LMFDB - Embedded newform 960.2.y.d.847.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(847,960)]

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([2, 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("960.847");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.y (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:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			847.1
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	960.847
Dual form			960.2.y.d.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-2.10278 - 2.10278i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-2.10278 - 2.10278i) q^{7} +1.00000 q^{9} +(-2.10278 + 2.10278i) q^{11} +(-1.00000 - 2.00000i) q^{15} +(-4.62721 - 4.62721i) q^{17} +(3.52444 - 3.52444i) q^{19} +(2.10278 + 2.10278i) q^{21} +(-3.52444 + 3.52444i) q^{23} +(-3.00000 + 4.00000i) q^{25} -1.00000 q^{27} +(-1.00000 - 1.00000i) q^{29} -4.20555i q^{31} +(2.10278 - 2.10278i) q^{33} +(2.10278 - 6.30833i) q^{35} -7.25443i q^{37} -4.00000i q^{41} -3.04888i q^{43} +(1.00000 + 2.00000i) q^{45} +(-4.68111 + 4.68111i) q^{47} +1.84333i q^{49} +(4.62721 + 4.62721i) q^{51} -3.15667 q^{53} +(-6.30833 - 2.10278i) q^{55} +(-3.52444 + 3.52444i) q^{57} +(-5.15165 - 5.15165i) q^{59} +(-6.62721 + 6.62721i) q^{61} +(-2.10278 - 2.10278i) q^{63} -7.45998i q^{67} +(3.52444 - 3.52444i) q^{69} +12.4111 q^{71} +(-10.2544 - 10.2544i) q^{73} +(3.00000 - 4.00000i) q^{75} +8.84333 q^{77} -12.4111 q^{79} +1.00000 q^{81} +16.4111 q^{83} +(4.62721 - 13.8816i) q^{85} +(1.00000 + 1.00000i) q^{87} -13.2544 q^{89} +4.20555i q^{93} +(10.5733 + 3.52444i) q^{95} +(-11.4111 - 11.4111i) q^{97} +(-2.10278 + 2.10278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9	$ 6 q - 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9} + 2 q^{11} - 6 q^{15} - 2 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 18 q^{25} - 6 q^{27} - 6 q^{29} - 2 q^{33} - 2 q^{35} + 6 q^{45} - 10 q^{47} + 2 q^{51} - 12 q^{53} + 6 q^{55} - 10 q^{57} + 6 q^{59} - 14 q^{61} + 2 q^{63} + 10 q^{69} + 16 q^{71} - 10 q^{73} + 18 q^{75} + 60 q^{77} - 16 q^{79} + 6 q^{81} + 40 q^{83} + 2 q^{85} + 6 q^{87} - 28 q^{89} + 30 q^{95} - 10 q^{97} + 2 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9 + 2 * q^11 - 6 * q^15 - 2 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 18 * q^25 - 6 * q^27 - 6 * q^29 - 2 * q^33 - 2 * q^35 + 6 * q^45 - 10 * q^47 + 2 * q^51 - 12 * q^53 + 6 * q^55 - 10 * q^57 + 6 * q^59 - 14 * q^61 + 2 * q^63 + 10 * q^69 + 16 * q^71 - 10 * q^73 + 18 * q^75 + 60 * q^77 - 16 * q^79 + 6 * q^81 + 40 * q^83 + 2 * q^85 + 6 * q^87 - 28 * q^89 + 30 * q^95 - 10 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$	−2.10278	−	2.10278i	−0.794774	−	0.794774i	0.187492	−	0.982266i	$-0.439964\pi$
$7$	−2.10278	−	2.10278i	−0.794774	−	0.794774i	−0.982266	+	0.187492i	$0.939964\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.10278	+	2.10278i	−0.634011	+	0.634011i	−0.949071	−	0.315061i	$-0.897975\pi$
$11$	−2.10278	+	2.10278i	−0.634011	+	0.634011i	0.315061	+	0.949071i	$0.397975\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−1.00000	−	2.00000i	−0.258199	−	0.516398i
$16$		0			0
$17$	−4.62721	−	4.62721i	−1.12226	−	1.12226i	−0.991400	−	0.130864i	$-0.958225\pi$
$17$	−4.62721	−	4.62721i	−1.12226	−	1.12226i	−0.130864	−	0.991400i	$-0.541775\pi$
$18$		0			0
$19$	3.52444	−	3.52444i	0.808562	−	0.808562i	−0.175855	−	0.984416i	$-0.556269\pi$
$19$	3.52444	−	3.52444i	0.808562	−	0.808562i	0.984416	+	0.175855i	$0.0562689\pi$
$20$		0			0
$21$	2.10278	+	2.10278i	0.458863	+	0.458863i
$22$		0			0
$23$	−3.52444	+	3.52444i	−0.734896	+	0.734896i	−0.971585	−	0.236689i	$-0.923938\pi$
$23$	−3.52444	+	3.52444i	−0.734896	+	0.734896i	0.236689	+	0.971585i	$0.423938\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	0.608137	−	0.793832i	$-0.291917\pi$
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	−0.793832	+	0.608137i	$0.791917\pi$
$30$		0			0
$31$		−	4.20555i		−	0.755339i	−0.925940	−	0.377670i	$-0.876726\pi$
$31$		−	4.20555i		−	0.755339i	0.925940	−	0.377670i	$-0.123274\pi$
$32$		0			0
$33$	2.10278	−	2.10278i	0.366046	−	0.366046i
$34$		0			0
$35$	2.10278	−	6.30833i	0.355434	−	1.06630i
$36$		0			0
$37$		−	7.25443i		−	1.19262i	−0.802754	−	0.596310i	$-0.796633\pi$
$37$		−	7.25443i		−	1.19262i	0.802754	−	0.596310i	$-0.203367\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$		−	3.04888i		−	0.464949i	−0.972602	−	0.232475i	$-0.925318\pi$
$43$		−	3.04888i		−	0.464949i	0.972602	−	0.232475i	$-0.0746823\pi$
$44$		0			0
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$		0			0
$47$	−4.68111	+	4.68111i	−0.682810	+	0.682810i	−0.960633	−	0.277822i	$-0.910387\pi$
$47$	−4.68111	+	4.68111i	−0.682810	+	0.682810i	0.277822	+	0.960633i	$0.410387\pi$
$48$		0			0
$49$			1.84333i			0.263332i
$50$		0			0
$51$	4.62721	+	4.62721i	0.647939	+	0.647939i
$52$		0			0
$53$	−3.15667			−0.433603			−0.216801	−	0.976216i	$-0.569562\pi$
$53$	−3.15667			−0.433603			−0.216801	+	0.976216i	$0.569562\pi$
$54$		0			0
$55$	−6.30833	−	2.10278i	−0.850614	−	0.283538i
$56$		0			0
$57$	−3.52444	+	3.52444i	−0.466823	+	0.466823i
$58$		0			0
$59$	−5.15165	−	5.15165i	−0.670688	−	0.670688i	0.287187	−	0.957875i	$-0.407280\pi$
$59$	−5.15165	−	5.15165i	−0.670688	−	0.670688i	−0.957875	+	0.287187i	$0.907280\pi$
$60$		0			0
$61$	−6.62721	+	6.62721i	−0.848528	+	0.848528i	−0.989949	−	0.141422i	$-0.954833\pi$
$61$	−6.62721	+	6.62721i	−0.848528	+	0.848528i	0.141422	+	0.989949i	$0.454833\pi$
$62$		0			0
$63$	−2.10278	−	2.10278i	−0.264925	−	0.264925i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	7.45998i		−	0.911381i	−0.890138	−	0.455691i	$-0.849392\pi$
$67$		−	7.45998i		−	0.911381i	0.890138	−	0.455691i	$-0.150608\pi$
$68$		0			0
$69$	3.52444	−	3.52444i	0.424292	−	0.424292i
$70$		0			0
$71$	12.4111			1.47293			0.736463	−	0.676477i	$-0.236494\pi$
$71$	12.4111			1.47293			0.736463	+	0.676477i	$0.236494\pi$
$72$		0			0
$73$	−10.2544	−	10.2544i	−1.20019	−	1.20019i	−0.974108	−	0.226081i	$-0.927408\pi$
$73$	−10.2544	−	10.2544i	−1.20019	−	1.20019i	−0.226081	−	0.974108i	$-0.572592\pi$
$74$		0			0
$75$	3.00000	−	4.00000i	0.346410	−	0.461880i
$76$		0			0
$77$	8.84333			1.00779
$78$		0			0
$79$	−12.4111			−1.39636			−0.698179	−	0.715923i	$-0.746006\pi$
$79$	−12.4111			−1.39636			−0.698179	+	0.715923i	$0.746006\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	16.4111			1.80135			0.900676	−	0.434491i	$-0.143072\pi$
$83$	16.4111			1.80135			0.900676	+	0.434491i	$0.143072\pi$
$84$		0			0
$85$	4.62721	−	13.8816i	0.501892	−	1.50568i
$86$		0			0
$87$	1.00000	+	1.00000i	0.107211	+	0.107211i
$88$		0			0
$89$	−13.2544			−1.40497			−0.702483	−	0.711700i	$-0.747925\pi$
$89$	−13.2544			−1.40497			−0.702483	+	0.711700i	$0.747925\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			4.20555i			0.436095i
$94$		0			0
$95$	10.5733	+	3.52444i	1.08480	+	0.361600i
$96$		0			0
$97$	−11.4111	−	11.4111i	−1.15862	−	1.15862i	−0.984772	−	0.173849i	$-0.944379\pi$
$97$	−11.4111	−	11.4111i	−1.15862	−	1.15862i	−0.173849	−	0.984772i	$-0.555621\pi$
$98$		0			0
$99$	−2.10278	+	2.10278i	−0.211337	+	0.211337i
$100$		0			0
$101$	6.25443	+	6.25443i	0.622339	+	0.622339i	0.946129	−	0.323790i	$-0.104957\pi$
$101$	6.25443	+	6.25443i	0.622339	+	0.622339i	−0.323790	+	0.946129i	$0.604957\pi$
$102$		0			0
$103$	−9.15165	+	9.15165i	−0.901739	+	0.901739i	−0.995587	−	0.0938476i	$-0.970083\pi$
$103$	−9.15165	+	9.15165i	−0.901739	+	0.901739i	0.0938476	+	0.995587i	$0.470083\pi$
$104$		0			0
$105$	−2.10278	+	6.30833i	−0.205210	+	0.615629i
$106$		0			0
$107$	−14.0978			−1.36288			−0.681441	−	0.731873i	$-0.738646\pi$
$107$	−14.0978			−1.36288			−0.681441	+	0.731873i	$0.738646\pi$
$108$		0			0
$109$	9.78389	+	9.78389i	0.937126	+	0.937126i	0.998137	−	0.0610107i	$-0.0194324\pi$
$109$	9.78389	+	9.78389i	0.937126	+	0.937126i	−0.0610107	+	0.998137i	$0.519432\pi$
$110$		0			0
$111$			7.25443i			0.688560i
$112$		0			0
$113$	6.62721	−	6.62721i	0.623436	−	0.623436i	−0.322973	−	0.946408i	$-0.604682\pi$
$113$	6.62721	−	6.62721i	0.623436	−	0.623436i	0.946408	+	0.322973i	$0.104682\pi$
$114$		0			0
$115$	−10.5733	−	3.52444i	−0.985967	−	0.328656i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			19.4600i			1.78389i
$120$		0			0
$121$			2.15667i			0.196061i
$122$		0			0
$123$			4.00000i			0.360668i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	−1.89722	+	1.89722i	−0.168351	+	0.168351i	−0.786254	−	0.617903i	$-0.787982\pi$
$127$	−1.89722	+	1.89722i	−0.168351	+	0.168351i	0.617903	+	0.786254i	$0.287982\pi$
$128$		0			0
$129$			3.04888i			0.268439i
$130$		0			0
$131$	5.35720	+	5.35720i	0.468061	+	0.468061i	0.901286	−	0.433225i	$-0.142624\pi$
$131$	5.35720	+	5.35720i	0.468061	+	0.468061i	−0.433225	+	0.901286i	$0.642624\pi$
$132$		0			0
$133$	−14.8222			−1.28525
$134$		0			0
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$		0			0
$137$	11.7839	−	11.7839i	1.00677	−	1.00677i	0.00678847	−	0.999977i	$-0.497839\pi$
$137$	11.7839	−	11.7839i	1.00677	−	1.00677i	0.999977	−	0.00678847i	$-0.00216085\pi$
$138$		0			0
$139$	3.72999	+	3.72999i	0.316373	+	0.316373i	0.847372	−	0.530999i	$-0.178183\pi$
$139$	3.72999	+	3.72999i	0.316373	+	0.316373i	−0.530999	+	0.847372i	$0.678183\pi$
$140$		0			0
$141$	4.68111	−	4.68111i	0.394221	−	0.394221i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	1.00000	−	3.00000i	0.0830455	−	0.249136i
$146$		0			0
$147$		−	1.84333i		−	0.152035i
$148$		0			0
$149$	−8.25443	+	8.25443i	−0.676229	+	0.676229i	−0.959145	−	0.282916i	$-0.908698\pi$
$149$	−8.25443	+	8.25443i	−0.676229	+	0.676229i	0.282916	+	0.959145i	$0.408698\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−4.62721	−	4.62721i	−0.374088	−	0.374088i
$154$		0			0
$155$	8.41110	−	4.20555i	0.675596	−	0.337798i
$156$		0			0
$157$	8.50885			0.679080			0.339540	−	0.940592i	$-0.389729\pi$
$157$	8.50885			0.679080			0.339540	+	0.940592i	$0.389729\pi$
$158$		0			0
$159$	3.15667			0.250341
$160$		0			0
$161$	14.8222			1.16815
$162$		0			0
$163$	−0.411100			−0.0321999			−0.0160999	−	0.999870i	$-0.505125\pi$
$163$	−0.411100			−0.0321999			−0.0160999	+	0.999870i	$0.505125\pi$
$164$		0			0
$165$	6.30833	+	2.10278i	0.491102	+	0.163701i
$166$		0			0
$167$	10.7789	+	10.7789i	0.834094	+	0.834094i	0.988074	−	0.153980i	$-0.0492093\pi$
$167$	10.7789	+	10.7789i	0.834094	+	0.834094i	−0.153980	+	0.988074i	$0.549209\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	3.52444	−	3.52444i	0.269521	−	0.269521i
$172$		0			0
$173$			18.5089i			1.40720i	0.710595	+	0.703601i	$0.248426\pi$
$173$			18.5089i			1.40720i	−0.710595	+	0.703601i	$0.751574\pi$
$174$		0			0
$175$	14.7194	−	2.10278i	1.11268	−	0.158955i
$176$		0			0
$177$	5.15165	+	5.15165i	0.387222	+	0.387222i
$178$		0			0
$179$	−9.35720	+	9.35720i	−0.699390	+	0.699390i	−0.964279	−	0.264889i	$-0.914665\pi$
$179$	−9.35720	+	9.35720i	−0.699390	+	0.699390i	0.264889	+	0.964279i	$0.414665\pi$
$180$		0			0
$181$	4.62721	+	4.62721i	0.343938	+	0.343938i	0.857846	−	0.513908i	$-0.171803\pi$
$181$	4.62721	+	4.62721i	0.343938	+	0.343938i	−0.513908	+	0.857846i	$0.671803\pi$
$182$		0			0
$183$	6.62721	−	6.62721i	0.489898	−	0.489898i
$184$		0			0
$185$	14.5089	−	7.25443i	1.06671	−	0.533356i
$186$		0			0
$187$	19.4600			1.42305
$188$		0			0
$189$	2.10278	+	2.10278i	0.152954	+	0.152954i
$190$		0			0
$191$		−	19.0489i		−	1.37833i	−0.724605	−	0.689164i	$-0.757978\pi$
$191$		−	19.0489i		−	1.37833i	0.724605	−	0.689164i	$-0.242022\pi$
$192$		0			0
$193$	−7.41110	+	7.41110i	−0.533463	+	0.533463i	−0.921601	−	0.388138i	$-0.873118\pi$
$193$	−7.41110	+	7.41110i	−0.533463	+	0.533463i	0.388138	+	0.921601i	$0.373118\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			15.6655i			1.11612i	0.829800	+	0.558061i	$0.188455\pi$
$197$			15.6655i			1.11612i	−0.829800	+	0.558061i	$0.811545\pi$
$198$		0			0
$199$		−	7.79445i		−	0.552534i	−0.961081	−	0.276267i	$-0.910903\pi$
$199$		−	7.79445i		−	0.552534i	0.961081	−	0.276267i	$-0.0890974\pi$
$200$		0			0
$201$			7.45998i			0.526186i
$202$		0			0
$203$			4.20555i			0.295172i
$204$		0			0
$205$	8.00000	−	4.00000i	0.558744	−	0.279372i
$206$		0			0
$207$	−3.52444	+	3.52444i	−0.244965	+	0.244965i
$208$		0			0
$209$			14.8222i			1.02527i
$210$		0			0
$211$	6.57331	+	6.57331i	0.452526	+	0.452526i	0.896192	−	0.443666i	$-0.146322\pi$
$211$	6.57331	+	6.57331i	0.452526	+	0.452526i	−0.443666	+	0.896192i	$0.646322\pi$
$212$		0			0
$213$	−12.4111			−0.850395
$214$		0			0
$215$	6.09775	−	3.04888i	0.415863	−	0.207932i
$216$		0			0
$217$	−8.84333	+	8.84333i	−0.600324	+	0.600324i
$218$		0			0
$219$	10.2544	+	10.2544i	0.692930	+	0.692930i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.35720	−	1.35720i	−0.0908849	−	0.0908849i	0.660203	−	0.751088i	$-0.270470\pi$
$223$	−1.35720	−	1.35720i	−0.0908849	−	0.0908849i	−0.751088	+	0.660203i	$0.770470\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$		0			0
$227$		−	12.2056i		−	0.810111i	−0.914292	−	0.405055i	$-0.867252\pi$
$227$		−	12.2056i		−	0.810111i	0.914292	−	0.405055i	$-0.132748\pi$
$228$		0			0
$229$	9.78389	−	9.78389i	0.646537	−	0.646537i	−0.305617	−	0.952155i	$-0.598863\pi$
$229$	9.78389	−	9.78389i	0.646537	−	0.646537i	0.952155	+	0.305617i	$0.0988627\pi$
$230$		0			0
$231$	−8.84333			−0.581848
$232$		0			0
$233$	7.78389	+	7.78389i	0.509939	+	0.509939i	0.914508	−	0.404568i	$-0.132578\pi$
$233$	7.78389	+	7.78389i	0.509939	+	0.509939i	−0.404568	+	0.914508i	$0.632578\pi$
$234$		0			0
$235$	−14.0433	−	4.68111i	−0.916086	−	0.305362i
$236$		0			0
$237$	12.4111			0.806188
$238$		0			0
$239$	−4.41110			−0.285330			−0.142665	−	0.989771i	$-0.545567\pi$
$239$	−4.41110			−0.285330			−0.142665	+	0.989771i	$0.545567\pi$
$240$		0			0
$241$	18.8222			1.21244			0.606222	−	0.795295i	$-0.292684\pi$
$241$	18.8222			1.21244			0.606222	+	0.795295i	$0.292684\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−3.68665	+	1.84333i	−0.235532	+	0.117766i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−16.4111			−1.04001
$250$		0			0
$251$	1.89722	−	1.89722i	0.119752	−	0.119752i	−0.644691	−	0.764443i	$-0.723014\pi$
$251$	1.89722	−	1.89722i	0.119752	−	0.119752i	0.764443	+	0.644691i	$0.223014\pi$
$252$		0			0
$253$		−	14.8222i		−	0.931864i
$254$		0			0
$255$	−4.62721	+	13.8816i	−0.289767	+	0.869302i
$256$		0			0
$257$	4.52946	+	4.52946i	0.282540	+	0.282540i	0.834121	−	0.551581i	$-0.185975\pi$
$257$	4.52946	+	4.52946i	0.282540	+	0.282540i	−0.551581	+	0.834121i	$0.685975\pi$
$258$		0			0
$259$	−15.2544	+	15.2544i	−0.947864	+	0.947864i
$260$		0			0
$261$	−1.00000	−	1.00000i	−0.0618984	−	0.0618984i
$262$		0			0
$263$	0.0644618	−	0.0644618i	0.00397489	−	0.00397489i	−0.705117	−	0.709091i	$-0.749105\pi$
$263$	0.0644618	−	0.0644618i	0.00397489	−	0.00397489i	0.709091	+	0.705117i	$0.249105\pi$
$264$		0			0
$265$	−3.15667	−	6.31335i	−0.193913	−	0.387826i
$266$		0			0
$267$	13.2544			0.811158
$268$		0			0
$269$	−12.6655	−	12.6655i	−0.772231	−	0.772231i	0.206265	−	0.978496i	$-0.433869\pi$
$269$	−12.6655	−	12.6655i	−0.772231	−	0.772231i	−0.978496	+	0.206265i	$0.933869\pi$
$270$		0			0
$271$		−	7.79445i		−	0.473479i	−0.971573	−	0.236740i	$-0.923921\pi$
$271$		−	7.79445i		−	0.473479i	0.971573	−	0.236740i	$-0.0760788\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.10278	−	14.7194i	−0.126802	−	0.887615i
$276$		0			0
$277$			17.5678i			1.05555i	0.849386	+	0.527773i	$0.176973\pi$
$277$			17.5678i			1.05555i	−0.849386	+	0.527773i	$0.823027\pi$
$278$		0			0
$279$		−	4.20555i		−	0.251780i
$280$		0			0
$281$			19.2544i			1.14862i	0.818637	+	0.574311i	$0.194730\pi$
$281$			19.2544i			1.14862i	−0.818637	+	0.574311i	$0.805270\pi$
$282$		0			0
$283$			17.3622i			1.03208i	0.856565	+	0.516039i	$0.172594\pi$
$283$			17.3622i			1.03208i	−0.856565	+	0.516039i	$0.827406\pi$
$284$		0			0
$285$	−10.5733	−	3.52444i	−0.626309	−	0.208770i
$286$		0			0
$287$	−8.41110	+	8.41110i	−0.496492	+	0.496492i
$288$		0			0
$289$			25.8222i			1.51895i
$290$		0			0
$291$	11.4111	+	11.4111i	0.668931	+	0.668931i
$292$		0			0
$293$	4.31335			0.251989			0.125994	−	0.992031i	$-0.459788\pi$
$293$	4.31335			0.251989			0.125994	+	0.992031i	$0.459788\pi$
$294$		0			0
$295$	5.15165	−	15.4550i	0.299941	−	0.899822i
$296$		0			0
$297$	2.10278	−	2.10278i	0.122015	−	0.122015i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−6.41110	+	6.41110i	−0.369530	+	0.369530i
$302$		0			0
$303$	−6.25443	−	6.25443i	−0.359307	−	0.359307i
$304$		0			0
$305$	−19.8816	−	6.62721i	−1.13842	−	0.379473i
$306$		0			0
$307$		−	19.0489i		−	1.08718i	−0.839352	−	0.543588i	$-0.817065\pi$
$307$		−	19.0489i		−	1.08718i	0.839352	−	0.543588i	$-0.182935\pi$
$308$		0			0
$309$	9.15165	−	9.15165i	0.520619	−	0.520619i
$310$		0			0
$311$	−18.0978			−1.02623			−0.513115	−	0.858320i	$-0.671508\pi$
$311$	−18.0978			−1.02623			−0.513115	+	0.858320i	$0.671508\pi$
$312$		0			0
$313$	−3.00000	−	3.00000i	−0.169570	−	0.169570i	0.617220	−	0.786790i	$-0.288259\pi$
$313$	−3.00000	−	3.00000i	−0.169570	−	0.169570i	−0.786790	+	0.617220i	$0.788259\pi$
$314$		0			0
$315$	2.10278	−	6.30833i	0.118478	−	0.355434i
$316$		0			0
$317$	−11.1567			−0.626621			−0.313311	−	0.949651i	$-0.601438\pi$
$317$	−11.1567			−0.626621			−0.313311	+	0.949651i	$0.601438\pi$
$318$		0			0
$319$	4.20555			0.235466
$320$		0			0
$321$	14.0978			0.786860
$322$		0			0
$323$	−32.6167			−1.81484
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.78389	−	9.78389i	−0.541050	−	0.541050i
$328$		0			0
$329$	19.6867			1.08536
$330$		0			0
$331$	−6.57331	+	6.57331i	−0.361302	+	0.361302i	−0.864292	−	0.502990i	$-0.832233\pi$
$331$	−6.57331	+	6.57331i	−0.361302	+	0.361302i	0.502990	+	0.864292i	$0.332233\pi$
$332$		0			0
$333$		−	7.25443i		−	0.397540i
$334$		0			0
$335$	14.9200	−	7.45998i	0.815164	−	0.407582i
$336$		0			0
$337$	−23.4111	−	23.4111i	−1.27528	−	1.27528i	−0.943277	−	0.332007i	$-0.892274\pi$
$337$	−23.4111	−	23.4111i	−1.27528	−	1.27528i	−0.332007	−	0.943277i	$-0.607726\pi$
$338$		0			0
$339$	−6.62721	+	6.62721i	−0.359941	+	0.359941i
$340$		0			0
$341$	8.84333	+	8.84333i	0.478893	+	0.478893i
$342$		0			0
$343$	−10.8433	+	10.8433i	−0.585485	+	0.585485i
$344$		0			0
$345$	10.5733	+	3.52444i	0.569248	+	0.189749i
$346$		0			0
$347$	−18.5089			−0.993607			−0.496804	−	0.867863i	$-0.665493\pi$
$347$	−18.5089			−0.993607			−0.496804	+	0.867863i	$0.665493\pi$
$348$		0			0
$349$	−13.4705	−	13.4705i	−0.721061	−	0.721061i	0.247760	−	0.968821i	$-0.420306\pi$
$349$	−13.4705	−	13.4705i	−0.721061	−	0.721061i	−0.968821	+	0.247760i	$0.920306\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.62721	+	4.62721i	−0.246282	+	0.246282i	−0.819443	−	0.573161i	$-0.805717\pi$
$353$	−4.62721	+	4.62721i	−0.246282	+	0.246282i	0.573161	+	0.819443i	$0.305717\pi$
$354$		0			0
$355$	12.4111	+	24.8222i	0.658713	+	1.31743i
$356$		0			0
$357$		−	19.4600i		−	1.02993i
$358$		0			0
$359$		−	5.14663i		−	0.271629i	−0.990734	−	0.135814i	$-0.956635\pi$
$359$		−	5.14663i		−	0.271629i	0.990734	−	0.135814i	$-0.0433651\pi$
$360$		0			0
$361$		−	5.84333i		−	0.307543i
$362$		0			0
$363$		−	2.15667i		−	0.113196i
$364$		0			0
$365$	10.2544	−	30.7633i	0.536741	−	1.61022i
$366$		0			0
$367$	11.2594	−	11.2594i	0.587738	−	0.587738i	−0.349280	−	0.937018i	$-0.613574\pi$
$367$	11.2594	−	11.2594i	0.587738	−	0.587738i	0.937018	+	0.349280i	$0.113574\pi$
$368$		0			0
$369$		−	4.00000i		−	0.208232i
$370$		0			0
$371$	6.63778	+	6.63778i	0.344616	+	0.344616i
$372$		0			0
$373$	−3.68665			−0.190888			−0.0954438	−	0.995435i	$-0.530427\pi$
$373$	−3.68665			−0.190888			−0.0954438	+	0.995435i	$0.530427\pi$
$374$		0			0
$375$	11.0000	+	2.00000i	0.568038	+	0.103280i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−13.0922	−	13.0922i	−0.672502	−	0.672502i	0.285790	−	0.958292i	$-0.407744\pi$
$379$	−13.0922	−	13.0922i	−0.672502	−	0.672502i	−0.958292	+	0.285790i	$0.907744\pi$
$380$		0			0
$381$	1.89722	−	1.89722i	0.0971978	−	0.0971978i
$382$		0			0
$383$	−8.47556	−	8.47556i	−0.433081	−	0.433081i	0.456594	−	0.889675i	$-0.349069\pi$
$383$	−8.47556	−	8.47556i	−0.433081	−	0.433081i	−0.889675	+	0.456594i	$0.849069\pi$
$384$		0			0
$385$	8.84333	+	17.6867i	0.450698	+	0.901395i
$386$		0			0
$387$		−	3.04888i		−	0.154983i
$388$		0			0
$389$	−0.254426	+	0.254426i	−0.0128999	+	0.0128999i	−0.713527	−	0.700627i	$-0.752904\pi$
$389$	−0.254426	+	0.254426i	−0.0128999	+	0.0128999i	0.700627	+	0.713527i	$0.252904\pi$
$390$		0			0
$391$	32.6167			1.64949
$392$		0			0
$393$	−5.35720	−	5.35720i	−0.270235	−	0.270235i
$394$		0			0
$395$	−12.4111	−	24.8222i	−0.624470	−	1.24894i
$396$		0			0
$397$	17.2544			0.865975			0.432987	−	0.901400i	$-0.357459\pi$
$397$	17.2544			0.865975			0.432987	+	0.901400i	$0.357459\pi$
$398$		0			0
$399$	14.8222			0.742038
$400$		0			0
$401$	−7.56777			−0.377917			−0.188958	−	0.981985i	$-0.560511\pi$
$401$	−7.56777			−0.377917			−0.188958	+	0.981985i	$0.560511\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$	15.2544	+	15.2544i	0.756134	+	0.756134i
$408$		0			0
$409$	3.35218			0.165755			0.0828773	−	0.996560i	$-0.473589\pi$
$409$	3.35218			0.165755			0.0828773	+	0.996560i	$0.473589\pi$
$410$		0			0
$411$	−11.7839	+	11.7839i	−0.581256	+	0.581256i
$412$		0			0
$413$			21.6655i			1.06609i
$414$		0			0
$415$	16.4111	+	32.8222i	0.805589	+	1.61118i
$416$		0			0
$417$	−3.72999	−	3.72999i	−0.182658	−	0.182658i
$418$		0			0
$419$	−0.946101	+	0.946101i	−0.0462201	+	0.0462201i	−0.729839	−	0.683619i	$-0.760405\pi$
$419$	−0.946101	+	0.946101i	−0.0462201	+	0.0462201i	0.683619	+	0.729839i	$0.260405\pi$
$420$		0			0
$421$	−19.7839	−	19.7839i	−0.964208	−	0.964208i	0.0351736	−	0.999381i	$-0.488802\pi$
$421$	−19.7839	−	19.7839i	−0.964208	−	0.964208i	−0.999381	+	0.0351736i	$0.988802\pi$
$422$		0			0
$423$	−4.68111	+	4.68111i	−0.227603	+	0.227603i
$424$		0			0
$425$	32.3905	−	4.62721i	1.57117	−	0.224453i
$426$		0			0
$427$	27.8711			1.34878
$428$		0			0
$429$		0			0
$430$		0			0
$431$			8.54002i			0.411358i	0.978619	+	0.205679i	$0.0659404\pi$
$431$			8.54002i			0.411358i	−0.978619	+	0.205679i	$0.934060\pi$
$432$		0			0
$433$	−0.156674	+	0.156674i	−0.00752928	+	0.00752928i	−0.710861	−	0.703332i	$-0.751695\pi$
$433$	−0.156674	+	0.156674i	−0.00752928	+	0.00752928i	0.703332	+	0.710861i	$0.251695\pi$
$434$		0			0
$435$	−1.00000	+	3.00000i	−0.0479463	+	0.143839i
$436$		0			0
$437$			24.8433i			1.18842i
$438$		0			0
$439$		−	22.3033i		−	1.06448i	−0.846594	−	0.532239i	$-0.821351\pi$
$439$		−	22.3033i		−	1.06448i	0.846594	−	0.532239i	$-0.178649\pi$
$440$		0			0
$441$			1.84333i			0.0877774i
$442$		0			0
$443$			11.1255i			0.528589i	0.964442	+	0.264294i	$0.0851390\pi$
$443$			11.1255i			0.528589i	−0.964442	+	0.264294i	$0.914861\pi$
$444$		0			0
$445$	−13.2544	−	26.5089i	−0.628320	−	1.25664i
$446$		0			0
$447$	8.25443	−	8.25443i	0.390421	−	0.390421i
$448$		0			0
$449$		−	17.7633i		−	0.838301i	−0.907917	−	0.419150i	$-0.862328\pi$
$449$		−	17.7633i		−	0.838301i	0.907917	−	0.419150i	$-0.137672\pi$
$450$		0			0
$451$	8.41110	+	8.41110i	0.396063	+	0.396063i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.41110	+	3.41110i	−0.159565	+	0.159565i	−0.782374	−	0.622809i	$-0.785991\pi$
$457$	−3.41110	+	3.41110i	−0.159565	+	0.159565i	0.622809	+	0.782374i	$0.285991\pi$
$458$		0			0
$459$	4.62721	+	4.62721i	0.215980	+	0.215980i
$460$		0			0
$461$	−3.84333	+	3.84333i	−0.179002	+	0.179002i	−0.790920	−	0.611919i	$-0.790398\pi$
$461$	−3.84333	+	3.84333i	−0.179002	+	0.179002i	0.611919	+	0.790920i	$0.290398\pi$
$462$		0			0
$463$	−21.3572	−	21.3572i	−0.992553	−	0.992553i	0.00741917	−	0.999972i	$-0.497638\pi$
$463$	−21.3572	−	21.3572i	−0.992553	−	0.992553i	−0.999972	+	0.00741917i	$0.997638\pi$
$464$		0			0
$465$	−8.41110	+	4.20555i	−0.390055	+	0.195028i
$466$		0			0
$467$		−	6.30330i		−	0.291682i	−0.989308	−	0.145841i	$-0.953411\pi$
$467$		−	6.30330i		−	0.291682i	0.989308	−	0.145841i	$-0.0465888\pi$
$468$		0			0
$469$	−15.6867	+	15.6867i	−0.724342	+	0.724342i
$470$		0			0
$471$	−8.50885			−0.392067
$472$		0			0
$473$	6.41110	+	6.41110i	0.294783	+	0.294783i
$474$		0			0
$475$	3.52444	+	24.6711i	0.161712	+	1.13199i
$476$		0			0
$477$	−3.15667			−0.144534
$478$		0			0
$479$	28.4111			1.29814			0.649068	−	0.760730i	$-0.275159\pi$
$479$	28.4111			1.29814			0.649068	+	0.760730i	$0.275159\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−14.8222			−0.674433
$484$		0			0
$485$	11.4111	−	34.2333i	0.518151	−	1.55445i
$486$		0			0
$487$	−22.9250	−	22.9250i	−1.03883	−	1.03883i	−0.999215	−	0.0396148i	$-0.987387\pi$
$487$	−22.9250	−	22.9250i	−1.03883	−	1.03883i	−0.0396148	−	0.999215i	$-0.512613\pi$
$488$		0			0
$489$	0.411100			0.0185906
$490$		0			0
$491$	−6.84835	+	6.84835i	−0.309062	+	0.309062i	−0.844545	−	0.535484i	$-0.820129\pi$
$491$	−6.84835	+	6.84835i	−0.309062	+	0.309062i	0.535484	+	0.844545i	$0.320129\pi$
$492$		0			0
$493$			9.25443i			0.416798i
$494$		0			0
$495$	−6.30833	−	2.10278i	−0.283538	−	0.0945127i
$496$		0			0
$497$	−26.0978	−	26.0978i	−1.17064	−	1.17064i
$498$		0			0
$499$	3.52444	−	3.52444i	0.157776	−	0.157776i	−0.623805	−	0.781580i	$-0.714414\pi$
$499$	3.52444	−	3.52444i	0.157776	−	0.157776i	0.781580	+	0.623805i	$0.214414\pi$
$500$		0			0
$501$	−10.7789	−	10.7789i	−0.481564	−	0.481564i
$502$		0			0
$503$	27.3955	−	27.3955i	1.22151	−	1.22151i	0.254409	−	0.967097i	$-0.418119\pi$
$503$	27.3955	−	27.3955i	1.22151	−	1.22151i	0.967097	−	0.254409i	$-0.0818809\pi$
$504$		0			0
$505$	−6.25443	+	18.7633i	−0.278318	+	0.834955i
$506$		0			0
$507$	−13.0000			−0.577350
$508$		0			0
$509$	−25.8222	−	25.8222i	−1.14455	−	1.14455i	−0.987608	−	0.156941i	$-0.949837\pi$
$509$	−25.8222	−	25.8222i	−1.14455	−	1.14455i	−0.156941	−	0.987608i	$-0.550163\pi$
$510$		0			0
$511$			43.1255i			1.90776i
$512$		0			0
$513$	−3.52444	+	3.52444i	−0.155608	+	0.155608i
$514$		0			0
$515$	−27.4550	−	9.15165i	−1.20981	−	0.403270i
$516$		0			0
$517$		−	19.6867i		−	0.865818i
$518$		0			0
$519$		−	18.5089i		−	0.812448i
$520$		0			0
$521$		−	41.7633i		−	1.82968i	−0.403814	−	0.914841i	$-0.632316\pi$
$521$		−	41.7633i		−	1.82968i	0.403814	−	0.914841i	$-0.367684\pi$
$522$		0			0
$523$		−	15.4600i		−	0.676018i	−0.941143	−	0.338009i	$-0.890247\pi$
$523$		−	15.4600i		−	0.676018i	0.941143	−	0.338009i	$-0.109753\pi$
$524$		0			0
$525$	−14.7194	+	2.10278i	−0.642408	+	0.0917726i
$526$		0			0
$527$	−19.4600	+	19.4600i	−0.847690	+	0.847690i
$528$		0			0
$529$		−	1.84333i		−	0.0801446i
$530$		0			0
$531$	−5.15165	−	5.15165i	−0.223563	−	0.223563i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−14.0978	−	28.1955i	−0.609499	−	1.21900i
$536$		0			0
$537$	9.35720	−	9.35720i	0.403793	−	0.403793i
$538$		0			0
$539$	−3.87610	−	3.87610i	−0.166955	−	0.166955i
$540$		0			0
$541$	−23.9794	+	23.9794i	−1.03095	+	1.03095i	−0.0314492	+	0.999505i	$0.510012\pi$
$541$	−23.9794	+	23.9794i	−1.03095	+	1.03095i	−0.999505	+	0.0314492i	$0.989988\pi$
$542$		0			0
$543$	−4.62721	−	4.62721i	−0.198573	−	0.198573i
$544$		0			0
$545$	−9.78389	+	29.3517i	−0.419096	+	1.25729i
$546$		0			0
$547$			20.9511i			0.895805i	0.894082	+	0.447903i	$0.147829\pi$
$547$			20.9511i			0.895805i	−0.894082	+	0.447903i	$0.852171\pi$
$548$		0			0
$549$	−6.62721	+	6.62721i	−0.282843	+	0.282843i
$550$		0			0
$551$	−7.04888			−0.300292
$552$		0			0
$553$	26.0978	+	26.0978i	1.10979	+	1.10979i
$554$		0			0
$555$	−14.5089	+	7.25443i	−0.615866	+	0.307933i
$556$		0			0
$557$	−6.82220			−0.289066			−0.144533	−	0.989500i	$-0.546168\pi$
$557$	−6.82220			−0.289066			−0.144533	+	0.989500i	$0.546168\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−19.4600			−0.821601
$562$		0			0
$563$	26.5089			1.11721			0.558607	−	0.829432i	$-0.311336\pi$
$563$	26.5089			1.11721			0.558607	+	0.829432i	$0.311336\pi$
$564$		0			0
$565$	19.8816	+	6.62721i	0.836427	+	0.278809i
$566$		0			0
$567$	−2.10278	−	2.10278i	−0.0883083	−	0.0883083i
$568$		0			0
$569$	−6.74557			−0.282789			−0.141395	−	0.989953i	$-0.545159\pi$
$569$	−6.74557			−0.282789			−0.141395	+	0.989953i	$0.545159\pi$
$570$		0			0
$571$	12.2700	−	12.2700i	0.513484	−	0.513484i	−0.402108	−	0.915592i	$-0.631722\pi$
$571$	12.2700	−	12.2700i	0.513484	−	0.513484i	0.915592	+	0.402108i	$0.131722\pi$
$572$		0			0
$573$			19.0489i			0.795778i
$574$		0			0
$575$	−3.52444	−	24.6711i	−0.146979	−	1.02885i
$576$		0			0
$577$	29.4111	+	29.4111i	1.22440	+	1.22440i	0.966052	+	0.258348i	$0.0831782\pi$
$577$	29.4111	+	29.4111i	1.22440	+	1.22440i	0.258348	+	0.966052i	$0.416822\pi$
$578$		0			0
$579$	7.41110	−	7.41110i	0.307995	−	0.307995i
$580$		0			0
$581$	−34.5089	−	34.5089i	−1.43167	−	1.43167i
$582$		0			0
$583$	6.63778	−	6.63778i	0.274909	−	0.274909i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	24.4111			1.00755			0.503777	−	0.863834i	$-0.331943\pi$
$587$	24.4111			1.00755			0.503777	+	0.863834i	$0.331943\pi$
$588$		0			0
$589$	−14.8222	−	14.8222i	−0.610738	−	0.610738i
$590$		0			0
$591$		−	15.6655i		−	0.644394i
$592$		0			0
$593$	16.1950	−	16.1950i	0.665048	−	0.665048i	−0.291517	−	0.956566i	$-0.594160\pi$
$593$	16.1950	−	16.1950i	0.665048	−	0.665048i	0.956566	+	0.291517i	$0.0941600\pi$
$594$		0			0
$595$	−38.9200	+	19.4600i	−1.59556	+	0.797781i
$596$		0			0
$597$			7.79445i			0.319006i
$598$		0			0
$599$		−	13.1466i		−	0.537157i	−0.963258	−	0.268578i	$-0.913446\pi$
$599$		−	13.1466i		−	0.537157i	0.963258	−	0.268578i	$-0.0865538\pi$
$600$		0			0
$601$			4.62670i			0.188727i	0.995538	+	0.0943634i	$0.0300816\pi$
$601$			4.62670i			0.188727i	−0.995538	+	0.0943634i	$0.969918\pi$
$602$		0			0
$603$		−	7.45998i		−	0.303794i
$604$		0			0
$605$	−4.31335	+	2.15667i	−0.175363	+	0.0876813i
$606$		0			0
$607$	−23.2494	+	23.2494i	−0.943664	+	0.943664i	−0.998496	−	0.0548315i	$-0.982538\pi$
$607$	−23.2494	+	23.2494i	−0.943664	+	0.943664i	0.0548315	+	0.998496i	$0.482538\pi$
$608$		0			0
$609$		−	4.20555i		−	0.170417i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	25.2544			1.02002			0.510008	−	0.860169i	$-0.329642\pi$
$613$	25.2544			1.02002			0.510008	+	0.860169i	$0.329642\pi$
$614$		0			0
$615$	−8.00000	+	4.00000i	−0.322591	+	0.161296i
$616$		0			0
$617$	−22.7250	+	22.7250i	−0.914873	+	0.914873i	−0.996651	−	0.0817779i	$-0.973940\pi$
$617$	−22.7250	+	22.7250i	−0.914873	+	0.914873i	0.0817779	+	0.996651i	$0.473940\pi$
$618$		0			0
$619$	3.72999	+	3.72999i	0.149921	+	0.149921i	0.778083	−	0.628162i	$-0.216192\pi$
$619$	3.72999	+	3.72999i	0.149921	+	0.149921i	−0.628162	+	0.778083i	$0.716192\pi$
$620$		0			0
$621$	3.52444	−	3.52444i	0.141431	−	0.141431i
$622$		0			0
$623$	27.8711	+	27.8711i	1.11663	+	1.11663i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		−	14.8222i		−	0.591942i
$628$		0			0
$629$	−33.5678	+	33.5678i	−1.33843	+	1.33843i
$630$		0			0
$631$	16.6066			0.661098			0.330549	−	0.943789i	$-0.392766\pi$
$631$	16.6066			0.661098			0.330549	+	0.943789i	$0.392766\pi$
$632$		0			0
$633$	−6.57331	−	6.57331i	−0.261266	−	0.261266i
$634$		0			0
$635$	−5.69167	−	1.89722i	−0.225867	−	0.0752891i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	12.4111			0.490976
$640$		0			0
$641$	1.17780			0.0465203			0.0232601	−	0.999729i	$-0.492595\pi$
$641$	1.17780			0.0465203			0.0232601	+	0.999729i	$0.492595\pi$
$642$		0			0
$643$	20.6066			0.812645			0.406323	−	0.913730i	$-0.366811\pi$
$643$	20.6066			0.812645			0.406323	+	0.913730i	$0.366811\pi$
$644$		0			0
$645$	−6.09775	+	3.04888i	−0.240099	+	0.120049i
$646$		0			0
$647$	−24.5522	−	24.5522i	−0.965246	−	0.965246i	0.0341699	−	0.999416i	$-0.489121\pi$
$647$	−24.5522	−	24.5522i	−0.965246	−	0.965246i	−0.999416	+	0.0341699i	$0.989121\pi$
$648$		0			0
$649$	21.6655			0.850446
$650$		0			0
$651$	8.84333	−	8.84333i	0.346597	−	0.346597i
$652$		0			0
$653$		−	9.15667i		−	0.358328i	−0.983819	−	0.179164i	$-0.942661\pi$
$653$		−	9.15667i		−	0.358328i	0.983819	−	0.179164i	$-0.0573393\pi$
$654$		0			0
$655$	−5.35720	+	16.0716i	−0.209323	+	0.627969i
$656$		0			0
$657$	−10.2544	−	10.2544i	−0.400063	−	0.400063i
$658$		0			0
$659$	−16.2005	+	16.2005i	−0.631083	+	0.631083i	−0.948340	−	0.317257i	$-0.897238\pi$
$659$	−16.2005	+	16.2005i	−0.631083	+	0.631083i	0.317257	+	0.948340i	$0.397238\pi$
$660$		0			0
$661$	30.7250	+	30.7250i	1.19506	+	1.19506i	0.975627	+	0.219436i	$0.0704216\pi$
$661$	30.7250	+	30.7250i	1.19506	+	1.19506i	0.219436	+	0.975627i	$0.429578\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.8222	−	29.6444i	−0.574780	−	1.14956i
$666$		0			0
$667$	7.04888			0.272934
$668$		0			0
$669$	1.35720	+	1.35720i	0.0524724	+	0.0524724i
$670$		0			0
$671$		−	27.8711i		−	1.07595i
$672$		0			0
$673$	36.3311	−	36.3311i	1.40046	−	1.40046i	0.601850	−	0.798609i	$-0.294431\pi$
$673$	36.3311	−	36.3311i	1.40046	−	1.40046i	0.798609	−	0.601850i	$-0.205569\pi$
$674$		0			0
$675$	3.00000	−	4.00000i	0.115470	−	0.153960i
$676$		0			0
$677$			7.66553i			0.294610i	0.989091	+	0.147305i	$0.0470599\pi$
$677$			7.66553i			0.294610i	−0.989091	+	0.147305i	$0.952940\pi$
$678$		0			0
$679$			47.9900i			1.84169i
$680$		0			0
$681$			12.2056i			0.467718i
$682$		0			0
$683$			21.8922i			0.837682i	0.908060	+	0.418841i	$0.137564\pi$
$683$			21.8922i			0.837682i	−0.908060	+	0.418841i	$0.862436\pi$
$684$		0			0
$685$	35.3517	+	11.7839i	1.35072	+	0.450239i
$686$		0			0
$687$	−9.78389	+	9.78389i	−0.373279	+	0.373279i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−30.7789	−	30.7789i	−1.17088	−	1.17088i	−0.981999	−	0.188884i	$-0.939513\pi$
$691$	−30.7789	−	30.7789i	−1.17088	−	1.17088i	−0.188884	−	0.981999i	$-0.560487\pi$
$692$		0			0
$693$	8.84333			0.335930
$694$		0			0
$695$	−3.72999	+	11.1900i	−0.141487	+	0.424460i
$696$		0			0
$697$	−18.5089	+	18.5089i	−0.701073	+	0.701073i
$698$		0			0
$699$	−7.78389	−	7.78389i	−0.294414	−	0.294414i
$700$		0			0
$701$	22.6655	−	22.6655i	0.856065	−	0.856065i	−0.134807	−	0.990872i	$-0.543041\pi$
$701$	22.6655	−	22.6655i	0.856065	−	0.856065i	0.990872	+	0.134807i	$0.0430414\pi$
$702$		0			0
$703$	−25.5678	−	25.5678i	−0.964307	−	0.964307i
$704$		0			0
$705$	14.0433	+	4.68111i	0.528903	+	0.176301i
$706$		0			0
$707$		−	26.3033i		−	0.989237i
$708$		0			0
$709$	13.3728	−	13.3728i	0.502226	−	0.502226i	−0.409903	−	0.912129i	$-0.634438\pi$
$709$	13.3728	−	13.3728i	0.502226	−	0.502226i	0.912129	+	0.409903i	$0.134438\pi$
$710$		0			0
$711$	−12.4111			−0.465453
$712$		0			0
$713$	14.8222	+	14.8222i	0.555096	+	0.555096i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.41110			0.164736
$718$		0			0
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	38.4877			1.43336
$722$		0			0
$723$	−18.8222			−0.700005
$724$		0			0
$725$	7.00000	−	1.00000i	0.259973	−	0.0371391i
$726$		0			0
$727$	30.9149	+	30.9149i	1.14657	+	1.14657i	0.987222	+	0.159349i	$0.0509395\pi$
$727$	30.9149	+	30.9149i	1.14657	+	1.14657i	0.159349	+	0.987222i	$0.449061\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−14.1078	+	14.1078i	−0.521796	+	0.521796i
$732$		0			0
$733$		−	29.7633i		−	1.09933i	−0.835385	−	0.549666i	$-0.814755\pi$
$733$		−	29.7633i		−	1.09933i	0.835385	−	0.549666i	$-0.185245\pi$
$734$		0			0
$735$	3.68665	−	1.84333i	0.135984	−	0.0679921i
$736$		0			0
$737$	15.6867	+	15.6867i	0.577825	+	0.577825i
$738$		0			0
$739$	31.9355	−	31.9355i	1.17477	−	1.17477i	0.193709	−	0.981059i	$-0.437948\pi$
$739$	31.9355	−	31.9355i	1.17477	−	1.17477i	0.981059	−	0.193709i	$-0.0620517\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.7789	+	22.7789i	−0.835675	+	0.835675i	−0.988286	−	0.152611i	$-0.951232\pi$
$743$	−22.7789	+	22.7789i	−0.835675	+	0.835675i	0.152611	+	0.988286i	$0.451232\pi$
$744$		0			0
$745$	−24.7633	−	8.25443i	−0.907256	−	0.302419i
$746$		0			0
$747$	16.4111			0.600451
$748$		0			0
$749$	29.6444	+	29.6444i	1.08318	+	1.08318i
$750$		0			0
$751$		−	34.7144i		−	1.26675i	−0.773846	−	0.633373i	$-0.781670\pi$
$751$		−	34.7144i		−	1.26675i	0.773846	−	0.633373i	$-0.218330\pi$
$752$		0			0
$753$	−1.89722	+	1.89722i	−0.0691387	+	0.0691387i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			3.05892i			0.111178i	0.998454	+	0.0555892i	$0.0177037\pi$
$757$			3.05892i			0.111178i	−0.998454	+	0.0555892i	$0.982296\pi$
$758$		0			0
$759$			14.8222i			0.538012i
$760$		0			0
$761$		−	20.0766i		−	0.727777i	−0.931442	−	0.363889i	$-0.881449\pi$
$761$		−	20.0766i		−	0.727777i	0.931442	−	0.363889i	$-0.118551\pi$
$762$		0			0
$763$		−	41.1466i		−	1.48961i
$764$		0			0
$765$	4.62721	−	13.8816i	0.167297	−	0.501892i
$766$		0			0
$767$		0			0
$768$		0			0
$769$			27.6655i			0.997644i	0.866704	+	0.498822i	$0.166234\pi$
$769$			27.6655i			0.997644i	−0.866704	+	0.498822i	$0.833766\pi$
$770$		0			0
$771$	−4.52946	−	4.52946i	−0.163125	−	0.163125i
$772$		0			0
$773$	17.0388			0.612844			0.306422	−	0.951896i	$-0.400868\pi$
$773$	17.0388			0.612844			0.306422	+	0.951896i	$0.400868\pi$
$774$		0			0
$775$	16.8222	+	12.6167i	0.604271	+	0.453203i
$776$		0			0
$777$	15.2544	−	15.2544i	0.547249	−	0.547249i
$778$		0			0
$779$	−14.0978	−	14.0978i	−0.505104	−	0.505104i
$780$		0			0
$781$	−26.0978	+	26.0978i	−0.933851	+	0.933851i
$782$		0			0
$783$	1.00000	+	1.00000i	0.0357371	+	0.0357371i
$784$		0			0
$785$	8.50885	+	17.0177i	0.303694	+	0.607388i
$786$		0			0
$787$			14.3799i			0.512589i	0.966599	+	0.256295i	$0.0825017\pi$
$787$			14.3799i			0.512589i	−0.966599	+	0.256295i	$0.917498\pi$
$788$		0			0
$789$	−0.0644618	+	0.0644618i	−0.00229490	+	0.00229490i
$790$		0			0
$791$	−27.8711			−0.990981
$792$		0			0
$793$		0			0
$794$		0			0
$795$	3.15667	+	6.31335i	0.111956	+	0.223911i
$796$		0			0
$797$	−6.52998			−0.231304			−0.115652	−	0.993290i	$-0.536896\pi$
$797$	−6.52998			−0.231304			−0.115652	+	0.993290i	$0.536896\pi$
$798$		0			0
$799$	43.3210			1.53259
$800$		0			0
$801$	−13.2544			−0.468322
$802$		0			0
$803$	43.1255			1.52187
$804$		0			0
$805$	14.8222	+	29.6444i	0.522414	+	1.04483i
$806$		0			0
$807$	12.6655	+	12.6655i	0.445848	+	0.445848i
$808$		0			0
$809$	−43.8399			−1.54133			−0.770664	−	0.637241i	$-0.780076\pi$
$809$	−43.8399			−1.54133			−0.770664	+	0.637241i	$0.780076\pi$
$810$		0			0
$811$	−26.5733	+	26.5733i	−0.933115	+	0.933115i	−0.997899	−	0.0647841i	$-0.979364\pi$
$811$	−26.5733	+	26.5733i	−0.933115	+	0.933115i	0.0647841	+	0.997899i	$0.479364\pi$
$812$		0			0
$813$			7.79445i			0.273363i
$814$		0			0
$815$	−0.411100	−	0.822200i	−0.0144002	−	0.0288004i
$816$		0			0
$817$	−10.7456	−	10.7456i	−0.375940	−	0.375940i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.7633	−	14.7633i	−0.515242	−	0.515242i	0.400886	−	0.916128i	$-0.368702\pi$
$821$	−14.7633	−	14.7633i	−0.515242	−	0.515242i	−0.916128	+	0.400886i	$0.868702\pi$
$822$		0			0
$823$	−18.0927	+	18.0927i	−0.630673	+	0.630673i	−0.948237	−	0.317564i	$-0.897135\pi$
$823$	−18.0927	+	18.0927i	−0.630673	+	0.630673i	0.317564	+	0.948237i	$0.397135\pi$
$824$		0			0
$825$	2.10278	+	14.7194i	0.0732092	+	0.512465i
$826$		0			0
$827$	6.31335			0.219537			0.109768	−	0.993957i	$-0.464989\pi$
$827$	6.31335			0.219537			0.109768	+	0.993957i	$0.464989\pi$
$828$		0			0
$829$	24.2927	+	24.2927i	0.843722	+	0.843722i	0.989341	−	0.145619i	$-0.0465174\pi$
$829$	24.2927	+	24.2927i	0.843722	+	0.843722i	−0.145619	+	0.989341i	$0.546517\pi$
$830$		0			0
$831$		−	17.5678i		−	0.609419i
$832$		0			0
$833$	8.52946	−	8.52946i	0.295528	−	0.295528i
$834$		0			0
$835$	−10.7789	+	32.3366i	−0.373018	+	1.11905i
$836$		0			0
$837$			4.20555i			0.145365i
$838$		0			0
$839$		−	19.2645i		−	0.665083i	−0.943089	−	0.332542i	$-0.892094\pi$
$839$		−	19.2645i		−	0.665083i	0.943089	−	0.332542i	$-0.107906\pi$
$840$		0			0
$841$		−	27.0000i		−	0.931034i
$842$		0			0
$843$		−	19.2544i		−	0.663158i
$844$		0			0
$845$	13.0000	+	26.0000i	0.447214	+	0.894427i
$846$		0			0
$847$	4.53500	−	4.53500i	0.155824	−	0.155824i
$848$		0			0
$849$		−	17.3622i		−	0.595870i
$850$		0			0
$851$	25.5678	+	25.5678i	0.876452	+	0.876452i
$852$		0			0
$853$	−45.2544			−1.54948			−0.774741	−	0.632279i	$-0.782120\pi$
$853$	−45.2544			−1.54948			−0.774741	+	0.632279i	$0.782120\pi$
$854$		0			0
$855$	10.5733	+	3.52444i	0.361600	+	0.120533i
$856$		0			0
$857$	−17.0383	+	17.0383i	−0.582018	+	0.582018i	−0.935457	−	0.353440i	$-0.885012\pi$
$857$	−17.0383	+	17.0383i	−0.582018	+	0.582018i	0.353440	+	0.935457i	$0.385012\pi$
$858$		0			0
$859$	−11.3088	−	11.3088i	−0.385853	−	0.385853i	0.487353	−	0.873205i	$-0.337963\pi$
$859$	−11.3088	−	11.3088i	−0.385853	−	0.385853i	−0.873205	+	0.487353i	$0.837963\pi$
$860$		0			0
$861$	8.41110	−	8.41110i	0.286650	−	0.286650i
$862$		0			0
$863$	0.681112	+	0.681112i	0.0231853	+	0.0231853i	0.718604	−	0.695419i	$-0.244781\pi$
$863$	0.681112	+	0.681112i	0.0231853	+	0.0231853i	−0.695419	+	0.718604i	$0.744781\pi$
$864$		0			0
$865$	−37.0177	+	18.5089i	−1.25864	+	0.629320i
$866$		0			0
$867$		−	25.8222i		−	0.876968i
$868$		0			0
$869$	26.0978	−	26.0978i	0.885306	−	0.885306i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−11.4111	−	11.4111i	−0.386207	−	0.386207i
$874$		0			0
$875$	18.9250	+	27.3361i	0.639781	+	0.924128i
$876$		0			0
$877$	32.5089			1.09775			0.548873	−	0.835906i	$-0.315057\pi$
$877$	32.5089			1.09775			0.548873	+	0.835906i	$0.315057\pi$
$878$		0			0
$879$	−4.31335			−0.145486
$880$		0			0
$881$	−1.05892			−0.0356760			−0.0178380	−	0.999841i	$-0.505678\pi$
$881$	−1.05892			−0.0356760			−0.0178380	+	0.999841i	$0.505678\pi$
$882$		0			0
$883$	23.7422			0.798987			0.399494	−	0.916736i	$-0.369186\pi$
$883$	23.7422			0.798987			0.399494	+	0.916736i	$0.369186\pi$
$884$		0			0
$885$	−5.15165	+	15.4550i	−0.173171	+	0.519513i
$886$		0			0
$887$	11.5244	+	11.5244i	0.386953	+	0.386953i	0.873599	−	0.486646i	$-0.161780\pi$
$887$	11.5244	+	11.5244i	0.386953	+	0.386953i	−0.486646	+	0.873599i	$0.661780\pi$
$888$		0			0
$889$	7.97887			0.267603
$890$		0			0
$891$	−2.10278	+	2.10278i	−0.0704456	+	0.0704456i
$892$		0			0
$893$			32.9966i			1.10419i
$894$		0			0
$895$	−28.0716	−	9.35720i	−0.938330	−	0.312777i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.20555	+	4.20555i	−0.140263	+	0.140263i
$900$		0			0
$901$	14.6066	+	14.6066i	0.486617	+	0.486617i
$902$		0			0
$903$	6.41110	−	6.41110i	0.213348	−	0.213348i
$904$		0			0
$905$	−4.62721	+	13.8816i	−0.153814	+	0.461441i
$906$		0			0
$907$	−26.5089			−0.880212			−0.440106	−	0.897946i	$-0.645059\pi$
$907$	−26.5089			−0.880212			−0.440106	+	0.897946i	$0.645059\pi$
$908$		0			0
$909$	6.25443	+	6.25443i	0.207446	+	0.207446i
$910$		0			0
$911$		−	1.77332i		−	0.0587529i	−0.999568	−	0.0293764i	$-0.990648\pi$
$911$		−	1.77332i		−	0.0587529i	0.999568	−	0.0293764i	$-0.00935215\pi$
$912$		0			0
$913$	−34.5089	+	34.5089i	−1.14208	+	1.14208i
$914$		0			0
$915$	19.8816	+	6.62721i	0.657267	+	0.219089i
$916$		0			0
$917$		−	22.5300i		−	0.744005i
$918$		0			0
$919$			19.1255i			0.630892i	0.948944	+	0.315446i	$0.102154\pi$
$919$			19.1255i			0.630892i	−0.948944	+	0.315446i	$0.897846\pi$
$920$		0			0
$921$			19.0489i			0.627682i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	29.0177	+	21.7633i	0.954096	+	0.715572i
$926$		0			0
$927$	−9.15165	+	9.15165i	−0.300580	+	0.300580i
$928$		0			0
$929$			14.6277i			0.479920i	0.970783	+	0.239960i	$0.0771344\pi$
$929$			14.6277i			0.479920i	−0.970783	+	0.239960i	$0.922866\pi$
$930$		0			0
$931$	6.49669	+	6.49669i	0.212920	+	0.212920i
$932$		0			0
$933$	18.0978			0.592494
$934$		0			0
$935$	19.4600	+	38.9200i	0.636409	+	1.27282i
$936$		0			0
$937$	3.31335	−	3.31335i	0.108242	−	0.108242i	−0.650911	−	0.759154i	$-0.725613\pi$
$937$	3.31335	−	3.31335i	0.108242	−	0.108242i	0.759154	+	0.650911i	$0.225613\pi$
$938$		0			0
$939$	3.00000	+	3.00000i	0.0979013	+	0.0979013i
$940$		0			0
$941$	−13.4111	+	13.4111i	−0.437189	+	0.437189i	−0.891065	−	0.453876i	$-0.850041\pi$
$941$	−13.4111	+	13.4111i	−0.437189	+	0.437189i	0.453876	+	0.891065i	$0.350041\pi$
$942$		0			0
$943$	14.0978	+	14.0978i	0.459086	+	0.459086i
$944$		0			0
$945$	−2.10278	+	6.30833i	−0.0684033	+	0.205210i
$946$		0			0
$947$			14.9300i			0.485160i	0.970131	+	0.242580i	$0.0779937\pi$
$947$			14.9300i			0.485160i	−0.970131	+	0.242580i	$0.922006\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	11.1567			0.361780
$952$		0			0
$953$	−24.6272	−	24.6272i	−0.797754	−	0.797754i	0.184987	−	0.982741i	$-0.440776\pi$
$953$	−24.6272	−	24.6272i	−0.797754	−	0.797754i	−0.982741	+	0.184987i	$0.940776\pi$
$954$		0			0
$955$	38.0978	−	19.0489i	1.23281	−	0.616407i
$956$		0			0
$957$	−4.20555			−0.135946
$958$		0			0
$959$	−49.5577			−1.60030
$960$		0			0
$961$	13.3133			0.429463
$962$		0			0
$963$	−14.0978			−0.454294
$964$		0			0
$965$	−22.2333	−	7.41110i	−0.715715	−	0.238572i
$966$		0			0
$967$	32.2872	+	32.2872i	1.03829	+	1.03829i	0.999237	+	0.0390491i	$0.0124329\pi$
$967$	32.2872	+	32.2872i	1.03829	+	1.03829i	0.0390491	+	0.999237i	$0.487567\pi$
$968$		0			0
$969$	32.6167			1.04780
$970$		0			0
$971$	27.2494	−	27.2494i	0.874475	−	0.874475i	−0.118481	−	0.992956i	$-0.537803\pi$
$971$	27.2494	−	27.2494i	0.874475	−	0.874475i	0.992956	+	0.118481i	$0.0378026\pi$
$972$		0			0
$973$		−	15.6867i		−	0.502891i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.5295	−	10.5295i	−0.336867	−	0.336867i	0.518320	−	0.855187i	$-0.326558\pi$
$977$	−10.5295	−	10.5295i	−0.336867	−	0.336867i	−0.855187	+	0.518320i	$0.826558\pi$
$978$		0			0
$979$	27.8711	−	27.8711i	0.890763	−	0.890763i
$980$		0			0
$981$	9.78389	+	9.78389i	0.312375	+	0.312375i
$982$		0			0
$983$	−9.62219	+	9.62219i	−0.306900	+	0.306900i	−0.843706	−	0.536806i	$-0.819631\pi$
$983$	−9.62219	+	9.62219i	−0.306900	+	0.306900i	0.536806	+	0.843706i	$0.319631\pi$
$984$		0			0
$985$	−31.3311	+	15.6655i	−0.998290	+	0.499145i
$986$		0			0
$987$	−19.6867			−0.626633
$988$		0			0
$989$	10.7456	+	10.7456i	0.341689	+	0.341689i
$990$		0			0
$991$			4.01005i			0.127383i	0.997970	+	0.0636917i	$0.0202874\pi$
$991$			4.01005i			0.127383i	−0.997970	+	0.0636917i	$0.979713\pi$
$992$		0			0
$993$	6.57331	−	6.57331i	0.208598	−	0.208598i
$994$		0			0
$995$	15.5889	−	7.79445i	0.494201	−	0.247101i
$996$		0			0
$997$		−	2.31335i		−	0.0732645i	−0.999329	−	0.0366322i	$-0.988337\pi$
$997$		−	2.31335i		−	0.0732645i	0.999329	−	0.0366322i	$-0.0116630\pi$
$998$		0			0
$999$			7.25443i			0.229520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.y.d.847.1		6
4.3	odd	2		240.2.y.d.187.2	yes	6
5.3	odd	4		960.2.bc.d.463.1		6
8.3	odd	2		1920.2.y.g.1567.3		6
8.5	even	2		1920.2.y.h.1567.1		6
12.11	even	2		720.2.z.e.667.2		6
16.3	odd	4		960.2.bc.d.367.1		6
16.5	even	4		1920.2.bc.g.607.3		6
16.11	odd	4		1920.2.bc.h.607.1		6
16.13	even	4		240.2.bc.d.67.1	yes	6
20.3	even	4		240.2.bc.d.43.1	yes	6
40.3	even	4		1920.2.bc.g.1183.3		6
40.13	odd	4		1920.2.bc.h.1183.1		6
48.29	odd	4		720.2.bd.e.307.3		6
60.23	odd	4		720.2.bd.e.523.3		6
80.3	even	4	inner	960.2.y.d.943.1		6
80.13	odd	4		240.2.y.d.163.2	✓	6
80.43	even	4		1920.2.y.h.223.1		6
80.53	odd	4		1920.2.y.g.223.3		6
240.173	even	4		720.2.z.e.163.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.2	✓	6	80.13	odd	4
240.2.y.d.187.2	yes	6	4.3	odd	2
240.2.bc.d.43.1	yes	6	20.3	even	4
240.2.bc.d.67.1	yes	6	16.13	even	4
720.2.z.e.163.2		6	240.173	even	4
720.2.z.e.667.2		6	12.11	even	2
720.2.bd.e.307.3		6	48.29	odd	4
720.2.bd.e.523.3		6	60.23	odd	4
960.2.y.d.847.1		6	1.1	even	1	trivial
960.2.y.d.943.1		6	80.3	even	4	inner
960.2.bc.d.367.1		6	16.3	odd	4
960.2.bc.d.463.1		6	5.3	odd	4
1920.2.y.g.223.3		6	80.53	odd	4
1920.2.y.g.1567.3		6	8.3	odd	2
1920.2.y.h.223.1		6	80.43	even	4
1920.2.y.h.1567.1		6	8.5	even	2
1920.2.bc.g.607.3		6	16.5	even	4
1920.2.bc.g.1183.3		6	40.3	even	4
1920.2.bc.h.607.1		6	16.11	odd	4
1920.2.bc.h.1183.1		6	40.13	odd	4

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.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-2.10278 - 2.10278i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-2.10278 - 2.10278i) q^{7} +1.00000 q^{9} +(-2.10278 + 2.10278i) q^{11} +(-1.00000 - 2.00000i) q^{15} +(-4.62721 - 4.62721i) q^{17} +(3.52444 - 3.52444i) q^{19} +(2.10278 + 2.10278i) q^{21} +(-3.52444 + 3.52444i) q^{23} +(-3.00000 + 4.00000i) q^{25} -1.00000 q^{27} +(-1.00000 - 1.00000i) q^{29} -4.20555i q^{31} +(2.10278 - 2.10278i) q^{33} +(2.10278 - 6.30833i) q^{35} -7.25443i q^{37} -4.00000i q^{41} -3.04888i q^{43} +(1.00000 + 2.00000i) q^{45} +(-4.68111 + 4.68111i) q^{47} +1.84333i q^{49} +(4.62721 + 4.62721i) q^{51} -3.15667 q^{53} +(-6.30833 - 2.10278i) q^{55} +(-3.52444 + 3.52444i) q^{57} +(-5.15165 - 5.15165i) q^{59} +(-6.62721 + 6.62721i) q^{61} +(-2.10278 - 2.10278i) q^{63} -7.45998i q^{67} +(3.52444 - 3.52444i) q^{69} +12.4111 q^{71} +(-10.2544 - 10.2544i) q^{73} +(3.00000 - 4.00000i) q^{75} +8.84333 q^{77} -12.4111 q^{79} +1.00000 q^{81} +16.4111 q^{83} +(4.62721 - 13.8816i) q^{85} +(1.00000 + 1.00000i) q^{87} -13.2544 q^{89} +4.20555i q^{93} +(10.5733 + 3.52444i) q^{95} +(-11.4111 - 11.4111i) q^{97} +(-2.10278 + 2.10278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9	\( 6 q - 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9} + 2 q^{11} - 6 q^{15} - 2 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 18 q^{25} - 6 q^{27} - 6 q^{29} - 2 q^{33} - 2 q^{35} + 6 q^{45} - 10 q^{47} + 2 q^{51} - 12 q^{53} + 6 q^{55} - 10 q^{57} + 6 q^{59} - 14 q^{61} + 2 q^{63} + 10 q^{69} + 16 q^{71} - 10 q^{73} + 18 q^{75} + 60 q^{77} - 16 q^{79} + 6 q^{81} + 40 q^{83} + 2 q^{85} + 6 q^{87} - 28 q^{89} + 30 q^{95} - 10 q^{97} + 2 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9 + 2 * q^11 - 6 * q^15 - 2 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 18 * q^25 - 6 * q^27 - 6 * q^29 - 2 * q^33 - 2 * q^35 + 6 * q^45 - 10 * q^47 + 2 * q^51 - 12 * q^53 + 6 * q^55 - 10 * q^57 + 6 * q^59 - 14 * q^61 + 2 * q^63 + 10 * q^69 + 16 * q^71 - 10 * q^73 + 18 * q^75 + 60 * q^77 - 16 * q^79 + 6 * q^81 + 40 * q^83 + 2 * q^85 + 6 * q^87 - 28 * q^89 + 30 * q^95 - 10 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more