LMFDB - Embedded newform 126.3.n.c.19.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(19,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.3.n.c.73.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(5.74264 + 3.31552i) q^{5} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} +(8.12132 - 4.68885i) q^{10} +(-2.37868 - 4.11999i) q^{11} -15.2913i q^{13} +(8.29289 - 5.40629i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(3.25736 - 1.88064i) q^{17} +(3.62132 + 2.09077i) q^{19} -13.2621i q^{20} -6.72792 q^{22} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} +(-18.7279 - 10.8126i) q^{26} +(-0.757359 - 13.9795i) q^{28} -3.51472 q^{29} +(-42.3198 + 24.4334i) q^{31} +(2.82843 + 4.89898i) q^{32} -5.31925i q^{34} +(25.3492 + 38.8841i) q^{35} +(1.47056 - 2.54709i) q^{37} +(5.12132 - 2.95680i) q^{38} +(-16.2426 - 9.37769i) q^{40} -27.9590i q^{41} -10.4853 q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(-45.6213 - 26.3395i) q^{47} +(28.9411 + 39.5400i) q^{49} +26.8284 q^{50} +(-26.4853 + 15.2913i) q^{52} +(27.9853 + 48.4719i) q^{53} -31.5462i q^{55} +(-17.6569 - 8.95743i) q^{56} +(-2.48528 + 4.30463i) q^{58} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +69.1080i q^{62} +8.00000 q^{64} +(50.6985 - 87.8124i) q^{65} +(17.3198 + 29.9988i) q^{67} +(-6.51472 - 3.76127i) q^{68} +(65.5477 - 3.55114i) q^{70} -36.4264 q^{71} +(45.5589 - 26.3034i) q^{73} +(-2.07969 - 3.60213i) q^{74} -8.36308i q^{76} +(-1.80152 - 33.2528i) q^{77} +(16.8934 - 29.2602i) q^{79} +(-22.9706 + 13.2621i) q^{80} +(-34.2426 - 19.7700i) q^{82} -127.577i q^{83} +24.9411 q^{85} +(-7.41421 + 12.8418i) q^{86} +(6.72792 + 11.6531i) q^{88} +(43.5883 + 25.1657i) q^{89} +(48.4264 - 95.4580i) q^{91} +55.4558 q^{92} +(-64.5183 + 37.2497i) q^{94} +(13.8640 + 24.0131i) q^{95} -101.792i q^{97} +(68.8909 - 7.48650i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 6 q^{5} + 8 q^{7} + 24 q^{10} - 18 q^{11} + 36 q^{14} - 8 q^{16} + 30 q^{17} + 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} - 24 q^{26} - 20 q^{28} - 48 q^{29} - 42 q^{31} + 42 q^{35} - 62 q^{37}+ \cdots + 120 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 6 * q^5 + 8 * q^7 + 24 * q^10 - 18 * q^11 + 36 * q^14 - 8 * q^16 + 30 * q^17 + 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 - 24 * q^26 - 20 * q^28 - 48 * q^29 - 42 * q^31 + 42 * q^35 - 62 * q^37 + 12 * q^38 - 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 - 174 * q^47 - 20 * q^49 + 96 * q^50 - 72 * q^52 + 78 * q^53 - 48 * q^56 + 24 * q^58 + 78 * q^59 - 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 - 60 * q^68 + 84 * q^70 + 24 * q^71 + 318 * q^73 - 96 * q^74 - 126 * q^77 + 110 * q^79 - 24 * q^80 - 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 + 378 * q^89 + 24 * q^91 + 120 * q^92 - 12 * q^94 + 30 * q^95 + 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	5.74264	+	3.31552i	1.14853	+	0.663103i	0.948528	−	0.316693i	$-0.102572\pi$
$5$	5.74264	+	3.31552i	1.14853	+	0.663103i	0.200000	+	0.979796i	$0.435906\pi$
$6$		0			0
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	8.12132	−	4.68885i	0.812132	−	0.468885i
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	0.737413	−	0.675442i	$-0.236047\pi$
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	−0.953657	+	0.300897i	$0.902714\pi$
$12$		0			0
$13$		−	15.2913i		−	1.17625i	−0.808769	−	0.588126i	$-0.799866\pi$
$13$		−	15.2913i		−	1.17625i	0.808769	−	0.588126i	$-0.200134\pi$
$14$	8.29289	−	5.40629i	0.592350	−	0.386163i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	3.25736	−	1.88064i	0.191609	−	0.110626i	−0.401126	−	0.916023i	$-0.631381\pi$
$17$	3.25736	−	1.88064i	0.191609	−	0.110626i	0.592736	+	0.805397i	$0.298048\pi$
$18$		0			0
$19$	3.62132	+	2.09077i	0.190596	+	0.110041i	0.592261	−	0.805746i	$-0.298235\pi$
$19$	3.62132	+	2.09077i	0.190596	+	0.110041i	−0.401666	+	0.915786i	$0.631569\pi$
$20$		−	13.2621i		−	0.663103i
$21$		0			0
$22$	−6.72792			−0.305815
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	0.389617	+	0.920977i	$0.372607\pi$
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	−0.992398	+	0.123070i	$0.960726\pi$
$24$		0			0
$25$	9.48528	+	16.4290i	0.379411	+	0.657160i
$26$	−18.7279	−	10.8126i	−0.720305	−	0.415868i
$27$		0			0
$28$	−0.757359	−	13.9795i	−0.0270485	−	0.499268i
$29$	−3.51472			−0.121197			−0.0605986	−	0.998162i	$-0.519301\pi$
$29$	−3.51472			−0.121197			−0.0605986	+	0.998162i	$0.519301\pi$
$30$		0			0
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.990305	−	0.138913i	$-0.955639\pi$
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.374850	+	0.927085i	$0.622306\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	5.31925i		−	0.156448i
$35$	25.3492	+	38.8841i	0.724264	+	1.11097i
$36$		0			0
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	−0.845469	−	0.534025i	$-0.820679\pi$
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	0.885214	+	0.465185i	$0.154012\pi$
$38$	5.12132	−	2.95680i	0.134772	−	0.0778104i
$39$		0			0
$40$	−16.2426	−	9.37769i	−0.406066	−	0.234442i
$41$		−	27.9590i		−	0.681927i	−0.940077	−	0.340963i	$-0.889247\pi$
$41$		−	27.9590i		−	0.681927i	0.940077	−	0.340963i	$-0.110753\pi$
$42$		0			0
$43$	−10.4853			−0.243844			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−10.4853			−0.243844			−0.121922	+	0.992540i	$0.538906\pi$
$44$	−4.75736	+	8.23999i	−0.108122	+	0.187272i
$45$		0			0
$46$	19.6066	+	33.9596i	0.426230	+	0.738253i
$47$	−45.6213	−	26.3395i	−0.970666	−	0.560415i	−0.0712271	−	0.997460i	$-0.522691\pi$
$47$	−45.6213	−	26.3395i	−0.970666	−	0.560415i	−0.899439	+	0.437046i	$0.856025\pi$
$48$		0			0
$49$	28.9411	+	39.5400i	0.590635	+	0.806939i
$50$	26.8284			0.536569
$51$		0			0
$52$	−26.4853	+	15.2913i	−0.509332	+	0.294063i
$53$	27.9853	+	48.4719i	0.528024	+	0.914565i	0.999466	+	0.0326677i	$0.0104003\pi$
$53$	27.9853	+	48.4719i	0.528024	+	0.914565i	−0.471442	+	0.881897i	$0.656266\pi$
$54$		0			0
$55$		−	31.5462i		−	0.573567i
$56$	−17.6569	−	8.95743i	−0.315301	−	0.159954i
$57$		0			0
$58$	−2.48528	+	4.30463i	−0.0428497	+	0.0742178i
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	−0.756492	−	0.654002i	$-0.773089\pi$
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	0.188136	+	0.982143i	$0.439755\pi$
$60$		0			0
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.307205	−	0.951643i	$-0.599394\pi$
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.977750	+	0.209774i	$0.932727\pi$
$62$			69.1080i			1.11464i
$63$		0			0
$64$	8.00000			0.125000
$65$	50.6985	−	87.8124i	0.779977	−	1.35096i
$66$		0			0
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	0.965842	−	0.259134i	$-0.0834370\pi$
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	−0.707337	+	0.706877i	$0.750104\pi$
$68$	−6.51472	−	3.76127i	−0.0958047	−	0.0553129i
$69$		0			0
$70$	65.5477	−	3.55114i	0.936396	−	0.0507306i
$71$	−36.4264			−0.513048			−0.256524	−	0.966538i	$-0.582577\pi$
$71$	−36.4264			−0.513048			−0.256524	+	0.966538i	$0.582577\pi$
$72$		0			0
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	−0.154367	−	0.988014i	$-0.549334\pi$
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	0.778461	+	0.627693i	$0.216001\pi$
$74$	−2.07969	−	3.60213i	−0.0281039	−	0.0486774i
$75$		0			0
$76$		−	8.36308i		−	0.110041i
$77$	−1.80152	−	33.2528i	−0.0233963	−	0.431854i
$78$		0			0
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	−0.739073	−	0.673626i	$-0.764736\pi$
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	0.952913	+	0.303243i	$0.0980694\pi$
$80$	−22.9706	+	13.2621i	−0.287132	+	0.165776i
$81$		0			0
$82$	−34.2426	−	19.7700i	−0.417593	−	0.241098i
$83$		−	127.577i		−	1.53708i	−0.639803	−	0.768539i	$-0.720984\pi$
$83$		−	127.577i		−	1.53708i	0.639803	−	0.768539i	$-0.279016\pi$
$84$		0			0
$85$	24.9411			0.293425
$86$	−7.41421	+	12.8418i	−0.0862118	+	0.149323i
$87$		0			0
$88$	6.72792	+	11.6531i	0.0764537	+	0.132422i
$89$	43.5883	+	25.1657i	0.489756	+	0.282761i	0.724473	−	0.689303i	$-0.242083\pi$
$89$	43.5883	+	25.1657i	0.489756	+	0.282761i	−0.234717	+	0.972064i	$0.575416\pi$
$90$		0			0
$91$	48.4264	−	95.4580i	0.532158	−	1.04899i
$92$	55.4558			0.602781
$93$		0			0
$94$	−64.5183	+	37.2497i	−0.686365	+	0.396273i
$95$	13.8640	+	24.0131i	0.145936	+	0.252769i
$96$		0			0
$97$		−	101.792i		−	1.04940i	−0.851287	−	0.524700i	$-0.824177\pi$
$97$		−	101.792i		−	1.04940i	0.851287	−	0.524700i	$-0.175823\pi$
$98$	68.8909	−	7.48650i	0.702968	−	0.0763928i
$99$		0			0
$100$	18.9706	−	32.8580i	0.189706	−	0.328580i
$101$	51.6838	−	29.8396i	0.511720	−	0.295442i	−0.221820	−	0.975088i	$-0.571200\pi$
$101$	51.6838	−	29.8396i	0.511720	−	0.295442i	0.733541	+	0.679646i	$0.237866\pi$
$102$		0			0
$103$	104.077	+	60.0890i	1.01046	+	0.583388i	0.911326	−	0.411686i	$-0.135060\pi$
$103$	104.077	+	60.0890i	1.01046	+	0.583388i	0.0991322	+	0.995074i	$0.468393\pi$
$104$			43.2503i			0.415868i
$105$		0			0
$106$	79.1543			0.746739
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	−0.999350	+	0.0360423i	$0.988525\pi$
$108$		0			0
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	0.978862	+	0.204524i	$0.0655645\pi$
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	−0.312308	+	0.949981i	$0.601102\pi$
$110$	−38.6360	−	22.3065i	−0.351237	−	0.202787i
$111$		0			0
$112$	−23.4558	+	15.2913i	−0.209427	+	0.136529i
$113$	−34.5442			−0.305700			−0.152850	−	0.988249i	$-0.548845\pi$
$113$	−34.5442			−0.305700			−0.152850	+	0.988249i	$0.548845\pi$
$114$		0			0
$115$	−159.231	+	91.9323i	−1.38462	+	0.799412i
$116$	3.51472	+	6.08767i	0.0302993	+	0.0524799i
$117$		0			0
$118$			54.7592i			0.464061i
$119$	26.2904	−	1.42432i	0.220927	−	0.0119691i
$120$		0			0
$121$	49.1838	−	85.1888i	0.406477	−	0.704040i
$122$	−110.849	+	63.9988i	−0.908600	+	0.524581i
$123$		0			0
$124$	84.6396	+	48.8667i	0.682578	+	0.394086i
$125$		−	39.9814i		−	0.319851i
$126$		0			0
$127$	−247.338			−1.94754			−0.973772	−	0.227526i	$-0.926936\pi$
$127$	−247.338			−1.94754			−0.973772	+	0.227526i	$0.926936\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−71.6985	−	124.185i	−0.551527	−	0.955272i
$131$	127.864	+	73.8223i	0.976061	+	0.563529i	0.901079	−	0.433656i	$-0.142777\pi$
$131$	127.864	+	73.8223i	0.976061	+	0.563529i	0.0749822	+	0.997185i	$0.476110\pi$
$132$		0			0
$133$	15.9853	+	24.5204i	0.120190	+	0.184364i
$134$	48.9878			0.365581
$135$		0			0
$136$	−9.21320	+	5.31925i	−0.0677441	+	0.0391121i
$137$	−16.2868	−	28.2096i	−0.118882	−	0.205909i	0.800443	−	0.599409i	$-0.204598\pi$
$137$	−16.2868	−	28.2096i	−0.118882	−	0.205909i	−0.919325	+	0.393500i	$0.871264\pi$
$138$		0			0
$139$		−	68.5857i		−	0.493422i	−0.969089	−	0.246711i	$-0.920650\pi$
$139$		−	68.5857i		−	0.493422i	0.969089	−	0.246711i	$-0.0793499\pi$
$140$	42.0000	−	82.7903i	0.300000	−	0.591359i
$141$		0			0
$142$	−25.7574	+	44.6131i	−0.181390	+	0.314176i
$143$	−63.0000	+	36.3731i	−0.440559	+	0.254357i
$144$		0			0
$145$	−20.1838	−	11.6531i	−0.139198	−	0.0803662i
$146$		−	74.3973i		−	0.509571i
$147$		0			0
$148$	−5.88225			−0.0397449
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	−0.668317	−	0.743876i	$-0.732985\pi$
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	0.978374	+	0.206842i	$0.0663185\pi$
$150$		0			0
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	0.977022	−	0.213136i	$-0.0683678\pi$
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	−0.673093	+	0.739558i	$0.735035\pi$
$152$	−10.2426	−	5.91359i	−0.0673858	−	0.0389052i
$153$		0			0
$154$	−42.0000	−	21.3068i	−0.272727	−	0.138356i
$155$	−324.037			−2.09056
$156$		0			0
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	−0.476496	−	0.879177i	$-0.658093\pi$
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	0.523142	+	0.852246i	$0.324760\pi$
$158$	−23.8909	−	41.3802i	−0.151208	−	0.261900i
$159$		0			0
$160$			37.5108i			0.234442i
$161$	−162.595	+	105.999i	−1.00991	+	0.658378i
$162$		0			0
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	0.293789	+	0.955870i	$0.405084\pi$
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	−0.974703	+	0.223506i	$0.928250\pi$
$164$	−48.4264	+	27.9590i	−0.295283	+	0.170482i
$165$		0			0
$166$	−156.250	−	90.2109i	−0.941264	−	0.543439i
$167$			168.841i			1.01102i	0.862820	+	0.505511i	$0.168696\pi$
$167$			168.841i			1.01102i	−0.862820	+	0.505511i	$0.831304\pi$
$168$		0			0
$169$	−64.8234			−0.383570
$170$	17.6360	−	30.5465i	0.103741	−	0.179685i
$171$		0			0
$172$	10.4853	+	18.1610i	0.0609609	+	0.105587i
$173$	142.323	+	82.1704i	0.822678	+	0.474974i	0.851339	−	0.524616i	$-0.175791\pi$
$173$	142.323	+	82.1704i	0.822678	+	0.474974i	−0.0286608	+	0.999589i	$0.509124\pi$
$174$		0			0
$175$	7.18377	+	132.599i	0.0410501	+	0.757711i
$176$	19.0294			0.108122
$177$		0			0
$178$	61.6432	−	35.5897i	0.346310	−	0.199942i
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	0.999799	+	0.0200614i	$0.00638618\pi$
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	−0.482526	+	0.875882i	$0.660280\pi$
$180$		0			0
$181$			155.086i			0.856830i	0.903582	+	0.428415i	$0.140928\pi$
$181$			155.086i			0.856830i	−0.903582	+	0.428415i	$0.859072\pi$
$182$	−82.6690	−	126.809i	−0.454226	−	0.696753i
$183$		0			0
$184$	39.2132	−	67.9193i	0.213115	−	0.369126i
$185$	16.8898	−	9.75135i	0.0912964	−	0.0527100i
$186$		0			0
$187$	−15.4964	−	8.94687i	−0.0828686	−	0.0478442i
$188$			105.358i			0.560415i
$189$		0			0
$190$	39.2132			0.206385
$191$	124.048	−	214.857i	0.649465	−	1.12491i	−0.333786	−	0.942649i	$-0.608326\pi$
$191$	124.048	−	214.857i	0.649465	−	1.12491i	0.983251	−	0.182257i	$-0.0583402\pi$
$192$		0			0
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	0.593866	−	0.804564i	$-0.297601\pi$
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	−0.993706	+	0.112021i	$0.964268\pi$
$194$	−124.669	−	71.9777i	−0.642624	−	0.371019i
$195$		0			0
$196$	39.5442	−	89.6675i	0.201756	−	0.457487i
$197$	181.103			0.919303			0.459651	−	0.888099i	$-0.347974\pi$
$197$	181.103			0.919303			0.459651	+	0.888099i	$0.347974\pi$
$198$		0			0
$199$	301.989	−	174.353i	1.51753	−	0.876147i	0.517744	−	0.855535i	$-0.326772\pi$
$199$	301.989	−	174.353i	1.51753	−	0.876147i	0.999788	−	0.0206121i	$-0.00656150\pi$
$200$	−26.8284	−	46.4682i	−0.134142	−	0.232341i
$201$		0			0
$202$		−	84.3992i		−	0.417818i
$203$	−21.9411	−	11.1309i	−0.108084	−	0.0548318i
$204$		0			0
$205$	92.6985	−	160.558i	0.452188	−	0.783212i
$206$	147.187	−	84.9786i	0.714502	−	0.412518i
$207$		0			0
$208$	52.9706	+	30.5826i	0.254666	+	0.147032i
$209$		−	19.8931i		−	0.0951823i
$210$		0			0
$211$	364.073			1.72547			0.862733	−	0.505660i	$-0.168751\pi$
$211$	364.073			1.72547			0.862733	+	0.505660i	$0.168751\pi$
$212$	55.9706	−	96.9439i	0.264012	−	0.457282i
$213$		0			0
$214$	80.3345	+	139.143i	0.375395	+	0.650203i
$215$	−60.2132	−	34.7641i	−0.280061	−	0.161694i
$216$		0			0
$217$	−341.566	+	18.5048i	−1.57404	+	0.0852757i
$218$	205.497			0.942649
$219$		0			0
$220$	−54.6396	+	31.5462i	−0.248362	+	0.143392i
$221$	−28.7574	−	49.8092i	−0.130124	−	0.225381i
$222$		0			0
$223$		−	123.231i		−	0.552603i	−0.961071	−	0.276302i	$-0.910891\pi$
$223$		−	123.231i		−	0.552603i	0.961071	−	0.276302i	$-0.0891089\pi$
$224$	2.14214	+	39.5400i	0.00956311	+	0.176518i
$225$		0			0
$226$	−24.4264	+	42.3078i	−0.108081	+	0.187203i
$227$	66.1432	−	38.1878i	0.291380	−	0.168228i	−0.347184	−	0.937797i	$-0.612862\pi$
$227$	66.1432	−	38.1878i	0.291380	−	0.168228i	0.638564	+	0.769569i	$0.279529\pi$
$228$		0			0
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.988414	−	0.151782i	$-0.0485012\pi$
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.362760	+	0.931883i	$0.381834\pi$
$230$			260.024i			1.13054i
$231$		0			0
$232$	9.94113			0.0428497
$233$	−136.537	+	236.488i	−0.585994	+	1.01497i	0.408757	+	0.912643i	$0.365962\pi$
$233$	−136.537	+	236.488i	−0.585994	+	1.01497i	−0.994751	+	0.102328i	$0.967371\pi$
$234$		0			0
$235$	−174.658	−	302.516i	−0.743225	−	1.28730i
$236$	67.0660	+	38.7206i	0.284178	+	0.164070i
$237$		0			0
$238$	16.8457	−	33.2061i	0.0707801	−	0.139522i
$239$	265.103			1.10922			0.554608	−	0.832112i	$-0.312868\pi$
$239$	265.103			1.10922			0.554608	+	0.832112i	$0.312868\pi$
$240$		0			0
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	−0.649128	−	0.760679i	$-0.724866\pi$
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	0.334203	+	0.942501i	$0.391533\pi$
$242$	−69.5563	−	120.475i	−0.287423	−	0.497831i
$243$		0			0
$244$			181.016i			0.741869i
$245$	35.1030	+	323.019i	0.143278	+	1.31844i
$246$		0			0
$247$	31.9706	−	55.3746i	0.129435	−	0.224189i
$248$	119.698	−	69.1080i	0.482655	−	0.278661i
$249$		0			0
$250$	−48.9670	−	28.2711i	−0.195868	−	0.113084i
$251$		−	495.655i		−	1.97472i	−0.158491	−	0.987360i	$-0.550663\pi$
$251$		−	495.655i		−	1.97472i	0.158491	−	0.987360i	$-0.449337\pi$
$252$		0			0
$253$	131.912			0.521390
$254$	−174.894	+	302.926i	−0.688561	+	1.19262i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−346.875	−	200.268i	−1.34971	−	0.779254i	−0.361499	−	0.932372i	$-0.617735\pi$
$257$	−346.875	−	200.268i	−1.34971	−	0.779254i	−0.988208	+	0.153119i	$0.951068\pi$
$258$		0			0
$259$	17.2466	−	11.2434i	0.0665894	−	0.0434108i
$260$	−202.794			−0.779977
$261$		0			0
$262$	180.827	−	104.400i	0.690179	−	0.398475i
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	0.833640	−	0.552308i	$-0.186253\pi$
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	−0.895133	+	0.445799i	$0.852919\pi$
$264$		0			0
$265$			371.142i			1.40054i
$266$	41.3345	−	2.23936i	0.155393	−	0.00841863i
$267$		0			0
$268$	34.6396	−	59.9976i	0.129252	−	0.223872i
$269$	265.838	−	153.482i	0.988246	−	0.570564i	0.0834963	−	0.996508i	$-0.473391\pi$
$269$	265.838	−	153.482i	0.988246	−	0.570564i	0.904749	+	0.425944i	$0.140058\pi$
$270$		0			0
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	0.373650	−	0.927570i	$-0.378106\pi$
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	−0.616474	+	0.787376i	$0.711439\pi$
$272$			15.0451i			0.0553129i
$273$		0			0
$274$	−46.0660			−0.168124
$275$	45.1249	−	78.1586i	0.164091	−	0.284213i
$276$		0			0
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	−0.999996	−	0.00294398i	$-0.999063\pi$
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	0.497448	−	0.867494i	$-0.334270\pi$
$278$	−84.0000	−	48.4974i	−0.302158	−	0.174451i
$279$		0			0
$280$	−71.6985	−	109.981i	−0.256066	−	0.392789i
$281$	−394.690			−1.40459			−0.702296	−	0.711885i	$-0.747842\pi$
$281$	−394.690			−1.40459			−0.702296	+	0.711885i	$0.747842\pi$
$282$		0			0
$283$	126.783	−	73.1981i	0.447996	−	0.258650i	−0.258988	−	0.965881i	$-0.583389\pi$
$283$	126.783	−	73.1981i	0.447996	−	0.258650i	0.706983	+	0.707230i	$0.250056\pi$
$284$	36.4264	+	63.0924i	0.128262	+	0.222156i
$285$		0			0
$286$			102.879i			0.359715i
$287$	88.5442	−	174.538i	0.308516	−	0.608146i
$288$		0			0
$289$	−137.426	+	238.030i	−0.475524	+	0.823632i
$290$	−28.5442	+	16.4800i	−0.0984281	+	0.0568275i
$291$		0			0
$292$	−91.1177	−	52.6069i	−0.312047	−	0.180160i
$293$			299.678i			1.02279i	0.859345	+	0.511396i	$0.170872\pi$
$293$			299.678i			1.02279i	−0.859345	+	0.511396i	$0.829128\pi$
$294$		0			0
$295$	−256.757			−0.870364
$296$	−4.15938	+	7.20426i	−0.0140520	+	0.0243387i
$297$		0			0
$298$	−65.3345	−	113.163i	−0.219243	−	0.379741i
$299$	367.191	+	211.998i	1.22806	+	0.709023i
$300$		0			0
$301$	−65.4558	−	33.2061i	−0.217461	−	0.110319i
$302$	129.806			0.429822
$303$		0			0
$304$	−14.4853	+	8.36308i	−0.0476490	+	0.0275101i
$305$	−300.081	−	519.755i	−0.983871	−	1.70412i
$306$		0			0
$307$			20.9886i			0.0683666i	0.999416	+	0.0341833i	$0.0108830\pi$
$307$			20.9886i			0.0683666i	−0.999416	+	0.0341833i	$0.989117\pi$
$308$	−55.7939	+	36.3731i	−0.181149	+	0.118094i
$309$		0			0
$310$	−229.128	+	396.862i	−0.739124	+	1.28020i
$311$	−157.651	+	91.0197i	−0.506916	+	0.292668i	−0.731565	−	0.681772i	$-0.761210\pi$
$311$	−157.651	+	91.0197i	−0.506916	+	0.292668i	0.224649	+	0.974440i	$0.427876\pi$
$312$		0			0
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	0.358367	−	0.933581i	$-0.383334\pi$
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	−0.629321	+	0.777145i	$0.716667\pi$
$314$		−	11.9590i		−	0.0380861i
$315$		0			0
$316$	−67.5736			−0.213840
$317$	−240.985	+	417.399i	−0.760206	+	1.31672i	0.182538	+	0.983199i	$0.441569\pi$
$317$	−240.985	+	417.399i	−0.760206	+	1.31672i	−0.942744	+	0.333517i	$0.891765\pi$
$318$		0			0
$319$	8.36039	+	14.4806i	0.0262081	+	0.0453938i
$320$	45.9411	+	26.5241i	0.143566	+	0.0828879i
$321$		0			0
$322$	14.8492	+	274.090i	0.0461157	+	0.851213i
$323$	15.7279			0.0486933
$324$		0			0
$325$	251.220	−	145.042i	0.772986	−	0.446283i
$326$	156.962	+	271.866i	0.481478	+	0.833945i
$327$		0			0
$328$			79.0800i			0.241098i
$329$	−201.382	−	308.907i	−0.612104	−	0.938928i
$330$		0			0
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	−0.984412	−	0.175879i	$-0.943723\pi$
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	0.644522	+	0.764586i	$0.277056\pi$
$332$	−220.971	+	127.577i	−0.665574	+	0.384269i
$333$		0			0
$334$	206.787	+	119.388i	0.619122	+	0.357450i
$335$			229.696i			0.685661i
$336$		0			0
$337$	−264.368			−0.784473			−0.392237	−	0.919864i	$-0.628299\pi$
$337$	−264.368			−0.784473			−0.392237	+	0.919864i	$0.628299\pi$
$338$	−45.8370	+	79.3921i	−0.135613	+	0.234888i
$339$		0			0
$340$	−24.9411	−	43.1993i	−0.0733563	−	0.127057i
$341$	201.331	+	116.238i	0.590412	+	0.340875i
$342$		0			0
$343$	55.4487	+	338.488i	0.161658	+	0.986847i
$344$	29.6569			0.0862118
$345$		0			0
$346$	201.276	−	116.207i	0.581722	−	0.335857i
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	0.694697	−	0.719303i	$-0.255539\pi$
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	−0.970283	+	0.241973i	$0.922205\pi$
$348$		0			0
$349$		−	135.448i		−	0.388104i	−0.980991	−	0.194052i	$-0.937837\pi$
$349$		−	135.448i		−	0.388104i	0.980991	−	0.194052i	$-0.0621630\pi$
$350$	167.480	+	84.9637i	0.478515	+	0.242753i
$351$		0			0
$352$	13.4558	−	23.3062i	0.0382268	−	0.0662108i
$353$	301.802	−	174.245i	0.854962	−	0.493612i	−0.00736010	−	0.999973i	$-0.502343\pi$
$353$	301.802	−	174.245i	0.854962	−	0.493612i	0.862322	+	0.506360i	$0.169009\pi$
$354$		0			0
$355$	−209.184	−	120.772i	−0.589250	−	0.340204i
$356$		−	100.663i		−	0.282761i
$357$		0			0
$358$	261.889			0.731535
$359$	152.415	−	263.991i	0.424555	−	0.735351i	−0.571824	−	0.820377i	$-0.693764\pi$
$359$	152.415	−	263.991i	0.424555	−	0.735351i	0.996379	+	0.0850256i	$0.0270972\pi$
$360$		0			0
$361$	−171.757	−	297.492i	−0.475782	−	0.824079i
$362$	189.941	+	109.663i	0.524699	+	0.302935i
$363$		0			0
$364$	−213.765	+	11.5810i	−0.587265	+	0.0318159i
$365$	348.838			0.955720
$366$		0			0
$367$	−82.2761	+	47.5021i	−0.224186	+	0.129434i	−0.607887	−	0.794024i	$-0.707983\pi$
$367$	−82.2761	+	47.5021i	−0.224186	+	0.129434i	0.383701	+	0.923457i	$0.374649\pi$
$368$	−55.4558	−	96.0523i	−0.150695	−	0.261012i
$369$		0			0
$370$		−	27.5810i		−	0.0745432i
$371$	21.1949	+	391.220i	0.0571291	+	1.05450i
$372$		0			0
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	−0.984412	−	0.175879i	$-0.943723\pi$
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	0.644521	+	0.764586i	$0.277057\pi$
$374$	−21.9153	+	12.6528i	−0.0585970	+	0.0338310i
$375$		0			0
$376$	129.037	+	74.4993i	0.343182	+	0.198136i
$377$			53.7446i			0.142559i
$378$		0			0
$379$	508.250			1.34103			0.670514	−	0.741897i	$-0.266074\pi$
$379$	508.250			1.34103			0.670514	+	0.741897i	$0.266074\pi$
$380$	27.7279	−	48.0262i	0.0729682	−	0.126385i
$381$		0			0
$382$	−175.430	−	303.854i	−0.459241	−	0.795428i
$383$	−413.753	−	238.881i	−1.08030	−	0.623709i	−0.149320	−	0.988789i	$-0.547708\pi$
$383$	−413.753	−	238.881i	−1.08030	−	0.623709i	−0.930976	+	0.365080i	$0.881042\pi$
$384$		0			0
$385$	99.9045	−	196.932i	0.259492	−	0.511511i
$386$	−218.267			−0.565459
$387$		0			0
$388$	−176.309	+	101.792i	−0.454404	+	0.262350i
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	0.954439	−	0.298406i	$-0.0964550\pi$
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	−0.735647	+	0.677365i	$0.763122\pi$
$390$		0			0
$391$			104.292i			0.266732i
$392$	−81.8579	−	111.836i	−0.208821	−	0.285296i
$393$		0			0
$394$	128.059	−	221.804i	0.325023	−	0.562956i
$395$	194.025	−	112.021i	0.491204	−	0.283597i
$396$		0			0
$397$	211.786	+	122.275i	0.533467	+	0.307997i	0.742427	−	0.669927i	$-0.233675\pi$
$397$	211.786	+	122.275i	0.533467	+	0.307997i	−0.208960	+	0.977924i	$0.567008\pi$
$398$		−	493.146i		−	1.23906i
$399$		0			0
$400$	−75.8823			−0.189706
$401$	−208.786	+	361.629i	−0.520664	+	0.901817i	0.479047	+	0.877789i	$0.340982\pi$
$401$	−208.786	+	361.629i	−0.520664	+	0.901817i	−0.999711	+	0.0240277i	$0.992351\pi$
$402$		0			0
$403$	373.617	+	647.124i	0.927090	+	1.60577i
$404$	−103.368	−	59.6793i	−0.255860	−	0.147721i
$405$		0			0
$406$	−29.1472	+	19.0016i	−0.0717911	+	0.0468019i
$407$	−13.9920			−0.0343784
$408$		0			0
$409$	266.919	−	154.106i	0.652614	−	0.376787i	−0.136843	−	0.990593i	$-0.543696\pi$
$409$	266.919	−	154.106i	0.652614	−	0.376787i	0.789457	+	0.613806i	$0.210362\pi$
$410$	−131.095	−	227.064i	−0.319745	−	0.553815i
$411$		0			0
$412$		−	240.356i		−	0.583388i
$413$	−270.647	+	14.6627i	−0.655320	+	0.0355029i
$414$		0			0
$415$	422.985	−	732.631i	1.01924	−	1.76538i
$416$	74.9117	−	43.2503i	0.180076	−	0.103967i
$417$		0			0
$418$	−24.3640	−	14.0665i	−0.0582870	−	0.0336520i
$419$		−	103.142i		−	0.246163i	−0.992397	−	0.123081i	$-0.960722\pi$
$419$		−	103.142i		−	0.246163i	0.992397	−	0.123081i	$-0.0392776\pi$
$420$		0			0
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$	257.439	−	445.897i	0.610044	−	1.05663i
$423$		0			0
$424$	−79.1543	−	137.099i	−0.186685	−	0.323347i
$425$	61.7939	+	35.6767i	0.145398	+	0.0839453i
$426$		0			0
$427$	−345.996	−	530.736i	−0.810295	−	1.24294i
$428$	227.220			0.530889
$429$		0			0
$430$	−85.1543	+	49.1639i	−0.198033	+	0.114335i
$431$	297.268	+	514.883i	0.689717	+	1.19463i	0.971929	+	0.235273i	$0.0755984\pi$
$431$	297.268	+	514.883i	0.689717	+	1.19463i	−0.282212	+	0.959352i	$0.591068\pi$
$432$		0			0
$433$			40.6267i			0.0938261i	0.998899	+	0.0469131i	$0.0149384\pi$
$433$			40.6267i			0.0938261i	−0.998899	+	0.0469131i	$0.985062\pi$
$434$	−218.860	+	431.416i	−0.504286	+	0.994046i
$435$		0			0
$436$	145.309	−	251.682i	0.333277	−	0.577252i
$437$	−100.412	+	57.9727i	−0.229775	+	0.132661i
$438$		0			0
$439$	126.959	+	73.3001i	0.289201	+	0.166971i	0.637582	−	0.770383i	$-0.279935\pi$
$439$	126.959	+	73.3001i	0.289201	+	0.166971i	−0.348380	+	0.937353i	$0.613268\pi$
$440$			89.2261i			0.202787i
$441$		0			0
$442$	−81.3381			−0.184023
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	−0.799057	−	0.601256i	$-0.794667\pi$
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	0.920231	+	0.391376i	$0.128001\pi$
$444$		0			0
$445$	166.875	+	289.035i	0.374999	+	0.649518i
$446$	−150.926	−	87.1372i	−0.338399	−	0.195375i
$447$		0			0
$448$	49.9411	+	25.3354i	0.111476	+	0.0565523i
$449$	−135.161			−0.301028			−0.150514	−	0.988608i	$-0.548093\pi$
$449$	−135.161			−0.301028			−0.150514	+	0.988608i	$0.548093\pi$
$450$		0			0
$451$	−115.191	+	66.5055i	−0.255412	+	0.147462i
$452$	34.5442	+	59.8322i	0.0764251	+	0.132372i
$453$		0			0
$454$		−	108.011i		−	0.237910i
$455$	594.588	−	387.622i	1.30679	−	0.851918i
$456$		0			0
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	−0.940080	−	0.340954i	$-0.889250\pi$
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	0.765315	+	0.643656i	$0.222583\pi$
$458$	437.584	−	252.639i	0.955424	−	0.551614i
$459$		0			0
$460$	318.463	+	183.865i	0.692311	+	0.399706i
$461$			310.250i			0.672993i	0.941685	+	0.336497i	$0.109242\pi$
$461$			310.250i			0.672993i	−0.941685	+	0.336497i	$0.890758\pi$
$462$		0			0
$463$	−326.014			−0.704135			−0.352067	−	0.935975i	$-0.614521\pi$
$463$	−326.014			−0.704135			−0.352067	+	0.935975i	$0.614521\pi$
$464$	7.02944	−	12.1753i	0.0151496	−	0.0262400i
$465$		0			0
$466$	193.092	+	334.445i	0.414360	+	0.717693i
$467$	−515.769	−	297.779i	−1.10443	−	0.637643i	−0.167048	−	0.985949i	$-0.553424\pi$
$467$	−515.769	−	297.779i	−1.10443	−	0.637643i	−0.937381	+	0.348306i	$0.886757\pi$
$468$		0			0
$469$	13.1173	+	242.122i	0.0279687	+	0.516252i
$470$	−494.007			−1.05108
$471$		0			0
$472$	94.8457	−	54.7592i	0.200944	−	0.116015i
$473$	24.9411	+	43.1993i	0.0527297	+	0.0913304i
$474$		0			0
$475$			79.3262i			0.167002i
$476$	−28.7574	−	44.1119i	−0.0604146	−	0.0926721i
$477$		0			0
$478$	187.456	−	324.683i	0.392167	−	0.679253i
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.882379	−	0.470539i	$-0.844060\pi$
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.0336914	+	0.999432i	$0.510726\pi$
$480$		0			0
$481$	−38.9483	−	22.4868i	−0.0809735	−	0.0467501i
$482$			123.939i			0.257135i
$483$		0			0
$484$	−196.735			−0.406477
$485$	337.492	−	584.554i	0.695861	−	1.20527i
$486$		0			0
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	0.736930	−	0.675970i	$-0.236275\pi$
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	−0.953872	+	0.300215i	$0.902942\pi$
$488$	221.698	+	127.998i	0.454300	+	0.262290i
$489$		0			0
$490$	420.437	+	185.416i	0.858035	+	0.378401i
$491$	784.161			1.59707			0.798534	−	0.601949i	$-0.205609\pi$
$491$	784.161			1.59707			0.798534	+	0.601949i	$0.205609\pi$
$492$		0			0
$493$	−11.4487	+	6.60991i	−0.0232225	+	0.0134075i
$494$	−45.2132	−	78.3116i	−0.0915247	−	0.158525i
$495$		0			0
$496$		−	195.467i		−	0.394086i
$497$	−227.397	−	115.360i	−0.457539	−	0.232112i
$498$		0			0
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	−0.767226	−	0.641377i	$-0.778363\pi$
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	0.939062	+	0.343748i	$0.111697\pi$
$500$	−69.2498	+	39.9814i	−0.138500	+	0.0799628i
$501$		0			0
$502$	−607.051	−	350.481i	−1.20926	−	0.698169i
$503$		−	20.0883i		−	0.0399370i	−0.999801	−	0.0199685i	$-0.993643\pi$
$503$		−	20.0883i		−	0.0399370i	0.999801	−	0.0199685i	$-0.00635659\pi$
$504$		0			0
$505$	395.735			0.783634
$506$	93.2756	−	161.558i	0.184339	−	0.319285i
$507$		0			0
$508$	247.338	+	428.402i	0.486886	+	0.843311i
$509$	412.890	+	238.382i	0.811178	+	0.468334i	0.847365	−	0.531011i	$-0.178188\pi$
$509$	412.890	+	238.382i	0.811178	+	0.468334i	−0.0361865	+	0.999345i	$0.511521\pi$
$510$		0			0
$511$	367.709	−	19.9211i	0.719587	−	0.0389846i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−490.555	+	283.222i	−0.954387	+	0.551016i
$515$	398.452	+	690.139i	0.773693	+	1.34008i
$516$		0			0
$517$			250.613i			0.484744i
$518$	−1.57507	−	29.0730i	−0.00304068	−	0.0561255i
$519$		0			0
$520$	−143.397	+	248.371i	−0.275763	+	0.477636i
$521$	−739.823	+	427.137i	−1.42001	+	0.819841i	−0.996299	−	0.0859587i	$-0.972605\pi$
$521$	−739.823	+	427.137i	−1.42001	+	0.819841i	−0.423707	+	0.905799i	$0.639271\pi$
$522$		0			0
$523$	−513.554	−	296.501i	−0.981940	−	0.566923i	−0.0790845	−	0.996868i	$-0.525200\pi$
$523$	−513.554	−	296.501i	−0.981940	−	0.566923i	−0.902855	+	0.429945i	$0.858533\pi$
$524$		−	295.289i		−	0.563529i
$525$		0			0
$526$	−45.7431			−0.0869640
$527$	−91.9005	+	159.176i	−0.174384	+	0.302043i
$528$		0			0
$529$	−119.919	−	207.706i	−0.226690	−	0.392638i
$530$	454.555	+	262.437i	0.857651	+	0.495165i
$531$		0			0
$532$	26.4853	−	52.2077i	0.0497844	−	0.0981348i
$533$	−427.529			−0.802118
$534$		0			0
$535$	−652.422	+	376.676i	−1.21948	+	0.704068i
$536$	−48.9878	−	84.8494i	−0.0913952	−	0.158301i
$537$		0			0
$538$		−	434.112i		−	0.806899i
$539$	94.0629	−	213.290i	0.174514	−	0.395715i
$540$		0			0
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	0.135352	+	0.990798i	$0.456783\pi$
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	−0.925732	+	0.378180i	$0.876550\pi$
$542$	−93.0624	+	53.7296i	−0.171702	+	0.0991322i
$543$		0			0
$544$	18.4264	+	10.6385i	0.0338721	+	0.0195560i
$545$			963.546i			1.76797i
$546$		0			0
$547$	415.897			0.760323			0.380161	−	0.924920i	$-0.375868\pi$
$547$	415.897			0.760323			0.380161	+	0.924920i	$0.375868\pi$
$548$	−32.5736	+	56.4191i	−0.0594409	+	0.102955i
$549$		0			0
$550$	−63.8162	−	110.533i	−0.116030	−	0.200969i
$551$	−12.7279	−	7.34847i	−0.0230997	−	0.0133366i
$552$		0			0
$553$	198.124	−	129.161i	0.358272	−	0.233564i
$554$	−393.733			−0.710709
$555$		0			0
$556$	−118.794	+	68.5857i	−0.213658	+	0.123356i
$557$	−292.110	−	505.950i	−0.524435	−	0.908348i	−0.999595	−	0.0284485i	$-0.990943\pi$
$557$	−292.110	−	505.950i	−0.524435	−	0.908348i	0.475160	−	0.879899i	$-0.342390\pi$
$558$		0			0
$559$			160.333i			0.286822i
$560$	−185.397	+	10.0441i	−0.331066	+	0.0179360i
$561$		0			0
$562$	−279.088	+	483.395i	−0.496598	+	0.860134i
$563$	−789.076	+	455.573i	−1.40156	+	0.809189i	−0.994552	−	0.104237i	$-0.966760\pi$
$563$	−789.076	+	455.573i	−1.40156	+	0.809189i	−0.407004	+	0.913426i	$0.633427\pi$
$564$		0			0
$565$	−198.375	−	114.532i	−0.351106	−	0.202711i
$566$		−	207.035i		−	0.365787i
$567$		0			0
$568$	103.029			0.181390
$569$	350.000	−	606.217i	0.615113	−	1.06541i	−0.375251	−	0.926923i	$-0.622444\pi$
$569$	350.000	−	606.217i	0.615113	−	1.06541i	0.990365	−	0.138485i	$-0.0442231\pi$
$570$		0			0
$571$	281.231	+	487.107i	0.492525	+	0.853077i	0.999963	−	0.00861055i	$-0.00274086\pi$
$571$	281.231	+	487.107i	0.492525	+	0.853077i	−0.507438	+	0.861688i	$0.669408\pi$
$572$	126.000	+	72.7461i	0.220280	+	0.127179i
$573$		0			0
$574$	−151.154	−	231.861i	−0.263335	−	0.403939i
$575$	−526.014			−0.914807
$576$		0			0
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.906197	−	0.422856i	$-0.861028\pi$
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.0868946	+	0.996218i	$0.527694\pi$
$578$	194.350	+	336.625i	0.336246	+	0.582395i
$579$		0			0
$580$			46.6124i			0.0803662i
$581$	404.029	−	796.420i	0.695402	−	1.37077i
$582$		0			0
$583$	133.136	−	230.598i	0.228364	−	0.395538i
$584$	−128.860	+	74.3973i	−0.220651	+	0.127393i
$585$		0			0
$586$	367.029	+	211.905i	0.626330	+	0.361612i
$587$		−	823.029i		−	1.40209i	−0.713116	−	0.701046i	$-0.752717\pi$
$587$		−	823.029i		−	1.40209i	0.713116	−	0.701046i	$-0.247283\pi$
$588$		0			0
$589$	−204.338			−0.346924
$590$	−181.555	+	314.462i	−0.307720	+	0.532987i
$591$		0			0
$592$	5.88225	+	10.1884i	0.00993623	+	0.0172101i
$593$	538.890	+	311.128i	0.908752	+	0.524668i	0.880029	−	0.474919i	$-0.157523\pi$
$593$	538.890	+	311.128i	0.908752	+	0.524668i	0.0287225	+	0.999587i	$0.490856\pi$
$594$		0			0
$595$	155.698	+	78.9868i	0.261678	+	0.132751i
$596$	−184.794			−0.310057
$597$		0			0
$598$	519.286	−	299.810i	0.868372	−	0.501355i
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	0.568619	−	0.822601i	$-0.307478\pi$
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	−0.996703	+	0.0811377i	$0.974145\pi$
$600$		0			0
$601$		−	680.160i		−	1.13171i	−0.824504	−	0.565857i	$-0.808546\pi$
$601$		−	680.160i		−	1.13171i	0.824504	−	0.565857i	$-0.191454\pi$
$602$	−86.9533	+	56.6864i	−0.144441	+	0.0941635i
$603$		0			0
$604$	91.7868	−	158.979i	0.151965	−	0.263211i
$605$	564.889	−	326.139i	0.933701	−	0.539073i
$606$		0			0
$607$	33.5482	+	19.3690i	0.0552688	+	0.0319095i	0.527380	−	0.849630i	$-0.323175\pi$
$607$	33.5482	+	19.3690i	0.0552688	+	0.0319095i	−0.472111	+	0.881539i	$0.656508\pi$
$608$			23.6544i			0.0389052i
$609$		0			0
$610$	−848.756			−1.39140
$611$	−402.765	+	697.609i	−0.659189	+	1.14175i
$612$		0			0
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	0.654784	−	0.755816i	$-0.272760\pi$
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	−0.981948	+	0.189151i	$0.939426\pi$
$614$	25.7056	+	14.8412i	0.0418658	+	0.0241713i
$615$		0			0
$616$	5.09545	+	94.0530i	0.00827184	+	0.152683i
$617$	959.044			1.55437			0.777183	−	0.629275i	$-0.216648\pi$
$617$	959.044			1.55437			0.777183	+	0.629275i	$0.216648\pi$
$618$		0			0
$619$	−869.951	+	502.267i	−1.40541	+	0.811416i	−0.994941	−	0.100457i	$-0.967970\pi$
$619$	−869.951	+	502.267i	−1.40541	+	0.811416i	−0.410473	+	0.911873i	$0.634636\pi$
$620$	324.037	+	561.248i	0.522640	+	0.905238i
$621$		0			0
$622$			257.443i			0.413895i
$623$	192.408	+	295.142i	0.308841	+	0.473743i
$624$		0			0
$625$	369.691	−	640.323i	0.591505	−	1.02452i
$626$	−119.938	+	69.2460i	−0.191594	+	0.110617i
$627$		0			0
$628$	−14.6468	−	8.45631i	−0.0233229	−	0.0134655i
$629$		−	11.0624i		−	0.0175873i
$630$		0			0
$631$	−386.514			−0.612542			−0.306271	−	0.951944i	$-0.599081\pi$
$631$	−386.514			−0.612542			−0.306271	+	0.951944i	$0.599081\pi$
$632$	−47.7817	+	82.7604i	−0.0756040	+	0.130950i
$633$		0			0
$634$	340.805	+	590.291i	0.537547	+	0.931058i
$635$	−1420.37	−	820.053i	−2.23681	−	1.29142i
$636$		0			0
$637$	604.617	−	442.547i	0.949164	−	0.694736i
$638$	23.6468			0.0370639
$639$		0			0
$640$	64.9706	−	37.5108i	0.101517	−	0.0586106i
$641$	−496.074	−	859.225i	−0.773906	−	1.34044i	−0.935407	−	0.353572i	$-0.884967\pi$
$641$	−496.074	−	859.225i	−0.773906	−	1.34044i	0.161502	−	0.986872i	$-0.448366\pi$
$642$		0			0
$643$		−	944.986i		−	1.46965i	−0.678256	−	0.734826i	$-0.737264\pi$
$643$		−	944.986i		−	1.46965i	0.678256	−	0.734826i	$-0.262736\pi$
$644$	346.191	+	175.625i	0.537564	+	0.272709i
$645$		0			0
$646$	11.1213	−	19.2627i	0.0172157	−	0.0298184i
$647$	−2.50357	+	1.44544i	−0.00386951	+	0.00223406i	−0.501934	−	0.864906i	$-0.667378\pi$
$647$	−2.50357	+	1.44544i	−0.00386951	+	0.00223406i	0.498064	+	0.867140i	$0.334044\pi$
$648$		0			0
$649$	159.529	+	92.1039i	0.245807	+	0.141917i
$650$		−	410.241i		−	0.631140i
$651$		0			0
$652$	443.955			0.680913
$653$	−161.529	+	279.777i	−0.247365	+	0.428449i	−0.962794	−	0.270237i	$-0.912898\pi$
$653$	−161.529	+	279.777i	−0.247365	+	0.428449i	0.715429	+	0.698686i	$0.246231\pi$
$654$		0			0
$655$	489.518	+	847.870i	0.747356	+	1.29446i
$656$	96.8528	+	55.9180i	0.147641	+	0.0852409i
$657$		0			0
$658$	−520.731	+	28.2114i	−0.791385	+	0.0428744i
$659$	−295.955			−0.449098			−0.224549	−	0.974463i	$-0.572091\pi$
$659$	−295.955			−0.449098			−0.224549	+	0.974463i	$0.572091\pi$
$660$		0			0
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	−0.486345	−	0.873767i	$-0.661670\pi$
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	0.513532	+	0.858070i	$0.328337\pi$
$662$	159.104	+	275.576i	0.240338	+	0.416278i
$663$		0			0
$664$			360.843i			0.543439i
$665$	10.5000	+	193.811i	0.0157895	+	0.291445i
$666$		0			0
$667$	48.7279	−	84.3992i	0.0730554	−	0.126536i
$668$	292.441	−	168.841i	0.437785	−	0.252756i
$669$		0			0
$670$	281.319	+	162.420i	0.419880	+	0.242418i
$671$			430.579i			0.641698i
$672$		0			0
$673$	627.044			0.931714			0.465857	−	0.884860i	$-0.345746\pi$
$673$	627.044			0.931714			0.465857	+	0.884860i	$0.345746\pi$
$674$	−186.936	+	323.783i	−0.277353	+	0.480390i
$675$		0			0
$676$	64.8234	+	112.277i	0.0958926	+	0.166091i
$677$	94.6097	+	54.6230i	0.139749	+	0.0806838i	0.568244	−	0.822860i	$-0.307623\pi$
$677$	94.6097	+	54.6230i	0.139749	+	0.0806838i	−0.428496	+	0.903544i	$0.640956\pi$
$678$		0			0
$679$	322.368	−	635.450i	0.474768	−	0.935861i
$680$	−70.5442			−0.103741
$681$		0			0
$682$	284.724	−	164.386i	0.417484	−	0.241035i
$683$	396.783	+	687.248i	0.580941	+	1.00622i	0.995368	+	0.0961370i	$0.0306487\pi$
$683$	396.783	+	687.248i	0.580941	+	1.00622i	−0.414427	+	0.910083i	$0.636018\pi$
$684$		0			0
$685$		−	215.996i		−	0.315323i
$686$	453.770	+	171.437i	0.661473	+	0.249908i
$687$		0			0
$688$	20.9706	−	36.3221i	0.0304805	−	0.0527937i
$689$	741.198	−	427.931i	1.07576	−	0.621090i
$690$		0			0
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	0.610788	−	0.791794i	$-0.290853\pi$
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	−0.380320	+	0.924855i	$0.624186\pi$
$692$		−	328.682i		−	0.474974i
$693$		0			0
$694$	−270.478			−0.389738
$695$	227.397	−	393.863i	0.327190	−	0.566710i
$696$		0			0
$697$	−52.5807	−	91.0725i	−0.0754386	−	0.130664i
$698$	−165.889	−	95.7763i	−0.237664	−	0.137215i
$699$		0			0
$700$	222.485	−	145.042i	0.317836	−	0.207203i
$701$	1043.82			1.48905			0.744525	−	0.667595i	$-0.232676\pi$
$701$	1043.82			1.48905			0.744525	+	0.667595i	$0.232676\pi$
$702$		0			0
$703$	10.6508	−	6.14922i	0.0151504	−	0.00874711i
$704$	−19.0294	−	32.9600i	−0.0270305	−	0.0468181i
$705$		0			0
$706$		−	492.840i		−	0.698073i
$707$	417.143	−	22.5993i	0.590019	−	0.0319651i
$708$		0			0
$709$	490.279	−	849.188i	0.691507	−	1.19773i	−0.279836	−	0.960048i	$-0.590280\pi$
$709$	490.279	−	849.188i	0.691507	−	1.19773i	0.971344	−	0.237678i	$-0.0763864\pi$
$710$	−295.831	+	170.798i	−0.416663	+	0.240560i
$711$		0			0
$712$	−123.286	−	71.1794i	−0.173155	−	0.0999711i
$713$		−	1354.97i		−	1.90038i
$714$		0			0
$715$	−482.382			−0.674660
$716$	185.184	−	320.748i	0.258637	−	0.447972i
$717$		0			0
$718$	−215.548	−	373.340i	−0.300206	−	0.519972i
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.889230	−	0.457460i	$-0.151241\pi$
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.0484429	+	0.998826i	$0.484574\pi$
$720$		0			0
$721$	459.419	+	704.719i	0.637197	+	0.977419i
$722$	−485.803			−0.672858
$723$		0			0
$724$	268.617	−	155.086i	0.371018	−	0.214208i
$725$	−33.3381	−	57.7433i	−0.0459836	−	0.0796459i
$726$		0			0
$727$			735.255i			1.01135i	0.862723	+	0.505677i	$0.168757\pi$
$727$			735.255i			1.01135i	−0.862723	+	0.505677i	$0.831243\pi$
$728$	−136.971	+	269.996i	−0.188146	+	0.370874i
$729$		0			0
$730$	246.665	−	427.237i	0.337898	−	0.585256i
$731$	−34.1543	+	19.7190i	−0.0467227	+	0.0269754i
$732$		0			0
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	0.189692	−	0.981844i	$-0.439251\pi$
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	−0.755456	+	0.655200i	$0.772585\pi$
$734$			134.356i			0.183047i
$735$		0			0
$736$	−156.853			−0.213115
$737$	82.3965	−	142.715i	0.111800	−	0.193643i
$738$		0			0
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	0.872680	−	0.488292i	$-0.162380\pi$
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	−0.859213	+	0.511618i	$0.829046\pi$
$740$	−33.7797	−	19.5027i	−0.0456482	−	0.0263550i
$741$		0			0
$742$	494.132	+	250.676i	0.665946	+	0.337838i
$743$	−43.3095			−0.0582901			−0.0291450	−	0.999575i	$-0.509278\pi$
$743$	−43.3095			−0.0582901			−0.0291450	+	0.999575i	$0.509278\pi$
$744$		0			0
$745$	530.603	−	306.344i	0.712218	−	0.411199i
$746$	179.293	+	310.544i	0.240339	+	0.416279i
$747$		0			0
$748$			35.7875i			0.0478442i
$749$	−666.206	+	434.311i	−0.889460	+	0.579855i
$750$		0			0
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	−0.931235	−	0.364420i	$-0.881267\pi$
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	0.781215	+	0.624263i	$0.214600\pi$
$752$	182.485	−	105.358i	0.242667	−	0.140104i
$753$		0			0
$754$	65.8234	+	38.0031i	0.0872989	+	0.0504020i
$755$			608.641i			0.806147i
$756$		0			0
$757$	935.779			1.23617			0.618084	−	0.786112i	$-0.287909\pi$
$757$	935.779			1.23617			0.618084	+	0.786112i	$0.287909\pi$
$758$	359.387	−	622.476i	0.474125	−	0.821209i
$759$		0			0
$760$	−39.2132	−	67.9193i	−0.0515963	−	0.0893674i
$761$	−1214.79	−	701.357i	−1.59630	−	0.921625i	−0.992191	−	0.124724i	$-0.960195\pi$
$761$	−1214.79	−	701.357i	−1.59630	−	0.921625i	−0.604110	−	0.796901i	$-0.706471\pi$
$762$		0			0
$763$	55.0254	+	1015.67i	0.0721172	+	1.33115i
$764$	−496.191			−0.649465
$765$		0			0
$766$	−585.136	+	337.828i	−0.763885	+	0.441029i
$767$	296.044	+	512.763i	0.385976	+	0.668530i
$768$		0			0
$769$		−	1.72330i		−	0.00224097i	−0.999999	−	0.00112048i	$-0.999643\pi$
$769$		−	1.72330i		−	0.00224097i	0.999999	−	0.00112048i	$-0.000356661\pi$
$770$	−170.548	−	261.609i	−0.221491	−	0.339752i
$771$		0			0
$772$	−154.338	+	267.321i	−0.199920	+	0.346271i
$773$	−194.213	+	112.129i	−0.251245	+	0.145057i	−0.620334	−	0.784337i	$-0.713003\pi$
$773$	−194.213	+	112.129i	−0.251245	+	0.145057i	0.369089	+	0.929394i	$0.379670\pi$
$774$		0			0
$775$	−802.831	−	463.514i	−1.03591	−	0.598083i
$776$			287.911i			0.371019i
$777$		0			0
$778$	240.728			0.309419
$779$	58.4558	−	101.248i	0.0750396	−	0.129972i
$780$		0			0
$781$	86.6468	+	150.077i	0.110943	+	0.192160i
$782$	127.731	+	73.7458i	0.163340	+	0.0943041i
$783$		0			0
$784$	−194.853	+	21.1750i	−0.248537	+	0.0270089i
$785$	56.0740			0.0714319
$786$		0			0
$787$	60.7979	−	35.1017i	0.0772528	−	0.0446019i	−0.460876	−	0.887465i	$-0.652465\pi$
$787$	60.7979	−	35.1017i	0.0772528	−	0.0446019i	0.538129	+	0.842863i	$0.319131\pi$
$788$	−181.103	−	313.679i	−0.229826	−	0.398070i
$789$		0			0
$790$		−	316.842i		−	0.401066i
$791$	−215.647	−	109.399i	−0.272625	−	0.138305i
$792$		0			0
$793$	−691.992	+	1198.57i	−0.872625	+	1.51143i
$794$	299.511	−	172.923i	0.377218	−	0.217787i
$795$		0			0
$796$	−603.978	−	348.707i	−0.758766	−	0.438074i
$797$			1305.38i			1.63787i	0.573889	+	0.818933i	$0.305434\pi$
$797$			1305.38i			1.63787i	−0.573889	+	0.818933i	$0.694566\pi$
$798$		0			0
$799$	−198.140			−0.247985
$800$	−53.6569	+	92.9364i	−0.0670711	+	0.116170i
$801$		0			0
$802$	295.269	+	511.420i	0.368165	+	0.637681i
$803$	−216.740	−	125.135i	−0.269913	−	0.155834i
$804$		0			0
$805$	−1285.17	+	69.6258i	−1.59648	+	0.0864917i
$806$	1056.75			1.31110
$807$		0			0
$808$	−146.184	+	84.3992i	−0.180921	+	0.104455i
$809$	381.382	+	660.573i	0.471424	+	0.816531i	0.999466	−	0.0326879i	$-0.0104067\pi$
$809$	381.382	+	660.573i	0.471424	+	0.816531i	−0.528041	+	0.849219i	$0.677073\pi$
$810$		0			0
$811$		−	1214.98i		−	1.49813i	−0.662498	−	0.749064i	$-0.730504\pi$
$811$		−	1214.98i		−	1.49813i	0.662498	−	0.749064i	$-0.269496\pi$
$812$	2.66190	+	49.1340i	0.00327821	+	0.0605099i
$813$		0			0
$814$	−9.89383	+	17.1366i	−0.0121546	+	0.0210524i
$815$	−1274.74	+	735.970i	−1.56410	+	0.903031i
$816$		0			0
$817$	−37.9706	−	21.9223i	−0.0464756	−	0.0268327i
$818$		−	435.877i		−	0.532857i
$819$		0			0
$820$	−370.794			−0.452188
$821$	−291.684	+	505.211i	−0.355279	+	0.615361i	−0.987166	−	0.159700i	$-0.948947\pi$
$821$	−291.684	+	505.211i	−0.355279	+	0.615361i	0.631887	+	0.775061i	$0.282281\pi$
$822$		0			0
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	−0.988306	−	0.152486i	$-0.951272\pi$
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	0.362096	−	0.932141i	$-0.382061\pi$
$824$	−294.375	−	169.957i	−0.357251	−	0.206259i
$825$		0			0
$826$	−173.418	+	341.842i	−0.209950	+	0.413852i
$827$	−152.102			−0.183920			−0.0919599	−	0.995763i	$-0.529313\pi$
$827$	−152.102			−0.183920			−0.0919599	+	0.995763i	$0.529313\pi$
$828$		0			0
$829$	532.095	−	307.205i	0.641852	−	0.370573i	−0.143476	−	0.989654i	$-0.545828\pi$
$829$	532.095	−	307.205i	0.641852	−	0.370573i	0.785327	+	0.619081i	$0.212495\pi$
$830$	−598.191	−	1036.10i	−0.720712	−	1.24831i
$831$		0			0
$832$		−	122.330i		−	0.147032i
$833$	168.632	+	74.3682i	0.202439	+	0.0892776i
$834$		0			0
$835$	−559.794	+	969.592i	−0.670412	+	1.16119i
$836$	−34.4558	+	19.8931i	−0.0412151	+	0.0237956i
$837$		0			0
$838$	−126.323	−	72.9326i	−0.150743	−	0.0870317i
$839$		−	1546.14i		−	1.84284i	−0.388568	−	0.921420i	$-0.627030\pi$
$839$		−	1546.14i		−	1.84284i	0.388568	−	0.921420i	$-0.372970\pi$
$840$		0			0
$841$	−828.647			−0.985311
$842$	−116.828	+	202.353i	−0.138751	+	0.240324i
$843$		0			0
$844$	−364.073	−	630.593i	−0.431366	−	0.747148i
$845$	−372.257	−	214.923i	−0.440541	−	0.254347i
$846$		0			0
$847$	576.823	−	376.041i	0.681019	−	0.443969i
$848$	−223.882			−0.264012
$849$		0			0
$850$	87.3898	−	50.4545i	0.102812	−	0.0593583i
$851$	40.7756	+	70.6255i	0.0479150	+	0.0829912i
$852$		0			0
$853$			1235.15i			1.44800i	0.689798	+	0.724002i	$0.257699\pi$
$853$			1235.15i			1.44800i	−0.689798	+	0.724002i	$0.742301\pi$
$854$	−894.672	+	48.4701i	−1.04763	+	0.0567566i
$855$		0			0
$856$	160.669	−	278.287i	0.187697	−	0.325102i
$857$	953.219	−	550.341i	1.11227	−	0.642172i	0.172857	−	0.984947i	$-0.444700\pi$
$857$	953.219	−	550.341i	1.11227	−	0.642172i	0.939417	+	0.342775i	$0.111367\pi$
$858$		0			0
$859$	512.488	+	295.885i	0.596610	+	0.344453i	0.767707	−	0.640801i	$-0.221398\pi$
$859$	512.488	+	295.885i	0.596610	+	0.344453i	−0.171096	+	0.985254i	$0.554731\pi$
$860$			139.056i			0.161694i
$861$		0			0
$862$	840.801			0.975407
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	−0.884167	−	0.467171i	$-0.845273\pi$
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	0.846666	+	0.532125i	$0.178606\pi$
$864$		0			0
$865$	544.875	+	943.751i	0.629913	+	1.09104i
$866$	49.7574	+	28.7274i	0.0574565	+	0.0331725i
$867$		0			0
$868$	373.617	+	573.105i	0.430435	+	0.660259i
$869$	−160.736			−0.184967
$870$		0			0
$871$	458.720	−	264.842i	0.526659	−	0.304067i
$872$	−205.497	−	355.932i	−0.235662	−	0.408179i
$873$		0			0
$874$			163.972i			0.187611i
$875$	126.618	−	249.589i	0.144706	−	0.285245i
$876$		0			0
$877$	152.096	−	263.438i	0.173427	−	0.300385i	−0.766188	−	0.642616i	$-0.777849\pi$
$877$	152.096	−	263.438i	0.173427	−	0.300385i	0.939616	+	0.342231i	$0.111182\pi$
$878$	179.548	−	103.662i	0.204496	−	0.118066i
$879$		0			0
$880$	109.279	+	63.0924i	0.124181	+	0.0716959i
$881$			863.732i			0.980400i	0.871610	+	0.490200i	$0.163076\pi$
$881$			863.732i			0.980400i	−0.871610	+	0.490200i	$0.836924\pi$
$882$		0			0
$883$	−567.456			−0.642645			−0.321323	−	0.946970i	$-0.604127\pi$
$883$	−567.456			−0.642645			−0.321323	+	0.946970i	$0.604127\pi$
$884$	−57.5147	+	99.6184i	−0.0650619	+	0.112691i
$885$		0			0
$886$	−75.9153	−	131.489i	−0.0856831	−	0.148408i
$887$	770.555	+	444.880i	0.868721	+	0.501556i	0.866923	−	0.498442i	$-0.166094\pi$
$887$	770.555	+	444.880i	0.868721	+	0.501556i	0.00179783	+	0.999998i	$0.499428\pi$
$888$		0			0
$889$	−1544.04	−	783.302i	−1.73683	−	0.881105i
$890$	471.993			0.530329
$891$		0			0
$892$	−213.442	+	123.231i	−0.239284	+	0.138151i
$893$	−110.140	−	190.767i	−0.123337	−	0.213625i
$894$		0			0
$895$			1227.96i			1.37202i
$896$	66.3431	−	43.2503i	0.0740437	−	0.0482704i
$897$		0			0
$898$	−95.5736	+	165.538i	−0.106429	+	0.184341i
$899$	148.742	−	85.8764i	0.165453	−	0.0955243i
$900$		0			0
$901$	182.316	+	105.260i	0.202349	+	0.116826i
$902$			188.106i			0.208543i
$903$		0			0
$904$	97.7056			0.108081
$905$	−514.191	+	890.605i	−0.568167	+	0.984094i
$906$		0			0
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	0.744340	−	0.667800i	$-0.232764\pi$
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	−0.950502	+	0.310717i	$0.899431\pi$
$908$	−132.286	−	76.3756i	−0.145690	−	0.0841141i
$909$		0			0
$910$	−54.3015	−	1002.31i	−0.0596720	−	1.10144i
$911$	−1133.75			−1.24451			−0.622256	−	0.782814i	$-0.713784\pi$
$911$	−1133.75			−1.24451			−0.622256	+	0.782814i	$0.713784\pi$
$912$		0			0
$913$	−525.618	+	303.466i	−0.575704	+	0.332383i
$914$	112.950	+	195.635i	0.123577	+	0.214042i
$915$		0			0
$916$		−	714.572i		−	0.780101i
$917$	564.419	+	865.782i	0.615506	+	0.944146i
$918$		0			0
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	−0.963043	−	0.269347i	$-0.913192\pi$
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	0.714783	+	0.699346i	$0.246525\pi$
$920$	450.375	−	260.024i	0.489538	−	0.282635i
$921$		0			0
$922$	379.977	+	219.380i	0.412122	+	0.237939i
$923$			557.007i			0.603474i
$924$		0			0
$925$	55.7948			0.0603187
$926$	−230.527	+	399.284i	−0.248949	+	0.431193i
$927$		0			0
$928$	−9.94113	−	17.2185i	−0.0107124	−	0.0185545i
$929$	824.058	+	475.770i	0.887037	+	0.512131i	0.872972	−	0.487770i	$-0.162189\pi$
$929$	824.058	+	475.770i	0.887037	+	0.512131i	0.0140650	+	0.999901i	$0.495523\pi$
$930$		0			0
$931$	22.1360	+	203.696i	0.0237766	+	0.218793i
$932$	546.146			0.585994
$933$		0			0
$934$	−729.407	+	421.123i	−0.780949	+	0.450881i
$935$	−59.3269	−	102.757i	−0.0634513	−	0.109901i
$936$		0			0
$937$			1295.71i			1.38283i	0.722460	+	0.691413i	$0.243011\pi$
$937$			1295.71i			1.38283i	−0.722460	+	0.691413i	$0.756989\pi$
$938$	305.813	+	155.141i	0.326027	+	0.165395i
$939$		0			0
$940$	−349.316	+	605.033i	−0.371613	+	0.643652i
$941$	1175.10	−	678.446i	1.24878	−	0.720984i	0.277915	−	0.960606i	$-0.410357\pi$
$941$	1175.10	−	678.446i	1.24878	−	0.720984i	0.970866	+	0.239622i	$0.0770234\pi$
$942$		0			0
$943$	671.382	+	387.622i	0.711964	+	0.411052i
$944$		−	154.882i		−	0.164070i
$945$		0			0
$946$	70.5442			0.0745710
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	−0.990265	−	0.139197i	$-0.955548\pi$
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	0.615681	+	0.787996i	$0.288881\pi$
$948$		0			0
$949$	−402.213	−	696.654i	−0.423828	−	0.734092i
$950$	97.1543	+	56.0921i	0.102268	+	0.0590443i
$951$		0			0
$952$	−74.3604	+	4.02858i	−0.0781097	+	0.00423170i
$953$	−936.603			−0.982794			−0.491397	−	0.870936i	$-0.663514\pi$
$953$	−936.603			−0.982794			−0.491397	+	0.870936i	$0.663514\pi$
$954$		0			0
$955$	1424.72	−	822.564i	1.49186	−	0.861324i
$956$	−265.103	−	459.171i	−0.277304	−	0.480305i
$957$		0			0
$958$			716.554i			0.747969i
$959$	−12.3350	−	227.681i	−0.0128623	−	0.237415i
$960$		0			0
$961$	713.477	−	1235.78i	0.742432	−	1.28593i
$962$	−55.0812	+	31.8011i	−0.0572569	+	0.0330573i
$963$		0			0
$964$	151.794	+	87.6383i	0.157463	+	0.0909111i
$965$		−	1023.42i		−	1.06054i
$966$		0			0
$967$	1374.37			1.42127			0.710635	−	0.703561i	$-0.248408\pi$
$967$	1374.37			1.42127			0.710635	+	0.703561i	$0.248408\pi$
$968$	−139.113	+	240.950i	−0.143711	+	0.248916i
$969$		0			0
$970$	−477.286	−	826.684i	−0.492048	−	0.852252i
$971$	27.2466	+	15.7309i	0.0280604	+	0.0162007i	0.513965	−	0.857811i	$-0.328176\pi$
$971$	27.2466	+	15.7309i	0.0280604	+	0.0162007i	−0.485904	+	0.874012i	$0.661510\pi$
$972$		0			0
$973$	217.206	−	428.156i	0.223233	−	0.440037i
$974$	−298.825			−0.306802
$975$		0			0
$976$	313.529	−	181.016i	0.321239	−	0.185467i
$977$	−270.949	−	469.297i	−0.277327	−	0.480345i	0.693392	−	0.720560i	$-0.256115\pi$
$977$	−270.949	−	469.297i	−0.277327	−	0.480345i	−0.970720	+	0.240215i	$0.922782\pi$
$978$		0			0
$979$		−	239.445i		−	0.244581i
$980$	524.382	−	383.819i	0.535083	−	0.391652i
$981$		0			0
$982$	554.485	−	960.397i	0.564649	−	0.978001i
$983$	−19.4161	+	11.2099i	−0.0197519	+	0.0114038i	−0.509843	−	0.860267i	$-0.670297\pi$
$983$	−19.4161	+	11.2099i	−0.0197519	+	0.0114038i	0.490092	+	0.871671i	$0.336963\pi$
$984$		0			0
$985$	1040.01	+	600.448i	1.05584	+	0.609592i
$986$			18.6957i			0.0189611i
$987$		0			0
$988$	−127.882			−0.129435
$989$	145.368	−	251.784i	0.146984	−	0.254584i
$990$		0			0
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	0.642726	−	0.766097i	$-0.277804\pi$
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	−0.984822	+	0.173568i	$0.944470\pi$
$992$	−239.397	−	138.216i	−0.241328	−	0.139331i
$993$		0			0
$994$	−302.080	+	196.932i	−0.303904	+	0.198120i
$995$	2312.28			2.32390
$996$		0			0
$997$	758.779	−	438.081i	0.761062	−	0.439400i	−0.0686147	−	0.997643i	$-0.521858\pi$
$997$	758.779	−	438.081i	0.761062	−	0.439400i	0.829677	+	0.558244i	$0.188525\pi$
$998$	−121.263	−	210.034i	−0.121506	−	0.210455i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.n.c.19.2		4
3.2	odd	2		14.3.d.a.5.1	yes	4
4.3	odd	2		1008.3.cg.l.145.2		4
7.2	even	3		882.3.c.f.685.1		4
7.3	odd	6	inner	126.3.n.c.73.2		4
7.4	even	3		882.3.n.b.325.2		4
7.5	odd	6		882.3.c.f.685.2		4
7.6	odd	2		882.3.n.b.19.2		4
12.11	even	2		112.3.s.b.33.1		4
15.2	even	4		350.3.i.a.299.2		8
15.8	even	4		350.3.i.a.299.3		8
15.14	odd	2		350.3.k.a.201.2		4
21.2	odd	6		98.3.b.b.97.4		4
21.5	even	6		98.3.b.b.97.3		4
21.11	odd	6		98.3.d.a.31.1		4
21.17	even	6		14.3.d.a.3.1	✓	4
21.20	even	2		98.3.d.a.19.1		4
24.5	odd	2		448.3.s.d.257.1		4
24.11	even	2		448.3.s.c.257.2		4
28.3	even	6		1008.3.cg.l.577.2		4
84.11	even	6		784.3.s.c.129.2		4
84.23	even	6		784.3.c.e.97.2		4
84.47	odd	6		784.3.c.e.97.3		4
84.59	odd	6		112.3.s.b.17.1		4
84.83	odd	2		784.3.s.c.705.2		4
105.17	odd	12		350.3.i.a.199.3		8
105.38	odd	12		350.3.i.a.199.2		8
105.59	even	6		350.3.k.a.101.2		4
168.59	odd	6		448.3.s.c.129.2		4
168.101	even	6		448.3.s.d.129.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	21.17	even	6
14.3.d.a.5.1	yes	4	3.2	odd	2
98.3.b.b.97.3		4	21.5	even	6
98.3.b.b.97.4		4	21.2	odd	6
98.3.d.a.19.1		4	21.20	even	2
98.3.d.a.31.1		4	21.11	odd	6
112.3.s.b.17.1		4	84.59	odd	6
112.3.s.b.33.1		4	12.11	even	2
126.3.n.c.19.2		4	1.1	even	1	trivial
126.3.n.c.73.2		4	7.3	odd	6	inner
350.3.i.a.199.2		8	105.38	odd	12
350.3.i.a.199.3		8	105.17	odd	12
350.3.i.a.299.2		8	15.2	even	4
350.3.i.a.299.3		8	15.8	even	4
350.3.k.a.101.2		4	105.59	even	6
350.3.k.a.201.2		4	15.14	odd	2
448.3.s.c.129.2		4	168.59	odd	6
448.3.s.c.257.2		4	24.11	even	2
448.3.s.d.129.1		4	168.101	even	6
448.3.s.d.257.1		4	24.5	odd	2
784.3.c.e.97.2		4	84.23	even	6
784.3.c.e.97.3		4	84.47	odd	6
784.3.s.c.129.2		4	84.11	even	6
784.3.s.c.705.2		4	84.83	odd	2
882.3.c.f.685.1		4	7.2	even	3
882.3.c.f.685.2		4	7.5	odd	6
882.3.n.b.19.2		4	7.6	odd	2
882.3.n.b.325.2		4	7.4	even	3
1008.3.cg.l.145.2		4	4.3	odd	2
1008.3.cg.l.577.2		4	28.3	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(5.74264 + 3.31552i) q^{5} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} +(8.12132 - 4.68885i) q^{10} +(-2.37868 - 4.11999i) q^{11} -15.2913i q^{13} +(8.29289 - 5.40629i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(3.25736 - 1.88064i) q^{17} +(3.62132 + 2.09077i) q^{19} -13.2621i q^{20} -6.72792 q^{22} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} +(-18.7279 - 10.8126i) q^{26} +(-0.757359 - 13.9795i) q^{28} -3.51472 q^{29} +(-42.3198 + 24.4334i) q^{31} +(2.82843 + 4.89898i) q^{32} -5.31925i q^{34} +(25.3492 + 38.8841i) q^{35} +(1.47056 - 2.54709i) q^{37} +(5.12132 - 2.95680i) q^{38} +(-16.2426 - 9.37769i) q^{40} -27.9590i q^{41} -10.4853 q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(-45.6213 - 26.3395i) q^{47} +(28.9411 + 39.5400i) q^{49} +26.8284 q^{50} +(-26.4853 + 15.2913i) q^{52} +(27.9853 + 48.4719i) q^{53} -31.5462i q^{55} +(-17.6569 - 8.95743i) q^{56} +(-2.48528 + 4.30463i) q^{58} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +69.1080i q^{62} +8.00000 q^{64} +(50.6985 - 87.8124i) q^{65} +(17.3198 + 29.9988i) q^{67} +(-6.51472 - 3.76127i) q^{68} +(65.5477 - 3.55114i) q^{70} -36.4264 q^{71} +(45.5589 - 26.3034i) q^{73} +(-2.07969 - 3.60213i) q^{74} -8.36308i q^{76} +(-1.80152 - 33.2528i) q^{77} +(16.8934 - 29.2602i) q^{79} +(-22.9706 + 13.2621i) q^{80} +(-34.2426 - 19.7700i) q^{82} -127.577i q^{83} +24.9411 q^{85} +(-7.41421 + 12.8418i) q^{86} +(6.72792 + 11.6531i) q^{88} +(43.5883 + 25.1657i) q^{89} +(48.4264 - 95.4580i) q^{91} +55.4558 q^{92} +(-64.5183 + 37.2497i) q^{94} +(13.8640 + 24.0131i) q^{95} -101.792i q^{97} +(68.8909 - 7.48650i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 6 q^{5} + 8 q^{7} + 24 q^{10} - 18 q^{11} + 36 q^{14} - 8 q^{16} + 30 q^{17} + 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} - 24 q^{26} - 20 q^{28} - 48 q^{29} - 42 q^{31} + 42 q^{35} - 62 q^{37}+ \cdots + 120 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 6 * q^5 + 8 * q^7 + 24 * q^10 - 18 * q^11 + 36 * q^14 - 8 * q^16 + 30 * q^17 + 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 - 24 * q^26 - 20 * q^28 - 48 * q^29 - 42 * q^31 + 42 * q^35 - 62 * q^37 + 12 * q^38 - 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 - 174 * q^47 - 20 * q^49 + 96 * q^50 - 72 * q^52 + 78 * q^53 - 48 * q^56 + 24 * q^58 + 78 * q^59 - 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 - 60 * q^68 + 84 * q^70 + 24 * q^71 + 318 * q^73 - 96 * q^74 - 126 * q^77 + 110 * q^79 - 24 * q^80 - 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 + 378 * q^89 + 24 * q^91 + 120 * q^92 - 12 * q^94 + 30 * q^95 + 120 * q^98

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