LMFDB - Embedded newform 960.2.v.g.833.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(257,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("960.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.v (of order $4$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			833.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	960.833
Dual form			960.2.v.g.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(1.00000 - 2.82843i) q^{9} +0.828427i q^{11} +(-3.82843 - 3.82843i) q^{13} +(0.585786 + 3.82843i) q^{15} +(-1.82843 - 1.82843i) q^{17} +0.828427i q^{19} +(-1.00000 + 5.82843i) q^{21} +(-4.41421 + 4.41421i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(1.41421 + 5.00000i) q^{27} -3.65685 q^{29} -5.65685 q^{31} +(-0.828427 - 1.17157i) q^{33} +(-2.41421 - 7.24264i) q^{35} +(5.82843 - 5.82843i) q^{37} +(9.24264 + 1.58579i) q^{39} +5.65685i q^{41} +(-0.414214 - 0.414214i) q^{43} +(-4.65685 - 4.82843i) q^{45} +(-3.58579 - 3.58579i) q^{47} -4.65685i q^{49} +(4.41421 + 0.757359i) q^{51} +(3.00000 - 3.00000i) q^{53} +(1.65685 + 0.828427i) q^{55} +(-0.828427 - 1.17157i) q^{57} -4.00000 q^{59} -0.343146 q^{61} +(-4.41421 - 9.24264i) q^{63} +(-11.4853 + 3.82843i) q^{65} +(10.0711 - 10.0711i) q^{67} +(1.82843 - 10.6569i) q^{69} -10.4853i q^{71} +(-4.65685 - 4.65685i) q^{73} +(8.24264 + 2.65685i) q^{75} +(2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 - 5.65685i) q^{81} +(3.24264 - 3.24264i) q^{83} +(-5.48528 + 1.82843i) q^{85} +(5.17157 - 3.65685i) q^{87} +15.6569 q^{89} -18.4853 q^{91} +(8.00000 - 5.65685i) q^{93} +(1.65685 + 0.828427i) q^{95} +(1.00000 - 1.00000i) q^{97} +(2.34315 + 0.828427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^5 + 4 * q^7 + 4 * q^9	$ 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9} - 4 q^{13} + 8 q^{15} + 4 q^{17} - 4 q^{21} - 12 q^{23} - 12 q^{25} + 8 q^{29} + 8 q^{33} - 4 q^{35} + 12 q^{37} + 20 q^{39} + 4 q^{43} + 4 q^{45} - 20 q^{47} + 12 q^{51} + 12 q^{53} - 16 q^{55} + 8 q^{57} - 16 q^{59} - 24 q^{61} - 12 q^{63} - 12 q^{65} + 12 q^{67} - 4 q^{69} + 4 q^{73} + 16 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} + 12 q^{85} + 32 q^{87} + 40 q^{89} - 40 q^{91} + 32 q^{93} - 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 4 * q + 4 * q^5 + 4 * q^7 + 4 * q^9 - 4 * q^13 + 8 * q^15 + 4 * q^17 - 4 * q^21 - 12 * q^23 - 12 * q^25 + 8 * q^29 + 8 * q^33 - 4 * q^35 + 12 * q^37 + 20 * q^39 + 4 * q^43 + 4 * q^45 - 20 * q^47 + 12 * q^51 + 12 * q^53 - 16 * q^55 + 8 * q^57 - 16 * q^59 - 24 * q^61 - 12 * q^63 - 12 * q^65 + 12 * q^67 - 4 * q^69 + 4 * q^73 + 16 * q^75 + 8 * q^77 - 28 * q^81 - 4 * q^83 + 12 * q^85 + 32 * q^87 + 40 * q^89 - 40 * q^91 + 32 * q^93 - 16 * q^95 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$4$		0			0
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$		0			0
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	−0.0839804	−	0.996467i	$-0.526763\pi$
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	0.996467	+	0.0839804i	$0.0267633\pi$
$8$		0			0
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$		0			0
$11$			0.828427i			0.249780i	0.992171	+	0.124890i	$0.0398578\pi$
$11$			0.828427i			0.249780i	−0.992171	+	0.124890i	$0.960142\pi$
$12$		0			0
$13$	−3.82843	−	3.82843i	−1.06181	−	1.06181i	−0.997959	−	0.0638555i	$-0.979660\pi$
$13$	−3.82843	−	3.82843i	−1.06181	−	1.06181i	−0.0638555	−	0.997959i	$-0.520340\pi$
$14$		0			0
$15$	0.585786	+	3.82843i	0.151249	+	0.988496i
$16$		0			0
$17$	−1.82843	−	1.82843i	−0.443459	−	0.443459i	0.449714	−	0.893173i	$-0.351526\pi$
$17$	−1.82843	−	1.82843i	−0.443459	−	0.443459i	−0.893173	+	0.449714i	$0.851526\pi$
$18$		0			0
$19$			0.828427i			0.190054i	0.995475	+	0.0950271i	$0.0302938\pi$
$19$			0.828427i			0.190054i	−0.995475	+	0.0950271i	$0.969706\pi$
$20$		0			0
$21$	−1.00000	+	5.82843i	−0.218218	+	1.27187i
$22$		0			0
$23$	−4.41421	+	4.41421i	−0.920427	+	0.920427i	−0.997059	−	0.0766323i	$-0.975583\pi$
$23$	−4.41421	+	4.41421i	−0.920427	+	0.920427i	0.0766323	+	0.997059i	$0.475583\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$		0			0
$29$	−3.65685			−0.679061			−0.339530	−	0.940595i	$-0.610268\pi$
$29$	−3.65685			−0.679061			−0.339530	+	0.940595i	$0.610268\pi$
$30$		0			0
$31$	−5.65685			−1.01600			−0.508001	−	0.861357i	$-0.669615\pi$
$31$	−5.65685			−1.01600			−0.508001	+	0.861357i	$0.669615\pi$
$32$		0			0
$33$	−0.828427	−	1.17157i	−0.144211	−	0.203945i
$34$		0			0
$35$	−2.41421	−	7.24264i	−0.408077	−	1.22423i
$36$		0			0
$37$	5.82843	−	5.82843i	0.958188	−	0.958188i	−0.0409727	−	0.999160i	$-0.513046\pi$
$37$	5.82843	−	5.82843i	0.958188	−	0.958188i	0.999160	+	0.0409727i	$0.0130457\pi$
$38$		0			0
$39$	9.24264	+	1.58579i	1.48001	+	0.253929i
$40$		0			0
$41$			5.65685i			0.883452i	0.897150	+	0.441726i	$0.145634\pi$
$41$			5.65685i			0.883452i	−0.897150	+	0.441726i	$0.854366\pi$
$42$		0			0
$43$	−0.414214	−	0.414214i	−0.0631670	−	0.0631670i	0.674818	−	0.737985i	$-0.264222\pi$
$43$	−0.414214	−	0.414214i	−0.0631670	−	0.0631670i	−0.737985	+	0.674818i	$0.764222\pi$
$44$		0			0
$45$	−4.65685	−	4.82843i	−0.694203	−	0.719779i
$46$		0			0
$47$	−3.58579	−	3.58579i	−0.523041	−	0.523041i	0.395448	−	0.918488i	$-0.370589\pi$
$47$	−3.58579	−	3.58579i	−0.523041	−	0.523041i	−0.918488	+	0.395448i	$0.870589\pi$
$48$		0			0
$49$		−	4.65685i		−	0.665265i
$50$		0			0
$51$	4.41421	+	0.757359i	0.618114	+	0.106052i
$52$		0			0
$53$	3.00000	−	3.00000i	0.412082	−	0.412082i	−0.470381	−	0.882463i	$-0.655884\pi$
$53$	3.00000	−	3.00000i	0.412082	−	0.412082i	0.882463	+	0.470381i	$0.155884\pi$
$54$		0			0
$55$	1.65685	+	0.828427i	0.223410	+	0.111705i
$56$		0			0
$57$	−0.828427	−	1.17157i	−0.109728	−	0.155179i
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	−0.343146			−0.0439353			−0.0219677	−	0.999759i	$-0.506993\pi$
$61$	−0.343146			−0.0439353			−0.0219677	+	0.999759i	$0.506993\pi$
$62$		0			0
$63$	−4.41421	−	9.24264i	−0.556139	−	1.16446i
$64$		0			0
$65$	−11.4853	+	3.82843i	−1.42457	+	0.474858i
$66$		0			0
$67$	10.0711	−	10.0711i	1.23038	−	1.23038i	0.266558	−	0.963819i	$-0.414114\pi$
$67$	10.0711	−	10.0711i	1.23038	−	1.23038i	0.963819	−	0.266558i	$-0.0858863\pi$
$68$		0			0
$69$	1.82843	−	10.6569i	0.220117	−	1.28293i
$70$		0			0
$71$		−	10.4853i		−	1.24437i	−0.782869	−	0.622187i	$-0.786244\pi$
$71$		−	10.4853i		−	1.24437i	0.782869	−	0.622187i	$-0.213756\pi$
$72$		0			0
$73$	−4.65685	−	4.65685i	−0.545044	−	0.545044i	0.379960	−	0.925003i	$-0.375938\pi$
$73$	−4.65685	−	4.65685i	−0.545044	−	0.545044i	−0.925003	+	0.379960i	$0.875938\pi$
$74$		0			0
$75$	8.24264	+	2.65685i	0.951778	+	0.306787i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$			0.828427i			0.0932053i	0.998914	+	0.0466027i	$0.0148395\pi$
$79$			0.828427i			0.0932053i	−0.998914	+	0.0466027i	$0.985161\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		0			0
$83$	3.24264	−	3.24264i	0.355926	−	0.355926i	−0.506383	−	0.862309i	$-0.669018\pi$
$83$	3.24264	−	3.24264i	0.355926	−	0.355926i	0.862309	+	0.506383i	$0.169018\pi$
$84$		0			0
$85$	−5.48528	+	1.82843i	−0.594962	+	0.198321i
$86$		0			0
$87$	5.17157	−	3.65685i	0.554451	−	0.392056i
$88$		0			0
$89$	15.6569			1.65962			0.829812	−	0.558044i	$-0.188448\pi$
$89$	15.6569			1.65962			0.829812	+	0.558044i	$0.188448\pi$
$90$		0			0
$91$	−18.4853			−1.93778
$92$		0			0
$93$	8.00000	−	5.65685i	0.829561	−	0.586588i
$94$		0			0
$95$	1.65685	+	0.828427i	0.169990	+	0.0849948i
$96$		0			0
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$98$		0			0
$99$	2.34315	+	0.828427i	0.235495	+	0.0832601i
$100$		0			0
$101$			9.65685i			0.960893i	0.877024	+	0.480446i	$0.159525\pi$
$101$			9.65685i			0.960893i	−0.877024	+	0.480446i	$0.840475\pi$
$102$		0			0
$103$	5.58579	+	5.58579i	0.550384	+	0.550384i	0.926552	−	0.376168i	$-0.122758\pi$
$103$	5.58579	+	5.58579i	0.550384	+	0.550384i	−0.376168	+	0.926552i	$0.622758\pi$
$104$		0			0
$105$	10.6569	+	7.82843i	1.04000	+	0.763976i
$106$		0			0
$107$	−9.58579	−	9.58579i	−0.926693	−	0.926693i	0.0707977	−	0.997491i	$-0.477446\pi$
$107$	−9.58579	−	9.58579i	−0.926693	−	0.926693i	−0.997491	+	0.0707977i	$0.977446\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$	−2.41421	+	14.0711i	−0.229147	+	1.33557i
$112$		0			0
$113$	9.48528	−	9.48528i	0.892300	−	0.892300i	−0.102439	−	0.994739i	$-0.532665\pi$
$113$	9.48528	−	9.48528i	0.892300	−	0.892300i	0.994739	+	0.102439i	$0.0326647\pi$
$114$		0			0
$115$	4.41421	+	13.2426i	0.411628	+	1.23488i
$116$		0			0
$117$	−14.6569	+	7.00000i	−1.35503	+	0.647150i
$118$		0			0
$119$	−8.82843			−0.809301
$120$		0			0
$121$	10.3137			0.937610
$122$		0			0
$123$	−5.65685	−	8.00000i	−0.510061	−	0.721336i
$124$		0			0
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$		0			0
$127$	−5.58579	+	5.58579i	−0.495658	+	0.495658i	−0.910083	−	0.414425i	$-0.863983\pi$
$127$	−5.58579	+	5.58579i	−0.495658	+	0.495658i	0.414425	+	0.910083i	$0.363983\pi$
$128$		0			0
$129$	1.00000	+	0.171573i	0.0880451	+	0.0151061i
$130$		0			0
$131$			8.82843i			0.771343i	0.922636	+	0.385672i	$0.126030\pi$
$131$			8.82843i			0.771343i	−0.922636	+	0.385672i	$0.873970\pi$
$132$		0			0
$133$	2.00000	+	2.00000i	0.173422	+	0.173422i
$134$		0			0
$135$	11.4142	+	2.17157i	0.982379	+	0.186899i
$136$		0			0
$137$	−9.82843	−	9.82843i	−0.839699	−	0.839699i	0.149120	−	0.988819i	$-0.452356\pi$
$137$	−9.82843	−	9.82843i	−0.839699	−	0.839699i	−0.988819	+	0.149120i	$0.952356\pi$
$138$		0			0
$139$			8.82843i			0.748817i	0.927264	+	0.374409i	$0.122154\pi$
$139$			8.82843i			0.748817i	−0.927264	+	0.374409i	$0.877846\pi$
$140$		0			0
$141$	8.65685	+	1.48528i	0.729039	+	0.125083i
$142$		0			0
$143$	3.17157	−	3.17157i	0.265220	−	0.265220i
$144$		0			0
$145$	−3.65685	+	7.31371i	−0.303685	+	0.607370i
$146$		0			0
$147$	4.65685	+	6.58579i	0.384091	+	0.543187i
$148$		0			0
$149$	13.3137			1.09070			0.545351	−	0.838208i	$-0.316396\pi$
$149$	13.3137			1.09070			0.545351	+	0.838208i	$0.316396\pi$
$150$		0			0
$151$	13.6569			1.11138			0.555690	−	0.831390i	$-0.312454\pi$
$151$	13.6569			1.11138			0.555690	+	0.831390i	$0.312454\pi$
$152$		0			0
$153$	−7.00000	+	3.34315i	−0.565916	+	0.270277i
$154$		0			0
$155$	−5.65685	+	11.3137i	−0.454369	+	0.908739i
$156$		0			0
$157$	−5.48528	+	5.48528i	−0.437773	+	0.437773i	−0.891262	−	0.453489i	$-0.850179\pi$
$157$	−5.48528	+	5.48528i	−0.437773	+	0.437773i	0.453489	+	0.891262i	$0.350179\pi$
$158$		0			0
$159$	−1.24264	+	7.24264i	−0.0985478	+	0.574379i
$160$		0			0
$161$			21.3137i			1.67976i
$162$		0			0
$163$	−0.414214	−	0.414214i	−0.0324437	−	0.0324437i	0.690699	−	0.723143i	$-0.257303\pi$
$163$	−0.414214	−	0.414214i	−0.0324437	−	0.0324437i	−0.723143	+	0.690699i	$0.757303\pi$
$164$		0			0
$165$	−3.17157	+	0.485281i	−0.246907	+	0.0377791i
$166$		0			0
$167$	−9.24264	−	9.24264i	−0.715217	−	0.715217i	0.252405	−	0.967622i	$-0.418779\pi$
$167$	−9.24264	−	9.24264i	−0.715217	−	0.715217i	−0.967622	+	0.252405i	$0.918779\pi$
$168$		0			0
$169$			16.3137i			1.25490i
$170$		0			0
$171$	2.34315	+	0.828427i	0.179185	+	0.0633514i
$172$		0			0
$173$	0.656854	−	0.656854i	0.0499397	−	0.0499397i	−0.681696	−	0.731636i	$-0.738757\pi$
$173$	0.656854	−	0.656854i	0.0499397	−	0.0499397i	0.731636	+	0.681696i	$0.238757\pi$
$174$		0			0
$175$	−16.8995	−	2.41421i	−1.27748	−	0.182497i
$176$		0			0
$177$	5.65685	−	4.00000i	0.425195	−	0.300658i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	5.31371			0.394965			0.197482	−	0.980306i	$-0.436723\pi$
$181$	5.31371			0.394965			0.197482	+	0.980306i	$0.436723\pi$
$182$		0			0
$183$	0.485281	−	0.343146i	0.0358730	−	0.0253661i
$184$		0			0
$185$	−5.82843	−	17.4853i	−0.428514	−	1.28554i
$186$		0			0
$187$	1.51472	−	1.51472i	0.110767	−	0.110767i
$188$		0			0
$189$	15.4853	+	8.65685i	1.12639	+	0.629693i
$190$		0			0
$191$			4.14214i			0.299714i	0.988708	+	0.149857i	$0.0478814\pi$
$191$			4.14214i			0.299714i	−0.988708	+	0.149857i	$0.952119\pi$
$192$		0			0
$193$	14.6569	+	14.6569i	1.05502	+	1.05502i	0.998395	+	0.0566281i	$0.0180349\pi$
$193$	14.6569	+	14.6569i	1.05502	+	1.05502i	0.0566281	+	0.998395i	$0.481965\pi$
$194$		0			0
$195$	12.4142	−	16.8995i	0.889000	−	1.21020i
$196$		0			0
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.998974	−	0.0452834i	$-0.985581\pi$
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.0452834	−	0.998974i	$-0.514419\pi$
$198$		0			0
$199$		−	18.4853i		−	1.31039i	−0.755461	−	0.655193i	$-0.772587\pi$
$199$		−	18.4853i		−	1.31039i	0.755461	−	0.655193i	$-0.227413\pi$
$200$		0			0
$201$	−4.17157	+	24.3137i	−0.294240	+	1.71496i
$202$		0			0
$203$	−8.82843	+	8.82843i	−0.619634	+	0.619634i
$204$		0			0
$205$	11.3137	+	5.65685i	0.790184	+	0.395092i
$206$		0			0
$207$	8.07107	+	16.8995i	0.560978	+	1.17460i
$208$		0			0
$209$	−0.686292			−0.0474718
$210$		0			0
$211$	20.9706			1.44367			0.721837	−	0.692064i	$-0.243298\pi$
$211$	20.9706			1.44367			0.721837	+	0.692064i	$0.243298\pi$
$212$		0			0
$213$	10.4853	+	14.8284i	0.718440	+	1.01603i
$214$		0			0
$215$	−1.24264	+	0.414214i	−0.0847474	+	0.0282491i
$216$		0			0
$217$	−13.6569	+	13.6569i	−0.927088	+	0.927088i
$218$		0			0
$219$	11.2426	+	1.92893i	0.759707	+	0.130345i
$220$		0			0
$221$			14.0000i			0.941742i
$222$		0			0
$223$	5.58579	+	5.58579i	0.374052	+	0.374052i	0.868951	−	0.494899i	$-0.164795\pi$
$223$	5.58579	+	5.58579i	0.374052	+	0.374052i	−0.494899	+	0.868951i	$0.664795\pi$
$224$		0			0
$225$	−14.3137	+	4.48528i	−0.954247	+	0.299019i
$226$		0			0
$227$	−4.89949	−	4.89949i	−0.325191	−	0.325191i	0.525563	−	0.850754i	$-0.323855\pi$
$227$	−4.89949	−	4.89949i	−0.325191	−	0.325191i	−0.850754	+	0.525563i	$0.823855\pi$
$228$		0			0
$229$			14.3431i			0.947822i	0.880573	+	0.473911i	$0.157158\pi$
$229$			14.3431i			0.947822i	−0.880573	+	0.473911i	$0.842842\pi$
$230$		0			0
$231$	−4.82843	−	0.828427i	−0.317687	−	0.0545065i
$232$		0			0
$233$	11.8284	−	11.8284i	0.774906	−	0.774906i	−0.204054	−	0.978960i	$-0.565412\pi$
$233$	11.8284	−	11.8284i	0.774906	−	0.774906i	0.978960	+	0.204054i	$0.0654117\pi$
$234$		0			0
$235$	−10.7574	+	3.58579i	−0.701733	+	0.233911i
$236$		0			0
$237$	−0.828427	−	1.17157i	−0.0538121	−	0.0761018i
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−0.343146			−0.0221040			−0.0110520	−	0.999939i	$-0.503518\pi$
$241$	−0.343146			−0.0221040			−0.0110520	+	0.999939i	$0.503518\pi$
$242$		0			0
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$		0			0
$245$	−9.31371	−	4.65685i	−0.595031	−	0.297516i
$246$		0			0
$247$	3.17157	−	3.17157i	0.201802	−	0.201802i
$248$		0			0
$249$	−1.34315	+	7.82843i	−0.0851184	+	0.496106i
$250$		0			0
$251$		−	26.4853i		−	1.67174i	−0.548930	−	0.835868i	$-0.684965\pi$
$251$		−	26.4853i		−	1.67174i	0.548930	−	0.835868i	$-0.315035\pi$
$252$		0			0
$253$	−3.65685	−	3.65685i	−0.229904	−	0.229904i
$254$		0			0
$255$	5.92893	−	8.07107i	0.371284	−	0.505430i
$256$		0			0
$257$	9.48528	+	9.48528i	0.591676	+	0.591676i	0.938084	−	0.346408i	$-0.112599\pi$
$257$	9.48528	+	9.48528i	0.591676	+	0.591676i	−0.346408	+	0.938084i	$0.612599\pi$
$258$		0			0
$259$		−	28.1421i		−	1.74867i
$260$		0			0
$261$	−3.65685	+	10.3431i	−0.226354	+	0.640225i
$262$		0			0
$263$	6.89949	−	6.89949i	0.425441	−	0.425441i	−0.461631	−	0.887072i	$-0.652736\pi$
$263$	6.89949	−	6.89949i	0.425441	−	0.425441i	0.887072	+	0.461631i	$0.152736\pi$
$264$		0			0
$265$	−3.00000	−	9.00000i	−0.184289	−	0.552866i
$266$		0			0
$267$	−22.1421	+	15.6569i	−1.35508	+	0.958184i
$268$		0			0
$269$	16.6274			1.01379			0.506896	−	0.862007i	$-0.330793\pi$
$269$	16.6274			1.01379			0.506896	+	0.862007i	$0.330793\pi$
$270$		0			0
$271$	−10.3431			−0.628301			−0.314151	−	0.949373i	$-0.601720\pi$
$271$	−10.3431			−0.628301			−0.314151	+	0.949373i	$0.601720\pi$
$272$		0			0
$273$	26.1421	−	18.4853i	1.58219	−	1.11878i
$274$		0			0
$275$	3.31371	−	2.48528i	0.199824	−	0.149868i
$276$		0			0
$277$	8.17157	−	8.17157i	0.490982	−	0.490982i	−0.417633	−	0.908616i	$-0.637140\pi$
$277$	8.17157	−	8.17157i	0.490982	−	0.490982i	0.908616	+	0.417633i	$0.137140\pi$
$278$		0			0
$279$	−5.65685	+	16.0000i	−0.338667	+	0.957895i
$280$		0			0
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$		0			0
$283$	5.24264	+	5.24264i	0.311643	+	0.311643i	0.845546	−	0.533903i	$-0.179275\pi$
$283$	5.24264	+	5.24264i	0.311643	+	0.311643i	−0.533903	+	0.845546i	$0.679275\pi$
$284$		0			0
$285$	−3.17157	+	0.485281i	−0.187868	+	0.0287456i
$286$		0			0
$287$	13.6569	+	13.6569i	0.806139	+	0.806139i
$288$		0			0
$289$		−	10.3137i		−	0.606689i
$290$		0			0
$291$	−0.414214	+	2.41421i	−0.0242816	+	0.141524i
$292$		0			0
$293$	16.6569	−	16.6569i	0.973104	−	0.973104i	−0.0265438	−	0.999648i	$-0.508450\pi$
$293$	16.6569	−	16.6569i	0.973104	−	0.973104i	0.999648	+	0.0265438i	$0.00845016\pi$
$294$		0			0
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$		0			0
$297$	−4.14214	+	1.17157i	−0.240351	+	0.0679816i
$298$		0			0
$299$	33.7990			1.95465
$300$		0			0
$301$	−2.00000			−0.115278
$302$		0			0
$303$	−9.65685	−	13.6569i	−0.554772	−	0.784566i
$304$		0			0
$305$	−0.343146	+	0.686292i	−0.0196485	+	0.0392969i
$306$		0			0
$307$	−6.89949	+	6.89949i	−0.393775	+	0.393775i	−0.876031	−	0.482256i	$-0.839818\pi$
$307$	−6.89949	+	6.89949i	−0.393775	+	0.393775i	0.482256	+	0.876031i	$0.339818\pi$
$308$		0			0
$309$	−13.4853	−	2.31371i	−0.767151	−	0.131622i
$310$		0			0
$311$			5.51472i			0.312711i	0.987701	+	0.156356i	$0.0499746\pi$
$311$			5.51472i			0.312711i	−0.987701	+	0.156356i	$0.950025\pi$
$312$		0			0
$313$	−2.31371	−	2.31371i	−0.130779	−	0.130779i	0.638688	−	0.769466i	$-0.279478\pi$
$313$	−2.31371	−	2.31371i	−0.130779	−	0.130779i	−0.769466	+	0.638688i	$0.779478\pi$
$314$		0			0
$315$	−22.8995	−	0.414214i	−1.29024	−	0.0233383i
$316$		0			0
$317$	4.65685	+	4.65685i	0.261555	+	0.261555i	0.825686	−	0.564131i	$-0.190789\pi$
$317$	4.65685	+	4.65685i	0.261555	+	0.261555i	−0.564131	+	0.825686i	$0.690789\pi$
$318$		0			0
$319$		−	3.02944i		−	0.169616i
$320$		0			0
$321$	23.1421	+	3.97056i	1.29167	+	0.221615i
$322$		0			0
$323$	1.51472	−	1.51472i	0.0842812	−	0.0842812i
$324$		0			0
$325$	−3.82843	+	26.7990i	−0.212363	+	1.48654i
$326$		0			0
$327$	−4.00000	−	5.65685i	−0.221201	−	0.312825i
$328$		0			0
$329$	−17.3137			−0.954536
$330$		0			0
$331$	−9.65685			−0.530789			−0.265394	−	0.964140i	$-0.585502\pi$
$331$	−9.65685			−0.530789			−0.265394	+	0.964140i	$0.585502\pi$
$332$		0			0
$333$	−10.6569	−	22.3137i	−0.583992	−	1.22278i
$334$		0			0
$335$	−10.0711	−	30.2132i	−0.550241	−	1.65072i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	−3.92893	+	22.8995i	−0.213390	+	1.24373i
$340$		0			0
$341$		−	4.68629i		−	0.253777i
$342$		0			0
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$		0			0
$345$	−19.4853	−	14.3137i	−1.04905	−	0.770624i
$346$		0			0
$347$	12.0711	+	12.0711i	0.648009	+	0.648009i	0.952511	−	0.304503i	$-0.0984902\pi$
$347$	12.0711	+	12.0711i	0.648009	+	0.648009i	−0.304503	+	0.952511i	$0.598490\pi$
$348$		0			0
$349$		−	9.65685i		−	0.516920i	−0.966022	−	0.258460i	$-0.916785\pi$
$349$		−	9.65685i		−	0.516920i	0.966022	−	0.258460i	$-0.0832149\pi$
$350$		0			0
$351$	13.7279	−	24.5563i	0.732742	−	1.31072i
$352$		0			0
$353$	−15.4853	+	15.4853i	−0.824198	+	0.824198i	−0.986707	−	0.162509i	$-0.948041\pi$
$353$	−15.4853	+	15.4853i	−0.824198	+	0.824198i	0.162509	+	0.986707i	$0.448041\pi$
$354$		0			0
$355$	−20.9706	−	10.4853i	−1.11300	−	0.556501i
$356$		0			0
$357$	12.4853	−	8.82843i	0.660791	−	0.467250i
$358$		0			0
$359$	35.3137			1.86379			0.931893	−	0.362733i	$-0.118156\pi$
$359$	35.3137			1.86379			0.931893	+	0.362733i	$0.118156\pi$
$360$		0			0
$361$	18.3137			0.963879
$362$		0			0
$363$	−14.5858	+	10.3137i	−0.765555	+	0.541329i
$364$		0			0
$365$	−13.9706	+	4.65685i	−0.731253	+	0.243751i
$366$		0			0
$367$	4.75736	−	4.75736i	0.248332	−	0.248332i	−0.571954	−	0.820286i	$-0.693814\pi$
$367$	4.75736	−	4.75736i	0.248332	−	0.248332i	0.820286	+	0.571954i	$0.193814\pi$
$368$		0			0
$369$	16.0000	+	5.65685i	0.832927	+	0.294484i
$370$		0			0
$371$		−	14.4853i		−	0.752038i
$372$		0			0
$373$	−0.514719	−	0.514719i	−0.0266511	−	0.0266511i	0.693656	−	0.720307i	$-0.255999\pi$
$373$	−0.514719	−	0.514719i	−0.0266511	−	0.0266511i	−0.720307	+	0.693656i	$0.755999\pi$
$374$		0			0
$375$	13.5563	−	13.8284i	0.700047	−	0.714097i
$376$		0			0
$377$	14.0000	+	14.0000i	0.721037	+	0.721037i
$378$		0			0
$379$		−	29.7990i		−	1.53067i	−0.643631	−	0.765336i	$-0.722573\pi$
$379$		−	29.7990i		−	1.53067i	0.643631	−	0.765336i	$-0.277427\pi$
$380$		0			0
$381$	2.31371	−	13.4853i	0.118535	−	0.690872i
$382$		0			0
$383$	−12.4142	+	12.4142i	−0.634337	+	0.634337i	−0.949153	−	0.314816i	$-0.898057\pi$
$383$	−12.4142	+	12.4142i	−0.634337	+	0.634337i	0.314816	+	0.949153i	$0.398057\pi$
$384$		0			0
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$		0			0
$387$	−1.58579	+	0.757359i	−0.0806101	+	0.0384987i
$388$		0			0
$389$	6.68629			0.339008			0.169504	−	0.985529i	$-0.445783\pi$
$389$	6.68629			0.339008			0.169504	+	0.985529i	$0.445783\pi$
$390$		0			0
$391$	16.1421			0.816343
$392$		0			0
$393$	−8.82843	−	12.4853i	−0.445335	−	0.629799i
$394$		0			0
$395$	1.65685	+	0.828427i	0.0833654	+	0.0416827i
$396$		0			0
$397$	−7.82843	+	7.82843i	−0.392897	+	0.392897i	−0.875719	−	0.482821i	$-0.839612\pi$
$397$	−7.82843	+	7.82843i	−0.392897	+	0.392897i	0.482821	+	0.875719i	$0.339612\pi$
$398$		0			0
$399$	−4.82843	−	0.828427i	−0.241724	−	0.0414732i
$400$		0			0
$401$			16.0000i			0.799002i	0.916733	+	0.399501i	$0.130817\pi$
$401$			16.0000i			0.799002i	−0.916733	+	0.399501i	$0.869183\pi$
$402$		0			0
$403$	21.6569	+	21.6569i	1.07880	+	1.07880i
$404$		0			0
$405$	−18.3137	+	8.34315i	−0.910015	+	0.414574i
$406$		0			0
$407$	4.82843	+	4.82843i	0.239336	+	0.239336i
$408$		0			0
$409$		−	21.6569i		−	1.07086i	−0.844579	−	0.535431i	$-0.820149\pi$
$409$		−	21.6569i		−	1.07086i	0.844579	−	0.535431i	$-0.179851\pi$
$410$		0			0
$411$	23.7279	+	4.07107i	1.17041	+	0.200811i
$412$		0			0
$413$	−9.65685	+	9.65685i	−0.475183	+	0.475183i
$414$		0			0
$415$	−3.24264	−	9.72792i	−0.159175	−	0.477525i
$416$		0			0
$417$	−8.82843	−	12.4853i	−0.432330	−	0.611407i
$418$		0			0
$419$	−29.9411			−1.46272			−0.731360	−	0.681992i	$-0.761114\pi$
$419$	−29.9411			−1.46272			−0.731360	+	0.681992i	$0.761114\pi$
$420$		0			0
$421$	−30.9706			−1.50941			−0.754706	−	0.656063i	$-0.772221\pi$
$421$	−30.9706			−1.50941			−0.754706	+	0.656063i	$0.772221\pi$
$422$		0			0
$423$	−13.7279	+	6.55635i	−0.667474	+	0.318781i
$424$		0			0
$425$	−1.82843	+	12.7990i	−0.0886917	+	0.620842i
$426$		0			0
$427$	−0.828427	+	0.828427i	−0.0400904	+	0.0400904i
$428$		0			0
$429$	−1.31371	+	7.65685i	−0.0634264	+	0.369676i
$430$		0			0
$431$			20.1421i			0.970213i	0.874455	+	0.485106i	$0.161219\pi$
$431$			20.1421i			0.970213i	−0.874455	+	0.485106i	$0.838781\pi$
$432$		0			0
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$		0			0
$435$	−2.14214	−	14.0000i	−0.102708	−	0.671249i
$436$		0			0
$437$	−3.65685	−	3.65685i	−0.174931	−	0.174931i
$438$		0			0
$439$		−	13.7990i		−	0.658590i	−0.944227	−	0.329295i	$-0.893189\pi$
$439$		−	13.7990i		−	0.658590i	0.944227	−	0.329295i	$-0.106811\pi$
$440$		0			0
$441$	−13.1716	−	4.65685i	−0.627218	−	0.221755i
$442$		0			0
$443$	−0.0710678	+	0.0710678i	−0.00337653	+	0.00337653i	−0.708793	−	0.705416i	$-0.750760\pi$
$443$	−0.0710678	+	0.0710678i	−0.00337653	+	0.00337653i	0.705416	+	0.708793i	$0.250760\pi$
$444$		0			0
$445$	15.6569	−	31.3137i	0.742206	−	1.48441i
$446$		0			0
$447$	−18.8284	+	13.3137i	−0.890554	+	0.629717i
$448$		0			0
$449$	−1.31371			−0.0619977			−0.0309989	−	0.999519i	$-0.509869\pi$
$449$	−1.31371			−0.0619977			−0.0309989	+	0.999519i	$0.509869\pi$
$450$		0			0
$451$	−4.68629			−0.220669
$452$		0			0
$453$	−19.3137	+	13.6569i	−0.907437	+	0.641655i
$454$		0			0
$455$	−18.4853	+	36.9706i	−0.866603	+	1.73321i
$456$		0			0
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	−0.683331	−	0.730109i	$-0.739469\pi$
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	0.730109	+	0.683331i	$0.239469\pi$
$458$		0			0
$459$	6.55635	−	11.7279i	0.306024	−	0.547413i
$460$		0			0
$461$			28.9706i			1.34929i	0.738141	+	0.674647i	$0.235704\pi$
$461$			28.9706i			1.34929i	−0.738141	+	0.674647i	$0.764296\pi$
$462$		0			0
$463$	21.5858	+	21.5858i	1.00318	+	1.00318i	0.999995	+	0.00318163i	$0.00101275\pi$
$463$	21.5858	+	21.5858i	1.00318	+	1.00318i	0.00318163	+	0.999995i	$0.498987\pi$
$464$		0			0
$465$	−3.31371	−	21.6569i	−0.153670	−	1.00431i
$466$		0			0
$467$	23.3848	+	23.3848i	1.08212	+	1.08212i	0.996312	+	0.0858066i	$0.0273467\pi$
$467$	23.3848	+	23.3848i	1.08212	+	1.08212i	0.0858066	+	0.996312i	$0.472653\pi$
$468$		0			0
$469$		−	48.6274i		−	2.24541i
$470$		0			0
$471$	2.27208	−	13.2426i	0.104692	−	0.610189i
$472$		0			0
$473$	0.343146	−	0.343146i	0.0157779	−	0.0157779i
$474$		0			0
$475$	3.31371	−	2.48528i	0.152043	−	0.114033i
$476$		0			0
$477$	−5.48528	−	11.4853i	−0.251154	−	0.525875i
$478$		0			0
$479$	−22.6274			−1.03387			−0.516937	−	0.856024i	$-0.672928\pi$
$479$	−22.6274			−1.03387			−0.516937	+	0.856024i	$0.672928\pi$
$480$		0			0
$481$	−44.6274			−2.03484
$482$		0			0
$483$	−21.3137	−	30.1421i	−0.969807	−	1.37151i
$484$		0			0
$485$	−1.00000	−	3.00000i	−0.0454077	−	0.136223i
$486$		0			0
$487$	−14.5563	+	14.5563i	−0.659611	+	0.659611i	−0.955288	−	0.295677i	$-0.904455\pi$
$487$	−14.5563	+	14.5563i	−0.659611	+	0.659611i	0.295677	+	0.955288i	$0.404455\pi$
$488$		0			0
$489$	1.00000	+	0.171573i	0.0452216	+	0.00775879i
$490$		0			0
$491$			21.5147i			0.970946i	0.874252	+	0.485473i	$0.161353\pi$
$491$			21.5147i			0.970946i	−0.874252	+	0.485473i	$0.838647\pi$
$492$		0			0
$493$	6.68629	+	6.68629i	0.301135	+	0.301135i
$494$		0			0
$495$	4.00000	−	3.85786i	0.179787	−	0.173398i
$496$		0			0
$497$	−25.3137	−	25.3137i	−1.13548	−	1.13548i
$498$		0			0
$499$			34.7696i			1.55650i	0.627955	+	0.778249i	$0.283892\pi$
$499$			34.7696i			1.55650i	−0.627955	+	0.778249i	$0.716108\pi$
$500$		0			0
$501$	22.3137	+	3.82843i	0.996903	+	0.171042i
$502$		0			0
$503$	5.92893	−	5.92893i	0.264358	−	0.264358i	−0.562464	−	0.826822i	$-0.690146\pi$
$503$	5.92893	−	5.92893i	0.264358	−	0.264358i	0.826822	+	0.562464i	$0.190146\pi$
$504$		0			0
$505$	19.3137	+	9.65685i	0.859449	+	0.429724i
$506$		0			0
$507$	−16.3137	−	23.0711i	−0.724517	−	1.02462i
$508$		0			0
$509$	−3.65685			−0.162087			−0.0810436	−	0.996711i	$-0.525825\pi$
$509$	−3.65685			−0.162087			−0.0810436	+	0.996711i	$0.525825\pi$
$510$		0			0
$511$	−22.4853			−0.994690
$512$		0			0
$513$	−4.14214	+	1.17157i	−0.182880	+	0.0517262i
$514$		0			0
$515$	16.7574	−	5.58579i	0.738417	−	0.246139i
$516$		0			0
$517$	2.97056	−	2.97056i	0.130645	−	0.130645i
$518$		0			0
$519$	−0.272078	+	1.58579i	−0.0119429	+	0.0696083i
$520$		0			0
$521$		−	24.0000i		−	1.05146i	−0.850652	−	0.525730i	$-0.823792\pi$
$521$		−	24.0000i		−	1.05146i	0.850652	−	0.525730i	$-0.176208\pi$
$522$		0			0
$523$	26.8995	+	26.8995i	1.17623	+	1.17623i	0.980696	+	0.195536i	$0.0626448\pi$
$523$	26.8995	+	26.8995i	1.17623	+	1.17623i	0.195536	+	0.980696i	$0.437355\pi$
$524$		0			0
$525$	26.3137	−	13.4853i	1.14842	−	0.588546i
$526$		0			0
$527$	10.3431	+	10.3431i	0.450555	+	0.450555i
$528$		0			0
$529$		−	15.9706i		−	0.694372i
$530$		0			0
$531$	−4.00000	+	11.3137i	−0.173585	+	0.490973i
$532$		0			0
$533$	21.6569	−	21.6569i	0.938062	−	0.938062i
$534$		0			0
$535$	−28.7574	+	9.58579i	−1.24329	+	0.414430i
$536$		0			0
$537$	16.9706	−	12.0000i	0.732334	−	0.517838i
$538$		0			0
$539$	3.85786			0.166170
$540$		0			0
$541$	29.3137			1.26029			0.630147	−	0.776476i	$-0.282994\pi$
$541$	29.3137			1.26029			0.630147	+	0.776476i	$0.282994\pi$
$542$		0			0
$543$	−7.51472	+	5.31371i	−0.322487	+	0.228033i
$544$		0			0
$545$	8.00000	+	4.00000i	0.342682	+	0.171341i
$546$		0			0
$547$	15.7279	−	15.7279i	0.672477	−	0.672477i	−0.285809	−	0.958287i	$-0.592262\pi$
$547$	15.7279	−	15.7279i	0.672477	−	0.672477i	0.958287	+	0.285809i	$0.0922623\pi$
$548$		0			0
$549$	−0.343146	+	0.970563i	−0.0146451	+	0.0414226i
$550$		0			0
$551$		−	3.02944i		−	0.129058i
$552$		0			0
$553$	2.00000	+	2.00000i	0.0850487	+	0.0850487i
$554$		0			0
$555$	25.7279	+	18.8995i	1.09209	+	0.802239i
$556$		0			0
$557$	−15.6274	−	15.6274i	−0.662155	−	0.662155i	0.293733	−	0.955888i	$-0.405102\pi$
$557$	−15.6274	−	15.6274i	−0.662155	−	0.662155i	−0.955888	+	0.293733i	$0.905102\pi$
$558$		0			0
$559$			3.17157i			0.134143i
$560$		0			0
$561$	−0.627417	+	3.65685i	−0.0264896	+	0.154393i
$562$		0			0
$563$	−1.44365	+	1.44365i	−0.0608426	+	0.0608426i	−0.736873	−	0.676031i	$-0.763699\pi$
$563$	−1.44365	+	1.44365i	−0.0608426	+	0.0608426i	0.676031	+	0.736873i	$0.263699\pi$
$564$		0			0
$565$	−9.48528	−	28.4558i	−0.399049	−	1.19715i
$566$		0			0
$567$	−30.5563	+	3.24264i	−1.28325	+	0.136178i
$568$		0			0
$569$	45.3137			1.89965			0.949825	−	0.312783i	$-0.101261\pi$
$569$	45.3137			1.89965			0.949825	+	0.312783i	$0.101261\pi$
$570$		0			0
$571$	−4.97056			−0.208012			−0.104006	−	0.994577i	$-0.533166\pi$
$571$	−4.97056			−0.208012			−0.104006	+	0.994577i	$0.533166\pi$
$572$		0			0
$573$	−4.14214	−	5.85786i	−0.173040	−	0.244716i
$574$		0			0
$575$	30.8995	+	4.41421i	1.28860	+	0.184085i
$576$		0			0
$577$	14.6569	−	14.6569i	0.610173	−	0.610173i	−0.332818	−	0.942991i	$-0.608000\pi$
$577$	14.6569	−	14.6569i	0.610173	−	0.610173i	0.942991	+	0.332818i	$0.108000\pi$
$578$		0			0
$579$	−35.3848	−	6.07107i	−1.47054	−	0.252305i
$580$		0			0
$581$		−	15.6569i		−	0.649556i
$582$		0			0
$583$	2.48528	+	2.48528i	0.102930	+	0.102930i
$584$		0			0
$585$	−0.656854	+	36.3137i	−0.0271576	+	1.50139i
$586$		0			0
$587$	−10.5563	−	10.5563i	−0.435707	−	0.435707i	0.454857	−	0.890564i	$-0.349690\pi$
$587$	−10.5563	−	10.5563i	−0.435707	−	0.435707i	−0.890564	+	0.454857i	$0.849690\pi$
$588$		0			0
$589$		−	4.68629i		−	0.193095i
$590$		0			0
$591$	35.3848	+	6.07107i	1.45554	+	0.249730i
$592$		0			0
$593$	−15.4853	+	15.4853i	−0.635904	+	0.635904i	−0.949543	−	0.313638i	$-0.898452\pi$
$593$	−15.4853	+	15.4853i	−0.635904	+	0.635904i	0.313638	+	0.949543i	$0.398452\pi$
$594$		0			0
$595$	−8.82843	+	17.6569i	−0.361930	+	0.723860i
$596$		0			0
$597$	18.4853	+	26.1421i	0.756552	+	1.06993i
$598$		0			0
$599$	41.9411			1.71367			0.856834	−	0.515592i	$-0.172428\pi$
$599$	41.9411			1.71367			0.856834	+	0.515592i	$0.172428\pi$
$600$		0			0
$601$	−14.9706			−0.610662			−0.305331	−	0.952246i	$-0.598767\pi$
$601$	−14.9706			−0.610662			−0.305331	+	0.952246i	$0.598767\pi$
$602$		0			0
$603$	−18.4142	−	38.5563i	−0.749885	−	1.57014i
$604$		0			0
$605$	10.3137	−	20.6274i	0.419312	−	0.838624i
$606$		0			0
$607$	33.0416	−	33.0416i	1.34112	−	1.34112i	0.446170	−	0.894948i	$-0.352788\pi$
$607$	33.0416	−	33.0416i	1.34112	−	1.34112i	0.894948	−	0.446170i	$-0.147212\pi$
$608$		0			0
$609$	3.65685	−	21.3137i	0.148183	−	0.863675i
$610$		0			0
$611$			27.4558i			1.11074i
$612$		0			0
$613$	−9.48528	−	9.48528i	−0.383107	−	0.383107i	0.489113	−	0.872220i	$-0.337320\pi$
$613$	−9.48528	−	9.48528i	−0.383107	−	0.383107i	−0.872220	+	0.489113i	$0.837320\pi$
$614$		0			0
$615$	−21.6569	+	3.31371i	−0.873289	+	0.133622i
$616$		0			0
$617$	−12.1716	−	12.1716i	−0.490009	−	0.490009i	0.418300	−	0.908309i	$-0.362626\pi$
$617$	−12.1716	−	12.1716i	−0.490009	−	0.490009i	−0.908309	+	0.418300i	$0.862626\pi$
$618$		0			0
$619$			20.1421i			0.809581i	0.914410	+	0.404790i	$0.132656\pi$
$619$			20.1421i			0.809581i	−0.914410	+	0.404790i	$0.867344\pi$
$620$		0			0
$621$	−28.3137	−	15.8284i	−1.13619	−	0.635173i
$622$		0			0
$623$	37.7990	−	37.7990i	1.51438	−	1.51438i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	0.970563	−	0.686292i	0.0387605	−	0.0274078i
$628$		0			0
$629$	−21.3137			−0.849833
$630$		0			0
$631$	−31.5980			−1.25790			−0.628948	−	0.777447i	$-0.716514\pi$
$631$	−31.5980			−1.25790			−0.628948	+	0.777447i	$0.716514\pi$
$632$		0			0
$633$	−29.6569	+	20.9706i	−1.17875	+	0.833505i
$634$		0			0
$635$	5.58579	+	16.7574i	0.221665	+	0.664996i
$636$		0			0
$637$	−17.8284	+	17.8284i	−0.706388	+	0.706388i
$638$		0			0
$639$	−29.6569	−	10.4853i	−1.17321	−	0.414791i
$640$		0			0
$641$		−	20.2843i		−	0.801181i	−0.916257	−	0.400590i	$-0.868805\pi$
$641$		−	20.2843i		−	0.801181i	0.916257	−	0.400590i	$-0.131195\pi$
$642$		0			0
$643$	−28.6985	−	28.6985i	−1.13176	−	1.13176i	−0.989885	−	0.141873i	$-0.954688\pi$
$643$	−28.6985	−	28.6985i	−1.13176	−	1.13176i	−0.141873	−	0.989885i	$-0.545312\pi$
$644$		0			0
$645$	1.34315	−	1.82843i	0.0528863	−	0.0719942i
$646$		0			0
$647$	−26.2132	−	26.2132i	−1.03055	−	1.03055i	−0.999518	−	0.0310289i	$-0.990122\pi$
$647$	−26.2132	−	26.2132i	−1.03055	−	1.03055i	−0.0310289	−	0.999518i	$-0.509878\pi$
$648$		0			0
$649$		−	3.31371i		−	0.130074i
$650$		0			0
$651$	5.65685	−	32.9706i	0.221710	−	1.29222i
$652$		0			0
$653$	−26.6569	+	26.6569i	−1.04316	+	1.04316i	−0.0441379	+	0.999025i	$0.514054\pi$
$653$	−26.6569	+	26.6569i	−1.04316	+	1.04316i	−0.999025	+	0.0441379i	$0.985946\pi$
$654$		0			0
$655$	17.6569	+	8.82843i	0.689910	+	0.344955i
$656$		0			0
$657$	−17.8284	+	8.51472i	−0.695553	+	0.332191i
$658$		0			0
$659$	10.6274			0.413985			0.206993	−	0.978342i	$-0.433632\pi$
$659$	10.6274			0.413985			0.206993	+	0.978342i	$0.433632\pi$
$660$		0			0
$661$	7.65685			0.297817			0.148909	−	0.988851i	$-0.452424\pi$
$661$	7.65685			0.297817			0.148909	+	0.988851i	$0.452424\pi$
$662$		0			0
$663$	−14.0000	−	19.7990i	−0.543715	−	0.768929i
$664$		0			0
$665$	6.00000	−	2.00000i	0.232670	−	0.0775567i
$666$		0			0
$667$	16.1421	−	16.1421i	0.625026	−	0.625026i
$668$		0			0
$669$	−13.4853	−	2.31371i	−0.521371	−	0.0894531i
$670$		0			0
$671$		−	0.284271i		−	0.0109742i
$672$		0			0
$673$	−3.68629	−	3.68629i	−0.142096	−	0.142096i	0.632480	−	0.774576i	$-0.282037\pi$
$673$	−3.68629	−	3.68629i	−0.142096	−	0.142096i	−0.774576	+	0.632480i	$0.782037\pi$
$674$		0			0
$675$	15.7574	−	20.6569i	0.606501	−	0.795083i
$676$		0			0
$677$	35.2843	+	35.2843i	1.35608	+	1.35608i	0.878688	+	0.477397i	$0.158420\pi$
$677$	35.2843	+	35.2843i	1.35608	+	1.35608i	0.477397	+	0.878688i	$0.341580\pi$
$678$		0			0
$679$		−	4.82843i		−	0.185298i
$680$		0			0
$681$	11.8284	+	2.02944i	0.453266	+	0.0777682i
$682$		0			0
$683$	22.5563	−	22.5563i	0.863095	−	0.863095i	−0.128602	−	0.991696i	$-0.541049\pi$
$683$	22.5563	−	22.5563i	0.863095	−	0.863095i	0.991696	+	0.128602i	$0.0410488\pi$
$684$		0			0
$685$	−29.4853	+	9.82843i	−1.12657	+	0.375525i
$686$		0			0
$687$	−14.3431	−	20.2843i	−0.547225	−	0.773893i
$688$		0			0
$689$	−22.9706			−0.875109
$690$		0			0
$691$	−33.6569			−1.28037			−0.640184	−	0.768222i	$-0.721142\pi$
$691$	−33.6569			−1.28037			−0.640184	+	0.768222i	$0.721142\pi$
$692$		0			0
$693$	7.65685	−	3.65685i	0.290860	−	0.138912i
$694$		0			0
$695$	17.6569	+	8.82843i	0.669763	+	0.334881i
$696$		0			0
$697$	10.3431	−	10.3431i	0.391775	−	0.391775i
$698$		0			0
$699$	−4.89949	+	28.5563i	−0.185316	+	1.08010i
$700$		0			0
$701$			4.00000i			0.151078i	0.997143	+	0.0755390i	$0.0240677\pi$
$701$			4.00000i			0.151078i	−0.997143	+	0.0755390i	$0.975932\pi$
$702$		0			0
$703$	4.82843	+	4.82843i	0.182108	+	0.182108i
$704$		0			0
$705$	11.6274	−	15.8284i	0.437914	−	0.596133i
$706$		0			0
$707$	23.3137	+	23.3137i	0.876802	+	0.876802i
$708$		0			0
$709$			32.2843i			1.21246i	0.795289	+	0.606231i	$0.207319\pi$
$709$			32.2843i			1.21246i	−0.795289	+	0.606231i	$0.792681\pi$
$710$		0			0
$711$	2.34315	+	0.828427i	0.0878748	+	0.0310684i
$712$		0			0
$713$	24.9706	−	24.9706i	0.935155	−	0.935155i
$714$		0			0
$715$	−3.17157	−	9.51472i	−0.118610	−	0.355830i
$716$		0			0
$717$	22.6274	−	16.0000i	0.845036	−	0.597531i
$718$		0			0
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$		0			0
$721$	26.9706			1.00444
$722$		0			0
$723$	0.485281	−	0.343146i	0.0180478	−	0.0127617i
$724$		0			0
$725$	10.9706	+	14.6274i	0.407436	+	0.543249i
$726$		0			0
$727$	12.7574	−	12.7574i	0.473144	−	0.473144i	−0.429786	−	0.902931i	$-0.641411\pi$
$727$	12.7574	−	12.7574i	0.473144	−	0.473144i	0.902931	+	0.429786i	$0.141411\pi$
$728$		0			0
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		0			0
$731$			1.51472i			0.0560239i
$732$		0			0
$733$	5.14214	+	5.14214i	0.189929	+	0.189929i	0.795665	−	0.605736i	$-0.207121\pi$
$733$	5.14214	+	5.14214i	0.189929	+	0.189929i	−0.605736	+	0.795665i	$0.707121\pi$
$734$		0			0
$735$	17.8284	−	2.72792i	0.657611	−	0.100621i
$736$		0			0
$737$	8.34315	+	8.34315i	0.307324	+	0.307324i
$738$		0			0
$739$		−	47.1716i		−	1.73523i	−0.497233	−	0.867617i	$-0.665650\pi$
$739$		−	47.1716i		−	1.73523i	0.497233	−	0.867617i	$-0.334350\pi$
$740$		0			0
$741$	−1.31371	+	7.65685i	−0.0482603	+	0.281282i
$742$		0			0
$743$	−37.3848	+	37.3848i	−1.37151	+	1.37151i	−0.513313	+	0.858202i	$0.671582\pi$
$743$	−37.3848	+	37.3848i	−1.37151	+	1.37151i	−0.858202	+	0.513313i	$0.828418\pi$
$744$		0			0
$745$	13.3137	−	26.6274i	0.487777	−	0.975553i
$746$		0			0
$747$	−5.92893	−	12.4142i	−0.216928	−	0.454212i
$748$		0			0
$749$	−46.2843			−1.69119
$750$		0			0
$751$	12.2843			0.448259			0.224130	−	0.974559i	$-0.428046\pi$
$751$	12.2843			0.448259			0.224130	+	0.974559i	$0.428046\pi$
$752$		0			0
$753$	26.4853	+	37.4558i	0.965177	+	1.36497i
$754$		0			0
$755$	13.6569	−	27.3137i	0.497024	−	0.994048i
$756$		0			0
$757$	−14.4558	+	14.4558i	−0.525407	+	0.525407i	−0.919199	−	0.393793i	$-0.871163\pi$
$757$	−14.4558	+	14.4558i	−0.525407	+	0.525407i	0.393793	+	0.919199i	$0.371163\pi$
$758$		0			0
$759$	8.82843	+	1.51472i	0.320452	+	0.0549808i
$760$		0			0
$761$		−	12.6863i		−	0.459878i	−0.973205	−	0.229939i	$-0.926147\pi$
$761$		−	12.6863i		−	0.459878i	0.973205	−	0.229939i	$-0.0738526\pi$
$762$		0			0
$763$	9.65685	+	9.65685i	0.349602	+	0.349602i
$764$		0			0
$765$	−0.313708	+	17.3431i	−0.0113422	+	0.627043i
$766$		0			0
$767$	15.3137	+	15.3137i	0.552946	+	0.552946i
$768$		0			0
$769$			49.9411i			1.80092i	0.434936	+	0.900462i	$0.356771\pi$
$769$			49.9411i			1.80092i	−0.434936	+	0.900462i	$0.643229\pi$
$770$		0			0
$771$	−22.8995	−	3.92893i	−0.824705	−	0.141497i
$772$		0			0
$773$	−10.6569	+	10.6569i	−0.383300	+	0.383300i	−0.872290	−	0.488989i	$-0.837366\pi$
$773$	−10.6569	+	10.6569i	−0.383300	+	0.383300i	0.488989	+	0.872290i	$0.337366\pi$
$774$		0			0
$775$	16.9706	+	22.6274i	0.609601	+	0.812801i
$776$		0			0
$777$	28.1421	+	39.7990i	1.00959	+	1.42778i
$778$		0			0
$779$	−4.68629			−0.167904
$780$		0			0
$781$	8.68629			0.310820
$782$		0			0
$783$	−5.17157	−	18.2843i	−0.184817	−	0.653427i
$784$		0			0
$785$	5.48528	+	16.4558i	0.195778	+	0.587334i
$786$		0			0
$787$	−27.5858	+	27.5858i	−0.983327	+	0.983327i	−0.999863	−	0.0165362i	$-0.994736\pi$
$787$	−27.5858	+	27.5858i	−0.983327	+	0.983327i	0.0165362	+	0.999863i	$0.494736\pi$
$788$		0			0
$789$	−2.85786	+	16.6569i	−0.101743	+	0.593000i
$790$		0			0
$791$		−	45.7990i		−	1.62842i
$792$		0			0
$793$	1.31371	+	1.31371i	0.0466512	+	0.0466512i
$794$		0			0
$795$	13.2426	+	9.72792i	0.469668	+	0.345014i
$796$		0			0
$797$	4.65685	+	4.65685i	0.164954	+	0.164954i	0.784757	−	0.619803i	$-0.212788\pi$
$797$	4.65685	+	4.65685i	0.164954	+	0.164954i	−0.619803	+	0.784757i	$0.712788\pi$
$798$		0			0
$799$			13.1127i			0.463894i
$800$		0			0
$801$	15.6569	−	44.2843i	0.553208	−	1.56471i
$802$		0			0
$803$	3.85786	−	3.85786i	0.136141	−	0.136141i
$804$		0			0
$805$	42.6274	+	21.3137i	1.50242	+	0.751210i
$806$		0			0
$807$	−23.5147	+	16.6274i	−0.827757	+	0.585313i
$808$		0			0
$809$	−32.3431			−1.13712			−0.568562	−	0.822640i	$-0.692500\pi$
$809$	−32.3431			−1.13712			−0.568562	+	0.822640i	$0.692500\pi$
$810$		0			0
$811$	33.6569			1.18185			0.590926	−	0.806726i	$-0.298763\pi$
$811$	33.6569			1.18185			0.590926	+	0.806726i	$0.298763\pi$
$812$		0			0
$813$	14.6274	−	10.3431i	0.513006	−	0.362750i
$814$		0			0
$815$	−1.24264	+	0.414214i	−0.0435278	+	0.0145093i
$816$		0			0
$817$	0.343146	−	0.343146i	0.0120052	−	0.0120052i
$818$		0			0
$819$	−18.4853	+	52.2843i	−0.645928	+	1.82696i
$820$		0			0
$821$		−	37.9411i		−	1.32415i	−0.749436	−	0.662077i	$-0.769675\pi$
$821$		−	37.9411i		−	1.32415i	0.749436	−	0.662077i	$-0.230325\pi$
$822$		0			0
$823$	−5.72792	−	5.72792i	−0.199663	−	0.199663i	0.600193	−	0.799855i	$-0.295091\pi$
$823$	−5.72792	−	5.72792i	−0.199663	−	0.199663i	−0.799855	+	0.600193i	$0.795091\pi$
$824$		0			0
$825$	−2.20101	+	6.82843i	−0.0766293	+	0.237735i
$826$		0			0
$827$	−27.5269	−	27.5269i	−0.957205	−	0.957205i	0.0419166	−	0.999121i	$-0.486654\pi$
$827$	−27.5269	−	27.5269i	−0.957205	−	0.957205i	−0.999121	+	0.0419166i	$0.986654\pi$
$828$		0			0
$829$			15.3137i			0.531867i	0.963991	+	0.265934i	$0.0856802\pi$
$829$			15.3137i			0.531867i	−0.963991	+	0.265934i	$0.914320\pi$
$830$		0			0
$831$	−3.38478	+	19.7279i	−0.117417	+	0.684354i
$832$		0			0
$833$	−8.51472	+	8.51472i	−0.295018	+	0.295018i
$834$		0			0
$835$	−27.7279	+	9.24264i	−0.959564	+	0.319855i
$836$		0			0
$837$	−8.00000	−	28.2843i	−0.276520	−	0.977647i
$838$		0			0
$839$	12.6863			0.437979			0.218990	−	0.975727i	$-0.429724\pi$
$839$	12.6863			0.437979			0.218990	+	0.975727i	$0.429724\pi$
$840$		0			0
$841$	−15.6274			−0.538876
$842$		0			0
$843$	5.65685	+	8.00000i	0.194832	+	0.275535i
$844$		0			0
$845$	32.6274	+	16.3137i	1.12242	+	0.561209i
$846$		0			0
$847$	24.8995	−	24.8995i	0.855557	−	0.855557i
$848$		0			0
$849$	−12.6569	−	2.17157i	−0.434382	−	0.0745282i
$850$		0			0
$851$			51.4558i			1.76388i
$852$		0			0
$853$	24.4558	+	24.4558i	0.837352	+	0.837352i	0.988510	−	0.151158i	$-0.0483001\pi$
$853$	24.4558	+	24.4558i	0.837352	+	0.837352i	−0.151158	+	0.988510i	$0.548300\pi$
$854$		0			0
$855$	4.00000	−	3.85786i	0.136797	−	0.131936i
$856$		0			0
$857$	33.4853	+	33.4853i	1.14384	+	1.14384i	0.987742	+	0.156093i	$0.0498900\pi$
$857$	33.4853	+	33.4853i	1.14384	+	1.14384i	0.156093	+	0.987742i	$0.450110\pi$
$858$		0			0
$859$		−	52.4264i		−	1.78877i	−0.447302	−	0.894383i	$-0.647615\pi$
$859$		−	52.4264i		−	1.78877i	0.447302	−	0.894383i	$-0.352385\pi$
$860$		0			0
$861$	−32.9706	−	5.65685i	−1.12363	−	0.192785i
$862$		0			0
$863$	3.58579	−	3.58579i	0.122062	−	0.122062i	−0.643437	−	0.765499i	$-0.722492\pi$
$863$	3.58579	−	3.58579i	0.122062	−	0.122062i	0.765499	+	0.643437i	$0.222492\pi$
$864$		0			0
$865$	−0.656854	−	1.97056i	−0.0223337	−	0.0670011i
$866$		0			0
$867$	10.3137	+	14.5858i	0.350272	+	0.495359i
$868$		0			0
$869$	−0.686292			−0.0232808
$870$		0			0
$871$	−77.1127			−2.61286
$872$		0			0
$873$	−1.82843	−	3.82843i	−0.0618829	−	0.129573i
$874$		0			0
$875$	−21.7279	+	31.3848i	−0.734538	+	1.06100i
$876$		0			0
$877$	12.4558	−	12.4558i	0.420604	−	0.420604i	−0.464808	−	0.885412i	$-0.653877\pi$
$877$	12.4558	−	12.4558i	0.420604	−	0.420604i	0.885412	+	0.464808i	$0.153877\pi$
$878$		0			0
$879$	−6.89949	+	40.2132i	−0.232714	+	1.35636i
$880$		0			0
$881$			8.97056i			0.302226i	0.988516	+	0.151113i	$0.0482857\pi$
$881$			8.97056i			0.302226i	−0.988516	+	0.151113i	$0.951714\pi$
$882$		0			0
$883$	31.5858	+	31.5858i	1.06295	+	1.06295i	0.997881	+	0.0650653i	$0.0207256\pi$
$883$	31.5858	+	31.5858i	1.06295	+	1.06295i	0.0650653	+	0.997881i	$0.479274\pi$
$884$		0			0
$885$	−2.34315	−	15.3137i	−0.0787640	−	0.514765i
$886$		0			0
$887$	7.72792	+	7.72792i	0.259478	+	0.259478i	0.824842	−	0.565364i	$-0.191264\pi$
$887$	7.72792	+	7.72792i	0.259478	+	0.259478i	−0.565364	+	0.824842i	$0.691264\pi$
$888$		0			0
$889$			26.9706i			0.904564i
$890$		0			0
$891$	4.68629	−	5.79899i	0.156997	−	0.194273i
$892$		0			0
$893$	2.97056	−	2.97056i	0.0994061	−	0.0994061i
$894$		0			0
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$		0			0
$897$	−47.7990	+	33.7990i	−1.59596	+	1.12852i
$898$		0			0
$899$	20.6863			0.689926
$900$		0			0
$901$	−10.9706			−0.365482
$902$		0			0
$903$	2.82843	−	2.00000i	0.0941242	−	0.0665558i
$904$		0			0
$905$	5.31371	−	10.6274i	0.176634	−	0.353267i
$906$		0			0
$907$	28.4142	−	28.4142i	0.943478	−	0.943478i	−0.0550075	−	0.998486i	$-0.517518\pi$
$907$	28.4142	−	28.4142i	0.943478	−	0.943478i	0.998486	+	0.0550075i	$0.0175183\pi$
$908$		0			0
$909$	27.3137	+	9.65685i	0.905939	+	0.320298i
$910$		0			0
$911$			40.8284i			1.35271i	0.736578	+	0.676353i	$0.236441\pi$
$911$			40.8284i			1.35271i	−0.736578	+	0.676353i	$0.763559\pi$
$912$		0			0
$913$	2.68629	+	2.68629i	0.0889033	+	0.0889033i
$914$		0			0
$915$	−0.201010	−	1.31371i	−0.00664519	−	0.0434299i
$916$		0			0
$917$	21.3137	+	21.3137i	0.703841	+	0.703841i
$918$		0			0
$919$			8.82843i			0.291223i	0.989342	+	0.145611i	$0.0465149\pi$
$919$			8.82843i			0.291223i	−0.989342	+	0.145611i	$0.953485\pi$
$920$		0			0
$921$	2.85786	−	16.6569i	0.0941698	−	0.548862i
$922$		0			0
$923$	−40.1421	+	40.1421i	−1.32129	+	1.32129i
$924$		0			0
$925$	−40.7990	−	5.82843i	−1.34146	−	0.191638i
$926$		0			0
$927$	21.3848	−	10.2132i	0.702368	−	0.335446i
$928$		0			0
$929$	11.9411			0.391776			0.195888	−	0.980626i	$-0.437241\pi$
$929$	11.9411			0.391776			0.195888	+	0.980626i	$0.437241\pi$
$930$		0			0
$931$	3.85786			0.126436
$932$		0			0
$933$	−5.51472	−	7.79899i	−0.180544	−	0.255327i
$934$		0			0
$935$	−1.51472	−	4.54416i	−0.0495366	−	0.148610i
$936$		0			0
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.0128079	+	0.999918i	$0.504077\pi$
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.999918	+	0.0128079i	$0.995923\pi$
$938$		0			0
$939$	5.58579	+	0.958369i	0.182285	+	0.0312752i
$940$		0			0
$941$		−	43.5980i		−	1.42125i	−0.703569	−	0.710627i	$-0.748411\pi$
$941$		−	43.5980i		−	1.42125i	0.703569	−	0.710627i	$-0.251589\pi$
$942$		0			0
$943$	−24.9706	−	24.9706i	−0.813153	−	0.813153i
$944$		0			0
$945$	32.7990	−	22.3137i	1.06695	−	0.725865i
$946$		0			0
$947$	1.72792	+	1.72792i	0.0561499	+	0.0561499i	0.734624	−	0.678474i	$-0.237359\pi$
$947$	1.72792	+	1.72792i	0.0561499	+	0.0561499i	−0.678474	+	0.734624i	$0.737359\pi$
$948$		0			0
$949$			35.6569i			1.15747i
$950$		0			0
$951$	−11.2426	−	1.92893i	−0.364568	−	0.0625499i
$952$		0			0
$953$	−15.4853	+	15.4853i	−0.501617	+	0.501617i	−0.911940	−	0.410323i	$-0.865416\pi$
$953$	−15.4853	+	15.4853i	−0.501617	+	0.501617i	0.410323	+	0.911940i	$0.365416\pi$
$954$		0			0
$955$	8.28427	+	4.14214i	0.268073	+	0.134036i
$956$		0			0
$957$	3.02944	+	4.28427i	0.0979278	+	0.138491i
$958$		0			0
$959$	−47.4558			−1.53243
$960$		0			0
$961$	1.00000			0.0322581
$962$		0			0
$963$	−36.6985	+	17.5269i	−1.18259	+	0.564797i
$964$		0			0
$965$	43.9706	−	14.6569i	1.41546	−	0.471821i
$966$		0			0
$967$	18.4142	−	18.4142i	0.592161	−	0.592161i	−0.346054	−	0.938215i	$-0.612478\pi$
$967$	18.4142	−	18.4142i	0.592161	−	0.592161i	0.938215	+	0.346054i	$0.112478\pi$
$968$		0			0
$969$	−0.627417	+	3.65685i	−0.0201555	+	0.117475i
$970$		0			0
$971$		−	42.4853i		−	1.36342i	−0.731624	−	0.681709i	$-0.761237\pi$
$971$		−	42.4853i		−	1.36342i	0.731624	−	0.681709i	$-0.238763\pi$
$972$		0			0
$973$	21.3137	+	21.3137i	0.683286	+	0.683286i
$974$		0			0
$975$	−21.3848	−	41.7279i	−0.684861	−	1.33636i
$976$		0			0
$977$	23.1421	+	23.1421i	0.740383	+	0.740383i	0.972652	−	0.232269i	$-0.0746150\pi$
$977$	23.1421	+	23.1421i	0.740383	+	0.740383i	−0.232269	+	0.972652i	$0.574615\pi$
$978$		0			0
$979$			12.9706i			0.414541i
$980$		0			0
$981$	11.3137	+	4.00000i	0.361219	+	0.127710i
$982$		0			0
$983$	−32.6985	+	32.6985i	−1.04292	+	1.04292i	−0.0438830	+	0.999037i	$0.513973\pi$
$983$	−32.6985	+	32.6985i	−1.04292	+	1.04292i	−0.999037	+	0.0438830i	$0.986027\pi$
$984$		0			0
$985$	−43.9706	+	14.6569i	−1.40102	+	0.467006i
$986$		0			0
$987$	24.4853	−	17.3137i	0.779375	−	0.551101i
$988$		0			0
$989$	3.65685			0.116281
$990$		0			0
$991$	48.9706			1.55560			0.777801	−	0.628511i	$-0.216335\pi$
$991$	48.9706			1.55560			0.777801	+	0.628511i	$0.216335\pi$
$992$		0			0
$993$	13.6569	−	9.65685i	0.433387	−	0.306451i
$994$		0			0
$995$	−36.9706	−	18.4853i	−1.17205	−	0.586023i
$996$		0			0
$997$	30.7990	−	30.7990i	0.975414	−	0.975414i	−0.0242911	−	0.999705i	$-0.507733\pi$
$997$	30.7990	−	30.7990i	0.975414	−	0.975414i	0.999705	+	0.0242911i	$0.00773287\pi$
$998$		0			0
$999$	37.3848	+	20.8995i	1.18280	+	0.661231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.v.g.833.1		4
3.2	odd	2		960.2.v.i.833.1		4
4.3	odd	2		960.2.v.f.833.2		4
5.2	odd	4		960.2.v.i.257.2		4
8.3	odd	2		120.2.r.b.113.1	yes	4
8.5	even	2		240.2.v.c.113.2		4
12.11	even	2		960.2.v.a.833.2		4
15.2	even	4	inner	960.2.v.g.257.1		4
20.7	even	4		960.2.v.a.257.1		4
24.5	odd	2		240.2.v.a.113.2		4
24.11	even	2		120.2.r.c.113.1	yes	4
40.3	even	4		600.2.r.b.257.1		4
40.13	odd	4		1200.2.v.j.257.2		4
40.19	odd	2		600.2.r.c.593.2		4
40.27	even	4		120.2.r.c.17.2	yes	4
40.29	even	2		1200.2.v.d.593.1		4
40.37	odd	4		240.2.v.a.17.1		4
60.47	odd	4		960.2.v.f.257.2		4
120.29	odd	2		1200.2.v.j.593.1		4
120.53	even	4		1200.2.v.d.257.1		4
120.59	even	2		600.2.r.b.593.2		4
120.77	even	4		240.2.v.c.17.2		4
120.83	odd	4		600.2.r.c.257.2		4
120.107	odd	4		120.2.r.b.17.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.r.b.17.1	✓	4	120.107	odd	4
120.2.r.b.113.1	yes	4	8.3	odd	2
120.2.r.c.17.2	yes	4	40.27	even	4
120.2.r.c.113.1	yes	4	24.11	even	2
240.2.v.a.17.1		4	40.37	odd	4
240.2.v.a.113.2		4	24.5	odd	2
240.2.v.c.17.2		4	120.77	even	4
240.2.v.c.113.2		4	8.5	even	2
600.2.r.b.257.1		4	40.3	even	4
600.2.r.b.593.2		4	120.59	even	2
600.2.r.c.257.2		4	120.83	odd	4
600.2.r.c.593.2		4	40.19	odd	2
960.2.v.a.257.1		4	20.7	even	4
960.2.v.a.833.2		4	12.11	even	2
960.2.v.f.257.2		4	60.47	odd	4
960.2.v.f.833.2		4	4.3	odd	2
960.2.v.g.257.1		4	15.2	even	4	inner
960.2.v.g.833.1		4	1.1	even	1	trivial
960.2.v.i.257.2		4	5.2	odd	4
960.2.v.i.833.1		4	3.2	odd	2
1200.2.v.d.257.1		4	120.53	even	4
1200.2.v.d.593.1		4	40.29	even	2
1200.2.v.j.257.2		4	40.13	odd	4
1200.2.v.j.593.1		4	120.29	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(1.00000 - 2.82843i) q^{9} +0.828427i q^{11} +(-3.82843 - 3.82843i) q^{13} +(0.585786 + 3.82843i) q^{15} +(-1.82843 - 1.82843i) q^{17} +0.828427i q^{19} +(-1.00000 + 5.82843i) q^{21} +(-4.41421 + 4.41421i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(1.41421 + 5.00000i) q^{27} -3.65685 q^{29} -5.65685 q^{31} +(-0.828427 - 1.17157i) q^{33} +(-2.41421 - 7.24264i) q^{35} +(5.82843 - 5.82843i) q^{37} +(9.24264 + 1.58579i) q^{39} +5.65685i q^{41} +(-0.414214 - 0.414214i) q^{43} +(-4.65685 - 4.82843i) q^{45} +(-3.58579 - 3.58579i) q^{47} -4.65685i q^{49} +(4.41421 + 0.757359i) q^{51} +(3.00000 - 3.00000i) q^{53} +(1.65685 + 0.828427i) q^{55} +(-0.828427 - 1.17157i) q^{57} -4.00000 q^{59} -0.343146 q^{61} +(-4.41421 - 9.24264i) q^{63} +(-11.4853 + 3.82843i) q^{65} +(10.0711 - 10.0711i) q^{67} +(1.82843 - 10.6569i) q^{69} -10.4853i q^{71} +(-4.65685 - 4.65685i) q^{73} +(8.24264 + 2.65685i) q^{75} +(2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 - 5.65685i) q^{81} +(3.24264 - 3.24264i) q^{83} +(-5.48528 + 1.82843i) q^{85} +(5.17157 - 3.65685i) q^{87} +15.6569 q^{89} -18.4853 q^{91} +(8.00000 - 5.65685i) q^{93} +(1.65685 + 0.828427i) q^{95} +(1.00000 - 1.00000i) q^{97} +(2.34315 + 0.828427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^5 + 4 * q^7 + 4 * q^9	\( 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9} - 4 q^{13} + 8 q^{15} + 4 q^{17} - 4 q^{21} - 12 q^{23} - 12 q^{25} + 8 q^{29} + 8 q^{33} - 4 q^{35} + 12 q^{37} + 20 q^{39} + 4 q^{43} + 4 q^{45} - 20 q^{47} + 12 q^{51} + 12 q^{53} - 16 q^{55} + 8 q^{57} - 16 q^{59} - 24 q^{61} - 12 q^{63} - 12 q^{65} + 12 q^{67} - 4 q^{69} + 4 q^{73} + 16 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} + 12 q^{85} + 32 q^{87} + 40 q^{89} - 40 q^{91} + 32 q^{93} - 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q + 4 * q^5 + 4 * q^7 + 4 * q^9 - 4 * q^13 + 8 * q^15 + 4 * q^17 - 4 * q^21 - 12 * q^23 - 12 * q^25 + 8 * q^29 + 8 * q^33 - 4 * q^35 + 12 * q^37 + 20 * q^39 + 4 * q^43 + 4 * q^45 - 20 * q^47 + 12 * q^51 + 12 * q^53 - 16 * q^55 + 8 * q^57 - 16 * q^59 - 24 * q^61 - 12 * q^63 - 12 * q^65 + 12 * q^67 - 4 * q^69 + 4 * q^73 + 16 * q^75 + 8 * q^77 - 28 * q^81 - 4 * q^83 + 12 * q^85 + 32 * q^87 + 40 * q^89 - 40 * q^91 + 32 * q^93 - 16 * q^95 + 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more