LMFDB - Embedded newform 1386.2.k.w.991.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.3
Root			$0.500000 - 0.0585812i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.w.793.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +(-1.37328 + 2.37860i) q^{10} +(0.500000 - 0.866025i) q^{11} +5.49314 q^{13} +(-2.64510 - 0.0585812i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(4.01839 + 6.96005i) q^{19} -2.74657 q^{20} +1.00000 q^{22} +(-0.645103 - 1.11735i) q^{23} +(-1.27182 + 2.20285i) q^{25} +(2.74657 + 4.75720i) q^{26} +(-1.27182 - 2.32002i) q^{28} -4.54364 q^{29} +(-2.54364 + 4.40571i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(-7.26496 - 0.160897i) q^{35} +(2.01839 + 3.49595i) q^{37} +(-4.01839 + 6.96005i) q^{38} +(-1.37328 - 2.37860i) q^{40} -5.54364 q^{41} -4.03677 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.645103 - 1.11735i) q^{46} +(-4.64510 - 8.04555i) q^{47} +(-3.22818 - 6.21119i) q^{49} -2.54364 q^{50} +(-2.74657 + 4.75720i) q^{52} +(2.74657 - 4.75720i) q^{53} +2.74657 q^{55} +(1.37328 - 2.26144i) q^{56} +(-2.27182 - 3.93491i) q^{58} +(-4.76496 + 8.25314i) q^{59} +(0.829647 + 1.43699i) q^{61} -5.08727 q^{62} +1.00000 q^{64} +(7.54364 + 13.0660i) q^{65} +(-1.77182 + 3.06888i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.49314 - 6.37208i) q^{70} -2.54364 q^{71} +(4.29021 - 7.43085i) q^{73} +(-2.01839 + 3.49595i) q^{74} -8.03677 q^{76} +(1.27182 + 2.32002i) q^{77} +(-6.11985 - 10.5999i) q^{79} +(1.37328 - 2.37860i) q^{80} +(-2.77182 - 4.80093i) q^{82} +14.5299 q^{83} +2.74657 q^{85} +(-2.01839 - 3.49595i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-3.25343 - 5.63511i) q^{89} +(-7.54364 + 12.4224i) q^{91} +1.29021 q^{92} +(4.64510 - 8.04555i) q^{94} +(-11.0368 + 19.1163i) q^{95} -0.0872743 q^{97} +(3.76496 - 5.90128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} + 3 q^{11} - 3 q^{14} - 3 q^{16} + 3 q^{17} + 3 q^{19} + 6 q^{22} + 9 q^{23} - 3 q^{25} - 3 q^{28} - 18 q^{29} - 6 q^{31} + 3 q^{32} + 6 q^{34} - 6 q^{35} - 9 q^{37} - 3 q^{38} - 24 q^{41} + 18 q^{43} + 3 q^{44} - 9 q^{46} - 15 q^{47} - 24 q^{49} - 6 q^{50} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} + 6 q^{64} + 36 q^{65} - 6 q^{67} + 3 q^{68} + 12 q^{70} - 6 q^{71} + 9 q^{74} - 6 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} + 12 q^{83} + 9 q^{86} - 3 q^{88} - 36 q^{89} - 36 q^{91} - 18 q^{92} + 15 q^{94} - 24 q^{95} + 18 q^{97} - 15 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 + 3 * q^11 - 3 * q^14 - 3 * q^16 + 3 * q^17 + 3 * q^19 + 6 * q^22 + 9 * q^23 - 3 * q^25 - 3 * q^28 - 18 * q^29 - 6 * q^31 + 3 * q^32 + 6 * q^34 - 6 * q^35 - 9 * q^37 - 3 * q^38 - 24 * q^41 + 18 * q^43 + 3 * q^44 - 9 * q^46 - 15 * q^47 - 24 * q^49 - 6 * q^50 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 + 6 * q^64 + 36 * q^65 - 6 * q^67 + 3 * q^68 + 12 * q^70 - 6 * q^71 + 9 * q^74 - 6 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 + 12 * q^83 + 9 * q^86 - 3 * q^88 - 36 * q^89 - 36 * q^91 - 18 * q^92 + 15 * q^94 - 24 * q^95 + 18 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.37328	+	2.37860i	0.614151	+	1.06374i	0.990533	+	0.137277i	$0.0438349\pi$
$5$	1.37328	+	2.37860i	0.614151	+	1.06374i	−0.376381	+	0.926465i	$0.622832\pi$
$6$		0			0
$7$	−1.37328	+	2.26144i	−0.519053	+	0.854742i
$7$	−1.37328	+	2.26144i	−0.519053	+	0.854742i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.37328	+	2.37860i	−0.434271	+	0.752179i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	5.49314			1.52352			0.761761	−	0.647858i	$-0.224335\pi$
$13$	5.49314			1.52352			0.761761	+	0.647858i	$0.224335\pi$
$14$	−2.64510	−	0.0585812i	−0.706933	−	0.0156565i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	4.01839	+	6.96005i	0.921881	+	1.59675i	0.796502	+	0.604636i	$0.206681\pi$
$19$	4.01839	+	6.96005i	0.921881	+	1.59675i	0.125379	+	0.992109i	$0.459985\pi$
$20$	−2.74657			−0.614151
$21$		0			0
$22$	1.00000			0.213201
$23$	−0.645103	−	1.11735i	−0.134513	−	0.232984i	0.790898	−	0.611948i	$-0.209614\pi$
$23$	−0.645103	−	1.11735i	−0.134513	−	0.232984i	−0.925411	+	0.378964i	$0.876280\pi$
$24$		0			0
$25$	−1.27182	+	2.20285i	−0.254364	+	0.440571i
$26$	2.74657	+	4.75720i	0.538646	+	0.932963i
$27$		0			0
$28$	−1.27182	−	2.32002i	−0.240351	−	0.438442i
$29$	−4.54364			−0.843732			−0.421866	−	0.906658i	$-0.638625\pi$
$29$	−4.54364			−0.843732			−0.421866	+	0.906658i	$0.638625\pi$
$30$		0			0
$31$	−2.54364	+	4.40571i	−0.456851	+	0.791289i	−0.998793	−	0.0491274i	$-0.984356\pi$
$31$	−2.54364	+	4.40571i	−0.456851	+	0.791289i	0.541942	+	0.840416i	$0.317689\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	1.00000			0.171499
$35$	−7.26496	−	0.160897i	−1.22800	−	0.0271966i
$36$		0			0
$37$	2.01839	+	3.49595i	0.331821	+	0.574730i	0.982869	−	0.184306i	$-0.0590038\pi$
$37$	2.01839	+	3.49595i	0.331821	+	0.574730i	−0.651048	+	0.759036i	$0.725670\pi$
$38$	−4.01839	+	6.96005i	−0.651868	+	1.12907i
$39$		0			0
$40$	−1.37328	−	2.37860i	−0.217135	−	0.376089i
$41$	−5.54364			−0.865771			−0.432885	−	0.901449i	$-0.642505\pi$
$41$	−5.54364			−0.865771			−0.432885	+	0.901449i	$0.642505\pi$
$42$		0			0
$43$	−4.03677			−0.615602			−0.307801	−	0.951451i	$-0.599593\pi$
$43$	−4.03677			−0.615602			−0.307801	+	0.951451i	$0.599593\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	0.645103	−	1.11735i	0.0951152	−	0.164744i
$47$	−4.64510	−	8.04555i	−0.677558	−	1.17356i	−0.975714	−	0.219048i	$-0.929705\pi$
$47$	−4.64510	−	8.04555i	−0.677558	−	1.17356i	0.298156	−	0.954517i	$-0.403628\pi$
$48$		0			0
$49$	−3.22818	−	6.21119i	−0.461169	−	0.887312i
$50$	−2.54364			−0.359725
$51$		0			0
$52$	−2.74657	+	4.75720i	−0.380880	+	0.659704i
$53$	2.74657	−	4.75720i	0.377270	−	0.653451i	−0.613394	−	0.789777i	$-0.710196\pi$
$53$	2.74657	−	4.75720i	0.377270	−	0.653451i	0.990664	+	0.136326i	$0.0435295\pi$
$54$		0			0
$55$	2.74657			0.370347
$56$	1.37328	−	2.26144i	0.183513	−	0.302197i
$57$		0			0
$58$	−2.27182	−	3.93491i	−0.298304	−	0.516678i
$59$	−4.76496	+	8.25314i	−0.620344	+	1.07447i	0.369077	+	0.929399i	$0.379674\pi$
$59$	−4.76496	+	8.25314i	−0.620344	+	1.07447i	−0.989422	+	0.145069i	$0.953660\pi$
$60$		0			0
$61$	0.829647	+	1.43699i	0.106225	+	0.183988i	0.914238	−	0.405177i	$-0.132790\pi$
$61$	0.829647	+	1.43699i	0.106225	+	0.183988i	−0.808013	+	0.589165i	$0.799457\pi$
$62$	−5.08727			−0.646084
$63$		0			0
$64$	1.00000			0.125000
$65$	7.54364	+	13.0660i	0.935673	+	1.62063i
$66$		0			0
$67$	−1.77182	+	3.06888i	−0.216462	+	0.374923i	−0.953724	−	0.300684i	$-0.902785\pi$
$67$	−1.77182	+	3.06888i	−0.216462	+	0.374923i	0.737262	+	0.675607i	$0.236118\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$		0			0
$70$	−3.49314	−	6.37208i	−0.417510	−	0.761610i
$71$	−2.54364			−0.301874			−0.150937	−	0.988543i	$-0.548229\pi$
$71$	−2.54364			−0.301874			−0.150937	+	0.988543i	$0.548229\pi$
$72$		0			0
$73$	4.29021	−	7.43085i	0.502131	−	0.869716i	−0.497866	−	0.867254i	$-0.665883\pi$
$73$	4.29021	−	7.43085i	0.502131	−	0.869716i	0.999997	−	0.00246191i	$-0.000783650\pi$
$74$	−2.01839	+	3.49595i	−0.234633	+	0.406396i
$75$		0			0
$76$	−8.03677			−0.921881
$77$	1.27182	+	2.32002i	0.144937	+	0.264390i
$78$		0			0
$79$	−6.11985	−	10.5999i	−0.688537	−	1.19258i	−0.972311	−	0.233690i	$-0.924920\pi$
$79$	−6.11985	−	10.5999i	−0.688537	−	1.19258i	0.283774	−	0.958891i	$-0.408413\pi$
$80$	1.37328	−	2.37860i	0.153538	−	0.265935i
$81$		0			0
$82$	−2.77182	−	4.80093i	−0.306096	−	0.530174i
$83$	14.5299			1.59486			0.797432	−	0.603408i	$-0.206191\pi$
$83$	14.5299			1.59486			0.797432	+	0.603408i	$0.206191\pi$
$84$		0			0
$85$	2.74657			0.297907
$86$	−2.01839	−	3.49595i	−0.217648	−	0.376978i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−3.25343	−	5.63511i	−0.344863	−	0.597320i	0.640466	−	0.767987i	$-0.278741\pi$
$89$	−3.25343	−	5.63511i	−0.344863	−	0.597320i	−0.985329	+	0.170666i	$0.945408\pi$
$90$		0			0
$91$	−7.54364	+	12.4224i	−0.790788	+	1.30222i
$92$	1.29021			0.134513
$93$		0			0
$94$	4.64510	−	8.04555i	0.479106	−	0.829836i
$95$	−11.0368	+	19.1163i	−1.13235	+	1.96129i
$96$		0			0
$97$	−0.0872743			−0.00886136			−0.00443068	−	0.999990i	$-0.501410\pi$
$97$	−0.0872743			−0.00886136			−0.00443068	+	0.999990i	$0.501410\pi$
$98$	3.76496	−	5.90128i	0.380318	−	0.596119i
$99$		0			0
$100$	−1.27182	−	2.20285i	−0.127182	−	0.220285i
$101$	6.51152	−	11.2783i	0.647921	−	1.12223i	−0.335698	−	0.941970i	$-0.608972\pi$
$101$	6.51152	−	11.2783i	0.647921	−	1.12223i	0.983619	−	0.180262i	$-0.0576946\pi$
$102$		0			0
$103$	9.03677	+	15.6522i	0.890420	+	1.54225i	0.839373	+	0.543556i	$0.182922\pi$
$103$	9.03677	+	15.6522i	0.890420	+	1.54225i	0.0510469	+	0.998696i	$0.483744\pi$
$104$	−5.49314			−0.538646
$105$		0			0
$106$	5.49314			0.533541
$107$	8.72132	+	15.1058i	0.843122	+	1.46033i	0.887243	+	0.461303i	$0.152618\pi$
$107$	8.72132	+	15.1058i	0.843122	+	1.46033i	−0.0441209	+	0.999026i	$0.514049\pi$
$108$		0			0
$109$	−0.829647	+	1.43699i	−0.0794658	+	0.137639i	−0.903020	−	0.429599i	$-0.858655\pi$
$109$	−0.829647	+	1.43699i	−0.0794658	+	0.137639i	0.823554	+	0.567238i	$0.191988\pi$
$110$	1.37328	+	2.37860i	0.130938	+	0.226790i
$111$		0			0
$112$	2.64510	+	0.0585812i	0.249939	+	0.00553540i
$113$	7.08727			0.666715			0.333357	−	0.942801i	$-0.391818\pi$
$113$	7.08727			0.666715			0.333357	+	0.942801i	$0.391818\pi$
$114$		0			0
$115$	1.77182	−	3.06888i	0.165223	−	0.286175i
$116$	2.27182	−	3.93491i	0.210933	−	0.365347i
$117$		0			0
$118$	−9.52991			−0.877299
$119$	1.27182	+	2.32002i	0.116587	+	0.212676i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.829647	+	1.43699i	−0.0751127	+	0.130099i
$123$		0			0
$124$	−2.54364	−	4.40571i	−0.228425	−	0.395644i
$125$	6.74657			0.603431
$126$		0			0
$127$	−6.78334			−0.601924			−0.300962	−	0.953636i	$-0.597308\pi$
$127$	−6.78334			−0.601924			−0.300962	+	0.953636i	$0.597308\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.54364	+	13.0660i	−0.661621	+	1.14596i
$131$	−6.94950	−	12.0369i	−0.607181	−	1.05167i	−0.991703	−	0.128552i	$-0.958967\pi$
$131$	−6.94950	−	12.0369i	−0.607181	−	1.05167i	0.384522	−	0.923116i	$-0.374366\pi$
$132$		0			0
$133$	−21.2581	−	0.470804i	−1.84331	−	0.0408238i
$134$	−3.54364			−0.306124
$135$		0			0
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	2.74657	−	4.75720i	0.234655	−	0.406435i	−0.724517	−	0.689257i	$-0.757937\pi$
$137$	2.74657	−	4.75720i	0.234655	−	0.406435i	0.959172	+	0.282822i	$0.0912706\pi$
$138$		0			0
$139$	13.6309			1.15616			0.578079	−	0.815981i	$-0.303802\pi$
$139$	13.6309			1.15616			0.578079	+	0.815981i	$0.303802\pi$
$140$	3.77182	−	6.21119i	0.318777	−	0.524941i
$141$		0			0
$142$	−1.27182	−	2.20285i	−0.106729	−	0.184859i
$143$	2.74657	−	4.75720i	0.229680	−	0.397817i
$144$		0			0
$145$	−6.23970	−	10.8075i	−0.518179	−	0.897513i
$146$	8.58041			0.710120
$147$		0			0
$148$	−4.03677			−0.331821
$149$	8.01839	+	13.8883i	0.656892	+	1.13777i	0.981416	+	0.191893i	$0.0614625\pi$
$149$	8.01839	+	13.8883i	0.656892	+	1.13777i	−0.324524	+	0.945877i	$0.605204\pi$
$150$		0			0
$151$	2.84803	−	4.93294i	0.231770	−	0.401437i	−0.726559	−	0.687104i	$-0.758882\pi$
$151$	2.84803	−	4.93294i	0.231770	−	0.401437i	0.958329	+	0.285667i	$0.0922151\pi$
$152$	−4.01839	−	6.96005i	−0.325934	−	0.564535i
$153$		0			0
$154$	−1.37328	+	2.26144i	−0.110662	+	0.182232i
$155$	−13.9725			−1.12230
$156$		0			0
$157$	−9.05516	+	15.6840i	−0.722680	+	1.25172i	0.237241	+	0.971451i	$0.423757\pi$
$157$	−9.05516	+	15.6840i	−0.722680	+	1.25172i	−0.959922	+	0.280269i	$0.909576\pi$
$158$	6.11985	−	10.5999i	0.486869	−	0.843282i
$159$		0			0
$160$	2.74657			0.217135
$161$	3.41273	+	0.0755817i	0.268960	+	0.00595668i
$162$		0			0
$163$	6.72132	+	11.6417i	0.526454	+	0.911846i	0.999525	+	0.0308210i	$0.00981219\pi$
$163$	6.72132	+	11.6417i	0.526454	+	0.911846i	−0.473071	+	0.881024i	$0.656854\pi$
$164$	2.77182	−	4.80093i	0.216443	−	0.374890i
$165$		0			0
$166$	7.26496	+	12.5833i	0.563870	+	0.976651i
$167$	−23.5667			−1.82364			−0.911822	−	0.410585i	$-0.865325\pi$
$167$	−23.5667			−1.82364			−0.911822	+	0.410585i	$0.865325\pi$
$168$		0			0
$169$	17.1745			1.32112
$170$	1.37328	+	2.37860i	0.105326	+	0.182430i
$171$		0			0
$172$	2.01839	−	3.49595i	0.153901	−	0.266564i
$173$	−5.45636	−	9.45070i	−0.414840	−	0.718523i	0.580572	−	0.814209i	$-0.302829\pi$
$173$	−5.45636	−	9.45070i	−0.414840	−	0.718523i	−0.995412	+	0.0956857i	$0.969496\pi$
$174$		0			0
$175$	−3.23504	−	5.90128i	−0.244546	−	0.446095i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	3.25343	−	5.63511i	0.243855	−	0.422369i
$179$	−6.47475	+	11.2146i	−0.483946	+	0.838218i	−0.999830	−	0.0184400i	$-0.994130\pi$
$179$	−6.47475	+	11.2146i	−0.483946	+	0.838218i	0.515884	+	0.856658i	$0.327463\pi$
$180$		0			0
$181$	7.59414			0.564468			0.282234	−	0.959346i	$-0.408925\pi$
$181$	7.59414			0.564468			0.282234	+	0.959346i	$0.408925\pi$
$182$	−14.5299	−	0.321794i	−1.07703	−	0.0238530i
$183$		0			0
$184$	0.645103	+	1.11735i	0.0475576	+	0.0823722i
$185$	−5.54364	+	9.60186i	−0.407576	+	0.705943i
$186$		0			0
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	9.29021			0.677558
$189$		0			0
$190$	−22.0735			−1.60138
$191$	9.49314	+	16.4426i	0.686899	+	1.18974i	0.972836	+	0.231496i	$0.0743620\pi$
$191$	9.49314	+	16.4426i	0.686899	+	1.18974i	−0.285937	+	0.958249i	$0.592305\pi$
$192$		0			0
$193$	10.7833	−	18.6773i	0.776202	−	1.34442i	−0.157915	−	0.987453i	$-0.550477\pi$
$193$	10.7833	−	18.6773i	0.776202	−	1.34442i	0.934116	−	0.356968i	$-0.116190\pi$
$194$	−0.0436371	−	0.0755817i	−0.00313296	−	0.00542645i
$195$		0			0
$196$	6.99314	+	0.309906i	0.499510	+	0.0221362i
$197$	3.12405			0.222579			0.111290	−	0.993788i	$-0.464502\pi$
$197$	3.12405			0.222579			0.111290	+	0.993788i	$0.464502\pi$
$198$		0			0
$199$	13.0368	−	22.5804i	0.924152	−	1.60068i	0.131234	−	0.991351i	$-0.458106\pi$
$199$	13.0368	−	22.5804i	0.924152	−	1.60068i	0.792919	−	0.609327i	$-0.208560\pi$
$200$	1.27182	−	2.20285i	0.0899312	−	0.155765i
$201$		0			0
$202$	13.0230			0.916298
$203$	6.23970	−	10.2751i	0.437941	−	0.721174i
$204$		0			0
$205$	−7.61299	−	13.1861i	−0.531714	−	0.920956i
$206$	−9.03677	+	15.6522i	−0.629622	+	1.09054i
$207$		0			0
$208$	−2.74657	−	4.75720i	−0.190440	−	0.329852i
$209$	8.03677			0.555915
$210$		0			0
$211$	15.6677			1.07861			0.539304	−	0.842111i	$-0.318687\pi$
$211$	15.6677			1.07861			0.539304	+	0.842111i	$0.318687\pi$
$212$	2.74657	+	4.75720i	0.188635	+	0.326726i
$213$		0			0
$214$	−8.72132	+	15.1058i	−0.596177	+	1.03261i
$215$	−5.54364	−	9.60186i	−0.378073	−	0.654841i
$216$		0			0
$217$	−6.47009	−	11.8026i	−0.439218	−	0.801210i
$218$	−1.65929			−0.112382
$219$		0			0
$220$	−1.37328	+	2.37860i	−0.0925868	+	0.160365i
$221$	2.74657	−	4.75720i	0.184754	−	0.320004i
$222$		0			0
$223$	2.40586			0.161108			0.0805542	−	0.996750i	$-0.474331\pi$
$223$	2.40586			0.161108			0.0805542	+	0.996750i	$0.474331\pi$
$224$	1.27182	+	2.32002i	0.0849770	+	0.155013i
$225$		0			0
$226$	3.54364	+	6.13776i	0.235719	+	0.408278i
$227$	1.22818	−	2.12727i	0.0815173	−	0.141192i	−0.822385	−	0.568932i	$-0.807357\pi$
$227$	1.22818	−	2.12727i	0.0815173	−	0.141192i	0.903902	+	0.427740i	$0.140690\pi$
$228$		0			0
$229$	5.29021	+	9.16290i	0.349587	+	0.605502i	0.986176	−	0.165701i	$-0.0529887\pi$
$229$	5.29021	+	9.16290i	0.349587	+	0.605502i	−0.636589	+	0.771203i	$0.719655\pi$
$230$	3.54364			0.233661
$231$		0			0
$232$	4.54364			0.298304
$233$	−3.53677	−	6.12587i	−0.231702	−	0.401319i	0.726607	−	0.687053i	$-0.241096\pi$
$233$	−3.53677	−	6.12587i	−0.231702	−	0.401319i	−0.958309	+	0.285734i	$0.907763\pi$
$234$		0			0
$235$	12.7581	−	22.0977i	0.832246	−	1.44149i
$236$	−4.76496	−	8.25314i	−0.310172	−	0.537234i
$237$		0			0
$238$	−1.37328	+	2.26144i	−0.0890168	+	0.146587i
$239$	−7.66769			−0.495981			−0.247991	−	0.968762i	$-0.579770\pi$
$239$	−7.66769			−0.495981			−0.247991	+	0.968762i	$0.579770\pi$
$240$		0			0
$241$	12.5299	−	21.7024i	0.807122	−	1.39798i	−0.107726	−	0.994181i	$-0.534357\pi$
$241$	12.5299	−	21.7024i	0.807122	−	1.39798i	0.914849	−	0.403797i	$-0.132310\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	−1.65929			−0.106225
$245$	10.3407	−	16.2083i	0.660643	−	1.03551i
$246$		0			0
$247$	22.0735	+	38.2325i	1.40451	+	2.43268i
$248$	2.54364	−	4.40571i	0.161521	−	0.279763i
$249$		0			0
$250$	3.37328	+	5.84270i	0.213345	+	0.369525i
$251$	25.0230			1.57944			0.789720	−	0.613467i	$-0.210226\pi$
$251$	25.0230			1.57944			0.789720	+	0.613467i	$0.210226\pi$
$252$		0			0
$253$	−1.29021			−0.0811145
$254$	−3.39167	−	5.87455i	−0.212812	−	0.368602i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.25343	−	9.09921i	−0.327700	−	0.567593i	0.654355	−	0.756187i	$-0.272940\pi$
$257$	−5.25343	−	9.09921i	−0.327700	−	0.567593i	−0.982055	+	0.188594i	$0.939607\pi$
$258$		0			0
$259$	−10.6777	−	0.236479i	−0.663479	−	0.0146941i
$260$	−15.0873			−0.935673
$261$		0			0
$262$	6.94950	−	12.0369i	0.429342	−	0.743641i
$263$	11.8201	−	20.4730i	0.728860	−	1.26242i	−0.228506	−	0.973543i	$-0.573384\pi$
$263$	11.8201	−	20.4730i	0.728860	−	1.26242i	0.957366	−	0.288879i	$-0.0932826\pi$
$264$		0			0
$265$	15.0873			0.926804
$266$	−10.2213	−	18.6454i	−0.626709	−	1.14323i
$267$		0			0
$268$	−1.77182	−	3.06888i	−0.108231	−	0.187462i
$269$	−7.57622	+	13.1224i	−0.461930	+	0.800086i	−0.999057	−	0.0434151i	$-0.986176\pi$
$269$	−7.57622	+	13.1224i	−0.461930	+	0.800086i	0.537127	+	0.843501i	$0.319510\pi$
$270$		0			0
$271$	−9.49314	−	16.4426i	−0.576667	−	0.998816i	−0.995858	−	0.0909186i	$-0.971020\pi$
$271$	−9.49314	−	16.4426i	−0.576667	−	0.998816i	0.419191	−	0.907898i	$-0.362314\pi$
$272$	−1.00000			−0.0606339
$273$		0			0
$274$	5.49314			0.331853
$275$	1.27182	+	2.20285i	0.0766935	+	0.132837i
$276$		0			0
$277$	−12.2397	+	21.1998i	−0.735413	+	1.27377i	0.219130	+	0.975696i	$0.429678\pi$
$277$	−12.2397	+	21.1998i	−0.735413	+	1.27377i	−0.954542	+	0.298076i	$0.903655\pi$
$278$	6.81546	+	11.8047i	0.408764	+	0.708000i
$279$		0			0
$280$	7.26496	+	0.160897i	0.434164	+	0.00961545i
$281$	12.0873			0.721066			0.360533	−	0.932746i	$-0.382595\pi$
$281$	12.0873			0.721066			0.360533	+	0.932746i	$0.382595\pi$
$282$		0			0
$283$	−2.34071	+	4.05422i	−0.139141	+	0.240998i	−0.927172	−	0.374637i	$-0.877767\pi$
$283$	−2.34071	+	4.05422i	−0.139141	+	0.240998i	0.788031	+	0.615636i	$0.211101\pi$
$284$	1.27182	−	2.20285i	0.0754685	−	0.130715i
$285$		0			0
$286$	5.49314			0.324816
$287$	7.61299	−	12.5366i	0.449381	−	0.740011i
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	6.23970	−	10.8075i	0.366408	−	0.634637i
$291$		0			0
$292$	4.29021	+	7.43085i	0.251065	+	0.434858i
$293$	11.6309			0.679485			0.339743	−	0.940518i	$-0.389660\pi$
$293$	11.6309			0.679485			0.339743	+	0.940518i	$0.389660\pi$
$294$		0			0
$295$	−26.1745			−1.52394
$296$	−2.01839	−	3.49595i	−0.117316	−	0.203198i
$297$		0			0
$298$	−8.01839	+	13.8883i	−0.464493	+	0.804525i
$299$	−3.54364	−	6.13776i	−0.204934	−	0.354956i
$300$		0			0
$301$	5.54364	−	9.12890i	0.319530	−	0.526181i
$302$	5.69607			0.327772
$303$		0			0
$304$	4.01839	−	6.96005i	0.230470	−	0.399186i
$305$	−2.27868	+	3.94679i	−0.130477	+	0.225993i
$306$		0			0
$307$	−14.0735			−0.803220			−0.401610	−	0.915811i	$-0.631549\pi$
$307$	−14.0735			−0.803220			−0.401610	+	0.915811i	$0.631549\pi$
$308$	−2.64510	−	0.0585812i	−0.150719	−	0.00333797i
$309$		0			0
$310$	−6.98627	−	12.1006i	−0.396794	−	0.687267i
$311$	6.13824	−	10.6317i	0.348068	−	0.602871i	−0.637839	−	0.770170i	$-0.720171\pi$
$311$	6.13824	−	10.6317i	0.348068	−	0.602871i	0.985906	+	0.167299i	$0.0535046\pi$
$312$		0			0
$313$	−11.7282	−	20.3138i	−0.662916	−	1.14820i	−0.979846	−	0.199755i	$-0.935985\pi$
$313$	−11.7282	−	20.3138i	−0.662916	−	1.14820i	0.316930	−	0.948449i	$-0.397348\pi$
$314$	−18.1103			−1.02202
$315$		0			0
$316$	12.2397			0.688537
$317$	−0.286010	−	0.495384i	−0.0160639	−	0.0278235i	0.857882	−	0.513847i	$-0.171780\pi$
$317$	−0.286010	−	0.495384i	−0.0160639	−	0.0278235i	−0.873946	+	0.486024i	$0.838447\pi$
$318$		0			0
$319$	−2.27182	+	3.93491i	−0.127197	+	0.220312i
$320$	1.37328	+	2.37860i	0.0767689	+	0.132968i
$321$		0			0
$322$	1.64091	+	2.99330i	0.0914442	+	0.166810i
$323$	8.03677			0.447178
$324$		0			0
$325$	−6.98627	+	12.1006i	−0.387529	+	0.671219i
$326$	−6.72132	+	11.6417i	−0.372259	+	0.644772i
$327$		0			0
$328$	5.54364			0.306096
$329$	24.5735	+	0.544231i	1.35478	+	0.0300044i
$330$		0			0
$331$	−3.85909	−	6.68414i	−0.212115	−	0.367394i	0.740261	−	0.672319i	$-0.234702\pi$
$331$	−3.85909	−	6.68414i	−0.212115	−	0.367394i	−0.952376	+	0.304925i	$0.901368\pi$
$332$	−7.26496	+	12.5833i	−0.398716	+	0.690597i
$333$		0			0
$334$	−11.7833	−	20.4093i	−0.644756	−	1.11675i
$335$	−9.73284			−0.531762
$336$		0			0
$337$	28.5530			1.55538			0.777689	−	0.628649i	$-0.216392\pi$
$337$	28.5530			1.55538			0.777689	+	0.628649i	$0.216392\pi$
$338$	8.58727	+	14.8736i	0.467086	+	0.809017i
$339$		0			0
$340$	−1.37328	+	2.37860i	−0.0744768	+	0.128998i
$341$	2.54364	+	4.40571i	0.137746	+	0.238583i
$342$		0			0
$343$	18.4794	+	1.22940i	0.997794	+	0.0663814i
$344$	4.03677			0.217648
$345$		0			0
$346$	5.45636	−	9.45070i	0.293336	−	0.508073i
$347$	−11.7213	+	20.3019i	−0.629233	+	1.08986i	0.358473	+	0.933540i	$0.383298\pi$
$347$	−11.7213	+	20.3019i	−0.629233	+	1.08986i	−0.987706	+	0.156324i	$0.950036\pi$
$348$		0			0
$349$	25.7328			1.37745			0.688724	−	0.725024i	$-0.258171\pi$
$349$	25.7328			1.37745			0.688724	+	0.725024i	$0.258171\pi$
$350$	3.49314	−	5.75227i	0.186716	−	0.307472i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−9.20293	+	15.9399i	−0.489823	+	0.848398i	−0.999931	−	0.0117122i	$-0.996272\pi$
$353$	−9.20293	+	15.9399i	−0.489823	+	0.848398i	0.510109	+	0.860110i	$0.329605\pi$
$354$		0			0
$355$	−3.49314	−	6.05029i	−0.185396	−	0.321116i
$356$	6.50686			0.344863
$357$		0			0
$358$	−12.9495			−0.684402
$359$	−15.9863	−	27.6890i	−0.843723	−	1.46137i	−0.886725	−	0.462297i	$-0.847026\pi$
$359$	−15.9863	−	27.6890i	−0.843723	−	1.46137i	0.0430022	−	0.999075i	$-0.486308\pi$
$360$		0			0
$361$	−22.7949	+	39.4819i	−1.19973	+	2.07799i
$362$	3.79707	+	6.57672i	0.199570	+	0.345665i
$363$		0			0
$364$	−6.98627	−	12.7442i	−0.366180	−	0.667976i
$365$	23.5667			1.23354
$366$		0			0
$367$	−18.2397	+	31.5921i	−0.952105	+	1.64909i	−0.211246	+	0.977433i	$0.567752\pi$
$367$	−18.2397	+	31.5921i	−0.952105	+	1.64909i	−0.740859	+	0.671661i	$0.765581\pi$
$368$	−0.645103	+	1.11735i	−0.0336283	+	0.0582459i
$369$		0			0
$370$	−11.0873			−0.576400
$371$	6.98627	+	12.7442i	0.362709	+	0.661644i
$372$		0			0
$373$	10.1566	+	17.5918i	0.525890	+	0.910868i	0.999545	+	0.0301580i	$0.00960104\pi$
$373$	10.1566	+	17.5918i	0.525890	+	0.910868i	−0.473655	+	0.880710i	$0.657066\pi$
$374$	0.500000	−	0.866025i	0.0258544	−	0.0447811i
$375$		0			0
$376$	4.64510	+	8.04555i	0.239553	+	0.414918i
$377$	−24.9588			−1.28544
$378$		0			0
$379$	9.44264			0.485036			0.242518	−	0.970147i	$-0.422027\pi$
$379$	9.44264			0.485036			0.242518	+	0.970147i	$0.422027\pi$
$380$	−11.0368	−	19.1163i	−0.566175	−	0.980643i
$381$		0			0
$382$	−9.49314	+	16.4426i	−0.485711	+	0.841276i
$383$	11.8522	+	20.5287i	0.605621	+	1.04897i	0.991953	+	0.126606i	$0.0404084\pi$
$383$	11.8522	+	20.5287i	0.605621	+	1.04897i	−0.386332	+	0.922360i	$0.626258\pi$
$384$		0			0
$385$	−3.77182	+	6.21119i	−0.192230	+	0.316551i
$386$	21.5667			1.09772
$387$		0			0
$388$	0.0436371	−	0.0755817i	0.00221534	−	0.00383708i
$389$	−0.626716	+	1.08550i	−0.0317758	+	0.0550372i	−0.881476	−	0.472229i	$-0.843450\pi$
$389$	−0.626716	+	1.08550i	−0.0317758	+	0.0550372i	0.849700	+	0.527266i	$0.176783\pi$
$390$		0			0
$391$	−1.29021			−0.0652485
$392$	3.22818	+	6.21119i	0.163048	+	0.313712i
$393$		0			0
$394$	1.56202	+	2.70550i	0.0786936	+	0.136301i
$395$	16.8086	−	29.1133i	0.845732	−	1.46485i
$396$		0			0
$397$	−14.3086	−	24.7832i	−0.718128	−	1.24383i	−0.961741	−	0.273961i	$-0.911666\pi$
$397$	−14.3086	−	24.7832i	−0.718128	−	1.24383i	0.243613	−	0.969872i	$-0.421667\pi$
$398$	26.0735			1.30695
$399$		0			0
$400$	2.54364			0.127182
$401$	0.202931	+	0.351487i	0.0101339	+	0.0175524i	0.871048	−	0.491198i	$-0.163441\pi$
$401$	0.202931	+	0.351487i	0.0101339	+	0.0175524i	−0.860914	+	0.508751i	$0.830108\pi$
$402$		0			0
$403$	−13.9725	+	24.2012i	−0.696022	+	1.20555i
$404$	6.51152	+	11.2783i	0.323960	+	0.561116i
$405$		0			0
$406$	12.0184	+	0.266172i	0.596463	+	0.0132099i
$407$	4.03677			0.200095
$408$		0			0
$409$	16.3775	−	28.3666i	0.809814	−	1.40264i	−0.103178	−	0.994663i	$-0.532901\pi$
$409$	16.3775	−	28.3666i	0.809814	−	1.40264i	0.912992	−	0.407977i	$-0.133765\pi$
$410$	7.61299	−	13.1861i	0.375979	−	0.651214i
$411$		0			0
$412$	−18.0735			−0.890420
$413$	−12.1203	−	22.1096i	−0.596402	−	1.08794i
$414$		0			0
$415$	19.9537	+	34.5608i	0.979488	+	1.69652i
$416$	2.74657	−	4.75720i	0.134662	−	0.233241i
$417$		0			0
$418$	4.01839	+	6.96005i	0.196546	+	0.340427i
$419$	15.9358			0.778513			0.389257	−	0.921129i	$-0.372732\pi$
$419$	15.9358			0.778513			0.389257	+	0.921129i	$0.372732\pi$
$420$		0			0
$421$	−27.1240			−1.32195			−0.660973	−	0.750410i	$-0.729856\pi$
$421$	−27.1240			−1.32195			−0.660973	+	0.750410i	$0.729856\pi$
$422$	7.83384	+	13.5686i	0.381345	+	0.660510i
$423$		0			0
$424$	−2.74657	+	4.75720i	−0.133385	+	0.231030i
$425$	1.27182	+	2.20285i	0.0616923	+	0.106854i
$426$		0			0
$427$	−4.38900	−	0.0972034i	−0.212399	−	0.00470400i
$428$	−17.4426			−0.843122
$429$		0			0
$430$	5.54364	−	9.60186i	0.267338	−	0.463043i
$431$	−20.3133	+	35.1836i	−0.978455	+	1.69473i	−0.310427	+	0.950597i	$0.600472\pi$
$431$	−20.3133	+	35.1836i	−0.978455	+	1.69473i	−0.668028	+	0.744137i	$0.732861\pi$
$432$		0			0
$433$	1.10100			0.0529107			0.0264554	−	0.999650i	$-0.491578\pi$
$433$	1.10100			0.0529107			0.0264554	+	0.999650i	$0.491578\pi$
$434$	6.98627	−	11.5045i	0.335352	−	0.552236i
$435$		0			0
$436$	−0.829647	−	1.43699i	−0.0397329	−	0.0688194i
$437$	5.18454	−	8.97989i	0.248010	−	0.429567i
$438$		0			0
$439$	−11.4284	−	19.7946i	−0.545450	−	0.944747i	−0.998578	−	0.0533018i	$-0.983025\pi$
$439$	−11.4284	−	19.7946i	−0.545450	−	0.944747i	0.453129	−	0.891445i	$-0.350308\pi$
$440$	−2.74657			−0.130938
$441$		0			0
$442$	5.49314			0.261282
$443$	−4.77868	−	8.27692i	−0.227042	−	0.393248i	0.729888	−	0.683567i	$-0.239572\pi$
$443$	−4.77868	−	8.27692i	−0.227042	−	0.393248i	−0.956930	+	0.290318i	$0.906239\pi$
$444$		0			0
$445$	8.93577	−	15.4772i	0.423596	−	0.733690i
$446$	1.20293	+	2.08354i	0.0569604	+	0.0986584i
$447$		0			0
$448$	−1.37328	+	2.26144i	−0.0648816	+	0.106843i
$449$	−0.681412			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$449$	−0.681412			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$450$		0			0
$451$	−2.77182	+	4.80093i	−0.130520	+	0.226067i
$452$	−3.54364	+	6.13776i	−0.166679	+	0.288696i
$453$		0			0
$454$	2.45636			0.115283
$455$	−39.9074	−	0.883830i	−1.87089	−	0.0414346i
$456$		0			0
$457$	−9.07355	−	15.7158i	−0.424443	−	0.735156i	0.571926	−	0.820306i	$-0.306197\pi$
$457$	−9.07355	−	15.7158i	−0.424443	−	0.735156i	−0.996368	+	0.0851493i	$0.972863\pi$
$458$	−5.29021	+	9.16290i	−0.247195	+	0.428154i
$459$		0			0
$460$	1.77182	+	3.06888i	0.0826115	+	0.143087i
$461$	41.7045			1.94237			0.971185	−	0.238326i	$-0.0765988\pi$
$461$	41.7045			1.94237			0.971185	+	0.238326i	$0.0765988\pi$
$462$		0			0
$463$	−28.5804			−1.32824			−0.664122	−	0.747624i	$-0.731195\pi$
$463$	−28.5804			−1.32824			−0.664122	+	0.747624i	$0.731195\pi$
$464$	2.27182	+	3.93491i	0.105467	+	0.182673i
$465$		0			0
$466$	3.53677	−	6.12587i	0.163838	−	0.283776i
$467$	2.69141	+	4.66166i	0.124544	+	0.215716i	0.921554	−	0.388249i	$-0.126920\pi$
$467$	2.69141	+	4.66166i	0.124544	+	0.215716i	−0.797011	+	0.603965i	$0.793587\pi$
$468$		0			0
$469$	−4.50686	−	8.22130i	−0.208108	−	0.379624i
$470$	25.5162			1.17697
$471$		0			0
$472$	4.76496	−	8.25314i	0.219325	−	0.379882i
$473$	−2.01839	+	3.49595i	−0.0928055	+	0.160744i
$474$		0			0
$475$	−20.4426			−0.937972
$476$	−2.64510	−	0.0585812i	−0.121238	−	0.00268506i
$477$		0			0
$478$	−3.83384	−	6.64041i	−0.175356	−	0.303725i
$479$	7.23970	−	12.5395i	0.330791	−	0.572946i	−0.651877	−	0.758325i	$-0.726018\pi$
$479$	7.23970	−	12.5395i	0.330791	−	0.572946i	0.982667	+	0.185379i	$0.0593513\pi$
$480$		0			0
$481$	11.0873	+	19.2037i	0.505536	+	0.875614i
$482$	25.0598			1.14144
$483$		0			0
$484$	1.00000			0.0454545
$485$	−0.119852	−	0.207590i	−0.00544222	−	0.00942619i
$486$		0			0
$487$	4.21666	−	7.30347i	0.191075	−	0.330952i	−0.754532	−	0.656264i	$-0.772136\pi$
$487$	4.21666	−	7.30347i	0.191075	−	0.330952i	0.945607	+	0.325312i	$0.105469\pi$
$488$	−0.829647	−	1.43699i	−0.0375564	−	0.0650495i
$489$		0			0
$490$	19.2071	+	0.851179i	0.867690	+	0.0384524i
$491$	38.6770			1.74547			0.872734	−	0.488195i	$-0.162345\pi$
$491$	38.6770			1.74547			0.872734	+	0.488195i	$0.162345\pi$
$492$		0			0
$493$	−2.27182	+	3.93491i	−0.102318	+	0.177219i
$494$	−22.0735	+	38.2325i	−0.993136	+	1.72016i
$495$		0			0
$496$	5.08727			0.228425
$497$	3.49314	−	5.75227i	0.156689	−	0.258025i
$498$		0			0
$499$	−19.0230	−	32.9489i	−0.851589	−	1.47499i	−0.879774	−	0.475392i	$-0.842306\pi$
$499$	−19.0230	−	32.9489i	−0.851589	−	1.47499i	0.0281856	−	0.999603i	$-0.491027\pi$
$500$	−3.37328	+	5.84270i	−0.150858	+	0.261293i
$501$		0			0
$502$	12.5115	+	21.6706i	0.558417	+	0.967206i
$503$	−21.5667			−0.961611			−0.480805	−	0.876827i	$-0.659656\pi$
$503$	−21.5667			−0.961611			−0.480805	+	0.876827i	$0.659656\pi$
$504$		0			0
$505$	35.7687			1.59169
$506$	−0.645103	−	1.11735i	−0.0286783	−	0.0496723i
$507$		0			0
$508$	3.39167	−	5.87455i	0.150481	−	0.260641i
$509$	−13.3270	−	23.0830i	−0.590708	−	1.02314i	−0.994137	−	0.108125i	$-0.965515\pi$
$509$	−13.3270	−	23.0830i	−0.590708	−	1.02314i	0.403429	−	0.915011i	$-0.367818\pi$
$510$		0			0
$511$	10.9127	+	19.9067i	0.482751	+	0.880620i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.25343	−	9.09921i	0.231719	−	0.401349i
$515$	−24.8201	+	42.9897i	−1.09370	+	1.89435i
$516$		0			0
$517$	−9.29021			−0.408583
$518$	−5.13404	−	9.36538i	−0.225577	−	0.411491i
$519$		0			0
$520$	−7.54364	−	13.0660i	−0.330810	−	0.572980i
$521$	−11.9863	+	20.7608i	−0.525128	+	0.909549i	0.474444	+	0.880286i	$0.342649\pi$
$521$	−11.9863	+	20.7608i	−0.525128	+	0.909549i	−0.999572	+	0.0292627i	$0.990684\pi$
$522$		0			0
$523$	−10.3407	−	17.9106i	−0.452168	−	0.783177i	0.546353	−	0.837555i	$-0.316016\pi$
$523$	−10.3407	−	17.9106i	−0.452168	−	0.783177i	−0.998520	+	0.0543780i	$0.982682\pi$
$524$	13.8990			0.607181
$525$		0			0
$526$	23.6402			1.03076
$527$	2.54364	+	4.40571i	0.110803	+	0.191916i
$528$		0			0
$529$	10.6677	−	18.4770i	0.463812	−	0.803347i
$530$	7.54364	+	13.0660i	0.327675	+	0.567549i
$531$		0			0
$532$	11.0368	−	18.1746i	0.478505	−	0.787971i
$533$	−30.4520			−1.31902
$534$		0			0
$535$	−23.9537	+	41.4890i	−1.03561	+	1.79373i
$536$	1.77182	−	3.06888i	0.0765309	−	0.132555i
$537$		0			0
$538$	−15.1524			−0.653268
$539$	−6.99314	−	0.309906i	−0.301216	−	0.0133486i
$540$		0			0
$541$	−17.9537	−	31.0967i	−0.771890	−	1.33695i	−0.936526	−	0.350598i	$-0.885978\pi$
$541$	−17.9537	−	31.0967i	−0.771890	−	1.33695i	0.164637	−	0.986354i	$-0.447355\pi$
$542$	9.49314	−	16.4426i	0.407765	−	0.706270i
$543$		0			0
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	−4.55736			−0.195216
$546$		0			0
$547$	−5.12405			−0.219088			−0.109544	−	0.993982i	$-0.534939\pi$
$547$	−5.12405			−0.219088			−0.109544	+	0.993982i	$0.534939\pi$
$548$	2.74657	+	4.75720i	0.117328	+	0.203217i
$549$		0			0
$550$	−1.27182	+	2.20285i	−0.0542305	+	0.0939300i
$551$	−18.2581	−	31.6239i	−0.777821	−	1.34723i
$552$		0			0
$553$	32.3753	+	0.717016i	1.37674	+	0.0304906i
$554$	−24.4794			−1.04003
$555$		0			0
$556$	−6.81546	+	11.8047i	−0.289040	+	0.500631i
$557$	−6.43798	+	11.1509i	−0.272786	+	0.472479i	−0.969574	−	0.244798i	$-0.921278\pi$
$557$	−6.43798	+	11.1509i	−0.272786	+	0.472479i	0.696788	+	0.717277i	$0.254612\pi$
$558$		0			0
$559$	−22.1745			−0.937883
$560$	3.49314	+	6.37208i	0.147612	+	0.269270i
$561$		0			0
$562$	6.04364	+	10.4679i	0.254935	+	0.441561i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	9.73284	+	16.8578i	0.409464	+	0.709212i
$566$	−4.68141			−0.196774
$567$		0			0
$568$	2.54364			0.106729
$569$	10.6777	+	18.4943i	0.447632	+	0.775321i	0.998231	−	0.0594486i	$-0.0189342\pi$
$569$	10.6777	+	18.4943i	0.447632	+	0.775321i	−0.550600	+	0.834769i	$0.685601\pi$
$570$		0			0
$571$	−3.72818	+	6.45740i	−0.156020	+	0.270234i	−0.933430	−	0.358760i	$-0.883200\pi$
$571$	−3.72818	+	6.45740i	−0.156020	+	0.270234i	0.777410	+	0.628994i	$0.216533\pi$
$572$	2.74657	+	4.75720i	0.114840	+	0.198908i
$573$		0			0
$574$	14.6635	+	0.324753i	0.612042	+	0.0135549i
$575$	3.28181			0.136861
$576$		0			0
$577$	−2.82232	+	4.88840i	−0.117495	+	0.203507i	−0.918774	−	0.394783i	$-0.870820\pi$
$577$	−2.82232	+	4.88840i	−0.117495	+	0.203507i	0.801280	+	0.598290i	$0.204153\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$		0			0
$580$	12.4794			0.518179
$581$	−19.9537	+	32.8585i	−0.827819	+	1.36320i
$582$		0			0
$583$	−2.74657	−	4.75720i	−0.113751	−	0.197023i
$584$	−4.29021	+	7.43085i	−0.177530	+	0.307491i
$585$		0			0
$586$	5.81546	+	10.0727i	0.240234	+	0.416098i
$587$	34.4059			1.42008			0.710041	−	0.704160i	$-0.248676\pi$
$587$	34.4059			1.42008			0.710041	+	0.704160i	$0.248676\pi$
$588$		0			0
$589$	−40.8853			−1.68465
$590$	−13.0873	−	22.6678i	−0.538795	−	0.933220i
$591$		0			0
$592$	2.01839	−	3.49595i	0.0829552	−	0.143683i
$593$	−9.35909	−	16.2104i	−0.384332	−	0.665682i	0.607344	−	0.794439i	$-0.292235\pi$
$593$	−9.35909	−	16.2104i	−0.384332	−	0.665682i	−0.991676	+	0.128756i	$0.958901\pi$
$594$		0			0
$595$	−3.77182	+	6.21119i	−0.154629	+	0.254634i
$596$	−16.0368			−0.656892
$597$		0			0
$598$	3.54364	−	6.13776i	0.144910	−	0.250992i
$599$	5.20713	−	9.01901i	0.212757	−	0.368507i	−0.739819	−	0.672806i	$-0.765089\pi$
$599$	5.20713	−	9.01901i	0.212757	−	0.368507i	0.952577	+	0.304299i	$0.0984223\pi$
$600$		0			0
$601$	25.0873			1.02333			0.511666	−	0.859185i	$-0.329029\pi$
$601$	25.0873			1.02333			0.511666	+	0.859185i	$0.329029\pi$
$602$	10.6777	+	0.236479i	0.435190	+	0.00963816i
$603$		0			0
$604$	2.84803	+	4.93294i	0.115885	+	0.200718i
$605$	1.37328	−	2.37860i	0.0558319	−	0.0967038i
$606$		0			0
$607$	−15.9537	−	27.6326i	−0.647541	−	1.12157i	−0.983708	−	0.179771i	$-0.942464\pi$
$607$	−15.9537	−	27.6326i	−0.647541	−	1.12157i	0.336168	−	0.941802i	$-0.390869\pi$
$608$	8.03677			0.325934
$609$		0			0
$610$	−4.55736			−0.184522
$611$	−25.5162	−	44.1953i	−1.03227	−	1.78795i
$612$		0			0
$613$	−1.71399	+	2.96872i	−0.0692274	+	0.119905i	−0.898561	−	0.438848i	$-0.855387\pi$
$613$	−1.71399	+	2.96872i	−0.0692274	+	0.119905i	0.829334	+	0.558753i	$0.188720\pi$
$614$	−7.03677	−	12.1880i	−0.283981	−	0.491870i
$615$		0			0
$616$	−1.27182	−	2.32002i	−0.0512430	−	0.0934761i
$617$	−12.7550			−0.513495			−0.256748	−	0.966478i	$-0.582651\pi$
$617$	−12.7550			−0.513495			−0.256748	+	0.966478i	$0.582651\pi$
$618$		0			0
$619$	10.7949	−	18.6973i	0.433882	−	0.751506i	−0.563321	−	0.826238i	$-0.690477\pi$
$619$	10.7949	−	18.6973i	0.433882	−	0.751506i	0.997204	+	0.0747317i	$0.0238100\pi$
$620$	6.98627	−	12.1006i	0.280575	−	0.485971i
$621$		0			0
$622$	12.2765			0.492242
$623$	17.2113	+	0.381180i	0.689557	+	0.0152716i
$624$		0			0
$625$	15.6240	+	27.0616i	0.624962	+	1.08247i
$626$	11.7282	−	20.3138i	0.468752	−	0.811903i
$627$		0			0
$628$	−9.05516	−	15.6840i	−0.361340	−	0.625860i
$629$	4.03677			0.160957
$630$		0			0
$631$	4.23131			0.168446			0.0842230	−	0.996447i	$-0.473159\pi$
$631$	4.23131			0.168446			0.0842230	+	0.996447i	$0.473159\pi$
$632$	6.11985	+	10.5999i	0.243435	+	0.421641i
$633$		0			0
$634$	0.286010	−	0.495384i	0.0113589	−	0.0196742i
$635$	−9.31546	−	16.1348i	−0.369673	−	0.640292i
$636$		0			0
$637$	−17.7328	−	34.1189i	−0.702601	−	1.35184i
$638$	−4.54364			−0.179884
$639$		0			0
$640$	−1.37328	+	2.37860i	−0.0542838	+	0.0940223i
$641$	2.03677	−	3.52780i	0.0804477	−	0.139340i	−0.822995	−	0.568049i	$-0.807698\pi$
$641$	2.03677	−	3.52780i	0.0804477	−	0.139340i	0.903442	+	0.428710i	$0.141032\pi$
$642$		0			0
$643$	−19.2618			−0.759612			−0.379806	−	0.925066i	$-0.624009\pi$
$643$	−19.2618			−0.759612			−0.379806	+	0.925066i	$0.624009\pi$
$644$	−1.77182	+	2.91772i	−0.0698194	+	0.114974i
$645$		0			0
$646$	4.01839	+	6.96005i	0.158101	+	0.273840i
$647$	−9.44683	+	16.3624i	−0.371393	+	0.643272i	−0.989780	−	0.142602i	$-0.954453\pi$
$647$	−9.44683	+	16.3624i	−0.371393	+	0.643272i	0.618387	+	0.785874i	$0.287786\pi$
$648$		0			0
$649$	4.76496	+	8.25314i	0.187041	+	0.323964i
$650$	−13.9725			−0.548048
$651$		0			0
$652$	−13.4426			−0.526454
$653$	−4.46056	−	7.72591i	−0.174555	−	0.302338i	0.765452	−	0.643493i	$-0.222515\pi$
$653$	−4.46056	−	7.72591i	−0.174555	−	0.302338i	−0.940007	+	0.341155i	$0.889182\pi$
$654$		0			0
$655$	19.0873	−	33.0601i	0.745802	−	1.29177i
$656$	2.77182	+	4.80093i	0.108221	+	0.187445i
$657$		0			0
$658$	11.8155	+	21.5534i	0.460614	+	0.840240i
$659$	−45.4426			−1.77019			−0.885097	−	0.465407i	$-0.845908\pi$
$659$	−45.4426			−1.77019			−0.885097	+	0.465407i	$0.845908\pi$
$660$		0			0
$661$	14.5115	−	25.1347i	0.564433	−	0.977626i	−0.432669	−	0.901553i	$-0.642428\pi$
$661$	14.5115	−	25.1347i	0.564433	−	0.977626i	0.997102	−	0.0760737i	$-0.0242384\pi$
$662$	3.85909	−	6.68414i	0.149988	−	0.259787i
$663$		0			0
$664$	−14.5299			−0.563870
$665$	−28.0735	−	51.2110i	−1.08865	−	1.98588i
$666$		0			0
$667$	2.93111	+	5.07684i	0.113493	+	0.196576i
$668$	11.7833	−	20.4093i	0.455911	−	0.789661i
$669$		0			0
$670$	−4.86642	−	8.42889i	−0.188006	−	0.325636i
$671$	1.65929			0.0640563
$672$		0			0
$673$	−16.2481			−0.626318			−0.313159	−	0.949701i	$-0.601387\pi$
$673$	−16.2481			−0.626318			−0.313159	+	0.949701i	$0.601387\pi$
$674$	14.2765	+	24.7276i	0.549909	+	0.952471i
$675$		0			0
$676$	−8.58727	+	14.8736i	−0.330280	+	0.572061i
$677$	−1.94484	−	3.36856i	−0.0747463	−	0.129464i	0.826230	−	0.563333i	$-0.190481\pi$
$677$	−1.94484	−	3.36856i	−0.0747463	−	0.129464i	−0.900976	+	0.433869i	$0.857148\pi$
$678$		0			0
$679$	0.119852	−	0.197365i	0.00459951	−	0.00757418i
$680$	−2.74657			−0.105326
$681$		0			0
$682$	−2.54364	+	4.40571i	−0.0974009	+	0.168703i
$683$	2.90273	−	5.02768i	0.111070	−	0.192379i	−0.805132	−	0.593096i	$-0.797906\pi$
$683$	2.90273	−	5.02768i	0.111070	−	0.192379i	0.916202	+	0.400717i	$0.131239\pi$
$684$		0			0
$685$	15.0873			0.576455
$686$	8.17501	+	16.6183i	0.312123	+	0.634491i
$687$		0			0
$688$	2.01839	+	3.49595i	0.0769503	+	0.133282i
$689$	15.0873	−	26.1319i	0.574779	−	0.995547i
$690$		0			0
$691$	3.17768	+	5.50390i	0.120885	+	0.209378i	0.920117	−	0.391644i	$-0.128094\pi$
$691$	3.17768	+	5.50390i	0.120885	+	0.209378i	−0.799232	+	0.601022i	$0.794760\pi$
$692$	10.9127			0.414840
$693$		0			0
$694$	−23.4426			−0.889870
$695$	18.7191	+	32.4225i	0.710056	+	1.22985i
$696$		0			0
$697$	−2.77182	+	4.80093i	−0.104990	+	0.181848i
$698$	12.8664	+	22.2853i	0.487001	+	0.843511i
$699$		0			0
$700$	6.72818	+	0.149009i	0.254301	+	0.00563202i
$701$	−5.86223			−0.221413			−0.110707	−	0.993853i	$-0.535311\pi$
$701$	−5.86223			−0.221413			−0.110707	+	0.993853i	$0.535311\pi$
$702$		0			0
$703$	−16.2213	+	28.0961i	−0.611799	+	1.05967i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	−18.4059			−0.692714
$707$	16.5630	+	30.2137i	0.622914	+	1.13630i
$708$		0			0
$709$	6.72818	+	11.6536i	0.252682	+	0.437658i	0.964263	−	0.264946i	$-0.0853540\pi$
$709$	6.72818	+	11.6536i	0.252682	+	0.437658i	−0.711581	+	0.702604i	$0.752021\pi$
$710$	3.49314	−	6.05029i	0.131095	−	0.227063i
$711$		0			0
$712$	3.25343	+	5.63511i	0.121928	+	0.211185i
$713$	6.56363			0.245810
$714$		0			0
$715$	15.0873			0.564232
$716$	−6.47475	−	11.2146i	−0.241973	−	0.419109i
$717$		0			0
$718$	15.9863	−	27.6890i	0.596602	−	1.03335i
$719$	−12.1382	−	21.0240i	−0.452680	−	0.784065i	0.545872	−	0.837869i	$-0.316199\pi$
$719$	−12.1382	−	21.0240i	−0.452680	−	0.784065i	−0.998552	+	0.0538042i	$0.982865\pi$
$720$		0			0
$721$	−47.8064	−	1.05877i	−1.78040	−	0.0394306i
$722$	−45.5897			−1.69667
$723$		0			0
$724$	−3.79707	+	6.57672i	−0.141117	+	0.244422i
$725$	5.77868	−	10.0090i	0.214615	−	0.371724i
$726$		0			0
$727$	−22.1471			−0.821390			−0.410695	−	0.911773i	$-0.634714\pi$
$727$	−22.1471			−0.821390			−0.410695	+	0.911773i	$0.634714\pi$
$728$	7.54364	−	12.4224i	0.279586	−	0.460404i
$729$		0			0
$730$	11.7833	+	20.4093i	0.436121	+	0.755384i
$731$	−2.01839	+	3.49595i	−0.0746527	+	0.129302i
$732$		0			0
$733$	2.66349	+	4.61330i	0.0983782	+	0.170396i	0.911014	−	0.412377i	$-0.135301\pi$
$733$	2.66349	+	4.61330i	0.0983782	+	0.170396i	−0.812635	+	0.582773i	$0.801968\pi$
$734$	−36.4794			−1.34648
$735$		0			0
$736$	−1.29021			−0.0475576
$737$	1.77182	+	3.06888i	0.0652658	+	0.113044i
$738$		0			0
$739$	12.6309	−	21.8774i	0.464636	−	0.804772i	−0.534549	−	0.845137i	$-0.679519\pi$
$739$	12.6309	−	21.8774i	0.464636	−	0.804772i	0.999185	+	0.0403648i	$0.0128520\pi$
$740$	−5.54364	−	9.60186i	−0.203788	−	0.352971i
$741$		0			0
$742$	−7.54364	+	12.4224i	−0.276936	+	0.456040i
$743$	25.4196			0.932554			0.466277	−	0.884639i	$-0.345595\pi$
$743$	25.4196			0.932554			0.466277	+	0.884639i	$0.345595\pi$
$744$		0			0
$745$	−22.0230	+	38.1450i	−0.806862	+	1.39753i
$746$	−10.1566	+	17.5918i	−0.371860	+	0.644081i
$747$		0			0
$748$	1.00000			0.0365636
$749$	−46.1376	−	1.02181i	−1.68583	−	0.0373361i
$750$		0			0
$751$	20.2765	+	35.1199i	0.739899	+	1.28154i	0.952540	+	0.304413i	$0.0984602\pi$
$751$	20.2765	+	35.1199i	0.739899	+	1.28154i	−0.212641	+	0.977130i	$0.568206\pi$
$752$	−4.64510	+	8.04555i	−0.169389	+	0.293391i
$753$		0			0
$754$	−12.4794	−	21.6150i	−0.454473	−	0.787171i
$755$	15.6446			0.569367
$756$		0			0
$757$	13.3554			0.485409			0.242704	−	0.970100i	$-0.421965\pi$
$757$	13.3554			0.485409			0.242704	+	0.970100i	$0.421965\pi$
$758$	4.72132	+	8.17756i	0.171486	+	0.297022i
$759$		0			0
$760$	11.0368	−	19.1163i	0.400346	−	0.693419i
$761$	9.22818	+	15.9837i	0.334521	+	0.579408i	0.983393	−	0.181490i	$-0.0580920\pi$
$761$	9.22818	+	15.9837i	0.334521	+	0.579408i	−0.648871	+	0.760898i	$0.724759\pi$
$762$		0			0
$763$	−2.11032	−	3.84959i	−0.0763987	−	0.139365i
$764$	−18.9863			−0.686899
$765$		0			0
$766$	−11.8522	+	20.5287i	−0.428238	+	0.741731i
$767$	−26.1745	+	45.3356i	−0.945108	+	1.63698i
$768$		0			0
$769$	49.9158			1.80001			0.900005	−	0.435881i	$-0.143563\pi$
$769$	49.9158			1.80001			0.900005	+	0.435881i	$0.143563\pi$
$770$	−7.26496	−	0.160897i	−0.261811	−	0.00579833i
$771$		0			0
$772$	10.7833	+	18.6773i	0.388101	+	0.672211i
$773$	−21.0694	+	36.4932i	−0.757812	+	1.31257i	0.186152	+	0.982521i	$0.440398\pi$
$773$	−21.0694	+	36.4932i	−0.757812	+	1.31257i	−0.943964	+	0.330048i	$0.892935\pi$
$774$		0			0
$775$	−6.47009	−	11.2065i	−0.232412	−	0.402550i
$776$	0.0872743			0.00313296
$777$		0			0
$778$	−1.25343			−0.0449377
$779$	−22.2765	−	38.5840i	−0.798138	−	1.38241i
$780$		0			0
$781$	−1.27182	+	2.20285i	−0.0455092	+	0.0788243i
$782$	−0.645103	−	1.11735i	−0.0230688	−	0.0399564i
$783$		0			0
$784$	−3.76496	+	5.90128i	−0.134463	+	0.210760i
$785$	−49.7412			−1.77534
$786$		0			0
$787$	17.1792	−	29.7553i	0.612373	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$787$	17.1792	−	29.7553i	0.612373	−	1.06066i	0.990839	−	0.135046i	$-0.0431181\pi$
$788$	−1.56202	+	2.70550i	−0.0556448	+	0.0963796i
$789$		0			0
$790$	33.6172			1.19605
$791$	−9.73284	+	16.0274i	−0.346060	+	0.569869i
$792$		0			0
$793$	4.55736	+	7.89359i	0.161837	+	0.280309i
$794$	14.3086	−	24.7832i	0.507793	−	0.879523i
$795$		0			0
$796$	13.0368	+	22.5804i	0.462076	+	0.800339i
$797$	18.1387			0.642506			0.321253	−	0.946993i	$-0.395896\pi$
$797$	18.1387			0.642506			0.321253	+	0.946993i	$0.395896\pi$
$798$		0			0
$799$	−9.29021			−0.328664
$800$	1.27182	+	2.20285i	0.0449656	+	0.0778827i
$801$		0			0
$802$	−0.202931	+	0.351487i	−0.00716575	+	0.0124114i
$803$	−4.29021	−	7.43085i	−0.151398	−	0.262229i
$804$		0			0
$805$	4.50686	+	8.22130i	0.158846	+	0.289763i
$806$	−27.9451			−0.984324
$807$		0			0
$808$	−6.51152	+	11.2783i	−0.229075	+	0.396769i
$809$	−8.77182	+	15.1932i	−0.308401	+	0.534166i	−0.978013	−	0.208545i	$-0.933127\pi$
$809$	−8.77182	+	15.1932i	−0.308401	+	0.534166i	0.669612	+	0.742711i	$0.266460\pi$
$810$		0			0
$811$	−43.0873			−1.51300			−0.756499	−	0.653994i	$-0.773092\pi$
$811$	−43.0873			−1.51300			−0.756499	+	0.653994i	$0.773092\pi$
$812$	5.77868	+	10.5413i	0.202792	+	0.369928i
$813$		0			0
$814$	2.01839	+	3.49595i	0.0707444	+	0.122533i
$815$	−18.4606	+	31.9746i	−0.646645	+	1.12002i
$816$		0			0
$817$	−16.2213	−	28.0961i	−0.567512	−	0.982960i
$818$	32.7550			1.14525
$819$		0			0
$820$	15.2260			0.531714
$821$	1.05050	+	1.81952i	0.0366627	+	0.0635017i	0.883775	−	0.467913i	$-0.154994\pi$
$821$	1.05050	+	1.81952i	0.0366627	+	0.0635017i	−0.847112	+	0.531415i	$0.821661\pi$
$822$		0			0
$823$	−9.87062	+	17.0964i	−0.344068	+	0.595943i	−0.985184	−	0.171501i	$-0.945138\pi$
$823$	−9.87062	+	17.0964i	−0.344068	+	0.595943i	0.641116	+	0.767444i	$0.278472\pi$
$824$	−9.03677	−	15.6522i	−0.314811	−	0.545269i
$825$		0			0
$826$	13.0873	−	21.5513i	0.455365	−	0.749865i
$827$	−23.7182			−0.824762			−0.412381	−	0.911011i	$-0.635303\pi$
$827$	−23.7182			−0.824762			−0.412381	+	0.911011i	$0.635303\pi$
$828$		0			0
$829$	−19.9816	+	34.6092i	−0.693990	+	1.20203i	0.276530	+	0.961005i	$0.410816\pi$
$829$	−19.9816	+	34.6092i	−0.693990	+	1.20203i	−0.970520	+	0.241021i	$0.922518\pi$
$830$	−19.9537	+	34.5608i	−0.692603	+	1.19962i
$831$		0			0
$832$	5.49314			0.190440
$833$	−6.99314	−	0.309906i	−0.242298	−	0.0107376i
$834$		0			0
$835$	−32.3638	−	56.0557i	−1.11999	−	1.93989i
$836$	−4.01839	+	6.96005i	−0.138979	+	0.240718i
$837$		0			0
$838$	7.96789	+	13.8008i	0.275246	+	0.476740i
$839$	−29.0682			−1.00355			−0.501773	−	0.864999i	$-0.667319\pi$
$839$	−29.0682			−1.00355			−0.501773	+	0.864999i	$0.667319\pi$
$840$		0			0
$841$	−8.35536			−0.288116
$842$	−13.5620	−	23.4901i	−0.467378	−	0.809523i
$843$		0			0
$844$	−7.83384	+	13.5686i	−0.269652	+	0.467051i
$845$	23.5855	+	40.8513i	0.811367	+	1.40533i
$846$		0			0
$847$	2.64510	+	0.0585812i	0.0908868	+	0.00201287i
$848$	−5.49314			−0.188635
$849$		0			0
$850$	−1.27182	+	2.20285i	−0.0436230	+	0.0755573i
$851$	2.60413	−	4.51049i	0.0892685	−	0.154618i
$852$		0			0
$853$	20.2397			0.692994			0.346497	−	0.938051i	$-0.387371\pi$
$853$	20.2397			0.692994			0.346497	+	0.938051i	$0.387371\pi$
$854$	−2.11032	−	3.84959i	−0.0722137	−	0.131730i
$855$		0			0
$856$	−8.72132	−	15.1058i	−0.298089	−	0.516304i
$857$	−6.08041	+	10.5316i	−0.207703	+	0.359752i	−0.950991	−	0.309220i	$-0.899932\pi$
$857$	−6.08041	+	10.5316i	−0.207703	+	0.359752i	0.743288	+	0.668972i	$0.233265\pi$
$858$		0			0
$859$	7.26496	+	12.5833i	0.247877	+	0.429336i	0.962937	−	0.269728i	$-0.0869338\pi$
$859$	7.26496	+	12.5833i	0.247877	+	0.429336i	−0.715060	+	0.699064i	$0.753600\pi$
$860$	11.0873			0.378073
$861$		0			0
$862$	−40.6265			−1.38374
$863$	−6.79287	−	11.7656i	−0.231232	−	0.400506i	0.726939	−	0.686702i	$-0.240942\pi$
$863$	−6.79287	−	11.7656i	−0.231232	−	0.400506i	−0.958171	+	0.286196i	$0.907609\pi$
$864$		0			0
$865$	14.9863	−	25.9570i	0.509549	−	0.882564i
$866$	0.550501	+	0.953495i	0.0187068	+	0.0324011i
$867$		0			0
$868$	13.4564	+	0.298018i	0.456739	+	0.0101154i
$869$	−12.2397			−0.415204
$870$		0			0
$871$	−9.73284	+	16.8578i	−0.329785	+	0.571204i
$872$	0.829647	−	1.43699i	0.0280954	−	0.0486626i
$873$		0			0
$874$	10.3691			0.350740
$875$	−9.26496	+	15.2569i	−0.313213	+	0.515778i
$876$		0			0
$877$	1.03258	+	1.78848i	0.0348677	+	0.0603926i	0.882933	−	0.469500i	$-0.155566\pi$
$877$	1.03258	+	1.78848i	0.0348677	+	0.0603926i	−0.848065	+	0.529892i	$0.822232\pi$
$878$	11.4284	−	19.7946i	0.385691	−	0.668037i
$879$		0			0
$880$	−1.37328	−	2.37860i	−0.0462934	−	0.0801825i
$881$	3.08727			0.104013			0.0520065	−	0.998647i	$-0.483438\pi$
$881$	3.08727			0.104013			0.0520065	+	0.998647i	$0.483438\pi$
$882$		0			0
$883$	21.8927			0.736749			0.368375	−	0.929677i	$-0.379914\pi$
$883$	21.8927			0.736749			0.368375	+	0.929677i	$0.379914\pi$
$884$	2.74657	+	4.75720i	0.0923771	+	0.160002i
$885$		0			0
$886$	4.77868	−	8.27692i	0.160543	−	0.278069i
$887$	18.8706	+	32.6849i	0.633613	+	1.09745i	0.986807	+	0.161900i	$0.0517623\pi$
$887$	18.8706	+	32.6849i	0.633613	+	1.09745i	−0.353194	+	0.935550i	$0.614904\pi$
$888$		0			0
$889$	9.31546	−	15.3401i	0.312430	−	0.514490i
$890$	17.8715			0.599056
$891$		0			0
$892$	−1.20293	+	2.08354i	−0.0402771	+	0.0697620i
$893$	37.3316	−	64.6603i	1.24926	−	2.16377i
$894$		0			0
$895$	−35.5667			−1.18886
$896$	−2.64510	−	0.0585812i	−0.0883667	−	0.00195706i
$897$		0			0
$898$	−0.340706	−	0.590120i	−0.0113695	−	0.0196926i
$899$	11.5574	−	20.0179i	0.385460	−	0.667636i
$900$		0			0
$901$	−2.74657	−	4.75720i	−0.0915015	−	0.158485i
$902$	−5.54364			−0.184583
$903$		0			0
$904$	−7.08727			−0.235719
$905$	10.4289	+	18.0634i	0.346669	+	0.600448i
$906$		0			0
$907$	−15.7949	+	27.3575i	−0.524460	+	0.908391i	0.475135	+	0.879913i	$0.342399\pi$
$907$	−15.7949	+	27.3575i	−0.524460	+	0.908391i	−0.999594	+	0.0284780i	$0.990934\pi$
$908$	1.22818	+	2.12727i	0.0407586	+	0.0705960i
$909$		0			0
$910$	−19.1883	−	35.0027i	−0.636085	−	1.16033i
$911$	27.7422			0.919139			0.459569	−	0.888142i	$-0.348004\pi$
$911$	27.7422			0.919139			0.459569	+	0.888142i	$0.348004\pi$
$912$		0			0
$913$	7.26496	−	12.5833i	0.240435	−	0.416445i
$914$	9.07355	−	15.7158i	0.300126	−	0.519834i
$915$		0			0
$916$	−10.5804			−0.349587
$917$	36.7643	+	0.814220i	1.21406	+	0.0268879i
$918$		0			0
$919$	−9.46522	−	16.3942i	−0.312229	−	0.540796i	0.666616	−	0.745401i	$-0.267742\pi$
$919$	−9.46522	−	16.3942i	−0.312229	−	0.540796i	−0.978845	+	0.204605i	$0.934409\pi$
$920$	−1.77182	+	3.06888i	−0.0584151	+	0.101178i
$921$		0			0
$922$	20.8522	+	36.1171i	0.686732	+	1.18945i
$923$	−13.9725			−0.459912
$924$		0			0
$925$	−10.2681			−0.337613
$926$	−14.2902	−	24.7514i	−0.469605	−	0.813380i
$927$		0			0
$928$	−2.27182	+	3.93491i	−0.0745761	+	0.129170i
$929$	6.88434	+	11.9240i	0.225868	+	0.391215i	0.956579	−	0.291472i	$-0.0941449\pi$
$929$	6.88434	+	11.9240i	0.225868	+	0.391215i	−0.730712	+	0.682686i	$0.760812\pi$
$930$		0			0
$931$	30.2581	−	47.4273i	0.991669	−	1.55437i
$932$	7.07355			0.231702
$933$		0			0
$934$	−2.69141	+	4.66166i	−0.0880656	+	0.152534i
$935$	1.37328	−	2.37860i	0.0449112	−	0.0777885i
$936$		0			0
$937$	−17.2618			−0.563919			−0.281960	−	0.959426i	$-0.590984\pi$
$937$	−17.2618			−0.563919			−0.281960	+	0.959426i	$0.590984\pi$
$938$	4.86642	−	8.01371i	0.158894	−	0.261657i
$939$		0			0
$940$	12.7581	+	22.0977i	0.416123	+	0.720746i
$941$	−18.8155	+	32.5893i	−0.613366	+	1.06238i	0.377302	+	0.926090i	$0.376852\pi$
$941$	−18.8155	+	32.5893i	−0.613366	+	1.06238i	−0.990669	+	0.136292i	$0.956482\pi$
$942$		0			0
$943$	3.57622	+	6.19419i	0.116458	+	0.201710i
$944$	9.52991			0.310172
$945$		0			0
$946$	−4.03677			−0.131247
$947$	−3.86596	−	6.69603i	−0.125627	−	0.217592i	0.796351	−	0.604835i	$-0.206761\pi$
$947$	−3.86596	−	6.69603i	−0.125627	−	0.217592i	−0.921978	+	0.387243i	$0.873427\pi$
$948$		0			0
$949$	23.5667	−	40.8187i	0.765007	−	1.32503i
$950$	−10.2213	−	17.7038i	−0.331623	−	0.574388i
$951$		0			0
$952$	−1.27182	−	2.32002i	−0.0412199	−	0.0751922i
$953$	20.6770			0.669794			0.334897	−	0.942255i	$-0.391298\pi$
$953$	20.6770			0.669794			0.334897	+	0.942255i	$0.391298\pi$
$954$		0			0
$955$	−26.0735	+	45.1607i	−0.843720	+	1.46137i
$956$	3.83384	−	6.64041i	0.123995	−	0.214766i
$957$		0			0
$958$	14.4794			0.467808
$959$	6.98627	+	12.7442i	0.225599	+	0.411531i
$960$		0			0
$961$	2.55982	+	4.43374i	0.0825748	+	0.143024i
$962$	−11.0873	+	19.2037i	−0.357468	+	0.619153i
$963$		0			0
$964$	12.5299	+	21.7024i	0.403561	+	0.698989i
$965$	59.2344			1.90682
$966$		0			0
$967$	15.7235			0.505634			0.252817	−	0.967514i	$-0.418643\pi$
$967$	15.7235			0.505634			0.252817	+	0.967514i	$0.418643\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	0.119852	−	0.207590i	0.00384823	−	0.00666533i
$971$	4.12405	+	7.14306i	0.132347	+	0.229232i	0.924581	−	0.380986i	$-0.124415\pi$
$971$	4.12405	+	7.14306i	0.132347	+	0.229232i	−0.792234	+	0.610218i	$0.791082\pi$
$972$		0			0
$973$	−18.7191	+	30.8254i	−0.600107	+	0.988218i
$974$	8.43332			0.270221
$975$		0			0
$976$	0.829647	−	1.43699i	0.0265564	−	0.0459970i
$977$	−17.6677	+	30.6013i	−0.565239	+	0.979023i	0.431788	+	0.901975i	$0.357883\pi$
$977$	−17.6677	+	30.6013i	−0.565239	+	0.979023i	−0.997027	+	0.0770481i	$0.975450\pi$
$978$		0			0
$979$	−6.50686			−0.207960
$980$	8.86642	+	17.0594i	0.283227	+	0.544944i
$981$		0			0
$982$	19.3385	+	33.4953i	0.617116	+	1.06888i
$983$	−4.57156	+	7.91817i	−0.145810	+	0.252550i	−0.929675	−	0.368381i	$-0.879912\pi$
$983$	−4.57156	+	7.91817i	−0.145810	+	0.252550i	0.783865	+	0.620931i	$0.213245\pi$
$984$		0			0
$985$	4.29021	+	7.43085i	0.136697	+	0.236767i
$986$	−4.54364			−0.144699
$987$		0			0
$988$	−44.1471			−1.40451
$989$	2.60413	+	4.51049i	0.0828066	+	0.143425i
$990$		0			0
$991$	−17.7328	+	30.7142i	−0.563302	+	0.975668i	0.433903	+	0.900960i	$0.357136\pi$
$991$	−17.7328	+	30.7142i	−0.563302	+	0.975668i	−0.997205	+	0.0747086i	$0.976197\pi$
$992$	2.54364	+	4.40571i	0.0807606	+	0.139881i
$993$		0			0
$994$	6.72818	+	0.149009i	0.213405	+	0.00472629i
$995$	71.6128			2.27028
$996$		0			0
$997$	−22.7466	+	39.3982i	−0.720391	+	1.24775i	0.240452	+	0.970661i	$0.422704\pi$
$997$	−22.7466	+	39.3982i	−0.720391	+	1.24775i	−0.960843	+	0.277093i	$0.910629\pi$
$998$	19.0230	−	32.9489i	0.602164	−	1.04298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.w.991.3		6
3.2	odd	2		462.2.i.f.67.1	✓	6
7.2	even	3	inner	1386.2.k.w.793.3		6
7.3	odd	6		9702.2.a.du.1.3		3
7.4	even	3		9702.2.a.dt.1.1		3
21.2	odd	6		462.2.i.f.331.1	yes	6
21.11	odd	6		3234.2.a.bi.1.3		3
21.17	even	6		3234.2.a.bg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.1	✓	6	3.2	odd	2
462.2.i.f.331.1	yes	6	21.2	odd	6
1386.2.k.w.793.3		6	7.2	even	3	inner
1386.2.k.w.991.3		6	1.1	even	1	trivial
3234.2.a.bg.1.1		3	21.17	even	6
3234.2.a.bi.1.3		3	21.11	odd	6
9702.2.a.dt.1.1		3	7.4	even	3
9702.2.a.du.1.3		3	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +(-1.37328 + 2.37860i) q^{10} +(0.500000 - 0.866025i) q^{11} +5.49314 q^{13} +(-2.64510 - 0.0585812i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(4.01839 + 6.96005i) q^{19} -2.74657 q^{20} +1.00000 q^{22} +(-0.645103 - 1.11735i) q^{23} +(-1.27182 + 2.20285i) q^{25} +(2.74657 + 4.75720i) q^{26} +(-1.27182 - 2.32002i) q^{28} -4.54364 q^{29} +(-2.54364 + 4.40571i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(-7.26496 - 0.160897i) q^{35} +(2.01839 + 3.49595i) q^{37} +(-4.01839 + 6.96005i) q^{38} +(-1.37328 - 2.37860i) q^{40} -5.54364 q^{41} -4.03677 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.645103 - 1.11735i) q^{46} +(-4.64510 - 8.04555i) q^{47} +(-3.22818 - 6.21119i) q^{49} -2.54364 q^{50} +(-2.74657 + 4.75720i) q^{52} +(2.74657 - 4.75720i) q^{53} +2.74657 q^{55} +(1.37328 - 2.26144i) q^{56} +(-2.27182 - 3.93491i) q^{58} +(-4.76496 + 8.25314i) q^{59} +(0.829647 + 1.43699i) q^{61} -5.08727 q^{62} +1.00000 q^{64} +(7.54364 + 13.0660i) q^{65} +(-1.77182 + 3.06888i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.49314 - 6.37208i) q^{70} -2.54364 q^{71} +(4.29021 - 7.43085i) q^{73} +(-2.01839 + 3.49595i) q^{74} -8.03677 q^{76} +(1.27182 + 2.32002i) q^{77} +(-6.11985 - 10.5999i) q^{79} +(1.37328 - 2.37860i) q^{80} +(-2.77182 - 4.80093i) q^{82} +14.5299 q^{83} +2.74657 q^{85} +(-2.01839 - 3.49595i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-3.25343 - 5.63511i) q^{89} +(-7.54364 + 12.4224i) q^{91} +1.29021 q^{92} +(4.64510 - 8.04555i) q^{94} +(-11.0368 + 19.1163i) q^{95} -0.0872743 q^{97} +(3.76496 - 5.90128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} + 3 q^{11} - 3 q^{14} - 3 q^{16} + 3 q^{17} + 3 q^{19} + 6 q^{22} + 9 q^{23} - 3 q^{25} - 3 q^{28} - 18 q^{29} - 6 q^{31} + 3 q^{32} + 6 q^{34} - 6 q^{35} - 9 q^{37} - 3 q^{38} - 24 q^{41} + 18 q^{43} + 3 q^{44} - 9 q^{46} - 15 q^{47} - 24 q^{49} - 6 q^{50} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} + 6 q^{64} + 36 q^{65} - 6 q^{67} + 3 q^{68} + 12 q^{70} - 6 q^{71} + 9 q^{74} - 6 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} + 12 q^{83} + 9 q^{86} - 3 q^{88} - 36 q^{89} - 36 q^{91} - 18 q^{92} + 15 q^{94} - 24 q^{95} + 18 q^{97} - 15 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 + 3 * q^11 - 3 * q^14 - 3 * q^16 + 3 * q^17 + 3 * q^19 + 6 * q^22 + 9 * q^23 - 3 * q^25 - 3 * q^28 - 18 * q^29 - 6 * q^31 + 3 * q^32 + 6 * q^34 - 6 * q^35 - 9 * q^37 - 3 * q^38 - 24 * q^41 + 18 * q^43 + 3 * q^44 - 9 * q^46 - 15 * q^47 - 24 * q^49 - 6 * q^50 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 + 6 * q^64 + 36 * q^65 - 6 * q^67 + 3 * q^68 + 12 * q^70 - 6 * q^71 + 9 * q^74 - 6 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 + 12 * q^83 + 9 * q^86 - 3 * q^88 - 36 * q^89 - 36 * q^91 - 18 * q^92 + 15 * q^94 - 24 * q^95 + 18 * q^97 - 15 * q^98

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