LMFDB - Embedded newform 1344.2.bb.f.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(31,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))

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

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

chi := DirichletCharacter("1344.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bb (of order $6$, degree $2$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.32905425960566784.37
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 $ x^12 + 36x^10 + 432x^8 + 2040x^6 + 3780x^4 + 2592*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$-0.802567i$ of defining polynomial
Character	$\chi$	$=$	1344.31
Dual form			1344.2.bb.f.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-1.29211 - 2.23800i) q^{5} +(-1.56777 - 2.13122i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(-1.29211 - 2.23800i) q^{5} +(-1.56777 - 2.13122i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.195786 + 0.339111i) q^{11} -1.67822 q^{13} -2.58423i q^{15} +(0.678221 + 0.391571i) q^{17} +(-4.19734 + 2.42334i) q^{19} +(-0.292113 - 2.62958i) q^{21} +(-4.47601 + 2.58423i) q^{23} +(-0.839111 + 1.45338i) q^{25} +1.00000i q^{27} -1.79505i q^{29} +(1.17619 - 2.03723i) q^{31} +(-0.339111 + 0.195786i) q^{33} +(-2.74396 + 6.26245i) q^{35} +(-4.83911 + 2.79386i) q^{37} +(-1.45338 - 0.839111i) q^{39} -4.24724i q^{41} -11.0756 q^{43} +(1.29211 - 2.23800i) q^{45} +(6.59963 + 11.4309i) q^{47} +(-2.08423 + 6.68251i) q^{49} +(0.391571 + 0.678221i) q^{51} +(-8.23278 - 4.75320i) q^{53} +1.01191 q^{55} -4.84667 q^{57} +(0.132786 + 0.0766640i) q^{59} +(-2.26245 - 3.91867i) q^{61} +(1.06181 - 2.42334i) q^{63} +(2.16845 + 3.75587i) q^{65} +(-2.46529 + 4.27001i) q^{67} -5.16845 q^{69} +0.524893i q^{71} +(-10.2700 - 5.92939i) q^{73} +(-1.45338 + 0.839111i) q^{75} +(1.02967 - 0.114383i) q^{77} +(-2.51667 + 1.45300i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.3716i q^{83} -2.02382i q^{85} +(0.897525 - 1.55456i) q^{87} +(10.8618 - 6.27106i) q^{89} +(2.63106 + 3.57666i) q^{91} +(2.03723 - 1.17619i) q^{93} +(10.8469 + 6.26245i) q^{95} -12.0245i q^{97} -0.391571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^9	$ 12 q + 6 q^{9} - 12 q^{13} + 12 q^{21} - 6 q^{25} - 54 q^{37} + 6 q^{49} - 36 q^{53} + 12 q^{57} + 12 q^{61} - 36 q^{65} - 18 q^{73} + 36 q^{77} - 6 q^{81} - 72 q^{89} - 18 q^{93}+O(q^{100}) $ 12 * q + 6 * q^9 - 12 * q^13 + 12 * q^21 - 6 * q^25 - 54 * q^37 + 6 * q^49 - 36 * q^53 + 12 * q^57 + 12 * q^61 - 36 * q^65 - 18 * q^73 + 36 * q^77 - 6 * q^81 - 72 * q^89 - 18 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−1.29211	−	2.23800i	−0.577850	−	1.00087i	−0.995726	−	0.0923617i	$-0.970558\pi$
$5$	−1.29211	−	2.23800i	−0.577850	−	1.00087i	0.417875	−	0.908504i	$-0.362775\pi$
$6$		0			0
$7$	−1.56777	−	2.13122i	−0.592559	−	0.805527i
$7$	−1.56777	−	2.13122i	−0.592559	−	0.805527i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.195786	+	0.339111i	−0.0590316	+	0.102246i	−0.894031	−	0.448005i	$-0.852135\pi$
$11$	−0.195786	+	0.339111i	−0.0590316	+	0.102246i	0.834999	+	0.550251i	$0.185468\pi$
$12$		0			0
$13$	−1.67822			−0.465455			−0.232727	−	0.972542i	$-0.574765\pi$
$13$	−1.67822			−0.465455			−0.232727	+	0.972542i	$0.574765\pi$
$14$		0			0
$15$		−	2.58423i		−	0.667244i
$16$		0			0
$17$	0.678221	+	0.391571i	0.164493	+	0.0949700i	0.579986	−	0.814626i	$-0.303058\pi$
$17$	0.678221	+	0.391571i	0.164493	+	0.0949700i	−0.415494	+	0.909596i	$0.636391\pi$
$18$		0			0
$19$	−4.19734	+	2.42334i	−0.962936	+	0.555951i	−0.897075	−	0.441877i	$-0.854313\pi$
$19$	−4.19734	+	2.42334i	−0.962936	+	0.555951i	−0.0658606	+	0.997829i	$0.520979\pi$
$20$		0			0
$21$	−0.292113	−	2.62958i	−0.0637442	−	0.573821i
$22$		0			0
$23$	−4.47601	+	2.58423i	−0.933313	+	0.538848i	−0.887858	−	0.460118i	$-0.847807\pi$
$23$	−4.47601	+	2.58423i	−0.933313	+	0.538848i	−0.0454549	+	0.998966i	$0.514474\pi$
$24$		0			0
$25$	−0.839111	+	1.45338i	−0.167822	+	0.290676i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	1.79505i		−	0.333333i	−0.986013	−	0.166666i	$-0.946700\pi$
$29$		−	1.79505i		−	0.333333i	0.986013	−	0.166666i	$-0.0533002\pi$
$30$		0			0
$31$	1.17619	−	2.03723i	0.211251	−	0.365897i	−0.740856	−	0.671664i	$-0.765580\pi$
$31$	1.17619	−	2.03723i	0.211251	−	0.365897i	0.952106	+	0.305768i	$0.0989130\pi$
$32$		0			0
$33$	−0.339111	+	0.195786i	−0.0590316	+	0.0340819i
$34$		0			0
$35$	−2.74396	+	6.26245i	−0.463814	+	1.05855i
$36$		0			0
$37$	−4.83911	+	2.79386i	−0.795545	+	0.459308i	−0.841911	−	0.539616i	$-0.818569\pi$
$37$	−4.83911	+	2.79386i	−0.795545	+	0.459308i	0.0463661	+	0.998925i	$0.485236\pi$
$38$		0			0
$39$	−1.45338	−	0.839111i	−0.232727	−	0.134365i
$40$		0			0
$41$		−	4.24724i		−	0.663308i	−0.943401	−	0.331654i	$-0.892393\pi$
$41$		−	4.24724i		−	0.663308i	0.943401	−	0.331654i	$-0.107607\pi$
$42$		0			0
$43$	−11.0756			−1.68902			−0.844510	−	0.535540i	$-0.820108\pi$
$43$	−11.0756			−1.68902			−0.844510	+	0.535540i	$0.820108\pi$
$44$		0			0
$45$	1.29211	−	2.23800i	0.192617	−	0.333622i
$46$		0			0
$47$	6.59963	+	11.4309i	0.962655	+	1.66737i	0.715787	+	0.698319i	$0.246068\pi$
$47$	6.59963	+	11.4309i	0.962655	+	1.66737i	0.246868	+	0.969049i	$0.420599\pi$
$48$		0			0
$49$	−2.08423	+	6.68251i	−0.297746	+	0.954645i
$50$		0			0
$51$	0.391571	+	0.678221i	0.0548309	+	0.0949700i
$52$		0			0
$53$	−8.23278	−	4.75320i	−1.13086	−	0.652902i	−0.186708	−	0.982415i	$-0.559782\pi$
$53$	−8.23278	−	4.75320i	−1.13086	−	0.652902i	−0.944151	+	0.329513i	$0.893115\pi$
$54$		0			0
$55$	1.01191			0.136446
$56$		0			0
$57$	−4.84667			−0.641957
$58$		0			0
$59$	0.132786	+	0.0766640i	0.0172873	+	0.00998080i	0.508619	−	0.860992i	$-0.330156\pi$
$59$	0.132786	+	0.0766640i	0.0172873	+	0.00998080i	−0.491331	+	0.870973i	$0.663490\pi$
$60$		0			0
$61$	−2.26245	−	3.91867i	−0.289677	−	0.501735i	0.684056	−	0.729430i	$-0.260214\pi$
$61$	−2.26245	−	3.91867i	−0.289677	−	0.501735i	−0.973733	+	0.227695i	$0.926881\pi$
$62$		0			0
$63$	1.06181	−	2.42334i	0.133776	−	0.305312i
$64$		0			0
$65$	2.16845	+	3.75587i	0.268963	+	0.465858i
$66$		0			0
$67$	−2.46529	+	4.27001i	−0.301183	+	0.521665i	−0.976404	−	0.215951i	$-0.930715\pi$
$67$	−2.46529	+	4.27001i	−0.301183	+	0.521665i	0.675221	+	0.737615i	$0.264048\pi$
$68$		0			0
$69$	−5.16845			−0.622208
$70$		0			0
$71$			0.524893i			0.0622934i	0.999515	+	0.0311467i	$0.00991590\pi$
$71$			0.524893i			0.0622934i	−0.999515	+	0.0311467i	$0.990084\pi$
$72$		0			0
$73$	−10.2700	−	5.92939i	−1.20201	−	0.693983i	−0.241011	−	0.970522i	$-0.577479\pi$
$73$	−10.2700	−	5.92939i	−1.20201	−	0.693983i	−0.961003	+	0.276540i	$0.910812\pi$
$74$		0			0
$75$	−1.45338	+	0.839111i	−0.167822	+	0.0968921i
$76$		0			0
$77$	1.02967	−	0.114383i	0.117341	−	0.0130351i
$78$		0			0
$79$	−2.51667	+	1.45300i	−0.283148	+	0.163476i	−0.634848	−	0.772637i	$-0.718937\pi$
$79$	−2.51667	+	1.45300i	−0.283148	+	0.163476i	0.351700	+	0.936113i	$0.385604\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			12.3716i			1.35796i	0.734159	+	0.678978i	$0.237577\pi$
$83$			12.3716i			1.35796i	−0.734159	+	0.678978i	$0.762423\pi$
$84$		0			0
$85$		−	2.02382i		−	0.219514i
$86$		0			0
$87$	0.897525	−	1.55456i	0.0962248	−	0.166666i
$88$		0			0
$89$	10.8618	−	6.27106i	1.15135	−	0.664731i	0.202133	−	0.979358i	$-0.435213\pi$
$89$	10.8618	−	6.27106i	1.15135	−	0.664731i	0.949215	+	0.314627i	$0.101879\pi$
$90$		0			0
$91$	2.63106	+	3.57666i	0.275810	+	0.374936i
$92$		0			0
$93$	2.03723	−	1.17619i	0.211251	−	0.121966i
$94$		0			0
$95$	10.8469	+	6.26245i	1.11287	+	0.642513i
$96$		0			0
$97$		−	12.0245i		−	1.22091i	−0.792052	−	0.610454i	$-0.790987\pi$
$97$		−	12.0245i		−	1.22091i	0.792052	−	0.610454i	$-0.209013\pi$
$98$		0			0
$99$	−0.391571			−0.0393544
$100$		0			0
$101$	5.58423	−	9.67216i	0.555651	−	0.962416i	−0.442201	−	0.896916i	$-0.645802\pi$
$101$	5.58423	−	9.67216i	0.555651	−	0.962416i	0.997853	−	0.0655003i	$-0.0208643\pi$
$102$		0			0
$103$	0.278669	+	0.482668i	0.0274580	+	0.0475587i	0.879428	−	0.476032i	$-0.157925\pi$
$103$	0.278669	+	0.482668i	0.0274580	+	0.0475587i	−0.851970	+	0.523591i	$0.824592\pi$
$104$		0			0
$105$	−5.50756	+	4.05146i	−0.537483	+	0.395382i
$106$		0			0
$107$	−6.79542	−	11.7700i	−0.656938	−	1.13785i	−0.981404	−	0.191952i	$-0.938518\pi$
$107$	−6.79542	−	11.7700i	−0.656938	−	1.13785i	0.324466	−	0.945897i	$-0.394815\pi$
$108$		0			0
$109$	−14.9136	−	8.61035i	−1.42846	−	0.824722i	−0.431461	−	0.902132i	$-0.642002\pi$
$109$	−14.9136	−	8.61035i	−1.42846	−	0.824722i	−0.996999	+	0.0774095i	$0.975335\pi$
$110$		0			0
$111$	−5.58772			−0.530363
$112$		0			0
$113$	17.6933			1.66445			0.832225	−	0.554438i	$-0.187067\pi$
$113$	17.6933			1.66445			0.832225	+	0.554438i	$0.187067\pi$
$114$		0			0
$115$	11.5670	+	6.67822i	1.07863	+	0.622747i
$116$		0			0
$117$	−0.839111	−	1.45338i	−0.0775758	−	0.134365i
$118$		0			0
$119$	−0.228766	−	2.05933i	−0.0209709	−	0.188779i
$120$		0			0
$121$	5.42334	+	9.39349i	0.493031	+	0.853954i
$122$		0			0
$123$	2.12362	−	3.67822i	0.191481	−	0.331654i
$124$		0			0
$125$	−8.58423			−0.767796
$126$		0			0
$127$		−	14.7873i		−	1.31216i	−0.754690	−	0.656082i	$-0.772212\pi$
$127$		−	14.7873i		−	1.31216i	0.754690	−	0.656082i	$-0.227788\pi$
$128$		0			0
$129$	−9.59179	−	5.53782i	−0.844510	−	0.487578i
$130$		0			0
$131$	−3.88865	+	2.24511i	−0.339753	+	0.196157i	−0.660163	−	0.751122i	$-0.729513\pi$
$131$	−3.88865	+	2.24511i	−0.339753	+	0.196157i	0.320410	+	0.947279i	$0.396179\pi$
$132$		0			0
$133$	11.7451	+	5.14625i	1.01843	+	0.446236i
$134$		0			0
$135$	2.23800	−	1.29211i	0.192617	−	0.111207i
$136$		0			0
$137$	6.52489	−	11.3014i	0.557459	−	0.965548i	−0.440248	−	0.897876i	$-0.645110\pi$
$137$	6.52489	−	11.3014i	0.557459	−	0.965548i	0.997708	−	0.0676717i	$-0.0215571\pi$
$138$		0			0
$139$		−	17.1836i		−	1.45749i	−0.684784	−	0.728746i	$-0.740104\pi$
$139$		−	17.1836i		−	1.45749i	0.684784	−	0.728746i	$-0.259896\pi$
$140$		0			0
$141$			13.1993i			1.11158i
$142$		0			0
$143$	0.328571	−	0.569103i	0.0274765	−	0.0475907i
$144$		0			0
$145$	−4.01733	+	2.31941i	−0.333621	+	0.192616i
$146$		0			0
$147$	−5.14625	+	4.74511i	−0.424456	+	0.391370i
$148$		0			0
$149$	−5.32178	+	3.07253i	−0.435977	+	0.251712i	−0.701890	−	0.712286i	$-0.747660\pi$
$149$	−5.32178	+	3.07253i	−0.435977	+	0.251712i	0.265913	+	0.963997i	$0.414327\pi$
$150$		0			0
$151$	−3.97006	−	2.29211i	−0.323079	−	0.186529i	0.329685	−	0.944091i	$-0.393057\pi$
$151$	−3.97006	−	2.29211i	−0.323079	−	0.186529i	−0.652764	+	0.757561i	$0.726391\pi$
$152$		0			0
$153$			0.783142i			0.0633133i
$154$		0			0
$155$	−6.07910			−0.488285
$156$		0			0
$157$	7.67822	−	13.2991i	0.612789	−	1.06138i	−0.377979	−	0.925814i	$-0.623381\pi$
$157$	7.67822	−	13.2991i	0.612789	−	1.06138i	0.990768	−	0.135567i	$-0.0432857\pi$
$158$		0			0
$159$	−4.75320	−	8.23278i	−0.376953	−	0.652902i
$160$		0			0
$161$	12.5249	+	5.48792i	0.987100	+	0.432509i
$162$		0			0
$163$	8.00311	+	13.8618i	0.626852	+	1.08574i	0.988180	+	0.153301i	$0.0489903\pi$
$163$	8.00311	+	13.8618i	0.626852	+	1.08574i	−0.361328	+	0.932439i	$0.617676\pi$
$164$		0			0
$165$	0.876338	+	0.505954i	0.0682228	+	0.0393885i
$166$		0			0
$167$	4.24724			0.328662			0.164331	−	0.986405i	$-0.447454\pi$
$167$	4.24724			0.328662			0.164331	+	0.986405i	$0.447454\pi$
$168$		0			0
$169$	−10.1836			−0.783352
$170$		0			0
$171$	−4.19734	−	2.42334i	−0.320979	−	0.185317i
$172$		0			0
$173$	9.26245	+	16.0430i	0.704211	+	1.21973i	0.966976	+	0.254869i	$0.0820323\pi$
$173$	9.26245	+	16.0430i	0.704211	+	1.21973i	−0.262765	+	0.964860i	$0.584634\pi$
$174$		0			0
$175$	4.41301	−	0.490230i	0.333592	−	0.0370579i
$176$		0			0
$177$	0.0766640	+	0.132786i	0.00576242	+	0.00998080i
$178$		0			0
$179$	8.66025	−	15.0000i	0.647298	−	1.12115i	−0.336468	−	0.941695i	$-0.609232\pi$
$179$	8.66025	−	15.0000i	0.647298	−	1.12115i	0.983766	−	0.179458i	$-0.0574343\pi$
$180$		0			0
$181$	17.1836			1.27724			0.638622	−	0.769520i	$-0.279505\pi$
$181$	17.1836			1.27724			0.638622	+	0.769520i	$0.279505\pi$
$182$		0			0
$183$		−	4.52489i		−	0.334490i
$184$		0			0
$185$	12.5054	+	7.21997i	0.919412	+	0.530823i
$186$		0			0
$187$	−0.265572	+	0.153328i	−0.0194205	+	0.0112125i
$188$		0			0
$189$	2.13122	−	1.56777i	0.155024	−	0.114038i
$190$		0			0
$191$	−15.3229	+	8.84667i	−1.10873	+	0.640123i	−0.938499	−	0.345282i	$-0.887783\pi$
$191$	−15.3229	+	8.84667i	−1.10873	+	0.640123i	−0.170226	+	0.985405i	$0.554450\pi$
$192$		0			0
$193$	−3.08423	+	5.34204i	−0.222007	+	0.384528i	−0.955417	−	0.295258i	$-0.904594\pi$
$193$	−3.08423	+	5.34204i	−0.222007	+	0.384528i	0.733410	+	0.679787i	$0.237928\pi$
$194$		0			0
$195$			4.33690i			0.310572i
$196$		0			0
$197$			25.6154i			1.82502i	0.409054	+	0.912510i	$0.365859\pi$
$197$			25.6154i			1.82502i	−0.409054	+	0.912510i	$0.634141\pi$
$198$		0			0
$199$	0.0629997	−	0.109119i	0.00446593	−	0.00773521i	−0.863784	−	0.503863i	$-0.831912\pi$
$199$	0.0629997	−	0.109119i	0.00446593	−	0.00773521i	0.868250	+	0.496127i	$0.165245\pi$
$200$		0			0
$201$	−4.27001	+	2.46529i	−0.301183	+	0.173888i
$202$		0			0
$203$	−3.82565	+	2.81422i	−0.268508	+	0.197519i
$204$		0			0
$205$	−9.50535	+	5.48792i	−0.663883	+	0.383293i
$206$		0			0
$207$	−4.47601	−	2.58423i	−0.311104	−	0.179616i
$208$		0			0
$209$		−	1.89782i		−	0.131275i
$210$		0			0
$211$	−8.82602			−0.607608			−0.303804	−	0.952735i	$-0.598257\pi$
$211$	−8.82602			−0.607608			−0.303804	+	0.952735i	$0.598257\pi$
$212$		0			0
$213$	−0.262447	+	0.454571i	−0.0179825	+	0.0311467i
$214$		0			0
$215$	14.3110	+	24.7873i	0.976001	+	1.69048i
$216$		0			0
$217$	−6.18578	+	0.687162i	−0.419918	+	0.0466476i
$218$		0			0
$219$	−5.92939	−	10.2700i	−0.400671	−	0.693983i
$220$		0			0
$221$	−1.13821	−	0.657143i	−0.0765640	−	0.0442042i
$222$		0			0
$223$	−19.1156			−1.28007			−0.640036	−	0.768345i	$-0.721081\pi$
$223$	−19.1156			−1.28007			−0.640036	+	0.768345i	$0.721081\pi$
$224$		0			0
$225$	−1.67822			−0.111881
$226$		0			0
$227$	19.9317	+	11.5076i	1.32291	+	0.763784i	0.984192	−	0.177104i	$-0.0566728\pi$
$227$	19.9317	+	11.5076i	1.32291	+	0.763784i	0.338720	+	0.940887i	$0.390006\pi$
$228$		0			0
$229$	3.10156	+	5.37205i	0.204957	+	0.354995i	0.950119	−	0.311888i	$-0.100961\pi$
$229$	3.10156	+	5.37205i	0.204957	+	0.354995i	−0.745162	+	0.666883i	$0.767628\pi$
$230$		0			0
$231$	0.948908	+	0.415775i	0.0624336	+	0.0273560i
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$	17.0549	−	29.5400i	1.11254	−	1.92698i
$236$		0			0
$237$	−2.90600			−0.188765
$238$		0			0
$239$			10.8618i			0.702591i	0.936265	+	0.351296i	$0.114259\pi$
$239$			10.8618i			0.702591i	−0.936265	+	0.351296i	$0.885741\pi$
$240$		0			0
$241$	−2.66089	−	1.53627i	−0.171403	−	0.0989595i	0.411844	−	0.911254i	$-0.364885\pi$
$241$	−2.66089	−	1.53627i	−0.171403	−	0.0989595i	−0.583247	+	0.812295i	$0.698218\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	17.6486	−	3.97006i	1.12752	−	0.253638i
$246$		0			0
$247$	7.04407	−	4.06689i	0.448203	−	0.258770i
$248$		0			0
$249$	−6.18578	+	10.7141i	−0.392008	+	0.678978i
$250$		0			0
$251$		−	21.0844i		−	1.33084i	−0.746470	−	0.665419i	$-0.768253\pi$
$251$		−	21.0844i		−	1.33084i	0.746470	−	0.665419i	$-0.231747\pi$
$252$		0			0
$253$		−	2.02382i		−	0.127236i
$254$		0			0
$255$	1.01191	−	1.75268i	0.0633681	−	0.109757i
$256$		0			0
$257$	−23.8271	+	13.7566i	−1.48630	+	0.858113i	−0.999878	−	0.0156133i	$-0.995030\pi$
$257$	−23.8271	+	13.7566i	−1.48630	+	0.858113i	−0.486418	+	0.873726i	$0.661697\pi$
$258$		0			0
$259$	13.5409	+	5.93311i	0.841393	+	0.368665i
$260$		0			0
$261$	1.55456	−	0.897525i	0.0962248	−	0.0555554i
$262$		0			0
$263$	4.47601	+	2.58423i	0.276003	+	0.159350i	0.631612	−	0.775284i	$-0.282393\pi$
$263$	4.47601	+	2.58423i	0.276003	+	0.159350i	−0.355610	+	0.934635i	$0.615727\pi$
$264$		0			0
$265$			24.5667i			1.50912i
$266$		0			0
$267$	12.5421			0.767565
$268$		0			0
$269$	4.86122	−	8.41987i	0.296394	−	0.513369i	−0.678915	−	0.734217i	$-0.737549\pi$
$269$	4.86122	−	8.41987i	0.296394	−	0.513369i	0.975308	+	0.220849i	$0.0708827\pi$
$270$		0			0
$271$	−5.70211	−	9.87634i	−0.346378	−	0.599945i	0.639225	−	0.769020i	$-0.279255\pi$
$271$	−5.70211	−	9.87634i	−0.346378	−	0.599945i	−0.985603	+	0.169075i	$0.945922\pi$
$272$		0			0
$273$	0.490230	+	4.41301i	0.0296701	+	0.267088i
$274$		0			0
$275$	−0.328571	−	0.569103i	−0.0198136	−	0.0343182i
$276$		0			0
$277$	−0.373550	−	0.215669i	−0.0224444	−	0.0129583i	0.488736	−	0.872432i	$-0.337458\pi$
$277$	−0.373550	−	0.215669i	−0.0224444	−	0.0129583i	−0.511180	+	0.859474i	$0.670792\pi$
$278$		0			0
$279$	2.35239			0.140834
$280$		0			0
$281$	13.0498			0.778485			0.389242	−	0.921135i	$-0.372737\pi$
$281$	13.0498			0.778485			0.389242	+	0.921135i	$0.372737\pi$
$282$		0			0
$283$	21.1922	+	12.2353i	1.25975	+	0.727316i	0.973025	−	0.230698i	$-0.0741009\pi$
$283$	21.1922	+	12.2353i	1.25975	+	0.727316i	0.286722	+	0.958014i	$0.407434\pi$
$284$		0			0
$285$	6.26245	+	10.8469i	0.370955	+	0.642513i
$286$		0			0
$287$	−9.05183	+	6.65868i	−0.534312	+	0.393049i
$288$		0			0
$289$	−8.19334	−	14.1913i	−0.481961	−	0.834782i
$290$		0			0
$291$	6.01227	−	10.4136i	0.352446	−	0.610454i
$292$		0			0
$293$	−6.92113			−0.404337			−0.202168	−	0.979351i	$-0.564799\pi$
$293$	−6.92113			−0.404337			−0.202168	+	0.979351i	$0.564799\pi$
$294$		0			0
$295$		−	0.396234i		−	0.0230696i
$296$		0			0
$297$	−0.339111	−	0.195786i	−0.0196772	−	0.0113606i
$298$		0			0
$299$	7.51173	−	4.33690i	0.434415	−	0.250810i
$300$		0			0
$301$	17.3640	+	23.6047i	1.00084	+	1.36055i
$302$		0			0
$303$	9.67216	−	5.58423i	0.555651	−	0.320805i
$304$		0			0
$305$	−5.84667	+	10.1267i	−0.334779	+	0.579855i
$306$		0			0
$307$		−	12.8467i		−	0.733198i	−0.930379	−	0.366599i	$-0.880522\pi$
$307$		−	12.8467i		−	0.733198i	0.930379	−	0.366599i	$-0.119478\pi$
$308$		0			0
$309$			0.557337i			0.0317058i
$310$		0			0
$311$	−8.39468	+	14.5400i	−0.476019	+	0.824489i	−0.999623	−	0.0274732i	$-0.991254\pi$
$311$	−8.39468	+	14.5400i	−0.476019	+	0.824489i	0.523604	+	0.851962i	$0.324587\pi$
$312$		0			0
$313$	2.06910	−	1.19460i	0.116953	−	0.0675226i	−0.440383	−	0.897810i	$-0.645157\pi$
$313$	2.06910	−	1.19460i	0.116953	−	0.0675226i	0.557335	+	0.830288i	$0.311824\pi$
$314$		0			0
$315$	−6.79542	+	0.754885i	−0.382878	+	0.0425330i
$316$		0			0
$317$	23.0599	−	13.3136i	1.29517	−	0.747769i	0.315607	−	0.948890i	$-0.397792\pi$
$317$	23.0599	−	13.3136i	1.29517	−	0.747769i	0.979566	+	0.201121i	$0.0644584\pi$
$318$		0			0
$319$	0.608721	+	0.351445i	0.0340818	+	0.0196771i
$320$		0			0
$321$		−	13.5908i		−	0.758566i
$322$		0			0
$323$	−3.79563			−0.211195
$324$		0			0
$325$	1.40821	−	2.43910i	0.0781136	−	0.135297i
$326$		0			0
$327$	−8.61035	−	14.9136i	−0.476154	−	0.824722i
$328$		0			0
$329$	14.0151	−	31.9863i	0.772679	−	1.76346i
$330$		0			0
$331$	−14.4239	−	24.9829i	−0.792808	−	1.37318i	−0.924222	−	0.381856i	$-0.875285\pi$
$331$	−14.4239	−	24.9829i	−0.792808	−	1.37318i	0.131414	−	0.991328i	$-0.458048\pi$
$332$		0			0
$333$	−4.83911	−	2.79386i	−0.265182	−	0.153103i
$334$		0			0
$335$	12.7417			0.696155
$336$		0			0
$337$	9.14891			0.498373			0.249186	−	0.968456i	$-0.419837\pi$
$337$	9.14891			0.498373			0.249186	+	0.968456i	$0.419837\pi$
$338$		0			0
$339$	15.3229	+	8.84667i	0.832225	+	0.480485i
$340$		0			0
$341$	0.460564	+	0.797720i	0.0249409	+	0.0431989i
$342$		0			0
$343$	17.5095	−	6.03466i	0.945425	−	0.325841i
$344$		0			0
$345$	6.67822	+	11.5670i	0.359543	+	0.622747i
$346$		0			0
$347$	17.0549	−	29.5400i	0.915557	−	1.58579i	0.109473	−	0.993990i	$-0.465084\pi$
$347$	17.0549	−	29.5400i	0.915557	−	1.58579i	0.806084	−	0.591801i	$-0.201583\pi$
$348$		0			0
$349$	12.0302			0.643964			0.321982	−	0.946746i	$-0.395651\pi$
$349$	12.0302			0.643964			0.321982	+	0.946746i	$0.395651\pi$
$350$		0			0
$351$		−	1.67822i		−	0.0895768i
$352$		0			0
$353$	15.6782	+	9.05183i	0.834468	+	0.481780i	0.855380	−	0.518001i	$-0.173324\pi$
$353$	15.6782	+	9.05183i	0.834468	+	0.481780i	−0.0209123	+	0.999781i	$0.506657\pi$
$354$		0			0
$355$	1.17471	−	0.678221i	0.0623473	−	0.0359962i
$356$		0			0
$357$	0.831549	−	1.89782i	0.0440102	−	0.100443i
$358$		0			0
$359$	0.909142	−	0.524893i	0.0479827	−	0.0277028i	−0.475817	−	0.879544i	$-0.657847\pi$
$359$	0.909142	−	0.524893i	0.0479827	−	0.0277028i	0.523799	+	0.851842i	$0.324514\pi$
$360$		0			0
$361$	2.24511	−	3.88865i	0.118164	−	0.204666i
$362$		0			0
$363$			10.8467i			0.569303i
$364$		0			0
$365$			30.6458i			1.60407i
$366$		0			0
$367$	−5.26063	+	9.11168i	−0.274603	+	0.475626i	−0.970035	−	0.242966i	$-0.921880\pi$
$367$	−5.26063	+	9.11168i	−0.274603	+	0.475626i	0.695432	+	0.718592i	$0.255213\pi$
$368$		0			0
$369$	3.67822	−	2.12362i	0.191481	−	0.110551i
$370$		0			0
$371$	2.77694	+	24.9978i	0.144172	+	1.29782i
$372$		0			0
$373$	−24.5918	+	14.1981i	−1.27331	+	0.735148i	−0.975610	−	0.219510i	$-0.929554\pi$
$373$	−24.5918	+	14.1981i	−1.27331	+	0.735148i	−0.297704	+	0.954658i	$0.596221\pi$
$374$		0			0
$375$	−7.43416	−	4.29211i	−0.383898	−	0.221644i
$376$		0			0
$377$			3.01249i			0.155151i
$378$		0			0
$379$	−31.0771			−1.59632			−0.798162	−	0.602443i	$-0.794194\pi$
$379$	−31.0771			−1.59632			−0.798162	+	0.602443i	$0.794194\pi$
$380$		0			0
$381$	7.39367	−	12.8062i	0.378789	−	0.656082i
$382$		0			0
$383$	−5.48792	−	9.50535i	−0.280420	−	0.485701i	0.691069	−	0.722789i	$-0.257140\pi$
$383$	−5.48792	−	9.50535i	−0.280420	−	0.485701i	−0.971488	+	0.237088i	$0.923807\pi$
$384$		0			0
$385$	−1.58643	−	2.15660i	−0.0808522	−	0.109911i
$386$		0			0
$387$	−5.53782	−	9.59179i	−0.281503	−	0.487578i
$388$		0			0
$389$	−0.287115	−	0.165766i	−0.0145573	−	0.00840468i	0.492704	−	0.870197i	$-0.336009\pi$
$389$	−0.287115	−	0.165766i	−0.0145573	−	0.00840468i	−0.507261	+	0.861792i	$0.669342\pi$
$390$		0			0
$391$	−4.04763			−0.204698
$392$		0			0
$393$	−4.49023			−0.226502
$394$		0			0
$395$	6.50365	+	3.75489i	0.327234	+	0.188929i
$396$		0			0
$397$	18.2700	+	31.6446i	0.916945	+	1.58820i	0.804028	+	0.594592i	$0.202686\pi$
$397$	18.2700	+	31.6446i	0.916945	+	1.58820i	0.112918	+	0.993604i	$0.463980\pi$
$398$		0			0
$399$	7.59844	+	10.3293i	0.380398	+	0.517114i
$400$		0			0
$401$	−9.81201	−	16.9949i	−0.489988	−	0.848685i	0.509945	−	0.860207i	$-0.329666\pi$
$401$	−9.81201	−	16.9949i	−0.489988	−	0.848685i	−0.999934	+	0.0115222i	$0.996332\pi$
$402$		0			0
$403$	−1.97391	+	3.41892i	−0.0983276	+	0.170308i
$404$		0			0
$405$	2.58423			0.128411
$406$		0			0
$407$		−	2.18799i		−	0.108455i
$408$		0			0
$409$	17.3965	+	10.0438i	0.860200	+	0.496636i	0.864079	−	0.503356i	$-0.167902\pi$
$409$	17.3965	+	10.0438i	0.860200	+	0.496636i	−0.00387959	+	0.999992i	$0.501235\pi$
$410$		0			0
$411$	11.3014	−	6.52489i	0.557459	−	0.321849i
$412$		0			0
$413$	−0.0447891	−	0.403188i	−0.00220393	−	0.0198396i
$414$		0			0
$415$	27.6876	−	15.9855i	1.35913	−	0.784695i
$416$		0			0
$417$	8.59179	−	14.8814i	0.420742	−	0.728746i
$418$		0			0
$419$		−	4.64356i		−	0.226853i	−0.993546	−	0.113426i	$-0.963817\pi$
$419$		−	4.64356i		−	0.226853i	0.993546	−	0.113426i	$-0.0361826\pi$
$420$		0			0
$421$			15.1969i			0.740651i	0.928902	+	0.370325i	$0.120754\pi$
$421$			15.1969i			0.740651i	−0.928902	+	0.370325i	$0.879246\pi$
$422$		0			0
$423$	−6.59963	+	11.4309i	−0.320885	+	0.555789i
$424$		0			0
$425$	−1.13821	+	0.657143i	−0.0552111	+	0.0318761i
$426$		0			0
$427$	−4.80458	+	10.9653i	−0.232510	+	0.530650i
$428$		0			0
$429$	0.569103	−	0.328571i	0.0274765	−	0.0158636i
$430$		0			0
$431$	−2.58115	−	1.49023i	−0.124330	−	0.0717818i	0.436545	−	0.899682i	$-0.356202\pi$
$431$	−2.58115	−	1.49023i	−0.124330	−	0.0717818i	−0.560875	+	0.827900i	$0.689535\pi$
$432$		0			0
$433$		−	25.9672i		−	1.24790i	−0.781463	−	0.623952i	$-0.785526\pi$
$433$		−	25.9672i		−	1.24790i	0.781463	−	0.623952i	$-0.214474\pi$
$434$		0			0
$435$	−4.63882			−0.222414
$436$		0			0
$437$	12.5249	−	21.6938i	0.599147	−	1.03775i
$438$		0			0
$439$	−13.6422	−	23.6290i	−0.651108	−	1.12775i	−0.982854	−	0.184383i	$-0.940971\pi$
$439$	−13.6422	−	23.6290i	−0.651108	−	1.12775i	0.331747	−	0.943368i	$-0.392362\pi$
$440$		0			0
$441$	−6.82934	+	1.53627i	−0.325207	+	0.0731555i
$442$		0			0
$443$	0.0300194	+	0.0519951i	0.00142627	+	0.00247036i	0.866738	−	0.498764i	$-0.166213\pi$
$443$	0.0300194	+	0.0519951i	0.00142627	+	0.00247036i	−0.865311	+	0.501235i	$0.832879\pi$
$444$		0			0
$445$	−28.0693	−	16.2058i	−1.33061	−	0.768230i
$446$		0			0
$447$	−6.14506			−0.290651
$448$		0			0
$449$	3.28712			0.155129			0.0775643	−	0.996987i	$-0.475286\pi$
$449$	3.28712			0.155129			0.0775643	+	0.996987i	$0.475286\pi$
$450$		0			0
$451$	1.44029	+	0.831549i	0.0678204	+	0.0391561i
$452$		0			0
$453$	−2.29211	−	3.97006i	−0.107693	−	0.186529i
$454$		0			0
$455$	4.60497	−	10.5098i	0.215884	−	0.492706i
$456$		0			0
$457$	4.17822	+	7.23689i	0.195449	+	0.338527i	0.947048	−	0.321093i	$-0.104050\pi$
$457$	4.17822	+	7.23689i	0.195449	+	0.338527i	−0.751599	+	0.659621i	$0.770717\pi$
$458$		0			0
$459$	−0.391571	+	0.678221i	−0.0182770	+	0.0316567i
$460$		0			0
$461$	−3.81201			−0.177543			−0.0887715	−	0.996052i	$-0.528294\pi$
$461$	−3.81201			−0.177543			−0.0887715	+	0.996052i	$0.528294\pi$
$462$		0			0
$463$			25.8965i			1.20351i	0.798681	+	0.601755i	$0.205532\pi$
$463$			25.8965i			1.20351i	−0.798681	+	0.601755i	$0.794468\pi$
$464$		0			0
$465$	−5.26466	−	3.03955i	−0.244143	−	0.140956i
$466$		0			0
$467$	−6.37087	+	3.67822i	−0.294809	+	0.170208i	−0.640108	−	0.768285i	$-0.721111\pi$
$467$	−6.37087	+	3.67822i	−0.294809	+	0.170208i	0.345300	+	0.938492i	$0.387777\pi$
$468$		0			0
$469$	12.9653	−	1.44029i	0.598684	−	0.0665062i
$470$		0			0
$471$	13.2991	−	7.67822i	0.612789	−	0.353794i
$472$		0			0
$473$	2.16845	−	3.75587i	0.0997055	−	0.172695i
$474$		0			0
$475$		−	8.13379i		−	0.373204i
$476$		0			0
$477$		−	9.50640i		−	0.435268i
$478$		0			0
$479$	18.3324	−	31.7527i	0.837629	−	1.45082i	−0.0542420	−	0.998528i	$-0.517274\pi$
$479$	18.3324	−	31.7527i	0.837629	−	1.45082i	0.891871	−	0.452289i	$-0.149392\pi$
$480$		0			0
$481$	8.12110	−	4.68872i	0.370290	−	0.213787i
$482$		0			0
$483$	8.10292	+	11.0151i	0.368695	+	0.501205i
$484$		0			0
$485$	−26.9110	+	15.5371i	−1.22197	+	0.705502i
$486$		0			0
$487$	−12.6172	−	7.28455i	−0.571740	−	0.330095i	0.186104	−	0.982530i	$-0.440414\pi$
$487$	−12.6172	−	7.28455i	−0.571740	−	0.330095i	−0.757844	+	0.652436i	$0.773747\pi$
$488$		0			0
$489$			16.0062i			0.723826i
$490$		0			0
$491$	−4.18128			−0.188699			−0.0943493	−	0.995539i	$-0.530077\pi$
$491$	−4.18128			−0.188699			−0.0943493	+	0.995539i	$0.530077\pi$
$492$		0			0
$493$	0.702890	−	1.21744i	0.0316566	−	0.0548308i
$494$		0			0
$495$	0.505954	+	0.876338i	0.0227409	+	0.0393885i
$496$		0			0
$497$	1.11866	−	0.822909i	0.0501790	−	0.0369125i
$498$		0			0
$499$	2.46529	+	4.27001i	0.110362	+	0.191152i	0.915916	−	0.401370i	$-0.131466\pi$
$499$	2.46529	+	4.27001i	0.110362	+	0.191152i	−0.805555	+	0.592522i	$0.798132\pi$
$500$		0			0
$501$	3.67822	+	2.12362i	0.164331	+	0.0948764i
$502$		0			0
$503$	−2.47543			−0.110374			−0.0551869	−	0.998476i	$-0.517575\pi$
$503$	−2.47543			−0.110374			−0.0551869	+	0.998476i	$0.517575\pi$
$504$		0			0
$505$	−28.8618			−1.28433
$506$		0			0
$507$	−8.81923	−	5.09179i	−0.391676	−	0.226134i
$508$		0			0
$509$	−5.07945	−	8.79787i	−0.225143	−	0.389959i	0.731219	−	0.682142i	$-0.238952\pi$
$509$	−5.07945	−	8.79787i	−0.225143	−	0.389959i	−0.956362	+	0.292184i	$0.905618\pi$
$510$		0			0
$511$	3.46410	+	31.1836i	0.153243	+	1.37948i
$512$		0			0
$513$	−2.42334	−	4.19734i	−0.106993	−	0.185317i
$514$		0			0
$515$	0.720143	−	1.24732i	0.0317333	−	0.0549636i
$516$		0			0
$517$	−5.16845			−0.227308
$518$		0			0
$519$			18.5249i			0.813153i
$520$		0			0
$521$	17.3218	+	10.0007i	0.758881	+	0.438140i	0.828894	−	0.559406i	$-0.188971\pi$
$521$	17.3218	+	10.0007i	0.758881	+	0.438140i	−0.0700129	+	0.997546i	$0.522304\pi$
$522$		0			0
$523$	−18.0799	+	10.4385i	−0.790581	+	0.456442i	−0.840167	−	0.542328i	$-0.817543\pi$
$523$	−18.0799	+	10.4385i	−0.790581	+	0.456442i	0.0495863	+	0.998770i	$0.484210\pi$
$524$		0			0
$525$	4.06689	+	1.78195i	0.177494	+	0.0777708i
$526$		0			0
$527$	1.59544	−	0.921127i	0.0694984	−	0.0401249i
$528$		0			0
$529$	1.85644	−	3.21545i	0.0807149	−	0.139802i
$530$		0			0
$531$			0.153328i			0.00665387i
$532$		0			0
$533$			7.12781i			0.308740i
$534$		0			0
$535$	−17.5609	+	30.4164i	−0.759223	+	1.31501i
$536$		0			0
$537$	15.0000	−	8.66025i	0.647298	−	0.373718i
$538$		0			0
$539$	−1.85805	−	2.01512i	−0.0800319	−	0.0867975i
$540$		0			0
$541$	14.7356	−	8.50758i	0.633532	−	0.365770i	−0.148587	−	0.988899i	$-0.547472\pi$
$541$	14.7356	−	8.50758i	0.633532	−	0.365770i	0.782119	+	0.623130i	$0.214139\pi$
$542$		0			0
$543$	14.8814	+	8.59179i	0.638622	+	0.368709i
$544$		0			0
$545$			44.5022i			1.90626i
$546$		0			0
$547$	−15.0912			−0.645251			−0.322626	−	0.946527i	$-0.604565\pi$
$547$	−15.0912			−0.645251			−0.322626	+	0.946527i	$0.604565\pi$
$548$		0			0
$549$	2.26245	−	3.91867i	0.0965589	−	0.167245i
$550$		0			0
$551$	4.35001	+	7.53444i	0.185317	+	0.320978i
$552$		0			0
$553$	7.04222	+	3.08563i	0.299466	+	0.131214i
$554$		0			0
$555$	7.21997	+	12.5054i	0.306471	+	0.530823i
$556$		0			0
$557$	−29.6290	−	17.1063i	−1.25542	−	0.724818i	−0.283241	−	0.959049i	$-0.591410\pi$
$557$	−29.6290	−	17.1063i	−1.25542	−	0.724818i	−0.972181	+	0.234231i	$0.924743\pi$
$558$		0			0
$559$	18.5874			0.786162
$560$		0			0
$561$	−0.306656			−0.0129470
$562$		0			0
$563$	21.3720	+	12.3391i	0.900721	+	0.520032i	0.877434	−	0.479697i	$-0.159254\pi$
$563$	21.3720	+	12.3391i	0.900721	+	0.520032i	0.0232870	+	0.999729i	$0.492587\pi$
$564$		0			0
$565$	−22.8618	−	39.5978i	−0.961803	−	1.66589i
$566$		0			0
$567$	2.62958	−	0.292113i	0.110432	−	0.0122676i
$568$		0			0
$569$	−16.8813	−	29.2393i	−0.707702	−	1.22578i	−0.965707	−	0.259633i	$-0.916398\pi$
$569$	−16.8813	−	29.2393i	−0.707702	−	1.22578i	0.258005	−	0.966144i	$-0.416935\pi$
$570$		0			0
$571$	3.97154	−	6.87890i	0.166204	−	0.287873i	−0.770878	−	0.636982i	$-0.780182\pi$
$571$	3.97154	−	6.87890i	0.166204	−	0.287873i	0.937082	+	0.349109i	$0.113516\pi$
$572$		0			0
$573$	−17.6933			−0.739150
$574$		0			0
$575$		−	8.67380i		−	0.361723i
$576$		0			0
$577$	−28.3220	−	16.3517i	−1.17906	−	0.680731i	−0.223263	−	0.974758i	$-0.571671\pi$
$577$	−28.3220	−	16.3517i	−1.17906	−	0.680731i	−0.955797	+	0.294027i	$0.905004\pi$
$578$		0			0
$579$	−5.34204	+	3.08423i	−0.222007	+	0.128176i
$580$		0			0
$581$	26.3666	−	19.3957i	1.09387	−	0.804670i
$582$		0			0
$583$	3.22372	−	1.86122i	0.133513	−	0.0770837i
$584$		0			0
$585$	−2.16845	+	3.75587i	−0.0896544	+	0.155286i
$586$		0			0
$587$			22.1836i			0.915614i	0.889052	+	0.457807i	$0.151365\pi$
$587$			22.1836i			0.915614i	−0.889052	+	0.457807i	$0.848635\pi$
$588$		0			0
$589$			11.4013i			0.469780i
$590$		0			0
$591$	−12.8077	+	22.1836i	−0.526838	+	0.912510i
$592$		0			0
$593$	−38.0800	+	21.9855i	−1.56376	+	0.902837i	−0.566888	+	0.823795i	$0.691853\pi$
$593$	−38.0800	+	21.9855i	−1.56376	+	0.902837i	−0.996871	+	0.0790422i	$0.974814\pi$
$594$		0			0
$595$	−4.31320	+	3.17287i	−0.176824	+	0.130075i
$596$		0			0
$597$	0.109119	−	0.0629997i	0.00446593	−	0.00257840i
$598$		0			0
$599$	−8.95202	−	5.16845i	−0.365770	−	0.211177i	0.305839	−	0.952083i	$-0.401063\pi$
$599$	−8.95202	−	5.16845i	−0.365770	−	0.211177i	−0.671609	+	0.740906i	$0.734396\pi$
$600$		0			0
$601$			6.88844i			0.280985i	0.990082	+	0.140493i	$0.0448686\pi$
$601$			6.88844i			0.280985i	−0.990082	+	0.140493i	$0.955131\pi$
$602$		0			0
$603$	−4.93058			−0.200789
$604$		0			0
$605$	14.0151	−	24.2749i	0.569796	−	0.986915i
$606$		0			0
$607$	−5.19763	−	9.00256i	−0.210965	−	0.365403i	0.741052	−	0.671448i	$-0.234327\pi$
$607$	−5.19763	−	9.00256i	−0.210965	−	0.365403i	−0.952017	+	0.306045i	$0.900994\pi$
$608$		0			0
$609$	−4.72022	+	0.524357i	−0.191273	+	0.0212480i
$610$		0			0
$611$	−11.0756	−	19.1836i	−0.448072	−	0.776084i
$612$		0			0
$613$	−21.3274	−	12.3134i	−0.861404	−	0.497332i	0.00307834	−	0.999995i	$-0.499020\pi$
$613$	−21.3274	−	12.3134i	−0.861404	−	0.497332i	−0.864482	+	0.502664i	$0.832353\pi$
$614$		0			0
$615$	−10.9758			−0.442588
$616$		0			0
$617$	−19.0498			−0.766916			−0.383458	−	0.923558i	$-0.625267\pi$
$617$	−19.0498			−0.766916			−0.383458	+	0.923558i	$0.625267\pi$
$618$		0			0
$619$	21.5178	+	12.4233i	0.864875	+	0.499336i	0.865642	−	0.500664i	$-0.166911\pi$
$619$	21.5178	+	12.4233i	0.864875	+	0.499336i	−0.000766513		1.00000i	$0.500244\pi$
$620$		0			0
$621$	−2.58423	−	4.47601i	−0.103701	−	0.179616i
$622$		0			0
$623$	−30.3938	−	13.3174i	−1.21770	−	0.533549i
$624$		0			0
$625$	15.2873	+	26.4784i	0.611494	+	1.05914i
$626$		0			0
$627$	0.948908	−	1.64356i	0.0378958	−	0.0656374i
$628$		0			0
$629$	−4.37598			−0.174482
$630$		0			0
$631$			13.6833i			0.544726i	0.962195	+	0.272363i	$0.0878051\pi$
$631$			13.6833i			0.544726i	−0.962195	+	0.272363i	$0.912195\pi$
$632$		0			0
$633$	−7.64356	−	4.41301i	−0.303804	−	0.175401i
$634$		0			0
$635$	−33.0941	+	19.1069i	−1.31330	+	0.758235i
$636$		0			0
$637$	3.49779	−	11.2147i	0.138588	−	0.444344i
$638$		0			0
$639$	−0.454571	+	0.262447i	−0.0179825	+	0.0103822i
$640$		0			0
$641$	−17.5400	+	30.3802i	−0.692789	+	1.19995i	0.278131	+	0.960543i	$0.410285\pi$
$641$	−17.5400	+	30.3802i	−0.692789	+	1.19995i	−0.970920	+	0.239403i	$0.923048\pi$
$642$		0			0
$643$			19.8965i			0.784640i	0.919829	+	0.392320i	$0.128327\pi$
$643$			19.8965i			0.784640i	−0.919829	+	0.392320i	$0.871673\pi$
$644$		0			0
$645$			28.6220i			1.12699i
$646$		0			0
$647$	17.9011	−	31.0056i	0.703764	−	1.21896i	−0.263372	−	0.964694i	$-0.584835\pi$
$647$	17.9011	−	31.0056i	0.703764	−	1.21896i	0.967136	−	0.254261i	$-0.0818321\pi$
$648$		0			0
$649$	−0.0519951	+	0.0300194i	−0.00204099	+	0.00117836i
$650$		0			0
$651$	−5.70063	−	2.49779i	−0.223425	−	0.0978962i
$652$		0			0
$653$	−32.9564	+	19.0274i	−1.28968	+	0.744598i	−0.978598	−	0.205784i	$-0.934026\pi$
$653$	−32.9564	+	19.0274i	−1.28968	+	0.744598i	−0.311085	+	0.950382i	$0.600692\pi$
$654$		0			0
$655$	10.0492	+	5.80188i	0.392653	+	0.226698i
$656$		0			0
$657$		−	11.8588i		−	0.462655i
$658$		0			0
$659$	−24.0491			−0.936820			−0.468410	−	0.883511i	$-0.655173\pi$
$659$	−24.0491			−0.936820			−0.468410	+	0.883511i	$0.655173\pi$
$660$		0			0
$661$	16.2107	−	28.0777i	0.630522	−	1.09210i	−0.356923	−	0.934134i	$-0.616174\pi$
$661$	16.2107	−	28.0777i	0.630522	−	1.09210i	0.987445	−	0.157963i	$-0.0504926\pi$
$662$		0			0
$663$	−0.657143	−	1.13821i	−0.0255213	−	0.0442042i
$664$		0			0
$665$	−3.65868	−	32.9352i	−0.141878	−	1.27717i
$666$		0			0
$667$	4.63882	+	8.03466i	0.179616	+	0.311103i
$668$		0			0
$669$	−16.5546	−	9.55778i	−0.640036	−	0.369525i
$670$		0			0
$671$	1.77182			0.0684003
$672$		0			0
$673$	22.0800			0.851123			0.425561	−	0.904930i	$-0.360077\pi$
$673$	22.0800			0.851123			0.425561	+	0.904930i	$0.360077\pi$
$674$		0			0
$675$	−1.45338	−	0.839111i	−0.0559407	−	0.0322974i
$676$		0			0
$677$	−3.06433	−	5.30757i	−0.117772	−	0.203987i	0.801113	−	0.598514i	$-0.204242\pi$
$677$	−3.06433	−	5.30757i	−0.117772	−	0.203987i	−0.918884	+	0.394527i	$0.870908\pi$
$678$		0			0
$679$	−25.6270	+	18.8517i	−0.983474	+	0.723461i
$680$		0			0
$681$	11.5076	+	19.9317i	0.440971	+	0.763784i
$682$		0			0
$683$	−11.3974	+	19.7409i	−0.436110	+	0.755365i	−0.997386	−	0.0722639i	$-0.976978\pi$
$683$	−11.3974	+	19.7409i	−0.436110	+	0.755365i	0.561275	+	0.827629i	$0.310311\pi$
$684$		0			0
$685$	−33.7236			−1.28851
$686$		0			0
$687$			6.20311i			0.236664i
$688$		0			0
$689$	13.8164	+	7.97692i	0.526364	+	0.303896i
$690$		0			0
$691$	5.60378	−	3.23534i	0.213178	−	0.123078i	−0.389610	−	0.920980i	$-0.627390\pi$
$691$	5.60378	−	3.23534i	0.213178	−	0.123078i	0.602787	+	0.797902i	$0.294057\pi$
$692$		0			0
$693$	0.613892	+	0.834526i	0.0233198	+	0.0317010i
$694$		0			0
$695$	−38.4569	+	22.2031i	−1.45875	+	0.842212i
$696$		0			0
$697$	1.66310	−	2.88057i	0.0629943	−	0.109109i
$698$		0			0
$699$		−	18.0000i		−	0.680823i
$700$		0			0
$701$		−	41.8445i		−	1.58044i	−0.612821	−	0.790222i	$-0.709965\pi$
$701$		−	41.8445i		−	1.58044i	0.612821	−	0.790222i	$-0.290035\pi$
$702$		0			0
$703$	13.5409	−	23.4536i	0.510706	−	0.884569i
$704$		0			0
$705$	29.5400	−	17.0549i	1.11254	−	0.642326i
$706$		0			0
$707$	−29.3683	+	3.26245i	−1.10451	+	0.122697i
$708$		0			0
$709$	−13.3564	+	7.71135i	−0.501612	+	0.289606i	−0.729379	−	0.684110i	$-0.760191\pi$
$709$	−13.3564	+	7.71135i	−0.501612	+	0.289606i	0.227767	+	0.973716i	$0.426857\pi$
$710$		0			0
$711$	−2.51667	−	1.45300i	−0.0943826	−	0.0544918i
$712$		0			0
$713$			12.1582i			0.455328i
$714$		0			0
$715$	−1.69821			−0.0635093
$716$		0			0
$717$	−5.43090	+	9.40659i	−0.202821	+	0.351296i
$718$		0			0
$719$	−3.68991	−	6.39111i	−0.137610	−	0.238348i	0.788981	−	0.614417i	$-0.210609\pi$
$719$	−3.68991	−	6.39111i	−0.137610	−	0.238348i	−0.926592	+	0.376069i	$0.877275\pi$
$720$		0			0
$721$	0.591787	−	1.35062i	0.0220393	−	0.0502996i
$722$		0			0
$723$	−1.53627	−	2.66089i	−0.0571343	−	0.0989595i
$724$		0			0
$725$	2.60889	+	1.50625i	0.0968919	+	0.0559406i
$726$		0			0
$727$	26.7271			0.991253			0.495627	−	0.868536i	$-0.334938\pi$
$727$	26.7271			0.991253			0.495627	+	0.868536i	$0.334938\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−7.51173	−	4.33690i	−0.277832	−	0.160406i
$732$		0			0
$733$	1.14577	+	1.98453i	0.0423199	+	0.0733001i	0.886409	−	0.462902i	$-0.153192\pi$
$733$	1.14577	+	1.98453i	0.0423199	+	0.0733001i	−0.844090	+	0.536202i	$0.819858\pi$
$734$		0			0
$735$	17.2691	+	5.38611i	0.636981	+	0.198670i
$736$		0			0
$737$	−0.965337	−	1.67201i	−0.0355586	−	0.0615894i
$738$		0			0
$739$	−5.14625	+	8.91357i	−0.189308	+	0.327891i	−0.945020	−	0.327013i	$-0.893958\pi$
$739$	−5.14625	+	8.91357i	−0.189308	+	0.327891i	0.755712	+	0.654904i	$0.227291\pi$
$740$		0			0
$741$	8.13379			0.298802
$742$		0			0
$743$		−	41.0800i		−	1.50708i	−0.657402	−	0.753540i	$-0.728345\pi$
$743$		−	41.0800i		−	1.50708i	0.657402	−	0.753540i	$-0.271655\pi$
$744$		0			0
$745$	13.7527	+	7.94011i	0.503859	+	0.290903i
$746$		0			0
$747$	−10.7141	+	6.18578i	−0.392008	+	0.226326i
$748$		0			0
$749$	−14.4309	+	32.9352i	−0.527294	+	1.20342i
$750$		0			0
$751$	−20.0524	+	11.5772i	−0.731722	+	0.422460i	−0.819052	−	0.573720i	$-0.805500\pi$
$751$	−20.0524	+	11.5772i	−0.731722	+	0.422460i	0.0873301	+	0.996179i	$0.472167\pi$
$752$		0			0
$753$	10.5422	−	18.2597i	0.384180	−	0.665419i
$754$		0			0
$755$			11.8467i			0.431145i
$756$		0			0
$757$			0.205533i			0.00747022i	0.999993	+	0.00373511i	$0.00118893\pi$
$757$			0.205533i			0.00747022i	−0.999993	+	0.00373511i	$0.998811\pi$
$758$		0			0
$759$	1.01191	−	1.75268i	0.0367299	−	0.0636181i
$760$		0			0
$761$	−20.0347	+	11.5670i	−0.726256	+	0.419304i	−0.817051	−	0.576566i	$-0.804393\pi$
$761$	−20.0347	+	11.5670i	−0.726256	+	0.419304i	0.0907949	+	0.995870i	$0.471059\pi$
$762$		0			0
$763$	5.03039	+	45.2831i	0.182112	+	1.63936i
$764$		0			0
$765$	1.75268	−	1.01191i	0.0633681	−	0.0365856i
$766$		0			0
$767$	−0.222844	−	0.128659i	−0.00804644	−	0.00464561i
$768$		0			0
$769$			3.42433i			0.123485i	0.998092	+	0.0617423i	$0.0196657\pi$
$769$			3.42433i			0.123485i	−0.998092	+	0.0617423i	$0.980334\pi$
$770$		0			0
$771$	−27.5132			−0.990864
$772$		0			0
$773$	−13.4656	+	23.3230i	−0.484323	+	0.838871i	−0.999838	−	0.0180091i	$-0.994267\pi$
$773$	−13.4656	+	23.3230i	−0.484323	+	0.838871i	0.515515	+	0.856880i	$0.327601\pi$
$774$		0			0
$775$	1.97391	+	3.41892i	0.0709051	+	0.122811i
$776$		0			0
$777$	8.76024	+	11.9087i	0.314272	+	0.427222i
$778$		0			0
$779$	10.2925	+	17.8271i	0.368767	+	0.638723i
$780$		0			0
$781$	−0.177997	−	0.102767i	−0.00636923	−	0.00367727i
$782$		0			0
$783$	1.79505			0.0641499
$784$		0			0
$785$	−39.6845			−1.41640
$786$		0			0
$787$	−26.9161	−	15.5400i	−0.959455	−	0.553942i	−0.0634499	−	0.997985i	$-0.520210\pi$
$787$	−26.9161	−	15.5400i	−0.959455	−	0.553942i	−0.896005	+	0.444043i	$0.853544\pi$
$788$		0			0
$789$	2.58423	+	4.47601i	0.0920009	+	0.159350i
$790$		0			0
$791$	−27.7390	−	37.7085i	−0.986286	−	1.34076i
$792$		0			0
$793$	3.79689	+	6.57640i	0.134831	+	0.233535i
$794$		0			0
$795$	−12.2833	+	21.2754i	−0.435645	+	0.754559i
$796$		0			0
$797$	5.25803			0.186249			0.0931245	−	0.995654i	$-0.470315\pi$
$797$	5.25803			0.186249			0.0931245	+	0.995654i	$0.470315\pi$
$798$		0			0
$799$			10.3369i			0.365693i
$800$		0			0
$801$	10.8618	+	6.27106i	0.383783	+	0.221577i
$802$		0			0
$803$	4.02144	−	2.32178i	0.141913	−	0.0819338i
$804$		0			0
$805$	−3.90159	−	35.1218i	−0.137513	−	1.23788i
$806$		0			0
$807$	8.41987	−	4.86122i	0.296394	−	0.171123i
$808$		0			0
$809$	7.18357	−	12.4423i	0.252561	−	0.437448i	−0.711669	−	0.702515i	$-0.752060\pi$
$809$	7.18357	−	12.4423i	0.252561	−	0.437448i	0.964230	+	0.265066i	$0.0853938\pi$
$810$		0			0
$811$			16.0000i			0.561836i	0.959732	+	0.280918i	$0.0906389\pi$
$811$			16.0000i			0.561836i	−0.959732	+	0.280918i	$0.909361\pi$
$812$		0			0
$813$		−	11.4042i		−	0.399963i
$814$		0			0
$815$	20.6818	−	35.8220i	0.724453	−	1.25479i
$816$		0			0
$817$	46.4882	−	26.8400i	1.62642	−	0.939013i
$818$		0			0
$819$	−1.78195	+	4.06689i	−0.0622665	+	0.142109i
$820$		0			0
$821$	−3.94009	+	2.27481i	−0.137510	+	0.0793914i	−0.567177	−	0.823596i	$-0.691964\pi$
$821$	−3.94009	+	2.27481i	−0.137510	+	0.0793914i	0.429667	+	0.902988i	$0.358631\pi$
$822$		0			0
$823$	−8.89198	−	5.13379i	−0.309955	−	0.178953i	0.336951	−	0.941522i	$-0.390604\pi$
$823$	−8.89198	−	5.13379i	−0.309955	−	0.178953i	−0.646906	+	0.762569i	$0.723938\pi$
$824$		0			0
$825$		−	0.657143i		−	0.0228788i
$826$		0			0
$827$	−13.9224			−0.484128			−0.242064	−	0.970260i	$-0.577824\pi$
$827$	−13.9224			−0.484128			−0.242064	+	0.970260i	$0.577824\pi$
$828$		0			0
$829$	16.0227	−	27.7521i	0.556491	−	0.963870i	−0.441295	−	0.897362i	$-0.645481\pi$
$829$	16.0227	−	27.7521i	0.556491	−	0.963870i	0.997786	−	0.0665083i	$-0.0211859\pi$
$830$		0			0
$831$	−0.215669	−	0.373550i	−0.00748147	−	0.0129583i
$832$		0			0
$833$	−4.03025	+	3.71610i	−0.139640	+	0.128755i
$834$		0			0
$835$	−5.48792	−	9.50535i	−0.189917	−	0.328946i
$836$		0			0
$837$	2.03723	+	1.17619i	0.0704169	+	0.0406552i
$838$		0			0
$839$	24.6267			0.850208			0.425104	−	0.905144i	$-0.360237\pi$
$839$	24.6267			0.850208			0.425104	+	0.905144i	$0.360237\pi$
$840$		0			0
$841$	25.7778			0.888889
$842$		0			0
$843$	11.3014	+	6.52489i	0.389242	+	0.224729i
$844$		0			0
$845$	13.1583	+	22.7909i	0.452660	+	0.784030i
$846$		0			0
$847$	11.5171	−	26.2851i	0.395733	−	0.903168i
$848$		0			0
$849$	12.2353	+	21.1922i	0.419916	+	0.727316i
$850$		0			0
$851$	14.4399	−	25.0107i	0.494995	−	0.857356i
$852$		0			0
$853$	−19.5205			−0.668368			−0.334184	−	0.942508i	$-0.608461\pi$
$853$	−19.5205			−0.668368			−0.334184	+	0.942508i	$0.608461\pi$
$854$		0			0
$855$			12.5249i			0.428342i
$856$		0			0
$857$	−28.4018	−	16.3978i	−0.970187	−	0.560138i	−0.0708940	−	0.997484i	$-0.522585\pi$
$857$	−28.4018	−	16.3978i	−0.970187	−	0.560138i	−0.899293	+	0.437346i	$0.855919\pi$
$858$		0			0
$859$	−13.5908	+	7.84667i	−0.463713	+	0.267725i	−0.713604	−	0.700549i	$-0.752939\pi$
$859$	−13.5908	+	7.84667i	−0.463713	+	0.267725i	0.249891	+	0.968274i	$0.419605\pi$
$860$		0			0
$861$	−11.1685	+	1.24067i	−0.380620	+	0.0422821i
$862$		0			0
$863$	−42.7101	+	24.6587i	−1.45387	+	0.839391i	−0.998698	−	0.0510131i	$-0.983755\pi$
$863$	−42.7101	+	24.6587i	−1.45387	+	0.839391i	−0.455170	+	0.890404i	$0.650422\pi$
$864$		0			0
$865$	23.9363	−	41.4588i	0.813857	−	1.40964i
$866$		0			0
$867$		−	16.3867i		−	0.556521i
$868$		0			0
$869$		−	1.13791i		−	0.0386009i
$870$		0			0
$871$	4.13730	−	7.16602i	0.140187	−	0.242811i
$872$		0			0
$873$	10.4136	−	6.01227i	0.352446	−	0.203485i
$874$		0			0
$875$	13.4580	+	18.2949i	0.454965	+	0.618481i
$876$		0			0
$877$	36.7925	−	21.2421i	1.24239	−	0.717296i	0.272812	−	0.962067i	$-0.412046\pi$
$877$	36.7925	−	21.2421i	1.24239	−	0.717296i	0.969581	+	0.244771i	$0.0787128\pi$
$878$		0			0
$879$	−5.99387	−	3.46056i	−0.202168	−	0.116722i
$880$		0			0
$881$			16.9890i			0.572373i	0.958174	+	0.286187i	$0.0923877\pi$
$881$			16.9890i			0.572373i	−0.958174	+	0.286187i	$0.907612\pi$
$882$		0			0
$883$	35.1247			1.18204			0.591021	−	0.806656i	$-0.298725\pi$
$883$	35.1247			1.18204			0.591021	+	0.806656i	$0.298725\pi$
$884$		0			0
$885$	0.198117	−	0.343149i	0.00665963	−	0.0115348i
$886$		0			0
$887$	17.6491	+	30.5691i	0.592598	+	1.02641i	0.993881	+	0.110456i	$0.0352311\pi$
$887$	17.6491	+	30.5691i	0.592598	+	1.02641i	−0.401283	+	0.915954i	$0.631436\pi$
$888$		0			0
$889$	−31.5151	+	23.1831i	−1.05698	+	0.777535i
$890$		0			0
$891$	−0.195786	−	0.339111i	−0.00655906	−	0.0113606i
$892$		0			0
$893$	−55.4018	−	31.9863i	−1.85395	−	1.07038i
$894$		0			0
$895$	−44.7601			−1.49617
$896$		0			0
$897$	8.67380			0.289610
$898$		0			0
$899$	−3.65693	−	2.11133i	−0.121965	−	0.0704167i
$900$		0			0
$901$	−3.72243	−	6.44744i	−0.124012	−	0.214795i
$902$		0			0
$903$	3.23534	+	29.1242i	0.107665	+	0.969194i
$904$		0			0
$905$	−22.2031	−	38.4569i	−0.738056	−	1.27835i
$906$		0			0
$907$	12.4660	−	21.5918i	0.413928	−	0.716944i	−0.581388	−	0.813627i	$-0.697490\pi$
$907$	12.4660	−	21.5918i	0.413928	−	0.716944i	0.995315	+	0.0966832i	$0.0308234\pi$
$908$		0			0
$909$	11.1685			0.370434
$910$		0			0
$911$		−	19.2680i		−	0.638378i	−0.947691	−	0.319189i	$-0.896590\pi$
$911$		−	19.2680i		−	0.638378i	0.947691	−	0.319189i	$-0.103410\pi$
$912$		0			0
$913$	−4.19533	−	2.42217i	−0.138845	−	0.0801623i
$914$		0			0
$915$	−10.1267	+	5.84667i	−0.334779	+	0.193285i
$916$		0			0
$917$	10.8813	+	4.76778i	0.359333	+	0.157446i
$918$		0			0
$919$	43.5634	−	25.1513i	1.43702	−	0.829666i	0.439382	−	0.898300i	$-0.355197\pi$
$919$	43.5634	−	25.1513i	1.43702	−	0.829666i	0.997642	+	0.0686339i	$0.0218641\pi$
$920$		0			0
$921$	6.42334	−	11.1255i	0.211656	−	0.366599i
$922$		0			0
$923$		−	0.880887i		−	0.0289947i
$924$		0			0
$925$		−	9.37744i		−	0.308328i
$926$		0			0
$927$	−0.278669	+	0.482668i	−0.00915268	+	0.0158529i
$928$		0			0
$929$	−23.7129	+	13.6906i	−0.777995	+	0.449175i	−0.835719	−	0.549157i	$-0.814949\pi$
$929$	−23.7129	+	13.6906i	−0.777995	+	0.449175i	0.0577246	+	0.998333i	$0.481615\pi$
$930$		0			0
$931$	−7.44577	−	33.0996i	−0.244025	−	1.08479i
$932$		0			0
$933$	−14.5400	+	8.39468i	−0.476019	+	0.274830i
$934$		0			0
$935$	0.686298	+	0.396234i	0.0224443	+	0.0129582i
$936$		0			0
$937$		−	20.6712i		−	0.675300i	−0.941272	−	0.337650i	$-0.890368\pi$
$937$		−	20.6712i		−	0.675300i	0.941272	−	0.337650i	$-0.109632\pi$
$938$		0			0
$939$	2.38919			0.0779684
$940$		0			0
$941$	−7.95079	+	13.7712i	−0.259188	+	0.448928i	−0.966025	−	0.258450i	$-0.916788\pi$
$941$	−7.95079	+	13.7712i	−0.259188	+	0.448928i	0.706836	+	0.707377i	$0.250122\pi$
$942$		0			0
$943$	10.9758	+	19.0107i	0.357422	+	0.619074i
$944$		0			0
$945$	−6.26245	−	2.74396i	−0.203717	−	0.0892610i
$946$		0			0
$947$	−19.3046	−	33.4365i	−0.627314	−	1.08654i	−0.988089	−	0.153886i	$-0.950821\pi$
$947$	−19.3046	−	33.4365i	−0.627314	−	1.08654i	0.360775	−	0.932653i	$-0.382512\pi$
$948$		0			0
$949$	17.2353	+	9.95083i	0.559483	+	0.323018i
$950$		0			0
$951$	26.6273			0.863449
$952$		0			0
$953$	−14.4062			−0.466664			−0.233332	−	0.972397i	$-0.574963\pi$
$953$	−14.4062			−0.466664			−0.233332	+	0.972397i	$0.574963\pi$
$954$		0			0
$955$	39.5978	+	22.8618i	1.28135	+	0.739790i
$956$		0			0
$957$	0.351445	+	0.608721i	0.0113606	+	0.0196771i
$958$		0			0
$959$	−34.3154	+	3.81201i	−1.10810	+	0.123096i
$960$		0			0
$961$	12.7331	+	22.0544i	0.410746	+	0.711433i
$962$		0			0
$963$	6.79542	−	11.7700i	0.218979	−	0.379283i
$964$		0			0
$965$	15.9407			0.513148
$966$		0			0
$967$			45.8371i			1.47402i	0.675880	+	0.737011i	$0.263764\pi$
$967$			45.8371i			1.47402i	−0.675880	+	0.737011i	$0.736236\pi$
$968$		0			0
$969$	−3.28712	−	1.89782i	−0.105597	−	0.0609667i
$970$		0			0
$971$	24.8623	−	14.3542i	0.797868	−	0.460649i	−0.0448572	−	0.998993i	$-0.514283\pi$
$971$	24.8623	−	14.3542i	0.797868	−	0.460649i	0.842725	+	0.538344i	$0.180950\pi$
$972$		0			0
$973$	−36.6220	+	26.9398i	−1.17405	+	0.863651i
$974$		0			0
$975$	2.43910	−	1.40821i	0.0781136	−	0.0450989i
$976$		0			0
$977$	−19.8618	+	34.4016i	−0.635435	+	1.10061i	0.350988	+	0.936380i	$0.385846\pi$
$977$	−19.8618	+	34.4016i	−0.635435	+	1.10061i	−0.986423	+	0.164226i	$0.947487\pi$
$978$		0			0
$979$			4.91113i			0.156960i
$980$		0			0
$981$		−	17.2207i		−	0.549815i
$982$		0			0
$983$	7.38573	−	12.7925i	0.235568	−	0.408016i	−0.723869	−	0.689937i	$-0.757638\pi$
$983$	7.38573	−	12.7925i	0.235568	−	0.408016i	0.959438	+	0.281921i	$0.0909715\pi$
$984$		0			0
$985$	57.3274	−	33.0980i	1.82660	−	1.05459i
$986$		0			0
$987$	28.1306	−	20.6933i	0.895406	−	0.658676i
$988$		0			0
$989$	49.5747	−	28.6220i	1.57638	−	0.910125i
$990$		0			0
$991$	30.1791	+	17.4239i	0.958671	+	0.553489i	0.895764	−	0.444530i	$-0.146629\pi$
$991$	30.1791	+	17.4239i	0.958671	+	0.553489i	0.0629072	+	0.998019i	$0.479963\pi$
$992$		0			0
$993$		−	28.8478i		−	0.915456i
$994$		0			0
$995$	−0.325611			−0.0103226
$996$		0			0
$997$	−7.10156	+	12.3003i	−0.224909	+	0.389553i	−0.956292	−	0.292413i	$-0.905542\pi$
$997$	−7.10156	+	12.3003i	−0.224909	+	0.389553i	0.731383	+	0.681966i	$0.238875\pi$
$998$		0			0
$999$	−2.79386	−	4.83911i	−0.0883939	−	0.153103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bb.f.31.4	yes	12
4.3	odd	2	inner	1344.2.bb.f.31.1	✓	12
7.5	odd	6		1344.2.bb.g.607.6	yes	12
8.3	odd	2		1344.2.bb.g.31.6	yes	12
8.5	even	2		1344.2.bb.g.31.3	yes	12
28.19	even	6		1344.2.bb.g.607.3	yes	12
56.5	odd	6	inner	1344.2.bb.f.607.1	yes	12
56.19	even	6	inner	1344.2.bb.f.607.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1344.2.bb.f.31.1	✓	12	4.3	odd	2	inner
1344.2.bb.f.31.4	yes	12	1.1	even	1	trivial
1344.2.bb.f.607.1	yes	12	56.5	odd	6	inner
1344.2.bb.f.607.4	yes	12	56.19	even	6	inner
1344.2.bb.g.31.3	yes	12	8.5	even	2
1344.2.bb.g.31.6	yes	12	8.3	odd	2
1344.2.bb.g.607.3	yes	12	28.19	even	6
1344.2.bb.g.607.6	yes	12	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.29211 - 2.23800i) q^{5} +(-1.56777 - 2.13122i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.29211 - 2.23800i) q^{5} +(-1.56777 - 2.13122i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.195786 + 0.339111i) q^{11} -1.67822 q^{13} -2.58423i q^{15} +(0.678221 + 0.391571i) q^{17} +(-4.19734 + 2.42334i) q^{19} +(-0.292113 - 2.62958i) q^{21} +(-4.47601 + 2.58423i) q^{23} +(-0.839111 + 1.45338i) q^{25} +1.00000i q^{27} -1.79505i q^{29} +(1.17619 - 2.03723i) q^{31} +(-0.339111 + 0.195786i) q^{33} +(-2.74396 + 6.26245i) q^{35} +(-4.83911 + 2.79386i) q^{37} +(-1.45338 - 0.839111i) q^{39} -4.24724i q^{41} -11.0756 q^{43} +(1.29211 - 2.23800i) q^{45} +(6.59963 + 11.4309i) q^{47} +(-2.08423 + 6.68251i) q^{49} +(0.391571 + 0.678221i) q^{51} +(-8.23278 - 4.75320i) q^{53} +1.01191 q^{55} -4.84667 q^{57} +(0.132786 + 0.0766640i) q^{59} +(-2.26245 - 3.91867i) q^{61} +(1.06181 - 2.42334i) q^{63} +(2.16845 + 3.75587i) q^{65} +(-2.46529 + 4.27001i) q^{67} -5.16845 q^{69} +0.524893i q^{71} +(-10.2700 - 5.92939i) q^{73} +(-1.45338 + 0.839111i) q^{75} +(1.02967 - 0.114383i) q^{77} +(-2.51667 + 1.45300i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.3716i q^{83} -2.02382i q^{85} +(0.897525 - 1.55456i) q^{87} +(10.8618 - 6.27106i) q^{89} +(2.63106 + 3.57666i) q^{91} +(2.03723 - 1.17619i) q^{93} +(10.8469 + 6.26245i) q^{95} -12.0245i q^{97} -0.391571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^9	\( 12 q + 6 q^{9} - 12 q^{13} + 12 q^{21} - 6 q^{25} - 54 q^{37} + 6 q^{49} - 36 q^{53} + 12 q^{57} + 12 q^{61} - 36 q^{65} - 18 q^{73} + 36 q^{77} - 6 q^{81} - 72 q^{89} - 18 q^{93}+O(q^{100}) \) 12 * q + 6 * q^9 - 12 * q^13 + 12 * q^21 - 6 * q^25 - 54 * q^37 + 6 * q^49 - 36 * q^53 + 12 * q^57 + 12 * q^61 - 36 * q^65 - 18 * q^73 + 36 * q^77 - 6 * q^81 - 72 * q^89 - 18 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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