LMFDB - Embedded newform 1242.2.e.b.415.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1242,2,Mod(415,1242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1242, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1242.415");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1242 = 2 \cdot 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1242.e (of order $3$, degree $2$, not 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:	$9.91741993104$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 414)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.4
Root			$-0.539982 + 0.935277i$ of defining polynomial
Character	$\chi$	$=$	1242.415
Dual form			1242.2.e.b.829.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.990153 - 1.71499i) q^{5} +(0.245502 + 0.425221i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.990153 - 1.71499i) q^{5} +(0.245502 + 0.425221i) q^{7} +1.00000 q^{8} -1.98031 q^{10} +(1.91763 + 3.32142i) q^{11} +(-2.84575 + 4.92899i) q^{13} +(0.245502 - 0.425221i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.35597 q^{17} +4.40294 q^{19} +(0.990153 + 1.71499i) q^{20} +(1.91763 - 3.32142i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.539195 + 0.933913i) q^{25} +5.69151 q^{26} -0.491003 q^{28} +(4.47632 + 7.75322i) q^{29} +(-4.82606 + 8.35898i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.17799 + 3.77238i) q^{34} +0.972336 q^{35} -9.12212 q^{37} +(-2.20147 - 3.81306i) q^{38} +(0.990153 - 1.71499i) q^{40} +(1.69182 - 2.93032i) q^{41} +(4.76500 + 8.25323i) q^{43} -3.83525 q^{44} -1.00000 q^{46} +(-6.30759 - 10.9251i) q^{47} +(3.37946 - 5.85339i) q^{49} +(0.539195 - 0.933913i) q^{50} +(-2.84575 - 4.92899i) q^{52} +0.481721 q^{53} +7.59497 q^{55} +(0.245502 + 0.425221i) q^{56} +(4.47632 - 7.75322i) q^{58} +(1.38506 - 2.39900i) q^{59} +(1.41327 + 2.44785i) q^{61} +9.65212 q^{62} +1.00000 q^{64} +(5.63546 + 9.76091i) q^{65} +(0.245502 - 0.425221i) q^{67} +(2.17799 - 3.77238i) q^{68} +(-0.486168 - 0.842068i) q^{70} -5.93089 q^{71} +6.59667 q^{73} +(4.56106 + 7.89998i) q^{74} +(-2.20147 + 3.81306i) q^{76} +(-0.941560 + 1.63083i) q^{77} +(6.68166 + 11.5730i) q^{79} -1.98031 q^{80} -3.38364 q^{82} +(0.956164 + 1.65612i) q^{83} +(-4.31308 + 7.47047i) q^{85} +(4.76500 - 8.25323i) q^{86} +(1.91763 + 3.32142i) q^{88} +5.17284 q^{89} -2.79455 q^{91} +(0.500000 + 0.866025i) q^{92} +(-6.30759 + 10.9251i) q^{94} +(4.35959 - 7.55102i) q^{95} +(6.47632 + 11.2173i) q^{97} -6.75892 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1242\mathbb{Z}\right)^\times$.

$n$	$461$	$649$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.990153	−	1.71499i	0.442810	−	0.766969i	−0.555087	−	0.831792i	$-0.687315\pi$
$5$	0.990153	−	1.71499i	0.442810	−	0.766969i	0.997897	+	0.0648233i	$0.0206484\pi$
$6$		0			0
$7$	0.245502	+	0.425221i	0.0927909	+	0.160719i	0.908684	−	0.417484i	$-0.137088\pi$
$7$	0.245502	+	0.425221i	0.0927909	+	0.160719i	−0.815894	+	0.578202i	$0.803755\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.98031			−0.626228
$11$	1.91763	+	3.32142i	0.578186	+	1.00145i	0.995687	+	0.0927710i	$0.0295725\pi$
$11$	1.91763	+	3.32142i	0.578186	+	1.00145i	−0.417502	+	0.908676i	$0.637094\pi$
$12$		0			0
$13$	−2.84575	+	4.92899i	−0.789270	+	1.36706i	0.137144	+	0.990551i	$0.456208\pi$
$13$	−2.84575	+	4.92899i	−0.789270	+	1.36706i	−0.926415	+	0.376505i	$0.877126\pi$
$14$	0.245502	−	0.425221i	0.0656131	−	0.113645i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.35597			−1.05648			−0.528239	−	0.849096i	$-0.677148\pi$
$17$	−4.35597			−1.05648			−0.528239	+	0.849096i	$0.677148\pi$
$18$		0			0
$19$	4.40294			1.01010			0.505052	−	0.863089i	$-0.331473\pi$
$19$	4.40294			1.01010			0.505052	+	0.863089i	$0.331473\pi$
$20$	0.990153	+	1.71499i	0.221405	+	0.383485i
$21$		0			0
$22$	1.91763	−	3.32142i	0.408839	−	0.708130i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	0.539195	+	0.933913i	0.107839	+	0.186783i
$26$	5.69151			1.11620
$27$		0			0
$28$	−0.491003			−0.0927909
$29$	4.47632	+	7.75322i	0.831232	+	1.43974i	0.897062	+	0.441905i	$0.145697\pi$
$29$	4.47632	+	7.75322i	0.831232	+	1.43974i	−0.0658299	+	0.997831i	$0.520969\pi$
$30$		0			0
$31$	−4.82606	+	8.35898i	−0.866786	+	1.50132i	−0.00152311	+	0.999999i	$0.500485\pi$
$31$	−4.82606	+	8.35898i	−0.866786	+	1.50132i	−0.865263	+	0.501318i	$0.832849\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.17799	+	3.77238i	0.373522	+	0.646958i
$35$	0.972336			0.164355
$36$		0			0
$37$	−9.12212			−1.49967			−0.749833	−	0.661627i	$-0.769866\pi$
$37$	−9.12212			−1.49967			−0.749833	+	0.661627i	$0.769866\pi$
$38$	−2.20147	−	3.81306i	−0.357126	−	0.618560i
$39$		0			0
$40$	0.990153	−	1.71499i	0.156557	−	0.271165i
$41$	1.69182	−	2.93032i	0.264218	−	0.457638i	−0.703141	−	0.711051i	$-0.748220\pi$
$41$	1.69182	−	2.93032i	0.264218	−	0.457638i	0.967358	+	0.253412i	$0.0815530\pi$
$42$		0			0
$43$	4.76500	+	8.25323i	0.726656	+	1.25861i	0.958289	+	0.285802i	$0.0922599\pi$
$43$	4.76500	+	8.25323i	0.726656	+	1.25861i	−0.231633	+	0.972803i	$0.574407\pi$
$44$	−3.83525			−0.578186
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−6.30759	−	10.9251i	−0.920056	−	1.59358i	−0.799325	−	0.600899i	$-0.794810\pi$
$47$	−6.30759	−	10.9251i	−0.920056	−	1.59358i	−0.120731	−	0.992685i	$-0.538524\pi$
$48$		0			0
$49$	3.37946	−	5.85339i	0.482780	−	0.836199i
$50$	0.539195	−	0.933913i	0.0762537	−	0.132075i
$51$		0			0
$52$	−2.84575	−	4.92899i	−0.394635	−	0.683528i
$53$	0.481721			0.0661695			0.0330847	−	0.999453i	$-0.489467\pi$
$53$	0.481721			0.0661695			0.0330847	+	0.999453i	$0.489467\pi$
$54$		0			0
$55$	7.59497			1.02411
$56$	0.245502	+	0.425221i	0.0328065	+	0.0568226i
$57$		0			0
$58$	4.47632	−	7.75322i	0.587770	−	1.01805i
$59$	1.38506	−	2.39900i	0.180320	−	0.312324i	−0.761669	−	0.647966i	$-0.775620\pi$
$59$	1.38506	−	2.39900i	0.180320	−	0.312324i	0.941990	+	0.335642i	$0.108953\pi$
$60$		0			0
$61$	1.41327	+	2.44785i	0.180951	+	0.313416i	0.942205	−	0.335038i	$-0.108749\pi$
$61$	1.41327	+	2.44785i	0.180951	+	0.313416i	−0.761254	+	0.648454i	$0.775416\pi$
$62$	9.65212			1.22582
$63$		0			0
$64$	1.00000			0.125000
$65$	5.63546	+	9.76091i	0.698993	+	1.21069i
$66$		0			0
$67$	0.245502	−	0.425221i	0.0299928	−	0.0519490i	−0.850639	−	0.525750i	$-0.823785\pi$
$67$	0.245502	−	0.425221i	0.0299928	−	0.0519490i	0.880632	+	0.473801i	$0.157118\pi$
$68$	2.17799	−	3.77238i	0.264120	−	0.457469i
$69$		0			0
$70$	−0.486168	−	0.842068i	−0.0581082	−	0.100646i
$71$	−5.93089			−0.703867			−0.351934	−	0.936025i	$-0.614476\pi$
$71$	−5.93089			−0.703867			−0.351934	+	0.936025i	$0.614476\pi$
$72$		0			0
$73$	6.59667			0.772082			0.386041	−	0.922482i	$-0.373842\pi$
$73$	6.59667			0.772082			0.386041	+	0.922482i	$0.373842\pi$
$74$	4.56106	+	7.89998i	0.530212	+	0.918354i
$75$		0			0
$76$	−2.20147	+	3.81306i	−0.252526	+	0.437388i
$77$	−0.941560	+	1.63083i	−0.107301	+	0.185850i
$78$		0			0
$79$	6.68166	+	11.5730i	0.751746	+	1.30206i	0.946976	+	0.321304i	$0.104121\pi$
$79$	6.68166	+	11.5730i	0.751746	+	1.30206i	−0.195230	+	0.980757i	$0.562545\pi$
$80$	−1.98031			−0.221405
$81$		0			0
$82$	−3.38364			−0.373660
$83$	0.956164	+	1.65612i	0.104953	+	0.181783i	0.913719	−	0.406347i	$-0.133198\pi$
$83$	0.956164	+	1.65612i	0.104953	+	0.181783i	−0.808766	+	0.588130i	$0.799864\pi$
$84$		0			0
$85$	−4.31308	+	7.47047i	−0.467819	+	0.810286i
$86$	4.76500	−	8.25323i	0.513823	−	0.889968i
$87$		0			0
$88$	1.91763	+	3.32142i	0.204420	+	0.354065i
$89$	5.17284			0.548320			0.274160	−	0.961684i	$-0.411600\pi$
$89$	5.17284			0.548320			0.274160	+	0.961684i	$0.411600\pi$
$90$		0			0
$91$	−2.79455			−0.292948
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$	−6.30759	+	10.9251i	−0.650578	+	1.12683i
$95$	4.35959	−	7.55102i	0.447284	−	0.774719i
$96$		0			0
$97$	6.47632	+	11.2173i	0.657571	+	1.13895i	0.981243	+	0.192777i	$0.0617493\pi$
$97$	6.47632	+	11.2173i	0.657571	+	1.13895i	−0.323672	+	0.946169i	$0.604917\pi$
$98$	−6.75892			−0.682754
$99$		0			0
$100$	−1.07839			−0.107839
$101$	7.03237	+	12.1804i	0.699747	+	1.21200i	0.968554	+	0.248803i	$0.0800371\pi$
$101$	7.03237	+	12.1804i	0.699747	+	1.21200i	−0.268808	+	0.963194i	$0.586630\pi$
$102$		0			0
$103$	8.28251	−	14.3457i	0.816100	−	1.41353i	−0.0924356	−	0.995719i	$-0.529465\pi$
$103$	8.28251	−	14.3457i	0.816100	−	1.41353i	0.908535	−	0.417808i	$-0.137201\pi$
$104$	−2.84575	+	4.92899i	−0.279049	+	0.483327i
$105$		0			0
$106$	−0.240860	−	0.417183i	−0.0233944	−	0.0405204i
$107$	−6.19254			−0.598655			−0.299328	−	0.954150i	$-0.596762\pi$
$107$	−6.19254			−0.598655			−0.299328	+	0.954150i	$0.596762\pi$
$108$		0			0
$109$	4.67294			0.447587			0.223793	−	0.974637i	$-0.428156\pi$
$109$	4.67294			0.447587			0.223793	+	0.974637i	$0.428156\pi$
$110$	−3.79748	−	6.57744i	−0.362076	−	0.627134i
$111$		0			0
$112$	0.245502	−	0.425221i	0.0231977	−	0.0401796i
$113$	2.36980	−	4.10462i	0.222932	−	0.386130i	−0.732765	−	0.680482i	$-0.761770\pi$
$113$	2.36980	−	4.10462i	0.222932	−	0.386130i	0.955697	+	0.294352i	$0.0951037\pi$
$114$		0			0
$115$	−0.990153	−	1.71499i	−0.0923322	−	0.159924i
$116$	−8.95264			−0.831232
$117$		0			0
$118$	−2.77013			−0.255011
$119$	−1.06940	−	1.85225i	−0.0980316	−	0.169796i
$120$		0			0
$121$	−1.85457	+	3.21222i	−0.168598	+	0.292020i
$122$	1.41327	−	2.44785i	0.127951	−	0.221618i
$123$		0			0
$124$	−4.82606	−	8.35898i	−0.433393	−	0.750659i
$125$	12.0371			1.07663
$126$		0			0
$127$	5.87595			0.521406			0.260703	−	0.965419i	$-0.416046\pi$
$127$	5.87595			0.521406			0.260703	+	0.965419i	$0.416046\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	5.63546	−	9.76091i	0.494263	−	0.856088i
$131$	1.16862	−	2.02411i	0.102103	−	0.176847i	−0.810448	−	0.585810i	$-0.800776\pi$
$131$	1.16862	−	2.02411i	0.102103	−	0.176847i	0.912551	+	0.408963i	$0.134110\pi$
$132$		0			0
$133$	1.08093	+	1.87222i	0.0937285	+	0.162342i
$134$	−0.491003			−0.0424162
$135$		0			0
$136$	−4.35597			−0.373522
$137$	1.30317	+	2.25716i	0.111337	+	0.192842i	0.916310	−	0.400470i	$-0.131153\pi$
$137$	1.30317	+	2.25716i	0.111337	+	0.192842i	−0.804972	+	0.593312i	$0.797820\pi$
$138$		0			0
$139$	5.42794	−	9.40146i	0.460391	−	0.797421i	−0.538589	−	0.842569i	$-0.681042\pi$
$139$	5.42794	−	9.40146i	0.460391	−	0.797421i	0.998980	+	0.0451473i	$0.0143757\pi$
$140$	−0.486168	+	0.842068i	−0.0410887	+	0.0711677i
$141$		0			0
$142$	2.96545	+	5.13630i	0.248855	+	0.431029i
$143$	−21.8284			−1.82538
$144$		0			0
$145$	17.7290			1.47231
$146$	−3.29833	−	5.71288i	−0.272972	−	0.472802i
$147$		0			0
$148$	4.56106	−	7.89998i	0.374917	−	0.649375i
$149$	−4.13281	+	7.15824i	−0.338573	+	0.586426i	−0.984165	−	0.177257i	$-0.943278\pi$
$149$	−4.13281	+	7.15824i	−0.338573	+	0.586426i	0.645591	+	0.763683i	$0.276611\pi$
$150$		0			0
$151$	−3.03757	−	5.26123i	−0.247194	−	0.428153i	0.715552	−	0.698559i	$-0.246175\pi$
$151$	−3.03757	−	5.26123i	−0.247194	−	0.428153i	−0.962746	+	0.270407i	$0.912842\pi$
$152$	4.40294			0.357126
$153$		0			0
$154$	1.88312			0.151746
$155$	9.55707	+	16.5533i	0.767643	+	1.32960i
$156$		0			0
$157$	−3.82728	+	6.62905i	−0.305450	+	0.529055i	−0.977361	−	0.211576i	$-0.932140\pi$
$157$	−3.82728	+	6.62905i	−0.305450	+	0.529055i	0.671911	+	0.740632i	$0.265474\pi$
$158$	6.68166	−	11.5730i	0.531564	−	0.920697i
$159$		0			0
$160$	0.990153	+	1.71499i	0.0782784	+	0.135582i
$161$	0.491003			0.0386965
$162$		0			0
$163$	−19.8556			−1.55521			−0.777607	−	0.628751i	$-0.783567\pi$
$163$	−19.8556			−1.55521			−0.777607	+	0.628751i	$0.783567\pi$
$164$	1.69182	+	2.93032i	0.132109	+	0.228819i
$165$		0			0
$166$	0.956164	−	1.65612i	0.0742127	−	0.128540i
$167$	2.18300	−	3.78106i	0.168926	−	0.292588i	−0.769117	−	0.639108i	$-0.779304\pi$
$167$	2.18300	−	3.78106i	0.168926	−	0.292588i	0.938042	+	0.346521i	$0.112637\pi$
$168$		0			0
$169$	−9.69664	−	16.7951i	−0.745895	−	1.29193i
$170$	8.62616			0.661596
$171$		0			0
$172$	−9.53000			−0.726656
$173$	3.42292	+	5.92868i	0.260240	+	0.450749i	0.966306	−	0.257398i	$-0.0828650\pi$
$173$	3.42292	+	5.92868i	0.260240	+	0.450749i	−0.706066	+	0.708146i	$0.749532\pi$
$174$		0			0
$175$	−0.264746	+	0.458554i	−0.0200130	+	0.0346634i
$176$	1.91763	−	3.32142i	0.144546	−	0.250362i
$177$		0			0
$178$	−2.58642	−	4.47981i	−0.193860	−	0.335776i
$179$	−11.4029			−0.852296			−0.426148	−	0.904653i	$-0.640130\pi$
$179$	−11.4029			−0.852296			−0.426148	+	0.904653i	$0.640130\pi$
$180$		0			0
$181$	15.7382			1.16981			0.584907	−	0.811100i	$-0.301131\pi$
$181$	15.7382			1.16981			0.584907	+	0.811100i	$0.301131\pi$
$182$	1.39727	+	2.42015i	0.103573	+	0.179393i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−9.03229	+	15.6444i	−0.664067	+	1.15020i
$186$		0			0
$187$	−8.35312	−	14.4680i	−0.610841	−	1.05801i
$188$	12.6152			0.920056
$189$		0			0
$190$	−8.71917			−0.632555
$191$	−8.87075	−	15.3646i	−0.641865	−	1.11174i	−0.985016	−	0.172462i	$-0.944828\pi$
$191$	−8.87075	−	15.3646i	−0.641865	−	1.11174i	0.343151	−	0.939280i	$-0.388506\pi$
$192$		0			0
$193$	2.95227	−	5.11348i	0.212509	−	0.368077i	−0.739990	−	0.672618i	$-0.765170\pi$
$193$	2.95227	−	5.11348i	0.212509	−	0.368077i	0.952499	+	0.304541i	$0.0985032\pi$
$194$	6.47632	−	11.2173i	0.464973	−	0.805356i
$195$		0			0
$196$	3.37946	+	5.85339i	0.241390	+	0.418099i
$197$	−10.0295			−0.714571			−0.357286	−	0.933995i	$-0.616298\pi$
$197$	−10.0295			−0.714571			−0.357286	+	0.933995i	$0.616298\pi$
$198$		0			0
$199$	−18.6534			−1.32231			−0.661153	−	0.750251i	$-0.729933\pi$
$199$	−18.6534			−1.32231			−0.661153	+	0.750251i	$0.729933\pi$
$200$	0.539195	+	0.933913i	0.0381268	+	0.0660376i
$201$		0			0
$202$	7.03237	−	12.1804i	0.494796	−	0.857011i
$203$	−2.19789	+	3.80685i	−0.154261	+	0.267189i
$204$		0			0
$205$	−3.35032	−	5.80292i	−0.233996	−	0.405293i
$206$	−16.5650			−1.15414
$207$		0			0
$208$	5.69151			0.394635
$209$	8.44320	+	14.6240i	0.584028	+	1.01157i
$210$		0			0
$211$	4.71584	−	8.16808i	0.324652	−	0.562314i	−0.656790	−	0.754074i	$-0.728086\pi$
$211$	4.71584	−	8.16808i	0.324652	−	0.562314i	0.981442	+	0.191760i	$0.0614194\pi$
$212$	−0.240860	+	0.417183i	−0.0165424	+	0.0286522i
$213$		0			0
$214$	3.09627	+	5.36289i	0.211657	+	0.366600i
$215$	18.8723			1.28708
$216$		0			0
$217$	−4.73922			−0.321719
$218$	−2.33647	−	4.04689i	−0.158246	−	0.274090i
$219$		0			0
$220$	−3.79748	+	6.57744i	−0.256026	+	0.443451i
$221$	12.3960	−	21.4706i	0.833847	−	1.44427i
$222$		0			0
$223$	1.72239	+	2.98326i	0.115340	+	0.199774i	0.917915	−	0.396776i	$-0.129871\pi$
$223$	1.72239	+	2.98326i	0.115340	+	0.199774i	−0.802576	+	0.596550i	$0.796538\pi$
$224$	−0.491003			−0.0328065
$225$		0			0
$226$	−4.73961			−0.315274
$227$	−8.69217	−	15.0553i	−0.576919	−	0.999253i	−0.995830	−	0.0912262i	$-0.970921\pi$
$227$	−8.69217	−	15.0553i	−0.576919	−	0.999253i	0.418911	−	0.908027i	$-0.362412\pi$
$228$		0			0
$229$	−1.23488	+	2.13888i	−0.0816033	+	0.141341i	−0.903939	−	0.427662i	$-0.859337\pi$
$229$	−1.23488	+	2.13888i	−0.0816033	+	0.141341i	0.822335	+	0.569003i	$0.192671\pi$
$230$	−0.990153	+	1.71499i	−0.0652887	+	0.113083i
$231$		0			0
$232$	4.47632	+	7.75322i	0.293885	+	0.509024i
$233$	−7.45708			−0.488530			−0.244265	−	0.969709i	$-0.578547\pi$
$233$	−7.45708			−0.488530			−0.244265	+	0.969709i	$0.578547\pi$
$234$		0			0
$235$	−24.9819			−1.62964
$236$	1.38506	+	2.39900i	0.0901600	+	0.156162i
$237$		0			0
$238$	−1.06940	+	1.85225i	−0.0693188	+	0.120064i
$239$	−13.0680	+	22.6345i	−0.845301	+	1.46410i	0.0400582	+	0.999197i	$0.487246\pi$
$239$	−13.0680	+	22.6345i	−0.845301	+	1.46410i	−0.885359	+	0.464907i	$0.846088\pi$
$240$		0			0
$241$	−5.14759	−	8.91589i	−0.331585	−	0.574323i	0.651238	−	0.758874i	$-0.274250\pi$
$241$	−5.14759	−	8.91589i	−0.331585	−	0.574323i	−0.982823	+	0.184551i	$0.940917\pi$
$242$	3.70915			0.238433
$243$		0			0
$244$	−2.82654			−0.180951
$245$	−6.69236	−	11.5915i	−0.427559	−	0.740554i
$246$		0			0
$247$	−12.5297	+	21.7021i	−0.797245	+	1.38087i
$248$	−4.82606	+	8.35898i	−0.306455	+	0.530796i
$249$		0			0
$250$	−6.01853	−	10.4244i	−0.380646	−	0.659297i
$251$	−14.0776			−0.888570			−0.444285	−	0.895886i	$-0.646542\pi$
$251$	−14.0776			−0.888570			−0.444285	+	0.895886i	$0.646542\pi$
$252$		0			0
$253$	3.83525			0.241120
$254$	−2.93798	−	5.08872i	−0.184345	−	0.319295i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.6086	+	20.1066i	−0.724123	+	1.25422i	0.235211	+	0.971944i	$0.424422\pi$
$257$	−11.6086	+	20.1066i	−0.724123	+	1.25422i	−0.959334	+	0.282273i	$0.908912\pi$
$258$		0			0
$259$	−2.23949	−	3.87892i	−0.139155	−	0.241024i
$260$	−11.2709			−0.698993
$261$		0			0
$262$	−2.33724			−0.144395
$263$	6.46220	+	11.1929i	0.398477	+	0.690182i	0.993538	−	0.113498i	$-0.0362057\pi$
$263$	6.46220	+	11.1929i	0.398477	+	0.690182i	−0.595062	+	0.803680i	$0.702872\pi$
$264$		0			0
$265$	0.476977	−	0.826149i	0.0293005	−	0.0507499i
$266$	1.08093	−	1.87222i	0.0662760	−	0.114793i
$267$		0			0
$268$	0.245502	+	0.425221i	0.0149964	+	0.0259745i
$269$	28.1514			1.71642			0.858212	−	0.513295i	$-0.171575\pi$
$269$	28.1514			1.71642			0.858212	+	0.513295i	$0.171575\pi$
$270$		0			0
$271$	−6.12742			−0.372214			−0.186107	−	0.982529i	$-0.559587\pi$
$271$	−6.12742			−0.372214			−0.186107	+	0.982529i	$0.559587\pi$
$272$	2.17799	+	3.77238i	0.132060	+	0.228734i
$273$		0			0
$274$	1.30317	−	2.25716i	0.0787274	−	0.136360i
$275$	−2.06795	+	3.58179i	−0.124702	+	0.215990i
$276$		0			0
$277$	−12.4804	−	21.6168i	−0.749877	−	1.29883i	−0.947881	−	0.318624i	$-0.896779\pi$
$277$	−12.4804	−	21.6168i	−0.749877	−	1.29883i	0.198004	−	0.980201i	$-0.436554\pi$
$278$	−10.8559			−0.651092
$279$		0			0
$280$	0.972336			0.0581082
$281$	−12.4119	−	21.4981i	−0.740433	−	1.28247i	−0.952298	−	0.305168i	$-0.901287\pi$
$281$	−12.4119	−	21.4981i	−0.740433	−	1.28247i	0.211866	−	0.977299i	$-0.432046\pi$
$282$		0			0
$283$	8.55622	−	14.8198i	0.508615	−	0.880946i	−0.491336	−	0.870970i	$-0.663491\pi$
$283$	8.55622	−	14.8198i	0.508615	−	0.880946i	0.999950	−	0.00997607i	$-0.00317554\pi$
$284$	2.96545	−	5.13630i	0.175967	−	0.304784i
$285$		0			0
$286$	10.9142	+	18.9039i	0.645369	+	1.11781i
$287$	1.66138			0.0980679
$288$		0			0
$289$	1.97450			0.116147
$290$	−8.86448	−	15.3537i	−0.520540	−	0.901602i
$291$		0			0
$292$	−3.29833	+	5.71288i	−0.193020	+	0.334321i
$293$	1.12470	−	1.94804i	0.0657059	−	0.113806i	−0.831301	−	0.555822i	$-0.812403\pi$
$293$	1.12470	−	1.94804i	0.0657059	−	0.113806i	0.897007	+	0.442017i	$0.145737\pi$
$294$		0			0
$295$	−2.74285	−	4.75076i	−0.159695	−	0.276600i
$296$	−9.12212			−0.530212
$297$		0			0
$298$	8.26563			0.478815
$299$	2.84575	+	4.92899i	0.164574	+	0.285051i
$300$		0			0
$301$	−2.33963	+	4.05236i	−0.134854	+	0.233574i
$302$	−3.03757	+	5.26123i	−0.174793	+	0.302750i
$303$		0			0
$304$	−2.20147	−	3.81306i	−0.126263	−	0.218694i
$305$	5.59741			0.320507
$306$		0			0
$307$	25.6490			1.46387			0.731933	−	0.681377i	$-0.238618\pi$
$307$	25.6490			1.46387			0.731933	+	0.681377i	$0.238618\pi$
$308$	−0.941560	−	1.63083i	−0.0536504	−	0.0929252i
$309$		0			0
$310$	9.55707	−	16.5533i	0.542805	−	0.940166i
$311$	9.92819	−	17.1961i	0.562976	−	0.975103i	−0.434259	−	0.900788i	$-0.642990\pi$
$311$	9.92819	−	17.1961i	0.562976	−	0.975103i	0.997235	−	0.0743150i	$-0.0236770\pi$
$312$		0			0
$313$	−5.45361	−	9.44593i	−0.308256	−	0.533915i	0.669725	−	0.742609i	$-0.266412\pi$
$313$	−5.45361	−	9.44593i	−0.308256	−	0.533915i	−0.977981	+	0.208694i	$0.933079\pi$
$314$	7.65456			0.431972
$315$		0			0
$316$	−13.3633			−0.751746
$317$	8.28174	+	14.3444i	0.465149	+	0.805662i	0.999208	−	0.0397852i	$-0.0126674\pi$
$317$	8.28174	+	14.3444i	0.465149	+	0.805662i	−0.534059	+	0.845447i	$0.679334\pi$
$318$		0			0
$319$	−17.1678	+	29.7355i	−0.961213	+	1.66487i
$320$	0.990153	−	1.71499i	0.0553512	−	0.0958711i
$321$		0			0
$322$	−0.245502	−	0.425221i	−0.0136813	−	0.0236967i
$323$	−19.1791			−1.06715
$324$		0			0
$325$	−6.13767			−0.340456
$326$	9.92782	+	17.1955i	0.549851	+	0.952370i
$327$		0			0
$328$	1.69182	−	2.93032i	0.0934150	−	0.161800i
$329$	3.09705	−	5.36424i	0.170746	−	0.295740i
$330$		0			0
$331$	0.974042	+	1.68709i	0.0535382	+	0.0927309i	0.891552	−	0.452917i	$-0.149617\pi$
$331$	0.974042	+	1.68709i	0.0535382	+	0.0927309i	−0.838014	+	0.545648i	$0.816283\pi$
$332$	−1.91233			−0.104953
$333$		0			0
$334$	−4.36600			−0.238897
$335$	−0.486168	−	0.842068i	−0.0265622	−	0.0460071i
$336$		0			0
$337$	−1.68898	+	2.92539i	−0.0920044	+	0.159356i	−0.908354	−	0.418201i	$-0.862661\pi$
$337$	−1.68898	+	2.92539i	−0.0920044	+	0.159356i	0.816350	+	0.577557i	$0.195994\pi$
$338$	−9.69664	+	16.7951i	−0.527427	+	0.913531i
$339$		0			0
$340$	−4.31308	−	7.47047i	−0.233910	−	0.405143i
$341$	−37.0183			−2.00465
$342$		0			0
$343$	6.75567			0.364772
$344$	4.76500	+	8.25323i	0.256912	+	0.444984i
$345$		0			0
$346$	3.42292	−	5.92868i	0.184017	−	0.318728i
$347$	5.27605	−	9.13839i	0.283233	−	0.490574i	−0.688946	−	0.724813i	$-0.741926\pi$
$347$	5.27605	−	9.13839i	0.283233	−	0.490574i	0.972179	+	0.234238i	$0.0752596\pi$
$348$		0			0
$349$	−0.196204	−	0.339835i	−0.0105025	−	0.0181909i	0.860726	−	0.509068i	$-0.170010\pi$
$349$	−0.196204	−	0.339835i	−0.0105025	−	0.0181909i	−0.871229	+	0.490877i	$0.836676\pi$
$350$	0.529493			0.0283026
$351$		0			0
$352$	−3.83525			−0.204420
$353$	0.936949	+	1.62284i	0.0498687	+	0.0863752i	0.889882	−	0.456190i	$-0.150786\pi$
$353$	0.936949	+	1.62284i	0.0498687	+	0.0863752i	−0.840014	+	0.542565i	$0.817453\pi$
$354$		0			0
$355$	−5.87249	+	10.1714i	−0.311679	+	0.539845i
$356$	−2.58642	+	4.47981i	−0.137080	+	0.237430i
$357$		0			0
$358$	5.70147	+	9.87524i	0.301332	+	0.521923i
$359$	−22.3446			−1.17930			−0.589651	−	0.807658i	$-0.700735\pi$
$359$	−22.3446			−1.17930			−0.589651	+	0.807658i	$0.700735\pi$
$360$		0			0
$361$	0.385908			0.0203109
$362$	−7.86912	−	13.6297i	−0.413592	−	0.716362i
$363$		0			0
$364$	1.39727	−	2.42015i	0.0732371	−	0.126850i
$365$	6.53171	−	11.3133i	0.341885	−	0.592163i
$366$		0			0
$367$	7.49849	+	12.9878i	0.391418	+	0.677956i	0.992637	−	0.121128i	$-0.0386513\pi$
$367$	7.49849	+	12.9878i	0.391418	+	0.677956i	−0.601219	+	0.799085i	$0.705318\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	18.0646			0.939133
$371$	0.118263	+	0.204838i	0.00613992	+	0.0106347i
$372$		0			0
$373$	−15.3152	+	26.5266i	−0.792989	+	1.37350i	0.131119	+	0.991367i	$0.458143\pi$
$373$	−15.3152	+	26.5266i	−0.792989	+	1.37350i	−0.924108	+	0.382131i	$0.875190\pi$
$374$	−8.35312	+	14.4680i	−0.431930	+	0.748124i
$375$		0			0
$376$	−6.30759	−	10.9251i	−0.325289	−	0.563417i
$377$	−50.9540			−2.62427
$378$		0			0
$379$	18.2092			0.935342			0.467671	−	0.883903i	$-0.345093\pi$
$379$	18.2092			0.935342			0.467671	+	0.883903i	$0.345093\pi$
$380$	4.35959	+	7.55102i	0.223642	+	0.387359i
$381$		0			0
$382$	−8.87075	+	15.3646i	−0.453867	+	0.786120i
$383$	−13.2106	+	22.8815i	−0.675032	+	1.16919i	0.301427	+	0.953489i	$0.402537\pi$
$383$	−13.2106	+	22.8815i	−0.675032	+	1.16919i	−0.976459	+	0.215701i	$0.930796\pi$
$384$		0			0
$385$	1.86458	+	3.22954i	0.0950276	+	0.164593i
$386$	−5.90454			−0.300533
$387$		0			0
$388$	−12.9526			−0.657571
$389$	5.03171	+	8.71518i	0.255118	+	0.441877i	0.964928	−	0.262516i	$-0.0845524\pi$
$389$	5.03171	+	8.71518i	0.255118	+	0.441877i	−0.709810	+	0.704394i	$0.751219\pi$
$390$		0			0
$391$	−2.17799	+	3.77238i	−0.110146	+	0.190778i
$392$	3.37946	−	5.85339i	0.170688	−	0.295641i
$393$		0			0
$394$	5.01474	+	8.68579i	0.252639	+	0.437584i
$395$	26.4635			1.33152
$396$		0			0
$397$	10.0383			0.503806			0.251903	−	0.967753i	$-0.418944\pi$
$397$	10.0383			0.503806			0.251903	+	0.967753i	$0.418944\pi$
$398$	9.32672	+	16.1543i	0.467506	+	0.809744i
$399$		0			0
$400$	0.539195	−	0.933913i	0.0269598	−	0.0466957i
$401$	17.5822	−	30.4533i	0.878015	−	1.52077i	0.0244997	−	0.999700i	$-0.492201\pi$
$401$	17.5822	−	30.4533i	0.878015	−	1.52077i	0.853516	−	0.521067i	$-0.174466\pi$
$402$		0			0
$403$	−27.4676	−	47.5752i	−1.36826	−	2.36989i
$404$	−14.0647			−0.699747
$405$		0			0
$406$	4.39578			0.218159
$407$	−17.4928	−	30.2984i	−0.867086	−	1.50184i
$408$		0			0
$409$	−3.54061	+	6.13252i	−0.175072	+	0.303233i	−0.940186	−	0.340661i	$-0.889349\pi$
$409$	−3.54061	+	6.13252i	−0.175072	+	0.303233i	0.765114	+	0.643895i	$0.222682\pi$
$410$	−3.35032	+	5.80292i	−0.165460	+	0.286586i
$411$		0			0
$412$	8.28251	+	14.3457i	0.408050	+	0.706763i
$413$	1.36014			0.0669282
$414$		0			0
$415$	3.78699			0.185896
$416$	−2.84575	−	4.92899i	−0.139525	−	0.241664i
$417$		0			0
$418$	8.44320	−	14.6240i	0.412970	−	0.715285i
$419$	−6.26384	+	10.8493i	−0.306009	+	0.530023i	−0.977485	−	0.211003i	$-0.932327\pi$
$419$	−6.26384	+	10.8493i	−0.306009	+	0.530023i	0.671477	+	0.741026i	$0.265660\pi$
$420$		0			0
$421$	16.2278	+	28.1074i	0.790897	+	1.36987i	0.925412	+	0.378962i	$0.123719\pi$
$421$	16.2278	+	28.1074i	0.790897	+	1.36987i	−0.134516	+	0.990911i	$0.542948\pi$
$422$	−9.43169			−0.459127
$423$		0			0
$424$	0.481721			0.0233944
$425$	−2.34872	−	4.06810i	−0.113930	−	0.197332i
$426$		0			0
$427$	−0.693920	+	1.20190i	−0.0335811	+	0.0581642i
$428$	3.09627	−	5.36289i	0.149664	−	0.259225i
$429$		0			0
$430$	−9.43616	−	16.3439i	−0.455052	−	0.788173i
$431$	7.22801			0.348161			0.174081	−	0.984731i	$-0.444305\pi$
$431$	7.22801			0.348161			0.174081	+	0.984731i	$0.444305\pi$
$432$		0			0
$433$	37.0157			1.77886			0.889430	−	0.457072i	$-0.151102\pi$
$433$	37.0157			1.77886			0.889430	+	0.457072i	$0.151102\pi$
$434$	2.36961	+	4.10429i	0.113745	+	0.197012i
$435$		0			0
$436$	−2.33647	+	4.04689i	−0.111897	+	0.193811i
$437$	2.20147	−	3.81306i	0.105311	−	0.182403i
$438$		0			0
$439$	9.41544	+	16.3080i	0.449374	+	0.778339i	0.998345	−	0.0575021i	$-0.0183136\pi$
$439$	9.41544	+	16.3080i	0.449374	+	0.778339i	−0.548971	+	0.835841i	$0.684980\pi$
$440$	7.59497			0.362076
$441$		0			0
$442$	−24.7921			−1.17924
$443$	−4.76549	−	8.25407i	−0.226415	−	0.392163i	0.730328	−	0.683097i	$-0.239367\pi$
$443$	−4.76549	−	8.25407i	−0.226415	−	0.392163i	−0.956743	+	0.290934i	$0.906034\pi$
$444$		0			0
$445$	5.12190	−	8.87140i	0.242802	−	0.420545i
$446$	1.72239	−	2.98326i	0.0815574	−	0.141262i
$447$		0			0
$448$	0.245502	+	0.425221i	0.0115989	+	0.0200898i
$449$	7.11135			0.335606			0.167803	−	0.985821i	$-0.446333\pi$
$449$	7.11135			0.335606			0.167803	+	0.985821i	$0.446333\pi$
$450$		0			0
$451$	12.9771			0.611068
$452$	2.36980	+	4.10462i	0.111466	+	0.193065i
$453$		0			0
$454$	−8.69217	+	15.0553i	−0.407944	+	0.706579i
$455$	−2.76703	+	4.79264i	−0.129720	+	0.224682i
$456$		0			0
$457$	−2.76634	−	4.79144i	−0.129404	−	0.224134i	0.794042	−	0.607863i	$-0.207973\pi$
$457$	−2.76634	−	4.79144i	−0.129404	−	0.224134i	−0.923446	+	0.383729i	$0.874640\pi$
$458$	2.46976			0.115405
$459$		0			0
$460$	1.98031			0.0923322
$461$	−7.97263	−	13.8090i	−0.371322	−	0.643149i	0.618447	−	0.785827i	$-0.287762\pi$
$461$	−7.97263	−	13.8090i	−0.371322	−	0.643149i	−0.989769	+	0.142678i	$0.954429\pi$
$462$		0			0
$463$	2.93221	−	5.07873i	0.136271	−	0.236029i	−0.789811	−	0.613350i	$-0.789822\pi$
$463$	2.93221	−	5.07873i	0.136271	−	0.236029i	0.926082	+	0.377322i	$0.123155\pi$
$464$	4.47632	−	7.75322i	0.207808	−	0.359934i
$465$		0			0
$466$	3.72854	+	6.45802i	0.172721	+	0.299162i
$467$	−5.82468			−0.269534			−0.134767	−	0.990877i	$-0.543029\pi$
$467$	−5.82468			−0.269534			−0.134767	+	0.990877i	$0.543029\pi$
$468$		0			0
$469$	0.241084			0.0111322
$470$	12.4909	+	21.6350i	0.576165	+	0.997946i
$471$		0			0
$472$	1.38506	−	2.39900i	0.0637528	−	0.110423i
$473$	−18.2750	+	31.6532i	−0.840284	+	1.45542i
$474$		0			0
$475$	2.37404	+	4.11197i	0.108929	+	0.188670i
$476$	2.13880			0.0980316
$477$		0			0
$478$	26.1361			1.19544
$479$	−11.3864	−	19.7218i	−0.520258	−	0.901114i	−0.999723	−	0.0235524i	$-0.992502\pi$
$479$	−11.3864	−	19.7218i	−0.520258	−	0.901114i	0.479464	−	0.877561i	$-0.340831\pi$
$480$		0			0
$481$	25.9593	−	44.9628i	1.18364	−	2.05013i
$482$	−5.14759	+	8.91589i	−0.234466	+	0.406107i
$483$		0			0
$484$	−1.85457	−	3.21222i	−0.0842988	−	0.146010i
$485$	25.6502			1.16472
$486$		0			0
$487$	−8.84186			−0.400663			−0.200332	−	0.979728i	$-0.564202\pi$
$487$	−8.84186			−0.400663			−0.200332	+	0.979728i	$0.564202\pi$
$488$	1.41327	+	2.44785i	0.0639757	+	0.110809i
$489$		0			0
$490$	−6.69236	+	11.5915i	−0.302330	+	0.523651i
$491$	10.8533	−	18.7985i	0.489803	−	0.848363i	−0.510129	−	0.860098i	$-0.670402\pi$
$491$	10.8533	−	18.7985i	0.489803	−	0.848363i	0.999931	+	0.0117352i	$0.00373550\pi$
$492$		0			0
$493$	−19.4987	−	33.7728i	−0.878179	−	1.52105i
$494$	25.0594			1.12748
$495$		0			0
$496$	9.65212			0.433393
$497$	−1.45604	−	2.52194i	−0.0653125	−	0.113125i
$498$		0			0
$499$	−9.67125	+	16.7511i	−0.432945	+	0.749882i	−0.997125	−	0.0757693i	$-0.975859\pi$
$499$	−9.67125	+	16.7511i	−0.432945	+	0.749882i	0.564181	+	0.825651i	$0.309192\pi$
$500$	−6.01853	+	10.4244i	−0.269157	+	0.466194i
$501$		0			0
$502$	7.03879	+	12.1915i	0.314157	+	0.544135i
$503$	9.04690			0.403381			0.201691	−	0.979449i	$-0.435356\pi$
$503$	9.04690			0.403381			0.201691	+	0.979449i	$0.435356\pi$
$504$		0			0
$505$	27.8525			1.23942
$506$	−1.91763	−	3.32142i	−0.0852488	−	0.147655i
$507$		0			0
$508$	−2.93798	+	5.08872i	−0.130352	+	0.225776i
$509$	6.18528	−	10.7132i	0.274158	−	0.474855i	−0.695765	−	0.718270i	$-0.744934\pi$
$509$	6.18528	−	10.7132i	0.274158	−	0.474855i	0.969922	+	0.243415i	$0.0782677\pi$
$510$		0			0
$511$	1.61949	+	2.80504i	0.0716421	+	0.124088i
$512$	1.00000			0.0441942
$513$		0			0
$514$	23.2171			1.02406
$515$	−16.4019	−	28.4089i	−0.722754	−	1.25185i
$516$		0			0
$517$	24.1912	−	41.9003i	1.06393	−	1.84278i
$518$	−2.23949	+	3.87892i	−0.0983977	+	0.170430i
$519$		0			0
$520$	5.63546	+	9.76091i	0.247131	+	0.428044i
$521$	34.6704			1.51894			0.759470	−	0.650543i	$-0.225459\pi$
$521$	34.6704			1.51894			0.759470	+	0.650543i	$0.225459\pi$
$522$		0			0
$523$	−36.3144			−1.58792			−0.793959	−	0.607971i	$-0.791984\pi$
$523$	−36.3144			−1.58792			−0.793959	+	0.607971i	$0.791984\pi$
$524$	1.16862	+	2.02411i	0.0510513	+	0.0884235i
$525$		0			0
$526$	6.46220	−	11.1929i	0.281765	−	0.488032i
$527$	21.0222	−	36.4115i	0.915741	−	1.58611i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−0.953955			−0.0414371
$531$		0			0
$532$	−2.16186			−0.0937285
$533$	9.62900	+	16.6779i	0.417078	+	0.722401i
$534$		0			0
$535$	−6.13156	+	10.6202i	−0.265090	+	0.459150i
$536$	0.245502	−	0.425221i	0.0106041	−	0.0183668i
$537$		0			0
$538$	−14.0757	−	24.3799i	−0.606848	−	1.05109i
$539$	25.9221			1.11655
$540$		0			0
$541$	40.1250			1.72511			0.862555	−	0.505964i	$-0.168863\pi$
$541$	40.1250			1.72511			0.862555	+	0.505964i	$0.168863\pi$
$542$	3.06371	+	5.30650i	0.131598	+	0.227934i
$543$		0			0
$544$	2.17799	−	3.77238i	0.0933804	−	0.161740i
$545$	4.62693	−	8.01408i	0.198196	−	0.343285i
$546$		0			0
$547$	−9.25852	−	16.0362i	−0.395866	−	0.685660i	0.597346	−	0.801984i	$-0.296222\pi$
$547$	−9.25852	−	16.0362i	−0.395866	−	0.685660i	−0.993211	+	0.116324i	$0.962889\pi$
$548$	−2.60634			−0.111337
$549$		0			0
$550$	4.13590			0.176355
$551$	19.7090	+	34.1370i	0.839631	+	1.45428i
$552$		0			0
$553$	−3.28072	+	5.68237i	−0.139510	+	0.241639i
$554$	−12.4804	+	21.6168i	−0.530243	+	0.918408i
$555$		0			0
$556$	5.42794	+	9.40146i	0.230196	+	0.398711i
$557$	13.4234			0.568767			0.284383	−	0.958711i	$-0.408211\pi$
$557$	13.4234			0.568767			0.284383	+	0.958711i	$0.408211\pi$
$558$		0			0
$559$	−54.2401			−2.29411
$560$	−0.486168	−	0.842068i	−0.0205444	−	0.0355839i
$561$		0			0
$562$	−12.4119	+	21.4981i	−0.523565	+	0.906841i
$563$	19.7884	−	34.2744i	0.833980	−	1.44450i	−0.0608787	−	0.998145i	$-0.519390\pi$
$563$	19.7884	−	34.2744i	0.833980	−	1.44450i	0.894858	−	0.446350i	$-0.147276\pi$
$564$		0			0
$565$	−4.69294	−	8.12841i	−0.197433	−	0.341965i
$566$	−17.1124			−0.719290
$567$		0			0
$568$	−5.93089			−0.248855
$569$	11.3717	+	19.6963i	0.476725	+	0.825711i	0.999644	−	0.0266706i	$-0.00849052\pi$
$569$	11.3717	+	19.6963i	0.476725	+	0.825711i	−0.522920	+	0.852382i	$0.675157\pi$
$570$		0			0
$571$	−3.89161	+	6.74046i	−0.162859	+	0.282079i	−0.935893	−	0.352285i	$-0.885405\pi$
$571$	−3.89161	+	6.74046i	−0.162859	+	0.282079i	0.773034	+	0.634364i	$0.218738\pi$
$572$	10.9142	−	18.9039i	0.456345	−	0.790412i
$573$		0			0
$574$	−0.830688	−	1.43879i	−0.0346723	−	0.0600541i
$575$	1.07839			0.0449720
$576$		0			0
$577$	−36.0241			−1.49970			−0.749852	−	0.661605i	$-0.769875\pi$
$577$	−36.0241			−1.49970			−0.749852	+	0.661605i	$0.769875\pi$
$578$	−0.987249	−	1.70997i	−0.0410642	−	0.0711252i
$579$		0			0
$580$	−8.86448	+	15.3537i	−0.368078	+	0.637529i
$581$	−0.469480	+	0.813162i	−0.0194773	+	0.0337357i
$582$		0			0
$583$	0.923760	+	1.60000i	0.0382582	+	0.0662652i
$584$	6.59667			0.272972
$585$		0			0
$586$	−2.24941			−0.0929222
$587$	−2.50701	−	4.34226i	−0.103475	−	0.179224i	0.809639	−	0.586928i	$-0.199663\pi$
$587$	−2.50701	−	4.34226i	−0.103475	−	0.179224i	−0.913114	+	0.407704i	$0.866330\pi$
$588$		0			0
$589$	−21.2489	+	36.8041i	−0.875544	+	1.51649i
$590$	−2.74285	+	4.75076i	−0.112921	+	0.195586i
$591$		0			0
$592$	4.56106	+	7.89998i	0.187458	+	0.324687i
$593$	13.7000			0.562594			0.281297	−	0.959621i	$-0.409235\pi$
$593$	13.7000			0.562594			0.281297	+	0.959621i	$0.409235\pi$
$594$		0			0
$595$	−4.23547			−0.173637
$596$	−4.13281	−	7.15824i	−0.169287	−	0.293213i
$597$		0			0
$598$	2.84575	−	4.92899i	0.116372	−	0.201561i
$599$	0.508335	−	0.880463i	0.0207700	−	0.0359747i	−0.855454	−	0.517880i	$-0.826722\pi$
$599$	0.508335	−	0.880463i	0.0207700	−	0.0359747i	0.876224	+	0.481905i	$0.160055\pi$
$600$		0			0
$601$	−0.747033	−	1.29390i	−0.0304721	−	0.0527792i	0.850387	−	0.526157i	$-0.176368\pi$
$601$	−0.747033	−	1.29390i	−0.0304721	−	0.0527792i	−0.880859	+	0.473378i	$0.843034\pi$
$602$	4.67926			0.190712
$603$		0			0
$604$	6.07515			0.247194
$605$	3.67262	+	6.36117i	0.149313	+	0.258618i
$606$		0			0
$607$	6.35637	−	11.0096i	0.257997	−	0.446864i	−0.707708	−	0.706505i	$-0.750271\pi$
$607$	6.35637	−	11.0096i	0.257997	−	0.446864i	0.965705	+	0.259641i	$0.0836041\pi$
$608$	−2.20147	+	3.81306i	−0.0892815	+	0.154640i
$609$		0			0
$610$	−2.79871	−	4.84750i	−0.113316	−	0.196270i
$611$	71.7994			2.90469
$612$		0			0
$613$	11.8172			0.477292			0.238646	−	0.971107i	$-0.423296\pi$
$613$	11.8172			0.477292			0.238646	+	0.971107i	$0.423296\pi$
$614$	−12.8245	−	22.2127i	−0.517555	−	0.896431i
$615$		0			0
$616$	−0.941560	+	1.63083i	−0.0379365	+	0.0657080i
$617$	−19.1596	+	33.1854i	−0.771336	+	1.33599i	0.165495	+	0.986211i	$0.447078\pi$
$617$	−19.1596	+	33.1854i	−0.771336	+	1.33599i	−0.936831	+	0.349782i	$0.886256\pi$
$618$		0			0
$619$	−8.98993	−	15.5710i	−0.361336	−	0.625852i	0.626845	−	0.779144i	$-0.284346\pi$
$619$	−8.98993	−	15.5710i	−0.361336	−	0.625852i	−0.988181	+	0.153292i	$0.951013\pi$
$620$	−19.1141			−0.767643
$621$		0			0
$622$	−19.8564			−0.796168
$623$	1.26994	+	2.19960i	0.0508791	+	0.0881252i
$624$		0			0
$625$	9.22256	−	15.9739i	0.368902	−	0.638958i
$626$	−5.45361	+	9.44593i	−0.217970	+	0.377535i
$627$		0			0
$628$	−3.82728	−	6.62905i	−0.152725	−	0.264528i
$629$	39.7357			1.58437
$630$		0			0
$631$	15.9861			0.636398			0.318199	−	0.948024i	$-0.396922\pi$
$631$	15.9861			0.636398			0.318199	+	0.948024i	$0.396922\pi$
$632$	6.68166	+	11.5730i	0.265782	+	0.460348i
$633$		0			0
$634$	8.28174	−	14.3444i	0.328910	−	0.569689i
$635$	5.81809	−	10.0772i	0.230884	−	0.399903i
$636$		0			0
$637$	19.2342	+	33.3146i	0.762087	+	1.31997i
$638$	34.3356			1.35936
$639$		0			0
$640$	−1.98031			−0.0782784
$641$	12.8109	+	22.1892i	0.506002	+	0.876421i	0.999976	+	0.00694409i	$0.00221039\pi$
$641$	12.8109	+	22.1892i	0.506002	+	0.876421i	−0.493974	+	0.869477i	$0.664456\pi$
$642$		0			0
$643$	−2.27841	+	3.94632i	−0.0898517	+	0.155628i	−0.907448	−	0.420164i	$-0.861973\pi$
$643$	−2.27841	+	3.94632i	−0.0898517	+	0.155628i	0.817597	+	0.575791i	$0.195306\pi$
$644$	−0.245502	+	0.425221i	−0.00967412	+	0.0167561i
$645$		0			0
$646$	9.58955	+	16.6096i	0.377296	+	0.653496i
$647$	29.1999			1.14796			0.573982	−	0.818868i	$-0.305398\pi$
$647$	29.1999			1.14796			0.573982	+	0.818868i	$0.305398\pi$
$648$		0			0
$649$	10.6241			0.417034
$650$	3.06883	+	5.31537i	0.120370	+	0.208486i
$651$		0			0
$652$	9.92782	−	17.1955i	0.388803	−	0.673427i
$653$	12.3427	−	21.3782i	0.483007	−	0.836592i	−0.516803	−	0.856104i	$-0.672878\pi$
$653$	12.3427	−	21.3782i	0.483007	−	0.836592i	0.999810	+	0.0195123i	$0.00621135\pi$
$654$		0			0
$655$	−2.31422	−	4.00835i	−0.0904241	−	0.156619i
$656$	−3.38364			−0.132109
$657$		0			0
$658$	−6.19409			−0.241471
$659$	2.39420	+	4.14688i	0.0932649	+	0.161539i	0.908883	−	0.417051i	$-0.136936\pi$
$659$	2.39420	+	4.14688i	0.0932649	+	0.161539i	−0.815618	+	0.578590i	$0.803603\pi$
$660$		0			0
$661$	−17.3401	+	30.0340i	−0.674453	+	1.16819i	0.302176	+	0.953252i	$0.402287\pi$
$661$	−17.3401	+	30.0340i	−0.674453	+	1.16819i	−0.976629	+	0.214934i	$0.931046\pi$
$662$	0.974042	−	1.68709i	0.0378572	−	0.0655706i
$663$		0			0
$664$	0.956164	+	1.65612i	0.0371064	+	0.0642701i
$665$	4.28114			0.166016
$666$		0			0
$667$	8.95264			0.346648
$668$	2.18300	+	3.78106i	0.0844628	+	0.146294i
$669$		0			0
$670$	−0.486168	+	0.842068i	−0.0187823	+	0.0325319i
$671$	−5.42024	+	9.38814i	−0.209246	+	0.362425i
$672$		0			0
$673$	15.6099	+	27.0372i	0.601719	+	1.04221i	0.992561	+	0.121750i	$0.0388506\pi$
$673$	15.6099	+	27.0372i	0.601719	+	1.04221i	−0.390842	+	0.920458i	$0.627816\pi$
$674$	3.37795			0.130114
$675$		0			0
$676$	19.3933			0.745895
$677$	−11.3284	−	19.6214i	−0.435387	−	0.754112i	0.561940	−	0.827178i	$-0.310055\pi$
$677$	−11.3284	−	19.6214i	−0.435387	−	0.754112i	−0.997327	+	0.0730658i	$0.976722\pi$
$678$		0			0
$679$	−3.17989	+	5.50774i	−0.122033	+	0.211368i
$680$	−4.31308	+	7.47047i	−0.165399	+	0.286479i
$681$		0			0
$682$	18.5091	+	32.0588i	0.708752	+	1.22759i
$683$	−4.28796			−0.164074			−0.0820371	−	0.996629i	$-0.526143\pi$
$683$	−4.28796			−0.164074			−0.0820371	+	0.996629i	$0.526143\pi$
$684$		0			0
$685$	5.16135			0.197205
$686$	−3.37784	−	5.85058i	−0.128966	−	0.223376i
$687$		0			0
$688$	4.76500	−	8.25323i	0.181664	−	0.314651i
$689$	−1.37086	+	2.37440i	−0.0522256	+	0.0904574i
$690$		0			0
$691$	13.6137	+	23.5797i	0.517891	+	0.897014i	0.999784	+	0.0207838i	$0.00661616\pi$
$691$	13.6137	+	23.5797i	0.517891	+	0.897014i	−0.481893	+	0.876230i	$0.660051\pi$
$692$	−6.84585			−0.260240
$693$		0			0
$694$	−10.5521			−0.400552
$695$	−10.7490	−	18.6178i	−0.407732	−	0.706212i
$696$		0			0
$697$	−7.36951	+	12.7644i	−0.279140	+	0.483485i
$698$	−0.196204	+	0.339835i	−0.00742642	+	0.0128629i
$699$		0			0
$700$	−0.264746	−	0.458554i	−0.0100065	−	0.0173317i
$701$	−29.0558			−1.09742			−0.548711	−	0.836012i	$-0.684881\pi$
$701$	−29.0558			−1.09742			−0.548711	+	0.836012i	$0.684881\pi$
$702$		0			0
$703$	−40.1642			−1.51482
$704$	1.91763	+	3.32142i	0.0722732	+	0.125181i
$705$		0			0
$706$	0.936949	−	1.62284i	0.0352625	−	0.0610765i
$707$	−3.45291	+	5.98062i	−0.129860	+	0.224924i
$708$		0			0
$709$	−3.10441	−	5.37700i	−0.116589	−	0.201938i	0.801825	−	0.597559i	$-0.203863\pi$
$709$	−3.10441	−	5.37700i	−0.116589	−	0.201938i	−0.918414	+	0.395621i	$0.870529\pi$
$710$	11.7450			0.440781
$711$		0			0
$712$	5.17284			0.193860
$713$	4.82606	+	8.35898i	0.180737	+	0.313046i
$714$		0			0
$715$	−21.6134	+	37.4355i	−0.808296	+	1.40001i
$716$	5.70147	−	9.87524i	0.213074	−	0.369055i
$717$		0			0
$718$	11.1723	+	19.3510i	0.416946	+	0.722172i
$719$	−2.20314			−0.0821633			−0.0410817	−	0.999156i	$-0.513080\pi$
$719$	−2.20314			−0.0821633			−0.0410817	+	0.999156i	$0.513080\pi$
$720$		0			0
$721$	8.13348			0.302906
$722$	−0.192954	−	0.334206i	−0.00718100	−	0.0124379i
$723$		0			0
$724$	−7.86912	+	13.6297i	−0.292454	+	0.506545i
$725$	−4.82722	+	8.36099i	−0.179278	+	0.310519i
$726$		0			0
$727$	−8.80940	−	15.2583i	−0.326723	−	0.565900i	0.655137	−	0.755510i	$-0.272611\pi$
$727$	−8.80940	−	15.2583i	−0.326723	−	0.565900i	−0.981859	+	0.189610i	$0.939278\pi$
$728$	−2.79455			−0.103573
$729$		0			0
$730$	−13.0634			−0.483499
$731$	−20.7562	−	35.9508i	−0.767697	−	1.32969i
$732$		0			0
$733$	25.4504	−	44.0815i	0.940033	−	1.62819i	0.174631	−	0.984634i	$-0.444127\pi$
$733$	25.4504	−	44.0815i	0.940033	−	1.62819i	0.765403	−	0.643552i	$-0.222540\pi$
$734$	7.49849	−	12.9878i	0.276774	−	0.479387i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	1.88312			0.0693656
$738$		0			0
$739$	6.05374			0.222690			0.111345	−	0.993782i	$-0.464484\pi$
$739$	6.05374			0.222690			0.111345	+	0.993782i	$0.464484\pi$
$740$	−9.03229	−	15.6444i	−0.332034	−	0.575099i
$741$		0			0
$742$	0.118263	−	0.204838i	0.00434158	−	0.00751984i
$743$	−23.4669	+	40.6459i	−0.860917	+	1.49115i	0.0101274	+	0.999949i	$0.496776\pi$
$743$	−23.4669	+	40.6459i	−0.860917	+	1.49115i	−0.871045	+	0.491204i	$0.836557\pi$
$744$		0			0
$745$	8.18423	+	14.1755i	0.299847	+	0.519350i
$746$	30.6303			1.12146
$747$		0			0
$748$	16.7062			0.610841
$749$	−1.52028	−	2.63320i	−0.0555497	−	0.0962150i
$750$		0			0
$751$	18.6436	−	32.2917i	0.680315	−	1.17834i	−0.294570	−	0.955630i	$-0.595176\pi$
$751$	18.6436	−	32.2917i	0.680315	−	1.17834i	0.974885	−	0.222710i	$-0.0714903\pi$
$752$	−6.30759	+	10.9251i	−0.230014	+	0.398396i
$753$		0			0
$754$	25.4770	+	44.1275i	0.927818	+	1.60703i
$755$	−12.0306			−0.437840
$756$		0			0
$757$	−45.8083			−1.66493			−0.832465	−	0.554077i	$-0.813071\pi$
$757$	−45.8083			−1.66493			−0.832465	+	0.554077i	$0.813071\pi$
$758$	−9.10458	−	15.7696i	−0.330693	−	0.572778i
$759$		0			0
$760$	4.35959	−	7.55102i	0.158139	−	0.273904i
$761$	−8.32774	+	14.4241i	−0.301880	+	0.522872i	−0.976562	−	0.215237i	$-0.930948\pi$
$761$	−8.32774	+	14.4241i	−0.301880	+	0.522872i	0.674681	+	0.738109i	$0.264281\pi$
$762$		0			0
$763$	1.14722	+	1.98704i	0.0415320	+	0.0719355i
$764$	17.7415			0.641865
$765$		0			0
$766$	26.4213			0.954640
$767$	7.88311	+	13.6539i	0.284643	+	0.493015i
$768$		0			0
$769$	11.3048	−	19.5805i	0.407663	−	0.706092i	−0.586965	−	0.809612i	$-0.699677\pi$
$769$	11.3048	−	19.5805i	0.407663	−	0.706092i	0.994627	+	0.103520i	$0.0330106\pi$
$770$	1.86458	−	3.22954i	0.0671947	−	0.116385i
$771$		0			0
$772$	2.95227	+	5.11348i	0.106255	+	0.184038i
$773$	−39.7217			−1.42869			−0.714345	−	0.699794i	$-0.753275\pi$
$773$	−39.7217			−1.42869			−0.714345	+	0.699794i	$0.753275\pi$
$774$		0			0
$775$	−10.4087			−0.373893
$776$	6.47632	+	11.2173i	0.232486	+	0.402678i
$777$		0			0
$778$	5.03171	−	8.71518i	0.180396	−	0.312454i
$779$	7.44898	−	12.9020i	0.266887	−	0.462263i
$780$		0			0
$781$	−11.3732	−	19.6990i	−0.406966	−	0.704886i
$782$	4.35597			0.155769
$783$		0			0
$784$	−6.75892			−0.241390
$785$	7.57919	+	13.1275i	0.270513	+	0.468542i
$786$		0			0
$787$	5.07395	−	8.78834i	0.180867	−	0.313270i	−0.761309	−	0.648389i	$-0.775443\pi$
$787$	5.07395	−	8.78834i	0.180867	−	0.313270i	0.942176	+	0.335119i	$0.108776\pi$
$788$	5.01474	−	8.68579i	0.178643	−	0.309419i
$789$		0			0
$790$	−13.2317	−	22.9180i	−0.470764	−	0.815387i
$791$	2.32716			0.0827444
$792$		0			0
$793$	−16.0873			−0.571276
$794$	−5.01913	−	8.69339i	−0.178122	−	0.308517i
$795$		0			0
$796$	9.32672	−	16.1543i	0.330577	−	0.572576i
$797$	1.73392	−	3.00323i	0.0614185	−	0.106380i	−0.833681	−	0.552246i	$-0.813771\pi$
$797$	1.73392	−	3.00323i	0.0614185	−	0.106380i	0.895100	+	0.445866i	$0.147104\pi$
$798$		0			0
$799$	27.4757	+	47.5893i	0.972020	+	1.68359i
$800$	−1.07839			−0.0381268
$801$		0			0
$802$	−35.1645			−1.24170
$803$	12.6499	+	21.9103i	0.446407	+	0.773199i
$804$		0			0
$805$	0.486168	−	0.842068i	0.0171352	−	0.0296790i
$806$	−27.4676	+	47.5752i	−0.967504	+	1.67577i
$807$		0			0
$808$	7.03237	+	12.1804i	0.247398	+	0.428506i
$809$	46.5003			1.63486			0.817431	−	0.576027i	$-0.195398\pi$
$809$	46.5003			1.63486			0.817431	+	0.576027i	$0.195398\pi$
$810$		0			0
$811$	−9.96119			−0.349785			−0.174892	−	0.984588i	$-0.555958\pi$
$811$	−9.96119			−0.349785			−0.174892	+	0.984588i	$0.555958\pi$
$812$	−2.19789	−	3.80685i	−0.0771307	−	0.133594i
$813$		0			0
$814$	−17.4928	+	30.2984i	−0.613122	+	1.06196i
$815$	−19.6601	+	34.0523i	−0.688664	+	1.19280i
$816$		0			0
$817$	20.9800	+	36.3385i	0.733998	+	1.27132i
$818$	7.08122			0.247589
$819$		0			0
$820$	6.70063			0.233996
$821$	−9.00462	−	15.5965i	−0.314263	−	0.544320i	0.665017	−	0.746828i	$-0.268424\pi$
$821$	−9.00462	−	15.5965i	−0.314263	−	0.544320i	−0.979281	+	0.202508i	$0.935091\pi$
$822$		0			0
$823$	21.9227	−	37.9712i	0.764176	−	1.32359i	−0.176505	−	0.984300i	$-0.556479\pi$
$823$	21.9227	−	37.9712i	0.764176	−	1.32359i	0.940681	−	0.339292i	$-0.110188\pi$
$824$	8.28251	−	14.3457i	0.288535	−	0.499757i
$825$		0			0
$826$	−0.680071	−	1.17792i	−0.0236627	−	0.0409850i
$827$	40.1574			1.39641			0.698205	−	0.715898i	$-0.253982\pi$
$827$	40.1574			1.39641			0.698205	+	0.715898i	$0.253982\pi$
$828$		0			0
$829$	35.0885			1.21868			0.609338	−	0.792911i	$-0.291435\pi$
$829$	35.0885			1.21868			0.609338	+	0.792911i	$0.291435\pi$
$830$	−1.89350	−	3.27963i	−0.0657242	−	0.113838i
$831$		0			0
$832$	−2.84575	+	4.92899i	−0.0986588	+	0.170882i
$833$	−14.7208	+	25.4972i	−0.510046	+	0.883426i
$834$		0			0
$835$	−4.32300	−	7.48766i	−0.149604	−	0.259121i
$836$	−16.8864			−0.584028
$837$		0			0
$838$	12.5277			0.432762
$839$	23.4482	+	40.6135i	0.809523	+	1.40214i	0.913195	+	0.407523i	$0.133608\pi$
$839$	23.4482	+	40.6135i	0.809523	+	1.40214i	−0.103672	+	0.994612i	$0.533059\pi$
$840$		0			0
$841$	−25.5749	+	44.2970i	−0.881893	+	1.52748i
$842$	16.2278	−	28.1074i	0.559248	−	0.968647i
$843$		0			0
$844$	4.71584	+	8.16808i	0.162326	+	0.281157i
$845$	−38.4046			−1.32116
$846$		0			0
$847$	−1.82120			−0.0625773
$848$	−0.240860	−	0.417183i	−0.00827118	−	0.0143261i
$849$		0			0
$850$	−2.34872	+	4.06810i	−0.0805604	+	0.139535i
$851$	−4.56106	+	7.89998i	−0.156351	+	0.270808i
$852$		0			0
$853$	−1.40121	−	2.42696i	−0.0479764	−	0.0830975i	0.841040	−	0.540973i	$-0.181944\pi$
$853$	−1.40121	−	2.42696i	−0.0479764	−	0.0830975i	−0.889016	+	0.457875i	$0.848611\pi$
$854$	1.38784			0.0474909
$855$		0			0
$856$	−6.19254			−0.211657
$857$	−11.4343	−	19.8048i	−0.390588	−	0.676518i	0.601940	−	0.798542i	$-0.294395\pi$
$857$	−11.4343	−	19.8048i	−0.390588	−	0.676518i	−0.992527	+	0.122024i	$0.961061\pi$
$858$		0			0
$859$	26.7021	−	46.2494i	0.911063	−	1.57801i	0.0984988	−	0.995137i	$-0.468596\pi$
$859$	26.7021	−	46.2494i	0.911063	−	1.57801i	0.812565	−	0.582871i	$-0.198071\pi$
$860$	−9.43616	+	16.3439i	−0.321770	+	0.557323i
$861$		0			0
$862$	−3.61401	−	6.25964i	−0.123094	−	0.213204i
$863$	31.9394			1.08723			0.543614	−	0.839335i	$-0.317055\pi$
$863$	31.9394			1.08723			0.543614	+	0.839335i	$0.317055\pi$
$864$		0			0
$865$	13.5569			0.460947
$866$	−18.5078	−	32.0565i	−0.628922	−	1.08932i
$867$		0			0
$868$	2.36961	−	4.10429i	0.0804298	−	0.139309i
$869$	−25.6258	+	44.3853i	−0.869297	+	1.50567i
$870$		0			0
$871$	1.39727	+	2.42015i	0.0473448	+	0.0820037i
$872$	4.67294			0.158246
$873$		0			0
$874$	−4.40294			−0.148932
$875$	2.95512	+	5.11842i	0.0999013	+	0.173034i
$876$		0			0
$877$	11.6178	−	20.1227i	0.392307	−	0.679495i	−0.600447	−	0.799665i	$-0.705011\pi$
$877$	11.6178	−	20.1227i	0.392307	−	0.679495i	0.992753	+	0.120170i	$0.0383439\pi$
$878$	9.41544	−	16.3080i	0.317756	−	0.550369i
$879$		0			0
$880$	−3.79748	−	6.57744i	−0.128013	−	0.221725i
$881$	−42.8183			−1.44259			−0.721293	−	0.692630i	$-0.756452\pi$
$881$	−42.8183			−1.44259			−0.721293	+	0.692630i	$0.756452\pi$
$882$		0			0
$883$	49.9493			1.68093			0.840465	−	0.541866i	$-0.182282\pi$
$883$	49.9493			1.68093			0.840465	+	0.541866i	$0.182282\pi$
$884$	12.3960	+	21.4706i	0.416924	+	0.722133i
$885$		0			0
$886$	−4.76549	+	8.25407i	−0.160100	+	0.277301i
$887$	9.77329	−	16.9278i	0.328155	−	0.568381i	−0.653991	−	0.756502i	$-0.726907\pi$
$887$	9.77329	−	16.9278i	0.328155	−	0.568381i	0.982146	+	0.188122i	$0.0602399\pi$
$888$		0			0
$889$	1.44256	+	2.49858i	0.0483818	+	0.0837997i
$890$	−10.2438			−0.343373
$891$		0			0
$892$	−3.44478			−0.115340
$893$	−27.7719	−	48.1024i	−0.929353	−	1.60969i
$894$		0			0
$895$	−11.2907	+	19.5560i	−0.377405	+	0.653685i
$896$	0.245502	−	0.425221i	0.00820163	−	0.0142056i
$897$		0			0
$898$	−3.55568	−	6.15861i	−0.118654	−	0.205516i
$899$	−86.4120			−2.88200
$900$		0			0
$901$	−2.09836			−0.0699066
$902$	−6.48855	−	11.2385i	−0.216045	−	0.374201i
$903$		0			0
$904$	2.36980	−	4.10462i	0.0788185	−	0.136518i
$905$	15.5833	−	26.9910i	0.518005	−	0.897212i
$906$		0			0
$907$	−27.0689	−	46.8848i	−0.898810	−	1.55678i	−0.829018	−	0.559223i	$-0.811100\pi$
$907$	−27.0689	−	46.8848i	−0.898810	−	1.55678i	−0.0697921	−	0.997562i	$-0.522234\pi$
$908$	17.3843			0.576919
$909$		0			0
$910$	5.53406			0.183452
$911$	−19.9195	−	34.5016i	−0.659963	−	1.14309i	−0.980625	−	0.195895i	$-0.937239\pi$
$911$	−19.9195	−	34.5016i	−0.659963	−	1.14309i	0.320662	−	0.947194i	$-0.396095\pi$
$912$		0			0
$913$	−3.66713	+	6.35165i	−0.121364	+	0.210209i
$914$	−2.76634	+	4.79144i	−0.0915024	+	0.158487i
$915$		0			0
$916$	−1.23488	−	2.13888i	−0.0408017	−	0.0706706i
$917$	1.14759			0.0378968
$918$		0			0
$919$	−32.7115			−1.07905			−0.539527	−	0.841968i	$-0.681397\pi$
$919$	−32.7115			−1.07905			−0.539527	+	0.841968i	$0.681397\pi$
$920$	−0.990153	−	1.71499i	−0.0326444	−	0.0565417i
$921$		0			0
$922$	−7.97263	+	13.8090i	−0.262564	+	0.454775i
$923$	16.8779	−	29.2333i	0.555542	−	0.962226i
$924$		0			0
$925$	−4.91860	−	8.51926i	−0.161723	−	0.280112i
$926$	−5.86441			−0.192716
$927$		0			0
$928$	−8.95264			−0.293885
$929$	18.6194	+	32.2497i	0.610881	+	1.05808i	0.991092	+	0.133177i	$0.0425180\pi$
$929$	18.6194	+	32.2497i	0.610881	+	1.05808i	−0.380211	+	0.924900i	$0.624149\pi$
$930$		0			0
$931$	14.8796	−	25.7722i	0.487658	−	0.844648i
$932$	3.72854	−	6.45802i	0.122132	−	0.211540i
$933$		0			0
$934$	2.91234	+	5.04432i	0.0952947	+	0.165055i
$935$	−33.0835			−1.08195
$936$		0			0
$937$	41.3670			1.35140			0.675700	−	0.737177i	$-0.263842\pi$
$937$	41.3670			1.35140			0.675700	+	0.737177i	$0.263842\pi$
$938$	−0.120542	−	0.208785i	−0.00393584	−	0.00681707i
$939$		0			0
$940$	12.4909	−	21.6350i	0.407410	−	0.705655i
$941$	3.96496	−	6.86751i	0.129254	−	0.223874i	−0.794134	−	0.607743i	$-0.792075\pi$
$941$	3.96496	−	6.86751i	0.129254	−	0.223874i	0.923388	+	0.383869i	$0.125408\pi$
$942$		0			0
$943$	−1.69182	−	2.93032i	−0.0550932	−	0.0954242i
$944$	−2.77013			−0.0901600
$945$		0			0
$946$	36.5500			1.18834
$947$	3.24044	+	5.61261i	0.105300	+	0.182385i	0.913861	−	0.406028i	$-0.133086\pi$
$947$	3.24044	+	5.61261i	0.105300	+	0.182385i	−0.808561	+	0.588413i	$0.799753\pi$
$948$		0			0
$949$	−18.7725	+	32.5149i	−0.609381	+	1.05548i
$950$	2.37404	−	4.11197i	0.0770242	−	0.133410i
$951$		0			0
$952$	−1.06940	−	1.85225i	−0.0346594	−	0.0600318i
$953$	3.25690			0.105501			0.0527507	−	0.998608i	$-0.483201\pi$
$953$	3.25690			0.105501			0.0527507	+	0.998608i	$0.483201\pi$
$954$		0			0
$955$	−35.1336			−1.13690
$956$	−13.0680	−	22.6345i	−0.422651	−	0.732052i
$957$		0			0
$958$	−11.3864	+	19.7218i	−0.367878	+	0.637184i
$959$	−0.639860	+	1.10827i	−0.0206622	+	0.0357879i
$960$		0			0
$961$	−31.0817	−	53.8351i	−1.00264	−	1.73662i
$962$	−51.9186			−1.67392
$963$		0			0
$964$	10.2952			0.331585
$965$	−5.84640	−	10.1263i	−0.188202	−	0.325976i
$966$		0			0
$967$	−2.46810	+	4.27487i	−0.0793686	+	0.137470i	−0.902978	−	0.429687i	$-0.858624\pi$
$967$	−2.46810	+	4.27487i	−0.0793686	+	0.137470i	0.823609	+	0.567158i	$0.191957\pi$
$968$	−1.85457	+	3.21222i	−0.0596083	+	0.103245i
$969$		0			0
$970$	−12.8251	−	22.2137i	−0.411789	−	0.713239i
$971$	−3.10588			−0.0996725			−0.0498363	−	0.998757i	$-0.515870\pi$
$971$	−3.10588			−0.0996725			−0.0498363	+	0.998757i	$0.515870\pi$
$972$		0			0
$973$	5.33027			0.170881
$974$	4.42093	+	7.65728i	0.141656	+	0.245355i
$975$		0			0
$976$	1.41327	−	2.44785i	0.0452377	−	0.0783539i
$977$	8.46066	−	14.6543i	0.270680	−	0.468832i	−0.698356	−	0.715751i	$-0.746085\pi$
$977$	8.46066	−	14.6543i	0.270680	−	0.468832i	0.969036	+	0.246918i	$0.0794180\pi$
$978$		0			0
$979$	9.91957	+	17.1812i	0.317031	+	0.549114i
$980$	13.3847			0.427559
$981$		0			0
$982$	−21.7066			−0.692686
$983$	−15.6073	−	27.0326i	−0.497794	−	0.862205i	0.502202	−	0.864750i	$-0.332523\pi$
$983$	−15.6073	−	27.0326i	−0.497794	−	0.862205i	−0.999997	+	0.00254491i	$0.999190\pi$
$984$		0			0
$985$	−9.93073	+	17.2005i	−0.316419	+	0.548054i
$986$	−19.4987	+	33.7728i	−0.620966	+	1.07554i
$987$		0			0
$988$	−12.5297	−	21.7021i	−0.398623	−	0.690435i
$989$	9.53000			0.303037
$990$		0			0
$991$	−8.49533			−0.269863			−0.134931	−	0.990855i	$-0.543081\pi$
$991$	−8.49533			−0.269863			−0.134931	+	0.990855i	$0.543081\pi$
$992$	−4.82606	−	8.35898i	−0.153228	−	0.265398i
$993$		0			0
$994$	−1.45604	+	2.52194i	−0.0461829	+	0.0799911i
$995$	−18.4697	+	31.9905i	−0.585530	+	1.01417i
$996$		0			0
$997$	16.7617	+	29.0321i	0.530848	+	0.919457i	0.999352	+	0.0359949i	$0.0114600\pi$
$997$	16.7617	+	29.0321i	0.530848	+	0.919457i	−0.468503	+	0.883462i	$0.655207\pi$
$998$	19.3425			0.612276
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1242.2.e.b.415.4		10
3.2	odd	2		414.2.e.d.139.3	✓	10
9.2	odd	6		414.2.e.d.277.3	yes	10
9.4	even	3		3726.2.a.u.1.2		5
9.5	odd	6		3726.2.a.r.1.4		5
9.7	even	3	inner	1242.2.e.b.829.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.3	✓	10	3.2	odd	2
414.2.e.d.277.3	yes	10	9.2	odd	6
1242.2.e.b.415.4		10	1.1	even	1	trivial
1242.2.e.b.829.4		10	9.7	even	3	inner
3726.2.a.r.1.4		5	9.5	odd	6
3726.2.a.u.1.2		5	9.4	even	3

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:	\( N \)	\(=\)	\( 1242 = 2 \cdot 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1242.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.990153 - 1.71499i) q^{5} +(0.245502 + 0.425221i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.990153 - 1.71499i) q^{5} +(0.245502 + 0.425221i) q^{7} +1.00000 q^{8} -1.98031 q^{10} +(1.91763 + 3.32142i) q^{11} +(-2.84575 + 4.92899i) q^{13} +(0.245502 - 0.425221i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.35597 q^{17} +4.40294 q^{19} +(0.990153 + 1.71499i) q^{20} +(1.91763 - 3.32142i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.539195 + 0.933913i) q^{25} +5.69151 q^{26} -0.491003 q^{28} +(4.47632 + 7.75322i) q^{29} +(-4.82606 + 8.35898i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.17799 + 3.77238i) q^{34} +0.972336 q^{35} -9.12212 q^{37} +(-2.20147 - 3.81306i) q^{38} +(0.990153 - 1.71499i) q^{40} +(1.69182 - 2.93032i) q^{41} +(4.76500 + 8.25323i) q^{43} -3.83525 q^{44} -1.00000 q^{46} +(-6.30759 - 10.9251i) q^{47} +(3.37946 - 5.85339i) q^{49} +(0.539195 - 0.933913i) q^{50} +(-2.84575 - 4.92899i) q^{52} +0.481721 q^{53} +7.59497 q^{55} +(0.245502 + 0.425221i) q^{56} +(4.47632 - 7.75322i) q^{58} +(1.38506 - 2.39900i) q^{59} +(1.41327 + 2.44785i) q^{61} +9.65212 q^{62} +1.00000 q^{64} +(5.63546 + 9.76091i) q^{65} +(0.245502 - 0.425221i) q^{67} +(2.17799 - 3.77238i) q^{68} +(-0.486168 - 0.842068i) q^{70} -5.93089 q^{71} +6.59667 q^{73} +(4.56106 + 7.89998i) q^{74} +(-2.20147 + 3.81306i) q^{76} +(-0.941560 + 1.63083i) q^{77} +(6.68166 + 11.5730i) q^{79} -1.98031 q^{80} -3.38364 q^{82} +(0.956164 + 1.65612i) q^{83} +(-4.31308 + 7.47047i) q^{85} +(4.76500 - 8.25323i) q^{86} +(1.91763 + 3.32142i) q^{88} +5.17284 q^{89} -2.79455 q^{91} +(0.500000 + 0.866025i) q^{92} +(-6.30759 + 10.9251i) q^{94} +(4.35959 - 7.55102i) q^{95} +(6.47632 + 11.2173i) q^{97} -6.75892 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

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