LMFDB - Embedded newform 336.3.z.g.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(47,336)]

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([3, 0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("336.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.z (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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 83 x^{18} + 2702 x^{16} + 44346 x^{14} + 396449 x^{12} + 1961403 x^{10} + 5268164 x^{8} + \cdots + 2304 $ x^20 + 83x^18 + 2702x^16 + 44346x^14 + 396449x^12 + 1961403x^10 + 5268164x^8 + 7444400x^6 + 5121988x^4 + 1338432*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.7
Root			$-5.07301i$ of defining polynomial
Character	$\chi$	$=$	336.47
Dual form			336.3.z.g.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43046 - 2.63700i) q^{3} +(-4.89508 + 8.47853i) q^{5} +(-1.55722 - 6.82459i) q^{7} +(-4.90756 - 7.54426i) q^{9} +O(q^{10})$	\(q+(1.43046 - 2.63700i) q^{3} +(-4.89508 + 8.47853i) q^{5} +(-1.55722 - 6.82459i) q^{7} +(-4.90756 - 7.54426i) q^{9} +(2.66502 + 4.61595i) q^{11} +15.7574i q^{13} +(15.3557 + 25.0366i) q^{15} +(7.79558 + 13.5023i) q^{17} +(-10.9740 + 19.0076i) q^{19} +(-20.2240 - 5.65593i) q^{21} +(-11.4600 + 19.8494i) q^{23} +(-35.4237 - 61.3556i) q^{25} +(-26.9143 + 2.14947i) q^{27} +24.5758i q^{29} +(10.8812 + 18.8467i) q^{31} +(15.9845 - 0.424724i) q^{33} +(65.4853 + 20.2040i) q^{35} +(-15.4747 + 26.8030i) q^{37} +(41.5524 + 22.5404i) q^{39} -14.7950 q^{41} -51.1900i q^{43} +(87.9872 - 4.67912i) q^{45} +(10.3662 + 5.98495i) q^{47} +(-44.1501 + 21.2548i) q^{49} +(46.7570 - 1.24238i) q^{51} +(47.4641 - 27.4034i) q^{53} -52.1820 q^{55} +(34.4251 + 56.1281i) q^{57} +(40.2875 - 23.2600i) q^{59} +(-27.2055 - 15.7071i) q^{61} +(-43.8444 + 45.2402i) q^{63} +(-133.600 - 77.1340i) q^{65} +(14.4100 - 8.31959i) q^{67} +(35.9497 + 58.6140i) q^{69} -73.0574 q^{71} +(34.4201 - 19.8724i) q^{73} +(-212.467 + 5.64547i) q^{75} +(27.3520 - 25.3757i) q^{77} +(4.29574 + 2.48015i) q^{79} +(-32.8317 + 74.0478i) q^{81} -56.0926i q^{83} -152.640 q^{85} +(64.8065 + 35.1547i) q^{87} +(4.12044 - 7.13681i) q^{89} +(107.538 - 24.5378i) q^{91} +(65.2639 - 1.73413i) q^{93} +(-107.438 - 186.087i) q^{95} +63.5054i q^{97} +(21.7452 - 42.7587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{3} - 16 q^{7} + 11 q^{9}+O(q^{10}) $ 20 * q + 3 * q^3 - 16 * q^7 + 11 * q^9	$ 20 q + 3 q^{3} - 16 q^{7} + 11 q^{9} - 44 q^{19} - 5 q^{21} - 98 q^{25} - 144 q^{27} - 70 q^{31} + 15 q^{33} - 64 q^{37} + 6 q^{39} + 21 q^{45} - 184 q^{49} - 33 q^{51} + 120 q^{55} + 218 q^{57} - 102 q^{61} + 27 q^{63} - 144 q^{67} + 372 q^{73} - 246 q^{75} + 258 q^{79} + 287 q^{81} - 108 q^{85} + 318 q^{87} + 510 q^{91} - 173 q^{93}+O(q^{100}) $ 20 * q + 3 * q^3 - 16 * q^7 + 11 * q^9 - 44 * q^19 - 5 * q^21 - 98 * q^25 - 144 * q^27 - 70 * q^31 + 15 * q^33 - 64 * q^37 + 6 * q^39 + 21 * q^45 - 184 * q^49 - 33 * q^51 + 120 * q^55 + 218 * q^57 - 102 * q^61 + 27 * q^63 - 144 * q^67 + 372 * q^73 - 246 * q^75 + 258 * q^79 + 287 * q^81 - 108 * q^85 + 318 * q^87 + 510 * q^91 - 173 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.43046	−	2.63700i	0.476821	−	0.879001i
$3$	1.43046	−	2.63700i	0.476821	−	0.879001i
$4$		0			0
$5$	−4.89508	+	8.47853i	−0.979017	+	1.69571i	−0.313030	+	0.949743i	$0.601344\pi$
$5$	−4.89508	+	8.47853i	−0.979017	+	1.69571i	−0.665987	+	0.745964i	$0.731989\pi$
$6$		0			0
$7$	−1.55722	−	6.82459i	−0.222460	−	0.974942i
$7$	−1.55722	−	6.82459i	−0.222460	−	0.974942i
$8$		0			0
$9$	−4.90756	−	7.54426i	−0.545284	−	0.838251i
$10$		0			0
$11$	2.66502	+	4.61595i	0.242275	+	0.419632i	0.961362	−	0.275288i	$-0.0887731\pi$
$11$	2.66502	+	4.61595i	0.242275	+	0.419632i	−0.719087	+	0.694920i	$0.755440\pi$
$12$		0			0
$13$			15.7574i			1.21211i	0.795422	+	0.606056i	$0.207249\pi$
$13$			15.7574i			1.21211i	−0.795422	+	0.606056i	$0.792751\pi$
$14$		0			0
$15$	15.3557	+	25.0366i	1.02371	+	1.66910i
$16$		0			0
$17$	7.79558	+	13.5023i	0.458563	+	0.794255i	0.998885	−	0.0472034i	$-0.0150309\pi$
$17$	7.79558	+	13.5023i	0.458563	+	0.794255i	−0.540322	+	0.841458i	$0.681698\pi$
$18$		0			0
$19$	−10.9740	+	19.0076i	−0.577580	+	1.00040i	0.418176	+	0.908366i	$0.362670\pi$
$19$	−10.9740	+	19.0076i	−0.577580	+	1.00040i	−0.995756	+	0.0920323i	$0.970664\pi$
$20$		0			0
$21$	−20.2240	−	5.65593i	−0.963048	−	0.269330i
$22$		0			0
$23$	−11.4600	+	19.8494i	−0.498263	+	0.863017i	−0.999998	−	0.00200458i	$-0.999362\pi$
$23$	−11.4600	+	19.8494i	−0.498263	+	0.863017i	0.501735	+	0.865021i	$0.332695\pi$
$24$		0			0
$25$	−35.4237	−	61.3556i	−1.41695	−	2.45423i
$26$		0			0
$27$	−26.9143	+	2.14947i	−0.996826	+	0.0796100i
$28$		0			0
$29$			24.5758i			0.847442i	0.905793	+	0.423721i	$0.139276\pi$
$29$			24.5758i			0.847442i	−0.905793	+	0.423721i	$0.860724\pi$
$30$		0			0
$31$	10.8812	+	18.8467i	0.351005	+	0.607958i	0.986426	−	0.164208i	$-0.0525067\pi$
$31$	10.8812	+	18.8467i	0.351005	+	0.607958i	−0.635421	+	0.772166i	$0.719173\pi$
$32$		0			0
$33$	15.9845	−	0.424724i	0.484378	−	0.0128704i
$34$		0			0
$35$	65.4853	+	20.2040i	1.87101	+	0.577258i
$36$		0			0
$37$	−15.4747	+	26.8030i	−0.418235	+	0.724404i	−0.995762	−	0.0919674i	$-0.970684\pi$
$37$	−15.4747	+	26.8030i	−0.418235	+	0.724404i	0.577527	+	0.816371i	$0.304018\pi$
$38$		0			0
$39$	41.5524	+	22.5404i	1.06545	+	0.577959i
$40$		0			0
$41$	−14.7950			−0.360854			−0.180427	−	0.983588i	$-0.557748\pi$
$41$	−14.7950			−0.360854			−0.180427	+	0.983588i	$0.557748\pi$
$42$		0			0
$43$		−	51.1900i		−	1.19047i	−0.803553	−	0.595233i	$-0.797060\pi$
$43$		−	51.1900i		−	1.19047i	0.803553	−	0.595233i	$-0.202940\pi$
$44$		0			0
$45$	87.9872	−	4.67912i	1.95527	−	0.103981i
$46$		0			0
$47$	10.3662	+	5.98495i	0.220558	+	0.127339i	0.606209	−	0.795306i	$-0.292690\pi$
$47$	10.3662	+	5.98495i	0.220558	+	0.127339i	−0.385650	+	0.922645i	$0.626023\pi$
$48$		0			0
$49$	−44.1501	+	21.2548i	−0.901023	+	0.433771i
$50$		0			0
$51$	46.7570	−	1.24238i	0.916803	−	0.0243604i
$52$		0			0
$53$	47.4641	−	27.4034i	0.895549	−	0.517045i	0.0197954	−	0.999804i	$-0.493699\pi$
$53$	47.4641	−	27.4034i	0.895549	−	0.517045i	0.875753	+	0.482759i	$0.160365\pi$
$54$		0			0
$55$	−52.1820			−0.948764
$56$		0			0
$57$	34.4251	+	56.1281i	0.603949	+	0.984704i
$58$		0			0
$59$	40.2875	−	23.2600i	0.682840	−	0.394238i	−0.118084	−	0.993004i	$-0.537675\pi$
$59$	40.2875	−	23.2600i	0.682840	−	0.394238i	0.800924	+	0.598766i	$0.204342\pi$
$60$		0			0
$61$	−27.2055	−	15.7071i	−0.445993	−	0.257494i	0.260144	−	0.965570i	$-0.416230\pi$
$61$	−27.2055	−	15.7071i	−0.445993	−	0.257494i	−0.706136	+	0.708076i	$0.749563\pi$
$62$		0			0
$63$	−43.8444	+	45.2402i	−0.695942	+	0.718098i
$64$		0			0
$65$	−133.600	−	77.1340i	−2.05539	−	1.18668i
$66$		0			0
$67$	14.4100	−	8.31959i	0.215074	−	0.124173i	−0.388593	−	0.921409i	$-0.627039\pi$
$67$	14.4100	−	8.31959i	0.215074	−	0.124173i	0.603667	+	0.797236i	$0.293706\pi$
$68$		0			0
$69$	35.9497	+	58.6140i	0.521010	+	0.849478i
$70$		0			0
$71$	−73.0574			−1.02898			−0.514489	−	0.857497i	$-0.672018\pi$
$71$	−73.0574			−1.02898			−0.514489	+	0.857497i	$0.672018\pi$
$72$		0			0
$73$	34.4201	−	19.8724i	0.471508	−	0.272225i	−0.245363	−	0.969431i	$-0.578907\pi$
$73$	34.4201	−	19.8724i	0.471508	−	0.272225i	0.716871	+	0.697206i	$0.245574\pi$
$74$		0			0
$75$	−212.467	+	5.64547i	−2.83290	+	0.0752729i
$76$		0			0
$77$	27.3520	−	25.3757i	0.355221	−	0.329555i
$78$		0			0
$79$	4.29574	+	2.48015i	0.0543765	+	0.0313943i	0.526942	−	0.849901i	$-0.323339\pi$
$79$	4.29574	+	2.48015i	0.0543765	+	0.0313943i	−0.472565	+	0.881296i	$0.656672\pi$
$80$		0			0
$81$	−32.8317	+	74.0478i	−0.405330	+	0.914170i
$82$		0			0
$83$		−	56.0926i		−	0.675815i	−0.941179	−	0.337907i	$-0.890281\pi$
$83$		−	56.0926i		−	0.675815i	0.941179	−	0.337907i	$-0.109719\pi$
$84$		0			0
$85$	−152.640			−1.79576
$86$		0			0
$87$	64.8065	+	35.1547i	0.744902	+	0.404078i
$88$		0			0
$89$	4.12044	−	7.13681i	0.0462971	−	0.0801889i	−0.841948	−	0.539558i	$-0.818591\pi$
$89$	4.12044	−	7.13681i	0.0462971	−	0.0801889i	0.888245	+	0.459369i	$0.151925\pi$
$90$		0			0
$91$	107.538	−	24.5378i	1.18174	−	0.269646i
$92$		0			0
$93$	65.2639	−	1.73413i	0.701762	−	0.0186465i
$94$		0			0
$95$	−107.438	−	186.087i	−1.13092	−	1.95881i
$96$		0			0
$97$			63.5054i			0.654695i	0.944904	+	0.327347i	$0.106155\pi$
$97$			63.5054i			0.654695i	−0.944904	+	0.327347i	$0.893845\pi$
$98$		0			0
$99$	21.7452	−	42.7587i	0.219648	−	0.431906i
$100$		0			0
$101$	−16.0741	−	27.8412i	−0.159150	−	0.275656i	0.775412	−	0.631455i	$-0.217542\pi$
$101$	−16.0741	−	27.8412i	−0.159150	−	0.275656i	−0.934562	+	0.355799i	$0.884209\pi$
$102$		0			0
$103$	85.1203	−	147.433i	0.826411	−	1.43139i	−0.0744256	−	0.997227i	$-0.523712\pi$
$103$	85.1203	−	147.433i	0.826411	−	1.43139i	0.900836	−	0.434159i	$-0.142954\pi$
$104$		0			0
$105$	146.952	−	143.784i	1.39954	−	1.36937i
$106$		0			0
$107$	−101.021	+	174.974i	−0.944124	+	1.63527i	−0.186629	+	0.982431i	$0.559756\pi$
$107$	−101.021	+	174.974i	−0.944124	+	1.63527i	−0.757495	+	0.652840i	$0.773577\pi$
$108$		0			0
$109$	17.6522	+	30.5745i	0.161947	+	0.280500i	0.935567	−	0.353150i	$-0.114889\pi$
$109$	17.6522	+	30.5745i	0.161947	+	0.280500i	−0.773620	+	0.633650i	$0.781556\pi$
$110$		0			0
$111$	48.5435	+	79.1474i	0.437329	+	0.713039i
$112$		0			0
$113$			92.2111i			0.816027i	0.912976	+	0.408014i	$0.133778\pi$
$113$			92.2111i			0.816027i	−0.912976	+	0.408014i	$0.866222\pi$
$114$		0			0
$115$	−112.196	−	194.329i	−0.975616	−	1.68982i
$116$		0			0
$117$	118.878	−	77.3306i	1.01605	−	0.660945i
$118$		0			0
$119$	80.0085	−	74.2277i	0.672340	−	0.623762i
$120$		0			0
$121$	46.2953	−	80.1858i	0.382606	−	0.662693i
$122$		0			0
$123$	−21.1637	+	39.0145i	−0.172063	+	0.317191i
$124$		0			0
$125$	448.854			3.59083
$126$		0			0
$127$		−	75.3464i		−	0.593279i	−0.954990	−	0.296640i	$-0.904134\pi$
$127$		−	75.3464i		−	0.593279i	0.954990	−	0.296640i	$-0.0958660\pi$
$128$		0			0
$129$	−134.988	−	73.2253i	−1.04642	−	0.567638i
$130$		0			0
$131$	36.9356	+	21.3248i	0.281951	+	0.162785i	0.634307	−	0.773082i	$-0.281286\pi$
$131$	36.9356	+	21.3248i	0.281951	+	0.162785i	−0.352355	+	0.935866i	$0.614619\pi$
$132$		0			0
$133$	146.808	+	45.2943i	1.10382	+	0.340559i
$134$		0			0
$135$	113.523	−	238.716i	0.840914	−	1.76826i
$136$		0			0
$137$	−88.8407	+	51.2922i	−0.648472	+	0.374396i	−0.787871	−	0.615841i	$-0.788816\pi$
$137$	−88.8407	+	51.2922i	−0.648472	+	0.374396i	0.139398	+	0.990236i	$0.455483\pi$
$138$		0			0
$139$	90.8399			0.653524			0.326762	−	0.945107i	$-0.394042\pi$
$139$	90.8399			0.653524			0.326762	+	0.945107i	$0.394042\pi$
$140$		0			0
$141$	30.6108	−	18.7746i	0.217098	−	0.133153i
$142$		0			0
$143$	−72.7356	+	41.9939i	−0.508641	+	0.293664i
$144$		0			0
$145$	−208.367	−	120.301i	−1.43701	−	0.829660i
$146$		0			0
$147$	−7.10621	+	146.828i	−0.0483416	+	0.998831i
$148$		0			0
$149$	−147.329	−	85.0603i	−0.988784	−	0.570874i	−0.0838731	−	0.996476i	$-0.526729\pi$
$149$	−147.329	−	85.0603i	−0.988784	−	0.570874i	−0.904910	+	0.425602i	$0.860062\pi$
$150$		0			0
$151$	−65.0630	+	37.5641i	−0.430881	+	0.248769i	−0.699722	−	0.714415i	$-0.746693\pi$
$151$	−65.0630	+	37.5641i	−0.430881	+	0.248769i	0.268841	+	0.963185i	$0.413359\pi$
$152$		0			0
$153$	63.6079	−	125.075i	0.415738	−	0.817486i
$154$		0			0
$155$	−213.057			−1.37456
$156$		0			0
$157$	−180.575	+	104.255i	−1.15016	+	0.664045i	−0.948926	−	0.315498i	$-0.897828\pi$
$157$	−180.575	+	104.255i	−1.15016	+	0.664045i	−0.201234	+	0.979543i	$0.564495\pi$
$158$		0			0
$159$	−4.36728	−	164.362i	−0.0274672	−	1.03373i
$160$		0			0
$161$	153.310	+	47.3003i	0.952235	+	0.293791i
$162$		0			0
$163$	256.887	+	148.314i	1.57599	+	0.909900i	0.995410	+	0.0956983i	$0.0305084\pi$
$163$	256.887	+	148.314i	1.57599	+	0.909900i	0.580582	+	0.814202i	$0.302825\pi$
$164$		0			0
$165$	−74.6444	+	137.604i	−0.452390	+	0.833964i
$166$		0			0
$167$			184.743i			1.10625i	0.833100	+	0.553123i	$0.186564\pi$
$167$			184.743i			1.10625i	−0.833100	+	0.553123i	$0.813436\pi$
$168$		0			0
$169$	−79.2971			−0.469213
$170$		0			0
$171$	197.254	−	10.4899i	1.15353	−	0.0613443i
$172$		0			0
$173$	−127.316	+	220.518i	−0.735931	+	1.27467i	0.218383	+	0.975863i	$0.429922\pi$
$173$	−127.316	+	220.518i	−0.735931	+	1.27467i	−0.954314	+	0.298807i	$0.903411\pi$
$174$		0			0
$175$	−363.565	+	337.296i	−2.07751	+	1.92741i
$176$		0			0
$177$	−3.70695	−	139.511i	−0.0209432	−	0.788197i
$178$		0			0
$179$	−58.7396	−	101.740i	−0.328154	−	0.568380i	0.653991	−	0.756502i	$-0.273093\pi$
$179$	−58.7396	−	101.740i	−0.328154	−	0.568380i	−0.982146	+	0.188122i	$0.939760\pi$
$180$		0			0
$181$			20.4562i			0.113017i	0.998402	+	0.0565087i	$0.0179969\pi$
$181$			20.4562i			0.113017i	−0.998402	+	0.0565087i	$0.982003\pi$
$182$		0			0
$183$	−80.3362	+	49.2726i	−0.438996	+	0.269249i
$184$		0			0
$185$	−151.500	−	262.405i	−0.818918	−	1.41841i
$186$		0			0
$187$	−41.5508	+	71.9680i	−0.222197	+	0.384856i
$188$		0			0
$189$	56.5807	+	180.332i	0.299369	+	0.954137i
$190$		0			0
$191$	92.0960	−	159.515i	0.482178	−	0.835157i	−0.517613	−	0.855615i	$-0.673179\pi$
$191$	92.0960	−	159.515i	0.482178	−	0.835157i	0.999791	+	0.0204581i	$0.00651248\pi$
$192$		0			0
$193$	2.02801	+	3.51262i	0.0105078	+	0.0182001i	0.871232	−	0.490872i	$-0.163322\pi$
$193$	2.02801	+	3.51262i	0.0105078	+	0.0182001i	−0.860724	+	0.509072i	$0.829989\pi$
$194$		0			0
$195$	−394.512	+	241.966i	−2.02314	+	1.24085i
$196$		0			0
$197$			176.763i			0.897272i	0.893714	+	0.448636i	$0.148090\pi$
$197$			176.763i			0.897272i	−0.893714	+	0.448636i	$0.851910\pi$
$198$		0			0
$199$	−21.5178	−	37.2699i	−0.108130	−	0.187286i	0.806883	−	0.590711i	$-0.201153\pi$
$199$	−21.5178	−	37.2699i	−0.108130	−	0.187286i	−0.915013	+	0.403425i	$0.867819\pi$
$200$		0			0
$201$	−1.32589	−	49.8999i	−0.00659648	−	0.248258i
$202$		0			0
$203$	167.720	−	38.2699i	0.826206	−	0.188522i
$204$		0			0
$205$	72.4229	−	125.440i	0.353283	−	0.611903i
$206$		0			0
$207$	205.990	−	10.9545i	0.995120	−	0.0529201i
$208$		0			0
$209$	−116.984			−0.559732
$210$		0			0
$211$		−	151.863i		−	0.719731i	−0.933004	−	0.359866i	$-0.882823\pi$
$211$		−	151.863i		−	0.719731i	0.933004	−	0.359866i	$-0.117177\pi$
$212$		0			0
$213$	−104.506	+	192.653i	−0.490638	+	0.904472i
$214$		0			0
$215$	434.016	+	250.579i	2.01868	+	1.16549i
$216$		0			0
$217$	111.677	−	103.608i	0.514639	−	0.477456i
$218$		0			0
$219$	−3.16707	−	119.193i	−0.0144615	−	0.544258i
$220$		0			0
$221$	−212.762	+	122.838i	−0.962725	+	0.555830i
$222$		0			0
$223$	159.992			0.717453			0.358726	−	0.933443i	$-0.383211\pi$
$223$	159.992			0.717453			0.358726	+	0.933443i	$0.383211\pi$
$224$		0			0
$225$	−289.039	+	568.352i	−1.28462	+	2.52601i
$226$		0			0
$227$	179.764	−	103.787i	0.791912	−	0.457210i	−0.0487235	−	0.998812i	$-0.515515\pi$
$227$	179.764	−	103.787i	0.791912	−	0.457210i	0.840635	+	0.541602i	$0.182182\pi$
$228$		0			0
$229$	318.721	+	184.014i	1.39179	+	0.803552i	0.993514	−	0.113711i	$-0.0362739\pi$
$229$	318.721	+	184.014i	1.39179	+	0.803552i	0.398280	+	0.917264i	$0.369607\pi$
$230$		0			0
$231$	−27.7899	−	108.426i	−0.120303	−	0.469378i
$232$		0			0
$233$	−13.9743	−	8.06808i	−0.0599757	−	0.0346270i	0.469712	−	0.882820i	$-0.344358\pi$
$233$	−13.9743	−	8.06808i	−0.0599757	−	0.0346270i	−0.529688	+	0.848193i	$0.677691\pi$
$234$		0			0
$235$	−101.487	+	58.5937i	−0.431861	+	0.249335i
$236$		0			0
$237$	12.6850	−	7.78012i	0.0535234	−	0.0328275i
$238$		0			0
$239$	86.2929			0.361058			0.180529	−	0.983570i	$-0.442219\pi$
$239$	86.2929			0.361058			0.180529	+	0.983570i	$0.442219\pi$
$240$		0			0
$241$	259.957	−	150.086i	1.07866	−	0.622765i	0.148126	−	0.988968i	$-0.452676\pi$
$241$	259.957	−	150.086i	1.07866	−	0.622765i	0.930535	+	0.366203i	$0.119342\pi$
$242$		0			0
$243$	148.300	+	192.500i	0.610287	+	0.792180i
$244$		0			0
$245$	35.9094	−	478.372i	0.146569	−	1.95254i
$246$		0			0
$247$	−299.511	−	172.923i	−1.21259	−	0.700092i
$248$		0			0
$249$	−147.916	−	80.2383i	−0.594042	−	0.322242i
$250$		0			0
$251$			298.636i			1.18979i	0.803805	+	0.594893i	$0.202805\pi$
$251$			298.636i			1.18979i	−0.803805	+	0.594893i	$0.797195\pi$
$252$		0			0
$253$	−122.165			−0.482866
$254$		0			0
$255$	−218.346	+	402.512i	−0.856257	+	1.57848i
$256$		0			0
$257$	−72.5522	+	125.664i	−0.282304	+	0.488965i	−0.971952	−	0.235180i	$-0.924432\pi$
$257$	−72.5522	+	125.664i	−0.282304	+	0.488965i	0.689648	+	0.724145i	$0.257765\pi$
$258$		0			0
$259$	207.017	+	63.8704i	0.799292	+	0.246604i
$260$		0			0
$261$	185.406	−	120.607i	0.710369	−	0.462097i
$262$		0			0
$263$	111.748	+	193.553i	0.424898	+	0.735945i	0.996411	−	0.0846482i	$-0.0269767\pi$
$263$	111.748	+	193.553i	0.424898	+	0.735945i	−0.571513	+	0.820593i	$0.693643\pi$
$264$		0			0
$265$			536.568i			2.02478i
$266$		0			0
$267$	−12.9257	−	21.0745i	−0.0484107	−	0.0789309i
$268$		0			0
$269$	6.39468	+	11.0759i	0.0237720	+	0.0411744i	0.877667	−	0.479272i	$-0.159099\pi$
$269$	6.39468	+	11.0759i	0.0237720	+	0.0411744i	−0.853895	+	0.520446i	$0.825766\pi$
$270$		0			0
$271$	−54.9222	+	95.1281i	−0.202665	+	0.351026i	−0.949386	−	0.314111i	$-0.898294\pi$
$271$	−54.9222	+	95.1281i	−0.202665	+	0.351026i	0.746721	+	0.665137i	$0.231627\pi$
$272$		0			0
$273$	89.1230	−	318.679i	0.326458	−	1.16732i
$274$		0			0
$275$	188.810	−	327.028i	0.686581	−	1.18919i
$276$		0			0
$277$	−245.860	−	425.843i	−0.887583	−	1.53734i	−0.842725	−	0.538345i	$-0.819050\pi$
$277$	−245.860	−	425.843i	−0.887583	−	1.53734i	−0.0448582	−	0.998993i	$-0.514284\pi$
$278$		0			0
$279$	88.7846	−	174.582i	0.318224	−	0.625740i
$280$		0			0
$281$			80.2824i			0.285703i	0.989744	+	0.142851i	$0.0456271\pi$
$281$			80.2824i			0.285703i	−0.989744	+	0.142851i	$0.954373\pi$
$282$		0			0
$283$	141.957	+	245.877i	0.501615	+	0.868823i	0.999998	+	0.00186632i	$0.000594068\pi$
$283$	141.957	+	245.877i	0.501615	+	0.868823i	−0.498383	+	0.866957i	$0.666073\pi$
$284$		0			0
$285$	−644.398	+	17.1223i	−2.26105	+	0.0600783i
$286$		0			0
$287$	23.0391	+	100.970i	0.0802756	+	0.351812i
$288$		0			0
$289$	22.9580	−	39.7644i	0.0794394	−	0.137593i
$290$		0			0
$291$	167.464	+	90.8420i	0.575477	+	0.312172i
$292$		0			0
$293$	327.509			1.11778			0.558890	−	0.829242i	$-0.311227\pi$
$293$	327.509			1.11778			0.558890	+	0.829242i	$0.311227\pi$
$294$		0			0
$295$			455.439i			1.54386i
$296$		0			0
$297$	−81.6491	−	118.507i	−0.274913	−	0.399013i
$298$		0			0
$299$	−312.776	−	180.581i	−1.04607	−	0.603950i
$300$		0			0
$301$	−349.351	+	79.7140i	−1.16063	+	0.264831i
$302$		0			0
$303$	−96.4108	+	2.56174i	−0.318188	+	0.00845457i
$304$		0			0
$305$	266.347	−	153.775i	0.873268	−	0.504182i
$306$		0			0
$307$	−204.668			−0.666671			−0.333335	−	0.942808i	$-0.608174\pi$
$307$	−204.668			−0.666671			−0.333335	+	0.942808i	$0.608174\pi$
$308$		0			0
$309$	−267.019	−	435.359i	−0.864139	−	1.40893i
$310$		0			0
$311$	−391.185	+	225.851i	−1.25783	+	0.726209i	−0.972652	−	0.232266i	$-0.925386\pi$
$311$	−391.185	+	225.851i	−1.25783	+	0.726209i	−0.285178	+	0.958475i	$0.592053\pi$
$312$		0			0
$313$	278.509	+	160.797i	0.889806	+	0.513730i	0.873879	−	0.486143i	$-0.161597\pi$
$313$	278.509	+	160.797i	0.889806	+	0.513730i	0.0159272	+	0.999873i	$0.494930\pi$
$314$		0			0
$315$	−168.948	−	593.190i	−0.536344	−	1.88314i
$316$		0			0
$317$	−203.355	−	117.407i	−0.641498	−	0.370369i	0.143693	−	0.989622i	$-0.454102\pi$
$317$	−203.355	−	117.407i	−0.641498	−	0.370369i	−0.785191	+	0.619253i	$0.787435\pi$
$318$		0			0
$319$	−113.441	+	65.4951i	−0.355614	+	0.205314i
$320$		0			0
$321$	316.900	+	516.687i	0.987227	+	1.60962i
$322$		0			0
$323$	−342.195			−1.05943
$324$		0			0
$325$	966.808	−	558.187i	2.97479	−	1.71750i
$326$		0			0
$327$	105.876	−	2.81323i	0.323779	−	0.00860314i
$328$		0			0
$329$	24.7024	−	80.0652i	0.0750831	−	0.243359i
$330$		0			0
$331$	136.729	+	78.9403i	0.413077	+	0.238490i	0.692111	−	0.721791i	$-0.256681\pi$
$331$	136.729	+	78.9403i	0.413077	+	0.238490i	−0.279034	+	0.960281i	$0.590014\pi$
$332$		0			0
$333$	278.151	−	14.7920i	0.835289	−	0.0444204i
$334$		0			0
$335$			162.900i			0.486270i
$336$		0			0
$337$	308.611			0.915759			0.457880	−	0.889014i	$-0.348609\pi$
$337$	308.611			0.915759			0.457880	+	0.889014i	$0.348609\pi$
$338$		0			0
$339$	243.161	+	131.904i	0.717289	+	0.389099i
$340$		0			0
$341$	−57.9970	+	100.454i	−0.170079	+	0.294586i
$342$		0			0
$343$	213.807	+	268.208i	0.623343	+	0.781949i
$344$		0			0
$345$	−672.937	+	17.8806i	−1.95054	+	0.0518279i
$346$		0			0
$347$	97.4526	+	168.793i	0.280843	+	0.486435i	0.971593	−	0.236659i	$-0.0760526\pi$
$347$	97.4526	+	168.793i	0.280843	+	0.486435i	−0.690749	+	0.723094i	$0.742719\pi$
$348$		0			0
$349$			353.944i			1.01417i	0.861897	+	0.507084i	$0.169276\pi$
$349$			353.944i			1.01417i	−0.861897	+	0.507084i	$0.830724\pi$
$350$		0			0
$351$	−33.8702	−	424.101i	−0.0964962	−	1.20826i
$352$		0			0
$353$	322.725	+	558.976i	0.914234	+	1.58350i	0.808018	+	0.589157i	$0.200540\pi$
$353$	322.725	+	558.976i	0.914234	+	1.58350i	0.106216	+	0.994343i	$0.466127\pi$
$354$		0			0
$355$	357.622	−	619.420i	1.00739	−	1.74484i
$356$		0			0
$357$	−81.2895	−	317.163i	−0.227702	−	0.888410i
$358$		0			0
$359$	265.046	−	459.074i	0.738291	−	1.27876i	−0.214973	−	0.976620i	$-0.568966\pi$
$359$	265.046	−	459.074i	0.738291	−	1.27876i	0.953264	−	0.302138i	$-0.0977002\pi$
$360$		0			0
$361$	−60.3585	−	104.544i	−0.167198	−	0.289596i
$362$		0			0
$363$	−145.227	−	236.784i	−0.400073	−	0.652296i
$364$		0			0
$365$			389.109i			1.06605i
$366$		0			0
$367$	−83.5711	−	144.749i	−0.227714	−	0.394412i	0.729416	−	0.684070i	$-0.239792\pi$
$367$	−83.5711	−	144.749i	−0.227714	−	0.394412i	−0.957130	+	0.289658i	$0.906458\pi$
$368$		0			0
$369$	72.6075	+	111.618i	0.196768	+	0.302487i
$370$		0			0
$371$	−260.929	−	281.250i	−0.703313	−	0.758086i
$372$		0			0
$373$	−56.0705	+	97.1169i	−0.150323	+	0.260367i	−0.931346	−	0.364135i	$-0.881365\pi$
$373$	−56.0705	+	97.1169i	−0.150323	+	0.260367i	0.781023	+	0.624502i	$0.214698\pi$
$374$		0			0
$375$	642.068	−	1183.63i	1.71218	−	3.15634i
$376$		0			0
$377$	−387.252			−1.02719
$378$		0			0
$379$		−	427.746i		−	1.12862i	−0.825564	−	0.564309i	$-0.809143\pi$
$379$		−	427.746i		−	1.12862i	0.825564	−	0.564309i	$-0.190857\pi$
$380$		0			0
$381$	−198.689	−	107.780i	−0.521493	−	0.282888i
$382$		0			0
$383$	−537.538	−	310.348i	−1.40349	−	0.810308i	−0.408745	−	0.912649i	$-0.634033\pi$
$383$	−537.538	−	310.348i	−1.40349	−	0.810308i	−0.994749	+	0.102341i	$0.967367\pi$
$384$		0			0
$385$	81.2588	+	356.121i	0.211062	+	0.924990i
$386$		0			0
$387$	−386.191	+	251.218i	−0.997909	+	0.649142i
$388$		0			0
$389$	−259.669	+	149.920i	−0.667530	+	0.385398i	−0.795140	−	0.606426i	$-0.792603\pi$
$389$	−259.669	+	149.920i	−0.667530	+	0.385398i	0.127610	+	0.991824i	$0.459269\pi$
$390$		0			0
$391$	−357.351			−0.913940
$392$		0			0
$393$	109.069	−	66.8951i	0.277528	−	0.170216i
$394$		0			0
$395$	−42.0560	+	24.2811i	−0.106471	+	0.0614710i
$396$		0			0
$397$	398.346	+	229.985i	1.00339	+	0.579307i	0.909249	−	0.416252i	$-0.136657\pi$
$397$	398.346	+	229.985i	1.00339	+	0.579307i	0.0941399	+	0.995559i	$0.469990\pi$
$398$		0			0
$399$	329.444	−	322.341i	0.825675	−	0.807872i
$400$		0			0
$401$	592.401	+	342.023i	1.47731	+	0.852925i	0.999671	−	0.0256326i	$-0.00816001\pi$
$401$	592.401	+	342.023i	1.47731	+	0.852925i	0.477637	+	0.878557i	$0.341493\pi$
$402$		0			0
$403$	−296.976	+	171.459i	−0.736913	+	0.425457i
$404$		0			0
$405$	−467.103	−	640.835i	−1.15334	−	1.58231i
$406$		0			0
$407$	−164.962			−0.405311
$408$		0			0
$409$	−325.542	+	187.952i	−0.795945	+	0.459539i	−0.842051	−	0.539397i	$-0.818652\pi$
$409$	−325.542	+	187.952i	−0.795945	+	0.459539i	0.0461061	+	0.998937i	$0.485319\pi$
$410$		0			0
$411$	8.17444	+	307.645i	0.0198891	+	0.748527i
$412$		0			0
$413$	−221.477	−	238.725i	−0.536263	−	0.578027i
$414$		0			0
$415$	475.583	+	274.578i	1.14598	+	0.661634i
$416$		0			0
$417$	129.943	−	239.545i	0.311614	−	0.574448i
$418$		0			0
$419$		−	285.762i		−	0.682010i	−0.940061	−	0.341005i	$-0.889233\pi$
$419$		−	285.762i		−	0.682010i	0.940061	−	0.341005i	$-0.110767\pi$
$420$		0			0
$421$	350.727			0.833081			0.416540	−	0.909117i	$-0.363242\pi$
$421$	350.727			0.833081			0.416540	+	0.909117i	$0.363242\pi$
$422$		0			0
$423$	−5.72091	−	107.577i	−0.0135246	−	0.254319i
$424$		0			0
$425$	552.296	−	956.605i	1.29952	−	2.25084i
$426$		0			0
$427$	−64.8298	+	210.126i	−0.151826	+	0.492099i
$428$		0			0
$429$	6.69257	+	251.875i	0.0156004	+	0.587121i
$430$		0			0
$431$	−233.727	−	404.826i	−0.542289	−	0.939272i	−0.998772	−	0.0495402i	$-0.984224\pi$
$431$	−233.727	−	404.826i	−0.542289	−	0.939272i	0.456483	−	0.889732i	$-0.349109\pi$
$432$		0			0
$433$		−	217.745i		−	0.502874i	−0.967874	−	0.251437i	$-0.919097\pi$
$433$		−	217.745i		−	0.502874i	0.967874	−	0.251437i	$-0.0809032\pi$
$434$		0			0
$435$	−615.294	+	377.378i	−1.41447	+	0.867536i
$436$		0			0
$437$	−251.526	−	435.655i	−0.575574	−	0.996923i
$438$		0			0
$439$	−230.686	+	399.560i	−0.525481	+	0.910160i	0.474078	+	0.880483i	$0.342781\pi$
$439$	−230.686	+	399.560i	−0.525481	+	0.910160i	−0.999560	+	0.0296775i	$0.990552\pi$
$440$		0			0
$441$	377.021	+	228.771i	0.854923	+	0.518755i
$442$		0			0
$443$	−78.2121	+	135.467i	−0.176551	+	0.305795i	−0.940697	−	0.339248i	$-0.889827\pi$
$443$	−78.2121	+	135.467i	−0.176551	+	0.305795i	0.764146	+	0.645043i	$0.223161\pi$
$444$		0			0
$445$	40.3398	+	69.8706i	0.0906513	+	0.157013i
$446$		0			0
$447$	−435.052	+	266.831i	−0.973271	+	0.596937i
$448$		0			0
$449$		−	49.2939i		−	0.109786i	−0.998492	−	0.0548930i	$-0.982518\pi$
$449$		−	49.2939i		−	0.109786i	0.998492	−	0.0548930i	$-0.0174818\pi$
$450$		0			0
$451$	−39.4291	−	68.2932i	−0.0874259	−	0.151426i
$452$		0			0
$453$	5.98659	+	225.305i	0.0132154	+	0.497363i
$454$		0			0
$455$	−318.364	+	1031.88i	−0.699701	+	2.26787i
$456$		0			0
$457$	130.664	−	226.317i	0.285917	−	0.495222i	−0.686914	−	0.726738i	$-0.741035\pi$
$457$	130.664	−	226.317i	0.285917	−	0.495222i	0.972831	+	0.231516i	$0.0743686\pi$
$458$		0			0
$459$	−238.835	−	346.650i	−0.520339	−	0.755228i
$460$		0			0
$461$	261.457			0.567151			0.283576	−	0.958950i	$-0.408479\pi$
$461$	261.457			0.567151			0.283576	+	0.958950i	$0.408479\pi$
$462$		0			0
$463$		−	410.629i		−	0.886887i	−0.896302	−	0.443444i	$-0.853757\pi$
$463$		−	410.629i		−	0.886887i	0.896302	−	0.443444i	$-0.146243\pi$
$464$		0			0
$465$	−304.769	+	561.831i	−0.655418	+	1.20824i
$466$		0			0
$467$	−377.906	−	218.184i	−0.809220	−	0.467203i	0.0374651	−	0.999298i	$-0.488072\pi$
$467$	−377.906	−	218.184i	−0.809220	−	0.467203i	−0.846685	+	0.532095i	$0.821405\pi$
$468$		0			0
$469$	−79.2173	−	85.3866i	−0.168907	−	0.182061i
$470$		0			0
$471$	16.6151	+	625.310i	0.0352763	+	1.32762i
$472$		0			0
$473$	236.291	−	136.422i	0.499557	−	0.288420i
$474$		0			0
$475$	1554.96			3.27360
$476$		0			0
$477$	−439.671	−	223.598i	−0.921743	−	0.468758i
$478$		0			0
$479$	712.054	−	411.104i	1.48654	−	0.858256i	0.486660	−	0.873592i	$-0.338215\pi$
$479$	712.054	−	411.104i	1.48654	−	0.858256i	0.999882	+	0.0153361i	$0.00488182\pi$
$480$		0			0
$481$	−422.346	−	243.842i	−0.878058	−	0.506947i
$482$		0			0
$483$	344.035	−	336.617i	0.712287	−	0.696929i
$484$		0			0
$485$	−538.432	−	310.864i	−1.11017	−	0.640957i
$486$		0			0
$487$	−617.211	+	356.347i	−1.26737	+	0.731719i	−0.974490	−	0.224429i	$-0.927948\pi$
$487$	−617.211	+	356.347i	−1.26737	+	0.731719i	−0.292884	+	0.956148i	$0.594615\pi$
$488$		0			0
$489$	758.570	−	465.254i	1.55127	−	0.951440i
$490$		0			0
$491$	806.962			1.64351			0.821754	−	0.569842i	$-0.192996\pi$
$491$	806.962			1.64351			0.821754	+	0.569842i	$0.192996\pi$
$492$		0			0
$493$	−331.831	+	191.583i	−0.673085	+	0.388606i
$494$		0			0
$495$	256.086	+	393.675i	0.517346	+	0.795303i
$496$		0			0
$497$	113.766	+	498.587i	0.228906	+	1.00319i
$498$		0			0
$499$	−45.1352	−	26.0588i	−0.0904513	−	0.0522221i	0.454092	−	0.890955i	$-0.349964\pi$
$499$	−45.1352	−	26.0588i	−0.0904513	−	0.0522221i	−0.544543	+	0.838733i	$0.683297\pi$
$500$		0			0
$501$	487.168	+	264.268i	0.972390	+	0.527481i
$502$		0			0
$503$		−	716.425i		−	1.42430i	−0.702025	−	0.712152i	$-0.747721\pi$
$503$		−	716.425i		−	1.42430i	0.702025	−	0.712152i	$-0.252279\pi$
$504$		0			0
$505$	314.737			0.623242
$506$		0			0
$507$	−113.431	+	209.107i	−0.223731	+	0.412439i
$508$		0			0
$509$	122.636	−	212.412i	0.240935	−	0.417312i	−0.720046	−	0.693926i	$-0.755879\pi$
$509$	122.636	−	212.412i	0.240935	−	0.417312i	0.960981	+	0.276615i	$0.0892126\pi$
$510$		0			0
$511$	−189.221	−	203.957i	−0.370295	−	0.399134i
$512$		0			0
$513$	254.502	−	535.164i	0.496105	−	1.04320i
$514$		0			0
$515$	833.342	+	1443.39i	1.61814	+	2.80270i
$516$		0			0
$517$			63.8001i			0.123404i
$518$		0			0
$519$	399.385	+	651.175i	0.769529	+	1.25467i
$520$		0			0
$521$	−278.097	−	481.679i	−0.533776	−	0.924527i	−0.999222	−	0.0394506i	$-0.987439\pi$
$521$	−278.097	−	481.679i	−0.533776	−	0.924527i	0.465446	−	0.885077i	$-0.345894\pi$
$522$		0			0
$523$	196.110	−	339.673i	0.374972	−	0.649470i	−0.615351	−	0.788253i	$-0.710986\pi$
$523$	196.110	−	339.673i	0.374972	−	0.649470i	0.990323	+	0.138783i	$0.0443191\pi$
$524$		0			0
$525$	369.386	+	1441.21i	0.703592	+	2.74516i
$526$		0			0
$527$	−169.650	+	293.842i	−0.321916	+	0.557575i
$528$		0			0
$529$	1.83458	+	3.17759i	0.00346802	+	0.00600678i
$530$		0			0
$531$	−373.193	−	189.790i	−0.702812	−	0.357419i
$532$		0			0
$533$		−	233.132i		−	0.437396i
$534$		0			0
$535$	−989.015	−	1713.02i	−1.84863	−	3.20192i
$536$		0			0
$537$	−352.313	+	9.36133i	−0.656077	+	0.0174326i
$538$		0			0
$539$	−215.772	−	147.151i	−0.400319	−	0.273007i
$540$		0			0
$541$	166.601	−	288.561i	0.307950	−	0.533384i	−0.669964	−	0.742394i	$-0.733691\pi$
$541$	166.601	−	288.561i	0.307950	−	0.533384i	0.977914	+	0.209009i	$0.0670239\pi$
$542$		0			0
$543$	53.9429	+	29.2617i	0.0993424	+	0.0538890i
$544$		0			0
$545$	−345.636			−0.634194
$546$		0			0
$547$			173.083i			0.316422i	0.987405	+	0.158211i	$0.0505726\pi$
$547$			173.083i			0.316422i	−0.987405	+	0.158211i	$0.949427\pi$
$548$		0			0
$549$	15.0142	+	282.329i	0.0273482	+	0.514261i
$550$		0			0
$551$	−467.126	−	269.696i	−0.847779	−	0.489466i
$552$		0			0
$553$	10.2366	−	33.1788i	0.0185110	−	0.0599979i
$554$		0			0
$555$	−908.678	+	24.1445i	−1.63726	+	0.0435036i
$556$		0			0
$557$	−918.753	+	530.442i	−1.64947	+	0.952320i	−0.672182	+	0.740386i	$0.734643\pi$
$557$	−918.753	+	530.442i	−1.64947	+	0.952320i	−0.977284	+	0.211934i	$0.932024\pi$
$558$		0			0
$559$	806.624			1.44298
$560$		0			0
$561$	130.343	+	212.517i	0.232341	+	0.378818i
$562$		0			0
$563$	550.654	−	317.920i	0.978071	−	0.564689i	0.0763835	−	0.997079i	$-0.475663\pi$
$563$	550.654	−	317.920i	0.978071	−	0.564689i	0.901687	+	0.432389i	$0.142329\pi$
$564$		0			0
$565$	−781.815	−	451.381i	−1.38374	−	0.798904i
$566$		0			0
$567$	556.472	+	108.754i	0.981433	+	0.191807i
$568$		0			0
$569$	704.449	+	406.714i	1.23805	+	0.714787i	0.968695	−	0.248255i	$-0.0798572\pi$
$569$	704.449	+	406.714i	1.23805	+	0.714787i	0.269352	+	0.963042i	$0.413190\pi$
$570$		0			0
$571$	−637.778	+	368.221i	−1.11695	+	0.644871i	−0.940620	−	0.339461i	$-0.889755\pi$
$571$	−637.778	+	368.221i	−1.11695	+	0.644871i	−0.176329	+	0.984331i	$0.556422\pi$
$572$		0			0
$573$	−288.902	−	471.037i	−0.504191	−	0.822055i
$574$		0			0
$575$	1623.83			2.82405
$576$		0			0
$577$	106.581	−	61.5346i	0.184716	−	0.106646i	−0.404791	−	0.914409i	$-0.632656\pi$
$577$	106.581	−	61.5346i	0.184716	−	0.106646i	0.589507	+	0.807764i	$0.299322\pi$
$578$		0			0
$579$	12.1638	−	0.323204i	0.0210082	−	0.000558211i
$580$		0			0
$581$	−382.809	+	87.3485i	−0.658880	+	0.150342i
$582$		0			0
$583$	252.986	+	146.061i	0.433938	+	0.250534i
$584$		0			0
$585$	73.7310	+	1386.45i	0.126036	+	2.37001i
$586$		0			0
$587$			939.308i			1.60018i	0.599878	+	0.800092i	$0.295216\pi$
$587$			939.308i			1.60018i	−0.599878	+	0.800092i	$0.704784\pi$
$588$		0			0
$589$	−477.640			−0.810934
$590$		0			0
$591$	466.124	+	252.852i	0.788703	+	0.427838i
$592$		0			0
$593$	−64.5058	+	111.727i	−0.108779	+	0.188410i	−0.915276	−	0.402828i	$-0.868027\pi$
$593$	−64.5058	+	111.727i	−0.108779	+	0.188410i	0.806497	+	0.591238i	$0.201361\pi$
$594$		0			0
$595$	237.694	+	1041.71i	0.399485	+	1.75077i
$596$		0			0
$597$	−129.061	+	3.42929i	−0.216183	+	0.00574420i
$598$		0			0
$599$	−444.320	−	769.585i	−0.741770	−	1.28478i	−0.951689	−	0.307064i	$-0.900653\pi$
$599$	−444.320	−	769.585i	−0.741770	−	1.28478i	0.209919	−	0.977719i	$-0.432680\pi$
$600$		0			0
$601$		−	634.763i		−	1.05618i	−0.849189	−	0.528089i	$-0.822909\pi$
$601$		−	634.763i		−	1.05618i	0.849189	−	0.528089i	$-0.177091\pi$
$602$		0			0
$603$	−133.483	−	67.8836i	−0.221365	−	0.112576i
$604$		0			0
$605$	453.239	+	785.033i	0.749155	+	1.29757i
$606$		0			0
$607$	−472.304	+	818.054i	−0.778095	+	1.34770i	0.154943	+	0.987923i	$0.450480\pi$
$607$	−472.304	+	818.054i	−0.778095	+	1.34770i	−0.933038	+	0.359777i	$0.882853\pi$
$608$		0			0
$609$	138.999	−	497.021i	0.228241	−	0.816127i
$610$		0			0
$611$	−94.3075	+	163.345i	−0.154349	+	0.267341i
$612$		0			0
$613$	50.2939	+	87.1115i	0.0820455	+	0.142107i	0.904128	−	0.427261i	$-0.140521\pi$
$613$	50.2939	+	87.1115i	0.0820455	+	0.142107i	−0.822083	+	0.569368i	$0.807188\pi$
$614$		0			0
$615$	−227.188	−	370.417i	−0.369411	−	0.602304i
$616$		0			0
$617$		−	544.570i		−	0.882610i	−0.897357	−	0.441305i	$-0.854516\pi$
$617$		−	544.570i		−	0.882610i	0.897357	−	0.441305i	$-0.145484\pi$
$618$		0			0
$619$	−33.3779	−	57.8123i	−0.0539224	−	0.0933963i	0.837804	−	0.545971i	$-0.183839\pi$
$619$	−33.3779	−	57.8123i	−0.0539224	−	0.0933963i	−0.891727	+	0.452574i	$0.850506\pi$
$620$		0			0
$621$	265.774	−	558.865i	0.427977	−	0.899944i
$622$		0			0
$623$	−55.1223	−	17.0068i	−0.0884788	−	0.0272982i
$624$		0			0
$625$	−1311.58	+	2271.73i	−2.09853	+	3.63477i
$626$		0			0
$627$	−167.341	+	308.487i	−0.266892	+	0.492005i
$628$		0			0
$629$	−482.537			−0.767149
$630$		0			0
$631$			738.431i			1.17026i	0.810941	+	0.585128i	$0.198956\pi$
$631$			738.431i			1.17026i	−0.810941	+	0.585128i	$0.801044\pi$
$632$		0			0
$633$	−400.464	−	217.235i	−0.632644	−	0.343183i
$634$		0			0
$635$	638.827	+	368.827i	1.00603	+	0.580830i
$636$		0			0
$637$	−334.921	−	695.693i	−0.525778	−	1.09214i
$638$		0			0
$639$	358.534	+	551.164i	0.561085	+	0.862542i
$640$		0			0
$641$	−148.471	+	85.7195i	−0.231623	+	0.133728i	−0.611321	−	0.791383i	$-0.709361\pi$
$641$	−148.471	+	85.7195i	−0.231623	+	0.133728i	0.379697	+	0.925111i	$0.376028\pi$
$642$		0			0
$643$	−749.426			−1.16551			−0.582757	−	0.812646i	$-0.698026\pi$
$643$	−749.426			−1.16551			−0.582757	+	0.812646i	$0.698026\pi$
$644$		0			0
$645$	1281.62	−	786.057i	1.98701	−	1.21869i
$646$		0			0
$647$	−589.924	+	340.593i	−0.911784	+	0.526419i	−0.881005	−	0.473108i	$-0.843132\pi$
$647$	−589.924	+	340.593i	−0.911784	+	0.526419i	−0.0307791	+	0.999526i	$0.509799\pi$
$648$		0			0
$649$	214.734	+	123.977i	0.330870	+	0.191028i
$650$		0			0
$651$	−113.465	−	442.699i	−0.174293	−	0.680029i
$652$		0			0
$653$	727.697	+	420.136i	1.11439	+	0.643394i	0.939963	−	0.341276i	$-0.110859\pi$
$653$	727.697	+	420.136i	1.11439	+	0.643394i	0.174428	+	0.984670i	$0.444192\pi$
$654$		0			0
$655$	−361.606	+	208.773i	−0.552070	+	0.318738i
$656$		0			0
$657$	−318.842	−	162.149i	−0.485299	−	0.246802i
$658$		0			0
$659$	−1035.77			−1.57172			−0.785862	−	0.618401i	$-0.787781\pi$
$659$	−1035.77			−1.57172			−0.785862	+	0.618401i	$0.787781\pi$
$660$		0			0
$661$	−624.364	+	360.477i	−0.944575	+	0.545351i	−0.891392	−	0.453234i	$-0.850270\pi$
$661$	−624.364	+	360.477i	−0.944575	+	0.545351i	−0.0531835	+	0.998585i	$0.516937\pi$
$662$		0			0
$663$	19.5767	+	736.770i	0.0295275	+	1.11127i
$664$		0			0
$665$	−1102.67	+	1023.00i	−1.65814	+	1.53834i
$666$		0			0
$667$	−487.815	−	281.640i	−0.731356	−	0.422249i
$668$		0			0
$669$	228.862	−	421.899i	0.342096	−	0.630641i
$670$		0			0
$671$		−	167.439i		−	0.249537i
$672$		0			0
$673$	−705.661			−1.04853			−0.524266	−	0.851555i	$-0.675660\pi$
$673$	−705.661			−1.04853			−0.524266	+	0.851555i	$0.675660\pi$
$674$		0			0
$675$	1085.29	+	1575.20i	1.60783	+	2.33363i
$676$		0			0
$677$	5.03682	−	8.72402i	0.00743990	−	0.0128863i	−0.862281	−	0.506429i	$-0.830965\pi$
$677$	5.03682	−	8.72402i	0.00743990	−	0.0128863i	0.869721	+	0.493543i	$0.164298\pi$
$678$		0			0
$679$	433.398	−	98.8918i	0.638289	−	0.145643i
$680$		0			0
$681$	−16.5405	−	622.501i	−0.0242885	−	0.914098i
$682$		0			0
$683$	−73.9512	−	128.087i	−0.108274	−	0.187536i	0.806797	−	0.590829i	$-0.201199\pi$
$683$	−73.9512	−	128.087i	−0.108274	−	0.187536i	−0.915071	+	0.403292i	$0.867866\pi$
$684$		0			0
$685$		−	1004.32i		−	1.46616i
$686$		0			0
$687$	941.162	−	577.243i	1.36996	−	0.840237i
$688$		0			0
$689$	431.808	+	747.913i	0.626716	+	1.08550i
$690$		0			0
$691$	605.873	−	1049.40i	0.876805	−	1.51867i	0.0219783	−	0.999758i	$-0.493004\pi$
$691$	605.873	−	1049.40i	0.876805	−	1.51867i	0.854827	−	0.518913i	$-0.173663\pi$
$692$		0			0
$693$	−325.673	−	81.8175i	−0.469946	−	0.118063i
$694$		0			0
$695$	−444.669	+	770.189i	−0.639811	+	1.10819i
$696$		0			0
$697$	−115.336	−	199.767i	−0.165475	−	0.286610i
$698$		0			0
$699$	−41.2653	+	25.3093i	−0.0590348	+	0.0362078i
$700$		0			0
$701$			34.2631i			0.0488775i	0.999701	+	0.0244387i	$0.00777986\pi$
$701$			34.2631i			0.0488775i	−0.999701	+	0.0244387i	$0.992220\pi$
$702$		0			0
$703$	−339.639	−	588.273i	−0.483129	−	0.836803i
$704$		0			0
$705$	9.33807	+	351.438i	0.0132455	+	0.498494i
$706$		0			0
$707$	−164.974	+	153.054i	−0.233344	+	0.216484i
$708$		0			0
$709$	207.128	−	358.756i	0.292141	−	0.506003i	−0.682175	−	0.731189i	$-0.738966\pi$
$709$	207.128	−	358.756i	0.292141	−	0.506003i	0.974316	+	0.225186i	$0.0722990\pi$
$710$		0			0
$711$	−2.37073	−	44.5797i	−0.00333436	−	0.0627000i
$712$		0			0
$713$	−498.794			−0.699571
$714$		0			0
$715$		−	822.255i		−	1.15001i
$716$		0			0
$717$	123.439	−	227.555i	0.172160	−	0.317370i
$718$		0			0
$719$	−68.9380	−	39.8014i	−0.0958804	−	0.0553566i	0.451293	−	0.892376i	$-0.350963\pi$
$719$	−68.9380	−	39.8014i	−0.0958804	−	0.0553566i	−0.547174	+	0.837019i	$0.684296\pi$
$720$		0			0
$721$	−1138.72	−	351.326i	−1.57936	−	0.487277i
$722$		0			0
$723$	−23.9193	−	900.201i	−0.0330834	−	1.24509i
$724$		0			0
$725$	1507.86	−	870.566i	2.07981	−	1.20078i
$726$		0			0
$727$	9.43364			0.0129761			0.00648806	−	0.999979i	$-0.497935\pi$
$727$	9.43364			0.0129761			0.00648806	+	0.999979i	$0.497935\pi$
$728$		0			0
$729$	719.760	−	115.703i	0.987324	−	0.158715i
$730$		0			0
$731$	691.185	−	399.056i	0.945533	−	0.545904i
$732$		0			0
$733$	193.869	+	111.930i	0.264487	+	0.152701i	0.626379	−	0.779518i	$-0.284536\pi$
$733$	193.869	+	111.930i	0.264487	+	0.152701i	−0.361893	+	0.932220i	$0.617869\pi$
$734$		0			0
$735$	−1210.10	−	778.986i	−1.64640	−	1.05985i
$736$		0			0
$737$	76.8057	+	44.3438i	0.104214	+	0.0601680i
$738$		0			0
$739$	541.551	−	312.665i	0.732816	−	0.423092i	−0.0866354	−	0.996240i	$-0.527612\pi$
$739$	541.551	−	312.665i	0.732816	−	0.423092i	0.819452	+	0.573148i	$0.194278\pi$
$740$		0			0
$741$	−884.436	+	542.451i	−1.19357	+	0.732053i
$742$		0			0
$743$	209.834			0.282415			0.141208	−	0.989980i	$-0.454902\pi$
$743$	209.834			0.282415			0.141208	+	0.989980i	$0.454902\pi$
$744$		0			0
$745$	1442.37	−	832.755i	1.93607	−	1.11779i
$746$		0			0
$747$	−423.177	+	275.278i	−0.566502	+	0.368511i
$748$		0			0
$749$	1351.44	+	416.956i	1.80432	+	0.556684i
$750$		0			0
$751$	836.749	+	483.097i	1.11418	+	0.643272i	0.939909	−	0.341426i	$-0.110910\pi$
$751$	836.749	+	483.097i	1.11418	+	0.643272i	0.174271	+	0.984698i	$0.444243\pi$
$752$		0			0
$753$	787.504	+	427.187i	1.04582	+	0.567314i
$754$		0			0
$755$		−	735.518i		−	0.974196i
$756$		0			0
$757$	318.215			0.420363			0.210181	−	0.977662i	$-0.432595\pi$
$757$	318.215			0.420363			0.210181	+	0.977662i	$0.432595\pi$
$758$		0			0
$759$	−174.753	+	322.150i	−0.230240	+	0.424440i
$760$		0			0
$761$	−333.550	+	577.725i	−0.438304	+	0.759165i	−0.997559	−	0.0698308i	$-0.977754\pi$
$761$	−333.550	+	577.725i	−0.438304	+	0.759165i	0.559255	+	0.828996i	$0.311087\pi$
$762$		0			0
$763$	181.170	−	168.080i	0.237444	−	0.220288i
$764$		0			0
$765$	749.090	+	1151.56i	0.979202	+	1.50530i
$766$		0			0
$767$	366.518	+	634.829i	0.477860	+	0.827678i
$768$		0			0
$769$			774.930i			1.00771i	0.863788	+	0.503856i	$0.168086\pi$
$769$			774.930i			1.00771i	−0.863788	+	0.503856i	$0.831914\pi$
$770$		0			0
$771$	227.593	+	371.078i	0.295192	+	0.481295i
$772$		0			0
$773$	−61.0922	−	105.815i	−0.0790326	−	0.136889i	0.823800	−	0.566880i	$-0.191850\pi$
$773$	−61.0922	−	105.815i	−0.0790326	−	0.136889i	−0.902833	+	0.429992i	$0.858516\pi$
$774$		0			0
$775$	770.901	−	1335.24i	0.994711	−	1.72289i
$776$		0			0
$777$	464.556	−	454.539i	0.597884	−	0.584993i
$778$		0			0
$779$	162.361	−	281.218i	0.208422	−	0.360998i
$780$		0			0
$781$	−194.700	−	337.230i	−0.249295	−	0.431792i
$782$		0			0
$783$	−52.8250	−	661.441i	−0.0674648	−	0.844752i
$784$		0			0
$785$		−	2041.35i		−	2.60045i
$786$		0			0
$787$	−351.265	−	608.408i	−0.446334	−	0.773073i	0.551810	−	0.833970i	$-0.313937\pi$
$787$	−351.265	−	608.408i	−0.446334	−	0.773073i	−0.998144	+	0.0608970i	$0.980604\pi$
$788$		0			0
$789$	670.252	−	17.8093i	0.849496	−	0.0225720i
$790$		0			0
$791$	629.303	−	143.593i	0.795579	−	0.181533i
$792$		0			0
$793$	247.504	−	428.690i	0.312111	−	0.540593i
$794$		0			0
$795$	1414.93	+	767.540i	1.77979	+	0.965459i
$796$		0			0
$797$	−615.706			−0.772530			−0.386265	−	0.922388i	$-0.626235\pi$
$797$	−615.706			−0.772530			−0.386265	+	0.922388i	$0.626235\pi$
$798$		0			0
$799$			186.625i			0.233573i
$800$		0			0
$801$	−74.0633	+	3.93866i	−0.0924635	+	0.00491717i
$802$		0			0
$803$	183.461	+	105.921i	0.228469	+	0.131907i
$804$		0			0
$805$	−1151.50	+	1068.30i	−1.43044	+	1.32708i
$806$		0			0
$807$	38.3545	−	1.01912i	0.0475273	−	0.00126285i
$808$		0			0
$809$	1077.98	−	622.375i	1.33249	−	0.769313i	0.346809	−	0.937936i	$-0.387265\pi$
$809$	1077.98	−	622.375i	1.33249	−	0.769313i	0.985681	+	0.168622i	$0.0539318\pi$
$810$		0			0
$811$	1339.58			1.65176			0.825881	−	0.563845i	$-0.190678\pi$
$811$	1339.58			1.65176			0.825881	+	0.563845i	$0.190678\pi$
$812$		0			0
$813$	172.289	+	280.907i	0.211917	+	0.345519i
$814$		0			0
$815$	−2514.97	+	1452.02i	−3.08585	+	1.78161i
$816$		0			0
$817$	972.998	+	561.760i	1.19094	+	0.687589i
$818$		0			0
$819$	−712.869	−	690.875i	−0.870414	−	0.843559i
$820$		0			0
$821$	−263.793	−	152.301i	−0.321307	−	0.185507i	0.330668	−	0.943747i	$-0.392726\pi$
$821$	−263.793	−	152.301i	−0.321307	−	0.185507i	−0.651975	+	0.758241i	$0.726059\pi$
$822$		0			0
$823$	297.149	−	171.559i	0.361056	−	0.208456i	−0.308488	−	0.951228i	$-0.599823\pi$
$823$	297.149	−	171.559i	0.361056	−	0.208456i	0.669544	+	0.742773i	$0.266490\pi$
$824$		0			0
$825$	−592.289	−	965.693i	−0.717926	−	1.17054i
$826$		0			0
$827$	−652.212			−0.788648			−0.394324	−	0.918972i	$-0.629021\pi$
$827$	−652.212			−0.788648			−0.394324	+	0.918972i	$0.629021\pi$
$828$		0			0
$829$	−314.990	+	181.859i	−0.379963	+	0.219372i	−0.677802	−	0.735244i	$-0.737067\pi$
$829$	−314.990	+	181.859i	−0.379963	+	0.219372i	0.297839	+	0.954616i	$0.403734\pi$
$830$		0			0
$831$	−1474.64	+	39.1828i	−1.77454	+	0.0471513i
$832$		0			0
$833$	−631.165	−	430.437i	−0.757701	−	0.516731i
$834$		0			0
$835$	−1566.35	−	904.332i	−1.87587	−	1.08303i
$836$		0			0
$837$	−333.369	−	483.857i	−0.398290	−	0.578085i
$838$		0			0
$839$		−	1070.44i		−	1.27585i	−0.770099	−	0.637925i	$-0.779793\pi$
$839$		−	1070.44i		−	1.27585i	0.770099	−	0.637925i	$-0.220207\pi$
$840$		0			0
$841$	237.030			0.281843
$842$		0			0
$843$	211.705	+	114.841i	0.251133	+	0.136229i
$844$		0			0
$845$	388.166	−	672.323i	0.459368	−	0.795648i
$846$		0			0
$847$	−619.328	−	191.080i	−0.731201	−	0.225596i
$848$		0			0
$849$	851.442	−	22.6237i	1.00288	−	0.0266475i
$850$		0			0
$851$	−354.681	−	614.326i	−0.416782	−	0.721887i
$852$		0			0
$853$			1557.63i			1.82606i	0.407891	+	0.913031i	$0.366264\pi$
$853$			1557.63i			1.82606i	−0.407891	+	0.913031i	$0.633736\pi$
$854$		0			0
$855$	−876.635	+	1723.77i	−1.02530	+	2.01611i
$856$		0			0
$857$	−117.943	−	204.284i	−0.137624	−	0.238371i	0.788973	−	0.614428i	$-0.210613\pi$
$857$	−117.943	−	204.284i	−0.137624	−	0.238371i	−0.926597	+	0.376057i	$0.877280\pi$
$858$		0			0
$859$	−557.231	+	965.153i	−0.648698	+	1.12358i	0.334737	+	0.942312i	$0.391353\pi$
$859$	−557.231	+	965.153i	−0.648698	+	1.12358i	−0.983434	+	0.181265i	$0.941981\pi$
$860$		0			0
$861$	299.215	+	83.6797i	0.347520	+	0.0971889i
$862$		0			0
$863$	375.824	−	650.946i	0.435486	−	0.754283i	−0.561849	−	0.827239i	$-0.689910\pi$
$863$	375.824	−	650.946i	0.435486	−	0.754283i	0.997335	+	0.0729562i	$0.0232433\pi$
$864$		0			0
$865$	−1246.45	−	2158.91i	−1.44098	−	2.49585i
$866$		0			0
$867$	−72.0183	−	117.422i	−0.0830661	−	0.135434i
$868$		0			0
$869$			26.4386i			0.0304242i
$870$		0			0
$871$	131.095	+	227.064i	0.150511	+	0.260694i
$872$		0			0
$873$	479.101	−	311.656i	0.548798	−	0.356995i
$874$		0			0
$875$	−698.963	−	3063.24i	−0.798815	−	3.50085i
$876$		0			0
$877$	−613.699	+	1062.96i	−0.699770	+	1.21204i	0.268776	+	0.963203i	$0.413381\pi$
$877$	−613.699	+	1062.96i	−0.699770	+	1.21204i	−0.968546	+	0.248835i	$0.919952\pi$
$878$		0			0
$879$	468.490	−	863.643i	0.532980	−	0.982529i
$880$		0			0
$881$	−1209.71			−1.37311			−0.686557	−	0.727076i	$-0.740879\pi$
$881$	−1209.71			−1.37311			−0.686557	+	0.727076i	$0.740879\pi$
$882$		0			0
$883$			990.879i			1.12217i	0.827757	+	0.561087i	$0.189617\pi$
$883$			990.879i			1.12217i	−0.827757	+	0.561087i	$0.810383\pi$
$884$		0			0
$885$	1200.99	+	651.488i	1.35705	+	0.736145i
$886$		0			0
$887$	1395.29	+	805.571i	1.57304	+	0.908198i	0.995793	+	0.0916309i	$0.0292080\pi$
$887$	1395.29	+	805.571i	1.57304	+	0.908198i	0.577251	+	0.816567i	$0.304125\pi$
$888$		0			0
$889$	−514.209	+	117.331i	−0.578413	+	0.131981i
$890$		0			0
$891$	−429.298	+	45.7893i	−0.481816	+	0.0513910i
$892$		0			0
$893$	−227.519	+	131.358i	−0.254780	+	0.147097i
$894$		0			0
$895$	1150.14			1.28507
$896$		0			0
$897$	−923.606	+	566.476i	−1.02966	+	0.631522i
$898$		0			0
$899$	−463.173	+	267.413i	−0.515209	+	0.297456i
$900$		0			0
$901$	740.020	+	427.251i	0.821332	+	0.474196i
$902$		0			0
$903$	−289.527	+	1035.27i	−0.320628	+	1.14648i
$904$		0			0
$905$	−173.438	−	100.135i	−0.191644	−	0.110646i
$906$		0			0
$907$	−967.470	+	558.569i	−1.06667	+	0.615842i	−0.927270	−	0.374394i	$-0.877851\pi$
$907$	−967.470	+	558.569i	−1.06667	+	0.615842i	−0.139400	+	0.990236i	$0.544517\pi$
$908$		0			0
$909$	−131.157	+	257.900i	−0.144287	+	0.283718i
$910$		0			0
$911$	−223.900			−0.245774			−0.122887	−	0.992421i	$-0.539215\pi$
$911$	−223.900			−0.245774			−0.122887	+	0.992421i	$0.539215\pi$
$912$		0			0
$913$	258.921	−	149.488i	0.283594	−	0.163733i
$914$		0			0
$915$	−24.5072	−	922.327i	−0.0267838	−	1.00801i
$916$		0			0
$917$	88.0162	−	285.278i	0.0959828	−	0.311099i
$918$		0			0
$919$	−412.009	−	237.874i	−0.448324	−	0.258840i	0.258798	−	0.965931i	$-0.416673\pi$
$919$	−412.009	−	237.874i	−0.448324	−	0.258840i	−0.707122	+	0.707092i	$0.750007\pi$
$920$		0			0
$921$	−292.770	+	539.710i	−0.317882	+	0.586004i
$922$		0			0
$923$		−	1151.20i		−	1.24724i
$924$		0			0
$925$	2192.68			2.37047
$926$		0			0
$927$	−1530.00	+	81.3650i	−1.65049	+	0.0877724i
$928$		0			0
$929$	−415.674	+	719.968i	−0.447442	+	0.774992i	−0.998219	−	0.0596603i	$-0.980998\pi$
$929$	−415.674	+	719.968i	−0.447442	+	0.774992i	0.550777	+	0.834653i	$0.314332\pi$
$930$		0			0
$931$	80.5033	−	1072.44i	0.0864697	−	1.15192i
$932$		0			0
$933$	35.9938	+	1354.63i	0.0385786	+	1.45190i
$934$		0			0
$935$	−406.789	−	704.579i	−0.435068	−	0.753561i
$936$		0			0
$937$		−	358.471i		−	0.382573i	−0.981534	−	0.191286i	$-0.938734\pi$
$937$		−	358.471i		−	0.382573i	0.981534	−	0.191286i	$-0.0612660\pi$
$938$		0			0
$939$	822.420	−	504.415i	0.875847	−	0.537183i
$940$		0			0
$941$	−485.287	−	840.541i	−0.515714	−	0.893243i	−0.999834	−	0.0182409i	$-0.994193\pi$
$941$	−485.287	−	840.541i	−0.515714	−	0.893243i	0.484120	−	0.875002i	$-0.339140\pi$
$942$		0			0
$943$	169.552	−	293.672i	0.179800	−	0.311423i
$944$		0			0
$945$	−1805.92	−	403.019i	−1.91102	−	0.426475i
$946$		0			0
$947$	−884.688	+	1532.32i	−0.934200	+	1.61808i	−0.158147	+	0.987416i	$0.550552\pi$
$947$	−884.688	+	1532.32i	−0.934200	+	1.61808i	−0.776054	+	0.630667i	$0.782781\pi$
$948$		0			0
$949$	313.139	+	542.373i	0.329967	+	0.571520i
$950$		0			0
$951$	−600.494	+	368.301i	−0.631434	+	0.387278i
$952$		0			0
$953$		−	1028.42i		−	1.07914i	−0.841941	−	0.539570i	$-0.818587\pi$
$953$		−	1028.42i		−	1.07914i	0.841941	−	0.539570i	$-0.181413\pi$
$954$		0			0
$955$	901.635	+	1561.68i	0.944121	+	1.63527i
$956$		0			0
$957$	10.4379	+	392.832i	0.0109069	+	0.410483i
$958$		0			0
$959$	488.393	+	526.429i	0.509273	+	0.548935i
$960$		0			0
$961$	243.701	−	422.103i	0.253591	−	0.439233i
$962$		0			0
$963$	1815.82	−	96.5644i	1.88558	−	0.100275i
$964$		0			0
$965$	−39.7091			−0.0411494
$966$		0			0
$967$		−	1136.76i		−	1.17555i	−0.809024	−	0.587776i	$-0.800004\pi$
$967$		−	1136.76i		−	1.17555i	0.809024	−	0.587776i	$-0.199996\pi$
$968$		0			0
$969$	−489.497	+	902.370i	−0.505157	+	0.931238i
$970$		0			0
$971$	418.792	+	241.790i	0.431300	+	0.249011i	0.699900	−	0.714241i	$-0.253228\pi$
$971$	418.792	+	241.790i	0.431300	+	0.249011i	−0.268600	+	0.963252i	$0.586561\pi$
$972$		0			0
$973$	−141.458	−	619.945i	−0.145383	−	0.637148i
$974$		0			0
$975$	−88.9582	−	3347.94i	−0.0912392	−	3.43378i
$976$		0			0
$977$	105.815	−	61.0925i	0.108306	−	0.0625307i	−0.444868	−	0.895596i	$-0.646750\pi$
$977$	105.815	−	61.0925i	0.108306	−	0.0625307i	0.553175	+	0.833065i	$0.313416\pi$
$978$		0			0
$979$	43.9243			0.0448665
$980$		0			0
$981$	144.033	−	283.219i	0.146822	−	0.288704i
$982$		0			0
$983$	1120.41	−	646.870i	1.13979	−	0.658057i	0.193410	−	0.981118i	$-0.438045\pi$
$983$	1120.41	−	646.870i	1.13979	−	0.658057i	0.946378	+	0.323061i	$0.104712\pi$
$984$		0			0
$985$	−1498.69	−	865.268i	−1.52151	−	0.878445i
$986$		0			0
$987$	−175.796	−	179.670i	−0.178112	−	0.182037i
$988$		0			0
$989$	1016.09	+	586.640i	1.02739	+	0.593165i
$990$		0			0
$991$	411.728	−	237.711i	0.415468	−	0.239870i	−0.277669	−	0.960677i	$-0.589562\pi$
$991$	411.728	−	237.711i	0.415468	−	0.239870i	0.693136	+	0.720807i	$0.256228\pi$
$992$		0			0
$993$	403.751	−	247.633i	0.406597	−	0.249378i
$994$		0			0
$995$	421.325			0.423443
$996$		0			0
$997$	−291.989	+	168.580i	−0.292868	+	0.169087i	−0.639235	−	0.769012i	$-0.720749\pi$
$997$	−291.989	+	168.580i	−0.292868	+	0.169087i	0.346367	+	0.938099i	$0.387415\pi$
$998$		0			0
$999$	358.878	−	754.645i	0.359238	−	0.755401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.z.g.47.7	yes	20
3.2	odd	2	inner	336.3.z.g.47.1	yes	20
4.3	odd	2		336.3.z.f.47.4	✓	20
7.3	odd	6		336.3.z.f.143.10	yes	20
12.11	even	2		336.3.z.f.47.10	yes	20
21.17	even	6		336.3.z.f.143.4	yes	20
28.3	even	6	inner	336.3.z.g.143.1	yes	20
84.59	odd	6	inner	336.3.z.g.143.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.z.f.47.4	✓	20	4.3	odd	2
336.3.z.f.47.10	yes	20	12.11	even	2
336.3.z.f.143.4	yes	20	21.17	even	6
336.3.z.f.143.10	yes	20	7.3	odd	6
336.3.z.g.47.1	yes	20	3.2	odd	2	inner
336.3.z.g.47.7	yes	20	1.1	even	1	trivial
336.3.z.g.143.1	yes	20	28.3	even	6	inner
336.3.z.g.143.7	yes	20	84.59	odd	6	inner

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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43046 - 2.63700i) q^{3} +(-4.89508 + 8.47853i) q^{5} +(-1.55722 - 6.82459i) q^{7} +(-4.90756 - 7.54426i) q^{9} +O(q^{10})\)	\(q+(1.43046 - 2.63700i) q^{3} +(-4.89508 + 8.47853i) q^{5} +(-1.55722 - 6.82459i) q^{7} +(-4.90756 - 7.54426i) q^{9} +(2.66502 + 4.61595i) q^{11} +15.7574i q^{13} +(15.3557 + 25.0366i) q^{15} +(7.79558 + 13.5023i) q^{17} +(-10.9740 + 19.0076i) q^{19} +(-20.2240 - 5.65593i) q^{21} +(-11.4600 + 19.8494i) q^{23} +(-35.4237 - 61.3556i) q^{25} +(-26.9143 + 2.14947i) q^{27} +24.5758i q^{29} +(10.8812 + 18.8467i) q^{31} +(15.9845 - 0.424724i) q^{33} +(65.4853 + 20.2040i) q^{35} +(-15.4747 + 26.8030i) q^{37} +(41.5524 + 22.5404i) q^{39} -14.7950 q^{41} -51.1900i q^{43} +(87.9872 - 4.67912i) q^{45} +(10.3662 + 5.98495i) q^{47} +(-44.1501 + 21.2548i) q^{49} +(46.7570 - 1.24238i) q^{51} +(47.4641 - 27.4034i) q^{53} -52.1820 q^{55} +(34.4251 + 56.1281i) q^{57} +(40.2875 - 23.2600i) q^{59} +(-27.2055 - 15.7071i) q^{61} +(-43.8444 + 45.2402i) q^{63} +(-133.600 - 77.1340i) q^{65} +(14.4100 - 8.31959i) q^{67} +(35.9497 + 58.6140i) q^{69} -73.0574 q^{71} +(34.4201 - 19.8724i) q^{73} +(-212.467 + 5.64547i) q^{75} +(27.3520 - 25.3757i) q^{77} +(4.29574 + 2.48015i) q^{79} +(-32.8317 + 74.0478i) q^{81} -56.0926i q^{83} -152.640 q^{85} +(64.8065 + 35.1547i) q^{87} +(4.12044 - 7.13681i) q^{89} +(107.538 - 24.5378i) q^{91} +(65.2639 - 1.73413i) q^{93} +(-107.438 - 186.087i) q^{95} +63.5054i q^{97} +(21.7452 - 42.7587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{3} - 16 q^{7} + 11 q^{9}+O(q^{10}) \) 20 * q + 3 * q^3 - 16 * q^7 + 11 * q^9	\( 20 q + 3 q^{3} - 16 q^{7} + 11 q^{9} - 44 q^{19} - 5 q^{21} - 98 q^{25} - 144 q^{27} - 70 q^{31} + 15 q^{33} - 64 q^{37} + 6 q^{39} + 21 q^{45} - 184 q^{49} - 33 q^{51} + 120 q^{55} + 218 q^{57} - 102 q^{61} + 27 q^{63} - 144 q^{67} + 372 q^{73} - 246 q^{75} + 258 q^{79} + 287 q^{81} - 108 q^{85} + 318 q^{87} + 510 q^{91} - 173 q^{93}+O(q^{100}) \) 20 * q + 3 * q^3 - 16 * q^7 + 11 * q^9 - 44 * q^19 - 5 * q^21 - 98 * q^25 - 144 * q^27 - 70 * q^31 + 15 * q^33 - 64 * q^37 + 6 * q^39 + 21 * q^45 - 184 * q^49 - 33 * q^51 + 120 * q^55 + 218 * q^57 - 102 * q^61 + 27 * q^63 - 144 * q^67 + 372 * q^73 - 246 * q^75 + 258 * q^79 + 287 * q^81 - 108 * q^85 + 318 * q^87 + 510 * q^91 - 173 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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