LMFDB - Embedded newform 819.2.o.d.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$-0.136945 - 0.237196i$ of defining polynomial
Character	$\chi$	$=$	819.757
Dual form			819.2.o.d.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18860 - 2.05872i) q^{2} +(-1.82555 + 3.16194i) q^{4} +4.02830 q^{5} +(0.500000 - 0.866025i) q^{7} +3.92498 q^{8} +O(q^{10})$	\(q+(-1.18860 - 2.05872i) q^{2} +(-1.82555 + 3.16194i) q^{4} +4.02830 q^{5} +(0.500000 - 0.866025i) q^{7} +3.92498 q^{8} +(-4.78804 - 8.29313i) q^{10} +(-1.63695 - 2.83527i) q^{11} +(0.910836 + 3.48861i) q^{13} -2.37720 q^{14} +(-1.01415 - 1.75656i) q^{16} +(-0.188601 + 0.326667i) q^{17} +(1.77389 - 3.07247i) q^{19} +(-7.35384 + 12.7372i) q^{20} +(-3.89135 + 6.74002i) q^{22} +(0.948344 + 1.64258i) q^{23} +11.2272 q^{25} +(6.09944 - 6.02172i) q^{26} +(1.82555 + 3.16194i) q^{28} +(-4.33969 - 7.51657i) q^{29} +6.33048 q^{31} +(1.51415 - 2.62258i) q^{32} +0.896688 q^{34} +(2.01415 - 3.48861i) q^{35} +(-2.01415 - 3.48861i) q^{37} -8.43380 q^{38} +15.8110 q^{40} +(3.75441 + 6.50282i) q^{41} +(4.32555 - 7.49207i) q^{43} +11.9533 q^{44} +(2.25441 - 3.90475i) q^{46} +12.1239 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-13.3446 - 23.1136i) q^{50} +(-12.6935 - 3.48861i) q^{52} -7.75441 q^{53} +(-6.59410 - 11.4213i) q^{55} +(1.96249 - 3.39914i) q^{56} +(-10.3163 + 17.8684i) q^{58} +(-1.05166 + 1.82152i) q^{59} +(-3.87720 + 6.71551i) q^{61} +(-7.52442 - 13.0327i) q^{62} -11.2555 q^{64} +(3.66912 + 14.0531i) q^{65} +(-2.79191 - 4.83574i) q^{67} +(-0.688601 - 1.19269i) q^{68} -9.57608 q^{70} +(1.99612 - 3.45739i) q^{71} +7.50106 q^{73} +(-4.78804 + 8.29313i) q^{74} +(6.47664 + 11.2179i) q^{76} -3.27389 q^{77} -1.16283 q^{79} +(-4.08529 - 7.07593i) q^{80} +(8.92498 - 15.4585i) q^{82} -15.1805 q^{83} +(-0.759742 + 1.31591i) q^{85} -20.5654 q^{86} +(-6.42498 - 11.1284i) q^{88} +(3.17939 + 5.50686i) q^{89} +(3.47664 + 0.955496i) q^{91} -6.92498 q^{92} +(-14.4104 - 24.9596i) q^{94} +(7.14576 - 12.3768i) q^{95} +(-2.48585 + 4.30562i) q^{97} +(-1.18860 + 2.05872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.18860	−	2.05872i	−0.840468	−	1.45573i	−0.889499	−	0.456936i	$-0.848947\pi$
$2$	−1.18860	−	2.05872i	−0.840468	−	1.45573i	0.0490313	−	0.998797i	$-0.484387\pi$
$3$		0			0
$3$		0			0
$4$	−1.82555	+	3.16194i	−0.912773	+	1.58097i
$5$	4.02830			1.80151			0.900754	−	0.434329i	$-0.143014\pi$
$5$	4.02830			1.80151			0.900754	+	0.434329i	$0.143014\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	3.92498			1.38769
$9$		0			0
$10$	−4.78804	−	8.29313i	−1.51411	−	2.62252i
$11$	−1.63695	−	2.83527i	−0.493558	−	0.854867i	0.506415	−	0.862290i	$-0.330970\pi$
$11$	−1.63695	−	2.83527i	−0.493558	−	0.854867i	−0.999972	+	0.00742317i	$0.997637\pi$
$12$		0			0
$13$	0.910836	+	3.48861i	0.252620	+	0.967565i
$13$	0.910836	+	3.48861i	0.252620	+	0.967565i
$14$	−2.37720			−0.635334
$15$		0			0
$16$	−1.01415	−	1.75656i	−0.253537	−	0.439139i
$17$	−0.188601	+	0.326667i	−0.0457426	+	0.0792284i	−0.887990	−	0.459862i	$-0.847899\pi$
$17$	−0.188601	+	0.326667i	−0.0457426	+	0.0792284i	0.842248	+	0.539091i	$0.181232\pi$
$18$		0			0
$19$	1.77389	−	3.07247i	0.406958	−	0.704873i	−0.587589	−	0.809160i	$-0.699923\pi$
$19$	1.77389	−	3.07247i	0.406958	−	0.704873i	0.994547	+	0.104287i	$0.0332561\pi$
$20$	−7.35384	+	12.7372i	−1.64437	+	2.84813i
$21$		0			0
$22$	−3.89135	+	6.74002i	−0.829639	+	1.43698i
$23$	0.948344	+	1.64258i	0.197743	+	0.342502i	0.947796	−	0.318876i	$-0.103305\pi$
$23$	0.948344	+	1.64258i	0.197743	+	0.342502i	−0.750053	+	0.661378i	$0.769972\pi$
$24$		0			0
$25$	11.2272			2.24543
$26$	6.09944	−	6.02172i	1.19620	−	1.18096i
$27$		0			0
$28$	1.82555	+	3.16194i	0.344996	+	0.597550i
$29$	−4.33969	−	7.51657i	−0.805861	−	1.39579i	−0.915708	−	0.401844i	$-0.868369\pi$
$29$	−4.33969	−	7.51657i	−0.805861	−	1.39579i	0.109847	−	0.993948i	$-0.464964\pi$
$30$		0			0
$31$	6.33048			1.13699			0.568494	−	0.822687i	$-0.307526\pi$
$31$	6.33048			1.13699			0.568494	+	0.822687i	$0.307526\pi$
$32$	1.51415	−	2.62258i	0.267666	−	0.463611i
$33$		0			0
$34$	0.896688			0.153781
$35$	2.01415	−	3.48861i	0.340453	−	0.589682i
$36$		0			0
$37$	−2.01415	−	3.48861i	−0.331124	−	0.573523i	0.651609	−	0.758555i	$-0.274094\pi$
$37$	−2.01415	−	3.48861i	−0.331124	−	0.573523i	−0.982733	+	0.185032i	$0.940761\pi$
$38$	−8.43380			−1.36814
$39$		0			0
$40$	15.8110			2.49994
$41$	3.75441	+	6.50282i	0.586340	+	1.01557i	0.994707	+	0.102752i	$0.0327649\pi$
$41$	3.75441	+	6.50282i	0.586340	+	1.01557i	−0.408367	+	0.912818i	$0.633902\pi$
$42$		0			0
$43$	4.32555	−	7.49207i	0.659640	−	1.14253i	−0.321069	−	0.947056i	$-0.604042\pi$
$43$	4.32555	−	7.49207i	0.659640	−	1.14253i	0.980709	−	0.195474i	$-0.0626244\pi$
$44$	11.9533			1.80202
$45$		0			0
$46$	2.25441	−	3.90475i	0.332394	−	0.575723i
$47$	12.1239			1.76845			0.884223	−	0.467064i	$-0.154688\pi$
$47$	12.1239			1.76845			0.884223	+	0.467064i	$0.154688\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−13.3446	−	23.1136i	−1.88722	−	3.26875i
$51$		0			0
$52$	−12.6935	−	3.48861i	−1.76028	−	0.483783i
$53$	−7.75441			−1.06515			−0.532575	−	0.846383i	$-0.678775\pi$
$53$	−7.75441			−1.06515			−0.532575	+	0.846383i	$0.678775\pi$
$54$		0			0
$55$	−6.59410	−	11.4213i	−0.889148	−	1.54005i
$56$	1.96249	−	3.39914i	0.262249	−	0.454229i
$57$		0			0
$58$	−10.3163	+	17.8684i	−1.35460	+	2.34624i
$59$	−1.05166	+	1.82152i	−0.136914	+	0.237142i	−0.926327	−	0.376720i	$-0.877052\pi$
$59$	−1.05166	+	1.82152i	−0.136914	+	0.237142i	0.789413	+	0.613862i	$0.210385\pi$
$60$		0			0
$61$	−3.87720	+	6.71551i	−0.496425	+	0.859833i	−0.999991	−	0.00412320i	$-0.998688\pi$
$61$	−3.87720	+	6.71551i	−0.496425	+	0.859833i	0.503567	+	0.863956i	$0.332021\pi$
$62$	−7.52442	−	13.0327i	−0.955602	−	1.65515i
$63$		0			0
$64$	−11.2555			−1.40693
$65$	3.66912	+	14.0531i	0.455098	+	1.74308i
$66$		0			0
$67$	−2.79191	−	4.83574i	−0.341087	−	0.590779i	0.643548	−	0.765406i	$-0.277462\pi$
$67$	−2.79191	−	4.83574i	−0.341087	−	0.590779i	−0.984635	+	0.174626i	$0.944128\pi$
$68$	−0.688601	−	1.19269i	−0.0835052	−	0.144635i
$69$		0			0
$70$	−9.57608			−1.14456
$71$	1.99612	−	3.45739i	0.236896	−	0.410317i	−0.722926	−	0.690926i	$-0.757203\pi$
$71$	1.99612	−	3.45739i	0.236896	−	0.410317i	0.959822	+	0.280609i	$0.0905365\pi$
$72$		0			0
$73$	7.50106			0.877933			0.438966	−	0.898503i	$-0.355345\pi$
$73$	7.50106			0.877933			0.438966	+	0.898503i	$0.355345\pi$
$74$	−4.78804	+	8.29313i	−0.556598	+	0.964056i
$75$		0			0
$76$	6.47664	+	11.2179i	0.742922	+	1.28678i
$77$	−3.27389			−0.373094
$78$		0			0
$79$	−1.16283			−0.130828			−0.0654142	−	0.997858i	$-0.520837\pi$
$79$	−1.16283			−0.130828			−0.0654142	+	0.997858i	$0.520837\pi$
$80$	−4.08529	−	7.07593i	−0.456749	−	0.791113i
$81$		0			0
$82$	8.92498	−	15.4585i	0.985600	−	1.70711i
$83$	−15.1805			−1.66627			−0.833135	−	0.553069i	$-0.813457\pi$
$83$	−15.1805			−1.66627			−0.833135	+	0.553069i	$0.813457\pi$
$84$		0			0
$85$	−0.759742	+	1.31591i	−0.0824056	+	0.142731i
$86$	−20.5654			−2.21762
$87$		0			0
$88$	−6.42498	−	11.1284i	−0.684906	−	1.18629i
$89$	3.17939	+	5.50686i	0.337015	+	0.583726i	0.983870	−	0.178886i	$-0.0572495\pi$
$89$	3.17939	+	5.50686i	0.337015	+	0.583726i	−0.646855	+	0.762613i	$0.723916\pi$
$90$		0			0
$91$	3.47664	+	0.955496i	0.364451	+	0.100163i
$92$	−6.92498			−0.721979
$93$		0			0
$94$	−14.4104	−	24.9596i	−1.48632	−	2.57439i
$95$	7.14576	−	12.3768i	0.733139	−	1.26983i
$96$		0			0
$97$	−2.48585	+	4.30562i	−0.252400	+	0.437170i	−0.964186	−	0.265227i	$-0.914553\pi$
$97$	−2.48585	+	4.30562i	−0.252400	+	0.437170i	0.711786	+	0.702396i	$0.247887\pi$
$98$	−1.18860	+	2.05872i	−0.120067	+	0.207962i
$99$		0			0
$100$	−20.4957	+	35.4996i	−2.04957	+	3.54996i
$101$	2.94834	+	5.10668i	0.293371	+	0.508134i	0.974605	−	0.223932i	$-0.0718895\pi$
$101$	2.94834	+	5.10668i	0.293371	+	0.508134i	−0.681233	+	0.732066i	$0.738556\pi$
$102$		0			0
$103$	10.5654			1.04104			0.520520	−	0.853849i	$-0.325738\pi$
$103$	10.5654			1.04104			0.520520	+	0.853849i	$0.325738\pi$
$104$	3.57502	+	13.6927i	0.350559	+	1.34268i
$105$		0			0
$106$	9.21690	+	15.9641i	0.895224	+	1.55057i
$107$	−6.20275	−	10.7435i	−0.599642	−	1.03861i	−0.992874	−	0.119172i	$-0.961976\pi$
$107$	−6.20275	−	10.7435i	−0.599642	−	1.03861i	0.393231	−	0.919440i	$-0.371357\pi$
$108$		0			0
$109$	−12.1316			−1.16200			−0.580999	−	0.813905i	$-0.697338\pi$
$109$	−12.1316			−1.16200			−0.580999	+	0.813905i	$0.697338\pi$
$110$	−15.6755	+	27.1508i	−1.49460	+	2.58873i
$111$		0			0
$112$	−2.02830			−0.191656
$113$	−5.33582	+	9.24191i	−0.501952	+	0.869406i	0.498046	+	0.867151i	$0.334051\pi$
$113$	−5.33582	+	9.24191i	−0.501952	+	0.869406i	−0.999997	+	0.00225510i	$0.999282\pi$
$114$		0			0
$115$	3.82021	+	6.61680i	0.356236	+	0.617020i
$116$	31.6893			2.94227
$117$		0			0
$118$	5.00000			0.460287
$119$	0.188601	+	0.326667i	0.0172891	+	0.0299455i
$120$		0			0
$121$	0.140820	−	0.243908i	0.0128018	−	0.0221734i
$122$	18.4338			1.66892
$123$		0			0
$124$	−11.5566	+	20.0166i	−1.03781	+	1.79754i
$125$	25.0849			2.24366
$126$		0			0
$127$	−3.66524	−	6.34838i	−0.325238	−	0.563328i	0.656323	−	0.754480i	$-0.272111\pi$
$127$	−3.66524	−	6.34838i	−0.325238	−	0.563328i	−0.981560	+	0.191152i	$0.938778\pi$
$128$	10.3500	+	17.9267i	0.914817	+	1.58451i
$129$		0			0
$130$	24.5703	−	24.2573i	2.15496	−	2.12750i
$131$	−11.4239			−0.998113			−0.499056	−	0.866570i	$-0.666320\pi$
$131$	−11.4239			−0.998113			−0.499056	+	0.866570i	$0.666320\pi$
$132$		0			0
$133$	−1.77389	−	3.07247i	−0.153816	−	0.266417i
$134$	−6.63695	+	11.4955i	−0.573345	+	0.993062i
$135$		0			0
$136$	−0.740258	+	1.28216i	−0.0634766	+	0.109945i
$137$	−1.59556	+	2.76359i	−0.136318	+	0.236110i	−0.926100	−	0.377278i	$-0.876860\pi$
$137$	−1.59556	+	2.76359i	−0.136318	+	0.236110i	0.789782	+	0.613387i	$0.210194\pi$
$138$		0			0
$139$	−2.68860	+	4.65679i	−0.228044	+	0.394984i	−0.957228	−	0.289333i	$-0.906566\pi$
$139$	−2.68860	+	4.65679i	−0.228044	+	0.394984i	0.729184	+	0.684317i	$0.239900\pi$
$140$	7.35384	+	12.7372i	0.621513	+	1.07649i
$141$		0			0
$142$	−9.49039			−0.796416
$143$	8.40016	−	8.29313i	0.702457	−	0.693506i
$144$		0			0
$145$	−17.4816	−	30.2790i	−1.45177	−	2.51453i
$146$	−8.91577	−	15.4426i	−0.737875	−	1.27804i
$147$		0			0
$148$	14.7077			1.20896
$149$	−5.01415	+	8.68476i	−0.410775	+	0.711483i	−0.994975	−	0.100127i	$-0.968075\pi$
$149$	−5.01415	+	8.68476i	−0.410775	+	0.711483i	0.584200	+	0.811610i	$0.301408\pi$
$150$		0			0
$151$	−9.71544			−0.790631			−0.395315	−	0.918545i	$-0.629365\pi$
$151$	−9.71544			−0.790631			−0.395315	+	0.918545i	$0.629365\pi$
$152$	6.96249	−	12.0594i	0.564733	−	0.978146i
$153$		0			0
$154$	3.89135	+	6.74002i	0.313574	+	0.543126i
$155$	25.5011			2.04829
$156$		0			0
$157$	17.5761			1.40272			0.701362	−	0.712805i	$-0.252576\pi$
$157$	17.5761			1.40272			0.701362	+	0.712805i	$0.252576\pi$
$158$	1.38214	+	2.39394i	0.109957	+	0.190451i
$159$		0			0
$160$	6.09944	−	10.5645i	0.482203	−	0.835200i
$161$	1.89669			0.149480
$162$		0			0
$163$	2.74559	−	4.75551i	0.215052	−	0.372480i	−0.738237	−	0.674541i	$-0.764341\pi$
$163$	2.74559	−	4.75551i	0.215052	−	0.372480i	0.953289	+	0.302061i	$0.0976747\pi$
$164$	−27.4154			−2.14078
$165$		0			0
$166$	18.0435	+	31.2523i	1.40045	+	2.42565i
$167$	2.21836	+	3.84231i	0.171662	+	0.297327i	0.939001	−	0.343914i	$-0.111753\pi$
$167$	2.21836	+	3.84231i	0.171662	+	0.297327i	−0.767339	+	0.641241i	$0.778420\pi$
$168$		0			0
$169$	−11.3408	+	6.35510i	−0.872366	+	0.488854i
$170$	3.61212			0.277037
$171$		0			0
$172$	15.7930	+	27.3542i	1.20420	+	2.08574i
$173$	11.0800	−	19.1910i	0.842393	−	1.45907i	−0.0454728	−	0.998966i	$-0.514479\pi$
$173$	11.0800	−	19.1910i	0.842393	−	1.45907i	0.887866	−	0.460102i	$-0.152187\pi$
$174$		0			0
$175$	5.61359	−	9.72302i	0.424347	−	0.734991i
$176$	−3.32021	+	5.75077i	−0.250270	+	0.433481i
$177$		0			0
$178$	7.55805	−	13.0909i	0.566500	−	0.981207i
$179$	−0.970242	−	1.68051i	−0.0725193	−	0.125607i	0.827486	−	0.561487i	$-0.189771\pi$
$179$	−0.970242	−	1.68051i	−0.0725193	−	0.125607i	−0.900005	+	0.435880i	$0.856437\pi$
$180$		0			0
$181$	−8.50106			−0.631879			−0.315939	−	0.948779i	$-0.602320\pi$
$181$	−8.50106			−0.631879			−0.315939	+	0.948779i	$0.602320\pi$
$182$	−2.16524	−	8.29313i	−0.160498	−	0.614727i
$183$		0			0
$184$	3.72223	+	6.44710i	0.274407	+	0.475286i
$185$	−8.11359	−	14.0531i	−0.596523	−	1.03321i
$186$		0			0
$187$	1.23492			0.0903064
$188$	−22.1327	+	38.3349i	−1.61419	+	2.79586i
$189$		0			0
$190$	−33.9738			−2.46472
$191$	0.325547	−	0.563863i	0.0235557	−	0.0407997i	−0.854007	−	0.520261i	$-0.825835\pi$
$191$	0.325547	−	0.563863i	0.0235557	−	0.0407997i	0.877563	+	0.479461i	$0.159168\pi$
$192$		0			0
$193$	−9.53217	−	16.5102i	−0.686141	−	1.18843i	−0.973077	−	0.230481i	$-0.925970\pi$
$193$	−9.53217	−	16.5102i	−0.686141	−	1.18843i	0.286936	−	0.957950i	$-0.407363\pi$
$194$	11.8187			0.848537
$195$		0			0
$196$	3.65109			0.260792
$197$	12.3549	+	21.3993i	0.880250	+	1.52464i	0.851062	+	0.525065i	$0.175959\pi$
$197$	12.3549	+	21.3993i	0.880250	+	1.52464i	0.0291881	+	0.999574i	$0.490708\pi$
$198$		0			0
$199$	−6.57220	+	11.3834i	−0.465891	+	0.806947i	−0.999241	−	0.0389475i	$-0.987599\pi$
$199$	−6.57220	+	11.3834i	−0.465891	+	0.806947i	0.533350	+	0.845895i	$0.320933\pi$
$200$	44.0665			3.11597
$201$		0			0
$202$	7.00881	−	12.1396i	0.493138	−	0.854141i
$203$	−8.67939			−0.609174
$204$		0			0
$205$	15.1239	+	26.1953i	1.05630	+	1.82956i
$206$	−12.5581	−	21.7512i	−0.874961	−	1.51548i
$207$		0			0
$208$	5.20421	−	5.13790i	0.360847	−	0.356249i
$209$	−11.6150			−0.803430
$210$		0			0
$211$	9.79831	+	16.9712i	0.674544	+	1.16834i	0.976602	+	0.215054i	$0.0689929\pi$
$211$	9.79831	+	16.9712i	0.674544	+	1.16834i	−0.302058	+	0.953289i	$0.597674\pi$
$212$	14.1560	−	24.5190i	0.972240	−	1.68397i
$213$		0			0
$214$	−14.7452	+	25.5394i	−1.00796	+	1.74584i
$215$	17.4246	−	30.1803i	1.18835	−	2.05828i
$216$		0			0
$217$	3.16524	−	5.48236i	0.214871	−	0.372167i
$218$	14.4196	+	24.9756i	0.976622	+	1.69156i
$219$		0			0
$220$	48.1514			3.24636
$221$	−1.31140	−	0.360416i	−0.0882142	−	0.0242442i
$222$		0			0
$223$	13.9338	+	24.1340i	0.933076	+	1.61613i	0.778029	+	0.628228i	$0.216219\pi$
$223$	13.9338	+	24.1340i	0.933076	+	1.61613i	0.155046	+	0.987907i	$0.450447\pi$
$224$	−1.51415	−	2.62258i	−0.101168	−	0.175229i
$225$		0			0
$226$	25.3687			1.68750
$227$	6.01521	−	10.4186i	0.399243	−	0.691510i	−0.594389	−	0.804177i	$-0.702606\pi$
$227$	6.01521	−	10.4186i	0.399243	−	0.691510i	0.993633	+	0.112667i	$0.0359395\pi$
$228$		0			0
$229$	−9.19887			−0.607879			−0.303939	−	0.952691i	$-0.598302\pi$
$229$	−9.19887			−0.607879			−0.303939	+	0.952691i	$0.598302\pi$
$230$	9.08141	−	15.7295i	0.598811	−	1.03717i
$231$		0			0
$232$	−17.0332	−	29.5024i	−1.11829	−	1.93693i
$233$	12.4522			0.815772			0.407886	−	0.913033i	$-0.366266\pi$
$233$	12.4522			0.815772			0.407886	+	0.913033i	$0.366266\pi$
$234$		0			0
$235$	48.8385			3.18587
$236$	−3.83969	−	6.65055i	−0.249943	−	0.432914i
$237$		0			0
$238$	0.448344	−	0.776554i	0.0290618	−	0.0503365i
$239$	3.24559			0.209940			0.104970	−	0.994475i	$-0.466525\pi$
$239$	3.24559			0.209940			0.104970	+	0.994475i	$0.466525\pi$
$240$		0			0
$241$	−4.71302	+	8.16319i	−0.303592	+	0.525838i	−0.976947	−	0.213482i	$-0.931519\pi$
$241$	−4.71302	+	8.16319i	−0.303592	+	0.525838i	0.673354	+	0.739320i	$0.264853\pi$
$242$	−0.669517			−0.0430382
$243$		0			0
$244$	−14.1560	−	24.5190i	−0.906247	−	1.56967i
$245$	−2.01415	−	3.48861i	−0.128679	−	0.222879i
$246$		0			0
$247$	12.3344	+	3.38989i	0.784816	+	0.215694i
$248$	24.8470			1.57779
$249$		0			0
$250$	−29.8159	−	51.6427i	−1.88573	−	3.26617i
$251$	−5.99466	+	10.3831i	−0.378380	+	0.655373i	−0.990827	−	0.135139i	$-0.956852\pi$
$251$	−5.99466	+	10.3831i	−0.378380	+	0.655373i	0.612447	+	0.790512i	$0.290185\pi$
$252$		0			0
$253$	3.10477	−	5.37763i	0.195195	−	0.338088i
$254$	−8.71302	+	15.0914i	−0.546704	+	0.946919i
$255$		0			0
$256$	13.3485	−	23.1203i	0.834282	−	1.44502i
$257$	7.29831	+	12.6410i	0.455256	+	0.788527i	0.998703	−	0.0509168i	$-0.0162143\pi$
$257$	7.29831	+	12.6410i	0.455256	+	0.788527i	−0.543447	+	0.839444i	$0.682881\pi$
$258$		0			0
$259$	−4.02830			−0.250306
$260$	−51.1333	−	14.0531i	−3.17115	−	0.871539i
$261$		0			0
$262$	13.5785	+	23.5186i	0.838882	+	1.45299i
$263$	11.3266	+	19.6183i	0.698429	+	1.20971i	0.969011	+	0.247017i	$0.0794504\pi$
$263$	11.3266	+	19.6183i	0.698429	+	1.20971i	−0.270583	+	0.962697i	$0.587216\pi$
$264$		0			0
$265$	−31.2370			−1.91888
$266$	−4.21690	+	7.30388i	−0.258555	+	0.447830i
$267$		0			0
$268$	20.3871			1.24534
$269$	−13.9947	+	24.2395i	−0.853270	+	1.47791i	0.0249713	+	0.999688i	$0.492051\pi$
$269$	−13.9947	+	24.2395i	−0.853270	+	1.47791i	−0.878241	+	0.478218i	$0.841283\pi$
$270$		0			0
$271$	3.80365	+	6.58811i	0.231055	+	0.400199i	0.958119	−	0.286371i	$-0.0924489\pi$
$271$	3.80365	+	6.58811i	0.231055	+	0.400199i	−0.727064	+	0.686570i	$0.759116\pi$
$272$	0.765079			0.0463897
$273$		0			0
$274$	7.58595			0.458284
$275$	−18.3783	−	31.8321i	−1.10825	−	1.91955i
$276$		0			0
$277$	3.44447	−	5.96599i	0.206958	−	0.358462i	−0.743797	−	0.668406i	$-0.766977\pi$
$277$	3.44447	−	5.96599i	0.206958	−	0.358462i	0.950755	+	0.309944i	$0.100310\pi$
$278$	12.7827			0.766656
$279$		0			0
$280$	7.90550	−	13.6927i	0.472444	−	0.818297i
$281$	−10.8062			−0.644642			−0.322321	−	0.946630i	$-0.604463\pi$
$281$	−10.8062			−0.644642			−0.322321	+	0.946630i	$0.604463\pi$
$282$		0			0
$283$	3.81246	+	6.60337i	0.226627	+	0.392530i	0.956806	−	0.290726i	$-0.0938968\pi$
$283$	3.81246	+	6.60337i	0.226627	+	0.392530i	−0.730179	+	0.683256i	$0.760563\pi$
$284$	7.28804	+	12.6233i	0.432466	+	0.749052i
$285$		0			0
$286$	−27.0577	−	7.43634i	−1.59995	−	0.439720i
$287$	7.50881			0.443231
$288$		0			0
$289$	8.42886	+	14.5992i	0.495815	+	0.858777i
$290$	−41.5573	+	71.9793i	−2.44033	+	4.22677i
$291$		0			0
$292$	−13.6935	+	23.7179i	−0.801354	+	1.38799i
$293$	−11.1458	+	19.3050i	−0.651142	+	1.12781i	0.331704	+	0.943384i	$0.392376\pi$
$293$	−11.1458	+	19.3050i	−0.651142	+	1.12781i	−0.982846	+	0.184428i	$0.940957\pi$
$294$		0			0
$295$	−4.23638	+	7.33763i	−0.246652	+	0.427213i
$296$	−7.90550	−	13.6927i	−0.459498	−	0.795874i
$297$		0			0
$298$	23.8393			1.38097
$299$	−4.86653	+	4.80452i	−0.281439	+	0.277853i
$300$		0			0
$301$	−4.32555	−	7.49207i	−0.249320	−	0.431836i
$302$	11.5478	+	20.0013i	0.664500	+	1.15095i
$303$		0			0
$304$	−7.19595			−0.412716
$305$	−15.6185	+	27.0521i	−0.894314	+	1.54900i
$306$		0			0
$307$	−28.2448			−1.61202			−0.806008	−	0.591905i	$-0.798376\pi$
$307$	−28.2448			−1.61202			−0.806008	+	0.591905i	$0.798376\pi$
$308$	5.97664	−	10.3518i	0.340551	−	0.589851i
$309$		0			0
$310$	−30.3106	−	52.4995i	−1.72153	−	2.98177i
$311$	2.66177			0.150935			0.0754675	−	0.997148i	$-0.475955\pi$
$311$	2.66177			0.150935			0.0754675	+	0.997148i	$0.475955\pi$
$312$		0			0
$313$	−22.4826			−1.27079			−0.635397	−	0.772186i	$-0.719163\pi$
$313$	−22.4826			−1.27079			−0.635397	+	0.772186i	$0.719163\pi$
$314$	−20.8910	−	36.1842i	−1.17894	−	2.04199i
$315$		0			0
$316$	2.12280	−	3.67679i	0.119417	−	0.206836i
$317$	−18.8315			−1.05768			−0.528842	−	0.848720i	$-0.677374\pi$
$317$	−18.8315			−1.05768			−0.528842	+	0.848720i	$0.677374\pi$
$318$		0			0
$319$	−14.2077	+	24.6084i	−0.795478	+	1.37781i
$320$	−45.3404			−2.53460
$321$		0			0
$322$	−2.25441	−	3.90475i	−0.125633	−	0.217603i
$323$	0.669117	+	1.15894i	0.0372306	+	0.0644854i
$324$		0			0
$325$	10.2261	+	39.1672i	0.567242	+	2.17260i
$326$	−13.0537			−0.722976
$327$		0			0
$328$	14.7360	+	25.5235i	0.813659	+	1.40930i
$329$	6.06193	−	10.4996i	0.334205	−	0.578860i
$330$		0			0
$331$	8.91577	−	15.4426i	0.490055	−	0.848800i	−0.509879	−	0.860246i	$-0.670310\pi$
$331$	8.91577	−	15.4426i	0.490055	−	0.848800i	0.999934	+	0.0114455i	$0.00364329\pi$
$332$	27.7126	−	47.9997i	1.52093	−	2.63432i
$333$		0			0
$334$	5.27349	−	9.13395i	0.288553	−	0.499788i
$335$	−11.2467	−	19.4798i	−0.614470	−	1.06429i
$336$		0			0
$337$	7.57608			0.412695			0.206348	−	0.978479i	$-0.433842\pi$
$337$	7.57608			0.412695			0.206348	+	0.978479i	$0.433842\pi$
$338$	26.5630	+	15.7937i	1.44484	+	0.859066i
$339$		0			0
$340$	−2.77389	−	4.80452i	−0.150435	−	0.260562i
$341$	−10.3627	−	17.9486i	−0.561169	−	0.971974i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	16.9777	−	29.4062i	0.915376	−	1.58548i
$345$		0			0
$346$	−52.6786			−2.83202
$347$	3.94407	−	6.83133i	0.211729	−	0.366725i	−0.740527	−	0.672027i	$-0.765424\pi$
$347$	3.94407	−	6.83133i	0.211729	−	0.366725i	0.952256	+	0.305302i	$0.0987573\pi$
$348$		0			0
$349$	5.86693	+	10.1618i	0.314050	+	0.543950i	0.979235	−	0.202728i	$-0.0649809\pi$
$349$	5.86693	+	10.1618i	0.314050	+	0.543950i	−0.665185	+	0.746678i	$0.731648\pi$
$350$	−26.6893			−1.42660
$351$		0			0
$352$	−9.91431			−0.528435
$353$	−6.26855	−	10.8575i	−0.333641	−	0.577884i	0.649581	−	0.760292i	$-0.274944\pi$
$353$	−6.26855	−	10.8575i	−0.333641	−	0.577884i	−0.983223	+	0.182408i	$0.941611\pi$
$354$		0			0
$355$	8.04098	−	13.9274i	0.426771	−	0.739189i
$356$	−23.2165			−1.23047
$357$		0			0
$358$	−2.30646	+	3.99491i	−0.121900	+	0.211138i
$359$	5.01762			0.264820			0.132410	−	0.991195i	$-0.457728\pi$
$359$	5.01762			0.264820			0.132410	+	0.991195i	$0.457728\pi$
$360$		0			0
$361$	3.20662	+	5.55404i	0.168770	+	0.292318i
$362$	10.1044	+	17.5013i	0.531074	+	0.919847i
$363$		0			0
$364$	−9.36799	+	9.24862i	−0.491016	+	0.484760i
$365$	30.2165			1.58160
$366$		0			0
$367$	−11.8549	−	20.5333i	−0.618821	−	1.07183i	−0.989701	−	0.143149i	$-0.954277\pi$
$367$	−11.8549	−	20.5333i	−0.618821	−	1.07183i	0.370880	−	0.928681i	$-0.379056\pi$
$368$	1.92352	−	3.33164i	0.100271	−	0.173674i
$369$		0			0
$370$	−19.2876	+	33.4072i	−1.00272	+	1.73676i
$371$	−3.87720	+	6.71551i	−0.201294	+	0.348652i
$372$		0			0
$373$	4.97664	−	8.61979i	0.257681	−	0.446316i	−0.707940	−	0.706273i	$-0.750375\pi$
$373$	4.97664	−	8.61979i	0.257681	−	0.446316i	0.965620	+	0.259957i	$0.0837084\pi$
$374$	−1.46783	−	2.54235i	−0.0758996	−	0.131462i
$375$		0			0
$376$	47.5860			2.45406
$377$	22.2696	−	21.9859i	1.14694	−	1.13233i
$378$		0			0
$379$	13.9250	+	24.1188i	0.715278	+	1.23890i	0.962852	+	0.270029i	$0.0870334\pi$
$379$	13.9250	+	24.1188i	0.715278	+	1.23890i	−0.247574	+	0.968869i	$0.579633\pi$
$380$	26.0898	+	45.1889i	1.33838	+	2.31814i
$381$		0			0
$382$	−1.54778			−0.0791914
$383$	−3.45222	+	5.97942i	−0.176400	+	0.305534i	−0.940645	−	0.339392i	$-0.889779\pi$
$383$	−3.45222	+	5.97942i	−0.176400	+	0.305534i	0.764245	+	0.644926i	$0.223112\pi$
$384$		0			0
$385$	−13.1882			−0.672133
$386$	−22.6599	+	39.2481i	−1.15336	+	1.99768i
$387$		0			0
$388$	−9.07608	−	15.7202i	−0.460768	−	0.798074i
$389$	28.3764			1.43874			0.719370	−	0.694627i	$-0.244430\pi$
$389$	28.3764			1.43874			0.719370	+	0.694627i	$0.244430\pi$
$390$		0			0
$391$	−0.715436			−0.0361812
$392$	−1.96249	−	3.39914i	−0.0991208	−	0.171682i
$393$		0			0
$394$	29.3701	−	50.8705i	1.47964	−	2.56282i
$395$	−4.68422			−0.235689
$396$		0			0
$397$	2.38360	−	4.12852i	0.119630	−	0.207204i	−0.799991	−	0.600011i	$-0.795163\pi$
$397$	2.38360	−	4.12852i	0.119630	−	0.207204i	0.919621	+	0.392807i	$0.128496\pi$
$398$	31.2469			1.56627
$399$		0			0
$400$	−11.3860	−	19.7212i	−0.569301	−	0.986058i
$401$	−4.13307	−	7.15869i	−0.206396	−	0.357488i	0.744181	−	0.667978i	$-0.232840\pi$
$401$	−4.13307	−	7.15869i	−0.206396	−	0.357488i	−0.950577	+	0.310490i	$0.899507\pi$
$402$		0			0
$403$	5.76603	+	22.0846i	0.287226	+	1.10011i
$404$	−21.5294			−1.07113
$405$		0			0
$406$	10.3163	+	17.8684i	0.511991	+	0.886795i
$407$	−6.59410	+	11.4213i	−0.326857	+	0.566134i
$408$		0			0
$409$	−10.7169	+	18.5622i	−0.529916	+	0.917842i	0.469474	+	0.882946i	$0.344443\pi$
$409$	−10.7169	+	18.5622i	−0.529916	+	0.917842i	−0.999391	+	0.0348962i	$0.988890\pi$
$410$	35.9525	−	62.2715i	1.77557	−	3.07537i
$411$		0			0
$412$	−19.2876	+	33.4072i	−0.950234	+	1.64585i
$413$	1.05166	+	1.82152i	0.0517486	+	0.0896312i
$414$		0			0
$415$	−61.1514			−3.00180
$416$	10.5283	+	2.89353i	0.516192	+	0.141867i
$417$		0			0
$418$	13.8057	+	23.9121i	0.675257	+	1.16958i
$419$	−1.14576	−	1.98451i	−0.0559739	−	0.0969496i	0.836681	−	0.547691i	$-0.184493\pi$
$419$	−1.14576	−	1.98451i	−0.0559739	−	0.0969496i	−0.892655	+	0.450741i	$0.851160\pi$
$420$		0			0
$421$	7.61292			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$421$	7.61292			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$422$	23.2926	−	40.3439i	1.13386	−	1.96391i
$423$		0			0
$424$	−30.4359			−1.47810
$425$	−2.11746	+	3.66755i	−0.102712	+	0.177902i
$426$		0			0
$427$	3.87720	+	6.71551i	0.187631	+	0.324986i
$428$	45.2936			2.18935
$429$		0			0
$430$	−82.8435			−3.99507
$431$	10.4314	+	18.0677i	0.502462	+	0.870290i	0.999996	+	0.00284520i	$0.000905656\pi$
$431$	10.4314	+	18.0677i	0.502462	+	0.870290i	−0.497534	+	0.867444i	$0.665761\pi$
$432$		0			0
$433$	11.6882	−	20.2446i	0.561699	−	0.972891i	−0.435649	−	0.900116i	$-0.643481\pi$
$433$	11.6882	−	20.2446i	0.561699	−	0.972891i	0.997348	−	0.0727749i	$-0.0231855\pi$
$434$	−15.0488			−0.722368
$435$		0			0
$436$	22.1468	−	38.3594i	1.06064	−	1.83708i
$437$	6.72903			0.321893
$438$		0			0
$439$	−4.57754	−	7.92853i	−0.218474	−	0.378408i	0.735868	−	0.677125i	$-0.236775\pi$
$439$	−4.57754	−	7.92853i	−0.218474	−	0.378408i	−0.954342	+	0.298717i	$0.903441\pi$
$440$	−25.8817	−	44.8285i	−1.23386	−	2.13711i
$441$		0			0
$442$	0.816735	+	3.12819i	0.0388481	+	0.148793i
$443$	−11.2632			−0.535132			−0.267566	−	0.963540i	$-0.586219\pi$
$443$	−11.2632			−0.535132			−0.267566	+	0.963540i	$0.586219\pi$
$444$		0			0
$445$	12.8075	+	22.1833i	0.607135	+	1.05159i
$446$	33.1235	−	57.3715i	1.56844	−	2.71662i
$447$		0			0
$448$	−5.62773	+	9.74752i	−0.265885	+	0.460527i
$449$	−16.8924	+	29.2585i	−0.797202	+	1.38079i	0.124229	+	0.992254i	$0.460354\pi$
$449$	−16.8924	+	29.2585i	−0.797202	+	1.38079i	−0.921431	+	0.388541i	$0.872979\pi$
$450$		0			0
$451$	12.2915	−	21.2895i	0.578785	−	1.00248i
$452$	−19.4816	−	33.7431i	−0.916336	−	1.58714i
$453$		0			0
$454$	−28.5987			−1.34221
$455$	14.0049	+	3.84902i	0.656562	+	0.180445i
$456$		0			0
$457$	−17.1472	−	29.6999i	−0.802113	−	1.38930i	−0.918223	−	0.396064i	$-0.870376\pi$
$457$	−17.1472	−	29.6999i	−0.802113	−	1.38930i	0.116110	−	0.993236i	$-0.462958\pi$
$458$	10.9338	+	18.9379i	0.510903	+	0.884909i
$459$		0			0
$460$	−27.8959			−1.30065
$461$	9.66630	−	16.7425i	0.450205	−	0.779777i	−0.548194	−	0.836351i	$-0.684684\pi$
$461$	9.66630	−	16.7425i	0.450205	−	0.779777i	0.998398	+	0.0565741i	$0.0180177\pi$
$462$		0			0
$463$	6.29444			0.292527			0.146264	−	0.989246i	$-0.453275\pi$
$463$	6.29444			0.292527			0.146264	+	0.989246i	$0.453275\pi$
$464$	−8.80219	+	15.2458i	−0.408631	+	0.707770i
$465$		0			0
$466$	−14.8007	−	25.6356i	−0.685630	−	1.18755i
$467$	−24.2293			−1.12120			−0.560599	−	0.828087i	$-0.689429\pi$
$467$	−24.2293			−1.12120			−0.560599	+	0.828087i	$0.689429\pi$
$468$		0			0
$469$	−5.58383			−0.257837
$470$	−58.0495	−	100.545i	−2.67762	−	4.63778i
$471$		0			0
$472$	−4.12773	+	7.14944i	−0.189994	+	0.329080i
$473$	−28.3227			−1.30228
$474$		0			0
$475$	19.9158	−	34.4951i	0.913798	−	1.58275i
$476$	−1.37720			−0.0631240
$477$		0			0
$478$	−3.85772	−	6.68176i	−0.176448	−	0.305617i
$479$	−16.8149	−	29.1242i	−0.768291	−	1.33072i	−0.938489	−	0.345309i	$-0.887774\pi$
$479$	−16.8149	−	29.1242i	−0.768291	−	1.33072i	0.170198	−	0.985410i	$-0.445559\pi$
$480$		0			0
$481$	10.3358	−	10.2041i	0.471273	−	0.465268i
$482$	22.4076			1.02064
$483$		0			0
$484$	0.514148	+	0.890531i	0.0233704	+	0.0404787i
$485$	−10.0137	+	17.3443i	−0.454701	+	0.787565i
$486$		0			0
$487$	3.96249	−	6.86324i	0.179558	−	0.311003i	−0.762171	−	0.647375i	$-0.775867\pi$
$487$	3.96249	−	6.86324i	0.179558	−	0.311003i	0.941729	+	0.336372i	$0.109200\pi$
$488$	−15.2180	+	26.3583i	−0.688885	+	1.19318i
$489$		0			0
$490$	−4.78804	+	8.29313i	−0.216302	+	0.374645i
$491$	1.21584	+	2.10589i	0.0548699	+	0.0950375i	0.892156	−	0.451728i	$-0.149192\pi$
$491$	1.21584	+	2.10589i	0.0548699	+	0.0950375i	−0.837286	+	0.546766i	$0.815859\pi$
$492$		0			0
$493$	3.27389			0.147449
$494$	−7.68180	−	29.4222i	−0.345621	−	1.32377i
$495$		0			0
$496$	−6.42005	−	11.1198i	−0.288269	−	0.499296i
$497$	−1.99612	−	3.45739i	−0.0895384	−	0.155085i
$498$		0			0
$499$	−18.5838			−0.831926			−0.415963	−	0.909381i	$-0.636555\pi$
$499$	−18.5838			−0.831926			−0.415963	+	0.909381i	$0.636555\pi$
$500$	−45.7936	+	79.3169i	−2.04795	+	3.54716i
$501$		0			0
$502$	28.5011			1.27206
$503$	−8.72717	+	15.1159i	−0.389125	+	0.673985i	−0.992332	−	0.123600i	$-0.960556\pi$
$503$	−8.72717	+	15.1159i	−0.389125	+	0.673985i	0.603207	+	0.797585i	$0.293889\pi$
$504$		0			0
$505$	11.8768	+	20.5712i	0.528511	+	0.915408i
$506$	−14.7614			−0.656222
$507$		0			0
$508$	26.7643			1.18747
$509$	1.38495	+	2.39881i	0.0613870	+	0.106325i	0.895086	−	0.445894i	$-0.147114\pi$
$509$	1.38495	+	2.39881i	0.0613870	+	0.106325i	−0.833699	+	0.552220i	$0.813781\pi$
$510$		0			0
$511$	3.75053	−	6.49611i	0.165914	−	0.287371i
$512$	−22.0643			−0.975115
$513$		0			0
$514$	17.3496	−	30.0503i	0.765257	−	1.32546i
$515$	42.5606			1.87544
$516$		0			0
$517$	−19.8461	−	34.3744i	−0.872830	−	1.51179i
$518$	4.78804	+	8.29313i	0.210374	+	0.364379i
$519$		0			0
$520$	14.4012	+	55.1584i	0.631535	+	2.41885i
$521$	26.2816			1.15142			0.575710	−	0.817654i	$-0.304726\pi$
$521$	26.2816			1.15142			0.575710	+	0.817654i	$0.304726\pi$
$522$		0			0
$523$	−2.62521	−	4.54700i	−0.114792	−	0.198826i	0.802904	−	0.596108i	$-0.203287\pi$
$523$	−2.62521	−	4.54700i	−0.114792	−	0.198826i	−0.917697	+	0.397282i	$0.869954\pi$
$524$	20.8549	−	36.1218i	0.911051	−	1.57799i
$525$		0			0
$526$	26.9256	−	46.6366i	1.17401	−	2.03345i
$527$	−1.19394	+	2.06796i	−0.0520088	+	0.0900818i
$528$		0			0
$529$	9.70129	−	16.8031i	0.421795	−	0.730571i
$530$	37.1284	+	64.3083i	1.61275	+	2.79337i
$531$		0			0
$532$	12.9533			0.561596
$533$	−19.2661	+	19.0206i	−0.834509	+	0.823876i
$534$		0			0
$535$	−24.9865	−	43.2779i	−1.08026	−	1.87107i
$536$	−10.9582	−	18.9802i	−0.473323	−	0.819819i
$537$		0			0
$538$	66.5363			2.86858
$539$	−1.63695	+	2.83527i	−0.0705082	+	0.122124i
$540$		0			0
$541$	−0.111863			−0.00480937			−0.00240468	−	0.999997i	$-0.500765\pi$
$541$	−0.111863			−0.00480937			−0.00240468	+	0.999997i	$0.500765\pi$
$542$	9.04204	−	15.6613i	0.388389	−	0.672710i
$543$		0			0
$544$	0.571141	+	0.989245i	0.0244875	+	0.0424135i
$545$	−48.8697			−2.09335
$546$		0			0
$547$	−33.7515			−1.44311			−0.721555	−	0.692358i	$-0.756572\pi$
$547$	−33.7515			−1.44311			−0.721555	+	0.692358i	$0.756572\pi$
$548$	−5.82555	−	10.0901i	−0.248855	−	0.431030i
$549$		0			0
$550$	−43.6889	+	75.6713i	−1.86290	+	3.22664i
$551$	−30.7926			−1.31181
$552$		0			0
$553$	−0.581414	+	1.00704i	−0.0247242	+	0.0428236i
$554$	−16.3764			−0.695767
$555$		0			0
$556$	−9.81633	−	17.0024i	−0.416305	−	0.721062i
$557$	14.5073	+	25.1275i	0.614696	+	1.06468i	0.990438	+	0.137960i	$0.0440547\pi$
$557$	14.5073	+	25.1275i	0.614696	+	1.06468i	−0.375742	+	0.926724i	$0.622612\pi$
$558$		0			0
$559$	30.0767	+	8.26609i	1.27211	+	0.349618i
$560$	−8.17058			−0.345270
$561$		0			0
$562$	12.8442	+	22.2469i	0.541801	+	0.938427i
$563$	0.715836	−	1.23986i	0.0301689	−	0.0522541i	−0.850547	−	0.525899i	$-0.823729\pi$
$563$	0.715836	−	1.23986i	0.0301689	−	0.0522541i	0.880716	+	0.473645i	$0.157062\pi$
$564$		0			0
$565$	−21.4943	+	37.2292i	−0.904270	+	1.56624i
$566$	9.06299	−	15.6976i	0.380946	−	0.659818i
$567$		0			0
$568$	7.83476	−	13.5702i	0.328739	−	0.569393i
$569$	−12.2505	−	21.2185i	−0.513569	−	0.889528i	−0.999876	−	0.0157396i	$-0.994990\pi$
$569$	−12.2505	−	21.2185i	−0.513569	−	0.889528i	0.486307	−	0.873788i	$-0.338344\pi$
$570$		0			0
$571$	−47.3735			−1.98252			−0.991259	−	0.131929i	$-0.957883\pi$
$571$	−47.3735			−1.98252			−0.991259	+	0.131929i	$0.957883\pi$
$572$	10.8875	+	41.7003i	0.455228	+	1.74358i
$573$		0			0
$574$	−8.92498	−	15.4585i	−0.372522	−	0.645226i
$575$	10.6472	+	18.4415i	0.444020	+	0.769065i
$576$		0			0
$577$	27.4055			1.14091			0.570453	−	0.821330i	$-0.306768\pi$
$577$	27.4055			1.14091			0.570453	+	0.821330i	$0.306768\pi$
$578$	20.0371	−	34.7053i	0.833434	−	1.44355i
$579$		0			0
$580$	127.654			5.30053
$581$	−7.59023	+	13.1467i	−0.314896	+	0.545415i
$582$		0			0
$583$	12.6935	+	21.9859i	0.525713	+	0.910561i
$584$	29.4415			1.21830
$585$		0			0
$586$	52.9914			2.18906
$587$	13.9479	+	24.1585i	0.575693	+	0.997130i	0.995966	+	0.0897321i	$0.0286011\pi$
$587$	13.9479	+	24.1585i	0.575693	+	0.997130i	−0.420273	+	0.907398i	$0.638066\pi$
$588$		0			0
$589$	11.2296	−	19.4502i	0.462707	−	0.801432i
$590$	20.1415			0.829212
$591$		0			0
$592$	−4.08529	+	7.07593i	−0.167904	+	0.290819i
$593$	16.6015			0.681740			0.340870	−	0.940110i	$-0.389278\pi$
$593$	16.6015			0.681740			0.340870	+	0.940110i	$0.389278\pi$
$594$		0			0
$595$	0.759742	+	1.31591i	0.0311464	+	0.0539472i
$596$	−18.3071	−	31.7089i	−0.749889	−	1.29885i
$597$		0			0
$598$	15.6755	+	4.30815i	0.641019	+	0.176173i
$599$	−11.7913			−0.481778			−0.240889	−	0.970553i	$-0.577439\pi$
$599$	−11.7913			−0.481778			−0.240889	+	0.970553i	$0.577439\pi$
$600$		0			0
$601$	−6.91084	−	11.9699i	−0.281899	−	0.488263i	0.689954	−	0.723854i	$-0.257631\pi$
$601$	−6.91084	−	11.9699i	−0.281899	−	0.488263i	−0.971852	+	0.235590i	$0.924298\pi$
$602$	−10.2827	+	17.8102i	−0.419092	+	0.725888i
$603$		0			0
$604$	17.7360	−	30.7196i	0.721667	−	1.24996i
$605$	0.567266	−	0.982533i	0.0230626	−	0.0399457i
$606$		0			0
$607$	10.5474	−	18.2686i	0.428105	−	0.741500i	−0.568600	−	0.822614i	$-0.692515\pi$
$607$	10.5474	−	18.2686i	0.428105	−	0.741500i	0.996705	+	0.0811147i	$0.0258480\pi$
$608$	−5.37187	−	9.30435i	−0.217858	−	0.377341i
$609$		0			0
$610$	74.2568			3.00657
$611$	11.0428	+	42.2954i	0.446746	+	1.71109i
$612$		0			0
$613$	−1.09691	−	1.89991i	−0.0443039	−	0.0767367i	0.843023	−	0.537877i	$-0.180774\pi$
$613$	−1.09691	−	1.89991i	−0.0443039	−	0.0767367i	−0.887327	+	0.461141i	$0.847440\pi$
$614$	33.5718	+	58.1481i	1.35485	+	2.34666i
$615$		0			0
$616$	−12.8500			−0.517740
$617$	−3.17405	+	5.49762i	−0.127783	+	0.221326i	−0.922817	−	0.385238i	$-0.874119\pi$
$617$	−3.17405	+	5.49762i	−0.127783	+	0.221326i	0.795035	+	0.606564i	$0.207453\pi$
$618$		0			0
$619$	−7.77203			−0.312384			−0.156192	−	0.987727i	$-0.549922\pi$
$619$	−7.77203			−0.312384			−0.156192	+	0.987727i	$0.549922\pi$
$620$	−46.5534	+	80.6328i	−1.86963	+	3.23829i
$621$		0			0
$622$	−3.16378	−	5.47983i	−0.126856	−	0.219721i
$623$	6.35878			0.254759
$624$		0			0
$625$	44.9135			1.79654
$626$	26.7229	+	46.2854i	1.06806	+	1.84994i
$627$		0			0
$628$	−32.0860	+	55.5745i	−1.28037	+	2.21766i
$629$	1.51948			0.0605858
$630$		0			0
$631$	−17.1312	+	29.6721i	−0.681983	+	1.18123i	0.292392	+	0.956298i	$0.405549\pi$
$631$	−17.1312	+	29.6721i	−0.681983	+	1.18123i	−0.974375	+	0.224930i	$0.927785\pi$
$632$	−4.56408			−0.181549
$633$		0			0
$634$	22.3832	+	38.7688i	0.888950	+	1.53971i
$635$	−14.7647	−	25.5732i	−0.585918	−	1.01484i
$636$		0			0
$637$	2.56580	−	2.53311i	0.101661	−	0.100365i
$638$	67.5491			2.67429
$639$		0			0
$640$	41.6927	+	72.2139i	1.64805	+	2.85451i
$641$	−11.6093	+	20.1079i	−0.458540	+	0.794215i	−0.998884	−	0.0472294i	$-0.984961\pi$
$641$	−11.6093	+	20.1079i	−0.458540	+	0.794215i	0.540344	+	0.841444i	$0.318294\pi$
$642$		0			0
$643$	−10.0400	+	17.3898i	−0.395940	+	0.685788i	−0.993221	−	0.116244i	$-0.962915\pi$
$643$	−10.0400	+	17.3898i	−0.395940	+	0.685788i	0.597281	+	0.802032i	$0.296248\pi$
$644$	−3.46249	+	5.99721i	−0.136441	+	0.236323i
$645$		0			0
$646$	1.59063	−	2.75504i	0.0625823	−	0.108396i
$647$	−8.26468	−	14.3148i	−0.324918	−	0.562775i	0.656578	−	0.754258i	$-0.272003\pi$
$647$	−8.26468	−	14.3148i	−0.324918	−	0.562775i	−0.981496	+	0.191484i	$0.938670\pi$
$648$		0			0
$649$	6.88601			0.270300
$650$	68.4794	−	67.6068i	2.68598	−	2.65176i
$651$		0			0
$652$	10.0244	+	17.3628i	0.392587	+	0.679980i
$653$	−0.463954	−	0.803591i	−0.0181559	−	0.0314470i	0.856805	−	0.515641i	$-0.172446\pi$
$653$	−0.463954	−	0.803591i	−0.0181559	−	0.0314470i	−0.874961	+	0.484194i	$0.839113\pi$
$654$		0			0
$655$	−46.0189			−1.79811
$656$	7.61505	−	13.1896i	0.297318	−	0.514969i
$657$		0			0
$658$	−28.8209			−1.12355
$659$	16.1284	−	27.9352i	0.628273	−	1.08820i	−0.359625	−	0.933097i	$-0.617095\pi$
$659$	16.1284	−	27.9352i	0.628273	−	1.08820i	0.987898	−	0.155104i	$-0.0495713\pi$
$660$		0			0
$661$	11.4285	+	19.7947i	0.444516	+	0.769923i	0.998018	−	0.0629238i	$-0.0200425\pi$
$661$	11.4285	+	19.7947i	0.444516	+	0.769923i	−0.553503	+	0.832847i	$0.686709\pi$
$662$	−42.3892			−1.64750
$663$		0			0
$664$	−59.5830			−2.31227
$665$	−7.14576	−	12.3768i	−0.277101	−	0.479952i
$666$		0			0
$667$	8.23105	−	14.2566i	0.318707	−	0.552017i
$668$	−16.1989			−0.626753
$669$		0			0
$670$	−26.7356	+	46.3074i	−1.03289	+	1.78901i
$671$	25.3871			0.980057
$672$		0			0
$673$	−0.542845	−	0.940235i	−0.0209251	−	0.0362434i	0.855373	−	0.518012i	$-0.173328\pi$
$673$	−0.542845	−	0.940235i	−0.0209251	−	0.0362434i	−0.876298	+	0.481769i	$0.839994\pi$
$674$	−9.00494	−	15.5970i	−0.346857	−	0.600774i
$675$		0			0
$676$	0.608649	−	47.4603i	0.0234096	−	1.82540i
$677$	8.60730			0.330805			0.165403	−	0.986226i	$-0.447108\pi$
$677$	8.60730			0.330805			0.165403	+	0.986226i	$0.447108\pi$
$678$		0			0
$679$	2.48585	+	4.30562i	0.0953982	+	0.165235i
$680$	−2.98198	+	5.16494i	−0.114354	+	0.198066i
$681$		0			0
$682$	−24.6341	+	42.6676i	−0.943290	+	1.63383i
$683$	16.7310	−	28.9790i	0.640196	−	1.10885i	−0.345193	−	0.938532i	$-0.612187\pi$
$683$	16.7310	−	28.9790i	0.640196	−	1.10885i	0.985389	−	0.170320i	$-0.0544801\pi$
$684$		0			0
$685$	−6.42740	+	11.1326i	−0.245578	+	0.425354i
$686$	1.18860	+	2.05872i	0.0453810	+	0.0786022i
$687$		0			0
$688$	−17.5470			−0.668972
$689$	−7.06299	−	27.0521i	−0.269079	−	1.03060i
$690$		0			0
$691$	2.34609	+	4.06355i	0.0892496	+	0.154585i	0.907194	−	0.420712i	$-0.138220\pi$
$691$	2.34609	+	4.06355i	0.0892496	+	0.154585i	−0.817945	+	0.575297i	$0.804886\pi$
$692$	40.4539	+	70.0683i	1.53783	+	2.66360i
$693$		0			0
$694$	−18.7517			−0.711805
$695$	−10.8305	+	18.7589i	−0.410824	+	0.711567i
$696$		0			0
$697$	−2.83235			−0.107283
$698$	13.9469	−	24.1567i	0.527897	−	0.914345i
$699$		0			0
$700$	20.4957	+	35.4996i	0.774666	+	1.34176i
$701$	−41.4535			−1.56568			−0.782839	−	0.622224i	$-0.786229\pi$
$701$	−41.4535			−1.56568			−0.782839	+	0.622224i	$0.786229\pi$
$702$		0			0
$703$	−14.2915			−0.539015
$704$	18.4246	+	31.9123i	0.694403	+	1.20274i
$705$		0			0
$706$	−14.9016	+	25.8104i	−0.560830	+	0.971386i
$707$	5.89669			0.221768
$708$		0			0
$709$	−1.92111	+	3.32746i	−0.0721488	+	0.124965i	−0.899843	−	0.436214i	$-0.856319\pi$
$709$	−1.92111	+	3.32746i	−0.0721488	+	0.124965i	0.827694	+	0.561180i	$0.189652\pi$
$710$	−38.2301			−1.43475
$711$		0			0
$712$	12.4791	+	21.6144i	0.467672	+	0.810032i
$713$	6.00347	+	10.3983i	0.224832	+	0.389420i
$714$		0			0
$715$	33.8383	−	33.4072i	1.26548	−	1.24936i
$716$	7.08489			0.264775
$717$		0			0
$718$	−5.96395	−	10.3299i	−0.222573	−	0.385507i
$719$	4.45609	−	7.71818i	0.166184	−	0.287840i	−0.770891	−	0.636967i	$-0.780189\pi$
$719$	4.45609	−	7.71818i	0.166184	−	0.287840i	0.937075	+	0.349128i	$0.113522\pi$
$720$		0			0
$721$	5.28270	−	9.14991i	0.196738	−	0.340760i
$722$	7.62280	−	13.2031i	0.283691	−	0.491367i
$723$		0			0
$724$	15.5191	−	26.8798i	0.576762	−	0.998981i
$725$	−48.7225	−	84.3898i	−1.80951	−	3.13416i
$726$		0			0
$727$	29.6815			1.10083			0.550413	−	0.834892i	$-0.314470\pi$
$727$	29.6815			1.10083			0.550413	+	0.834892i	$0.314470\pi$
$728$	13.6458	+	3.75031i	0.505745	+	0.138996i
$729$		0			0
$730$	−35.9154	−	62.2072i	−1.32929	−	2.30239i
$731$	1.63161	+	2.82603i	0.0603472	+	0.104524i
$732$		0			0
$733$	5.30299			0.195870			0.0979352	−	0.995193i	$-0.468776\pi$
$733$	5.30299			0.195870			0.0979352	+	0.995193i	$0.468776\pi$
$734$	−28.1815	+	48.8118i	−1.04020	+	1.80168i
$735$		0			0
$736$	5.74373			0.211717
$737$	−9.14042	+	15.8317i	−0.336692	+	0.583167i
$738$		0			0
$739$	10.4572	+	18.1123i	0.384673	+	0.666273i	0.991724	−	0.128390i	$-0.0409810\pi$
$739$	10.4572	+	18.1123i	0.384673	+	0.666273i	−0.607051	+	0.794663i	$0.707648\pi$
$740$	59.2469			2.17796
$741$		0			0
$742$	18.4338			0.676726
$743$	−0.159244	−	0.275818i	−0.00584209	−	0.0101188i	0.863090	−	0.505051i	$-0.168526\pi$
$743$	−0.159244	−	0.275818i	−0.00584209	−	0.0101188i	−0.868932	+	0.494932i	$0.835193\pi$
$744$		0			0
$745$	−20.1985	+	34.9848i	−0.740015	+	1.28174i
$746$	−23.6610			−0.866290
$747$		0			0
$748$	−2.25441	+	3.90475i	−0.0824292	+	0.142772i
$749$	−12.4055			−0.453287
$750$		0			0
$751$	−19.7940	−	34.2843i	−0.722295	−	1.25105i	−0.960078	−	0.279733i	$-0.909754\pi$
$751$	−19.7940	−	34.2843i	−0.722295	−	1.25105i	0.237783	−	0.971318i	$-0.423579\pi$
$752$	−12.2954	−	21.2962i	−0.448367	−	0.776594i
$753$		0			0
$754$	−71.7324	−	19.7144i	−2.61234	−	0.717958i
$755$	−39.1367			−1.42433
$756$		0			0
$757$	5.12667	+	8.87966i	0.186332	+	0.322737i	0.944025	−	0.329875i	$-0.107007\pi$
$757$	5.12667	+	8.87966i	0.186332	+	0.322737i	−0.757693	+	0.652612i	$0.773673\pi$
$758$	33.1025	−	57.3352i	1.20234	−	2.08251i
$759$		0			0
$760$	28.0470	−	48.5788i	1.01737	−	1.76214i
$761$	−8.73920	+	15.1367i	−0.316796	+	0.548706i	−0.979818	−	0.199894i	$-0.935940\pi$
$761$	−8.73920	+	15.1367i	−0.316796	+	0.548706i	0.663022	+	0.748600i	$0.269274\pi$
$762$		0			0
$763$	−6.06580	+	10.5063i	−0.219597	+	0.380353i
$764$	1.18860	+	2.05872i	0.0430021	+	0.0744818i
$765$		0			0
$766$	16.4132			0.593035
$767$	−7.31246	−	2.00971i	−0.264038	−	0.0725663i
$768$		0			0
$769$	−18.0283	−	31.2259i	−0.650117	−	1.12604i	−0.983094	−	0.183101i	$-0.941387\pi$
$769$	−18.0283	−	31.2259i	−0.650117	−	1.12604i	0.332977	−	0.942935i	$-0.391947\pi$
$770$	15.6755	+	27.1508i	0.564906	+	0.978446i
$771$		0			0
$772$	69.6057			2.50516
$773$	−5.35918	+	9.28237i	−0.192756	+	0.333864i	−0.946163	−	0.323691i	$-0.895076\pi$
$773$	−5.35918	+	9.28237i	−0.192756	+	0.333864i	0.753406	+	0.657555i	$0.228409\pi$
$774$		0			0
$775$	71.0734			2.55303
$776$	−9.75693	+	16.8995i	−0.350253	+	0.606657i
$777$		0			0
$778$	−33.7282	−	58.4190i	−1.20922	−	2.09442i
$779$	26.6396			0.954463
$780$		0			0
$781$	−13.0702			−0.467688
$782$	0.850368	+	1.47288i	0.0304091	+	0.0526701i
$783$		0			0
$784$	−1.01415	+	1.75656i	−0.0362196	+	0.0627341i
$785$	70.8016			2.52702
$786$		0			0
$787$	4.47905	−	7.75795i	0.159661	−	0.276541i	−0.775085	−	0.631856i	$-0.782293\pi$
$787$	4.47905	−	7.75795i	0.159661	−	0.276541i	0.934746	+	0.355315i	$0.115627\pi$
$788$	−90.2178			−3.21388
$789$		0			0
$790$	5.56767	+	9.64348i	0.198089	+	0.343100i
$791$	5.33582	+	9.24191i	0.189720	+	0.328605i
$792$		0			0
$793$	−26.9593	−	7.40931i	−0.957352	−	0.263112i
$794$	−11.3326			−0.402179
$795$		0			0
$796$	−23.9957	−	41.5618i	−0.850506	−	1.47312i
$797$	−18.0343	+	31.2363i	−0.638807	+	1.10645i	0.346887	+	0.937907i	$0.387239\pi$
$797$	−18.0343	+	31.2363i	−0.638807	+	1.10645i	−0.985695	+	0.168540i	$0.946095\pi$
$798$		0			0
$799$	−2.28658	+	3.96047i	−0.0808933	+	0.140111i
$800$	16.9996	−	29.4442i	0.601027	−	1.04101i
$801$		0			0
$802$	−9.82515	+	17.0177i	−0.346938	+	0.600914i
$803$	−12.2788	−	21.2676i	−0.433310	−	0.750516i
$804$		0			0
$805$	7.64042			0.269289
$806$	38.6124	−	38.1204i	1.36006	−	1.34273i
$807$		0			0
$808$	11.5722	+	20.0436i	0.407109	+	0.705133i
$809$	23.7647	+	41.1616i	0.835522	+	1.44717i	0.893605	+	0.448854i	$0.148168\pi$
$809$	23.7647	+	41.1616i	0.835522	+	1.44717i	−0.0580834	+	0.998312i	$0.518499\pi$
$810$		0			0
$811$	−5.34678			−0.187751			−0.0938755	−	0.995584i	$-0.529926\pi$
$811$	−5.34678			−0.187751			−0.0938755	+	0.995584i	$0.529926\pi$
$812$	15.8446	−	27.4437i	0.556038	−	0.963085i
$813$		0			0
$814$	31.3510			1.09885
$815$	11.0601	−	19.1566i	0.387417	−	0.671026i
$816$		0			0
$817$	−15.3461	−	26.5802i	−0.536892	−	0.929924i
$818$	50.9525			1.78151
$819$		0			0
$820$	−110.437			−3.85664
$821$	−10.9349	−	18.9397i	−0.381629	−	0.661001i	0.609666	−	0.792658i	$-0.291304\pi$
$821$	−10.9349	−	18.9397i	−0.381629	−	0.661001i	−0.991295	+	0.131657i	$0.957970\pi$
$822$		0			0
$823$	−11.4971	+	19.9135i	−0.400763	+	0.694142i	−0.993818	−	0.111020i	$-0.964588\pi$
$823$	−11.4971	+	19.9135i	−0.400763	+	0.694142i	0.593055	+	0.805162i	$0.297922\pi$
$824$	41.4690			1.44464
$825$		0			0
$826$	2.50000	−	4.33013i	0.0869861	−	0.150664i
$827$	−21.3425			−0.742151			−0.371075	−	0.928603i	$-0.621011\pi$
$827$	−21.3425			−0.742151			−0.371075	+	0.928603i	$0.621011\pi$
$828$		0			0
$829$	−13.7154	−	23.7558i	−0.476357	−	0.825074i	0.523276	−	0.852163i	$-0.324710\pi$
$829$	−13.7154	−	23.7558i	−0.476357	−	0.825074i	−0.999633	+	0.0270890i	$0.991376\pi$
$830$	72.6846	+	125.893i	2.52292	+	4.36982i
$831$		0			0
$832$	−10.2519	−	39.2659i	−0.355420	−	1.36130i
$833$	0.377203			0.0130693
$834$		0			0
$835$	8.93621	+	15.4780i	0.309250	+	0.535637i
$836$	21.2038	−	36.7261i	0.733349	−	1.27020i
$837$		0			0
$838$	−2.72370	+	4.71758i	−0.0940885	+	0.162966i
$839$	−2.21584	+	3.83794i	−0.0764992	+	0.132500i	−0.901737	−	0.432285i	$-0.857708\pi$
$839$	−2.21584	+	3.83794i	−0.0764992	+	0.132500i	0.825238	+	0.564785i	$0.191041\pi$
$840$		0			0
$841$	−23.1659	+	40.1245i	−0.798824	+	1.38360i
$842$	−9.04873	−	15.6729i	−0.311840	−	0.540123i
$843$		0			0
$844$	−71.5491			−2.46282
$845$	−45.6839	+	25.6002i	−1.57157	+	0.880674i
$846$		0			0
$847$	−0.140820	−	0.243908i	−0.00483864	−	0.00838078i
$848$	7.86412	+	13.6210i	0.270055	+	0.467749i
$849$		0			0
$850$	10.0673			0.345304
$851$	3.82021	−	6.61680i	0.130955	−	0.226821i
$852$		0			0
$853$	43.0040			1.47243			0.736215	−	0.676748i	$-0.236611\pi$
$853$	43.0040			1.47243			0.736215	+	0.676748i	$0.236611\pi$
$854$	9.21690	−	15.9641i	0.315396	−	0.546281i
$855$		0			0
$856$	−24.3457	−	42.1680i	−0.832119	−	1.44127i
$857$	−0.866269			−0.0295912			−0.0147956	−	0.999891i	$-0.504710\pi$
$857$	−0.866269			−0.0295912			−0.0147956	+	0.999891i	$0.504710\pi$
$858$		0			0
$859$	−15.3481			−0.523671			−0.261835	−	0.965113i	$-0.584328\pi$
$859$	−15.3481			−0.523671			−0.261835	+	0.965113i	$0.584328\pi$
$860$	63.6188	+	110.191i	2.16938	+	3.75748i
$861$		0			0
$862$	24.7975	−	42.9505i	0.844607	−	1.46290i
$863$	37.0275			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$863$	37.0275			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$864$		0			0
$865$	44.6333	−	77.3072i	1.51758	−	2.62852i
$866$	−55.5704			−1.88836
$867$		0			0
$868$	11.5566	+	20.0166i	0.392256	+	0.679408i
$869$	1.90349	+	3.29693i	0.0645713	+	0.111841i
$870$		0			0
$871$	14.3270	−	14.1445i	0.485452	−	0.479266i
$872$	−47.6164			−1.61249
$873$		0			0
$874$	−7.99814	−	13.8532i	−0.270541	−	0.468591i
$875$	12.5424	−	21.7242i	0.424012	−	0.734410i
$876$		0			0
$877$	−11.5103	+	19.9364i	−0.388674	+	0.673204i	−0.992271	−	0.124086i	$-0.960400\pi$
$877$	−11.5103	+	19.9364i	−0.388674	+	0.673204i	0.603597	+	0.797289i	$0.293734\pi$
$878$	−10.8817	+	18.8477i	−0.367241	+	0.636080i
$879$		0			0
$880$	−13.3748	+	23.1658i	−0.450864	+	0.780919i
$881$	19.0084	+	32.9235i	0.640410	+	1.10922i	0.985341	+	0.170594i	$0.0545687\pi$
$881$	19.0084	+	32.9235i	0.640410	+	1.10922i	−0.344932	+	0.938628i	$0.612098\pi$
$882$		0			0
$883$	−6.95620			−0.234095			−0.117047	−	0.993126i	$-0.537343\pi$
$883$	−6.95620			−0.234095			−0.117047	+	0.993126i	$0.537343\pi$
$884$	3.53363	−	3.48861i	0.118849	−	0.117335i
$885$		0			0
$886$	13.3875	+	23.1878i	0.449761	+	0.779009i
$887$	−12.9066	−	22.3548i	−0.433360	−	0.750601i	0.563800	−	0.825911i	$-0.309339\pi$
$887$	−12.9066	−	22.3548i	−0.433360	−	0.750601i	−0.997160	+	0.0753098i	$0.976005\pi$
$888$		0			0
$889$	−7.33048			−0.245857
$890$	30.4461	−	52.7342i	1.02055	−	1.76765i
$891$		0			0
$892$	−101.747			−3.40675
$893$	21.5064	−	37.2502i	0.719684	−	1.24653i
$894$		0			0
$895$	−3.90842	−	6.76959i	−0.130644	−	0.226282i
$896$	20.6999			0.691536
$897$		0			0
$898$	80.3134			2.68009
$899$	−27.4724	−	47.5835i	−0.916255	−	1.58700i
$900$		0			0
$901$	1.46249	−	2.53311i	0.0487227	−	0.0843901i
$902$	−58.4388			−1.94580
$903$		0			0
$904$	−20.9430	+	36.2744i	−0.696554	+	1.20647i
$905$	−34.2448			−1.13834
$906$		0			0
$907$	1.29579	+	2.24437i	0.0430260	+	0.0745231i	0.886736	−	0.462275i	$-0.152967\pi$
$907$	1.29579	+	2.24437i	0.0430260	+	0.0745231i	−0.843710	+	0.536799i	$0.819634\pi$
$908$	21.9621	+	38.0395i	0.728838	+	1.26238i
$909$		0			0
$910$	−8.72223	−	33.4072i	−0.289139	−	1.10744i
$911$	−36.7507			−1.21760			−0.608802	−	0.793322i	$-0.708350\pi$
$911$	−36.7507			−1.21760			−0.608802	+	0.793322i	$0.708350\pi$
$912$		0			0
$913$	24.8496	+	43.0407i	0.822401	+	1.42444i
$914$	−40.7624	+	70.6026i	−1.34830	+	2.33533i
$915$		0			0
$916$	16.7930	−	29.0863i	0.554856	−	0.961038i
$917$	−5.71196	+	9.89341i	−0.188626	+	0.326709i
$918$		0			0
$919$	1.58141	−	2.73909i	0.0521660	−	0.0903542i	−0.838763	−	0.544496i	$-0.816721\pi$
$919$	1.58141	−	2.73909i	0.0521660	−	0.0903542i	0.890929	+	0.454142i	$0.150054\pi$
$920$	14.9943	+	25.9708i	0.494346	+	0.856233i
$921$		0			0
$922$	−45.9575			−1.51353
$923$	13.8796	+	3.81458i	0.456853	+	0.125558i
$924$		0			0
$925$	−22.6132	−	39.1672i	−0.743517	−	1.28781i
$926$	−7.48158	−	12.9585i	−0.245860	−	0.425842i
$927$		0			0
$928$	−26.2838			−0.862807
$929$	19.7964	−	34.2885i	0.649500	−	1.12497i	−0.333742	−	0.942664i	$-0.608311\pi$
$929$	19.7964	−	34.2885i	0.649500	−	1.12497i	0.983242	−	0.182303i	$-0.0583553\pi$
$930$		0			0
$931$	−3.54778			−0.116274
$932$	−22.7321	+	39.3732i	−0.744615	+	1.28971i
$933$		0			0
$934$	28.7990	+	49.8813i	0.942331	+	1.63217i
$935$	4.97463			0.162688
$936$		0			0
$937$	2.94553			0.0962263			0.0481131	−	0.998842i	$-0.484679\pi$
$937$	2.94553			0.0962263			0.0481131	+	0.998842i	$0.484679\pi$
$938$	6.63695	+	11.4955i	0.216704	+	0.375342i
$939$		0			0
$940$	−89.1570	+	154.424i	−2.90798	+	5.03677i
$941$	−20.9893			−0.684232			−0.342116	−	0.939658i	$-0.611144\pi$
$941$	−20.9893			−0.684232			−0.342116	+	0.939658i	$0.611144\pi$
$942$		0			0
$943$	−7.12094	+	12.3338i	−0.231890	+	0.401644i
$944$	4.26614			0.138851
$945$		0			0
$946$	33.6644	+	58.3085i	1.09453	+	1.89577i
$947$	−3.18367	−	5.51427i	−0.103455	−	0.179190i	0.809651	−	0.586912i	$-0.199657\pi$
$947$	−3.18367	−	5.51427i	−0.103455	−	0.179190i	−0.913106	+	0.407722i	$0.866323\pi$
$948$		0			0
$949$	6.83224	+	26.1683i	0.221784	+	0.849457i
$950$	−94.6877			−3.07207
$951$		0			0
$952$	0.740258	+	1.28216i	0.0239919	+	0.0415552i
$953$	30.2268	−	52.3543i	0.979141	−	1.69592i	0.313610	−	0.949552i	$-0.398461\pi$
$953$	30.2268	−	52.3543i	0.979141	−	1.69592i	0.665531	−	0.746370i	$-0.268205\pi$
$954$		0			0
$955$	1.31140	−	2.27141i	0.0424359	−	0.0735011i
$956$	−5.92498	+	10.2624i	−0.191628	+	0.331909i
$957$		0			0
$958$	−39.9724	+	69.2342i	−1.29145	+	2.23685i
$959$	1.59556	+	2.76359i	0.0515234	+	0.0892411i
$960$		0			0
$961$	9.07502			0.292742
$962$	−33.2926	−	9.14991i	−1.07340	−	0.295005i
$963$		0			0
$964$	−17.2077	−	29.8046i	−0.554222	−	0.959941i
$965$	−38.3984	−	66.5080i	−1.23609	−	2.14097i
$966$		0			0
$967$	48.1719			1.54910			0.774552	−	0.632510i	$-0.217975\pi$
$967$	48.1719			1.54910			0.774552	+	0.632510i	$0.217975\pi$
$968$	0.552717	−	0.957335i	0.0177650	−	0.0307699i
$969$		0			0
$970$	47.6094			1.52865
$971$	8.98264	−	15.5584i	0.288267	−	0.499292i	−0.685130	−	0.728421i	$-0.740254\pi$
$971$	8.98264	−	15.5584i	0.288267	−	0.499292i	0.973396	+	0.229129i	$0.0735877\pi$
$972$		0			0
$973$	2.68860	+	4.65679i	0.0861926	+	0.149290i
$974$	−18.8393			−0.603650
$975$		0			0
$976$	15.7282			0.503448
$977$	−1.41336	−	2.44801i	−0.0452174	−	0.0783188i	0.842531	−	0.538648i	$-0.181065\pi$
$977$	−1.41336	−	2.44801i	−0.0452174	−	0.0783188i	−0.887748	+	0.460329i	$0.847731\pi$
$978$		0			0
$979$	10.4090	−	18.0289i	0.332672	−	0.576205i
$980$	14.7077			0.469820
$981$		0			0
$982$	2.89029	−	5.00613i	0.0922328	−	0.159752i
$983$	29.8873			0.953258			0.476629	−	0.879105i	$-0.341859\pi$
$983$	29.8873			0.953258			0.476629	+	0.879105i	$0.341859\pi$
$984$		0			0
$985$	49.7692	+	86.2028i	1.58578	+	2.74665i
$986$	−3.89135	−	6.74002i	−0.123926	−	0.214646i
$987$		0			0
$988$	−33.2356	+	32.8121i	−1.05736	+	1.04389i
$989$	16.4084			0.521757
$990$		0			0
$991$	−18.4734	−	31.9969i	−0.586828	−	1.01642i	−0.994645	−	0.103352i	$-0.967043\pi$
$991$	−18.4734	−	31.9969i	−0.586828	−	1.01642i	0.407817	−	0.913064i	$-0.366290\pi$
$992$	9.58529	−	16.6022i	0.304333	−	0.527121i
$993$		0			0
$994$	−4.74519	+	8.21892i	−0.150508	+	0.260688i
$995$	−26.4748	+	45.8557i	−0.839307	+	1.45372i
$996$		0			0
$997$	−5.35878	+	9.28168i	−0.169714	+	0.293954i	−0.938319	−	0.345770i	$-0.887618\pi$
$997$	−5.35878	+	9.28168i	−0.169714	+	0.293954i	0.768605	+	0.639724i	$0.220951\pi$
$998$	22.0888	+	38.2589i	0.699208	+	1.21106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.d.757.1		6
3.2	odd	2		273.2.k.d.211.3	yes	6
13.9	even	3	inner	819.2.o.d.568.1		6
39.23	odd	6		3549.2.a.s.1.3		3
39.29	odd	6		3549.2.a.h.1.1		3
39.35	odd	6		273.2.k.d.22.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.3	✓	6	39.35	odd	6
273.2.k.d.211.3	yes	6	3.2	odd	2
819.2.o.d.568.1		6	13.9	even	3	inner
819.2.o.d.757.1		6	1.1	even	1	trivial
3549.2.a.h.1.1		3	39.29	odd	6
3549.2.a.s.1.3		3	39.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18860 - 2.05872i) q^{2} +(-1.82555 + 3.16194i) q^{4} +4.02830 q^{5} +(0.500000 - 0.866025i) q^{7} +3.92498 q^{8} +O(q^{10})\)	\(q+(-1.18860 - 2.05872i) q^{2} +(-1.82555 + 3.16194i) q^{4} +4.02830 q^{5} +(0.500000 - 0.866025i) q^{7} +3.92498 q^{8} +(-4.78804 - 8.29313i) q^{10} +(-1.63695 - 2.83527i) q^{11} +(0.910836 + 3.48861i) q^{13} -2.37720 q^{14} +(-1.01415 - 1.75656i) q^{16} +(-0.188601 + 0.326667i) q^{17} +(1.77389 - 3.07247i) q^{19} +(-7.35384 + 12.7372i) q^{20} +(-3.89135 + 6.74002i) q^{22} +(0.948344 + 1.64258i) q^{23} +11.2272 q^{25} +(6.09944 - 6.02172i) q^{26} +(1.82555 + 3.16194i) q^{28} +(-4.33969 - 7.51657i) q^{29} +6.33048 q^{31} +(1.51415 - 2.62258i) q^{32} +0.896688 q^{34} +(2.01415 - 3.48861i) q^{35} +(-2.01415 - 3.48861i) q^{37} -8.43380 q^{38} +15.8110 q^{40} +(3.75441 + 6.50282i) q^{41} +(4.32555 - 7.49207i) q^{43} +11.9533 q^{44} +(2.25441 - 3.90475i) q^{46} +12.1239 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-13.3446 - 23.1136i) q^{50} +(-12.6935 - 3.48861i) q^{52} -7.75441 q^{53} +(-6.59410 - 11.4213i) q^{55} +(1.96249 - 3.39914i) q^{56} +(-10.3163 + 17.8684i) q^{58} +(-1.05166 + 1.82152i) q^{59} +(-3.87720 + 6.71551i) q^{61} +(-7.52442 - 13.0327i) q^{62} -11.2555 q^{64} +(3.66912 + 14.0531i) q^{65} +(-2.79191 - 4.83574i) q^{67} +(-0.688601 - 1.19269i) q^{68} -9.57608 q^{70} +(1.99612 - 3.45739i) q^{71} +7.50106 q^{73} +(-4.78804 + 8.29313i) q^{74} +(6.47664 + 11.2179i) q^{76} -3.27389 q^{77} -1.16283 q^{79} +(-4.08529 - 7.07593i) q^{80} +(8.92498 - 15.4585i) q^{82} -15.1805 q^{83} +(-0.759742 + 1.31591i) q^{85} -20.5654 q^{86} +(-6.42498 - 11.1284i) q^{88} +(3.17939 + 5.50686i) q^{89} +(3.47664 + 0.955496i) q^{91} -6.92498 q^{92} +(-14.4104 - 24.9596i) q^{94} +(7.14576 - 12.3768i) q^{95} +(-2.48585 + 4.30562i) q^{97} +(-1.18860 + 2.05872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

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