LMFDB - Embedded newform 1960.2.q.u.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.u.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.35234i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.280776 + 0.486319i) q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.35234i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.280776 + 0.486319i) q^{9} +(-0.780776 + 1.35234i) q^{11} -6.68466 q^{13} -1.56155 q^{15} +(3.78078 - 6.54850i) q^{17} +(-3.56155 - 6.16879i) q^{19} +(-1.56155 - 2.70469i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.56155 q^{27} +0.438447 q^{29} +(3.12311 - 5.40938i) q^{31} +(-1.21922 - 2.11176i) q^{33} +(4.12311 + 7.14143i) q^{37} +(5.21922 - 9.03996i) q^{39} +1.12311 q^{41} -7.12311 q^{43} +(-0.280776 + 0.486319i) q^{45} +(1.21922 + 2.11176i) q^{47} +(5.90388 + 10.2258i) q^{51} +(6.56155 - 11.3649i) q^{53} -1.56155 q^{55} +11.1231 q^{57} +(-2.00000 + 3.46410i) q^{59} +(-3.43845 - 5.95557i) q^{61} +(-3.34233 - 5.78908i) q^{65} +(-1.12311 + 1.94528i) q^{67} +4.87689 q^{69} +(-2.12311 + 3.67733i) q^{73} +(-0.780776 - 1.35234i) q^{75} +(-0.342329 - 0.592932i) q^{79} +(3.50000 - 6.06218i) q^{81} -12.0000 q^{83} +7.56155 q^{85} +(-0.342329 + 0.592932i) q^{87} +(2.56155 + 4.43674i) q^{89} +(4.87689 + 8.44703i) q^{93} +(3.56155 - 6.16879i) q^{95} -1.31534 q^{97} -0.876894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 2 q^{5} - 3 q^{9}+O(q^{10}) $ 4 * q + q^3 + 2 * q^5 - 3 * q^9	$ 4 q + q^{3} + 2 q^{5} - 3 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} + 11 q^{17} - 6 q^{19} + 2 q^{23} - 2 q^{25} - 14 q^{27} + 10 q^{29} - 4 q^{31} - 9 q^{33} + 25 q^{39} - 12 q^{41} - 12 q^{43} + 3 q^{45} + 9 q^{47} + 3 q^{51} + 18 q^{53} + 2 q^{55} + 28 q^{57} - 8 q^{59} - 22 q^{61} - q^{65} + 12 q^{67} + 36 q^{69} + 8 q^{73} + q^{75} + 11 q^{79} + 14 q^{81} - 48 q^{83} + 22 q^{85} + 11 q^{87} + 2 q^{89} + 36 q^{93} + 6 q^{95} - 30 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q + q^3 + 2 * q^5 - 3 * q^9 + q^11 - 2 * q^13 + 2 * q^15 + 11 * q^17 - 6 * q^19 + 2 * q^23 - 2 * q^25 - 14 * q^27 + 10 * q^29 - 4 * q^31 - 9 * q^33 + 25 * q^39 - 12 * q^41 - 12 * q^43 + 3 * q^45 + 9 * q^47 + 3 * q^51 + 18 * q^53 + 2 * q^55 + 28 * q^57 - 8 * q^59 - 22 * q^61 - q^65 + 12 * q^67 + 36 * q^69 + 8 * q^73 + q^75 + 11 * q^79 + 14 * q^81 - 48 * q^83 + 22 * q^85 + 11 * q^87 + 2 * q^89 + 36 * q^93 + 6 * q^95 - 30 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.780776	+	1.35234i	−0.450781	+	0.780776i	−0.998435	−	0.0559290i	$-0.982188\pi$
$3$	−0.780776	+	1.35234i	−0.450781	+	0.780776i	0.547653	+	0.836705i	$0.315521\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.280776	+	0.486319i	0.0935921	+	0.162106i
$10$		0			0
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	−0.959393	−	0.282074i	$-0.908978\pi$
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	0.723980	+	0.689821i	$0.242311\pi$
$12$		0			0
$13$	−6.68466			−1.85399			−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−6.68466			−1.85399			−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	−1.56155			−0.403191
$16$		0			0
$17$	3.78078	−	6.54850i	0.916973	−	1.58824i	0.112986	−	0.993597i	$-0.463958\pi$
$17$	3.78078	−	6.54850i	0.916973	−	1.58824i	0.803987	−	0.594647i	$-0.202708\pi$
$18$		0			0
$19$	−3.56155	−	6.16879i	−0.817076	−	1.41522i	−0.907827	−	0.419344i	$-0.862260\pi$
$19$	−3.56155	−	6.16879i	−0.817076	−	1.41522i	0.0907512	−	0.995874i	$-0.471073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.56155	−	2.70469i	−0.325606	−	0.563967i	0.656029	−	0.754736i	$-0.272235\pi$
$23$	−1.56155	−	2.70469i	−0.325606	−	0.563967i	−0.981635	+	0.190769i	$0.938902\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−5.56155			−1.07032
$28$		0			0
$29$	0.438447			0.0814176			0.0407088	−	0.999171i	$-0.487038\pi$
$29$	0.438447			0.0814176			0.0407088	+	0.999171i	$0.487038\pi$
$30$		0			0
$31$	3.12311	−	5.40938i	0.560926	−	0.971553i	−0.436490	−	0.899709i	$-0.643778\pi$
$31$	3.12311	−	5.40938i	0.560926	−	0.971553i	0.997416	−	0.0718436i	$-0.0228882\pi$
$32$		0			0
$33$	−1.21922	−	2.11176i	−0.212240	−	0.367610i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.12311	+	7.14143i	0.677834	+	1.17404i	0.975632	+	0.219414i	$0.0704147\pi$
$37$	4.12311	+	7.14143i	0.677834	+	1.17404i	−0.297797	+	0.954629i	$0.596252\pi$
$38$		0			0
$39$	5.21922	−	9.03996i	0.835745	−	1.44755i
$40$		0			0
$41$	1.12311			0.175400			0.0876998	−	0.996147i	$-0.472048\pi$
$41$	1.12311			0.175400			0.0876998	+	0.996147i	$0.472048\pi$
$42$		0			0
$43$	−7.12311			−1.08626			−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311			−1.08626			−0.543132	+	0.839648i	$0.682762\pi$
$44$		0			0
$45$	−0.280776	+	0.486319i	−0.0418557	+	0.0724962i
$46$		0			0
$47$	1.21922	+	2.11176i	0.177842	+	0.308031i	0.941141	−	0.338014i	$-0.109755\pi$
$47$	1.21922	+	2.11176i	0.177842	+	0.308031i	−0.763299	+	0.646045i	$0.776422\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	5.90388	+	10.2258i	0.826709	+	1.43190i
$52$		0			0
$53$	6.56155	−	11.3649i	0.901299	−	1.56109i	0.0754885	−	0.997147i	$-0.475948\pi$
$53$	6.56155	−	11.3649i	0.901299	−	1.56109i	0.825810	−	0.563948i	$-0.190718\pi$
$54$		0			0
$55$	−1.56155			−0.210560
$56$		0			0
$57$	11.1231			1.47329
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−3.43845	−	5.95557i	−0.440248	−	0.762532i	0.557460	−	0.830204i	$-0.311776\pi$
$61$	−3.43845	−	5.95557i	−0.440248	−	0.762532i	−0.997708	+	0.0676721i	$0.978443\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.34233	−	5.78908i	−0.414565	−	0.718048i
$66$		0			0
$67$	−1.12311	+	1.94528i	−0.137209	+	0.237653i	−0.926439	−	0.376444i	$-0.877147\pi$
$67$	−1.12311	+	1.94528i	−0.137209	+	0.237653i	0.789230	+	0.614098i	$0.210480\pi$
$68$		0			0
$69$	4.87689			0.587109
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−2.12311	+	3.67733i	−0.248491	+	0.430399i	−0.963107	−	0.269118i	$-0.913268\pi$
$73$	−2.12311	+	3.67733i	−0.248491	+	0.430399i	0.714617	+	0.699516i	$0.246601\pi$
$74$		0			0
$75$	−0.780776	−	1.35234i	−0.0901563	−	0.156155i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.342329	−	0.592932i	−0.0385150	−	0.0667100i	0.846125	−	0.532984i	$-0.178929\pi$
$79$	−0.342329	−	0.592932i	−0.0385150	−	0.0667100i	−0.884640	+	0.466274i	$0.845596\pi$
$80$		0			0
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	7.56155			0.820166
$86$		0			0
$87$	−0.342329	+	0.592932i	−0.0367015	+	0.0635689i
$88$		0			0
$89$	2.56155	+	4.43674i	0.271524	+	0.470293i	0.969252	−	0.246069i	$-0.0791390\pi$
$89$	2.56155	+	4.43674i	0.271524	+	0.470293i	−0.697728	+	0.716363i	$0.745806\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.87689	+	8.44703i	0.505710	+	0.875916i
$94$		0			0
$95$	3.56155	−	6.16879i	0.365408	−	0.632905i
$96$		0			0
$97$	−1.31534			−0.133553			−0.0667764	−	0.997768i	$-0.521271\pi$
$97$	−1.31534			−0.133553			−0.0667764	+	0.997768i	$0.521271\pi$
$98$		0			0
$99$	−0.876894			−0.0881312
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	−5.90388	−	10.2258i	−0.581727	−	1.00758i	−0.995275	−	0.0970980i	$-0.969044\pi$
$103$	−5.90388	−	10.2258i	−0.581727	−	1.00758i	0.413548	−	0.910482i	$-0.364289\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.56155	−	13.0970i	−0.731003	−	1.26613i	−0.956455	−	0.291880i	$-0.905719\pi$
$107$	−7.56155	−	13.0970i	−0.731003	−	1.26613i	0.225452	−	0.974254i	$-0.427614\pi$
$108$		0			0
$109$	2.21922	−	3.84381i	0.212563	−	0.368170i	−0.739953	−	0.672659i	$-0.765152\pi$
$109$	2.21922	−	3.84381i	0.212563	−	0.368170i	0.952516	+	0.304489i	$0.0984856\pi$
$110$		0			0
$111$	−12.8769			−1.22222
$112$		0			0
$113$	8.24621			0.775738			0.387869	−	0.921714i	$-0.373211\pi$
$113$	8.24621			0.775738			0.387869	+	0.921714i	$0.373211\pi$
$114$		0			0
$115$	1.56155	−	2.70469i	0.145616	−	0.252214i
$116$		0			0
$117$	−1.87689	−	3.25088i	−0.173519	−	0.300544i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$		0			0
$123$	−0.876894	+	1.51883i	−0.0790669	+	0.136948i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.24621			−0.554262			−0.277131	−	0.960832i	$-0.589384\pi$
$127$	−6.24621			−0.554262			−0.277131	+	0.960832i	$0.589384\pi$
$128$		0			0
$129$	5.56155	−	9.63289i	0.489667	−	0.848129i
$130$		0			0
$131$	7.56155	+	13.0970i	0.660656	+	1.14429i	0.980444	+	0.196800i	$0.0630551\pi$
$131$	7.56155	+	13.0970i	0.660656	+	1.14429i	−0.319788	+	0.947489i	$0.603612\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.78078	−	4.81645i	−0.239331	−	0.414534i
$136$		0			0
$137$	3.68466	−	6.38202i	0.314802	−	0.545252i	−0.664594	−	0.747205i	$-0.731395\pi$
$137$	3.68466	−	6.38202i	0.314802	−	0.545252i	0.979395	+	0.201953i	$0.0647287\pi$
$138$		0			0
$139$	21.3693			1.81252			0.906261	−	0.422719i	$-0.138924\pi$
$139$	21.3693			1.81252			0.906261	+	0.422719i	$0.138924\pi$
$140$		0			0
$141$	−3.80776			−0.320672
$142$		0			0
$143$	5.21922	−	9.03996i	0.436453	−	0.755959i
$144$		0			0
$145$	0.219224	+	0.379706i	0.0182055	+	0.0315329i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.123106	+	0.213225i	0.0100852	+	0.0174681i	0.871024	−	0.491241i	$-0.163456\pi$
$149$	0.123106	+	0.213225i	0.0100852	+	0.0174681i	−0.860939	+	0.508709i	$0.830123\pi$
$150$		0			0
$151$	9.90388	−	17.1540i	0.805966	−	1.39597i	−0.109670	−	0.993968i	$-0.534979\pi$
$151$	9.90388	−	17.1540i	0.805966	−	1.39597i	0.915637	−	0.402007i	$-0.131687\pi$
$152$		0			0
$153$	4.24621			0.343286
$154$		0			0
$155$	6.24621			0.501708
$156$		0			0
$157$	2.12311	−	3.67733i	0.169442	−	0.293483i	−0.768782	−	0.639511i	$-0.779137\pi$
$157$	2.12311	−	3.67733i	0.169442	−	0.293483i	0.938224	+	0.346029i	$0.112470\pi$
$158$		0			0
$159$	10.2462	+	17.7470i	0.812577	+	1.40743i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−9.80776	−	16.9875i	−0.768203	−	1.33057i	−0.938536	−	0.345181i	$-0.887818\pi$
$163$	−9.80776	−	16.9875i	−0.768203	−	1.33057i	0.170333	−	0.985387i	$-0.445516\pi$
$164$		0			0
$165$	1.21922	−	2.11176i	0.0949164	−	0.164400i
$166$		0			0
$167$	−4.19224			−0.324405			−0.162202	−	0.986757i	$-0.551860\pi$
$167$	−4.19224			−0.324405			−0.162202	+	0.986757i	$0.551860\pi$
$168$		0			0
$169$	31.6847			2.43728
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$		0			0
$173$	−11.5885	−	20.0719i	−0.881060	−	1.52604i	−0.850163	−	0.526519i	$-0.823497\pi$
$173$	−11.5885	−	20.0719i	−0.881060	−	1.52604i	−0.0308969	−	0.999523i	$-0.509836\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.12311	−	5.40938i	−0.234747	−	0.406594i
$178$		0			0
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		0			0
$181$	5.12311			0.380797			0.190399	−	0.981707i	$-0.439022\pi$
$181$	5.12311			0.380797			0.190399	+	0.981707i	$0.439022\pi$
$182$		0			0
$183$	10.7386			0.793823
$184$		0			0
$185$	−4.12311	+	7.14143i	−0.303137	+	0.525048i
$186$		0			0
$187$	5.90388	+	10.2258i	0.431735	+	0.747786i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.342329	+	0.592932i	0.0247701	+	0.0429030i	0.878145	−	0.478395i	$-0.158781\pi$
$191$	0.342329	+	0.592932i	0.0247701	+	0.0429030i	−0.853375	+	0.521298i	$0.825448\pi$
$192$		0			0
$193$	−6.56155	+	11.3649i	−0.472311	+	0.818066i	−0.999498	−	0.0316828i	$-0.989913\pi$
$193$	−6.56155	+	11.3649i	−0.472311	+	0.818066i	0.527187	+	0.849749i	$0.323247\pi$
$194$		0			0
$195$	10.4384			0.747513
$196$		0			0
$197$	−13.1231			−0.934983			−0.467491	−	0.883998i	$-0.654842\pi$
$197$	−13.1231			−0.934983			−0.467491	+	0.883998i	$0.654842\pi$
$198$		0			0
$199$	−7.12311	+	12.3376i	−0.504944	+	0.874588i	0.495040	+	0.868870i	$0.335153\pi$
$199$	−7.12311	+	12.3376i	−0.504944	+	0.874588i	−0.999984	+	0.00571778i	$0.998180\pi$
$200$		0			0
$201$	−1.75379	−	3.03765i	−0.123703	−	0.214259i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.561553	+	0.972638i	0.0392205	+	0.0679320i
$206$		0			0
$207$	0.876894	−	1.51883i	0.0609484	−	0.105566i
$208$		0			0
$209$	11.1231			0.769401
$210$		0			0
$211$	−17.5616			−1.20899			−0.604494	−	0.796610i	$-0.706624\pi$
$211$	−17.5616			−1.20899			−0.604494	+	0.796610i	$0.706624\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.56155	−	6.16879i	−0.242896	−	0.420708i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.31534	−	5.74234i	−0.224030	−	0.388031i
$220$		0			0
$221$	−25.2732	+	43.7745i	−1.70006	+	2.94459i
$222$		0			0
$223$	−24.6847			−1.65301			−0.826503	−	0.562932i	$-0.809673\pi$
$223$	−24.6847			−1.65301			−0.826503	+	0.562932i	$0.809673\pi$
$224$		0			0
$225$	−0.561553			−0.0374369
$226$		0			0
$227$	−5.65767	+	9.79937i	−0.375513	+	0.650407i	−0.990404	−	0.138205i	$-0.955867\pi$
$227$	−5.65767	+	9.79937i	−0.375513	+	0.650407i	0.614891	+	0.788612i	$0.289200\pi$
$228$		0			0
$229$	−5.68466	−	9.84612i	−0.375653	−	0.650650i	0.614772	−	0.788705i	$-0.289248\pi$
$229$	−5.68466	−	9.84612i	−0.375653	−	0.650650i	−0.990425	+	0.138055i	$0.955915\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.43845	+	9.41967i	0.356285	+	0.617103i	0.987337	−	0.158637i	$-0.0507101\pi$
$233$	5.43845	+	9.41967i	0.356285	+	0.617103i	−0.631052	+	0.775740i	$0.717377\pi$
$234$		0			0
$235$	−1.21922	+	2.11176i	−0.0795334	+	0.137756i
$236$		0			0
$237$	1.06913			0.0694475
$238$		0			0
$239$	−18.0540			−1.16781			−0.583907	−	0.811820i	$-0.698477\pi$
$239$	−18.0540			−1.16781			−0.583907	+	0.811820i	$0.698477\pi$
$240$		0			0
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$		0			0
$243$	−2.87689	−	4.98293i	−0.184553	−	0.319655i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	23.8078	+	41.2363i	1.51485	+	2.62380i
$248$		0			0
$249$	9.36932	−	16.2281i	0.593756	−	1.02842i
$250$		0			0
$251$	−13.3693			−0.843864			−0.421932	−	0.906628i	$-0.638648\pi$
$251$	−13.3693			−0.843864			−0.421932	+	0.906628i	$0.638648\pi$
$252$		0			0
$253$	4.87689			0.306608
$254$		0			0
$255$	−5.90388	+	10.2258i	−0.369715	+	0.640366i
$256$		0			0
$257$	−9.24621	−	16.0149i	−0.576763	−	0.998982i	−0.995848	−	0.0910354i	$-0.970982\pi$
$257$	−9.24621	−	16.0149i	−0.576763	−	0.998982i	0.419085	−	0.907947i	$-0.362351\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.123106	+	0.213225i	0.00762005	+	0.0131983i
$262$		0			0
$263$	−4.68466	+	8.11407i	−0.288868	+	0.500335i	−0.973540	−	0.228517i	$-0.926612\pi$
$263$	−4.68466	+	8.11407i	−0.288868	+	0.500335i	0.684672	+	0.728852i	$0.259946\pi$
$264$		0			0
$265$	13.1231			0.806146
$266$		0			0
$267$	−8.00000			−0.489592
$268$		0			0
$269$	2.12311	−	3.67733i	0.129448	−	0.224211i	−0.794015	−	0.607898i	$-0.792013\pi$
$269$	2.12311	−	3.67733i	0.129448	−	0.224211i	0.923463	+	0.383688i	$0.125346\pi$
$270$		0			0
$271$	−3.12311	−	5.40938i	−0.189715	−	0.328596i	0.755440	−	0.655218i	$-0.227423\pi$
$271$	−3.12311	−	5.40938i	−0.189715	−	0.328596i	−0.945155	+	0.326621i	$0.894090\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.780776	−	1.35234i	−0.0470826	−	0.0815494i
$276$		0			0
$277$	4.12311	−	7.14143i	0.247733	−	0.429087i	−0.715163	−	0.698958i	$-0.753648\pi$
$277$	4.12311	−	7.14143i	0.247733	−	0.429087i	0.962897	+	0.269871i	$0.0869810\pi$
$278$		0			0
$279$	3.50758			0.209993
$280$		0			0
$281$	−19.5616			−1.16694			−0.583472	−	0.812133i	$-0.698306\pi$
$281$	−19.5616			−1.16694			−0.583472	+	0.812133i	$0.698306\pi$
$282$		0			0
$283$	−2.34233	+	4.05703i	−0.139237	+	0.241166i	−0.927208	−	0.374547i	$-0.877798\pi$
$283$	−2.34233	+	4.05703i	−0.139237	+	0.241166i	0.787971	+	0.615712i	$0.211132\pi$
$284$		0			0
$285$	5.56155	+	9.63289i	0.329438	+	0.570603i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−20.0885	−	34.7944i	−1.18168	−	2.04673i
$290$		0			0
$291$	1.02699	−	1.77879i	0.0602031	−	0.104275i
$292$		0			0
$293$	−32.0540			−1.87261			−0.936307	−	0.351184i	$-0.885779\pi$
$293$	−32.0540			−1.87261			−0.936307	+	0.351184i	$0.885779\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	4.34233	−	7.52113i	0.251967	−	0.436421i
$298$		0			0
$299$	10.4384	+	18.0799i	0.603671	+	1.04559i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4.68466	+	8.11407i	0.269127	+	0.466141i
$304$		0			0
$305$	3.43845	−	5.95557i	0.196885	−	0.341015i
$306$		0			0
$307$	28.6847			1.63712			0.818560	−	0.574421i	$-0.194773\pi$
$307$	28.6847			1.63712			0.818560	+	0.574421i	$0.194773\pi$
$308$		0			0
$309$	18.4384			1.04893
$310$		0			0
$311$	−6.43845	+	11.1517i	−0.365091	+	0.632356i	−0.988791	−	0.149308i	$-0.952295\pi$
$311$	−6.43845	+	11.1517i	−0.365091	+	0.632356i	0.623700	+	0.781664i	$0.285629\pi$
$312$		0			0
$313$	13.3423	+	23.1096i	0.754153	+	1.30623i	0.945794	+	0.324766i	$0.105286\pi$
$313$	13.3423	+	23.1096i	0.754153	+	1.30623i	−0.191641	+	0.981465i	$0.561381\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$	−0.342329	+	0.592932i	−0.0191668	+	0.0331978i
$320$		0			0
$321$	23.6155			1.31809
$322$		0			0
$323$	−53.8617			−2.99695
$324$		0			0
$325$	3.34233	−	5.78908i	0.185399	−	0.321121i
$326$		0			0
$327$	3.46543	+	6.00231i	0.191639	+	0.331928i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	0.982470	−	0.186421i	$-0.0596888\pi$
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$332$		0			0
$333$	−2.31534	+	4.01029i	−0.126880	+	0.219762i
$334$		0			0
$335$	−2.24621			−0.122724
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	−6.43845	+	11.1517i	−0.349688	+	0.605678i
$340$		0			0
$341$	4.87689	+	8.44703i	0.264099	+	0.457432i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.43845	+	4.22351i	0.131282	+	0.227386i
$346$		0			0
$347$	−7.56155	+	13.0970i	−0.405925	+	0.703083i	−0.994429	−	0.105411i	$-0.966384\pi$
$347$	−7.56155	+	13.0970i	−0.405925	+	0.703083i	0.588503	+	0.808495i	$0.299717\pi$
$348$		0			0
$349$	11.7538			0.629166			0.314583	−	0.949230i	$-0.398135\pi$
$349$	11.7538			0.629166			0.314583	+	0.949230i	$0.398135\pi$
$350$		0			0
$351$	37.1771			1.98437
$352$		0			0
$353$	−1.09612	+	1.89853i	−0.0583405	+	0.101049i	−0.893721	−	0.448624i	$-0.851914\pi$
$353$	−1.09612	+	1.89853i	−0.0583405	+	0.101049i	0.835380	+	0.549673i	$0.185248\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	−0.886100	−	0.463494i	$-0.846596\pi$
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	0.0416523	−	0.999132i	$-0.486738\pi$
$360$		0			0
$361$	−15.8693	+	27.4865i	−0.835227	+	1.44666i
$362$		0			0
$363$	−13.3693			−0.701707
$364$		0			0
$365$	−4.24621			−0.222257
$366$		0			0
$367$	7.46543	−	12.9305i	0.389693	−	0.674967i	−0.602716	−	0.797956i	$-0.705915\pi$
$367$	7.46543	−	12.9305i	0.389693	−	0.674967i	0.992408	+	0.122989i	$0.0392480\pi$
$368$		0			0
$369$	0.315342	+	0.546188i	0.0164160	+	0.0284334i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.68466	−	13.3102i	−0.397897	−	0.689177i	0.595570	−	0.803304i	$-0.296926\pi$
$373$	−7.68466	−	13.3102i	−0.397897	−	0.689177i	−0.993466	+	0.114127i	$0.963593\pi$
$374$		0			0
$375$	0.780776	−	1.35234i	0.0403191	−	0.0698348i
$376$		0			0
$377$	−2.93087			−0.150947
$378$		0			0
$379$	32.4924			1.66902			0.834512	−	0.550990i	$-0.185750\pi$
$379$	32.4924			1.66902			0.834512	+	0.550990i	$0.185750\pi$
$380$		0			0
$381$	4.87689	−	8.44703i	0.249851	−	0.432754i
$382$		0			0
$383$	−4.87689	−	8.44703i	−0.249198	−	0.431623i	0.714106	−	0.700038i	$-0.246834\pi$
$383$	−4.87689	−	8.44703i	−0.249198	−	0.431623i	−0.963303	+	0.268415i	$0.913500\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$		0			0
$389$	−11.1501	+	19.3125i	−0.565332	+	0.979184i	0.431687	+	0.902024i	$0.357919\pi$
$389$	−11.1501	+	19.3125i	−0.565332	+	0.979184i	−0.997019	+	0.0771603i	$0.975415\pi$
$390$		0			0
$391$	−23.6155			−1.19429
$392$		0			0
$393$	−23.6155			−1.19125
$394$		0			0
$395$	0.342329	−	0.592932i	0.0172245	−	0.0298336i
$396$		0			0
$397$	−11.5885	−	20.0719i	−0.581612	−	1.00738i	−0.995288	−	0.0969578i	$-0.969089\pi$
$397$	−11.5885	−	20.0719i	−0.581612	−	1.00738i	0.413676	−	0.910424i	$-0.364245\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.46543	+	11.1985i	0.322868	+	0.559224i	0.981079	−	0.193610i	$-0.0620195\pi$
$401$	6.46543	+	11.1985i	0.322868	+	0.559224i	−0.658210	+	0.752834i	$0.728686\pi$
$402$		0			0
$403$	−20.8769	+	36.1598i	−1.03995	+	1.80125i
$404$		0			0
$405$	7.00000			0.347833
$406$		0			0
$407$	−12.8769			−0.638284
$408$		0			0
$409$	−9.24621	+	16.0149i	−0.457196	+	0.791886i	−0.998812	−	0.0487399i	$-0.984479\pi$
$409$	−9.24621	+	16.0149i	−0.457196	+	0.791886i	0.541616	+	0.840626i	$0.317813\pi$
$410$		0			0
$411$	5.75379	+	9.96585i	0.283813	+	0.491579i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$		0			0
$417$	−16.6847	+	28.8987i	−0.817051	+	1.41517i
$418$		0			0
$419$	18.2462			0.891386			0.445693	−	0.895186i	$-0.352957\pi$
$419$	18.2462			0.891386			0.445693	+	0.895186i	$0.352957\pi$
$420$		0			0
$421$	3.56155			0.173579			0.0867897	−	0.996227i	$-0.472339\pi$
$421$	3.56155			0.173579			0.0867897	+	0.996227i	$0.472339\pi$
$422$		0			0
$423$	−0.684658	+	1.18586i	−0.0332892	+	0.0576586i
$424$		0			0
$425$	3.78078	+	6.54850i	0.183395	+	0.317649i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	8.15009	+	14.1164i	0.393490	+	0.681545i
$430$		0			0
$431$	11.4654	−	19.8587i	0.552271	−	0.956561i	−0.445840	−	0.895113i	$-0.647095\pi$
$431$	11.4654	−	19.8587i	0.552271	−	0.956561i	0.998110	−	0.0614479i	$-0.0195718\pi$
$432$		0			0
$433$	−19.7538			−0.949307			−0.474653	−	0.880173i	$-0.657427\pi$
$433$	−19.7538			−0.949307			−0.474653	+	0.880173i	$0.657427\pi$
$434$		0			0
$435$	−0.684658			−0.0328269
$436$		0			0
$437$	−11.1231	+	19.2658i	−0.532090	+	0.921607i
$438$		0			0
$439$	9.56155	+	16.5611i	0.456348	+	0.790418i	0.998765	−	0.0496917i	$-0.0158239\pi$
$439$	9.56155	+	16.5611i	0.456348	+	0.790418i	−0.542417	+	0.840110i	$0.682491\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.80776	+	16.9875i	0.465981	+	0.807103i	0.999245	−	0.0388461i	$-0.0123682\pi$
$443$	9.80776	+	16.9875i	0.465981	+	0.807103i	−0.533264	+	0.845949i	$0.679035\pi$
$444$		0			0
$445$	−2.56155	+	4.43674i	−0.121429	+	0.210322i
$446$		0			0
$447$	−0.384472			−0.0181849
$448$		0			0
$449$	−21.3153			−1.00593			−0.502967	−	0.864306i	$-0.667758\pi$
$449$	−21.3153			−1.00593			−0.502967	+	0.864306i	$0.667758\pi$
$450$		0			0
$451$	−0.876894	+	1.51883i	−0.0412913	+	0.0715187i
$452$		0			0
$453$	15.4654	+	26.7869i	0.726630	+	1.25856i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.31534	−	7.47439i	−0.201863	−	0.349637i	0.747266	−	0.664525i	$-0.231366\pi$
$457$	−4.31534	−	7.47439i	−0.201863	−	0.349637i	−0.949129	+	0.314888i	$0.898033\pi$
$458$		0			0
$459$	−21.0270	+	36.4198i	−0.981456	+	1.69993i
$460$		0			0
$461$	−18.8769			−0.879185			−0.439592	−	0.898197i	$-0.644877\pi$
$461$	−18.8769			−0.879185			−0.439592	+	0.898197i	$0.644877\pi$
$462$		0			0
$463$	−6.24621			−0.290286			−0.145143	−	0.989411i	$-0.546364\pi$
$463$	−6.24621			−0.290286			−0.145143	+	0.989411i	$0.546364\pi$
$464$		0			0
$465$	−4.87689	+	8.44703i	−0.226161	+	0.391722i
$466$		0			0
$467$	12.7808	+	22.1370i	0.591424	+	1.02438i	0.994041	+	0.109008i	$0.0347673\pi$
$467$	12.7808	+	22.1370i	0.591424	+	1.02438i	−0.402617	+	0.915368i	$0.631899\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.31534	+	5.74234i	0.152763	+	0.264593i
$472$		0			0
$473$	5.56155	−	9.63289i	0.255720	−	0.442921i
$474$		0			0
$475$	7.12311			0.326831
$476$		0			0
$477$	7.36932			0.337418
$478$		0			0
$479$	8.68466	−	15.0423i	0.396812	−	0.687299i	−0.596518	−	0.802599i	$-0.703450\pi$
$479$	8.68466	−	15.0423i	0.396812	−	0.687299i	0.993331	+	0.115300i	$0.0367831\pi$
$480$		0			0
$481$	−27.5616	−	47.7380i	−1.25670	−	2.17667i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.657671	−	1.13912i	−0.0298633	−	0.0517247i
$486$		0			0
$487$	−1.56155	+	2.70469i	−0.0707607	+	0.122561i	−0.899235	−	0.437466i	$-0.855876\pi$
$487$	−1.56155	+	2.70469i	−0.0707607	+	0.122561i	0.828474	+	0.560027i	$0.189209\pi$
$488$		0			0
$489$	30.6307			1.38517
$490$		0			0
$491$	−3.31534			−0.149619			−0.0748096	−	0.997198i	$-0.523835\pi$
$491$	−3.31534			−0.149619			−0.0748096	+	0.997198i	$0.523835\pi$
$492$		0			0
$493$	1.65767	−	2.87117i	0.0746577	−	0.129311i
$494$		0			0
$495$	−0.438447	−	0.759413i	−0.0197067	−	0.0341331i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.0961180	+	0.166481i	0.00430283	+	0.00745272i	0.868169	−	0.496269i	$-0.165297\pi$
$499$	0.0961180	+	0.166481i	0.00430283	+	0.00745272i	−0.863866	+	0.503722i	$0.831964\pi$
$500$		0			0
$501$	3.27320	−	5.66935i	0.146236	−	0.253288i
$502$		0			0
$503$	29.1771			1.30094			0.650471	−	0.759531i	$-0.274572\pi$
$503$	29.1771			1.30094			0.650471	+	0.759531i	$0.274572\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	−24.7386	+	42.8486i	−1.09868	+	1.90297i
$508$		0			0
$509$	16.3693	+	28.3525i	0.725557	+	1.25670i	0.958744	+	0.284270i	$0.0917512\pi$
$509$	16.3693	+	28.3525i	0.725557	+	1.25670i	−0.233187	+	0.972432i	$0.574915\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	19.8078	+	34.3081i	0.874534	+	1.51474i
$514$		0			0
$515$	5.90388	−	10.2258i	0.260156	−	0.450604i
$516$		0			0
$517$	−3.80776			−0.167465
$518$		0			0
$519$	36.1922			1.58866
$520$		0			0
$521$	−6.12311	+	10.6055i	−0.268258	+	0.464637i	−0.968412	−	0.249355i	$-0.919781\pi$
$521$	−6.12311	+	10.6055i	−0.268258	+	0.464637i	0.700154	+	0.713992i	$0.253115\pi$
$522$		0			0
$523$	−6.00000	−	10.3923i	−0.262362	−	0.454424i	0.704507	−	0.709697i	$-0.251168\pi$
$523$	−6.00000	−	10.3923i	−0.262362	−	0.454424i	−0.966869	+	0.255273i	$0.917835\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−23.6155	−	40.9033i	−1.02871	−	1.78178i
$528$		0			0
$529$	6.62311	−	11.4716i	0.287961	−	0.498763i
$530$		0			0
$531$	−2.24621			−0.0974773
$532$		0			0
$533$	−7.50758			−0.325189
$534$		0			0
$535$	7.56155	−	13.0970i	0.326914	−	0.566232i
$536$		0			0
$537$	3.12311	+	5.40938i	0.134772	+	0.233432i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−20.7116	−	35.8736i	−0.890463	−	1.54233i	−0.839321	−	0.543636i	$-0.817047\pi$
$541$	−20.7116	−	35.8736i	−0.890463	−	1.54233i	−0.0511422	−	0.998691i	$-0.516286\pi$
$542$		0			0
$543$	−4.00000	+	6.92820i	−0.171656	+	0.297318i
$544$		0			0
$545$	4.43845			0.190122
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	1.93087	−	3.34436i	0.0824075	−	0.142734i
$550$		0			0
$551$	−1.56155	−	2.70469i	−0.0665244	−	0.115224i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.43845	−	11.1517i	−0.273297	−	0.473364i
$556$		0			0
$557$	8.80776	−	15.2555i	0.373197	−	0.646396i	−0.616858	−	0.787074i	$-0.711595\pi$
$557$	8.80776	−	15.2555i	0.373197	−	0.646396i	0.990055	+	0.140678i	$0.0449282\pi$
$558$		0			0
$559$	47.6155			2.01392
$560$		0			0
$561$	−18.4384			−0.778472
$562$		0			0
$563$	−3.75379	+	6.50175i	−0.158203	+	0.274016i	−0.934221	−	0.356695i	$-0.883903\pi$
$563$	−3.75379	+	6.50175i	−0.158203	+	0.274016i	0.776017	+	0.630711i	$0.217237\pi$
$564$		0			0
$565$	4.12311	+	7.14143i	0.173460	+	0.300442i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.49242	−	16.4414i	−0.397943	−	0.689258i	0.595529	−	0.803334i	$-0.296943\pi$
$569$	−9.49242	−	16.4414i	−0.397943	−	0.689258i	−0.993472	+	0.114076i	$0.963609\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$	−1.06913			−0.0446636
$574$		0			0
$575$	3.12311			0.130243
$576$		0			0
$577$	−1.78078	+	3.08440i	−0.0741347	+	0.128405i	−0.900710	−	0.434422i	$-0.856953\pi$
$577$	−1.78078	+	3.08440i	−0.0741347	+	0.128405i	0.826575	+	0.562827i	$0.190286\pi$
$578$		0			0
$579$	−10.2462	−	17.7470i	−0.425818	−	0.737538i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	10.2462	+	17.7470i	0.424355	+	0.735004i
$584$		0			0
$585$	1.87689	−	3.25088i	0.0776000	−	0.134407i
$586$		0			0
$587$	−10.2462			−0.422906			−0.211453	−	0.977388i	$-0.567820\pi$
$587$	−10.2462			−0.422906			−0.211453	+	0.977388i	$0.567820\pi$
$588$		0			0
$589$	−44.4924			−1.83328
$590$		0			0
$591$	10.2462	−	17.7470i	0.421473	−	0.730012i
$592$		0			0
$593$	18.7116	+	32.4095i	0.768395	+	1.33090i	0.938433	+	0.345462i	$0.112278\pi$
$593$	18.7116	+	32.4095i	0.768395	+	1.33090i	−0.170038	+	0.985438i	$0.554389\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.1231	−	19.2658i	−0.455238	−	0.788496i
$598$		0			0
$599$	23.4654	−	40.6433i	0.958772	−	1.66064i	0.233281	−	0.972409i	$-0.425054\pi$
$599$	23.4654	−	40.6433i	0.958772	−	1.66064i	0.725491	−	0.688232i	$-0.241613\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$	−1.26137			−0.0513668
$604$		0			0
$605$	−4.28078	+	7.41452i	−0.174038	+	0.301443i
$606$		0			0
$607$	−4.34233	−	7.52113i	−0.176250	−	0.305273i	0.764343	−	0.644809i	$-0.223063\pi$
$607$	−4.34233	−	7.52113i	−0.176250	−	0.305273i	−0.940593	+	0.339536i	$0.889730\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.15009	−	14.1164i	−0.329717	−	0.571087i
$612$		0			0
$613$	−8.36932	+	14.4961i	−0.338034	+	0.585491i	−0.984063	−	0.177821i	$-0.943095\pi$
$613$	−8.36932	+	14.4961i	−0.338034	+	0.585491i	0.646029	+	0.763313i	$0.276428\pi$
$614$		0			0
$615$	−1.75379			−0.0707196
$616$		0			0
$617$	−15.7538			−0.634224			−0.317112	−	0.948388i	$-0.602713\pi$
$617$	−15.7538			−0.634224			−0.317112	+	0.948388i	$0.602713\pi$
$618$		0			0
$619$	5.31534	−	9.20644i	0.213642	−	0.370038i	−0.739210	−	0.673475i	$-0.764801\pi$
$619$	5.31534	−	9.20644i	0.213642	−	0.370038i	0.952852	+	0.303437i	$0.0981342\pi$
$620$		0			0
$621$	8.68466	+	15.0423i	0.348503	+	0.603625i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−8.68466	+	15.0423i	−0.346832	+	0.600730i
$628$		0			0
$629$	62.3542			2.48622
$630$		0			0
$631$	−27.4233			−1.09170			−0.545852	−	0.837882i	$-0.683794\pi$
$631$	−27.4233			−1.09170			−0.545852	+	0.837882i	$0.683794\pi$
$632$		0			0
$633$	13.7116	−	23.7493i	0.544989	−	0.943949i
$634$		0			0
$635$	−3.12311	−	5.40938i	−0.123937	−	0.214665i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.4924	−	19.9055i	0.453923	−	0.786218i	−0.544702	−	0.838630i	$-0.683357\pi$
$641$	11.4924	−	19.9055i	0.453923	−	0.786218i	0.998626	+	0.0524112i	$0.0166906\pi$
$642$		0			0
$643$	30.0540			1.18521			0.592607	−	0.805492i	$-0.298099\pi$
$643$	30.0540			1.18521			0.592607	+	0.805492i	$0.298099\pi$
$644$		0			0
$645$	11.1231			0.437972
$646$		0			0
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	−0.776622	−	0.629967i	$-0.783068\pi$
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	0.933878	+	0.357591i	$0.116402\pi$
$648$		0			0
$649$	−3.12311	−	5.40938i	−0.122593	−	0.212337i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.2462	+	33.3354i	0.753162	+	1.30452i	0.946283	+	0.323341i	$0.104806\pi$
$653$	19.2462	+	33.3354i	0.753162	+	1.30452i	−0.193120	+	0.981175i	$0.561861\pi$
$654$		0			0
$655$	−7.56155	+	13.0970i	−0.295454	+	0.511742i
$656$		0			0
$657$	−2.38447			−0.0930271
$658$		0			0
$659$	−0.192236			−0.00748845			−0.00374422	−	0.999993i	$-0.501192\pi$
$659$	−0.192236			−0.00748845			−0.00374422	+	0.999993i	$0.501192\pi$
$660$		0			0
$661$	−8.80776	+	15.2555i	−0.342582	+	0.593370i	−0.984911	−	0.173059i	$-0.944635\pi$
$661$	−8.80776	+	15.2555i	−0.342582	+	0.593370i	0.642329	+	0.766429i	$0.277968\pi$
$662$		0			0
$663$	−39.4654	−	68.3561i	−1.53271	−	2.65473i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.684658	−	1.18586i	−0.0265101	−	0.0459168i
$668$		0			0
$669$	19.2732	−	33.3822i	0.745145	−	1.29063i
$670$		0			0
$671$	10.7386			0.414560
$672$		0			0
$673$	41.6155			1.60416			0.802080	−	0.597216i	$-0.203727\pi$
$673$	41.6155			1.60416			0.802080	+	0.597216i	$0.203727\pi$
$674$		0			0
$675$	2.78078	−	4.81645i	0.107032	−	0.185385i
$676$		0			0
$677$	−0.657671	−	1.13912i	−0.0252763	−	0.0437799i	0.853111	−	0.521730i	$-0.174713\pi$
$677$	−0.657671	−	1.13912i	−0.0252763	−	0.0437799i	−0.878387	+	0.477950i	$0.841380\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−8.83475	−	15.3022i	−0.338548	−	0.586383i
$682$		0			0
$683$	−22.4924	+	38.9580i	−0.860649	+	1.49069i	0.0106552	+	0.999943i	$0.496608\pi$
$683$	−22.4924	+	38.9580i	−0.860649	+	1.49069i	−0.871304	+	0.490744i	$0.836725\pi$
$684$		0			0
$685$	7.36932			0.281567
$686$		0			0
$687$	17.7538			0.677349
$688$		0			0
$689$	−43.8617	+	75.9708i	−1.67100	+	2.89426i
$690$		0			0
$691$	8.24621	+	14.2829i	0.313701	+	0.543345i	0.979160	−	0.203088i	$-0.0650978\pi$
$691$	8.24621	+	14.2829i	0.313701	+	0.543345i	−0.665460	+	0.746434i	$0.731764\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.6847	+	18.5064i	0.405292	+	0.701987i
$696$		0			0
$697$	4.24621	−	7.35465i	0.160837	−	0.278577i
$698$		0			0
$699$	−16.9848			−0.642426
$700$		0			0
$701$	−9.31534			−0.351836			−0.175918	−	0.984405i	$-0.556289\pi$
$701$	−9.31534			−0.351836			−0.175918	+	0.984405i	$0.556289\pi$
$702$		0			0
$703$	29.3693	−	50.8691i	1.10768	−	1.91857i
$704$		0			0
$705$	−1.90388	−	3.29762i	−0.0717043	−	0.124196i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2.02699	+	3.51085i	0.0761251	+	0.131853i	0.901575	−	0.432623i	$-0.142412\pi$
$709$	2.02699	+	3.51085i	0.0761251	+	0.131853i	−0.825450	+	0.564475i	$0.809078\pi$
$710$		0			0
$711$	0.192236	−	0.332962i	0.00720941	−	0.0124871i
$712$		0			0
$713$	−19.5076			−0.730565
$714$		0			0
$715$	10.4384			0.390376
$716$		0			0
$717$	14.0961	−	24.4152i	0.526429	−	0.911802i
$718$		0			0
$719$	−11.8078	−	20.4516i	−0.440355	−	0.762718i	0.557360	−	0.830271i	$-0.311814\pi$
$719$	−11.8078	−	20.4516i	−0.440355	−	0.762718i	−0.997716	+	0.0675529i	$0.978481\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.56155	+	2.70469i	0.0580748	+	0.100588i
$724$		0			0
$725$	−0.219224	+	0.379706i	−0.00814176	+	0.0141019i
$726$		0			0
$727$	−48.9848			−1.81675			−0.908374	−	0.418159i	$-0.862675\pi$
$727$	−48.9848			−1.81675			−0.908374	+	0.418159i	$0.862675\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$		0			0
$731$	−26.9309	+	46.6456i	−0.996074	+	1.72525i
$732$		0			0
$733$	8.21922	+	14.2361i	0.303584	+	0.525823i	0.976945	−	0.213491i	$-0.0684834\pi$
$733$	8.21922	+	14.2361i	0.303584	+	0.525823i	−0.673361	+	0.739314i	$0.735150\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.75379	−	3.03765i	−0.0646016	−	0.111893i
$738$		0			0
$739$	3.21922	−	5.57586i	0.118421	−	0.205111i	−0.800721	−	0.599037i	$-0.795550\pi$
$739$	3.21922	−	5.57586i	0.118421	−	0.205111i	0.919142	+	0.393926i	$0.128883\pi$
$740$		0			0
$741$	−74.3542			−2.73147
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	−0.123106	+	0.213225i	−0.00451024	+	0.00781197i
$746$		0			0
$747$	−3.36932	−	5.83583i	−0.123277	−	0.213522i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15.6577	+	27.1199i	0.571357	+	0.989619i	0.996427	+	0.0844583i	$0.0269160\pi$
$751$	15.6577	+	27.1199i	0.571357	+	0.989619i	−0.425070	+	0.905160i	$0.639751\pi$
$752$		0			0
$753$	10.4384	−	18.0799i	0.380398	−	0.658869i
$754$		0			0
$755$	19.8078			0.720878
$756$		0			0
$757$	15.3693			0.558607			0.279304	−	0.960203i	$-0.409896\pi$
$757$	15.3693			0.558607			0.279304	+	0.960203i	$0.409896\pi$
$758$		0			0
$759$	−3.80776	+	6.59524i	−0.138213	+	0.239392i
$760$		0			0
$761$	13.0000	+	22.5167i	0.471250	+	0.816228i	0.999459	−	0.0328858i	$-0.0104698\pi$
$761$	13.0000	+	22.5167i	0.471250	+	0.816228i	−0.528209	+	0.849114i	$0.677136\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.12311	+	3.67733i	0.0767610	+	0.132954i
$766$		0			0
$767$	13.3693	−	23.1563i	0.482738	−	0.836127i
$768$		0			0
$769$	−42.9848			−1.55007			−0.775037	−	0.631916i	$-0.782269\pi$
$769$	−42.9848			−1.55007			−0.775037	+	0.631916i	$0.782269\pi$
$770$		0			0
$771$	28.8769			1.03998
$772$		0			0
$773$	−14.9039	+	25.8143i	−0.536055	+	0.928475i	0.463056	+	0.886329i	$0.346753\pi$
$773$	−14.9039	+	25.8143i	−0.536055	+	0.928475i	−0.999111	+	0.0421462i	$0.986580\pi$
$774$		0			0
$775$	3.12311	+	5.40938i	0.112185	+	0.194311i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.00000	−	6.92820i	−0.143315	−	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.43845			−0.0871430
$784$		0			0
$785$	4.24621			0.151554
$786$		0			0
$787$	16.5885	−	28.7322i	0.591318	−	1.02419i	−0.402738	−	0.915315i	$-0.631941\pi$
$787$	16.5885	−	28.7322i	0.591318	−	1.02419i	0.994055	−	0.108877i	$-0.0347254\pi$
$788$		0			0
$789$	−7.31534	−	12.6705i	−0.260433	−	0.451083i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	22.9848	+	39.8109i	0.816216	+	1.41373i
$794$		0			0
$795$	−10.2462	+	17.7470i	−0.363396	+	0.629420i
$796$		0			0
$797$	−17.8078			−0.630783			−0.315392	−	0.948962i	$-0.602136\pi$
$797$	−17.8078			−0.630783			−0.315392	+	0.948962i	$0.602136\pi$
$798$		0			0
$799$	18.4384			0.652305
$800$		0			0
$801$	−1.43845	+	2.49146i	−0.0508250	+	0.0880315i
$802$		0			0
$803$	−3.31534	−	5.74234i	−0.116996	−	0.202643i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.31534	+	5.74234i	0.116706	+	0.202140i
$808$		0			0
$809$	−2.02699	+	3.51085i	−0.0712651	+	0.123435i	−0.899456	−	0.437011i	$-0.856037\pi$
$809$	−2.02699	+	3.51085i	−0.0712651	+	0.123435i	0.828191	+	0.560446i	$0.189370\pi$
$810$		0			0
$811$	27.6155			0.969712			0.484856	−	0.874594i	$-0.338872\pi$
$811$	27.6155			0.969712			0.484856	+	0.874594i	$0.338872\pi$
$812$		0			0
$813$	9.75379			0.342080
$814$		0			0
$815$	9.80776	−	16.9875i	0.343551	−	0.595048i
$816$		0			0
$817$	25.3693	+	43.9409i	0.887560	+	1.53730i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−27.1501	−	47.0253i	−0.947545	−	1.64120i	−0.750574	−	0.660786i	$-0.770223\pi$
$821$	−27.1501	−	47.0253i	−0.947545	−	1.64120i	−0.196971	−	0.980409i	$-0.563110\pi$
$822$		0			0
$823$	8.87689	−	15.3752i	0.309429	−	0.535947i	−0.668809	−	0.743435i	$-0.733195\pi$
$823$	8.87689	−	15.3752i	0.309429	−	0.535947i	0.978238	+	0.207488i	$0.0665287\pi$
$824$		0			0
$825$	2.43845			0.0848958
$826$		0			0
$827$	24.8769			0.865054			0.432527	−	0.901621i	$-0.357622\pi$
$827$	24.8769			0.865054			0.432527	+	0.901621i	$0.357622\pi$
$828$		0			0
$829$	2.80776	−	4.86319i	0.0975177	−	0.168906i	−0.813139	−	0.582070i	$-0.802243\pi$
$829$	2.80776	−	4.86319i	0.0975177	−	0.168906i	0.910657	+	0.413164i	$0.135576\pi$
$830$		0			0
$831$	6.43845	+	11.1517i	0.223347	+	0.386849i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.09612	−	3.63058i	−0.0725392	−	0.125641i
$836$		0			0
$837$	−17.3693	+	30.0845i	−0.600371	+	1.03987i
$838$		0			0
$839$	−19.1231			−0.660203			−0.330101	−	0.943945i	$-0.607083\pi$
$839$	−19.1231			−0.660203			−0.330101	+	0.943945i	$0.607083\pi$
$840$		0			0
$841$	−28.8078			−0.993371
$842$		0			0
$843$	15.2732	−	26.4540i	0.526037	−	0.911123i
$844$		0			0
$845$	15.8423	+	27.4397i	0.544993	+	0.943955i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.65767	−	6.33527i	−0.125531	−	0.217426i
$850$		0			0
$851$	12.8769	−	22.3034i	0.441414	−	0.764552i
$852$		0			0
$853$	−15.7538			−0.539399			−0.269700	−	0.962944i	$-0.586924\pi$
$853$	−15.7538			−0.539399			−0.269700	+	0.962944i	$0.586924\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	26.3693	−	45.6730i	0.900759	−	1.56016i	0.0742473	−	0.997240i	$-0.476345\pi$
$857$	26.3693	−	45.6730i	0.900759	−	1.56016i	0.826511	−	0.562920i	$-0.190322\pi$
$858$		0			0
$859$	18.4924	+	32.0298i	0.630953	+	1.09284i	0.987357	+	0.158511i	$0.0506694\pi$
$859$	18.4924	+	32.0298i	0.630953	+	1.09284i	−0.356404	+	0.934332i	$0.615997\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.2462	−	24.6752i	−0.484947	−	0.839952i	0.514904	−	0.857248i	$-0.327828\pi$
$863$	−14.2462	−	24.6752i	−0.484947	−	0.839952i	−0.999850	+	0.0172957i	$0.994494\pi$
$864$		0			0
$865$	11.5885	−	20.0719i	0.394022	−	0.682466i
$866$		0			0
$867$	62.7386			2.13072
$868$		0			0
$869$	1.06913			0.0362678
$870$		0			0
$871$	7.50758	−	13.0035i	0.254385	−	0.440607i
$872$		0			0
$873$	−0.369317	−	0.639676i	−0.0124995	−	0.0216497i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.75379	+	11.6979i	0.228059	+	0.395010i	0.957233	−	0.289319i	$-0.0934287\pi$
$877$	6.75379	+	11.6979i	0.228059	+	0.395010i	−0.729174	+	0.684329i	$0.760095\pi$
$878$		0			0
$879$	25.0270	−	43.3480i	0.844139	−	1.46209i
$880$		0			0
$881$	−54.1080			−1.82294			−0.911472	−	0.411363i	$-0.865053\pi$
$881$	−54.1080			−1.82294			−0.911472	+	0.411363i	$0.865053\pi$
$882$		0			0
$883$	21.7538			0.732073			0.366037	−	0.930600i	$-0.380714\pi$
$883$	21.7538			0.732073			0.366037	+	0.930600i	$0.380714\pi$
$884$		0			0
$885$	3.12311	−	5.40938i	0.104982	−	0.181834i
$886$		0			0
$887$	−18.2462	−	31.6034i	−0.612648	−	1.06114i	−0.990792	−	0.135391i	$-0.956771\pi$
$887$	−18.2462	−	31.6034i	−0.612648	−	1.06114i	0.378144	−	0.925747i	$-0.376562\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.46543	+	9.46641i	0.183099	+	0.317137i
$892$		0			0
$893$	8.68466	−	15.0423i	0.290621	−	0.503370i
$894$		0			0
$895$	4.00000			0.133705
$896$		0			0
$897$	−32.6004			−1.08849
$898$		0			0
$899$	1.36932	−	2.37173i	0.0456693	−	0.0791015i
$900$		0			0
$901$	−49.6155	−	85.9366i	−1.65293	−	2.86296i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.56155	+	4.43674i	0.0851489	+	0.147482i
$906$		0			0
$907$	24.0540	−	41.6627i	0.798699	−	1.38339i	−0.121764	−	0.992559i	$-0.538855\pi$
$907$	24.0540	−	41.6627i	0.798699	−	1.38339i	0.920464	−	0.390828i	$-0.127811\pi$
$908$		0			0
$909$	3.36932			0.111753
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	9.36932	−	16.2281i	0.310079	−	0.537073i
$914$		0			0
$915$	5.36932	+	9.29993i	0.177504	+	0.307446i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.21922	−	2.11176i	−0.0402185	−	0.0696604i	0.845215	−	0.534426i	$-0.179472\pi$
$919$	−1.21922	−	2.11176i	−0.0402185	−	0.0696604i	−0.885434	+	0.464765i	$0.846139\pi$
$920$		0			0
$921$	−22.3963	+	38.7915i	−0.737983	+	1.27822i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−8.24621			−0.271134
$926$		0			0
$927$	3.31534	−	5.74234i	0.108890	−	0.188603i
$928$		0			0
$929$	−1.43845	−	2.49146i	−0.0471939	−	0.0817423i	0.841463	−	0.540314i	$-0.181695\pi$
$929$	−1.43845	−	2.49146i	−0.0471939	−	0.0817423i	−0.888657	+	0.458572i	$0.848361\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−10.0540	−	17.4140i	−0.329152	−	0.570109i
$934$		0			0
$935$	−5.90388	+	10.2258i	−0.193078	+	0.334420i
$936$		0			0
$937$	−37.8078			−1.23513			−0.617563	−	0.786521i	$-0.711880\pi$
$937$	−37.8078			−1.23513			−0.617563	+	0.786521i	$0.711880\pi$
$938$		0			0
$939$	−41.6695			−1.35983
$940$		0			0
$941$	14.3153	−	24.7949i	0.466667	−	0.808291i	−0.532608	−	0.846362i	$-0.678788\pi$
$941$	14.3153	−	24.7949i	0.466667	−	0.808291i	0.999275	+	0.0380713i	$0.0121214\pi$
$942$		0			0
$943$	−1.75379	−	3.03765i	−0.0571112	−	0.0989195i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.6155	+	30.5110i	0.572428	+	0.991474i	0.996316	+	0.0857594i	$0.0273316\pi$
$947$	17.6155	+	30.5110i	0.572428	+	0.991474i	−0.423888	+	0.905715i	$0.639335\pi$
$948$		0			0
$949$	14.1922	−	24.5817i	0.460699	−	0.797955i
$950$		0			0
$951$	−15.6155			−0.506368
$952$		0			0
$953$	−51.8617			−1.67997			−0.839983	−	0.542612i	$-0.817435\pi$
$953$	−51.8617			−1.67997			−0.839983	+	0.542612i	$0.817435\pi$
$954$		0			0
$955$	−0.342329	+	0.592932i	−0.0110775	+	0.0191868i
$956$		0			0
$957$	−0.534565	−	0.925894i	−0.0172800	−	0.0299299i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−4.00758	−	6.94133i	−0.129277	−	0.223914i
$962$		0			0
$963$	4.24621	−	7.35465i	0.136832	−	0.237000i
$964$		0			0
$965$	−13.1231			−0.422448
$966$		0			0
$967$	44.1080			1.41842			0.709208	−	0.704999i	$-0.249053\pi$
$967$	44.1080			1.41842			0.709208	+	0.704999i	$0.249053\pi$
$968$		0			0
$969$	42.0540	−	72.8396i	1.35097	−	2.33995i
$970$		0			0
$971$	−11.3693	−	19.6922i	−0.364859	−	0.631954i	0.623895	−	0.781508i	$-0.285549\pi$
$971$	−11.3693	−	19.6922i	−0.364859	−	0.631954i	−0.988753	+	0.149555i	$0.952216\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	5.21922	+	9.03996i	0.167149	+	0.289510i
$976$		0			0
$977$	−5.49242	+	9.51315i	−0.175718	+	0.304353i	−0.940410	−	0.340044i	$-0.889558\pi$
$977$	−5.49242	+	9.51315i	−0.175718	+	0.304353i	0.764691	+	0.644397i	$0.222891\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$		0			0
$981$	2.49242			0.0795769
$982$		0			0
$983$	−14.5885	+	25.2681i	−0.465302	+	0.805927i	−0.999215	−	0.0396124i	$-0.987388\pi$
$983$	−14.5885	+	25.2681i	−0.465302	+	0.805927i	0.533913	+	0.845539i	$0.320721\pi$
$984$		0			0
$985$	−6.56155	−	11.3649i	−0.209068	−	0.362117i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	11.1231	+	19.2658i	0.353694	+	0.612616i
$990$		0			0
$991$	10.2462	−	17.7470i	0.325482	−	0.563751i	−0.656128	−	0.754650i	$-0.727807\pi$
$991$	10.2462	−	17.7470i	0.325482	−	0.563751i	0.981610	+	0.190899i	$0.0611402\pi$
$992$		0			0
$993$	−18.7386			−0.594653
$994$		0			0
$995$	−14.2462			−0.451635
$996$		0			0
$997$	−28.4654	+	49.3036i	−0.901509	+	1.56146i	−0.0759739	+	0.997110i	$0.524207\pi$
$997$	−28.4654	+	49.3036i	−0.901509	+	1.56146i	−0.825535	+	0.564350i	$0.809127\pi$
$998$		0			0
$999$	−22.9309	−	39.7174i	−0.725501	−	1.25660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.u.361.1		4
7.2	even	3	inner	1960.2.q.u.961.1		4
7.3	odd	6		280.2.a.d.1.1	✓	2
7.4	even	3		1960.2.a.r.1.2		2
7.5	odd	6		1960.2.q.s.961.2		4
7.6	odd	2		1960.2.q.s.361.2		4
21.17	even	6		2520.2.a.w.1.1		2
28.3	even	6		560.2.a.g.1.2		2
28.11	odd	6		3920.2.a.bu.1.1		2
35.3	even	12		1400.2.g.k.449.2		4
35.4	even	6		9800.2.a.by.1.1		2
35.17	even	12		1400.2.g.k.449.3		4
35.24	odd	6		1400.2.a.p.1.2		2
56.3	even	6		2240.2.a.bi.1.1		2
56.45	odd	6		2240.2.a.be.1.2		2
84.59	odd	6		5040.2.a.bq.1.2		2
140.3	odd	12		2800.2.g.u.449.3		4
140.59	even	6		2800.2.a.bn.1.1		2
140.87	odd	12		2800.2.g.u.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.a.d.1.1	✓	2	7.3	odd	6
560.2.a.g.1.2		2	28.3	even	6
1400.2.a.p.1.2		2	35.24	odd	6
1400.2.g.k.449.2		4	35.3	even	12
1400.2.g.k.449.3		4	35.17	even	12
1960.2.a.r.1.2		2	7.4	even	3
1960.2.q.s.361.2		4	7.6	odd	2
1960.2.q.s.961.2		4	7.5	odd	6
1960.2.q.u.361.1		4	1.1	even	1	trivial
1960.2.q.u.961.1		4	7.2	even	3	inner
2240.2.a.be.1.2		2	56.45	odd	6
2240.2.a.bi.1.1		2	56.3	even	6
2520.2.a.w.1.1		2	21.17	even	6
2800.2.a.bn.1.1		2	140.59	even	6
2800.2.g.u.449.2		4	140.87	odd	12
2800.2.g.u.449.3		4	140.3	odd	12
3920.2.a.bu.1.1		2	28.11	odd	6
5040.2.a.bq.1.2		2	84.59	odd	6
9800.2.a.by.1.1		2	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.35234i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.280776 + 0.486319i) q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.35234i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.280776 + 0.486319i) q^{9} +(-0.780776 + 1.35234i) q^{11} -6.68466 q^{13} -1.56155 q^{15} +(3.78078 - 6.54850i) q^{17} +(-3.56155 - 6.16879i) q^{19} +(-1.56155 - 2.70469i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.56155 q^{27} +0.438447 q^{29} +(3.12311 - 5.40938i) q^{31} +(-1.21922 - 2.11176i) q^{33} +(4.12311 + 7.14143i) q^{37} +(5.21922 - 9.03996i) q^{39} +1.12311 q^{41} -7.12311 q^{43} +(-0.280776 + 0.486319i) q^{45} +(1.21922 + 2.11176i) q^{47} +(5.90388 + 10.2258i) q^{51} +(6.56155 - 11.3649i) q^{53} -1.56155 q^{55} +11.1231 q^{57} +(-2.00000 + 3.46410i) q^{59} +(-3.43845 - 5.95557i) q^{61} +(-3.34233 - 5.78908i) q^{65} +(-1.12311 + 1.94528i) q^{67} +4.87689 q^{69} +(-2.12311 + 3.67733i) q^{73} +(-0.780776 - 1.35234i) q^{75} +(-0.342329 - 0.592932i) q^{79} +(3.50000 - 6.06218i) q^{81} -12.0000 q^{83} +7.56155 q^{85} +(-0.342329 + 0.592932i) q^{87} +(2.56155 + 4.43674i) q^{89} +(4.87689 + 8.44703i) q^{93} +(3.56155 - 6.16879i) q^{95} -1.31534 q^{97} -0.876894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 2 q^{5} - 3 q^{9}+O(q^{10}) \) 4 * q + q^3 + 2 * q^5 - 3 * q^9	\( 4 q + q^{3} + 2 q^{5} - 3 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} + 11 q^{17} - 6 q^{19} + 2 q^{23} - 2 q^{25} - 14 q^{27} + 10 q^{29} - 4 q^{31} - 9 q^{33} + 25 q^{39} - 12 q^{41} - 12 q^{43} + 3 q^{45} + 9 q^{47} + 3 q^{51} + 18 q^{53} + 2 q^{55} + 28 q^{57} - 8 q^{59} - 22 q^{61} - q^{65} + 12 q^{67} + 36 q^{69} + 8 q^{73} + q^{75} + 11 q^{79} + 14 q^{81} - 48 q^{83} + 22 q^{85} + 11 q^{87} + 2 q^{89} + 36 q^{93} + 6 q^{95} - 30 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q + q^3 + 2 * q^5 - 3 * q^9 + q^11 - 2 * q^13 + 2 * q^15 + 11 * q^17 - 6 * q^19 + 2 * q^23 - 2 * q^25 - 14 * q^27 + 10 * q^29 - 4 * q^31 - 9 * q^33 + 25 * q^39 - 12 * q^41 - 12 * q^43 + 3 * q^45 + 9 * q^47 + 3 * q^51 + 18 * q^53 + 2 * q^55 + 28 * q^57 - 8 * q^59 - 22 * q^61 - q^65 + 12 * q^67 + 36 * q^69 + 8 * q^73 + q^75 + 11 * q^79 + 14 * q^81 - 48 * q^83 + 22 * q^85 + 11 * q^87 + 2 * q^89 + 36 * q^93 + 6 * q^95 - 30 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more