LMFDB - Embedded newform 882.4.g.bi.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-2.34521 - 4.06202i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.bi.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +(9.38083 - 16.2481i) q^{10} +(10.0000 - 17.3205i) q^{11} -65.6658 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-28.1425 + 48.7442i) q^{17} +(4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(24.0000 + 41.5692i) q^{23} +(18.5000 - 32.0429i) q^{25} +(-65.6658 - 113.737i) q^{26} +166.000 q^{29} +(-103.189 + 178.729i) q^{31} +(16.0000 - 27.7128i) q^{32} -112.570 q^{34} +(39.0000 + 67.5500i) q^{37} +(-9.38083 + 16.2481i) q^{38} +(37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(40.0000 + 69.2820i) q^{44} +(-48.0000 + 83.1384i) q^{46} +(-103.189 - 178.729i) q^{47} +74.0000 q^{50} +(131.332 - 227.473i) q^{52} +(31.0000 - 53.6936i) q^{53} -187.617 q^{55} +(166.000 + 287.520i) q^{58} +(333.020 - 576.807i) q^{59} +(136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(308.000 + 533.472i) q^{65} +(-290.000 + 502.295i) q^{67} +(-112.570 - 194.977i) q^{68} +544.000 q^{71} +(-300.187 + 519.938i) q^{73} +(-78.0000 + 135.100i) q^{74} -37.5233 q^{76} +(340.000 + 588.897i) q^{79} +(-75.0467 + 129.985i) q^{80} +(393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(436.000 + 755.174i) q^{86} +(-80.0000 + 138.564i) q^{88} +(750.467 + 1299.85i) q^{89} -192.000 q^{92} +(206.378 - 357.458i) q^{94} +(44.0000 - 76.2102i) q^{95} +656.658 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 40 q^{11} - 32 q^{16} + 160 q^{22} + 96 q^{23} + 74 q^{25} + 664 q^{29} + 64 q^{32} + 156 q^{37} + 1744 q^{43} + 160 q^{44} - 192 q^{46} + 296 q^{50} + 124 q^{53} + 664 q^{58} + 256 q^{64} + 1232 q^{65} - 1160 q^{67} + 2176 q^{71} - 312 q^{74} + 1360 q^{79} + 2112 q^{85} + 1744 q^{86} - 320 q^{88} - 768 q^{92} + 176 q^{95}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 40 * q^11 - 32 * q^16 + 160 * q^22 + 96 * q^23 + 74 * q^25 + 664 * q^29 + 64 * q^32 + 156 * q^37 + 1744 * q^43 + 160 * q^44 - 192 * q^46 + 296 * q^50 + 124 * q^53 + 664 * q^58 + 256 * q^64 + 1232 * q^65 - 1160 * q^67 + 2176 * q^71 - 312 * q^74 + 1360 * q^79 + 2112 * q^85 + 1744 * q^86 - 320 * q^88 - 768 * q^92 + 176 * q^95

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
$5$	−4.69042	−	8.12404i	−0.419524	−	0.726636i	0.576368	−	0.817190i	$-0.304470\pi$
$5$	−4.69042	−	8.12404i	−0.419524	−	0.726636i	−0.995892	+	0.0905542i	$0.971136\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	9.38083	−	16.2481i	0.296648	−	0.513809i
$11$	10.0000	−	17.3205i	0.274101	−	0.474757i	−0.695807	−	0.718229i	$-0.744953\pi$
$11$	10.0000	−	17.3205i	0.274101	−	0.474757i	0.969908	+	0.243472i	$0.0782863\pi$
$12$		0			0
$13$	−65.6658			−1.40096			−0.700478	−	0.713674i	$-0.747030\pi$
$13$	−65.6658			−1.40096			−0.700478	+	0.713674i	$0.747030\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−28.1425	+	48.7442i	−0.401503	+	0.695424i	−0.993908	−	0.110217i	$-0.964846\pi$
$17$	−28.1425	+	48.7442i	−0.401503	+	0.695424i	0.592404	+	0.805641i	$0.298179\pi$
$18$		0			0
$19$	4.69042	+	8.12404i	0.0566345	+	0.0980938i	0.892953	−	0.450151i	$-0.148630\pi$
$19$	4.69042	+	8.12404i	0.0566345	+	0.0980938i	−0.836318	+	0.548244i	$0.815296\pi$
$20$	37.5233			0.419524
$21$		0			0
$22$	40.0000			0.387638
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	0.954068	−	0.299591i	$-0.0968503\pi$
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	−0.736487	+	0.676451i	$0.763517\pi$
$24$		0			0
$25$	18.5000	−	32.0429i	0.148000	−	0.256344i
$26$	−65.6658	−	113.737i	−0.495313	−	0.857907i
$27$		0			0
$28$		0			0
$29$	166.000			1.06295			0.531473	−	0.847075i	$-0.321639\pi$
$29$	166.000			1.06295			0.531473	+	0.847075i	$0.321639\pi$
$30$		0			0
$31$	−103.189	+	178.729i	−0.597849	+	1.03550i	0.395289	+	0.918557i	$0.370644\pi$
$31$	−103.189	+	178.729i	−0.597849	+	1.03550i	−0.993138	+	0.116948i	$0.962689\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−112.570			−0.567812
$35$		0			0
$36$		0			0
$37$	39.0000	+	67.5500i	0.173285	+	0.300139i	0.939567	−	0.342366i	$-0.111228\pi$
$37$	39.0000	+	67.5500i	0.173285	+	0.300139i	−0.766281	+	0.642505i	$0.777895\pi$
$38$	−9.38083	+	16.2481i	−0.0400466	+	0.0693628i
$39$		0			0
$40$	37.5233	+	64.9923i	0.148324	+	0.256905i
$41$	393.995			1.50077			0.750386	−	0.661000i	$-0.229868\pi$
$41$	393.995			1.50077			0.750386	+	0.661000i	$0.229868\pi$
$42$		0			0
$43$	436.000			1.54626			0.773132	−	0.634245i	$-0.218689\pi$
$43$	436.000			1.54626			0.773132	+	0.634245i	$0.218689\pi$
$44$	40.0000	+	69.2820i	0.137051	+	0.237379i
$45$		0			0
$46$	−48.0000	+	83.1384i	−0.153852	+	0.266480i
$47$	−103.189	−	178.729i	−0.320249	−	0.554687i	0.660291	−	0.751010i	$-0.270433\pi$
$47$	−103.189	−	178.729i	−0.320249	−	0.554687i	−0.980539	+	0.196323i	$0.937100\pi$
$48$		0			0
$49$		0			0
$50$	74.0000			0.209304
$51$		0			0
$52$	131.332	−	227.473i	0.350239	−	0.606632i
$53$	31.0000	−	53.6936i	0.0803430	−	0.139158i	−0.823054	−	0.567963i	$-0.807732\pi$
$53$	31.0000	−	53.6936i	0.0803430	−	0.139158i	0.903397	+	0.428805i	$0.141065\pi$
$54$		0			0
$55$	−187.617			−0.459968
$56$		0			0
$57$		0			0
$58$	166.000	+	287.520i	0.375808	+	0.650919i
$59$	333.020	−	576.807i	0.734838	−	1.27278i	−0.219956	−	0.975510i	$-0.570591\pi$
$59$	333.020	−	576.807i	0.734838	−	1.27278i	0.954794	−	0.297267i	$-0.0960752\pi$
$60$		0			0
$61$	136.022	+	235.597i	0.285506	+	0.494510i	0.972732	−	0.231933i	$-0.0745052\pi$
$61$	136.022	+	235.597i	0.285506	+	0.494510i	−0.687226	+	0.726444i	$0.741172\pi$
$62$	−412.757			−0.845486
$63$		0			0
$64$	64.0000			0.125000
$65$	308.000	+	533.472i	0.587734	+	1.01798i
$66$		0			0
$67$	−290.000	+	502.295i	−0.528793	+	0.915897i	0.470643	+	0.882324i	$0.344022\pi$
$67$	−290.000	+	502.295i	−0.528793	+	0.915897i	−0.999436	+	0.0335729i	$0.989311\pi$
$68$	−112.570	−	194.977i	−0.200752	−	0.347712i
$69$		0			0
$70$		0			0
$71$	544.000			0.909309			0.454654	−	0.890668i	$-0.349763\pi$
$71$	544.000			0.909309			0.454654	+	0.890668i	$0.349763\pi$
$72$		0			0
$73$	−300.187	+	519.938i	−0.481290	+	0.833619i	−0.999769	−	0.0214711i	$-0.993165\pi$
$73$	−300.187	+	519.938i	−0.481290	+	0.833619i	0.518479	+	0.855090i	$0.326498\pi$
$74$	−78.0000	+	135.100i	−0.122531	+	0.212230i
$75$		0			0
$76$	−37.5233			−0.0566345
$77$		0			0
$78$		0			0
$79$	340.000	+	588.897i	0.484215	+	0.838685i	0.999836	−	0.0181320i	$-0.00577190\pi$
$79$	340.000	+	588.897i	0.484215	+	0.838685i	−0.515621	+	0.856817i	$0.672439\pi$
$80$	−75.0467	+	129.985i	−0.104881	+	0.181659i
$81$		0			0
$82$	393.995	+	682.419i	0.530603	+	0.919032i
$83$	196.997			0.260521			0.130261	−	0.991480i	$-0.458419\pi$
$83$	196.997			0.260521			0.130261	+	0.991480i	$0.458419\pi$
$84$		0			0
$85$	528.000			0.673760
$86$	436.000	+	755.174i	0.546687	+	0.946890i
$87$		0			0
$88$	−80.0000	+	138.564i	−0.0969094	+	0.167852i
$89$	750.467	+	1299.85i	0.893812	+	1.54813i	0.835268	+	0.549843i	$0.185313\pi$
$89$	750.467	+	1299.85i	0.893812	+	1.54813i	0.0585446	+	0.998285i	$0.481354\pi$
$90$		0			0
$91$		0			0
$92$	−192.000			−0.217580
$93$		0			0
$94$	206.378	−	357.458i	0.226450	−	0.392223i
$95$	44.0000	−	76.2102i	0.0475190	−	0.0823053i
$96$		0			0
$97$	656.658			0.687356			0.343678	−	0.939088i	$-0.388327\pi$
$97$	656.658			0.687356			0.343678	+	0.939088i	$0.388327\pi$
$98$		0			0
$99$		0			0
$100$	74.0000	+	128.172i	0.0740000	+	0.128172i
$101$	−60.9754	+	105.612i	−0.0600721	+	0.104048i	−0.894497	−	0.447073i	$-0.852466\pi$
$101$	−60.9754	+	105.612i	−0.0600721	+	0.104048i	0.834425	+	0.551121i	$0.185800\pi$
$102$		0			0
$103$	−684.801	−	1186.11i	−0.655101	−	1.13467i	−0.981868	−	0.189564i	$-0.939293\pi$
$103$	−684.801	−	1186.11i	−0.655101	−	1.13467i	0.326767	−	0.945105i	$-0.394041\pi$
$104$	525.327			0.495313
$105$		0			0
$106$	124.000			0.113622
$107$	−130.000	−	225.167i	−0.117454	−	0.203436i	0.801304	−	0.598257i	$-0.204140\pi$
$107$	−130.000	−	225.167i	−0.117454	−	0.203436i	−0.918758	+	0.394821i	$0.870807\pi$
$108$		0			0
$109$	−941.000	+	1629.86i	−0.826894	+	1.43222i	0.0735690	+	0.997290i	$0.476561\pi$
$109$	−941.000	+	1629.86i	−0.826894	+	1.43222i	−0.900463	+	0.434932i	$0.856772\pi$
$110$	−187.617	−	324.962i	−0.162623	−	0.281672i
$111$		0			0
$112$		0			0
$113$	1286.00			1.07059			0.535295	−	0.844665i	$-0.320200\pi$
$113$	1286.00			1.07059			0.535295	+	0.844665i	$0.320200\pi$
$114$		0			0
$115$	225.140	−	389.954i	0.182560	−	0.316203i
$116$	−332.000	+	575.041i	−0.265736	+	0.460269i
$117$		0			0
$118$	1332.08			1.03922
$119$		0			0
$120$		0			0
$121$	465.500	+	806.270i	0.349737	+	0.605762i
$122$	−272.044	+	471.194i	−0.201883	+	0.349671i
$123$		0			0
$124$	−412.757	−	714.915i	−0.298924	−	0.517752i
$125$	−1519.69			−1.08741
$126$		0			0
$127$	2312.00			1.61541			0.807704	−	0.589588i	$-0.200710\pi$
$127$	2312.00			1.61541			0.807704	+	0.589588i	$0.200710\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−616.000	+	1066.94i	−0.415591	+	0.719824i
$131$	126.641	+	219.349i	0.0844633	+	0.146295i	0.905162	−	0.425066i	$-0.139749\pi$
$131$	126.641	+	219.349i	0.0844633	+	0.146295i	−0.820699	+	0.571361i	$0.806416\pi$
$132$		0			0
$133$		0			0
$134$	−1160.00			−0.747826
$135$		0			0
$136$	225.140	−	389.954i	0.141953	−	0.245870i
$137$	−557.000	+	964.752i	−0.347356	+	0.601638i	−0.985779	−	0.168048i	$-0.946254\pi$
$137$	−557.000	+	964.752i	−0.347356	+	0.601638i	0.638423	+	0.769686i	$0.279587\pi$
$138$		0			0
$139$	−1378.98			−0.841466			−0.420733	−	0.907185i	$-0.638227\pi$
$139$	−1378.98			−0.841466			−0.420733	+	0.907185i	$0.638227\pi$
$140$		0			0
$141$		0			0
$142$	544.000	+	942.236i	0.321489	+	0.556836i
$143$	−656.658	+	1137.37i	−0.384004	+	0.665114i
$144$		0			0
$145$	−778.609	−	1348.59i	−0.445931	−	0.772375i
$146$	−1200.75			−0.680647
$147$		0			0
$148$	−312.000			−0.173285
$149$	−473.000	−	819.260i	−0.260065	−	0.450446i	0.706194	−	0.708018i	$-0.250411\pi$
$149$	−473.000	−	819.260i	−0.260065	−	0.450446i	−0.966259	+	0.257573i	$0.917077\pi$
$150$		0			0
$151$	−416.000	+	720.533i	−0.224196	+	0.388319i	−0.956078	−	0.293113i	$-0.905309\pi$
$151$	−416.000	+	720.533i	−0.224196	+	0.388319i	0.731882	+	0.681431i	$0.238642\pi$
$152$	−37.5233	−	64.9923i	−0.0200233	−	0.0346814i
$153$		0			0
$154$		0			0
$155$	1936.00			1.00325
$156$		0			0
$157$	1439.96	−	2494.08i	0.731982	−	1.26783i	−0.224053	−	0.974577i	$-0.571929\pi$
$157$	1439.96	−	2494.08i	0.731982	−	1.26783i	0.956035	−	0.293253i	$-0.0947377\pi$
$158$	−680.000	+	1177.79i	−0.342392	+	0.593040i
$159$		0			0
$160$	−300.187			−0.148324
$161$		0			0
$162$		0			0
$163$	−318.000	−	550.792i	−0.152808	−	0.264671i	0.779451	−	0.626463i	$-0.215498\pi$
$163$	−318.000	−	550.792i	−0.152808	−	0.264671i	−0.932259	+	0.361792i	$0.882165\pi$
$164$	−787.990	+	1364.84i	−0.375193	+	0.649854i
$165$		0			0
$166$	196.997	+	341.210i	0.0921082	+	0.159536i
$167$	−656.658			−0.304274			−0.152137	−	0.988359i	$-0.548615\pi$
$167$	−656.658			−0.304274			−0.152137	+	0.988359i	$0.548615\pi$
$168$		0			0
$169$	2115.00			0.962676
$170$	528.000	+	914.523i	0.238210	+	0.412592i
$171$		0			0
$172$	−872.000	+	1510.35i	−0.386566	+	0.669552i
$173$	−333.020	−	576.807i	−0.146353	−	0.253490i	0.783524	−	0.621361i	$-0.213420\pi$
$173$	−333.020	−	576.807i	−0.146353	−	0.253490i	−0.929877	+	0.367871i	$0.880087\pi$
$174$		0			0
$175$		0			0
$176$	−320.000			−0.137051
$177$		0			0
$178$	−1500.93	+	2599.69i	−0.632021	+	1.09469i
$179$	−1614.00	+	2795.53i	−0.673944	+	1.16731i	0.302832	+	0.953044i	$0.402068\pi$
$179$	−1614.00	+	2795.53i	−0.673944	+	1.16731i	−0.976776	+	0.214262i	$0.931265\pi$
$180$		0			0
$181$	2823.63			1.15955			0.579776	−	0.814776i	$-0.303140\pi$
$181$	2823.63			1.15955			0.579776	+	0.814776i	$0.303140\pi$
$182$		0			0
$183$		0			0
$184$	−192.000	−	332.554i	−0.0769262	−	0.133240i
$185$	365.852	−	633.675i	0.145395	−	0.251831i
$186$		0			0
$187$	562.850	+	974.885i	0.220105	+	0.381233i
$188$	825.513			0.320249
$189$		0			0
$190$	176.000			0.0672020
$191$	−1068.00	−	1849.83i	−0.404596	−	0.700780i	0.589679	−	0.807638i	$-0.299254\pi$
$191$	−1068.00	−	1849.83i	−0.404596	−	0.700780i	−0.994274	+	0.106858i	$0.965921\pi$
$192$		0			0
$193$	−829.000	+	1435.87i	−0.309185	+	0.535524i	−0.978184	−	0.207739i	$-0.933390\pi$
$193$	−829.000	+	1435.87i	−0.309185	+	0.535524i	0.668999	+	0.743263i	$0.266723\pi$
$194$	656.658	+	1137.37i	0.243017	+	0.420918i
$195$		0			0
$196$		0			0
$197$	978.000			0.353704			0.176852	−	0.984237i	$-0.443409\pi$
$197$	978.000			0.353704			0.176852	+	0.984237i	$0.443409\pi$
$198$		0			0
$199$	−2467.16	+	4273.24i	−0.878855	+	1.52222i	−0.0262574	+	0.999655i	$0.508359\pi$
$199$	−2467.16	+	4273.24i	−0.878855	+	1.52222i	−0.852598	+	0.522567i	$0.824974\pi$
$200$	−148.000	+	256.344i	−0.0523259	+	0.0906311i
$201$		0			0
$202$	−243.902			−0.0849547
$203$		0			0
$204$		0			0
$205$	−1848.00	−	3200.83i	−0.629609	−	1.09052i
$206$	1369.60	−	2372.22i	0.463226	−	0.802332i
$207$		0			0
$208$	525.327	+	909.892i	0.175119	+	0.303316i
$209$	187.617			0.0620943
$210$		0			0
$211$	1556.00			0.507675			0.253838	−	0.967247i	$-0.418307\pi$
$211$	1556.00			0.507675			0.253838	+	0.967247i	$0.418307\pi$
$212$	124.000	+	214.774i	0.0401715	+	0.0695791i
$213$		0			0
$214$	260.000	−	450.333i	0.0830525	−	0.143851i
$215$	−2045.02	−	3542.08i	−0.648694	−	1.12357i
$216$		0			0
$217$		0			0
$218$	−3764.00			−1.16940
$219$		0			0
$220$	375.233	−	649.923i	0.114992	−	0.199172i
$221$	1848.00	−	3200.83i	0.562488	−	0.974258i
$222$		0			0
$223$	−2889.30			−0.867630			−0.433815	−	0.901002i	$-0.642833\pi$
$223$	−2889.30			−0.867630			−0.433815	+	0.901002i	$0.642833\pi$
$224$		0			0
$225$		0			0
$226$	1286.00	+	2227.42i	0.378511	+	0.655600i
$227$	989.678	−	1714.17i	0.289371	−	0.501205i	−0.684289	−	0.729211i	$-0.739887\pi$
$227$	989.678	−	1714.17i	0.289371	−	0.501205i	0.973660	+	0.228006i	$0.0732205\pi$
$228$		0			0
$229$	1383.67	+	2396.59i	0.399282	+	0.691577i	0.993638	−	0.112625i	$-0.0359260\pi$
$229$	1383.67	+	2396.59i	0.399282	+	0.691577i	−0.594355	+	0.804203i	$0.702593\pi$
$230$	900.560			0.258179
$231$		0			0
$232$	−1328.00			−0.375808
$233$	−3245.00	−	5620.50i	−0.912391	−	1.58031i	−0.810677	−	0.585493i	$-0.800901\pi$
$233$	−3245.00	−	5620.50i	−0.912391	−	1.58031i	−0.101713	−	0.994814i	$-0.532432\pi$
$234$		0			0
$235$	−968.000	+	1676.63i	−0.268704	+	0.465408i
$236$	1332.08	+	2307.23i	0.367419	+	0.636388i
$237$		0			0
$238$		0			0
$239$	4296.00			1.16270			0.581350	−	0.813654i	$-0.302525\pi$
$239$	4296.00			1.16270			0.581350	+	0.813654i	$0.302525\pi$
$240$		0			0
$241$	2260.78	−	3915.79i	0.604272	−	1.04663i	−0.387894	−	0.921704i	$-0.626797\pi$
$241$	2260.78	−	3915.79i	0.604272	−	1.04663i	0.992166	−	0.124926i	$-0.0398695\pi$
$242$	−931.000	+	1612.54i	−0.247301	+	0.428339i
$243$		0			0
$244$	−1088.18			−0.285506
$245$		0			0
$246$		0			0
$247$	−308.000	−	533.472i	−0.0793424	−	0.137425i
$248$	825.513	−	1429.83i	0.211372	−	0.366106i
$249$		0			0
$250$	−1519.69	−	2632.19i	−0.384456	−	0.665897i
$251$	5581.59			1.40361			0.701807	−	0.712367i	$-0.252377\pi$
$251$	5581.59			1.40361			0.701807	+	0.712367i	$0.252377\pi$
$252$		0			0
$253$	960.000			0.238556
$254$	2312.00	+	4004.50i	0.571133	+	0.989231i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	750.467	+	1299.85i	0.182151	+	0.315495i	0.942613	−	0.333888i	$-0.108361\pi$
$257$	750.467	+	1299.85i	0.182151	+	0.315495i	−0.760462	+	0.649383i	$0.775027\pi$
$258$		0			0
$259$		0			0
$260$	−2464.00			−0.587734
$261$		0			0
$262$	−253.282	+	438.698i	−0.0597246	+	0.103446i
$263$	−200.000	+	346.410i	−0.0468917	+	0.0812189i	−0.888519	−	0.458841i	$-0.848265\pi$
$263$	−200.000	+	346.410i	−0.0468917	+	0.0812189i	0.841627	+	0.540059i	$0.181598\pi$
$264$		0			0
$265$	−581.612			−0.134823
$266$		0			0
$267$		0			0
$268$	−1160.00	−	2009.18i	−0.264397	−	0.457948i
$269$	136.022	−	235.597i	0.0308305	−	0.0534000i	−0.850198	−	0.526462i	$-0.823518\pi$
$269$	136.022	−	235.597i	0.0308305	−	0.0534000i	0.881029	+	0.473062i	$0.156851\pi$
$270$		0			0
$271$	3452.15	+	5979.29i	0.773812	+	1.34028i	0.935460	+	0.353433i	$0.114986\pi$
$271$	3452.15	+	5979.29i	0.773812	+	1.34028i	−0.161648	+	0.986848i	$0.551681\pi$
$272$	900.560			0.200752
$273$		0			0
$274$	−2228.00			−0.491235
$275$	−370.000	−	640.859i	−0.0811340	−	0.140528i
$276$		0			0
$277$	3385.00	−	5862.99i	0.734242	−	1.27174i	−0.220814	−	0.975316i	$-0.570871\pi$
$277$	3385.00	−	5862.99i	0.734242	−	1.27174i	0.955055	−	0.296428i	$-0.0957954\pi$
$278$	−1378.98	−	2388.47i	−0.297503	−	0.515290i
$279$		0			0
$280$		0			0
$281$	−1878.00			−0.398691			−0.199345	−	0.979929i	$-0.563882\pi$
$281$	−1878.00			−0.398691			−0.199345	+	0.979929i	$0.563882\pi$
$282$		0			0
$283$	192.307	−	333.086i	0.0403939	−	0.0699642i	−0.845122	−	0.534574i	$-0.820472\pi$
$283$	192.307	−	333.086i	0.0403939	−	0.0699642i	0.885516	+	0.464610i	$0.153805\pi$
$284$	−1088.00	+	1884.47i	−0.227327	+	0.393742i
$285$		0			0
$286$	−2626.63			−0.543063
$287$		0			0
$288$		0			0
$289$	872.500	+	1511.21i	0.177590	+	0.307595i
$290$	1557.22	−	2697.18i	0.315321	−	0.546151i
$291$		0			0
$292$	−1200.75	−	2079.75i	−0.240645	−	0.416810i
$293$	−3742.95			−0.746299			−0.373149	−	0.927771i	$-0.621722\pi$
$293$	−3742.95			−0.746299			−0.373149	+	0.927771i	$0.621722\pi$
$294$		0			0
$295$	−6248.00			−1.23313
$296$	−312.000	−	540.400i	−0.0612656	−	0.106115i
$297$		0			0
$298$	946.000	−	1638.52i	0.183894	−	0.318513i
$299$	−1575.98	−	2729.68i	−0.304820	−	0.527964i
$300$		0			0
$301$		0			0
$302$	−1664.00			−0.317061
$303$		0			0
$304$	75.0467	−	129.985i	0.0141586	−	0.0245235i
$305$	1276.00	−	2210.10i	0.239553	−	0.414917i
$306$		0			0
$307$	−722.324			−0.134284			−0.0671420	−	0.997743i	$-0.521388\pi$
$307$	−722.324			−0.134284			−0.0671420	+	0.997743i	$0.521388\pi$
$308$		0			0
$309$		0			0
$310$	1936.00	+	3353.25i	0.354701	+	0.614361i
$311$	−3639.76	+	6304.25i	−0.663640	+	1.14946i	0.316012	+	0.948755i	$0.397656\pi$
$311$	−3639.76	+	6304.25i	−0.663640	+	1.14946i	−0.979652	+	0.200703i	$0.935677\pi$
$312$		0			0
$313$	759.847	+	1316.09i	0.137218	+	0.237668i	0.926442	−	0.376437i	$-0.122851\pi$
$313$	759.847	+	1316.09i	0.137218	+	0.237668i	−0.789225	+	0.614104i	$0.789517\pi$
$314$	5759.83			1.03518
$315$		0			0
$316$	−2720.00			−0.484215
$317$	1179.00	+	2042.09i	0.208893	+	0.361814i	0.951366	−	0.308062i	$-0.0996805\pi$
$317$	1179.00	+	2042.09i	0.208893	+	0.361814i	−0.742473	+	0.669876i	$0.766347\pi$
$318$		0			0
$319$	1660.00	−	2875.20i	0.291355	−	0.504641i
$320$	−300.187	−	519.938i	−0.0524404	−	0.0908295i
$321$		0			0
$322$		0			0
$323$	−528.000			−0.0909557
$324$		0			0
$325$	−1214.82	+	2104.13i	−0.207341	+	0.359126i
$326$	636.000	−	1101.58i	0.108051	−	0.187151i
$327$		0			0
$328$	−3151.96			−0.530603
$329$		0			0
$330$		0			0
$331$	−1186.00	−	2054.21i	−0.196944	−	0.341117i	0.750592	−	0.660766i	$-0.229768\pi$
$331$	−1186.00	−	2054.21i	−0.196944	−	0.341117i	−0.947536	+	0.319649i	$0.896435\pi$
$332$	−393.995	+	682.419i	−0.0651304	+	0.112809i
$333$		0			0
$334$	−656.658	−	1137.37i	−0.107577	−	0.186329i
$335$	5440.88			0.887365
$336$		0			0
$337$	−250.000			−0.0404106			−0.0202053	−	0.999796i	$-0.506432\pi$
$337$	−250.000			−0.0404106			−0.0202053	+	0.999796i	$0.506432\pi$
$338$	2115.00	+	3663.29i	0.340357	+	0.589516i
$339$		0			0
$340$	−1056.00	+	1829.05i	−0.168440	+	0.291747i
$341$	2063.78	+	3574.58i	0.327742	+	0.567666i
$342$		0			0
$343$		0			0
$344$	−3488.00			−0.546687
$345$		0			0
$346$	666.039	−	1153.61i	0.103487	−	0.179245i
$347$	4770.00	−	8261.88i	0.737945	−	1.27816i	−0.215474	−	0.976510i	$-0.569130\pi$
$347$	4770.00	−	8261.88i	0.737945	−	1.27816i	0.953419	−	0.301649i	$-0.0975371\pi$
$348$		0			0
$349$	5712.93			0.876235			0.438117	−	0.898918i	$-0.355645\pi$
$349$	5712.93			0.876235			0.438117	+	0.898918i	$0.355645\pi$
$350$		0			0
$351$		0			0
$352$	−320.000	−	554.256i	−0.0484547	−	0.0839260i
$353$	−2195.11	+	3802.05i	−0.330975	+	0.573265i	−0.982703	−	0.185187i	$-0.940711\pi$
$353$	−2195.11	+	3802.05i	−0.330975	+	0.573265i	0.651728	+	0.758452i	$0.274044\pi$
$354$		0			0
$355$	−2551.59	−	4419.48i	−0.381476	−	0.660737i
$356$	−6003.73			−0.893812
$357$		0			0
$358$	−6456.00			−0.953101
$359$	920.000	+	1593.49i	0.135253	+	0.234265i	0.925694	−	0.378273i	$-0.123482\pi$
$359$	920.000	+	1593.49i	0.135253	+	0.234265i	−0.790441	+	0.612538i	$0.790149\pi$
$360$		0			0
$361$	3385.50	−	5863.86i	0.493585	−	0.854914i
$362$	2823.63	+	4890.67i	0.409963	+	0.710077i
$363$		0			0
$364$		0			0
$365$	5632.00			0.807650
$366$		0			0
$367$	−1482.17	+	2567.20i	−0.210814	+	0.365140i	−0.951969	−	0.306193i	$-0.900945\pi$
$367$	−1482.17	+	2567.20i	−0.210814	+	0.365140i	0.741156	+	0.671333i	$0.234278\pi$
$368$	384.000	−	665.108i	0.0543951	−	0.0942150i
$369$		0			0
$370$	1463.41			0.205619
$371$		0			0
$372$		0			0
$373$	−1991.00	−	3448.51i	−0.276381	−	0.478706i	0.694102	−	0.719877i	$-0.255802\pi$
$373$	−1991.00	−	3448.51i	−0.276381	−	0.478706i	−0.970483	+	0.241171i	$0.922468\pi$
$374$	−1125.70	+	1949.77i	−0.155638	+	0.269573i
$375$		0			0
$376$	825.513	+	1429.83i	0.113225	+	0.196111i
$377$	−10900.5			−1.48914
$378$		0			0
$379$	2676.00			0.362683			0.181342	−	0.983420i	$-0.441956\pi$
$379$	2676.00			0.362683			0.181342	+	0.983420i	$0.441956\pi$
$380$	176.000	+	304.841i	0.0237595	+	0.0411527i
$381$		0			0
$382$	2136.00	−	3699.66i	0.286092	−	0.495526i
$383$	−3517.81	−	6093.03i	−0.469326	−	0.812896i	0.530059	−	0.847961i	$-0.322170\pi$
$383$	−3517.81	−	6093.03i	−0.469326	−	0.812896i	−0.999385	+	0.0350645i	$0.988836\pi$
$384$		0			0
$385$		0			0
$386$	−3316.00			−0.437254
$387$		0			0
$388$	−1313.32	+	2274.73i	−0.171839	+	0.297634i
$389$	4329.00	−	7498.05i	0.564239	−	0.977291i	−0.432881	−	0.901451i	$-0.642503\pi$
$389$	4329.00	−	7498.05i	0.564239	−	0.977291i	0.997120	−	0.0758397i	$-0.0241637\pi$
$390$		0			0
$391$	−2701.68			−0.349437
$392$		0			0
$393$		0			0
$394$	978.000	+	1693.95i	0.125053	+	0.216598i
$395$	3189.48	−	5524.35i	0.406279	−	0.703696i
$396$		0			0
$397$	−4526.25	−	7839.70i	−0.572207	−	0.991091i	−0.996339	−	0.0854907i	$-0.972754\pi$
$397$	−4526.25	−	7839.70i	−0.572207	−	0.991091i	0.424132	−	0.905600i	$-0.360579\pi$
$398$	−9868.63			−1.24289
$399$		0			0
$400$	−592.000			−0.0740000
$401$	−2853.00	−	4941.54i	−0.355292	−	0.615383i	0.631876	−	0.775069i	$-0.282285\pi$
$401$	−2853.00	−	4941.54i	−0.355292	−	0.615383i	−0.987168	+	0.159686i	$0.948952\pi$
$402$		0			0
$403$	6776.00	−	11736.4i	0.837560	−	1.45070i
$404$	−243.902	−	422.450i	−0.0300360	−	0.0520239i
$405$		0			0
$406$		0			0
$407$	1560.00			0.189991
$408$		0			0
$409$	1210.13	−	2096.00i	0.146301	−	0.253400i	−0.783557	−	0.621320i	$-0.786597\pi$
$409$	1210.13	−	2096.00i	0.146301	−	0.253400i	0.929857	+	0.367920i	$0.119930\pi$
$410$	3696.00	−	6401.66i	0.445201	−	0.771111i
$411$		0			0
$412$	5478.41			0.655101
$413$		0			0
$414$		0			0
$415$	−924.000	−	1600.41i	−0.109295	−	0.189304i
$416$	−1050.65	+	1819.78i	−0.123828	+	0.214477i
$417$		0			0
$418$	187.617	+	324.962i	0.0219537	+	0.0380249i
$419$	−1510.31			−0.176095			−0.0880473	−	0.996116i	$-0.528063\pi$
$419$	−1510.31			−0.176095			−0.0880473	+	0.996116i	$0.528063\pi$
$420$		0			0
$421$	−16770.0			−1.94138			−0.970689	−	0.240341i	$-0.922741\pi$
$421$	−16770.0			−1.94138			−0.970689	+	0.240341i	$0.922741\pi$
$422$	1556.00	+	2695.07i	0.179490	+	0.310886i
$423$		0			0
$424$	−248.000	+	429.549i	−0.0284055	+	0.0491998i
$425$	1041.27	+	1803.54i	0.118845	+	0.205846i
$426$		0			0
$427$		0			0
$428$	1040.00			0.117454
$429$		0			0
$430$	4090.04	−	7084.16i	0.458696	−	0.794485i
$431$	668.000	−	1157.01i	0.0746553	−	0.129307i	−0.826281	−	0.563258i	$-0.809548\pi$
$431$	668.000	−	1157.01i	0.0746553	−	0.129307i	0.900936	+	0.433951i	$0.142881\pi$
$432$		0			0
$433$	11163.2			1.23896			0.619479	−	0.785013i	$-0.287344\pi$
$433$	11163.2			1.23896			0.619479	+	0.785013i	$0.287344\pi$
$434$		0			0
$435$		0			0
$436$	−3764.00	−	6519.44i	−0.413447	−	0.716111i
$437$	−225.140	+	389.954i	−0.0246451	+	0.0426865i
$438$		0			0
$439$	−1801.12	−	3119.63i	−0.195815	−	0.339161i	0.751352	−	0.659901i	$-0.229402\pi$
$439$	−1801.12	−	3119.63i	−0.195815	−	0.339161i	−0.947167	+	0.320740i	$0.896069\pi$
$440$	1500.93			0.162623
$441$		0			0
$442$	7392.00			0.795479
$443$	3174.00	+	5497.53i	0.340409	+	0.589606i	0.984509	−	0.175336i	$-0.0561011\pi$
$443$	3174.00	+	5497.53i	0.340409	+	0.589606i	−0.644099	+	0.764942i	$0.722768\pi$
$444$		0			0
$445$	7040.00	−	12193.6i	0.749951	−	1.29895i
$446$	−2889.30	−	5004.41i	−0.306754	−	0.531313i
$447$		0			0
$448$		0			0
$449$	−7170.00			−0.753615			−0.376808	−	0.926292i	$-0.622978\pi$
$449$	−7170.00			−0.753615			−0.376808	+	0.926292i	$0.622978\pi$
$450$		0			0
$451$	3939.95	−	6824.19i	0.411364	−	0.712503i
$452$	−2572.00	+	4454.83i	−0.267648	+	0.463579i
$453$		0			0
$454$	3958.71			0.409232
$455$		0			0
$456$		0			0
$457$	−3433.00	−	5946.13i	−0.351398	−	0.608639i	0.635097	−	0.772433i	$-0.280960\pi$
$457$	−3433.00	−	5946.13i	−0.351398	−	0.608639i	−0.986495	+	0.163793i	$0.947627\pi$
$458$	−2767.35	+	4793.18i	−0.282335	+	0.489019i
$459$		0			0
$460$	900.560	+	1559.82i	0.0912800	+	0.158102i
$461$	1378.98			0.139318			0.0696590	−	0.997571i	$-0.477809\pi$
$461$	1378.98			0.139318			0.0696590	+	0.997571i	$0.477809\pi$
$462$		0			0
$463$	2648.00			0.265795			0.132897	−	0.991130i	$-0.457572\pi$
$463$	2648.00			0.265795			0.132897	+	0.991130i	$0.457572\pi$
$464$	−1328.00	−	2300.16i	−0.132868	−	0.230135i
$465$		0			0
$466$	6490.00	−	11241.0i	0.645158	−	1.11745i
$467$	6167.90	+	10683.1i	0.611170	+	1.05858i	0.991044	+	0.133539i	$0.0426340\pi$
$467$	6167.90	+	10683.1i	0.611170	+	1.05858i	−0.379874	+	0.925038i	$0.624033\pi$
$468$		0			0
$469$		0			0
$470$	−3872.00			−0.380004
$471$		0			0
$472$	−2664.16	+	4614.45i	−0.259805	+	0.449995i
$473$	4360.00	−	7551.74i	0.423833	−	0.734100i
$474$		0			0
$475$	347.091			0.0335276
$476$		0			0
$477$		0			0
$478$	4296.00	+	7440.89i	0.411076	+	0.712005i
$479$	6669.77	−	11552.4i	0.636221	−	1.10197i	−0.350035	−	0.936737i	$-0.613830\pi$
$479$	6669.77	−	11552.4i	0.636221	−	1.10197i	0.986255	−	0.165229i	$-0.0528365\pi$
$480$		0			0
$481$	−2560.97	−	4435.72i	−0.242765	−	0.420482i
$482$	9043.12			0.854570
$483$		0			0
$484$	−3724.00			−0.349737
$485$	−3080.00	−	5334.72i	−0.288362	−	0.499458i
$486$		0			0
$487$	−6968.00	+	12068.9i	−0.648358	+	1.12299i	0.335157	+	0.942162i	$0.391211\pi$
$487$	−6968.00	+	12068.9i	−0.648358	+	1.12299i	−0.983515	+	0.180826i	$0.942123\pi$
$488$	−1088.18	−	1884.78i	−0.100941	−	0.174836i
$489$		0			0
$490$		0			0
$491$	12276.0			1.12833			0.564163	−	0.825663i	$-0.309199\pi$
$491$	12276.0			1.12833			0.564163	+	0.825663i	$0.309199\pi$
$492$		0			0
$493$	−4671.65	+	8091.54i	−0.426776	+	0.739198i
$494$	616.000	−	1066.94i	0.0561035	−	0.0971742i
$495$		0			0
$496$	3302.05			0.298924
$497$		0			0
$498$		0			0
$499$	1110.00	+	1922.58i	0.0995800	+	0.172478i	0.911511	−	0.411276i	$-0.134917\pi$
$499$	1110.00	+	1922.58i	0.0995800	+	0.172478i	−0.811931	+	0.583754i	$0.801583\pi$
$500$	3039.39	−	5264.38i	0.271851	−	0.470860i
$501$		0			0
$502$	5581.59	+	9667.61i	0.496253	+	0.859535i
$503$	−11294.5			−1.00119			−0.500594	−	0.865682i	$-0.666885\pi$
$503$	−11294.5			−1.00119			−0.500594	+	0.865682i	$0.666885\pi$
$504$		0			0
$505$	1144.00			0.100807
$506$	960.000	+	1662.77i	0.0843423	+	0.146085i
$507$		0			0
$508$	−4624.00	+	8009.00i	−0.403852	+	0.699492i
$509$	7940.87	+	13754.0i	0.691499	+	1.19771i	0.971347	+	0.237667i	$0.0763827\pi$
$509$	7940.87	+	13754.0i	0.691499	+	1.19771i	−0.279848	+	0.960044i	$0.590284\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1500.93	+	2599.69i	−0.128800	+	0.223089i
$515$	−6424.00	+	11126.7i	−0.549661	+	0.952040i
$516$		0			0
$517$	−4127.57			−0.351122
$518$		0			0
$519$		0			0
$520$	−2464.00	−	4267.77i	−0.207795	−	0.359912i
$521$	−5806.73	+	10057.6i	−0.488287	+	0.845738i	−0.999909	−	0.0134723i	$-0.995712\pi$
$521$	−5806.73	+	10057.6i	−0.488287	+	0.845738i	0.511622	+	0.859211i	$0.329045\pi$
$522$		0			0
$523$	6308.61	+	10926.8i	0.527450	+	0.913570i	0.999488	+	0.0319918i	$0.0101850\pi$
$523$	6308.61	+	10926.8i	0.527450	+	0.913570i	−0.472038	+	0.881578i	$0.656482\pi$
$524$	−1013.13			−0.0844633
$525$		0			0
$526$	−800.000			−0.0663149
$527$	−5808.00	−	10059.8i	−0.480077	−	0.831517i
$528$		0			0
$529$	4931.50	−	8541.61i	0.405318	−	0.702031i
$530$	−581.612	−	1007.38i	−0.0476672	−	0.0825619i
$531$		0			0
$532$		0			0
$533$	−25872.0			−2.10252
$534$		0			0
$535$	−1219.51	+	2112.25i	−0.0985494	+	0.170693i
$536$	2320.00	−	4018.36i	0.186957	−	0.323818i
$537$		0			0
$538$	544.088			0.0436009
$539$		0			0
$540$		0			0
$541$	−899.000	−	1557.11i	−0.0714437	−	0.123744i	0.828091	−	0.560594i	$-0.189427\pi$
$541$	−899.000	−	1557.11i	−0.0714437	−	0.123744i	−0.899534	+	0.436850i	$0.856094\pi$
$542$	−6904.29	+	11958.6i	−0.547167	+	0.947722i
$543$		0			0
$544$	900.560	+	1559.82i	0.0709764	+	0.122935i
$545$	17654.7			1.38761
$546$		0			0
$547$	1276.00			0.0997401			0.0498700	−	0.998756i	$-0.484119\pi$
$547$	1276.00			0.0997401			0.0498700	+	0.998756i	$0.484119\pi$
$548$	−2228.00	−	3859.01i	−0.173678	−	0.300819i
$549$		0			0
$550$	740.000	−	1281.72i	0.0573704	−	0.0993684i
$551$	778.609	+	1348.59i	0.0601994	+	0.104268i
$552$		0			0
$553$		0			0
$554$	13540.0			1.03837
$555$		0			0
$556$	2757.96	−	4776.93i	0.210366	−	0.364365i
$557$	1347.00	−	2333.07i	0.102467	−	0.177478i	−0.810233	−	0.586107i	$-0.800660\pi$
$557$	1347.00	−	2333.07i	0.102467	−	0.177478i	0.912701	+	0.408629i	$0.133993\pi$
$558$		0			0
$559$	−28630.3			−2.16625
$560$		0			0
$561$		0			0
$562$	−1878.00	−	3252.79i	−0.140958	−	0.244147i
$563$	7884.59	−	13656.5i	0.590223	−	1.02230i	−0.403979	−	0.914768i	$-0.632373\pi$
$563$	7884.59	−	13656.5i	0.590223	−	1.02230i	0.994202	−	0.107529i	$-0.0342937\pi$
$564$		0			0
$565$	−6031.87	−	10447.5i	−0.449138	−	0.777930i
$566$	769.228			0.0571256
$567$		0			0
$568$	−4352.00			−0.321489
$569$	6303.00	+	10917.1i	0.464386	+	0.804340i	0.999174	−	0.0406466i	$-0.0129418\pi$
$569$	6303.00	+	10917.1i	0.464386	+	0.804340i	−0.534788	+	0.844986i	$0.679608\pi$
$570$		0			0
$571$	−3426.00	+	5934.01i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−3426.00	+	5934.01i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	−2626.63	−	4549.46i	−0.192002	−	0.332557i
$573$		0			0
$574$		0			0
$575$	1776.00			0.128808
$576$		0			0
$577$	7185.72	−	12446.0i	0.518449	−	0.897981i	−0.481321	−	0.876545i	$-0.659843\pi$
$577$	7185.72	−	12446.0i	0.518449	−	0.897981i	0.999770	−	0.0214362i	$-0.00682388\pi$
$578$	−1745.00	+	3022.43i	−0.125575	+	0.217503i
$579$		0			0
$580$	6228.87			0.445931
$581$		0			0
$582$		0			0
$583$	−620.000	−	1073.87i	−0.0440442	−	0.0762868i
$584$	2401.49	−	4159.51i	0.170162	−	0.294729i
$585$		0			0
$586$	−3742.95	−	6482.98i	−0.263857	−	0.457013i
$587$	18977.4			1.33438			0.667191	−	0.744887i	$-0.267497\pi$
$587$	18977.4			1.33438			0.667191	+	0.744887i	$0.267497\pi$
$588$		0			0
$589$	−1936.00			−0.135435
$590$	−6248.00	−	10821.9i	−0.435976	−	0.755133i
$591$		0			0
$592$	624.000	−	1080.80i	0.0433214	−	0.0750348i
$593$	−4108.80	−	7116.66i	−0.284534	−	0.492826i	0.687962	−	0.725746i	$-0.258505\pi$
$593$	−4108.80	−	7116.66i	−0.284534	−	0.492826i	−0.972496	+	0.232920i	$0.925172\pi$
$594$		0			0
$595$		0			0
$596$	3784.00			0.260065
$597$		0			0
$598$	3151.96	−	5459.35i	0.215540	−	0.373327i
$599$	−9552.00	+	16544.5i	−0.651559	+	1.12853i	0.331185	+	0.943566i	$0.392552\pi$
$599$	−9552.00	+	16544.5i	−0.651559	+	1.12853i	−0.982744	+	0.184968i	$0.940782\pi$
$600$		0			0
$601$	−21538.4			−1.46185			−0.730923	−	0.682460i	$-0.760910\pi$
$601$	−21538.4			−1.46185			−0.730923	+	0.682460i	$0.760910\pi$
$602$		0			0
$603$		0			0
$604$	−1664.00	−	2882.13i	−0.112098	−	0.194159i
$605$	4366.78	−	7563.48i	0.293446	−	0.508263i
$606$		0			0
$607$	6866.77	+	11893.6i	0.459166	+	0.795298i	0.998917	−	0.0465262i	$-0.0148151\pi$
$607$	6866.77	+	11893.6i	0.459166	+	0.795298i	−0.539751	+	0.841824i	$0.681482\pi$
$608$	300.187			0.0200233
$609$		0			0
$610$	5104.00			0.338779
$611$	6776.00	+	11736.4i	0.448654	+	0.777092i
$612$		0			0
$613$	−14017.0	+	24278.2i	−0.923558	+	1.59965i	−0.129695	+	0.991554i	$0.541400\pi$
$613$	−14017.0	+	24278.2i	−0.923558	+	1.59965i	−0.793863	+	0.608096i	$0.791934\pi$
$614$	−722.324	−	1251.10i	−0.0474766	−	0.0822319i
$615$		0			0
$616$		0			0
$617$	8258.00			0.538824			0.269412	−	0.963025i	$-0.413171\pi$
$617$	8258.00			0.538824			0.269412	+	0.963025i	$0.413171\pi$
$618$		0			0
$619$	−2565.66	+	4443.85i	−0.166595	+	0.288551i	−0.937221	−	0.348737i	$-0.886611\pi$
$619$	−2565.66	+	4443.85i	−0.166595	+	0.288551i	0.770625	+	0.637288i	$0.219944\pi$
$620$	−3872.00	+	6706.50i	−0.250812	+	0.434419i
$621$		0			0
$622$	−14559.1			−0.938529
$623$		0			0
$624$		0			0
$625$	4815.50	+	8340.69i	0.308192	+	0.533804i
$626$	−1519.69	+	2632.19i	−0.0970275	+	0.168057i
$627$		0			0
$628$	5759.83	+	9976.32i	0.365991	+	0.633915i
$629$	−4390.23			−0.278299
$630$		0			0
$631$	912.000			0.0575375			0.0287687	−	0.999586i	$-0.490841\pi$
$631$	912.000			0.0575375			0.0287687	+	0.999586i	$0.490841\pi$
$632$	−2720.00	−	4711.18i	−0.171196	−	0.296520i
$633$		0			0
$634$	−2358.00	+	4084.18i	−0.147710	+	0.255841i
$635$	−10844.2	−	18782.8i	−0.677702	−	1.17381i
$636$		0			0
$637$		0			0
$638$	6640.00			0.412038
$639$		0			0
$640$	600.373	−	1039.88i	0.0370810	−	0.0642262i
$641$	−445.000	+	770.763i	−0.0274203	+	0.0474934i	−0.879410	−	0.476065i	$-0.842063\pi$
$641$	−445.000	+	770.763i	−0.0274203	+	0.0474934i	0.851990	+	0.523559i	$0.175396\pi$
$642$		0			0
$643$	29352.6			1.80024			0.900120	−	0.435642i	$-0.143479\pi$
$643$	29352.6			1.80024			0.900120	+	0.435642i	$0.143479\pi$
$644$		0			0
$645$		0			0
$646$	−528.000	−	914.523i	−0.0321577	−	0.0556988i
$647$	−5938.07	+	10285.0i	−0.360818	+	0.624956i	−0.988096	−	0.153840i	$-0.950836\pi$
$647$	−5938.07	+	10285.0i	−0.360818	+	0.624956i	0.627277	+	0.778796i	$0.284169\pi$
$648$		0			0
$649$	−6660.39	−	11536.1i	−0.402840	−	0.697739i
$650$	−4859.27			−0.293225
$651$		0			0
$652$	2544.00			0.152808
$653$	−10763.0	−	18642.1i	−0.645006	−	1.11718i	−0.984300	−	0.176502i	$-0.943522\pi$
$653$	−10763.0	−	18642.1i	−0.645006	−	1.11718i	0.339294	−	0.940680i	$-0.389812\pi$
$654$		0			0
$655$	1188.00	−	2057.68i	0.0708687	−	0.122748i
$656$	−3151.96	−	5459.35i	−0.187597	−	0.324927i
$657$		0			0
$658$		0			0
$659$	−23452.0			−1.38628			−0.693141	−	0.720802i	$-0.743774\pi$
$659$	−23452.0			−1.38628			−0.693141	+	0.720802i	$0.743774\pi$
$660$		0			0
$661$	−13334.9	+	23096.6i	−0.784668	+	1.35909i	0.144529	+	0.989501i	$0.453833\pi$
$661$	−13334.9	+	23096.6i	−0.784668	+	1.35909i	−0.929197	+	0.369584i	$0.879500\pi$
$662$	2372.00	−	4108.42i	0.139260	−	0.241206i
$663$		0			0
$664$	−1575.98			−0.0921082
$665$		0			0
$666$		0			0
$667$	3984.00	+	6900.49i	0.231276	+	0.400582i
$668$	1313.32	−	2274.73i	0.0760685	−	0.131754i
$669$		0			0
$670$	5440.88	+	9423.88i	0.313731	+	0.543398i
$671$	5440.88			0.313030
$672$		0			0
$673$	−13858.0			−0.793739			−0.396870	−	0.917875i	$-0.629904\pi$
$673$	−13858.0			−0.793739			−0.396870	+	0.917875i	$0.629904\pi$
$674$	−250.000	−	433.013i	−0.0142873	−	0.0247463i
$675$		0			0
$676$	−4230.00	+	7326.57i	−0.240669	+	0.416851i
$677$	−16224.1	−	28101.0i	−0.921041	−	1.59529i	−0.797808	−	0.602912i	$-0.794007\pi$
$677$	−16224.1	−	28101.0i	−0.921041	−	1.59529i	−0.123233	−	0.992378i	$-0.539326\pi$
$678$		0			0
$679$		0			0
$680$	−4224.00			−0.238210
$681$		0			0
$682$	−4127.57	+	7149.15i	−0.231749	+	0.401401i
$683$	−13906.0	+	24085.9i	−0.779060	+	1.34937i	0.153423	+	0.988161i	$0.450970\pi$
$683$	−13906.0	+	24085.9i	−0.779060	+	1.34937i	−0.932484	+	0.361212i	$0.882363\pi$
$684$		0			0
$685$	10450.2			0.582895
$686$		0			0
$687$		0			0
$688$	−3488.00	−	6041.39i	−0.193283	−	0.334776i
$689$	−2035.64	+	3525.83i	−0.112557	+	0.194954i
$690$		0			0
$691$	−651.968	−	1129.24i	−0.0358929	−	0.0621684i	0.847521	−	0.530762i	$-0.178094\pi$
$691$	−651.968	−	1129.24i	−0.0358929	−	0.0621684i	−0.883414	+	0.468594i	$0.844761\pi$
$692$	2664.16			0.146353
$693$		0			0
$694$	19080.0			1.04361
$695$	6468.00	+	11202.9i	0.353015	+	0.611439i
$696$		0			0
$697$	−11088.0	+	19205.0i	−0.602565	+	1.04367i
$698$	5712.93	+	9895.08i	0.309796	+	0.536582i
$699$		0			0
$700$		0			0
$701$	−22906.0			−1.23416			−0.617081	−	0.786900i	$-0.711685\pi$
$701$	−22906.0			−1.23416			−0.617081	+	0.786900i	$0.711685\pi$
$702$		0			0
$703$	−365.852	+	633.675i	−0.0196279	+	0.0339965i
$704$	640.000	−	1108.51i	0.0342627	−	0.0593447i
$705$		0			0
$706$	−8780.46			−0.468069
$707$		0			0
$708$		0			0
$709$	7543.00	+	13064.9i	0.399553	+	0.692047i	0.993671	−	0.112332i	$-0.0358319\pi$
$709$	7543.00	+	13064.9i	0.399553	+	0.692047i	−0.594117	+	0.804378i	$0.702499\pi$
$710$	5103.17	−	8838.95i	0.269745	−	0.467211i
$711$		0			0
$712$	−6003.73	−	10398.8i	−0.316010	−	0.547346i
$713$	−9906.16			−0.520321
$714$		0			0
$715$	12320.0			0.644394
$716$	−6456.00	−	11182.1i	−0.336972	−	0.583653i
$717$		0			0
$718$	−1840.00	+	3186.97i	−0.0956381	+	0.165650i
$719$	10272.0	+	17791.6i	0.532797	+	0.922832i	0.999266	+	0.0382947i	$0.0121926\pi$
$719$	10272.0	+	17791.6i	0.532797	+	0.922832i	−0.466469	+	0.884538i	$0.654474\pi$
$720$		0			0
$721$		0			0
$722$	13542.0			0.698035
$723$		0			0
$724$	−5647.26	+	9781.34i	−0.289888	+	0.502100i
$725$	3071.00	−	5319.13i	0.157316	−	0.272479i
$726$		0			0
$727$	7223.24			0.368494			0.184247	−	0.982880i	$-0.441015\pi$
$727$	7223.24			0.368494			0.184247	+	0.982880i	$0.441015\pi$
$728$		0			0
$729$		0			0
$730$	5632.00	+	9754.91i	0.285547	+	0.494583i
$731$	−12270.1	+	21252.5i	−0.620830	+	1.07531i
$732$		0			0
$733$	14713.8	+	25485.1i	0.741430	+	1.28419i	0.951844	+	0.306581i	$0.0991852\pi$
$733$	14713.8	+	25485.1i	0.741430	+	1.28419i	−0.210415	+	0.977612i	$0.567481\pi$
$734$	−5928.69			−0.298136
$735$		0			0
$736$	1536.00			0.0769262
$737$	5800.00	+	10045.9i	0.289886	+	0.502097i
$738$		0			0
$739$	−16334.0	+	28291.3i	−0.813066	+	1.40827i	0.0976420	+	0.995222i	$0.468870\pi$
$739$	−16334.0	+	28291.3i	−0.813066	+	1.40827i	−0.910708	+	0.413050i	$0.864463\pi$
$740$	1463.41	+	2534.70i	0.0726973	+	0.125915i
$741$		0			0
$742$		0			0
$743$	37056.0			1.82968			0.914840	−	0.403816i	$-0.132316\pi$
$743$	37056.0			1.82968			0.914840	+	0.403816i	$0.132316\pi$
$744$		0			0
$745$	−4437.13	+	7685.34i	−0.218207	+	0.377945i
$746$	3982.00	−	6897.03i	0.195431	−	0.338496i
$747$		0			0
$748$	−4502.80			−0.220105
$749$		0			0
$750$		0			0
$751$	9804.00	+	16981.0i	0.476369	+	0.825095i	0.999633	−	0.0270752i	$-0.00861935\pi$
$751$	9804.00	+	16981.0i	0.476369	+	0.825095i	−0.523265	+	0.852170i	$0.675286\pi$
$752$	−1651.03	+	2859.66i	−0.0800621	+	0.138672i
$753$		0			0
$754$	−10900.5	−	18880.3i	−0.526490	−	0.911908i
$755$	7804.85			0.376222
$756$		0			0
$757$	19378.0			0.930390			0.465195	−	0.885208i	$-0.345984\pi$
$757$	19378.0			0.930390			0.465195	+	0.885208i	$0.345984\pi$
$758$	2676.00	+	4634.97i	0.128228	+	0.222097i
$759$		0			0
$760$	−352.000	+	609.682i	−0.0168005	+	0.0290993i
$761$	6988.72	+	12104.8i	0.332905	+	0.576609i	0.983080	−	0.183176i	$-0.0586377\pi$
$761$	6988.72	+	12104.8i	0.332905	+	0.576609i	−0.650175	+	0.759785i	$0.725304\pi$
$762$		0			0
$763$		0			0
$764$	8544.00			0.404596
$765$		0			0
$766$	7035.62	−	12186.1i	0.331863	−	0.574804i
$767$	−21868.0	+	37876.5i	−1.02948	+	1.78310i
$768$		0			0
$769$	−8536.56			−0.400307			−0.200154	−	0.979765i	$-0.564144\pi$
$769$	−8536.56			−0.400307			−0.200154	+	0.979765i	$0.564144\pi$
$770$		0			0
$771$		0			0
$772$	−3316.00	−	5743.48i	−0.154593	−	0.267762i
$773$	14648.2	−	25371.4i	0.681576	−	1.18052i	−0.292924	−	0.956136i	$-0.594628\pi$
$773$	14648.2	−	25371.4i	0.681576	−	1.18052i	0.974500	−	0.224388i	$-0.0720383\pi$
$774$		0			0
$775$	3818.00	+	6612.97i	0.176963	+	0.306509i
$776$	−5253.27			−0.243017
$777$		0			0
$778$	17316.0			0.797955
$779$	1848.00	+	3200.83i	0.0849955	+	0.147216i
$780$		0			0
$781$	5440.00	−	9422.36i	0.249243	−	0.431701i
$782$	−2701.68	−	4679.45i	−0.123545	−	0.213985i
$783$		0			0
$784$		0			0
$785$	−27016.0			−1.22833
$786$		0			0
$787$	6890.22	−	11934.2i	0.312084	−	0.540545i	−0.666730	−	0.745300i	$-0.732306\pi$
$787$	6890.22	−	11934.2i	0.312084	−	0.540545i	0.978813	+	0.204755i	$0.0656397\pi$
$788$	−1956.00	+	3387.89i	−0.0884259	+	0.153158i
$789$		0			0
$790$	12757.9			0.574566
$791$		0			0
$792$		0			0
$793$	−8932.00	−	15470.7i	−0.399981	−	0.692787i
$794$	9052.50	−	15679.4i	0.404611	−	0.700807i
$795$		0			0
$796$	−9868.63	−	17093.0i	−0.439428	−	0.761111i
$797$	−34868.6			−1.54970			−0.774848	−	0.632148i	$-0.782174\pi$
$797$	−34868.6			−1.54970			−0.774848	+	0.632148i	$0.782174\pi$
$798$		0			0
$799$	11616.0			0.514324
$800$	−592.000	−	1025.37i	−0.0261630	−	0.0453156i
$801$		0			0
$802$	5706.00	−	9883.08i	0.251229	−	0.435142i
$803$	6003.73	+	10398.8i	0.263844	+	0.456992i
$804$		0			0
$805$		0			0
$806$	27104.0			1.18449
$807$		0			0
$808$	487.803	−	844.900i	0.0212387	−	0.0367865i
$809$	7017.00	−	12153.8i	0.304950	−	0.528189i	−0.672300	−	0.740279i	$-0.734694\pi$
$809$	7017.00	−	12153.8i	0.304950	−	0.528189i	0.977250	+	0.212090i	$0.0680269\pi$
$810$		0			0
$811$	6632.25			0.287164			0.143582	−	0.989638i	$-0.454138\pi$
$811$	6632.25			0.287164			0.143582	+	0.989638i	$0.454138\pi$
$812$		0			0
$813$		0			0
$814$	1560.00	+	2702.00i	0.0671720	+	0.116345i
$815$	−2983.10	+	5166.89i	−0.128213	+	0.222071i
$816$		0			0
$817$	2045.02	+	3542.08i	0.0875719	+	0.151679i
$818$	4840.51			0.206900
$819$		0			0
$820$	14784.0			0.629609
$821$	14311.0	+	24787.4i	0.608352	+	1.05370i	0.991512	+	0.130015i	$0.0415026\pi$
$821$	14311.0	+	24787.4i	0.608352	+	1.05370i	−0.383160	+	0.923682i	$0.625164\pi$
$822$		0			0
$823$	−12344.0	+	21380.4i	−0.522825	+	0.905559i	0.476822	+	0.879000i	$0.341788\pi$
$823$	−12344.0	+	21380.4i	−0.522825	+	0.905559i	−0.999647	+	0.0265595i	$0.991545\pi$
$824$	5478.41	+	9488.88i	0.231613	+	0.401166i
$825$		0			0
$826$		0			0
$827$	30756.0			1.29322			0.646609	−	0.762822i	$-0.276187\pi$
$827$	30756.0			1.29322			0.646609	+	0.762822i	$0.276187\pi$
$828$		0			0
$829$	11618.2	−	20123.2i	0.486750	−	0.843075i	−0.513134	−	0.858308i	$-0.671516\pi$
$829$	11618.2	−	20123.2i	0.486750	−	0.843075i	0.999884	+	0.0152333i	$0.00484910\pi$
$830$	1848.00	−	3200.83i	0.0772832	−	0.133858i
$831$		0			0
$832$	−4202.61			−0.175119
$833$		0			0
$834$		0			0
$835$	3080.00	+	5334.72i	0.127650	+	0.221096i
$836$	−375.233	+	649.923i	−0.0155236	+	0.0268876i
$837$		0			0
$838$	−1510.31	−	2615.94i	−0.0622589	−	0.107836i
$839$	−24033.7			−0.988957			−0.494479	−	0.869190i	$-0.664641\pi$
$839$	−24033.7			−0.988957			−0.494479	+	0.869190i	$0.664641\pi$
$840$		0			0
$841$	3167.00			0.129854
$842$	−16770.0	−	29046.5i	−0.686380	−	1.18885i
$843$		0			0
$844$	−3112.00	+	5390.14i	−0.126919	+	0.219830i
$845$	−9920.23	−	17182.3i	−0.403865	−	0.699515i
$846$		0			0
$847$		0			0
$848$	−992.000			−0.0401715
$849$		0			0
$850$	−2082.54	+	3607.07i	−0.0840361	+	0.145555i
$851$	−1872.00	+	3242.40i	−0.0754070	+	0.130609i
$852$		0			0
$853$	23574.0			0.946260			0.473130	−	0.880993i	$-0.343124\pi$
$853$	23574.0			0.946260			0.473130	+	0.880993i	$0.343124\pi$
$854$		0			0
$855$		0			0
$856$	1040.00	+	1801.33i	0.0415262	+	0.0719256i
$857$	−12242.0	+	21203.7i	−0.487956	+	0.845164i	−0.999904	−	0.0138519i	$-0.995591\pi$
$857$	−12242.0	+	21203.7i	−0.487956	+	0.845164i	0.511948	+	0.859016i	$0.328924\pi$
$858$		0			0
$859$	−16477.4	−	28539.7i	−0.654485	−	1.13360i	−0.982023	−	0.188763i	$-0.939552\pi$
$859$	−16477.4	−	28539.7i	−0.654485	−	1.13360i	0.327538	−	0.944838i	$-0.393781\pi$
$860$	16360.2			0.648694
$861$		0			0
$862$	2672.00			0.105579
$863$	20436.0	+	35396.2i	0.806083	+	1.39618i	0.915558	+	0.402187i	$0.131750\pi$
$863$	20436.0	+	35396.2i	0.806083	+	1.39618i	−0.109475	+	0.993990i	$0.534917\pi$
$864$		0			0
$865$	−3124.00	+	5410.93i	−0.122797	+	0.212690i
$866$	11163.2	+	19335.2i	0.438038	+	0.758703i
$867$		0			0
$868$		0			0
$869$	13600.0			0.530896
$870$		0			0
$871$	19043.1	−	32983.6i	0.740816	−	1.28313i
$872$	7528.00	−	13038.9i	0.292351	−	0.506367i
$873$		0			0
$874$	−900.560			−0.0348534
$875$		0			0
$876$		0			0
$877$	6003.00	+	10397.5i	0.231137	+	0.400341i	0.958143	−	0.286290i	$-0.0924222\pi$
$877$	6003.00	+	10397.5i	0.231137	+	0.400341i	−0.727006	+	0.686631i	$0.759089\pi$
$878$	3602.24	−	6239.26i	0.138462	−	0.239823i
$879$		0			0
$880$	1500.93	+	2599.69i	0.0574960	+	0.0995859i
$881$	35722.2			1.36607			0.683037	−	0.730383i	$-0.260659\pi$
$881$	35722.2			1.36607			0.683037	+	0.730383i	$0.260659\pi$
$882$		0			0
$883$	19588.0			0.746533			0.373267	−	0.927724i	$-0.378238\pi$
$883$	19588.0			0.746533			0.373267	+	0.927724i	$0.378238\pi$
$884$	7392.00	+	12803.3i	0.281244	+	0.487129i
$885$		0			0
$886$	−6348.00	+	10995.1i	−0.240706	+	0.416914i
$887$	20121.9	+	34852.1i	0.761699	+	1.31930i	0.941974	+	0.335685i	$0.108968\pi$
$887$	20121.9	+	34852.1i	0.761699	+	1.31930i	−0.180276	+	0.983616i	$0.557699\pi$
$888$		0			0
$889$		0			0
$890$	28160.0			1.06059
$891$		0			0
$892$	5778.59	−	10008.8i	0.216908	−	0.375695i
$893$	968.000	−	1676.63i	0.0362742	−	0.0628288i
$894$		0			0
$895$	30281.3			1.13094
$896$		0			0
$897$		0			0
$898$	−7170.00	−	12418.8i	−0.266443	−	0.461493i
$899$	−17129.4	+	29669.0i	−0.635481	+	1.10069i
$900$		0			0
$901$	1744.83	+	3022.14i	0.0645159	+	0.111745i
$902$	15759.8			0.581756
$903$		0			0
$904$	−10288.0			−0.378511
$905$	−13244.0	−	22939.3i	−0.486459	−	0.842572i
$906$		0			0
$907$	−7934.00	+	13742.1i	−0.290457	+	0.503086i	−0.973918	−	0.226901i	$-0.927141\pi$
$907$	−7934.00	+	13742.1i	−0.290457	+	0.503086i	0.683461	+	0.729987i	$0.260474\pi$
$908$	3958.71	+	6856.69i	0.144686	+	0.250603i
$909$		0			0
$910$		0			0
$911$	−39832.0			−1.44862			−0.724310	−	0.689474i	$-0.757842\pi$
$911$	−39832.0			−1.44862			−0.724310	+	0.689474i	$0.757842\pi$
$912$		0			0
$913$	1969.97	−	3412.10i	0.0714092	−	0.123684i
$914$	6866.00	−	11892.3i	0.248476	−	0.430373i
$915$		0			0
$916$	−11069.4			−0.399282
$917$		0			0
$918$		0			0
$919$	15264.0	+	26438.0i	0.547892	+	0.948977i	0.998419	+	0.0562141i	$0.0179029\pi$
$919$	15264.0	+	26438.0i	0.547892	+	0.948977i	−0.450527	+	0.892763i	$0.648764\pi$
$920$	−1801.12	+	3119.63i	−0.0645447	+	0.111795i
$921$		0			0
$922$	1378.98	+	2388.47i	0.0492564	+	0.0853145i
$923$	−35722.2			−1.27390
$924$		0			0
$925$	2886.00			0.102585
$926$	2648.00	+	4586.47i	0.0939727	+	0.162765i
$927$		0			0
$928$	2656.00	−	4600.33i	0.0939520	−	0.162730i
$929$	8302.04	+	14379.5i	0.293198	+	0.507834i	0.974564	−	0.224109i	$-0.0719471\pi$
$929$	8302.04	+	14379.5i	0.293198	+	0.507834i	−0.681366	+	0.731943i	$0.738614\pi$
$930$		0			0
$931$		0			0
$932$	25960.0			0.912391
$933$		0			0
$934$	−12335.8	+	21366.2i	−0.432162	+	0.748527i
$935$	5280.00	−	9145.23i	0.184679	−	0.319873i
$936$		0			0
$937$	−29943.6			−1.04399			−0.521993	−	0.852950i	$-0.674811\pi$
$937$	−29943.6			−1.04399			−0.521993	+	0.852950i	$0.674811\pi$
$938$		0			0
$939$		0			0
$940$	−3872.00	−	6706.50i	−0.134352	−	0.232704i
$941$	−2687.61	+	4655.07i	−0.0931068	+	0.161266i	−0.908817	−	0.417195i	$-0.863013\pi$
$941$	−2687.61	+	4655.07i	−0.0931068	+	0.161266i	0.815710	+	0.578461i	$0.196346\pi$
$942$		0			0
$943$	9455.88	+	16378.1i	0.326538	+	0.565581i
$944$	−10656.6			−0.367419
$945$		0			0
$946$	17440.0			0.599390
$947$	22606.0	+	39154.7i	0.775709	+	1.34357i	0.934395	+	0.356238i	$0.115941\pi$
$947$	22606.0	+	39154.7i	0.775709	+	1.34357i	−0.158686	+	0.987329i	$0.550726\pi$
$948$		0			0
$949$	19712.0	−	34142.2i	0.674266	−	1.16786i
$950$	347.091	+	601.179i	0.0118538	+	0.0205314i
$951$		0			0
$952$		0			0
$953$	−34218.0			−1.16310			−0.581548	−	0.813512i	$-0.697553\pi$
$953$	−34218.0			−1.16310			−0.581548	+	0.813512i	$0.697553\pi$
$954$		0			0
$955$	−10018.7	+	17352.9i	−0.339475	+	0.587988i
$956$	−8592.00	+	14881.8i	−0.290675	+	0.503464i
$957$		0			0
$958$	26679.1			0.899752
$959$		0			0
$960$		0			0
$961$	−6400.50	−	11086.0i	−0.214847	−	0.372126i
$962$	5121.93	−	8871.45i	0.171661	−	0.297325i
$963$		0			0
$964$	9043.12	+	15663.1i	0.302136	+	0.523315i
$965$	15553.4			0.518842
$966$		0			0
$967$	14464.0			0.481004			0.240502	−	0.970649i	$-0.422688\pi$
$967$	14464.0			0.481004			0.240502	+	0.970649i	$0.422688\pi$
$968$	−3724.00	−	6450.16i	−0.123651	−	0.214169i
$969$		0			0
$970$	6160.00	−	10669.4i	0.203903	−	0.353170i
$971$	−18916.4	−	32764.2i	−0.625188	−	1.08286i	−0.988504	−	0.151192i	$-0.951689\pi$
$971$	−18916.4	−	32764.2i	−0.625188	−	1.08286i	0.363316	−	0.931666i	$-0.381644\pi$
$972$		0			0
$973$		0			0
$974$	−27872.0			−0.916916
$975$		0			0
$976$	2176.35	−	3769.55i	0.0713764	−	0.123628i
$977$	21031.0	−	36426.8i	0.688681	−	1.19283i	−0.283584	−	0.958947i	$-0.591523\pi$
$977$	21031.0	−	36426.8i	0.688681	−	1.19283i	0.972265	−	0.233883i	$-0.0751433\pi$
$978$		0			0
$979$	30018.7			0.979980
$980$		0			0
$981$		0			0
$982$	12276.0	+	21262.7i	0.398924	+	0.690956i
$983$	21510.2	−	37256.8i	0.697935	−	1.20886i	−0.271246	−	0.962510i	$-0.587436\pi$
$983$	21510.2	−	37256.8i	0.697935	−	1.20886i	0.969181	−	0.246349i	$-0.0792310\pi$
$984$		0			0
$985$	−4587.23	−	7945.31i	−0.148387	−	0.257014i
$986$	−18686.6			−0.603553
$987$		0			0
$988$	2464.00			0.0793424
$989$	10464.0	+	18124.2i	0.336437	+	0.582725i
$990$		0			0
$991$	−10636.0	+	18422.1i	−0.340932	+	0.590512i	−0.984606	−	0.174788i	$-0.944076\pi$
$991$	−10636.0	+	18422.1i	−0.340932	+	0.590512i	0.643674	+	0.765300i	$0.277409\pi$
$992$	3302.05	+	5719.32i	0.105686	+	0.183053i
$993$		0			0
$994$		0			0
$995$	46288.0			1.47480
$996$		0			0
$997$	60.9754	−	105.612i	0.00193692	−	0.00335485i	−0.865055	−	0.501676i	$-0.832717\pi$
$997$	60.9754	−	105.612i	0.00193692	−	0.00335485i	0.866992	+	0.498322i	$0.166050\pi$
$998$	−2220.00	+	3845.15i	−0.0704137	+	0.121960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bi.361.1		4
3.2	odd	2		98.4.c.g.67.1		4
7.2	even	3	inner	882.4.g.bi.667.1		4
7.3	odd	6		882.4.a.w.1.1		2
7.4	even	3		882.4.a.w.1.2		2
7.5	odd	6	inner	882.4.g.bi.667.2		4
7.6	odd	2	inner	882.4.g.bi.361.2		4
21.2	odd	6		98.4.c.g.79.1		4
21.5	even	6		98.4.c.g.79.2		4
21.11	odd	6		98.4.a.h.1.2	yes	2
21.17	even	6		98.4.a.h.1.1	✓	2
21.20	even	2		98.4.c.g.67.2		4
84.11	even	6		784.4.a.z.1.1		2
84.59	odd	6		784.4.a.z.1.2		2
105.59	even	6		2450.4.a.bs.1.2		2
105.74	odd	6		2450.4.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.4.a.h.1.1	✓	2	21.17	even	6
98.4.a.h.1.2	yes	2	21.11	odd	6
98.4.c.g.67.1		4	3.2	odd	2
98.4.c.g.67.2		4	21.20	even	2
98.4.c.g.79.1		4	21.2	odd	6
98.4.c.g.79.2		4	21.5	even	6
784.4.a.z.1.1		2	84.11	even	6
784.4.a.z.1.2		2	84.59	odd	6
882.4.a.w.1.1		2	7.3	odd	6
882.4.a.w.1.2		2	7.4	even	3
882.4.g.bi.361.1		4	1.1	even	1	trivial
882.4.g.bi.361.2		4	7.6	odd	2	inner
882.4.g.bi.667.1		4	7.2	even	3	inner
882.4.g.bi.667.2		4	7.5	odd	6	inner
2450.4.a.bs.1.1		2	105.74	odd	6
2450.4.a.bs.1.2		2	105.59	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +(9.38083 - 16.2481i) q^{10} +(10.0000 - 17.3205i) q^{11} -65.6658 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-28.1425 + 48.7442i) q^{17} +(4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(24.0000 + 41.5692i) q^{23} +(18.5000 - 32.0429i) q^{25} +(-65.6658 - 113.737i) q^{26} +166.000 q^{29} +(-103.189 + 178.729i) q^{31} +(16.0000 - 27.7128i) q^{32} -112.570 q^{34} +(39.0000 + 67.5500i) q^{37} +(-9.38083 + 16.2481i) q^{38} +(37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(40.0000 + 69.2820i) q^{44} +(-48.0000 + 83.1384i) q^{46} +(-103.189 - 178.729i) q^{47} +74.0000 q^{50} +(131.332 - 227.473i) q^{52} +(31.0000 - 53.6936i) q^{53} -187.617 q^{55} +(166.000 + 287.520i) q^{58} +(333.020 - 576.807i) q^{59} +(136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(308.000 + 533.472i) q^{65} +(-290.000 + 502.295i) q^{67} +(-112.570 - 194.977i) q^{68} +544.000 q^{71} +(-300.187 + 519.938i) q^{73} +(-78.0000 + 135.100i) q^{74} -37.5233 q^{76} +(340.000 + 588.897i) q^{79} +(-75.0467 + 129.985i) q^{80} +(393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(436.000 + 755.174i) q^{86} +(-80.0000 + 138.564i) q^{88} +(750.467 + 1299.85i) q^{89} -192.000 q^{92} +(206.378 - 357.458i) q^{94} +(44.0000 - 76.2102i) q^{95} +656.658 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 40 q^{11} - 32 q^{16} + 160 q^{22} + 96 q^{23} + 74 q^{25} + 664 q^{29} + 64 q^{32} + 156 q^{37} + 1744 q^{43} + 160 q^{44} - 192 q^{46} + 296 q^{50} + 124 q^{53} + 664 q^{58} + 256 q^{64} + 1232 q^{65} - 1160 q^{67} + 2176 q^{71} - 312 q^{74} + 1360 q^{79} + 2112 q^{85} + 1744 q^{86} - 320 q^{88} - 768 q^{92} + 176 q^{95}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 40 * q^11 - 32 * q^16 + 160 * q^22 + 96 * q^23 + 74 * q^25 + 664 * q^29 + 64 * q^32 + 156 * q^37 + 1744 * q^43 + 160 * q^44 - 192 * q^46 + 296 * q^50 + 124 * q^53 + 664 * q^58 + 256 * q^64 + 1232 * q^65 - 1160 * q^67 + 2176 * q^71 - 312 * q^74 + 1360 * q^79 + 2112 * q^85 + 1744 * q^86 - 320 * q^88 - 768 * q^92 + 176 * q^95

Introduction

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