LMFDB - Embedded newform 882.4.g.o.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.o.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-9.00000 - 15.5885i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-9.00000 - 15.5885i) q^{5} -8.00000 q^{8} +(18.0000 - 31.1769i) q^{10} +(-36.0000 + 62.3538i) q^{11} +34.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(46.0000 + 79.6743i) q^{19} +72.0000 q^{20} -144.000 q^{22} +(-90.0000 - 155.885i) q^{23} +(-99.5000 + 172.339i) q^{25} +(34.0000 + 58.8897i) q^{26} +114.000 q^{29} +(28.0000 - 48.4974i) q^{31} +(16.0000 - 27.7128i) q^{32} -12.0000 q^{34} +(17.0000 + 29.4449i) q^{37} +(-92.0000 + 159.349i) q^{38} +(72.0000 + 124.708i) q^{40} +6.00000 q^{41} +164.000 q^{43} +(-144.000 - 249.415i) q^{44} +(180.000 - 311.769i) q^{46} +(-84.0000 - 145.492i) q^{47} -398.000 q^{50} +(-68.0000 + 117.779i) q^{52} +(327.000 - 566.381i) q^{53} +1296.00 q^{55} +(114.000 + 197.454i) q^{58} +(246.000 - 426.084i) q^{59} +(-125.000 - 216.506i) q^{61} +112.000 q^{62} +64.0000 q^{64} +(-306.000 - 530.008i) q^{65} +(62.0000 - 107.387i) q^{67} +(-12.0000 - 20.7846i) q^{68} -36.0000 q^{71} +(505.000 - 874.686i) q^{73} +(-34.0000 + 58.8897i) q^{74} -368.000 q^{76} +(-28.0000 - 48.4974i) q^{79} +(-144.000 + 249.415i) q^{80} +(6.00000 + 10.3923i) q^{82} +228.000 q^{83} +108.000 q^{85} +(164.000 + 284.056i) q^{86} +(288.000 - 498.831i) q^{88} +(-195.000 - 337.750i) q^{89} +720.000 q^{92} +(168.000 - 290.985i) q^{94} +(828.000 - 1434.14i) q^{95} +70.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 18 q^{5} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 - 18 * q^5 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} - 18 q^{5} - 16 q^{8} + 36 q^{10} - 72 q^{11} + 68 q^{13} - 16 q^{16} - 6 q^{17} + 92 q^{19} + 144 q^{20} - 288 q^{22} - 180 q^{23} - 199 q^{25} + 68 q^{26} + 228 q^{29} + 56 q^{31} + 32 q^{32} - 24 q^{34} + 34 q^{37} - 184 q^{38} + 144 q^{40} + 12 q^{41} + 328 q^{43} - 288 q^{44} + 360 q^{46} - 168 q^{47} - 796 q^{50} - 136 q^{52} + 654 q^{53} + 2592 q^{55} + 228 q^{58} + 492 q^{59} - 250 q^{61} + 224 q^{62} + 128 q^{64} - 612 q^{65} + 124 q^{67} - 24 q^{68} - 72 q^{71} + 1010 q^{73} - 68 q^{74} - 736 q^{76} - 56 q^{79} - 288 q^{80} + 12 q^{82} + 456 q^{83} + 216 q^{85} + 328 q^{86} + 576 q^{88} - 390 q^{89} + 1440 q^{92} + 336 q^{94} + 1656 q^{95} + 140 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 18 * q^5 - 16 * q^8 + 36 * q^10 - 72 * q^11 + 68 * q^13 - 16 * q^16 - 6 * q^17 + 92 * q^19 + 144 * q^20 - 288 * q^22 - 180 * q^23 - 199 * q^25 + 68 * q^26 + 228 * q^29 + 56 * q^31 + 32 * q^32 - 24 * q^34 + 34 * q^37 - 184 * q^38 + 144 * q^40 + 12 * q^41 + 328 * q^43 - 288 * q^44 + 360 * q^46 - 168 * q^47 - 796 * q^50 - 136 * q^52 + 654 * q^53 + 2592 * q^55 + 228 * q^58 + 492 * q^59 - 250 * q^61 + 224 * q^62 + 128 * q^64 - 612 * q^65 + 124 * q^67 - 24 * q^68 - 72 * q^71 + 1010 * q^73 - 68 * q^74 - 736 * q^76 - 56 * q^79 - 288 * q^80 + 12 * q^82 + 456 * q^83 + 216 * q^85 + 328 * q^86 + 576 * q^88 - 390 * q^89 + 1440 * q^92 + 336 * q^94 + 1656 * q^95 + 140 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	−0.916302	−	0.400489i	$-0.868840\pi$
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	0.111317	−	0.993785i	$-0.464493\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	18.0000	−	31.1769i	0.569210	−	0.985901i
$11$	−36.0000	+	62.3538i	−0.986764	+	1.70913i	−0.352947	+	0.935643i	$0.614820\pi$
$11$	−36.0000	+	62.3538i	−0.986764	+	1.70913i	−0.633817	+	0.773483i	$0.718513\pi$
$12$		0			0
$13$	34.0000			0.725377			0.362689	−	0.931910i	$-0.381859\pi$
$13$	34.0000			0.725377			0.362689	+	0.931910i	$0.381859\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−3.00000	+	5.19615i	−0.0428004	+	0.0741325i	−0.886632	−	0.462476i	$-0.846961\pi$
$17$	−3.00000	+	5.19615i	−0.0428004	+	0.0741325i	0.843832	+	0.536608i	$0.180295\pi$
$18$		0			0
$19$	46.0000	+	79.6743i	0.555428	+	0.962029i	0.997870	+	0.0652319i	$0.0207787\pi$
$19$	46.0000	+	79.6743i	0.555428	+	0.962029i	−0.442443	+	0.896797i	$0.645888\pi$
$20$	72.0000			0.804984
$21$		0			0
$22$	−144.000			−1.39550
$23$	−90.0000	−	155.885i	−0.815926	−	1.41323i	−0.908661	−	0.417534i	$-0.862894\pi$
$23$	−90.0000	−	155.885i	−0.815926	−	1.41323i	0.0927351	−	0.995691i	$-0.470439\pi$
$24$		0			0
$25$	−99.5000	+	172.339i	−0.796000	+	1.37871i
$26$	34.0000	+	58.8897i	0.256460	+	0.444201i
$27$		0			0
$28$		0			0
$29$	114.000			0.729975			0.364987	−	0.931012i	$-0.381073\pi$
$29$	114.000			0.729975			0.364987	+	0.931012i	$0.381073\pi$
$30$		0			0
$31$	28.0000	−	48.4974i	0.162224	−	0.280980i	−0.773442	−	0.633867i	$-0.781467\pi$
$31$	28.0000	−	48.4974i	0.162224	−	0.280980i	0.935666	+	0.352887i	$0.114800\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−12.0000			−0.0605289
$35$		0			0
$36$		0			0
$37$	17.0000	+	29.4449i	0.0755347	+	0.130830i	0.901319	−	0.433157i	$-0.142600\pi$
$37$	17.0000	+	29.4449i	0.0755347	+	0.130830i	−0.825784	+	0.563987i	$0.809267\pi$
$38$	−92.0000	+	159.349i	−0.392747	+	0.680257i
$39$		0			0
$40$	72.0000	+	124.708i	0.284605	+	0.492950i
$41$	6.00000			0.0228547			0.0114273	−	0.999935i	$-0.496362\pi$
$41$	6.00000			0.0228547			0.0114273	+	0.999935i	$0.496362\pi$
$42$		0			0
$43$	164.000			0.581622			0.290811	−	0.956780i	$-0.406075\pi$
$43$	164.000			0.581622			0.290811	+	0.956780i	$0.406075\pi$
$44$	−144.000	−	249.415i	−0.493382	−	0.854563i
$45$		0			0
$46$	180.000	−	311.769i	0.576947	−	0.999301i
$47$	−84.0000	−	145.492i	−0.260695	−	0.451537i	0.705732	−	0.708479i	$-0.250618\pi$
$47$	−84.0000	−	145.492i	−0.260695	−	0.451537i	−0.966427	+	0.256942i	$0.917285\pi$
$48$		0			0
$49$		0			0
$50$	−398.000			−1.12571
$51$		0			0
$52$	−68.0000	+	117.779i	−0.181344	+	0.314098i
$53$	327.000	−	566.381i	0.847489	−	1.46789i	−0.0359535	−	0.999353i	$-0.511447\pi$
$53$	327.000	−	566.381i	0.847489	−	1.46789i	0.883442	−	0.468540i	$-0.155220\pi$
$54$		0			0
$55$	1296.00			3.17732
$56$		0			0
$57$		0			0
$58$	114.000	+	197.454i	0.258085	+	0.447016i
$59$	246.000	−	426.084i	0.542822	−	0.940195i	−0.455919	−	0.890021i	$-0.650689\pi$
$59$	246.000	−	426.084i	0.542822	−	0.940195i	0.998741	−	0.0501732i	$-0.0159773\pi$
$60$		0			0
$61$	−125.000	−	216.506i	−0.262371	−	0.454439i	0.704501	−	0.709703i	$-0.251171\pi$
$61$	−125.000	−	216.506i	−0.262371	−	0.454439i	−0.966871	+	0.255264i	$0.917838\pi$
$62$	112.000			0.229420
$63$		0			0
$64$	64.0000			0.125000
$65$	−306.000	−	530.008i	−0.583917	−	1.01137i
$66$		0			0
$67$	62.0000	−	107.387i	0.113052	−	0.195812i	−0.803947	−	0.594701i	$-0.797271\pi$
$67$	62.0000	−	107.387i	0.113052	−	0.195812i	0.917000	+	0.398888i	$0.130604\pi$
$68$	−12.0000	−	20.7846i	−0.0214002	−	0.0370662i
$69$		0			0
$70$		0			0
$71$	−36.0000			−0.0601748			−0.0300874	−	0.999547i	$-0.509579\pi$
$71$	−36.0000			−0.0601748			−0.0300874	+	0.999547i	$0.509579\pi$
$72$		0			0
$73$	505.000	−	874.686i	0.809668	−	1.40239i	−0.103426	−	0.994637i	$-0.532980\pi$
$73$	505.000	−	874.686i	0.809668	−	1.40239i	0.913094	−	0.407749i	$-0.133686\pi$
$74$	−34.0000	+	58.8897i	−0.0534111	+	0.0925107i
$75$		0			0
$76$	−368.000			−0.555428
$77$		0			0
$78$		0			0
$79$	−28.0000	−	48.4974i	−0.0398765	−	0.0690682i	0.845398	−	0.534136i	$-0.179363\pi$
$79$	−28.0000	−	48.4974i	−0.0398765	−	0.0690682i	−0.885275	+	0.465068i	$0.846030\pi$
$80$	−144.000	+	249.415i	−0.201246	+	0.348569i
$81$		0			0
$82$	6.00000	+	10.3923i	0.00808036	+	0.0139956i
$83$	228.000			0.301521			0.150761	−	0.988570i	$-0.451828\pi$
$83$	228.000			0.301521			0.150761	+	0.988570i	$0.451828\pi$
$84$		0			0
$85$	108.000			0.137815
$86$	164.000	+	284.056i	0.205635	+	0.356170i
$87$		0			0
$88$	288.000	−	498.831i	0.348874	−	0.604267i
$89$	−195.000	−	337.750i	−0.232247	−	0.402263i	0.726222	−	0.687460i	$-0.241274\pi$
$89$	−195.000	−	337.750i	−0.232247	−	0.402263i	−0.958469	+	0.285197i	$0.907941\pi$
$90$		0			0
$91$		0			0
$92$	720.000			0.815926
$93$		0			0
$94$	168.000	−	290.985i	0.184339	−	0.319285i
$95$	828.000	−	1434.14i	0.894221	−	1.54884i
$96$		0			0
$97$	70.0000			0.0732724			0.0366362	−	0.999329i	$-0.488336\pi$
$97$	70.0000			0.0732724			0.0366362	+	0.999329i	$0.488336\pi$
$98$		0			0
$99$		0			0
$100$	−398.000	−	689.356i	−0.398000	−	0.689356i
$101$	675.000	−	1169.13i	0.665000	−	1.15181i	−0.314285	−	0.949329i	$-0.601765\pi$
$101$	675.000	−	1169.13i	0.665000	−	1.15181i	0.979285	−	0.202485i	$-0.0649019\pi$
$102$		0			0
$103$	1000.00	+	1732.05i	0.956630	+	1.65693i	0.730592	+	0.682814i	$0.239244\pi$
$103$	1000.00	+	1732.05i	0.956630	+	1.65693i	0.226038	+	0.974118i	$0.427423\pi$
$104$	−272.000			−0.256460
$105$		0			0
$106$	1308.00			1.19853
$107$	348.000	+	602.754i	0.314415	+	0.544583i	0.979313	−	0.202351i	$-0.0648582\pi$
$107$	348.000	+	602.754i	0.314415	+	0.544583i	−0.664898	+	0.746934i	$0.731525\pi$
$108$		0			0
$109$	557.000	−	964.752i	0.489458	−	0.847766i	−0.510468	−	0.859897i	$-0.670528\pi$
$109$	557.000	−	964.752i	0.489458	−	0.847766i	0.999926	+	0.0121304i	$0.00386131\pi$
$110$	1296.00	+	2244.74i	1.12335	+	1.94570i
$111$		0			0
$112$		0			0
$113$	462.000			0.384613			0.192307	−	0.981335i	$-0.438403\pi$
$113$	462.000			0.384613			0.192307	+	0.981335i	$0.438403\pi$
$114$		0			0
$115$	−1620.00	+	2805.92i	−1.31362	+	2.27525i
$116$	−228.000	+	394.908i	−0.182494	+	0.316088i
$117$		0			0
$118$	984.000			0.767666
$119$		0			0
$120$		0			0
$121$	−1926.50	−	3336.80i	−1.44741	−	2.50698i
$122$	250.000	−	433.013i	0.185524	−	0.321337i
$123$		0			0
$124$	112.000	+	193.990i	0.0811121	+	0.140490i
$125$	1332.00			0.953102
$126$		0			0
$127$	1064.00			0.743423			0.371712	−	0.928348i	$-0.378771\pi$
$127$	1064.00			0.743423			0.371712	+	0.928348i	$0.378771\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	612.000	−	1060.02i	0.412892	−	0.715150i
$131$	−90.0000	−	155.885i	−0.0600255	−	0.103967i	0.834451	−	0.551082i	$-0.185785\pi$
$131$	−90.0000	−	155.885i	−0.0600255	−	0.103967i	−0.894477	+	0.447115i	$0.852452\pi$
$132$		0			0
$133$		0			0
$134$	248.000			0.159880
$135$		0			0
$136$	24.0000	−	41.5692i	0.0151322	−	0.0262098i
$137$	−1359.00	+	2353.86i	−0.847498	+	1.46791i	0.0359363	+	0.999354i	$0.488559\pi$
$137$	−1359.00	+	2353.86i	−0.847498	+	1.46791i	−0.883434	+	0.468555i	$0.844775\pi$
$138$		0			0
$139$	1348.00			0.822560			0.411280	−	0.911509i	$-0.365082\pi$
$139$	1348.00			0.822560			0.411280	+	0.911509i	$0.365082\pi$
$140$		0			0
$141$		0			0
$142$	−36.0000	−	62.3538i	−0.0212750	−	0.0368494i
$143$	−1224.00	+	2120.03i	−0.715776	+	1.23976i
$144$		0			0
$145$	−1026.00	−	1777.08i	−0.587618	−	1.01778i
$146$	2020.00			1.14504
$147$		0			0
$148$	−136.000			−0.0755347
$149$	279.000	+	483.242i	0.153400	+	0.265696i	0.932475	−	0.361234i	$-0.117644\pi$
$149$	279.000	+	483.242i	0.153400	+	0.265696i	−0.779075	+	0.626930i	$0.784311\pi$
$150$		0			0
$151$	−964.000	+	1669.70i	−0.519531	+	0.899854i	0.480211	+	0.877153i	$0.340560\pi$
$151$	−964.000	+	1669.70i	−0.519531	+	0.899854i	−0.999742	+	0.0227014i	$0.992773\pi$
$152$	−368.000	−	637.395i	−0.196373	−	0.340129i
$153$		0			0
$154$		0			0
$155$	−1008.00			−0.522352
$156$		0			0
$157$	−1205.00	+	2087.12i	−0.612544	+	1.06096i	0.378266	+	0.925697i	$0.376521\pi$
$157$	−1205.00	+	2087.12i	−0.612544	+	1.06096i	−0.990810	+	0.135261i	$0.956813\pi$
$158$	56.0000	−	96.9948i	0.0281970	−	0.0488386i
$159$		0			0
$160$	−576.000			−0.284605
$161$		0			0
$162$		0			0
$163$	−370.000	−	640.859i	−0.177795	−	0.307951i	0.763330	−	0.646009i	$-0.223563\pi$
$163$	−370.000	−	640.859i	−0.177795	−	0.307951i	−0.941125	+	0.338058i	$0.890230\pi$
$164$	−12.0000	+	20.7846i	−0.00571367	+	0.00989637i
$165$		0			0
$166$	228.000	+	394.908i	0.106604	+	0.184643i
$167$	3984.00			1.84605			0.923027	−	0.384734i	$-0.125707\pi$
$167$	3984.00			1.84605			0.923027	+	0.384734i	$0.125707\pi$
$168$		0			0
$169$	−1041.00			−0.473828
$170$	108.000	+	187.061i	0.0487248	+	0.0843939i
$171$		0			0
$172$	−328.000	+	568.113i	−0.145406	+	0.251850i
$173$	519.000	+	898.934i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	519.000	+	898.934i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	1152.00			0.493382
$177$		0			0
$178$	390.000	−	675.500i	0.164223	−	0.284443i
$179$	−1284.00	+	2223.95i	−0.536149	+	0.928637i	0.462958	+	0.886380i	$0.346788\pi$
$179$	−1284.00	+	2223.95i	−0.536149	+	0.928637i	−0.999107	+	0.0422569i	$0.986545\pi$
$180$		0			0
$181$	2698.00			1.10796			0.553980	−	0.832530i	$-0.313108\pi$
$181$	2698.00			1.10796			0.553980	+	0.832530i	$0.313108\pi$
$182$		0			0
$183$		0			0
$184$	720.000	+	1247.08i	0.288473	+	0.499651i
$185$	306.000	−	530.008i	0.121608	−	0.210632i
$186$		0			0
$187$	−216.000	−	374.123i	−0.0844678	−	0.146303i
$188$	672.000			0.260695
$189$		0			0
$190$	3312.00			1.26462
$191$	−2058.00	−	3564.56i	−0.779642	−	1.35038i	−0.932148	−	0.362077i	$-0.882068\pi$
$191$	−2058.00	−	3564.56i	−0.779642	−	1.35038i	0.152506	−	0.988303i	$-0.451266\pi$
$192$		0			0
$193$	1655.00	−	2866.54i	0.617251	−	1.06911i	−0.372734	−	0.927938i	$-0.621580\pi$
$193$	1655.00	−	2866.54i	0.617251	−	1.06911i	0.989985	−	0.141172i	$-0.0450872\pi$
$194$	70.0000	+	121.244i	0.0259057	+	0.0448700i
$195$		0			0
$196$		0			0
$197$	−1278.00			−0.462202			−0.231101	−	0.972930i	$-0.574233\pi$
$197$	−1278.00			−0.462202			−0.231101	+	0.972930i	$0.574233\pi$
$198$		0			0
$199$	1468.00	−	2542.65i	0.522933	−	0.905747i	−0.476710	−	0.879060i	$-0.658171\pi$
$199$	1468.00	−	2542.65i	0.522933	−	0.905747i	0.999644	−	0.0266869i	$-0.00849572\pi$
$200$	796.000	−	1378.71i	0.281428	−	0.487448i
$201$		0			0
$202$	2700.00			0.940452
$203$		0			0
$204$		0			0
$205$	−54.0000	−	93.5307i	−0.0183977	−	0.0318657i
$206$	−2000.00	+	3464.10i	−0.676440	+	1.17163i
$207$		0			0
$208$	−272.000	−	471.118i	−0.0906721	−	0.157049i
$209$	−6624.00			−2.19230
$210$		0			0
$211$	−3508.00			−1.14455			−0.572276	−	0.820061i	$-0.693940\pi$
$211$	−3508.00			−1.14455			−0.572276	+	0.820061i	$0.693940\pi$
$212$	1308.00	+	2265.52i	0.423744	+	0.733947i
$213$		0			0
$214$	−696.000	+	1205.51i	−0.222325	+	0.385078i
$215$	−1476.00	−	2556.51i	−0.468197	−	0.810941i
$216$		0			0
$217$		0			0
$218$	2228.00			0.692198
$219$		0			0
$220$	−2592.00	+	4489.48i	−0.794330	+	1.37582i
$221$	−102.000	+	176.669i	−0.0310464	+	0.0537740i
$222$		0			0
$223$	1888.00			0.566950			0.283475	−	0.958980i	$-0.408513\pi$
$223$	1888.00			0.566950			0.283475	+	0.958980i	$0.408513\pi$
$224$		0			0
$225$		0			0
$226$	462.000	+	800.207i	0.135981	+	0.235527i
$227$	−1782.00	+	3086.51i	−0.521037	+	0.902463i	0.478663	+	0.877999i	$0.341121\pi$
$227$	−1782.00	+	3086.51i	−0.521037	+	0.902463i	−0.999701	+	0.0244647i	$0.992212\pi$
$228$		0			0
$229$	667.000	+	1155.28i	0.192474	+	0.333375i	0.946070	−	0.323963i	$-0.105015\pi$
$229$	667.000	+	1155.28i	0.192474	+	0.333375i	−0.753595	+	0.657339i	$0.771682\pi$
$230$	−6480.00			−1.85773
$231$		0			0
$232$	−912.000			−0.258085
$233$	1329.00	+	2301.90i	0.373672	+	0.647220i	0.990127	−	0.140171i	$-0.0447651\pi$
$233$	1329.00	+	2301.90i	0.373672	+	0.647220i	−0.616455	+	0.787390i	$0.711432\pi$
$234$		0			0
$235$	−1512.00	+	2618.86i	−0.419711	+	0.726960i
$236$	984.000	+	1704.34i	0.271411	+	0.470097i
$237$		0			0
$238$		0			0
$239$	588.000			0.159140			0.0795702	−	0.996829i	$-0.474645\pi$
$239$	588.000			0.159140			0.0795702	+	0.996829i	$0.474645\pi$
$240$		0			0
$241$	2845.00	−	4927.68i	0.760426	−	1.31710i	−0.182206	−	0.983260i	$-0.558324\pi$
$241$	2845.00	−	4927.68i	0.760426	−	1.31710i	0.942631	−	0.333835i	$-0.108343\pi$
$242$	3853.00	−	6673.59i	1.02347	−	1.77271i
$243$		0			0
$244$	1000.00			0.262371
$245$		0			0
$246$		0			0
$247$	1564.00	+	2708.93i	0.402894	+	0.697834i
$248$	−224.000	+	387.979i	−0.0573549	+	0.0993416i
$249$		0			0
$250$	1332.00	+	2307.09i	0.336972	+	0.583653i
$251$	180.000			0.0452649			0.0226325	−	0.999744i	$-0.492795\pi$
$251$	180.000			0.0452649			0.0226325	+	0.999744i	$0.492795\pi$
$252$		0			0
$253$	12960.0			3.22051
$254$	1064.00	+	1842.90i	0.262840	+	0.455252i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2655.00	−	4598.59i	−0.644414	−	1.11616i	−0.984437	−	0.175740i	$-0.943768\pi$
$257$	−2655.00	−	4598.59i	−0.644414	−	1.11616i	0.340023	−	0.940417i	$-0.389565\pi$
$258$		0			0
$259$		0			0
$260$	2448.00			0.583917
$261$		0			0
$262$	180.000	−	311.769i	0.0424444	−	0.0735159i
$263$	414.000	−	717.069i	0.0970659	−	0.168123i	−0.813403	−	0.581701i	$-0.802388\pi$
$263$	414.000	−	717.069i	0.0970659	−	0.168123i	0.910469	+	0.413577i	$0.135721\pi$
$264$		0			0
$265$	−11772.0			−2.72886
$266$		0			0
$267$		0			0
$268$	248.000	+	429.549i	0.0565262	+	0.0979062i
$269$	2067.00	−	3580.15i	0.468503	−	0.811470i	−0.530849	−	0.847466i	$-0.678127\pi$
$269$	2067.00	−	3580.15i	0.468503	−	0.811470i	0.999352	+	0.0359958i	$0.0114603\pi$
$270$		0			0
$271$	−1484.00	−	2570.36i	−0.332644	−	0.576157i	0.650385	−	0.759605i	$-0.274607\pi$
$271$	−1484.00	−	2570.36i	−0.332644	−	0.576157i	−0.983029	+	0.183448i	$0.941274\pi$
$272$	96.0000			0.0214002
$273$		0			0
$274$	−5436.00			−1.19854
$275$	−7164.00	−	12408.4i	−1.57093	−	2.72093i
$276$		0			0
$277$	2393.00	−	4144.80i	0.519067	−	0.899050i	−0.480688	−	0.876892i	$-0.659613\pi$
$277$	2393.00	−	4144.80i	0.519067	−	0.899050i	0.999754	−	0.0221579i	$-0.00705366\pi$
$278$	1348.00	+	2334.80i	0.290819	+	0.503713i
$279$		0			0
$280$		0			0
$281$	4398.00			0.933675			0.466838	−	0.884343i	$-0.345393\pi$
$281$	4398.00			0.933675			0.466838	+	0.884343i	$0.345393\pi$
$282$		0			0
$283$	2386.00	−	4132.67i	0.501177	−	0.868063i	−0.498822	−	0.866704i	$-0.666234\pi$
$283$	2386.00	−	4132.67i	0.501177	−	0.868063i	0.999999	−	0.00135915i	$-0.000432632\pi$
$284$	72.0000	−	124.708i	0.0150437	−	0.0260565i
$285$		0			0
$286$	−4896.00			−1.01226
$287$		0			0
$288$		0			0
$289$	2438.50	+	4223.61i	0.496336	+	0.859680i
$290$	2052.00	−	3554.17i	0.415509	−	0.719683i
$291$		0			0
$292$	2020.00	+	3498.74i	0.404834	+	0.701193i
$293$	6522.00			1.30041			0.650204	−	0.759760i	$-0.274684\pi$
$293$	6522.00			1.30041			0.650204	+	0.759760i	$0.274684\pi$
$294$		0			0
$295$	−8856.00			−1.74785
$296$	−136.000	−	235.559i	−0.0267055	−	0.0462553i
$297$		0			0
$298$	−558.000	+	966.484i	−0.108470	+	0.187876i
$299$	−3060.00	−	5300.08i	−0.591854	−	1.02512i
$300$		0			0
$301$		0			0
$302$	−3856.00			−0.734728
$303$		0			0
$304$	736.000	−	1274.79i	0.138857	−	0.240507i
$305$	−2250.00	+	3897.11i	−0.422409	+	0.731633i
$306$		0			0
$307$	6244.00			1.16079			0.580397	−	0.814333i	$-0.302897\pi$
$307$	6244.00			1.16079			0.580397	+	0.814333i	$0.302897\pi$
$308$		0			0
$309$		0			0
$310$	−1008.00	−	1745.91i	−0.184679	−	0.319874i
$311$	264.000	−	457.261i	0.0481353	−	0.0833727i	−0.840954	−	0.541107i	$-0.818005\pi$
$311$	264.000	−	457.261i	0.0481353	−	0.0833727i	0.889089	+	0.457734i	$0.151339\pi$
$312$		0			0
$313$	−2915.00	−	5048.93i	−0.526407	−	0.911765i	−0.999527	−	0.0307660i	$-0.990205\pi$
$313$	−2915.00	−	5048.93i	−0.526407	−	0.911765i	0.473119	−	0.880998i	$-0.343128\pi$
$314$	−4820.00			−0.866269
$315$		0			0
$316$	224.000			0.0398765
$317$	2523.00	+	4369.96i	0.447021	+	0.774264i	0.998191	−	0.0601297i	$-0.0191514\pi$
$317$	2523.00	+	4369.96i	0.447021	+	0.774264i	−0.551169	+	0.834394i	$0.685818\pi$
$318$		0			0
$319$	−4104.00	+	7108.34i	−0.720313	+	1.24762i
$320$	−576.000	−	997.661i	−0.100623	−	0.174284i
$321$		0			0
$322$		0			0
$323$	−552.000			−0.0950901
$324$		0			0
$325$	−3383.00	+	5859.53i	−0.577400	+	1.00009i
$326$	740.000	−	1281.72i	0.125720	−	0.217754i
$327$		0			0
$328$	−48.0000			−0.00808036
$329$		0			0
$330$		0			0
$331$	2510.00	+	4347.45i	0.416804	+	0.721925i	0.995616	−	0.0935355i	$-0.0298169\pi$
$331$	2510.00	+	4347.45i	0.416804	+	0.721925i	−0.578812	+	0.815461i	$0.696484\pi$
$332$	−456.000	+	789.815i	−0.0753803	+	0.130562i
$333$		0			0
$334$	3984.00	+	6900.49i	0.652679	+	1.13047i
$335$	−2232.00			−0.364021
$336$		0			0
$337$	−7486.00			−1.21005			−0.605027	−	0.796205i	$-0.706838\pi$
$337$	−7486.00			−1.21005			−0.605027	+	0.796205i	$0.706838\pi$
$338$	−1041.00	−	1803.06i	−0.167523	−	0.290159i
$339$		0			0
$340$	−216.000	+	374.123i	−0.0344537	+	0.0596755i
$341$	2016.00	+	3491.81i	0.320154	+	0.554523i
$342$		0			0
$343$		0			0
$344$	−1312.00			−0.205635
$345$		0			0
$346$	−1038.00	+	1797.87i	−0.161281	+	0.279347i
$347$	−5016.00	+	8687.97i	−0.776003	+	1.34408i	0.158226	+	0.987403i	$0.449422\pi$
$347$	−5016.00	+	8687.97i	−0.776003	+	1.34408i	−0.934229	+	0.356673i	$0.883911\pi$
$348$		0			0
$349$	−5942.00			−0.911370			−0.455685	−	0.890141i	$-0.650606\pi$
$349$	−5942.00			−0.911370			−0.455685	+	0.890141i	$0.650606\pi$
$350$		0			0
$351$		0			0
$352$	1152.00	+	1995.32i	0.174437	+	0.302134i
$353$	45.0000	−	77.9423i	0.00678501	−	0.0117520i	−0.862613	−	0.505864i	$-0.831174\pi$
$353$	45.0000	−	77.9423i	0.00678501	−	0.0117520i	0.869398	+	0.494113i	$0.164507\pi$
$354$		0			0
$355$	324.000	+	561.184i	0.0484398	+	0.0839002i
$356$	1560.00			0.232247
$357$		0			0
$358$	−5136.00			−0.758229
$359$	5298.00	+	9176.41i	0.778880	+	1.34906i	0.932588	+	0.360943i	$0.117545\pi$
$359$	5298.00	+	9176.41i	0.778880	+	1.34906i	−0.153708	+	0.988116i	$0.549122\pi$
$360$		0			0
$361$	−802.500	+	1389.97i	−0.117000	+	0.202649i
$362$	2698.00	+	4673.07i	0.391723	+	0.678484i
$363$		0			0
$364$		0			0
$365$	−18180.0			−2.60708
$366$		0			0
$367$	2008.00	−	3477.96i	0.285604	−	0.494681i	−0.687151	−	0.726514i	$-0.741139\pi$
$367$	2008.00	−	3477.96i	0.285604	−	0.494681i	0.972756	+	0.231833i	$0.0744724\pi$
$368$	−1440.00	+	2494.15i	−0.203981	+	0.353306i
$369$		0			0
$370$	1224.00			0.171980
$371$		0			0
$372$		0			0
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	0.729554	−	0.683923i	$-0.239728\pi$
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	−0.957072	+	0.289851i	$0.906394\pi$
$374$	432.000	−	748.246i	0.0597278	−	0.103452i
$375$		0			0
$376$	672.000	+	1163.94i	0.0921696	+	0.159642i
$377$	3876.00			0.529507
$378$		0			0
$379$	4628.00			0.627241			0.313621	−	0.949548i	$-0.398458\pi$
$379$	4628.00			0.627241			0.313621	+	0.949548i	$0.398458\pi$
$380$	3312.00	+	5736.55i	0.447111	+	0.774418i
$381$		0			0
$382$	4116.00	−	7129.12i	0.551290	−	0.954863i
$383$	1440.00	+	2494.15i	0.192116	+	0.332755i	0.945951	−	0.324308i	$-0.105132\pi$
$383$	1440.00	+	2494.15i	0.192116	+	0.332755i	−0.753835	+	0.657064i	$0.771798\pi$
$384$		0			0
$385$		0			0
$386$	6620.00			0.872925
$387$		0			0
$388$	−140.000	+	242.487i	−0.0183181	+	0.0317279i
$389$	3987.00	−	6905.69i	0.519663	−	0.900083i	−0.480076	−	0.877227i	$-0.659391\pi$
$389$	3987.00	−	6905.69i	0.519663	−	0.900083i	0.999739	−	0.0228557i	$-0.00727584\pi$
$390$		0			0
$391$	1080.00			0.139688
$392$		0			0
$393$		0			0
$394$	−1278.00	−	2213.56i	−0.163413	−	0.283040i
$395$	−504.000	+	872.954i	−0.0642000	+	0.111198i
$396$		0			0
$397$	−6173.00	−	10691.9i	−0.780388	−	1.35167i	−0.931716	−	0.363188i	$-0.881688\pi$
$397$	−6173.00	−	10691.9i	−0.780388	−	1.35167i	0.151328	−	0.988484i	$-0.451645\pi$
$398$	5872.00			0.739540
$399$		0			0
$400$	3184.00			0.398000
$401$	4869.00	+	8433.36i	0.606350	+	1.05023i	0.991837	+	0.127515i	$0.0407002\pi$
$401$	4869.00	+	8433.36i	0.606350	+	1.05023i	−0.385487	+	0.922713i	$0.625966\pi$
$402$		0			0
$403$	952.000	−	1648.91i	0.117674	−	0.203817i
$404$	2700.00	+	4676.54i	0.332500	+	0.575907i
$405$		0			0
$406$		0			0
$407$	−2448.00			−0.298140
$408$		0			0
$409$	−215.000	+	372.391i	−0.0259928	+	0.0450209i	−0.878729	−	0.477321i	$-0.841608\pi$
$409$	−215.000	+	372.391i	−0.0259928	+	0.0450209i	0.852736	+	0.522342i	$0.174941\pi$
$410$	108.000	−	187.061i	0.0130091	−	0.0225325i
$411$		0			0
$412$	−8000.00			−0.956630
$413$		0			0
$414$		0			0
$415$	−2052.00	−	3554.17i	−0.242720	−	0.420403i
$416$	544.000	−	942.236i	0.0641149	−	0.111050i
$417$		0			0
$418$	−6624.00	−	11473.1i	−0.775097	−	1.34251i
$419$	−1812.00			−0.211270			−0.105635	−	0.994405i	$-0.533687\pi$
$419$	−1812.00			−0.211270			−0.105635	+	0.994405i	$0.533687\pi$
$420$		0			0
$421$	−10690.0			−1.23753			−0.618763	−	0.785577i	$-0.712366\pi$
$421$	−10690.0			−1.23753			−0.618763	+	0.785577i	$0.712366\pi$
$422$	−3508.00	−	6076.03i	−0.404661	−	0.700893i
$423$		0			0
$424$	−2616.00	+	4531.04i	−0.299633	+	0.518979i
$425$	−597.000	−	1034.03i	−0.0681382	−	0.118019i
$426$		0			0
$427$		0			0
$428$	−2784.00			−0.314415
$429$		0			0
$430$	2952.00	−	5113.01i	0.331065	−	0.573422i
$431$	−2058.00	+	3564.56i	−0.230001	+	0.398373i	−0.957808	−	0.287409i	$-0.907206\pi$
$431$	−2058.00	+	3564.56i	−0.230001	+	0.398373i	0.727807	+	0.685782i	$0.240540\pi$
$432$		0			0
$433$	−9938.00			−1.10298			−0.551489	−	0.834182i	$-0.685940\pi$
$433$	−9938.00			−1.10298			−0.551489	+	0.834182i	$0.685940\pi$
$434$		0			0
$435$		0			0
$436$	2228.00	+	3859.01i	0.244729	+	0.423883i
$437$	8280.00	−	14341.4i	0.906376	−	1.56989i
$438$		0			0
$439$	892.000	+	1544.99i	0.0969769	+	0.167969i	0.910432	−	0.413659i	$-0.135749\pi$
$439$	892.000	+	1544.99i	0.0969769	+	0.167969i	−0.813455	+	0.581628i	$0.802416\pi$
$440$	−10368.0			−1.12335
$441$		0			0
$442$	−408.000			−0.0439063
$443$	−5856.00	−	10142.9i	−0.628052	−	1.08782i	−0.987942	−	0.154823i	$-0.950519\pi$
$443$	−5856.00	−	10142.9i	−0.628052	−	1.08782i	0.359890	−	0.932995i	$-0.382814\pi$
$444$		0			0
$445$	−3510.00	+	6079.50i	−0.373910	+	0.647631i
$446$	1888.00	+	3270.11i	0.200447	+	0.347185i
$447$		0			0
$448$		0			0
$449$	−7650.00			−0.804066			−0.402033	−	0.915625i	$-0.631696\pi$
$449$	−7650.00			−0.804066			−0.402033	+	0.915625i	$0.631696\pi$
$450$		0			0
$451$	−216.000	+	374.123i	−0.0225522	+	0.0390616i
$452$	−924.000	+	1600.41i	−0.0961533	+	0.166542i
$453$		0			0
$454$	−7128.00			−0.736858
$455$		0			0
$456$		0			0
$457$	−1837.00	−	3181.78i	−0.188033	−	0.325683i	0.756561	−	0.653923i	$-0.226878\pi$
$457$	−1837.00	−	3181.78i	−0.188033	−	0.325683i	−0.944594	+	0.328240i	$0.893545\pi$
$458$	−1334.00	+	2310.56i	−0.136100	+	0.235732i
$459$		0			0
$460$	−6480.00	−	11223.7i	−0.656808	−	1.13762i
$461$	−3102.00			−0.313394			−0.156697	−	0.987647i	$-0.550085\pi$
$461$	−3102.00			−0.313394			−0.156697	+	0.987647i	$0.550085\pi$
$462$		0			0
$463$	8984.00			0.901775			0.450888	−	0.892581i	$-0.351108\pi$
$463$	8984.00			0.901775			0.450888	+	0.892581i	$0.351108\pi$
$464$	−912.000	−	1579.63i	−0.0912468	−	0.158044i
$465$		0			0
$466$	−2658.00	+	4603.79i	−0.264226	+	0.457653i
$467$	−1806.00	−	3128.08i	−0.178954	−	0.309958i	0.762568	−	0.646908i	$-0.223938\pi$
$467$	−1806.00	−	3128.08i	−0.178954	−	0.309958i	−0.941523	+	0.336950i	$0.890605\pi$
$468$		0			0
$469$		0			0
$470$	−6048.00			−0.593561
$471$		0			0
$472$	−1968.00	+	3408.68i	−0.191916	+	0.332409i
$473$	−5904.00	+	10226.0i	−0.573924	+	0.994066i
$474$		0			0
$475$	−18308.0			−1.76848
$476$		0			0
$477$		0			0
$478$	588.000	+	1018.45i	0.0562646	+	0.0974532i
$479$	4644.00	−	8043.64i	0.442985	−	0.767272i	−0.554924	−	0.831901i	$-0.687253\pi$
$479$	4644.00	−	8043.64i	0.442985	−	0.767272i	0.997909	+	0.0646283i	$0.0205862\pi$
$480$		0			0
$481$	578.000	+	1001.13i	0.0547911	+	0.0949010i
$482$	11380.0			1.07540
$483$		0			0
$484$	15412.0			1.44741
$485$	−630.000	−	1091.19i	−0.0589831	−	0.102162i
$486$		0			0
$487$	2924.00	−	5064.52i	0.272072	−	0.471243i	−0.697320	−	0.716760i	$-0.745624\pi$
$487$	2924.00	−	5064.52i	0.272072	−	0.471243i	0.969392	+	0.245517i	$0.0789578\pi$
$488$	1000.00	+	1732.05i	0.0927620	+	0.160669i
$489$		0			0
$490$		0			0
$491$	5952.00			0.547067			0.273534	−	0.961862i	$-0.411808\pi$
$491$	5952.00			0.547067			0.273534	+	0.961862i	$0.411808\pi$
$492$		0			0
$493$	−342.000	+	592.361i	−0.0312432	+	0.0541148i
$494$	−3128.00	+	5417.85i	−0.284889	+	0.493443i
$495$		0			0
$496$	−896.000			−0.0811121
$497$		0			0
$498$		0			0
$499$	−5374.00	−	9308.04i	−0.482111	−	0.835040i	0.517678	−	0.855575i	$-0.326796\pi$
$499$	−5374.00	−	9308.04i	−0.482111	−	0.835040i	−0.999789	+	0.0205349i	$0.993463\pi$
$500$	−2664.00	+	4614.18i	−0.238275	+	0.412705i
$501$		0			0
$502$	180.000	+	311.769i	0.0160036	+	0.0277190i
$503$	−16488.0			−1.46156			−0.730779	−	0.682614i	$-0.760843\pi$
$503$	−16488.0			−1.46156			−0.730779	+	0.682614i	$0.760843\pi$
$504$		0			0
$505$	−24300.0			−2.14126
$506$	12960.0	+	22447.4i	1.13862	+	1.97215i
$507$		0			0
$508$	−2128.00	+	3685.80i	−0.185856	+	0.321912i
$509$	−7029.00	−	12174.6i	−0.612092	−	1.06017i	−0.990887	−	0.134694i	$-0.956995\pi$
$509$	−7029.00	−	12174.6i	−0.612092	−	1.06017i	0.378795	−	0.925481i	$-0.376339\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	5310.00	−	9197.19i	0.455669	−	0.789243i
$515$	18000.0	−	31176.9i	1.54015	−	2.66761i
$516$		0			0
$517$	12096.0			1.02898
$518$		0			0
$519$		0			0
$520$	2448.00	+	4240.06i	0.206446	+	0.357575i
$521$	7233.00	−	12527.9i	0.608222	−	1.05347i	−0.383312	−	0.923619i	$-0.625217\pi$
$521$	7233.00	−	12527.9i	0.608222	−	1.05347i	0.991533	−	0.129852i	$-0.0414502\pi$
$522$		0			0
$523$	9262.00	+	16042.3i	0.774377	+	1.34126i	0.935144	+	0.354267i	$0.115270\pi$
$523$	9262.00	+	16042.3i	0.774377	+	1.34126i	−0.160768	+	0.986992i	$0.551397\pi$
$524$	720.000			0.0600255
$525$		0			0
$526$	1656.00			0.137272
$527$	168.000	+	290.985i	0.0138865	+	0.0240522i
$528$		0			0
$529$	−10116.5	+	17522.3i	−0.831470	+	1.44015i
$530$	−11772.0	−	20389.7i	−0.964798	−	1.67108i
$531$		0			0
$532$		0			0
$533$	204.000			0.0165783
$534$		0			0
$535$	6264.00	−	10849.6i	0.506199	−	0.876762i
$536$	−496.000	+	859.097i	−0.0399700	+	0.0692301i
$537$		0			0
$538$	8268.00			0.662563
$539$		0			0
$540$		0			0
$541$	−2179.00	−	3774.14i	−0.173165	−	0.299931i	0.766359	−	0.642412i	$-0.222066\pi$
$541$	−2179.00	−	3774.14i	−0.173165	−	0.299931i	−0.939525	+	0.342481i	$0.888733\pi$
$542$	2968.00	−	5140.73i	0.235215	−	0.407404i
$543$		0			0
$544$	96.0000	+	166.277i	0.00756611	+	0.0131049i
$545$	−20052.0			−1.57602
$546$		0			0
$547$	−2140.00			−0.167276			−0.0836378	−	0.996496i	$-0.526654\pi$
$547$	−2140.00			−0.167276			−0.0836378	+	0.996496i	$0.526654\pi$
$548$	−5436.00	−	9415.43i	−0.423749	−	0.733955i
$549$		0			0
$550$	14328.0	−	24816.8i	1.11081	−	1.92399i
$551$	5244.00	+	9082.87i	0.405448	+	0.702257i
$552$		0			0
$553$		0			0
$554$	9572.00			0.734071
$555$		0			0
$556$	−2696.00	+	4669.61i	−0.205640	+	0.356179i
$557$	1011.00	−	1751.10i	0.0769074	−	0.133208i	−0.825007	−	0.565123i	$-0.808829\pi$
$557$	1011.00	−	1751.10i	0.0769074	−	0.133208i	0.901914	+	0.431915i	$0.142162\pi$
$558$		0			0
$559$	5576.00			0.421896
$560$		0			0
$561$		0			0
$562$	4398.00	+	7617.56i	0.330104	+	0.571757i
$563$	−3678.00	+	6370.48i	−0.275327	+	0.476881i	−0.970218	−	0.242235i	$-0.922120\pi$
$563$	−3678.00	+	6370.48i	−0.275327	+	0.476881i	0.694890	+	0.719116i	$0.255453\pi$
$564$		0			0
$565$	−4158.00	−	7201.87i	−0.309608	−	0.536256i
$566$	9544.00			0.708771
$567$		0			0
$568$	288.000			0.0212750
$569$	5601.00	+	9701.22i	0.412665	+	0.714756i	0.995180	−	0.0980635i	$-0.0312648\pi$
$569$	5601.00	+	9701.22i	0.412665	+	0.714756i	−0.582516	+	0.812820i	$0.697932\pi$
$570$		0			0
$571$	5282.00	−	9148.69i	0.387119	−	0.670509i	−0.604942	−	0.796270i	$-0.706804\pi$
$571$	5282.00	−	9148.69i	0.387119	−	0.670509i	0.992061	+	0.125760i	$0.0401370\pi$
$572$	−4896.00	−	8480.12i	−0.357888	−	0.619881i
$573$		0			0
$574$		0			0
$575$	35820.0			2.59791
$576$		0			0
$577$	−9287.00	+	16085.6i	−0.670057	+	1.16057i	0.307831	+	0.951441i	$0.400397\pi$
$577$	−9287.00	+	16085.6i	−0.670057	+	1.16057i	−0.977888	+	0.209132i	$0.932936\pi$
$578$	−4877.00	+	8447.21i	−0.350963	+	0.607885i
$579$		0			0
$580$	8208.00			0.587618
$581$		0			0
$582$		0			0
$583$	23544.0	+	40779.4i	1.67254	+	2.89693i
$584$	−4040.00	+	6997.49i	−0.286261	+	0.495818i
$585$		0			0
$586$	6522.00	+	11296.4i	0.459763	+	0.796334i
$587$	13188.0			0.927303			0.463652	−	0.886018i	$-0.346539\pi$
$587$	13188.0			0.927303			0.463652	+	0.886018i	$0.346539\pi$
$588$		0			0
$589$	5152.00			0.360415
$590$	−8856.00	−	15339.0i	−0.617959	−	1.07034i
$591$		0			0
$592$	272.000	−	471.118i	0.0188837	−	0.0327075i
$593$	11253.0	+	19490.8i	0.779267	+	1.34973i	0.932365	+	0.361519i	$0.117742\pi$
$593$	11253.0	+	19490.8i	0.779267	+	1.34973i	−0.153098	+	0.988211i	$0.548925\pi$
$594$		0			0
$595$		0			0
$596$	−2232.00			−0.153400
$597$		0			0
$598$	6120.00	−	10600.2i	0.418504	−	0.724870i
$599$	5298.00	−	9176.41i	0.361386	−	0.625939i	−0.626803	−	0.779178i	$-0.715637\pi$
$599$	5298.00	−	9176.41i	0.361386	−	0.625939i	0.988189	+	0.153238i	$0.0489702\pi$
$600$		0			0
$601$	−14618.0			−0.992148			−0.496074	−	0.868280i	$-0.665225\pi$
$601$	−14618.0			−0.992148			−0.496074	+	0.868280i	$0.665225\pi$
$602$		0			0
$603$		0			0
$604$	−3856.00	−	6678.79i	−0.259766	−	0.449927i
$605$	−34677.0	+	60062.3i	−2.33028	+	4.03617i
$606$		0			0
$607$	2584.00	+	4475.62i	0.172786	+	0.299275i	0.939393	−	0.342842i	$-0.111390\pi$
$607$	2584.00	+	4475.62i	0.172786	+	0.299275i	−0.766607	+	0.642117i	$0.778056\pi$
$608$	2944.00			0.196373
$609$		0			0
$610$	−9000.00			−0.597376
$611$	−2856.00	−	4946.74i	−0.189102	−	0.327534i
$612$		0			0
$613$	−2863.00	+	4958.86i	−0.188639	+	0.326732i	−0.944797	−	0.327657i	$-0.893741\pi$
$613$	−2863.00	+	4958.86i	−0.188639	+	0.326732i	0.756158	+	0.654389i	$0.227074\pi$
$614$	6244.00	+	10814.9i	0.410403	+	0.710839i
$615$		0			0
$616$		0			0
$617$	7806.00			0.509332			0.254666	−	0.967029i	$-0.418035\pi$
$617$	7806.00			0.509332			0.254666	+	0.967029i	$0.418035\pi$
$618$		0			0
$619$	−9026.00	+	15633.5i	−0.586083	+	1.01513i	0.408656	+	0.912688i	$0.365998\pi$
$619$	−9026.00	+	15633.5i	−0.586083	+	1.01513i	−0.994739	+	0.102438i	$0.967336\pi$
$620$	2016.00	−	3491.81i	0.130588	−	0.226185i
$621$		0			0
$622$	1056.00			0.0680735
$623$		0			0
$624$		0			0
$625$	449.500	+	778.557i	0.0287680	+	0.0498276i
$626$	5830.00	−	10097.9i	0.372226	−	0.644715i
$627$		0			0
$628$	−4820.00	−	8348.48i	−0.306272	−	0.530479i
$629$	−204.000			−0.0129317
$630$		0			0
$631$	−6208.00			−0.391659			−0.195829	−	0.980638i	$-0.562740\pi$
$631$	−6208.00			−0.391659			−0.195829	+	0.980638i	$0.562740\pi$
$632$	224.000	+	387.979i	0.0140985	+	0.0244193i
$633$		0			0
$634$	−5046.00	+	8739.93i	−0.316092	+	0.547487i
$635$	−9576.00	−	16586.1i	−0.598444	−	1.03654i
$636$		0			0
$637$		0			0
$638$	−16416.0			−1.01868
$639$		0			0
$640$	1152.00	−	1995.32i	0.0711512	−	0.123238i
$641$	−10755.0	+	18628.2i	−0.662710	+	1.14785i	0.317191	+	0.948362i	$0.397260\pi$
$641$	−10755.0	+	18628.2i	−0.662710	+	1.14785i	−0.979901	+	0.199485i	$0.936073\pi$
$642$		0			0
$643$	11140.0			0.683233			0.341616	−	0.939839i	$-0.389026\pi$
$643$	11140.0			0.683233			0.341616	+	0.939839i	$0.389026\pi$
$644$		0			0
$645$		0			0
$646$	−552.000	−	956.092i	−0.0336194	−	0.0582306i
$647$	−4656.00	+	8064.43i	−0.282915	+	0.490024i	−0.972102	−	0.234561i	$-0.924635\pi$
$647$	−4656.00	+	8064.43i	−0.282915	+	0.490024i	0.689186	+	0.724584i	$0.257968\pi$
$648$		0			0
$649$	17712.0	+	30678.1i	1.07127	+	1.85550i
$650$	−13532.0			−0.816567
$651$		0			0
$652$	2960.00			0.177795
$653$	2439.00	+	4224.47i	0.146165	+	0.253164i	0.929807	−	0.368048i	$-0.119974\pi$
$653$	2439.00	+	4224.47i	0.146165	+	0.253164i	−0.783642	+	0.621212i	$0.786640\pi$
$654$		0			0
$655$	−1620.00	+	2805.92i	−0.0966391	+	0.167384i
$656$	−48.0000	−	83.1384i	−0.00285684	−	0.00494819i
$657$		0			0
$658$		0			0
$659$	9744.00			0.575982			0.287991	−	0.957633i	$-0.407013\pi$
$659$	9744.00			0.575982			0.287991	+	0.957633i	$0.407013\pi$
$660$		0			0
$661$	1495.00	−	2589.42i	0.0879709	−	0.152370i	−0.818682	−	0.574247i	$-0.805295\pi$
$661$	1495.00	−	2589.42i	0.0879709	−	0.152370i	0.906653	+	0.421876i	$0.138628\pi$
$662$	−5020.00	+	8694.90i	−0.294725	+	0.510478i
$663$		0			0
$664$	−1824.00			−0.106604
$665$		0			0
$666$		0			0
$667$	−10260.0	−	17770.8i	−0.595605	−	1.03162i
$668$	−7968.00	+	13801.0i	−0.461514	+	0.799365i
$669$		0			0
$670$	−2232.00	−	3865.94i	−0.128701	−	0.222917i
$671$	18000.0			1.03559
$672$		0			0
$673$	33266.0			1.90536			0.952682	−	0.303969i	$-0.0983118\pi$
$673$	33266.0			1.90536			0.952682	+	0.303969i	$0.0983118\pi$
$674$	−7486.00	−	12966.1i	−0.427819	−	0.741004i
$675$		0			0
$676$	2082.00	−	3606.13i	0.118457	−	0.205174i
$677$	−2685.00	−	4650.56i	−0.152427	−	0.264011i	0.779692	−	0.626163i	$-0.215375\pi$
$677$	−2685.00	−	4650.56i	−0.152427	−	0.264011i	−0.932119	+	0.362152i	$0.882042\pi$
$678$		0			0
$679$		0			0
$680$	−864.000			−0.0487248
$681$		0			0
$682$	−4032.00	+	6983.63i	−0.226383	+	0.392107i
$683$	192.000	−	332.554i	0.0107565	−	0.0186308i	−0.860597	−	0.509286i	$-0.829909\pi$
$683$	192.000	−	332.554i	0.0107565	−	0.0186308i	0.871354	+	0.490656i	$0.163243\pi$
$684$		0			0
$685$	48924.0			2.72889
$686$		0			0
$687$		0			0
$688$	−1312.00	−	2272.45i	−0.0727028	−	0.125925i
$689$	11118.0	−	19256.9i	0.614749	−	1.06478i
$690$		0			0
$691$	−7262.00	−	12578.2i	−0.399797	−	0.692468i	0.593904	−	0.804536i	$-0.297586\pi$
$691$	−7262.00	−	12578.2i	−0.399797	−	0.692468i	−0.993701	+	0.112068i	$0.964253\pi$
$692$	−4152.00			−0.228086
$693$		0			0
$694$	−20064.0			−1.09743
$695$	−12132.0	−	21013.2i	−0.662148	−	1.14687i
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.000978190	+	0.00169428i
$698$	−5942.00	−	10291.8i	−0.322218	−	0.558098i
$699$		0			0
$700$		0			0
$701$	−24750.0			−1.33352			−0.666758	−	0.745274i	$-0.732318\pi$
$701$	−24750.0			−1.33352			−0.666758	+	0.745274i	$0.732318\pi$
$702$		0			0
$703$	−1564.00	+	2708.93i	−0.0839081	+	0.145333i
$704$	−2304.00	+	3990.65i	−0.123346	+	0.213641i
$705$		0			0
$706$	180.000			0.00959545
$707$		0			0
$708$		0			0
$709$	521.000	+	902.398i	0.0275974	+	0.0478001i	0.879494	−	0.475909i	$-0.157881\pi$
$709$	521.000	+	902.398i	0.0275974	+	0.0478001i	−0.851897	+	0.523710i	$0.824548\pi$
$710$	−648.000	+	1122.37i	−0.0342521	+	0.0593264i
$711$		0			0
$712$	1560.00	+	2702.00i	0.0821116	+	0.142221i
$713$	−10080.0			−0.529452
$714$		0			0
$715$	44064.0			2.30476
$716$	−5136.00	−	8895.81i	−0.268074	−	0.464319i
$717$		0			0
$718$	−10596.0	+	18352.8i	−0.550751	+	0.953929i
$719$	18480.0	+	32008.3i	0.958536	+	1.66023i	0.726059	+	0.687632i	$0.241350\pi$
$719$	18480.0	+	32008.3i	0.958536	+	1.66023i	0.232477	+	0.972602i	$0.425317\pi$
$720$		0			0
$721$		0			0
$722$	−3210.00			−0.165462
$723$		0			0
$724$	−5396.00	+	9346.15i	−0.276990	+	0.479761i
$725$	−11343.0	+	19646.7i	−0.581060	+	1.00643i
$726$		0			0
$727$	16288.0			0.830933			0.415467	−	0.909608i	$-0.363618\pi$
$727$	16288.0			0.830933			0.415467	+	0.909608i	$0.363618\pi$
$728$		0			0
$729$		0			0
$730$	−18180.0	−	31488.7i	−0.921742	−	1.59650i
$731$	−492.000	+	852.169i	−0.0248937	+	0.0431171i
$732$		0			0
$733$	−3905.00	−	6763.66i	−0.196773	−	0.340820i	0.750707	−	0.660635i	$-0.229713\pi$
$733$	−3905.00	−	6763.66i	−0.196773	−	0.340820i	−0.947480	+	0.319814i	$0.896379\pi$
$734$	8032.00			0.403905
$735$		0			0
$736$	−5760.00			−0.288473
$737$	4464.00	+	7731.87i	0.223112	+	0.386441i
$738$		0			0
$739$	18350.0	−	31783.1i	0.913418	−	1.58209i	0.104216	−	0.994555i	$-0.466767\pi$
$739$	18350.0	−	31783.1i	0.913418	−	1.58209i	0.809202	−	0.587531i	$-0.199900\pi$
$740$	1224.00	+	2120.03i	0.0608042	+	0.105316i
$741$		0			0
$742$		0			0
$743$	−29508.0			−1.45699			−0.728495	−	0.685051i	$-0.759780\pi$
$743$	−29508.0			−1.45699			−0.728495	+	0.685051i	$0.759780\pi$
$744$		0			0
$745$	5022.00	−	8698.36i	0.246969	−	0.427763i
$746$	3278.00	−	5677.66i	0.160880	−	0.278651i
$747$		0			0
$748$	1728.00			0.0844678
$749$		0			0
$750$		0			0
$751$	7568.00	+	13108.2i	0.367723	+	0.636916i	0.989209	−	0.146510i	$-0.0468040\pi$
$751$	7568.00	+	13108.2i	0.367723	+	0.636916i	−0.621486	+	0.783425i	$0.713471\pi$
$752$	−1344.00	+	2327.88i	−0.0651737	+	0.112884i
$753$		0			0
$754$	3876.00	+	6713.43i	0.187209	+	0.324256i
$755$	34704.0			1.67286
$756$		0			0
$757$	3422.00			0.164299			0.0821497	−	0.996620i	$-0.473821\pi$
$757$	3422.00			0.164299			0.0821497	+	0.996620i	$0.473821\pi$
$758$	4628.00	+	8015.93i	0.221763	+	0.384105i
$759$		0			0
$760$	−6624.00	+	11473.1i	−0.316155	+	0.547596i
$761$	−15723.0	−	27233.0i	−0.748960	−	1.29724i	−0.948322	−	0.317310i	$-0.897220\pi$
$761$	−15723.0	−	27233.0i	−0.748960	−	1.29724i	0.199362	−	0.979926i	$-0.436113\pi$
$762$		0			0
$763$		0			0
$764$	16464.0			0.779642
$765$		0			0
$766$	−2880.00	+	4988.31i	−0.135847	+	0.235294i
$767$	8364.00	−	14486.9i	0.393750	−	0.681996i
$768$		0			0
$769$	18718.0			0.877748			0.438874	−	0.898549i	$-0.355377\pi$
$769$	18718.0			0.877748			0.438874	+	0.898549i	$0.355377\pi$
$770$		0			0
$771$		0			0
$772$	6620.00	+	11466.2i	0.308626	+	0.534555i
$773$	843.000	−	1460.12i	0.0392246	−	0.0679390i	−0.845747	−	0.533585i	$-0.820845\pi$
$773$	843.000	−	1460.12i	0.0392246	−	0.0679390i	0.884971	+	0.465646i	$0.154178\pi$
$774$		0			0
$775$	5572.00	+	9650.99i	0.258261	+	0.447321i
$776$	−560.000			−0.0259057
$777$		0			0
$778$	15948.0			0.734915
$779$	276.000	+	478.046i	0.0126941	+	0.0219869i
$780$		0			0
$781$	1296.00	−	2244.74i	0.0593784	−	0.102846i
$782$	1080.00	+	1870.61i	0.0493871	+	0.0855410i
$783$		0			0
$784$		0			0
$785$	43380.0			1.97235
$786$		0			0
$787$	2746.00	−	4756.21i	0.124377	−	0.215426i	−0.797113	−	0.603831i	$-0.793640\pi$
$787$	2746.00	−	4756.21i	0.124377	−	0.215426i	0.921489	+	0.388404i	$0.126974\pi$
$788$	2556.00	−	4427.12i	0.115550	−	0.200139i
$789$		0			0
$790$	−2016.00			−0.0907925
$791$		0			0
$792$		0			0
$793$	−4250.00	−	7361.22i	−0.190318	−	0.329640i
$794$	12346.0	−	21383.9i	0.551818	−	0.955776i
$795$		0			0
$796$	5872.00	+	10170.6i	0.261467	+	0.452874i
$797$	−17310.0			−0.769325			−0.384662	−	0.923057i	$-0.625682\pi$
$797$	−17310.0			−0.769325			−0.384662	+	0.923057i	$0.625682\pi$
$798$		0			0
$799$	1008.00			0.0446314
$800$	3184.00	+	5514.85i	0.140714	+	0.243724i
$801$		0			0
$802$	−9738.00	+	16866.7i	−0.428754	+	0.742624i
$803$	36360.0	+	62977.4i	1.59790	+	2.76765i
$804$		0			0
$805$		0			0
$806$	3808.00			0.166416
$807$		0			0
$808$	−5400.00	+	9353.07i	−0.235113	+	0.407228i
$809$	17877.0	−	30963.9i	0.776912	−	1.34565i	−0.156801	−	0.987630i	$-0.550118\pi$
$809$	17877.0	−	30963.9i	0.776912	−	1.34565i	0.933714	−	0.358021i	$-0.116548\pi$
$810$		0			0
$811$	−33644.0			−1.45672			−0.728360	−	0.685194i	$-0.759717\pi$
$811$	−33644.0			−1.45672			−0.728360	+	0.685194i	$0.759717\pi$
$812$		0			0
$813$		0			0
$814$	−2448.00	−	4240.06i	−0.105408	−	0.182573i
$815$	−6660.00	+	11535.5i	−0.286245	+	0.495791i
$816$		0			0
$817$	7544.00	+	13066.6i	0.323049	+	0.559538i
$818$	−860.000			−0.0367594
$819$		0			0
$820$	432.000			0.0183977
$821$	14367.0	+	24884.4i	0.610733	+	1.05782i	0.991117	+	0.132992i	$0.0424584\pi$
$821$	14367.0	+	24884.4i	0.610733	+	1.05782i	−0.380384	+	0.924829i	$0.624208\pi$
$822$		0			0
$823$	14336.0	−	24830.7i	0.607195	−	1.05169i	−0.384505	−	0.923123i	$-0.625628\pi$
$823$	14336.0	−	24830.7i	0.607195	−	1.05169i	0.991700	−	0.128570i	$-0.0410387\pi$
$824$	−8000.00	−	13856.4i	−0.338220	−	0.585814i
$825$		0			0
$826$		0			0
$827$	15912.0			0.669062			0.334531	−	0.942385i	$-0.391422\pi$
$827$	15912.0			0.669062			0.334531	+	0.942385i	$0.391422\pi$
$828$		0			0
$829$	8767.00	−	15184.9i	0.367299	−	0.636180i	−0.621844	−	0.783141i	$-0.713616\pi$
$829$	8767.00	−	15184.9i	0.367299	−	0.636180i	0.989142	+	0.146962i	$0.0469494\pi$
$830$	4104.00	−	7108.34i	0.171629	−	0.297270i
$831$		0			0
$832$	2176.00			0.0906721
$833$		0			0
$834$		0			0
$835$	−35856.0	−	62104.4i	−1.48605	−	2.57391i
$836$	13248.0	−	22946.2i	0.548076	−	0.949296i
$837$		0			0
$838$	−1812.00	−	3138.48i	−0.0746951	−	0.129376i
$839$	40656.0			1.67295			0.836473	−	0.548009i	$-0.184614\pi$
$839$	40656.0			1.67295			0.836473	+	0.548009i	$0.184614\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$	−10690.0	−	18515.6i	−0.437532	−	0.757827i
$843$		0			0
$844$	7016.00	−	12152.1i	0.286138	−	0.495606i
$845$	9369.00	+	16227.6i	0.381424	+	0.660646i
$846$		0			0
$847$		0			0
$848$	−10464.0			−0.423744
$849$		0			0
$850$	1194.00	−	2068.07i	0.0481810	−	0.0834520i
$851$	3060.00	−	5300.08i	0.123261	−	0.213495i
$852$		0			0
$853$	−23870.0			−0.958140			−0.479070	−	0.877777i	$-0.659026\pi$
$853$	−23870.0			−0.958140			−0.479070	+	0.877777i	$0.659026\pi$
$854$		0			0
$855$		0			0
$856$	−2784.00	−	4822.03i	−0.111163	−	0.192539i
$857$	14805.0	−	25643.0i	0.590116	−	1.02211i	−0.404101	−	0.914715i	$-0.632415\pi$
$857$	14805.0	−	25643.0i	0.590116	−	1.02211i	0.994216	−	0.107396i	$-0.0342512\pi$
$858$		0			0
$859$	−22742.0	−	39390.3i	−0.903314	−	1.56459i	−0.823164	−	0.567804i	$-0.807793\pi$
$859$	−22742.0	−	39390.3i	−0.903314	−	1.56459i	−0.0801503	−	0.996783i	$-0.525540\pi$
$860$	11808.0			0.468197
$861$		0			0
$862$	−8232.00			−0.325270
$863$	23082.0	+	39979.2i	0.910452	+	1.57695i	0.813426	+	0.581668i	$0.197600\pi$
$863$	23082.0	+	39979.2i	0.910452	+	1.57695i	0.0970261	+	0.995282i	$0.469067\pi$
$864$		0			0
$865$	9342.00	−	16180.8i	0.367211	−	0.636028i
$866$	−9938.00	−	17213.1i	−0.389962	−	0.675434i
$867$		0			0
$868$		0			0
$869$	4032.00			0.157395
$870$		0			0
$871$	2108.00	−	3651.16i	0.0820056	−	0.142038i
$872$	−4456.00	+	7718.02i	−0.173050	+	0.299731i
$873$		0			0
$874$	33120.0			1.28181
$875$		0			0
$876$		0			0
$877$	1493.00	+	2585.95i	0.0574858	+	0.0995683i	0.893336	−	0.449389i	$-0.148358\pi$
$877$	1493.00	+	2585.95i	0.0574858	+	0.0995683i	−0.835850	+	0.548957i	$0.815025\pi$
$878$	−1784.00	+	3089.98i	−0.0685730	+	0.118772i
$879$		0			0
$880$	−10368.0	−	17957.9i	−0.397165	−	0.687910i
$881$	6534.00			0.249871			0.124935	−	0.992165i	$-0.460128\pi$
$881$	6534.00			0.249871			0.124935	+	0.992165i	$0.460128\pi$
$882$		0			0
$883$	29756.0			1.13405			0.567027	−	0.823699i	$-0.308094\pi$
$883$	29756.0			1.13405			0.567027	+	0.823699i	$0.308094\pi$
$884$	−408.000	−	706.677i	−0.0155232	−	0.0268870i
$885$		0			0
$886$	11712.0	−	20285.8i	0.444100	−	0.769203i
$887$	−14976.0	−	25939.2i	−0.566905	−	0.981909i	−0.996870	−	0.0790627i	$-0.974807\pi$
$887$	−14976.0	−	25939.2i	−0.566905	−	0.981909i	0.429964	−	0.902846i	$-0.358526\pi$
$888$		0			0
$889$		0			0
$890$	−14040.0			−0.528789
$891$		0			0
$892$	−3776.00	+	6540.22i	−0.141737	+	0.245497i
$893$	7728.00	−	13385.3i	0.289594	−	0.501592i
$894$		0			0
$895$	46224.0			1.72637
$896$		0			0
$897$		0			0
$898$	−7650.00	−	13250.2i	−0.284280	−	0.492388i
$899$	3192.00	−	5528.71i	0.118420	−	0.205109i
$900$		0			0
$901$	1962.00	+	3398.28i	0.0725457	+	0.125653i
$902$	−864.000			−0.0318936
$903$		0			0
$904$	−3696.00			−0.135981
$905$	−24282.0	−	42057.7i	−0.891891	−	1.54480i
$906$		0			0
$907$	18134.0	−	31409.0i	0.663869	−	1.14986i	−0.315721	−	0.948852i	$-0.602246\pi$
$907$	18134.0	−	31409.0i	0.663869	−	1.14986i	0.979591	−	0.201004i	$-0.0644203\pi$
$908$	−7128.00	−	12346.1i	−0.260519	−	0.451232i
$909$		0			0
$910$		0			0
$911$	23604.0			0.858436			0.429218	−	0.903201i	$-0.358789\pi$
$911$	23604.0			0.858436			0.429218	+	0.903201i	$0.358789\pi$
$912$		0			0
$913$	−8208.00	+	14216.7i	−0.297530	+	0.515338i
$914$	3674.00	−	6363.55i	0.132960	−	0.230293i
$915$		0			0
$916$	−5336.00			−0.192474
$917$		0			0
$918$		0			0
$919$	−17092.0	−	29604.2i	−0.613507	−	1.06263i	−0.990644	−	0.136468i	$-0.956425\pi$
$919$	−17092.0	−	29604.2i	−0.613507	−	1.06263i	0.377137	−	0.926157i	$-0.376908\pi$
$920$	12960.0	−	22447.4i	0.464433	−	0.804422i
$921$		0			0
$922$	−3102.00	−	5372.82i	−0.110801	−	0.191914i
$923$	−1224.00			−0.0436495
$924$		0			0
$925$	−6766.00			−0.240502
$926$	8984.00	+	15560.7i	0.318826	+	0.552222i
$927$		0			0
$928$	1824.00	−	3159.26i	0.0645213	−	0.111754i
$929$	26961.0	+	46697.8i	0.952165	+	1.64920i	0.740725	+	0.671808i	$0.234482\pi$
$929$	26961.0	+	46697.8i	0.952165	+	1.64920i	0.211440	+	0.977391i	$0.432185\pi$
$930$		0			0
$931$		0			0
$932$	−10632.0			−0.373672
$933$		0			0
$934$	3612.00	−	6256.17i	0.126540	−	0.219174i
$935$	−3888.00	+	6734.21i	−0.135991	+	0.235543i
$936$		0			0
$937$	−40538.0			−1.41336			−0.706680	−	0.707533i	$-0.749808\pi$
$937$	−40538.0			−1.41336			−0.706680	+	0.707533i	$0.749808\pi$
$938$		0			0
$939$		0			0
$940$	−6048.00	−	10475.4i	−0.209855	−	0.363480i
$941$	1803.00	−	3122.89i	0.0624613	−	0.108186i	−0.833104	−	0.553117i	$-0.813438\pi$
$941$	1803.00	−	3122.89i	0.0624613	−	0.108186i	0.895565	+	0.444931i	$0.146772\pi$
$942$		0			0
$943$	−540.000	−	935.307i	−0.0186477	−	0.0322988i
$944$	−7872.00			−0.271411
$945$		0			0
$946$	−23616.0			−0.811652
$947$	7032.00	+	12179.8i	0.241298	+	0.417941i	0.961084	−	0.276255i	$-0.0890935\pi$
$947$	7032.00	+	12179.8i	0.241298	+	0.417941i	−0.719786	+	0.694196i	$0.755760\pi$
$948$		0			0
$949$	17170.0	−	29739.3i	0.587315	−	1.01726i
$950$	−18308.0	−	31710.4i	−0.625253	−	1.08297i
$951$		0			0
$952$		0			0
$953$	−33066.0			−1.12394			−0.561969	−	0.827158i	$-0.689956\pi$
$953$	−33066.0			−1.12394			−0.561969	+	0.827158i	$0.689956\pi$
$954$		0			0
$955$	−37044.0	+	64162.1i	−1.25520	+	2.17407i
$956$	−1176.00	+	2036.89i	−0.0397851	+	0.0689098i
$957$		0			0
$958$	18576.0			0.626475
$959$		0			0
$960$		0			0
$961$	13327.5	+	23083.9i	0.447367	+	0.774862i
$962$	−1156.00	+	2002.25i	−0.0387432	+	0.0671052i
$963$		0			0
$964$	11380.0	+	19710.7i	0.380213	+	0.658548i
$965$	−59580.0			−1.98751
$966$		0			0
$967$	−26368.0			−0.876875			−0.438437	−	0.898762i	$-0.644468\pi$
$967$	−26368.0			−0.876875			−0.438437	+	0.898762i	$0.644468\pi$
$968$	15412.0	+	26694.4i	0.511736	+	0.886353i
$969$		0			0
$970$	1260.00	−	2182.38i	0.0417074	−	0.0722393i
$971$	−27942.0	−	48397.0i	−0.923482	−	1.59952i	−0.793984	−	0.607939i	$-0.791997\pi$
$971$	−27942.0	−	48397.0i	−0.923482	−	1.59952i	−0.129499	−	0.991580i	$-0.541337\pi$
$972$		0			0
$973$		0			0
$974$	11696.0			0.384768
$975$		0			0
$976$	−2000.00	+	3464.10i	−0.0655927	+	0.113610i
$977$	−25563.0	+	44276.4i	−0.837086	+	1.44988i	0.0552350	+	0.998473i	$0.482409\pi$
$977$	−25563.0	+	44276.4i	−0.837086	+	1.44988i	−0.892321	+	0.451402i	$0.850924\pi$
$978$		0			0
$979$	28080.0			0.916691
$980$		0			0
$981$		0			0
$982$	5952.00	+	10309.2i	0.193417	+	0.335009i
$983$	7092.00	−	12283.7i	0.230112	−	0.398565i	−0.727729	−	0.685865i	$-0.759424\pi$
$983$	7092.00	−	12283.7i	0.230112	−	0.398565i	0.957841	+	0.287300i	$0.0927576\pi$
$984$		0			0
$985$	11502.0	+	19922.0i	0.372065	+	0.644436i
$986$	−1368.00			−0.0441846
$987$		0			0
$988$	−12512.0			−0.402894
$989$	−14760.0	−	25565.1i	−0.474561	−	0.821964i
$990$		0			0
$991$	−25840.0	+	44756.2i	−0.828289	+	1.43464i	0.0710900	+	0.997470i	$0.477352\pi$
$991$	−25840.0	+	44756.2i	−0.828289	+	1.43464i	−0.899379	+	0.437169i	$0.855981\pi$
$992$	−896.000	−	1551.92i	−0.0286774	−	0.0496708i
$993$		0			0
$994$		0			0
$995$	−52848.0			−1.68381
$996$		0			0
$997$	26047.0	−	45114.7i	0.827399	−	1.43310i	−0.0726730	−	0.997356i	$-0.523153\pi$
$997$	26047.0	−	45114.7i	0.827399	−	1.43310i	0.900072	−	0.435741i	$-0.143514\pi$
$998$	10748.0	−	18616.1i	0.340904	−	0.590463i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.o.361.1		2
3.2	odd	2		294.4.e.b.67.1		2
7.2	even	3	inner	882.4.g.o.667.1		2
7.3	odd	6		126.4.a.a.1.1		1
7.4	even	3		882.4.a.g.1.1		1
7.5	odd	6		882.4.g.w.667.1		2
7.6	odd	2		882.4.g.w.361.1		2
21.2	odd	6		294.4.e.b.79.1		2
21.5	even	6		294.4.e.c.79.1		2
21.11	odd	6		294.4.a.i.1.1		1
21.17	even	6		42.4.a.a.1.1	✓	1
21.20	even	2		294.4.e.c.67.1		2
28.3	even	6		1008.4.a.b.1.1		1
84.11	even	6		2352.4.a.a.1.1		1
84.59	odd	6		336.4.a.l.1.1		1
105.17	odd	12		1050.4.g.a.799.2		2
105.38	odd	12		1050.4.g.a.799.1		2
105.59	even	6		1050.4.a.g.1.1		1
168.59	odd	6		1344.4.a.a.1.1		1
168.101	even	6		1344.4.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.a.1.1	✓	1	21.17	even	6
126.4.a.a.1.1		1	7.3	odd	6
294.4.a.i.1.1		1	21.11	odd	6
294.4.e.b.67.1		2	3.2	odd	2
294.4.e.b.79.1		2	21.2	odd	6
294.4.e.c.67.1		2	21.20	even	2
294.4.e.c.79.1		2	21.5	even	6
336.4.a.l.1.1		1	84.59	odd	6
882.4.a.g.1.1		1	7.4	even	3
882.4.g.o.361.1		2	1.1	even	1	trivial
882.4.g.o.667.1		2	7.2	even	3	inner
882.4.g.w.361.1		2	7.6	odd	2
882.4.g.w.667.1		2	7.5	odd	6
1008.4.a.b.1.1		1	28.3	even	6
1050.4.a.g.1.1		1	105.59	even	6
1050.4.g.a.799.1		2	105.38	odd	12
1050.4.g.a.799.2		2	105.17	odd	12
1344.4.a.a.1.1		1	168.59	odd	6
1344.4.a.o.1.1		1	168.101	even	6
2352.4.a.a.1.1		1	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-9.00000 - 15.5885i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-9.00000 - 15.5885i) q^{5} -8.00000 q^{8} +(18.0000 - 31.1769i) q^{10} +(-36.0000 + 62.3538i) q^{11} +34.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(46.0000 + 79.6743i) q^{19} +72.0000 q^{20} -144.000 q^{22} +(-90.0000 - 155.885i) q^{23} +(-99.5000 + 172.339i) q^{25} +(34.0000 + 58.8897i) q^{26} +114.000 q^{29} +(28.0000 - 48.4974i) q^{31} +(16.0000 - 27.7128i) q^{32} -12.0000 q^{34} +(17.0000 + 29.4449i) q^{37} +(-92.0000 + 159.349i) q^{38} +(72.0000 + 124.708i) q^{40} +6.00000 q^{41} +164.000 q^{43} +(-144.000 - 249.415i) q^{44} +(180.000 - 311.769i) q^{46} +(-84.0000 - 145.492i) q^{47} -398.000 q^{50} +(-68.0000 + 117.779i) q^{52} +(327.000 - 566.381i) q^{53} +1296.00 q^{55} +(114.000 + 197.454i) q^{58} +(246.000 - 426.084i) q^{59} +(-125.000 - 216.506i) q^{61} +112.000 q^{62} +64.0000 q^{64} +(-306.000 - 530.008i) q^{65} +(62.0000 - 107.387i) q^{67} +(-12.0000 - 20.7846i) q^{68} -36.0000 q^{71} +(505.000 - 874.686i) q^{73} +(-34.0000 + 58.8897i) q^{74} -368.000 q^{76} +(-28.0000 - 48.4974i) q^{79} +(-144.000 + 249.415i) q^{80} +(6.00000 + 10.3923i) q^{82} +228.000 q^{83} +108.000 q^{85} +(164.000 + 284.056i) q^{86} +(288.000 - 498.831i) q^{88} +(-195.000 - 337.750i) q^{89} +720.000 q^{92} +(168.000 - 290.985i) q^{94} +(828.000 - 1434.14i) q^{95} +70.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 18 q^{5} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 18 * q^5 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 18 q^{5} - 16 q^{8} + 36 q^{10} - 72 q^{11} + 68 q^{13} - 16 q^{16} - 6 q^{17} + 92 q^{19} + 144 q^{20} - 288 q^{22} - 180 q^{23} - 199 q^{25} + 68 q^{26} + 228 q^{29} + 56 q^{31} + 32 q^{32} - 24 q^{34} + 34 q^{37} - 184 q^{38} + 144 q^{40} + 12 q^{41} + 328 q^{43} - 288 q^{44} + 360 q^{46} - 168 q^{47} - 796 q^{50} - 136 q^{52} + 654 q^{53} + 2592 q^{55} + 228 q^{58} + 492 q^{59} - 250 q^{61} + 224 q^{62} + 128 q^{64} - 612 q^{65} + 124 q^{67} - 24 q^{68} - 72 q^{71} + 1010 q^{73} - 68 q^{74} - 736 q^{76} - 56 q^{79} - 288 q^{80} + 12 q^{82} + 456 q^{83} + 216 q^{85} + 328 q^{86} + 576 q^{88} - 390 q^{89} + 1440 q^{92} + 336 q^{94} + 1656 q^{95} + 140 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 18 * q^5 - 16 * q^8 + 36 * q^10 - 72 * q^11 + 68 * q^13 - 16 * q^16 - 6 * q^17 + 92 * q^19 + 144 * q^20 - 288 * q^22 - 180 * q^23 - 199 * q^25 + 68 * q^26 + 228 * q^29 + 56 * q^31 + 32 * q^32 - 24 * q^34 + 34 * q^37 - 184 * q^38 + 144 * q^40 + 12 * q^41 + 328 * q^43 - 288 * q^44 + 360 * q^46 - 168 * q^47 - 796 * q^50 - 136 * q^52 + 654 * q^53 + 2592 * q^55 + 228 * q^58 + 492 * q^59 - 250 * q^61 + 224 * q^62 + 128 * q^64 - 612 * q^65 + 124 * q^67 - 24 * q^68 - 72 * q^71 + 1010 * q^73 - 68 * q^74 - 736 * q^76 - 56 * q^79 - 288 * q^80 + 12 * q^82 + 456 * q^83 + 216 * q^85 + 328 * q^86 + 576 * q^88 - 390 * q^89 + 1440 * q^92 + 336 * q^94 + 1656 * q^95 + 140 * q^97

Introduction

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Database

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