LMFDB - Embedded newform 441.4.e.e.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 7)
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.e.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +(-8.00000 - 13.8564i) q^{10} +(-4.00000 - 6.92820i) q^{11} -28.0000 q^{13} +(-20.5000 + 35.5070i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(-55.0000 + 95.2628i) q^{19} -112.000 q^{20} +8.00000 q^{22} +(24.0000 - 41.5692i) q^{23} +(-65.5000 - 113.449i) q^{25} +(14.0000 - 24.2487i) q^{26} +110.000 q^{29} +(6.00000 + 10.3923i) q^{31} +(-80.5000 - 139.430i) q^{32} +54.0000 q^{34} +(123.000 - 213.042i) q^{37} +(-55.0000 - 95.2628i) q^{38} +(120.000 - 207.846i) q^{40} +182.000 q^{41} +128.000 q^{43} +(28.0000 - 48.4974i) q^{44} +(24.0000 + 41.5692i) q^{46} +(-162.000 + 280.592i) q^{47} +131.000 q^{50} +(-98.0000 - 169.741i) q^{52} +(-81.0000 - 140.296i) q^{53} +128.000 q^{55} +(-55.0000 + 95.2628i) q^{58} +(-405.000 - 701.481i) q^{59} +(-244.000 + 422.620i) q^{61} -12.0000 q^{62} -167.000 q^{64} +(224.000 - 387.979i) q^{65} +(-122.000 - 211.310i) q^{67} +(189.000 - 327.358i) q^{68} +768.000 q^{71} +(-351.000 - 607.950i) q^{73} +(123.000 + 213.042i) q^{74} -770.000 q^{76} +(-220.000 + 381.051i) q^{79} +(-328.000 - 568.113i) q^{80} +(-91.0000 + 157.617i) q^{82} -1302.00 q^{83} +864.000 q^{85} +(-64.0000 + 110.851i) q^{86} +(60.0000 + 103.923i) q^{88} +(-365.000 + 632.199i) q^{89} +336.000 q^{92} +(-162.000 - 280.592i) q^{94} +(-880.000 - 1524.20i) q^{95} -294.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 7 q^{4} - 16 q^{5} - 30 q^{8}+O(q^{10}) $ 2 * q - q^2 + 7 * q^4 - 16 * q^5 - 30 * q^8	$ 2 q - q^{2} + 7 q^{4} - 16 q^{5} - 30 q^{8} - 16 q^{10} - 8 q^{11} - 56 q^{13} - 41 q^{16} - 54 q^{17} - 110 q^{19} - 224 q^{20} + 16 q^{22} + 48 q^{23} - 131 q^{25} + 28 q^{26} + 220 q^{29} + 12 q^{31} - 161 q^{32} + 108 q^{34} + 246 q^{37} - 110 q^{38} + 240 q^{40} + 364 q^{41} + 256 q^{43} + 56 q^{44} + 48 q^{46} - 324 q^{47} + 262 q^{50} - 196 q^{52} - 162 q^{53} + 256 q^{55} - 110 q^{58} - 810 q^{59} - 488 q^{61} - 24 q^{62} - 334 q^{64} + 448 q^{65} - 244 q^{67} + 378 q^{68} + 1536 q^{71} - 702 q^{73} + 246 q^{74} - 1540 q^{76} - 440 q^{79} - 656 q^{80} - 182 q^{82} - 2604 q^{83} + 1728 q^{85} - 128 q^{86} + 120 q^{88} - 730 q^{89} + 672 q^{92} - 324 q^{94} - 1760 q^{95} - 588 q^{97}+O(q^{100}) $ 2 * q - q^2 + 7 * q^4 - 16 * q^5 - 30 * q^8 - 16 * q^10 - 8 * q^11 - 56 * q^13 - 41 * q^16 - 54 * q^17 - 110 * q^19 - 224 * q^20 + 16 * q^22 + 48 * q^23 - 131 * q^25 + 28 * q^26 + 220 * q^29 + 12 * q^31 - 161 * q^32 + 108 * q^34 + 246 * q^37 - 110 * q^38 + 240 * q^40 + 364 * q^41 + 256 * q^43 + 56 * q^44 + 48 * q^46 - 324 * q^47 + 262 * q^50 - 196 * q^52 - 162 * q^53 + 256 * q^55 - 110 * q^58 - 810 * q^59 - 488 * q^61 - 24 * q^62 - 334 * q^64 + 448 * q^65 - 244 * q^67 + 378 * q^68 + 1536 * q^71 - 702 * q^73 + 246 * q^74 - 1540 * q^76 - 440 * q^79 - 656 * q^80 - 182 * q^82 - 2604 * q^83 + 1728 * q^85 - 128 * q^86 + 120 * q^88 - 730 * q^89 + 672 * q^92 - 324 * q^94 - 1760 * q^95 - 588 * 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
$5$	−8.00000	+	13.8564i	−0.715542	+	1.23935i	0.247208	+	0.968962i	$0.420487\pi$
$5$	−8.00000	+	13.8564i	−0.715542	+	1.23935i	−0.962750	+	0.270392i	$0.912847\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−15.0000			−0.662913
$9$		0			0
$10$	−8.00000	−	13.8564i	−0.252982	−	0.438178i
$11$	−4.00000	−	6.92820i	−0.109640	−	0.189903i	0.805984	−	0.591937i	$-0.201637\pi$
$11$	−4.00000	−	6.92820i	−0.109640	−	0.189903i	−0.915625	+	0.402034i	$0.868303\pi$
$12$		0			0
$13$	−28.0000			−0.597369			−0.298685	−	0.954352i	$-0.596548\pi$
$13$	−28.0000			−0.597369			−0.298685	+	0.954352i	$0.596548\pi$
$14$		0			0
$15$		0			0
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	−27.0000	−	46.7654i	−0.385204	−	0.667192i	0.606594	−	0.795012i	$-0.292535\pi$
$17$	−27.0000	−	46.7654i	−0.385204	−	0.667192i	−0.991797	+	0.127820i	$0.959202\pi$
$18$		0			0
$19$	−55.0000	+	95.2628i	−0.664098	+	1.15025i	0.315431	+	0.948949i	$0.397851\pi$
$19$	−55.0000	+	95.2628i	−0.664098	+	1.15025i	−0.979529	+	0.201303i	$0.935482\pi$
$20$	−112.000			−1.25220
$21$		0			0
$22$	8.00000			0.0775275
$23$	24.0000	−	41.5692i	0.217580	−	0.376860i	−0.736487	−	0.676451i	$-0.763517\pi$
$23$	24.0000	−	41.5692i	0.217580	−	0.376860i	0.954068	+	0.299591i	$0.0968503\pi$
$24$		0			0
$25$	−65.5000	−	113.449i	−0.524000	−	0.907595i
$26$	14.0000	−	24.2487i	0.105601	−	0.182906i
$27$		0			0
$28$		0			0
$29$	110.000			0.704362			0.352181	−	0.935932i	$-0.385440\pi$
$29$	110.000			0.704362			0.352181	+	0.935932i	$0.385440\pi$
$30$		0			0
$31$	6.00000	+	10.3923i	0.0347623	+	0.0602101i	0.882883	−	0.469593i	$-0.155599\pi$
$31$	6.00000	+	10.3923i	0.0347623	+	0.0602101i	−0.848121	+	0.529803i	$0.822266\pi$
$32$	−80.5000	−	139.430i	−0.444704	−	0.770250i
$33$		0			0
$34$	54.0000			0.272380
$35$		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	$-0.0173794\pi$
$38$	−55.0000	−	95.2628i	−0.234794	−	0.406675i
$39$		0			0
$40$	120.000	−	207.846i	0.474342	−	0.821584i
$41$	182.000			0.693259			0.346630	−	0.938002i	$-0.387326\pi$
$41$	182.000			0.693259			0.346630	+	0.938002i	$0.387326\pi$
$42$		0			0
$43$	128.000			0.453949			0.226975	−	0.973901i	$-0.427117\pi$
$43$	128.000			0.453949			0.226975	+	0.973901i	$0.427117\pi$
$44$	28.0000	−	48.4974i	0.0959354	−	0.166165i
$45$		0			0
$46$	24.0000	+	41.5692i	0.0769262	+	0.133240i
$47$	−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
$50$	131.000			0.370524
$51$		0			0
$52$	−98.0000	−	169.741i	−0.261349	−	0.452670i
$53$	−81.0000	−	140.296i	−0.209928	−	0.363607i	0.741763	−	0.670662i	$-0.233990\pi$
$53$	−81.0000	−	140.296i	−0.209928	−	0.363607i	−0.951692	+	0.307055i	$0.900656\pi$
$54$		0			0
$55$	128.000			0.313809
$56$		0			0
$57$		0			0
$58$	−55.0000	+	95.2628i	−0.124515	+	0.215666i
$59$	−405.000	−	701.481i	−0.893670	−	1.54788i	−0.835442	−	0.549578i	$-0.814789\pi$
$59$	−405.000	−	701.481i	−0.893670	−	1.54788i	−0.0582271	−	0.998303i	$-0.518545\pi$
$60$		0			0
$61$	−244.000	+	422.620i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−244.000	+	422.620i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−12.0000			−0.0245807
$63$		0			0
$64$	−167.000			−0.326172
$65$	224.000	−	387.979i	0.427443	−	0.740353i
$66$		0			0
$67$	−122.000	−	211.310i	−0.222458	−	0.385308i	0.733096	−	0.680125i	$-0.238075\pi$
$67$	−122.000	−	211.310i	−0.222458	−	0.385308i	−0.955554	+	0.294817i	$0.904741\pi$
$68$	189.000	−	327.358i	0.337053	−	0.583793i
$69$		0			0
$70$		0			0
$71$	768.000			1.28373			0.641865	−	0.766818i	$-0.278161\pi$
$71$	768.000			1.28373			0.641865	+	0.766818i	$0.278161\pi$
$72$		0			0
$73$	−351.000	−	607.950i	−0.562759	−	0.974728i	−0.997254	−	0.0740537i	$-0.976406\pi$
$73$	−351.000	−	607.950i	−0.562759	−	0.974728i	0.434495	−	0.900674i	$-0.356927\pi$
$74$	123.000	+	213.042i	0.193222	+	0.334671i
$75$		0			0
$76$	−770.000			−1.16217
$77$		0			0
$78$		0			0
$79$	−220.000	+	381.051i	−0.313316	+	0.542679i	−0.979078	−	0.203485i	$-0.934773\pi$
$79$	−220.000	+	381.051i	−0.313316	+	0.542679i	0.665762	+	0.746164i	$0.268106\pi$
$80$	−328.000	−	568.113i	−0.458394	−	0.793962i
$81$		0			0
$82$	−91.0000	+	157.617i	−0.122552	+	0.212266i
$83$	−1302.00			−1.72184			−0.860922	−	0.508737i	$-0.830113\pi$
$83$	−1302.00			−1.72184			−0.860922	+	0.508737i	$0.830113\pi$
$84$		0			0
$85$	864.000			1.10252
$86$	−64.0000	+	110.851i	−0.0802476	+	0.138993i
$87$		0			0
$88$	60.0000	+	103.923i	0.0726821	+	0.125889i
$89$	−365.000	+	632.199i	−0.434718	+	0.752954i	−0.997273	−	0.0738062i	$-0.976485\pi$
$89$	−365.000	+	632.199i	−0.434718	+	0.752954i	0.562554	+	0.826760i	$0.309819\pi$
$90$		0			0
$91$		0			0
$92$	336.000			0.380765
$93$		0			0
$94$	−162.000	−	280.592i	−0.177756	−	0.307882i
$95$	−880.000	−	1524.20i	−0.950380	−	1.64611i
$96$		0			0
$97$	−294.000			−0.307744			−0.153872	−	0.988091i	$-0.549174\pi$
$97$	−294.000			−0.307744			−0.153872	+	0.988091i	$0.549174\pi$
$98$		0			0
$99$		0			0
$100$	458.500	−	794.145i	0.458500	−	0.794145i
$101$	344.000	+	595.825i	0.338904	+	0.586999i	0.984227	−	0.176911i	$-0.0566106\pi$
$101$	344.000	+	595.825i	0.338904	+	0.586999i	−0.645323	+	0.763910i	$0.723277\pi$
$102$		0			0
$103$	694.000	−	1202.04i	0.663901	−	1.14991i	−0.315680	−	0.948866i	$-0.602233\pi$
$103$	694.000	−	1202.04i	0.663901	−	1.14991i	0.979582	−	0.201046i	$-0.0644339\pi$
$104$	420.000			0.396004
$105$		0			0
$106$	162.000			0.148442
$107$	122.000	−	211.310i	0.110226	−	0.190917i	−0.805635	−	0.592412i	$-0.798176\pi$
$107$	122.000	−	211.310i	0.110226	−	0.190917i	0.915861	+	0.401495i	$0.131509\pi$
$108$		0			0
$109$	−45.0000	−	77.9423i	−0.0395433	−	0.0684910i	0.845576	−	0.533854i	$-0.179257\pi$
$109$	−45.0000	−	77.9423i	−0.0395433	−	0.0684910i	−0.885120	+	0.465363i	$0.845924\pi$
$110$	−64.0000	+	110.851i	−0.0554742	+	0.0960841i
$111$		0			0
$112$		0			0
$113$	−1318.00			−1.09723			−0.548615	−	0.836075i	$-0.684845\pi$
$113$	−1318.00			−1.09723			−0.548615	+	0.836075i	$0.684845\pi$
$114$		0			0
$115$	384.000	+	665.108i	0.311376	+	0.539318i
$116$	385.000	+	666.840i	0.308158	+	0.533746i
$117$		0			0
$118$	810.000			0.631920
$119$		0			0
$120$		0			0
$121$	633.500	−	1097.25i	0.475958	−	0.824383i
$122$	−244.000	−	422.620i	−0.181071	−	0.313625i
$123$		0			0
$124$	−42.0000	+	72.7461i	−0.0304170	+	0.0526838i
$125$	96.0000			0.0686920
$126$		0			0
$127$	−1776.00			−1.24090			−0.620451	−	0.784245i	$-0.713050\pi$
$127$	−1776.00			−1.24090			−0.620451	+	0.784245i	$0.713050\pi$
$128$	727.500	−	1260.07i	0.502363	−	0.870119i
$129$		0			0
$130$	224.000	+	387.979i	0.151124	+	0.261754i
$131$	559.000	−	968.216i	0.372825	−	0.645752i	−0.617174	−	0.786827i	$-0.711723\pi$
$131$	559.000	−	968.216i	0.372825	−	0.645752i	0.989999	+	0.141075i	$0.0450559\pi$
$132$		0			0
$133$		0			0
$134$	244.000			0.157301
$135$		0			0
$136$	405.000	+	701.481i	0.255356	+	0.442290i
$137$	1137.00	+	1969.34i	0.709054	+	1.22812i	0.965208	+	0.261482i	$0.0842113\pi$
$137$	1137.00	+	1969.34i	0.709054	+	1.22812i	−0.256154	+	0.966636i	$0.582455\pi$
$138$		0			0
$139$	210.000			0.128144			0.0640718	−	0.997945i	$-0.479591\pi$
$139$	210.000			0.128144			0.0640718	+	0.997945i	$0.479591\pi$
$140$		0			0
$141$		0			0
$142$	−384.000	+	665.108i	−0.226934	+	0.393060i
$143$	112.000	+	193.990i	0.0654959	+	0.113442i
$144$		0			0
$145$	−880.000	+	1524.20i	−0.504000	+	0.872954i
$146$	702.000			0.397931
$147$		0			0
$148$	1722.00			0.956402
$149$	−1005.00	+	1740.71i	−0.552569	+	0.957078i	0.445519	+	0.895272i	$0.353019\pi$
$149$	−1005.00	+	1740.71i	−0.552569	+	0.957078i	−0.998088	+	0.0618054i	$0.980314\pi$
$150$		0			0
$151$	−556.000	−	963.020i	−0.299647	−	0.519003i	0.676408	−	0.736527i	$-0.263535\pi$
$151$	−556.000	−	963.020i	−0.299647	−	0.519003i	−0.976055	+	0.217524i	$0.930202\pi$
$152$	825.000	−	1428.94i	0.440239	−	0.762516i
$153$		0			0
$154$		0			0
$155$	−192.000			−0.0994956
$156$		0			0
$157$	62.0000	+	107.387i	0.0315168	+	0.0545887i	0.881354	−	0.472457i	$-0.156633\pi$
$157$	62.0000	+	107.387i	0.0315168	+	0.0545887i	−0.849837	+	0.527046i	$0.823300\pi$
$158$	−220.000	−	381.051i	−0.110774	−	0.191866i
$159$		0			0
$160$	2576.00			1.27282
$161$		0			0
$162$		0			0
$163$	−1004.00	+	1738.98i	−0.482450	+	0.835628i	−0.999797	−	0.0201478i	$-0.993586\pi$
$163$	−1004.00	+	1738.98i	−0.482450	+	0.835628i	0.517347	+	0.855776i	$0.326920\pi$
$164$	637.000	+	1103.32i	0.303301	+	0.525333i
$165$		0			0
$166$	651.000	−	1127.57i	0.304382	−	0.527205i
$167$	2884.00			1.33635			0.668176	−	0.744004i	$-0.267076\pi$
$167$	2884.00			1.33635			0.668176	+	0.744004i	$0.267076\pi$
$168$		0			0
$169$	−1413.00			−0.643150
$170$	−432.000	+	748.246i	−0.194899	+	0.337576i
$171$		0			0
$172$	448.000	+	775.959i	0.198603	+	0.343990i
$173$	−1114.00	+	1929.50i	−0.489571	+	0.847963i	−0.999928	−	0.0120003i	$-0.996180\pi$
$173$	−1114.00	+	1929.50i	−0.489571	+	0.847963i	0.510357	+	0.859963i	$0.329513\pi$
$174$		0			0
$175$		0			0
$176$	328.000			0.140477
$177$		0			0
$178$	−365.000	−	632.199i	−0.153696	−	0.266209i
$179$	−410.000	−	710.141i	−0.171200	−	0.296527i	0.767640	−	0.640882i	$-0.221431\pi$
$179$	−410.000	−	710.141i	−0.171200	−	0.296527i	−0.938840	+	0.344354i	$0.888098\pi$
$180$		0			0
$181$	−3892.00			−1.59829			−0.799144	−	0.601140i	$-0.794713\pi$
$181$	−3892.00			−1.59829			−0.799144	+	0.601140i	$0.794713\pi$
$182$		0			0
$183$		0			0
$184$	−360.000	+	623.538i	−0.144237	+	0.249825i
$185$	1968.00	+	3408.68i	0.782109	+	1.35465i
$186$		0			0
$187$	−216.000	+	374.123i	−0.0844678	+	0.146303i
$188$	−2268.00			−0.879845
$189$		0			0
$190$	1760.00			0.672020
$191$	−2524.00	+	4371.70i	−0.956179	+	1.65615i	−0.224533	+	0.974466i	$0.572086\pi$
$191$	−2524.00	+	4371.70i	−0.956179	+	1.65615i	−0.731646	+	0.681684i	$0.761248\pi$
$192$		0			0
$193$	1481.00	+	2565.17i	0.552356	+	0.956709i	0.998104	+	0.0615502i	$0.0196044\pi$
$193$	1481.00	+	2565.17i	0.552356	+	0.956709i	−0.445748	+	0.895159i	$0.647062\pi$
$194$	147.000	−	254.611i	0.0544020	−	0.0942270i
$195$		0			0
$196$		0			0
$197$	−3334.00			−1.20577			−0.602887	−	0.797826i	$-0.705983\pi$
$197$	−3334.00			−1.20577			−0.602887	+	0.797826i	$0.705983\pi$
$198$		0			0
$199$	930.000	+	1610.81i	0.331286	+	0.573805i	0.982764	−	0.184863i	$-0.0591841\pi$
$199$	930.000	+	1610.81i	0.331286	+	0.573805i	−0.651478	+	0.758667i	$0.725851\pi$
$200$	982.500	+	1701.74i	0.347366	+	0.601656i
$201$		0			0
$202$	−688.000			−0.239641
$203$		0			0
$204$		0			0
$205$	−1456.00	+	2521.87i	−0.496056	+	0.859194i
$206$	694.000	+	1202.04i	0.234725	+	0.406555i
$207$		0			0
$208$	574.000	−	994.197i	0.191345	−	0.331419i
$209$	880.000			0.291248
$210$		0			0
$211$	−4268.00			−1.39252			−0.696259	−	0.717791i	$-0.745153\pi$
$211$	−4268.00			−1.39252			−0.696259	+	0.717791i	$0.745153\pi$
$212$	567.000	−	982.073i	0.183687	−	0.318156i
$213$		0			0
$214$	122.000	+	211.310i	0.0389708	+	0.0674994i
$215$	−1024.00	+	1773.62i	−0.324820	+	0.562604i
$216$		0			0
$217$		0			0
$218$	90.0000			0.0279613
$219$		0			0
$220$	448.000	+	775.959i	0.137292	+	0.237796i
$221$	756.000	+	1309.43i	0.230109	+	0.398560i
$222$		0			0
$223$	5432.00			1.63118			0.815591	−	0.578629i	$-0.196412\pi$
$223$	5432.00			1.63118			0.815591	+	0.578629i	$0.196412\pi$
$224$		0			0
$225$		0			0
$226$	659.000	−	1141.42i	0.193965	−	0.335957i
$227$	1023.00	+	1771.89i	0.299114	+	0.518081i	0.975934	−	0.218068i	$-0.0699756\pi$
$227$	1023.00	+	1771.89i	0.299114	+	0.518081i	−0.676819	+	0.736149i	$0.736642\pi$
$228$		0			0
$229$	−1490.00	+	2580.76i	−0.429965	+	0.744721i	−0.996870	−	0.0790622i	$-0.974807\pi$
$229$	−1490.00	+	2580.76i	−0.429965	+	0.744721i	0.566905	+	0.823783i	$0.308141\pi$
$230$	−768.000			−0.220176
$231$		0			0
$232$	−1650.00			−0.466930
$233$	2229.00	−	3860.74i	0.626724	−	1.08552i	−0.361481	−	0.932379i	$-0.617729\pi$
$233$	2229.00	−	3860.74i	0.626724	−	1.08552i	0.988205	−	0.153138i	$-0.0489379\pi$
$234$		0			0
$235$	−2592.00	−	4489.48i	−0.719504	−	1.24622i
$236$	2835.00	−	4910.36i	0.781961	−	1.35440i
$237$		0			0
$238$		0			0
$239$	−4440.00			−1.20167			−0.600836	−	0.799372i	$-0.705166\pi$
$239$	−4440.00			−1.20167			−0.600836	+	0.799372i	$0.705166\pi$
$240$		0			0
$241$	1651.00	+	2859.62i	0.441287	+	0.764332i	0.997785	−	0.0665168i	$-0.0211886\pi$
$241$	1651.00	+	2859.62i	0.441287	+	0.764332i	−0.556498	+	0.830849i	$0.687855\pi$
$242$	633.500	+	1097.25i	0.168277	+	0.291464i
$243$		0			0
$244$	−3416.00			−0.896258
$245$		0			0
$246$		0			0
$247$	1540.00	−	2667.36i	0.396712	−	0.687125i
$248$	−90.0000	−	155.885i	−0.0230444	−	0.0399140i
$249$		0			0
$250$	−48.0000	+	83.1384i	−0.0121431	+	0.0210325i
$251$	1582.00			0.397829			0.198914	−	0.980017i	$-0.436258\pi$
$251$	1582.00			0.397829			0.198914	+	0.980017i	$0.436258\pi$
$252$		0			0
$253$	−384.000			−0.0954224
$254$	888.000	−	1538.06i	0.219363	−	0.379947i
$255$		0			0
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	−1177.00	+	2038.62i	−0.285678	+	0.494809i	−0.972773	−	0.231758i	$-0.925552\pi$
$257$	−1177.00	+	2038.62i	−0.285678	+	0.494809i	0.687095	+	0.726567i	$0.258885\pi$
$258$		0			0
$259$		0			0
$260$	3136.00			0.748025
$261$		0			0
$262$	559.000	+	968.216i	0.131813	+	0.228308i
$263$	−1936.00	−	3353.25i	−0.453912	−	0.786199i	0.544713	−	0.838623i	$-0.316639\pi$
$263$	−1936.00	−	3353.25i	−0.453912	−	0.786199i	−0.998625	+	0.0524239i	$0.983305\pi$
$264$		0			0
$265$	2592.00			0.600850
$266$		0			0
$267$		0			0
$268$	854.000	−	1479.17i	0.194651	−	0.337145i
$269$	−90.0000	−	155.885i	−0.0203992	−	0.0353325i	0.855646	−	0.517562i	$-0.173160\pi$
$269$	−90.0000	−	155.885i	−0.0203992	−	0.0353325i	−0.876045	+	0.482230i	$0.839827\pi$
$270$		0			0
$271$	1016.00	−	1759.76i	0.227740	−	0.394458i	−0.729398	−	0.684090i	$-0.760200\pi$
$271$	1016.00	−	1759.76i	0.227740	−	0.394458i	0.957138	+	0.289632i	$0.0935330\pi$
$272$	2214.00			0.493542
$273$		0			0
$274$	−2274.00			−0.501377
$275$	−524.000	+	907.595i	−0.114903	+	0.199018i
$276$		0			0
$277$	2713.00	+	4699.05i	0.588478	+	1.01927i	0.994432	+	0.105380i	$0.0336059\pi$
$277$	2713.00	+	4699.05i	0.588478	+	1.01927i	−0.405954	+	0.913893i	$0.633061\pi$
$278$	−105.000	+	181.865i	−0.0226528	+	0.0392358i
$279$		0			0
$280$		0			0
$281$	−842.000			−0.178753			−0.0893764	−	0.995998i	$-0.528487\pi$
$281$	−842.000			−0.178753			−0.0893764	+	0.995998i	$0.528487\pi$
$282$		0			0
$283$	−1891.00	−	3275.31i	−0.397202	−	0.687975i	0.596177	−	0.802853i	$-0.296686\pi$
$283$	−1891.00	−	3275.31i	−0.397202	−	0.687975i	−0.993380	+	0.114878i	$0.963352\pi$
$284$	2688.00	+	4655.75i	0.561632	+	0.972775i
$285$		0			0
$286$	−224.000			−0.0463126
$287$		0			0
$288$		0			0
$289$	998.500	−	1729.45i	0.203236	−	0.352016i
$290$	−880.000	−	1524.20i	−0.178191	−	0.308636i
$291$		0			0
$292$	2457.00	−	4255.65i	0.492415	−	0.852887i
$293$	−4312.00			−0.859760			−0.429880	−	0.902886i	$-0.641444\pi$
$293$	−4312.00			−0.859760			−0.429880	+	0.902886i	$0.641444\pi$
$294$		0			0
$295$	12960.0			2.55783
$296$	−1845.00	+	3195.63i	−0.362292	+	0.627508i
$297$		0			0
$298$	−1005.00	−	1740.71i	−0.195363	−	0.338378i
$299$	−672.000	+	1163.94i	−0.129976	+	0.225125i
$300$		0			0
$301$		0			0
$302$	1112.00			0.211882
$303$		0			0
$304$	−2255.00	−	3905.77i	−0.425438	−	0.736880i
$305$	−3904.00	−	6761.93i	−0.732926	−	1.26946i
$306$		0			0
$307$	−2674.00			−0.497112			−0.248556	−	0.968618i	$-0.579956\pi$
$307$	−2674.00			−0.497112			−0.248556	+	0.968618i	$0.579956\pi$
$308$		0			0
$309$		0			0
$310$	96.0000	−	166.277i	0.0175885	−	0.0304642i
$311$	1884.00	+	3263.18i	0.343511	+	0.594978i	0.985082	−	0.172085i	$-0.0550505\pi$
$311$	1884.00	+	3263.18i	0.343511	+	0.594978i	−0.641571	+	0.767063i	$0.721717\pi$
$312$		0			0
$313$	1219.00	−	2111.37i	0.220134	−	0.381283i	−0.734714	−	0.678376i	$-0.762684\pi$
$313$	1219.00	−	2111.37i	0.220134	−	0.381283i	0.954849	+	0.297093i	$0.0960172\pi$
$314$	−124.000			−0.0222857
$315$		0			0
$316$	−3080.00			−0.548302
$317$	−1593.00	+	2759.16i	−0.282245	+	0.488863i	−0.971937	−	0.235239i	$-0.924413\pi$
$317$	−1593.00	+	2759.16i	−0.282245	+	0.488863i	0.689692	+	0.724103i	$0.257746\pi$
$318$		0			0
$319$	−440.000	−	762.102i	−0.0772266	−	0.133760i
$320$	1336.00	−	2314.02i	0.233390	−	0.404243i
$321$		0			0
$322$		0			0
$323$	5940.00			1.02325
$324$		0			0
$325$	1834.00	+	3176.58i	0.313022	+	0.542169i
$326$	−1004.00	−	1738.98i	−0.170572	−	0.295439i
$327$		0			0
$328$	−2730.00			−0.459570
$329$		0			0
$330$		0			0
$331$	−4336.00	+	7510.17i	−0.720025	+	1.24712i	0.240965	+	0.970534i	$0.422536\pi$
$331$	−4336.00	+	7510.17i	−0.720025	+	1.24712i	−0.960989	+	0.276585i	$0.910797\pi$
$332$	−4557.00	−	7892.96i	−0.753307	−	1.30477i
$333$		0			0
$334$	−1442.00	+	2497.62i	−0.236236	+	0.409172i
$335$	3904.00			0.636711
$336$		0			0
$337$	814.000			0.131577			0.0657884	−	0.997834i	$-0.479044\pi$
$337$	814.000			0.131577			0.0657884	+	0.997834i	$0.479044\pi$
$338$	706.500	−	1223.69i	0.113694	−	0.196924i
$339$		0			0
$340$	3024.00	+	5237.72i	0.482351	+	0.835457i
$341$	48.0000	−	83.1384i	0.00762271	−	0.0132029i
$342$		0			0
$343$		0			0
$344$	−1920.00			−0.300929
$345$		0			0
$346$	−1114.00	−	1929.50i	−0.173090	−	0.299800i
$347$	4672.00	+	8092.14i	0.722784	+	1.25190i	0.959880	+	0.280413i	$0.0904713\pi$
$347$	4672.00	+	8092.14i	0.722784	+	1.25190i	−0.237095	+	0.971486i	$0.576195\pi$
$348$		0			0
$349$	5180.00			0.794496			0.397248	−	0.917711i	$-0.369965\pi$
$349$	5180.00			0.794496			0.397248	+	0.917711i	$0.369965\pi$
$350$		0			0
$351$		0			0
$352$	−644.000	+	1115.44i	−0.0975151	+	0.168901i
$353$	−6089.00	−	10546.5i	−0.918087	−	1.59017i	−0.802317	−	0.596898i	$-0.796400\pi$
$353$	−6089.00	−	10546.5i	−0.918087	−	1.59017i	−0.115770	−	0.993276i	$-0.536933\pi$
$354$		0			0
$355$	−6144.00	+	10641.7i	−0.918562	+	1.59100i
$356$	−5110.00			−0.760757
$357$		0			0
$358$	820.000			0.121057
$359$	220.000	−	381.051i	0.0323431	−	0.0560198i	−0.849401	−	0.527748i	$-0.823036\pi$
$359$	220.000	−	381.051i	0.0323431	−	0.0560198i	0.881744	+	0.471729i	$0.156370\pi$
$360$		0			0
$361$	−2620.50	−	4538.84i	−0.382053	−	0.661735i
$362$	1946.00	−	3370.57i	0.282540	−	0.489374i
$363$		0			0
$364$		0			0
$365$	11232.0			1.61071
$366$		0			0
$367$	−4908.00	−	8500.91i	−0.698080	−	1.20911i	−0.969131	−	0.246546i	$-0.920704\pi$
$367$	−4908.00	−	8500.91i	−0.698080	−	1.20911i	0.271051	−	0.962565i	$-0.412629\pi$
$368$	984.000	+	1704.34i	0.139387	+	0.241426i
$369$		0			0
$370$	−3936.00			−0.553035
$371$		0			0
$372$		0			0
$373$	221.000	−	382.783i	0.0306781	−	0.0531361i	−0.850279	−	0.526333i	$-0.823567\pi$
$373$	221.000	−	382.783i	0.0306781	−	0.0531361i	0.880957	+	0.473197i	$0.156900\pi$
$374$	−216.000	−	374.123i	−0.0298639	−	0.0517258i
$375$		0			0
$376$	2430.00	−	4208.88i	0.333292	−	0.577278i
$377$	−3080.00			−0.420764
$378$		0			0
$379$	−3960.00			−0.536706			−0.268353	−	0.963321i	$-0.586479\pi$
$379$	−3960.00			−0.536706			−0.268353	+	0.963321i	$0.586479\pi$
$380$	6160.00	−	10669.4i	0.831582	−	1.44034i
$381$		0			0
$382$	−2524.00	−	4371.70i	−0.338060	−	0.585538i
$383$	−3354.00	+	5809.30i	−0.447471	+	0.775043i	−0.998221	−	0.0596280i	$-0.981009\pi$
$383$	−3354.00	+	5809.30i	−0.447471	+	0.775043i	0.550750	+	0.834670i	$0.314342\pi$
$384$		0			0
$385$		0			0
$386$	−2962.00			−0.390575
$387$		0			0
$388$	−1029.00	−	1782.28i	−0.134638	−	0.233200i
$389$	−6675.00	−	11561.4i	−0.870015	−	1.50691i	−0.861980	−	0.506943i	$-0.830775\pi$
$389$	−6675.00	−	11561.4i	−0.870015	−	1.50691i	−0.00803563	−	0.999968i	$-0.502558\pi$
$390$		0			0
$391$	−2592.00			−0.335251
$392$		0			0
$393$		0			0
$394$	1667.00	−	2887.33i	0.213153	−	0.369192i
$395$	−3520.00	−	6096.82i	−0.448381	−	0.776618i
$396$		0			0
$397$	−678.000	+	1174.33i	−0.0857125	+	0.148458i	−0.905695	−	0.423931i	$-0.860650\pi$
$397$	−678.000	+	1174.33i	−0.0857125	+	0.148458i	0.819982	+	0.572389i	$0.193983\pi$
$398$	−1860.00			−0.234255
$399$		0			0
$400$	5371.00			0.671375
$401$	3111.00	−	5388.41i	0.387421	−	0.671033i	−0.604681	−	0.796468i	$-0.706699\pi$
$401$	3111.00	−	5388.41i	0.387421	−	0.671033i	0.992102	+	0.125435i	$0.0400326\pi$
$402$		0			0
$403$	−168.000	−	290.985i	−0.0207659	−	0.0359677i
$404$	−2408.00	+	4170.78i	−0.296541	+	0.513624i
$405$		0			0
$406$		0			0
$407$	−1968.00			−0.239681
$408$		0			0
$409$	2575.00	+	4460.03i	0.311309	+	0.539204i	0.978646	−	0.205552i	$-0.0658991\pi$
$409$	2575.00	+	4460.03i	0.311309	+	0.539204i	−0.667337	+	0.744756i	$0.732566\pi$
$410$	−1456.00	−	2521.87i	−0.175382	−	0.303771i
$411$		0			0
$412$	9716.00			1.16183
$413$		0			0
$414$		0			0
$415$	10416.0	−	18041.0i	1.23205	−	2.13398i
$416$	2254.00	+	3904.04i	0.265653	+	0.460124i
$417$		0			0
$418$	−440.000	+	762.102i	−0.0514859	+	0.0891762i
$419$	2310.00			0.269334			0.134667	−	0.990891i	$-0.457004\pi$
$419$	2310.00			0.269334			0.134667	+	0.990891i	$0.457004\pi$
$420$		0			0
$421$	1262.00			0.146095			0.0730476	−	0.997328i	$-0.476727\pi$
$421$	1262.00			0.146095			0.0730476	+	0.997328i	$0.476727\pi$
$422$	2134.00	−	3696.20i	0.246165	−	0.426370i
$423$		0			0
$424$	1215.00	+	2104.44i	0.139164	+	0.241039i
$425$	−3537.00	+	6126.26i	−0.403693	+	0.699218i
$426$		0			0
$427$		0			0
$428$	1708.00			0.192896
$429$		0			0
$430$	−1024.00	−	1773.62i	−0.114841	−	0.198911i
$431$	−2244.00	−	3886.72i	−0.250788	−	0.434378i	0.712955	−	0.701210i	$-0.247356\pi$
$431$	−2244.00	−	3886.72i	−0.250788	−	0.434378i	−0.963743	+	0.266832i	$0.914023\pi$
$432$		0			0
$433$	−17038.0			−1.89098			−0.945490	−	0.325652i	$-0.894416\pi$
$433$	−17038.0			−1.89098			−0.945490	+	0.325652i	$0.894416\pi$
$434$		0			0
$435$		0			0
$436$	315.000	−	545.596i	0.0346004	−	0.0599296i
$437$	2640.00	+	4572.61i	0.288989	+	0.500544i
$438$		0			0
$439$	8100.00	−	14029.6i	0.880619	−	1.52528i	0.0299658	−	0.999551i	$-0.490460\pi$
$439$	8100.00	−	14029.6i	0.880619	−	1.52528i	0.850654	−	0.525727i	$-0.176206\pi$
$440$	−1920.00			−0.208028
$441$		0			0
$442$	−1512.00			−0.162712
$443$	−4386.00	+	7596.77i	−0.470395	+	0.814749i	−0.999427	−	0.0338535i	$-0.989222\pi$
$443$	−4386.00	+	7596.77i	−0.470395	+	0.814749i	0.529031	+	0.848602i	$0.322555\pi$
$444$		0			0
$445$	−5840.00	−	10115.2i	−0.622118	−	1.07754i
$446$	−2716.00	+	4704.25i	−0.288355	+	0.499446i
$447$		0			0
$448$		0			0
$449$	−2130.00			−0.223877			−0.111939	−	0.993715i	$-0.535706\pi$
$449$	−2130.00			−0.223877			−0.111939	+	0.993715i	$0.535706\pi$
$450$		0			0
$451$	−728.000	−	1260.93i	−0.0760093	−	0.131652i
$452$	−4613.00	−	7989.95i	−0.480038	−	0.831451i
$453$		0			0
$454$	−2046.00			−0.211506
$455$		0			0
$456$		0			0
$457$	−5267.00	+	9122.71i	−0.539124	+	0.933791i	0.459827	+	0.888009i	$0.347911\pi$
$457$	−5267.00	+	9122.71i	−0.539124	+	0.933791i	−0.998951	+	0.0457824i	$0.985422\pi$
$458$	−1490.00	−	2580.76i	−0.152016	−	0.263299i
$459$		0			0
$460$	−2688.00	+	4655.75i	−0.272454	+	0.471903i
$461$	−9268.00			−0.936342			−0.468171	−	0.883638i	$-0.655087\pi$
$461$	−9268.00			−0.936342			−0.468171	+	0.883638i	$0.655087\pi$
$462$		0			0
$463$	−9392.00			−0.942728			−0.471364	−	0.881939i	$-0.656238\pi$
$463$	−9392.00			−0.942728			−0.471364	+	0.881939i	$0.656238\pi$
$464$	−2255.00	+	3905.77i	−0.225616	+	0.390778i
$465$		0			0
$466$	2229.00	+	3860.74i	0.221580	+	0.383788i
$467$	5403.00	−	9358.27i	0.535377	−	0.927300i	−0.463768	−	0.885957i	$-0.653503\pi$
$467$	5403.00	−	9358.27i	0.535377	−	0.927300i	0.999145	−	0.0413434i	$-0.0131638\pi$
$468$		0			0
$469$		0			0
$470$	5184.00			0.508766
$471$		0			0
$472$	6075.00	+	10522.2i	0.592425	+	1.02611i
$473$	−512.000	−	886.810i	−0.0497712	−	0.0862063i
$474$		0			0
$475$	14410.0			1.39195
$476$		0			0
$477$		0			0
$478$	2220.00	−	3845.15i	0.212428	−	0.367936i
$479$	−2470.00	−	4278.17i	−0.235610	−	0.408088i	0.723840	−	0.689968i	$-0.242375\pi$
$479$	−2470.00	−	4278.17i	−0.235610	−	0.408088i	−0.959450	+	0.281880i	$0.909042\pi$
$480$		0			0
$481$	−3444.00	+	5965.18i	−0.326472	+	0.565466i
$482$	−3302.00			−0.312037
$483$		0			0
$484$	8869.00			0.832926
$485$	2352.00	−	4073.78i	0.220204	−	0.381404i
$486$		0			0
$487$	2608.00	+	4517.19i	0.242669	+	0.420315i	0.961474	−	0.274897i	$-0.0886438\pi$
$487$	2608.00	+	4517.19i	0.242669	+	0.420315i	−0.718805	+	0.695212i	$0.755310\pi$
$488$	3660.00	−	6339.31i	0.339509	−	0.588047i
$489$		0			0
$490$		0			0
$491$	−4412.00			−0.405521			−0.202760	−	0.979228i	$-0.564991\pi$
$491$	−4412.00			−0.405521			−0.202760	+	0.979228i	$0.564991\pi$
$492$		0			0
$493$	−2970.00	−	5144.19i	−0.271323	−	0.469945i
$494$	1540.00	+	2667.36i	0.140259	+	0.242935i
$495$		0			0
$496$	−492.000			−0.0445392
$497$		0			0
$498$		0			0
$499$	−9530.00	+	16506.4i	−0.854953	+	1.48082i	0.0217362	+	0.999764i	$0.493081\pi$
$499$	−9530.00	+	16506.4i	−0.854953	+	1.48082i	−0.876689	+	0.481058i	$0.840253\pi$
$500$	336.000	+	581.969i	0.0300528	+	0.0520529i
$501$		0			0
$502$	−791.000	+	1370.05i	−0.0703268	+	0.121810i
$503$	12768.0			1.13180			0.565902	−	0.824473i	$-0.308528\pi$
$503$	12768.0			1.13180			0.565902	+	0.824473i	$0.308528\pi$
$504$		0			0
$505$	−11008.0			−0.969999
$506$	192.000	−	332.554i	0.0168685	−	0.0292170i
$507$		0			0
$508$	−6216.00	−	10766.4i	−0.542894	−	0.940321i
$509$	2750.00	−	4763.14i	0.239473	−	0.414779i	−0.721090	−	0.692841i	$-0.756359\pi$
$509$	2750.00	−	4763.14i	0.239473	−	0.414779i	0.960563	+	0.278062i	$0.0896921\pi$
$510$		0			0
$511$		0			0
$512$	11521.0			0.994455
$513$		0			0
$514$	−1177.00	−	2038.62i	−0.101002	−	0.174941i
$515$	11104.0	+	19232.7i	0.950098	+	1.64562i
$516$		0			0
$517$	2592.00			0.220495
$518$		0			0
$519$		0			0
$520$	−3360.00	+	5819.69i	−0.283357	+	0.490789i
$521$	3669.00	+	6354.89i	0.308526	+	0.534382i	0.978040	−	0.208417i	$-0.0668311\pi$
$521$	3669.00	+	6354.89i	0.308526	+	0.534382i	−0.669514	+	0.742799i	$0.733498\pi$
$522$		0			0
$523$	−8791.00	+	15226.5i	−0.734997	+	1.27305i	0.219727	+	0.975561i	$0.429483\pi$
$523$	−8791.00	+	15226.5i	−0.734997	+	1.27305i	−0.954725	+	0.297491i	$0.903850\pi$
$524$	7826.00			0.652444
$525$		0			0
$526$	3872.00			0.320964
$527$	324.000	−	561.184i	0.0267811	−	0.0463863i
$528$		0			0
$529$	4931.50	+	8541.61i	0.405318	+	0.702031i
$530$	−1296.00	+	2244.74i	−0.106216	+	0.183972i
$531$		0			0
$532$		0			0
$533$	−5096.00			−0.414132
$534$		0			0
$535$	1952.00	+	3380.96i	0.157743	+	0.273218i
$536$	1830.00	+	3169.65i	0.147470	+	0.255426i
$537$		0			0
$538$	180.000			0.0144244
$539$		0			0
$540$		0			0
$541$	809.000	−	1401.23i	0.0642914	−	0.111356i	−0.832088	−	0.554644i	$-0.812855\pi$
$541$	809.000	−	1401.23i	0.0642914	−	0.111356i	0.896379	+	0.443288i	$0.146188\pi$
$542$	1016.00	+	1759.76i	0.0805183	+	0.139462i
$543$		0			0
$544$	−4347.00	+	7529.22i	−0.342603	+	0.593406i
$545$	1440.00			0.113179
$546$		0			0
$547$	16144.0			1.26192			0.630958	−	0.775817i	$-0.282662\pi$
$547$	16144.0			1.26192			0.630958	+	0.775817i	$0.282662\pi$
$548$	−7959.00	+	13785.4i	−0.620423	+	1.07460i
$549$		0			0
$550$	−524.000	−	907.595i	−0.0406244	−	0.0703636i
$551$	−6050.00	+	10478.9i	−0.467765	+	0.810193i
$552$		0			0
$553$		0			0
$554$	−5426.00			−0.416117
$555$		0			0
$556$	735.000	+	1273.06i	0.0560628	+	0.0971037i
$557$	2327.00	+	4030.48i	0.177016	+	0.306601i	0.940857	−	0.338803i	$-0.110022\pi$
$557$	2327.00	+	4030.48i	0.177016	+	0.306601i	−0.763841	+	0.645405i	$0.776689\pi$
$558$		0			0
$559$	−3584.00			−0.271175
$560$		0			0
$561$		0			0
$562$	421.000	−	729.193i	0.0315993	−	0.0547316i
$563$	−5039.00	−	8727.80i	−0.377209	−	0.653345i	0.613446	−	0.789736i	$-0.289783\pi$
$563$	−5039.00	−	8727.80i	−0.377209	−	0.653345i	−0.990655	+	0.136392i	$0.956449\pi$
$564$		0			0
$565$	10544.0	−	18262.7i	0.785114	−	1.35986i
$566$	3782.00			0.280865
$567$		0			0
$568$	−11520.0			−0.851001
$569$	−2965.00	+	5135.53i	−0.218452	+	0.378370i	−0.954335	−	0.298739i	$-0.903434\pi$
$569$	−2965.00	+	5135.53i	−0.218452	+	0.378370i	0.735883	+	0.677109i	$0.236767\pi$
$570$		0			0
$571$	9524.00	+	16496.1i	0.698016	+	1.20900i	0.969153	+	0.246458i	$0.0792668\pi$
$571$	9524.00	+	16496.1i	0.698016	+	1.20900i	−0.271138	+	0.962541i	$0.587400\pi$
$572$	−784.000	+	1357.93i	−0.0573089	+	0.0992619i
$573$		0			0
$574$		0			0
$575$	−6288.00			−0.456048
$576$		0			0
$577$	−7183.00	−	12441.3i	−0.518253	−	0.897641i	−0.999775	−	0.0212070i	$-0.993249\pi$
$577$	−7183.00	−	12441.3i	−0.518253	−	0.897641i	0.481522	−	0.876434i	$-0.340084\pi$
$578$	998.500	+	1729.45i	0.0718549	+	0.124456i
$579$		0			0
$580$	−12320.0			−0.882000
$581$		0			0
$582$		0			0
$583$	−648.000	+	1122.37i	−0.0460333	+	0.0797320i
$584$	5265.00	+	9119.25i	0.373060	+	0.646159i
$585$		0			0
$586$	2156.00	−	3734.30i	0.151986	−	0.263247i
$587$	−3626.00			−0.254959			−0.127480	−	0.991841i	$-0.540689\pi$
$587$	−3626.00			−0.254959			−0.127480	+	0.991841i	$0.540689\pi$
$588$		0			0
$589$	−1320.00			−0.0923424
$590$	−6480.00	+	11223.7i	−0.452165	+	0.783173i
$591$		0			0
$592$	5043.00	+	8734.73i	0.350112	+	0.606411i
$593$	531.000	−	919.719i	0.0367716	−	0.0636903i	−0.847054	−	0.531507i	$-0.821626\pi$
$593$	531.000	−	919.719i	0.0367716	−	0.0636903i	0.883826	+	0.467817i	$0.154959\pi$
$594$		0			0
$595$		0			0
$596$	−14070.0			−0.966996
$597$		0			0
$598$	−672.000	−	1163.94i	−0.0459534	−	0.0795936i
$599$	−5100.00	−	8833.46i	−0.347880	−	0.602547i	0.637992	−	0.770043i	$-0.279765\pi$
$599$	−5100.00	−	8833.46i	−0.347880	−	0.602547i	−0.985873	+	0.167496i	$0.946432\pi$
$600$		0			0
$601$	25158.0			1.70751			0.853757	−	0.520671i	$-0.174318\pi$
$601$	25158.0			1.70751			0.853757	+	0.520671i	$0.174318\pi$
$602$		0			0
$603$		0			0
$604$	3892.00	−	6741.14i	0.262191	−	0.454128i
$605$	10136.0	+	17556.1i	0.681136	+	1.17976i
$606$		0			0
$607$	12832.0	−	22225.7i	0.858047	−	1.48618i	−0.0157413	−	0.999876i	$-0.505011\pi$
$607$	12832.0	−	22225.7i	0.858047	−	1.48618i	0.873789	−	0.486306i	$-0.161656\pi$
$608$	17710.0			1.18131
$609$		0			0
$610$	7808.00			0.518257
$611$	4536.00	−	7856.58i	0.300339	−	0.520202i
$612$		0			0
$613$	−9509.00	−	16470.1i	−0.626533	−	1.08519i	−0.988242	−	0.152896i	$-0.951140\pi$
$613$	−9509.00	−	16470.1i	−0.626533	−	1.08519i	0.361709	−	0.932291i	$-0.382193\pi$
$614$	1337.00	−	2315.75i	0.0878777	−	0.152209i
$615$		0			0
$616$		0			0
$617$	−17334.0			−1.13102			−0.565511	−	0.824741i	$-0.691321\pi$
$617$	−17334.0			−1.13102			−0.565511	+	0.824741i	$0.691321\pi$
$618$		0			0
$619$	9365.00	+	16220.7i	0.608096	+	1.05325i	0.991554	+	0.129694i	$0.0413996\pi$
$619$	9365.00	+	16220.7i	0.608096	+	1.05325i	−0.383459	+	0.923558i	$0.625267\pi$
$620$	−672.000	−	1163.94i	−0.0435293	−	0.0753950i
$621$		0			0
$622$	−3768.00			−0.242899
$623$		0			0
$624$		0			0
$625$	7419.50	−	12851.0i	0.474848	−	0.822461i
$626$	1219.00	+	2111.37i	0.0778291	+	0.134804i
$627$		0			0
$628$	−434.000	+	751.710i	−0.0275772	+	0.0477651i
$629$	−13284.0			−0.842079
$630$		0			0
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$	3300.00	−	5715.77i	0.207701	−	0.359748i
$633$		0			0
$634$	−1593.00	−	2759.16i	−0.0997888	−	0.172839i
$635$	14208.0	−	24609.0i	0.887917	−	1.53792i
$636$		0			0
$637$		0			0
$638$	880.000			0.0546074
$639$		0			0
$640$	11640.0	+	20161.1i	0.718924	+	1.24521i
$641$	8151.00	+	14117.9i	0.502255	+	0.869930i	0.999997	+	0.00260525i	$0.000829277\pi$
$641$	8151.00	+	14117.9i	0.502255	+	0.869930i	−0.497742	+	0.867325i	$0.665837\pi$
$642$		0			0
$643$	−4718.00			−0.289362			−0.144681	−	0.989478i	$-0.546216\pi$
$643$	−4718.00			−0.289362			−0.144681	+	0.989478i	$0.546216\pi$
$644$		0			0
$645$		0			0
$646$	−2970.00	+	5144.19i	−0.180887	+	0.313306i
$647$	10718.0	+	18564.1i	0.651264	+	1.12802i	0.982816	+	0.184586i	$0.0590944\pi$
$647$	10718.0	+	18564.1i	0.651264	+	1.12802i	−0.331552	+	0.943437i	$0.607572\pi$
$648$		0			0
$649$	−3240.00	+	5611.84i	−0.195965	+	0.339421i
$650$	−3668.00			−0.221340
$651$		0			0
$652$	−14056.0			−0.844287
$653$	2229.00	−	3860.74i	0.133580	−	0.231367i	−0.791474	−	0.611202i	$-0.790686\pi$
$653$	2229.00	−	3860.74i	0.133580	−	0.231367i	0.925054	+	0.379836i	$0.124019\pi$
$654$		0			0
$655$	8944.00	+	15491.5i	0.533544	+	0.924124i
$656$	−3731.00	+	6462.28i	−0.222060	+	0.384618i
$657$		0			0
$658$		0			0
$659$	26640.0			1.57473			0.787365	−	0.616487i	$-0.211445\pi$
$659$	26640.0			1.57473			0.787365	+	0.616487i	$0.211445\pi$
$660$		0			0
$661$	3716.00	+	6436.30i	0.218662	+	0.378734i	0.954399	−	0.298533i	$-0.0964974\pi$
$661$	3716.00	+	6436.30i	0.218662	+	0.378734i	−0.735737	+	0.677267i	$0.763164\pi$
$662$	−4336.00	−	7510.17i	−0.254567	−	0.440923i
$663$		0			0
$664$	19530.0			1.14143
$665$		0			0
$666$		0			0
$667$	2640.00	−	4572.61i	0.153255	−	0.265446i
$668$	10094.0	+	17483.3i	0.584654	+	1.01265i
$669$		0			0
$670$	−1952.00	+	3380.96i	−0.112556	+	0.194952i
$671$	3904.00			0.224608
$672$		0			0
$673$	58.0000			0.00332204			0.00166102	−	0.999999i	$-0.499471\pi$
$673$	58.0000			0.00332204			0.00166102	+	0.999999i	$0.499471\pi$
$674$	−407.000	+	704.945i	−0.0232597	+	0.0402870i
$675$		0			0
$676$	−4945.50	−	8565.86i	−0.281378	−	0.487361i
$677$	10758.0	−	18633.4i	0.610729	−	1.05781i	−0.380389	−	0.924827i	$-0.624210\pi$
$677$	10758.0	−	18633.4i	0.610729	−	1.05781i	0.991118	−	0.132987i	$-0.0424568\pi$
$678$		0			0
$679$		0			0
$680$	−12960.0			−0.730873
$681$		0			0
$682$	48.0000	+	83.1384i	0.00269504	+	0.00466794i
$683$	9054.00	+	15682.0i	0.507235	+	0.878557i	0.999965	+	0.00837480i	$0.00266581\pi$
$683$	9054.00	+	15682.0i	0.507235	+	0.878557i	−0.492730	+	0.870182i	$0.664001\pi$
$684$		0			0
$685$	−36384.0			−2.02943
$686$		0			0
$687$		0			0
$688$	−2624.00	+	4544.90i	−0.145406	+	0.251850i
$689$	2268.00	+	3928.29i	0.125405	+	0.217208i
$690$		0			0
$691$	−5039.00	+	8727.80i	−0.277413	+	0.480494i	−0.970741	−	0.240128i	$-0.922810\pi$
$691$	−5039.00	+	8727.80i	−0.277413	+	0.480494i	0.693328	+	0.720622i	$0.256144\pi$
$692$	−15596.0			−0.856750
$693$		0			0
$694$	−9344.00			−0.511086
$695$	−1680.00	+	2909.85i	−0.0916921	+	0.158815i
$696$		0			0
$697$	−4914.00	−	8511.30i	−0.267046	−	0.462537i
$698$	−2590.00	+	4486.01i	−0.140448	+	0.243264i
$699$		0			0
$700$		0			0
$701$	−18762.0			−1.01089			−0.505443	−	0.862860i	$-0.668671\pi$
$701$	−18762.0			−1.01089			−0.505443	+	0.862860i	$0.668671\pi$
$702$		0			0
$703$	13530.0	+	23434.6i	0.725880	+	1.25726i
$704$	668.000	+	1157.01i	0.0357616	+	0.0619410i
$705$		0			0
$706$	12178.0			0.649186
$707$		0			0
$708$		0			0
$709$	−3405.00	+	5897.63i	−0.180363	+	0.312398i	−0.942004	−	0.335601i	$-0.891061\pi$
$709$	−3405.00	+	5897.63i	−0.180363	+	0.312398i	0.761641	+	0.647999i	$0.224394\pi$
$710$	−6144.00	−	10641.7i	−0.324761	−	0.562502i
$711$		0			0
$712$	5475.00	−	9482.98i	0.288180	−	0.499143i
$713$	576.000			0.0302544
$714$		0			0
$715$	−3584.00			−0.187460
$716$	2870.00	−	4970.99i	0.149800	−	0.259462i
$717$		0			0
$718$	220.000	+	381.051i	0.0114350	+	0.0198060i
$719$	−2430.00	+	4208.88i	−0.126041	+	0.218310i	−0.922140	−	0.386858i	$-0.873561\pi$
$719$	−2430.00	+	4208.88i	−0.126041	+	0.218310i	0.796098	+	0.605167i	$0.206894\pi$
$720$		0			0
$721$		0			0
$722$	5241.00			0.270152
$723$		0			0
$724$	−13622.0	−	23594.0i	−0.699251	−	1.21114i
$725$	−7205.00	−	12479.4i	−0.369085	−	0.639275i
$726$		0			0
$727$	13636.0			0.695641			0.347821	−	0.937561i	$-0.386922\pi$
$727$	13636.0			0.695641			0.347821	+	0.937561i	$0.386922\pi$
$728$		0			0
$729$		0			0
$730$	−5616.00	+	9727.20i	−0.284736	+	0.493178i
$731$	−3456.00	−	5985.97i	−0.174863	−	0.302871i
$732$		0			0
$733$	1044.00	−	1808.26i	0.0526071	−	0.0911182i	−0.838523	−	0.544867i	$-0.816580\pi$
$733$	1044.00	−	1808.26i	0.0526071	−	0.0911182i	0.891130	+	0.453749i	$0.149914\pi$
$734$	9816.00			0.493617
$735$		0			0
$736$	−7728.00			−0.387035
$737$	−976.000	+	1690.48i	−0.0487808	+	0.0844908i
$738$		0			0
$739$	2580.00	+	4468.69i	0.128426	+	0.222440i	0.923067	−	0.384639i	$-0.125674\pi$
$739$	2580.00	+	4468.69i	0.128426	+	0.222440i	−0.794641	+	0.607080i	$0.792341\pi$
$740$	−13776.0	+	23860.7i	−0.684346	+	1.18532i
$741$		0			0
$742$		0			0
$743$	28152.0			1.39004			0.695018	−	0.718992i	$-0.255396\pi$
$743$	28152.0			1.39004			0.695018	+	0.718992i	$0.255396\pi$
$744$		0			0
$745$	−16080.0	−	27851.4i	−0.790773	−	1.36966i
$746$	221.000	+	382.783i	0.0108464	+	0.0187864i
$747$		0			0
$748$	−3024.00			−0.147819
$749$		0			0
$750$		0			0
$751$	8404.00	−	14556.2i	0.408344	−	0.707272i	−0.586360	−	0.810050i	$-0.699440\pi$
$751$	8404.00	−	14556.2i	0.408344	−	0.707272i	0.994704	+	0.102778i	$0.0327731\pi$
$752$	−6642.00	−	11504.3i	−0.322086	−	0.557870i
$753$		0			0
$754$	1540.00	−	2667.36i	0.0743813	−	0.128832i
$755$	17792.0			0.857639
$756$		0			0
$757$	21674.0			1.04063			0.520314	−	0.853975i	$-0.325815\pi$
$757$	21674.0			1.04063			0.520314	+	0.853975i	$0.325815\pi$
$758$	1980.00	−	3429.46i	0.0948771	−	0.164332i
$759$		0			0
$760$	13200.0	+	22863.1i	0.630019	+	1.09122i
$761$	−3711.00	+	6427.64i	−0.176772	+	0.306178i	−0.940773	−	0.339037i	$-0.889899\pi$
$761$	−3711.00	+	6427.64i	−0.176772	+	0.306178i	0.764001	+	0.645215i	$0.223232\pi$
$762$		0			0
$763$		0			0
$764$	−35336.0			−1.67331
$765$		0			0
$766$	−3354.00	−	5809.30i	−0.158205	−	0.274019i
$767$	11340.0	+	19641.5i	0.533851	+	0.924657i
$768$		0			0
$769$	−13790.0			−0.646658			−0.323329	−	0.946287i	$-0.604802\pi$
$769$	−13790.0			−0.646658			−0.323329	+	0.946287i	$0.604802\pi$
$770$		0			0
$771$		0			0
$772$	−10367.0	+	17956.2i	−0.483312	+	0.837120i
$773$	3116.00	+	5397.07i	0.144987	+	0.251124i	0.929368	−	0.369155i	$-0.120353\pi$
$773$	3116.00	+	5397.07i	0.144987	+	0.251124i	−0.784381	+	0.620279i	$0.787019\pi$
$774$		0			0
$775$	786.000	−	1361.39i	0.0364309	−	0.0631002i
$776$	4410.00			0.204007
$777$		0			0
$778$	13350.0			0.615194
$779$	−10010.0	+	17337.8i	−0.460392	+	0.797423i
$780$		0			0
$781$	−3072.00	−	5320.86i	−0.140749	−	0.243784i
$782$	1296.00	−	2244.74i	0.0592645	−	0.102649i
$783$		0			0
$784$		0			0
$785$	−1984.00			−0.0902064
$786$		0			0
$787$	−883.000	−	1529.40i	−0.0399943	−	0.0692722i	0.845335	−	0.534236i	$-0.179401\pi$
$787$	−883.000	−	1529.40i	−0.0399943	−	0.0692722i	−0.885330	+	0.464964i	$0.846067\pi$
$788$	−11669.0	−	20211.3i	−0.527527	−	0.913703i
$789$		0			0
$790$	7040.00			0.317053
$791$		0			0
$792$		0			0
$793$	6832.00	−	11833.4i	0.305941	−	0.529906i
$794$	−678.000	−	1174.33i	−0.0303039	−	0.0524879i
$795$		0			0
$796$	−6510.00	+	11275.7i	−0.289875	+	0.502079i
$797$	1204.00			0.0535105			0.0267552	−	0.999642i	$-0.491483\pi$
$797$	1204.00			0.0535105			0.0267552	+	0.999642i	$0.491483\pi$
$798$		0			0
$799$	17496.0			0.774673
$800$	−10545.5	+	18265.3i	−0.466050	+	0.807222i
$801$		0			0
$802$	3111.00	+	5388.41i	0.136974	+	0.237246i
$803$	−2808.00	+	4863.60i	−0.123402	+	0.213739i
$804$		0			0
$805$		0			0
$806$	336.000			0.0146837
$807$		0			0
$808$	−5160.00	−	8937.38i	−0.224664	−	0.389129i
$809$	−3525.00	−	6105.48i	−0.153192	−	0.265336i	0.779207	−	0.626766i	$-0.215622\pi$
$809$	−3525.00	−	6105.48i	−0.153192	−	0.265336i	−0.932399	+	0.361430i	$0.882289\pi$
$810$		0			0
$811$	−23282.0			−1.00807			−0.504033	−	0.863684i	$-0.668151\pi$
$811$	−23282.0			−1.00807			−0.504033	+	0.863684i	$0.668151\pi$
$812$		0			0
$813$		0			0
$814$	984.000	−	1704.34i	0.0423700	−	0.0733870i
$815$	−16064.0	−	27823.7i	−0.690426	−	1.19585i
$816$		0			0
$817$	−7040.00	+	12193.6i	−0.301467	+	0.522156i
$818$	−5150.00			−0.220129
$819$		0			0
$820$	−20384.0			−0.868098
$821$	5071.00	−	8783.23i	0.215565	−	0.373370i	−0.737882	−	0.674930i	$-0.764174\pi$
$821$	5071.00	−	8783.23i	0.215565	−	0.373370i	0.953447	+	0.301560i	$0.0975073\pi$
$822$		0			0
$823$	4596.00	+	7960.51i	0.194662	+	0.337164i	0.946790	−	0.321853i	$-0.104306\pi$
$823$	4596.00	+	7960.51i	0.194662	+	0.337164i	−0.752128	+	0.659017i	$0.770972\pi$
$824$	−10410.0	+	18030.6i	−0.440109	+	0.762291i
$825$		0			0
$826$		0			0
$827$	46716.0			1.96430			0.982149	−	0.188104i	$-0.0602344\pi$
$827$	46716.0			1.96430			0.982149	+	0.188104i	$0.0602344\pi$
$828$		0			0
$829$	5620.00	+	9734.13i	0.235453	+	0.407817i	0.959404	−	0.282034i	$-0.0910092\pi$
$829$	5620.00	+	9734.13i	0.235453	+	0.407817i	−0.723951	+	0.689851i	$0.757676\pi$
$830$	10416.0	+	18041.0i	0.435596	+	0.754474i
$831$		0			0
$832$	4676.00			0.194845
$833$		0			0
$834$		0			0
$835$	−23072.0	+	39961.9i	−0.956215	+	1.65621i
$836$	3080.00	+	5334.72i	0.127421	+	0.220700i
$837$		0			0
$838$	−1155.00	+	2000.52i	−0.0476119	+	0.0824663i
$839$	700.000			0.0288042			0.0144021	−	0.999896i	$-0.495416\pi$
$839$	700.000			0.0288042			0.0144021	+	0.999896i	$0.495416\pi$
$840$		0			0
$841$	−12289.0			−0.503875
$842$	−631.000	+	1092.92i	−0.0258262	+	0.0447324i
$843$		0			0
$844$	−14938.0	−	25873.4i	−0.609226	−	1.05521i
$845$	11304.0	−	19579.1i	0.460200	−	0.797091i
$846$		0			0
$847$		0			0
$848$	6642.00			0.268971
$849$		0			0
$850$	−3537.00	−	6126.26i	−0.142727	−	0.247211i
$851$	−5904.00	−	10226.0i	−0.237822	−	0.411920i
$852$		0			0
$853$	37492.0			1.50493			0.752463	−	0.658635i	$-0.228866\pi$
$853$	37492.0			1.50493			0.752463	+	0.658635i	$0.228866\pi$
$854$		0			0
$855$		0			0
$856$	−1830.00	+	3169.65i	−0.0730702	+	0.126561i
$857$	−14447.0	−	25022.9i	−0.575846	−	0.997395i	−0.995949	−	0.0899183i	$-0.971339\pi$
$857$	−14447.0	−	25022.9i	−0.575846	−	0.997395i	0.420103	−	0.907476i	$-0.361994\pi$
$858$		0			0
$859$	−1385.00	+	2398.89i	−0.0550123	+	0.0952841i	−0.892220	−	0.451601i	$-0.850853\pi$
$859$	−1385.00	+	2398.89i	−0.0550123	+	0.0952841i	0.837208	+	0.546885i	$0.184186\pi$
$860$	−14336.0			−0.568434
$861$		0			0
$862$	4488.00			0.177334
$863$	8844.00	−	15318.3i	0.348845	−	0.604217i	−0.637200	−	0.770699i	$-0.719907\pi$
$863$	8844.00	−	15318.3i	0.348845	−	0.604217i	0.986045	+	0.166482i	$0.0532406\pi$
$864$		0			0
$865$	−17824.0	−	30872.1i	−0.700618	−	1.21351i
$866$	8519.00	−	14755.3i	0.334281	−	0.578992i
$867$		0			0
$868$		0			0
$869$	3520.00			0.137408
$870$		0			0
$871$	3416.00	+	5916.69i	0.132889	+	0.230171i
$872$	675.000	+	1169.13i	0.0262137	+	0.0454035i
$873$		0			0
$874$	−5280.00			−0.204346
$875$		0			0
$876$		0			0
$877$	16783.0	−	29069.0i	0.646205	−	1.11926i	−0.337817	−	0.941212i	$-0.609688\pi$
$877$	16783.0	−	29069.0i	0.646205	−	1.11926i	0.984022	−	0.178048i	$-0.0569782\pi$
$878$	8100.00	+	14029.6i	0.311346	+	0.539267i
$879$		0			0
$880$	−2624.00	+	4544.90i	−0.100517	+	0.174101i
$881$	−16758.0			−0.640853			−0.320426	−	0.947273i	$-0.603826\pi$
$881$	−16758.0			−0.640853			−0.320426	+	0.947273i	$0.603826\pi$
$882$		0			0
$883$	11468.0			0.437066			0.218533	−	0.975830i	$-0.429873\pi$
$883$	11468.0			0.437066			0.218533	+	0.975830i	$0.429873\pi$
$884$	−5292.00	+	9166.01i	−0.201345	+	0.348740i
$885$		0			0
$886$	−4386.00	−	7596.77i	−0.166310	−	0.288057i
$887$	25178.0	−	43609.6i	0.953094	−	1.65081i	0.214424	−	0.976741i	$-0.431213\pi$
$887$	25178.0	−	43609.6i	0.953094	−	1.65081i	0.738670	−	0.674067i	$-0.235454\pi$
$888$		0			0
$889$		0			0
$890$	11680.0			0.439904
$891$		0			0
$892$	19012.0	+	32929.7i	0.713642	+	1.23606i
$893$	−17820.0	−	30865.1i	−0.667776	−	1.15662i
$894$		0			0
$895$	13120.0			0.490004
$896$		0			0
$897$		0			0
$898$	1065.00	−	1844.63i	0.0395763	−	0.0685481i
$899$	660.000	+	1143.15i	0.0244852	+	0.0424097i
$900$		0			0
$901$	−4374.00	+	7575.99i	−0.161730	+	0.280125i
$902$	1456.00			0.0537467
$903$		0			0
$904$	19770.0			0.727368
$905$	31136.0	−	53929.1i	1.14364	−	1.98085i
$906$		0			0
$907$	4358.00	+	7548.28i	0.159542	+	0.276336i	0.934704	−	0.355428i	$-0.115665\pi$
$907$	4358.00	+	7548.28i	0.159542	+	0.276336i	−0.775161	+	0.631763i	$0.782331\pi$
$908$	−7161.00	+	12403.2i	−0.261725	+	0.453321i
$909$		0			0
$910$		0			0
$911$	−7632.00			−0.277563			−0.138781	−	0.990323i	$-0.544318\pi$
$911$	−7632.00			−0.277563			−0.138781	+	0.990323i	$0.544318\pi$
$912$		0			0
$913$	5208.00	+	9020.52i	0.188784	+	0.326983i
$914$	−5267.00	−	9122.71i	−0.190609	−	0.330145i
$915$		0			0
$916$	−20860.0			−0.752439
$917$		0			0
$918$		0			0
$919$	11540.0	−	19987.9i	0.414221	−	0.717453i	−0.581125	−	0.813814i	$-0.697387\pi$
$919$	11540.0	−	19987.9i	0.414221	−	0.717453i	0.995346	+	0.0963618i	$0.0307206\pi$
$920$	−5760.00	−	9976.61i	−0.206415	−	0.357521i
$921$		0			0
$922$	4634.00	−	8026.32i	0.165523	−	0.286695i
$923$	−21504.0			−0.766861
$924$		0			0
$925$	−32226.0			−1.14550
$926$	4696.00	−	8133.71i	0.166652	−	0.288650i
$927$		0			0
$928$	−8855.00	−	15337.3i	−0.313232	−	0.542534i
$929$	−22555.0	+	39066.4i	−0.796561	+	1.37968i	0.125282	+	0.992121i	$0.460017\pi$
$929$	−22555.0	+	39066.4i	−0.796561	+	1.37968i	−0.921843	+	0.387564i	$0.873317\pi$
$930$		0			0
$931$		0			0
$932$	31206.0			1.09677
$933$		0			0
$934$	5403.00	+	9358.27i	0.189284	+	0.327850i
$935$	−3456.00	−	5985.97i	−0.120881	−	0.209371i
$936$		0			0
$937$	−16674.0			−0.581340			−0.290670	−	0.956823i	$-0.593878\pi$
$937$	−16674.0			−0.581340			−0.290670	+	0.956823i	$0.593878\pi$
$938$		0			0
$939$		0			0
$940$	18144.0	−	31426.3i	0.629566	−	1.09044i
$941$	−21916.0	−	37959.6i	−0.759236	−	1.31504i	−0.943241	−	0.332110i	$-0.892239\pi$
$941$	−21916.0	−	37959.6i	−0.759236	−	1.31504i	0.184005	−	0.982925i	$-0.441094\pi$
$942$		0			0
$943$	4368.00	−	7565.60i	0.150840	−	0.261262i
$944$	33210.0			1.14501
$945$		0			0
$946$	1024.00			0.0351936
$947$	−368.000	+	637.395i	−0.0126277	+	0.0218717i	−0.872270	−	0.489024i	$-0.837353\pi$
$947$	−368.000	+	637.395i	−0.0126277	+	0.0218717i	0.859643	+	0.510896i	$0.170686\pi$
$948$		0			0
$949$	9828.00	+	17022.6i	0.336175	+	0.582273i
$950$	−7205.00	+	12479.4i	−0.246064	+	0.426196i
$951$		0			0
$952$		0			0
$953$	−38138.0			−1.29634			−0.648169	−	0.761496i	$-0.724465\pi$
$953$	−38138.0			−1.29634			−0.648169	+	0.761496i	$0.724465\pi$
$954$		0			0
$955$	−40384.0	−	69947.1i	−1.36837	−	2.37009i
$956$	−15540.0	−	26916.1i	−0.525732	−	0.910594i
$957$		0			0
$958$	4940.00			0.166601
$959$		0			0
$960$		0			0
$961$	14823.5	−	25675.1i	0.497583	−	0.861839i
$962$	−3444.00	−	5965.18i	−0.115425	−	0.199922i
$963$		0			0
$964$	−11557.0	+	20017.3i	−0.386126	+	0.668791i
$965$	−47392.0			−1.58094
$966$		0			0
$967$	26224.0			0.872086			0.436043	−	0.899926i	$-0.356380\pi$
$967$	26224.0			0.872086			0.436043	+	0.899926i	$0.356380\pi$
$968$	−9502.50	+	16458.8i	−0.315519	+	0.546494i
$969$		0			0
$970$	2352.00	+	4073.78i	0.0778538	+	0.134847i
$971$	−9381.00	+	16248.4i	−0.310042	+	0.537008i	−0.978371	−	0.206857i	$-0.933676\pi$
$971$	−9381.00	+	16248.4i	−0.310042	+	0.537008i	0.668329	+	0.743866i	$0.267010\pi$
$972$		0			0
$973$		0			0
$974$	−5216.00			−0.171593
$975$		0			0
$976$	−10004.0	−	17327.4i	−0.328095	−	0.568276i
$977$	19197.0	+	33250.2i	0.628625	+	1.08881i	0.987828	+	0.155551i	$0.0497152\pi$
$977$	19197.0	+	33250.2i	0.628625	+	1.08881i	−0.359203	+	0.933259i	$0.616951\pi$
$978$		0			0
$979$	5840.00			0.190651
$980$		0			0
$981$		0			0
$982$	2206.00	−	3820.90i	0.0716866	−	0.124165i
$983$	−2694.00	−	4666.14i	−0.0874112	−	0.151401i	0.819005	−	0.573787i	$-0.194526\pi$
$983$	−2694.00	−	4666.14i	−0.0874112	−	0.151401i	−0.906416	+	0.422386i	$0.861193\pi$
$984$		0			0
$985$	26672.0	−	46197.3i	0.862782	−	1.49438i
$986$	5940.00			0.191854
$987$		0			0
$988$	21560.0			0.694246
$989$	3072.00	−	5320.86i	0.0987704	−	0.171075i
$990$		0			0
$991$	−12736.0	−	22059.4i	−0.408247	−	0.707104i	0.586447	−	0.809988i	$-0.300526\pi$
$991$	−12736.0	−	22059.4i	−0.408247	−	0.707104i	−0.994693	+	0.102884i	$0.967193\pi$
$992$	966.000	−	1673.16i	0.0309179	−	0.0535513i
$993$		0			0
$994$		0			0
$995$	−29760.0			−0.948196
$996$		0			0
$997$	−8548.00	−	14805.6i	−0.271532	−	0.470308i	0.697722	−	0.716369i	$-0.254197\pi$
$997$	−8548.00	−	14805.6i	−0.271532	−	0.470308i	−0.969254	+	0.246061i	$0.920864\pi$
$998$	−9530.00	−	16506.4i	−0.302271	−	0.523549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.e.226.1		2
3.2	odd	2		49.4.c.b.30.1		2
7.2	even	3		441.4.a.i.1.1		1
7.3	odd	6		441.4.e.h.361.1		2
7.4	even	3	inner	441.4.e.e.361.1		2
7.5	odd	6		63.4.a.b.1.1		1
7.6	odd	2		441.4.e.h.226.1		2
21.2	odd	6		49.4.a.b.1.1		1
21.5	even	6		7.4.a.a.1.1	✓	1
21.11	odd	6		49.4.c.b.18.1		2
21.17	even	6		49.4.c.c.18.1		2
21.20	even	2		49.4.c.c.30.1		2
28.19	even	6		1008.4.a.c.1.1		1
35.19	odd	6		1575.4.a.e.1.1		1
84.23	even	6		784.4.a.g.1.1		1
84.47	odd	6		112.4.a.f.1.1		1
105.44	odd	6		1225.4.a.j.1.1		1
105.47	odd	12		175.4.b.b.99.1		2
105.68	odd	12		175.4.b.b.99.2		2
105.89	even	6		175.4.a.b.1.1		1
168.5	even	6		448.4.a.i.1.1		1
168.131	odd	6		448.4.a.e.1.1		1
231.131	odd	6		847.4.a.b.1.1		1
273.194	even	6		1183.4.a.b.1.1		1
357.152	even	6		2023.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.a.a.1.1	✓	1	21.5	even	6
49.4.a.b.1.1		1	21.2	odd	6
49.4.c.b.18.1		2	21.11	odd	6
49.4.c.b.30.1		2	3.2	odd	2
49.4.c.c.18.1		2	21.17	even	6
49.4.c.c.30.1		2	21.20	even	2
63.4.a.b.1.1		1	7.5	odd	6
112.4.a.f.1.1		1	84.47	odd	6
175.4.a.b.1.1		1	105.89	even	6
175.4.b.b.99.1		2	105.47	odd	12
175.4.b.b.99.2		2	105.68	odd	12
441.4.a.i.1.1		1	7.2	even	3
441.4.e.e.226.1		2	1.1	even	1	trivial
441.4.e.e.361.1		2	7.4	even	3	inner
441.4.e.h.226.1		2	7.6	odd	2
441.4.e.h.361.1		2	7.3	odd	6
448.4.a.e.1.1		1	168.131	odd	6
448.4.a.i.1.1		1	168.5	even	6
784.4.a.g.1.1		1	84.23	even	6
847.4.a.b.1.1		1	231.131	odd	6
1008.4.a.c.1.1		1	28.19	even	6
1183.4.a.b.1.1		1	273.194	even	6
1225.4.a.j.1.1		1	105.44	odd	6
1575.4.a.e.1.1		1	35.19	odd	6
2023.4.a.a.1.1		1	357.152	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +(-8.00000 - 13.8564i) q^{10} +(-4.00000 - 6.92820i) q^{11} -28.0000 q^{13} +(-20.5000 + 35.5070i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(-55.0000 + 95.2628i) q^{19} -112.000 q^{20} +8.00000 q^{22} +(24.0000 - 41.5692i) q^{23} +(-65.5000 - 113.449i) q^{25} +(14.0000 - 24.2487i) q^{26} +110.000 q^{29} +(6.00000 + 10.3923i) q^{31} +(-80.5000 - 139.430i) q^{32} +54.0000 q^{34} +(123.000 - 213.042i) q^{37} +(-55.0000 - 95.2628i) q^{38} +(120.000 - 207.846i) q^{40} +182.000 q^{41} +128.000 q^{43} +(28.0000 - 48.4974i) q^{44} +(24.0000 + 41.5692i) q^{46} +(-162.000 + 280.592i) q^{47} +131.000 q^{50} +(-98.0000 - 169.741i) q^{52} +(-81.0000 - 140.296i) q^{53} +128.000 q^{55} +(-55.0000 + 95.2628i) q^{58} +(-405.000 - 701.481i) q^{59} +(-244.000 + 422.620i) q^{61} -12.0000 q^{62} -167.000 q^{64} +(224.000 - 387.979i) q^{65} +(-122.000 - 211.310i) q^{67} +(189.000 - 327.358i) q^{68} +768.000 q^{71} +(-351.000 - 607.950i) q^{73} +(123.000 + 213.042i) q^{74} -770.000 q^{76} +(-220.000 + 381.051i) q^{79} +(-328.000 - 568.113i) q^{80} +(-91.0000 + 157.617i) q^{82} -1302.00 q^{83} +864.000 q^{85} +(-64.0000 + 110.851i) q^{86} +(60.0000 + 103.923i) q^{88} +(-365.000 + 632.199i) q^{89} +336.000 q^{92} +(-162.000 - 280.592i) q^{94} +(-880.000 - 1524.20i) q^{95} -294.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 7 q^{4} - 16 q^{5} - 30 q^{8}+O(q^{10}) \) 2 * q - q^2 + 7 * q^4 - 16 * q^5 - 30 * q^8	\( 2 q - q^{2} + 7 q^{4} - 16 q^{5} - 30 q^{8} - 16 q^{10} - 8 q^{11} - 56 q^{13} - 41 q^{16} - 54 q^{17} - 110 q^{19} - 224 q^{20} + 16 q^{22} + 48 q^{23} - 131 q^{25} + 28 q^{26} + 220 q^{29} + 12 q^{31} - 161 q^{32} + 108 q^{34} + 246 q^{37} - 110 q^{38} + 240 q^{40} + 364 q^{41} + 256 q^{43} + 56 q^{44} + 48 q^{46} - 324 q^{47} + 262 q^{50} - 196 q^{52} - 162 q^{53} + 256 q^{55} - 110 q^{58} - 810 q^{59} - 488 q^{61} - 24 q^{62} - 334 q^{64} + 448 q^{65} - 244 q^{67} + 378 q^{68} + 1536 q^{71} - 702 q^{73} + 246 q^{74} - 1540 q^{76} - 440 q^{79} - 656 q^{80} - 182 q^{82} - 2604 q^{83} + 1728 q^{85} - 128 q^{86} + 120 q^{88} - 730 q^{89} + 672 q^{92} - 324 q^{94} - 1760 q^{95} - 588 q^{97}+O(q^{100}) \) 2 * q - q^2 + 7 * q^4 - 16 * q^5 - 30 * q^8 - 16 * q^10 - 8 * q^11 - 56 * q^13 - 41 * q^16 - 54 * q^17 - 110 * q^19 - 224 * q^20 + 16 * q^22 + 48 * q^23 - 131 * q^25 + 28 * q^26 + 220 * q^29 + 12 * q^31 - 161 * q^32 + 108 * q^34 + 246 * q^37 - 110 * q^38 + 240 * q^40 + 364 * q^41 + 256 * q^43 + 56 * q^44 + 48 * q^46 - 324 * q^47 + 262 * q^50 - 196 * q^52 - 162 * q^53 + 256 * q^55 - 110 * q^58 - 810 * q^59 - 488 * q^61 - 24 * q^62 - 334 * q^64 + 448 * q^65 - 244 * q^67 + 378 * q^68 + 1536 * q^71 - 702 * q^73 + 246 * q^74 - 1540 * q^76 - 440 * q^79 - 656 * q^80 - 182 * q^82 - 2604 * q^83 + 1728 * q^85 - 128 * q^86 + 120 * q^88 - 730 * q^89 + 672 * q^92 - 324 * q^94 - 1760 * q^95 - 588 * q^97

Introduction

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