LMFDB - Embedded newform 144.2.l.a.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(35,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("144.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.l (of order $4$, 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.5
Root			$-0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	144.107
Dual form			144.2.l.a.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.263185 + 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(-2.63251 + 2.63251i) q^{5} -0.207188 q^{7} +(-1.50619 - 2.39403i) q^{8} +O(q^{10})$	\(q+(0.263185 + 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(-2.63251 + 2.63251i) q^{5} -0.207188 q^{7} +(-1.50619 - 2.39403i) q^{8} +(-4.35074 - 2.96506i) q^{10} +(3.66686 + 3.66686i) q^{11} +(0.255601 - 0.255601i) q^{13} +(-0.0545288 - 0.287890i) q^{14} +(2.93012 - 2.72294i) q^{16} -0.654483i q^{17} +(4.46733 + 4.46733i) q^{19} +(2.97493 - 6.82574i) q^{20} +(-4.13007 + 6.06020i) q^{22} -3.48934i q^{23} -8.86025i q^{25} +(0.422430 + 0.287890i) q^{26} +(0.385674 - 0.151536i) q^{28} +(-4.33973 - 4.33973i) q^{29} +6.16426i q^{31} +(4.55471 + 3.35480i) q^{32} +(0.909410 - 0.172250i) q^{34} +(0.545426 - 0.545426i) q^{35} +(4.39291 + 4.39291i) q^{37} +(-5.03166 + 7.38313i) q^{38} +(10.2674 + 2.33726i) q^{40} -0.0684664 q^{41} +(5.65306 - 5.65306i) q^{43} +(-9.50767 - 4.14382i) q^{44} +(4.84846 - 0.918340i) q^{46} +9.14619 q^{47} -6.95707 q^{49} +(12.3114 - 2.33188i) q^{50} +(-0.288848 + 0.662739i) q^{52} +(-1.51131 + 1.51131i) q^{53} -19.3061 q^{55} +(0.312065 + 0.496015i) q^{56} +(4.88795 - 7.17225i) q^{58} +(-2.53542 - 2.53542i) q^{59} +(-5.46733 + 5.46733i) q^{61} +(-8.56529 + 1.62234i) q^{62} +(-3.46279 + 7.21173i) q^{64} +1.34575i q^{65} +(-4.77135 - 4.77135i) q^{67} +(0.478686 + 1.21830i) q^{68} +(0.901421 + 0.614326i) q^{70} -5.94986i q^{71} -6.93467i q^{73} +(-4.94784 + 7.26014i) q^{74} +(-11.5832 - 5.04841i) q^{76} +(-0.759730 - 0.759730i) q^{77} -4.72748i q^{79} +(-0.545426 + 14.8817i) q^{80} +(-0.0180193 - 0.0951346i) q^{82} +(-4.32777 + 4.32777i) q^{83} +(1.72294 + 1.72294i) q^{85} +(9.34277 + 6.36717i) q^{86} +(3.25560 - 14.3016i) q^{88} +11.9443 q^{89} +(-0.0529576 + 0.0529576i) q^{91} +(2.55208 + 6.49529i) q^{92} +(2.40714 + 12.7087i) q^{94} -23.5206 q^{95} -0.925579 q^{97} +(-1.83100 - 9.66691i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.263185	+	1.38951i	0.186100	+	0.982531i
$2$	0.263185	+	1.38951i	0.186100	+	0.982531i
$3$		0			0
$3$		0			0
$4$	−1.86147	+	0.731395i	−0.930734	+	0.365697i
$5$	−2.63251	+	2.63251i	−1.17730	+	1.17730i	−0.196865	+	0.980431i	$0.563076\pi$
$5$	−2.63251	+	2.63251i	−1.17730	+	1.17730i	−0.980431	+	0.196865i	$0.936924\pi$
$6$		0			0
$7$	−0.207188			−0.0783098			−0.0391549	−	0.999233i	$-0.512467\pi$
$7$	−0.207188			−0.0783098			−0.0391549	+	0.999233i	$0.512467\pi$
$8$	−1.50619	−	2.39403i	−0.532518	−	0.846419i
$9$		0			0
$10$	−4.35074	−	2.96506i	−1.37582	−	0.937635i
$11$	3.66686	+	3.66686i	1.10560	+	1.10560i	0.993722	+	0.111878i	$0.0356867\pi$
$11$	3.66686	+	3.66686i	1.10560	+	1.10560i	0.111878	+	0.993722i	$0.464313\pi$
$12$		0			0
$13$	0.255601	−	0.255601i	0.0708910	−	0.0708910i	−0.670772	−	0.741663i	$-0.734037\pi$
$13$	0.255601	−	0.255601i	0.0708910	−	0.0708910i	0.741663	+	0.670772i	$0.234037\pi$
$14$	−0.0545288	−	0.287890i	−0.0145734	−	0.0769418i
$15$		0			0
$16$	2.93012	−	2.72294i	0.732531	−	0.680734i
$17$		−	0.654483i		−	0.158735i	−0.996845	−	0.0793677i	$-0.974710\pi$
$17$		−	0.654483i		−	0.158735i	0.996845	−	0.0793677i	$-0.0252901\pi$
$18$		0			0
$19$	4.46733	+	4.46733i	1.02488	+	1.02488i	0.999683	+	0.0251941i	$0.00802039\pi$
$19$	4.46733	+	4.46733i	1.02488	+	1.02488i	0.0251941	+	0.999683i	$0.491980\pi$
$20$	2.97493	−	6.82574i	0.665215	−	1.52628i
$21$		0			0
$22$	−4.13007	+	6.06020i	−0.880534	+	1.29204i
$23$		−	3.48934i		−	0.727577i	−0.931482	−	0.363789i	$-0.881483\pi$
$23$		−	3.48934i		−	0.727577i	0.931482	−	0.363789i	$-0.118517\pi$
$24$		0			0
$25$		−	8.86025i		−	1.77205i
$26$	0.422430	+	0.287890i	0.0828454	+	0.0564598i
$27$		0			0
$28$	0.385674	−	0.151536i	0.0728856	−	0.0286377i
$29$	−4.33973	−	4.33973i	−0.805869	−	0.805869i	0.178137	−	0.984006i	$-0.442993\pi$
$29$	−4.33973	−	4.33973i	−0.805869	−	0.805869i	−0.984006	+	0.178137i	$0.942993\pi$
$30$		0			0
$31$			6.16426i			1.10713i	0.832805	+	0.553567i	$0.186734\pi$
$31$			6.16426i			1.10713i	−0.832805	+	0.553567i	$0.813266\pi$
$32$	4.55471	+	3.35480i	0.805166	+	0.593050i
$33$		0			0
$34$	0.909410	−	0.172250i	0.155963	−	0.0295406i
$35$	0.545426	−	0.545426i	0.0921938	−	0.0921938i
$36$		0			0
$37$	4.39291	+	4.39291i	0.722190	+	0.722190i	0.969051	−	0.246861i	$-0.0793990\pi$
$37$	4.39291	+	4.39291i	0.722190	+	0.722190i	−0.246861	+	0.969051i	$0.579399\pi$
$38$	−5.03166	+	7.38313i	−0.816244	+	1.19770i
$39$		0			0
$40$	10.2674	+	2.33726i	1.62342	+	0.369553i
$41$	−0.0684664			−0.0106927			−0.00534633	−	0.999986i	$-0.501702\pi$
$41$	−0.0684664			−0.0106927			−0.00534633	+	0.999986i	$0.501702\pi$
$42$		0			0
$43$	5.65306	−	5.65306i	0.862083	−	0.862083i	−0.129497	−	0.991580i	$-0.541336\pi$
$43$	5.65306	−	5.65306i	0.862083	−	0.862083i	0.991580	+	0.129497i	$0.0413361\pi$
$44$	−9.50767	−	4.14382i	−1.43333	−	0.624704i
$45$		0			0
$46$	4.84846	−	0.918340i	0.714867	−	0.135402i
$47$	9.14619			1.33411			0.667055	−	0.745009i	$-0.267555\pi$
$47$	9.14619			1.33411			0.667055	+	0.745009i	$0.267555\pi$
$48$		0			0
$49$	−6.95707			−0.993868
$50$	12.3114	−	2.33188i	1.74109	−	0.329778i
$51$		0			0
$52$	−0.288848	+	0.662739i	−0.0400560	+	0.0919053i
$53$	−1.51131	+	1.51131i	−0.207594	+	0.207594i	−0.803244	−	0.595650i	$-0.796895\pi$
$53$	−1.51131	+	1.51131i	−0.207594	+	0.207594i	0.595650	+	0.803244i	$0.296895\pi$
$54$		0			0
$55$	−19.3061			−2.60324
$56$	0.312065	+	0.496015i	0.0417014	+	0.0662829i
$57$		0			0
$58$	4.88795	−	7.17225i	0.641819	−	0.941763i
$59$	−2.53542	−	2.53542i	−0.330083	−	0.330083i	0.522535	−	0.852618i	$-0.324987\pi$
$59$	−2.53542	−	2.53542i	−0.330083	−	0.330083i	−0.852618	+	0.522535i	$0.824987\pi$
$60$		0			0
$61$	−5.46733	+	5.46733i	−0.700020	+	0.700020i	−0.964415	−	0.264394i	$-0.914828\pi$
$61$	−5.46733	+	5.46733i	−0.700020	+	0.700020i	0.264394	+	0.964415i	$0.414828\pi$
$62$	−8.56529	+	1.62234i	−1.08779	+	0.206037i
$63$		0			0
$64$	−3.46279	+	7.21173i	−0.432849	+	0.901467i
$65$			1.34575i			0.166919i
$66$		0			0
$67$	−4.77135	−	4.77135i	−0.582913	−	0.582913i	0.352790	−	0.935703i	$-0.385233\pi$
$67$	−4.77135	−	4.77135i	−0.582913	−	0.582913i	−0.935703	+	0.352790i	$0.885233\pi$
$68$	0.478686	+	1.21830i	0.0580491	+	0.147740i
$69$		0			0
$70$	0.901421	+	0.614326i	0.107740	+	0.0734260i
$71$		−	5.94986i		−	0.706119i	−0.935601	−	0.353059i	$-0.885141\pi$
$71$		−	5.94986i		−	0.706119i	0.935601	−	0.353059i	$-0.114859\pi$
$72$		0			0
$73$		−	6.93467i		−	0.811641i	−0.913953	−	0.405821i	$-0.866986\pi$
$73$		−	6.93467i		−	0.811641i	0.913953	−	0.405821i	$-0.133014\pi$
$74$	−4.94784	+	7.26014i	−0.575175	+	0.843974i
$75$		0			0
$76$	−11.5832	−	5.04841i	−1.32868	−	0.579093i
$77$	−0.759730	−	0.759730i	−0.0865793	−	0.0865793i
$78$		0			0
$79$		−	4.72748i		−	0.531883i	−0.963989	−	0.265942i	$-0.914317\pi$
$79$		−	4.72748i		−	0.531883i	0.963989	−	0.265942i	$-0.0856828\pi$
$80$	−0.545426	+	14.8817i	−0.0609804	+	1.66383i
$81$		0			0
$82$	−0.0180193	−	0.0951346i	−0.00198990	−	0.0105059i
$83$	−4.32777	+	4.32777i	−0.475035	+	0.475035i	−0.903539	−	0.428505i	$-0.859040\pi$
$83$	−4.32777	+	4.32777i	−0.475035	+	0.475035i	0.428505	+	0.903539i	$0.359040\pi$
$84$		0			0
$85$	1.72294	+	1.72294i	0.186879	+	0.186879i
$86$	9.34277	+	6.36717i	1.00746	+	0.686590i
$87$		0			0
$88$	3.25560	−	14.3016i	0.347048	−	1.52455i
$89$	11.9443			1.26609			0.633045	−	0.774115i	$-0.281805\pi$
$89$	11.9443			1.26609			0.633045	+	0.774115i	$0.281805\pi$
$90$		0			0
$91$	−0.0529576	+	0.0529576i	−0.00555146	+	0.00555146i
$92$	2.55208	+	6.49529i	0.266073	+	0.677181i
$93$		0			0
$94$	2.40714	+	12.7087i	0.248277	+	1.31080i
$95$	−23.5206			−2.41317
$96$		0			0
$97$	−0.925579			−0.0939783			−0.0469892	−	0.998895i	$-0.514963\pi$
$97$	−0.925579			−0.0939783			−0.0469892	+	0.998895i	$0.514963\pi$
$98$	−1.83100	−	9.66691i	−0.184958	−	0.976506i
$99$		0			0
$100$	6.48034	+	16.4931i	0.648034	+	1.64931i
$101$	2.27104	−	2.27104i	0.225977	−	0.225977i	−0.585033	−	0.811010i	$-0.698918\pi$
$101$	2.27104	−	2.27104i	0.225977	−	0.225977i	0.811010	+	0.585033i	$0.198918\pi$
$102$		0			0
$103$	14.1643			1.39565			0.697823	−	0.716270i	$-0.254152\pi$
$103$	14.1643			1.39565			0.697823	+	0.716270i	$0.254152\pi$
$104$	−0.996902	−	0.226934i	−0.0977543	−	0.0222527i
$105$		0			0
$106$	−2.49773	−	1.70222i	−0.242601	−	0.165334i
$107$	8.85318	+	8.85318i	0.855870	+	0.855870i	0.990848	−	0.134979i	$-0.0430967\pi$
$107$	8.85318	+	8.85318i	0.855870	+	0.855870i	−0.134979	+	0.990848i	$0.543097\pi$
$108$		0			0
$109$	−2.66998	+	2.66998i	−0.255737	+	0.255737i	−0.823318	−	0.567580i	$-0.807880\pi$
$109$	−2.66998	+	2.66998i	−0.255737	+	0.255737i	0.567580	+	0.823318i	$0.307880\pi$
$110$	−5.08107	−	26.8260i	−0.484461	−	2.55776i
$111$		0			0
$112$	−0.607087	+	0.564160i	−0.0573643	+	0.0533081i
$113$		−	8.39289i		−	0.789536i	−0.918781	−	0.394768i	$-0.870825\pi$
$113$		−	8.39289i		−	0.789536i	0.918781	−	0.394768i	$-0.129175\pi$
$114$		0			0
$115$	9.18572	+	9.18572i	0.856573	+	0.856573i
$116$	11.2523	+	4.90422i	1.04475	+	0.455345i
$117$		0			0
$118$	2.85570	−	4.19027i	0.262889	−	0.385746i
$119$			0.135601i			0.0124305i
$120$		0			0
$121$			15.8917i			1.44470i
$122$	−9.03583	−	6.15799i	−0.818065	−	0.557518i
$123$		0			0
$124$	−4.50851	−	11.4746i	−0.404876	−	1.03045i
$125$	10.1621	+	10.1621i	0.908930	+	0.908930i
$126$		0			0
$127$		−	9.64397i		−	0.855764i	−0.903835	−	0.427882i	$-0.859260\pi$
$127$		−	9.64397i		−	0.855764i	0.903835	−	0.427882i	$-0.140740\pi$
$128$	−10.9321	−	2.91356i	−0.966272	−	0.257525i
$129$		0			0
$130$	−1.86993	+	0.354180i	−0.164003	+	0.0310636i
$131$	−5.07084	+	5.07084i	−0.443041	+	0.443041i	−0.893033	−	0.449992i	$-0.851427\pi$
$131$	−5.07084	+	5.07084i	−0.443041	+	0.443041i	0.449992	+	0.893033i	$0.351427\pi$
$132$		0			0
$133$	−0.925579	−	0.925579i	−0.0802579	−	0.0802579i
$134$	5.37408	−	7.88557i	0.464250	−	0.681210i
$135$		0			0
$136$	−1.56685	+	0.985775i	−0.134357	+	0.0845295i
$137$	11.9075			1.01732			0.508662	−	0.860966i	$-0.330140\pi$
$137$	11.9075			1.01732			0.508662	+	0.860966i	$0.330140\pi$
$138$		0			0
$139$	0.771348	−	0.771348i	0.0654249	−	0.0654249i	−0.673637	−	0.739062i	$-0.735269\pi$
$139$	0.771348	−	0.771348i	0.0654249	−	0.0654249i	0.739062	+	0.673637i	$0.235269\pi$
$140$	−0.616371	+	1.41421i	−0.0520928	+	0.119523i
$141$		0			0
$142$	8.26738	−	1.56591i	0.693784	−	0.131408i
$143$	1.87451			0.156754
$144$		0			0
$145$	22.8488			1.89749
$146$	9.63578	−	1.82510i	0.797463	−	0.151046i
$147$		0			0
$148$	−11.3902	−	4.96431i	−0.936270	−	0.408064i
$149$	−3.02434	+	3.02434i	−0.247764	+	0.247764i	−0.820052	−	0.572289i	$-0.806056\pi$
$149$	−3.02434	+	3.02434i	−0.247764	+	0.247764i	0.572289	+	0.820052i	$0.306056\pi$
$150$		0			0
$151$	6.57864			0.535362			0.267681	−	0.963508i	$-0.413743\pi$
$151$	6.57864			0.535362			0.267681	+	0.963508i	$0.413743\pi$
$152$	3.96630	−	17.4236i	0.321709	−	1.41324i
$153$		0			0
$154$	0.855702	−	1.25560i	0.0689545	−	0.101179i
$155$	−16.2275	−	16.2275i	−1.30342	−	1.30342i
$156$		0			0
$157$	7.46733	−	7.46733i	0.595958	−	0.595958i	−0.343276	−	0.939234i	$-0.611537\pi$
$157$	7.46733	−	7.46733i	0.595958	−	0.595958i	0.939234	+	0.343276i	$0.111537\pi$
$158$	6.56887	−	1.24420i	0.522591	−	0.0989833i
$159$		0			0
$160$	−20.8219	+	3.15878i	−1.64611	+	0.249723i
$161$			0.722950i			0.0569764i
$162$		0			0
$163$	−14.0674	−	14.0674i	−1.10185	−	1.10185i	−0.994188	−	0.107659i	$-0.965665\pi$
$163$	−14.0674	−	14.0674i	−1.10185	−	1.10185i	−0.107659	−	0.994188i	$-0.534335\pi$
$164$	0.127448	−	0.0500760i	0.00995201	−	0.00391028i
$165$		0			0
$166$	−7.15248	−	4.87447i	−0.555140	−	0.378332i
$167$			6.55006i			0.506859i	0.967354	+	0.253430i	$0.0815586\pi$
$167$			6.55006i			0.506859i	−0.967354	+	0.253430i	$0.918441\pi$
$168$		0			0
$169$			12.8693i			0.989949i
$170$	−1.94058	+	2.84748i	−0.148836	+	0.218392i
$171$		0			0
$172$	−6.38837	+	14.6576i	−0.487109	+	1.11763i
$173$	0.955645	+	0.955645i	0.0726563	+	0.0726563i	0.742501	−	0.669845i	$-0.233639\pi$
$173$	0.955645	+	0.955645i	0.0726563	+	0.0726563i	−0.669845	+	0.742501i	$0.733639\pi$
$174$		0			0
$175$			1.83574i			0.138769i
$176$	20.7290	+	0.759730i	1.56251	+	0.0572668i
$177$		0			0
$178$	3.14355	+	16.5967i	0.235619	+	1.24397i
$179$	8.77829	−	8.77829i	0.656120	−	0.656120i	−0.298340	−	0.954460i	$-0.596433\pi$
$179$	8.77829	−	8.77829i	0.656120	−	0.656120i	0.954460	+	0.298340i	$0.0964328\pi$
$180$		0			0
$181$	6.25560	+	6.25560i	0.464975	+	0.464975i	0.900282	−	0.435307i	$-0.143360\pi$
$181$	6.25560	+	6.25560i	0.464975	+	0.464975i	−0.435307	+	0.900282i	$0.643360\pi$
$182$	−0.0875226	−	0.0596474i	−0.00648761	−	0.00442136i
$183$		0			0
$184$	−8.35359	+	5.25560i	−0.615835	+	0.387448i
$185$	−23.1288			−1.70046
$186$		0			0
$187$	2.39990	−	2.39990i	0.175498	−	0.175498i
$188$	−17.0253	+	6.68948i	−1.24170	+	0.487880i
$189$		0			0
$190$	−6.19027	−	32.6821i	−0.449089	−	2.37101i
$191$	7.13608			0.516349			0.258174	−	0.966098i	$-0.416879\pi$
$191$	7.13608			0.516349			0.258174	+	0.966098i	$0.416879\pi$
$192$		0			0
$193$	−10.9347			−0.787095			−0.393547	−	0.919304i	$-0.628752\pi$
$193$	−10.9347			−0.787095			−0.393547	+	0.919304i	$0.628752\pi$
$194$	−0.243598	−	1.28610i	−0.0174893	−	0.0923366i
$195$		0			0
$196$	12.9504	−	5.08837i	0.925026	−	0.363455i
$197$	10.3277	−	10.3277i	0.735819	−	0.735819i	−0.235947	−	0.971766i	$-0.575819\pi$
$197$	10.3277	−	10.3277i	0.735819	−	0.735819i	0.971766	+	0.235947i	$0.0758192\pi$
$198$		0			0
$199$	7.18478			0.509316			0.254658	−	0.967031i	$-0.418037\pi$
$199$	7.18478			0.509316			0.254658	+	0.967031i	$0.418037\pi$
$200$	−21.2117	+	13.3452i	−1.49990	+	0.943649i
$201$		0			0
$202$	3.75333	+	2.55792i	0.264083	+	0.179975i
$203$	0.899142	+	0.899142i	0.0631074	+	0.0631074i
$204$		0			0
$205$	0.180239	−	0.180239i	0.0125884	−	0.0125884i
$206$	3.72782	+	19.6814i	0.259729	+	1.37127i
$207$		0			0
$208$	0.0529576	−	1.44493i	0.00367195	−	0.100188i
$209$			32.7622i			2.26621i
$210$		0			0
$211$	−0.163320	−	0.163320i	−0.0112434	−	0.0112434i	0.701463	−	0.712706i	$-0.252531\pi$
$211$	−0.163320	−	0.163320i	−0.0112434	−	0.0112434i	−0.712706	+	0.701463i	$0.752531\pi$
$212$	1.70789	−	3.91861i	0.117298	−	0.269131i
$213$		0			0
$214$	−9.97155	+	14.6316i	−0.681641	+	1.00020i
$215$			29.7635i			2.02985i
$216$		0			0
$217$		−	1.27716i		−	0.0866994i
$218$	−4.41265	−	3.00726i	−0.298863	−	0.203677i
$219$		0			0
$220$	35.9377	−	14.1204i	2.42292	−	0.951997i
$221$	−0.167287	−	0.167287i	−0.0112529	−	0.0112529i
$222$		0			0
$223$			0.621565i			0.0416230i	0.999783	+	0.0208115i	$0.00662499\pi$
$223$			0.621565i			0.0416230i	−0.999783	+	0.0208115i	$0.993375\pi$
$224$	−0.943681	−	0.695074i	−0.0630524	−	0.0464416i
$225$		0			0
$226$	11.6620	−	2.20888i	0.775744	−	0.146932i
$227$	−10.9257	+	10.9257i	−0.725164	+	0.725164i	−0.969652	−	0.244489i	$-0.921380\pi$
$227$	−10.9257	+	10.9257i	−0.725164	+	0.725164i	0.244489	+	0.969652i	$0.421380\pi$
$228$		0			0
$229$	−17.9761	−	17.9761i	−1.18789	−	1.18789i	−0.977649	−	0.210245i	$-0.932574\pi$
$229$	−17.9761	−	17.9761i	−1.18789	−	1.18789i	−0.210245	−	0.977649i	$-0.567426\pi$
$230$	−10.3461	+	15.1812i	−0.682202	+	1.00102i
$231$		0			0
$232$	−3.85301	+	16.9259i	−0.252962	+	1.11124i
$233$	−21.5409			−1.41119			−0.705595	−	0.708616i	$-0.749320\pi$
$233$	−21.5409			−1.41119			−0.705595	+	0.708616i	$0.749320\pi$
$234$		0			0
$235$	−24.0775	+	24.0775i	−1.57064	+	1.57064i
$236$	6.57399	+	2.86521i	0.427930	+	0.186509i
$237$		0			0
$238$	−0.188419	+	0.0356882i	−0.0122134	+	0.00231332i
$239$	16.5420			1.07001			0.535005	−	0.844849i	$-0.320310\pi$
$239$	16.5420			1.07001			0.535005	+	0.844849i	$0.320310\pi$
$240$		0			0
$241$	−24.9008			−1.60400			−0.802002	−	0.597322i	$-0.796232\pi$
$241$	−24.9008			−1.60400			−0.802002	+	0.597322i	$0.796232\pi$
$242$	−22.0817	+	4.18246i	−1.41947	+	0.268859i
$243$		0			0
$244$	6.17849	−	14.1760i	0.395537	−	0.907528i
$245$	18.3146	−	18.3146i	1.17008	−	1.17008i
$246$		0			0
$247$	2.28371			0.145309
$248$	14.7574	−	9.28454i	0.937099	−	0.589569i
$249$		0			0
$250$	−11.4459	+	16.7949i	−0.723900	+	1.06220i
$251$	−8.73770	−	8.73770i	−0.551519	−	0.551519i	0.375360	−	0.926879i	$-0.377519\pi$
$251$	−8.73770	−	8.73770i	−0.551519	−	0.551519i	−0.926879	+	0.375360i	$0.877519\pi$
$252$		0			0
$253$	12.7949	−	12.7949i	0.804409	−	0.804409i
$254$	13.4004	−	2.53815i	0.840814	−	0.159257i
$255$		0			0
$256$	1.17125	−	15.9571i	0.0732029	−	0.997317i
$257$		−	18.7732i		−	1.17104i	−0.810659	−	0.585519i	$-0.800891\pi$
$257$		−	18.7732i		−	1.17104i	0.810659	−	0.585519i	$-0.199109\pi$
$258$		0			0
$259$	−0.910160	−	0.910160i	−0.0565546	−	0.0565546i
$260$	−0.984272	−	2.50506i	−0.0610420	−	0.155358i
$261$		0			0
$262$	−8.38054	−	5.71140i	−0.517751	−	0.352852i
$263$		−	19.1523i		−	1.18098i	−0.807045	−	0.590490i	$-0.798935\pi$
$263$		−	19.1523i		−	1.18098i	0.807045	−	0.590490i	$-0.201065\pi$
$264$		0			0
$265$		−	7.95707i		−	0.488799i
$266$	1.04250	−	1.52970i	0.0639199	−	0.0937918i
$267$		0			0
$268$	12.3714	+	5.39197i	0.755707	+	0.329367i
$269$	−4.69478	−	4.69478i	−0.286246	−	0.286246i	0.549348	−	0.835594i	$-0.314876\pi$
$269$	−4.69478	−	4.69478i	−0.286246	−	0.286246i	−0.835594	+	0.549348i	$0.814876\pi$
$270$		0			0
$271$			25.2478i			1.53369i	0.641831	+	0.766846i	$0.278175\pi$
$271$			25.2478i			1.53369i	−0.641831	+	0.766846i	$0.721825\pi$
$272$	−1.78212	−	1.91772i	−0.108057	−	0.116279i
$273$		0			0
$274$	3.13387	+	16.5455i	0.189324	+	0.999553i
$275$	32.4893	−	32.4893i	1.95918	−	1.95918i
$276$		0			0
$277$	−21.1473	−	21.1473i	−1.27062	−	1.27062i	−0.945763	−	0.324858i	$-0.894684\pi$
$277$	−21.1473	−	21.1473i	−1.27062	−	1.27062i	−0.324858	−	0.945763i	$-0.605316\pi$
$278$	1.27480	+	0.868788i	0.0764575	+	0.0521064i
$279$		0			0
$280$	−2.12728	−	0.484253i	−0.127129	−	0.0289396i
$281$	−6.34812			−0.378697			−0.189348	−	0.981910i	$-0.560638\pi$
$281$	−6.34812			−0.378697			−0.189348	+	0.981910i	$0.560638\pi$
$282$		0			0
$283$	2.56322	−	2.56322i	0.152368	−	0.152368i	−0.626807	−	0.779175i	$-0.715639\pi$
$283$	2.56322	−	2.56322i	0.152368	−	0.152368i	0.779175	+	0.626807i	$0.215639\pi$
$284$	4.35170	+	11.0755i	0.258226	+	0.657209i
$285$		0			0
$286$	0.493342	+	2.60465i	0.0291719	+	0.154016i
$287$	0.0141854			0.000837339
$288$		0			0
$289$	16.5717			0.974803
$290$	6.01346	+	31.7486i	0.353122	+	1.86434i
$291$		0			0
$292$	5.07198	+	12.9087i	0.296815	+	0.755422i
$293$	−11.7102	+	11.7102i	−0.684119	+	0.684119i	−0.960926	−	0.276806i	$-0.910724\pi$
$293$	−11.7102	+	11.7102i	−0.684119	+	0.684119i	0.276806	+	0.960926i	$0.410724\pi$
$294$		0			0
$295$	13.3490			0.777211
$296$	3.90022	−	17.1333i	0.226696	−	0.995855i
$297$		0			0
$298$	−4.99831	−	3.40639i	−0.289544	−	0.197327i
$299$	−0.891879	−	0.891879i	−0.0515787	−	0.0515787i
$300$		0			0
$301$	−1.17125	+	1.17125i	−0.0675096	+	0.0675096i
$302$	1.73140	+	9.14107i	0.0996307	+	0.526010i
$303$		0			0
$304$	25.2541	+	0.925579i	1.44842	+	0.0530856i
$305$		−	28.7857i		−	1.64826i
$306$		0			0
$307$	−11.5572	−	11.5572i	−0.659603	−	0.659603i	0.295683	−	0.955286i	$-0.404453\pi$
$307$	−11.5572	−	11.5572i	−0.659603	−	0.659603i	−0.955286	+	0.295683i	$0.904453\pi$
$308$	1.96988	+	0.858551i	0.112244	+	0.0489205i
$309$		0			0
$310$	18.2774	−	26.8191i	1.03809	−	1.52322i
$311$			13.9316i			0.789991i	0.918683	+	0.394995i	$0.129254\pi$
$311$			13.9316i			0.789991i	−0.918683	+	0.394995i	$0.870746\pi$
$312$		0			0
$313$			17.8264i			1.00761i	0.863818	+	0.503804i	$0.168067\pi$
$313$			17.8264i			1.00761i	−0.863818	+	0.503804i	$0.831933\pi$
$314$	12.3412	+	8.41064i	0.696455	+	0.474640i
$315$		0			0
$316$	3.45765	+	8.80005i	0.194508	+	0.495042i
$317$	−11.6127	−	11.6127i	−0.652237	−	0.652237i	0.301294	−	0.953531i	$-0.402581\pi$
$317$	−11.6127	−	11.6127i	−0.652237	−	0.652237i	−0.953531	+	0.301294i	$0.902581\pi$
$318$		0			0
$319$		−	31.8264i		−	1.78194i
$320$	−9.86914	−	28.1008i	−0.551702	−	1.57088i
$321$		0			0
$322$	−1.00454	+	0.190269i	−0.0559811	+	0.0106033i
$323$	2.92379	−	2.92379i	0.162684	−	0.162684i
$324$		0			0
$325$	−2.26469	−	2.26469i	−0.125622	−	0.125622i
$326$	15.8445	−	23.2492i	0.877545	−	1.28765i
$327$		0			0
$328$	0.103123	+	0.163911i	0.00569403	+	0.00905046i
$329$	−1.89498			−0.104474
$330$		0			0
$331$	−23.5572	+	23.5572i	−1.29482	+	1.29482i	−0.363050	+	0.931770i	$0.618264\pi$
$331$	−23.5572	+	23.5572i	−1.29482	+	1.29482i	−0.931770	+	0.363050i	$0.881736\pi$
$332$	4.89070	−	11.2213i	0.268412	−	0.615850i
$333$		0			0
$334$	−9.10137	+	1.72388i	−0.498005	+	0.0943263i
$335$	25.1213			1.37252
$336$		0			0
$337$	22.8488			1.24465			0.622327	−	0.782757i	$-0.286187\pi$
$337$	22.8488			1.24465			0.622327	+	0.782757i	$0.286187\pi$
$338$	−17.8821	+	3.38701i	−0.972655	+	0.184229i
$339$		0			0
$340$	−4.46733	−	1.94704i	−0.242275	−	0.105593i
$341$	−22.6035	+	22.6035i	−1.22405	+	1.22405i
$342$		0			0
$343$	2.89174			0.156139
$344$	−22.0482	−	5.01904i	−1.18876	−	0.270608i
$345$		0			0
$346$	−1.07637	+	1.57939i	−0.0578658	+	0.0849084i
$347$	18.0542	+	18.0542i	0.969198	+	0.969198i	0.999540	−	0.0303420i	$-0.00965963\pi$
$347$	18.0542	+	18.0542i	0.969198	+	0.969198i	−0.0303420	+	0.999540i	$0.509660\pi$
$348$		0			0
$349$	−3.32758	+	3.32758i	−0.178121	+	0.178121i	−0.790536	−	0.612415i	$-0.790198\pi$
$349$	−3.32758	+	3.32758i	−0.178121	+	0.178121i	0.612415	+	0.790536i	$0.290198\pi$
$350$	−2.55077	+	0.483138i	−0.136345	+	0.0258248i
$351$		0			0
$352$	4.39990	+	29.0030i	0.234515	+	1.54587i
$353$			18.9229i			1.00717i	0.863947	+	0.503583i	$0.167985\pi$
$353$			18.9229i			1.00717i	−0.863947	+	0.503583i	$0.832015\pi$
$354$		0			0
$355$	15.6631	+	15.6631i	0.831310	+	0.831310i
$356$	−22.2339	+	8.73597i	−1.17839	+	0.463006i
$357$		0			0
$358$	14.5078	+	9.88720i	0.766762	+	0.522555i
$359$		−	32.0808i		−	1.69316i	−0.532262	−	0.846580i	$-0.678658\pi$
$359$		−	32.0808i		−	1.69316i	0.532262	−	0.846580i	$-0.321342\pi$
$360$		0			0
$361$			20.9141i			1.10074i
$362$	−7.04583	+	10.3386i	−0.370321	+	0.543384i
$363$		0			0
$364$	0.0598459	−	0.137312i	0.00313678	−	0.00719709i
$365$	18.2556	+	18.2556i	0.955542	+	0.955542i
$366$		0			0
$367$			19.0989i			0.996956i	0.866902	+	0.498478i	$0.166108\pi$
$367$			19.0989i			0.996956i	−0.866902	+	0.498478i	$0.833892\pi$
$368$	−9.50124	−	10.2242i	−0.495286	−	0.532973i
$369$		0			0
$370$	−6.08715	−	32.1377i	−0.316456	−	1.67076i
$371$	0.313125	−	0.313125i	0.0162566	−	0.0162566i
$372$		0			0
$373$	3.51026	+	3.51026i	0.181754	+	0.181754i	0.792120	−	0.610365i	$-0.208977\pi$
$373$	3.51026	+	3.51026i	0.181754	+	0.181754i	−0.610365	+	0.792120i	$0.708977\pi$
$374$	3.96630	+	2.70306i	0.205092	+	0.139772i
$375$		0			0
$376$	−13.7759	−	21.8963i	−0.710437	−	1.12921i
$377$	−2.21848			−0.114258
$378$		0			0
$379$	9.07536	−	9.07536i	0.466170	−	0.466170i	−0.434501	−	0.900671i	$-0.643075\pi$
$379$	9.07536	−	9.07536i	0.466170	−	0.466170i	0.900671	+	0.434501i	$0.143075\pi$
$380$	43.7829	−	17.2029i	2.24601	−	0.882488i
$381$		0			0
$382$	1.87811	+	9.91565i	0.0960923	+	0.507329i
$383$	−28.3176			−1.44696			−0.723481	−	0.690344i	$-0.757459\pi$
$383$	−28.3176			−1.44696			−0.723481	+	0.690344i	$0.757459\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	−2.87784	−	15.1938i	−0.146478	−	0.773345i
$387$		0			0
$388$	1.72294	−	0.676964i	0.0874688	−	0.0343676i
$389$	−0.490254	+	0.490254i	−0.0248569	+	0.0248569i	−0.719426	−	0.694569i	$-0.755595\pi$
$389$	−0.490254	+	0.490254i	−0.0248569	+	0.0248569i	0.694569	+	0.719426i	$0.255595\pi$
$390$		0			0
$391$	−2.28371			−0.115492
$392$	10.4787	+	16.6555i	0.529253	+	0.841228i
$393$		0			0
$394$	17.0685	+	11.6323i	0.859900	+	0.586029i
$395$	12.4452	+	12.4452i	0.626183	+	0.626183i
$396$		0			0
$397$	24.4559	−	24.4559i	1.22741	−	1.22741i	0.262465	−	0.964942i	$-0.415465\pi$
$397$	24.4559	−	24.4559i	1.22741	−	1.22741i	0.964942	−	0.262465i	$-0.0845354\pi$
$398$	1.89092	+	9.98332i	0.0947835	+	0.500418i
$399$		0			0
$400$	−24.1259	−	25.9616i	−1.20629	−	1.29808i
$401$		−	0.517550i		−	0.0258452i	−0.999916	−	0.0129226i	$-0.995886\pi$
$401$		−	0.517550i		−	0.0258452i	0.999916	−	0.0129226i	$-0.00411351\pi$
$402$		0			0
$403$	1.57559	+	1.57559i	0.0784859	+	0.0784859i
$404$	−2.56644	+	5.88849i	−0.127685	+	0.292963i
$405$		0			0
$406$	−1.01272	+	1.48601i	−0.0502607	+	0.0737492i
$407$			32.2164i			1.59691i
$408$		0			0
$409$		−	36.5602i		−	1.80779i	−0.427758	−	0.903893i	$-0.640696\pi$
$409$		−	36.5602i		−	1.80779i	0.427758	−	0.903893i	$-0.359304\pi$
$410$	0.297879	+	0.203007i	0.0147112	+	0.0100258i
$411$		0			0
$412$	−26.3663	+	10.3597i	−1.29898	+	0.510384i
$413$	0.525309	+	0.525309i	0.0258488	+	0.0258488i
$414$		0			0
$415$		−	22.7858i		−	1.11851i
$416$	2.02168	−	0.306698i	0.0991210	−	0.0150371i
$417$		0			0
$418$	−45.5233	+	8.62251i	−2.22662	+	0.421741i
$419$	−20.9433	+	20.9433i	−1.02315	+	1.02315i	−0.0234208	+	0.999726i	$0.507456\pi$
$419$	−20.9433	+	20.9433i	−1.02315	+	1.02315i	−0.999726	+	0.0234208i	$0.992544\pi$
$420$		0			0
$421$	14.2218	+	14.2218i	0.693126	+	0.693126i	0.962919	−	0.269792i	$-0.0869550\pi$
$421$	14.2218	+	14.2218i	0.693126	+	0.693126i	−0.269792	+	0.962919i	$0.586955\pi$
$422$	0.183951	−	0.269917i	0.00895459	−	0.0131394i
$423$		0			0
$424$	5.89444	+	1.34181i	0.286259	+	0.0651638i
$425$	−5.79888			−0.281287
$426$		0			0
$427$	1.13277	−	1.13277i	0.0548184	−	0.0548184i
$428$	−22.9551	−	10.0047i	−1.10958	−	0.483597i
$429$		0			0
$430$	−41.3566	+	7.83330i	−1.99439	+	0.377755i
$431$	−27.9032			−1.34405			−0.672024	−	0.740529i	$-0.734575\pi$
$431$	−27.9032			−1.34405			−0.672024	+	0.740529i	$0.734575\pi$
$432$		0			0
$433$	−28.4634			−1.36786			−0.683932	−	0.729546i	$-0.739731\pi$
$433$	−28.4634			−1.36786			−0.683932	+	0.729546i	$0.739731\pi$
$434$	1.77463	−	0.336130i	0.0851849	−	0.0161347i
$435$		0			0
$436$	3.01727	−	6.92288i	0.144501	−	0.331546i
$437$	15.5880	−	15.5880i	0.745677	−	0.745677i
$438$		0			0
$439$	18.2702			0.871988			0.435994	−	0.899950i	$-0.356397\pi$
$439$	18.2702			0.871988			0.435994	+	0.899950i	$0.356397\pi$
$440$	29.0787	+	46.2195i	1.38627	+	2.20343i
$441$		0			0
$442$	0.188419	−	0.276474i	0.00896218	−	0.0131505i
$443$	−13.9646	−	13.9646i	−0.663479	−	0.663479i	0.292720	−	0.956198i	$-0.405440\pi$
$443$	−13.9646	−	13.9646i	−0.663479	−	0.663479i	−0.956198	+	0.292720i	$0.905440\pi$
$444$		0			0
$445$	−31.4434	+	31.4434i	−1.49056	+	1.49056i
$446$	−0.863669	+	0.163586i	−0.0408959	+	0.00774604i
$447$		0			0
$448$	0.717449	−	1.49419i	0.0338963	−	0.0705937i
$449$			23.8072i			1.12353i	0.827296	+	0.561766i	$0.189878\pi$
$449$			23.8072i			1.12353i	−0.827296	+	0.561766i	$0.810122\pi$
$450$		0			0
$451$	−0.251057	−	0.251057i	−0.0118218	−	0.0118218i
$452$	6.13851	+	15.6231i	0.288731	+	0.734848i
$453$		0			0
$454$	−18.0568	−	12.3059i	−0.847448	−	0.577543i
$455$		−	0.278823i		−	0.0130714i
$456$		0			0
$457$		−	13.9662i		−	0.653310i	−0.945144	−	0.326655i	$-0.894079\pi$
$457$		−	13.9662i		−	0.653310i	0.945144	−	0.326655i	$-0.105921\pi$
$458$	20.2469	−	29.7090i	0.946076	−	1.38821i
$459$		0			0
$460$	−23.8173	−	10.3805i	−1.11049	−	0.483995i
$461$	−19.4422	−	19.4422i	−0.905514	−	0.905514i	0.0903920	−	0.995906i	$-0.471188\pi$
$461$	−19.4422	−	19.4422i	−0.905514	−	0.905514i	−0.995906	+	0.0903920i	$0.971188\pi$
$462$		0			0
$463$			27.9277i			1.29791i	0.760827	+	0.648955i	$0.224794\pi$
$463$			27.9277i			1.29791i	−0.760827	+	0.648955i	$0.775206\pi$
$464$	−24.5328	−	0.899142i	−1.13891	−	0.0417416i
$465$		0			0
$466$	−5.66923	−	29.9312i	−0.262622	−	1.38654i
$467$	−4.32777	+	4.32777i	−0.200265	+	0.200265i	−0.800114	−	0.599848i	$-0.795228\pi$
$467$	−4.32777	+	4.32777i	−0.200265	+	0.200265i	0.599848	+	0.800114i	$0.295228\pi$
$468$		0			0
$469$	0.988567	+	0.988567i	0.0456478	+	0.0456478i
$470$	−39.7927	−	27.1190i	−1.83550	−	1.25091i
$471$		0			0
$472$	−2.25106	+	9.88870i	−0.103613	+	0.455164i
$473$	41.4580			1.90624
$474$		0			0
$475$	39.5817	−	39.5817i	1.81613	−	1.81613i
$476$	−0.0991780	−	0.252417i	−0.00454582	−	0.0115695i
$477$		0			0
$478$	4.35359	+	22.9852i	0.199129	+	1.05132i
$479$	30.0898			1.37484			0.687420	−	0.726260i	$-0.258743\pi$
$479$	30.0898			1.37484			0.687420	+	0.726260i	$0.258743\pi$
$480$		0			0
$481$	2.24567			0.102394
$482$	−6.55352	−	34.5999i	−0.298505	−	1.57598i
$483$		0			0
$484$	−11.6231	−	29.5820i	−0.528324	−	1.34463i
$485$	2.43660	−	2.43660i	0.110640	−	0.110640i
$486$		0			0
$487$	−27.3397			−1.23888			−0.619440	−	0.785044i	$-0.712640\pi$
$487$	−27.3397			−1.23888			−0.619440	+	0.785044i	$0.712640\pi$
$488$	21.3238	+	4.85414i	0.965284	+	0.219737i
$489$		0			0
$490$	30.2684	+	20.6282i	1.36739	+	0.931885i
$491$	−3.78368	−	3.78368i	−0.170755	−	0.170755i	0.616556	−	0.787311i	$-0.288527\pi$
$491$	−3.78368	−	3.78368i	−0.170755	−	0.170755i	−0.787311	+	0.616556i	$0.788527\pi$
$492$		0			0
$493$	−2.84028	+	2.84028i	−0.127920	+	0.127920i
$494$	0.601038	+	3.17324i	0.0270420	+	0.142771i
$495$		0			0
$496$	16.7849	+	18.0620i	0.753664	+	0.811010i
$497$			1.23274i			0.0552960i
$498$		0			0
$499$	15.2002	+	15.2002i	0.680455	+	0.680455i	0.960103	−	0.279648i	$-0.0902178\pi$
$499$	15.2002	+	15.2002i	0.680455	+	0.680455i	−0.279648	+	0.960103i	$0.590218\pi$
$500$	−26.3491	−	11.4840i	−1.17837	−	0.513579i
$501$		0			0
$502$	9.84148	−	14.4407i	0.439247	−	0.644522i
$503$			12.6164i			0.562537i	0.959629	+	0.281268i	$0.0907551\pi$
$503$			12.6164i			0.562537i	−0.959629	+	0.281268i	$0.909245\pi$
$504$		0			0
$505$			11.9571i			0.532083i
$506$	21.1461	+	14.4112i	0.940057	+	0.640657i
$507$		0			0
$508$	7.05355	+	17.9519i	0.312951	+	0.796488i
$509$	26.3204	+	26.3204i	1.16663	+	1.16663i	0.982994	+	0.183639i	$0.0587876\pi$
$509$	26.3204	+	26.3204i	1.16663	+	1.16663i	0.183639	+	0.982994i	$0.441212\pi$
$510$		0			0
$511$			1.43678i			0.0635595i
$512$	22.4807	−	2.57220i	0.993518	−	0.113676i
$513$		0			0
$514$	26.0855	−	4.94081i	1.15058	−	0.217930i
$515$	−37.2876	+	37.2876i	−1.64309	+	1.64309i
$516$		0			0
$517$	33.5378	+	33.5378i	1.47499	+	1.47499i
$518$	1.02513	−	1.50421i	0.0450418	−	0.0660914i
$519$		0			0
$520$	3.22176	−	2.02695i	0.141284	−	0.0888876i
$521$	9.60170			0.420658			0.210329	−	0.977631i	$-0.432546\pi$
$521$	9.60170			0.420658			0.210329	+	0.977631i	$0.432546\pi$
$522$		0			0
$523$	11.2532	−	11.2532i	0.492066	−	0.492066i	−0.416890	−	0.908957i	$-0.636880\pi$
$523$	11.2532	−	11.2532i	0.492066	−	0.492066i	0.908957	+	0.416890i	$0.136880\pi$
$524$	5.73042	−	13.1480i	0.250334	−	0.574372i
$525$		0			0
$526$	26.6122	−	5.04058i	1.16035	−	0.219780i
$527$	4.03441			0.175741
$528$		0			0
$529$	10.8245			0.470632
$530$	11.0564	−	2.09418i	0.480260	−	0.0909654i
$531$		0			0
$532$	2.39990	+	1.04597i	0.104049	+	0.0453486i
$533$	−0.0175001	+	0.0175001i	−0.000758013	+	0.000758013i
$534$		0			0
$535$	−46.6122			−2.01522
$536$	−4.23621	+	18.6093i	−0.182977	+	0.803800i
$537$		0			0
$538$	5.28785	−	7.75904i	0.227975	−	0.334516i
$539$	−25.5106	−	25.5106i	−1.09882	−	1.09882i
$540$		0			0
$541$	4.66998	−	4.66998i	0.200778	−	0.200778i	−0.599555	−	0.800333i	$-0.704656\pi$
$541$	4.66998	−	4.66998i	0.200778	−	0.200778i	0.800333	+	0.599555i	$0.204656\pi$
$542$	−35.0820	+	6.64483i	−1.50690	+	0.285420i
$543$		0			0
$544$	2.19566	−	2.98098i	0.0941381	−	0.127808i
$545$		−	14.0575i		−	0.602157i
$546$		0			0
$547$	−18.6755	−	18.6755i	−0.798505	−	0.798505i	0.184355	−	0.982860i	$-0.440981\pi$
$547$	−18.6755	−	18.6755i	−0.798505	−	0.798505i	−0.982860	+	0.184355i	$0.940981\pi$
$548$	−22.1654	+	8.70907i	−0.946859	+	0.372033i
$549$		0			0
$550$	53.6948	+	36.5935i	2.28956	+	1.56035i
$551$		−	38.7741i		−	1.65183i
$552$		0			0
$553$			0.979478i			0.0416516i
$554$	23.8188	−	34.9501i	1.01196	−	1.48489i
$555$		0			0
$556$	−0.871680	+	2.00000i	−0.0369675	+	0.0848189i
$557$	3.20568	+	3.20568i	0.135829	+	0.135829i	0.771752	−	0.635923i	$-0.219381\pi$
$557$	3.20568	+	3.20568i	0.135829	+	0.135829i	−0.635923	+	0.771752i	$0.719381\pi$
$558$		0			0
$559$		−	2.88986i		−	0.122228i
$560$	0.113006	−	3.08332i	0.00477536	−	0.130294i
$561$		0			0
$562$	−1.67073	−	8.82076i	−0.0704754	−	0.372081i
$563$	32.4157	−	32.4157i	1.36616	−	1.36616i	0.500319	−	0.865841i	$-0.333216\pi$
$563$	32.4157	−	32.4157i	1.36616	−	1.36616i	0.865841	−	0.500319i	$-0.166784\pi$
$564$		0			0
$565$	22.0944	+	22.0944i	0.929518	+	0.929518i
$566$	4.23621	+	2.88701i	0.178061	+	0.121350i
$567$		0			0
$568$	−14.2442	+	8.96162i	−0.597672	+	0.376021i
$569$	11.1238			0.466335			0.233168	−	0.972437i	$-0.425091\pi$
$569$	11.1238			0.466335			0.233168	+	0.972437i	$0.425091\pi$
$570$		0			0
$571$	16.1349	−	16.1349i	0.675223	−	0.675223i	−0.283692	−	0.958915i	$-0.591559\pi$
$571$	16.1349	−	16.1349i	0.675223	−	0.675223i	0.958915	+	0.283692i	$0.0915594\pi$
$572$	−3.48934	+	1.37101i	−0.145897	+	0.0573246i
$573$		0			0
$574$	0.00373339	+	0.0197108i	0.000155829	+	0.000822712i
$575$	−30.9164			−1.28930
$576$		0			0
$577$	−10.9795			−0.457082			−0.228541	−	0.973534i	$-0.573395\pi$
$577$	−10.9795			−0.457082			−0.228541	+	0.973534i	$0.573395\pi$
$578$	4.36141	+	23.0265i	0.181411	+	0.957774i
$579$		0			0
$580$	−42.5323	+	16.7115i	−1.76606	+	0.693907i
$581$	0.896663	−	0.896663i	0.0371999	−	0.0371999i
$582$		0			0
$583$	−11.0835			−0.459032
$584$	−16.6018	+	10.4449i	−0.686988	+	0.432214i
$585$		0			0
$586$	−19.3534	−	13.1895i	−0.799483	−	0.544854i
$587$	7.40862	+	7.40862i	0.305786	+	0.305786i	0.843273	−	0.537486i	$-0.180626\pi$
$587$	7.40862	+	7.40862i	0.305786	+	0.305786i	−0.537486	+	0.843273i	$0.680626\pi$
$588$		0			0
$589$	−27.5378	+	27.5378i	−1.13468	+	1.13468i
$590$	3.51326	+	18.5486i	0.144639	+	0.763634i
$591$		0			0
$592$	24.8334	+	0.910160i	1.02065	+	0.0374073i
$593$		−	12.3933i		−	0.508934i	−0.967081	−	0.254467i	$-0.918100\pi$
$593$		−	12.3933i		−	0.508934i	0.967081	−	0.254467i	$-0.0819000\pi$
$594$		0			0
$595$	−0.356972	−	0.356972i	−0.0146344	−	0.0146344i
$596$	3.41773	−	7.84170i	0.139996	−	0.321209i
$597$		0			0
$598$	1.00454	−	1.47400i	0.0410789	−	0.0602764i
$599$		−	41.2488i		−	1.68538i	−0.538399	−	0.842690i	$-0.680971\pi$
$599$		−	41.2488i		−	1.68538i	0.538399	−	0.842690i	$-0.319029\pi$
$600$		0			0
$601$		−	20.4615i		−	0.834642i	−0.908759	−	0.417321i	$-0.862969\pi$
$601$		−	20.4615i		−	0.834642i	0.908759	−	0.417321i	$-0.137031\pi$
$602$	−1.93571	−	1.31920i	−0.0788937	−	0.0537667i
$603$		0			0
$604$	−12.2459	+	4.81158i	−0.498279	+	0.195780i
$605$	−41.8352	−	41.8352i	−1.70084	−	1.70084i
$606$		0			0
$607$		−	30.1643i		−	1.22433i	−0.790730	−	0.612165i	$-0.790299\pi$
$607$		−	30.1643i		−	1.22433i	0.790730	−	0.612165i	$-0.209701\pi$
$608$	5.36039	+	35.3344i	0.217393	+	1.43300i
$609$		0			0
$610$	39.9979	−	7.57594i	1.61947	−	0.306741i
$611$	2.33778	−	2.33778i	0.0945764	−	0.0945764i
$612$		0			0
$613$	−1.80074	−	1.80074i	−0.0727312	−	0.0727312i	0.669805	−	0.742537i	$-0.266377\pi$
$613$	−1.80074	−	1.80074i	−0.0727312	−	0.0727312i	−0.742537	+	0.669805i	$0.766377\pi$
$614$	13.0171	−	19.1005i	0.525328	−	0.770832i
$615$		0			0
$616$	−0.674522	+	2.96312i	−0.0271773	+	0.119387i
$617$	30.8098			1.24036			0.620178	−	0.784461i	$-0.287060\pi$
$617$	30.8098			1.24036			0.620178	+	0.784461i	$0.287060\pi$
$618$		0			0
$619$	−10.0429	+	10.0429i	−0.403659	+	0.403659i	−0.879520	−	0.475861i	$-0.842136\pi$
$619$	−10.0429	+	10.0429i	−0.403659	+	0.403659i	0.475861	+	0.879520i	$0.342136\pi$
$620$	42.0757	+	18.3383i	1.68980	+	0.736482i
$621$		0			0
$622$	−19.3581	+	3.66659i	−0.776190	+	0.147017i
$623$	−2.47471			−0.0991472
$624$		0			0
$625$	−9.20274			−0.368110
$626$	−24.7699	+	4.69164i	−0.990006	+	0.187516i
$627$		0			0
$628$	−8.43863	+	19.3618i	−0.336738	+	0.772619i
$629$	2.87509	−	2.87509i	0.114637	−	0.114637i
$630$		0			0
$631$	−4.91925			−0.195832			−0.0979161	−	0.995195i	$-0.531218\pi$
$631$	−4.91925			−0.195832			−0.0979161	+	0.995195i	$0.531218\pi$
$632$	−11.3177	+	7.12048i	−0.450196	+	0.283237i
$633$		0			0
$634$	13.0797	−	19.1923i	0.519462	−	0.762224i
$635$	25.3879	+	25.3879i	1.00749	+	1.00749i
$636$		0			0
$637$	−1.77824	+	1.77824i	−0.0704563	+	0.0704563i
$638$	44.2231	−	8.37622i	1.75081	−	0.331618i
$639$		0			0
$640$	36.4489	−	21.1090i	1.44077	−	0.834405i
$641$		−	15.0833i		−	0.595756i	−0.954604	−	0.297878i	$-0.903721\pi$
$641$		−	15.0833i		−	0.595756i	0.954604	−	0.297878i	$-0.0962789\pi$
$642$		0			0
$643$	−2.26109	−	2.26109i	−0.0891686	−	0.0891686i	0.661116	−	0.750284i	$-0.270083\pi$
$643$	−2.26109	−	2.26109i	−0.0891686	−	0.0891686i	−0.750284	+	0.661116i	$0.770083\pi$
$644$	−0.528761	−	1.34575i	−0.0208361	−	0.0530299i
$645$		0			0
$646$	4.83214	+	3.29314i	0.190118	+	0.129567i
$647$		−	12.1851i		−	0.479046i	−0.970891	−	0.239523i	$-0.923009\pi$
$647$		−	12.1851i		−	0.479046i	0.970891	−	0.239523i	$-0.0769911\pi$
$648$		0			0
$649$		−	18.5941i		−	0.729881i
$650$	2.55077	−	3.74284i	0.100050	−	0.146806i
$651$		0			0
$652$	36.4749	+	15.8972i	1.42847	+	0.622583i
$653$	11.4822	+	11.4822i	0.449335	+	0.449335i	0.895133	−	0.445798i	$-0.147080\pi$
$653$	11.4822	+	11.4822i	0.449335	+	0.449335i	−0.445798	+	0.895133i	$0.647080\pi$
$654$		0			0
$655$		−	26.6981i		−	1.04318i
$656$	−0.200615	+	0.186430i	−0.00783270	+	0.00727885i
$657$		0			0
$658$	−0.498731	−	2.63310i	−0.0194425	−	0.102649i
$659$	−16.6502	+	16.6502i	−0.648599	+	0.648599i	−0.952654	−	0.304056i	$-0.901659\pi$
$659$	−16.6502	+	16.6502i	−0.648599	+	0.648599i	0.304056	+	0.952654i	$0.401659\pi$
$660$		0			0
$661$	−14.6386	−	14.6386i	−0.569375	−	0.569375i	0.362578	−	0.931953i	$-0.381896\pi$
$661$	−14.6386	−	14.6386i	−0.569375	−	0.569375i	−0.931953	+	0.362578i	$0.881896\pi$
$662$	−38.9328	−	26.5330i	−1.51317	−	1.03123i
$663$		0			0
$664$	16.8793	+	3.84239i	0.655043	+	0.149114i
$665$	4.87320			0.188974
$666$		0			0
$667$	−15.1428	+	15.1428i	−0.586331	+	0.586331i
$668$	−4.79068	−	12.1927i	−0.185357	−	0.471751i
$669$		0			0
$670$	6.61153	+	34.9062i	0.255426	+	1.34854i
$671$	−40.0959			−1.54789
$672$		0			0
$673$	−20.5492			−0.792115			−0.396058	−	0.918226i	$-0.629622\pi$
$673$	−20.5492			−0.792115			−0.396058	+	0.918226i	$0.629622\pi$
$674$	6.01346	+	31.7486i	0.231630	+	1.22291i
$675$		0			0
$676$	−9.41256	−	23.9559i	−0.362022	−	0.921379i
$677$	−6.72550	+	6.72550i	−0.258482	+	0.258482i	−0.824437	−	0.565954i	$-0.808508\pi$
$677$	−6.72550	+	6.72550i	−0.258482	+	0.258482i	0.565954	+	0.824437i	$0.308508\pi$
$678$		0			0
$679$	0.191769			0.00735942
$680$	1.52970	−	6.71983i	0.0586612	−	0.257694i
$681$		0			0
$682$	−37.3566	−	25.4588i	−1.43046	−	0.974870i
$683$	30.5399	+	30.5399i	1.16858	+	1.16858i	0.982543	+	0.186033i	$0.0595632\pi$
$683$	30.5399	+	30.5399i	1.16858	+	1.16858i	0.186033	+	0.982543i	$0.440437\pi$
$684$		0			0
$685$	−31.3466	+	31.3466i	−1.19769	+	1.19769i
$686$	0.761062	+	4.01810i	0.0290575	+	0.153412i
$687$		0			0
$688$	1.17125	−	31.9571i	0.0446534	−	1.21835i
$689$			0.772584i			0.0294331i
$690$		0			0
$691$	10.8672	+	10.8672i	0.413409	+	0.413409i	0.882924	−	0.469515i	$-0.155571\pi$
$691$	10.8672	+	10.8672i	0.413409	+	0.413409i	−0.469515	+	0.882924i	$0.655571\pi$
$692$	−2.47786	−	1.07995i	−0.0941939	−	0.0410535i
$693$		0			0
$694$	−20.3348	+	29.8380i	−0.771899	+	1.13263i
$695$			4.06117i			0.154049i
$696$		0			0
$697$			0.0448101i			0.00169730i
$698$	−5.49947	−	3.74793i	−0.208158	−	0.141861i
$699$		0			0
$700$	−1.34265	−	3.41717i	−0.0507474	−	0.129157i
$701$	20.5506	+	20.5506i	0.776184	+	0.776184i	0.979180	−	0.202995i	$-0.0650677\pi$
$701$	20.5506	+	20.5506i	0.776184	+	0.776184i	−0.202995	+	0.979180i	$0.565068\pi$
$702$		0			0
$703$			39.2492i			1.48031i
$704$	−39.1420	+	13.7469i	−1.47522	+	0.518104i
$705$		0			0
$706$	−26.2936	+	4.98023i	−0.989572	+	0.187433i
$707$	−0.470532	+	0.470532i	−0.0176962	+	0.0176962i
$708$		0			0
$709$	−33.4311	−	33.4311i	−1.25553	−	1.25553i	−0.953205	−	0.302325i	$-0.902237\pi$
$709$	−33.4311	−	33.4311i	−1.25553	−	1.25553i	−0.302325	−	0.953205i	$-0.597763\pi$
$710$	−17.6417	+	25.8863i	−0.662082	+	0.971495i
$711$		0			0
$712$	−17.9903	−	28.5950i	−0.674216	−	1.07164i
$713$	21.5092			0.805525
$714$		0			0
$715$	−4.93467	+	4.93467i	−0.184546	+	0.184546i
$716$	−9.92011	+	22.7609i	−0.370732	+	0.850615i
$717$		0			0
$718$	44.5765	−	8.44318i	1.66358	−	0.315097i
$719$	9.15381			0.341380			0.170690	−	0.985325i	$-0.445400\pi$
$719$	9.15381			0.341380			0.170690	+	0.985325i	$0.445400\pi$
$720$		0			0
$721$	−2.93467			−0.109293
$722$	−29.0604	+	5.50428i	−1.08152	+	0.204848i
$723$		0			0
$724$	−16.2199	−	7.06929i	−0.602808	−	0.262728i
$725$	−38.4511	+	38.4511i	−1.42804	+	1.42804i
$726$		0			0
$727$	−37.6052			−1.39470			−0.697351	−	0.716730i	$-0.745638\pi$
$727$	−37.6052			−1.39470			−0.697351	+	0.716730i	$0.745638\pi$
$728$	0.206546	+	0.0470181i	0.00765511	+	0.00174261i
$729$		0			0
$730$	−20.5617	+	30.1709i	−0.761023	+	1.11668i
$731$	−3.69983	−	3.69983i	−0.136843	−	0.136843i
$732$		0			0
$733$	33.4129	−	33.4129i	1.23413	−	1.23413i	0.271771	−	0.962362i	$-0.412391\pi$
$733$	33.4129	−	33.4129i	1.23413	−	1.23413i	0.962362	−	0.271771i	$-0.0876092\pi$
$734$	−26.5381	+	5.02655i	−0.979540	+	0.185533i
$735$		0			0
$736$	11.7060	−	15.8929i	0.431489	−	0.585820i
$737$		−	34.9917i		−	1.28894i
$738$		0			0
$739$	21.9860	+	21.9860i	0.808769	+	0.808769i	0.984448	−	0.175678i	$-0.0562119\pi$
$739$	21.9860	+	21.9860i	0.808769	+	0.808769i	−0.175678	+	0.984448i	$0.556212\pi$
$740$	43.0535	−	16.9163i	1.58268	−	0.621855i
$741$		0			0
$742$	0.517500	+	0.352680i	0.0189980	+	0.0129473i
$743$			20.6315i			0.756896i	0.925623	+	0.378448i	$0.123542\pi$
$743$			20.6315i			0.756896i	−0.925623	+	0.378448i	$0.876458\pi$
$744$		0			0
$745$		−	15.9232i		−	0.583382i
$746$	−3.95369	+	5.80138i	−0.144755	+	0.212404i
$747$		0			0
$748$	−2.71206	+	6.22261i	−0.0991628	+	0.227521i
$749$	−1.83428	−	1.83428i	−0.0670230	−	0.0670230i
$750$		0			0
$751$			21.1419i			0.771477i	0.922608	+	0.385739i	$0.126053\pi$
$751$			21.1419i			0.771477i	−0.922608	+	0.385739i	$0.873947\pi$
$752$	26.7995	−	24.9045i	0.977276	−	0.908173i
$753$		0			0
$754$	−0.583871	−	3.08260i	−0.0212633	−	0.112262i
$755$	−17.3183	+	17.3183i	−0.630279	+	0.630279i
$756$		0			0
$757$	16.9156	+	16.9156i	0.614810	+	0.614810i	0.944195	−	0.329386i	$-0.106842\pi$
$757$	16.9156	+	16.9156i	0.614810	+	0.614810i	−0.329386	+	0.944195i	$0.606842\pi$
$758$	14.9988	+	10.2218i	0.544781	+	0.371272i
$759$		0			0
$760$	35.4265	+	56.3092i	1.28505	+	2.04255i
$761$	−29.0688			−1.05374			−0.526871	−	0.849945i	$-0.676635\pi$
$761$	−29.0688			−1.05374			−0.526871	+	0.849945i	$0.676635\pi$
$762$		0			0
$763$	0.553188	−	0.553188i	0.0200267	−	0.0200267i
$764$	−13.2836	+	5.21929i	−0.480583	+	0.188827i
$765$		0			0
$766$	−7.45276	−	39.3475i	−0.269279	−	1.42168i
$767$	−1.29611			−0.0467999
$768$		0			0
$769$	17.9123			0.645933			0.322966	−	0.946410i	$-0.395320\pi$
$769$	17.9123			0.645933			0.322966	+	0.946410i	$0.395320\pi$
$770$	1.05274	+	5.55803i	0.0379381	+	0.200298i
$771$		0			0
$772$	20.3545	−	7.99756i	0.732576	−	0.287838i
$773$	−19.1937	+	19.1937i	−0.690351	+	0.690351i	−0.962309	−	0.271958i	$-0.912329\pi$
$773$	−19.1937	+	19.1937i	−0.690351	+	0.690351i	0.271958	+	0.962309i	$0.412329\pi$
$774$		0			0
$775$	54.6169			1.96190
$776$	1.39410	+	2.21587i	0.0500452	+	0.0795450i
$777$		0			0
$778$	−0.810240	−	0.552185i	−0.0290485	−	0.0197968i
$779$	−0.305862	−	0.305862i	−0.0109587	−	0.0109587i
$780$		0			0
$781$	21.8173	−	21.8173i	0.780685	−	0.780685i
$782$	−0.601038	−	3.17324i	−0.0214931	−	0.113475i
$783$		0			0
$784$	−20.3851	+	18.9437i	−0.728039	+	0.676559i
$785$			39.3157i			1.40324i
$786$		0			0
$787$	5.09354	+	5.09354i	0.181565	+	0.181565i	0.792038	−	0.610472i	$-0.209020\pi$
$787$	5.09354	+	5.09354i	0.181565	+	0.181565i	−0.610472	+	0.792038i	$0.709020\pi$
$788$	−11.6711	+	26.7783i	−0.415764	+	0.953939i
$789$		0			0
$790$	−14.0173	+	20.5680i	−0.498712	+	0.731777i
$791$			1.73891i			0.0618284i
$792$		0			0
$793$			2.79491i			0.0992503i
$794$	40.4181	+	27.5453i	1.43438	+	0.977545i
$795$		0			0
$796$	−13.3742	+	5.25491i	−0.474037	+	0.186255i
$797$	−22.2946	−	22.2946i	−0.789714	−	0.789714i	0.191733	−	0.981447i	$-0.438589\pi$
$797$	−22.2946	−	22.2946i	−0.789714	−	0.789714i	−0.981447	+	0.191733i	$0.938589\pi$
$798$		0			0
$799$		−	5.98603i		−	0.211770i
$800$	29.7243	−	40.3558i	1.05091	−	1.42679i
$801$		0			0
$802$	0.719141	−	0.136211i	0.0253937	−	0.00480979i
$803$	25.4285	−	25.4285i	0.897351	−	0.897351i
$804$		0			0
$805$	−1.90317	−	1.90317i	−0.0670781	−	0.0670781i
$806$	−1.77463	+	2.60397i	−0.0625086	+	0.0917210i
$807$		0			0
$808$	−8.85755	−	2.01633i	−0.311608	−	0.0709342i
$809$	−16.9021			−0.594246			−0.297123	−	0.954839i	$-0.596027\pi$
$809$	−16.9021			−0.594246			−0.297123	+	0.954839i	$0.596027\pi$
$810$		0			0
$811$	38.2508	−	38.2508i	1.34317	−	1.34317i	0.450281	−	0.892887i	$-0.351324\pi$
$811$	38.2508	−	38.2508i	1.34317	−	1.34317i	0.892887	−	0.450281i	$-0.148676\pi$
$812$	−2.33135	−	1.01610i	−0.0818144	−	0.0356580i
$813$		0			0
$814$	−44.7650	+	8.47886i	−1.56901	+	0.297184i
$815$	74.0654			2.59440
$816$		0			0
$817$	50.5082			1.76706
$818$	50.8007	−	9.62209i	1.77621	−	0.336428i
$819$		0			0
$820$	−0.203683	+	0.467334i	−0.00711291	+	0.0163200i
$821$	15.6774	−	15.6774i	0.547144	−	0.547144i	−0.378470	−	0.925614i	$-0.623550\pi$
$821$	15.6774	−	15.6774i	0.547144	−	0.547144i	0.925614	+	0.378470i	$0.123550\pi$
$822$		0			0
$823$	−0.813334			−0.0283510			−0.0141755	−	0.999900i	$-0.504512\pi$
$823$	−0.813334			−0.0283510			−0.0141755	+	0.999900i	$0.504512\pi$
$824$	−21.3341	−	33.9097i	−0.743207	−	1.18130i
$825$		0			0
$826$	−0.591668	+	0.868174i	−0.0205868	+	0.0302077i
$827$	−12.7929	−	12.7929i	−0.444854	−	0.444854i	0.448786	−	0.893639i	$-0.351857\pi$
$827$	−12.7929	−	12.7929i	−0.444854	−	0.444854i	−0.893639	+	0.448786i	$0.851857\pi$
$828$		0			0
$829$	−29.2623	+	29.2623i	−1.01632	+	1.01632i	−0.0164588	+	0.999865i	$0.505239\pi$
$829$	−29.2623	+	29.2623i	−1.01632	+	1.01632i	−0.999865	+	0.0164588i	$0.994761\pi$
$830$	31.6611	−	5.99688i	1.09897	−	0.208155i
$831$		0			0
$832$	0.958235	+	2.72842i	0.0332208	+	0.0945910i
$833$			4.55329i			0.157762i
$834$		0			0
$835$	−17.2431	−	17.2431i	−0.596723	−	0.596723i
$836$	−23.9621	−	60.9858i	−0.828746	−	2.10924i
$837$		0			0
$838$	−34.6128	−	23.5889i	−1.19568	−	0.814866i
$839$			1.42409i			0.0491652i	0.999698	+	0.0245826i	$0.00782567\pi$
$839$			1.42409i			0.0491652i	−0.999698	+	0.0245826i	$0.992174\pi$
$840$		0			0
$841$			8.66659i			0.298848i
$842$	−16.0183	+	23.5042i	−0.552027	+	0.810009i
$843$		0			0
$844$	0.423465	+	0.184563i	0.0145763	+	0.00635293i
$845$	−33.8787	−	33.8787i	−1.16546	−	1.16546i
$846$		0			0
$847$		−	3.29258i		−	0.113134i
$848$	−0.313125	+	8.54351i	−0.0107528	+	0.293385i
$849$		0			0
$850$	−1.52618	−	8.05760i	−0.0523474	−	0.276373i
$851$	15.3284	−	15.3284i	0.525449	−	0.525449i
$852$		0			0
$853$	26.0796	+	26.0796i	0.892947	+	0.892947i	0.994800	−	0.101852i	$-0.0324769\pi$
$853$	26.0796	+	26.0796i	0.892947	+	0.892947i	−0.101852	+	0.994800i	$0.532477\pi$
$854$	1.87212	+	1.27586i	0.0640625	+	0.0436591i
$855$		0			0
$856$	7.86025	−	34.5294i	0.268658	−	1.18019i
$857$	−46.9249			−1.60293			−0.801463	−	0.598045i	$-0.795944\pi$
$857$	−46.9249			−1.60293			−0.801463	+	0.598045i	$0.795944\pi$
$858$		0			0
$859$	−29.1799	+	29.1799i	−0.995605	+	0.995605i	−0.999990	−	0.00438503i	$-0.998604\pi$
$859$	−29.1799	+	29.1799i	−0.995605	+	0.995605i	0.00438503	+	0.999990i	$0.498604\pi$
$860$	−21.7689	−	55.4038i	−0.742312	−	1.88925i
$861$		0			0
$862$	−7.34369	−	38.7717i	−0.250127	−	1.32057i
$863$	21.9276			0.746424			0.373212	−	0.927746i	$-0.378256\pi$
$863$	21.9276			0.746424			0.373212	+	0.927746i	$0.378256\pi$
$864$		0			0
$865$	−5.03149			−0.171076
$866$	−7.49113	−	39.5501i	−0.254559	−	1.34397i
$867$		0			0
$868$	0.934110	+	2.37740i	0.0317058	+	0.0806941i
$869$	17.3350	−	17.3350i	0.588050	−	0.588050i
$870$		0			0
$871$	−2.43913			−0.0826466
$872$	10.4135	+	2.37052i	0.352646	+	0.0802761i
$873$		0			0
$874$	25.7622	+	17.5572i	0.871421	+	0.593880i
$875$	−2.10548	−	2.10548i	−0.0711781	−	0.0711781i
$876$		0			0
$877$	29.1540	−	29.1540i	0.984460	−	0.984460i	−0.0154208	−	0.999881i	$-0.504909\pi$
$877$	29.1540	−	29.1540i	0.984460	−	0.984460i	0.999881	+	0.0154208i	$0.00490879\pi$
$878$	4.80843	+	25.3866i	0.162277	+	0.856755i
$879$		0			0
$880$	−56.5693	+	52.5693i	−1.90695	+	1.77211i
$881$			22.0859i			0.744094i	0.928214	+	0.372047i	$0.121344\pi$
$881$			22.0859i			0.744094i	−0.928214	+	0.372047i	$0.878656\pi$
$882$		0			0
$883$	15.8038	+	15.8038i	0.531840	+	0.531840i	0.921120	−	0.389280i	$-0.127276\pi$
$883$	15.8038	+	15.8038i	0.531840	+	0.531840i	−0.389280	+	0.921120i	$0.627276\pi$
$884$	0.433751	+	0.189046i	0.0145886	+	0.00635831i
$885$		0			0
$886$	15.7287	−	23.0792i	0.528415	−	0.775362i
$887$			28.0131i			0.940587i	0.882510	+	0.470293i	$0.155852\pi$
$887$			28.0131i			0.940587i	−0.882510	+	0.470293i	$0.844148\pi$
$888$		0			0
$889$			1.99812i			0.0670147i
$890$	−51.9663	−	35.4155i	−1.74192	−	1.18713i
$891$		0			0
$892$	−0.454609	−	1.15702i	−0.0152214	−	0.0387400i
$893$	40.8591	+	40.8591i	1.36730	+	1.36730i
$894$		0			0
$895$			46.2179i			1.54489i
$896$	2.26501	+	0.603655i	0.0756685	+	0.0201667i
$897$		0			0
$898$	−33.0803	+	6.26569i	−1.10390	+	0.209089i
$899$	26.7513	−	26.7513i	0.892204	−	0.892204i
$900$		0			0
$901$	0.989125	+	0.989125i	0.0329525	+	0.0329525i
$902$	0.282771	−	0.414920i	0.00941525	−	0.0138153i
$903$		0			0
$904$	−20.0929	+	12.6413i	−0.668278	+	0.420443i
$905$	−32.9359			−1.09483
$906$		0			0
$907$	−2.86723	+	2.86723i	−0.0952049	+	0.0952049i	−0.753105	−	0.657900i	$-0.771445\pi$
$907$	−2.86723	+	2.86723i	−0.0952049	+	0.0952049i	0.657900	+	0.753105i	$0.271445\pi$
$908$	12.3468	−	28.3288i	0.409744	−	0.940125i
$909$		0			0
$910$	0.387427	−	0.0733819i	0.0128431	−	0.00243259i
$911$	13.6528			0.452338			0.226169	−	0.974088i	$-0.427380\pi$
$911$	13.6528			0.452338			0.226169	+	0.974088i	$0.427380\pi$
$912$		0			0
$913$	−31.7387			−1.05040
$914$	19.4061	−	3.67568i	0.641897	−	0.121581i
$915$		0			0
$916$	46.6095	+	20.3143i	1.54002	+	0.671203i
$917$	1.05062	−	1.05062i	0.0346945	−	0.0346945i
$918$		0			0
$919$	16.4461			0.542506			0.271253	−	0.962508i	$-0.412562\pi$
$919$	16.4461			0.542506			0.271253	+	0.962508i	$0.412562\pi$
$920$	8.15549	−	35.8264i	0.268879	−	1.18116i
$921$		0			0
$922$	21.8982	−	32.1320i	0.721180	−	1.05821i
$923$	−1.52079	−	1.52079i	−0.0500575	−	0.0500575i
$924$		0			0
$925$	38.9223	−	38.9223i	1.27976	−	1.27976i
$926$	−38.8058	+	7.35014i	−1.27524	+	0.241541i
$927$		0			0
$928$	−5.20729	−	34.3251i	−0.170938	−	1.12678i
$929$			58.8247i			1.92997i	0.262297	+	0.964987i	$0.415520\pi$
$929$			58.8247i			1.92997i	−0.262297	+	0.964987i	$0.584480\pi$
$930$		0			0
$931$	−31.0796	−	31.0796i	−1.01859	−	1.01859i
$932$	40.0976	−	15.7549i	1.31344	−	0.516068i
$933$		0			0
$934$	−7.15248	−	4.87447i	−0.234036	−	0.159498i
$935$			12.6355i			0.413226i
$936$		0			0
$937$		−	31.5717i		−	1.03140i	−0.856769	−	0.515700i	$-0.827532\pi$
$937$		−	31.5717i		−	1.03140i	0.856769	−	0.515700i	$-0.172468\pi$
$938$	−1.11345	+	1.63380i	−0.0363553	+	0.0533454i
$939$		0			0
$940$	27.2093	−	62.4296i	0.887469	−	2.03623i
$941$	5.30353	+	5.30353i	0.172890	+	0.172890i	0.788248	−	0.615358i	$-0.210988\pi$
$941$	5.30353	+	5.30353i	0.172890	+	0.172890i	−0.615358	+	0.788248i	$0.710988\pi$
$942$		0			0
$943$			0.238902i			0.00777973i
$944$	−14.3329	−	0.525309i	−0.466495	−	0.0170973i
$945$		0			0
$946$	10.9111	+	57.6062i	0.354751	+	1.87294i
$947$	−11.9011	+	11.9011i	−0.386732	+	0.386732i	−0.873520	−	0.486788i	$-0.838168\pi$
$947$	−11.9011	+	11.9011i	−0.386732	+	0.386732i	0.486788	+	0.873520i	$0.338168\pi$
$948$		0			0
$949$	−1.77251	−	1.77251i	−0.0575381	−	0.0575381i
$950$	65.4164	+	44.5818i	2.12239	+	1.44642i
$951$		0			0
$952$	0.324634	−	0.204241i	0.0105214	−	0.00661949i
$953$	−18.1504			−0.587948			−0.293974	−	0.955813i	$-0.594978\pi$
$953$	−18.1504			−0.587948			−0.293974	+	0.955813i	$0.594978\pi$
$954$		0			0
$955$	−18.7858	+	18.7858i	−0.607895	+	0.607895i
$956$	−30.7923	+	12.0987i	−0.995894	+	0.391300i
$957$		0			0
$958$	7.91918	+	41.8101i	0.255857	+	1.35082i
$959$	−2.46709			−0.0796665
$960$		0			0
$961$	−6.99812			−0.225746
$962$	0.591026	+	3.12037i	0.0190554	+	0.100605i
$963$		0			0
$964$	46.3521	−	18.2123i	1.49290	−	0.586580i
$965$	28.7857	−	28.7857i	0.926643	−	0.926643i
$966$		0			0
$967$	48.0626			1.54559			0.772794	−	0.634657i	$-0.218859\pi$
$967$	48.0626			1.54559			0.772794	+	0.634657i	$0.218859\pi$
$968$	38.0454	−	23.9360i	1.22282	−	0.769331i
$969$		0			0
$970$	4.02695	+	2.74440i	0.129298	+	0.0881173i
$971$	8.81259	+	8.81259i	0.282810	+	0.282810i	0.834228	−	0.551419i	$-0.185913\pi$
$971$	8.81259	+	8.81259i	0.282810	+	0.282810i	−0.551419	+	0.834228i	$0.685913\pi$
$972$		0			0
$973$	−0.159814	+	0.159814i	−0.00512341	+	0.00512341i
$974$	−7.19539	−	37.9888i	−0.230555	−	1.21724i
$975$		0			0
$976$	−1.13277	+	30.9072i	−0.0362590	+	0.989314i
$977$		−	40.9404i		−	1.30980i	−0.755716	−	0.654900i	$-0.772711\pi$
$977$		−	40.9404i		−	1.30980i	0.755716	−	0.654900i	$-0.227289\pi$
$978$		0			0
$979$	43.7980	+	43.7980i	1.39979	+	1.39979i
$980$	−20.6968	+	47.4872i	−0.661135	+	1.51692i
$981$		0			0
$982$	4.26165	−	6.25326i	0.135995	−	0.199549i
$983$		−	15.0884i		−	0.481246i	−0.970619	−	0.240623i	$-0.922648\pi$
$983$		−	15.0884i		−	0.481246i	0.970619	−	0.240623i	$-0.0773518\pi$
$984$		0			0
$985$			54.3757i			1.73255i
$986$	−4.69412	−	3.19908i	−0.149491	−	0.101879i
$987$		0			0
$988$	−4.25106	+	1.67030i	−0.135244	+	0.0531392i
$989$	−19.7254	−	19.7254i	−0.627232	−	0.627232i
$990$		0			0
$991$		−	3.48435i		−	0.110684i	−0.998467	−	0.0553420i	$-0.982375\pi$
$991$		−	3.48435i		−	0.110684i	0.998467	−	0.0553420i	$-0.0176249\pi$
$992$	−20.6798	+	28.0764i	−0.656586	+	0.891426i
$993$		0			0
$994$	−1.71290	+	0.324439i	−0.0543300	+	0.0102906i
$995$	−18.9140	+	18.9140i	−0.599615	+	0.599615i
$996$		0			0
$997$	−10.5079	−	10.5079i	−0.332789	−	0.332789i	0.520856	−	0.853645i	$-0.325613\pi$
$997$	−10.5079	−	10.5079i	−0.332789	−	0.332789i	−0.853645	+	0.520856i	$0.825613\pi$
$998$	−17.1203	+	25.1213i	−0.541935	+	0.795200i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.l.a.107.5	yes	16
3.2	odd	2	inner	144.2.l.a.107.4	yes	16
4.3	odd	2		576.2.l.a.143.1		16
8.3	odd	2		1152.2.l.b.287.8		16
8.5	even	2		1152.2.l.a.287.8		16
12.11	even	2		576.2.l.a.143.8		16
16.3	odd	4	inner	144.2.l.a.35.4	✓	16
16.5	even	4		1152.2.l.b.863.1		16
16.11	odd	4		1152.2.l.a.863.1		16
16.13	even	4		576.2.l.a.431.8		16
24.5	odd	2		1152.2.l.a.287.1		16
24.11	even	2		1152.2.l.b.287.1		16
48.5	odd	4		1152.2.l.b.863.8		16
48.11	even	4		1152.2.l.a.863.8		16
48.29	odd	4		576.2.l.a.431.1		16
48.35	even	4	inner	144.2.l.a.35.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.l.a.35.4	✓	16	16.3	odd	4	inner
144.2.l.a.35.5	yes	16	48.35	even	4	inner
144.2.l.a.107.4	yes	16	3.2	odd	2	inner
144.2.l.a.107.5	yes	16	1.1	even	1	trivial
576.2.l.a.143.1		16	4.3	odd	2
576.2.l.a.143.8		16	12.11	even	2
576.2.l.a.431.1		16	48.29	odd	4
576.2.l.a.431.8		16	16.13	even	4
1152.2.l.a.287.1		16	24.5	odd	2
1152.2.l.a.287.8		16	8.5	even	2
1152.2.l.a.863.1		16	16.11	odd	4
1152.2.l.a.863.8		16	48.11	even	4
1152.2.l.b.287.1		16	24.11	even	2
1152.2.l.b.287.8		16	8.3	odd	2
1152.2.l.b.863.1		16	16.5	even	4
1152.2.l.b.863.8		16	48.5	odd	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.263185 + 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(-2.63251 + 2.63251i) q^{5} -0.207188 q^{7} +(-1.50619 - 2.39403i) q^{8} +O(q^{10})\)	\(q+(0.263185 + 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(-2.63251 + 2.63251i) q^{5} -0.207188 q^{7} +(-1.50619 - 2.39403i) q^{8} +(-4.35074 - 2.96506i) q^{10} +(3.66686 + 3.66686i) q^{11} +(0.255601 - 0.255601i) q^{13} +(-0.0545288 - 0.287890i) q^{14} +(2.93012 - 2.72294i) q^{16} -0.654483i q^{17} +(4.46733 + 4.46733i) q^{19} +(2.97493 - 6.82574i) q^{20} +(-4.13007 + 6.06020i) q^{22} -3.48934i q^{23} -8.86025i q^{25} +(0.422430 + 0.287890i) q^{26} +(0.385674 - 0.151536i) q^{28} +(-4.33973 - 4.33973i) q^{29} +6.16426i q^{31} +(4.55471 + 3.35480i) q^{32} +(0.909410 - 0.172250i) q^{34} +(0.545426 - 0.545426i) q^{35} +(4.39291 + 4.39291i) q^{37} +(-5.03166 + 7.38313i) q^{38} +(10.2674 + 2.33726i) q^{40} -0.0684664 q^{41} +(5.65306 - 5.65306i) q^{43} +(-9.50767 - 4.14382i) q^{44} +(4.84846 - 0.918340i) q^{46} +9.14619 q^{47} -6.95707 q^{49} +(12.3114 - 2.33188i) q^{50} +(-0.288848 + 0.662739i) q^{52} +(-1.51131 + 1.51131i) q^{53} -19.3061 q^{55} +(0.312065 + 0.496015i) q^{56} +(4.88795 - 7.17225i) q^{58} +(-2.53542 - 2.53542i) q^{59} +(-5.46733 + 5.46733i) q^{61} +(-8.56529 + 1.62234i) q^{62} +(-3.46279 + 7.21173i) q^{64} +1.34575i q^{65} +(-4.77135 - 4.77135i) q^{67} +(0.478686 + 1.21830i) q^{68} +(0.901421 + 0.614326i) q^{70} -5.94986i q^{71} -6.93467i q^{73} +(-4.94784 + 7.26014i) q^{74} +(-11.5832 - 5.04841i) q^{76} +(-0.759730 - 0.759730i) q^{77} -4.72748i q^{79} +(-0.545426 + 14.8817i) q^{80} +(-0.0180193 - 0.0951346i) q^{82} +(-4.32777 + 4.32777i) q^{83} +(1.72294 + 1.72294i) q^{85} +(9.34277 + 6.36717i) q^{86} +(3.25560 - 14.3016i) q^{88} +11.9443 q^{89} +(-0.0529576 + 0.0529576i) q^{91} +(2.55208 + 6.49529i) q^{92} +(2.40714 + 12.7087i) q^{94} -23.5206 q^{95} -0.925579 q^{97} +(-1.83100 - 9.66691i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Introduction

L-functions

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