LMFDB - Embedded newform 360.2.q.e.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	360.121
Dual form			360.2.q.e.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24624 + 1.20287i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.433868 - 0.751481i) q^{7} +(0.106223 + 2.99812i) q^{9} +O(q^{10})$	\(q+(1.24624 + 1.20287i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.433868 - 0.751481i) q^{7} +(0.106223 + 2.99812i) q^{9} +(2.04334 + 3.53916i) q^{11} +(-0.606223 + 1.05001i) q^{13} +(-1.66483 + 0.477841i) q^{15} +7.82214 q^{17} -4.51156 q^{19} +(0.363229 - 1.45841i) q^{21} +(-1.43387 + 2.48353i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.47396 + 3.86414i) q^{27} +(-3.14956 - 5.45520i) q^{29} +(1.26151 - 2.18500i) q^{31} +(-1.71066 + 6.86850i) q^{33} +0.867736 q^{35} -0.523026 q^{37} +(-2.01852 + 0.579356i) q^{39} +(4.06063 - 7.03322i) q^{41} +(-1.91107 - 3.31007i) q^{43} +(-2.64956 - 1.40707i) q^{45} +(0.695381 + 1.20444i) q^{47} +(3.12352 - 5.41009i) q^{49} +(9.74826 + 9.40900i) q^{51} +13.9088 q^{53} -4.08667 q^{55} +(-5.62248 - 5.42681i) q^{57} +(-3.43711 + 5.95325i) q^{59} +(-4.54334 - 7.86929i) q^{61} +(2.20694 - 1.38061i) q^{63} +(-0.606223 - 1.05001i) q^{65} +(-1.68965 + 2.92656i) q^{67} +(-4.77430 + 1.37032i) q^{69} +3.21245 q^{71} +8.60970 q^{73} +(0.418594 - 1.68071i) q^{75} +(1.77308 - 3.07106i) q^{77} +(-8.12126 - 14.0664i) q^{79} +(-8.97743 + 0.636937i) q^{81} +(-3.22142 - 5.57967i) q^{83} +(-3.91107 + 6.77417i) q^{85} +(2.63677 - 10.5870i) q^{87} -10.2079 q^{89} +1.05208 q^{91} +(4.20042 - 1.20561i) q^{93} +(2.25578 - 3.90713i) q^{95} +(4.38503 + 7.59510i) q^{97} +(-10.3938 + 6.50210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + q^7	$ 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.24624	+	1.20287i	0.719516	+	0.694475i
$3$	1.24624	+	1.20287i	0.719516	+	0.694475i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.433868	−	0.751481i	−0.163987	−	0.284033i	0.772308	−	0.635248i	$-0.219102\pi$
$7$	−0.433868	−	0.751481i	−0.163987	−	0.284033i	−0.936295	+	0.351215i	$0.885769\pi$
$8$		0			0
$9$	0.106223	+	2.99812i	0.0354076	+	0.999373i
$10$		0			0
$11$	2.04334	+	3.53916i	0.616089	+	1.06710i	0.990192	+	0.139710i	$0.0446171\pi$
$11$	2.04334	+	3.53916i	0.616089	+	1.06710i	−0.374104	+	0.927387i	$0.622050\pi$
$12$		0			0
$13$	−0.606223	+	1.05001i	−0.168136	+	0.291220i	−0.937764	−	0.347272i	$-0.887108\pi$
$13$	−0.606223	+	1.05001i	−0.168136	+	0.291220i	0.769629	+	0.638492i	$0.220441\pi$
$14$		0			0
$15$	−1.66483	+	0.477841i	−0.429858	+	0.123378i
$16$		0			0
$17$	7.82214			1.89715			0.948574	−	0.316555i	$-0.102526\pi$
$17$	7.82214			1.89715			0.948574	+	0.316555i	$0.102526\pi$
$18$		0			0
$19$	−4.51156			−1.03502			−0.517512	−	0.855676i	$-0.673142\pi$
$19$	−4.51156			−1.03502			−0.517512	+	0.855676i	$0.673142\pi$
$20$		0			0
$21$	0.363229	−	1.45841i	0.0792630	−	0.318251i
$22$		0			0
$23$	−1.43387	+	2.48353i	−0.298982	+	0.517852i	−0.975903	−	0.218203i	$-0.929980\pi$
$23$	−1.43387	+	2.48353i	−0.298982	+	0.517852i	0.676921	+	0.736055i	$0.263314\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−3.47396	+	3.86414i	−0.668564	+	0.743655i
$28$		0			0
$29$	−3.14956	−	5.45520i	−0.584858	−	1.01300i	−0.994893	−	0.100934i	$-0.967817\pi$
$29$	−3.14956	−	5.45520i	−0.584858	−	1.01300i	0.410035	−	0.912070i	$-0.365517\pi$
$30$		0			0
$31$	1.26151	−	2.18500i	0.226574	−	0.392438i	−0.730216	−	0.683216i	$-0.760581\pi$
$31$	1.26151	−	2.18500i	0.226574	−	0.392438i	0.956791	+	0.290778i	$0.0939140\pi$
$32$		0			0
$33$	−1.71066	+	6.86850i	−0.297787	+	1.19565i
$34$		0			0
$35$	0.867736			0.146674
$36$		0			0
$37$	−0.523026			−0.0859850			−0.0429925	−	0.999075i	$-0.513689\pi$
$37$	−0.523026			−0.0859850			−0.0429925	+	0.999075i	$0.513689\pi$
$38$		0			0
$39$	−2.01852	+	0.579356i	−0.323222	+	0.0927713i
$40$		0			0
$41$	4.06063	−	7.03322i	0.634164	−	1.09840i	−0.352528	−	0.935801i	$-0.614678\pi$
$41$	4.06063	−	7.03322i	0.634164	−	1.09840i	0.986692	−	0.162603i	$-0.0519889\pi$
$42$		0			0
$43$	−1.91107	−	3.31007i	−0.291436	−	0.504781i	0.682714	−	0.730686i	$-0.260800\pi$
$43$	−1.91107	−	3.31007i	−0.291436	−	0.504781i	−0.974149	+	0.225905i	$0.927466\pi$
$44$		0			0
$45$	−2.64956	−	1.40707i	−0.394973	−	0.209753i
$46$		0			0
$47$	0.695381	+	1.20444i	0.101432	+	0.175685i	0.912275	−	0.409579i	$-0.134324\pi$
$47$	0.695381	+	1.20444i	0.101432	+	0.175685i	−0.810843	+	0.585264i	$0.800991\pi$
$48$		0			0
$49$	3.12352	−	5.41009i	0.446217	−	0.772870i
$50$		0			0
$51$	9.74826	+	9.40900i	1.36503	+	1.31752i
$52$		0			0
$53$	13.9088			1.91052			0.955261	−	0.295763i	$-0.0955739\pi$
$53$	13.9088			1.91052			0.955261	+	0.295763i	$0.0955739\pi$
$54$		0			0
$55$	−4.08667			−0.551047
$56$		0			0
$57$	−5.62248	−	5.42681i	−0.744716	−	0.718798i
$58$		0			0
$59$	−3.43711	+	5.95325i	−0.447474	+	0.775048i	−0.998221	−	0.0596246i	$-0.981010\pi$
$59$	−3.43711	+	5.95325i	−0.447474	+	0.775048i	0.550747	+	0.834672i	$0.314343\pi$
$60$		0			0
$61$	−4.54334	−	7.86929i	−0.581715	−	1.00756i	−0.995276	−	0.0970830i	$-0.969049\pi$
$61$	−4.54334	−	7.86929i	−0.581715	−	1.00756i	0.413562	−	0.910476i	$-0.364285\pi$
$62$		0			0
$63$	2.20694	−	1.38061i	0.278049	−	0.173941i
$64$		0			0
$65$	−0.606223	−	1.05001i	−0.0751927	−	0.130238i
$66$		0			0
$67$	−1.68965	+	2.92656i	−0.206424	+	0.357536i	−0.950585	−	0.310463i	$-0.899516\pi$
$67$	−1.68965	+	2.92656i	−0.206424	+	0.357536i	0.744162	+	0.667999i	$0.232849\pi$
$68$		0			0
$69$	−4.77430	+	1.37032i	−0.574758	+	0.164967i
$70$		0			0
$71$	3.21245			0.381247			0.190624	−	0.981663i	$-0.438949\pi$
$71$	3.21245			0.381247			0.190624	+	0.981663i	$0.438949\pi$
$72$		0			0
$73$	8.60970			1.00769			0.503844	−	0.863794i	$-0.331918\pi$
$73$	8.60970			1.00769			0.503844	+	0.863794i	$0.331918\pi$
$74$		0			0
$75$	0.418594	−	1.68071i	0.0483350	−	0.194071i
$76$		0			0
$77$	1.77308	−	3.07106i	0.202061	−	0.349979i
$78$		0			0
$79$	−8.12126	−	14.0664i	−0.913713	−	1.58260i	−0.808774	−	0.588119i	$-0.799869\pi$
$79$	−8.12126	−	14.0664i	−0.913713	−	1.58260i	−0.104939	−	0.994479i	$-0.533465\pi$
$80$		0			0
$81$	−8.97743	+	0.636937i	−0.997493	+	0.0707708i
$82$		0			0
$83$	−3.22142	−	5.57967i	−0.353597	−	0.612448i	0.633280	−	0.773923i	$-0.281708\pi$
$83$	−3.22142	−	5.57967i	−0.353597	−	0.612448i	−0.986877	+	0.161475i	$0.948375\pi$
$84$		0			0
$85$	−3.91107	+	6.77417i	−0.424215	+	0.734762i
$86$		0			0
$87$	2.63677	−	10.5870i	0.282692	−	1.13504i
$88$		0			0
$89$	−10.2079			−1.08204			−0.541019	−	0.841010i	$-0.681961\pi$
$89$	−10.2079			−1.08204			−0.541019	+	0.841010i	$0.681961\pi$
$90$		0			0
$91$	1.05208			0.110288
$92$		0			0
$93$	4.20042	−	1.20561i	0.435563	−	0.125015i
$94$		0			0
$95$	2.25578	−	3.90713i	0.231438	−	0.400863i
$96$		0			0
$97$	4.38503	+	7.59510i	0.445232	+	0.771165i	0.998068	−	0.0621250i	$-0.0197877\pi$
$97$	4.38503	+	7.59510i	0.445232	+	0.771165i	−0.552836	+	0.833290i	$0.686454\pi$
$98$		0			0
$99$	−10.3938	+	6.50210i	−1.04461	+	0.653486i
$100$		0			0
$101$	−1.13226	−	1.96114i	−0.112664	−	0.195141i	0.804179	−	0.594387i	$-0.202605\pi$
$101$	−1.13226	−	1.96114i	−0.112664	−	0.195141i	−0.916844	+	0.399246i	$0.869272\pi$
$102$		0			0
$103$	7.69289	−	13.3245i	0.758003	−	1.31290i	−0.185864	−	0.982575i	$-0.559508\pi$
$103$	7.69289	−	13.3245i	0.758003	−	1.31290i	0.943867	−	0.330325i	$-0.107158\pi$
$104$		0			0
$105$	1.08141	+	1.04377i	0.105534	+	0.101862i
$106$		0			0
$107$	14.3402			1.38632			0.693160	−	0.720784i	$-0.256218\pi$
$107$	14.3402			1.38632			0.693160	+	0.720784i	$0.256218\pi$
$108$		0			0
$109$	−5.35120			−0.512552			−0.256276	−	0.966604i	$-0.582496\pi$
$109$	−5.35120			−0.512552			−0.256276	+	0.966604i	$0.582496\pi$
$110$		0			0
$111$	−0.651816	−	0.629131i	−0.0618676	−	0.0597145i
$112$		0			0
$113$	−1.34471	+	2.32911i	−0.126500	+	0.219104i	−0.922318	−	0.386431i	$-0.873708\pi$
$113$	−1.34471	+	2.32911i	−0.126500	+	0.219104i	0.795818	+	0.605535i	$0.207041\pi$
$114$		0			0
$115$	−1.43387	−	2.48353i	−0.133709	−	0.231591i
$116$		0			0
$117$	−3.21245	−	1.70599i	−0.296991	−	0.157719i
$118$		0			0
$119$	−3.39378	−	5.87819i	−0.311107	−	0.538853i
$120$		0			0
$121$	−2.85044	+	4.93711i	−0.259131	+	0.448828i
$122$		0			0
$123$	13.5205	−	3.88067i	1.21911	−	0.349908i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−21.5641			−1.91350			−0.956752	−	0.290903i	$-0.906044\pi$
$127$	−21.5641			−1.91350			−0.956752	+	0.290903i	$0.906044\pi$
$128$		0			0
$129$	1.59993	−	6.42391i	0.140866	−	0.565593i
$130$		0			0
$131$	−9.24703	+	16.0163i	−0.807917	+	1.39935i	0.106387	+	0.994325i	$0.466072\pi$
$131$	−9.24703	+	16.0163i	−0.807917	+	1.39935i	−0.914304	+	0.405029i	$0.867262\pi$
$132$		0			0
$133$	1.95742	+	3.39036i	0.169730	+	0.293981i
$134$		0			0
$135$	−1.60947	−	4.94061i	−0.138521	−	0.425220i
$136$		0			0
$137$	−4.86200	−	8.42124i	−0.415389	−	0.719475i	0.580080	−	0.814559i	$-0.303021\pi$
$137$	−4.86200	−	8.42124i	−0.415389	−	0.719475i	−0.995469	+	0.0950845i	$0.969688\pi$
$138$		0			0
$139$	8.04032	−	13.9262i	0.681971	−	1.18121i	−0.292407	−	0.956294i	$-0.594456\pi$
$139$	8.04032	−	13.9262i	0.681971	−	1.18121i	0.974378	−	0.224915i	$-0.0722104\pi$
$140$		0			0
$141$	−0.582164	+	2.33746i	−0.0490271	+	0.196850i
$142$		0			0
$143$	−4.95487			−0.414347
$144$		0			0
$145$	6.29912			0.523113
$146$		0			0
$147$	10.4003	−	2.98509i	0.857800	−	0.246206i
$148$		0			0
$149$	−7.92263	+	13.7224i	−0.649047	+	1.12418i	0.334303	+	0.942466i	$0.391499\pi$
$149$	−7.92263	+	13.7224i	−0.649047	+	1.12418i	−0.983351	+	0.181718i	$0.941834\pi$
$150$		0			0
$151$	7.56063	+	13.0954i	0.615275	+	1.06569i	0.990336	+	0.138688i	$0.0442885\pi$
$151$	7.56063	+	13.0954i	0.615275	+	1.06569i	−0.375061	+	0.927000i	$0.622378\pi$
$152$		0			0
$153$	0.830890	+	23.4517i	0.0671735	+	1.89596i
$154$		0			0
$155$	1.26151	+	2.18500i	0.101327	+	0.175504i
$156$		0			0
$157$	−8.77655	+	15.2014i	−0.700445	+	1.21321i	0.267865	+	0.963456i	$0.413682\pi$
$157$	−8.77655	+	15.2014i	−0.700445	+	1.21321i	−0.968310	+	0.249750i	$0.919652\pi$
$158$		0			0
$159$	17.3337	+	16.7305i	1.37465	+	1.32681i
$160$		0			0
$161$	2.48844			0.196116
$162$		0			0
$163$	6.85673			0.537061			0.268530	−	0.963271i	$-0.413462\pi$
$163$	6.85673			0.537061			0.268530	+	0.963271i	$0.413462\pi$
$164$		0			0
$165$	−5.09297	−	4.91572i	−0.396487	−	0.382688i
$166$		0			0
$167$	−1.95991	+	3.39466i	−0.151662	+	0.262687i	−0.931839	−	0.362873i	$-0.881796\pi$
$167$	−1.95991	+	3.39466i	−0.151662	+	0.262687i	0.780176	+	0.625560i	$0.215129\pi$
$168$		0			0
$169$	5.76499	+	9.98525i	0.443461	+	0.768096i
$170$		0			0
$171$	−0.479231	−	13.5262i	−0.0366477	−	1.03437i
$172$		0			0
$173$	4.08667	+	7.07832i	0.310704	+	0.538155i	0.978515	−	0.206176i	$-0.0661019\pi$
$173$	4.08667	+	7.07832i	0.310704	+	0.538155i	−0.667811	+	0.744331i	$0.732769\pi$
$174$		0			0
$175$	−0.433868	+	0.751481i	−0.0327973	+	0.0568066i
$176$		0			0
$177$	−11.4444	+	3.28479i	−0.860216	+	0.246900i
$178$		0			0
$179$	−6.85673			−0.512496			−0.256248	−	0.966611i	$-0.582486\pi$
$179$	−6.85673			−0.512496			−0.256248	+	0.966611i	$0.582486\pi$
$180$		0			0
$181$	16.2991			1.21150			0.605752	−	0.795654i	$-0.292872\pi$
$181$	16.2991			1.21150			0.605752	+	0.795654i	$0.292872\pi$
$182$		0			0
$183$	3.80362	−	15.2720i	0.281172	−	1.12894i
$184$		0			0
$185$	0.261513	−	0.452954i	0.0192268	−	0.0333018i
$186$		0			0
$187$	15.9833	+	27.6838i	1.16881	+	2.02444i
$188$		0			0
$189$	4.41107	+	0.934087i	0.320858	+	0.0679448i
$190$		0			0
$191$	−5.91680	−	10.2482i	−0.428125	−	0.741534i	0.568582	−	0.822627i	$-0.307492\pi$
$191$	−5.91680	−	10.2482i	−0.428125	−	0.741534i	−0.996707	+	0.0810928i	$0.974159\pi$
$192$		0			0
$193$	0.911072	−	1.57802i	0.0655804	−	0.113589i	−0.831371	−	0.555718i	$-0.812443\pi$
$193$	0.911072	−	1.57802i	0.0655804	−	0.113589i	0.896951	+	0.442129i	$0.145777\pi$
$194$		0			0
$195$	0.507522	−	2.03777i	0.0363444	−	0.145928i
$196$		0			0
$197$	19.3798			1.38075			0.690375	−	0.723451i	$-0.257445\pi$
$197$	19.3798			1.38075			0.690375	+	0.723451i	$0.257445\pi$
$198$		0			0
$199$	6.69637			0.474693			0.237347	−	0.971425i	$-0.423722\pi$
$199$	6.69637			0.474693			0.237347	+	0.971425i	$0.423722\pi$
$200$		0			0
$201$	−5.62597	+	1.61477i	−0.396825	+	0.113897i
$202$		0			0
$203$	−2.73298	+	4.73367i	−0.191818	+	0.332238i
$204$		0			0
$205$	4.06063	+	7.03322i	0.283607	+	0.491221i
$206$		0			0
$207$	−7.59823	−	4.03510i	−0.528114	−	0.280459i
$208$		0			0
$209$	−9.21864	−	15.9671i	−0.637666	−	1.10447i
$210$		0			0
$211$	−4.26151	+	7.38116i	−0.293375	+	0.508140i	−0.974605	−	0.223929i	$-0.928112\pi$
$211$	−4.26151	+	7.38116i	−0.293375	+	0.508140i	0.681231	+	0.732069i	$0.261445\pi$
$212$		0			0
$213$	4.00347	+	3.86414i	0.274314	+	0.264767i
$214$		0			0
$215$	3.82214			0.260668
$216$		0			0
$217$	−2.18932			−0.148621
$218$		0			0
$219$	10.7297	+	10.3563i	0.725049	+	0.699815i
$220$		0			0
$221$	−4.74196	+	8.21332i	−0.318979	+	0.552488i
$222$		0			0
$223$	5.43085	+	9.40651i	0.363677	+	0.629907i	0.988563	−	0.150809i	$-0.0481879\pi$
$223$	5.43085	+	9.40651i	0.363677	+	0.629907i	−0.624886	+	0.780716i	$0.714855\pi$
$224$		0			0
$225$	2.54334	−	1.59105i	0.169556	−	0.106070i
$226$		0			0
$227$	9.34245	+	16.1816i	0.620080	+	1.07401i	0.989470	+	0.144736i	$0.0462334\pi$
$227$	9.34245	+	16.1816i	0.620080	+	1.07401i	−0.369390	+	0.929274i	$0.620433\pi$
$228$		0			0
$229$	−4.79836	+	8.31100i	−0.317084	+	0.549206i	−0.979878	−	0.199595i	$-0.936037\pi$
$229$	−4.79836	+	8.31100i	−0.317084	+	0.549206i	0.662794	+	0.748802i	$0.269371\pi$
$230$		0			0
$231$	5.90375	−	1.69450i	0.388438	−	0.111490i
$232$		0			0
$233$	−20.5807			−1.34829			−0.674145	−	0.738599i	$-0.735488\pi$
$233$	−20.5807			−1.34829			−0.674145	+	0.738599i	$0.735488\pi$
$234$		0			0
$235$	−1.39076			−0.0907233
$236$		0			0
$237$	6.79902	−	27.2989i	0.441644	−	1.77326i
$238$		0			0
$239$	−5.08018	+	8.79913i	−0.328610	+	0.569169i	−0.982236	−	0.187649i	$-0.939913\pi$
$239$	−5.08018	+	8.79913i	−0.328610	+	0.569169i	0.653627	+	0.756817i	$0.273247\pi$
$240$		0			0
$241$	−7.10622	−	12.3083i	−0.457752	−	0.792850i	0.541090	−	0.840965i	$-0.318012\pi$
$241$	−7.10622	−	12.3083i	−0.457752	−	0.792850i	−0.998842	+	0.0481150i	$0.984679\pi$
$242$		0			0
$243$	−11.9542	−	10.0049i	−0.766861	−	0.641813i
$244$		0			0
$245$	3.12352	+	5.41009i	0.199554	+	0.345638i
$246$		0			0
$247$	2.73501	−	4.73718i	0.174025	−	0.301420i
$248$		0			0
$249$	2.69693	−	10.8285i	0.170911	−	0.686231i
$250$		0			0
$251$	−0.247034			−0.0155927			−0.00779634	−	0.999970i	$-0.502482\pi$
$251$	−0.247034			−0.0155927			−0.00779634	+	0.999970i	$0.502482\pi$
$252$		0			0
$253$	−11.7195			−0.736798
$254$		0			0
$255$	−13.0226	+	3.73774i	−0.815504	+	0.234066i
$256$		0			0
$257$	−2.43062	+	4.20996i	−0.151618	+	0.262610i	−0.931822	−	0.362914i	$-0.881782\pi$
$257$	−2.43062	+	4.20996i	−0.151618	+	0.262610i	0.780204	+	0.625525i	$0.215115\pi$
$258$		0			0
$259$	0.226924	+	0.393044i	0.0141004	+	0.0244226i
$260$		0			0
$261$	16.0208	−	10.0222i	0.991661	−	0.620360i
$262$		0			0
$263$	−10.2159	−	17.6945i	−0.629941	−	1.09109i	−0.987563	−	0.157223i	$-0.949746\pi$
$263$	−10.2159	−	17.6945i	−0.629941	−	1.09109i	0.357622	−	0.933866i	$-0.383587\pi$
$264$		0			0
$265$	−6.95441	+	12.0454i	−0.427206	+	0.739942i
$266$		0			0
$267$	−12.7215	−	12.2788i	−0.778544	−	0.751449i
$268$		0			0
$269$	−25.5125			−1.55552			−0.777762	−	0.628559i	$-0.783645\pi$
$269$	−25.5125			−1.55552			−0.777762	+	0.628559i	$0.783645\pi$
$270$		0			0
$271$	5.12126			0.311094			0.155547	−	0.987828i	$-0.450286\pi$
$271$	5.12126			0.311094			0.155547	+	0.987828i	$0.450286\pi$
$272$		0			0
$273$	1.31115	+	1.26552i	0.0793542	+	0.0765925i
$274$		0			0
$275$	2.04334	−	3.53916i	0.123218	−	0.213419i
$276$		0			0
$277$	−5.70436	−	9.88024i	−0.342742	−	0.593646i	0.642199	−	0.766538i	$-0.278022\pi$
$277$	−5.70436	−	9.88024i	−0.342742	−	0.593646i	−0.984941	+	0.172892i	$0.944689\pi$
$278$		0			0
$279$	6.68491	+	3.55007i	0.400215	+	0.212537i
$280$		0			0
$281$	−10.7969	−	18.7007i	−0.644087	−	1.11559i	−0.984512	−	0.175319i	$-0.943904\pi$
$281$	−10.7969	−	18.7007i	−0.644087	−	1.11559i	0.340425	−	0.940272i	$-0.389429\pi$
$282$		0			0
$283$	−9.96338	+	17.2571i	−0.592262	+	1.02583i	0.401665	+	0.915787i	$0.368432\pi$
$283$	−9.96338	+	17.2571i	−0.592262	+	1.02583i	−0.993927	+	0.110041i	$0.964902\pi$
$284$		0			0
$285$	7.51100	−	2.15581i	0.444913	−	0.127699i
$286$		0			0
$287$	−7.04711			−0.415978
$288$		0			0
$289$	44.1859			2.59917
$290$		0			0
$291$	−3.67109	+	14.7399i	−0.215203	+	0.864069i
$292$		0			0
$293$	−0.916803	+	1.58795i	−0.0535602	+	0.0927690i	−0.891562	−	0.452898i	$-0.850390\pi$
$293$	−0.916803	+	1.58795i	−0.0535602	+	0.0927690i	0.838002	+	0.545667i	$0.183724\pi$
$294$		0			0
$295$	−3.43711	−	5.95325i	−0.200116	−	0.346612i
$296$		0			0
$297$	−20.7743	−	4.39916i	−1.20545	−	0.255265i
$298$		0			0
$299$	−1.73849	−	3.01115i	−0.100539	−	0.174139i
$300$		0			0
$301$	−1.65831	+	2.87227i	−0.0955831	+	0.165555i
$302$		0			0
$303$	0.947917	−	3.80601i	0.0544564	−	0.218650i
$304$		0			0
$305$	9.08667			0.520301
$306$		0			0
$307$	9.02962			0.515347			0.257674	−	0.966232i	$-0.417044\pi$
$307$	9.02962			0.515347			0.257674	+	0.966232i	$0.417044\pi$
$308$		0			0
$309$	25.6148	−	7.35196i	1.45717	−	0.418239i
$310$		0			0
$311$	−1.48045	+	2.56421i	−0.0839485	+	0.145403i	−0.904943	−	0.425533i	$-0.860086\pi$
$311$	−1.48045	+	2.56421i	−0.0839485	+	0.145403i	0.820994	+	0.570937i	$0.193420\pi$
$312$		0			0
$313$	−9.64157	−	16.6997i	−0.544974	−	0.943922i	−0.998609	−	0.0527345i	$-0.983206\pi$
$313$	−9.64157	−	16.6997i	−0.544974	−	0.943922i	0.453635	−	0.891188i	$-0.350127\pi$
$314$		0			0
$315$	0.0921733	+	2.60158i	0.00519338	+	0.146582i
$316$		0			0
$317$	3.08366	+	5.34105i	0.173195	+	0.299983i	0.939535	−	0.342452i	$-0.111257\pi$
$317$	3.08366	+	5.34105i	0.173195	+	0.299983i	−0.766340	+	0.642435i	$0.777924\pi$
$318$		0			0
$319$	12.8712	−	22.2936i	0.720649	−	1.24820i
$320$		0			0
$321$	17.8713	+	17.2493i	0.997479	+	0.962765i
$322$		0			0
$323$	−35.2901			−1.96359
$324$		0			0
$325$	1.21245			0.0672544
$326$		0			0
$327$	−6.66887	−	6.43678i	−0.368790	−	0.355955i
$328$		0			0
$329$	0.603407	−	1.04513i	0.0332669	−	0.0576200i
$330$		0			0
$331$	−10.3447	−	17.9176i	−0.568597	−	0.984838i	−0.996705	−	0.0811109i	$-0.974153\pi$
$331$	−10.3447	−	17.9176i	−0.568597	−	0.984838i	0.428108	−	0.903727i	$-0.359180\pi$
$332$		0			0
$333$	−0.0555573	−	1.56809i	−0.00304452	−	0.0859311i
$334$		0			0
$335$	−1.68965	−	2.92656i	−0.0923154	−	0.159895i
$336$		0			0
$337$	0.862004	−	1.49303i	0.0469564	−	0.0813308i	−0.841592	−	0.540114i	$-0.818381\pi$
$337$	0.862004	−	1.49303i	0.0469564	−	0.0813308i	0.888548	+	0.458783i	$0.151714\pi$
$338$		0			0
$339$	−4.47743	+	1.28512i	−0.243181	+	0.0697979i
$340$		0			0
$341$	10.3108			0.558360
$342$		0			0
$343$	−11.4949			−0.620668
$344$		0			0
$345$	1.20042	−	4.81983i	0.0646282	−	0.259491i
$346$		0			0
$347$	16.2448	−	28.1368i	0.872065	−	1.51046i	0.0122090	−	0.999925i	$-0.496114\pi$
$347$	16.2448	−	28.1368i	0.872065	−	1.51046i	0.859856	−	0.510536i	$-0.170553\pi$
$348$		0			0
$349$	−2.59240	−	4.49017i	−0.138768	−	0.240354i	0.788262	−	0.615339i	$-0.210981\pi$
$349$	−2.59240	−	4.49017i	−0.138768	−	0.240354i	−0.927031	+	0.374986i	$0.877648\pi$
$350$		0			0
$351$	−1.95139	−	5.99022i	−0.104158	−	0.319734i
$352$		0			0
$353$	1.43062	+	2.47791i	0.0761444	+	0.131886i	0.901583	−	0.432605i	$-0.142406\pi$
$353$	1.43062	+	2.47791i	0.0761444	+	0.131886i	−0.825439	+	0.564491i	$0.809072\pi$
$354$		0			0
$355$	−1.60622	+	2.78206i	−0.0852495	+	0.147656i
$356$		0			0
$357$	2.84123	−	11.4079i	0.150374	−	0.603770i
$358$		0			0
$359$	37.0301			1.95437			0.977186	−	0.212384i	$-0.0681227\pi$
$359$	37.0301			1.95437			0.977186	+	0.212384i	$0.0681227\pi$
$360$		0			0
$361$	1.35420			0.0712736
$362$		0			0
$363$	−9.49102	+	2.72412i	−0.498149	+	0.142979i
$364$		0			0
$365$	−4.30485	+	7.45622i	−0.225326	+	0.390276i
$366$		0			0
$367$	18.2159	+	31.5509i	0.950863	+	1.64694i	0.743563	+	0.668666i	$0.233135\pi$
$367$	18.2159	+	31.5509i	0.950863	+	1.64694i	0.207301	+	0.978277i	$0.433532\pi$
$368$		0			0
$369$	21.5178	+	11.4272i	1.12017	+	0.594874i
$370$		0			0
$371$	−6.03459	−	10.4522i	−0.313300	−	0.542652i
$372$		0			0
$373$	8.26499	−	14.3154i	0.427945	−	0.741222i	−0.568746	−	0.822514i	$-0.692571\pi$
$373$	8.26499	−	14.3154i	0.427945	−	0.741222i	0.996690	+	0.0812913i	$0.0259044\pi$
$374$		0			0
$375$	1.24624	+	1.20287i	0.0643555	+	0.0621158i
$376$		0			0
$377$	7.63734			0.393343
$378$		0			0
$379$	−31.8062			−1.63377			−0.816886	−	0.576798i	$-0.804302\pi$
$379$	−31.8062			−1.63377			−0.816886	+	0.576798i	$0.804302\pi$
$380$		0			0
$381$	−26.8740	−	25.9387i	−1.37680	−	1.32888i
$382$		0			0
$383$	−10.1178	+	17.5245i	−0.516995	+	0.895461i	0.482811	+	0.875725i	$0.339616\pi$
$383$	−10.1178	+	17.5245i	−0.516995	+	0.895461i	−0.999805	+	0.0197362i	$0.993717\pi$
$384$		0			0
$385$	1.77308	+	3.07106i	0.0903643	+	0.156516i
$386$		0			0
$387$	9.72099	−	6.08123i	0.494146	−	0.309126i
$388$		0			0
$389$	12.0028	+	20.7895i	0.608567	+	1.05407i	0.991477	+	0.130283i	$0.0415886\pi$
$389$	12.0028	+	20.7895i	0.608567	+	1.05407i	−0.382910	+	0.923786i	$0.625078\pi$
$390$		0			0
$391$	−11.2159	+	19.4265i	−0.567213	+	0.982443i
$392$		0			0
$393$	−30.7895	+	8.83723i	−1.55313	+	0.445779i
$394$		0			0
$395$	16.2425			0.817250
$396$		0			0
$397$	−35.8868			−1.80111			−0.900554	−	0.434745i	$-0.856839\pi$
$397$	−35.8868			−1.80111			−0.900554	+	0.434745i	$0.856839\pi$
$398$		0			0
$399$	−1.63873	+	6.57971i	−0.0820391	+	0.329398i
$400$		0			0
$401$	1.60894	−	2.78676i	0.0803466	−	0.139164i	−0.823052	−	0.567966i	$-0.807731\pi$
$401$	1.60894	−	2.78676i	0.0803466	−	0.139164i	0.903399	+	0.428801i	$0.141064\pi$
$402$		0			0
$403$	1.52952	+	2.64920i	0.0761906	+	0.131966i
$404$		0			0
$405$	3.93711	−	8.09315i	0.195637	−	0.402152i
$406$		0			0
$407$	−1.06872	−	1.85107i	−0.0529744	−	0.0917543i
$408$		0			0
$409$	13.1155	−	22.7168i	0.648521	−	1.12327i	−0.334955	−	0.942234i	$-0.608721\pi$
$409$	13.1155	−	22.7168i	0.648521	−	1.12327i	0.983476	−	0.181037i	$-0.0579455\pi$
$410$		0			0
$411$	4.07041	−	16.3432i	0.200778	−	0.806151i
$412$		0			0
$413$	5.96501			0.293519
$414$		0			0
$415$	6.44284			0.316267
$416$		0			0
$417$	26.7716	−	7.68399i	1.31101	−	0.376287i
$418$		0			0
$419$	11.3828	−	19.7155i	0.556085	−	0.963167i	−0.441733	−	0.897146i	$-0.645636\pi$
$419$	11.3828	−	19.7155i	0.556085	−	0.963167i	0.997818	−	0.0660209i	$-0.0210304\pi$
$420$		0			0
$421$	−14.1213	−	24.4587i	−0.688228	−	1.19205i	−0.972411	−	0.233276i	$-0.925055\pi$
$421$	−14.1213	−	24.4587i	−0.688228	−	1.19205i	0.284182	−	0.958770i	$-0.408278\pi$
$422$		0			0
$423$	−3.53717	+	2.21277i	−0.171983	+	0.107589i
$424$		0			0
$425$	−3.91107	−	6.77417i	−0.189715	−	0.328596i
$426$		0			0
$427$	−3.94242	+	6.82846i	−0.190787	+	0.330453i
$428$		0			0
$429$	−6.17495	−	5.96004i	−0.298129	−	0.287754i
$430$		0			0
$431$	−21.4480			−1.03311			−0.516557	−	0.856253i	$-0.672787\pi$
$431$	−21.4480			−1.03311			−0.516557	+	0.856253i	$0.672787\pi$
$432$		0			0
$433$	−0.498583			−0.0239604			−0.0119802	−	0.999928i	$-0.503814\pi$
$433$	−0.498583			−0.0239604			−0.0119802	+	0.999928i	$0.503814\pi$
$434$		0			0
$435$	7.85020	+	7.57700i	0.376389	+	0.363289i
$436$		0			0
$437$	6.46899	−	11.2046i	0.309454	−	0.535989i
$438$		0			0
$439$	12.2075	+	21.1440i	0.582631	+	1.00915i	0.995166	+	0.0982047i	$0.0313100\pi$
$439$	12.2075	+	21.1440i	0.582631	+	1.00915i	−0.412535	+	0.910942i	$0.635357\pi$
$440$		0			0
$441$	16.5519	+	8.79000i	0.788185	+	0.418571i
$442$		0			0
$443$	−8.07544	−	13.9871i	−0.383676	−	0.664546i	0.607909	−	0.794007i	$-0.292009\pi$
$443$	−8.07544	−	13.9871i	−0.383676	−	0.664546i	−0.991584	+	0.129461i	$0.958675\pi$
$444$		0			0
$445$	5.10397	−	8.84033i	0.241951	−	0.419072i
$446$		0			0
$447$	−26.3797	+	7.57152i	−1.24772	+	0.358121i
$448$		0			0
$449$	−30.8392			−1.45539			−0.727697	−	0.685899i	$-0.759409\pi$
$449$	−30.8392			−1.45539			−0.727697	+	0.685899i	$0.759409\pi$
$450$		0			0
$451$	33.1889			1.56281
$452$		0			0
$453$	−6.32967	+	25.4144i	−0.297394	+	1.19407i
$454$		0			0
$455$	−0.526041	+	0.911130i	−0.0246612	+	0.0427144i
$456$		0			0
$457$	7.61844	+	13.1955i	0.356376	+	0.617261i	0.987352	−	0.158541i	$-0.0506790\pi$
$457$	7.61844	+	13.1955i	0.356376	+	0.617261i	−0.630977	+	0.775802i	$0.717346\pi$
$458$		0			0
$459$	−27.1738	+	30.2259i	−1.26836	+	1.41082i
$460$		0			0
$461$	20.8805	+	36.1661i	0.972503	+	1.68442i	0.687942	+	0.725766i	$0.258514\pi$
$461$	20.8805	+	36.1661i	0.972503	+	1.68442i	0.284561	+	0.958658i	$0.408152\pi$
$462$		0			0
$463$	9.47396	−	16.4094i	0.440292	−	0.762608i	−0.557419	−	0.830232i	$-0.688208\pi$
$463$	9.47396	−	16.4094i	0.440292	−	0.762608i	0.997711	+	0.0676230i	$0.0215415\pi$
$464$		0			0
$465$	−1.05612	+	4.24047i	−0.0489765	+	0.196647i
$466$		0			0
$467$	−1.90035			−0.0879377			−0.0439688	−	0.999033i	$-0.514000\pi$
$467$	−1.90035			−0.0879377			−0.0439688	+	0.999033i	$0.514000\pi$
$468$		0			0
$469$	2.93234			0.135403
$470$		0			0
$471$	−29.2230	+	8.38759i	−1.34652	+	0.386480i
$472$		0			0
$473$	7.80992	−	13.5272i	0.359101	−	0.621980i
$474$		0			0
$475$	2.25578	+	3.90713i	0.103502	+	0.179271i
$476$		0			0
$477$	1.47743	+	41.7003i	0.0676470	+	1.90932i
$478$		0			0
$479$	14.9088	+	25.8228i	0.681201	+	1.17987i	0.974615	+	0.223889i	$0.0718754\pi$
$479$	14.9088	+	25.8228i	0.681201	+	1.17987i	−0.293413	+	0.955986i	$0.594791\pi$
$480$		0			0
$481$	0.317070	−	0.549182i	0.0144572	−	0.0250405i
$482$		0			0
$483$	3.10119	+	2.99326i	0.141109	+	0.136198i
$484$		0			0
$485$	−8.77006			−0.398228
$486$		0			0
$487$	−43.1213			−1.95401			−0.977005	−	0.213215i	$-0.931607\pi$
$487$	−43.1213			−1.95401			−0.977005	+	0.213215i	$0.931607\pi$
$488$		0			0
$489$	8.54513	+	8.24774i	0.386424	+	0.372975i
$490$		0			0
$491$	5.89659	−	10.2132i	0.266110	−	0.460915i	−0.701744	−	0.712429i	$-0.747595\pi$
$491$	5.89659	−	10.2132i	0.266110	−	0.460915i	0.967854	+	0.251514i	$0.0809284\pi$
$492$		0			0
$493$	−24.6363	−	42.6713i	−1.10956	−	1.92182i
$494$		0			0
$495$	−0.434098	−	12.2523i	−0.0195112	−	0.550701i
$496$		0			0
$497$	−1.39378	−	2.41409i	−0.0625195	−	0.108287i
$498$		0			0
$499$	9.55837	−	16.5556i	0.427892	−	0.741130i	−0.568794	−	0.822480i	$-0.692590\pi$
$499$	9.55837	−	16.5556i	0.427892	−	0.741130i	0.996686	+	0.0813501i	$0.0259232\pi$
$500$		0			0
$501$	−6.52584	+	1.87305i	−0.291553	+	0.0836817i
$502$		0			0
$503$	21.1522			0.943130			0.471565	−	0.881831i	$-0.343689\pi$
$503$	21.1522			0.943130			0.471565	+	0.881831i	$0.343689\pi$
$504$		0			0
$505$	2.26453			0.100770
$506$		0			0
$507$	−4.82638	+	19.3785i	−0.214347	+	0.860630i
$508$		0			0
$509$	0.982706	−	1.70210i	0.0435577	−	0.0754441i	−0.843425	−	0.537247i	$-0.819464\pi$
$509$	0.982706	−	1.70210i	0.0435577	−	0.0754441i	0.886982	+	0.461803i	$0.152797\pi$
$510$		0			0
$511$	−3.73547	−	6.47003i	−0.165248	−	0.286217i
$512$		0			0
$513$	15.6730	−	17.4333i	0.691979	−	0.769700i
$514$		0			0
$515$	7.69289	+	13.3245i	0.338989	+	0.587147i
$516$		0			0
$517$	−2.84179	+	4.92213i	−0.124982	+	0.216475i
$518$		0			0
$519$	−3.42131	+	13.7370i	−0.150179	+	0.602987i
$520$		0			0
$521$	−14.1143			−0.618359			−0.309180	−	0.951004i	$-0.600054\pi$
$521$	−14.1143			−0.618359			−0.309180	+	0.951004i	$0.600054\pi$
$522$		0			0
$523$	5.03413			0.220127			0.110064	−	0.993925i	$-0.464895\pi$
$523$	5.03413			0.220127			0.110064	+	0.993925i	$0.464895\pi$
$524$		0			0
$525$	−1.44464	+	0.414640i	−0.0630490	+	0.0180964i
$526$		0			0
$527$	9.86774	−	17.0914i	0.429845	−	0.744514i
$528$		0			0
$529$	7.38805	+	12.7965i	0.321219	+	0.556368i
$530$		0			0
$531$	−18.2137	−	9.67250i	−0.790406	−	0.419751i
$532$		0			0
$533$	4.92329	+	8.52739i	0.213252	+	0.369362i
$534$		0			0
$535$	−7.17010	+	12.4190i	−0.309990	+	0.536919i
$536$		0			0
$537$	−8.54513	−	8.24774i	−0.368749	−	0.355916i
$538$		0			0
$539$	25.5296			1.09964
$540$		0			0
$541$	−9.30926			−0.400236			−0.200118	−	0.979772i	$-0.564133\pi$
$541$	−9.30926			−0.400236			−0.200118	+	0.979772i	$0.564133\pi$
$542$		0			0
$543$	20.3126	+	19.6057i	0.871697	+	0.841360i
$544$		0			0
$545$	2.67560	−	4.63427i	0.114610	−	0.198511i
$546$		0			0
$547$	−15.1245	−	26.1964i	−0.646677	−	1.12008i	−0.983911	−	0.178657i	$-0.942825\pi$
$547$	−15.1245	−	26.1964i	−0.646677	−	1.12008i	0.337234	−	0.941421i	$-0.390509\pi$
$548$		0			0
$549$	23.1105	−	14.4574i	0.986330	−	0.617025i
$550$		0			0
$551$	14.2094	+	24.6115i	0.605342	+	1.04848i
$552$		0			0
$553$	−7.04711	+	12.2060i	−0.299674	+	0.519050i
$554$		0			0
$555$	0.870751	−	0.249923i	0.0369613	−	0.0106087i
$556$		0			0
$557$	14.6903			0.622450			0.311225	−	0.950336i	$-0.399261\pi$
$557$	14.6903			0.622450			0.311225	+	0.950336i	$0.399261\pi$
$558$		0			0
$559$	4.63414			0.196003
$560$		0			0
$561$	−13.3810	+	53.7264i	−0.564946	+	2.26833i
$562$		0			0
$563$	1.64857	−	2.85541i	0.0694790	−	0.120341i	−0.829193	−	0.558962i	$-0.811200\pi$
$563$	1.64857	−	2.85541i	0.0694790	−	0.120341i	0.898672	+	0.438621i	$0.144533\pi$
$564$		0			0
$565$	−1.34471	−	2.32911i	−0.0565724	−	0.0979862i
$566$		0			0
$567$	4.37367	+	6.47003i	0.183677	+	0.271716i
$568$		0			0
$569$	11.9943	+	20.7747i	0.502826	+	0.870920i	0.999995	+	0.00326613i	$0.00103964\pi$
$569$	11.9943	+	20.7747i	0.502826	+	0.870920i	−0.497169	+	0.867654i	$0.665627\pi$
$570$		0			0
$571$	−10.0403	+	17.3903i	−0.420174	+	0.727763i	−0.995956	−	0.0898400i	$-0.971364\pi$
$571$	−10.0403	+	17.3903i	−0.420174	+	0.727763i	0.575782	+	0.817603i	$0.304698\pi$
$572$		0			0
$573$	4.95347	−	19.8888i	0.206934	−	0.830868i
$574$		0			0
$575$	2.86774			0.119593
$576$		0			0
$577$	22.8622			0.951764			0.475882	−	0.879509i	$-0.342129\pi$
$577$	22.8622			0.951764			0.475882	+	0.879509i	$0.342129\pi$
$578$		0			0
$579$	3.03356	−	0.870695i	0.126071	−	0.0361848i
$580$		0			0
$581$	−2.79534	+	4.84168i	−0.115970	+	0.200867i
$582$		0			0
$583$	28.4204	+	49.2255i	1.17705	+	2.03871i
$584$		0			0
$585$	3.08366	−	1.92906i	0.127493	−	0.0797569i
$586$		0			0
$587$	12.9447	+	22.4208i	0.534284	+	0.925407i	0.999198	+	0.0400508i	$0.0127520\pi$
$587$	12.9447	+	22.4208i	0.534284	+	0.925407i	−0.464914	+	0.885356i	$0.653915\pi$
$588$		0			0
$589$	−5.69140	+	9.85779i	−0.234510	+	0.406183i
$590$		0			0
$591$	24.1518	+	23.3113i	0.993473	+	0.958897i
$592$		0			0
$593$	39.7887			1.63392			0.816962	−	0.576691i	$-0.195656\pi$
$593$	39.7887			1.63392			0.816962	+	0.576691i	$0.195656\pi$
$594$		0			0
$595$	6.78755			0.278263
$596$		0			0
$597$	8.34528	+	8.05484i	0.341549	+	0.329663i
$598$		0			0
$599$	13.9434	−	24.1507i	0.569712	−	0.986770i	−0.426882	−	0.904307i	$-0.640388\pi$
$599$	13.9434	−	24.1507i	0.569712	−	0.986770i	0.996594	−	0.0824629i	$-0.0262786\pi$
$600$		0			0
$601$	−13.5633	−	23.4924i	−0.553260	−	0.958275i	−0.998037	−	0.0626334i	$-0.980050\pi$
$601$	−13.5633	−	23.4924i	−0.553260	−	0.958275i	0.444776	−	0.895642i	$-0.353283\pi$
$602$		0			0
$603$	−8.95365	−	4.75490i	−0.364621	−	0.193635i
$604$		0			0
$605$	−2.85044	−	4.93711i	−0.115887	−	0.200722i
$606$		0			0
$607$	6.43085	−	11.1386i	0.261020	−	0.452100i	−0.705493	−	0.708717i	$-0.749274\pi$
$607$	6.43085	−	11.1386i	0.261020	−	0.452100i	0.966513	+	0.256616i	$0.0826077\pi$
$608$		0			0
$609$	−9.09993	+	2.61187i	−0.368748	+	0.105838i
$610$		0			0
$611$	−1.68622			−0.0682173
$612$		0			0
$613$	−29.2726			−1.18231			−0.591154	−	0.806558i	$-0.701328\pi$
$613$	−29.2726			−1.18231			−0.591154	+	0.806558i	$0.701328\pi$
$614$		0			0
$615$	−3.39951	+	13.6495i	−0.137081	+	0.550400i
$616$		0			0
$617$	−17.3865	+	30.1144i	−0.699956	+	1.21236i	0.268525	+	0.963273i	$0.413464\pi$
$617$	−17.3865	+	30.1144i	−0.699956	+	1.21236i	−0.968481	+	0.249087i	$0.919870\pi$
$618$		0			0
$619$	−17.7282	−	30.7062i	−0.712558	−	1.23419i	−0.963894	−	0.266287i	$-0.914203\pi$
$619$	−17.7282	−	30.7062i	−0.712558	−	1.23419i	0.251336	−	0.967900i	$-0.419130\pi$
$620$		0			0
$621$	−4.61553	−	14.1684i	−0.185215	−	0.568557i
$622$		0			0
$623$	4.42889	+	7.67107i	0.177440	+	0.307335i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	7.71773	−	30.9877i	0.308216	−	1.23753i
$628$		0			0
$629$	−4.09119			−0.163126
$630$		0			0
$631$	6.68942			0.266302			0.133151	−	0.991096i	$-0.457491\pi$
$631$	6.68942			0.266302			0.133151	+	0.991096i	$0.457491\pi$
$632$		0			0
$633$	−14.1894	+	4.07265i	−0.563979	+	0.161873i
$634$		0			0
$635$	10.7821	−	18.6751i	0.427873	−	0.741097i
$636$		0			0
$637$	3.78709	+	6.55944i	0.150050	+	0.259894i
$638$		0			0
$639$	0.341235	+	9.63129i	0.0134990	+	0.381008i
$640$		0			0
$641$	2.46889	+	4.27624i	0.0975151	+	0.168901i	0.910656	−	0.413166i	$-0.135577\pi$
$641$	2.46889	+	4.27624i	0.0975151	+	0.168901i	−0.813140	+	0.582068i	$0.802244\pi$
$642$		0			0
$643$	7.64406	−	13.2399i	0.301452	−	0.522130i	−0.675013	−	0.737806i	$-0.735862\pi$
$643$	7.64406	−	13.2399i	0.301452	−	0.522130i	0.976465	+	0.215675i	$0.0691953\pi$
$644$		0			0
$645$	4.76330	+	4.59753i	0.187555	+	0.181028i
$646$		0			0
$647$	−31.2304			−1.22779			−0.613897	−	0.789386i	$-0.710399\pi$
$647$	−31.2304			−1.22779			−0.613897	+	0.789386i	$0.710399\pi$
$648$		0			0
$649$	−28.0927			−1.10273
$650$		0			0
$651$	−2.72842	−	2.63346i	−0.106935	−	0.103213i
$652$		0			0
$653$	3.82516	−	6.62537i	0.149690	−	0.259271i	−0.781423	−	0.624002i	$-0.785506\pi$
$653$	3.82516	−	6.62537i	0.149690	−	0.259271i	0.931113	+	0.364731i	$0.118839\pi$
$654$		0			0
$655$	−9.24703	−	16.0163i	−0.361312	−	0.625810i
$656$		0			0
$657$	0.914546	+	25.8129i	0.0356798	+	1.00706i
$658$		0			0
$659$	−20.9775	−	36.3342i	−0.817169	−	1.41538i	−0.907760	−	0.419489i	$-0.862209\pi$
$659$	−20.9775	−	36.3342i	−0.817169	−	1.41538i	0.0905915	−	0.995888i	$-0.471124\pi$
$660$		0			0
$661$	−20.2991	+	35.1591i	−0.789544	+	1.36753i	0.136702	+	0.990612i	$0.456350\pi$
$661$	−20.2991	+	35.1591i	−0.789544	+	1.36753i	−0.926246	+	0.376918i	$0.876984\pi$
$662$		0			0
$663$	−15.7891	+	4.53181i	−0.613200	+	0.176001i
$664$		0			0
$665$	−3.91484			−0.151811
$666$		0			0
$667$	18.0642			0.699449
$668$		0			0
$669$	−4.54664	+	18.2554i	−0.175783	+	0.705793i
$670$		0			0
$671$	18.5671	−	32.1592i	0.716776	−	1.24149i
$672$		0			0
$673$	−7.43486	−	12.8775i	−0.286593	−	0.496393i	0.686402	−	0.727223i	$-0.259189\pi$
$673$	−7.43486	−	12.8775i	−0.286593	−	0.496393i	−0.972994	+	0.230830i	$0.925856\pi$
$674$		0			0
$675$	5.08343	+	1.07646i	0.195661	+	0.0414331i
$676$		0			0
$677$	5.61271	+	9.72150i	0.215714	+	0.373628i	0.953493	−	0.301414i	$-0.0974588\pi$
$677$	5.61271	+	9.72150i	0.215714	+	0.373628i	−0.737779	+	0.675042i	$0.764125\pi$
$678$		0			0
$679$	3.80505	−	6.59054i	0.146024	−	0.252922i
$680$		0			0
$681$	−7.82139	+	31.4039i	−0.299716	+	1.20340i
$682$		0			0
$683$	−6.60275			−0.252647			−0.126324	−	0.991989i	$-0.540318\pi$
$683$	−6.60275			−0.252647			−0.126324	+	0.991989i	$0.540318\pi$
$684$		0			0
$685$	9.72401			0.371535
$686$		0			0
$687$	−15.9769	+	4.58571i	−0.609558	+	0.174956i
$688$		0			0
$689$	−8.43184	+	14.6044i	−0.321228	+	0.556382i
$690$		0			0
$691$	−5.87423	−	10.1745i	−0.223466	−	0.387055i	0.732392	−	0.680883i	$-0.238404\pi$
$691$	−5.87423	−	10.1745i	−0.223466	−	0.387055i	−0.955858	+	0.293829i	$0.905071\pi$
$692$		0			0
$693$	9.39574	+	4.98968i	0.356914	+	0.189542i
$694$		0			0
$695$	8.04032	+	13.9262i	0.304987	+	0.528253i
$696$		0			0
$697$	31.7628	−	55.0148i	1.20310	−	2.08384i
$698$		0			0
$699$	−25.6485	−	24.7559i	−0.970116	−	0.936354i
$700$		0			0
$701$	−6.21396			−0.234698			−0.117349	−	0.993091i	$-0.537440\pi$
$701$	−6.21396			−0.234698			−0.117349	+	0.993091i	$0.537440\pi$
$702$		0			0
$703$	2.35967			0.0889965
$704$		0			0
$705$	−1.73322	−	1.67290i	−0.0652769	−	0.0630051i
$706$		0			0
$707$	−0.982506	+	1.70175i	−0.0369509	+	0.0640009i
$708$		0			0
$709$	6.49473	+	11.2492i	0.243915	+	0.422473i	0.961826	−	0.273662i	$-0.0882350\pi$
$709$	6.49473	+	11.2492i	0.243915	+	0.422473i	−0.717911	+	0.696135i	$0.754902\pi$
$710$		0			0
$711$	41.3102	−	25.8427i	1.54925	−	0.969176i
$712$		0			0
$713$	3.61769	+	6.26602i	0.135483	+	0.234664i
$714$		0			0
$715$	2.47743	−	4.29104i	0.0926508	−	0.160476i
$716$		0			0
$717$	−16.9153	+	4.85504i	−0.631714	+	0.181315i
$718$		0			0
$719$	15.4610			0.576598			0.288299	−	0.957540i	$-0.406910\pi$
$719$	15.4610			0.576598			0.288299	+	0.957540i	$0.406910\pi$
$720$		0			0
$721$	−13.3508			−0.497210
$722$		0			0
$723$	5.94924	−	23.8870i	0.221255	−	0.888366i
$724$		0			0
$725$	−3.14956	+	5.45520i	−0.116972	+	0.202601i
$726$		0			0
$727$	−6.42588	−	11.1299i	−0.238323	−	0.412787i	0.721910	−	0.691986i	$-0.243264\pi$
$727$	−6.42588	−	11.1299i	−0.238323	−	0.412787i	−0.960233	+	0.279200i	$0.909931\pi$
$728$		0			0
$729$	−2.86322	−	26.8478i	−0.106045	−	0.994361i
$730$		0			0
$731$	−14.9487	−	25.8919i	−0.552897	−	0.957645i
$732$		0			0
$733$	10.5636	−	18.2968i	0.390177	−	0.675807i	−0.602295	−	0.798273i	$-0.705747\pi$
$733$	10.5636	−	18.2968i	0.390177	−	0.675807i	0.992473	+	0.122467i	$0.0390804\pi$
$734$		0			0
$735$	−2.61497	+	10.4994i	−0.0964546	+	0.387278i
$736$		0			0
$737$	−13.8101			−0.508701
$738$		0			0
$739$	−18.8652			−0.693968			−0.346984	−	0.937871i	$-0.612794\pi$
$739$	−18.8652			−0.693968			−0.346984	+	0.937871i	$0.612794\pi$
$740$		0			0
$741$	9.10668	−	2.61380i	0.334542	−	0.0960204i
$742$		0			0
$743$	3.99751	−	6.92390i	0.146655	−	0.254013i	−0.783334	−	0.621600i	$-0.786483\pi$
$743$	3.99751	−	6.92390i	0.146655	−	0.254013i	0.929989	+	0.367587i	$0.119816\pi$
$744$		0			0
$745$	−7.92263	−	13.7224i	−0.290263	−	0.502750i
$746$		0			0
$747$	16.3863	−	10.2509i	0.599544	−	0.375061i
$748$		0			0
$749$	−6.22175	−	10.7764i	−0.227338	−	0.393761i
$750$		0			0
$751$	15.2390	−	26.3948i	0.556081	−	0.963160i	−0.441738	−	0.897144i	$-0.645638\pi$
$751$	15.2390	−	26.3948i	0.556081	−	0.963160i	0.997819	−	0.0660158i	$-0.0210288\pi$
$752$		0			0
$753$	−0.307864	−	0.297150i	−0.0112192	−	0.0108287i
$754$		0			0
$755$	−15.1213			−0.550319
$756$		0			0
$757$	−30.4318			−1.10606			−0.553032	−	0.833160i	$-0.686529\pi$
$757$	−30.4318			−1.10606			−0.553032	+	0.833160i	$0.686529\pi$
$758$		0			0
$759$	−14.6053	−	14.0970i	−0.530138	−	0.511688i
$760$		0			0
$761$	23.3575	−	40.4564i	0.846708	−	1.46654i	−0.0374210	−	0.999300i	$-0.511914\pi$
$761$	23.3575	−	40.4564i	0.846708	−	1.46654i	0.884129	−	0.467242i	$-0.154752\pi$
$762$		0			0
$763$	2.32171	+	4.02133i	0.0840517	+	0.145582i
$764$		0			0
$765$	−20.7252	−	11.0063i	−0.749322	−	0.397933i
$766$		0			0
$767$	−4.16731	−	7.21800i	−0.150473	−	0.260627i
$768$		0			0
$769$	−18.4947	+	32.0338i	−0.666937	+	1.15517i	0.311819	+	0.950141i	$0.399062\pi$
$769$	−18.4947	+	32.0338i	−0.666937	+	1.15517i	−0.978756	+	0.205027i	$0.934272\pi$
$770$		0			0
$771$	−8.09316	+	2.32290i	−0.291468	+	0.0836573i
$772$		0			0
$773$	−33.7485			−1.21385			−0.606924	−	0.794760i	$-0.707597\pi$
$773$	−33.7485			−1.21385			−0.606924	+	0.794760i	$0.707597\pi$
$774$		0			0
$775$	−2.52303			−0.0906298
$776$		0			0
$777$	−0.189978	+	0.762787i	−0.00681543	+	0.0273648i
$778$		0			0
$779$	−18.3198	+	31.7308i	−0.656374	+	1.13687i
$780$		0			0
$781$	6.56410	+	11.3694i	0.234882	+	0.406828i
$782$		0			0
$783$	32.0211	+	6.78077i	1.14434	+	0.242325i
$784$		0			0
$785$	−8.77655	−	15.2014i	−0.313249	−	0.542562i
$786$		0			0
$787$	20.9745	−	36.3289i	0.747661	−	1.29499i	−0.201280	−	0.979534i	$-0.564510\pi$
$787$	20.9745	−	36.3289i	0.747661	−	1.29499i	0.948941	−	0.315453i	$-0.102156\pi$
$788$		0			0
$789$	8.55264	−	34.3400i	0.304482	−	1.22253i
$790$		0			0
$791$	2.33371			0.0829770
$792$		0			0
$793$	11.0171			0.391229
$794$		0			0
$795$	−23.1558	+	6.64620i	−0.821253	+	0.235717i
$796$		0			0
$797$	−6.56666	+	11.3738i	−0.232603	+	0.402880i	−0.958573	−	0.284846i	$-0.908058\pi$
$797$	−6.56666	+	11.3738i	−0.232603	+	0.402880i	0.725970	+	0.687726i	$0.241391\pi$
$798$		0			0
$799$	5.43937	+	9.42127i	0.192431	+	0.333300i
$800$		0			0
$801$	−1.08432	−	30.6046i	−0.0383124	−	1.08136i
$802$		0			0
$803$	17.5925	+	30.4711i	0.620826	+	1.07530i
$804$		0			0
$805$	−1.24422	+	2.15505i	−0.0438529	+	0.0759555i
$806$		0			0
$807$	−31.7946	−	30.6881i	−1.11922	−	1.08027i
$808$		0			0
$809$	−26.0015			−0.914165			−0.457082	−	0.889424i	$-0.651106\pi$
$809$	−26.0015			−0.914165			−0.457082	+	0.889424i	$0.651106\pi$
$810$		0			0
$811$	14.9425			0.524702			0.262351	−	0.964973i	$-0.415502\pi$
$811$	14.9425			0.524702			0.262351	+	0.964973i	$0.415502\pi$
$812$		0			0
$813$	6.38231	+	6.16019i	0.223838	+	0.216047i
$814$		0			0
$815$	−3.42837	+	5.93810i	−0.120090	+	0.208003i
$816$		0			0
$817$	8.62192	+	14.9336i	0.301643	+	0.522461i
$818$		0			0
$819$	0.111755	+	3.15427i	0.00390504	+	0.110219i
$820$		0			0
$821$	10.8310	+	18.7598i	0.378004	+	0.654722i	0.990772	−	0.135541i	$-0.0432772\pi$
$821$	10.8310	+	18.7598i	0.378004	+	0.654722i	−0.612768	+	0.790263i	$0.709944\pi$
$822$		0			0
$823$	−19.9770	+	34.6012i	−0.696355	+	1.20612i	0.273367	+	0.961910i	$0.411863\pi$
$823$	−19.9770	+	34.6012i	−0.696355	+	1.20612i	−0.969722	+	0.244212i	$0.921471\pi$
$824$		0			0
$825$	6.80362	−	1.95278i	0.236872	−	0.0679871i
$826$		0			0
$827$	−7.04711			−0.245052			−0.122526	−	0.992465i	$-0.539099\pi$
$827$	−7.04711			−0.245052			−0.122526	+	0.992465i	$0.539099\pi$
$828$		0			0
$829$	−7.21376			−0.250544			−0.125272	−	0.992122i	$-0.539980\pi$
$829$	−7.21376			−0.250544			−0.125272	+	0.992122i	$0.539980\pi$
$830$		0			0
$831$	4.77562	−	19.1747i	0.165664	−	0.665164i
$832$		0			0
$833$	24.4326	−	42.3185i	0.846539	−	1.46625i
$834$		0			0
$835$	−1.95991	−	3.39466i	−0.0678255	−	0.117477i
$836$		0			0
$837$	4.06073	+	12.4653i	0.140359	+	0.430863i
$838$		0			0
$839$	−1.16338	−	2.01503i	−0.0401643	−	0.0695666i	0.845244	−	0.534380i	$-0.179455\pi$
$839$	−1.16338	−	2.01503i	−0.0401643	−	0.0695666i	−0.885409	+	0.464813i	$0.846121\pi$
$840$		0			0
$841$	−5.33944	+	9.24818i	−0.184119	+	0.318903i
$842$		0			0
$843$	9.03900	−	36.2927i	0.311320	−	1.24999i
$844$		0			0
$845$	−11.5300			−0.396643
$846$		0			0
$847$	4.94686			0.169976
$848$		0			0
$849$	−33.1747	+	9.52183i	−1.13855	+	0.326788i
$850$		0			0
$851$	0.749950	−	1.29895i	0.0257080	−	0.0445275i
$852$		0			0
$853$	18.3713	+	31.8200i	0.629022	+	1.08950i	0.987748	+	0.156055i	$0.0498777\pi$
$853$	18.3713	+	31.8200i	0.629022	+	1.08950i	−0.358727	+	0.933443i	$0.616789\pi$
$854$		0			0
$855$	11.9536	+	6.34807i	0.408806	+	0.217100i
$856$		0			0
$857$	−4.45732	−	7.72031i	−0.152259	−	0.263721i	0.779798	−	0.626031i	$-0.215322\pi$
$857$	−4.45732	−	7.72031i	−0.152259	−	0.263721i	−0.932058	+	0.362310i	$0.881988\pi$
$858$		0			0
$859$	−19.4817	+	33.7432i	−0.664706	+	1.15130i	0.314659	+	0.949205i	$0.398110\pi$
$859$	−19.4817	+	33.7432i	−0.664706	+	1.15130i	−0.979365	+	0.202100i	$0.935224\pi$
$860$		0			0
$861$	−8.78238	−	8.47673i	−0.299303	−	0.288886i
$862$		0			0
$863$	−15.2084			−0.517700			−0.258850	−	0.965918i	$-0.583343\pi$
$863$	−15.2084			−0.517700			−0.258850	+	0.965918i	$0.583343\pi$
$864$		0			0
$865$	−8.17334			−0.277902
$866$		0			0
$867$	55.0662	+	53.1498i	1.87015	+	1.80506i
$868$		0			0
$869$	33.1889	−	57.4849i	1.12586	−	1.95004i
$870$		0			0
$871$	−2.04861	−	3.54829i	−0.0694144	−	0.120229i
$872$		0			0
$873$	−22.3052	+	13.9536i	−0.754917	+	0.472258i
$874$		0			0
$875$	−0.433868	−	0.751481i	−0.0146674	−	0.0254047i
$876$		0			0
$877$	5.21592	−	9.03424i	0.176129	−	0.305065i	−0.764422	−	0.644716i	$-0.776976\pi$
$877$	5.21592	−	9.03424i	0.176129	−	0.305065i	0.940551	+	0.339651i	$0.110309\pi$
$878$		0			0
$879$	−3.05265	+	0.876173i	−0.102963	+	0.0295526i
$880$		0			0
$881$	22.9272			0.772438			0.386219	−	0.922407i	$-0.373781\pi$
$881$	22.9272			0.772438			0.386219	+	0.922407i	$0.373781\pi$
$882$		0			0
$883$	10.9773			0.369417			0.184708	−	0.982793i	$-0.440866\pi$
$883$	10.9773			0.369417			0.184708	+	0.982793i	$0.440866\pi$
$884$		0			0
$885$	2.87751	−	11.5536i	0.0967264	−	0.388369i
$886$		0			0
$887$	6.48496	−	11.2323i	0.217744	−	0.377143i	−0.736374	−	0.676575i	$-0.763464\pi$
$887$	6.48496	−	11.2323i	0.217744	−	0.377143i	0.954118	+	0.299431i	$0.0967970\pi$
$888$		0			0
$889$	9.35597	+	16.2050i	0.313789	+	0.543499i
$890$		0			0
$891$	−20.5981	−	30.4711i	−0.690063	−	1.02082i
$892$		0			0
$893$	−3.13726	−	5.43389i	−0.104984	−	0.181838i
$894$		0			0
$895$	3.42837	−	5.93810i	0.114598	−	0.198489i
$896$		0			0
$897$	1.45544	−	5.84378i	0.0485957	−	0.195118i
$898$		0			0
$899$	−15.8928			−0.530056
$900$		0			0
$901$	108.797			3.62454
$902$		0			0
$903$	−5.52160	+	1.58481i	−0.183747	+	0.0527393i
$904$		0			0
$905$	−8.14956	+	14.1154i	−0.270900	+	0.469213i
$906$		0			0
$907$	5.74173	+	9.94497i	0.190651	+	0.330217i	0.945466	−	0.325720i	$-0.105607\pi$
$907$	5.74173	+	9.94497i	0.190651	+	0.330217i	−0.754815	+	0.655938i	$0.772273\pi$
$908$		0			0
$909$	5.75946	−	3.60298i	0.191029	−	0.119503i
$910$		0			0
$911$	7.64383	+	13.2395i	0.253251	+	0.438644i	0.964419	−	0.264378i	$-0.0851667\pi$
$911$	7.64383	+	13.2395i	0.253251	+	0.438644i	−0.711168	+	0.703022i	$0.751833\pi$
$912$		0			0
$913$	13.1649	−	22.8023i	0.435694	−	0.754645i
$914$		0			0
$915$	11.3242	+	10.9301i	0.374365	+	0.361336i
$916$		0			0
$917$	16.0480			0.529951
$918$		0			0
$919$	−43.5890			−1.43787			−0.718934	−	0.695078i	$-0.755370\pi$
$919$	−43.5890			−1.43787			−0.718934	+	0.695078i	$0.755370\pi$
$920$		0			0
$921$	11.2531	+	10.8614i	0.370801	+	0.357896i
$922$		0			0
$923$	−1.94746	+	3.37310i	−0.0641014	+	0.111027i
$924$		0			0
$925$	0.261513	+	0.452954i	0.00859850	+	0.0148930i
$926$		0			0
$927$	40.7655	+	21.6488i	1.33892	+	0.711041i
$928$		0			0
$929$	−0.741502	−	1.28432i	−0.0243279	−	0.0421371i	0.853605	−	0.520921i	$-0.174411\pi$
$929$	−0.741502	−	1.28432i	−0.0243279	−	0.0421371i	−0.877933	+	0.478783i	$0.841078\pi$
$930$		0			0
$931$	−14.0919	+	24.4080i	−0.461845	+	0.799939i
$932$		0			0
$933$	−4.92940	+	1.41484i	−0.161381	+	0.0463197i
$934$		0			0
$935$	−31.9665			−1.04542
$936$		0			0
$937$	5.12821			0.167531			0.0837657	−	0.996485i	$-0.473305\pi$
$937$	5.12821			0.167531			0.0837657	+	0.996485i	$0.473305\pi$
$938$		0			0
$939$	8.07180	−	32.4093i	0.263413	−	1.05764i
$940$		0			0
$941$	−23.4381	+	40.5960i	−0.764061	+	1.32339i	0.176680	+	0.984268i	$0.443464\pi$
$941$	−23.4381	+	40.5960i	−0.764061	+	1.32339i	−0.940741	+	0.339125i	$0.889869\pi$
$942$		0			0
$943$	11.6448	+	20.1694i	0.379207	+	0.656806i
$944$		0			0
$945$	−3.01448	+	3.35306i	−0.0980610	+	0.109075i
$946$		0			0
$947$	−17.1850	−	29.7654i	−0.558439	−	0.967244i	−0.997627	−	0.0688491i	$-0.978067\pi$
$947$	−17.1850	−	29.7654i	−0.558439	−	0.967244i	0.439188	−	0.898395i	$-0.355266\pi$
$948$		0			0
$949$	−5.21940	+	9.04026i	−0.169429	+	0.293459i
$950$		0			0
$951$	−2.58160	+	10.3655i	−0.0837141	+	0.336123i
$952$		0			0
$953$	−23.8092			−0.771254			−0.385627	−	0.922655i	$-0.626015\pi$
$953$	−23.8092			−0.771254			−0.385627	+	0.922655i	$0.626015\pi$
$954$		0			0
$955$	11.8336			0.382927
$956$		0			0
$957$	42.8568	−	12.3008i	1.38536	−	0.397628i
$958$		0			0
$959$	−4.21894	+	7.30741i	−0.136237	+	0.235969i
$960$		0			0
$961$	12.3172	+	21.3340i	0.397328	+	0.688192i
$962$		0			0
$963$	1.52326	+	42.9936i	0.0490862	+	1.38545i
$964$		0			0
$965$	0.911072	+	1.57802i	0.0293284	+	0.0507983i
$966$		0			0
$967$	−1.42889	+	2.47492i	−0.0459501	+	0.0795880i	−0.888086	−	0.459678i	$-0.847965\pi$
$967$	−1.42889	+	2.47492i	−0.0459501	+	0.0795880i	0.842136	+	0.539266i	$0.181298\pi$
$968$		0			0
$969$	−43.9799	−	42.4493i	−1.41284	−	1.36367i
$970$		0			0
$971$	3.55821			0.114188			0.0570942	−	0.998369i	$-0.481816\pi$
$971$	3.55821			0.114188			0.0570942	+	0.998369i	$0.481816\pi$
$972$		0			0
$973$	−13.9537			−0.447337
$974$		0			0
$975$	1.51100	+	1.45841i	0.0483906	+	0.0467065i
$976$		0			0
$977$	−14.8480	+	25.7175i	−0.475029	+	0.822775i	−0.999591	−	0.0285977i	$-0.990896\pi$
$977$	−14.8480	+	25.7175i	−0.475029	+	0.822775i	0.524562	+	0.851372i	$0.324229\pi$
$978$		0			0
$979$	−20.8582	−	36.1275i	−0.666632	−	1.15464i
$980$		0			0
$981$	−0.568419	−	16.0435i	−0.0181482	−	0.512231i
$982$		0			0
$983$	29.0557	+	50.3259i	0.926732	+	1.60515i	0.788751	+	0.614713i	$0.210728\pi$
$983$	29.0557	+	50.3259i	0.926732	+	1.60515i	0.137982	+	0.990435i	$0.455939\pi$
$984$		0			0
$985$	−9.68988	+	16.7834i	−0.308745	+	0.534762i
$986$		0			0
$987$	2.00914	−	0.576665i	0.0639517	−	0.0183555i
$988$		0			0
$989$	10.9609			0.348536
$990$		0			0
$991$	−19.4489			−0.617816			−0.308908	−	0.951092i	$-0.599963\pi$
$991$	−19.4489			−0.617816			−0.308908	+	0.951092i	$0.599963\pi$
$992$		0			0
$993$	8.66046	−	34.7729i	0.274831	−	1.10348i
$994$		0			0
$995$	−3.34818	+	5.79923i	−0.106145	+	0.183848i
$996$		0			0
$997$	4.25201	+	7.36469i	0.134662	+	0.233242i	0.925468	−	0.378825i	$-0.123672\pi$
$997$	4.25201	+	7.36469i	0.134662	+	0.233242i	−0.790806	+	0.612067i	$0.790338\pi$
$998$		0			0
$999$	1.81697	−	2.02105i	0.0574864	−	0.0639431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.e.121.4	✓	8
3.2	odd	2		1080.2.q.e.361.2		8
4.3	odd	2		720.2.q.l.481.1		8
9.2	odd	6		1080.2.q.e.721.2		8
9.4	even	3		3240.2.a.u.1.3		4
9.5	odd	6		3240.2.a.s.1.3		4
9.7	even	3	inner	360.2.q.e.241.4	yes	8
12.11	even	2		2160.2.q.l.1441.3		8
36.7	odd	6		720.2.q.l.241.1		8
36.11	even	6		2160.2.q.l.721.3		8
36.23	even	6		6480.2.a.bz.1.2		4
36.31	odd	6		6480.2.a.cb.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.e.121.4	✓	8	1.1	even	1	trivial
360.2.q.e.241.4	yes	8	9.7	even	3	inner
720.2.q.l.241.1		8	36.7	odd	6
720.2.q.l.481.1		8	4.3	odd	2
1080.2.q.e.361.2		8	3.2	odd	2
1080.2.q.e.721.2		8	9.2	odd	6
2160.2.q.l.721.3		8	36.11	even	6
2160.2.q.l.1441.3		8	12.11	even	2
3240.2.a.s.1.3		4	9.5	odd	6
3240.2.a.u.1.3		4	9.4	even	3
6480.2.a.bz.1.2		4	36.23	even	6
6480.2.a.cb.1.2		4	36.31	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24624 + 1.20287i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.433868 - 0.751481i) q^{7} +(0.106223 + 2.99812i) q^{9} +O(q^{10})\)	\(q+(1.24624 + 1.20287i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.433868 - 0.751481i) q^{7} +(0.106223 + 2.99812i) q^{9} +(2.04334 + 3.53916i) q^{11} +(-0.606223 + 1.05001i) q^{13} +(-1.66483 + 0.477841i) q^{15} +7.82214 q^{17} -4.51156 q^{19} +(0.363229 - 1.45841i) q^{21} +(-1.43387 + 2.48353i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.47396 + 3.86414i) q^{27} +(-3.14956 - 5.45520i) q^{29} +(1.26151 - 2.18500i) q^{31} +(-1.71066 + 6.86850i) q^{33} +0.867736 q^{35} -0.523026 q^{37} +(-2.01852 + 0.579356i) q^{39} +(4.06063 - 7.03322i) q^{41} +(-1.91107 - 3.31007i) q^{43} +(-2.64956 - 1.40707i) q^{45} +(0.695381 + 1.20444i) q^{47} +(3.12352 - 5.41009i) q^{49} +(9.74826 + 9.40900i) q^{51} +13.9088 q^{53} -4.08667 q^{55} +(-5.62248 - 5.42681i) q^{57} +(-3.43711 + 5.95325i) q^{59} +(-4.54334 - 7.86929i) q^{61} +(2.20694 - 1.38061i) q^{63} +(-0.606223 - 1.05001i) q^{65} +(-1.68965 + 2.92656i) q^{67} +(-4.77430 + 1.37032i) q^{69} +3.21245 q^{71} +8.60970 q^{73} +(0.418594 - 1.68071i) q^{75} +(1.77308 - 3.07106i) q^{77} +(-8.12126 - 14.0664i) q^{79} +(-8.97743 + 0.636937i) q^{81} +(-3.22142 - 5.57967i) q^{83} +(-3.91107 + 6.77417i) q^{85} +(2.63677 - 10.5870i) q^{87} -10.2079 q^{89} +1.05208 q^{91} +(4.20042 - 1.20561i) q^{93} +(2.25578 - 3.90713i) q^{95} +(4.38503 + 7.59510i) q^{97} +(-10.3938 + 6.50210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + q^7	\( 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Introduction

L-functions

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