LMFDB - Embedded newform 1050.2.b.b.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(251,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1050.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.b (of order $2$, degree $1$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.b.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} +1.00000i q^{8} -3.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} +1.00000i q^{8} -3.00000i q^{9} +(1.22474 - 1.22474i) q^{12} +2.44949i q^{13} +(-2.44949 - 1.00000i) q^{14} +1.00000 q^{16} -4.89898 q^{17} -3.00000 q^{18} +2.44949i q^{19} +(1.77526 + 4.22474i) q^{21} -6.00000i q^{23} +(-1.22474 - 1.22474i) q^{24} +2.44949 q^{26} +(3.67423 + 3.67423i) q^{27} +(-1.00000 + 2.44949i) q^{28} -6.00000i q^{29} -1.00000i q^{32} +4.89898i q^{34} +3.00000i q^{36} +2.00000 q^{37} +2.44949 q^{38} +(-3.00000 - 3.00000i) q^{39} -4.89898 q^{41} +(4.22474 - 1.77526i) q^{42} -4.00000 q^{43} -6.00000 q^{46} -4.89898 q^{47} +(-1.22474 + 1.22474i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(6.00000 - 6.00000i) q^{51} -2.44949i q^{52} -6.00000i q^{53} +(3.67423 - 3.67423i) q^{54} +(2.44949 + 1.00000i) q^{56} +(-3.00000 - 3.00000i) q^{57} -6.00000 q^{58} -12.2474 q^{59} -12.2474i q^{61} +(-7.34847 - 3.00000i) q^{63} -1.00000 q^{64} -8.00000 q^{67} +4.89898 q^{68} +(7.34847 + 7.34847i) q^{69} +3.00000 q^{72} -9.79796i q^{73} -2.00000i q^{74} -2.44949i q^{76} +(-3.00000 + 3.00000i) q^{78} -10.0000 q^{79} -9.00000 q^{81} +4.89898i q^{82} -2.44949 q^{83} +(-1.77526 - 4.22474i) q^{84} +4.00000i q^{86} +(7.34847 + 7.34847i) q^{87} +(6.00000 + 2.44949i) q^{91} +6.00000i q^{92} +4.89898i q^{94} +(1.22474 + 1.22474i) q^{96} -4.89898i q^{97} +(-4.89898 + 5.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^7	$ 4 q - 4 q^{4} + 4 q^{7} + 4 q^{16} - 12 q^{18} + 12 q^{21} - 4 q^{28} + 8 q^{37} - 12 q^{39} + 12 q^{42} - 16 q^{43} - 24 q^{46} - 20 q^{49} + 24 q^{51} - 12 q^{57} - 24 q^{58} - 4 q^{64} - 32 q^{67} + 12 q^{72} - 12 q^{78} - 40 q^{79} - 36 q^{81} - 12 q^{84} + 24 q^{91}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^7 + 4 * q^16 - 12 * q^18 + 12 * q^21 - 4 * q^28 + 8 * q^37 - 12 * q^39 + 12 * q^42 - 16 * q^43 - 24 * q^46 - 20 * q^49 + 24 * q^51 - 12 * q^57 - 24 * q^58 - 4 * q^64 - 32 * q^67 + 12 * q^72 - 12 * q^78 - 40 * q^79 - 36 * q^81 - 12 * q^84 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	1.22474	+	1.22474i	0.500000	+	0.500000i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$			1.00000i			0.353553i
$9$		−	3.00000i		−	1.00000i
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	−2.44949	−	1.00000i	−0.654654	−	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	−4.89898			−1.18818			−0.594089	−	0.804400i	$-0.702487\pi$
$17$	−4.89898			−1.18818			−0.594089	+	0.804400i	$0.702487\pi$
$18$	−3.00000			−0.707107
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$		0			0
$21$	1.77526	+	4.22474i	0.387392	+	0.921915i
$22$		0			0
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	−1.22474	−	1.22474i	−0.250000	−	0.250000i
$25$		0			0
$26$	2.44949			0.480384
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$	−1.00000	+	2.44949i	−0.188982	+	0.462910i
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			4.89898i			0.840168i
$35$		0			0
$36$			3.00000i			0.500000i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	2.44949			0.397360
$39$	−3.00000	−	3.00000i	−0.480384	−	0.480384i
$40$		0			0
$41$	−4.89898			−0.765092			−0.382546	−	0.923936i	$-0.624953\pi$
$41$	−4.89898			−0.765092			−0.382546	+	0.923936i	$0.624953\pi$
$42$	4.22474	−	1.77526i	0.651892	−	0.273928i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$		0			0
$46$	−6.00000			−0.884652
$47$	−4.89898			−0.714590			−0.357295	−	0.933992i	$-0.616301\pi$
$47$	−4.89898			−0.714590			−0.357295	+	0.933992i	$0.616301\pi$
$48$	−1.22474	+	1.22474i	−0.176777	+	0.176777i
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$	6.00000	−	6.00000i	0.840168	−	0.840168i
$52$		−	2.44949i		−	0.339683i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	3.67423	−	3.67423i	0.500000	−	0.500000i
$55$		0			0
$56$	2.44949	+	1.00000i	0.327327	+	0.133631i
$57$	−3.00000	−	3.00000i	−0.397360	−	0.397360i
$58$	−6.00000			−0.787839
$59$	−12.2474			−1.59448			−0.797241	−	0.603661i	$-0.793708\pi$
$59$	−12.2474			−1.59448			−0.797241	+	0.603661i	$0.793708\pi$
$60$		0			0
$61$		−	12.2474i		−	1.56813i	−0.620682	−	0.784063i	$-0.713144\pi$
$61$		−	12.2474i		−	1.56813i	0.620682	−	0.784063i	$-0.286856\pi$
$62$		0			0
$63$	−7.34847	−	3.00000i	−0.925820	−	0.377964i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$	4.89898			0.594089
$69$	7.34847	+	7.34847i	0.884652	+	0.884652i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	3.00000			0.353553
$73$		−	9.79796i		−	1.14676i	−0.819288	−	0.573382i	$-0.805631\pi$
$73$		−	9.79796i		−	1.14676i	0.819288	−	0.573382i	$-0.194369\pi$
$74$		−	2.00000i		−	0.232495i
$75$		0			0
$76$		−	2.44949i		−	0.280976i
$77$		0			0
$78$	−3.00000	+	3.00000i	−0.339683	+	0.339683i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$			4.89898i			0.541002i
$83$	−2.44949			−0.268866			−0.134433	−	0.990923i	$-0.542921\pi$
$83$	−2.44949			−0.268866			−0.134433	+	0.990923i	$0.542921\pi$
$84$	−1.77526	−	4.22474i	−0.193696	−	0.460957i
$85$		0			0
$86$			4.00000i			0.431331i
$87$	7.34847	+	7.34847i	0.787839	+	0.787839i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$			6.00000i			0.625543i
$93$		0			0
$94$			4.89898i			0.505291i
$95$		0			0
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$		−	4.89898i		−	0.497416i	−0.968579	−	0.248708i	$-0.919994\pi$
$97$		−	4.89898i		−	0.497416i	0.968579	−	0.248708i	$-0.0800060\pi$
$98$	−4.89898	+	5.00000i	−0.494872	+	0.505076i
$99$		0			0
$100$		0			0
$101$	7.34847			0.731200			0.365600	−	0.930772i	$-0.380864\pi$
$101$	7.34847			0.731200			0.365600	+	0.930772i	$0.380864\pi$
$102$	−6.00000	−	6.00000i	−0.594089	−	0.594089i
$103$		−	9.79796i		−	0.965422i	−0.875780	−	0.482711i	$-0.839652\pi$
$103$		−	9.79796i		−	0.965422i	0.875780	−	0.482711i	$-0.160348\pi$
$104$	−2.44949			−0.240192
$105$		0			0
$106$	−6.00000			−0.582772
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	−3.67423	−	3.67423i	−0.353553	−	0.353553i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−2.44949	+	2.44949i	−0.232495	+	0.232495i
$112$	1.00000	−	2.44949i	0.0944911	−	0.231455i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−3.00000	+	3.00000i	−0.280976	+	0.280976i
$115$		0			0
$116$			6.00000i			0.557086i
$117$	7.34847			0.679366
$118$			12.2474i			1.12747i
$119$	−4.89898	+	12.0000i	−0.449089	+	1.10004i
$120$		0			0
$121$	11.0000			1.00000
$122$	−12.2474			−1.10883
$123$	6.00000	−	6.00000i	0.541002	−	0.541002i
$124$		0			0
$125$		0			0
$126$	−3.00000	+	7.34847i	−0.267261	+	0.654654i
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$			1.00000i			0.0883883i
$129$	4.89898	−	4.89898i	0.431331	−	0.431331i
$130$		0			0
$131$	7.34847			0.642039			0.321019	−	0.947073i	$-0.395975\pi$
$131$	7.34847			0.642039			0.321019	+	0.947073i	$0.395975\pi$
$132$		0			0
$133$	6.00000	+	2.44949i	0.520266	+	0.212398i
$134$			8.00000i			0.691095i
$135$		0			0
$136$		−	4.89898i		−	0.420084i
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	7.34847	−	7.34847i	0.625543	−	0.625543i
$139$			2.44949i			0.207763i	0.994590	+	0.103882i	$0.0331263\pi$
$139$			2.44949i			0.207763i	−0.994590	+	0.103882i	$0.966874\pi$
$140$		0			0
$141$	6.00000	−	6.00000i	0.505291	−	0.505291i
$142$		0			0
$143$		0			0
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−9.79796			−0.810885
$147$	12.1237	−	0.123724i	0.999948	−	0.0102046i
$148$	−2.00000			−0.164399
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	−2.44949			−0.198680
$153$			14.6969i			1.18818i
$154$		0			0
$155$		0			0
$156$	3.00000	+	3.00000i	0.240192	+	0.240192i
$157$			7.34847i			0.586472i	0.956040	+	0.293236i	$0.0947321\pi$
$157$			7.34847i			0.586472i	−0.956040	+	0.293236i	$0.905268\pi$
$158$			10.0000i			0.795557i
$159$	7.34847	+	7.34847i	0.582772	+	0.582772i
$160$		0			0
$161$	−14.6969	−	6.00000i	−1.15828	−	0.472866i
$162$			9.00000i			0.707107i
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$	4.89898			0.382546
$165$		0			0
$166$			2.44949i			0.190117i
$167$	−4.89898			−0.379094			−0.189547	−	0.981872i	$-0.560702\pi$
$167$	−4.89898			−0.379094			−0.189547	+	0.981872i	$0.560702\pi$
$168$	−4.22474	+	1.77526i	−0.325946	+	0.136964i
$169$	7.00000			0.538462
$170$		0			0
$171$	7.34847			0.561951
$172$	4.00000			0.304997
$173$	22.0454			1.67608			0.838041	−	0.545608i	$-0.183701\pi$
$173$	22.0454			1.67608			0.838041	+	0.545608i	$0.183701\pi$
$174$	7.34847	−	7.34847i	0.557086	−	0.557086i
$175$		0			0
$176$		0			0
$177$	15.0000	−	15.0000i	1.12747	−	1.12747i
$178$		0			0
$179$			24.0000i			1.79384i	0.442189	+	0.896922i	$0.354202\pi$
$179$			24.0000i			1.79384i	−0.442189	+	0.896922i	$0.645798\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	2.44949	−	6.00000i	0.181568	−	0.444750i
$183$	15.0000	+	15.0000i	1.10883	+	1.10883i
$184$	6.00000			0.442326
$185$		0			0
$186$		0			0
$187$		0			0
$188$	4.89898			0.357295
$189$	12.6742	−	5.32577i	0.921915	−	0.387392i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	1.22474	−	1.22474i	0.0883883	−	0.0883883i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	−4.89898			−0.351726
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$		−	9.79796i		−	0.694559i	−0.937762	−	0.347279i	$-0.887106\pi$
$199$		−	9.79796i		−	0.694559i	0.937762	−	0.347279i	$-0.112894\pi$
$200$		0			0
$201$	9.79796	−	9.79796i	0.691095	−	0.691095i
$202$		−	7.34847i		−	0.517036i
$203$	−14.6969	−	6.00000i	−1.03152	−	0.421117i
$204$	−6.00000	+	6.00000i	−0.420084	+	0.420084i
$205$		0			0
$206$	−9.79796			−0.682656
$207$	−18.0000			−1.25109
$208$			2.44949i			0.169842i
$209$		0			0
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	12.0000			0.820303
$215$		0			0
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$		−	10.0000i		−	0.677285i
$219$	12.0000	+	12.0000i	0.810885	+	0.810885i
$220$		0			0
$221$		−	12.0000i		−	0.807207i
$222$	2.44949	+	2.44949i	0.164399	+	0.164399i
$223$			14.6969i			0.984180i	0.870544	+	0.492090i	$0.163767\pi$
$223$			14.6969i			0.984180i	−0.870544	+	0.492090i	$0.836233\pi$
$224$	−2.44949	−	1.00000i	−0.163663	−	0.0668153i
$225$		0			0
$226$	−6.00000			−0.399114
$227$	7.34847			0.487735			0.243868	−	0.969809i	$-0.421584\pi$
$227$	7.34847			0.487735			0.243868	+	0.969809i	$0.421584\pi$
$228$	3.00000	+	3.00000i	0.198680	+	0.198680i
$229$		−	22.0454i		−	1.45680i	−0.685151	−	0.728401i	$-0.740264\pi$
$229$		−	22.0454i		−	1.45680i	0.685151	−	0.728401i	$-0.259736\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$			24.0000i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$233$			24.0000i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$234$		−	7.34847i		−	0.480384i
$235$		0			0
$236$	12.2474			0.797241
$237$	12.2474	−	12.2474i	0.795557	−	0.795557i
$238$	12.0000	+	4.89898i	0.777844	+	0.317554i
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$		0			0
$241$			24.4949i			1.57786i	0.614486	+	0.788928i	$0.289363\pi$
$241$			24.4949i			1.57786i	−0.614486	+	0.788928i	$0.710637\pi$
$242$		−	11.0000i		−	0.707107i
$243$	11.0227	−	11.0227i	0.707107	−	0.707107i
$244$			12.2474i			0.784063i
$245$		0			0
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$	−6.00000			−0.381771
$248$		0			0
$249$	3.00000	−	3.00000i	0.190117	−	0.190117i
$250$		0			0
$251$	−17.1464			−1.08227			−0.541136	−	0.840935i	$-0.682006\pi$
$251$	−17.1464			−1.08227			−0.541136	+	0.840935i	$0.682006\pi$
$252$	7.34847	+	3.00000i	0.462910	+	0.188982i
$253$		0			0
$254$			8.00000i			0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−29.3939			−1.83354			−0.916770	−	0.399416i	$-0.869213\pi$
$257$	−29.3939			−1.83354			−0.916770	+	0.399416i	$0.869213\pi$
$258$	−4.89898	−	4.89898i	−0.304997	−	0.304997i
$259$	2.00000	−	4.89898i	0.124274	−	0.304408i
$260$		0			0
$261$	−18.0000			−1.11417
$262$		−	7.34847i		−	0.453990i
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		0			0
$265$		0			0
$266$	2.44949	−	6.00000i	0.150188	−	0.367884i
$267$		0			0
$268$	8.00000			0.488678
$269$	−12.2474			−0.746740			−0.373370	−	0.927682i	$-0.621798\pi$
$269$	−12.2474			−0.746740			−0.373370	+	0.927682i	$0.621798\pi$
$270$		0			0
$271$		−	24.4949i		−	1.48796i	−0.668202	−	0.743980i	$-0.732936\pi$
$271$		−	24.4949i		−	1.48796i	0.668202	−	0.743980i	$-0.267064\pi$
$272$	−4.89898			−0.297044
$273$	−10.3485	+	4.34847i	−0.626318	+	0.263181i
$274$	12.0000			0.724947
$275$		0			0
$276$	−7.34847	−	7.34847i	−0.442326	−	0.442326i
$277$	22.0000			1.32185			0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000			1.32185			0.660926	+	0.750451i	$0.270164\pi$
$278$	2.44949			0.146911
$279$		0			0
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−6.00000	−	6.00000i	−0.357295	−	0.357295i
$283$		−	22.0454i		−	1.31046i	−0.755428	−	0.655232i	$-0.772571\pi$
$283$		−	22.0454i		−	1.31046i	0.755428	−	0.655232i	$-0.227429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.89898	+	12.0000i	−0.289178	+	0.708338i
$288$	−3.00000			−0.176777
$289$	7.00000			0.411765
$290$		0			0
$291$	6.00000	+	6.00000i	0.351726	+	0.351726i
$292$			9.79796i			0.573382i
$293$	−2.44949			−0.143101			−0.0715504	−	0.997437i	$-0.522795\pi$
$293$	−2.44949			−0.143101			−0.0715504	+	0.997437i	$0.522795\pi$
$294$	−0.123724	−	12.1237i	−0.00721575	−	0.707070i
$295$		0			0
$296$			2.00000i			0.116248i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	14.6969			0.849946
$300$		0			0
$301$	−4.00000	+	9.79796i	−0.230556	+	0.564745i
$302$			8.00000i			0.460348i
$303$	−9.00000	+	9.00000i	−0.517036	+	0.517036i
$304$			2.44949i			0.140488i
$305$		0			0
$306$	14.6969			0.840168
$307$			7.34847i			0.419399i	0.977766	+	0.209700i	$0.0672486\pi$
$307$			7.34847i			0.419399i	−0.977766	+	0.209700i	$0.932751\pi$
$308$		0			0
$309$	12.0000	+	12.0000i	0.682656	+	0.682656i
$310$		0			0
$311$	19.5959			1.11118			0.555591	−	0.831456i	$-0.312492\pi$
$311$	19.5959			1.11118			0.555591	+	0.831456i	$0.312492\pi$
$312$	3.00000	−	3.00000i	0.169842	−	0.169842i
$313$		−	34.2929i		−	1.93835i	−0.246380	−	0.969173i	$-0.579241\pi$
$313$		−	34.2929i		−	1.93835i	0.246380	−	0.969173i	$-0.420759\pi$
$314$	7.34847			0.414698
$315$		0			0
$316$	10.0000			0.562544
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	7.34847	−	7.34847i	0.412082	−	0.412082i
$319$		0			0
$320$		0			0
$321$	−14.6969	−	14.6969i	−0.820303	−	0.820303i
$322$	−6.00000	+	14.6969i	−0.334367	+	0.819028i
$323$		−	12.0000i		−	0.667698i
$324$	9.00000			0.500000
$325$		0			0
$326$		−	16.0000i		−	0.886158i
$327$	−12.2474	+	12.2474i	−0.677285	+	0.677285i
$328$		−	4.89898i		−	0.270501i
$329$	−4.89898	+	12.0000i	−0.270089	+	0.661581i
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	2.44949			0.134433
$333$		−	6.00000i		−	0.328798i
$334$			4.89898i			0.268060i
$335$		0			0
$336$	1.77526	+	4.22474i	0.0968481	+	0.230479i
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$		−	7.00000i		−	0.380750i
$339$	7.34847	+	7.34847i	0.399114	+	0.399114i
$340$		0			0
$341$		0			0
$342$		−	7.34847i		−	0.397360i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		−	4.00000i		−	0.215666i
$345$		0			0
$346$		−	22.0454i		−	1.18517i
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$	−7.34847	−	7.34847i	−0.393919	−	0.393919i
$349$			2.44949i			0.131118i	0.997849	+	0.0655591i	$0.0208831\pi$
$349$			2.44949i			0.131118i	−0.997849	+	0.0655591i	$0.979117\pi$
$350$		0			0
$351$	−9.00000	+	9.00000i	−0.480384	+	0.480384i
$352$		0			0
$353$	9.79796			0.521493			0.260746	−	0.965407i	$-0.416031\pi$
$353$	9.79796			0.521493			0.260746	+	0.965407i	$0.416031\pi$
$354$	−15.0000	−	15.0000i	−0.797241	−	0.797241i
$355$		0			0
$356$		0			0
$357$	−8.69694	−	20.6969i	−0.460291	−	1.09540i
$358$	24.0000			1.26844
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$		0			0
$361$	13.0000			0.684211
$362$	12.2474			0.643712
$363$	−13.4722	+	13.4722i	−0.707107	+	0.707107i
$364$	−6.00000	−	2.44949i	−0.314485	−	0.128388i
$365$		0			0
$366$	15.0000	−	15.0000i	0.784063	−	0.784063i
$367$		−	4.89898i		−	0.255725i	−0.991792	−	0.127862i	$-0.959188\pi$
$367$		−	4.89898i		−	0.255725i	0.991792	−	0.127862i	$-0.0408116\pi$
$368$		−	6.00000i		−	0.312772i
$369$			14.6969i			0.765092i
$370$		0			0
$371$	−14.6969	−	6.00000i	−0.763027	−	0.311504i
$372$		0			0
$373$	−14.0000			−0.724893			−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000			−0.724893			−0.362446	+	0.932005i	$0.618058\pi$
$374$		0			0
$375$		0			0
$376$		−	4.89898i		−	0.252646i
$377$	14.6969			0.756931
$378$	−5.32577	−	12.6742i	−0.273928	−	0.651892i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	9.79796	−	9.79796i	0.501965	−	0.501965i
$382$		0			0
$383$	34.2929			1.75228			0.876142	−	0.482054i	$-0.160109\pi$
$383$	34.2929			1.75228			0.876142	+	0.482054i	$0.160109\pi$
$384$	−1.22474	−	1.22474i	−0.0625000	−	0.0625000i
$385$		0			0
$386$			4.00000i			0.203595i
$387$			12.0000i			0.609994i
$388$			4.89898i			0.248708i
$389$		−	6.00000i		−	0.304212i	−0.988364	−	0.152106i	$-0.951394\pi$
$389$		−	6.00000i		−	0.304212i	0.988364	−	0.152106i	$-0.0486055\pi$
$390$		0			0
$391$			29.3939i			1.48651i
$392$	4.89898	−	5.00000i	0.247436	−	0.252538i
$393$	−9.00000	+	9.00000i	−0.453990	+	0.453990i
$394$	−18.0000			−0.906827
$395$		0			0
$396$		0			0
$397$			7.34847i			0.368809i	0.982850	+	0.184405i	$0.0590357\pi$
$397$			7.34847i			0.368809i	−0.982850	+	0.184405i	$0.940964\pi$
$398$	−9.79796			−0.491127
$399$	−10.3485	+	4.34847i	−0.518071	+	0.217696i
$400$		0			0
$401$			30.0000i			1.49813i	0.662497	+	0.749064i	$0.269497\pi$
$401$			30.0000i			1.49813i	−0.662497	+	0.749064i	$0.730503\pi$
$402$	−9.79796	−	9.79796i	−0.488678	−	0.488678i
$403$		0			0
$404$	−7.34847			−0.365600
$405$		0			0
$406$	−6.00000	+	14.6969i	−0.297775	+	0.729397i
$407$		0			0
$408$	6.00000	+	6.00000i	0.297044	+	0.297044i
$409$		−	34.2929i		−	1.69567i	−0.530258	−	0.847836i	$-0.677905\pi$
$409$		−	34.2929i		−	1.69567i	0.530258	−	0.847836i	$-0.322095\pi$
$410$		0			0
$411$	−14.6969	−	14.6969i	−0.724947	−	0.724947i
$412$			9.79796i			0.482711i
$413$	−12.2474	+	30.0000i	−0.602658	+	1.47620i
$414$			18.0000i			0.884652i
$415$		0			0
$416$	2.44949			0.120096
$417$	−3.00000	−	3.00000i	−0.146911	−	0.146911i
$418$		0			0
$419$	12.2474			0.598327			0.299164	−	0.954202i	$-0.403292\pi$
$419$	12.2474			0.598327			0.299164	+	0.954202i	$0.403292\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$			8.00000i			0.389434i
$423$			14.6969i			0.714590i
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	−30.0000	−	12.2474i	−1.45180	−	0.592696i
$428$		−	12.0000i		−	0.580042i
$429$		0			0
$430$		0			0
$431$			30.0000i			1.44505i	0.691345	+	0.722525i	$0.257018\pi$
$431$			30.0000i			1.44505i	−0.691345	+	0.722525i	$0.742982\pi$
$432$	3.67423	+	3.67423i	0.176777	+	0.176777i
$433$			14.6969i			0.706290i	0.935569	+	0.353145i	$0.114888\pi$
$433$			14.6969i			0.706290i	−0.935569	+	0.353145i	$0.885112\pi$
$434$		0			0
$435$		0			0
$436$	−10.0000			−0.478913
$437$	14.6969			0.703050
$438$	12.0000	−	12.0000i	0.573382	−	0.573382i
$439$			14.6969i			0.701447i	0.936479	+	0.350723i	$0.114064\pi$
$439$			14.6969i			0.701447i	−0.936479	+	0.350723i	$0.885936\pi$
$440$		0			0
$441$	−14.6969	+	15.0000i	−0.699854	+	0.714286i
$442$	−12.0000			−0.570782
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	2.44949	−	2.44949i	0.116248	−	0.116248i
$445$		0			0
$446$	14.6969			0.695920
$447$	7.34847	+	7.34847i	0.347571	+	0.347571i
$448$	−1.00000	+	2.44949i	−0.0472456	+	0.115728i
$449$		−	36.0000i		−	1.69895i	−0.527633	−	0.849473i	$-0.676920\pi$
$449$		−	36.0000i		−	1.69895i	0.527633	−	0.849473i	$-0.323080\pi$
$450$		0			0
$451$		0			0
$452$			6.00000i			0.282216i
$453$	9.79796	−	9.79796i	0.460348	−	0.460348i
$454$		−	7.34847i		−	0.344881i
$455$		0			0
$456$	3.00000	−	3.00000i	0.140488	−	0.140488i
$457$	−28.0000			−1.30978			−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000			−1.30978			−0.654892	+	0.755722i	$0.727286\pi$
$458$	−22.0454			−1.03011
$459$	−18.0000	−	18.0000i	−0.840168	−	0.840168i
$460$		0			0
$461$	31.8434			1.48309			0.741547	−	0.670901i	$-0.234093\pi$
$461$	31.8434			1.48309			0.741547	+	0.670901i	$0.234093\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$		−	6.00000i		−	0.278543i
$465$		0			0
$466$	24.0000			1.11178
$467$	7.34847			0.340047			0.170023	−	0.985440i	$-0.445616\pi$
$467$	7.34847			0.340047			0.170023	+	0.985440i	$0.445616\pi$
$468$	−7.34847			−0.339683
$469$	−8.00000	+	19.5959i	−0.369406	+	0.904855i
$470$		0			0
$471$	−9.00000	−	9.00000i	−0.414698	−	0.414698i
$472$		−	12.2474i		−	0.563735i
$473$		0			0
$474$	−12.2474	−	12.2474i	−0.562544	−	0.562544i
$475$		0			0
$476$	4.89898	−	12.0000i	0.224544	−	0.550019i
$477$	−18.0000			−0.824163
$478$	−6.00000			−0.274434
$479$	24.4949			1.11920			0.559600	−	0.828763i	$-0.310955\pi$
$479$	24.4949			1.11920			0.559600	+	0.828763i	$0.310955\pi$
$480$		0			0
$481$			4.89898i			0.223374i
$482$	24.4949			1.11571
$483$	25.3485	−	10.6515i	1.15340	−	0.484661i
$484$	−11.0000			−0.500000
$485$		0			0
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$	12.2474			0.554416
$489$	−19.5959	+	19.5959i	−0.886158	+	0.886158i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−6.00000	+	6.00000i	−0.270501	+	0.270501i
$493$			29.3939i			1.32383i
$494$			6.00000i			0.269953i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−3.00000	−	3.00000i	−0.134433	−	0.134433i
$499$	−20.0000			−0.895323			−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000			−0.895323			−0.447661	+	0.894203i	$0.647743\pi$
$500$		0			0
$501$	6.00000	−	6.00000i	0.268060	−	0.268060i
$502$			17.1464i			0.765283i
$503$	−39.1918			−1.74748			−0.873739	−	0.486395i	$-0.838311\pi$
$503$	−39.1918			−1.74748			−0.873739	+	0.486395i	$0.838311\pi$
$504$	3.00000	−	7.34847i	0.133631	−	0.327327i
$505$		0			0
$506$		0			0
$507$	−8.57321	+	8.57321i	−0.380750	+	0.380750i
$508$	8.00000			0.354943
$509$	−12.2474			−0.542859			−0.271429	−	0.962458i	$-0.587496\pi$
$509$	−12.2474			−0.542859			−0.271429	+	0.962458i	$0.587496\pi$
$510$		0			0
$511$	−24.0000	−	9.79796i	−1.06170	−	0.433436i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.00000	+	9.00000i	−0.397360	+	0.397360i
$514$			29.3939i			1.29651i
$515$		0			0
$516$	−4.89898	+	4.89898i	−0.215666	+	0.215666i
$517$		0			0
$518$	−4.89898	−	2.00000i	−0.215249	−	0.0878750i
$519$	−27.0000	+	27.0000i	−1.18517	+	1.18517i
$520$		0			0
$521$	−4.89898			−0.214628			−0.107314	−	0.994225i	$-0.534225\pi$
$521$	−4.89898			−0.214628			−0.107314	+	0.994225i	$0.534225\pi$
$522$			18.0000i			0.787839i
$523$			2.44949i			0.107109i	0.998565	+	0.0535544i	$0.0170550\pi$
$523$			2.44949i			0.107109i	−0.998565	+	0.0535544i	$0.982945\pi$
$524$	−7.34847			−0.321019
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	−13.0000			−0.565217
$530$		0			0
$531$			36.7423i			1.59448i
$532$	−6.00000	−	2.44949i	−0.260133	−	0.106199i
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$		0			0
$536$		−	8.00000i		−	0.345547i
$537$	−29.3939	−	29.3939i	−1.26844	−	1.26844i
$538$			12.2474i			0.528025i
$539$		0			0
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	−24.4949			−1.05215
$543$	−15.0000	−	15.0000i	−0.643712	−	0.643712i
$544$			4.89898i			0.210042i
$545$		0			0
$546$	4.34847	+	10.3485i	0.186097	+	0.442874i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$		−	12.0000i		−	0.512615i
$549$	−36.7423			−1.56813
$550$		0			0
$551$	14.6969			0.626111
$552$	−7.34847	+	7.34847i	−0.312772	+	0.312772i
$553$	−10.0000	+	24.4949i	−0.425243	+	1.04163i
$554$		−	22.0000i		−	0.934690i
$555$		0			0
$556$		−	2.44949i		−	0.103882i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$		0			0
$559$		−	9.79796i		−	0.414410i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.0454			0.929103			0.464552	−	0.885546i	$-0.346216\pi$
$563$	22.0454			0.929103			0.464552	+	0.885546i	$0.346216\pi$
$564$	−6.00000	+	6.00000i	−0.252646	+	0.252646i
$565$		0			0
$566$	−22.0454			−0.926638
$567$	−9.00000	+	22.0454i	−0.377964	+	0.925820i
$568$		0			0
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$		0			0
$574$	12.0000	+	4.89898i	0.500870	+	0.204479i
$575$		0			0
$576$			3.00000i			0.125000i
$577$			19.5959i			0.815789i	0.913029	+	0.407894i	$0.133737\pi$
$577$			19.5959i			0.815789i	−0.913029	+	0.407894i	$0.866263\pi$
$578$		−	7.00000i		−	0.291162i
$579$	4.89898	−	4.89898i	0.203595	−	0.203595i
$580$		0			0
$581$	−2.44949	+	6.00000i	−0.101622	+	0.248922i
$582$	6.00000	−	6.00000i	0.248708	−	0.248708i
$583$		0			0
$584$	9.79796			0.405442
$585$		0			0
$586$			2.44949i			0.101187i
$587$	7.34847			0.303304			0.151652	−	0.988434i	$-0.451541\pi$
$587$	7.34847			0.303304			0.151652	+	0.988434i	$0.451541\pi$
$588$	−12.1237	+	0.123724i	−0.499974	+	0.00510231i
$589$		0			0
$590$		0			0
$591$	22.0454	+	22.0454i	0.906827	+	0.906827i
$592$	2.00000			0.0821995
$593$	−39.1918			−1.60942			−0.804708	−	0.593671i	$-0.797678\pi$
$593$	−39.1918			−1.60942			−0.804708	+	0.593671i	$0.797678\pi$
$594$		0			0
$595$		0			0
$596$			6.00000i			0.245770i
$597$	12.0000	+	12.0000i	0.491127	+	0.491127i
$598$		−	14.6969i		−	0.601003i
$599$			24.0000i			0.980613i	0.871550	+	0.490307i	$0.163115\pi$
$599$			24.0000i			0.980613i	−0.871550	+	0.490307i	$0.836885\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	9.79796	+	4.00000i	0.399335	+	0.163028i
$603$			24.0000i			0.977356i
$604$	8.00000			0.325515
$605$		0			0
$606$	9.00000	+	9.00000i	0.365600	+	0.365600i
$607$		−	4.89898i		−	0.198843i	−0.995045	−	0.0994217i	$-0.968301\pi$
$607$		−	4.89898i		−	0.198843i	0.995045	−	0.0994217i	$-0.0316993\pi$
$608$	2.44949			0.0993399
$609$	25.3485	−	10.6515i	1.02717	−	0.431622i
$610$		0			0
$611$		−	12.0000i		−	0.485468i
$612$		−	14.6969i		−	0.594089i
$613$	−14.0000			−0.565455			−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000			−0.565455			−0.282727	+	0.959200i	$0.591239\pi$
$614$	7.34847			0.296560
$615$		0			0
$616$		0			0
$617$		−	18.0000i		−	0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$		−	18.0000i		−	0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$	12.0000	−	12.0000i	0.482711	−	0.482711i
$619$			26.9444i			1.08299i	0.840705	+	0.541493i	$0.182141\pi$
$619$			26.9444i			1.08299i	−0.840705	+	0.541493i	$0.817859\pi$
$620$		0			0
$621$	22.0454	−	22.0454i	0.884652	−	0.884652i
$622$		−	19.5959i		−	0.785725i
$623$		0			0
$624$	−3.00000	−	3.00000i	−0.120096	−	0.120096i
$625$		0			0
$626$	−34.2929			−1.37062
$627$		0			0
$628$		−	7.34847i		−	0.293236i
$629$	−9.79796			−0.390670
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$		−	10.0000i		−	0.397779i
$633$	9.79796	−	9.79796i	0.389434	−	0.389434i
$634$	−18.0000			−0.714871
$635$		0			0
$636$	−7.34847	−	7.34847i	−0.291386	−	0.291386i
$637$	12.0000	−	12.2474i	0.475457	−	0.485262i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	30.0000i		−	1.18493i	−0.805597	−	0.592464i	$-0.798155\pi$
$641$		−	30.0000i		−	1.18493i	0.805597	−	0.592464i	$-0.201845\pi$
$642$	−14.6969	+	14.6969i	−0.580042	+	0.580042i
$643$		−	22.0454i		−	0.869386i	−0.900579	−	0.434693i	$-0.856857\pi$
$643$		−	22.0454i		−	0.869386i	0.900579	−	0.434693i	$-0.143143\pi$
$644$	14.6969	+	6.00000i	0.579141	+	0.236433i
$645$		0			0
$646$	−12.0000			−0.472134
$647$	44.0908			1.73339			0.866694	−	0.498839i	$-0.166240\pi$
$647$	44.0908			1.73339			0.866694	+	0.498839i	$0.166240\pi$
$648$		−	9.00000i		−	0.353553i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−16.0000			−0.626608
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	12.2474	+	12.2474i	0.478913	+	0.478913i
$655$		0			0
$656$	−4.89898			−0.191273
$657$	−29.3939			−1.14676
$658$	12.0000	+	4.89898i	0.467809	+	0.190982i
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$		0			0
$661$			12.2474i			0.476371i	0.971220	+	0.238185i	$0.0765525\pi$
$661$			12.2474i			0.476371i	−0.971220	+	0.238185i	$0.923447\pi$
$662$			8.00000i			0.310929i
$663$	14.6969	+	14.6969i	0.570782	+	0.570782i
$664$		−	2.44949i		−	0.0950586i
$665$		0			0
$666$	−6.00000			−0.232495
$667$	−36.0000			−1.39393
$668$	4.89898			0.189547
$669$	−18.0000	−	18.0000i	−0.695920	−	0.695920i
$670$		0			0
$671$		0			0
$672$	4.22474	−	1.77526i	0.162973	−	0.0684820i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$		−	32.0000i		−	1.23259i
$675$		0			0
$676$	−7.00000			−0.269231
$677$	7.34847			0.282425			0.141212	−	0.989979i	$-0.454900\pi$
$677$	7.34847			0.282425			0.141212	+	0.989979i	$0.454900\pi$
$678$	7.34847	−	7.34847i	0.282216	−	0.282216i
$679$	−12.0000	−	4.89898i	−0.460518	−	0.188006i
$680$		0			0
$681$	−9.00000	+	9.00000i	−0.344881	+	0.344881i
$682$		0			0
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	−7.34847			−0.280976
$685$		0			0
$686$	7.34847	+	17.0000i	0.280566	+	0.649063i
$687$	27.0000	+	27.0000i	1.03011	+	1.03011i
$688$	−4.00000			−0.152499
$689$	14.6969			0.559909
$690$		0			0
$691$		−	36.7423i		−	1.39774i	−0.715246	−	0.698872i	$-0.753686\pi$
$691$		−	36.7423i		−	1.39774i	0.715246	−	0.698872i	$-0.246314\pi$
$692$	−22.0454			−0.838041
$693$		0			0
$694$	12.0000			0.455514
$695$		0			0
$696$	−7.34847	+	7.34847i	−0.278543	+	0.278543i
$697$	24.0000			0.909065
$698$	2.44949			0.0927146
$699$	−29.3939	−	29.3939i	−1.11178	−	1.11178i
$700$		0			0
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	9.00000	+	9.00000i	0.339683	+	0.339683i
$703$			4.89898i			0.184769i
$704$		0			0
$705$		0			0
$706$		−	9.79796i		−	0.368751i
$707$	7.34847	−	18.0000i	0.276368	−	0.676960i
$708$	−15.0000	+	15.0000i	−0.563735	+	0.563735i
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$		0			0
$711$			30.0000i			1.12509i
$712$		0			0
$713$		0			0
$714$	−20.6969	+	8.69694i	−0.774563	+	0.325475i
$715$		0			0
$716$		−	24.0000i		−	0.896922i
$717$	7.34847	+	7.34847i	0.274434	+	0.274434i
$718$	−6.00000			−0.223918
$719$	24.4949			0.913506			0.456753	−	0.889594i	$-0.349012\pi$
$719$	24.4949			0.913506			0.456753	+	0.889594i	$0.349012\pi$
$720$		0			0
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$		−	13.0000i		−	0.483810i
$723$	−30.0000	−	30.0000i	−1.11571	−	1.11571i
$724$		−	12.2474i		−	0.455173i
$725$		0			0
$726$	13.4722	+	13.4722i	0.500000	+	0.500000i
$727$		−	29.3939i		−	1.09016i	−0.838385	−	0.545079i	$-0.816500\pi$
$727$		−	29.3939i		−	1.09016i	0.838385	−	0.545079i	$-0.183500\pi$
$728$	−2.44949	+	6.00000i	−0.0907841	+	0.222375i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	19.5959			0.724781
$732$	−15.0000	−	15.0000i	−0.554416	−	0.554416i
$733$		−	22.0454i		−	0.814266i	−0.913369	−	0.407133i	$-0.866529\pi$
$733$		−	22.0454i		−	0.814266i	0.913369	−	0.407133i	$-0.133471\pi$
$734$	−4.89898			−0.180825
$735$		0			0
$736$	−6.00000			−0.221163
$737$		0			0
$738$	14.6969			0.541002
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$		0			0
$741$	7.34847	−	7.34847i	0.269953	−	0.269953i
$742$	−6.00000	+	14.6969i	−0.220267	+	0.539542i
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$		0			0
$746$			14.0000i			0.512576i
$747$			7.34847i			0.268866i
$748$		0			0
$749$	29.3939	+	12.0000i	1.07403	+	0.438470i
$750$		0			0
$751$	−8.00000			−0.291924			−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000			−0.291924			−0.145962	+	0.989290i	$0.546628\pi$
$752$	−4.89898			−0.178647
$753$	21.0000	−	21.0000i	0.765283	−	0.765283i
$754$		−	14.6969i		−	0.535231i
$755$		0			0
$756$	−12.6742	+	5.32577i	−0.460957	+	0.193696i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$			20.0000i			0.726433i
$759$		0			0
$760$		0			0
$761$	−4.89898			−0.177588			−0.0887939	−	0.996050i	$-0.528301\pi$
$761$	−4.89898			−0.177588			−0.0887939	+	0.996050i	$0.528301\pi$
$762$	−9.79796	−	9.79796i	−0.354943	−	0.354943i
$763$	10.0000	−	24.4949i	0.362024	−	0.886775i
$764$		0			0
$765$		0			0
$766$		−	34.2929i		−	1.23905i
$767$		−	30.0000i		−	1.08324i
$768$	−1.22474	+	1.22474i	−0.0441942	+	0.0441942i
$769$		−	34.2929i		−	1.23663i	−0.785930	−	0.618316i	$-0.787815\pi$
$769$		−	34.2929i		−	1.23663i	0.785930	−	0.618316i	$-0.212185\pi$
$770$		0			0
$771$	36.0000	−	36.0000i	1.29651	−	1.29651i
$772$	4.00000			0.143963
$773$	−26.9444			−0.969122			−0.484561	−	0.874757i	$-0.661021\pi$
$773$	−26.9444			−0.969122			−0.484561	+	0.874757i	$0.661021\pi$
$774$	12.0000			0.431331
$775$		0			0
$776$	4.89898			0.175863
$777$	3.55051	+	8.44949i	0.127374	+	0.303124i
$778$	−6.00000			−0.215110
$779$		−	12.0000i		−	0.429945i
$780$		0			0
$781$		0			0
$782$	29.3939			1.05112
$783$	22.0454	−	22.0454i	0.787839	−	0.787839i
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$		0			0
$786$	9.00000	+	9.00000i	0.321019	+	0.321019i
$787$			31.8434i			1.13509i	0.823341	+	0.567547i	$0.192107\pi$
$787$			31.8434i			1.13509i	−0.823341	+	0.567547i	$0.807893\pi$
$788$			18.0000i			0.641223i
$789$	−29.3939	−	29.3939i	−1.04645	−	1.04645i
$790$		0			0
$791$	−14.6969	−	6.00000i	−0.522563	−	0.213335i
$792$		0			0
$793$	30.0000			1.06533
$794$	7.34847			0.260787
$795$		0			0
$796$			9.79796i			0.347279i
$797$	7.34847			0.260296			0.130148	−	0.991495i	$-0.458455\pi$
$797$	7.34847			0.260296			0.130148	+	0.991495i	$0.458455\pi$
$798$	4.34847	+	10.3485i	0.153934	+	0.366332i
$799$	24.0000			0.849059
$800$		0			0
$801$		0			0
$802$	30.0000			1.05934
$803$		0			0
$804$	−9.79796	+	9.79796i	−0.345547	+	0.345547i
$805$		0			0
$806$		0			0
$807$	15.0000	−	15.0000i	0.528025	−	0.528025i
$808$			7.34847i			0.258518i
$809$		−	6.00000i		−	0.210949i	−0.994422	−	0.105474i	$-0.966364\pi$
$809$		−	6.00000i		−	0.210949i	0.994422	−	0.105474i	$-0.0336361\pi$
$810$		0			0
$811$		−	36.7423i		−	1.29020i	−0.764099	−	0.645099i	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$	14.6969	+	6.00000i	0.515761	+	0.210559i
$813$	30.0000	+	30.0000i	1.05215	+	1.05215i
$814$		0			0
$815$		0			0
$816$	6.00000	−	6.00000i	0.210042	−	0.210042i
$817$		−	9.79796i		−	0.342787i
$818$	−34.2929			−1.19902
$819$	7.34847	−	18.0000i	0.256776	−	0.628971i
$820$		0			0
$821$		−	30.0000i		−	1.04701i	−0.852023	−	0.523504i	$-0.824625\pi$
$821$		−	30.0000i		−	1.04701i	0.852023	−	0.523504i	$-0.175375\pi$
$822$	−14.6969	+	14.6969i	−0.512615	+	0.512615i
$823$	−14.0000			−0.488009			−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000			−0.488009			−0.244005	+	0.969774i	$0.578461\pi$
$824$	9.79796			0.341328
$825$		0			0
$826$	30.0000	+	12.2474i	1.04383	+	0.426143i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	18.0000			0.625543
$829$			26.9444i			0.935817i	0.883777	+	0.467909i	$0.154992\pi$
$829$			26.9444i			0.935817i	−0.883777	+	0.467909i	$0.845008\pi$
$830$		0			0
$831$	−26.9444	+	26.9444i	−0.934690	+	0.934690i
$832$		−	2.44949i		−	0.0849208i
$833$	24.4949	+	24.0000i	0.848698	+	0.831551i
$834$	−3.00000	+	3.00000i	−0.103882	+	0.103882i
$835$		0			0
$836$		0			0
$837$		0			0
$838$		−	12.2474i		−	0.423081i
$839$	−24.4949			−0.845658			−0.422829	−	0.906210i	$-0.638963\pi$
$839$	−24.4949			−0.845658			−0.422829	+	0.906210i	$0.638963\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$		−	2.00000i		−	0.0689246i
$843$		0			0
$844$	8.00000			0.275371
$845$		0			0
$846$	14.6969			0.505291
$847$	11.0000	−	26.9444i	0.377964	−	0.925820i
$848$		−	6.00000i		−	0.206041i
$849$	27.0000	+	27.0000i	0.926638	+	0.926638i
$850$		0			0
$851$		−	12.0000i		−	0.411355i
$852$		0			0
$853$			2.44949i			0.0838689i	0.999120	+	0.0419345i	$0.0133521\pi$
$853$			2.44949i			0.0838689i	−0.999120	+	0.0419345i	$0.986648\pi$
$854$	−12.2474	+	30.0000i	−0.419099	+	1.02658i
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−4.89898			−0.167346			−0.0836730	−	0.996493i	$-0.526665\pi$
$857$	−4.89898			−0.167346			−0.0836730	+	0.996493i	$0.526665\pi$
$858$		0			0
$859$			26.9444i			0.919331i	0.888092	+	0.459665i	$0.152031\pi$
$859$			26.9444i			0.919331i	−0.888092	+	0.459665i	$0.847969\pi$
$860$		0			0
$861$	−8.69694	−	20.6969i	−0.296391	−	0.705350i
$862$	30.0000			1.02180
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	3.67423	−	3.67423i	0.125000	−	0.125000i
$865$		0			0
$866$	14.6969			0.499422
$867$	−8.57321	+	8.57321i	−0.291162	+	0.291162i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	19.5959i		−	0.663982i
$872$			10.0000i			0.338643i
$873$	−14.6969			−0.497416
$874$		−	14.6969i		−	0.497131i
$875$		0			0
$876$	−12.0000	−	12.0000i	−0.405442	−	0.405442i
$877$	22.0000			0.742887			0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000			0.742887			0.371444	+	0.928456i	$0.378863\pi$
$878$	14.6969			0.495998
$879$	3.00000	−	3.00000i	0.101187	−	0.101187i
$880$		0			0
$881$	−29.3939			−0.990305			−0.495152	−	0.868806i	$-0.664888\pi$
$881$	−29.3939			−0.990305			−0.495152	+	0.868806i	$0.664888\pi$
$882$	15.0000	+	14.6969i	0.505076	+	0.494872i
$883$	56.0000			1.88455			0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000			1.88455			0.942275	+	0.334840i	$0.108682\pi$
$884$			12.0000i			0.403604i
$885$		0			0
$886$	−36.0000			−1.20944
$887$	−4.89898			−0.164492			−0.0822458	−	0.996612i	$-0.526209\pi$
$887$	−4.89898			−0.164492			−0.0822458	+	0.996612i	$0.526209\pi$
$888$	−2.44949	−	2.44949i	−0.0821995	−	0.0821995i
$889$	−8.00000	+	19.5959i	−0.268311	+	0.657226i
$890$		0			0
$891$		0			0
$892$		−	14.6969i		−	0.492090i
$893$		−	12.0000i		−	0.401565i
$894$	7.34847	−	7.34847i	0.245770	−	0.245770i
$895$		0			0
$896$	2.44949	+	1.00000i	0.0818317	+	0.0334077i
$897$	−18.0000	+	18.0000i	−0.601003	+	0.601003i
$898$	−36.0000			−1.20134
$899$		0			0
$900$		0			0
$901$			29.3939i			0.979252i
$902$		0			0
$903$	−7.10102	−	16.8990i	−0.236307	−	0.562363i
$904$	6.00000			0.199557
$905$		0			0
$906$	−9.79796	−	9.79796i	−0.325515	−	0.325515i
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$	−7.34847			−0.243868
$909$		−	22.0454i		−	0.731200i
$910$		0			0
$911$			30.0000i			0.993944i	0.867766	+	0.496972i	$0.165555\pi$
$911$			30.0000i			0.993944i	−0.867766	+	0.496972i	$0.834445\pi$
$912$	−3.00000	−	3.00000i	−0.0993399	−	0.0993399i
$913$		0			0
$914$			28.0000i			0.926158i
$915$		0			0
$916$			22.0454i			0.728401i
$917$	7.34847	−	18.0000i	0.242668	−	0.594412i
$918$	−18.0000	+	18.0000i	−0.594089	+	0.594089i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	−9.00000	−	9.00000i	−0.296560	−	0.296560i
$922$		−	31.8434i		−	1.04871i
$923$		0			0
$924$		0			0
$925$		0			0
$926$			14.0000i			0.460069i
$927$	−29.3939			−0.965422
$928$	−6.00000			−0.196960
$929$	−24.4949			−0.803652			−0.401826	−	0.915716i	$-0.631624\pi$
$929$	−24.4949			−0.803652			−0.401826	+	0.915716i	$0.631624\pi$
$930$		0			0
$931$	12.0000	−	12.2474i	0.393284	−	0.401394i
$932$		−	24.0000i		−	0.786146i
$933$	−24.0000	+	24.0000i	−0.785725	+	0.785725i
$934$		−	7.34847i		−	0.240449i
$935$		0			0
$936$			7.34847i			0.240192i
$937$			19.5959i			0.640171i	0.947389	+	0.320085i	$0.103712\pi$
$937$			19.5959i			0.640171i	−0.947389	+	0.320085i	$0.896288\pi$
$938$	19.5959	+	8.00000i	0.639829	+	0.261209i
$939$	42.0000	+	42.0000i	1.37062	+	1.37062i
$940$		0			0
$941$	31.8434			1.03806			0.519032	−	0.854755i	$-0.326293\pi$
$941$	31.8434			1.03806			0.519032	+	0.854755i	$0.326293\pi$
$942$	−9.00000	+	9.00000i	−0.293236	+	0.293236i
$943$			29.3939i			0.957196i
$944$	−12.2474			−0.398621
$945$		0			0
$946$		0			0
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$	−12.2474	+	12.2474i	−0.397779	+	0.397779i
$949$	24.0000			0.779073
$950$		0			0
$951$	22.0454	+	22.0454i	0.714871	+	0.714871i
$952$	−12.0000	−	4.89898i	−0.388922	−	0.158777i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$			18.0000i			0.582772i
$955$		0			0
$956$			6.00000i			0.194054i
$957$		0			0
$958$		−	24.4949i		−	0.791394i
$959$	29.3939	+	12.0000i	0.949178	+	0.387500i
$960$		0			0
$961$	31.0000			1.00000
$962$	4.89898			0.157949
$963$	36.0000			1.16008
$964$		−	24.4949i		−	0.788928i
$965$		0			0
$966$	−10.6515	−	25.3485i	−0.342707	−	0.815574i
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$			11.0000i			0.353553i
$969$	14.6969	+	14.6969i	0.472134	+	0.472134i
$970$		0			0
$971$	−41.6413			−1.33633			−0.668167	−	0.744011i	$-0.732921\pi$
$971$	−41.6413			−1.33633			−0.668167	+	0.744011i	$0.732921\pi$
$972$	−11.0227	+	11.0227i	−0.353553	+	0.353553i
$973$	6.00000	+	2.44949i	0.192351	+	0.0785270i
$974$		−	32.0000i		−	1.02535i
$975$		0			0
$976$		−	12.2474i		−	0.392031i
$977$			12.0000i			0.383914i	0.981403	+	0.191957i	$0.0614834\pi$
$977$			12.0000i			0.383914i	−0.981403	+	0.191957i	$0.938517\pi$
$978$	19.5959	+	19.5959i	0.626608	+	0.626608i
$979$		0			0
$980$		0			0
$981$		−	30.0000i		−	0.957826i
$982$		0			0
$983$	34.2929			1.09377			0.546886	−	0.837207i	$-0.315813\pi$
$983$	34.2929			1.09377			0.546886	+	0.837207i	$0.315813\pi$
$984$	6.00000	+	6.00000i	0.191273	+	0.191273i
$985$		0			0
$986$	29.3939			0.936092
$987$	−8.69694	−	20.6969i	−0.276827	−	0.658791i
$988$	6.00000			0.190885
$989$			24.0000i			0.763156i
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$		0			0
$993$	9.79796	−	9.79796i	0.310929	−	0.310929i
$994$		0			0
$995$		0			0
$996$	−3.00000	+	3.00000i	−0.0950586	+	0.0950586i
$997$			7.34847i			0.232728i	0.993207	+	0.116364i	$0.0371240\pi$
$997$			7.34847i			0.232728i	−0.993207	+	0.116364i	$0.962876\pi$
$998$			20.0000i			0.633089i
$999$	7.34847	+	7.34847i	0.232495	+	0.232495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.b.b.251.1		4
3.2	odd	2	inner	1050.2.b.b.251.4		4
5.2	odd	4		1050.2.d.e.1049.4		4
5.3	odd	4		1050.2.d.b.1049.1		4
5.4	even	2		42.2.d.a.41.4	yes	4
7.6	odd	2	inner	1050.2.b.b.251.2		4
15.2	even	4		1050.2.d.b.1049.3		4
15.8	even	4		1050.2.d.e.1049.2		4
15.14	odd	2		42.2.d.a.41.1	✓	4
20.19	odd	2		336.2.k.b.209.2		4
21.20	even	2	inner	1050.2.b.b.251.3		4
35.4	even	6		294.2.f.b.215.1		8
35.9	even	6		294.2.f.b.227.4		8
35.13	even	4		1050.2.d.b.1049.4		4
35.19	odd	6		294.2.f.b.227.3		8
35.24	odd	6		294.2.f.b.215.2		8
35.27	even	4		1050.2.d.e.1049.1		4
35.34	odd	2		42.2.d.a.41.3	yes	4
40.19	odd	2		1344.2.k.d.1217.3		4
40.29	even	2		1344.2.k.c.1217.2		4
45.4	even	6		1134.2.m.g.755.2		8
45.14	odd	6		1134.2.m.g.755.3		8
45.29	odd	6		1134.2.m.g.377.1		8
45.34	even	6		1134.2.m.g.377.4		8
60.59	even	2		336.2.k.b.209.4		4
105.44	odd	6		294.2.f.b.227.2		8
105.59	even	6		294.2.f.b.215.4		8
105.62	odd	4		1050.2.d.b.1049.2		4
105.74	odd	6		294.2.f.b.215.3		8
105.83	odd	4		1050.2.d.e.1049.3		4
105.89	even	6		294.2.f.b.227.1		8
105.104	even	2		42.2.d.a.41.2	yes	4
120.29	odd	2		1344.2.k.c.1217.4		4
120.59	even	2		1344.2.k.d.1217.1		4
140.139	even	2		336.2.k.b.209.3		4
280.69	odd	2		1344.2.k.c.1217.3		4
280.139	even	2		1344.2.k.d.1217.2		4
315.34	odd	6		1134.2.m.g.377.3		8
315.104	even	6		1134.2.m.g.755.4		8
315.139	odd	6		1134.2.m.g.755.1		8
315.209	even	6		1134.2.m.g.377.2		8
420.419	odd	2		336.2.k.b.209.1		4
840.419	odd	2		1344.2.k.d.1217.4		4
840.629	even	2		1344.2.k.c.1217.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.d.a.41.1	✓	4	15.14	odd	2
42.2.d.a.41.2	yes	4	105.104	even	2
42.2.d.a.41.3	yes	4	35.34	odd	2
42.2.d.a.41.4	yes	4	5.4	even	2
294.2.f.b.215.1		8	35.4	even	6
294.2.f.b.215.2		8	35.24	odd	6
294.2.f.b.215.3		8	105.74	odd	6
294.2.f.b.215.4		8	105.59	even	6
294.2.f.b.227.1		8	105.89	even	6
294.2.f.b.227.2		8	105.44	odd	6
294.2.f.b.227.3		8	35.19	odd	6
294.2.f.b.227.4		8	35.9	even	6
336.2.k.b.209.1		4	420.419	odd	2
336.2.k.b.209.2		4	20.19	odd	2
336.2.k.b.209.3		4	140.139	even	2
336.2.k.b.209.4		4	60.59	even	2
1050.2.b.b.251.1		4	1.1	even	1	trivial
1050.2.b.b.251.2		4	7.6	odd	2	inner
1050.2.b.b.251.3		4	21.20	even	2	inner
1050.2.b.b.251.4		4	3.2	odd	2	inner
1050.2.d.b.1049.1		4	5.3	odd	4
1050.2.d.b.1049.2		4	105.62	odd	4
1050.2.d.b.1049.3		4	15.2	even	4
1050.2.d.b.1049.4		4	35.13	even	4
1050.2.d.e.1049.1		4	35.27	even	4
1050.2.d.e.1049.2		4	15.8	even	4
1050.2.d.e.1049.3		4	105.83	odd	4
1050.2.d.e.1049.4		4	5.2	odd	4
1134.2.m.g.377.1		8	45.29	odd	6
1134.2.m.g.377.2		8	315.209	even	6
1134.2.m.g.377.3		8	315.34	odd	6
1134.2.m.g.377.4		8	45.34	even	6
1134.2.m.g.755.1		8	315.139	odd	6
1134.2.m.g.755.2		8	45.4	even	6
1134.2.m.g.755.3		8	45.14	odd	6
1134.2.m.g.755.4		8	315.104	even	6
1344.2.k.c.1217.1		4	840.629	even	2
1344.2.k.c.1217.2		4	40.29	even	2
1344.2.k.c.1217.3		4	280.69	odd	2
1344.2.k.c.1217.4		4	120.29	odd	2
1344.2.k.d.1217.1		4	120.59	even	2
1344.2.k.d.1217.2		4	280.139	even	2
1344.2.k.d.1217.3		4	40.19	odd	2
1344.2.k.d.1217.4		4	840.419	odd	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} +1.00000i q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} +1.00000i q^{8} -3.00000i q^{9} +(1.22474 - 1.22474i) q^{12} +2.44949i q^{13} +(-2.44949 - 1.00000i) q^{14} +1.00000 q^{16} -4.89898 q^{17} -3.00000 q^{18} +2.44949i q^{19} +(1.77526 + 4.22474i) q^{21} -6.00000i q^{23} +(-1.22474 - 1.22474i) q^{24} +2.44949 q^{26} +(3.67423 + 3.67423i) q^{27} +(-1.00000 + 2.44949i) q^{28} -6.00000i q^{29} -1.00000i q^{32} +4.89898i q^{34} +3.00000i q^{36} +2.00000 q^{37} +2.44949 q^{38} +(-3.00000 - 3.00000i) q^{39} -4.89898 q^{41} +(4.22474 - 1.77526i) q^{42} -4.00000 q^{43} -6.00000 q^{46} -4.89898 q^{47} +(-1.22474 + 1.22474i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(6.00000 - 6.00000i) q^{51} -2.44949i q^{52} -6.00000i q^{53} +(3.67423 - 3.67423i) q^{54} +(2.44949 + 1.00000i) q^{56} +(-3.00000 - 3.00000i) q^{57} -6.00000 q^{58} -12.2474 q^{59} -12.2474i q^{61} +(-7.34847 - 3.00000i) q^{63} -1.00000 q^{64} -8.00000 q^{67} +4.89898 q^{68} +(7.34847 + 7.34847i) q^{69} +3.00000 q^{72} -9.79796i q^{73} -2.00000i q^{74} -2.44949i q^{76} +(-3.00000 + 3.00000i) q^{78} -10.0000 q^{79} -9.00000 q^{81} +4.89898i q^{82} -2.44949 q^{83} +(-1.77526 - 4.22474i) q^{84} +4.00000i q^{86} +(7.34847 + 7.34847i) q^{87} +(6.00000 + 2.44949i) q^{91} +6.00000i q^{92} +4.89898i q^{94} +(1.22474 + 1.22474i) q^{96} -4.89898i q^{97} +(-4.89898 + 5.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^7	\( 4 q - 4 q^{4} + 4 q^{7} + 4 q^{16} - 12 q^{18} + 12 q^{21} - 4 q^{28} + 8 q^{37} - 12 q^{39} + 12 q^{42} - 16 q^{43} - 24 q^{46} - 20 q^{49} + 24 q^{51} - 12 q^{57} - 24 q^{58} - 4 q^{64} - 32 q^{67} + 12 q^{72} - 12 q^{78} - 40 q^{79} - 36 q^{81} - 12 q^{84} + 24 q^{91}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^7 + 4 * q^16 - 12 * q^18 + 12 * q^21 - 4 * q^28 + 8 * q^37 - 12 * q^39 + 12 * q^42 - 16 * q^43 - 24 * q^46 - 20 * q^49 + 24 * q^51 - 12 * q^57 - 24 * q^58 - 4 * q^64 - 32 * q^67 + 12 * q^72 - 12 * q^78 - 40 * q^79 - 36 * q^81 - 12 * q^84 + 24 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more