LMFDB - Embedded newform 1680.2.bg.v.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29428272.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 $ x^6 - 6x^4 - 4x^3 - 42*x^2 + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$-0.0741344 - 2.64471i$ of defining polynomial
Character	$\chi$	$=$	1680.961
Dual form			1680.2.bg.v.1201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.0741344 - 2.64471i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.0741344 - 2.64471i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.08078 + 5.33606i) q^{11} +2.50664 q^{13} +1.00000 q^{15} +(-2.90159 - 5.02570i) q^{17} +(0.500000 - 0.866025i) q^{19} +(2.32746 - 1.25815i) q^{21} +(-0.425866 + 0.737621i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +5.50664 q^{29} +(3.67919 + 6.37254i) q^{31} +(-3.08078 + 5.33606i) q^{33} +(-2.25332 - 1.38656i) q^{35} +(4.90823 - 8.50131i) q^{37} +(1.25332 + 2.17082i) q^{39} -3.14827 q^{41} +7.16155 q^{43} +(0.500000 + 0.866025i) q^{45} +(-1.17919 + 2.04241i) q^{47} +(-6.98901 - 0.392129i) q^{49} +(2.90159 - 5.02570i) q^{51} +(0.672545 + 1.16488i) q^{53} +6.16155 q^{55} +1.00000 q^{57} +(3.24668 + 5.62341i) q^{59} +(2.25332 + 1.38656i) q^{63} +(1.25332 - 2.17082i) q^{65} +(-3.58078 - 6.20209i) q^{67} -0.851731 q^{69} +15.1130 q^{71} +(-2.92587 - 5.06775i) q^{73} +(0.500000 - 0.866025i) q^{75} +(14.3407 - 7.75218i) q^{77} +(6.33410 - 10.9710i) q^{79} +(-0.500000 - 0.866025i) q^{81} -5.50664 q^{83} -5.80318 q^{85} +(2.75332 + 4.76889i) q^{87} +(5.40823 - 9.36733i) q^{89} +(0.185828 - 6.62935i) q^{91} +(-3.67919 + 6.37254i) q^{93} +(-0.500000 - 0.866025i) q^{95} +8.00000 q^{97} -6.16155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9	$ 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{15} - 6 q^{17} + 3 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{25} - 6 q^{27} + 12 q^{29} + 12 q^{31} + 3 q^{33} - 3 q^{35} - 3 q^{37} - 3 q^{39} - 18 q^{41} + 3 q^{45} + 3 q^{47} + 12 q^{49} + 6 q^{51} + 15 q^{53} - 6 q^{55} + 6 q^{57} + 30 q^{59} + 3 q^{63} - 3 q^{65} - 6 q^{69} + 24 q^{71} - 18 q^{73} + 3 q^{75} + 33 q^{77} + 6 q^{79} - 3 q^{81} - 12 q^{83} - 12 q^{85} + 6 q^{87} - 30 q^{91} - 12 q^{93} - 3 q^{95} + 48 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^15 - 6 * q^17 + 3 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^25 - 6 * q^27 + 12 * q^29 + 12 * q^31 + 3 * q^33 - 3 * q^35 - 3 * q^37 - 3 * q^39 - 18 * q^41 + 3 * q^45 + 3 * q^47 + 12 * q^49 + 6 * q^51 + 15 * q^53 - 6 * q^55 + 6 * q^57 + 30 * q^59 + 3 * q^63 - 3 * q^65 - 6 * q^69 + 24 * q^71 - 18 * q^73 + 3 * q^75 + 33 * q^77 + 6 * q^79 - 3 * q^81 - 12 * q^83 - 12 * q^85 + 6 * q^87 - 30 * q^91 - 12 * q^93 - 3 * q^95 + 48 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.0741344	−	2.64471i	0.0280202	−	0.999607i
$7$	0.0741344	−	2.64471i	0.0280202	−	0.999607i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.08078	+	5.33606i	0.928889	+	1.60888i	0.785184	+	0.619262i	$0.212568\pi$
$11$	3.08078	+	5.33606i	0.928889	+	1.60888i	0.143705	+	0.989621i	$0.454098\pi$
$12$		0			0
$13$	2.50664			0.695217			0.347609	−	0.937640i	$-0.386994\pi$
$13$	2.50664			0.695217			0.347609	+	0.937640i	$0.386994\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−2.90159	−	5.02570i	−0.703739	−	1.21891i	−0.967145	−	0.254226i	$-0.918179\pi$
$17$	−2.90159	−	5.02570i	−0.703739	−	1.21891i	0.263406	−	0.964685i	$-0.415154\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	2.32746	−	1.25815i	0.507892	−	0.274552i
$22$		0			0
$23$	−0.425866	+	0.737621i	−0.0887991	+	0.153805i	−0.907004	−	0.421122i	$-0.861636\pi$
$23$	−0.425866	+	0.737621i	−0.0887991	+	0.153805i	0.818205	+	0.574927i	$0.194970\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	5.50664			1.02256			0.511279	−	0.859415i	$-0.329172\pi$
$29$	5.50664			1.02256			0.511279	+	0.859415i	$0.329172\pi$
$30$		0			0
$31$	3.67919	+	6.37254i	0.660801	+	1.14454i	0.980405	+	0.196990i	$0.0631168\pi$
$31$	3.67919	+	6.37254i	0.660801	+	1.14454i	−0.319604	+	0.947551i	$0.603550\pi$
$32$		0			0
$33$	−3.08078	+	5.33606i	−0.536294	+	0.928889i
$34$		0			0
$35$	−2.25332	−	1.38656i	−0.380881	−	0.234371i
$36$		0			0
$37$	4.90823	−	8.50131i	0.806908	−	1.39761i	−0.108087	−	0.994141i	$-0.534472\pi$
$37$	4.90823	−	8.50131i	0.806908	−	1.39761i	0.914995	−	0.403465i	$-0.132194\pi$
$38$		0			0
$39$	1.25332	+	2.17082i	0.200692	+	0.347609i
$40$		0			0
$41$	−3.14827			−0.491677			−0.245838	−	0.969311i	$-0.579063\pi$
$41$	−3.14827			−0.491677			−0.245838	+	0.969311i	$0.579063\pi$
$42$		0			0
$43$	7.16155			1.09213			0.546063	−	0.837744i	$-0.316126\pi$
$43$	7.16155			1.09213			0.546063	+	0.837744i	$0.316126\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	−1.17919	+	2.04241i	−0.172002	+	0.297916i	−0.939120	−	0.343590i	$-0.888357\pi$
$47$	−1.17919	+	2.04241i	−0.172002	+	0.297916i	0.767118	+	0.641506i	$0.221690\pi$
$48$		0			0
$49$	−6.98901	−	0.392129i	−0.998430	−	0.0560184i
$50$		0			0
$51$	2.90159	−	5.02570i	0.406304	−	0.703739i
$52$		0			0
$53$	0.672545	+	1.16488i	0.0923811	+	0.160009i	0.908513	−	0.417857i	$-0.137219\pi$
$53$	0.672545	+	1.16488i	0.0923811	+	0.160009i	−0.816131	+	0.577866i	$0.803886\pi$
$54$		0			0
$55$	6.16155			0.830824
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	3.24668	+	5.62341i	0.422682	+	0.732106i	0.996201	−	0.0870861i	$-0.0277555\pi$
$59$	3.24668	+	5.62341i	0.422682	+	0.732106i	−0.573519	+	0.819192i	$0.694422\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$	2.25332	+	1.38656i	0.283892	+	0.174690i
$64$		0			0
$65$	1.25332	−	2.17082i	0.155455	−	0.269257i
$66$		0			0
$67$	−3.58078	−	6.20209i	−0.437461	−	0.757705i	0.560031	−	0.828471i	$-0.310789\pi$
$67$	−3.58078	−	6.20209i	−0.437461	−	0.757705i	−0.997493	+	0.0707658i	$0.977456\pi$
$68$		0			0
$69$	−0.851731			−0.102536
$70$		0			0
$71$	15.1130			1.79358			0.896792	−	0.442453i	$-0.145892\pi$
$71$	15.1130			1.79358			0.896792	+	0.442453i	$0.145892\pi$
$72$		0			0
$73$	−2.92587	−	5.06775i	−0.342447	−	0.593135i	0.642440	−	0.766336i	$-0.277922\pi$
$73$	−2.92587	−	5.06775i	−0.342447	−	0.593135i	−0.984886	+	0.173201i	$0.944589\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	14.3407	−	7.75218i	1.63428	−	0.883443i
$78$		0			0
$79$	6.33410	−	10.9710i	0.712642	−	1.23433i	−0.251220	−	0.967930i	$-0.580832\pi$
$79$	6.33410	−	10.9710i	0.712642	−	1.23433i	0.963862	−	0.266402i	$-0.0858347\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−5.50664			−0.604432			−0.302216	−	0.953239i	$-0.597726\pi$
$83$	−5.50664			−0.604432			−0.302216	+	0.953239i	$0.597726\pi$
$84$		0			0
$85$	−5.80318			−0.629443
$86$		0			0
$87$	2.75332	+	4.76889i	0.295187	+	0.511279i
$88$		0			0
$89$	5.40823	−	9.36733i	0.573271	−	0.992935i	−0.422956	−	0.906150i	$-0.639007\pi$
$89$	5.40823	−	9.36733i	0.573271	−	0.992935i	0.996227	−	0.0867848i	$-0.0276593\pi$
$90$		0			0
$91$	0.185828	−	6.62935i	0.0194801	−	0.694944i
$92$		0			0
$93$	−3.67919	+	6.37254i	−0.381514	+	0.660801i
$94$		0			0
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−6.16155			−0.619259
$100$		0			0
$101$	−1.09841	−	1.90250i	−0.109296	−	0.189306i	0.806189	−	0.591658i	$-0.201526\pi$
$101$	−1.09841	−	1.90250i	−0.109296	−	0.189306i	−0.915485	+	0.402352i	$0.868193\pi$
$102$		0			0
$103$	−5.08742	+	8.81167i	−0.501278	+	0.868239i	0.498721	+	0.866763i	$0.333803\pi$
$103$	−5.08742	+	8.81167i	−0.501278	+	0.868239i	−0.999999	+	0.00147659i	$0.999530\pi$
$104$		0			0
$105$	0.0741344	−	2.64471i	0.00723478	−	0.258098i
$106$		0			0
$107$	−5.55650	+	9.62414i	−0.537167	+	0.930401i	0.461888	+	0.886938i	$0.347172\pi$
$107$	−5.55650	+	9.62414i	−0.537167	+	0.930401i	−0.999055	+	0.0434625i	$0.986161\pi$
$108$		0			0
$109$	3.33410	+	5.77483i	0.319349	+	0.553128i	0.980352	−	0.197255i	$-0.0632026\pi$
$109$	3.33410	+	5.77483i	0.319349	+	0.553128i	−0.661004	+	0.750383i	$0.729869\pi$
$110$		0			0
$111$	9.81646			0.931737
$112$		0			0
$113$	20.6196			1.93973			0.969866	−	0.243637i	$-0.0783406\pi$
$113$	20.6196			1.93973			0.969866	+	0.243637i	$0.0783406\pi$
$114$		0			0
$115$	0.425866	+	0.737621i	0.0397122	+	0.0687835i
$116$		0			0
$117$	−1.25332	+	2.17082i	−0.115870	+	0.200692i
$118$		0			0
$119$	−13.5066	+	7.30129i	−1.23815	+	0.669308i
$120$		0			0
$121$	−13.4824	+	23.3521i	−1.22567	+	2.12292i
$122$		0			0
$123$	−1.57413	−	2.72648i	−0.141935	−	0.245838i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.11300			−0.719912			−0.359956	−	0.932969i	$-0.617208\pi$
$127$	−8.11300			−0.719912			−0.359956	+	0.932969i	$0.617208\pi$
$128$		0			0
$129$	3.58078	+	6.20209i	0.315270	+	0.546063i
$130$		0			0
$131$	2.32746	−	4.03127i	0.203351	−	0.352214i	−0.746255	−	0.665660i	$-0.768150\pi$
$131$	2.32746	−	4.03127i	0.203351	−	0.352214i	0.949606	+	0.313446i	$0.101484\pi$
$132$		0			0
$133$	−2.25332	−	1.38656i	−0.195388	−	0.120230i
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	10.7666	+	18.6483i	0.919853	+	1.59323i	0.799636	+	0.600485i	$0.205026\pi$
$137$	10.7666	+	18.6483i	0.919853	+	1.59323i	0.120217	+	0.992748i	$0.461641\pi$
$138$		0			0
$139$	−16.9647			−1.43893			−0.719465	−	0.694529i	$-0.755613\pi$
$139$	−16.9647			−1.43893			−0.719465	+	0.694529i	$0.755613\pi$
$140$		0			0
$141$	−2.35837			−0.198611
$142$		0			0
$143$	7.72240	+	13.3756i	0.645780	+	1.11852i
$144$		0			0
$145$	2.75332	−	4.76889i	0.228651	−	0.396035i
$146$		0			0
$147$	−3.15491	−	6.24872i	−0.260213	−	0.515386i
$148$		0			0
$149$	−11.0133	+	19.0756i	−0.902243	+	1.56273i	−0.0776680	+	0.996979i	$0.524747\pi$
$149$	−11.0133	+	19.0756i	−0.902243	+	1.56273i	−0.824575	+	0.565752i	$0.808586\pi$
$150$		0			0
$151$	−4.30982	−	7.46483i	−0.350728	−	0.607479i	0.635649	−	0.771978i	$-0.280733\pi$
$151$	−4.30982	−	7.46483i	−0.350728	−	0.607479i	−0.986377	+	0.164499i	$0.947399\pi$
$152$		0			0
$153$	5.80318			0.469159
$154$		0			0
$155$	7.35837			0.591039
$156$		0			0
$157$	2.03092	+	3.51765i	0.162085	+	0.280739i	0.935616	−	0.353019i	$-0.114845\pi$
$157$	2.03092	+	3.51765i	0.162085	+	0.280739i	−0.773531	+	0.633758i	$0.781511\pi$
$158$		0			0
$159$	−0.672545	+	1.16488i	−0.0533363	+	0.0923811i
$160$		0			0
$161$	1.91922	+	1.18098i	0.151256	+	0.0930739i
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$	3.08078	+	5.33606i	0.239838	+	0.415412i
$166$		0			0
$167$	9.47137			0.732917			0.366458	−	0.930434i	$-0.380570\pi$
$167$	9.47137			0.732917			0.366458	+	0.930434i	$0.380570\pi$
$168$		0			0
$169$	−6.71675			−0.516673
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$		0			0
$173$	−1.03092	+	1.78560i	−0.0783792	+	0.135757i	−0.902551	−	0.430583i	$-0.858308\pi$
$173$	−1.03092	+	1.78560i	−0.0783792	+	0.135757i	0.824172	+	0.566340i	$0.191641\pi$
$174$		0			0
$175$	−2.32746	+	1.25815i	−0.175939	+	0.0951075i
$176$		0			0
$177$	−3.24668	+	5.62341i	−0.244035	+	0.422682i
$178$		0			0
$179$	−0.524276	−	0.908072i	−0.0391862	−	0.0678725i	0.845767	−	0.533552i	$-0.179143\pi$
$179$	−0.524276	−	0.908072i	−0.0391862	−	0.0678725i	−0.884953	+	0.465680i	$0.845810\pi$
$180$		0			0
$181$	−4.37166			−0.324943			−0.162471	−	0.986713i	$-0.551947\pi$
$181$	−4.37166			−0.324943			−0.162471	+	0.986713i	$0.551947\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.90823	−	8.50131i	−0.360860	−	0.625029i
$186$		0			0
$187$	17.8783	−	30.9661i	1.30739	−	2.26447i
$188$		0			0
$189$	−0.0741344	+	2.64471i	−0.00539249	+	0.192375i
$190$		0			0
$191$	−10.0133	+	17.3435i	−0.724536	+	1.25493i	0.234629	+	0.972085i	$0.424612\pi$
$191$	−10.0133	+	17.3435i	−0.724536	+	1.25493i	−0.959165	+	0.282848i	$0.908721\pi$
$192$		0			0
$193$	−4.08742	−	7.07962i	−0.294219	−	0.509602i	0.680584	−	0.732670i	$-0.261726\pi$
$193$	−4.08742	−	7.07962i	−0.294219	−	0.509602i	−0.974803	+	0.223068i	$0.928393\pi$
$194$		0			0
$195$	2.50664			0.179504
$196$		0			0
$197$	9.17484			0.653680			0.326840	−	0.945080i	$-0.394016\pi$
$197$	9.17484			0.653680			0.326840	+	0.945080i	$0.394016\pi$
$198$		0			0
$199$	−1.35837	−	2.35277i	−0.0962925	−	0.166784i	0.813855	−	0.581068i	$-0.197365\pi$
$199$	−1.35837	−	2.35277i	−0.0962925	−	0.166784i	−0.910147	+	0.414285i	$0.864032\pi$
$200$		0			0
$201$	3.58078	−	6.20209i	0.252568	−	0.437461i
$202$		0			0
$203$	0.408232	−	14.5635i	0.0286523	−	1.02216i
$204$		0			0
$205$	−1.57413	+	2.72648i	−0.109942	+	0.190426i
$206$		0			0
$207$	−0.425866	−	0.737621i	−0.0295997	−	0.0512682i
$208$		0			0
$209$	6.16155			0.426204
$210$		0			0
$211$	−2.95145			−0.203186			−0.101593	−	0.994826i	$-0.532394\pi$
$211$	−2.95145			−0.203186			−0.101593	+	0.994826i	$0.532394\pi$
$212$		0			0
$213$	7.55650	+	13.0882i	0.517763	+	0.896792i
$214$		0			0
$215$	3.58078	−	6.20209i	0.244207	−	0.422979i
$216$		0			0
$217$	17.1263	−	9.25797i	1.16261	−	0.628472i
$218$		0			0
$219$	2.92587	−	5.06775i	0.197712	−	0.342447i
$220$		0			0
$221$	−7.27325	−	12.5976i	−0.489252	−	0.847408i
$222$		0			0
$223$	−23.0133			−1.54108			−0.770542	−	0.637390i	$-0.780014\pi$
$223$	−23.0133			−1.54108			−0.770542	+	0.637390i	$0.780014\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−4.55650	−	7.89209i	−0.302426	−	0.523816i	0.674259	−	0.738495i	$-0.264463\pi$
$227$	−4.55650	−	7.89209i	−0.302426	−	0.523816i	−0.976685	+	0.214678i	$0.931130\pi$
$228$		0			0
$229$	9.67919	−	16.7648i	0.639619	−	1.10785i	−0.345898	−	0.938272i	$-0.612426\pi$
$229$	9.67919	−	16.7648i	0.639619	−	1.10785i	0.985516	−	0.169580i	$-0.0542411\pi$
$230$		0			0
$231$	13.8840	+	8.54335i	0.913497	+	0.562111i
$232$		0			0
$233$	−6.50664	+	11.2698i	−0.426264	+	0.738311i	−0.996538	−	0.0831436i	$-0.973504\pi$
$233$	−6.50664	+	11.2698i	−0.426264	+	0.738311i	0.570273	+	0.821455i	$0.306837\pi$
$234$		0			0
$235$	1.17919	+	2.04241i	0.0769216	+	0.133232i
$236$		0			0
$237$	12.6682			0.822888
$238$		0			0
$239$	−4.02657			−0.260457			−0.130229	−	0.991484i	$-0.541571\pi$
$239$	−4.02657			−0.260457			−0.130229	+	0.991484i	$0.541571\pi$
$240$		0			0
$241$	−6.67254	−	11.5572i	−0.429816	−	0.744464i	0.567040	−	0.823690i	$-0.308088\pi$
$241$	−6.67254	−	11.5572i	−0.429816	−	0.744464i	−0.996857	+	0.0792263i	$0.974755\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−3.83410	+	5.85659i	−0.244951	+	0.374164i
$246$		0			0
$247$	1.25332	−	2.17082i	0.0797469	−	0.138126i
$248$		0			0
$249$	−2.75332	−	4.76889i	−0.174485	−	0.302216i
$250$		0			0
$251$	−29.7945			−1.88061			−0.940305	−	0.340332i	$-0.889461\pi$
$251$	−29.7945			−1.88061			−0.940305	+	0.340332i	$0.889461\pi$
$252$		0			0
$253$	−5.24799			−0.329938
$254$		0			0
$255$	−2.90159	−	5.02570i	−0.181705	−	0.314722i
$256$		0			0
$257$	4.06314	−	7.03757i	0.253452	−	0.438992i	−0.711022	−	0.703170i	$-0.751767\pi$
$257$	4.06314	−	7.03757i	0.253452	−	0.438992i	0.964474	+	0.264178i	$0.0851007\pi$
$258$		0			0
$259$	−22.1196	−	13.6111i	−1.37445	−	0.845753i
$260$		0			0
$261$	−2.75332	+	4.76889i	−0.170426	+	0.295187i
$262$		0			0
$263$	−5.50664	−	9.53778i	−0.339554	−	0.588125i	0.644795	−	0.764356i	$-0.276943\pi$
$263$	−5.50664	−	9.53778i	−0.339554	−	0.588125i	−0.984349	+	0.176231i	$0.943609\pi$
$264$		0			0
$265$	1.34509			0.0826282
$266$		0			0
$267$	10.8165			0.661957
$268$		0			0
$269$	−1.85173	−	3.20729i	−0.112902	−	0.195552i	0.804037	−	0.594579i	$-0.202681\pi$
$269$	−1.85173	−	3.20729i	−0.112902	−	0.195552i	−0.916939	+	0.399027i	$0.869348\pi$
$270$		0			0
$271$	13.6549	−	23.6510i	0.829477	−	1.43670i	−0.0689725	−	0.997619i	$-0.521972\pi$
$271$	13.6549	−	23.6510i	0.829477	−	1.43670i	0.898449	−	0.439077i	$-0.144695\pi$
$272$		0			0
$273$	5.83410	−	3.15374i	0.353096	−	0.190873i
$274$		0			0
$275$	3.08078	−	5.33606i	0.185778	−	0.321777i
$276$		0			0
$277$	−3.74233	−	6.48190i	−0.224855	−	0.389460i	0.731421	−	0.681926i	$-0.238857\pi$
$277$	−3.74233	−	6.48190i	−0.224855	−	0.389460i	−0.956276	+	0.292466i	$0.905524\pi$
$278$		0			0
$279$	−7.35837			−0.440534
$280$		0			0
$281$	−24.2878			−1.44889			−0.724445	−	0.689332i	$-0.757904\pi$
$281$	−24.2878			−1.44889			−0.724445	+	0.689332i	$0.757904\pi$
$282$		0			0
$283$	12.5808	+	21.7905i	0.747850	+	1.29531i	0.948852	+	0.315723i	$0.102247\pi$
$283$	12.5808	+	21.7905i	0.747850	+	1.29531i	−0.201002	+	0.979591i	$0.564420\pi$
$284$		0			0
$285$	0.500000	−	0.866025i	0.0296174	−	0.0512989i
$286$		0			0
$287$	−0.233395	+	8.32627i	−0.0137769	+	0.491484i
$288$		0			0
$289$	−8.33845	+	14.4426i	−0.490497	+	0.849566i
$290$		0			0
$291$	4.00000	+	6.92820i	0.234484	+	0.406138i
$292$		0			0
$293$	−25.6682			−1.49955			−0.749776	−	0.661692i	$-0.769839\pi$
$293$	−25.6682			−1.49955			−0.749776	+	0.661692i	$0.769839\pi$
$294$		0			0
$295$	6.49336			0.378058
$296$		0			0
$297$	−3.08078	−	5.33606i	−0.178765	−	0.309630i
$298$		0			0
$299$	−1.06749	+	1.84895i	−0.0617347	+	0.106928i
$300$		0			0
$301$	0.530918	−	18.9402i	0.0306016	−	1.09170i
$302$		0			0
$303$	1.09841	−	1.90250i	0.0631020	−	0.109296i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−31.0644			−1.77294			−0.886471	−	0.462784i	$-0.846850\pi$
$307$	−31.0644			−1.77294			−0.886471	+	0.462784i	$0.846850\pi$
$308$		0			0
$309$	−10.1748			−0.578826
$310$		0			0
$311$	13.4215	+	23.2467i	0.761064	+	1.31820i	0.942302	+	0.334763i	$0.108656\pi$
$311$	13.4215	+	23.2467i	0.761064	+	1.31820i	−0.181238	+	0.983439i	$0.558010\pi$
$312$		0			0
$313$	−9.03887	+	15.6558i	−0.510907	+	0.884917i	0.489013	+	0.872276i	$0.337357\pi$
$313$	−9.03887	+	15.6558i	−0.510907	+	0.884917i	−0.999920	+	0.0126404i	$0.995976\pi$
$314$		0			0
$315$	2.32746	−	1.25815i	0.131137	−	0.0708889i
$316$		0			0
$317$	7.75332	−	13.4291i	0.435470	−	0.754256i	−0.561864	−	0.827230i	$-0.689916\pi$
$317$	7.75332	−	13.4291i	0.435470	−	0.754256i	0.997334	+	0.0729737i	$0.0232489\pi$
$318$		0			0
$319$	16.9647	+	29.3838i	0.949843	+	1.64518i
$320$		0			0
$321$	−11.1130			−0.620267
$322$		0			0
$323$	−5.80318			−0.322898
$324$		0			0
$325$	−1.25332	−	2.17082i	−0.0695217	−	0.120415i
$326$		0			0
$327$	−3.33410	+	5.77483i	−0.184376	+	0.319349i
$328$		0			0
$329$	5.31417	+	3.27002i	0.292980	+	0.180282i
$330$		0			0
$331$	10.3650	−	17.9527i	0.569713	−	0.986771i	−0.426881	−	0.904308i	$-0.640388\pi$
$331$	10.3650	−	17.9527i	0.569713	−	0.986771i	0.996594	−	0.0824638i	$-0.0262789\pi$
$332$		0			0
$333$	4.90823	+	8.50131i	0.268969	+	0.465869i
$334$		0			0
$335$	−7.16155			−0.391277
$336$		0			0
$337$	−27.7546			−1.51189			−0.755945	−	0.654635i	$-0.772823\pi$
$337$	−27.7546			−1.51189			−0.755945	+	0.654635i	$0.772823\pi$
$338$		0			0
$339$	10.3098	+	17.8571i	0.559953	+	0.969866i
$340$		0			0
$341$	−22.6695	+	39.2647i	−1.22762	+	2.12630i
$342$		0			0
$343$	−1.55519	+	18.4548i	−0.0839725	+	0.996468i
$344$		0			0
$345$	−0.425866	+	0.737621i	−0.0229278	+	0.0397122i
$346$		0			0
$347$	−13.9647	−	24.1876i	−0.749666	−	1.29846i	−0.947983	−	0.318322i	$-0.896881\pi$
$347$	−13.9647	−	24.1876i	−0.749666	−	1.29846i	0.198317	−	0.980138i	$-0.436453\pi$
$348$		0			0
$349$	6.71675			0.359539			0.179770	−	0.983709i	$-0.442465\pi$
$349$	6.71675			0.359539			0.179770	+	0.983709i	$0.442465\pi$
$350$		0			0
$351$	−2.50664			−0.133795
$352$		0			0
$353$	−3.74004	−	6.47793i	−0.199062	−	0.344786i	0.749162	−	0.662386i	$-0.230456\pi$
$353$	−3.74004	−	6.47793i	−0.199062	−	0.344786i	−0.948225	+	0.317601i	$0.897123\pi$
$354$		0			0
$355$	7.55650	−	13.0882i	0.401057	−	0.694652i
$356$		0			0
$357$	−13.0764	−	8.04645i	−0.692078	−	0.425863i
$358$		0			0
$359$	−15.7666	+	27.3086i	−0.832130	+	1.44129i	0.0642167	+	0.997936i	$0.479545\pi$
$359$	−15.7666	+	27.3086i	−0.832130	+	1.44129i	−0.896346	+	0.443355i	$0.853788\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$	−26.9647			−1.41528
$364$		0			0
$365$	−5.85173			−0.306294
$366$		0			0
$367$	−16.0565	−	27.8107i	−0.838143	−	1.45171i	−0.891446	−	0.453127i	$-0.850308\pi$
$367$	−16.0565	−	27.8107i	−0.838143	−	1.45171i	0.0533034	−	0.998578i	$-0.483025\pi$
$368$		0			0
$369$	1.57413	−	2.72648i	0.0819462	−	0.141935i
$370$		0			0
$371$	3.13064	−	1.69233i	0.162534	−	0.0878614i
$372$		0			0
$373$	9.79088	−	16.9583i	0.506953	−	0.878068i	−0.493015	−	0.870021i	$-0.664105\pi$
$373$	9.79088	−	16.9583i	0.506953	−	0.878068i	0.999968	−	0.00804684i	$-0.00256142\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	13.8032			0.710900
$378$		0			0
$379$	−23.0266			−1.18280			−0.591398	−	0.806380i	$-0.701424\pi$
$379$	−23.0266			−1.18280			−0.591398	+	0.806380i	$0.701424\pi$
$380$		0			0
$381$	−4.05650	−	7.02607i	−0.207821	−	0.359956i
$382$		0			0
$383$	−0.637277	+	1.10380i	−0.0325633	+	0.0564014i	−0.881848	−	0.471534i	$-0.843700\pi$
$383$	−0.637277	+	1.10380i	−0.0325633	+	0.0564014i	0.849284	+	0.527936i	$0.177034\pi$
$384$		0			0
$385$	0.456783	−	16.2955i	0.0232798	−	0.830497i
$386$		0			0
$387$	−3.58078	+	6.20209i	−0.182021	+	0.315270i
$388$		0			0
$389$	13.0631	+	22.6260i	0.662328	+	1.14719i	0.980002	+	0.198985i	$0.0637646\pi$
$389$	13.0631	+	22.6260i	0.662328	+	1.14719i	−0.317675	+	0.948200i	$0.602902\pi$
$390$		0			0
$391$	4.94275			0.249966
$392$		0			0
$393$	4.65491			0.234809
$394$		0			0
$395$	−6.33410	−	10.9710i	−0.318703	−	0.552010i
$396$		0			0
$397$	15.7423	−	27.2665i	0.790085	−	1.36847i	−0.135829	−	0.990732i	$-0.543370\pi$
$397$	15.7423	−	27.2665i	0.790085	−	1.36847i	0.925914	−	0.377735i	$-0.123297\pi$
$398$		0			0
$399$	0.0741344	−	2.64471i	0.00371136	−	0.132401i
$400$		0			0
$401$	8.34074	−	14.4466i	0.416517	−	0.721428i	−0.579070	−	0.815278i	$-0.696584\pi$
$401$	8.34074	−	14.4466i	0.416517	−	0.721428i	0.995586	+	0.0938501i	$0.0299174\pi$
$402$		0			0
$403$	9.22240	+	15.9737i	0.459401	+	0.795705i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	60.4847			2.99811
$408$		0			0
$409$	−7.03756	−	12.1894i	−0.347985	−	0.602728i	0.637906	−	0.770114i	$-0.279801\pi$
$409$	−7.03756	−	12.1894i	−0.347985	−	0.602728i	−0.985891	+	0.167386i	$0.946467\pi$
$410$		0			0
$411$	−10.7666	+	18.6483i	−0.531077	+	0.919853i
$412$		0			0
$413$	15.1130	−	8.16964i	0.743662	−	0.402002i
$414$		0			0
$415$	−2.75332	+	4.76889i	−0.135155	+	0.234096i
$416$		0			0
$417$	−8.48237	−	14.6919i	−0.415383	−	0.719465i
$418$		0			0
$419$	32.5844			1.59185			0.795925	−	0.605395i	$-0.206985\pi$
$419$	32.5844			1.59185			0.795925	+	0.605395i	$0.206985\pi$
$420$		0			0
$421$	14.5711			0.710152			0.355076	−	0.934838i	$-0.384455\pi$
$421$	14.5711			0.710152			0.355076	+	0.934838i	$0.384455\pi$
$422$		0			0
$423$	−1.17919	−	2.04241i	−0.0573340	−	0.0993054i
$424$		0			0
$425$	−2.90159	+	5.02570i	−0.140748	+	0.243782i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7.72240	+	13.3756i	−0.372841	+	0.645780i
$430$		0			0
$431$	0.148269	+	0.256809i	0.00714186	+	0.0123701i	0.869574	−	0.493802i	$-0.164393\pi$
$431$	0.148269	+	0.256809i	0.00714186	+	0.0123701i	−0.862432	+	0.506172i	$0.831060\pi$
$432$		0			0
$433$	−33.0910			−1.59025			−0.795126	−	0.606444i	$-0.792596\pi$
$433$	−33.0910			−1.59025			−0.795126	+	0.606444i	$0.792596\pi$
$434$		0			0
$435$	5.50664			0.264023
$436$		0			0
$437$	0.425866	+	0.737621i	0.0203719	+	0.0352852i
$438$		0			0
$439$	−14.4714	+	25.0652i	−0.690681	+	1.19629i	0.280934	+	0.959727i	$0.409356\pi$
$439$	−14.4714	+	25.0652i	−0.690681	+	1.19629i	−0.971615	+	0.236568i	$0.923978\pi$
$440$		0			0
$441$	3.83410	−	5.85659i	0.182576	−	0.278885i
$442$		0			0
$443$	5.50664	−	9.53778i	0.261628	−	0.453154i	−0.705046	−	0.709161i	$-0.749074\pi$
$443$	5.50664	−	9.53778i	0.261628	−	0.453154i	0.966675	+	0.256007i	$0.0824072\pi$
$444$		0			0
$445$	−5.40823	−	9.36733i	−0.256375	−	0.444054i
$446$		0			0
$447$	−22.0266			−1.04182
$448$		0			0
$449$	−16.9780			−0.801242			−0.400621	−	0.916244i	$-0.631206\pi$
$449$	−16.9780			−0.801242			−0.400621	+	0.916244i	$0.631206\pi$
$450$		0			0
$451$	−9.69911	−	16.7994i	−0.456713	−	0.791051i
$452$		0			0
$453$	4.30982	−	7.46483i	0.202493	−	0.350728i
$454$		0			0
$455$	−5.64827	−	3.47561i	−0.264795	−	0.162939i
$456$		0			0
$457$	−11.1007	+	19.2270i	−0.519269	+	0.899400i	0.480480	+	0.877006i	$0.340462\pi$
$457$	−11.1007	+	19.2270i	−0.519269	+	0.899400i	−0.999749	+	0.0223947i	$0.992871\pi$
$458$		0			0
$459$	2.90159	+	5.02570i	0.135435	+	0.234580i
$460$		0			0
$461$	−33.5066			−1.56056			−0.780280	−	0.625430i	$-0.784923\pi$
$461$	−33.5066			−1.56056			−0.780280	+	0.625430i	$0.784923\pi$
$462$		0			0
$463$	−1.59046			−0.0739150			−0.0369575	−	0.999317i	$-0.511767\pi$
$463$	−1.59046			−0.0739150			−0.0369575	+	0.999317i	$0.511767\pi$
$464$		0			0
$465$	3.67919	+	6.37254i	0.170618	+	0.295519i
$466$		0			0
$467$	−0.668195	+	1.15735i	−0.0309204	+	0.0535556i	−0.881071	−	0.472983i	$-0.843177\pi$
$467$	−0.668195	+	1.15735i	−0.0309204	+	0.0535556i	0.850151	+	0.526539i	$0.176510\pi$
$468$		0			0
$469$	−16.6682	+	9.01034i	−0.769666	+	0.416059i
$470$		0			0
$471$	−2.03092	+	3.51765i	−0.0935797	+	0.162085i
$472$		0			0
$473$	22.0631	+	38.2145i	1.01446	+	1.75710i
$474$		0			0
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	−1.34509			−0.0615874
$478$		0			0
$479$	12.6549	+	21.9189i	0.578218	+	1.00150i	0.995684	+	0.0928099i	$0.0295849\pi$
$479$	12.6549	+	21.9189i	0.578218	+	1.00150i	−0.417466	+	0.908692i	$0.637082\pi$
$480$		0			0
$481$	12.3032	−	21.3097i	0.560977	−	0.971640i
$482$		0			0
$483$	−0.0631426	+	2.25258i	−0.00287309	+	0.102496i
$484$		0			0
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$		0			0
$487$	17.2357	+	29.8531i	0.781024	+	1.35277i	0.931346	+	0.364135i	$0.118635\pi$
$487$	17.2357	+	29.8531i	0.781024	+	1.35277i	−0.150322	+	0.988637i	$0.548031\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−21.6329			−0.976280			−0.488140	−	0.872765i	$-0.662325\pi$
$491$	−21.6329			−0.976280			−0.488140	+	0.872765i	$0.662325\pi$
$492$		0			0
$493$	−15.9780	−	27.6747i	−0.719614	−	1.24641i
$494$		0			0
$495$	−3.08078	+	5.33606i	−0.138471	+	0.239838i
$496$		0			0
$497$	1.12039	−	39.9695i	0.0502565	−	1.79288i
$498$		0			0
$499$	−15.0023	+	25.9847i	−0.671595	+	1.16324i	0.305857	+	0.952077i	$0.401057\pi$
$499$	−15.0023	+	25.9847i	−0.671595	+	1.16324i	−0.977452	+	0.211159i	$0.932276\pi$
$500$		0			0
$501$	4.73569	+	8.20245i	0.211575	+	0.366458i
$502$		0			0
$503$	−20.2965			−0.904978			−0.452489	−	0.891770i	$-0.649464\pi$
$503$	−20.2965			−0.904978			−0.452489	+	0.891770i	$0.649464\pi$
$504$		0			0
$505$	−2.19682			−0.0977572
$506$		0			0
$507$	−3.35837	−	5.81687i	−0.149151	−	0.258336i
$508$		0			0
$509$	3.49336	−	6.05067i	0.154840	−	0.268191i	−0.778161	−	0.628065i	$-0.783847\pi$
$509$	3.49336	−	6.05067i	0.154840	−	0.268191i	0.933001	+	0.359874i	$0.117180\pi$
$510$		0			0
$511$	−13.6196	+	7.36238i	−0.602498	+	0.325692i
$512$		0			0
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$		0			0
$515$	5.08742	+	8.81167i	0.224178	+	0.388288i
$516$		0			0
$517$	−14.5312			−0.639083
$518$		0			0
$519$	−2.06184			−0.0905045
$520$		0			0
$521$	−15.6858	−	27.1687i	−0.687209	−	1.19028i	−0.972737	−	0.231910i	$-0.925502\pi$
$521$	−15.6858	−	27.1687i	−0.687209	−	1.19028i	0.285529	−	0.958370i	$-0.407831\pi$
$522$		0			0
$523$	0.0608505	−	0.105396i	0.00266081	−	0.00460866i	−0.864692	−	0.502303i	$-0.832486\pi$
$523$	0.0608505	−	0.105396i	0.00266081	−	0.00460866i	0.867353	+	0.497694i	$0.165820\pi$
$524$		0			0
$525$	−2.25332	−	1.38656i	−0.0983430	−	0.0605144i
$526$		0			0
$527$	21.3510	−	36.9810i	0.930063	−	1.61092i
$528$		0			0
$529$	11.1373	+	19.2903i	0.484229	+	0.838710i
$530$		0			0
$531$	−6.49336			−0.281788
$532$		0			0
$533$	−7.89158			−0.341822
$534$		0			0
$535$	5.55650	+	9.62414i	0.240228	+	0.416088i
$536$		0			0
$537$	0.524276	−	0.908072i	0.0226242	−	0.0391862i
$538$		0			0
$539$	−19.4391	−	38.5018i	−0.837303	−	1.65839i
$540$		0			0
$541$	−5.33410	+	9.23893i	−0.229331	+	0.397213i	−0.957610	−	0.288068i	$-0.906987\pi$
$541$	−5.33410	+	9.23893i	−0.229331	+	0.397213i	0.728279	+	0.685281i	$0.240320\pi$
$542$		0			0
$543$	−2.18583	−	3.78597i	−0.0938029	−	0.162471i
$544$		0			0
$545$	6.66819			0.285634
$546$		0			0
$547$	−17.6329			−0.753930			−0.376965	−	0.926228i	$-0.623032\pi$
$547$	−17.6329			−0.753930			−0.376965	+	0.926228i	$0.623032\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.75332	−	4.76889i	0.117295	−	0.203162i
$552$		0			0
$553$	−28.5455	−	17.5652i	−1.21388	−	0.746948i
$554$		0			0
$555$	4.90823	−	8.50131i	0.208343	−	0.360860i
$556$		0			0
$557$	1.86936	+	3.23783i	0.0792075	+	0.137191i	0.902908	−	0.429833i	$-0.141428\pi$
$557$	1.86936	+	3.23783i	0.0792075	+	0.137191i	−0.823701	+	0.567025i	$0.808094\pi$
$558$		0			0
$559$	17.9514			0.759265
$560$		0			0
$561$	35.7566			1.50964
$562$		0			0
$563$	11.7167	+	20.2940i	0.493802	+	0.855290i	0.999974	−	0.00714214i	$-0.00227343\pi$
$563$	11.7167	+	20.2940i	0.493802	+	0.855290i	−0.506173	+	0.862432i	$0.668940\pi$
$564$		0			0
$565$	10.3098	−	17.8571i	0.433737	−	0.751255i
$566$		0			0
$567$	−2.32746	+	1.25815i	−0.0977439	+	0.0528375i
$568$		0			0
$569$	−11.5741	+	20.0470i	−0.485213	+	0.840413i	−0.999856	−	0.0169913i	$-0.994591\pi$
$569$	−11.5741	+	20.0470i	−0.485213	+	0.840413i	0.514643	+	0.857405i	$0.327925\pi$
$570$		0			0
$571$	−2.33410	−	4.04278i	−0.0976789	−	0.169185i	0.813045	−	0.582201i	$-0.197808\pi$
$571$	−2.33410	−	4.04278i	−0.0976789	−	0.169185i	−0.910724	+	0.413017i	$0.864475\pi$
$572$		0			0
$573$	−20.0266			−0.836622
$574$		0			0
$575$	0.851731			0.0355196
$576$		0			0
$577$	16.3840	+	28.3778i	0.682073	+	1.18139i	0.974347	+	0.225051i	$0.0722547\pi$
$577$	16.3840	+	28.3778i	0.682073	+	1.18139i	−0.292274	+	0.956335i	$0.594412\pi$
$578$		0			0
$579$	4.08742	−	7.07962i	0.169867	−	0.294219i
$580$		0			0
$581$	−0.408232	+	14.5635i	−0.0169363	+	0.604195i
$582$		0			0
$583$	−4.14392	+	7.17748i	−0.171624	+	0.297261i
$584$		0			0
$585$	1.25332	+	2.17082i	0.0518184	+	0.0897522i
$586$		0			0
$587$	36.1529			1.49219			0.746094	−	0.665841i	$-0.231927\pi$
$587$	36.1529			1.49219			0.746094	+	0.665841i	$0.231927\pi$
$588$		0			0
$589$	7.35837			0.303196
$590$		0			0
$591$	4.58742	+	7.94564i	0.188701	+	0.326840i
$592$		0			0
$593$	−12.5565	+	21.7485i	−0.515634	+	0.893104i	0.484202	+	0.874956i	$0.339110\pi$
$593$	−12.5565	+	21.7485i	−0.515634	+	0.893104i	−0.999835	+	0.0181473i	$0.994223\pi$
$594$		0			0
$595$	−0.430215	+	15.3477i	−0.0176371	+	0.629196i
$596$		0			0
$597$	1.35837	−	2.35277i	0.0555945	−	0.0962925i
$598$		0			0
$599$	0.555193	+	0.961623i	0.0226846	+	0.0392909i	0.877145	−	0.480226i	$-0.159445\pi$
$599$	0.555193	+	0.961623i	0.0226846	+	0.0392909i	−0.854460	+	0.519517i	$0.826112\pi$
$600$		0			0
$601$	41.8809			1.70836			0.854179	−	0.519979i	$-0.174060\pi$
$601$	41.8809			1.70836			0.854179	+	0.519979i	$0.174060\pi$
$602$		0			0
$603$	7.16155			0.291641
$604$		0			0
$605$	13.4824	+	23.3521i	0.548136	+	0.949400i
$606$		0			0
$607$	10.2048	−	17.6752i	0.414199	−	0.717413i	−0.581145	−	0.813800i	$-0.697395\pi$
$607$	10.2048	−	17.6752i	0.414199	−	0.717413i	0.995344	+	0.0963865i	$0.0307285\pi$
$608$		0			0
$609$	12.8165	−	6.92820i	0.519349	−	0.280745i
$610$		0			0
$611$	−2.95580	+	5.11959i	−0.119579	+	0.207117i
$612$		0			0
$613$	−2.47572	−	4.28808i	−0.0999936	−	0.173194i	0.811688	−	0.584091i	$-0.198549\pi$
$613$	−2.47572	−	4.28808i	−0.0999936	−	0.173194i	−0.911682	+	0.410897i	$0.865216\pi$
$614$		0			0
$615$	−3.14827			−0.126950
$616$		0			0
$617$	−13.6769			−0.550611			−0.275306	−	0.961357i	$-0.588779\pi$
$617$	−13.6769			−0.550611			−0.275306	+	0.961357i	$0.588779\pi$
$618$		0			0
$619$	−5.30318	−	9.18538i	−0.213153	−	0.369191i	0.739547	−	0.673105i	$-0.235040\pi$
$619$	−5.30318	−	9.18538i	−0.213153	−	0.369191i	−0.952700	+	0.303914i	$0.901707\pi$
$620$		0			0
$621$	0.425866	−	0.737621i	0.0170894	−	0.0295997i
$622$		0			0
$623$	−24.3730	−	14.9977i	−0.976482	−	0.600869i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	3.08078	+	5.33606i	0.123034	+	0.213102i
$628$		0			0
$629$	−56.9667			−2.27141
$630$		0			0
$631$	19.3364			0.769770			0.384885	−	0.922965i	$-0.374241\pi$
$631$	19.3364			0.769770			0.384885	+	0.922965i	$0.374241\pi$
$632$		0			0
$633$	−1.47572	−	2.55603i	−0.0586548	−	0.101593i
$634$		0			0
$635$	−4.05650	+	7.02607i	−0.160977	+	0.278821i
$636$		0			0
$637$	−17.5189	−	0.982926i	−0.694126	−	0.0389449i
$638$		0			0
$639$	−7.55650	+	13.0882i	−0.298931	+	0.517763i
$640$		0			0
$641$	5.42587	+	9.39787i	0.214309	+	0.371194i	0.953059	−	0.302786i	$-0.0979168\pi$
$641$	5.42587	+	9.39787i	0.214309	+	0.371194i	−0.738750	+	0.673980i	$0.764583\pi$
$642$		0			0
$643$	27.3876			1.08006			0.540030	−	0.841646i	$-0.318413\pi$
$643$	27.3876			1.08006			0.540030	+	0.841646i	$0.318413\pi$
$644$		0			0
$645$	7.16155			0.281986
$646$		0			0
$647$	−0.574134	−	0.994430i	−0.0225716	−	0.0390951i	0.854519	−	0.519420i	$-0.173852\pi$
$647$	−0.574134	−	0.994430i	−0.0225716	−	0.0390951i	−0.877091	+	0.480325i	$0.840519\pi$
$648$		0			0
$649$	−20.0046	+	34.6490i	−0.785249	+	1.36009i
$650$		0			0
$651$	16.5808	+	10.2028i	0.649852	+	0.399880i
$652$		0			0
$653$	11.2643	−	19.5104i	0.440807	−	0.763499i	−0.556943	−	0.830551i	$-0.688026\pi$
$653$	11.2643	−	19.5104i	0.440807	−	0.763499i	0.997750	+	0.0670513i	$0.0213591\pi$
$654$		0			0
$655$	−2.32746	−	4.03127i	−0.0909412	−	0.157515i
$656$		0			0
$657$	5.85173			0.228298
$658$		0			0
$659$	24.0531			0.936977			0.468489	−	0.883470i	$-0.344799\pi$
$659$	24.0531			0.936977			0.468489	+	0.883470i	$0.344799\pi$
$660$		0			0
$661$	7.84074	+	13.5806i	0.304969	+	0.528223i	0.977255	−	0.212070i	$-0.0680204\pi$
$661$	7.84074	+	13.5806i	0.304969	+	0.528223i	−0.672285	+	0.740292i	$0.734687\pi$
$662$		0			0
$663$	7.27325	−	12.5976i	0.282469	−	0.489252i
$664$		0			0
$665$	−2.32746	+	1.25815i	−0.0902548	+	0.0487891i
$666$		0			0
$667$	−2.34509	+	4.06181i	−0.0908022	+	0.157274i
$668$		0			0
$669$	−11.5066	−	19.9301i	−0.444872	−	0.770542i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	25.7812			0.993792			0.496896	−	0.867810i	$-0.334473\pi$
$673$	25.7812			0.993792			0.496896	+	0.867810i	$0.334473\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	−14.5874	+	25.2661i	−0.560640	+	0.971057i	0.436801	+	0.899558i	$0.356112\pi$
$677$	−14.5874	+	25.2661i	−0.560640	+	0.971057i	−0.997441	+	0.0714987i	$0.977222\pi$
$678$		0			0
$679$	0.593075	−	21.1577i	0.0227601	−	0.811958i
$680$		0			0
$681$	4.55650	−	7.89209i	0.174605	−	0.302426i
$682$		0			0
$683$	−2.70477	−	4.68480i	−0.103495	−	0.179259i	0.809627	−	0.586944i	$-0.199669\pi$
$683$	−2.70477	−	4.68480i	−0.103495	−	0.179259i	−0.913122	+	0.407686i	$0.866336\pi$
$684$		0			0
$685$	21.5332			0.822742
$686$		0			0
$687$	19.3584			0.738568
$688$		0			0
$689$	1.68583	+	2.91994i	0.0642250	+	0.111241i
$690$		0			0
$691$	−6.43381	+	11.1437i	−0.244754	+	0.423926i	−0.962062	−	0.272830i	$-0.912040\pi$
$691$	−6.43381	+	11.1437i	−0.244754	+	0.423926i	0.717309	+	0.696756i	$0.245374\pi$
$692$		0			0
$693$	−0.456783	+	16.2955i	−0.0173518	+	0.619016i
$694$		0			0
$695$	−8.48237	+	14.6919i	−0.321754	+	0.557295i
$696$		0			0
$697$	9.13498	+	15.8223i	0.346012	+	0.599311i
$698$		0			0
$699$	−13.0133			−0.492208
$700$		0			0
$701$	−2.81646			−0.106376			−0.0531882	−	0.998585i	$-0.516938\pi$
$701$	−2.81646			−0.106376			−0.0531882	+	0.998585i	$0.516938\pi$
$702$		0			0
$703$	−4.90823	−	8.50131i	−0.185117	−	0.320633i
$704$		0			0
$705$	−1.17919	+	2.04241i	−0.0444107	+	0.0769216i
$706$		0			0
$707$	−5.11300	+	2.76394i	−0.192294	+	0.103949i
$708$		0			0
$709$	−5.70346	+	9.87869i	−0.214198	+	0.371002i	−0.953024	−	0.302894i	$-0.902047\pi$
$709$	−5.70346	+	9.87869i	−0.214198	+	0.371002i	0.738826	+	0.673896i	$0.235380\pi$
$710$		0			0
$711$	6.33410	+	10.9710i	0.237547	+	0.411444i
$712$		0			0
$713$	−6.26736			−0.234714
$714$		0			0
$715$	15.4448			0.577603
$716$		0			0
$717$	−2.01328	−	3.48711i	−0.0751875	−	0.130229i
$718$		0			0
$719$	18.1130	−	31.3726i	0.675501	−	1.17000i	−0.300821	−	0.953681i	$-0.597261\pi$
$719$	18.1130	−	31.3726i	0.675501	−	1.17000i	0.976322	−	0.216321i	$-0.0694059\pi$
$720$		0			0
$721$	22.9272	+	14.1080i	0.853853	+	0.525410i
$722$		0			0
$723$	6.67254	−	11.5572i	0.248155	−	0.429816i
$724$		0			0
$725$	−2.75332	−	4.76889i	−0.102256	−	0.177112i
$726$		0			0
$727$	−49.3523			−1.83038			−0.915188	−	0.403028i	$-0.867958\pi$
$727$	−49.3523			−1.83038			−0.915188	+	0.403028i	$0.867958\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−20.7799	−	35.9918i	−0.768572	−	1.33121i
$732$		0			0
$733$	23.9215	−	41.4333i	0.883561	−	1.53037i	0.0362076	−	0.999344i	$-0.488472\pi$
$733$	23.9215	−	41.4333i	0.883561	−	1.53037i	0.847354	−	0.531029i	$-0.178194\pi$
$734$		0			0
$735$	−6.98901	−	0.392129i	−0.257793	−	0.0144639i
$736$		0			0
$737$	22.0631	−	38.2145i	0.812706	−	1.40765i
$738$		0			0
$739$	−0.316464	−	0.548131i	−0.0116413	−	0.0201633i	0.860146	−	0.510048i	$-0.170372\pi$
$739$	−0.316464	−	0.548131i	−0.0116413	−	0.0201633i	−0.871787	+	0.489884i	$0.837039\pi$
$740$		0			0
$741$	2.50664			0.0920838
$742$		0			0
$743$	−24.8078			−0.910109			−0.455054	−	0.890464i	$-0.650380\pi$
$743$	−24.8078			−0.910109			−0.455054	+	0.890464i	$0.650380\pi$
$744$		0			0
$745$	11.0133	+	19.0756i	0.403496	+	0.698875i
$746$		0			0
$747$	2.75332	−	4.76889i	0.100739	−	0.174485i
$748$		0			0
$749$	25.0412	+	15.4088i	0.914984	+	0.563026i
$750$		0			0
$751$	−2.15056	+	3.72488i	−0.0784751	+	0.135923i	−0.902592	−	0.430497i	$-0.858338\pi$
$751$	−2.15056	+	3.72488i	−0.0784751	+	0.135923i	0.824117	+	0.566419i	$0.191672\pi$
$752$		0			0
$753$	−14.8972	−	25.8028i	−0.542886	−	0.940305i
$754$		0			0
$755$	−8.61964			−0.313701
$756$		0			0
$757$	−4.02657			−0.146348			−0.0731740	−	0.997319i	$-0.523313\pi$
$757$	−4.02657			−0.146348			−0.0731740	+	0.997319i	$0.523313\pi$
$758$		0			0
$759$	−2.62399	−	4.54489i	−0.0952449	−	0.164969i
$760$		0			0
$761$	11.6871	−	20.2427i	0.423658	−	0.733798i	−0.572636	−	0.819810i	$-0.694079\pi$
$761$	11.6871	−	20.2427i	0.423658	−	0.733798i	0.996294	+	0.0860121i	$0.0274124\pi$
$762$		0			0
$763$	15.5199	−	8.38962i	0.561859	−	0.303724i
$764$		0			0
$765$	2.90159	−	5.02570i	0.104907	−	0.181705i
$766$		0			0
$767$	8.13826	+	14.0959i	0.293856	+	0.508973i
$768$		0			0
$769$	3.88961			0.140263			0.0701315	−	0.997538i	$-0.477658\pi$
$769$	3.88961			0.140263			0.0701315	+	0.997538i	$0.477658\pi$
$770$		0			0
$771$	8.12629			0.292661
$772$		0			0
$773$	23.0588	+	39.9390i	0.829367	+	1.43651i	0.898535	+	0.438901i	$0.144632\pi$
$773$	23.0588	+	39.9390i	0.829367	+	1.43651i	−0.0691683	+	0.997605i	$0.522035\pi$
$774$		0			0
$775$	3.67919	−	6.37254i	0.132160	−	0.228908i
$776$		0			0
$777$	0.727738	−	25.9617i	0.0261075	−	0.931372i
$778$		0			0
$779$	−1.57413	+	2.72648i	−0.0563992	+	0.0976863i
$780$		0			0
$781$	46.5598	+	80.6439i	1.66604	+	2.88567i
$782$		0			0
$783$	−5.50664			−0.196791
$784$		0			0
$785$	4.06184			0.144973
$786$		0			0
$787$	1.47137	+	2.54850i	0.0524488	+	0.0908440i	0.891058	−	0.453890i	$-0.149964\pi$
$787$	1.47137	+	2.54850i	0.0524488	+	0.0908440i	−0.838609	+	0.544734i	$0.816631\pi$
$788$		0			0
$789$	5.50664	−	9.53778i	0.196042	−	0.339554i
$790$		0			0
$791$	1.52863	−	54.5330i	0.0543517	−	1.93897i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.672545	+	1.16488i	0.0238527	+	0.0413141i
$796$		0			0
$797$	12.5465			0.444420			0.222210	−	0.974999i	$-0.428673\pi$
$797$	12.5465			0.444420			0.222210	+	0.974999i	$0.428673\pi$
$798$		0			0
$799$	13.6861			0.484178
$800$		0			0
$801$	5.40823	+	9.36733i	0.191090	+	0.330978i
$802$		0			0
$803$	18.0279	−	31.2252i	0.636190	−	1.10191i
$804$		0			0
$805$	1.98237	−	1.07161i	0.0698692	−	0.0377692i
$806$		0			0
$807$	1.85173	−	3.20729i	0.0651840	−	0.112902i
$808$		0			0
$809$	−10.1925	−	17.6539i	−0.358348	−	0.620677i	0.629337	−	0.777133i	$-0.283327\pi$
$809$	−10.1925	−	17.6539i	−0.358348	−	0.620677i	−0.987685	+	0.156455i	$0.949993\pi$
$810$		0			0
$811$	−38.6109			−1.35581			−0.677907	−	0.735148i	$-0.737113\pi$
$811$	−38.6109			−1.35581			−0.677907	+	0.735148i	$0.737113\pi$
$812$		0			0
$813$	27.3098			0.957797
$814$		0			0
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	3.58078	−	6.20209i	0.125276	−	0.216984i
$818$		0			0
$819$	5.64827	+	3.47561i	0.197366	+	0.121447i
$820$		0			0
$821$	13.7533	−	23.8215i	0.479994	−	0.831374i	−0.519742	−	0.854323i	$-0.673972\pi$
$821$	13.7533	−	23.8215i	0.479994	−	0.831374i	0.999737	+	0.0229486i	$0.00730542\pi$
$822$		0			0
$823$	19.1616	+	33.1888i	0.667930	+	1.15689i	0.978482	+	0.206332i	$0.0661527\pi$
$823$	19.1616	+	33.1888i	0.667930	+	1.15689i	−0.310552	+	0.950556i	$0.600514\pi$
$824$		0			0
$825$	6.16155			0.214518
$826$		0			0
$827$	13.0133			0.452516			0.226258	−	0.974067i	$-0.427351\pi$
$827$	13.0133			0.452516			0.226258	+	0.974067i	$0.427351\pi$
$828$		0			0
$829$	−11.4471	−	19.8270i	−0.397574	−	0.688619i	0.595852	−	0.803094i	$-0.296815\pi$
$829$	−11.4471	−	19.8270i	−0.397574	−	0.688619i	−0.993426	+	0.114476i	$0.963481\pi$
$830$		0			0
$831$	3.74233	−	6.48190i	0.129820	−	0.224855i
$832$		0			0
$833$	18.3085	+	36.2625i	0.634352	+	1.25642i
$834$		0			0
$835$	4.73569	−	8.20245i	0.163885	−	0.283858i
$836$		0			0
$837$	−3.67919	−	6.37254i	−0.127171	−	0.220267i
$838$		0			0
$839$	−15.1396			−0.522676			−0.261338	−	0.965247i	$-0.584164\pi$
$839$	−15.1396			−0.522676			−0.261338	+	0.965247i	$0.584164\pi$
$840$		0			0
$841$	1.32311			0.0456243
$842$		0			0
$843$	−12.1439	−	21.0339i	−0.418259	−	0.724445i
$844$		0			0
$845$	−3.35837	+	5.81687i	−0.115532	+	0.200107i
$846$		0			0
$847$	60.7602	+	37.3882i	2.08775	+	1.28467i
$848$		0			0
$849$	−12.5808	+	21.7905i	−0.431771	+	0.747850i
$850$		0			0
$851$	4.18049	+	7.24083i	0.143305	+	0.248212i
$852$		0			0
$853$	−2.55061			−0.0873312			−0.0436656	−	0.999046i	$-0.513904\pi$
$853$	−2.55061			−0.0873312			−0.0436656	+	0.999046i	$0.513904\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	9.06314	+	15.6978i	0.309591	+	0.536227i	0.978273	−	0.207321i	$-0.0664745\pi$
$857$	9.06314	+	15.6978i	0.309591	+	0.536227i	−0.668682	+	0.743549i	$0.733141\pi$
$858$		0			0
$859$	−12.8650	+	22.2829i	−0.438949	+	0.760281i	−0.997609	−	0.0691154i	$-0.977982\pi$
$859$	−12.8650	+	22.2829i	−0.438949	+	0.760281i	0.558660	+	0.829397i	$0.311316\pi$
$860$		0			0
$861$	−7.32746	+	3.96101i	−0.249719	+	0.134991i
$862$		0			0
$863$	3.73438	−	6.46814i	0.127120	−	0.220178i	−0.795440	−	0.606033i	$-0.792760\pi$
$863$	3.73438	−	6.46814i	0.127120	−	0.220178i	0.922560	+	0.385855i	$0.126093\pi$
$864$		0			0
$865$	1.03092	+	1.78560i	0.0350523	+	0.0607123i
$866$		0			0
$867$	−16.6769			−0.566377
$868$		0			0
$869$	78.0558			2.64786
$870$		0			0
$871$	−8.97572	−	15.5464i	−0.304131	−	0.526770i
$872$		0			0
$873$	−4.00000	+	6.92820i	−0.135379	+	0.234484i
$874$		0			0
$875$	−0.0741344	+	2.64471i	−0.00250620	+	0.0894076i
$876$		0			0
$877$	24.1306	−	41.7955i	0.814834	−	1.41133i	−0.0946136	−	0.995514i	$-0.530162\pi$
$877$	24.1306	−	41.7955i	0.814834	−	1.41133i	0.909447	−	0.415819i	$-0.136505\pi$
$878$		0			0
$879$	−12.8341	−	22.2293i	−0.432883	−	0.749776i
$880$		0			0
$881$	−16.2347			−0.546961			−0.273481	−	0.961878i	$-0.588175\pi$
$881$	−16.2347			−0.546961			−0.273481	+	0.961878i	$0.588175\pi$
$882$		0			0
$883$	−19.8252			−0.667170			−0.333585	−	0.942720i	$-0.608258\pi$
$883$	−19.8252			−0.667170			−0.333585	+	0.942720i	$0.608258\pi$
$884$		0			0
$885$	3.24668	+	5.62341i	0.109136	+	0.189029i
$886$		0			0
$887$	17.8663	−	30.9454i	0.599892	−	1.03904i	−0.392944	−	0.919562i	$-0.628543\pi$
$887$	17.8663	−	30.9454i	0.599892	−	1.03904i	0.992836	−	0.119482i	$-0.0381233\pi$
$888$		0			0
$889$	−0.601453	+	21.4566i	−0.0201721	+	0.719630i
$890$		0			0
$891$	3.08078	−	5.33606i	0.103210	−	0.178765i
$892$		0			0
$893$	1.17919	+	2.04241i	0.0394600	+	0.0683467i
$894$		0			0
$895$	−1.04855			−0.0350492
$896$		0			0
$897$	−2.13498			−0.0712851
$898$		0			0
$899$	20.2600	+	35.0913i	0.675708	+	1.17036i
$900$		0			0
$901$	3.90290	−	6.76002i	0.130024	−	0.225209i
$902$		0			0
$903$	16.6682	−	9.01034i	0.554683	−	0.299845i
$904$		0			0
$905$	−2.18583	+	3.78597i	−0.0726594	+	0.125850i
$906$		0			0
$907$	2.60276	+	4.50811i	0.0864232	+	0.149689i	0.905997	−	0.423285i	$-0.139123\pi$
$907$	2.60276	+	4.50811i	0.0864232	+	0.149689i	−0.819574	+	0.572974i	$0.805790\pi$
$908$		0			0
$909$	2.19682			0.0728639
$910$		0			0
$911$	−37.4361			−1.24031			−0.620157	−	0.784478i	$-0.712931\pi$
$911$	−37.4361			−1.24031			−0.620157	+	0.784478i	$0.712931\pi$
$912$		0			0
$913$	−16.9647	−	29.3838i	−0.561451	−	0.972461i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.4890	−	6.45431i	−0.346378	−	0.213140i
$918$		0			0
$919$	22.8055	−	39.5002i	0.752283	−	1.30299i	−0.194431	−	0.980916i	$-0.562286\pi$
$919$	22.8055	−	39.5002i	0.752283	−	1.30299i	0.946714	−	0.322076i	$-0.104381\pi$
$920$		0			0
$921$	−15.5322	−	26.9026i	−0.511804	−	0.886471i
$922$		0			0
$923$	37.8829			1.24693
$924$		0			0
$925$	−9.81646			−0.322763
$926$		0			0
$927$	−5.08742	−	8.81167i	−0.167093	−	0.289413i
$928$		0			0
$929$	18.9458	−	32.8151i	0.621591	−	1.07663i	−0.367598	−	0.929985i	$-0.619820\pi$
$929$	18.9458	−	32.8151i	0.621591	−	1.07663i	0.989189	−	0.146643i	$-0.0468468\pi$
$930$		0			0
$931$	−3.83410	+	5.85659i	−0.125657	+	0.191942i
$932$		0			0
$933$	−13.4215	+	23.2467i	−0.439401	+	0.761064i
$934$		0			0
$935$	−17.8783	−	30.9661i	−0.584683	−	1.01270i
$936$		0			0
$937$	−35.6083			−1.16327			−0.581637	−	0.813449i	$-0.697587\pi$
$937$	−35.6083			−1.16327			−0.581637	+	0.813449i	$0.697587\pi$
$938$		0			0
$939$	−18.0777			−0.589945
$940$		0			0
$941$	−6.71805	−	11.6360i	−0.219002	−	0.379323i	0.735501	−	0.677524i	$-0.236947\pi$
$941$	−6.71805	−	11.6360i	−0.219002	−	0.379323i	−0.954503	+	0.298201i	$0.903614\pi$
$942$		0			0
$943$	1.34074	−	2.32223i	0.0436605	−	0.0756222i
$944$		0			0
$945$	2.25332	+	1.38656i	0.0733005	+	0.0451048i
$946$		0			0
$947$	−14.3218	+	24.8061i	−0.465396	+	0.806089i	−0.999219	−	0.0395066i	$-0.987421\pi$
$947$	−14.3218	+	24.8061i	−0.465396	+	0.806089i	0.533823	+	0.845596i	$0.320755\pi$
$948$		0			0
$949$	−7.33410	−	12.7030i	−0.238075	−	0.412358i
$950$		0			0
$951$	15.5066			0.502837
$952$		0			0
$953$	−26.2791			−0.851265			−0.425632	−	0.904896i	$-0.639948\pi$
$953$	−26.2791			−0.851265			−0.425632	+	0.904896i	$0.639948\pi$
$954$		0			0
$955$	10.0133	+	17.3435i	0.324022	+	0.561223i
$956$		0			0
$957$	−16.9647	+	29.3838i	−0.548392	+	0.949843i
$958$		0			0
$959$	50.1176	−	27.0921i	1.61838	−	0.874849i
$960$		0			0
$961$	−11.5728	+	20.0447i	−0.373317	+	0.646604i
$962$		0			0
$963$	−5.55650	−	9.62414i	−0.179056	−	0.310134i
$964$		0			0
$965$	−8.17484			−0.263157
$966$		0			0
$967$	27.4581			0.882993			0.441496	−	0.897263i	$-0.354448\pi$
$967$	27.4581			0.882993			0.441496	+	0.897263i	$0.354448\pi$
$968$		0			0
$969$	−2.90159	−	5.02570i	−0.0932125	−	0.161449i
$970$		0			0
$971$	−24.7370	+	42.8457i	−0.793848	+	1.37498i	0.129720	+	0.991551i	$0.458592\pi$
$971$	−24.7370	+	42.8457i	−0.793848	+	1.37498i	−0.923568	+	0.383434i	$0.874741\pi$
$972$		0			0
$973$	−1.25767	+	44.8668i	−0.0403191	+	1.43836i
$974$		0			0
$975$	1.25332	−	2.17082i	0.0401384	−	0.0695217i
$976$		0			0
$977$	5.11169	+	8.85371i	0.163538	+	0.283255i	0.936135	−	0.351641i	$-0.114376\pi$
$977$	5.11169	+	8.85371i	0.163538	+	0.283255i	−0.772597	+	0.634896i	$0.781043\pi$
$978$		0			0
$979$	66.6462			2.13002
$980$		0			0
$981$	−6.66819			−0.212899
$982$		0			0
$983$	−3.57413	−	6.19058i	−0.113997	−	0.197449i	0.803381	−	0.595465i	$-0.203032\pi$
$983$	−3.57413	−	6.19058i	−0.113997	−	0.197449i	−0.917378	+	0.398016i	$0.869699\pi$
$984$		0			0
$985$	4.58742	−	7.94564i	0.146167	−	0.253169i
$986$		0			0
$987$	−0.174837	+	6.23722i	−0.00556511	+	0.198533i
$988$		0			0
$989$	−3.04986	+	5.28251i	−0.0969799	+	0.167974i
$990$		0			0
$991$	21.0376	+	36.4381i	0.668280	+	1.15750i	0.978385	+	0.206793i	$0.0663026\pi$
$991$	21.0376	+	36.4381i	0.668280	+	1.15750i	−0.310105	+	0.950702i	$0.600364\pi$
$992$		0			0
$993$	20.7300			0.657848
$994$		0			0
$995$	−2.71675			−0.0861266
$996$		0			0
$997$	20.7290	+	35.9038i	0.656495	+	1.13708i	0.981517	+	0.191377i	$0.0612952\pi$
$997$	20.7290	+	35.9038i	0.656495	+	1.13708i	−0.325021	+	0.945707i	$0.605371\pi$
$998$		0			0
$999$	−4.90823	+	8.50131i	−0.155290	+	0.268969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.v.961.2		6
4.3	odd	2		840.2.bg.j.121.2	✓	6
7.4	even	3	inner	1680.2.bg.v.1201.2		6
12.11	even	2		2520.2.bi.n.1801.2		6
28.11	odd	6		840.2.bg.j.361.2	yes	6
28.19	even	6		5880.2.a.bu.1.3		3
28.23	odd	6		5880.2.a.bv.1.3		3
84.11	even	6		2520.2.bi.n.361.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.j.121.2	✓	6	4.3	odd	2
840.2.bg.j.361.2	yes	6	28.11	odd	6
1680.2.bg.v.961.2		6	1.1	even	1	trivial
1680.2.bg.v.1201.2		6	7.4	even	3	inner
2520.2.bi.n.361.2		6	84.11	even	6
2520.2.bi.n.1801.2		6	12.11	even	2
5880.2.a.bu.1.3		3	28.19	even	6
5880.2.a.bv.1.3		3	28.23	odd	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.0741344 - 2.64471i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.0741344 - 2.64471i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.08078 + 5.33606i) q^{11} +2.50664 q^{13} +1.00000 q^{15} +(-2.90159 - 5.02570i) q^{17} +(0.500000 - 0.866025i) q^{19} +(2.32746 - 1.25815i) q^{21} +(-0.425866 + 0.737621i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +5.50664 q^{29} +(3.67919 + 6.37254i) q^{31} +(-3.08078 + 5.33606i) q^{33} +(-2.25332 - 1.38656i) q^{35} +(4.90823 - 8.50131i) q^{37} +(1.25332 + 2.17082i) q^{39} -3.14827 q^{41} +7.16155 q^{43} +(0.500000 + 0.866025i) q^{45} +(-1.17919 + 2.04241i) q^{47} +(-6.98901 - 0.392129i) q^{49} +(2.90159 - 5.02570i) q^{51} +(0.672545 + 1.16488i) q^{53} +6.16155 q^{55} +1.00000 q^{57} +(3.24668 + 5.62341i) q^{59} +(2.25332 + 1.38656i) q^{63} +(1.25332 - 2.17082i) q^{65} +(-3.58078 - 6.20209i) q^{67} -0.851731 q^{69} +15.1130 q^{71} +(-2.92587 - 5.06775i) q^{73} +(0.500000 - 0.866025i) q^{75} +(14.3407 - 7.75218i) q^{77} +(6.33410 - 10.9710i) q^{79} +(-0.500000 - 0.866025i) q^{81} -5.50664 q^{83} -5.80318 q^{85} +(2.75332 + 4.76889i) q^{87} +(5.40823 - 9.36733i) q^{89} +(0.185828 - 6.62935i) q^{91} +(-3.67919 + 6.37254i) q^{93} +(-0.500000 - 0.866025i) q^{95} +8.00000 q^{97} -6.16155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9	\( 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{15} - 6 q^{17} + 3 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{25} - 6 q^{27} + 12 q^{29} + 12 q^{31} + 3 q^{33} - 3 q^{35} - 3 q^{37} - 3 q^{39} - 18 q^{41} + 3 q^{45} + 3 q^{47} + 12 q^{49} + 6 q^{51} + 15 q^{53} - 6 q^{55} + 6 q^{57} + 30 q^{59} + 3 q^{63} - 3 q^{65} - 6 q^{69} + 24 q^{71} - 18 q^{73} + 3 q^{75} + 33 q^{77} + 6 q^{79} - 3 q^{81} - 12 q^{83} - 12 q^{85} + 6 q^{87} - 30 q^{91} - 12 q^{93} - 3 q^{95} + 48 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^15 - 6 * q^17 + 3 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^25 - 6 * q^27 + 12 * q^29 + 12 * q^31 + 3 * q^33 - 3 * q^35 - 3 * q^37 - 3 * q^39 - 18 * q^41 + 3 * q^45 + 3 * q^47 + 12 * q^49 + 6 * q^51 + 15 * q^53 - 6 * q^55 + 6 * q^57 + 30 * q^59 + 3 * q^63 - 3 * q^65 - 6 * q^69 + 24 * q^71 - 18 * q^73 + 3 * q^75 + 33 * q^77 + 6 * q^79 - 3 * q^81 - 12 * q^83 - 12 * q^85 + 6 * q^87 - 30 * q^91 - 12 * q^93 - 3 * q^95 + 48 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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