LMFDB - Embedded newform 441.4.e.q.226.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.q.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13746 - 1.97014i) q^{2} +(1.41238 + 2.44631i) q^{4} +(-2.27492 + 3.94027i) q^{5} +24.6254 q^{8} +O(q^{10})$	\(q+(1.13746 - 1.97014i) q^{2} +(1.41238 + 2.44631i) q^{4} +(-2.27492 + 3.94027i) q^{5} +24.6254 q^{8} +(5.17525 + 8.96379i) q^{10} +(-20.3746 - 35.2898i) q^{11} +53.2990 q^{13} +(16.7114 - 28.9450i) q^{16} +(2.27492 + 3.94027i) q^{17} +(-61.2990 + 106.173i) q^{19} -12.8522 q^{20} -92.7010 q^{22} +(65.6736 - 113.750i) q^{23} +(52.1495 + 90.3256i) q^{25} +(60.6254 - 105.006i) q^{26} +216.598 q^{29} +(125.897 + 218.060i) q^{31} +(60.4846 + 104.762i) q^{32} +10.3505 q^{34} +(-5.94851 + 10.3031i) q^{37} +(139.450 + 241.535i) q^{38} +(-56.0208 + 97.0308i) q^{40} +111.752 q^{41} +369.196 q^{43} +(57.5531 - 99.6850i) q^{44} +(-149.402 - 258.772i) q^{46} +(-131.347 + 227.500i) q^{47} +237.272 q^{50} +(75.2782 + 130.386i) q^{52} +(-283.550 - 491.123i) q^{53} +185.402 q^{55} +(246.371 - 426.728i) q^{58} +(419.945 + 727.366i) q^{59} +(242.897 - 420.710i) q^{61} +572.811 q^{62} +542.577 q^{64} +(-121.251 + 210.013i) q^{65} +(166.846 + 288.985i) q^{67} +(-6.42608 + 11.1303i) q^{68} -590.248 q^{71} +(-245.350 - 424.960i) q^{73} +(13.5324 + 23.4387i) q^{74} -346.309 q^{76} +(-60.8455 + 105.388i) q^{79} +(76.0340 + 131.695i) q^{80} +(127.114 - 220.168i) q^{82} -609.608 q^{83} -20.7010 q^{85} +(419.945 - 727.366i) q^{86} +(-501.733 - 869.026i) q^{88} +(359.519 - 622.705i) q^{89} +371.023 q^{92} +(298.804 + 517.544i) q^{94} +(-278.900 - 483.070i) q^{95} -637.877 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 17 q^{4} + 6 q^{5} + 174 q^{8}+O(q^{10}) $ 4 * q - 3 * q^2 - 17 * q^4 + 6 * q^5 + 174 * q^8	$ 4 q - 3 q^{2} - 17 q^{4} + 6 q^{5} + 174 q^{8} + 66 q^{10} - 6 q^{11} + 32 q^{13} - 137 q^{16} - 6 q^{17} - 64 q^{19} - 444 q^{20} - 552 q^{22} + 6 q^{23} + 118 q^{25} + 318 q^{26} + 504 q^{29} - 40 q^{31} - 279 q^{32} + 132 q^{34} + 248 q^{37} + 588 q^{38} + 546 q^{40} + 900 q^{41} + 752 q^{43} + 804 q^{44} - 960 q^{46} - 12 q^{47} + 330 q^{50} + 890 q^{52} - 1104 q^{53} + 1104 q^{55} + 306 q^{58} + 804 q^{59} + 428 q^{61} + 4224 q^{62} + 2578 q^{64} - 636 q^{65} - 148 q^{67} - 222 q^{68} - 1908 q^{71} - 1072 q^{73} + 1398 q^{74} - 3016 q^{76} + 572 q^{79} + 1950 q^{80} - 1530 q^{82} - 3888 q^{83} - 264 q^{85} + 804 q^{86} + 1164 q^{88} + 366 q^{89} + 5712 q^{92} + 1920 q^{94} - 1176 q^{95} + 1616 q^{97}+O(q^{100}) $ 4 * q - 3 * q^2 - 17 * q^4 + 6 * q^5 + 174 * q^8 + 66 * q^10 - 6 * q^11 + 32 * q^13 - 137 * q^16 - 6 * q^17 - 64 * q^19 - 444 * q^20 - 552 * q^22 + 6 * q^23 + 118 * q^25 + 318 * q^26 + 504 * q^29 - 40 * q^31 - 279 * q^32 + 132 * q^34 + 248 * q^37 + 588 * q^38 + 546 * q^40 + 900 * q^41 + 752 * q^43 + 804 * q^44 - 960 * q^46 - 12 * q^47 + 330 * q^50 + 890 * q^52 - 1104 * q^53 + 1104 * q^55 + 306 * q^58 + 804 * q^59 + 428 * q^61 + 4224 * q^62 + 2578 * q^64 - 636 * q^65 - 148 * q^67 - 222 * q^68 - 1908 * q^71 - 1072 * q^73 + 1398 * q^74 - 3016 * q^76 + 572 * q^79 + 1950 * q^80 - 1530 * q^82 - 3888 * q^83 - 264 * q^85 + 804 * q^86 + 1164 * q^88 + 366 * q^89 + 5712 * q^92 + 1920 * q^94 - 1176 * q^95 + 1616 * 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 $

$2$	1.13746	−	1.97014i	0.402152	−	0.696548i	−0.591833	−	0.806061i	$-0.701596\pi$
$2$	1.13746	−	1.97014i	0.402152	−	0.696548i	0.993985	+	0.109512i	$0.0349289\pi$
$3$		0			0
$3$		0			0
$4$	1.41238	+	2.44631i	0.176547	+	0.305788i
$5$	−2.27492	+	3.94027i	−0.203475	+	0.352429i	−0.949646	−	0.313326i	$-0.898557\pi$
$5$	−2.27492	+	3.94027i	−0.203475	+	0.352429i	0.746171	+	0.665754i	$0.231890\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	24.6254			1.08830
$9$		0			0
$10$	5.17525	+	8.96379i	0.163656	+	0.283460i
$11$	−20.3746	−	35.2898i	−0.558470	−	0.967298i	−0.997624	−	0.0688867i	$-0.978055\pi$
$11$	−20.3746	−	35.2898i	−0.558470	−	0.967298i	0.439155	−	0.898412i	$-0.355278\pi$
$12$		0			0
$13$	53.2990			1.13711			0.568557	−	0.822644i	$-0.307502\pi$
$13$	53.2990			1.13711			0.568557	+	0.822644i	$0.307502\pi$
$14$		0			0
$15$		0			0
$16$	16.7114	−	28.9450i	0.261115	−	0.452265i
$17$	2.27492	+	3.94027i	0.0324558	+	0.0562151i	0.881797	−	0.471629i	$-0.156334\pi$
$17$	2.27492	+	3.94027i	0.0324558	+	0.0562151i	−0.849341	+	0.527844i	$0.823001\pi$
$18$		0			0
$19$	−61.2990	+	106.173i	−0.740156	+	1.28199i	0.212269	+	0.977211i	$0.431915\pi$
$19$	−61.2990	+	106.173i	−0.740156	+	1.28199i	−0.952424	+	0.304776i	$0.901418\pi$
$20$	−12.8522			−0.143691
$21$		0			0
$22$	−92.7010			−0.898360
$23$	65.6736	−	113.750i	0.595387	−	1.03124i	−0.398106	−	0.917340i	$-0.630332\pi$
$23$	65.6736	−	113.750i	0.595387	−	1.03124i	0.993492	−	0.113900i	$-0.0363344\pi$
$24$		0			0
$25$	52.1495	+	90.3256i	0.417196	+	0.722605i
$26$	60.6254	−	105.006i	0.457293	−	0.792055i
$27$		0			0
$28$		0			0
$29$	216.598			1.38694			0.693470	−	0.720486i	$-0.256081\pi$
$29$	216.598			1.38694			0.693470	+	0.720486i	$0.256081\pi$
$30$		0			0
$31$	125.897	+	218.060i	0.729412	+	1.26338i	0.957132	+	0.289652i	$0.0935396\pi$
$31$	125.897	+	218.060i	0.729412	+	1.26338i	−0.227720	+	0.973727i	$0.573127\pi$
$32$	60.4846	+	104.762i	0.334134	+	0.578736i
$33$		0			0
$34$	10.3505			0.0522087
$35$		0			0
$36$		0			0
$37$	−5.94851	+	10.3031i	−0.0264305	+	0.0457790i	−0.878938	−	0.476936i	$-0.841747\pi$
$37$	−5.94851	+	10.3031i	−0.0264305	+	0.0457790i	0.852508	+	0.522715i	$0.175081\pi$
$38$	139.450	+	241.535i	0.595311	+	1.03111i
$39$		0			0
$40$	−56.0208	+	97.0308i	−0.221442	+	0.383548i
$41$	111.752			0.425678			0.212839	−	0.977087i	$-0.431729\pi$
$41$	111.752			0.425678			0.212839	+	0.977087i	$0.431729\pi$
$42$		0			0
$43$	369.196			1.30935			0.654673	−	0.755912i	$-0.272806\pi$
$43$	369.196			1.30935			0.654673	+	0.755912i	$0.272806\pi$
$44$	57.5531	−	99.6850i	0.197192	−	0.341547i
$45$		0			0
$46$	−149.402	−	258.772i	−0.478872	−	0.829431i
$47$	−131.347	+	227.500i	−0.407637	+	0.706049i	−0.994624	−	0.103548i	$-0.966981\pi$
$47$	−131.347	+	227.500i	−0.407637	+	0.706049i	0.586987	+	0.809596i	$0.300314\pi$
$48$		0			0
$49$		0			0
$50$	237.272			0.671105
$51$		0			0
$52$	75.2782	+	130.386i	0.200754	+	0.347716i
$53$	−283.550	−	491.123i	−0.734879	−	1.27285i	−0.954777	−	0.297324i	$-0.903906\pi$
$53$	−283.550	−	491.123i	−0.734879	−	1.27285i	0.219898	−	0.975523i	$-0.429428\pi$
$54$		0			0
$55$	185.402			0.454538
$56$		0			0
$57$		0			0
$58$	246.371	−	426.728i	0.557761	−	0.966070i
$59$	419.945	+	727.366i	0.926648	+	1.60500i	0.788890	+	0.614535i	$0.210656\pi$
$59$	419.945	+	727.366i	0.926648	+	1.60500i	0.137758	+	0.990466i	$0.456010\pi$
$60$		0			0
$61$	242.897	−	420.710i	0.509832	−	0.883056i	−0.490103	−	0.871665i	$-0.663041\pi$
$61$	242.897	−	420.710i	0.509832	−	0.883056i	0.999935	−	0.0113909i	$-0.00362593\pi$
$62$	572.811			1.17334
$63$		0			0
$64$	542.577			1.05972
$65$	−121.251	+	210.013i	−0.231374	+	0.400752i
$66$		0			0
$67$	166.846	+	288.985i	0.304230	+	0.526942i	0.977090	−	0.212828i	$-0.0682675\pi$
$67$	166.846	+	288.985i	0.304230	+	0.526942i	−0.672859	+	0.739770i	$0.734934\pi$
$68$	−6.42608	+	11.1303i	−0.0114599	+	0.0198492i
$69$		0			0
$70$		0			0
$71$	−590.248			−0.986613			−0.493306	−	0.869856i	$-0.664212\pi$
$71$	−590.248			−0.986613			−0.493306	+	0.869856i	$0.664212\pi$
$72$		0			0
$73$	−245.350	−	424.960i	−0.393371	−	0.681339i	0.599521	−	0.800359i	$-0.295358\pi$
$73$	−245.350	−	424.960i	−0.393371	−	0.681339i	−0.992892	+	0.119020i	$0.962025\pi$
$74$	13.5324	+	23.4387i	0.0212582	+	0.0368203i
$75$		0			0
$76$	−346.309			−0.522689
$77$		0			0
$78$		0			0
$79$	−60.8455	+	105.388i	−0.0866539	+	0.150089i	−0.906095	−	0.423075i	$-0.860951\pi$
$79$	−60.8455	+	105.388i	−0.0866539	+	0.150089i	0.819441	+	0.573164i	$0.194284\pi$
$80$	76.0340	+	131.695i	0.106261	+	0.184049i
$81$		0			0
$82$	127.114	−	220.168i	0.171187	−	0.296505i
$83$	−609.608			−0.806183			−0.403091	−	0.915160i	$-0.632064\pi$
$83$	−609.608			−0.806183			−0.403091	+	0.915160i	$0.632064\pi$
$84$		0			0
$85$	−20.7010			−0.0264157
$86$	419.945	−	727.366i	0.526556	−	0.912023i
$87$		0			0
$88$	−501.733	−	869.026i	−0.607783	−	1.05271i
$89$	359.519	−	622.705i	0.428190	−	0.741648i	−0.568522	−	0.822668i	$-0.692485\pi$
$89$	359.519	−	622.705i	0.428190	−	0.741648i	0.996712	+	0.0810204i	$0.0258179\pi$
$90$		0			0
$91$		0			0
$92$	371.023			0.420455
$93$		0			0
$94$	298.804	+	517.544i	0.327865	+	0.567878i
$95$	−278.900	−	483.070i	−0.301206	−	0.521704i
$96$		0			0
$97$	−637.877			−0.667697			−0.333849	−	0.942627i	$-0.608347\pi$
$97$	−637.877			−0.667697			−0.333849	+	0.942627i	$0.608347\pi$
$98$		0			0
$99$		0			0
$100$	−147.309	+	255.147i	−0.147309	+	0.255147i
$101$	335.574	+	581.231i	0.330603	+	0.572620i	0.982630	−	0.185575i	$-0.0594147\pi$
$101$	335.574	+	581.231i	0.330603	+	0.572620i	−0.652028	+	0.758195i	$0.726081\pi$
$102$		0			0
$103$	456.206	−	790.172i	0.436420	−	0.755902i	−0.560990	−	0.827823i	$-0.689579\pi$
$103$	456.206	−	790.172i	0.436420	−	0.755902i	0.997410	+	0.0719202i	$0.0229127\pi$
$104$	1312.51			1.23752
$105$		0			0
$106$	−1290.10			−1.18213
$107$	−58.3680	+	101.096i	−0.0527350	+	0.0913397i	−0.891188	−	0.453634i	$-0.850127\pi$
$107$	−58.3680	+	101.096i	−0.0527350	+	0.0913397i	0.838453	+	0.544974i	$0.183461\pi$
$108$		0			0
$109$	−418.588	−	725.016i	−0.367830	−	0.637100i	0.621396	−	0.783497i	$-0.286566\pi$
$109$	−418.588	−	725.016i	−0.367830	−	0.637100i	−0.989226	+	0.146396i	$0.953232\pi$
$110$	210.887	−	365.267i	0.182794	−	0.316608i
$111$		0			0
$112$		0			0
$113$	1086.58			0.904572			0.452286	−	0.891873i	$-0.350609\pi$
$113$	1086.58			0.904572			0.452286	+	0.891873i	$0.350609\pi$
$114$		0			0
$115$	298.804	+	517.544i	0.242292	+	0.419663i
$116$	305.918	+	529.865i	0.244860	+	0.424110i
$117$		0			0
$118$	1910.68			1.49061
$119$		0			0
$120$		0			0
$121$	−164.748	+	285.351i	−0.123777	+	0.214388i
$122$	−552.571	−	957.080i	−0.410061	−	0.710246i
$123$		0			0
$124$	−355.628	+	615.965i	−0.257551	+	0.446091i
$125$	−1043.27			−0.746505
$126$		0			0
$127$	−537.113			−0.375284			−0.187642	−	0.982237i	$-0.560084\pi$
$127$	−537.113			−0.375284			−0.187642	+	0.982237i	$0.560084\pi$
$128$	133.282	−	230.851i	0.0920357	−	0.159411i
$129$		0			0
$130$	275.836	+	477.761i	0.186095	+	0.322326i
$131$	748.694	−	1296.78i	0.499341	−	0.864885i	−0.500658	−	0.865645i	$-0.666909\pi$
$131$	748.694	−	1296.78i	0.499341	−	0.864885i	1.00000		0.000760253i	$0.000241996\pi$
$132$		0			0
$133$		0			0
$134$	759.120			0.489388
$135$		0			0
$136$	56.0208	+	97.0308i	0.0353216	+	0.0611789i
$137$	−690.045	−	1195.19i	−0.430325	−	0.745345i	0.566576	−	0.824009i	$-0.308268\pi$
$137$	−690.045	−	1195.19i	−0.430325	−	0.745345i	−0.996901	+	0.0786647i	$0.974934\pi$
$138$		0			0
$139$	−141.980			−0.0866374			−0.0433187	−	0.999061i	$-0.513793\pi$
$139$	−141.980			−0.0866374			−0.0433187	+	0.999061i	$0.513793\pi$
$140$		0			0
$141$		0			0
$142$	−671.382	+	1162.87i	−0.396769	+	0.687223i
$143$	−1085.95	−	1880.91i	−0.635044	−	1.09993i
$144$		0			0
$145$	−492.743	+	853.455i	−0.282207	+	0.488797i
$146$	−1116.30			−0.632781
$147$		0			0
$148$	−33.6061			−0.0186649
$149$	−971.935	+	1683.44i	−0.534390	+	0.925590i	0.464803	+	0.885414i	$0.346125\pi$
$149$	−971.935	+	1683.44i	−0.534390	+	0.925590i	−0.999193	+	0.0401757i	$0.987208\pi$
$150$		0			0
$151$	1327.38	+	2299.09i	0.715370	+	1.23906i	0.962817	+	0.270155i	$0.0870750\pi$
$151$	1327.38	+	2299.09i	0.715370	+	1.23906i	−0.247447	+	0.968901i	$0.579592\pi$
$152$	−1509.51	+	2614.55i	−0.805511	+	1.39519i
$153$		0			0
$154$		0			0
$155$	−1145.62			−0.593668
$156$		0			0
$157$	−832.608	−	1442.12i	−0.423244	−	0.733081i	0.573010	−	0.819548i	$-0.305775\pi$
$157$	−832.608	−	1442.12i	−0.423244	−	0.733081i	−0.996255	+	0.0864675i	$0.972442\pi$
$158$	138.419	+	239.748i	0.0696961	+	0.120717i
$159$		0			0
$160$	−550.390			−0.271951
$161$		0			0
$162$		0			0
$163$	16.5366	−	28.6422i	0.00794629	−	0.0137634i	−0.862025	−	0.506866i	$-0.830804\pi$
$163$	16.5366	−	28.6422i	0.00794629	−	0.0137634i	0.869971	+	0.493103i	$0.164137\pi$
$164$	157.837	+	273.381i	0.0751522	+	0.130167i
$165$		0			0
$166$	−693.404	+	1201.01i	−0.324208	+	0.561545i
$167$	−1654.48			−0.766630			−0.383315	−	0.923618i	$-0.625218\pi$
$167$	−1654.48			−0.766630			−0.383315	+	0.923618i	$0.625218\pi$
$168$		0			0
$169$	643.784			0.293029
$170$	−23.5465	+	40.7838i	−0.0106232	+	0.0183998i
$171$		0			0
$172$	521.444	+	903.167i	0.231161	+	0.400383i
$173$	32.0954	−	55.5909i	0.0141050	−	0.0244306i	−0.858887	−	0.512166i	$-0.828843\pi$
$173$	32.0954	−	55.5909i	0.0141050	−	0.0244306i	0.872992	+	0.487735i	$0.162177\pi$
$174$		0			0
$175$		0			0
$176$	−1361.95			−0.583300
$177$		0			0
$178$	−817.876	−	1416.60i	−0.344396	−	0.596511i
$179$	1957.34	+	3390.21i	0.817309	+	1.41562i	0.907658	+	0.419711i	$0.137868\pi$
$179$	1957.34	+	3390.21i	0.817309	+	1.41562i	−0.0903489	+	0.995910i	$0.528798\pi$
$180$		0			0
$181$	−2058.04			−0.845156			−0.422578	−	0.906327i	$-0.638875\pi$
$181$	−2058.04			−0.845156			−0.422578	+	0.906327i	$0.638875\pi$
$182$		0			0
$183$		0			0
$184$	1617.24	−	2801.14i	0.647959	−	1.12230i
$185$	−27.0647	−	46.8775i	−0.0107559	−	0.0186297i
$186$		0			0
$187$	92.7010	−	160.563i	0.0362512	−	0.0627889i
$188$	−742.046			−0.287869
$189$		0			0
$190$	−1268.95			−0.484523
$191$	214.024	−	370.701i	0.0810798	−	0.140434i	−0.822634	−	0.568571i	$-0.807496\pi$
$191$	214.024	−	370.701i	0.0810798	−	0.140434i	0.903714	+	0.428137i	$0.140830\pi$
$192$		0			0
$193$	−802.463	−	1389.91i	−0.299288	−	0.518382i	0.676685	−	0.736272i	$-0.263416\pi$
$193$	−802.463	−	1389.91i	−0.299288	−	0.518382i	−0.975973	+	0.217890i	$0.930082\pi$
$194$	−725.559	+	1256.70i	−0.268516	+	0.465083i
$195$		0			0
$196$		0			0
$197$	−3738.83			−1.35218			−0.676092	−	0.736817i	$-0.736328\pi$
$197$	−3738.83			−1.35218			−0.676092	+	0.736817i	$0.736328\pi$
$198$		0			0
$199$	174.515	+	302.269i	0.0621660	+	0.107675i	0.895433	−	0.445196i	$-0.146866\pi$
$199$	174.515	+	302.269i	0.0621660	+	0.107675i	−0.833267	+	0.552870i	$0.813533\pi$
$200$	1284.20	+	2224.31i	0.454034	+	0.786411i
$201$		0			0
$202$	1526.81			0.531810
$203$		0			0
$204$		0			0
$205$	−254.228	+	440.335i	−0.0866148	+	0.150021i
$206$	−1037.83	−	1797.58i	−0.351015	−	0.607976i
$207$		0			0
$208$	890.700	−	1542.74i	0.296918	−	0.514277i
$209$	4995.77			1.65342
$210$		0			0
$211$	2588.58			0.844574			0.422287	−	0.906462i	$-0.361227\pi$
$211$	2588.58			0.844574			0.422287	+	0.906462i	$0.361227\pi$
$212$	800.958	−	1387.30i	0.259481	−	0.449435i
$213$		0			0
$214$	132.782	+	229.986i	0.0424150	+	0.0734649i
$215$	−839.890	+	1454.73i	−0.266419	+	0.461451i
$216$		0			0
$217$		0			0
$218$	−1904.51			−0.591695
$219$		0			0
$220$	261.857	+	453.550i	0.0802473	+	0.138992i
$221$	121.251	+	210.013i	0.0369059	+	0.0639230i
$222$		0			0
$223$	−3236.21			−0.971804			−0.485902	−	0.874013i	$-0.661509\pi$
$223$	−3236.21			−0.971804			−0.485902	+	0.874013i	$0.661509\pi$
$224$		0			0
$225$		0			0
$226$	1235.94	−	2140.71i	0.363776	−	0.630078i
$227$	−2815.81	−	4877.12i	−0.823312	−	1.42602i	−0.903203	−	0.429215i	$-0.858790\pi$
$227$	−2815.81	−	4877.12i	−0.823312	−	1.42602i	0.0798906	−	0.996804i	$-0.474543\pi$
$228$		0			0
$229$	−1885.12	+	3265.13i	−0.543985	+	0.942210i	0.454685	+	0.890652i	$0.349752\pi$
$229$	−1885.12	+	3265.13i	−0.543985	+	0.942210i	−0.998670	+	0.0515573i	$0.983582\pi$
$230$	1359.51			0.389754
$231$		0			0
$232$	5333.82			1.50941
$233$	−3280.45	+	5681.91i	−0.922358	+	1.59757i	−0.126602	+	0.991954i	$0.540407\pi$
$233$	−3280.45	+	5681.91i	−0.922358	+	1.59757i	−0.795756	+	0.605618i	$0.792926\pi$
$234$		0			0
$235$	−597.608	−	1035.09i	−0.165888	−	0.287326i
$236$	−1186.24	+	2054.63i	−0.327194	+	0.566716i
$237$		0			0
$238$		0			0
$239$	771.444			0.208789			0.104394	−	0.994536i	$-0.466710\pi$
$239$	771.444			0.208789			0.104394	+	0.994536i	$0.466710\pi$
$240$		0			0
$241$	−626.051	−	1084.35i	−0.167334	−	0.289831i	0.770148	−	0.637866i	$-0.220183\pi$
$241$	−626.051	−	1084.35i	−0.167334	−	0.289831i	−0.937482	+	0.348035i	$0.886849\pi$
$242$	374.787	+	649.150i	0.0995546	+	0.172434i
$243$		0			0
$244$	1372.25			0.360037
$245$		0			0
$246$		0			0
$247$	−3267.18	+	5658.92i	−0.841641	+	1.45777i
$248$	3100.27	+	5369.82i	0.793819	+	1.37493i
$249$		0			0
$250$	−1186.68	+	2055.39i	−0.300209	+	0.519977i
$251$	−5166.27			−1.29917			−0.649586	−	0.760288i	$-0.725058\pi$
$251$	−5166.27			−1.29917			−0.649586	+	0.760288i	$0.725058\pi$
$252$		0			0
$253$	−5352.29			−1.33002
$254$	−610.944	+	1058.19i	−0.150921	+	0.261403i
$255$		0			0
$256$	1867.10	+	3233.92i	0.455836	+	0.789531i
$257$	1383.73	−	2396.68i	0.335854	−	0.581716i	−0.647795	−	0.761815i	$-0.724309\pi$
$257$	1383.73	−	2396.68i	0.335854	−	0.581716i	0.983648	+	0.180099i	$0.0576419\pi$
$258$		0			0
$259$		0			0
$260$	−685.007			−0.163394
$261$		0			0
$262$	−1703.22	−	2950.06i	−0.401623	−	0.695631i
$263$	−2050.89	−	3552.25i	−0.480849	−	0.832855i	0.518909	−	0.854829i	$-0.326338\pi$
$263$	−2050.89	−	3552.25i	−0.480849	−	0.832855i	−0.999759	+	0.0219739i	$0.993005\pi$
$264$		0			0
$265$	2580.21			0.598117
$266$		0			0
$267$		0			0
$268$	−471.297	+	816.311i	−0.107422	+	0.186060i
$269$	−3475.42	−	6019.60i	−0.787732	−	1.36439i	−0.927353	−	0.374187i	$-0.877922\pi$
$269$	−3475.42	−	6019.60i	−0.787732	−	1.36439i	0.139621	−	0.990205i	$-0.455412\pi$
$270$		0			0
$271$	3570.15	−	6183.67i	0.800262	−	1.38609i	−0.119182	−	0.992872i	$-0.538027\pi$
$271$	3570.15	−	6183.67i	0.800262	−	1.38609i	0.919444	−	0.393222i	$-0.128639\pi$
$272$	152.068			0.0338988
$273$		0			0
$274$	−3139.59			−0.692225
$275$	2125.05	−	3680.69i	0.465983	−	0.807106i
$276$		0			0
$277$	−660.257	−	1143.60i	−0.143217	−	0.248059i	0.785490	−	0.618875i	$-0.212411\pi$
$277$	−660.257	−	1143.60i	−0.143217	−	0.248059i	−0.928706	+	0.370816i	$0.879078\pi$
$278$	−161.497	+	279.720i	−0.0348414	+	0.0603471i
$279$		0			0
$280$		0			0
$281$	204.309			0.0433738			0.0216869	−	0.999765i	$-0.493096\pi$
$281$	204.309			0.0433738			0.0216869	+	0.999765i	$0.493096\pi$
$282$		0			0
$283$	−487.897	−	845.062i	−0.102482	−	0.177504i	0.810225	−	0.586120i	$-0.199345\pi$
$283$	−487.897	−	845.062i	−0.102482	−	0.177504i	−0.912707	+	0.408615i	$0.866012\pi$
$284$	−833.651	−	1443.93i	−0.174183	−	0.301695i
$285$		0			0
$286$	−4940.87			−1.02154
$287$		0			0
$288$		0			0
$289$	2446.15	−	4236.86i	0.497893	−	0.862376i
$290$	1120.95	+	1941.54i	0.226981	+	0.393142i
$291$		0			0
$292$	693.054	−	1200.41i	0.138897	−	0.240577i
$293$	−607.919			−0.121212			−0.0606058	−	0.998162i	$-0.519303\pi$
$293$	−607.919			−0.121212			−0.0606058	+	0.998162i	$0.519303\pi$
$294$		0			0
$295$	−3821.36			−0.754198
$296$	−146.485	+	253.719i	−0.0287643	+	0.0498213i
$297$		0			0
$298$	2211.07	+	3829.69i	0.429812	+	0.744456i
$299$	3500.34	−	6062.76i	0.677023	−	1.17264i
$300$		0			0
$301$		0			0
$302$	6039.37			1.15075
$303$		0			0
$304$	2048.78	+	3548.60i	0.386532	+	0.669493i
$305$	1105.14	+	1914.16i	0.207476	+	0.359359i
$306$		0			0
$307$	8037.08			1.49414			0.747069	−	0.664747i	$-0.231461\pi$
$307$	8037.08			1.49414			0.747069	+	0.664747i	$0.231461\pi$
$308$		0			0
$309$		0			0
$310$	−1303.10	+	2257.03i	−0.238745	+	0.413518i
$311$	2655.80	+	4599.98i	0.484234	+	0.838718i	0.999836	−	0.0181104i	$-0.00576505\pi$
$311$	2655.80	+	4599.98i	0.484234	+	0.838718i	−0.515602	+	0.856828i	$0.672432\pi$
$312$		0			0
$313$	765.804	−	1326.41i	0.138293	−	0.239531i	−0.788557	−	0.614961i	$-0.789172\pi$
$313$	765.804	−	1326.41i	0.138293	−	0.239531i	0.926851	+	0.375430i	$0.122505\pi$
$314$	−3788.23			−0.680835
$315$		0			0
$316$	−343.747			−0.0611939
$317$	2109.59	−	3653.92i	0.373775	−	0.647397i	−0.616368	−	0.787458i	$-0.711397\pi$
$317$	2109.59	−	3653.92i	0.373775	−	0.647397i	0.990143	+	0.140061i	$0.0447300\pi$
$318$		0			0
$319$	−4413.09	−	7643.70i	−0.774564	−	1.34158i
$320$	−1234.32	+	2137.90i	−0.215627	+	0.373476i
$321$		0			0
$322$		0			0
$323$	−557.801			−0.0960893
$324$		0			0
$325$	2779.52	+	4814.26i	0.474400	+	0.821684i
$326$	−37.6194	−	65.1587i	−0.00639124	−	0.0110700i
$327$		0			0
$328$	2751.95			0.463265
$329$		0			0
$330$		0			0
$331$	−4149.09	+	7186.44i	−0.688987	+	1.19336i	0.283179	+	0.959067i	$0.408611\pi$
$331$	−4149.09	+	7186.44i	−0.688987	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$332$	−860.996	−	1491.29i	−0.142329	−	0.246521i
$333$		0			0
$334$	−1881.90	+	3259.54i	−0.308302	+	0.533994i
$335$	−1518.24			−0.247613
$336$		0			0
$337$	−4348.44			−0.702892			−0.351446	−	0.936208i	$-0.614310\pi$
$337$	−4348.44			−0.702892			−0.351446	+	0.936208i	$0.614310\pi$
$338$	732.278	−	1268.34i	0.117842	−	0.204109i
$339$		0			0
$340$	−29.2376	−	50.6410i	−0.00466362	−	0.00807763i
$341$	5130.20	−	8885.77i	0.814709	−	1.41112i
$342$		0			0
$343$		0			0
$344$	9091.60			1.42496
$345$		0			0
$346$	−73.0145	−	126.465i	−0.0113447	−	0.0196497i
$347$	−4172.77	−	7227.45i	−0.645550	−	1.11813i	−0.984174	−	0.177204i	$-0.943295\pi$
$347$	−4172.77	−	7227.45i	−0.645550	−	1.11813i	0.338624	−	0.940922i	$-0.390039\pi$
$348$		0			0
$349$	−9982.54			−1.53110			−0.765549	−	0.643378i	$-0.777532\pi$
$349$	−9982.54			−1.53110			−0.765549	+	0.643378i	$0.777532\pi$
$350$		0			0
$351$		0			0
$352$	2464.70	−	4268.98i	0.373207	−	0.646414i
$353$	4400.79	+	7622.40i	0.663543	+	1.14929i	0.979678	+	0.200576i	$0.0642813\pi$
$353$	4400.79	+	7622.40i	0.663543	+	1.14929i	−0.316135	+	0.948714i	$0.602385\pi$
$354$		0			0
$355$	1342.76	−	2325.74i	0.200751	−	0.347711i
$356$	2031.10			0.302383
$357$		0			0
$358$	8905.56			1.31473
$359$	−262.019	+	453.831i	−0.0385205	+	0.0667194i	−0.884643	−	0.466269i	$-0.845598\pi$
$359$	−262.019	+	453.831i	−0.0385205	+	0.0667194i	0.846122	+	0.532989i	$0.178931\pi$
$360$		0			0
$361$	−4085.64	−	7076.53i	−0.595661	−	1.03171i
$362$	−2340.94	+	4054.63i	−0.339881	+	0.588692i
$363$		0			0
$364$		0			0
$365$	2232.61			0.320165
$366$		0			0
$367$	3181.36	+	5510.28i	0.452495	+	0.783745i	0.998540	−	0.0540110i	$-0.0172006\pi$
$367$	3181.36	+	5510.28i	0.452495	+	0.783745i	−0.546045	+	0.837756i	$0.683867\pi$
$368$	−2194.99	−	3801.84i	−0.310929	−	0.538545i
$369$		0			0
$370$	−123.140			−0.0173020
$371$		0			0
$372$		0			0
$373$	5632.92	−	9756.50i	0.781935	−	1.35435i	−0.148879	−	0.988855i	$-0.547566\pi$
$373$	5632.92	−	9756.50i	0.781935	−	1.35435i	0.930813	−	0.365495i	$-0.119100\pi$
$374$	−210.887	−	365.267i	−0.0291570	−	0.0505014i
$375$		0			0
$376$	−3234.48	+	5602.28i	−0.443632	+	0.768393i
$377$	11544.5			1.57711
$378$		0			0
$379$	−1151.71			−0.156094			−0.0780470	−	0.996950i	$-0.524868\pi$
$379$	−1151.71			−0.156094			−0.0780470	+	0.996950i	$0.524868\pi$
$380$	787.824	−	1364.55i	0.106354	−	0.184211i
$381$		0			0
$382$	−486.887	−	843.313i	−0.0652129	−	0.112952i
$383$	−75.7772	+	131.250i	−0.0101097	+	0.0175106i	−0.871036	−	0.491219i	$-0.836551\pi$
$383$	−75.7772	+	131.250i	−0.0101097	+	0.0175106i	0.860926	+	0.508730i	$0.169885\pi$
$384$		0			0
$385$		0			0
$386$	−3651.08			−0.481437
$387$		0			0
$388$	−900.922	−	1560.44i	−0.117880	−	0.204174i
$389$	2397.09	+	4151.88i	0.312435	+	0.541154i	0.978889	−	0.204393i	$-0.0655220\pi$
$389$	2397.09	+	4151.88i	0.312435	+	0.541154i	−0.666454	+	0.745546i	$0.732189\pi$
$390$		0			0
$391$	597.608			0.0772950
$392$		0			0
$393$		0			0
$394$	−4252.76	+	7366.00i	−0.543784	+	0.941862i
$395$	−276.837	−	479.496i	−0.0352638	−	0.0610786i
$396$		0			0
$397$	2311.97	−	4004.45i	0.292278	−	0.506241i	−0.682070	−	0.731287i	$-0.738920\pi$
$397$	2311.97	−	4004.45i	0.292278	−	0.506241i	0.974348	+	0.225046i	$0.0722533\pi$
$398$	794.014			0.100001
$399$		0			0
$400$	3485.96			0.435745
$401$	−1805.32	+	3126.90i	−0.224821	+	0.389402i	−0.956266	−	0.292499i	$-0.905513\pi$
$401$	−1805.32	+	3126.90i	−0.224821	+	0.389402i	0.731445	+	0.681901i	$0.238846\pi$
$402$		0			0
$403$	6710.19	+	11622.4i	0.829425	+	1.43661i
$404$	−947.913	+	1641.83i	−0.116734	+	0.202189i
$405$		0			0
$406$		0			0
$407$	484.794			0.0590426
$408$		0			0
$409$	−4479.79	−	7759.22i	−0.541592	−	0.938065i	−0.998813	−	0.0487118i	$-0.984488\pi$
$409$	−4479.79	−	7759.22i	−0.541592	−	0.938065i	0.457221	−	0.889353i	$-0.348845\pi$
$410$	578.347	+	1001.73i	0.0696647	+	0.120663i
$411$		0			0
$412$	2577.34			0.308195
$413$		0			0
$414$		0			0
$415$	1386.81	−	2402.02i	0.164038	−	0.284122i
$416$	3223.77	+	5583.74i	0.379948	+	0.658089i
$417$		0			0
$418$	5682.48	−	9842.34i	0.664926	−	1.15169i
$419$	7078.28			0.825290			0.412645	−	0.910892i	$-0.364605\pi$
$419$	7078.28			0.825290			0.412645	+	0.910892i	$0.364605\pi$
$420$		0			0
$421$	11551.5			1.33725			0.668626	−	0.743599i	$-0.266883\pi$
$421$	11551.5			1.33725			0.668626	+	0.743599i	$0.266883\pi$
$422$	2944.40	−	5099.85i	0.339647	−	0.588286i
$423$		0			0
$424$	−6982.53	−	12094.1i	−0.799768	−	1.38524i
$425$	−237.272	+	410.966i	−0.0270809	+	0.0469054i
$426$		0			0
$427$		0			0
$428$	−329.750			−0.0372408
$429$		0			0
$430$	1910.68	+	3309.40i	0.214282	+	0.371147i
$431$	−2032.19	−	3519.85i	−0.227116	−	0.393377i	0.729836	−	0.683622i	$-0.239596\pi$
$431$	−2032.19	−	3519.85i	−0.227116	−	0.393377i	−0.956952	+	0.290245i	$0.906263\pi$
$432$		0			0
$433$	17456.3			1.93740			0.968701	−	0.248229i	$-0.0798487\pi$
$433$	17456.3			1.93740			0.968701	+	0.248229i	$0.0798487\pi$
$434$		0			0
$435$		0			0
$436$	1182.41	−	2047.99i	0.129879	−	0.224956i
$437$	8051.45	+	13945.5i	0.881357	+	1.52656i
$438$		0			0
$439$	−2297.69	+	3979.72i	−0.249802	+	0.432669i	−0.963471	−	0.267814i	$-0.913699\pi$
$439$	−2297.69	+	3979.72i	−0.249802	+	0.432669i	0.713669	+	0.700483i	$0.247032\pi$
$440$	4565.60			0.494674
$441$		0			0
$442$	551.671			0.0593672
$443$	−153.107	+	265.189i	−0.0164206	+	0.0284413i	−0.874119	−	0.485712i	$-0.838560\pi$
$443$	−153.107	+	265.189i	−0.0164206	+	0.0284413i	0.857698	+	0.514153i	$0.171894\pi$
$444$		0			0
$445$	1635.75	+	2833.21i	0.174252	+	0.301813i
$446$	−3681.05	+	6375.77i	−0.390813	+	0.676909i
$447$		0			0
$448$		0			0
$449$	−9229.22			−0.970053			−0.485026	−	0.874500i	$-0.661190\pi$
$449$	−9229.22			−0.970053			−0.485026	+	0.874500i	$0.661190\pi$
$450$		0			0
$451$	−2276.91	−	3943.72i	−0.237728	−	0.411758i
$452$	1534.66	+	2658.10i	0.159700	+	0.276608i
$453$		0			0
$454$	−12811.5			−1.32439
$455$		0			0
$456$		0			0
$457$	5496.12	−	9519.55i	0.562577	−	0.974411i	−0.434694	−	0.900578i	$-0.643143\pi$
$457$	5496.12	−	9519.55i	0.562577	−	0.974411i	0.997271	−	0.0738330i	$-0.0235232\pi$
$458$	4288.50	+	7427.90i	0.437530	+	0.757824i
$459$		0			0
$460$	−844.047	+	1461.93i	−0.0855519	+	0.148180i
$461$	−7387.88			−0.746394			−0.373197	−	0.927752i	$-0.621739\pi$
$461$	−7387.88			−0.746394			−0.373197	+	0.927752i	$0.621739\pi$
$462$		0			0
$463$	10163.8			1.02020			0.510101	−	0.860114i	$-0.329608\pi$
$463$	10163.8			1.02020			0.510101	+	0.860114i	$0.329608\pi$
$464$	3619.65	−	6269.42i	0.362151	−	0.627264i
$465$		0			0
$466$	7462.75	+	12925.9i	0.741857	+	1.28493i
$467$	−7907.29	+	13695.8i	−0.783524	+	1.35710i	0.146353	+	0.989232i	$0.453246\pi$
$467$	−7907.29	+	13695.8i	−0.783524	+	1.35710i	−0.929877	+	0.367871i	$0.880087\pi$
$468$		0			0
$469$		0			0
$470$	−2719.02			−0.266849
$471$		0			0
$472$	10341.3	+	17911.7i	1.00847	+	1.74672i
$473$	−7522.22	−	13028.9i	−0.731230	−	1.26653i
$474$		0			0
$475$	−12786.9			−1.23516
$476$		0			0
$477$		0			0
$478$	877.485	−	1519.85i	0.0839649	−	0.145432i
$479$	−722.427	−	1251.28i	−0.0689113	−	0.119358i	0.829511	−	0.558490i	$-0.188619\pi$
$479$	−722.427	−	1251.28i	−0.0689113	−	0.119358i	−0.898422	+	0.439132i	$0.855286\pi$
$480$		0			0
$481$	−317.050	+	549.146i	−0.0300545	+	0.0520559i
$482$	−2848.43			−0.269175
$483$		0			0
$484$	−930.742			−0.0874100
$485$	1451.12	−	2513.41i	0.135860	−	0.235316i
$486$		0			0
$487$	244.701	+	423.835i	0.0227689	+	0.0394369i	0.877185	−	0.480152i	$-0.159418\pi$
$487$	244.701	+	423.835i	0.0227689	+	0.0394369i	−0.854416	+	0.519589i	$0.826085\pi$
$488$	5981.44	−	10360.2i	0.554851	−	0.961029i
$489$		0			0
$490$		0			0
$491$	3941.30			0.362257			0.181129	−	0.983459i	$-0.442025\pi$
$491$	3941.30			0.362257			0.181129	+	0.983459i	$0.442025\pi$
$492$		0			0
$493$	492.743	+	853.455i	0.0450142	+	0.0779669i
$494$	7432.56	+	12873.6i	0.676936	+	1.17249i
$495$		0			0
$496$	8415.65			0.761843
$497$		0			0
$498$		0			0
$499$	−5.54470	+	9.60371i	−0.000497425	+	0.000861565i	−0.866274	−	0.499569i	$-0.833492\pi$
$499$	−5.54470	+	9.60371i	−0.000497425	+	0.000861565i	0.865777	+	0.500431i	$0.166825\pi$
$500$	−1473.49	−	2552.16i	−0.131793	−	0.228273i
$501$		0			0
$502$	−5876.42	+	10178.3i	−0.522465	+	0.904936i
$503$	−7088.41			−0.628343			−0.314172	−	0.949366i	$-0.601727\pi$
$503$	−7088.41			−0.628343			−0.314172	+	0.949366i	$0.601727\pi$
$504$		0			0
$505$	−3053.61			−0.269077
$506$	−6088.01	+	10544.7i	−0.534871	+	0.926424i
$507$		0			0
$508$	−758.605	−	1313.94i	−0.0662553	−	0.114757i
$509$	8794.22	−	15232.0i	0.765810	−	1.32642i	−0.174008	−	0.984744i	$-0.555672\pi$
$509$	8794.22	−	15232.0i	0.765810	−	1.32642i	0.939817	−	0.341677i	$-0.110995\pi$
$510$		0			0
$511$		0			0
$512$	10627.5			0.917333
$513$		0			0
$514$	−3147.86	−	5452.25i	−0.270129	−	0.467877i
$515$	2075.66	+	3595.15i	0.177601	+	0.307614i
$516$		0			0
$517$	10704.6			0.910613
$518$		0			0
$519$		0			0
$520$	−2985.85	+	5171.65i	−0.251804	+	0.436138i
$521$	−5823.30	−	10086.2i	−0.489680	−	0.848151i	0.510249	−	0.860026i	$-0.329553\pi$
$521$	−5823.30	−	10086.2i	−0.489680	−	0.848151i	−0.999929	+	0.0118758i	$0.996220\pi$
$522$		0			0
$523$	−4482.91	+	7764.63i	−0.374807	+	0.649185i	−0.990298	−	0.138959i	$-0.955624\pi$
$523$	−4482.91	+	7764.63i	−0.374807	+	0.649185i	0.615491	+	0.788144i	$0.288958\pi$
$524$	4229.75			0.352629
$525$		0			0
$526$	−9331.22			−0.773499
$527$	−572.811	+	992.137i	−0.0473473	+	0.0820079i
$528$		0			0
$529$	−2542.54	−	4403.81i	−0.208970	−	0.361947i
$530$	2934.88	−	5083.36i	0.240534	−	0.416617i
$531$		0			0
$532$		0			0
$533$	5956.30			0.484045
$534$		0			0
$535$	−265.565	−	459.971i	−0.0214605	−	0.0371706i
$536$	4108.64	+	7116.37i	0.331094	+	0.573471i
$537$		0			0
$538$	−15812.6			−1.26715
$539$		0			0
$540$		0			0
$541$	97.6359	−	169.110i	0.00775914	−	0.0134392i	−0.862120	−	0.506705i	$-0.830863\pi$
$541$	97.6359	−	169.110i	0.00775914	−	0.0134392i	0.869879	+	0.493265i	$0.164197\pi$
$542$	−8121.79	−	14067.3i	−0.643654	−	1.11484i
$543$		0			0
$544$	−275.195	+	476.652i	−0.0216891	+	0.0375667i
$545$	3809.01			0.299376
$546$		0			0
$547$	−1399.26			−0.109375			−0.0546874	−	0.998504i	$-0.517416\pi$
$547$	−1399.26			−0.109375			−0.0546874	+	0.998504i	$0.517416\pi$
$548$	1949.21	−	3376.12i	0.151945	−	0.263177i
$549$		0			0
$550$	−4834.31	−	8373.27i	−0.374792	−	0.649159i
$551$	−13277.2	+	22996.9i	−1.02655	+	1.77804i
$552$		0			0
$553$		0			0
$554$	−3004.06			−0.230380
$555$		0			0
$556$	−200.529	−	347.327i	−0.0152956	−	0.0264927i
$557$	21.5233	+	37.2795i	0.00163730	+	0.00283588i	0.866843	−	0.498581i	$-0.166145\pi$
$557$	21.5233	+	37.2795i	0.00163730	+	0.00283588i	−0.865206	+	0.501417i	$0.832812\pi$
$558$		0			0
$559$	19677.8			1.48888
$560$		0			0
$561$		0			0
$562$	232.393	−	402.516i	0.0174429	−	0.0302120i
$563$	−9616.43	−	16656.1i	−0.719865	−	1.24684i	−0.961053	−	0.276365i	$-0.910870\pi$
$563$	−9616.43	−	16656.1i	−0.719865	−	1.24684i	0.241187	−	0.970479i	$-0.422463\pi$
$564$		0			0
$565$	−2471.88	+	4281.41i	−0.184058	+	0.318797i
$566$	−2219.85			−0.164854
$567$		0			0
$568$	−14535.1			−1.07373
$569$	2581.99	−	4472.14i	0.190233	−	0.329493i	−0.755094	−	0.655616i	$-0.772409\pi$
$569$	2581.99	−	4472.14i	0.190233	−	0.329493i	0.945327	+	0.326123i	$0.105742\pi$
$570$		0			0
$571$	5115.96	+	8861.10i	0.374950	+	0.649432i	0.990319	−	0.138807i	$-0.0443267\pi$
$571$	5115.96	+	8861.10i	0.374950	+	0.649432i	−0.615370	+	0.788238i	$0.710993\pi$
$572$	3067.53	−	5313.11i	0.224230	−	0.388378i
$573$		0			0
$574$		0			0
$575$	13699.4			0.993572
$576$		0			0
$577$	−8281.87	−	14344.6i	−0.597537	−	1.03496i	−0.993184	−	0.116561i	$-0.962813\pi$
$577$	−8281.87	−	14344.6i	−0.597537	−	1.03496i	0.395647	−	0.918403i	$-0.370520\pi$
$578$	−5564.79	−	9638.49i	−0.400458	−	0.693613i
$579$		0			0
$580$	−2783.75			−0.199291
$581$		0			0
$582$		0			0
$583$	−11554.4	+	20012.8i	−0.820815	+	1.42169i
$584$	−6041.86	−	10464.8i	−0.428106	−	0.741501i
$585$		0			0
$586$	−691.482	+	1197.68i	−0.0487455	+	0.0844297i
$587$	−16020.6			−1.12648			−0.563239	−	0.826294i	$-0.690445\pi$
$587$	−16020.6			−1.12648			−0.563239	+	0.826294i	$0.690445\pi$
$588$		0			0
$589$	−30869.4			−2.15951
$590$	−4346.64	+	7528.60i	−0.303302	+	0.525335i
$591$		0			0
$592$	198.816	+	344.359i	0.0138028	+	0.0239072i
$593$	−3385.57	+	5863.98i	−0.234450	+	0.406079i	−0.959113	−	0.283025i	$-0.908662\pi$
$593$	−3385.57	+	5863.98i	−0.234450	+	0.406079i	0.724663	+	0.689104i	$0.241996\pi$
$594$		0			0
$595$		0			0
$596$	−5490.95			−0.377379
$597$		0			0
$598$	−7962.98	−	13792.3i	−0.544532	−	0.943158i
$599$	5535.11	+	9587.09i	0.377560	+	0.653953i	0.990707	−	0.136016i	$-0.0434299\pi$
$599$	5535.11	+	9587.09i	0.377560	+	0.653953i	−0.613147	+	0.789969i	$0.710097\pi$
$600$		0			0
$601$	−24187.7			−1.64166			−0.820830	−	0.571173i	$-0.806489\pi$
$601$	−24187.7			−1.64166			−0.820830	+	0.571173i	$0.806489\pi$
$602$		0			0
$603$		0			0
$604$	−3749.52	+	6494.37i	−0.252593	+	0.437503i
$605$	−749.574	−	1298.30i	−0.0503711	−	0.0872453i
$606$		0			0
$607$	5037.04	−	8724.40i	0.336816	−	0.583382i	−0.647016	−	0.762476i	$-0.723983\pi$
$607$	5037.04	−	8724.40i	0.336816	−	0.583382i	0.983832	+	0.179095i	$0.0573168\pi$
$608$	−14830.6			−0.989243
$609$		0			0
$610$	5028.21			0.333748
$611$	−7000.67	+	12125.5i	−0.463530	+	0.802858i
$612$		0			0
$613$	5557.29	+	9625.51i	0.366161	+	0.634210i	0.988962	−	0.148171i	$-0.0473385\pi$
$613$	5557.29	+	9625.51i	0.366161	+	0.634210i	−0.622800	+	0.782381i	$0.714005\pi$
$614$	9141.84	−	15834.1i	0.600871	−	1.04074i
$615$		0			0
$616$		0			0
$617$	−20496.4			−1.33737			−0.668683	−	0.743548i	$-0.733142\pi$
$617$	−20496.4			−1.33737			−0.668683	+	0.743548i	$0.733142\pi$
$618$		0			0
$619$	8357.22	+	14475.1i	0.542658	+	0.939910i	0.998750	+	0.0499782i	$0.0159152\pi$
$619$	8357.22	+	14475.1i	0.542658	+	0.939910i	−0.456093	+	0.889932i	$0.650751\pi$
$620$	−1618.05	−	2802.54i	−0.104810	−	0.181537i
$621$		0			0
$622$	12083.5			0.778943
$623$		0			0
$624$		0			0
$625$	−4145.33	+	7179.92i	−0.265301	+	0.459515i
$626$	−1742.14	−	3017.48i	−0.111230	−	0.192656i
$627$		0			0
$628$	2351.91	−	4073.63i	0.149445	−	0.258846i
$629$	−54.1295			−0.00343129
$630$		0			0
$631$	9168.53			0.578437			0.289218	−	0.957263i	$-0.406605\pi$
$631$	9168.53			0.578437			0.289218	+	0.957263i	$0.406605\pi$
$632$	−1498.35	+	2595.21i	−0.0943054	+	0.163342i
$633$		0			0
$634$	−4799.15	−	8312.37i	−0.300629	−	0.520704i
$635$	1221.89	−	2116.37i	0.0763608	−	0.132261i
$636$		0			0
$637$		0			0
$638$	−20078.9			−1.24597
$639$		0			0
$640$	606.411	+	1050.33i	0.0374539	+	0.0648721i
$641$	−2136.68	−	3700.84i	−0.131660	−	0.228041i	0.792657	−	0.609668i	$-0.208697\pi$
$641$	−2136.68	−	3700.84i	−0.131660	−	0.228041i	−0.924316	+	0.381627i	$0.875364\pi$
$642$		0			0
$643$	2955.75			0.181281			0.0906404	−	0.995884i	$-0.471109\pi$
$643$	2955.75			0.181281			0.0906404	+	0.995884i	$0.471109\pi$
$644$		0			0
$645$		0			0
$646$	−634.475	+	1098.94i	−0.0386426	+	0.0669309i
$647$	11350.6	+	19659.8i	0.689704	+	1.19460i	0.971934	+	0.235256i	$0.0755927\pi$
$647$	11350.6	+	19659.8i	0.689704	+	1.19460i	−0.282229	+	0.959347i	$0.591074\pi$
$648$		0			0
$649$	17112.4	−	29639.6i	1.03501	−	1.79269i
$650$	12646.3			0.763124
$651$		0			0
$652$	93.4235			0.00561158
$653$	768.907	−	1331.79i	0.0460791	−	0.0798113i	−0.842066	−	0.539375i	$-0.818661\pi$
$653$	768.907	−	1331.79i	0.0460791	−	0.0798113i	0.888145	+	0.459563i	$0.151994\pi$
$654$		0			0
$655$	3406.44	+	5900.12i	0.203207	+	0.351964i
$656$	1867.54	−	3234.67i	0.111151	−	0.192519i
$657$		0			0
$658$		0			0
$659$	−12338.1			−0.729323			−0.364661	−	0.931140i	$-0.618815\pi$
$659$	−12338.1			−0.729323			−0.364661	+	0.931140i	$0.618815\pi$
$660$		0			0
$661$	−922.548	−	1597.90i	−0.0542859	−	0.0940259i	0.837605	−	0.546276i	$-0.183955\pi$
$661$	−922.548	−	1597.90i	−0.0542859	−	0.0940259i	−0.891891	+	0.452250i	$0.850622\pi$
$662$	9438.84	+	16348.6i	0.554156	+	0.959826i
$663$		0			0
$664$	−15011.8			−0.877369
$665$		0			0
$666$		0			0
$667$	14224.8	−	24638.0i	0.825765	−	1.43027i
$668$	−2336.74	−	4047.35i	−0.135346	−	0.234426i
$669$		0			0
$670$	−1726.93	+	2991.14i	−0.0995780	+	0.172474i
$671$	−19795.7			−1.13890
$672$		0			0
$673$	23955.4			1.37208			0.686041	−	0.727563i	$-0.259347\pi$
$673$	23955.4			1.37208			0.686041	+	0.727563i	$0.259347\pi$
$674$	−4946.17	+	8567.02i	−0.282670	+	0.489598i
$675$		0			0
$676$	909.265	+	1574.89i	0.0517333	+	0.0896048i
$677$	−1839.13	+	3185.46i	−0.104407	+	0.180838i	−0.913496	−	0.406848i	$-0.866628\pi$
$677$	−1839.13	+	3185.46i	−0.104407	+	0.180838i	0.809089	+	0.587686i	$0.199961\pi$
$678$		0			0
$679$		0			0
$680$	−509.771			−0.0287482
$681$		0			0
$682$	−11670.8	−	20214.4i	−0.655275	−	1.13497i
$683$	2195.43	+	3802.60i	0.122996	+	0.213034i	0.920948	−	0.389686i	$-0.127417\pi$
$683$	2195.43	+	3802.60i	0.122996	+	0.213034i	−0.797952	+	0.602721i	$0.794083\pi$
$684$		0			0
$685$	6279.18			0.350241
$686$		0			0
$687$		0			0
$688$	6169.78	−	10686.4i	0.341890	−	0.592171i
$689$	−15112.9	−	26176.4i	−0.835641	−	1.44737i
$690$		0			0
$691$	−5185.84	+	8982.13i	−0.285497	+	0.494496i	−0.972730	−	0.231942i	$-0.925492\pi$
$691$	−5185.84	+	8982.13i	−0.285497	+	0.494496i	0.687232	+	0.726438i	$0.258825\pi$
$692$	181.323			0.00996081
$693$		0			0
$694$	−18985.4			−1.03844
$695$	322.993	−	559.440i	0.0176285	−	0.0305335i
$696$		0			0
$697$	254.228	+	440.335i	0.0138157	+	0.0239295i
$698$	−11354.7	+	19667.0i	−0.615734	+	1.06648i
$699$		0			0
$700$		0			0
$701$	−109.675			−0.00590922			−0.00295461	−	0.999996i	$-0.500940\pi$
$701$	−109.675			−0.00590922			−0.00295461	+	0.999996i	$0.500940\pi$
$702$		0			0
$703$	−729.275	−	1263.14i	−0.0391254	−	0.0677672i
$704$	−11054.8	−	19147.5i	−0.591822	−	1.02507i
$705$		0			0
$706$	20022.9			1.06738
$707$		0			0
$708$		0			0
$709$	−13459.4	+	23312.3i	−0.712944	+	1.23486i	0.250803	+	0.968038i	$0.419306\pi$
$709$	−13459.4	+	23312.3i	−0.712944	+	1.23486i	−0.963747	+	0.266818i	$0.914028\pi$
$710$	−3054.68	−	5290.86i	−0.161465	−	0.279665i
$711$		0			0
$712$	8853.31	−	15334.4i	0.466000	−	0.807135i
$713$	33072.4			1.73713
$714$		0			0
$715$	9881.74			0.516862
$716$	−5528.99	+	9576.50i	−0.288587	+	0.499847i
$717$		0			0
$718$	596.072	+	1032.43i	0.0309822	+	0.0536627i
$719$	7585.38	−	13138.3i	0.393445	−	0.681466i	−0.599457	−	0.800407i	$-0.704617\pi$
$719$	7585.38	−	13138.3i	0.393445	−	0.681466i	0.992901	+	0.118941i	$0.0379499\pi$
$720$		0			0
$721$		0			0
$722$	−18589.0			−0.958185
$723$		0			0
$724$	−2906.73	−	5034.61i	−0.149210	−	0.258439i
$725$	11295.5	+	19564.3i	0.578626	+	1.00221i
$726$		0			0
$727$	−33286.9			−1.69813			−0.849066	−	0.528288i	$-0.822834\pi$
$727$	−33286.9			−1.69813			−0.849066	+	0.528288i	$0.822834\pi$
$728$		0			0
$729$		0			0
$730$	2539.50	−	4398.54i	0.128755	−	0.223010i
$731$	839.890	+	1454.73i	0.0424959	+	0.0736050i
$732$		0			0
$733$	−10272.0	+	17791.7i	−0.517607	+	0.896521i	0.482184	+	0.876070i	$0.339844\pi$
$733$	−10272.0	+	17791.7i	−0.517607	+	0.896521i	−0.999791	+	0.0204512i	$0.993490\pi$
$734$	14474.7			0.727888
$735$		0			0
$736$	15889.0			0.795755
$737$	6798.82	−	11775.9i	0.339807	−	0.588563i
$738$		0			0
$739$	−17178.6	−	29754.2i	−0.855109	−	1.48109i	−0.876544	−	0.481321i	$-0.840157\pi$
$739$	−17178.6	−	29754.2i	−0.855109	−	1.48109i	0.0214356	−	0.999770i	$-0.493176\pi$
$740$	76.4512	−	132.417i	0.00379784	−	0.00657805i
$741$		0			0
$742$		0			0
$743$	−8166.99			−0.403254			−0.201627	−	0.979462i	$-0.564623\pi$
$743$	−8166.99			−0.403254			−0.201627	+	0.979462i	$0.564623\pi$
$744$		0			0
$745$	−4422.14	−	7659.38i	−0.217470	−	0.376668i
$746$	−12814.4	−	22195.2i	−0.628914	−	1.08931i
$747$		0			0
$748$	523.715			0.0256001
$749$		0			0
$750$		0			0
$751$	−8540.05	+	14791.8i	−0.414954	+	0.718722i	−0.995424	−	0.0955601i	$-0.969536\pi$
$751$	−8540.05	+	14791.8i	−0.414954	+	0.718722i	0.580469	+	0.814282i	$0.302869\pi$
$752$	4389.99	+	7603.68i	0.212881	+	0.368720i
$753$		0			0
$754$	13131.3	−	22744.2i	0.634238	−	1.09853i
$755$	−12078.7			−0.582239
$756$		0			0
$757$	−16324.0			−0.783758			−0.391879	−	0.920017i	$-0.628175\pi$
$757$	−16324.0			−0.783758			−0.391879	+	0.920017i	$0.628175\pi$
$758$	−1310.03	+	2269.03i	−0.0627735	+	0.108727i
$759$		0			0
$760$	−6868.04	−	11895.8i	−0.327802	−	0.567770i
$761$	−16183.1	+	28029.9i	−0.770875	+	1.33520i	0.166208	+	0.986091i	$0.446848\pi$
$761$	−16183.1	+	28029.9i	−0.770875	+	1.33520i	−0.937084	+	0.349105i	$0.886486\pi$
$762$		0			0
$763$		0			0
$764$	1209.13			0.0572576
$765$		0			0
$766$	172.387	+	298.583i	0.00813131	+	0.0140838i
$767$	22382.7	+	38767.9i	1.05370	+	1.82507i
$768$		0			0
$769$	−7948.44			−0.372728			−0.186364	−	0.982481i	$-0.559670\pi$
$769$	−7948.44			−0.372728			−0.186364	+	0.982481i	$0.559670\pi$
$770$		0			0
$771$		0			0
$772$	2266.76	−	3926.14i	0.105677	−	0.183038i
$773$	8909.64	+	15432.0i	0.414564	+	0.718045i	0.995383	−	0.0959876i	$-0.0306009\pi$
$773$	8909.64	+	15432.0i	0.414564	+	0.718045i	−0.580819	+	0.814033i	$0.697268\pi$
$774$		0			0
$775$	−13130.9	+	22743.4i	−0.608616	+	1.05415i
$776$	−15708.0			−0.726655
$777$		0			0
$778$	10906.4			0.502586
$779$	−6850.32	+	11865.1i	−0.315068	+	0.545714i
$780$		0			0
$781$	12026.0	+	20829.7i	0.550993	+	0.954349i
$782$	679.754	−	1177.37i	0.0310844	−	0.0538397i
$783$		0			0
$784$		0			0
$785$	7576.46			0.344478
$786$		0			0
$787$	−1456.19	−	2522.19i	−0.0659562	−	0.114240i	0.831162	−	0.556031i	$-0.187676\pi$
$787$	−1456.19	−	2522.19i	−0.0659562	−	0.114240i	−0.897118	+	0.441791i	$0.854343\pi$
$788$	−5280.63	−	9146.32i	−0.238724	−	0.413482i
$789$		0			0
$790$	−1259.56			−0.0567256
$791$		0			0
$792$		0			0
$793$	12946.2	−	22423.4i	0.579738	−	1.00414i
$794$	−5259.54	−	9109.79i	−0.235081	−	0.407172i
$795$		0			0
$796$	−492.961	+	853.834i	−0.0219504	+	0.0380193i
$797$	33789.1			1.50172			0.750861	−	0.660460i	$-0.229639\pi$
$797$	33789.1			1.50172			0.750861	+	0.660460i	$0.229639\pi$
$798$		0			0
$799$	−1195.22			−0.0529208
$800$	−6308.49	+	10926.6i	−0.278798	+	0.482893i
$801$		0			0
$802$	4106.95	+	7113.44i	0.180825	+	0.313197i
$803$	−9997.83	+	17316.7i	−0.439372	+	0.761015i
$804$		0			0
$805$		0			0
$806$	30530.2			1.33422
$807$		0			0
$808$	8263.65	+	14313.1i	0.359795	+	0.623183i
$809$	626.064	+	1084.37i	0.0272079	+	0.0471255i	0.879309	−	0.476252i	$-0.158005\pi$
$809$	626.064	+	1084.37i	0.0272079	+	0.0471255i	−0.852101	+	0.523378i	$0.824672\pi$
$810$		0			0
$811$	−31913.1			−1.38178			−0.690889	−	0.722961i	$-0.742781\pi$
$811$	−31913.1			−1.38178			−0.690889	+	0.722961i	$0.742781\pi$
$812$		0			0
$813$		0			0
$814$	551.433	−	955.110i	0.0237441	−	0.0411260i
$815$	75.2387	+	130.317i	0.00323374	+	0.00560100i
$816$		0			0
$817$	−22631.3	+	39198.6i	−0.969120	+	1.67856i
$818$	−20382.3			−0.871210
$819$		0			0
$820$	−1436.26			−0.0611663
$821$	15371.2	−	26623.7i	0.653421	−	1.13176i	−0.328866	−	0.944376i	$-0.606667\pi$
$821$	15371.2	−	26623.7i	0.653421	−	1.13176i	0.982287	−	0.187382i	$-0.0600001\pi$
$822$		0			0
$823$	6911.28	+	11970.7i	0.292724	+	0.507014i	0.974453	−	0.224592i	$-0.0721048\pi$
$823$	6911.28	+	11970.7i	0.292724	+	0.507014i	−0.681729	+	0.731605i	$0.738771\pi$
$824$	11234.3	−	19458.3i	0.474956	−	0.822648i
$825$		0			0
$826$		0			0
$827$	42107.1			1.77051			0.885253	−	0.465110i	$-0.153985\pi$
$827$	42107.1			1.77051			0.885253	+	0.465110i	$0.153985\pi$
$828$		0			0
$829$	19381.9	+	33570.4i	0.812015	+	1.40645i	0.911451	+	0.411408i	$0.134963\pi$
$829$	19381.9	+	33570.4i	0.812015	+	1.40645i	−0.0994360	+	0.995044i	$0.531704\pi$
$830$	−3154.87	−	5464.40i	−0.131936	−	0.228521i
$831$		0			0
$832$	28918.8			1.20502
$833$		0			0
$834$		0			0
$835$	3763.79	−	6519.08i	0.155990	−	0.270182i
$836$	7055.90	+	12221.2i	0.291906	+	0.505596i
$837$		0			0
$838$	8051.25	−	13945.2i	0.331892	−	0.574854i
$839$	−16896.3			−0.695262			−0.347631	−	0.937631i	$-0.613014\pi$
$839$	−16896.3			−0.695262			−0.347631	+	0.937631i	$0.613014\pi$
$840$		0			0
$841$	22525.7			0.923601
$842$	13139.3	−	22757.9i	0.537779	−	0.931461i
$843$		0			0
$844$	3656.05	+	6332.46i	0.149107	+	0.258261i
$845$	−1464.56	+	2536.68i	−0.0596240	+	0.103272i
$846$		0			0
$847$		0			0
$848$	−18954.0			−0.767552
$849$		0			0
$850$	539.773	+	934.915i	0.0217813	+	0.0377262i
$851$	781.320	+	1353.29i	0.0314727	+	0.0545124i
$852$		0			0
$853$	46429.3			1.86367			0.931833	−	0.362887i	$-0.118209\pi$
$853$	46429.3			1.86367			0.931833	+	0.362887i	$0.118209\pi$
$854$		0			0
$855$		0			0
$856$	−1437.34	+	2489.54i	−0.0573915	+	0.0994050i
$857$	10603.2	+	18365.3i	0.422636	+	0.732027i	0.996196	−	0.0871364i	$-0.0277716\pi$
$857$	10603.2	+	18365.3i	0.422636	+	0.732027i	−0.573561	+	0.819163i	$0.694438\pi$
$858$		0			0
$859$	−6938.09	+	12017.1i	−0.275581	+	0.477321i	−0.970282	−	0.241978i	$-0.922204\pi$
$859$	−6938.09	+	12017.1i	−0.275581	+	0.477321i	0.694700	+	0.719299i	$0.255537\pi$
$860$	−4744.96			−0.188142
$861$		0			0
$862$	−9246.12			−0.365341
$863$	7168.53	−	12416.3i	0.282757	−	0.489750i	−0.689306	−	0.724471i	$-0.742084\pi$
$863$	7168.53	−	12416.3i	0.282757	−	0.489750i	0.972063	+	0.234721i	$0.0754176\pi$
$864$		0			0
$865$	146.029	+	252.930i	0.00574004	+	0.00994204i
$866$	19855.8	−	34391.2i	0.779131	−	1.34949i
$867$		0			0
$868$		0			0
$869$	4958.81			0.193574
$870$		0			0
$871$	8892.70	+	15402.6i	0.345945	+	0.599193i
$872$	−10307.9	−	17853.8i	−0.400309	−	0.693356i
$873$		0			0
$874$	36632.8			1.41776
$875$		0			0
$876$		0			0
$877$	12184.6	−	21104.4i	0.469152	−	0.812595i	−0.530226	−	0.847856i	$-0.677893\pi$
$877$	12184.6	−	21104.4i	0.469152	−	0.812595i	0.999378	+	0.0352614i	$0.0112264\pi$
$878$	5227.07	+	9053.54i	0.200917	+	0.347998i
$879$		0			0
$880$	3098.32	−	5366.45i	0.118687	−	0.205572i
$881$	26127.0			0.999140			0.499570	−	0.866273i	$-0.333491\pi$
$881$	26127.0			0.999140			0.499570	+	0.866273i	$0.333491\pi$
$882$		0			0
$883$	−15713.1			−0.598855			−0.299428	−	0.954119i	$-0.596796\pi$
$883$	−15713.1			−0.598855			−0.299428	+	0.954119i	$0.596796\pi$
$884$	−342.503	+	593.233i	−0.0130313	+	0.0225708i
$885$		0			0
$886$	348.305	+	603.283i	0.0132072	+	0.0228755i
$887$	6569.74	−	11379.1i	0.248692	−	0.430748i	−0.714471	−	0.699665i	$-0.753333\pi$
$887$	6569.74	−	11379.1i	0.248692	−	0.430748i	0.963163	+	0.268917i	$0.0866658\pi$
$888$		0			0
$889$		0			0
$890$	7442.40			0.280303
$891$		0			0
$892$	−4570.74	−	7916.75i	−0.171569	−	0.297166i
$893$	−16102.9	−	27891.0i	−0.603430	−	1.04517i
$894$		0			0
$895$	−17811.1			−0.665207
$896$		0			0
$897$		0			0
$898$	−10497.9	+	18182.8i	−0.390109	+	0.675689i
$899$	27269.0	+	47231.4i	1.01165	+	1.75223i
$900$		0			0
$901$	1290.10	−	2234.53i	0.0477021	−	0.0826225i
$902$	−10359.6			−0.382412
$903$		0			0
$904$	26757.4			0.984446
$905$	4681.88	−	8109.25i	0.171968	−	0.297857i
$906$		0			0
$907$	1899.85	+	3290.64i	0.0695519	+	0.120467i	0.898704	−	0.438555i	$-0.144510\pi$
$907$	1899.85	+	3290.64i	0.0695519	+	0.120467i	−0.829152	+	0.559023i	$0.811176\pi$
$908$	7953.96	−	13776.7i	0.290706	−	0.503518i
$909$		0			0
$910$		0			0
$911$	51528.4			1.87400			0.936998	−	0.349334i	$-0.113592\pi$
$911$	51528.4			1.87400			0.936998	+	0.349334i	$0.113592\pi$
$912$		0			0
$913$	12420.5	+	21513.0i	0.450229	+	0.779819i
$914$	−12503.2	−	21656.2i	−0.452483	−	0.783723i
$915$		0			0
$916$	−10650.0			−0.384156
$917$		0			0
$918$		0			0
$919$	8492.37	−	14709.2i	0.304828	−	0.527978i	−0.672395	−	0.740193i	$-0.734734\pi$
$919$	8492.37	−	14709.2i	0.304828	−	0.527978i	0.977223	+	0.212214i	$0.0680675\pi$
$920$	7358.17	+	12744.7i	0.263687	+	0.456719i
$921$		0			0
$922$	−8403.41	+	14555.1i	−0.300164	+	0.519900i
$923$	−31459.6			−1.12189
$924$		0			0
$925$	−1240.85			−0.0441068
$926$	11560.9	−	20024.1i	0.410277	−	0.710620i
$927$		0			0
$928$	13100.9	+	22691.3i	0.463423	+	0.802672i
$929$	−2725.93	+	4721.44i	−0.0962699	+	0.166744i	−0.910138	−	0.414305i	$-0.864025\pi$
$929$	−2725.93	+	4721.44i	−0.0962699	+	0.166744i	0.813868	+	0.581050i	$0.197358\pi$
$930$		0			0
$931$		0			0
$932$	−18532.9			−0.651358
$933$		0			0
$934$	17988.4	+	31156.9i	0.630192	+	1.09152i
$935$	421.774	+	730.534i	0.0147524	+	0.0255519i
$936$		0			0
$937$	42429.4			1.47930			0.739652	−	0.672989i	$-0.234990\pi$
$937$	42429.4			1.47930			0.739652	+	0.672989i	$0.234990\pi$
$938$		0			0
$939$		0			0
$940$	1688.09	−	2923.86i	0.0585740	−	0.101453i
$941$	−16488.9	−	28559.7i	−0.571226	−	0.989393i	−0.996440	−	0.0843003i	$-0.973134\pi$
$941$	−16488.9	−	28559.7i	−0.571226	−	0.989393i	0.425214	−	0.905093i	$-0.360199\pi$
$942$		0			0
$943$	7339.19	−	12711.8i	0.253443	−	0.438976i
$944$	28071.5			0.967848
$945$		0			0
$946$	−34224.8			−1.17626
$947$	−11876.7	+	20571.1i	−0.407541	+	0.705882i	−0.994614	−	0.103653i	$-0.966947\pi$
$947$	−11876.7	+	20571.1i	−0.407541	+	0.705882i	0.587073	+	0.809534i	$0.300280\pi$
$948$		0			0
$949$	−13076.9	−	22649.9i	−0.447308	−	0.774760i
$950$	−14544.5	+	25191.8i	−0.496722	+	0.860349i
$951$		0			0
$952$		0			0
$953$	28074.3			0.954267			0.477134	−	0.878831i	$-0.341676\pi$
$953$	28074.3			0.954267			0.477134	+	0.878831i	$0.341676\pi$
$954$		0			0
$955$	973.774	+	1686.63i	0.0329954	+	0.0571497i
$956$	1089.57	+	1887.19i	0.0368610	+	0.0638452i
$957$		0			0
$958$	−3286.92			−0.110851
$959$		0			0
$960$		0			0
$961$	−16804.6	+	29106.5i	−0.564084	+	0.977022i
$962$	721.262	+	1249.26i	0.0241730	+	0.0418688i
$963$		0			0
$964$	1768.44	−	3063.03i	0.0590847	−	0.102338i
$965$	7302.15			0.243590
$966$		0			0
$967$	−11150.3			−0.370806			−0.185403	−	0.982663i	$-0.559359\pi$
$967$	−11150.3			−0.370806			−0.185403	+	0.982663i	$0.559359\pi$
$968$	−4056.98	+	7026.89i	−0.134707	+	0.233319i
$969$		0			0
$970$	−3301.17	−	5717.80i	−0.109272	−	0.189265i
$971$	3029.52	−	5247.29i	0.100126	−	0.173423i	−0.811611	−	0.584199i	$-0.801409\pi$
$971$	3029.52	−	5247.29i	0.100126	−	0.173423i	0.911736	+	0.410776i	$0.134742\pi$
$972$		0			0
$973$		0			0
$974$	1113.35			0.0366263
$975$		0			0
$976$	−8118.29	−	14061.3i	−0.266250	−	0.461159i
$977$	2850.24	+	4936.77i	0.0933341	+	0.161659i	0.908912	−	0.416988i	$-0.136914\pi$
$977$	2850.24	+	4936.77i	0.0933341	+	0.161659i	−0.815578	+	0.578647i	$0.803581\pi$
$978$		0			0
$979$	−29300.2			−0.956526
$980$		0			0
$981$		0			0
$982$	4483.06	−	7764.89i	0.145683	−	0.252330i
$983$	98.7401	+	171.023i	0.00320378	+	0.00554912i	0.867623	−	0.497223i	$-0.165647\pi$
$983$	98.7401	+	171.023i	0.00320378	+	0.00554912i	−0.864419	+	0.502772i	$0.832314\pi$
$984$		0			0
$985$	8505.52	−	14732.0i	0.275136	−	0.476549i
$986$	2241.90			0.0724103
$987$		0			0
$988$	−18457.9			−0.594357
$989$	24246.4	−	41996.0i	0.779567	−	1.35025i
$990$		0			0
$991$	−10310.4	−	17858.1i	−0.330495	−	0.572434i	0.652114	−	0.758121i	$-0.273882\pi$
$991$	−10310.4	−	17858.1i	−0.330495	−	0.572434i	−0.982609	+	0.185687i	$0.940549\pi$
$992$	−15229.7	+	26378.6i	−0.487442	+	0.844275i
$993$		0			0
$994$		0			0
$995$	−1588.03			−0.0505969
$996$		0			0
$997$	−9663.41	−	16737.5i	−0.306964	−	0.531678i	0.670733	−	0.741699i	$-0.265980\pi$
$997$	−9663.41	−	16737.5i	−0.306964	−	0.531678i	−0.977697	+	0.210022i	$0.932647\pi$
$998$	12.6137	+	21.8476i	0.000400081	+	0.000692961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.q.226.2		4
3.2	odd	2		147.4.e.l.79.1		4
7.2	even	3		63.4.a.e.1.1		2
7.3	odd	6		441.4.e.p.361.2		4
7.4	even	3	inner	441.4.e.q.361.2		4
7.5	odd	6		441.4.a.r.1.1		2
7.6	odd	2		441.4.e.p.226.2		4
21.2	odd	6		21.4.a.c.1.2	✓	2
21.5	even	6		147.4.a.i.1.2		2
21.11	odd	6		147.4.e.l.67.1		4
21.17	even	6		147.4.e.m.67.1		4
21.20	even	2		147.4.e.m.79.1		4
28.23	odd	6		1008.4.a.ba.1.2		2
35.9	even	6		1575.4.a.p.1.2		2
84.23	even	6		336.4.a.m.1.1		2
84.47	odd	6		2352.4.a.bz.1.2		2
105.2	even	12		525.4.d.g.274.3		4
105.23	even	12		525.4.d.g.274.2		4
105.44	odd	6		525.4.a.n.1.1		2
168.107	even	6		1344.4.a.bo.1.2		2
168.149	odd	6		1344.4.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.2	✓	2	21.2	odd	6
63.4.a.e.1.1		2	7.2	even	3
147.4.a.i.1.2		2	21.5	even	6
147.4.e.l.67.1		4	21.11	odd	6
147.4.e.l.79.1		4	3.2	odd	2
147.4.e.m.67.1		4	21.17	even	6
147.4.e.m.79.1		4	21.20	even	2
336.4.a.m.1.1		2	84.23	even	6
441.4.a.r.1.1		2	7.5	odd	6
441.4.e.p.226.2		4	7.6	odd	2
441.4.e.p.361.2		4	7.3	odd	6
441.4.e.q.226.2		4	1.1	even	1	trivial
441.4.e.q.361.2		4	7.4	even	3	inner
525.4.a.n.1.1		2	105.44	odd	6
525.4.d.g.274.2		4	105.23	even	12
525.4.d.g.274.3		4	105.2	even	12
1008.4.a.ba.1.2		2	28.23	odd	6
1344.4.a.bg.1.2		2	168.149	odd	6
1344.4.a.bo.1.2		2	168.107	even	6
1575.4.a.p.1.2		2	35.9	even	6
2352.4.a.bz.1.2		2	84.47	odd	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)

\(f(q)\)	\(=\)	\(q+(1.13746 - 1.97014i) q^{2} +(1.41238 + 2.44631i) q^{4} +(-2.27492 + 3.94027i) q^{5} +24.6254 q^{8} +O(q^{10})\)	\(q+(1.13746 - 1.97014i) q^{2} +(1.41238 + 2.44631i) q^{4} +(-2.27492 + 3.94027i) q^{5} +24.6254 q^{8} +(5.17525 + 8.96379i) q^{10} +(-20.3746 - 35.2898i) q^{11} +53.2990 q^{13} +(16.7114 - 28.9450i) q^{16} +(2.27492 + 3.94027i) q^{17} +(-61.2990 + 106.173i) q^{19} -12.8522 q^{20} -92.7010 q^{22} +(65.6736 - 113.750i) q^{23} +(52.1495 + 90.3256i) q^{25} +(60.6254 - 105.006i) q^{26} +216.598 q^{29} +(125.897 + 218.060i) q^{31} +(60.4846 + 104.762i) q^{32} +10.3505 q^{34} +(-5.94851 + 10.3031i) q^{37} +(139.450 + 241.535i) q^{38} +(-56.0208 + 97.0308i) q^{40} +111.752 q^{41} +369.196 q^{43} +(57.5531 - 99.6850i) q^{44} +(-149.402 - 258.772i) q^{46} +(-131.347 + 227.500i) q^{47} +237.272 q^{50} +(75.2782 + 130.386i) q^{52} +(-283.550 - 491.123i) q^{53} +185.402 q^{55} +(246.371 - 426.728i) q^{58} +(419.945 + 727.366i) q^{59} +(242.897 - 420.710i) q^{61} +572.811 q^{62} +542.577 q^{64} +(-121.251 + 210.013i) q^{65} +(166.846 + 288.985i) q^{67} +(-6.42608 + 11.1303i) q^{68} -590.248 q^{71} +(-245.350 - 424.960i) q^{73} +(13.5324 + 23.4387i) q^{74} -346.309 q^{76} +(-60.8455 + 105.388i) q^{79} +(76.0340 + 131.695i) q^{80} +(127.114 - 220.168i) q^{82} -609.608 q^{83} -20.7010 q^{85} +(419.945 - 727.366i) q^{86} +(-501.733 - 869.026i) q^{88} +(359.519 - 622.705i) q^{89} +371.023 q^{92} +(298.804 + 517.544i) q^{94} +(-278.900 - 483.070i) q^{95} -637.877 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 17 q^{4} + 6 q^{5} + 174 q^{8}+O(q^{10}) \) 4 * q - 3 * q^2 - 17 * q^4 + 6 * q^5 + 174 * q^8	\( 4 q - 3 q^{2} - 17 q^{4} + 6 q^{5} + 174 q^{8} + 66 q^{10} - 6 q^{11} + 32 q^{13} - 137 q^{16} - 6 q^{17} - 64 q^{19} - 444 q^{20} - 552 q^{22} + 6 q^{23} + 118 q^{25} + 318 q^{26} + 504 q^{29} - 40 q^{31} - 279 q^{32} + 132 q^{34} + 248 q^{37} + 588 q^{38} + 546 q^{40} + 900 q^{41} + 752 q^{43} + 804 q^{44} - 960 q^{46} - 12 q^{47} + 330 q^{50} + 890 q^{52} - 1104 q^{53} + 1104 q^{55} + 306 q^{58} + 804 q^{59} + 428 q^{61} + 4224 q^{62} + 2578 q^{64} - 636 q^{65} - 148 q^{67} - 222 q^{68} - 1908 q^{71} - 1072 q^{73} + 1398 q^{74} - 3016 q^{76} + 572 q^{79} + 1950 q^{80} - 1530 q^{82} - 3888 q^{83} - 264 q^{85} + 804 q^{86} + 1164 q^{88} + 366 q^{89} + 5712 q^{92} + 1920 q^{94} - 1176 q^{95} + 1616 q^{97}+O(q^{100}) \) 4 * q - 3 * q^2 - 17 * q^4 + 6 * q^5 + 174 * q^8 + 66 * q^10 - 6 * q^11 + 32 * q^13 - 137 * q^16 - 6 * q^17 - 64 * q^19 - 444 * q^20 - 552 * q^22 + 6 * q^23 + 118 * q^25 + 318 * q^26 + 504 * q^29 - 40 * q^31 - 279 * q^32 + 132 * q^34 + 248 * q^37 + 588 * q^38 + 546 * q^40 + 900 * q^41 + 752 * q^43 + 804 * q^44 - 960 * q^46 - 12 * q^47 + 330 * q^50 + 890 * q^52 - 1104 * q^53 + 1104 * q^55 + 306 * q^58 + 804 * q^59 + 428 * q^61 + 4224 * q^62 + 2578 * q^64 - 636 * q^65 - 148 * q^67 - 222 * q^68 - 1908 * q^71 - 1072 * q^73 + 1398 * q^74 - 3016 * q^76 + 572 * q^79 + 1950 * q^80 - 1530 * q^82 - 3888 * q^83 - 264 * q^85 + 804 * q^86 + 1164 * q^88 + 366 * q^89 + 5712 * q^92 + 1920 * q^94 - 1176 * q^95 + 1616 * q^97

Introduction

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