LMFDB - Embedded newform 252.2.w.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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, 5, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.8
Root			$-0.544978 + 1.64408i$ of defining polynomial
Character	$\chi$	$=$	252.5
Dual form			252.2.w.a.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +O(q^{10})$	\(q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +(-3.19958 - 1.84728i) q^{11} +(0.480242 + 0.277268i) q^{13} +(-2.41122 - 6.33747i) q^{15} +(2.91916 + 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(1.66177 - 4.27066i) q^{21} +(-1.96965 + 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(4.60867 + 2.40003i) q^{27} +(3.53638 - 2.04173i) q^{29} +8.08443i q^{31} +(-4.96114 - 4.04183i) q^{33} +(-9.85583 + 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(0.744643 + 0.606659i) q^{39} +(3.59234 - 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +(-2.37374 - 11.5021i) q^{45} -2.82833 q^{47} +(-6.38563 - 2.86770i) q^{49} +(3.59594 + 9.45130i) q^{51} +(-0.0415658 + 0.0239980i) q^{53} +14.4635i q^{55} +(7.17031 + 5.84164i) q^{57} -8.91313 q^{59} +6.96680i q^{61} +(4.02026 - 6.84379i) q^{63} -2.17091i q^{65} +1.17480 q^{67} +(-3.68181 + 1.40082i) q^{69} +6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-11.2964 + 13.8658i) q^{75} +(-6.55234 + 7.25364i) q^{77} -3.94747 q^{79} +(7.21799 + 5.37592i) q^{81} +(3.84674 + 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(6.61047 - 2.51509i) q^{87} +(-2.71300 + 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(-2.23143 + 13.8237i) q^{93} -20.9041i q^{95} +(13.9874 - 8.07563i) q^{97} +(-7.36753 - 8.28055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.70992	+	0.276016i	0.987221	+	0.159358i
$3$	1.70992	+	0.276016i	0.987221	+	0.159358i
$4$		0			0
$5$	−1.95741	−	3.39033i	−0.875381	−	1.51620i	−0.856357	−	0.516385i	$-0.827278\pi$
$5$	−1.95741	−	3.39033i	−0.875381	−	1.51620i	−0.0190238	−	0.999819i	$-0.506056\pi$
$6$		0			0
$7$	0.554241	−	2.58705i	0.209483	−	0.977812i
$7$	0.554241	−	2.58705i	0.209483	−	0.977812i
$8$		0			0
$9$	2.84763	+	0.943929i	0.949210	+	0.314643i
$10$		0			0
$11$	−3.19958	−	1.84728i	−0.964710	−	0.556976i	−0.0670908	−	0.997747i	$-0.521372\pi$
$11$	−3.19958	−	1.84728i	−0.964710	−	0.556976i	−0.897620	+	0.440771i	$0.854705\pi$
$12$		0			0
$13$	0.480242	+	0.277268i	0.133195	+	0.0769002i	0.565117	−	0.825011i	$-0.308831\pi$
$13$	0.480242	+	0.277268i	0.133195	+	0.0769002i	−0.431922	+	0.901911i	$0.642164\pi$
$14$		0			0
$15$	−2.41122	−	6.33747i	−0.622575	−	1.63633i
$16$		0			0
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	0.965598	+	0.260040i	$0.0837356\pi$
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	−0.257598	+	0.966252i	$0.582931\pi$
$18$		0			0
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.925680	−	0.378307i	$-0.123494\pi$
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.135216	+	0.990816i	$0.456827\pi$
$20$		0			0
$21$	1.66177	−	4.27066i	0.362629	−	0.931934i
$22$		0			0
$23$	−1.96965	+	1.13718i	−0.410700	+	0.237118i	−0.691090	−	0.722768i	$-0.742869\pi$
$23$	−1.96965	+	1.13718i	−0.410700	+	0.237118i	0.280390	+	0.959886i	$0.409536\pi$
$24$		0			0
$25$	−5.16291	+	8.94242i	−1.03258	+	1.78848i
$26$		0			0
$27$	4.60867	+	2.40003i	0.886939	+	0.461887i
$28$		0			0
$29$	3.53638	−	2.04173i	0.656690	−	0.379140i	−0.134325	−	0.990937i	$-0.542887\pi$
$29$	3.53638	−	2.04173i	0.656690	−	0.379140i	0.791014	+	0.611797i	$0.209553\pi$
$30$		0			0
$31$			8.08443i			1.45201i	0.687691	+	0.726004i	$0.258624\pi$
$31$			8.08443i			1.45201i	−0.687691	+	0.726004i	$0.741376\pi$
$32$		0			0
$33$	−4.96114	−	4.04183i	−0.863624	−	0.703592i
$34$		0			0
$35$	−9.85583	+	3.18485i	−1.66594	+	0.538338i
$36$		0			0
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	−0.344322	−	0.938852i	$-0.611891\pi$
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	0.985230	−	0.171235i	$-0.0547756\pi$
$38$		0			0
$39$	0.744643	+	0.606659i	0.119238	+	0.0971432i
$40$		0			0
$41$	3.59234	−	6.22212i	0.561030	−	0.971732i	−0.436377	−	0.899764i	$-0.643739\pi$
$41$	3.59234	−	6.22212i	0.561030	−	0.971732i	0.997407	−	0.0719684i	$-0.0229281\pi$
$42$		0			0
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	0.802789	−	0.596264i	$-0.203349\pi$
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	−0.917774	+	0.397103i	$0.870015\pi$
$44$		0			0
$45$	−2.37374	−	11.5021i	−0.353857	−	1.71463i
$46$		0			0
$47$	−2.82833			−0.412554			−0.206277	−	0.978494i	$-0.566135\pi$
$47$	−2.82833			−0.412554			−0.206277	+	0.978494i	$0.566135\pi$
$48$		0			0
$49$	−6.38563	−	2.86770i	−0.912233	−	0.409671i
$50$		0			0
$51$	3.59594	+	9.45130i	0.503533	+	1.32345i
$52$		0			0
$53$	−0.0415658	+	0.0239980i	−0.00570950	+	0.00329638i	−0.502852	−	0.864373i	$-0.667716\pi$
$53$	−0.0415658	+	0.0239980i	−0.00570950	+	0.00329638i	0.497143	+	0.867669i	$0.334383\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$	7.17031	+	5.84164i	0.949731	+	0.773744i
$58$		0			0
$59$	−8.91313			−1.16039			−0.580195	−	0.814477i	$-0.697024\pi$
$59$	−8.91313			−1.16039			−0.580195	+	0.814477i	$0.697024\pi$
$60$		0			0
$61$			6.96680i			0.892008i	0.895031	+	0.446004i	$0.147153\pi$
$61$			6.96680i			0.892008i	−0.895031	+	0.446004i	$0.852847\pi$
$62$		0			0
$63$	4.02026	−	6.84379i	0.506506	−	0.862237i
$64$		0			0
$65$		−	2.17091i		−	0.269268i
$66$		0			0
$67$	1.17480			0.143525			0.0717626	−	0.997422i	$-0.477138\pi$
$67$	1.17480			0.143525			0.0717626	+	0.997422i	$0.477138\pi$
$68$		0			0
$69$	−3.68181	+	1.40082i	−0.443238	+	0.168639i
$70$		0			0
$71$			6.71061i			0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$71$			6.71061i			0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$72$		0			0
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	−0.691990	−	0.721907i	$-0.743266\pi$
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	0.279195	+	0.960234i	$0.409932\pi$
$74$		0			0
$75$	−11.2964	+	13.8658i	−1.30440	+	1.60108i
$76$		0			0
$77$	−6.55234	+	7.25364i	−0.746709	+	0.826628i
$78$		0			0
$79$	−3.94747			−0.444125			−0.222063	−	0.975032i	$-0.571279\pi$
$79$	−3.94747			−0.444125			−0.222063	+	0.975032i	$0.571279\pi$
$80$		0			0
$81$	7.21799	+	5.37592i	0.801999	+	0.597325i
$82$		0			0
$83$	3.84674	+	6.66275i	0.422235	+	0.731332i	0.996158	−	0.0875774i	$-0.0279125\pi$
$83$	3.84674	+	6.66275i	0.422235	+	0.731332i	−0.573923	+	0.818909i	$0.694579\pi$
$84$		0			0
$85$	11.4280	−	19.7938i	1.23954	−	2.14694i
$86$		0			0
$87$	6.61047	−	2.51509i	0.708717	−	0.269646i
$88$		0			0
$89$	−2.71300	+	4.69905i	−0.287577	+	0.498099i	−0.973231	−	0.229829i	$-0.926183\pi$
$89$	−2.71300	+	4.69905i	−0.287577	+	0.498099i	0.685654	+	0.727928i	$0.259517\pi$
$90$		0			0
$91$	0.983474	−	1.08874i	0.103096	−	0.114130i
$92$		0			0
$93$	−2.23143	+	13.8237i	−0.231389	+	1.43345i
$94$		0			0
$95$		−	20.9041i		−	2.14471i
$96$		0			0
$97$	13.9874	−	8.07563i	1.42021	−	0.819956i	0.423890	−	0.905714i	$-0.360664\pi$
$97$	13.9874	−	8.07563i	1.42021	−	0.819956i	0.996316	+	0.0857571i	$0.0273309\pi$
$98$		0			0
$99$	−7.36753	−	8.28055i	−0.740464	−	0.832227i
$100$		0			0
$101$	0.811750	−	1.40599i	0.0807722	−	0.139901i	−0.822810	−	0.568317i	$-0.807595\pi$
$101$	0.811750	−	1.40599i	0.0807722	−	0.139901i	0.903582	+	0.428416i	$0.140928\pi$
$102$		0			0
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	−0.516786	−	0.856114i	$-0.672872\pi$
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	0.483024	+	0.875607i	$0.339539\pi$
$104$		0			0
$105$	−17.7317	+	2.72546i	−1.73044	+	0.265978i
$106$		0			0
$107$	−4.90777	−	2.83350i	−0.474452	−	0.273925i	0.243650	−	0.969863i	$-0.421655\pi$
$107$	−4.90777	−	2.83350i	−0.474452	−	0.273925i	−0.718101	+	0.695938i	$0.754989\pi$
$108$		0			0
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	−0.983795	−	0.179294i	$-0.942619\pi$
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	0.336624	−	0.941639i	$-0.390715\pi$
$110$		0			0
$111$	8.52987	−	10.4700i	0.809619	−	0.993766i
$112$		0			0
$113$	1.13651	+	0.656162i	0.106913	+	0.0617265i	0.552503	−	0.833511i	$-0.313673\pi$
$113$	1.13651	+	0.656162i	0.106913	+	0.0617265i	−0.445590	+	0.895237i	$0.647006\pi$
$114$		0			0
$115$	7.71082	+	4.45184i	0.719038	+	0.415137i
$116$		0			0
$117$	1.10583	+	1.24287i	0.102234	+	0.114903i
$118$		0			0
$119$	14.6984	−	4.74969i	1.34740	−	0.435403i
$120$		0			0
$121$	1.32489	+	2.29477i	0.120444	+	0.208615i
$122$		0			0
$123$	7.86002	−	9.64777i	0.708714	−	0.869910i
$124$		0			0
$125$	20.8496			1.86485
$126$		0			0
$127$	−17.3935			−1.54342			−0.771710	−	0.635975i	$-0.780598\pi$
$127$	−17.3935			−1.54342			−0.771710	+	0.635975i	$0.780598\pi$
$128$		0			0
$129$	−0.928820	−	2.44124i	−0.0817780	−	0.214939i
$130$		0			0
$131$	5.45361	+	9.44593i	0.476484	+	0.825295i	0.999637	−	0.0269442i	$-0.00857764\pi$
$131$	5.45361	+	9.44593i	0.476484	+	0.825295i	−0.523153	+	0.852239i	$0.675244\pi$
$132$		0			0
$133$	9.47007	−	10.4836i	0.821159	−	0.909047i
$134$		0			0
$135$	−0.884146	−	20.3228i	−0.0760952	−	1.74911i
$136$		0			0
$137$	7.62547	+	4.40257i	0.651488	+	0.376137i	0.789026	−	0.614360i	$-0.210586\pi$
$137$	7.62547	+	4.40257i	0.651488	+	0.376137i	−0.137538	+	0.990496i	$0.543919\pi$
$138$		0			0
$139$	−14.2352	−	8.21869i	−1.20741	−	0.697100i	−0.245220	−	0.969468i	$-0.578860\pi$
$139$	−14.2352	−	8.21869i	−1.20741	−	0.697100i	−0.962193	+	0.272367i	$0.912193\pi$
$140$		0			0
$141$	−4.83621	−	0.780664i	−0.407282	−	0.0657438i
$142$		0			0
$143$	−1.02438	−	1.77428i	−0.0856631	−	0.148373i
$144$		0			0
$145$	−13.8443	−	7.99301i	−1.14971	−	0.663783i
$146$		0			0
$147$	−10.1274	−	6.66606i	−0.835292	−	0.549807i
$148$		0			0
$149$	12.5814	−	7.26390i	1.03071	−	0.595082i	0.113523	−	0.993535i	$-0.463786\pi$
$149$	12.5814	−	7.26390i	1.03071	−	0.595082i	0.917188	+	0.398454i	$0.130453\pi$
$150$		0			0
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	−0.957248	−	0.289268i	$-0.906588\pi$
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	0.729138	+	0.684367i	$0.239921\pi$
$152$		0			0
$153$	3.54005	+	17.1535i	0.286196	+	1.38678i
$154$		0			0
$155$	27.4089	−	15.8246i	2.20154	−	1.27106i
$156$		0			0
$157$			17.8299i			1.42298i	0.702697	+	0.711489i	$0.251979\pi$
$157$			17.8299i			1.42298i	−0.702697	+	0.711489i	$0.748021\pi$
$158$		0			0
$159$	−0.0776978	+	0.0295618i	−0.00616184	+	0.00234440i
$160$		0			0
$161$	1.85027	+	5.72584i	0.145822	+	0.451260i
$162$		0			0
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	−0.887737	−	0.460350i	$-0.847724\pi$
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	0.842544	+	0.538628i	$0.181057\pi$
$164$		0			0
$165$	−3.99217	+	24.7314i	−0.310790	+	1.92534i
$166$		0			0
$167$	−8.95550	+	15.5114i	−0.692997	+	1.20031i	0.277854	+	0.960623i	$0.410377\pi$
$167$	−8.95550	+	15.5114i	−0.692997	+	1.20031i	−0.970851	+	0.239683i	$0.922957\pi$
$168$		0			0
$169$	−6.34625	−	10.9920i	−0.488173	−	0.845540i
$170$		0			0
$171$	10.6482	+	11.9678i	0.814292	+	0.915203i
$172$		0			0
$173$	7.49629			0.569932			0.284966	−	0.958538i	$-0.408018\pi$
$173$	7.49629			0.569932			0.284966	+	0.958538i	$0.408018\pi$
$174$		0			0
$175$	20.2730	+	18.3130i	1.53249	+	1.38433i
$176$		0			0
$177$	−15.2407	−	2.46017i	−1.14556	−	0.184918i
$178$		0			0
$179$	0.624382	−	0.360487i	0.0466685	−	0.0269441i	−0.476484	−	0.879183i	$-0.658089\pi$
$179$	0.624382	−	0.360487i	0.0466685	−	0.0269441i	0.523153	+	0.852239i	$0.324756\pi$
$180$		0			0
$181$		−	5.07121i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$181$		−	5.07121i		−	0.376940i	0.982079	−	0.188470i	$-0.0603529\pi$
$182$		0			0
$183$	−1.92295	+	11.9127i	−0.142149	+	0.880609i
$184$		0			0
$185$	−30.5238			−2.24416
$186$		0			0
$187$		−	21.5700i		−	1.57736i
$188$		0			0
$189$	8.76331	−	10.5927i	0.637437	−	0.770502i
$190$		0			0
$191$			12.7022i			0.919101i	0.888152	+	0.459551i	$0.151989\pi$
$191$			12.7022i			0.919101i	−0.888152	+	0.459551i	$0.848011\pi$
$192$		0			0
$193$	−22.8153			−1.64228			−0.821140	−	0.570726i	$-0.806662\pi$
$193$	−22.8153			−1.64228			−0.821140	+	0.570726i	$0.806662\pi$
$194$		0			0
$195$	0.599205	−	3.71207i	0.0429100	−	0.265827i
$196$		0			0
$197$			0.0311360i			0.00221835i	0.999999	+	0.00110918i	$0.000353062\pi$
$197$			0.0311360i			0.00221835i	−0.999999	+	0.00110918i	$0.999647\pi$
$198$		0			0
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.416146	−	0.909298i	$-0.363380\pi$
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.995548	+	0.0942556i	$0.0300471\pi$
$200$		0			0
$201$	2.00882	+	0.324265i	0.141691	+	0.0228719i
$202$		0			0
$203$	−3.32205	−	10.2804i	−0.233162	−	0.721543i
$204$		0			0
$205$	−28.1268			−1.96446
$206$		0			0
$207$	−6.68225	+	1.37905i	−0.464448	+	0.0958506i
$208$		0			0
$209$	−9.86397	−	17.0849i	−0.682305	−	1.18179i
$210$		0			0
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	−0.405154	−	0.914248i	$-0.632782\pi$
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	0.994339	−	0.106250i	$-0.0338845\pi$
$212$		0			0
$213$	−1.85224	+	11.4746i	−0.126913	+	0.786226i
$214$		0			0
$215$	−2.95181	+	5.11268i	−0.201312	+	0.348682i
$216$		0			0
$217$	20.9148	+	4.48072i	1.41979	+	0.304171i
$218$		0			0
$219$	−6.59278	+	2.50836i	−0.445499	+	0.169499i
$220$		0			0
$221$			3.23755i			0.217781i
$222$		0			0
$223$	1.25230	−	0.723016i	0.0838602	−	0.0484167i	−0.457484	−	0.889218i	$-0.651249\pi$
$223$	1.25230	−	0.723016i	0.0838602	−	0.0484167i	0.541344	+	0.840801i	$0.317916\pi$
$224$		0			0
$225$	−23.1431	+	20.5913i	−1.54287	+	1.37275i
$226$		0			0
$227$	−2.23596	+	3.87280i	−0.148406	+	0.257047i	−0.930639	−	0.365940i	$-0.880748\pi$
$227$	−2.23596	+	3.87280i	−0.148406	+	0.257047i	0.782232	+	0.622987i	$0.214081\pi$
$228$		0			0
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	−0.424134	−	0.905599i	$-0.639421\pi$
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	0.572205	+	0.820111i	$0.306088\pi$
$230$		0			0
$231$	−13.2061	+	10.5946i	−0.868896	+	0.697071i
$232$		0			0
$233$	15.0756	+	8.70389i	0.987634	+	0.570211i	0.904566	−	0.426333i	$-0.140195\pi$
$233$	15.0756	+	8.70389i	0.987634	+	0.570211i	0.0830679	+	0.996544i	$0.473528\pi$
$234$		0			0
$235$	5.53620	+	9.58898i	0.361142	+	0.625516i
$236$		0			0
$237$	−6.74985	−	1.08957i	−0.438450	−	0.0707750i
$238$		0			0
$239$	4.23642	+	2.44590i	0.274031	+	0.158212i	0.630718	−	0.776012i	$-0.282760\pi$
$239$	4.23642	+	2.44590i	0.274031	+	0.158212i	−0.356687	+	0.934224i	$0.616094\pi$
$240$		0			0
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	0.709378	−	0.704828i	$-0.248976\pi$
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	−0.255710	+	0.966754i	$0.582309\pi$
$242$		0			0
$243$	10.8583	+	11.1847i	0.696562	+	0.717497i
$244$		0			0
$245$	2.77686	+	27.2627i	0.177407	+	1.74175i
$246$		0			0
$247$	1.48053	+	2.56436i	0.0942041	+	0.163166i
$248$		0			0
$249$	4.73858	+	12.4545i	0.300295	+	0.789272i
$250$		0			0
$251$	−25.9341			−1.63694			−0.818472	−	0.574546i	$-0.805179\pi$
$251$	−25.9341			−1.63694			−0.818472	+	0.574546i	$0.805179\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$	25.0043	−	30.6915i	1.56583	−	1.92198i
$256$		0			0
$257$	15.4115	+	26.6935i	0.961344	+	1.66510i	0.719131	+	0.694874i	$0.244540\pi$
$257$	15.4115	+	26.6935i	0.961344	+	1.66510i	0.242213	+	0.970223i	$0.422127\pi$
$258$		0			0
$259$	−15.3081	−	13.8280i	−0.951196	−	0.859233i
$260$		0			0
$261$	11.9976	−	2.47600i	0.742630	−	0.153261i
$262$		0			0
$263$	−15.6625	−	9.04276i	−0.965792	−	0.557600i	−0.0678413	−	0.997696i	$-0.521611\pi$
$263$	−15.6625	−	9.04276i	−0.965792	−	0.557600i	−0.897951	+	0.440096i	$0.854944\pi$
$264$		0			0
$265$	0.162723	+	0.0939479i	0.00999597	+	0.00577117i
$266$		0			0
$267$	−5.93602	+	7.28616i	−0.363278	+	0.445906i
$268$		0			0
$269$	−10.8203	−	18.7413i	−0.659725	−	1.14268i	−0.980687	−	0.195585i	$-0.937339\pi$
$269$	−10.8203	−	18.7413i	−0.659725	−	1.14268i	0.320961	−	0.947092i	$-0.395994\pi$
$270$		0			0
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	0.0757430	−	0.997127i	$-0.475867\pi$
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	−0.825666	+	0.564159i	$0.809200\pi$
$272$		0			0
$273$	1.98217	−	1.59019i	0.119966	−	0.0962428i
$274$		0			0
$275$	33.0383	−	19.0747i	1.99229	−	1.15025i
$276$		0			0
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	−0.967424	−	0.253160i	$-0.918530\pi$
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	0.702956	+	0.711234i	$0.251863\pi$
$278$		0			0
$279$	−7.63113	+	23.0215i	−0.456864	+	1.37826i
$280$		0			0
$281$	−16.6889	+	9.63537i	−0.995579	+	0.574798i	−0.906937	−	0.421266i	$-0.861586\pi$
$281$	−16.6889	+	9.63537i	−0.995579	+	0.574798i	−0.0886417	+	0.996064i	$0.528253\pi$
$282$		0			0
$283$			9.61660i			0.571647i	0.958282	+	0.285824i	$0.0922672\pi$
$283$			9.61660i			0.571647i	−0.958282	+	0.285824i	$0.907733\pi$
$284$		0			0
$285$	5.76987	−	35.7442i	0.341777	−	2.11731i
$286$		0			0
$287$	−14.1059	−	12.7421i	−0.832645	−	0.752144i
$288$		0			0
$289$	−8.54297	+	14.7969i	−0.502528	+	0.870404i
$290$		0			0
$291$	26.1463	−	9.94791i	1.53272	−	0.583157i
$292$		0			0
$293$	1.22598	−	2.12346i	0.0716225	−	0.124054i	−0.827990	−	0.560743i	$-0.810516\pi$
$293$	1.22598	−	2.12346i	0.0716225	−	0.124054i	0.899613	+	0.436689i	$0.143849\pi$
$294$		0			0
$295$	17.4467	+	30.2185i	1.01578	+	1.75939i
$296$		0			0
$297$	−10.3123	−	16.1926i	−0.598380	−	0.939590i
$298$		0			0
$299$	−1.26121			−0.0729376
$300$		0			0
$301$	−3.79654	+	1.22683i	−0.218829	+	0.0707132i
$302$		0			0
$303$	1.77610	−	2.18007i	0.102034	−	0.125242i
$304$		0			0
$305$	23.6198	−	13.6369i	1.35247	−	0.780846i
$306$		0			0
$307$		−	10.6839i		−	0.609760i	−0.952391	−	0.304880i	$-0.901384\pi$
$307$		−	10.6839i		−	0.609760i	0.952391	−	0.304880i	$-0.0986163\pi$
$308$		0			0
$309$	−0.640513	+	0.243697i	−0.0364375	+	0.0138634i
$310$		0			0
$311$	−20.7665			−1.17756			−0.588780	−	0.808293i	$-0.700392\pi$
$311$	−20.7665			−1.17756			−0.588780	+	0.808293i	$0.700392\pi$
$312$		0			0
$313$			3.93117i			0.222203i	0.993809	+	0.111101i	$0.0354378\pi$
$313$			3.93117i			0.222203i	−0.993809	+	0.111101i	$0.964562\pi$
$314$		0			0
$315$	−31.0720	−	0.233929i	−1.75071	−	0.0131804i
$316$		0			0
$317$		−	2.29057i		−	0.128651i	−0.997929	−	0.0643256i	$-0.979510\pi$
$317$		−	2.29057i		−	0.128651i	0.997929	−	0.0643256i	$-0.0204896\pi$
$318$		0			0
$319$	−15.0866			−0.844687
$320$		0			0
$321$	−7.60978	−	6.19967i	−0.424736	−	0.346032i
$322$		0			0
$323$			31.1750i			1.73462i
$324$		0			0
$325$	−4.95889	+	2.86302i	−0.275070	+	0.158812i
$326$		0			0
$327$	−8.32315	−	21.8759i	−0.460271	−	1.20974i
$328$		0			0
$329$	−1.56757	+	7.31702i	−0.0864232	+	0.403400i
$330$		0			0
$331$	6.93577			0.381224			0.190612	−	0.981665i	$-0.438953\pi$
$331$	6.93577			0.381224			0.190612	+	0.981665i	$0.438953\pi$
$332$		0			0
$333$	17.4753	−	15.5484i	0.957638	−	0.852047i
$334$		0			0
$335$	−2.29957	−	3.98298i	−0.125639	−	0.217613i
$336$		0			0
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	0.476827	+	0.878997i	$0.341787\pi$
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	−0.999647	+	0.0265545i	$0.991546\pi$
$338$		0			0
$339$	1.76222	+	1.43568i	0.0957106	+	0.0779752i
$340$		0			0
$341$	14.9342	−	25.8668i	0.808733	−	1.40077i
$342$		0			0
$343$	−10.9580	+	14.9305i	−0.591679	+	0.806174i
$344$		0			0
$345$	11.9561	+	9.74059i	0.643694	+	0.524416i
$346$		0			0
$347$		−	8.49036i		−	0.455786i	−0.973686	−	0.227893i	$-0.926816\pi$
$347$		−	8.49036i		−	0.455786i	0.973686	−	0.227893i	$-0.0731837\pi$
$348$		0			0
$349$	−16.5478	+	9.55386i	−0.885782	+	0.511407i	−0.872560	−	0.488506i	$-0.837542\pi$
$349$	−16.5478	+	9.55386i	−0.885782	+	0.511407i	−0.0132216	+	0.999913i	$0.504209\pi$
$350$		0			0
$351$	1.54782	+	2.43043i	0.0826167	+	0.129727i
$352$		0			0
$353$	6.82951	−	11.8291i	0.363498	−	0.629597i	−0.625036	−	0.780596i	$-0.714916\pi$
$353$	6.82951	−	11.8291i	0.363498	−	0.629597i	0.988534	+	0.150999i	$0.0482490\pi$
$354$		0			0
$355$	22.7512	−	13.1354i	1.20751	−	0.697156i
$356$		0			0
$357$	26.4440	−	4.06458i	1.39956	−	0.215121i
$358$		0			0
$359$	−14.8909	−	8.59724i	−0.785909	−	0.453745i	0.0526113	−	0.998615i	$-0.483246\pi$
$359$	−14.8909	−	8.59724i	−0.785909	−	0.453745i	−0.838520	+	0.544870i	$0.816579\pi$
$360$		0			0
$361$	4.75635	+	8.23824i	0.250334	+	0.433592i
$362$		0			0
$363$	1.63205	+	4.28955i	0.0856604	+	0.225143i
$364$		0			0
$365$	13.8073	+	7.97162i	0.722705	+	0.417254i
$366$		0			0
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	0.830056	−	0.557680i	$-0.188309\pi$
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	−0.0679376	+	0.997690i	$0.521642\pi$
$368$		0			0
$369$	16.1029	−	14.3274i	0.838284	−	0.745854i
$370$		0			0
$371$	0.0390466	+	0.120833i	0.00202720	+	0.00627335i
$372$		0			0
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	0.883683	−	0.468086i	$-0.155056\pi$
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	−0.847216	+	0.531248i	$0.821723\pi$
$374$		0			0
$375$	35.6511	+	5.75484i	1.84102	+	0.297179i
$376$		0			0
$377$	2.26442			0.116624
$378$		0			0
$379$	−0.598572			−0.0307466			−0.0153733	−	0.999882i	$-0.504894\pi$
$379$	−0.598572			−0.0307466			−0.0153733	+	0.999882i	$0.504894\pi$
$380$		0			0
$381$	−29.7414	−	4.80088i	−1.52370	−	0.245956i
$382$		0			0
$383$	−4.26039	−	7.37921i	−0.217696	−	0.377060i	0.736407	−	0.676538i	$-0.236521\pi$
$383$	−4.26039	−	7.37921i	−0.217696	−	0.377060i	−0.954103	+	0.299478i	$0.903187\pi$
$384$		0			0
$385$	37.4179	+	8.01628i	1.90699	+	0.408548i
$386$		0			0
$387$	−0.914384	−	4.43068i	−0.0464807	−	0.225224i
$388$		0			0
$389$	−29.9624	−	17.2988i	−1.51915	−	0.877084i	−0.999746	−	0.0225587i	$-0.992819\pi$
$389$	−29.9624	−	17.2988i	−1.51915	−	0.877084i	−0.519409	−	0.854526i	$-0.673848\pi$
$390$		0			0
$391$	−11.4994	−	6.63920i	−0.581551	−	0.335759i
$392$		0			0
$393$	6.71799	+	17.6570i	0.338878	+	0.890680i
$394$		0			0
$395$	7.72683	+	13.3833i	0.388779	+	0.673385i
$396$		0			0
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.994712	−	0.102699i	$-0.0327478\pi$
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.408416	+	0.912796i	$0.366081\pi$
$398$		0			0
$399$	19.0867	−	15.3123i	0.955529	−	0.766572i
$400$		0			0
$401$	11.3473	−	6.55139i	0.566659	−	0.327161i	−0.189155	−	0.981947i	$-0.560575\pi$
$401$	11.3473	−	6.55139i	0.566659	−	0.327161i	0.755814	+	0.654787i	$0.227242\pi$
$402$		0			0
$403$	−2.24155	+	3.88248i	−0.111660	+	0.193400i
$404$		0			0
$405$	4.09760	−	34.9943i	0.203611	−	1.73888i
$406$		0			0
$407$	−24.9471	+	14.4032i	−1.23658	+	0.713941i
$408$		0			0
$409$		−	37.3538i		−	1.84703i	−0.383568	−	0.923513i	$-0.625305\pi$
$409$		−	37.3538i		−	1.84703i	0.383568	−	0.923513i	$-0.374695\pi$
$410$		0			0
$411$	11.8237	+	9.63278i	0.583222	+	0.475150i
$412$		0			0
$413$	−4.94002	+	23.0587i	−0.243082	+	1.13464i
$414$		0			0
$415$	15.0593	−	26.0835i	0.739232	−	1.28039i
$416$		0			0
$417$	−22.0725	−	17.9824i	−1.08089	−	0.880603i
$418$		0			0
$419$	14.1954	−	24.5871i	0.693490	−	1.20116i	−0.277198	−	0.960813i	$-0.589406\pi$
$419$	14.1954	−	24.5871i	0.693490	−	1.20116i	0.970687	−	0.240346i	$-0.0772610\pi$
$420$		0			0
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	−0.885707	−	0.464245i	$-0.846326\pi$
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	0.0408054	−	0.999167i	$-0.487008\pi$
$422$		0			0
$423$	−8.05403	−	2.66974i	−0.391600	−	0.129807i
$424$		0			0
$425$	−60.2854			−2.92427
$426$		0			0
$427$	18.0235	+	3.86129i	0.872216	+	0.186861i
$428$		0			0
$429$	−1.26188	−	3.31662i	−0.0609240	−	0.160128i
$430$		0			0
$431$	13.1844	−	7.61200i	0.635069	−	0.366657i	−0.147643	−	0.989041i	$-0.547169\pi$
$431$	13.1844	−	7.61200i	0.635069	−	0.366657i	0.782713	+	0.622383i	$0.213835\pi$
$432$		0			0
$433$			3.97041i			0.190806i	0.995439	+	0.0954028i	$0.0304139\pi$
$433$			3.97041i			0.190806i	−0.995439	+	0.0954028i	$0.969586\pi$
$434$		0			0
$435$	−21.4664	−	17.4886i	−1.02924	−	0.838516i
$436$		0			0
$437$	−12.1444			−0.580947
$438$		0			0
$439$			9.49060i			0.452962i	0.974016	+	0.226481i	$0.0727221\pi$
$439$			9.49060i			0.452962i	−0.974016	+	0.226481i	$0.927278\pi$
$440$		0			0
$441$	−15.4770	−	14.1937i	−0.737001	−	0.675892i
$442$		0			0
$443$			32.7883i			1.55782i	0.627135	+	0.778910i	$0.284227\pi$
$443$			32.7883i			1.55782i	−0.627135	+	0.778910i	$0.715773\pi$
$444$		0			0
$445$	21.2418			1.00696
$446$		0			0
$447$	23.5182	−	8.94798i	1.11237	−	0.423225i
$448$		0			0
$449$		−	0.658896i		−	0.0310952i	−0.999879	−	0.0155476i	$-0.995051\pi$
$449$		−	0.658896i		−	0.0310952i	0.999879	−	0.0155476i	$-0.00494916\pi$
$450$		0			0
$451$	−22.9880	+	13.2721i	−1.08246	+	0.624960i
$452$		0			0
$453$	−6.13308	+	7.52804i	−0.288157	+	0.353698i
$454$		0			0
$455$	−5.61624	−	1.20321i	−0.263293	−	0.0564071i
$456$		0			0
$457$	15.8903			0.743316			0.371658	−	0.928370i	$-0.378789\pi$
$457$	15.8903			0.743316			0.371658	+	0.928370i	$0.378789\pi$
$458$		0			0
$459$	1.31856	+	30.3081i	0.0615451	+	1.41466i
$460$		0			0
$461$	−9.81626	−	17.0023i	−0.457189	−	0.791874i	0.541622	−	0.840622i	$-0.317810\pi$
$461$	−9.81626	−	17.0023i	−0.457189	−	0.791874i	−0.998811	+	0.0487477i	$0.984477\pi$
$462$		0			0
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	−0.851743	−	0.523960i	$-0.824454\pi$
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	0.879634	+	0.475651i	$0.157787\pi$
$464$		0			0
$465$	51.2348	−	19.4934i	2.37596	−	0.903983i
$466$		0			0
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.0549972	−	0.998487i	$-0.482485\pi$
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.837216	−	0.546872i	$-0.184182\pi$
$468$		0			0
$469$	0.651124	−	3.03927i	0.0300661	−	0.140341i
$470$		0			0
$471$	−4.92133	+	30.4876i	−0.226763	+	1.40479i
$472$		0			0
$473$			5.57146i			0.256176i
$474$		0			0
$475$	−47.7501	+	27.5685i	−2.19093	+	1.26493i
$476$		0			0
$477$	−0.141016	+	0.0291023i	−0.00645670	+	0.00133250i
$478$		0			0
$479$	−3.61289	+	6.25771i	−0.165077	+	0.285922i	−0.936683	−	0.350179i	$-0.886121\pi$
$479$	−3.61289	+	6.25771i	−0.165077	+	0.285922i	0.771606	+	0.636101i	$0.219454\pi$
$480$		0			0
$481$	3.74444	−	2.16185i	0.170732	−	0.0985720i
$482$		0			0
$483$	1.58338	+	10.3014i	0.0720465	+	0.468731i
$484$		0			0
$485$	−54.7582	−	31.6147i	−2.48644	−	1.43555i
$486$		0			0
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	0.954845	−	0.297104i	$-0.0960207\pi$
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	−0.734722	+	0.678368i	$0.762687\pi$
$488$		0			0
$489$	−1.26246	+	1.54960i	−0.0570903	+	0.0700754i
$490$		0			0
$491$	17.2480	+	9.95814i	0.778392	+	0.449405i	0.835860	−	0.548943i	$-0.184969\pi$
$491$	17.2480	+	9.95814i	0.778392	+	0.449405i	−0.0574682	+	0.998347i	$0.518303\pi$
$492$		0			0
$493$	20.6465	+	11.9203i	0.929872	+	0.536862i
$494$		0			0
$495$	−13.6526	+	41.1868i	−0.613637	+	1.85121i
$496$		0			0
$497$	17.3607	+	3.71930i	0.778733	+	0.166833i
$498$		0			0
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	−0.937770	−	0.347258i	$-0.887113\pi$
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	0.168150	−	0.985761i	$-0.446221\pi$
$500$		0			0
$501$	−19.5945	+	24.0513i	−0.875420	+	1.07453i
$502$		0			0
$503$	1.22542			0.0546388			0.0273194	−	0.999627i	$-0.491303\pi$
$503$	1.22542			0.0546388			0.0273194	+	0.999627i	$0.491303\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$	−7.81758	−	20.5471i	−0.347191	−	0.912529i
$508$		0			0
$509$	5.05078	+	8.74820i	0.223872	+	0.387757i	0.955980	−	0.293431i	$-0.0947970\pi$
$509$	5.05078	+	8.74820i	0.223872	+	0.387757i	−0.732109	+	0.681188i	$0.761464\pi$
$510$		0			0
$511$	3.31316	+	10.2529i	0.146565	+	0.453561i
$512$		0			0
$513$	14.9043	+	23.4031i	0.658041	+	1.03327i
$514$		0			0
$515$	1.34143	+	0.774473i	0.0591103	+	0.0341274i
$516$		0			0
$517$	9.04947	+	5.22471i	0.397995	+	0.229783i
$518$		0			0
$519$	12.8180	+	2.06910i	0.562649	+	0.0908233i
$520$		0			0
$521$	10.5390	+	18.2541i	0.461723	+	0.799728i	0.999047	−	0.0436480i	$-0.0138980\pi$
$521$	10.5390	+	18.2541i	0.461723	+	0.799728i	−0.537324	+	0.843376i	$0.680565\pi$
$522$		0			0
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	0.824451	−	0.565934i	$-0.191484\pi$
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	−0.0778877	+	0.996962i	$0.524818\pi$
$524$		0			0
$525$	29.6104	+	36.9093i	1.29231	+	1.61085i
$526$		0			0
$527$	−40.8760	+	23.5997i	−1.78058	+	1.02802i
$528$		0			0
$529$	−8.91366	+	15.4389i	−0.387550	+	0.671257i
$530$		0			0
$531$	−25.3813	−	8.41336i	−1.10145	−	0.365109i
$532$		0			0
$533$	3.45039	−	1.99208i	0.149453	−	0.0862866i
$534$		0			0
$535$			22.1853i			0.959154i
$536$		0			0
$537$	1.16714	−	0.444063i	0.0503658	−	0.0191627i
$538$		0			0
$539$	15.1339	+	20.9715i	0.651864	+	0.903306i
$540$		0			0
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	−0.942438	−	0.334381i	$-0.891473\pi$
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	0.760802	+	0.648984i	$0.224806\pi$
$542$		0			0
$543$	1.39974	−	8.67135i	0.0600685	−	0.372123i
$544$		0			0
$545$	−26.4511	+	45.8147i	−1.13304	+	1.96249i
$546$		0			0
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	0.766948	−	0.641709i	$-0.221774\pi$
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	−0.939211	+	0.343342i	$0.888441\pi$
$548$		0			0
$549$	−6.57617	+	19.8389i	−0.280664	+	0.846703i
$550$		0			0
$551$	21.8046			0.928906
$552$		0			0
$553$	−2.18785	+	10.2123i	−0.0930369	+	0.434271i
$554$		0			0
$555$	−52.1932	−	8.42507i	−2.21548	−	0.357624i
$556$		0			0
$557$	−18.2294	+	10.5247i	−0.772403	+	0.445947i	−0.833731	−	0.552170i	$-0.813800\pi$
$557$	−18.2294	+	10.5247i	−0.772403	+	0.445947i	0.0613279	+	0.998118i	$0.480466\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$	5.95367	−	36.8829i	0.251364	−	1.55720i
$562$		0			0
$563$	41.2821			1.73983			0.869916	−	0.493200i	$-0.164173\pi$
$563$	41.2821			1.73983			0.869916	+	0.493200i	$0.164173\pi$
$564$		0			0
$565$		−	5.13751i		−	0.216137i
$566$		0			0
$567$	17.9083	−	15.6937i	0.752077	−	0.659075i
$568$		0			0
$569$		−	36.1064i		−	1.51366i	−0.653612	−	0.756829i	$-0.726747\pi$
$569$		−	36.1064i		−	1.51366i	0.653612	−	0.756829i	$-0.273253\pi$
$570$		0			0
$571$	−19.2422			−0.805262			−0.402631	−	0.915362i	$-0.631904\pi$
$571$	−19.2422			−0.805262			−0.402631	+	0.915362i	$0.631904\pi$
$572$		0			0
$573$	−3.50602	+	21.7198i	−0.146466	+	0.907356i
$574$		0			0
$575$		−	23.4846i		−	0.979375i
$576$		0			0
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.929406	−	0.369060i	$-0.879680\pi$
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.145088	+	0.989419i	$0.546346\pi$
$578$		0			0
$579$	−39.0123	−	6.29739i	−1.62129	−	0.261711i
$580$		0			0
$581$	19.3689	−	6.25893i	0.803556	−	0.259664i
$582$		0			0
$583$	0.177324			0.00734402
$584$		0			0
$585$	2.04918	−	6.18194i	0.0847233	−	0.255592i
$586$		0			0
$587$	4.72218	+	8.17905i	0.194905	+	0.337586i	0.946869	−	0.321618i	$-0.104227\pi$
$587$	4.72218	+	8.17905i	0.194905	+	0.337586i	−0.751964	+	0.659204i	$0.770893\pi$
$588$		0			0
$589$	−21.5843	+	37.3852i	−0.889367	+	1.54043i
$590$		0			0
$591$	−0.00859405	+	0.0532400i	−0.000353512	+	0.00219000i
$592$		0			0
$593$	12.4176	−	21.5079i	0.509929	−	0.883223i	−0.490005	−	0.871720i	$-0.663005\pi$
$593$	12.4176	−	21.5079i	0.509929	−	0.883223i	0.999934	−	0.0115033i	$-0.00366171\pi$
$594$		0			0
$595$	−44.8738	−	40.5353i	−1.83965	−	1.66179i
$596$		0			0
$597$	37.2255	−	14.1632i	1.52354	−	0.579662i
$598$		0			0
$599$		−	11.8995i		−	0.486199i	−0.970001	−	0.243100i	$-0.921836\pi$
$599$		−	11.8995i		−	0.486199i	0.970001	−	0.243100i	$-0.0781642\pi$
$600$		0			0
$601$	22.1276	−	12.7754i	0.902604	−	0.521118i	0.0245596	−	0.999698i	$-0.492182\pi$
$601$	22.1276	−	12.7754i	0.902604	−	0.521118i	0.878044	+	0.478580i	$0.158848\pi$
$602$		0			0
$603$	3.34541	+	1.10893i	0.136236	+	0.0451592i
$604$		0			0
$605$	5.18669	−	8.98361i	0.210869	−	0.365236i
$606$		0			0
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	−0.841259	−	0.540632i	$-0.818185\pi$
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	0.0475718	+	0.998868i	$0.484852\pi$
$608$		0			0
$609$	−2.84287	−	18.4956i	−0.115199	−	0.749478i
$610$		0			0
$611$	−1.35828	−	0.784204i	−0.0549502	−	0.0317255i
$612$		0			0
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	0.537414	−	0.843319i	$-0.319401\pi$
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	−0.999042	+	0.0437549i	$0.986068\pi$
$614$		0			0
$615$	−48.0944	−	7.76344i	−1.93935	−	0.313052i
$616$		0			0
$617$	1.78792	+	1.03226i	0.0719791	+	0.0415572i	0.535558	−	0.844499i	$-0.320101\pi$
$617$	1.78792	+	1.03226i	0.0719791	+	0.0415572i	−0.463578	+	0.886056i	$0.653435\pi$
$618$		0			0
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.189354	−	0.981909i	$-0.560639\pi$
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.945035	+	0.326969i	$0.893973\pi$
$620$		0			0
$621$	−11.8067	+	0.513653i	−0.473787	+	0.0206122i
$622$		0			0
$623$	10.6530	+	9.62307i	0.426804	+	0.385540i
$624$		0			0
$625$	−14.9967	−	25.9751i	−0.599870	−	1.03901i
$626$		0			0
$627$	−12.1509	−	31.9364i	−0.485259	−	1.27542i
$628$		0			0
$629$	45.5213			1.81505
$630$		0			0
$631$	38.4706			1.53149			0.765744	−	0.643145i	$-0.222371\pi$
$631$	38.4706			1.53149			0.765744	+	0.643145i	$0.222371\pi$
$632$		0			0
$633$	18.7257	−	22.9849i	0.744281	−	0.913566i
$634$		0			0
$635$	34.0461	+	58.9696i	1.35108	+	2.34014i
$636$		0			0
$637$	−2.27153	−	3.14772i	−0.0900012	−	0.124717i
$638$		0			0
$639$	−6.33434	+	19.1093i	−0.250583	+	0.755954i
$640$		0			0
$641$	41.3645	+	23.8818i	1.63380	+	0.943274i	0.982907	+	0.184104i	$0.0589384\pi$
$641$	41.3645	+	23.8818i	1.63380	+	0.943274i	0.650892	+	0.759170i	$0.274395\pi$
$642$		0			0
$643$	29.2346	+	16.8786i	1.15290	+	0.665626i	0.949592	−	0.313489i	$-0.101498\pi$
$643$	29.2346	+	16.8786i	1.15290	+	0.665626i	0.203306	+	0.979115i	$0.434831\pi$
$644$		0			0
$645$	−6.45853	+	7.92752i	−0.254304	+	0.312146i
$646$		0			0
$647$	0.536008	+	0.928393i	0.0210727	+	0.0364989i	0.876369	−	0.481640i	$-0.159959\pi$
$647$	0.536008	+	0.928393i	0.0210727	+	0.0364989i	−0.855297	+	0.518138i	$0.826625\pi$
$648$		0			0
$649$	28.5183	+	16.4650i	1.11944	+	0.646309i
$650$		0			0
$651$	34.5258	+	13.4345i	1.35317	+	0.526539i
$652$		0			0
$653$	28.8503	−	16.6567i	1.12900	−	0.651828i	0.185317	−	0.982679i	$-0.440669\pi$
$653$	28.8503	−	16.6567i	1.12900	−	0.651828i	0.943683	+	0.330851i	$0.107336\pi$
$654$		0			0
$655$	21.3499	−	36.9791i	0.834210	−	1.44489i
$656$		0			0
$657$	−11.9654	+	2.46937i	−0.466817	+	0.0963394i
$658$		0			0
$659$	−8.41890	+	4.86065i	−0.327954	+	0.189344i	−0.654932	−	0.755688i	$-0.727303\pi$
$659$	−8.41890	+	4.86065i	−0.327954	+	0.189344i	0.326979	+	0.945032i	$0.393969\pi$
$660$		0			0
$661$			17.0729i			0.664060i	0.943269	+	0.332030i	$0.107734\pi$
$661$			17.0729i			0.664060i	−0.943269	+	0.332030i	$0.892266\pi$
$662$		0			0
$663$	−0.893617	+	5.53595i	−0.0347052	+	0.214998i
$664$		0			0
$665$	−54.0799	−	11.5859i	−2.09713	−	0.449282i
$666$		0			0
$667$	−4.64362	+	8.04298i	−0.179802	+	0.311426i
$668$		0			0
$669$	2.34089	−	0.890642i	0.0905041	−	0.0344342i
$670$		0			0
$671$	12.8696	−	22.2909i	0.496827	−	0.860529i
$672$		0			0
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	−0.966039	−	0.258398i	$-0.916805\pi$
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	0.259240	−	0.965813i	$-0.416528\pi$
$674$		0			0
$675$	−45.2563	+	28.8215i	−1.74191	+	1.10934i
$676$		0			0
$677$	−40.3538			−1.55092			−0.775461	−	0.631395i	$-0.782483\pi$
$677$	−40.3538			−1.55092			−0.775461	+	0.631395i	$0.782483\pi$
$678$		0			0
$679$	−13.1397	−	40.6619i	−0.504254	−	1.56046i
$680$		0			0
$681$	−4.89227	+	6.00501i	−0.187472	+	0.230112i
$682$		0			0
$683$	8.23662	−	4.75541i	0.315165	−	0.181961i	−0.334070	−	0.942548i	$-0.608422\pi$
$683$	8.23662	−	4.75541i	0.315165	−	0.181961i	0.649236	+	0.760587i	$0.275089\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$	4.18852	−	1.59361i	0.159802	−	0.0608000i
$688$		0			0
$689$	−0.0266155			−0.00101397
$690$		0			0
$691$		−	7.70784i		−	0.293220i	−0.989194	−	0.146610i	$-0.953164\pi$
$691$		−	7.70784i		−	0.293220i	0.989194	−	0.146610i	$-0.0468363\pi$
$692$		0			0
$693$	−25.5056	+	14.4707i	−0.968876	+	0.549697i
$694$		0			0
$695$			64.3494i			2.44091i
$696$		0			0
$697$	41.9465			1.58884
$698$		0			0
$699$	23.3756	+	19.0440i	0.884145	+	0.720311i
$700$		0			0
$701$		−	15.6388i		−	0.590671i	−0.955394	−	0.295336i	$-0.904569\pi$
$701$		−	15.6388i		−	0.590671i	0.955394	−	0.295336i	$-0.0954314\pi$
$702$		0			0
$703$	36.0559	−	20.8169i	1.35988	−	0.785124i
$704$		0			0
$705$	6.81973	+	17.9244i	0.256846	+	0.675073i
$706$		0			0
$707$	−3.18747	−	2.87930i	−0.119877	−	0.108287i
$708$		0			0
$709$	13.4405			0.504769			0.252384	−	0.967627i	$-0.418785\pi$
$709$	13.4405			0.504769			0.252384	+	0.967627i	$0.418785\pi$
$710$		0			0
$711$	−11.2409	−	3.72614i	−0.421568	−	0.139741i
$712$		0			0
$713$	−9.19343	−	15.9235i	−0.344297	−	0.596339i
$714$		0			0
$715$	−4.01027	+	6.94599i	−0.149976	+	0.259765i
$716$		0			0
$717$	6.56881	+	5.35160i	0.245317	+	0.199859i
$718$		0			0
$719$	20.0309	−	34.6946i	0.747027	−	1.29389i	−0.202214	−	0.979341i	$-0.564814\pi$
$719$	20.0309	−	34.6946i	0.747027	−	1.29389i	0.949242	−	0.314548i	$-0.101853\pi$
$720$		0			0
$721$	0.321886	+	0.996107i	0.0119877	+	0.0370970i
$722$		0			0
$723$	10.9203	+	8.89675i	0.406131	+	0.330874i
$724$		0			0
$725$			42.1651i			1.56597i
$726$		0			0
$727$	43.2091	−	24.9468i	1.60254	−	0.925225i	0.611560	−	0.791198i	$-0.290542\pi$
$727$	43.2091	−	24.9468i	1.60254	−	0.925225i	0.990978	−	0.134027i	$-0.0427910\pi$
$728$		0			0
$729$	15.4797	+	22.1219i	0.573322	+	0.819330i
$730$		0			0
$731$	4.40214	−	7.62473i	0.162819	−	0.282011i
$732$		0			0
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	−0.671794	−	0.740738i	$-0.734476\pi$
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	0.305601	+	0.952160i	$0.401143\pi$
$734$		0			0
$735$	−2.77674	+	47.3834i	−0.102422	+	1.74776i
$736$		0			0
$737$	−3.75888	−	2.17019i	−0.138460	−	0.0799400i
$738$		0			0
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	0.936362	−	0.351036i	$-0.114170\pi$
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	−0.772187	+	0.635396i	$0.780837\pi$
$740$		0			0
$741$	1.82378	+	4.79349i	0.0669984	+	0.176093i
$742$		0			0
$743$	−45.8621	−	26.4785i	−1.68252	−	0.971403i	−0.959979	−	0.280074i	$-0.909641\pi$
$743$	−45.8621	−	26.4785i	−1.68252	−	0.971403i	−0.722540	−	0.691329i	$-0.757026\pi$
$744$		0			0
$745$	−49.2541	−	28.4369i	−1.80453	−	1.04185i
$746$		0			0
$747$	4.66493	+	22.6041i	0.170681	+	0.827041i
$748$		0			0
$749$	−10.0505	+	11.1262i	−0.367237	+	0.406542i
$750$		0			0
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	0.999806	−	0.0196744i	$-0.00626295\pi$
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	−0.516942	+	0.856021i	$0.672930\pi$
$752$		0			0
$753$	−44.3451	−	7.15823i	−1.61603	−	0.260860i
$754$		0			0
$755$	21.9470			0.798733
$756$		0			0
$757$	8.46749			0.307756			0.153878	−	0.988090i	$-0.450824\pi$
$757$	8.46749			0.307756			0.153878	+	0.988090i	$0.450824\pi$
$758$		0			0
$759$	14.3680	+	2.31929i	0.521525	+	0.0841849i
$760$		0			0
$761$	−26.9968	−	46.7599i	−0.978635	−	1.69505i	−0.667377	−	0.744720i	$-0.732583\pi$
$761$	−26.9968	−	46.7599i	−0.978635	−	1.69505i	−0.311258	−	0.950325i	$-0.600750\pi$
$762$		0			0
$763$	−34.0208	+	10.9936i	−1.23163	+	0.397995i
$764$		0			0
$765$	51.2267	−	45.5783i	1.85210	−	1.64789i
$766$		0			0
$767$	−4.28046	−	2.47132i	−0.154558	−	0.0892343i
$768$		0			0
$769$	30.1912	+	17.4309i	1.08872	+	0.628575i	0.933236	−	0.359263i	$-0.116972\pi$
$769$	30.1912	+	17.4309i	1.08872	+	0.628575i	0.155487	+	0.987838i	$0.450305\pi$
$770$		0			0
$771$	18.9846	+	49.8976i	0.683713	+	1.79702i
$772$		0			0
$773$	−1.06375	−	1.84246i	−0.0382603	−	0.0662688i	0.846261	−	0.532768i	$-0.178848\pi$
$773$	−1.06375	−	1.84246i	−0.0382603	−	0.0662688i	−0.884521	+	0.466499i	$0.845515\pi$
$774$		0			0
$775$	−72.2944	−	41.7392i	−2.59689	−	1.49932i
$776$		0			0
$777$	−22.3587	−	27.8701i	−0.802115	−	0.999833i
$778$		0			0
$779$	33.2244	−	19.1821i	1.19039	−	0.687272i
$780$		0			0
$781$	12.3964	−	21.4712i	0.443577	−	0.768298i
$782$		0			0
$783$	21.1982	−	0.922233i	0.757563	−	0.0329579i
$784$		0			0
$785$	60.4492	−	34.9004i	2.15752	−	1.24565i
$786$		0			0
$787$		−	28.3429i		−	1.01032i	−0.863027	−	0.505158i	$-0.831434\pi$
$787$		−	28.3429i		−	1.01032i	0.863027	−	0.505158i	$-0.168566\pi$
$788$		0			0
$789$	−24.2856	−	19.7855i	−0.864592	−	0.704381i
$790$		0			0
$791$	2.32742	−	2.57652i	0.0827535	−	0.0916106i
$792$		0			0
$793$	−1.93167	+	3.34575i	−0.0685956	+	0.118811i
$794$		0			0
$795$	0.252311	+	0.205557i	0.00894854	+	0.00729036i
$796$		0			0
$797$	−18.9123	+	32.7570i	−0.669907	+	1.16031i	0.308022	+	0.951379i	$0.400333\pi$
$797$	−18.9123	+	32.7570i	−0.669907	+	1.16031i	−0.977930	+	0.208935i	$0.933000\pi$
$798$		0			0
$799$	−8.25634	−	14.3004i	−0.292088	−	0.505912i
$800$		0			0
$801$	−12.1612	+	10.8203i	−0.429695	+	0.382316i
$802$		0			0
$803$	15.0462			0.530970
$804$		0			0
$805$	15.7908	−	17.4809i	0.556552	−	0.616120i
$806$		0			0
$807$	−13.3289	−	35.0327i	−0.469200	−	1.23321i
$808$		0			0
$809$	39.2475	−	22.6595i	1.37987	−	0.796667i	0.387724	−	0.921776i	$-0.373261\pi$
$809$	39.2475	−	22.6595i	1.37987	−	0.796667i	0.992143	+	0.125109i	$0.0399280\pi$
$810$		0			0
$811$		−	5.45145i		−	0.191426i	−0.995409	−	0.0957132i	$-0.969487\pi$
$811$		−	5.45145i		−	0.191426i	0.995409	−	0.0957132i	$-0.0305132\pi$
$812$		0			0
$813$	−19.1421	−	15.5950i	−0.671343	−	0.546942i
$814$		0			0
$815$	4.51766			0.158247
$816$		0			0
$817$		−	8.05240i		−	0.281718i
$818$		0			0
$819$	3.82826	−	2.17198i	0.133770	−	0.0758953i
$820$		0			0
$821$			49.3196i			1.72127i	0.509225	+	0.860634i	$0.329932\pi$
$821$			49.3196i			1.72127i	−0.509225	+	0.860634i	$0.670068\pi$
$822$		0			0
$823$	−23.6992			−0.826101			−0.413050	−	0.910708i	$-0.635537\pi$
$823$	−23.6992			−0.826101			−0.413050	+	0.910708i	$0.635537\pi$
$824$		0			0
$825$	61.7577	−	23.4970i	2.15013	−	0.818061i
$826$		0			0
$827$			19.9706i			0.694445i	0.937783	+	0.347222i	$0.112875\pi$
$827$			19.9706i			0.694445i	−0.937783	+	0.347222i	$0.887125\pi$
$828$		0			0
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	−0.713936	−	0.700211i	$-0.753089\pi$
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	0.249433	+	0.968392i	$0.419756\pi$
$830$		0			0
$831$	−9.63074	+	11.8212i	−0.334087	+	0.410074i
$832$		0			0
$833$	−4.14124	−	40.6579i	−0.143485	−	1.40871i
$834$		0			0
$835$	70.1183			2.42654
$836$		0			0
$837$	−19.4029	+	37.2585i	−0.670663	+	1.28784i
$838$		0			0
$839$	−5.53910	−	9.59401i	−0.191231	−	0.331222i	0.754427	−	0.656383i	$-0.227915\pi$
$839$	−5.53910	−	9.59401i	−0.191231	−	0.331222i	−0.945658	+	0.325162i	$0.894581\pi$
$840$		0			0
$841$	−6.16267	+	10.6741i	−0.212506	+	0.368071i
$842$		0			0
$843$	−31.1962	+	11.8693i	−1.07445	+	0.408799i
$844$		0			0
$845$	−24.8444	+	43.0318i	−0.854674	+	1.48034i
$846$		0			0
$847$	6.67098	−	2.15569i	0.229218	−	0.0740703i
$848$		0			0
$849$	−2.65434	+	16.4436i	−0.0910966	+	0.564342i
$850$		0			0
$851$			17.7331i			0.607883i
$852$		0			0
$853$	−42.1706	+	24.3472i	−1.44389	+	0.833633i	−0.998107	−	0.0615058i	$-0.980410\pi$
$853$	−42.1706	+	24.3472i	−1.44389	+	0.833633i	−0.445788	+	0.895139i	$0.647076\pi$
$854$		0			0
$855$	19.7320	−	59.5271i	0.674819	−	2.03578i
$856$		0			0
$857$	8.39130	−	14.5342i	0.286641	−	0.496477i	−0.686365	−	0.727258i	$-0.740795\pi$
$857$	8.39130	−	14.5342i	0.286641	−	0.496477i	0.973006	+	0.230780i	$0.0741279\pi$
$858$		0			0
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	−0.823058	−	0.567957i	$-0.807734\pi$
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	0.0803361	+	0.996768i	$0.474401\pi$
$860$		0			0
$861$	−20.6029	−	25.6814i	−0.702145	−	0.875221i
$862$		0			0
$863$	5.87377	+	3.39122i	0.199945	+	0.115438i	0.596630	−	0.802516i	$-0.296506\pi$
$863$	5.87377	+	3.39122i	0.199945	+	0.115438i	−0.396685	+	0.917955i	$0.629839\pi$
$864$		0			0
$865$	−14.6733	−	25.4149i	−0.498907	−	0.864133i
$866$		0			0
$867$	−18.6919	+	22.9434i	−0.634812	+	0.779199i
$868$		0			0
$869$	12.6303	+	7.29209i	0.428452	+	0.247367i
$870$		0			0
$871$	0.564190	+	0.325735i	0.0191168	+	0.0110371i
$872$		0			0
$873$	47.4538	−	9.79329i	1.60607	−	0.331453i
$874$		0			0
$875$	11.5557	−	53.9390i	0.390655	−	1.82347i
$876$		0			0
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	0.953278	+	0.302093i	$0.0976854\pi$
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	−0.215019	+	0.976610i	$0.568981\pi$
$878$		0			0
$879$	2.68243	−	3.29255i	0.0904761	−	0.111055i
$880$		0			0
$881$	−27.5307			−0.927531			−0.463766	−	0.885958i	$-0.653502\pi$
$881$	−27.5307			−0.927531			−0.463766	+	0.885958i	$0.653502\pi$
$882$		0			0
$883$	5.56040			0.187122			0.0935612	−	0.995614i	$-0.470175\pi$
$883$	5.56040			0.187122			0.0935612	+	0.995614i	$0.470175\pi$
$884$		0			0
$885$	21.4915	+	56.4867i	0.722430	+	1.89878i
$886$		0			0
$887$	12.3092	+	21.3202i	0.413303	+	0.715862i	0.995249	−	0.0973655i	$-0.0310416\pi$
$887$	12.3092	+	21.3202i	0.413303	+	0.715862i	−0.581945	+	0.813228i	$0.697708\pi$
$888$		0			0
$889$	−9.64017	+	44.9977i	−0.323321	+	1.50917i
$890$		0			0
$891$	−13.1637	−	30.5344i	−0.441002	−	1.02294i
$892$		0			0
$893$	−13.0792	−	7.55125i	−0.437677	−	0.252693i
$894$		0			0
$895$	−2.44434	−	1.41124i	−0.0817054	−	0.0471726i
$896$		0			0
$897$	−2.15656	−	0.348114i	−0.0720056	−	0.0116232i
$898$		0			0
$899$	16.5062	+	28.5896i	0.550514	+	0.953518i
$900$		0			0
$901$	−0.242674	−	0.140108i	−0.00808465	−	0.00466767i
$902$		0			0
$903$	−6.83039	+	1.04987i	−0.227301	+	0.0349374i
$904$		0			0
$905$	−17.1931	+	9.92644i	−0.571518	+	0.329966i
$906$		0			0
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	−0.770065	−	0.637966i	$-0.779776\pi$
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	0.937527	+	0.347913i	$0.113109\pi$
$908$		0			0
$909$	3.63872	−	3.23751i	0.120689	−	0.107381i
$910$		0			0
$911$	23.5808	−	13.6144i	0.781267	−	0.451065i	−0.0556121	−	0.998452i	$-0.517711\pi$
$911$	23.5808	−	13.6144i	0.781267	−	0.451065i	0.836879	+	0.547388i	$0.184378\pi$
$912$		0			0
$913$		−	28.4240i		−	0.940698i
$914$		0			0
$915$	44.1519	−	16.7985i	1.45962	−	0.555341i
$916$		0			0
$917$	27.4597	−	8.87343i	0.906799	−	0.293026i
$918$		0			0
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	0.327183	+	0.944961i	$0.393901\pi$
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	−0.981952	+	0.189132i	$0.939433\pi$
$920$		0			0
$921$	2.94892	−	18.2685i	0.0971701	−	0.601968i
$922$		0			0
$923$	−1.86064	+	3.22272i	−0.0612436	+	0.106077i
$924$		0			0
$925$	40.2552	+	69.7240i	1.32358	+	2.29251i
$926$		0			0
$927$	−1.16249	+	0.239909i	−0.0381811	+	0.00787965i
$928$		0			0
$929$	−0.284567			−0.00933633			−0.00466816	−	0.999989i	$-0.501486\pi$
$929$	−0.284567			−0.00933633			−0.00466816	+	0.999989i	$0.501486\pi$
$930$		0			0
$931$	−21.8730	−	30.3100i	−0.716858	−	0.993369i
$932$		0			0
$933$	−35.5090	−	5.73189i	−1.16251	−	0.187654i
$934$		0			0
$935$	−73.1295	+	42.2214i	−2.39159	+	1.38079i
$936$		0			0
$937$			21.7298i			0.709881i	0.934889	+	0.354940i	$0.115499\pi$
$937$			21.7298i			0.709881i	−0.934889	+	0.354940i	$0.884501\pi$
$938$		0			0
$939$	−1.08507	+	6.72197i	−0.0354098	+	0.219363i
$940$		0			0
$941$	−11.2848			−0.367875			−0.183938	−	0.982938i	$-0.558884\pi$
$941$	−11.2848			−0.367875			−0.183938	+	0.982938i	$0.558884\pi$
$942$		0			0
$943$			16.3405i			0.532121i
$944$		0			0
$945$	−53.0660	−	8.97639i	−1.72624	−	0.292002i
$946$		0			0
$947$		−	22.7131i		−	0.738077i	−0.929414	−	0.369039i	$-0.879687\pi$
$947$		−	22.7131i		−	0.738077i	0.929414	−	0.369039i	$-0.120313\pi$
$948$		0			0
$949$	−2.25836			−0.0733096
$950$		0			0
$951$	0.632234	−	3.91668i	0.0205016	−	0.127007i
$952$		0			0
$953$		−	16.5638i		−	0.536554i	−0.963342	−	0.268277i	$-0.913546\pi$
$953$		−	16.5638i		−	0.536554i	0.963342	−	0.268277i	$-0.0864543\pi$
$954$		0			0
$955$	43.0648	−	24.8635i	1.39354	−	0.804563i
$956$		0			0
$957$	−25.7968	−	4.16414i	−0.833893	−	0.134608i
$958$		0			0
$959$	15.6160	−	17.2874i	0.504267	−	0.558239i
$960$		0			0
$961$	−34.3581			−1.10832
$962$		0			0
$963$	−11.3009	−	12.7013i	−0.364166	−	0.409295i
$964$		0			0
$965$	44.6589	+	77.3515i	1.43762	+	2.49003i
$966$		0			0
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	−0.699039	−	0.715084i	$-0.746388\pi$
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	0.968800	+	0.247843i	$0.0797218\pi$
$968$		0			0
$969$	−8.60481	+	53.3067i	−0.276426	+	1.71246i
$970$		0			0
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	0.496734	+	0.867903i	$0.334532\pi$
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	−0.999993	+	0.00376705i	$0.998801\pi$
$972$		0			0
$973$	−29.1519	+	32.2720i	−0.934566	+	1.03459i
$974$		0			0
$975$	−9.26953	+	3.52679i	−0.296862	+	0.112948i
$976$		0			0
$977$			56.6904i			1.81369i	0.421469	+	0.906843i	$0.361515\pi$
$977$			56.6904i			1.81369i	−0.421469	+	0.906843i	$0.638485\pi$
$978$		0			0
$979$	17.3609	−	10.0233i	0.554858	−	0.320347i
$980$		0			0
$981$	−8.19378	−	39.7033i	−0.261607	−	1.26763i
$982$		0			0
$983$	19.9204	−	34.5032i	0.635362	−	1.10048i	−0.351076	−	0.936347i	$-0.614184\pi$
$983$	19.9204	−	34.5032i	0.635362	−	1.10048i	0.986438	−	0.164133i	$-0.0524825\pi$
$984$		0			0
$985$	0.105562	−	0.0609460i	0.00336347	−	0.00194190i
$986$		0			0
$987$	−4.70004	+	12.0788i	−0.149604	+	0.384473i
$988$		0			0
$989$	2.97026	+	1.71488i	0.0944489	+	0.0545301i
$990$		0			0
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.590247	+	0.807223i	$0.299030\pi$
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.403952	+	0.914780i	$0.367636\pi$
$992$		0			0
$993$	11.8596	+	1.91438i	0.376352	+	0.0607511i
$994$		0			0
$995$	−77.9613	−	45.0110i	−2.47154	−	1.42694i
$996$		0			0
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.968497	−	0.249025i	$-0.0801102\pi$
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.268586	+	0.963256i	$0.413444\pi$
$998$		0			0
$999$	34.1728	−	21.7630i	1.08118	−	0.688552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.w.a.5.8	✓	16
3.2	odd	2		756.2.w.a.341.8		16
4.3	odd	2		1008.2.ca.d.257.1		16
7.2	even	3		1764.2.x.a.293.3		16
7.3	odd	6		252.2.bm.a.185.6	yes	16
7.4	even	3		1764.2.bm.a.1697.3		16
7.5	odd	6		1764.2.x.b.293.6		16
7.6	odd	2		1764.2.w.b.509.1		16
9.2	odd	6		252.2.bm.a.173.6	yes	16
9.4	even	3		2268.2.t.b.2105.1		16
9.5	odd	6		2268.2.t.a.2105.8		16
9.7	even	3		756.2.bm.a.89.8		16
12.11	even	2		3024.2.ca.d.2609.8		16
21.2	odd	6		5292.2.x.a.881.8		16
21.5	even	6		5292.2.x.b.881.1		16
21.11	odd	6		5292.2.bm.a.2285.1		16
21.17	even	6		756.2.bm.a.17.8		16
21.20	even	2		5292.2.w.b.1097.1		16
28.3	even	6		1008.2.df.d.689.3		16
36.7	odd	6		3024.2.df.d.1601.8		16
36.11	even	6		1008.2.df.d.929.3		16
63.2	odd	6		1764.2.x.b.1469.6		16
63.11	odd	6		1764.2.w.b.1109.1		16
63.16	even	3		5292.2.x.b.4409.1		16
63.20	even	6		1764.2.bm.a.1685.3		16
63.25	even	3		5292.2.w.b.521.1		16
63.31	odd	6		2268.2.t.a.1781.8		16
63.34	odd	6		5292.2.bm.a.4625.1		16
63.38	even	6	inner	252.2.w.a.101.8	yes	16
63.47	even	6		1764.2.x.a.1469.3		16
63.52	odd	6		756.2.w.a.521.8		16
63.59	even	6		2268.2.t.b.1781.1		16
63.61	odd	6		5292.2.x.a.4409.8		16
84.59	odd	6		3024.2.df.d.17.8		16
252.115	even	6		3024.2.ca.d.2033.8		16
252.227	odd	6		1008.2.ca.d.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	1.1	even	1	trivial
252.2.w.a.101.8	yes	16	63.38	even	6	inner
252.2.bm.a.173.6	yes	16	9.2	odd	6
252.2.bm.a.185.6	yes	16	7.3	odd	6
756.2.w.a.341.8		16	3.2	odd	2
756.2.w.a.521.8		16	63.52	odd	6
756.2.bm.a.17.8		16	21.17	even	6
756.2.bm.a.89.8		16	9.7	even	3
1008.2.ca.d.257.1		16	4.3	odd	2
1008.2.ca.d.353.1		16	252.227	odd	6
1008.2.df.d.689.3		16	28.3	even	6
1008.2.df.d.929.3		16	36.11	even	6
1764.2.w.b.509.1		16	7.6	odd	2
1764.2.w.b.1109.1		16	63.11	odd	6
1764.2.x.a.293.3		16	7.2	even	3
1764.2.x.a.1469.3		16	63.47	even	6
1764.2.x.b.293.6		16	7.5	odd	6
1764.2.x.b.1469.6		16	63.2	odd	6
1764.2.bm.a.1685.3		16	63.20	even	6
1764.2.bm.a.1697.3		16	7.4	even	3
2268.2.t.a.1781.8		16	63.31	odd	6
2268.2.t.a.2105.8		16	9.5	odd	6
2268.2.t.b.1781.1		16	63.59	even	6
2268.2.t.b.2105.1		16	9.4	even	3
3024.2.ca.d.2033.8		16	252.115	even	6
3024.2.ca.d.2609.8		16	12.11	even	2
3024.2.df.d.17.8		16	84.59	odd	6
3024.2.df.d.1601.8		16	36.7	odd	6
5292.2.w.b.521.1		16	63.25	even	3
5292.2.w.b.1097.1		16	21.20	even	2
5292.2.x.a.881.8		16	21.2	odd	6
5292.2.x.a.4409.8		16	63.61	odd	6
5292.2.x.b.881.1		16	21.5	even	6
5292.2.x.b.4409.1		16	63.16	even	3
5292.2.bm.a.2285.1		16	21.11	odd	6
5292.2.bm.a.4625.1		16	63.34	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +O(q^{10})\)	\(q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +(-3.19958 - 1.84728i) q^{11} +(0.480242 + 0.277268i) q^{13} +(-2.41122 - 6.33747i) q^{15} +(2.91916 + 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(1.66177 - 4.27066i) q^{21} +(-1.96965 + 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(4.60867 + 2.40003i) q^{27} +(3.53638 - 2.04173i) q^{29} +8.08443i q^{31} +(-4.96114 - 4.04183i) q^{33} +(-9.85583 + 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(0.744643 + 0.606659i) q^{39} +(3.59234 - 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +(-2.37374 - 11.5021i) q^{45} -2.82833 q^{47} +(-6.38563 - 2.86770i) q^{49} +(3.59594 + 9.45130i) q^{51} +(-0.0415658 + 0.0239980i) q^{53} +14.4635i q^{55} +(7.17031 + 5.84164i) q^{57} -8.91313 q^{59} +6.96680i q^{61} +(4.02026 - 6.84379i) q^{63} -2.17091i q^{65} +1.17480 q^{67} +(-3.68181 + 1.40082i) q^{69} +6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-11.2964 + 13.8658i) q^{75} +(-6.55234 + 7.25364i) q^{77} -3.94747 q^{79} +(7.21799 + 5.37592i) q^{81} +(3.84674 + 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(6.61047 - 2.51509i) q^{87} +(-2.71300 + 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(-2.23143 + 13.8237i) q^{93} -20.9041i q^{95} +(13.9874 - 8.07563i) q^{97} +(-7.36753 - 8.28055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

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