LMFDB - Embedded newform 168.4.u.a.17.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(17,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("168.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, 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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.14
Character	$\chi$	$=$	168.17
Dual form			168.4.u.a.89.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.919514 + 5.11415i) q^{3} +(-6.04693 - 10.4736i) q^{5} +(15.9632 + 9.39028i) q^{7} +(-25.3090 + 9.40505i) q^{9} +O(q^{10})$	\(q+(0.919514 + 5.11415i) q^{3} +(-6.04693 - 10.4736i) q^{5} +(15.9632 + 9.39028i) q^{7} +(-25.3090 + 9.40505i) q^{9} +(30.2732 + 17.4782i) q^{11} +81.1032i q^{13} +(48.0032 - 40.5555i) q^{15} +(-4.14503 + 7.17941i) q^{17} +(-52.7556 + 30.4585i) q^{19} +(-33.3449 + 90.2725i) q^{21} +(-157.219 + 90.7706i) q^{23} +(-10.6306 + 18.4128i) q^{25} +(-71.3708 - 120.786i) q^{27} +75.6434i q^{29} +(77.3344 + 44.6491i) q^{31} +(-61.5496 + 170.893i) q^{33} +(1.82179 - 223.974i) q^{35} +(-58.4106 - 101.170i) q^{37} +(-414.774 + 74.5755i) q^{39} +147.344 q^{41} +389.121 q^{43} +(251.546 + 208.204i) q^{45} +(99.8765 + 172.991i) q^{47} +(166.645 + 299.797i) q^{49} +(-40.5279 - 14.5967i) q^{51} +(578.226 + 333.839i) q^{53} -422.758i q^{55} +(-204.278 - 241.793i) q^{57} +(8.54890 - 14.8071i) q^{59} +(-661.389 + 381.853i) q^{61} +(-492.328 - 87.5240i) q^{63} +(849.442 - 490.425i) q^{65} +(428.169 - 741.610i) q^{67} +(-608.780 - 720.578i) q^{69} -700.045i q^{71} +(-748.329 - 432.048i) q^{73} +(-103.941 - 37.4358i) q^{75} +(319.130 + 563.281i) q^{77} +(-463.245 - 802.364i) q^{79} +(552.090 - 476.065i) q^{81} +1053.69 q^{83} +100.259 q^{85} +(-386.851 + 69.5551i) q^{87} +(-224.645 - 389.097i) q^{89} +(-761.582 + 1294.66i) q^{91} +(-157.232 + 436.555i) q^{93} +(638.018 + 368.360i) q^{95} +213.360i q^{97} +(-930.566 - 157.635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q + 12 * q^7 + 14 * q^9	$ 48 q + 12 q^{7} + 14 q^{9} - 88 q^{15} - 270 q^{19} + 50 q^{21} - 438 q^{25} + 216 q^{31} - 372 q^{33} + 66 q^{37} + 242 q^{39} + 900 q^{43} - 294 q^{45} + 60 q^{49} - 138 q^{51} + 1384 q^{57} + 108 q^{61} + 1096 q^{63} + 6 q^{67} - 1206 q^{73} - 594 q^{75} - 588 q^{79} - 54 q^{81} - 240 q^{85} - 3522 q^{87} + 234 q^{91} - 608 q^{93} + 1988 q^{99}+O(q^{100}) $ 48 * q + 12 * q^7 + 14 * q^9 - 88 * q^15 - 270 * q^19 + 50 * q^21 - 438 * q^25 + 216 * q^31 - 372 * q^33 + 66 * q^37 + 242 * q^39 + 900 * q^43 - 294 * q^45 + 60 * q^49 - 138 * q^51 + 1384 * q^57 + 108 * q^61 + 1096 * q^63 + 6 * q^67 - 1206 * q^73 - 594 * q^75 - 588 * q^79 - 54 * q^81 - 240 * q^85 - 3522 * q^87 + 234 * q^91 - 608 * q^93 + 1988 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$	0.919514	+	5.11415i	0.176960	+	0.984218i
$3$	0.919514	+	5.11415i	0.176960	+	0.984218i
$4$		0			0
$5$	−6.04693	−	10.4736i	−0.540854	−	0.936786i	−0.998855	−	0.0478345i	$-0.984768\pi$
$5$	−6.04693	−	10.4736i	−0.540854	−	0.936786i	0.458002	−	0.888951i	$-0.348565\pi$
$6$		0			0
$7$	15.9632	+	9.39028i	0.861930	+	0.507027i
$7$	15.9632	+	9.39028i	0.861930	+	0.507027i
$8$		0			0
$9$	−25.3090	+	9.40505i	−0.937370	+	0.348335i
$10$		0			0
$11$	30.2732	+	17.4782i	0.829791	+	0.479080i	0.853781	−	0.520632i	$-0.174304\pi$
$11$	30.2732	+	17.4782i	0.829791	+	0.479080i	−0.0239903	+	0.999712i	$0.507637\pi$
$12$		0			0
$13$			81.1032i			1.73031i	0.501507	+	0.865154i	$0.332779\pi$
$13$			81.1032i			1.73031i	−0.501507	+	0.865154i	$0.667221\pi$
$14$		0			0
$15$	48.0032	−	40.5555i	0.826292	−	0.698092i
$16$		0			0
$17$	−4.14503	+	7.17941i	−0.0591364	+	0.102427i	−0.894078	−	0.447911i	$-0.852168\pi$
$17$	−4.14503	+	7.17941i	−0.0591364	+	0.102427i	0.834942	+	0.550339i	$0.185501\pi$
$18$		0			0
$19$	−52.7556	+	30.4585i	−0.636998	+	0.367771i	−0.783457	−	0.621446i	$-0.786546\pi$
$19$	−52.7556	+	30.4585i	−0.636998	+	0.367771i	0.146459	+	0.989217i	$0.453212\pi$
$20$		0			0
$21$	−33.3449	+	90.2725i	−0.346498	+	0.938051i
$22$		0			0
$23$	−157.219	+	90.7706i	−1.42533	+	0.822912i	−0.996747	−	0.0805920i	$-0.974319\pi$
$23$	−157.219	+	90.7706i	−1.42533	+	0.822912i	−0.428579	+	0.903504i	$0.640986\pi$
$24$		0			0
$25$	−10.6306	+	18.4128i	−0.0850451	+	0.147302i
$26$		0			0
$27$	−71.3708	−	120.786i	−0.508715	−	0.860935i
$28$		0			0
$29$			75.6434i			0.484366i	0.970231	+	0.242183i	$0.0778635\pi$
$29$			75.6434i			0.484366i	−0.970231	+	0.242183i	$0.922137\pi$
$30$		0			0
$31$	77.3344	+	44.6491i	0.448054	+	0.258684i	0.707008	−	0.707206i	$-0.250044\pi$
$31$	77.3344	+	44.6491i	0.448054	+	0.258684i	−0.258954	+	0.965890i	$0.583378\pi$
$32$		0			0
$33$	−61.5496	+	170.893i	−0.324679	+	0.901473i
$34$		0			0
$35$	1.82179	−	223.974i	0.00879825	−	1.08167i
$36$		0			0
$37$	−58.4106	−	101.170i	−0.259531	−	0.449521i	0.706585	−	0.707628i	$-0.250235\pi$
$37$	−58.4106	−	101.170i	−0.259531	−	0.449521i	−0.966116	+	0.258107i	$0.916901\pi$
$38$		0			0
$39$	−414.774	+	74.5755i	−1.70300	+	0.306196i
$40$		0			0
$41$	147.344			0.561249			0.280625	−	0.959818i	$-0.409458\pi$
$41$	147.344			0.561249			0.280625	+	0.959818i	$0.409458\pi$
$42$		0			0
$43$	389.121			1.38001			0.690005	−	0.723804i	$-0.257608\pi$
$43$	389.121			1.38001			0.690005	+	0.723804i	$0.257608\pi$
$44$		0			0
$45$	251.546	+	208.204i	0.833295	+	0.689716i
$46$		0			0
$47$	99.8765	+	172.991i	0.309968	+	0.536880i	0.978355	−	0.206934i	$-0.0663484\pi$
$47$	99.8765	+	172.991i	0.309968	+	0.536880i	−0.668387	+	0.743814i	$0.733015\pi$
$48$		0			0
$49$	166.645	+	299.797i	0.485846	+	0.874044i
$50$		0			0
$51$	−40.5279	−	14.5967i	−0.111275	−	0.0400775i
$52$		0			0
$53$	578.226	+	333.839i	1.49859	+	0.865214i	0.999999	−	0.00162105i	$-0.000515997\pi$
$53$	578.226	+	333.839i	1.49859	+	0.865214i	0.498595	+	0.866835i	$0.333849\pi$
$54$		0			0
$55$		−	422.758i		−	1.03645i
$56$		0			0
$57$	−204.278	−	241.793i	−0.474690	−	0.561864i
$58$		0			0
$59$	8.54890	−	14.8071i	0.0188639	−	0.0326733i	−0.856439	−	0.516248i	$-0.827328\pi$
$59$	8.54890	−	14.8071i	0.0188639	−	0.0326733i	0.875303	+	0.483574i	$0.160662\pi$
$60$		0			0
$61$	−661.389	+	381.853i	−1.38823	+	0.801497i	−0.993116	−	0.117134i	$-0.962629\pi$
$61$	−661.389	+	381.853i	−1.38823	+	0.801497i	−0.395117	+	0.918631i	$0.629296\pi$
$62$		0			0
$63$	−492.328	−	87.5240i	−0.984563	−	0.175032i
$64$		0			0
$65$	849.442	−	490.425i	1.62093	−	0.935843i
$66$		0			0
$67$	428.169	−	741.610i	0.780733	−	1.35227i	−0.150782	−	0.988567i	$-0.548179\pi$
$67$	428.169	−	741.610i	0.780733	−	1.35227i	0.931515	−	0.363703i	$-0.118488\pi$
$68$		0			0
$69$	−608.780	−	720.578i	−1.06215	−	1.25721i
$70$		0			0
$71$		−	700.045i		−	1.17014i	−0.810982	−	0.585070i	$-0.801067\pi$
$71$		−	700.045i		−	1.17014i	0.810982	−	0.585070i	$-0.198933\pi$
$72$		0			0
$73$	−748.329	−	432.048i	−1.19980	−	0.692704i	−0.239288	−	0.970949i	$-0.576914\pi$
$73$	−748.329	−	432.048i	−1.19980	−	0.692704i	−0.960510	+	0.278245i	$0.910247\pi$
$74$		0			0
$75$	−103.941	−	37.4358i	−0.160027	−	0.0576362i
$76$		0			0
$77$	319.130	+	563.281i	0.472315	+	0.833660i
$78$		0			0
$79$	−463.245	−	802.364i	−0.659736	−	1.14270i	−0.980684	−	0.195600i	$-0.937335\pi$
$79$	−463.245	−	802.364i	−0.659736	−	1.14270i	0.320947	−	0.947097i	$-0.395999\pi$
$80$		0			0
$81$	552.090	−	476.065i	0.757325	−	0.653038i
$82$		0			0
$83$	1053.69			1.39347			0.696734	−	0.717329i	$-0.254636\pi$
$83$	1053.69			1.39347			0.696734	+	0.717329i	$0.254636\pi$
$84$		0			0
$85$	100.259			0.127936
$86$		0			0
$87$	−386.851	+	69.5551i	−0.476722	+	0.0857137i
$88$		0			0
$89$	−224.645	−	389.097i	−0.267554	−	0.463418i	0.700675	−	0.713480i	$-0.252882\pi$
$89$	−224.645	−	389.097i	−0.267554	−	0.463418i	−0.968230	+	0.250063i	$0.919549\pi$
$90$		0			0
$91$	−761.582	+	1294.66i	−0.877313	+	1.49140i
$92$		0			0
$93$	−157.232	+	436.555i	−0.175314	+	0.486760i
$94$		0			0
$95$	638.018	+	368.360i	0.689045	+	0.397820i
$96$		0			0
$97$			213.360i			0.223334i	0.993746	+	0.111667i	$0.0356190\pi$
$97$			213.360i			0.223334i	−0.993746	+	0.111667i	$0.964381\pi$
$98$		0			0
$99$	−930.566	−	157.635i	−0.944701	−	0.160030i
$100$		0			0
$101$	−404.582	+	700.756i	−0.398588	+	0.690375i	−0.993552	−	0.113378i	$-0.963833\pi$
$101$	−404.582	+	700.756i	−0.398588	+	0.690375i	0.594964	+	0.803752i	$0.297166\pi$
$102$		0			0
$103$	855.486	−	493.915i	0.818384	−	0.472494i	−0.0314750	−	0.999505i	$-0.510020\pi$
$103$	855.486	−	493.915i	0.818384	−	0.472494i	0.849859	+	0.527010i	$0.176687\pi$
$104$		0			0
$105$	1147.11	−	196.630i	1.06616	−	0.182754i
$106$		0			0
$107$	502.297	−	290.002i	0.453822	−	0.262014i	−0.255621	−	0.966777i	$-0.582280\pi$
$107$	502.297	−	290.002i	0.453822	−	0.262014i	0.709443	+	0.704763i	$0.248947\pi$
$108$		0			0
$109$	121.714	−	210.814i	0.106955	−	0.185251i	−0.807580	−	0.589757i	$-0.799223\pi$
$109$	121.714	−	210.814i	0.106955	−	0.185251i	0.914535	+	0.404507i	$0.132557\pi$
$110$		0			0
$111$	463.689	−	391.748i	0.396499	−	0.334982i
$112$		0			0
$113$			176.852i			0.147229i	0.997287	+	0.0736143i	$0.0234534\pi$
$113$			176.852i			0.147229i	−0.997287	+	0.0736143i	$0.976547\pi$
$114$		0			0
$115$	1901.39	+	1097.77i	1.54179	+	0.890150i
$116$		0			0
$117$	−762.780	−	2052.64i	−0.602727	−	1.62194i
$118$		0			0
$119$	−133.584	+	75.6830i	−0.102905	+	0.0583013i
$120$		0			0
$121$	−54.5242	−	94.4387i	−0.0409648	−	0.0709532i
$122$		0			0
$123$	135.485	+	753.537i	0.0993190	+	0.552392i
$124$		0			0
$125$	−1254.60			−0.897719
$126$		0			0
$127$	−709.586			−0.495792			−0.247896	−	0.968787i	$-0.579739\pi$
$127$	−709.586			−0.495792			−0.247896	+	0.968787i	$0.579739\pi$
$128$		0			0
$129$	357.802	+	1990.02i	0.244207	+	1.35823i
$130$		0			0
$131$	45.5566	+	78.9063i	0.0303839	+	0.0526265i	0.880818	−	0.473456i	$-0.156994\pi$
$131$	45.5566	+	78.9063i	0.0303839	+	0.0526265i	−0.850434	+	0.526082i	$0.823660\pi$
$132$		0			0
$133$	−1128.16	−	9.17638i	−0.735518	−	0.00598266i
$134$		0			0
$135$	−833.486	+	1477.89i	−0.531371	+	0.942197i
$136$		0			0
$137$	−805.981	−	465.333i	−0.502625	−	0.290191i	0.227172	−	0.973855i	$-0.427052\pi$
$137$	−805.981	−	465.333i	−0.502625	−	0.290191i	−0.729797	+	0.683664i	$0.760385\pi$
$138$		0			0
$139$			1704.57i			1.04014i	0.854124	+	0.520070i	$0.174094\pi$
$139$			1704.57i			1.04014i	−0.854124	+	0.520070i	$0.825906\pi$
$140$		0			0
$141$	−792.865	+	669.851i	−0.473555	+	0.400082i
$142$		0			0
$143$	−1417.54	+	2455.25i	−0.828955	+	1.43579i
$144$		0			0
$145$	792.257	−	457.410i	0.453748	−	0.261971i
$146$		0			0
$147$	−1379.97	+	1127.92i	−0.774274	+	0.632850i
$148$		0			0
$149$	2848.50	−	1644.58i	1.56616	−	0.904225i	0.569555	−	0.821954i	$-0.307116\pi$
$149$	2848.50	−	1644.58i	1.56616	−	0.904225i	0.996610	−	0.0822720i	$-0.0262176\pi$
$150$		0			0
$151$	995.034	−	1723.45i	0.536256	−	0.928823i	−0.462845	−	0.886439i	$-0.653171\pi$
$151$	995.034	−	1723.45i	0.536256	−	0.928823i	0.999101	−	0.0423842i	$-0.0134954\pi$
$152$		0			0
$153$	37.3839	−	220.688i	0.0197536	−	0.116611i
$154$		0			0
$155$		−	1079.96i		−	0.559641i
$156$		0			0
$157$	3247.22	+	1874.78i	1.65068	+	0.953019i	0.976794	+	0.214180i	$0.0687078\pi$
$157$	3247.22	+	1874.78i	1.65068	+	0.953019i	0.673882	+	0.738839i	$0.264626\pi$
$158$		0			0
$159$	−1175.62	+	3264.10i	−0.586367	+	1.62805i
$160$		0			0
$161$	−3362.08	−	27.3470i	−1.64577	−	0.0133866i
$162$		0			0
$163$	83.7914	+	145.131i	0.0402641	+	0.0697395i	0.885455	−	0.464725i	$-0.153847\pi$
$163$	83.7914	+	145.131i	0.0402641	+	0.0697395i	−0.845191	+	0.534464i	$0.820513\pi$
$164$		0			0
$165$	2162.05	−	388.732i	1.02009	−	0.183410i
$166$		0			0
$167$	−676.970			−0.313686			−0.156843	−	0.987624i	$-0.550132\pi$
$167$	−676.970			−0.313686			−0.156843	+	0.987624i	$0.550132\pi$
$168$		0			0
$169$	−4380.74			−1.99396
$170$		0			0
$171$	1048.73	−	1267.04i	0.468995	−	0.566626i
$172$		0			0
$173$	−716.045	−	1240.23i	−0.314682	−	0.545045i	0.664688	−	0.747121i	$-0.268564\pi$
$173$	−716.045	−	1240.23i	−0.314682	−	0.545045i	−0.979370	+	0.202076i	$0.935231\pi$
$174$		0			0
$175$	−342.600	+	194.102i	−0.147989	+	0.0838441i
$176$		0			0
$177$	83.5867	+	30.1050i	0.0354958	+	0.0127843i
$178$		0			0
$179$	2583.90	+	1491.82i	1.07894	+	0.622925i	0.930610	−	0.366013i	$-0.119277\pi$
$179$	2583.90	+	1491.82i	1.07894	+	0.622925i	0.148328	+	0.988938i	$0.452611\pi$
$180$		0			0
$181$			420.728i			0.172776i	0.996262	+	0.0863880i	$0.0275325\pi$
$181$			420.728i			0.172776i	−0.996262	+	0.0863880i	$0.972468\pi$
$182$		0			0
$183$	−2561.01	−	3031.32i	−1.03451	−	1.22449i
$184$		0			0
$185$	−706.409	+	1223.54i	−0.280736	+	0.486250i
$186$		0			0
$187$	−250.966	+	144.896i	−0.0981416	+	0.0566621i
$188$		0			0
$189$	−5.09124	−	2598.32i	−0.00195943	−	0.999998i
$190$		0			0
$191$	−3537.32	+	2042.27i	−1.34006	+	0.773684i	−0.986816	−	0.161847i	$-0.948255\pi$
$191$	−3537.32	+	2042.27i	−1.34006	+	0.773684i	−0.353245	+	0.935531i	$0.614922\pi$
$192$		0			0
$193$	807.596	−	1398.80i	0.301202	−	0.521697i	−0.675206	−	0.737629i	$-0.735945\pi$
$193$	807.596	−	1398.80i	0.301202	−	0.521697i	0.976409	+	0.215931i	$0.0692788\pi$
$194$		0			0
$195$	3289.18	+	3893.22i	1.20791	+	1.42974i
$196$		0			0
$197$		−	596.168i		−	0.215610i	−0.994172	−	0.107805i	$-0.965618\pi$
$197$		−	596.168i		−	0.215610i	0.994172	−	0.107805i	$-0.0343822\pi$
$198$		0			0
$199$	134.161	+	77.4579i	0.0477910	+	0.0275922i	0.523705	−	0.851900i	$-0.324549\pi$
$199$	134.161	+	77.4579i	0.0477910	+	0.0275922i	−0.475914	+	0.879492i	$0.657883\pi$
$200$		0			0
$201$	4186.41	+	1507.80i	1.46909	+	0.529113i
$202$		0			0
$203$	−710.313	+	1207.51i	−0.245587	+	0.417490i
$204$		0			0
$205$	−890.977	−	1543.22i	−0.303554	−	0.525770i
$206$		0			0
$207$	3125.36	−	3775.97i	1.04941	−	1.26786i
$208$		0			0
$209$	−2129.44			−0.704767
$210$		0			0
$211$	2328.06			0.759576			0.379788	−	0.925074i	$-0.375997\pi$
$211$	2328.06			0.759576			0.379788	+	0.925074i	$0.375997\pi$
$212$		0			0
$213$	3580.13	−	643.700i	1.15167	−	0.207069i
$214$		0			0
$215$	−2352.99	−	4075.49i	−0.746383	−	1.29277i
$216$		0			0
$217$	815.235	+	1438.93i	0.255031	+	0.450143i
$218$		0			0
$219$	1521.46	−	4224.34i	0.469455	−	1.30344i
$220$		0			0
$221$	−582.273	−	336.176i	−0.177230	−	0.102324i
$222$		0			0
$223$			1385.14i			0.415945i	0.978135	+	0.207973i	$0.0666865\pi$
$223$			1385.14i			0.415945i	−0.978135	+	0.207973i	$0.933314\pi$
$224$		0			0
$225$	95.8772	−	565.991i	0.0284081	−	0.167701i
$226$		0			0
$227$	605.053	−	1047.98i	0.176911	−	0.306419i	−0.763910	−	0.645323i	$-0.776723\pi$
$227$	605.053	−	1047.98i	0.176911	−	0.306419i	0.940821	+	0.338904i	$0.110056\pi$
$228$		0			0
$229$	−5041.96	+	2910.98i	−1.45494	+	0.840012i	−0.998756	−	0.0498722i	$-0.984119\pi$
$229$	−5041.96	+	2910.98i	−1.45494	+	0.840012i	−0.456187	+	0.889884i	$0.650785\pi$
$230$		0			0
$231$	−2587.26	+	2150.02i	−0.736922	+	0.612386i
$232$		0			0
$233$	1233.80	−	712.335i	0.346905	−	0.200286i	−0.316416	−	0.948620i	$-0.602480\pi$
$233$	1233.80	−	712.335i	0.346905	−	0.200286i	0.663321	+	0.748335i	$0.269146\pi$
$234$		0			0
$235$	1207.89	−	2092.13i	0.335294	−	0.580747i
$236$		0			0
$237$	3677.45	−	3106.89i	1.00792	−	0.851537i
$238$		0			0
$239$		−	1673.51i		−	0.452929i	−0.974019	−	0.226465i	$-0.927283\pi$
$239$		−	1673.51i		−	0.452929i	0.974019	−	0.226465i	$-0.0727168\pi$
$240$		0			0
$241$	1907.97	+	1101.57i	0.509971	+	0.294432i	0.732822	−	0.680421i	$-0.238203\pi$
$241$	1907.97	+	1101.57i	0.509971	+	0.294432i	−0.222851	+	0.974853i	$0.571536\pi$
$242$		0			0
$243$	2942.32	+	2385.72i	0.776749	+	0.629811i
$244$		0			0
$245$	2132.26	−	3558.22i	0.556020	−	0.927864i
$246$		0			0
$247$	−2470.28	−	4278.65i	−0.636357	−	1.10220i
$248$		0			0
$249$	968.886	+	5388.74i	0.246589	+	1.37148i
$250$		0			0
$251$	6110.91			1.53672			0.768361	−	0.640016i	$-0.221072\pi$
$251$	6110.91			1.53672			0.768361	+	0.640016i	$0.221072\pi$
$252$		0			0
$253$	−6346.03			−1.57696
$254$		0			0
$255$	92.1893	+	512.738i	0.0226397	+	0.125917i
$256$		0			0
$257$	586.762	+	1016.30i	0.142417	+	0.246674i	0.928406	−	0.371567i	$-0.121179\pi$
$257$	586.762	+	1016.30i	0.142417	+	0.246674i	−0.785989	+	0.618240i	$0.787846\pi$
$258$		0			0
$259$	17.5977	−	2163.49i	0.00422188	−	0.519044i
$260$		0			0
$261$	−711.430	−	1914.46i	−0.168722	−	0.454030i
$262$		0			0
$263$	−2283.56	−	1318.41i	−0.535400	−	0.309113i	0.207813	−	0.978169i	$-0.433366\pi$
$263$	−2283.56	−	1318.41i	−0.535400	−	0.309113i	−0.743212	+	0.669055i	$0.766699\pi$
$264$		0			0
$265$		−	8074.80i		−	1.87182i
$266$		0			0
$267$	1783.33	−	1506.65i	0.408757	−	0.345338i
$268$		0			0
$269$	−3876.21	+	6713.78i	−0.878574	+	1.52173i	−0.0256678	+	0.999671i	$0.508171\pi$
$269$	−3876.21	+	6713.78i	−0.878574	+	1.52173i	−0.852906	+	0.522064i	$0.825162\pi$
$270$		0			0
$271$	3512.22	−	2027.78i	0.787277	−	0.454535i	−0.0517260	−	0.998661i	$-0.516472\pi$
$271$	3512.22	−	2027.78i	0.787277	−	0.454535i	0.839003	+	0.544127i	$0.183139\pi$
$272$		0			0
$273$	−7321.39	−	2704.38i	−1.62312	−	0.599548i
$274$		0			0
$275$	−643.646	+	371.609i	−0.141139	+	0.0814868i
$276$		0			0
$277$	576.130	−	997.886i	0.124968	−	0.216452i	−0.796752	−	0.604306i	$-0.793450\pi$
$277$	576.130	−	997.886i	0.124968	−	0.216452i	0.921721	+	0.387854i	$0.126784\pi$
$278$		0			0
$279$	−2377.18	−	402.688i	−0.510101	−	0.0864097i
$280$		0			0
$281$			1042.40i			0.221296i	0.993860	+	0.110648i	$0.0352926\pi$
$281$			1042.40i			0.221296i	−0.993860	+	0.110648i	$0.964707\pi$
$282$		0			0
$283$	−1873.40	−	1081.61i	−0.393506	−	0.227191i	0.290172	−	0.956975i	$-0.406288\pi$
$283$	−1873.40	−	1081.61i	−0.393506	−	0.227191i	−0.683678	+	0.729783i	$0.739621\pi$
$284$		0			0
$285$	−1297.18	+	3601.63i	−0.269608	+	0.748569i
$286$		0			0
$287$	2352.07	+	1383.60i	0.483758	+	0.284569i
$288$		0			0
$289$	2422.14	+	4195.27i	0.493006	+	0.853911i
$290$		0			0
$291$	−1091.15	+	196.187i	−0.219810	+	0.0395213i
$292$		0			0
$293$	−5371.61			−1.07103			−0.535517	−	0.844525i	$-0.679883\pi$
$293$	−5371.61			−1.07103			−0.535517	+	0.844525i	$0.679883\pi$
$294$		0			0
$295$	−206.778			−0.0408105
$296$		0			0
$297$	−49.4987	−	4904.00i	−0.00967073	−	0.958111i
$298$		0			0
$299$	−7361.79	−	12751.0i	−1.42389	−	2.46625i
$300$		0			0
$301$	6211.61	+	3653.96i	1.18947	+	0.699703i
$302$		0			0
$303$	−3955.79	−	1424.74i	−0.750014	−	0.270129i
$304$		0			0
$305$	7998.74	+	4618.08i	1.50166	+	0.866985i
$306$		0			0
$307$		−	3027.33i		−	0.562797i	−0.959591	−	0.281399i	$-0.909202\pi$
$307$		−	3027.33i		−	0.562797i	0.959591	−	0.281399i	$-0.0907983\pi$
$308$		0			0
$309$	3312.58	+	3920.92i	0.609859	+	0.721855i
$310$		0			0
$311$	−4481.30	+	7761.84i	−0.817078	+	1.41522i	0.0907478	+	0.995874i	$0.471074\pi$
$311$	−4481.30	+	7761.84i	−0.817078	+	1.41522i	−0.907826	+	0.419347i	$0.862259\pi$
$312$		0			0
$313$	1548.33	−	893.927i	0.279606	−	0.161431i	−0.353639	−	0.935382i	$-0.615056\pi$
$313$	1548.33	−	893.927i	0.279606	−	0.161431i	0.633245	+	0.773951i	$0.281723\pi$
$314$		0			0
$315$	2060.38	+	5685.69i	0.368537	+	1.01699i
$316$		0			0
$317$	5728.18	−	3307.17i	1.01491	−	0.585959i	0.102285	−	0.994755i	$-0.467385\pi$
$317$	5728.18	−	3307.17i	1.01491	−	0.585959i	0.912626	+	0.408796i	$0.134051\pi$
$318$		0			0
$319$	−1322.11	+	2289.96i	−0.232050	+	0.401923i
$320$		0			0
$321$	1944.98	+	2302.16i	0.338187	+	0.400293i
$322$		0			0
$323$		−	505.005i		−	0.0869945i
$324$		0			0
$325$	−1493.34	−	862.179i	−0.254878	−	0.147154i
$326$		0			0
$327$	1190.05	+	428.615i	0.201254	+	0.0724846i
$328$		0			0
$329$	−30.0903	+	3699.36i	−0.00504235	+	0.619915i
$330$		0			0
$331$	3731.74	+	6463.57i	0.619684	+	1.07332i	0.989543	+	0.144236i	$0.0460724\pi$
$331$	3731.74	+	6463.57i	0.619684	+	1.07332i	−0.369860	+	0.929088i	$0.620594\pi$
$332$		0			0
$333$	2429.82	+	2011.16i	0.399860	+	0.330963i
$334$		0			0
$335$	−10356.4			−1.68905
$336$		0			0
$337$	589.545			0.0952954			0.0476477	−	0.998864i	$-0.484828\pi$
$337$	589.545			0.0952954			0.0476477	+	0.998864i	$0.484828\pi$
$338$		0			0
$339$	−904.447	+	162.618i	−0.144905	+	0.0260536i
$340$		0			0
$341$	1560.77	+	2703.34i	0.247861	+	0.429307i
$342$		0			0
$343$	−154.993	+	6350.56i	−0.0243989	+	0.999702i
$344$		0			0
$345$	−3865.79	+	10733.4i	−0.603267	+	1.67497i
$346$		0			0
$347$	−8535.10	−	4927.74i	−1.32043	−	0.762349i	−0.336631	−	0.941637i	$-0.609287\pi$
$347$	−8535.10	−	4927.74i	−1.32043	−	0.762349i	−0.983797	+	0.179288i	$0.942621\pi$
$348$		0			0
$349$			3853.61i			0.591057i	0.955334	+	0.295528i	$0.0954957\pi$
$349$			3853.61i			0.591057i	−0.955334	+	0.295528i	$0.904504\pi$
$350$		0			0
$351$	9796.12	−	5788.40i	1.48968	−	0.880234i
$352$		0			0
$353$	5226.31	−	9052.23i	0.788012	−	1.36488i	−0.139171	−	0.990268i	$-0.544444\pi$
$353$	5226.31	−	9052.23i	0.788012	−	1.36488i	0.927183	−	0.374608i	$-0.122223\pi$
$354$		0			0
$355$	−7331.97	+	4233.12i	−1.09617	+	0.632875i
$356$		0			0
$357$	−509.887	−	613.579i	−0.0755912	−	0.0909637i
$358$		0			0
$359$	9947.70	−	5743.31i	1.46245	−	0.844346i	0.463326	−	0.886188i	$-0.346656\pi$
$359$	9947.70	−	5743.31i	1.46245	−	0.844346i	0.999124	+	0.0418417i	$0.0133225\pi$
$360$		0			0
$361$	−1574.06	+	2726.36i	−0.229489	+	0.397487i
$362$		0			0
$363$	432.838	−	365.682i	0.0625842	−	0.0528742i
$364$		0			0
$365$			10450.2i			1.49861i
$366$		0			0
$367$	1546.71	+	892.995i	0.219994	+	0.127014i	0.605947	−	0.795505i	$-0.292794\pi$
$367$	1546.71	+	892.995i	0.219994	+	0.127014i	−0.385953	+	0.922518i	$0.626127\pi$
$368$		0			0
$369$	−3729.12	+	1385.78i	−0.526098	+	0.195503i
$370$		0			0
$371$	6095.48	+	10758.8i	0.852996	+	1.50558i
$372$		0			0
$373$	5796.80	+	10040.4i	0.804683	+	1.39375i	0.916505	+	0.400024i	$0.130998\pi$
$373$	5796.80	+	10040.4i	0.804683	+	1.39375i	−0.111821	+	0.993728i	$0.535668\pi$
$374$		0			0
$375$	−1153.62	−	6416.21i	−0.158861	−	0.883552i
$376$		0			0
$377$	−6134.92			−0.838103
$378$		0			0
$379$	7025.12			0.952128			0.476064	−	0.879411i	$-0.342063\pi$
$379$	7025.12			0.952128			0.476064	+	0.879411i	$0.342063\pi$
$380$		0			0
$381$	−652.474	−	3628.93i	−0.0877356	−	0.487968i
$382$		0			0
$383$	4735.12	+	8201.47i	0.631732	+	1.09419i	0.987197	+	0.159503i	$0.0509891\pi$
$383$	4735.12	+	8201.47i	0.631732	+	1.09419i	−0.355465	+	0.934689i	$0.615678\pi$
$384$		0			0
$385$	3969.81	−	6748.55i	0.525508	−	0.893346i
$386$		0			0
$387$	−9848.27	+	3659.71i	−1.29358	+	0.480706i
$388$		0			0
$389$	−12106.3	−	6989.56i	−1.57792	−	0.911015i	−0.995149	−	0.0983806i	$-0.968634\pi$
$389$	−12106.3	−	6989.56i	−1.57792	−	0.911015i	−0.582775	−	0.812634i	$-0.698033\pi$
$390$		0			0
$391$		−	1504.99i		−	0.194656i
$392$		0			0
$393$	−361.648	+	305.538i	−0.0464192	+	0.0392172i
$394$		0			0
$395$	−5602.42	+	9703.68i	−0.713641	+	1.23606i
$396$		0			0
$397$	453.470	−	261.811i	0.0573274	−	0.0330980i	−0.471062	−	0.882100i	$-0.656129\pi$
$397$	453.470	−	261.811i	0.0573274	−	0.0330980i	0.528390	+	0.849002i	$0.322796\pi$
$398$		0			0
$399$	−990.429	−	5778.01i	−0.124269	−	0.724968i
$400$		0			0
$401$	4171.52	−	2408.43i	0.519491	−	0.299928i	−0.217235	−	0.976119i	$-0.569704\pi$
$401$	4171.52	−	2408.43i	0.519491	−	0.299928i	0.736726	+	0.676191i	$0.236371\pi$
$402$		0			0
$403$	−3621.18	+	6272.07i	−0.447603	+	0.775271i
$404$		0			0
$405$	−8324.55	−	2903.63i	−1.02136	−	0.356253i
$406$		0			0
$407$		−	4083.65i		−	0.497344i
$408$		0			0
$409$	−10923.1	−	6306.47i	−1.32057	−	0.762432i	−0.336751	−	0.941594i	$-0.609328\pi$
$409$	−10923.1	−	6306.47i	−1.32057	−	0.762432i	−0.983820	+	0.179161i	$0.942662\pi$
$410$		0			0
$411$	1638.67	−	4549.78i	0.196666	−	0.546045i
$412$		0			0
$413$	275.511	−	156.092i	0.0328256	−	0.0185976i
$414$		0			0
$415$	−6371.61	−	11036.0i	−0.753663	−	1.30538i
$416$		0			0
$417$	−8717.40	+	1567.37i	−1.02372	+	0.184064i
$418$		0			0
$419$	16375.7			1.90932			0.954659	−	0.297701i	$-0.0962198\pi$
$419$	16375.7			1.90932			0.954659	+	0.297701i	$0.0962198\pi$
$420$		0			0
$421$	6148.10			0.711734			0.355867	−	0.934537i	$-0.384186\pi$
$421$	6148.10			0.711734			0.355867	+	0.934537i	$0.384186\pi$
$422$		0			0
$423$	−4154.77	−	3438.89i	−0.477569	−	0.395282i
$424$		0			0
$425$	−88.1286	−	152.643i	−0.0100585	−	0.0174219i
$426$		0			0
$427$	−14143.6	−	115.043i	−1.60294	−	0.0130382i
$428$		0			0
$429$	−13860.0	−	4991.87i	−1.55983	−	0.561794i
$430$		0			0
$431$	5503.76	+	3177.60i	0.615097	+	0.355127i	0.774958	−	0.632013i	$-0.217771\pi$
$431$	5503.76	+	3177.60i	0.615097	+	0.355127i	−0.159861	+	0.987140i	$0.551104\pi$
$432$		0			0
$433$		−	11089.9i		−	1.23083i	−0.788204	−	0.615414i	$-0.788989\pi$
$433$		−	11089.9i		−	1.23083i	0.788204	−	0.615414i	$-0.211011\pi$
$434$		0			0
$435$	3067.75	+	3631.13i	0.338132	+	0.400228i
$436$		0			0
$437$	5529.47	−	9577.32i	0.605287	−	1.04839i
$438$		0			0
$439$	−389.043	+	224.614i	−0.0422962	+	0.0244197i	−0.520999	−	0.853557i	$-0.674440\pi$
$439$	−389.043	+	224.614i	−0.0422962	+	0.0244197i	0.478703	+	0.877977i	$0.341107\pi$
$440$		0			0
$441$	−7037.23	−	6020.26i	−0.759878	−	0.650065i
$442$		0			0
$443$	6182.74	−	3569.61i	0.663094	−	0.382838i	−0.130361	−	0.991467i	$-0.541614\pi$
$443$	6182.74	−	3569.61i	0.663094	−	0.382838i	0.793455	+	0.608629i	$0.208280\pi$
$444$		0			0
$445$	−2716.82	+	4705.68i	−0.289415	+	0.501282i
$446$		0			0
$447$	11029.9	+	13055.4i	1.16710	+	1.38144i
$448$		0			0
$449$		−	2229.59i		−	0.234345i	−0.993112	−	0.117172i	$-0.962617\pi$
$449$		−	2229.59i		−	0.234345i	0.993112	−	0.117172i	$-0.0373830\pi$
$450$		0			0
$451$	4460.56	+	2575.31i	0.465720	+	0.268883i
$452$		0			0
$453$	9728.92	+	3504.01i	1.00906	+	0.363428i
$454$		0			0
$455$	18165.0	+	147.753i	1.87162	+	0.0152237i
$456$		0			0
$457$	−173.693	−	300.845i	−0.0177790	−	0.0307942i	0.856999	−	0.515318i	$-0.172326\pi$
$457$	−173.693	−	300.845i	−0.0177790	−	0.0307942i	−0.874778	+	0.484524i	$0.838993\pi$
$458$		0			0
$459$	1163.00	−	11.7388i	0.118267	−	0.00119373i
$460$		0			0
$461$	499.529			0.0504672			0.0252336	−	0.999682i	$-0.491967\pi$
$461$	499.529			0.0504672			0.0252336	+	0.999682i	$0.491967\pi$
$462$		0			0
$463$	2521.67			0.253114			0.126557	−	0.991959i	$-0.459607\pi$
$463$	2521.67			0.253114			0.126557	+	0.991959i	$0.459607\pi$
$464$		0			0
$465$	5523.06	−	993.036i	0.550809	−	0.0990343i
$466$		0			0
$467$	−1963.45	−	3400.79i	−0.194556	−	0.336980i	0.752199	−	0.658936i	$-0.228993\pi$
$467$	−1963.45	−	3400.79i	−0.194556	−	0.336980i	−0.946755	+	0.321956i	$0.895660\pi$
$468$		0			0
$469$	13798.9	−	7817.82i	1.35858	−	0.769709i
$470$		0			0
$471$	−6602.05	+	18330.6i	−0.645873	+	1.79327i
$472$		0			0
$473$	11779.9	+	6801.15i	1.14512	+	0.661135i
$474$		0			0
$475$		−	1295.17i		−	0.125108i
$476$		0			0
$477$	−17774.1	−	3010.88i	−1.70612	−	0.289012i
$478$		0			0
$479$	5680.39	−	9838.73i	0.541845	−	0.938503i	−0.456953	−	0.889491i	$-0.651059\pi$
$479$	5680.39	−	9838.73i	0.541845	−	0.938503i	0.998798	−	0.0490121i	$-0.0156073\pi$
$480$		0			0
$481$	8205.22	−	4737.29i	0.777809	−	0.449068i
$482$		0			0
$483$	−2951.62	−	17219.3i	−0.278061	−	1.62217i
$484$		0			0
$485$	2234.64	−	1290.17i	0.209216	−	0.120791i
$486$		0			0
$487$	−9543.14	+	16529.2i	−0.887969	+	1.53801i	−0.0456972	+	0.998955i	$0.514551\pi$
$487$	−9543.14	+	16529.2i	−0.887969	+	1.53801i	−0.842272	+	0.539053i	$0.818782\pi$
$488$		0			0
$489$	−665.174	+	561.972i	−0.0615137	+	0.0519698i
$490$		0			0
$491$			16255.8i			1.49412i	0.664756	+	0.747060i	$0.268535\pi$
$491$			16255.8i			1.49412i	−0.664756	+	0.747060i	$0.731465\pi$
$492$		0			0
$493$	−543.075	−	313.544i	−0.0496123	−	0.0286437i
$494$		0			0
$495$	3976.06	+	10699.6i	0.361032	+	0.971535i
$496$		0			0
$497$	6573.61	−	11174.9i	0.593294	−	1.00858i
$498$		0			0
$499$	−5281.57	−	9147.95i	−0.473819	−	0.820679i	0.525732	−	0.850650i	$-0.323792\pi$
$499$	−5281.57	−	9147.95i	−0.473819	−	0.820679i	−0.999551	+	0.0299718i	$0.990458\pi$
$500$		0			0
$501$	−622.483	−	3462.12i	−0.0555099	−	0.308735i
$502$		0			0
$503$	2625.85			0.232766			0.116383	−	0.993204i	$-0.462870\pi$
$503$	2625.85			0.232766			0.116383	+	0.993204i	$0.462870\pi$
$504$		0			0
$505$	9785.91			0.862311
$506$		0			0
$507$	−4028.15	−	22403.7i	−0.352853	−	1.96249i
$508$		0			0
$509$	−3951.26	−	6843.79i	−0.344080	−	0.595964i	0.641106	−	0.767452i	$-0.278476\pi$
$509$	−3951.26	−	6843.79i	−0.344080	−	0.595964i	−0.985186	+	0.171488i	$0.945142\pi$
$510$		0			0
$511$	−7888.65	−	13923.9i	−0.682922	−	1.20539i
$512$		0			0
$513$	7444.16	+	4198.28i	0.640678	+	0.361323i
$514$		0			0
$515$	−10346.1	−	5973.34i	−0.885252	−	0.511100i
$516$		0			0
$517$			6982.65i			0.593997i
$518$		0			0
$519$	5684.29	−	4802.37i	0.480756	−	0.406167i
$520$		0			0
$521$	−4428.45	+	7670.29i	−0.372387	+	0.644993i	−0.989932	−	0.141542i	$-0.954794\pi$
$521$	−4428.45	+	7670.29i	−0.372387	+	0.644993i	0.617545	+	0.786535i	$0.288127\pi$
$522$		0			0
$523$	7370.81	−	4255.54i	0.616258	−	0.355797i	−0.159152	−	0.987254i	$-0.550876\pi$
$523$	7370.81	−	4255.54i	0.616258	−	0.355797i	0.775411	+	0.631457i	$0.217543\pi$
$524$		0			0
$525$	−1307.69	−	1573.63i	−0.108709	−	0.130817i
$526$		0			0
$527$	−641.107	+	370.144i	−0.0529926	+	0.0305953i
$528$		0			0
$529$	10395.1	−	18004.9i	0.854370	−	1.47981i
$530$		0			0
$531$	−77.1022	+	455.156i	−0.00630122	+	0.0371979i
$532$		0			0
$533$			11950.1i			0.971134i
$534$		0			0
$535$	−6074.71	−	3507.24i	−0.490902	−	0.283422i
$536$		0			0
$537$	−5253.44	+	14586.2i	−0.422165	+	1.17214i
$538$		0			0
$539$	−195.040	+	11988.5i	−0.0155862	+	0.958033i
$540$		0			0
$541$	−3515.29	−	6088.65i	−0.279360	−	0.483866i	0.691866	−	0.722026i	$-0.256789\pi$
$541$	−3515.29	−	6088.65i	−0.279360	−	0.483866i	−0.971226	+	0.238160i	$0.923456\pi$
$542$		0			0
$543$	−2151.66	+	386.865i	−0.170049	+	0.0305745i
$544$		0			0
$545$	−2943.97			−0.231387
$546$		0			0
$547$	−13482.4			−1.05387			−0.526935	−	0.849905i	$-0.676659\pi$
$547$	−13482.4			−1.05387			−0.526935	+	0.849905i	$0.676659\pi$
$548$		0			0
$549$	13147.7	−	15884.7i	1.02210	−	1.23487i
$550$		0			0
$551$	−2303.98	−	3990.61i	−0.178136	−	0.308540i
$552$		0			0
$553$	139.564	−	17158.3i	0.0107322	−	1.31943i
$554$		0			0
$555$	−6906.90	−	2487.62i	−0.528255	−	0.190259i
$556$		0			0
$557$	−1711.26	−	987.995i	−0.130177	−	0.0751575i	0.433498	−	0.901155i	$-0.357279\pi$
$557$	−1711.26	−	987.995i	−0.130177	−	0.0751575i	−0.563674	+	0.825997i	$0.690613\pi$
$558$		0			0
$559$			31559.0i			2.38784i
$560$		0			0
$561$	−971.784	−	1150.25i	−0.0731350	−	0.0865658i
$562$		0			0
$563$	3293.90	−	5705.20i	0.246574	−	0.427079i	−0.715999	−	0.698101i	$-0.754028\pi$
$563$	3293.90	−	5705.20i	0.246574	−	0.427079i	0.962573	+	0.271022i	$0.0873618\pi$
$564$		0			0
$565$	1852.27	−	1069.41i	0.137922	−	0.0796291i
$566$		0			0
$567$	13283.5	−	2415.22i	0.983869	−	0.178889i
$568$		0			0
$569$	−1886.69	+	1089.28i	−0.139006	+	0.0802549i	−0.567890	−	0.823104i	$-0.692240\pi$
$569$	−1886.69	+	1089.28i	−0.139006	+	0.0802549i	0.428884	+	0.903359i	$0.358907\pi$
$570$		0			0
$571$	35.0470	−	60.7032i	0.00256860	−	0.00444895i	−0.864738	−	0.502223i	$-0.832516\pi$
$571$	35.0470	−	60.7032i	0.00256860	−	0.00444895i	0.867307	+	0.497774i	$0.165849\pi$
$572$		0			0
$573$	−13697.1	−	16212.5i	−0.998612	−	1.18200i
$574$		0			0
$575$		−	3859.80i		−	0.279939i
$576$		0			0
$577$	−12250.2	−	7072.64i	−0.883850	−	0.510291i	−0.0119244	−	0.999929i	$-0.503796\pi$
$577$	−12250.2	−	7072.64i	−0.883850	−	0.510291i	−0.871926	+	0.489638i	$0.837129\pi$
$578$		0			0
$579$	7896.25	+	2843.95i	0.566765	+	0.204129i
$580$		0			0
$581$	16820.3	+	9894.48i	1.20107	+	0.706527i
$582$		0			0
$583$	11669.8	+	20212.7i	0.829013	+	1.43589i
$584$		0			0
$585$	−16886.0	+	20401.2i	−1.19342	+	1.44186i
$586$		0			0
$587$	−8833.09			−0.621091			−0.310546	−	0.950558i	$-0.600512\pi$
$587$	−8833.09			−0.621091			−0.310546	+	0.950558i	$0.600512\pi$
$588$		0			0
$589$	−5439.77			−0.380546
$590$		0			0
$591$	3048.89	−	548.184i	0.212207	−	0.0381545i
$592$		0			0
$593$	−11738.8	−	20332.2i	−0.812910	−	1.40800i	−0.910819	−	0.412806i	$-0.864549\pi$
$593$	−11738.8	−	20332.2i	−0.812910	−	1.40800i	0.0979090	−	0.995195i	$-0.468785\pi$
$594$		0			0
$595$	1600.45	+	941.458i	0.110272	+	0.0648673i
$596$		0			0
$597$	−272.768	+	757.342i	−0.0186996	+	0.0519195i
$598$		0			0
$599$	−2426.76	−	1401.09i	−0.165534	−	0.0955710i	0.414944	−	0.909847i	$-0.363801\pi$
$599$	−2426.76	−	1401.09i	−0.165534	−	0.0955710i	−0.580478	+	0.814276i	$0.697134\pi$
$600$		0			0
$601$			24832.3i			1.68541i	0.538376	+	0.842705i	$0.319038\pi$
$601$			24832.3i			1.68541i	−0.538376	+	0.842705i	$0.680962\pi$
$602$		0			0
$603$	−3861.64	+	22796.4i	−0.260793	+	1.53953i
$604$		0			0
$605$	−659.408	+	1142.13i	−0.0443120	+	0.0767506i
$606$		0			0
$607$	7023.78	−	4055.18i	0.469665	−	0.271161i	−0.246435	−	0.969159i	$-0.579259\pi$
$607$	7023.78	−	4055.18i	0.469665	−	0.271161i	0.716099	+	0.697998i	$0.245926\pi$
$608$		0			0
$609$	−6828.51	−	2522.32i	−0.454360	−	0.167832i
$610$		0			0
$611$	−14030.1	+	8100.31i	−0.928967	+	0.536340i
$612$		0			0
$613$	−7061.93	+	12231.6i	−0.465300	+	0.805923i	−0.999215	−	0.0396154i	$-0.987387\pi$
$613$	−7061.93	+	12231.6i	−0.465300	+	0.805923i	0.533915	+	0.845538i	$0.320720\pi$
$614$		0			0
$615$	7072.97	−	5975.59i	0.463756	−	0.391804i
$616$		0			0
$617$			22028.2i			1.43731i	0.695364	+	0.718657i	$0.255243\pi$
$617$			22028.2i			1.43731i	−0.695364	+	0.718657i	$0.744757\pi$
$618$		0			0
$619$	−10812.4	−	6242.54i	−0.702080	−	0.405346i	0.106042	−	0.994362i	$-0.466182\pi$
$619$	−10812.4	−	6242.54i	−0.702080	−	0.405346i	−0.808121	+	0.589016i	$0.799516\pi$
$620$		0			0
$621$	22184.7	+	12511.5i	1.43356	+	0.808485i
$622$		0			0
$623$	67.6800	−	8320.69i	0.00435240	−	0.535091i
$624$		0			0
$625$	8915.31	+	15441.8i	0.570580	+	0.988273i
$626$		0			0
$627$	−1958.05	−	10890.3i	−0.124716	−	0.693644i
$628$		0			0
$629$	968.455			0.0613908
$630$		0			0
$631$	15068.0			0.950630			0.475315	−	0.879816i	$-0.342334\pi$
$631$	15068.0			0.950630			0.475315	+	0.879816i	$0.342334\pi$
$632$		0			0
$633$	2140.69	+	11906.1i	0.134415	+	0.747588i
$634$		0			0
$635$	4290.82	+	7431.91i	0.268151	+	0.464451i
$636$		0			0
$637$	−24314.5	+	13515.5i	−1.51236	+	0.840663i
$638$		0			0
$639$	6583.96	+	17717.4i	0.407601	+	1.09685i
$640$		0			0
$641$	−23791.9	−	13736.2i	−1.46603	−	0.846411i	−0.466748	−	0.884391i	$-0.654574\pi$
$641$	−23791.9	−	13736.2i	−1.46603	−	0.846411i	−0.999278	+	0.0379800i	$0.987908\pi$
$642$		0			0
$643$		−	4302.73i		−	0.263893i	−0.991257	−	0.131946i	$-0.957877\pi$
$643$		−	4302.73i		−	0.263893i	0.991257	−	0.131946i	$-0.0421227\pi$
$644$		0			0
$645$	18679.1	−	15781.0i	1.14029	−	0.963374i
$646$		0			0
$647$	−713.937	+	1236.58i	−0.0433814	+	0.0751388i	−0.886901	−	0.461960i	$-0.847146\pi$
$647$	−713.937	+	1236.58i	−0.0433814	+	0.0751388i	0.843519	+	0.537099i	$0.180480\pi$
$648$		0			0
$649$	517.604	−	298.839i	0.0313062	−	0.0180747i
$650$		0			0
$651$	−6609.29	+	5492.35i	−0.397909	+	0.330664i
$652$		0			0
$653$	6918.20	−	3994.22i	0.414594	−	0.239366i	−0.278168	−	0.960533i	$-0.589727\pi$
$653$	6918.20	−	3994.22i	0.414594	−	0.239366i	0.692762	+	0.721167i	$0.256394\pi$
$654$		0			0
$655$	550.954	−	954.281i	0.0328665	−	0.0569265i
$656$		0			0
$657$	23002.9	+	3896.62i	1.36595	+	0.231388i
$658$		0			0
$659$		−	22182.4i		−	1.31123i	−0.755094	−	0.655616i	$-0.772409\pi$
$659$		−	22182.4i		−	1.31123i	0.755094	−	0.655616i	$-0.227591\pi$
$660$		0			0
$661$	16557.2	+	9559.29i	0.974280	+	0.562501i	0.900538	−	0.434776i	$-0.143173\pi$
$661$	16557.2	+	9559.29i	0.974280	+	0.562501i	0.0737417	+	0.997277i	$0.476506\pi$
$662$		0			0
$663$	1183.84	−	3286.95i	0.0693464	−	0.192541i
$664$		0			0
$665$	6725.79	+	11871.4i	0.392203	+	0.692258i
$666$		0			0
$667$	−6866.20	−	11892.6i	−0.398591	−	0.690380i
$668$		0			0
$669$	−7083.80	+	1273.65i	−0.409381	+	0.0736058i
$670$		0			0
$671$	−26696.4			−1.53592
$672$		0			0
$673$	13725.7			0.786164			0.393082	−	0.919503i	$-0.371409\pi$
$673$	13725.7			0.786164			0.393082	+	0.919503i	$0.371409\pi$
$674$		0			0
$675$	2982.72	−	30.1062i	0.170081	−	0.00171672i
$676$		0			0
$677$	−14678.4	−	25423.8i	−0.833292	−	1.44330i	−0.895414	−	0.445235i	$-0.853120\pi$
$677$	−14678.4	−	25423.8i	−0.833292	−	1.44330i	0.0621223	−	0.998069i	$-0.480213\pi$
$678$		0			0
$679$	−2003.51	+	3405.90i	−0.113237	+	0.192498i
$680$		0			0
$681$	5915.89	+	2130.69i	0.332889	+	0.119895i
$682$		0			0
$683$	−18237.7	−	10529.5i	−1.02173	−	0.589899i	−0.107129	−	0.994245i	$-0.534166\pi$
$683$	−18237.7	−	10529.5i	−1.02173	−	0.589899i	−0.914606	+	0.404346i	$0.867499\pi$
$684$		0			0
$685$			11255.3i			0.627802i
$686$		0			0
$687$	−19523.3	−	23108.6i	−1.08422	−	1.28333i
$688$		0			0
$689$	−27075.4	+	46896.0i	−1.49709	+	2.59303i
$690$		0			0
$691$	10470.0	−	6044.86i	0.576408	−	0.332789i	−0.183297	−	0.983058i	$-0.558677\pi$
$691$	10470.0	−	6044.86i	0.576408	−	0.332789i	0.759705	+	0.650268i	$0.225344\pi$
$692$		0			0
$693$	−13374.5	−	11254.6i	−0.733127	−	0.616924i
$694$		0			0
$695$	17852.9	−	10307.4i	0.974388	−	0.562563i
$696$		0			0
$697$	−610.745	+	1057.84i	−0.0331902	+	0.0574872i
$698$		0			0
$699$	4777.48	+	5654.83i	0.258513	+	0.305988i
$700$		0			0
$701$			26152.8i			1.40910i	0.709655	+	0.704549i	$0.248851\pi$
$701$			26152.8i			1.40910i	−0.709655	+	0.704549i	$0.751149\pi$
$702$		0			0
$703$	6162.97	+	3558.19i	0.330641	+	0.190896i
$704$		0			0
$705$	11810.1	+	4253.59i	0.630915	+	0.227233i
$706$		0			0
$707$	−13038.7	+	7387.15i	−0.693594	+	0.392960i
$708$		0			0
$709$	7450.21	+	12904.1i	0.394638	+	0.683533i	0.993055	−	0.117652i	$-0.0375367\pi$
$709$	7450.21	+	12904.1i	0.394638	+	0.683533i	−0.598417	+	0.801185i	$0.704203\pi$
$710$		0			0
$711$	19270.6	+	15950.2i	1.01646	+	0.841320i
$712$		0			0
$713$	−16211.3			−0.851497
$714$		0			0
$715$	34287.0			1.79337
$716$		0			0
$717$	8558.55	−	1538.81i	0.445781	−	0.0801506i
$718$		0			0
$719$	4510.47	+	7812.37i	0.233953	+	0.405219i	0.958968	−	0.283515i	$-0.0915004\pi$
$719$	4510.47	+	7812.37i	0.233953	+	0.405219i	−0.725015	+	0.688733i	$0.758167\pi$
$720$		0			0
$721$	18294.3	+	148.804i	0.944957	+	0.00768622i
$722$		0			0
$723$	−3879.17	+	10770.5i	−0.199540	+	0.554025i
$724$		0			0
$725$	−1392.81	−	804.137i	−0.0713483	−	0.0411930i
$726$		0			0
$727$		−	32781.8i		−	1.67236i	−0.548452	−	0.836182i	$-0.684783\pi$
$727$		−	32781.8i		−	1.67236i	0.548452	−	0.836182i	$-0.315217\pi$
$728$		0			0
$729$	−9495.42	+	17241.2i	−0.482417	+	0.875941i
$730$		0			0
$731$	−1612.92	+	2793.66i	−0.0816088	+	0.141351i
$732$		0			0
$733$	−16798.2	+	9698.47i	−0.846463	+	0.488706i	−0.859456	−	0.511210i	$-0.829197\pi$
$733$	−16798.2	+	9698.47i	−0.846463	+	0.488706i	0.0129930	+	0.999916i	$0.495864\pi$
$734$		0			0
$735$	20157.9	+	7632.85i	1.01161	+	0.383050i
$736$		0			0
$737$	25924.0	−	14967.2i	1.29569	−	0.748067i
$738$		0			0
$739$	1168.95	−	2024.68i	0.0581875	−	0.100784i	−0.835464	−	0.549545i	$-0.814801\pi$
$739$	1168.95	−	2024.68i	0.0581875	−	0.100784i	0.893652	+	0.448761i	$0.148135\pi$
$740$		0			0
$741$	19610.2	−	16567.6i	0.972197	−	0.821360i
$742$		0			0
$743$			10849.6i			0.535711i	0.963459	+	0.267856i	$0.0863150\pi$
$743$			10849.6i			0.535711i	−0.963459	+	0.267856i	$0.913685\pi$
$744$		0			0
$745$	−34449.4	−	19889.4i	−1.69413	−	0.978107i
$746$		0			0
$747$	−26667.9	+	9910.05i	−1.30620	+	0.485395i
$748$		0			0
$749$	10741.5	+	87.3703i	0.524011	+	0.00426227i
$750$		0			0
$751$	−680.252	−	1178.23i	−0.0330529	−	0.0572494i	0.849026	−	0.528351i	$-0.177190\pi$
$751$	−680.252	−	1178.23i	−0.0330529	−	0.0572494i	−0.882079	+	0.471102i	$0.843856\pi$
$752$		0			0
$753$	5619.07	+	31252.1i	0.271939	+	1.51247i
$754$		0			0
$755$	−24067.6			−1.16014
$756$		0			0
$757$	−30917.4			−1.48443			−0.742214	−	0.670163i	$-0.766224\pi$
$757$	−30917.4			−1.48443			−0.742214	+	0.670163i	$0.766224\pi$
$758$		0			0
$759$	−5835.26	−	32454.5i	−0.279060	−	1.55208i
$760$		0			0
$761$	−5386.71	−	9330.06i	−0.256594	−	0.444434i	0.708733	−	0.705477i	$-0.249267\pi$
$761$	−5386.71	−	9330.06i	−0.256594	−	0.444434i	−0.965327	+	0.261043i	$0.915934\pi$
$762$		0			0
$763$	3922.54	−	2222.34i	0.186115	−	0.105444i
$764$		0			0
$765$	−2537.45	+	942.940i	−0.119924	+	0.0445648i
$766$		0			0
$767$	1200.91	+	693.344i	0.0565348	+	0.0326404i
$768$		0			0
$769$		−	5088.61i		−	0.238621i	−0.992857	−	0.119311i	$-0.961932\pi$
$769$		−	5088.61i		−	0.238621i	0.992857	−	0.119311i	$-0.0380685\pi$
$770$		0			0
$771$	−4657.98	+	3935.29i	−0.217578	+	0.183821i
$772$		0			0
$773$	16560.6	−	28683.9i	0.770562	−	1.33465i	−0.166693	−	0.986009i	$-0.553309\pi$
$773$	16560.6	−	28683.9i	0.770562	−	1.33465i	0.937255	−	0.348644i	$-0.113358\pi$
$774$		0			0
$775$	−1644.23	+	949.296i	−0.0762096	+	0.0439996i
$776$		0			0
$777$	11080.6	−	1899.36i	0.511600	−	0.0876951i
$778$		0			0
$779$	−7773.21	+	4487.86i	−0.357515	+	0.206411i
$780$		0			0
$781$	12235.5	−	21192.6i	0.560591	−	0.970972i
$782$		0			0
$783$	9136.65	−	5398.73i	0.417008	−	0.246405i
$784$		0			0
$785$		−	45346.7i		−	2.06177i
$786$		0			0
$787$	−12144.6	−	7011.70i	−0.550075	−	0.317586i	0.199077	−	0.979984i	$-0.436206\pi$
$787$	−12144.6	−	7011.70i	−0.550075	−	0.317586i	−0.749152	+	0.662398i	$0.769539\pi$
$788$		0			0
$789$	4642.79	−	12890.7i	0.209490	−	0.581651i
$790$		0			0
$791$	−1660.69	+	2823.12i	−0.0746489	+	0.126901i
$792$		0			0
$793$	−30969.5	−	53640.8i	−1.38684	−	2.40207i
$794$		0			0
$795$	41295.7	−	7424.89i	1.84227	−	0.331237i
$796$		0			0
$797$	5707.05			0.253644			0.126822	−	0.991926i	$-0.459522\pi$
$797$	5707.05			0.253644			0.126822	+	0.991926i	$0.459522\pi$
$798$		0			0
$799$	−1655.97			−0.0733215
$800$		0			0
$801$	9345.02	+	7734.84i	0.412222	+	0.341195i
$802$		0			0
$803$	−15102.9	−	26158.9i	−0.663721	−	1.14960i
$804$		0			0
$805$	20043.8	+	35378.4i	0.877580	+	1.54897i
$806$		0			0
$807$	−37899.5	−	13650.1i	−1.65319	−	0.595421i
$808$		0			0
$809$	15291.3	+	8828.45i	0.664542	+	0.383674i	0.794005	−	0.607911i	$-0.207992\pi$
$809$	15291.3	+	8828.45i	0.664542	+	0.383674i	−0.129463	+	0.991584i	$0.541325\pi$
$810$		0			0
$811$		−	23363.4i		−	1.01159i	−0.862654	−	0.505794i	$-0.831199\pi$
$811$		−	23363.4i		−	1.01159i	0.862654	−	0.505794i	$-0.168801\pi$
$812$		0			0
$813$	13599.9	+	16097.4i	0.586678	+	0.694418i
$814$		0			0
$815$	1013.36	−	1755.19i	0.0435540	−	0.0754377i
$816$		0			0
$817$	−20528.3	+	11852.0i	−0.879064	+	0.507528i
$818$		0			0
$819$	7098.48	−	39929.4i	0.302858	−	1.70360i
$820$		0			0
$821$	−21621.7	+	12483.3i	−0.919124	+	0.530657i	−0.883356	−	0.468704i	$-0.844721\pi$
$821$	−21621.7	+	12483.3i	−0.919124	+	0.530657i	−0.0357685	+	0.999360i	$0.511388\pi$
$822$		0			0
$823$	1873.90	−	3245.69i	0.0793683	−	0.137470i	−0.823609	−	0.567158i	$-0.808043\pi$
$823$	1873.90	−	3245.69i	0.0793683	−	0.137470i	0.902978	+	0.429688i	$0.141376\pi$
$824$		0			0
$825$	−2492.30	−	2950.00i	−0.105177	−	0.124492i
$826$		0			0
$827$			21381.4i			0.899037i	0.893271	+	0.449519i	$0.148404\pi$
$827$			21381.4i			0.899037i	−0.893271	+	0.449519i	$0.851596\pi$
$828$		0			0
$829$	−21555.1	−	12444.8i	−0.903062	−	0.521383i	−0.0248698	−	0.999691i	$-0.507917\pi$
$829$	−21555.1	−	12444.8i	−0.903062	−	0.521383i	−0.878192	+	0.478307i	$0.841250\pi$
$830$		0			0
$831$	5633.09	+	2028.84i	0.235150	+	0.0846928i
$832$		0			0
$833$	−2843.12	−	46.2545i	−0.118257	−	0.00192392i
$834$		0			0
$835$	4093.59	+	7090.30i	0.169658	+	0.293856i
$836$		0			0
$837$	−126.447	−	12527.5i	−0.00522181	−	0.517342i
$838$		0			0
$839$	8042.30			0.330931			0.165466	−	0.986216i	$-0.447087\pi$
$839$	8042.30			0.330931			0.165466	+	0.986216i	$0.447087\pi$
$840$		0			0
$841$	18667.1			0.765389
$842$		0			0
$843$	−5330.96	+	958.497i	−0.217803	+	0.0391606i
$844$		0			0
$845$	26490.0	+	45882.0i	1.07844	+	1.86792i
$846$		0			0
$847$	16.4268	−	2019.54i	0.000666389	−	0.0819270i
$848$		0			0
$849$	3808.89	−	10575.4i	0.153970	−	0.427500i
$850$		0			0
$851$	18366.5	+	10603.9i	0.739832	+	0.427142i
$852$		0			0
$853$		−	6230.54i		−	0.250093i	−0.992151	−	0.125047i	$-0.960092\pi$
$853$		−	6230.54i		−	0.250093i	0.992151	−	0.125047i	$-0.0399080\pi$
$854$		0			0
$855$	−19612.0	−	3322.22i	−0.784465	−	0.132886i
$856$		0			0
$857$	−259.511	+	449.486i	−0.0103439	+	0.0179162i	−0.871151	−	0.491015i	$-0.836626\pi$
$857$	−259.511	+	449.486i	−0.0103439	+	0.0179162i	0.860807	+	0.508931i	$0.169959\pi$
$858$		0			0
$859$	−2239.34	+	1292.89i	−0.0889469	+	0.0513535i	−0.543814	−	0.839206i	$-0.683020\pi$
$859$	−2239.34	+	1292.89i	−0.0889469	+	0.0513535i	0.454867	+	0.890559i	$0.349687\pi$
$860$		0			0
$861$	−4913.16	+	13301.1i	−0.194472	+	0.526480i
$862$		0			0
$863$	22261.6	−	12852.7i	0.878091	−	0.506966i	0.00806261	−	0.999967i	$-0.497434\pi$
$863$	22261.6	−	12852.7i	0.878091	−	0.506966i	0.870029	+	0.493001i	$0.164100\pi$
$864$		0			0
$865$	−8659.75	+	14999.1i	−0.340393	+	0.589578i
$866$		0			0
$867$	−19228.0	+	16244.8i	−0.753192	+	0.636334i
$868$		0			0
$869$		−	32386.8i		−	1.26427i
$870$		0			0
$871$	60147.0	+	34725.9i	2.33984	+	1.35091i
$872$		0			0
$873$	−2006.66	−	5399.93i	−0.0777952	−	0.209347i
$874$		0			0
$875$	−20027.4	−	11781.1i	−0.773771	−	0.455168i
$876$		0			0
$877$	7737.34	+	13401.5i	0.297915	+	0.516004i	0.975659	−	0.219294i	$-0.0703755\pi$
$877$	7737.34	+	13401.5i	0.297915	+	0.516004i	−0.677744	+	0.735298i	$0.737042\pi$
$878$		0			0
$879$	−4939.27	−	27471.2i	−0.189531	−	1.05413i
$880$		0			0
$881$	21804.4			0.833836			0.416918	−	0.908944i	$-0.363110\pi$
$881$	21804.4			0.833836			0.416918	+	0.908944i	$0.363110\pi$
$882$		0			0
$883$	−24982.9			−0.952142			−0.476071	−	0.879407i	$-0.657940\pi$
$883$	−24982.9			−0.952142			−0.476071	+	0.879407i	$0.657940\pi$
$884$		0			0
$885$	−190.135	−	1057.49i	−0.00722185	−	0.0401664i
$886$		0			0
$887$	6136.40	+	10628.6i	0.232289	+	0.402336i	0.958481	−	0.285156i	$-0.0920453\pi$
$887$	6136.40	+	10628.6i	0.232289	+	0.402336i	−0.726193	+	0.687491i	$0.758712\pi$
$888$		0			0
$889$	−11327.2	−	6663.21i	−0.427338	−	0.251380i
$890$		0			0
$891$	25034.3	−	4762.44i	0.941279	−	0.179066i
$892$		0			0
$893$	−10538.1	−	6084.17i	−0.394898	−	0.227994i
$894$		0			0
$895$		−	36083.6i		−	1.34765i
$896$		0			0
$897$	58441.2	−	49374.0i	2.17536	−	1.83785i
$898$		0			0
$899$	−3377.41	+	5849.84i	−0.125298	+	0.217022i
$900$		0			0
$901$	−4793.53	+	2767.55i	−0.177243	+	0.102331i
$902$		0			0
$903$	−12975.2	+	35126.9i	−0.478171	+	1.29452i
$904$		0			0
$905$	4406.53	−	2544.11i	0.161854	−	0.0934465i
$906$		0			0
$907$	−21298.9	+	36890.8i	−0.779735	+	1.35054i	0.152360	+	0.988325i	$0.451313\pi$
$907$	−21298.9	+	36890.8i	−0.779735	+	1.35054i	−0.932095	+	0.362215i	$0.882021\pi$
$908$		0			0
$909$	3648.91	−	21540.6i	0.133143	−	0.785979i
$910$		0			0
$911$		−	3752.25i		−	0.136463i	−0.997670	−	0.0682313i	$-0.978264\pi$
$911$		−	3752.25i		−	0.136463i	0.997670	−	0.0682313i	$-0.0217356\pi$
$912$		0			0
$913$	31898.6	+	18416.7i	1.15629	+	0.667583i
$914$		0			0
$915$	−16262.6	+	45153.1i	−0.587567	+	1.63138i
$916$		0			0
$917$	−13.7251	+	1687.38i	−0.000494266	+	0.0607659i
$918$		0			0
$919$	3227.42	+	5590.05i	0.115846	+	0.200651i	0.918118	−	0.396308i	$-0.129709\pi$
$919$	3227.42	+	5590.05i	0.115846	+	0.200651i	−0.802272	+	0.596959i	$0.796375\pi$
$920$		0			0
$921$	15482.2	−	2783.67i	0.553915	−	0.0995929i
$922$		0			0
$923$	56775.9			2.02470
$924$		0			0
$925$	2483.77			0.0882873
$926$		0			0
$927$	−17006.2	+	20546.4i	−0.602542	+	0.727974i
$928$		0			0
$929$	−9970.85	−	17270.0i	−0.352135	−	0.609915i	0.634489	−	0.772932i	$-0.281211\pi$
$929$	−9970.85	−	17270.0i	−0.352135	−	0.609915i	−0.986623	+	0.163017i	$0.947877\pi$
$930$		0			0
$931$	−17922.8	−	10740.2i	−0.630931	−	0.378084i
$932$		0			0
$933$	−43815.8	−	15780.9i	−1.53748	−	0.553745i
$934$		0			0
$935$	3035.15	+	1752.34i	0.106160	+	0.0612918i
$936$		0			0
$937$			20595.3i			0.718057i	0.933327	+	0.359029i	$0.116892\pi$
$937$			20595.3i			0.718057i	−0.933327	+	0.359029i	$0.883108\pi$
$938$		0			0
$939$	5995.38	+	7096.40i	0.208362	+	0.246626i
$940$		0			0
$941$	−20620.5	+	35715.8i	−0.714357	+	1.23730i	0.248850	+	0.968542i	$0.419947\pi$
$941$	−20620.5	+	35715.8i	−0.714357	+	1.23730i	−0.963207	+	0.268760i	$0.913386\pi$
$942$		0			0
$943$	−23165.3	+	13374.5i	−0.799963	+	0.461859i
$944$		0			0
$945$	−27182.9	+	15765.1i	−0.935724	+	0.542688i
$946$		0			0
$947$	32099.0	−	18532.4i	1.10145	−	0.635925i	0.164852	−	0.986318i	$-0.447285\pi$
$947$	32099.0	−	18532.4i	1.10145	−	0.635925i	0.936603	+	0.350393i	$0.113952\pi$
$948$		0			0
$949$	35040.5	−	60691.9i	1.19859	−	2.07602i
$950$		0			0
$951$	22180.5	+	26253.8i	0.756311	+	0.895202i
$952$		0			0
$953$		−	32868.6i		−	1.11723i	−0.829428	−	0.558614i	$-0.811333\pi$
$953$		−	32868.6i		−	1.11723i	0.829428	−	0.558614i	$-0.188667\pi$
$954$		0			0
$955$	42779.8	+	24699.0i	1.44955	+	0.836900i
$956$		0			0
$957$	−12926.9	−	4655.82i	−0.436643	−	0.157264i
$958$		0			0
$959$	−8496.40	−	14996.6i	−0.286093	−	0.504968i
$960$		0			0
$961$	−10908.4	−	18893.9i	−0.366165	−	0.634216i
$962$		0			0
$963$	−9985.16	+	12063.8i	−0.334130	+	0.403686i
$964$		0			0
$965$	−19533.9			−0.651625
$966$		0			0
$967$	−30226.5			−1.00519			−0.502595	−	0.864522i	$-0.667621\pi$
$967$	−30226.5			−1.00519			−0.502595	+	0.864522i	$0.667621\pi$
$968$		0			0
$969$	2582.67	−	464.359i	0.0856216	−	0.0153946i
$970$		0			0
$971$	6665.95	+	11545.8i	0.220310	+	0.381588i	0.954902	−	0.296921i	$-0.0959599\pi$
$971$	6665.95	+	11545.8i	0.220310	+	0.381588i	−0.734592	+	0.678509i	$0.762627\pi$
$972$		0			0
$973$	−16006.4	+	27210.3i	−0.527379	+	0.896528i
$974$		0			0
$975$	3036.16	−	8429.93i	0.0997283	−	0.276896i
$976$		0			0
$977$	21717.6	+	12538.7i	0.711166	+	0.410592i	0.811492	−	0.584363i	$-0.198656\pi$
$977$	21717.6	+	12538.7i	0.711166	+	0.410592i	−0.100327	+	0.994955i	$0.531989\pi$
$978$		0			0
$979$		−	15705.6i		−	0.512720i
$980$		0			0
$981$	−1097.73	+	6480.22i	−0.0357266	+	0.210905i
$982$		0			0
$983$	−13328.7	+	23086.0i	−0.432472	+	0.749063i	−0.997086	−	0.0762919i	$-0.975692\pi$
$983$	−13328.7	+	23086.0i	−0.432472	+	0.749063i	0.564614	+	0.825355i	$0.309025\pi$
$984$		0			0
$985$	−6244.01	+	3604.98i	−0.201980	+	0.116613i
$986$		0			0
$987$	−18946.7	+	3247.72i	−0.611024	+	0.104738i
$988$		0			0
$989$	−61177.4	+	35320.8i	−1.96696	+	1.13563i
$990$		0			0
$991$	−10219.7	+	17701.0i	−0.327588	+	0.567398i	−0.982033	−	0.188711i	$-0.939569\pi$
$991$	−10219.7	+	17701.0i	−0.327588	+	0.567398i	0.654445	+	0.756110i	$0.272902\pi$
$992$		0			0
$993$	−29624.3	+	25028.0i	−0.946725	+	0.799839i
$994$		0			0
$995$		−	1873.53i		−	0.0596933i
$996$		0			0
$997$	12044.5	+	6953.91i	0.382602	+	0.220895i	0.678950	−	0.734185i	$-0.262435\pi$
$997$	12044.5	+	6953.91i	0.382602	+	0.220895i	−0.296348	+	0.955080i	$0.595769\pi$
$998$		0			0
$999$	−8051.10	+	14275.8i	−0.254981	+	0.452117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.u.a.17.14	✓	48
3.2	odd	2	inner	168.4.u.a.17.21	yes	48
4.3	odd	2		336.4.bc.f.17.11		48
7.5	odd	6	inner	168.4.u.a.89.21	yes	48
12.11	even	2		336.4.bc.f.17.4		48
21.5	even	6	inner	168.4.u.a.89.14	yes	48
28.19	even	6		336.4.bc.f.257.4		48
84.47	odd	6		336.4.bc.f.257.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.14	✓	48	1.1	even	1	trivial
168.4.u.a.17.21	yes	48	3.2	odd	2	inner
168.4.u.a.89.14	yes	48	21.5	even	6	inner
168.4.u.a.89.21	yes	48	7.5	odd	6	inner
336.4.bc.f.17.4		48	12.11	even	2
336.4.bc.f.17.11		48	4.3	odd	2
336.4.bc.f.257.4		48	28.19	even	6
336.4.bc.f.257.11		48	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.919514 + 5.11415i) q^{3} +(-6.04693 - 10.4736i) q^{5} +(15.9632 + 9.39028i) q^{7} +(-25.3090 + 9.40505i) q^{9} +O(q^{10})\)	\(q+(0.919514 + 5.11415i) q^{3} +(-6.04693 - 10.4736i) q^{5} +(15.9632 + 9.39028i) q^{7} +(-25.3090 + 9.40505i) q^{9} +(30.2732 + 17.4782i) q^{11} +81.1032i q^{13} +(48.0032 - 40.5555i) q^{15} +(-4.14503 + 7.17941i) q^{17} +(-52.7556 + 30.4585i) q^{19} +(-33.3449 + 90.2725i) q^{21} +(-157.219 + 90.7706i) q^{23} +(-10.6306 + 18.4128i) q^{25} +(-71.3708 - 120.786i) q^{27} +75.6434i q^{29} +(77.3344 + 44.6491i) q^{31} +(-61.5496 + 170.893i) q^{33} +(1.82179 - 223.974i) q^{35} +(-58.4106 - 101.170i) q^{37} +(-414.774 + 74.5755i) q^{39} +147.344 q^{41} +389.121 q^{43} +(251.546 + 208.204i) q^{45} +(99.8765 + 172.991i) q^{47} +(166.645 + 299.797i) q^{49} +(-40.5279 - 14.5967i) q^{51} +(578.226 + 333.839i) q^{53} -422.758i q^{55} +(-204.278 - 241.793i) q^{57} +(8.54890 - 14.8071i) q^{59} +(-661.389 + 381.853i) q^{61} +(-492.328 - 87.5240i) q^{63} +(849.442 - 490.425i) q^{65} +(428.169 - 741.610i) q^{67} +(-608.780 - 720.578i) q^{69} -700.045i q^{71} +(-748.329 - 432.048i) q^{73} +(-103.941 - 37.4358i) q^{75} +(319.130 + 563.281i) q^{77} +(-463.245 - 802.364i) q^{79} +(552.090 - 476.065i) q^{81} +1053.69 q^{83} +100.259 q^{85} +(-386.851 + 69.5551i) q^{87} +(-224.645 - 389.097i) q^{89} +(-761.582 + 1294.66i) q^{91} +(-157.232 + 436.555i) q^{93} +(638.018 + 368.360i) q^{95} +213.360i q^{97} +(-930.566 - 157.635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q + 12 * q^7 + 14 * q^9	\( 48 q + 12 q^{7} + 14 q^{9} - 88 q^{15} - 270 q^{19} + 50 q^{21} - 438 q^{25} + 216 q^{31} - 372 q^{33} + 66 q^{37} + 242 q^{39} + 900 q^{43} - 294 q^{45} + 60 q^{49} - 138 q^{51} + 1384 q^{57} + 108 q^{61} + 1096 q^{63} + 6 q^{67} - 1206 q^{73} - 594 q^{75} - 588 q^{79} - 54 q^{81} - 240 q^{85} - 3522 q^{87} + 234 q^{91} - 608 q^{93} + 1988 q^{99}+O(q^{100}) \) 48 * q + 12 * q^7 + 14 * q^9 - 88 * q^15 - 270 * q^19 + 50 * q^21 - 438 * q^25 + 216 * q^31 - 372 * q^33 + 66 * q^37 + 242 * q^39 + 900 * q^43 - 294 * q^45 + 60 * q^49 - 138 * q^51 + 1384 * q^57 + 108 * q^61 + 1096 * q^63 + 6 * q^67 - 1206 * q^73 - 594 * q^75 - 588 * q^79 - 54 * q^81 - 240 * q^85 - 3522 * q^87 + 234 * q^91 - 608 * q^93 + 1988 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more