LMFDB - Embedded newform 728.2.bm.c.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(225,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("728.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.bm (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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.3
Character	$\chi$	$=$	728.225
Dual form			728.2.bm.c.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21632 + 2.10672i) q^{3} +3.98804i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.45886 - 2.52682i) q^{9} +(2.90265 + 1.67585i) q^{11} +(0.364104 + 3.58712i) q^{13} +(-8.40170 - 4.85073i) q^{15} +(3.40418 + 5.89621i) q^{17} +(0.621861 - 0.359032i) q^{19} -2.43264i q^{21} +(0.509352 - 0.882224i) q^{23} -10.9045 q^{25} -0.200166 q^{27} +(4.79947 - 8.31293i) q^{29} -4.52613i q^{31} +(-7.06109 + 4.07672i) q^{33} +(-1.99402 - 3.45375i) q^{35} +(4.53684 + 2.61935i) q^{37} +(-7.99994 - 3.59601i) q^{39} +(-0.985057 - 0.568723i) q^{41} +(-4.25951 - 7.37769i) q^{43} +(10.0771 - 5.81799i) q^{45} -11.0842i q^{47} +(0.500000 - 0.866025i) q^{49} -16.5622 q^{51} +3.19732 q^{53} +(-6.68334 + 11.5759i) q^{55} +1.74679i q^{57} +(6.50131 - 3.75353i) q^{59} +(1.90489 + 3.29937i) q^{61} +(2.52682 + 1.45886i) q^{63} +(-14.3056 + 1.45206i) q^{65} +(12.6609 + 7.30975i) q^{67} +(1.23907 + 2.14613i) q^{69} +(-11.0774 + 6.39557i) q^{71} +7.44426i q^{73} +(13.2633 - 22.9727i) q^{75} -3.35169 q^{77} +3.61316 q^{79} +(4.62004 - 8.00214i) q^{81} +3.31234i q^{83} +(-23.5143 + 13.5760i) q^{85} +(11.6754 + 20.2223i) q^{87} +(5.96558 + 3.44423i) q^{89} +(-2.10888 - 2.92448i) q^{91} +(9.53530 + 5.50521i) q^{93} +(1.43183 + 2.48001i) q^{95} +(-10.3519 + 5.97665i) q^{97} -9.77929i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.21632	+	2.10672i	−0.702241	+	1.21632i	0.265436	+	0.964128i	$0.414484\pi$
$3$	−1.21632	+	2.10672i	−0.702241	+	1.21632i	−0.967678	+	0.252189i	$0.918849\pi$
$4$		0			0
$5$			3.98804i			1.78351i	0.452522	+	0.891753i	$0.350524\pi$
$5$			3.98804i			1.78351i	−0.452522	+	0.891753i	$0.649476\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	−1.45886	−	2.52682i	−0.486286	−	0.842272i
$10$		0			0
$11$	2.90265	+	1.67585i	0.875182	+	0.505287i	0.869067	−	0.494695i	$-0.164720\pi$
$11$	2.90265	+	1.67585i	0.875182	+	0.505287i	0.00611528	+	0.999981i	$0.498053\pi$
$12$		0			0
$13$	0.364104	+	3.58712i	0.100984	+	0.994888i
$13$	0.364104	+	3.58712i	0.100984	+	0.994888i
$14$		0			0
$15$	−8.40170	−	4.85073i	−2.16931	−	1.25245i
$16$		0			0
$17$	3.40418	+	5.89621i	0.825634	+	1.43004i	0.901434	+	0.432917i	$0.142516\pi$
$17$	3.40418	+	5.89621i	0.825634	+	1.43004i	−0.0757999	+	0.997123i	$0.524151\pi$
$18$		0			0
$19$	0.621861	−	0.359032i	0.142665	−	0.0823675i	−0.426969	−	0.904266i	$-0.640419\pi$
$19$	0.621861	−	0.359032i	0.142665	−	0.0823675i	0.569633	+	0.821899i	$0.307085\pi$
$20$		0			0
$21$		−	2.43264i		−	0.530845i
$22$		0			0
$23$	0.509352	−	0.882224i	0.106207	−	0.183956i	−0.808024	−	0.589150i	$-0.799463\pi$
$23$	0.509352	−	0.882224i	0.106207	−	0.183956i	0.914231	+	0.405194i	$0.132796\pi$
$24$		0			0
$25$	−10.9045			−2.18090
$26$		0			0
$27$	−0.200166			−0.0385219
$28$		0			0
$29$	4.79947	−	8.31293i	0.891240	−	1.54367i	0.0528493	−	0.998602i	$-0.483170\pi$
$29$	4.79947	−	8.31293i	0.891240	−	1.54367i	0.838390	−	0.545070i	$-0.183497\pi$
$30$		0			0
$31$		−	4.52613i		−	0.812916i	−0.913669	−	0.406458i	$-0.866764\pi$
$31$		−	4.52613i		−	0.812916i	0.913669	−	0.406458i	$-0.133236\pi$
$32$		0			0
$33$	−7.06109	+	4.07672i	−1.22918	+	0.709666i
$34$		0			0
$35$	−1.99402	−	3.45375i	−0.337051	−	0.583790i
$36$		0			0
$37$	4.53684	+	2.61935i	0.745852	+	0.430618i	0.824193	−	0.566309i	$-0.191629\pi$
$37$	4.53684	+	2.61935i	0.745852	+	0.430618i	−0.0783409	+	0.996927i	$0.524962\pi$
$38$		0			0
$39$	−7.99994	−	3.59601i	−1.28102	−	0.575823i
$40$		0			0
$41$	−0.985057	−	0.568723i	−0.153840	−	0.0888196i	0.421104	−	0.907012i	$-0.361643\pi$
$41$	−0.985057	−	0.568723i	−0.153840	−	0.0888196i	−0.574944	+	0.818193i	$0.694976\pi$
$42$		0			0
$43$	−4.25951	−	7.37769i	−0.649569	−	1.12509i	−0.983226	−	0.182392i	$-0.941616\pi$
$43$	−4.25951	−	7.37769i	−0.649569	−	1.12509i	0.333657	−	0.942695i	$-0.391717\pi$
$44$		0			0
$45$	10.0771	−	5.81799i	1.50220	−	0.867294i
$46$		0			0
$47$		−	11.0842i		−	1.61679i	−0.588637	−	0.808397i	$-0.700335\pi$
$47$		−	11.0842i		−	1.61679i	0.588637	−	0.808397i	$-0.299665\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−16.5622			−2.31918
$52$		0			0
$53$	3.19732			0.439185			0.219593	−	0.975592i	$-0.429527\pi$
$53$	3.19732			0.439185			0.219593	+	0.975592i	$0.429527\pi$
$54$		0			0
$55$	−6.68334	+	11.5759i	−0.901182	+	1.56089i
$56$		0			0
$57$			1.74679i			0.231367i
$58$		0			0
$59$	6.50131	−	3.75353i	0.846398	−	0.488668i	−0.0130358	−	0.999915i	$-0.504150\pi$
$59$	6.50131	−	3.75353i	0.846398	−	0.488668i	0.859434	+	0.511247i	$0.170816\pi$
$60$		0			0
$61$	1.90489	+	3.29937i	0.243896	+	0.422441i	0.961821	−	0.273680i	$-0.0882410\pi$
$61$	1.90489	+	3.29937i	0.243896	+	0.422441i	−0.717924	+	0.696121i	$0.754908\pi$
$62$		0			0
$63$	2.52682	+	1.45886i	0.318349	+	0.183799i
$64$		0			0
$65$	−14.3056	+	1.45206i	−1.77439	+	0.180106i
$66$		0			0
$67$	12.6609	+	7.30975i	1.54677	+	0.893028i	0.998386	+	0.0568011i	$0.0180901\pi$
$67$	12.6609	+	7.30975i	1.54677	+	0.893028i	0.548384	+	0.836227i	$0.315243\pi$
$68$		0			0
$69$	1.23907	+	2.14613i	0.149166	+	0.258364i
$70$		0			0
$71$	−11.0774	+	6.39557i	−1.31465	+	0.759014i	−0.982863	−	0.184340i	$-0.940985\pi$
$71$	−11.0774	+	6.39557i	−1.31465	+	0.759014i	−0.331788	+	0.943354i	$0.607652\pi$
$72$		0			0
$73$			7.44426i			0.871285i	0.900120	+	0.435643i	$0.143479\pi$
$73$			7.44426i			0.871285i	−0.900120	+	0.435643i	$0.856521\pi$
$74$		0			0
$75$	13.2633	−	22.9727i	1.53152	−	2.65266i
$76$		0			0
$77$	−3.35169			−0.381961
$78$		0			0
$79$	3.61316			0.406512			0.203256	−	0.979126i	$-0.434848\pi$
$79$	3.61316			0.406512			0.203256	+	0.979126i	$0.434848\pi$
$80$		0			0
$81$	4.62004	−	8.00214i	0.513338	−	0.889127i
$82$		0			0
$83$			3.31234i			0.363576i	0.983338	+	0.181788i	$0.0581885\pi$
$83$			3.31234i			0.363576i	−0.983338	+	0.181788i	$0.941811\pi$
$84$		0			0
$85$	−23.5143	+	13.5760i	−2.55049	+	1.47252i
$86$		0			0
$87$	11.6754	+	20.2223i	1.25173	+	2.16806i
$88$		0			0
$89$	5.96558	+	3.44423i	0.632351	+	0.365088i	0.781662	−	0.623702i	$-0.214372\pi$
$89$	5.96558	+	3.44423i	0.632351	+	0.365088i	−0.149311	+	0.988790i	$0.547706\pi$
$90$		0			0
$91$	−2.10888	−	2.92448i	−0.221071	−	0.306569i
$92$		0			0
$93$	9.53530	+	5.50521i	0.988765	+	0.570863i
$94$		0			0
$95$	1.43183	+	2.48001i	0.146903	+	0.254443i
$96$		0			0
$97$	−10.3519	+	5.97665i	−1.05107	+	0.606837i	−0.922950	−	0.384921i	$-0.874229\pi$
$97$	−10.3519	+	5.97665i	−1.05107	+	0.606837i	−0.128123	+	0.991758i	$0.540895\pi$
$98$		0			0
$99$		−	9.77929i		−	0.982855i
$100$		0			0
$101$	5.64792	−	9.78248i	0.561989	−	0.973393i	−0.435334	−	0.900269i	$-0.643370\pi$
$101$	5.64792	−	9.78248i	0.561989	−	0.973393i	0.997323	−	0.0731239i	$-0.0232968\pi$
$102$		0			0
$103$	2.13103			0.209976			0.104988	−	0.994473i	$-0.466520\pi$
$103$	2.13103			0.209976			0.104988	+	0.994473i	$0.466520\pi$
$104$		0			0
$105$	9.70145			0.946765
$106$		0			0
$107$	−8.79045	+	15.2255i	−0.849805	+	1.47191i	0.0315771	+	0.999501i	$0.489947\pi$
$107$	−8.79045	+	15.2255i	−0.849805	+	1.47191i	−0.881382	+	0.472404i	$0.843386\pi$
$108$		0			0
$109$		−	5.94894i		−	0.569805i	−0.958557	−	0.284902i	$-0.908039\pi$
$109$		−	5.94894i		−	0.569805i	0.958557	−	0.284902i	$-0.0919612\pi$
$110$		0			0
$111$	−11.0365	+	6.37192i	−1.04754	+	0.604796i
$112$		0			0
$113$	1.55550	+	2.69421i	0.146330	+	0.253450i	0.929868	−	0.367893i	$-0.119921\pi$
$113$	1.55550	+	2.69421i	0.146330	+	0.253450i	−0.783539	+	0.621343i	$0.786587\pi$
$114$		0			0
$115$	3.51835	+	2.03132i	0.328087	+	0.189421i
$116$		0			0
$117$	8.53282	−	6.15312i	0.788859	−	0.568856i
$118$		0			0
$119$	−5.89621	−	3.40418i	−0.540504	−	0.312060i
$120$		0			0
$121$	0.116921	+	0.202513i	0.0106292	+	0.0184103i
$122$		0			0
$123$	2.39628	−	1.38350i	0.216066	−	0.124746i
$124$		0			0
$125$		−	23.5473i		−	2.10614i
$126$		0			0
$127$	5.87191	−	10.1704i	0.521047	−	0.902481i	−0.478653	−	0.878004i	$-0.658875\pi$
$127$	5.87191	−	10.1704i	0.521047	−	0.902481i	0.999700	−	0.0244765i	$-0.00779189\pi$
$128$		0			0
$129$	20.7237			1.82462
$130$		0			0
$131$	−7.96449			−0.695860			−0.347930	−	0.937520i	$-0.613115\pi$
$131$	−7.96449			−0.695860			−0.347930	+	0.937520i	$0.613115\pi$
$132$		0			0
$133$	−0.359032	+	0.621861i	−0.0311320	+	0.0539222i
$134$		0			0
$135$		−	0.798270i		−	0.0687041i
$136$		0			0
$137$	16.8986	−	9.75643i	1.44375	−	0.833548i	0.445651	−	0.895207i	$-0.352972\pi$
$137$	16.8986	−	9.75643i	1.44375	−	0.833548i	0.998097	+	0.0616585i	$0.0196390\pi$
$138$		0			0
$139$	3.54000	+	6.13147i	0.300259	+	0.520064i	0.976195	−	0.216897i	$-0.0695935\pi$
$139$	3.54000	+	6.13147i	0.300259	+	0.520064i	−0.675935	+	0.736961i	$0.736260\pi$
$140$		0			0
$141$	23.3513	+	13.4819i	1.96654	+	1.13538i
$142$		0			0
$143$	−4.95459	+	11.0223i	−0.414324	+	0.921734i
$144$		0			0
$145$	33.1523	+	19.1405i	2.75315	+	1.58953i
$146$		0			0
$147$	1.21632	+	2.10672i	0.100320	+	0.173760i
$148$		0			0
$149$	4.07836	−	2.35464i	0.334112	−	0.192900i	−0.323553	−	0.946210i	$-0.604877\pi$
$149$	4.07836	−	2.35464i	0.334112	−	0.192900i	0.657665	+	0.753310i	$0.271544\pi$
$150$		0			0
$151$			8.99006i			0.731600i	0.930693	+	0.365800i	$0.119205\pi$
$151$			8.99006i			0.731600i	−0.930693	+	0.365800i	$0.880795\pi$
$152$		0			0
$153$	9.93242	−	17.2035i	0.802989	−	1.39082i
$154$		0			0
$155$	18.0504			1.44984
$156$		0			0
$157$	−3.64545			−0.290938			−0.145469	−	0.989363i	$-0.546469\pi$
$157$	−3.64545			−0.290938			−0.145469	+	0.989363i	$0.546469\pi$
$158$		0			0
$159$	−3.88895	+	6.73586i	−0.308414	+	0.534189i
$160$		0			0
$161$			1.01870i			0.0802851i
$162$		0			0
$163$	9.57892	−	5.53039i	0.750279	−	0.433174i	−0.0755156	−	0.997145i	$-0.524060\pi$
$163$	9.57892	−	5.53039i	0.750279	−	0.433174i	0.825795	+	0.563971i	$0.190727\pi$
$164$		0			0
$165$	−16.2581	−	28.1599i	−1.26569	−	2.19225i
$166$		0			0
$167$	−6.10346	−	3.52384i	−0.472300	−	0.272683i	0.244902	−	0.969548i	$-0.421244\pi$
$167$	−6.10346	−	3.52384i	−0.472300	−	0.272683i	−0.717202	+	0.696865i	$0.754578\pi$
$168$		0			0
$169$	−12.7349	+	2.61217i	−0.979604	+	0.200936i
$170$		0			0
$171$	−1.81441	−	1.04755i	−0.138752	−	0.0801083i
$172$		0			0
$173$	−7.54568	−	13.0695i	−0.573688	−	0.993656i	−0.996183	−	0.0872910i	$-0.972179\pi$
$173$	−7.54568	−	13.0695i	−0.573688	−	0.993656i	0.422495	−	0.906365i	$-0.361154\pi$
$174$		0			0
$175$	9.44356	−	5.45224i	0.713866	−	0.412151i
$176$		0			0
$177$			18.2619i			1.37265i
$178$		0			0
$179$	−6.29634	+	10.9056i	−0.470611	+	0.815122i	−0.999435	−	0.0336095i	$-0.989300\pi$
$179$	−6.29634	+	10.9056i	−0.470611	+	0.815122i	0.528824	+	0.848731i	$0.322633\pi$
$180$		0			0
$181$	−10.8101			−0.803511			−0.401756	−	0.915747i	$-0.631600\pi$
$181$	−10.8101			−0.803511			−0.401756	+	0.915747i	$0.631600\pi$
$182$		0			0
$183$	−9.26782			−0.685097
$184$		0			0
$185$	−10.4461	+	18.0931i	−0.768010	+	1.33023i
$186$		0			0
$187$			22.8195i			1.66873i
$188$		0			0
$189$	0.173349	−	0.100083i	0.0126093	−	0.00727996i
$190$		0			0
$191$	6.60184	+	11.4347i	0.477692	+	0.827387i	0.999673	−	0.0255702i	$-0.00814014\pi$
$191$	6.60184	+	11.4347i	0.477692	+	0.827387i	−0.521981	+	0.852957i	$0.674807\pi$
$192$		0			0
$193$	−4.83035	−	2.78880i	−0.347696	−	0.200743i	0.315974	−	0.948768i	$-0.397669\pi$
$193$	−4.83035	−	2.78880i	−0.347696	−	0.200743i	−0.663670	+	0.748025i	$0.731002\pi$
$194$		0			0
$195$	14.3410	−	31.9041i	1.02698	−	2.28470i
$196$		0			0
$197$	2.74329	+	1.58384i	0.195452	+	0.112844i	0.594532	−	0.804072i	$-0.297337\pi$
$197$	2.74329	+	1.58384i	0.195452	+	0.112844i	−0.399081	+	0.916916i	$0.630671\pi$
$198$		0			0
$199$	3.10818	+	5.38353i	0.220333	+	0.381629i	0.954909	−	0.296898i	$-0.0959521\pi$
$199$	3.10818	+	5.38353i	0.220333	+	0.381629i	−0.734576	+	0.678527i	$0.762619\pi$
$200$		0			0
$201$	−30.7992	+	17.7820i	−2.17241	+	1.25424i
$202$		0			0
$203$			9.59895i			0.673714i
$204$		0			0
$205$	2.26809	−	3.92845i	0.158410	−	0.274375i
$206$		0			0
$207$	−2.97229			−0.206588
$208$		0			0
$209$	2.40673			0.166477
$210$		0			0
$211$	−7.13911	+	12.3653i	−0.491477	+	0.851262i	−0.999952	−	0.00981417i	$-0.996876\pi$
$211$	−7.13911	+	12.3653i	−0.491477	+	0.851262i	0.508475	+	0.861077i	$0.330209\pi$
$212$		0			0
$213$		−	31.1162i		−	2.13204i
$214$		0			0
$215$	29.4225	−	16.9871i	2.00660	−	1.15851i
$216$		0			0
$217$	2.26306	+	3.91974i	0.153627	+	0.266089i
$218$		0			0
$219$	−15.6830	−	9.05459i	−1.05976	−	0.611853i
$220$		0			0
$221$	−19.9109	+	14.3580i	−1.33935	+	0.965825i
$222$		0			0
$223$	−6.50691	−	3.75677i	−0.435735	−	0.251572i	0.266052	−	0.963959i	$-0.414281\pi$
$223$	−6.50691	−	3.75677i	−0.435735	−	0.251572i	−0.701787	+	0.712387i	$0.747614\pi$
$224$		0			0
$225$	15.9081	+	27.5536i	1.06054	+	1.83691i
$226$		0			0
$227$	9.98521	−	5.76496i	0.662742	−	0.382634i	−0.130579	−	0.991438i	$-0.541684\pi$
$227$	9.98521	−	5.76496i	0.662742	−	0.382634i	0.793321	+	0.608804i	$0.208350\pi$
$228$		0			0
$229$		−	5.92000i		−	0.391204i	−0.980683	−	0.195602i	$-0.937334\pi$
$229$		−	5.92000i		−	0.391204i	0.980683	−	0.195602i	$-0.0626661\pi$
$230$		0			0
$231$	4.07672	−	7.06109i	0.268229	−	0.464586i
$232$		0			0
$233$	−27.3769			−1.79352			−0.896759	−	0.442519i	$-0.854085\pi$
$233$	−27.3769			−1.79352			−0.896759	+	0.442519i	$0.854085\pi$
$234$		0			0
$235$	44.2042			2.88356
$236$		0			0
$237$	−4.39475	+	7.61192i	−0.285469	+	0.494448i
$238$		0			0
$239$		−	25.9440i		−	1.67818i	−0.543996	−	0.839088i	$-0.683089\pi$
$239$		−	25.9440i		−	1.67818i	0.543996	−	0.839088i	$-0.316911\pi$
$240$		0			0
$241$	20.8922	−	12.0621i	1.34578	−	0.776988i	0.358134	−	0.933670i	$-0.383413\pi$
$241$	20.8922	−	12.0621i	1.34578	−	0.776988i	0.987649	+	0.156682i	$0.0500797\pi$
$242$		0			0
$243$	10.9386	+	18.9463i	0.701713	+	1.21540i
$244$		0			0
$245$	3.45375	+	1.99402i	0.220652	+	0.127393i
$246$		0			0
$247$	1.51431	+	2.09996i	0.0963533	+	0.133618i
$248$		0			0
$249$	−6.97819	−	4.02886i	−0.442225	−	0.255318i
$250$		0			0
$251$	1.58994	+	2.75386i	0.100356	+	0.173822i	0.911832	−	0.410565i	$-0.134668\pi$
$251$	1.58994	+	2.75386i	0.100356	+	0.173822i	−0.811475	+	0.584387i	$0.801335\pi$
$252$		0			0
$253$	2.95694	−	1.70719i	0.185901	−	0.107330i
$254$		0			0
$255$		−	66.0509i		−	4.13627i
$256$		0			0
$257$	10.4090	−	18.0288i	0.649293	−	1.12461i	−0.333999	−	0.942573i	$-0.608398\pi$
$257$	10.4090	−	18.0288i	0.649293	−	1.12461i	0.983292	−	0.182035i	$-0.0582684\pi$
$258$		0			0
$259$	−5.23869			−0.325517
$260$		0			0
$261$	−28.0070			−1.73359
$262$		0			0
$263$	2.33273	−	4.04041i	0.143842	−	0.249142i	−0.785098	−	0.619371i	$-0.787388\pi$
$263$	2.33273	−	4.04041i	0.143842	−	0.249142i	0.928940	+	0.370229i	$0.120721\pi$
$264$		0			0
$265$			12.7510i			0.783289i
$266$		0			0
$267$	−14.5121	+	8.37856i	−0.888126	+	0.512760i
$268$		0			0
$269$	−2.79744	−	4.84531i	−0.170563	−	0.295424i	0.768054	−	0.640385i	$-0.221225\pi$
$269$	−2.79744	−	4.84531i	−0.170563	−	0.295424i	−0.938617	+	0.344961i	$0.887892\pi$
$270$		0			0
$271$	−1.28702	−	0.743063i	−0.0781810	−	0.0451378i	0.460400	−	0.887712i	$-0.347706\pi$
$271$	−1.28702	−	0.743063i	−0.0781810	−	0.0451378i	−0.538581	+	0.842574i	$0.681039\pi$
$272$		0			0
$273$	8.72616	−	0.885732i	0.528131	−	0.0536069i
$274$		0			0
$275$	−31.6519	−	18.2742i	−1.90868	−	1.10198i
$276$		0			0
$277$	14.2101	+	24.6127i	0.853804	+	1.47883i	0.877750	+	0.479119i	$0.159044\pi$
$277$	14.2101	+	24.6127i	0.853804	+	1.47883i	−0.0239462	+	0.999713i	$0.507623\pi$
$278$		0			0
$279$	−11.4367	+	6.60298i	−0.684697	+	0.395310i
$280$		0			0
$281$		−	19.5795i		−	1.16801i	−0.811749	−	0.584007i	$-0.801484\pi$
$281$		−	19.5795i		−	1.16801i	0.811749	−	0.584007i	$-0.198516\pi$
$282$		0			0
$283$	−6.44095	+	11.1561i	−0.382875	+	0.663158i	−0.991472	−	0.130321i	$-0.958399\pi$
$283$	−6.44095	+	11.1561i	−0.382875	+	0.663158i	0.608597	+	0.793479i	$0.291733\pi$
$284$		0			0
$285$	−6.96626			−0.412645
$286$		0			0
$287$	1.13745			0.0671413
$288$		0			0
$289$	−14.6768	+	25.4210i	−0.863343	+	1.49535i
$290$		0			0
$291$		−	29.0780i		−	1.70459i
$292$		0			0
$293$	−10.7014	+	6.17846i	−0.625183	+	0.360950i	−0.778884	−	0.627168i	$-0.784214\pi$
$293$	−10.7014	+	6.17846i	−0.625183	+	0.360950i	0.153701	+	0.988117i	$0.450881\pi$
$294$		0			0
$295$	14.9692	+	25.9275i	0.871543	+	1.50956i
$296$		0			0
$297$	−0.581012	−	0.335447i	−0.0337137	−	0.0194646i
$298$		0			0
$299$	3.35010	+	1.50589i	0.193741	+	0.0870876i
$300$		0			0
$301$	7.37769	+	4.25951i	0.425243	+	0.245514i
$302$		0			0
$303$	13.7393	+	23.7972i	0.789303	+	1.36711i
$304$		0			0
$305$	−13.1580	+	7.59679i	−0.753426	+	0.434991i
$306$		0			0
$307$		−	0.570197i		−	0.0325429i	−0.999868	−	0.0162714i	$-0.994820\pi$
$307$		−	0.570197i		−	0.0325429i	0.999868	−	0.0162714i	$-0.00517959\pi$
$308$		0			0
$309$	−2.59200	+	4.48948i	−0.147454	+	0.255398i
$310$		0			0
$311$	−27.5957			−1.56481			−0.782404	−	0.622771i	$-0.786007\pi$
$311$	−27.5957			−1.56481			−0.782404	+	0.622771i	$0.786007\pi$
$312$		0			0
$313$	−2.85101			−0.161149			−0.0805744	−	0.996749i	$-0.525675\pi$
$313$	−2.85101			−0.161149			−0.0805744	+	0.996749i	$0.525675\pi$
$314$		0			0
$315$	−5.81799	+	10.0771i	−0.327806	+	0.567777i
$316$		0			0
$317$			32.7278i			1.83818i	0.394052	+	0.919088i	$0.371073\pi$
$317$			32.7278i			1.83818i	−0.394052	+	0.919088i	$0.628927\pi$
$318$		0			0
$319$	27.8624	−	16.0864i	1.55999	−	0.900663i
$320$		0			0
$321$	−21.3840	−	37.0381i	−1.19354	−	2.06727i
$322$		0			0
$323$	4.23385	+	2.44441i	0.235578	+	0.136011i
$324$		0			0
$325$	−3.97036	−	39.1157i	−0.220236	−	2.16975i
$326$		0			0
$327$	12.5328	+	7.23580i	0.693064	+	0.400141i
$328$		0			0
$329$	5.54209	+	9.59919i	0.305546	+	0.529220i
$330$		0			0
$331$	1.88365	−	1.08753i	0.103535	−	0.0597759i	−0.447338	−	0.894365i	$-0.647628\pi$
$331$	1.88365	−	1.08753i	0.103535	−	0.0597759i	0.550873	+	0.834589i	$0.314295\pi$
$332$		0			0
$333$		−	15.2850i		−	0.837614i
$334$		0			0
$335$	−29.1516	+	50.4920i	−1.59272	+	2.75867i
$336$		0			0
$337$	6.15505			0.335287			0.167644	−	0.985848i	$-0.446384\pi$
$337$	6.15505			0.335287			0.167644	+	0.985848i	$0.446384\pi$
$338$		0			0
$339$	−7.56795			−0.411035
$340$		0			0
$341$	7.58509	−	13.1378i	0.410756	−	0.711450i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−8.55885	+	4.94146i	−0.460793	+	0.266039i
$346$		0			0
$347$	−0.620250	−	1.07430i	−0.0332968	−	0.0576717i	0.848897	−	0.528559i	$-0.177267\pi$
$347$	−0.620250	−	1.07430i	−0.0332968	−	0.0576717i	−0.882194	+	0.470887i	$0.843934\pi$
$348$		0			0
$349$	−15.5980	−	9.00554i	−0.834944	−	0.482055i	0.0205981	−	0.999788i	$-0.493443\pi$
$349$	−15.5980	−	9.00554i	−0.834944	−	0.482055i	−0.855543	+	0.517732i	$0.826776\pi$
$350$		0			0
$351$	−0.0728812	−	0.718019i	−0.00389011	−	0.0383250i
$352$		0			0
$353$	−8.93323	−	5.15760i	−0.475468	−	0.274511i	0.243058	−	0.970012i	$-0.421849\pi$
$353$	−8.93323	−	5.15760i	−0.475468	−	0.274511i	−0.718526	+	0.695500i	$0.755183\pi$
$354$		0			0
$355$	−25.5058	−	44.1773i	−1.35371	−	2.34469i
$356$		0			0
$357$	14.3433	−	8.28112i	0.759129	−	0.438283i
$358$		0			0
$359$		−	19.7883i		−	1.04439i	−0.852827	−	0.522193i	$-0.825114\pi$
$359$		−	19.7883i		−	1.04439i	0.852827	−	0.522193i	$-0.174886\pi$
$360$		0			0
$361$	−9.24219	+	16.0079i	−0.486431	+	0.842524i
$362$		0			0
$363$	−0.568852			−0.0298570
$364$		0			0
$365$	−29.6880			−1.55394
$366$		0			0
$367$	6.77618	−	11.7367i	0.353714	−	0.612650i	−0.633183	−	0.774002i	$-0.718252\pi$
$367$	6.77618	−	11.7367i	0.353714	−	0.612650i	0.986897	+	0.161352i	$0.0515854\pi$
$368$		0			0
$369$			3.31874i			0.172767i
$370$		0			0
$371$	−2.76896	+	1.59866i	−0.143757	+	0.0829982i
$372$		0			0
$373$	−6.70165	−	11.6076i	−0.346998	−	0.601019i	0.638716	−	0.769442i	$-0.279466\pi$
$373$	−6.70165	−	11.6076i	−0.346998	−	0.601019i	−0.985715	+	0.168424i	$0.946132\pi$
$374$		0			0
$375$	49.6077	+	28.6410i	2.56173	+	1.47902i
$376$		0			0
$377$	31.5670	+	14.1895i	1.62578	+	0.730797i
$378$		0			0
$379$	14.9512	+	8.63206i	0.767990	+	0.443399i	0.832157	−	0.554540i	$-0.187106\pi$
$379$	14.9512	+	8.63206i	0.767990	+	0.443399i	−0.0641670	+	0.997939i	$0.520439\pi$
$380$		0			0
$381$	14.2842	+	24.7410i	0.731802	+	1.26752i
$382$		0			0
$383$	10.0074	−	5.77775i	0.511352	−	0.295229i	−0.222037	−	0.975038i	$-0.571271\pi$
$383$	10.0074	−	5.77775i	0.511352	−	0.295229i	0.733389	+	0.679809i	$0.237937\pi$
$384$		0			0
$385$		−	13.3667i		−	0.681230i
$386$		0			0
$387$	−12.4280	+	21.5260i	−0.631753	+	1.09423i
$388$		0			0
$389$	−21.4305			−1.08657			−0.543284	−	0.839549i	$-0.682819\pi$
$389$	−21.4305			−1.08657			−0.543284	+	0.839549i	$0.682819\pi$
$390$		0			0
$391$	6.93570			0.350753
$392$		0			0
$393$	9.68735	−	16.7790i	0.488662	−	0.846387i
$394$		0			0
$395$			14.4094i			0.725016i
$396$		0			0
$397$	10.2782	−	5.93414i	0.515850	−	0.297826i	−0.219385	−	0.975638i	$-0.570405\pi$
$397$	10.2782	−	5.93414i	0.515850	−	0.297826i	0.735235	+	0.677812i	$0.237072\pi$
$398$		0			0
$399$	−0.873393	−	1.51276i	−0.0437243	−	0.0757328i
$400$		0			0
$401$	5.71607	+	3.30017i	0.285447	+	0.164803i	0.635887	−	0.771782i	$-0.280635\pi$
$401$	5.71607	+	3.30017i	0.285447	+	0.164803i	−0.350440	+	0.936585i	$0.613968\pi$
$402$		0			0
$403$	16.2358	−	1.64798i	0.808761	−	0.0820917i
$404$		0			0
$405$	31.9129	+	18.4249i	1.58576	+	0.915541i
$406$		0			0
$407$	8.77925	+	15.2061i	0.435171	+	0.753738i
$408$		0			0
$409$	−27.8315	+	16.0685i	−1.37618	+	0.794538i	−0.991697	−	0.128594i	$-0.958953\pi$
$409$	−27.8315	+	16.0685i	−1.37618	+	0.794538i	−0.384483	+	0.923132i	$0.625620\pi$
$410$		0			0
$411$			47.4677i			2.34141i
$412$		0			0
$413$	−3.75353	+	6.50131i	−0.184699	+	0.319908i
$414$		0			0
$415$	−13.2097			−0.648441
$416$		0			0
$417$	−17.2231			−0.843418
$418$		0			0
$419$	−6.57238	+	11.3837i	−0.321082	+	0.556130i	−0.980712	−	0.195461i	$-0.937380\pi$
$419$	−6.57238	+	11.3837i	−0.321082	+	0.556130i	0.659630	+	0.751591i	$0.270713\pi$
$420$		0			0
$421$		−	33.7473i		−	1.64474i	−0.568952	−	0.822371i	$-0.692651\pi$
$421$		−	33.7473i		−	1.64474i	0.568952	−	0.822371i	$-0.307349\pi$
$422$		0			0
$423$	−28.0077	+	16.1703i	−1.36178	+	0.786225i
$424$		0			0
$425$	−37.1208	−	64.2950i	−1.80062	−	3.11877i
$426$		0			0
$427$	−3.29937	−	1.90489i	−0.159668	−	0.0921842i
$428$		0			0
$429$	−17.1947	−	23.8446i	−0.830166	−	1.15123i
$430$		0			0
$431$	7.61484	+	4.39643i	0.366794	+	0.211769i	0.672057	−	0.740500i	$-0.265411\pi$
$431$	7.61484	+	4.39643i	0.366794	+	0.211769i	−0.305263	+	0.952268i	$0.598744\pi$
$432$		0			0
$433$	15.3059	+	26.5106i	0.735556	+	1.27402i	0.954479	+	0.298278i	$0.0964122\pi$
$433$	15.3059	+	26.5106i	0.735556	+	1.27402i	−0.218923	+	0.975742i	$0.570254\pi$
$434$		0			0
$435$	−80.6475	+	46.5619i	−3.86675	+	2.23247i
$436$		0			0
$437$		−	0.731494i		−	0.0349921i
$438$		0			0
$439$	−9.30460	+	16.1160i	−0.444084	+	0.769176i	−0.997988	−	0.0634044i	$-0.979804\pi$
$439$	−9.30460	+	16.1160i	−0.444084	+	0.769176i	0.553904	+	0.832581i	$0.313138\pi$
$440$		0			0
$441$	−2.91772			−0.138939
$442$		0			0
$443$	0.0390168			0.00185374			0.000926871	−	1.00000i	$-0.499705\pi$
$443$	0.0390168			0.00185374			0.000926871		1.00000i	$0.499705\pi$
$444$		0			0
$445$	−13.7357	+	23.7910i	−0.651136	+	1.12780i
$446$		0			0
$447$			11.4560i			0.541849i
$448$		0			0
$449$	30.4435	−	17.5765i	1.43672	−	0.829488i	0.439095	−	0.898440i	$-0.355299\pi$
$449$	30.4435	−	17.5765i	1.43672	−	0.829488i	0.997620	+	0.0689525i	$0.0219657\pi$
$450$		0			0
$451$	−1.90618	−	3.30161i	−0.0897587	−	0.155467i
$452$		0			0
$453$	−18.9396	−	10.9348i	−0.889859	−	0.513760i
$454$		0			0
$455$	11.6630	−	8.41031i	0.546768	−	0.394282i
$456$		0			0
$457$	−1.80481	−	1.04201i	−0.0844254	−	0.0487430i	0.457193	−	0.889368i	$-0.348855\pi$
$457$	−1.80481	−	1.04201i	−0.0844254	−	0.0487430i	−0.541618	+	0.840624i	$0.682188\pi$
$458$		0			0
$459$	−0.681400	−	1.18022i	−0.0318050	−	0.0550879i
$460$		0			0
$461$	18.8011	−	10.8548i	0.875652	−	0.505558i	0.00642998	−	0.999979i	$-0.497953\pi$
$461$	18.8011	−	10.8548i	0.875652	−	0.505558i	0.869222	+	0.494421i	$0.164620\pi$
$462$		0			0
$463$		−	3.23290i		−	0.150246i	−0.997174	−	0.0751229i	$-0.976065\pi$
$463$		−	3.23290i		−	0.150246i	0.997174	−	0.0751229i	$-0.0239349\pi$
$464$		0			0
$465$	−21.9550	+	38.0272i	−1.01814	+	1.76347i
$466$		0			0
$467$	−6.13695			−0.283984			−0.141992	−	0.989868i	$-0.545351\pi$
$467$	−6.13695			−0.283984			−0.141992	+	0.989868i	$0.545351\pi$
$468$		0			0
$469$	−14.6195			−0.675066
$470$		0			0
$471$	4.43402	−	7.67995i	0.204309	−	0.353874i
$472$		0			0
$473$		−	28.5531i		−	1.31287i
$474$		0			0
$475$	−6.78107	+	3.91505i	−0.311137	+	0.179635i
$476$		0			0
$477$	−4.66443	−	8.07903i	−0.213570	−	0.369913i
$478$		0			0
$479$	5.93664	+	3.42752i	0.271252	+	0.156607i	0.629456	−	0.777036i	$-0.283278\pi$
$479$	5.93664	+	3.42752i	0.271252	+	0.156607i	−0.358204	+	0.933643i	$0.616611\pi$
$480$		0			0
$481$	−7.74403	+	17.2279i	−0.353097	+	0.785525i
$482$		0			0
$483$	−2.14613	−	1.23907i	−0.0976522	−	0.0563796i
$484$		0			0
$485$	−23.8351	−	41.2837i	−1.08230	−	1.87460i
$486$		0			0
$487$	−33.1986	+	19.1672i	−1.50437	+	0.868551i	−0.504387	+	0.863478i	$0.668281\pi$
$487$	−33.1986	+	19.1672i	−1.50437	+	0.868551i	−0.999987	+	0.00507302i	$0.998385\pi$
$488$		0			0
$489$			26.9069i			1.21677i
$490$		0			0
$491$	11.7060	−	20.2754i	0.528284	−	0.915015i	−0.471172	−	0.882041i	$-0.656169\pi$
$491$	11.7060	−	20.2754i	0.528284	−	0.915015i	0.999456	−	0.0329734i	$-0.0104977\pi$
$492$		0			0
$493$	65.3530			2.94335
$494$		0			0
$495$	39.0002			1.75293
$496$		0			0
$497$	6.39557	−	11.0774i	0.286880	−	0.496891i
$498$		0			0
$499$		−	15.7127i		−	0.703395i	−0.936114	−	0.351697i	$-0.885605\pi$
$499$		−	15.7127i		−	0.703395i	0.936114	−	0.351697i	$-0.114395\pi$
$500$		0			0
$501$	14.8475	−	8.57221i	0.663338	−	0.382978i
$502$		0			0
$503$	−16.9329	−	29.3286i	−0.755000	−	1.30770i	−0.945374	−	0.325987i	$-0.894303\pi$
$503$	−16.9329	−	29.3286i	−0.755000	−	1.30770i	0.190374	−	0.981712i	$-0.439030\pi$
$504$		0			0
$505$	39.0129	+	22.5241i	1.73605	+	1.00231i
$506$		0			0
$507$	9.98652	−	30.0061i	0.443517	−	1.33262i
$508$		0			0
$509$	6.74442	+	3.89389i	0.298941	+	0.172594i	0.641967	−	0.766732i	$-0.278119\pi$
$509$	6.74442	+	3.89389i	0.298941	+	0.172594i	−0.343026	+	0.939326i	$0.611452\pi$
$510$		0			0
$511$	−3.72213	−	6.44692i	−0.164657	−	0.285195i
$512$		0			0
$513$	−0.124475	+	0.0718659i	−0.00549572	+	0.00317296i
$514$		0			0
$515$			8.49862i			0.374494i
$516$		0			0
$517$	18.5754	−	32.1735i	0.816945	−	1.41499i
$518$		0			0
$519$	36.7118			1.61147
$520$		0			0
$521$	−22.6954			−0.994302			−0.497151	−	0.867664i	$-0.665621\pi$
$521$	−22.6954			−0.994302			−0.497151	+	0.867664i	$0.665621\pi$
$522$		0			0
$523$	−16.6328	+	28.8088i	−0.727301	+	1.25972i	0.230718	+	0.973021i	$0.425892\pi$
$523$	−16.6328	+	28.8088i	−0.727301	+	1.25972i	−0.958020	+	0.286702i	$0.907441\pi$
$524$		0			0
$525$			26.5266i			1.15772i
$526$		0			0
$527$	26.6870	−	15.4077i	1.16250	−	0.671171i
$528$		0			0
$529$	10.9811	+	19.0199i	0.477440	+	0.826950i
$530$		0			0
$531$	−18.9690	−	10.9517i	−0.823183	−	0.475265i
$532$		0			0
$533$	1.68141	−	3.74059i	0.0728301	−	0.162023i
$534$		0			0
$535$	−60.7200	−	35.0567i	−2.62515	−	1.51563i
$536$		0			0
$537$	−15.3167	−	26.5293i	−0.660965	−	1.14482i
$538$		0			0
$539$	2.90265	−	1.67585i	0.125026	−	0.0721838i
$540$		0			0
$541$		−	34.2525i		−	1.47263i	−0.676640	−	0.736314i	$-0.736565\pi$
$541$		−	34.2525i		−	1.47263i	0.676640	−	0.736314i	$-0.263435\pi$
$542$		0			0
$543$	13.1486	−	22.7740i	0.564259	−	0.977325i
$544$		0			0
$545$	23.7246			1.01625
$546$		0			0
$547$	−17.4809			−0.747428			−0.373714	−	0.927544i	$-0.621916\pi$
$547$	−17.4809			−0.747428			−0.373714	+	0.927544i	$0.621916\pi$
$548$		0			0
$549$	5.55794	−	9.62663i	0.237207	−	0.410854i
$550$		0			0
$551$		−	6.89265i		−	0.293637i
$552$		0			0
$553$	−3.12908	+	1.80658i	−0.133062	+	0.0768235i
$554$		0			0
$555$	−25.4115	−	44.0140i	−1.07866	−	1.86829i
$556$		0			0
$557$	12.5934	+	7.27078i	0.533598	+	0.308073i	0.742480	−	0.669868i	$-0.233649\pi$
$557$	12.5934	+	7.27078i	0.533598	+	0.308073i	−0.208883	+	0.977941i	$0.566983\pi$
$558$		0			0
$559$	24.9137	−	17.9656i	1.05374	−	0.759864i
$560$		0			0
$561$	−48.0744	−	27.7558i	−2.02970	−	1.17185i
$562$		0			0
$563$	21.4677	+	37.1832i	0.904757	+	1.56708i	0.821244	+	0.570578i	$0.193281\pi$
$563$	21.4677	+	37.1832i	0.904757	+	1.56708i	0.0835128	+	0.996507i	$0.473386\pi$
$564$		0			0
$565$	−10.7446	+	6.20342i	−0.452030	+	0.260980i
$566$		0			0
$567$			9.24008i			0.388047i
$568$		0			0
$569$	8.12537	−	14.0736i	0.340633	−	0.589994i	−0.643917	−	0.765095i	$-0.722692\pi$
$569$	8.12537	−	14.0736i	0.340633	−	0.589994i	0.984550	+	0.175101i	$0.0560252\pi$
$570$		0			0
$571$	16.4589			0.688784			0.344392	−	0.938826i	$-0.388085\pi$
$571$	16.4589			0.688784			0.344392	+	0.938826i	$0.388085\pi$
$572$		0			0
$573$	−32.1197			−1.34182
$574$		0			0
$575$	−5.55422	+	9.62019i	−0.231627	+	0.401190i
$576$		0			0
$577$			34.1900i			1.42335i	0.702509	+	0.711674i	$0.252063\pi$
$577$			34.1900i			1.42335i	−0.702509	+	0.711674i	$0.747937\pi$
$578$		0			0
$579$	11.7505	−	6.78414i	0.488333	−	0.281939i
$580$		0			0
$581$	−1.65617	−	2.86857i	−0.0687095	−	0.119008i
$582$		0			0
$583$	9.28069	+	5.35821i	0.384367	+	0.221914i
$584$		0			0
$585$	24.5389	+	34.0292i	1.01456	+	1.40694i
$586$		0			0
$587$	27.9942	+	16.1624i	1.15544	+	0.667095i	0.950208	−	0.311618i	$-0.100871\pi$
$587$	27.9942	+	16.1624i	1.15544	+	0.667095i	0.205235	+	0.978713i	$0.434204\pi$
$588$		0			0
$589$	−1.62502	−	2.81462i	−0.0669579	−	0.115974i
$590$		0			0
$591$	−6.67343	+	3.85291i	−0.274508	+	0.158487i
$592$		0			0
$593$		−	12.7618i		−	0.524064i	−0.965059	−	0.262032i	$-0.915607\pi$
$593$		−	12.7618i		−	0.524064i	0.965059	−	0.262032i	$-0.0843925\pi$
$594$		0			0
$595$	13.5760	−	23.5143i	0.556562	−	0.963993i
$596$		0			0
$597$	−15.1222			−0.618909
$598$		0			0
$599$	−36.3602			−1.48564			−0.742818	−	0.669493i	$-0.766511\pi$
$599$	−36.3602			−1.48564			−0.742818	+	0.669493i	$0.766511\pi$
$600$		0			0
$601$	−12.2231	+	21.1711i	−0.498592	+	0.863586i	−0.999999	−	0.00162539i	$-0.999483\pi$
$601$	−12.2231	+	21.1711i	−0.498592	+	0.863586i	0.501407	+	0.865212i	$0.332816\pi$
$602$		0			0
$603$		−	42.6555i		−	1.73707i
$604$		0			0
$605$	−0.807630	+	0.466285i	−0.0328348	+	0.0189572i
$606$		0			0
$607$	−3.87641	−	6.71413i	−0.157338	−	0.272518i	0.776570	−	0.630031i	$-0.216958\pi$
$607$	−3.87641	−	6.71413i	−0.157338	−	0.272518i	−0.933908	+	0.357513i	$0.883625\pi$
$608$		0			0
$609$	−20.2223	−	11.6754i	−0.819450	−	0.473110i
$610$		0			0
$611$	39.7603	−	4.03579i	1.60853	−	0.163271i
$612$		0			0
$613$	20.6221	+	11.9062i	0.832918	+	0.480885i	0.854851	−	0.518874i	$-0.173649\pi$
$613$	20.6221	+	11.9062i	0.832918	+	0.480885i	−0.0219327	+	0.999759i	$0.506982\pi$
$614$		0			0
$615$	5.51744	+	9.55648i	0.222485	+	0.385355i
$616$		0			0
$617$	29.4007	−	16.9745i	1.18363	−	0.683369i	0.226778	−	0.973947i	$-0.427181\pi$
$617$	29.4007	−	16.9745i	1.18363	−	0.683369i	0.956851	+	0.290578i	$0.0938476\pi$
$618$		0			0
$619$			16.8377i			0.676764i	0.941009	+	0.338382i	$0.109880\pi$
$619$			16.8377i			0.676764i	−0.941009	+	0.338382i	$0.890120\pi$
$620$		0			0
$621$	−0.101955	+	0.176591i	−0.00409131	+	0.00708636i
$622$		0			0
$623$	−6.88846			−0.275980
$624$		0			0
$625$	39.3853			1.57541
$626$		0			0
$627$	−2.92734	+	5.07031i	−0.116907	+	0.202489i
$628$		0			0
$629$			35.6669i			1.42213i
$630$		0			0
$631$	−15.3064	+	8.83718i	−0.609340	+	0.351803i	−0.772707	−	0.634763i	$-0.781098\pi$
$631$	−15.3064	+	8.83718i	−0.609340	+	0.351803i	0.163367	+	0.986565i	$0.447765\pi$
$632$		0			0
$633$	−17.3669	−	30.0803i	−0.690270	−	1.19558i
$634$		0			0
$635$	40.5601	+	23.4174i	1.60958	+	0.929292i
$636$		0			0
$637$	3.28859	+	1.47824i	0.130299	+	0.0585699i
$638$		0			0
$639$	32.3208	+	18.6604i	1.27859	+	0.738196i
$640$		0			0
$641$	−18.9020	−	32.7392i	−0.746583	−	1.29312i	−0.949451	−	0.313914i	$-0.898360\pi$
$641$	−18.9020	−	32.7392i	−0.746583	−	1.29312i	0.202868	−	0.979206i	$-0.434974\pi$
$642$		0			0
$643$	−16.8674	+	9.73842i	−0.665187	+	0.384046i	−0.794250	−	0.607590i	$-0.792136\pi$
$643$	−16.8674	+	9.73842i	−0.665187	+	0.384046i	0.129064	+	0.991636i	$0.458803\pi$
$644$		0			0
$645$			82.6469i			3.25422i
$646$		0			0
$647$	20.3452	−	35.2389i	0.799851	−	1.38538i	−0.119862	−	0.992791i	$-0.538245\pi$
$647$	20.3452	−	35.2389i	0.799851	−	1.38538i	0.919713	−	0.392592i	$-0.128422\pi$
$648$		0			0
$649$	25.1614			0.987670
$650$		0			0
$651$	−11.0104			−0.431532
$652$		0			0
$653$	9.47968	−	16.4193i	0.370969	−	0.642536i	−0.618746	−	0.785591i	$-0.712359\pi$
$653$	9.47968	−	16.4193i	0.370969	−	0.642536i	0.989715	+	0.143055i	$0.0456924\pi$
$654$		0			0
$655$		−	31.7627i		−	1.24107i
$656$		0			0
$657$	18.8103	−	10.8601i	0.733859	−	0.423694i
$658$		0			0
$659$	4.03079	+	6.98153i	0.157017	+	0.271962i	0.933792	−	0.357817i	$-0.116479\pi$
$659$	4.03079	+	6.98153i	0.157017	+	0.271962i	−0.776775	+	0.629779i	$0.783146\pi$
$660$		0			0
$661$	17.7393	+	10.2418i	0.689978	+	0.398359i	0.803604	−	0.595165i	$-0.202913\pi$
$661$	17.7393	+	10.2418i	0.689978	+	0.398359i	−0.113626	+	0.993524i	$0.536246\pi$
$662$		0			0
$663$	−6.03037	−	59.4107i	−0.234200	−	2.30732i
$664$		0			0
$665$	−2.48001	−	1.43183i	−0.0961706	−	0.0555241i
$666$		0			0
$667$	−4.88924	−	8.46842i	−0.189312	−	0.327898i
$668$		0			0
$669$	15.8289	−	9.13884i	0.611982	−	0.353328i
$670$		0			0
$671$			12.7692i			0.492951i
$672$		0			0
$673$	−7.70562	+	13.3465i	−0.297030	+	0.514471i	−0.975455	−	0.220199i	$-0.929329\pi$
$673$	−7.70562	+	13.3465i	−0.297030	+	0.514471i	0.678425	+	0.734669i	$0.262663\pi$
$674$		0			0
$675$	2.18270			0.0840123
$676$		0			0
$677$	51.5750			1.98219			0.991093	−	0.133169i	$-0.0425151\pi$
$677$	51.5750			1.98219			0.991093	+	0.133169i	$0.0425151\pi$
$678$		0			0
$679$	5.97665	−	10.3519i	0.229363	−	0.397268i
$680$		0			0
$681$			28.0481i			1.07481i
$682$		0			0
$683$	−10.8294	+	6.25234i	−0.414374	+	0.239239i	−0.692668	−	0.721257i	$-0.743565\pi$
$683$	−10.8294	+	6.25234i	−0.414374	+	0.239239i	0.278293	+	0.960496i	$0.410231\pi$
$684$		0			0
$685$	38.9091	+	67.3925i	1.48664	+	2.57493i
$686$		0			0
$687$	12.4718	+	7.20060i	0.475829	+	0.274720i
$688$		0			0
$689$	1.16415	+	11.4692i	0.0443508	+	0.436940i
$690$		0			0
$691$	−6.42282	−	3.70822i	−0.244336	−	0.141067i	0.372832	−	0.927899i	$-0.378387\pi$
$691$	−6.42282	−	3.70822i	−0.244336	−	0.141067i	−0.617168	+	0.786832i	$0.711720\pi$
$692$		0			0
$693$	4.88964	+	8.46911i	0.185742	+	0.321715i
$694$		0			0
$695$	−24.4525	+	14.1177i	−0.927538	+	0.535514i
$696$		0			0
$697$		−	7.74413i		−	0.293330i
$698$		0			0
$699$	33.2990	−	57.6755i	1.25948	−	2.18149i
$700$		0			0
$701$	23.9330			0.903938			0.451969	−	0.892034i	$-0.350722\pi$
$701$	23.9330			0.903938			0.451969	+	0.892034i	$0.350722\pi$
$702$		0			0
$703$	3.76171			0.141876
$704$		0			0
$705$	−53.7664	+	93.1261i	−2.02496	+	3.50733i
$706$		0			0
$707$			11.2958i			0.424823i
$708$		0			0
$709$	−3.36015	+	1.93998i	−0.126193	+	0.0728575i	−0.561768	−	0.827295i	$-0.689879\pi$
$709$	−3.36015	+	1.93998i	−0.126193	+	0.0728575i	0.435575	+	0.900153i	$0.356545\pi$
$710$		0			0
$711$	−5.27108	−	9.12978i	−0.197681	−	0.342394i
$712$		0			0
$713$	−3.99306	−	2.30539i	−0.149541	−	0.0863376i
$714$		0			0
$715$	−43.9575	−	19.7591i	−1.64392	−	0.738950i
$716$		0			0
$717$	54.6568	+	31.5561i	2.04119	+	1.17848i
$718$		0			0
$719$	2.95792	+	5.12327i	0.110312	+	0.191066i	0.915896	−	0.401416i	$-0.131482\pi$
$719$	2.95792	+	5.12327i	0.110312	+	0.191066i	−0.805584	+	0.592481i	$0.798148\pi$
$720$		0			0
$721$	−1.84552	+	1.06551i	−0.0687308	+	0.0396818i
$722$		0			0
$723$			58.6854i			2.18253i
$724$		0			0
$725$	−52.3358	+	90.6482i	−1.94370	+	3.36659i
$726$		0			0
$727$	−21.9599			−0.814447			−0.407223	−	0.913329i	$-0.633503\pi$
$727$	−21.9599			−0.814447			−0.407223	+	0.913329i	$0.633503\pi$
$728$		0			0
$729$	−25.4991			−0.944413
$730$		0			0
$731$	29.0002	−	50.2299i	1.07261	−	1.85782i
$732$		0			0
$733$		−	26.5800i		−	0.981753i	−0.871229	−	0.490877i	$-0.836677\pi$
$733$		−	26.5800i		−	0.981753i	0.871229	−	0.490877i	$-0.163323\pi$
$734$		0			0
$735$	−8.40170	+	4.85073i	−0.309902	+	0.178922i
$736$		0			0
$737$	24.5000	+	42.4353i	0.902470	+	1.56312i
$738$		0			0
$739$	20.8757	+	12.0526i	0.767924	+	0.443361i	0.832133	−	0.554576i	$-0.187119\pi$
$739$	20.8757	+	12.0526i	0.767924	+	0.443361i	−0.0642098	+	0.997936i	$0.520453\pi$
$740$		0			0
$741$	−6.26593	+	0.636011i	−0.230185	+	0.0233645i
$742$		0			0
$743$	−0.650327	−	0.375466i	−0.0238582	−	0.0137745i	0.488023	−	0.872831i	$-0.337718\pi$
$743$	−0.650327	−	0.375466i	−0.0238582	−	0.0137745i	−0.511882	+	0.859056i	$0.671051\pi$
$744$		0			0
$745$	9.39042	+	16.2647i	0.344038	+	0.595892i
$746$		0			0
$747$	8.36967	−	4.83223i	0.306230	−	0.176802i
$748$		0			0
$749$		−	17.5809i		−	0.642392i
$750$		0			0
$751$	−21.2580	+	36.8199i	−0.775716	+	1.34358i	0.158676	+	0.987331i	$0.449278\pi$
$751$	−21.2580	+	36.8199i	−0.775716	+	1.34358i	−0.934391	+	0.356248i	$0.884056\pi$
$752$		0			0
$753$	−7.73551			−0.281898
$754$		0			0
$755$	−35.8527			−1.30481
$756$		0			0
$757$	12.0058	−	20.7947i	0.436360	−	0.755797i	−0.561046	−	0.827785i	$-0.689601\pi$
$757$	12.0058	−	20.7947i	0.436360	−	0.755797i	0.997406	+	0.0719875i	$0.0229342\pi$
$758$		0			0
$759$			8.30595i			0.301487i
$760$		0			0
$761$	−10.6240	+	6.13375i	−0.385118	+	0.222348i	−0.680043	−	0.733172i	$-0.738039\pi$
$761$	−10.6240	+	6.13375i	−0.385118	+	0.222348i	0.294924	+	0.955521i	$0.404706\pi$
$762$		0			0
$763$	2.97447	+	5.15193i	0.107683	+	0.186512i
$764$		0			0
$765$	68.6081	+	39.6109i	2.48053	+	1.43214i
$766$		0			0
$767$	15.8315	+	21.9543i	0.571643	+	0.792724i
$768$		0			0
$769$	−6.22357	−	3.59318i	−0.224428	−	0.129573i	0.383571	−	0.923511i	$-0.374694\pi$
$769$	−6.22357	−	3.59318i	−0.224428	−	0.129573i	−0.607999	+	0.793938i	$0.708027\pi$
$770$		0			0
$771$	25.3212	+	43.8576i	0.911921	+	1.57949i
$772$		0			0
$773$	19.6003	−	11.3162i	0.704972	−	0.407016i	−0.104224	−	0.994554i	$-0.533236\pi$
$773$	19.6003	−	11.3162i	0.704972	−	0.407016i	0.809197	+	0.587538i	$0.199903\pi$
$774$		0			0
$775$			49.3550i			1.77289i
$776$		0			0
$777$	6.37192	−	11.0365i	0.228591	−	0.395932i
$778$		0			0
$779$	−0.816758			−0.0292634
$780$		0			0
$781$	−42.8719			−1.53408
$782$		0			0
$783$	−0.960691	+	1.66397i	−0.0343323	+	0.0594653i
$784$		0			0
$785$		−	14.5382i		−	0.518890i
$786$		0			0
$787$	−10.4705	+	6.04512i	−0.373232	+	0.215485i	−0.674869	−	0.737937i	$-0.735800\pi$
$787$	−10.4705	+	6.04512i	−0.373232	+	0.215485i	0.301638	+	0.953423i	$0.402467\pi$
$788$		0			0
$789$	5.67468	+	9.82883i	0.202024	+	0.349916i
$790$		0			0
$791$	−2.69421	−	1.55550i	−0.0957952	−	0.0553074i
$792$		0			0
$793$	−11.1417	+	8.03439i	−0.395652	+	0.285310i
$794$		0			0
$795$	−26.8629	−	15.5093i	−0.952729	−	0.550058i
$796$		0			0
$797$	1.83514	+	3.17855i	0.0650039	+	0.112590i	0.896696	−	0.442647i	$-0.145961\pi$
$797$	1.83514	+	3.17855i	0.0650039	+	0.112590i	−0.831692	+	0.555238i	$0.812627\pi$
$798$		0			0
$799$	65.3547	−	37.7325i	2.31208	−	1.33488i
$800$		0			0
$801$		−	20.0986i		−	0.710148i
$802$		0			0
$803$	−12.4754	+	21.6081i	−0.440249	+	0.762533i
$804$		0			0
$805$	−4.06264			−0.143189
$806$		0			0
$807$	13.6103			0.479106
$808$		0			0
$809$	4.76432	−	8.25204i	0.167504	−	0.290126i	−0.770037	−	0.637999i	$-0.779762\pi$
$809$	4.76432	−	8.25204i	0.167504	−	0.290126i	0.937542	+	0.347873i	$0.113096\pi$
$810$		0			0
$811$		−	27.9316i		−	0.980812i	−0.871494	−	0.490406i	$-0.836849\pi$
$811$		−	27.9316i		−	0.980812i	0.871494	−	0.490406i	$-0.163151\pi$
$812$		0			0
$813$	3.13086	−	1.80760i	0.109804	−	0.0633953i
$814$		0			0
$815$	22.0554	+	38.2011i	0.772568	+	1.33813i
$816$		0			0
$817$	−5.29764	−	3.05860i	−0.185341	−	0.107007i
$818$		0			0
$819$	−4.31308	+	9.59517i	−0.150711	+	0.335282i
$820$		0			0
$821$	−7.09938	−	4.09883i	−0.247770	−	0.143050i	0.370973	−	0.928644i	$-0.379024\pi$
$821$	−7.09938	−	4.09883i	−0.247770	−	0.143050i	−0.618743	+	0.785594i	$0.712358\pi$
$822$		0			0
$823$	−26.3063	−	45.5639i	−0.916981	−	1.58826i	−0.803974	−	0.594664i	$-0.797285\pi$
$823$	−26.3063	−	45.5639i	−0.916981	−	1.58826i	−0.113007	−	0.993594i	$-0.536048\pi$
$824$		0			0
$825$	76.9975	−	44.4545i	2.68071	−	1.54771i
$826$		0			0
$827$		−	45.2254i		−	1.57264i	−0.617818	−	0.786321i	$-0.711983\pi$
$827$		−	45.2254i		−	1.57264i	0.617818	−	0.786321i	$-0.288017\pi$
$828$		0			0
$829$	10.6849	−	18.5068i	0.371101	−	0.642766i	−0.618634	−	0.785679i	$-0.712314\pi$
$829$	10.6849	−	18.5068i	0.371101	−	0.642766i	0.989735	+	0.142913i	$0.0456470\pi$
$830$		0			0
$831$	−69.1361			−2.39831
$832$		0			0
$833$	6.80835			0.235895
$834$		0			0
$835$	14.0532	−	24.3409i	0.486331	−	0.842350i
$836$		0			0
$837$			0.905976i			0.0313151i
$838$		0			0
$839$	38.6504	−	22.3148i	1.33436	−	0.770392i	0.348394	−	0.937348i	$-0.386727\pi$
$839$	38.6504	−	22.3148i	1.33436	−	0.770392i	0.985964	+	0.166956i	$0.0533938\pi$
$840$		0			0
$841$	−31.5699	−	54.6806i	−1.08862	−	1.88554i
$842$		0			0
$843$	41.2486	+	23.8149i	1.42068	+	0.820228i
$844$		0			0
$845$	−10.4174	−	50.7871i	−0.358371	−	1.74713i
$846$		0			0
$847$	−0.202513	−	0.116921i	−0.00695843	−	0.00401745i
$848$		0			0
$849$	−15.6685	−	27.1386i	−0.537741	−	0.931395i
$850$		0			0
$851$	4.62170	−	2.66834i	0.158430	−	0.0914695i
$852$		0			0
$853$		−	2.36345i		−	0.0809230i	−0.999181	−	0.0404615i	$-0.987117\pi$
$853$		−	2.36345i		−	0.0809230i	0.999181	−	0.0404615i	$-0.0128828\pi$
$854$		0			0
$855$	4.17768	−	7.23596i	0.142874	−	0.247465i
$856$		0			0
$857$	20.0305			0.684227			0.342114	−	0.939659i	$-0.388857\pi$
$857$	20.0305			0.684227			0.342114	+	0.939659i	$0.388857\pi$
$858$		0			0
$859$	3.79217			0.129387			0.0646936	−	0.997905i	$-0.479393\pi$
$859$	3.79217			0.129387			0.0646936	+	0.997905i	$0.479393\pi$
$860$		0			0
$861$	−1.38350	+	2.39628i	−0.0471494	+	0.0816651i
$862$		0			0
$863$			43.7312i			1.48863i	0.667830	+	0.744314i	$0.267223\pi$
$863$			43.7312i			1.48863i	−0.667830	+	0.744314i	$0.732777\pi$
$864$		0			0
$865$	52.1217	−	30.0925i	1.77219	−	1.02318i
$866$		0			0
$867$	−35.7034	−	61.8401i	−1.21255	−	2.10020i
$868$		0			0
$869$	10.4877	+	6.05509i	0.355772	+	0.205405i
$870$		0			0
$871$	−21.6111	+	48.0775i	−0.732263	+	1.62904i
$872$		0			0
$873$	30.2038	+	17.4382i	1.02224	+	0.590193i
$874$		0			0
$875$	11.7737	+	20.3926i	0.398022	+	0.689395i
$876$		0			0
$877$	27.1327	−	15.6650i	0.916205	−	0.528971i	0.0337825	−	0.999429i	$-0.489245\pi$
$877$	27.1327	−	15.6650i	0.916205	−	0.528971i	0.882422	+	0.470458i	$0.155911\pi$
$878$		0			0
$879$		−	30.0599i		−	1.01389i
$880$		0			0
$881$	−0.262517	+	0.454693i	−0.00884443	+	0.0153190i	−0.870414	−	0.492321i	$-0.836149\pi$
$881$	−0.262517	+	0.454693i	−0.00884443	+	0.0153190i	0.861569	+	0.507640i	$0.169482\pi$
$882$		0			0
$883$	26.9929			0.908383			0.454191	−	0.890904i	$-0.349928\pi$
$883$	26.9929			0.908383			0.454191	+	0.890904i	$0.349928\pi$
$884$		0			0
$885$	−72.8294			−2.44813
$886$		0			0
$887$	−2.80959	+	4.86635i	−0.0943367	+	0.163396i	−0.909332	−	0.416072i	$-0.863406\pi$
$887$	−2.80959	+	4.86635i	−0.0943367	+	0.163396i	0.814995	+	0.579468i	$0.196740\pi$
$888$		0			0
$889$			11.7438i			0.393875i
$890$		0			0
$891$	26.8207	−	15.4850i	0.898528	−	0.518765i
$892$		0			0
$893$	−3.97957	−	6.89282i	−0.133171	−	0.230660i
$894$		0			0
$895$	−43.4919	−	25.1101i	−1.45378	−	0.839337i
$896$		0			0
$897$	−7.24727	+	5.22610i	−0.241979	+	0.174494i
$898$		0			0
$899$	−37.6254	−	21.7230i	−1.25488	−	0.724503i
$900$		0			0
$901$	10.8842	+	18.8520i	0.362606	+	0.628052i
$902$		0			0
$903$	−17.9472	+	10.3618i	−0.597246	+	0.344820i
$904$		0			0
$905$		−	43.1113i		−	1.43307i
$906$		0			0
$907$	8.60233	−	14.8997i	0.285636	−	0.494735i	−0.687128	−	0.726537i	$-0.741129\pi$
$907$	8.60233	−	14.8997i	0.285636	−	0.494735i	0.972763	+	0.231802i	$0.0744620\pi$
$908$		0			0
$909$	−32.9580			−1.09315
$910$		0			0
$911$	−50.1900			−1.66287			−0.831434	−	0.555623i	$-0.812480\pi$
$911$	−50.1900			−1.66287			−0.831434	+	0.555623i	$0.812480\pi$
$912$		0			0
$913$	−5.55097	+	9.61456i	−0.183710	+	0.318196i
$914$		0			0
$915$		−	36.9604i		−	1.22187i
$916$		0			0
$917$	6.89745	−	3.98224i	0.227774	−	0.131505i
$918$		0			0
$919$	1.43694	+	2.48885i	0.0474002	+	0.0820996i	0.888752	−	0.458388i	$-0.151573\pi$
$919$	1.43694	+	2.48885i	0.0474002	+	0.0820996i	−0.841352	+	0.540488i	$0.818240\pi$
$920$		0			0
$921$	1.20125	+	0.693541i	0.0395825	+	0.0228529i
$922$		0			0
$923$	−26.9750	−	37.4075i	−0.887893	−	1.23128i
$924$		0			0
$925$	−49.4719	−	28.5626i	−1.62663	−	0.939133i
$926$		0			0
$927$	−3.10886	−	5.38471i	−0.102108	−	0.176857i
$928$		0			0
$929$	50.4339	−	29.1180i	1.65468	−	0.955332i	0.679574	−	0.733607i	$-0.262164\pi$
$929$	50.4339	−	29.1180i	1.65468	−	0.955332i	0.975109	−	0.221725i	$-0.0711689\pi$
$930$		0			0
$931$		−	0.718063i		−	0.0235336i
$932$		0			0
$933$	33.5651	−	58.1365i	1.09887	−	1.90330i
$934$		0			0
$935$	−91.0051			−2.97619
$936$		0			0
$937$	−16.7420			−0.546937			−0.273468	−	0.961881i	$-0.588171\pi$
$937$	−16.7420			−0.546937			−0.273468	+	0.961881i	$0.588171\pi$
$938$		0			0
$939$	3.46774	−	6.00630i	0.113165	−	0.196008i
$940$		0			0
$941$			46.8173i			1.52620i	0.646279	+	0.763101i	$0.276324\pi$
$941$			46.8173i			1.52620i	−0.646279	+	0.763101i	$0.723676\pi$
$942$		0			0
$943$	−1.00348	+	0.579360i	−0.0326778	+	0.0188666i
$944$		0			0
$945$	0.399135	+	0.691322i	0.0129839	+	0.0224887i
$946$		0			0
$947$	0.00591719	+	0.00341629i	0.000192283	+	0.000111015i	0.500096	−	0.865970i	$-0.333298\pi$
$947$	0.00591719	+	0.00341629i	0.000192283	+	0.000111015i	−0.499904	+	0.866081i	$0.666631\pi$
$948$		0			0
$949$	−26.7035	+	2.71048i	−0.866831	+	0.0879861i
$950$		0			0
$951$	−68.9484	−	39.8074i	−2.23581	−	1.29084i
$952$		0			0
$953$	2.79166	+	4.83530i	0.0904308	+	0.156631i	0.907692	−	0.419636i	$-0.137842\pi$
$953$	2.79166	+	4.83530i	0.0904308	+	0.156631i	−0.817262	+	0.576267i	$0.804509\pi$
$954$		0			0
$955$	−45.6021	+	26.3284i	−1.47565	+	0.851967i
$956$		0			0
$957$			78.2645i			2.52993i
$958$		0			0
$959$	−9.75643	+	16.8986i	−0.315052	+	0.545686i
$960$		0			0
$961$	10.5142			0.339167
$962$		0			0
$963$	51.2961			1.65299
$964$		0			0
$965$	11.1219	−	19.2636i	0.358026	−	0.620119i
$966$		0			0
$967$		−	4.02297i		−	0.129370i	−0.997906	−	0.0646851i	$-0.979396\pi$
$967$		−	4.02297i		−	0.129370i	0.997906	−	0.0646851i	$-0.0206043\pi$
$968$		0			0
$969$	−10.2994	+	5.94637i	−0.330865	+	0.191025i
$970$		0			0
$971$	12.0274	+	20.8321i	0.385979	+	0.668535i	0.991904	−	0.126986i	$-0.0405305\pi$
$971$	12.0274	+	20.8321i	0.385979	+	0.668535i	−0.605926	+	0.795521i	$0.707197\pi$
$972$		0			0
$973$	−6.13147	−	3.54000i	−0.196566	−	0.113487i
$974$		0			0
$975$	87.2352	+	39.2126i	2.79376	+	1.25581i
$976$		0			0
$977$	−37.6961	−	21.7639i	−1.20601	−	0.696287i	−0.244121	−	0.969745i	$-0.578499\pi$
$977$	−37.6961	−	21.7639i	−1.20601	−	0.696287i	−0.961884	+	0.273457i	$0.911833\pi$
$978$		0			0
$979$	11.5440	+	19.9948i	0.368948	+	0.639037i
$980$		0			0
$981$	−15.0319	+	8.67866i	−0.479931	+	0.277088i
$982$		0			0
$983$			52.7712i			1.68314i	0.540149	+	0.841570i	$0.318368\pi$
$983$			52.7712i			1.68314i	−0.540149	+	0.841570i	$0.681632\pi$
$984$		0			0
$985$	−6.31642	+	10.9404i	−0.201258	+	0.348589i
$986$		0			0
$987$	−26.9638			−0.858267
$988$		0			0
$989$	−8.67836			−0.275956
$990$		0			0
$991$	0.578566	−	1.00211i	0.0183788	−	0.0318330i	−0.856690	−	0.515832i	$-0.827483\pi$
$991$	0.578566	−	1.00211i	0.0183788	−	0.0318330i	0.875069	+	0.483999i	$0.160816\pi$
$992$		0			0
$993$			5.29112i			0.167909i
$994$		0			0
$995$	−21.4698	+	12.3956i	−0.680637	+	0.392966i
$996$		0			0
$997$	−3.65812	−	6.33605i	−0.115854	−	0.200665i	0.802267	−	0.596965i	$-0.203627\pi$
$997$	−3.65812	−	6.33605i	−0.115854	−	0.200665i	−0.918121	+	0.396301i	$0.870294\pi$
$998$		0			0
$999$	−0.908121	−	0.524304i	−0.0287317	−	0.0165882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.bm.c.225.3	✓	24
4.3	odd	2		1456.2.cc.g.225.10		24
13.6	odd	12		9464.2.a.bm.1.10		12
13.7	odd	12		9464.2.a.bl.1.10		12
13.10	even	6	inner	728.2.bm.c.673.3	yes	24
52.23	odd	6		1456.2.cc.g.673.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.3	✓	24	1.1	even	1	trivial
728.2.bm.c.673.3	yes	24	13.10	even	6	inner
1456.2.cc.g.225.10		24	4.3	odd	2
1456.2.cc.g.673.10		24	52.23	odd	6
9464.2.a.bl.1.10		12	13.7	odd	12
9464.2.a.bm.1.10		12	13.6	odd	12

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21632 + 2.10672i) q^{3} +3.98804i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.45886 - 2.52682i) q^{9} +(2.90265 + 1.67585i) q^{11} +(0.364104 + 3.58712i) q^{13} +(-8.40170 - 4.85073i) q^{15} +(3.40418 + 5.89621i) q^{17} +(0.621861 - 0.359032i) q^{19} -2.43264i q^{21} +(0.509352 - 0.882224i) q^{23} -10.9045 q^{25} -0.200166 q^{27} +(4.79947 - 8.31293i) q^{29} -4.52613i q^{31} +(-7.06109 + 4.07672i) q^{33} +(-1.99402 - 3.45375i) q^{35} +(4.53684 + 2.61935i) q^{37} +(-7.99994 - 3.59601i) q^{39} +(-0.985057 - 0.568723i) q^{41} +(-4.25951 - 7.37769i) q^{43} +(10.0771 - 5.81799i) q^{45} -11.0842i q^{47} +(0.500000 - 0.866025i) q^{49} -16.5622 q^{51} +3.19732 q^{53} +(-6.68334 + 11.5759i) q^{55} +1.74679i q^{57} +(6.50131 - 3.75353i) q^{59} +(1.90489 + 3.29937i) q^{61} +(2.52682 + 1.45886i) q^{63} +(-14.3056 + 1.45206i) q^{65} +(12.6609 + 7.30975i) q^{67} +(1.23907 + 2.14613i) q^{69} +(-11.0774 + 6.39557i) q^{71} +7.44426i q^{73} +(13.2633 - 22.9727i) q^{75} -3.35169 q^{77} +3.61316 q^{79} +(4.62004 - 8.00214i) q^{81} +3.31234i q^{83} +(-23.5143 + 13.5760i) q^{85} +(11.6754 + 20.2223i) q^{87} +(5.96558 + 3.44423i) q^{89} +(-2.10888 - 2.92448i) q^{91} +(9.53530 + 5.50521i) q^{93} +(1.43183 + 2.48001i) q^{95} +(-10.3519 + 5.97665i) q^{97} -9.77929i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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