LMFDB - Embedded newform 2280.2.bg.l.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2280,2,Mod(121,2280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2280, 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("2280.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2280.bg (of order $3$, degree $2$, 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:	$18.2058916609$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	2280.961
Dual form			2280.2.bg.l.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.12311 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.12311 q^{7} +(-0.500000 - 0.866025i) q^{9} +2.56155 q^{11} +(-1.78078 - 3.08440i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{17} +(1.84233 - 3.95042i) q^{19} +(2.06155 - 3.57071i) q^{21} +(-0.280776 - 0.486319i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.561553 - 0.972638i) q^{29} +8.68466 q^{31} +(-1.28078 + 2.21837i) q^{33} +(2.06155 - 3.57071i) q^{35} -9.00000 q^{37} +3.56155 q^{39} +(-1.84233 + 3.19101i) q^{41} +(3.78078 - 6.54850i) q^{43} +1.00000 q^{45} +(2.43845 + 4.22351i) q^{47} +10.0000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(3.71922 + 6.44188i) q^{53} +(-1.28078 + 2.21837i) q^{55} +(2.50000 + 3.57071i) q^{57} +(3.12311 - 5.40938i) q^{59} +(2.34233 + 4.05703i) q^{61} +(2.06155 + 3.57071i) q^{63} +3.56155 q^{65} +(6.34233 + 10.9852i) q^{67} +0.561553 q^{69} +(6.12311 - 10.6055i) q^{71} +(5.34233 - 9.25319i) q^{73} +1.00000 q^{75} -10.5616 q^{77} +(-3.78078 + 6.54850i) q^{79} +(-0.500000 + 0.866025i) q^{81} +2.87689 q^{83} +(-2.00000 - 3.46410i) q^{85} +1.12311 q^{87} +(5.84233 + 10.1192i) q^{89} +(7.34233 + 12.7173i) q^{91} +(-4.34233 + 7.52113i) q^{93} +(2.50000 + 3.57071i) q^{95} +(3.00000 - 5.19615i) q^{97} +(-1.28078 - 2.21837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} + 2 q^{11} - 3 q^{13} - 2 q^{15} - 8 q^{17} - 5 q^{19} + 3 q^{23} - 2 q^{25} + 4 q^{27} + 6 q^{29} + 10 q^{31} - q^{33} - 36 q^{37} + 6 q^{39} + 5 q^{41} + 11 q^{43} + 4 q^{45} + 18 q^{47} + 40 q^{49} - 8 q^{51} + 19 q^{53} - q^{55} + 10 q^{57} - 4 q^{59} - 3 q^{61} + 6 q^{65} + 13 q^{67} - 6 q^{69} + 8 q^{71} + 9 q^{73} + 4 q^{75} - 34 q^{77} - 11 q^{79} - 2 q^{81} + 28 q^{83} - 8 q^{85} - 12 q^{87} + 11 q^{89} + 17 q^{91} - 5 q^{93} + 10 q^{95} + 12 q^{97} - q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 + 2 * q^11 - 3 * q^13 - 2 * q^15 - 8 * q^17 - 5 * q^19 + 3 * q^23 - 2 * q^25 + 4 * q^27 + 6 * q^29 + 10 * q^31 - q^33 - 36 * q^37 + 6 * q^39 + 5 * q^41 + 11 * q^43 + 4 * q^45 + 18 * q^47 + 40 * q^49 - 8 * q^51 + 19 * q^53 - q^55 + 10 * q^57 - 4 * q^59 - 3 * q^61 + 6 * q^65 + 13 * q^67 - 6 * q^69 + 8 * q^71 + 9 * q^73 + 4 * q^75 - 34 * q^77 - 11 * q^79 - 2 * q^81 + 28 * q^83 - 8 * q^85 - 12 * q^87 + 11 * q^89 + 17 * q^91 - 5 * q^93 + 10 * q^95 + 12 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2280\mathbb{Z}\right)^\times$.

$n$	$457$	$761$	$1141$	$1711$	$1921$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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
$7$	−4.12311			−1.55839			−0.779194	−	0.626783i	$-0.784371\pi$
$7$	−4.12311			−1.55839			−0.779194	+	0.626783i	$0.784371\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.56155			0.772337			0.386169	−	0.922428i	$-0.373798\pi$
$11$	2.56155			0.772337			0.386169	+	0.922428i	$0.373798\pi$
$12$		0			0
$13$	−1.78078	−	3.08440i	−0.493899	−	0.855457i	0.506077	−	0.862488i	$-0.331095\pi$
$13$	−1.78078	−	3.08440i	−0.493899	−	0.855457i	−0.999975	+	0.00703112i	$0.997762\pi$
$14$		0			0
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$		0			0
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	1.84233	−	3.95042i	0.422659	−	0.906289i
$19$	1.84233	−	3.95042i	0.422659	−	0.906289i
$20$		0			0
$21$	2.06155	−	3.57071i	0.449868	−	0.779194i
$22$		0			0
$23$	−0.280776	−	0.486319i	−0.0585459	−	0.101405i	0.835267	−	0.549845i	$-0.185313\pi$
$23$	−0.280776	−	0.486319i	−0.0585459	−	0.101405i	−0.893813	+	0.448440i	$0.851980\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.561553	−	0.972638i	−0.104278	−	0.180614i	0.809165	−	0.587581i	$-0.199920\pi$
$29$	−0.561553	−	0.972638i	−0.104278	−	0.180614i	−0.913443	+	0.406967i	$0.866586\pi$
$30$		0			0
$31$	8.68466			1.55981			0.779905	−	0.625897i	$-0.215267\pi$
$31$	8.68466			1.55981			0.779905	+	0.625897i	$0.215267\pi$
$32$		0			0
$33$	−1.28078	+	2.21837i	−0.222955	+	0.386169i
$34$		0			0
$35$	2.06155	−	3.57071i	0.348466	−	0.603561i
$36$		0			0
$37$	−9.00000			−1.47959			−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000			−1.47959			−0.739795	+	0.672832i	$0.765078\pi$
$38$		0			0
$39$	3.56155			0.570305
$40$		0			0
$41$	−1.84233	+	3.19101i	−0.287723	+	0.498352i	−0.973266	−	0.229681i	$-0.926232\pi$
$41$	−1.84233	+	3.19101i	−0.287723	+	0.498352i	0.685542	+	0.728033i	$0.259565\pi$
$42$		0			0
$43$	3.78078	−	6.54850i	0.576563	−	0.998636i	−0.419307	−	0.907845i	$-0.637727\pi$
$43$	3.78078	−	6.54850i	0.576563	−	0.998636i	0.995870	−	0.0907919i	$-0.0289398\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	2.43845	+	4.22351i	0.355684	+	0.616063i	0.987235	−	0.159272i	$-0.0509146\pi$
$47$	2.43845	+	4.22351i	0.355684	+	0.616063i	−0.631551	+	0.775335i	$0.717581\pi$
$48$		0			0
$49$	10.0000			1.42857
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	3.71922	+	6.44188i	0.510875	+	0.884861i	0.999921	+	0.0126028i	$0.00401171\pi$
$53$	3.71922	+	6.44188i	0.510875	+	0.884861i	−0.489046	+	0.872258i	$0.662655\pi$
$54$		0			0
$55$	−1.28078	+	2.21837i	−0.172700	+	0.299125i
$56$		0			0
$57$	2.50000	+	3.57071i	0.331133	+	0.472953i
$58$		0			0
$59$	3.12311	−	5.40938i	0.406594	−	0.704241i	−0.587912	−	0.808925i	$-0.700050\pi$
$59$	3.12311	−	5.40938i	0.406594	−	0.704241i	0.994506	+	0.104684i	$0.0333831\pi$
$60$		0			0
$61$	2.34233	+	4.05703i	0.299905	+	0.519450i	0.976114	−	0.217260i	$-0.0697118\pi$
$61$	2.34233	+	4.05703i	0.299905	+	0.519450i	−0.676209	+	0.736710i	$0.736379\pi$
$62$		0			0
$63$	2.06155	+	3.57071i	0.259731	+	0.449868i
$64$		0			0
$65$	3.56155			0.441756
$66$		0			0
$67$	6.34233	+	10.9852i	0.774839	+	1.34206i	0.934885	+	0.354951i	$0.115502\pi$
$67$	6.34233	+	10.9852i	0.774839	+	1.34206i	−0.160046	+	0.987110i	$0.551164\pi$
$68$		0			0
$69$	0.561553			0.0676030
$70$		0			0
$71$	6.12311	−	10.6055i	0.726679	−	1.25864i	−0.231600	−	0.972811i	$-0.574396\pi$
$71$	6.12311	−	10.6055i	0.726679	−	1.25864i	0.958279	−	0.285834i	$-0.0922705\pi$
$72$		0			0
$73$	5.34233	−	9.25319i	0.625272	−	1.08300i	−0.363216	−	0.931705i	$-0.618321\pi$
$73$	5.34233	−	9.25319i	0.625272	−	1.08300i	0.988488	−	0.151298i	$-0.0483454\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−10.5616			−1.20360
$78$		0			0
$79$	−3.78078	+	6.54850i	−0.425371	+	0.736763i	−0.996455	−	0.0841279i	$-0.973190\pi$
$79$	−3.78078	+	6.54850i	−0.425371	+	0.736763i	0.571084	+	0.820891i	$0.306523\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	2.87689			0.315780			0.157890	−	0.987457i	$-0.449531\pi$
$83$	2.87689			0.315780			0.157890	+	0.987457i	$0.449531\pi$
$84$		0			0
$85$	−2.00000	−	3.46410i	−0.216930	−	0.375735i
$86$		0			0
$87$	1.12311			0.120410
$88$		0			0
$89$	5.84233	+	10.1192i	0.619286	+	1.07263i	0.989616	+	0.143734i	$0.0459110\pi$
$89$	5.84233	+	10.1192i	0.619286	+	1.07263i	−0.370331	+	0.928900i	$0.620756\pi$
$90$		0			0
$91$	7.34233	+	12.7173i	0.769685	+	1.33313i
$92$		0			0
$93$	−4.34233	+	7.52113i	−0.450279	+	0.779905i
$94$		0			0
$95$	2.50000	+	3.57071i	0.256495	+	0.366348i
$96$		0			0
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$		0			0
$99$	−1.28078	−	2.21837i	−0.128723	−	0.222955i
$100$		0			0
$101$	2.12311	+	3.67733i	0.211257	+	0.365908i	0.952108	−	0.305761i	$-0.0989110\pi$
$101$	2.12311	+	3.67733i	0.211257	+	0.365908i	−0.740851	+	0.671669i	$0.765578\pi$
$102$		0			0
$103$	−1.87689			−0.184936			−0.0924679	−	0.995716i	$-0.529476\pi$
$103$	−1.87689			−0.184936			−0.0924679	+	0.995716i	$0.529476\pi$
$104$		0			0
$105$	2.06155	+	3.57071i	0.201187	+	0.348466i
$106$		0			0
$107$	7.12311			0.688617			0.344308	−	0.938857i	$-0.388113\pi$
$107$	7.12311			0.688617			0.344308	+	0.938857i	$0.388113\pi$
$108$		0			0
$109$	−2.43845	+	4.22351i	−0.233561	+	0.404539i	−0.958853	−	0.283901i	$-0.908371\pi$
$109$	−2.43845	+	4.22351i	−0.233561	+	0.404539i	0.725293	+	0.688441i	$0.241704\pi$
$110$		0			0
$111$	4.50000	−	7.79423i	0.427121	−	0.739795i
$112$		0			0
$113$	10.2462			0.963882			0.481941	−	0.876204i	$-0.339932\pi$
$113$	10.2462			0.963882			0.481941	+	0.876204i	$0.339932\pi$
$114$		0			0
$115$	0.561553			0.0523651
$116$		0			0
$117$	−1.78078	+	3.08440i	−0.164633	+	0.285152i
$118$		0			0
$119$	8.24621	−	14.2829i	0.755929	−	1.30931i
$120$		0			0
$121$	−4.43845			−0.403495
$122$		0			0
$123$	−1.84233	−	3.19101i	−0.166117	−	0.287723i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.15767	+	7.20130i	0.368934	+	0.639012i	0.989399	−	0.145222i	$-0.0463896\pi$
$127$	4.15767	+	7.20130i	0.368934	+	0.639012i	−0.620465	+	0.784234i	$0.713056\pi$
$128$		0			0
$129$	3.78078	+	6.54850i	0.332879	+	0.576563i
$130$		0			0
$131$	8.52699	−	14.7692i	0.745006	−	1.29039i	−0.205185	−	0.978723i	$-0.565780\pi$
$131$	8.52699	−	14.7692i	0.745006	−	1.29039i	0.950192	−	0.311666i	$-0.100887\pi$
$132$		0			0
$133$	−7.59612	+	16.2880i	−0.658667	+	1.41235i
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−0.438447	−	0.759413i	−0.0374591	−	0.0648810i	0.846688	−	0.532090i	$-0.178593\pi$
$137$	−0.438447	−	0.759413i	−0.0374591	−	0.0648810i	−0.884147	+	0.467209i	$0.845260\pi$
$138$		0			0
$139$	10.7808	+	18.6729i	0.914414	+	1.58381i	0.807758	+	0.589515i	$0.200681\pi$
$139$	10.7808	+	18.6729i	0.914414	+	1.58381i	0.106656	+	0.994296i	$0.465986\pi$
$140$		0			0
$141$	−4.87689			−0.410709
$142$		0			0
$143$	−4.56155	−	7.90084i	−0.381456	−	0.660702i
$144$		0			0
$145$	1.12311			0.0932688
$146$		0			0
$147$	−5.00000	+	8.66025i	−0.412393	+	0.714286i
$148$		0			0
$149$	1.12311	−	1.94528i	0.0920084	−	0.159363i	−0.816348	−	0.577561i	$-0.804005\pi$
$149$	1.12311	−	1.94528i	0.0920084	−	0.159363i	0.908356	+	0.418198i	$0.137338\pi$
$150$		0			0
$151$	−2.24621			−0.182794			−0.0913970	−	0.995815i	$-0.529133\pi$
$151$	−2.24621			−0.182794			−0.0913970	+	0.995815i	$0.529133\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−4.34233	+	7.52113i	−0.348784	+	0.604112i
$156$		0			0
$157$	−5.18466	+	8.98009i	−0.413781	+	0.716689i	−0.995300	−	0.0968436i	$-0.969125\pi$
$157$	−5.18466	+	8.98009i	−0.413781	+	0.716689i	0.581519	+	0.813533i	$0.302459\pi$
$158$		0			0
$159$	−7.43845			−0.589907
$160$		0			0
$161$	1.15767	+	2.00514i	0.0912372	+	0.158028i
$162$		0			0
$163$	−9.31534			−0.729634			−0.364817	−	0.931079i	$-0.618868\pi$
$163$	−9.31534			−0.729634			−0.364817	+	0.931079i	$0.618868\pi$
$164$		0			0
$165$	−1.28078	−	2.21837i	−0.0997083	−	0.172700i
$166$		0			0
$167$	−0.157671	−	0.273094i	−0.0122009	−	0.0211326i	0.859860	−	0.510529i	$-0.170550\pi$
$167$	−0.157671	−	0.273094i	−0.0122009	−	0.0211326i	−0.872061	+	0.489396i	$0.837217\pi$
$168$		0			0
$169$	0.157671	−	0.273094i	0.0121285	−	0.0210072i
$170$		0			0
$171$	−4.34233	+	0.379706i	−0.332066	+	0.0290369i
$172$		0			0
$173$	10.4039	−	18.0201i	0.790993	−	1.37004i	−0.134360	−	0.990933i	$-0.542898\pi$
$173$	10.4039	−	18.0201i	0.790993	−	1.37004i	0.925353	−	0.379107i	$-0.123769\pi$
$174$		0			0
$175$	2.06155	+	3.57071i	0.155839	+	0.269921i
$176$		0			0
$177$	3.12311	+	5.40938i	0.234747	+	0.406594i
$178$		0			0
$179$	21.0540			1.57365			0.786824	−	0.617177i	$-0.211724\pi$
$179$	21.0540			1.57365			0.786824	+	0.617177i	$0.211724\pi$
$180$		0			0
$181$	−8.12311	−	14.0696i	−0.603786	−	1.04579i	−0.992242	−	0.124320i	$-0.960325\pi$
$181$	−8.12311	−	14.0696i	−0.603786	−	1.04579i	0.388456	−	0.921467i	$-0.373008\pi$
$182$		0			0
$183$	−4.68466			−0.346300
$184$		0			0
$185$	4.50000	−	7.79423i	0.330847	−	0.573043i
$186$		0			0
$187$	−5.12311	+	8.87348i	−0.374639	+	0.648893i
$188$		0			0
$189$	−4.12311			−0.299912
$190$		0			0
$191$	−18.4924			−1.33806			−0.669032	−	0.743233i	$-0.733291\pi$
$191$	−18.4924			−1.33806			−0.669032	+	0.743233i	$0.733291\pi$
$192$		0			0
$193$	3.21922	−	5.57586i	0.231725	−	0.401359i	−0.726591	−	0.687070i	$-0.758896\pi$
$193$	3.21922	−	5.57586i	0.231725	−	0.401359i	0.958316	+	0.285711i	$0.0922298\pi$
$194$		0			0
$195$	−1.78078	+	3.08440i	−0.127524	+	0.220878i
$196$		0			0
$197$	11.0540			0.787563			0.393782	−	0.919204i	$-0.371167\pi$
$197$	11.0540			0.787563			0.393782	+	0.919204i	$0.371167\pi$
$198$		0			0
$199$	−12.5885	−	21.8040i	−0.892378	−	1.54564i	−0.837017	−	0.547178i	$-0.815702\pi$
$199$	−12.5885	−	21.8040i	−0.892378	−	1.54564i	−0.0553614	−	0.998466i	$-0.517631\pi$
$200$		0			0
$201$	−12.6847			−0.894707
$202$		0			0
$203$	2.31534	+	4.01029i	0.162505	+	0.281467i
$204$		0			0
$205$	−1.84233	−	3.19101i	−0.128674	−	0.222870i
$206$		0			0
$207$	−0.280776	+	0.486319i	−0.0195153	+	0.0338015i
$208$		0			0
$209$	4.71922	−	10.1192i	0.326436	−	0.699960i
$210$		0			0
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	−0.882723	−	0.469894i	$-0.844292\pi$
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	0.848301	+	0.529514i	$0.177626\pi$
$212$		0			0
$213$	6.12311	+	10.6055i	0.419548	+	0.726679i
$214$		0			0
$215$	3.78078	+	6.54850i	0.257847	+	0.446604i
$216$		0			0
$217$	−35.8078			−2.43079
$218$		0			0
$219$	5.34233	+	9.25319i	0.361001	+	0.625272i
$220$		0			0
$221$	14.2462			0.958304
$222$		0			0
$223$	5.18466	−	8.98009i	0.347190	−	0.601351i	−0.638559	−	0.769573i	$-0.720469\pi$
$223$	5.18466	−	8.98009i	0.347190	−	0.601351i	0.985749	+	0.168222i	$0.0538024\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	8.24621			0.547320			0.273660	−	0.961826i	$-0.411766\pi$
$227$	8.24621			0.547320			0.273660	+	0.961826i	$0.411766\pi$
$228$		0			0
$229$	1.31534			0.0869202			0.0434601	−	0.999055i	$-0.486162\pi$
$229$	1.31534			0.0869202			0.0434601	+	0.999055i	$0.486162\pi$
$230$		0			0
$231$	5.28078	−	9.14657i	0.347450	−	0.601800i
$232$		0			0
$233$	−2.12311	+	3.67733i	−0.139089	+	0.240910i	−0.927152	−	0.374685i	$-0.877751\pi$
$233$	−2.12311	+	3.67733i	−0.139089	+	0.240910i	0.788063	+	0.615595i	$0.211084\pi$
$234$		0			0
$235$	−4.87689			−0.318134
$236$		0			0
$237$	−3.78078	−	6.54850i	−0.245588	−	0.425371i
$238$		0			0
$239$	27.1231			1.75445			0.877224	−	0.480081i	$-0.159393\pi$
$239$	27.1231			1.75445			0.877224	+	0.480081i	$0.159393\pi$
$240$		0			0
$241$	6.21922	+	10.7720i	0.400615	+	0.693886i	0.993800	−	0.111180i	$-0.0354630\pi$
$241$	6.21922	+	10.7720i	0.400615	+	0.693886i	−0.593185	+	0.805066i	$0.702130\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−5.00000	+	8.66025i	−0.319438	+	0.553283i
$246$		0			0
$247$	−15.4654	+	1.35234i	−0.984042	+	0.0860476i
$248$		0			0
$249$	−1.43845	+	2.49146i	−0.0911579	+	0.157890i
$250$		0			0
$251$	−2.68466	−	4.64996i	−0.169454	−	0.293503i	0.768774	−	0.639521i	$-0.220867\pi$
$251$	−2.68466	−	4.64996i	−0.169454	−	0.293503i	−0.938228	+	0.346017i	$0.887534\pi$
$252$		0			0
$253$	−0.719224	−	1.24573i	−0.0452172	−	0.0783185i
$254$		0			0
$255$	4.00000			0.250490
$256$		0			0
$257$	−8.12311	−	14.0696i	−0.506705	−	0.877640i	−0.999970	−	0.00776012i	$-0.997530\pi$
$257$	−8.12311	−	14.0696i	−0.506705	−	0.877640i	0.493264	−	0.869879i	$-0.335803\pi$
$258$		0			0
$259$	37.1080			2.30578
$260$		0			0
$261$	−0.561553	+	0.972638i	−0.0347592	+	0.0602048i
$262$		0			0
$263$	12.5270	−	21.6974i	0.772447	−	1.33792i	−0.163771	−	0.986498i	$-0.552366\pi$
$263$	12.5270	−	21.6974i	0.772447	−	1.33792i	0.936218	−	0.351419i	$-0.114301\pi$
$264$		0			0
$265$	−7.43845			−0.456940
$266$		0			0
$267$	−11.6847			−0.715089
$268$		0			0
$269$	−6.24621	+	10.8188i	−0.380838	+	0.659631i	−0.991182	−	0.132505i	$-0.957698\pi$
$269$	−6.24621	+	10.8188i	−0.380838	+	0.659631i	0.610344	+	0.792136i	$0.291031\pi$
$270$		0			0
$271$	−12.8078	+	22.1837i	−0.778016	+	1.34756i	0.155067	+	0.987904i	$0.450441\pi$
$271$	−12.8078	+	22.1837i	−0.778016	+	1.34756i	−0.933084	+	0.359660i	$0.882893\pi$
$272$		0			0
$273$	−14.6847			−0.888756
$274$		0			0
$275$	−1.28078	−	2.21837i	−0.0772337	−	0.133773i
$276$		0			0
$277$	24.2462			1.45681			0.728407	−	0.685145i	$-0.240261\pi$
$277$	24.2462			1.45681			0.728407	+	0.685145i	$0.240261\pi$
$278$		0			0
$279$	−4.34233	−	7.52113i	−0.259968	−	0.450279i
$280$		0			0
$281$	6.52699	+	11.3051i	0.389367	+	0.674404i	0.992365	−	0.123339i	$-0.0393603\pi$
$281$	6.52699	+	11.3051i	0.389367	+	0.674404i	−0.602997	+	0.797743i	$0.706027\pi$
$282$		0			0
$283$	7.43845	−	12.8838i	0.442170	−	0.765861i	−0.555680	−	0.831396i	$-0.687542\pi$
$283$	7.43845	−	12.8838i	0.442170	−	0.765861i	0.997850	+	0.0655354i	$0.0208755\pi$
$284$		0			0
$285$	−4.34233	+	0.379706i	−0.257217	+	0.0224919i
$286$		0			0
$287$	7.59612	−	13.1569i	0.448385	−	0.776625i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$		0			0
$293$	−29.0540			−1.69735			−0.848676	−	0.528914i	$-0.822600\pi$
$293$	−29.0540			−1.69735			−0.848676	+	0.528914i	$0.822600\pi$
$294$		0			0
$295$	3.12311	+	5.40938i	0.181834	+	0.314946i
$296$		0			0
$297$	2.56155			0.148636
$298$		0			0
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−15.5885	+	27.0001i	−0.898509	+	1.55626i
$302$		0			0
$303$	−4.24621			−0.243938
$304$		0			0
$305$	−4.68466			−0.268243
$306$		0			0
$307$	12.5616	−	21.7572i	0.716926	−	1.24175i	−0.245286	−	0.969451i	$-0.578882\pi$
$307$	12.5616	−	21.7572i	0.716926	−	1.24175i	0.962212	−	0.272301i	$-0.0877847\pi$
$308$		0			0
$309$	0.938447	−	1.62544i	0.0533864	−	0.0924679i
$310$		0			0
$311$	−10.2462			−0.581009			−0.290505	−	0.956874i	$-0.593823\pi$
$311$	−10.2462			−0.581009			−0.290505	+	0.956874i	$0.593823\pi$
$312$		0			0
$313$	−0.684658	−	1.18586i	−0.0386992	−	0.0670290i	0.846027	−	0.533140i	$-0.178988\pi$
$313$	−0.684658	−	1.18586i	−0.0386992	−	0.0670290i	−0.884726	+	0.466111i	$0.845655\pi$
$314$		0			0
$315$	−4.12311			−0.232311
$316$		0			0
$317$	2.84233	+	4.92306i	0.159641	+	0.276507i	0.934739	−	0.355334i	$-0.115633\pi$
$317$	2.84233	+	4.92306i	0.159641	+	0.276507i	−0.775098	+	0.631841i	$0.782300\pi$
$318$		0			0
$319$	−1.43845	−	2.49146i	−0.0805376	−	0.139495i
$320$		0			0
$321$	−3.56155	+	6.16879i	−0.198786	+	0.344308i
$322$		0			0
$323$	10.0000	+	14.2829i	0.556415	+	0.794719i
$324$		0			0
$325$	−1.78078	+	3.08440i	−0.0987797	+	0.171091i
$326$		0			0
$327$	−2.43845	−	4.22351i	−0.134846	−	0.233561i
$328$		0			0
$329$	−10.0540	−	17.4140i	−0.554294	−	0.960065i
$330$		0			0
$331$	29.7386			1.63458			0.817292	−	0.576224i	$-0.195475\pi$
$331$	29.7386			1.63458			0.817292	+	0.576224i	$0.195475\pi$
$332$		0			0
$333$	4.50000	+	7.79423i	0.246598	+	0.427121i
$334$		0			0
$335$	−12.6847			−0.693037
$336$		0			0
$337$	−6.02699	+	10.4390i	−0.328311	+	0.568651i	−0.982177	−	0.187959i	$-0.939813\pi$
$337$	−6.02699	+	10.4390i	−0.328311	+	0.568651i	0.653866	+	0.756610i	$0.273146\pi$
$338$		0			0
$339$	−5.12311	+	8.87348i	−0.278249	+	0.481941i
$340$		0			0
$341$	22.2462			1.20470
$342$		0			0
$343$	−12.3693			−0.667880
$344$		0			0
$345$	−0.280776	+	0.486319i	−0.0151165	+	0.0261825i
$346$		0			0
$347$	5.00000	−	8.66025i	0.268414	−	0.464907i	−0.700038	−	0.714105i	$-0.746834\pi$
$347$	5.00000	−	8.66025i	0.268414	−	0.464907i	0.968452	+	0.249198i	$0.0801671\pi$
$348$		0			0
$349$	35.8078			1.91675			0.958373	−	0.285520i	$-0.0921662\pi$
$349$	35.8078			1.91675			0.958373	+	0.285520i	$0.0921662\pi$
$350$		0			0
$351$	−1.78078	−	3.08440i	−0.0950508	−	0.164633i
$352$		0			0
$353$	13.3693			0.711577			0.355788	−	0.934567i	$-0.384212\pi$
$353$	13.3693			0.711577			0.355788	+	0.934567i	$0.384212\pi$
$354$		0			0
$355$	6.12311	+	10.6055i	0.324981	+	0.562883i
$356$		0			0
$357$	8.24621	+	14.2829i	0.436436	+	0.755929i
$358$		0			0
$359$	13.6847	−	23.7025i	0.722249	−	1.25097i	−0.237848	−	0.971302i	$-0.576442\pi$
$359$	13.6847	−	23.7025i	0.722249	−	1.25097i	0.960096	−	0.279669i	$-0.0902247\pi$
$360$		0			0
$361$	−12.2116	−	14.5560i	−0.642718	−	0.766103i
$362$		0			0
$363$	2.21922	−	3.84381i	0.116479	−	0.201748i
$364$		0			0
$365$	5.34233	+	9.25319i	0.279630	+	0.484334i
$366$		0			0
$367$	5.46543	+	9.46641i	0.285293	+	0.494143i	0.972680	−	0.232149i	$-0.0745756\pi$
$367$	5.46543	+	9.46641i	0.285293	+	0.494143i	−0.687387	+	0.726291i	$0.741242\pi$
$368$		0			0
$369$	3.68466			0.191816
$370$		0			0
$371$	−15.3348	−	26.5606i	−0.796141	−	1.37896i
$372$		0			0
$373$	1.19224			0.0617316			0.0308658	−	0.999524i	$-0.490174\pi$
$373$	1.19224			0.0617316			0.0308658	+	0.999524i	$0.490174\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−2.00000	+	3.46410i	−0.103005	+	0.178410i
$378$		0			0
$379$	−20.6847			−1.06250			−0.531250	−	0.847215i	$-0.678277\pi$
$379$	−20.6847			−1.06250			−0.531250	+	0.847215i	$0.678277\pi$
$380$		0			0
$381$	−8.31534			−0.426008
$382$		0			0
$383$	0.876894	−	1.51883i	0.0448072	−	0.0776084i	−0.842752	−	0.538302i	$-0.819066\pi$
$383$	0.876894	−	1.51883i	0.0448072	−	0.0776084i	0.887559	+	0.460694i	$0.152399\pi$
$384$		0			0
$385$	5.28078	−	9.14657i	0.269133	−	0.466153i
$386$		0			0
$387$	−7.56155			−0.384375
$388$		0			0
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	−0.997686	−	0.0679877i	$-0.978342\pi$
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	0.439964	−	0.898015i	$-0.354991\pi$
$390$		0			0
$391$	2.24621			0.113596
$392$		0			0
$393$	8.52699	+	14.7692i	0.430130	+	0.745006i
$394$		0			0
$395$	−3.78078	−	6.54850i	−0.190232	−	0.329491i
$396$		0			0
$397$	−1.74621	+	3.02453i	−0.0876398	+	0.151797i	−0.906513	−	0.422178i	$-0.861266\pi$
$397$	−1.74621	+	3.02453i	−0.0876398	+	0.151797i	0.818873	+	0.573974i	$0.194599\pi$
$398$		0			0
$399$	−10.3078	−	14.7224i	−0.516034	−	0.737043i
$400$		0			0
$401$	1.68466	−	2.91791i	0.0841278	−	0.145714i	−0.820891	−	0.571084i	$-0.806523\pi$
$401$	1.68466	−	2.91791i	0.0841278	−	0.145714i	0.905019	+	0.425371i	$0.139856\pi$
$402$		0			0
$403$	−15.4654	−	26.7869i	−0.770388	−	1.33435i
$404$		0			0
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		0			0
$407$	−23.0540			−1.14274
$408$		0			0
$409$	−9.96543	−	17.2606i	−0.492759	−	0.853484i	0.507206	−	0.861825i	$-0.330678\pi$
$409$	−9.96543	−	17.2606i	−0.492759	−	0.853484i	−0.999965	+	0.00834106i	$0.997345\pi$
$410$		0			0
$411$	0.876894			0.0432540
$412$		0			0
$413$	−12.8769	+	22.3034i	−0.633631	+	1.09748i
$414$		0			0
$415$	−1.43845	+	2.49146i	−0.0706106	+	0.122301i
$416$		0			0
$417$	−21.5616			−1.05587
$418$		0			0
$419$	−20.1771			−0.985715			−0.492857	−	0.870110i	$-0.664048\pi$
$419$	−20.1771			−0.985715			−0.492857	+	0.870110i	$0.664048\pi$
$420$		0			0
$421$	−17.5616	+	30.4175i	−0.855898	+	1.48246i	0.0199120	+	0.999802i	$0.493661\pi$
$421$	−17.5616	+	30.4175i	−0.855898	+	1.48246i	−0.875810	+	0.482657i	$0.839672\pi$
$422$		0			0
$423$	2.43845	−	4.22351i	0.118561	−	0.205354i
$424$		0			0
$425$	4.00000			0.194029
$426$		0			0
$427$	−9.65767	−	16.7276i	−0.467367	−	0.809504i
$428$		0			0
$429$	9.12311			0.440468
$430$		0			0
$431$	−13.8078	−	23.9157i	−0.665097	−	1.15198i	−0.979259	−	0.202612i	$-0.935057\pi$
$431$	−13.8078	−	23.9157i	−0.665097	−	1.15198i	0.314163	−	0.949369i	$-0.398276\pi$
$432$		0			0
$433$	−7.34233	−	12.7173i	−0.352850	−	0.611154i	0.633898	−	0.773417i	$-0.281454\pi$
$433$	−7.34233	−	12.7173i	−0.352850	−	0.611154i	−0.986748	+	0.162263i	$0.948121\pi$
$434$		0			0
$435$	−0.561553	+	0.972638i	−0.0269244	+	0.0466344i
$436$		0			0
$437$	−2.43845	+	0.213225i	−0.116647	+	0.0101999i
$438$		0			0
$439$	5.21922	−	9.03996i	0.249100	−	0.431454i	−0.714176	−	0.699966i	$-0.753199\pi$
$439$	5.21922	−	9.03996i	0.249100	−	0.431454i	0.963276	+	0.268512i	$0.0865319\pi$
$440$		0			0
$441$	−5.00000	−	8.66025i	−0.238095	−	0.412393i
$442$		0			0
$443$	15.1231	+	26.1940i	0.718520	+	1.24451i	0.961586	+	0.274504i	$0.0885137\pi$
$443$	15.1231	+	26.1940i	0.718520	+	1.24451i	−0.243066	+	0.970010i	$0.578153\pi$
$444$		0			0
$445$	−11.6847			−0.553906
$446$		0			0
$447$	1.12311	+	1.94528i	0.0531211	+	0.0920084i
$448$		0			0
$449$	−17.4384			−0.822971			−0.411486	−	0.911416i	$-0.634990\pi$
$449$	−17.4384			−0.822971			−0.411486	+	0.911416i	$0.634990\pi$
$450$		0			0
$451$	−4.71922	+	8.17394i	−0.222220	+	0.384896i
$452$		0			0
$453$	1.12311	−	1.94528i	0.0527681	−	0.0913970i
$454$		0			0
$455$	−14.6847			−0.688427
$456$		0			0
$457$	−26.0540			−1.21875			−0.609377	−	0.792881i	$-0.708580\pi$
$457$	−26.0540			−1.21875			−0.609377	+	0.792881i	$0.708580\pi$
$458$		0			0
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	12.5616	−	21.7572i	0.585050	−	1.01334i	−0.409819	−	0.912167i	$-0.634408\pi$
$461$	12.5616	−	21.7572i	0.585050	−	1.01334i	0.994869	−	0.101169i	$-0.0322584\pi$
$462$		0			0
$463$	−9.49242			−0.441150			−0.220575	−	0.975370i	$-0.570793\pi$
$463$	−9.49242			−0.441150			−0.220575	+	0.975370i	$0.570793\pi$
$464$		0			0
$465$	−4.34233	−	7.52113i	−0.201371	−	0.348784i
$466$		0			0
$467$	−19.3693			−0.896305			−0.448153	−	0.893957i	$-0.647918\pi$
$467$	−19.3693			−0.896305			−0.448153	+	0.893957i	$0.647918\pi$
$468$		0			0
$469$	−26.1501	−	45.2933i	−1.20750	−	2.09145i
$470$		0			0
$471$	−5.18466	−	8.98009i	−0.238896	−	0.413781i
$472$		0			0
$473$	9.68466	−	16.7743i	0.445301	−	0.771284i
$474$		0			0
$475$	−4.34233	+	0.379706i	−0.199240	+	0.0174221i
$476$		0			0
$477$	3.71922	−	6.44188i	0.170292	−	0.294954i
$478$		0			0
$479$	7.87689	+	13.6432i	0.359904	+	0.623373i	0.987945	−	0.154808i	$-0.0494759\pi$
$479$	7.87689	+	13.6432i	0.359904	+	0.623373i	−0.628040	+	0.778181i	$0.716143\pi$
$480$		0			0
$481$	16.0270	+	27.7596i	0.730768	+	1.26573i
$482$		0			0
$483$	−2.31534			−0.105352
$484$		0			0
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−24.3153			−1.10183			−0.550917	−	0.834560i	$-0.685722\pi$
$487$	−24.3153			−1.10183			−0.550917	+	0.834560i	$0.685722\pi$
$488$		0			0
$489$	4.65767	−	8.06732i	0.210627	−	0.364817i
$490$		0			0
$491$	10.8423	−	18.7795i	0.489307	−	0.847505i	−0.510617	−	0.859808i	$-0.670583\pi$
$491$	10.8423	−	18.7795i	0.489307	−	0.847505i	0.999924	+	0.0123030i	$0.00391626\pi$
$492$		0			0
$493$	4.49242			0.202329
$494$		0			0
$495$	2.56155			0.115133
$496$		0			0
$497$	−25.2462	+	43.7277i	−1.13245	+	1.96146i
$498$		0			0
$499$	0.623106	−	1.07925i	0.0278940	−	0.0483139i	−0.851741	−	0.523962i	$-0.824453\pi$
$499$	0.623106	−	1.07925i	0.0278940	−	0.0483139i	0.879635	+	0.475648i	$0.157787\pi$
$500$		0			0
$501$	0.315342			0.0140884
$502$		0			0
$503$	−5.28078	−	9.14657i	−0.235458	−	0.407826i	0.723948	−	0.689855i	$-0.242326\pi$
$503$	−5.28078	−	9.14657i	−0.235458	−	0.407826i	−0.959406	+	0.282029i	$0.908992\pi$
$504$		0			0
$505$	−4.24621			−0.188954
$506$		0			0
$507$	0.157671	+	0.273094i	0.00700241	+	0.0121285i
$508$		0			0
$509$	−13.4924	−	23.3696i	−0.598041	−	1.03584i	−0.993110	−	0.117186i	$-0.962613\pi$
$509$	−13.4924	−	23.3696i	−0.598041	−	1.03584i	0.395069	−	0.918652i	$-0.370721\pi$
$510$		0			0
$511$	−22.0270	+	38.1519i	−0.974417	+	1.68774i
$512$		0			0
$513$	1.84233	−	3.95042i	0.0813408	−	0.174415i
$514$		0			0
$515$	0.938447	−	1.62544i	0.0413529	−	0.0716254i
$516$		0			0
$517$	6.24621	+	10.8188i	0.274708	+	0.475808i
$518$		0			0
$519$	10.4039	+	18.0201i	0.456680	+	0.790993i
$520$		0			0
$521$	−43.8617			−1.92162			−0.960809	−	0.277212i	$-0.910590\pi$
$521$	−43.8617			−1.92162			−0.960809	+	0.277212i	$0.910590\pi$
$522$		0			0
$523$	−6.90388	−	11.9579i	−0.301886	−	0.522881i	0.674677	−	0.738113i	$-0.264283\pi$
$523$	−6.90388	−	11.9579i	−0.301886	−	0.522881i	−0.976563	+	0.215231i	$0.930949\pi$
$524$		0			0
$525$	−4.12311			−0.179947
$526$		0			0
$527$	−17.3693	+	30.0845i	−0.756619	+	1.31050i
$528$		0			0
$529$	11.3423	−	19.6455i	0.493145	−	0.854152i
$530$		0			0
$531$	−6.24621			−0.271062
$532$		0			0
$533$	13.1231			0.568425
$534$		0			0
$535$	−3.56155	+	6.16879i	−0.153979	+	0.266700i
$536$		0			0
$537$	−10.5270	+	18.2333i	−0.454273	+	0.786824i
$538$		0			0
$539$	25.6155			1.10334
$540$		0			0
$541$	9.02699	+	15.6352i	0.388101	+	0.672210i	0.992194	−	0.124704i	$-0.0397980\pi$
$541$	9.02699	+	15.6352i	0.388101	+	0.672210i	−0.604094	+	0.796913i	$0.706465\pi$
$542$		0			0
$543$	16.2462			0.697192
$544$		0			0
$545$	−2.43845	−	4.22351i	−0.104452	−	0.180915i
$546$		0			0
$547$	6.90388	+	11.9579i	0.295189	+	0.511282i	0.975029	−	0.222079i	$-0.0712842\pi$
$547$	6.90388	+	11.9579i	0.295189	+	0.511282i	−0.679840	+	0.733360i	$0.737951\pi$
$548$		0			0
$549$	2.34233	−	4.05703i	0.0999682	−	0.173150i
$550$		0			0
$551$	−4.87689	+	0.426450i	−0.207763	+	0.0181674i
$552$		0			0
$553$	15.5885	−	27.0001i	0.662892	−	1.14816i
$554$		0			0
$555$	4.50000	+	7.79423i	0.191014	+	0.330847i
$556$		0			0
$557$	−0.842329	−	1.45896i	−0.0356906	−	0.0618180i	0.847628	−	0.530590i	$-0.178030\pi$
$557$	−0.842329	−	1.45896i	−0.0356906	−	0.0618180i	−0.883319	+	0.468772i	$0.844696\pi$
$558$		0			0
$559$	−26.9309			−1.13905
$560$		0			0
$561$	−5.12311	−	8.87348i	−0.216298	−	0.374639i
$562$		0			0
$563$	−33.3693			−1.40635			−0.703175	−	0.711017i	$-0.748235\pi$
$563$	−33.3693			−1.40635			−0.703175	+	0.711017i	$0.748235\pi$
$564$		0			0
$565$	−5.12311	+	8.87348i	−0.215531	+	0.373310i
$566$		0			0
$567$	2.06155	−	3.57071i	0.0865771	−	0.149956i
$568$		0			0
$569$	33.3002			1.39602			0.698008	−	0.716090i	$-0.254070\pi$
$569$	33.3002			1.39602			0.698008	+	0.716090i	$0.254070\pi$
$570$		0			0
$571$	20.6847			0.865626			0.432813	−	0.901484i	$-0.357521\pi$
$571$	20.6847			0.865626			0.432813	+	0.901484i	$0.357521\pi$
$572$		0			0
$573$	9.24621	−	16.0149i	0.386266	−	0.669032i
$574$		0			0
$575$	−0.280776	+	0.486319i	−0.0117092	+	0.0202809i
$576$		0			0
$577$	14.6307			0.609083			0.304542	−	0.952499i	$-0.401497\pi$
$577$	14.6307			0.609083			0.304542	+	0.952499i	$0.401497\pi$
$578$		0			0
$579$	3.21922	+	5.57586i	0.133786	+	0.231725i
$580$		0			0
$581$	−11.8617			−0.492108
$582$		0			0
$583$	9.52699	+	16.5012i	0.394568	+	0.683411i
$584$		0			0
$585$	−1.78078	−	3.08440i	−0.0736260	−	0.127524i
$586$		0			0
$587$	−10.8769	+	18.8393i	−0.448937	+	0.777583i	−0.998317	−	0.0579903i	$-0.981531\pi$
$587$	−10.8769	+	18.8393i	−0.448937	+	0.777583i	0.549380	+	0.835573i	$0.314864\pi$
$588$		0			0
$589$	16.0000	−	34.3081i	0.659269	−	1.41364i
$590$		0			0
$591$	−5.52699	+	9.57302i	−0.227350	+	0.393782i
$592$		0			0
$593$	5.68466	+	9.84612i	0.233441	+	0.404332i	0.958818	−	0.284020i	$-0.0916681\pi$
$593$	5.68466	+	9.84612i	0.233441	+	0.404332i	−0.725378	+	0.688351i	$0.758335\pi$
$594$		0			0
$595$	8.24621	+	14.2829i	0.338062	+	0.585540i
$596$		0			0
$597$	25.1771			1.03043
$598$		0			0
$599$	17.3693	+	30.0845i	0.709691	+	1.22922i	0.964972	+	0.262354i	$0.0844988\pi$
$599$	17.3693	+	30.0845i	0.709691	+	1.22922i	−0.255281	+	0.966867i	$0.582168\pi$
$600$		0			0
$601$	−26.6155			−1.08567			−0.542835	−	0.839839i	$-0.682649\pi$
$601$	−26.6155			−1.08567			−0.542835	+	0.839839i	$0.682649\pi$
$602$		0			0
$603$	6.34233	−	10.9852i	0.258280	−	0.447353i
$604$		0			0
$605$	2.21922	−	3.84381i	0.0902243	−	0.156273i
$606$		0			0
$607$	−26.8617			−1.09028			−0.545142	−	0.838344i	$-0.683524\pi$
$607$	−26.8617			−1.09028			−0.545142	+	0.838344i	$0.683524\pi$
$608$		0			0
$609$	−4.63068			−0.187645
$610$		0			0
$611$	8.68466	−	15.0423i	0.351344	−	0.608545i
$612$		0			0
$613$	−16.7732	+	29.0520i	−0.677463	+	1.17340i	0.298279	+	0.954479i	$0.403587\pi$
$613$	−16.7732	+	29.0520i	−0.677463	+	1.17340i	−0.975742	+	0.218922i	$0.929746\pi$
$614$		0			0
$615$	3.68466			0.148580
$616$		0			0
$617$	10.2462	+	17.7470i	0.412497	+	0.714466i	0.995162	−	0.0982467i	$-0.0313234\pi$
$617$	10.2462	+	17.7470i	0.412497	+	0.714466i	−0.582665	+	0.812712i	$0.697990\pi$
$618$		0			0
$619$	−8.61553			−0.346287			−0.173144	−	0.984897i	$-0.555392\pi$
$619$	−8.61553			−0.346287			−0.173144	+	0.984897i	$0.555392\pi$
$620$		0			0
$621$	−0.280776	−	0.486319i	−0.0112672	−	0.0195153i
$622$		0			0
$623$	−24.0885	−	41.7226i	−0.965087	−	1.67158i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	6.40388	+	9.14657i	0.255746	+	0.365279i
$628$		0			0
$629$	18.0000	−	31.1769i	0.717707	−	1.24310i
$630$		0			0
$631$	−20.9039	−	36.2066i	−0.832170	−	1.44136i	−0.896314	−	0.443421i	$-0.853765\pi$
$631$	−20.9039	−	36.2066i	−0.832170	−	1.44136i	0.0641432	−	0.997941i	$-0.479569\pi$
$632$		0			0
$633$	−0.500000	−	0.866025i	−0.0198732	−	0.0344214i
$634$		0			0
$635$	−8.31534			−0.329984
$636$		0			0
$637$	−17.8078	−	30.8440i	−0.705569	−	1.22208i
$638$		0			0
$639$	−12.2462			−0.484453
$640$		0			0
$641$	3.24621	−	5.62260i	0.128218	−	0.222079i	−0.794768	−	0.606913i	$-0.792408\pi$
$641$	3.24621	−	5.62260i	0.128218	−	0.222079i	0.922986	+	0.384833i	$0.125741\pi$
$642$		0			0
$643$	3.90388	−	6.76172i	0.153954	−	0.266656i	−0.778724	−	0.627367i	$-0.784133\pi$
$643$	3.90388	−	6.76172i	0.153954	−	0.266656i	0.932678	+	0.360711i	$0.117466\pi$
$644$		0			0
$645$	−7.56155			−0.297736
$646$		0			0
$647$	3.19224			0.125500			0.0627499	−	0.998029i	$-0.480013\pi$
$647$	3.19224			0.125500			0.0627499	+	0.998029i	$0.480013\pi$
$648$		0			0
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$		0			0
$651$	17.9039	−	31.0104i	0.701708	−	1.21539i
$652$		0			0
$653$	5.19224			0.203188			0.101594	−	0.994826i	$-0.467606\pi$
$653$	5.19224			0.203188			0.101594	+	0.994826i	$0.467606\pi$
$654$		0			0
$655$	8.52699	+	14.7692i	0.333177	+	0.577079i
$656$		0			0
$657$	−10.6847			−0.416848
$658$		0			0
$659$	15.8423	+	27.4397i	0.617130	+	1.06890i	0.990007	+	0.141019i	$0.0450379\pi$
$659$	15.8423	+	27.4397i	0.617130	+	1.06890i	−0.372877	+	0.927881i	$0.621629\pi$
$660$		0			0
$661$	4.93087	+	8.54052i	0.191789	+	0.332188i	0.945843	−	0.324624i	$-0.105238\pi$
$661$	4.93087	+	8.54052i	0.191789	+	0.332188i	−0.754054	+	0.656812i	$0.771905\pi$
$662$		0			0
$663$	−7.12311	+	12.3376i	−0.276638	+	0.479152i
$664$		0			0
$665$	−10.3078	−	14.7224i	−0.399718	−	0.570911i
$666$		0			0
$667$	−0.315342	+	0.546188i	−0.0122101	+	0.0211485i
$668$		0			0
$669$	5.18466	+	8.98009i	0.200450	+	0.347190i
$670$		0			0
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$		0			0
$673$	19.8078			0.763533			0.381767	−	0.924259i	$-0.375316\pi$
$673$	19.8078			0.763533			0.381767	+	0.924259i	$0.375316\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	13.6847			0.525944			0.262972	−	0.964803i	$-0.415297\pi$
$677$	13.6847			0.525944			0.262972	+	0.964803i	$0.415297\pi$
$678$		0			0
$679$	−12.3693	+	21.4243i	−0.474691	+	0.822189i
$680$		0			0
$681$	−4.12311	+	7.14143i	−0.157998	+	0.273660i
$682$		0			0
$683$	51.1231			1.95617			0.978086	−	0.208203i	$-0.0667615\pi$
$683$	51.1231			1.95617			0.978086	+	0.208203i	$0.0667615\pi$
$684$		0			0
$685$	0.876894			0.0335044
$686$		0			0
$687$	−0.657671	+	1.13912i	−0.0250917	+	0.0434601i
$688$		0			0
$689$	13.2462	−	22.9431i	0.504640	−	0.874063i
$690$		0			0
$691$	2.56155			0.0974461			0.0487230	−	0.998812i	$-0.484485\pi$
$691$	2.56155			0.0974461			0.0487230	+	0.998812i	$0.484485\pi$
$692$		0			0
$693$	5.28078	+	9.14657i	0.200600	+	0.347450i
$694$		0			0
$695$	−21.5616			−0.817876
$696$		0			0
$697$	−7.36932	−	12.7640i	−0.279133	−	0.483472i
$698$		0			0
$699$	−2.12311	−	3.67733i	−0.0803032	−	0.139089i
$700$		0			0
$701$	14.1231	−	24.4619i	0.533422	−	0.923915i	−0.465816	−	0.884882i	$-0.654239\pi$
$701$	14.1231	−	24.4619i	0.533422	−	0.923915i	0.999238	−	0.0390328i	$-0.0124277\pi$
$702$		0			0
$703$	−16.5810	+	35.5538i	−0.625363	+	1.34094i
$704$		0			0
$705$	2.43845	−	4.22351i	0.0918372	−	0.159067i
$706$		0			0
$707$	−8.75379	−	15.1620i	−0.329220	−	0.570226i
$708$		0			0
$709$	−9.46543	−	16.3946i	−0.355482	−	0.615713i	0.631718	−	0.775198i	$-0.282350\pi$
$709$	−9.46543	−	16.3946i	−0.355482	−	0.615713i	−0.987200	+	0.159485i	$0.949017\pi$
$710$		0			0
$711$	7.56155			0.283580
$712$		0			0
$713$	−2.43845	−	4.22351i	−0.0913206	−	0.158172i
$714$		0			0
$715$	9.12311			0.341185
$716$		0			0
$717$	−13.5616	+	23.4893i	−0.506465	+	0.877224i
$718$		0			0
$719$	−8.43845	+	14.6158i	−0.314701	+	0.545078i	−0.979374	−	0.202056i	$-0.935238\pi$
$719$	−8.43845	+	14.6158i	−0.314701	+	0.545078i	0.664673	+	0.747134i	$0.268571\pi$
$720$		0			0
$721$	7.73863			0.288202
$722$		0			0
$723$	−12.4384			−0.462591
$724$		0			0
$725$	−0.561553	+	0.972638i	−0.0208555	+	0.0361229i
$726$		0			0
$727$	10.7808	−	18.6729i	0.399837	−	0.692538i	−0.593869	−	0.804562i	$-0.702400\pi$
$727$	10.7808	−	18.6729i	0.399837	−	0.692538i	0.993705	+	0.112024i	$0.0357334\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.1231	+	26.1940i	0.559348	+	0.968820i
$732$		0			0
$733$	22.8078			0.842424			0.421212	−	0.906962i	$-0.361605\pi$
$733$	22.8078			0.842424			0.421212	+	0.906962i	$0.361605\pi$
$734$		0			0
$735$	−5.00000	−	8.66025i	−0.184428	−	0.319438i
$736$		0			0
$737$	16.2462	+	28.1393i	0.598437	+	1.03652i
$738$		0			0
$739$	−21.4309	+	37.1194i	−0.788347	+	1.36546i	0.138632	+	0.990344i	$0.455730\pi$
$739$	−21.4309	+	37.1194i	−0.788347	+	1.36546i	−0.926979	+	0.375114i	$0.877604\pi$
$740$		0			0
$741$	6.56155	−	14.0696i	0.241045	−	0.516861i
$742$		0			0
$743$	20.4039	−	35.3406i	0.748546	−	1.29652i	−0.199974	−	0.979801i	$-0.564086\pi$
$743$	20.4039	−	35.3406i	0.748546	−	1.29652i	0.948520	−	0.316718i	$-0.102581\pi$
$744$		0			0
$745$	1.12311	+	1.94528i	0.0411474	+	0.0712694i
$746$		0			0
$747$	−1.43845	−	2.49146i	−0.0526300	−	0.0911579i
$748$		0			0
$749$	−29.3693			−1.07313
$750$		0			0
$751$	11.2732	+	19.5258i	0.411365	+	0.712505i	0.995039	−	0.0994830i	$-0.0317189\pi$
$751$	11.2732	+	19.5258i	0.411365	+	0.712505i	−0.583674	+	0.811988i	$0.698386\pi$
$752$		0			0
$753$	5.36932			0.195669
$754$		0			0
$755$	1.12311	−	1.94528i	0.0408740	−	0.0707958i
$756$		0			0
$757$	−13.3078	+	23.0497i	−0.483679	+	0.837756i	−0.999824	−	0.0187445i	$-0.994033\pi$
$757$	−13.3078	+	23.0497i	−0.483679	+	0.837756i	0.516145	+	0.856501i	$0.327366\pi$
$758$		0			0
$759$	1.43845			0.0522123
$760$		0			0
$761$	47.5464			1.72356			0.861778	−	0.507286i	$-0.169351\pi$
$761$	47.5464			1.72356			0.861778	+	0.507286i	$0.169351\pi$
$762$		0			0
$763$	10.0540	−	17.4140i	0.363978	−	0.630429i
$764$		0			0
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$		0			0
$767$	−22.2462			−0.803264
$768$		0			0
$769$	−11.8348	−	20.4984i	−0.426772	−	0.739191i	0.569812	−	0.821775i	$-0.307016\pi$
$769$	−11.8348	−	20.4984i	−0.426772	−	0.739191i	−0.996584	+	0.0825842i	$0.973683\pi$
$770$		0			0
$771$	16.2462			0.585093
$772$		0			0
$773$	17.9654	+	31.1170i	0.646172	+	1.11920i	0.984030	+	0.178005i	$0.0569644\pi$
$773$	17.9654	+	31.1170i	0.646172	+	1.11920i	−0.337858	+	0.941197i	$0.609702\pi$
$774$		0			0
$775$	−4.34233	−	7.52113i	−0.155981	−	0.270167i
$776$		0			0
$777$	−18.5540	+	32.1364i	−0.665620	+	1.15289i
$778$		0			0
$779$	9.21165	+	13.1569i	0.330041	+	0.471394i
$780$		0			0
$781$	15.6847	−	27.1666i	0.561241	−	0.972098i
$782$		0			0
$783$	−0.561553	−	0.972638i	−0.0200683	−	0.0347592i
$784$		0			0
$785$	−5.18466	−	8.98009i	−0.185048	−	0.320513i
$786$		0			0
$787$	−10.6847			−0.380867			−0.190433	−	0.981700i	$-0.560989\pi$
$787$	−10.6847			−0.380867			−0.190433	+	0.981700i	$0.560989\pi$
$788$		0			0
$789$	12.5270	+	21.6974i	0.445973	+	0.772447i
$790$		0			0
$791$	−42.2462			−1.50210
$792$		0			0
$793$	8.34233	−	14.4493i	0.296245	−	0.513111i
$794$		0			0
$795$	3.71922	−	6.44188i	0.131907	−	0.228470i
$796$		0			0
$797$	31.3002			1.10871			0.554355	−	0.832280i	$-0.312965\pi$
$797$	31.3002			1.10871			0.554355	+	0.832280i	$0.312965\pi$
$798$		0			0
$799$	−19.5076			−0.690128
$800$		0			0
$801$	5.84233	−	10.1192i	0.206429	−	0.357545i
$802$		0			0
$803$	13.6847	−	23.7025i	0.482921	−	0.836444i
$804$		0			0
$805$	−2.31534			−0.0816051
$806$		0			0
$807$	−6.24621	−	10.8188i	−0.219877	−	0.380838i
$808$		0			0
$809$	−26.9848			−0.948737			−0.474368	−	0.880326i	$-0.657323\pi$
$809$	−26.9848			−0.948737			−0.474368	+	0.880326i	$0.657323\pi$
$810$		0			0
$811$	17.5270	+	30.3576i	0.615456	+	1.06600i	0.990304	+	0.138915i	$0.0443614\pi$
$811$	17.5270	+	30.3576i	0.615456	+	1.06600i	−0.374849	+	0.927086i	$0.622305\pi$
$812$		0			0
$813$	−12.8078	−	22.1837i	−0.449188	−	0.778016i
$814$		0			0
$815$	4.65767	−	8.06732i	0.163151	−	0.282586i
$816$		0			0
$817$	−18.9039	−	27.0001i	−0.661363	−	0.944615i
$818$		0			0
$819$	7.34233	−	12.7173i	0.256562	−	0.444378i
$820$		0			0
$821$	10.8078	+	18.7196i	0.377194	+	0.653318i	0.990653	−	0.136408i	$-0.0435558\pi$
$821$	10.8078	+	18.7196i	0.377194	+	0.653318i	−0.613459	+	0.789726i	$0.710222\pi$
$822$		0			0
$823$	21.8423	+	37.8320i	0.761376	+	1.31874i	0.942142	+	0.335215i	$0.108809\pi$
$823$	21.8423	+	37.8320i	0.761376	+	1.31874i	−0.180766	+	0.983526i	$0.557858\pi$
$824$		0			0
$825$	2.56155			0.0891818
$826$		0			0
$827$	−0.315342	−	0.546188i	−0.0109655	−	0.0189928i	0.860491	−	0.509466i	$-0.170157\pi$
$827$	−0.315342	−	0.546188i	−0.0109655	−	0.0189928i	−0.871456	+	0.490474i	$0.836824\pi$
$828$		0			0
$829$	1.94602			0.0675882			0.0337941	−	0.999429i	$-0.489241\pi$
$829$	1.94602			0.0675882			0.0337941	+	0.999429i	$0.489241\pi$
$830$		0			0
$831$	−12.1231	+	20.9978i	−0.420546	+	0.728407i
$832$		0			0
$833$	−20.0000	+	34.6410i	−0.692959	+	1.20024i
$834$		0			0
$835$	0.315342			0.0109128
$836$		0			0
$837$	8.68466			0.300186
$838$		0			0
$839$	−25.7386	+	44.5806i	−0.888596	+	1.53909i	−0.0470609	+	0.998892i	$0.514985\pi$
$839$	−25.7386	+	44.5806i	−0.888596	+	1.53909i	−0.841535	+	0.540202i	$0.818348\pi$
$840$		0			0
$841$	13.8693	−	24.0224i	0.478252	−	0.828357i
$842$		0			0
$843$	−13.0540			−0.449603
$844$		0			0
$845$	0.157671	+	0.273094i	0.00542404	+	0.00939471i
$846$		0			0
$847$	18.3002			0.628802
$848$		0			0
$849$	7.43845	+	12.8838i	0.255287	+	0.442170i
$850$		0			0
$851$	2.52699	+	4.37687i	0.0866240	+	0.150037i
$852$		0			0
$853$	−21.3423	+	36.9660i	−0.730747	+	1.26569i	0.225817	+	0.974170i	$0.427495\pi$
$853$	−21.3423	+	36.9660i	−0.730747	+	1.26569i	−0.956564	+	0.291522i	$0.905838\pi$
$854$		0			0
$855$	1.84233	−	3.95042i	0.0630063	−	0.135102i
$856$		0			0
$857$	−17.8078	+	30.8440i	−0.608302	+	1.05361i	0.383219	+	0.923658i	$0.374816\pi$
$857$	−17.8078	+	30.8440i	−0.608302	+	1.05361i	−0.991520	+	0.129952i	$0.958518\pi$
$858$		0			0
$859$	12.7462	+	22.0771i	0.434895	+	0.753260i	0.997287	−	0.0736103i	$-0.0234521\pi$
$859$	12.7462	+	22.0771i	0.434895	+	0.753260i	−0.562392	+	0.826871i	$0.690119\pi$
$860$		0			0
$861$	7.59612	+	13.1569i	0.258875	+	0.448385i
$862$		0			0
$863$	−50.1771			−1.70805			−0.854024	−	0.520234i	$-0.825845\pi$
$863$	−50.1771			−1.70805			−0.854024	+	0.520234i	$0.825845\pi$
$864$		0			0
$865$	10.4039	+	18.0201i	0.353743	+	0.612700i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	−9.68466	+	16.7743i	−0.328530	+	0.569030i
$870$		0			0
$871$	22.5885	−	39.1245i	0.765383	−	1.32568i
$872$		0			0
$873$	−6.00000			−0.203069
$874$		0			0
$875$	−4.12311			−0.139386
$876$		0			0
$877$	10.8153	−	18.7327i	0.365208	−	0.632559i	−0.623601	−	0.781742i	$-0.714331\pi$
$877$	10.8153	−	18.7327i	0.365208	−	0.632559i	0.988810	+	0.149183i	$0.0476645\pi$
$878$		0			0
$879$	14.5270	−	25.1615i	0.489983	−	0.848676i
$880$		0			0
$881$	−31.3002			−1.05453			−0.527265	−	0.849701i	$-0.676783\pi$
$881$	−31.3002			−1.05453			−0.527265	+	0.849701i	$0.676783\pi$
$882$		0			0
$883$	20.5885	+	35.6604i	0.692860	+	1.20007i	0.970897	+	0.239498i	$0.0769828\pi$
$883$	20.5885	+	35.6604i	0.692860	+	1.20007i	−0.278037	+	0.960570i	$0.589684\pi$
$884$		0			0
$885$	−6.24621			−0.209964
$886$		0			0
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$		0			0
$889$	−17.1425	−	29.6917i	−0.574942	−	0.995828i
$890$		0			0
$891$	−1.28078	+	2.21837i	−0.0429076	+	0.0743182i
$892$		0			0
$893$	21.1771	−	1.85179i	0.708664	−	0.0619677i
$894$		0			0
$895$	−10.5270	+	18.2333i	−0.351878	+	0.609471i
$896$		0			0
$897$	−1.00000	−	1.73205i	−0.0333890	−	0.0578315i
$898$		0			0
$899$	−4.87689	−	8.44703i	−0.162654	−	0.281724i
$900$		0			0
$901$	−29.7538			−0.991242
$902$		0			0
$903$	−15.5885	−	27.0001i	−0.518754	−	0.898509i
$904$		0			0
$905$	16.2462			0.540042
$906$		0			0
$907$	−28.5616	+	49.4701i	−0.948371	+	1.64263i	−0.199514	+	0.979895i	$0.563936\pi$
$907$	−28.5616	+	49.4701i	−0.948371	+	1.64263i	−0.748857	+	0.662731i	$0.769397\pi$
$908$		0			0
$909$	2.12311	−	3.67733i	0.0704190	−	0.121969i
$910$		0			0
$911$	51.8617			1.71826			0.859128	−	0.511761i	$-0.171007\pi$
$911$	51.8617			1.71826			0.859128	+	0.511761i	$0.171007\pi$
$912$		0			0
$913$	7.36932			0.243889
$914$		0			0
$915$	2.34233	−	4.05703i	0.0774350	−	0.134121i
$916$		0			0
$917$	−35.1577	+	60.8949i	−1.16101	+	2.01093i
$918$		0			0
$919$	47.6695			1.57247			0.786236	−	0.617926i	$-0.212027\pi$
$919$	47.6695			1.57247			0.786236	+	0.617926i	$0.212027\pi$
$920$		0			0
$921$	12.5616	+	21.7572i	0.413917	+	0.716926i
$922$		0			0
$923$	−43.6155			−1.43562
$924$		0			0
$925$	4.50000	+	7.79423i	0.147959	+	0.256273i
$926$		0			0
$927$	0.938447	+	1.62544i	0.0308226	+	0.0533864i
$928$		0			0
$929$	13.4039	−	23.2162i	0.439767	−	0.761699i	−0.557904	−	0.829905i	$-0.688394\pi$
$929$	13.4039	−	23.2162i	0.439767	−	0.761699i	0.997671	+	0.0682064i	$0.0217277\pi$
$930$		0			0
$931$	18.4233	−	39.5042i	0.603799	−	1.29470i
$932$		0			0
$933$	5.12311	−	8.87348i	0.167723	−	0.290505i
$934$		0			0
$935$	−5.12311	−	8.87348i	−0.167543	−	0.290194i
$936$		0			0
$937$	−11.5885	−	20.0719i	−0.378581	−	0.655722i	0.612275	−	0.790645i	$-0.290255\pi$
$937$	−11.5885	−	20.0719i	−0.378581	−	0.655722i	−0.990856	+	0.134923i	$0.956921\pi$
$938$		0			0
$939$	1.36932			0.0446860
$940$		0			0
$941$	−19.6847	−	34.0948i	−0.641702	−	1.11146i	−0.985053	−	0.172253i	$-0.944895\pi$
$941$	−19.6847	−	34.0948i	−0.641702	−	1.11146i	0.343351	−	0.939207i	$-0.388438\pi$
$942$		0			0
$943$	2.06913			0.0673802
$944$		0			0
$945$	2.06155	−	3.57071i	0.0670623	−	0.116155i
$946$		0			0
$947$	−21.1771	+	36.6798i	−0.688163	+	1.19193i	0.284269	+	0.958745i	$0.408249\pi$
$947$	−21.1771	+	36.6798i	−0.688163	+	1.19193i	−0.972432	+	0.233188i	$0.925084\pi$
$948$		0			0
$949$	−38.0540			−1.23528
$950$		0			0
$951$	−5.68466			−0.184338
$952$		0			0
$953$	28.7386	−	49.7768i	0.930936	−	1.61243i	0.149210	−	0.988806i	$-0.452327\pi$
$953$	28.7386	−	49.7768i	0.930936	−	1.61243i	0.781726	−	0.623622i	$-0.214340\pi$
$954$		0			0
$955$	9.24621	−	16.0149i	0.299200	−	0.518230i
$956$		0			0
$957$	2.87689			0.0929968
$958$		0			0
$959$	1.80776	+	3.13114i	0.0583757	+	0.101110i
$960$		0			0
$961$	44.4233			1.43301
$962$		0			0
$963$	−3.56155	−	6.16879i	−0.114769	−	0.198786i
$964$		0			0
$965$	3.21922	+	5.57586i	0.103630	+	0.179493i
$966$		0			0
$967$	26.5885	−	46.0527i	0.855030	−	1.48096i	−0.0215875	−	0.999767i	$-0.506872\pi$
$967$	26.5885	−	46.0527i	0.855030	−	1.48096i	0.876617	−	0.481188i	$-0.159795\pi$
$968$		0			0
$969$	−17.3693	+	1.51883i	−0.557983	+	0.0487917i
$970$		0			0
$971$	22.6847	−	39.2910i	0.727985	−	1.26091i	−0.229748	−	0.973250i	$-0.573790\pi$
$971$	22.6847	−	39.2910i	0.727985	−	1.26091i	0.957733	−	0.287657i	$-0.0928765\pi$
$972$		0			0
$973$	−44.4503	−	76.9901i	−1.42501	−	2.46819i
$974$		0			0
$975$	−1.78078	−	3.08440i	−0.0570305	−	0.0987797i
$976$		0			0
$977$	6.49242			0.207711			0.103855	−	0.994592i	$-0.466882\pi$
$977$	6.49242			0.207711			0.103855	+	0.994592i	$0.466882\pi$
$978$		0			0
$979$	14.9654	+	25.9209i	0.478297	+	0.828435i
$980$		0			0
$981$	4.87689			0.155707
$982$		0			0
$983$	11.7732	−	20.3918i	0.375507	−	0.650397i	−0.614896	−	0.788608i	$-0.710802\pi$
$983$	11.7732	−	20.3918i	0.375507	−	0.650397i	0.990403	+	0.138211i	$0.0441354\pi$
$984$		0			0
$985$	−5.52699	+	9.57302i	−0.176104	+	0.305022i
$986$		0			0
$987$	20.1080			0.640043
$988$		0			0
$989$	−4.24621			−0.135022
$990$		0			0
$991$	−6.21922	+	10.7720i	−0.197560	+	0.342184i	−0.947737	−	0.319053i	$-0.896635\pi$
$991$	−6.21922	+	10.7720i	−0.197560	+	0.342184i	0.750177	+	0.661237i	$0.229968\pi$
$992$		0			0
$993$	−14.8693	+	25.7544i	−0.471864	+	0.817292i
$994$		0			0
$995$	25.1771			0.798167
$996$		0			0
$997$	−3.81534	−	6.60837i	−0.120833	−	0.209289i	0.799263	−	0.600981i	$-0.205223\pi$
$997$	−3.81534	−	6.60837i	−0.120833	−	0.209289i	−0.920096	+	0.391692i	$0.871890\pi$
$998$		0			0
$999$	−9.00000			−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2280.2.bg.l.961.1	yes	4
19.7	even	3	inner	2280.2.bg.l.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2280.2.bg.l.121.1	✓	4	19.7	even	3	inner
2280.2.bg.l.961.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2280.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.12311 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.12311 q^{7} +(-0.500000 - 0.866025i) q^{9} +2.56155 q^{11} +(-1.78078 - 3.08440i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{17} +(1.84233 - 3.95042i) q^{19} +(2.06155 - 3.57071i) q^{21} +(-0.280776 - 0.486319i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.561553 - 0.972638i) q^{29} +8.68466 q^{31} +(-1.28078 + 2.21837i) q^{33} +(2.06155 - 3.57071i) q^{35} -9.00000 q^{37} +3.56155 q^{39} +(-1.84233 + 3.19101i) q^{41} +(3.78078 - 6.54850i) q^{43} +1.00000 q^{45} +(2.43845 + 4.22351i) q^{47} +10.0000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(3.71922 + 6.44188i) q^{53} +(-1.28078 + 2.21837i) q^{55} +(2.50000 + 3.57071i) q^{57} +(3.12311 - 5.40938i) q^{59} +(2.34233 + 4.05703i) q^{61} +(2.06155 + 3.57071i) q^{63} +3.56155 q^{65} +(6.34233 + 10.9852i) q^{67} +0.561553 q^{69} +(6.12311 - 10.6055i) q^{71} +(5.34233 - 9.25319i) q^{73} +1.00000 q^{75} -10.5616 q^{77} +(-3.78078 + 6.54850i) q^{79} +(-0.500000 + 0.866025i) q^{81} +2.87689 q^{83} +(-2.00000 - 3.46410i) q^{85} +1.12311 q^{87} +(5.84233 + 10.1192i) q^{89} +(7.34233 + 12.7173i) q^{91} +(-4.34233 + 7.52113i) q^{93} +(2.50000 + 3.57071i) q^{95} +(3.00000 - 5.19615i) q^{97} +(-1.28078 - 2.21837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} + 2 q^{11} - 3 q^{13} - 2 q^{15} - 8 q^{17} - 5 q^{19} + 3 q^{23} - 2 q^{25} + 4 q^{27} + 6 q^{29} + 10 q^{31} - q^{33} - 36 q^{37} + 6 q^{39} + 5 q^{41} + 11 q^{43} + 4 q^{45} + 18 q^{47} + 40 q^{49} - 8 q^{51} + 19 q^{53} - q^{55} + 10 q^{57} - 4 q^{59} - 3 q^{61} + 6 q^{65} + 13 q^{67} - 6 q^{69} + 8 q^{71} + 9 q^{73} + 4 q^{75} - 34 q^{77} - 11 q^{79} - 2 q^{81} + 28 q^{83} - 8 q^{85} - 12 q^{87} + 11 q^{89} + 17 q^{91} - 5 q^{93} + 10 q^{95} + 12 q^{97} - q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 + 2 * q^11 - 3 * q^13 - 2 * q^15 - 8 * q^17 - 5 * q^19 + 3 * q^23 - 2 * q^25 + 4 * q^27 + 6 * q^29 + 10 * q^31 - q^33 - 36 * q^37 + 6 * q^39 + 5 * q^41 + 11 * q^43 + 4 * q^45 + 18 * q^47 + 40 * q^49 - 8 * q^51 + 19 * q^53 - q^55 + 10 * q^57 - 4 * q^59 - 3 * q^61 + 6 * q^65 + 13 * q^67 - 6 * q^69 + 8 * q^71 + 9 * q^73 + 4 * q^75 - 34 * q^77 - 11 * q^79 - 2 * q^81 + 28 * q^83 - 8 * q^85 - 12 * q^87 + 11 * q^89 + 17 * q^91 - 5 * q^93 + 10 * q^95 + 12 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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