LMFDB - Embedded newform 1014.2.e.m.991.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,2,Mod(529,1014)] 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("1014.529"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [6,3,-3,-3,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.3
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.m.529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.04892 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.346011 + 0.599308i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.02446 + 3.50647i) q^{10} +(2.42543 + 4.20096i) q^{11} +1.00000 q^{12} -0.692021 q^{14} +(-2.02446 - 3.50647i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.69202 + 6.39477i) q^{17} -1.00000 q^{18} +(0.890084 - 1.54167i) q^{19} +(-2.02446 + 3.50647i) q^{20} +0.692021 q^{21} +(-2.42543 + 4.20096i) q^{22} +(-2.55496 - 4.42532i) q^{23} +(0.500000 + 0.866025i) q^{24} +11.3937 q^{25} +1.00000 q^{27} +(-0.346011 - 0.599308i) q^{28} +(1.67241 + 2.89669i) q^{29} +(2.02446 - 3.50647i) q^{30} +0.972853 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.42543 - 4.20096i) q^{33} -7.38404 q^{34} +(-1.40097 + 2.42655i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.643104 - 1.11389i) q^{37} +1.78017 q^{38} -4.04892 q^{40} +(-0.753020 - 1.30427i) q^{41} +(0.346011 + 0.599308i) q^{42} +(4.15883 - 7.20331i) q^{43} -4.85086 q^{44} +(-2.02446 + 3.50647i) q^{45} +(2.55496 - 4.42532i) q^{46} -7.20775 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.26055 + 5.64744i) q^{49} +(5.69687 + 9.86726i) q^{50} +7.38404 q^{51} +13.4765 q^{53} +(0.500000 + 0.866025i) q^{54} +(9.82036 + 17.0094i) q^{55} +(0.346011 - 0.599308i) q^{56} -1.78017 q^{57} +(-1.67241 + 2.89669i) q^{58} +(-0.653989 + 1.13274i) q^{59} +4.04892 q^{60} +(0.198062 - 0.343054i) q^{61} +(0.486426 + 0.842515i) q^{62} +(-0.346011 - 0.599308i) q^{63} +1.00000 q^{64} +4.85086 q^{66} +(-3.02715 - 5.24317i) q^{67} +(-3.69202 - 6.39477i) q^{68} +(-2.55496 + 4.42532i) q^{69} -2.80194 q^{70} +(0.664874 - 1.15160i) q^{71} +(0.500000 - 0.866025i) q^{72} -7.65279 q^{73} +(0.643104 - 1.11389i) q^{74} +(-5.69687 - 9.86726i) q^{75} +(0.890084 + 1.54167i) q^{76} -3.35690 q^{77} -8.33944 q^{79} +(-2.02446 - 3.50647i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.753020 - 1.30427i) q^{82} +15.3274 q^{83} +(-0.346011 + 0.599308i) q^{84} +(-14.9487 + 25.8919i) q^{85} +8.31767 q^{86} +(1.67241 - 2.89669i) q^{87} +(-2.42543 - 4.20096i) q^{88} +(-1.55496 - 2.69327i) q^{89} -4.04892 q^{90} +5.10992 q^{92} +(-0.486426 - 0.842515i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(3.60388 - 6.24210i) q^{95} -1.00000 q^{96} +(4.27144 - 7.39835i) q^{97} +(-3.26055 + 5.64744i) q^{98} -4.85086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} - 3 q^{16} - 12 q^{17} - 6 q^{18} + 4 q^{19} - 3 q^{20} - 6 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 - 3 * q^16 - 12 * q^17 - 6 * q^18 + 4 * q^19 - 3 * q^20 - 6 * q^21 - q^22 - 16 * q^23 + 3 * q^24 + 4 * q^25 + 6 * q^27 + 3 * q^28 - 13 * q^29 + 3 * q^30 + 18 * q^31 + 3 * q^32 + q^33 - 24 * q^34 - 4 * q^35 - 3 * q^36 - 12 * q^37 + 8 * q^38 - 6 * q^40 - 14 * q^41 - 3 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 16 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^49 + 2 * q^50 + 24 * q^51 + 30 * q^53 + 3 * q^54 + 22 * q^55 - 3 * q^56 - 8 * q^57 + 13 * q^58 - 9 * q^59 + 6 * q^60 + 10 * q^61 + 9 * q^62 + 3 * q^63 + 6 * q^64 + 2 * q^66 - 6 * q^67 - 12 * q^68 - 16 * q^69 - 8 * q^70 + 6 * q^71 + 3 * q^72 - 10 * q^73 + 12 * q^74 - 2 * q^75 + 4 * q^76 - 12 * q^77 - 10 * q^79 - 3 * q^80 - 3 * q^81 + 14 * q^82 + 14 * q^83 + 3 * q^84 - 26 * q^85 + 16 * q^86 - 13 * q^87 - q^88 - 10 * q^89 - 6 * q^90 + 32 * q^92 - 9 * q^93 - 4 * q^94 + 4 * q^95 - 6 * q^96 + 7 * q^97 - 4 * q^98 - 2 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	4.04892			1.81073			0.905365	−	0.424633i	$-0.139597\pi$
$5$	4.04892			1.81073			0.905365	+	0.424633i	$0.139597\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.346011	+	0.599308i	−0.130780	+	0.226517i	−0.923977	−	0.382447i	$-0.875081\pi$
$7$	−0.346011	+	0.599308i	−0.130780	+	0.226517i	0.793198	+	0.608964i	$0.208415\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.02446	+	3.50647i	0.640190	+	1.10884i
$11$	2.42543	+	4.20096i	0.731294	+	1.26664i	0.956330	+	0.292288i	$0.0944165\pi$
$11$	2.42543	+	4.20096i	0.731294	+	1.26664i	−0.225036	+	0.974350i	$0.572250\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−0.692021			−0.184951
$15$	−2.02446	−	3.50647i	−0.522713	−	0.905365i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.69202	+	6.39477i	−0.895447	+	1.55096i	−0.0621960	+	0.998064i	$0.519810\pi$
$17$	−3.69202	+	6.39477i	−0.895447	+	1.55096i	−0.833251	+	0.552895i	$0.813523\pi$
$18$	−1.00000			−0.235702
$19$	0.890084	−	1.54167i	0.204199	−	0.353683i	−0.745678	−	0.666306i	$-0.767874\pi$
$19$	0.890084	−	1.54167i	0.204199	−	0.353683i	0.949877	+	0.312623i	$0.101208\pi$
$20$	−2.02446	+	3.50647i	−0.452683	+	0.784069i
$21$	0.692021			0.151011
$22$	−2.42543	+	4.20096i	−0.517103	+	0.895648i
$23$	−2.55496	−	4.42532i	−0.532746	−	0.922742i	−0.999269	−	0.0382335i	$-0.987827\pi$
$23$	−2.55496	−	4.42532i	−0.532746	−	0.922742i	0.466523	−	0.884509i	$-0.345506\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	11.3937			2.27875
$26$		0			0
$27$	1.00000			0.192450
$28$	−0.346011	−	0.599308i	−0.0653899	−	0.113259i
$29$	1.67241	+	2.89669i	0.310558	+	0.537903i	0.978483	−	0.206326i	$-0.0661507\pi$
$29$	1.67241	+	2.89669i	0.310558	+	0.537903i	−0.667925	+	0.744228i	$0.732817\pi$
$30$	2.02446	−	3.50647i	0.369614	−	0.640190i
$31$	0.972853			0.174730			0.0873648	−	0.996176i	$-0.472155\pi$
$31$	0.972853			0.174730			0.0873648	+	0.996176i	$0.472155\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.42543	−	4.20096i	0.422213	−	0.731294i
$34$	−7.38404			−1.26635
$35$	−1.40097	+	2.42655i	−0.236807	+	0.410162i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.643104	−	1.11389i	−0.105726	−	0.183122i	0.808309	−	0.588759i	$-0.200383\pi$
$37$	−0.643104	−	1.11389i	−0.105726	−	0.183122i	−0.914034	+	0.405637i	$0.867050\pi$
$38$	1.78017			0.288781
$39$		0			0
$40$	−4.04892			−0.640190
$41$	−0.753020	−	1.30427i	−0.117602	−	0.203693i	0.801215	−	0.598377i	$-0.204187\pi$
$41$	−0.753020	−	1.30427i	−0.117602	−	0.203693i	−0.918817	+	0.394684i	$0.870854\pi$
$42$	0.346011	+	0.599308i	0.0533906	+	0.0924753i
$43$	4.15883	−	7.20331i	0.634216	−	1.09849i	−0.352464	−	0.935825i	$-0.614656\pi$
$43$	4.15883	−	7.20331i	0.634216	−	1.09849i	0.986681	−	0.162669i	$-0.0520104\pi$
$44$	−4.85086			−0.731294
$45$	−2.02446	+	3.50647i	−0.301788	+	0.522713i
$46$	2.55496	−	4.42532i	0.376708	−	0.652477i
$47$	−7.20775			−1.05136			−0.525679	−	0.850683i	$-0.676189\pi$
$47$	−7.20775			−1.05136			−0.525679	+	0.850683i	$0.676189\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.26055	+	5.64744i	0.465793	+	0.806778i
$50$	5.69687	+	9.86726i	0.805658	+	1.39544i
$51$	7.38404			1.03397
$52$		0			0
$53$	13.4765			1.85114			0.925570	−	0.378577i	$-0.123586\pi$
$53$	13.4765			1.85114			0.925570	+	0.378577i	$0.123586\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	9.82036	+	17.0094i	1.32418	+	2.29354i
$56$	0.346011	−	0.599308i	0.0462376	−	0.0800859i
$57$	−1.78017			−0.235789
$58$	−1.67241	+	2.89669i	−0.219598	+	0.380355i
$59$	−0.653989	+	1.13274i	−0.0851422	+	0.147471i	−0.905452	−	0.424449i	$-0.860468\pi$
$59$	−0.653989	+	1.13274i	−0.0851422	+	0.147471i	0.820310	+	0.571920i	$0.193801\pi$
$60$	4.04892			0.522713
$61$	0.198062	−	0.343054i	0.0253593	−	0.0439236i	−0.853067	−	0.521801i	$-0.825260\pi$
$61$	0.198062	−	0.343054i	0.0253593	−	0.0439236i	0.878427	+	0.477877i	$0.158594\pi$
$62$	0.486426	+	0.842515i	0.0617762	+	0.107000i
$63$	−0.346011	−	0.599308i	−0.0435933	−	0.0755057i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.85086			0.597099
$67$	−3.02715	−	5.24317i	−0.369825	−	0.640555i	0.619713	−	0.784828i	$-0.287249\pi$
$67$	−3.02715	−	5.24317i	−0.369825	−	0.640555i	−0.989538	+	0.144273i	$0.953916\pi$
$68$	−3.69202	−	6.39477i	−0.447723	−	0.775480i
$69$	−2.55496	+	4.42532i	−0.307581	+	0.532746i
$70$	−2.80194			−0.334896
$71$	0.664874	−	1.15160i	0.0789061	−	0.136669i	−0.823872	−	0.566776i	$-0.808191\pi$
$71$	0.664874	−	1.15160i	0.0789061	−	0.136669i	0.902778	+	0.430106i	$0.141524\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−7.65279			−0.895692			−0.447846	−	0.894111i	$-0.647809\pi$
$73$	−7.65279			−0.895692			−0.447846	+	0.894111i	$0.647809\pi$
$74$	0.643104	−	1.11389i	0.0747593	−	0.129487i
$75$	−5.69687	−	9.86726i	−0.657817	−	1.13937i
$76$	0.890084	+	1.54167i	0.102100	+	0.176842i
$77$	−3.35690			−0.382554
$78$		0			0
$79$	−8.33944			−0.938260			−0.469130	−	0.883129i	$-0.655432\pi$
$79$	−8.33944			−0.938260			−0.469130	+	0.883129i	$0.655432\pi$
$80$	−2.02446	−	3.50647i	−0.226341	−	0.392035i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.753020	−	1.30427i	0.0831572	−	0.144032i
$83$	15.3274			1.68240			0.841198	−	0.540727i	$-0.181851\pi$
$83$	15.3274			1.68240			0.841198	+	0.540727i	$0.181851\pi$
$84$	−0.346011	+	0.599308i	−0.0377529	+	0.0653899i
$85$	−14.9487	+	25.8919i	−1.62141	+	2.80837i
$86$	8.31767			0.896917
$87$	1.67241	−	2.89669i	0.179301	−	0.310558i
$88$	−2.42543	−	4.20096i	−0.258551	−	0.447824i
$89$	−1.55496	−	2.69327i	−0.164825	−	0.285486i	0.771768	−	0.635904i	$-0.219373\pi$
$89$	−1.55496	−	2.69327i	−0.164825	−	0.285486i	−0.936593	+	0.350419i	$0.886039\pi$
$90$	−4.04892			−0.426793
$91$		0			0
$92$	5.10992			0.532746
$93$	−0.486426	−	0.842515i	−0.0504401	−	0.0873648i
$94$	−3.60388	−	6.24210i	−0.371711	−	0.643823i
$95$	3.60388	−	6.24210i	0.369750	−	0.640425i
$96$	−1.00000			−0.102062
$97$	4.27144	−	7.39835i	0.433699	−	0.751188i	−0.563490	−	0.826123i	$-0.690542\pi$
$97$	4.27144	−	7.39835i	0.433699	−	0.751188i	0.997188	+	0.0749347i	$0.0238748\pi$
$98$	−3.26055	+	5.64744i	−0.329366	+	0.570478i
$99$	−4.85086			−0.487529
$100$	−5.69687	+	9.86726i	−0.569687	+	0.986726i
$101$	5.99880	+	10.3902i	0.596903	+	1.03387i	0.993275	+	0.115777i	$0.0369357\pi$
$101$	5.99880	+	10.3902i	0.596903	+	1.03387i	−0.396372	+	0.918090i	$0.629731\pi$
$102$	3.69202	+	6.39477i	0.365565	+	0.633176i
$103$	−12.3230			−1.21423			−0.607113	−	0.794616i	$-0.707672\pi$
$103$	−12.3230			−1.21423			−0.607113	+	0.794616i	$0.707672\pi$
$104$		0			0
$105$	2.80194			0.273441
$106$	6.73825	+	11.6710i	0.654477	+	1.13359i
$107$	−2.94989	−	5.10935i	−0.285176	−	0.493940i	0.687476	−	0.726207i	$-0.258719\pi$
$107$	−2.94989	−	5.10935i	−0.285176	−	0.493940i	−0.972652	+	0.232268i	$0.925385\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	0.792249			0.0758837			0.0379418	−	0.999280i	$-0.487920\pi$
$109$	0.792249			0.0758837			0.0379418	+	0.999280i	$0.487920\pi$
$110$	−9.82036	+	17.0094i	−0.936334	+	1.62178i
$111$	−0.643104	+	1.11389i	−0.0610407	+	0.105726i
$112$	0.692021			0.0653899
$113$	−3.10992	+	5.38653i	−0.292556	+	0.506722i	−0.974413	−	0.224763i	$-0.927839\pi$
$113$	−3.10992	+	5.38653i	−0.292556	+	0.506722i	0.681857	+	0.731485i	$0.261173\pi$
$114$	−0.890084	−	1.54167i	−0.0833640	−	0.144391i
$115$	−10.3448	−	17.9177i	−0.964659	−	1.67084i
$116$	−3.34481			−0.310558
$117$		0			0
$118$	−1.30798			−0.120409
$119$	−2.55496	−	4.42532i	−0.234213	−	0.405668i
$120$	2.02446	+	3.50647i	0.184807	+	0.320095i
$121$	−6.26540	+	10.8520i	−0.569582	+	0.986544i
$122$	0.396125			0.0358634
$123$	−0.753020	+	1.30427i	−0.0678976	+	0.117602i
$124$	−0.486426	+	0.842515i	−0.0436824	+	0.0756601i
$125$	25.8877			2.31547
$126$	0.346011	−	0.599308i	0.0308251	−	0.0533906i
$127$	3.00269	+	5.20081i	0.266446	+	0.461497i	0.967941	−	0.251176i	$-0.0808174\pi$
$127$	3.00269	+	5.20081i	0.266446	+	0.461497i	−0.701496	+	0.712674i	$0.747484\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−8.31767			−0.732330
$130$		0			0
$131$	8.81700			0.770345			0.385173	−	0.922845i	$-0.374142\pi$
$131$	8.81700			0.770345			0.385173	+	0.922845i	$0.374142\pi$
$132$	2.42543	+	4.20096i	0.211106	+	0.365647i
$133$	0.615957	+	1.06687i	0.0534103	+	0.0925093i
$134$	3.02715	−	5.24317i	0.261506	−	0.452941i
$135$	4.04892			0.348475
$136$	3.69202	−	6.39477i	0.316588	−	0.548347i
$137$	7.87800	−	13.6451i	0.673063	−	1.16578i	−0.303968	−	0.952682i	$-0.598312\pi$
$137$	7.87800	−	13.6451i	0.673063	−	1.16578i	0.977031	−	0.213097i	$-0.0683551\pi$
$138$	−5.10992			−0.434985
$139$	3.04892	−	5.28088i	0.258606	−	0.447918i	−0.707263	−	0.706951i	$-0.750070\pi$
$139$	3.04892	−	5.28088i	0.258606	−	0.447918i	0.965869	+	0.259032i	$0.0834036\pi$
$140$	−1.40097	−	2.42655i	−0.118403	−	0.205081i
$141$	3.60388	+	6.24210i	0.303501	+	0.525679i
$142$	1.32975			0.111590
$143$		0			0
$144$	1.00000			0.0833333
$145$	6.77144	+	11.7285i	0.562337	+	0.973997i
$146$	−3.82640	−	6.62751i	−0.316675	−	0.548497i
$147$	3.26055	−	5.64744i	0.268926	−	0.465793i
$148$	1.28621			0.105726
$149$	1.27628	−	2.21059i	0.104557	−	0.181098i	−0.809000	−	0.587809i	$-0.799991\pi$
$149$	1.27628	−	2.21059i	0.104557	−	0.181098i	0.913557	+	0.406710i	$0.133324\pi$
$150$	5.69687	−	9.86726i	0.465147	−	0.805658i
$151$	−17.7168			−1.44177			−0.720885	−	0.693054i	$-0.756265\pi$
$151$	−17.7168			−1.44177			−0.720885	+	0.693054i	$0.756265\pi$
$152$	−0.890084	+	1.54167i	−0.0721953	+	0.125046i
$153$	−3.69202	−	6.39477i	−0.298482	−	0.516986i
$154$	−1.67845	−	2.90716i	−0.135253	−	0.234265i
$155$	3.93900			0.316388
$156$		0			0
$157$	−6.31767			−0.504205			−0.252102	−	0.967701i	$-0.581122\pi$
$157$	−6.31767			−0.504205			−0.252102	+	0.967701i	$0.581122\pi$
$158$	−4.16972	−	7.22216i	−0.331725	−	0.574565i
$159$	−6.73825	−	11.6710i	−0.534378	−	0.925570i
$160$	2.02446	−	3.50647i	0.160048	−	0.277210i
$161$	3.53617			0.278689
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	7.29590	−	12.6369i	0.571459	−	0.989796i	−0.424958	−	0.905213i	$-0.639711\pi$
$163$	7.29590	−	12.6369i	0.571459	−	0.989796i	0.996416	−	0.0845824i	$-0.0269556\pi$
$164$	1.50604			0.117602
$165$	9.82036	−	17.0094i	0.764514	−	1.32418i
$166$	7.66368	+	13.2739i	0.594817	+	1.03025i
$167$	−9.75063	−	16.8886i	−0.754526	−	1.30688i	−0.945610	−	0.325304i	$-0.894533\pi$
$167$	−9.75063	−	16.8886i	−0.754526	−	1.30688i	0.191083	−	0.981574i	$-0.438800\pi$
$168$	−0.692021			−0.0533906
$169$		0			0
$170$	−29.8974			−2.29302
$171$	0.890084	+	1.54167i	0.0680664	+	0.117894i
$172$	4.15883	+	7.20331i	0.317108	+	0.549247i
$173$	4.64526	−	8.04583i	0.353173	−	0.611713i	−0.633631	−	0.773636i	$-0.718436\pi$
$173$	4.64526	−	8.04583i	0.353173	−	0.611713i	0.986803	+	0.161923i	$0.0517695\pi$
$174$	3.34481			0.253570
$175$	−3.94235	+	6.82836i	−0.298014	+	0.516175i
$176$	2.42543	−	4.20096i	0.182823	−	0.316660i
$177$	1.30798			0.0983137
$178$	1.55496	−	2.69327i	0.116549	−	0.201869i
$179$	−11.3964	−	19.7392i	−0.851808	−	1.47538i	−0.879575	−	0.475761i	$-0.842173\pi$
$179$	−11.3964	−	19.7392i	−0.851808	−	1.47538i	0.0277662	−	0.999614i	$-0.491161\pi$
$180$	−2.02446	−	3.50647i	−0.150894	−	0.261356i
$181$	0.537500			0.0399520			0.0199760	−	0.999800i	$-0.493641\pi$
$181$	0.537500			0.0399520			0.0199760	+	0.999800i	$0.493641\pi$
$182$		0			0
$183$	−0.396125			−0.0292824
$184$	2.55496	+	4.42532i	0.188354	+	0.326239i
$185$	−2.60388	−	4.51004i	−0.191441	−	0.331585i
$186$	0.486426	−	0.842515i	0.0356665	−	0.0617762i
$187$	−35.8189			−2.61934
$188$	3.60388	−	6.24210i	0.262840	−	0.455252i
$189$	−0.346011	+	0.599308i	−0.0251686	+	0.0435933i
$190$	7.20775			0.522905
$191$	4.89977	−	8.48665i	0.354535	−	0.614073i	−0.632503	−	0.774558i	$-0.717972\pi$
$191$	4.89977	−	8.48665i	0.354535	−	0.614073i	0.987038	+	0.160485i	$0.0513058\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−7.09783	−	12.2938i	−0.510913	−	0.884928i	−0.999920	−	0.0126478i	$-0.995974\pi$
$193$	−7.09783	−	12.2938i	−0.510913	−	0.884928i	0.489007	−	0.872280i	$-0.337359\pi$
$194$	8.54288			0.613343
$195$		0			0
$196$	−6.52111			−0.465793
$197$	−1.50484	−	2.60647i	−0.107216	−	0.185703i	0.807426	−	0.589969i	$-0.200860\pi$
$197$	−1.50484	−	2.60647i	−0.107216	−	0.185703i	−0.914641	+	0.404266i	$0.867527\pi$
$198$	−2.42543	−	4.20096i	−0.172368	−	0.298549i
$199$	−6.44720	+	11.1669i	−0.457030	+	0.791599i	−0.998802	−	0.0489263i	$-0.984420\pi$
$199$	−6.44720	+	11.1669i	−0.457030	+	0.791599i	0.541773	+	0.840525i	$0.317753\pi$
$200$	−11.3937			−0.805658
$201$	−3.02715	+	5.24317i	−0.213518	+	0.369825i
$202$	−5.99880	+	10.3902i	−0.422074	+	0.731054i
$203$	−2.31468			−0.162459
$204$	−3.69202	+	6.39477i	−0.258493	+	0.447723i
$205$	−3.04892	−	5.28088i	−0.212946	−	0.368833i
$206$	−6.16152	−	10.6721i	−0.429294	−	0.743558i
$207$	5.10992			0.355164
$208$		0			0
$209$	8.63533			0.597319
$210$	1.40097	+	2.42655i	0.0966760	+	0.167448i
$211$	−3.89977	−	6.75460i	−0.268471	−	0.465006i	0.699996	−	0.714147i	$-0.253185\pi$
$211$	−3.89977	−	6.75460i	−0.268471	−	0.465006i	−0.968467	+	0.249141i	$0.919852\pi$
$212$	−6.73825	+	11.6710i	−0.462785	+	0.801567i
$213$	−1.32975			−0.0911129
$214$	2.94989	−	5.10935i	0.201650	−	0.349268i
$215$	16.8388	−	29.1656i	1.14839	−	1.98908i
$216$	−1.00000			−0.0680414
$217$	−0.336618	+	0.583039i	−0.0228511	+	0.0395792i
$218$	0.396125	+	0.686108i	0.0268289	+	0.0464691i
$219$	3.82640	+	6.62751i	0.258564	+	0.447846i
$220$	−19.6407			−1.32418
$221$		0			0
$222$	−1.28621			−0.0863246
$223$	−6.09783	−	10.5618i	−0.408341	−	0.707268i	0.586363	−	0.810049i	$-0.300559\pi$
$223$	−6.09783	−	10.5618i	−0.408341	−	0.707268i	−0.994704	+	0.102781i	$0.967226\pi$
$224$	0.346011	+	0.599308i	0.0231188	+	0.0400430i
$225$	−5.69687	+	9.86726i	−0.379791	+	0.657817i
$226$	−6.21983			−0.413737
$227$	3.37167	−	5.83990i	0.223785	−	0.387608i	−0.732169	−	0.681123i	$-0.761492\pi$
$227$	3.37167	−	5.83990i	0.223785	−	0.387608i	0.955954	+	0.293515i	$0.0948252\pi$
$228$	0.890084	−	1.54167i	0.0589472	−	0.102100i
$229$	19.8237			1.30999			0.654994	−	0.755634i	$-0.272671\pi$
$229$	19.8237			1.30999			0.654994	+	0.755634i	$0.272671\pi$
$230$	10.3448	−	17.9177i	0.682117	−	1.18146i
$231$	1.67845	+	2.90716i	0.110434	+	0.191277i
$232$	−1.67241	−	2.89669i	−0.109799	−	0.190177i
$233$	−30.0301			−1.96734			−0.983670	−	0.179983i	$-0.942396\pi$
$233$	−30.0301			−1.96734			−0.983670	+	0.179983i	$0.942396\pi$
$234$		0			0
$235$	−29.1836			−1.90373
$236$	−0.653989	−	1.13274i	−0.0425711	−	0.0737353i
$237$	4.16972	+	7.22216i	0.270852	+	0.469130i
$238$	2.55496	−	4.42532i	0.165613	−	0.286851i
$239$	−22.0978			−1.42939			−0.714695	−	0.699436i	$-0.753435\pi$
$239$	−22.0978			−1.42939			−0.714695	+	0.699436i	$0.753435\pi$
$240$	−2.02446	+	3.50647i	−0.130678	+	0.226341i
$241$	5.06369	−	8.77056i	0.326181	−	0.564962i	−0.655570	−	0.755135i	$-0.727572\pi$
$241$	5.06369	−	8.77056i	0.326181	−	0.564962i	0.981751	+	0.190173i	$0.0609048\pi$
$242$	−12.5308			−0.805510
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.198062	+	0.343054i	0.0126796	+	0.0219618i
$245$	13.2017	+	22.8660i	0.843426	+	1.46086i
$246$	−1.50604			−0.0960217
$247$		0			0
$248$	−0.972853			−0.0617762
$249$	−7.66368	−	13.2739i	−0.485666	−	0.841198i
$250$	12.9438	+	22.4194i	0.818641	+	1.41793i
$251$	−2.77359	+	4.80401i	−0.175068	+	0.303226i	−0.940185	−	0.340665i	$-0.889348\pi$
$251$	−2.77359	+	4.80401i	−0.175068	+	0.303226i	0.765117	+	0.643891i	$0.222681\pi$
$252$	0.692021			0.0435933
$253$	12.3937	−	21.4666i	0.779187	−	1.34959i
$254$	−3.00269	+	5.20081i	−0.188405	+	0.326328i
$255$	29.8974			1.87225
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.89977	+	11.9508i	0.430396	+	0.745468i	0.996907	−	0.0785862i	$-0.0250406\pi$
$257$	6.89977	+	11.9508i	0.430396	+	0.745468i	−0.566511	+	0.824054i	$0.691707\pi$
$258$	−4.15883	−	7.20331i	−0.258918	−	0.448459i
$259$	0.890084			0.0553071
$260$		0			0
$261$	−3.34481			−0.207039
$262$	4.40850	+	7.63575i	0.272358	+	0.471738i
$263$	11.2349	+	19.4594i	0.692773	+	1.19992i	0.970926	+	0.239382i	$0.0769448\pi$
$263$	11.2349	+	19.4594i	0.692773	+	1.19992i	−0.278152	+	0.960537i	$0.589722\pi$
$264$	−2.42543	+	4.20096i	−0.149275	+	0.258551i
$265$	54.5652			3.35192
$266$	−0.615957	+	1.06687i	−0.0377668	+	0.0654139i
$267$	−1.55496	+	2.69327i	−0.0951619	+	0.164825i
$268$	6.05429			0.369825
$269$	13.0070	−	22.5288i	0.793051	−	1.37360i	−0.131019	−	0.991380i	$-0.541825\pi$
$269$	13.0070	−	22.5288i	0.793051	−	1.37360i	0.924070	−	0.382224i	$-0.124842\pi$
$270$	2.02446	+	3.50647i	0.123205	+	0.213397i
$271$	1.44235	+	2.49823i	0.0876167	+	0.151757i	0.906503	−	0.422199i	$-0.138742\pi$
$271$	1.44235	+	2.49823i	0.0876167	+	0.151757i	−0.818887	+	0.573955i	$0.805408\pi$
$272$	7.38404			0.447723
$273$		0			0
$274$	15.7560			0.951855
$275$	27.6347	+	47.8647i	1.66643	+	2.88635i
$276$	−2.55496	−	4.42532i	−0.153790	−	0.266373i
$277$	0.731250	−	1.26656i	0.0439366	−	0.0761004i	−0.843221	−	0.537567i	$-0.819343\pi$
$277$	0.731250	−	1.26656i	0.0439366	−	0.0761004i	0.887157	+	0.461467i	$0.152677\pi$
$278$	6.09783			0.365724
$279$	−0.486426	+	0.842515i	−0.0291216	+	0.0504401i
$280$	1.40097	−	2.42655i	0.0837239	−	0.145014i
$281$	−5.68233			−0.338980			−0.169490	−	0.985532i	$-0.554212\pi$
$281$	−5.68233			−0.338980			−0.169490	+	0.985532i	$0.554212\pi$
$282$	−3.60388	+	6.24210i	−0.214608	+	0.371711i
$283$	12.6039	+	21.8306i	0.749223	+	1.29769i	0.948196	+	0.317687i	$0.102906\pi$
$283$	12.6039	+	21.8306i	0.749223	+	1.29769i	−0.198973	+	0.980005i	$0.563761\pi$
$284$	0.664874	+	1.15160i	0.0394530	+	0.0683347i
$285$	−7.20775			−0.426950
$286$		0			0
$287$	1.04221			0.0615199
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−18.7620	−	32.4968i	−1.10365	−	1.91158i
$290$	−6.77144	+	11.7285i	−0.397633	+	0.688720i
$291$	−8.54288			−0.500792
$292$	3.82640	−	6.62751i	0.223923	−	0.387846i
$293$	−3.57457	+	6.19134i	−0.208829	+	0.361702i	−0.951346	−	0.308125i	$-0.900298\pi$
$293$	−3.57457	+	6.19134i	−0.208829	+	0.361702i	0.742517	+	0.669827i	$0.233632\pi$
$294$	6.52111			0.380319
$295$	−2.64795	+	4.58638i	−0.154170	+	0.267029i
$296$	0.643104	+	1.11389i	0.0373797	+	0.0647435i
$297$	2.42543	+	4.20096i	0.140738	+	0.243765i
$298$	2.55257			0.147866
$299$		0			0
$300$	11.3937			0.657817
$301$	2.87800	+	4.98485i	0.165885	+	0.287322i
$302$	−8.85839	−	15.3432i	−0.509743	−	0.882901i
$303$	5.99880	−	10.3902i	0.344622	−	0.596903i
$304$	−1.78017			−0.102100
$305$	0.801938	−	1.38900i	0.0459188	−	0.0795337i
$306$	3.69202	−	6.39477i	0.211059	−	0.365565i
$307$	17.9952			1.02704			0.513521	−	0.858077i	$-0.328341\pi$
$307$	17.9952			1.02704			0.513521	+	0.858077i	$0.328341\pi$
$308$	1.67845	−	2.90716i	0.0956384	−	0.165651i
$309$	6.16152	+	10.6721i	0.350517	+	0.607113i
$310$	1.96950	+	3.41127i	0.111860	+	0.193747i
$311$	3.32975			0.188813			0.0944064	−	0.995534i	$-0.469905\pi$
$311$	3.32975			0.188813			0.0944064	+	0.995534i	$0.469905\pi$
$312$		0			0
$313$	−17.8834			−1.01083			−0.505414	−	0.862877i	$-0.668660\pi$
$313$	−17.8834			−1.01083			−0.505414	+	0.862877i	$0.668660\pi$
$314$	−3.15883	−	5.47126i	−0.178263	−	0.308761i
$315$	−1.40097	−	2.42655i	−0.0789357	−	0.136721i
$316$	4.16972	−	7.22216i	0.234565	−	0.406279i
$317$	−4.39373			−0.246777			−0.123388	−	0.992358i	$-0.539376\pi$
$317$	−4.39373			−0.246777			−0.123388	+	0.992358i	$0.539376\pi$
$318$	6.73825	−	11.6710i	0.377862	−	0.654477i
$319$	−8.11260	+	14.0514i	−0.454219	+	0.786730i
$320$	4.04892			0.226341
$321$	−2.94989	+	5.10935i	−0.164647	+	0.285176i
$322$	1.76809	+	3.06241i	0.0985316	+	0.170662i
$323$	6.57242	+	11.3838i	0.365699	+	0.633409i
$324$	1.00000			0.0555556
$325$		0			0
$326$	14.5918			0.808165
$327$	−0.396125	−	0.686108i	−0.0219057	−	0.0379418i
$328$	0.753020	+	1.30427i	0.0415786	+	0.0720162i
$329$	2.49396	−	4.31966i	0.137496	−	0.238151i
$330$	19.6407			1.08119
$331$	−12.8388	+	22.2374i	−0.705683	+	1.22228i	0.260762	+	0.965403i	$0.416026\pi$
$331$	−12.8388	+	22.2374i	−0.705683	+	1.22228i	−0.966445	+	0.256875i	$0.917307\pi$
$332$	−7.66368	+	13.2739i	−0.420599	+	0.728499i
$333$	1.28621			0.0704838
$334$	9.75063	−	16.8886i	0.533531	−	0.924102i
$335$	−12.2567	−	21.2292i	−0.669653	−	1.15987i
$336$	−0.346011	−	0.599308i	−0.0188764	−	0.0326949i
$337$	−24.6504			−1.34279			−0.671396	−	0.741098i	$-0.734305\pi$
$337$	−24.6504			−1.34279			−0.671396	+	0.741098i	$0.734305\pi$
$338$		0			0
$339$	6.21983			0.337815
$340$	−14.9487	−	25.8919i	−0.810707	−	1.40418i
$341$	2.35958	+	4.08692i	0.127779	+	0.221319i
$342$	−0.890084	+	1.54167i	−0.0481302	+	0.0833640i
$343$	−9.35690			−0.505225
$344$	−4.15883	+	7.20331i	−0.224229	+	0.388377i
$345$	−10.3448	+	17.9177i	−0.556946	+	0.964659i
$346$	9.29052			0.499461
$347$	−7.14795	+	12.3806i	−0.383722	+	0.664626i	−0.991591	−	0.129411i	$-0.958691\pi$
$347$	−7.14795	+	12.3806i	−0.383722	+	0.664626i	0.607869	+	0.794037i	$0.292025\pi$
$348$	1.67241	+	2.89669i	0.0896504	+	0.155279i
$349$	5.53079	+	9.57962i	0.296057	+	0.512785i	0.975230	−	0.221193i	$-0.0709949\pi$
$349$	5.53079	+	9.57962i	0.296057	+	0.512785i	−0.679173	+	0.733978i	$0.737662\pi$
$350$	−7.88471			−0.421455
$351$		0			0
$352$	4.85086			0.258551
$353$	−5.25236	−	9.09735i	−0.279555	−	0.484203i	0.691719	−	0.722166i	$-0.256854\pi$
$353$	−5.25236	−	9.09735i	−0.279555	−	0.484203i	−0.971274	+	0.237963i	$0.923520\pi$
$354$	0.653989	+	1.13274i	0.0347591	+	0.0602046i
$355$	2.69202	−	4.66272i	0.142878	−	0.247471i
$356$	3.10992			0.164825
$357$	−2.55496	+	4.42532i	−0.135223	+	0.234213i
$358$	11.3964	−	19.7392i	0.602320	−	1.04325i
$359$	−5.10992			−0.269691			−0.134846	−	0.990867i	$-0.543054\pi$
$359$	−5.10992			−0.269691			−0.134846	+	0.990867i	$0.543054\pi$
$360$	2.02446	−	3.50647i	0.106698	−	0.184807i
$361$	7.91550	+	13.7101i	0.416605	+	0.721582i
$362$	0.268750	+	0.465488i	0.0141252	+	0.0244655i
$363$	12.5308			0.657696
$364$		0			0
$365$	−30.9855			−1.62186
$366$	−0.198062	−	0.343054i	−0.0103529	−	0.0179317i
$367$	4.22401	+	7.31620i	0.220492	+	0.381903i	0.954957	−	0.296743i	$-0.0959005\pi$
$367$	4.22401	+	7.31620i	0.220492	+	0.381903i	−0.734466	+	0.678646i	$0.762567\pi$
$368$	−2.55496	+	4.42532i	−0.133186	+	0.230686i
$369$	1.50604			0.0784014
$370$	2.60388	−	4.51004i	0.135369	−	0.234466i
$371$	−4.66301	+	8.07658i	−0.242092	+	0.419315i
$372$	0.972853			0.0504401
$373$	−3.84548	+	6.66056i	−0.199111	+	0.344871i	−0.948241	−	0.317553i	$-0.897139\pi$
$373$	−3.84548	+	6.66056i	−0.199111	+	0.344871i	0.749129	+	0.662424i	$0.230472\pi$
$374$	−17.9095	−	31.0201i	−0.926076	−	1.60401i
$375$	−12.9438	−	22.4194i	−0.668417	−	1.15773i
$376$	7.20775			0.371711
$377$		0			0
$378$	−0.692021			−0.0355937
$379$	−5.70171	−	9.87565i	−0.292877	−	0.507278i	0.681612	−	0.731714i	$-0.261279\pi$
$379$	−5.70171	−	9.87565i	−0.292877	−	0.507278i	−0.974489	+	0.224436i	$0.927946\pi$
$380$	3.60388	+	6.24210i	0.184875	+	0.320213i
$381$	3.00269	−	5.20081i	0.153832	−	0.266446i
$382$	9.79954			0.501388
$383$	10.3351	−	17.9010i	0.528100	−	0.914696i	−0.471363	−	0.881939i	$-0.656238\pi$
$383$	10.3351	−	17.9010i	0.528100	−	0.914696i	0.999463	−	0.0327572i	$-0.0104288\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−13.5918			−0.692702
$386$	7.09783	−	12.2938i	0.361270	−	0.625738i
$387$	4.15883	+	7.20331i	0.211405	+	0.366165i
$388$	4.27144	+	7.39835i	0.216849	+	0.375594i
$389$	17.4776			0.886148			0.443074	−	0.896485i	$-0.353888\pi$
$389$	17.4776			0.886148			0.443074	+	0.896485i	$0.353888\pi$
$390$		0			0
$391$	37.7318			1.90818
$392$	−3.26055	−	5.64744i	−0.164683	−	0.285239i
$393$	−4.40850	−	7.63575i	−0.222379	−	0.385173i
$394$	1.50484	−	2.60647i	0.0758130	−	0.131312i
$395$	−33.7657			−1.69894
$396$	2.42543	−	4.20096i	0.121882	−	0.211106i
$397$	−9.67994	+	16.7661i	−0.485822	+	0.841469i	−0.999867	−	0.0162944i	$-0.994813\pi$
$397$	−9.67994	+	16.7661i	−0.485822	+	0.841469i	0.514045	+	0.857763i	$0.328146\pi$
$398$	−12.8944			−0.646338
$399$	0.615957	−	1.06687i	0.0308364	−	0.0534103i
$400$	−5.69687	−	9.86726i	−0.284843	−	0.493363i
$401$	−7.24160	−	12.5428i	−0.361628	−	0.626359i	0.626601	−	0.779341i	$-0.284446\pi$
$401$	−7.24160	−	12.5428i	−0.361628	−	0.626359i	−0.988229	+	0.152982i	$0.951112\pi$
$402$	−6.05429			−0.301961
$403$		0			0
$404$	−11.9976			−0.596903
$405$	−2.02446	−	3.50647i	−0.100596	−	0.174238i
$406$	−1.15734	−	2.00457i	−0.0574379	−	0.0994854i
$407$	3.11960	−	5.40331i	0.154633	−	0.267832i
$408$	−7.38404			−0.365565
$409$	−9.44922	+	16.3665i	−0.467234	+	0.809273i	−0.999299	−	0.0374304i	$-0.988083\pi$
$409$	−9.44922	+	16.3665i	−0.467234	+	0.809273i	0.532065	+	0.846703i	$0.321416\pi$
$410$	3.04892	−	5.28088i	0.150575	−	0.260804i
$411$	−15.7560			−0.777186
$412$	6.16152	−	10.6721i	0.303556	−	0.525775i
$413$	−0.452575	−	0.783882i	−0.0222697	−	0.0385723i
$414$	2.55496	+	4.42532i	0.125569	+	0.217492i
$415$	62.0592			3.04637
$416$		0			0
$417$	−6.09783			−0.298612
$418$	4.31767	+	7.47842i	0.211184	+	0.365781i
$419$	10.8802	+	18.8450i	0.531531	+	0.920638i	0.999323	+	0.0367993i	$0.0117162\pi$
$419$	10.8802	+	18.8450i	0.531531	+	0.920638i	−0.467792	+	0.883838i	$0.654950\pi$
$420$	−1.40097	+	2.42655i	−0.0683603	+	0.118403i
$421$	−20.5918			−1.00358			−0.501791	−	0.864989i	$-0.667325\pi$
$421$	−20.5918			−1.00358			−0.501791	+	0.864989i	$0.667325\pi$
$422$	3.89977	−	6.75460i	0.189838	−	0.328809i
$423$	3.60388	−	6.24210i	0.175226	−	0.303501i
$424$	−13.4765			−0.654477
$425$	−42.0659	+	72.8603i	−2.04050	+	3.53424i
$426$	−0.664874	−	1.15160i	−0.0322133	−	0.0557950i
$427$	0.137063	+	0.237401i	0.00663296	+	0.0114886i
$428$	5.89977			0.285176
$429$		0			0
$430$	33.6775			1.62408
$431$	17.2567	+	29.8894i	0.831224	+	1.43972i	0.897068	+	0.441893i	$0.145693\pi$
$431$	17.2567	+	29.8894i	0.831224	+	1.43972i	−0.0658433	+	0.997830i	$0.520974\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	1.06315	−	1.84144i	0.0510920	−	0.0884939i	−0.839348	−	0.543594i	$-0.817063\pi$
$433$	1.06315	−	1.84144i	0.0510920	−	0.0884939i	0.890440	+	0.455100i	$0.150397\pi$
$434$	−0.673235			−0.0323163
$435$	6.77144	−	11.7285i	0.324666	−	0.562337i
$436$	−0.396125	+	0.686108i	−0.0189709	+	0.0328586i
$437$	−9.09651			−0.435145
$438$	−3.82640	+	6.62751i	−0.182832	+	0.316675i
$439$	−10.9160	−	18.9071i	−0.520994	−	0.902388i	−0.999702	−	0.0244137i	$-0.992228\pi$
$439$	−10.9160	−	18.9071i	−0.520994	−	0.902388i	0.478708	−	0.877974i	$-0.341105\pi$
$440$	−9.82036	−	17.0094i	−0.468167	−	0.810889i
$441$	−6.52111			−0.310529
$442$		0			0
$443$	−7.54048			−0.358259			−0.179130	−	0.983825i	$-0.557328\pi$
$443$	−7.54048			−0.358259			−0.179130	+	0.983825i	$0.557328\pi$
$444$	−0.643104	−	1.11389i	−0.0305204	−	0.0528628i
$445$	−6.29590	−	10.9048i	−0.298454	−	0.516938i
$446$	6.09783	−	10.5618i	0.288741	−	0.500114i
$447$	−2.55257			−0.120732
$448$	−0.346011	+	0.599308i	−0.0163475	+	0.0283146i
$449$	9.87800	−	17.1092i	0.466172	−	0.807433i	−0.533082	−	0.846064i	$-0.678966\pi$
$449$	9.87800	−	17.1092i	0.466172	−	0.807433i	0.999254	+	0.0386305i	$0.0122995\pi$
$450$	−11.3937			−0.537106
$451$	3.65279	−	6.32682i	0.172003	−	0.297918i
$452$	−3.10992	−	5.38653i	−0.146278	−	0.253361i
$453$	8.85839	+	15.3432i	0.416203	+	0.720885i
$454$	6.74333			0.316480
$455$		0			0
$456$	1.78017			0.0833640
$457$	11.9291	+	20.6618i	0.558019	+	0.966517i	0.997662	+	0.0683441i	$0.0217716\pi$
$457$	11.9291	+	20.6618i	0.558019	+	0.966517i	−0.439643	+	0.898173i	$0.644895\pi$
$458$	9.91185	+	17.1678i	0.463151	+	0.802200i
$459$	−3.69202	+	6.39477i	−0.172329	+	0.298482i
$460$	20.6896			0.964659
$461$	−8.78866	+	15.2224i	−0.409329	+	0.708978i	−0.994815	−	0.101704i	$-0.967570\pi$
$461$	−8.78866	+	15.2224i	−0.409329	+	0.708978i	0.585486	+	0.810683i	$0.300904\pi$
$462$	−1.67845	+	2.90716i	−0.0780885	+	0.135253i
$463$	−23.8431			−1.10808			−0.554041	−	0.832489i	$-0.686915\pi$
$463$	−23.8431			−1.10808			−0.554041	+	0.832489i	$0.686915\pi$
$464$	1.67241	−	2.89669i	0.0776396	−	0.134476i
$465$	−1.96950	−	3.41127i	−0.0913334	−	0.158194i
$466$	−15.0151	−	26.0069i	−0.695559	−	1.20474i
$467$	8.61058			0.398450			0.199225	−	0.979954i	$-0.436158\pi$
$467$	8.61058			0.398450			0.199225	+	0.979954i	$0.436158\pi$
$468$		0			0
$469$	4.18970			0.193462
$470$	−14.5918	−	25.2737i	−0.673069	−	1.16579i
$471$	3.15883	+	5.47126i	0.145551	+	0.252102i
$472$	0.653989	−	1.13274i	0.0301023	−	0.0521387i
$473$	40.3478			1.85519
$474$	−4.16972	+	7.22216i	−0.191522	+	0.331725i
$475$	10.1414	−	17.5654i	0.465318	−	0.805955i
$476$	5.10992			0.234213
$477$	−6.73825	+	11.6710i	−0.308523	+	0.534378i
$478$	−11.0489	−	19.1373i	−0.505366	−	0.875319i
$479$	3.29052	+	5.69935i	0.150348	+	0.260410i	0.931355	−	0.364112i	$-0.118627\pi$
$479$	3.29052	+	5.69935i	0.150348	+	0.260410i	−0.781008	+	0.624522i	$0.785294\pi$
$480$	−4.04892			−0.184807
$481$		0			0
$482$	10.1274			0.461289
$483$	−1.76809	−	3.06241i	−0.0804507	−	0.139345i
$484$	−6.26540	−	10.8520i	−0.284791	−	0.493272i
$485$	17.2947	−	29.9553i	0.785312	−	1.36020i
$486$	−1.00000			−0.0453609
$487$	−11.6380	+	20.1576i	−0.527369	+	0.913430i	0.472122	+	0.881533i	$0.343488\pi$
$487$	−11.6380	+	20.1576i	−0.527369	+	0.913430i	−0.999491	+	0.0318970i	$0.989845\pi$
$488$	−0.198062	+	0.343054i	−0.00896586	+	0.0155293i
$489$	−14.5918			−0.659864
$490$	−13.2017	+	22.8660i	−0.596392	+	1.03298i
$491$	7.77024	+	13.4585i	0.350666	+	0.607372i	0.986366	−	0.164565i	$-0.0526219\pi$
$491$	7.77024	+	13.4585i	0.350666	+	0.607372i	−0.635700	+	0.771936i	$0.719289\pi$
$492$	−0.753020	−	1.30427i	−0.0339488	−	0.0588010i
$493$	−24.6983			−1.11235
$494$		0			0
$495$	−19.6407			−0.882784
$496$	−0.486426	−	0.842515i	−0.0218412	−	0.0378301i
$497$	0.460107	+	0.796929i	0.0206386	+	0.0357472i
$498$	7.66368	−	13.2739i	0.343418	−	0.594817i
$499$	−9.53617			−0.426898			−0.213449	−	0.976954i	$-0.568470\pi$
$499$	−9.53617			−0.426898			−0.213449	+	0.976954i	$0.568470\pi$
$500$	−12.9438	+	22.4194i	−0.578866	+	1.00263i
$501$	−9.75063	+	16.8886i	−0.435626	+	0.754526i
$502$	−5.54719			−0.247583
$503$	6.91723	−	11.9810i	0.308424	−	0.534206i	−0.669594	−	0.742728i	$-0.733532\pi$
$503$	6.91723	−	11.9810i	0.308424	−	0.534206i	0.978018	+	0.208521i	$0.0668651\pi$
$504$	0.346011	+	0.599308i	0.0154125	+	0.0266953i
$505$	24.2887	+	42.0692i	1.08083	+	1.87205i
$506$	24.7875			1.10194
$507$		0			0
$508$	−6.00538			−0.266446
$509$	−20.4819	−	35.4757i	−0.907843	−	1.57243i	−0.817054	−	0.576560i	$-0.804395\pi$
$509$	−20.4819	−	35.4757i	−0.907843	−	1.57243i	−0.0907888	−	0.995870i	$-0.528939\pi$
$510$	14.9487	+	25.8919i	0.661939	+	1.14651i
$511$	2.64795	−	4.58638i	0.117138	−	0.202890i
$512$	−1.00000			−0.0441942
$513$	0.890084	−	1.54167i	0.0392982	−	0.0680664i
$514$	−6.89977	+	11.9508i	−0.304336	+	0.527125i
$515$	−49.8950			−2.19864
$516$	4.15883	−	7.20331i	0.183082	−	0.317108i
$517$	−17.4819	−	30.2795i	−0.768852	−	1.33169i
$518$	0.445042	+	0.770835i	0.0195540	+	0.0338686i
$519$	−9.29052			−0.407809
$520$		0			0
$521$	36.3672			1.59327			0.796637	−	0.604457i	$-0.206610\pi$
$521$	36.3672			1.59327			0.796637	+	0.604457i	$0.206610\pi$
$522$	−1.67241	−	2.89669i	−0.0731993	−	0.126785i
$523$	3.01507	+	5.22225i	0.131840	+	0.228353i	0.924386	−	0.381459i	$-0.124578\pi$
$523$	3.01507	+	5.22225i	0.131840	+	0.228353i	−0.792546	+	0.609812i	$0.791245\pi$
$524$	−4.40850	+	7.63575i	−0.192586	+	0.333569i
$525$	7.88471			0.344117
$526$	−11.2349	+	19.4594i	−0.489865	+	0.848471i
$527$	−3.59179	+	6.22117i	−0.156461	+	0.270998i
$528$	−4.85086			−0.211106
$529$	−1.55562	+	2.69442i	−0.0676357	+	0.117149i
$530$	27.2826	+	47.2549i	1.18508	+	2.05262i
$531$	−0.653989	−	1.13274i	−0.0283807	−	0.0491568i
$532$	−1.23191			−0.0534103
$533$		0			0
$534$	−3.10992			−0.134579
$535$	−11.9438	−	20.6873i	−0.516377	−	0.894392i
$536$	3.02715	+	5.24317i	0.130753	+	0.226471i
$537$	−11.3964	+	19.7392i	−0.491792	+	0.851808i
$538$	26.0140			1.12154
$539$	−15.8165	+	27.3949i	−0.681264	+	1.17998i
$540$	−2.02446	+	3.50647i	−0.0871188	+	0.150894i
$541$	7.92154			0.340574			0.170287	−	0.985395i	$-0.445531\pi$
$541$	7.92154			0.340574			0.170287	+	0.985395i	$0.445531\pi$
$542$	−1.44235	+	2.49823i	−0.0619544	+	0.107308i
$543$	−0.268750	−	0.465488i	−0.0115332	−	0.0199760i
$544$	3.69202	+	6.39477i	0.158294	+	0.274173i
$545$	3.20775			0.137405
$546$		0			0
$547$	18.4155			0.787390			0.393695	−	0.919241i	$-0.371197\pi$
$547$	18.4155			0.787390			0.393695	+	0.919241i	$0.371197\pi$
$548$	7.87800	+	13.6451i	0.336532	+	0.582890i
$549$	0.198062	+	0.343054i	0.00845309	+	0.0146412i
$550$	−27.6347	+	47.8647i	−1.17835	+	2.04096i
$551$	5.95433			0.253663
$552$	2.55496	−	4.42532i	0.108746	−	0.188354i
$553$	2.88553	−	4.99789i	0.122705	−	0.212532i
$554$	1.46250			0.0621357
$555$	−2.60388	+	4.51004i	−0.110528	+	0.191441i
$556$	3.04892	+	5.28088i	0.129303	+	0.223959i
$557$	−11.9879	−	20.7637i	−0.507944	−	0.879786i	−0.999958	−	0.00919783i	$-0.997072\pi$
$557$	−11.9879	−	20.7637i	−0.507944	−	0.879786i	0.492013	−	0.870588i	$-0.336261\pi$
$558$	−0.972853			−0.0411841
$559$		0			0
$560$	2.80194			0.118403
$561$	17.9095	+	31.0201i	0.756138	+	1.30967i
$562$	−2.84117	−	4.92104i	−0.119847	−	0.207582i
$563$	1.14646	−	1.98572i	0.0483174	−	0.0836882i	−0.840855	−	0.541260i	$-0.817947\pi$
$563$	1.14646	−	1.98572i	0.0483174	−	0.0836882i	0.889173	+	0.457572i	$0.151281\pi$
$564$	−7.20775			−0.303501
$565$	−12.5918	+	21.8096i	−0.529741	+	0.917538i
$566$	−12.6039	+	21.8306i	−0.529780	+	0.917607i
$567$	0.692021			0.0290622
$568$	−0.664874	+	1.15160i	−0.0278975	+	0.0483199i
$569$	22.1715	+	38.4022i	0.929478	+	1.60990i	0.784197	+	0.620513i	$0.213075\pi$
$569$	22.1715	+	38.4022i	0.929478	+	1.60990i	0.145281	+	0.989390i	$0.453591\pi$
$570$	−3.60388	−	6.24210i	−0.150950	−	0.261453i
$571$	−15.2707			−0.639058			−0.319529	−	0.947577i	$-0.603525\pi$
$571$	−15.2707			−0.639058			−0.319529	+	0.947577i	$0.603525\pi$
$572$		0			0
$573$	−9.79954			−0.409382
$574$	0.521106	+	0.902583i	0.0217506	+	0.0376731i
$575$	−29.1105	−	50.4209i	−1.21399	−	2.10270i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.77048			−0.365120			−0.182560	−	0.983195i	$-0.558438\pi$
$577$	−8.77048			−0.365120			−0.182560	+	0.983195i	$0.558438\pi$
$578$	18.7620	−	32.4968i	0.780398	−	1.35169i
$579$	−7.09783	+	12.2938i	−0.294976	+	0.510913i
$580$	−13.5429			−0.562337
$581$	−5.30343	+	9.18581i	−0.220023	+	0.381092i
$582$	−4.27144	−	7.39835i	−0.177057	−	0.306671i
$583$	32.6863	+	56.6143i	1.35373	+	2.34472i
$584$	7.65279			0.316675
$585$		0			0
$586$	−7.14914			−0.295328
$587$	−19.0715	−	33.0328i	−0.787166	−	1.36341i	−0.927697	−	0.373335i	$-0.878214\pi$
$587$	−19.0715	−	33.0328i	−0.787166	−	1.36341i	0.140531	−	0.990076i	$-0.455119\pi$
$588$	3.26055	+	5.64744i	0.134463	+	0.232897i
$589$	0.865921	−	1.49982i	0.0356796	−	0.0617989i
$590$	−5.29590			−0.218029
$591$	−1.50484	+	2.60647i	−0.0619010	+	0.107216i
$592$	−0.643104	+	1.11389i	−0.0264314	+	0.0457806i
$593$	37.9517			1.55849			0.779244	−	0.626720i	$-0.215603\pi$
$593$	37.9517			1.55849			0.779244	+	0.626720i	$0.215603\pi$
$594$	−2.42543	+	4.20096i	−0.0995165	+	0.172368i
$595$	−10.3448	−	17.9177i	−0.424096	−	0.734556i
$596$	1.27628	+	2.21059i	0.0522786	+	0.0905491i
$597$	12.8944			0.527732
$598$		0			0
$599$	−3.57971			−0.146263			−0.0731315	−	0.997322i	$-0.523299\pi$
$599$	−3.57971			−0.146263			−0.0731315	+	0.997322i	$0.523299\pi$
$600$	5.69687	+	9.86726i	0.232574	+	0.402829i
$601$	2.85839	+	4.95087i	0.116596	+	0.201950i	0.918417	−	0.395615i	$-0.129468\pi$
$601$	2.85839	+	4.95087i	0.116596	+	0.201950i	−0.801821	+	0.597565i	$0.796135\pi$
$602$	−2.87800	+	4.98485i	−0.117299	+	0.203167i
$603$	6.05429			0.246550
$604$	8.85839	−	15.3432i	0.360443	−	0.624305i
$605$	−25.3681	+	43.9388i	−1.03136	+	1.78637i
$606$	11.9976			0.487369
$607$	−11.2143	+	19.4238i	−0.455175	+	0.788387i	−0.998698	−	0.0510075i	$-0.983757\pi$
$607$	−11.2143	+	19.4238i	−0.455175	+	0.788387i	0.543523	+	0.839394i	$0.317090\pi$
$608$	−0.890084	−	1.54167i	−0.0360977	−	0.0625230i
$609$	1.15734	+	2.00457i	0.0468979	+	0.0812295i
$610$	1.60388			0.0649390
$611$		0			0
$612$	7.38404			0.298482
$613$	−19.9801	−	34.6066i	−0.806991	−	1.39775i	−0.914939	−	0.403592i	$-0.867761\pi$
$613$	−19.9801	−	34.6066i	−0.806991	−	1.39775i	0.107948	−	0.994157i	$-0.465572\pi$
$614$	8.99761	+	15.5843i	0.363114	+	0.628932i
$615$	−3.04892	+	5.28088i	−0.122944	+	0.212946i
$616$	3.35690			0.135253
$617$	15.7235	−	27.2339i	0.633003	−	1.09639i	−0.353931	−	0.935272i	$-0.615155\pi$
$617$	15.7235	−	27.2339i	0.633003	−	1.09639i	0.986934	−	0.161123i	$-0.0515115\pi$
$618$	−6.16152	+	10.6721i	−0.247853	+	0.429294i
$619$	29.3685			1.18042			0.590210	−	0.807250i	$-0.299045\pi$
$619$	29.3685			1.18042			0.590210	+	0.807250i	$0.299045\pi$
$620$	−1.96950	+	3.41127i	−0.0790970	+	0.137000i
$621$	−2.55496	−	4.42532i	−0.102527	−	0.177582i
$622$	1.66487	+	2.88365i	0.0667554	+	0.115624i
$623$	2.15213			0.0862232
$624$		0			0
$625$	47.8485			1.91394
$626$	−8.94169	−	15.4875i	−0.357382	−	0.619003i
$627$	−4.31767	−	7.47842i	−0.172431	−	0.298659i
$628$	3.15883	−	5.47126i	0.126051	−	0.218327i
$629$	9.49742			0.378687
$630$	1.40097	−	2.42655i	0.0558159	−	0.0966760i
$631$	10.8400	−	18.7754i	0.431532	−	0.747436i	−0.565473	−	0.824767i	$-0.691306\pi$
$631$	10.8400	−	18.7754i	0.431532	−	0.747436i	0.997005	+	0.0773307i	$0.0246397\pi$
$632$	8.33944			0.331725
$633$	−3.89977	+	6.75460i	−0.155002	+	0.268471i
$634$	−2.19687	−	3.80508i	−0.0872487	−	0.151119i
$635$	12.1576	+	21.0576i	0.482461	+	0.835647i
$636$	13.4765			0.534378
$637$		0			0
$638$	−16.2252			−0.642362
$639$	0.664874	+	1.15160i	0.0263020	+	0.0455564i
$640$	2.02446	+	3.50647i	0.0800238	+	0.138605i
$641$	−7.00538	+	12.1337i	−0.276696	+	0.479251i	−0.970562	−	0.240853i	$-0.922573\pi$
$641$	−7.00538	+	12.1337i	−0.276696	+	0.479251i	0.693866	+	0.720104i	$0.255906\pi$
$642$	−5.89977			−0.232845
$643$	15.3937	−	26.6627i	0.607070	−	1.05148i	−0.384651	−	0.923062i	$-0.625678\pi$
$643$	15.3937	−	26.6627i	0.607070	−	1.05148i	0.991721	−	0.128413i	$-0.0409884\pi$
$644$	−1.76809	+	3.06241i	−0.0696723	+	0.120676i
$645$	−33.6775			−1.32605
$646$	−6.57242	+	11.3838i	−0.258588	+	0.447888i
$647$	8.30127	+	14.3782i	0.326357	+	0.565266i	0.981786	−	0.189990i	$-0.0608456\pi$
$647$	8.30127	+	14.3782i	0.326357	+	0.565266i	−0.655429	+	0.755257i	$0.727512\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−6.34481			−0.249056
$650$		0			0
$651$	0.673235			0.0263862
$652$	7.29590	+	12.6369i	0.285729	+	0.494898i
$653$	−14.2729	−	24.7214i	−0.558543	−	0.967425i	−0.997618	−	0.0689745i	$-0.978027\pi$
$653$	−14.2729	−	24.7214i	−0.558543	−	0.967425i	0.439075	−	0.898450i	$-0.355306\pi$
$654$	0.396125	−	0.686108i	0.0154897	−	0.0268289i
$655$	35.6993			1.39489
$656$	−0.753020	+	1.30427i	−0.0294005	+	0.0509232i
$657$	3.82640	−	6.62751i	0.149282	−	0.258564i
$658$	4.98792			0.194449
$659$	−13.8593	+	24.0051i	−0.539884	+	0.935106i	0.459026	+	0.888423i	$0.348198\pi$
$659$	−13.8593	+	24.0051i	−0.539884	+	0.935106i	−0.998910	+	0.0466830i	$0.985135\pi$
$660$	9.82036	+	17.0094i	0.382257	+	0.662088i
$661$	5.40044	+	9.35383i	0.210053	+	0.363822i	0.951731	−	0.306934i	$-0.0993031\pi$
$661$	5.40044	+	9.35383i	0.210053	+	0.363822i	−0.741678	+	0.670756i	$0.765970\pi$
$662$	−25.6775			−0.997986
$663$		0			0
$664$	−15.3274			−0.594817
$665$	2.49396	+	4.31966i	0.0967116	+	0.167509i
$666$	0.643104	+	1.11389i	0.0249198	+	0.0431623i
$667$	8.54586	−	14.8019i	0.330897	−	0.573130i
$668$	19.5013			0.754526
$669$	−6.09783	+	10.5618i	−0.235756	+	0.408341i
$670$	12.2567	−	21.2292i	0.473516	−	0.820154i
$671$	1.92154			0.0741803
$672$	0.346011	−	0.599308i	0.0133477	−	0.0231188i
$673$	−8.16301	−	14.1388i	−0.314661	−	0.545009i	0.664704	−	0.747107i	$-0.268558\pi$
$673$	−8.16301	−	14.1388i	−0.314661	−	0.545009i	−0.979365	+	0.202098i	$0.935224\pi$
$674$	−12.3252	−	21.3479i	−0.474749	−	0.822289i
$675$	11.3937			0.438545
$676$		0			0
$677$	41.4252			1.59210			0.796050	−	0.605231i	$-0.206919\pi$
$677$	41.4252			1.59210			0.796050	+	0.605231i	$0.206919\pi$
$678$	3.10992	+	5.38653i	0.119436	+	0.206869i
$679$	2.95593	+	5.11982i	0.113438	+	0.196480i
$680$	14.9487	−	25.8919i	0.573256	−	0.992909i
$681$	−6.74333			−0.258405
$682$	−2.35958	+	4.08692i	−0.0903532	+	0.156496i
$683$	15.6163	−	27.0481i	0.597539	−	1.03497i	−0.395644	−	0.918404i	$-0.629479\pi$
$683$	15.6163	−	27.0481i	0.597539	−	1.03497i	0.993183	−	0.116564i	$-0.0371881\pi$
$684$	−1.78017			−0.0680664
$685$	31.8974	−	55.2479i	1.21874	−	2.11091i
$686$	−4.67845	−	8.10331i	−0.178624	−	0.309386i
$687$	−9.91185	−	17.1678i	−0.378161	−	0.654994i
$688$	−8.31767			−0.317108
$689$		0			0
$690$	−20.6896			−0.787641
$691$	12.4819	+	21.6192i	0.474833	+	0.822435i	0.999585	−	0.0288205i	$-0.00917513\pi$
$691$	12.4819	+	21.6192i	0.474833	+	0.822435i	−0.524752	+	0.851255i	$0.675842\pi$
$692$	4.64526	+	8.04583i	0.176586	+	0.305856i
$693$	1.67845	−	2.90716i	0.0637590	−	0.110434i
$694$	−14.2959			−0.542665
$695$	12.3448	−	21.3818i	0.468265	−	0.811060i
$696$	−1.67241	+	2.89669i	−0.0633924	+	0.109799i
$697$	11.1207			0.421225
$698$	−5.53079	+	9.57962i	−0.209344	+	0.362594i
$699$	15.0151	+	26.0069i	0.567922	+	0.983670i
$700$	−3.94235	−	6.82836i	−0.149007	−	0.258088i
$701$	8.17151			0.308634			0.154317	−	0.988021i	$-0.450682\pi$
$701$	8.17151			0.308634			0.154317	+	0.988021i	$0.450682\pi$
$702$		0			0
$703$	−2.28967			−0.0863564
$704$	2.42543	+	4.20096i	0.0914117	+	0.158330i
$705$	14.5918	+	25.2737i	0.549559	+	0.951864i
$706$	5.25236	−	9.09735i	0.197675	−	0.342383i
$707$	−8.30260			−0.312251
$708$	−0.653989	+	1.13274i	−0.0245784	+	0.0425711i
$709$	−18.3991	+	31.8682i	−0.690993	+	1.19684i	0.280520	+	0.959848i	$0.409493\pi$
$709$	−18.3991	+	31.8682i	−0.690993	+	1.19684i	−0.971513	+	0.236987i	$0.923840\pi$
$710$	5.38404			0.202060
$711$	4.16972	−	7.22216i	0.156377	−	0.270852i
$712$	1.55496	+	2.69327i	0.0582745	+	0.100934i
$713$	−2.48560	−	4.30518i	−0.0930864	−	0.161230i
$714$	−5.10992			−0.191234
$715$		0			0
$716$	22.7928			0.851808
$717$	11.0489	+	19.1373i	0.412629	+	0.714695i
$718$	−2.55496	−	4.42532i	−0.0953502	−	0.165151i
$719$	−17.6112	+	30.5034i	−0.656786	+	1.13759i	0.324657	+	0.945832i	$0.394751\pi$
$719$	−17.6112	+	30.5034i	−0.656786	+	1.13759i	−0.981443	+	0.191755i	$0.938582\pi$
$720$	4.04892			0.150894
$721$	4.26391	−	7.38530i	0.158796	−	0.275043i
$722$	−7.91550	+	13.7101i	−0.294584	+	0.510235i
$723$	−10.1274			−0.376641
$724$	−0.268750	+	0.465488i	−0.00998801	+	0.0172997i
$725$	19.0550	+	33.0042i	0.707683	+	1.22574i
$726$	6.26540	+	10.8520i	0.232531	+	0.402755i
$727$	40.6872			1.50901			0.754503	−	0.656297i	$-0.227878\pi$
$727$	40.6872			1.50901			0.754503	+	0.656297i	$0.227878\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−15.4928	−	26.8343i	−0.573413	−	0.993180i
$731$	30.7090	+	53.1896i	1.13581	+	1.96729i
$732$	0.198062	−	0.343054i	0.00732059	−	0.0126796i
$733$	−27.1400			−1.00244			−0.501220	−	0.865320i	$-0.667115\pi$
$733$	−27.1400			−1.00244			−0.501220	+	0.865320i	$0.667115\pi$
$734$	−4.22401	+	7.31620i	−0.155911	+	0.270046i
$735$	13.2017	−	22.8660i	0.486952	−	0.843426i
$736$	−5.10992			−0.188354
$737$	14.6843	−	25.4339i	0.540901	−	0.936869i
$738$	0.753020	+	1.30427i	0.0277191	+	0.0480108i
$739$	1.86294	+	3.22670i	0.0685292	+	0.118696i	0.898254	−	0.439476i	$-0.144836\pi$
$739$	1.86294	+	3.22670i	0.0685292	+	0.118696i	−0.829725	+	0.558173i	$0.811503\pi$
$740$	5.20775			0.191441
$741$		0			0
$742$	−9.32603			−0.342369
$743$	10.9293	+	18.9301i	0.400958	+	0.694479i	0.993842	−	0.110809i	$-0.0353441\pi$
$743$	10.9293	+	18.9301i	0.400958	+	0.694479i	−0.592884	+	0.805288i	$0.702011\pi$
$744$	0.486426	+	0.842515i	0.0178333	+	0.0308881i
$745$	5.16756	−	8.95048i	0.189325	−	0.327920i
$746$	−7.69096			−0.281586
$747$	−7.66368	+	13.2739i	−0.280399	+	0.485666i
$748$	17.9095	−	31.0201i	0.654835	−	1.13421i
$749$	4.08277			0.149181
$750$	12.9438	−	22.4194i	0.472642	−	0.818641i
$751$	−26.6821	−	46.2147i	−0.973644	−	1.68640i	−0.684341	−	0.729162i	$-0.739910\pi$
$751$	−26.6821	−	46.2147i	−0.973644	−	1.68640i	−0.289303	−	0.957238i	$-0.593423\pi$
$752$	3.60388	+	6.24210i	0.131420	+	0.227626i
$753$	5.54719			0.202151
$754$		0			0
$755$	−71.7338			−2.61066
$756$	−0.346011	−	0.599308i	−0.0125843	−	0.0217966i
$757$	2.31767	+	4.01432i	0.0842370	+	0.145903i	0.905066	−	0.425271i	$-0.139821\pi$
$757$	2.31767	+	4.01432i	0.0842370	+	0.145903i	−0.820829	+	0.571174i	$0.806488\pi$
$758$	5.70171	−	9.87565i	0.207095	−	0.358700i
$759$	−24.7875			−0.899728
$760$	−3.60388	+	6.24210i	−0.130726	+	0.226425i
$761$	5.78017	−	10.0115i	0.209531	−	0.362918i	−0.742036	−	0.670360i	$-0.766140\pi$
$761$	5.78017	−	10.0115i	0.209531	−	0.362918i	0.951567	+	0.307442i	$0.0994730\pi$
$762$	6.00538			0.217552
$763$	−0.274127	+	0.474801i	−0.00992405	+	0.0171890i
$764$	4.89977	+	8.48665i	0.177268	+	0.307036i
$765$	−14.9487	−	25.8919i	−0.540471	−	0.936123i
$766$	20.6703			0.746847
$767$		0			0
$768$	1.00000			0.0360844
$769$	7.37196	+	12.7686i	0.265840	+	0.460448i	0.967783	−	0.251785i	$-0.0810175\pi$
$769$	7.37196	+	12.7686i	0.265840	+	0.460448i	−0.701944	+	0.712233i	$0.747684\pi$
$770$	−6.79590	−	11.7708i	−0.244907	−	0.424192i
$771$	6.89977	−	11.9508i	0.248489	−	0.430396i
$772$	14.1957			0.510913
$773$	−3.21134	+	5.56220i	−0.115504	+	0.200059i	−0.917981	−	0.396624i	$-0.870182\pi$
$773$	−3.21134	+	5.56220i	−0.115504	+	0.200059i	0.802477	+	0.596683i	$0.203515\pi$
$774$	−4.15883	+	7.20331i	−0.149486	+	0.258918i
$775$	11.0844			0.398164
$776$	−4.27144	+	7.39835i	−0.153336	+	0.265585i
$777$	−0.445042	−	0.770835i	−0.0159658	−	0.0276536i
$778$	8.73878	+	15.1360i	0.313301	+	0.542652i
$779$	−2.68100			−0.0960570
$780$		0			0
$781$	6.45042			0.230814
$782$	18.8659	+	32.6767i	0.674644	+	1.16852i
$783$	1.67241	+	2.89669i	0.0597670	+	0.103519i
$784$	3.26055	−	5.64744i	0.116448	−	0.201694i
$785$	−25.5797			−0.912979
$786$	4.40850	−	7.63575i	0.157246	−	0.272358i
$787$	21.7168	−	37.6146i	0.774119	−	1.34081i	−0.161169	−	0.986927i	$-0.551526\pi$
$787$	21.7168	−	37.6146i	0.774119	−	1.34081i	0.935288	−	0.353887i	$-0.115140\pi$
$788$	3.00969			0.107216
$789$	11.2349	−	19.4594i	0.399973	−	0.692773i
$790$	−16.8828	−	29.2419i	−0.600665	−	1.04038i
$791$	−2.15213	−	3.72760i	−0.0765209	−	0.132538i
$792$	4.85086			0.172368
$793$		0			0
$794$	−19.3599			−0.687056
$795$	−27.2826	−	47.2549i	−0.967615	−	1.67596i
$796$	−6.44720	−	11.1669i	−0.228515	−	0.395799i
$797$	−10.5082	+	18.2007i	−0.372219	+	0.644703i	−0.989907	−	0.141721i	$-0.954736\pi$
$797$	−10.5082	+	18.2007i	−0.372219	+	0.644703i	0.617687	+	0.786424i	$0.288070\pi$
$798$	1.23191			0.0436093
$799$	26.6112	−	46.0919i	0.941436	−	1.63061i
$800$	5.69687	−	9.86726i	0.201415	−	0.348860i
$801$	3.10992			0.109883
$802$	7.24160	−	12.5428i	0.255710	−	0.442903i
$803$	−18.5613	−	32.1491i	−0.655014	−	1.13452i
$804$	−3.02715	−	5.24317i	−0.106759	−	0.184912i
$805$	14.3177			0.504631
$806$		0			0
$807$	−26.0140			−0.915736
$808$	−5.99880	−	10.3902i	−0.211037	−	0.365527i
$809$	4.16123	+	7.20746i	0.146301	+	0.253401i	0.929858	−	0.367920i	$-0.119930\pi$
$809$	4.16123	+	7.20746i	0.146301	+	0.253401i	−0.783557	+	0.621320i	$0.786597\pi$
$810$	2.02446	−	3.50647i	0.0711322	−	0.123205i
$811$	−14.4638			−0.507894			−0.253947	−	0.967218i	$-0.581729\pi$
$811$	−14.4638			−0.507894			−0.253947	+	0.967218i	$0.581729\pi$
$812$	1.15734	−	2.00457i	0.0406147	−	0.0703468i
$813$	1.44235	−	2.49823i	0.0505855	−	0.0876167i
$814$	6.23921			0.218684
$815$	29.5405	−	51.1656i	1.03476	−	1.79225i
$816$	−3.69202	−	6.39477i	−0.129247	−	0.223862i
$817$	−7.40342	−	12.8231i	−0.259013	−	0.448623i
$818$	−18.8984			−0.660769
$819$		0			0
$820$	6.09783			0.212946
$821$	19.2080	+	33.2693i	0.670365	+	1.16111i	0.977801	+	0.209538i	$0.0671960\pi$
$821$	19.2080	+	33.2693i	0.670365	+	1.16111i	−0.307435	+	0.951569i	$0.599471\pi$
$822$	−7.87800	−	13.6451i	−0.274777	−	0.475928i
$823$	20.4874	−	35.4852i	0.714145	−	1.23694i	−0.249143	−	0.968467i	$-0.580149\pi$
$823$	20.4874	−	35.4852i	0.714145	−	1.23694i	0.963288	−	0.268469i	$-0.0865178\pi$
$824$	12.3230			0.429294
$825$	27.6347	−	47.8647i	0.962116	−	1.66643i
$826$	0.452575	−	0.783882i	0.0157471	−	0.0272748i
$827$	3.51035			0.122067			0.0610335	−	0.998136i	$-0.480560\pi$
$827$	3.51035			0.122067			0.0610335	+	0.998136i	$0.480560\pi$
$828$	−2.55496	+	4.42532i	−0.0887909	+	0.153790i
$829$	6.60925	+	11.4476i	0.229549	+	0.397590i	0.957674	−	0.287853i	$-0.0929416\pi$
$829$	6.60925	+	11.4476i	0.229549	+	0.397590i	−0.728126	+	0.685444i	$0.759608\pi$
$830$	31.0296	+	53.7448i	1.07705	+	1.86551i
$831$	−1.46250			−0.0507336
$832$		0			0
$833$	−48.1521			−1.66837
$834$	−3.04892	−	5.28088i	−0.105575	−	0.182862i
$835$	−39.4795	−	68.3805i	−1.36624	−	2.36640i
$836$	−4.31767	+	7.47842i	−0.149330	+	0.258647i
$837$	0.972853			0.0336267
$838$	−10.8802	+	18.8450i	−0.375849	+	0.650989i
$839$	−27.9245	+	48.3667i	−0.964062	+	1.66980i	−0.251947	+	0.967741i	$0.581071\pi$
$839$	−27.9245	+	48.3667i	−0.964062	+	1.66980i	−0.712115	+	0.702063i	$0.752263\pi$
$840$	−2.80194			−0.0966760
$841$	8.90611	−	15.4258i	0.307107	−	0.531925i
$842$	−10.2959	−	17.8330i	−0.354820	−	0.614566i
$843$	2.84117	+	4.92104i	0.0978550	+	0.169490i
$844$	7.79954			0.268471
$845$		0			0
$846$	7.20775			0.247808
$847$	−4.33579	−	7.50981i	−0.148979	−	0.258040i
$848$	−6.73825	−	11.6710i	−0.231392	−	0.400784i
$849$	12.6039	−	21.8306i	0.432564	−	0.749223i
$850$	−84.1318			−2.88570
$851$	−3.28621	+	5.69188i	−0.112650	+	0.195115i
$852$	0.664874	−	1.15160i	0.0227782	−	0.0394530i
$853$	21.8103			0.746770			0.373385	−	0.927676i	$-0.378197\pi$
$853$	21.8103			0.746770			0.373385	+	0.927676i	$0.378197\pi$
$854$	−0.137063	+	0.237401i	−0.00469021	+	0.00812368i
$855$	3.60388	+	6.24210i	0.123250	+	0.213475i
$856$	2.94989	+	5.10935i	0.100825	+	0.174634i
$857$	28.8961			0.987070			0.493535	−	0.869726i	$-0.335704\pi$
$857$	28.8961			0.987070			0.493535	+	0.869726i	$0.335704\pi$
$858$		0			0
$859$	−17.2755			−0.589431			−0.294715	−	0.955585i	$-0.595225\pi$
$859$	−17.2755			−0.589431			−0.294715	+	0.955585i	$0.595225\pi$
$860$	16.8388	+	29.1656i	0.574197	+	0.994539i
$861$	−0.521106	−	0.902583i	−0.0177593	−	0.0307599i
$862$	−17.2567	+	29.8894i	−0.587764	+	1.01804i
$863$	44.7741			1.52413			0.762063	−	0.647503i	$-0.224187\pi$
$863$	44.7741			1.52413			0.762063	+	0.647503i	$0.224187\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	18.8083	−	32.5769i	0.639501	−	1.10765i
$866$	2.12631			0.0722549
$867$	−18.7620	+	32.4968i	−0.637192	+	1.10365i
$868$	−0.336618	−	0.583039i	−0.0114255	−	0.0197896i
$869$	−20.2267	−	35.0337i	−0.686144	−	1.18844i
$870$	13.5429			0.459147
$871$		0			0
$872$	−0.792249			−0.0268289
$873$	4.27144	+	7.39835i	0.144566	+	0.250396i
$874$	−4.54825	−	7.87781i	−0.153847	−	0.266471i
$875$	−8.95742	+	15.5147i	−0.302816	+	0.524493i
$876$	−7.65279			−0.258564
$877$	−20.1371	+	34.8784i	−0.679980	+	1.17776i	0.295006	+	0.955495i	$0.404678\pi$
$877$	−20.1371	+	34.8784i	−0.679980	+	1.17776i	−0.974986	+	0.222265i	$0.928655\pi$
$878$	10.9160	−	18.9071i	0.368398	−	0.638085i
$879$	7.14914			0.241135
$880$	9.82036	−	17.0094i	0.331044	−	0.573385i
$881$	−4.70410	−	8.14775i	−0.158485	−	0.274505i	0.775837	−	0.630933i	$-0.217328\pi$
$881$	−4.70410	−	8.14775i	−0.158485	−	0.274505i	−0.934323	+	0.356428i	$0.883994\pi$
$882$	−3.26055	−	5.64744i	−0.109789	−	0.190159i
$883$	−51.2271			−1.72393			−0.861965	−	0.506968i	$-0.830766\pi$
$883$	−51.2271			−1.72393			−0.861965	+	0.506968i	$0.830766\pi$
$884$		0			0
$885$	5.29590			0.178020
$886$	−3.77024	−	6.53025i	−0.126664	−	0.219388i
$887$	19.9608	+	34.5731i	0.670217	+	1.16085i	0.977842	+	0.209342i	$0.0671324\pi$
$887$	19.9608	+	34.5731i	0.670217	+	1.16085i	−0.307625	+	0.951508i	$0.599534\pi$
$888$	0.643104	−	1.11389i	0.0215812	−	0.0373797i
$889$	−4.15585			−0.139383
$890$	6.29590	−	10.9048i	0.211039	−	0.365530i
$891$	2.42543	−	4.20096i	0.0812549	−	0.140738i
$892$	12.1957			0.408341
$893$	−6.41550	+	11.1120i	−0.214687	+	0.371848i
$894$	−1.27628	−	2.21059i	−0.0426853	−	0.0739331i
$895$	−46.1432	−	79.9223i	−1.54240	−	2.67151i
$896$	−0.692021			−0.0231188
$897$		0			0
$898$	19.7560			0.659266
$899$	1.62701	+	2.81806i	0.0542637	+	0.0939875i
$900$	−5.69687	−	9.86726i	−0.189896	−	0.328909i
$901$	−49.7555	+	86.1791i	−1.65760	+	2.87104i
$902$	7.30559			0.243249
$903$	2.87800	−	4.98485i	0.0957739	−	0.165885i
$904$	3.10992	−	5.38653i	0.103434	−	0.179153i
$905$	2.17629			0.0723424
$906$	−8.85839	+	15.3432i	−0.294300	+	0.509743i
$907$	17.4155	+	30.1645i	0.578272	+	1.00160i	0.995678	+	0.0928765i	$0.0296062\pi$
$907$	17.4155	+	30.1645i	0.578272	+	1.00160i	−0.417405	+	0.908720i	$0.637060\pi$
$908$	3.37167	+	5.83990i	0.111893	+	0.193804i
$909$	−11.9976			−0.397936
$910$		0			0
$911$	13.2125			0.437751			0.218875	−	0.975753i	$-0.429761\pi$
$911$	13.2125			0.437751			0.218875	+	0.975753i	$0.429761\pi$
$912$	0.890084	+	1.54167i	0.0294736	+	0.0510498i
$913$	37.1754	+	64.3897i	1.23033	+	2.13099i
$914$	−11.9291	+	20.6618i	−0.394579	+	0.683430i
$915$	−1.60388			−0.0530225
$916$	−9.91185	+	17.1678i	−0.327497	+	0.567241i
$917$	−3.05078	+	5.28410i	−0.100746	+	0.174496i
$918$	−7.38404			−0.243710
$919$	−10.5087	+	18.2017i	−0.346651	+	0.600417i	−0.985652	−	0.168789i	$-0.946015\pi$
$919$	−10.5087	+	18.2017i	−0.346651	+	0.600417i	0.639001	+	0.769206i	$0.279348\pi$
$920$	10.3448	+	17.9177i	0.341058	+	0.590731i
$921$	−8.99761	−	15.5843i	−0.296481	−	0.513521i
$922$	−17.5773			−0.578878
$923$		0			0
$924$	−3.35690			−0.110434
$925$	−7.32736	−	12.6914i	−0.240922	−	0.417289i
$926$	−11.9215	−	20.6487i	−0.391766	−	0.678559i
$927$	6.16152	−	10.6721i	0.202371	−	0.350517i
$928$	3.34481			0.109799
$929$	−13.4983	+	23.3797i	−0.442864	+	0.767063i	−0.997901	−	0.0647630i	$-0.979371\pi$
$929$	−13.4983	+	23.3797i	−0.442864	+	0.767063i	0.555037	+	0.831826i	$0.312704\pi$
$930$	1.96950	−	3.41127i	0.0645825	−	0.111860i
$931$	11.6087			0.380459
$932$	15.0151	−	26.0069i	0.491835	−	0.851883i
$933$	−1.66487	−	2.88365i	−0.0545055	−	0.0944064i
$934$	4.30529	+	7.45698i	0.140873	+	0.244000i
$935$	−145.028			−4.74292
$936$		0			0
$937$	23.1745			0.757078			0.378539	−	0.925585i	$-0.376427\pi$
$937$	23.1745			0.757078			0.378539	+	0.925585i	$0.376427\pi$
$938$	2.09485	+	3.62839i	0.0683993	+	0.118471i
$939$	8.94169	+	15.4875i	0.291801	+	0.505414i
$940$	14.5918	−	25.2737i	0.475932	−	0.824338i
$941$	−7.54048			−0.245813			−0.122906	−	0.992418i	$-0.539221\pi$
$941$	−7.54048			−0.245813			−0.122906	+	0.992418i	$0.539221\pi$
$942$	−3.15883	+	5.47126i	−0.102920	+	0.178263i
$943$	−3.84787	+	6.66471i	−0.125304	+	0.217033i
$944$	1.30798			0.0425711
$945$	−1.40097	+	2.42655i	−0.0455735	+	0.0789357i
$946$	20.1739	+	34.9422i	0.655910	+	1.13607i
$947$	10.3300	+	17.8922i	0.335681	+	0.581417i	0.983615	−	0.180279i	$-0.0577001\pi$
$947$	10.3300	+	17.8922i	0.335681	+	0.581417i	−0.647934	+	0.761696i	$0.724367\pi$
$948$	−8.33944			−0.270852
$949$		0			0
$950$	20.2828			0.658059
$951$	2.19687	+	3.80508i	0.0712383	+	0.123388i
$952$	2.55496	+	4.42532i	0.0828067	+	0.143425i
$953$	15.1468	−	26.2349i	0.490651	−	0.849833i	−0.509291	−	0.860595i	$-0.670092\pi$
$953$	15.1468	−	26.2349i	0.490651	−	0.849833i	0.999942	+	0.0107614i	$0.00342552\pi$
$954$	−13.4765			−0.436318
$955$	19.8388	−	34.3618i	0.641968	−	1.11192i
$956$	11.0489	−	19.1373i	0.357348	−	0.618944i
$957$	16.2252			0.524487
$958$	−3.29052	+	5.69935i	−0.106312	+	0.184138i
$959$	5.45175	+	9.44270i	0.176046	+	0.304921i
$960$	−2.02446	−	3.50647i	−0.0653391	−	0.113171i
$961$	−30.0536			−0.969470
$962$		0			0
$963$	5.89977			0.190118
$964$	5.06369	+	8.77056i	0.163090	+	0.282481i
$965$	−28.7385	−	49.7766i	−0.925127	−	1.60237i
$966$	1.76809	−	3.06241i	0.0568872	−	0.0985316i
$967$	20.7289			0.666595			0.333298	−	0.942822i	$-0.391839\pi$
$967$	20.7289			0.666595			0.333298	+	0.942822i	$0.391839\pi$
$968$	6.26540	−	10.8520i	0.201378	−	0.348796i
$969$	6.57242	−	11.3838i	0.211136	−	0.365699i
$970$	34.5894			1.11060
$971$	19.5547	−	33.8698i	0.627541	−	1.08693i	−0.360503	−	0.932758i	$-0.617395\pi$
$971$	19.5547	−	33.8698i	0.627541	−	1.08693i	0.988044	−	0.154175i	$-0.0492718\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	2.10992	+	3.65448i	0.0676408	+	0.117157i
$974$	−23.2760			−0.745813
$975$		0			0
$976$	−0.396125			−0.0126796
$977$	3.63773	+	6.30073i	0.116381	+	0.201578i	0.918331	−	0.395813i	$-0.129537\pi$
$977$	3.63773	+	6.30073i	0.116381	+	0.201578i	−0.801950	+	0.597391i	$0.796204\pi$
$978$	−7.29590	−	12.6369i	−0.233297	−	0.404082i
$979$	7.54288	−	13.0646i	0.241071	−	0.417548i
$980$	−26.4034			−0.843426
$981$	−0.396125	+	0.686108i	−0.0126473	+	0.0219057i
$982$	−7.77024	+	13.4585i	−0.247958	+	0.429477i
$983$	−53.4857			−1.70593			−0.852965	−	0.521969i	$-0.825198\pi$
$983$	−53.4857			−1.70593			−0.852965	+	0.521969i	$0.825198\pi$
$984$	0.753020	−	1.30427i	0.0240054	−	0.0415786i
$985$	−6.09299	−	10.5534i	−0.194139	−	0.336258i
$986$	−12.3491	−	21.3893i	−0.393276	−	0.681175i
$987$	−4.98792			−0.158767
$988$		0			0
$989$	−42.5026			−1.35150
$990$	−9.82036	−	17.0094i	−0.312111	−	0.540593i
$991$	−8.02877	−	13.9062i	−0.255042	−	0.441746i	0.709865	−	0.704338i	$-0.248756\pi$
$991$	−8.02877	−	13.9062i	−0.255042	−	0.441746i	−0.964907	+	0.262592i	$0.915423\pi$
$992$	0.486426	−	0.842515i	0.0154441	−	0.0267499i
$993$	25.6775			0.814852
$994$	−0.460107	+	0.796929i	−0.0145937	+	0.0252771i
$995$	−26.1042	+	45.2138i	−0.827558	+	1.43337i
$996$	15.3274			0.485666
$997$	−11.2131	+	19.4217i	−0.355123	+	0.615092i	−0.987139	−	0.159864i	$-0.948894\pi$
$997$	−11.2131	+	19.4217i	−0.355123	+	0.615092i	0.632016	+	0.774956i	$0.282228\pi$
$998$	−4.76809	−	8.25857i	−0.150931	−	0.261420i
$999$	−0.643104	−	1.11389i	−0.0203469	−	0.0352419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.m.991.3		6
13.2	odd	12		1014.2.b.g.337.4		6
13.3	even	3		1014.2.a.m.1.3	✓	3
13.4	even	6		1014.2.e.k.529.1		6
13.5	odd	4		1014.2.i.g.361.4		12
13.6	odd	12		1014.2.i.g.823.1		12
13.7	odd	12		1014.2.i.g.823.6		12
13.8	odd	4		1014.2.i.g.361.3		12
13.9	even	3	inner	1014.2.e.m.529.3		6
13.10	even	6		1014.2.a.o.1.1	yes	3
13.11	odd	12		1014.2.b.g.337.3		6
13.12	even	2		1014.2.e.k.991.1		6
39.2	even	12		3042.2.b.r.1351.3		6
39.11	even	12		3042.2.b.r.1351.4		6
39.23	odd	6		3042.2.a.bd.1.3		3
39.29	odd	6		3042.2.a.be.1.1		3
52.3	odd	6		8112.2.a.ce.1.3		3
52.23	odd	6		8112.2.a.bz.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.3	✓	3	13.3	even	3
1014.2.a.o.1.1	yes	3	13.10	even	6
1014.2.b.g.337.3		6	13.11	odd	12
1014.2.b.g.337.4		6	13.2	odd	12
1014.2.e.k.529.1		6	13.4	even	6
1014.2.e.k.991.1		6	13.12	even	2
1014.2.e.m.529.3		6	13.9	even	3	inner
1014.2.e.m.991.3		6	1.1	even	1	trivial
1014.2.i.g.361.3		12	13.8	odd	4
1014.2.i.g.361.4		12	13.5	odd	4
1014.2.i.g.823.1		12	13.6	odd	12
1014.2.i.g.823.6		12	13.7	odd	12
3042.2.a.bd.1.3		3	39.23	odd	6
3042.2.a.be.1.1		3	39.29	odd	6
3042.2.b.r.1351.3		6	39.2	even	12
3042.2.b.r.1351.4		6	39.11	even	12
8112.2.a.bz.1.1		3	52.23	odd	6
8112.2.a.ce.1.3		3	52.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.04892 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.346011 + 0.599308i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.02446 + 3.50647i) q^{10} +(2.42543 + 4.20096i) q^{11} +1.00000 q^{12} -0.692021 q^{14} +(-2.02446 - 3.50647i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.69202 + 6.39477i) q^{17} -1.00000 q^{18} +(0.890084 - 1.54167i) q^{19} +(-2.02446 + 3.50647i) q^{20} +0.692021 q^{21} +(-2.42543 + 4.20096i) q^{22} +(-2.55496 - 4.42532i) q^{23} +(0.500000 + 0.866025i) q^{24} +11.3937 q^{25} +1.00000 q^{27} +(-0.346011 - 0.599308i) q^{28} +(1.67241 + 2.89669i) q^{29} +(2.02446 - 3.50647i) q^{30} +0.972853 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.42543 - 4.20096i) q^{33} -7.38404 q^{34} +(-1.40097 + 2.42655i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.643104 - 1.11389i) q^{37} +1.78017 q^{38} -4.04892 q^{40} +(-0.753020 - 1.30427i) q^{41} +(0.346011 + 0.599308i) q^{42} +(4.15883 - 7.20331i) q^{43} -4.85086 q^{44} +(-2.02446 + 3.50647i) q^{45} +(2.55496 - 4.42532i) q^{46} -7.20775 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.26055 + 5.64744i) q^{49} +(5.69687 + 9.86726i) q^{50} +7.38404 q^{51} +13.4765 q^{53} +(0.500000 + 0.866025i) q^{54} +(9.82036 + 17.0094i) q^{55} +(0.346011 - 0.599308i) q^{56} -1.78017 q^{57} +(-1.67241 + 2.89669i) q^{58} +(-0.653989 + 1.13274i) q^{59} +4.04892 q^{60} +(0.198062 - 0.343054i) q^{61} +(0.486426 + 0.842515i) q^{62} +(-0.346011 - 0.599308i) q^{63} +1.00000 q^{64} +4.85086 q^{66} +(-3.02715 - 5.24317i) q^{67} +(-3.69202 - 6.39477i) q^{68} +(-2.55496 + 4.42532i) q^{69} -2.80194 q^{70} +(0.664874 - 1.15160i) q^{71} +(0.500000 - 0.866025i) q^{72} -7.65279 q^{73} +(0.643104 - 1.11389i) q^{74} +(-5.69687 - 9.86726i) q^{75} +(0.890084 + 1.54167i) q^{76} -3.35690 q^{77} -8.33944 q^{79} +(-2.02446 - 3.50647i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.753020 - 1.30427i) q^{82} +15.3274 q^{83} +(-0.346011 + 0.599308i) q^{84} +(-14.9487 + 25.8919i) q^{85} +8.31767 q^{86} +(1.67241 - 2.89669i) q^{87} +(-2.42543 - 4.20096i) q^{88} +(-1.55496 - 2.69327i) q^{89} -4.04892 q^{90} +5.10992 q^{92} +(-0.486426 - 0.842515i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(3.60388 - 6.24210i) q^{95} -1.00000 q^{96} +(4.27144 - 7.39835i) q^{97} +(-3.26055 + 5.64744i) q^{98} -4.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} - 3 q^{16} - 12 q^{17} - 6 q^{18} + 4 q^{19} - 3 q^{20} - 6 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 - 3 * q^16 - 12 * q^17 - 6 * q^18 + 4 * q^19 - 3 * q^20 - 6 * q^21 - q^22 - 16 * q^23 + 3 * q^24 + 4 * q^25 + 6 * q^27 + 3 * q^28 - 13 * q^29 + 3 * q^30 + 18 * q^31 + 3 * q^32 + q^33 - 24 * q^34 - 4 * q^35 - 3 * q^36 - 12 * q^37 + 8 * q^38 - 6 * q^40 - 14 * q^41 - 3 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 16 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^49 + 2 * q^50 + 24 * q^51 + 30 * q^53 + 3 * q^54 + 22 * q^55 - 3 * q^56 - 8 * q^57 + 13 * q^58 - 9 * q^59 + 6 * q^60 + 10 * q^61 + 9 * q^62 + 3 * q^63 + 6 * q^64 + 2 * q^66 - 6 * q^67 - 12 * q^68 - 16 * q^69 - 8 * q^70 + 6 * q^71 + 3 * q^72 - 10 * q^73 + 12 * q^74 - 2 * q^75 + 4 * q^76 - 12 * q^77 - 10 * q^79 - 3 * q^80 - 3 * q^81 + 14 * q^82 + 14 * q^83 + 3 * q^84 - 26 * q^85 + 16 * q^86 - 13 * q^87 - q^88 - 10 * q^89 - 6 * q^90 + 32 * q^92 - 9 * q^93 - 4 * q^94 + 4 * q^95 - 6 * q^96 + 7 * q^97 - 4 * q^98 - 2 * q^99

Introduction

L-functions

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