	+	7.55154i	−0.272670	+	0.272670i
$768$	1.22474	+	1.22474i	0.0441942	+	0.0441942i
$769$		−	18.6410i		−	0.672212i	−0.941824	−	0.336106i	$-0.890890\pi$
$769$		−	18.6410i		−	0.672212i	0.941824	−	0.336106i	$-0.109110\pi$
$770$	−29.4954	+	6.03579i	−1.06294	+	0.217515i
$771$	10.1436			0.365313
$772$	10.6340	+	10.6340i	0.382725	+	0.382725i
$773$	−2.07055	−	2.07055i	−0.0744726	−	0.0744726i	0.668889	−	0.743362i	$-0.266770\pi$
$773$	−2.07055	−	2.07055i	−0.0744726	−	0.0744726i	−0.743362	+	0.668889i	$0.766770\pi$
$774$	−14.6969			−0.528271
$775$	4.59808	−	1.96410i	0.165168	−	0.0705526i
$776$			9.38186i			0.336789i
$777$	−31.6675	+	31.6675i	−1.13607	+	1.13607i
$778$	−6.19615	+	6.19615i	−0.222143	+	0.222143i
$779$	−16.9706			−0.608034
$780$	−8.76795	+	1.79423i	−0.313943	+	0.0642437i
$781$	−14.6077			−0.522704
$782$	2.44949	−	2.44949i	0.0875936	−	0.0875936i
$783$	−34.9808	+	34.9808i	−1.25011	+	1.25011i
$784$		−	1.00000i		−	0.0357143i
$785$	2.20925	−	3.34607i	0.0788516	−	0.119426i
$786$			12.9038i			0.460263i
$787$	−5.12436	−	5.12436i	−0.182664	−	0.182664i	0.609852	−	0.792515i	$-0.291229\pi$
$787$	−5.12436	−	5.12436i	−0.182664	−	0.182664i	−0.792515	+	0.609852i	$0.791229\pi$
$788$	−16.1112	−	16.1112i	−0.573936	−	0.573936i
$789$		−	45.4641i		−	1.61856i
$790$	−0.330127	+	0.500000i	−0.0117454	+	0.0177892i
$791$		−	18.0802i		−	0.642857i
$792$	−10.0981	−	10.0981i	−0.358820	−	0.358820i
$793$	−23.0788	+	23.0788i	−0.819554	+	0.819554i
$794$	24.7723			0.879136
$795$	−26.2880	+	5.37945i	−0.932341	+	0.190790i
$796$	−17.3923			−0.616454
$797$	−21.0101	+	21.0101i	−0.744217	+	0.744217i	−0.973387	−	0.229169i	$-0.926399\pi$
$797$	−21.0101	+	21.0101i	−0.744217	+	0.744217i	0.229169	+	0.973387i	$0.426399\pi$
$798$	10.3923	−	10.3923i	0.367884	−	0.367884i
$799$			3.73205i			0.132030i
$800$	1.86250	−	4.64016i	0.0658494	−	0.164054i
$801$			29.6985i			1.04934i
$802$	−2.56218	−	2.56218i	−0.0904736	−	0.0904736i
$803$	12.0716	+	12.0716i	0.425997	+	0.425997i
$804$	21.6293			0.762807
$805$	21.4641	−	4.39230i	0.756510	−	0.154808i
$806$			2.31079i			0.0813941i
$807$	−23.3205	−	23.3205i	−0.820921	−	0.820921i
$808$	−7.00000	+	7.00000i	−0.246259	+	0.246259i
$809$	−30.9468			−1.08803			−0.544016	−	0.839075i	$-0.683097\pi$
$809$	−30.9468			−1.08803			−0.544016	+	0.839075i	$0.683097\pi$
$810$	16.7942	+	11.0885i	0.590089	+	0.389609i
$811$	17.6077			0.618290			0.309145	−	0.951015i	$-0.399957\pi$
$811$	17.6077			0.618290			0.309145	+	0.951015i	$0.399957\pi$
$812$	19.0411	−	19.0411i	0.668212	−	0.668212i
$813$	6.84443	+	6.84443i	0.240045	+	0.240045i
$814$		−	43.5167i		−	1.52526i
$815$	−4.31199	−	2.84701i	−0.151042	−	0.0997264i
$816$	−1.73205			−0.0606339
$817$	10.3923	+	10.3923i	0.363581	+	0.363581i
$818$	−23.4596	−	23.4596i	−0.820246	−	0.820246i
$819$			19.6077i			0.685148i
$820$	2.53590	+	12.3923i	0.0885574	+	0.432758i
$821$		−	31.8706i		−	1.11229i	−0.831085	−	0.556145i	$-0.812280\pi$
$821$		−	31.8706i		−	1.11229i	0.831085	−	0.556145i	$-0.187720\pi$
$822$	−8.66115	+	8.66115i	−0.302092	+	0.302092i
$823$	−9.56218	+	9.56218i	−0.333317	+	0.333317i	−0.853845	−	0.520528i	$-0.825735\pi$
$823$	−9.56218	+	9.56218i	−0.333317	+	0.333317i	0.520528	+	0.853845i	$0.325735\pi$
$824$	−2.07055			−0.0721311
$825$	−15.3564	+	38.2583i	−0.534641	+	1.33198i
$826$	−13.0718			−0.454826
$827$	−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
$829$			50.9282i			1.76881i	0.466721	+	0.884405i	$0.345435\pi$
$829$			50.9282i			1.76881i	−0.466721	+	0.884405i	$0.654565\pi$
$830$	−4.36276	−	21.3197i	−0.151434	−	0.740018i
$831$		−	19.0040i		−	0.659240i
$832$	1.63397	+	1.63397i	0.0566479	+	0.0566479i
$833$	0.707107	+	0.707107i	0.0244998	+	0.0244998i
$834$			32.5359i			1.12663i
$835$	41.7846	+	27.5885i	1.44602	+	0.954738i
$836$			14.2808i			0.493913i
$837$	3.67423	−	3.67423i	0.127000	−	0.127000i
$838$	8.58846	−	8.58846i	0.296683	−	0.296683i
$839$	−13.9663			−0.482169			−0.241085	−	0.970504i	$-0.577503\pi$
$839$	−13.9663			−0.482169			−0.241085	+	0.970504i	$0.577503\pi$
$840$	−9.14162	−	6.03579i	−0.315416	−	0.208255i
$841$	61.6410			2.12555
$842$	−6.31319	+	6.31319i	−0.217567	+	0.217567i
$843$	−36.2487	+	36.2487i	−1.24847	+	1.24847i
$844$		−	26.3923i		−	0.908461i
$845$	16.7811	−	3.43400i	0.577287	−	0.118133i
$846$	−11.1962			−0.384932
$847$	−23.3205	−	23.3205i	−0.801302	−	0.801302i
$848$	4.89898	+	4.89898i	0.168232	+	0.168232i
$849$	24.7351			0.848908
$850$	1.96410	+	4.59808i	0.0673681	+	0.157713i
$851$			31.6675i			1.08555i
$852$	−3.75833	−	3.75833i	−0.128758	−	0.128758i
$853$	−1.80385	+	1.80385i	−0.0617626	+	0.0617626i	−0.737313	−	0.675551i	$-0.763906\pi$
$853$	−1.80385	+	1.80385i	−0.0617626	+	0.0617626i	0.675551	+	0.737313i	$0.263906\pi$
$854$	−39.9497			−1.36705
$855$	−4.03459	−	19.7160i	−0.137980	−	0.674274i
$856$	17.3205			0.592003
$857$	−12.0716	+	12.0716i	−0.412357	+	0.412357i	−0.882559	−	0.470202i	$-0.844181\pi$
$857$	−12.0716	+	12.0716i	−0.412357	+	0.412357i	0.470202	+	0.882559i	$0.344181\pi$
$858$	−13.4722	−	13.4722i	−0.459933	−	0.459933i
$859$		−	44.6410i		−	1.52313i	−0.648087	−	0.761566i	$-0.724431\pi$
$859$		−	44.6410i		−	1.52313i	0.648087	−	0.761566i	$-0.275569\pi$
$860$	6.03579	−	9.14162i	0.205819	−	0.311727i
$861$	27.7128			0.944450
$862$	24.5167	+	24.5167i	0.835041	+	0.835041i
$863$	30.3548	+	30.3548i	1.03329	+	1.03329i	0.999426	+	0.0338638i	$0.0107812\pi$
$863$	30.3548	+	30.3548i	1.03329	+	1.03329i	0.0338638	+	0.999426i	$0.489219\pi$
$864$		−	5.19615i		−	0.176777i
$865$	1.65064	−	2.50000i	0.0561233	−	0.0850026i
$866$		−	2.27362i		−	0.0772609i
$867$	−19.5959	+	19.5959i	−0.665512	+	0.665512i
$868$	−2.00000	+	2.00000i	−0.0678844	+	0.0678844i
$869$	−1.27551			−0.0432688
$870$	−7.39230	−	36.1244i	−0.250623	−	1.22473i
$871$	28.8564			0.977762
$872$	10.5558	−	10.5558i	0.357466	−	0.357466i
$873$	19.9019	−	19.9019i	0.673578	−	0.673578i
$874$		−	10.3923i		−	0.351525i
$875$	−5.65685	+	31.1127i	−0.191237	+	1.05180i
$876$			6.21166i			0.209872i
$877$	11.2679	+	11.2679i	0.380492	+	0.380492i	0.871279	−	0.490788i	$-0.163291\pi$
$877$	11.2679	+	11.2679i	0.380492	+	0.380492i	−0.490788	+	0.871279i	$0.663291\pi$
$878$	7.07107	+	7.07107i	0.238637	+	0.238637i
$879$		−	3.21539i		−	0.108452i
$880$	10.4282	−	2.13397i	0.351535	−	0.0719363i
$881$			43.3230i			1.45959i	0.683667	+	0.729794i	$0.260384\pi$
$881$			43.3230i			1.45959i	−0.683667	+	0.729794i	$0.739616\pi$
$882$	−2.12132	+	2.12132i	−0.0714286	+	0.0714286i
$883$	1.26795	−	1.26795i	0.0426699	−	0.0426699i	−0.685450	−	0.728120i	$-0.740394\pi$
$883$	1.26795	−	1.26795i	0.0426699	−	0.0426699i	0.728120	+	0.685450i	$0.240394\pi$
$884$	−2.31079			−0.0777202
$885$	−9.86233	+	14.9372i	−0.331519	+	0.502108i
$886$	19.0718			0.640730
$887$	37.7033	−	37.7033i	1.26595	−	1.26595i	0.317792	−	0.948160i	$-0.397059\pi$
$887$	37.7033	−	37.7033i	1.26595	−	1.26595i	0.948160	−	0.317792i	$-0.102941\pi$
$888$	11.1962	−	11.1962i	0.375718	−	0.375718i
$889$			1.07180i			0.0359469i
$890$	−18.4727	−	12.1967i	−0.619207	−	0.408834i
$891$			42.8425i			1.43528i
$892$	−4.09808	−	4.09808i	−0.137214	−	0.137214i
$893$	7.91688	+	7.91688i	0.264928	+	0.264928i
$894$	−20.9730			−0.701441
$895$	1.03590	+	5.06218i	0.0346263	+	0.169210i
$896$			2.82843i			0.0944911i
$897$	9.80385	+	9.80385i	0.327341	+	0.327341i
$898$	1.56218	−	1.56218i	0.0521305	−	0.0521305i
$899$	−9.52056			−0.317528
$900$	−13.7942	+	5.89230i	−0.459808	+	0.196410i
$901$	−6.92820			−0.230812
$902$	−19.0411	+	19.0411i	−0.634000	+	0.634000i
$903$	−16.9706	−	16.9706i	−0.564745	−	0.564745i
$904$			6.39230i			0.212605i
$905$	−0.416102	−	2.03339i	−0.0138317	−	0.0675921i
$906$	−35.1962			−1.16931
$907$	17.2417	+	17.2417i	0.572500	+	0.572500i	0.932826	−	0.360326i	$-0.117335\pi$
$907$	17.2417	+	17.2417i	0.572500	+	0.572500i	−0.360326	+	0.932826i	$0.617335\pi$
$908$	−6.96953	−	6.96953i	−0.231292	−	0.231292i
$909$	29.6985			0.985037
$910$	−12.1962	−	8.05256i	−0.404299	−	0.266940i
$911$			35.0507i			1.16128i	0.814160	+	0.580641i	$0.197198\pi$
$911$			35.0507i			1.16128i	−0.814160	+	0.580641i	$0.802802\pi$
$912$	−3.67423	+	3.67423i	−0.121666	+	0.121666i
$913$	32.7583	−	32.7583i	1.08414	−	1.08414i
$914$	−3.10583			−0.102732
$915$	−30.1410	+	45.6506i	−0.996431	+	1.50916i
$916$	10.3205			0.340999
$917$	−14.9000	+	14.9000i	−0.492042	+	0.492042i
$918$	3.67423	+	3.67423i	0.121268	+	0.121268i
$919$			4.53590i			0.149625i	0.997198	+	0.0748127i	$0.0238359\pi$
$919$			4.53590i			0.149625i	−0.997198	+	0.0748127i	$0.976164\pi$
$920$	−7.58871	+	1.55291i	−0.250192	+	0.0511981i
$921$			28.3858i			0.935344i
$922$	−22.7321	−	22.7321i	−0.748640	−	0.748640i
$923$	−5.01412	−	5.01412i	−0.165042	−	0.165042i
$924$		−	23.3205i		−	0.767188i
$925$	−42.4186	−	17.0263i	−1.39471	−	0.559821i
$926$		−	41.1509i		−	1.35230i
$927$	4.39230	+	4.39230i	0.144262	+	0.144262i
$928$	−6.73205	+	6.73205i	−0.220990	+	0.220990i
$929$	6.31319			0.207129			0.103565	−	0.994623i	$-0.466975\pi$
$929$	6.31319			0.207129			0.103565	+	0.994623i	$0.466975\pi$
$930$	0.776457	+	3.79435i	0.0254610	+	0.124422i
$931$	3.00000			0.0983210
$932$	3.10583	−	3.10583i	0.101735	−	0.101735i
$933$	−3.16987	+	3.16987i	−0.103777	+	0.103777i
$934$		−	32.7846i		−	1.07275i
$935$	−5.86491	+	8.88280i	−0.191803	+	0.290499i
$936$		−	6.93237i		−	0.226592i
$937$	−31.3468	−	31.3468i	−1.02405	−	1.02405i	−0.999703	−	0.0243515i	$-0.992248\pi$
$937$	−31.3468	−	31.3468i	−1.02405	−	1.02405i	−0.0243515	−	0.999703i	$-0.507752\pi$
$938$	24.9754	+	24.9754i	0.815475	+	0.815475i
$939$	38.8401			1.26750
$940$	4.59808	−	6.96410i	0.149973	−	0.227144i
$941$		−	28.5617i		−	0.931084i	−0.885026	−	0.465542i	$-0.845859\pi$
$941$		−	28.5617i		−	0.931084i	0.885026	−	0.465542i	$-0.154141\pi$
$942$	2.19615	+	2.19615i	0.0715545	+	0.0715545i
$943$	13.8564	−	13.8564i	0.451227	−	0.451227i
$944$	4.62158			0.150420
$945$	6.58846	+	32.1962i	0.214323	+	1.04734i
$946$	23.3205			0.758215
$947$	−19.7482	+	19.7482i	−0.641731	+	0.641731i	−0.950981	−	0.309250i	$-0.899922\pi$
$947$	−19.7482	+	19.7482i	−0.641731	+	0.641731i	0.309250	+	0.950981i	$0.399922\pi$
$948$	−0.328169	−	0.328169i	−0.0106584	−	0.0106584i
$949$			8.28719i			0.269013i
$950$	13.9205	+	5.58750i	0.451640	+	0.181283i
$951$	−0.803848			−0.0260665
$952$	−2.00000	−	2.00000i	−0.0648204	−	0.0648204i
$953$	−6.29959	−	6.29959i	−0.204064	−	0.204064i	0.597675	−	0.801739i	$-0.296091\pi$
$953$	−6.29959	−	6.29959i	−0.204064	−	0.204064i	−0.801739	+	0.597675i	$0.796091\pi$
$954$		−	20.7846i		−	0.672927i
$955$	−22.2942	+	4.56218i	−0.721424	+	0.147629i
$956$			17.2480i			0.557839i
$957$	55.5061	−	55.5061i	1.79426	−	1.79426i
$958$	−28.8827	+	28.8827i	−0.933157	+	0.933157i
$959$	−20.0021			−0.645900
$960$	3.23205	+	2.13397i	0.104314	+	0.0688737i
$961$	1.00000			0.0322581
$962$	14.9372	−	14.9372i	0.481594	−	0.481594i
$963$	−36.7423	−	36.7423i	−1.18401	−	1.18401i
$964$		−	4.39230i		−	0.141467i
$965$	28.0626	+	18.5285i	0.903368	+	0.596452i
$966$			16.9706i			0.546019i
$967$	−0.418584	−	0.418584i	−0.0134608	−	0.0134608i	0.700344	−	0.713805i	$-0.253030\pi$
$967$	−0.418584	−	0.418584i	−0.0134608	−	0.0134608i	−0.713805	+	0.700344i	$0.753030\pi$
$968$	8.24504	+	8.24504i	0.265006	+	0.265006i
$969$		−	5.19615i		−	0.166924i
$970$	4.20577	+	20.5526i	0.135039	+	0.659903i
$971$			10.6302i			0.341138i	0.985346	+	0.170569i	$0.0545606\pi$
$971$			10.6302i			0.341138i	−0.985346	+	0.170569i	$0.945439\pi$
$972$	−11.0227	+	11.0227i	−0.353553	+	0.353553i
$973$	−37.5692	+	37.5692i	−1.20441	+	1.20441i
$974$	−25.2156			−0.807960
$975$	−18.4034	+	7.86113i	−0.589379	+	0.251758i
$976$	14.1244			0.452110
$977$	−40.8091	+	40.8091i	−1.30560	+	1.30560i	−0.381042	+	0.924558i	$0.624435\pi$
$977$	−40.8091	+	40.8091i	−1.30560	+	1.30560i	−0.924558	+	0.381042i	$0.875565\pi$
$978$	2.83013	−	2.83013i	0.0904975	−	0.0904975i
$979$		−	47.1244i		−	1.50610i
$980$	−0.448288	−	2.19067i	−0.0143200	−	0.0699784i
$981$	−44.7846			−1.42986
$982$	8.26795	+	8.26795i	0.263841	+	0.263841i
$983$	−23.8386	−	23.8386i	−0.760332	−	0.760332i	0.216050	−	0.976382i	$-0.430682\pi$
$983$	−23.8386	−	23.8386i	−0.760332	−	0.760332i	−0.976382	+	0.216050i	$0.930682\pi$
$984$	−9.79796			−0.312348
$985$	−42.5167	−	28.0718i	−1.35469	−	0.894442i
$986$		−	9.52056i		−	0.303196i
$987$	−12.9282	−	12.9282i	−0.411509	−	0.411509i
$988$	−4.90192	+	4.90192i	−0.155951	+	0.155951i
$989$	−16.9706			−0.539633
$990$	−26.6484	−	17.5947i	−0.846942	−	0.559197i
$991$	−23.4641			−0.745362			−0.372681	−	0.927960i	$-0.621561\pi$
$991$	−23.4641			−0.745362			−0.372681	+	0.927960i	$0.621561\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−2.92996	−	2.92996i	−0.0929796	−	0.0929796i
$994$		−	8.67949i		−	0.275297i
$995$	−38.1008	+	7.79676i	−1.20788	+	0.247174i
$996$	16.8564			0.534116
$997$	−1.26795	−	1.26795i	−0.0401564	−	0.0401564i	0.686743	−	0.726900i	$-0.259040\pi$
$997$	−1.26795	−	1.26795i	−0.0401564	−	0.0401564i	−0.726900	+	0.686743i	$0.759040\pi$
$998$	−21.1117	−	21.1117i	−0.668278	−	0.668278i
$999$	−47.5013			−1.50287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.e.497.4	yes	8
3.2	odd	2	inner	930.2.j.e.497.1	✓	8
5.3	odd	4	inner	930.2.j.e.683.1	yes	8
15.8	even	4	inner	930.2.j.e.683.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.e.497.1	✓	8	3.2	odd	2	inner
930.2.j.e.497.4	yes	8	1.1	even	1	trivial
930.2.j.e.683.1	yes	8	5.3	odd	4	inner
930.2.j.e.683.4	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} +(-0.448288 - 2.19067i) q^{5} +1.73205 q^{6} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(-1.86603 - 1.23205i) q^{10} -4.76028i q^{11} +(1.22474 - 1.22474i) q^{12} +(1.63397 - 1.63397i) q^{13} +2.82843 q^{14} +(2.13397 - 3.23205i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(2.12132 + 2.12132i) q^{18} -3.00000i q^{19} +(-2.19067 + 0.448288i) q^{20} +4.89898i q^{21} +(-3.36603 - 3.36603i) q^{22} +(2.44949 + 2.44949i) q^{23} -1.73205i q^{24} +(-4.59808 + 1.96410i) q^{25} -2.31079i q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 2.00000i) q^{28} +9.52056 q^{29} +(-0.776457 - 3.79435i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.83013 - 5.83013i) q^{33} -1.00000i q^{34} +(3.48477 - 5.27792i) q^{35} +3.00000 q^{36} +(6.46410 + 6.46410i) q^{37} +(-2.12132 - 2.12132i) q^{38} +4.00240 q^{39} +(-1.23205 + 1.86603i) q^{40} -5.65685i q^{41} +(3.46410 + 3.46410i) q^{42} +(-3.46410 + 3.46410i) q^{43} -4.76028 q^{44} +(6.57201 - 1.34486i) q^{45} +3.46410 q^{46} +(-2.63896 + 2.63896i) q^{47} +(-1.22474 - 1.22474i) q^{48} +1.00000i q^{49} +(-1.86250 + 4.64016i) q^{50} +1.73205 q^{51} +(-1.63397 - 1.63397i) q^{52} +(-4.89898 - 4.89898i) q^{53} +5.19615i q^{54} +(-10.4282 + 2.13397i) q^{55} -2.82843i q^{56} +(3.67423 - 3.67423i) q^{57} +(6.73205 - 6.73205i) q^{58} -4.62158 q^{59} +(-3.23205 - 2.13397i) q^{60} -14.1244 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.00000 + 6.00000i) q^{63} +1.00000i q^{64} +(-4.31199 - 2.84701i) q^{65} -8.24504i q^{66} +(8.83013 + 8.83013i) q^{67} +(-0.707107 - 0.707107i) q^{68} +6.00000i q^{69} +(-1.26795 - 6.19615i) q^{70} -3.06866i q^{71} +(2.12132 - 2.12132i) q^{72} +(-2.53590 + 2.53590i) q^{73} +9.14162 q^{74} +(-8.03699 - 3.22595i) q^{75} -3.00000 q^{76} +(9.52056 - 9.52056i) q^{77} +(2.83013 - 2.83013i) q^{78} -0.267949i q^{79} +(0.448288 + 2.19067i) q^{80} -9.00000 q^{81} +(-4.00000 - 4.00000i) q^{82} +(6.88160 + 6.88160i) q^{83} +4.89898 q^{84} +(-1.86603 - 1.23205i) q^{85} +4.89898i q^{86} +(11.6603 + 11.6603i) q^{87} +(-3.36603 + 3.36603i) q^{88} +9.89949 q^{89} +(3.69615 - 5.59808i) q^{90} +6.53590 q^{91} +(2.44949 - 2.44949i) q^{92} +(-1.22474 - 1.22474i) q^{93} +3.73205i q^{94} +(-6.57201 + 1.34486i) q^{95} -1.73205 q^{96} +(-6.63397 - 6.63397i) q^{97} +(0.707107 + 0.707107i) q^{98} +14.2808 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

Related objects

Downloads

Learn more