LMFDB - Embedded newform 441.4.e.n.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (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:	$26.0198423125$
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 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.n.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +(-8.00000 - 13.8564i) q^{10} +(31.0000 + 53.6936i) q^{11} +62.0000 q^{13} +(32.0000 - 55.4256i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(50.0000 - 86.6025i) q^{19} -32.0000 q^{20} +248.000 q^{22} +(-21.0000 + 36.3731i) q^{23} +(54.5000 + 94.3968i) q^{25} +(124.000 - 214.774i) q^{26} +10.0000 q^{29} +(-24.0000 - 41.5692i) q^{31} +(-128.000 - 221.703i) q^{32} -336.000 q^{34} +(123.000 - 213.042i) q^{37} +(-200.000 - 346.410i) q^{38} -248.000 q^{41} +68.0000 q^{43} +(248.000 - 429.549i) q^{44} +(84.0000 + 145.492i) q^{46} +(-162.000 + 280.592i) q^{47} +436.000 q^{50} +(-248.000 - 429.549i) q^{52} +(129.000 + 223.435i) q^{53} +248.000 q^{55} +(20.0000 - 34.6410i) q^{58} +(-60.0000 - 103.923i) q^{59} +(311.000 - 538.668i) q^{61} -192.000 q^{62} -512.000 q^{64} +(124.000 - 214.774i) q^{65} +(-452.000 - 782.887i) q^{67} +(-336.000 + 581.969i) q^{68} +678.000 q^{71} +(-321.000 - 555.988i) q^{73} +(-492.000 - 852.169i) q^{74} -800.000 q^{76} +(-370.000 + 640.859i) q^{79} +(-128.000 - 221.703i) q^{80} +(-496.000 + 859.097i) q^{82} +468.000 q^{83} -336.000 q^{85} +(136.000 - 235.559i) q^{86} +(-100.000 + 173.205i) q^{89} +336.000 q^{92} +(648.000 + 1122.37i) q^{94} +(-200.000 - 346.410i) q^{95} +1266.00 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 8 q^{4} + 4 q^{5}+O(q^{10}) $ 2 * q + 4 * q^2 - 8 * q^4 + 4 * q^5	$ 2 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 16 q^{10} + 62 q^{11} + 124 q^{13} + 64 q^{16} - 84 q^{17} + 100 q^{19} - 64 q^{20} + 496 q^{22} - 42 q^{23} + 109 q^{25} + 248 q^{26} + 20 q^{29} - 48 q^{31} - 256 q^{32} - 672 q^{34} + 246 q^{37} - 400 q^{38} - 496 q^{41} + 136 q^{43} + 496 q^{44} + 168 q^{46} - 324 q^{47} + 872 q^{50} - 496 q^{52} + 258 q^{53} + 496 q^{55} + 40 q^{58} - 120 q^{59} + 622 q^{61} - 384 q^{62} - 1024 q^{64} + 248 q^{65} - 904 q^{67} - 672 q^{68} + 1356 q^{71} - 642 q^{73} - 984 q^{74} - 1600 q^{76} - 740 q^{79} - 256 q^{80} - 992 q^{82} + 936 q^{83} - 672 q^{85} + 272 q^{86} - 200 q^{89} + 672 q^{92} + 1296 q^{94} - 400 q^{95} + 2532 q^{97}+O(q^{100}) $ 2 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 16 * q^10 + 62 * q^11 + 124 * q^13 + 64 * q^16 - 84 * q^17 + 100 * q^19 - 64 * q^20 + 496 * q^22 - 42 * q^23 + 109 * q^25 + 248 * q^26 + 20 * q^29 - 48 * q^31 - 256 * q^32 - 672 * q^34 + 246 * q^37 - 400 * q^38 - 496 * q^41 + 136 * q^43 + 496 * q^44 + 168 * q^46 - 324 * q^47 + 872 * q^50 - 496 * q^52 + 258 * q^53 + 496 * q^55 + 40 * q^58 - 120 * q^59 + 622 * q^61 - 384 * q^62 - 1024 * q^64 + 248 * q^65 - 904 * q^67 - 672 * q^68 + 1356 * q^71 - 642 * q^73 - 984 * q^74 - 1600 * q^76 - 740 * q^79 - 256 * q^80 - 992 * q^82 + 936 * q^83 - 672 * q^85 + 272 * q^86 - 200 * q^89 + 672 * q^92 + 1296 * q^94 - 400 * q^95 + 2532 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$		0			0
$3$		0			0
$4$	−4.00000	−	6.92820i	−0.500000	−	0.866025i
$5$	2.00000	−	3.46410i	0.178885	−	0.309839i	−0.762614	−	0.646854i	$-0.776084\pi$
$5$	2.00000	−	3.46410i	0.178885	−	0.309839i	0.941499	+	0.337016i	$0.109418\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$	−8.00000	−	13.8564i	−0.252982	−	0.438178i
$11$	31.0000	+	53.6936i	0.849714	+	1.47175i	0.881464	+	0.472252i	$0.156559\pi$
$11$	31.0000	+	53.6936i	0.849714	+	1.47175i	−0.0317500	+	0.999496i	$0.510108\pi$
$12$		0			0
$13$	62.0000			1.32275			0.661373	−	0.750057i	$-0.269974\pi$
$13$	62.0000			1.32275			0.661373	+	0.750057i	$0.269974\pi$
$14$		0			0
$15$		0			0
$16$	32.0000	−	55.4256i	0.500000	−	0.866025i
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	−0.992939	−	0.118630i	$-0.962150\pi$
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	0.393733	−	0.919225i	$-0.371183\pi$
$18$		0			0
$19$	50.0000	−	86.6025i	0.603726	−	1.04568i	−0.388526	−	0.921438i	$-0.627016\pi$
$19$	50.0000	−	86.6025i	0.603726	−	1.04568i	0.992251	−	0.124246i	$-0.0396511\pi$
$20$	−32.0000			−0.357771
$21$		0			0
$22$	248.000			2.40335
$23$	−21.0000	+	36.3731i	−0.190383	+	0.329753i	−0.945377	−	0.325979i	$-0.894306\pi$
$23$	−21.0000	+	36.3731i	−0.190383	+	0.329753i	0.754994	+	0.655731i	$0.227640\pi$
$24$		0			0
$25$	54.5000	+	94.3968i	0.436000	+	0.755174i
$26$	124.000	−	214.774i	0.935323	−	1.62003i
$27$		0			0
$28$		0			0
$29$	10.0000			0.0640329			0.0320164	−	0.999487i	$-0.489807\pi$
$29$	10.0000			0.0640329			0.0320164	+	0.999487i	$0.489807\pi$
$30$		0			0
$31$	−24.0000	−	41.5692i	−0.139049	−	0.240840i	0.788088	−	0.615563i	$-0.211071\pi$
$31$	−24.0000	−	41.5692i	−0.139049	−	0.240840i	−0.927137	+	0.374723i	$0.877738\pi$
$32$	−128.000	−	221.703i	−0.707107	−	1.22474i
$33$		0			0
$34$	−336.000			−1.69481
$35$		0			0
$36$		0			0
$37$	123.000	−	213.042i	0.546516	−	0.946593i	−0.451994	−	0.892021i	$-0.649287\pi$
$37$	123.000	−	213.042i	0.546516	−	0.946593i	0.998510	−	0.0545719i	$-0.0173794\pi$
$38$	−200.000	−	346.410i	−0.853797	−	1.47882i
$39$		0			0
$40$		0			0
$41$	−248.000			−0.944661			−0.472330	−	0.881422i	$-0.656587\pi$
$41$	−248.000			−0.944661			−0.472330	+	0.881422i	$0.656587\pi$
$42$		0			0
$43$	68.0000			0.241161			0.120580	−	0.992704i	$-0.461524\pi$
$43$	68.0000			0.241161			0.120580	+	0.992704i	$0.461524\pi$
$44$	248.000	−	429.549i	0.849714	−	1.47175i
$45$		0			0
$46$	84.0000	+	145.492i	0.269242	+	0.466341i
$47$	−162.000	+	280.592i	−0.502769	+	0.870821i	0.497226	+	0.867621i	$0.334352\pi$
$47$	−162.000	+	280.592i	−0.502769	+	0.870821i	−0.999995	+	0.00319997i	$0.998981\pi$
$48$		0			0
$49$		0			0
$50$	436.000			1.23319
$51$		0			0
$52$	−248.000	−	429.549i	−0.661373	−	1.14553i
$53$	129.000	+	223.435i	0.334330	+	0.579077i	0.983356	−	0.181689i	$-0.0581565\pi$
$53$	129.000	+	223.435i	0.334330	+	0.579077i	−0.649026	+	0.760767i	$0.724823\pi$
$54$		0			0
$55$	248.000			0.608006
$56$		0			0
$57$		0			0
$58$	20.0000	−	34.6410i	0.0452781	−	0.0784239i
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	0.792204	−	0.610256i	$-0.208934\pi$
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	−0.924600	+	0.380941i	$0.875600\pi$
$60$		0			0
$61$	311.000	−	538.668i	0.652778	−	1.13064i	−0.329668	−	0.944097i	$-0.606937\pi$
$61$	311.000	−	538.668i	0.652778	−	1.13064i	0.982446	−	0.186548i	$-0.0597300\pi$
$62$	−192.000			−0.393291
$63$		0			0
$64$	−512.000			−1.00000
$65$	124.000	−	214.774i	0.236620	−	0.409838i
$66$		0			0
$67$	−452.000	−	782.887i	−0.824188	−	1.42754i	−0.902538	−	0.430609i	$-0.858299\pi$
$67$	−452.000	−	782.887i	−0.824188	−	1.42754i	0.0783505	−	0.996926i	$-0.475035\pi$
$68$	−336.000	+	581.969i	−0.599206	+	1.03785i
$69$		0			0
$70$		0			0
$71$	678.000			1.13329			0.566646	−	0.823961i	$-0.308241\pi$
$71$	678.000			1.13329			0.566646	+	0.823961i	$0.308241\pi$
$72$		0			0
$73$	−321.000	−	555.988i	−0.514660	−	0.891418i	−0.999855	−	0.0170119i	$-0.994585\pi$
$73$	−321.000	−	555.988i	−0.514660	−	0.891418i	0.485195	−	0.874406i	$-0.338749\pi$
$74$	−492.000	−	852.169i	−0.772890	−	1.33868i
$75$		0			0
$76$	−800.000			−1.20745
$77$		0			0
$78$		0			0
$79$	−370.000	+	640.859i	−0.526940	+	0.912687i	0.472567	+	0.881295i	$0.343327\pi$
$79$	−370.000	+	640.859i	−0.526940	+	0.912687i	−0.999507	+	0.0313921i	$0.990006\pi$
$80$	−128.000	−	221.703i	−0.178885	−	0.309839i
$81$		0			0
$82$	−496.000	+	859.097i	−0.667976	+	1.15697i
$83$	468.000			0.618912			0.309456	−	0.950914i	$-0.399853\pi$
$83$	468.000			0.618912			0.309456	+	0.950914i	$0.399853\pi$
$84$		0			0
$85$	−336.000			−0.428757
$86$	136.000	−	235.559i	0.170526	−	0.295360i
$87$		0			0
$88$		0			0
$89$	−100.000	+	173.205i	−0.119101	+	0.206289i	−0.919412	−	0.393297i	$-0.871335\pi$
$89$	−100.000	+	173.205i	−0.119101	+	0.206289i	0.800311	+	0.599585i	$0.204668\pi$
$90$		0			0
$91$		0			0
$92$	336.000			0.380765
$93$		0			0
$94$	648.000	+	1122.37i	0.711022	+	1.23153i
$95$	−200.000	−	346.410i	−0.215995	−	0.374115i
$96$		0			0
$97$	1266.00			1.32518			0.662592	−	0.748981i	$-0.269456\pi$
$97$	1266.00			1.32518			0.662592	+	0.748981i	$0.269456\pi$
$98$		0			0
$99$		0			0
$100$	436.000	−	755.174i	0.436000	−	0.755174i
$101$	−116.000	−	200.918i	−0.114281	−	0.197941i	0.803211	−	0.595695i	$-0.203123\pi$
$101$	−116.000	−	200.918i	−0.114281	−	0.197941i	−0.917492	+	0.397754i	$0.869790\pi$
$102$		0			0
$103$	−896.000	+	1551.92i	−0.857141	+	1.48461i	0.0175038	+	0.999847i	$0.494428\pi$
$103$	−896.000	+	1551.92i	−0.857141	+	1.48461i	−0.874645	+	0.484765i	$0.838905\pi$
$104$		0			0
$105$		0			0
$106$	1032.00			0.945629
$107$	−953.000	+	1650.64i	−0.861028	+	1.49134i	0.00990992	+	0.999951i	$0.496846\pi$
$107$	−953.000	+	1650.64i	−0.861028	+	1.49134i	−0.870938	+	0.491393i	$0.836488\pi$
$108$		0			0
$109$	45.0000	+	77.9423i	0.0395433	+	0.0684910i	0.885120	−	0.465363i	$-0.154076\pi$
$109$	45.0000	+	77.9423i	0.0395433	+	0.0684910i	−0.845576	+	0.533854i	$0.820743\pi$
$110$	496.000	−	859.097i	0.429925	−	0.744652i
$111$		0			0
$112$		0			0
$113$	−458.000			−0.381283			−0.190642	−	0.981660i	$-0.561057\pi$
$113$	−458.000			−0.381283			−0.190642	+	0.981660i	$0.561057\pi$
$114$		0			0
$115$	84.0000	+	145.492i	0.0681134	+	0.117976i
$116$	−40.0000	−	69.2820i	−0.0320164	−	0.0554541i
$117$		0			0
$118$	−480.000			−0.374471
$119$		0			0
$120$		0			0
$121$	−1256.50	+	2176.32i	−0.944027	+	1.63510i
$122$	−1244.00	−	2154.67i	−0.923168	−	1.59897i
$123$		0			0
$124$	−192.000	+	332.554i	−0.139049	+	0.240840i
$125$	936.000			0.669747
$126$		0			0
$127$	804.000			0.561760			0.280880	−	0.959743i	$-0.409374\pi$
$127$	804.000			0.561760			0.280880	+	0.959743i	$0.409374\pi$
$128$		0			0
$129$		0			0
$130$	−496.000	−	859.097i	−0.334631	−	0.579599i
$131$	−406.000	+	703.213i	−0.270782	+	0.469007i	−0.969062	−	0.246817i	$-0.920615\pi$
$131$	−406.000	+	703.213i	−0.270782	+	0.469007i	0.698281	+	0.715824i	$0.253949\pi$
$132$		0			0
$133$		0			0
$134$	−3616.00			−2.33116
$135$		0			0
$136$		0			0
$137$	207.000	+	358.535i	0.129089	+	0.223589i	0.923324	−	0.384022i	$-0.125461\pi$
$137$	207.000	+	358.535i	0.129089	+	0.223589i	−0.794235	+	0.607611i	$0.792128\pi$
$138$		0			0
$139$	1620.00			0.988537			0.494268	−	0.869309i	$-0.335436\pi$
$139$	1620.00			0.988537			0.494268	+	0.869309i	$0.335436\pi$
$140$		0			0
$141$		0			0
$142$	1356.00	−	2348.66i	0.801359	−	1.38799i
$143$	1922.00	+	3329.00i	1.12396	+	1.94675i
$144$		0			0
$145$	20.0000	−	34.6410i	0.0114545	−	0.0198399i
$146$	−2568.00			−1.45568
$147$		0			0
$148$	−1968.00			−1.09303
$149$	1185.00	−	2052.48i	0.651537	−	1.12849i	−0.331213	−	0.943556i	$-0.607458\pi$
$149$	1185.00	−	2052.48i	0.651537	−	1.12849i	0.982750	−	0.184939i	$-0.0592087\pi$
$150$		0			0
$151$	284.000	+	491.902i	0.153057	+	0.265102i	0.932350	−	0.361558i	$-0.117755\pi$
$151$	284.000	+	491.902i	0.153057	+	0.265102i	−0.779293	+	0.626660i	$0.784422\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−192.000			−0.0994956
$156$		0			0
$157$	−133.000	−	230.363i	−0.0676086	−	0.117102i	0.830240	−	0.557407i	$-0.188204\pi$
$157$	−133.000	−	230.363i	−0.0676086	−	0.117102i	−0.897848	+	0.440305i	$0.854870\pi$
$158$	1480.00	+	2563.44i	0.745206	+	1.29073i
$159$		0			0
$160$	−1024.00			−0.505964
$161$		0			0
$162$		0			0
$163$	136.000	−	235.559i	0.0653518	−	0.113193i	−0.831498	−	0.555527i	$-0.812516\pi$
$163$	136.000	−	235.559i	0.0653518	−	0.113193i	0.896850	+	0.442335i	$0.145850\pi$
$164$	992.000	+	1718.19i	0.472330	+	0.818100i
$165$		0			0
$166$	936.000	−	1621.20i	0.437637	−	0.758009i
$167$	−1876.00			−0.869277			−0.434638	−	0.900605i	$-0.643124\pi$
$167$	−1876.00			−0.869277			−0.434638	+	0.900605i	$0.643124\pi$
$168$		0			0
$169$	1647.00			0.749659
$170$	−672.000	+	1163.94i	−0.303177	+	0.525118i
$171$		0			0
$172$	−272.000	−	471.118i	−0.120580	−	0.208851i
$173$	76.0000	−	131.636i	0.0333998	−	0.0578502i	−0.848842	−	0.528646i	$-0.822700\pi$
$173$	76.0000	−	131.636i	0.0333998	−	0.0578502i	0.882242	+	0.470796i	$0.156033\pi$
$174$		0			0
$175$		0			0
$176$	3968.00			1.69943
$177$		0			0
$178$	400.000	+	692.820i	0.168434	+	0.291736i
$179$	305.000	+	528.275i	0.127356	+	0.220588i	0.922652	−	0.385635i	$-0.126018\pi$
$179$	305.000	+	528.275i	0.127356	+	0.220588i	−0.795295	+	0.606222i	$0.792684\pi$
$180$		0			0
$181$	−1042.00			−0.427907			−0.213954	−	0.976844i	$-0.568634\pi$
$181$	−1042.00			−0.427907			−0.213954	+	0.976844i	$0.568634\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−492.000	−	852.169i	−0.195527	−	0.338663i
$186$		0			0
$187$	2604.00	−	4510.26i	1.01831	−	1.76376i
$188$	2592.00			1.00554
$189$		0			0
$190$	−1600.00			−0.610927
$191$	−1019.00	+	1764.96i	−0.386033	+	0.668628i	−0.991912	−	0.126928i	$-0.959488\pi$
$191$	−1019.00	+	1764.96i	−0.386033	+	0.668628i	0.605879	+	0.795557i	$0.292821\pi$
$192$		0			0
$193$	1301.00	+	2253.40i	0.485223	+	0.840431i	0.999856	−	0.0169798i	$-0.00540511\pi$
$193$	1301.00	+	2253.40i	0.485223	+	0.840431i	−0.514633	+	0.857411i	$0.672072\pi$
$194$	2532.00	−	4385.55i	0.937046	−	1.62301i
$195$		0			0
$196$		0			0
$197$	−2354.00			−0.851348			−0.425674	−	0.904877i	$-0.639963\pi$
$197$	−2354.00			−0.851348			−0.425674	+	0.904877i	$0.639963\pi$
$198$		0			0
$199$	840.000	+	1454.92i	0.299226	+	0.518275i	0.975959	−	0.217954i	$-0.0699381\pi$
$199$	840.000	+	1454.92i	0.299226	+	0.518275i	−0.676733	+	0.736229i	$0.736605\pi$
$200$		0			0
$201$		0			0
$202$	−928.000			−0.323237
$203$		0			0
$204$		0			0
$205$	−496.000	+	859.097i	−0.168986	+	0.292692i
$206$	3584.00	+	6207.67i	1.21218	+	2.09956i
$207$		0			0
$208$	1984.00	−	3436.39i	0.661373	−	1.14553i
$209$	6200.00			2.05198
$210$		0			0
$211$	−668.000			−0.217948			−0.108974	−	0.994045i	$-0.534757\pi$
$211$	−668.000			−0.217948			−0.108974	+	0.994045i	$0.534757\pi$
$212$	1032.00	−	1787.48i	0.334330	−	0.579077i
$213$		0			0
$214$	3812.00	+	6602.58i	1.21768	+	2.10908i
$215$	136.000	−	235.559i	0.0431401	−	0.0747209i
$216$		0			0
$217$		0			0
$218$	360.000			0.111845
$219$		0			0
$220$	−992.000	−	1718.19i	−0.304003	−	0.526548i
$221$	−2604.00	−	4510.26i	−0.792597	−	1.37282i
$222$		0			0
$223$	1832.00			0.550134			0.275067	−	0.961425i	$-0.411300\pi$
$223$	1832.00			0.550134			0.275067	+	0.961425i	$0.411300\pi$
$224$		0			0
$225$		0			0
$226$	−916.000	+	1586.56i	−0.269608	+	0.466975i
$227$	−2472.00	−	4281.63i	−0.722786	−	1.25190i	−0.959879	−	0.280415i	$-0.909528\pi$
$227$	−2472.00	−	4281.63i	−0.722786	−	1.25190i	0.237093	−	0.971487i	$-0.423805\pi$
$228$		0			0
$229$	−2735.00	+	4737.16i	−0.789231	+	1.36699i	0.137208	+	0.990542i	$0.456187\pi$
$229$	−2735.00	+	4737.16i	−0.789231	+	1.36699i	−0.926439	+	0.376446i	$0.877146\pi$
$230$	672.000			0.192654
$231$		0			0
$232$		0			0
$233$	−1401.00	+	2426.60i	−0.393917	+	0.682284i	−0.992962	−	0.118431i	$-0.962213\pi$
$233$	−1401.00	+	2426.60i	−0.393917	+	0.682284i	0.599046	+	0.800715i	$0.295547\pi$
$234$		0			0
$235$	648.000	+	1122.37i	0.179876	+	0.311554i
$236$	−480.000	+	831.384i	−0.132396	+	0.229316i
$237$		0			0
$238$		0			0
$239$	1170.00			0.316657			0.158328	−	0.987386i	$-0.449390\pi$
$239$	1170.00			0.316657			0.158328	+	0.987386i	$0.449390\pi$
$240$		0			0
$241$	−1169.00	−	2024.77i	−0.312456	−	0.541190i	0.666437	−	0.745561i	$-0.267818\pi$
$241$	−1169.00	−	2024.77i	−0.312456	−	0.541190i	−0.978893	+	0.204371i	$0.934485\pi$
$242$	5026.00	+	8705.29i	1.33506	+	2.31238i
$243$		0			0
$244$	−4976.00			−1.30556
$245$		0			0
$246$		0			0
$247$	3100.00	−	5369.36i	0.798576	−	1.38317i
$248$		0			0
$249$		0			0
$250$	1872.00	−	3242.40i	0.473583	−	0.820269i
$251$	2792.00			0.702109			0.351055	−	0.936355i	$-0.385823\pi$
$251$	2792.00			0.702109			0.351055	+	0.936355i	$0.385823\pi$
$252$		0			0
$253$	−2604.00			−0.647083
$254$	1608.00	−	2785.14i	0.397224	−	0.688012i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.500000	−	0.866025i
$257$	−3512.00	+	6082.96i	−0.852422	+	1.47644i	0.0265936	+	0.999646i	$0.491534\pi$
$257$	−3512.00	+	6082.96i	−0.852422	+	1.47644i	−0.879016	+	0.476792i	$0.841799\pi$
$258$		0			0
$259$		0			0
$260$	−1984.00			−0.473240
$261$		0			0
$262$	1624.00	+	2812.85i	0.382943	+	0.663277i
$263$	1219.00	+	2111.37i	0.285805	+	0.495029i	0.972804	−	0.231629i	$-0.0744056\pi$
$263$	1219.00	+	2111.37i	0.285805	+	0.495029i	−0.686999	+	0.726658i	$0.741072\pi$
$264$		0			0
$265$	1032.00			0.239227
$266$		0			0
$267$		0			0
$268$	−3616.00	+	6263.10i	−0.824188	+	1.42754i
$269$	3390.00	+	5871.65i	0.768372	+	1.33086i	0.938446	+	0.345427i	$0.112266\pi$
$269$	3390.00	+	5871.65i	0.768372	+	1.33086i	−0.170074	+	0.985431i	$0.554401\pi$
$270$		0			0
$271$	−964.000	+	1669.70i	−0.216084	+	0.374269i	−0.953607	−	0.301053i	$-0.902662\pi$
$271$	−964.000	+	1669.70i	−0.216084	+	0.374269i	0.737523	+	0.675322i	$0.235995\pi$
$272$	−5376.00			−1.19841
$273$		0			0
$274$	1656.00			0.365119
$275$	−3379.00	+	5852.60i	−0.740950	+	1.28336i
$276$		0			0
$277$	−2777.00	−	4809.91i	−0.602360	−	1.04332i	−0.992463	−	0.122547i	$-0.960894\pi$
$277$	−2777.00	−	4809.91i	−0.602360	−	1.04332i	0.390103	−	0.920771i	$-0.372440\pi$
$278$	3240.00	−	5611.84i	0.699001	−	1.21071i
$279$		0			0
$280$		0			0
$281$	−1942.00			−0.412278			−0.206139	−	0.978523i	$-0.566090\pi$
$281$	−1942.00			−0.412278			−0.206139	+	0.978523i	$0.566090\pi$
$282$		0			0
$283$	2414.00	+	4181.17i	0.507058	+	0.878250i	0.999967	+	0.00816911i	$0.00260034\pi$
$283$	2414.00	+	4181.17i	0.507058	+	0.878250i	−0.492909	+	0.870081i	$0.664066\pi$
$284$	−2712.00	−	4697.32i	−0.566646	−	0.981460i
$285$		0			0
$286$	15376.0			3.17903
$287$		0			0
$288$		0			0
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	−80.0000	−	138.564i	−0.0161992	−	0.0280578i
$291$		0			0
$292$	−2568.00	+	4447.91i	−0.514660	+	0.891418i
$293$	−6152.00			−1.22663			−0.613317	−	0.789837i	$-0.710165\pi$
$293$	−6152.00			−1.22663			−0.613317	+	0.789837i	$0.710165\pi$
$294$		0			0
$295$	−480.000			−0.0947345
$296$		0			0
$297$		0			0
$298$	−4740.00	−	8209.92i	−0.921412	−	1.59593i
$299$	−1302.00	+	2255.13i	−0.251828	+	0.436179i
$300$		0			0
$301$		0			0
$302$	2272.00			0.432910
$303$		0			0
$304$	−3200.00	−	5542.56i	−0.603726	−	1.04568i
$305$	−1244.00	−	2154.67i	−0.233545	−	0.404512i
$306$		0			0
$307$	−5884.00			−1.09387			−0.546934	−	0.837176i	$-0.684205\pi$
$307$	−5884.00			−1.09387			−0.546934	+	0.837176i	$0.684205\pi$
$308$		0			0
$309$		0			0
$310$	−384.000	+	665.108i	−0.0703540	+	0.121857i
$311$	−4566.00	−	7908.54i	−0.832521	−	1.44197i	−0.896033	−	0.443988i	$-0.853563\pi$
$311$	−4566.00	−	7908.54i	−0.832521	−	1.44197i	0.0635115	−	0.997981i	$-0.479770\pi$
$312$		0			0
$313$	−4691.00	+	8125.05i	−0.847128	+	1.46727i	0.0366327	+	0.999329i	$0.488337\pi$
$313$	−4691.00	+	8125.05i	−0.847128	+	1.46727i	−0.883760	+	0.467940i	$0.844996\pi$
$314$	−1064.00			−0.191226
$315$		0			0
$316$	5920.00			1.05388
$317$	1557.00	−	2696.80i	0.275867	−	0.477816i	−0.694487	−	0.719506i	$-0.744368\pi$
$317$	1557.00	−	2696.80i	0.275867	−	0.477816i	0.970353	+	0.241690i	$0.0777017\pi$
$318$		0			0
$319$	310.000	+	536.936i	0.0544096	+	0.0942402i
$320$	−1024.00	+	1773.62i	−0.178885	+	0.309839i
$321$		0			0
$322$		0			0
$323$	−8400.00			−1.44702
$324$		0			0
$325$	3379.00	+	5852.60i	0.576718	+	0.998904i
$326$	−544.000	−	942.236i	−0.0924214	−	0.160079i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−766.000	+	1326.75i	−0.127200	+	0.220317i	−0.922591	−	0.385780i	$-0.873932\pi$
$331$	−766.000	+	1326.75i	−0.127200	+	0.220317i	0.795391	+	0.606097i	$0.207266\pi$
$332$	−1872.00	−	3242.40i	−0.309456	−	0.535993i
$333$		0			0
$334$	−3752.00	+	6498.65i	−0.614672	+	1.06464i
$335$	−3616.00			−0.589741
$336$		0			0
$337$	−4166.00			−0.673402			−0.336701	−	0.941612i	$-0.609311\pi$
$337$	−4166.00			−0.673402			−0.336701	+	0.941612i	$0.609311\pi$
$338$	3294.00	−	5705.38i	0.530089	−	0.918141i
$339$		0			0
$340$	1344.00	+	2327.88i	0.214378	+	0.371314i
$341$	1488.00	−	2577.29i	0.236304	−	0.409291i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−304.000	−	526.543i	−0.0472345	−	0.0818126i
$347$	−5683.00	−	9843.24i	−0.879191	−	1.52280i	−0.852230	−	0.523168i	$-0.824750\pi$
$347$	−5683.00	−	9843.24i	−0.879191	−	1.52280i	−0.0269617	−	0.999636i	$-0.508583\pi$
$348$		0			0
$349$	−9310.00			−1.42795			−0.713973	−	0.700174i	$-0.753106\pi$
$349$	−9310.00			−1.42795			−0.713973	+	0.700174i	$0.753106\pi$
$350$		0			0
$351$		0			0
$352$	7936.00	−	13745.6i	1.20168	−	2.08137i
$353$	4286.00	+	7423.57i	0.646234	+	1.11931i	0.984015	+	0.178086i	$0.0569905\pi$
$353$	4286.00	+	7423.57i	0.646234	+	1.11931i	−0.337780	+	0.941225i	$0.609676\pi$
$354$		0			0
$355$	1356.00	−	2348.66i	0.202730	−	0.351138i
$356$	1600.00			0.238202
$357$		0			0
$358$	2440.00			0.360218
$359$	−2395.00	+	4148.26i	−0.352098	+	0.609852i	−0.986617	−	0.163056i	$-0.947865\pi$
$359$	−2395.00	+	4148.26i	−0.352098	+	0.609852i	0.634519	+	0.772908i	$0.281198\pi$
$360$		0			0
$361$	−1570.50	−	2720.19i	−0.228969	−	0.396586i
$362$	−2084.00	+	3609.59i	−0.302576	+	0.524077i
$363$		0			0
$364$		0			0
$365$	−2568.00			−0.368261
$366$		0			0
$367$	2712.00	+	4697.32i	0.385736	+	0.668115i	0.991871	−	0.127247i	$-0.0406141\pi$
$367$	2712.00	+	4697.32i	0.385736	+	0.668115i	−0.606135	+	0.795362i	$0.707281\pi$
$368$	1344.00	+	2327.88i	0.190383	+	0.329753i
$369$		0			0
$370$	−3936.00			−0.553035
$371$		0			0
$372$		0			0
$373$	−919.000	+	1591.75i	−0.127571	+	0.220960i	−0.922735	−	0.385435i	$-0.874051\pi$
$373$	−919.000	+	1591.75i	−0.127571	+	0.220960i	0.795164	+	0.606395i	$0.207385\pi$
$374$	−10416.0	−	18041.0i	−1.44010	−	2.49433i
$375$		0			0
$376$		0			0
$377$	620.000			0.0846993
$378$		0			0
$379$	−4260.00			−0.577365			−0.288683	−	0.957425i	$-0.593217\pi$
$379$	−4260.00			−0.577365			−0.288683	+	0.957425i	$0.593217\pi$
$380$	−1600.00	+	2771.28i	−0.215995	+	0.374115i
$381$		0			0
$382$	4076.00	+	7059.84i	0.545933	+	0.945583i
$383$	−4524.00	+	7835.80i	−0.603566	+	1.04541i	0.388711	+	0.921360i	$0.372920\pi$
$383$	−4524.00	+	7835.80i	−0.603566	+	1.04541i	−0.992276	+	0.124046i	$0.960413\pi$
$384$		0			0
$385$		0			0
$386$	10408.0			1.37242
$387$		0			0
$388$	−5064.00	−	8771.11i	−0.662592	−	1.14764i
$389$	−5745.00	−	9950.63i	−0.748800	−	1.29696i	−0.948398	−	0.317081i	$-0.897297\pi$
$389$	−5745.00	−	9950.63i	−0.748800	−	1.29696i	0.199599	−	0.979878i	$-0.436036\pi$
$390$		0			0
$391$	3528.00			0.456314
$392$		0			0
$393$		0			0
$394$	−4708.00	+	8154.50i	−0.601994	+	1.04268i
$395$	1480.00	+	2563.44i	0.188524	+	0.326533i
$396$		0			0
$397$	−933.000	+	1616.00i	−0.117949	+	0.204294i	−0.918955	−	0.394363i	$-0.870965\pi$
$397$	−933.000	+	1616.00i	−0.117949	+	0.204294i	0.801005	+	0.598657i	$0.204299\pi$
$398$	6720.00			0.846340
$399$		0			0
$400$	6976.00			0.872000
$401$	6831.00	−	11831.6i	0.850683	−	1.47343i	−0.0299100	−	0.999553i	$-0.509522\pi$
$401$	6831.00	−	11831.6i	0.850683	−	1.47343i	0.880593	−	0.473873i	$-0.157145\pi$
$402$		0			0
$403$	−1488.00	−	2577.29i	−0.183927	−	0.318571i
$404$	−928.000	+	1607.34i	−0.114281	+	0.197941i
$405$		0			0
$406$		0			0
$407$	15252.0			1.85753
$408$		0			0
$409$	−6605.00	−	11440.2i	−0.798524	−	1.38308i	−0.920577	−	0.390560i	$-0.872281\pi$
$409$	−6605.00	−	11440.2i	−0.798524	−	1.38308i	0.122054	−	0.992524i	$-0.461052\pi$
$410$	1984.00	+	3436.39i	0.238982	+	0.413930i
$411$		0			0
$412$	14336.0			1.71428
$413$		0			0
$414$		0			0
$415$	936.000	−	1621.20i	0.110714	−	0.191763i
$416$	−7936.00	−	13745.6i	−0.935323	−	1.62003i
$417$		0			0
$418$	12400.0	−	21477.4i	1.45097	−	2.51315i
$419$	6960.00			0.811499			0.405750	−	0.913984i	$-0.367010\pi$
$419$	6960.00			0.811499			0.405750	+	0.913984i	$0.367010\pi$
$420$		0			0
$421$	8162.00			0.944873			0.472437	−	0.881365i	$-0.343375\pi$
$421$	8162.00			0.944873			0.472437	+	0.881365i	$0.343375\pi$
$422$	−1336.00	+	2314.02i	−0.154112	+	0.266931i
$423$		0			0
$424$		0			0
$425$	4578.00	−	7929.33i	0.522507	−	0.905009i
$426$		0			0
$427$		0			0
$428$	15248.0			1.72206
$429$		0			0
$430$	−544.000	−	942.236i	−0.0610093	−	0.105671i
$431$	8301.00	+	14377.8i	0.927715	+	1.60685i	0.787136	+	0.616780i	$0.211563\pi$
$431$	8301.00	+	14377.8i	0.927715	+	1.60685i	0.140579	+	0.990069i	$0.455104\pi$
$432$		0			0
$433$	−7738.00			−0.858810			−0.429405	−	0.903112i	$-0.641277\pi$
$433$	−7738.00			−0.858810			−0.429405	+	0.903112i	$0.641277\pi$
$434$		0			0
$435$		0			0
$436$	360.000	−	623.538i	0.0395433	−	0.0684910i
$437$	2100.00	+	3637.31i	0.229878	+	0.398160i
$438$		0			0
$439$	−420.000	+	727.461i	−0.0456617	+	0.0790885i	−0.887953	−	0.459934i	$-0.847873\pi$
$439$	−420.000	+	727.461i	−0.0456617	+	0.0790885i	0.842291	+	0.539023i	$0.181206\pi$
$440$		0			0
$441$		0			0
$442$	−20832.0			−2.24180
$443$	3309.00	−	5731.36i	0.354888	−	0.614684i	−0.632211	−	0.774796i	$-0.717852\pi$
$443$	3309.00	−	5731.36i	0.354888	−	0.614684i	0.987099	+	0.160113i	$0.0511857\pi$
$444$		0			0
$445$	400.000	+	692.820i	0.0426108	+	0.0738041i
$446$	3664.00	−	6346.23i	0.389003	−	0.673773i
$447$		0			0
$448$		0			0
$449$	−3090.00			−0.324780			−0.162390	−	0.986727i	$-0.551920\pi$
$449$	−3090.00			−0.324780			−0.162390	+	0.986727i	$0.551920\pi$
$450$		0			0
$451$	−7688.00	−	13316.0i	−0.802691	−	1.39030i
$452$	1832.00	+	3173.12i	0.190642	+	0.330201i
$453$		0			0
$454$	−19776.0			−2.04435
$455$		0			0
$456$		0			0
$457$	−2957.00	+	5121.67i	−0.302675	+	0.524249i	−0.976741	−	0.214422i	$-0.931213\pi$
$457$	−2957.00	+	5121.67i	−0.302675	+	0.524249i	0.674066	+	0.738671i	$0.264546\pi$
$458$	10940.0	+	18948.6i	1.11614	+	1.93321i
$459$		0			0
$460$	672.000	−	1163.94i	0.0681134	−	0.117976i
$461$	−15968.0			−1.61324			−0.806620	−	0.591070i	$-0.798706\pi$
$461$	−15968.0			−1.61324			−0.806620	+	0.591070i	$0.798706\pi$
$462$		0			0
$463$	−1172.00			−0.117640			−0.0588202	−	0.998269i	$-0.518734\pi$
$463$	−1172.00			−0.117640			−0.0588202	+	0.998269i	$0.518734\pi$
$464$	320.000	−	554.256i	0.0320164	−	0.0554541i
$465$		0			0
$466$	5604.00	+	9706.41i	0.557082	+	0.964895i
$467$	−2652.00	+	4593.40i	−0.262784	+	0.455154i	−0.966981	−	0.254850i	$-0.917974\pi$
$467$	−2652.00	+	4593.40i	−0.262784	+	0.455154i	0.704197	+	0.710005i	$0.251307\pi$
$468$		0			0
$469$		0			0
$470$	5184.00			0.508766
$471$		0			0
$472$		0			0
$473$	2108.00	+	3651.16i	0.204917	+	0.354927i
$474$		0			0
$475$	10900.0			1.05290
$476$		0			0
$477$		0			0
$478$	2340.00	−	4053.00i	0.223910	−	0.387824i
$479$	−2870.00	−	4970.99i	−0.273765	−	0.474176i	0.696057	−	0.717986i	$-0.254936\pi$
$479$	−2870.00	−	4970.99i	−0.273765	−	0.474176i	−0.969823	+	0.243810i	$0.921603\pi$
$480$		0			0
$481$	7626.00	−	13208.6i	0.722902	−	1.25210i
$482$	−9352.00			−0.883759
$483$		0			0
$484$	20104.0			1.88805
$485$	2532.00	−	4385.55i	0.237056	−	0.410593i
$486$		0			0
$487$	−4472.00	−	7745.73i	−0.416110	−	0.720724i	0.579434	−	0.815019i	$-0.303274\pi$
$487$	−4472.00	−	7745.73i	−0.416110	−	0.720724i	−0.995544	+	0.0942951i	$0.969940\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5558.00			0.510853			0.255427	−	0.966828i	$-0.417784\pi$
$491$	5558.00			0.510853			0.255427	+	0.966828i	$0.417784\pi$
$492$		0			0
$493$	−420.000	−	727.461i	−0.0383689	−	0.0664568i
$494$	−12400.0	−	21477.4i	−1.12936	−	1.95610i
$495$		0			0
$496$	−3072.00			−0.278099
$497$		0			0
$498$		0			0
$499$	9910.00	−	17164.6i	0.889043	−	1.53987i	0.0480349	−	0.998846i	$-0.484704\pi$
$499$	9910.00	−	17164.6i	0.889043	−	1.53987i	0.841008	−	0.541022i	$-0.181963\pi$
$500$	−3744.00	−	6484.80i	−0.334874	−	0.580018i
$501$		0			0
$502$	5584.00	−	9671.77i	0.496466	−	0.859905i
$503$	1848.00			0.163814			0.0819068	−	0.996640i	$-0.473899\pi$
$503$	1848.00			0.163814			0.0819068	+	0.996640i	$0.473899\pi$
$504$		0			0
$505$	−928.000			−0.0817732
$506$	−5208.00	+	9020.52i	−0.457557	+	0.792512i
$507$		0			0
$508$	−3216.00	−	5570.28i	−0.280880	−	0.486498i
$509$	−170.000	+	294.449i	−0.0148038	+	0.0256409i	−0.873332	−	0.487125i	$-0.838046\pi$
$509$	−170.000	+	294.449i	−0.0148038	+	0.0256409i	0.858529	+	0.512766i	$0.171379\pi$
$510$		0			0
$511$		0			0
$512$	−16384.0			−1.41421
$513$		0			0
$514$	14048.0	+	24331.8i	1.20551	+	2.08800i
$515$	3584.00	+	6207.67i	0.306660	+	0.531151i
$516$		0			0
$517$	−20088.0			−1.70884
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5106.00	−	8843.85i	−0.429363	−	0.743678i	0.567454	−	0.823405i	$-0.307928\pi$
$521$	−5106.00	−	8843.85i	−0.429363	−	0.743678i	−0.996817	+	0.0797272i	$0.974595\pi$
$522$		0			0
$523$	−4666.00	+	8081.75i	−0.390115	+	0.675698i	−0.992464	−	0.122534i	$-0.960898\pi$
$523$	−4666.00	+	8081.75i	−0.390115	+	0.675698i	0.602350	+	0.798232i	$0.294231\pi$
$524$	6496.00			0.541563
$525$		0			0
$526$	9752.00			0.808379
$527$	−2016.00	+	3491.81i	−0.166638	+	0.288626i
$528$		0			0
$529$	5201.50	+	9009.26i	0.427509	+	0.740467i
$530$	2064.00	−	3574.95i	0.169159	−	0.292993i
$531$		0			0
$532$		0			0
$533$	−15376.0			−1.24955
$534$		0			0
$535$	3812.00	+	6602.58i	0.308051	+	0.533559i
$536$		0			0
$537$		0			0
$538$	27120.0			2.17328
$539$		0			0
$540$		0			0
$541$	4499.00	−	7792.50i	0.357536	−	0.619271i	−0.630012	−	0.776585i	$-0.716950\pi$
$541$	4499.00	−	7792.50i	0.357536	−	0.619271i	0.987549	+	0.157314i	$0.0502835\pi$
$542$	3856.00	+	6678.79i	0.305589	+	0.529296i
$543$		0			0
$544$	−10752.0	+	18623.0i	−0.847405	+	1.46775i
$545$	360.000			0.0282949
$546$		0			0
$547$	−3416.00			−0.267016			−0.133508	−	0.991048i	$-0.542624\pi$
$547$	−3416.00			−0.267016			−0.133508	+	0.991048i	$0.542624\pi$
$548$	1656.00	−	2868.28i	0.129089	−	0.223589i
$549$		0			0
$550$	13516.0	+	23410.4i	1.04786	+	1.81495i
$551$	500.000	−	866.025i	0.0386583	−	0.0669581i
$552$		0			0
$553$		0			0
$554$	−22216.0			−1.70373
$555$		0			0
$556$	−6480.00	−	11223.7i	−0.494268	−	0.856098i
$557$	−263.000	−	455.529i	−0.0200066	−	0.0346524i	0.855849	−	0.517226i	$-0.173035\pi$
$557$	−263.000	−	455.529i	−0.0200066	−	0.0346524i	−0.875855	+	0.482574i	$0.839702\pi$
$558$		0			0
$559$	4216.00			0.318994
$560$		0			0
$561$		0			0
$562$	−3884.00	+	6727.29i	−0.291524	+	0.504935i
$563$	3356.00	+	5812.76i	0.251223	+	0.435131i	0.963863	−	0.266399i	$-0.0858339\pi$
$563$	3356.00	+	5812.76i	0.251223	+	0.435131i	−0.712640	+	0.701530i	$0.752501\pi$
$564$		0			0
$565$	−916.000	+	1586.56i	−0.0682060	+	0.118136i
$566$	19312.0			1.43418
$567$		0			0
$568$		0			0
$569$	2095.00	−	3628.65i	0.154353	−	0.267348i	−0.778470	−	0.627682i	$-0.784004\pi$
$569$	2095.00	−	3628.65i	0.154353	−	0.267348i	0.932823	+	0.360334i	$0.117337\pi$
$570$		0			0
$571$	−1516.00	−	2625.79i	−0.111108	−	0.192445i	0.805109	−	0.593126i	$-0.202107\pi$
$571$	−1516.00	−	2625.79i	−0.111108	−	0.192445i	−0.916217	+	0.400682i	$0.868773\pi$
$572$	15376.0	−	26632.0i	1.12396	−	1.94675i
$573$		0			0
$574$		0			0
$575$	−4578.00			−0.332027
$576$		0			0
$577$	2717.00	+	4705.98i	0.196032	+	0.339537i	0.947238	−	0.320531i	$-0.103861\pi$
$577$	2717.00	+	4705.98i	0.196032	+	0.339537i	−0.751207	+	0.660067i	$0.770528\pi$
$578$	4286.00	+	7423.57i	0.308433	+	0.534221i
$579$		0			0
$580$	−320.000			−0.0229091
$581$		0			0
$582$		0			0
$583$	−7998.00	+	13852.9i	−0.568170	+	0.984100i
$584$		0			0
$585$		0			0
$586$	−12304.0	+	21311.2i	−0.867361	+	1.50231i
$587$	464.000			0.0326258			0.0163129	−	0.999867i	$-0.494807\pi$
$587$	464.000			0.0326258			0.0163129	+	0.999867i	$0.494807\pi$
$588$		0			0
$589$	−4800.00			−0.335790
$590$	−960.000	+	1662.77i	−0.0669874	+	0.116026i
$591$		0			0
$592$	−7872.00	−	13634.7i	−0.546516	−	0.946593i
$593$	−5874.00	+	10174.1i	−0.406773	+	0.704551i	−0.994526	−	0.104489i	$-0.966679\pi$
$593$	−5874.00	+	10174.1i	−0.406773	+	0.704551i	0.587753	+	0.809040i	$0.300013\pi$
$594$		0			0
$595$		0			0
$596$	−18960.0			−1.30307
$597$		0			0
$598$	5208.00	+	9020.52i	0.356139	+	0.616850i
$599$	3825.00	+	6625.09i	0.260910	+	0.451910i	0.966484	−	0.256727i	$-0.0826440\pi$
$599$	3825.00	+	6625.09i	0.260910	+	0.451910i	−0.705574	+	0.708636i	$0.749311\pi$
$600$		0			0
$601$	22878.0			1.55277			0.776384	−	0.630261i	$-0.217052\pi$
$601$	22878.0			1.55277			0.776384	+	0.630261i	$0.217052\pi$
$602$		0			0
$603$		0			0
$604$	2272.00	−	3935.22i	0.153057	−	0.265102i
$605$	5026.00	+	8705.29i	0.337745	+	0.584992i
$606$		0			0
$607$	352.000	−	609.682i	0.0235375	−	0.0407681i	−0.854017	−	0.520246i	$-0.825840\pi$
$607$	352.000	−	609.682i	0.0235375	−	0.0407681i	0.877554	+	0.479477i	$0.159174\pi$
$608$	−25600.0			−1.70759
$609$		0			0
$610$	−9952.00			−0.660565
$611$	−10044.0	+	17396.7i	−0.665036	+	1.15188i
$612$		0			0
$613$	−12479.0	−	21614.3i	−0.822222	−	1.42413i	−0.904024	−	0.427482i	$-0.859401\pi$
$613$	−12479.0	−	21614.3i	−0.822222	−	1.42413i	0.0818021	−	0.996649i	$-0.473932\pi$
$614$	−11768.0	+	20382.8i	−0.773482	+	1.33971i
$615$		0			0
$616$		0			0
$617$	8826.00			0.575886			0.287943	−	0.957648i	$-0.407029\pi$
$617$	8826.00			0.575886			0.287943	+	0.957648i	$0.407029\pi$
$618$		0			0
$619$	10610.0	+	18377.1i	0.688937	+	1.19327i	0.972182	+	0.234226i	$0.0752556\pi$
$619$	10610.0	+	18377.1i	0.688937	+	1.19327i	−0.283245	+	0.959047i	$0.591411\pi$
$620$	768.000	+	1330.22i	0.0497478	+	0.0861657i
$621$		0			0
$622$	−36528.0			−2.35473
$623$		0			0
$624$		0			0
$625$	−4940.50	+	8557.20i	−0.316192	+	0.547661i
$626$	18764.0	+	32500.2i	1.19802	+	2.07503i
$627$		0			0
$628$	−1064.00	+	1842.90i	−0.0676086	+	0.117102i
$629$	−20664.0			−1.30990
$630$		0			0
$631$	−3268.00			−0.206176			−0.103088	−	0.994672i	$-0.532872\pi$
$631$	−3268.00			−0.206176			−0.103088	+	0.994672i	$0.532872\pi$
$632$		0			0
$633$		0			0
$634$	−6228.00	−	10787.2i	−0.390135	−	0.675733i
$635$	1608.00	−	2785.14i	0.100491	−	0.174055i
$636$		0			0
$637$		0			0
$638$	2480.00			0.153894
$639$		0			0
$640$		0			0
$641$	6531.00	+	11312.0i	0.402432	+	0.697033i	0.994019	−	0.109208i	$-0.0348316\pi$
$641$	6531.00	+	11312.0i	0.402432	+	0.697033i	−0.591587	+	0.806241i	$0.701498\pi$
$642$		0			0
$643$	28012.0			1.71802			0.859009	−	0.511961i	$-0.171081\pi$
$643$	28012.0			1.71802			0.859009	+	0.511961i	$0.171081\pi$
$644$		0			0
$645$		0			0
$646$	−16800.0	+	29098.5i	−1.02320	+	1.77223i
$647$	−1922.00	−	3329.00i	−0.116788	−	0.202282i	0.801705	−	0.597720i	$-0.203926\pi$
$647$	−1922.00	−	3329.00i	−0.116788	−	0.202282i	−0.918493	+	0.395437i	$0.870593\pi$
$648$		0			0
$649$	3720.00	−	6443.23i	0.224997	−	0.389705i
$650$	27032.0			1.63120
$651$		0			0
$652$	−2176.00			−0.130704
$653$	−14241.0	+	24666.1i	−0.853436	+	1.47819i	0.0246533	+	0.999696i	$0.492152\pi$
$653$	−14241.0	+	24666.1i	−0.853436	+	1.47819i	−0.878089	+	0.478498i	$0.841182\pi$
$654$		0			0
$655$	1624.00	+	2812.85i	0.0968778	+	0.167797i
$656$	−7936.00	+	13745.6i	−0.472330	+	0.818100i
$657$		0			0
$658$		0			0
$659$	9330.00			0.551510			0.275755	−	0.961228i	$-0.411072\pi$
$659$	9330.00			0.551510			0.275755	+	0.961228i	$0.411072\pi$
$660$		0			0
$661$	4391.00	+	7605.44i	0.258381	+	0.447530i	0.965808	−	0.259257i	$-0.0834775\pi$
$661$	4391.00	+	7605.44i	0.258381	+	0.447530i	−0.707427	+	0.706786i	$0.750144\pi$
$662$	3064.00	+	5307.00i	0.179888	+	0.311575i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−210.000	+	363.731i	−0.0121908	+	0.0211150i
$668$	7504.00	+	12997.3i	0.434638	+	0.752816i
$669$		0			0
$670$	−7232.00	+	12526.2i	−0.417010	+	0.722282i
$671$	38564.0			2.21870
$672$		0			0
$673$	−10562.0			−0.604956			−0.302478	−	0.953156i	$-0.597814\pi$
$673$	−10562.0			−0.604956			−0.302478	+	0.953156i	$0.597814\pi$
$674$	−8332.00	+	14431.4i	−0.476167	+	0.824746i
$675$		0			0
$676$	−6588.00	−	11410.8i	−0.374829	−	0.649223i
$677$	13008.0	−	22530.5i	0.738461	−	1.27905i	−0.214727	−	0.976674i	$-0.568886\pi$
$677$	13008.0	−	22530.5i	0.738461	−	1.27905i	0.953188	−	0.302378i	$-0.0977804\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−5952.00	−	10309.2i	−0.334185	−	0.578825i
$683$	4449.00	+	7705.89i	0.249248	+	0.431710i	0.963317	−	0.268365i	$-0.0864833\pi$
$683$	4449.00	+	7705.89i	0.249248	+	0.431710i	−0.714070	+	0.700075i	$0.753150\pi$
$684$		0			0
$685$	1656.00			0.0923686
$686$		0			0
$687$		0			0
$688$	2176.00	−	3768.94i	0.120580	−	0.208851i
$689$	7998.00	+	13852.9i	0.442234	+	0.765973i
$690$		0			0
$691$	15286.0	−	26476.1i	0.841544	−	1.45760i	−0.0470452	−	0.998893i	$-0.514980\pi$
$691$	15286.0	−	26476.1i	0.841544	−	1.45760i	0.888589	−	0.458704i	$-0.151686\pi$
$692$	−1216.00			−0.0667997
$693$		0			0
$694$	−45464.0			−2.48673
$695$	3240.00	−	5611.84i	0.176835	−	0.306287i
$696$		0			0
$697$	10416.0	+	18041.0i	0.566046	+	0.980421i
$698$	−18620.0	+	32250.8i	−1.00971	+	1.74887i
$699$		0			0
$700$		0			0
$701$	30618.0			1.64968			0.824840	−	0.565366i	$-0.191265\pi$
$701$	30618.0			1.64968			0.824840	+	0.565366i	$0.191265\pi$
$702$		0			0
$703$	−12300.0	−	21304.2i	−0.659891	−	1.14296i
$704$	−15872.0	−	27491.1i	−0.849714	−	1.47175i
$705$		0			0
$706$	34288.0			1.82783
$707$		0			0
$708$		0			0
$709$	4065.00	−	7040.79i	0.215323	−	0.372951i	−0.738049	−	0.674747i	$-0.764253\pi$
$709$	4065.00	−	7040.79i	0.215323	−	0.372951i	0.953373	+	0.301796i	$0.0975861\pi$
$710$	−5424.00	−	9394.64i	−0.286703	−	0.496584i
$711$		0			0
$712$		0			0
$713$	2016.00			0.105890
$714$		0			0
$715$	15376.0			0.804237
$716$	2440.00	−	4226.20i	0.127356	−	0.220588i
$717$		0			0
$718$	9580.00	+	16593.0i	0.497942	+	0.862461i
$719$	13920.0	−	24110.1i	0.722014	−	1.25057i	−0.238177	−	0.971222i	$-0.576550\pi$
$719$	13920.0	−	24110.1i	0.722014	−	1.25057i	0.960191	−	0.279344i	$-0.0901169\pi$
$720$		0			0
$721$		0			0
$722$	−12564.0			−0.647623
$723$		0			0
$724$	4168.00	+	7219.19i	0.213954	+	0.370579i
$725$	545.000	+	943.968i	0.0279183	+	0.0483560i
$726$		0			0
$727$	−14624.0			−0.746044			−0.373022	−	0.927822i	$-0.621678\pi$
$727$	−14624.0			−0.746044			−0.373022	+	0.927822i	$0.621678\pi$
$728$		0			0
$729$		0			0
$730$	−5136.00	+	8895.81i	−0.260400	+	0.451026i
$731$	−2856.00	−	4946.74i	−0.144505	−	0.250290i
$732$		0			0
$733$	−10431.0	+	18067.0i	−0.525618	+	0.910397i	0.473937	+	0.880559i	$0.342832\pi$
$733$	−10431.0	+	18067.0i	−0.525618	+	0.910397i	−0.999555	+	0.0298378i	$0.990501\pi$
$734$	21696.0			1.09103
$735$		0			0
$736$	10752.0			0.538484
$737$	28024.0	−	48539.0i	1.40065	−	2.42599i
$738$		0			0
$739$	6960.00	+	12055.1i	0.346452	+	0.600072i	0.985616	−	0.168998i	$-0.0540532\pi$
$739$	6960.00	+	12055.1i	0.346452	+	0.600072i	−0.639165	+	0.769070i	$0.720720\pi$
$740$	−3936.00	+	6817.35i	−0.195527	+	0.338663i
$741$		0			0
$742$		0			0
$743$	−25578.0			−1.26294			−0.631471	−	0.775400i	$-0.717548\pi$
$743$	−25578.0			−1.26294			−0.631471	+	0.775400i	$0.717548\pi$
$744$		0			0
$745$	−4740.00	−	8209.92i	−0.233101	−	0.403743i
$746$	3676.00	+	6367.02i	0.180413	+	0.312484i
$747$		0			0
$748$	−41664.0			−2.03661
$749$		0			0
$750$		0			0
$751$	−16736.0	+	28987.6i	−0.813189	+	1.40849i	0.0974312	+	0.995242i	$0.468937\pi$
$751$	−16736.0	+	28987.6i	−0.813189	+	1.40849i	−0.910621	+	0.413243i	$0.864396\pi$
$752$	10368.0	+	17957.9i	0.502769	+	0.870821i
$753$		0			0
$754$	1240.00	−	2147.74i	0.0598914	−	0.103735i
$755$	2272.00			0.109519
$756$		0			0
$757$	25934.0			1.24516			0.622581	−	0.782556i	$-0.286084\pi$
$757$	25934.0			1.24516			0.622581	+	0.782556i	$0.286084\pi$
$758$	−8520.00	+	14757.1i	−0.408259	+	0.707125i
$759$		0			0
$760$		0			0
$761$	−13476.0	+	23341.1i	−0.641925	+	1.11185i	0.343078	+	0.939307i	$0.388530\pi$
$761$	−13476.0	+	23341.1i	−0.641925	+	1.11185i	−0.985003	+	0.172539i	$0.944803\pi$
$762$		0			0
$763$		0			0
$764$	16304.0			0.772065
$765$		0			0
$766$	18096.0	+	31343.2i	0.853571	+	1.47843i
$767$	−3720.00	−	6443.23i	−0.175126	−	0.303327i
$768$		0			0
$769$	−23450.0			−1.09965			−0.549824	−	0.835281i	$-0.685305\pi$
$769$	−23450.0			−1.09965			−0.549824	+	0.835281i	$0.685305\pi$
$770$		0			0
$771$		0			0
$772$	10408.0	−	18027.2i	0.485223	−	0.840431i
$773$	−19784.0	−	34266.9i	−0.920545	−	1.59443i	−0.798574	−	0.601896i	$-0.794412\pi$
$773$	−19784.0	−	34266.9i	−0.920545	−	1.59443i	−0.121970	−	0.992534i	$-0.538921\pi$
$774$		0			0
$775$	2616.00	−	4531.04i	0.121251	−	0.210013i
$776$		0			0
$777$		0			0
$778$	−45960.0			−2.11793
$779$	−12400.0	+	21477.4i	−0.570316	+	0.987816i
$780$		0			0
$781$	21018.0	+	36404.2i	0.962975	+	1.66792i
$782$	7056.00	−	12221.4i	0.322662	−	0.558868i
$783$		0			0
$784$		0			0
$785$	−1064.00			−0.0483768
$786$		0			0
$787$	−6178.00	−	10700.6i	−0.279825	−	0.484670i	0.691516	−	0.722361i	$-0.256943\pi$
$787$	−6178.00	−	10700.6i	−0.279825	−	0.484670i	−0.971341	+	0.237690i	$0.923610\pi$
$788$	9416.00	+	16309.0i	0.425674	+	0.737289i
$789$		0			0
$790$	11840.0			0.533226
$791$		0			0
$792$		0			0
$793$	19282.0	−	33397.4i	0.863460	−	1.49556i
$794$	3732.00	+	6464.01i	0.166806	+	0.288916i
$795$		0			0
$796$	6720.00	−	11639.4i	0.299226	−	0.518275i
$797$	−21736.0			−0.966033			−0.483017	−	0.875611i	$-0.660459\pi$
$797$	−21736.0			−0.966033			−0.483017	+	0.875611i	$0.660459\pi$
$798$		0			0
$799$	27216.0			1.20505
$800$	13952.0	−	24165.6i	0.616597	−	1.06798i
$801$		0			0
$802$	−27324.0	−	47326.6i	−1.20305	−	2.08374i
$803$	19902.0	−	34471.3i	0.874628	−	1.51490i
$804$		0			0
$805$		0			0
$806$	−11904.0			−0.520224
$807$		0			0
$808$		0			0
$809$	−19155.0	−	33177.4i	−0.832452	−	1.44185i	−0.896088	−	0.443877i	$-0.853603\pi$
$809$	−19155.0	−	33177.4i	−0.832452	−	1.44185i	0.0636356	−	0.997973i	$-0.479730\pi$
$810$		0			0
$811$	−2132.00			−0.0923115			−0.0461558	−	0.998934i	$-0.514697\pi$
$811$	−2132.00			−0.0923115			−0.0461558	+	0.998934i	$0.514697\pi$
$812$		0			0
$813$		0			0
$814$	30504.0	−	52834.5i	1.31347	−	2.27500i
$815$	−544.000	−	942.236i	−0.0233810	−	0.0404970i
$816$		0			0
$817$	3400.00	−	5888.97i	0.145595	−	0.252178i
$818$	−52840.0			−2.25857
$819$		0			0
$820$	7936.00			0.337972
$821$	2501.00	−	4331.86i	0.106316	−	0.184145i	−0.807959	−	0.589239i	$-0.799428\pi$
$821$	2501.00	−	4331.86i	0.106316	−	0.184145i	0.914275	+	0.405094i	$0.132761\pi$
$822$		0			0
$823$	1806.00	+	3128.08i	0.0764923	+	0.132489i	0.901734	−	0.432291i	$-0.142295\pi$
$823$	1806.00	+	3128.08i	0.0764923	+	0.132489i	−0.825242	+	0.564779i	$0.808961\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27666.0			1.16329			0.581645	−	0.813443i	$-0.302409\pi$
$827$	27666.0			1.16329			0.581645	+	0.813443i	$0.302409\pi$
$828$		0			0
$829$	6445.00	+	11163.1i	0.270017	+	0.467683i	0.968866	−	0.247586i	$-0.0796373\pi$
$829$	6445.00	+	11163.1i	0.270017	+	0.467683i	−0.698849	+	0.715269i	$0.746304\pi$
$830$	−3744.00	−	6484.80i	−0.156574	−	0.271194i
$831$		0			0
$832$	−31744.0			−1.32275
$833$		0			0
$834$		0			0
$835$	−3752.00	+	6498.65i	−0.155501	+	0.269336i
$836$	−24800.0	−	42954.9i	−1.02599	−	1.77706i
$837$		0			0
$838$	13920.0	−	24110.1i	0.573817	−	0.993880i
$839$	−9340.00			−0.384330			−0.192165	−	0.981363i	$-0.561551\pi$
$839$	−9340.00			−0.384330			−0.192165	+	0.981363i	$0.561551\pi$
$840$		0			0
$841$	−24289.0			−0.995900
$842$	16324.0	−	28274.0i	0.668126	−	1.15723i
$843$		0			0
$844$	2672.00	+	4628.04i	0.108974	+	0.188748i
$845$	3294.00	−	5705.38i	0.134103	−	0.232273i
$846$		0			0
$847$		0			0
$848$	16512.0			0.668661
$849$		0			0
$850$	−18312.0	−	31717.3i	−0.738937	−	1.27988i
$851$	5166.00	+	8947.77i	0.208094	+	0.360430i
$852$		0			0
$853$	33082.0			1.32791			0.663954	−	0.747773i	$-0.268877\pi$
$853$	33082.0			1.32791			0.663954	+	0.747773i	$0.268877\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3772.00	−	6533.30i	−0.150349	−	0.260412i	0.781007	−	0.624523i	$-0.214706\pi$
$857$	−3772.00	−	6533.30i	−0.150349	−	0.260412i	−0.931356	+	0.364110i	$0.881373\pi$
$858$		0			0
$859$	4090.00	−	7084.09i	0.162455	−	0.281381i	−0.773293	−	0.634048i	$-0.781392\pi$
$859$	4090.00	−	7084.09i	0.162455	−	0.281381i	0.935749	+	0.352668i	$0.114725\pi$
$860$	−2176.00			−0.0862802
$861$		0			0
$862$	66408.0			2.62397
$863$	5259.00	−	9108.86i	0.207437	−	0.359292i	−0.743469	−	0.668770i	$-0.766821\pi$
$863$	5259.00	−	9108.86i	0.207437	−	0.359292i	0.950907	+	0.309478i	$0.100154\pi$
$864$		0			0
$865$	−304.000	−	526.543i	−0.0119495	−	0.0206971i
$866$	−15476.0	+	26805.2i	−0.607270	+	1.05182i
$867$		0			0
$868$		0			0
$869$	−45880.0			−1.79099
$870$		0			0
$871$	−28024.0	−	48539.0i	−1.09019	−	1.88827i
$872$		0			0
$873$		0			0
$874$	16800.0			0.650193
$875$		0			0
$876$		0			0
$877$	−7067.00	+	12240.4i	−0.272104	+	0.471299i	−0.969401	−	0.245484i	$-0.921053\pi$
$877$	−7067.00	+	12240.4i	−0.272104	+	0.471299i	0.697296	+	0.716783i	$0.254386\pi$
$878$	1680.00	+	2909.85i	0.0645755	+	0.111848i
$879$		0			0
$880$	7936.00	−	13745.6i	0.304003	−	0.526548i
$881$	6492.00			0.248265			0.124132	−	0.992266i	$-0.460385\pi$
$881$	6492.00			0.248265			0.124132	+	0.992266i	$0.460385\pi$
$882$		0			0
$883$	38228.0			1.45694			0.728468	−	0.685080i	$-0.240233\pi$
$883$	38228.0			1.45694			0.728468	+	0.685080i	$0.240233\pi$
$884$	−20832.0	+	36082.1i	−0.792597	+	1.37282i
$885$		0			0
$886$	−13236.0	−	22925.4i	−0.501887	−	0.869294i
$887$	21538.0	−	37304.9i	0.815305	−	1.41215i	−0.0938042	−	0.995591i	$-0.529903\pi$
$887$	21538.0	−	37304.9i	0.815305	−	1.41215i	0.909109	−	0.416558i	$-0.136764\pi$
$888$		0			0
$889$		0			0
$890$	3200.00			0.120522
$891$		0			0
$892$	−7328.00	−	12692.5i	−0.275067	−	0.476430i
$893$	16200.0	+	28059.2i	0.607069	+	1.05147i
$894$		0			0
$895$	2440.00			0.0911287
$896$		0			0
$897$		0			0
$898$	−6180.00	+	10704.1i	−0.229654	+	0.397772i
$899$	−240.000	−	415.692i	−0.00890372	−	0.0154217i
$900$		0			0
$901$	10836.0	−	18768.5i	0.400665	−	0.693973i
$902$	−61504.0			−2.27035
$903$		0			0
$904$		0			0
$905$	−2084.00	+	3609.59i	−0.0765464	+	0.132582i
$906$		0			0
$907$	16118.0	+	27917.2i	0.590065	+	1.02202i	0.994223	+	0.107334i	$0.0342314\pi$
$907$	16118.0	+	27917.2i	0.590065	+	1.02202i	−0.404158	+	0.914689i	$0.632435\pi$
$908$	−19776.0	+	34253.0i	−0.722786	+	1.25190i
$909$		0			0
$910$		0			0
$911$	46518.0			1.69178			0.845889	−	0.533359i	$-0.179070\pi$
$911$	46518.0			1.69178			0.845889	+	0.533359i	$0.179070\pi$
$912$		0			0
$913$	14508.0	+	25128.6i	0.525898	+	0.910882i
$914$	11828.0	+	20486.7i	0.428048	+	0.741400i
$915$		0			0
$916$	43760.0			1.57846
$917$		0			0
$918$		0			0
$919$	−8920.00	+	15449.9i	−0.320178	+	0.554565i	−0.980525	−	0.196396i	$-0.937076\pi$
$919$	−8920.00	+	15449.9i	−0.320178	+	0.554565i	0.660347	+	0.750961i	$0.270409\pi$
$920$		0			0
$921$		0			0
$922$	−31936.0	+	55314.8i	−1.14073	+	1.97581i
$923$	42036.0			1.49906
$924$		0			0
$925$	26814.0			0.953123
$926$	−2344.00	+	4059.93i	−0.0831843	+	0.144079i
$927$		0			0
$928$	−1280.00	−	2217.03i	−0.0452781	−	0.0784239i
$929$	−3500.00	+	6062.18i	−0.123607	+	0.214094i	−0.921188	−	0.389118i	$-0.872780\pi$
$929$	−3500.00	+	6062.18i	−0.123607	+	0.214094i	0.797580	+	0.603213i	$0.206113\pi$
$930$		0			0
$931$		0			0
$932$	22416.0			0.787833
$933$		0			0
$934$	10608.0	+	18373.6i	0.371632	+	0.643686i
$935$	−10416.0	−	18041.0i	−0.364320	−	0.631022i
$936$		0			0
$937$	−36114.0			−1.25912			−0.629559	−	0.776953i	$-0.716764\pi$
$937$	−36114.0			−1.25912			−0.629559	+	0.776953i	$0.716764\pi$
$938$		0			0
$939$		0			0
$940$	5184.00	−	8978.95i	0.179876	−	0.311554i
$941$	2374.00	+	4111.89i	0.0822425	+	0.142448i	0.904213	−	0.427082i	$-0.140458\pi$
$941$	2374.00	+	4111.89i	0.0822425	+	0.142448i	−0.821970	+	0.569530i	$0.807125\pi$
$942$		0			0
$943$	5208.00	−	9020.52i	0.179847	−	0.311504i
$944$	−7680.00			−0.264791
$945$		0			0
$946$	16864.0			0.579594
$947$	21347.0	−	36974.1i	0.732507	−	1.26874i	−0.223301	−	0.974749i	$-0.571683\pi$
$947$	21347.0	−	36974.1i	0.732507	−	1.26874i	0.955808	−	0.293990i	$-0.0949833\pi$
$948$		0			0
$949$	−19902.0	−	34471.3i	−0.680765	−	1.17912i
$950$	21800.0	−	37758.7i	0.744511	−	1.28953i
$951$		0			0
$952$		0			0
$953$	16742.0			0.569073			0.284537	−	0.958665i	$-0.408160\pi$
$953$	16742.0			0.569073			0.284537	+	0.958665i	$0.408160\pi$
$954$		0			0
$955$	4076.00	+	7059.84i	0.138111	+	0.239216i
$956$	−4680.00	−	8106.00i	−0.158328	−	0.274233i
$957$		0			0
$958$	−22960.0			−0.774326
$959$		0			0
$960$		0			0
$961$	13743.5	−	23804.4i	0.461331	−	0.799048i
$962$	−30504.0	−	52834.5i	−1.02234	−	1.77074i
$963$		0			0
$964$	−9352.00	+	16198.1i	−0.312456	+	0.541190i
$965$	10408.0			0.347197
$966$		0			0
$967$	−9956.00			−0.331089			−0.165545	−	0.986202i	$-0.552938\pi$
$967$	−9956.00			−0.331089			−0.165545	+	0.986202i	$0.552938\pi$
$968$		0			0
$969$		0			0
$970$	−10128.0	−	17542.2i	−0.335248	−	0.580666i
$971$	13194.0	−	22852.7i	0.436061	−	0.755280i	−0.561320	−	0.827599i	$-0.689706\pi$
$971$	13194.0	−	22852.7i	0.436061	−	0.755280i	0.997382	+	0.0723182i	$0.0230397\pi$
$972$		0			0
$973$		0			0
$974$	−35776.0			−1.17694
$975$		0			0
$976$	−19904.0	−	34474.7i	−0.652778	−	1.13064i
$977$	−393.000	−	680.696i	−0.0128692	−	0.0222901i	0.859519	−	0.511104i	$-0.170763\pi$
$977$	−393.000	−	680.696i	−0.0128692	−	0.0222901i	−0.872388	+	0.488814i	$0.837430\pi$
$978$		0			0
$979$	−12400.0			−0.404807
$980$		0			0
$981$		0			0
$982$	11116.0	−	19253.5i	0.361228	−	0.625665i
$983$	−25944.0	−	44936.3i	−0.841796	−	1.45803i	−0.888375	−	0.459118i	$-0.848165\pi$
$983$	−25944.0	−	44936.3i	−0.841796	−	1.45803i	0.0465796	−	0.998915i	$-0.485168\pi$
$984$		0			0
$985$	−4708.00	+	8154.50i	−0.152294	+	0.263781i
$986$	−3360.00			−0.108524
$987$		0			0
$988$	−49600.0			−1.59715
$989$	−1428.00	+	2473.37i	−0.0459128	+	0.0795233i
$990$		0			0
$991$	25964.0	+	44971.0i	0.832264	+	1.44152i	0.896239	+	0.443572i	$0.146289\pi$
$991$	25964.0	+	44971.0i	0.832264	+	1.44152i	−0.0639747	+	0.997952i	$0.520378\pi$
$992$	−6144.00	+	10641.7i	−0.196645	+	0.340600i
$993$		0			0
$994$		0			0
$995$	6720.00			0.214109
$996$		0			0
$997$	−193.000	−	334.286i	−0.00613076	−	0.0106188i	0.862944	−	0.505300i	$-0.168618\pi$
$997$	−193.000	−	334.286i	−0.00613076	−	0.0106188i	−0.869075	+	0.494681i	$0.835285\pi$
$998$	−39640.0	−	68658.5i	−1.25730	−	2.17770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.n.226.1		2
3.2	odd	2		147.4.e.b.79.1		2
7.2	even	3		441.4.a.b.1.1		1
7.3	odd	6		441.4.e.m.361.1		2
7.4	even	3	inner	441.4.e.n.361.1		2
7.5	odd	6		63.4.a.a.1.1		1
7.6	odd	2		441.4.e.m.226.1		2
21.2	odd	6		147.4.a.g.1.1		1
21.5	even	6		21.4.a.b.1.1	✓	1
21.11	odd	6		147.4.e.b.67.1		2
21.17	even	6		147.4.e.c.67.1		2
21.20	even	2		147.4.e.c.79.1		2
28.19	even	6		1008.4.a.m.1.1		1
35.19	odd	6		1575.4.a.k.1.1		1
84.23	even	6		2352.4.a.l.1.1		1
84.47	odd	6		336.4.a.h.1.1		1
105.47	odd	12		525.4.d.b.274.2		2
105.68	odd	12		525.4.d.b.274.1		2
105.89	even	6		525.4.a.b.1.1		1
168.5	even	6		1344.4.a.w.1.1		1
168.131	odd	6		1344.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.b.1.1	✓	1	21.5	even	6
63.4.a.a.1.1		1	7.5	odd	6
147.4.a.g.1.1		1	21.2	odd	6
147.4.e.b.67.1		2	21.11	odd	6
147.4.e.b.79.1		2	3.2	odd	2
147.4.e.c.67.1		2	21.17	even	6
147.4.e.c.79.1		2	21.20	even	2
336.4.a.h.1.1		1	84.47	odd	6
441.4.a.b.1.1		1	7.2	even	3
441.4.e.m.226.1		2	7.6	odd	2
441.4.e.m.361.1		2	7.3	odd	6
441.4.e.n.226.1		2	1.1	even	1	trivial
441.4.e.n.361.1		2	7.4	even	3	inner
525.4.a.b.1.1		1	105.89	even	6
525.4.d.b.274.1		2	105.68	odd	12
525.4.d.b.274.2		2	105.47	odd	12
1008.4.a.m.1.1		1	28.19	even	6
1344.4.a.i.1.1		1	168.131	odd	6
1344.4.a.w.1.1		1	168.5	even	6
1575.4.a.k.1.1		1	35.19	odd	6
2352.4.a.l.1.1		1	84.23	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +(-8.00000 - 13.8564i) q^{10} +(31.0000 + 53.6936i) q^{11} +62.0000 q^{13} +(32.0000 - 55.4256i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(50.0000 - 86.6025i) q^{19} -32.0000 q^{20} +248.000 q^{22} +(-21.0000 + 36.3731i) q^{23} +(54.5000 + 94.3968i) q^{25} +(124.000 - 214.774i) q^{26} +10.0000 q^{29} +(-24.0000 - 41.5692i) q^{31} +(-128.000 - 221.703i) q^{32} -336.000 q^{34} +(123.000 - 213.042i) q^{37} +(-200.000 - 346.410i) q^{38} -248.000 q^{41} +68.0000 q^{43} +(248.000 - 429.549i) q^{44} +(84.0000 + 145.492i) q^{46} +(-162.000 + 280.592i) q^{47} +436.000 q^{50} +(-248.000 - 429.549i) q^{52} +(129.000 + 223.435i) q^{53} +248.000 q^{55} +(20.0000 - 34.6410i) q^{58} +(-60.0000 - 103.923i) q^{59} +(311.000 - 538.668i) q^{61} -192.000 q^{62} -512.000 q^{64} +(124.000 - 214.774i) q^{65} +(-452.000 - 782.887i) q^{67} +(-336.000 + 581.969i) q^{68} +678.000 q^{71} +(-321.000 - 555.988i) q^{73} +(-492.000 - 852.169i) q^{74} -800.000 q^{76} +(-370.000 + 640.859i) q^{79} +(-128.000 - 221.703i) q^{80} +(-496.000 + 859.097i) q^{82} +468.000 q^{83} -336.000 q^{85} +(136.000 - 235.559i) q^{86} +(-100.000 + 173.205i) q^{89} +336.000 q^{92} +(648.000 + 1122.37i) q^{94} +(-200.000 - 346.410i) q^{95} +1266.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 8 q^{4} + 4 q^{5}+O(q^{10}) \) 2 * q + 4 * q^2 - 8 * q^4 + 4 * q^5	\( 2 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 16 q^{10} + 62 q^{11} + 124 q^{13} + 64 q^{16} - 84 q^{17} + 100 q^{19} - 64 q^{20} + 496 q^{22} - 42 q^{23} + 109 q^{25} + 248 q^{26} + 20 q^{29} - 48 q^{31} - 256 q^{32} - 672 q^{34} + 246 q^{37} - 400 q^{38} - 496 q^{41} + 136 q^{43} + 496 q^{44} + 168 q^{46} - 324 q^{47} + 872 q^{50} - 496 q^{52} + 258 q^{53} + 496 q^{55} + 40 q^{58} - 120 q^{59} + 622 q^{61} - 384 q^{62} - 1024 q^{64} + 248 q^{65} - 904 q^{67} - 672 q^{68} + 1356 q^{71} - 642 q^{73} - 984 q^{74} - 1600 q^{76} - 740 q^{79} - 256 q^{80} - 992 q^{82} + 936 q^{83} - 672 q^{85} + 272 q^{86} - 200 q^{89} + 672 q^{92} + 1296 q^{94} - 400 q^{95} + 2532 q^{97}+O(q^{100}) \) 2 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 16 * q^10 + 62 * q^11 + 124 * q^13 + 64 * q^16 - 84 * q^17 + 100 * q^19 - 64 * q^20 + 496 * q^22 - 42 * q^23 + 109 * q^25 + 248 * q^26 + 20 * q^29 - 48 * q^31 - 256 * q^32 - 672 * q^34 + 246 * q^37 - 400 * q^38 - 496 * q^41 + 136 * q^43 + 496 * q^44 + 168 * q^46 - 324 * q^47 + 872 * q^50 - 496 * q^52 + 258 * q^53 + 496 * q^55 + 40 * q^58 - 120 * q^59 + 622 * q^61 - 384 * q^62 - 1024 * q^64 + 248 * q^65 - 904 * q^67 - 672 * q^68 + 1356 * q^71 - 642 * q^73 - 984 * q^74 - 1600 * q^76 - 740 * q^79 - 256 * q^80 - 992 * q^82 + 936 * q^83 - 672 * q^85 + 272 * q^86 - 200 * q^89 + 672 * q^92 + 1296 * q^94 - 400 * q^95 + 2532 * q^97

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