LMFDB - Embedded newform 576.2.p.c.95.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(95,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("576.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.p (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:	$4.59938315643$
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} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.7
Root			$-0.192865 - 0.334053i$ of defining polynomial
Character	$\chi$	$=$	576.95
Dual form			576.2.p.c.479.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46399 + 0.925606i) q^{3} +(2.06470 - 3.57617i) q^{5} +(-0.287429 + 0.165947i) q^{7} +(1.28651 + 2.71015i) q^{9} +O(q^{10})$	\(q+(1.46399 + 0.925606i) q^{3} +(2.06470 - 3.57617i) q^{5} +(-0.287429 + 0.165947i) q^{7} +(1.28651 + 2.71015i) q^{9} +(-3.62268 + 2.09155i) q^{11} +(4.27682 + 2.46922i) q^{13} +(6.33282 - 3.32436i) q^{15} -3.20639i q^{17} +5.42029 q^{19} +(-0.574394 - 0.0231017i) q^{21} +(1.39438 - 2.41514i) q^{23} +(-6.02601 - 10.4374i) q^{25} +(-0.625100 + 5.15842i) q^{27} +(-1.03570 - 1.79388i) q^{29} +(-3.60828 - 2.08324i) q^{31} +(-7.23950 - 0.291167i) q^{33} +1.37053i q^{35} -2.21390i q^{37} +(3.97567 + 7.57355i) q^{39} +(1.41298 + 0.815784i) q^{41} +(2.99758 + 5.19195i) q^{43} +(12.3482 + 0.994880i) q^{45} +(-3.97567 - 6.88607i) q^{47} +(-3.44492 + 5.96678i) q^{49} +(2.96786 - 4.69411i) q^{51} -2.05801 q^{53} +17.2738i q^{55} +(7.93523 + 5.01706i) q^{57} +(5.40497 + 3.12056i) q^{59} +(-9.10709 + 5.25798i) q^{61} +(-0.819522 - 0.565483i) q^{63} +(17.6607 - 10.1964i) q^{65} +(-5.83658 + 10.1093i) q^{67} +(4.27682 - 2.24508i) q^{69} -7.66299 q^{71} -6.21742 q^{73} +(0.838886 - 20.8578i) q^{75} +(0.694175 - 1.20235i) q^{77} +(-0.719039 + 0.415137i) q^{79} +(-5.68980 + 6.97325i) q^{81} +(-5.96543 + 3.44414i) q^{83} +(-11.4666 - 6.62025i) q^{85} +(0.144180 - 3.58486i) q^{87} +9.14211i q^{89} -1.63904 q^{91} +(-3.35421 - 6.38968i) q^{93} +(11.1913 - 19.3839i) q^{95} +(-0.749190 - 1.29763i) q^{97} +(-10.3290 - 7.12719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^5 + 6 * q^9	$ 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.46399	+	0.925606i	0.845232	+	0.534399i
$3$	1.46399	+	0.925606i	0.845232	+	0.534399i
$4$		0			0
$5$	2.06470	−	3.57617i	0.923364	−	1.59931i	0.129192	−	0.991620i	$-0.458762\pi$
$5$	2.06470	−	3.57617i	0.923364	−	1.59931i	0.794172	−	0.607693i	$-0.207905\pi$
$6$		0			0
$7$	−0.287429	+	0.165947i	−0.108638	+	0.0627222i	−0.553335	−	0.832959i	$-0.686645\pi$
$7$	−0.287429	+	0.165947i	−0.108638	+	0.0627222i	0.444696	+	0.895681i	$0.353312\pi$
$8$		0			0
$9$	1.28651	+	2.71015i	0.428836	+	0.903382i
$10$		0			0
$11$	−3.62268	+	2.09155i	−1.09228	+	0.630627i	−0.934182	−	0.356797i	$-0.883869\pi$
$11$	−3.62268	+	2.09155i	−1.09228	+	0.630627i	−0.158096	+	0.987424i	$0.550536\pi$
$12$		0			0
$13$	4.27682	+	2.46922i	1.18618	+	0.684839i	0.957435	−	0.288648i	$-0.0932059\pi$
$13$	4.27682	+	2.46922i	1.18618	+	0.684839i	0.228741	+	0.973487i	$0.426539\pi$
$14$		0			0
$15$	6.33282	−	3.32436i	1.63513	−	0.858347i
$16$		0			0
$17$		−	3.20639i		−	0.777664i	−0.921309	−	0.388832i	$-0.872879\pi$
$17$		−	3.20639i		−	0.777664i	0.921309	−	0.388832i	$-0.127121\pi$
$18$		0			0
$19$	5.42029			1.24350			0.621750	−	0.783215i	$-0.286422\pi$
$19$	5.42029			1.24350			0.621750	+	0.783215i	$0.286422\pi$
$20$		0			0
$21$	−0.574394	−	0.0231017i	−0.125343	−	0.00504120i
$22$		0			0
$23$	1.39438	−	2.41514i	0.290748	−	0.503591i	−0.683239	−	0.730195i	$-0.739429\pi$
$23$	1.39438	−	2.41514i	0.290748	−	0.503591i	0.973987	+	0.226604i	$0.0727624\pi$
$24$		0			0
$25$	−6.02601	−	10.4374i	−1.20520	−	2.08747i
$26$		0			0
$27$	−0.625100	+	5.15842i	−0.120301	+	0.992738i
$28$		0			0
$29$	−1.03570	−	1.79388i	−0.192324	−	0.333115i	0.753696	−	0.657223i	$-0.228269\pi$
$29$	−1.03570	−	1.79388i	−0.192324	−	0.333115i	−0.946020	+	0.324108i	$0.894936\pi$
$30$		0			0
$31$	−3.60828	−	2.08324i	−0.648067	−	0.374161i	0.139649	−	0.990201i	$-0.455403\pi$
$31$	−3.60828	−	2.08324i	−0.648067	−	0.374161i	−0.787715	+	0.616040i	$0.788736\pi$
$32$		0			0
$33$	−7.23950	−	0.291167i	−1.26024	−	0.0506857i
$34$		0			0
$35$			1.37053i			0.231662i
$36$		0			0
$37$		−	2.21390i		−	0.363963i	−0.983302	−	0.181982i	$-0.941749\pi$
$37$		−	2.21390i		−	0.363963i	0.983302	−	0.181982i	$-0.0582511\pi$
$38$		0			0
$39$	3.97567	+	7.57355i	0.636617	+	1.21274i
$40$		0			0
$41$	1.41298	+	0.815784i	0.220670	+	0.127404i	0.606261	−	0.795266i	$-0.292669\pi$
$41$	1.41298	+	0.815784i	0.220670	+	0.127404i	−0.385590	+	0.922670i	$0.626002\pi$
$42$		0			0
$43$	2.99758	+	5.19195i	0.457126	+	0.791766i	0.998808	−	0.0488181i	$-0.0155455\pi$
$43$	2.99758	+	5.19195i	0.457126	+	0.791766i	−0.541682	+	0.840584i	$0.682212\pi$
$44$		0			0
$45$	12.3482	+	0.994880i	1.84076	+	0.148308i
$46$		0			0
$47$	−3.97567	−	6.88607i	−0.579912	−	1.00444i	−0.995489	−	0.0948784i	$-0.969754\pi$
$47$	−3.97567	−	6.88607i	−0.579912	−	1.00444i	0.415577	−	0.909558i	$-0.363580\pi$
$48$		0			0
$49$	−3.44492	+	5.96678i	−0.492132	+	0.852397i
$50$		0			0
$51$	2.96786	−	4.69411i	0.415583	−	0.657307i
$52$		0			0
$53$	−2.05801			−0.282690			−0.141345	−	0.989960i	$-0.545143\pi$
$53$	−2.05801			−0.282690			−0.141345	+	0.989960i	$0.545143\pi$
$54$		0			0
$55$			17.2738i			2.32919i
$56$		0			0
$57$	7.93523	+	5.01706i	1.05105	+	0.664525i
$58$		0			0
$59$	5.40497	+	3.12056i	0.703667	+	0.406262i	0.808712	−	0.588205i	$-0.200165\pi$
$59$	5.40497	+	3.12056i	0.703667	+	0.406262i	−0.105045	+	0.994467i	$0.533499\pi$
$60$		0			0
$61$	−9.10709	+	5.25798i	−1.16604	+	0.673216i	−0.952745	−	0.303771i	$-0.901754\pi$
$61$	−9.10709	+	5.25798i	−1.16604	+	0.673216i	−0.213299	+	0.976987i	$0.568421\pi$
$62$		0			0
$63$	−0.819522	−	0.565483i	−0.103250	−	0.0712442i
$64$		0			0
$65$	17.6607	−	10.1964i	2.19054	−	1.26471i
$66$		0			0
$67$	−5.83658	+	10.1093i	−0.713052	+	1.23504i	0.250655	+	0.968077i	$0.419354\pi$
$67$	−5.83658	+	10.1093i	−0.713052	+	1.23504i	−0.963706	+	0.266965i	$0.913979\pi$
$68$		0			0
$69$	4.27682	−	2.24508i	0.514868	−	0.270276i
$70$		0			0
$71$	−7.66299			−0.909429			−0.454715	−	0.890637i	$-0.650259\pi$
$71$	−7.66299			−0.909429			−0.454715	+	0.890637i	$0.650259\pi$
$72$		0			0
$73$	−6.21742			−0.727695			−0.363847	−	0.931459i	$-0.618537\pi$
$73$	−6.21742			−0.727695			−0.363847	+	0.931459i	$0.618537\pi$
$74$		0			0
$75$	0.838886	−	20.8578i	0.0968662	−	2.40846i
$76$		0			0
$77$	0.694175	−	1.20235i	0.0791086	−	0.137020i
$78$		0			0
$79$	−0.719039	+	0.415137i	−0.0808982	+	0.0467066i	−0.539903	−	0.841727i	$-0.681539\pi$
$79$	−0.719039	+	0.415137i	−0.0808982	+	0.0467066i	0.459005	+	0.888434i	$0.348206\pi$
$80$		0			0
$81$	−5.68980	+	6.97325i	−0.632200	+	0.774806i
$82$		0			0
$83$	−5.96543	+	3.44414i	−0.654791	+	0.378044i	−0.790289	−	0.612734i	$-0.790070\pi$
$83$	−5.96543	+	3.44414i	−0.654791	+	0.378044i	0.135498	+	0.990778i	$0.456737\pi$
$84$		0			0
$85$	−11.4666	−	6.62025i	−1.24373	−	0.718067i
$86$		0			0
$87$	0.144180	−	3.58486i	0.0154578	−	0.384338i
$88$		0			0
$89$			9.14211i			0.969061i	0.874774	+	0.484531i	$0.161010\pi$
$89$			9.14211i			0.969061i	−0.874774	+	0.484531i	$0.838990\pi$
$90$		0			0
$91$	−1.63904			−0.171818
$92$		0			0
$93$	−3.35421	−	6.38968i	−0.347815	−	0.662579i
$94$		0			0
$95$	11.1913	−	19.3839i	1.14820	−	1.98875i
$96$		0			0
$97$	−0.749190	−	1.29763i	−0.0760687	−	0.131755i	0.825482	−	0.564429i	$-0.190904\pi$
$97$	−0.749190	−	1.29763i	−0.0760687	−	0.131755i	−0.901551	+	0.432674i	$0.857570\pi$
$98$		0			0
$99$	−10.3290	−	7.12719i	−1.03811	−	0.716309i
$100$		0			0
$101$	4.82358	+	8.35469i	0.479965	+	0.831323i	0.999736	−	0.0229825i	$-0.00731619\pi$
$101$	4.82358	+	8.35469i	0.479965	+	0.831323i	−0.519771	+	0.854305i	$0.673983\pi$
$102$		0			0
$103$	−4.32639	−	2.49784i	−0.426292	−	0.246120i	0.271474	−	0.962446i	$-0.412489\pi$
$103$	−4.32639	−	2.49784i	−0.426292	−	0.246120i	−0.697766	+	0.716326i	$0.745822\pi$
$104$		0			0
$105$	−1.26857	+	2.00643i	−0.123800	+	0.195808i
$106$		0			0
$107$		−	13.1294i		−	1.26927i	−0.772813	−	0.634634i	$-0.781151\pi$
$107$		−	13.1294i		−	1.26927i	0.772813	−	0.634634i	$-0.218849\pi$
$108$		0			0
$109$			10.7401i			1.02872i	0.857576	+	0.514358i	$0.171970\pi$
$109$			10.7401i			1.02872i	−0.857576	+	0.514358i	$0.828030\pi$
$110$		0			0
$111$	2.04920	−	3.24112i	0.194502	−	0.307634i
$112$		0			0
$113$	4.02870	+	2.32597i	0.378989	+	0.218809i	0.677378	−	0.735635i	$-0.263116\pi$
$113$	4.02870	+	2.32597i	0.378989	+	0.218809i	−0.298390	+	0.954444i	$0.596449\pi$
$114$		0			0
$115$	−5.75797	−	9.97309i	−0.536933	−	0.929995i
$116$		0			0
$117$	−1.18980	+	14.7675i	−0.109997	+	1.36525i
$118$		0			0
$119$	0.532092	+	0.921611i	0.0487768	+	0.0844839i
$120$		0			0
$121$	3.24919	−	5.62776i	0.295381	−	0.511615i
$122$		0			0
$123$	1.31349	+	2.50216i	0.118433	+	0.225612i
$124$		0			0
$125$	−29.1207			−2.60463
$126$		0			0
$127$			0.663789i			0.0589018i	0.999566	+	0.0294509i	$0.00937587\pi$
$127$			0.663789i			0.0589018i	−0.999566	+	0.0294509i	$0.990624\pi$
$128$		0			0
$129$	−0.417295	+	10.3755i	−0.0367408	+	0.913514i
$130$		0			0
$131$	−4.77467	−	2.75666i	−0.417165	−	0.240850i	0.276699	−	0.960957i	$-0.410760\pi$
$131$	−4.77467	−	2.75666i	−0.417165	−	0.240850i	−0.693864	+	0.720106i	$0.744093\pi$
$132$		0			0
$133$	−1.55795	+	0.899484i	−0.135092	+	0.0779951i
$134$		0			0
$135$	17.1567	+	12.8861i	1.47662	+	1.10906i
$136$		0			0
$137$	3.41730	−	1.97298i	0.291959	−	0.168563i	−0.346866	−	0.937915i	$-0.612754\pi$
$137$	3.41730	−	1.97298i	0.291959	−	0.168563i	0.638825	+	0.769352i	$0.279421\pi$
$138$		0			0
$139$	9.09321	−	15.7499i	0.771276	−	1.33589i	−0.165588	−	0.986195i	$-0.552952\pi$
$139$	9.09321	−	15.7499i	0.771276	−	1.33589i	0.936864	−	0.349695i	$-0.113715\pi$
$140$		0			0
$141$	0.553457	−	13.7610i	0.0466095	−	1.15889i
$142$		0			0
$143$	−20.6580			−1.72751
$144$		0			0
$145$	−8.55364			−0.710341
$146$		0			0
$147$	−10.5662	+	5.54664i	−0.871486	+	0.457479i
$148$		0			0
$149$	7.33052	−	12.6968i	0.600539	−	1.04016i	−0.392200	−	0.919880i	$-0.628286\pi$
$149$	7.33052	−	12.6968i	0.600539	−	1.04016i	0.992739	−	0.120285i	$-0.0383807\pi$
$150$		0			0
$151$	−18.4236	+	10.6369i	−1.49929	+	0.865617i	−1.00000		0.000816542i	$-0.999740\pi$
$151$	−18.4236	+	10.6369i	−1.49929	+	0.865617i	−0.499293	+	0.866433i	$0.666407\pi$
$152$		0			0
$153$	8.68980	−	4.12505i	0.702528	−	0.333490i
$154$		0			0
$155$	−14.9001	+	8.60256i	−1.19680	+	0.690974i
$156$		0			0
$157$	9.74343	+	5.62537i	0.777611	+	0.448954i	0.835583	−	0.549365i	$-0.185130\pi$
$157$	9.74343	+	5.62537i	0.777611	+	0.448954i	−0.0579722	+	0.998318i	$0.518463\pi$
$158$		0			0
$159$	−3.01290	−	1.90491i	−0.238939	−	0.151069i
$160$		0			0
$161$			0.925575i			0.0729455i
$162$		0			0
$163$	13.3410			1.04495			0.522473	−	0.852656i	$-0.325009\pi$
$163$	13.3410			1.04495			0.522473	+	0.852656i	$0.325009\pi$
$164$		0			0
$165$	−15.9887	+	25.2885i	−1.24472	+	1.96871i
$166$		0			0
$167$	−12.3782	+	21.4397i	−0.957855	+	1.65905i	−0.230161	+	0.973153i	$0.573925\pi$
$167$	−12.3782	+	21.4397i	−0.957855	+	1.65905i	−0.727694	+	0.685901i	$0.759408\pi$
$168$		0			0
$169$	5.69411	+	9.86249i	0.438009	+	0.758653i
$170$		0			0
$171$	6.97325	+	14.6898i	0.533258	+	1.12336i
$172$		0			0
$173$	−4.13610	−	7.16393i	−0.314462	−	0.544664i	0.664861	−	0.746967i	$-0.268491\pi$
$173$	−4.13610	−	7.16393i	−0.314462	−	0.544664i	−0.979323	+	0.202303i	$0.935157\pi$
$174$		0			0
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$		0			0
$177$	5.02439	+	9.57133i	0.377656	+	0.719425i
$178$		0			0
$179$		−	12.3748i		−	0.924939i	−0.886635	−	0.462470i	$-0.846963\pi$
$179$		−	12.3748i		−	0.924939i	0.886635	−	0.462470i	$-0.153037\pi$
$180$		0			0
$181$			2.41487i			0.179496i	0.995965	+	0.0897478i	$0.0286061\pi$
$181$			2.41487i			0.179496i	−0.995965	+	0.0897478i	$0.971394\pi$
$182$		0			0
$183$	−18.1995	−	0.731968i	−1.34534	−	0.0541086i
$184$		0			0
$185$	−7.91730	−	4.57105i	−0.582091	−	0.336070i
$186$		0			0
$187$	6.70634	+	11.6157i	0.490416	+	0.849426i
$188$		0			0
$189$	−0.676353	−	1.58641i	−0.0491975	−	0.115395i
$190$		0			0
$191$	7.21563	+	12.4978i	0.522105	+	0.904312i	0.999669	+	0.0257154i	$0.00818637\pi$
$191$	7.21563	+	12.4978i	0.522105	+	0.904312i	−0.477564	+	0.878597i	$0.658480\pi$
$192$		0			0
$193$	8.63904	−	14.9632i	0.621851	−	1.07708i	−0.367289	−	0.930107i	$-0.619714\pi$
$193$	8.63904	−	14.9632i	0.621851	−	1.07708i	0.989141	−	0.146971i	$-0.0469526\pi$
$194$		0			0
$195$	35.2929	+	1.41945i	2.52738	+	0.101649i
$196$		0			0
$197$	15.1427			1.07887			0.539435	−	0.842027i	$-0.318638\pi$
$197$	15.1427			1.07887			0.539435	+	0.842027i	$0.318638\pi$
$198$		0			0
$199$		−	21.6057i		−	1.53158i	−0.643088	−	0.765792i	$-0.722347\pi$
$199$		−	21.6057i		−	1.53158i	0.643088	−	0.765792i	$-0.277653\pi$
$200$		0			0
$201$	−17.9018	+	9.39743i	−1.26270	+	0.662843i
$202$		0			0
$203$	0.595379	+	0.343742i	0.0417874	+	0.0241260i
$204$		0			0
$205$	5.83477	−	3.36871i	0.407518	−	0.235281i
$206$		0			0
$207$	8.33926	+	0.671883i	0.579619	+	0.0466991i
$208$		0			0
$209$	−19.6360	+	11.3368i	−1.35825	+	0.784185i
$210$		0			0
$211$	3.70129	−	6.41082i	0.254807	−	0.441339i	−0.710036	−	0.704166i	$-0.751321\pi$
$211$	3.70129	−	6.41082i	0.254807	−	0.441339i	0.964843	+	0.262826i	$0.0846546\pi$
$212$		0			0
$213$	−11.2185	−	7.09290i	−0.768679	−	0.485998i
$214$		0			0
$215$	24.7564			1.68837
$216$		0			0
$217$	1.38283			0.0938729
$218$		0			0
$219$	−9.10222	−	5.75488i	−0.615071	−	0.388879i
$220$		0			0
$221$	7.91730	−	13.7132i	0.532575	−	0.922447i
$222$		0			0
$223$	−2.60181	+	1.50216i	−0.174230	+	0.100592i	−0.584579	−	0.811337i	$-0.698740\pi$
$223$	−2.60181	+	1.50216i	−0.174230	+	0.100592i	0.410349	+	0.911929i	$0.365407\pi$
$224$		0			0
$225$	20.5343	−	29.7591i	1.36895	−	1.98394i
$226$		0			0
$227$	−7.28027	+	4.20326i	−0.483208	+	0.278980i	−0.721753	−	0.692151i	$-0.756663\pi$
$227$	−7.28027	+	4.20326i	−0.483208	+	0.278980i	0.238544	+	0.971132i	$0.423330\pi$
$228$		0			0
$229$	−2.74775	−	1.58641i	−0.181576	−	0.104833i	0.406457	−	0.913670i	$-0.366764\pi$
$229$	−2.74775	−	1.58641i	−0.181576	−	0.104833i	−0.588033	+	0.808837i	$0.700098\pi$
$230$		0			0
$231$	2.12916	−	1.11769i	0.140089	−	0.0735383i
$232$		0			0
$233$		−	10.0341i		−	0.657357i	−0.944442	−	0.328678i	$-0.893397\pi$
$233$		−	10.0341i		−	0.657357i	0.944442	−	0.328678i	$-0.106603\pi$
$234$		0			0
$235$	−32.8344			−2.14188
$236$		0			0
$237$	−1.43692	−	0.0577916i	−0.0933377	−	0.00375397i
$238$		0			0
$239$	4.95896	−	8.58918i	0.320769	−	0.555588i	−0.659878	−	0.751373i	$-0.729392\pi$
$239$	4.95896	−	8.58918i	0.320769	−	0.555588i	0.980647	+	0.195785i	$0.0627254\pi$
$240$		0			0
$241$	0.334590	+	0.579528i	0.0215529	+	0.0373307i	0.876601	−	0.481219i	$-0.159806\pi$
$241$	0.334590	+	0.579528i	0.0215529	+	0.0373307i	−0.855048	+	0.518549i	$0.826472\pi$
$242$		0			0
$243$	−14.7843	+	4.94223i	−0.948411	+	0.317044i
$244$		0			0
$245$	14.2255	+	24.6393i	0.908833	+	1.57415i
$246$		0			0
$247$	23.1816	+	13.3839i	1.47501	+	0.851598i
$248$		0			0
$249$	−11.9212	−	0.479462i	−0.755477	−	0.0303847i
$250$		0			0
$251$			3.38823i			0.213863i	0.994266	+	0.106931i	$0.0341025\pi$
$251$			3.38823i			0.213863i	−0.994266	+	0.106931i	$0.965897\pi$
$252$		0			0
$253$			11.6657i			0.733415i
$254$		0			0
$255$	−10.6592	−	20.3055i	−0.667506	−	1.27158i
$256$		0			0
$257$	−19.5531	−	11.2890i	−1.21969	−	0.704187i	−0.254837	−	0.966984i	$-0.582022\pi$
$257$	−19.5531	−	11.2890i	−1.21969	−	0.704187i	−0.964851	+	0.262797i	$0.915355\pi$
$258$		0			0
$259$	0.367391	+	0.636340i	0.0228286	+	0.0395403i
$260$		0			0
$261$	3.52925	−	5.11473i	0.218455	−	0.316594i
$262$		0			0
$263$	−3.70876	−	6.42377i	−0.228692	−	0.396107i	0.728729	−	0.684803i	$-0.240112\pi$
$263$	−3.70876	−	6.42377i	−0.228692	−	0.396107i	−0.957421	+	0.288696i	$0.906778\pi$
$264$		0			0
$265$	−4.24919	+	7.35981i	−0.261026	+	0.452110i
$266$		0			0
$267$	−8.46199	+	13.3839i	−0.517865	+	0.819082i
$268$		0			0
$269$	−19.9774			−1.21804			−0.609021	−	0.793154i	$-0.708438\pi$
$269$	−19.9774			−1.21804			−0.609021	+	0.793154i	$0.708438\pi$
$270$		0			0
$271$		−	26.1040i		−	1.58571i	−0.609412	−	0.792853i	$-0.708595\pi$
$271$		−	26.1040i		−	1.58571i	0.609412	−	0.792853i	$-0.291405\pi$
$272$		0			0
$273$	−2.39954	−	1.51711i	−0.145227	−	0.0918196i
$274$		0			0
$275$	43.6606	+	25.2074i	2.63283	+	1.52007i
$276$		0			0
$277$	21.2472	−	12.2671i	1.27662	−	0.737057i	0.300395	−	0.953815i	$-0.402881\pi$
$277$	21.2472	−	12.2671i	1.27662	−	0.737057i	0.976225	+	0.216757i	$0.0695481\pi$
$278$		0			0
$279$	1.00381	−	12.4591i	0.0600967	−	0.745906i
$280$		0			0
$281$	23.8348	−	13.7610i	1.42186	−	0.820913i	0.425405	−	0.905003i	$-0.360132\pi$
$281$	23.8348	−	13.7610i	1.42186	−	0.820913i	0.996458	+	0.0840901i	$0.0267983\pi$
$282$		0			0
$283$	−0.480920	+	0.832977i	−0.0285877	+	0.0495154i	−0.879965	−	0.475038i	$-0.842434\pi$
$283$	−0.480920	+	0.832977i	−0.0285877	+	0.0495154i	0.851378	+	0.524553i	$0.175768\pi$
$284$		0			0
$285$	34.3258	−	18.0190i	2.03328	−	1.06735i
$286$		0			0
$287$	−0.541509			−0.0319643
$288$		0			0
$289$	6.71904			0.395238
$290$		0			0
$291$	0.104295	−	2.59317i	0.00611390	−	0.152015i
$292$		0			0
$293$	1.36384	−	2.36224i	0.0796763	−	0.138003i	−0.823434	−	0.567412i	$-0.807945\pi$
$293$	1.36384	−	2.36224i	0.0796763	−	0.138003i	0.903110	+	0.429409i	$0.141278\pi$
$294$		0			0
$295$	22.3193	−	12.8861i	1.29948	−	0.750256i
$296$		0			0
$297$	−8.52457	−	19.9947i	−0.494645	−	1.16021i
$298$		0			0
$299$	11.9270	−	6.88607i	0.689757	−	0.398232i
$300$		0			0
$301$	−1.72318	−	0.994880i	−0.0993226	−	0.0573439i
$302$		0			0
$303$	−0.671495	+	16.6959i	−0.0385764	+	0.959154i
$304$		0			0
$305$			43.4247i			2.48649i
$306$		0			0
$307$	−5.29186			−0.302022			−0.151011	−	0.988532i	$-0.548253\pi$
$307$	−5.29186			−0.302022			−0.151011	+	0.988532i	$0.548253\pi$
$308$		0			0
$309$	−4.02175	−	7.66134i	−0.228790	−	0.435838i
$310$		0			0
$311$	12.1708	−	21.0804i	0.690140	−	1.19536i	−0.281652	−	0.959517i	$-0.590882\pi$
$311$	12.1708	−	21.0804i	0.690140	−	1.19536i	0.971792	−	0.235841i	$-0.0757844\pi$
$312$		0			0
$313$	15.2158	+	26.3545i	0.860048	+	1.48965i	0.871881	+	0.489717i	$0.162900\pi$
$313$	15.2158	+	26.3545i	0.860048	+	1.48965i	−0.0118333	+	0.999930i	$0.503767\pi$
$314$		0			0
$315$	−3.71434	+	1.76320i	−0.209279	+	0.0993448i
$316$		0			0
$317$	14.8885	+	25.7876i	0.836220	+	1.44837i	0.893034	+	0.449990i	$0.148572\pi$
$317$	14.8885	+	25.7876i	0.836220	+	1.44837i	−0.0568140	+	0.998385i	$0.518094\pi$
$318$		0			0
$319$	7.50399	+	4.33243i	0.420143	+	0.242570i
$320$		0			0
$321$	12.1527	−	19.2213i	0.678295	−	1.07283i
$322$		0			0
$323$		−	17.3796i		−	0.967026i
$324$		0			0
$325$		−	59.5182i		−	3.30148i
$326$		0			0
$327$	−9.94111	+	15.7234i	−0.549744	+	0.869504i
$328$		0			0
$329$	2.28545	+	1.31950i	0.126001	+	0.0727467i
$330$		0			0
$331$	9.53922	+	16.5224i	0.524323	+	0.908154i	0.999599	+	0.0283170i	$0.00901480\pi$
$331$	9.53922	+	16.5224i	0.524323	+	0.908154i	−0.475276	+	0.879837i	$0.657652\pi$
$332$		0			0
$333$	6.00000	−	2.84820i	0.328798	−	0.156080i
$334$		0			0
$335$	24.1016	+	41.7452i	1.31681	+	2.28079i
$336$		0			0
$337$	−1.33027	+	2.30410i	−0.0724647	+	0.125512i	−0.899981	−	0.435929i	$-0.856420\pi$
$337$	−1.33027	+	2.30410i	−0.0724647	+	0.125512i	0.827516	+	0.561442i	$0.189753\pi$
$338$		0			0
$339$	3.74503	+	7.13418i	0.203402	+	0.387476i
$340$		0			0
$341$	17.4289			0.943825
$342$		0			0
$343$		−	4.60997i		−	0.248915i
$344$		0			0
$345$	0.801571	−	19.9301i	0.0431551	−	1.07300i
$346$		0			0
$347$	19.1413	+	11.0512i	1.02756	+	0.593261i	0.916284	−	0.400528i	$-0.131173\pi$
$347$	19.1413	+	11.0512i	1.02756	+	0.593261i	0.111275	+	0.993790i	$0.464507\pi$
$348$		0			0
$349$	17.9088	−	10.3397i	0.958638	−	0.553470i	0.0628846	−	0.998021i	$-0.479970\pi$
$349$	17.9088	−	10.3397i	0.958638	−	0.553470i	0.895754	+	0.444551i	$0.146637\pi$
$350$		0			0
$351$	−15.4107	+	20.5181i	−0.822563	+	1.09517i
$352$		0			0
$353$	−11.7969	+	6.81094i	−0.627885	+	0.362510i	−0.779933	−	0.625864i	$-0.784747\pi$
$353$	−11.7969	+	6.81094i	−0.627885	+	0.362510i	0.152047	+	0.988373i	$0.451413\pi$
$354$		0			0
$355$	−15.8218	+	27.4042i	−0.839734	+	1.45446i
$356$		0			0
$357$	−0.0740730	+	1.84173i	−0.00392036	+	0.0974749i
$358$		0			0
$359$	−17.3818			−0.917377			−0.458688	−	0.888597i	$-0.651681\pi$
$359$	−17.3818			−0.917377			−0.458688	+	0.888597i	$0.651681\pi$
$360$		0			0
$361$	10.3796			0.546294
$362$		0			0
$363$	9.96586	−	5.23149i	0.523072	−	0.274582i
$364$		0			0
$365$	−12.8371	+	22.2346i	−0.671927	+	1.16381i
$366$		0			0
$367$	16.3976	−	9.46715i	0.855947	−	0.494181i	−0.00670584	−	0.999978i	$-0.502135\pi$
$367$	16.3976	−	9.46715i	0.855947	−	0.494181i	0.862653	+	0.505796i	$0.168801\pi$
$368$		0			0
$369$	−0.393086	+	4.87889i	−0.0204633	+	0.253985i
$370$		0			0
$371$	0.591533	−	0.341522i	0.0307109	−	0.0177309i
$372$		0			0
$373$	−24.2230	−	13.9852i	−1.25422	−	0.724124i	−0.282275	−	0.959334i	$-0.591089\pi$
$373$	−24.2230	−	13.9852i	−1.25422	−	0.724124i	−0.971945	+	0.235210i	$0.924422\pi$
$374$		0			0
$375$	−42.6322	−	26.9542i	−2.20152	−	1.39191i
$376$		0			0
$377$		−	10.2295i		−	0.526844i
$378$		0			0
$379$	11.7997			0.606111			0.303056	−	0.952973i	$-0.401993\pi$
$379$	11.7997			0.606111			0.303056	+	0.952973i	$0.401993\pi$
$380$		0			0
$381$	−0.614407	+	0.971778i	−0.0314770	+	0.0497857i
$382$		0			0
$383$	−9.87782	+	17.1089i	−0.504733	+	0.874223i	0.495252	+	0.868749i	$0.335076\pi$
$383$	−9.87782	+	17.1089i	−0.504733	+	0.874223i	−0.999985	+	0.00547380i	$0.998258\pi$
$384$		0			0
$385$	−2.86653	−	4.96498i	−0.146092	−	0.253039i
$386$		0			0
$387$	−10.2146	+	14.8034i	−0.519235	+	0.752497i
$388$		0			0
$389$	2.76557	+	4.79011i	0.140220	+	0.242868i	0.927579	−	0.373626i	$-0.121886\pi$
$389$	2.76557	+	4.79011i	0.140220	+	0.242868i	−0.787359	+	0.616494i	$0.788552\pi$
$390$		0			0
$391$	−7.74388	−	4.47093i	−0.391625	−	0.226105i
$392$		0			0
$393$	−4.43847	−	8.45518i	−0.223891	−	0.426507i
$394$		0			0
$395$			3.42854i			0.172509i
$396$		0			0
$397$			31.5247i			1.58218i	0.611700	+	0.791090i	$0.290486\pi$
$397$			31.5247i			1.58218i	−0.611700	+	0.791090i	$0.709514\pi$
$398$		0			0
$399$	−3.11339	−	0.125218i	−0.155864	−	0.00626873i
$400$		0			0
$401$	−17.9709	−	10.3755i	−0.897425	−	0.518129i	−0.0210614	−	0.999778i	$-0.506705\pi$
$401$	−17.9709	−	10.3755i	−0.897425	−	0.518129i	−0.876364	+	0.481649i	$0.840038\pi$
$402$		0			0
$403$	−10.2880	−	17.8193i	−0.512481	−	0.887642i
$404$		0			0
$405$	13.1898	+	34.7454i	0.655406	+	1.72651i
$406$		0			0
$407$	4.63049	+	8.02025i	0.229525	+	0.397549i
$408$		0			0
$409$	−5.99838	+	10.3895i	−0.296601	+	0.513728i	−0.975356	−	0.220637i	$-0.929186\pi$
$409$	−5.99838	+	10.3895i	−0.296601	+	0.513728i	0.678755	+	0.734365i	$0.262520\pi$
$410$		0			0
$411$	6.82907	+	0.274660i	0.336853	+	0.0135480i
$412$		0			0
$413$	−2.07139			−0.101927
$414$		0			0
$415$			28.4446i			1.39629i
$416$		0			0
$417$	27.8905	−	14.6409i	1.36581	−	0.716968i
$418$		0			0
$419$	−20.8617	−	12.0445i	−1.01916	−	0.588412i	−0.105299	−	0.994441i	$-0.533580\pi$
$419$	−20.8617	−	12.0445i	−1.01916	−	0.588412i	−0.913860	+	0.406029i	$0.866913\pi$
$420$		0			0
$421$	−26.3884	+	15.2354i	−1.28609	+	0.742526i	−0.977955	−	0.208816i	$-0.933039\pi$
$421$	−26.3884	+	15.2354i	−1.28609	+	0.742526i	−0.308137	+	0.951342i	$0.599706\pi$
$422$		0			0
$423$	13.5475	−	19.6336i	0.658703	−	0.954620i
$424$		0			0
$425$	−33.4662	+	19.3217i	−1.62335	+	0.937242i
$426$		0			0
$427$	1.74510	−	3.02260i	0.0844511	−	0.146274i
$428$		0			0
$429$	−30.2431	−	19.1212i	−1.46015	−	0.923180i
$430$		0			0
$431$	−0.902398			−0.0434670			−0.0217335	−	0.999764i	$-0.506919\pi$
$431$	−0.902398			−0.0434670			−0.0217335	+	0.999764i	$0.506919\pi$
$432$		0			0
$433$	0.559027			0.0268651			0.0134326	−	0.999910i	$-0.495724\pi$
$433$	0.559027			0.0268651			0.0134326	+	0.999910i	$0.495724\pi$
$434$		0			0
$435$	−12.5224	−	7.91730i	−0.600403	−	0.379605i
$436$		0			0
$437$	7.55795	−	13.0908i	0.361546	−	0.626216i
$438$		0			0
$439$	20.1482	−	11.6326i	0.961621	−	0.555192i	0.0649491	−	0.997889i	$-0.479311\pi$
$439$	20.1482	−	11.6326i	0.961621	−	0.555192i	0.896671	+	0.442697i	$0.145978\pi$
$440$		0			0
$441$	−20.6028	−	1.65994i	−0.981085	−	0.0790447i
$442$		0			0
$443$	22.0835	−	12.7499i	1.04922	−	0.605766i	0.126788	−	0.991930i	$-0.459533\pi$
$443$	22.0835	−	12.7499i	1.04922	−	0.605766i	0.922430	+	0.386164i	$0.126200\pi$
$444$		0			0
$445$	32.6937	+	18.8757i	1.54983	+	0.894796i
$446$		0			0
$447$	22.4840	−	11.8028i	1.06346	−	0.558253i
$448$		0			0
$449$		−	16.6758i		−	0.786981i	−0.919329	−	0.393490i	$-0.871268\pi$
$449$		−	16.6758i		−	0.786981i	0.919329	−	0.393490i	$-0.128732\pi$
$450$		0			0
$451$	−6.82502			−0.321378
$452$		0			0
$453$	−36.8175	−	1.48077i	−1.72984	−	0.0695726i
$454$		0			0
$455$	−3.38414	+	5.86150i	−0.158651	+	0.274791i
$456$		0			0
$457$	3.30283	+	5.72066i	0.154500	+	0.267601i	0.932877	−	0.360196i	$-0.117290\pi$
$457$	3.30283	+	5.72066i	0.154500	+	0.267601i	−0.778377	+	0.627797i	$0.783957\pi$
$458$		0			0
$459$	16.5399	+	2.00432i	0.772017	+	0.0935535i
$460$		0			0
$461$	−9.40191	−	16.2846i	−0.437891	−	0.758449i	0.559636	−	0.828739i	$-0.310941\pi$
$461$	−9.40191	−	16.2846i	−0.437891	−	0.758449i	−0.997527	+	0.0702897i	$0.977608\pi$
$462$		0			0
$463$	−21.5994	−	12.4704i	−1.00381	−	0.579548i	−0.0944346	−	0.995531i	$-0.530104\pi$
$463$	−21.5994	−	12.4704i	−1.00381	−	0.579548i	−0.909372	+	0.415983i	$0.863438\pi$
$464$		0			0
$465$	−29.7761	−	1.19757i	−1.38083	−	0.0555360i
$466$		0			0
$467$			10.2003i			0.472015i	0.971751	+	0.236007i	$0.0758389\pi$
$467$			10.2003i			0.472015i	−0.971751	+	0.236007i	$0.924161\pi$
$468$		0			0
$469$		−	3.87426i		−	0.178897i
$470$		0			0
$471$	9.05737	+	17.2540i	0.417341	+	0.795024i
$472$		0			0
$473$	−21.7185	−	12.5392i	−0.998618	−	0.576552i
$474$		0			0
$475$	−32.6627	−	56.5735i	−1.49867	−	2.59577i
$476$		0			0
$477$	−2.64765	−	5.57752i	−0.121228	−	0.255377i
$478$		0			0
$479$	5.43334	+	9.41082i	0.248256	+	0.429991i	0.963042	−	0.269352i	$-0.0868094\pi$
$479$	5.43334	+	9.41082i	0.248256	+	0.429991i	−0.714786	+	0.699343i	$0.753476\pi$
$480$		0			0
$481$	5.46661	−	9.46845i	0.249256	−	0.431724i
$482$		0			0
$483$	−0.856717	+	1.35503i	−0.0389820	+	0.0616559i
$484$		0			0
$485$	−6.18742			−0.280956
$486$		0			0
$487$		−	21.1073i		−	0.956462i	−0.878234	−	0.478231i	$-0.841278\pi$
$487$		−	21.1073i		−	0.956462i	0.878234	−	0.478231i	$-0.158722\pi$
$488$		0			0
$489$	19.5310	+	12.3485i	0.883223	+	0.558418i
$490$		0			0
$491$	−18.5189	−	10.6919i	−0.835746	−	0.482518i	0.0200698	−	0.999799i	$-0.493611\pi$
$491$	−18.5189	−	10.6919i	−0.835746	−	0.482518i	−0.855816	+	0.517280i	$0.826944\pi$
$492$		0			0
$493$	−5.75189	+	3.32085i	−0.259052	+	0.149564i
$494$		0			0
$495$	−46.8144	+	22.2228i	−2.10415	+	0.998841i
$496$		0			0
$497$	2.20257	−	1.27165i	0.0987986	−	0.0570414i
$498$		0			0
$499$	12.9981	−	22.5134i	0.581876	−	1.00784i	−0.413381	−	0.910558i	$-0.635652\pi$
$499$	12.9981	−	22.5134i	0.581876	−	1.00784i	0.995257	−	0.0972805i	$-0.0310144\pi$
$500$		0			0
$501$	−37.9662	+	19.9301i	−1.69621	+	0.890410i
$502$		0			0
$503$	28.4476			1.26842			0.634208	−	0.773163i	$-0.281326\pi$
$503$	28.4476			1.26842			0.634208	+	0.773163i	$0.281326\pi$
$504$		0			0
$505$	39.8371			1.77273
$506$		0			0
$507$	−0.792682	+	19.7091i	−0.0352043	+	0.875310i
$508$		0			0
$509$	−0.928302	+	1.60787i	−0.0411462	+	0.0712674i	−0.885865	−	0.463943i	$-0.846434\pi$
$509$	−0.928302	+	1.60787i	−0.0411462	+	0.0712674i	0.844719	+	0.535210i	$0.179768\pi$
$510$		0			0
$511$	1.78707	−	1.03177i	0.0790553	−	0.0456426i
$512$		0			0
$513$	−3.38823	+	27.9601i	−0.149594	+	1.23447i
$514$		0			0
$515$	−17.8654	+	10.3146i	−0.787245	+	0.454516i
$516$		0			0
$517$	28.8052	+	16.6307i	1.26685	+	0.731416i
$518$		0			0
$519$	0.575790	−	14.3163i	0.0252744	−	0.628416i
$520$		0			0
$521$			40.2415i			1.76301i	0.472173	+	0.881506i	$0.343470\pi$
$521$			40.2415i			1.76301i	−0.472173	+	0.881506i	$0.656530\pi$
$522$		0			0
$523$	21.0040			0.918440			0.459220	−	0.888323i	$-0.348129\pi$
$523$	21.0040			0.918440			0.459220	+	0.888323i	$0.348129\pi$
$524$		0			0
$525$	3.22018	+	6.13436i	0.140540	+	0.267726i
$526$		0			0
$527$	−6.67969	+	11.5696i	−0.290972	+	0.503978i
$528$		0			0
$529$	7.61141	+	13.1833i	0.330931	+	0.573189i
$530$		0			0
$531$	−1.50364	+	18.6629i	−0.0652526	+	0.809900i
$532$		0			0
$533$	4.02870	+	6.97792i	0.174503	+	0.302247i
$534$		0			0
$535$	−46.9530	−	27.1083i	−2.02996	−	1.17200i
$536$		0			0
$537$	11.4542	−	18.1166i	0.494286	−	0.781789i
$538$		0			0
$539$		−	28.8210i		−	1.24141i
$540$		0			0
$541$		−	5.33020i		−	0.229163i	−0.993414	−	0.114582i	$-0.963447\pi$
$541$		−	5.33020i		−	0.229163i	0.993414	−	0.114582i	$-0.0365528\pi$
$542$		0			0
$543$	−2.23522	+	3.53533i	−0.0959223	+	0.151716i
$544$		0			0
$545$	38.4085	+	22.1751i	1.64524	+	0.949879i
$546$		0			0
$547$	−1.09162	−	1.89075i	−0.0466745	−	0.0808426i	0.841744	−	0.539876i	$-0.181529\pi$
$547$	−1.09162	−	1.89075i	−0.0466745	−	0.0808426i	−0.888419	+	0.459034i	$0.848196\pi$
$548$		0			0
$549$	−25.9662	−	17.9171i	−1.10821	−	0.764684i
$550$		0			0
$551$	−5.61378	−	9.72336i	−0.239155	−	0.414229i
$552$		0			0
$553$	0.137782	−	0.238645i	0.00585908	−	0.0101482i
$554$		0			0
$555$	−7.35981	−	14.0202i	−0.312407	−	0.595126i
$556$		0			0
$557$	−14.6744			−0.621775			−0.310887	−	0.950447i	$-0.600626\pi$
$557$	−14.6744			−0.621775			−0.310887	+	0.950447i	$0.600626\pi$
$558$		0			0
$559$			29.6067i			1.25223i
$560$		0			0
$561$	−0.933596	+	23.2127i	−0.0394164	+	0.980040i
$562$		0			0
$563$	−4.62742	−	2.67164i	−0.195023	−	0.112596i	0.399309	−	0.916816i	$-0.369250\pi$
$563$	−4.62742	−	2.67164i	−0.195023	−	0.112596i	−0.594332	+	0.804220i	$0.702583\pi$
$564$		0			0
$565$	16.6362	−	9.60489i	0.699889	−	0.404081i
$566$		0			0
$567$	0.478222	−	2.94852i	0.0200834	−	0.123826i
$568$		0			0
$569$	1.77232	−	1.02325i	0.0742997	−	0.0428969i	−0.462390	−	0.886677i	$-0.653008\pi$
$569$	1.77232	−	1.02325i	0.0742997	−	0.0428969i	0.536690	+	0.843780i	$0.319675\pi$
$570$		0			0
$571$	4.29802	−	7.44439i	0.179866	−	0.311538i	−0.761968	−	0.647614i	$-0.775767\pi$
$571$	4.29802	−	7.44439i	0.179866	−	0.311538i	0.941835	+	0.336077i	$0.109100\pi$
$572$		0			0
$573$	−1.00449	+	24.9755i	−0.0419634	+	1.04337i
$574$		0			0
$575$	−33.6102			−1.40164
$576$		0			0
$577$	26.6609			1.10991			0.554954	−	0.831881i	$-0.312736\pi$
$577$	26.6609			1.10991			0.554954	+	0.831881i	$0.312736\pi$
$578$		0			0
$579$	26.4975	−	13.9096i	1.10120	−	0.578065i
$580$		0			0
$581$	1.14309	−	1.97990i	0.0474235	−	0.0821399i
$582$		0			0
$583$	7.45552	−	4.30445i	0.308776	−	0.178272i
$584$		0			0
$585$	50.3545	+	34.7454i	2.08190	+	1.43655i
$586$		0			0
$587$	−39.9759	+	23.0801i	−1.64998	+	0.952618i	−0.672908	+	0.739726i	$0.734955\pi$
$587$	−39.9759	+	23.0801i	−1.64998	+	0.952618i	−0.977076	+	0.212892i	$0.931712\pi$
$588$		0			0
$589$	−19.5580	−	11.2918i	−0.805871	−	0.465270i
$590$		0			0
$591$	22.1686	+	14.0161i	0.911896	+	0.576547i
$592$		0			0
$593$		−	15.7409i		−	0.646402i	−0.946330	−	0.323201i	$-0.895241\pi$
$593$		−	15.7409i		−	0.646402i	0.946330	−	0.323201i	$-0.104759\pi$
$594$		0			0
$595$	4.39445			0.180155
$596$		0			0
$597$	19.9983	−	31.6304i	0.818477	−	1.29454i
$598$		0			0
$599$	−21.5203	+	37.2743i	−0.879297	+	1.52299i	−0.0271823	+	0.999630i	$0.508653\pi$
$599$	−21.5203	+	37.2743i	−0.879297	+	1.52299i	−0.852114	+	0.523356i	$0.824680\pi$
$600$		0			0
$601$	−19.6867	−	34.0984i	−0.803039	−	1.39090i	−0.917607	−	0.397488i	$-0.869882\pi$
$601$	−19.6867	−	34.0984i	−0.803039	−	1.39090i	0.114569	−	0.993415i	$-0.463451\pi$
$602$		0			0
$603$	−34.9064	−	2.81236i	−1.42150	−	0.114528i
$604$		0			0
$605$	−13.4172	−	23.2393i	−0.545488	−	0.944813i
$606$		0			0
$607$	25.7834	+	14.8861i	1.04652	+	0.604207i	0.921672	−	0.387969i	$-0.126823\pi$
$607$	25.7834	+	14.8861i	1.04652	+	0.604207i	0.124845	+	0.992176i	$0.460157\pi$
$608$		0			0
$609$	0.553457	+	1.05432i	0.0224272	+	0.0427232i
$610$		0			0
$611$		−	39.2673i		−	1.58858i
$612$		0			0
$613$			0.615900i			0.0248760i	0.999923	+	0.0124380i	$0.00395924\pi$
$613$			0.615900i			0.0248760i	−0.999923	+	0.0124380i	$0.996041\pi$
$614$		0			0
$615$	11.6601	+	0.468960i	0.470181	+	0.0189103i
$616$		0			0
$617$	2.03339	+	1.17398i	0.0818610	+	0.0472625i	0.540372	−	0.841426i	$-0.318284\pi$
$617$	2.03339	+	1.17398i	0.0818610	+	0.0472625i	−0.458511	+	0.888689i	$0.651617\pi$
$618$		0			0
$619$	9.58718	+	16.6055i	0.385341	+	0.667431i	0.991816	−	0.127672i	$-0.0407504\pi$
$619$	9.58718	+	16.6055i	0.385341	+	0.667431i	−0.606475	+	0.795102i	$0.707417\pi$
$620$		0			0
$621$	11.5867	+	8.70249i	0.464956	+	0.349219i
$622$		0			0
$623$	−1.51711	−	2.62771i	−0.0607817	−	0.105277i
$624$		0			0
$625$	−29.9955	+	51.9537i	−1.19982	+	2.07815i
$626$		0			0
$627$	−39.2402	−	1.57821i	−1.56710	−	0.0630277i
$628$		0			0
$629$	−7.09864			−0.283041
$630$		0			0
$631$			3.77969i			0.150467i	0.997166	+	0.0752336i	$0.0239702\pi$
$631$			3.77969i			0.150467i	−0.997166	+	0.0752336i	$0.976030\pi$
$632$		0			0
$633$	11.3525	−	5.95941i	0.451222	−	0.236865i
$634$		0			0
$635$	2.37383	+	1.37053i	0.0942024	+	0.0543878i
$636$		0			0
$637$	−29.4666	+	17.0126i	−1.16751	+	0.674062i
$638$		0			0
$639$	−9.85849	−	20.7678i	−0.389996	−	0.821562i
$640$		0			0
$641$	12.1609	−	7.02110i	0.480327	−	0.277317i	−0.240226	−	0.970717i	$-0.577221\pi$
$641$	12.1609	−	7.02110i	0.480327	−	0.277317i	0.720553	+	0.693400i	$0.243888\pi$
$642$		0			0
$643$	4.39850	−	7.61843i	0.173460	−	0.300441i	−0.766167	−	0.642641i	$-0.777839\pi$
$643$	4.39850	−	7.61843i	0.173460	−	0.300441i	0.939627	+	0.342200i	$0.111172\pi$
$644$		0			0
$645$	36.2431	+	22.9147i	1.42707	+	0.902266i
$646$		0			0
$647$	29.5118			1.16023			0.580114	−	0.814535i	$-0.303008\pi$
$647$	29.5118			1.16023			0.580114	+	0.814535i	$0.303008\pi$
$648$		0			0
$649$	−26.1073			−1.02480
$650$		0			0
$651$	2.02445	+	1.27996i	0.0793444	+	0.0501656i
$652$		0			0
$653$	0.00669049	−	0.0115883i	0.000261819	−	0.000453484i	−0.865894	−	0.500227i	$-0.833250\pi$
$653$	0.00669049	−	0.0115883i	0.000261819	−	0.000453484i	0.866156	+	0.499773i	$0.166583\pi$
$654$		0			0
$655$	−19.7166	+	11.3834i	−0.770390	+	0.444785i
$656$		0			0
$657$	−7.99876	−	16.8501i	−0.312061	−	0.657386i
$658$		0			0
$659$	34.3244	−	19.8172i	1.33709	−	0.771970i	0.350715	−	0.936482i	$-0.385938\pi$
$659$	34.3244	−	19.8172i	1.33709	−	0.771970i	0.986375	+	0.164513i	$0.0526051\pi$
$660$		0			0
$661$	−11.8008	−	6.81322i	−0.458999	−	0.265003i	0.252624	−	0.967565i	$-0.418706\pi$
$661$	−11.8008	−	6.81322i	−0.458999	−	0.265003i	−0.711623	+	0.702561i	$0.752040\pi$
$662$		0			0
$663$	24.2838	−	12.7476i	0.943104	−	0.495075i
$664$		0			0
$665$			7.42867i			0.288071i
$666$		0			0
$667$	−5.77662			−0.223672
$668$		0			0
$669$	−5.19942	−	0.209117i	−0.201021	−	0.00808492i
$670$		0			0
$671$	21.9947	−	38.0959i	0.849096	−	1.47068i
$672$		0			0
$673$	−3.22156	−	5.57991i	−0.124182	−	0.215090i	0.797231	−	0.603675i	$-0.206297\pi$
$673$	−3.22156	−	5.57991i	−0.124182	−	0.215090i	−0.921413	+	0.388585i	$0.872964\pi$
$674$		0			0
$675$	57.6071	−	24.5603i	2.21730	−	0.945325i
$676$		0			0
$677$	7.67204	+	13.2884i	0.294860	+	0.510713i	0.974952	−	0.222414i	$-0.0713935\pi$
$677$	7.67204	+	13.2884i	0.294860	+	0.510713i	−0.680092	+	0.733127i	$0.738060\pi$
$678$		0			0
$679$	0.430678	+	0.248652i	0.0165279	+	0.00954239i
$680$		0			0
$681$	−14.5488	−	0.585140i	−0.557510	−	0.0224226i
$682$		0			0
$683$			17.2454i			0.659878i	0.944002	+	0.329939i	$0.107028\pi$
$683$			17.2454i			0.659878i	−0.944002	+	0.329939i	$0.892972\pi$
$684$		0			0
$685$		−	16.2945i		−	0.622579i
$686$		0			0
$687$	−2.55427	−	4.86582i	−0.0974515	−	0.185643i
$688$		0			0
$689$	−8.80175	−	5.08169i	−0.335320	−	0.193597i
$690$		0			0
$691$	9.97083	+	17.2700i	0.379308	+	0.656981i	0.990962	−	0.134145i	$-0.0428287\pi$
$691$	9.97083	+	17.2700i	0.379308	+	0.656981i	−0.611654	+	0.791126i	$0.709495\pi$
$692$		0			0
$693$	4.15160	+	0.334489i	0.157706	+	0.0127062i
$694$		0			0
$695$	−37.5496	−	65.0378i	−1.42434	−	2.46702i
$696$		0			0
$697$	2.61572	−	4.53057i	0.0990776	−	0.171607i
$698$		0			0
$699$	9.28763	−	14.6898i	0.351291	−	0.555619i
$700$		0			0
$701$	3.45975			0.130673			0.0653364	−	0.997863i	$-0.479188\pi$
$701$	3.45975			0.130673			0.0653364	+	0.997863i	$0.479188\pi$
$702$		0			0
$703$		−	12.0000i		−	0.452589i
$704$		0			0
$705$	−48.0690	−	30.3917i	−1.81038	−	1.14462i
$706$		0			0
$707$	−2.77288	−	1.60092i	−0.104285	−	0.0602089i
$708$		0			0
$709$	−34.2429	+	19.7701i	−1.28602	+	0.742483i	−0.977942	−	0.208878i	$-0.933019\pi$
$709$	−34.2429	+	19.7701i	−1.28602	+	0.742483i	−0.308077	+	0.951361i	$0.599685\pi$
$710$		0			0
$711$	−2.05013	−	1.41462i	−0.0768860	−	0.0530525i
$712$		0			0
$713$	−10.0626	+	5.80966i	−0.376849	+	0.217574i
$714$		0			0
$715$	−42.6527	+	73.8767i	−1.59512	+	2.76283i
$716$		0			0
$717$	15.2100	−	7.98439i	0.568030	−	0.298182i
$718$		0			0
$719$	−4.62877			−0.172624			−0.0863120	−	0.996268i	$-0.527508\pi$
$719$	−4.62877			−0.172624			−0.0863120	+	0.996268i	$0.527508\pi$
$720$		0			0
$721$	1.65804			0.0617487
$722$		0			0
$723$	−0.0465786	+	1.15812i	−0.00173228	+	0.0430709i
$724$		0			0
$725$	−12.4822	+	21.6199i	−0.463579	+	0.802942i
$726$		0			0
$727$	−5.33286	+	3.07893i	−0.197785	+	0.114191i	−0.595622	−	0.803265i	$-0.703094\pi$
$727$	−5.33286	+	3.07893i	−0.197785	+	0.114191i	0.397837	+	0.917456i	$0.369761\pi$
$728$		0			0
$729$	−26.2185	−	6.44905i	−0.971056	−	0.238854i
$730$		0			0
$731$	16.6474	−	9.61141i	0.615728	−	0.355491i
$732$		0			0
$733$	−18.9417	−	10.9360i	−0.699627	−	0.403930i	0.107581	−	0.994196i	$-0.465689\pi$
$733$	−18.9417	−	10.9360i	−0.699627	−	0.403930i	−0.807208	+	0.590266i	$0.799023\pi$
$734$		0			0
$735$	−1.98034	+	49.2388i	−0.0730461	+	1.81620i
$736$		0			0
$737$		−	48.8301i		−	1.79868i
$738$		0			0
$739$	−24.5677			−0.903738			−0.451869	−	0.892084i	$-0.649243\pi$
$739$	−24.5677			−0.903738			−0.451869	+	0.892084i	$0.649243\pi$
$740$		0			0
$741$	21.5493	+	41.0509i	0.791634	+	1.50804i
$742$		0			0
$743$	3.52447	−	6.10457i	0.129300	−	0.223955i	−0.794105	−	0.607780i	$-0.792060\pi$
$743$	3.52447	−	6.10457i	0.129300	−	0.223955i	0.923406	+	0.383825i	$0.125394\pi$
$744$		0			0
$745$	−30.2707	−	52.4304i	−1.10903	−	1.92090i
$746$		0			0
$747$	−17.0087	−	11.7363i	−0.622316	−	0.429408i
$748$		0			0
$749$	2.17879	+	3.77378i	0.0796113	+	0.137891i
$750$		0			0
$751$	20.9770	+	12.1110i	0.765460	+	0.441938i	0.831253	−	0.555895i	$-0.187624\pi$
$751$	20.9770	+	12.1110i	0.765460	+	0.441938i	−0.0657928	+	0.997833i	$0.520958\pi$
$752$		0			0
$753$	−3.13616	+	4.96031i	−0.114288	+	0.180764i
$754$		0			0
$755$			87.8480i			3.19712i
$756$		0			0
$757$			29.8780i			1.08593i	0.839754	+	0.542967i	$0.182699\pi$
$757$			29.8780i			1.08593i	−0.839754	+	0.542967i	$0.817301\pi$
$758$		0			0
$759$	−10.7978	+	17.0784i	−0.391936	+	0.619906i
$760$		0			0
$761$	36.2631	+	20.9365i	1.31454	+	0.758949i	0.982844	−	0.184438i	$-0.0590466\pi$
$761$	36.2631	+	20.9365i	1.31454	+	0.758949i	0.331694	+	0.943387i	$0.392380\pi$
$762$		0			0
$763$	−1.78229	−	3.08702i	−0.0645233	−	0.111758i
$764$		0			0
$765$	3.18998	−	39.5932i	0.115334	−	1.43150i
$766$		0			0
$767$	15.4107	+	26.6921i	0.556449	+	0.963797i
$768$		0			0
$769$	6.30858	−	10.9268i	0.227493	−	0.394030i	−0.729571	−	0.683905i	$-0.760280\pi$
$769$	6.30858	−	10.9268i	0.227493	−	0.394030i	0.957065	+	0.289875i	$0.0936137\pi$
$770$		0			0
$771$	−18.1763	−	34.6254i	−0.654603	−	1.24700i
$772$		0			0
$773$	28.6390			1.03007			0.515037	−	0.857168i	$-0.327778\pi$
$773$	28.6390			1.03007			0.515037	+	0.857168i	$0.327778\pi$
$774$		0			0
$775$			50.2145i			1.80376i
$776$		0			0
$777$	−0.0511448	+	1.27165i	−0.00183481	+	0.0456203i
$778$		0			0
$779$	7.65876	+	4.42179i	0.274404	+	0.158427i
$780$		0			0
$781$	27.7605	−	16.0275i	0.993349	−	0.573511i
$782$		0			0
$783$	9.90100	−	4.22120i	0.353833	−	0.150853i
$784$		0			0
$785$	40.2346	−	23.2295i	1.43603	−	0.829095i
$786$		0			0
$787$	19.7520	−	34.2115i	0.704083	−	1.21951i	−0.262938	−	0.964813i	$-0.584692\pi$
$787$	19.7520	−	34.2115i	0.704083	−	1.21951i	0.967021	−	0.254695i	$-0.0819751\pi$
$788$		0			0
$789$	0.516300	−	12.8372i	0.0183808	−	0.457015i
$790$		0			0
$791$	−1.54396			−0.0548968
$792$		0			0
$793$	−51.9325			−1.84418
$794$		0			0
$795$	−13.0330	+	6.84158i	−0.462234	+	0.242646i
$796$		0			0
$797$	−13.6253	+	23.5998i	−0.482634	+	0.835947i	−0.999801	−	0.0199377i	$-0.993653\pi$
$797$	−13.6253	+	23.5998i	−0.482634	+	0.835947i	0.517167	+	0.855884i	$0.326987\pi$
$798$		0			0
$799$	−22.0794	+	12.7476i	−0.781114	+	0.450977i
$800$		0			0
$801$	−24.7765	+	11.7614i	−0.875433	+	0.415568i
$802$		0			0
$803$	22.5237	−	13.0041i	0.794845	−	0.458904i
$804$		0			0
$805$	3.31002	+	1.91104i	0.116663	+	0.0673552i
$806$		0			0
$807$	−29.2466	−	18.4912i	−1.02953	−	0.650920i
$808$		0			0
$809$		−	32.7182i		−	1.15031i	−0.818045	−	0.575155i	$-0.804942\pi$
$809$		−	32.7182i		−	1.15031i	0.818045	−	0.575155i	$-0.195058\pi$
$810$		0			0
$811$	23.3901			0.821336			0.410668	−	0.911785i	$-0.365296\pi$
$811$	23.3901			0.821336			0.410668	+	0.911785i	$0.365296\pi$
$812$		0			0
$813$	24.1620	−	38.2159i	0.847400	−	1.34029i
$814$		0			0
$815$	27.5452	−	47.7097i	0.964866	−	1.67120i
$816$		0			0
$817$	16.2477	+	28.1419i	0.568437	+	0.984561i
$818$		0			0
$819$	−2.10864	−	4.44205i	−0.0736819	−	0.155218i
$820$		0			0
$821$	−15.4953	−	26.8387i	−0.540790	−	0.936676i	−0.998859	−	0.0477594i	$-0.984792\pi$
$821$	−15.4953	−	26.8387i	−0.540790	−	0.936676i	0.458069	−	0.888917i	$-0.348541\pi$
$822$		0			0
$823$	41.9067	+	24.1948i	1.46077	+	0.843379i	0.999047	−	0.0436430i	$-0.0138964\pi$
$823$	41.9067	+	24.1948i	1.46077	+	0.843379i	0.461728	+	0.887022i	$0.347230\pi$
$824$		0			0
$825$	40.5863	+	77.3158i	1.41303	+	2.69179i
$826$		0			0
$827$			53.6957i			1.86718i	0.358340	+	0.933591i	$0.383343\pi$
$827$			53.6957i			1.86718i	−0.358340	+	0.933591i	$0.616657\pi$
$828$		0			0
$829$		−	14.1371i		−	0.491001i	−0.969396	−	0.245500i	$-0.921048\pi$
$829$		−	14.1371i		−	0.491001i	0.969396	−	0.245500i	$-0.0789523\pi$
$830$		0			0
$831$	42.4601	+	1.70771i	1.47292	+	0.0592398i
$832$		0			0
$833$	19.1318	+	11.0458i	0.662879	+	0.382713i
$834$		0			0
$835$	51.1147	+	88.5333i	1.76890	+	3.06382i
$836$		0			0
$837$	13.0018	−	17.3108i	0.449407	−	0.598348i
$838$		0			0
$839$	−21.1957	−	36.7120i	−0.731757	−	1.26744i	−0.956132	−	0.292937i	$-0.905367\pi$
$839$	−21.1957	−	36.7120i	−0.731757	−	1.26744i	0.224375	−	0.974503i	$-0.427966\pi$
$840$		0			0
$841$	12.3547	−	21.3989i	0.426023	−	0.737893i
$842$		0			0
$843$	47.6310	+	1.91568i	1.64050	+	0.0659796i
$844$		0			0
$845$	47.0266			1.61777
$846$		0			0
$847$			2.15678i			0.0741078i
$848$		0			0
$849$	−1.47507	+	0.774325i	−0.0506242	+	0.0265747i
$850$		0			0
$851$	−5.34688	−	3.08702i	−0.183289	−	0.105822i
$852$		0			0
$853$	20.7766	−	11.9954i	0.711378	−	0.410714i	−0.100193	−	0.994968i	$-0.531946\pi$
$853$	20.7766	−	11.9954i	0.711378	−	0.410714i	0.811571	+	0.584254i	$0.198613\pi$
$854$		0			0
$855$	66.9309	+	5.39254i	2.28899	+	0.184421i
$856$		0			0
$857$	14.4336	−	8.33324i	0.493042	−	0.284658i	−0.232793	−	0.972526i	$-0.574787\pi$
$857$	14.4336	−	8.33324i	0.493042	−	0.284658i	0.725836	+	0.687868i	$0.241453\pi$
$858$		0			0
$859$	9.78253	−	16.9438i	0.333776	−	0.578116i	−0.649473	−	0.760384i	$-0.725011\pi$
$859$	9.78253	−	16.9438i	0.333776	−	0.578116i	0.983249	+	0.182268i	$0.0583439\pi$
$860$		0			0
$861$	−0.792761	−	0.501224i	−0.0270172	−	0.0170817i
$862$		0			0
$863$	−30.5794			−1.04094			−0.520468	−	0.853881i	$-0.674242\pi$
$863$	−30.5794			−1.04094			−0.520468	+	0.853881i	$0.674242\pi$
$864$		0			0
$865$	−34.1593			−1.16145
$866$		0			0
$867$	9.83658	+	6.21919i	0.334068	+	0.211215i
$868$		0			0
$869$	1.73656	−	3.00782i	0.0589089	−	0.102033i
$870$		0			0
$871$	−49.9240	+	28.8236i	−1.69161	+	0.976651i
$872$		0			0
$873$	2.55294	−	3.69983i	0.0864040	−	0.125220i
$874$		0			0
$875$	8.37013	−	4.83250i	0.282962	−	0.163368i
$876$		0			0
$877$	33.9915	+	19.6250i	1.14781	+	0.662690i	0.948353	−	0.317216i	$-0.102748\pi$
$877$	33.9915	+	19.6250i	1.14781	+	0.662690i	0.199460	+	0.979906i	$0.436081\pi$
$878$		0			0
$879$	4.18314	−	2.19590i	0.141094	−	0.0740660i
$880$		0			0
$881$			20.2971i			0.683828i	0.939731	+	0.341914i	$0.111075\pi$
$881$			20.2971i			0.683828i	−0.939731	+	0.341914i	$0.888925\pi$
$882$		0			0
$883$	−13.2658			−0.446431			−0.223216	−	0.974769i	$-0.571655\pi$
$883$	−13.2658			−0.446431			−0.223216	+	0.974769i	$0.571655\pi$
$884$		0			0
$885$	44.6026	+	1.79388i	1.49930	+	0.0603006i
$886$		0			0
$887$	−12.2973	+	21.2996i	−0.412904	+	0.715170i	−0.995206	−	0.0978022i	$-0.968819\pi$
$887$	−12.2973	+	21.2996i	−0.412904	+	0.715170i	0.582302	+	0.812972i	$0.302152\pi$
$888$		0			0
$889$	−0.110154	−	0.190792i	−0.00369445	−	0.00639897i
$890$		0			0
$891$	6.02737	−	37.1623i	0.201925	−	1.24499i
$892$		0			0
$893$	−21.5493	−	37.3245i	−0.721120	−	1.24902i
$894$		0			0
$895$	−44.2546	−	25.5504i	−1.47927	−	0.854056i
$896$		0			0
$897$	23.8348	+	0.958615i	0.795820	+	0.0320072i
$898$		0			0
$899$			8.63044i			0.287841i
$900$		0			0
$901$			6.59880i			0.219838i
$902$		0			0
$903$	−1.60185	−	3.05148i	−0.0533061	−	0.101547i
$904$		0			0
$905$	8.63598	+	4.98599i	0.287070	+	0.165740i
$906$		0			0
$907$	−4.21712	−	7.30427i	−0.140027	−	0.242534i	0.787479	−	0.616341i	$-0.211386\pi$
$907$	−4.21712	−	7.30427i	−0.140027	−	0.242534i	−0.927507	+	0.373807i	$0.878052\pi$
$908$		0			0
$909$	−16.4369	+	23.8210i	−0.545177	+	0.790093i
$910$		0			0
$911$	−7.35597	−	12.7409i	−0.243714	−	0.422125i	0.718055	−	0.695986i	$-0.245033\pi$
$911$	−7.35597	−	12.7409i	−0.243714	−	0.422125i	−0.961769	+	0.273861i	$0.911699\pi$
$912$		0			0
$913$	14.4072	−	24.9540i	0.476809	−	0.825858i
$914$		0			0
$915$	−40.1942	+	63.5732i	−1.32878	+	2.10166i
$916$		0			0
$917$	1.82984			0.0604267
$918$		0			0
$919$		−	38.4521i		−	1.26842i	−0.773162	−	0.634209i	$-0.781326\pi$
$919$		−	38.4521i		−	1.26842i	0.773162	−	0.634209i	$-0.218674\pi$
$920$		0			0
$921$	−7.74720	−	4.89817i	−0.255279	−	0.161400i
$922$		0			0
$923$	−32.7732	−	18.9216i	−1.07874	−	0.622812i
$924$		0			0
$925$	−23.1073	+	13.3410i	−0.759762	+	0.438649i
$926$		0			0
$927$	1.20359	−	14.9386i	0.0395310	−	0.490649i
$928$		0			0
$929$	−3.88859	+	2.24508i	−0.127581	+	0.0736587i	−0.562432	−	0.826844i	$-0.690134\pi$
$929$	−3.88859	+	2.24508i	−0.127581	+	0.0736587i	0.434851	+	0.900502i	$0.356801\pi$
$930$		0			0
$931$	−18.6725	+	32.3417i	−0.611966	+	1.05996i
$932$		0			0
$933$	37.3299	−	19.5960i	1.22213	−	0.641545i
$934$		0			0
$935$	55.3864			1.81133
$936$		0			0
$937$	−22.9267			−0.748984			−0.374492	−	0.927230i	$-0.622183\pi$
$937$	−22.9267			−0.748984			−0.374492	+	0.927230i	$0.622183\pi$
$938$		0			0
$939$	−2.11821	+	52.6665i	−0.0691250	+	1.71871i
$940$		0			0
$941$	27.6316	−	47.8593i	0.900764	−	1.56017i	0.0742601	−	0.997239i	$-0.476341\pi$
$941$	27.6316	−	47.8593i	0.900764	−	1.56017i	0.826504	−	0.562931i	$-0.190326\pi$
$942$		0			0
$943$	3.94046	−	2.27503i	0.128319	−	0.0740850i
$944$		0			0
$945$	−7.06976	−	0.856717i	−0.229979	−	0.0278690i
$946$		0			0
$947$	−20.4482	+	11.8058i	−0.664479	+	0.383637i	−0.793981	−	0.607942i	$-0.791995\pi$
$947$	−20.4482	+	11.8058i	−0.664479	+	0.383637i	0.129503	+	0.991579i	$0.458662\pi$
$948$		0			0
$949$	−26.5908	−	15.3522i	−0.863174	−	0.498354i
$950$		0			0
$951$	−2.07264	+	51.5335i	−0.0672098	+	1.67109i
$952$		0			0
$953$		−	0.892008i		−	0.0288950i	−0.999896	−	0.0144475i	$-0.995401\pi$
$953$		−	0.892008i		−	0.0288950i	0.999896	−	0.0144475i	$-0.00459894\pi$
$954$		0			0
$955$	59.5926			1.92837
$956$		0			0
$957$	6.97561	+	13.2884i	0.225490	+	0.429552i
$958$		0			0
$959$	−0.654820	+	1.13418i	−0.0211453	+	0.0366247i
$960$		0			0
$961$	−6.82020	−	11.8129i	−0.220006	−	0.381062i
$962$		0			0
$963$	35.5826	−	16.8911i	1.14663	−	0.544308i
$964$		0			0
$965$	−35.6741	−	61.7894i	−1.14839	−	1.98907i
$966$		0			0
$967$	31.3105	+	18.0771i	1.00688	+	0.581321i	0.910276	−	0.414002i	$-0.135869\pi$
$967$	31.3105	+	18.0771i	1.00688	+	0.581321i	0.0966015	+	0.995323i	$0.469203\pi$
$968$		0			0
$969$	16.0867	−	25.4435i	0.516778	−	0.817362i
$970$		0			0
$971$		−	42.0395i		−	1.34911i	−0.738223	−	0.674556i	$-0.764335\pi$
$971$		−	42.0395i		−	1.34911i	0.738223	−	0.674556i	$-0.235665\pi$
$972$		0			0
$973$			6.03598i			0.193505i
$974$		0			0
$975$	55.0904	−	87.1338i	1.76430	−	2.79051i
$976$		0			0
$977$	−13.2808	−	7.66765i	−0.424889	−	0.245310i	0.272278	−	0.962219i	$-0.412223\pi$
$977$	−13.2808	−	7.66765i	−0.424889	−	0.245310i	−0.697167	+	0.716909i	$0.745556\pi$
$978$		0			0
$979$	−19.1212	−	33.1189i	−0.611116	−	1.05848i
$980$		0			0
$981$	−29.1073	+	13.8172i	−0.929324	+	0.441150i
$982$		0			0
$983$	−2.90976	−	5.03986i	−0.0928071	−	0.160747i	0.815884	−	0.578215i	$-0.196251\pi$
$983$	−2.90976	−	5.03986i	−0.0928071	−	0.160747i	−0.908691	+	0.417469i	$0.862917\pi$
$984$		0			0
$985$	31.2651	−	54.1528i	0.996190	−	1.72545i
$986$		0			0
$987$	2.12452	+	4.04716i	0.0676243	+	0.128823i
$988$		0			0
$989$	16.7190			0.531635
$990$		0			0
$991$		−	42.7700i		−	1.35863i	−0.733845	−	0.679316i	$-0.762276\pi$
$991$		−	42.7700i		−	1.35863i	0.733845	−	0.679316i	$-0.237724\pi$
$992$		0			0
$993$	−1.32796	+	33.0181i	−0.0421416	+	1.04780i
$994$		0			0
$995$	−77.2655	−	44.6093i	−2.44948	−	1.41421i
$996$		0			0
$997$	45.0247	−	25.9950i	1.42595	−	0.823271i	0.429150	−	0.903233i	$-0.358813\pi$
$997$	45.0247	−	25.9950i	1.42595	−	0.823271i	0.996798	+	0.0799618i	$0.0254798\pi$
$998$		0			0
$999$	11.4202	+	1.38391i	0.361320	+	0.0437850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.p.c.95.7	yes	16
3.2	odd	2		1728.2.p.a.287.1		16
4.3	odd	2	inner	576.2.p.c.95.2	yes	16
8.3	odd	2		576.2.p.a.95.7	yes	16
8.5	even	2		576.2.p.a.95.2	✓	16
9.2	odd	6		576.2.p.a.479.7	yes	16
9.4	even	3		5184.2.f.a.2591.1		16
9.5	odd	6		5184.2.f.f.2591.13		16
9.7	even	3		1728.2.p.c.1439.8		16
12.11	even	2		1728.2.p.a.287.2		16
24.5	odd	2		1728.2.p.c.287.7		16
24.11	even	2		1728.2.p.c.287.8		16
36.7	odd	6		1728.2.p.c.1439.7		16
36.11	even	6		576.2.p.a.479.2	yes	16
36.23	even	6		5184.2.f.f.2591.15		16
36.31	odd	6		5184.2.f.a.2591.3		16
72.5	odd	6		5184.2.f.a.2591.2		16
72.11	even	6	inner	576.2.p.c.479.7	yes	16
72.13	even	6		5184.2.f.f.2591.14		16
72.29	odd	6	inner	576.2.p.c.479.2	yes	16
72.43	odd	6		1728.2.p.a.1439.1		16
72.59	even	6		5184.2.f.a.2591.4		16
72.61	even	6		1728.2.p.a.1439.2		16
72.67	odd	6		5184.2.f.f.2591.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.p.a.95.2	✓	16	8.5	even	2
576.2.p.a.95.7	yes	16	8.3	odd	2
576.2.p.a.479.2	yes	16	36.11	even	6
576.2.p.a.479.7	yes	16	9.2	odd	6
576.2.p.c.95.2	yes	16	4.3	odd	2	inner
576.2.p.c.95.7	yes	16	1.1	even	1	trivial
576.2.p.c.479.2	yes	16	72.29	odd	6	inner
576.2.p.c.479.7	yes	16	72.11	even	6	inner
1728.2.p.a.287.1		16	3.2	odd	2
1728.2.p.a.287.2		16	12.11	even	2
1728.2.p.a.1439.1		16	72.43	odd	6
1728.2.p.a.1439.2		16	72.61	even	6
1728.2.p.c.287.7		16	24.5	odd	2
1728.2.p.c.287.8		16	24.11	even	2
1728.2.p.c.1439.7		16	36.7	odd	6
1728.2.p.c.1439.8		16	9.7	even	3
5184.2.f.a.2591.1		16	9.4	even	3
5184.2.f.a.2591.2		16	72.5	odd	6
5184.2.f.a.2591.3		16	36.31	odd	6
5184.2.f.a.2591.4		16	72.59	even	6
5184.2.f.f.2591.13		16	9.5	odd	6
5184.2.f.f.2591.14		16	72.13	even	6
5184.2.f.f.2591.15		16	36.23	even	6
5184.2.f.f.2591.16		16	72.67	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46399 + 0.925606i) q^{3} +(2.06470 - 3.57617i) q^{5} +(-0.287429 + 0.165947i) q^{7} +(1.28651 + 2.71015i) q^{9} +O(q^{10})\)	\(q+(1.46399 + 0.925606i) q^{3} +(2.06470 - 3.57617i) q^{5} +(-0.287429 + 0.165947i) q^{7} +(1.28651 + 2.71015i) q^{9} +(-3.62268 + 2.09155i) q^{11} +(4.27682 + 2.46922i) q^{13} +(6.33282 - 3.32436i) q^{15} -3.20639i q^{17} +5.42029 q^{19} +(-0.574394 - 0.0231017i) q^{21} +(1.39438 - 2.41514i) q^{23} +(-6.02601 - 10.4374i) q^{25} +(-0.625100 + 5.15842i) q^{27} +(-1.03570 - 1.79388i) q^{29} +(-3.60828 - 2.08324i) q^{31} +(-7.23950 - 0.291167i) q^{33} +1.37053i q^{35} -2.21390i q^{37} +(3.97567 + 7.57355i) q^{39} +(1.41298 + 0.815784i) q^{41} +(2.99758 + 5.19195i) q^{43} +(12.3482 + 0.994880i) q^{45} +(-3.97567 - 6.88607i) q^{47} +(-3.44492 + 5.96678i) q^{49} +(2.96786 - 4.69411i) q^{51} -2.05801 q^{53} +17.2738i q^{55} +(7.93523 + 5.01706i) q^{57} +(5.40497 + 3.12056i) q^{59} +(-9.10709 + 5.25798i) q^{61} +(-0.819522 - 0.565483i) q^{63} +(17.6607 - 10.1964i) q^{65} +(-5.83658 + 10.1093i) q^{67} +(4.27682 - 2.24508i) q^{69} -7.66299 q^{71} -6.21742 q^{73} +(0.838886 - 20.8578i) q^{75} +(0.694175 - 1.20235i) q^{77} +(-0.719039 + 0.415137i) q^{79} +(-5.68980 + 6.97325i) q^{81} +(-5.96543 + 3.44414i) q^{83} +(-11.4666 - 6.62025i) q^{85} +(0.144180 - 3.58486i) q^{87} +9.14211i q^{89} -1.63904 q^{91} +(-3.35421 - 6.38968i) q^{93} +(11.1913 - 19.3839i) q^{95} +(-0.749190 - 1.29763i) q^{97} +(-10.3290 - 7.12719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^5 + 6 * q^9	\( 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

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Database

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