LMFDB - Embedded newform 720.2.q.i.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (of order $3$, degree $2$, not 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.1
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.i.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25707 + 1.19154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +(0.160442 - 2.99571i) q^{9} +O(q^{10})$	\(q+(-1.25707 + 1.19154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +(0.160442 - 2.99571i) q^{9} +(-1.66044 - 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +(-0.403374 - 1.68443i) q^{15} -3.32088 q^{17} +1.32088 q^{19} +(0.853695 + 0.253408i) q^{21} +(2.06382 - 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.36783 + 3.95698i) q^{27} +(0.693252 + 1.20075i) q^{29} +(4.36783 - 7.56531i) q^{31} +(5.51414 + 1.63680i) q^{33} +0.514137 q^{35} +0.292611 q^{37} +(0.532810 + 2.22493i) q^{39} +(5.67458 - 9.82866i) q^{41} +(5.17458 + 8.96263i) q^{43} +(2.51414 + 1.63680i) q^{45} +(-2.43165 - 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(4.17458 - 3.95698i) q^{51} -5.02827 q^{53} +3.32088 q^{55} +(-1.66044 + 1.57389i) q^{57} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} +(-1.37510 + 0.698664i) q^{63} +(0.660442 + 1.14392i) q^{65} +(4.72426 - 8.18266i) q^{67} +(1.66498 + 6.95269i) q^{69} -8.99093 q^{71} +6.05655 q^{73} +(1.66044 + 0.492881i) q^{75} +(-0.853695 + 1.47864i) q^{77} +(-4.02827 - 6.97717i) q^{79} +(-8.94852 - 0.961276i) q^{81} +(0.771205 + 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +(-2.30221 - 0.683382i) q^{87} -3.00000 q^{89} -0.679116 q^{91} +(3.52374 + 14.7146i) q^{93} +(-0.660442 + 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +(-8.88197 + 4.51277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 - 2 * q^11 - 4 * q^13 - q^15 - 4 * q^17 - 8 * q^19 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 8 * q^31 + 20 * q^33 - 10 * q^35 + 12 * q^37 + 14 * q^39 + 13 * q^41 + 10 * q^43 + 2 * q^45 + 13 * q^47 + 2 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^55 - 2 * q^57 - 2 * q^59 - q^61 - 33 * q^63 - 4 * q^65 + 11 * q^67 + 39 * q^69 + 20 * q^71 - 16 * q^73 + 2 * q^75 + 2 * q^79 - 19 * q^81 - 15 * q^83 + 2 * q^85 + 26 * q^87 - 18 * q^89 - 20 * q^91 - 42 * q^93 + 4 * q^95 + 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.25707	+	1.19154i	−0.725769	+	0.687939i
$3$	−1.25707	+	1.19154i	−0.725769	+	0.687939i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.257068	−	0.445256i	−0.0971627	−	0.168291i	0.813346	−	0.581780i	$-0.197643\pi$
$7$	−0.257068	−	0.445256i	−0.0971627	−	0.168291i	−0.910509	+	0.413489i	$0.864310\pi$
$8$		0			0
$9$	0.160442	−	2.99571i	0.0534807	−	0.998569i
$10$		0			0
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	−1.00000		0.000741679i	$-0.999764\pi$
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	0.499358	−	0.866396i	$-0.333569\pi$
$12$		0			0
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	−0.759786	−	0.650173i	$-0.774696\pi$
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	0.942960	+	0.332907i	$0.108030\pi$
$14$		0			0
$15$	−0.403374	−	1.68443i	−0.104151	−	0.434917i
$16$		0			0
$17$	−3.32088			−0.805433			−0.402716	−	0.915325i	$-0.631934\pi$
$17$	−3.32088			−0.805433			−0.402716	+	0.915325i	$0.631934\pi$
$18$		0			0
$19$	1.32088			0.303032			0.151516	−	0.988455i	$-0.451585\pi$
$19$	1.32088			0.303032			0.151516	+	0.988455i	$0.451585\pi$
$20$		0			0
$21$	0.853695	+	0.253408i	0.186291	+	0.0552982i
$22$		0			0
$23$	2.06382	−	3.57463i	0.430335	−	0.745363i	−0.566567	−	0.824016i	$-0.691729\pi$
$23$	2.06382	−	3.57463i	0.430335	−	0.745363i	0.996902	+	0.0786532i	$0.0250620\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	3.36783	+	3.95698i	0.648139	+	0.761522i
$28$		0			0
$29$	0.693252	+	1.20075i	0.128734	+	0.222973i	0.923186	−	0.384353i	$-0.125575\pi$
$29$	0.693252	+	1.20075i	0.128734	+	0.222973i	−0.794453	+	0.607326i	$0.792242\pi$
$30$		0			0
$31$	4.36783	−	7.56531i	0.784486	−	1.35877i	−0.144820	−	0.989458i	$-0.546260\pi$
$31$	4.36783	−	7.56531i	0.784486	−	1.35877i	0.929306	−	0.369311i	$-0.120406\pi$
$32$		0			0
$33$	5.51414	+	1.63680i	0.959888	+	0.284930i
$34$		0			0
$35$	0.514137			0.0869050
$36$		0			0
$37$	0.292611			0.0481049			0.0240524	−	0.999711i	$-0.492343\pi$
$37$	0.292611			0.0481049			0.0240524	+	0.999711i	$0.492343\pi$
$38$		0			0
$39$	0.532810	+	2.22493i	0.0853179	+	0.356274i
$40$		0			0
$41$	5.67458	−	9.82866i	0.886220	−	1.53498i	0.0419119	−	0.999121i	$-0.486655\pi$
$41$	5.67458	−	9.82866i	0.886220	−	1.53498i	0.844308	−	0.535857i	$-0.180012\pi$
$42$		0			0
$43$	5.17458	+	8.96263i	0.789116	+	1.36679i	0.926509	+	0.376272i	$0.122794\pi$
$43$	5.17458	+	8.96263i	0.789116	+	1.36679i	−0.137393	+	0.990517i	$0.543872\pi$
$44$		0			0
$45$	2.51414	+	1.63680i	0.374785	+	0.244000i
$46$		0			0
$47$	−2.43165	−	4.21174i	−0.354692	−	0.614345i	0.632373	−	0.774664i	$-0.282081\pi$
$47$	−2.43165	−	4.21174i	−0.354692	−	0.614345i	−0.987065	+	0.160319i	$0.948748\pi$
$48$		0			0
$49$	3.36783	−	5.83326i	0.481119	−	0.833322i
$50$		0			0
$51$	4.17458	−	3.95698i	0.584558	−	0.554088i
$52$		0			0
$53$	−5.02827			−0.690687			−0.345343	−	0.938476i	$-0.612238\pi$
$53$	−5.02827			−0.690687			−0.345343	+	0.938476i	$0.612238\pi$
$54$		0			0
$55$	3.32088			0.447788
$56$		0			0
$57$	−1.66044	+	1.57389i	−0.219931	+	0.208467i
$58$		0			0
$59$	−2.51414	+	4.35461i	−0.327313	+	0.566922i	−0.981978	−	0.188997i	$-0.939476\pi$
$59$	−2.51414	+	4.35461i	−0.327313	+	0.566922i	0.654665	+	0.755919i	$0.272810\pi$
$60$		0			0
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	0.528948	−	0.848654i	$-0.322586\pi$
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	−0.999430	+	0.0337558i	$0.989253\pi$
$62$		0			0
$63$	−1.37510	+	0.698664i	−0.173246	+	0.0880234i
$64$		0			0
$65$	0.660442	+	1.14392i	0.0819178	+	0.141886i
$66$		0			0
$67$	4.72426	−	8.18266i	0.577160	−	0.999670i	−0.418643	−	0.908151i	$-0.637494\pi$
$67$	4.72426	−	8.18266i	0.577160	−	0.999670i	0.995803	−	0.0915197i	$-0.0291724\pi$
$68$		0			0
$69$	1.66498	+	6.95269i	0.200440	+	0.837005i
$70$		0			0
$71$	−8.99093			−1.06703			−0.533513	−	0.845792i	$-0.679129\pi$
$71$	−8.99093			−1.06703			−0.533513	+	0.845792i	$0.679129\pi$
$72$		0			0
$73$	6.05655			0.708865			0.354433	−	0.935082i	$-0.384674\pi$
$73$	6.05655			0.708865			0.354433	+	0.935082i	$0.384674\pi$
$74$		0			0
$75$	1.66044	+	0.492881i	0.191731	+	0.0569130i
$76$		0			0
$77$	−0.853695	+	1.47864i	−0.0972875	+	0.168507i
$78$		0			0
$79$	−4.02827	−	6.97717i	−0.453216	−	0.784994i	0.545367	−	0.838197i	$-0.316390\pi$
$79$	−4.02827	−	6.97717i	−0.453216	−	0.784994i	−0.998584	+	0.0532036i	$0.983057\pi$
$80$		0			0
$81$	−8.94852	−	0.961276i	−0.994280	−	0.106808i
$82$		0			0
$83$	0.771205	+	1.33577i	0.0846508	+	0.146619i	0.905242	−	0.424896i	$-0.139689\pi$
$83$	0.771205	+	1.33577i	0.0846508	+	0.146619i	−0.820592	+	0.571515i	$0.806356\pi$
$84$		0			0
$85$	1.66044	−	2.87597i	0.180100	−	0.311943i
$86$		0			0
$87$	−2.30221	−	0.683382i	−0.246823	−	0.0732662i
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−0.679116			−0.0711906
$92$		0			0
$93$	3.52374	+	14.7146i	0.365395	+	1.52583i
$94$		0			0
$95$	−0.660442	+	1.14392i	−0.0677599	+	0.117364i
$96$		0			0
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	0.989081	+	0.147370i	$0.0470808\pi$
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	−0.366915	+	0.930255i	$0.619586\pi$
$98$		0			0
$99$	−8.88197	+	4.51277i	−0.892671	+	0.453551i
$100$		0			0
$101$	−5.83502	−	10.1066i	−0.580606	−	1.00564i	−0.995408	−	0.0957276i	$-0.969482\pi$
$101$	−5.83502	−	10.1066i	−0.580606	−	1.00564i	0.414801	−	0.909912i	$-0.363851\pi$
$102$		0			0
$103$	0.146305	−	0.253408i	0.0144159	−	0.0249691i	−0.858727	−	0.512433i	$-0.828744\pi$
$103$	0.146305	−	0.253408i	0.0144159	−	0.0249691i	0.873143	+	0.487464i	$0.162078\pi$
$104$		0			0
$105$	−0.646305	+	0.612617i	−0.0630729	+	0.0597853i
$106$		0			0
$107$	−1.87237			−0.181009			−0.0905043	−	0.995896i	$-0.528848\pi$
$107$	−1.87237			−0.181009			−0.0905043	+	0.995896i	$0.528848\pi$
$108$		0			0
$109$	5.54787			0.531390			0.265695	−	0.964057i	$-0.414399\pi$
$109$	5.54787			0.531390			0.265695	+	0.964057i	$0.414399\pi$
$110$		0			0
$111$	−0.367832	+	0.348659i	−0.0349130	+	0.0330932i
$112$		0			0
$113$	−3.90064	+	6.75611i	−0.366942	+	0.635561i	−0.989086	−	0.147341i	$-0.952928\pi$
$113$	−3.90064	+	6.75611i	−0.366942	+	0.635561i	0.622144	+	0.782903i	$0.286262\pi$
$114$		0			0
$115$	2.06382	+	3.57463i	0.192452	+	0.333336i
$116$		0			0
$117$	−3.32088	−	2.16202i	−0.307016	−	0.199879i
$118$		0			0
$119$	0.853695	+	1.47864i	0.0782581	+	0.135547i
$120$		0			0
$121$	−0.0141369	+	0.0244859i	−0.00128518	+	0.00222599i
$122$		0			0
$123$	4.57795	+	19.1168i	0.412780	+	1.72370i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−17.8916			−1.58762			−0.793810	−	0.608166i	$-0.791906\pi$
$127$	−17.8916			−1.58762			−0.793810	+	0.608166i	$0.791906\pi$
$128$		0			0
$129$	−17.1842	−	5.10090i	−1.51298	−	0.449109i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−0.339558	−	0.588131i	−0.0294434	−	0.0509974i
$134$		0			0
$135$	−5.11076	+	0.938136i	−0.439864	+	0.0807419i
$136$		0			0
$137$	−2.83502	−	4.91040i	−0.242212	−	0.419524i	0.719132	−	0.694874i	$-0.244540\pi$
$137$	−2.83502	−	4.91040i	−0.242212	−	0.419524i	−0.961344	+	0.275350i	$0.911206\pi$
$138$		0			0
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		0			0
$141$	8.07522	+	2.39703i	0.680056	+	0.201866i
$142$		0			0
$143$	−4.38650			−0.366818
$144$		0			0
$145$	−1.38650			−0.115143
$146$		0			0
$147$	2.71699	+	11.3457i	0.224094	+	0.935780i
$148$		0			0
$149$	−8.83049	+	15.2948i	−0.723422	+	1.25300i	0.236199	+	0.971705i	$0.424098\pi$
$149$	−8.83049	+	15.2948i	−0.723422	+	1.25300i	−0.959620	+	0.281298i	$0.909235\pi$
$150$		0			0
$151$	0.632168	+	1.09495i	0.0514451	+	0.0891056i	0.890601	−	0.454785i	$-0.150284\pi$
$151$	0.632168	+	1.09495i	0.0514451	+	0.0891056i	−0.839156	+	0.543891i	$0.816951\pi$
$152$		0			0
$153$	−0.532810	+	9.94840i	−0.0430752	+	0.804280i
$154$		0			0
$155$	4.36783	+	7.56531i	0.350833	+	0.607660i
$156$		0			0
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	−0.363179	−	0.931719i	$-0.618309\pi$
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	0.988482	−	0.151337i	$-0.0483579\pi$
$158$		0			0
$159$	6.32088	−	5.99141i	0.501279	−	0.475150i
$160$		0			0
$161$	−2.12217			−0.167250
$162$		0			0
$163$	−15.7074			−1.23030			−0.615149	−	0.788411i	$-0.710904\pi$
$163$	−15.7074			−1.23030			−0.615149	+	0.788411i	$0.710904\pi$
$164$		0			0
$165$	−4.17458	+	3.95698i	−0.324991	+	0.308051i
$166$		0			0
$167$	3.08249	−	5.33903i	0.238530	−	0.413146i	−0.721763	−	0.692141i	$-0.756668\pi$
$167$	3.08249	−	5.33903i	0.238530	−	0.413146i	0.960293	+	0.278994i	$0.0900011\pi$
$168$		0			0
$169$	5.62763	+	9.74734i	0.432895	+	0.749796i
$170$		0			0
$171$	0.211926	−	3.95698i	0.0162064	−	0.302598i
$172$		0			0
$173$	−4.29261	−	7.43502i	−0.326361	−	0.565274i	0.655426	−	0.755260i	$-0.272489\pi$
$173$	−4.29261	−	7.43502i	−0.326361	−	0.565274i	−0.981787	+	0.189986i	$0.939156\pi$
$174$		0			0
$175$	−0.257068	+	0.445256i	−0.0194325	+	0.0336582i
$176$		0			0
$177$	−2.02827	−	8.46975i	−0.152454	−	0.636626i
$178$		0			0
$179$	1.06562			0.0796482			0.0398241	−	0.999207i	$-0.487320\pi$
$179$	1.06562			0.0796482			0.0398241	+	0.999207i	$0.487320\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$		0			0
$183$	12.2029	+	3.62226i	0.902061	+	0.267765i
$184$		0			0
$185$	−0.146305	+	0.253408i	−0.0107566	+	0.0186309i
$186$		0			0
$187$	5.51414	+	9.55077i	0.403234	+	0.698421i
$188$		0			0
$189$	0.896105	−	2.51676i	0.0651821	−	0.183067i
$190$		0			0
$191$	−8.46719	−	14.6656i	−0.612664	−	1.06117i	−0.990789	−	0.135411i	$-0.956764\pi$
$191$	−8.46719	−	14.6656i	−0.612664	−	1.06117i	0.378125	−	0.925754i	$-0.376569\pi$
$192$		0			0
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.243060	+	0.970011i	$0.578151\pi$
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.718524	+	0.695502i	$0.755182\pi$
$194$		0			0
$195$	−2.19325	−	0.651039i	−0.157062	−	0.0466218i
$196$		0			0
$197$	−14.2553			−1.01565			−0.507823	−	0.861462i	$-0.669550\pi$
$197$	−14.2553			−1.01565			−0.507823	+	0.861462i	$0.669550\pi$
$198$		0			0
$199$	24.6610			1.74817			0.874085	−	0.485773i	$-0.161462\pi$
$199$	24.6610			1.74817			0.874085	+	0.485773i	$0.161462\pi$
$200$		0			0
$201$	3.81128	+	15.9153i	0.268827	+	1.12258i
$202$		0			0
$203$	0.356427	−	0.617349i	0.0250162	−	0.0433294i
$204$		0			0
$205$	5.67458	+	9.82866i	0.396330	+	0.686463i
$206$		0			0
$207$	−10.3774	−	6.75611i	−0.721281	−	0.469582i
$208$		0			0
$209$	−2.19325	−	3.79882i	−0.151710	−	0.262770i
$210$		0			0
$211$	−2.68872	+	4.65699i	−0.185099	+	0.320601i	−0.943610	−	0.331060i	$-0.892594\pi$
$211$	−2.68872	+	4.65699i	−0.185099	+	0.320601i	0.758511	+	0.651660i	$0.225927\pi$
$212$		0			0
$213$	11.3022	−	10.7131i	0.774415	−	0.734049i
$214$		0			0
$215$	−10.3492			−0.705807
$216$		0			0
$217$	−4.49133			−0.304891
$218$		0			0
$219$	−7.61350	+	7.21665i	−0.514472	+	0.487656i
$220$		0			0
$221$	−2.19325	+	3.79882i	−0.147534	+	0.255537i
$222$		0			0
$223$	4.33229	+	7.50375i	0.290112	+	0.502488i	0.973836	−	0.227252i	$-0.0729743\pi$
$223$	4.33229	+	7.50375i	0.290112	+	0.502488i	−0.683724	+	0.729740i	$0.739641\pi$
$224$		0			0
$225$	−2.67458	+	1.35891i	−0.178305	+	0.0905938i
$226$		0			0
$227$	1.66044	+	2.87597i	0.110207	+	0.190885i	0.915854	−	0.401512i	$-0.131515\pi$
$227$	1.66044	+	2.87597i	0.110207	+	0.190885i	−0.805646	+	0.592397i	$0.798182\pi$
$228$		0			0
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	−0.0566206	−	0.998396i	$-0.518033\pi$
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	0.892946	−	0.450163i	$-0.148634\pi$
$230$		0			0
$231$	−0.688716	−	2.87597i	−0.0453142	−	0.189225i
$232$		0			0
$233$	27.6327			1.81028			0.905139	−	0.425116i	$-0.139767\pi$
$233$	27.6327			1.81028			0.905139	+	0.425116i	$0.139767\pi$
$234$		0			0
$235$	4.86330			0.317246
$236$		0			0
$237$	13.3774	+	3.97092i	0.868958	+	0.257939i
$238$		0			0
$239$	−2.09936	+	3.63620i	−0.135796	+	0.235206i	−0.925901	−	0.377765i	$-0.876693\pi$
$239$	−2.09936	+	3.63620i	−0.135796	+	0.235206i	0.790105	+	0.612971i	$0.210026\pi$
$240$		0			0
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	0.802125	−	0.597157i	$-0.203703\pi$
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	−0.918215	+	0.396082i	$0.870370\pi$
$242$		0			0
$243$	12.3943	−	9.45417i	0.795095	−	0.606485i
$244$		0			0
$245$	3.36783	+	5.83326i	0.215163	+	0.372673i
$246$		0			0
$247$	0.872368	−	1.51099i	0.0555074	−	0.0961417i
$248$		0			0
$249$	−2.56108	−	0.760225i	−0.162302	−	0.0481773i
$250$		0			0
$251$	6.87783			0.434125			0.217062	−	0.976158i	$-0.430352\pi$
$251$	6.87783			0.434125			0.217062	+	0.976158i	$0.430352\pi$
$252$		0			0
$253$	−13.7074			−0.861776
$254$		0			0
$255$	1.33956	+	5.59378i	0.0838864	+	0.350296i
$256$		0			0
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$	−0.0752210	−	0.130287i	−0.00467400	−	0.00809561i
$260$		0			0
$261$	3.70832	−	1.88413i	0.229539	−	0.116625i
$262$		0			0
$263$	3.11803	+	5.40059i	0.192266	+	0.333015i	0.946001	−	0.324164i	$-0.105083\pi$
$263$	3.11803	+	5.40059i	0.192266	+	0.333015i	−0.753735	+	0.657179i	$0.771750\pi$
$264$		0			0
$265$	2.51414	−	4.35461i	0.154442	−	0.267502i
$266$		0			0
$267$	3.77121	−	3.57463i	0.230794	−	0.218764i
$268$		0			0
$269$	9.92345			0.605044			0.302522	−	0.953142i	$-0.402172\pi$
$269$	9.92345			0.605044			0.302522	+	0.953142i	$0.402172\pi$
$270$		0			0
$271$	−6.60442			−0.401190			−0.200595	−	0.979674i	$-0.564288\pi$
$271$	−6.60442			−0.401190			−0.200595	+	0.979674i	$0.564288\pi$
$272$		0			0
$273$	0.853695	−	0.809197i	0.0516680	−	0.0489748i
$274$		0			0
$275$	−1.66044	+	2.87597i	−0.100128	+	0.173428i
$276$		0			0
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	−0.974742	−	0.223333i	$-0.928306\pi$
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	0.293959	−	0.955818i	$-0.405027\pi$
$278$		0			0
$279$	−21.9627	−	14.2985i	−1.31487	−	0.856031i
$280$		0			0
$281$	7.77394	+	13.4649i	0.463754	+	0.803246i	0.999144	−	0.0413590i	$-0.0131687\pi$
$281$	7.77394	+	13.4649i	0.463754	+	0.803246i	−0.535390	+	0.844605i	$0.679835\pi$
$282$		0			0
$283$	0.322689	−	0.558913i	0.0191819	−	0.0332240i	−0.856275	−	0.516520i	$-0.827227\pi$
$283$	0.322689	−	0.558913i	0.0191819	−	0.0332240i	0.875457	+	0.483296i	$0.160561\pi$
$284$		0			0
$285$	−0.532810	−	2.22493i	−0.0315610	−	0.131794i
$286$		0			0
$287$	−5.83502			−0.344430
$288$		0			0
$289$	−5.97173			−0.351278
$290$		0			0
$291$	−20.3492	−	6.04039i	−1.19289	−	0.354094i
$292$		0			0
$293$	0.688716	−	1.19289i	0.0402352	−	0.0696895i	−0.845207	−	0.534440i	$-0.820523\pi$
$293$	0.688716	−	1.19289i	0.0402352	−	0.0696895i	0.885442	+	0.464750i	$0.153856\pi$
$294$		0			0
$295$	−2.51414	−	4.35461i	−0.146379	−	0.253535i
$296$		0			0
$297$	5.78807	−	16.2561i	0.335858	−	0.943276i
$298$		0			0
$299$	−2.72606	−	4.72168i	−0.157652	−	0.273062i
$300$		0			0
$301$	2.66044	−	4.60802i	0.153345	−	0.265602i
$302$		0			0
$303$	19.3774	+	5.75194i	1.11320	+	0.330440i
$304$		0			0
$305$	7.34916			0.420812
$306$		0			0
$307$	7.98546			0.455754			0.227877	−	0.973690i	$-0.426822\pi$
$307$	7.98546			0.455754			0.227877	+	0.973690i	$0.426822\pi$
$308$		0			0
$309$	0.118031	+	0.492881i	0.00671458	+	0.0280390i
$310$		0			0
$311$	4.81635	−	8.34216i	0.273110	−	0.473040i	−0.696547	−	0.717512i	$-0.745281\pi$
$311$	4.81635	−	8.34216i	0.273110	−	0.473040i	0.969657	+	0.244471i	$0.0786143\pi$
$312$		0			0
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	0.970699	+	0.240300i	$0.0772458\pi$
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	−0.277244	+	0.960800i	$0.589421\pi$
$314$		0			0
$315$	0.0824893	−	1.54020i	0.00464774	−	0.0867806i
$316$		0			0
$317$	10.1746	+	17.6229i	0.571461	+	0.989800i	0.996416	+	0.0845855i	$0.0269566\pi$
$317$	10.1746	+	17.6229i	0.571461	+	0.989800i	−0.424955	+	0.905215i	$0.639710\pi$
$318$		0			0
$319$	2.30221	−	3.98755i	0.128899	−	0.223260i
$320$		0			0
$321$	2.35369	−	2.23101i	0.131370	−	0.124523i
$322$		0			0
$323$	−4.38650			−0.244072
$324$		0			0
$325$	−1.32088			−0.0732695
$326$		0			0
$327$	−6.97406	+	6.61054i	−0.385666	+	0.365564i
$328$		0			0
$329$	−1.25020	+	2.16541i	−0.0689257	+	0.119383i
$330$		0			0
$331$	8.22153	+	14.2401i	0.451896	+	0.782707i	0.998504	−	0.0546819i	$-0.0174145\pi$
$331$	8.22153	+	14.2401i	0.451896	+	0.782707i	−0.546608	+	0.837389i	$0.684081\pi$
$332$		0			0
$333$	0.0469471	−	0.876576i	0.00257269	−	0.0480360i
$334$		0			0
$335$	4.72426	+	8.18266i	0.258114	+	0.447066i
$336$		0			0
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	−0.924977	−	0.380023i	$-0.875916\pi$
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	0.791598	+	0.611042i	$0.209249\pi$
$338$		0			0
$339$	−3.14683	−	13.1407i	−0.170913	−	0.713704i
$340$		0			0
$341$	−29.0101			−1.57099
$342$		0			0
$343$	−7.06201			−0.381313
$344$		0			0
$345$	−6.85369	−	2.03443i	−0.368991	−	0.109530i
$346$		0			0
$347$	11.1372	−	19.2903i	0.597878	−	1.03556i	−0.395256	−	0.918571i	$-0.629344\pi$
$347$	11.1372	−	19.2903i	0.597878	−	1.03556i	0.993134	−	0.116984i	$-0.0373226\pi$
$348$		0			0
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	0.902724	−	0.430221i	$-0.141564\pi$
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	−0.823944	+	0.566671i	$0.808231\pi$
$350$		0			0
$351$	6.75073	−	1.23917i	0.360327	−	0.0661420i
$352$		0			0
$353$	−9.41478	−	16.3069i	−0.501098	−	0.867927i	−0.999999	−	0.00126845i	$-0.999596\pi$
$353$	−9.41478	−	16.3069i	−0.501098	−	0.867927i	0.498901	−	0.866659i	$-0.333737\pi$
$354$		0			0
$355$	4.49546	−	7.78637i	0.238594	−	0.413258i
$356$		0			0
$357$	−2.83502	−	0.841540i	−0.150045	−	0.0445390i
$358$		0			0
$359$	31.8770			1.68241			0.841203	−	0.540720i	$-0.181848\pi$
$359$	31.8770			1.68241			0.841203	+	0.540720i	$0.181848\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$		0			0
$363$	−0.0114049	−	0.0476252i	−0.000598604	−	0.00249968i
$364$		0			0
$365$	−3.02827	+	5.24512i	−0.158507	+	0.274542i
$366$		0			0
$367$	−9.17458	−	15.8908i	−0.478909	−	0.829495i	0.520798	−	0.853680i	$-0.325634\pi$
$367$	−9.17458	−	15.8908i	−0.478909	−	0.829495i	−0.999708	+	0.0241848i	$0.992301\pi$
$368$		0			0
$369$	−28.5333	−	18.5763i	−1.48539	−	0.967044i
$370$		0			0
$371$	1.29261	+	2.23887i	0.0671090	+	0.116236i
$372$		0			0
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	−0.836160	−	0.548486i	$-0.815205\pi$
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	0.893083	+	0.449893i	$0.148538\pi$
$374$		0			0
$375$	−1.25707	+	1.19154i	−0.0649147	+	0.0615311i
$376$		0			0
$377$	1.83141			0.0943226
$378$		0			0
$379$	−15.4713			−0.794709			−0.397354	−	0.917665i	$-0.630072\pi$
$379$	−15.4713			−0.794709			−0.397354	+	0.917665i	$0.630072\pi$
$380$		0			0
$381$	22.4909	−	21.3186i	1.15225	−	1.09219i
$382$		0			0
$383$	3.85369	−	6.67479i	0.196915	−	0.341066i	−0.750612	−	0.660743i	$-0.770241\pi$
$383$	3.85369	−	6.67479i	0.196915	−	0.341066i	0.947526	+	0.319677i	$0.103574\pi$
$384$		0			0
$385$	−0.853695	−	1.47864i	−0.0435083	−	0.0753586i
$386$		0			0
$387$	27.6796	−	14.0635i	1.40704	−	0.714890i
$388$		0			0
$389$	12.3163	+	21.3325i	0.624464	+	1.08160i	0.988644	+	0.150274i	$0.0480157\pi$
$389$	12.3163	+	21.3325i	0.624464	+	1.08160i	−0.364181	+	0.931328i	$0.618651\pi$
$390$		0			0
$391$	−6.85369	+	11.8709i	−0.346606	+	0.600340i
$392$		0			0
$393$	−2.42024	−	10.1066i	−0.122085	−	0.509808i
$394$		0			0
$395$	8.05655			0.405369
$396$		0			0
$397$	−6.77301			−0.339928			−0.169964	−	0.985450i	$-0.554365\pi$
$397$	−6.77301			−0.339928			−0.169964	+	0.985450i	$0.554365\pi$
$398$		0			0
$399$	1.12763	+	0.334723i	0.0564522	+	0.0167571i
$400$		0			0
$401$	9.24980	−	16.0211i	0.461913	−	0.800057i	−0.537143	−	0.843491i	$-0.680497\pi$
$401$	9.24980	−	16.0211i	0.461913	−	0.800057i	0.999056	+	0.0434343i	$0.0138299\pi$
$402$		0			0
$403$	−5.76940	−	9.99290i	−0.287394	−	0.497782i
$404$		0			0
$405$	5.30675	−	7.26900i	0.263694	−	0.361200i
$406$		0			0
$407$	−0.485863	−	0.841540i	−0.0240833	−	0.0417136i
$408$		0			0
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	−0.651178	−	0.758925i	$-0.725725\pi$
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	0.982837	+	0.184474i	$0.0590583\pi$
$410$		0			0
$411$	9.41478	+	2.79466i	0.464397	+	0.137850i
$412$		0			0
$413$	2.58522			0.127210
$414$		0			0
$415$	−1.54241			−0.0757140
$416$		0			0
$417$	3.22699	+	13.4754i	0.158026	+	0.659893i
$418$		0			0
$419$	−16.5575	+	28.6784i	−0.808886	+	1.40103i	0.104751	+	0.994499i	$0.466596\pi$
$419$	−16.5575	+	28.6784i	−0.808886	+	1.40103i	−0.913636	+	0.406532i	$0.866738\pi$
$420$		0			0
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	0.987656	−	0.156637i	$-0.0500654\pi$
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	−0.629480	+	0.777017i	$0.716732\pi$
$422$		0			0
$423$	−13.0073	+	6.60876i	−0.632435	+	0.321329i
$424$		0			0
$425$	1.66044	+	2.87597i	0.0805433	+	0.139505i
$426$		0			0
$427$	−1.88924	+	3.27225i	−0.0914266	+	0.158355i
$428$		0			0
$429$	5.51414	−	5.22672i	0.266225	−	0.252348i
$430$		0			0
$431$	32.7549			1.57775			0.788873	−	0.614556i	$-0.210665\pi$
$431$	32.7549			1.57775			0.788873	+	0.614556i	$0.210665\pi$
$432$		0			0
$433$	−11.8314			−0.568581			−0.284291	−	0.958738i	$-0.591758\pi$
$433$	−11.8314			−0.568581			−0.284291	+	0.958738i	$0.591758\pi$
$434$		0			0
$435$	1.74293	−	1.65208i	0.0835672	−	0.0792113i
$436$		0			0
$437$	2.72606	−	4.72168i	0.130405	−	0.225869i
$438$		0			0
$439$	4.15591	+	7.19824i	0.198351	+	0.343553i	0.947994	−	0.318289i	$-0.103108\pi$
$439$	4.15591	+	7.19824i	0.198351	+	0.343553i	−0.749643	+	0.661842i	$0.769775\pi$
$440$		0			0
$441$	−16.9344	−	11.0249i	−0.806399	−	0.524997i
$442$		0			0
$443$	−14.5876	−	25.2664i	−0.693076	−	1.20044i	−0.970825	−	0.239789i	$-0.922922\pi$
$443$	−14.5876	−	25.2664i	−0.693076	−	1.20044i	0.277750	−	0.960654i	$-0.410411\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$	−7.12397	−	29.7486i	−0.336952	−	1.40706i
$448$		0			0
$449$	18.9717			0.895331			0.447666	−	0.894201i	$-0.352256\pi$
$449$	18.9717			0.895331			0.447666	+	0.894201i	$0.352256\pi$
$450$		0			0
$451$	−37.6892			−1.77472
$452$		0			0
$453$	−2.09936	−	0.623167i	−0.0986365	−	0.0292790i
$454$		0			0
$455$	0.339558	−	0.588131i	0.0159187	−	0.0275720i
$456$		0			0
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	0.998703	+	0.0509206i	$0.0162155\pi$
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	−0.455253	+	0.890362i	$0.650451\pi$
$458$		0			0
$459$	−11.1842	−	13.1407i	−0.522033	−	0.613354i
$460$		0			0
$461$	−2.21285	−	3.83277i	−0.103063	−	0.178510i	0.809882	−	0.586592i	$-0.199531\pi$
$461$	−2.21285	−	3.83277i	−0.103063	−	0.178510i	−0.912945	+	0.408082i	$0.866198\pi$
$462$		0			0
$463$	−9.75434	+	16.8950i	−0.453322	+	0.785178i	−0.998590	−	0.0530845i	$-0.983095\pi$
$463$	−9.75434	+	16.8950i	−0.453322	+	0.785178i	0.545268	+	0.838262i	$0.316428\pi$
$464$		0			0
$465$	−14.5051	−	4.30564i	−0.672656	−	0.199669i
$466$		0			0
$467$	24.5935			1.13805			0.569026	−	0.822320i	$-0.307321\pi$
$467$	24.5935			1.13805			0.569026	+	0.822320i	$0.307321\pi$
$468$		0			0
$469$	−4.85783			−0.224314
$470$		0			0
$471$	6.32088	+	26.3950i	0.291251	+	1.21622i
$472$		0			0
$473$	17.1842	−	29.7639i	0.790129	−	1.36854i
$474$		0			0
$475$	−0.660442	−	1.14392i	−0.0303032	−	0.0524866i
$476$		0			0
$477$	−0.806748	+	15.0632i	−0.0369384	+	0.689698i
$478$		0			0
$479$	16.3774	+	28.3665i	0.748304	+	1.29610i	0.948635	+	0.316372i	$0.102465\pi$
$479$	16.3774	+	28.3665i	0.748304	+	1.29610i	−0.200331	+	0.979728i	$0.564202\pi$
$480$		0			0
$481$	0.193252	−	0.334723i	0.00881155	−	0.0152621i
$482$		0			0
$483$	2.66771	−	2.52866i	0.121385	−	0.115058i
$484$		0			0
$485$	−12.2553			−0.556483
$486$		0			0
$487$	6.03735			0.273578			0.136789	−	0.990600i	$-0.456322\pi$
$487$	6.03735			0.273578			0.136789	+	0.990600i	$0.456322\pi$
$488$		0			0
$489$	19.7453	−	18.7161i	0.892912	−	0.846369i
$490$		0			0
$491$	7.22153	−	12.5081i	0.325903	−	0.564480i	−0.655792	−	0.754942i	$-0.727665\pi$
$491$	7.22153	−	12.5081i	0.325903	−	0.564480i	0.981695	+	0.190461i	$0.0609984\pi$
$492$		0			0
$493$	−2.30221	−	3.98755i	−0.103686	−	0.179590i
$494$		0			0
$495$	0.532810	−	9.94840i	0.0239480	−	0.447147i
$496$		0			0
$497$	2.31128	+	4.00326i	0.103675	+	0.179571i
$498$		0			0
$499$	10.4859	−	18.1620i	0.469412	−	0.813045i	−0.529977	−	0.848012i	$-0.677799\pi$
$499$	10.4859	−	18.1620i	0.469412	−	0.813045i	0.999388	+	0.0349673i	$0.0111327\pi$
$500$		0			0
$501$	2.48679	+	10.3844i	0.111102	+	0.463943i
$502$		0			0
$503$	5.31728			0.237086			0.118543	−	0.992949i	$-0.462178\pi$
$503$	5.31728			0.237086			0.118543	+	0.992949i	$0.462178\pi$
$504$		0			0
$505$	11.6700			0.519310
$506$		0			0
$507$	−18.6887	−	5.54750i	−0.829995	−	0.246373i
$508$		0			0
$509$	−9.11350	+	15.7850i	−0.403949	+	0.699659i	−0.994198	−	0.107561i	$-0.965696\pi$
$509$	−9.11350	+	15.7850i	−0.403949	+	0.699659i	0.590250	+	0.807221i	$0.299029\pi$
$510$		0			0
$511$	−1.55695	−	2.69671i	−0.0688753	−	0.119296i
$512$		0			0
$513$	4.44852	+	5.22672i	0.196407	+	0.230765i
$514$		0			0
$515$	0.146305	+	0.253408i	0.00644698	+	0.0111665i
$516$		0			0
$517$	−8.07522	+	13.9867i	−0.355148	+	0.615134i
$518$		0			0
$519$	14.2553	+	4.23149i	0.625737	+	0.185742i
$520$		0			0
$521$	40.1232			1.75783			0.878915	−	0.476978i	$-0.158268\pi$
$521$	40.1232			1.75783			0.878915	+	0.476978i	$0.158268\pi$
$522$		0			0
$523$	−18.9873			−0.830257			−0.415129	−	0.909763i	$-0.636263\pi$
$523$	−18.9873			−0.830257			−0.415129	+	0.909763i	$0.636263\pi$
$524$		0			0
$525$	−0.207389	−	0.866025i	−0.00905121	−	0.0377964i
$526$		0			0
$527$	−14.5051	+	25.1235i	−0.631851	+	1.09440i
$528$		0			0
$529$	2.98133	+	5.16381i	0.129623	+	0.224513i
$530$		0			0
$531$	12.6418	+	8.23028i	0.548606	+	0.357164i
$532$		0			0
$533$	−7.49546	−	12.9825i	−0.324665	−	0.562336i
$534$		0			0
$535$	0.936184	−	1.62152i	0.0404748	−	0.0701043i
$536$		0			0
$537$	−1.33956	+	1.26973i	−0.0578062	+	0.0547931i
$538$		0			0
$539$	−22.3684			−0.963473
$540$		0			0
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$		0			0
$543$	15.9271	−	15.0969i	0.683498	−	0.647871i
$544$		0			0
$545$	−2.77394	+	4.80460i	−0.118822	+	0.205806i
$546$		0			0
$547$	8.83683	+	15.3058i	0.377835	+	0.654430i	0.990747	−	0.135721i	$-0.0433352\pi$
$547$	8.83683	+	15.3058i	0.377835	+	0.654430i	−0.612912	+	0.790151i	$0.710002\pi$
$548$		0			0
$549$	−19.6559	+	9.98682i	−0.838894	+	0.426227i
$550$		0			0
$551$	0.915706	+	1.58605i	0.0390104	+	0.0675680i
$552$		0			0
$553$	−2.07108	+	3.58722i	−0.0880715	+	0.152544i
$554$		0			0
$555$	−0.118031	−	0.492881i	−0.00501016	−	0.0209216i
$556$		0			0
$557$	17.3401			0.734723			0.367362	−	0.930078i	$-0.380261\pi$
$557$	17.3401			0.734723			0.367362	+	0.930078i	$0.380261\pi$
$558$		0			0
$559$	13.6700			0.578181
$560$		0			0
$561$	−18.3118	−	5.43563i	−0.773125	−	0.229492i
$562$		0			0
$563$	6.49727	−	11.2536i	0.273827	−	0.474283i	−0.696011	−	0.718031i	$-0.745044\pi$
$563$	6.49727	−	11.2536i	0.273827	−	0.474283i	0.969839	+	0.243748i	$0.0783770\pi$
$564$		0			0
$565$	−3.90064	−	6.75611i	−0.164101	−	0.284232i
$566$		0			0
$567$	1.87237	+	4.23149i	0.0786321	+	0.177706i
$568$		0			0
$569$	8.34009	+	14.4455i	0.349635	+	0.605585i	0.986184	−	0.165651i	$-0.0529724\pi$
$569$	8.34009	+	14.4455i	0.349635	+	0.605585i	−0.636550	+	0.771236i	$0.719639\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$	28.1186	+	8.34663i	1.17467	+	0.348686i
$574$		0			0
$575$	−4.12763			−0.172134
$576$		0			0
$577$	−23.5953			−0.982287			−0.491144	−	0.871079i	$-0.663421\pi$
$577$	−23.5953			−0.982287			−0.491144	+	0.871079i	$0.663421\pi$
$578$		0			0
$579$	−10.7771	−	45.0037i	−0.447883	−	1.87029i
$580$		0			0
$581$	0.396505	−	0.686767i	0.0164498	−	0.0284919i
$582$		0			0
$583$	8.34916	+	14.4612i	0.345787	+	0.598920i
$584$		0			0
$585$	3.53281	−	1.79496i	0.146064	−	0.0742124i
$586$		0			0
$587$	14.0638	+	24.3592i	0.580476	+	1.00541i	0.995423	+	0.0955681i	$0.0304668\pi$
$587$	14.0638	+	24.3592i	0.580476	+	1.00541i	−0.414947	+	0.909846i	$0.636200\pi$
$588$		0			0
$589$	5.76940	−	9.99290i	0.237724	−	0.411750i
$590$		0			0
$591$	17.9198	−	16.9858i	0.737124	−	0.698702i
$592$		0			0
$593$	−9.17872			−0.376925			−0.188462	−	0.982080i	$-0.560350\pi$
$593$	−9.17872			−0.376925			−0.188462	+	0.982080i	$0.560350\pi$
$594$		0			0
$595$	−1.70739			−0.0699961
$596$		0			0
$597$	−31.0005	+	29.3846i	−1.26877	+	1.20263i
$598$		0			0
$599$	−15.7357	+	27.2550i	−0.642942	+	1.11361i	0.341831	+	0.939761i	$0.388953\pi$
$599$	−15.7357	+	27.2550i	−0.642942	+	1.11361i	−0.984773	+	0.173846i	$0.944380\pi$
$600$		0			0
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	0.993279	+	0.115748i	$0.0369265\pi$
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	−0.396398	+	0.918079i	$0.629740\pi$
$602$		0			0
$603$	−23.7549	−	15.4653i	−0.967373	−	0.629797i
$604$		0			0
$605$	−0.0141369	−	0.0244859i	−0.000574748	−	0.000995493i
$606$		0			0
$607$	−22.1017	+	38.2813i	−0.897080	+	1.55379i	−0.0658708	+	0.997828i	$0.520983\pi$
$607$	−22.1017	+	38.2813i	−0.897080	+	1.55379i	−0.831209	+	0.555960i	$0.812351\pi$
$608$		0			0
$609$	0.287546	+	1.20075i	0.0116520	+	0.0486568i
$610$		0			0
$611$	−6.42385			−0.259881
$612$		0			0
$613$	−35.1715			−1.42056			−0.710282	−	0.703918i	$-0.751432\pi$
$613$	−35.1715			−1.42056			−0.710282	+	0.703918i	$0.751432\pi$
$614$		0			0
$615$	−18.8446	−	5.59378i	−0.759889	−	0.225563i
$616$		0			0
$617$	3.71285	−	6.43085i	0.149474	−	0.258896i	−0.781559	−	0.623831i	$-0.785575\pi$
$617$	3.71285	−	6.43085i	0.149474	−	0.258896i	0.931033	+	0.364935i	$0.118909\pi$
$618$		0			0
$619$	4.27394	+	7.40268i	0.171784	+	0.297539i	0.939044	−	0.343798i	$-0.111714\pi$
$619$	4.27394	+	7.40268i	0.171784	+	0.297539i	−0.767260	+	0.641337i	$0.778380\pi$
$620$		0			0
$621$	21.0953	−	3.87228i	0.846527	−	0.155389i
$622$		0			0
$623$	0.771205	+	1.33577i	0.0308977	+	0.0535164i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	7.28354	+	2.16202i	0.290876	+	0.0863429i
$628$		0			0
$629$	−0.971726			−0.0387453
$630$		0			0
$631$	2.36836			0.0942829			0.0471415	−	0.998888i	$-0.484989\pi$
$631$	2.36836			0.0942829			0.0471415	+	0.998888i	$0.484989\pi$
$632$		0			0
$633$	−2.16912	−	9.05788i	−0.0862146	−	0.360019i
$634$		0			0
$635$	8.94578	−	15.4946i	0.355003	−	0.614883i
$636$		0			0
$637$	−4.44852	−	7.70506i	−0.176257	−	0.305285i
$638$		0			0
$639$	−1.44252	+	26.9342i	−0.0570654	+	1.06550i
$640$		0			0
$641$	0.0665480	+	0.115265i	0.00262849	+	0.00455268i	0.867337	−	0.497722i	$-0.165830\pi$
$641$	0.0665480	+	0.115265i	0.00262849	+	0.00455268i	−0.864708	+	0.502275i	$0.832497\pi$
$642$		0			0
$643$	−11.3232	+	19.6124i	−0.446544	+	0.773437i	−0.998158	−	0.0606623i	$-0.980679\pi$
$643$	−11.3232	+	19.6124i	−0.446544	+	0.773437i	0.551614	+	0.834099i	$0.314012\pi$
$644$		0			0
$645$	13.0096	−	12.3315i	0.512253	−	0.485552i
$646$		0			0
$647$	−46.3912			−1.82383			−0.911913	−	0.410385i	$-0.865394\pi$
$647$	−46.3912			−1.82383			−0.911913	+	0.410385i	$0.865394\pi$
$648$		0			0
$649$	16.6983			0.655466
$650$		0			0
$651$	5.64591	−	5.35162i	0.221280	−	0.209746i
$652$		0			0
$653$	−18.2029	+	31.5283i	−0.712333	+	1.23380i	0.251647	+	0.967819i	$0.419028\pi$
$653$	−18.2029	+	31.5283i	−0.712333	+	1.23380i	−0.963979	+	0.265977i	$0.914305\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$		0			0
$657$	0.971726	−	18.1436i	0.0379106	−	0.707851i
$658$		0			0
$659$	9.57068	+	16.5769i	0.372821	+	0.645745i	0.989998	−	0.141079i	$-0.0450572\pi$
$659$	9.57068	+	16.5769i	0.372821	+	0.645745i	−0.617177	+	0.786824i	$0.711724\pi$
$660$		0			0
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	0.158067	+	0.987428i	$0.449474\pi$
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	−0.934172	+	0.356824i	$0.883860\pi$
$662$		0			0
$663$	−1.76940	−	7.38874i	−0.0687178	−	0.286955i
$664$		0			0
$665$	0.679116			0.0263350
$666$		0			0
$667$	5.72298			0.221595
$668$		0			0
$669$	−14.3870	−	4.27061i	−0.556235	−	0.165111i
$670$		0			0
$671$	−12.2029	+	21.1360i	−0.471086	+	0.815945i
$672$		0			0
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	0.542899	−	0.839798i	$-0.317326\pi$
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	−0.998736	+	0.0502658i	$0.983993\pi$
$674$		0			0
$675$	1.74293	−	4.89512i	0.0670855	−	0.188413i
$676$		0			0
$677$	7.40157	+	12.8199i	0.284465	+	0.492709i	0.972479	−	0.232989i	$-0.0748506\pi$
$677$	7.40157	+	12.8199i	0.284465	+	0.492709i	−0.688014	+	0.725697i	$0.741517\pi$
$678$		0			0
$679$	3.15044	−	5.45673i	0.120903	−	0.209410i
$680$		0			0
$681$	−5.51414	−	1.63680i	−0.211302	−	0.0627223i
$682$		0			0
$683$	4.95252			0.189503			0.0947515	−	0.995501i	$-0.469794\pi$
$683$	4.95252			0.189503			0.0947515	+	0.995501i	$0.469794\pi$
$684$		0			0
$685$	5.67004			0.216641
$686$		0			0
$687$	10.2101	+	42.6359i	0.389540	+	1.62666i
$688$		0			0
$689$	−3.32088	+	5.75194i	−0.126516	+	0.219131i
$690$		0			0
$691$	−9.60442	−	16.6353i	−0.365369	−	0.632838i	0.623466	−	0.781851i	$-0.285724\pi$
$691$	−9.60442	−	16.6353i	−0.365369	−	0.632838i	−0.988835	+	0.149012i	$0.952391\pi$
$692$		0			0
$693$	4.29261	+	2.79466i	0.163063	+	0.106160i
$694$		0			0
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	−18.8446	+	32.6398i	−0.713791	+	1.23632i
$698$		0			0
$699$	−34.7362	+	32.9256i	−1.31384	+	1.24536i
$700$		0			0
$701$	−29.3492			−1.10850			−0.554251	−	0.832349i	$-0.686995\pi$
$701$	−29.3492			−1.10850			−0.554251	+	0.832349i	$0.686995\pi$
$702$		0			0
$703$	0.386505			0.0145773
$704$		0			0
$705$	−6.11350	+	5.79483i	−0.230248	+	0.218246i
$706$		0			0
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	−0.958060	−	0.286566i	$-0.907486\pi$
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	0.230857	−	0.972988i	$-0.425847\pi$
$710$		0			0
$711$	−21.5479	+	10.9481i	−0.808108	+	0.410586i
$712$		0			0
$713$	−18.0288	−	31.2268i	−0.675184	−	1.16945i
$714$		0			0
$715$	2.19325	−	3.79882i	0.0820230	−	0.142068i
$716$		0			0
$717$	−1.69365	−	7.07243i	−0.0632506	−	0.264125i
$718$		0			0
$719$	15.0848			0.562569			0.281284	−	0.959624i	$-0.409240\pi$
$719$	15.0848			0.562569			0.281284	+	0.959624i	$0.409240\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$		0			0
$723$	5.98494	+	1.77655i	0.222582	+	0.0660706i
$724$		0			0
$725$	0.693252	−	1.20075i	0.0257467	−	0.0445947i
$726$		0			0
$727$	6.17277	+	10.6916i	0.228936	+	0.396528i	0.957493	−	0.288457i	$-0.0931422\pi$
$727$	6.17277	+	10.6916i	0.228936	+	0.396528i	−0.728557	+	0.684985i	$0.759809\pi$
$728$		0			0
$729$	−4.31542	+	26.6529i	−0.159830	+	0.987144i
$730$		0			0
$731$	−17.1842	−	29.7639i	−0.635580	−	1.10086i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$	−11.1842	−	3.31988i	−0.412535	−	0.122456i
$736$		0			0
$737$	−31.3774			−1.15580
$738$		0			0
$739$	−29.7266			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$739$	−29.7266			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$740$		0			0
$741$	0.703781	+	2.93888i	0.0258540	+	0.107962i
$742$		0			0
$743$	24.1824	−	41.8851i	0.887165	−	1.53662i	0.0439537	−	0.999034i	$-0.486005\pi$
$743$	24.1824	−	41.8851i	0.887165	−	1.53662i	0.843212	−	0.537582i	$-0.180662\pi$
$744$		0			0
$745$	−8.83049	−	15.2948i	−0.323524	−	0.560360i
$746$		0			0
$747$	4.12530	−	2.09599i	0.150937	−	0.0766883i
$748$		0			0
$749$	0.481327	+	0.833682i	0.0175873	+	0.0304621i
$750$		0			0
$751$	−15.9102	+	27.5573i	−0.580573	+	1.00558i	0.414838	+	0.909895i	$0.363838\pi$
$751$	−15.9102	+	27.5573i	−0.580573	+	1.00558i	−0.995411	+	0.0956869i	$0.969495\pi$
$752$		0			0
$753$	−8.64591	+	8.19524i	−0.315074	+	0.298651i
$754$		0			0
$755$	−1.26434			−0.0460139
$756$		0			0
$757$	4.94531			0.179740			0.0898701	−	0.995953i	$-0.471355\pi$
$757$	4.94531			0.179740			0.0898701	+	0.995953i	$0.471355\pi$
$758$		0			0
$759$	17.2311	−	16.3330i	0.625450	−	0.592849i
$760$		0			0
$761$	−17.7125	+	30.6789i	−0.642076	+	1.11211i	0.342893	+	0.939375i	$0.388593\pi$
$761$	−17.7125	+	30.6789i	−0.642076	+	1.11211i	−0.984969	+	0.172734i	$0.944740\pi$
$762$		0			0
$763$	−1.42618	−	2.47022i	−0.0516313	−	0.0894281i
$764$		0			0
$765$	−8.34916	−	5.43563i	−0.301864	−	0.196525i
$766$		0			0
$767$	3.32088	+	5.75194i	0.119910	+	0.207691i
$768$		0			0
$769$	−24.7125	+	42.8032i	−0.891154	+	1.54352i	−0.0526602	+	0.998612i	$0.516770\pi$
$769$	−24.7125	+	42.8032i	−0.891154	+	1.54352i	−0.838494	+	0.544911i	$0.816563\pi$
$770$		0			0
$771$	7.26073	+	30.3197i	0.261489	+	1.09194i
$772$		0			0
$773$	12.6599			0.455345			0.227673	−	0.973738i	$-0.426888\pi$
$773$	12.6599			0.455345			0.227673	+	0.973738i	$0.426888\pi$
$774$		0			0
$775$	−8.73566			−0.313794
$776$		0			0
$777$	0.249800	+	0.0741499i	0.00896153	+	0.00266011i
$778$		0			0
$779$	7.49546	−	12.9825i	0.268553	−	0.465147i
$780$		0			0
$781$	14.9289	+	25.8576i	0.534199	+	0.925259i
$782$		0			0
$783$	−2.41658	+	6.78711i	−0.0863616	+	0.242551i
$784$		0			0
$785$	7.83502	+	13.5707i	0.279644	+	0.484357i
$786$		0			0
$787$	15.4672	−	26.7900i	0.551346	−	0.954959i	−0.446832	−	0.894618i	$-0.647448\pi$
$787$	15.4672	−	26.7900i	0.551346	−	0.954959i	0.998178	−	0.0603410i	$-0.0192188\pi$
$788$		0			0
$789$	−10.3546	−	3.07364i	−0.368634	−	0.109424i
$790$		0			0
$791$	4.01093			0.142612
$792$		0			0
$793$	−9.70739			−0.344720
$794$		0			0
$795$	2.02827	+	8.46975i	0.0719355	+	0.300391i
$796$		0			0
$797$	15.2967	−	26.4947i	0.541839	−	0.938492i	−0.456960	−	0.889487i	$-0.651062\pi$
$797$	15.2967	−	26.4947i	0.541839	−	0.938492i	0.998799	−	0.0490047i	$-0.0156049\pi$
$798$		0			0
$799$	8.07522	+	13.9867i	0.285681	+	0.494814i
$800$		0			0
$801$	−0.481327	+	8.98712i	−0.0170068	+	0.317544i
$802$		0			0
$803$	−10.0565	−	17.4185i	−0.354888	−	0.614684i
$804$		0			0
$805$	1.06108	−	1.83785i	0.0373983	−	0.0647758i
$806$		0			0
$807$	−12.4745	+	11.8242i	−0.439122	+	0.416233i
$808$		0			0
$809$	−2.89703			−0.101854			−0.0509271	−	0.998702i	$-0.516218\pi$
$809$	−2.89703			−0.101854			−0.0509271	+	0.998702i	$0.516218\pi$
$810$		0			0
$811$	14.8861			0.522722			0.261361	−	0.965241i	$-0.415829\pi$
$811$	14.8861			0.522722			0.261361	+	0.965241i	$0.415829\pi$
$812$		0			0
$813$	8.30221	−	7.86946i	0.291171	−	0.275994i
$814$		0			0
$815$	7.85369	−	13.6030i	0.275103	−	0.476492i
$816$		0			0
$817$	6.83502	+	11.8386i	0.239127	+	0.414180i
$818$		0			0
$819$	−0.108959	+	2.03443i	−0.00380733	+	0.0710888i
$820$		0			0
$821$	4.47586	+	7.75242i	0.156209	+	0.270561i	0.933498	−	0.358581i	$-0.116739\pi$
$821$	4.47586	+	7.75242i	0.156209	+	0.270561i	−0.777290	+	0.629143i	$0.783406\pi$
$822$		0			0
$823$	1.49727	−	2.59334i	0.0521915	−	0.0903983i	−0.838749	−	0.544518i	$-0.816713\pi$
$823$	1.49727	−	2.59334i	0.0521915	−	0.0903983i	0.890941	+	0.454119i	$0.150046\pi$
$824$		0			0
$825$	−1.33956	−	5.59378i	−0.0466374	−	0.194751i
$826$		0			0
$827$	−31.9663			−1.11158			−0.555788	−	0.831324i	$-0.687583\pi$
$827$	−31.9663			−1.11158			−0.555788	+	0.831324i	$0.687583\pi$
$828$		0			0
$829$	22.7458			0.789994			0.394997	−	0.918682i	$-0.370746\pi$
$829$	22.7458			0.789994			0.394997	+	0.918682i	$0.370746\pi$
$830$		0			0
$831$	37.6272	+	11.1692i	1.30527	+	0.387454i
$832$		0			0
$833$	−11.1842	+	19.3716i	−0.387509	+	0.671185i
$834$		0			0
$835$	3.08249	+	5.33903i	0.106674	+	0.184765i
$836$		0			0
$837$	44.6459	−	8.19524i	1.54319	−	0.283269i
$838$		0			0
$839$	−11.6322	−	20.1475i	−0.401587	−	0.695569i	0.592331	−	0.805695i	$-0.298208\pi$
$839$	−11.6322	−	20.1475i	−0.401587	−	0.695569i	−0.993918	+	0.110126i	$0.964875\pi$
$840$		0			0
$841$	13.5388	−	23.4499i	0.466855	−	0.808617i
$842$		0			0
$843$	−25.8163	−	7.66325i	−0.889162	−	0.263936i
$844$		0			0
$845$	−11.2553			−0.387193
$846$		0			0
$847$	0.0145366			0.000499485
$848$		0			0
$849$	0.260328	+	1.08709i	0.00893445	+	0.0373089i
$850$		0			0
$851$	0.603895	−	1.04598i	0.0207012	−	0.0358556i
$852$		0			0
$853$	−5.49546	−	9.51842i	−0.188161	−	0.325905i	0.756476	−	0.654021i	$-0.226919\pi$
$853$	−5.49546	−	9.51842i	−0.188161	−	0.325905i	−0.944637	+	0.328117i	$0.893586\pi$
$854$		0			0
$855$	3.32088	+	2.16202i	0.113572	+	0.0739397i
$856$		0			0
$857$	8.07522	+	13.9867i	0.275844	+	0.477776i	0.970348	−	0.241713i	$-0.0777093\pi$
$857$	8.07522	+	13.9867i	0.275844	+	0.477776i	−0.694503	+	0.719489i	$0.744376\pi$
$858$		0			0
$859$	14.2594	−	24.6980i	0.486524	−	0.842685i	−0.513356	−	0.858176i	$-0.671598\pi$
$859$	14.2594	−	24.6980i	0.486524	−	0.842685i	0.999880	+	0.0154909i	$0.00493111\pi$
$860$		0			0
$861$	7.33502	−	6.95269i	0.249977	−	0.236947i
$862$		0			0
$863$	−12.2890			−0.418322			−0.209161	−	0.977881i	$-0.567073\pi$
$863$	−12.2890			−0.418322			−0.209161	+	0.977881i	$0.567073\pi$
$864$		0			0
$865$	8.58522			0.291906
$866$		0			0
$867$	7.50687	−	7.11558i	0.254947	−	0.241658i
$868$		0			0
$869$	−13.3774	+	23.1704i	−0.453798	+	0.786002i
$870$		0			0
$871$	−6.24020	−	10.8083i	−0.211441	−	0.366227i
$872$		0			0
$873$	32.7777	−	16.6538i	1.10936	−	0.563644i
$874$		0			0
$875$	−0.257068	−	0.445256i	−0.00869050	−	0.0150524i
$876$		0			0
$877$	19.8501	−	34.3814i	0.670290	−	1.16098i	−0.307532	−	0.951538i	$-0.599503\pi$
$877$	19.8501	−	34.3814i	0.670290	−	1.16098i	0.977822	−	0.209438i	$-0.0671635\pi$
$878$		0			0
$879$	0.555620	+	2.32018i	0.0187406	+	0.0782578i
$880$		0			0
$881$	32.1040			1.08161			0.540806	−	0.841147i	$-0.318119\pi$
$881$	32.1040			1.08161			0.540806	+	0.841147i	$0.318119\pi$
$882$		0			0
$883$	−13.5051			−0.454482			−0.227241	−	0.973839i	$-0.572970\pi$
$883$	−13.5051			−0.454482			−0.227241	+	0.973839i	$0.572970\pi$
$884$		0			0
$885$	8.34916	+	2.47834i	0.280654	+	0.0833085i
$886$		0			0
$887$	17.5611	−	30.4167i	0.589643	−	1.02129i	−0.404635	−	0.914478i	$-0.632602\pi$
$887$	17.5611	−	30.4167i	0.589643	−	1.02129i	0.994279	−	0.106814i	$-0.0340651\pi$
$888$		0			0
$889$	4.59936	+	7.96632i	0.154258	+	0.267182i
$890$		0			0
$891$	12.0939	+	27.3318i	0.405161	+	0.915650i
$892$		0			0
$893$	−3.21193	−	5.56322i	−0.107483	−	0.186166i
$894$		0			0
$895$	−0.532810	+	0.922854i	−0.0178099	+	0.0308476i
$896$		0			0
$897$	9.05294	+	2.68725i	0.302269	+	0.0897246i
$898$		0			0
$899$	12.1120			0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$		0			0
$903$	2.14631	+	8.96263i	0.0714246	+	0.298258i
$904$		0			0
$905$	6.33502	−	10.9726i	0.210583	−	0.364741i
$906$		0			0
$907$	7.55928	+	13.0931i	0.251002	+	0.434748i	0.963802	−	0.266619i	$-0.0859067\pi$
$907$	7.55928	+	13.0931i	0.251002	+	0.434748i	−0.712800	+	0.701367i	$0.752573\pi$
$908$		0			0
$909$	−31.2125	+	15.8585i	−1.03525	+	0.525993i
$910$		0			0
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.861345	+	0.508021i	$0.169623\pi$
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.00928675	+	0.999957i	$0.497044\pi$
$912$		0			0
$913$	2.56108	−	4.43593i	0.0847595	−	0.146808i
$914$		0			0
$915$	−9.23840	+	8.75685i	−0.305412	+	0.289493i
$916$		0			0
$917$	3.08482			0.101870
$918$		0			0
$919$	54.5489			1.79940			0.899702	−	0.436505i	$-0.143784\pi$
$919$	54.5489			1.79940			0.899702	+	0.436505i	$0.143784\pi$
$920$		0			0
$921$	−10.0383	+	9.51504i	−0.330772	+	0.313531i
$922$		0			0
$923$	−5.93799	+	10.2849i	−0.195451	+	0.338532i
$924$		0			0
$925$	−0.146305	−	0.253408i	−0.00481049	−	0.00833201i
$926$		0			0
$927$	−0.735663	−	0.478945i	−0.0241624	−	0.0157306i
$928$		0			0
$929$	−10.1896	−	17.6490i	−0.334311	−	0.579044i	0.649041	−	0.760753i	$-0.275170\pi$
$929$	−10.1896	−	17.6490i	−0.334311	−	0.579044i	−0.983352	+	0.181709i	$0.941837\pi$
$930$		0			0
$931$	4.44852	−	7.70506i	0.145794	−	0.252523i
$932$		0			0
$933$	3.88558	+	16.2256i	0.127208	+	0.531201i
$934$		0			0
$935$	−11.0283			−0.360663
$936$		0			0
$937$	49.1979			1.60723			0.803613	−	0.595152i	$-0.202908\pi$
$937$	49.1979			1.60723			0.803613	+	0.595152i	$0.202908\pi$
$938$		0			0
$939$	−40.7422	−	12.0938i	−1.32957	−	0.394666i
$940$		0			0
$941$	11.6186	−	20.1239i	0.378754	−	0.656022i	−0.612127	−	0.790759i	$-0.709686\pi$
$941$	11.6186	−	20.1239i	0.378754	−	0.656022i	0.990881	+	0.134738i	$0.0430192\pi$
$942$		0			0
$943$	−23.4226	−	40.5691i	−0.762744	−	1.32111i
$944$		0			0
$945$	1.73153	+	2.03443i	0.0563266	+	0.0661800i
$946$		0			0
$947$	18.5821	+	32.1851i	0.603837	+	1.04588i	0.992234	+	0.124384i	$0.0396955\pi$
$947$	18.5821	+	32.1851i	0.603837	+	1.04588i	−0.388397	+	0.921492i	$0.626971\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	−33.7886	−	10.0297i	−1.09567	−	0.325236i
$952$		0			0
$953$	−23.5761			−0.763706			−0.381853	−	0.924223i	$-0.624714\pi$
$953$	−23.5761			−0.763706			−0.381853	+	0.924223i	$0.624714\pi$
$954$		0			0
$955$	16.9344			0.547984
$956$		0			0
$957$	1.85730	+	7.75581i	0.0600381	+	0.250710i
$958$		0			0
$959$	−1.45759	+	2.52462i	−0.0470680	+	0.0815242i
$960$		0			0
$961$	−22.6559	−	39.2412i	−0.730836	−	1.26584i
$962$		0			0
$963$	−0.300407	+	5.60907i	−0.00968048	+	0.180750i
$964$		0			0
$965$	−13.3588	−	23.1380i	−0.430034	−	0.744840i
$966$		0			0
$967$	4.19145	−	7.25980i	0.134788	−	0.233459i	−0.790729	−	0.612167i	$-0.790298\pi$
$967$	4.19145	−	7.25980i	0.134788	−	0.233459i	0.925516	+	0.378708i	$0.123631\pi$
$968$		0			0
$969$	5.51414	−	5.22672i	0.177140	−	0.167906i
$970$		0			0
$971$	−13.2078			−0.423858			−0.211929	−	0.977285i	$-0.567975\pi$
$971$	−13.2078			−0.423858			−0.211929	+	0.977285i	$0.567975\pi$
$972$		0			0
$973$	−4.11310			−0.131860
$974$		0			0
$975$	1.66044	−	1.57389i	0.0531767	−	0.0504049i
$976$		0			0
$977$	7.16551	−	12.4110i	0.229245	−	0.397064i	−0.728340	−	0.685216i	$-0.759708\pi$
$977$	7.16551	−	12.4110i	0.229245	−	0.397064i	0.957585	+	0.288153i	$0.0930410\pi$
$978$		0			0
$979$	4.98133	+	8.62791i	0.159204	+	0.275749i
$980$		0			0
$981$	0.890114	−	16.6198i	0.0284191	−	0.530630i
$982$		0			0
$983$	−16.1541	−	27.9797i	−0.515236	−	0.892415i	−0.999844	−	0.0176831i	$-0.994371\pi$
$983$	−16.1541	−	27.9797i	−0.515236	−	0.892415i	0.484608	−	0.874732i	$-0.338962\pi$
$984$		0			0
$985$	7.12763	−	12.3454i	0.227105	−	0.393358i
$986$		0			0
$987$	−1.00860	−	4.21174i	−0.0321040	−	0.134061i
$988$		0			0
$989$	42.7175			1.35834
$990$		0			0
$991$	39.6700			1.26016			0.630080	−	0.776530i	$-0.283022\pi$
$991$	39.6700			1.26016			0.630080	+	0.776530i	$0.283022\pi$
$992$		0			0
$993$	−27.3027	−	8.10447i	−0.866426	−	0.257187i
$994$		0			0
$995$	−12.3305	+	21.3570i	−0.390903	+	0.677063i
$996$		0			0
$997$	−19.3437	−	33.5043i	−0.612621	−	1.06109i	−0.990797	−	0.135357i	$-0.956782\pi$
$997$	−19.3437	−	33.5043i	−0.612621	−	1.06109i	0.378176	−	0.925734i	$-0.376551\pi$
$998$		0			0
$999$	0.985463	+	1.15786i	0.0311787	+	0.0366329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.i.481.1		6
3.2	odd	2		2160.2.q.k.1441.1		6
4.3	odd	2		45.2.e.b.31.1	yes	6
9.2	odd	6		2160.2.q.k.721.1		6
9.4	even	3		6480.2.a.bv.1.3		3
9.5	odd	6		6480.2.a.bs.1.3		3
9.7	even	3	inner	720.2.q.i.241.1		6
12.11	even	2		135.2.e.b.91.3		6
20.3	even	4		225.2.k.b.49.1		12
20.7	even	4		225.2.k.b.49.6		12
20.19	odd	2		225.2.e.b.76.3		6
36.7	odd	6		45.2.e.b.16.1	✓	6
36.11	even	6		135.2.e.b.46.3		6
36.23	even	6		405.2.a.i.1.1		3
36.31	odd	6		405.2.a.j.1.3		3
60.23	odd	4		675.2.k.b.199.6		12
60.47	odd	4		675.2.k.b.199.1		12
60.59	even	2		675.2.e.b.226.1		6
180.7	even	12		225.2.k.b.124.1		12
180.23	odd	12		2025.2.b.m.649.6		6
180.43	even	12		225.2.k.b.124.6		12
180.47	odd	12		675.2.k.b.424.6		12
180.59	even	6		2025.2.a.o.1.3		3
180.67	even	12		2025.2.b.l.649.6		6
180.79	odd	6		225.2.e.b.151.3		6
180.83	odd	12		675.2.k.b.424.1		12
180.103	even	12		2025.2.b.l.649.1		6
180.119	even	6		675.2.e.b.451.1		6
180.139	odd	6		2025.2.a.n.1.1		3
180.167	odd	12		2025.2.b.m.649.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	36.7	odd	6
45.2.e.b.31.1	yes	6	4.3	odd	2
135.2.e.b.46.3		6	36.11	even	6
135.2.e.b.91.3		6	12.11	even	2
225.2.e.b.76.3		6	20.19	odd	2
225.2.e.b.151.3		6	180.79	odd	6
225.2.k.b.49.1		12	20.3	even	4
225.2.k.b.49.6		12	20.7	even	4
225.2.k.b.124.1		12	180.7	even	12
225.2.k.b.124.6		12	180.43	even	12
405.2.a.i.1.1		3	36.23	even	6
405.2.a.j.1.3		3	36.31	odd	6
675.2.e.b.226.1		6	60.59	even	2
675.2.e.b.451.1		6	180.119	even	6
675.2.k.b.199.1		12	60.47	odd	4
675.2.k.b.199.6		12	60.23	odd	4
675.2.k.b.424.1		12	180.83	odd	12
675.2.k.b.424.6		12	180.47	odd	12
720.2.q.i.241.1		6	9.7	even	3	inner
720.2.q.i.481.1		6	1.1	even	1	trivial
2025.2.a.n.1.1		3	180.139	odd	6
2025.2.a.o.1.3		3	180.59	even	6
2025.2.b.l.649.1		6	180.103	even	12
2025.2.b.l.649.6		6	180.67	even	12
2025.2.b.m.649.1		6	180.167	odd	12
2025.2.b.m.649.6		6	180.23	odd	12
2160.2.q.k.721.1		6	9.2	odd	6
2160.2.q.k.1441.1		6	3.2	odd	2
6480.2.a.bs.1.3		3	9.5	odd	6
6480.2.a.bv.1.3		3	9.4	even	3

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.25707 + 1.19154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +(0.160442 - 2.99571i) q^{9} +O(q^{10})\)	\(q+(-1.25707 + 1.19154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +(0.160442 - 2.99571i) q^{9} +(-1.66044 - 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +(-0.403374 - 1.68443i) q^{15} -3.32088 q^{17} +1.32088 q^{19} +(0.853695 + 0.253408i) q^{21} +(2.06382 - 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.36783 + 3.95698i) q^{27} +(0.693252 + 1.20075i) q^{29} +(4.36783 - 7.56531i) q^{31} +(5.51414 + 1.63680i) q^{33} +0.514137 q^{35} +0.292611 q^{37} +(0.532810 + 2.22493i) q^{39} +(5.67458 - 9.82866i) q^{41} +(5.17458 + 8.96263i) q^{43} +(2.51414 + 1.63680i) q^{45} +(-2.43165 - 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(4.17458 - 3.95698i) q^{51} -5.02827 q^{53} +3.32088 q^{55} +(-1.66044 + 1.57389i) q^{57} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} +(-1.37510 + 0.698664i) q^{63} +(0.660442 + 1.14392i) q^{65} +(4.72426 - 8.18266i) q^{67} +(1.66498 + 6.95269i) q^{69} -8.99093 q^{71} +6.05655 q^{73} +(1.66044 + 0.492881i) q^{75} +(-0.853695 + 1.47864i) q^{77} +(-4.02827 - 6.97717i) q^{79} +(-8.94852 - 0.961276i) q^{81} +(0.771205 + 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +(-2.30221 - 0.683382i) q^{87} -3.00000 q^{89} -0.679116 q^{91} +(3.52374 + 14.7146i) q^{93} +(-0.660442 + 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +(-8.88197 + 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 - 2 * q^11 - 4 * q^13 - q^15 - 4 * q^17 - 8 * q^19 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 8 * q^31 + 20 * q^33 - 10 * q^35 + 12 * q^37 + 14 * q^39 + 13 * q^41 + 10 * q^43 + 2 * q^45 + 13 * q^47 + 2 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^55 - 2 * q^57 - 2 * q^59 - q^61 - 33 * q^63 - 4 * q^65 + 11 * q^67 + 39 * q^69 + 20 * q^71 - 16 * q^73 + 2 * q^75 + 2 * q^79 - 19 * q^81 - 15 * q^83 + 2 * q^85 + 26 * q^87 - 18 * q^89 - 20 * q^91 - 42 * q^93 + 4 * q^95 + 18 * q^97 - 22 * q^99

Introduction

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