LMFDB - Embedded newform 252.4.bm.a.173.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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:	$14.8684813214$
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			173.11
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17430 + 5.06172i) q^{3} -6.49181 q^{5} +(18.4099 - 2.01918i) q^{7} +(-24.2420 - 11.8880i) q^{9} +O(q^{10})$	\(q+(-1.17430 + 5.06172i) q^{3} -6.49181 q^{5} +(18.4099 - 2.01918i) q^{7} +(-24.2420 - 11.8880i) q^{9} +37.0005i q^{11} +(-39.5861 + 22.8550i) q^{13} +(7.62336 - 32.8597i) q^{15} +(55.2592 + 95.7117i) q^{17} +(-131.772 - 76.0785i) q^{19} +(-11.3983 + 95.5567i) q^{21} -123.781i q^{23} -82.8564 q^{25} +(88.6413 - 108.746i) q^{27} +(-89.2268 - 51.5151i) q^{29} +(-162.719 - 93.9461i) q^{31} +(-187.286 - 43.4499i) q^{33} +(-119.513 + 13.1081i) q^{35} +(131.982 - 228.600i) q^{37} +(-69.1996 - 227.212i) q^{39} +(-152.493 - 264.126i) q^{41} +(-167.894 + 290.802i) q^{43} +(157.375 + 77.1746i) q^{45} +(214.225 + 371.048i) q^{47} +(334.846 - 74.3456i) q^{49} +(-549.357 + 167.312i) q^{51} +(-35.3859 + 20.4301i) q^{53} -240.200i q^{55} +(539.828 - 577.653i) q^{57} +(-82.1345 + 142.261i) q^{59} +(-674.424 + 389.379i) q^{61} +(-470.296 - 169.907i) q^{63} +(256.985 - 148.370i) q^{65} +(-163.632 + 283.419i) q^{67} +(626.546 + 145.357i) q^{69} -94.0461i q^{71} +(-334.530 + 193.141i) q^{73} +(97.2987 - 419.396i) q^{75} +(74.7108 + 681.175i) q^{77} +(-245.324 - 424.914i) q^{79} +(446.351 + 576.378i) q^{81} +(-621.666 + 1076.76i) q^{83} +(-358.732 - 621.342i) q^{85} +(365.534 - 391.147i) q^{87} +(-560.989 + 971.661i) q^{89} +(-682.625 + 500.689i) q^{91} +(666.611 - 713.319i) q^{93} +(855.437 + 493.887i) q^{95} +(1017.85 + 587.656i) q^{97} +(439.863 - 896.968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.17430	+	5.06172i	−0.225995	+	0.974128i
$3$	−1.17430	+	5.06172i	−0.225995	+	0.974128i
$4$		0			0
$5$	−6.49181			−0.580645			−0.290322	−	0.956929i	$-0.593763\pi$
$5$	−6.49181			−0.580645			−0.290322	+	0.956929i	$0.593763\pi$
$6$		0			0
$7$	18.4099	−	2.01918i	0.994039	−	0.109025i
$7$	18.4099	−	2.01918i	0.994039	−	0.109025i
$8$		0			0
$9$	−24.2420	−	11.8880i	−0.897852	−	0.440296i
$10$		0			0
$11$			37.0005i			1.01419i	0.861890	+	0.507095i	$0.169281\pi$
$11$			37.0005i			1.01419i	−0.861890	+	0.507095i	$0.830719\pi$
$12$		0			0
$13$	−39.5861	+	22.8550i	−0.844554	+	0.487603i	−0.858809	−	0.512295i	$-0.828795\pi$
$13$	−39.5861	+	22.8550i	−0.844554	+	0.487603i	0.0142559	+	0.999898i	$0.495462\pi$
$14$		0			0
$15$	7.62336	−	32.8597i	0.131223	−	0.565623i
$16$		0			0
$17$	55.2592	+	95.7117i	0.788371	+	1.36550i	0.926964	+	0.375150i	$0.122409\pi$
$17$	55.2592	+	95.7117i	0.788371	+	1.36550i	−0.138593	+	0.990349i	$0.544258\pi$
$18$		0			0
$19$	−131.772	−	76.0785i	−1.59108	−	0.918611i	−0.993122	−	0.117084i	$-0.962645\pi$
$19$	−131.772	−	76.0785i	−1.59108	−	0.918611i	−0.597958	−	0.801527i	$-0.704021\pi$
$20$		0			0
$21$	−11.3983	+	95.5567i	−0.118443	+	0.992961i
$22$		0			0
$23$		−	123.781i		−	1.12218i	−0.827755	−	0.561090i	$-0.810382\pi$
$23$		−	123.781i		−	1.12218i	0.827755	−	0.561090i	$-0.189618\pi$
$24$		0			0
$25$	−82.8564			−0.662851
$26$		0			0
$27$	88.6413	−	108.746i	0.631816	−	0.775119i
$28$		0			0
$29$	−89.2268	−	51.5151i	−0.571345	−	0.329866i	0.186342	−	0.982485i	$-0.440337\pi$
$29$	−89.2268	−	51.5151i	−0.571345	−	0.329866i	−0.757686	+	0.652619i	$0.773670\pi$
$30$		0			0
$31$	−162.719	−	93.9461i	−0.942751	−	0.544297i	−0.0519293	−	0.998651i	$-0.516537\pi$
$31$	−162.719	−	93.9461i	−0.942751	−	0.544297i	−0.890822	+	0.454353i	$0.849870\pi$
$32$		0			0
$33$	−187.286	−	43.4499i	−0.987951	−	0.229202i
$34$		0			0
$35$	−119.513	+	13.1081i	−0.577184	+	0.0633051i
$36$		0			0
$37$	131.982	−	228.600i	0.586426	−	1.01572i	−0.408270	−	0.912861i	$-0.633868\pi$
$37$	131.982	−	228.600i	0.586426	−	1.01572i	0.994696	−	0.102859i	$-0.0327989\pi$
$38$		0			0
$39$	−69.1996	−	227.212i	−0.284123	−	0.932900i
$40$		0			0
$41$	−152.493	−	264.126i	−0.580864	−	1.00609i	−0.995377	−	0.0960429i	$-0.969381\pi$
$41$	−152.493	−	264.126i	−0.580864	−	1.00609i	0.414513	−	0.910043i	$-0.363952\pi$
$42$		0			0
$43$	−167.894	+	290.802i	−0.595434	+	1.03132i	0.398052	+	0.917363i	$0.369686\pi$
$43$	−167.894	+	290.802i	−0.595434	+	1.03132i	−0.993486	+	0.113958i	$0.963647\pi$
$44$		0			0
$45$	157.375	+	77.1746i	0.521333	+	0.255656i
$46$		0			0
$47$	214.225	+	371.048i	0.664849	+	1.15155i	0.979326	+	0.202287i	$0.0648374\pi$
$47$	214.225	+	371.048i	0.664849	+	1.15155i	−0.314478	+	0.949265i	$0.601829\pi$
$48$		0			0
$49$	334.846	−	74.3456i	0.976227	−	0.216751i
$50$		0			0
$51$	−549.357	+	167.312i	−1.50834	+	0.459379i
$52$		0			0
$53$	−35.3859	+	20.4301i	−0.0917101	+	0.0529488i	−0.545154	−	0.838336i	$-0.683529\pi$
$53$	−35.3859	+	20.4301i	−0.0917101	+	0.0529488i	0.453444	+	0.891285i	$0.350195\pi$
$54$		0			0
$55$		−	240.200i		−	0.588884i
$56$		0			0
$57$	539.828	−	577.653i	1.25442	−	1.34232i
$58$		0			0
$59$	−82.1345	+	142.261i	−0.181237	+	0.313912i	−0.942302	−	0.334764i	$-0.891344\pi$
$59$	−82.1345	+	142.261i	−0.181237	+	0.313912i	0.761065	+	0.648676i	$0.224677\pi$
$60$		0			0
$61$	−674.424	+	389.379i	−1.41559	+	0.817293i	−0.995908	−	0.0903765i	$-0.971193\pi$
$61$	−674.424	+	389.379i	−1.41559	+	0.817293i	−0.419686	+	0.907670i	$0.637860\pi$
$62$		0			0
$63$	−470.296	−	169.907i	−0.940504	−	0.339783i
$64$		0			0
$65$	256.985	−	148.370i	0.490386	−	0.283124i
$66$		0			0
$67$	−163.632	+	283.419i	−0.298371	+	0.516793i	−0.975763	−	0.218828i	$-0.929776\pi$
$67$	−163.632	+	283.419i	−0.298371	+	0.516793i	0.677393	+	0.735622i	$0.263110\pi$
$68$		0			0
$69$	626.546	+	145.357i	1.09315	+	0.253607i
$70$		0			0
$71$		−	94.0461i		−	0.157200i	−0.996906	−	0.0786001i	$-0.974955\pi$
$71$		−	94.0461i		−	0.157200i	0.996906	−	0.0786001i	$-0.0250450\pi$
$72$		0			0
$73$	−334.530	+	193.141i	−0.536353	+	0.309663i	−0.743599	−	0.668625i	$-0.766883\pi$
$73$	−334.530	+	193.141i	−0.536353	+	0.309663i	0.207247	+	0.978289i	$0.433550\pi$
$74$		0			0
$75$	97.2987	−	419.396i	0.149801	−	0.645702i
$76$		0			0
$77$	74.7108	+	681.175i	0.110572	+	1.00814i
$78$		0			0
$79$	−245.324	−	424.914i	−0.349381	−	0.605146i	0.636758	−	0.771063i	$-0.280275\pi$
$79$	−245.324	−	424.914i	−0.349381	−	0.605146i	−0.986140	+	0.165917i	$0.946942\pi$
$80$		0			0
$81$	446.351	+	576.378i	0.612278	+	0.790643i
$82$		0			0
$83$	−621.666	+	1076.76i	−0.822129	+	1.42397i	0.0819655	+	0.996635i	$0.473880\pi$
$83$	−621.666	+	1076.76i	−0.822129	+	1.42397i	−0.904094	+	0.427333i	$0.859453\pi$
$84$		0			0
$85$	−358.732	−	621.342i	−0.457764	−	0.792870i
$86$		0			0
$87$	365.534	−	391.147i	0.450453	−	0.482015i
$88$		0			0
$89$	−560.989	+	971.661i	−0.668142	+	1.15726i	0.310281	+	0.950645i	$0.399577\pi$
$89$	−560.989	+	971.661i	−0.668142	+	1.15726i	−0.978423	+	0.206611i	$0.933756\pi$
$90$		0			0
$91$	−682.625	+	500.689i	−0.786358	+	0.576774i
$92$		0			0
$93$	666.611	−	713.319i	0.743273	−	0.795352i
$94$		0			0
$95$	855.437	+	493.887i	0.923853	+	0.533387i
$96$		0			0
$97$	1017.85	+	587.656i	1.06543	+	0.615129i	0.926930	−	0.375233i	$-0.122437\pi$
$97$	1017.85	+	587.656i	1.06543	+	0.615129i	0.138504	+	0.990362i	$0.455771\pi$
$98$		0			0
$99$	439.863	−	896.968i	0.446544	−	0.910593i
$100$		0			0
$101$	1700.43			1.67523			0.837617	−	0.546257i	$-0.183948\pi$
$101$	1700.43			1.67523			0.837617	+	0.546257i	$0.183948\pi$
$102$		0			0
$103$			181.064i			0.173212i	0.996243	+	0.0866058i	$0.0276021\pi$
$103$			181.064i			0.173212i	−0.996243	+	0.0866058i	$0.972398\pi$
$104$		0			0
$105$	73.9953	−	620.336i	0.0687734	−	0.576558i
$106$		0			0
$107$	−29.9862	−	17.3125i	−0.0270923	−	0.0156417i	0.486393	−	0.873740i	$-0.338312\pi$
$107$	−29.9862	−	17.3125i	−0.0270923	−	0.0156417i	−0.513485	+	0.858099i	$0.671646\pi$
$108$		0			0
$109$	−659.496	−	1142.28i	−0.579526	−	1.00377i	−0.995534	−	0.0944071i	$-0.969904\pi$
$109$	−659.496	−	1142.28i	−0.579526	−	1.00377i	0.416008	−	0.909361i	$-0.363429\pi$
$110$		0			0
$111$	1002.12	+	936.504i	0.856912	+	0.800802i
$112$		0			0
$113$	2001.89	−	1155.79i	1.66657	−	0.962194i	0.697102	−	0.716972i	$-0.254472\pi$
$113$	2001.89	−	1155.79i	1.66657	−	0.962194i	0.969467	−	0.245222i	$-0.0788609\pi$
$114$		0			0
$115$			803.563i			0.651589i
$116$		0			0
$117$	1231.35	−	83.4526i	0.972975	−	0.0659418i
$118$		0			0
$119$	1210.57	+	1650.46i	0.932546	+	1.27141i
$120$		0			0
$121$	−38.0404			−0.0285803
$122$		0			0
$123$	1516.00	−	461.713i	1.11133	−	0.338466i
$124$		0			0
$125$	1349.36			0.965526
$126$		0			0
$127$	−1227.05			−0.857345			−0.428673	−	0.903460i	$-0.641019\pi$
$127$	−1227.05			−0.857345			−0.428673	+	0.903460i	$0.641019\pi$
$128$		0			0
$129$	−1274.80	−	1191.32i	−0.870074	−	0.813102i
$130$		0			0
$131$	−2373.37			−1.58292			−0.791460	−	0.611221i	$-0.790679\pi$
$131$	−2373.37			−1.58292			−0.791460	+	0.611221i	$0.790679\pi$
$132$		0			0
$133$	−2579.52	−	1134.52i	−1.68175	−	0.739667i
$134$		0			0
$135$	−575.442	+	705.959i	−0.366861	+	0.450069i
$136$		0			0
$137$			508.377i			0.317033i	0.987356	+	0.158517i	$0.0506711\pi$
$137$			508.377i			0.317033i	−0.987356	+	0.158517i	$0.949329\pi$
$138$		0			0
$139$	1304.07	−	752.902i	0.795751	−	0.459427i	−0.0462323	−	0.998931i	$-0.514721\pi$
$139$	1304.07	−	752.902i	0.795751	−	0.459427i	0.841983	+	0.539504i	$0.181388\pi$
$140$		0			0
$141$	−2129.71	+	648.622i	−1.27201	+	0.387403i
$142$		0			0
$143$	−845.648	−	1464.71i	−0.494522	−	0.856537i
$144$		0			0
$145$	579.243	+	334.426i	0.331748	+	0.191535i
$146$		0			0
$147$	−16.8943	+	1782.20i	−0.00947902	+	0.999955i
$148$		0			0
$149$			2066.30i			1.13609i	0.822996	+	0.568047i	$0.192301\pi$
$149$			2066.30i			1.13609i	−0.822996	+	0.568047i	$0.807699\pi$
$150$		0			0
$151$	2044.77			1.10199			0.550996	−	0.834508i	$-0.314248\pi$
$151$	2044.77			1.10199			0.550996	+	0.834508i	$0.314248\pi$
$152$		0			0
$153$	−201.773	−	2977.16i	−0.106617	−	1.57313i
$154$		0			0
$155$	1056.34	+	609.880i	0.547404	+	0.316044i
$156$		0			0
$157$	547.345	+	316.010i	0.278235	+	0.160639i	0.632624	−	0.774459i	$-0.281978\pi$
$157$	547.345	+	316.010i	0.278235	+	0.160639i	−0.354389	+	0.935098i	$0.615311\pi$
$158$		0			0
$159$	−61.8575	−	203.105i	−0.0308529	−	0.101304i
$160$		0			0
$161$	−249.936	−	2278.79i	−0.122346	−	1.11549i
$162$		0			0
$163$	497.565	−	861.807i	0.239094	−	0.414122i	−0.721361	−	0.692559i	$-0.756483\pi$
$163$	497.565	−	861.807i	0.239094	−	0.414122i	0.960454	+	0.278437i	$0.0898164\pi$
$164$		0			0
$165$	1215.83	+	282.069i	0.573649	+	0.133085i
$166$		0			0
$167$	521.379	+	903.055i	0.241590	+	0.418446i	0.961167	−	0.275966i	$-0.0889978\pi$
$167$	521.379	+	903.055i	0.241590	+	0.418446i	−0.719577	+	0.694412i	$0.755664\pi$
$168$		0			0
$169$	−53.7960	+	93.1774i	−0.0244861	+	0.0424112i
$170$		0			0
$171$	2289.99	+	3410.80i	1.02409	+	1.52532i
$172$		0			0
$173$	1889.17	+	3272.13i	0.830235	+	1.43801i	0.897851	+	0.440298i	$0.145127\pi$
$173$	1889.17	+	3272.13i	0.830235	+	1.43801i	−0.0676161	+	0.997711i	$0.521539\pi$
$174$		0			0
$175$	−1525.38	+	167.302i	−0.658900	+	0.0722677i
$176$		0			0
$177$	−623.635	−	582.800i	−0.264832	−	0.247491i
$178$		0			0
$179$	−3494.32	+	2017.45i	−1.45909	+	0.842407i	−0.998967	−	0.0454464i	$-0.985529\pi$
$179$	−3494.32	+	2017.45i	−1.45909	+	0.842407i	−0.460126	+	0.887854i	$0.652196\pi$
$180$		0			0
$181$			50.7288i			0.0208323i	0.999946	+	0.0104161i	$0.00331562\pi$
$181$			50.7288i			0.0208323i	−0.999946	+	0.0104161i	$0.996684\pi$
$182$		0			0
$183$	−1178.95	−	3871.00i	−0.476231	−	1.56367i
$184$		0			0
$185$	−856.804	+	1484.03i	−0.340505	+	0.589773i
$186$		0			0
$187$	−3541.38	+	2044.62i	−1.38488	+	0.799558i
$188$		0			0
$189$	1412.30	−	2180.98i	0.543542	−	0.839382i
$190$		0			0
$191$	486.076	−	280.636i	0.184143	−	0.106315i	−0.405095	−	0.914275i	$-0.632762\pi$
$191$	486.076	−	280.636i	0.184143	−	0.106315i	0.589238	+	0.807960i	$0.299428\pi$
$192$		0			0
$193$	−929.308	+	1609.61i	−0.346596	+	0.600322i	−0.985642	−	0.168846i	$-0.945996\pi$
$193$	−929.308	+	1609.61i	−0.346596	+	0.600322i	0.639046	+	0.769168i	$0.279329\pi$
$194$		0			0
$195$	449.231	+	1475.02i	0.164975	+	0.541683i
$196$		0			0
$197$		−	1749.92i		−	0.632877i	−0.948613	−	0.316438i	$-0.897513\pi$
$197$		−	1749.92i		−	0.632877i	0.948613	−	0.316438i	$-0.102487\pi$
$198$		0			0
$199$	−766.410	+	442.487i	−0.273012	+	0.157624i	−0.630256	−	0.776388i	$-0.717050\pi$
$199$	−766.410	+	442.487i	−0.273012	+	0.157624i	0.357244	+	0.934011i	$0.383717\pi$
$200$		0			0
$201$	−1242.43	−	1161.08i	−0.435993	−	0.407444i
$202$		0			0
$203$	−1746.67	−	768.221i	−0.603903	−	0.265609i
$204$		0			0
$205$	989.956	+	1714.65i	0.337276	+	0.584179i
$206$		0			0
$207$	−1471.51	+	3000.70i	−0.494092	+	1.00755i
$208$		0			0
$209$	2814.95	−	4875.63i	0.931645	−	1.61366i
$210$		0			0
$211$	−1618.68	−	2803.64i	−0.528126	−	0.914741i	−0.999462	−	0.0327877i	$-0.989561\pi$
$211$	−1618.68	−	2803.64i	−0.528126	−	0.914741i	0.471336	−	0.881954i	$-0.343772\pi$
$212$		0			0
$213$	476.035	+	110.439i	0.153133	+	0.0355265i
$214$		0			0
$215$	1089.94	−	1887.83i	0.345736	−	0.598832i
$216$		0			0
$217$	−3185.34	−	1400.98i	−0.996473	−	0.438269i
$218$		0			0
$219$	−584.785	−	1920.10i	−0.180439	−	0.592459i
$220$		0			0
$221$	−4374.98	−	2525.90i	−1.33164	−	0.768825i
$222$		0			0
$223$	−1557.56	−	899.259i	−0.467723	−	0.270040i	0.247563	−	0.968872i	$-0.420370\pi$
$223$	−1557.56	−	899.259i	−0.467723	−	0.270040i	−0.715286	+	0.698832i	$0.753704\pi$
$224$		0			0
$225$	2008.61	+	984.998i	0.595143	+	0.291851i
$226$		0			0
$227$	−1980.94			−0.579206			−0.289603	−	0.957147i	$-0.593523\pi$
$227$	−1980.94			−0.579206			−0.289603	+	0.957147i	$0.593523\pi$
$228$		0			0
$229$			2704.72i			0.780493i	0.920710	+	0.390247i	$0.127610\pi$
$229$			2704.72i			0.780493i	−0.920710	+	0.390247i	$0.872390\pi$
$230$		0			0
$231$	−3535.65	−	421.742i	−1.00705	−	0.120124i
$232$		0			0
$233$	814.698	+	470.366i	0.229067	+	0.132252i	0.610142	−	0.792292i	$-0.291113\pi$
$233$	814.698	+	470.366i	0.229067	+	0.132252i	−0.381074	+	0.924544i	$0.624446\pi$
$234$		0			0
$235$	−1390.71	−	2408.77i	−0.386041	−	0.668643i
$236$		0			0
$237$	2438.88	−	742.784i	0.668449	−	0.203582i
$238$		0			0
$239$	−3438.55	+	1985.25i	−0.930633	+	0.537301i	−0.887012	−	0.461747i	$-0.847223\pi$
$239$	−3438.55	+	1985.25i	−0.930633	+	0.537301i	−0.0436214	+	0.999048i	$0.513890\pi$
$240$		0			0
$241$		−	2568.76i		−	0.686592i	−0.939227	−	0.343296i	$-0.888457\pi$
$241$		−	2568.76i		−	0.686592i	0.939227	−	0.343296i	$-0.111543\pi$
$242$		0			0
$243$	−3441.62	+	1582.46i	−0.908559	+	0.417756i
$244$		0			0
$245$	−2173.75	+	482.638i	−0.566841	+	0.125855i
$246$		0			0
$247$	6955.10			1.79167
$248$		0			0
$249$	−4720.22	−	4411.14i	−1.20133	−	1.12267i
$250$		0			0
$251$	1570.81			0.395014			0.197507	−	0.980301i	$-0.436715\pi$
$251$	1570.81			0.395014			0.197507	+	0.980301i	$0.436715\pi$
$252$		0			0
$253$	4579.97			1.13810
$254$		0			0
$255$	3566.32	−	1086.16i	0.875810	−	0.266736i
$256$		0			0
$257$	−760.869			−0.184676			−0.0923380	−	0.995728i	$-0.529434\pi$
$257$	−760.869			−0.184676			−0.0923380	+	0.995728i	$0.529434\pi$
$258$		0			0
$259$	1968.19	−	4474.99i	0.472191	−	1.07360i
$260$		0			0
$261$	1550.63	+	2309.56i	0.367744	+	0.547732i
$262$		0			0
$263$		−	1566.87i		−	0.367367i	−0.982985	−	0.183683i	$-0.941198\pi$
$263$		−	1566.87i		−	0.367367i	0.982985	−	0.183683i	$-0.0588021\pi$
$264$		0			0
$265$	229.719	−	132.628i	0.0532510	−	0.0307445i
$266$		0			0
$267$	−4259.50	−	3980.59i	−0.976319	−	0.912391i
$268$		0			0
$269$	1990.54	+	3447.71i	0.451172	+	0.781453i	0.998459	−	0.0554919i	$-0.0176727\pi$
$269$	1990.54	+	3447.71i	0.451172	+	0.781453i	−0.547287	+	0.836945i	$0.684339\pi$
$270$		0			0
$271$	4275.00	+	2468.17i	0.958257	+	0.553250i	0.895636	−	0.444787i	$-0.146721\pi$
$271$	4275.00	+	2468.17i	0.958257	+	0.553250i	0.0626210	+	0.998037i	$0.480054\pi$
$272$		0			0
$273$	−1732.74	−	4043.22i	−0.384139	−	0.896362i
$274$		0			0
$275$		−	3065.73i		−	0.672257i
$276$		0			0
$277$	−223.332			−0.0484430			−0.0242215	−	0.999707i	$-0.507711\pi$
$277$	−223.332			−0.0484430			−0.0242215	+	0.999707i	$0.507711\pi$
$278$		0			0
$279$	2827.82	+	4211.85i	0.606799	+	0.903789i
$280$		0			0
$281$	−1909.57	−	1102.49i	−0.405392	−	0.234053i	0.283416	−	0.958997i	$-0.408532\pi$
$281$	−1909.57	−	1102.49i	−0.405392	−	0.234053i	−0.688808	+	0.724944i	$0.741866\pi$
$282$		0			0
$283$	−1562.45	−	902.080i	−0.328190	−	0.189481i	0.326847	−	0.945077i	$-0.394014\pi$
$283$	−1562.45	−	902.080i	−0.328190	−	0.189481i	−0.655037	+	0.755596i	$0.727347\pi$
$284$		0			0
$285$	−3504.46	+	3750.01i	−0.728373	+	0.779409i
$286$		0			0
$287$	−3340.70	−	4554.61i	−0.687091	−	0.936760i
$288$		0			0
$289$	−3650.65	+	6323.11i	−0.743059	+	1.28702i
$290$		0			0
$291$	−4169.82	+	4461.99i	−0.839997	+	0.898853i
$292$		0			0
$293$	−53.8959	−	93.3504i	−0.0107462	−	0.0186129i	0.860602	−	0.509278i	$-0.170087\pi$
$293$	−53.8959	−	93.3504i	−0.0107462	−	0.0186129i	−0.871348	+	0.490665i	$0.836754\pi$
$294$		0			0
$295$	533.201	−	923.532i	0.105235	−	0.182272i
$296$		0			0
$297$	4023.67	+	3279.78i	0.786117	+	0.640781i
$298$		0			0
$299$	2829.02	+	4900.01i	0.547179	+	0.947742i
$300$		0			0
$301$	−2503.73	+	5692.62i	−0.479444	+	1.09009i
$302$		0			0
$303$	−1996.82	+	8607.08i	−0.378595	+	1.63189i
$304$		0			0
$305$	4378.23	−	2527.77i	0.821957	−	0.474557i
$306$		0			0
$307$			1706.43i			0.317235i	0.987340	+	0.158617i	$0.0507036\pi$
$307$			1706.43i			0.317235i	−0.987340	+	0.158617i	$0.949296\pi$
$308$		0			0
$309$	−916.496	−	212.625i	−0.168730	−	0.0391450i
$310$		0			0
$311$	−2624.54	+	4545.84i	−0.478534	+	0.828846i	−0.999697	−	0.0246115i	$-0.992165\pi$
$311$	−2624.54	+	4545.84i	−0.478534	+	0.828846i	0.521163	+	0.853457i	$0.325498\pi$
$312$		0			0
$313$	8106.61	−	4680.35i	1.46394	−	0.845205i	0.464748	−	0.885443i	$-0.346145\pi$
$313$	8106.61	−	4680.35i	1.46394	−	0.845205i	0.999190	+	0.0402378i	$0.0128116\pi$
$314$		0			0
$315$	3053.07	+	1103.01i	0.546099	+	0.197293i
$316$		0			0
$317$	1914.90	−	1105.57i	0.339280	−	0.195883i	−0.320674	−	0.947190i	$-0.603909\pi$
$317$	1914.90	−	1105.57i	0.339280	−	0.195883i	0.659953	+	0.751306i	$0.270576\pi$
$318$		0			0
$319$	1906.09	−	3301.44i	0.334547	−	0.579452i
$320$		0			0
$321$	122.844	−	131.452i	0.0213598	−	0.0228564i
$322$		0			0
$323$		−	16816.1i		−	2.89683i
$324$		0			0
$325$	3279.96	−	1893.69i	0.559814	−	0.323209i
$326$		0			0
$327$	6556.36	−	1996.80i	1.10877	−	0.337686i
$328$		0			0
$329$	4693.06	+	6398.39i	0.786434	+	1.07220i
$330$		0			0
$331$	583.251	+	1010.22i	0.0968531	+	0.167755i	0.910381	−	0.413772i	$-0.135789\pi$
$331$	583.251	+	1010.22i	0.0968531	+	0.167755i	−0.813527	+	0.581527i	$0.802456\pi$
$332$		0			0
$333$	−5917.12	+	3972.72i	−0.973742	+	0.653765i
$334$		0			0
$335$	1062.27	−	1839.90i	0.173247	−	0.300073i
$336$		0			0
$337$	−272.698	−	472.327i	−0.0440796	−	0.0763481i	0.843144	−	0.537688i	$-0.180702\pi$
$337$	−272.698	−	472.327i	−0.0440796	−	0.0763481i	−0.887223	+	0.461340i	$0.847369\pi$
$338$		0			0
$339$	3499.47	+	11490.3i	0.560664	+	1.84090i
$340$		0			0
$341$	3476.06	−	6020.71i	0.552021	−	0.956128i
$342$		0			0
$343$	6014.35	−	2044.81i	0.946776	−	0.321893i
$344$		0			0
$345$	−4067.41	−	943.629i	−0.634731	−	0.147256i
$346$		0			0
$347$	−6888.64	−	3977.16i	−1.06571	−	0.615288i	−0.138704	−	0.990334i	$-0.544294\pi$
$347$	−6888.64	−	3977.16i	−1.06571	−	0.615288i	−0.927006	+	0.375046i	$0.877627\pi$
$348$		0			0
$349$	8709.56	+	5028.47i	1.33585	+	0.771254i	0.986189	−	0.165622i	$-0.0529632\pi$
$349$	8709.56	+	5028.47i	1.33585	+	0.771254i	0.349662	+	0.936876i	$0.386296\pi$
$350$		0			0
$351$	−1023.56	+	6330.73i	−0.155652	+	0.962705i
$352$		0			0
$353$	−146.489			−0.0220873			−0.0110437	−	0.999939i	$-0.503515\pi$
$353$	−146.489			−0.0220873			−0.0110437	+	0.999939i	$0.503515\pi$
$354$		0			0
$355$			610.529i			0.0912776i
$356$		0			0
$357$	−9775.75	+	4189.43i	−1.44926	+	0.621088i
$358$		0			0
$359$	−2577.66	−	1488.22i	−0.378952	−	0.218788i	0.298410	−	0.954438i	$-0.403544\pi$
$359$	−2577.66	−	1488.22i	−0.378952	−	0.218788i	−0.677362	+	0.735650i	$0.736877\pi$
$360$		0			0
$361$	8146.37	+	14109.9i	1.18769	+	2.05714i
$362$		0			0
$363$	44.6710	−	192.550i	0.00645901	−	0.0278409i
$364$		0			0
$365$	2171.70	−	1253.83i	0.311430	−	0.179804i
$366$		0			0
$367$			548.129i			0.0779622i	0.999240	+	0.0389811i	$0.0124112\pi$
$367$			548.129i			0.0779622i	−0.999240	+	0.0389811i	$0.987589\pi$
$368$		0			0
$369$	556.812	+	8215.78i	0.0785541	+	1.15907i
$370$		0			0
$371$	−610.198	+	447.566i	−0.0853906	+	0.0626319i
$372$		0			0
$373$	−6781.89			−0.941429			−0.470715	−	0.882286i	$-0.656004\pi$
$373$	−6781.89			−0.941429			−0.470715	+	0.882286i	$0.656004\pi$
$374$		0			0
$375$	−1584.56	+	6830.10i	−0.218204	+	0.940547i
$376$		0			0
$377$	4709.52			0.643375
$378$		0			0
$379$	3888.82			0.527058			0.263529	−	0.964651i	$-0.415114\pi$
$379$	3888.82			0.527058			0.263529	+	0.964651i	$0.415114\pi$
$380$		0			0
$381$	1440.93	−	6210.97i	0.193756	−	0.835165i
$382$		0			0
$383$	−9792.03			−1.30640			−0.653198	−	0.757187i	$-0.726573\pi$
$383$	−9792.03			−1.30640			−0.653198	+	0.757187i	$0.726573\pi$
$384$		0			0
$385$	−485.008	−	4422.06i	−0.0642034	−	0.585374i
$386$		0			0
$387$	7527.15	−	5053.69i	0.988699	−	0.663807i
$388$		0			0
$389$		−	2005.10i		−	0.261343i	−0.991426	−	0.130671i	$-0.958287\pi$
$389$		−	2005.10i		−	0.261343i	0.991426	−	0.130671i	$-0.0417133\pi$
$390$		0			0
$391$	11847.3	−	6840.04i	1.53234	−	0.884695i
$392$		0			0
$393$	2787.06	−	12013.3i	0.357732	−	1.54197i
$394$		0			0
$395$	1592.60	+	2758.46i	0.202866	+	0.351375i
$396$		0			0
$397$	−2249.78	−	1298.91i	−0.284416	−	0.164208i	0.351005	−	0.936374i	$-0.385840\pi$
$397$	−2249.78	−	1298.91i	−0.284416	−	0.164208i	−0.635421	+	0.772166i	$0.719173\pi$
$398$		0			0
$399$	8771.78	−	11724.5i	1.10060	−	1.47108i
$400$		0			0
$401$			7467.50i			0.929948i	0.885324	+	0.464974i	$0.153936\pi$
$401$			7467.50i			0.929948i	−0.885324	+	0.464974i	$0.846064\pi$
$402$		0			0
$403$	8588.56			1.06160
$404$		0			0
$405$	−2897.62	−	3741.74i	−0.355516	−	0.459083i
$406$		0			0
$407$	8458.33	+	4883.42i	1.03013	+	0.594747i
$408$		0			0
$409$	−8802.59	−	5082.18i	−1.06421	−	0.614419i	−0.137613	−	0.990486i	$-0.543943\pi$
$409$	−8802.59	−	5082.18i	−1.06421	−	0.614419i	−0.926592	+	0.376067i	$0.877276\pi$
$410$		0			0
$411$	−2573.26	−	596.989i	−0.308831	−	0.0716479i
$412$		0			0
$413$	−1224.83	+	2784.85i	−0.145932	+	0.331800i
$414$		0			0
$415$	4035.73	−	6990.10i	0.477365	−	0.826820i
$416$		0			0
$417$	2279.61	+	7484.95i	0.267705	+	0.878992i
$418$		0			0
$419$	−63.1813	−	109.433i	−0.00736660	−	0.0127593i	0.862319	−	0.506366i	$-0.169012\pi$
$419$	−63.1813	−	109.433i	−0.00736660	−	0.0127593i	−0.869685	+	0.493607i	$0.835678\pi$
$420$		0			0
$421$	−2820.71	+	4885.61i	−0.326539	+	0.565582i	−0.981823	−	0.189801i	$-0.939216\pi$
$421$	−2820.71	+	4885.61i	−0.326539	+	0.565582i	0.655284	+	0.755383i	$0.272549\pi$
$422$		0			0
$423$	−782.218	−	11541.7i	−0.0899119	−	1.32665i
$424$		0			0
$425$	−4578.58	−	7930.33i	−0.522573	−	0.905123i
$426$		0			0
$427$	−11629.8	+	8530.20i	−1.31805	+	0.966757i
$428$		0			0
$429$	8406.98	−	2560.42i	0.946137	−	0.288155i
$430$		0			0
$431$	7131.94	−	4117.63i	0.797061	−	0.460184i	−0.0453813	−	0.998970i	$-0.514450\pi$
$431$	7131.94	−	4117.63i	0.797061	−	0.460184i	0.842443	+	0.538786i	$0.181117\pi$
$432$		0			0
$433$		−	372.717i		−	0.0413663i	−0.999786	−	0.0206832i	$-0.993416\pi$
$433$		−	372.717i		−	0.0413663i	0.999786	−	0.0206832i	$-0.00658413\pi$
$434$		0			0
$435$	−2372.98	+	2539.25i	−0.261553	+	0.279880i
$436$		0			0
$437$	−9417.08	+	16310.9i	−1.03085	+	1.78548i
$438$		0			0
$439$	−10585.0	+	6111.25i	−1.15078	+	0.664405i	−0.949078	−	0.315041i	$-0.897982\pi$
$439$	−10585.0	+	6111.25i	−1.15078	+	0.664405i	−0.201706	+	0.979446i	$0.564648\pi$
$440$		0			0
$441$	−9001.16	−	2178.36i	−0.971942	−	0.235219i
$442$		0			0
$443$	4511.56	−	2604.75i	0.483862	−	0.279358i	−0.238162	−	0.971225i	$-0.576545\pi$
$443$	4511.56	−	2604.75i	0.483862	−	0.279358i	0.722025	+	0.691867i	$0.243212\pi$
$444$		0			0
$445$	3641.83	−	6307.83i	0.387953	−	0.671955i
$446$		0			0
$447$	−10459.0	−	2426.47i	−1.10670	−	0.256752i
$448$		0			0
$449$		−	9082.98i		−	0.954683i	−0.878718	−	0.477341i	$-0.841601\pi$
$449$		−	9082.98i		−	0.954683i	0.878718	−	0.477341i	$-0.158399\pi$
$450$		0			0
$451$	9772.80	−	5642.33i	1.02036	−	0.589106i
$452$		0			0
$453$	−2401.18	+	10350.0i	−0.249045	+	1.07348i
$454$		0			0
$455$	4431.47	−	3250.38i	0.456595	−	0.334901i
$456$		0			0
$457$	−2769.31	−	4796.58i	−0.283463	−	0.490973i	0.688772	−	0.724978i	$-0.258150\pi$
$457$	−2769.31	−	4796.58i	−0.283463	−	0.490973i	−0.972235	+	0.234005i	$0.924817\pi$
$458$		0			0
$459$	15306.5	+	2474.78i	1.55653	+	0.251662i
$460$		0			0
$461$	−509.939	+	883.239i	−0.0515189	+	0.0892333i	−0.890635	−	0.454719i	$-0.849740\pi$
$461$	−509.939	+	883.239i	−0.0515189	+	0.0892333i	0.839116	+	0.543953i	$0.183073\pi$
$462$		0			0
$463$	1154.35	+	1999.39i	0.115869	+	0.200691i	0.918127	−	0.396287i	$-0.129701\pi$
$463$	1154.35	+	1999.39i	0.115869	+	0.200691i	−0.802258	+	0.596978i	$0.796368\pi$
$464$		0			0
$465$	−4327.51	+	4630.73i	−0.431578	+	0.461817i
$466$		0			0
$467$	−1109.62	+	1921.92i	−0.109951	+	0.190441i	−0.915750	−	0.401748i	$-0.868403\pi$
$467$	−1109.62	+	1921.92i	−0.109951	+	0.190441i	0.805799	+	0.592189i	$0.201736\pi$
$468$		0			0
$469$	−2440.17	+	5548.11i	−0.240248	+	0.546243i
$470$		0			0
$471$	−2242.30	+	2399.41i	−0.219363	+	0.234733i
$472$		0			0
$473$	−10759.8	−	6212.18i	−1.04596	−	0.603883i
$474$		0			0
$475$	10918.1	+	6303.59i	1.05465	+	0.608902i
$476$		0			0
$477$	1100.70	−	74.5982i	0.105655	−	0.00716062i
$478$		0			0
$479$	−2710.15			−0.258517			−0.129259	−	0.991611i	$-0.541260\pi$
$479$	−2710.15			−0.258517			−0.129259	+	0.991611i	$0.541260\pi$
$480$		0			0
$481$			12065.8i			1.14377i
$482$		0			0
$483$	11828.1	+	1410.89i	1.11428	+	0.132915i
$484$		0			0
$485$	−6607.69	−	3814.95i	−0.618639	−	0.357171i
$486$		0			0
$487$	−2907.08	−	5035.21i	−0.270498	−	0.468516i	0.698492	−	0.715618i	$-0.253855\pi$
$487$	−2907.08	−	5035.21i	−0.270498	−	0.468516i	−0.968989	+	0.247102i	$0.920522\pi$
$488$		0			0
$489$	3777.93	+	3530.56i	0.349374	+	0.326498i
$490$		0			0
$491$	−3856.83	+	2226.74i	−0.354494	+	0.204667i	−0.666663	−	0.745360i	$-0.732278\pi$
$491$	−3856.83	+	2226.74i	−0.354494	+	0.204667i	0.312169	+	0.950027i	$0.398945\pi$
$492$		0			0
$493$		−	11386.7i		−	1.04023i
$494$		0			0
$495$	−2855.50	+	5822.94i	−0.259284	+	0.528731i
$496$		0			0
$497$	−189.896	−	1731.38i	−0.0171388	−	0.156263i
$498$		0			0
$499$	15569.7			1.39678			0.698392	−	0.715715i	$-0.253899\pi$
$499$	15569.7			1.39678			0.698392	+	0.715715i	$0.253899\pi$
$500$		0			0
$501$	−5183.27	+	1578.61i	−0.462218	+	0.140773i
$502$		0			0
$503$	−17745.1			−1.57299			−0.786497	−	0.617594i	$-0.788107\pi$
$503$	−17745.1			−1.57299			−0.786497	+	0.617594i	$0.788107\pi$
$504$		0			0
$505$	−11038.8			−0.972717
$506$		0			0
$507$	−408.465	−	381.719i	−0.0357802	−	0.0334374i
$508$		0			0
$509$	11953.6			1.04093			0.520465	−	0.853883i	$-0.325759\pi$
$509$	11953.6			1.04093			0.520465	+	0.853883i	$0.325759\pi$
$510$		0			0
$511$	−5768.66	+	4231.17i	−0.499394	+	0.366294i
$512$		0			0
$513$	−19953.7	+	7585.98i	−1.71730	+	0.652884i
$514$		0			0
$515$		−	1175.43i		−	0.100574i
$516$		0			0
$517$	−13729.0	+	7926.43i	−1.16789	+	0.674283i
$518$		0			0
$519$	−18781.1	+	5719.95i	−1.58844	+	0.483773i
$520$		0			0
$521$	−7217.74	−	12501.5i	−0.606939	−	1.05125i	−0.991742	−	0.128250i	$-0.959064\pi$
$521$	−7217.74	−	12501.5i	−0.606939	−	1.05125i	0.384803	−	0.922999i	$-0.374269\pi$
$522$		0			0
$523$	−11592.4	−	6692.86i	−0.969215	−	0.559576i	−0.0702180	−	0.997532i	$-0.522369\pi$
$523$	−11592.4	−	6692.86i	−0.969215	−	0.559576i	−0.898997	+	0.437955i	$0.855703\pi$
$524$		0			0
$525$	944.419	−	7917.49i	0.0785102	−	0.658186i
$526$		0			0
$527$		−	20765.5i		−	1.71643i
$528$		0			0
$529$	−3154.77			−0.259289
$530$		0			0
$531$	3682.31	−	2472.28i	0.300939	−	0.202049i
$532$		0			0
$533$	12073.2	+	6970.47i	0.981142	+	0.566463i
$534$		0			0
$535$	194.665	+	112.390i	0.0157310	+	0.00908230i
$536$		0			0
$537$	−6108.35	−	20056.4i	−0.490865	−	1.61172i
$538$		0			0
$539$	2750.83	+	12389.5i	0.219827	+	0.990079i
$540$		0			0
$541$	−7650.45	+	13251.0i	−0.607983	+	1.05306i	0.383590	+	0.923504i	$0.374688\pi$
$541$	−7650.45	+	13251.0i	−0.607983	+	1.05306i	−0.991572	+	0.129553i	$0.958646\pi$
$542$		0			0
$543$	−256.775	−	59.5710i	−0.0202933	−	0.00470799i
$544$		0			0
$545$	4281.32	+	7415.47i	0.336499	+	0.582833i
$546$		0			0
$547$	−2612.52	+	4525.02i	−0.204211	+	0.353703i	−0.949881	−	0.312612i	$-0.898796\pi$
$547$	−2612.52	+	4525.02i	−0.204211	+	0.353703i	0.745670	+	0.666315i	$0.232129\pi$
$548$		0			0
$549$	20978.3	−	1421.77i	1.63085	−	0.110528i
$550$		0			0
$551$	7838.38	+	13576.5i	0.606037	+	1.04969i
$552$		0			0
$553$	−5374.36	−	7327.25i	−0.413275	−	0.563447i
$554$		0			0
$555$	−6505.59	−	6079.60i	−0.497562	−	0.464982i
$556$		0			0
$557$	−8899.53	+	5138.15i	−0.676993	+	0.390862i	−0.798721	−	0.601701i	$-0.794490\pi$
$557$	−8899.53	+	5138.15i	−0.676993	+	0.390862i	0.121728	+	0.992563i	$0.461156\pi$
$558$		0			0
$559$		−	15348.9i		−	1.16134i
$560$		0			0
$561$	−6190.62	−	20326.5i	−0.465897	−	1.52974i
$562$		0			0
$563$	−4484.61	+	7767.57i	−0.335708	+	0.581463i	−0.983621	−	0.180251i	$-0.942309\pi$
$563$	−4484.61	+	7767.57i	−0.335708	+	0.581463i	0.647912	+	0.761715i	$0.275642\pi$
$564$		0			0
$565$	−12995.9	+	7503.19i	−0.967685	+	0.558693i
$566$		0			0
$567$	9381.07	+	9709.78i	0.694828	+	0.719176i
$568$		0			0
$569$	16726.3	−	9656.96i	1.23235	−	0.711495i	0.264828	−	0.964296i	$-0.414685\pi$
$569$	16726.3	−	9656.96i	1.23235	−	0.711495i	0.967518	+	0.252800i	$0.0813516\pi$
$570$		0			0
$571$	12387.0	−	21454.9i	0.907847	−	1.57244i	0.0907968	−	0.995869i	$-0.471059\pi$
$571$	12387.0	−	21454.9i	0.907847	−	1.57244i	0.817050	−	0.576567i	$-0.195608\pi$
$572$		0			0
$573$	849.701	+	2789.93i	0.0619490	+	0.203405i
$574$		0			0
$575$			10256.1i			0.743839i
$576$		0			0
$577$	−571.398	+	329.897i	−0.0412264	+	0.0238021i	−0.520472	−	0.853879i	$-0.674244\pi$
$577$	−571.398	+	329.897i	−0.0412264	+	0.0238021i	0.479245	+	0.877681i	$0.340910\pi$
$578$		0			0
$579$	−7056.10	−	6594.07i	−0.506462	−	0.473299i
$580$		0			0
$581$	−9270.61	+	21078.2i	−0.661979	+	1.50511i
$582$		0			0
$583$	−755.924	−	1309.30i	−0.0537001	−	0.0930114i
$584$		0			0
$585$	−7993.66	+	541.758i	−0.564953	+	0.0382888i
$586$		0			0
$587$	−981.728	+	1700.40i	−0.0690294	+	0.119562i	−0.898474	−	0.439026i	$-0.855324\pi$
$587$	−981.728	+	1700.40i	−0.0690294	+	0.119562i	0.829445	+	0.558589i	$0.188657\pi$
$588$		0			0
$589$	14294.6	+	24758.9i	0.999995	+	1.73204i
$590$		0			0
$591$	8857.61	+	2054.94i	0.616503	+	0.143027i
$592$		0			0
$593$	2959.64	−	5126.25i	0.204954	−	0.354991i	−0.745164	−	0.666881i	$-0.767629\pi$
$593$	2959.64	−	5126.25i	0.204954	−	0.354991i	0.950118	+	0.311890i	$0.100962\pi$
$594$		0			0
$595$	−7858.80	−	10714.5i	−0.541478	−	0.738236i
$596$		0			0
$597$	−1339.75	−	4398.97i	−0.0918462	−	0.301571i
$598$		0			0
$599$	−8972.05	−	5180.02i	−0.612000	−	0.353339i	0.161748	−	0.986832i	$-0.448287\pi$
$599$	−8972.05	−	5180.02i	−0.612000	−	0.353339i	−0.773748	+	0.633494i	$0.781620\pi$
$600$		0			0
$601$	−17593.4	−	10157.6i	−1.19410	−	0.689412i	−0.234863	−	0.972028i	$-0.575464\pi$
$601$	−17593.4	−	10157.6i	−1.19410	−	0.689412i	−0.959233	+	0.282617i	$0.908797\pi$
$602$		0			0
$603$	7336.06	−	4925.39i	0.495435	−	0.332632i
$604$		0			0
$605$	246.951			0.0165950
$606$		0			0
$607$		−	18108.2i		−	1.21086i	−0.795899	−	0.605429i	$-0.793001\pi$
$607$		−	18108.2i		−	1.21086i	0.795899	−	0.605429i	$-0.206999\pi$
$608$		0			0
$609$	5939.64	−	7939.03i	0.395216	−	0.528253i
$610$		0			0
$611$	−16960.6	−	9792.22i	−1.12300	−	0.648365i
$612$		0			0
$613$	−464.949	−	805.315i	−0.0306347	−	0.0530609i	0.850302	−	0.526296i	$-0.176420\pi$
$613$	−464.949	−	805.315i	−0.0306347	−	0.0530609i	−0.880936	+	0.473235i	$0.843086\pi$
$614$		0			0
$615$	−9841.61	+	2997.35i	−0.645288	+	0.196528i
$616$		0			0
$617$	18475.1	−	10666.6i	1.20548	−	0.695984i	0.243712	−	0.969848i	$-0.421635\pi$
$617$	18475.1	−	10666.6i	1.20548	−	0.695984i	0.961769	+	0.273863i	$0.0883016\pi$
$618$		0			0
$619$		−	29004.6i		−	1.88335i	−0.336525	−	0.941675i	$-0.609252\pi$
$619$		−	29004.6i		−	1.88335i	0.336525	−	0.941675i	$-0.390748\pi$
$620$		0			0
$621$	−13460.7	−	10972.1i	−0.869823	−	0.709011i
$622$		0			0
$623$	−8365.76	+	19020.9i	−0.537989	+	1.22320i
$624$		0			0
$625$	1597.24			0.102223
$626$		0			0
$627$	21373.5	+	19973.9i	1.36136	+	1.27222i
$628$		0			0
$629$	29172.9			1.84929
$630$		0			0
$631$	−3444.88			−0.217335			−0.108668	−	0.994078i	$-0.534658\pi$
$631$	−3444.88			−0.217335			−0.108668	+	0.994078i	$0.534658\pi$
$632$		0			0
$633$	16092.1	−	4900.99i	1.01043	−	0.307736i
$634$		0			0
$635$	7965.76			0.497813
$636$		0			0
$637$	−11556.1	+	10596.0i	−0.718787	+	0.659069i
$638$		0			0
$639$	−1118.02	+	2279.87i	−0.0692147	+	0.141143i
$640$		0			0
$641$			4349.27i			0.267997i	0.990982	+	0.133998i	$0.0427817\pi$
$641$			4349.27i			0.267997i	−0.990982	+	0.133998i	$0.957218\pi$
$642$		0			0
$643$	−19144.5	+	11053.1i	−1.17416	+	0.677902i	−0.954657	−	0.297710i	$-0.903777\pi$
$643$	−19144.5	+	11053.1i	−1.17416	+	0.677902i	−0.219504	+	0.975612i	$0.570444\pi$
$644$		0			0
$645$	8275.74	+	7733.85i	0.505204	+	0.472124i
$646$		0			0
$647$	13635.6	+	23617.6i	0.828549	+	1.43509i	0.899176	+	0.437586i	$0.144167\pi$
$647$	13635.6	+	23617.6i	0.828549	+	1.43509i	−0.0706273	+	0.997503i	$0.522500\pi$
$648$		0			0
$649$	−5263.74	−	3039.02i	−0.318366	−	0.183809i
$650$		0			0
$651$	10831.9	−	14478.1i	0.652128	−	0.871646i
$652$		0			0
$653$		−	2671.42i		−	0.160093i	−0.996791	−	0.0800464i	$-0.974493\pi$
$653$		−	2671.42i		−	0.160093i	0.996791	−	0.0800464i	$-0.0255068\pi$
$654$		0			0
$655$	15407.5			0.919114
$656$		0			0
$657$	10405.7	−	705.232i	0.617909	−	0.0418778i
$658$		0			0
$659$	5245.11	+	3028.27i	0.310046	+	0.179005i	0.646947	−	0.762535i	$-0.276045\pi$
$659$	5245.11	+	3028.27i	0.310046	+	0.179005i	−0.336901	+	0.941540i	$0.609379\pi$
$660$		0			0
$661$	−17284.5	−	9979.24i	−1.01708	−	0.587212i	−0.103824	−	0.994596i	$-0.533108\pi$
$661$	−17284.5	−	9979.24i	−1.01708	−	0.587212i	−0.913257	+	0.407383i	$0.866441\pi$
$662$		0			0
$663$	17923.0	−	19178.8i	1.04988	−	1.12344i
$664$		0			0
$665$	16745.7	+	7365.11i	0.976498	+	0.429484i
$666$		0			0
$667$	−6376.60	+	11044.6i	−0.370169	+	0.641152i
$668$		0			0
$669$	6380.85	−	6827.94i	0.368756	−	0.394594i
$670$		0			0
$671$	−14407.2	−	24954.1i	−0.828890	−	1.43568i
$672$		0			0
$673$	−12905.7	+	22353.3i	−0.739194	+	1.28032i	0.213665	+	0.976907i	$0.431460\pi$
$673$	−12905.7	+	22353.3i	−0.739194	+	1.28032i	−0.952859	+	0.303414i	$0.901873\pi$
$674$		0			0
$675$	−7344.50	+	9010.32i	−0.418800	+	0.513789i
$676$		0			0
$677$	10877.0	+	18839.5i	0.617484	+	1.06951i	0.989943	+	0.141465i	$0.0451811\pi$
$677$	10877.0	+	18839.5i	0.617484	+	1.06951i	−0.372460	+	0.928048i	$0.621486\pi$
$678$		0			0
$679$	19925.1	+	8763.45i	1.12615	+	0.495302i
$680$		0			0
$681$	2326.23	−	10027.0i	0.130898	−	0.564221i
$682$		0			0
$683$	−13382.6	+	7726.43i	−0.749736	+	0.432860i	−0.825599	−	0.564258i	$-0.809162\pi$
$683$	−13382.6	+	7726.43i	−0.749736	+	0.432860i	0.0758624	+	0.997118i	$0.475829\pi$
$684$		0			0
$685$		−	3300.28i		−	0.184084i
$686$		0			0
$687$	−13690.5	−	3176.17i	−0.760301	−	0.176388i
$688$		0			0
$689$	933.860	−	1617.49i	0.0516360	−	0.0894362i
$690$		0			0
$691$	−2290.38	+	1322.35i	−0.126093	+	0.0727999i	−0.561720	−	0.827328i	$-0.689860\pi$
$691$	−2290.38	+	1322.35i	−0.126093	+	0.0727999i	0.435627	+	0.900127i	$0.356527\pi$
$692$		0			0
$693$	6286.67	−	17401.2i	0.344604	−	0.953849i
$694$		0			0
$695$	−8465.74	+	4887.70i	−0.462049	+	0.266764i
$696$		0			0
$697$	16853.3	−	29190.7i	0.915873	−	1.58634i
$698$		0			0
$699$	−3337.57	+	3571.42i	−0.180599	+	0.193253i
$700$		0			0
$701$			34540.5i			1.86102i	0.366263	+	0.930511i	$0.380637\pi$
$701$			34540.5i			1.86102i	−0.366263	+	0.930511i	$0.619363\pi$
$702$		0			0
$703$	−34783.1	+	20082.0i	−1.86610	+	1.07739i
$704$		0			0
$705$	13825.6	−	4210.73i	0.738587	−	0.224944i
$706$		0			0
$707$	31304.6	−	3433.47i	1.66525	−	0.182643i
$708$		0			0
$709$	17248.9	+	29875.9i	0.913675	+	1.58253i	0.808830	+	0.588042i	$0.200101\pi$
$709$	17248.9	+	29875.9i	0.913675	+	1.58253i	0.104844	+	0.994489i	$0.466566\pi$
$710$		0			0
$711$	895.774	+	13217.2i	0.0472491	+	0.697163i
$712$		0			0
$713$	−11628.8	+	20141.6i	−0.610800	+	1.05794i
$714$		0			0
$715$	5489.79	+	9508.59i	0.287142	+	0.497344i
$716$		0			0
$717$	−6010.86	−	19736.3i	−0.313082	−	1.02798i
$718$		0			0
$719$	4548.93	−	7878.97i	0.235948	−	0.408673i	−0.723600	−	0.690219i	$-0.757514\pi$
$719$	4548.93	−	7878.97i	0.235948	−	0.408673i	0.959548	+	0.281546i	$0.0908473\pi$
$720$		0			0
$721$	365.601	+	3333.37i	0.0188845	+	0.172179i
$722$		0			0
$723$	13002.4	+	3016.51i	0.668829	+	0.155166i
$724$		0			0
$725$	7393.01	+	4268.36i	0.378717	+	0.218652i
$726$		0			0
$727$	4975.26	+	2872.47i	0.253813	+	0.146539i	0.621509	−	0.783407i	$-0.286520\pi$
$727$	4975.26	+	2872.47i	0.253813	+	0.146539i	−0.367696	+	0.929946i	$0.619853\pi$
$728$		0			0
$729$	−3968.45	−	19278.8i	−0.201618	−	0.979464i
$730$		0			0
$731$	−37110.8			−1.87769
$732$		0			0
$733$			1551.59i			0.0781844i	0.999236	+	0.0390922i	$0.0124466\pi$
$733$			1551.59i			0.0781844i	−0.999236	+	0.0390922i	$0.987553\pi$
$734$		0			0
$735$	109.674	−	11569.7i	0.00550395	−	0.580619i
$736$		0			0
$737$	−10486.7	−	6054.47i	−0.524126	−	0.302604i
$738$		0			0
$739$	4102.55	+	7105.82i	0.204215	+	0.353710i	0.949882	−	0.312608i	$-0.101203\pi$
$739$	4102.55	+	7105.82i	0.204215	+	0.353710i	−0.745668	+	0.666318i	$0.767869\pi$
$740$		0			0
$741$	−8167.41	+	35204.8i	−0.404909	+	1.74532i
$742$		0			0
$743$	28507.4	−	16458.8i	1.40758	−	0.812669i	0.412429	−	0.910990i	$-0.364680\pi$
$743$	28507.4	−	16458.8i	1.40758	−	0.812669i	0.995155	+	0.0983208i	$0.0313471\pi$
$744$		0			0
$745$		−	13414.0i		−	0.659668i
$746$		0			0
$747$	27870.9	−	18712.4i	1.36512	−	0.916533i
$748$		0			0
$749$	−586.999	−	258.174i	−0.0286361	−	0.0125948i
$750$		0			0
$751$	−14843.9			−0.721255			−0.360628	−	0.932710i	$-0.617437\pi$
$751$	−14843.9			−0.721255			−0.360628	+	0.932710i	$0.617437\pi$
$752$		0			0
$753$	−1844.61	+	7951.00i	−0.0892713	+	0.384795i
$754$		0			0
$755$	−13274.2			−0.639866
$756$		0			0
$757$	17386.7			0.834782			0.417391	−	0.908727i	$-0.362945\pi$
$757$	17386.7			0.834782			0.417391	+	0.908727i	$0.362945\pi$
$758$		0			0
$759$	−5378.28	+	23182.5i	−0.257206	+	1.10866i
$760$		0			0
$761$	21498.3			1.02406			0.512032	−	0.858966i	$-0.328893\pi$
$761$	21498.3			1.02406			0.512032	+	0.858966i	$0.328893\pi$
$762$		0			0
$763$	−14447.7	−	19697.6i	−0.685507	−	0.934601i
$764$		0			0
$765$	1309.87	+	19327.2i	0.0619064	+	0.913432i
$766$		0			0
$767$		−	7508.74i		−	0.353488i
$768$		0			0
$769$	−11917.1	+	6880.35i	−0.558833	+	0.322642i	−0.752677	−	0.658390i	$-0.771238\pi$
$769$	−11917.1	+	6880.35i	−0.558833	+	0.322642i	0.193844	+	0.981032i	$0.437904\pi$
$770$		0			0
$771$	893.492	−	3851.31i	0.0417359	−	0.179898i
$772$		0			0
$773$	5414.03	+	9377.37i	0.251913	+	0.436327i	0.964053	−	0.265712i	$-0.0856069\pi$
$773$	5414.03	+	9377.37i	0.251913	+	0.436327i	−0.712139	+	0.702038i	$0.752274\pi$
$774$		0			0
$775$	13482.4	+	7784.04i	0.624904	+	0.360788i
$776$		0			0
$777$	20339.9	+	15217.4i	0.939112	+	0.702603i
$778$		0			0
$779$			46405.8i			2.13435i
$780$		0			0
$781$	3479.76			0.159431
$782$		0			0
$783$	−13511.2	+	5136.71i	−0.616670	+	0.234446i
$784$		0			0
$785$	−3553.26	−	2051.47i	−0.161556	−	0.0932742i
$786$		0			0
$787$	15968.2	+	9219.24i	0.723259	+	0.417574i	0.815951	−	0.578121i	$-0.196214\pi$
$787$	15968.2	+	9219.24i	0.723259	+	0.417574i	−0.0926920	+	0.995695i	$0.529547\pi$
$788$		0			0
$789$	7931.06	+	1839.98i	0.357862	+	0.0830231i
$790$		0			0
$791$	34520.8	−	25320.2i	1.55173	−	1.13816i
$792$		0			0
$793$	17798.5	−	30828.0i	0.797030	−	1.38050i
$794$		0			0
$795$	401.567	+	1318.52i	0.0179146	+	0.0588214i
$796$		0			0
$797$	−15862.0	−	27473.9i	−0.704971	−	1.22105i	−0.966702	−	0.255905i	$-0.917627\pi$
$797$	−15862.0	−	27473.9i	−0.704971	−	1.22105i	0.261731	−	0.965141i	$-0.415707\pi$
$798$		0			0
$799$	−23675.8	+	41007.6i	−1.04830	+	1.81570i
$800$		0			0
$801$	25150.6	−	16886.0i	1.10943	−	0.744865i
$802$		0			0
$803$	−7146.32	−	12377.8i	−0.314057	−	0.543963i
$804$		0			0
$805$	1622.54	+	14793.5i	0.0710397	+	0.647704i
$806$		0			0
$807$	−19788.9	+	6026.88i	−0.863198	+	0.262895i
$808$		0			0
$809$	−19207.3	+	11089.4i	−0.834727	+	0.481930i	−0.855468	−	0.517855i	$-0.826731\pi$
$809$	−19207.3	+	11089.4i	−0.834727	+	0.481930i	0.0207412	+	0.999785i	$0.493397\pi$
$810$		0			0
$811$		−	22033.0i		−	0.953986i	−0.878907	−	0.476993i	$-0.841727\pi$
$811$		−	22033.0i		−	0.953986i	0.878907	−	0.476993i	$-0.158273\pi$
$812$		0			0
$813$	−17513.3	+	18740.5i	−0.755498	+	0.808434i
$814$		0			0
$815$	−3230.09	+	5594.69i	−0.138829	+	0.240458i
$816$		0			0
$817$	44247.5	−	25546.3i	1.89477	−	1.09394i
$818$		0			0
$819$	22500.4	−	4022.66i	0.959985	−	0.171628i
$820$		0			0
$821$	29822.4	−	17218.0i	1.26773	−	0.731926i	0.293174	−	0.956059i	$-0.405288\pi$
$821$	29822.4	−	17218.0i	1.26773	−	0.731926i	0.974558	+	0.224133i	$0.0719551\pi$
$822$		0			0
$823$	−16707.3	+	28938.0i	−0.707632	+	1.22565i	0.258101	+	0.966118i	$0.416903\pi$
$823$	−16707.3	+	28938.0i	−0.707632	+	1.22565i	−0.965733	+	0.259537i	$0.916430\pi$
$824$		0			0
$825$	15517.9	+	3600.11i	0.654865	+	0.151927i
$826$		0			0
$827$			14117.7i			0.593617i	0.954937	+	0.296809i	$0.0959224\pi$
$827$			14117.7i			0.593617i	−0.954937	+	0.296809i	$0.904078\pi$
$828$		0			0
$829$	809.222	−	467.205i	0.0339028	−	0.0195738i	−0.482953	−	0.875646i	$-0.660436\pi$
$829$	809.222	−	467.205i	0.0339028	−	0.0195738i	0.516856	+	0.856073i	$0.327102\pi$
$830$		0			0
$831$	262.259	−	1130.44i	0.0109479	−	0.0471897i
$832$		0			0
$833$	25619.0	+	27940.4i	1.06560	+	1.16216i
$834$		0			0
$835$	−3384.69	−	5862.46i	−0.140278	−	0.242969i
$836$		0			0
$837$	−24639.9	+	9367.61i	−1.01754	+	0.386848i
$838$		0			0
$839$	−8184.66	+	14176.2i	−0.336789	+	0.583335i	−0.983827	−	0.179122i	$-0.942674\pi$
$839$	−8184.66	+	14176.2i	−0.336789	+	0.583335i	0.647038	+	0.762458i	$0.276008\pi$
$840$		0			0
$841$	−6886.89	−	11928.4i	−0.282377	−	0.489091i
$842$		0			0
$843$	7822.90	−	8371.03i	0.319615	−	0.342009i
$844$		0			0
$845$	349.233	−	604.890i	0.0142177	−	0.0246259i
$846$		0			0
$847$	−700.319	+	76.8105i	−0.0284100	+	0.00311598i
$848$		0			0
$849$	6400.87	−	6849.36i	0.258748	−	0.276878i
$850$		0			0
$851$	−28296.4	−	16336.9i	−1.13982	−	0.658076i
$852$		0			0
$853$	12082.5	+	6975.83i	0.484990	+	0.280009i	0.722494	−	0.691377i	$-0.242996\pi$
$853$	12082.5	+	6975.83i	0.484990	+	0.280009i	−0.237504	+	0.971387i	$0.576329\pi$
$854$		0			0
$855$	−14866.2	−	22142.3i	−0.594635	−	0.885672i
$856$		0			0
$857$	−15169.5			−0.604646			−0.302323	−	0.953205i	$-0.597762\pi$
$857$	−15169.5			−0.604646			−0.302323	+	0.953205i	$0.597762\pi$
$858$		0			0
$859$		−	13135.6i		−	0.521749i	−0.965373	−	0.260874i	$-0.915989\pi$
$859$		−	13135.6i		−	0.521749i	0.965373	−	0.260874i	$-0.0840109\pi$
$860$		0			0
$861$	26977.2	−	11561.2i	1.06780	−	0.457611i
$862$		0			0
$863$	−4798.70	−	2770.53i	−0.189281	−	0.109282i	0.402365	−	0.915479i	$-0.368188\pi$
$863$	−4798.70	−	2770.53i	−0.189281	−	0.109282i	−0.591646	+	0.806198i	$0.701522\pi$
$864$		0			0
$865$	−12264.1	−	21242.1i	−0.482072	−	0.834973i
$866$		0			0
$867$	−27718.8	−	25903.8i	−1.08579	−	1.01469i
$868$		0			0
$869$	15722.0	−	9077.13i	0.613733	−	0.354339i
$870$		0			0
$871$		−	14959.3i		−	0.581946i
$872$		0			0
$873$	−17688.7	−	26346.2i	−0.685764	−	1.02140i
$874$		0			0
$875$	24841.6	−	2724.61i	0.959771	−	0.105267i
$876$		0			0
$877$	29006.8			1.11687			0.558433	−	0.829550i	$-0.311403\pi$
$877$	29006.8			1.11687			0.558433	+	0.829550i	$0.311403\pi$
$878$		0			0
$879$	535.804	−	163.184i	0.0205600	−	0.00626173i
$880$		0			0
$881$	−46444.1			−1.77610			−0.888048	−	0.459750i	$-0.847939\pi$
$881$	−46444.1			−1.77610			−0.888048	+	0.459750i	$0.847939\pi$
$882$		0			0
$883$	−24326.1			−0.927111			−0.463555	−	0.886068i	$-0.653427\pi$
$883$	−24326.1			−0.927111			−0.463555	+	0.886068i	$0.653427\pi$
$884$		0			0
$885$	4048.52	+	3783.42i	0.153773	+	0.143704i
$886$		0			0
$887$	−18033.6			−0.682649			−0.341324	−	0.939946i	$-0.610875\pi$
$887$	−18033.6			−0.682649			−0.341324	+	0.939946i	$0.610875\pi$
$888$		0			0
$889$	−22589.8	+	2477.63i	−0.852235	+	0.0934725i
$890$		0			0
$891$	−21326.3	+	16515.2i	−0.801861	+	0.620966i
$892$		0			0
$893$		−	65191.6i		−	2.44295i
$894$		0			0
$895$	22684.4	−	13096.9i	0.847215	−	0.489140i
$896$		0			0
$897$	−28124.6	+	8565.61i	−1.04688	+	0.318838i
$898$		0			0
$899$	9679.29	+	16765.0i	0.359091	+	0.621963i
$900$		0			0
$901$	−3910.79	−	2257.90i	−0.144603	−	0.0834867i
$902$		0			0
$903$	−25874.3	−	19358.1i	−0.953537	−	0.713395i
$904$		0			0
$905$		−	329.321i		−	0.0120961i
$906$		0			0
$907$	48238.3			1.76596			0.882981	−	0.469409i	$-0.155533\pi$
$907$	48238.3			1.76596			0.882981	+	0.469409i	$0.155533\pi$
$908$		0			0
$909$	−41221.8	−	20214.7i	−1.50411	−	0.737600i
$910$		0			0
$911$	39814.8	+	22987.1i	1.44799	+	0.835999i	0.998362	−	0.0572149i	$-0.0182220\pi$
$911$	39814.8	+	22987.1i	1.44799	+	0.835999i	0.449631	+	0.893214i	$0.351555\pi$
$912$		0			0
$913$	−39840.6	−	23002.0i	−1.44417	−	0.833794i
$914$		0			0
$915$	7653.50	+	25129.8i	0.276521	+	0.907939i
$916$		0			0
$917$	−43693.4	+	4792.27i	−1.57348	+	0.172579i
$918$		0			0
$919$	6140.67	−	10635.9i	0.220416	−	0.381771i	−0.734519	−	0.678589i	$-0.762592\pi$
$919$	6140.67	−	10635.9i	0.220416	−	0.381771i	0.954934	+	0.296818i	$0.0959253\pi$
$920$		0			0
$921$	−8637.46	−	2003.87i	−0.309027	−	0.0716934i
$922$		0			0
$923$	2149.43	+	3722.92i	0.0766514	+	0.132764i
$924$		0			0
$925$	−10935.6	+	18941.0i	−0.388713	+	0.673271i
$926$		0			0
$927$	2152.49	−	4389.36i	0.0762644	−	0.155518i
$928$		0			0
$929$	−19605.0	−	33956.8i	−0.692378	−	1.19923i	−0.971057	−	0.238849i	$-0.923230\pi$
$929$	−19605.0	−	33956.8i	−0.692378	−	1.19923i	0.278679	−	0.960384i	$-0.410103\pi$
$930$		0			0
$931$	−49779.3	−	15677.9i	−1.75237	−	0.551904i
$932$		0			0
$933$	−19927.8	−	18622.9i	−0.699256	−	0.653469i
$934$		0			0
$935$	22990.0	−	13273.3i	0.804121	−	0.464259i
$936$		0			0
$937$			44889.9i			1.56509i	0.622595	+	0.782544i	$0.286079\pi$
$937$			44889.9i			1.56509i	−0.622595	+	0.782544i	$0.713921\pi$
$938$		0			0
$939$	14171.0	+	46529.5i	0.492496	+	1.61708i
$940$		0			0
$941$	12954.0	−	22437.0i	0.448767	−	0.777287i	−0.549539	−	0.835468i	$-0.685197\pi$
$941$	12954.0	−	22437.0i	0.448767	−	0.777287i	0.998306	+	0.0581813i	$0.0185301\pi$
$942$		0			0
$943$	−32693.8	+	18875.8i	−1.12901	+	0.651835i
$944$		0			0
$945$	−9168.35	+	14158.5i	−0.315605	+	0.487383i
$946$		0			0
$947$	−13928.7	+	8041.76i	−0.477955	+	0.275947i	−0.719564	−	0.694426i	$-0.755658\pi$
$947$	−13928.7	+	8041.76i	−0.477955	+	0.275947i	0.241609	+	0.970374i	$0.422325\pi$
$948$		0			0
$949$	8828.47	−	15291.4i	0.301986	−	0.523055i
$950$		0			0
$951$	3347.41	+	10991.0i	0.114140	+	0.374771i
$952$		0			0
$953$			18660.5i			0.634283i	0.948378	+	0.317142i	$0.102723\pi$
$953$			18660.5i			0.634283i	−0.948378	+	0.317142i	$0.897277\pi$
$954$		0			0
$955$	−3155.51	+	1821.84i	−0.106922	+	0.0617312i
$956$		0			0
$957$	14472.6	+	13525.0i	0.488855	+	0.456845i
$958$		0			0
$959$	1026.50	+	9359.14i	0.0345647	+	0.315143i
$960$		0			0
$961$	2756.25	+	4773.96i	0.0925195	+	0.160248i
$962$		0			0
$963$	521.114	+	776.167i	0.0174379	+	0.0259726i
$964$		0			0
$965$	6032.89	−	10449.3i	0.201249	−	0.348574i
$966$		0			0
$967$	16045.9	+	27792.3i	0.533611	+	0.924241i	0.999229	+	0.0392555i	$0.0124986\pi$
$967$	16045.9	+	27792.3i	0.533611	+	0.924241i	−0.465618	+	0.884986i	$0.654168\pi$
$968$		0			0
$969$	85118.6	+	19747.3i	2.82188	+	0.654668i
$970$		0			0
$971$	12332.4	−	21360.4i	0.407586	−	0.705960i	−0.587032	−	0.809564i	$-0.699704\pi$
$971$	12332.4	−	21360.4i	0.407586	−	0.705960i	0.994619	+	0.103603i	$0.0330372\pi$
$972$		0			0
$973$	22487.4	−	16494.0i	0.740918	−	0.543445i
$974$		0			0
$975$	5733.63	+	18826.0i	0.188332	+	0.618374i
$976$		0			0
$977$	−31710.6	−	18308.1i	−1.03840	−	0.599518i	−0.119017	−	0.992892i	$-0.537974\pi$
$977$	−31710.6	−	18308.1i	−1.03840	−	0.599518i	−0.919379	+	0.393374i	$0.871308\pi$
$978$		0			0
$979$	−35952.0	−	20756.9i	−1.17368	−	0.677623i
$980$		0			0
$981$	2408.08	+	35531.3i	0.0783731	+	1.15640i
$982$		0			0
$983$	−57292.5			−1.85895			−0.929475	−	0.368886i	$-0.879739\pi$
$983$	−57292.5			−1.85895			−0.929475	+	0.368886i	$0.879739\pi$
$984$		0			0
$985$			11360.1i			0.367477i
$986$		0			0
$987$	−37897.9	+	16241.3i	−1.22219	+	0.523775i
$988$		0			0
$989$	35995.8	+	20782.2i	1.15733	+	0.668184i
$990$		0			0
$991$	22467.2	+	38914.3i	0.720176	+	1.24738i	0.960929	+	0.276795i	$0.0892723\pi$
$991$	22467.2	+	38914.3i	0.720176	+	1.24738i	−0.240753	+	0.970586i	$0.577394\pi$
$992$		0			0
$993$	−5798.37	+	1765.95i	−0.185303	+	0.0564357i
$994$		0			0
$995$	4975.39	−	2872.54i	0.158523	−	0.0915233i
$996$		0			0
$997$		−	57923.3i		−	1.83997i	−0.391955	−	0.919985i	$-0.628201\pi$
$997$		−	57923.3i		−	1.83997i	0.391955	−	0.919985i	$-0.371799\pi$
$998$		0			0
$999$	−13160.3	−	34616.0i	−0.416790	−	1.09630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.11	yes	48
3.2	odd	2		756.4.bm.a.89.16		48
7.3	odd	6		252.4.w.a.101.3	yes	48
9.4	even	3		756.4.w.a.341.16		48
9.5	odd	6		252.4.w.a.5.3	✓	48
21.17	even	6		756.4.w.a.521.16		48
63.31	odd	6		756.4.bm.a.17.16		48
63.59	even	6	inner	252.4.bm.a.185.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.3	✓	48	9.5	odd	6
252.4.w.a.101.3	yes	48	7.3	odd	6
252.4.bm.a.173.11	yes	48	1.1	even	1	trivial
252.4.bm.a.185.11	yes	48	63.59	even	6	inner
756.4.w.a.341.16		48	9.4	even	3
756.4.w.a.521.16		48	21.17	even	6
756.4.bm.a.17.16		48	63.31	odd	6
756.4.bm.a.89.16		48	3.2	odd	2

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17430 + 5.06172i) q^{3} -6.49181 q^{5} +(18.4099 - 2.01918i) q^{7} +(-24.2420 - 11.8880i) q^{9} +O(q^{10})\)	\(q+(-1.17430 + 5.06172i) q^{3} -6.49181 q^{5} +(18.4099 - 2.01918i) q^{7} +(-24.2420 - 11.8880i) q^{9} +37.0005i q^{11} +(-39.5861 + 22.8550i) q^{13} +(7.62336 - 32.8597i) q^{15} +(55.2592 + 95.7117i) q^{17} +(-131.772 - 76.0785i) q^{19} +(-11.3983 + 95.5567i) q^{21} -123.781i q^{23} -82.8564 q^{25} +(88.6413 - 108.746i) q^{27} +(-89.2268 - 51.5151i) q^{29} +(-162.719 - 93.9461i) q^{31} +(-187.286 - 43.4499i) q^{33} +(-119.513 + 13.1081i) q^{35} +(131.982 - 228.600i) q^{37} +(-69.1996 - 227.212i) q^{39} +(-152.493 - 264.126i) q^{41} +(-167.894 + 290.802i) q^{43} +(157.375 + 77.1746i) q^{45} +(214.225 + 371.048i) q^{47} +(334.846 - 74.3456i) q^{49} +(-549.357 + 167.312i) q^{51} +(-35.3859 + 20.4301i) q^{53} -240.200i q^{55} +(539.828 - 577.653i) q^{57} +(-82.1345 + 142.261i) q^{59} +(-674.424 + 389.379i) q^{61} +(-470.296 - 169.907i) q^{63} +(256.985 - 148.370i) q^{65} +(-163.632 + 283.419i) q^{67} +(626.546 + 145.357i) q^{69} -94.0461i q^{71} +(-334.530 + 193.141i) q^{73} +(97.2987 - 419.396i) q^{75} +(74.7108 + 681.175i) q^{77} +(-245.324 - 424.914i) q^{79} +(446.351 + 576.378i) q^{81} +(-621.666 + 1076.76i) q^{83} +(-358.732 - 621.342i) q^{85} +(365.534 - 391.147i) q^{87} +(-560.989 + 971.661i) q^{89} +(-682.625 + 500.689i) q^{91} +(666.611 - 713.319i) q^{93} +(855.437 + 493.887i) q^{95} +(1017.85 + 587.656i) q^{97} +(439.863 - 896.968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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