LMFDB - Embedded newform 441.4.e.g.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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
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.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +(6.00000 + 10.3923i) q^{10} +(10.0000 + 17.3205i) q^{11} -84.0000 q^{13} +(-20.5000 + 35.5070i) q^{16} +(-48.0000 - 83.1384i) q^{17} +(-6.00000 + 10.3923i) q^{19} +84.0000 q^{20} -20.0000 q^{22} +(-88.0000 + 152.420i) q^{23} +(-9.50000 - 16.4545i) q^{25} +(42.0000 - 72.7461i) q^{26} -58.0000 q^{29} +(132.000 + 228.631i) q^{31} +(-80.5000 - 139.430i) q^{32} +96.0000 q^{34} +(-129.000 + 223.435i) q^{37} +(-6.00000 - 10.3923i) q^{38} +(-90.0000 + 155.885i) q^{40} +156.000 q^{43} +(-70.0000 + 121.244i) q^{44} +(-88.0000 - 152.420i) q^{46} +(-204.000 + 353.338i) q^{47} +19.0000 q^{50} +(-294.000 - 509.223i) q^{52} +(-361.000 - 625.270i) q^{53} +240.000 q^{55} +(29.0000 - 50.2295i) q^{58} +(246.000 + 426.084i) q^{59} +(246.000 - 426.084i) q^{61} -264.000 q^{62} -167.000 q^{64} +(-504.000 + 872.954i) q^{65} +(-206.000 - 356.802i) q^{67} +(336.000 - 581.969i) q^{68} -296.000 q^{71} +(-120.000 - 207.846i) q^{73} +(-129.000 - 223.435i) q^{74} -84.0000 q^{76} +(-388.000 + 672.036i) q^{79} +(246.000 + 426.084i) q^{80} -924.000 q^{83} -1152.00 q^{85} +(-78.0000 + 135.100i) q^{86} +(-150.000 - 259.808i) q^{88} +(-372.000 + 644.323i) q^{89} -1232.00 q^{92} +(-204.000 - 353.338i) q^{94} +(72.0000 + 124.708i) q^{95} -168.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 7 q^{4} + 12 q^{5} - 30 q^{8}+O(q^{10}) $ 2 * q - q^2 + 7 * q^4 + 12 * q^5 - 30 * q^8	$ 2 q - q^{2} + 7 q^{4} + 12 q^{5} - 30 q^{8} + 12 q^{10} + 20 q^{11} - 168 q^{13} - 41 q^{16} - 96 q^{17} - 12 q^{19} + 168 q^{20} - 40 q^{22} - 176 q^{23} - 19 q^{25} + 84 q^{26} - 116 q^{29} + 264 q^{31} - 161 q^{32} + 192 q^{34} - 258 q^{37} - 12 q^{38} - 180 q^{40} + 312 q^{43} - 140 q^{44} - 176 q^{46} - 408 q^{47} + 38 q^{50} - 588 q^{52} - 722 q^{53} + 480 q^{55} + 58 q^{58} + 492 q^{59} + 492 q^{61} - 528 q^{62} - 334 q^{64} - 1008 q^{65} - 412 q^{67} + 672 q^{68} - 592 q^{71} - 240 q^{73} - 258 q^{74} - 168 q^{76} - 776 q^{79} + 492 q^{80} - 1848 q^{83} - 2304 q^{85} - 156 q^{86} - 300 q^{88} - 744 q^{89} - 2464 q^{92} - 408 q^{94} + 144 q^{95} - 336 q^{97}+O(q^{100}) $ 2 * q - q^2 + 7 * q^4 + 12 * q^5 - 30 * q^8 + 12 * q^10 + 20 * q^11 - 168 * q^13 - 41 * q^16 - 96 * q^17 - 12 * q^19 + 168 * q^20 - 40 * q^22 - 176 * q^23 - 19 * q^25 + 84 * q^26 - 116 * q^29 + 264 * q^31 - 161 * q^32 + 192 * q^34 - 258 * q^37 - 12 * q^38 - 180 * q^40 + 312 * q^43 - 140 * q^44 - 176 * q^46 - 408 * q^47 + 38 * q^50 - 588 * q^52 - 722 * q^53 + 480 * q^55 + 58 * q^58 + 492 * q^59 + 492 * q^61 - 528 * q^62 - 334 * q^64 - 1008 * q^65 - 412 * q^67 + 672 * q^68 - 592 * q^71 - 240 * q^73 - 258 * q^74 - 168 * q^76 - 776 * q^79 + 492 * q^80 - 1848 * q^83 - 2304 * q^85 - 156 * q^86 - 300 * q^88 - 744 * q^89 - 2464 * q^92 - 408 * q^94 + 144 * q^95 - 336 * 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 $

$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	−0.940775	−	0.339032i	$-0.889900\pi$
$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	0.763998	+	0.645219i	$0.223234\pi$
$3$		0			0
$3$		0			0
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	−0.462425	−	0.886658i	$-0.653021\pi$
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	0.999081	−	0.0428575i	$-0.0136462\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−15.0000			−0.662913
$9$		0			0
$10$	6.00000	+	10.3923i	0.189737	+	0.328634i
$11$	10.0000	+	17.3205i	0.274101	+	0.474757i	0.969908	−	0.243472i	$-0.0782863\pi$
$11$	10.0000	+	17.3205i	0.274101	+	0.474757i	−0.695807	+	0.718229i	$0.744953\pi$
$12$		0			0
$13$	−84.0000			−1.79211			−0.896054	−	0.443945i	$-0.853579\pi$
$13$	−84.0000			−1.79211			−0.896054	+	0.443945i	$0.853579\pi$
$14$		0			0
$15$		0			0
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	−48.0000	−	83.1384i	−0.684806	−	1.18612i	−0.973498	−	0.228697i	$-0.926553\pi$
$17$	−48.0000	−	83.1384i	−0.684806	−	1.18612i	0.288691	−	0.957422i	$-0.406780\pi$
$18$		0			0
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	−0.899973	−	0.435945i	$-0.856414\pi$
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	0.827526	+	0.561427i	$0.189748\pi$
$20$	84.0000			0.939149
$21$		0			0
$22$	−20.0000			−0.193819
$23$	−88.0000	+	152.420i	−0.797794	+	1.38182i	0.123255	+	0.992375i	$0.460667\pi$
$23$	−88.0000	+	152.420i	−0.797794	+	1.38182i	−0.921050	+	0.389445i	$0.872667\pi$
$24$		0			0
$25$	−9.50000	−	16.4545i	−0.0760000	−	0.131636i
$26$	42.0000	−	72.7461i	0.316803	−	0.548719i
$27$		0			0
$28$		0			0
$29$	−58.0000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−58.0000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	132.000	+	228.631i	0.764771	+	1.32462i	0.940368	+	0.340160i	$0.110481\pi$
$31$	132.000	+	228.631i	0.764771	+	1.32462i	−0.175597	+	0.984462i	$0.556185\pi$
$32$	−80.5000	−	139.430i	−0.444704	−	0.770250i
$33$		0			0
$34$	96.0000			0.484231
$35$		0			0
$36$		0			0
$37$	−129.000	+	223.435i	−0.573175	+	0.992768i	0.423062	+	0.906101i	$0.360955\pi$
$37$	−129.000	+	223.435i	−0.573175	+	0.992768i	−0.996237	+	0.0866674i	$0.972378\pi$
$38$	−6.00000	−	10.3923i	−0.0256139	−	0.0443646i
$39$		0			0
$40$	−90.0000	+	155.885i	−0.355756	+	0.616188i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	156.000			0.553251			0.276625	−	0.960978i	$-0.410784\pi$
$43$	156.000			0.553251			0.276625	+	0.960978i	$0.410784\pi$
$44$	−70.0000	+	121.244i	−0.239839	+	0.415413i
$45$		0			0
$46$	−88.0000	−	152.420i	−0.282063	−	0.488547i
$47$	−204.000	+	353.338i	−0.633116	+	1.09659i	0.353795	+	0.935323i	$0.384891\pi$
$47$	−204.000	+	353.338i	−0.633116	+	1.09659i	−0.986911	+	0.161266i	$0.948442\pi$
$48$		0			0
$49$		0			0
$50$	19.0000			0.0537401
$51$		0			0
$52$	−294.000	−	509.223i	−0.784047	−	1.35801i
$53$	−361.000	−	625.270i	−0.935607	−	1.62052i	−0.773548	−	0.633737i	$-0.781520\pi$
$53$	−361.000	−	625.270i	−0.935607	−	1.62052i	−0.162059	−	0.986781i	$-0.551813\pi$
$54$		0			0
$55$	240.000			0.588393
$56$		0			0
$57$		0			0
$58$	29.0000	−	50.2295i	0.0656532	−	0.113715i
$59$	246.000	+	426.084i	0.542822	+	0.940195i	0.998741	+	0.0501732i	$0.0159773\pi$
$59$	246.000	+	426.084i	0.542822	+	0.940195i	−0.455919	+	0.890021i	$0.650689\pi$
$60$		0			0
$61$	246.000	−	426.084i	0.516345	−	0.894337i	−0.483474	−	0.875358i	$-0.660625\pi$
$61$	246.000	−	426.084i	0.516345	−	0.894337i	0.999820	−	0.0189781i	$-0.00604127\pi$
$62$	−264.000			−0.540775
$63$		0			0
$64$	−167.000			−0.326172
$65$	−504.000	+	872.954i	−0.961746	+	1.66579i
$66$		0			0
$67$	−206.000	−	356.802i	−0.375625	−	0.650602i	0.614795	−	0.788687i	$-0.289239\pi$
$67$	−206.000	−	356.802i	−0.375625	−	0.650602i	−0.990420	+	0.138085i	$0.955905\pi$
$68$	336.000	−	581.969i	0.599206	−	1.03785i
$69$		0			0
$70$		0			0
$71$	−296.000			−0.494771			−0.247385	−	0.968917i	$-0.579571\pi$
$71$	−296.000			−0.494771			−0.247385	+	0.968917i	$0.579571\pi$
$72$		0			0
$73$	−120.000	−	207.846i	−0.192396	−	0.333240i	0.753647	−	0.657279i	$-0.228293\pi$
$73$	−120.000	−	207.846i	−0.192396	−	0.333240i	−0.946044	+	0.324038i	$0.894959\pi$
$74$	−129.000	−	223.435i	−0.202648	−	0.350996i
$75$		0			0
$76$	−84.0000			−0.126782
$77$		0			0
$78$		0			0
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	0.445513	+	0.895275i	$0.353021\pi$
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	−0.998088	+	0.0618122i	$0.980312\pi$
$80$	246.000	+	426.084i	0.343795	+	0.595471i
$81$		0			0
$82$		0			0
$83$	−924.000			−1.22195			−0.610977	−	0.791648i	$-0.709223\pi$
$83$	−924.000			−1.22195			−0.610977	+	0.791648i	$0.709223\pi$
$84$		0			0
$85$	−1152.00			−1.47002
$86$	−78.0000	+	135.100i	−0.0978018	+	0.169398i
$87$		0			0
$88$	−150.000	−	259.808i	−0.181705	−	0.314723i
$89$	−372.000	+	644.323i	−0.443055	+	0.767394i	−0.997914	−	0.0645500i	$-0.979439\pi$
$89$	−372.000	+	644.323i	−0.443055	+	0.767394i	0.554859	+	0.831944i	$0.312772\pi$
$90$		0			0
$91$		0			0
$92$	−1232.00			−1.39614
$93$		0			0
$94$	−204.000	−	353.338i	−0.223840	−	0.387703i
$95$	72.0000	+	124.708i	0.0777584	+	0.134681i
$96$		0			0
$97$	−168.000			−0.175854			−0.0879269	−	0.996127i	$-0.528024\pi$
$97$	−168.000			−0.175854			−0.0879269	+	0.996127i	$0.528024\pi$
$98$		0			0
$99$		0			0
$100$	66.5000	−	115.181i	0.0665000	−	0.115181i
$101$	−762.000	−	1319.82i	−0.750711	−	1.30027i	−0.947478	−	0.319820i	$-0.896378\pi$
$101$	−762.000	−	1319.82i	−0.750711	−	1.30027i	0.196767	−	0.980450i	$-0.436956\pi$
$102$		0			0
$103$	204.000	−	353.338i	0.195153	−	0.338014i	−0.751798	−	0.659394i	$-0.770813\pi$
$103$	204.000	−	353.338i	0.195153	−	0.338014i	0.946951	+	0.321379i	$0.104146\pi$
$104$	1260.00			1.18801
$105$		0			0
$106$	722.000			0.661574
$107$	−410.000	+	710.141i	−0.370432	+	0.641607i	−0.989632	−	0.143627i	$-0.954124\pi$
$107$	−410.000	+	710.141i	−0.370432	+	0.641607i	0.619200	+	0.785233i	$0.287457\pi$
$108$		0			0
$109$	459.000	+	795.011i	0.403342	+	0.698608i	0.994127	−	0.108221i	$-0.0345153\pi$
$109$	459.000	+	795.011i	0.403342	+	0.698608i	−0.590785	+	0.806829i	$0.701182\pi$
$110$	−120.000	+	207.846i	−0.104014	+	0.180158i
$111$		0			0
$112$		0			0
$113$	110.000			0.0915746			0.0457873	−	0.998951i	$-0.485420\pi$
$113$	110.000			0.0915746			0.0457873	+	0.998951i	$0.485420\pi$
$114$		0			0
$115$	1056.00	+	1829.05i	0.856283	+	1.48313i
$116$	−203.000	−	351.606i	−0.162483	−	0.281430i
$117$		0			0
$118$	−492.000			−0.383833
$119$		0			0
$120$		0			0
$121$	465.500	−	806.270i	0.349737	−	0.605762i
$122$	246.000	+	426.084i	0.182556	+	0.316196i
$123$		0			0
$124$	−924.000	+	1600.41i	−0.669175	+	1.15904i
$125$	1272.00			0.910169
$126$		0			0
$127$	16.0000			0.0111793			0.00558965	−	0.999984i	$-0.498221\pi$
$127$	16.0000			0.0111793			0.00558965	+	0.999984i	$0.498221\pi$
$128$	727.500	−	1260.07i	0.502363	−	0.870119i
$129$		0			0
$130$	−504.000	−	872.954i	−0.340029	−	0.588947i
$131$	846.000	−	1465.31i	0.564239	−	0.977291i	−0.432881	−	0.901451i	$-0.642503\pi$
$131$	846.000	−	1465.31i	0.564239	−	0.977291i	0.997120	−	0.0758401i	$-0.0241638\pi$
$132$		0			0
$133$		0			0
$134$	412.000			0.265607
$135$		0			0
$136$	720.000	+	1247.08i	0.453967	+	0.786294i
$137$	563.000	+	975.145i	0.351097	+	0.608118i	0.986442	−	0.164110i	$-0.0524753\pi$
$137$	563.000	+	975.145i	0.351097	+	0.608118i	−0.635345	+	0.772229i	$0.719142\pi$
$138$		0			0
$139$	1092.00			0.666347			0.333173	−	0.942866i	$-0.391881\pi$
$139$	1092.00			0.666347			0.333173	+	0.942866i	$0.391881\pi$
$140$		0			0
$141$		0			0
$142$	148.000	−	256.344i	0.0874640	−	0.151492i
$143$	−840.000	−	1454.92i	−0.491219	−	0.850816i
$144$		0			0
$145$	−348.000	+	602.754i	−0.199309	+	0.345214i
$146$	240.000			0.136045
$147$		0			0
$148$	−1806.00			−1.00306
$149$	535.000	−	926.647i	0.294154	−	0.509489i	−0.680634	−	0.732624i	$-0.738296\pi$
$149$	535.000	−	926.647i	0.294154	−	0.509489i	0.974788	+	0.223134i	$0.0716289\pi$
$150$		0			0
$151$	60.0000	+	103.923i	0.0323360	+	0.0560075i	0.881741	−	0.471735i	$-0.156372\pi$
$151$	60.0000	+	103.923i	0.0323360	+	0.0560075i	−0.849405	+	0.527742i	$0.823039\pi$
$152$	90.0000	−	155.885i	0.0480261	−	0.0831836i
$153$		0			0
$154$		0			0
$155$	3168.00			1.64168
$156$		0			0
$157$	−918.000	−	1590.02i	−0.466652	−	0.808265i	0.532622	−	0.846353i	$-0.321207\pi$
$157$	−918.000	−	1590.02i	−0.466652	−	0.808265i	−0.999274	+	0.0380879i	$0.987873\pi$
$158$	−388.000	−	672.036i	−0.195365	−	0.338382i
$159$		0			0
$160$	−1932.00			−0.954613
$161$		0			0
$162$		0			0
$163$	−458.000	+	793.279i	−0.220082	+	0.381193i	−0.954833	−	0.297144i	$-0.903966\pi$
$163$	−458.000	+	793.279i	−0.220082	+	0.381193i	0.734751	+	0.678337i	$0.237299\pi$
$164$		0			0
$165$		0			0
$166$	462.000	−	800.207i	0.216013	−	0.374145i
$167$	−504.000			−0.233537			−0.116769	−	0.993159i	$-0.537254\pi$
$167$	−504.000			−0.233537			−0.116769	+	0.993159i	$0.537254\pi$
$168$		0			0
$169$	4859.00			2.21165
$170$	576.000	−	997.661i	0.259866	−	0.450101i
$171$		0			0
$172$	546.000	+	945.700i	0.242047	+	0.419238i
$173$	−918.000	+	1590.02i	−0.403435	+	0.698770i	−0.994138	−	0.108119i	$-0.965517\pi$
$173$	−918.000	+	1590.02i	−0.403435	+	0.698770i	0.590703	+	0.806889i	$0.298851\pi$
$174$		0			0
$175$		0			0
$176$	−820.000			−0.351192
$177$		0			0
$178$	−372.000	−	644.323i	−0.156644	−	0.271315i
$179$	1186.00	+	2054.21i	0.495228	+	0.857760i	0.999985	−	0.00550156i	$-0.00175121\pi$
$179$	1186.00	+	2054.21i	0.495228	+	0.857760i	−0.504757	+	0.863262i	$0.668418\pi$
$180$		0			0
$181$	−1092.00			−0.448440			−0.224220	−	0.974539i	$-0.571983\pi$
$181$	−1092.00			−0.448440			−0.224220	+	0.974539i	$0.571983\pi$
$182$		0			0
$183$		0			0
$184$	1320.00	−	2286.31i	0.528868	−	0.916026i
$185$	1548.00	+	2681.21i	0.615196	+	1.06555i
$186$		0			0
$187$	960.000	−	1662.77i	0.375413	−	0.650234i
$188$	−2856.00			−1.10795
$189$		0			0
$190$	−144.000			−0.0549835
$191$	1256.00	−	2175.46i	0.475817	−	0.824139i	−0.523800	−	0.851842i	$-0.675486\pi$
$191$	1256.00	−	2175.46i	0.475817	−	0.824139i	0.999616	+	0.0277030i	$0.00881927\pi$
$192$		0			0
$193$	1215.00	+	2104.44i	0.453148	+	0.784876i	0.998580	−	0.0532797i	$-0.0169675\pi$
$193$	1215.00	+	2104.44i	0.453148	+	0.784876i	−0.545431	+	0.838155i	$0.683634\pi$
$194$	84.0000	−	145.492i	0.0310868	−	0.0538440i
$195$		0			0
$196$		0			0
$197$	1762.00			0.637245			0.318623	−	0.947882i	$-0.396780\pi$
$197$	1762.00			0.637245			0.318623	+	0.947882i	$0.396780\pi$
$198$		0			0
$199$	−1548.00	−	2681.21i	−0.551431	−	0.955107i	−0.998172	−	0.0604433i	$-0.980749\pi$
$199$	−1548.00	−	2681.21i	−0.551431	−	0.955107i	0.446740	−	0.894664i	$-0.352585\pi$
$200$	142.500	+	246.817i	0.0503814	+	0.0872631i
$201$		0			0
$202$	1524.00			0.530833
$203$		0			0
$204$		0			0
$205$		0			0
$206$	204.000	+	353.338i	0.0689969	+	0.119506i
$207$		0			0
$208$	1722.00	−	2982.59i	0.574035	−	0.994257i
$209$	−240.000			−0.0794313
$210$		0			0
$211$	156.000			0.0508980			0.0254490	−	0.999676i	$-0.491898\pi$
$211$	156.000			0.0508980			0.0254490	+	0.999676i	$0.491898\pi$
$212$	2527.00	−	4376.89i	0.818656	−	1.41795i
$213$		0			0
$214$	−410.000	−	710.141i	−0.130967	−	0.226842i
$215$	936.000	−	1621.20i	0.296905	−	0.514255i
$216$		0			0
$217$		0			0
$218$	−918.000			−0.285206
$219$		0			0
$220$	840.000	+	1454.92i	0.257422	+	0.445868i
$221$	4032.00	+	6983.63i	1.22725	+	2.12565i
$222$		0			0
$223$	5040.00			1.51347			0.756734	−	0.653723i	$-0.226794\pi$
$223$	5040.00			1.51347			0.756734	+	0.653723i	$0.226794\pi$
$224$		0			0
$225$		0			0
$226$	−55.0000	+	95.2628i	−0.0161883	+	0.0280389i
$227$	1086.00	+	1881.01i	0.317535	+	0.549986i	0.979973	−	0.199130i	$-0.0638117\pi$
$227$	1086.00	+	1881.01i	0.317535	+	0.549986i	−0.662438	+	0.749116i	$0.730478\pi$
$228$		0			0
$229$	−1350.00	+	2338.27i	−0.389566	+	0.674747i	−0.992391	−	0.123126i	$-0.960708\pi$
$229$	−1350.00	+	2338.27i	−0.389566	+	0.674747i	0.602826	+	0.797873i	$0.294041\pi$
$230$	−2112.00			−0.605483
$231$		0			0
$232$	870.000			0.246200
$233$	−1901.00	+	3292.63i	−0.534501	+	0.925782i	0.464687	+	0.885475i	$0.346167\pi$
$233$	−1901.00	+	3292.63i	−0.534501	+	0.925782i	−0.999187	+	0.0403071i	$0.987166\pi$
$234$		0			0
$235$	2448.00	+	4240.06i	0.679532	+	1.17698i
$236$	−1722.00	+	2982.59i	−0.474969	+	0.822670i
$237$		0			0
$238$		0			0
$239$	4408.00			1.19301			0.596506	−	0.802609i	$-0.296555\pi$
$239$	4408.00			1.19301			0.596506	+	0.802609i	$0.296555\pi$
$240$		0			0
$241$	−1548.00	−	2681.21i	−0.413757	−	0.716648i	0.581540	−	0.813518i	$-0.302450\pi$
$241$	−1548.00	−	2681.21i	−0.413757	−	0.716648i	−0.995297	+	0.0968696i	$0.969117\pi$
$242$	465.500	+	806.270i	0.123651	+	0.214169i
$243$		0			0
$244$	3444.00			0.903605
$245$		0			0
$246$		0			0
$247$	504.000	−	872.954i	0.129833	−	0.224877i
$248$	−1980.00	−	3429.46i	−0.506976	−	0.878109i
$249$		0			0
$250$	−636.000	+	1101.58i	−0.160897	+	0.278681i
$251$	924.000			0.232360			0.116180	−	0.993228i	$-0.462935\pi$
$251$	924.000			0.232360			0.116180	+	0.993228i	$0.462935\pi$
$252$		0			0
$253$	−3520.00			−0.874706
$254$	−8.00000	+	13.8564i	−0.00197624	+	0.00342295i
$255$		0			0
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	−1380.00	+	2390.23i	−0.334950	+	0.580150i	−0.983475	−	0.181043i	$-0.942053\pi$
$257$	−1380.00	+	2390.23i	−0.334950	+	0.580150i	0.648526	+	0.761193i	$0.275386\pi$
$258$		0			0
$259$		0			0
$260$	−7056.00			−1.68306
$261$		0			0
$262$	846.000	+	1465.31i	0.199489	+	0.345525i
$263$	−1180.00	−	2043.82i	−0.276661	−	0.479191i	0.693892	−	0.720079i	$-0.255895\pi$
$263$	−1180.00	−	2043.82i	−0.276661	−	0.479191i	−0.970553	+	0.240888i	$0.922561\pi$
$264$		0			0
$265$	−8664.00			−2.00840
$266$		0			0
$267$		0			0
$268$	1442.00	−	2497.62i	0.328672	−	0.569277i
$269$	2010.00	+	3481.42i	0.455583	+	0.789093i	0.998722	−	0.0505501i	$-0.0160974\pi$
$269$	2010.00	+	3481.42i	0.455583	+	0.789093i	−0.543138	+	0.839643i	$0.682764\pi$
$270$		0			0
$271$	−2400.00	+	4156.92i	−0.537969	+	0.931790i	0.461044	+	0.887377i	$0.347475\pi$
$271$	−2400.00	+	4156.92i	−0.537969	+	0.931790i	−0.999013	+	0.0444126i	$0.985858\pi$
$272$	3936.00			0.877408
$273$		0			0
$274$	−1126.00			−0.248263
$275$	190.000	−	329.090i	0.0416634	−	0.0721631i
$276$		0			0
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	−0.968778	−	0.247929i	$-0.920250\pi$
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	0.269676	−	0.962951i	$-0.413083\pi$
$278$	−546.000	+	945.700i	−0.117795	+	0.204026i
$279$		0			0
$280$		0			0
$281$	2602.00			0.552393			0.276196	−	0.961101i	$-0.410926\pi$
$281$	2602.00			0.552393			0.276196	+	0.961101i	$0.410926\pi$
$282$		0			0
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	0.959110	+	0.283033i	$0.0913405\pi$
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	−0.234442	+	0.972130i	$0.575326\pi$
$284$	−1036.00	−	1794.40i	−0.216462	−	0.374924i
$285$		0			0
$286$	1680.00			0.347344
$287$		0			0
$288$		0			0
$289$	−2151.50	+	3726.51i	−0.437920	+	0.758499i
$290$	−348.000	−	602.754i	−0.0704664	−	0.122051i
$291$		0			0
$292$	840.000	−	1454.92i	0.168347	−	0.291585i
$293$	4452.00			0.887674			0.443837	−	0.896107i	$-0.353617\pi$
$293$	4452.00			0.887674			0.443837	+	0.896107i	$0.353617\pi$
$294$		0			0
$295$	5904.00			1.16523
$296$	1935.00	−	3351.52i	0.379965	−	0.658118i
$297$		0			0
$298$	535.000	+	926.647i	0.103999	+	0.180132i
$299$	7392.00	−	12803.3i	1.42973	−	2.47637i
$300$		0			0
$301$		0			0
$302$	−120.000			−0.0228650
$303$		0			0
$304$	−246.000	−	426.084i	−0.0464114	−	0.0803869i
$305$	−2952.00	−	5113.01i	−0.554200	−	0.959903i
$306$		0			0
$307$	−2436.00			−0.452866			−0.226433	−	0.974027i	$-0.572706\pi$
$307$	−2436.00			−0.452866			−0.226433	+	0.974027i	$0.572706\pi$
$308$		0			0
$309$		0			0
$310$	−1584.00	+	2743.57i	−0.290210	+	0.502659i
$311$	−3744.00	−	6484.80i	−0.682646	−	1.18238i	−0.974171	−	0.225814i	$-0.927496\pi$
$311$	−3744.00	−	6484.80i	−0.682646	−	1.18238i	0.291525	−	0.956563i	$-0.405837\pi$
$312$		0			0
$313$	876.000	−	1517.28i	0.158193	−	0.273999i	−0.776024	−	0.630703i	$-0.782766\pi$
$313$	876.000	−	1517.28i	0.158193	−	0.273999i	0.934217	+	0.356705i	$0.116100\pi$
$314$	1836.00			0.329973
$315$		0			0
$316$	−5432.00			−0.967006
$317$	−781.000	+	1352.73i	−0.138376	+	0.239675i	−0.926882	−	0.375352i	$-0.877522\pi$
$317$	−781.000	+	1352.73i	−0.138376	+	0.239675i	0.788506	+	0.615027i	$0.210855\pi$
$318$		0			0
$319$	−580.000	−	1004.59i	−0.101799	−	0.176320i
$320$	−1002.00	+	1735.51i	−0.175042	+	0.303182i
$321$		0			0
$322$		0			0
$323$	1152.00			0.198449
$324$		0			0
$325$	798.000	+	1382.18i	0.136200	+	0.235906i
$326$	−458.000	−	793.279i	−0.0778107	−	0.134772i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3546.00	−	6141.85i	0.588839	−	1.01990i	−0.405546	−	0.914075i	$-0.632918\pi$
$331$	3546.00	−	6141.85i	0.588839	−	1.01990i	0.994385	−	0.105825i	$-0.0337482\pi$
$332$	−3234.00	−	5601.45i	−0.534605	−	0.925963i
$333$		0			0
$334$	252.000	−	436.477i	0.0412839	−	0.0715058i
$335$	−4944.00			−0.806327
$336$		0			0
$337$	366.000			0.0591611			0.0295805	−	0.999562i	$-0.490583\pi$
$337$	366.000			0.0591611			0.0295805	+	0.999562i	$0.490583\pi$
$338$	−2429.50	+	4208.02i	−0.390969	+	0.677177i
$339$		0			0
$340$	−4032.00	−	6983.63i	−0.643135	−	1.11394i
$341$	−2640.00	+	4572.61i	−0.419249	+	0.726161i
$342$		0			0
$343$		0			0
$344$	−2340.00			−0.366757
$345$		0			0
$346$	−918.000	−	1590.02i	−0.142636	−	0.247052i
$347$	−3182.00	−	5511.39i	−0.492273	−	0.852642i	0.507687	−	0.861541i	$-0.330500\pi$
$347$	−3182.00	−	5511.39i	−0.492273	−	0.852642i	−0.999960	+	0.00889958i	$0.997167\pi$
$348$		0			0
$349$	−10500.0			−1.61046			−0.805232	−	0.592960i	$-0.797959\pi$
$349$	−10500.0			−1.61046			−0.805232	+	0.592960i	$0.797959\pi$
$350$		0			0
$351$		0			0
$352$	1610.00	−	2788.60i	0.243788	−	0.422253i
$353$	204.000	+	353.338i	0.0307587	+	0.0532756i	0.880995	−	0.473126i	$-0.156874\pi$
$353$	204.000	+	353.338i	0.0307587	+	0.0532756i	−0.850236	+	0.526401i	$0.823541\pi$
$354$		0			0
$355$	−1776.00	+	3076.12i	−0.265522	+	0.459898i
$356$	−5208.00			−0.775347
$357$		0			0
$358$	−2372.00			−0.350179
$359$	−5968.00	+	10336.9i	−0.877379	+	1.51966i	−0.0231719	+	0.999731i	$0.507376\pi$
$359$	−5968.00	+	10336.9i	−0.877379	+	1.51966i	−0.854207	+	0.519933i	$0.825957\pi$
$360$		0			0
$361$	3357.50	+	5815.36i	0.489503	+	0.847844i
$362$	546.000	−	945.700i	0.0792738	−	0.137306i
$363$		0			0
$364$		0			0
$365$	−2880.00			−0.413003
$366$		0			0
$367$	1224.00	+	2120.03i	0.174093	+	0.301539i	0.939847	−	0.341595i	$-0.110967\pi$
$367$	1224.00	+	2120.03i	0.174093	+	0.301539i	−0.765754	+	0.643134i	$0.777634\pi$
$368$	−3608.00	−	6249.24i	−0.511087	−	0.885229i
$369$		0			0
$370$	−3096.00			−0.435009
$371$		0			0
$372$		0			0
$373$	−5687.00	+	9850.17i	−0.789442	+	1.36735i	0.136868	+	0.990589i	$0.456296\pi$
$373$	−5687.00	+	9850.17i	−0.789442	+	1.36735i	−0.926309	+	0.376764i	$0.877037\pi$
$374$	960.000	+	1662.77i	0.132728	+	0.229892i
$375$		0			0
$376$	3060.00	−	5300.08i	0.419701	−	0.726943i
$377$	4872.00			0.665572
$378$		0			0
$379$	−5892.00			−0.798553			−0.399277	−	0.916830i	$-0.630739\pi$
$379$	−5892.00			−0.798553			−0.399277	+	0.916830i	$0.630739\pi$
$380$	−504.000	+	872.954i	−0.0680386	+	0.117846i
$381$		0			0
$382$	1256.00	+	2175.46i	0.168227	+	0.291377i
$383$	−5244.00	+	9082.87i	−0.699624	+	1.21178i	0.268973	+	0.963148i	$0.413316\pi$
$383$	−5244.00	+	9082.87i	−0.699624	+	1.21178i	−0.968597	+	0.248636i	$0.920018\pi$
$384$		0			0
$385$		0			0
$386$	−2430.00			−0.320424
$387$		0			0
$388$	−588.000	−	1018.45i	−0.0769360	−	0.133257i
$389$	2257.00	+	3909.24i	0.294176	+	0.509528i	0.974793	−	0.223112i	$-0.0716215\pi$
$389$	2257.00	+	3909.24i	0.294176	+	0.509528i	−0.680617	+	0.732639i	$0.738288\pi$
$390$		0			0
$391$	16896.0			2.18534
$392$		0			0
$393$		0			0
$394$	−881.000	+	1525.94i	−0.112650	+	0.195116i
$395$	4656.00	+	8064.43i	0.593086	+	1.02725i
$396$		0			0
$397$	3018.00	−	5227.33i	0.381534	−	0.660837i	−0.609748	−	0.792596i	$-0.708729\pi$
$397$	3018.00	−	5227.33i	0.381534	−	0.660837i	0.991282	+	0.131759i	$0.0420625\pi$
$398$	3096.00			0.389921
$399$		0			0
$400$	779.000			0.0973750
$401$	−3385.00	+	5862.99i	−0.421543	+	0.730134i	−0.996091	−	0.0883370i	$-0.971845\pi$
$401$	−3385.00	+	5862.99i	−0.421543	+	0.730134i	0.574547	+	0.818471i	$0.305178\pi$
$402$		0			0
$403$	−11088.0	−	19205.0i	−1.37055	−	2.37387i
$404$	5334.00	−	9238.76i	0.656872	−	1.13774i
$405$		0			0
$406$		0			0
$407$	−5160.00			−0.628432
$408$		0			0
$409$	−6252.00	−	10828.8i	−0.755847	−	1.30917i	−0.944952	−	0.327209i	$-0.893892\pi$
$409$	−6252.00	−	10828.8i	−0.755847	−	1.30917i	0.189105	−	0.981957i	$-0.439441\pi$
$410$		0			0
$411$		0			0
$412$	2856.00			0.341517
$413$		0			0
$414$		0			0
$415$	−5544.00	+	9602.49i	−0.655769	+	1.13583i
$416$	6762.00	+	11712.1i	0.796958	+	1.38037i
$417$		0			0
$418$	120.000	−	207.846i	0.0140416	−	0.0243208i
$419$	−9492.00			−1.10672			−0.553359	−	0.832943i	$-0.686654\pi$
$419$	−9492.00			−1.10672			−0.553359	+	0.832943i	$0.686654\pi$
$420$		0			0
$421$	5182.00			0.599894			0.299947	−	0.953956i	$-0.403031\pi$
$421$	5182.00			0.599894			0.299947	+	0.953956i	$0.403031\pi$
$422$	−78.0000	+	135.100i	−0.00899758	+	0.0155843i
$423$		0			0
$424$	5415.00	+	9379.06i	0.620226	+	1.07426i
$425$	−912.000	+	1579.63i	−0.104091	+	0.180290i
$426$		0			0
$427$		0			0
$428$	−5740.00			−0.648256
$429$		0			0
$430$	936.000	+	1621.20i	0.104972	+	0.181817i
$431$	−2860.00	−	4953.67i	−0.319632	−	0.553619i	0.660779	−	0.750580i	$-0.270226\pi$
$431$	−2860.00	−	4953.67i	−0.319632	−	0.553619i	−0.980411	+	0.196962i	$0.936893\pi$
$432$		0			0
$433$	13608.0			1.51030			0.755149	−	0.655554i	$-0.227565\pi$
$433$	13608.0			1.51030			0.755149	+	0.655554i	$0.227565\pi$
$434$		0			0
$435$		0			0
$436$	−3213.00	+	5565.08i	−0.352924	+	0.611282i
$437$	−1056.00	−	1829.05i	−0.115596	−	0.200218i
$438$		0			0
$439$	−6432.00	+	11140.6i	−0.699277	+	1.21118i	0.269440	+	0.963017i	$0.413161\pi$
$439$	−6432.00	+	11140.6i	−0.699277	+	1.21118i	−0.968717	+	0.248166i	$0.920172\pi$
$440$	−3600.00			−0.390053
$441$		0			0
$442$	−8064.00			−0.867795
$443$	−6626.00	+	11476.6i	−0.710634	+	1.23085i	0.253986	+	0.967208i	$0.418258\pi$
$443$	−6626.00	+	11476.6i	−0.710634	+	1.23085i	−0.964620	+	0.263646i	$0.915075\pi$
$444$		0			0
$445$	4464.00	+	7731.87i	0.475537	+	0.823654i
$446$	−2520.00	+	4364.77i	−0.267546	+	0.463403i
$447$		0			0
$448$		0			0
$449$	−226.000			−0.0237541			−0.0118771	−	0.999929i	$-0.503781\pi$
$449$	−226.000			−0.0237541			−0.0118771	+	0.999929i	$0.503781\pi$
$450$		0			0
$451$		0			0
$452$	385.000	+	666.840i	0.0400639	+	0.0693927i
$453$		0			0
$454$	−2172.00			−0.224531
$455$		0			0
$456$		0			0
$457$	5667.00	−	9815.53i	0.580068	−	1.00471i	−0.415403	−	0.909638i	$-0.636359\pi$
$457$	5667.00	−	9815.53i	0.580068	−	1.00471i	0.995471	−	0.0950696i	$-0.0303074\pi$
$458$	−1350.00	−	2338.27i	−0.137732	−	0.238559i
$459$		0			0
$460$	−7392.00	+	12803.3i	−0.749247	+	1.29773i
$461$	1596.00			0.161243			0.0806216	−	0.996745i	$-0.474309\pi$
$461$	1596.00			0.161243			0.0806216	+	0.996745i	$0.474309\pi$
$462$		0			0
$463$	12728.0			1.27758			0.638791	−	0.769380i	$-0.279435\pi$
$463$	12728.0			1.27758			0.638791	+	0.769380i	$0.279435\pi$
$464$	1189.00	−	2059.41i	0.118961	−	0.206047i
$465$		0			0
$466$	−1901.00	−	3292.63i	−0.188975	−	0.327313i
$467$	−1506.00	+	2608.47i	−0.149228	+	0.258470i	−0.930942	−	0.365166i	$-0.881012\pi$
$467$	−1506.00	+	2608.47i	−0.149228	+	0.258470i	0.781715	+	0.623636i	$0.214345\pi$
$468$		0			0
$469$		0			0
$470$	−4896.00			−0.480501
$471$		0			0
$472$	−3690.00	−	6391.27i	−0.359843	−	0.623267i
$473$	1560.00	+	2702.00i	0.151647	+	0.262660i
$474$		0			0
$475$	228.000			0.0220239
$476$		0			0
$477$		0			0
$478$	−2204.00	+	3817.44i	−0.210897	+	0.365284i
$479$	−2148.00	−	3720.45i	−0.204895	−	0.354888i	0.745204	−	0.666836i	$-0.232352\pi$
$479$	−2148.00	−	3720.45i	−0.204895	−	0.354888i	−0.950099	+	0.311948i	$0.899019\pi$
$480$		0			0
$481$	10836.0	−	18768.5i	1.02719	−	1.77915i
$482$	3096.00			0.292570
$483$		0			0
$484$	6517.00			0.612040
$485$	−1008.00	+	1745.91i	−0.0943730	+	0.163459i
$486$		0			0
$487$	4092.00	+	7087.55i	0.380752	+	0.659482i	0.991170	−	0.132598i	$-0.0423318\pi$
$487$	4092.00	+	7087.55i	0.380752	+	0.659482i	−0.610418	+	0.792079i	$0.708998\pi$
$488$	−3690.00	+	6391.27i	−0.342292	+	0.592867i
$489$		0			0
$490$		0			0
$491$	12164.0			1.11803			0.559016	−	0.829157i	$-0.311179\pi$
$491$	12164.0			1.11803			0.559016	+	0.829157i	$0.311179\pi$
$492$		0			0
$493$	2784.00	+	4822.03i	0.254331	+	0.440514i
$494$	504.000	+	872.954i	0.0459029	+	0.0795062i
$495$		0			0
$496$	−10824.0			−0.979863
$497$		0			0
$498$		0			0
$499$	−486.000	+	841.777i	−0.0435999	+	0.0755172i	−0.887002	−	0.461766i	$-0.847216\pi$
$499$	−486.000	+	841.777i	−0.0435999	+	0.0755172i	0.843402	+	0.537283i	$0.180549\pi$
$500$	4452.00	+	7711.09i	0.398199	+	0.689701i
$501$		0			0
$502$	−462.000	+	800.207i	−0.0410758	+	0.0711454i
$503$	−7728.00			−0.685039			−0.342519	−	0.939511i	$-0.611280\pi$
$503$	−7728.00			−0.685039			−0.342519	+	0.939511i	$0.611280\pi$
$504$		0			0
$505$	−18288.0			−1.61150
$506$	1760.00	−	3048.41i	0.154628	−	0.267823i
$507$		0			0
$508$	56.0000	+	96.9948i	0.00489094	+	0.00847136i
$509$	5802.00	−	10049.4i	0.505244	−	0.875108i	−0.494738	−	0.869042i	$-0.664736\pi$
$509$	5802.00	−	10049.4i	0.505244	−	0.875108i	0.999982	−	0.00606572i	$-0.00193079\pi$
$510$		0			0
$511$		0			0
$512$	11521.0			0.994455
$513$		0			0
$514$	−1380.00	−	2390.23i	−0.118423	−	0.205114i
$515$	−2448.00	−	4240.06i	−0.209460	−	0.362795i
$516$		0			0
$517$	−8160.00			−0.694152
$518$		0			0
$519$		0			0
$520$	7560.00	−	13094.3i	0.637554	−	1.10428i
$521$	−5424.00	−	9394.64i	−0.456103	−	0.789994i	0.542648	−	0.839960i	$-0.317422\pi$
$521$	−5424.00	−	9394.64i	−0.456103	−	0.789994i	−0.998751	+	0.0499665i	$0.984089\pi$
$522$		0			0
$523$	9066.00	−	15702.8i	0.757989	−	1.31288i	−0.185885	−	0.982572i	$-0.559515\pi$
$523$	9066.00	−	15702.8i	0.757989	−	1.31288i	0.943874	−	0.330305i	$-0.107152\pi$
$524$	11844.0			0.987419
$525$		0			0
$526$	2360.00			0.195629
$527$	12672.0	−	21948.5i	1.04744	−	1.81422i
$528$		0			0
$529$	−9404.50	−	16289.1i	−0.772951	−	1.33879i
$530$	4332.00	−	7503.24i	0.355038	−	0.614944i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4920.00	+	8521.69i	0.397589	+	0.688644i
$536$	3090.00	+	5352.04i	0.249007	+	0.431293i
$537$		0			0
$538$	−4020.00			−0.322146
$539$		0			0
$540$		0			0
$541$	−3475.00	+	6018.88i	−0.276159	+	0.478321i	−0.970427	−	0.241395i	$-0.922395\pi$
$541$	−3475.00	+	6018.88i	−0.276159	+	0.478321i	0.694268	+	0.719717i	$0.255728\pi$
$542$	−2400.00	−	4156.92i	−0.190201	−	0.329437i
$543$		0			0
$544$	−7728.00	+	13385.3i	−0.609072	+	1.05494i
$545$	11016.0			0.865823
$546$		0			0
$547$	17012.0			1.32976			0.664882	−	0.746949i	$-0.268482\pi$
$547$	17012.0			1.32976			0.664882	+	0.746949i	$0.268482\pi$
$548$	−3941.00	+	6826.01i	−0.307210	+	0.532104i
$549$		0			0
$550$	190.000	+	329.090i	0.0147302	+	0.0255135i
$551$	348.000	−	602.754i	0.0269062	−	0.0466028i
$552$		0			0
$553$		0			0
$554$	6446.00			0.494340
$555$		0			0
$556$	3822.00	+	6619.90i	0.291527	+	0.504939i
$557$	1963.00	+	3400.02i	0.149327	+	0.258641i	0.930979	−	0.365073i	$-0.118956\pi$
$557$	1963.00	+	3400.02i	0.149327	+	0.258641i	−0.781652	+	0.623715i	$0.785623\pi$
$558$		0			0
$559$	−13104.0			−0.991485
$560$		0			0
$561$		0			0
$562$	−1301.00	+	2253.40i	−0.0976501	+	0.169135i
$563$	−9414.00	−	16305.5i	−0.704712	−	1.22060i	−0.966795	−	0.255552i	$-0.917743\pi$
$563$	−9414.00	−	16305.5i	−0.704712	−	1.22060i	0.262084	−	0.965045i	$-0.415590\pi$
$564$		0			0
$565$	660.000	−	1143.15i	0.0491441	−	0.0851201i
$566$	−6900.00			−0.512418
$567$		0			0
$568$	4440.00			0.327990
$569$	5995.00	−	10383.6i	0.441693	−	0.765035i	−0.556122	−	0.831101i	$-0.687711\pi$
$569$	5995.00	−	10383.6i	0.441693	−	0.765035i	0.997815	+	0.0660655i	$0.0210446\pi$
$570$		0			0
$571$	7858.00	+	13610.5i	0.575914	+	0.997513i	0.995942	+	0.0900014i	$0.0286871\pi$
$571$	7858.00	+	13610.5i	0.575914	+	0.997513i	−0.420027	+	0.907511i	$0.637980\pi$
$572$	5880.00	−	10184.5i	0.429817	−	0.744464i
$573$		0			0
$574$		0			0
$575$	3344.00			0.242529
$576$		0			0
$577$	6936.00	+	12013.5i	0.500432	+	0.866774i	1.00000		0.000499291i	$0.000158929\pi$
$577$	6936.00	+	12013.5i	0.500432	+	0.866774i	−0.499568	+	0.866275i	$0.666508\pi$
$578$	−2151.50	−	3726.51i	−0.154828	−	0.268170i
$579$		0			0
$580$	−4872.00			−0.348791
$581$		0			0
$582$		0			0
$583$	7220.00	−	12505.4i	0.512902	−	0.888372i
$584$	1800.00	+	3117.69i	0.127542	+	0.220909i
$585$		0			0
$586$	−2226.00	+	3855.55i	−0.156920	+	0.271794i
$587$	−8820.00			−0.620171			−0.310085	−	0.950709i	$-0.600358\pi$
$587$	−8820.00			−0.620171			−0.310085	+	0.950709i	$0.600358\pi$
$588$		0			0
$589$	−3168.00			−0.221622
$590$	−2952.00	+	5113.01i	−0.205986	+	0.356779i
$591$		0			0
$592$	−5289.00	−	9160.82i	−0.367190	−	0.635992i
$593$	−8436.00	+	14611.6i	−0.584191	+	1.01185i	0.410785	+	0.911732i	$0.365255\pi$
$593$	−8436.00	+	14611.6i	−0.584191	+	1.01185i	−0.994976	+	0.100116i	$0.968079\pi$
$594$		0			0
$595$		0			0
$596$	7490.00			0.514769
$597$		0			0
$598$	7392.00	+	12803.3i	0.505487	+	0.875530i
$599$	−3028.00	−	5244.65i	−0.206545	−	0.357747i	0.744079	−	0.668092i	$-0.232889\pi$
$599$	−3028.00	−	5244.65i	−0.206545	−	0.357747i	−0.950624	+	0.310345i	$0.899555\pi$
$600$		0			0
$601$	10752.0			0.729756			0.364878	−	0.931055i	$-0.381111\pi$
$601$	10752.0			0.729756			0.364878	+	0.931055i	$0.381111\pi$
$602$		0			0
$603$		0			0
$604$	−420.000	+	727.461i	−0.0282940	+	0.0490066i
$605$	−5586.00	−	9675.24i	−0.375377	−	0.650172i
$606$		0			0
$607$	−10128.0	+	17542.2i	−0.677237	+	1.17301i	0.298573	+	0.954387i	$0.403489\pi$
$607$	−10128.0	+	17542.2i	−0.677237	+	1.17301i	−0.975810	+	0.218622i	$0.929844\pi$
$608$	1932.00			0.128870
$609$		0			0
$610$	5904.00			0.391879
$611$	17136.0	−	29680.4i	1.13461	−	1.96521i
$612$		0			0
$613$	14095.0	+	24413.3i	0.928698	+	1.60855i	0.785504	+	0.618857i	$0.212404\pi$
$613$	14095.0	+	24413.3i	0.928698	+	1.60855i	0.143194	+	0.989695i	$0.454263\pi$
$614$	1218.00	−	2109.64i	0.0800562	−	0.138661i
$615$		0			0
$616$		0			0
$617$	−29318.0			−1.91296			−0.956482	−	0.291793i	$-0.905748\pi$
$617$	−29318.0			−1.91296			−0.956482	+	0.291793i	$0.905748\pi$
$618$		0			0
$619$	−12174.0	−	21086.0i	−0.790492	−	1.36917i	−0.925663	−	0.378350i	$-0.876492\pi$
$619$	−12174.0	−	21086.0i	−0.790492	−	1.36917i	0.135171	−	0.990822i	$-0.456842\pi$
$620$	11088.0	+	19205.0i	0.718234	+	1.24402i
$621$		0			0
$622$	7488.00			0.482703
$623$		0			0
$624$		0			0
$625$	8819.50	−	15275.8i	0.564448	−	0.977653i
$626$	876.000	+	1517.28i	0.0559297	+	0.0968731i
$627$		0			0
$628$	6426.00	−	11130.2i	0.408321	−	0.707232i
$629$	24768.0			1.57006
$630$		0			0
$631$	−25184.0			−1.58884			−0.794421	−	0.607368i	$-0.792226\pi$
$631$	−25184.0			−1.58884			−0.794421	+	0.607368i	$0.792226\pi$
$632$	5820.00	−	10080.5i	0.366309	−	0.634465i
$633$		0			0
$634$	−781.000	−	1352.73i	−0.0489235	−	0.0847379i
$635$	96.0000	−	166.277i	0.00599944	−	0.0103913i
$636$		0			0
$637$		0			0
$638$	1160.00			0.0719825
$639$		0			0
$640$	−8730.00	−	15120.8i	−0.539193	−	0.933910i
$641$	16159.0	+	27988.2i	0.995698	+	1.72460i	0.578097	+	0.815968i	$0.303795\pi$
$641$	16159.0	+	27988.2i	0.995698	+	1.72460i	0.417600	+	0.908631i	$0.362871\pi$
$642$		0			0
$643$	−3948.00			−0.242137			−0.121068	−	0.992644i	$-0.538632\pi$
$643$	−3948.00			−0.242137			−0.121068	+	0.992644i	$0.538632\pi$
$644$		0			0
$645$		0			0
$646$	−576.000	+	997.661i	−0.0350811	+	0.0607623i
$647$	6924.00	+	11992.7i	0.420727	+	0.728721i	0.996011	−	0.0892331i	$-0.0284416\pi$
$647$	6924.00	+	11992.7i	0.420727	+	0.728721i	−0.575284	+	0.817954i	$0.695108\pi$
$648$		0			0
$649$	−4920.00	+	8521.69i	−0.297576	+	0.515417i
$650$	−1596.00			−0.0963081
$651$		0			0
$652$	−6412.00			−0.385143
$653$	−1579.00	+	2734.91i	−0.0946264	+	0.163898i	−0.909453	−	0.415808i	$-0.863499\pi$
$653$	−1579.00	+	2734.91i	−0.0946264	+	0.163898i	0.814826	+	0.579705i	$0.196832\pi$
$654$		0			0
$655$	−10152.0	−	17583.8i	−0.605605	−	1.04894i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	24596.0			1.45391			0.726953	−	0.686687i	$-0.240936\pi$
$659$	24596.0			1.45391			0.726953	+	0.686687i	$0.240936\pi$
$660$		0			0
$661$	7734.00	+	13395.7i	0.455095	+	0.788248i	0.998694	−	0.0510977i	$-0.0162720\pi$
$661$	7734.00	+	13395.7i	0.455095	+	0.788248i	−0.543599	+	0.839345i	$0.682939\pi$
$662$	3546.00	+	6141.85i	0.208186	+	0.360589i
$663$		0			0
$664$	13860.0			0.810049
$665$		0			0
$666$		0			0
$667$	5104.00	−	8840.39i	0.296293	−	0.513195i
$668$	−1764.00	−	3055.34i	−0.102172	−	0.176968i
$669$		0			0
$670$	2472.00	−	4281.63i	0.142540	−	0.246886i
$671$	9840.00			0.566124
$672$		0			0
$673$	13470.0			0.771516			0.385758	−	0.922600i	$-0.373940\pi$
$673$	13470.0			0.771516			0.385758	+	0.922600i	$0.373940\pi$
$674$	−183.000	+	316.965i	−0.0104583	+	0.0181143i
$675$		0			0
$676$	17006.5	+	29456.1i	0.967598	+	1.67593i
$677$	−4782.00	+	8282.67i	−0.271473	+	0.470205i	−0.969239	−	0.246121i	$-0.920844\pi$
$677$	−4782.00	+	8282.67i	−0.271473	+	0.470205i	0.697766	+	0.716326i	$0.254177\pi$
$678$		0			0
$679$		0			0
$680$	17280.0			0.974497
$681$		0			0
$682$	−2640.00	−	4572.61i	−0.148227	−	0.256737i
$683$	6926.00	+	11996.2i	0.388018	+	0.672066i	0.992183	−	0.124793i	$-0.0398266\pi$
$683$	6926.00	+	11996.2i	0.388018	+	0.672066i	−0.604165	+	0.796859i	$0.706493\pi$
$684$		0			0
$685$	13512.0			0.753674
$686$		0			0
$687$		0			0
$688$	−3198.00	+	5539.10i	−0.177213	+	0.306942i
$689$	30324.0	+	52522.7i	1.67671	+	2.90414i
$690$		0			0
$691$	162.000	−	280.592i	0.00891863	−	0.0154475i	−0.861532	−	0.507704i	$-0.830494\pi$
$691$	162.000	−	280.592i	0.00891863	−	0.0154475i	0.870450	+	0.492256i	$0.163828\pi$
$692$	−12852.0			−0.706011
$693$		0			0
$694$	6364.00			0.348090
$695$	6552.00	−	11348.4i	0.357599	−	0.619380i
$696$		0			0
$697$		0			0
$698$	5250.00	−	9093.27i	0.284693	−	0.493102i
$699$		0			0
$700$		0			0
$701$	−24922.0			−1.34278			−0.671392	−	0.741103i	$-0.734303\pi$
$701$	−24922.0			−1.34278			−0.671392	+	0.741103i	$0.734303\pi$
$702$		0			0
$703$	−1548.00	−	2681.21i	−0.0830497	−	0.143846i
$704$	−1670.00	−	2892.52i	−0.0894041	−	0.154852i
$705$		0			0
$706$	−408.000			−0.0217497
$707$		0			0
$708$		0			0
$709$	8943.00	−	15489.7i	0.473711	−	0.820492i	−0.525836	−	0.850586i	$-0.676247\pi$
$709$	8943.00	−	15489.7i	0.473711	−	0.820492i	0.999547	+	0.0300939i	$0.00958064\pi$
$710$	−1776.00	−	3076.12i	−0.0938762	−	0.162598i
$711$		0			0
$712$	5580.00	−	9664.84i	0.293707	−	0.508715i
$713$	−46464.0			−2.44052
$714$		0			0
$715$	−20160.0			−1.05446
$716$	−8302.00	+	14379.5i	−0.433324	+	0.750540i
$717$		0			0
$718$	−5968.00	−	10336.9i	−0.310200	−	0.537283i
$719$	−3396.00	+	5882.04i	−0.176147	+	0.305095i	−0.940557	−	0.339635i	$-0.889697\pi$
$719$	−3396.00	+	5882.04i	−0.176147	+	0.305095i	0.764411	+	0.644729i	$0.223030\pi$
$720$		0			0
$721$		0			0
$722$	−6715.00			−0.346131
$723$		0			0
$724$	−3822.00	−	6619.90i	−0.196193	−	0.339816i
$725$	551.000	+	954.360i	0.0282257	+	0.0488883i
$726$		0			0
$727$	1512.00			0.0771348			0.0385674	−	0.999256i	$-0.487721\pi$
$727$	1512.00			0.0771348			0.0385674	+	0.999256i	$0.487721\pi$
$728$		0			0
$729$		0			0
$730$	1440.00	−	2494.15i	0.0730093	−	0.126456i
$731$	−7488.00	−	12969.6i	−0.378870	−	0.656221i
$732$		0			0
$733$	5622.00	−	9737.59i	0.283292	−	0.490677i	−0.688901	−	0.724855i	$-0.741907\pi$
$733$	5622.00	−	9737.59i	0.283292	−	0.490677i	0.972194	+	0.234178i	$0.0752400\pi$
$734$	−2448.00			−0.123103
$735$		0			0
$736$	28336.0			1.41913
$737$	4120.00	−	7136.05i	0.205919	−	0.356662i
$738$		0			0
$739$	998.000	+	1728.59i	0.0496780	+	0.0860448i	0.889795	−	0.456360i	$-0.150847\pi$
$739$	998.000	+	1728.59i	0.0496780	+	0.0860448i	−0.840117	+	0.542405i	$0.817514\pi$
$740$	−10836.0	+	18768.5i	−0.538296	+	0.932357i
$741$		0			0
$742$		0			0
$743$	656.000			0.0323907			0.0161954	−	0.999869i	$-0.494845\pi$
$743$	656.000			0.0323907			0.0161954	+	0.999869i	$0.494845\pi$
$744$		0			0
$745$	−6420.00	−	11119.8i	−0.315719	−	0.546841i
$746$	−5687.00	−	9850.17i	−0.279110	−	0.483432i
$747$		0			0
$748$	13440.0			0.656972
$749$		0			0
$750$		0			0
$751$	−528.000	+	914.523i	−0.0256551	+	0.0444360i	−0.878568	−	0.477617i	$-0.841501\pi$
$751$	−528.000	+	914.523i	−0.0256551	+	0.0444360i	0.852913	+	0.522053i	$0.174834\pi$
$752$	−8364.00	−	14486.9i	−0.405590	−	0.702503i
$753$		0			0
$754$	−2436.00	+	4219.28i	−0.117658	+	0.203789i
$755$	1440.00			0.0694132
$756$		0			0
$757$	−18702.0			−0.897934			−0.448967	−	0.893548i	$-0.648208\pi$
$757$	−18702.0			−0.897934			−0.448967	+	0.893548i	$0.648208\pi$
$758$	2946.00	−	5102.62i	0.141166	−	0.244506i
$759$		0			0
$760$	−1080.00	−	1870.61i	−0.0515470	−	0.0892820i
$761$	8952.00	−	15505.3i	0.426425	−	0.738590i	−0.570127	−	0.821557i	$-0.693106\pi$
$761$	8952.00	−	15505.3i	0.426425	−	0.738590i	0.996552	+	0.0829661i	$0.0264393\pi$
$762$		0			0
$763$		0			0
$764$	17584.0			0.832679
$765$		0			0
$766$	−5244.00	−	9082.87i	−0.247354	−	0.428430i
$767$	−20664.0	−	35791.1i	−0.972795	−	1.68493i
$768$		0			0
$769$	−7560.00			−0.354513			−0.177257	−	0.984165i	$-0.556722\pi$
$769$	−7560.00			−0.354513			−0.177257	+	0.984165i	$0.556722\pi$
$770$		0			0
$771$		0			0
$772$	−8505.00	+	14731.1i	−0.396505	+	0.686766i
$773$	−7146.00	−	12377.2i	−0.332502	−	0.575910i	0.650500	−	0.759506i	$-0.274559\pi$
$773$	−7146.00	−	12377.2i	−0.332502	−	0.575910i	−0.983002	+	0.183596i	$0.941226\pi$
$774$		0			0
$775$	2508.00	−	4343.98i	0.116245	−	0.201343i
$776$	2520.00			0.116576
$777$		0			0
$778$	−4514.00			−0.208014
$779$		0			0
$780$		0			0
$781$	−2960.00	−	5126.87i	−0.135617	−	0.234896i
$782$	−8448.00	+	14632.4i	−0.386317	+	0.669121i
$783$		0			0
$784$		0			0
$785$	−22032.0			−1.00173
$786$		0			0
$787$	−13182.0	−	22831.9i	−0.597062	−	1.03414i	−0.993252	−	0.115973i	$-0.963001\pi$
$787$	−13182.0	−	22831.9i	−0.597062	−	1.03414i	0.396191	−	0.918168i	$-0.370332\pi$
$788$	6167.00	+	10681.6i	0.278795	+	0.482887i
$789$		0			0
$790$	−9312.00			−0.419375
$791$		0			0
$792$		0			0
$793$	−20664.0	+	35791.1i	−0.925347	+	1.60275i
$794$	3018.00	+	5227.33i	0.134893	+	0.233641i
$795$		0			0
$796$	10836.0	−	18768.5i	0.482502	−	0.835719i
$797$	−17220.0			−0.765325			−0.382662	−	0.923888i	$-0.624993\pi$
$797$	−17220.0			−0.765325			−0.382662	+	0.923888i	$0.624993\pi$
$798$		0			0
$799$	39168.0			1.73425
$800$	−1529.50	+	2649.17i	−0.0675950	+	0.117078i
$801$		0			0
$802$	−3385.00	−	5862.99i	−0.149038	−	0.258141i
$803$	2400.00	−	4156.92i	0.105472	−	0.182683i
$804$		0			0
$805$		0			0
$806$	22176.0			0.969127
$807$		0			0
$808$	11430.0	+	19797.3i	0.497656	+	0.861965i
$809$	8221.00	+	14239.2i	0.357274	+	0.618817i	0.987504	−	0.157591i	$-0.0503728\pi$
$809$	8221.00	+	14239.2i	0.357274	+	0.618817i	−0.630230	+	0.776408i	$0.717039\pi$
$810$		0			0
$811$	−31332.0			−1.35662			−0.678308	−	0.734778i	$-0.737286\pi$
$811$	−31332.0			−1.35662			−0.678308	+	0.734778i	$0.737286\pi$
$812$		0			0
$813$		0			0
$814$	2580.00	−	4468.69i	0.111092	−	0.192417i
$815$	5496.00	+	9519.35i	0.236217	+	0.409139i
$816$		0			0
$817$	−936.000	+	1621.20i	−0.0400814	+	0.0694230i
$818$	12504.0			0.534465
$819$		0			0
$820$		0			0
$821$	−12905.0	+	22352.1i	−0.548584	+	0.950176i	0.449788	+	0.893135i	$0.351500\pi$
$821$	−12905.0	+	22352.1i	−0.548584	+	0.950176i	−0.998372	+	0.0570402i	$0.981834\pi$
$822$		0			0
$823$	−6184.00	−	10711.0i	−0.261921	−	0.453660i	0.704832	−	0.709375i	$-0.251023\pi$
$823$	−6184.00	−	10711.0i	−0.261921	−	0.453660i	−0.966752	+	0.255715i	$0.917689\pi$
$824$	−3060.00	+	5300.08i	−0.129369	+	0.224074i
$825$		0			0
$826$		0			0
$827$	−6316.00			−0.265573			−0.132786	−	0.991145i	$-0.542392\pi$
$827$	−6316.00			−0.265573			−0.132786	+	0.991145i	$0.542392\pi$
$828$		0			0
$829$	11934.0	+	20670.3i	0.499982	+	0.865994i	1.00000		2.09597e-5i	$-6.67166e-6\pi$
$829$	11934.0	+	20670.3i	0.499982	+	0.865994i	−0.500018	+	0.866015i	$0.666673\pi$
$830$	−5544.00	−	9602.49i	−0.231849	−	0.401575i
$831$		0			0
$832$	14028.0			0.584535
$833$		0			0
$834$		0			0
$835$	−3024.00	+	5237.72i	−0.125329	+	0.217076i
$836$	−840.000	−	1454.92i	−0.0347512	−	0.0601909i
$837$		0			0
$838$	4746.00	−	8220.31i	0.195642	−	0.338862i
$839$	48216.0			1.98403			0.992015	−	0.126120i	$-0.0402524\pi$
$839$	48216.0			1.98403			0.992015	+	0.126120i	$0.0402524\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	−2591.00	+	4487.74i	−0.106047	+	0.183679i
$843$		0			0
$844$	546.000	+	945.700i	0.0222679	+	0.0385691i
$845$	29154.0	−	50496.2i	1.18690	−	2.05577i
$846$		0			0
$847$		0			0
$848$	29602.0			1.19875
$849$		0			0
$850$	−912.000	−	1579.63i	−0.0368016	−	0.0637422i
$851$	−22704.0	−	39324.5i	−0.914551	−	1.58405i
$852$		0			0
$853$	−27300.0			−1.09582			−0.547910	−	0.836537i	$-0.684576\pi$
$853$	−27300.0			−1.09582			−0.547910	+	0.836537i	$0.684576\pi$
$854$		0			0
$855$		0			0
$856$	6150.00	−	10652.1i	0.245564	−	0.425329i
$857$	4320.00	+	7482.46i	0.172192	+	0.298245i	0.939186	−	0.343409i	$-0.111582\pi$
$857$	4320.00	+	7482.46i	0.172192	+	0.298245i	−0.766994	+	0.641654i	$0.778248\pi$
$858$		0			0
$859$	−12186.0	+	21106.8i	−0.484029	+	0.838363i	−0.999832	−	0.0183445i	$-0.994160\pi$
$859$	−12186.0	+	21106.8i	−0.484029	+	0.838363i	0.515803	+	0.856707i	$0.327494\pi$
$860$	13104.0			0.519585
$861$		0			0
$862$	5720.00			0.226014
$863$	1088.00	−	1884.47i	0.0429154	−	0.0743316i	−0.843770	−	0.536705i	$-0.819669\pi$
$863$	1088.00	−	1884.47i	0.0429154	−	0.0743316i	0.886685	+	0.462374i	$0.153002\pi$
$864$		0			0
$865$	11016.0	+	19080.3i	0.433012	+	0.749998i
$866$	−6804.00	+	11784.9i	−0.266985	+	0.462432i
$867$		0			0
$868$		0			0
$869$	−15520.0			−0.605846
$870$		0			0
$871$	17304.0	+	29971.4i	0.673162	+	1.16595i
$872$	−6885.00	−	11925.2i	−0.267380	−	0.463116i
$873$		0			0
$874$	2112.00			0.0817385
$875$		0			0
$876$		0			0
$877$	13787.0	−	23879.8i	0.530848	−	0.919456i	−0.468504	−	0.883462i	$-0.655207\pi$
$877$	13787.0	−	23879.8i	0.530848	−	0.919456i	0.999352	−	0.0359946i	$-0.0114599\pi$
$878$	−6432.00	−	11140.6i	−0.247232	−	0.428218i
$879$		0			0
$880$	−4920.00	+	8521.69i	−0.188470	+	0.326439i
$881$	−16968.0			−0.648884			−0.324442	−	0.945906i	$-0.605176\pi$
$881$	−16968.0			−0.648884			−0.324442	+	0.945906i	$0.605176\pi$
$882$		0			0
$883$	−1860.00			−0.0708879			−0.0354439	−	0.999372i	$-0.511285\pi$
$883$	−1860.00			−0.0708879			−0.0354439	+	0.999372i	$0.511285\pi$
$884$	−28224.0	+	48885.4i	−1.07384	+	1.85995i
$885$		0			0
$886$	−6626.00	−	11476.6i	−0.251247	−	0.435173i
$887$	1140.00	−	1974.54i	0.0431538	−	0.0747446i	−0.843642	−	0.536907i	$-0.819593\pi$
$887$	1140.00	−	1974.54i	0.0431538	−	0.0747446i	0.886796	+	0.462162i	$0.152926\pi$
$888$		0			0
$889$		0			0
$890$	−8928.00			−0.336255
$891$		0			0
$892$	17640.0	+	30553.4i	0.662142	+	1.14686i
$893$	−2448.00	−	4240.06i	−0.0917348	−	0.158889i
$894$		0			0
$895$	28464.0			1.06307
$896$		0			0
$897$		0			0
$898$	113.000	−	195.722i	0.00419917	−	0.00727318i
$899$	−7656.00	−	13260.6i	−0.284029	−	0.491952i
$900$		0			0
$901$	−34656.0	+	60026.0i	−1.28142	+	2.21948i
$902$		0			0
$903$		0			0
$904$	−1650.00			−0.0607060
$905$	−6552.00	+	11348.4i	−0.240658	+	0.416833i
$906$		0			0
$907$	−18042.0	−	31249.7i	−0.660501	−	1.14402i	−0.980484	−	0.196599i	$-0.937010\pi$
$907$	−18042.0	−	31249.7i	−0.660501	−	1.14402i	0.319983	−	0.947423i	$-0.396323\pi$
$908$	−7602.00	+	13167.1i	−0.277843	+	0.481238i
$909$		0			0
$910$		0			0
$911$	−24152.0			−0.878366			−0.439183	−	0.898398i	$-0.644732\pi$
$911$	−24152.0			−0.878366			−0.439183	+	0.898398i	$0.644732\pi$
$912$		0			0
$913$	−9240.00	−	16004.1i	−0.334939	−	0.580131i
$914$	5667.00	+	9815.53i	0.205085	+	0.355218i
$915$		0			0
$916$	−18900.0			−0.681740
$917$		0			0
$918$		0			0
$919$	−18168.0	+	31467.9i	−0.652130	+	1.12952i	0.330476	+	0.943815i	$0.392791\pi$
$919$	−18168.0	+	31467.9i	−0.652130	+	1.12952i	−0.982605	+	0.185707i	$0.940542\pi$
$920$	−15840.0	−	27435.7i	−0.567641	−	0.983182i
$921$		0			0
$922$	−798.000	+	1382.18i	−0.0285040	+	0.0493705i
$923$	24864.0			0.886683
$924$		0			0
$925$	4902.00			0.174245
$926$	−6364.00	+	11022.8i	−0.225847	+	0.391178i
$927$		0			0
$928$	4669.00	+	8086.95i	0.165159	+	0.286064i
$929$	216.000	−	374.123i	0.00762834	−	0.0132127i	−0.862186	−	0.506592i	$-0.830905\pi$
$929$	216.000	−	374.123i	0.00762834	−	0.0132127i	0.869814	+	0.493379i	$0.164238\pi$
$930$		0			0
$931$		0			0
$932$	−26614.0			−0.935376
$933$		0			0
$934$	−1506.00	−	2608.47i	−0.0527600	−	0.0913830i
$935$	−11520.0	−	19953.2i	−0.402935	−	0.697904i
$936$		0			0
$937$	22176.0			0.773168			0.386584	−	0.922254i	$-0.373655\pi$
$937$	22176.0			0.773168			0.386584	+	0.922254i	$0.373655\pi$
$938$		0			0
$939$		0			0
$940$	−17136.0	+	29680.4i	−0.594590	+	1.02986i
$941$	−21762.0	−	37692.9i	−0.753901	−	1.30579i	−0.945919	−	0.324404i	$-0.894836\pi$
$941$	−21762.0	−	37692.9i	−0.753901	−	1.30579i	0.192018	−	0.981391i	$-0.438497\pi$
$942$		0			0
$943$		0			0
$944$	−20172.0			−0.695490
$945$		0			0
$946$	−3120.00			−0.107230
$947$	934.000	−	1617.74i	0.0320495	−	0.0555114i	−0.849556	−	0.527499i	$-0.823130\pi$
$947$	934.000	−	1617.74i	0.0320495	−	0.0555114i	0.881605	+	0.471987i	$0.156463\pi$
$948$		0			0
$949$	10080.0	+	17459.1i	0.344795	+	0.597203i
$950$	−114.000	+	197.454i	−0.00389331	+	0.00674342i
$951$		0			0
$952$		0			0
$953$	9238.00			0.314006			0.157003	−	0.987598i	$-0.449817\pi$
$953$	9238.00			0.314006			0.157003	+	0.987598i	$0.449817\pi$
$954$		0			0
$955$	−15072.0	−	26105.5i	−0.510700	−	0.884558i
$956$	15428.0	+	26722.1i	0.521943	+	0.904031i
$957$		0			0
$958$	4296.00			0.144883
$959$		0			0
$960$		0			0
$961$	−19952.5	+	34558.7i	−0.669749	+	1.16004i
$962$	10836.0	+	18768.5i	0.363167	+	0.629024i
$963$		0			0
$964$	10836.0	−	18768.5i	0.362037	−	0.627067i
$965$	29160.0			0.972739
$966$		0			0
$967$	−30616.0			−1.01814			−0.509071	−	0.860724i	$-0.670011\pi$
$967$	−30616.0			−1.01814			−0.509071	+	0.860724i	$0.670011\pi$
$968$	−6982.50	+	12094.0i	−0.231845	+	0.401567i
$969$		0			0
$970$	−1008.00	−	1745.91i	−0.0333659	−	0.0577914i
$971$	−13770.0	+	23850.3i	−0.455098	+	0.788253i	−0.998694	−	0.0510941i	$-0.983729\pi$
$971$	−13770.0	+	23850.3i	−0.455098	+	0.788253i	0.543596	+	0.839347i	$0.317063\pi$
$972$		0			0
$973$		0			0
$974$	−8184.00			−0.269232
$975$		0			0
$976$	10086.0	+	17469.5i	0.330784	+	0.572934i
$977$	−8201.00	−	14204.5i	−0.268550	−	0.465142i	0.699938	−	0.714204i	$-0.253211\pi$
$977$	−8201.00	−	14204.5i	−0.268550	−	0.465142i	−0.968488	+	0.249062i	$0.919878\pi$
$978$		0			0
$979$	−14880.0			−0.485768
$980$		0			0
$981$		0			0
$982$	−6082.00	+	10534.3i	−0.197642	+	0.342326i
$983$	27588.0	+	47783.8i	0.895138	+	1.55042i	0.833634	+	0.552317i	$0.186256\pi$
$983$	27588.0	+	47783.8i	0.895138	+	1.55042i	0.0615040	+	0.998107i	$0.480410\pi$
$984$		0			0
$985$	10572.0	−	18311.2i	0.341982	−	0.592330i
$986$	−5568.00			−0.179839
$987$		0			0
$988$	7056.00			0.227208
$989$	−13728.0	+	23777.6i	−0.441380	+	0.764493i
$990$		0			0
$991$	−13548.0	−	23465.8i	−0.434275	−	0.752186i	0.562961	−	0.826483i	$-0.309662\pi$
$991$	−13548.0	−	23465.8i	−0.434275	−	0.752186i	−0.997236	+	0.0742971i	$0.976329\pi$
$992$	21252.0	−	36809.5i	0.680193	−	1.17813i
$993$		0			0
$994$		0			0
$995$	−37152.0			−1.18372
$996$		0			0
$997$	8406.00	+	14559.6i	0.267022	+	0.462495i	0.968091	−	0.250598i	$-0.0806271\pi$
$997$	8406.00	+	14559.6i	0.267022	+	0.462495i	−0.701070	+	0.713093i	$0.747294\pi$
$998$	−486.000	−	841.777i	−0.0154149	−	0.0266994i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.g.226.1		2
3.2	odd	2		147.4.e.f.79.1		2
7.2	even	3		441.4.a.g.1.1		1
7.3	odd	6		441.4.e.f.361.1		2
7.4	even	3	inner	441.4.e.g.361.1		2
7.5	odd	6		441.4.a.h.1.1		1
7.6	odd	2		441.4.e.f.226.1		2
21.2	odd	6		147.4.a.d.1.1	✓	1
21.5	even	6		147.4.a.e.1.1	yes	1
21.11	odd	6		147.4.e.f.67.1		2
21.17	even	6		147.4.e.e.67.1		2
21.20	even	2		147.4.e.e.79.1		2
84.23	even	6		2352.4.a.bi.1.1		1
84.47	odd	6		2352.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.d.1.1	✓	1	21.2	odd	6
147.4.a.e.1.1	yes	1	21.5	even	6
147.4.e.e.67.1		2	21.17	even	6
147.4.e.e.79.1		2	21.20	even	2
147.4.e.f.67.1		2	21.11	odd	6
147.4.e.f.79.1		2	3.2	odd	2
441.4.a.g.1.1		1	7.2	even	3
441.4.a.h.1.1		1	7.5	odd	6
441.4.e.f.226.1		2	7.6	odd	2
441.4.e.f.361.1		2	7.3	odd	6
441.4.e.g.226.1		2	1.1	even	1	trivial
441.4.e.g.361.1		2	7.4	even	3	inner
2352.4.a.b.1.1		1	84.47	odd	6
2352.4.a.bi.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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +(6.00000 + 10.3923i) q^{10} +(10.0000 + 17.3205i) q^{11} -84.0000 q^{13} +(-20.5000 + 35.5070i) q^{16} +(-48.0000 - 83.1384i) q^{17} +(-6.00000 + 10.3923i) q^{19} +84.0000 q^{20} -20.0000 q^{22} +(-88.0000 + 152.420i) q^{23} +(-9.50000 - 16.4545i) q^{25} +(42.0000 - 72.7461i) q^{26} -58.0000 q^{29} +(132.000 + 228.631i) q^{31} +(-80.5000 - 139.430i) q^{32} +96.0000 q^{34} +(-129.000 + 223.435i) q^{37} +(-6.00000 - 10.3923i) q^{38} +(-90.0000 + 155.885i) q^{40} +156.000 q^{43} +(-70.0000 + 121.244i) q^{44} +(-88.0000 - 152.420i) q^{46} +(-204.000 + 353.338i) q^{47} +19.0000 q^{50} +(-294.000 - 509.223i) q^{52} +(-361.000 - 625.270i) q^{53} +240.000 q^{55} +(29.0000 - 50.2295i) q^{58} +(246.000 + 426.084i) q^{59} +(246.000 - 426.084i) q^{61} -264.000 q^{62} -167.000 q^{64} +(-504.000 + 872.954i) q^{65} +(-206.000 - 356.802i) q^{67} +(336.000 - 581.969i) q^{68} -296.000 q^{71} +(-120.000 - 207.846i) q^{73} +(-129.000 - 223.435i) q^{74} -84.0000 q^{76} +(-388.000 + 672.036i) q^{79} +(246.000 + 426.084i) q^{80} -924.000 q^{83} -1152.00 q^{85} +(-78.0000 + 135.100i) q^{86} +(-150.000 - 259.808i) q^{88} +(-372.000 + 644.323i) q^{89} -1232.00 q^{92} +(-204.000 - 353.338i) q^{94} +(72.0000 + 124.708i) q^{95} -168.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 7 q^{4} + 12 q^{5} - 30 q^{8}+O(q^{10}) \) 2 * q - q^2 + 7 * q^4 + 12 * q^5 - 30 * q^8	\( 2 q - q^{2} + 7 q^{4} + 12 q^{5} - 30 q^{8} + 12 q^{10} + 20 q^{11} - 168 q^{13} - 41 q^{16} - 96 q^{17} - 12 q^{19} + 168 q^{20} - 40 q^{22} - 176 q^{23} - 19 q^{25} + 84 q^{26} - 116 q^{29} + 264 q^{31} - 161 q^{32} + 192 q^{34} - 258 q^{37} - 12 q^{38} - 180 q^{40} + 312 q^{43} - 140 q^{44} - 176 q^{46} - 408 q^{47} + 38 q^{50} - 588 q^{52} - 722 q^{53} + 480 q^{55} + 58 q^{58} + 492 q^{59} + 492 q^{61} - 528 q^{62} - 334 q^{64} - 1008 q^{65} - 412 q^{67} + 672 q^{68} - 592 q^{71} - 240 q^{73} - 258 q^{74} - 168 q^{76} - 776 q^{79} + 492 q^{80} - 1848 q^{83} - 2304 q^{85} - 156 q^{86} - 300 q^{88} - 744 q^{89} - 2464 q^{92} - 408 q^{94} + 144 q^{95} - 336 q^{97}+O(q^{100}) \) 2 * q - q^2 + 7 * q^4 + 12 * q^5 - 30 * q^8 + 12 * q^10 + 20 * q^11 - 168 * q^13 - 41 * q^16 - 96 * q^17 - 12 * q^19 + 168 * q^20 - 40 * q^22 - 176 * q^23 - 19 * q^25 + 84 * q^26 - 116 * q^29 + 264 * q^31 - 161 * q^32 + 192 * q^34 - 258 * q^37 - 12 * q^38 - 180 * q^40 + 312 * q^43 - 140 * q^44 - 176 * q^46 - 408 * q^47 + 38 * q^50 - 588 * q^52 - 722 * q^53 + 480 * q^55 + 58 * q^58 + 492 * q^59 + 492 * q^61 - 528 * q^62 - 334 * q^64 - 1008 * q^65 - 412 * q^67 + 672 * q^68 - 592 * q^71 - 240 * q^73 - 258 * q^74 - 168 * q^76 - 776 * q^79 + 492 * q^80 - 1848 * q^83 - 2304 * q^85 - 156 * q^86 - 300 * q^88 - 744 * q^89 - 2464 * q^92 - 408 * q^94 + 144 * q^95 - 336 * q^97

Introduction

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