LMFDB - Embedded newform 336.3.bh.f.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{65})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 17x^{2} + 16x + 256 $ x^4 - x^3 + 17x^2 + 16x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.2
Root			$2.26556 - 3.92407i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.f.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(3.79669 - 2.19202i) q^{5} +(-0.500000 + 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(3.79669 - 2.19202i) q^{5} +(-0.500000 + 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-9.79669 + 16.9684i) q^{11} +6.11609i q^{13} +7.59339 q^{15} +(7.59339 + 4.38404i) q^{17} +(26.2967 - 15.1824i) q^{19} +(-6.79669 + 10.0402i) q^{21} +(-12.0000 - 20.7846i) q^{23} +(-2.89008 + 5.00577i) q^{25} +5.19615i q^{27} +13.5934 q^{29} +(24.2802 + 14.0182i) q^{31} +(-29.3901 + 16.9684i) q^{33} +(13.4066 + 27.6050i) q^{35} +(24.2967 + 42.0831i) q^{37} +(-5.29669 + 9.17414i) q^{39} -7.14387i q^{41} -53.7802 q^{43} +(11.3901 + 6.57607i) q^{45} +(34.5934 - 19.9725i) q^{47} +(-48.5000 - 6.98212i) q^{49} +(7.59339 + 13.1521i) q^{51} +(30.7967 - 53.3414i) q^{53} +85.8983i q^{55} +52.5934 q^{57} +(-66.7967 - 38.5651i) q^{59} +(0.373546 - 0.215667i) q^{61} +(-18.8901 + 9.17414i) q^{63} +(13.4066 + 23.2209i) q^{65} +(-28.4835 + 49.3348i) q^{67} -41.5692i q^{69} +123.560 q^{71} +(31.0769 + 17.9422i) q^{73} +(-8.67024 + 5.00577i) q^{75} +(-113.577 - 76.8859i) q^{77} +(-26.0934 - 45.1951i) q^{79} +(-4.50000 + 7.79423i) q^{81} -136.883i q^{83} +38.4397 q^{85} +(20.3901 + 11.7722i) q^{87} +(13.2198 - 7.63248i) q^{89} +(-42.7033 - 3.05805i) q^{91} +(24.2802 + 42.0545i) q^{93} +(66.5603 - 115.286i) q^{95} +34.1524i q^{97} -58.7802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9} - 15 q^{11} - 18 q^{15} - 18 q^{17} + 81 q^{19} - 3 q^{21} - 48 q^{23} + 61 q^{25} + 6 q^{29} - 48 q^{31} - 45 q^{33} + 102 q^{35} + 73 q^{37} + 3 q^{39} - 70 q^{43} - 27 q^{45} + 90 q^{47} - 194 q^{49} - 18 q^{51} + 99 q^{53} + 162 q^{57} - 243 q^{59} - 192 q^{61} - 3 q^{63} + 102 q^{65} + 7 q^{67} + 204 q^{71} - 45 q^{73} + 183 q^{75} - 285 q^{77} - 56 q^{79} - 18 q^{81} + 444 q^{85} + 9 q^{87} + 198 q^{89} - 195 q^{91} - 48 q^{93} - 24 q^{95} - 90 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9 - 15 * q^11 - 18 * q^15 - 18 * q^17 + 81 * q^19 - 3 * q^21 - 48 * q^23 + 61 * q^25 + 6 * q^29 - 48 * q^31 - 45 * q^33 + 102 * q^35 + 73 * q^37 + 3 * q^39 - 70 * q^43 - 27 * q^45 + 90 * q^47 - 194 * q^49 - 18 * q^51 + 99 * q^53 + 162 * q^57 - 243 * q^59 - 192 * q^61 - 3 * q^63 + 102 * q^65 + 7 * q^67 + 204 * q^71 - 45 * q^73 + 183 * q^75 - 285 * q^77 - 56 * q^79 - 18 * q^81 + 444 * q^85 + 9 * q^87 + 198 * q^89 - 195 * q^91 - 48 * q^93 - 24 * q^95 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	3.79669	−	2.19202i	0.759339	−	0.438404i	−0.0697196	−	0.997567i	$-0.522210\pi$
$5$	3.79669	−	2.19202i	0.759339	−	0.438404i	0.829058	+	0.559162i	$0.188877\pi$
$6$		0			0
$7$	−0.500000	+	6.98212i	−0.0714286	+	0.997446i
$7$	−0.500000	+	6.98212i	−0.0714286	+	0.997446i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−9.79669	+	16.9684i	−0.890608	+	1.54258i	−0.0514611	+	0.998675i	$0.516388\pi$
$11$	−9.79669	+	16.9684i	−0.890608	+	1.54258i	−0.839147	+	0.543904i	$0.816946\pi$
$12$		0			0
$13$			6.11609i			0.470469i	0.971939	+	0.235234i	$0.0755858\pi$
$13$			6.11609i			0.470469i	−0.971939	+	0.235234i	$0.924414\pi$
$14$		0			0
$15$	7.59339			0.506226
$16$		0			0
$17$	7.59339	+	4.38404i	0.446670	+	0.257885i	0.706423	−	0.707790i	$-0.250308\pi$
$17$	7.59339	+	4.38404i	0.446670	+	0.257885i	−0.259753	+	0.965675i	$0.583641\pi$
$18$		0			0
$19$	26.2967	−	15.1824i	1.38404	−	0.799074i	0.391402	−	0.920220i	$-0.371990\pi$
$19$	26.2967	−	15.1824i	1.38404	−	0.799074i	0.992635	+	0.121146i	$0.0386569\pi$
$20$		0			0
$21$	−6.79669	+	10.0402i	−0.323652	+	0.478103i
$22$		0			0
$23$	−12.0000	−	20.7846i	−0.521739	−	0.903679i	−0.999680	−	0.0252868i	$-0.991950\pi$
$23$	−12.0000	−	20.7846i	−0.521739	−	0.903679i	0.477941	−	0.878392i	$-0.341383\pi$
$24$		0			0
$25$	−2.89008	+	5.00577i	−0.115603	+	0.200231i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	13.5934			0.468737			0.234369	−	0.972148i	$-0.424698\pi$
$29$	13.5934			0.468737			0.234369	+	0.972148i	$0.424698\pi$
$30$		0			0
$31$	24.2802	+	14.0182i	0.783231	+	0.452199i	0.837574	−	0.546324i	$-0.183973\pi$
$31$	24.2802	+	14.0182i	0.783231	+	0.452199i	−0.0543432	+	0.998522i	$0.517306\pi$
$32$		0			0
$33$	−29.3901	+	16.9684i	−0.890608	+	0.514193i
$34$		0			0
$35$	13.4066	+	27.6050i	0.383046	+	0.788714i
$36$		0			0
$37$	24.2967	+	42.0831i	0.656667	+	1.13738i	0.981473	+	0.191600i	$0.0613678\pi$
$37$	24.2967	+	42.0831i	0.656667	+	1.13738i	−0.324806	+	0.945781i	$0.605299\pi$
$38$		0			0
$39$	−5.29669	+	9.17414i	−0.135813	+	0.235234i
$40$		0			0
$41$		−	7.14387i		−	0.174241i	−0.996198	−	0.0871204i	$-0.972234\pi$
$41$		−	7.14387i		−	0.174241i	0.996198	−	0.0871204i	$-0.0277665\pi$
$42$		0			0
$43$	−53.7802			−1.25070			−0.625351	−	0.780344i	$-0.715044\pi$
$43$	−53.7802			−1.25070			−0.625351	+	0.780344i	$0.715044\pi$
$44$		0			0
$45$	11.3901	+	6.57607i	0.253113	+	0.146135i
$46$		0			0
$47$	34.5934	−	19.9725i	0.736030	−	0.424947i	−0.0845944	−	0.996415i	$-0.526959\pi$
$47$	34.5934	−	19.9725i	0.736030	−	0.424947i	0.820624	+	0.571469i	$0.193626\pi$
$48$		0			0
$49$	−48.5000	−	6.98212i	−0.989796	−	0.142492i
$50$		0			0
$51$	7.59339	+	13.1521i	0.148890	+	0.257885i
$52$		0			0
$53$	30.7967	−	53.3414i	0.581070	−	1.00644i	−0.414283	−	0.910148i	$-0.635968\pi$
$53$	30.7967	−	53.3414i	0.581070	−	1.00644i	0.995353	−	0.0962942i	$-0.0306990\pi$
$54$		0			0
$55$			85.8983i			1.56179i
$56$		0			0
$57$	52.5934			0.922691
$58$		0			0
$59$	−66.7967	−	38.5651i	−1.13215	−	0.653646i	−0.187673	−	0.982232i	$-0.560095\pi$
$59$	−66.7967	−	38.5651i	−1.13215	−	0.653646i	−0.944474	+	0.328586i	$0.893428\pi$
$60$		0			0
$61$	0.373546	−	0.215667i	0.00612371	−	0.00353553i	−0.496935	−	0.867788i	$-0.665541\pi$
$61$	0.373546	−	0.215667i	0.00612371	−	0.00353553i	0.503059	+	0.864252i	$0.332208\pi$
$62$		0			0
$63$	−18.8901	+	9.17414i	−0.299843	+	0.145621i
$64$		0			0
$65$	13.4066	+	23.2209i	0.206256	+	0.357245i
$66$		0			0
$67$	−28.4835	+	49.3348i	−0.425126	+	0.736340i	−0.996432	−	0.0843968i	$-0.973104\pi$
$67$	−28.4835	+	49.3348i	−0.425126	+	0.736340i	0.571306	+	0.820737i	$0.306437\pi$
$68$		0			0
$69$		−	41.5692i		−	0.602452i
$70$		0			0
$71$	123.560			1.74029			0.870143	−	0.492799i	$-0.164026\pi$
$71$	123.560			1.74029			0.870143	+	0.492799i	$0.164026\pi$
$72$		0			0
$73$	31.0769	+	17.9422i	0.425710	+	0.245784i	0.697517	−	0.716568i	$-0.254288\pi$
$73$	31.0769	+	17.9422i	0.425710	+	0.245784i	−0.271807	+	0.962352i	$0.587621\pi$
$74$		0			0
$75$	−8.67024	+	5.00577i	−0.115603	+	0.0667435i
$76$		0			0
$77$	−113.577	−	76.8859i	−1.47502	−	0.998518i
$78$		0			0
$79$	−26.0934	−	45.1951i	−0.330296	−	0.572090i	0.652274	−	0.757983i	$-0.273815\pi$
$79$	−26.0934	−	45.1951i	−0.330296	−	0.572090i	−0.982570	+	0.185894i	$0.940482\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	136.883i		−	1.64919i	−0.565725	−	0.824594i	$-0.691404\pi$
$83$		−	136.883i		−	1.64919i	0.565725	−	0.824594i	$-0.308596\pi$
$84$		0			0
$85$	38.4397			0.452232
$86$		0			0
$87$	20.3901	+	11.7722i	0.234369	+	0.135313i
$88$		0			0
$89$	13.2198	−	7.63248i	0.148538	−	0.0857582i	−0.423889	−	0.905714i	$-0.639335\pi$
$89$	13.2198	−	7.63248i	0.148538	−	0.0857582i	0.572427	+	0.819956i	$0.306002\pi$
$90$		0			0
$91$	−42.7033	−	3.05805i	−0.469267	−	0.0336049i
$92$		0			0
$93$	24.2802	+	42.0545i	0.261077	+	0.452199i
$94$		0			0
$95$	66.5603	−	115.286i	0.700635	−	1.21354i
$96$		0			0
$97$			34.1524i			0.352087i	0.984382	+	0.176043i	$0.0563299\pi$
$97$			34.1524i			0.352087i	−0.984382	+	0.176043i	$0.943670\pi$
$98$		0			0
$99$	−58.7802			−0.593739
$100$		0			0
$101$	−113.340	−	65.4372i	−1.12218	−	0.647893i	−0.180226	−	0.983625i	$-0.557683\pi$
$101$	−113.340	−	65.4372i	−1.12218	−	0.647893i	−0.941957	+	0.335733i	$0.891016\pi$
$102$		0			0
$103$	140.857	−	81.3238i	1.36754	−	0.789552i	0.376930	−	0.926242i	$-0.376980\pi$
$103$	140.857	−	81.3238i	1.36754	−	0.789552i	0.990614	+	0.136690i	$0.0436464\pi$
$104$		0			0
$105$	−3.79669	+	53.0179i	−0.0361590	+	0.504933i
$106$		0			0
$107$	−51.9835	−	90.0380i	−0.485827	−	0.841477i	0.514041	−	0.857766i	$-0.328148\pi$
$107$	−51.9835	−	90.0380i	−0.485827	−	0.841477i	−0.999867	+	0.0162892i	$0.994815\pi$
$108$		0			0
$109$	7.89008	−	13.6660i	0.0723861	−	0.125376i	−0.827561	−	0.561377i	$-0.810272\pi$
$109$	7.89008	−	13.6660i	0.0723861	−	0.125376i	0.899947	+	0.436000i	$0.143605\pi$
$110$		0			0
$111$			84.1662i			0.758254i
$112$		0			0
$113$	−59.6265			−0.527668			−0.263834	−	0.964568i	$-0.584987\pi$
$113$	−59.6265			−0.527668			−0.263834	+	0.964568i	$0.584987\pi$
$114$		0			0
$115$	−91.1206	−	52.6085i	−0.792353	−	0.457465i
$116$		0			0
$117$	−15.8901	+	9.17414i	−0.135813	+	0.0784115i
$118$		0			0
$119$	−34.4066	+	50.8259i	−0.289131	+	0.427109i
$120$		0			0
$121$	−131.450	−	227.679i	−1.08637	−	1.88164i
$122$		0			0
$123$	6.18677	−	10.7158i	0.0502990	−	0.0871204i
$124$		0			0
$125$			134.942i			1.07953i
$126$		0			0
$127$	25.0000			0.196850			0.0984252	−	0.995144i	$-0.468619\pi$
$127$	25.0000			0.196850			0.0984252	+	0.995144i	$0.468619\pi$
$128$		0			0
$129$	−80.6702	−	46.5750i	−0.625351	−	0.361046i
$130$		0			0
$131$	−196.170	+	113.259i	−1.49748	+	0.864572i	−0.999996	−	0.00289939i	$-0.999077\pi$
$131$	−196.170	+	113.259i	−1.49748	+	0.864572i	−0.497487	+	0.867471i	$0.665744\pi$
$132$		0			0
$133$	92.8570	+	191.198i	0.698173	+	1.43758i
$134$		0			0
$135$	11.3901	+	19.7282i	0.0843710	+	0.146135i
$136$		0			0
$137$	123.560	−	214.013i	0.901900	−	1.56214i	0.0768751	−	0.997041i	$-0.475506\pi$
$137$	123.560	−	214.013i	0.901900	−	1.56214i	0.825025	−	0.565096i	$-0.191161\pi$
$138$		0			0
$139$			147.383i			1.06031i	0.847902	+	0.530154i	$0.177866\pi$
$139$			147.383i			1.06031i	−0.847902	+	0.530154i	$0.822134\pi$
$140$		0			0
$141$	69.1868			0.490686
$142$		0			0
$143$	−103.780	−	59.9175i	−0.725735	−	0.419004i
$144$		0			0
$145$	51.6099	−	29.7970i	0.355930	−	0.205497i
$146$		0			0
$147$	−66.7033	−	52.4754i	−0.453764	−	0.356976i
$148$		0			0
$149$	−64.4066	−	111.556i	−0.432259	−	0.748695i	0.564808	−	0.825222i	$-0.308950\pi$
$149$	−64.4066	−	111.556i	−0.432259	−	0.748695i	−0.997067	+	0.0765273i	$0.975617\pi$
$150$		0			0
$151$	31.0165	−	53.7222i	0.205408	−	0.355776i	−0.744855	−	0.667226i	$-0.767481\pi$
$151$	31.0165	−	53.7222i	0.205408	−	0.355776i	0.950262	+	0.311450i	$0.100815\pi$
$152$		0			0
$153$			26.3043i			0.171923i
$154$		0			0
$155$	122.912			0.792983
$156$		0			0
$157$	−217.121	−	125.355i	−1.38293	−	0.798437i	−0.390428	−	0.920633i	$-0.627673\pi$
$157$	−217.121	−	125.355i	−1.38293	−	0.798437i	−0.992506	+	0.122196i	$0.961006\pi$
$158$		0			0
$159$	92.3901	−	53.3414i	0.581070	−	0.335481i
$160$		0			0
$161$	151.121	−	73.3931i	0.938638	−	0.455858i
$162$		0			0
$163$	−48.9669	−	84.8132i	−0.300411	−	0.520326i	0.675818	−	0.737068i	$-0.263790\pi$
$163$	−48.9669	−	84.8132i	−0.300411	−	0.520326i	−0.976229	+	0.216742i	$0.930457\pi$
$164$		0			0
$165$	−74.3901	+	128.847i	−0.450849	+	0.780893i
$166$		0			0
$167$			71.7689i			0.429754i	0.976641	+	0.214877i	$0.0689351\pi$
$167$			71.7689i			0.429754i	−0.976641	+	0.214877i	$0.931065\pi$
$168$		0			0
$169$	131.593			0.778659
$170$		0			0
$171$	78.8901	+	45.5472i	0.461345	+	0.266358i
$172$		0			0
$173$	261.560	−	151.012i	1.51191	−	0.872901i	0.512006	−	0.858982i	$-0.328902\pi$
$173$	261.560	−	151.012i	1.51191	−	0.872901i	0.999903	−	0.0139196i	$-0.00443087\pi$
$174$		0			0
$175$	−33.5058	−	22.6818i	−0.191462	−	0.129610i
$176$		0			0
$177$	−66.7967	−	115.695i	−0.377382	−	0.653646i
$178$		0			0
$179$	69.0000	−	119.512i	0.385475	−	0.667662i	−0.606360	−	0.795190i	$-0.707371\pi$
$179$	69.0000	−	119.512i	0.385475	−	0.667662i	0.991835	+	0.127528i	$0.0407043\pi$
$180$		0			0
$181$			82.9733i			0.458416i	0.973377	+	0.229208i	$0.0736136\pi$
$181$			82.9733i			0.458416i	−0.973377	+	0.229208i	$0.926386\pi$
$182$		0			0
$183$	0.747093			0.00408248
$184$		0			0
$185$	184.494	+	106.518i	0.997266	+	0.575772i
$186$		0			0
$187$	−148.780	+	85.8983i	−0.795616	+	0.459349i
$188$		0			0
$189$	−36.2802	−	2.59808i	−0.191959	−	0.0137464i
$190$		0			0
$191$	86.1537	+	149.223i	0.451067	+	0.781270i	0.998453	−	0.0556101i	$-0.0177104\pi$
$191$	86.1537	+	149.223i	0.451067	+	0.781270i	−0.547386	+	0.836880i	$0.684377\pi$
$192$		0			0
$193$	−137.654	+	238.423i	−0.713232	+	1.23535i	0.250406	+	0.968141i	$0.419436\pi$
$193$	−137.654	+	238.423i	−0.713232	+	1.23535i	−0.963638	+	0.267213i	$0.913897\pi$
$194$		0			0
$195$			46.4419i			0.238163i
$196$		0			0
$197$	−154.307			−0.783286			−0.391643	−	0.920117i	$-0.628093\pi$
$197$	−154.307			−0.783286			−0.391643	+	0.920117i	$0.628093\pi$
$198$		0			0
$199$	162.747	+	93.9621i	0.817825	+	0.472171i	0.849666	−	0.527322i	$-0.176804\pi$
$199$	162.747	+	93.9621i	0.817825	+	0.472171i	−0.0318411	+	0.999493i	$0.510137\pi$
$200$		0			0
$201$	−85.4504	+	49.3348i	−0.425126	+	0.245447i
$202$		0			0
$203$	−6.79669	+	94.9107i	−0.0334812	+	0.467540i
$204$		0			0
$205$	−15.6595	−	27.1231i	−0.0763879	−	0.132308i
$206$		0			0
$207$	36.0000	−	62.3538i	0.173913	−	0.301226i
$208$		0			0
$209$			594.949i			2.84665i
$210$		0			0
$211$	348.307			1.65075			0.825373	−	0.564588i	$-0.190965\pi$
$211$	348.307			1.65075			0.825373	+	0.564588i	$0.190965\pi$
$212$		0			0
$213$	185.340	+	107.006i	0.870143	+	0.502377i
$214$		0			0
$215$	−204.187	+	117.887i	−0.949706	+	0.548313i
$216$		0			0
$217$	−110.017	+	162.518i	−0.506989	+	0.748930i
$218$		0			0
$219$	31.0769	+	53.8267i	0.141903	+	0.245784i
$220$		0			0
$221$	−26.8132	+	46.4419i	−0.121327	+	0.210144i
$222$		0			0
$223$		−	30.3581i		−	0.136135i	−0.997681	−	0.0680675i	$-0.978317\pi$
$223$		−	30.3581i		−	0.136135i	0.997681	−	0.0680675i	$-0.0216833\pi$
$224$		0			0
$225$	−17.3405			−0.0770688
$226$		0			0
$227$	−55.8298	−	32.2333i	−0.245946	−	0.141997i	0.371961	−	0.928249i	$-0.378686\pi$
$227$	−55.8298	−	32.2333i	−0.245946	−	0.141997i	−0.617907	+	0.786252i	$0.712019\pi$
$228$		0			0
$229$	8.67024	−	5.00577i	0.0378613	−	0.0218592i	−0.480950	−	0.876748i	$-0.659708\pi$
$229$	8.67024	−	5.00577i	0.0378613	−	0.0218592i	0.518811	+	0.854889i	$0.326375\pi$
$230$		0			0
$231$	−103.780	−	213.689i	−0.449265	−	0.925062i
$232$		0			0
$233$	−14.2529	−	24.6868i	−0.0611713	−	0.105952i	0.833818	−	0.552040i	$-0.186150\pi$
$233$	−14.2529	−	24.6868i	−0.0611713	−	0.105952i	−0.894989	+	0.446088i	$0.852817\pi$
$234$		0			0
$235$	87.5603	−	151.659i	0.372597	−	0.645357i
$236$		0			0
$237$		−	90.3901i		−	0.381393i
$238$		0			0
$239$	256.307			1.07242			0.536208	−	0.844086i	$-0.319856\pi$
$239$	256.307			1.07242			0.536208	+	0.844086i	$0.319856\pi$
$240$		0			0
$241$	186.797	+	107.847i	0.775090	+	0.447498i	0.834687	−	0.550724i	$-0.185648\pi$
$241$	186.797	+	107.847i	0.775090	+	0.447498i	−0.0595974	+	0.998222i	$0.518982\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−199.445	+	79.8041i	−0.814060	+	0.325731i
$246$		0			0
$247$	92.8570	+	160.833i	0.375939	+	0.651146i
$248$		0			0
$249$	118.544	−	205.324i	0.476079	−	0.824594i
$250$		0			0
$251$			371.680i			1.48080i	0.672168	+	0.740398i	$0.265363\pi$
$251$			371.680i			1.48080i	−0.672168	+	0.740398i	$0.734637\pi$
$252$		0			0
$253$	470.241			1.85866
$254$		0			0
$255$	57.6595	+	33.2897i	0.226116	+	0.130548i
$256$		0			0
$257$	−64.1206	+	37.0201i	−0.249497	+	0.144047i	−0.619534	−	0.784970i	$-0.712678\pi$
$257$	−64.1206	+	37.0201i	−0.249497	+	0.144047i	0.370037	+	0.929017i	$0.379345\pi$
$258$		0			0
$259$	−305.978	+	148.601i	−1.18138	+	0.573749i
$260$		0			0
$261$	20.3901	+	35.3167i	0.0781229	+	0.135313i
$262$		0			0
$263$	9.65952	−	16.7308i	0.0367282	−	0.0636151i	−0.847077	−	0.531470i	$-0.821640\pi$
$263$	9.65952	−	16.7308i	0.0367282	−	0.0636151i	0.883805	+	0.467855i	$0.154973\pi$
$264$		0			0
$265$		−	270.028i		−	1.01897i
$266$		0			0
$267$	26.4397			0.0990250
$268$		0			0
$269$	−180.983	−	104.491i	−0.672801	−	0.388442i	0.124336	−	0.992240i	$-0.460320\pi$
$269$	−180.983	−	104.491i	−0.672801	−	0.388442i	−0.797137	+	0.603798i	$0.793653\pi$
$270$		0			0
$271$	−106.357	+	61.4053i	−0.392461	+	0.226588i	−0.683226	−	0.730207i	$-0.739424\pi$
$271$	−106.357	+	61.4053i	−0.392461	+	0.226588i	0.290765	+	0.956795i	$0.406090\pi$
$272$		0			0
$273$	−61.4066	−	41.5692i	−0.224933	−	0.152268i
$274$		0			0
$275$	−56.6265	−	98.0799i	−0.205914	−	0.356654i
$276$		0			0
$277$	−13.8901	+	24.0583i	−0.0501447	+	0.0868532i	−0.890008	−	0.455944i	$-0.849302\pi$
$277$	−13.8901	+	24.0583i	−0.0501447	+	0.0868532i	0.839864	+	0.542798i	$0.182635\pi$
$278$		0			0
$279$			84.1089i			0.301466i
$280$		0			0
$281$	61.4942			0.218841			0.109420	−	0.993996i	$-0.465101\pi$
$281$	61.4942			0.218841			0.109420	+	0.993996i	$0.465101\pi$
$282$		0			0
$283$	38.0107	+	21.9455i	0.134313	+	0.0775459i	0.565651	−	0.824645i	$-0.308625\pi$
$283$	38.0107	+	21.9455i	0.134313	+	0.0775459i	−0.431338	+	0.902191i	$0.641958\pi$
$284$		0			0
$285$	199.681	−	115.286i	0.700635	−	0.404512i
$286$		0			0
$287$	49.8794	+	3.57194i	0.173796	+	0.0124458i
$288$		0			0
$289$	−106.060	−	183.702i	−0.366991	−	0.635647i
$290$		0			0
$291$	−29.5769	+	51.2286i	−0.101639	+	0.176043i
$292$		0			0
$293$			223.600i			0.763139i	0.924340	+	0.381569i	$0.124616\pi$
$293$			223.600i			0.763139i	−0.924340	+	0.381569i	$0.875384\pi$
$294$		0			0
$295$	−338.142			−1.14624
$296$		0			0
$297$	−88.1702	−	50.9051i	−0.296869	−	0.171398i
$298$		0			0
$299$	127.121	−	73.3931i	0.425153	−	0.245462i
$300$		0			0
$301$	26.8901	−	375.500i	0.0893358	−	1.24751i
$302$		0			0
$303$	−113.340	−	196.311i	−0.374061	−	0.647893i
$304$		0			0
$305$	0.945494	−	1.63764i	0.00309998	−	0.00536933i
$306$		0			0
$307$		−	66.8457i		−	0.217738i	−0.994056	−	0.108869i	$-0.965277\pi$
$307$		−	66.8457i		−	0.217738i	0.994056	−	0.108869i	$-0.0347230\pi$
$308$		0			0
$309$	281.714			0.911696
$310$		0			0
$311$	25.3074	+	14.6112i	0.0813743	+	0.0469815i	0.540135	−	0.841578i	$-0.318373\pi$
$311$	25.3074	+	14.6112i	0.0813743	+	0.0469815i	−0.458761	+	0.888560i	$0.651706\pi$
$312$		0			0
$313$	−214.874	+	124.057i	−0.686497	+	0.396349i	−0.802298	−	0.596923i	$-0.796390\pi$
$313$	−214.874	+	124.057i	−0.686497	+	0.396349i	0.115801	+	0.993272i	$0.463056\pi$
$314$		0			0
$315$	−51.6099	+	76.2389i	−0.163841	+	0.242028i
$316$		0			0
$317$	−6.32395	−	10.9534i	−0.0199494	−	0.0345533i	0.855878	−	0.517177i	$-0.173017\pi$
$317$	−6.32395	−	10.9534i	−0.0199494	−	0.0345533i	−0.875828	+	0.482624i	$0.839684\pi$
$318$		0			0
$319$	−133.170	+	230.658i	−0.417462	+	0.723065i
$320$		0			0
$321$		−	180.076i		−	0.560984i
$322$		0			0
$323$	266.241			0.824276
$324$		0			0
$325$	−30.6157	−	17.6760i	−0.0942023	−	0.0543877i
$326$		0			0
$327$	23.6702	−	13.6660i	0.0723861	−	0.0417921i
$328$		0			0
$329$	122.154	+	251.521i	0.371288	+	0.764503i
$330$		0			0
$331$	−251.450	−	435.525i	−0.759669	−	1.31579i	−0.943019	−	0.332738i	$-0.892028\pi$
$331$	−251.450	−	435.525i	−0.759669	−	1.31579i	0.183351	−	0.983048i	$-0.441306\pi$
$332$		0			0
$333$	−72.8901	+	126.249i	−0.218889	+	0.379127i
$334$		0			0
$335$			249.746i			0.745509i
$336$		0			0
$337$	−123.681			−0.367006			−0.183503	−	0.983019i	$-0.558744\pi$
$337$	−123.681			−0.367006			−0.183503	+	0.983019i	$0.558744\pi$
$338$		0			0
$339$	−89.4397	−	51.6380i	−0.263834	−	0.152325i
$340$		0			0
$341$	−475.731	+	274.663i	−1.39510	+	0.805464i
$342$		0			0
$343$	73.0000	−	335.142i	0.212828	−	0.977090i
$344$		0			0
$345$	−91.1206	−	157.826i	−0.264118	−	0.457465i
$346$		0			0
$347$	−113.154	+	195.988i	−0.326091	+	0.564807i	−0.981733	−	0.190266i	$-0.939065\pi$
$347$	−113.154	+	195.988i	−0.326091	+	0.564807i	0.655641	+	0.755073i	$0.272398\pi$
$348$		0			0
$349$			155.669i			0.446043i	0.974814	+	0.223021i	$0.0715920\pi$
$349$			155.669i			0.446043i	−0.974814	+	0.223021i	$0.928408\pi$
$350$		0			0
$351$	−31.7802			−0.0905418
$352$		0			0
$353$	−55.4066	−	31.9890i	−0.156959	−	0.0906205i	0.419463	−	0.907772i	$-0.362218\pi$
$353$	−55.4066	−	31.9890i	−0.156959	−	0.0906205i	−0.576422	+	0.817152i	$0.695552\pi$
$354$		0			0
$355$	469.121	−	270.847i	1.32147	−	0.762949i
$356$		0			0
$357$	−95.6265	+	46.4419i	−0.267861	+	0.130089i
$358$		0			0
$359$	−151.494	−	262.396i	−0.421989	−	0.730907i	0.574145	−	0.818754i	$-0.305335\pi$
$359$	−151.494	−	262.396i	−0.421989	−	0.730907i	−0.996134	+	0.0878469i	$0.972001\pi$
$360$		0			0
$361$	280.511	−	485.859i	0.777038	−	1.34587i
$362$		0			0
$363$		−	455.358i		−	1.25443i
$364$		0			0
$365$	157.319			0.431011
$366$		0			0
$367$	0.00581404	+	0.00335674i	1.58421e−5	+	9.14643e-6i	0.500008	−	0.866021i	$-0.333330\pi$
$367$	0.00581404	+	0.00335674i	1.58421e−5	+	9.14643e-6i	−0.499992	+	0.866030i	$0.666664\pi$
$368$		0			0
$369$	18.5603	−	10.7158i	0.0502990	−	0.0290401i
$370$		0			0
$371$	357.038	+	241.697i	0.962367	+	0.651474i
$372$		0			0
$373$	62.8901	+	108.929i	0.168606	+	0.292034i	0.937930	−	0.346825i	$-0.112740\pi$
$373$	62.8901	+	108.929i	0.168606	+	0.292034i	−0.769324	+	0.638859i	$0.779407\pi$
$374$		0			0
$375$	−116.863	+	202.412i	−0.311634	+	0.539766i
$376$		0			0
$377$			83.1384i			0.220526i
$378$		0			0
$379$	485.076			1.27988			0.639942	−	0.768423i	$-0.278958\pi$
$379$	485.076			1.27988			0.639942	+	0.768423i	$0.278958\pi$
$380$		0			0
$381$	37.5000	+	21.6506i	0.0984252	+	0.0568258i
$382$		0			0
$383$	225.286	−	130.069i	0.588214	−	0.339606i	−0.176177	−	0.984359i	$-0.556373\pi$
$383$	225.286	−	130.069i	0.588214	−	0.339606i	0.764391	+	0.644753i	$0.223040\pi$
$384$		0			0
$385$	−599.752	−	42.9491i	−1.55780	−	0.111556i
$386$		0			0
$387$	−80.6702	−	139.725i	−0.208450	−	0.361046i
$388$		0			0
$389$	−42.9339	+	74.3636i	−0.110370	+	0.191166i	−0.915919	−	0.401362i	$-0.868537\pi$
$389$	−42.9339	+	74.3636i	−0.110370	+	0.191166i	0.805550	+	0.592528i	$0.201870\pi$
$390$		0			0
$391$		−	210.434i		−	0.538195i
$392$		0			0
$393$	−392.340			−0.998322
$394$		0			0
$395$	−198.137	−	114.395i	−0.501613	−	0.289606i
$396$		0			0
$397$	401.670	−	231.904i	1.01176	−	0.584142i	0.100056	−	0.994982i	$-0.468098\pi$
$397$	401.670	−	231.904i	1.01176	−	0.584142i	0.911708	+	0.410840i	$0.134764\pi$
$398$		0			0
$399$	−26.2967	+	367.213i	−0.0659065	+	0.920334i
$400$		0			0
$401$	231.934	+	401.721i	0.578389	+	1.00180i	0.995664	+	0.0930186i	$0.0296516\pi$
$401$	231.934	+	401.721i	0.578389	+	1.00180i	−0.417276	+	0.908780i	$0.637015\pi$
$402$		0			0
$403$	−85.7364	+	148.500i	−0.212745	+	0.368486i
$404$		0			0
$405$			39.4564i			0.0974232i
$406$		0			0
$407$	−952.109			−2.33933
$408$		0			0
$409$	403.687	+	233.069i	0.987009	+	0.569850i	0.904379	−	0.426730i	$-0.140335\pi$
$409$	403.687	+	233.069i	0.987009	+	0.569850i	0.0826303	+	0.996580i	$0.473668\pi$
$410$		0			0
$411$	370.681	−	214.013i	0.901900	−	0.520712i
$412$		0			0
$413$	302.664	−	447.100i	0.732844	−	1.08257i
$414$		0			0
$415$	−300.050	−	519.701i	−0.723011	−	1.25229i
$416$		0			0
$417$	−127.637	+	221.074i	−0.306084	+	0.530154i
$418$		0			0
$419$			89.9655i			0.214715i	0.994220	+	0.107357i	$0.0342389\pi$
$419$			89.9655i			0.214715i	−0.994220	+	0.107357i	$0.965761\pi$
$420$		0			0
$421$	−413.582			−0.982379			−0.491190	−	0.871053i	$-0.663438\pi$
$421$	−413.582			−0.982379			−0.491190	+	0.871053i	$0.663438\pi$
$422$		0			0
$423$	103.780	+	59.9175i	0.245343	+	0.141649i
$424$		0			0
$425$	−43.8910	+	25.3405i	−0.103273	+	0.0596246i
$426$		0			0
$427$	1.31904	+	2.71598i	0.00308909	+	0.00636061i
$428$		0			0
$429$	−103.780	−	179.753i	−0.241912	−	0.419004i
$430$		0			0
$431$	35.0661	−	60.7363i	0.0813599	−	0.140920i	−0.822474	−	0.568802i	$-0.807407\pi$
$431$	35.0661	−	60.7363i	0.0813599	−	0.140920i	0.903834	+	0.427883i	$0.140740\pi$
$432$		0			0
$433$		−	431.223i		−	0.995897i	−0.867207	−	0.497948i	$-0.834087\pi$
$433$		−	431.223i		−	0.995897i	0.867207	−	0.497948i	$-0.165913\pi$
$434$		0			0
$435$	103.220			0.237287
$436$		0			0
$437$	−631.121	−	364.378i	−1.44421	−	0.833816i
$438$		0			0
$439$	81.7091	−	47.1748i	0.186126	−	0.107460i	−0.404042	−	0.914740i	$-0.632395\pi$
$439$	81.7091	−	47.1748i	0.186126	−	0.107460i	0.590168	+	0.807281i	$0.299062\pi$
$440$		0			0
$441$	−54.6099	−	136.480i	−0.123832	−	0.309478i
$442$		0			0
$443$	206.291	+	357.306i	0.465668	+	0.806560i	0.999231	−	0.0391995i	$-0.0124808\pi$
$443$	206.291	+	357.306i	0.465668	+	0.806560i	−0.533564	+	0.845760i	$0.679147\pi$
$444$		0			0
$445$	33.4611	−	57.9564i	0.0751935	−	0.130239i
$446$		0			0
$447$		−	223.111i		−	0.499130i
$448$		0			0
$449$	617.802			1.37595			0.687975	−	0.725734i	$-0.258500\pi$
$449$	617.802			1.37595			0.687975	+	0.725734i	$0.258500\pi$
$450$		0			0
$451$	121.220	+	69.9863i	0.268780	+	0.155180i
$452$		0			0
$453$	93.0496	−	53.7222i	0.205408	−	0.118592i
$454$		0			0
$455$	−168.835	+	81.9961i	−0.371065	+	0.180211i
$456$		0			0
$457$	5.50000	+	9.52628i	0.0120350	+	0.0208453i	0.871980	−	0.489541i	$-0.162836\pi$
$457$	5.50000	+	9.52628i	0.0120350	+	0.0208453i	−0.859945	+	0.510386i	$0.829502\pi$
$458$		0			0
$459$	−22.7802	+	39.4564i	−0.0496300	+	0.0859616i
$460$		0			0
$461$		−	859.960i		−	1.86542i	−0.360624	−	0.932711i	$-0.617436\pi$
$461$		−	859.960i		−	1.86542i	0.360624	−	0.932711i	$-0.382564\pi$
$462$		0			0
$463$	−397.340			−0.858187			−0.429093	−	0.903260i	$-0.641167\pi$
$463$	−397.340			−0.858187			−0.429093	+	0.903260i	$0.641167\pi$
$464$		0			0
$465$	184.369	+	106.445i	0.396492	+	0.228915i
$466$		0			0
$467$	−257.340	+	148.576i	−0.551050	+	0.318149i	−0.749545	−	0.661953i	$-0.769728\pi$
$467$	−257.340	+	148.576i	−0.551050	+	0.318149i	0.198495	+	0.980102i	$0.436395\pi$
$468$		0			0
$469$	−330.220	−	223.542i	−0.704093	−	0.476636i
$470$		0			0
$471$	−217.121	−	376.064i	−0.460978	−	0.798437i
$472$		0			0
$473$	526.868	−	912.562i	1.11389	−	1.92931i
$474$		0			0
$475$			175.513i			0.369502i
$476$		0			0
$477$	184.780			0.387380
$478$		0			0
$479$	−696.648	−	402.210i	−1.45438	−	0.839687i	−0.455654	−	0.890157i	$-0.650595\pi$
$479$	−696.648	−	402.210i	−1.45438	−	0.839687i	−0.998726	+	0.0504704i	$0.983928\pi$
$480$		0			0
$481$	−257.384	+	148.601i	−0.535102	+	0.308942i
$482$		0			0
$483$	290.241	+	20.7846i	0.600914	+	0.0430323i
$484$		0			0
$485$	74.8628	+	129.666i	0.154356	+	0.267353i
$486$		0			0
$487$	30.4008	−	52.6557i	0.0624246	−	0.108123i	−0.833124	−	0.553086i	$-0.813450\pi$
$487$	30.4008	−	52.6557i	0.0624246	−	0.108123i	0.895549	+	0.444964i	$0.146783\pi$
$488$		0			0
$489$		−	169.626i		−	0.346884i
$490$		0			0
$491$	−514.955			−1.04879			−0.524394	−	0.851475i	$-0.675708\pi$
$491$	−514.955			−1.04879			−0.524394	+	0.851475i	$0.675708\pi$
$492$		0			0
$493$	103.220	+	59.5940i	0.209371	+	0.120880i
$494$		0			0
$495$	−223.170	+	128.847i	−0.450849	+	0.260298i
$496$		0			0
$497$	−61.7802	+	862.713i	−0.124306	+	1.73584i
$498$		0			0
$499$	444.450	+	769.811i	0.890682	+	1.54271i	0.839059	+	0.544040i	$0.183106\pi$
$499$	444.450	+	769.811i	0.890682	+	1.54271i	0.0516230	+	0.998667i	$0.483561\pi$
$500$		0			0
$501$	−62.1537	+	107.653i	−0.124059	+	0.214877i
$502$		0			0
$503$			822.920i			1.63602i	0.575202	+	0.818012i	$0.304924\pi$
$503$			822.920i			1.63602i	−0.575202	+	0.818012i	$0.695076\pi$
$504$		0			0
$505$	−573.759			−1.13616
$506$		0			0
$507$	197.390	+	113.963i	0.389330	+	0.224780i
$508$		0			0
$509$	−492.038	+	284.078i	−0.966676	+	0.558111i	−0.898221	−	0.439544i	$-0.855140\pi$
$509$	−492.038	+	284.078i	−0.966676	+	0.558111i	−0.0684546	+	0.997654i	$0.521807\pi$
$510$		0			0
$511$	−140.813	+	208.011i	−0.275564	+	0.407067i
$512$		0			0
$513$	78.8901	+	136.642i	0.153782	+	0.266358i
$514$		0			0
$515$	356.527	−	617.523i	0.692286	−	1.19907i
$516$		0			0
$517$			782.658i			1.51385i
$518$		0			0
$519$	523.121			1.00794
$520$		0			0
$521$	118.407	+	68.3621i	0.227268	+	0.131213i	0.609311	−	0.792931i	$-0.291446\pi$
$521$	118.407	+	68.3621i	0.227268	+	0.131213i	−0.382043	+	0.924145i	$0.624779\pi$
$522$		0			0
$523$	−12.6157	+	7.28370i	−0.0241219	+	0.0139268i	−0.512012	−	0.858978i	$-0.671100\pi$
$523$	−12.6157	+	7.28370i	−0.0241219	+	0.0139268i	0.487891	+	0.872905i	$0.337767\pi$
$524$		0			0
$525$	−30.6157	−	63.0395i	−0.0583157	−	0.120075i
$526$		0			0
$527$	122.912	+	212.891i	0.233230	+	0.403967i
$528$		0			0
$529$	−23.5000	+	40.7032i	−0.0444234	+	0.0769437i
$530$		0			0
$531$		−	231.391i		−	0.435764i
$532$		0			0
$533$	43.6926			0.0819748
$534$		0			0
$535$	−394.731	−	227.898i	−0.737814	−	0.425977i
$536$		0			0
$537$	207.000	−	119.512i	0.385475	−	0.222554i
$538$		0			0
$539$	593.615	−	754.564i	1.10133	−	1.39993i
$540$		0			0
$541$	462.450	+	800.988i	0.854807	+	1.48057i	0.876824	+	0.480811i	$0.159658\pi$
$541$	462.450	+	800.988i	0.854807	+	1.48057i	−0.0220176	+	0.999758i	$0.507009\pi$
$542$		0			0
$543$	−71.8570	+	124.460i	−0.132333	+	0.229208i
$544$		0			0
$545$		−	69.1809i		−	0.126937i
$546$		0			0
$547$	−103.626			−0.189445			−0.0947225	−	0.995504i	$-0.530196\pi$
$547$	−103.626			−0.189445			−0.0947225	+	0.995504i	$0.530196\pi$
$548$		0			0
$549$	1.12064	+	0.647001i	0.00204124	+	0.00117851i
$550$		0			0
$551$	357.461	−	206.380i	0.648750	−	0.374556i
$552$		0			0
$553$	328.604	−	159.590i	0.594221	−	0.288589i
$554$		0			0
$555$	184.494	+	319.553i	0.332422	+	0.575772i
$556$		0			0
$557$	−206.203	+	357.155i	−0.370203	+	0.641211i	−0.989597	−	0.143870i	$-0.954045\pi$
$557$	−206.203	+	357.155i	−0.370203	+	0.641211i	0.619393	+	0.785081i	$0.287379\pi$
$558$		0			0
$559$		−	328.925i		−	0.588416i
$560$		0			0
$561$	−297.560			−0.530411
$562$		0			0
$563$	594.412	+	343.184i	1.05579	+	0.609562i	0.924266	−	0.381750i	$-0.124678\pi$
$563$	594.412	+	343.184i	1.05579	+	0.609562i	0.131528	+	0.991313i	$0.458012\pi$
$564$		0			0
$565$	−226.383	+	130.702i	−0.400679	+	0.231332i
$566$		0			0
$567$	−52.1702	−	35.3167i	−0.0920110	−	0.0622869i
$568$		0			0
$569$	73.3074	+	126.972i	0.128836	+	0.223150i	0.923226	−	0.384258i	$-0.125543\pi$
$569$	73.3074	+	126.972i	0.128836	+	0.223150i	−0.794390	+	0.607408i	$0.792209\pi$
$570$		0			0
$571$	178.131	−	308.533i	0.311964	−	0.540337i	−0.666824	−	0.745216i	$-0.732347\pi$
$571$	178.131	−	308.533i	0.311964	−	0.540337i	0.978787	+	0.204878i	$0.0656799\pi$
$572$		0			0
$573$			298.445i			0.520847i
$574$		0			0
$575$	138.724			0.241259
$576$		0			0
$577$	−148.115	−	85.5141i	−0.256698	−	0.148205i	0.366129	−	0.930564i	$-0.380683\pi$
$577$	−148.115	−	85.5141i	−0.256698	−	0.148205i	−0.622827	+	0.782359i	$0.714016\pi$
$578$		0			0
$579$	−412.961	+	238.423i	−0.713232	+	0.411784i
$580$		0			0
$581$	955.731	+	68.4413i	1.64498	+	0.117799i
$582$		0			0
$583$	603.412	+	1045.14i	1.03501	+	1.79269i
$584$		0			0
$585$	−40.2198	+	69.6628i	−0.0687519	+	0.119082i
$586$		0			0
$587$		−	24.8384i		−	0.0423142i	−0.999776	−	0.0211571i	$-0.993265\pi$
$587$		−	24.8384i		−	0.0423142i	0.999776	−	0.0211571i	$-0.00673502\pi$
$588$		0			0
$589$	851.317			1.44536
$590$		0			0
$591$	−231.461	−	133.634i	−0.391643	−	0.226115i
$592$		0			0
$593$	−117.846	+	68.0386i	−0.198729	+	0.114736i	−0.596062	−	0.802938i	$-0.703269\pi$
$593$	−117.846	+	68.0386i	−0.198729	+	0.114736i	0.397333	+	0.917674i	$0.369936\pi$
$594$		0			0
$595$	−19.2198	+	268.390i	−0.0323023	+	0.451076i
$596$		0			0
$597$	162.747	+	281.886i	0.272608	+	0.472171i
$598$		0			0
$599$	494.615	−	856.698i	0.825734	−	1.43021i	−0.0756226	−	0.997137i	$-0.524094\pi$
$599$	494.615	−	856.698i	0.825734	−	1.43021i	0.901357	−	0.433077i	$-0.142572\pi$
$600$		0			0
$601$		−	78.8184i		−	0.131145i	−0.997848	−	0.0655727i	$-0.979113\pi$
$601$		−	78.8184i		−	0.131145i	0.997848	−	0.0655727i	$-0.0208874\pi$
$602$		0			0
$603$	−170.901			−0.283418
$604$		0			0
$605$	−998.154	−	576.284i	−1.64984	−	0.952536i
$606$		0			0
$607$	−727.850	+	420.225i	−1.19909	+	0.692297i	−0.960353	−	0.278786i	$-0.910068\pi$
$607$	−727.850	+	420.225i	−1.19909	+	0.692297i	−0.238741	+	0.971083i	$0.576735\pi$
$608$		0			0
$609$	−92.3901	+	136.480i	−0.151708	+	0.224105i
$610$		0			0
$611$	122.154	+	211.576i	0.199924	+	0.346279i
$612$		0			0
$613$	−423.714	+	733.894i	−0.691214	+	1.19722i	0.280227	+	0.959934i	$0.409590\pi$
$613$	−423.714	+	733.894i	−0.691214	+	1.19722i	−0.971440	+	0.237283i	$0.923743\pi$
$614$		0			0
$615$		−	54.2462i		−	0.0882052i
$616$		0			0
$617$	−649.669			−1.05295			−0.526474	−	0.850191i	$-0.676486\pi$
$617$	−649.669			−1.05295			−0.526474	+	0.850191i	$0.676486\pi$
$618$		0			0
$619$	422.659	+	244.022i	0.682809	+	0.394220i	0.800912	−	0.598781i	$-0.204348\pi$
$619$	422.659	+	244.022i	0.682809	+	0.394220i	−0.118104	+	0.993001i	$0.537682\pi$
$620$		0			0
$621$	108.000	−	62.3538i	0.173913	−	0.100409i
$622$		0			0
$623$	46.6810	+	96.1187i	0.0749293	+	0.154284i
$624$		0			0
$625$	223.543	+	387.188i	0.357669	+	0.619500i
$626$		0			0
$627$	−515.241	+	892.424i	−0.821756	+	1.42332i
$628$		0			0
$629$			426.071i			0.677378i
$630$		0			0
$631$	820.473			1.30027			0.650137	−	0.759817i	$-0.274712\pi$
$631$	820.473			1.30027			0.650137	+	0.759817i	$0.274712\pi$
$632$		0			0
$633$	522.461	+	301.643i	0.825373	+	0.476529i
$634$		0			0
$635$	94.9173	−	54.8005i	0.149476	−	0.0863001i
$636$		0			0
$637$	42.7033	−	296.631i	0.0670382	−	0.465668i
$638$		0			0
$639$	185.340	+	321.019i	0.290048	+	0.502377i
$640$		0			0
$641$	9.93387	−	17.2060i	0.0154975	−	0.0268424i	−0.858173	−	0.513361i	$-0.828400\pi$
$641$	9.93387	−	17.2060i	0.0154975	−	0.0268424i	0.873670	+	0.486519i	$0.161733\pi$
$642$		0			0
$643$		−	1013.95i		−	1.57691i	−0.615092	−	0.788456i	$-0.710881\pi$
$643$		−	1013.95i		−	1.57691i	0.615092	−	0.788456i	$-0.289119\pi$
$644$		0			0
$645$	−408.374			−0.633137
$646$		0			0
$647$	−115.582	−	66.7312i	−0.178643	−	0.103139i	0.408012	−	0.912976i	$-0.366222\pi$
$647$	−115.582	−	66.7312i	−0.178643	−	0.103139i	−0.586655	+	0.809837i	$0.699555\pi$
$648$		0			0
$649$	1308.77	−	755.621i	2.01660	−	1.16428i
$650$		0			0
$651$	−305.769	+	148.500i	−0.469692	+	0.228110i
$652$		0			0
$653$	−302.378	−	523.735i	−0.463060	−	0.802044i	0.536051	−	0.844185i	$-0.319915\pi$
$653$	−302.378	−	523.735i	−0.463060	−	0.802044i	−0.999112	+	0.0421413i	$0.986582\pi$
$654$		0			0
$655$	−496.532	+	860.019i	−0.758064	+	1.31301i
$656$		0			0
$657$			107.653i			0.163856i
$658$		0			0
$659$	−335.451			−0.509031			−0.254515	−	0.967069i	$-0.581916\pi$
$659$	−335.451			−0.509031			−0.254515	+	0.967069i	$0.581916\pi$
$660$		0			0
$661$	608.186	+	351.136i	0.920100	+	0.531220i	0.883667	−	0.468116i	$-0.155067\pi$
$661$	608.186	+	351.136i	0.920100	+	0.531220i	0.0364328	+	0.999336i	$0.488401\pi$
$662$		0			0
$663$	−80.4397	+	46.4419i	−0.121327	+	0.0700481i
$664$		0			0
$665$	771.660	+	522.375i	1.16039	+	0.785526i
$666$		0			0
$667$	−163.121	−	282.533i	−0.244559	−	0.423588i
$668$		0			0
$669$	26.2909	−	45.5371i	0.0392988	−	0.0680675i
$670$		0			0
$671$			8.45130i			0.0125951i
$672$		0			0
$673$	−1119.48			−1.66342			−0.831711	−	0.555209i	$-0.812638\pi$
$673$	−1119.48			−1.66342			−0.831711	+	0.555209i	$0.812638\pi$
$674$		0			0
$675$	−26.0107	−	15.0173i	−0.0385344	−	0.0222478i
$676$		0			0
$677$	225.709	−	130.313i	0.333396	−	0.192486i	−0.323952	−	0.946074i	$-0.605012\pi$
$677$	225.709	−	130.313i	0.333396	−	0.192486i	0.657348	+	0.753587i	$0.271678\pi$
$678$		0			0
$679$	−238.456	−	17.0762i	−0.351187	−	0.0251490i
$680$		0			0
$681$	−55.8298	−	96.7000i	−0.0819820	−	0.141997i
$682$		0			0
$683$	−100.258	+	173.652i	−0.146790	+	0.254248i	−0.930039	−	0.367460i	$-0.880228\pi$
$683$	−100.258	+	173.652i	−0.146790	+	0.254248i	0.783249	+	0.621708i	$0.213561\pi$
$684$		0			0
$685$		−	1083.39i		−	1.58159i
$686$		0			0
$687$	17.3405			0.0252409
$688$		0			0
$689$	326.241	+	188.355i	0.473500	+	0.273375i
$690$		0			0
$691$	−860.933	+	497.060i	−1.24592	+	0.719334i	−0.970294	−	0.241930i	$-0.922220\pi$
$691$	−860.933	+	497.060i	−1.24592	+	0.719334i	−0.275629	+	0.961264i	$0.588886\pi$
$692$		0			0
$693$	29.3901	−	410.410i	0.0424099	−	0.592222i
$694$		0			0
$695$	323.066	+	559.567i	0.464843	+	0.805132i
$696$		0			0
$697$	31.3190	−	54.2462i	0.0449341	−	0.0778281i
$698$		0			0
$699$		−	49.3735i		−	0.0706345i
$700$		0			0
$701$	−148.231			−0.211457			−0.105729	−	0.994395i	$-0.533717\pi$
$701$	−148.231			−0.211457			−0.105729	+	0.994395i	$0.533717\pi$
$702$		0			0
$703$	1277.85	+	737.764i	1.81770	+	1.04945i
$704$		0			0
$705$	262.681	−	151.659i	0.372597	−	0.215119i
$706$		0			0
$707$	513.560	−	758.638i	0.726394	−	1.07304i
$708$		0			0
$709$	−355.988	−	616.590i	−0.502099	−	0.869661i	−0.999997	−	0.00242571i	$-0.999228\pi$
$709$	−355.988	−	616.590i	−0.502099	−	0.869661i	0.497898	−	0.867236i	$-0.334105\pi$
$710$		0			0
$711$	78.2802	−	135.585i	0.110099	−	0.190697i
$712$		0			0
$713$		−	672.872i		−	0.943719i
$714$		0			0
$715$	−525.362			−0.734772
$716$		0			0
$717$	384.461	+	221.969i	0.536208	+	0.309580i
$718$		0			0
$719$	649.109	−	374.763i	0.902794	−	0.521228i	0.0246885	−	0.999695i	$-0.492141\pi$
$719$	649.109	−	374.763i	0.902794	−	0.521228i	0.878106	+	0.478467i	$0.158807\pi$
$720$		0			0
$721$	497.384	+	1024.14i	0.689853	+	1.42045i
$722$		0			0
$723$	186.797	+	323.541i	0.258363	+	0.447498i
$724$		0			0
$725$	−39.2860	+	68.0453i	−0.0541876	+	0.0938556i
$726$		0			0
$727$		−	865.702i		−	1.19079i	−0.803434	−	0.595393i	$-0.796996\pi$
$727$		−	865.702i		−	1.19079i	0.803434	−	0.595393i	$-0.203004\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−408.374	−	235.775i	−0.558651	−	0.322537i
$732$		0			0
$733$	83.5710	−	48.2498i	0.114012	−	0.0658251i	−0.441909	−	0.897060i	$-0.645699\pi$
$733$	83.5710	−	48.2498i	0.114012	−	0.0658251i	0.555922	+	0.831235i	$0.312365\pi$
$734$		0			0
$735$	−368.279	−	53.0179i	−0.501060	−	0.0721332i
$736$		0			0
$737$	−558.088	−	966.636i	−0.757242	−	1.31158i
$738$		0			0
$739$	−210.450	+	364.511i	−0.284777	+	0.493249i	−0.972555	−	0.232673i	$-0.925253\pi$
$739$	−210.450	+	364.511i	−0.284777	+	0.493249i	0.687778	+	0.725921i	$0.258586\pi$
$740$		0			0
$741$			321.666i			0.434097i
$742$		0			0
$743$	−920.043			−1.23828			−0.619141	−	0.785280i	$-0.712519\pi$
$743$	−920.043			−1.23828			−0.619141	+	0.785280i	$0.712519\pi$
$744$		0			0
$745$	−489.064	−	282.361i	−0.656462	−	0.379009i
$746$		0			0
$747$	355.631	−	205.324i	0.476079	−	0.274865i
$748$		0			0
$749$	654.648	−	317.936i	0.874029	−	0.424480i
$750$		0			0
$751$	−160.181	−	277.442i	−0.213290	−	0.369430i	0.739452	−	0.673209i	$-0.235085\pi$
$751$	−160.181	−	277.442i	−0.213290	−	0.369430i	−0.952742	+	0.303780i	$0.901751\pi$
$752$		0			0
$753$	−321.884	+	557.520i	−0.427469	+	0.740398i
$754$		0			0
$755$		−	271.956i		−	0.360206i
$756$		0			0
$757$	330.813			0.437006			0.218503	−	0.975836i	$-0.429883\pi$
$757$	330.813			0.437006			0.218503	+	0.975836i	$0.429883\pi$
$758$		0			0
$759$	705.362	+	407.241i	0.929331	+	0.536549i
$760$		0			0
$761$	230.615	−	133.146i	0.303042	−	0.174961i	−0.340767	−	0.940148i	$-0.610687\pi$
$761$	230.615	−	133.146i	0.303042	−	0.174961i	0.643809	+	0.765187i	$0.277353\pi$
$762$		0			0
$763$	91.4727	+	61.9225i	0.119886	+	0.0811566i
$764$		0			0
$765$	57.6595	+	99.8692i	0.0753719	+	0.130548i
$766$		0			0
$767$	235.868	−	408.535i	0.307520	−	0.532640i
$768$		0			0
$769$			241.301i			0.313785i	0.987616	+	0.156893i	$0.0501477\pi$
$769$			241.301i			0.313785i	−0.987616	+	0.156893i	$0.949852\pi$
$770$		0			0
$771$	−128.241			−0.166331
$772$		0			0
$773$	−805.208	−	464.887i	−1.04167	−	0.601406i	−0.121362	−	0.992608i	$-0.538726\pi$
$773$	−805.208	−	464.887i	−1.04167	−	0.601406i	−0.920305	+	0.391202i	$0.872059\pi$
$774$		0			0
$775$	−140.343	+	81.0272i	−0.181088	+	0.104551i
$776$		0			0
$777$	−587.659	−	42.0831i	−0.756317	−	0.0541610i
$778$		0			0
$779$	−108.461	−	187.860i	−0.139231	−	0.241156i
$780$		0			0
$781$	−1210.48	+	2096.62i	−1.54991	+	2.68453i
$782$		0			0
$783$			70.6333i			0.0902086i
$784$		0			0
$785$	−1099.12			−1.40015
$786$		0			0
$787$	−961.097	−	554.890i	−1.22122	−	0.705070i	−0.256039	−	0.966666i	$-0.582418\pi$
$787$	−961.097	−	554.890i	−1.22122	−	0.705070i	−0.965177	+	0.261597i	$0.915751\pi$
$788$		0			0
$789$	28.9786	−	16.7308i	0.0367282	−	0.0212050i
$790$		0			0
$791$	29.8132	−	416.319i	0.0376906	−	0.526320i
$792$		0			0
$793$	1.31904	+	2.28465i	0.00166336	+	0.00288102i
$794$		0			0
$795$	233.851	−	405.042i	0.294152	−	0.509487i
$796$		0			0
$797$		−	231.047i		−	0.289896i	−0.989439	−	0.144948i	$-0.953699\pi$
$797$		−	231.047i		−	0.289896i	0.989439	−	0.144948i	$-0.0463014\pi$
$798$		0			0
$799$	350.241			0.438350
$800$		0			0
$801$	39.6595	+	22.8974i	0.0495125	+	0.0285861i
$802$		0			0
$803$	−608.901	+	351.549i	−0.758282	+	0.437795i
$804$		0			0
$805$	412.879	−	609.911i	0.512894	−	0.757653i
$806$		0			0
$807$	−180.983	−	313.473i	−0.224267	−	0.388442i
$808$		0			0
$809$	159.473	−	276.215i	0.197123	−	0.341428i	−0.750471	−	0.660903i	$-0.770173\pi$
$809$	159.473	−	276.215i	0.197123	−	0.341428i	0.947595	+	0.319476i	$0.103507\pi$
$810$		0			0
$811$			196.807i			0.242672i	0.992612	+	0.121336i	$0.0387178\pi$
$811$			196.807i			0.242672i	−0.992612	+	0.121336i	$0.961282\pi$
$812$		0			0
$813$	−212.714			−0.261641
$814$		0			0
$815$	−371.825	−	214.673i	−0.456227	−	0.263403i
$816$		0			0
$817$	−1414.24	+	816.512i	−1.73102	+	0.999403i
$818$		0			0
$819$	−56.1099	−	115.534i	−0.0685103	−	0.141067i
$820$		0			0
$821$	692.005	+	1198.59i	0.842881	+	1.45991i	0.887449	+	0.460906i	$0.152475\pi$
$821$	692.005	+	1198.59i	0.842881	+	1.45991i	−0.0445687	+	0.999006i	$0.514191\pi$
$822$		0			0
$823$	138.253	−	239.461i	0.167987	−	0.290961i	−0.769725	−	0.638375i	$-0.779607\pi$
$823$	138.253	−	239.461i	0.167987	−	0.290961i	0.937712	+	0.347414i	$0.112940\pi$
$824$		0			0
$825$		−	196.160i		−	0.237769i
$826$		0			0
$827$	−1467.81			−1.77486			−0.887431	−	0.460940i	$-0.847512\pi$
$827$	−1467.81			−1.77486			−0.887431	+	0.460940i	$0.847512\pi$
$828$		0			0
$829$	68.1859	+	39.3671i	0.0822507	+	0.0474875i	0.540561	−	0.841305i	$-0.318212\pi$
$829$	68.1859	+	39.3671i	0.0822507	+	0.0474875i	−0.458311	+	0.888792i	$0.651545\pi$
$830$		0			0
$831$	−41.6702	+	24.0583i	−0.0501447	+	0.0289511i
$832$		0			0
$833$	−337.669	−	265.644i	−0.405365	−	0.318900i
$834$		0			0
$835$	157.319	+	272.485i	0.188406	+	0.326329i
$836$		0			0
$837$	−72.8405	+	126.163i	−0.0870257	+	0.150733i
$838$		0			0
$839$		−	591.398i		−	0.704884i	−0.935834	−	0.352442i	$-0.885351\pi$
$839$		−	591.398i		−	0.704884i	0.935834	−	0.352442i	$-0.114649\pi$
$840$		0			0
$841$	−656.220			−0.780285
$842$		0			0
$843$	92.2413	+	53.2555i	0.109420	+	0.0631738i
$844$		0			0
$845$	499.620	−	288.456i	0.591266	−	0.341368i
$846$		0			0
$847$	1655.41	−	803.963i	1.95443	−	0.949189i
$848$		0			0
$849$	38.0107	+	65.8365i	0.0447712	+	0.0775459i
$850$		0			0
$851$	583.121	−	1009.99i	0.685218	−	1.18683i
$852$		0			0
$853$		−	1048.80i		−	1.22954i	−0.788707	−	0.614770i	$-0.789249\pi$
$853$		−	1048.80i		−	1.22954i	0.788707	−	0.614770i	$-0.210751\pi$
$854$		0			0
$855$	399.362			0.467090
$856$		0			0
$857$	92.8132	+	53.5857i	0.108300	+	0.0625271i	0.553172	−	0.833067i	$-0.313417\pi$
$857$	92.8132	+	53.5857i	0.108300	+	0.0625271i	−0.444872	+	0.895594i	$0.646751\pi$
$858$		0			0
$859$	1304.52	−	753.162i	1.51864	−	0.876790i	0.518885	−	0.854844i	$-0.326347\pi$
$859$	1304.52	−	753.162i	1.51864	−	0.876790i	0.999759	−	0.0219460i	$-0.00698618\pi$
$860$		0			0
$861$	71.7257	+	48.5547i	0.0833051	+	0.0563934i
$862$		0			0
$863$	187.681	+	325.073i	0.217475	+	0.376678i	0.954035	−	0.299694i	$-0.0968846\pi$
$863$	187.681	+	325.073i	0.217475	+	0.376678i	−0.736560	+	0.676372i	$0.763551\pi$
$864$		0			0
$865$	662.043	−	1146.69i	0.765367	−	1.32566i
$866$		0			0
$867$		−	367.404i		−	0.423764i
$868$		0			0
$869$	1022.52			1.17666
$870$		0			0
$871$	−301.736	−	174.208i	−0.346425	−	0.200009i
$872$		0			0
$873$	−88.7306	+	51.2286i	−0.101639	+	0.0586811i
$874$		0			0
$875$	−942.178	−	67.4708i	−1.07678	−	0.0771095i
$876$		0			0
$877$	−704.395	−	1220.05i	−0.803187	−	1.39116i	−0.917508	−	0.397717i	$-0.869803\pi$
$877$	−704.395	−	1220.05i	−0.803187	−	1.39116i	0.114321	−	0.993444i	$-0.463531\pi$
$878$		0			0
$879$	−193.643	+	335.399i	−0.220299	+	0.381569i
$880$		0			0
$881$		−	1236.04i		−	1.40299i	−0.712673	−	0.701497i	$-0.752515\pi$
$881$		−	1236.04i		−	1.40299i	0.712673	−	0.701497i	$-0.247485\pi$
$882$		0			0
$883$	72.9437			0.0826089			0.0413045	−	0.999147i	$-0.486849\pi$
$883$	72.9437			0.0826089			0.0413045	+	0.999147i	$0.486849\pi$
$884$		0			0
$885$	−507.213	−	292.840i	−0.573122	−	0.330892i
$886$		0			0
$887$	−1249.01	+	721.116i	−1.40813	+	0.812983i	−0.995208	−	0.0977838i	$-0.968825\pi$
$887$	−1249.01	+	721.116i	−1.40813	+	0.812983i	−0.412921	+	0.910767i	$0.635491\pi$
$888$		0			0
$889$	−12.5000	+	174.553i	−0.0140607	+	0.196348i
$890$		0			0
$891$	−88.1702	−	152.715i	−0.0989565	−	0.171398i
$892$		0			0
$893$	606.461	−	1050.42i	0.679128	−	1.17628i
$894$		0			0
$895$		−	604.998i		−	0.675975i
$896$		0			0
$897$	254.241			0.283435
$898$		0			0
$899$	330.050	+	190.554i	0.367130	+	0.211962i
$900$		0			0
$901$	467.702	−	270.028i	0.519093	−	0.299698i
$902$		0			0
$903$	365.527	−	539.962i	0.404792	−	0.597964i
$904$		0			0
$905$	181.879	+	315.024i	0.200972	+	0.348093i
$906$		0			0
$907$	−604.878	+	1047.68i	−0.666900	+	1.15510i	0.311866	+	0.950126i	$0.399046\pi$
$907$	−604.878	+	1047.68i	−0.666900	+	1.15510i	−0.978766	+	0.204979i	$0.934287\pi$
$908$		0			0
$909$		−	392.623i		−	0.431928i
$910$		0			0
$911$	1328.22			1.45798			0.728989	−	0.684525i	$-0.239991\pi$
$911$	1328.22			1.45798			0.728989	+	0.684525i	$0.239991\pi$
$912$		0			0
$913$	2322.67	+	1341.00i	2.54400	+	1.46878i
$914$		0			0
$915$	2.83648	−	1.63764i	0.00309998	−	0.00178978i
$916$		0			0
$917$	−692.702	−	1426.31i	−0.755401	−	1.55541i
$918$		0			0
$919$	−244.429	−	423.363i	−0.265973	−	0.460678i	0.701845	−	0.712329i	$-0.252360\pi$
$919$	−244.429	−	423.363i	−0.265973	−	0.460678i	−0.967818	+	0.251651i	$0.919026\pi$
$920$		0			0
$921$	57.8901	−	100.269i	0.0628557	−	0.108869i
$922$		0			0
$923$			755.707i			0.818750i
$924$		0			0
$925$	−280.878			−0.303651
$926$		0			0
$927$	422.571	+	243.972i	0.455848	+	0.263184i
$928$		0			0
$929$	−824.055	+	475.768i	−0.887034	+	0.512129i	−0.872971	−	0.487772i	$-0.837810\pi$
$929$	−824.055	+	475.768i	−0.887034	+	0.512129i	−0.0140628	+	0.999901i	$0.504476\pi$
$930$		0			0
$931$	−1381.39	+	552.740i	−1.48378	+	0.593706i
$932$		0			0
$933$	25.3074	+	43.8337i	0.0271248	+	0.0469815i
$934$		0			0
$935$	−376.582	+	652.259i	−0.402761	+	0.697603i
$936$		0			0
$937$			309.707i			0.330530i	0.986249	+	0.165265i	$0.0528480\pi$
$937$			309.707i			0.330530i	−0.986249	+	0.165265i	$0.947152\pi$
$938$		0			0
$939$	−429.747			−0.457665
$940$		0			0
$941$	1015.42	+	586.254i	1.07909	+	0.623011i	0.930650	−	0.365910i	$-0.119242\pi$
$941$	1015.42	+	586.254i	1.07909	+	0.623011i	0.148437	+	0.988922i	$0.452576\pi$
$942$		0			0
$943$	−148.483	+	85.7264i	−0.157458	+	0.0909082i
$944$		0			0
$945$	−143.440	+	69.6628i	−0.151788	+	0.0737173i
$946$		0			0
$947$	−362.428	−	627.744i	−0.382712	−	0.662876i	0.608737	−	0.793372i	$-0.291676\pi$
$947$	−362.428	−	627.744i	−0.382712	−	0.662876i	−0.991449	+	0.130496i	$0.958343\pi$
$948$		0			0
$949$	−109.736	+	190.069i	−0.115634	+	0.200283i
$950$		0			0
$951$		−	21.9068i		−	0.0230355i
$952$		0			0
$953$	27.5371			0.0288951			0.0144476	−	0.999896i	$-0.495401\pi$
$953$	27.5371			0.0288951			0.0144476	+	0.999896i	$0.495401\pi$
$954$		0			0
$955$	654.198	+	377.702i	0.685025	+	0.395499i
$956$		0			0
$957$	−399.511	+	230.658i	−0.417462	+	0.241022i
$958$		0			0
$959$	1432.48	+	969.719i	1.49373	+	1.01118i
$960$		0			0
$961$	−87.4826	−	151.524i	−0.0910328	−	0.157674i
$962$		0			0
$963$	155.950	−	270.114i	0.161942	−	0.280492i
$964$		0			0
$965$			1206.96i			1.25074i
$966$		0			0
$967$	−1279.81			−1.32349			−0.661744	−	0.749730i	$-0.730183\pi$
$967$	−1279.81			−1.32349			−0.661744	+	0.749730i	$0.730183\pi$
$968$		0			0
$969$	399.362	+	230.572i	0.412138	+	0.237948i
$970$		0			0
$971$	−963.686	+	556.384i	−0.992467	+	0.573001i	−0.906011	−	0.423254i	$-0.860888\pi$
$971$	−963.686	+	556.384i	−0.992467	+	0.573001i	−0.0864565	+	0.996256i	$0.527554\pi$
$972$		0			0
$973$	−1029.04	−	73.6914i	−1.05760	−	0.0757362i
$974$		0			0
$975$	−30.6157	−	53.0280i	−0.0314008	−	0.0543877i
$976$		0			0
$977$	217.879	−	377.378i	0.223009	−	0.386262i	−0.732712	−	0.680539i	$-0.761746\pi$
$977$	217.879	−	377.378i	0.223009	−	0.386262i	0.955720	+	0.294277i	$0.0950789\pi$
$978$		0			0
$979$			299.092i			0.305508i
$980$		0			0
$981$	47.3405			0.0482574
$982$		0			0
$983$	243.835	+	140.778i	0.248052	+	0.143213i	0.618872	−	0.785492i	$-0.287590\pi$
$983$	243.835	+	140.778i	0.248052	+	0.143213i	−0.370820	+	0.928705i	$0.620923\pi$
$984$		0			0
$985$	−585.858	+	338.245i	−0.594780	+	0.343396i
$986$		0			0
$987$	−34.5934	+	483.070i	−0.0350490	+	0.489433i
$988$		0			0
$989$	645.362	+	1117.80i	0.652540	+	1.13023i
$990$		0			0
$991$	−308.786	+	534.833i	−0.311590	+	0.539690i	−0.978707	−	0.205263i	$-0.934195\pi$
$991$	−308.786	+	534.833i	−0.311590	+	0.539690i	0.667117	+	0.744953i	$0.267528\pi$
$992$		0			0
$993$		−	871.050i		−	0.877190i
$994$		0			0
$995$	823.868			0.828008
$996$		0			0
$997$	−1303.91	−	752.814i	−1.30784	−	0.755079i	−0.326101	−	0.945335i	$-0.605735\pi$
$997$	−1303.91	−	752.814i	−1.30784	−	0.755079i	−0.981734	+	0.190256i	$0.939068\pi$
$998$		0			0
$999$	−218.670	+	126.249i	−0.218889	+	0.126376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.f.241.2		4
3.2	odd	2		1008.3.cg.m.577.1		4
4.3	odd	2		84.3.m.b.73.2	yes	4
7.3	odd	6		2352.3.f.f.97.3		4
7.4	even	3		2352.3.f.f.97.2		4
7.5	odd	6	inner	336.3.bh.f.145.2		4
12.11	even	2		252.3.z.e.73.1		4
20.3	even	4		2100.3.be.d.1249.3		8
20.7	even	4		2100.3.be.d.1249.2		8
20.19	odd	2		2100.3.bd.f.1501.2		4
21.5	even	6		1008.3.cg.m.145.1		4
28.3	even	6		588.3.d.b.97.1		4
28.11	odd	6		588.3.d.b.97.4		4
28.19	even	6		84.3.m.b.61.2	✓	4
28.23	odd	6		588.3.m.d.313.1		4
28.27	even	2		588.3.m.d.325.1		4
84.11	even	6		1764.3.d.f.685.2		4
84.23	even	6		1764.3.z.h.901.2		4
84.47	odd	6		252.3.z.e.145.1		4
84.59	odd	6		1764.3.d.f.685.3		4
84.83	odd	2		1764.3.z.h.325.2		4
140.19	even	6		2100.3.bd.f.901.1		4
140.47	odd	12		2100.3.be.d.649.3		8
140.103	odd	12		2100.3.be.d.649.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.m.b.61.2	✓	4	28.19	even	6
84.3.m.b.73.2	yes	4	4.3	odd	2
252.3.z.e.73.1		4	12.11	even	2
252.3.z.e.145.1		4	84.47	odd	6
336.3.bh.f.145.2		4	7.5	odd	6	inner
336.3.bh.f.241.2		4	1.1	even	1	trivial
588.3.d.b.97.1		4	28.3	even	6
588.3.d.b.97.4		4	28.11	odd	6
588.3.m.d.313.1		4	28.23	odd	6
588.3.m.d.325.1		4	28.27	even	2
1008.3.cg.m.145.1		4	21.5	even	6
1008.3.cg.m.577.1		4	3.2	odd	2
1764.3.d.f.685.2		4	84.11	even	6
1764.3.d.f.685.3		4	84.59	odd	6
1764.3.z.h.325.2		4	84.83	odd	2
1764.3.z.h.901.2		4	84.23	even	6
2100.3.bd.f.901.1		4	140.19	even	6
2100.3.bd.f.1501.2		4	20.19	odd	2
2100.3.be.d.649.2		8	140.103	odd	12
2100.3.be.d.649.3		8	140.47	odd	12
2100.3.be.d.1249.2		8	20.7	even	4
2100.3.be.d.1249.3		8	20.3	even	4
2352.3.f.f.97.2		4	7.4	even	3
2352.3.f.f.97.3		4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(3.79669 - 2.19202i) q^{5} +(-0.500000 + 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(3.79669 - 2.19202i) q^{5} +(-0.500000 + 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-9.79669 + 16.9684i) q^{11} +6.11609i q^{13} +7.59339 q^{15} +(7.59339 + 4.38404i) q^{17} +(26.2967 - 15.1824i) q^{19} +(-6.79669 + 10.0402i) q^{21} +(-12.0000 - 20.7846i) q^{23} +(-2.89008 + 5.00577i) q^{25} +5.19615i q^{27} +13.5934 q^{29} +(24.2802 + 14.0182i) q^{31} +(-29.3901 + 16.9684i) q^{33} +(13.4066 + 27.6050i) q^{35} +(24.2967 + 42.0831i) q^{37} +(-5.29669 + 9.17414i) q^{39} -7.14387i q^{41} -53.7802 q^{43} +(11.3901 + 6.57607i) q^{45} +(34.5934 - 19.9725i) q^{47} +(-48.5000 - 6.98212i) q^{49} +(7.59339 + 13.1521i) q^{51} +(30.7967 - 53.3414i) q^{53} +85.8983i q^{55} +52.5934 q^{57} +(-66.7967 - 38.5651i) q^{59} +(0.373546 - 0.215667i) q^{61} +(-18.8901 + 9.17414i) q^{63} +(13.4066 + 23.2209i) q^{65} +(-28.4835 + 49.3348i) q^{67} -41.5692i q^{69} +123.560 q^{71} +(31.0769 + 17.9422i) q^{73} +(-8.67024 + 5.00577i) q^{75} +(-113.577 - 76.8859i) q^{77} +(-26.0934 - 45.1951i) q^{79} +(-4.50000 + 7.79423i) q^{81} -136.883i q^{83} +38.4397 q^{85} +(20.3901 + 11.7722i) q^{87} +(13.2198 - 7.63248i) q^{89} +(-42.7033 - 3.05805i) q^{91} +(24.2802 + 42.0545i) q^{93} +(66.5603 - 115.286i) q^{95} +34.1524i q^{97} -58.7802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9} - 15 q^{11} - 18 q^{15} - 18 q^{17} + 81 q^{19} - 3 q^{21} - 48 q^{23} + 61 q^{25} + 6 q^{29} - 48 q^{31} - 45 q^{33} + 102 q^{35} + 73 q^{37} + 3 q^{39} - 70 q^{43} - 27 q^{45} + 90 q^{47} - 194 q^{49} - 18 q^{51} + 99 q^{53} + 162 q^{57} - 243 q^{59} - 192 q^{61} - 3 q^{63} + 102 q^{65} + 7 q^{67} + 204 q^{71} - 45 q^{73} + 183 q^{75} - 285 q^{77} - 56 q^{79} - 18 q^{81} + 444 q^{85} + 9 q^{87} + 198 q^{89} - 195 q^{91} - 48 q^{93} - 24 q^{95} - 90 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9 - 15 * q^11 - 18 * q^15 - 18 * q^17 + 81 * q^19 - 3 * q^21 - 48 * q^23 + 61 * q^25 + 6 * q^29 - 48 * q^31 - 45 * q^33 + 102 * q^35 + 73 * q^37 + 3 * q^39 - 70 * q^43 - 27 * q^45 + 90 * q^47 - 194 * q^49 - 18 * q^51 + 99 * q^53 + 162 * q^57 - 243 * q^59 - 192 * q^61 - 3 * q^63 + 102 * q^65 + 7 * q^67 + 204 * q^71 - 45 * q^73 + 183 * q^75 - 285 * q^77 - 56 * q^79 - 18 * q^81 + 444 * q^85 + 9 * q^87 + 198 * q^89 - 195 * q^91 - 48 * q^93 - 24 * q^95 - 90 * q^99

Introduction

L-functions

Modular forms

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