LMFDB - Embedded newform 1242.2.e.b.415.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1242,2,Mod(415,1242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1242, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1242.415");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1242 = 2 \cdot 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1242.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.91741993104$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 414)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.5
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	1242.415
Dual form			1242.2.e.b.829.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.69714 - 2.93953i) q^{5} +(-1.74607 - 3.02428i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.69714 - 2.93953i) q^{5} +(-1.74607 - 3.02428i) q^{7} +1.00000 q^{8} -3.39428 q^{10} +(2.39735 + 4.15233i) q^{11} +(2.56373 - 4.44052i) q^{13} +(-1.74607 + 3.02428i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.35504 q^{17} +3.15998 q^{19} +(1.69714 + 2.93953i) q^{20} +(2.39735 - 4.15233i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-3.26058 - 5.64748i) q^{25} -5.12747 q^{26} +3.49214 q^{28} +(-1.22952 - 2.12959i) q^{29} +(-0.830547 + 1.43855i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.17752 - 5.50362i) q^{34} -11.8533 q^{35} -9.88582 q^{37} +(-1.57999 - 2.73662i) q^{38} +(1.69714 - 2.93953i) q^{40} +(2.74914 - 4.76165i) q^{41} +(0.387635 + 0.671404i) q^{43} -4.79470 q^{44} -1.00000 q^{46} +(5.55862 + 9.62781i) q^{47} +(-2.59753 + 4.49906i) q^{49} +(-3.26058 + 5.64748i) q^{50} +(2.56373 + 4.44052i) q^{52} -6.41715 q^{53} +16.2746 q^{55} +(-1.74607 - 3.02428i) q^{56} +(-1.22952 + 2.12959i) q^{58} +(3.08029 - 5.33522i) q^{59} +(-0.632287 - 1.09515i) q^{61} +1.66109 q^{62} +1.00000 q^{64} +(-8.70204 - 15.0724i) q^{65} +(-1.74607 + 3.02428i) q^{67} +(-3.17752 + 5.50362i) q^{68} +(5.92666 + 10.2653i) q^{70} -16.4462 q^{71} +5.89600 q^{73} +(4.94291 + 8.56138i) q^{74} +(-1.57999 + 2.73662i) q^{76} +(8.37189 - 14.5005i) q^{77} +(-3.43033 - 5.94150i) q^{79} -3.39428 q^{80} -5.49828 q^{82} +(3.29807 + 5.71243i) q^{83} +(10.7854 - 18.6809i) q^{85} +(0.387635 - 0.671404i) q^{86} +(2.39735 + 4.15233i) q^{88} -14.4886 q^{89} -17.9059 q^{91} +(0.500000 + 0.866025i) q^{92} +(5.55862 - 9.62781i) q^{94} +(5.36292 - 9.28886i) q^{95} +(0.770482 + 1.33451i) q^{97} +5.19506 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1242\mathbb{Z}\right)^\times$.

$n$	$461$	$649$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	1.69714	−	2.93953i	0.758985	−	1.31460i	−0.184384	−	0.982854i	$-0.559029\pi$
$5$	1.69714	−	2.93953i	0.758985	−	1.31460i	0.943369	−	0.331746i	$-0.107638\pi$
$6$		0			0
$7$	−1.74607	−	3.02428i	−0.659953	−	1.14307i	−0.980627	−	0.195883i	$-0.937243\pi$
$7$	−1.74607	−	3.02428i	−0.659953	−	1.14307i	0.320674	−	0.947189i	$-0.396090\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.39428			−1.07337
$11$	2.39735	+	4.15233i	0.722828	+	1.25198i	0.959862	+	0.280474i	$0.0904917\pi$
$11$	2.39735	+	4.15233i	0.722828	+	1.25198i	−0.237033	+	0.971502i	$0.576175\pi$
$12$		0			0
$13$	2.56373	−	4.44052i	0.711052	−	1.23158i	−0.253410	−	0.967359i	$-0.581552\pi$
$13$	2.56373	−	4.44052i	0.711052	−	1.23158i	0.964463	−	0.264219i	$-0.0851143\pi$
$14$	−1.74607	+	3.02428i	−0.466657	+	0.808274i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.35504			1.54132			0.770662	−	0.637245i	$-0.219926\pi$
$17$	6.35504			1.54132			0.770662	+	0.637245i	$0.219926\pi$
$18$		0			0
$19$	3.15998			0.724948			0.362474	−	0.931994i	$-0.381932\pi$
$19$	3.15998			0.724948			0.362474	+	0.931994i	$0.381932\pi$
$20$	1.69714	+	2.93953i	0.379492	+	0.657300i
$21$		0			0
$22$	2.39735	−	4.15233i	0.511117	−	0.885280i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	−3.26058	−	5.64748i	−0.652115	−	1.12950i
$26$	−5.12747			−1.00558
$27$		0			0
$28$	3.49214			0.659953
$29$	−1.22952	−	2.12959i	−0.228316	−	0.395455i	0.728993	−	0.684521i	$-0.239989\pi$
$29$	−1.22952	−	2.12959i	−0.228316	−	0.395455i	−0.957309	+	0.289066i	$0.906655\pi$
$30$		0			0
$31$	−0.830547	+	1.43855i	−0.149171	+	0.258371i	−0.930921	−	0.365220i	$-0.880994\pi$
$31$	−0.830547	+	1.43855i	−0.149171	+	0.258371i	0.781750	+	0.623591i	$0.214327\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.17752	−	5.50362i	−0.544940	−	0.943864i
$35$	−11.8533			−2.00358
$36$		0			0
$37$	−9.88582			−1.62522			−0.812610	−	0.582808i	$-0.801954\pi$
$37$	−9.88582			−1.62522			−0.812610	+	0.582808i	$0.801954\pi$
$38$	−1.57999	−	2.73662i	−0.256308	−	0.443938i
$39$		0			0
$40$	1.69714	−	2.93953i	0.268342	−	0.464781i
$41$	2.74914	−	4.76165i	0.429344	−	0.743645i	−0.567471	−	0.823393i	$-0.692078\pi$
$41$	2.74914	−	4.76165i	0.429344	−	0.743645i	0.996815	+	0.0797482i	$0.0254116\pi$
$42$		0			0
$43$	0.387635	+	0.671404i	0.0591138	+	0.102388i	0.894068	−	0.447932i	$-0.147839\pi$
$43$	0.387635	+	0.671404i	0.0591138	+	0.102388i	−0.834954	+	0.550320i	$0.814506\pi$
$44$	−4.79470			−0.722828
$45$		0			0
$46$	−1.00000			−0.147442
$47$	5.55862	+	9.62781i	0.810808	+	1.40436i	0.912300	+	0.409524i	$0.134305\pi$
$47$	5.55862	+	9.62781i	0.810808	+	1.40436i	−0.101492	+	0.994836i	$0.532362\pi$
$48$		0			0
$49$	−2.59753	+	4.49906i	−0.371076	+	0.642722i
$50$	−3.26058	+	5.64748i	−0.461115	+	0.798675i
$51$		0			0
$52$	2.56373	+	4.44052i	0.355526	+	0.615789i
$53$	−6.41715			−0.881464			−0.440732	−	0.897639i	$-0.645281\pi$
$53$	−6.41715			−0.881464			−0.440732	+	0.897639i	$0.645281\pi$
$54$		0			0
$55$	16.2746			2.19446
$56$	−1.74607	−	3.02428i	−0.233329	−	0.404137i
$57$		0			0
$58$	−1.22952	+	2.12959i	−0.161444	+	0.279629i
$59$	3.08029	−	5.33522i	0.401019	−	0.694586i	−0.592830	−	0.805328i	$-0.701989\pi$
$59$	3.08029	−	5.33522i	0.401019	−	0.694586i	0.993849	+	0.110742i	$0.0353227\pi$
$60$		0			0
$61$	−0.632287	−	1.09515i	−0.0809561	−	0.140220i	0.822705	−	0.568469i	$-0.192464\pi$
$61$	−0.632287	−	1.09515i	−0.0809561	−	0.140220i	−0.903661	+	0.428249i	$0.859131\pi$
$62$	1.66109			0.210959
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.70204	−	15.0724i	−1.07936	−	1.86950i
$66$		0			0
$67$	−1.74607	+	3.02428i	−0.213317	+	0.369475i	−0.952751	−	0.303754i	$-0.901760\pi$
$67$	−1.74607	+	3.02428i	−0.213317	+	0.369475i	0.739434	+	0.673229i	$0.235093\pi$
$68$	−3.17752	+	5.50362i	−0.385331	+	0.667412i
$69$		0			0
$70$	5.92666	+	10.2653i	0.708371	+	1.22694i
$71$	−16.4462			−1.95180			−0.975900	−	0.218218i	$-0.929976\pi$
$71$	−16.4462			−1.95180			−0.975900	+	0.218218i	$0.929976\pi$
$72$		0			0
$73$	5.89600			0.690075			0.345037	−	0.938589i	$-0.387866\pi$
$73$	5.89600			0.690075			0.345037	+	0.938589i	$0.387866\pi$
$74$	4.94291	+	8.56138i	0.574602	+	0.995240i
$75$		0			0
$76$	−1.57999	+	2.73662i	−0.181237	+	0.313912i
$77$	8.37189	−	14.5005i	0.954066	−	1.65249i
$78$		0			0
$79$	−3.43033	−	5.94150i	−0.385942	−	0.668471i	0.605957	−	0.795497i	$-0.292790\pi$
$79$	−3.43033	−	5.94150i	−0.385942	−	0.668471i	−0.991899	+	0.127026i	$0.959457\pi$
$80$	−3.39428			−0.379492
$81$		0			0
$82$	−5.49828			−0.607183
$83$	3.29807	+	5.71243i	0.362010	+	0.627020i	0.988292	−	0.152577i	$-0.0487572\pi$
$83$	3.29807	+	5.71243i	0.362010	+	0.627020i	−0.626281	+	0.779597i	$0.715424\pi$
$84$		0			0
$85$	10.7854	−	18.6809i	1.16984	−	2.02622i
$86$	0.387635	−	0.671404i	0.0417998	−	0.0723993i
$87$		0			0
$88$	2.39735	+	4.15233i	0.255558	+	0.442640i
$89$	−14.4886			−1.53579			−0.767897	−	0.640574i	$-0.778697\pi$
$89$	−14.4886			−1.53579			−0.767897	+	0.640574i	$0.778697\pi$
$90$		0			0
$91$	−17.9059			−1.87704
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$	5.55862	−	9.62781i	0.573328	−	0.993032i
$95$	5.36292	−	9.28886i	0.550224	−	0.953017i
$96$		0			0
$97$	0.770482	+	1.33451i	0.0782306	+	0.135499i	0.902487	−	0.430718i	$-0.141740\pi$
$97$	0.770482	+	1.33451i	0.0782306	+	0.135499i	−0.824256	+	0.566217i	$0.808406\pi$
$98$	5.19506			0.524781
$99$		0			0
$100$	6.52115			0.652115
$101$	4.84505	+	8.39188i	0.482101	+	0.835023i	0.999789	−	0.0205465i	$-0.00654062\pi$
$101$	4.84505	+	8.39188i	0.482101	+	0.835023i	−0.517688	+	0.855569i	$0.673207\pi$
$102$		0			0
$103$	5.56148	−	9.63277i	0.547989	−	0.949145i	−0.450423	−	0.892815i	$-0.648727\pi$
$103$	5.56148	−	9.63277i	0.547989	−	0.949145i	0.998412	−	0.0563301i	$-0.0179399\pi$
$104$	2.56373	−	4.44052i	0.251395	−	0.435429i
$105$		0			0
$106$	3.20858	+	5.55742i	0.311644	+	0.539784i
$107$	14.8829			1.43879			0.719393	−	0.694603i	$-0.244420\pi$
$107$	14.8829			1.43879			0.719393	+	0.694603i	$0.244420\pi$
$108$		0			0
$109$	−11.9775			−1.14724			−0.573618	−	0.819123i	$-0.694460\pi$
$109$	−11.9775			−1.14724			−0.573618	+	0.819123i	$0.694460\pi$
$110$	−8.13728	−	14.0942i	−0.775860	−	1.34383i
$111$		0			0
$112$	−1.74607	+	3.02428i	−0.164988	+	0.285768i
$113$	−1.92838	+	3.34005i	−0.181407	+	0.314205i	−0.942360	−	0.334601i	$-0.891398\pi$
$113$	−1.92838	+	3.34005i	−0.181407	+	0.314205i	0.760953	+	0.648807i	$0.224732\pi$
$114$		0			0
$115$	−1.69714	−	2.93953i	−0.158259	−	0.274113i
$116$	2.45904			0.228316
$117$		0			0
$118$	−6.16058			−0.567127
$119$	−11.0964	−	19.2194i	−1.01720	−	1.76184i
$120$		0			0
$121$	−5.99458	+	10.3829i	−0.544962	+	0.943902i
$122$	−0.632287	+	1.09515i	−0.0572446	+	0.0991506i
$123$		0			0
$124$	−0.830547	−	1.43855i	−0.0745854	−	0.129186i
$125$	−5.16322			−0.461812
$126$		0			0
$127$	−7.31645			−0.649230			−0.324615	−	0.945846i	$-0.605235\pi$
$127$	−7.31645			−0.649230			−0.324615	+	0.945846i	$0.605235\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.70204	+	15.0724i	−0.763219	+	1.32193i
$131$	−3.57550	+	6.19295i	−0.312393	+	0.541080i	−0.978880	−	0.204436i	$-0.934464\pi$
$131$	−3.57550	+	6.19295i	−0.312393	+	0.541080i	0.666487	+	0.745517i	$0.267797\pi$
$132$		0			0
$133$	−5.51754	−	9.55667i	−0.478432	−	0.828668i
$134$	3.49214			0.301675
$135$		0			0
$136$	6.35504			0.544940
$137$	3.38252	+	5.85869i	0.288988	+	0.500542i	0.973568	−	0.228395i	$-0.0733479\pi$
$137$	3.38252	+	5.85869i	0.288988	+	0.500542i	−0.684581	+	0.728937i	$0.740015\pi$
$138$		0			0
$139$	−1.43310	+	2.48220i	−0.121554	+	0.210537i	−0.920381	−	0.391024i	$-0.872121\pi$
$139$	−1.43310	+	2.48220i	−0.121554	+	0.210537i	0.798827	+	0.601561i	$0.205454\pi$
$140$	5.92666	−	10.2653i	0.500894	−	0.867574i
$141$		0			0
$142$	8.22308	+	14.2428i	0.690066	+	1.19523i
$143$	24.5847			2.05587
$144$		0			0
$145$	−8.34666			−0.693153
$146$	−2.94800	−	5.10609i	−0.243978	−	0.422583i
$147$		0			0
$148$	4.94291	−	8.56138i	0.406305	−	0.703741i
$149$	0.500601	−	0.867066i	0.0410108	−	0.0710328i	−0.844791	−	0.535096i	$-0.820276\pi$
$149$	0.500601	−	0.867066i	0.0410108	−	0.0710328i	0.885802	+	0.464063i	$0.153609\pi$
$150$		0			0
$151$	1.31459	+	2.27694i	0.106980	+	0.185295i	0.914546	−	0.404483i	$-0.132549\pi$
$151$	1.31459	+	2.27694i	0.106980	+	0.185295i	−0.807565	+	0.589778i	$0.799215\pi$
$152$	3.15998			0.256308
$153$		0			0
$154$	−16.7438			−1.34925
$155$	2.81911	+	4.88285i	0.226437	+	0.392200i
$156$		0			0
$157$	9.45290	−	16.3729i	0.754423	−	1.30670i	−0.191237	−	0.981544i	$-0.561250\pi$
$157$	9.45290	−	16.3729i	0.754423	−	1.30670i	0.945660	−	0.325156i	$-0.105417\pi$
$158$	−3.43033	+	5.94150i	−0.272902	+	0.472681i
$159$		0			0
$160$	1.69714	+	2.93953i	0.134171	+	0.232391i
$161$	−3.49214			−0.275219
$162$		0			0
$163$	15.6754			1.22779			0.613896	−	0.789387i	$-0.289602\pi$
$163$	15.6754			1.22779			0.613896	+	0.789387i	$0.289602\pi$
$164$	2.74914	+	4.76165i	0.214672	+	0.371822i
$165$		0			0
$166$	3.29807	−	5.71243i	0.255980	−	0.443370i
$167$	−6.30918	+	10.9278i	−0.488219	+	0.845620i	−0.999908	−	0.0135508i	$-0.995686\pi$
$167$	−6.30918	+	10.9278i	−0.488219	+	0.845620i	0.511689	+	0.859170i	$0.329020\pi$
$168$		0			0
$169$	−6.64547	−	11.5103i	−0.511190	−	0.885407i
$170$	−21.5708			−1.65440
$171$		0			0
$172$	−0.775270			−0.0591138
$173$	−0.301440	−	0.522109i	−0.0229180	−	0.0396952i	0.854339	−	0.519716i	$-0.173962\pi$
$173$	−0.301440	−	0.522109i	−0.0229180	−	0.0396952i	−0.877257	+	0.480021i	$0.840629\pi$
$174$		0			0
$175$	−11.3864	+	19.7218i	−0.860731	+	1.49083i
$176$	2.39735	−	4.15233i	0.180707	−	0.312994i
$177$		0			0
$178$	7.24432	+	12.5475i	0.542985	+	0.940477i
$179$	−10.1600			−0.759392			−0.379696	−	0.925111i	$-0.623971\pi$
$179$	−10.1600			−0.759392			−0.379696	+	0.925111i	$0.623971\pi$
$180$		0			0
$181$	−7.42165			−0.551647			−0.275824	−	0.961208i	$-0.588951\pi$
$181$	−7.42165			−0.551647			−0.275824	+	0.961208i	$0.588951\pi$
$182$	8.95293	+	15.5069i	0.663635	+	1.14945i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−16.7776	+	29.0597i	−1.23352	+	2.13651i
$186$		0			0
$187$	15.2353	+	26.3882i	1.11411	+	1.92970i
$188$	−11.1172			−0.810808
$189$		0			0
$190$	−10.7258			−0.778135
$191$	2.15681	+	3.73570i	0.156061	+	0.270306i	0.933445	−	0.358721i	$-0.116787\pi$
$191$	2.15681	+	3.73570i	0.156061	+	0.270306i	−0.777384	+	0.629027i	$0.783454\pi$
$192$		0			0
$193$	−3.86487	+	6.69416i	−0.278200	+	0.481856i	−0.970937	−	0.239334i	$-0.923071\pi$
$193$	−3.86487	+	6.69416i	−0.278200	+	0.481856i	0.692738	+	0.721190i	$0.256404\pi$
$194$	0.770482	−	1.33451i	0.0553174	−	0.0958125i
$195$		0			0
$196$	−2.59753	−	4.49906i	−0.185538	−	0.321361i
$197$	19.4668			1.38695			0.693476	−	0.720480i	$-0.256078\pi$
$197$	19.4668			1.38695			0.693476	+	0.720480i	$0.256078\pi$
$198$		0			0
$199$	0.661496			0.0468922			0.0234461	−	0.999725i	$-0.492536\pi$
$199$	0.661496			0.0468922			0.0234461	+	0.999725i	$0.492536\pi$
$200$	−3.26058	−	5.64748i	−0.230558	−	0.399337i
$201$		0			0
$202$	4.84505	−	8.39188i	0.340897	−	0.590450i
$203$	−4.29365	+	7.43682i	−0.301355	+	0.521963i
$204$		0			0
$205$	−9.33136	−	16.1624i	−0.651730	−	1.12883i
$206$	−11.1230			−0.774974
$207$		0			0
$208$	−5.12747			−0.355526
$209$	7.57557	+	13.1213i	0.524013	+	0.907617i
$210$		0			0
$211$	−6.05925	+	10.4949i	−0.417136	+	0.722500i	−0.995650	−	0.0931719i	$-0.970299\pi$
$211$	−6.05925	+	10.4949i	−0.417136	+	0.722500i	0.578514	+	0.815672i	$0.303633\pi$
$212$	3.20858	−	5.55742i	0.220366	−	0.381685i
$213$		0			0
$214$	−7.44146	−	12.8890i	−0.508688	−	0.881073i
$215$	2.63149			0.179466
$216$		0			0
$217$	5.80078			0.393783
$218$	5.98874	+	10.3728i	0.405609	+	0.702535i
$219$		0			0
$220$	−8.13728	+	14.0942i	−0.548616	+	0.950230i
$221$	16.2926	−	28.2197i	1.09596	−	1.89826i
$222$		0			0
$223$	−9.59774	−	16.6238i	−0.642712	−	1.11321i	−0.984825	−	0.173551i	$-0.944476\pi$
$223$	−9.59774	−	16.6238i	−0.642712	−	1.11321i	0.342113	−	0.939659i	$-0.388858\pi$
$224$	3.49214			0.233329
$225$		0			0
$226$	3.85676			0.256548
$227$	7.78876	+	13.4905i	0.516958	+	0.895398i	0.999806	+	0.0196939i	$0.00626918\pi$
$227$	7.78876	+	13.4905i	0.516958	+	0.895398i	−0.482848	+	0.875704i	$0.660397\pi$
$228$		0			0
$229$	5.29223	−	9.16642i	0.349721	−	0.605734i	−0.636479	−	0.771294i	$-0.719610\pi$
$229$	5.29223	−	9.16642i	0.349721	−	0.605734i	0.986200	+	0.165560i	$0.0529432\pi$
$230$	−1.69714	+	2.93953i	−0.111906	+	0.193827i
$231$		0			0
$232$	−1.22952	−	2.12959i	−0.0807218	−	0.139814i
$233$	−10.2477			−0.671346			−0.335673	−	0.941978i	$-0.608964\pi$
$233$	−10.2477			−0.671346			−0.335673	+	0.941978i	$0.608964\pi$
$234$		0			0
$235$	37.7350			2.46156
$236$	3.08029	+	5.33522i	0.200510	+	0.347293i
$237$		0			0
$238$	−11.0964	+	19.2194i	−0.719270	+	1.24581i
$239$	6.67263	−	11.5573i	0.431617	−	0.747582i	−0.565396	−	0.824820i	$-0.691277\pi$
$239$	6.67263	−	11.5573i	0.431617	−	0.747582i	0.997013	+	0.0772376i	$0.0246100\pi$
$240$		0			0
$241$	15.0065	+	25.9919i	0.966651	+	1.67429i	0.705113	+	0.709095i	$0.250896\pi$
$241$	15.0065	+	25.9919i	0.966651	+	1.67429i	0.261538	+	0.965193i	$0.415770\pi$
$242$	11.9892			0.770693
$243$		0			0
$244$	1.26457			0.0809561
$245$	8.81675	+	15.2711i	0.563282	+	0.975633i
$246$		0			0
$247$	8.10134	−	14.0319i	0.515476	−	0.892830i
$248$	−0.830547	+	1.43855i	−0.0527398	+	0.0913480i
$249$		0			0
$250$	2.58161	+	4.47148i	0.163275	+	0.282801i
$251$	13.1961			0.832929			0.416465	−	0.909152i	$-0.363269\pi$
$251$	13.1961			0.832929			0.416465	+	0.909152i	$0.363269\pi$
$252$		0			0
$253$	4.79470			0.301440
$254$	3.65823	+	6.33623i	0.229538	+	0.397571i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.89203	+	8.47325i	−0.305157	+	0.528547i	−0.977296	−	0.211878i	$-0.932042\pi$
$257$	−4.89203	+	8.47325i	−0.305157	+	0.528547i	0.672140	+	0.740424i	$0.265375\pi$
$258$		0			0
$259$	17.2614	+	29.8975i	1.07257	+	1.85774i
$260$	17.4041			1.07936
$261$		0			0
$262$	7.15100			0.441790
$263$	−4.58904	−	7.94846i	−0.282973	−	0.490123i	0.689143	−	0.724625i	$-0.257987\pi$
$263$	−4.58904	−	7.94846i	−0.282973	−	0.490123i	−0.972116	+	0.234503i	$0.924654\pi$
$264$		0			0
$265$	−10.8908	+	18.8634i	−0.669017	+	1.15877i
$266$	−5.51754	+	9.55667i	−0.338302	+	0.585957i
$267$		0			0
$268$	−1.74607	−	3.02428i	−0.106658	−	0.184738i
$269$	19.2842			1.17578			0.587889	−	0.808941i	$-0.299959\pi$
$269$	19.2842			1.17578			0.587889	+	0.808941i	$0.299959\pi$
$270$		0			0
$271$	12.5171			0.760357			0.380178	−	0.924913i	$-0.375863\pi$
$271$	12.5171			0.760357			0.380178	+	0.924913i	$0.375863\pi$
$272$	−3.17752	−	5.50362i	−0.192665	−	0.333706i
$273$		0			0
$274$	3.38252	−	5.85869i	0.204345	−	0.353936i
$275$	15.6335	−	27.0780i	0.942735	−	1.63286i
$276$		0			0
$277$	12.5091	+	21.6664i	0.751598	+	1.30181i	0.947048	+	0.321092i	$0.104050\pi$
$277$	12.5091	+	21.6664i	0.751598	+	1.30181i	−0.195451	+	0.980714i	$0.562617\pi$
$278$	2.86619			0.171903
$279$		0			0
$280$	−11.8533			−0.708371
$281$	−2.20838	−	3.82502i	−0.131741	−	0.228182i	0.792607	−	0.609733i	$-0.208723\pi$
$281$	−2.20838	−	3.82502i	−0.131741	−	0.228182i	−0.924348	+	0.381551i	$0.875390\pi$
$282$		0			0
$283$	6.50840	−	11.2729i	0.386884	−	0.670103i	−0.605145	−	0.796116i	$-0.706885\pi$
$283$	6.50840	−	11.2729i	0.386884	−	0.670103i	0.992029	+	0.126013i	$0.0402181\pi$
$284$	8.22308	−	14.2428i	0.487950	−	0.845154i
$285$		0			0
$286$	−12.2923	−	21.2910i	−0.726861	−	1.25896i
$287$	−19.2008			−1.13339
$288$		0			0
$289$	23.3865			1.37568
$290$	4.17333	+	7.22842i	0.245066	+	0.424468i
$291$		0			0
$292$	−2.94800	+	5.10609i	−0.172519	+	0.298811i
$293$	8.65516	−	14.9912i	0.505640	−	0.875794i	−0.494339	−	0.869269i	$-0.664590\pi$
$293$	8.65516	−	14.9912i	0.505640	−	0.875794i	0.999979	−	0.00652448i	$-0.00207682\pi$
$294$		0			0
$295$	−10.4554	−	18.1092i	−0.608735	−	1.05436i
$296$	−9.88582			−0.574602
$297$		0			0
$298$	−1.00120			−0.0579980
$299$	−2.56373	−	4.44052i	−0.148265	−	0.256802i
$300$		0			0
$301$	1.35368	−	2.34464i	0.0780247	−	0.135143i
$302$	1.31459	−	2.27694i	0.0756464	−	0.131023i
$303$		0			0
$304$	−1.57999	−	2.73662i	−0.0906185	−	0.156956i
$305$	−4.29232			−0.245778
$306$		0			0
$307$	−16.3885			−0.935340			−0.467670	−	0.883903i	$-0.654906\pi$
$307$	−16.3885			−0.935340			−0.467670	+	0.883903i	$0.654906\pi$
$308$	8.37189	+	14.5005i	0.477033	+	0.826245i
$309$		0			0
$310$	2.81911	−	4.88285i	0.160115	−	0.277327i
$311$	−12.4319	+	21.5326i	−0.704946	+	1.22100i	0.261765	+	0.965132i	$0.415695\pi$
$311$	−12.4319	+	21.5326i	−0.704946	+	1.22100i	−0.966711	+	0.255871i	$0.917638\pi$
$312$		0			0
$313$	−0.256278	−	0.443887i	−0.0144857	−	0.0250900i	0.858692	−	0.512493i	$-0.171278\pi$
$313$	−0.256278	−	0.443887i	−0.0144857	−	0.0250900i	−0.873177	+	0.487403i	$0.837944\pi$
$314$	−18.9058			−1.06692
$315$		0			0
$316$	6.86066			0.385942
$317$	6.72374	+	11.6459i	0.377643	+	0.654097i	0.990719	−	0.135927i	$-0.0434014\pi$
$317$	6.72374	+	11.6459i	0.377643	+	0.654097i	−0.613076	+	0.790024i	$0.710068\pi$
$318$		0			0
$319$	5.89517	−	10.2107i	0.330066	−	0.571692i
$320$	1.69714	−	2.93953i	0.0948731	−	0.164325i
$321$		0			0
$322$	1.74607	+	3.02428i	0.0973048	+	0.168537i
$323$	20.0818			1.11738
$324$		0			0
$325$	−33.4370			−1.85475
$326$	−7.83770	−	13.5753i	−0.434090	−	0.751866i
$327$		0			0
$328$	2.74914	−	4.76165i	0.151796	−	0.262918i
$329$	19.4115	−	33.6217i	1.07019	−	1.85362i
$330$		0			0
$331$	0.377758	+	0.654296i	0.0207635	+	0.0359634i	0.876220	−	0.481911i	$-0.160057\pi$
$331$	0.377758	+	0.654296i	0.0207635	+	0.0359634i	−0.855457	+	0.517874i	$0.826724\pi$
$332$	−6.59614			−0.362010
$333$		0			0
$334$	12.6184			0.690446
$335$	5.92666	+	10.2653i	0.323808	+	0.560852i
$336$		0			0
$337$	3.72552	−	6.45279i	0.202942	−	0.351506i	−0.746533	−	0.665348i	$-0.768283\pi$
$337$	3.72552	−	6.45279i	0.202942	−	0.351506i	0.949475	+	0.313842i	$0.101616\pi$
$338$	−6.64547	+	11.5103i	−0.361466	+	0.626077i
$339$		0			0
$340$	10.7854	+	18.6809i	0.584920	+	1.01311i
$341$	−7.96445			−0.431299
$342$		0			0
$343$	−6.30310			−0.340335
$344$	0.387635	+	0.671404i	0.0208999	+	0.0361997i
$345$		0			0
$346$	−0.301440	+	0.522109i	−0.0162055	+	0.0280687i
$347$	−0.427050	+	0.739673i	−0.0229253	+	0.0397077i	−0.877260	−	0.480015i	$-0.840631\pi$
$347$	−0.427050	+	0.739673i	−0.0229253	+	0.0397077i	0.854335	+	0.519722i	$0.173965\pi$
$348$		0			0
$349$	−18.2104	−	31.5413i	−0.974781	−	1.68837i	−0.680657	−	0.732602i	$-0.738306\pi$
$349$	−18.2104	−	31.5413i	−0.974781	−	1.68837i	−0.294124	−	0.955767i	$-0.595028\pi$
$350$	22.7728			1.21726
$351$		0			0
$352$	−4.79470			−0.255558
$353$	4.59723	+	7.96264i	0.244686	+	0.423808i	0.962043	−	0.272897i	$-0.0879818\pi$
$353$	4.59723	+	7.96264i	0.244686	+	0.423808i	−0.717357	+	0.696705i	$0.754648\pi$
$354$		0			0
$355$	−27.9115	+	48.3441i	−1.48139	+	2.56584i
$356$	7.24432	−	12.5475i	0.383948	−	0.665018i
$357$		0			0
$358$	5.07999	+	8.79880i	0.268486	+	0.465031i
$359$	27.0648			1.42843			0.714213	−	0.699929i	$-0.246785\pi$
$359$	27.0648			1.42843			0.714213	+	0.699929i	$0.246785\pi$
$360$		0			0
$361$	−9.01455			−0.474450
$362$	3.71083	+	6.42734i	0.195037	+	0.337813i
$363$		0			0
$364$	8.95293	−	15.5069i	0.469261	−	0.812784i
$365$	10.0063	−	17.3315i	0.523756	−	0.907172i
$366$		0			0
$367$	17.8506	+	30.9181i	0.931793	+	1.61391i	0.780256	+	0.625461i	$0.215089\pi$
$367$	17.8506	+	30.9181i	0.931793	+	1.61391i	0.151537	+	0.988452i	$0.451578\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	33.5553			1.74446
$371$	11.2048	+	19.4073i	0.581725	+	1.00758i
$372$		0			0
$373$	−15.7450	+	27.2711i	−0.815243	+	1.41204i	0.0939100	+	0.995581i	$0.470063\pi$
$373$	−15.7450	+	27.2711i	−0.815243	+	1.41204i	−0.909153	+	0.416462i	$0.863270\pi$
$374$	15.2353	−	26.3882i	0.787796	−	1.36450i
$375$		0			0
$376$	5.55862	+	9.62781i	0.286664	+	0.496516i
$377$	−12.6086			−0.649378
$378$		0			0
$379$	−9.46354			−0.486109			−0.243055	−	0.970013i	$-0.578149\pi$
$379$	−9.46354			−0.486109			−0.243055	+	0.970013i	$0.578149\pi$
$380$	5.36292	+	9.28886i	0.275112	+	0.476508i
$381$		0			0
$382$	2.15681	−	3.73570i	0.110352	−	0.191135i
$383$	−11.0060	+	19.0629i	−0.562378	+	0.974068i	0.434910	+	0.900474i	$0.356780\pi$
$383$	−11.0060	+	19.0629i	−0.562378	+	0.974068i	−0.997288	+	0.0735937i	$0.976553\pi$
$384$		0			0
$385$	−28.4166	−	49.2189i	−1.44824	−	2.50843i
$386$	7.72975			0.393434
$387$		0			0
$388$	−1.54096			−0.0782306
$389$	8.50635	+	14.7334i	0.431289	+	0.747014i	0.996985	−	0.0775998i	$-0.0247256\pi$
$389$	8.50635	+	14.7334i	0.431289	+	0.747014i	−0.565696	+	0.824614i	$0.691392\pi$
$390$		0			0
$391$	3.17752	−	5.50362i	0.160694	−	0.278330i
$392$	−2.59753	+	4.49906i	−0.131195	+	0.227237i
$393$		0			0
$394$	−9.73340	−	16.8587i	−0.490361	−	0.849331i
$395$	−23.2870			−1.17170
$396$		0			0
$397$	14.4557			0.725513			0.362756	−	0.931884i	$-0.381836\pi$
$397$	14.4557			0.725513			0.362756	+	0.931884i	$0.381836\pi$
$398$	−0.330748	−	0.572872i	−0.0165789	−	0.0287155i
$399$		0			0
$400$	−3.26058	+	5.64748i	−0.163029	+	0.282374i
$401$	−0.340134	+	0.589129i	−0.0169855	+	0.0294197i	−0.874393	−	0.485218i	$-0.838740\pi$
$401$	−0.340134	+	0.589129i	−0.0169855	+	0.0294197i	0.857408	+	0.514638i	$0.172074\pi$
$402$		0			0
$403$	4.25861	+	7.37612i	0.212136	+	0.367431i
$404$	−9.69010			−0.482101
$405$		0			0
$406$	8.58731			0.426181
$407$	−23.6998	−	41.0492i	−1.17475	−	2.03474i
$408$		0			0
$409$	8.57201	−	14.8472i	0.423859	−	0.734145i	−0.572454	−	0.819937i	$-0.694009\pi$
$409$	8.57201	−	14.8472i	0.423859	−	0.734145i	0.996313	+	0.0857918i	$0.0273420\pi$
$410$	−9.33136	+	16.1624i	−0.460843	+	0.798203i
$411$		0			0
$412$	5.56148	+	9.63277i	0.273995	+	0.474573i
$413$	−21.5136			−1.05862
$414$		0			0
$415$	22.3892			1.09904
$416$	2.56373	+	4.44052i	0.125697	+	0.217714i
$417$		0			0
$418$	7.57557	−	13.1213i	0.370533	−	0.641782i
$419$	5.29969	−	9.17933i	0.258907	−	0.448440i	−0.707043	−	0.707171i	$-0.749971\pi$
$419$	5.29969	−	9.17933i	0.258907	−	0.448440i	0.965949	+	0.258731i	$0.0833044\pi$
$420$		0			0
$421$	3.80320	+	6.58733i	0.185356	+	0.321047i	0.943697	−	0.330812i	$-0.107323\pi$
$421$	3.80320	+	6.58733i	0.185356	+	0.321047i	−0.758340	+	0.651859i	$0.773989\pi$
$422$	12.1185			0.589919
$423$		0			0
$424$	−6.41715			−0.311644
$425$	−20.7211	−	35.8900i	−1.00512	−	1.74092i
$426$		0			0
$427$	−2.20804	+	3.82443i	−0.106854	+	0.185077i
$428$	−7.44146	+	12.8890i	−0.359697	+	0.623013i
$429$		0			0
$430$	−1.31574	−	2.27893i	−0.0634508	−	0.109900i
$431$	33.0832			1.59356			0.796780	−	0.604269i	$-0.206535\pi$
$431$	33.0832			1.59356			0.796780	+	0.604269i	$0.206535\pi$
$432$		0			0
$433$	30.6096			1.47101			0.735503	−	0.677522i	$-0.236946\pi$
$433$	30.6096			1.47101			0.735503	+	0.677522i	$0.236946\pi$
$434$	−2.90039	−	5.02362i	−0.139223	−	0.241142i
$435$		0			0
$436$	5.98874	−	10.3728i	0.286809	−	0.496767i
$437$	1.57999	−	2.73662i	0.0755811	−	0.130910i
$438$		0			0
$439$	−2.23860	−	3.87738i	−0.106843	−	0.185057i	0.807647	−	0.589666i	$-0.200741\pi$
$439$	−2.23860	−	3.87738i	−0.106843	−	0.185057i	−0.914490	+	0.404609i	$0.867407\pi$
$440$	16.2746			0.775860
$441$		0			0
$442$	−32.5853			−1.54992
$443$	−6.69807	−	11.6014i	−0.318235	−	0.551199i	0.661885	−	0.749606i	$-0.269757\pi$
$443$	−6.69807	−	11.6014i	−0.318235	−	0.551199i	−0.980120	+	0.198406i	$0.936423\pi$
$444$		0			0
$445$	−24.5893	+	42.5899i	−1.16564	+	2.01895i
$446$	−9.59774	+	16.6238i	−0.454466	+	0.787159i
$447$		0			0
$448$	−1.74607	−	3.02428i	−0.0824941	−	0.142884i
$449$	−7.07071			−0.333687			−0.166844	−	0.985983i	$-0.553358\pi$
$449$	−7.07071			−0.333687			−0.166844	+	0.985983i	$0.553358\pi$
$450$		0			0
$451$	26.3626			1.24137
$452$	−1.92838	−	3.34005i	−0.0907033	−	0.157103i
$453$		0			0
$454$	7.78876	−	13.4905i	0.365545	−	0.633142i
$455$	−30.3888	+	52.6349i	−1.42465	+	2.46756i
$456$		0			0
$457$	−0.00878737	−	0.0152202i	−0.000411056	−	0.000711969i	0.865820	−	0.500356i	$-0.166798\pi$
$457$	−0.00878737	−	0.0152202i	−0.000411056	−	0.000711969i	−0.866231	+	0.499644i	$0.833464\pi$
$458$	−10.5845			−0.494580
$459$		0			0
$460$	3.39428			0.158259
$461$	−15.6892	−	27.1745i	−0.730719	−	1.26564i	−0.956576	−	0.291481i	$-0.905852\pi$
$461$	−15.6892	−	27.1745i	−0.730719	−	1.26564i	0.225858	−	0.974160i	$-0.427481\pi$
$462$		0			0
$463$	2.12357	−	3.67813i	0.0986907	−	0.170937i	−0.812452	−	0.583028i	$-0.801868\pi$
$463$	2.12357	−	3.67813i	0.0986907	−	0.170937i	0.911143	+	0.412090i	$0.135201\pi$
$464$	−1.22952	+	2.12959i	−0.0570789	+	0.0988636i
$465$		0			0
$466$	5.12383	+	8.87473i	0.237357	+	0.411114i
$467$	−30.9792			−1.43354			−0.716772	−	0.697307i	$-0.754381\pi$
$467$	−30.9792			−1.43354			−0.716772	+	0.697307i	$0.754381\pi$
$468$		0			0
$469$	12.1951			0.563116
$470$	−18.8675	−	32.6795i	−0.870293	−	1.50739i
$471$		0			0
$472$	3.08029	−	5.33522i	0.141782	−	0.245573i
$473$	−1.85859	+	3.21918i	−0.0854583	+	0.148018i
$474$		0			0
$475$	−10.3033	−	17.8459i	−0.472750	−	0.818826i
$476$	22.1927			1.01720
$477$		0			0
$478$	−13.3453			−0.610398
$479$	13.9406	+	24.1459i	0.636963	+	1.10325i	0.986096	+	0.166179i	$0.0531429\pi$
$479$	13.9406	+	24.1459i	0.636963	+	1.10325i	−0.349133	+	0.937073i	$0.613524\pi$
$480$		0			0
$481$	−25.3446	+	43.8982i	−1.15562	+	2.00159i
$482$	15.0065	−	25.9919i	0.683525	−	1.18390i
$483$		0			0
$484$	−5.99458	−	10.3829i	−0.272481	−	0.471951i
$485$	5.23047			0.237503
$486$		0			0
$487$	20.9308			0.948464			0.474232	−	0.880400i	$-0.342726\pi$
$487$	20.9308			0.948464			0.474232	+	0.880400i	$0.342726\pi$
$488$	−0.632287	−	1.09515i	−0.0286223	−	0.0495753i
$489$		0			0
$490$	8.81675	−	15.2711i	0.398300	−	0.689876i
$491$	−18.3014	+	31.6990i	−0.825932	+	1.43056i	0.0752731	+	0.997163i	$0.476017\pi$
$491$	−18.3014	+	31.6990i	−0.825932	+	1.43056i	−0.901205	+	0.433393i	$0.857316\pi$
$492$		0			0
$493$	−7.81363	−	13.5336i	−0.351908	−	0.609523i
$494$	−16.2027			−0.728993
$495$		0			0
$496$	1.66109			0.0745854
$497$	28.7162	+	49.7379i	1.28810	+	2.23105i
$498$		0			0
$499$	−3.88896	+	6.73588i	−0.174094	+	0.301540i	−0.939847	−	0.341595i	$-0.889033\pi$
$499$	−3.88896	+	6.73588i	−0.174094	+	0.301540i	0.765753	+	0.643134i	$0.222366\pi$
$500$	2.58161	−	4.47148i	0.115453	−	0.199970i
$501$		0			0
$502$	−6.59804	−	11.4281i	−0.294485	−	0.510063i
$503$	−23.1594			−1.03262			−0.516312	−	0.856400i	$-0.672696\pi$
$503$	−23.1594			−1.03262			−0.516312	+	0.856400i	$0.672696\pi$
$504$		0			0
$505$	32.8909			1.46363
$506$	−2.39735	−	4.15233i	−0.106575	−	0.184594i
$507$		0			0
$508$	3.65823	−	6.33623i	0.162308	−	0.281125i
$509$	−7.41645	+	12.8457i	−0.328728	+	0.569374i	−0.982260	−	0.187525i	$-0.939953\pi$
$509$	−7.41645	+	12.8457i	−0.328728	+	0.569374i	0.653531	+	0.756899i	$0.273287\pi$
$510$		0			0
$511$	−10.2948	−	17.8312i	−0.455417	−	0.788805i
$512$	1.00000			0.0441942
$513$		0			0
$514$	9.78406			0.431557
$515$	−18.8772	−	32.6964i	−0.831831	−	1.44077i
$516$		0			0
$517$	−26.6519	+	46.1625i	−1.17215	+	2.03022i
$518$	17.2614	−	29.8975i	0.758420	−	1.31362i
$519$		0			0
$520$	−8.70204	−	15.0724i	−0.381610	−	0.660967i
$521$	40.8448			1.78944			0.894722	−	0.446623i	$-0.147373\pi$
$521$	40.8448			1.78944			0.894722	+	0.446623i	$0.147373\pi$
$522$		0			0
$523$	5.80630			0.253892			0.126946	−	0.991910i	$-0.459483\pi$
$523$	5.80630			0.253892			0.126946	+	0.991910i	$0.459483\pi$
$524$	−3.57550	−	6.19295i	−0.156196	−	0.270540i
$525$		0			0
$526$	−4.58904	+	7.94846i	−0.200092	+	0.346569i
$527$	−5.27816	+	9.14204i	−0.229920	+	0.398234i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	21.7816			0.946133
$531$		0			0
$532$	11.0351			0.478432
$533$	−14.0961	−	24.4152i	−0.610571	−	1.05754i
$534$		0			0
$535$	25.2584	−	43.7489i	1.09202	−	1.89143i
$536$	−1.74607	+	3.02428i	−0.0754188	+	0.130629i
$537$		0			0
$538$	−9.64210	−	16.7006i	−0.415701	−	0.720014i
$539$	−24.9088			−1.07290
$540$		0			0
$541$	−34.5661			−1.48611			−0.743056	−	0.669229i	$-0.766624\pi$
$541$	−34.5661			−1.48611			−0.743056	+	0.669229i	$0.766624\pi$
$542$	−6.25853	−	10.8401i	−0.268827	−	0.465622i
$543$		0			0
$544$	−3.17752	+	5.50362i	−0.136235	+	0.235966i
$545$	−20.3275	+	35.2082i	−0.870734	+	1.50816i
$546$		0			0
$547$	11.0446	+	19.1299i	0.472235	+	0.817935i	0.999495	−	0.0317690i	$-0.0101141\pi$
$547$	11.0446	+	19.1299i	0.472235	+	0.817935i	−0.527260	+	0.849704i	$0.676781\pi$
$548$	−6.76503			−0.288988
$549$		0			0
$550$	−31.2670			−1.33323
$551$	−3.88525	−	6.72945i	−0.165517	−	0.286684i
$552$		0			0
$553$	−11.9792	+	20.7486i	−0.509407	+	0.882319i
$554$	12.5091	−	21.6664i	0.531460	−	0.920515i
$555$		0			0
$556$	−1.43310	−	2.48220i	−0.0607768	−	0.105269i
$557$	1.57737			0.0668353			0.0334176	−	0.999441i	$-0.489361\pi$
$557$	1.57737			0.0668353			0.0334176	+	0.999441i	$0.489361\pi$
$558$		0			0
$559$	3.97517			0.168132
$560$	5.92666	+	10.2653i	0.250447	+	0.433787i
$561$		0			0
$562$	−2.20838	+	3.82502i	−0.0931547	+	0.161349i
$563$	2.70236	−	4.68062i	0.113891	−	0.197265i	−0.803445	−	0.595379i	$-0.797002\pi$
$563$	2.70236	−	4.68062i	0.113891	−	0.197265i	0.917336	+	0.398114i	$0.130335\pi$
$564$		0			0
$565$	6.54546	+	11.3371i	0.275370	+	0.476954i
$566$	−13.0168			−0.547137
$567$		0			0
$568$	−16.4462			−0.690066
$569$	−20.8169	−	36.0559i	−0.872688	−	1.51154i	−0.859205	−	0.511631i	$-0.829041\pi$
$569$	−20.8169	−	36.0559i	−0.872688	−	1.51154i	−0.0134832	−	0.999909i	$-0.504292\pi$
$570$		0			0
$571$	−20.2459	+	35.0669i	−0.847264	+	1.46750i	0.0363770	+	0.999338i	$0.488418\pi$
$571$	−20.2459	+	35.0669i	−0.847264	+	1.46750i	−0.883641	+	0.468166i	$0.844915\pi$
$572$	−12.2923	+	21.2910i	−0.513969	+	0.890220i
$573$		0			0
$574$	9.60039	+	16.6284i	0.400713	+	0.694055i
$575$	−6.52115			−0.271951
$576$		0			0
$577$	−0.0485978			−0.00202315			−0.00101158	−	0.999999i	$-0.500322\pi$
$577$	−0.0485978			−0.00202315			−0.00101158	+	0.999999i	$0.500322\pi$
$578$	−11.6933	−	20.2533i	−0.486375	−	0.842427i
$579$		0			0
$580$	4.17333	−	7.22842i	0.173288	−	0.300144i
$581$	11.5173	−	19.9486i	0.477820	−	0.827608i
$582$		0			0
$583$	−15.3842	−	26.6462i	−0.637147	−	1.10357i
$584$	5.89600			0.243978
$585$		0			0
$586$	−17.3103			−0.715083
$587$	4.67180	+	8.09180i	0.192826	+	0.333984i	0.946186	−	0.323624i	$-0.104901\pi$
$587$	4.67180	+	8.09180i	0.192826	+	0.333984i	−0.753360	+	0.657609i	$0.771568\pi$
$588$		0			0
$589$	−2.62451	+	4.54578i	−0.108141	+	0.187306i
$590$	−10.4554	+	18.1092i	−0.430441	+	0.745545i
$591$		0			0
$592$	4.94291	+	8.56138i	0.203152	+	0.351870i
$593$	14.9859			0.615396			0.307698	−	0.951484i	$-0.400441\pi$
$593$	14.9859			0.615396			0.307698	+	0.951484i	$0.400441\pi$
$594$		0			0
$595$	−75.3283			−3.08816
$596$	0.500601	+	0.867066i	0.0205054	+	0.0355164i
$597$		0			0
$598$	−2.56373	+	4.44052i	−0.104839	+	0.181586i
$599$	−11.4562	+	19.8427i	−0.468088	+	0.810752i	−0.999335	−	0.0364650i	$-0.988390\pi$
$599$	−11.4562	+	19.8427i	−0.468088	+	0.810752i	0.531247	+	0.847217i	$0.321724\pi$
$600$		0			0
$601$	−1.34709	−	2.33323i	−0.0549490	−	0.0951745i	0.837242	−	0.546832i	$-0.184166\pi$
$601$	−1.34709	−	2.33323i	−0.0549490	−	0.0951745i	−0.892191	+	0.451657i	$0.850833\pi$
$602$	−2.70735			−0.110344
$603$		0			0
$604$	−2.62919			−0.106980
$605$	20.3473	+	35.2426i	0.827235	+	1.43281i
$606$		0			0
$607$	20.6865	−	35.8301i	0.839640	−	1.45430i	−0.0505565	−	0.998721i	$-0.516099\pi$
$607$	20.6865	−	35.8301i	0.839640	−	1.45430i	0.890196	−	0.455577i	$-0.150567\pi$
$608$	−1.57999	+	2.73662i	−0.0640770	+	0.110985i
$609$		0			0
$610$	2.14616	+	3.71726i	0.0868955	+	0.150507i
$611$	57.0033			2.30611
$612$		0			0
$613$	−24.0528			−0.971485			−0.485743	−	0.874102i	$-0.661451\pi$
$613$	−24.0528			−0.971485			−0.485743	+	0.874102i	$0.661451\pi$
$614$	8.19424	+	14.1928i	0.330693	+	0.572777i
$615$		0			0
$616$	8.37189	−	14.5005i	0.337313	−	0.584243i
$617$	9.04957	−	15.6743i	0.364322	−	0.631024i	−0.624345	−	0.781149i	$-0.714634\pi$
$617$	9.04957	−	15.6743i	0.364322	−	0.631024i	0.988667	+	0.150124i	$0.0479674\pi$
$618$		0			0
$619$	5.70650	+	9.88394i	0.229364	+	0.397269i	0.957620	−	0.288036i	$-0.0930022\pi$
$619$	5.70650	+	9.88394i	0.229364	+	0.397269i	−0.728256	+	0.685305i	$0.759669\pi$
$620$	−5.63822			−0.226437
$621$		0			0
$622$	24.8637			0.996944
$623$	25.2982	+	43.8178i	1.01355	+	1.75552i
$624$		0			0
$625$	7.54017	−	13.0600i	0.301607	−	0.522398i
$626$	−0.256278	+	0.443887i	−0.0102429	+	0.0177413i
$627$		0			0
$628$	9.45290	+	16.3729i	0.377212	+	0.653350i
$629$	−62.8248			−2.50499
$630$		0			0
$631$	10.2132			0.406580			0.203290	−	0.979119i	$-0.434837\pi$
$631$	10.2132			0.406580			0.203290	+	0.979119i	$0.434837\pi$
$632$	−3.43033	−	5.94150i	−0.136451	−	0.236340i
$633$		0			0
$634$	6.72374	−	11.6459i	0.267034	−	0.462516i
$635$	−12.4171	+	21.5070i	−0.492756	+	0.853478i
$636$		0			0
$637$	13.3188	+	23.0688i	0.527709	+	0.914018i
$638$	−11.7903			−0.466784
$639$		0			0
$640$	−3.39428			−0.134171
$641$	−23.5815	−	40.8443i	−0.931412	−	1.61325i	−0.780910	−	0.624644i	$-0.785244\pi$
$641$	−23.5815	−	40.8443i	−0.931412	−	1.61325i	−0.150503	−	0.988610i	$-0.548089\pi$
$642$		0			0
$643$	18.4669	−	31.9856i	0.728264	−	1.26139i	−0.229352	−	0.973343i	$-0.573661\pi$
$643$	18.4669	−	31.9856i	0.728264	−	1.26139i	0.957616	−	0.288047i	$-0.0930059\pi$
$644$	1.74607	−	3.02428i	0.0688049	−	0.119174i
$645$		0			0
$646$	−10.0409	−	17.3913i	−0.395053	−	0.684252i
$647$	−14.4649			−0.568674			−0.284337	−	0.958724i	$-0.591774\pi$
$647$	−14.4649			−0.568674			−0.284337	+	0.958724i	$0.591774\pi$
$648$		0			0
$649$	29.5381			1.15947
$650$	16.7185	+	28.9573i	0.655754	+	1.13580i
$651$		0			0
$652$	−7.83770	+	13.5753i	−0.306948	+	0.531649i
$653$	0.262054	−	0.453890i	0.0102550	−	0.0177621i	−0.860852	−	0.508855i	$-0.830069\pi$
$653$	0.262054	−	0.453890i	0.0102550	−	0.0177621i	0.871107	+	0.491093i	$0.163402\pi$
$654$		0			0
$655$	12.1363	+	21.0206i	0.474203	+	0.821343i
$656$	−5.49828			−0.214672
$657$		0			0
$658$	−38.8230			−1.51348
$659$	−18.3309	−	31.7501i	−0.714072	−	1.23681i	−0.963317	−	0.268368i	$-0.913516\pi$
$659$	−18.3309	−	31.7501i	−0.714072	−	1.23681i	0.249245	−	0.968440i	$-0.419818\pi$
$660$		0			0
$661$	8.68530	−	15.0434i	0.337819	−	0.585119i	−0.646203	−	0.763165i	$-0.723644\pi$
$661$	8.68530	−	15.0434i	0.337819	−	0.585119i	0.984022	+	0.178046i	$0.0569775\pi$
$662$	0.377758	−	0.654296i	0.0146820	−	0.0254299i
$663$		0			0
$664$	3.29807	+	5.71243i	0.127990	+	0.221685i
$665$	−37.4562			−1.45249
$666$		0			0
$667$	−2.45904			−0.0952143
$668$	−6.30918	−	10.9278i	−0.244109	−	0.422810i
$669$		0			0
$670$	5.92666	−	10.2653i	0.228967	−	0.396582i
$671$	3.03163	−	5.25093i	0.117035	−	0.202710i
$672$		0			0
$673$	−20.3892	−	35.3152i	−0.785946	−	1.36130i	−0.928432	−	0.371502i	$-0.878843\pi$
$673$	−20.3892	−	35.3152i	−0.785946	−	1.36130i	0.142486	−	0.989797i	$-0.454491\pi$
$674$	−7.45104			−0.287003
$675$		0			0
$676$	13.2909			0.511190
$677$	1.30376	+	2.25817i	0.0501075	+	0.0867887i	0.889991	−	0.455978i	$-0.150710\pi$
$677$	1.30376	+	2.25817i	0.0501075	+	0.0867887i	−0.839884	+	0.542766i	$0.817377\pi$
$678$		0			0
$679$	2.69063	−	4.66031i	0.103257	−	0.178846i
$680$	10.7854	−	18.6809i	0.413601	−	0.716378i
$681$		0			0
$682$	3.98223	+	6.89742i	0.152487	+	0.264116i
$683$	16.2295			0.621006			0.310503	−	0.950572i	$-0.399502\pi$
$683$	16.2295			0.621006			0.310503	+	0.950572i	$0.399502\pi$
$684$		0			0
$685$	22.9624			0.877350
$686$	3.15155	+	5.45865i	0.120327	+	0.208412i
$687$		0			0
$688$	0.387635	−	0.671404i	0.0147785	−	0.0255970i
$689$	−16.4519	+	28.4955i	−0.626767	+	1.08559i
$690$		0			0
$691$	−9.69924	−	16.7996i	−0.368977	−	0.639086i	0.620429	−	0.784262i	$-0.286958\pi$
$691$	−9.69924	−	16.7996i	−0.368977	−	0.639086i	−0.989406	+	0.145176i	$0.953625\pi$
$692$	0.602879			0.0229180
$693$		0			0
$694$	0.854101			0.0324212
$695$	4.86433	+	8.42528i	0.184515	+	0.319589i
$696$		0			0
$697$	17.4709	−	30.2605i	0.661757	−	1.14620i
$698$	−18.2104	+	31.5413i	−0.689274	+	1.19386i
$699$		0			0
$700$	−11.3864	−	19.7218i	−0.430365	−	0.745415i
$701$	−27.9645			−1.05621			−0.528103	−	0.849180i	$-0.677097\pi$
$701$	−27.9645			−1.05621			−0.528103	+	0.849180i	$0.677097\pi$
$702$		0			0
$703$	−31.2390			−1.17820
$704$	2.39735	+	4.15233i	0.0903536	+	0.156497i
$705$		0			0
$706$	4.59723	−	7.96264i	0.173019	−	0.299678i
$707$	16.9196	−	29.3056i	0.636327	−	1.10215i
$708$		0			0
$709$	−1.23996	−	2.14768i	−0.0465678	−	0.0806578i	0.841802	−	0.539786i	$-0.181495\pi$
$709$	−1.23996	−	2.14768i	−0.0465678	−	0.0806578i	−0.888370	+	0.459129i	$0.848162\pi$
$710$	55.8229			2.09500
$711$		0			0
$712$	−14.4886			−0.542985
$713$	0.830547	+	1.43855i	0.0311042	+	0.0538741i
$714$		0			0
$715$	41.7237	−	72.2675i	1.56038	−	2.70265i
$716$	5.07999	−	8.79880i	0.189848	−	0.328826i
$717$		0			0
$718$	−13.5324	−	23.4388i	−0.505025	−	0.874728i
$719$	−15.9388			−0.594416			−0.297208	−	0.954813i	$-0.596056\pi$
$719$	−15.9388			−0.594416			−0.297208	+	0.954813i	$0.596056\pi$
$720$		0			0
$721$	−38.8430			−1.44659
$722$	4.50728	+	7.80683i	0.167743	+	0.290540i
$723$		0			0
$724$	3.71083	−	6.42734i	0.137912	−	0.238870i
$725$	−8.01787	+	13.8874i	−0.297776	+	0.515764i
$726$		0			0
$727$	−13.6715	−	23.6797i	−0.507048	−	0.878233i	−0.999967	−	0.00815739i	$-0.997403\pi$
$727$	−13.6715	−	23.6797i	−0.507048	−	0.878233i	0.492919	−	0.870075i	$-0.335930\pi$
$728$	−17.9059			−0.663635
$729$		0			0
$730$	−20.0127			−0.740703
$731$	2.46344	+	4.26680i	0.0911135	+	0.157813i
$732$		0			0
$733$	10.5709	−	18.3094i	0.390446	−	0.676271i	−0.602063	−	0.798449i	$-0.705654\pi$
$733$	10.5709	−	18.3094i	0.390446	−	0.676271i	0.992508	+	0.122177i	$0.0389877\pi$
$734$	17.8506	−	30.9181i	0.658877	−	1.14121i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−16.7438			−0.616765
$738$		0			0
$739$	−4.66746			−0.171695			−0.0858476	−	0.996308i	$-0.527360\pi$
$739$	−4.66746			−0.171695			−0.0858476	+	0.996308i	$0.527360\pi$
$740$	−16.7776	−	29.0597i	−0.616758	−	1.06826i
$741$		0			0
$742$	11.2048	−	19.4073i	0.411341	−	0.712464i
$743$	2.59731	−	4.49867i	0.0952861	−	0.165040i	−0.814442	−	0.580245i	$-0.802957\pi$
$743$	2.59731	−	4.49867i	0.0952861	−	0.165040i	0.909728	+	0.415205i	$0.136290\pi$
$744$		0			0
$745$	−1.69918	−	2.94307i	−0.0622531	−	0.107826i
$746$	31.4899			1.15293
$747$		0			0
$748$	−30.4705			−1.11411
$749$	−25.9867	−	45.0102i	−0.949532	−	1.64464i
$750$		0			0
$751$	12.9794	−	22.4810i	0.473625	−	0.820342i	−0.525920	−	0.850534i	$-0.676279\pi$
$751$	12.9794	−	22.4810i	0.473625	−	0.820342i	0.999544	+	0.0301925i	$0.00961203\pi$
$752$	5.55862	−	9.62781i	0.202702	−	0.351090i
$753$		0			0
$754$	6.30432	+	10.9194i	0.229590	+	0.397661i
$755$	8.92421			0.324785
$756$		0			0
$757$	−11.6767			−0.424397			−0.212198	−	0.977227i	$-0.568062\pi$
$757$	−11.6767			−0.424397			−0.212198	+	0.977227i	$0.568062\pi$
$758$	4.73177	+	8.19566i	0.171866	+	0.297680i
$759$		0			0
$760$	5.36292	−	9.28886i	0.194534	−	0.336942i
$761$	11.5862	−	20.0679i	0.420000	−	0.727461i	−0.575939	−	0.817492i	$-0.695364\pi$
$761$	11.5862	−	20.0679i	0.420000	−	0.727461i	0.995939	+	0.0900318i	$0.0286969\pi$
$762$		0			0
$763$	20.9136	+	36.2233i	0.757121	+	1.31137i
$764$	−4.31361			−0.156061
$765$		0			0
$766$	22.0119			0.795323
$767$	−15.7941	−	27.3562i	−0.570291	−	0.987774i
$768$		0			0
$769$	−15.4780	+	26.8086i	−0.558150	+	0.966744i	0.439501	+	0.898242i	$0.355155\pi$
$769$	−15.4780	+	26.8086i	−0.558150	+	0.966744i	−0.997651	+	0.0685023i	$0.978178\pi$
$770$	−28.4166	+	49.2189i	−1.02406	+	1.77373i
$771$		0			0
$772$	−3.86487	−	6.69416i	−0.139100	−	0.240928i
$773$	35.6701			1.28296			0.641482	−	0.767138i	$-0.278320\pi$
$773$	35.6701			1.28296			0.641482	+	0.767138i	$0.278320\pi$
$774$		0			0
$775$	10.8322			0.389106
$776$	0.770482	+	1.33451i	0.0276587	+	0.0479063i
$777$		0			0
$778$	8.50635	−	14.7334i	0.304967	−	0.528219i
$779$	8.68722	−	15.0467i	0.311252	−	0.539104i
$780$		0			0
$781$	−39.4272	−	68.2899i	−1.41082	−	2.44361i
$782$	−6.35504			−0.227256
$783$		0			0
$784$	5.19506			0.185538
$785$	−32.0858	−	55.5742i	−1.14519	−	1.98353i
$786$		0			0
$787$	18.5980	−	32.2127i	0.662947	−	1.14826i	−0.316890	−	0.948462i	$-0.602639\pi$
$787$	18.5980	−	32.2127i	0.662947	−	1.14826i	0.979838	−	0.199796i	$-0.0640279\pi$
$788$	−9.73340	+	16.8587i	−0.346738	+	0.600568i
$789$		0			0
$790$	11.6435	+	20.1671i	0.414257	+	0.717515i
$791$	13.4683			0.478879
$792$		0			0
$793$	−6.48407			−0.230256
$794$	−7.22787	−	12.5190i	−0.256507	−	0.444284i
$795$		0			0
$796$	−0.330748	+	0.572872i	−0.0117230	+	0.0203049i
$797$	−11.0075	+	19.0656i	−0.389907	+	0.675339i	−0.992437	−	0.122757i	$-0.960826\pi$
$797$	−11.0075	+	19.0656i	−0.389907	+	0.675339i	0.602529	+	0.798097i	$0.294160\pi$
$798$		0			0
$799$	35.3252	+	61.1851i	1.24972	+	2.16457i
$800$	6.52115			0.230558
$801$		0			0
$802$	0.680268			0.0240211
$803$	14.1348	+	24.4822i	0.498806	+	0.863957i
$804$		0			0
$805$	−5.92666	+	10.2653i	−0.208887	+	0.361803i
$806$	4.25861	−	7.37612i	0.150003	−	0.259813i
$807$		0			0
$808$	4.84505	+	8.39188i	0.170448	+	0.295225i
$809$	32.3565			1.13759			0.568797	−	0.822478i	$-0.307409\pi$
$809$	32.3565			1.13759			0.568797	+	0.822478i	$0.307409\pi$
$810$		0			0
$811$	−53.8736			−1.89176			−0.945879	−	0.324520i	$-0.894797\pi$
$811$	−53.8736			−1.89176			−0.945879	+	0.324520i	$0.894797\pi$
$812$	−4.29365	−	7.43682i	−0.150678	−	0.260981i
$813$		0			0
$814$	−23.6998	+	41.0492i	−0.830677	+	1.43878i
$815$	26.6033	−	46.0784i	0.931875	−	1.61405i
$816$		0			0
$817$	1.22492	+	2.12162i	0.0428544	+	0.0742261i
$818$	−17.1440			−0.599427
$819$		0			0
$820$	18.6627			0.651730
$821$	17.6853	+	30.6319i	0.617222	+	1.06906i	0.989990	+	0.141135i	$0.0450753\pi$
$821$	17.6853	+	30.6319i	0.617222	+	1.06906i	−0.372768	+	0.927924i	$0.621591\pi$
$822$		0			0
$823$	−11.6367	+	20.1554i	−0.405630	+	0.702572i	−0.994395	−	0.105733i	$-0.966281\pi$
$823$	−11.6367	+	20.1554i	−0.405630	+	0.702572i	0.588765	+	0.808305i	$0.299615\pi$
$824$	5.56148	−	9.63277i	0.193744	−	0.335574i
$825$		0			0
$826$	10.7568	+	18.6313i	0.374277	+	0.648267i
$827$	−8.57319			−0.298119			−0.149060	−	0.988828i	$-0.547625\pi$
$827$	−8.57319			−0.298119			−0.149060	+	0.988828i	$0.547625\pi$
$828$		0			0
$829$	31.4933			1.09381			0.546903	−	0.837196i	$-0.315806\pi$
$829$	31.4933			1.09381			0.546903	+	0.837196i	$0.315806\pi$
$830$	−11.1946	−	19.3896i	−0.388570	−	0.673022i
$831$		0			0
$832$	2.56373	−	4.44052i	0.0888815	−	0.153947i
$833$	−16.5074	+	28.5917i	−0.571948	+	0.990643i
$834$		0			0
$835$	21.4151	+	37.0921i	0.741101	+	1.28362i
$836$	−15.1511			−0.524013
$837$		0			0
$838$	−10.5994			−0.366150
$839$	3.74560	+	6.48757i	0.129312	+	0.223976i	0.923410	−	0.383814i	$-0.125390\pi$
$839$	3.74560	+	6.48757i	0.129312	+	0.223976i	−0.794098	+	0.607790i	$0.792056\pi$
$840$		0			0
$841$	11.4766	−	19.8780i	0.395744	−	0.685448i
$842$	3.80320	−	6.58733i	0.131067	−	0.227014i
$843$		0			0
$844$	−6.05925	−	10.4949i	−0.208568	−	0.361250i
$845$	−45.1132			−1.55194
$846$		0			0
$847$	41.8679			1.43860
$848$	3.20858	+	5.55742i	0.110183	+	0.190842i
$849$		0			0
$850$	−20.7211	+	35.8900i	−0.710727	+	1.23102i
$851$	−4.94291	+	8.56138i	−0.169441	+	0.293480i
$852$		0			0
$853$	11.2986	+	19.5698i	0.386858	+	0.670058i	0.992025	−	0.126041i	$-0.0402270\pi$
$853$	11.2986	+	19.5698i	0.386858	+	0.670058i	−0.605167	+	0.796099i	$0.706894\pi$
$854$	4.41607			0.151115
$855$		0			0
$856$	14.8829			0.508688
$857$	−18.2605	−	31.6281i	−0.623766	−	1.08039i	−0.988778	−	0.149392i	$-0.952268\pi$
$857$	−18.2605	−	31.6281i	−0.623766	−	1.08039i	0.365012	−	0.931003i	$-0.381065\pi$
$858$		0			0
$859$	0.936765	−	1.62252i	0.0319620	−	0.0553598i	−0.849602	−	0.527424i	$-0.823158\pi$
$859$	0.936765	−	1.62252i	0.0319620	−	0.0553598i	0.881564	+	0.472065i	$0.156491\pi$
$860$	−1.31574	+	2.27893i	−0.0448665	+	0.0777110i
$861$		0			0
$862$	−16.5416	−	28.6509i	−0.563409	−	0.975852i
$863$	25.6962			0.874710			0.437355	−	0.899289i	$-0.355915\pi$
$863$	25.6962			0.874710			0.437355	+	0.899289i	$0.355915\pi$
$864$		0			0
$865$	−2.04634			−0.0695777
$866$	−15.3048	−	26.5087i	−0.520079	−	0.900803i
$867$		0			0
$868$	−2.90039	+	5.02362i	−0.0984457	+	0.170513i
$869$	16.4474	−	28.4877i	0.557940	−	0.966380i
$870$		0			0
$871$	8.95293	+	15.5069i	0.303358	+	0.525432i
$872$	−11.9775			−0.405609
$873$		0			0
$874$	−3.15998			−0.106888
$875$	9.01534	+	15.6150i	0.304774	+	0.527884i
$876$		0			0
$877$	−15.2805	+	26.4666i	−0.515985	+	0.893713i	0.483842	+	0.875155i	$0.339241\pi$
$877$	−15.2805	+	26.4666i	−0.515985	+	0.893713i	−0.999828	+	0.0185578i	$0.994093\pi$
$878$	−2.23860	+	3.87738i	−0.0755492	+	0.130855i
$879$		0			0
$880$	−8.13728	−	14.0942i	−0.274308	−	0.475115i
$881$	10.3977			0.350309			0.175154	−	0.984541i	$-0.443958\pi$
$881$	10.3977			0.350309			0.175154	+	0.984541i	$0.443958\pi$
$882$		0			0
$883$	11.5454			0.388535			0.194267	−	0.980949i	$-0.437767\pi$
$883$	11.5454			0.388535			0.194267	+	0.980949i	$0.437767\pi$
$884$	16.2926	+	28.2197i	0.547980	+	0.949130i
$885$		0			0
$886$	−6.69807	+	11.6014i	−0.225026	+	0.389757i
$887$	2.86979	−	4.97062i	0.0963581	−	0.166897i	−0.813817	−	0.581122i	$-0.802614\pi$
$887$	2.86979	−	4.97062i	0.0963581	−	0.166897i	0.910175	+	0.414225i	$0.135947\pi$
$888$		0			0
$889$	12.7751	+	22.1270i	0.428461	+	0.742117i
$890$	49.1785			1.64847
$891$		0			0
$892$	19.1955			0.642712
$893$	17.5651	+	30.4236i	0.587793	+	1.01809i
$894$		0			0
$895$	−17.2429	+	29.8656i	−0.576367	+	0.998297i
$896$	−1.74607	+	3.02428i	−0.0583322	+	0.101034i
$897$		0			0
$898$	3.53535	+	6.12341i	0.117976	+	0.204341i
$899$	4.08469			0.136232
$900$		0			0
$901$	−40.7812			−1.35862
$902$	−13.1813	−	22.8307i	−0.438890	−	0.760179i
$903$		0			0
$904$	−1.92838	+	3.34005i	−0.0641369	+	0.111088i
$905$	−12.5956	+	21.8162i	−0.418692	+	0.725195i
$906$		0			0
$907$	−1.37140	−	2.37533i	−0.0455366	−	0.0788717i	0.842359	−	0.538917i	$-0.181166\pi$
$907$	−1.37140	−	2.37533i	−0.0455366	−	0.0788717i	−0.887895	+	0.460046i	$0.847833\pi$
$908$	−15.5775			−0.516958
$909$		0			0
$910$	60.7775			2.01476
$911$	23.1894	+	40.1653i	0.768301	+	1.33074i	0.938484	+	0.345323i	$0.112231\pi$
$911$	23.1894	+	40.1653i	0.768301	+	1.33074i	−0.170183	+	0.985412i	$0.554436\pi$
$912$		0			0
$913$	−15.8133	+	27.3894i	−0.523343	+	0.906456i
$914$	−0.00878737	+	0.0152202i	−0.000290660	+	0.000503438i
$915$		0			0
$916$	5.29223	+	9.16642i	0.174860	+	0.302867i
$917$	24.9723			0.824658
$918$		0			0
$919$	3.46521			0.114307			0.0571534	−	0.998365i	$-0.481798\pi$
$919$	3.46521			0.114307			0.0571534	+	0.998365i	$0.481798\pi$
$920$	−1.69714	−	2.93953i	−0.0559531	−	0.0969136i
$921$		0			0
$922$	−15.6892	+	27.1745i	−0.516696	+	0.894944i
$923$	−42.1636	+	73.0295i	−1.38783	+	2.40379i
$924$		0			0
$925$	32.2335	+	55.8300i	1.05983	+	1.83568i
$926$	−4.24714			−0.139570
$927$		0			0
$928$	2.45904			0.0807218
$929$	2.97858	+	5.15905i	0.0977240	+	0.169263i	0.910742	−	0.412975i	$-0.135510\pi$
$929$	2.97858	+	5.15905i	0.0977240	+	0.169263i	−0.813018	+	0.582238i	$0.802177\pi$
$930$		0			0
$931$	−8.20814	+	14.2169i	−0.269011	+	0.465940i
$932$	5.12383	−	8.87473i	0.167837	−	0.290702i
$933$		0			0
$934$	15.4896	+	26.8287i	0.506835	+	0.877863i
$935$	103.426			3.38238
$936$		0			0
$937$	24.1914			0.790299			0.395149	−	0.918617i	$-0.370693\pi$
$937$	24.1914			0.790299			0.395149	+	0.918617i	$0.370693\pi$
$938$	−6.09753	−	10.5612i	−0.199091	−	0.344837i
$939$		0			0
$940$	−18.8675	+	32.6795i	−0.615390	+	1.06589i
$941$	2.91264	−	5.04485i	0.0949495	−	0.164457i	−0.814638	−	0.579970i	$-0.803064\pi$
$941$	2.91264	−	5.04485i	0.0949495	−	0.164457i	0.909588	+	0.415512i	$0.136398\pi$
$942$		0			0
$943$	−2.74914	−	4.76165i	−0.0895243	−	0.155061i
$944$	−6.16058			−0.200510
$945$		0			0
$946$	3.71719			0.120856
$947$	−1.38014	−	2.39047i	−0.0448485	−	0.0776799i	0.842730	−	0.538337i	$-0.180947\pi$
$947$	−1.38014	−	2.39047i	−0.0448485	−	0.0776799i	−0.887578	+	0.460657i	$0.847614\pi$
$948$		0			0
$949$	15.1158	−	26.1813i	0.490679	−	0.849881i
$950$	−10.3033	+	17.8459i	−0.334284	+	0.578998i
$951$		0			0
$952$	−11.0964	−	19.2194i	−0.359635	−	0.622906i
$953$	−14.0362			−0.454679			−0.227339	−	0.973816i	$-0.573003\pi$
$953$	−14.0362			−0.454679			−0.227339	+	0.973816i	$0.573003\pi$
$954$		0			0
$955$	14.6416			0.473792
$956$	6.67263	+	11.5573i	0.215808	+	0.373791i
$957$		0			0
$958$	13.9406	−	24.1459i	0.450401	−	0.780117i
$959$	11.8122	−	20.4594i	0.381437	−	0.660668i
$960$		0			0
$961$	14.1204	+	24.4572i	0.455496	+	0.788943i
$962$	50.6893			1.63429
$963$		0			0
$964$	−30.0129			−0.966651
$965$	13.1185	+	22.7219i	0.422299	+	0.731443i
$966$		0			0
$967$	1.97836	−	3.42662i	0.0636197	−	0.110193i	−0.832461	−	0.554083i	$-0.813069\pi$
$967$	1.97836	−	3.42662i	0.0636197	−	0.110193i	0.896081	+	0.443891i	$0.146402\pi$
$968$	−5.99458	+	10.3829i	−0.192673	+	0.333720i
$969$		0			0
$970$	−2.61523	−	4.52972i	−0.0839701	−	0.145440i
$971$	−15.3862			−0.493767			−0.246884	−	0.969045i	$-0.579407\pi$
$971$	−15.3862			−0.493767			−0.246884	+	0.969045i	$0.579407\pi$
$972$		0			0
$973$	10.0092			0.320879
$974$	−10.4654	−	18.1266i	−0.335332	−	0.580813i
$975$		0			0
$976$	−0.632287	+	1.09515i	−0.0202390	+	0.0350550i
$977$	−13.0757	+	22.6477i	−0.418327	+	0.724564i	−0.995771	−	0.0918663i	$-0.970717\pi$
$977$	−13.0757	+	22.6477i	−0.418327	+	0.724564i	0.577444	+	0.816430i	$0.304050\pi$
$978$		0			0
$979$	−34.7344	−	60.1617i	−1.11012	−	1.92278i
$980$	−17.6335			−0.563282
$981$		0			0
$982$	36.6029			1.16804
$983$	23.6315	+	40.9310i	0.753728	+	1.30550i	0.946004	+	0.324155i	$0.105080\pi$
$983$	23.6315	+	40.9310i	0.753728	+	1.30550i	−0.192276	+	0.981341i	$0.561587\pi$
$984$		0			0
$985$	33.0379	−	57.2233i	1.05267	−	1.82329i
$986$	−7.81363	+	13.5336i	−0.248837	+	0.430998i
$987$		0			0
$988$	8.10134	+	14.0319i	0.257738	+	0.446415i
$989$	0.775270			0.0246522
$990$		0			0
$991$	−2.89228			−0.0918763			−0.0459382	−	0.998944i	$-0.514628\pi$
$991$	−2.89228			−0.0918763			−0.0459382	+	0.998944i	$0.514628\pi$
$992$	−0.830547	−	1.43855i	−0.0263699	−	0.0456740i
$993$		0			0
$994$	28.7162	−	49.7379i	0.910822	−	1.57759i
$995$	1.12265	−	1.94449i	0.0355905	−	0.0616445i
$996$		0			0
$997$	−16.0958	−	27.8787i	−0.509758	−	0.882927i	−0.999936	−	0.0113048i	$-0.996402\pi$
$997$	−16.0958	−	27.8787i	−0.509758	−	0.882927i	0.490178	−	0.871622i	$-0.336932\pi$
$998$	7.77793			0.246206
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1242.2.e.b.415.5		10
3.2	odd	2		414.2.e.d.139.4	✓	10
9.2	odd	6		414.2.e.d.277.4	yes	10
9.4	even	3		3726.2.a.u.1.1		5
9.5	odd	6		3726.2.a.r.1.5		5
9.7	even	3	inner	1242.2.e.b.829.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.4	✓	10	3.2	odd	2
414.2.e.d.277.4	yes	10	9.2	odd	6
1242.2.e.b.415.5		10	1.1	even	1	trivial
1242.2.e.b.829.5		10	9.7	even	3	inner
3726.2.a.r.1.5		5	9.5	odd	6
3726.2.a.u.1.1		5	9.4	even	3

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:	\( N \)	\(=\)	\( 1242 = 2 \cdot 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1242.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.69714 - 2.93953i) q^{5} +(-1.74607 - 3.02428i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.69714 - 2.93953i) q^{5} +(-1.74607 - 3.02428i) q^{7} +1.00000 q^{8} -3.39428 q^{10} +(2.39735 + 4.15233i) q^{11} +(2.56373 - 4.44052i) q^{13} +(-1.74607 + 3.02428i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.35504 q^{17} +3.15998 q^{19} +(1.69714 + 2.93953i) q^{20} +(2.39735 - 4.15233i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-3.26058 - 5.64748i) q^{25} -5.12747 q^{26} +3.49214 q^{28} +(-1.22952 - 2.12959i) q^{29} +(-0.830547 + 1.43855i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.17752 - 5.50362i) q^{34} -11.8533 q^{35} -9.88582 q^{37} +(-1.57999 - 2.73662i) q^{38} +(1.69714 - 2.93953i) q^{40} +(2.74914 - 4.76165i) q^{41} +(0.387635 + 0.671404i) q^{43} -4.79470 q^{44} -1.00000 q^{46} +(5.55862 + 9.62781i) q^{47} +(-2.59753 + 4.49906i) q^{49} +(-3.26058 + 5.64748i) q^{50} +(2.56373 + 4.44052i) q^{52} -6.41715 q^{53} +16.2746 q^{55} +(-1.74607 - 3.02428i) q^{56} +(-1.22952 + 2.12959i) q^{58} +(3.08029 - 5.33522i) q^{59} +(-0.632287 - 1.09515i) q^{61} +1.66109 q^{62} +1.00000 q^{64} +(-8.70204 - 15.0724i) q^{65} +(-1.74607 + 3.02428i) q^{67} +(-3.17752 + 5.50362i) q^{68} +(5.92666 + 10.2653i) q^{70} -16.4462 q^{71} +5.89600 q^{73} +(4.94291 + 8.56138i) q^{74} +(-1.57999 + 2.73662i) q^{76} +(8.37189 - 14.5005i) q^{77} +(-3.43033 - 5.94150i) q^{79} -3.39428 q^{80} -5.49828 q^{82} +(3.29807 + 5.71243i) q^{83} +(10.7854 - 18.6809i) q^{85} +(0.387635 - 0.671404i) q^{86} +(2.39735 + 4.15233i) q^{88} -14.4886 q^{89} -17.9059 q^{91} +(0.500000 + 0.866025i) q^{92} +(5.55862 - 9.62781i) q^{94} +(5.36292 - 9.28886i) q^{95} +(0.770482 + 1.33451i) q^{97} +5.19506 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

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