LMFDB - Embedded newform 1320.2.bw.e.1081.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7 x^{10} - 6 x^{9} + 130 x^{8} - 768 x^{7} + 3132 x^{6} - 7488 x^{5} + 18450 x^{4} + \cdots + 9801 $ x^12 - 2x^11 + 7x^10 - 6x^9 + 130x^8 - 768x^7 + 3132x^6 - 7488x^5 + 18450x^4 - 35046x^3 + 44847x^2 - 19602*x + 9801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.2
Root			$1.03688 - 3.19120i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.e.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.232215 + 0.714683i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.232215 + 0.714683i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.31420 - 0.126898i) q^{11} +(0.212453 - 0.154356i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(4.31422 + 3.13446i) q^{17} +(0.375731 + 1.15638i) q^{19} +0.751462 q^{21} -4.61807 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.313364 + 0.964436i) q^{29} +(7.30095 - 5.30445i) q^{31} +(-1.14483 - 3.11277i) q^{33} +(0.607946 - 0.441698i) q^{35} +(1.09444 - 3.36834i) q^{37} +(-0.212453 - 0.154356i) q^{39} +(-0.0987863 - 0.304033i) q^{41} +5.18935 q^{43} +1.00000 q^{45} +(-1.28942 - 3.96843i) q^{47} +(5.20627 + 3.78258i) q^{49} +(1.64788 - 5.07167i) q^{51} +(4.27733 - 3.10766i) q^{53} +(-2.75583 - 1.84537i) q^{55} +(0.983677 - 0.714683i) q^{57} +(3.75772 - 11.5651i) q^{59} +(3.67492 + 2.66998i) q^{61} +(-0.232215 - 0.714683i) q^{63} -0.262606 q^{65} +13.3597 q^{67} +(1.42706 + 4.39205i) q^{69} +(-7.25759 - 5.27295i) q^{71} +(-4.66821 + 14.3673i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-0.678913 + 2.39807i) q^{77} +(11.2868 - 8.20032i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-13.5534 - 9.84709i) q^{83} +(-1.64788 - 5.07167i) q^{85} +1.01407 q^{87} -2.88722 q^{89} +(0.0609810 + 0.187680i) q^{91} +(-7.30095 - 5.30445i) q^{93} +(0.375731 - 1.15638i) q^{95} +(-5.24469 + 3.81049i) q^{97} +(-2.60665 + 2.05070i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 3 q^{15} - 13 q^{17} + 20 q^{23} - 3 q^{25} + 3 q^{27} - 3 q^{29} - 3 q^{31} - q^{33} + 5 q^{35} + 5 q^{37} - 12 q^{39} + q^{41} + 6 q^{43} + 12 q^{45} - 10 q^{47} - 12 q^{51} - 3 q^{53} + q^{55} + 5 q^{57} + 23 q^{59} - 7 q^{61} - 5 q^{63} - 28 q^{65} + 44 q^{67} + 5 q^{69} - 9 q^{71} - 27 q^{73} + 3 q^{75} + 65 q^{77} - q^{79} - 3 q^{81} - 21 q^{83} + 12 q^{85} + 28 q^{87} + 32 q^{89} - 19 q^{91} + 3 q^{93} + 5 q^{97} - 4 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 3 * q^15 - 13 * q^17 + 20 * q^23 - 3 * q^25 + 3 * q^27 - 3 * q^29 - 3 * q^31 - q^33 + 5 * q^35 + 5 * q^37 - 12 * q^39 + q^41 + 6 * q^43 + 12 * q^45 - 10 * q^47 - 12 * q^51 - 3 * q^53 + q^55 + 5 * q^57 + 23 * q^59 - 7 * q^61 - 5 * q^63 - 28 * q^65 + 44 * q^67 + 5 * q^69 - 9 * q^71 - 27 * q^73 + 3 * q^75 + 65 * q^77 - q^79 - 3 * q^81 - 21 * q^83 + 12 * q^85 + 28 * q^87 + 32 * q^89 - 19 * q^91 + 3 * q^93 + 5 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.232215	+	0.714683i	−0.0877689	+	0.270125i	−0.985302	−	0.170823i	$-0.945357\pi$
$7$	−0.232215	+	0.714683i	−0.0877689	+	0.270125i	0.897533	+	0.440947i	$0.145357\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	3.31420	−	0.126898i	0.999268	−	0.0382611i
$11$	3.31420	−	0.126898i	0.999268	−	0.0382611i
$12$		0			0
$13$	0.212453	−	0.154356i	0.0589238	−	0.0428107i	−0.557933	−	0.829886i	$-0.688406\pi$
$13$	0.212453	−	0.154356i	0.0589238	−	0.0428107i	0.616857	+	0.787075i	$0.288406\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	4.31422	+	3.13446i	1.04635	+	0.760219i	0.971515	−	0.236977i	$-0.0761567\pi$
$17$	4.31422	+	3.13446i	1.04635	+	0.760219i	0.0748360	+	0.997196i	$0.476157\pi$
$18$		0			0
$19$	0.375731	+	1.15638i	0.0861986	+	0.265292i	0.984860	−	0.173351i	$-0.0554594\pi$
$19$	0.375731	+	1.15638i	0.0861986	+	0.265292i	−0.898662	+	0.438643i	$0.855459\pi$
$20$		0			0
$21$	0.751462			0.163983
$22$		0			0
$23$	−4.61807			−0.962935			−0.481468	−	0.876464i	$-0.659896\pi$
$23$	−4.61807			−0.962935			−0.481468	+	0.876464i	$0.659896\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−0.313364	+	0.964436i	−0.0581903	+	0.179091i	−0.975927	−	0.218099i	$-0.930015\pi$
$29$	−0.313364	+	0.964436i	−0.0581903	+	0.179091i	0.917736	+	0.397190i	$0.130015\pi$
$30$		0			0
$31$	7.30095	−	5.30445i	1.31129	−	0.952707i	0.311292	−	0.950314i	$-0.399238\pi$
$31$	7.30095	−	5.30445i	1.31129	−	0.952707i	0.999997	−	0.00239271i	$-0.000761625\pi$
$32$		0			0
$33$	−1.14483	−	3.11277i	−0.199289	−	0.541864i
$34$		0			0
$35$	0.607946	−	0.441698i	0.102762	−	0.0746607i
$36$		0			0
$37$	1.09444	−	3.36834i	0.179925	−	0.553751i	−0.819899	−	0.572508i	$-0.805971\pi$
$37$	1.09444	−	3.36834i	0.179925	−	0.553751i	0.999824	+	0.0187564i	$0.00597071\pi$
$38$		0			0
$39$	−0.212453	−	0.154356i	−0.0340197	−	0.0247167i
$40$		0			0
$41$	−0.0987863	−	0.304033i	−0.0154278	−	0.0474820i	0.943046	−	0.332662i	$-0.107947\pi$
$41$	−0.0987863	−	0.304033i	−0.0154278	−	0.0474820i	−0.958474	+	0.285180i	$0.907947\pi$
$42$		0			0
$43$	5.18935			0.791369			0.395684	−	0.918387i	$-0.370507\pi$
$43$	5.18935			0.791369			0.395684	+	0.918387i	$0.370507\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−1.28942	−	3.96843i	−0.188082	−	0.578856i	0.811906	−	0.583788i	$-0.198430\pi$
$47$	−1.28942	−	3.96843i	−0.188082	−	0.578856i	−0.999988	+	0.00493227i	$0.998430\pi$
$48$		0			0
$49$	5.20627	+	3.78258i	0.743753	+	0.540368i
$50$		0			0
$51$	1.64788	−	5.07167i	0.230750	−	0.710175i
$52$		0			0
$53$	4.27733	−	3.10766i	0.587537	−	0.426870i	−0.253897	−	0.967231i	$-0.581712\pi$
$53$	4.27733	−	3.10766i	0.587537	−	0.426870i	0.841433	+	0.540361i	$0.181712\pi$
$54$		0			0
$55$	−2.75583	−	1.84537i	−0.371596	−	0.248830i
$56$		0			0
$57$	0.983677	−	0.714683i	0.130291	−	0.0946621i
$58$		0			0
$59$	3.75772	−	11.5651i	0.489213	−	1.50564i	−0.336572	−	0.941658i	$-0.609267\pi$
$59$	3.75772	−	11.5651i	0.489213	−	1.50564i	0.825785	−	0.563985i	$-0.190733\pi$
$60$		0			0
$61$	3.67492	+	2.66998i	0.470525	+	0.341856i	0.797646	−	0.603126i	$-0.206078\pi$
$61$	3.67492	+	2.66998i	0.470525	+	0.341856i	−0.327121	+	0.944983i	$0.606078\pi$
$62$		0			0
$63$	−0.232215	−	0.714683i	−0.0292563	−	0.0900416i
$64$		0			0
$65$	−0.262606			−0.0325723
$66$		0			0
$67$	13.3597			1.63215			0.816075	−	0.577946i	$-0.196146\pi$
$67$	13.3597			1.63215			0.816075	+	0.577946i	$0.196146\pi$
$68$		0			0
$69$	1.42706	+	4.39205i	0.171798	+	0.528741i
$70$		0			0
$71$	−7.25759	−	5.27295i	−0.861318	−	0.625784i	0.0669256	−	0.997758i	$-0.478681\pi$
$71$	−7.25759	−	5.27295i	−0.861318	−	0.625784i	−0.928243	+	0.371974i	$0.878681\pi$
$72$		0			0
$73$	−4.66821	+	14.3673i	−0.546372	+	1.68156i	0.171332	+	0.985213i	$0.445193\pi$
$73$	−4.66821	+	14.3673i	−0.546372	+	1.68156i	−0.717704	+	0.696348i	$0.754807\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$		0			0
$77$	−0.678913	+	2.39807i	−0.0773693	+	0.273285i
$78$		0			0
$79$	11.2868	−	8.20032i	1.26986	−	0.922608i	0.270664	−	0.962674i	$-0.412757\pi$
$79$	11.2868	−	8.20032i	1.26986	−	0.922608i	0.999197	+	0.0400661i	$0.0127568\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−13.5534	−	9.84709i	−1.48767	−	1.08086i	−0.974981	−	0.222287i	$-0.928648\pi$
$83$	−13.5534	−	9.84709i	−1.48767	−	1.08086i	−0.512693	−	0.858572i	$-0.671352\pi$
$84$		0			0
$85$	−1.64788	−	5.07167i	−0.178738	−	0.550099i
$86$		0			0
$87$	1.01407			0.108720
$88$		0			0
$89$	−2.88722			−0.306045			−0.153023	−	0.988223i	$-0.548901\pi$
$89$	−2.88722			−0.306045			−0.153023	+	0.988223i	$0.548901\pi$
$90$		0			0
$91$	0.0609810	+	0.187680i	0.00639254	+	0.0196742i
$92$		0			0
$93$	−7.30095	−	5.30445i	−0.757073	−	0.550046i
$94$		0			0
$95$	0.375731	−	1.15638i	0.0385492	−	0.118642i
$96$		0			0
$97$	−5.24469	+	3.81049i	−0.532517	+	0.386896i	−0.821298	−	0.570499i	$-0.806750\pi$
$97$	−5.24469	+	3.81049i	−0.532517	+	0.386896i	0.288781	+	0.957395i	$0.406750\pi$
$98$		0			0
$99$	−2.60665	+	2.05070i	−0.261978	+	0.206103i
$100$		0			0
$101$	10.8211	−	7.86197i	1.07674	−	0.782295i	0.0996258	−	0.995025i	$-0.468235\pi$
$101$	10.8211	−	7.86197i	1.07674	−	0.782295i	0.977111	+	0.212730i	$0.0682354\pi$
$102$		0			0
$103$	1.68393	−	5.18260i	0.165922	−	0.510657i	−0.833181	−	0.553001i	$-0.813483\pi$
$103$	1.68393	−	5.18260i	0.165922	−	0.510657i	0.999103	+	0.0423442i	$0.0134826\pi$
$104$		0			0
$105$	−0.607946	−	0.441698i	−0.0593294	−	0.0431054i
$106$		0			0
$107$	2.12083	+	6.52725i	0.205029	+	0.631013i	0.999712	+	0.0239892i	$0.00763673\pi$
$107$	2.12083	+	6.52725i	0.205029	+	0.631013i	−0.794684	+	0.607024i	$0.792363\pi$
$108$		0			0
$109$	−0.534741			−0.0512189			−0.0256095	−	0.999672i	$-0.508153\pi$
$109$	−0.534741			−0.0512189			−0.0256095	+	0.999672i	$0.508153\pi$
$110$		0			0
$111$	−3.54168			−0.336161
$112$		0			0
$113$	1.87392	+	5.76734i	0.176284	+	0.542546i	0.999690	−	0.0249068i	$-0.00792890\pi$
$113$	1.87392	+	5.76734i	0.176284	+	0.542546i	−0.823406	+	0.567453i	$0.807929\pi$
$114$		0			0
$115$	3.73610	+	2.71444i	0.348393	+	0.253122i
$116$		0			0
$117$	−0.0811497	+	0.249753i	−0.00750230	+	0.0230897i
$118$		0			0
$119$	−3.24197	+	2.35543i	−0.297191	+	0.215922i
$120$		0			0
$121$	10.9678	−	0.841129i	0.997072	−	0.0764662i
$122$		0			0
$123$	−0.258626	+	0.187903i	−0.0233195	+	0.0169426i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−7.10347	−	5.16097i	−0.630331	−	0.457962i	0.226184	−	0.974085i	$-0.427375\pi$
$127$	−7.10347	−	5.16097i	−0.630331	−	0.457962i	−0.856515	+	0.516122i	$0.827375\pi$
$128$		0			0
$129$	−1.60360	−	4.93537i	−0.141189	−	0.434535i
$130$		0			0
$131$	15.9822			1.39637			0.698187	−	0.715915i	$-0.253990\pi$
$131$	15.9822			1.39637			0.698187	+	0.715915i	$0.253990\pi$
$132$		0			0
$133$	−0.913697			−0.0792275
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	−10.6888	−	7.76590i	−0.913209	−	0.663485i	0.0286153	−	0.999590i	$-0.490890\pi$
$137$	−10.6888	−	7.76590i	−0.913209	−	0.663485i	−0.941824	+	0.336105i	$0.890890\pi$
$138$		0			0
$139$	−2.07826	+	6.39624i	−0.176276	+	0.542522i	−0.999689	−	0.0249202i	$-0.992067\pi$
$139$	−2.07826	+	6.39624i	−0.176276	+	0.542522i	0.823413	+	0.567442i	$0.192067\pi$
$140$		0			0
$141$	−3.37575	+	2.45263i	−0.284290	+	0.206548i
$142$		0			0
$143$	0.684523	−	0.538526i	0.0572427	−	0.0450338i
$144$		0			0
$145$	0.820399	−	0.596054i	0.0681304	−	0.0494996i
$146$		0			0
$147$	1.98862	−	6.12034i	0.164018	−	0.504797i
$148$		0			0
$149$	1.78907	+	1.29983i	0.146566	+	0.106486i	0.658652	−	0.752448i	$-0.271127\pi$
$149$	1.78907	+	1.29983i	0.146566	+	0.106486i	−0.512086	+	0.858934i	$0.671127\pi$
$150$		0			0
$151$	2.39802	+	7.38035i	0.195148	+	0.600604i	0.999975	+	0.00709431i	$0.00225821\pi$
$151$	2.39802	+	7.38035i	0.195148	+	0.600604i	−0.804827	+	0.593510i	$0.797742\pi$
$152$		0			0
$153$	−5.33266			−0.431120
$154$		0			0
$155$	−9.02447			−0.724863
$156$		0			0
$157$	5.48108	+	16.8690i	0.437438	+	1.34629i	0.890568	+	0.454850i	$0.150307\pi$
$157$	5.48108	+	16.8690i	0.437438	+	1.34629i	−0.453130	+	0.891444i	$0.649693\pi$
$158$		0			0
$159$	−4.27733	−	3.10766i	−0.339215	−	0.246454i
$160$		0			0
$161$	1.07238	−	3.30046i	0.0845157	−	0.260113i
$162$		0			0
$163$	−2.73817	+	1.98940i	−0.214470	+	0.155822i	−0.689834	−	0.723968i	$-0.742316\pi$
$163$	−2.73817	+	1.98940i	−0.214470	+	0.155822i	0.475364	+	0.879789i	$0.342316\pi$
$164$		0			0
$165$	−0.903456	+	3.19120i	−0.0703340	+	0.248435i
$166$		0			0
$167$	5.62456	−	4.08648i	0.435241	−	0.316221i	−0.348500	−	0.937309i	$-0.613309\pi$
$167$	5.62456	−	4.08648i	0.435241	−	0.316221i	0.783741	+	0.621087i	$0.213309\pi$
$168$		0			0
$169$	−3.99591	+	12.2981i	−0.307378	+	0.946011i
$170$		0			0
$171$	−0.983677	−	0.714683i	−0.0752237	−	0.0546532i
$172$		0			0
$173$	5.38513	+	16.5737i	0.409424	+	1.26008i	0.917144	+	0.398555i	$0.130488\pi$
$173$	5.38513	+	16.5737i	0.409424	+	1.26008i	−0.507720	+	0.861522i	$0.669512\pi$
$174$		0			0
$175$	−0.751462			−0.0568052
$176$		0			0
$177$	−12.1602			−0.914019
$178$		0			0
$179$	1.44163	+	4.43689i	0.107753	+	0.331629i	0.990367	−	0.138470i	$-0.0442184\pi$
$179$	1.44163	+	4.43689i	0.107753	+	0.331629i	−0.882614	+	0.470099i	$0.844218\pi$
$180$		0			0
$181$	5.22816	+	3.79848i	0.388606	+	0.282339i	0.764884	−	0.644168i	$-0.222796\pi$
$181$	5.22816	+	3.79848i	0.388606	+	0.282339i	−0.376278	+	0.926507i	$0.622796\pi$
$182$		0			0
$183$	1.40369	−	4.32012i	0.103764	−	0.319353i
$184$		0			0
$185$	−2.86528	+	2.08175i	−0.210659	+	0.153053i
$186$		0			0
$187$	14.6959	+	9.84076i	1.07467	+	0.719627i
$188$		0			0
$189$	−0.607946	+	0.441698i	−0.0442215	+	0.0321288i
$190$		0			0
$191$	−1.67007	+	5.13996i	−0.120842	+	0.371915i	−0.993121	−	0.117095i	$-0.962642\pi$
$191$	−1.67007	+	5.13996i	−0.120842	+	0.371915i	0.872278	+	0.489010i	$0.162642\pi$
$192$		0			0
$193$	−13.3643	−	9.70973i	−0.961983	−	0.698921i	−0.00837235	−	0.999965i	$-0.502665\pi$
$193$	−13.3643	−	9.70973i	−0.961983	−	0.698921i	−0.953610	+	0.301044i	$0.902665\pi$
$194$		0			0
$195$	0.0811497	+	0.249753i	0.00581125	+	0.0178852i
$196$		0			0
$197$	−0.843768			−0.0601160			−0.0300580	−	0.999548i	$-0.509569\pi$
$197$	−0.843768			−0.0601160			−0.0300580	+	0.999548i	$0.509569\pi$
$198$		0			0
$199$	−1.64783			−0.116812			−0.0584059	−	0.998293i	$-0.518602\pi$
$199$	−1.64783			−0.116812			−0.0584059	+	0.998293i	$0.518602\pi$
$200$		0			0
$201$	−4.12838	−	12.7058i	−0.291193	−	0.896201i
$202$		0			0
$203$	−0.616499	−	0.447912i	−0.0432697	−	0.0314373i
$204$		0			0
$205$	−0.0987863	+	0.304033i	−0.00689954	+	0.0212346i
$206$		0			0
$207$	3.73610	−	2.71444i	0.259677	−	0.188666i
$208$		0			0
$209$	1.39199	+	3.78480i	0.0962859	+	0.261800i
$210$		0			0
$211$	4.77137	−	3.46660i	0.328475	−	0.238651i	−0.411309	−	0.911496i	$-0.634928\pi$
$211$	4.77137	−	3.46660i	0.328475	−	0.238651i	0.739783	+	0.672845i	$0.234928\pi$
$212$		0			0
$213$	−2.77215	+	8.53181i	−0.189945	+	0.584590i
$214$		0			0
$215$	−4.19828	−	3.05023i	−0.286320	−	0.208024i
$216$		0			0
$217$	2.09561	+	6.44963i	0.142259	+	0.437830i
$218$		0			0
$219$	15.1066			1.02081
$220$		0			0
$221$	1.40039			0.0942004
$222$		0			0
$223$	0.139859	+	0.430440i	0.00936562	+	0.0288244i	0.955630	−	0.294569i	$-0.0951762\pi$
$223$	0.139859	+	0.430440i	0.00936562	+	0.0288244i	−0.946264	+	0.323394i	$0.895176\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	−1.85812	+	5.71871i	−0.123328	+	0.379564i	−0.993593	−	0.113020i	$-0.963948\pi$
$227$	−1.85812	+	5.71871i	−0.123328	+	0.379564i	0.870265	+	0.492584i	$0.163948\pi$
$228$		0			0
$229$	−3.65839	+	2.65798i	−0.241753	+	0.175644i	−0.702064	−	0.712114i	$-0.747738\pi$
$229$	−3.65839	+	2.65798i	−0.241753	+	0.175644i	0.460311	+	0.887758i	$0.347738\pi$
$230$		0			0
$231$	2.49049	−	0.0953589i	0.163862	−	0.00627416i
$232$		0			0
$233$	−9.75695	+	7.08884i	−0.639199	+	0.464405i	−0.859575	−	0.511010i	$-0.829272\pi$
$233$	−9.75695	+	7.08884i	−0.639199	+	0.464405i	0.220376	+	0.975415i	$0.429272\pi$
$234$		0			0
$235$	−1.28942	+	3.96843i	−0.0841126	+	0.258872i
$236$		0			0
$237$	−11.2868	−	8.20032i	−0.733154	−	0.532668i
$238$		0			0
$239$	−8.59407	−	26.4498i	−0.555904	−	1.71090i	−0.693544	−	0.720415i	$-0.743952\pi$
$239$	−8.59407	−	26.4498i	−0.555904	−	1.71090i	0.137640	−	0.990482i	$-0.456048\pi$
$240$		0			0
$241$	15.7467			1.01434			0.507168	−	0.861847i	$-0.330692\pi$
$241$	15.7467			1.01434			0.507168	+	0.861847i	$0.330692\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.98862	−	6.12034i	−0.127048	−	0.391014i
$246$		0			0
$247$	0.258320	+	0.187680i	0.0164365	+	0.0119418i
$248$		0			0
$249$	−5.17692	+	15.9329i	−0.328074	+	1.00971i
$250$		0			0
$251$	−20.4911	+	14.8877i	−1.29339	+	0.939700i	−0.999868	−	0.0162528i	$-0.994826\pi$
$251$	−20.4911	+	14.8877i	−1.29339	+	0.939700i	−0.293519	+	0.955953i	$0.594826\pi$
$252$		0			0
$253$	−15.3052	+	0.586024i	−0.962230	+	0.0368430i
$254$		0			0
$255$	−4.31422	+	3.13446i	−0.270167	+	0.196288i
$256$		0			0
$257$	−2.21346	+	6.81232i	−0.138072	+	0.424941i	−0.996055	−	0.0887365i	$-0.971717\pi$
$257$	−2.21346	+	6.81232i	−0.138072	+	0.424941i	0.857984	+	0.513677i	$0.171717\pi$
$258$		0			0
$259$	2.15315	+	1.56435i	0.133790	+	0.0972042i
$260$		0			0
$261$	−0.313364	−	0.964436i	−0.0193968	−	0.0596971i
$262$		0			0
$263$	−25.5964			−1.57834			−0.789170	−	0.614175i	$-0.789489\pi$
$263$	−25.5964			−1.57834			−0.789170	+	0.614175i	$0.789489\pi$
$264$		0			0
$265$	−5.28707			−0.324782
$266$		0			0
$267$	0.892201	+	2.74591i	0.0546018	+	0.168047i
$268$		0			0
$269$	−15.4935	−	11.2567i	−0.944655	−	0.686332i	0.00488155	−	0.999988i	$-0.498446\pi$
$269$	−15.4935	−	11.2567i	−0.944655	−	0.686332i	−0.949537	+	0.313656i	$0.898446\pi$
$270$		0			0
$271$	−3.42034	+	10.5267i	−0.207771	+	0.639453i	0.791817	+	0.610758i	$0.209135\pi$
$271$	−3.42034	+	10.5267i	−0.207771	+	0.639453i	−0.999588	+	0.0286949i	$0.990865\pi$
$272$		0			0
$273$	0.159650	−	0.115993i	0.00966247	−	0.00702020i
$274$		0			0
$275$	1.14483	+	3.11277i	0.0690358	+	0.187707i
$276$		0			0
$277$	12.0191	−	8.73241i	0.722159	−	0.524680i	−0.164914	−	0.986308i	$-0.552735\pi$
$277$	12.0191	−	8.73241i	0.722159	−	0.524680i	0.887073	+	0.461628i	$0.152735\pi$
$278$		0			0
$279$	−2.78871	+	8.58278i	−0.166956	+	0.513837i
$280$		0			0
$281$	12.9526	+	9.41063i	0.772689	+	0.561391i	0.902776	−	0.430111i	$-0.141526\pi$
$281$	12.9526	+	9.41063i	0.772689	+	0.561391i	−0.130087	+	0.991503i	$0.541526\pi$
$282$		0			0
$283$	2.61041	+	8.03403i	0.155173	+	0.477573i	0.998178	−	0.0603318i	$-0.0192159\pi$
$283$	2.61041	+	8.03403i	0.155173	+	0.477573i	−0.843005	+	0.537905i	$0.819216\pi$
$284$		0			0
$285$	−1.21589			−0.0720232
$286$		0			0
$287$	0.240227			0.0141801
$288$		0			0
$289$	3.53432	+	10.8775i	0.207901	+	0.639855i
$290$		0			0
$291$	5.24469	+	3.81049i	0.307449	+	0.223375i
$292$		0			0
$293$	−3.55695	+	10.9472i	−0.207799	+	0.639541i	0.791787	+	0.610797i	$0.209151\pi$
$293$	−3.55695	+	10.9472i	−0.207799	+	0.639541i	−0.999587	+	0.0287439i	$0.990849\pi$
$294$		0			0
$295$	−9.83783	+	7.14760i	−0.572781	+	0.416150i
$296$		0			0
$297$	2.75583	+	1.84537i	0.159909	+	0.107079i
$298$		0			0
$299$	−0.981123	+	0.712827i	−0.0567398	+	0.0412239i
$300$		0			0
$301$	−1.20504	+	3.70874i	−0.0694576	+	0.213768i
$302$		0			0
$303$	−10.8211	−	7.86197i	−0.621654	−	0.451658i
$304$		0			0
$305$	−1.40369	−	4.32012i	−0.0803753	−	0.247370i
$306$		0			0
$307$	22.5607			1.28761			0.643803	−	0.765191i	$-0.277356\pi$
$307$	22.5607			1.28761			0.643803	+	0.765191i	$0.277356\pi$
$308$		0			0
$309$	−5.44931			−0.310000
$310$		0			0
$311$	4.95278	+	15.2431i	0.280846	+	0.864356i	0.987613	+	0.156910i	$0.0501531\pi$
$311$	4.95278	+	15.2431i	0.280846	+	0.864356i	−0.706767	+	0.707447i	$0.749847\pi$
$312$		0			0
$313$	−27.2579	−	19.8041i	−1.54071	−	1.11939i	−0.949888	−	0.312589i	$-0.898804\pi$
$313$	−27.2579	−	19.8041i	−1.54071	−	1.11939i	−0.590822	−	0.806802i	$-0.701196\pi$
$314$		0			0
$315$	−0.232215	+	0.714683i	−0.0130838	+	0.0402678i
$316$		0			0
$317$	−1.19920	+	0.871267i	−0.0673536	+	0.0489352i	−0.620953	−	0.783848i	$-0.713254\pi$
$317$	−1.19920	+	0.871267i	−0.0673536	+	0.0489352i	0.553599	+	0.832783i	$0.313254\pi$
$318$		0			0
$319$	−0.916166	+	3.23610i	−0.0512955	+	0.181187i
$320$		0			0
$321$	5.55241	−	4.03406i	0.309905	−	0.225159i
$322$		0			0
$323$	−2.00365	+	6.16660i	−0.111486	+	0.343119i
$324$		0			0
$325$	0.212453	+	0.154356i	0.0117848	+	0.00856213i
$326$		0			0
$327$	0.165244	+	0.508569i	0.00913803	+	0.0281239i
$328$		0			0
$329$	3.13560			0.172871
$330$		0			0
$331$	−3.58164			−0.196865			−0.0984323	−	0.995144i	$-0.531383\pi$
$331$	−3.58164			−0.196865			−0.0984323	+	0.995144i	$0.531383\pi$
$332$		0			0
$333$	1.09444	+	3.36834i	0.0599749	+	0.184584i
$334$		0			0
$335$	−10.8082	−	7.85265i	−0.590517	−	0.429036i
$336$		0			0
$337$	−2.34423	+	7.21481i	−0.127699	+	0.393016i	−0.994383	−	0.105841i	$-0.966247\pi$
$337$	−2.34423	+	7.21481i	−0.127699	+	0.393016i	0.866685	+	0.498857i	$0.166247\pi$
$338$		0			0
$339$	4.90600	−	3.56441i	0.266457	−	0.193592i
$340$		0			0
$341$	23.5236	−	18.5065i	1.27388	−	1.00218i
$342$		0			0
$343$	−8.16794	+	5.93435i	−0.441027	+	0.320425i
$344$		0			0
$345$	1.42706	−	4.39205i	0.0768305	−	0.236460i
$346$		0			0
$347$	6.21227	+	4.51348i	0.333492	+	0.242296i	0.741911	−	0.670498i	$-0.233920\pi$
$347$	6.21227	+	4.51348i	0.333492	+	0.242296i	−0.408419	+	0.912795i	$0.633920\pi$
$348$		0			0
$349$	3.32515	+	10.2338i	0.177991	+	0.547801i	0.999757	−	0.0220239i	$-0.00701098\pi$
$349$	3.32515	+	10.2338i	0.177991	+	0.547801i	−0.821766	+	0.569825i	$0.807011\pi$
$350$		0			0
$351$	0.262606			0.0140169
$352$		0			0
$353$	−24.5512			−1.30673			−0.653364	−	0.757044i	$-0.726643\pi$
$353$	−24.5512			−1.30673			−0.653364	+	0.757044i	$0.726643\pi$
$354$		0			0
$355$	2.77215	+	8.53181i	0.147131	+	0.452821i
$356$		0			0
$357$	3.24197	+	2.35543i	0.171583	+	0.124663i
$358$		0			0
$359$	5.29614	−	16.2998i	0.279520	−	0.860273i	−0.708468	−	0.705742i	$-0.750614\pi$
$359$	5.29614	−	16.2998i	0.279520	−	0.860273i	0.987988	−	0.154530i	$-0.0493864\pi$
$360$		0			0
$361$	14.1753	−	10.2989i	0.746067	−	0.542050i
$362$		0			0
$363$	−4.18920	−	10.1711i	−0.219876	−	0.533843i
$364$		0			0
$365$	12.2215	−	8.87946i	0.639704	−	0.464772i
$366$		0			0
$367$	4.83286	−	14.8740i	0.252273	−	0.776417i	−0.742081	−	0.670310i	$-0.766161\pi$
$367$	4.83286	−	14.8740i	0.252273	−	0.776417i	0.994355	−	0.106107i	$-0.0338387\pi$
$368$		0			0
$369$	0.258626	+	0.187903i	0.0134635	+	0.00978183i
$370$		0			0
$371$	1.22774	+	3.77858i	0.0637409	+	0.196174i
$372$		0			0
$373$	−11.5004			−0.595470			−0.297735	−	0.954649i	$-0.596231\pi$
$373$	−11.5004			−0.595470			−0.297735	+	0.954649i	$0.596231\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	0.0822914	+	0.253267i	0.00423822	+	0.0130439i
$378$		0			0
$379$	18.0583	+	13.1201i	0.927594	+	0.673937i	0.945403	−	0.325905i	$-0.105669\pi$
$379$	18.0583	+	13.1201i	0.927594	+	0.673937i	−0.0178084	+	0.999841i	$0.505669\pi$
$380$		0			0
$381$	−2.71328	+	8.35063i	−0.139006	+	0.427816i
$382$		0			0
$383$	−29.8645	+	21.6978i	−1.52600	+	1.10871i	−0.567593	+	0.823309i	$0.692125\pi$
$383$	−29.8645	+	21.6978i	−1.52600	+	1.10871i	−0.958410	+	0.285396i	$0.907875\pi$
$384$		0			0
$385$	1.95880	−	1.54102i	0.0998297	−	0.0785378i
$386$		0			0
$387$	−4.19828	+	3.05023i	−0.213410	+	0.155052i
$388$		0			0
$389$	8.80586	−	27.1016i	0.446475	−	1.37411i	−0.434384	−	0.900728i	$-0.643034\pi$
$389$	8.80586	−	27.1016i	0.446475	−	1.37411i	0.880858	−	0.473380i	$-0.156966\pi$
$390$		0			0
$391$	−19.9234	−	14.4752i	−1.00757	−	0.732041i
$392$		0			0
$393$	−4.93878	−	15.2000i	−0.249129	−	0.766739i
$394$		0			0
$395$	−13.9512			−0.701962
$396$		0			0
$397$	−25.8229			−1.29601			−0.648007	−	0.761634i	$-0.724397\pi$
$397$	−25.8229			−1.29601			−0.648007	+	0.761634i	$0.724397\pi$
$398$		0			0
$399$	0.282348	+	0.868977i	0.0141351	+	0.0435033i
$400$		0			0
$401$	21.7126	+	15.7751i	1.08428	+	0.787773i	0.978424	−	0.206609i	$-0.0662428\pi$
$401$	21.7126	+	15.7751i	1.08428	+	0.787773i	0.105853	+	0.994382i	$0.466243\pi$
$402$		0			0
$403$	0.732333	−	2.25389i	0.0364801	−	0.112274i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	3.19975	−	11.3022i	0.158606	−	0.560230i
$408$		0			0
$409$	3.25852	−	2.36745i	0.161123	−	0.117063i	−0.504302	−	0.863527i	$-0.668250\pi$
$409$	3.25852	−	2.36745i	0.161123	−	0.117063i	0.665425	+	0.746464i	$0.268250\pi$
$410$		0			0
$411$	−4.08277	+	12.5655i	−0.201388	+	0.619810i
$412$		0			0
$413$	7.39276	+	5.37115i	0.363774	+	0.264297i
$414$		0			0
$415$	5.17692	+	15.9329i	0.254125	+	0.782117i
$416$		0			0
$417$	6.72540			0.329344
$418$		0			0
$419$	−18.6525			−0.911236			−0.455618	−	0.890175i	$-0.650582\pi$
$419$	−18.6525			−0.911236			−0.455618	+	0.890175i	$0.650582\pi$
$420$		0			0
$421$	4.82295	+	14.8435i	0.235056	+	0.723429i	0.997114	+	0.0759197i	$0.0241893\pi$
$421$	4.82295	+	14.8435i	0.235056	+	0.723429i	−0.762058	+	0.647509i	$0.775811\pi$
$422$		0			0
$423$	3.37575	+	2.45263i	0.164135	+	0.119251i
$424$		0			0
$425$	−1.64788	+	5.07167i	−0.0799341	+	0.246012i
$426$		0			0
$427$	−2.76156	+	2.00639i	−0.133641	+	0.0970961i
$428$		0			0
$429$	−0.723698	−	0.484606i	−0.0349405	−	0.0233970i
$430$		0			0
$431$	−19.6935	+	14.3081i	−0.948601	+	0.689199i	−0.950475	−	0.310800i	$-0.899403\pi$
$431$	−19.6935	+	14.3081i	−0.948601	+	0.689199i	0.00187486	+	0.999998i	$0.499403\pi$
$432$		0			0
$433$	9.41246	−	28.9686i	0.452334	−	1.39214i	−0.421903	−	0.906641i	$-0.638638\pi$
$433$	9.41246	−	28.9686i	0.452334	−	1.39214i	0.874237	−	0.485500i	$-0.161362\pi$
$434$		0			0
$435$	−0.820399	−	0.596054i	−0.0393351	−	0.0285786i
$436$		0			0
$437$	−1.73515	−	5.34026i	−0.0830037	−	0.255459i
$438$		0			0
$439$	−0.658702			−0.0314381			−0.0157191	−	0.999876i	$-0.505004\pi$
$439$	−0.658702			−0.0314381			−0.0157191	+	0.999876i	$0.505004\pi$
$440$		0			0
$441$	−6.43530			−0.306443
$442$		0			0
$443$	4.77376	+	14.6921i	0.226808	+	0.698043i	0.998103	+	0.0615656i	$0.0196093\pi$
$443$	4.77376	+	14.6921i	0.226808	+	0.698043i	−0.771295	+	0.636478i	$0.780391\pi$
$444$		0			0
$445$	2.33581	+	1.69707i	0.110728	+	0.0804487i
$446$		0			0
$447$	0.683362	−	2.10317i	0.0323219	−	0.0994767i
$448$		0			0
$449$	5.54224	−	4.02668i	0.261555	−	0.190031i	−0.449277	−	0.893392i	$-0.648319\pi$
$449$	5.54224	−	4.02668i	0.261555	−	0.190031i	0.710832	+	0.703362i	$0.248319\pi$
$450$		0			0
$451$	−0.365978	−	0.995089i	−0.0172332	−	0.0468569i
$452$		0			0
$453$	6.27810	−	4.56131i	0.294971	−	0.214309i
$454$		0			0
$455$	0.0609810	−	0.187680i	0.00285883	−	0.00879858i
$456$		0			0
$457$	4.28730	+	3.11490i	0.200551	+	0.145709i	0.683528	−	0.729924i	$-0.260445\pi$
$457$	4.28730	+	3.11490i	0.200551	+	0.145709i	−0.482977	+	0.875633i	$0.660445\pi$
$458$		0			0
$459$	1.64788	+	5.07167i	0.0769166	+	0.236725i
$460$		0			0
$461$	−10.0343			−0.467345			−0.233673	−	0.972315i	$-0.575074\pi$
$461$	−10.0343			−0.467345			−0.233673	+	0.972315i	$0.575074\pi$
$462$		0			0
$463$	5.11597			0.237759			0.118880	−	0.992909i	$-0.462070\pi$
$463$	5.11597			0.237759			0.118880	+	0.992909i	$0.462070\pi$
$464$		0			0
$465$	2.78871	+	8.58278i	0.129324	+	0.398017i
$466$		0			0
$467$	−14.7675	−	10.7292i	−0.683358	−	0.496489i	0.191112	−	0.981568i	$-0.438791\pi$
$467$	−14.7675	−	10.7292i	−0.683358	−	0.496489i	−0.874470	+	0.485079i	$0.838791\pi$
$468$		0			0
$469$	−3.10232	+	9.54797i	−0.143252	+	0.440884i
$470$		0			0
$471$	14.3496	−	10.4256i	0.661197	−	0.480388i
$472$		0			0
$473$	17.1985	−	0.658518i	0.790790	−	0.0302787i
$474$		0			0
$475$	−0.983677	+	0.714683i	−0.0451342	+	0.0327919i
$476$		0			0
$477$	−1.63380	+	5.02831i	−0.0748064	+	0.230230i
$478$		0			0
$479$	−34.8594	−	25.3268i	−1.59277	−	1.15721i	−0.899854	−	0.436192i	$-0.856327\pi$
$479$	−34.8594	−	25.3268i	−1.59277	−	1.15721i	−0.692913	−	0.721021i	$-0.743673\pi$
$480$		0			0
$481$	−0.287406	−	0.884546i	−0.0131046	−	0.0403318i
$482$		0			0
$483$	−3.47031			−0.157905
$484$		0			0
$485$	6.48279			0.294368
$486$		0			0
$487$	−0.217804	−	0.670330i	−0.00986962	−	0.0303756i	0.946000	−	0.324165i	$-0.105083\pi$
$487$	−0.217804	−	0.670330i	−0.00986962	−	0.0303756i	−0.955870	+	0.293790i	$0.905083\pi$
$488$		0			0
$489$	2.73817	+	1.98940i	0.123824	+	0.0899637i
$490$		0			0
$491$	−0.609230	+	1.87502i	−0.0274942	+	0.0846183i	−0.963862	−	0.266402i	$-0.914165\pi$
$491$	−0.609230	+	1.87502i	−0.0274942	+	0.0846183i	0.936368	+	0.351020i	$0.114165\pi$
$492$		0			0
$493$	−4.37491	+	3.17856i	−0.197036	+	0.143155i
$494$		0			0
$495$	3.31420	−	0.126898i	0.148962	−	0.00570363i
$496$		0			0
$497$	5.45381	−	3.96242i	0.244637	−	0.177739i
$498$		0			0
$499$	−0.595158	+	1.83171i	−0.0266429	+	0.0819985i	−0.963494	−	0.267730i	$-0.913726\pi$
$499$	−0.595158	+	1.83171i	−0.0266429	+	0.0819985i	0.936851	+	0.349729i	$0.113726\pi$
$500$		0			0
$501$	−5.62456	−	4.08648i	−0.251287	−	0.182571i
$502$		0			0
$503$	5.58817	+	17.1986i	0.249164	+	0.766849i	0.994924	+	0.100633i	$0.0320869\pi$
$503$	5.58817	+	17.1986i	0.249164	+	0.766849i	−0.745759	+	0.666216i	$0.767913\pi$
$504$		0			0
$505$	−13.3756			−0.595205
$506$		0			0
$507$	12.9310			0.574288
$508$		0			0
$509$	0.276880	+	0.852150i	0.0122725	+	0.0377709i	0.957005	−	0.290071i	$-0.0936788\pi$
$509$	0.276880	+	0.852150i	0.0122725	+	0.0377709i	−0.944733	+	0.327841i	$0.893679\pi$
$510$		0			0
$511$	−9.18402	−	6.67258i	−0.406277	−	0.295177i
$512$		0			0
$513$	−0.375731	+	1.15638i	−0.0165889	+	0.0510555i
$514$		0			0
$515$	−4.40858	+	3.20302i	−0.194265	+	0.141142i
$516$		0			0
$517$	−4.77698	−	12.9885i	−0.210092	−	0.571235i
$518$		0			0
$519$	14.0985	−	10.2431i	0.618854	−	0.449623i
$520$		0			0
$521$	−2.32413	+	7.15292i	−0.101822	+	0.313375i	−0.988971	−	0.148107i	$-0.952682\pi$
$521$	−2.32413	+	7.15292i	−0.101822	+	0.313375i	0.887150	+	0.461482i	$0.152682\pi$
$522$		0			0
$523$	−21.9083	−	15.9173i	−0.957985	−	0.696017i	−0.00530277	−	0.999986i	$-0.501688\pi$
$523$	−21.9083	−	15.9173i	−0.957985	−	0.696017i	−0.952682	+	0.303969i	$0.901688\pi$
$524$		0			0
$525$	0.232215	+	0.714683i	0.0101347	+	0.0311913i
$526$		0			0
$527$	48.1245			2.09633
$528$		0			0
$529$	−1.67339			−0.0727561
$530$		0			0
$531$	3.75772	+	11.5651i	0.163071	+	0.501881i
$532$		0			0
$533$	−0.0679168	−	0.0493444i	−0.00294180	−	0.00213734i
$534$		0			0
$535$	2.12083	−	6.52725i	0.0916916	−	0.282198i
$536$		0			0
$537$	3.77425	−	2.74215i	0.162871	−	0.118333i
$538$		0			0
$539$	17.7346	+	11.8755i	0.763883	+	0.511516i
$540$		0			0
$541$	33.0494	−	24.0118i	1.42090	−	1.03235i	0.429283	−	0.903170i	$-0.358766\pi$
$541$	33.0494	−	24.0118i	1.42090	−	1.03235i	0.991621	−	0.129178i	$-0.0412337\pi$
$542$		0			0
$543$	1.99698	−	6.14607i	0.0856986	−	0.263753i
$544$		0			0
$545$	0.432615	+	0.314313i	0.0185312	+	0.0134637i
$546$		0			0
$547$	−8.87013	−	27.2995i	−0.379260	−	1.16724i	−0.940560	−	0.339629i	$-0.889699\pi$
$547$	−8.87013	−	27.2995i	−0.379260	−	1.16724i	0.561300	−	0.827612i	$-0.310301\pi$
$548$		0			0
$549$	−4.54245			−0.193867
$550$		0			0
$551$	−1.23300			−0.0525274
$552$		0			0
$553$	3.23968	+	9.97070i	0.137765	+	0.423997i
$554$		0			0
$555$	2.86528	+	2.08175i	0.121624	+	0.0883652i
$556$		0			0
$557$	−2.62090	+	8.06630i	−0.111051	+	0.341780i	−0.991103	−	0.133098i	$-0.957508\pi$
$557$	−2.62090	+	8.06630i	−0.111051	+	0.341780i	0.880052	+	0.474878i	$0.157508\pi$
$558$		0			0
$559$	1.10249	−	0.801008i	0.0466305	−	0.0338790i
$560$		0			0
$561$	4.81783	−	17.0176i	0.203409	−	0.718484i
$562$		0			0
$563$	31.4281	−	22.8339i	1.32454	−	0.962333i	0.324674	−	0.945826i	$-0.394745\pi$
$563$	31.4281	−	22.8339i	1.32454	−	0.962333i	0.999864	−	0.0165073i	$-0.00525469\pi$
$564$		0			0
$565$	1.87392	−	5.76734i	0.0788366	−	0.242634i
$566$		0			0
$567$	0.607946	+	0.441698i	0.0255313	+	0.0185496i
$568$		0			0
$569$	−1.38605	−	4.26582i	−0.0581062	−	0.178833i	0.917791	−	0.397064i	$-0.129971\pi$
$569$	−1.38605	−	4.26582i	−0.0581062	−	0.178833i	−0.975897	+	0.218232i	$0.929971\pi$
$570$		0			0
$571$	10.8106			0.452409			0.226204	−	0.974080i	$-0.427368\pi$
$571$	10.8106			0.452409			0.226204	+	0.974080i	$0.427368\pi$
$572$		0			0
$573$	5.40448			0.225775
$574$		0			0
$575$	−1.42706	−	4.39205i	−0.0595127	−	0.183161i
$576$		0			0
$577$	−14.0187	−	10.1852i	−0.583606	−	0.424015i	0.256416	−	0.966566i	$-0.417458\pi$
$577$	−14.0187	−	10.1852i	−0.583606	−	0.424015i	−0.840022	+	0.542552i	$0.817458\pi$
$578$		0			0
$579$	−5.10471	+	15.7107i	−0.212144	+	0.652913i
$580$		0			0
$581$	10.1848	−	7.39972i	0.422538	−	0.306992i
$582$		0			0
$583$	13.7816	−	10.8422i	0.570774	−	0.449038i
$584$		0			0
$585$	0.212453	−	0.154356i	0.00878384	−	0.00638184i
$586$		0			0
$587$	0.194315	−	0.598039i	0.00802022	−	0.0246837i	−0.946966	−	0.321333i	$-0.895869\pi$
$587$	0.194315	−	0.598039i	0.00802022	−	0.0246837i	0.954987	+	0.296649i	$0.0958692\pi$
$588$		0			0
$589$	8.87716	+	6.44963i	0.365777	+	0.265753i
$590$		0			0
$591$	0.260739	+	0.802471i	0.0107254	+	0.0330093i
$592$		0			0
$593$	26.1874			1.07539			0.537694	−	0.843140i	$-0.319296\pi$
$593$	26.1874			1.07539			0.537694	+	0.843140i	$0.319296\pi$
$594$		0			0
$595$	4.00730			0.164283
$596$		0			0
$597$	0.509209	+	1.56718i	0.0208405	+	0.0641406i
$598$		0			0
$599$	−8.58294	−	6.23587i	−0.350689	−	0.254791i	0.398469	−	0.917182i	$-0.369542\pi$
$599$	−8.58294	−	6.23587i	−0.350689	−	0.254791i	−0.749158	+	0.662391i	$0.769542\pi$
$600$		0			0
$601$	8.22068	−	25.3007i	0.335329	−	1.03204i	−0.631231	−	0.775595i	$-0.717450\pi$
$601$	8.22068	−	25.3007i	0.335329	−	1.03204i	0.966560	−	0.256441i	$-0.0825498\pi$
$602$		0			0
$603$	−10.8082	+	7.85265i	−0.440146	+	0.319784i
$604$		0			0
$605$	−9.36753	−	5.76622i	−0.380844	−	0.234430i
$606$		0			0
$607$	3.31040	−	2.40515i	0.134365	−	0.0976218i	−0.518573	−	0.855034i	$-0.673536\pi$
$607$	3.31040	−	2.40515i	0.134365	−	0.0976218i	0.652938	+	0.757412i	$0.273536\pi$
$608$		0			0
$609$	−0.235482	+	0.724738i	−0.00954219	+	0.0293678i
$610$		0			0
$611$	−0.886493	−	0.644075i	−0.0358637	−	0.0260565i
$612$		0			0
$613$	−2.37882	−	7.32127i	−0.0960798	−	0.295703i	0.891454	−	0.453112i	$-0.149686\pi$
$613$	−2.37882	−	7.32127i	−0.0960798	−	0.295703i	−0.987534	+	0.157408i	$0.949686\pi$
$614$		0			0
$615$	0.319679			0.0128907
$616$		0			0
$617$	28.8591			1.16182			0.580912	−	0.813966i	$-0.302696\pi$
$617$	28.8591			1.16182			0.580912	+	0.813966i	$0.302696\pi$
$618$		0			0
$619$	14.0349	+	43.1950i	0.564110	+	1.73615i	0.670581	+	0.741836i	$0.266045\pi$
$619$	14.0349	+	43.1950i	0.564110	+	1.73615i	−0.106471	+	0.994316i	$0.533955\pi$
$620$		0			0
$621$	−3.73610	−	2.71444i	−0.149925	−	0.108927i
$622$		0			0
$623$	0.670456	−	2.06345i	0.0268612	−	0.0826704i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	3.16941	−	2.49343i	0.126574	−	0.0995779i
$628$		0			0
$629$	15.2796	−	11.1013i	0.609236	−	0.442636i
$630$		0			0
$631$	−12.0377	+	37.0482i	−0.479212	+	1.47486i	0.360979	+	0.932574i	$0.382443\pi$
$631$	−12.0377	+	37.0482i	−0.479212	+	1.47486i	−0.840191	+	0.542290i	$0.817557\pi$
$632$		0			0
$633$	−4.77137	−	3.46660i	−0.189645	−	0.137785i
$634$		0			0
$635$	2.71328	+	8.35063i	0.107673	+	0.331385i
$636$		0			0
$637$	1.68995			0.0669583
$638$		0			0
$639$	8.97088			0.354882
$640$		0			0
$641$	5.48149	+	16.8703i	0.216506	+	0.666337i	0.999043	+	0.0437330i	$0.0139251\pi$
$641$	5.48149	+	16.8703i	0.216506	+	0.666337i	−0.782537	+	0.622604i	$0.786075\pi$
$642$		0			0
$643$	4.14716	+	3.01309i	0.163548	+	0.118825i	0.666549	−	0.745461i	$-0.267771\pi$
$643$	4.14716	+	3.01309i	0.163548	+	0.118825i	−0.503001	+	0.864286i	$0.667771\pi$
$644$		0			0
$645$	−1.60360	+	4.93537i	−0.0631416	+	0.194330i
$646$		0			0
$647$	−23.4321	+	17.0244i	−0.921212	+	0.669300i	−0.943825	−	0.330445i	$-0.892801\pi$
$647$	−23.4321	+	17.0244i	−0.921212	+	0.669300i	0.0226134	+	0.999744i	$0.492801\pi$
$648$		0			0
$649$	10.9862	−	38.8057i	0.431247	−	1.52326i
$650$		0			0
$651$	5.48639	−	3.98609i	0.215028	−	0.156227i
$652$		0			0
$653$	12.0973	−	37.2316i	0.473403	−	1.45698i	−0.374696	−	0.927148i	$-0.622253\pi$
$653$	12.0973	−	37.2316i	0.473403	−	1.45698i	0.848099	−	0.529837i	$-0.177747\pi$
$654$		0			0
$655$	−12.9299	−	9.39412i	−0.505213	−	0.367059i
$656$		0			0
$657$	−4.66821	−	14.3673i	−0.182124	−	0.560520i
$658$		0			0
$659$	20.2819			0.790071			0.395036	−	0.918666i	$-0.370732\pi$
$659$	20.2819			0.790071			0.395036	+	0.918666i	$0.370732\pi$
$660$		0			0
$661$	−25.4310			−0.989152			−0.494576	−	0.869134i	$-0.664677\pi$
$661$	−25.4310			−0.989152			−0.494576	+	0.869134i	$0.664677\pi$
$662$		0			0
$663$	−0.432744	−	1.33185i	−0.0168064	−	0.0517248i
$664$		0			0
$665$	0.739196	+	0.537057i	0.0286648	+	0.0208262i
$666$		0			0
$667$	1.44714	−	4.45384i	0.0560335	−	0.172453i
$668$		0			0
$669$	0.366154	−	0.266027i	0.0141563	−	0.0102852i
$670$		0			0
$671$	12.5182	+	8.38251i	0.483260	+	0.323603i
$672$		0			0
$673$	8.46729	−	6.15184i	0.326390	−	0.237136i	−0.412507	−	0.910954i	$-0.635347\pi$
$673$	8.46729	−	6.15184i	0.326390	−	0.237136i	0.738897	+	0.673818i	$0.235347\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	23.2492	+	16.8915i	0.893539	+	0.649194i	0.936798	−	0.349870i	$-0.113774\pi$
$677$	23.2492	+	16.8915i	0.893539	+	0.649194i	−0.0432597	+	0.999064i	$0.513774\pi$
$678$		0			0
$679$	−1.50540	−	4.63314i	−0.0577719	−	0.177804i
$680$		0			0
$681$	6.01301			0.230419
$682$		0			0
$683$	11.1538			0.426790			0.213395	−	0.976966i	$-0.431548\pi$
$683$	11.1538			0.426790			0.213395	+	0.976966i	$0.431548\pi$
$684$		0			0
$685$	4.08277	+	12.5655i	0.155995	+	0.480102i
$686$		0			0
$687$	3.65839	+	2.65798i	0.139576	+	0.101408i
$688$		0			0
$689$	0.429045	−	1.32046i	0.0163453	−	0.0503057i
$690$		0			0
$691$	−22.9447	+	16.6703i	−0.872857	+	0.634168i	−0.931352	−	0.364120i	$-0.881370\pi$
$691$	−22.9447	+	16.6703i	−0.872857	+	0.634168i	0.0584951	+	0.998288i	$0.481370\pi$
$692$		0			0
$693$	−0.860297	−	2.33913i	−0.0326800	−	0.0888563i
$694$		0			0
$695$	5.44096	−	3.95309i	0.206387	−	0.149949i
$696$		0			0
$697$	0.526794	−	1.62131i	0.0199538	−	0.0614114i
$698$		0			0
$699$	9.75695	+	7.08884i	0.369042	+	0.268125i
$700$		0			0
$701$	−2.75126	−	8.46750i	−0.103914	−	0.319813i	0.885560	−	0.464524i	$-0.153775\pi$
$701$	−2.75126	−	8.46750i	−0.103914	−	0.319813i	−0.989474	+	0.144711i	$0.953775\pi$
$702$		0			0
$703$	4.30630			0.162415
$704$		0			0
$705$	4.17266			0.157151
$706$		0			0
$707$	3.10601	+	9.55930i	0.116813	+	0.359514i
$708$		0			0
$709$	−33.3253	−	24.2123i	−1.25156	−	0.909310i	−0.253247	−	0.967402i	$-0.581499\pi$
$709$	−33.3253	−	24.2123i	−1.25156	−	0.909310i	−0.998311	+	0.0580913i	$0.981499\pi$
$710$		0			0
$711$	−4.31116	+	13.2684i	−0.161681	+	0.497604i
$712$		0			0
$713$	−33.7163	+	24.4963i	−1.26269	+	0.917395i
$714$		0			0
$715$	−0.870328	+	0.0333241i	−0.0325484	+	0.00124625i
$716$		0			0
$717$	−22.4996	+	16.3469i	−0.840262	+	0.610486i
$718$		0			0
$719$	−1.00933	+	3.10640i	−0.0376417	+	0.115849i	−0.968112	−	0.250519i	$-0.919399\pi$
$719$	−1.00933	+	3.10640i	−0.0376417	+	0.115849i	0.930470	+	0.366368i	$0.119399\pi$
$720$		0			0
$721$	3.31288	+	2.40695i	0.123378	+	0.0896395i
$722$		0			0
$723$	−4.86601	−	14.9760i	−0.180969	−	0.556965i
$724$		0			0
$725$	−1.01407			−0.0376616
$726$		0			0
$727$	−17.7831			−0.659539			−0.329770	−	0.944061i	$-0.606971\pi$
$727$	−17.7831			−0.659539			−0.329770	+	0.944061i	$0.606971\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	22.3880	+	16.2658i	0.828050	+	0.601613i
$732$		0			0
$733$	3.27285	−	10.0728i	0.120885	−	0.372047i	−0.872244	−	0.489072i	$-0.837336\pi$
$733$	3.27285	−	10.0728i	0.120885	−	0.372047i	0.993129	+	0.117025i	$0.0373356\pi$
$734$		0			0
$735$	−5.20627	+	3.78258i	−0.192036	+	0.139522i
$736$		0			0
$737$	44.2767	−	1.69532i	1.63095	−	0.0624479i
$738$		0			0
$739$	0.524995	−	0.381431i	0.0193123	−	0.0140312i	−0.578087	−	0.815975i	$-0.696201\pi$
$739$	0.524995	−	0.381431i	0.0193123	−	0.0140312i	0.597400	+	0.801944i	$0.296201\pi$
$740$		0			0
$741$	0.0986693	−	0.303673i	0.00362471	−	0.0111557i
$742$		0			0
$743$	17.8875	+	12.9960i	0.656229	+	0.476779i	0.865387	−	0.501103i	$-0.167072\pi$
$743$	17.8875	+	12.9960i	0.656229	+	0.476779i	−0.209158	+	0.977882i	$0.567072\pi$
$744$		0			0
$745$	−0.683362	−	2.10317i	−0.0250365	−	0.0770543i
$746$		0			0
$747$	16.7529			0.612956
$748$		0			0
$749$	−5.15740			−0.188447
$750$		0			0
$751$	−4.45922	−	13.7241i	−0.162719	−	0.500798i	0.836142	−	0.548513i	$-0.184806\pi$
$751$	−4.45922	−	13.7241i	−0.162719	−	0.500798i	−0.998861	+	0.0477152i	$0.984806\pi$
$752$		0			0
$753$	20.4911	+	14.8877i	0.746737	+	0.542536i
$754$		0			0
$755$	2.39802	−	7.38035i	0.0872729	−	0.268598i
$756$		0			0
$757$	18.3362	−	13.3221i	0.666442	−	0.484199i	−0.202390	−	0.979305i	$-0.564871\pi$
$757$	18.3362	−	13.3221i	0.666442	−	0.484199i	0.868832	+	0.495106i	$0.164871\pi$
$758$		0			0
$759$	5.28691	+	14.3750i	0.191903	+	0.521780i
$760$		0			0
$761$	21.0314	−	15.2802i	0.762388	−	0.553907i	−0.137254	−	0.990536i	$-0.543828\pi$
$761$	21.0314	−	15.2802i	0.762388	−	0.553907i	0.899642	+	0.436629i	$0.143828\pi$
$762$		0			0
$763$	0.124175	−	0.382171i	0.00449543	−	0.0138355i
$764$		0			0
$765$	4.31422	+	3.13446i	0.155981	+	0.113327i
$766$		0			0
$767$	−0.986800	−	3.03706i	−0.0356313	−	0.109662i
$768$		0			0
$769$	9.56088			0.344774			0.172387	−	0.985029i	$-0.444852\pi$
$769$	9.56088			0.344774			0.172387	+	0.985029i	$0.444852\pi$
$770$		0			0
$771$	7.16290			0.257965
$772$		0			0
$773$	7.00484	+	21.5587i	0.251947	+	0.775412i	0.994416	+	0.105532i	$0.0336545\pi$
$773$	7.00484	+	21.5587i	0.251947	+	0.775412i	−0.742469	+	0.669880i	$0.766345\pi$
$774$		0			0
$775$	7.30095	+	5.30445i	0.262258	+	0.190541i
$776$		0			0
$777$	0.822430	−	2.53118i	0.0295045	−	0.0908055i
$778$		0			0
$779$	0.314461	−	0.228469i	0.0112667	−	0.00818576i
$780$		0			0
$781$	−24.7222	−	16.5546i	−0.884630	−	0.592371i
$782$		0			0
$783$	−0.820399	+	0.596054i	−0.0293187	+	0.0213012i
$784$		0			0
$785$	5.48108	−	16.8690i	0.195628	−	0.602081i
$786$		0			0
$787$	−29.5497	−	21.4691i	−1.05333	−	0.765291i	−0.0804896	−	0.996755i	$-0.525648\pi$
$787$	−29.5497	−	21.4691i	−1.05333	−	0.765291i	−0.972843	+	0.231464i	$0.925648\pi$
$788$		0			0
$789$	7.90971	+	24.3436i	0.281593	+	0.866655i
$790$		0			0
$791$	−4.55698			−0.162027
$792$		0			0
$793$	1.19287			0.0423602
$794$		0			0
$795$	1.63380	+	5.02831i	0.0579448	+	0.178336i
$796$		0			0
$797$	−36.0493	−	26.1913i	−1.27693	−	0.927744i	−0.277475	−	0.960733i	$-0.589498\pi$
$797$	−36.0493	−	26.1913i	−1.27693	−	0.927744i	−0.999456	+	0.0329885i	$0.989498\pi$
$798$		0			0
$799$	6.87606	−	21.1623i	0.243257	−	0.748669i
$800$		0			0
$801$	2.33581	−	1.69707i	0.0825319	−	0.0599629i
$802$		0			0
$803$	−13.6482	+	48.2083i	−0.481634	+	1.70123i
$804$		0			0
$805$	−2.80754	+	2.03980i	−0.0989527	+	0.0718934i
$806$		0			0
$807$	−5.91799	+	18.2137i	−0.208323	+	0.641153i
$808$		0			0
$809$	−29.2878	−	21.2789i	−1.02971	−	0.748125i	−0.0614558	−	0.998110i	$-0.519574\pi$
$809$	−29.2878	−	21.2789i	−1.02971	−	0.748125i	−0.968250	+	0.249985i	$0.919574\pi$
$810$		0			0
$811$	−9.40984	−	28.9605i	−0.330424	−	1.01694i	−0.968932	−	0.247326i	$-0.920448\pi$
$811$	−9.40984	−	28.9605i	−0.330424	−	1.01694i	0.638508	−	0.769615i	$-0.279552\pi$
$812$		0			0
$813$	11.0685			0.388188
$814$		0			0
$815$	3.38457			0.118556
$816$		0			0
$817$	1.94980	+	6.00087i	0.0682149	+	0.209944i
$818$		0			0
$819$	−0.159650	−	0.115993i	−0.00557863	−	0.00405311i
$820$		0			0
$821$	8.46115	−	26.0407i	0.295296	−	0.908828i	−0.687826	−	0.725876i	$-0.741435\pi$
$821$	8.46115	−	26.0407i	0.295296	−	0.908828i	0.983122	−	0.182952i	$-0.0585653\pi$
$822$		0			0
$823$	1.53365	−	1.11426i	0.0534597	−	0.0388408i	−0.560734	−	0.827996i	$-0.689481\pi$
$823$	1.53365	−	1.11426i	0.0534597	−	0.0388408i	0.614194	+	0.789155i	$0.289481\pi$
$824$		0			0
$825$	2.60665	−	2.05070i	0.0907520	−	0.0713961i
$826$		0			0
$827$	22.4548	−	16.3144i	0.780830	−	0.567306i	−0.124398	−	0.992232i	$-0.539700\pi$
$827$	22.4548	−	16.3144i	0.780830	−	0.567306i	0.905228	+	0.424926i	$0.139700\pi$
$828$		0			0
$829$	−13.4845	+	41.5009i	−0.468335	+	1.44139i	0.386404	+	0.922330i	$0.373717\pi$
$829$	−13.4845	+	41.5009i	−0.468335	+	1.44139i	−0.854739	+	0.519058i	$0.826283\pi$
$830$		0			0
$831$	−12.0191	−	8.73241i	−0.416939	−	0.302924i
$832$		0			0
$833$	10.6046	+	32.6377i	0.367429	+	1.13083i
$834$		0			0
$835$	−6.95234			−0.240596
$836$		0			0
$837$	9.02447			0.311931
$838$		0			0
$839$	−7.10502	−	21.8670i	−0.245293	−	0.754933i	−0.995588	−	0.0938306i	$-0.970089\pi$
$839$	−7.10502	−	21.8670i	−0.245293	−	0.754933i	0.750296	−	0.661103i	$-0.229911\pi$
$840$		0			0
$841$	22.6296	+	16.4413i	0.780329	+	0.566942i
$842$		0			0
$843$	4.94746	−	15.2267i	0.170400	−	0.524436i
$844$		0			0
$845$	10.4614	−	7.60067i	0.359884	−	0.261471i
$846$		0			0
$847$	−1.94574	+	8.03382i	−0.0668565	+	0.276045i
$848$		0			0
$849$	6.83415	−	4.96530i	0.234547	−	0.170409i
$850$		0			0
$851$	−5.05420	+	15.5552i	−0.173256	+	0.533226i
$852$		0			0
$853$	−20.8733	−	15.1653i	−0.714687	−	0.519250i	0.169995	−	0.985445i	$-0.445625\pi$
$853$	−20.8733	−	15.1653i	−0.714687	−	0.519250i	−0.884682	+	0.466194i	$0.845625\pi$
$854$		0			0
$855$	0.375731	+	1.15638i	0.0128497	+	0.0395474i
$856$		0			0
$857$	−49.2710			−1.68307			−0.841533	−	0.540206i	$-0.818346\pi$
$857$	−49.2710			−1.68307			−0.841533	+	0.540206i	$0.818346\pi$
$858$		0			0
$859$	54.3769			1.85531			0.927657	−	0.373433i	$-0.121819\pi$
$859$	54.3769			1.85531			0.927657	+	0.373433i	$0.121819\pi$
$860$		0			0
$861$	−0.0742342	−	0.228469i	−0.00252989	−	0.00778622i
$862$		0			0
$863$	4.44680	+	3.23079i	0.151371	+	0.109977i	0.660893	−	0.750480i	$-0.270178\pi$
$863$	4.44680	+	3.23079i	0.151371	+	0.109977i	−0.509522	+	0.860458i	$0.670178\pi$
$864$		0			0
$865$	5.38513	−	16.5737i	0.183100	−	0.563524i
$866$		0			0
$867$	9.25298	−	6.72268i	0.314248	−	0.228314i
$868$		0			0
$869$	36.3660	−	28.6097i	1.23363	−	0.970519i
$870$		0			0
$871$	2.83831	−	2.06215i	0.0961725	−	0.0698734i
$872$		0			0
$873$	2.00329	−	6.16550i	0.0678012	−	0.208670i
$874$		0			0
$875$	0.607946	+	0.441698i	0.0205523	+	0.0149321i
$876$		0			0
$877$	−5.61200	−	17.2720i	−0.189504	−	0.583233i	0.810493	−	0.585748i	$-0.199199\pi$
$877$	−5.61200	−	17.2720i	−0.189504	−	0.583233i	−0.999997	+	0.00251548i	$0.999199\pi$
$878$		0			0
$879$	11.5105			0.388241
$880$		0			0
$881$	−10.3537			−0.348825			−0.174413	−	0.984673i	$-0.555803\pi$
$881$	−10.3537			−0.348825			−0.174413	+	0.984673i	$0.555803\pi$
$882$		0			0
$883$	1.72717	+	5.31567i	0.0581238	+	0.178887i	0.975903	−	0.218204i	$-0.0700198\pi$
$883$	1.72717	+	5.31567i	0.0581238	+	0.178887i	−0.917779	+	0.397091i	$0.870020\pi$
$884$		0			0
$885$	9.83783	+	7.14760i	0.330695	+	0.240264i
$886$		0			0
$887$	8.91988	−	27.4526i	0.299500	−	0.921767i	−0.682172	−	0.731191i	$-0.738965\pi$
$887$	8.91988	−	27.4526i	0.299500	−	0.921767i	0.981673	−	0.190575i	$-0.0610353\pi$
$888$		0			0
$889$	5.33799	−	3.87828i	0.179030	−	0.130073i
$890$		0			0
$891$	0.903456	−	3.19120i	0.0302669	−	0.106909i
$892$		0			0
$893$	4.10455	−	2.98213i	0.137353	−	0.0997931i
$894$		0			0
$895$	1.44163	−	4.43689i	0.0481885	−	0.148309i
$896$		0			0
$897$	0.981123	+	0.712827i	0.0327587	+	0.0238006i
$898$		0			0
$899$	2.82795	+	8.70352i	0.0943173	+	0.290279i
$900$		0			0
$901$	28.1942			0.939285
$902$		0			0
$903$	3.89960			0.129771
$904$		0			0
$905$	−1.99698	−	6.14607i	−0.0663818	−	0.204302i
$906$		0			0
$907$	21.7109	+	15.7739i	0.720898	+	0.523763i	0.886671	−	0.462401i	$-0.153012\pi$
$907$	21.7109	+	15.7739i	0.720898	+	0.523763i	−0.165773	+	0.986164i	$0.553012\pi$
$908$		0			0
$909$	−4.13328	+	12.7209i	−0.137092	+	0.421927i
$910$		0			0
$911$	−30.4418	+	22.1173i	−1.00858	+	0.732778i	−0.963911	−	0.266224i	$-0.914224\pi$
$911$	−30.4418	+	22.1173i	−1.00858	+	0.732778i	−0.0446709	+	0.999002i	$0.514224\pi$
$912$		0			0
$913$	−46.1681	−	30.9153i	−1.52794	−	1.02315i
$914$		0			0
$915$	−3.67492	+	2.66998i	−0.121489	+	0.0882670i
$916$		0			0
$917$	−3.71131	+	11.4222i	−0.122558	+	0.377195i
$918$		0			0
$919$	−40.2904	−	29.2727i	−1.32906	−	0.965618i	−0.999771	−	0.0213879i	$-0.993192\pi$
$919$	−40.2904	−	29.2727i	−1.32906	−	0.965618i	−0.329287	−	0.944230i	$-0.606808\pi$
$920$		0			0
$921$	−6.97163	−	21.4565i	−0.229723	−	0.707015i
$922$		0			0
$923$	−2.35581			−0.0775423
$924$		0			0
$925$	3.54168			0.116450
$926$		0			0
$927$	1.68393	+	5.18260i	0.0553075	+	0.170219i
$928$		0			0
$929$	−18.2883	−	13.2872i	−0.600019	−	0.435939i	0.245867	−	0.969304i	$-0.420927\pi$
$929$	−18.2883	−	13.2872i	−0.600019	−	0.435939i	−0.845885	+	0.533365i	$0.820927\pi$
$930$		0			0
$931$	−2.41794	+	7.44167i	−0.0792449	+	0.243891i
$932$		0			0
$933$	12.9665	−	9.42075i	0.424506	−	0.308421i
$934$		0			0
$935$	−6.10499	−	16.5994i	−0.199655	−	0.542858i
$936$		0			0
$937$	−33.2199	+	24.1357i	−1.08525	+	0.788478i	−0.978590	−	0.205818i	$-0.934015\pi$
$937$	−33.2199	+	24.1357i	−1.08525	+	0.788478i	−0.106657	+	0.994296i	$0.534015\pi$
$938$		0			0
$939$	−10.4116	+	32.0436i	−0.339770	+	1.04570i
$940$		0			0
$941$	34.4950	+	25.0621i	1.12450	+	0.817000i	0.984886	−	0.173205i	$-0.0554124\pi$
$941$	34.4950	+	25.0621i	1.12450	+	0.817000i	0.139618	+	0.990205i	$0.455412\pi$
$942$		0			0
$943$	0.456203	+	1.40405i	0.0148560	+	0.0457221i
$944$		0			0
$945$	0.751462			0.0244451
$946$		0			0
$947$	5.11363			0.166171			0.0830854	−	0.996542i	$-0.473523\pi$
$947$	5.11363			0.166171			0.0830854	+	0.996542i	$0.473523\pi$
$948$		0			0
$949$	1.22590	+	3.77293i	0.0397944	+	0.122475i
$950$		0			0
$951$	1.19920	+	0.871267i	0.0388866	+	0.0282528i
$952$		0			0
$953$	−10.2558	+	31.5642i	−0.332219	+	1.02246i	0.635857	+	0.771807i	$0.280647\pi$
$953$	−10.2558	+	31.5642i	−0.332219	+	1.02246i	−0.968076	+	0.250657i	$0.919353\pi$
$954$		0			0
$955$	4.37231	−	3.17667i	0.141485	−	0.102795i
$956$		0			0
$957$	3.36082	−	0.128683i	0.108640	−	0.00415973i
$958$		0			0
$959$	8.03226	−	5.83578i	0.259375	−	0.188447i
$960$		0			0
$961$	15.5871	−	47.9722i	0.502811	−	1.54749i
$962$		0			0
$963$	−5.55241	−	4.03406i	−0.178924	−	0.129996i
$964$		0			0
$965$	5.10471	+	15.7107i	0.164326	+	0.505744i
$966$		0			0
$967$	14.7001			0.472723			0.236361	−	0.971665i	$-0.424045\pi$
$967$	14.7001			0.472723			0.236361	+	0.971665i	$0.424045\pi$
$968$		0			0
$969$	6.48394			0.208294
$970$		0			0
$971$	−2.56032	−	7.87984i	−0.0821645	−	0.252876i	0.901532	−	0.432712i	$-0.142443\pi$
$971$	−2.56032	−	7.87984i	−0.0821645	−	0.252876i	−0.983697	+	0.179836i	$0.942443\pi$
$972$		0			0
$973$	−4.08868	−	2.97060i	−0.131077	−	0.0952330i
$974$		0			0
$975$	0.0811497	−	0.249753i	0.00259887	−	0.00799851i
$976$		0			0
$977$	−31.8325	+	23.1276i	−1.01841	+	0.739919i	−0.965957	−	0.258704i	$-0.916704\pi$
$977$	−31.8325	+	23.1276i	−1.01841	+	0.739919i	−0.0524545	+	0.998623i	$0.516704\pi$
$978$		0			0
$979$	−9.56883	+	0.366382i	−0.305821	+	0.0117096i
$980$		0			0
$981$	0.432615	−	0.314313i	0.0138123	−	0.0100352i
$982$		0			0
$983$	7.56126	−	23.2712i	0.241167	−	0.742235i	−0.755076	−	0.655637i	$-0.772400\pi$
$983$	7.56126	−	23.2712i	0.241167	−	0.742235i	0.996243	−	0.0865985i	$-0.0275997\pi$
$984$		0			0
$985$	0.682623	+	0.495955i	0.0217502	+	0.0158024i
$986$		0			0
$987$	−0.968952	−	2.98213i	−0.0308421	−	0.0949222i
$988$		0			0
$989$	−23.9648			−0.762037
$990$		0			0
$991$	−32.2889			−1.02569			−0.512845	−	0.858481i	$-0.671409\pi$
$991$	−32.2889			−1.02569			−0.512845	+	0.858481i	$0.671409\pi$
$992$		0			0
$993$	1.10679	+	3.40634i	0.0351228	+	0.108097i
$994$		0			0
$995$	1.33313	+	0.968573i	0.0422629	+	0.0307058i
$996$		0			0
$997$	−16.2030	+	49.8677i	−0.513154	+	1.57933i	0.273462	+	0.961883i	$0.411831\pi$
$997$	−16.2030	+	49.8677i	−0.513154	+	1.57933i	−0.786616	+	0.617442i	$0.788169\pi$
$998$		0			0
$999$	2.86528	−	2.08175i	0.0906534	−	0.0658635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.e.1081.2	yes	12
11.4	even	5	inner	1320.2.bw.e.961.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.e.961.2	✓	12	11.4	even	5	inner
1320.2.bw.e.1081.2	yes	12	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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.232215 + 0.714683i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.232215 + 0.714683i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(3.31420 - 0.126898i) q^{11} +(0.212453 - 0.154356i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(4.31422 + 3.13446i) q^{17} +(0.375731 + 1.15638i) q^{19} +0.751462 q^{21} -4.61807 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.313364 + 0.964436i) q^{29} +(7.30095 - 5.30445i) q^{31} +(-1.14483 - 3.11277i) q^{33} +(0.607946 - 0.441698i) q^{35} +(1.09444 - 3.36834i) q^{37} +(-0.212453 - 0.154356i) q^{39} +(-0.0987863 - 0.304033i) q^{41} +5.18935 q^{43} +1.00000 q^{45} +(-1.28942 - 3.96843i) q^{47} +(5.20627 + 3.78258i) q^{49} +(1.64788 - 5.07167i) q^{51} +(4.27733 - 3.10766i) q^{53} +(-2.75583 - 1.84537i) q^{55} +(0.983677 - 0.714683i) q^{57} +(3.75772 - 11.5651i) q^{59} +(3.67492 + 2.66998i) q^{61} +(-0.232215 - 0.714683i) q^{63} -0.262606 q^{65} +13.3597 q^{67} +(1.42706 + 4.39205i) q^{69} +(-7.25759 - 5.27295i) q^{71} +(-4.66821 + 14.3673i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-0.678913 + 2.39807i) q^{77} +(11.2868 - 8.20032i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-13.5534 - 9.84709i) q^{83} +(-1.64788 - 5.07167i) q^{85} +1.01407 q^{87} -2.88722 q^{89} +(0.0609810 + 0.187680i) q^{91} +(-7.30095 - 5.30445i) q^{93} +(0.375731 - 1.15638i) q^{95} +(-5.24469 + 3.81049i) q^{97} +(-2.60665 + 2.05070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{5} - 5 q^{7} - 3 q^{9} + 6 q^{11} + 12 q^{13} + 3 q^{15} - 13 q^{17} + 20 q^{23} - 3 q^{25} + 3 q^{27} - 3 q^{29} - 3 q^{31} - q^{33} + 5 q^{35} + 5 q^{37} - 12 q^{39} + q^{41} + 6 q^{43} + 12 q^{45} - 10 q^{47} - 12 q^{51} - 3 q^{53} + q^{55} + 5 q^{57} + 23 q^{59} - 7 q^{61} - 5 q^{63} - 28 q^{65} + 44 q^{67} + 5 q^{69} - 9 q^{71} - 27 q^{73} + 3 q^{75} + 65 q^{77} - q^{79} - 3 q^{81} - 21 q^{83} + 12 q^{85} + 28 q^{87} + 32 q^{89} - 19 q^{91} + 3 q^{93} + 5 q^{97} - 4 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^5 - 5 * q^7 - 3 * q^9 + 6 * q^11 + 12 * q^13 + 3 * q^15 - 13 * q^17 + 20 * q^23 - 3 * q^25 + 3 * q^27 - 3 * q^29 - 3 * q^31 - q^33 + 5 * q^35 + 5 * q^37 - 12 * q^39 + q^41 + 6 * q^43 + 12 * q^45 - 10 * q^47 - 12 * q^51 - 3 * q^53 + q^55 + 5 * q^57 + 23 * q^59 - 7 * q^61 - 5 * q^63 - 28 * q^65 + 44 * q^67 + 5 * q^69 - 9 * q^71 - 27 * q^73 + 3 * q^75 + 65 * q^77 - q^79 - 3 * q^81 - 21 * q^83 + 12 * q^85 + 28 * q^87 + 32 * q^89 - 19 * q^91 + 3 * q^93 + 5 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more