LMFDB - Embedded newform 336.3.z.f.143.10

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			143.10
Root			$-0.0416279i$ of defining polynomial
Character	$\chi$	$=$	336.143
Dual form			336.3.z.f.47.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99894 - 0.0796850i) q^{3} +(4.89508 + 8.47853i) q^{5} +(1.55722 - 6.82459i) q^{7} +(8.98730 - 0.477941i) q^{9} +O(q^{10})$	\(q+(2.99894 - 0.0796850i) q^{3} +(4.89508 + 8.47853i) q^{5} +(1.55722 - 6.82459i) q^{7} +(8.98730 - 0.477941i) q^{9} +(2.66502 - 4.61595i) q^{11} -15.7574i q^{13} +(15.3557 + 25.0366i) q^{15} +(-7.79558 + 13.5023i) q^{17} +(10.9740 + 19.0076i) q^{19} +(4.12619 - 20.5906i) q^{21} +(-11.4600 - 19.8494i) q^{23} +(-35.4237 + 61.3556i) q^{25} +(26.9143 - 2.14947i) q^{27} +24.5758i q^{29} +(-10.8812 + 18.8467i) q^{31} +(7.62442 - 14.0553i) q^{33} +(65.4853 - 20.2040i) q^{35} +(-15.4747 - 26.8030i) q^{37} +(-1.25563 - 47.2557i) q^{39} +14.7950 q^{41} -51.1900i q^{43} +(48.0458 + 73.8596i) q^{45} +(10.3662 - 5.98495i) q^{47} +(-44.1501 - 21.2548i) q^{49} +(-22.3025 + 41.1139i) q^{51} +(-47.4641 - 27.4034i) q^{53} +52.1820 q^{55} +(34.4251 + 56.1281i) q^{57} +(40.2875 + 23.2600i) q^{59} +(-27.2055 + 15.7071i) q^{61} +(10.7334 - 62.0789i) q^{63} +(133.600 - 77.1340i) q^{65} +(-14.4100 - 8.31959i) q^{67} +(-35.9497 - 58.6140i) q^{69} -73.0574 q^{71} +(34.4201 + 19.8724i) q^{73} +(-101.344 + 186.825i) q^{75} +(-27.3520 - 25.3757i) q^{77} +(-4.29574 + 2.48015i) q^{79} +(80.5431 - 8.59080i) q^{81} +56.0926i q^{83} -152.640 q^{85} +(1.95832 + 73.7014i) q^{87} +(-4.12044 - 7.13681i) q^{89} +(-107.538 - 24.5378i) q^{91} +(-31.1301 + 57.3872i) q^{93} +(-107.438 + 186.087i) q^{95} -63.5054i q^{97} +(21.7452 - 42.7587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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
$3$	2.99894	−	0.0796850i	0.999647	−	0.0265617i
$3$	2.99894	−	0.0796850i	0.999647	−	0.0265617i
$4$		0			0
$5$	4.89508	+	8.47853i	0.979017	+	1.69571i	0.665987	+	0.745964i	$0.268011\pi$
$5$	4.89508	+	8.47853i	0.979017	+	1.69571i	0.313030	+	0.949743i	$0.398656\pi$
$6$		0			0
$7$	1.55722	−	6.82459i	0.222460	−	0.974942i
$7$	1.55722	−	6.82459i	0.222460	−	0.974942i
$8$		0			0
$9$	8.98730	−	0.477941i	0.998589	−	0.0531046i
$10$		0			0
$11$	2.66502	−	4.61595i	0.242275	−	0.419632i	−0.719087	−	0.694920i	$-0.755440\pi$
$11$	2.66502	−	4.61595i	0.242275	−	0.419632i	0.961362	+	0.275288i	$0.0887731\pi$
$12$		0			0
$13$		−	15.7574i		−	1.21211i	−0.795422	−	0.606056i	$-0.792751\pi$
$13$		−	15.7574i		−	1.21211i	0.795422	−	0.606056i	$-0.207249\pi$
$14$		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	$-0.984969\pi$
$17$	−7.79558	+	13.5023i	−0.458563	+	0.794255i	0.540322	+	0.841458i	$0.318302\pi$
$18$		0			0
$19$	10.9740	+	19.0076i	0.577580	+	1.00040i	0.995756	+	0.0920323i	$0.0293363\pi$
$19$	10.9740	+	19.0076i	0.577580	+	1.00040i	−0.418176	+	0.908366i	$0.637330\pi$
$20$		0			0
$21$	4.12619	−	20.5906i	0.196485	−	0.980507i
$22$		0			0
$23$	−11.4600	−	19.8494i	−0.498263	−	0.863017i	0.501735	−	0.865021i	$-0.332695\pi$
$23$	−11.4600	−	19.8494i	−0.498263	−	0.863017i	−0.999998	+	0.00200458i	$0.999362\pi$
$24$		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	$-0.947493\pi$
$31$	−10.8812	+	18.8467i	−0.351005	+	0.607958i	0.635421	+	0.772166i	$0.280827\pi$
$32$		0			0
$33$	7.62442	−	14.0553i	0.231043	−	0.425919i
$34$		0			0
$35$	65.4853	−	20.2040i	1.87101	−	0.577258i
$36$		0			0
$37$	−15.4747	−	26.8030i	−0.418235	−	0.724404i	0.577527	−	0.816371i	$-0.304018\pi$
$37$	−15.4747	−	26.8030i	−0.418235	−	0.724404i	−0.995762	+	0.0919674i	$0.970684\pi$
$38$		0			0
$39$	−1.25563	−	47.2557i	−0.0321957	−	1.21168i
$40$		0			0
$41$	14.7950			0.360854			0.180427	−	0.983588i	$-0.442252\pi$
$41$	14.7950			0.360854			0.180427	+	0.983588i	$0.442252\pi$
$42$		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
$45$	48.0458	+	73.8596i	1.06769	+	1.64132i
$46$		0			0
$47$	10.3662	−	5.98495i	0.220558	−	0.127339i	−0.385650	−	0.922645i	$-0.626023\pi$
$47$	10.3662	−	5.98495i	0.220558	−	0.127339i	0.606209	+	0.795306i	$0.292690\pi$
$48$		0			0
$49$	−44.1501	−	21.2548i	−0.901023	−	0.433771i
$50$		0			0
$51$	−22.3025	+	41.1139i	−0.437305	+	0.806155i
$52$		0			0
$53$	−47.4641	−	27.4034i	−0.895549	−	0.517045i	−0.0197954	−	0.999804i	$-0.506301\pi$
$53$	−47.4641	−	27.4034i	−0.895549	−	0.517045i	−0.875753	+	0.482759i	$0.839635\pi$
$54$		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	0.800924	−	0.598766i	$-0.204342\pi$
$59$	40.2875	+	23.2600i	0.682840	+	0.394238i	−0.118084	+	0.993004i	$0.537675\pi$
$60$		0			0
$61$	−27.2055	+	15.7071i	−0.445993	+	0.257494i	−0.706136	−	0.708076i	$-0.749563\pi$
$61$	−27.2055	+	15.7071i	−0.445993	+	0.257494i	0.260144	+	0.965570i	$0.416230\pi$
$62$		0			0
$63$	10.7334	−	62.0789i	0.170372	−	0.985380i
$64$		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	$-0.372961\pi$
$67$	−14.4100	−	8.31959i	−0.215074	−	0.124173i	−0.603667	+	0.797236i	$0.706294\pi$
$68$		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	0.716871	−	0.697206i	$-0.245574\pi$
$73$	34.4201	+	19.8724i	0.471508	+	0.272225i	−0.245363	+	0.969431i	$0.578907\pi$
$74$		0			0
$75$	−101.344	+	186.825i	−1.35126	+	2.49100i
$76$		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	$-0.676661\pi$
$79$	−4.29574	+	2.48015i	−0.0543765	+	0.0313943i	0.472565	+	0.881296i	$0.343328\pi$
$80$		0			0
$81$	80.5431	−	8.59080i	0.994360	−	0.106059i
$82$		0			0
$83$			56.0926i			0.675815i	0.941179	+	0.337907i	$0.109719\pi$
$83$			56.0926i			0.675815i	−0.941179	+	0.337907i	$0.890281\pi$
$84$		0			0
$85$	−152.640			−1.79576
$86$		0			0
$87$	1.95832	+	73.7014i	0.0225095	+	0.847143i
$88$		0			0
$89$	−4.12044	−	7.13681i	−0.0462971	−	0.0801889i	0.841948	−	0.539558i	$-0.181409\pi$
$89$	−4.12044	−	7.13681i	−0.0462971	−	0.0801889i	−0.888245	+	0.459369i	$0.848075\pi$
$90$		0			0
$91$	−107.538	−	24.5378i	−1.18174	−	0.269646i
$92$		0			0
$93$	−31.1301	+	57.3872i	−0.334733	+	0.617067i
$94$		0			0
$95$	−107.438	+	186.087i	−1.13092	+	1.95881i
$96$		0			0
$97$		−	63.5054i		−	0.654695i	−0.944904	−	0.327347i	$-0.893845\pi$
$97$		−	63.5054i		−	0.654695i	0.944904	−	0.327347i	$-0.106155\pi$
$98$		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	$-0.782458\pi$
$101$	16.0741	−	27.8412i	0.159150	−	0.275656i	0.934562	+	0.355799i	$0.115791\pi$
$102$		0			0
$103$	−85.1203	−	147.433i	−0.826411	−	1.43139i	−0.900836	−	0.434159i	$-0.857046\pi$
$103$	−85.1203	−	147.433i	−0.826411	−	1.43139i	0.0744256	−	0.997227i	$-0.476288\pi$
$104$		0			0
$105$	194.777	−	65.8089i	1.85501	−	0.626751i
$106$		0			0
$107$	−101.021	−	174.974i	−0.944124	−	1.63527i	−0.757495	−	0.652840i	$-0.773577\pi$
$107$	−101.021	−	174.974i	−0.944124	−	1.63527i	−0.186629	−	0.982431i	$-0.559756\pi$
$108$		0			0
$109$	17.6522	−	30.5745i	0.161947	−	0.280500i	−0.773620	−	0.633650i	$-0.781556\pi$
$109$	17.6522	−	30.5745i	0.161947	−	0.280500i	0.935567	+	0.353150i	$0.114889\pi$
$110$		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
$117$	−7.53113	−	141.617i	−0.0643686	−	1.21040i
$118$		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
$123$	44.3694	−	1.17894i	0.360727	−	0.00958489i
$124$		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
$129$	−4.07907	−	153.516i	−0.0316207	−	1.19005i
$130$		0			0
$131$	36.9356	−	21.3248i	0.281951	−	0.162785i	−0.352355	−	0.935866i	$-0.614619\pi$
$131$	36.9356	−	21.3248i	0.281951	−	0.162785i	0.634307	+	0.773082i	$0.281286\pi$
$132$		0			0
$133$	146.808	−	45.2943i	1.10382	−	0.340559i
$134$		0			0
$135$	149.972	+	217.672i	1.11090	+	1.61239i
$136$		0			0
$137$	88.8407	+	51.2922i	0.648472	+	0.374396i	0.787871	−	0.615841i	$-0.211184\pi$
$137$	88.8407	+	51.2922i	0.648472	+	0.374396i	−0.139398	+	0.990236i	$0.544517\pi$
$138$		0			0
$139$	−90.8399			−0.653524			−0.326762	−	0.945107i	$-0.605958\pi$
$139$	−90.8399			−0.653524			−0.326762	+	0.945107i	$0.605958\pi$
$140$		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
$147$	−134.097	−	60.2237i	−0.912227	−	0.409685i
$148$		0			0
$149$	147.329	−	85.0603i	0.988784	−	0.570874i	0.0838731	−	0.996476i	$-0.473271\pi$
$149$	147.329	−	85.0603i	0.988784	−	0.570874i	0.904910	+	0.425602i	$0.139938\pi$
$150$		0			0
$151$	65.0630	+	37.5641i	0.430881	+	0.248769i	0.699722	−	0.714415i	$-0.253307\pi$
$151$	65.0630	+	37.5641i	0.430881	+	0.248769i	−0.268841	+	0.963185i	$0.586641\pi$
$152$		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	−0.201234	−	0.979543i	$-0.564495\pi$
$157$	−180.575	−	104.255i	−1.15016	−	0.664045i	−0.948926	+	0.315498i	$0.897828\pi$
$158$		0			0
$159$	−144.526	−	78.3990i	−0.908966	−	0.493076i
$160$		0			0
$161$	−153.310	+	47.3003i	−0.952235	+	0.293791i
$162$		0			0
$163$	−256.887	+	148.314i	−1.57599	+	0.909900i	−0.580582	+	0.814202i	$0.697175\pi$
$163$	−256.887	+	148.314i	−1.57599	+	0.909900i	−0.995410	+	0.0956983i	$0.969492\pi$
$164$		0			0
$165$	156.491	−	4.15812i	0.948429	−	0.0252007i
$166$		0			0
$167$		−	184.743i		−	1.10625i	−0.833100	−	0.553123i	$-0.813436\pi$
$167$		−	184.743i		−	1.10625i	0.833100	−	0.553123i	$-0.186564\pi$
$168$		0			0
$169$	−79.2971			−0.469213
$170$		0			0
$171$	107.711	+	165.582i	0.629891	+	0.968315i
$172$		0			0
$173$	127.316	+	220.518i	0.735931	+	1.27467i	0.954314	+	0.298807i	$0.0965885\pi$
$173$	127.316	+	220.518i	0.735931	+	1.27467i	−0.218383	+	0.975863i	$0.570078\pi$
$174$		0			0
$175$	363.565	+	337.296i	2.07751	+	1.92741i
$176$		0			0
$177$	122.673	+	66.5451i	0.693070	+	0.375961i
$178$		0			0
$179$	−58.7396	+	101.740i	−0.328154	+	0.568380i	−0.982146	−	0.188122i	$-0.939760\pi$
$179$	−58.7396	+	101.740i	−0.328154	+	0.568380i	0.653991	+	0.756502i	$0.273093\pi$
$180$		0			0
$181$		−	20.4562i		−	0.113017i	−0.998402	−	0.0565087i	$-0.982003\pi$
$181$		−	20.4562i		−	0.113017i	0.998402	−	0.0565087i	$-0.0179969\pi$
$182$		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
$189$	27.2422	−	187.026i	0.144139	−	0.989558i
$190$		0			0
$191$	92.0960	+	159.515i	0.482178	+	0.835157i	0.999791	−	0.0204581i	$-0.00651248\pi$
$191$	92.0960	+	159.515i	0.482178	+	0.835157i	−0.517613	+	0.855615i	$0.673179\pi$
$192$		0			0
$193$	2.02801	−	3.51262i	0.0105078	−	0.0182001i	−0.860724	−	0.509072i	$-0.829989\pi$
$193$	2.02801	−	3.51262i	0.0105078	−	0.0182001i	0.871232	+	0.490872i	$0.163322\pi$
$194$		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	$-0.798847\pi$
$199$	21.5178	−	37.2699i	0.108130	−	0.187286i	0.915013	+	0.403425i	$0.132181\pi$
$200$		0			0
$201$	−43.8776	−	23.8017i	−0.218296	−	0.118416i
$202$		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
$207$	−112.482	−	172.915i	−0.543390	−	0.835339i
$208$		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
$213$	−219.095	+	5.82158i	−1.02861	+	0.0273313i
$214$		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
$219$	104.807	+	56.8535i	0.478572	+	0.259605i
$220$		0			0
$221$	212.762	+	122.838i	0.962725	+	0.555830i
$222$		0			0
$223$	−159.992			−0.717453			−0.358726	−	0.933443i	$-0.616789\pi$
$223$	−159.992			−0.717453			−0.358726	+	0.933443i	$0.616789\pi$
$224$		0			0
$225$	−289.039	+	568.352i	−1.28462	+	2.52601i
$226$		0			0
$227$	179.764	+	103.787i	0.791912	+	0.457210i	0.840635	−	0.541602i	$-0.182182\pi$
$227$	179.764	+	103.787i	0.791912	+	0.457210i	−0.0487235	+	0.998812i	$0.515515\pi$
$228$		0			0
$229$	318.721	−	184.014i	1.39179	−	0.803552i	0.398280	−	0.917264i	$-0.369607\pi$
$229$	318.721	−	184.014i	1.39179	−	0.803552i	0.993514	+	0.113711i	$0.0362739\pi$
$230$		0			0
$231$	−84.0491	−	73.9208i	−0.363849	−	0.320004i
$232$		0			0
$233$	13.9743	−	8.06808i	0.0599757	−	0.0346270i	−0.469712	−	0.882820i	$-0.655642\pi$
$233$	13.9743	−	8.06808i	0.0599757	−	0.0346270i	0.529688	+	0.848193i	$0.322309\pi$
$234$		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	0.930535	−	0.366203i	$-0.119342\pi$
$241$	259.957	+	150.086i	1.07866	+	0.622765i	0.148126	+	0.988968i	$0.452676\pi$
$242$		0			0
$243$	240.860	−	32.1814i	0.991192	−	0.132434i
$244$		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
$249$	4.46974	+	168.218i	0.0179508	+	0.675576i
$250$		0			0
$251$		−	298.636i		−	1.18979i	−0.803805	−	0.594893i	$-0.797195\pi$
$251$		−	298.636i		−	1.18979i	0.803805	−	0.594893i	$-0.202805\pi$
$252$		0			0
$253$	−122.165			−0.482866
$254$		0			0
$255$	−457.758	+	12.1631i	−1.79513	+	0.0476985i
$256$		0			0
$257$	72.5522	+	125.664i	0.282304	+	0.488965i	0.971952	−	0.235180i	$-0.0755679\pi$
$257$	72.5522	+	125.664i	0.282304	+	0.488965i	−0.689648	+	0.724145i	$0.742235\pi$
$258$		0			0
$259$	−207.017	+	63.8704i	−0.799292	+	0.246604i
$260$		0			0
$261$	11.7458	+	220.870i	0.0450030	+	0.846246i
$262$		0			0
$263$	111.748	−	193.553i	0.424898	−	0.735945i	−0.571513	−	0.820593i	$-0.693643\pi$
$263$	111.748	−	193.553i	0.424898	−	0.735945i	0.996411	+	0.0846482i	$0.0269767\pi$
$264$		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	$-0.840901\pi$
$269$	−6.39468	+	11.0759i	−0.0237720	+	0.0411744i	0.853895	+	0.520446i	$0.174234\pi$
$270$		0			0
$271$	54.9222	+	95.1281i	0.202665	+	0.351026i	0.949386	−	0.314111i	$-0.101706\pi$
$271$	54.9222	+	95.1281i	0.202665	+	0.351026i	−0.746721	+	0.665137i	$0.768373\pi$
$272$		0			0
$273$	−324.456	−	65.0182i	−1.18848	−	0.238162i
$274$		0			0
$275$	188.810	+	327.028i	0.686581	+	1.18919i
$276$		0			0
$277$	−245.860	+	425.843i	−0.887583	+	1.53734i	−0.0448582	+	0.998993i	$0.514284\pi$
$277$	−245.860	+	425.843i	−0.887583	+	1.53734i	−0.842725	+	0.538345i	$0.819050\pi$
$278$		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	0.498383	+	0.866957i	$0.333927\pi$
$283$	−141.957	+	245.877i	−0.501615	+	0.868823i	−0.999998	+	0.00186632i	$0.999406\pi$
$284$		0			0
$285$	−307.371	+	566.626i	−1.07849	+	1.98816i
$286$		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
$291$	−5.06042	−	190.449i	−0.0173898	−	0.654464i
$292$		0			0
$293$	−327.509			−1.11778			−0.558890	−	0.829242i	$-0.688773\pi$
$293$	−327.509			−1.11778			−0.558890	+	0.829242i	$0.688773\pi$
$294$		0			0
$295$			455.439i			1.54386i
$296$		0			0
$297$	61.8054	−	129.964i	0.208099	−	0.437588i
$298$		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
$303$	45.9869	−	84.7751i	0.151772	−	0.279786i
$304$		0			0
$305$	−266.347	−	153.775i	−0.873268	−	0.504182i
$306$		0			0
$307$	204.668			0.666671			0.333335	−	0.942808i	$-0.391826\pi$
$307$	204.668			0.666671			0.333335	+	0.942808i	$0.391826\pi$
$308$		0			0
$309$	−267.019	−	435.359i	−0.864139	−	1.40893i
$310$		0			0
$311$	−391.185	−	225.851i	−1.25783	−	0.726209i	−0.285178	−	0.958475i	$-0.592053\pi$
$311$	−391.185	−	225.851i	−1.25783	−	0.726209i	−0.972652	+	0.232266i	$0.925386\pi$
$312$		0			0
$313$	278.509	−	160.797i	0.889806	−	0.513730i	0.0159272	−	0.999873i	$-0.494930\pi$
$313$	278.509	−	160.797i	0.889806	−	0.513730i	0.873879	+	0.486143i	$0.161597\pi$
$314$		0			0
$315$	578.879	−	212.878i	1.83771	−	0.675802i
$316$		0			0
$317$	203.355	−	117.407i	0.641498	−	0.370369i	−0.143693	−	0.989622i	$-0.545898\pi$
$317$	203.355	−	117.407i	0.641498	−	0.370369i	0.785191	+	0.619253i	$0.212565\pi$
$318$		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
$327$	50.5015	−	93.0977i	0.154439	−	0.284702i
$328$		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	$-0.743319\pi$
$331$	−136.729	+	78.9403i	−0.413077	+	0.238490i	0.279034	+	0.960281i	$0.409986\pi$
$332$		0			0
$333$	−151.886	−	233.490i	−0.456114	−	0.701172i
$334$		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
$339$	7.34784	+	276.536i	0.0216750	+	0.815739i
$340$		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
$345$	320.984	−	591.721i	0.930387	−	1.71513i
$346$		0			0
$347$	97.4526	−	168.793i	0.280843	−	0.486435i	−0.690749	−	0.723094i	$-0.742719\pi$
$347$	97.4526	−	168.793i	0.280843	−	0.486435i	0.971593	+	0.236659i	$0.0760526\pi$
$348$		0			0
$349$		−	353.944i		−	1.01417i	−0.861897	−	0.507084i	$-0.830724\pi$
$349$		−	353.944i		−	1.01417i	0.861897	−	0.507084i	$-0.169276\pi$
$350$		0			0
$351$	−33.8702	−	424.101i	−0.0964962	−	1.20826i
$352$		0			0
$353$	−322.725	+	558.976i	−0.914234	+	1.58350i	−0.106216	+	0.994343i	$0.533873\pi$
$353$	−322.725	+	558.976i	−0.914234	+	1.58350i	−0.808018	+	0.589157i	$0.799460\pi$
$354$		0			0
$355$	−357.622	−	619.420i	−1.00739	−	1.74484i
$356$		0			0
$357$	245.856	+	216.229i	0.688671	+	0.605684i
$358$		0			0
$359$	265.046	+	459.074i	0.738291	+	1.27876i	0.953264	+	0.302138i	$0.0977002\pi$
$359$	265.046	+	459.074i	0.738291	+	1.27876i	−0.214973	+	0.976620i	$0.568966\pi$
$360$		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	$-0.760208\pi$
$367$	83.5711	−	144.749i	0.227714	−	0.394412i	0.957130	+	0.289658i	$0.0935415\pi$
$368$		0			0
$369$	132.967	−	7.07115i	0.360345	−	0.0191630i
$370$		0			0
$371$	−260.929	+	281.250i	−0.703313	+	0.758086i
$372$		0			0
$373$	−56.0705	−	97.1169i	−0.150323	−	0.260367i	0.781023	−	0.624502i	$-0.214698\pi$
$373$	−56.0705	−	97.1169i	−0.150323	−	0.260367i	−0.931346	+	0.364135i	$0.881365\pi$
$374$		0			0
$375$	−1346.09	+	35.7669i	−3.58956	+	0.0953783i
$376$		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
$381$	−6.00398	−	225.960i	−0.0157585	−	0.593070i
$382$		0			0
$383$	−537.538	+	310.348i	−1.40349	+	0.810308i	−0.994749	−	0.102341i	$-0.967367\pi$
$383$	−537.538	+	310.348i	−1.40349	+	0.810308i	−0.408745	+	0.912649i	$0.634033\pi$
$384$		0			0
$385$	81.2588	−	356.121i	0.211062	−	0.924990i
$386$		0			0
$387$	−24.4658	−	460.060i	−0.0632191	−	1.18879i
$388$		0			0
$389$	259.669	+	149.920i	0.667530	+	0.385398i	0.795140	−	0.606426i	$-0.207397\pi$
$389$	259.669	+	149.920i	0.667530	+	0.385398i	−0.127610	+	0.991824i	$0.540731\pi$
$390$		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	0.0941399	−	0.995559i	$-0.469990\pi$
$397$	398.346	−	229.985i	1.00339	−	0.579307i	0.909249	+	0.416252i	$0.136657\pi$
$398$		0			0
$399$	436.659	−	147.533i	1.09438	−	0.369758i
$400$		0			0
$401$	−592.401	+	342.023i	−1.47731	+	0.852925i	−0.999671	−	0.0256326i	$-0.991840\pi$
$401$	−592.401	+	342.023i	−1.47731	+	0.852925i	−0.477637	+	0.878557i	$0.658507\pi$
$402$		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	0.0461061	−	0.998937i	$-0.485319\pi$
$409$	−325.542	−	187.952i	−0.795945	−	0.459539i	−0.842051	+	0.539397i	$0.818652\pi$
$410$		0			0
$411$	270.515	+	146.743i	0.658188	+	0.357039i
$412$		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
$417$	−272.423	+	7.23857i	−0.653294	+	0.0173587i
$418$		0			0
$419$			285.762i			0.682010i	0.940061	+	0.341005i	$0.110767\pi$
$419$			285.762i			0.682010i	−0.940061	+	0.341005i	$0.889233\pi$
$420$		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
$423$	90.3041	−	58.7430i	0.213485	−	0.138872i
$424$		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
$429$	−221.476	−	120.141i	−0.516261	−	0.280050i
$430$		0			0
$431$	−233.727	+	404.826i	−0.542289	+	0.939272i	0.456483	+	0.889732i	$0.349109\pi$
$431$	−233.727	+	404.826i	−0.542289	+	0.939272i	−0.998772	+	0.0495402i	$0.984224\pi$
$432$		0			0
$433$			217.745i			0.502874i	0.967874	+	0.251437i	$0.0809032\pi$
$433$			217.745i			0.502874i	−0.967874	+	0.251437i	$0.919097\pi$
$434$		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	0.999560	+	0.0296775i	$0.00944802\pi$
$439$	230.686	+	399.560i	0.525481	+	0.910160i	−0.474078	+	0.880483i	$0.657219\pi$
$440$		0			0
$441$	−406.949	−	169.922i	−0.922787	−	0.385310i
$442$		0			0
$443$	−78.2121	−	135.467i	−0.176551	−	0.305795i	0.764146	−	0.645043i	$-0.223161\pi$
$443$	−78.2121	−	135.467i	−0.176551	−	0.305795i	−0.940697	+	0.339248i	$0.889827\pi$
$444$		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
$453$	198.113	+	107.468i	0.437336	+	0.237236i
$454$		0			0
$455$	−318.364	−	1031.88i	−0.699701	−	2.26787i
$456$		0			0
$457$	130.664	+	226.317i	0.285917	+	0.495222i	0.972831	−	0.231516i	$-0.0743686\pi$
$457$	130.664	+	226.317i	0.285917	+	0.495222i	−0.686914	+	0.726738i	$0.741035\pi$
$458$		0			0
$459$	−180.790	+	380.162i	−0.393877	+	0.828240i
$460$		0			0
$461$	−261.457			−0.567151			−0.283576	−	0.958950i	$-0.591521\pi$
$461$	−261.457			−0.567151			−0.283576	+	0.958950i	$0.591521\pi$
$462$		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
$465$	−638.944	+	16.9774i	−1.37407	+	0.0365105i
$466$		0			0
$467$	−377.906	+	218.184i	−0.809220	+	0.467203i	−0.846685	−	0.532095i	$-0.821405\pi$
$467$	−377.906	+	218.184i	−0.809220	+	0.467203i	0.0374651	+	0.999298i	$0.488072\pi$
$468$		0			0
$469$	−79.2173	+	85.3866i	−0.168907	+	0.182061i
$470$		0			0
$471$	−549.842	−	298.266i	−1.16739	−	0.633261i
$472$		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	0.999882	−	0.0153361i	$-0.00488182\pi$
$479$	712.054	+	411.104i	1.48654	+	0.858256i	0.486660	+	0.873592i	$0.338215\pi$
$480$		0			0
$481$	−422.346	+	243.842i	−0.878058	+	0.506947i
$482$		0			0
$483$	−455.998	+	154.067i	−0.944095	+	0.318980i
$484$		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	$-0.0720518\pi$
$487$	617.211	+	356.347i	1.26737	+	0.731719i	0.292884	+	0.956148i	$0.405385\pi$
$488$		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
$495$	468.976	−	24.9399i	0.947425	−	0.0503837i
$496$		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	$-0.650036\pi$
$499$	45.1352	−	26.0588i	0.0904513	−	0.0522221i	0.544543	+	0.838733i	$0.316703\pi$
$500$		0			0
$501$	−14.7212	−	554.033i	−0.0293837	−	1.10586i
$502$		0			0
$503$			716.425i			1.42430i	0.702025	+	0.712152i	$0.252279\pi$
$503$			716.425i			1.42430i	−0.702025	+	0.712152i	$0.747721\pi$
$504$		0			0
$505$	314.737			0.623242
$506$		0			0
$507$	−237.807	+	6.31878i	−0.469048	+	0.0124631i
$508$		0			0
$509$	−122.636	−	212.412i	−0.240935	−	0.417312i	0.720046	−	0.693926i	$-0.244121\pi$
$509$	−122.636	−	212.412i	−0.240935	−	0.417312i	−0.960981	+	0.276615i	$0.910787\pi$
$510$		0			0
$511$	189.221	−	203.957i	0.370295	−	0.399134i
$512$		0			0
$513$	336.214	+	487.987i	0.655389	+	0.951242i
$514$		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	−0.465446	−	0.885077i	$-0.654106\pi$
$521$	278.097	−	481.679i	0.533776	−	0.924527i	0.999222	−	0.0394506i	$-0.0125608\pi$
$522$		0			0
$523$	−196.110	−	339.673i	−0.374972	−	0.649470i	0.615351	−	0.788253i	$-0.289014\pi$
$523$	−196.110	−	339.673i	−0.374972	−	0.649470i	−0.990323	+	0.138783i	$0.955681\pi$
$524$		0			0
$525$	1117.19	+	982.562i	2.12798	+	1.87155i
$526$		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
$537$	−168.050	+	309.793i	−0.312941	+	0.576896i
$538$		0			0
$539$	−215.772	+	147.151i	−0.400319	+	0.273007i
$540$		0			0
$541$	166.601	+	288.561i	0.307950	+	0.533384i	0.977914	−	0.209009i	$-0.0670239\pi$
$541$	166.601	+	288.561i	0.307950	+	0.533384i	−0.669964	+	0.742394i	$0.733691\pi$
$542$		0			0
$543$	−1.63005	−	61.3468i	−0.00300193	−	0.112978i
$544$		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
$549$	−236.997	+	154.167i	−0.431689	+	0.280815i
$550$		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
$555$	433.429	−	799.011i	0.780954	−	1.43966i
$556$		0			0
$557$	918.753	+	530.442i	1.64947	+	0.952320i	0.977284	+	0.211934i	$0.0679763\pi$
$557$	918.753	+	530.442i	1.64947	+	0.952320i	0.672182	+	0.740386i	$0.265357\pi$
$558$		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	0.901687	−	0.432389i	$-0.142329\pi$
$563$	550.654	+	317.920i	0.978071	+	0.564689i	0.0763835	+	0.997079i	$0.475663\pi$
$564$		0			0
$565$	−781.815	+	451.381i	−1.38374	+	0.798904i
$566$		0			0
$567$	66.7946	−	563.052i	0.117803	−	0.993037i
$568$		0			0
$569$	−704.449	+	406.714i	−1.23805	+	0.714787i	−0.968695	−	0.248255i	$-0.920143\pi$
$569$	−704.449	+	406.714i	−1.23805	+	0.714787i	−0.269352	+	0.963042i	$0.586810\pi$
$570$		0			0
$571$	637.778	+	368.221i	1.11695	+	0.644871i	0.940620	−	0.339461i	$-0.110245\pi$
$571$	637.778	+	368.221i	1.11695	+	0.644871i	0.176329	+	0.984331i	$0.443578\pi$
$572$		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	0.589507	−	0.807764i	$-0.299322\pi$
$577$	106.581	+	61.5346i	0.184716	+	0.106646i	−0.404791	+	0.914409i	$0.632656\pi$
$578$		0			0
$579$	5.80198	−	10.6957i	0.0100207	−	0.0184728i
$580$		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
$585$	1163.84	−	757.079i	1.98947	−	1.29415i
$586$		0			0
$587$		−	939.308i		−	1.60018i	−0.599878	−	0.800092i	$-0.704784\pi$
$587$		−	939.308i		−	1.60018i	0.599878	−	0.800092i	$-0.295216\pi$
$588$		0			0
$589$	−477.640			−0.810934
$590$		0			0
$591$	14.0853	+	530.101i	0.0238330	+	0.896956i
$592$		0			0
$593$	64.5058	+	111.727i	0.108779	+	0.188410i	0.915276	−	0.402828i	$-0.131973\pi$
$593$	64.5058	+	111.727i	0.108779	+	0.188410i	−0.806497	+	0.591238i	$0.798639\pi$
$594$		0			0
$595$	−237.694	+	1041.71i	−0.399485	+	1.75077i
$596$		0			0
$597$	61.5607	−	113.485i	0.103117	−	0.190092i
$598$		0			0
$599$	−444.320	+	769.585i	−0.741770	+	1.28478i	0.209919	+	0.977719i	$0.432680\pi$
$599$	−444.320	+	769.585i	−0.741770	+	1.28478i	−0.951689	+	0.307064i	$0.900653\pi$
$600$		0			0
$601$			634.763i			1.05618i	0.849189	+	0.528089i	$0.177091\pi$
$601$			634.763i			1.05618i	−0.849189	+	0.528089i	$0.822909\pi$
$602$		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	0.933038	+	0.359777i	$0.117147\pi$
$607$	472.304	+	818.054i	0.778095	+	1.34770i	−0.154943	+	0.987923i	$0.549520\pi$
$608$		0			0
$609$	506.032	+	101.404i	0.830922	+	0.166510i
$610$		0			0
$611$	−94.3075	−	163.345i	−0.154349	−	0.267341i
$612$		0			0
$613$	50.2939	−	87.1115i	0.0820455	−	0.142107i	−0.822083	−	0.569368i	$-0.807188\pi$
$613$	50.2939	−	87.1115i	0.0820455	−	0.142107i	0.904128	+	0.427261i	$0.140521\pi$
$614$		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	$-0.816161\pi$
$619$	33.3779	−	57.8123i	0.0539224	−	0.0933963i	0.891727	+	0.452574i	$0.149494\pi$
$620$		0			0
$621$	−351.105	−	509.599i	−0.565386	−	0.820611i
$622$		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
$627$	350.828	−	9.32187i	0.559535	−	0.0148674i
$628$		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
$633$	−12.1012	−	455.429i	−0.0191173	−	0.719477i
$634$		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
$639$	−656.589	+	34.9171i	−1.02753	+	0.0546434i
$640$		0			0
$641$	148.471	+	85.7195i	0.231623	+	0.133728i	0.611321	−	0.791383i	$-0.290639\pi$
$641$	148.471	+	85.7195i	0.231623	+	0.133728i	−0.379697	+	0.925111i	$0.623972\pi$
$642$		0			0
$643$	749.426			1.16551			0.582757	−	0.812646i	$-0.301974\pi$
$643$	749.426			1.16551			0.582757	+	0.812646i	$0.301974\pi$
$644$		0			0
$645$	1281.62	−	786.057i	1.98701	−	1.21869i
$646$		0			0
$647$	−589.924	−	340.593i	−0.911784	−	0.526419i	−0.0307791	−	0.999526i	$-0.509799\pi$
$647$	−589.924	−	340.593i	−0.911784	−	0.526419i	−0.881005	+	0.473108i	$0.843132\pi$
$648$		0			0
$649$	214.734	−	123.977i	0.330870	−	0.191028i
$650$		0			0
$651$	343.168	+	301.815i	0.527140	+	0.463617i
$652$		0			0
$653$	−727.697	+	420.136i	−1.11439	+	0.643394i	−0.939963	−	0.341276i	$-0.889141\pi$
$653$	−727.697	+	420.136i	−1.11439	+	0.643394i	−0.174428	+	0.984670i	$0.555808\pi$
$654$		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	−0.0531835	−	0.998585i	$-0.516937\pi$
$661$	−624.364	−	360.477i	−0.944575	−	0.545351i	−0.891392	+	0.453234i	$0.850270\pi$
$662$		0			0
$663$	647.850	+	351.431i	0.977149	+	0.530062i
$664$		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
$669$	−479.807	+	12.7490i	−0.717200	+	0.0190567i
$670$		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
$675$	−821.522	+	1727.49i	−1.21707	+	2.55924i
$676$		0			0
$677$	−5.03682	−	8.72402i	−0.00743990	−	0.0128863i	0.862281	−	0.506429i	$-0.169035\pi$
$677$	−5.03682	−	8.72402i	−0.00743990	−	0.0128863i	−0.869721	+	0.493543i	$0.835702\pi$
$678$		0			0
$679$	−433.398	−	98.8918i	−0.638289	−	0.145643i
$680$		0			0
$681$	547.372	+	296.926i	0.803776	+	0.436015i
$682$		0			0
$683$	−73.9512	+	128.087i	−0.108274	+	0.187536i	−0.915071	−	0.403292i	$-0.867866\pi$
$683$	−73.9512	+	128.087i	−0.108274	+	0.187536i	0.806797	+	0.590829i	$0.201199\pi$
$684$		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	−0.854827	−	0.518913i	$-0.826337\pi$
$691$	−605.873	−	1049.40i	−0.876805	−	1.51867i	−0.0219783	−	0.999758i	$-0.506996\pi$
$692$		0			0
$693$	−257.949	−	214.987i	−0.372220	−	0.310226i
$694$		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
$705$	309.023	+	167.632i	0.438331	+	0.237776i
$706$		0			0
$707$	−164.974	−	153.054i	−0.233344	−	0.216484i
$708$		0			0
$709$	207.128	+	358.756i	0.292141	+	0.506003i	0.974316	−	0.225186i	$-0.0722990\pi$
$709$	207.128	+	358.756i	0.292141	+	0.506003i	−0.682175	+	0.731189i	$0.738966\pi$
$710$		0			0
$711$	−37.4218	+	24.3429i	−0.0526326	+	0.0342376i
$712$		0			0
$713$	498.794			0.699571
$714$		0			0
$715$		−	822.255i		−	1.15001i
$716$		0			0
$717$	258.787	−	6.87625i	0.360931	−	0.00959031i
$718$		0			0
$719$	−68.9380	+	39.8014i	−0.0958804	+	0.0553566i	−0.547174	−	0.837019i	$-0.684296\pi$
$719$	−68.9380	+	39.8014i	−0.0958804	+	0.0553566i	0.451293	+	0.892376i	$0.350963\pi$
$720$		0			0
$721$	−1138.72	+	351.326i	−1.57936	+	0.487277i
$722$		0			0
$723$	791.556	+	429.386i	1.09482	+	0.593895i
$724$		0			0
$725$	−1507.86	−	870.566i	−2.07981	−	1.20078i
$726$		0			0
$727$	−9.43364			−0.0129761			−0.00648806	−	0.999979i	$-0.502065\pi$
$727$	−9.43364			−0.0129761			−0.00648806	+	0.999979i	$0.502065\pi$
$728$		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	−0.361893	−	0.932220i	$-0.617869\pi$
$733$	193.869	−	111.930i	0.264487	−	0.152701i	0.626379	+	0.779518i	$0.284536\pi$
$734$		0			0
$735$	−145.809	−	1431.75i	−0.198380	−	1.94796i
$736$		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	$-0.472388\pi$
$739$	−541.551	−	312.665i	−0.732816	−	0.423092i	−0.819452	+	0.573148i	$0.805722\pi$
$740$		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
$747$	26.8090	+	504.121i	0.0358888	+	0.674861i
$748$		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	$-0.889090\pi$
$751$	−836.749	+	483.097i	−1.11418	+	0.643272i	−0.174271	+	0.984698i	$0.555757\pi$
$752$		0			0
$753$	−23.7968	−	895.592i	−0.0316027	−	1.18937i
$754$		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
$759$	−366.366	+	9.73472i	−0.482696	+	0.0128257i
$760$		0			0
$761$	333.550	+	577.725i	0.438304	+	0.759165i	0.997559	−	0.0698308i	$-0.0222459\pi$
$761$	333.550	+	577.725i	0.438304	+	0.759165i	−0.559255	+	0.828996i	$0.688913\pi$
$762$		0			0
$763$	−181.170	−	168.080i	−0.237444	−	0.220288i
$764$		0			0
$765$	−1371.82	+	72.9529i	−1.79323	+	0.0953633i
$766$		0			0
$767$	366.518	−	634.829i	0.477860	−	0.827678i
$768$		0			0
$769$		−	774.930i		−	1.00771i	−0.863788	−	0.503856i	$-0.831914\pi$
$769$		−	774.930i		−	1.00771i	0.863788	−	0.503856i	$-0.168086\pi$
$770$		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	$-0.808150\pi$
$773$	61.0922	−	105.815i	0.0790326	−	0.136889i	0.902833	+	0.429992i	$0.141484\pi$
$774$		0			0
$775$	−770.901	−	1335.24i	−0.994711	−	1.72289i
$776$		0			0
$777$	−615.742	+	208.040i	−0.792460	+	0.267747i
$778$		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	$-0.686063\pi$
$787$	351.265	−	608.408i	0.446334	−	0.773073i	0.998144	+	0.0608970i	$0.0193961\pi$
$788$		0			0
$789$	319.703	−	589.360i	0.405200	−	0.746971i
$790$		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
$795$	−42.7564	−	1609.14i	−0.0537816	−	2.02407i
$796$		0			0
$797$	615.706			0.772530			0.386265	−	0.922388i	$-0.373765\pi$
$797$	615.706			0.772530			0.386265	+	0.922388i	$0.373765\pi$
$798$		0			0
$799$			186.625i			0.233573i
$800$		0			0
$801$	−40.4426	−	62.1714i	−0.0504902	−	0.0776172i
$802$		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
$807$	−18.2947	+	33.7255i	−0.0226700	+	0.0417913i
$808$		0			0
$809$	−1077.98	−	622.375i	−1.33249	−	0.769313i	−0.346809	−	0.937936i	$-0.612735\pi$
$809$	−1077.98	−	622.375i	−1.33249	−	0.769313i	−0.985681	+	0.168622i	$0.946068\pi$
$810$		0			0
$811$	−1339.58			−1.65176			−0.825881	−	0.563845i	$-0.809322\pi$
$811$	−1339.58			−1.65176			−0.825881	+	0.563845i	$0.809322\pi$
$812$		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
$819$	−978.205	−	169.132i	−1.19439	−	0.206510i
$820$		0			0
$821$	263.793	−	152.301i	0.321307	−	0.185507i	−0.330668	−	0.943747i	$-0.607274\pi$
$821$	263.793	−	152.301i	0.321307	−	0.185507i	0.651975	+	0.758241i	$0.273941\pi$
$822$		0			0
$823$	−297.149	−	171.559i	−0.361056	−	0.208456i	0.308488	−	0.951228i	$-0.400177\pi$
$823$	−297.149	−	171.559i	−0.361056	−	0.208456i	−0.669544	+	0.742773i	$0.733510\pi$
$824$		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	0.297839	−	0.954616i	$-0.403734\pi$
$829$	−314.990	−	181.859i	−0.379963	−	0.219372i	−0.677802	+	0.735244i	$0.737067\pi$
$830$		0			0
$831$	−703.388	+	1296.67i	−0.846435	+	1.56037i
$832$		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
$837$	−252.348	+	530.635i	−0.301491	+	0.633972i
$838$		0			0
$839$			1070.44i			1.27585i	0.770099	+	0.637925i	$0.220207\pi$
$839$			1070.44i			1.27585i	−0.770099	+	0.637925i	$0.779793\pi$
$840$		0			0
$841$	237.030			0.281843
$842$		0			0
$843$	6.39730	+	240.762i	0.00758873	+	0.285602i
$844$		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
$849$	−406.129	+	748.683i	−0.478361	+	0.881841i
$850$		0			0
$851$	−354.681	+	614.326i	−0.416782	+	0.721887i
$852$		0			0
$853$		−	1557.63i		−	1.82606i	−0.407891	−	0.913031i	$-0.633736\pi$
$853$		−	1557.63i		−	1.82606i	0.407891	−	0.913031i	$-0.366264\pi$
$854$		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	$-0.789387\pi$
$857$	117.943	−	204.284i	0.137624	−	0.238371i	0.926597	+	0.376057i	$0.122720\pi$
$858$		0			0
$859$	557.231	+	965.153i	0.648698	+	1.12358i	0.983434	+	0.181265i	$0.0580193\pi$
$859$	557.231	+	965.153i	0.648698	+	1.12358i	−0.334737	+	0.942312i	$0.608647\pi$
$860$		0			0
$861$	61.0471	−	304.639i	0.0709026	−	0.353820i
$862$		0			0
$863$	375.824	+	650.946i	0.435486	+	0.754283i	0.997335	−	0.0729562i	$-0.0232433\pi$
$863$	375.824	+	650.946i	0.435486	+	0.754283i	−0.561849	+	0.827239i	$0.689910\pi$
$864$		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
$873$	−30.3518	−	570.742i	−0.0347673	−	0.653771i
$874$		0			0
$875$	−698.963	+	3063.24i	−0.798815	+	3.50085i
$876$		0			0
$877$	−613.699	−	1062.96i	−0.699770	−	1.21204i	−0.968546	−	0.248835i	$-0.919952\pi$
$877$	−613.699	−	1062.96i	−0.699770	−	1.21204i	0.268776	−	0.963203i	$-0.413381\pi$
$878$		0			0
$879$	−982.182	+	26.0976i	−1.11739	+	0.0296901i
$880$		0			0
$881$	1209.71			1.37311			0.686557	−	0.727076i	$-0.259121\pi$
$881$	1209.71			1.37311			0.686557	+	0.727076i	$0.259121\pi$
$882$		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
$885$	36.2916	+	1365.83i	0.0410075	+	1.54332i
$886$		0			0
$887$	1395.29	−	805.571i	1.57304	−	0.908198i	0.577251	−	0.816567i	$-0.304125\pi$
$887$	1395.29	−	805.571i	1.57304	−	0.908198i	0.995793	−	0.0916309i	$-0.0292080\pi$
$888$		0			0
$889$	−514.209	−	117.331i	−0.578413	−	0.131981i
$890$		0			0
$891$	174.995	−	394.678i	0.196402	−	0.442961i
$892$		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
$903$	−1054.04	−	211.220i	−1.16726	−	0.233909i
$904$		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	$-0.122149\pi$
$907$	967.470	+	558.569i	1.06667	+	0.615842i	0.139400	+	0.990236i	$0.455483\pi$
$908$		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
$915$	−811.012	−	439.940i	−0.886352	−	0.480808i
$916$		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	$-0.583327\pi$
$919$	412.009	−	237.874i	0.448324	−	0.258840i	0.707122	+	0.707092i	$0.249993\pi$
$920$		0			0
$921$	613.787	−	16.3090i	0.666436	−	0.0177079i
$922$		0			0
$923$			1151.20i			1.24724i
$924$		0			0
$925$	2192.68			2.37047
$926$		0			0
$927$	−835.466	−	1284.34i	−0.901258	−	1.38548i
$928$		0			0
$929$	415.674	+	719.968i	0.447442	+	0.774992i	0.998219	−	0.0596603i	$-0.0190018\pi$
$929$	415.674	+	719.968i	0.447442	+	0.774992i	−0.550777	+	0.834653i	$0.685668\pi$
$930$		0			0
$931$	−80.5033	−	1072.44i	−0.0864697	−	1.15192i
$932$		0			0
$933$	−1191.14	−	646.142i	−1.27668	−	0.692542i
$934$		0			0
$935$	−406.789	+	704.579i	−0.435068	+	0.753561i
$936$		0			0
$937$			358.471i			0.382573i	0.981534	+	0.191286i	$0.0612660\pi$
$937$			358.471i			0.382573i	−0.981534	+	0.191286i	$0.938734\pi$
$938$		0			0
$939$	822.420	−	504.415i	0.875847	−	0.537183i
$940$		0			0
$941$	485.287	−	840.541i	0.515714	−	0.893243i	−0.484120	−	0.875002i	$-0.660860\pi$
$941$	485.287	−	840.541i	0.515714	−	0.893243i	0.999834	−	0.0182409i	$-0.00580657\pi$
$942$		0			0
$943$	−169.552	−	293.672i	−0.179800	−	0.311423i
$944$		0			0
$945$	1719.06	−	684.536i	1.81911	−	0.724377i
$946$		0			0
$947$	−884.688	−	1532.32i	−0.934200	−	1.61808i	−0.776054	−	0.630667i	$-0.782781\pi$
$947$	−884.688	−	1532.32i	−0.934200	−	1.61808i	−0.158147	−	0.987416i	$-0.550552\pi$
$948$		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
$957$	345.421	+	187.376i	0.360942	+	0.195796i
$958$		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
$963$	−991.536	−	1524.26i	−1.02963	−	1.58283i
$964$		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
$969$	−1026.22	+	27.2678i	−1.05905	+	0.0281402i
$970$		0			0
$971$	418.792	−	241.790i	0.431300	−	0.249011i	−0.268600	−	0.963252i	$-0.586561\pi$
$971$	418.792	−	241.790i	0.431300	−	0.249011i	0.699900	+	0.714241i	$0.253228\pi$
$972$		0			0
$973$	−141.458	+	619.945i	−0.145383	+	0.637148i
$974$		0			0
$975$	2943.88	+	1596.93i	3.01936	+	1.63788i
$976$		0			0
$977$	−105.815	−	61.0925i	−0.108306	−	0.0625307i	0.444868	−	0.895596i	$-0.353250\pi$
$977$	−105.815	−	61.0925i	−0.108306	−	0.0625307i	−0.553175	+	0.833065i	$0.686584\pi$
$978$		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	0.946378	−	0.323061i	$-0.104712\pi$
$983$	1120.41	+	646.870i	1.13979	+	0.658057i	0.193410	+	0.981118i	$0.438045\pi$
$984$		0			0
$985$	−1498.69	+	865.268i	−1.52151	+	0.878445i
$986$		0			0
$987$	−80.4609	−	238.143i	−0.0815207	−	0.241279i
$988$		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	$-0.410438\pi$
$991$	−411.728	−	237.711i	−0.415468	−	0.239870i	−0.693136	+	0.720807i	$0.743772\pi$
$992$		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	0.346367	−	0.938099i	$-0.387415\pi$
$997$	−291.989	−	168.580i	−0.292868	−	0.169087i	−0.639235	+	0.769012i	$0.720749\pi$
$998$		0			0
$999$	−474.103	−	688.120i	−0.474577	−	0.688809i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.z.f.47.4	✓	20	28.19	even	6	inner
336.3.z.f.47.10	yes	20	84.47	odd	6	inner
336.3.z.f.143.4	yes	20	3.2	odd	2	inner
336.3.z.f.143.10	yes	20	1.1	even	1	trivial
336.3.z.g.47.1	yes	20	21.5	even	6
336.3.z.g.47.7	yes	20	7.5	odd	6
336.3.z.g.143.1	yes	20	4.3	odd	2
336.3.z.g.143.7	yes	20	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99894 - 0.0796850i) q^{3} +(4.89508 + 8.47853i) q^{5} +(1.55722 - 6.82459i) q^{7} +(8.98730 - 0.477941i) q^{9} +O(q^{10})\)	\(q+(2.99894 - 0.0796850i) q^{3} +(4.89508 + 8.47853i) q^{5} +(1.55722 - 6.82459i) q^{7} +(8.98730 - 0.477941i) q^{9} +(2.66502 - 4.61595i) q^{11} -15.7574i q^{13} +(15.3557 + 25.0366i) q^{15} +(-7.79558 + 13.5023i) q^{17} +(10.9740 + 19.0076i) q^{19} +(4.12619 - 20.5906i) q^{21} +(-11.4600 - 19.8494i) q^{23} +(-35.4237 + 61.3556i) q^{25} +(26.9143 - 2.14947i) q^{27} +24.5758i q^{29} +(-10.8812 + 18.8467i) q^{31} +(7.62442 - 14.0553i) q^{33} +(65.4853 - 20.2040i) q^{35} +(-15.4747 - 26.8030i) q^{37} +(-1.25563 - 47.2557i) q^{39} +14.7950 q^{41} -51.1900i q^{43} +(48.0458 + 73.8596i) q^{45} +(10.3662 - 5.98495i) q^{47} +(-44.1501 - 21.2548i) q^{49} +(-22.3025 + 41.1139i) q^{51} +(-47.4641 - 27.4034i) q^{53} +52.1820 q^{55} +(34.4251 + 56.1281i) q^{57} +(40.2875 + 23.2600i) q^{59} +(-27.2055 + 15.7071i) q^{61} +(10.7334 - 62.0789i) q^{63} +(133.600 - 77.1340i) q^{65} +(-14.4100 - 8.31959i) q^{67} +(-35.9497 - 58.6140i) q^{69} -73.0574 q^{71} +(34.4201 + 19.8724i) q^{73} +(-101.344 + 186.825i) q^{75} +(-27.3520 - 25.3757i) q^{77} +(-4.29574 + 2.48015i) q^{79} +(80.5431 - 8.59080i) q^{81} +56.0926i q^{83} -152.640 q^{85} +(1.95832 + 73.7014i) q^{87} +(-4.12044 - 7.13681i) q^{89} +(-107.538 - 24.5378i) q^{91} +(-31.1301 + 57.3872i) q^{93} +(-107.438 + 186.087i) q^{95} -63.5054i q^{97} +(21.7452 - 42.7587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{3} + 16 q^{7} + 11 q^{9}+O(q^{10}) \) 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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