LMFDB - Embedded newform 126.3.n.c.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,3,Mod(19,126)]

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

lf = mfeigenbasis(mf)

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")

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

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			73.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.3.n.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.200000	−	0.979796i	$-0.435906\pi$
$5$	5.74264	−	3.31552i	1.14853	−	0.663103i	0.948528	+	0.316693i	$0.102572\pi$
$6$		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	−0.953657	−	0.300897i	$-0.902714\pi$
$11$	−2.37868	+	4.11999i	−0.216244	+	0.374545i	0.737413	+	0.675442i	$0.236047\pi$
$12$		0			0
$13$			15.2913i			1.17625i	0.808769	+	0.588126i	$0.200134\pi$
$13$			15.2913i			1.17625i	−0.808769	+	0.588126i	$0.799866\pi$
$14$	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	0.592736	−	0.805397i	$-0.298048\pi$
$17$	3.25736	+	1.88064i	0.191609	+	0.110626i	−0.401126	+	0.916023i	$0.631381\pi$
$18$		0			0
$19$	3.62132	−	2.09077i	0.190596	−	0.110041i	−0.401666	−	0.915786i	$-0.631569\pi$
$19$	3.62132	−	2.09077i	0.190596	−	0.110041i	0.592261	+	0.805746i	$0.298235\pi$
$20$			13.2621i			0.663103i
$21$		0			0
$22$	−6.72792			−0.305815
$23$	−13.8640	−	24.0131i	−0.602781	−	1.04405i	−0.992398	−	0.123070i	$-0.960726\pi$
$23$	−13.8640	−	24.0131i	−0.602781	−	1.04405i	0.389617	−	0.920977i	$-0.372607\pi$
$24$		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	−0.374850	−	0.927085i	$-0.622306\pi$
$31$	−42.3198	−	24.4334i	−1.36516	−	0.788173i	−0.990305	+	0.138913i	$0.955639\pi$
$32$	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	0.885214	−	0.465185i	$-0.154012\pi$
$37$	1.47056	+	2.54709i	0.0397449	+	0.0688403i	−0.845469	+	0.534025i	$0.820679\pi$
$38$	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	$0.110753\pi$
$41$			27.9590i			0.681927i	−0.940077	+	0.340963i	$0.889247\pi$
$42$		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	−0.899439	−	0.437046i	$-0.856025\pi$
$47$	−45.6213	+	26.3395i	−0.970666	+	0.560415i	−0.0712271	+	0.997460i	$0.522691\pi$
$48$		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	−0.471442	−	0.881897i	$-0.656266\pi$
$53$	27.9853	−	48.4719i	0.528024	−	0.914565i	0.999466	−	0.0326677i	$-0.0104003\pi$
$54$		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	0.188136	−	0.982143i	$-0.439755\pi$
$59$	−33.5330	−	19.3603i	−0.568356	−	0.328141i	−0.756492	+	0.654002i	$0.773089\pi$
$60$		0			0
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.977750	−	0.209774i	$-0.932727\pi$
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.307205	+	0.951643i	$0.599394\pi$
$62$		−	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	−0.707337	−	0.706877i	$-0.750104\pi$
$67$	17.3198	−	29.9988i	0.258505	−	0.447743i	0.965842	+	0.259134i	$0.0834370\pi$
$68$	−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	0.778461	−	0.627693i	$-0.216001\pi$
$73$	45.5589	+	26.3034i	0.624094	+	0.360321i	−0.154367	+	0.988014i	$0.549334\pi$
$74$	−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	0.952913	−	0.303243i	$-0.0980694\pi$
$79$	16.8934	+	29.2602i	0.213840	+	0.370383i	−0.739073	+	0.673626i	$0.764736\pi$
$80$	−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	$0.279016\pi$
$83$			127.577i			1.53708i	−0.639803	+	0.768539i	$0.720984\pi$
$84$		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	−0.234717	−	0.972064i	$-0.575416\pi$
$89$	43.5883	−	25.1657i	0.489756	−	0.282761i	0.724473	+	0.689303i	$0.242083\pi$
$90$		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	$0.175823\pi$
$97$			101.792i			1.04940i	−0.851287	+	0.524700i	$0.824177\pi$
$98$	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	0.733541	−	0.679646i	$-0.237866\pi$
$101$	51.6838	+	29.8396i	0.511720	+	0.295442i	−0.221820	+	0.975088i	$0.571200\pi$
$102$		0			0
$103$	104.077	−	60.0890i	1.01046	−	0.583388i	0.0991322	−	0.995074i	$-0.468393\pi$
$103$	104.077	−	60.0890i	1.01046	−	0.583388i	0.911326	+	0.411686i	$0.135060\pi$
$104$		−	43.2503i		−	0.415868i
$105$		0			0
$106$	79.1543			0.746739
$107$	−56.8051	−	98.3893i	−0.530889	−	0.919526i	−0.999350	−	0.0360423i	$-0.988525\pi$
$107$	−56.8051	−	98.3893i	−0.530889	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$108$		0			0
$109$	72.6543	−	125.841i	0.666553	−	1.15450i	−0.312308	−	0.949981i	$-0.601102\pi$
$109$	72.6543	−	125.841i	0.666553	−	1.15450i	0.978862	−	0.204524i	$-0.0655645\pi$
$110$	−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	0.0749822	−	0.997185i	$-0.476110\pi$
$131$	127.864	−	73.8223i	0.976061	−	0.563529i	0.901079	+	0.433656i	$0.142777\pi$
$132$		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	−0.919325	−	0.393500i	$-0.871264\pi$
$137$	−16.2868	+	28.2096i	−0.118882	+	0.205909i	0.800443	+	0.599409i	$0.204598\pi$
$138$		0			0
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$	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	0.978374	−	0.206842i	$-0.0663185\pi$
$149$	46.1985	+	80.0181i	0.310057	+	0.537034i	−0.668317	+	0.743876i	$0.732985\pi$
$150$		0			0
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	−0.673093	−	0.739558i	$-0.735035\pi$
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	0.977022	+	0.213136i	$0.0683678\pi$
$152$	−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	0.523142	−	0.852246i	$-0.324760\pi$
$157$	7.32338	+	4.22815i	0.0466457	+	0.0269309i	−0.476496	+	0.879177i	$0.658093\pi$
$158$	−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	−0.974703	−	0.223506i	$-0.928250\pi$
$163$	−110.989	−	192.238i	−0.680913	−	1.17938i	0.293789	−	0.955870i	$-0.405084\pi$
$164$	−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	$-0.831304\pi$
$167$		−	168.841i		−	1.01102i	0.862820	−	0.505511i	$-0.168696\pi$
$168$		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	−0.0286608	−	0.999589i	$-0.509124\pi$
$173$	142.323	−	82.1704i	0.822678	−	0.474974i	0.851339	+	0.524616i	$0.175791\pi$
$174$		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	−0.482526	−	0.875882i	$-0.660280\pi$
$179$	92.5919	−	160.374i	0.517273	−	0.895943i	0.999799	−	0.0200614i	$-0.00638618\pi$
$180$		0			0
$181$		−	155.086i		−	0.856830i	−0.903582	−	0.428415i	$-0.859072\pi$
$181$		−	155.086i		−	0.856830i	0.903582	−	0.428415i	$-0.140928\pi$
$182$	−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	0.983251	+	0.182257i	$0.0583402\pi$
$191$	124.048	+	214.857i	0.649465	+	1.12491i	−0.333786	+	0.942649i	$0.608326\pi$
$192$		0			0
$193$	−77.1690	+	133.661i	−0.399840	+	0.692543i	−0.993706	−	0.112021i	$-0.964268\pi$
$193$	−77.1690	+	133.661i	−0.399840	+	0.692543i	0.593866	+	0.804564i	$0.297601\pi$
$194$	−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	0.999788	+	0.0206121i	$0.00656150\pi$
$199$	301.989	+	174.353i	1.51753	+	0.876147i	0.517744	+	0.855535i	$0.326772\pi$
$200$	−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	$0.0891089\pi$
$223$			123.231i			0.552603i	−0.961071	+	0.276302i	$0.910891\pi$
$224$	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	0.638564	−	0.769569i	$-0.279529\pi$
$227$	66.1432	+	38.1878i	0.291380	+	0.168228i	−0.347184	+	0.937797i	$0.612862\pi$
$228$		0			0
$229$	309.419	−	178.643i	1.35117	−	0.780101i	0.362760	−	0.931883i	$-0.381834\pi$
$229$	309.419	−	178.643i	1.35117	−	0.780101i	0.988414	+	0.151782i	$0.0485012\pi$
$230$		−	260.024i		−	1.13054i
$231$		0			0
$232$	9.94113			0.0428497
$233$	−136.537	−	236.488i	−0.585994	−	1.01497i	−0.994751	−	0.102328i	$-0.967371\pi$
$233$	−136.537	−	236.488i	−0.585994	−	1.01497i	0.408757	−	0.912643i	$-0.365962\pi$
$234$		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	0.334203	−	0.942501i	$-0.391533\pi$
$241$	−75.8970	−	43.8191i	−0.314925	−	0.181822i	−0.649128	+	0.760679i	$0.724866\pi$
$242$	−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	$0.449337\pi$
$251$			495.655i			1.97472i	−0.158491	+	0.987360i	$0.550663\pi$
$252$		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	−0.988208	−	0.153119i	$-0.951068\pi$
$257$	−346.875	+	200.268i	−1.34971	+	0.779254i	−0.361499	+	0.932372i	$0.617735\pi$
$258$		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	−0.895133	−	0.445799i	$-0.852919\pi$
$263$	−16.1726	+	28.0118i	−0.0614928	+	0.106509i	0.833640	+	0.552308i	$0.186253\pi$
$264$		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	0.904749	−	0.425944i	$-0.140058\pi$
$269$	265.838	+	153.482i	0.988246	+	0.570564i	0.0834963	+	0.996508i	$0.473391\pi$
$270$		0			0
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	−0.616474	−	0.787376i	$-0.711439\pi$
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	0.373650	+	0.927570i	$0.378106\pi$
$272$		−	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	0.497448	+	0.867494i	$0.334270\pi$
$277$	−139.206	+	241.111i	−0.502547	+	0.870438i	−0.999996	+	0.00294398i	$0.999063\pi$
$278$	−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	0.706983	−	0.707230i	$-0.250056\pi$
$283$	126.783	+	73.1981i	0.447996	+	0.258650i	−0.258988	+	0.965881i	$0.583389\pi$
$284$	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	$-0.829128\pi$
$293$		−	299.678i		−	1.02279i	0.859345	−	0.511396i	$-0.170872\pi$
$294$		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	$-0.989117\pi$
$307$		−	20.9886i		−	0.0683666i	0.999416	−	0.0341833i	$-0.0108830\pi$
$308$	−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	0.224649	−	0.974440i	$-0.427876\pi$
$311$	−157.651	−	91.0197i	−0.506916	−	0.292668i	−0.731565	+	0.681772i	$0.761210\pi$
$312$		0			0
$313$	−84.8087	+	48.9643i	−0.270954	+	0.156435i	−0.629321	−	0.777145i	$-0.716667\pi$
$313$	−84.8087	+	48.9643i	−0.270954	+	0.156435i	0.358367	+	0.933581i	$0.383334\pi$
$314$			11.9590i			0.0380861i
$315$		0			0
$316$	−67.5736			−0.213840
$317$	−240.985	−	417.399i	−0.760206	−	1.31672i	−0.942744	−	0.333517i	$-0.891765\pi$
$317$	−240.985	−	417.399i	−0.760206	−	1.31672i	0.182538	−	0.983199i	$-0.441569\pi$
$318$		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	0.644522	−	0.764586i	$-0.277056\pi$
$331$	−112.504	−	194.862i	−0.339890	−	0.588707i	−0.984412	+	0.175879i	$0.943723\pi$
$332$	−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	−0.970283	−	0.241973i	$-0.922205\pi$
$347$	−95.6285	+	165.633i	−0.275586	+	0.477330i	0.694697	+	0.719303i	$0.255539\pi$
$348$		0			0
$349$			135.448i			0.388104i	0.980991	+	0.194052i	$0.0621630\pi$
$349$			135.448i			0.388104i	−0.980991	+	0.194052i	$0.937837\pi$
$350$	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	0.862322	−	0.506360i	$-0.169009\pi$
$353$	301.802	+	174.245i	0.854962	+	0.493612i	−0.00736010	+	0.999973i	$0.502343\pi$
$354$		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	0.996379	−	0.0850256i	$-0.0270972\pi$
$359$	152.415	+	263.991i	0.424555	+	0.735351i	−0.571824	+	0.820377i	$0.693764\pi$
$360$		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	0.383701	−	0.923457i	$-0.374649\pi$
$367$	−82.2761	−	47.5021i	−0.224186	−	0.129434i	−0.607887	+	0.794024i	$0.707983\pi$
$368$	−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	0.644521	−	0.764586i	$-0.277057\pi$
$373$	−126.779	−	219.588i	−0.339891	−	0.588708i	−0.984412	+	0.175879i	$0.943723\pi$
$374$	−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	−0.930976	−	0.365080i	$-0.881042\pi$
$383$	−413.753	+	238.881i	−1.08030	+	0.623709i	−0.149320	+	0.988789i	$0.547708\pi$
$384$		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	−0.735647	−	0.677365i	$-0.763122\pi$
$389$	85.1102	−	147.415i	0.218792	−	0.378959i	0.954439	+	0.298406i	$0.0964550\pi$
$390$		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	−0.208960	−	0.977924i	$-0.567008\pi$
$397$	211.786	−	122.275i	0.533467	−	0.307997i	0.742427	+	0.669927i	$0.233675\pi$
$398$			493.146i			1.23906i
$399$		0			0
$400$	−75.8823			−0.189706
$401$	−208.786	−	361.629i	−0.520664	−	0.901817i	−0.999711	−	0.0240277i	$-0.992351\pi$
$401$	−208.786	−	361.629i	−0.520664	−	0.901817i	0.479047	−	0.877789i	$-0.340982\pi$
$402$		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	0.789457	−	0.613806i	$-0.210362\pi$
$409$	266.919	+	154.106i	0.652614	+	0.376787i	−0.136843	+	0.990593i	$0.543696\pi$
$410$	−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	$0.0392776\pi$
$419$			103.142i			0.246163i	−0.992397	+	0.123081i	$0.960722\pi$
$420$		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	−0.282212	−	0.959352i	$-0.591068\pi$
$431$	297.268	−	514.883i	0.689717	−	1.19463i	0.971929	−	0.235273i	$-0.0755984\pi$
$432$		0			0
$433$		−	40.6267i		−	0.0938261i	−0.998899	−	0.0469131i	$-0.985062\pi$
$433$		−	40.6267i		−	0.0938261i	0.998899	−	0.0469131i	$-0.0149384\pi$
$434$	−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	−0.348380	−	0.937353i	$-0.613268\pi$
$439$	126.959	−	73.3001i	0.289201	−	0.166971i	0.637582	+	0.770383i	$0.279935\pi$
$440$		−	89.2261i		−	0.202787i
$441$		0			0
$442$	−81.3381			−0.184023
$443$	53.6802	+	92.9768i	0.121174	+	0.209880i	0.920231	−	0.391376i	$-0.128001\pi$
$443$	53.6802	+	92.9768i	0.121174	+	0.209880i	−0.799057	+	0.601256i	$0.794667\pi$
$444$		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	0.765315	−	0.643656i	$-0.222583\pi$
$457$	−79.8675	−	138.335i	−0.174765	−	0.302702i	−0.940080	+	0.340954i	$0.889250\pi$
$458$	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	$-0.890758\pi$
$461$		−	310.250i		−	0.672993i	0.941685	−	0.336497i	$-0.109242\pi$
$462$		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	−0.937381	−	0.348306i	$-0.886757\pi$
$467$	−515.769	+	297.779i	−1.10443	+	0.637643i	−0.167048	+	0.985949i	$0.553424\pi$
$468$		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	−0.0336914	−	0.999432i	$-0.510726\pi$
$479$	−438.798	−	253.340i	−0.916071	−	0.528894i	−0.882379	+	0.470539i	$0.844060\pi$
$480$		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	−0.953872	−	0.300215i	$-0.902942\pi$
$487$	−105.651	+	182.992i	−0.216942	+	0.375755i	0.736930	+	0.675970i	$0.236275\pi$
$488$	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	0.939062	−	0.343748i	$-0.111697\pi$
$499$	85.7462	+	148.517i	0.171836	+	0.297629i	−0.767226	+	0.641377i	$0.778363\pi$
$500$	−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	$0.00635659\pi$
$503$			20.0883i			0.0399370i	−0.999801	+	0.0199685i	$0.993643\pi$
$504$		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	−0.0361865	−	0.999345i	$-0.511521\pi$
$509$	412.890	−	238.382i	0.811178	−	0.468334i	0.847365	+	0.531011i	$0.178188\pi$
$510$		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	−0.423707	−	0.905799i	$-0.639271\pi$
$521$	−739.823	−	427.137i	−1.42001	−	0.819841i	−0.996299	+	0.0859587i	$0.972605\pi$
$522$		0			0
$523$	−513.554	+	296.501i	−0.981940	+	0.566923i	−0.902855	−	0.429945i	$-0.858533\pi$
$523$	−513.554	+	296.501i	−0.981940	+	0.566923i	−0.0790845	+	0.996868i	$0.525200\pi$
$524$			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	−0.925732	−	0.378180i	$-0.876550\pi$
$541$	−427.595	−	740.617i	−0.790380	−	1.36898i	0.135352	−	0.990798i	$-0.456783\pi$
$542$	−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	0.475160	+	0.879899i	$0.342390\pi$
$557$	−292.110	+	505.950i	−0.524435	+	0.908348i	−0.999595	+	0.0284485i	$0.990943\pi$
$558$		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	−0.407004	−	0.913426i	$-0.633427\pi$
$563$	−789.076	−	455.573i	−1.40156	−	0.809189i	−0.994552	+	0.104237i	$0.966760\pi$
$564$		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	0.990365	+	0.138485i	$0.0442231\pi$
$569$	350.000	+	606.217i	0.615113	+	1.06541i	−0.375251	+	0.926923i	$0.622444\pi$
$570$		0			0
$571$	281.231	−	487.107i	0.492525	−	0.853077i	−0.507438	−	0.861688i	$-0.669408\pi$
$571$	281.231	−	487.107i	0.492525	−	0.853077i	0.999963	+	0.00861055i	$0.00274086\pi$
$572$	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	−0.0868946	−	0.996218i	$-0.527694\pi$
$577$	−573.014	−	330.830i	−0.993092	−	0.573362i	−0.906197	+	0.422856i	$0.861028\pi$
$578$	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	$0.247283\pi$
$587$			823.029i			1.40209i	−0.713116	+	0.701046i	$0.752717\pi$
$588$		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	0.0287225	−	0.999587i	$-0.490856\pi$
$593$	538.890	−	311.128i	0.908752	−	0.524668i	0.880029	+	0.474919i	$0.157523\pi$
$594$		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	−0.996703	−	0.0811377i	$-0.974145\pi$
$599$	−256.422	+	444.137i	−0.428084	+	0.741463i	0.568619	+	0.822601i	$0.307478\pi$
$600$		0			0
$601$			680.160i			1.13171i	0.824504	+	0.565857i	$0.191454\pi$
$601$			680.160i			1.13171i	−0.824504	+	0.565857i	$0.808546\pi$
$602$	−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	−0.472111	−	0.881539i	$-0.656508\pi$
$607$	33.5482	−	19.3690i	0.0552688	−	0.0319095i	0.527380	+	0.849630i	$0.323175\pi$
$608$		−	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	−0.981948	−	0.189151i	$-0.939426\pi$
$613$	−200.552	+	347.366i	−0.327164	+	0.566665i	0.654784	+	0.755816i	$0.272760\pi$
$614$	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	−0.410473	−	0.911873i	$-0.634636\pi$
$619$	−869.951	−	502.267i	−1.40541	−	0.811416i	−0.994941	+	0.100457i	$0.967970\pi$
$620$	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	0.161502	+	0.986872i	$0.448366\pi$
$641$	−496.074	+	859.225i	−0.773906	+	1.34044i	−0.935407	+	0.353572i	$0.884967\pi$
$642$		0			0
$643$			944.986i			1.46965i	0.678256	+	0.734826i	$0.262736\pi$
$643$			944.986i			1.46965i	−0.678256	+	0.734826i	$0.737264\pi$
$644$	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	0.498064	−	0.867140i	$-0.334044\pi$
$647$	−2.50357	−	1.44544i	−0.00386951	−	0.00223406i	−0.501934	+	0.864906i	$0.667378\pi$
$648$		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	0.715429	−	0.698686i	$-0.246231\pi$
$653$	−161.529	−	279.777i	−0.247365	−	0.428449i	−0.962794	+	0.270237i	$0.912898\pi$
$654$		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	0.513532	−	0.858070i	$-0.328337\pi$
$661$	17.9710	+	10.3756i	0.0271876	+	0.0156968i	−0.486345	+	0.873767i	$0.661670\pi$
$662$	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	−0.428496	−	0.903544i	$-0.640956\pi$
$677$	94.6097	−	54.6230i	0.139749	−	0.0806838i	0.568244	+	0.822860i	$0.307623\pi$
$678$		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	−0.414427	−	0.910083i	$-0.636018\pi$
$683$	396.783	−	687.248i	0.580941	−	1.00622i	0.995368	−	0.0961370i	$-0.0306487\pi$
$684$		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	−0.380320	−	0.924855i	$-0.624186\pi$
$691$	159.253	−	91.9447i	0.230467	−	0.133060i	0.610788	+	0.791794i	$0.290853\pi$
$692$			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	0.971344	+	0.237678i	$0.0763864\pi$
$709$	490.279	+	849.188i	0.691507	+	1.19773i	−0.279836	+	0.960048i	$0.590280\pi$
$710$	−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	0.0484429	−	0.998826i	$-0.484574\pi$
$719$	674.187	−	389.242i	0.937673	−	0.541366i	0.889230	+	0.457460i	$0.151241\pi$
$720$		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	$-0.831243\pi$
$727$		−	735.255i		−	1.01135i	0.862723	−	0.505677i	$-0.168757\pi$
$728$	−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	−0.755456	−	0.655200i	$-0.772585\pi$
$733$	−414.705	+	239.430i	−0.565764	+	0.326644i	0.189692	+	0.981844i	$0.439251\pi$
$734$		−	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	−0.859213	−	0.511618i	$-0.829046\pi$
$739$	9.95227	−	17.2378i	0.0134672	−	0.0233259i	0.872680	+	0.488292i	$0.162380\pi$
$740$	−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	0.781215	−	0.624263i	$-0.214600\pi$
$751$	−112.665	−	195.142i	−0.150020	−	0.259842i	−0.931235	+	0.364420i	$0.881267\pi$
$752$	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	−0.604110	+	0.796901i	$0.706471\pi$
$761$	−1214.79	+	701.357i	−1.59630	+	0.921625i	−0.992191	+	0.124724i	$0.960195\pi$
$762$		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	$0.000356661\pi$
$769$			1.72330i			0.00224097i	−0.999999	+	0.00112048i	$0.999643\pi$
$770$	−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	0.369089	−	0.929394i	$-0.379670\pi$
$773$	−194.213	−	112.129i	−0.251245	−	0.145057i	−0.620334	+	0.784337i	$0.713003\pi$
$774$		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	0.538129	−	0.842863i	$-0.319131\pi$
$787$	60.7979	+	35.1017i	0.0772528	+	0.0446019i	−0.460876	+	0.887465i	$0.652465\pi$
$788$	−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	$-0.694566\pi$
$797$		−	1305.38i		−	1.63787i	0.573889	−	0.818933i	$-0.305434\pi$
$798$		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	−0.528041	−	0.849219i	$-0.677073\pi$
$809$	381.382	−	660.573i	0.471424	−	0.816531i	0.999466	+	0.0326879i	$0.0104067\pi$
$810$		0			0
$811$			1214.98i			1.49813i	0.662498	+	0.749064i	$0.269496\pi$
$811$			1214.98i			1.49813i	−0.662498	+	0.749064i	$0.730504\pi$
$812$	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	0.631887	−	0.775061i	$-0.282281\pi$
$821$	−291.684	−	505.211i	−0.355279	−	0.615361i	−0.987166	+	0.159700i	$0.948947\pi$
$822$		0			0
$823$	−515.371	+	892.648i	−0.626210	+	1.08463i	0.362096	+	0.932141i	$0.382061\pi$
$823$	−515.371	+	892.648i	−0.626210	+	1.08463i	−0.988306	+	0.152486i	$0.951272\pi$
$824$	−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	0.785327	−	0.619081i	$-0.212495\pi$
$829$	532.095	+	307.205i	0.641852	+	0.370573i	−0.143476	+	0.989654i	$0.545828\pi$
$830$	−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	$0.372970\pi$
$839$			1546.14i			1.84284i	−0.388568	+	0.921420i	$0.627030\pi$
$840$		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	$-0.742301\pi$
$853$		−	1235.15i		−	1.44800i	0.689798	−	0.724002i	$-0.257699\pi$
$854$	−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	0.939417	−	0.342775i	$-0.111367\pi$
$857$	953.219	+	550.341i	1.11227	+	0.642172i	0.172857	+	0.984947i	$0.444700\pi$
$858$		0			0
$859$	512.488	−	295.885i	0.596610	−	0.344453i	−0.171096	−	0.985254i	$-0.554731\pi$
$859$	512.488	−	295.885i	0.596610	−	0.344453i	0.767707	+	0.640801i	$0.221398\pi$
$860$		−	139.056i		−	0.161694i
$861$		0			0
$862$	840.801			0.975407
$863$	−32.3635	−	56.0553i	−0.0375012	−	0.0649540i	0.846666	−	0.532125i	$-0.178606\pi$
$863$	−32.3635	−	56.0553i	−0.0375012	−	0.0649540i	−0.884167	+	0.467171i	$0.845273\pi$
$864$		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	0.939616	−	0.342231i	$-0.111182\pi$
$877$	152.096	+	263.438i	0.173427	+	0.300385i	−0.766188	+	0.642616i	$0.777849\pi$
$878$	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	$-0.836924\pi$
$881$		−	863.732i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$882$		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	0.00179783	−	0.999998i	$-0.499428\pi$
$887$	770.555	−	444.880i	0.868721	−	0.501556i	0.866923	+	0.498442i	$0.166094\pi$
$888$		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	−0.950502	−	0.310717i	$-0.899431\pi$
$907$	−186.989	+	323.874i	−0.206162	+	0.357083i	0.744340	+	0.667800i	$0.232764\pi$
$908$	−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	0.714783	−	0.699346i	$-0.246525\pi$
$919$	−228.151	−	395.169i	−0.248260	−	0.429999i	−0.963043	+	0.269347i	$0.913192\pi$
$920$	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	0.0140650	−	0.999901i	$-0.495523\pi$
$929$	824.058	−	475.770i	0.887037	−	0.512131i	0.872972	+	0.487770i	$0.162189\pi$
$930$		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	$-0.756989\pi$
$937$		−	1295.71i		−	1.38283i	0.722460	−	0.691413i	$-0.243011\pi$
$938$	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	0.970866	−	0.239622i	$-0.0770234\pi$
$941$	1175.10	+	678.446i	1.24878	+	0.720984i	0.277915	+	0.960606i	$0.410357\pi$
$942$		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	0.615681	−	0.787996i	$-0.288881\pi$
$947$	−354.731	−	614.412i	−0.374584	−	0.648799i	−0.990265	+	0.139197i	$0.955548\pi$
$948$		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	−0.485904	−	0.874012i	$-0.661510\pi$
$971$	27.2466	−	15.7309i	0.0280604	−	0.0162007i	0.513965	+	0.857811i	$0.328176\pi$
$972$		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	−0.970720	−	0.240215i	$-0.922782\pi$
$977$	−270.949	+	469.297i	−0.277327	+	0.480345i	0.693392	+	0.720560i	$0.256115\pi$
$978$		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	0.490092	−	0.871671i	$-0.336963\pi$
$983$	−19.4161	−	11.2099i	−0.0197519	−	0.0114038i	−0.509843	+	0.860267i	$0.670297\pi$
$984$		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	−0.984822	−	0.173568i	$-0.944470\pi$
$991$	−339.017	+	587.195i	−0.342096	+	0.592528i	0.642726	+	0.766097i	$0.277804\pi$
$992$	−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	0.829677	−	0.558244i	$-0.188525\pi$
$997$	758.779	+	438.081i	0.761062	+	0.439400i	−0.0686147	+	0.997643i	$0.521858\pi$
$998$	−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.73.2		4
3.2	odd	2		14.3.d.a.3.1	✓	4
4.3	odd	2		1008.3.cg.l.577.2		4
7.2	even	3		882.3.n.b.19.2		4
7.3	odd	6		882.3.c.f.685.1		4
7.4	even	3		882.3.c.f.685.2		4
7.5	odd	6	inner	126.3.n.c.19.2		4
7.6	odd	2		882.3.n.b.325.2		4
12.11	even	2		112.3.s.b.17.1		4
15.2	even	4		350.3.i.a.199.3		8
15.8	even	4		350.3.i.a.199.2		8
15.14	odd	2		350.3.k.a.101.2		4
21.2	odd	6		98.3.d.a.19.1		4
21.5	even	6		14.3.d.a.5.1	yes	4
21.11	odd	6		98.3.b.b.97.3		4
21.17	even	6		98.3.b.b.97.4		4
21.20	even	2		98.3.d.a.31.1		4
24.5	odd	2		448.3.s.d.129.1		4
24.11	even	2		448.3.s.c.129.2		4
28.19	even	6		1008.3.cg.l.145.2		4
84.11	even	6		784.3.c.e.97.3		4
84.23	even	6		784.3.s.c.705.2		4
84.47	odd	6		112.3.s.b.33.1		4
84.59	odd	6		784.3.c.e.97.2		4
84.83	odd	2		784.3.s.c.129.2		4
105.47	odd	12		350.3.i.a.299.2		8
105.68	odd	12		350.3.i.a.299.3		8
105.89	even	6		350.3.k.a.201.2		4
168.5	even	6		448.3.s.d.257.1		4
168.131	odd	6		448.3.s.c.257.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	3.2	odd	2
14.3.d.a.5.1	yes	4	21.5	even	6
98.3.b.b.97.3		4	21.11	odd	6
98.3.b.b.97.4		4	21.17	even	6
98.3.d.a.19.1		4	21.2	odd	6
98.3.d.a.31.1		4	21.20	even	2
112.3.s.b.17.1		4	12.11	even	2
112.3.s.b.33.1		4	84.47	odd	6
126.3.n.c.19.2		4	7.5	odd	6	inner
126.3.n.c.73.2		4	1.1	even	1	trivial
350.3.i.a.199.2		8	15.8	even	4
350.3.i.a.199.3		8	15.2	even	4
350.3.i.a.299.2		8	105.47	odd	12
350.3.i.a.299.3		8	105.68	odd	12
350.3.k.a.101.2		4	15.14	odd	2
350.3.k.a.201.2		4	105.89	even	6
448.3.s.c.129.2		4	24.11	even	2
448.3.s.c.257.2		4	168.131	odd	6
448.3.s.d.129.1		4	24.5	odd	2
448.3.s.d.257.1		4	168.5	even	6
784.3.c.e.97.2		4	84.59	odd	6
784.3.c.e.97.3		4	84.11	even	6
784.3.s.c.129.2		4	84.83	odd	2
784.3.s.c.705.2		4	84.23	even	6
882.3.c.f.685.1		4	7.3	odd	6
882.3.c.f.685.2		4	7.4	even	3
882.3.n.b.19.2		4	7.2	even	3
882.3.n.b.325.2		4	7.6	odd	2
1008.3.cg.l.145.2		4	28.19	even	6
1008.3.cg.l.577.2		4	4.3	odd	2

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

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