LMFDB - Embedded newform 252.3.m.a.65.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(65,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("252.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.m (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:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.16
Character	$\chi$	$=$	252.65
Dual form			252.3.m.a.221.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99793 + 0.111527i) q^{3} -8.05008i q^{5} +(-6.58302 + 2.37987i) q^{7} +(8.97512 + 0.668699i) q^{9} +O(q^{10})$	\(q+(2.99793 + 0.111527i) q^{3} -8.05008i q^{5} +(-6.58302 + 2.37987i) q^{7} +(8.97512 + 0.668699i) q^{9} -19.2134i q^{11} +(0.782606 + 1.35551i) q^{13} +(0.897800 - 24.1335i) q^{15} +(-8.39721 + 4.84813i) q^{17} +(5.84871 - 10.1303i) q^{19} +(-20.0008 + 6.40050i) q^{21} +2.07535i q^{23} -39.8037 q^{25} +(26.8322 + 3.00568i) q^{27} +(40.2492 + 23.2379i) q^{29} +(11.1747 - 19.3552i) q^{31} +(2.14281 - 57.6003i) q^{33} +(19.1582 + 52.9938i) q^{35} +(-30.6213 + 53.0376i) q^{37} +(2.19502 + 4.15101i) q^{39} +(48.9545 - 28.2639i) q^{41} +(21.6300 - 37.4643i) q^{43} +(5.38308 - 72.2504i) q^{45} +(-5.50180 + 3.17647i) q^{47} +(37.6724 - 31.3335i) q^{49} +(-25.7149 + 13.5978i) q^{51} +(-55.3510 + 31.9569i) q^{53} -154.669 q^{55} +(18.6638 - 29.7175i) q^{57} +(27.7798 + 16.0387i) q^{59} +(37.2708 + 64.5549i) q^{61} +(-60.6749 + 16.9576i) q^{63} +(10.9120 - 6.30004i) q^{65} +(-2.38096 + 4.12394i) q^{67} +(-0.231458 + 6.22176i) q^{69} +33.1772i q^{71} +(6.60726 + 11.4441i) q^{73} +(-119.329 - 4.43919i) q^{75} +(45.7254 + 126.482i) q^{77} +(-23.1230 - 40.0502i) q^{79} +(80.1057 + 12.0033i) q^{81} +(81.0445 + 46.7910i) q^{83} +(39.0278 + 67.5982i) q^{85} +(118.072 + 74.1543i) q^{87} +(55.9009 + 32.2744i) q^{89} +(-8.37786 - 7.06087i) q^{91} +(35.6596 - 56.7791i) q^{93} +(-81.5494 - 47.0826i) q^{95} +(-96.6875 + 167.468i) q^{97} +(12.8480 - 172.442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{7} + 10 q^{9}+O(q^{10}) $ 32 * q - q^7 + 10 * q^9	$ 32 q - q^{7} + 10 q^{9} - 5 q^{13} - 29 q^{15} - 27 q^{17} - 14 q^{19} - 20 q^{21} - 160 q^{25} + 45 q^{27} + 36 q^{29} - 8 q^{31} + 5 q^{33} - 45 q^{35} - 11 q^{37} + 37 q^{39} + 72 q^{41} + 16 q^{43} + 59 q^{45} - 108 q^{47} + 35 q^{49} + 77 q^{51} + 180 q^{53} - 24 q^{55} + 57 q^{57} + 45 q^{59} - 41 q^{61} + 117 q^{63} - 81 q^{65} - 35 q^{67} - 97 q^{69} - 98 q^{73} + 313 q^{75} + 225 q^{77} - 71 q^{79} - 74 q^{81} - 30 q^{85} + 97 q^{87} - 189 q^{89} + 109 q^{91} - 149 q^{93} - 288 q^{95} + 19 q^{97} - 101 q^{99}+O(q^{100}) $ 32 * q - q^7 + 10 * q^9 - 5 * q^13 - 29 * q^15 - 27 * q^17 - 14 * q^19 - 20 * q^21 - 160 * q^25 + 45 * q^27 + 36 * q^29 - 8 * q^31 + 5 * q^33 - 45 * q^35 - 11 * q^37 + 37 * q^39 + 72 * q^41 + 16 * q^43 + 59 * q^45 - 108 * q^47 + 35 * q^49 + 77 * q^51 + 180 * q^53 - 24 * q^55 + 57 * q^57 + 45 * q^59 - 41 * q^61 + 117 * q^63 - 81 * q^65 - 35 * q^67 - 97 * q^69 - 98 * q^73 + 313 * q^75 + 225 * q^77 - 71 * q^79 - 74 * q^81 - 30 * q^85 + 97 * q^87 - 189 * q^89 + 109 * q^91 - 149 * q^93 - 288 * q^95 + 19 * q^97 - 101 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.99793	+	0.111527i	0.999309	+	0.0371756i
$3$	2.99793	+	0.111527i	0.999309	+	0.0371756i
$4$		0			0
$5$		−	8.05008i		−	1.61002i	−0.593264	−	0.805008i	$-0.702161\pi$
$5$		−	8.05008i		−	1.61002i	0.593264	−	0.805008i	$-0.297839\pi$
$6$		0			0
$7$	−6.58302	+	2.37987i	−0.940432	+	0.339982i
$7$	−6.58302	+	2.37987i	−0.940432	+	0.339982i
$8$		0			0
$9$	8.97512	+	0.668699i	0.997236	+	0.0742999i
$10$		0			0
$11$		−	19.2134i		−	1.74667i	−0.487120	−	0.873335i	$-0.661952\pi$
$11$		−	19.2134i		−	1.74667i	0.487120	−	0.873335i	$-0.338048\pi$
$12$		0			0
$13$	0.782606	+	1.35551i	0.0602005	+	0.104270i	0.894555	−	0.446958i	$-0.147493\pi$
$13$	0.782606	+	1.35551i	0.0602005	+	0.104270i	−0.834354	+	0.551228i	$0.814159\pi$
$14$		0			0
$15$	0.897800	−	24.1335i	0.0598533	−	1.60890i
$16$		0			0
$17$	−8.39721	+	4.84813i	−0.493953	+	0.285184i	−0.726213	−	0.687470i	$-0.758721\pi$
$17$	−8.39721	+	4.84813i	−0.493953	+	0.285184i	0.232260	+	0.972654i	$0.425388\pi$
$18$		0			0
$19$	5.84871	−	10.1303i	0.307827	−	0.533172i	−0.670060	−	0.742307i	$-0.733732\pi$
$19$	5.84871	−	10.1303i	0.307827	−	0.533172i	0.977887	+	0.209135i	$0.0670649\pi$
$20$		0			0
$21$	−20.0008	+	6.40050i	−0.952421	+	0.304786i
$22$		0			0
$23$			2.07535i			0.0902328i	0.998982	+	0.0451164i	$0.0143659\pi$
$23$			2.07535i			0.0902328i	−0.998982	+	0.0451164i	$0.985634\pi$
$24$		0			0
$25$	−39.8037			−1.59215
$26$		0			0
$27$	26.8322	+	3.00568i	0.993784	+	0.111321i
$28$		0			0
$29$	40.2492	+	23.2379i	1.38790	+	0.801306i	0.993079	−	0.117451i	$-0.0374725\pi$
$29$	40.2492	+	23.2379i	1.38790	+	0.801306i	0.394823	+	0.918757i	$0.370806\pi$
$30$		0			0
$31$	11.1747	−	19.3552i	0.360474	−	0.624360i	−0.627564	−	0.778565i	$-0.715948\pi$
$31$	11.1747	−	19.3552i	0.360474	−	0.624360i	0.988039	+	0.154205i	$0.0492815\pi$
$32$		0			0
$33$	2.14281	−	57.6003i	0.0649336	−	1.74546i
$34$		0			0
$35$	19.1582	+	52.9938i	0.547376	+	1.51411i
$36$		0			0
$37$	−30.6213	+	53.0376i	−0.827603	+	1.43345i	0.0723114	+	0.997382i	$0.476962\pi$
$37$	−30.6213	+	53.0376i	−0.827603	+	1.43345i	−0.899914	+	0.436068i	$0.856371\pi$
$38$		0			0
$39$	2.19502	+	4.15101i	0.0562825	+	0.106436i
$40$		0			0
$41$	48.9545	−	28.2639i	1.19401	−	0.689363i	0.234797	−	0.972044i	$-0.424557\pi$
$41$	48.9545	−	28.2639i	1.19401	−	0.689363i	0.959214	+	0.282682i	$0.0912240\pi$
$42$		0			0
$43$	21.6300	−	37.4643i	0.503023	−	0.871262i	−0.496971	−	0.867767i	$-0.665554\pi$
$43$	21.6300	−	37.4643i	0.503023	−	0.871262i	0.999994	−	0.00349442i	$-0.00111231\pi$
$44$		0			0
$45$	5.38308	−	72.2504i	0.119624	−	1.60557i
$46$		0			0
$47$	−5.50180	+	3.17647i	−0.117060	+	0.0675844i	−0.557387	−	0.830253i	$-0.688196\pi$
$47$	−5.50180	+	3.17647i	−0.117060	+	0.0675844i	0.440327	+	0.897837i	$0.354863\pi$
$48$		0			0
$49$	37.6724	−	31.3335i	0.768824	−	0.639460i
$50$		0			0
$51$	−25.7149	+	13.5978i	−0.504214	+	0.266624i
$52$		0			0
$53$	−55.3510	+	31.9569i	−1.04436	+	0.602960i	−0.921065	−	0.389410i	$-0.872679\pi$
$53$	−55.3510	+	31.9569i	−1.04436	+	0.602960i	−0.123293	+	0.992370i	$0.539346\pi$
$54$		0			0
$55$	−154.669			−2.81217
$56$		0			0
$57$	18.6638	−	29.7175i	0.327435	−	0.521359i
$58$		0			0
$59$	27.7798	+	16.0387i	0.470844	+	0.271842i	0.716593	−	0.697492i	$-0.245701\pi$
$59$	27.7798	+	16.0387i	0.470844	+	0.271842i	−0.245749	+	0.969333i	$0.579034\pi$
$60$		0			0
$61$	37.2708	+	64.5549i	0.610997	+	1.05828i	0.991073	+	0.133322i	$0.0425645\pi$
$61$	37.2708	+	64.5549i	0.610997	+	1.05828i	−0.380076	+	0.924955i	$0.624102\pi$
$62$		0			0
$63$	−60.6749	+	16.9576i	−0.963093	+	0.269168i
$64$		0			0
$65$	10.9120	−	6.30004i	0.167877	−	0.0969237i
$66$		0			0
$67$	−2.38096	+	4.12394i	−0.0355367	+	0.0615514i	−0.883247	−	0.468908i	$-0.844647\pi$
$67$	−2.38096	+	4.12394i	−0.0355367	+	0.0615514i	0.847710	+	0.530460i	$0.177981\pi$
$68$		0			0
$69$	−0.231458	+	6.22176i	−0.00335446	+	0.0901704i
$70$		0			0
$71$			33.1772i			0.467284i	0.972323	+	0.233642i	$0.0750644\pi$
$71$			33.1772i			0.467284i	−0.972323	+	0.233642i	$0.924936\pi$
$72$		0			0
$73$	6.60726	+	11.4441i	0.0905104	+	0.156769i	0.907726	−	0.419563i	$-0.137817\pi$
$73$	6.60726	+	11.4441i	0.0905104	+	0.156769i	−0.817216	+	0.576332i	$0.804483\pi$
$74$		0			0
$75$	−119.329	−	4.43919i	−1.59105	−	0.0591892i
$76$		0			0
$77$	45.7254	+	126.482i	0.593837	+	1.64262i
$78$		0			0
$79$	−23.1230	−	40.0502i	−0.292696	−	0.506965i	0.681750	−	0.731585i	$-0.261219\pi$
$79$	−23.1230	−	40.0502i	−0.292696	−	0.506965i	−0.974446	+	0.224620i	$0.927886\pi$
$80$		0			0
$81$	80.1057	+	12.0033i	0.988959	+	0.148189i
$82$		0			0
$83$	81.0445	+	46.7910i	0.976439	+	0.563748i	0.901193	−	0.433417i	$-0.142692\pi$
$83$	81.0445	+	46.7910i	0.976439	+	0.563748i	0.0752462	+	0.997165i	$0.476026\pi$
$84$		0			0
$85$	39.0278	+	67.5982i	0.459151	+	0.795273i
$86$		0			0
$87$	118.072	+	74.1543i	1.35715	+	0.852348i
$88$		0			0
$89$	55.9009	+	32.2744i	0.628099	+	0.362633i	0.780016	−	0.625760i	$-0.215211\pi$
$89$	55.9009	+	32.2744i	0.628099	+	0.362633i	−0.151916	+	0.988393i	$0.548544\pi$
$90$		0			0
$91$	−8.37786	−	7.06087i	−0.0920644	−	0.0775920i
$92$		0			0
$93$	35.6596	−	56.7791i	0.383436	−	0.610528i
$94$		0			0
$95$	−81.5494	−	47.0826i	−0.858415	−	0.495606i
$96$		0			0
$97$	−96.6875	+	167.468i	−0.996779	+	1.72647i	−0.428933	+	0.903337i	$0.641110\pi$
$97$	−96.6875	+	167.468i	−0.996779	+	1.72647i	−0.567846	+	0.823135i	$0.692223\pi$
$98$		0			0
$99$	12.8480	−	172.442i	0.129777	−	1.74184i
$100$		0			0
$101$		−	67.4181i		−	0.667506i	−0.942661	−	0.333753i	$-0.891685\pi$
$101$		−	67.4181i		−	0.667506i	0.942661	−	0.333753i	$-0.108315\pi$
$102$		0			0
$103$	−80.2840			−0.779456			−0.389728	−	0.920930i	$-0.627431\pi$
$103$	−80.2840			−0.779456			−0.389728	+	0.920930i	$0.627431\pi$
$104$		0			0
$105$	51.5245	+	161.008i	0.490710	+	1.53341i
$106$		0			0
$107$	−108.086	−	62.4035i	−1.01015	−	0.583210i	−0.0989143	−	0.995096i	$-0.531537\pi$
$107$	−108.086	−	62.4035i	−1.01015	−	0.583210i	−0.911236	+	0.411886i	$0.864870\pi$
$108$		0			0
$109$	80.8079	+	139.963i	0.741357	+	1.28407i	0.951878	+	0.306478i	$0.0991506\pi$
$109$	80.8079	+	139.963i	0.741357	+	1.28407i	−0.210521	+	0.977589i	$0.567516\pi$
$110$		0			0
$111$	−97.7155	+	155.588i	−0.880320	+	1.40169i
$112$		0			0
$113$	28.7804	−	16.6164i	0.254694	−	0.147048i	−0.367218	−	0.930135i	$-0.619690\pi$
$113$	28.7804	−	16.6164i	0.254694	−	0.147048i	0.621912	+	0.783087i	$0.286356\pi$
$114$		0			0
$115$	16.7068			0.145276
$116$		0			0
$117$	6.11755	+	12.6892i	0.0522868	+	0.108455i
$118$		0			0
$119$	43.7411	−	51.8997i	0.367572	−	0.436132i
$120$		0			0
$121$	−248.154			−2.05086
$122$		0			0
$123$	149.914	−	79.2732i	1.21881	−	0.644498i
$124$		0			0
$125$			119.171i			0.953370i
$126$		0			0
$127$	−194.763			−1.53357			−0.766785	−	0.641904i	$-0.778145\pi$
$127$	−194.763			−1.53357			−0.766785	+	0.641904i	$0.778145\pi$
$128$		0			0
$129$	69.0234	−	109.903i	0.535065	−	0.851959i
$130$		0			0
$131$			117.044i			0.893463i	0.894668	+	0.446731i	$0.147412\pi$
$131$			117.044i			0.893463i	−0.894668	+	0.446731i	$0.852588\pi$
$132$		0			0
$133$	−14.3934	+	80.6069i	−0.108221	+	0.606067i
$134$		0			0
$135$	24.1959	−	216.001i	0.179229	−	1.60001i
$136$		0			0
$137$		−	79.8132i		−	0.582578i	−0.956635	−	0.291289i	$-0.905916\pi$
$137$		−	79.8132i		−	0.582578i	0.956635	−	0.291289i	$-0.0940841\pi$
$138$		0			0
$139$	−37.9101	−	65.6622i	−0.272734	−	0.472390i	0.696827	−	0.717240i	$-0.254595\pi$
$139$	−37.9101	−	65.6622i	−0.272734	−	0.472390i	−0.969561	+	0.244850i	$0.921261\pi$
$140$		0			0
$141$	−16.8483	+	8.90922i	−0.119491	+	0.0631859i
$142$		0			0
$143$	26.0440	−	15.0365i	0.182126	−	0.105150i
$144$		0			0
$145$	187.067	−	324.009i	1.29011	−	2.23454i
$146$		0			0
$147$	116.434	−	89.7341i	0.792065	−	0.610436i
$148$		0			0
$149$		−	108.954i		−	0.731236i	−0.930765	−	0.365618i	$-0.880858\pi$
$149$		−	108.954i		−	0.731236i	0.930765	−	0.365618i	$-0.119142\pi$
$150$		0			0
$151$	163.434			1.08234			0.541172	−	0.840912i	$-0.317981\pi$
$151$	163.434			1.08234			0.541172	+	0.840912i	$0.317981\pi$
$152$		0			0
$153$	−78.6079	+	37.8974i	−0.513777	+	0.247695i
$154$		0			0
$155$	−155.811	−	89.9573i	−1.00523	−	0.580369i
$156$		0			0
$157$	15.7565	−	27.2910i	0.100360	−	0.173828i	−0.811473	−	0.584390i	$-0.801334\pi$
$157$	15.7565	−	27.2910i	0.100360	−	0.173828i	0.911833	+	0.410561i	$0.134667\pi$
$158$		0			0
$159$	−169.502	+	89.6313i	−1.06605	+	0.563719i
$160$		0			0
$161$	−4.93908	−	13.6621i	−0.0306775	−	0.0848578i
$162$		0			0
$163$	149.467	−	258.884i	0.916974	−	1.58824i	0.112988	−	0.993596i	$-0.463958\pi$
$163$	149.467	−	258.884i	0.916974	−	1.58824i	0.803986	−	0.594648i	$-0.202709\pi$
$164$		0			0
$165$	−463.687	−	17.2498i	−2.81022	−	0.104544i
$166$		0			0
$167$	226.397	−	130.710i	1.35567	−	0.782695i	0.366632	−	0.930366i	$-0.380511\pi$
$167$	226.397	−	130.710i	1.35567	−	0.782695i	0.989037	+	0.147671i	$0.0471776\pi$
$168$		0			0
$169$	83.2751	−	144.237i	0.492752	−	0.853471i
$170$		0			0
$171$	59.2670	−	87.0093i	0.346591	−	0.508826i
$172$		0			0
$173$	166.695	−	96.2412i	0.963553	−	0.556307i	0.0662881	−	0.997801i	$-0.478884\pi$
$173$	166.695	−	96.2412i	0.963553	−	0.556307i	0.897265	+	0.441493i	$0.145551\pi$
$174$		0			0
$175$	262.029	−	94.7279i	1.49731	−	0.541302i
$176$		0			0
$177$	81.4930	+	51.1809i	0.460412	+	0.289158i
$178$		0			0
$179$	−303.708	+	175.346i	−1.69669	+	0.979585i	−0.747831	+	0.663889i	$0.768905\pi$
$179$	−303.708	+	175.346i	−1.69669	+	0.979585i	−0.948860	+	0.315696i	$0.897762\pi$
$180$		0			0
$181$	227.913			1.25919			0.629594	−	0.776925i	$-0.283221\pi$
$181$	227.913			1.25919			0.629594	+	0.776925i	$0.283221\pi$
$182$		0			0
$183$	104.535	+	197.688i	0.571232	+	1.08026i
$184$		0			0
$185$	426.957	+	246.504i	2.30788	+	1.33245i
$186$		0			0
$187$	93.1490	+	161.339i	0.498123	+	0.862774i
$188$		0			0
$189$	−183.790	+	44.0708i	−0.972434	+	0.233179i
$190$		0			0
$191$	−162.483	+	93.8095i	−0.850695	+	0.491149i	−0.860885	−	0.508799i	$-0.830090\pi$
$191$	−162.483	+	93.8095i	−0.850695	+	0.491149i	0.0101901	+	0.999948i	$0.496756\pi$
$192$		0			0
$193$	17.9056	−	31.0135i	0.0927753	−	0.160691i	−0.815903	−	0.578189i	$-0.803760\pi$
$193$	17.9056	−	31.0135i	0.0927753	−	0.160691i	0.908678	+	0.417498i	$0.137093\pi$
$194$		0			0
$195$	33.4160	−	17.6701i	0.171364	−	0.0906157i
$196$		0			0
$197$		−	110.071i		−	0.558736i	−0.960184	−	0.279368i	$-0.909875\pi$
$197$		−	110.071i		−	0.558736i	0.960184	−	0.279368i	$-0.0901250\pi$
$198$		0			0
$199$	34.5156	+	59.7829i	0.173445	+	0.300416i	0.939622	−	0.342214i	$-0.111177\pi$
$199$	34.5156	+	59.7829i	0.173445	+	0.300416i	−0.766177	+	0.642630i	$0.777843\pi$
$200$		0			0
$201$	−7.59787	+	12.0977i	−0.0378004	+	0.0601878i
$202$		0			0
$203$	−320.264	−	57.1875i	−1.57766	−	0.281712i
$204$		0			0
$205$	−227.526	−	394.087i	−1.10988	−	1.92238i
$206$		0			0
$207$	−1.38779	+	18.6266i	−0.00670429	+	0.0899834i
$208$		0			0
$209$	−194.637	−	112.373i	−0.931275	−	0.537672i
$210$		0			0
$211$	122.482	+	212.145i	0.580484	+	1.00543i	0.995422	+	0.0955775i	$0.0304698\pi$
$211$	122.482	+	212.145i	0.580484	+	1.00543i	−0.414938	+	0.909849i	$0.636197\pi$
$212$		0			0
$213$	−3.70015	+	99.4628i	−0.0173716	+	0.466961i
$214$		0			0
$215$	−301.590	−	174.123i	−1.40274	−	0.809875i
$216$		0			0
$217$	−27.5005	+	154.010i	−0.126730	+	0.709723i
$218$		0			0
$219$	18.5317	+	35.0455i	0.0846199	+	0.160025i
$220$		0			0
$221$	−13.1434	−	7.58835i	−0.0594724	−	0.0343364i
$222$		0			0
$223$	−50.2344	+	87.0085i	−0.225266	+	0.390173i	−0.956399	−	0.292062i	$-0.905659\pi$
$223$	−50.2344	+	87.0085i	−0.225266	+	0.390173i	0.731133	+	0.682235i	$0.238992\pi$
$224$		0			0
$225$	−357.243	−	26.6167i	−1.58775	−	0.118297i
$226$		0			0
$227$		−	166.877i		−	0.735142i	−0.929996	−	0.367571i	$-0.880190\pi$
$227$		−	166.877i		−	0.735142i	0.929996	−	0.367571i	$-0.119810\pi$
$228$		0			0
$229$	−277.529			−1.21192			−0.605959	−	0.795496i	$-0.707210\pi$
$229$	−277.529			−1.21192			−0.605959	+	0.795496i	$0.707210\pi$
$230$		0			0
$231$	122.975	+	384.284i	0.532361	+	1.66357i
$232$		0			0
$233$	41.2378	+	23.8087i	0.176986	+	0.102183i	0.585876	−	0.810401i	$-0.300751\pi$
$233$	41.2378	+	23.8087i	0.176986	+	0.102183i	−0.408890	+	0.912584i	$0.634084\pi$
$234$		0			0
$235$	25.5708	+	44.2899i	0.108812	+	0.188468i
$236$		0			0
$237$	−64.8544	−	122.646i	−0.273647	−	0.517496i
$238$		0			0
$239$	199.849	−	115.383i	0.836187	−	0.482773i	−0.0197796	−	0.999804i	$-0.506296\pi$
$239$	199.849	−	115.383i	0.836187	−	0.482773i	0.855966	+	0.517032i	$0.172963\pi$
$240$		0			0
$241$	297.477			1.23434			0.617172	−	0.786828i	$-0.288278\pi$
$241$	297.477			1.23434			0.617172	+	0.786828i	$0.288278\pi$
$242$		0			0
$243$	238.812	+	44.9190i	0.982766	+	0.184852i
$244$		0			0
$245$	−252.237	−	303.266i	−1.02954	−	1.23782i
$246$		0			0
$247$	18.3089			0.0741252
$248$		0			0
$249$	237.747	+	149.315i	0.954807	+	0.599658i
$250$		0			0
$251$			85.2548i			0.339661i	0.985473	+	0.169830i	$0.0543220\pi$
$251$			85.2548i			0.339661i	−0.985473	+	0.169830i	$0.945678\pi$
$252$		0			0
$253$	39.8746			0.157607
$254$		0			0
$255$	109.464	+	207.007i	0.429269	+	0.811792i
$256$		0			0
$257$		−	71.7566i		−	0.279208i	−0.990207	−	0.139604i	$-0.955417\pi$
$257$		−	71.7566i		−	0.279208i	0.990207	−	0.139604i	$-0.0445830\pi$
$258$		0			0
$259$	75.3578	−	422.023i	0.290957	−	1.62943i
$260$		0			0
$261$	345.702	+	235.477i	1.32453	+	0.902212i
$262$		0			0
$263$		−	341.324i		−	1.29781i	−0.760869	−	0.648906i	$-0.775227\pi$
$263$		−	341.324i		−	1.29781i	0.760869	−	0.648906i	$-0.224773\pi$
$264$		0			0
$265$	257.255	+	445.580i	0.970775	+	1.68143i
$266$		0			0
$267$	163.987	+	102.991i	0.614184	+	0.385733i
$268$		0			0
$269$	182.681	−	105.471i	0.679111	−	0.392085i	−0.120409	−	0.992724i	$-0.538421\pi$
$269$	182.681	−	105.471i	0.679111	−	0.392085i	0.799520	+	0.600639i	$0.205087\pi$
$270$		0			0
$271$	−129.425	+	224.171i	−0.477584	+	0.827199i	−0.999670	−	0.0256934i	$-0.991821\pi$
$271$	−129.425	+	224.171i	−0.477584	+	0.827199i	0.522086	+	0.852893i	$0.325154\pi$
$272$		0			0
$273$	−24.3287	−	22.1023i	−0.0891163	−	0.0809609i
$274$		0			0
$275$			764.764i			2.78096i
$276$		0			0
$277$	−409.257			−1.47746			−0.738731	−	0.674000i	$-0.764575\pi$
$277$	−409.257			−1.47746			−0.738731	+	0.674000i	$0.764575\pi$
$278$		0			0
$279$	113.237	−	166.242i	0.405868	−	0.595851i
$280$		0			0
$281$	−277.104	−	159.986i	−0.986134	−	0.569344i	−0.0820173	−	0.996631i	$-0.526136\pi$
$281$	−277.104	−	159.986i	−0.986134	−	0.569344i	−0.904116	+	0.427286i	$0.859470\pi$
$282$		0			0
$283$	−61.8838	+	107.186i	−0.218671	+	0.378749i	−0.954402	−	0.298525i	$-0.903505\pi$
$283$	−61.8838	+	107.186i	−0.218671	+	0.378749i	0.735731	+	0.677274i	$0.236839\pi$
$284$		0			0
$285$	−239.228	−	150.245i	−0.839397	−	0.527175i
$286$		0			0
$287$	−255.004	+	302.567i	−0.888515	+	1.05424i
$288$		0			0
$289$	−97.4913	+	168.860i	−0.337340	+	0.584290i
$290$		0			0
$291$	−308.539	+	491.273i	−1.06027	+	1.68822i
$292$		0			0
$293$	16.0474	−	9.26498i	0.0547693	−	0.0316211i	−0.472365	−	0.881403i	$-0.656600\pi$
$293$	16.0474	−	9.26498i	0.0547693	−	0.0316211i	0.527135	+	0.849782i	$0.323266\pi$
$294$		0			0
$295$	129.112	−	223.629i	0.437669	−	0.758066i
$296$		0			0
$297$	57.7492	−	515.537i	0.194442	−	1.73581i
$298$		0			0
$299$	−2.81317	+	1.62418i	−0.00940860	+	0.00543206i
$300$		0			0
$301$	−53.2306	+	298.105i	−0.176846	+	0.990381i
$302$		0			0
$303$	7.51894	−	202.115i	0.0248150	−	0.667045i
$304$		0			0
$305$	519.672	−	300.033i	1.70384	−	0.983714i
$306$		0			0
$307$	363.739			1.18482			0.592408	−	0.805638i	$-0.298177\pi$
$307$	363.739			1.18482			0.592408	+	0.805638i	$0.298177\pi$
$308$		0			0
$309$	−240.685	−	8.95382i	−0.778917	−	0.0289768i
$310$		0			0
$311$	−130.067	−	75.0941i	−0.418221	−	0.241460i	0.276095	−	0.961130i	$-0.410960\pi$
$311$	−130.067	−	75.0941i	−0.418221	−	0.241460i	−0.694316	+	0.719670i	$0.744293\pi$
$312$		0			0
$313$	117.107	+	202.836i	0.374145	+	0.648038i	0.990199	−	0.139666i	$-0.0446029\pi$
$313$	117.107	+	202.836i	0.374145	+	0.648038i	−0.616054	+	0.787704i	$0.711270\pi$
$314$		0			0
$315$	136.510	+	488.437i	0.433365	+	1.55059i
$316$		0			0
$317$	−340.075	+	196.342i	−1.07279	+	0.619377i	−0.928943	−	0.370223i	$-0.879281\pi$
$317$	−340.075	+	196.342i	−1.07279	+	0.619377i	−0.143849	+	0.989600i	$0.545948\pi$
$318$		0			0
$319$	446.478	−	773.322i	1.39962	−	2.42421i
$320$		0			0
$321$	−317.074	−	199.136i	−0.987770	−	0.620360i
$322$		0			0
$323$			113.421i			0.351149i
$324$		0			0
$325$	−31.1506	−	53.9545i	−0.0958481	−	0.166014i
$326$		0			0
$327$	226.646	+	428.612i	0.693108	+	1.31074i
$328$		0			0
$329$	28.6589	−	34.0044i	0.0871091	−	0.103357i
$330$		0			0
$331$	−76.0134	−	131.659i	−0.229648	−	0.397761i	0.728056	−	0.685518i	$-0.240424\pi$
$331$	−76.0134	−	131.659i	−0.229648	−	0.397761i	−0.957704	+	0.287756i	$0.907091\pi$
$332$		0			0
$333$	−310.296	+	455.543i	−0.931820	+	1.36800i
$334$		0			0
$335$	33.1981	+	19.1669i	0.0990987	+	0.0572147i
$336$		0			0
$337$	−142.286	−	246.447i	−0.422214	−	0.731295i	0.573942	−	0.818896i	$-0.305413\pi$
$337$	−142.286	−	246.447i	−0.422214	−	0.731295i	−0.996156	+	0.0876006i	$0.972080\pi$
$338$		0			0
$339$	88.1347	−	46.6049i	0.259984	−	0.137478i
$340$		0			0
$341$	−371.878	−	214.704i	−1.09055	−	0.629630i
$342$		0			0
$343$	−173.428	+	295.925i	−0.505622	+	0.862755i
$344$		0			0
$345$	50.0856	+	1.86325i	0.145176	+	0.00540073i
$346$		0			0
$347$	115.858	+	66.8907i	0.333885	+	0.192768i	0.657565	−	0.753398i	$-0.271587\pi$
$347$	115.858	+	66.8907i	0.333885	+	0.192768i	−0.323680	+	0.946167i	$0.604920\pi$
$348$		0			0
$349$	−231.018	+	400.135i	−0.661943	+	1.14652i	0.318162	+	0.948036i	$0.396934\pi$
$349$	−231.018	+	400.135i	−0.661943	+	1.14652i	−0.980105	+	0.198482i	$0.936399\pi$
$350$		0			0
$351$	16.9248	+	38.7236i	0.0482188	+	0.110324i
$352$		0			0
$353$			644.199i			1.82492i	0.409160	+	0.912462i	$0.365822\pi$
$353$			644.199i			1.82492i	−0.409160	+	0.912462i	$0.634178\pi$
$354$		0			0
$355$	267.079			0.752335
$356$		0			0
$357$	136.921	−	150.713i	0.383531	−	0.422165i
$358$		0			0
$359$	−157.335	−	90.8373i	−0.438259	−	0.253029i	0.264600	−	0.964358i	$-0.414760\pi$
$359$	−157.335	−	90.8373i	−0.438259	−	0.253029i	−0.702859	+	0.711329i	$0.748093\pi$
$360$		0			0
$361$	112.085	+	194.137i	0.310485	+	0.537776i
$362$		0			0
$363$	−743.947	−	27.6758i	−2.04944	−	0.0762420i
$364$		0			0
$365$	92.1260	−	53.1889i	0.252400	−	0.145723i
$366$		0			0
$367$	−563.242			−1.53472			−0.767360	−	0.641217i	$-0.778430\pi$
$367$	−563.242			−1.53472			−0.767360	+	0.641217i	$0.778430\pi$
$368$		0			0
$369$	458.272	−	220.936i	1.24193	−	0.598742i
$370$		0			0
$371$	288.323	−	342.101i	0.777152	−	0.922106i
$372$		0			0
$373$	−44.1540			−0.118375			−0.0591877	−	0.998247i	$-0.518851\pi$
$373$	−44.1540			−0.118375			−0.0591877	+	0.998247i	$0.518851\pi$
$374$		0			0
$375$	−13.2908	+	357.267i	−0.0354421	+	0.952711i
$376$		0			0
$377$			72.7444i			0.192956i
$378$		0			0
$379$	106.066			0.279857			0.139928	−	0.990162i	$-0.455313\pi$
$379$	106.066			0.279857			0.139928	+	0.990162i	$0.455313\pi$
$380$		0			0
$381$	−583.886	−	21.7214i	−1.53251	−	0.0570114i
$382$		0			0
$383$		−	313.826i		−	0.819390i	−0.912223	−	0.409695i	$-0.865635\pi$
$383$		−	313.826i		−	0.819390i	0.912223	−	0.409695i	$-0.134365\pi$
$384$		0			0
$385$	1018.19	−	368.093i	2.64465	−	0.956086i
$386$		0			0
$387$	219.184	−	321.782i	0.566367	−	0.831479i
$388$		0			0
$389$			61.5101i			0.158124i	0.996870	+	0.0790618i	$0.0251924\pi$
$389$			61.5101i			0.158124i	−0.996870	+	0.0790618i	$0.974808\pi$
$390$		0			0
$391$	−10.0616	−	17.4272i	−0.0257330	−	0.0445708i
$392$		0			0
$393$	−13.0535	+	350.888i	−0.0332150	+	0.892845i
$394$		0			0
$395$	−322.407	+	186.142i	−0.816221	+	0.471245i
$396$		0			0
$397$	−65.6615	+	113.729i	−0.165394	+	0.286471i	−0.936795	−	0.349878i	$-0.886223\pi$
$397$	−65.6615	+	113.729i	−0.165394	+	0.286471i	0.771401	+	0.636349i	$0.219556\pi$
$398$		0			0
$399$	−52.1403	+	240.048i	−0.130677	+	0.601625i
$400$		0			0
$401$			209.667i			0.522861i	0.965222	+	0.261431i	$0.0841943\pi$
$401$			209.667i			0.522861i	−0.965222	+	0.261431i	$0.915806\pi$
$402$		0			0
$403$	34.9816			0.0868029
$404$		0			0
$405$	96.6276	−	644.857i	0.238587	−	1.59224i
$406$		0			0
$407$	1019.03	+	588.338i	2.50376	+	1.44555i
$408$		0			0
$409$	−136.488	+	236.404i	−0.333711	+	0.578005i	−0.983236	−	0.182335i	$-0.941634\pi$
$409$	−136.488	+	236.404i	−0.333711	+	0.578005i	0.649525	+	0.760340i	$0.274968\pi$
$410$		0			0
$411$	8.90132	−	239.274i	0.0216577	−	0.582175i
$412$		0			0
$413$	−221.045	−	39.4705i	−0.535218	−	0.0955702i
$414$		0			0
$415$	376.672	−	652.414i	0.907642	−	1.57208i
$416$		0			0
$417$	−106.329	−	201.078i	−0.254984	−	0.482202i
$418$		0			0
$419$	93.8050	−	54.1584i	0.223878	−	0.129256i	−0.383866	−	0.923389i	$-0.625408\pi$
$419$	93.8050	−	54.1584i	0.223878	−	0.129256i	0.607745	+	0.794132i	$0.292074\pi$
$420$		0			0
$421$	−268.137	+	464.427i	−0.636905	+	1.10315i	0.349203	+	0.937047i	$0.386452\pi$
$421$	−268.137	+	464.427i	−0.636905	+	1.10315i	−0.986108	+	0.166104i	$0.946881\pi$
$422$		0			0
$423$	−51.5035	+	24.8301i	−0.121758	+	0.0587001i
$424$		0			0
$425$	334.240	−	192.974i	0.786448	−	0.454056i
$426$		0			0
$427$	−398.987	−	336.267i	−0.934396	−	0.787510i
$428$		0			0
$429$	79.7549	−	42.1737i	0.185909	−	0.0983070i
$430$		0			0
$431$	235.401	−	135.909i	0.546173	−	0.315333i	−0.201404	−	0.979508i	$-0.564550\pi$
$431$	235.401	−	135.909i	0.546173	−	0.315333i	0.747577	+	0.664175i	$0.231217\pi$
$432$		0			0
$433$	−428.323			−0.989199			−0.494600	−	0.869121i	$-0.664685\pi$
$433$	−428.323			−0.989199			−0.494600	+	0.869121i	$0.664685\pi$
$434$		0			0
$435$	596.947	−	950.492i	1.37229	−	2.18504i
$436$		0			0
$437$	21.0239	+	12.1381i	0.0481096	+	0.0277761i
$438$		0			0
$439$	153.290	+	265.505i	0.349179	+	0.604795i	0.986104	−	0.166130i	$-0.0531272\pi$
$439$	153.290	+	265.505i	0.349179	+	0.604795i	−0.636925	+	0.770926i	$0.719794\pi$
$440$		0			0
$441$	359.067	−	256.031i	0.814211	−	0.580569i
$442$		0			0
$443$	−251.820	+	145.388i	−0.568443	+	0.328191i	−0.756527	−	0.653962i	$-0.773105\pi$
$443$	−251.820	+	145.388i	−0.568443	+	0.328191i	0.188084	+	0.982153i	$0.439772\pi$
$444$		0			0
$445$	259.811	−	450.006i	0.583845	−	1.01125i
$446$		0			0
$447$	12.1513	−	326.637i	0.0271842	−	0.730731i
$448$		0			0
$449$		−	278.892i		−	0.621140i	−0.950550	−	0.310570i	$-0.899480\pi$
$449$		−	278.892i		−	0.621140i	0.950550	−	0.310570i	$-0.100520\pi$
$450$		0			0
$451$	−543.044	−	940.580i	−1.20409	−	2.08554i
$452$		0			0
$453$	489.963	+	18.2273i	1.08160	+	0.0402368i
$454$		0			0
$455$	−56.8406	+	67.4425i	−0.124924	+	0.148225i
$456$		0			0
$457$	−221.608	−	383.836i	−0.484919	−	0.839904i	0.514931	−	0.857232i	$-0.327818\pi$
$457$	−221.608	−	383.836i	−0.484919	−	0.839904i	−0.999850	+	0.0173275i	$0.994484\pi$
$458$		0			0
$459$	−239.887	+	104.847i	−0.522630	+	0.228424i
$460$		0			0
$461$	134.497	+	77.6519i	0.291751	+	0.168442i	0.638731	−	0.769430i	$-0.279460\pi$
$461$	134.497	+	77.6519i	0.291751	+	0.168442i	−0.346980	+	0.937872i	$0.612793\pi$
$462$		0			0
$463$	201.958	+	349.802i	0.436195	+	0.755511i	0.997392	−	0.0721704i	$-0.0229925\pi$
$463$	201.958	+	349.802i	0.436195	+	0.755511i	−0.561198	+	0.827682i	$0.689659\pi$
$464$		0			0
$465$	−457.076	−	287.062i	−0.982959	−	0.617338i
$466$		0			0
$467$	358.548	+	207.008i	0.767769	+	0.443272i	0.832078	−	0.554658i	$-0.187151\pi$
$467$	358.548	+	207.008i	0.767769	+	0.443272i	−0.0643092	+	0.997930i	$0.520484\pi$
$468$		0			0
$469$	5.85945	−	32.8144i	0.0124935	−	0.0699668i
$470$		0			0
$471$	50.2805	−	80.0592i	0.106753	−	0.169977i
$472$		0			0
$473$	−719.815	−	415.585i	−1.52181	−	0.878616i
$474$		0			0
$475$	−232.800	+	403.222i	−0.490106	+	0.848889i
$476$		0			0
$477$	−518.151	+	249.804i	−1.08627	+	0.523698i
$478$		0			0
$479$		−	832.818i		−	1.73866i	−0.494232	−	0.869330i	$-0.664551\pi$
$479$		−	832.818i		−	1.73866i	0.494232	−	0.869330i	$-0.335449\pi$
$480$		0			0
$481$	−95.8576			−0.199288
$482$		0			0
$483$	−13.2833	−	41.5088i	−0.0275017	−	0.0859396i
$484$		0			0
$485$	1348.13	+	778.342i	2.77965	+	1.60483i
$486$		0			0
$487$	90.7601	+	157.201i	0.186366	+	0.322795i	0.944036	−	0.329843i	$-0.106996\pi$
$487$	90.7601	+	157.201i	0.186366	+	0.322795i	−0.757670	+	0.652638i	$0.773662\pi$
$488$		0			0
$489$	476.963	−	759.445i	0.975384	−	1.55306i
$490$		0			0
$491$	−213.443	+	123.232i	−0.434712	+	0.250981i	−0.701352	−	0.712815i	$-0.747420\pi$
$491$	−213.443	+	123.232i	−0.434712	+	0.250981i	0.266640	+	0.963796i	$0.414086\pi$
$492$		0			0
$493$	−450.641			−0.914079
$494$		0			0
$495$	−1388.17	−	103.427i	−2.80439	−	0.208944i
$496$		0			0
$497$	−78.9575	−	218.406i	−0.158868	−	0.439449i
$498$		0			0
$499$	−927.638			−1.85899			−0.929497	−	0.368829i	$-0.879759\pi$
$499$	−927.638			−1.85899			−0.929497	+	0.368829i	$0.879759\pi$
$500$		0			0
$501$	693.298	−	366.610i	1.38383	−	0.731757i
$502$		0			0
$503$			569.020i			1.13125i	0.824662	+	0.565626i	$0.191366\pi$
$503$			569.020i			1.13125i	−0.824662	+	0.565626i	$0.808634\pi$
$504$		0			0
$505$	−542.721			−1.07470
$506$		0			0
$507$	265.739	−	423.123i	0.524140	−	0.834563i
$508$		0			0
$509$		−	631.624i		−	1.24091i	−0.784242	−	0.620456i	$-0.786948\pi$
$509$		−	631.624i		−	1.24091i	0.784242	−	0.620456i	$-0.213052\pi$
$510$		0			0
$511$	−70.7313	−	59.6124i	−0.138417	−	0.116658i
$512$		0			0
$513$	187.382	−	254.238i	0.365267	−	0.495590i
$514$		0			0
$515$			646.292i			1.25494i
$516$		0			0
$517$	61.0307	+	105.708i	0.118048	+	0.204465i
$518$		0			0
$519$	510.472	−	269.933i	0.983568	−	0.520102i
$520$		0			0
$521$	−278.992	+	161.076i	−0.535494	+	0.309168i	−0.743251	−	0.669013i	$-0.766717\pi$
$521$	−278.992	+	161.076i	−0.535494	+	0.309168i	0.207757	+	0.978181i	$0.433384\pi$
$522$		0			0
$523$	−204.092	+	353.498i	−0.390233	+	0.675904i	−0.992480	−	0.122406i	$-0.960939\pi$
$523$	−204.092	+	353.498i	−0.390233	+	0.675904i	0.602247	+	0.798310i	$0.294272\pi$
$524$		0			0
$525$	796.108	−	254.764i	1.51640	−	0.485265i
$526$		0			0
$527$			216.706i			0.411206i
$528$		0			0
$529$	524.693			0.991858
$530$		0			0
$531$	238.602	+	162.525i	0.449344	+	0.306074i
$532$		0			0
$533$	76.6241	+	44.2389i	0.143760	+	0.0829999i
$534$		0			0
$535$	−502.353	+	870.101i	−0.938977	+	1.62636i
$536$		0			0
$537$	−930.049	+	491.802i	−1.73194	+	0.915833i
$538$		0			0
$539$	−602.023	−	723.814i	−1.11693	−	1.34288i
$540$		0			0
$541$	−182.747	+	316.528i	−0.337795	+	0.585079i	−0.984018	−	0.178070i	$-0.943015\pi$
$541$	−182.747	+	316.528i	−0.337795	+	0.585079i	0.646222	+	0.763149i	$0.276348\pi$
$542$		0			0
$543$	683.266	+	25.4184i	1.25832	+	0.0468111i
$544$		0			0
$545$	1126.72	−	650.510i	2.06737	−	1.19360i
$546$		0			0
$547$	−294.880	+	510.747i	−0.539086	+	0.933724i	0.459868	+	0.887987i	$0.347897\pi$
$547$	−294.880	+	510.747i	−0.539086	+	0.933724i	−0.998954	+	0.0457367i	$0.985436\pi$
$548$		0			0
$549$	291.342	+	604.311i	0.530678	+	1.10075i
$550$		0			0
$551$	470.811	−	271.823i	0.854467	−	0.493327i
$552$		0			0
$553$	247.534	+	208.622i	0.447620	+	0.377254i
$554$		0			0
$555$	1252.49	+	786.617i	2.25675	+	1.41733i
$556$		0			0
$557$	−426.103	+	246.011i	−0.764996	+	0.441671i	−0.831087	−	0.556143i	$-0.812281\pi$
$557$	−426.103	+	246.011i	−0.764996	+	0.441671i	0.0660907	+	0.997814i	$0.478947\pi$
$558$		0			0
$559$	67.7111			0.121129
$560$		0			0
$561$	261.260	+	494.070i	0.465704	+	0.880696i
$562$		0			0
$563$	−18.3180	−	10.5759i	−0.0325365	−	0.0187850i	0.483644	−	0.875265i	$-0.339313\pi$
$563$	−18.3180	−	10.5759i	−0.0325365	−	0.0187850i	−0.516180	+	0.856480i	$0.672646\pi$
$564$		0			0
$565$	−133.763	−	231.685i	−0.236749	−	0.410061i
$566$		0			0
$567$	−555.904	+	111.623i	−0.980430	+	0.196867i
$568$		0			0
$569$	−133.437	+	77.0401i	−0.234512	+	0.135396i	−0.612652	−	0.790353i	$-0.709897\pi$
$569$	−133.437	+	77.0401i	−0.234512	+	0.135396i	0.378140	+	0.925749i	$0.376564\pi$
$570$		0			0
$571$	−22.5846	+	39.1178i	−0.0395528	+	0.0685075i	−0.885124	−	0.465355i	$-0.845927\pi$
$571$	−22.5846	+	39.1178i	−0.0395528	+	0.0685075i	0.845571	+	0.533862i	$0.179260\pi$
$572$		0			0
$573$	−497.574	+	263.113i	−0.868366	+	0.459184i
$574$		0			0
$575$		−	82.6069i		−	0.143664i
$576$		0			0
$577$	13.1264	+	22.7356i	0.0227494	+	0.0394032i	0.877176	−	0.480169i	$-0.159425\pi$
$577$	13.1264	+	22.7356i	0.0227494	+	0.0394032i	−0.854427	+	0.519572i	$0.826091\pi$
$578$		0			0
$579$	57.1386	−	90.9791i	0.0986850	−	0.157131i
$580$		0			0
$581$	−644.875	−	115.151i	−1.10994	−	0.198194i
$582$		0			0
$583$	614.000	+	1063.48i	1.05317	+	1.82415i
$584$		0			0
$585$	102.149	−	49.2468i	0.174614	−	0.0841825i
$586$		0			0
$587$	606.599	+	350.220i	1.03339	+	0.596627i	0.917953	−	0.396688i	$-0.129841\pi$
$587$	606.599	+	350.220i	1.03339	+	0.596627i	0.115434	+	0.993315i	$0.463174\pi$
$588$		0			0
$589$	−130.715	−	226.405i	−0.221927	−	0.384389i
$590$		0			0
$591$	12.2759	−	329.985i	0.0207714	−	0.558350i
$592$		0			0
$593$	679.184	+	392.127i	1.14534	+	0.661260i	0.947746	−	0.319025i	$-0.103355\pi$
$593$	679.184	+	392.127i	1.14534	+	0.661260i	0.197589	+	0.980285i	$0.436689\pi$
$594$		0			0
$595$	−417.796	−	352.119i	−0.702179	−	0.591797i
$596$		0			0
$597$	96.8080	+	183.074i	0.162157	+	0.306657i
$598$		0			0
$599$	−449.279	−	259.391i	−0.750048	−	0.433041i	0.0756631	−	0.997133i	$-0.475893\pi$
$599$	−449.279	−	259.391i	−0.750048	−	0.433041i	−0.825711	+	0.564093i	$0.809226\pi$
$600$		0			0
$601$	1.71229	−	2.96577i	0.00284907	−	0.00493473i	−0.864597	−	0.502465i	$-0.832426\pi$
$601$	1.71229	−	2.96577i	0.00284907	−	0.00493473i	0.867446	+	0.497531i	$0.165760\pi$
$602$		0			0
$603$	−24.1271	+	35.4208i	−0.0400118	+	0.0587409i
$604$		0			0
$605$			1997.66i			3.30191i
$606$		0			0
$607$	439.277			0.723686			0.361843	−	0.932239i	$-0.382148\pi$
$607$	439.277			0.723686			0.361843	+	0.932239i	$0.382148\pi$
$608$		0			0
$609$	−953.751	−	207.162i	−1.56609	−	0.340167i
$610$		0			0
$611$	−8.61149	−	4.97184i	−0.0140941	−	0.00813722i
$612$		0			0
$613$	56.2801	+	97.4800i	0.0918109	+	0.159021i	0.908273	−	0.418378i	$-0.137401\pi$
$613$	56.2801	+	97.4800i	0.0918109	+	0.159021i	−0.816462	+	0.577399i	$0.804068\pi$
$614$		0			0
$615$	−638.156	−	1206.82i	−1.03765	−	1.96231i
$616$		0			0
$617$	−259.198	+	149.648i	−0.420094	+	0.242541i	−0.695117	−	0.718896i	$-0.744648\pi$
$617$	−259.198	+	149.648i	−0.420094	+	0.242541i	0.275024	+	0.961437i	$0.411314\pi$
$618$		0			0
$619$	286.982			0.463621			0.231811	−	0.972761i	$-0.425535\pi$
$619$	286.982			0.463621			0.231811	+	0.972761i	$0.425535\pi$
$620$		0			0
$621$	−6.23785	+	55.6863i	−0.0100448	+	0.0896719i
$622$		0			0
$623$	−444.806	−	79.4259i	−0.713974	−	0.127489i
$624$		0			0
$625$	−35.7559			−0.0572095
$626$		0			0
$627$	−570.973	−	358.595i	−0.910643	−	0.571921i
$628$		0			0
$629$		−	593.824i		−	0.944077i
$630$		0			0
$631$	−263.760			−0.418003			−0.209001	−	0.977915i	$-0.567021\pi$
$631$	−263.760			−0.418003			−0.209001	+	0.977915i	$0.567021\pi$
$632$		0			0
$633$	343.532	+	649.655i	0.542705	+	1.02631i
$634$		0			0
$635$			1567.86i			2.46907i
$636$		0			0
$637$	71.9557	+	26.5436i	0.112960	+	0.0416697i
$638$		0			0
$639$	−22.1856	+	297.769i	−0.0347192	+	0.465993i
$640$		0			0
$641$		−	120.631i		−	0.188192i	−0.995563	−	0.0940960i	$-0.970004\pi$
$641$		−	120.631i		−	0.188192i	0.995563	−	0.0940960i	$-0.0299961\pi$
$642$		0			0
$643$	−477.894	−	827.737i	−0.743226	−	1.28730i	−0.951019	−	0.309132i	$-0.899962\pi$
$643$	−477.894	−	827.737i	−0.743226	−	1.28730i	0.207794	−	0.978173i	$-0.433372\pi$
$644$		0			0
$645$	−884.726	−	555.644i	−1.37167	−	0.861463i
$646$		0			0
$647$	340.484	−	196.578i	0.526250	−	0.303831i	−0.213238	−	0.977000i	$-0.568401\pi$
$647$	340.484	−	196.578i	0.526250	−	0.303831i	0.739488	+	0.673170i	$0.235068\pi$
$648$		0			0
$649$	308.157	−	533.743i	0.474818	−	0.822409i
$650$		0			0
$651$	−99.6208	+	458.643i	−0.153027	+	0.704521i
$652$		0			0
$653$			693.093i			1.06140i	0.847560	+	0.530699i	$0.178071\pi$
$653$			693.093i			1.06140i	−0.847560	+	0.530699i	$0.821929\pi$
$654$		0			0
$655$	942.210			1.43849
$656$		0			0
$657$	51.6483	+	107.131i	0.0786123	+	0.163060i
$658$		0			0
$659$	−120.779	−	69.7321i	−0.183277	−	0.105815i	0.405554	−	0.914071i	$-0.367078\pi$
$659$	−120.779	−	69.7321i	−0.183277	−	0.105815i	−0.588831	+	0.808256i	$0.700412\pi$
$660$		0			0
$661$	101.266	−	175.398i	0.153201	−	0.265352i	−0.779201	−	0.626774i	$-0.784375\pi$
$661$	101.266	−	175.398i	0.153201	−	0.265352i	0.932403	+	0.361421i	$0.117708\pi$
$662$		0			0
$663$	−38.5567	−	24.2152i	−0.0581549	−	0.0365236i
$664$		0			0
$665$	648.892	+	115.868i	0.975778	+	0.174238i
$666$		0			0
$667$	−48.2268	+	83.5313i	−0.0723040	+	0.125234i
$668$		0			0
$669$	−160.303	+	255.243i	−0.239615	+	0.381528i
$670$		0			0
$671$	1240.32	−	716.098i	1.84846	−	1.06721i
$672$		0			0
$673$	−319.572	+	553.515i	−0.474847	+	0.822459i	−0.999585	−	0.0288047i	$-0.990830\pi$
$673$	−319.572	+	553.515i	−0.474847	+	0.822459i	0.524738	+	0.851264i	$0.324163\pi$
$674$		0			0
$675$	−1068.02	−	119.637i	−1.58225	−	0.177240i
$676$		0			0
$677$	−298.599	+	172.396i	−0.441062	+	0.254647i	−0.704048	−	0.710152i	$-0.748626\pi$
$677$	−298.599	+	172.396i	−0.441062	+	0.254647i	0.262986	+	0.964800i	$0.415293\pi$
$678$		0			0
$679$	237.944	−	1332.55i	0.350433	−	1.96252i
$680$		0			0
$681$	18.6113	−	500.285i	0.0273294	−	0.734633i
$682$		0			0
$683$	392.616	−	226.677i	0.574840	−	0.331884i	−0.184240	−	0.982881i	$-0.558982\pi$
$683$	392.616	−	226.677i	0.574840	−	0.331884i	0.759080	+	0.650997i	$0.225649\pi$
$684$		0			0
$685$	−642.502			−0.937959
$686$		0			0
$687$	−832.012	−	30.9520i	−1.21108	−	0.0450538i
$688$		0			0
$689$	−86.6360	−	50.0193i	−0.125742	−	0.0725970i
$690$		0			0
$691$	10.8436	+	18.7816i	0.0156926	+	0.0271804i	0.873765	−	0.486348i	$-0.161671\pi$
$691$	10.8436	+	18.7816i	0.0156926	+	0.0271804i	−0.858072	+	0.513529i	$0.828338\pi$
$692$		0			0
$693$	325.813	+	1165.77i	0.470148	+	1.68221i
$694$		0			0
$695$	−528.586	+	305.179i	−0.760555	+	0.439107i
$696$		0			0
$697$	−274.054	+	474.675i	−0.393191	+	0.681026i
$698$		0			0
$699$	120.973	+	75.9757i	0.173065	+	0.108692i
$700$		0			0
$701$			988.932i			1.41074i	0.708837	+	0.705372i	$0.249220\pi$
$701$			988.932i			1.41074i	−0.708837	+	0.705372i	$0.750780\pi$
$702$		0			0
$703$	358.190	+	620.403i	0.509516	+	0.882508i
$704$		0			0
$705$	71.7199	+	135.630i	0.101730	+	0.192383i
$706$		0			0
$707$	160.447	+	443.815i	0.226940	+	0.627744i
$708$		0			0
$709$	−328.607	−	569.164i	−0.463480	−	0.802771i	0.535652	−	0.844439i	$-0.320066\pi$
$709$	−328.607	−	569.164i	−0.463480	−	0.802771i	−0.999131	+	0.0416683i	$0.986733\pi$
$710$		0			0
$711$	−180.750	−	374.918i	−0.254220	−	0.527311i
$712$		0			0
$713$	40.1688	+	23.1915i	0.0563378	+	0.0325266i
$714$		0			0
$715$	−121.045	−	209.656i	−0.169294	−	0.293225i
$716$		0			0
$717$	612.000	−	323.620i	0.853556	−	0.451353i
$718$		0			0
$719$	−490.350	−	283.104i	−0.681988	−	0.393746i	0.118615	−	0.992940i	$-0.462154\pi$
$719$	−490.350	−	283.104i	−0.681988	−	0.393746i	−0.800604	+	0.599194i	$0.795488\pi$
$720$		0			0
$721$	528.511	−	191.066i	0.733025	−	0.265001i
$722$		0			0
$723$	891.814	+	33.1767i	1.23349	+	0.0458875i
$724$		0			0
$725$	−1602.07	−	924.954i	−2.20975	−	1.27580i
$726$		0			0
$727$	61.6116	−	106.714i	0.0847478	−	0.146787i	−0.820536	−	0.571595i	$-0.806325\pi$
$727$	61.6116	−	106.714i	0.0847478	−	0.146787i	0.905284	+	0.424807i	$0.139658\pi$
$728$		0			0
$729$	710.932	+	161.298i	0.975215	+	0.221259i
$730$		0			0
$731$			419.460i			0.573817i
$732$		0			0
$733$	1037.13			1.41492			0.707458	−	0.706756i	$-0.249842\pi$
$733$	1037.13			1.41492			0.707458	+	0.706756i	$0.249842\pi$
$734$		0			0
$735$	−722.367	−	937.299i	−0.982812	−	1.27524i
$736$		0			0
$737$	79.2349	+	45.7463i	0.107510	+	0.0620709i
$738$		0			0
$739$	536.011	+	928.397i	0.725319	+	1.25629i	0.958843	+	0.283938i	$0.0916409\pi$
$739$	536.011	+	928.397i	0.725319	+	1.25629i	−0.233524	+	0.972351i	$0.575026\pi$
$740$		0			0
$741$	54.8888	+	2.04194i	0.0740740	+	0.00275565i
$742$		0			0
$743$	−645.464	+	372.659i	−0.868727	+	0.501560i	−0.866925	−	0.498439i	$-0.833907\pi$
$743$	−645.464	+	372.659i	−0.868727	+	0.501560i	−0.00180187	+	0.999998i	$0.500574\pi$
$744$		0			0
$745$	−877.090			−1.17730
$746$		0			0
$747$	696.095	+	474.150i	0.931854	+	0.634739i
$748$		0			0
$749$	860.045	+	153.573i	1.14826	+	0.205037i
$750$		0			0
$751$	−6.37835			−0.00849314			−0.00424657	−	0.999991i	$-0.501352\pi$
$751$	−6.37835			−0.00849314			−0.00424657	+	0.999991i	$0.501352\pi$
$752$		0			0
$753$	−9.50820	+	255.588i	−0.0126271	+	0.339426i
$754$		0			0
$755$		−	1315.66i		−	1.74259i
$756$		0			0
$757$	1187.30			1.56843			0.784216	−	0.620488i	$-0.213066\pi$
$757$	1187.30			1.56843			0.784216	+	0.620488i	$0.213066\pi$
$758$		0			0
$759$	119.541	+	4.44709i	0.157498	+	0.00585914i
$760$		0			0
$761$		−	271.035i		−	0.356157i	−0.984016	−	0.178078i	$-0.943012\pi$
$761$		−	271.035i		−	0.356157i	0.984016	−	0.178078i	$-0.0569880\pi$
$762$		0			0
$763$	−865.055	−	729.069i	−1.13376	−	0.955530i
$764$		0			0
$765$	305.077	+	632.800i	0.398793	+	0.827189i
$766$		0			0
$767$			50.2078i			0.0654600i
$768$		0			0
$769$	−12.4068	−	21.4892i	−0.0161337	−	0.0279443i	0.857846	−	0.513907i	$-0.171802\pi$
$769$	−12.4068	−	21.4892i	−0.0161337	−	0.0279443i	−0.873980	+	0.485963i	$0.838469\pi$
$770$		0			0
$771$	8.00279	−	215.121i	0.0103798	−	0.279015i
$772$		0			0
$773$	780.685	−	450.729i	1.00994	−	0.583090i	0.0987672	−	0.995111i	$-0.468510\pi$
$773$	780.685	−	450.729i	1.00994	−	0.583090i	0.911175	+	0.412020i	$0.135177\pi$
$774$		0			0
$775$	−444.795	+	770.408i	−0.573929	+	0.994075i
$776$		0			0
$777$	272.984	−	1256.79i	0.351331	−	1.61749i
$778$		0			0
$779$		−	661.229i		−	0.848817i
$780$		0			0
$781$	637.446			0.816192
$782$		0			0
$783$	1010.13	+	744.499i	1.29007	+	0.950828i
$784$		0			0
$785$	−219.695	−	126.841i	−0.279866	−	0.161581i
$786$		0			0
$787$	−389.427	+	674.508i	−0.494825	+	0.857063i	−0.999982	−	0.00596498i	$-0.998101\pi$
$787$	−389.427	+	674.508i	−0.494825	+	0.857063i	0.505157	+	0.863028i	$0.331435\pi$
$788$		0			0
$789$	38.0669	−	1023.27i	0.0482470	−	1.29691i
$790$		0			0
$791$	−149.917	+	177.880i	−0.189529	+	0.224880i
$792$		0			0
$793$	−58.3367	+	101.042i	−0.0735646	+	0.127418i
$794$		0			0
$795$	721.539	+	1364.51i	0.907596	+	1.71636i
$796$		0			0
$797$	492.791	−	284.513i	0.618307	−	0.356980i	−0.157903	−	0.987455i	$-0.550473\pi$
$797$	492.791	−	284.513i	0.618307	−	0.356980i	0.776210	+	0.630475i	$0.217140\pi$
$798$		0			0
$799$	30.7999	−	53.3469i	0.0385480	−	0.0667671i
$800$		0			0
$801$	480.135	+	327.047i	0.599420	+	0.408299i
$802$		0			0
$803$	219.880	−	126.948i	0.273823	−	0.158092i
$804$		0			0
$805$	−109.981	+	39.7600i	−0.136622	+	0.0493913i
$806$		0			0
$807$	559.427	−	295.820i	0.693218	−	0.366568i
$808$		0			0
$809$	888.209	−	512.808i	1.09791	−	0.633878i	0.162238	−	0.986752i	$-0.448129\pi$
$809$	888.209	−	512.808i	1.09791	−	0.633878i	0.935671	+	0.352873i	$0.114795\pi$
$810$		0			0
$811$	−276.040			−0.340370			−0.170185	−	0.985412i	$-0.554437\pi$
$811$	−276.040			−0.340370			−0.170185	+	0.985412i	$0.554437\pi$
$812$		0			0
$813$	−413.008	+	657.614i	−0.508005	+	0.808873i
$814$		0			0
$815$	−2084.04	−	1203.22i	−2.55710	−	1.47634i
$816$		0			0
$817$	−253.015	−	438.235i	−0.309688	−	0.536395i
$818$		0			0
$819$	−70.4708	−	68.9745i	−0.0860449	−	0.0842179i
$820$		0			0
$821$	−176.195	+	101.726i	−0.214610	+	0.123905i	−0.603452	−	0.797399i	$-0.706208\pi$
$821$	−176.195	+	101.726i	−0.214610	+	0.123905i	0.388842	+	0.921304i	$0.372875\pi$
$822$		0			0
$823$	−410.181	+	710.454i	−0.498397	+	0.863249i	−0.999998	−	0.00185026i	$-0.999411\pi$
$823$	−410.181	+	710.454i	−0.498397	+	0.863249i	0.501602	+	0.865099i	$0.332744\pi$
$824$		0			0
$825$	−85.2918	+	2292.71i	−0.103384	+	2.77904i
$826$		0			0
$827$		−	1580.90i		−	1.91161i	−0.293998	−	0.955806i	$-0.594986\pi$
$827$		−	1580.90i		−	1.91161i	0.293998	−	0.955806i	$-0.405014\pi$
$828$		0			0
$829$	51.7377	+	89.6124i	0.0624098	+	0.108097i	0.895542	−	0.444977i	$-0.146788\pi$
$829$	51.7377	+	89.6124i	0.0624098	+	0.108097i	−0.833132	+	0.553074i	$0.813455\pi$
$830$		0			0
$831$	−1226.92	−	45.6432i	−1.47644	−	0.0549256i
$832$		0			0
$833$	−164.434	+	445.755i	−0.197400	+	0.535120i
$834$		0			0
$835$	−1052.23	−	1822.51i	−1.26015	−	2.18265i
$836$		0			0
$837$	358.017	−	485.754i	0.427739	−	0.580351i
$838$		0			0
$839$	−1258.61	−	726.657i	−1.50013	−	0.866099i	−1.00000		0.000147057i	$-0.999953\pi$
$839$	−1258.61	−	726.657i	−1.50013	−	0.866099i	−0.500127	−	0.865952i	$-0.666713\pi$
$840$		0			0
$841$	659.496	+	1142.28i	0.784181	+	1.35824i
$842$		0			0
$843$	−812.893	−	510.530i	−0.964286	−	0.605611i
$844$		0			0
$845$	−1161.12	−	670.371i	−1.37410	−	0.793338i
$846$		0			0
$847$	1633.60	−	590.575i	1.92869	−	0.697255i
$848$		0			0
$849$	−197.477	+	314.434i	−0.232600	+	0.370357i
$850$		0			0
$851$	−110.072	−	63.5500i	−0.129344	−	0.0746769i
$852$		0			0
$853$	−52.3396	+	90.6549i	−0.0613595	+	0.106278i	−0.895073	−	0.445919i	$-0.852877\pi$
$853$	−52.3396	+	90.6549i	−0.0613595	+	0.106278i	0.833714	+	0.552197i	$0.186210\pi$
$854$		0			0
$855$	−700.432	−	477.104i	−0.819218	−	0.558016i
$856$		0			0
$857$		−	225.718i		−	0.263382i	−0.991291	−	0.131691i	$-0.957959\pi$
$857$		−	225.718i		−	0.263382i	0.991291	−	0.131691i	$-0.0420407\pi$
$858$		0			0
$859$	583.238			0.678973			0.339486	−	0.940611i	$-0.389747\pi$
$859$	583.238			0.678973			0.339486	+	0.940611i	$0.389747\pi$
$860$		0			0
$861$	−798.227	+	878.634i	−0.927093	+	1.02048i
$862$		0			0
$863$	−306.120	−	176.739i	−0.354716	−	0.204796i	0.312044	−	0.950068i	$-0.398986\pi$
$863$	−306.120	−	176.739i	−0.354716	−	0.204796i	−0.666761	+	0.745272i	$0.732320\pi$
$864$		0			0
$865$	−774.749	−	1341.90i	−0.895664	−	1.55133i
$866$		0			0
$867$	−311.104	+	495.356i	−0.358828	+	0.571345i
$868$		0			0
$869$	−769.500	+	444.271i	−0.885500	+	0.511244i
$870$		0			0
$871$	−7.45341			−0.00855731
$872$		0			0
$873$	−979.768	+	1438.39i	−1.12230	+	1.64764i
$874$		0			0
$875$	−283.613	−	784.507i	−0.324129	−	0.896579i
$876$		0			0
$877$	916.182			1.04468			0.522339	−	0.852738i	$-0.325060\pi$
$877$	916.182			1.04468			0.522339	+	0.852738i	$0.325060\pi$
$878$		0			0
$879$	49.1422	−	25.9860i	0.0559070	−	0.0295631i
$880$		0			0
$881$			1041.09i			1.18172i	0.806775	+	0.590859i	$0.201211\pi$
$881$			1041.09i			1.18172i	−0.806775	+	0.590859i	$0.798789\pi$
$882$		0			0
$883$	247.115			0.279858			0.139929	−	0.990162i	$-0.455313\pi$
$883$	247.115			0.279858			0.139929	+	0.990162i	$0.455313\pi$
$884$		0			0
$885$	412.010	−	656.025i	0.465548	−	0.741271i
$886$		0			0
$887$			1077.91i			1.21523i	0.794231	+	0.607616i	$0.207874\pi$
$887$			1077.91i			1.21523i	−0.794231	+	0.607616i	$0.792126\pi$
$888$		0			0
$889$	1282.13	−	463.512i	1.44222	−	0.521386i
$890$		0			0
$891$	230.624	−	1539.10i	0.258837	−	1.72739i
$892$		0			0
$893$			74.3129i			0.0832172i
$894$		0			0
$895$	1411.55	+	2444.87i	1.57715	+	2.73170i
$896$		0			0
$897$	−8.61482	+	4.55544i	−0.00960403	+	0.00507853i
$898$		0			0
$899$	899.545	−	519.353i	1.00061	−	0.577700i
$900$		0			0
$901$	309.862	−	536.697i	0.343909	−	0.595669i
$902$		0			0
$903$	−192.828	+	887.759i	−0.213542	+	0.983122i
$904$		0			0
$905$		−	1834.72i		−	2.02731i
$906$		0			0
$907$	−867.280			−0.956208			−0.478104	−	0.878303i	$-0.658676\pi$
$907$	−867.280			−0.956208			−0.478104	+	0.878303i	$0.658676\pi$
$908$		0			0
$909$	45.0824	−	605.086i	0.0495956	−	0.665661i
$910$		0			0
$911$	987.899	+	570.364i	1.08441	+	0.626085i	0.932083	−	0.362245i	$-0.117990\pi$
$911$	987.899	+	570.364i	1.08441	+	0.626085i	0.152328	+	0.988330i	$0.451323\pi$
$912$		0			0
$913$	899.014	−	1557.14i	0.984681	−	1.70552i
$914$		0			0
$915$	1591.40	−	841.519i	1.73924	−	0.919693i
$916$		0			0
$917$	−278.549	−	770.501i	−0.303761	−	0.840241i
$918$		0			0
$919$	308.533	−	534.394i	0.335726	−	0.581495i	−0.647898	−	0.761727i	$-0.724352\pi$
$919$	308.533	−	534.394i	0.335726	−	0.581495i	0.983624	+	0.180232i	$0.0576849\pi$
$920$		0			0
$921$	1090.46	+	40.5666i	1.18400	+	0.0440463i
$922$		0			0
$923$	−44.9721	+	25.9647i	−0.0487239	+	0.0281307i
$924$		0			0
$925$	1218.84	−	2111.10i	1.31767	−	2.28227i
$926$		0			0
$927$	−720.558	−	53.6858i	−0.777301	−	0.0579135i
$928$		0			0
$929$	−460.934	+	266.120i	−0.496161	+	0.286459i	−0.727127	−	0.686503i	$-0.759145\pi$
$929$	−460.934	+	266.120i	−0.496161	+	0.286459i	0.230966	+	0.972962i	$0.425811\pi$
$930$		0			0
$931$	−97.0820	−	564.892i	−0.104277	−	0.606758i
$932$		0			0
$933$	−381.556	−	239.633i	−0.408956	−	0.256841i
$934$		0			0
$935$	1298.79	−	749.856i	1.38908	−	0.801985i
$936$		0			0
$937$	−1506.24			−1.60751			−0.803755	−	0.594960i	$-0.797168\pi$
$937$	−1506.24			−1.60751			−0.803755	+	0.594960i	$0.797168\pi$
$938$		0			0
$939$	328.458	+	621.148i	0.349795	+	0.661499i
$940$		0			0
$941$	176.771	+	102.059i	0.187855	+	0.108458i	0.590978	−	0.806688i	$-0.298742\pi$
$941$	176.771	+	102.059i	0.187855	+	0.108458i	−0.403123	+	0.915146i	$0.632075\pi$
$942$		0			0
$943$	58.6575	+	101.598i	0.0622031	+	0.107739i
$944$		0			0
$945$	354.773	+	1479.52i	0.375421	+	1.56563i
$946$		0			0
$947$	−430.653	+	248.638i	−0.454755	+	0.262553i	−0.709836	−	0.704367i	$-0.751231\pi$
$947$	−430.653	+	248.638i	−0.454755	+	0.262553i	0.255081	+	0.966920i	$0.417898\pi$
$948$		0			0
$949$	−10.3418	+	17.9125i	−0.0108975	+	0.0188751i
$950$		0			0
$951$	−1041.42	+	550.693i	−1.09508	+	0.579067i
$952$		0			0
$953$		−	582.144i		−	0.610854i	−0.952215	−	0.305427i	$-0.901201\pi$
$953$		−	582.144i		−	0.610854i	0.952215	−	0.305427i	$-0.0987992\pi$
$954$		0			0
$955$	755.174	+	1308.00i	0.790758	+	1.36963i
$956$		0			0
$957$	1424.75	−	2268.57i	1.48877	−	2.37050i
$958$		0			0
$959$	189.945	+	525.412i	0.198066	+	0.547875i
$960$		0			0
$961$	230.752	+	399.674i	0.240116	+	0.415894i
$962$		0			0
$963$	−928.356	−	632.356i	−0.964025	−	0.656652i
$964$		0			0
$965$	−249.661	−	144.142i	−0.258716	−	0.149370i
$966$		0			0
$967$	−239.897	−	415.514i	−0.248084	−	0.429694i	0.714910	−	0.699216i	$-0.246468\pi$
$967$	−239.897	−	415.514i	−0.248084	−	0.429694i	−0.962994	+	0.269522i	$0.913134\pi$
$968$		0			0
$969$	−12.6495	+	340.028i	−0.0130542	+	0.350907i
$970$		0			0
$971$	−311.099	−	179.613i	−0.320391	−	0.184978i	0.331176	−	0.943569i	$-0.392555\pi$
$971$	−311.099	−	179.613i	−0.320391	−	0.184978i	−0.651567	+	0.758591i	$0.725888\pi$
$972$		0			0
$973$	405.831	+	342.034i	0.417092	+	0.351526i
$974$		0			0
$975$	−87.3699	−	165.226i	−0.0896102	−	0.169462i
$976$		0			0
$977$	8.54385	+	4.93279i	0.00874498	+	0.00504892i	0.504366	−	0.863490i	$-0.331726\pi$
$977$	8.54385	+	4.93279i	0.00874498	+	0.00504892i	−0.495621	+	0.868539i	$0.665060\pi$
$978$		0			0
$979$	620.100	−	1074.04i	0.633401	−	1.09708i
$980$		0			0
$981$	631.667	+	1310.22i	0.643901	+	1.33560i
$982$		0			0
$983$			205.281i			0.208831i	0.994534	+	0.104415i	$0.0332972\pi$
$983$			205.281i			0.208831i	−0.994534	+	0.104415i	$0.966703\pi$
$984$		0			0
$985$	−886.080			−0.899574
$986$		0			0
$987$	89.7097	−	98.7463i	0.0908913	−	0.100047i
$988$		0			0
$989$	77.7516	+	44.8899i	0.0786164	+	0.0453892i
$990$		0			0
$991$	−204.103	−	353.517i	−0.205957	−	0.356728i	0.744480	−	0.667645i	$-0.232697\pi$
$991$	−204.103	−	353.517i	−0.205957	−	0.356728i	−0.950437	+	0.310917i	$0.899364\pi$
$992$		0			0
$993$	−213.199	−	403.182i	−0.214702	−	0.406024i
$994$		0			0
$995$	481.257	−	277.854i	0.483675	−	0.279250i
$996$		0			0
$997$	−650.652			−0.652610			−0.326305	−	0.945264i	$-0.605804\pi$
$997$	−650.652			−0.652610			−0.326305	+	0.945264i	$0.605804\pi$
$998$		0			0
$999$	−981.050	+	1331.08i	−0.982032	+	1.33241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.m.a.65.16	✓	32
3.2	odd	2		756.3.m.a.737.15		32
7.4	even	3		252.3.bh.a.137.6	yes	32
9.4	even	3		756.3.bh.a.233.2		32
9.5	odd	6		252.3.bh.a.149.6	yes	32
21.11	odd	6		756.3.bh.a.305.2		32
63.4	even	3		756.3.m.a.557.2		32
63.32	odd	6	inner	252.3.m.a.221.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.3.m.a.65.16	✓	32	1.1	even	1	trivial
252.3.m.a.221.16	yes	32	63.32	odd	6	inner
252.3.bh.a.137.6	yes	32	7.4	even	3
252.3.bh.a.149.6	yes	32	9.5	odd	6
756.3.m.a.557.2		32	63.4	even	3
756.3.m.a.737.15		32	3.2	odd	2
756.3.bh.a.233.2		32	9.4	even	3
756.3.bh.a.305.2		32	21.11	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99793 + 0.111527i) q^{3} -8.05008i q^{5} +(-6.58302 + 2.37987i) q^{7} +(8.97512 + 0.668699i) q^{9} +O(q^{10})\)	\(q+(2.99793 + 0.111527i) q^{3} -8.05008i q^{5} +(-6.58302 + 2.37987i) q^{7} +(8.97512 + 0.668699i) q^{9} -19.2134i q^{11} +(0.782606 + 1.35551i) q^{13} +(0.897800 - 24.1335i) q^{15} +(-8.39721 + 4.84813i) q^{17} +(5.84871 - 10.1303i) q^{19} +(-20.0008 + 6.40050i) q^{21} +2.07535i q^{23} -39.8037 q^{25} +(26.8322 + 3.00568i) q^{27} +(40.2492 + 23.2379i) q^{29} +(11.1747 - 19.3552i) q^{31} +(2.14281 - 57.6003i) q^{33} +(19.1582 + 52.9938i) q^{35} +(-30.6213 + 53.0376i) q^{37} +(2.19502 + 4.15101i) q^{39} +(48.9545 - 28.2639i) q^{41} +(21.6300 - 37.4643i) q^{43} +(5.38308 - 72.2504i) q^{45} +(-5.50180 + 3.17647i) q^{47} +(37.6724 - 31.3335i) q^{49} +(-25.7149 + 13.5978i) q^{51} +(-55.3510 + 31.9569i) q^{53} -154.669 q^{55} +(18.6638 - 29.7175i) q^{57} +(27.7798 + 16.0387i) q^{59} +(37.2708 + 64.5549i) q^{61} +(-60.6749 + 16.9576i) q^{63} +(10.9120 - 6.30004i) q^{65} +(-2.38096 + 4.12394i) q^{67} +(-0.231458 + 6.22176i) q^{69} +33.1772i q^{71} +(6.60726 + 11.4441i) q^{73} +(-119.329 - 4.43919i) q^{75} +(45.7254 + 126.482i) q^{77} +(-23.1230 - 40.0502i) q^{79} +(80.1057 + 12.0033i) q^{81} +(81.0445 + 46.7910i) q^{83} +(39.0278 + 67.5982i) q^{85} +(118.072 + 74.1543i) q^{87} +(55.9009 + 32.2744i) q^{89} +(-8.37786 - 7.06087i) q^{91} +(35.6596 - 56.7791i) q^{93} +(-81.5494 - 47.0826i) q^{95} +(-96.6875 + 167.468i) q^{97} +(12.8480 - 172.442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{7} + 10 q^{9}+O(q^{10}) \) 32 * q - q^7 + 10 * q^9	\( 32 q - q^{7} + 10 q^{9} - 5 q^{13} - 29 q^{15} - 27 q^{17} - 14 q^{19} - 20 q^{21} - 160 q^{25} + 45 q^{27} + 36 q^{29} - 8 q^{31} + 5 q^{33} - 45 q^{35} - 11 q^{37} + 37 q^{39} + 72 q^{41} + 16 q^{43} + 59 q^{45} - 108 q^{47} + 35 q^{49} + 77 q^{51} + 180 q^{53} - 24 q^{55} + 57 q^{57} + 45 q^{59} - 41 q^{61} + 117 q^{63} - 81 q^{65} - 35 q^{67} - 97 q^{69} - 98 q^{73} + 313 q^{75} + 225 q^{77} - 71 q^{79} - 74 q^{81} - 30 q^{85} + 97 q^{87} - 189 q^{89} + 109 q^{91} - 149 q^{93} - 288 q^{95} + 19 q^{97} - 101 q^{99}+O(q^{100}) \) 32 * q - q^7 + 10 * q^9 - 5 * q^13 - 29 * q^15 - 27 * q^17 - 14 * q^19 - 20 * q^21 - 160 * q^25 + 45 * q^27 + 36 * q^29 - 8 * q^31 + 5 * q^33 - 45 * q^35 - 11 * q^37 + 37 * q^39 + 72 * q^41 + 16 * q^43 + 59 * q^45 - 108 * q^47 + 35 * q^49 + 77 * q^51 + 180 * q^53 - 24 * q^55 + 57 * q^57 + 45 * q^59 - 41 * q^61 + 117 * q^63 - 81 * q^65 - 35 * q^67 - 97 * q^69 - 98 * q^73 + 313 * q^75 + 225 * q^77 - 71 * q^79 - 74 * q^81 - 30 * q^85 + 97 * q^87 - 189 * q^89 + 109 * q^91 - 149 * q^93 - 288 * q^95 + 19 * q^97 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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