LMFDB - Embedded newform 560.4.g.f.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(449,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("560.449");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.g (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.1
Root			$1.85474i$ of defining polynomial
Character	$\chi$	$=$	560.449
Dual form			560.4.g.f.449.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.98858i q^{3} +(3.91321 + 10.4731i) q^{5} +7.00000i q^{7} -53.7945 q^{9} -37.4408 q^{11} +3.96370i q^{13} +(94.1387 - 35.1742i) q^{15} -51.6780i q^{17} +25.9323 q^{19} +62.9200 q^{21} +173.454i q^{23} +(-94.3736 + 81.9673i) q^{25} +240.845i q^{27} +245.676 q^{29} +172.074 q^{31} +336.539i q^{33} +(-73.3120 + 27.3925i) q^{35} +250.699i q^{37} +35.6281 q^{39} -48.8649 q^{41} +143.612i q^{43} +(-210.509 - 563.398i) q^{45} -36.6415i q^{47} -49.0000 q^{49} -464.511 q^{51} +645.286i q^{53} +(-146.514 - 392.123i) q^{55} -233.094i q^{57} +395.495 q^{59} +47.5130 q^{61} -376.562i q^{63} +(-41.5125 + 15.5108i) q^{65} +263.189i q^{67} +1559.11 q^{69} +268.177 q^{71} +199.757i q^{73} +(736.769 + 848.284i) q^{75} -262.085i q^{77} +473.640 q^{79} +712.399 q^{81} +72.7028i q^{83} +(541.231 - 202.227i) q^{85} -2208.28i q^{87} +1552.25 q^{89} -27.7459 q^{91} -1546.70i q^{93} +(101.478 + 271.593i) q^{95} -243.338i q^{97} +2014.11 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{5} - 46 q^{9} - 84 q^{11} - 8 q^{15} - 72 q^{19} + 140 q^{21} - 362 q^{25} + 88 q^{29} - 120 q^{31} + 28 q^{35} - 212 q^{39} - 852 q^{41} - 510 q^{45} - 490 q^{49} - 1276 q^{51} + 1136 q^{55}+ \cdots + 5304 q^{99}+O(q^{100}) $ 10 * q + 6 * q^5 - 46 * q^9 - 84 * q^11 - 8 * q^15 - 72 * q^19 + 140 * q^21 - 362 * q^25 + 88 * q^29 - 120 * q^31 + 28 * q^35 - 212 * q^39 - 852 * q^41 - 510 * q^45 - 490 * q^49 - 1276 * q^51 + 1136 * q^55 - 864 * q^59 - 884 * q^61 + 520 * q^65 + 4808 * q^69 - 880 * q^71 - 720 * q^75 + 3580 * q^79 - 302 * q^81 + 1572 * q^85 - 1492 * q^89 - 476 * q^91 + 1628 * q^95 + 5304 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	8.98858i		−	1.72985i	−0.501899	−	0.864926i	$-0.667365\pi$
$3$		−	8.98858i		−	1.72985i	0.501899	−	0.864926i	$-0.332635\pi$
$4$		0			0
$5$	3.91321	+	10.4731i	0.350008	+	0.936747i
$5$	3.91321	+	10.4731i	0.350008	+	0.936747i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$		0			0
$9$	−53.7945			−1.99239
$10$		0			0
$11$	−37.4408			−1.02626			−0.513128	−	0.858312i	$-0.671513\pi$
$11$	−37.4408			−1.02626			−0.513128	+	0.858312i	$0.671513\pi$
$12$		0			0
$13$			3.96370i			0.0845641i	0.999106	+	0.0422821i	$0.0134628\pi$
$13$			3.96370i			0.0845641i	−0.999106	+	0.0422821i	$0.986537\pi$
$14$		0			0
$15$	94.1387	−	35.1742i	1.62043	−	0.605463i
$16$		0			0
$17$		−	51.6780i		−	0.737279i	−0.929572	−	0.368640i	$-0.879824\pi$
$17$		−	51.6780i		−	0.737279i	0.929572	−	0.368640i	$-0.120176\pi$
$18$		0			0
$19$	25.9323			0.313120			0.156560	−	0.987668i	$-0.449960\pi$
$19$	25.9323			0.313120			0.156560	+	0.987668i	$0.449960\pi$
$20$		0			0
$21$	62.9200			0.653823
$22$		0			0
$23$			173.454i			1.57251i	0.617902	+	0.786255i	$0.287983\pi$
$23$			173.454i			1.57251i	−0.617902	+	0.786255i	$0.712017\pi$
$24$		0			0
$25$	−94.3736	+	81.9673i	−0.754988	+	0.655738i
$26$		0			0
$27$			240.845i			1.71669i
$28$		0			0
$29$	245.676			1.57314			0.786568	−	0.617503i	$-0.211856\pi$
$29$	245.676			1.57314			0.786568	+	0.617503i	$0.211856\pi$
$30$		0			0
$31$	172.074			0.996951			0.498475	−	0.866904i	$-0.333893\pi$
$31$	172.074			0.996951			0.498475	+	0.866904i	$0.333893\pi$
$32$		0			0
$33$			336.539i			1.77527i
$34$		0			0
$35$	−73.3120	+	27.3925i	−0.354057	+	0.132291i
$36$		0			0
$37$			250.699i			1.11391i	0.830543	+	0.556954i	$0.188030\pi$
$37$			250.699i			1.11391i	−0.830543	+	0.556954i	$0.811970\pi$
$38$		0			0
$39$	35.6281			0.146283
$40$		0			0
$41$	−48.8649			−0.186132			−0.0930661	−	0.995660i	$-0.529667\pi$
$41$	−48.8649			−0.186132			−0.0930661	+	0.995660i	$0.529667\pi$
$42$		0			0
$43$			143.612i			0.509317i	0.967031	+	0.254658i	$0.0819630\pi$
$43$			143.612i			0.509317i	−0.967031	+	0.254658i	$0.918037\pi$
$44$		0			0
$45$	−210.509	−	563.398i	−0.697353	−	1.86636i
$46$		0			0
$47$		−	36.6415i		−	0.113717i	−0.998382	−	0.0568587i	$-0.981892\pi$
$47$		−	36.6415i		−	0.113717i	0.998382	−	0.0568587i	$-0.0181085\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$		0			0
$51$	−464.511			−1.27538
$52$		0			0
$53$			645.286i			1.67239i	0.548430	+	0.836196i	$0.315226\pi$
$53$			645.286i			1.67239i	−0.548430	+	0.836196i	$0.684774\pi$
$54$		0			0
$55$	−146.514	−	392.123i	−0.359198	−	0.961342i
$56$		0			0
$57$		−	233.094i		−	0.541651i
$58$		0			0
$59$	395.495			0.872696			0.436348	−	0.899778i	$-0.356272\pi$
$59$	395.495			0.872696			0.436348	+	0.899778i	$0.356272\pi$
$60$		0			0
$61$	47.5130			0.0997282			0.0498641	−	0.998756i	$-0.484121\pi$
$61$	47.5130			0.0997282			0.0498641	+	0.998756i	$0.484121\pi$
$62$		0			0
$63$		−	376.562i		−	0.753053i
$64$		0			0
$65$	−41.5125	+	15.5108i	−0.0792152	+	0.0295981i
$66$		0			0
$67$			263.189i			0.479906i	0.970785	+	0.239953i	$0.0771320\pi$
$67$			263.189i			0.479906i	−0.970785	+	0.239953i	$0.922868\pi$
$68$		0			0
$69$	1559.11			2.72021
$70$		0			0
$71$	268.177			0.448264			0.224132	−	0.974559i	$-0.428045\pi$
$71$	268.177			0.448264			0.224132	+	0.974559i	$0.428045\pi$
$72$		0			0
$73$			199.757i			0.320271i	0.987095	+	0.160136i	$0.0511931\pi$
$73$			199.757i			0.320271i	−0.987095	+	0.160136i	$0.948807\pi$
$74$		0			0
$75$	736.769	+	848.284i	1.13433	+	1.30602i
$76$		0			0
$77$		−	262.085i		−	0.387888i
$78$		0			0
$79$	473.640			0.674540			0.337270	−	0.941408i	$-0.390497\pi$
$79$	473.640			0.674540			0.337270	+	0.941408i	$0.390497\pi$
$80$		0			0
$81$	712.399			0.977227
$82$		0			0
$83$			72.7028i			0.0961466i	0.998844	+	0.0480733i	$0.0153081\pi$
$83$			72.7028i			0.0961466i	−0.998844	+	0.0480733i	$0.984692\pi$
$84$		0			0
$85$	541.231	−	202.227i	0.690644	−	0.258054i
$86$		0			0
$87$		−	2208.28i		−	2.72129i
$88$		0			0
$89$	1552.25			1.84874			0.924369	−	0.381500i	$-0.124592\pi$
$89$	1552.25			1.84874			0.924369	+	0.381500i	$0.124592\pi$
$90$		0			0
$91$	−27.7459			−0.0319622
$92$		0			0
$93$		−	1546.70i		−	1.72458i
$94$		0			0
$95$	101.478	+	271.593i	0.109594	+	0.293314i
$96$		0			0
$97$		−	243.338i		−	0.254714i	−0.991857	−	0.127357i	$-0.959351\pi$
$97$		−	243.338i		−	0.254714i	0.991857	−	0.127357i	$-0.0406494\pi$
$98$		0			0
$99$	2014.11			2.04470
$100$		0			0
$101$	−1539.34			−1.51653			−0.758265	−	0.651946i	$-0.773953\pi$
$101$	−1539.34			−1.51653			−0.758265	+	0.651946i	$0.773953\pi$
$102$		0			0
$103$		−	948.628i		−	0.907486i	−0.891133	−	0.453743i	$-0.850088\pi$
$103$		−	948.628i		−	0.907486i	0.891133	−	0.453743i	$-0.149912\pi$
$104$		0			0
$105$	246.219	+	658.971i	0.228843	+	0.612466i
$106$		0			0
$107$			863.983i			0.780602i	0.920687	+	0.390301i	$0.127629\pi$
$107$			863.983i			0.780602i	−0.920687	+	0.390301i	$0.872371\pi$
$108$		0			0
$109$	−886.319			−0.778844			−0.389422	−	0.921060i	$-0.627325\pi$
$109$	−886.319			−0.778844			−0.389422	+	0.921060i	$0.627325\pi$
$110$		0			0
$111$	2253.42			1.92690
$112$		0			0
$113$			765.957i			0.637657i	0.947812	+	0.318828i	$0.103289\pi$
$113$			765.957i			0.637657i	−0.947812	+	0.318828i	$0.896711\pi$
$114$		0			0
$115$	−1816.61	+	678.763i	−1.47304	+	0.550391i
$116$		0			0
$117$		−	213.226i		−	0.168485i
$118$		0			0
$119$	361.746			0.278665
$120$		0			0
$121$	70.8116			0.0532018
$122$		0			0
$123$			439.226i			0.321981i
$124$		0			0
$125$	−1227.76	−	667.633i	−0.878513	−	0.477719i
$126$		0			0
$127$			505.042i			0.352876i	0.984312	+	0.176438i	$0.0564575\pi$
$127$			505.042i			0.352876i	−0.984312	+	0.176438i	$0.943543\pi$
$128$		0			0
$129$	1290.87			0.881043
$130$		0			0
$131$	−672.930			−0.448811			−0.224405	−	0.974496i	$-0.572044\pi$
$131$	−672.930			−0.448811			−0.224405	+	0.974496i	$0.572044\pi$
$132$		0			0
$133$			181.526i			0.118348i
$134$		0			0
$135$	−2522.40	+	942.476i	−1.60810	+	0.600855i
$136$		0			0
$137$		−	1552.28i		−	0.968032i	−0.875059	−	0.484016i	$-0.839178\pi$
$137$		−	1552.28i		−	0.968032i	0.875059	−	0.484016i	$-0.160822\pi$
$138$		0			0
$139$	−1072.02			−0.654154			−0.327077	−	0.944998i	$-0.606064\pi$
$139$	−1072.02			−0.654154			−0.327077	+	0.944998i	$0.606064\pi$
$140$		0			0
$141$	−329.355			−0.196714
$142$		0			0
$143$		−	148.404i		−	0.0867845i
$144$		0			0
$145$	961.384	+	2573.00i	0.550611	+	1.47363i
$146$		0			0
$147$			440.440i			0.247122i
$148$		0			0
$149$	−645.936			−0.355149			−0.177574	−	0.984107i	$-0.556825\pi$
$149$	−645.936			−0.355149			−0.177574	+	0.984107i	$0.556825\pi$
$150$		0			0
$151$	−243.194			−0.131065			−0.0655326	−	0.997850i	$-0.520875\pi$
$151$	−243.194			−0.131065			−0.0655326	+	0.997850i	$0.520875\pi$
$152$		0			0
$153$			2779.99i			1.46895i
$154$		0			0
$155$	673.363	+	1802.16i	0.348941	+	0.933890i
$156$		0			0
$157$			1552.56i			0.789223i	0.918848	+	0.394611i	$0.129121\pi$
$157$			1552.56i			0.789223i	−0.918848	+	0.394611i	$0.870879\pi$
$158$		0			0
$159$	5800.20			2.89299
$160$		0			0
$161$	−1214.18			−0.594353
$162$		0			0
$163$		−	2553.65i		−	1.22710i	−0.789656	−	0.613550i	$-0.789741\pi$
$163$		−	2553.65i		−	1.22710i	0.789656	−	0.613550i	$-0.210259\pi$
$164$		0			0
$165$	−3524.63	+	1316.95i	−1.66298	+	0.621360i
$166$		0			0
$167$			3573.14i			1.65568i	0.560966	+	0.827839i	$0.310430\pi$
$167$			3573.14i			1.65568i	−0.560966	+	0.827839i	$0.689570\pi$
$168$		0			0
$169$	2181.29			0.992849
$170$		0			0
$171$	−1395.01			−0.623856
$172$		0			0
$173$			2234.71i			0.982090i	0.871134	+	0.491045i	$0.163385\pi$
$173$			2234.71i			0.982090i	−0.871134	+	0.491045i	$0.836615\pi$
$174$		0			0
$175$	−573.771	−	660.615i	−0.247846	−	0.285359i
$176$		0			0
$177$		−	3554.94i		−	1.50964i
$178$		0			0
$179$	−1830.53			−0.764361			−0.382180	−	0.924088i	$-0.624827\pi$
$179$	−1830.53			−0.764361			−0.382180	+	0.924088i	$0.624827\pi$
$180$		0			0
$181$	2437.22			1.00087			0.500433	−	0.865775i	$-0.333174\pi$
$181$	2437.22			1.00087			0.500433	+	0.865775i	$0.333174\pi$
$182$		0			0
$183$		−	427.075i		−	0.172515i
$184$		0			0
$185$	−2625.60	+	981.037i	−1.04345	+	0.389877i
$186$		0			0
$187$			1934.86i			0.756638i
$188$		0			0
$189$	−1685.91			−0.648847
$190$		0			0
$191$	−5079.50			−1.92429			−0.962145	−	0.272538i	$-0.912137\pi$
$191$	−5079.50			−1.92429			−0.962145	+	0.272538i	$0.912137\pi$
$192$		0			0
$193$		−	2805.09i		−	1.04619i	−0.852274	−	0.523095i	$-0.824777\pi$
$193$		−	2805.09i		−	1.04619i	0.852274	−	0.523095i	$-0.175223\pi$
$194$		0			0
$195$	139.420	+	373.138i	0.0512004	+	0.137031i
$196$		0			0
$197$			3107.79i			1.12396i	0.827149	+	0.561982i	$0.189961\pi$
$197$			3107.79i			1.12396i	−0.827149	+	0.561982i	$0.810039\pi$
$198$		0			0
$199$	−2145.63			−0.764321			−0.382161	−	0.924096i	$-0.624820\pi$
$199$	−2145.63			−0.764321			−0.382161	+	0.924096i	$0.624820\pi$
$200$		0			0
$201$	2365.70			0.830166
$202$		0			0
$203$			1719.73i			0.594590i
$204$		0			0
$205$	−191.219	−	511.769i	−0.0651478	−	0.174359i
$206$		0			0
$207$		−	9330.89i		−	3.13305i
$208$		0			0
$209$	−970.925			−0.321341
$210$		0			0
$211$	−2837.45			−0.925772			−0.462886	−	0.886418i	$-0.653186\pi$
$211$	−2837.45			−0.925772			−0.462886	+	0.886418i	$0.653186\pi$
$212$		0			0
$213$		−	2410.53i		−	0.775430i
$214$		0			0
$215$	−1504.07	+	561.984i	−0.477101	+	0.178265i
$216$		0			0
$217$			1204.52i			0.376812i
$218$		0			0
$219$	1795.53			0.554022
$220$		0			0
$221$	204.836			0.0623474
$222$		0			0
$223$			4741.40i			1.42380i	0.702280	+	0.711901i	$0.252166\pi$
$223$			4741.40i			1.42380i	−0.702280	+	0.711901i	$0.747834\pi$
$224$		0			0
$225$	5076.78	−	4409.39i	1.50423	−	1.30649i
$226$		0			0
$227$		−	960.790i		−	0.280925i	−0.990086	−	0.140462i	$-0.955141\pi$
$227$		−	960.790i		−	0.280925i	0.990086	−	0.140462i	$-0.0448589\pi$
$228$		0			0
$229$	−744.006			−0.214696			−0.107348	−	0.994222i	$-0.534236\pi$
$229$	−744.006			−0.214696			−0.107348	+	0.994222i	$0.534236\pi$
$230$		0			0
$231$	−2355.78			−0.670990
$232$		0			0
$233$			1550.56i			0.435968i	0.975952	+	0.217984i	$0.0699480\pi$
$233$			1550.56i			0.435968i	−0.975952	+	0.217984i	$0.930052\pi$
$234$		0			0
$235$	383.752	−	143.386i	0.106524	−	0.0398020i
$236$		0			0
$237$		−	4257.35i		−	1.16685i
$238$		0			0
$239$	2775.00			0.751045			0.375523	−	0.926813i	$-0.377463\pi$
$239$	2775.00			0.751045			0.375523	+	0.926813i	$0.377463\pi$
$240$		0			0
$241$	−2550.20			−0.681630			−0.340815	−	0.940130i	$-0.610703\pi$
$241$	−2550.20			−0.681630			−0.340815	+	0.940130i	$0.610703\pi$
$242$		0			0
$243$			99.3558i			0.0262291i
$244$		0			0
$245$	−191.747	−	513.184i	−0.0500012	−	0.133821i
$246$		0			0
$247$			102.788i			0.0264787i
$248$		0			0
$249$	653.494			0.166319
$250$		0			0
$251$	2933.00			0.737568			0.368784	−	0.929515i	$-0.379774\pi$
$251$	2933.00			0.737568			0.368784	+	0.929515i	$0.379774\pi$
$252$		0			0
$253$		−	6494.26i		−	1.61380i
$254$		0			0
$255$	−1817.73	−	4864.90i	−0.446395	−	1.19471i
$256$		0			0
$257$		−	2725.22i		−	0.661459i	−0.943726	−	0.330729i	$-0.892705\pi$
$257$		−	2725.22i		−	0.661459i	0.943726	−	0.330729i	$-0.107295\pi$
$258$		0			0
$259$	−1754.89			−0.421018
$260$		0			0
$261$	−13216.0			−3.13430
$262$		0			0
$263$		−	3027.26i		−	0.709767i	−0.934910	−	0.354884i	$-0.884520\pi$
$263$		−	3027.26i		−	0.709767i	0.934910	−	0.354884i	$-0.115480\pi$
$264$		0			0
$265$	−6758.17	+	2525.14i	−1.56661	+	0.585351i
$266$		0			0
$267$		−	13952.5i		−	3.19804i
$268$		0			0
$269$	1442.46			0.326946			0.163473	−	0.986548i	$-0.447730\pi$
$269$	1442.46			0.326946			0.163473	+	0.986548i	$0.447730\pi$
$270$		0			0
$271$	6464.45			1.44903			0.724516	−	0.689258i	$-0.242063\pi$
$271$	6464.45			1.44903			0.724516	+	0.689258i	$0.242063\pi$
$272$		0			0
$273$			249.396i			0.0552900i
$274$		0			0
$275$	3533.42	−	3068.92i	0.774812	−	0.672955i
$276$		0			0
$277$			876.614i			0.190147i	0.995470	+	0.0950733i	$0.0303086\pi$
$277$			876.614i			0.190147i	−0.995470	+	0.0950733i	$0.969691\pi$
$278$		0			0
$279$	−9256.66			−1.98631
$280$		0			0
$281$	6252.19			1.32731			0.663655	−	0.748038i	$-0.269004\pi$
$281$	6252.19			1.32731			0.663655	+	0.748038i	$0.269004\pi$
$282$		0			0
$283$			2250.07i			0.472625i	0.971677	+	0.236312i	$0.0759389\pi$
$283$			2250.07i			0.472625i	−0.971677	+	0.236312i	$0.924061\pi$
$284$		0			0
$285$	2441.23	−	912.147i	0.507390	−	0.189582i
$286$		0			0
$287$		−	342.054i		−	0.0703513i
$288$		0			0
$289$	2242.39			0.456419
$290$		0			0
$291$	−2187.26			−0.440617
$292$		0			0
$293$			5917.86i			1.17995i	0.807422	+	0.589975i	$0.200862\pi$
$293$			5917.86i			1.17995i	−0.807422	+	0.589975i	$0.799138\pi$
$294$		0			0
$295$	1547.66	+	4142.08i	0.305451	+	0.817495i
$296$		0			0
$297$		−	9017.41i		−	1.76176i
$298$		0			0
$299$	−687.522			−0.132978
$300$		0			0
$301$	−1005.28			−0.192504
$302$		0			0
$303$			13836.4i			2.62337i
$304$		0			0
$305$	185.929	+	497.611i	0.0349057	+	0.0934200i
$306$		0			0
$307$		−	9458.47i		−	1.75838i	−0.476469	−	0.879191i	$-0.658084\pi$
$307$		−	9458.47i		−	1.75838i	0.476469	−	0.879191i	$-0.341916\pi$
$308$		0			0
$309$	−8526.81			−1.56982
$310$		0			0
$311$	7576.78			1.38148			0.690739	−	0.723104i	$-0.257285\pi$
$311$	7576.78			1.38148			0.690739	+	0.723104i	$0.257285\pi$
$312$		0			0
$313$			9172.41i			1.65641i	0.560427	+	0.828204i	$0.310637\pi$
$313$			9172.41i			1.65641i	−0.560427	+	0.828204i	$0.689363\pi$
$314$		0			0
$315$	3943.79	−	1473.57i	0.705419	−	0.263575i
$316$		0			0
$317$		−	3077.94i		−	0.545345i	−0.962107	−	0.272672i	$-0.912092\pi$
$317$		−	3077.94i		−	0.545345i	0.962107	−	0.272672i	$-0.0879075\pi$
$318$		0			0
$319$	−9198.31			−1.61444
$320$		0			0
$321$	7765.98			1.35033
$322$		0			0
$323$		−	1340.13i		−	0.230857i
$324$		0			0
$325$	−324.894	−	374.069i	−0.0554519	−	0.0638449i
$326$		0			0
$327$			7966.75i			1.34728i
$328$		0			0
$329$	256.491			0.0429811
$330$		0			0
$331$	−3234.50			−0.537113			−0.268557	−	0.963264i	$-0.586547\pi$
$331$	−3234.50			−0.537113			−0.268557	+	0.963264i	$0.586547\pi$
$332$		0			0
$333$		−	13486.2i		−	2.21934i
$334$		0			0
$335$	−2756.42	+	1029.92i	−0.449550	+	0.167971i
$336$		0			0
$337$		−	3777.84i		−	0.610658i	−0.952247	−	0.305329i	$-0.901234\pi$
$337$		−	3777.84i		−	0.610658i	0.952247	−	0.305329i	$-0.0987665\pi$
$338$		0			0
$339$	6884.87			1.10305
$340$		0			0
$341$	−6442.60			−1.02313
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$		0			0
$345$	6101.12	+	16328.8i	0.952096	+	2.54815i
$346$		0			0
$347$			8244.08i			1.27540i	0.770283	+	0.637702i	$0.220115\pi$
$347$			8244.08i			1.27540i	−0.770283	+	0.637702i	$0.779885\pi$
$348$		0			0
$349$	−7173.78			−1.10030			−0.550148	−	0.835067i	$-0.685429\pi$
$349$	−7173.78			−1.10030			−0.550148	+	0.835067i	$0.685429\pi$
$350$		0			0
$351$	−954.637			−0.145170
$352$		0			0
$353$			4191.51i			0.631987i	0.948761	+	0.315994i	$0.102338\pi$
$353$			4191.51i			0.631987i	−0.948761	+	0.315994i	$0.897662\pi$
$354$		0			0
$355$	1049.43	+	2808.65i	0.156896	+	0.419910i
$356$		0			0
$357$		−	3251.58i		−	0.482050i
$358$		0			0
$359$	−3136.29			−0.461078			−0.230539	−	0.973063i	$-0.574049\pi$
$359$	−3136.29			−0.461078			−0.230539	+	0.973063i	$0.574049\pi$
$360$		0			0
$361$	−6186.52			−0.901956
$362$		0			0
$363$		−	636.496i		−	0.0920313i
$364$		0			0
$365$	−2092.08	+	781.691i	−0.300013	+	0.112098i
$366$		0			0
$367$		−	1723.30i		−	0.245110i	−0.992462	−	0.122555i	$-0.960891\pi$
$367$		−	1723.30i		−	0.245110i	0.992462	−	0.122555i	$-0.0391088\pi$
$368$		0			0
$369$	2628.67			0.370848
$370$		0			0
$371$	−4517.00			−0.632105
$372$		0			0
$373$			2818.55i			0.391258i	0.980678	+	0.195629i	$0.0626748\pi$
$373$			2818.55i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$374$		0			0
$375$	−6001.07	+	11035.8i	−0.826384	+	1.51970i
$376$		0			0
$377$			973.788i			0.133031i
$378$		0			0
$379$	−10466.1			−1.41849			−0.709246	−	0.704961i	$-0.750964\pi$
$379$	−10466.1			−1.41849			−0.709246	+	0.704961i	$0.750964\pi$
$380$		0			0
$381$	4539.61			0.610423
$382$		0			0
$383$			258.055i			0.0344282i	0.999852	+	0.0172141i	$0.00547969\pi$
$383$			258.055i			0.0344282i	−0.999852	+	0.0172141i	$0.994520\pi$
$384$		0			0
$385$	2744.86	−	1025.60i	0.363353	−	0.135764i
$386$		0			0
$387$		−	7725.54i		−	1.01476i
$388$		0			0
$389$	−4573.87			−0.596156			−0.298078	−	0.954542i	$-0.596346\pi$
$389$	−4573.87			−0.596156			−0.298078	+	0.954542i	$0.596346\pi$
$390$		0			0
$391$	8963.77			1.15938
$392$		0			0
$393$			6048.69i			0.776376i
$394$		0			0
$395$	1853.45	+	4960.50i	0.236094	+	0.631873i
$396$		0			0
$397$		−	3624.55i		−	0.458215i	−0.973401	−	0.229107i	$-0.926419\pi$
$397$		−	3624.55i		−	0.458215i	0.973401	−	0.229107i	$-0.0735807\pi$
$398$		0			0
$399$	1631.66			0.204725
$400$		0			0
$401$	6358.32			0.791819			0.395910	−	0.918289i	$-0.370429\pi$
$401$	6358.32			0.791819			0.395910	+	0.918289i	$0.370429\pi$
$402$		0			0
$403$			682.052i			0.0843063i
$404$		0			0
$405$	2787.77	+	7461.05i	0.342038	+	0.915414i
$406$		0			0
$407$		−	9386.35i		−	1.14316i
$408$		0			0
$409$	6536.39			0.790228			0.395114	−	0.918632i	$-0.370705\pi$
$409$	6536.39			0.790228			0.395114	+	0.918632i	$0.370705\pi$
$410$		0			0
$411$	−13952.8			−1.67455
$412$		0			0
$413$			2768.47i			0.329848i
$414$		0			0
$415$	−761.427	+	284.501i	−0.0900650	+	0.0336521i
$416$		0			0
$417$			9635.91i			1.13159i
$418$		0			0
$419$	6333.56			0.738460			0.369230	−	0.929338i	$-0.379621\pi$
$419$	6333.56			0.738460			0.369230	+	0.929338i	$0.379621\pi$
$420$		0			0
$421$	−8139.62			−0.942282			−0.471141	−	0.882058i	$-0.656158\pi$
$421$	−8139.62			−0.942282			−0.471141	+	0.882058i	$0.656158\pi$
$422$		0			0
$423$			1971.11i			0.226569i
$424$		0			0
$425$	4235.90	+	4877.03i	0.483462	+	0.556637i
$426$		0			0
$427$			332.591i			0.0376937i
$428$		0			0
$429$	−1333.94			−0.150124
$430$		0			0
$431$	14367.6			1.60571			0.802856	−	0.596173i	$-0.203313\pi$
$431$	14367.6			1.60571			0.802856	+	0.596173i	$0.203313\pi$
$432$		0			0
$433$		−	8399.05i		−	0.932176i	−0.884738	−	0.466088i	$-0.845663\pi$
$433$		−	8399.05i		−	0.932176i	0.884738	−	0.466088i	$-0.154337\pi$
$434$		0			0
$435$	23127.6	−	8641.47i	2.54916	−	0.952475i
$436$		0			0
$437$			4498.07i			0.492384i
$438$		0			0
$439$	−17860.8			−1.94180			−0.970901	−	0.239482i	$-0.923022\pi$
$439$	−17860.8			−1.94180			−0.970901	+	0.239482i	$0.923022\pi$
$440$		0			0
$441$	2635.93			0.284627
$442$		0			0
$443$		−	1901.57i		−	0.203942i	−0.994787	−	0.101971i	$-0.967485\pi$
$443$		−	1901.57i		−	0.203942i	0.994787	−	0.101971i	$-0.0325148\pi$
$444$		0			0
$445$	6074.26	+	16256.9i	0.647074	+	1.73180i
$446$		0			0
$447$			5806.05i			0.614355i
$448$		0			0
$449$	5185.68			0.545050			0.272525	−	0.962149i	$-0.412141\pi$
$449$	5185.68			0.545050			0.272525	+	0.962149i	$0.412141\pi$
$450$		0			0
$451$	1829.54			0.191019
$452$		0			0
$453$			2185.97i			0.226723i
$454$		0			0
$455$	−108.576	−	290.587i	−0.0111870	−	0.0299405i
$456$		0			0
$457$			11198.8i			1.14630i	0.819451	+	0.573149i	$0.194278\pi$
$457$			11198.8i			1.14630i	−0.819451	+	0.573149i	$0.805722\pi$
$458$		0			0
$459$	12446.4			1.26568
$460$		0			0
$461$	17270.7			1.74485			0.872427	−	0.488744i	$-0.162545\pi$
$461$	17270.7			1.74485			0.872427	+	0.488744i	$0.162545\pi$
$462$		0			0
$463$		−	385.660i		−	0.0387109i	−0.999813	−	0.0193554i	$-0.993839\pi$
$463$		−	385.660i		−	0.0387109i	0.999813	−	0.0193554i	$-0.00616141\pi$
$464$		0			0
$465$	16198.9	−	6052.58i	1.61549	−	0.603616i
$466$		0			0
$467$			5035.36i			0.498947i	0.968382	+	0.249474i	$0.0802576\pi$
$467$			5035.36i			0.498947i	−0.968382	+	0.249474i	$0.919742\pi$
$468$		0			0
$469$	−1842.33			−0.181387
$470$		0			0
$471$	13955.3			1.36524
$472$		0			0
$473$		−	5376.94i		−	0.522689i
$474$		0			0
$475$	−2447.32	+	2125.60i	−0.236402	+	0.205324i
$476$		0			0
$477$		−	34712.8i		−	3.33206i
$478$		0			0
$479$	−8681.99			−0.828163			−0.414082	−	0.910240i	$-0.635897\pi$
$479$	−8681.99			−0.828163			−0.414082	+	0.910240i	$0.635897\pi$
$480$		0			0
$481$	−993.695			−0.0941967
$482$		0			0
$483$			10913.8i			1.02814i
$484$		0			0
$485$	2548.51	−	952.233i	0.238602	−	0.0891519i
$486$		0			0
$487$			890.476i			0.0828569i	0.999141	+	0.0414284i	$0.0131909\pi$
$487$			890.476i			0.0828569i	−0.999141	+	0.0414284i	$0.986809\pi$
$488$		0			0
$489$	−22953.7			−2.12270
$490$		0			0
$491$	−1562.48			−0.143613			−0.0718063	−	0.997419i	$-0.522876\pi$
$491$	−1562.48			−0.143613			−0.0718063	+	0.997419i	$0.522876\pi$
$492$		0			0
$493$		−	12696.1i		−	1.15984i
$494$		0			0
$495$	7881.63	+	21094.1i	0.715663	+	1.91537i
$496$		0			0
$497$			1877.24i			0.169428i
$498$		0			0
$499$	8234.33			0.738716			0.369358	−	0.929287i	$-0.379578\pi$
$499$	8234.33			0.738716			0.369358	+	0.929287i	$0.379578\pi$
$500$		0			0
$501$	32117.5			2.86408
$502$		0			0
$503$		−	72.5340i		−	0.00642969i	−0.999995	−	0.00321484i	$-0.998977\pi$
$503$		−	72.5340i		−	0.00642969i	0.999995	−	0.00321484i	$-0.00102332\pi$
$504$		0			0
$505$	−6023.75	−	16121.7i	−0.530798	−	1.42061i
$506$		0			0
$507$		−	19606.7i		−	1.71748i
$508$		0			0
$509$	−7793.44			−0.678660			−0.339330	−	0.940667i	$-0.610200\pi$
$509$	−7793.44			−0.678660			−0.339330	+	0.940667i	$0.610200\pi$
$510$		0			0
$511$	−1398.30			−0.121051
$512$		0			0
$513$			6245.65i			0.537529i
$514$		0			0
$515$	9935.12	−	3712.18i	0.850084	−	0.317628i
$516$		0			0
$517$			1371.89i			0.116703i
$518$		0			0
$519$	20086.8			1.69887
$520$		0			0
$521$	4645.42			0.390633			0.195316	−	0.980740i	$-0.437427\pi$
$521$	4645.42			0.390633			0.195316	+	0.980740i	$0.437427\pi$
$522$		0			0
$523$		−	8783.88i		−	0.734402i	−0.930142	−	0.367201i	$-0.880316\pi$
$523$		−	8783.88i		−	0.734402i	0.930142	−	0.367201i	$-0.119684\pi$
$524$		0			0
$525$	−5937.99	+	5157.38i	−0.493629	+	0.428737i
$526$		0			0
$527$		−	8892.46i		−	0.735031i
$528$		0			0
$529$	−17919.4			−1.47279
$530$		0			0
$531$	−21275.5			−1.73875
$532$		0			0
$533$		−	193.686i		−	0.0157401i
$534$		0			0
$535$	−9048.62	+	3380.95i	−0.731226	+	0.273217i
$536$		0			0
$537$			16453.9i			1.32223i
$538$		0			0
$539$	1834.60			0.146608
$540$		0			0
$541$	−7054.13			−0.560593			−0.280296	−	0.959913i	$-0.590433\pi$
$541$	−7054.13			−0.560593			−0.280296	+	0.959913i	$0.590433\pi$
$542$		0			0
$543$		−	21907.1i		−	1.73135i
$544$		0			0
$545$	−3468.35	−	9282.55i	−0.272602	−	0.729579i
$546$		0			0
$547$		−	5776.83i		−	0.451553i	−0.974179	−	0.225776i	$-0.927508\pi$
$547$		−	5776.83i		−	0.451553i	0.974179	−	0.225776i	$-0.0724919\pi$
$548$		0			0
$549$	−2555.94			−0.198697
$550$		0			0
$551$	6370.95			0.492580
$552$		0			0
$553$			3315.48i			0.254952i
$554$		0			0
$555$	8818.12	+	23600.4i	0.674430	+	1.80501i
$556$		0			0
$557$		−	20562.6i		−	1.56421i	−0.623145	−	0.782106i	$-0.714146\pi$
$557$		−	20562.6i		−	1.56421i	0.623145	−	0.782106i	$-0.285854\pi$
$558$		0			0
$559$	−569.235			−0.0430699
$560$		0			0
$561$	17391.7			1.30887
$562$		0			0
$563$			24009.5i			1.79730i	0.438666	+	0.898650i	$0.355451\pi$
$563$			24009.5i			1.79730i	−0.438666	+	0.898650i	$0.644549\pi$
$564$		0			0
$565$	−8021.98	+	2997.35i	−0.597323	+	0.223185i
$566$		0			0
$567$			4986.79i			0.369357i
$568$		0			0
$569$	24157.5			1.77985			0.889925	−	0.456107i	$-0.150757\pi$
$569$	24157.5			1.77985			0.889925	+	0.456107i	$0.150757\pi$
$570$		0			0
$571$	706.993			0.0518157			0.0259078	−	0.999664i	$-0.491752\pi$
$571$	706.993			0.0518157			0.0259078	+	0.999664i	$0.491752\pi$
$572$		0			0
$573$			45657.4i			3.32874i
$574$		0			0
$575$	−14217.6	−	16369.5i	−1.03115	−	1.18723i
$576$		0			0
$577$		−	16057.2i		−	1.15853i	−0.815139	−	0.579265i	$-0.803340\pi$
$577$		−	16057.2i		−	1.15853i	0.815139	−	0.579265i	$-0.196660\pi$
$578$		0			0
$579$	−25213.8			−1.80976
$580$		0			0
$581$	−508.919			−0.0363400
$582$		0			0
$583$		−	24160.0i		−	1.71630i
$584$		0			0
$585$	2233.14	−	834.397i	0.157827	−	0.0589710i
$586$		0			0
$587$			8605.63i			0.605098i	0.953134	+	0.302549i	$0.0978376\pi$
$587$			8605.63i			0.605098i	−0.953134	+	0.302549i	$0.902162\pi$
$588$		0			0
$589$	4462.28			0.312165
$590$		0			0
$591$	27934.6			1.94429
$592$		0			0
$593$		−	20355.6i		−	1.40962i	−0.709397	−	0.704809i	$-0.751033\pi$
$593$		−	20355.6i		−	1.40962i	0.709397	−	0.704809i	$-0.248967\pi$
$594$		0			0
$595$	1415.59	+	3788.62i	0.0975352	+	0.261039i
$596$		0			0
$597$			19286.2i			1.32216i
$598$		0			0
$599$	22635.7			1.54402			0.772010	−	0.635610i	$-0.219251\pi$
$599$	22635.7			1.54402			0.772010	+	0.635610i	$0.219251\pi$
$600$		0			0
$601$	−22553.8			−1.53077			−0.765383	−	0.643575i	$-0.777450\pi$
$601$	−22553.8			−1.53077			−0.765383	+	0.643575i	$0.777450\pi$
$602$		0			0
$603$		−	14158.1i		−	0.956159i
$604$		0			0
$605$	277.101	+	741.620i	0.0186211	+	0.0498366i
$606$		0			0
$607$		−	17534.2i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$607$		−	17534.2i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$608$		0			0
$609$	15458.0			1.02855
$610$		0			0
$611$	145.236			0.00961641
$612$		0			0
$613$		−	10445.5i		−	0.688238i	−0.938926	−	0.344119i	$-0.888178\pi$
$613$		−	10445.5i		−	0.688238i	0.938926	−	0.344119i	$-0.111822\pi$
$614$		0			0
$615$	−4600.08	+	1718.78i	−0.301615	+	0.112696i
$616$		0			0
$617$		−	13218.9i		−	0.862516i	−0.902229	−	0.431258i	$-0.858070\pi$
$617$		−	13218.9i		−	0.862516i	0.902229	−	0.431258i	$-0.141930\pi$
$618$		0			0
$619$	23438.9			1.52195			0.760976	−	0.648780i	$-0.224720\pi$
$619$	23438.9			1.52195			0.760976	+	0.648780i	$0.224720\pi$
$620$		0			0
$621$	−41775.5			−2.69951
$622$		0			0
$623$			10865.7i			0.698757i
$624$		0			0
$625$	2187.74	−	15471.1i	0.140015	−	0.990149i
$626$		0			0
$627$			8727.23i			0.555873i
$628$		0			0
$629$	12955.6			0.821262
$630$		0			0
$631$	874.004			0.0551403			0.0275702	−	0.999620i	$-0.491223\pi$
$631$	874.004			0.0551403			0.0275702	+	0.999620i	$0.491223\pi$
$632$		0			0
$633$			25504.6i			1.60145i
$634$		0			0
$635$	−5289.38	+	1976.34i	−0.330555	+	0.123509i
$636$		0			0
$637$		−	194.222i		−	0.0120806i
$638$		0			0
$639$	−14426.4			−0.893116
$640$		0			0
$641$	23977.0			1.47743			0.738715	−	0.674017i	$-0.235433\pi$
$641$	23977.0			1.47743			0.738715	+	0.674017i	$0.235433\pi$
$642$		0			0
$643$			27698.0i			1.69876i	0.527782	+	0.849380i	$0.323024\pi$
$643$			27698.0i			1.69876i	−0.527782	+	0.849380i	$0.676976\pi$
$644$		0			0
$645$	5051.44	+	13519.4i	0.308372	+	0.825314i
$646$		0			0
$647$		−	10965.1i		−	0.666282i	−0.942877	−	0.333141i	$-0.891891\pi$
$647$		−	10965.1i		−	0.666282i	0.942877	−	0.333141i	$-0.108109\pi$
$648$		0			0
$649$	−14807.6			−0.895610
$650$		0			0
$651$	10826.9			0.651829
$652$		0			0
$653$		−	12336.2i		−	0.739285i	−0.929174	−	0.369642i	$-0.879480\pi$
$653$		−	12336.2i		−	0.739285i	0.929174	−	0.369642i	$-0.120520\pi$
$654$		0			0
$655$	−2633.32	−	7047.70i	−0.157087	−	0.420422i
$656$		0			0
$657$		−	10745.8i		−	0.638105i
$658$		0			0
$659$	−25275.6			−1.49408			−0.747040	−	0.664779i	$-0.768526\pi$
$659$	−25275.6			−1.49408			−0.747040	+	0.664779i	$0.768526\pi$
$660$		0			0
$661$	−4447.92			−0.261731			−0.130865	−	0.991400i	$-0.541776\pi$
$661$	−4447.92			−0.261731			−0.130865	+	0.991400i	$0.541776\pi$
$662$		0			0
$663$		−	1841.19i		−	0.107852i
$664$		0			0
$665$	−1901.15	+	710.349i	−0.110862	+	0.0414228i
$666$		0			0
$667$			42613.6i			2.47377i
$668$		0			0
$669$	42618.5			2.46297
$670$		0			0
$671$	−1778.92			−0.102347
$672$		0			0
$673$			30358.9i			1.73885i	0.494061	+	0.869427i	$0.335512\pi$
$673$			30358.9i			1.73885i	−0.494061	+	0.869427i	$0.664488\pi$
$674$		0			0
$675$	−19741.4	−	22729.4i	−1.12570	−	1.29608i
$676$		0			0
$677$		−	6916.48i		−	0.392647i	−0.980539	−	0.196324i	$-0.937100\pi$
$677$		−	6916.48i		−	0.392647i	0.980539	−	0.196324i	$-0.0629003\pi$
$678$		0			0
$679$	1703.37			0.0962728
$680$		0			0
$681$	−8636.14			−0.485958
$682$		0			0
$683$		−	4532.72i		−	0.253938i	−0.991907	−	0.126969i	$-0.959475\pi$
$683$		−	4532.72i		−	0.253938i	0.991907	−	0.126969i	$-0.0405249\pi$
$684$		0			0
$685$	16257.3	−	6074.40i	0.906800	−	0.338819i
$686$		0			0
$687$			6687.56i			0.371392i
$688$		0			0
$689$	−2557.72			−0.141424
$690$		0			0
$691$	−27235.2			−1.49939			−0.749694	−	0.661785i	$-0.769799\pi$
$691$	−27235.2			−1.49939			−0.749694	+	0.661785i	$0.769799\pi$
$692$		0			0
$693$			14098.8i			0.772825i
$694$		0			0
$695$	−4195.03	−	11227.4i	−0.228959	−	0.612776i
$696$		0			0
$697$			2525.24i			0.137231i
$698$		0			0
$699$	13937.3			0.754160
$700$		0			0
$701$	−17144.3			−0.923726			−0.461863	−	0.886951i	$-0.652819\pi$
$701$	−17144.3			−0.923726			−0.461863	+	0.886951i	$0.652819\pi$
$702$		0			0
$703$			6501.19i			0.348787i
$704$		0			0
$705$	−1288.84	−	3449.39i	−0.0688516	−	0.184271i
$706$		0			0
$707$		−	10775.3i		−	0.573195i
$708$		0			0
$709$	−16724.1			−0.885877			−0.442939	−	0.896552i	$-0.646064\pi$
$709$	−16724.1			−0.885877			−0.442939	+	0.896552i	$0.646064\pi$
$710$		0			0
$711$	−25479.2			−1.34395
$712$		0			0
$713$			29847.0i			1.56771i
$714$		0			0
$715$	1554.26	−	580.737i	0.0812951	−	0.0303753i
$716$		0			0
$717$		−	24943.3i		−	1.29920i
$718$		0			0
$719$	4308.66			0.223485			0.111743	−	0.993737i	$-0.464357\pi$
$719$	4308.66			0.223485			0.111743	+	0.993737i	$0.464357\pi$
$720$		0			0
$721$	6640.39			0.342997
$722$		0			0
$723$			22922.7i			1.17912i
$724$		0			0
$725$	−23185.4	+	20137.4i	−1.18770	+	1.03157i
$726$		0			0
$727$		−	29435.6i		−	1.50166i	−0.660496	−	0.750830i	$-0.729654\pi$
$727$		−	29435.6i		−	1.50166i	0.660496	−	0.750830i	$-0.270346\pi$
$728$		0			0
$729$	20127.8			1.02260
$730$		0			0
$731$	7421.58			0.375509
$732$		0			0
$733$		−	6587.69i		−	0.331954i	−0.986130	−	0.165977i	$-0.946922\pi$
$733$		−	6587.69i		−	0.331954i	0.986130	−	0.165977i	$-0.0530777\pi$
$734$		0			0
$735$	−4612.80	+	1723.54i	−0.231490	+	0.0864947i
$736$		0			0
$737$		−	9854.01i		−	0.492506i
$738$		0			0
$739$	3684.46			0.183404			0.0917018	−	0.995787i	$-0.470769\pi$
$739$	3684.46			0.183404			0.0917018	+	0.995787i	$0.470769\pi$
$740$		0			0
$741$	923.917			0.0458042
$742$		0			0
$743$		−	12271.9i		−	0.605940i	−0.953000	−	0.302970i	$-0.902022\pi$
$743$		−	12271.9i		−	0.605940i	0.953000	−	0.302970i	$-0.0979783\pi$
$744$		0			0
$745$	−2527.68	−	6764.98i	−0.124305	−	0.332684i
$746$		0			0
$747$		−	3911.01i		−	0.191561i
$748$		0			0
$749$	−6047.88			−0.295040
$750$		0			0
$751$	30871.0			1.50000			0.749999	−	0.661439i	$-0.230054\pi$
$751$	30871.0			1.50000			0.749999	+	0.661439i	$0.230054\pi$
$752$		0			0
$753$		−	26363.5i		−	1.27588i
$754$		0			0
$755$	−951.669	−	2547.00i	−0.0458739	−	0.122775i
$756$		0			0
$757$		−	11442.1i		−	0.549368i	−0.961535	−	0.274684i	$-0.911427\pi$
$757$		−	11442.1i		−	0.549368i	0.961535	−	0.274684i	$-0.0885732\pi$
$758$		0			0
$759$	−58374.2			−2.79163
$760$		0			0
$761$	14423.3			0.687048			0.343524	−	0.939144i	$-0.388379\pi$
$761$	14423.3			0.687048			0.343524	+	0.939144i	$0.388379\pi$
$762$		0			0
$763$		−	6204.23i		−	0.294375i
$764$		0			0
$765$	−29115.3	+	10878.7i	−1.37603	+	0.514144i
$766$		0			0
$767$			1567.63i			0.0737988i
$768$		0			0
$769$	−26772.8			−1.25546			−0.627731	−	0.778430i	$-0.716016\pi$
$769$	−26772.8			−1.25546			−0.627731	+	0.778430i	$0.716016\pi$
$770$		0			0
$771$	−24495.9			−1.14423
$772$		0			0
$773$			27669.3i			1.28745i	0.765258	+	0.643724i	$0.222611\pi$
$773$			27669.3i			1.28745i	−0.765258	+	0.643724i	$0.777389\pi$
$774$		0			0
$775$	−16239.3	+	14104.5i	−0.752686	+	0.653739i
$776$		0			0
$777$			15774.0i			0.728299i
$778$		0			0
$779$	−1267.18			−0.0582816
$780$		0			0
$781$	−10040.7			−0.460034
$782$		0			0
$783$			59169.8i			2.70058i
$784$		0			0
$785$	−16260.2	+	6075.51i	−0.739302	+	0.276235i
$786$		0			0
$787$		−	10934.5i		−	0.495263i	−0.968854	−	0.247632i	$-0.920348\pi$
$787$		−	10934.5i		−	0.495263i	0.968854	−	0.247632i	$-0.0796523\pi$
$788$		0			0
$789$	−27210.8			−1.22779
$790$		0			0
$791$	−5361.70			−0.241012
$792$		0			0
$793$			188.328i			0.00843343i
$794$		0			0

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-8.98858i q^{3} +(3.91321 + 10.4731i) q^{5} +7.00000i q^{7} -53.7945 q^{9} -37.4408 q^{11} +3.96370i q^{13} +(94.1387 - 35.1742i) q^{15} -51.6780i q^{17} +25.9323 q^{19} +62.9200 q^{21} +173.454i q^{23} +(-94.3736 + 81.9673i) q^{25} +240.845i q^{27} +245.676 q^{29} +172.074 q^{31} +336.539i q^{33} +(-73.3120 + 27.3925i) q^{35} +250.699i q^{37} +35.6281 q^{39} -48.8649 q^{41} +143.612i q^{43} +(-210.509 - 563.398i) q^{45} -36.6415i q^{47} -49.0000 q^{49} -464.511 q^{51} +645.286i q^{53} +(-146.514 - 392.123i) q^{55} -233.094i q^{57} +395.495 q^{59} +47.5130 q^{61} -376.562i q^{63} +(-41.5125 + 15.5108i) q^{65} +263.189i q^{67} +1559.11 q^{69} +268.177 q^{71} +199.757i q^{73} +(736.769 + 848.284i) q^{75} -262.085i q^{77} +473.640 q^{79} +712.399 q^{81} +72.7028i q^{83} +(541.231 - 202.227i) q^{85} -2208.28i q^{87} +1552.25 q^{89} -27.7459 q^{91} -1546.70i q^{93} +(101.478 + 271.593i) q^{95} -243.338i q^{97} +2014.11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{5} - 46 q^{9} - 84 q^{11} - 8 q^{15} - 72 q^{19} + 140 q^{21} - 362 q^{25} + 88 q^{29} - 120 q^{31} + 28 q^{35} - 212 q^{39} - 852 q^{41} - 510 q^{45} - 490 q^{49} - 1276 q^{51} + 1136 q^{55}+ \cdots + 5304 q^{99}+O(q^{100}) \) 10 * q + 6 * q^5 - 46 * q^9 - 84 * q^11 - 8 * q^15 - 72 * q^19 + 140 * q^21 - 362 * q^25 + 88 * q^29 - 120 * q^31 + 28 * q^35 - 212 * q^39 - 852 * q^41 - 510 * q^45 - 490 * q^49 - 1276 * q^51 + 1136 * q^55 - 864 * q^59 - 884 * q^61 + 520 * q^65 + 4808 * q^69 - 880 * q^71 - 720 * q^75 + 3580 * q^79 - 302 * q^81 + 1572 * q^85 - 1492 * q^89 - 476 * q^91 + 1628 * q^95 + 5304 * q^99

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