LMFDB - Embedded newform 546.2.e.f.545.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(545,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.545");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.10070523904.11
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 10x^{4} + 81 $ x^8 - 10*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.7
Root			$1.68014 + 0.420861i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.f.545.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.68014 - 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(-1.68014 + 0.420861i) q^{6} +(-0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.68014 - 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(-1.68014 + 0.420861i) q^{6} +(-0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} -0.841723i q^{10} +(1.68014 - 0.420861i) q^{12} +(2.27533 + 2.79694i) q^{13} +(0.595188 - 2.57794i) q^{14} +(0.354249 + 1.41421i) q^{15} +1.00000 q^{16} -4.33981 q^{17} +(-2.64575 + 1.41421i) q^{18} +4.55066 q^{19} +0.841723i q^{20} +(0.0849536 + 4.58179i) q^{21} +7.98430i q^{23} +(-1.68014 + 0.420861i) q^{24} +4.29150 q^{25} +(-2.27533 - 2.79694i) q^{26} +(3.85005 - 3.48957i) q^{27} +(-0.595188 + 2.57794i) q^{28} -2.32744i q^{29} +(-0.354249 - 1.41421i) q^{30} -5.53019 q^{31} -1.00000 q^{32} +4.33981 q^{34} +(-2.16991 - 0.500983i) q^{35} +(2.64575 - 1.41421i) q^{36} +5.15587i q^{37} -4.55066 q^{38} +(5.00000 + 3.74166i) q^{39} -0.841723i q^{40} -10.8896i q^{41} +(-0.0849536 - 4.58179i) q^{42} +8.00000 q^{43} +(1.19038 + 2.22699i) q^{45} -7.98430i q^{46} -7.82087i q^{47} +(1.68014 - 0.420861i) q^{48} +(-6.29150 - 3.06871i) q^{49} -4.29150 q^{50} +(-7.29150 + 1.82646i) q^{51} +(2.27533 + 2.79694i) q^{52} +7.98430i q^{53} +(-3.85005 + 3.48957i) q^{54} +(0.595188 - 2.57794i) q^{56} +(7.64575 - 1.91520i) q^{57} +2.32744i q^{58} +3.91044i q^{59} +(0.354249 + 1.41421i) q^{60} -5.59388i q^{61} +5.53019 q^{62} +(2.07103 + 7.66230i) q^{63} +1.00000 q^{64} +(-2.35425 + 1.91520i) q^{65} +1.82646i q^{67} -4.33981 q^{68} +(3.36028 + 13.4148i) q^{69} +(2.16991 + 0.500983i) q^{70} +14.5830 q^{71} +(-2.64575 + 1.41421i) q^{72} +3.14944 q^{73} -5.15587i q^{74} +(7.21033 - 1.80613i) q^{75} +4.55066 q^{76} +(-5.00000 - 3.74166i) q^{78} -11.2915 q^{79} +0.841723i q^{80} +(5.00000 - 7.48331i) q^{81} +10.8896i q^{82} -7.27733i q^{83} +(0.0849536 + 4.58179i) q^{84} -3.65292i q^{85} -8.00000 q^{86} +(-0.979531 - 3.91044i) q^{87} +12.5730i q^{89} +(-1.19038 - 2.22699i) q^{90} +(-8.56458 + 4.20095i) q^{91} +7.98430i q^{92} +(-9.29150 + 2.32744i) q^{93} +7.82087i q^{94} +3.83039i q^{95} +(-1.68014 + 0.420861i) q^{96} -9.87000 q^{97} +(6.29150 + 3.06871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 24 q^{15} + 8 q^{16} - 8 q^{21} - 8 q^{25} - 24 q^{30} - 8 q^{32} + 40 q^{39} + 8 q^{42} + 64 q^{43} - 8 q^{49} + 8 q^{50} - 16 q^{51} + 40 q^{57} + 24 q^{60} + 8 q^{63} + 8 q^{64} - 40 q^{65} + 32 q^{71} - 40 q^{78} - 48 q^{79} + 40 q^{81} - 8 q^{84} - 64 q^{86} - 32 q^{91} - 32 q^{93} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 24 * q^15 + 8 * q^16 - 8 * q^21 - 8 * q^25 - 24 * q^30 - 8 * q^32 + 40 * q^39 + 8 * q^42 + 64 * q^43 - 8 * q^49 + 8 * q^50 - 16 * q^51 + 40 * q^57 + 24 * q^60 + 8 * q^63 + 8 * q^64 - 40 * q^65 + 32 * q^71 - 40 * q^78 - 48 * q^79 + 40 * q^81 - 8 * q^84 - 64 * q^86 - 32 * q^91 - 32 * q^93 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.68014	−	0.420861i	0.970030	−	0.242984i
$3$	1.68014	−	0.420861i	0.970030	−	0.242984i
$4$	1.00000			0.500000
$5$			0.841723i			0.376430i	0.982128	+	0.188215i	$0.0602702\pi$
$5$			0.841723i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$6$	−1.68014	+	0.420861i	−0.685915	+	0.171816i
$7$	−0.595188	+	2.57794i	−0.224960	+	0.974368i
$7$	−0.595188	+	2.57794i	−0.224960	+	0.974368i
$8$	−1.00000			−0.353553
$9$	2.64575	−	1.41421i	0.881917	−	0.471405i
$10$		−	0.841723i		−	0.266176i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	1.68014	−	0.420861i	0.485015	−	0.121492i
$13$	2.27533	+	2.79694i	0.631063	+	0.775732i
$13$	2.27533	+	2.79694i	0.631063	+	0.775732i
$14$	0.595188	−	2.57794i	0.159071	−	0.688982i
$15$	0.354249	+	1.41421i	0.0914666	+	0.365148i
$16$	1.00000			0.250000
$17$	−4.33981			−1.05256			−0.526280	−	0.850311i	$-0.676414\pi$
$17$	−4.33981			−1.05256			−0.526280	+	0.850311i	$0.676414\pi$
$18$	−2.64575	+	1.41421i	−0.623610	+	0.333333i
$19$	4.55066			1.04399			0.521996	−	0.852948i	$-0.325187\pi$
$19$	4.55066			1.04399			0.521996	+	0.852948i	$0.325187\pi$
$20$			0.841723i			0.188215i
$21$	0.0849536	+	4.58179i	0.0185384	+	0.999828i
$22$		0			0
$23$			7.98430i			1.66484i	0.554144	+	0.832421i	$0.313046\pi$
$23$			7.98430i			1.66484i	−0.554144	+	0.832421i	$0.686954\pi$
$24$	−1.68014	+	0.420861i	−0.342957	+	0.0859080i
$25$	4.29150			0.858301
$26$	−2.27533	−	2.79694i	−0.446229	−	0.548525i
$27$	3.85005	−	3.48957i	0.740942	−	0.671569i
$28$	−0.595188	+	2.57794i	−0.112480	+	0.487184i
$29$		−	2.32744i		−	0.432195i	−0.976372	−	0.216098i	$-0.930667\pi$
$29$		−	2.32744i		−	0.432195i	0.976372	−	0.216098i	$-0.0693330\pi$
$30$	−0.354249	−	1.41421i	−0.0646767	−	0.258199i
$31$	−5.53019			−0.993252			−0.496626	−	0.867965i	$-0.665428\pi$
$31$	−5.53019			−0.993252			−0.496626	+	0.867965i	$0.665428\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	4.33981			0.744272
$35$	−2.16991	−	0.500983i	−0.366781	−	0.0846816i
$36$	2.64575	−	1.41421i	0.440959	−	0.235702i
$37$			5.15587i			0.847620i	0.905751	+	0.423810i	$0.139308\pi$
$37$			5.15587i			0.847620i	−0.905751	+	0.423810i	$0.860692\pi$
$38$	−4.55066			−0.738214
$39$	5.00000	+	3.74166i	0.800641	+	0.599145i
$40$		−	0.841723i		−	0.133088i
$41$		−	10.8896i		−	1.70067i	−0.526244	−	0.850334i	$-0.676400\pi$
$41$		−	10.8896i		−	1.70067i	0.526244	−	0.850334i	$-0.323600\pi$
$42$	−0.0849536	−	4.58179i	−0.0131086	−	0.706985i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	1.19038	+	2.22699i	0.177451	+	0.331980i
$46$		−	7.98430i		−	1.17722i
$47$		−	7.82087i		−	1.14079i	−0.821370	−	0.570396i	$-0.806790\pi$
$47$		−	7.82087i		−	1.14079i	0.821370	−	0.570396i	$-0.193210\pi$
$48$	1.68014	−	0.420861i	0.242508	−	0.0607461i
$49$	−6.29150	−	3.06871i	−0.898786	−	0.438387i
$50$	−4.29150			−0.606910
$51$	−7.29150	+	1.82646i	−1.02101	+	0.255756i
$52$	2.27533	+	2.79694i	0.315531	+	0.387866i
$53$			7.98430i			1.09673i	0.836240	+	0.548364i	$0.184749\pi$
$53$			7.98430i			1.09673i	−0.836240	+	0.548364i	$0.815251\pi$
$54$	−3.85005	+	3.48957i	−0.523925	+	0.474871i
$55$		0			0
$56$	0.595188	−	2.57794i	0.0795353	−	0.344491i
$57$	7.64575	−	1.91520i	1.01270	−	0.253674i
$58$			2.32744i			0.305608i
$59$			3.91044i			0.509095i	0.967060	+	0.254548i	$0.0819266\pi$
$59$			3.91044i			0.509095i	−0.967060	+	0.254548i	$0.918073\pi$
$60$	0.354249	+	1.41421i	0.0457333	+	0.182574i
$61$		−	5.59388i		−	0.716223i	−0.933679	−	0.358112i	$-0.883421\pi$
$61$		−	5.59388i		−	0.716223i	0.933679	−	0.358112i	$-0.116579\pi$
$62$	5.53019			0.702335
$63$	2.07103	+	7.66230i	0.260926	+	0.965359i
$64$	1.00000			0.125000
$65$	−2.35425	+	1.91520i	−0.292009	+	0.237551i
$66$		0			0
$67$			1.82646i			0.223138i	0.993757	+	0.111569i	$0.0355876\pi$
$67$			1.82646i			0.223138i	−0.993757	+	0.111569i	$0.964412\pi$
$68$	−4.33981			−0.526280
$69$	3.36028	+	13.4148i	0.404531	+	1.61495i
$70$	2.16991	+	0.500983i	0.259354	+	0.0598790i
$71$	14.5830			1.73068			0.865342	−	0.501182i	$-0.167101\pi$
$71$	14.5830			1.73068			0.865342	+	0.501182i	$0.167101\pi$
$72$	−2.64575	+	1.41421i	−0.311805	+	0.166667i
$73$	3.14944			0.368614			0.184307	−	0.982869i	$-0.440996\pi$
$73$	3.14944			0.368614			0.184307	+	0.982869i	$0.440996\pi$
$74$		−	5.15587i		−	0.599358i
$75$	7.21033	−	1.80613i	0.832577	−	0.208554i
$76$	4.55066			0.521996
$77$		0			0
$78$	−5.00000	−	3.74166i	−0.566139	−	0.423659i
$79$	−11.2915			−1.27039			−0.635197	−	0.772350i	$-0.719081\pi$
$79$	−11.2915			−1.27039			−0.635197	+	0.772350i	$0.719081\pi$
$80$			0.841723i			0.0941075i
$81$	5.00000	−	7.48331i	0.555556	−	0.831479i
$82$			10.8896i			1.20255i
$83$		−	7.27733i		−	0.798790i	−0.916779	−	0.399395i	$-0.869220\pi$
$83$		−	7.27733i		−	0.798790i	0.916779	−	0.399395i	$-0.130780\pi$
$84$	0.0849536	+	4.58179i	0.00926920	+	0.499914i
$85$		−	3.65292i		−	0.396215i
$86$	−8.00000			−0.862662
$87$	−0.979531	−	3.91044i	−0.105017	−	0.419243i
$88$		0			0
$89$			12.5730i			1.33274i	0.745622	+	0.666369i	$0.232152\pi$
$89$			12.5730i			1.33274i	−0.745622	+	0.666369i	$0.767848\pi$
$90$	−1.19038	−	2.22699i	−0.125477	−	0.234745i
$91$	−8.56458	+	4.20095i	−0.897812	+	0.440379i
$92$			7.98430i			0.832421i
$93$	−9.29150	+	2.32744i	−0.963484	+	0.241345i
$94$			7.82087i			0.806661i
$95$			3.83039i			0.392990i
$96$	−1.68014	+	0.420861i	−0.171479	+	0.0429540i
$97$	−9.87000			−1.00215			−0.501074	−	0.865405i	$-0.667061\pi$
$97$	−9.87000			−1.00215			−0.501074	+	0.865405i	$0.667061\pi$
$98$	6.29150	+	3.06871i	0.635538	+	0.309987i
$99$		0			0
$100$	4.29150			0.429150
$101$	−5.74103			−0.571254			−0.285627	−	0.958341i	$-0.592202\pi$
$101$	−5.74103			−0.571254			−0.285627	+	0.958341i	$0.592202\pi$
$102$	7.29150	−	1.82646i	0.721966	−	0.180847i
$103$		−	9.20614i		−	0.907108i	−0.891229	−	0.453554i	$-0.850156\pi$
$103$		−	9.20614i		−	0.907108i	0.891229	−	0.453554i	$-0.149844\pi$
$104$	−2.27533	−	2.79694i	−0.223114	−	0.274263i
$105$	−3.85660	+	0.0715074i	−0.376365	+	0.00697841i
$106$		−	7.98430i		−	0.775504i
$107$		−	5.65685i		−	0.546869i	−0.961891	−	0.273434i	$-0.911840\pi$
$107$		−	5.65685i		−	0.546869i	0.961891	−	0.273434i	$-0.0881596\pi$
$108$	3.85005	−	3.48957i	0.370471	−	0.335784i
$109$		−	15.4676i		−	1.48153i	−0.671765	−	0.740764i	$-0.734464\pi$
$109$		−	15.4676i		−	1.48153i	0.671765	−	0.740764i	$-0.265536\pi$
$110$		0			0
$111$	2.16991	+	8.66259i	0.205958	+	0.822217i
$112$	−0.595188	+	2.57794i	−0.0562400	+	0.243592i
$113$		−	14.1421i		−	1.33038i	−0.746674	−	0.665190i	$-0.768350\pi$
$113$		−	14.1421i		−	1.33038i	0.746674	−	0.665190i	$-0.231650\pi$
$114$	−7.64575	+	1.91520i	−0.716090	+	0.179375i
$115$	−6.72057			−0.626696
$116$		−	2.32744i		−	0.216098i
$117$	9.97543	+	4.18221i	0.922229	+	0.386645i
$118$		−	3.91044i		−	0.359985i
$119$	2.58301	−	11.1878i	0.236784	−	1.02558i
$120$	−0.354249	−	1.41421i	−0.0323383	−	0.129099i
$121$	−11.0000			−1.00000
$122$			5.59388i			0.506446i
$123$	−4.58301	−	18.2960i	−0.413236	−	1.64970i
$124$	−5.53019			−0.496626
$125$			7.82087i			0.699520i
$126$	−2.07103	−	7.66230i	−0.184502	−	0.682612i
$127$	−6.58301			−0.584147			−0.292074	−	0.956396i	$-0.594345\pi$
$127$	−6.58301			−0.584147			−0.292074	+	0.956396i	$0.594345\pi$
$128$	−1.00000			−0.0883883
$129$	13.4411	−	3.36689i	1.18343	−	0.296438i
$130$	2.35425	−	1.91520i	0.206481	−	0.167974i
$131$	−1.40122			−0.122425			−0.0612126	−	0.998125i	$-0.519497\pi$
$131$	−1.40122			−0.122425			−0.0612126	+	0.998125i	$0.519497\pi$
$132$		0			0
$133$	−2.70850	+	11.7313i	−0.234857	+	1.01723i
$134$		−	1.82646i		−	0.157782i
$135$	2.93725	+	3.24067i	0.252799	+	0.278913i
$136$	4.33981			0.372136
$137$	−1.29150			−0.110341			−0.0551703	−	0.998477i	$-0.517570\pi$
$137$	−1.29150			−0.110341			−0.0551703	+	0.998477i	$0.517570\pi$
$138$	−3.36028	−	13.4148i	−0.286046	−	1.14194i
$139$		−	8.66259i		−	0.734752i	−0.930073	−	0.367376i	$-0.880256\pi$
$139$		−	8.66259i		−	0.734752i	0.930073	−	0.367376i	$-0.119744\pi$
$140$	−2.16991	−	0.500983i	−0.183391	−	0.0423408i
$141$	−3.29150	−	13.1402i	−0.277195	−	1.10660i
$142$	−14.5830			−1.22378
$143$		0			0
$144$	2.64575	−	1.41421i	0.220479	−	0.117851i
$145$	1.95906			0.162691
$146$	−3.14944			−0.260649
$147$	−11.8621	−	2.50802i	−0.978371	−	0.206858i
$148$			5.15587i			0.423810i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	−7.21033	+	1.80613i	−0.588721	+	0.147470i
$151$		−	13.6412i		−	1.11010i	−0.831817	−	0.555051i	$-0.812699\pi$
$151$		−	13.6412i		−	1.11010i	0.831817	−	0.555051i	$-0.187301\pi$
$152$	−4.55066			−0.369107
$153$	−11.4821	+	6.13742i	−0.928270	+	0.496181i
$154$		0			0
$155$		−	4.65489i		−	0.373890i
$156$	5.00000	+	3.74166i	0.400320	+	0.299572i
$157$		−	17.8687i		−	1.42608i	−0.701123	−	0.713040i	$-0.747318\pi$
$157$		−	17.8687i		−	1.42608i	0.701123	−	0.713040i	$-0.252682\pi$
$158$	11.2915			0.898304
$159$	3.36028	+	13.4148i	0.266488	+	1.06386i
$160$		−	0.841723i		−	0.0665440i
$161$	−20.5830	−	4.75216i	−1.62217	−	0.374523i
$162$	−5.00000	+	7.48331i	−0.392837	+	0.587945i
$163$			8.48528i			0.664619i	0.943170	+	0.332309i	$0.107828\pi$
$163$			8.48528i			0.664619i	−0.943170	+	0.332309i	$0.892172\pi$
$164$		−	10.8896i		−	0.850334i
$165$		0			0
$166$			7.27733i			0.564830i
$167$		−	1.68345i		−	0.130269i	−0.997876	−	0.0651345i	$-0.979252\pi$
$167$		−	1.68345i		−	0.130269i	0.997876	−	0.0651345i	$-0.0207476\pi$
$168$	−0.0849536	−	4.58179i	−0.00655431	−	0.353493i
$169$	−2.64575	+	12.7279i	−0.203519	+	0.979071i
$170$			3.65292i			0.280166i
$171$	12.0399	−	6.43560i	0.920715	−	0.492143i
$172$	8.00000			0.609994
$173$	−14.4207			−1.09638			−0.548191	−	0.836353i	$-0.684683\pi$
$173$	−14.4207			−1.09638			−0.548191	+	0.836353i	$0.684683\pi$
$174$	0.979531	+	3.91044i	0.0742581	+	0.296449i
$175$	−2.55425	+	11.0632i	−0.193083	+	0.836301i
$176$		0			0
$177$	1.64575	+	6.57008i	0.123702	+	0.493838i
$178$		−	12.5730i		−	0.942388i
$179$			11.3137i			0.845626i	0.906217	+	0.422813i	$0.138957\pi$
$179$			11.3137i			0.845626i	−0.906217	+	0.422813i	$0.861043\pi$
$180$	1.19038	+	2.22699i	0.0887254	+	0.165990i
$181$		−	10.6442i		−	0.791178i	−0.918428	−	0.395589i	$-0.870540\pi$
$181$		−	10.6442i		−	0.791178i	0.918428	−	0.395589i	$-0.129460\pi$
$182$	8.56458	−	4.20095i	0.634849	−	0.311395i
$183$	−2.35425	−	9.39851i	−0.174031	−	0.694758i
$184$		−	7.98430i		−	0.588610i
$185$	−4.33981			−0.319070
$186$	9.29150	−	2.32744i	0.681286	−	0.170656i
$187$		0			0
$188$		−	7.82087i		−	0.570396i
$189$	6.70439	+	12.0021i	0.487673	+	0.873026i
$190$		−	3.83039i		−	0.277886i
$191$		−	0.500983i		−	0.0362499i	−0.999836	−	0.0181249i	$-0.994230\pi$
$191$		−	0.500983i		−	0.0362499i	0.999836	−	0.0181249i	$-0.00576966\pi$
$192$	1.68014	−	0.420861i	0.121254	−	0.0303731i
$193$		−	8.48528i		−	0.610784i	−0.952227	−	0.305392i	$-0.901213\pi$
$193$		−	8.48528i		−	0.610784i	0.952227	−	0.305392i	$-0.0987875\pi$
$194$	9.87000			0.708625
$195$	−3.14944	+	4.20861i	−0.225536	+	0.301385i
$196$	−6.29150	−	3.06871i	−0.449393	−	0.219194i
$197$	−8.58301			−0.611514			−0.305757	−	0.952110i	$-0.598909\pi$
$197$	−8.58301			−0.611514			−0.305757	+	0.952110i	$0.598909\pi$
$198$		0			0
$199$			25.4442i			1.80369i	0.432056	+	0.901847i	$0.357788\pi$
$199$			25.4442i			1.80369i	−0.432056	+	0.901847i	$0.642212\pi$
$200$	−4.29150			−0.303455
$201$	0.768687	+	3.06871i	0.0542190	+	0.216450i
$202$	5.74103			0.403938
$203$	6.00000	+	1.38527i	0.421117	+	0.0972266i
$204$	−7.29150	+	1.82646i	−0.510507	+	0.127878i
$205$	9.16601			0.640182
$206$			9.20614i			0.641422i
$207$	11.2915	+	21.1245i	0.784814	+	1.46825i
$208$	2.27533	+	2.79694i	0.157766	+	0.193933i
$209$		0			0
$210$	3.85660	−	0.0715074i	0.266130	−	0.00493448i
$211$	10.5830			0.728564			0.364282	−	0.931289i	$-0.381314\pi$
$211$	10.5830			0.728564			0.364282	+	0.931289i	$0.381314\pi$
$212$			7.98430i			0.548364i
$213$	24.5015	−	6.13742i	1.67882	−	0.420529i
$214$			5.65685i			0.386695i
$215$			6.73378i			0.459240i
$216$	−3.85005	+	3.48957i	−0.261963	+	0.237435i
$217$	3.29150	−	14.2565i	0.223442	−	0.967793i
$218$			15.4676i			1.04760i
$219$	5.29150	−	1.32548i	0.357567	−	0.0895675i
$220$		0			0
$221$	−9.87451	−	12.1382i	−0.664231	−	0.816504i
$222$	−2.16991	−	8.66259i	−0.145635	−	0.581395i
$223$	14.6315			0.979798			0.489899	−	0.871779i	$-0.337034\pi$
$223$	14.6315			0.979798			0.489899	+	0.871779i	$0.337034\pi$
$224$	0.595188	−	2.57794i	0.0397677	−	0.172246i
$225$	11.3542	−	6.06910i	0.756950	−	0.404607i
$226$			14.1421i			0.940721i
$227$			8.96077i			0.594747i	0.954761	+	0.297374i	$0.0961107\pi$
$227$			8.96077i			0.594747i	−0.954761	+	0.297374i	$0.903889\pi$
$228$	7.64575	−	1.91520i	0.506352	−	0.126837i
$229$	−24.2907			−1.60517			−0.802586	−	0.596536i	$-0.796543\pi$
$229$	−24.2907			−1.60517			−0.802586	+	0.596536i	$0.796543\pi$
$230$	6.72057			0.443141
$231$		0			0
$232$			2.32744i			0.152804i
$233$		−	22.6274i		−	1.48237i	−0.671300	−	0.741186i	$-0.734264\pi$
$233$		−	22.6274i		−	1.48237i	0.671300	−	0.741186i	$-0.265736\pi$
$234$	−9.97543	−	4.18221i	−0.652114	−	0.273399i
$235$	6.58301			0.429428
$236$			3.91044i			0.254548i
$237$	−18.9713	+	4.75216i	−1.23232	+	0.308686i
$238$	−2.58301	+	11.1878i	−0.167431	+	0.725195i
$239$	21.8745			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$239$	21.8745			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$240$	0.354249	+	1.41421i	0.0228667	+	0.0912871i
$241$	−25.6919			−1.65496			−0.827480	−	0.561495i	$-0.810226\pi$
$241$	−25.6919			−1.65496			−0.827480	+	0.561495i	$0.810226\pi$
$242$	11.0000			0.707107
$243$	5.25127	−	14.6773i	0.336869	−	0.941551i
$244$		−	5.59388i		−	0.358112i
$245$	2.58301	−	5.29570i	0.165022	−	0.338330i
$246$	4.58301	+	18.2960i	0.292202	+	1.16651i
$247$	10.3542	+	12.7279i	0.658825	+	0.809858i
$248$	5.53019			0.351167
$249$	−3.06275	−	12.2269i	−0.194094	−	0.774851i
$250$		−	7.82087i		−	0.494635i
$251$	5.74103			0.362371			0.181185	−	0.983449i	$-0.442007\pi$
$251$	5.74103			0.362371			0.181185	+	0.983449i	$0.442007\pi$
$252$	2.07103	+	7.66230i	0.130463	+	0.482679i
$253$		0			0
$254$	6.58301			0.413054
$255$	−1.53737	−	6.13742i	−0.0962741	−	0.384340i
$256$	1.00000			0.0625000
$257$	15.8219			0.986942			0.493471	−	0.869762i	$-0.335728\pi$
$257$	15.8219			0.986942			0.493471	+	0.869762i	$0.335728\pi$
$258$	−13.4411	+	3.36689i	−0.836808	+	0.209614i
$259$	−13.2915	−	3.06871i	−0.825894	−	0.190681i
$260$	−2.35425	+	1.91520i	−0.146004	+	0.118775i
$261$	−3.29150	−	6.15784i	−0.203739	−	0.381161i
$262$	1.40122			0.0865677
$263$			16.4696i			1.01556i	0.861487	+	0.507779i	$0.169533\pi$
$263$			16.4696i			1.01556i	−0.861487	+	0.507779i	$0.830467\pi$
$264$		0			0
$265$	−6.72057			−0.412841
$266$	2.70850	−	11.7313i	0.166069	−	0.719292i
$267$	5.29150	+	21.1245i	0.323835	+	1.29280i
$268$			1.82646i			0.111569i
$269$	23.1003			1.40845			0.704225	−	0.709977i	$-0.251295\pi$
$269$	23.1003			1.40845			0.704225	+	0.709977i	$0.251295\pi$
$270$	−2.93725	−	3.24067i	−0.178756	−	0.197221i
$271$	23.3111			1.41605			0.708025	−	0.706187i	$-0.249586\pi$
$271$	23.3111			1.41605			0.708025	+	0.706187i	$0.249586\pi$
$272$	−4.33981			−0.263140
$273$	−12.6217	+	10.6627i	−0.763899	+	0.645335i
$274$	1.29150			0.0780225
$275$		0			0
$276$	3.36028	+	13.4148i	0.202265	+	0.807473i
$277$	31.1660			1.87258			0.936292	−	0.351222i	$-0.114234\pi$
$277$	31.1660			1.87258			0.936292	+	0.351222i	$0.114234\pi$
$278$			8.66259i			0.519548i
$279$	−14.6315	+	7.82087i	−0.875965	+	0.468223i
$280$	2.16991	+	0.500983i	0.129677	+	0.0299395i
$281$	−13.2915			−0.792905			−0.396452	−	0.918055i	$-0.629759\pi$
$281$	−13.2915			−0.792905			−0.396452	+	0.918055i	$0.629759\pi$
$282$	3.29150	+	13.1402i	0.196006	+	0.782486i
$283$			14.8000i			0.879770i	0.898054	+	0.439885i	$0.144981\pi$
$283$			14.8000i			0.879770i	−0.898054	+	0.439885i	$0.855019\pi$
$284$	14.5830			0.865342
$285$	1.61206	+	6.43560i	0.0954905	+	0.381212i
$286$		0			0
$287$	28.0726	+	6.48135i	1.65708	+	0.382582i
$288$	−2.64575	+	1.41421i	−0.155902	+	0.0833333i
$289$	1.83399			0.107882
$290$	−1.95906			−0.115040
$291$	−16.5830	+	4.15390i	−0.972113	+	0.243506i
$292$	3.14944			0.184307
$293$			13.1166i			0.766278i	0.923691	+	0.383139i	$0.125157\pi$
$293$			13.1166i			0.766278i	−0.923691	+	0.383139i	$0.874843\pi$
$294$	11.8621	+	2.50802i	0.691813	+	0.146271i
$295$	−3.29150			−0.191639
$296$		−	5.15587i		−	0.299679i
$297$		0			0
$298$	6.00000			0.347571
$299$	−22.3316	+	18.1669i	−1.29147	+	1.05062i
$300$	7.21033	−	1.80613i	0.416289	−	0.104277i
$301$	−4.76150	+	20.6235i	−0.274449	+	1.18872i
$302$			13.6412i			0.784960i
$303$	−9.64575	+	2.41618i	−0.554134	+	0.138806i
$304$	4.55066			0.260998
$305$	4.70850			0.269608
$306$	11.4821	−	6.13742i	0.656386	−	0.350853i
$307$	8.89047			0.507406			0.253703	−	0.967282i	$-0.418351\pi$
$307$	8.89047			0.507406			0.253703	+	0.967282i	$0.418351\pi$
$308$		0			0
$309$	−3.87451	−	15.4676i	−0.220413	−	0.879922i
$310$			4.65489i			0.264380i
$311$	−7.14226			−0.405000			−0.202500	−	0.979282i	$-0.564907\pi$
$311$	−7.14226			−0.405000			−0.202500	+	0.979282i	$0.564907\pi$
$312$	−5.00000	−	3.74166i	−0.283069	−	0.211830i
$313$		−	33.5633i		−	1.89711i	−0.316614	−	0.948555i	$-0.602546\pi$
$313$		−	33.5633i		−	1.89711i	0.316614	−	0.948555i	$-0.397454\pi$
$314$			17.8687i			1.00839i
$315$	−6.44953	+	1.74324i	−0.363390	+	0.0982202i
$316$	−11.2915			−0.635197
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$	−3.36028	−	13.4148i	−0.188435	−	0.752262i
$319$		0			0
$320$			0.841723i			0.0470537i
$321$	−2.38075	−	9.50432i	−0.132881	−	0.530479i
$322$	20.5830	+	4.75216i	1.14705	+	0.264827i
$323$	−19.7490			−1.09886
$324$	5.00000	−	7.48331i	0.277778	−	0.415740i
$325$	9.76458	+	12.0031i	0.541642	+	0.665811i
$326$		−	8.48528i		−	0.469956i
$327$	−6.50972	−	25.9878i	−0.359988	−	1.43713i
$328$			10.8896i			0.601277i
$329$	20.1617	+	4.65489i	1.11155	+	0.256632i
$330$		0			0
$331$			8.48528i			0.466393i	0.972430	+	0.233197i	$0.0749186\pi$
$331$			8.48528i			0.466393i	−0.972430	+	0.233197i	$0.925081\pi$
$332$		−	7.27733i		−	0.399395i
$333$	7.29150	+	13.6412i	0.399572	+	0.747531i
$334$			1.68345i			0.0921141i
$335$	−1.53737			−0.0839957
$336$	0.0849536	+	4.58179i	0.00463460	+	0.249957i
$337$	11.8745			0.646846			0.323423	−	0.946255i	$-0.395166\pi$
$337$	11.8745			0.646846			0.323423	+	0.946255i	$0.395166\pi$
$338$	2.64575	−	12.7279i	0.143910	−	0.692308i
$339$	−5.95188	−	23.7608i	−0.323262	−	1.29051i
$340$		−	3.65292i		−	0.198107i
$341$		0			0
$342$	−12.0399	+	6.43560i	−0.651044	+	0.347998i
$343$	11.6556	−	14.3926i	0.629342	−	0.777129i
$344$	−8.00000			−0.431331
$345$	−11.2915	+	2.82843i	−0.607914	+	0.152277i
$346$	14.4207			0.775260
$347$		−	2.00393i		−	0.107577i	−0.998552	−	0.0537884i	$-0.982870\pi$
$347$		−	2.00393i		−	0.107577i	0.998552	−	0.0537884i	$-0.0171296\pi$
$348$	−0.979531	−	3.91044i	−0.0525084	−	0.209621i
$349$	−15.6110			−0.835640			−0.417820	−	0.908530i	$-0.637206\pi$
$349$	−15.6110			−0.835640			−0.417820	+	0.908530i	$0.637206\pi$
$350$	2.55425	−	11.0632i	0.136530	−	0.591354i
$351$	18.5203	+	2.82843i	0.988538	+	0.150970i
$352$		0			0
$353$		−	5.83925i		−	0.310792i	−0.987852	−	0.155396i	$-0.950335\pi$
$353$		−	5.83925i		−	0.310792i	0.987852	−	0.155396i	$-0.0496653\pi$
$354$	−1.64575	−	6.57008i	−0.0874707	−	0.349196i
$355$			12.2748i			0.651481i
$356$			12.5730i			0.666369i
$357$	−0.368683	−	19.8841i	−0.0195128	−	1.05238i
$358$		−	11.3137i		−	0.597948i
$359$	16.7085			0.881841			0.440920	−	0.897546i	$-0.354652\pi$
$359$	16.7085			0.881841			0.440920	+	0.897546i	$0.354652\pi$
$360$	−1.19038	−	2.22699i	−0.0627383	−	0.117373i
$361$	1.70850			0.0899209
$362$			10.6442i			0.559448i
$363$	−18.4816	+	4.62948i	−0.970030	+	0.242984i
$364$	−8.56458	+	4.20095i	−0.448906	+	0.220189i
$365$			2.65095i			0.138757i
$366$	2.35425	+	9.39851i	0.123059	+	0.491268i
$367$			8.11905i			0.423811i	0.977290	+	0.211905i	$0.0679669\pi$
$367$			8.11905i			0.423811i	−0.977290	+	0.211905i	$0.932033\pi$
$368$			7.98430i			0.416210i
$369$	−15.4002	−	28.8111i	−0.801702	−	1.49985i
$370$	4.33981			0.225616
$371$	−20.5830	−	4.75216i	−1.06862	−	0.246720i
$372$	−9.29150	+	2.32744i	−0.481742	+	0.120672i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	3.29150	+	13.1402i	0.169972	+	0.678555i
$376$			7.82087i			0.403331i
$377$	6.50972	−	5.29570i	0.335268	−	0.272743i
$378$	−6.70439	−	12.0021i	−0.344837	−	0.617323i
$379$		−	15.1441i		−	0.777900i	−0.921259	−	0.388950i	$-0.872838\pi$
$379$		−	15.1441i		−	0.777900i	0.921259	−	0.388950i	$-0.127162\pi$
$380$			3.83039i			0.196495i
$381$	−11.0604	+	2.77053i	−0.566640	+	0.141939i
$382$			0.500983i			0.0256325i
$383$			39.1044i			1.99814i	0.0431294	+	0.999069i	$0.486267\pi$
$383$			39.1044i			1.99814i	−0.0431294	+	0.999069i	$0.513733\pi$
$384$	−1.68014	+	0.420861i	−0.0857394	+	0.0214770i
$385$		0			0
$386$			8.48528i			0.431889i
$387$	21.1660	−	11.3137i	1.07593	−	0.575108i
$388$	−9.87000			−0.501074
$389$		−	12.6392i		−	0.640832i	−0.947277	−	0.320416i	$-0.896177\pi$
$389$		−	12.6392i		−	0.640832i	0.947277	−	0.320416i	$-0.103823\pi$
$390$	3.14944	−	4.20861i	0.159478	−	0.213111i
$391$		−	34.6504i		−	1.75234i
$392$	6.29150	+	3.06871i	0.317769	+	0.154993i
$393$	−2.35425	+	0.589720i	−0.118756	+	0.0297474i
$394$	8.58301			0.432406
$395$		−	9.50432i		−	0.478214i
$396$		0			0
$397$	16.0327			0.804660			0.402330	−	0.915495i	$-0.368201\pi$
$397$	16.0327			0.804660			0.402330	+	0.915495i	$0.368201\pi$
$398$		−	25.4442i		−	1.27540i
$399$	0.386595	+	20.8502i	0.0193540	+	1.04381i
$400$	4.29150			0.214575
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$	−0.768687	−	3.06871i	−0.0383386	−	0.153053i
$403$	−12.5830	−	15.4676i	−0.626804	−	0.770497i
$404$	−5.74103			−0.285627
$405$	6.29888	+	4.20861i	0.312994	+	0.209128i
$406$	−6.00000	−	1.38527i	−0.297775	−	0.0687496i
$407$		0			0
$408$	7.29150	−	1.82646i	0.360983	−	0.0904233i
$409$	−1.19038			−0.0588603			−0.0294301	−	0.999567i	$-0.509369\pi$
$409$	−1.19038			−0.0588603			−0.0294301	+	0.999567i	$0.509369\pi$
$410$	−9.16601			−0.452677
$411$	−2.16991	+	0.543544i	−0.107034	+	0.0268110i
$412$		−	9.20614i		−	0.453554i
$413$	−10.0808	−	2.32744i	−0.496046	−	0.114526i
$414$	−11.2915	−	21.1245i	−0.554947	−	1.03821i
$415$	6.12549			0.300689
$416$	−2.27533	−	2.79694i	−0.111557	−	0.137131i
$417$	−3.64575	−	14.5544i	−0.178533	−	0.712731i
$418$		0			0
$419$	25.9027			1.26543			0.632716	−	0.774384i	$-0.281940\pi$
$419$	25.9027			1.26543			0.632716	+	0.774384i	$0.281940\pi$
$420$	−3.85660	+	0.0715074i	−0.188183	+	0.00348920i
$421$			11.8147i			0.575813i	0.957659	+	0.287906i	$0.0929592\pi$
$421$			11.8147i			0.575813i	−0.957659	+	0.287906i	$0.907041\pi$
$422$	−10.5830			−0.515173
$423$	−11.0604	−	20.6921i	−0.537774	−	1.00608i
$424$		−	7.98430i		−	0.387752i
$425$	−18.6243			−0.903412
$426$	−24.5015	+	6.13742i	−1.18710	+	0.297359i
$427$	14.4207	+	3.32941i	0.697865	+	0.161121i
$428$		−	5.65685i		−	0.273434i
$429$		0			0
$430$		−	6.73378i		−	0.324732i
$431$	−7.29150			−0.351219			−0.175610	−	0.984460i	$-0.556190\pi$
$431$	−7.29150			−0.351219			−0.175610	+	0.984460i	$0.556190\pi$
$432$	3.85005	−	3.48957i	0.185236	−	0.167892i
$433$			17.3252i			0.832595i	0.909228	+	0.416298i	$0.136673\pi$
$433$			17.3252i			0.832595i	−0.909228	+	0.416298i	$0.863327\pi$
$434$	−3.29150	+	14.2565i	−0.157997	+	0.684333i
$435$	3.29150	−	0.824494i	0.157815	−	0.0395315i
$436$		−	15.4676i		−	0.740764i
$437$			36.3338i			1.73808i
$438$	−5.29150	+	1.32548i	−0.252838	+	0.0633338i
$439$			8.11905i			0.387501i	0.981051	+	0.193751i	$0.0620652\pi$
$439$			8.11905i			0.387501i	−0.981051	+	0.193751i	$0.937935\pi$
$440$		0			0
$441$	−20.9856	+	0.778479i	−0.999313	+	0.0370704i
$442$	9.87451	+	12.1382i	0.469682	+	0.577355i
$443$		−	5.65685i		−	0.268765i	−0.990930	−	0.134383i	$-0.957095\pi$
$443$		−	5.65685i		−	0.268765i	0.990930	−	0.134383i	$-0.0429051\pi$
$444$	2.16991	+	8.66259i	0.102979	+	0.411108i
$445$	−10.5830			−0.501683
$446$	−14.6315			−0.692822
$447$	−10.0808	+	2.52517i	−0.476808	+	0.119436i
$448$	−0.595188	+	2.57794i	−0.0281200	+	0.121796i
$449$	30.4575			1.43738			0.718689	−	0.695331i	$-0.244742\pi$
$449$	30.4575			1.43738			0.718689	+	0.695331i	$0.244742\pi$
$450$	−11.3542	+	6.06910i	−0.535244	+	0.286100i
$451$		0			0
$452$		−	14.1421i		−	0.665190i
$453$	−5.74103	−	22.9191i	−0.269737	−	1.07683i
$454$		−	8.96077i		−	0.420550i
$455$	−3.53603	−	7.20900i	−0.165772	−	0.337963i
$456$	−7.64575	+	1.91520i	−0.358045	+	0.0896873i
$457$			12.1382i			0.567801i	0.958854	+	0.283901i	$0.0916286\pi$
$457$			12.1382i			0.567801i	−0.958854	+	0.283901i	$0.908371\pi$
$458$	24.2907			1.13503
$459$	−16.7085	+	15.1441i	−0.779886	+	0.706866i
$460$	−6.72057			−0.313348
$461$		−	15.3964i		−	0.717081i	−0.933514	−	0.358540i	$-0.883275\pi$
$461$		−	15.3964i		−	0.717081i	0.933514	−	0.358540i	$-0.116725\pi$
$462$		0			0
$463$		−	25.7794i		−	1.19807i	−0.800724	−	0.599034i	$-0.795551\pi$
$463$		−	25.7794i		−	1.19807i	0.800724	−	0.599034i	$-0.204449\pi$
$464$		−	2.32744i		−	0.108049i
$465$	−1.95906	−	7.82087i	−0.0908494	−	0.362684i
$466$			22.6274i			1.04819i
$467$	7.27841			0.336805			0.168402	−	0.985718i	$-0.446139\pi$
$467$	7.27841			0.336805			0.168402	+	0.985718i	$0.446139\pi$
$468$	9.97543	+	4.18221i	0.461114	+	0.193323i
$469$	−4.70850	−	1.08709i	−0.217418	−	0.0501970i
$470$	−6.58301			−0.303651
$471$	−7.52026	−	30.0220i	−0.346515	−	1.38334i
$472$		−	3.91044i		−	0.179992i
$473$		0			0
$474$	18.9713	−	4.75216i	0.871382	−	0.218274i
$475$	19.5292			0.896060
$476$	2.58301	−	11.1878i	0.118392	−	0.512790i
$477$	11.2915	+	21.1245i	0.517002	+	0.967223i
$478$	−21.8745			−1.00052
$479$		−	17.9215i		−	0.818856i	−0.912342	−	0.409428i	$-0.865728\pi$
$479$		−	17.9215i		−	0.818856i	0.912342	−	0.409428i	$-0.134272\pi$
$480$	−0.354249	−	1.41421i	−0.0161692	−	0.0645497i
$481$	−14.4207	+	11.7313i	−0.657526	+	0.534901i
$482$	25.6919			1.17023
$483$	−36.5824	+	0.678295i	−1.66456	+	0.0308635i
$484$	−11.0000			−0.500000
$485$		−	8.30781i		−	0.377238i
$486$	−5.25127	+	14.6773i	−0.238202	+	0.665777i
$487$			17.2941i			0.783669i	0.920036	+	0.391835i	$0.128159\pi$
$487$			17.2941i			0.783669i	−0.920036	+	0.391835i	$0.871841\pi$
$488$			5.59388i			0.253223i
$489$	3.57113	+	14.2565i	0.161492	+	0.644700i
$490$	−2.58301	+	5.29570i	−0.116688	+	0.239235i
$491$		−	26.2803i		−	1.18602i	−0.805197	−	0.593008i	$-0.797940\pi$
$491$		−	26.2803i		−	1.18602i	0.805197	−	0.593008i	$-0.202060\pi$
$492$	−4.58301	−	18.2960i	−0.206618	−	0.824849i
$493$			10.1007i			0.454911i
$494$	−10.3542	−	12.7279i	−0.465860	−	0.572656i
$495$		0			0
$496$	−5.53019			−0.248313
$497$	−8.67963	+	37.5940i	−0.389335	+	1.68632i
$498$	3.06275	+	12.2269i	0.137245	+	0.547902i
$499$		−	18.7970i		−	0.841470i	−0.907184	−	0.420735i	$-0.861772\pi$
$499$		−	18.7970i		−	0.841470i	0.907184	−	0.420735i	$-0.138228\pi$
$500$			7.82087i			0.349760i
$501$	−0.708497	−	2.82843i	−0.0316533	−	0.126365i
$502$	−5.74103			−0.256235
$503$	8.67963			0.387006			0.193503	−	0.981100i	$-0.438015\pi$
$503$	8.67963			0.387006			0.193503	+	0.981100i	$0.438015\pi$
$504$	−2.07103	−	7.66230i	−0.0922511	−	0.341306i
$505$		−	4.83236i		−	0.215037i
$506$		0			0
$507$	0.911455	+	22.4982i	0.0404791	+	0.999180i
$508$	−6.58301			−0.292074
$509$		−	15.3964i		−	0.682432i	−0.939985	−	0.341216i	$-0.889161\pi$
$509$		−	15.3964i		−	0.682432i	0.939985	−	0.341216i	$-0.110839\pi$
$510$	1.53737	+	6.13742i	0.0680760	+	0.271770i
$511$	−1.87451	+	8.11905i	−0.0829233	+	0.359166i
$512$	−1.00000			−0.0441942
$513$	17.5203	−	15.8799i	0.773538	−	0.701113i
$514$	−15.8219			−0.697873
$515$	7.74902			0.341462
$516$	13.4411	−	3.36689i	0.591713	−	0.148219i
$517$		0			0
$518$	13.2915	+	3.06871i	0.583995	+	0.134831i
$519$	−24.2288	+	6.06910i	−1.06352	+	0.266404i
$520$	2.35425	−	1.91520i	0.103241	−	0.0839869i
$521$	2.80244			0.122777			0.0613886	−	0.998114i	$-0.480447\pi$
$521$	2.80244			0.122777			0.0613886	+	0.998114i	$0.480447\pi$
$522$	3.29150	+	6.15784i	0.144065	+	0.269521i
$523$			32.1252i			1.40474i	0.711813	+	0.702369i	$0.247874\pi$
$523$			32.1252i			1.40474i	−0.711813	+	0.702369i	$0.752126\pi$
$524$	−1.40122			−0.0612126
$525$	0.364579	+	19.6628i	0.0159115	+	0.858153i
$526$		−	16.4696i		−	0.718108i
$527$	24.0000			1.04546
$528$		0			0
$529$	−40.7490			−1.77170
$530$	6.72057			0.291923
$531$	5.53019	+	10.3460i	0.239990	+	0.448980i
$532$	−2.70850	+	11.7313i	−0.117428	+	0.508617i
$533$	30.4575	−	24.7774i	1.31926	−	1.07323i
$534$	−5.29150	−	21.1245i	−0.228986	−	0.914145i
$535$	4.76150			0.205858
$536$		−	1.82646i		−	0.0788911i
$537$	4.76150	+	19.0086i	0.205474	+	0.820283i
$538$	−23.1003			−0.995924
$539$		0			0
$540$	2.93725	+	3.24067i	0.126399	+	0.139456i
$541$		−	29.4323i		−	1.26539i	−0.774400	−	0.632696i	$-0.781948\pi$
$541$		−	29.4323i		−	1.26539i	0.774400	−	0.632696i	$-0.218052\pi$
$542$	−23.3111			−1.00130
$543$	−4.47974	−	17.8838i	−0.192244	−	0.767467i
$544$	4.33981			0.186068
$545$	13.0194			0.557692
$546$	12.6217	−	10.6627i	0.540159	−	0.456321i
$547$	−6.58301			−0.281469			−0.140734	−	0.990047i	$-0.544946\pi$
$547$	−6.58301			−0.281469			−0.140734	+	0.990047i	$0.544946\pi$
$548$	−1.29150			−0.0551703
$549$	−7.91094	−	14.8000i	−0.337631	−	0.631649i
$550$		0			0
$551$		−	10.5914i		−	0.451209i
$552$	−3.36028	−	13.4148i	−0.143023	−	0.570970i
$553$	6.72057	−	29.1088i	0.285788	−	1.23783i
$554$	−31.1660			−1.32412
$555$	−7.29150	+	1.82646i	−0.309507	+	0.0775289i
$556$		−	8.66259i		−	0.367376i
$557$	23.1660			0.981575			0.490788	−	0.871279i	$-0.336709\pi$
$557$	23.1660			0.981575			0.490788	+	0.871279i	$0.336709\pi$
$558$	14.6315	−	7.82087i	0.619401	−	0.331084i
$559$	18.2026	+	22.3755i	0.769889	+	0.946384i
$560$	−2.16991	−	0.500983i	−0.0916953	−	0.0211704i
$561$		0			0
$562$	13.2915			0.560668
$563$	7.27841			0.306748			0.153374	−	0.988168i	$-0.450986\pi$
$563$	7.27841			0.306748			0.153374	+	0.988168i	$0.450986\pi$
$564$	−3.29150	−	13.1402i	−0.138597	−	0.553301i
$565$	11.9038			0.500795
$566$		−	14.8000i		−	0.622091i
$567$	16.3156	+	17.3437i	0.685189	+	0.728365i
$568$	−14.5830			−0.611889
$569$			30.1107i			1.26231i	0.775658	+	0.631154i	$0.217418\pi$
$569$			30.1107i			1.26231i	−0.775658	+	0.631154i	$0.782582\pi$
$570$	−1.61206	−	6.43560i	−0.0675220	−	0.269558i
$571$	−1.41699			−0.0592994			−0.0296497	−	0.999560i	$-0.509439\pi$
$571$	−1.41699			−0.0592994			−0.0296497	+	0.999560i	$0.509439\pi$
$572$		0			0
$573$	−0.210845	−	0.841723i	−0.00880816	−	0.0351635i
$574$	−28.0726	−	6.48135i	−1.17173	−	0.270526i
$575$			34.2646i			1.42893i
$576$	2.64575	−	1.41421i	0.110240	−	0.0589256i
$577$	−5.53019			−0.230225			−0.115112	−	0.993352i	$-0.536723\pi$
$577$	−5.53019			−0.230225			−0.115112	+	0.993352i	$0.536723\pi$
$578$	−1.83399			−0.0762839
$579$	−3.57113	−	14.2565i	−0.148411	−	0.592479i
$580$	1.95906			0.0813457
$581$	18.7605	+	4.33138i	0.778316	+	0.179696i
$582$	16.5830	−	4.15390i	0.687388	−	0.172185i
$583$		0			0
$584$	−3.14944			−0.130325
$585$	−3.52026	+	8.39655i	−0.145545	+	0.347154i
$586$		−	13.1166i		−	0.541841i
$587$		−	8.36441i		−	0.345236i	−0.984989	−	0.172618i	$-0.944777\pi$
$587$		−	8.36441i		−	0.345236i	0.984989	−	0.172618i	$-0.0552227\pi$
$588$	−11.8621	−	2.50802i	−0.489185	−	0.103429i
$589$	−25.1660			−1.03695
$590$	3.29150			0.135509
$591$	−14.4207	+	3.61226i	−0.593187	+	0.148588i
$592$			5.15587i			0.211905i
$593$			41.0860i			1.68720i	0.536973	+	0.843599i	$0.319568\pi$
$593$			41.0860i			1.68720i	−0.536973	+	0.843599i	$0.680432\pi$
$594$		0			0
$595$	9.41699	+	2.17417i	0.386059	+	0.0891325i
$596$	−6.00000			−0.245770
$597$	10.7085	+	42.7499i	0.438270	+	1.74964i
$598$	22.3316	−	18.1669i	0.913207	−	0.742900i
$599$			23.7754i			0.971437i	0.874115	+	0.485719i	$0.161442\pi$
$599$			23.7754i			0.971437i	−0.874115	+	0.485719i	$0.838558\pi$
$600$	−7.21033	+	1.80613i	−0.294361	+	0.0737349i
$601$			22.3755i			0.912717i	0.889796	+	0.456358i	$0.150846\pi$
$601$			22.3755i			0.912717i	−0.889796	+	0.456358i	$0.849154\pi$
$602$	4.76150	−	20.6235i	0.194064	−	0.840550i
$603$	2.58301	+	4.83236i	0.105188	+	0.196789i
$604$		−	13.6412i		−	0.555051i
$605$		−	9.25895i		−	0.376430i
$606$	9.64575	−	2.41618i	0.391832	−	0.0981506i
$607$		−	26.5313i		−	1.07687i	−0.842666	−	0.538437i	$-0.819015\pi$
$607$		−	26.5313i		−	1.07687i	0.842666	−	0.538437i	$-0.180985\pi$
$608$	−4.55066			−0.184554
$609$	10.6639	−	0.197725i	0.432121	−	0.00801221i
$610$	−4.70850			−0.190641
$611$	21.8745	−	17.7951i	0.884948	−	0.719911i
$612$	−11.4821	+	6.13742i	−0.464135	+	0.248091i
$613$			32.4382i			1.31017i	0.755557	+	0.655083i	$0.227366\pi$
$613$			32.4382i			1.31017i	−0.755557	+	0.655083i	$0.772634\pi$
$614$	−8.89047			−0.358790
$615$	15.4002	−	3.85762i	0.620996	−	0.155554i
$616$		0			0
$617$	−11.1660			−0.449527			−0.224763	−	0.974413i	$-0.572161\pi$
$617$	−11.1660			−0.449527			−0.224763	+	0.974413i	$0.572161\pi$
$618$	3.87451	+	15.4676i	0.155856	+	0.622199i
$619$	26.2497			1.05507			0.527533	−	0.849535i	$-0.323117\pi$
$619$	26.2497			1.05507			0.527533	+	0.849535i	$0.323117\pi$
$620$		−	4.65489i		−	0.186945i
$621$	27.8618	+	30.7399i	1.11806	+	1.23355i
$622$	7.14226			0.286378
$623$	−32.4125	−	7.48331i	−1.29858	−	0.299813i
$624$	5.00000	+	3.74166i	0.200160	+	0.149786i
$625$	14.8745			0.594980
$626$			33.5633i			1.34146i
$627$		0			0
$628$		−	17.8687i		−	0.713040i
$629$		−	22.3755i		−	0.892171i
$630$	6.44953	−	1.74324i	0.256956	−	0.0694521i
$631$			19.1205i			0.761176i	0.924745	+	0.380588i	$0.124278\pi$
$631$			19.1205i			0.761176i	−0.924745	+	0.380588i	$0.875722\pi$
$632$	11.2915			0.449152
$633$	17.7809	−	4.45398i	0.706729	−	0.177030i
$634$	−6.00000			−0.238290
$635$		−	5.54107i		−	0.219890i
$636$	3.36028	+	13.4148i	0.133244	+	0.531929i
$637$	−5.73224	−	24.5793i	−0.227119	−	0.973867i
$638$		0			0
$639$	38.5830	−	20.6235i	1.52632	−	0.815852i
$640$		−	0.841723i		−	0.0332720i
$641$			13.1402i			0.519005i	0.965742	+	0.259503i	$0.0835587\pi$
$641$			13.1402i			0.519005i	−0.965742	+	0.259503i	$0.916441\pi$
$642$	2.38075	+	9.50432i	0.0939608	+	0.375105i
$643$	4.55066			0.179460			0.0897302	−	0.995966i	$-0.471400\pi$
$643$	4.55066			0.179460			0.0897302	+	0.995966i	$0.471400\pi$
$644$	−20.5830	−	4.75216i	−0.811084	−	0.187261i
$645$	2.83399	+	11.3137i	0.111588	+	0.445477i
$646$	19.7490			0.777015
$647$	2.80244			0.110175			0.0550877	−	0.998482i	$-0.482456\pi$
$647$	2.80244			0.110175			0.0550877	+	0.998482i	$0.482456\pi$
$648$	−5.00000	+	7.48331i	−0.196419	+	0.293972i
$649$		0			0
$650$	−9.76458	−	12.0031i	−0.382998	−	0.470799i
$651$	−0.469810	−	25.3382i	−0.0184133	−	0.993081i
$652$			8.48528i			0.332309i
$653$			32.2607i			1.26246i	0.775596	+	0.631229i	$0.217449\pi$
$653$			32.2607i			1.26246i	−0.775596	+	0.631229i	$0.782551\pi$
$654$	6.50972	+	25.9878i	0.254550	+	1.01620i
$655$		−	1.17944i		−	0.0460845i
$656$		−	10.8896i		−	0.425167i
$657$	8.33263	−	4.45398i	0.325087	−	0.173766i
$658$	−20.1617	−	4.65489i	−0.785985	−	0.181466i
$659$			1.00197i			0.0390311i	0.999810	+	0.0195155i	$0.00621238\pi$
$659$			1.00197i			0.0390311i	−0.999810	+	0.0195155i	$0.993788\pi$
$660$		0			0
$661$	−31.4329			−1.22260			−0.611300	−	0.791399i	$-0.709353\pi$
$661$	−31.4329			−1.22260			−0.611300	+	0.791399i	$0.709353\pi$
$662$		−	8.48528i		−	0.329790i
$663$	−21.6991	−	16.2381i	−0.842722	−	0.630636i
$664$			7.27733i			0.282415i
$665$	−9.87451	−	2.27980i	−0.382917	−	0.0884070i
$666$	−7.29150	−	13.6412i	−0.282540	−	0.528584i
$667$	18.5830			0.719537
$668$		−	1.68345i		−	0.0651345i
$669$	24.5830	−	6.15784i	0.950434	−	0.238076i
$670$	1.53737			0.0593939
$671$		0			0
$672$	−0.0849536	−	4.58179i	−0.00327716	−	0.176746i
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	−11.8745			−0.457389
$675$	16.5225	−	14.9755i	0.635951	−	0.576408i
$676$	−2.64575	+	12.7279i	−0.101760	+	0.489535i
$677$	−43.2620			−1.66269			−0.831347	−	0.555754i	$-0.812430\pi$
$677$	−43.2620			−1.66269			−0.831347	+	0.555754i	$0.812430\pi$
$678$	5.95188	+	23.7608i	0.228581	+	0.912528i
$679$	5.87451	−	25.4442i	0.225443	−	0.976460i
$680$			3.65292i			0.140083i
$681$	3.77124	+	15.0554i	0.144514	+	0.576923i
$682$		0			0
$683$	−50.5830			−1.93550			−0.967752	−	0.251903i	$-0.918944\pi$
$683$	−50.5830			−1.93550			−0.967752	+	0.251903i	$0.918944\pi$
$684$	12.0399	−	6.43560i	0.460358	−	0.246071i
$685$		−	1.08709i		−	0.0415355i
$686$	−11.6556	+	14.3926i	−0.445012	+	0.549513i
$687$	−40.8118	+	10.2230i	−1.55707	+	0.390032i
$688$	8.00000			0.304997
$689$	−22.3316	+	18.1669i	−0.850766	+	0.692104i
$690$	11.2915	−	2.82843i	0.429860	−	0.107676i
$691$	−15.6110			−0.593872			−0.296936	−	0.954897i	$-0.595965\pi$
$691$	−15.6110			−0.593872			−0.296936	+	0.954897i	$0.595965\pi$
$692$	−14.4207			−0.548191
$693$		0			0
$694$			2.00393i			0.0760683i
$695$	7.29150			0.276582
$696$	0.979531	+	3.91044i	0.0371290	+	0.148225i
$697$			47.2588i			1.79005i
$698$	15.6110			0.590887
$699$	−9.52301	−	38.0173i	−0.360193	−	1.43794i
$700$	−2.55425	+	11.0632i	−0.0965416	+	0.418150i
$701$		−	8.98626i		−	0.339407i	−0.985495	−	0.169703i	$-0.945719\pi$
$701$		−	8.98626i		−	0.339407i	0.985495	−	0.169703i	$-0.0542809\pi$
$702$	−18.5203	−	2.82843i	−0.699002	−	0.106752i
$703$			23.4626i			0.884909i
$704$		0			0
$705$	11.0604	−	2.77053i	0.416558	−	0.104344i
$706$			5.83925i			0.219763i
$707$	3.41699	−	14.8000i	0.128509	−	0.556612i
$708$	1.64575	+	6.57008i	0.0618511	+	0.246919i
$709$		−	28.7853i		−	1.08105i	−0.841327	−	0.540526i	$-0.818225\pi$
$709$		−	28.7853i		−	1.08105i	0.841327	−	0.540526i	$-0.181775\pi$
$710$		−	12.2748i		−	0.460667i
$711$	−29.8745	+	15.9686i	−1.12038	+	0.598869i
$712$		−	12.5730i		−	0.471194i
$713$		−	44.1547i		−	1.65361i
$714$	0.368683	+	19.8841i	0.0137976	+	0.744144i
$715$		0			0
$716$			11.3137i			0.422813i
$717$	36.7523	−	9.20614i	1.37254	−	0.343809i
$718$	−16.7085			−0.623556
$719$	−27.3040			−1.01827			−0.509133	−	0.860688i	$-0.670034\pi$
$719$	−27.3040			−1.01827			−0.509133	+	0.860688i	$0.670034\pi$
$720$	1.19038	+	2.22699i	0.0443627	+	0.0829950i
$721$	23.7328	+	5.47938i	0.883857	+	0.204063i
$722$	−1.70850			−0.0635837
$723$	−43.1660	+	10.8127i	−1.60536	+	0.402130i
$724$		−	10.6442i		−	0.395589i
$725$		−	9.98823i		−	0.370954i
$726$	18.4816	−	4.62948i	0.685915	−	0.171816i
$727$		−	13.1694i		−	0.488426i	−0.969722	−	0.244213i	$-0.921470\pi$
$727$		−	13.1694i		−	0.488426i	0.969722	−	0.244213i	$-0.0785295\pi$
$728$	8.56458	−	4.20095i	0.317424	−	0.155697i
$729$	2.64575	−	26.8701i	0.0979908	−	0.995187i
$730$		−	2.65095i		−	0.0981162i
$731$	−34.7185			−1.28411
$732$	−2.35425	−	9.39851i	−0.0870155	−	0.347379i
$733$	10.4278			0.385161			0.192581	−	0.981281i	$-0.438314\pi$
$733$	10.4278			0.385161			0.192581	+	0.981281i	$0.438314\pi$
$734$		−	8.11905i		−	0.299680i
$735$	2.11106	−	9.98462i	0.0778675	−	0.368288i
$736$		−	7.98430i		−	0.294305i
$737$		0			0
$738$	15.4002	+	28.8111i	0.566889	+	1.06055i
$739$			18.7970i			0.691460i	0.938334	+	0.345730i	$0.112369\pi$
$739$			18.7970i			0.691460i	−0.938334	+	0.345730i	$0.887631\pi$
$740$	−4.33981			−0.159535
$741$	22.7533	+	17.0270i	0.835863	+	0.625503i
$742$	20.5830	+	4.75216i	0.755626	+	0.174457i
$743$	7.29150			0.267499			0.133750	−	0.991015i	$-0.457298\pi$
$743$	7.29150			0.267499			0.133750	+	0.991015i	$0.457298\pi$
$744$	9.29150	−	2.32744i	0.340643	−	0.0853282i
$745$		−	5.05034i		−	0.185030i
$746$	22.0000			0.805477
$747$	−10.2917	−	19.2540i	−0.376553	−	0.704467i
$748$		0			0
$749$	14.5830	+	3.36689i	0.532851	+	0.123024i
$750$	−3.29150	−	13.1402i	−0.120189	−	0.479811i
$751$	13.1660			0.480435			0.240217	−	0.970719i	$-0.422781\pi$
$751$	13.1660			0.480435			0.240217	+	0.970719i	$0.422781\pi$
$752$		−	7.82087i		−	0.285198i
$753$	9.64575	−	2.41618i	0.351511	−	0.0880505i
$754$	−6.50972	+	5.29570i	−0.237070	+	0.192858i
$755$	11.4821			0.417875
$756$	6.70439	+	12.0021i	0.243836	+	0.436513i
$757$	4.58301			0.166572			0.0832861	−	0.996526i	$-0.473458\pi$
$757$	4.58301			0.166572			0.0832861	+	0.996526i	$0.473458\pi$
$758$			15.1441i			0.550059i
$759$		0			0
$760$		−	3.83039i		−	0.138943i
$761$			11.4859i			0.416365i	0.978090	+	0.208183i	$0.0667548\pi$
$761$			11.4859i			0.416365i	−0.978090	+	0.208183i	$0.933245\pi$
$762$	11.0604	−	2.77053i	0.400675	−	0.100366i
$763$	39.8745	+	9.20614i	1.44355	+	0.333285i
$764$		−	0.500983i		−	0.0181249i
$765$	−5.16601	−	9.66472i	−0.186778	−	0.349429i
$766$		−	39.1044i		−	1.41290i
$767$	−10.9373	+	8.89753i	−0.394921	+	0.321271i
$768$	1.68014	−	0.420861i	0.0606269	−	0.0151865i
$769$	21.7738			0.785182			0.392591	−	0.919713i	$-0.371579\pi$
$769$	21.7738			0.785182			0.392591	+	0.919713i	$0.371579\pi$
$770$		0			0
$771$	26.5830	−	6.65882i	0.957364	−	0.239812i
$772$		−	8.48528i		−	0.305392i
$773$		−	10.3460i		−	0.372121i	−0.982538	−	0.186061i	$-0.940428\pi$
$773$		−	10.3460i		−	0.372121i	0.982538	−	0.186061i	$-0.0595721\pi$
$774$	−21.1660	+	11.3137i	−0.760797	+	0.406663i
$775$	−23.7328			−0.852508
$776$	9.87000			0.354313
$777$	−23.6231	+	0.438010i	−0.847474	+	0.0157135i
$778$			12.6392i			0.453137i
$779$		−	49.5548i		−	1.77548i
$780$	−3.14944	+	4.20861i	−0.112768	+	0.150693i
$781$		0			0
$782$			34.6504i			1.23909i
$783$	−8.12179	−	8.96077i	−0.290249	−	0.320232i
$784$	−6.29150	−	3.06871i	−0.224697	−	0.109597i
$785$	15.0405			0.536819
$786$	2.35425	−	0.589720i	0.0839733	−	0.0210346i
$787$	−54.3971			−1.93905			−0.969523	−	0.245001i	$-0.921212\pi$
$787$	−54.3971			−1.93905			−0.969523	+	0.245001i	$0.921212\pi$
$788$	−8.58301			−0.305757
$789$	6.93141	+	27.6712i	0.246765	+	0.985122i
$790$			9.50432i			0.338148i
$791$	36.4575	+	8.41723i	1.29628	+	0.299282i
$792$		0			0
$793$	15.6458	−	12.7279i	0.555597	−	0.451982i
$794$	−16.0327			−0.568980
$795$	−11.2915	+	2.82843i	−0.400468	+	0.100314i
$796$			25.4442i			0.901847i
$797$	8.54348			0.302625			0.151313	−	0.988486i	$-0.451650\pi$
$797$	8.54348			0.302625			0.151313	+	0.988486i	$0.451650\pi$
$798$	−0.386595	−	20.8502i	−0.0136853	−	0.738088i
$799$			33.9411i			1.20075i
$800$	−4.29150			−0.151728
$801$	17.7809	+	33.2651i	0.628259	+	1.17536i
$802$	6.00000			0.211867
$803$		0			0
$804$	0.768687	+	3.06871i	0.0271095	+	0.108225i
$805$	4.00000	−	17.3252i	0.140981	−	0.610633i
$806$	12.5830	+	15.4676i	0.443217	+	0.544823i
$807$	38.8118	−	9.72202i	1.36624	−	0.342231i
$808$	5.74103			0.201969
$809$		−	0.177473i		−	0.00623961i	−0.999995	−	0.00311980i	$-0.999007\pi$
$809$		−	0.177473i		−	0.00623961i	0.999995	−	0.00311980i	$-0.000993066\pi$
$810$	−6.29888	−	4.20861i	−0.221320	−	0.147876i
$811$	6.08803			0.213780			0.106890	−	0.994271i	$-0.465911\pi$
$811$	6.08803			0.213780			0.106890	+	0.994271i	$0.465911\pi$
$812$	6.00000	+	1.38527i	0.210559	+	0.0486133i
$813$	39.1660	−	9.81076i	1.37361	−	0.344078i
$814$		0			0
$815$	−7.14226			−0.250182
$816$	−7.29150	+	1.82646i	−0.255254	+	0.0639389i
$817$	36.4053			1.27366
$818$	1.19038			0.0416205
$819$	−16.7187	+	23.2268i	−0.584199	+	0.811610i
$820$	9.16601			0.320091
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$	2.16991	−	0.543544i	0.0756842	−	0.0189583i
$823$	−25.8745			−0.901929			−0.450964	−	0.892542i	$-0.648920\pi$
$823$	−25.8745			−0.901929			−0.450964	+	0.892542i	$0.648920\pi$
$824$			9.20614i			0.320711i
$825$		0			0
$826$	10.0808	+	2.32744i	0.350758	+	0.0809821i
$827$	−43.7490			−1.52130			−0.760651	−	0.649161i	$-0.775120\pi$
$827$	−43.7490			−1.52130			−0.760651	+	0.649161i	$0.775120\pi$
$828$	11.2915	+	21.1245i	0.392407	+	0.734126i
$829$		−	30.1436i		−	1.04693i	−0.852047	−	0.523465i	$-0.824639\pi$
$829$		−	30.1436i		−	1.04693i	0.852047	−	0.523465i	$-0.175361\pi$
$830$	−6.12549			−0.212619
$831$	52.3633	−	13.1166i	1.81646	−	0.455009i
$832$	2.27533	+	2.79694i	0.0788829	+	0.0969665i
$833$	27.3040	+	13.3176i	0.946026	+	0.461429i
$834$	3.64575	+	14.5544i	0.126242	+	0.503977i
$835$	1.41699			0.0490371
$836$		0			0
$837$	−21.2915	+	19.2980i	−0.735942	+	0.667037i
$838$	−25.9027			−0.894795
$839$		−	48.6087i		−	1.67816i	−0.544010	−	0.839079i	$-0.683095\pi$
$839$		−	48.6087i		−	1.67816i	0.544010	−	0.839079i	$-0.316905\pi$
$840$	3.85660	−	0.0715074i	0.133065	−	0.00246724i
$841$	23.5830			0.813207
$842$		−	11.8147i		−	0.407161i
$843$	−22.3316	+	5.59388i	−0.769141	+	0.192663i
$844$	10.5830			0.364282
$845$	−10.7134	−	2.22699i	−0.368552	−	0.0766108i
$846$	11.0604	+	20.6921i	0.380264	+	0.711408i
$847$	6.54707	−	28.3573i	0.224960	−	0.974368i
$848$			7.98430i			0.274182i
$849$	6.22876	+	24.8661i	0.213770	+	0.853403i
$850$	18.6243			0.638809
$851$	−41.1660			−1.41115
$852$	24.5015	−	6.13742i	0.839408	−	0.210265i
$853$	−35.7727			−1.22484			−0.612418	−	0.790534i	$-0.709803\pi$
$853$	−35.7727			−1.22484			−0.612418	+	0.790534i	$0.709803\pi$
$854$	−14.4207	−	3.32941i	−0.493465	−	0.113930i
$855$	5.41699	+	10.1343i	0.185257	+	0.346585i
$856$			5.65685i			0.193347i
$857$	20.1617			0.688711			0.344355	−	0.938839i	$-0.388098\pi$
$857$	20.1617			0.688711			0.344355	+	0.938839i	$0.388098\pi$
$858$		0			0
$859$			33.2123i			1.13319i	0.823997	+	0.566594i	$0.191739\pi$
$859$			33.2123i			1.13319i	−0.823997	+	0.566594i	$0.808261\pi$
$860$			6.73378i			0.229620i
$861$	49.8938	−	0.925109i	1.70037	−	0.0315276i
$862$	7.29150			0.248350
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	−3.85005	+	3.48957i	−0.130981	+	0.118718i
$865$		−	12.1382i		−	0.412711i
$866$		−	17.3252i		−	0.588734i
$867$	3.08136	−	0.771855i	0.104649	−	0.0262136i
$868$	3.29150	−	14.2565i	0.111721	−	0.483896i
$869$		0			0
$870$	−3.29150	+	0.824494i	−0.111592	+	0.0279530i
$871$	−5.10850	+	4.15580i	−0.173095	+	0.140814i
$872$			15.4676i			0.523799i
$873$	−26.1136	+	13.9583i	−0.883811	+	0.472417i
$874$		−	36.3338i		−	1.22901i
$875$	−20.1617	−	4.65489i	−0.681590	−	0.157364i
$876$	5.29150	−	1.32548i	0.178783	−	0.0447837i
$877$			36.0911i			1.21871i	0.792898	+	0.609355i	$0.208572\pi$
$877$			36.0911i			1.21871i	−0.792898	+	0.609355i	$0.791428\pi$
$878$		−	8.11905i		−	0.274005i
$879$	5.52026	+	22.0377i	0.186194	+	0.743313i
$880$		0			0
$881$	−24.5015			−0.825477			−0.412738	−	0.910850i	$-0.635428\pi$
$881$	−24.5015			−0.825477			−0.412738	+	0.910850i	$0.635428\pi$
$882$	20.9856	−	0.778479i	0.706621	−	0.0262127i
$883$	−6.58301			−0.221536			−0.110768	−	0.993846i	$-0.535331\pi$
$883$	−6.58301			−0.221536			−0.110768	+	0.993846i	$0.535331\pi$
$884$	−9.87451	−	12.1382i	−0.332116	−	0.408252i
$885$	−5.53019	+	1.38527i	−0.185895	+	0.0465652i
$886$			5.65685i			0.190046i
$887$	44.6632			1.49964			0.749822	−	0.661640i	$-0.230139\pi$
$887$	44.6632			1.49964			0.749822	+	0.661640i	$0.230139\pi$
$888$	−2.16991	−	8.66259i	−0.0728173	−	0.290698i
$889$	3.91813	−	16.9706i	0.131410	−	0.569174i
$890$	10.5830			0.354743
$891$		0			0
$892$	14.6315			0.489899
$893$		−	35.5901i		−	1.19098i
$894$	10.0808	−	2.52517i	0.337154	−	0.0844543i
$895$	−9.52301			−0.318319
$896$	0.595188	−	2.57794i	0.0198838	−	0.0861228i
$897$	−29.8745	+	39.9215i	−0.997481	+	1.33294i
$898$	−30.4575			−1.01638
$899$			12.8712i			0.429279i
$900$	11.3542	−	6.06910i	0.378475	−	0.202303i
$901$		−	34.6504i		−	1.15437i
$902$		0			0
$903$	0.679629	+	36.6543i	0.0226166	+	1.21978i
$904$			14.1421i			0.470360i
$905$	8.95948			0.297823
$906$	5.74103	+	22.9191i	0.190733	+	0.761435i
$907$	−4.00000			−0.132818			−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000			−0.132818			−0.0664089	+	0.997792i	$0.521154\pi$
$908$			8.96077i			0.297374i
$909$	−15.1894	+	8.11905i	−0.503799	+	0.269292i
$910$	3.53603	+	7.20900i	0.117218	+	0.238976i
$911$			21.3019i			0.705765i	0.935668	+	0.352882i	$0.114798\pi$
$911$			21.3019i			0.705765i	−0.935668	+	0.352882i	$0.885202\pi$
$912$	7.64575	−	1.91520i	0.253176	−	0.0634185i
$913$		0			0
$914$		−	12.1382i		−	0.401496i
$915$	7.91094	−	1.98162i	0.261528	−	0.0655105i
$916$	−24.2907			−0.802586
$917$	0.833990	−	3.61226i	0.0275408	−	0.119287i
$918$	16.7085	−	15.1441i	0.551463	−	0.499830i
$919$	−1.87451			−0.0618343			−0.0309172	−	0.999522i	$-0.509843\pi$
$919$	−1.87451			−0.0618343			−0.0309172	+	0.999522i	$0.509843\pi$
$920$	6.72057			0.221571
$921$	14.9373	−	3.74166i	0.492199	−	0.123292i
$922$			15.3964i			0.507053i
$923$	33.1811	+	40.7878i	1.09217	+	1.34255i
$924$		0			0
$925$			22.1264i			0.727513i
$926$			25.7794i			0.847162i
$927$	−13.0194	−	24.3571i	−0.427615	−	0.799994i
$928$			2.32744i			0.0764021i
$929$		−	35.4393i		−	1.16273i	−0.813645	−	0.581363i	$-0.802520\pi$
$929$		−	35.4393i		−	1.16273i	0.813645	−	0.581363i	$-0.197480\pi$
$930$	1.95906	+	7.82087i	0.0642402	+	0.256456i
$931$	−28.6305	−	13.9647i	−0.938326	−	0.457673i
$932$		−	22.6274i		−	0.741186i
$933$	−12.0000	+	3.00590i	−0.392862	+	0.0984087i
$934$	−7.27841			−0.238157
$935$		0			0
$936$	−9.97543	−	4.18221i	−0.326057	−	0.136700i
$937$			40.7878i			1.33248i	0.745738	+	0.666240i	$0.232097\pi$
$937$			40.7878i			1.33248i	−0.745738	+	0.666240i	$0.767903\pi$
$938$	4.70850	+	1.08709i	0.153738	+	0.0354947i
$939$	−14.1255	−	56.3911i	−0.460968	−	1.84025i
$940$	6.58301			0.214714
$941$			10.9424i			0.356712i	0.983966	+	0.178356i	$0.0570779\pi$
$941$			10.9424i			0.356712i	−0.983966	+	0.178356i	$0.942922\pi$
$942$	7.52026	+	30.0220i	0.245023	+	0.978169i
$943$	86.9457			2.83134
$944$			3.91044i			0.127274i
$945$	−10.1025	+	5.64324i	−0.328633	+	0.183575i
$946$		0			0
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$	−18.9713	+	4.75216i	−0.616160	+	0.154343i
$949$	7.16601	+	8.80879i	0.232619	+	0.285945i
$950$	−19.5292			−0.633610
$951$	10.0808	−	2.52517i	0.326894	−	0.0818842i
$952$	−2.58301	+	11.1878i	−0.0837157	+	0.362597i
$953$		−	19.6215i		−	0.635603i	−0.948157	−	0.317802i	$-0.897055\pi$
$953$		−	19.6215i		−	0.635603i	0.948157	−	0.317802i	$-0.102945\pi$
$954$	−11.2915	−	21.1245i	−0.365576	−	0.683930i
$955$	0.421689			0.0136455
$956$	21.8745			0.707472
$957$		0			0
$958$			17.9215i			0.579019i
$959$	0.768687	−	3.32941i	0.0248222	−	0.107512i
$960$	0.354249	+	1.41421i	0.0114333	+	0.0456435i
$961$	−0.416995			−0.0134514
$962$	14.4207	−	11.7313i	0.464941	−	0.378232i
$963$	−8.00000	−	14.9666i	−0.257796	−	0.482293i
$964$	−25.6919			−0.827480
$965$	7.14226			0.229917
$966$	36.5824	−	0.678295i	1.17702	−	0.0218238i
$967$			23.9529i			0.770273i	0.922860	+	0.385137i	$0.125846\pi$
$967$			23.9529i			0.770273i	−0.922860	+	0.385137i	$0.874154\pi$
$968$	11.0000			0.353553
$969$	−33.1811	+	8.31160i	−1.06593	+	0.267007i
$970$			8.30781i			0.266748i
$971$	−36.1197			−1.15914			−0.579569	−	0.814923i	$-0.696779\pi$
$971$	−36.1197			−1.15914			−0.579569	+	0.814923i	$0.696779\pi$
$972$	5.25127	−	14.6773i	0.168435	−	0.470776i
$973$	22.3316	+	5.15587i	0.715918	+	0.165290i
$974$		−	17.2941i		−	0.554138i
$975$	21.4575	+	16.0573i	0.687190	+	0.514246i
$976$		−	5.59388i		−	0.179056i
$977$	54.4575			1.74225			0.871125	−	0.491061i	$-0.163391\pi$
$977$	54.4575			1.74225			0.871125	+	0.491061i	$0.163391\pi$
$978$	−3.57113	−	14.2565i	−0.114192	−	0.455872i
$979$		0			0
$980$	2.58301	−	5.29570i	0.0825111	−	0.169165i
$981$	−21.8745	−	40.9235i	−0.698399	−	1.30659i
$982$			26.2803i			0.838639i
$983$		−	3.85762i		−	0.123039i	−0.998106	−	0.0615195i	$-0.980405\pi$
$983$		−	3.85762i		−	0.123039i	0.998106	−	0.0615195i	$-0.0195946\pi$
$984$	4.58301	+	18.2960i	0.146101	+	0.583256i
$985$		−	7.22451i		−	0.230192i
$986$		−	10.1007i		−	0.321671i
$987$	35.8336	−	0.664411i	1.14060	−	0.0211484i
$988$	10.3542	+	12.7279i	0.329413	+	0.404929i
$989$			63.8744i			2.03109i
$990$		0			0
$991$	−11.2915			−0.358686			−0.179343	−	0.983787i	$-0.557397\pi$
$991$	−11.2915			−0.358686			−0.179343	+	0.983787i	$0.557397\pi$
$992$	5.53019			0.175584
$993$	3.57113	+	14.2565i	0.113326	+	0.452416i
$994$	8.67963	−	37.5940i	0.275301	−	1.19241i
$995$	−21.4170			−0.678964
$996$	−3.06275	−	12.2269i	−0.0970468	−	0.387425i
$997$			12.8184i			0.405963i	0.979183	+	0.202981i	$0.0650631\pi$
$997$			12.8184i			0.405963i	−0.979183	+	0.202981i	$0.934937\pi$
$998$			18.7970i			0.595009i
$999$	17.9918	+	19.8504i	0.569235	+	0.628037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.e.f.545.7	yes	8
3.2	odd	2		546.2.e.h.545.1	yes	8
7.6	odd	2	inner	546.2.e.f.545.2	yes	8
13.12	even	2		546.2.e.h.545.7	yes	8
21.20	even	2		546.2.e.h.545.8	yes	8
39.38	odd	2	inner	546.2.e.f.545.1	✓	8
91.90	odd	2		546.2.e.h.545.2	yes	8
273.272	even	2	inner	546.2.e.f.545.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.e.f.545.1	✓	8	39.38	odd	2	inner
546.2.e.f.545.2	yes	8	7.6	odd	2	inner
546.2.e.f.545.7	yes	8	1.1	even	1	trivial
546.2.e.f.545.8	yes	8	273.272	even	2	inner
546.2.e.h.545.1	yes	8	3.2	odd	2
546.2.e.h.545.2	yes	8	91.90	odd	2
546.2.e.h.545.7	yes	8	13.12	even	2
546.2.e.h.545.8	yes	8	21.20	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.68014 - 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(-1.68014 + 0.420861i) q^{6} +(-0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.68014 - 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(-1.68014 + 0.420861i) q^{6} +(-0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} -0.841723i q^{10} +(1.68014 - 0.420861i) q^{12} +(2.27533 + 2.79694i) q^{13} +(0.595188 - 2.57794i) q^{14} +(0.354249 + 1.41421i) q^{15} +1.00000 q^{16} -4.33981 q^{17} +(-2.64575 + 1.41421i) q^{18} +4.55066 q^{19} +0.841723i q^{20} +(0.0849536 + 4.58179i) q^{21} +7.98430i q^{23} +(-1.68014 + 0.420861i) q^{24} +4.29150 q^{25} +(-2.27533 - 2.79694i) q^{26} +(3.85005 - 3.48957i) q^{27} +(-0.595188 + 2.57794i) q^{28} -2.32744i q^{29} +(-0.354249 - 1.41421i) q^{30} -5.53019 q^{31} -1.00000 q^{32} +4.33981 q^{34} +(-2.16991 - 0.500983i) q^{35} +(2.64575 - 1.41421i) q^{36} +5.15587i q^{37} -4.55066 q^{38} +(5.00000 + 3.74166i) q^{39} -0.841723i q^{40} -10.8896i q^{41} +(-0.0849536 - 4.58179i) q^{42} +8.00000 q^{43} +(1.19038 + 2.22699i) q^{45} -7.98430i q^{46} -7.82087i q^{47} +(1.68014 - 0.420861i) q^{48} +(-6.29150 - 3.06871i) q^{49} -4.29150 q^{50} +(-7.29150 + 1.82646i) q^{51} +(2.27533 + 2.79694i) q^{52} +7.98430i q^{53} +(-3.85005 + 3.48957i) q^{54} +(0.595188 - 2.57794i) q^{56} +(7.64575 - 1.91520i) q^{57} +2.32744i q^{58} +3.91044i q^{59} +(0.354249 + 1.41421i) q^{60} -5.59388i q^{61} +5.53019 q^{62} +(2.07103 + 7.66230i) q^{63} +1.00000 q^{64} +(-2.35425 + 1.91520i) q^{65} +1.82646i q^{67} -4.33981 q^{68} +(3.36028 + 13.4148i) q^{69} +(2.16991 + 0.500983i) q^{70} +14.5830 q^{71} +(-2.64575 + 1.41421i) q^{72} +3.14944 q^{73} -5.15587i q^{74} +(7.21033 - 1.80613i) q^{75} +4.55066 q^{76} +(-5.00000 - 3.74166i) q^{78} -11.2915 q^{79} +0.841723i q^{80} +(5.00000 - 7.48331i) q^{81} +10.8896i q^{82} -7.27733i q^{83} +(0.0849536 + 4.58179i) q^{84} -3.65292i q^{85} -8.00000 q^{86} +(-0.979531 - 3.91044i) q^{87} +12.5730i q^{89} +(-1.19038 - 2.22699i) q^{90} +(-8.56458 + 4.20095i) q^{91} +7.98430i q^{92} +(-9.29150 + 2.32744i) q^{93} +7.82087i q^{94} +3.83039i q^{95} +(-1.68014 + 0.420861i) q^{96} -9.87000 q^{97} +(6.29150 + 3.06871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 24 q^{15} + 8 q^{16} - 8 q^{21} - 8 q^{25} - 24 q^{30} - 8 q^{32} + 40 q^{39} + 8 q^{42} + 64 q^{43} - 8 q^{49} + 8 q^{50} - 16 q^{51} + 40 q^{57} + 24 q^{60} + 8 q^{63} + 8 q^{64} - 40 q^{65} + 32 q^{71} - 40 q^{78} - 48 q^{79} + 40 q^{81} - 8 q^{84} - 64 q^{86} - 32 q^{91} - 32 q^{93} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 24 * q^15 + 8 * q^16 - 8 * q^21 - 8 * q^25 - 24 * q^30 - 8 * q^32 + 40 * q^39 + 8 * q^42 + 64 * q^43 - 8 * q^49 + 8 * q^50 - 16 * q^51 + 40 * q^57 + 24 * q^60 + 8 * q^63 + 8 * q^64 - 40 * q^65 + 32 * q^71 - 40 * q^78 - 48 * q^79 + 40 * q^81 - 8 * q^84 - 64 * q^86 - 32 * q^91 - 32 * q^93 + 8 * q^98

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