LMFDB - Embedded newform 144.2.i.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("144.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.i (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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	144.49
Dual form			144.2.i.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +4.00000 q^{19} +(1.50000 - 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} +(2.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(1.50000 + 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(4.50000 - 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(3.00000 - 5.19615i) q^{49} +10.3923i q^{51} -6.00000 q^{53} -9.00000 q^{55} +6.92820i q^{57} +(-1.50000 + 2.59808i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{63} +(1.50000 + 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-4.50000 - 2.59808i) q^{69} +12.0000 q^{71} -10.0000 q^{73} +(6.00000 - 3.46410i) q^{75} +(1.50000 - 2.59808i) q^{77} +(5.50000 + 9.52628i) q^{79} +9.00000 q^{81} +(-4.50000 - 7.79423i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(4.50000 - 2.59808i) q^{87} +6.00000 q^{89} -1.00000 q^{91} +(7.50000 + 4.33013i) q^{93} +(-6.00000 + 10.3923i) q^{95} +(-5.50000 - 9.52628i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^5 - q^7 - 6 * q^9	$ 2 q - 3 q^{5} - q^{7} - 6 q^{9} + 3 q^{11} + q^{13} - 9 q^{15} + 12 q^{17} + 8 q^{19} + 3 q^{21} - 3 q^{23} - 4 q^{25} - 3 q^{29} + 5 q^{31} - 9 q^{33} + 6 q^{35} + 4 q^{37} + 3 q^{39} - 3 q^{41} - q^{43} + 9 q^{45} - 9 q^{47} + 6 q^{49} - 12 q^{53} - 18 q^{55} - 3 q^{59} + 13 q^{61} + 3 q^{63} + 3 q^{65} - 7 q^{67} - 9 q^{69} + 24 q^{71} - 20 q^{73} + 12 q^{75} + 3 q^{77} + 11 q^{79} + 18 q^{81} - 9 q^{83} - 18 q^{85} + 9 q^{87} + 12 q^{89} - 2 q^{91} + 15 q^{93} - 12 q^{95} - 11 q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q - 3 * q^5 - q^7 - 6 * q^9 + 3 * q^11 + q^13 - 9 * q^15 + 12 * q^17 + 8 * q^19 + 3 * q^21 - 3 * q^23 - 4 * q^25 - 3 * q^29 + 5 * q^31 - 9 * q^33 + 6 * q^35 + 4 * q^37 + 3 * q^39 - 3 * q^41 - q^43 + 9 * q^45 - 9 * q^47 + 6 * q^49 - 12 * q^53 - 18 * q^55 - 3 * q^59 + 13 * q^61 + 3 * q^63 + 3 * q^65 - 7 * q^67 - 9 * q^69 + 24 * q^71 - 20 * q^73 + 12 * q^75 + 3 * q^77 + 11 * q^79 + 18 * q^81 - 9 * q^83 - 18 * q^85 + 9 * q^87 + 12 * q^89 - 2 * q^91 + 15 * q^93 - 12 * q^95 - 11 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$		0			0
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$		0			0
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$	1.50000	−	0.866025i	0.327327	−	0.188982i
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$		0			0
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$			10.3923i			1.45521i
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$			6.92820i			0.917663i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$		0			0
$77$	1.50000	−	2.59808i	0.170941	−	0.296078i
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$		0			0
$87$	4.50000	−	2.59808i	0.482451	−	0.278543i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$		0			0
$93$	7.50000	+	4.33013i	0.777714	+	0.449013i
$94$		0			0
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	−0.997627	−	0.0688512i	$-0.978067\pi$
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	0.439187	−	0.898396i	$-0.355267\pi$
$98$		0			0
$99$	−4.50000	−	7.79423i	−0.452267	−	0.783349i
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$			5.19615i			0.507093i
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$			3.46410i			0.328798i
$112$		0			0
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$		0			0
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$		0			0
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$		0			0
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.114024	−	0.993478i	$-0.463626\pi$
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.803365	−	0.595487i	$-0.203041\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$		0			0
$135$	13.5000	+	7.79423i	1.16190	+	0.670820i
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$	13.5000	−	7.79423i	1.13691	−	0.656392i
$142$		0			0
$143$	3.00000			0.250873
$144$		0			0
$145$	9.00000			0.747409
$146$		0			0
$147$	9.00000	+	5.19615i	0.742307	+	0.428571i
$148$		0			0
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	−0.999430	−	0.0337724i	$-0.989248\pi$
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	0.470467	−	0.882418i	$-0.344085\pi$
$152$		0			0
$153$	−18.0000			−1.45521
$154$		0			0
$155$	7.50000	+	12.9904i	0.602414	+	1.04341i
$156$		0			0
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$		0			0
$159$		−	10.3923i		−	0.824163i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$		0			0
$165$		−	15.5885i		−	1.21356i
$166$		0			0
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−12.0000			−0.917663
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$		0			0
$177$	−4.50000	−	2.59808i	−0.338241	−	0.195283i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−19.5000	+	11.2583i	−1.44148	+	0.832240i
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$		0			0
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	0.998749	+	0.0500060i	$0.0159241\pi$
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	−0.456068	+	0.889945i	$0.650743\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		0			0
$195$	−4.50000	+	2.59808i	−0.322252	+	0.186052i
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$	−10.5000	−	6.06218i	−0.740613	−	0.427593i
$202$		0			0
$203$	−1.50000	+	2.59808i	−0.105279	+	0.182349i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$		0			0
$209$	6.00000	+	10.3923i	0.415029	+	0.718851i
$210$		0			0
$211$	8.50000	−	14.7224i	0.585164	−	1.01353i	−0.409691	−	0.912224i	$-0.634363\pi$
$211$	8.50000	−	14.7224i	0.585164	−	1.01353i	0.994855	−	0.101310i	$-0.0323033\pi$
$212$		0			0
$213$			20.7846i			1.42414i
$214$		0			0
$215$	3.00000			0.204598
$216$		0			0
$217$	−5.00000			−0.339422
$218$		0			0
$219$		−	17.3205i		−	1.17041i
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		0			0
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	0.848799	−	0.528716i	$-0.177326\pi$
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	−0.882281	+	0.470723i	$0.843993\pi$
$224$		0			0
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$		0			0
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$	4.50000	+	2.59808i	0.296078	+	0.170941i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	27.0000			1.76129
$236$		0			0
$237$	−16.5000	+	9.52628i	−1.07179	+	0.618798i
$238$		0			0
$239$	−13.5000	+	23.3827i	−0.873242	+	1.51250i	−0.0146191	+	0.999893i	$0.504654\pi$
$239$	−13.5000	+	23.3827i	−0.873242	+	1.51250i	−0.858623	+	0.512607i	$0.828680\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$			15.5885i			1.00000i
$244$		0			0
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$		0			0
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$		0			0
$249$	13.5000	−	7.79423i	0.855528	−	0.493939i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$		0			0
$255$	−27.0000	−	15.5885i	−1.69081	−	0.976187i
$256$		0			0
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	−0.690856	−	0.722993i	$-0.742766\pi$
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	0.971558	+	0.236802i	$0.0760993\pi$
$258$		0			0
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$		0			0
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$		0			0
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	−0.983728	−	0.179664i	$-0.942499\pi$
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	0.336270	−	0.941766i	$-0.390834\pi$
$264$		0			0
$265$	9.00000	−	15.5885i	0.552866	−	0.957591i
$266$		0			0
$267$			10.3923i			0.635999i
$268$		0			0
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		−	1.73205i		−	0.104828i
$274$		0			0
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		0			0
$279$	−7.50000	+	12.9904i	−0.449013	+	0.777714i
$280$		0			0
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	0.817810	−	0.575488i	$-0.195188\pi$
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	−0.907293	+	0.420500i	$0.861855\pi$
$282$		0			0
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$		0			0
$285$	−18.0000	−	10.3923i	−1.06623	−	0.615587i
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	16.5000	−	9.52628i	0.967247	−	0.558440i
$292$		0			0
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$		0			0
$295$	−4.50000	−	7.79423i	−0.262000	−	0.453798i
$296$		0			0
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$		0			0
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$	22.5000	−	12.9904i	1.29259	−	0.746278i
$304$		0			0
$305$	−39.0000			−2.23313
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−10.5000	−	6.06218i	−0.597324	−	0.344865i
$310$		0			0
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	−0.398090	−	0.917346i	$-0.630327\pi$
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	0.993490	−	0.113917i	$-0.0363399\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$		0			0
$315$	−9.00000			−0.507093
$316$		0			0
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		−	20.7846i		−	1.16008i
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	−4.00000			−0.221880
$326$		0			0
$327$			3.46410i			0.191565i
$328$		0			0
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	5.50000	+	9.52628i	0.302307	+	0.523612i	0.976658	−	0.214799i	$-0.0689098\pi$
$331$	5.50000	+	9.52628i	0.302307	+	0.523612i	−0.674351	+	0.738411i	$0.735576\pi$
$332$		0			0
$333$	−6.00000			−0.328798
$334$		0			0
$335$	−10.5000	−	18.1865i	−0.573676	−	0.993636i
$336$		0			0
$337$	−11.5000	+	19.9186i	−0.626445	+	1.08503i	0.361815	+	0.932250i	$0.382157\pi$
$337$	−11.5000	+	19.9186i	−0.626445	+	1.08503i	−0.988260	+	0.152784i	$0.951176\pi$
$338$		0			0
$339$	13.5000	+	7.79423i	0.733219	+	0.423324i
$340$		0			0
$341$	15.0000			0.812296
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	13.5000	−	7.79423i	0.726816	−	0.419627i
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	0.879097	−	0.476642i	$-0.158146\pi$
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	−0.852333	+	0.523000i	$0.824813\pi$
$350$		0			0
$351$	−4.50000	−	2.59808i	−0.240192	−	0.138675i
$352$		0			0
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$		0			0
$357$	9.00000	−	5.19615i	0.476331	−	0.275010i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$	3.00000	+	1.73205i	0.157459	+	0.0909091i
$364$		0			0
$365$	15.0000	−	25.9808i	0.785136	−	1.35990i
$366$		0			0
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	0.645003	−	0.764180i	$-0.276856\pi$
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	−0.984301	+	0.176500i	$0.943523\pi$
$368$		0			0
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$		0			0
$375$		−	5.19615i		−	0.268328i
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$			27.7128i			1.41977i
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	4.50000	+	7.79423i	0.229341	+	0.397231i
$386$		0			0
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$		0			0
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$		0			0
$393$	31.5000	+	18.1865i	1.58896	+	0.917389i
$394$		0			0
$395$	−33.0000			−1.66041
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$	6.00000	−	3.46410i	0.300376	−	0.173422i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$		0			0
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$		0			0
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$		0			0
$411$	4.50000	−	2.59808i	0.221969	−	0.128154i
$412$		0			0
$413$	3.00000			0.147620
$414$		0			0
$415$	27.0000			1.32538
$416$		0			0
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$		0			0
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$		0			0
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$		0			0
$425$	−12.0000	−	20.7846i	−0.582086	−	1.00820i
$426$		0			0
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$		0			0
$429$			5.19615i			0.250873i
$430$		0			0
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$			15.5885i			0.747409i
$436$		0			0
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	0.739100	−	0.673596i	$-0.235251\pi$
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	−0.952901	+	0.303281i	$0.901918\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$		0			0
$447$	−22.5000	−	12.9904i	−1.06421	−	0.614424i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$		0			0
$453$	19.5000	−	11.2583i	0.916190	−	0.528962i
$454$		0			0
$455$	1.50000	−	2.59808i	0.0703211	−	0.121800i
$456$		0			0
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	0.866656	+	0.498906i	$0.166265\pi$
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	−0.00126243	+	0.999999i	$0.500402\pi$
$458$		0			0
$459$		−	31.1769i		−	1.45521i
$460$		0			0
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	0.828978	−	0.559281i	$-0.188923\pi$
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	−0.898840	+	0.438276i	$0.855589\pi$
$462$		0			0
$463$	−9.50000	+	16.4545i	−0.441502	+	0.764705i	−0.997801	−	0.0662777i	$-0.978888\pi$
$463$	−9.50000	+	16.4545i	−0.441502	+	0.764705i	0.556299	+	0.830982i	$0.312221\pi$
$464$		0			0
$465$	−22.5000	+	12.9904i	−1.04341	+	0.602414i
$466$		0			0
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$		0			0
$475$	−8.00000	−	13.8564i	−0.367065	−	0.635776i
$476$		0			0
$477$	18.0000			0.824163
$478$		0			0
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	0.990060	+	0.140643i	$0.0449170\pi$
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	−0.373230	+	0.927739i	$0.621750\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$		0			0
$483$			5.19615i			0.236433i
$484$		0			0
$485$	33.0000			1.49845
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$		0			0
$489$		−	34.6410i		−	1.56652i
$490$		0			0
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$492$		0			0
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$		0			0
$495$	27.0000			1.21356
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$		0			0
$501$	13.5000	+	7.79423i	0.603136	+	0.348220i
$502$		0			0
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$	45.0000			2.00247
$506$		0			0
$507$	−18.0000	+	10.3923i	−0.799408	+	0.461538i
$508$		0			0
$509$	−19.5000	+	33.7750i	−0.864322	+	1.49705i	0.00339621	+	0.999994i	$0.498919\pi$
$509$	−19.5000	+	33.7750i	−0.864322	+	1.49705i	−0.867719	+	0.497056i	$0.834414\pi$
$510$		0			0
$511$	5.00000	+	8.66025i	0.221187	+	0.383107i
$512$		0			0
$513$		−	20.7846i		−	0.917663i
$514$		0			0
$515$	−10.5000	−	18.1865i	−0.462685	−	0.801394i
$516$		0			0
$517$	13.5000	−	23.3827i	0.593729	−	1.02837i
$518$		0			0
$519$	−13.5000	+	7.79423i	−0.592584	+	0.342129i
$520$		0			0
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	−8.00000			−0.349816			−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000			−0.349816			−0.174908	+	0.984585i	$0.555963\pi$
$524$		0			0
$525$	−6.00000	−	3.46410i	−0.261861	−	0.151186i
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$		0			0
$533$	1.50000	+	2.59808i	0.0649722	+	0.112535i
$534$		0			0
$535$	18.0000	−	31.1769i	0.778208	−	1.34790i
$536$		0			0
$537$		−	20.7846i		−	0.896922i
$538$		0			0
$539$	18.0000			0.775315
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$		0			0
$543$			3.46410i			0.148659i
$544$		0			0
$545$	−3.00000	+	5.19615i	−0.128506	+	0.222579i
$546$		0			0
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	0.692948	−	0.720988i	$-0.256312\pi$
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	−0.970868	+	0.239616i	$0.922978\pi$
$548$		0			0
$549$	−19.5000	−	33.7750i	−0.832240	−	1.44148i
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$	5.50000	−	9.52628i	0.233884	−	0.405099i
$554$		0			0
$555$	−9.00000	−	5.19615i	−0.382029	−	0.220564i
$556$		0			0
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$	−27.0000	+	15.5885i	−1.13994	+	0.658145i
$562$		0			0
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	−0.755482	−	0.655169i	$-0.772597\pi$
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	0.945134	+	0.326682i	$0.105931\pi$
$564$		0			0
$565$	13.5000	+	23.3827i	0.567949	+	0.983717i
$566$		0			0
$567$	−4.50000	−	7.79423i	−0.188982	−	0.327327i
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	−15.5000	+	26.8468i	−0.648655	+	1.12350i	0.334790	+	0.942293i	$0.391335\pi$
$571$	−15.5000	+	26.8468i	−0.648655	+	1.12350i	−0.983444	+	0.181210i	$0.941999\pi$
$572$		0			0
$573$	−22.5000	+	12.9904i	−0.939951	+	0.542681i
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$	−16.5000	−	9.52628i	−0.685717	−	0.395899i
$580$		0			0
$581$	−4.50000	+	7.79423i	−0.186691	+	0.323359i
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$		0			0
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$		0			0
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	0.978266	−	0.207355i	$-0.0664855\pi$
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	−0.668708	+	0.743525i	$0.733152\pi$
$588$		0			0
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$		0			0
$591$			10.3923i			0.427482i
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$		0			0
$597$			6.92820i			0.283552i
$598$		0			0
$599$	−19.5000	+	33.7750i	−0.796748	+	1.38001i	0.124975	+	0.992160i	$0.460115\pi$
$599$	−19.5000	+	33.7750i	−0.796748	+	1.38001i	−0.921723	+	0.387849i	$0.873218\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$	10.5000	−	18.1865i	0.427593	−	0.740613i
$604$		0			0
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	−0.0643251	−	0.997929i	$-0.520489\pi$
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	0.896394	−	0.443257i	$-0.146177\pi$
$608$		0			0
$609$	−4.50000	−	2.59808i	−0.182349	−	0.105279i
$610$		0			0
$611$	−9.00000			−0.364101
$612$		0			0
$613$	26.0000			1.05013			0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000			1.05013			0.525065	+	0.851062i	$0.324041\pi$
$614$		0			0
$615$	13.5000	−	7.79423i	0.544373	−	0.314294i
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		0			0
$619$	−6.50000	−	11.2583i	−0.261257	−	0.452510i	0.705319	−	0.708890i	$-0.250804\pi$
$619$	−6.50000	−	11.2583i	−0.261257	−	0.452510i	−0.966576	+	0.256379i	$0.917470\pi$
$620$		0			0
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		0			0
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	−18.0000	+	10.3923i	−0.718851	+	0.415029i
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		0			0
$633$	25.5000	+	14.7224i	1.01353	+	0.585164i
$634$		0			0
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$		0			0
$639$	−36.0000			−1.42414
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	−0.105502	−	0.994419i	$-0.533645\pi$
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	0.913943	−	0.405842i	$-0.133022\pi$
$644$		0			0
$645$			5.19615i			0.204598i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$		−	8.66025i		−	0.339422i
$652$		0			0
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	−0.584091	−	0.811688i	$-0.698549\pi$
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	0.994988	+	0.0999939i	$0.0318823\pi$
$654$		0			0
$655$	31.5000	+	54.5596i	1.23081	+	2.13182i
$656$		0			0
$657$	30.0000			1.17041
$658$		0			0
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	0.739014	+	0.673690i	$0.235292\pi$
$662$		0			0
$663$	9.00000	+	5.19615i	0.349531	+	0.201802i
$664$		0			0
$665$	12.0000			0.465340
$666$		0			0
$667$	9.00000			0.348481
$668$		0			0
$669$	1.50000	−	0.866025i	0.0579934	−	0.0334825i
$670$		0			0
$671$	−19.5000	+	33.7750i	−0.752789	+	1.30387i
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$		0			0
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$		0			0
$677$	−7.50000	−	12.9904i	−0.288248	−	0.499261i	0.685143	−	0.728408i	$-0.259740\pi$
$677$	−7.50000	−	12.9904i	−0.288248	−	0.499261i	−0.973392	+	0.229147i	$0.926406\pi$
$678$		0			0
$679$	−5.50000	+	9.52628i	−0.211071	+	0.365585i
$680$		0			0
$681$	−40.5000	+	23.3827i	−1.55196	+	0.896026i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$		0			0
$687$	19.5000	+	11.2583i	0.743971	+	0.429532i
$688$		0			0
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$		0			0
$693$	−4.50000	+	7.79423i	−0.170941	+	0.296078i
$694$		0			0
$695$	7.50000	+	12.9904i	0.284491	+	0.492753i
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$		0			0
$699$		−	10.3923i		−	0.393073i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$		0			0
$705$			46.7654i			1.76129i
$706$		0			0
$707$	−7.50000	+	12.9904i	−0.282067	+	0.488554i
$708$		0			0
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	0.999390	−	0.0349269i	$-0.0111198\pi$
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	−0.529943	+	0.848034i	$0.677787\pi$
$710$		0			0
$711$	−16.5000	−	28.5788i	−0.618798	−	1.07179i
$712$		0			0
$713$	7.50000	+	12.9904i	0.280877	+	0.486494i
$714$		0			0
$715$	−4.50000	+	7.79423i	−0.168290	+	0.291488i
$716$		0			0
$717$	−40.5000	−	23.3827i	−1.51250	−	0.873242i
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	7.00000			0.260694
$722$		0			0
$723$	−1.50000	+	0.866025i	−0.0557856	+	0.0322078i
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	−0.973081	−	0.230463i	$-0.925976\pi$
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	0.286954	−	0.957944i	$-0.407357\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$		0			0
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	−0.996398	−	0.0847976i	$-0.972976\pi$
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	0.571636	+	0.820507i	$0.306309\pi$
$734$		0			0
$735$	−27.0000	+	15.5885i	−0.995910	+	0.574989i
$736$		0			0
$737$	−21.0000			−0.773545
$738$		0			0
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$		0			0
$741$	6.00000	+	3.46410i	0.220416	+	0.127257i
$742$		0			0
$743$	4.50000	−	7.79423i	0.165089	−	0.285943i	−0.771598	−	0.636111i	$-0.780542\pi$
$743$	4.50000	−	7.79423i	0.165089	−	0.285943i	0.936687	+	0.350168i	$0.113876\pi$
$744$		0			0
$745$	−22.5000	−	38.9711i	−0.824336	−	1.42779i
$746$		0			0
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$		0			0
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$		0			0
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	0.431390	+	0.902165i	$0.358023\pi$
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	−0.996993	+	0.0774878i	$0.975310\pi$
$752$		0			0
$753$		−	20.7846i		−	0.757433i
$754$		0			0
$755$	39.0000			1.41936
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		−	15.5885i		−	0.565825i
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$		0			0
$765$	27.0000	−	46.7654i	0.976187	−	1.69081i
$766$		0			0
$767$	1.50000	+	2.59808i	0.0541619	+	0.0938111i
$768$		0			0
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$	13.5000	+	7.79423i	0.486191	+	0.280702i
$772$		0			0
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	−20.0000			−0.718421
$776$		0			0
$777$	3.00000	−	1.73205i	0.107624	−	0.0621370i
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	−13.5000	+	7.79423i	−0.482451	+	0.278543i
$784$		0			0
$785$	19.5000	+	33.7750i	0.695985	+	1.20548i
$786$		0			0
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	0.173115	+	0.984902i	$0.444617\pi$
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	−0.939507	+	0.342529i	$0.888717\pi$
$788$		0			0
$789$	31.5000	−	18.1865i	1.12143	−	0.647458i
$790$		0			0
$791$	−9.00000			−0.320003
$792$		0			0
$793$	13.0000			0.461644
$794$		0			0
$795$	27.0000	+	15.5885i	0.957591	+	0.552866i
$796$		0			0
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	−0.775254	−	0.631650i	$-0.782378\pi$
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	0.934652	+	0.355564i	$0.115711\pi$
$798$		0			0
$799$	−27.0000	−	46.7654i	−0.955191	−	1.65444i
$800$		0			0
$801$	−18.0000			−0.635999
$802$		0			0
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$		0			0
$805$	−4.50000	+	7.79423i	−0.158604	+	0.274710i
$806$		0			0
$807$		−	10.3923i		−	0.365826i
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		−	13.8564i		−	0.485965i
$814$		0			0
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$		0			0
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$		0			0
$819$	3.00000			0.104828
$820$		0			0
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.839926	−	0.542702i	$-0.817401\pi$
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.0500305	−	0.998748i	$-0.515932\pi$
$822$		0			0
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	−0.982737	−	0.185006i	$-0.940770\pi$
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	0.651588	+	0.758573i	$0.274103\pi$
$824$		0			0
$825$	18.0000	+	10.3923i	0.626680	+	0.361814i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	50.0000			1.73657			0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000			1.73657			0.868286	+	0.496064i	$0.165222\pi$
$830$		0			0
$831$	−1.50000	+	0.866025i	−0.0520344	+	0.0300421i
$832$		0			0
$833$	18.0000	−	31.1769i	0.623663	−	1.08022i
$834$		0			0
$835$	13.5000	+	23.3827i	0.467187	+	0.809191i
$836$		0			0
$837$	−22.5000	−	12.9904i	−0.777714	−	0.449013i
$838$		0			0
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	0.777832	−	0.628473i	$-0.216320\pi$
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	−0.933189	+	0.359386i	$0.882986\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	4.50000	−	2.59808i	0.154988	−	0.0894825i
$844$		0			0
$845$	−36.0000			−1.23844
$846$		0			0
$847$	−2.00000			−0.0687208
$848$		0			0
$849$	7.50000	+	4.33013i	0.257399	+	0.148610i
$850$		0			0
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$		0			0
$853$	6.50000	+	11.2583i	0.222556	+	0.385478i	0.955583	−	0.294721i	$-0.0952267\pi$
$853$	6.50000	+	11.2583i	0.222556	+	0.385478i	−0.733028	+	0.680199i	$0.761893\pi$
$854$		0			0
$855$	18.0000	−	31.1769i	0.615587	−	1.06623i
$856$		0			0
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	0.537867	−	0.843029i	$-0.319230\pi$
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	−0.999019	+	0.0442921i	$0.985897\pi$
$858$		0			0
$859$	20.5000	−	35.5070i	0.699451	−	1.21148i	−0.269206	−	0.963083i	$-0.586761\pi$
$859$	20.5000	−	35.5070i	0.699451	−	1.21148i	0.968657	−	0.248402i	$-0.0799054\pi$
$860$		0			0
$861$			5.19615i			0.177084i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	−27.0000			−0.918028
$866$		0			0
$867$			32.9090i			1.11765i
$868$		0			0
$869$	−16.5000	+	28.5788i	−0.559724	+	0.969471i
$870$		0			0
$871$	3.50000	+	6.06218i	0.118593	+	0.205409i
$872$		0			0
$873$	16.5000	+	28.5788i	0.558440	+	0.967247i
$874$		0			0
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$		0			0
$879$	31.5000	+	18.1865i	1.06247	+	0.613417i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$	13.5000	−	7.79423i	0.453798	−	0.262000i
$886$		0			0
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	−0.634141	−	0.773217i	$-0.718646\pi$
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	0.986696	+	0.162573i	$0.0519794\pi$
$888$		0			0
$889$	−8.00000	−	13.8564i	−0.268311	−	0.464729i
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$		0			0
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$		0			0
$895$	18.0000	−	31.1769i	0.601674	−	1.04213i
$896$		0			0
$897$	−4.50000	+	2.59808i	−0.150251	+	0.0867472i
$898$		0			0
$899$	−15.0000			−0.500278
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$	−1.50000	−	0.866025i	−0.0499169	−	0.0288195i
$904$		0			0
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$		0			0
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	0.931764	+	0.363064i	$0.118269\pi$
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	−0.151460	+	0.988463i	$0.548397\pi$
$908$		0			0
$909$	22.5000	+	38.9711i	0.746278	+	1.29259i
$910$		0			0
$911$	−22.5000	−	38.9711i	−0.745458	−	1.29117i	−0.949980	−	0.312310i	$-0.898897\pi$
$911$	−22.5000	−	38.9711i	−0.745458	−	1.29117i	0.204522	−	0.978862i	$-0.434436\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$		0			0
$915$		−	67.5500i		−	2.23313i
$916$		0			0
$917$	−21.0000			−0.693481
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		−	34.6410i		−	1.14146i
$922$		0			0
$923$	6.00000	−	10.3923i	0.197492	−	0.342067i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$		0			0
$927$	10.5000	−	18.1865i	0.344865	−	0.597324i
$928$		0			0
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	12.0000	−	20.7846i	0.393284	−	0.681188i
$932$		0			0
$933$	31.5000	+	18.1865i	1.03126	+	0.595400i
$934$		0			0
$935$	−54.0000			−1.76599
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	−1.50000	+	0.866025i	−0.0489506	+	0.0282617i
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$		0			0
$945$		−	15.5885i		−	0.507093i
$946$		0			0
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		0			0
$951$	−31.5000	+	18.1865i	−1.02146	+	0.589739i
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	−45.0000			−1.45617
$956$		0			0
$957$	13.5000	+	7.79423i	0.436393	+	0.251952i
$958$		0			0
$959$	−1.50000	+	2.59808i	−0.0484375	+	0.0838963i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	36.0000			1.16008
$964$		0			0
$965$	−16.5000	−	28.5788i	−0.531154	−	0.919985i
$966$		0			0
$967$	−21.5000	+	37.2391i	−0.691393	+	1.19753i	0.279988	+	0.960003i	$0.409669\pi$
$967$	−21.5000	+	37.2391i	−0.691393	+	1.19753i	−0.971381	+	0.237525i	$0.923664\pi$
$968$		0			0
$969$			41.5692i			1.33540i
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	−5.00000			−0.160293
$974$		0			0
$975$		−	6.92820i		−	0.221880i
$976$		0			0
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.100270	−	0.994960i	$-0.468029\pi$
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.811526	−	0.584316i	$-0.198637\pi$
$978$		0			0
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$		0			0
$981$	−6.00000			−0.191565
$982$		0			0
$983$	25.5000	+	44.1673i	0.813324	+	1.40872i	0.910525	+	0.413453i	$0.135677\pi$
$983$	25.5000	+	44.1673i	0.813324	+	1.40872i	−0.0972017	+	0.995265i	$0.530989\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$	−13.5000	−	7.79423i	−0.429710	−	0.248093i
$988$		0			0
$989$	3.00000			0.0953945
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$		0			0
$993$	−16.5000	+	9.52628i	−0.523612	+	0.302307i
$994$		0			0
$995$	−6.00000	+	10.3923i	−0.190213	+	0.329458i
$996$		0			0
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	0.873834	−	0.486224i	$-0.161626\pi$
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	−0.857999	+	0.513651i	$0.828293\pi$
$998$		0			0
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.i.a.49.1		2
3.2	odd	2		432.2.i.c.145.1		2
4.3	odd	2		36.2.e.a.13.1	✓	2
8.3	odd	2		576.2.i.f.193.1		2
8.5	even	2		576.2.i.e.193.1		2
9.2	odd	6		432.2.i.c.289.1		2
9.4	even	3		1296.2.a.k.1.1		1
9.5	odd	6		1296.2.a.b.1.1		1
9.7	even	3	inner	144.2.i.a.97.1		2
12.11	even	2		108.2.e.a.37.1		2
20.3	even	4		900.2.s.b.49.2		4
20.7	even	4		900.2.s.b.49.1		4
20.19	odd	2		900.2.i.b.301.1		2
24.5	odd	2		1728.2.i.c.577.1		2
24.11	even	2		1728.2.i.d.577.1		2
28.3	even	6		1764.2.i.c.373.1		2
28.11	odd	6		1764.2.i.a.373.1		2
28.19	even	6		1764.2.l.a.949.1		2
28.23	odd	6		1764.2.l.c.949.1		2
28.27	even	2		1764.2.j.b.589.1		2
36.7	odd	6		36.2.e.a.25.1	yes	2
36.11	even	6		108.2.e.a.73.1		2
36.23	even	6		324.2.a.a.1.1		1
36.31	odd	6		324.2.a.c.1.1		1
60.23	odd	4		2700.2.s.b.1549.2		4
60.47	odd	4		2700.2.s.b.1549.1		4
60.59	even	2		2700.2.i.b.901.1		2
72.5	odd	6		5184.2.a.bb.1.1		1
72.11	even	6		1728.2.i.d.1153.1		2
72.13	even	6		5184.2.a.f.1.1		1
72.29	odd	6		1728.2.i.c.1153.1		2
72.43	odd	6		576.2.i.f.385.1		2
72.59	even	6		5184.2.a.ba.1.1		1
72.61	even	6		576.2.i.e.385.1		2
72.67	odd	6		5184.2.a.e.1.1		1
84.11	even	6		5292.2.i.c.1549.1		2
84.23	even	6		5292.2.l.a.361.1		2
84.47	odd	6		5292.2.l.c.361.1		2
84.59	odd	6		5292.2.i.a.1549.1		2
84.83	odd	2		5292.2.j.a.1765.1		2
180.7	even	12		900.2.s.b.349.2		4
180.23	odd	12		8100.2.d.c.649.2		2
180.43	even	12		900.2.s.b.349.1		4
180.47	odd	12		2700.2.s.b.2449.2		4
180.59	even	6		8100.2.a.g.1.1		1
180.67	even	12		8100.2.d.h.649.1		2
180.79	odd	6		900.2.i.b.601.1		2
180.83	odd	12		2700.2.s.b.2449.1		4
180.103	even	12		8100.2.d.h.649.2		2
180.119	even	6		2700.2.i.b.1801.1		2
180.139	odd	6		8100.2.a.j.1.1		1
180.167	odd	12		8100.2.d.c.649.1		2
252.11	even	6		5292.2.l.a.3313.1		2
252.47	odd	6		5292.2.i.a.2125.1		2
252.79	odd	6		1764.2.i.a.1537.1		2
252.83	odd	6		5292.2.j.a.3529.1		2
252.115	even	6		1764.2.l.a.961.1		2
252.151	odd	6		1764.2.l.c.961.1		2
252.187	even	6		1764.2.i.c.1537.1		2
252.191	even	6		5292.2.i.c.2125.1		2
252.223	even	6		1764.2.j.b.1177.1		2
252.227	odd	6		5292.2.l.c.3313.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.e.a.13.1	✓	2	4.3	odd	2
36.2.e.a.25.1	yes	2	36.7	odd	6
108.2.e.a.37.1		2	12.11	even	2
108.2.e.a.73.1		2	36.11	even	6
144.2.i.a.49.1		2	1.1	even	1	trivial
144.2.i.a.97.1		2	9.7	even	3	inner
324.2.a.a.1.1		1	36.23	even	6
324.2.a.c.1.1		1	36.31	odd	6
432.2.i.c.145.1		2	3.2	odd	2
432.2.i.c.289.1		2	9.2	odd	6
576.2.i.e.193.1		2	8.5	even	2
576.2.i.e.385.1		2	72.61	even	6
576.2.i.f.193.1		2	8.3	odd	2
576.2.i.f.385.1		2	72.43	odd	6
900.2.i.b.301.1		2	20.19	odd	2
900.2.i.b.601.1		2	180.79	odd	6
900.2.s.b.49.1		4	20.7	even	4
900.2.s.b.49.2		4	20.3	even	4
900.2.s.b.349.1		4	180.43	even	12
900.2.s.b.349.2		4	180.7	even	12
1296.2.a.b.1.1		1	9.5	odd	6
1296.2.a.k.1.1		1	9.4	even	3
1728.2.i.c.577.1		2	24.5	odd	2
1728.2.i.c.1153.1		2	72.29	odd	6
1728.2.i.d.577.1		2	24.11	even	2
1728.2.i.d.1153.1		2	72.11	even	6
1764.2.i.a.373.1		2	28.11	odd	6
1764.2.i.a.1537.1		2	252.79	odd	6
1764.2.i.c.373.1		2	28.3	even	6
1764.2.i.c.1537.1		2	252.187	even	6
1764.2.j.b.589.1		2	28.27	even	2
1764.2.j.b.1177.1		2	252.223	even	6
1764.2.l.a.949.1		2	28.19	even	6
1764.2.l.a.961.1		2	252.115	even	6
1764.2.l.c.949.1		2	28.23	odd	6
1764.2.l.c.961.1		2	252.151	odd	6
2700.2.i.b.901.1		2	60.59	even	2
2700.2.i.b.1801.1		2	180.119	even	6
2700.2.s.b.1549.1		4	60.47	odd	4
2700.2.s.b.1549.2		4	60.23	odd	4
2700.2.s.b.2449.1		4	180.83	odd	12
2700.2.s.b.2449.2		4	180.47	odd	12
5184.2.a.e.1.1		1	72.67	odd	6
5184.2.a.f.1.1		1	72.13	even	6
5184.2.a.ba.1.1		1	72.59	even	6
5184.2.a.bb.1.1		1	72.5	odd	6
5292.2.i.a.1549.1		2	84.59	odd	6
5292.2.i.a.2125.1		2	252.47	odd	6
5292.2.i.c.1549.1		2	84.11	even	6
5292.2.i.c.2125.1		2	252.191	even	6
5292.2.j.a.1765.1		2	84.83	odd	2
5292.2.j.a.3529.1		2	252.83	odd	6
5292.2.l.a.361.1		2	84.23	even	6
5292.2.l.a.3313.1		2	252.11	even	6
5292.2.l.c.361.1		2	84.47	odd	6
5292.2.l.c.3313.1		2	252.227	odd	6
8100.2.a.g.1.1		1	180.59	even	6
8100.2.a.j.1.1		1	180.139	odd	6
8100.2.d.c.649.1		2	180.167	odd	12
8100.2.d.c.649.2		2	180.23	odd	12
8100.2.d.h.649.1		2	180.67	even	12
8100.2.d.h.649.2		2	180.103	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +4.00000 q^{19} +(1.50000 - 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} +(2.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(1.50000 + 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(4.50000 - 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(3.00000 - 5.19615i) q^{49} +10.3923i q^{51} -6.00000 q^{53} -9.00000 q^{55} +6.92820i q^{57} +(-1.50000 + 2.59808i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{63} +(1.50000 + 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-4.50000 - 2.59808i) q^{69} +12.0000 q^{71} -10.0000 q^{73} +(6.00000 - 3.46410i) q^{75} +(1.50000 - 2.59808i) q^{77} +(5.50000 + 9.52628i) q^{79} +9.00000 q^{81} +(-4.50000 - 7.79423i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(4.50000 - 2.59808i) q^{87} +6.00000 q^{89} -1.00000 q^{91} +(7.50000 + 4.33013i) q^{93} +(-6.00000 + 10.3923i) q^{95} +(-5.50000 - 9.52628i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^5 - q^7 - 6 * q^9	\( 2 q - 3 q^{5} - q^{7} - 6 q^{9} + 3 q^{11} + q^{13} - 9 q^{15} + 12 q^{17} + 8 q^{19} + 3 q^{21} - 3 q^{23} - 4 q^{25} - 3 q^{29} + 5 q^{31} - 9 q^{33} + 6 q^{35} + 4 q^{37} + 3 q^{39} - 3 q^{41} - q^{43} + 9 q^{45} - 9 q^{47} + 6 q^{49} - 12 q^{53} - 18 q^{55} - 3 q^{59} + 13 q^{61} + 3 q^{63} + 3 q^{65} - 7 q^{67} - 9 q^{69} + 24 q^{71} - 20 q^{73} + 12 q^{75} + 3 q^{77} + 11 q^{79} + 18 q^{81} - 9 q^{83} - 18 q^{85} + 9 q^{87} + 12 q^{89} - 2 q^{91} + 15 q^{93} - 12 q^{95} - 11 q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q - 3 * q^5 - q^7 - 6 * q^9 + 3 * q^11 + q^13 - 9 * q^15 + 12 * q^17 + 8 * q^19 + 3 * q^21 - 3 * q^23 - 4 * q^25 - 3 * q^29 + 5 * q^31 - 9 * q^33 + 6 * q^35 + 4 * q^37 + 3 * q^39 - 3 * q^41 - q^43 + 9 * q^45 - 9 * q^47 + 6 * q^49 - 12 * q^53 - 18 * q^55 - 3 * q^59 + 13 * q^61 + 3 * q^63 + 3 * q^65 - 7 * q^67 - 9 * q^69 + 24 * q^71 - 20 * q^73 + 12 * q^75 + 3 * q^77 + 11 * q^79 + 18 * q^81 - 9 * q^83 - 18 * q^85 + 9 * q^87 + 12 * q^89 - 2 * q^91 + 15 * q^93 - 12 * q^95 - 11 * q^97 - 9 * q^99

Introduction

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