LMFDB - Embedded newform 1782.2.e.s.1189.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1782,2,Mod(595,1782)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1782, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1782.595");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1782 = 2 \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1782.e (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:	$14.2293416402$
Analytic rank:	$1$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1189.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1782.1189
Dual form			1782.2.e.s.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{11} +(2.00000 + 3.46410i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +4.00000 q^{26} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -10.0000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} -1.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(2.00000 - 3.46410i) q^{52} +(1.00000 - 1.73205i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +6.00000 q^{71} +2.00000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(1.00000 + 1.73205i) q^{77} +(-7.00000 + 12.1244i) q^{79} -6.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(4.00000 + 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} -6.00000 q^{89} -8.00000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-7.00000 + 12.1244i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + q^{11} + 4 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 8 q^{19} - q^{22} - 6 q^{23} + 5 q^{25} + 8 q^{26} + 4 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} - 6 q^{34} - 20 q^{37} - 4 q^{38} - 6 q^{41} - 8 q^{43} - 2 q^{44} - 12 q^{46} + 6 q^{47} + 3 q^{49} - 5 q^{50} + 4 q^{52} + 2 q^{56} + 6 q^{58} - 8 q^{61} - 16 q^{62} + 2 q^{64} + 4 q^{67} + 6 q^{68} + 12 q^{71} + 4 q^{73} - 10 q^{74} + 4 q^{76} + 2 q^{77} - 14 q^{79} - 12 q^{82} + 12 q^{83} + 8 q^{86} - q^{88} - 12 q^{89} - 16 q^{91} - 6 q^{92} - 6 q^{94} - 14 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + q^11 + 4 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 8 * q^19 - q^22 - 6 * q^23 + 5 * q^25 + 8 * q^26 + 4 * q^28 - 6 * q^29 - 8 * q^31 + q^32 - 6 * q^34 - 20 * q^37 - 4 * q^38 - 6 * q^41 - 8 * q^43 - 2 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^49 - 5 * q^50 + 4 * q^52 + 2 * q^56 + 6 * q^58 - 8 * q^61 - 16 * q^62 + 2 * q^64 + 4 * q^67 + 6 * q^68 + 12 * q^71 + 4 * q^73 - 10 * q^74 + 4 * q^76 + 2 * q^77 - 14 * q^79 - 12 * q^82 + 12 * q^83 + 8 * q^86 - q^88 - 12 * q^89 - 16 * q^91 - 6 * q^92 - 6 * q^94 - 14 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1782\mathbb{Z}\right)^\times$.

$n$	$1135$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	4.00000			0.784465
$27$		0			0
$28$	2.00000			0.377964
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	−6.00000			−0.884652
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−5.00000	+	8.66025i	−0.581238	+	1.00673i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	1.00000	+	1.73205i	0.113961	+	0.197386i
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$		0			0
$81$		0			0
$82$	−6.00000			−0.662589
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	−5.00000			−0.500000
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$		0			0
$106$		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
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$		0			0
$112$	−1.00000	−	1.73205i	−0.0944911	−	0.163663i
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$		0			0
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		0			0
$126$		0			0
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$	4.00000			0.345547
$135$		0			0
$136$	6.00000			0.514496
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	4.00000			0.334497
$144$		0			0
$145$		0			0
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$	2.00000			0.161165
$155$		0			0
$156$		0			0
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	7.00000	+	12.1244i	0.556890	+	0.964562i
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	5.00000	+	8.66025i	0.377964	+	0.654654i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−6.00000			−0.437595
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	7.00000	+	12.1244i	0.502571	+	0.870478i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	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	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$		0			0
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$	−6.00000	−	10.3923i	−0.421117	−	0.729397i
$204$		0			0
$205$		0			0
$206$	4.00000			0.278693
$207$		0			0
$208$	−4.00000			−0.277350
$209$	−2.00000	+	3.46410i	−0.138343	+	0.239617i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$		0			0
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$		0			0
$216$		0			0
$217$	16.0000			1.08615
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$		0			0
$220$		0			0
$221$	−12.0000	−	20.7846i	−0.807207	−	1.39812i
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	−18.0000			−1.19734
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−1.00000			−0.0642824
$243$		0			0
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	7.00000	−	12.1244i	0.439219	−	0.760750i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$		0			0
$259$	10.0000	−	17.3205i	0.621370	−	1.07624i
$260$		0			0
$261$		0			0
$262$	12.0000			0.741362
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$	−4.00000	−	6.92820i	−0.245256	−	0.424795i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$		0			0
$274$	−9.00000	−	15.5885i	−0.543710	−	0.941733i
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	4.00000			0.239904
$279$		0			0
$280$		0			0
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	−0.762561	−	0.646916i	$-0.776058\pi$
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	0.941526	+	0.336939i	$0.109392\pi$
$282$		0			0
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	0.722300	−	0.691580i	$-0.243085\pi$
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	−0.960076	+	0.279741i	$0.909752\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	2.00000	−	3.46410i	0.118262	−	0.204837i
$287$	12.0000			0.708338
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	0.940252	−	0.340480i	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$		0			0
$295$		0			0
$296$	10.0000			0.581238
$297$		0			0
$298$	6.00000			0.347571
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$		0			0
$310$		0			0
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$		0			0
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	0.220006	+	0.975499i	$0.429392\pi$
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	−0.954810	+	0.297218i	$0.903941\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	14.0000			0.787562
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$		0			0
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	24.0000			1.33540
$324$		0			0
$325$	20.0000			1.10940
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	−12.0000			−0.656611
$335$		0			0
$336$		0			0
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	0.837503	−	0.546433i	$-0.184015\pi$
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	−0.891976	+	0.452082i	$0.850681\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$		0			0
$340$		0			0
$341$	−8.00000			−0.433224
$342$		0			0
$343$	−20.0000			−1.07990
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.706107	−	0.708105i	$-0.749550\pi$
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.260184	−	0.965559i	$-0.583783\pi$
$348$		0			0
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	−0.807519	−	0.589841i	$-0.799190\pi$
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	0.914577	+	0.404412i	$0.132524\pi$
$350$	10.0000			0.534522
$351$		0			0
$352$	1.00000			0.0533002
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$		0			0
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$		0			0
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$		0			0
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	6.00000			0.312772
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	−0.999787	−	0.0206542i	$-0.993425\pi$
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	0.482006	−	0.876168i	$-0.339908\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−24.0000			−1.23606
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$		0			0
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$		0			0
$385$		0			0
$386$	−14.0000			−0.712581
$387$		0			0
$388$	14.0000			0.710742
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$		0			0
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$		0			0
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	−2.00000	+	3.46410i	−0.100251	+	0.173640i
$399$		0			0
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$		0			0
$403$	16.0000	−	27.7128i	0.797017	−	1.38047i
$404$	6.00000			0.298511
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−5.00000	+	8.66025i	−0.247841	+	0.429273i
$408$		0			0
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	0.889392	+	0.457146i	$0.151128\pi$
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	−0.0487958	+	0.998809i	$0.515538\pi$
$410$		0			0
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		0			0
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	−0.994720	−	0.102628i	$-0.967275\pi$
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	0.408481	−	0.912767i	$-0.366058\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	−8.00000			−0.389434
$423$		0			0
$424$		0			0
$425$	−15.0000	+	25.9808i	−0.727607	+	1.26025i
$426$		0			0
$427$	−8.00000	−	13.8564i	−0.387147	−	0.670559i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$		0			0
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	22.0000			1.02799
$459$		0			0
$460$		0			0
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.308651	+	0.951175i	$0.599877\pi$
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.669417	+	0.742887i	$0.733456\pi$
$462$		0			0
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	−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
$469$	−8.00000			−0.369406
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$		0			0
$475$	−10.0000	+	17.3205i	−0.458831	+	0.794719i
$476$	−12.0000			−0.550019
$477$		0			0
$478$	12.0000			0.548867
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	−20.0000	−	34.6410i	−0.911922	−	1.57949i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$		0			0
$486$		0			0
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$		0			0
$490$		0			0
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$		0			0
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$		0			0
$508$	−7.00000	−	12.1244i	−0.310575	−	0.537931i
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	−0.999307	−	0.0372243i	$-0.988148\pi$
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	0.467416	−	0.884037i	$-0.345185\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	30.0000			1.32324
$515$		0			0
$516$		0			0
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$	−10.0000	−	17.3205i	−0.439375	−	0.761019i
$519$		0			0
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$		0			0
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$	−8.00000			−0.346844
$533$	12.0000	−	20.7846i	0.519778	−	0.900281i
$534$		0			0
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	−12.0000	+	20.7846i	−0.517357	+	0.896088i
$539$	3.00000			0.129219
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	1.00000	−	1.73205i	0.0429537	−	0.0743980i
$543$		0			0
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$		0			0
$546$		0			0
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	0.993028	−	0.117875i	$-0.0376081\pi$
$548$	−18.0000			−0.768922
$549$		0			0
$550$	−5.00000			−0.213201
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$		0			0
$553$	−14.0000	−	24.2487i	−0.595341	−	1.03116i
$554$	−8.00000	−	13.8564i	−0.339887	−	0.588702i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$	−32.0000			−1.35346
$560$		0			0
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$		0			0
$566$	−8.00000			−0.336265
$567$		0			0
$568$	−6.00000			−0.251754
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		0			0
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$	−30.0000			−1.25109
$576$		0			0
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$		0			0
$581$	12.0000	+	20.7846i	0.497844	+	0.862291i
$582$		0			0
$583$		0			0
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	6.00000			0.247858
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	−0.999985	−	0.00542667i	$-0.998273\pi$
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	0.504692	+	0.863299i	$0.331606\pi$
$588$		0			0
$589$	16.0000	+	27.7128i	0.659269	+	1.14189i
$590$		0			0
$591$		0			0
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		0			0
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$	−16.0000			−0.652111
$603$		0			0
$604$	−10.0000			−0.406894
$605$		0			0
$606$		0			0
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$		0			0
$610$		0			0
$611$	24.0000			0.970936
$612$		0			0
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	−1.00000	−	1.73205i	−0.0402911	−	0.0697863i
$617$	15.0000	+	25.9808i	0.603877	+	1.04595i	0.992228	+	0.124434i	$0.0397116\pi$
$617$	15.0000	+	25.9808i	0.603877	+	1.04595i	−0.388351	+	0.921512i	$0.626955\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$		0			0
$621$		0			0
$622$	18.0000			0.721734
$623$	6.00000	−	10.3923i	0.240385	−	0.416359i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	60.0000			2.39236
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	7.00000	−	12.1244i	0.278445	−	0.482281i
$633$		0			0
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$		0			0
$636$		0			0
$637$	−6.00000	+	10.3923i	−0.237729	+	0.411758i
$638$	6.00000			0.237542
$639$		0			0
$640$		0			0
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		0			0
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$		0			0
$650$	10.0000	−	17.3205i	0.392232	−	0.679366i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$		0			0
$655$		0			0
$656$	6.00000			0.234261
$657$		0			0
$658$	12.0000			0.467809
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$	36.0000			1.39393
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$		0			0
$670$		0			0
$671$	4.00000	+	6.92820i	0.154418	+	0.267460i
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	−2.00000			−0.0770371
$675$		0			0
$676$	3.00000			0.115385
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	−0.995877	+	0.0907112i	$0.971086\pi$
$678$		0			0
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$		0			0
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$		0			0
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$		0			0
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−36.0000			−1.36654
$695$		0			0
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$		0			0
$700$	5.00000	−	8.66025i	0.188982	−	0.327327i
$701$	−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
$703$	40.0000			1.50863
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	−3.00000	−	5.19615i	−0.112906	−	0.195560i
$707$	−6.00000	−	10.3923i	−0.225653	−	0.390843i
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$		0			0
$712$	6.00000			0.224860
$713$	−24.0000	+	41.5692i	−0.898807	+	1.55678i
$714$		0			0
$715$		0			0
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		0			0
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	30.0000			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$		0			0
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	15.0000	+	25.9808i	0.557086	+	0.964901i
$726$		0			0
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$	8.00000			0.296500
$729$		0			0
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$		0			0
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	0.900595	−	0.434659i	$-0.143131\pi$
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	−0.826723	+	0.562609i	$0.809798\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	4.00000			0.147342
$738$		0			0
$739$	8.00000			0.294285			0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000			0.294285			0.147142	+	0.989115i	$0.452992\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$		0			0
$745$		0			0
$746$	−20.0000			−0.732252
$747$		0			0
$748$	6.00000			0.219382
$749$	12.0000	−	20.7846i	0.438470	−	0.759453i
$750$		0			0
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	−12.0000	+	20.7846i	−0.437014	+	0.756931i
$755$		0			0
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$		0			0
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	18.0000			0.651217
$765$		0			0
$766$	−6.00000			−0.216789
$767$		0			0
$768$		0			0
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$	−40.0000			−1.43684
$776$	7.00000	−	12.1244i	0.251285	−	0.435239i
$777$		0			0
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$	36.0000			1.28736
$783$		0			0
$784$	−3.00000			−0.107143
$785$		0			0
$786$		0			0
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$		0			0
$790$		0			0
$791$	36.0000			1.28001
$792$		0			0
$793$	−32.0000			−1.13635
$794$	13.0000	−	22.5167i	0.461353	−	0.799086i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$	−18.0000	+	31.1769i	−0.636794	+	1.10296i
$800$	5.00000			0.176777
$801$		0			0
$802$	−30.0000			−1.05934
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$		0			0
$805$		0			0
$806$	−16.0000	−	27.7128i	−0.563576	−	0.976142i
$807$		0			0
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	−6.00000	+	10.3923i	−0.210559	+	0.364698i
$813$		0			0
$814$	5.00000	+	8.66025i	0.175250	+	0.303542i
$815$		0			0
$816$		0			0
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$	34.0000			1.18878
$819$		0			0
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$		0			0
$831$		0			0
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$	−9.00000	−	15.5885i	−0.311832	−	0.540108i
$834$		0			0
$835$		0			0
$836$	4.00000			0.138343
$837$		0			0
$838$	−24.0000			−0.829066
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$		0			0
$846$		0			0
$847$	2.00000			0.0687208
$848$		0			0
$849$		0			0
$850$	15.0000	+	25.9808i	0.514496	+	0.891133i
$851$	30.0000	+	51.9615i	1.02839	+	1.78122i
$852$		0			0
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	−0.926343	−	0.376680i	$-0.877066\pi$
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	0.789386	+	0.613897i	$0.210399\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$	12.0000			0.410152
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.126459	+	0.991972i	$0.540361\pi$
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.795843	+	0.605503i	$0.792972\pi$
$858$		0			0
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	0.643459	−	0.765480i	$-0.277499\pi$
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	−0.984655	+	0.174512i	$0.944165\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	42.0000			1.42970			0.714848	−	0.699280i	$-0.246496\pi$
$863$	42.0000			1.42970			0.714848	+	0.699280i	$0.246496\pi$
$864$		0			0
$865$		0			0
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$		0			0
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	7.00000	+	12.1244i	0.237459	+	0.411291i
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	4.00000			0.135457
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	26.0000	+	45.0333i	0.877958	+	1.52067i	0.853578	+	0.520964i	$0.174428\pi$
$877$	26.0000	+	45.0333i	0.877958	+	1.52067i	0.0243792	+	0.999703i	$0.492239\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	−14.0000	+	24.2487i	−0.469545	+	0.813276i
$890$		0			0
$891$		0			0
$892$	−16.0000			−0.535720
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$		0			0
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$		0			0
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	48.0000			1.60089
$900$		0			0
$901$		0			0
$902$	−3.00000	+	5.19615i	−0.0998891	+	0.173013i
$903$		0			0
$904$	9.00000	+	15.5885i	0.299336	+	0.518464i
$905$		0			0
$906$		0			0
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$		0			0
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	−0.274162	−	0.961683i	$-0.588401\pi$
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	0.969923	−	0.243410i	$-0.0782661\pi$
$912$		0			0
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	−24.0000			−0.792550
$918$		0			0
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$		0			0
$921$		0			0
$922$	21.0000	+	36.3731i	0.691598	+	1.19788i
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$		0			0
$925$	−25.0000	+	43.3013i	−0.821995	+	1.42374i
$926$	4.00000			0.131448
$927$		0			0
$928$	−6.00000			−0.196960
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$	−6.00000	−	10.3923i	−0.196642	−	0.340594i
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−4.00000	+	6.92820i	−0.130605	+	0.226214i
$939$		0			0
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$		0			0
$945$		0			0
$946$	8.00000			0.260102
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	10.0000	+	17.3205i	0.324443	+	0.561951i
$951$		0			0
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$		0			0
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−40.0000			−1.28965
$963$		0			0
$964$	−10.0000			−0.322078
$965$		0			0
$966$		0			0
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	0.731246	−	0.682114i	$-0.238939\pi$
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	−0.956351	+	0.292221i	$0.905606\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$	10.0000	−	17.3205i	0.320421	−	0.554985i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$		0			0
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$		0			0
$981$		0			0
$982$	−12.0000			−0.382935
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	−0.999694	−	0.0247352i	$-0.992126\pi$
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	0.521268	+	0.853393i	$0.325459\pi$
$984$		0			0
$985$		0			0
$986$	−18.0000	−	31.1769i	−0.573237	−	0.992875i
$987$		0			0
$988$	−8.00000	+	13.8564i	−0.254514	+	0.440831i
$989$	48.0000			1.52631
$990$		0			0
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$		0			0
$994$	6.00000	+	10.3923i	0.190308	+	0.329624i
$995$		0			0
$996$		0			0
$997$	−22.0000	+	38.1051i	−0.696747	+	1.20680i	0.272841	+	0.962059i	$0.412037\pi$
$997$	−22.0000	+	38.1051i	−0.696747	+	1.20680i	−0.969588	+	0.244742i	$0.921297\pi$
$998$	4.00000			0.126618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1782.2.e.s.1189.1		2
3.2	odd	2		1782.2.e.f.1189.1		2
9.2	odd	6		198.2.a.e.1.1		1
9.4	even	3	inner	1782.2.e.s.595.1		2
9.5	odd	6		1782.2.e.f.595.1		2
9.7	even	3		66.2.a.a.1.1	✓	1
36.7	odd	6		528.2.a.d.1.1		1
36.11	even	6		1584.2.a.h.1.1		1
45.2	even	12		4950.2.c.r.199.2		2
45.7	odd	12		1650.2.c.d.199.1		2
45.29	odd	6		4950.2.a.g.1.1		1
45.34	even	6		1650.2.a.m.1.1		1
45.38	even	12		4950.2.c.r.199.1		2
45.43	odd	12		1650.2.c.d.199.2		2
63.20	even	6		9702.2.a.bu.1.1		1
63.34	odd	6		3234.2.a.d.1.1		1
72.11	even	6		6336.2.a.bf.1.1		1
72.29	odd	6		6336.2.a.bj.1.1		1
72.43	odd	6		2112.2.a.v.1.1		1
72.61	even	6		2112.2.a.i.1.1		1
99.7	odd	30		726.2.e.b.511.1		4
99.16	even	15		726.2.e.k.487.1		4
99.25	even	15		726.2.e.k.493.1		4
99.43	odd	6		726.2.a.i.1.1		1
99.52	odd	30		726.2.e.b.493.1		4
99.61	odd	30		726.2.e.b.487.1		4
99.65	even	6		2178.2.a.b.1.1		1
99.70	even	15		726.2.e.k.511.1		4
99.79	odd	30		726.2.e.b.565.1		4
99.97	even	15		726.2.e.k.565.1		4
396.43	even	6		5808.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.a.1.1	✓	1	9.7	even	3
198.2.a.e.1.1		1	9.2	odd	6
528.2.a.d.1.1		1	36.7	odd	6
726.2.a.i.1.1		1	99.43	odd	6
726.2.e.b.487.1		4	99.61	odd	30
726.2.e.b.493.1		4	99.52	odd	30
726.2.e.b.511.1		4	99.7	odd	30
726.2.e.b.565.1		4	99.79	odd	30
726.2.e.k.487.1		4	99.16	even	15
726.2.e.k.493.1		4	99.25	even	15
726.2.e.k.511.1		4	99.70	even	15
726.2.e.k.565.1		4	99.97	even	15
1584.2.a.h.1.1		1	36.11	even	6
1650.2.a.m.1.1		1	45.34	even	6
1650.2.c.d.199.1		2	45.7	odd	12
1650.2.c.d.199.2		2	45.43	odd	12
1782.2.e.f.595.1		2	9.5	odd	6
1782.2.e.f.1189.1		2	3.2	odd	2
1782.2.e.s.595.1		2	9.4	even	3	inner
1782.2.e.s.1189.1		2	1.1	even	1	trivial
2112.2.a.i.1.1		1	72.61	even	6
2112.2.a.v.1.1		1	72.43	odd	6
2178.2.a.b.1.1		1	99.65	even	6
3234.2.a.d.1.1		1	63.34	odd	6
4950.2.a.g.1.1		1	45.29	odd	6
4950.2.c.r.199.1		2	45.38	even	12
4950.2.c.r.199.2		2	45.2	even	12
5808.2.a.l.1.1		1	396.43	even	6
6336.2.a.bf.1.1		1	72.11	even	6
6336.2.a.bj.1.1		1	72.29	odd	6
9702.2.a.bu.1.1		1	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1782 = 2 \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1782.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{11} +(2.00000 + 3.46410i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +4.00000 q^{26} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -10.0000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} -1.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(2.00000 - 3.46410i) q^{52} +(1.00000 - 1.73205i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +6.00000 q^{71} +2.00000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(1.00000 + 1.73205i) q^{77} +(-7.00000 + 12.1244i) q^{79} -6.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(4.00000 + 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} -6.00000 q^{89} -8.00000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-7.00000 + 12.1244i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 2 q^{7} - 2 q^{8} + q^{11} + 4 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 8 q^{19} - q^{22} - 6 q^{23} + 5 q^{25} + 8 q^{26} + 4 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} - 6 q^{34} - 20 q^{37} - 4 q^{38} - 6 q^{41} - 8 q^{43} - 2 q^{44} - 12 q^{46} + 6 q^{47} + 3 q^{49} - 5 q^{50} + 4 q^{52} + 2 q^{56} + 6 q^{58} - 8 q^{61} - 16 q^{62} + 2 q^{64} + 4 q^{67} + 6 q^{68} + 12 q^{71} + 4 q^{73} - 10 q^{74} + 4 q^{76} + 2 q^{77} - 14 q^{79} - 12 q^{82} + 12 q^{83} + 8 q^{86} - q^{88} - 12 q^{89} - 16 q^{91} - 6 q^{92} - 6 q^{94} - 14 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^7 - 2 * q^8 + q^11 + 4 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 8 * q^19 - q^22 - 6 * q^23 + 5 * q^25 + 8 * q^26 + 4 * q^28 - 6 * q^29 - 8 * q^31 + q^32 - 6 * q^34 - 20 * q^37 - 4 * q^38 - 6 * q^41 - 8 * q^43 - 2 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^49 - 5 * q^50 + 4 * q^52 + 2 * q^56 + 6 * q^58 - 8 * q^61 - 16 * q^62 + 2 * q^64 + 4 * q^67 + 6 * q^68 + 12 * q^71 + 4 * q^73 - 10 * q^74 + 4 * q^76 + 2 * q^77 - 14 * q^79 - 12 * q^82 + 12 * q^83 + 8 * q^86 - q^88 - 12 * q^89 - 16 * q^91 - 6 * q^92 - 6 * q^94 - 14 * q^97 + 6 * q^98

Introduction

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