LMFDB - Embedded newform 216.4.n.a.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	216.37
Dual form			216.4.n.a.181.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59019 - 2.33908i) q^{2} +(-2.94259 + 7.43916i) q^{4} +(11.0897 + 6.40265i) q^{5} +(11.0213 + 19.0894i) q^{7} +(22.0801 - 4.94672i) q^{8} +O(q^{10})$	\(q+(-1.59019 - 2.33908i) q^{2} +(-2.94259 + 7.43916i) q^{4} +(11.0897 + 6.40265i) q^{5} +(11.0213 + 19.0894i) q^{7} +(22.0801 - 4.94672i) q^{8} +(-2.65844 - 36.1212i) q^{10} +(-45.1623 + 26.0744i) q^{11} +(-27.1714 - 15.6874i) q^{13} +(27.1257 - 56.1353i) q^{14} +(-46.6823 - 43.7809i) q^{16} -119.141 q^{17} +72.0120i q^{19} +(-80.2629 + 63.6578i) q^{20} +(132.807 + 64.1748i) q^{22} +(6.65920 - 11.5341i) q^{23} +(19.4879 + 33.7540i) q^{25} +(6.51355 + 88.5020i) q^{26} +(-174.440 + 25.8166i) q^{28} +(-133.796 + 77.2471i) q^{29} +(111.239 - 192.671i) q^{31} +(-28.1733 + 178.813i) q^{32} +(189.457 + 278.681i) q^{34} +282.261i q^{35} +172.235i q^{37} +(168.442 - 114.513i) q^{38} +(276.534 + 86.5134i) q^{40} +(61.0938 - 105.818i) q^{41} +(44.2394 - 25.5416i) q^{43} +(-61.0778 - 412.696i) q^{44} +(-37.5685 + 2.76496i) q^{46} +(116.835 + 202.364i) q^{47} +(-71.4361 + 123.731i) q^{49} +(47.9640 - 99.2591i) q^{50} +(196.656 - 155.971i) q^{52} +310.412i q^{53} -667.782 q^{55} +(337.780 + 366.976i) q^{56} +(393.448 + 190.122i) q^{58} +(613.956 + 354.468i) q^{59} +(-747.786 + 431.734i) q^{61} +(-627.564 + 46.1873i) q^{62} +(463.060 - 218.448i) q^{64} +(-200.882 - 347.938i) q^{65} +(4.78278 + 2.76134i) q^{67} +(350.585 - 886.313i) q^{68} +(660.231 - 448.849i) q^{70} +61.9318 q^{71} +273.216 q^{73} +(402.871 - 273.886i) q^{74} +(-535.709 - 211.902i) q^{76} +(-995.490 - 574.746i) q^{77} +(194.002 + 336.022i) q^{79} +(-237.380 - 784.408i) q^{80} +(-344.666 + 25.3667i) q^{82} +(-677.357 + 391.072i) q^{83} +(-1321.25 - 762.821i) q^{85} +(-130.093 - 62.8635i) q^{86} +(-868.204 + 799.131i) q^{88} +949.710 q^{89} -691.580i q^{91} +(66.2085 + 83.4790i) q^{92} +(287.557 - 595.085i) q^{94} +(-461.068 + 798.593i) q^{95} +(-85.8899 - 148.766i) q^{97} +(403.014 - 29.6609i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8}+O(q^{10}) $ 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8	$ 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 20 q^{10} + 10 q^{14} - q^{16} + 8 q^{17} + 52 q^{20} - 17 q^{22} - 274 q^{23} + 648 q^{25} - 368 q^{26} + 124 q^{28} - 2 q^{31} - 259 q^{32} + 189 q^{34} - 319 q^{38} + 214 q^{40} + 22 q^{41} - 282 q^{44} - 24 q^{46} + 942 q^{47} - 1080 q^{49} - 53 q^{50} - 588 q^{52} - 508 q^{55} + 502 q^{56} + 280 q^{58} - 1744 q^{62} + 410 q^{64} + 502 q^{65} - 1149 q^{68} - 586 q^{70} + 3984 q^{71} - 8 q^{73} - 1778 q^{74} + 621 q^{76} - 2 q^{79} - 4704 q^{80} + 714 q^{82} + 2923 q^{86} - 533 q^{88} + 856 q^{89} - 3342 q^{92} + 1518 q^{94} + 2792 q^{95} - 2 q^{97} + 6414 q^{98}+O(q^{100}) $ 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 20 * q^10 + 10 * q^14 - q^16 + 8 * q^17 + 52 * q^20 - 17 * q^22 - 274 * q^23 + 648 * q^25 - 368 * q^26 + 124 * q^28 - 2 * q^31 - 259 * q^32 + 189 * q^34 - 319 * q^38 + 214 * q^40 + 22 * q^41 - 282 * q^44 - 24 * q^46 + 942 * q^47 - 1080 * q^49 - 53 * q^50 - 588 * q^52 - 508 * q^55 + 502 * q^56 + 280 * q^58 - 1744 * q^62 + 410 * q^64 + 502 * q^65 - 1149 * q^68 - 586 * q^70 + 3984 * q^71 - 8 * q^73 - 1778 * q^74 + 621 * q^76 - 2 * q^79 - 4704 * q^80 + 714 * q^82 + 2923 * q^86 - 533 * q^88 + 856 * q^89 - 3342 * q^92 + 1518 * q^94 + 2792 * q^95 - 2 * q^97 + 6414 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.59019	−	2.33908i	−0.562217	−	0.826990i
$2$	−1.59019	−	2.33908i	−0.562217	−	0.826990i
$3$		0			0
$3$		0			0
$4$	−2.94259	+	7.43916i	−0.367824	+	0.929895i
$5$	11.0897	+	6.40265i	0.991895	+	0.572671i	0.905840	−	0.423620i	$-0.139241\pi$
$5$	11.0897	+	6.40265i	0.991895	+	0.572671i	0.0860545	+	0.996290i	$0.472574\pi$
$6$		0			0
$7$	11.0213	+	19.0894i	0.595092	+	1.03073i	0.993534	+	0.113536i	$0.0362177\pi$
$7$	11.0213	+	19.0894i	0.595092	+	1.03073i	−0.398442	+	0.917194i	$0.630449\pi$
$8$	22.0801	−	4.94672i	0.975811	−	0.218616i
$9$		0			0
$10$	−2.65844	−	36.1212i	−0.0840672	−	1.14225i
$11$	−45.1623	+	26.0744i	−1.23790	+	0.714704i	−0.968665	−	0.248370i	$-0.920105\pi$
$11$	−45.1623	+	26.0744i	−1.23790	+	0.714704i	−0.269238	+	0.963074i	$0.586772\pi$
$12$		0			0
$13$	−27.1714	−	15.6874i	−0.579692	−	0.334685i	0.181319	−	0.983424i	$-0.441963\pi$
$13$	−27.1714	−	15.6874i	−0.579692	−	0.334685i	−0.761011	+	0.648739i	$0.775297\pi$
$14$	27.1257	−	56.1353i	0.517832	−	1.07163i
$15$		0			0
$16$	−46.6823	−	43.7809i	−0.729411	−	0.684076i
$17$	−119.141			−1.69977			−0.849884	−	0.526970i	$-0.823328\pi$
$17$	−119.141			−1.69977			−0.849884	+	0.526970i	$0.823328\pi$
$18$		0			0
$19$			72.0120i			0.869510i	0.900549	+	0.434755i	$0.143165\pi$
$19$			72.0120i			0.869510i	−0.900549	+	0.434755i	$0.856835\pi$
$20$	−80.2629	+	63.6578i	−0.897367	+	0.711716i
$21$		0			0
$22$	132.807	+	64.1748i	1.28702	+	0.621915i
$23$	6.65920	−	11.5341i	0.0603713	−	0.104566i	−0.834260	−	0.551371i	$-0.814105\pi$
$23$	6.65920	−	11.5341i	0.0603713	−	0.104566i	0.894631	+	0.446805i	$0.147438\pi$
$24$		0			0
$25$	19.4879	+	33.7540i	0.155903	+	0.270032i
$26$	6.51355	+	88.5020i	0.0491313	+	0.667565i
$27$		0			0
$28$	−174.440	+	25.8166i	−1.17736	+	0.174246i
$29$	−133.796	+	77.2471i	−0.856733	+	0.494635i	−0.862917	−	0.505346i	$-0.831365\pi$
$29$	−133.796	+	77.2471i	−0.856733	+	0.494635i	0.00618373	+	0.999981i	$0.498032\pi$
$30$		0			0
$31$	111.239	−	192.671i	0.644486	−	1.11628i	−0.339934	−	0.940449i	$-0.610405\pi$
$31$	111.239	−	192.671i	0.644486	−	1.11628i	0.984420	−	0.175833i	$-0.0562618\pi$
$32$	−28.1733	+	178.813i	−0.155637	+	0.987814i
$33$		0			0
$34$	189.457	+	278.681i	0.955638	+	1.40569i
$35$			282.261i			1.36317i
$36$		0			0
$37$			172.235i			0.765276i	0.923898	+	0.382638i	$0.124984\pi$
$37$			172.235i			0.765276i	−0.923898	+	0.382638i	$0.875016\pi$
$38$	168.442	−	114.513i	0.719076	−	0.488853i
$39$		0			0
$40$	276.534	+	86.5134i	1.09310	+	0.341974i
$41$	61.0938	−	105.818i	0.232713	−	0.403071i	−0.725892	−	0.687808i	$-0.758573\pi$
$41$	61.0938	−	105.818i	0.232713	−	0.403071i	0.958606	+	0.284737i	$0.0919063\pi$
$42$		0			0
$43$	44.2394	−	25.5416i	0.156894	−	0.0905829i	−0.419497	−	0.907757i	$-0.637794\pi$
$43$	44.2394	−	25.5416i	0.156894	−	0.0905829i	0.576392	+	0.817174i	$0.304460\pi$
$44$	−61.0778	−	412.696i	−0.209269	−	1.41401i
$45$		0			0
$46$	−37.5685	+	2.76496i	−0.120417	+	0.00886241i
$47$	116.835	+	202.364i	0.362599	+	0.628040i	0.988388	−	0.151952i	$-0.0485561\pi$
$47$	116.835	+	202.364i	0.362599	+	0.628040i	−0.625789	+	0.779993i	$0.715223\pi$
$48$		0			0
$49$	−71.4361	+	123.731i	−0.208269	+	0.360732i
$50$	47.9640	−	99.2591i	0.135663	−	0.280747i
$51$		0			0
$52$	196.656	−	155.971i	0.524447	−	0.415947i
$53$			310.412i			0.804498i	0.915530	+	0.402249i	$0.131771\pi$
$53$			310.412i			0.804498i	−0.915530	+	0.402249i	$0.868229\pi$
$54$		0			0
$55$	−667.782			−1.63716
$56$	337.780	+	366.976i	0.806031	+	0.875700i
$57$		0			0
$58$	393.448	+	190.122i	0.890728	+	0.430417i
$59$	613.956	+	354.468i	1.35475	+	0.782166i	0.988911	−	0.148512i	$-0.0474484\pi$
$59$	613.956	+	354.468i	1.35475	+	0.782166i	0.365840	+	0.930678i	$0.380782\pi$
$60$		0			0
$61$	−747.786	+	431.734i	−1.56958	+	0.906195i	−0.573358	+	0.819305i	$0.694360\pi$
$61$	−747.786	+	431.734i	−1.56958	+	0.906195i	−0.996218	+	0.0868901i	$0.972307\pi$
$62$	−627.564	+	46.1873i	−1.28549	+	0.0946095i
$63$		0			0
$64$	463.060	−	218.448i	0.904414	−	0.426656i
$65$	−200.882	−	347.938i	−0.383329	−	0.663945i
$66$		0			0
$67$	4.78278	+	2.76134i	0.00872105	+	0.00503510i	0.504354	−	0.863497i	$-0.331731\pi$
$67$	4.78278	+	2.76134i	0.00872105	+	0.00503510i	−0.495633	+	0.868532i	$0.665064\pi$
$68$	350.585	−	886.313i	0.625216	−	1.58061i
$69$		0			0
$70$	660.231	−	448.849i	1.12732	−	0.766395i
$71$	61.9318			0.103520			0.0517602	−	0.998660i	$-0.483517\pi$
$71$	61.9318			0.103520			0.0517602	+	0.998660i	$0.483517\pi$
$72$		0			0
$73$	273.216			0.438047			0.219024	−	0.975720i	$-0.429713\pi$
$73$	273.216			0.438047			0.219024	+	0.975720i	$0.429713\pi$
$74$	402.871	−	273.886i	0.632876	−	0.430251i
$75$		0			0
$76$	−535.709	−	211.902i	−0.808553	−	0.319827i
$77$	−995.490	−	574.746i	−1.47333	−	0.850629i
$78$		0			0
$79$	194.002	+	336.022i	0.276291	+	0.478549i	0.970460	−	0.241262i	$-0.0775614\pi$
$79$	194.002	+	336.022i	0.276291	+	0.478549i	−0.694169	+	0.719812i	$0.744228\pi$
$80$	−237.380	−	784.408i	−0.331748	−	1.09624i
$81$		0			0
$82$	−344.666	+	25.3667i	−0.464171	+	0.0341620i
$83$	−677.357	+	391.072i	−0.895778	+	0.517178i	−0.875828	−	0.482623i	$-0.839684\pi$
$83$	−677.357	+	391.072i	−0.895778	+	0.517178i	−0.0199499	+	0.999801i	$0.506351\pi$
$84$		0			0
$85$	−1321.25	−	762.821i	−1.68599	−	0.973407i
$86$	−130.093	−	62.8635i	−0.163120	−	0.0788226i
$87$		0			0
$88$	−868.204	+	799.131i	−1.05171	+	0.968041i
$89$	949.710			1.13111			0.565557	−	0.824710i	$-0.308661\pi$
$89$	949.710			1.13111			0.565557	+	0.824710i	$0.308661\pi$
$90$		0			0
$91$		−	691.580i		−	0.796673i
$92$	66.2085	+	83.4790i	0.0750295	+	0.0946009i
$93$		0			0
$94$	287.557	−	595.085i	0.315523	−	0.652961i
$95$	−461.068	+	798.593i	−0.497943	+	0.862462i
$96$		0			0
$97$	−85.8899	−	148.766i	−0.0899051	−	0.155720i	0.817566	−	0.575835i	$-0.195323\pi$
$97$	−85.8899	−	148.766i	−0.0899051	−	0.155720i	−0.907471	+	0.420115i	$0.861990\pi$
$98$	403.014	−	29.6609i	0.415414	−	0.0305735i
$99$		0			0
$100$	−308.447	+	45.6493i	−0.308447	+	0.0456493i
$101$	621.680	−	358.927i	0.612470	−	0.353610i	−0.161462	−	0.986879i	$-0.551621\pi$
$101$	621.680	−	358.927i	0.612470	−	0.353610i	0.773931	+	0.633269i	$0.218287\pi$
$102$		0			0
$103$	411.395	−	712.557i	0.393553	−	0.681654i	−0.599362	−	0.800478i	$-0.704579\pi$
$103$	411.395	−	712.557i	0.393553	−	0.681654i	0.992915	+	0.118824i	$0.0379124\pi$
$104$	−677.548	−	211.970i	−0.638837	−	0.199860i
$105$		0			0
$106$	726.079	−	493.614i	0.665312	−	0.452302i
$107$			117.180i			0.105871i	0.998598	+	0.0529354i	$0.0168578\pi$
$107$			117.180i			0.105871i	−0.998598	+	0.0529354i	$0.983142\pi$
$108$		0			0
$109$		−	463.675i		−	0.407450i	−0.979028	−	0.203725i	$-0.934695\pi$
$109$		−	463.675i		−	0.407450i	0.979028	−	0.203725i	$-0.0653048\pi$
$110$	1061.90	+	1562.00i	0.920439	+	1.35391i
$111$		0			0
$112$	321.252	−	1373.66i	0.271031	−	1.15891i
$113$	−577.706	+	1000.62i	−0.480938	+	0.833010i	−0.999761	−	0.0218723i	$-0.993037\pi$
$113$	−577.706	+	1000.62i	−0.480938	+	0.833010i	0.518822	+	0.854882i	$0.326371\pi$
$114$		0			0
$115$	147.697	−	85.2731i	0.119764	−	0.0691457i
$116$	−180.947	−	1222.64i	−0.144832	−	0.978611i
$117$		0			0
$118$	−147.178	−	1999.76i	−0.114821	−	1.56011i
$119$	−1313.09	−	2274.34i	−1.01152	−	1.75200i
$120$		0			0
$121$	694.253	−	1202.48i	0.521603	−	0.903442i
$122$	2198.98	+	1062.59i	1.63186	+	0.788545i
$123$		0			0
$124$	1105.98	+	1394.48i	0.800968	+	1.00990i
$125$		−	1101.57i		−	0.788216i
$126$		0			0
$127$	463.231			0.323662			0.161831	−	0.986818i	$-0.448260\pi$
$127$	463.231			0.323662			0.161831	+	0.986818i	$0.448260\pi$
$128$	−1247.32	−	735.761i	−0.861317	−	0.508068i
$129$		0			0
$130$	−494.414	+	1023.17i	−0.333562	+	0.690290i
$131$	1835.89	+	1059.95i	1.22445	+	0.706935i	0.965863	−	0.259054i	$-0.0834108\pi$
$131$	1835.89	+	1059.95i	1.22445	+	0.706935i	0.258584	+	0.965989i	$0.416744\pi$
$132$		0			0
$133$	−1374.66	+	793.663i	−0.896229	+	0.517438i
$134$	−1.14653	−	15.5784i	−0.000739145	−	0.0100430i
$135$		0			0
$136$	−2630.65	+	589.359i	−1.65865	+	0.371596i
$137$	115.052	+	199.275i	0.0717484	+	0.124272i	0.899668	−	0.436575i	$-0.143809\pi$
$137$	115.052	+	199.275i	0.0717484	+	0.124272i	−0.827919	+	0.560847i	$0.810475\pi$
$138$		0			0
$139$	2365.28	+	1365.59i	1.44331	+	0.833296i	0.998069	−	0.0621137i	$-0.0197841\pi$
$139$	2365.28	+	1365.59i	1.44331	+	0.833296i	0.445243	+	0.895410i	$0.353117\pi$
$140$	−2099.79	−	830.580i	−1.26760	−	0.501406i
$141$		0			0
$142$	−98.4832	−	144.863i	−0.0582009	−	0.0856103i
$143$	1636.16			0.956803
$144$		0			0
$145$	−1978.34			−1.13305
$146$	−434.465	−	639.073i	−0.246278	−	0.362261i
$147$		0			0
$148$	−1281.28	−	506.817i	−0.711627	−	0.281487i
$149$	−2162.36	−	1248.44i	−1.18891	−	0.686416i	−0.230849	−	0.972990i	$-0.574150\pi$
$149$	−2162.36	−	1248.44i	−1.18891	−	0.686416i	−0.958058	+	0.286574i	$0.907484\pi$
$150$		0			0
$151$	1722.41	+	2983.29i	0.928260	+	1.60779i	0.786232	+	0.617932i	$0.212029\pi$
$151$	1722.41	+	2983.29i	0.928260	+	1.60779i	0.142029	+	0.989863i	$0.454637\pi$
$152$	356.223	+	1590.03i	0.190089	+	0.848477i
$153$		0			0
$154$	238.640	+	3242.49i	0.124871	+	1.69667i
$155$	2467.21	−	1424.45i	1.27852	−	0.738156i
$156$		0			0
$157$	1794.05	+	1035.79i	0.911978	+	0.526531i	0.881067	−	0.472992i	$-0.156826\pi$
$157$	1794.05	+	1035.79i	0.911978	+	0.526531i	0.0309108	+	0.999522i	$0.490159\pi$
$158$	477.482	−	988.125i	0.240420	−	0.497538i
$159$		0			0
$160$	−1457.31	+	1802.61i	−0.720068	+	0.890679i
$161$	293.571			0.143706
$162$		0			0
$163$		−	431.131i		−	0.207171i	−0.994621	−	0.103585i	$-0.966969\pi$
$163$		−	431.131i		−	0.207171i	0.994621	−	0.103585i	$-0.0330315\pi$
$164$	607.420	+	765.865i	0.289216	+	0.364658i
$165$		0			0
$166$	1991.87	+	962.513i	0.931322	+	0.450033i
$167$	−174.716	+	302.618i	−0.0809579	+	0.140223i	−0.903662	−	0.428247i	$-0.859131\pi$
$167$	−174.716	+	302.618i	−0.0809579	+	0.140223i	0.822704	+	0.568470i	$0.192465\pi$
$168$		0			0
$169$	−606.310	−	1050.16i	−0.275972	−	0.477997i
$170$	316.730	+	4303.53i	0.142895	+	1.94156i
$171$		0			0
$172$	59.8298	+	404.263i	0.0265231	+	0.179214i
$173$	−738.539	+	426.396i	−0.324567	+	0.187389i	−0.653426	−	0.756990i	$-0.726669\pi$
$173$	−738.539	+	426.396i	−0.324567	+	0.187389i	0.328859	+	0.944379i	$0.393336\pi$
$174$		0			0
$175$	−429.562	+	744.024i	−0.185554	+	0.321388i
$176$	3249.84	+	760.029i	1.39185	+	0.325507i
$177$		0			0
$178$	−1510.22	−	2221.45i	−0.635931	−	0.935419i
$179$			2609.48i			1.08962i	0.838560	+	0.544809i	$0.183398\pi$
$179$			2609.48i			1.08962i	−0.838560	+	0.544809i	$0.816602\pi$
$180$		0			0
$181$			1163.96i			0.477992i	0.971021	+	0.238996i	$0.0768182\pi$
$181$			1163.96i			0.477992i	−0.971021	+	0.238996i	$0.923182\pi$
$182$	−1617.66	+	1099.74i	−0.658841	+	0.447903i
$183$		0			0
$184$	89.9799	−	287.614i	0.0360511	−	0.115235i
$185$	−1102.76	+	1910.04i	−0.438251	+	0.759074i
$186$		0			0
$187$	5380.70	−	3106.55i	2.10415	−	1.21483i
$188$	−1849.22	+	273.679i	−0.717385	+	0.106171i
$189$		0			0
$190$	2601.16	−	191.439i	0.993199	−	0.0730972i
$191$	509.268	+	882.078i	0.192928	+	0.334162i	0.946219	−	0.323526i	$-0.104868\pi$
$191$	509.268	+	882.078i	0.192928	+	0.334162i	−0.753291	+	0.657687i	$0.771535\pi$
$192$		0			0
$193$	−1705.67	+	2954.30i	−0.636149	+	1.10184i	0.350122	+	0.936704i	$0.386140\pi$
$193$	−1705.67	+	2954.30i	−0.636149	+	1.10184i	−0.986271	+	0.165138i	$0.947193\pi$
$194$	−211.394	+	437.469i	−0.0782329	+	0.161899i
$195$		0			0
$196$	−710.248	−	895.515i	−0.258837	−	0.326354i
$197$		−	2988.80i		−	1.08093i	−0.841367	−	0.540464i	$-0.818249\pi$
$197$		−	2988.80i		−	1.08093i	0.841367	−	0.540464i	$-0.181751\pi$
$198$		0			0
$199$	−1274.96			−0.454170			−0.227085	−	0.973875i	$-0.572920\pi$
$199$	−1274.96			−0.454170			−0.227085	+	0.973875i	$0.572920\pi$
$200$	597.266	+	648.891i	0.211165	+	0.229418i
$201$		0			0
$202$	−1828.15	−	883.397i	−0.636772	−	0.307701i
$203$	−2949.20	−	1702.72i	−1.01967	−	0.588707i
$204$		0			0
$205$	1355.03	−	782.324i	0.461654	−	0.266536i
$206$	−2320.92	+	170.815i	−0.784983	+	0.0577730i
$207$		0			0
$208$	581.614	+	1921.91i	0.193883	+	0.640676i
$209$	−1877.67	−	3252.22i	−0.621442	−	1.07637i
$210$		0			0
$211$	902.267	+	520.924i	0.294382	+	0.169961i	0.639916	−	0.768445i	$-0.278969\pi$
$211$	902.267	+	520.924i	0.294382	+	0.169961i	−0.345534	+	0.938406i	$0.612302\pi$
$212$	−2309.21	−	913.417i	−0.748099	−	0.295914i
$213$		0			0
$214$	274.093	−	186.338i	0.0875541	−	0.0595224i
$215$	654.137			0.207497
$216$		0			0
$217$	4903.96			1.53411
$218$	−1084.57	+	737.331i	−0.336957	+	0.229075i
$219$		0			0
$220$	1965.01	−	4967.74i	0.602187	−	1.52239i
$221$	3237.24	+	1869.02i	0.985341	+	0.568887i
$222$		0			0
$223$	−3124.81	−	5412.33i	−0.938353	−	1.62528i	−0.768542	−	0.639799i	$-0.779017\pi$
$223$	−3124.81	−	5412.33i	−0.938353	−	1.62528i	−0.169811	−	0.985477i	$-0.554316\pi$
$224$	−3723.94	+	1432.94i	−1.11079	+	0.427421i
$225$		0			0
$226$	3259.19	−	239.869i	0.959282	−	0.0706010i
$227$	1309.43	−	755.998i	0.382862	−	0.221046i	−0.296201	−	0.955126i	$-0.595720\pi$
$227$	1309.43	−	755.998i	0.382862	−	0.221046i	0.679063	+	0.734080i	$0.262386\pi$
$228$		0			0
$229$	−2425.02	−	1400.09i	−0.699781	−	0.404019i	0.107485	−	0.994207i	$-0.465720\pi$
$229$	−2425.02	−	1400.09i	−0.699781	−	0.404019i	−0.807266	+	0.590188i	$0.799054\pi$
$230$	−434.327	−	209.876i	−0.124516	−	0.0601686i
$231$		0			0
$232$	−2572.10	+	2367.47i	−0.727875	+	0.669966i
$233$	6398.07			1.79893			0.899467	−	0.436989i	$-0.143955\pi$
$233$	6398.07			1.79893			0.899467	+	0.436989i	$0.143955\pi$
$234$		0			0
$235$			2992.22i			0.830600i
$236$	−4443.57	+	3524.27i	−1.22564	+	0.972077i
$237$		0			0
$238$	−3231.79	+	6688.04i	−0.880194	+	1.82152i
$239$	−1486.27	+	2574.30i	−0.402255	+	0.696726i	−0.993998	−	0.109401i	$-0.965107\pi$
$239$	−1486.27	+	2574.30i	−0.402255	+	0.696726i	0.591743	+	0.806127i	$0.298440\pi$
$240$		0			0
$241$	85.1832	+	147.542i	0.0227682	+	0.0394356i	0.877185	−	0.480153i	$-0.159419\pi$
$241$	85.1832	+	147.542i	0.0227682	+	0.0394356i	−0.854417	+	0.519588i	$0.826085\pi$
$242$	−3916.70	+	288.260i	−1.04039	+	0.0765705i
$243$		0			0
$244$	−1011.31	−	6833.32i	−0.265338	−	1.79286i
$245$	−1584.41	+	914.761i	−0.413161	+	0.238539i
$246$		0			0
$247$	1129.68	−	1956.67i	0.291012	−	0.504047i
$248$	1503.07	−	4804.46i	0.384859	−	1.23018i
$249$		0			0
$250$	−2576.65	+	1751.70i	−0.651847	+	0.443149i
$251$			1.37424i			0.000345582i	1.00000		0.000172791i	$5.50011e-5\pi$
$251$			1.37424i			0.000345582i	−1.00000		0.000172791i	$0.999945\pi$
$252$		0			0
$253$			694.540i			0.172590i
$254$	−736.624	−	1083.53i	−0.181968	−	0.267665i
$255$		0			0
$256$	262.471	+	4087.58i	0.0640798	+	0.997945i
$257$	1552.91	−	2689.71i	0.376917	−	0.652839i	−0.613695	−	0.789543i	$-0.710318\pi$
$257$	1552.91	−	2689.71i	0.376917	−	0.652839i	0.990612	+	0.136704i	$0.0436510\pi$
$258$		0			0
$259$	−3287.85	+	1898.24i	−0.788793	+	0.455410i
$260$	3179.48	−	470.554i	0.758397	−	0.112241i
$261$		0			0
$262$	−440.101	−	5979.82i	−0.103777	−	1.41006i
$263$	−17.2346	−	29.8512i	−0.00404080	−	0.00699887i	0.863998	−	0.503495i	$-0.167953\pi$
$263$	−17.2346	−	29.8512i	−0.00404080	−	0.00699887i	−0.868039	+	0.496496i	$0.834620\pi$
$264$		0			0
$265$	−1987.46	+	3442.38i	−0.460712	+	0.797977i
$266$	4042.42	+	1953.38i	0.931791	+	0.450260i
$267$		0			0
$268$	−34.6159	+	27.4544i	−0.00788993	+	0.00625763i
$269$		−	2451.69i		−	0.555695i	−0.960625	−	0.277848i	$-0.910379\pi$
$269$		−	2451.69i		−	0.555695i	0.960625	−	0.277848i	$-0.0896210\pi$
$270$		0			0
$271$	−6038.45			−1.35354			−0.676771	−	0.736194i	$-0.736621\pi$
$271$	−6038.45			−1.35354			−0.676771	+	0.736194i	$0.736621\pi$
$272$	5561.79	+	5216.12i	1.23983	+	1.16277i
$273$		0			0
$274$	283.167	−	586.000i	0.0624334	−	0.129203i
$275$	−1760.24	−	1016.27i	−0.385986	−	0.222849i
$276$		0			0
$277$	6469.90	−	3735.40i	1.40339	−	0.810247i	0.408650	−	0.912691i	$-0.366000\pi$
$277$	6469.90	−	3735.40i	1.40339	−	0.810247i	0.994739	+	0.102445i	$0.0326665\pi$
$278$	−567.007	−	7704.13i	−0.122327	−	1.66210i
$279$		0			0
$280$	1396.27	+	6232.35i	0.298010	+	1.33019i
$281$	−1864.69	−	3229.74i	−0.395866	−	0.685660i	0.597345	−	0.801984i	$-0.296222\pi$
$281$	−1864.69	−	3229.74i	−0.395866	−	0.685660i	−0.993211	+	0.116324i	$0.962889\pi$
$282$		0			0
$283$	−4950.23	−	2858.01i	−1.03979	−	0.600323i	−0.120016	−	0.992772i	$-0.538295\pi$
$283$	−4950.23	−	2858.01i	−1.03979	−	0.600323i	−0.919774	+	0.392449i	$0.871628\pi$
$284$	−182.240	+	460.720i	−0.0380773	+	0.0962631i
$285$		0			0
$286$	−2601.81	−	3827.12i	−0.537931	−	0.791266i
$287$	2693.32			0.553943
$288$		0			0
$289$	9281.68			1.88921
$290$	3145.94	+	4627.51i	0.637021	+	0.937023i
$291$		0			0
$292$	−803.963	+	2032.50i	−0.161124	+	0.407338i
$293$	1089.44	+	628.987i	0.217220	+	0.125412i	0.604663	−	0.796482i	$-0.293308\pi$
$293$	1089.44	+	628.987i	0.217220	+	0.125412i	−0.387442	+	0.921894i	$0.626641\pi$
$294$		0			0
$295$	4539.07	+	7861.90i	0.895847	+	1.55165i
$296$	851.997	+	3802.96i	0.167302	+	0.746765i
$297$		0			0
$298$	518.362	+	7043.18i	0.100765	+	1.36913i
$299$	−361.880	+	208.931i	−0.0699934	+	0.0404107i
$300$		0			0
$301$	975.148	+	563.002i	0.186733	+	0.107810i
$302$	4239.21	−	8772.85i	0.807746	−	1.67159i
$303$		0			0
$304$	3152.75	−	3361.68i	0.594811	−	0.634230i
$305$	−11057.0			−2.07581
$306$		0			0
$307$		−	5465.07i		−	1.01599i	−0.861361	−	0.507994i	$-0.830387\pi$
$307$		−	5465.07i		−	1.01599i	0.861361	−	0.507994i	$-0.169613\pi$
$308$	7204.95	−	5714.36i	1.33292	−	1.05716i
$309$		0			0
$310$	−7255.23	−	3505.87i	−1.32926	−	0.642322i
$311$	−999.244	+	1730.74i	−0.182193	+	0.315567i	−0.942627	−	0.333848i	$-0.891653\pi$
$311$	−999.244	+	1730.74i	−0.182193	+	0.315567i	0.760434	+	0.649415i	$0.224986\pi$
$312$		0			0
$313$	−4049.59	−	7014.09i	−0.731298	−	1.26665i	−0.956329	−	0.292294i	$-0.905582\pi$
$313$	−4049.59	−	7014.09i	−0.731298	−	1.26665i	0.225031	−	0.974352i	$-0.427752\pi$
$314$	−430.071	−	5843.53i	−0.0772939	−	1.05022i
$315$		0			0
$316$	−3070.59	+	454.439i	−0.546627	+	0.0808993i
$317$	5897.37	−	3404.85i	1.04489	−	0.603266i	0.123674	−	0.992323i	$-0.460532\pi$
$317$	5897.37	−	3404.85i	1.04489	−	0.603266i	0.921214	+	0.389057i	$0.127199\pi$
$318$		0			0
$319$	4028.35	−	6977.30i	0.707035	−	1.22462i
$320$	6533.85	+	542.288i	1.14142	+	0.0947338i
$321$		0			0
$322$	−466.833	−	686.686i	−0.0807938	−	0.118843i
$323$		−	8579.61i		−	1.47796i
$324$		0			0
$325$		−	1222.86i		−	0.208714i
$326$	−1008.45	+	685.580i	−0.171328	+	0.116475i
$327$		0			0
$328$	825.506	−	2638.67i	0.138966	−	0.444196i
$329$	−2575.34	+	4460.62i	−0.431560	+	0.747483i
$330$		0			0
$331$	−9099.01	+	5253.31i	−1.51096	+	0.872351i	−0.511038	+	0.859558i	$0.670739\pi$
$331$	−9099.01	+	5253.31i	−1.51096	+	0.872351i	−0.999918	+	0.0127931i	$0.995928\pi$
$332$	−916.063	−	6189.73i	−0.151432	−	1.02321i
$333$		0			0
$334$	985.680	−	72.5438i	0.161479	−	0.0118845i
$335$	35.3598	+	61.2450i	0.00576691	+	0.00998857i
$336$		0			0
$337$	−4385.48	+	7595.88i	−0.708880	+	1.22782i	0.256393	+	0.966572i	$0.417466\pi$
$337$	−4385.48	+	7595.88i	−0.708880	+	1.22782i	−0.965273	+	0.261243i	$0.915868\pi$
$338$	−1492.26	+	3088.16i	−0.240143	+	0.496964i
$339$		0			0
$340$	9562.64	−	7584.28i	1.52531	−	1.20975i
$341$			11601.9i			1.84247i
$342$		0			0
$343$	4411.32			0.694428
$344$	850.463	−	782.801i	0.133296	−	0.122691i
$345$		0			0
$346$	2171.79	+	1049.45i	0.337446	+	0.163060i
$347$	421.359	+	243.272i	0.0651865	+	0.0376355i	0.532239	−	0.846594i	$-0.321351\pi$
$347$	421.359	+	243.272i	0.0651865	+	0.0376355i	−0.467052	+	0.884230i	$0.654684\pi$
$348$		0			0
$349$	−8884.95	+	5129.73i	−1.36275	+	0.786785i	−0.989989	−	0.141142i	$-0.954923\pi$
$349$	−8884.95	+	5129.73i	−1.36275	+	0.786785i	−0.372762	+	0.927927i	$0.621589\pi$
$350$	2423.42	−	178.358i	0.370106	−	0.0272390i
$351$		0			0
$352$	−3390.09	−	8810.22i	−0.513331	−	1.33405i
$353$	5950.60	+	10306.7i	0.897220	+	1.55403i	0.831033	+	0.556223i	$0.187750\pi$
$353$	5950.60	+	10306.7i	0.897220	+	1.55403i	0.0661869	+	0.997807i	$0.478917\pi$
$354$		0			0
$355$	686.806	+	396.528i	0.102681	+	0.0592831i
$356$	−2794.61	+	7065.05i	−0.416051	+	1.05182i
$357$		0			0
$358$	6103.78	−	4149.57i	0.901103	−	0.612602i
$359$	−3155.03			−0.463833			−0.231916	−	0.972736i	$-0.574500\pi$
$359$	−3155.03			−0.463833			−0.231916	+	0.972736i	$0.574500\pi$
$360$		0			0
$361$	1673.27			0.243953
$362$	2722.60	−	1850.92i	0.395294	−	0.268735i
$363$		0			0
$364$	5144.78	+	2035.04i	0.740823	+	0.293036i
$365$	3029.88	+	1749.30i	0.434497	+	0.250857i
$366$		0			0
$367$	1543.73	+	2673.82i	0.219570	+	0.380306i	0.954677	−	0.297645i	$-0.0962013\pi$
$367$	1543.73	+	2673.82i	0.219570	+	0.380306i	−0.735107	+	0.677952i	$0.762868\pi$
$368$	−815.838	+	246.891i	−0.115567	+	0.0349731i
$369$		0			0
$370$	6221.32	−	457.875i	0.874138	−	0.0643346i
$371$	−5925.57	+	3421.13i	−0.829220	+	0.478750i
$372$		0			0
$373$	1115.37	+	643.956i	0.154830	+	0.0893909i	0.575413	−	0.817863i	$-0.304841\pi$
$373$	1115.37	+	643.956i	0.154830	+	0.0893909i	−0.420584	+	0.907254i	$0.638175\pi$
$374$	−15822.8	−	7645.88i	−2.18764	−	1.05711i
$375$		0			0
$376$	3580.77	+	3890.27i	0.491128	+	0.533579i
$377$	4847.23			0.662188
$378$		0			0
$379$			3010.49i			0.408018i	0.978969	+	0.204009i	$0.0653971\pi$
$379$			3010.49i			0.408018i	−0.978969	+	0.204009i	$0.934603\pi$
$380$	−4584.13	−	5779.89i	−0.618844	−	0.780269i
$381$		0			0
$382$	1253.42	−	2593.89i	0.167881	−	0.347421i
$383$	4585.16	−	7941.74i	0.611726	−	1.05954i	−0.379224	−	0.925305i	$-0.623809\pi$
$383$	4585.16	−	7941.74i	0.611726	−	1.05954i	0.990950	−	0.134235i	$-0.0428577\pi$
$384$		0			0
$385$	−7359.80	−	12747.5i	−0.974260	−	1.68747i
$386$	9622.69	−	708.208i	1.26887	−	0.0933856i
$387$		0			0
$388$	1359.43	−	201.192i	0.177873	−	0.0263247i
$389$	−8274.43	+	4777.24i	−1.07848	+	0.622663i	−0.930487	−	0.366325i	$-0.880616\pi$
$389$	−8274.43	+	4777.24i	−1.07848	+	0.622663i	−0.147996	+	0.988988i	$0.547282\pi$
$390$		0			0
$391$	−793.387	+	1374.19i	−0.102617	+	0.177738i
$392$	−965.254	+	3085.36i	−0.124369	+	0.397537i
$393$		0			0
$394$	−6991.03	+	4752.75i	−0.893917	+	0.607716i
$395$			4968.52i			0.632894i
$396$		0			0
$397$		−	3277.01i		−	0.414278i	−0.978312	−	0.207139i	$-0.933585\pi$
$397$		−	3277.01i		−	0.414278i	0.978312	−	0.207139i	$-0.0664152\pi$
$398$	2027.43	+	2982.24i	0.255342	+	0.375594i
$399$		0			0
$400$	568.042	−	2428.91i	0.0710052	−	0.303614i
$401$	1858.40	−	3218.85i	0.231432	−	0.400852i	−0.726798	−	0.686851i	$-0.758992\pi$
$401$	1858.40	−	3218.85i	0.231432	−	0.400852i	0.958230	+	0.286000i	$0.0923256\pi$
$402$		0			0
$403$	−6045.02	+	3490.09i	−0.747206	+	0.431400i
$404$	840.765	+	5680.95i	0.103539	+	0.699599i
$405$		0			0
$406$	706.984	+	9606.05i	0.0864213	+	1.17424i
$407$	−4490.93	−	7778.51i	−0.546946	−	0.947338i
$408$		0			0
$409$	−912.006	+	1579.64i	−0.110259	+	0.190974i	−0.915875	−	0.401465i	$-0.868501\pi$
$409$	−912.006	+	1579.64i	−0.110259	+	0.190974i	0.805616	+	0.592438i	$0.201835\pi$
$410$	−3984.67	−	1925.47i	−0.479972	−	0.231932i
$411$		0			0
$412$	4090.26	+	5157.20i	0.489108	+	0.616692i
$413$			15626.7i			1.86184i
$414$		0			0
$415$	−10015.6			−1.18469
$416$	3570.63	−	4416.65i	0.420828	−	0.520538i
$417$		0			0
$418$	−4621.36	+	9563.68i	−0.540761	+	1.11908i
$419$	−5167.33	−	2983.36i	−0.602484	−	0.347844i	0.167534	−	0.985866i	$-0.446419\pi$
$419$	−5167.33	−	2983.36i	−0.602484	−	0.347844i	−0.770018	+	0.638022i	$0.779753\pi$
$420$		0			0
$421$	6264.66	−	3616.90i	0.725228	−	0.418710i	−0.0914460	−	0.995810i	$-0.529149\pi$
$421$	6264.66	−	3616.90i	0.725228	−	0.418710i	0.816674	+	0.577100i	$0.195816\pi$
$422$	−216.292	−	2938.84i	−0.0249501	−	0.339006i
$423$		0			0
$424$	1535.52	+	6853.93i	0.175876	+	0.785038i
$425$	−2321.82	−	4021.51i	−0.264999	−	0.458992i
$426$		0			0
$427$	−16483.1	−	9516.51i	−1.86808	−	1.07854i
$428$	−871.718	−	344.812i	−0.0984488	−	0.0389419i
$429$		0			0
$430$	−1040.20	−	1530.08i	−0.116658	−	0.171598i
$431$	−1176.30			−0.131463			−0.0657314	−	0.997837i	$-0.520938\pi$
$431$	−1176.30			−0.131463			−0.0657314	+	0.997837i	$0.520938\pi$
$432$		0			0
$433$	−5783.94			−0.641937			−0.320968	−	0.947090i	$-0.604008\pi$
$433$	−5783.94			−0.641937			−0.320968	+	0.947090i	$0.604008\pi$
$434$	−7798.23	−	11470.8i	−0.862504	−	1.26870i
$435$		0			0
$436$	3449.35	+	1364.41i	0.378886	+	0.149870i
$437$	830.592	+	479.542i	0.0909212	+	0.0524934i
$438$		0			0
$439$	3132.78	+	5426.13i	0.340591	+	0.589921i	0.984543	−	0.175145i	$-0.0560395\pi$
$439$	3132.78	+	5426.13i	0.340591	+	0.589921i	−0.643952	+	0.765066i	$0.722706\pi$
$440$	−14744.7	+	3303.33i	−1.59756	+	0.357909i
$441$		0			0
$442$	−776.034	−	10544.3i	−0.0835117	−	1.13470i
$443$	−11214.4	+	6474.66i	−1.20274	+	0.694402i	−0.961163	−	0.275980i	$-0.910998\pi$
$443$	−11214.4	+	6474.66i	−1.20274	+	0.694402i	−0.241576	+	0.970382i	$0.577664\pi$
$444$		0			0
$445$	10532.0	+	6080.66i	1.12195	+	0.647755i
$446$	−7690.84	+	15915.8i	−0.816528	+	1.68977i
$447$		0			0
$448$	9273.53	+	6431.96i	0.977976	+	0.678307i
$449$	6748.62			0.709325			0.354662	−	0.934994i	$-0.384596\pi$
$449$	6748.62			0.709325			0.354662	+	0.934994i	$0.384596\pi$
$450$		0			0
$451$			6371.95i			0.665284i
$452$	−5743.80	−	7242.06i	−0.597711	−	0.753624i
$453$		0			0
$454$	−3850.58	−	1860.68i	−0.398054	−	0.192348i
$455$	4427.95	−	7669.43i	0.456231	−	0.790216i
$456$		0			0
$457$	1698.32	+	2941.58i	0.173839	+	0.301097i	0.939759	−	0.341839i	$-0.111050\pi$
$457$	1698.32	+	2941.58i	0.173839	+	0.301097i	−0.765920	+	0.642936i	$0.777716\pi$
$458$	581.328	+	7898.72i	0.0593094	+	0.805858i
$459$		0			0
$460$	199.747	+	1349.67i	0.0202462	+	0.136801i
$461$	7036.41	−	4062.48i	0.710886	−	0.410430i	−0.100503	−	0.994937i	$-0.532045\pi$
$461$	7036.41	−	4062.48i	0.710886	−	0.410430i	0.811389	+	0.584507i	$0.198712\pi$
$462$		0			0
$463$	3264.81	−	5654.81i	0.327707	−	0.567606i	−0.654349	−	0.756192i	$-0.727057\pi$
$463$	3264.81	−	5654.81i	0.327707	−	0.567606i	0.982057	+	0.188587i	$0.0603907\pi$
$464$	9627.84	+	2251.63i	0.963278	+	0.225279i
$465$		0			0
$466$	−10174.1	−	14965.6i	−1.01139	−	1.48770i
$467$		−	3225.20i		−	0.319581i	−0.987151	−	0.159791i	$-0.948918\pi$
$467$		−	3225.20i		−	0.319581i	0.987151	−	0.159791i	$-0.0510819\pi$
$468$		0			0
$469$			121.734i			0.0119854i
$470$	6999.04	−	4758.20i	0.686897	−	0.466977i
$471$		0			0
$472$	15309.7	+	4789.61i	1.49297	+	0.467076i
$473$	−1331.97	+	2307.04i	−0.129480	+	0.224266i
$474$		0			0
$475$	−2430.70	+	1403.36i	−0.234796	+	0.135559i
$476$	20783.0	−	3075.83i	2.00124	−	0.296177i
$477$		0			0
$478$	8384.95	−	617.114i	0.802340	−	0.0590504i
$479$	8085.45	+	14004.4i	0.771261	+	1.33586i	0.936872	+	0.349671i	$0.113707\pi$
$479$	8085.45	+	14004.4i	0.771261	+	1.33586i	−0.165612	+	0.986191i	$0.552960\pi$
$480$		0			0
$481$	2701.92	−	4679.86i	0.256127	−	0.443624i
$482$	209.654	−	433.869i	0.0198122	−	0.0410004i
$483$		0			0
$484$	6902.55	+	8703.08i	0.648249	+	0.817344i
$485$		−	2199.69i		−	0.205944i
$486$		0			0
$487$	−6187.90			−0.575771			−0.287886	−	0.957665i	$-0.592952\pi$
$487$	−6187.90			−0.575771			−0.287886	+	0.957665i	$0.592952\pi$
$488$	−14375.5	+	13231.8i	−1.33350	+	1.22741i
$489$		0			0
$490$	4659.22	+	2251.43i	0.429555	+	0.207569i
$491$	508.795	+	293.753i	0.0467650	+	0.0269998i	0.523200	−	0.852210i	$-0.324738\pi$
$491$	508.795	+	293.753i	0.0467650	+	0.0269998i	−0.476435	+	0.879210i	$0.658071\pi$
$492$		0			0
$493$	15940.6	−	9203.33i	1.45625	−	0.840765i
$494$	−6373.21	+	469.054i	−0.580454	+	0.0427201i
$495$		0			0
$496$	−13628.2	+	4124.20i	−1.23372	+	0.373351i
$497$	682.566	+	1182.24i	0.0616041	+	0.106701i
$498$		0			0
$499$	15174.8	+	8761.17i	1.36136	+	0.785980i	0.989805	−	0.142432i	$-0.0454922\pi$
$499$	15174.8	+	8761.17i	1.36136	+	0.785980i	0.371553	+	0.928412i	$0.378825\pi$
$500$	8194.73	+	3241.46i	0.732959	+	0.289925i
$501$		0			0
$502$	3.21445	−	2.18530i	0.000285793	−	0.000194292i
$503$	−8880.13			−0.787168			−0.393584	−	0.919289i	$-0.628765\pi$
$503$	−8880.13			−0.787168			−0.393584	+	0.919289i	$0.628765\pi$
$504$		0			0
$505$	9192.34			0.810007
$506$	1624.58	−	1104.45i	0.142730	−	0.0970332i
$507$		0			0
$508$	−1363.10	+	3446.05i	−0.119051	+	0.300972i
$509$	11665.3	+	6734.95i	1.01582	+	0.586486i	0.912891	−	0.408203i	$-0.133844\pi$
$509$	11665.3	+	6734.95i	1.01582	+	0.586486i	0.102932	+	0.994688i	$0.467178\pi$
$510$		0			0
$511$	3011.18	+	5215.51i	0.260678	+	0.451508i
$512$	9143.80	−	7113.97i	0.789263	−	0.614055i
$513$		0			0
$514$	−8760.86	+	644.780i	−0.751800	+	0.0553308i
$515$	9124.51	−	5268.04i	0.780726	−	0.450752i
$516$		0			0
$517$	−10553.1	−	6092.82i	−0.897725	−	0.518302i
$518$	9668.46	+	4671.99i	0.820092	+	0.396285i
$519$		0			0
$520$	−6156.64	−	6688.79i	−0.519205	−	0.564083i
$521$	−13988.7			−1.17631			−0.588153	−	0.808749i	$-0.700145\pi$
$521$	−13988.7			−1.17631			−0.588153	+	0.808749i	$0.700145\pi$
$522$		0			0
$523$			9180.29i			0.767545i	0.923428	+	0.383772i	$0.125375\pi$
$523$			9180.29i			0.767545i	−0.923428	+	0.383772i	$0.874625\pi$
$524$	−13287.4	+	10538.5i	−1.10776	+	0.878580i
$525$		0			0
$526$	−42.4180	+	87.7821i	−0.00351619	+	0.00727658i
$527$	−13253.1	+	22955.1i	−1.09548	+	1.89742i
$528$		0			0
$529$	5994.81	+	10383.3i	0.492711	+	0.853400i
$530$	11212.5	−	825.211i	0.918939	−	0.0676319i
$531$		0			0
$532$	−1859.11	−	12561.8i	−0.151508	−	1.02373i
$533$	−3320.01	+	1916.81i	−0.269804	+	0.155771i
$534$		0			0
$535$	−750.260	+	1299.49i	−0.0606291	+	0.105013i
$536$	119.264	+	37.3116i	0.00961085	+	0.00300674i
$537$		0			0
$538$	−5734.69	+	3898.65i	−0.459554	+	0.312421i
$539$		−	7450.63i		−	0.595401i
$540$		0			0
$541$			16856.7i			1.33961i	0.742538	+	0.669804i	$0.233622\pi$
$541$			16856.7i			1.33961i	−0.742538	+	0.669804i	$0.766378\pi$
$542$	9602.28	+	14124.4i	0.760984	+	1.11936i
$543$		0			0
$544$	3356.61	−	21304.1i	0.264547	−	1.67905i
$545$	2968.75	−	5142.03i	0.233334	−	0.404147i
$546$		0			0
$547$	3417.56	−	1973.13i	0.267138	−	0.154232i	−0.360448	−	0.932779i	$-0.617376\pi$
$547$	3417.56	−	1973.13i	0.267138	−	0.154232i	0.627586	+	0.778547i	$0.284043\pi$
$548$	−1820.99	+	269.502i	−0.141951	+	0.0210083i
$549$		0			0
$550$	421.965	+	5733.40i	0.0327139	+	0.444496i
$551$	−5562.72	−	9634.91i	−0.430090	−	0.744938i
$552$		0			0
$553$	−4276.30	+	7406.76i	−0.328837	+	0.569562i
$554$	−19025.8	−	9193.62i	−1.45907	−	0.705053i
$555$		0			0
$556$	−17118.9	+	13577.3i	−1.30576	+	1.03562i
$557$		−	12854.6i		−	0.977859i	−0.872323	−	0.488929i	$-0.837388\pi$
$557$		−	12854.6i		−	0.977859i	0.872323	−	0.488929i	$-0.162612\pi$
$558$		0			0
$559$	−1602.73			−0.121267
$560$	12357.6	−	13176.6i	0.932510	−	0.994308i
$561$		0			0
$562$	−4589.41	+	9497.57i	−0.344471	+	0.712866i
$563$	333.326	+	192.446i	0.0249521	+	0.0144061i	0.512424	−	0.858732i	$-0.328748\pi$
$563$	333.326	+	192.446i	0.0249521	+	0.0144061i	−0.487472	+	0.873139i	$0.662081\pi$
$564$		0			0
$565$	−12813.2	+	7397.71i	−0.954080	+	0.550839i
$566$	1186.67	+	16123.8i	0.0881265	+	1.19741i
$567$		0			0
$568$	1367.46	−	306.359i	0.101016	−	0.0226312i
$569$	672.481	+	1164.77i	0.0495463	+	0.0858167i	0.889735	−	0.456478i	$-0.150889\pi$
$569$	672.481	+	1164.77i	0.0495463	+	0.0858167i	−0.840189	+	0.542294i	$0.817556\pi$
$570$		0			0
$571$	4938.01	+	2850.96i	0.361908	+	0.208947i	0.669917	−	0.742436i	$-0.266330\pi$
$571$	4938.01	+	2850.96i	0.361908	+	0.208947i	−0.308010	+	0.951383i	$0.599663\pi$
$572$	−4814.56	+	12171.7i	−0.351935	+	0.889726i
$573$		0			0
$574$	−4282.89	−	6299.89i	−0.311436	−	0.458105i
$575$	519.095			0.0376483
$576$		0			0
$577$	10836.2			0.781833			0.390916	−	0.920426i	$-0.372158\pi$
$577$	10836.2			0.781833			0.390916	+	0.920426i	$0.372158\pi$
$578$	−14759.6	−	21710.6i	−1.06215	−	1.56236i
$579$		0			0
$580$	5821.46	−	14717.2i	0.416764	−	1.05362i
$581$	−14930.6	−	8620.21i	−1.06614	−	0.615536i
$582$		0			0
$583$	−8093.83	−	14018.9i	−0.574978	−	0.995891i
$584$	6032.62	−	1351.52i	0.427452	−	0.0957642i
$585$		0			0
$586$	−261.161	−	3548.49i	−0.0184103	−	0.250148i
$587$	7672.50	−	4429.72i	0.539486	−	0.311472i	−0.205385	−	0.978681i	$-0.565845\pi$
$587$	7672.50	−	4429.72i	0.539486	−	0.311472i	0.744870	+	0.667209i	$0.232511\pi$
$588$		0			0
$589$	13874.6	+	8010.52i	0.970618	+	0.560387i
$590$	11171.6	−	23119.2i	0.779540	−	1.61322i
$591$		0			0
$592$	7540.59	−	8040.31i	0.523507	−	0.558201i
$593$	−3444.82			−0.238553			−0.119276	−	0.992861i	$-0.538057\pi$
$593$	−3444.82			−0.238553			−0.119276	+	0.992861i	$0.538057\pi$
$594$		0			0
$595$		−	33629.0i		−	2.31707i
$596$	15650.3	−	12412.5i	1.07560	−	0.853079i
$597$		0			0
$598$	1064.16	+	514.225i	0.0727707	+	0.0351643i
$599$	6935.24	−	12012.2i	0.473066	−	0.819374i	−0.526459	−	0.850200i	$-0.676481\pi$
$599$	6935.24	−	12012.2i	0.473066	−	0.819374i	0.999525	+	0.0308268i	$0.00981404\pi$
$600$		0			0
$601$	6480.55	+	11224.6i	0.439845	+	0.761834i	0.997677	−	0.0681195i	$-0.0216999\pi$
$601$	6480.55	+	11224.6i	0.439845	+	0.761834i	−0.557832	+	0.829954i	$0.688367\pi$
$602$	−233.763	−	3176.23i	−0.0158264	−	0.215039i
$603$		0			0
$604$	−27261.5	+	4034.63i	−1.83652	+	0.271799i
$605$	15398.1	−	8890.12i	1.03475	−	0.597413i
$606$		0			0
$607$	10120.6	−	17529.4i	0.676744	−	1.17215i	−0.299212	−	0.954187i	$-0.596724\pi$
$607$	10120.6	−	17529.4i	0.676744	−	1.17215i	0.975956	−	0.217968i	$-0.0699429\pi$
$608$	−12876.7	−	2028.82i	−0.858914	−	0.135328i
$609$		0			0
$610$	17582.7	+	25863.2i	1.16705	+	1.71667i
$611$		−	7331.37i		−	0.485426i
$612$		0			0
$613$		−	22878.4i		−	1.50742i	−0.657205	−	0.753712i	$-0.728261\pi$
$613$		−	22878.4i		−	1.50742i	0.657205	−	0.753712i	$-0.271739\pi$
$614$	−12783.2	+	8690.50i	−0.840211	+	0.571205i
$615$		0			0
$616$	−24823.6	−	7766.04i	−1.62365	−	0.507959i
$617$	10055.6	−	17416.9i	0.656118	−	1.13643i	−0.325495	−	0.945544i	$-0.605531\pi$
$617$	10055.6	−	17416.9i	0.656118	−	1.13643i	0.981612	−	0.190885i	$-0.0611359\pi$
$618$		0			0
$619$	25325.6	−	14621.7i	1.64446	−	0.949429i	0.665239	−	0.746631i	$-0.268330\pi$
$619$	25325.6	−	14621.7i	1.64446	−	0.949429i	0.979221	−	0.202798i	$-0.0650036\pi$
$620$	3336.68	+	22545.6i	0.216136	+	1.46041i
$621$		0			0
$622$	5637.33	−	414.895i	0.363402	−	0.0267456i
$623$	10467.0	+	18129.4i	0.673116	+	1.16587i
$624$		0			0
$625$	9488.93	−	16435.3i	0.607292	−	1.05186i
$626$	−9966.91	+	20626.0i	−0.636355	+	1.31691i
$627$		0			0
$628$	−12984.6	+	10298.3i	−0.825066	+	0.654373i
$629$		−	20520.3i		−	1.30079i
$630$		0			0
$631$	−3809.08			−0.240312			−0.120156	−	0.992755i	$-0.538339\pi$
$631$	−3809.08			−0.240312			−0.120156	+	0.992755i	$0.538339\pi$
$632$	5945.79	+	6459.71i	0.374226	+	0.406572i
$633$		0			0
$634$	−17342.2	−	8380.07i	−1.08635	−	0.524945i
$635$	5137.10	+	2965.90i	0.321039	+	0.185352i
$636$		0			0
$637$	3882.04	−	2241.30i	0.241463	−	0.139409i
$638$	−22726.3	+	1672.61i	−1.41026	+	0.103792i
$639$		0			0
$640$	−9121.61	−	16145.5i	−0.563380	−	0.997201i
$641$	7103.19	+	12303.1i	0.437690	+	0.758101i	0.997511	−	0.0705123i	$-0.0224634\pi$
$641$	7103.19	+	12303.1i	0.437690	+	0.758101i	−0.559821	+	0.828614i	$0.689130\pi$
$642$		0			0
$643$	−4455.55	−	2572.41i	−0.273265	−	0.157770i	0.357105	−	0.934064i	$-0.383764\pi$
$643$	−4455.55	−	2572.41i	−0.273265	−	0.157770i	−0.630371	+	0.776294i	$0.717097\pi$
$644$	−863.860	+	2183.92i	−0.0528585	+	0.133631i
$645$		0			0
$646$	−20068.4	+	13643.2i	−1.22226	+	0.830936i
$647$	13544.4			0.823007			0.411504	−	0.911408i	$-0.365004\pi$
$647$	13544.4			0.823007			0.411504	+	0.911408i	$0.365004\pi$
$648$		0			0
$649$	−36970.2			−2.23607
$650$	−2860.37	+	1944.58i	−0.172604	+	0.117343i
$651$		0			0
$652$	3207.26	+	1268.64i	0.192647	+	0.0762024i
$653$	−12523.7	−	7230.55i	−0.750520	−	0.433313i	0.0753621	−	0.997156i	$-0.475989\pi$
$653$	−12523.7	−	7230.55i	−0.750520	−	0.433313i	−0.825882	+	0.563844i	$0.809322\pi$
$654$		0			0
$655$	13573.0	+	23509.1i	0.809681	+	1.40241i
$656$	−7484.78	+	2265.06i	−0.445475	+	0.134811i
$657$		0			0
$658$	14529.0	−	1069.30i	0.860791	−	0.0633523i
$659$	10653.2	−	6150.62i	0.629726	−	0.363572i	−0.150920	−	0.988546i	$-0.548224\pi$
$659$	10653.2	−	6150.62i	0.629726	−	0.363572i	0.780646	+	0.624974i	$0.214890\pi$
$660$		0			0
$661$	−27310.4	−	15767.7i	−1.60704	−	0.927824i	−0.990028	−	0.140870i	$-0.955010\pi$
$661$	−27310.4	−	15767.7i	−1.60704	−	0.927824i	−0.617011	−	0.786954i	$-0.711657\pi$
$662$	26757.1	+	12929.5i	1.57091	+	0.759095i
$663$		0			0
$664$	−13021.6	+	11985.6i	−0.761047	+	0.700499i
$665$	−20326.2			−1.18529
$666$		0			0
$667$			2057.61i			0.119447i
$668$	−1737.10	−	2190.23i	−0.100615	−	0.126860i
$669$		0			0
$670$	87.0282	−	180.101i	0.00501820	−	0.0103849i
$671$	22514.5	−	38996.2i	1.29532	−	2.24356i
$672$		0			0
$673$	−2971.12	−	5146.13i	−0.170176	−	0.294753i	0.768306	−	0.640083i	$-0.221100\pi$
$673$	−2971.12	−	5146.13i	−0.170176	−	0.294753i	−0.938481	+	0.345330i	$0.887767\pi$
$674$	24741.1	−	1820.89i	1.41394	−	0.104062i
$675$		0			0
$676$	9596.43	−	1420.25i	0.545996	−	0.0808059i
$677$	−11809.4	+	6818.16i	−0.670416	+	0.387065i	−0.796234	−	0.604988i	$-0.793178\pi$
$677$	−11809.4	+	6818.16i	−0.670416	+	0.387065i	0.125818	+	0.992053i	$0.459844\pi$
$678$		0			0
$679$	1893.23	−	3279.17i	0.107004	−	0.185336i
$680$	−32946.7	−	10307.3i	−1.85801	−	0.581277i
$681$		0			0
$682$	27137.9	−	18449.3i	1.52370	−	1.03587i
$683$		−	5073.36i		−	0.284227i	−0.989850	−	0.142113i	$-0.954610\pi$
$683$		−	5073.36i		−	0.284227i	0.989850	−	0.142113i	$-0.0453898\pi$
$684$		0			0
$685$			2946.54i			0.164353i
$686$	−7014.83	−	10318.4i	−0.390419	−	0.574285i
$687$		0			0
$688$	−3183.43	−	744.498i	−0.176406	−	0.0412554i
$689$	4869.56	−	8434.33i	0.269253	−	0.466361i
$690$		0			0
$691$	−2356.51	+	1360.53i	−0.129734	+	0.0749018i	−0.563462	−	0.826142i	$-0.690531\pi$
$691$	−2356.51	+	1360.53i	−0.129734	+	0.0749018i	0.433729	+	0.901044i	$0.357198\pi$
$692$	−998.807	−	6748.82i	−0.0548684	−	0.370740i
$693$		0			0
$694$	−101.009	−	1372.44i	−0.00552483	−	0.0750679i
$695$	17486.8	+	30288.1i	0.954409	+	1.65308i
$696$		0			0
$697$	−7278.80	+	12607.3i	−0.395558	+	0.685127i
$698$	26127.6	+	12625.4i	1.41683	+	0.684638i
$699$		0			0
$700$	−4270.89	−	5384.94i	−0.230606	−	0.290760i
$701$		−	18126.1i		−	0.976625i	−0.872669	−	0.488312i	$-0.837613\pi$
$701$		−	18126.1i		−	0.976625i	0.872669	−	0.488312i	$-0.162387\pi$
$702$		0			0
$703$	−12403.0			−0.665415
$704$	−15216.9	+	21939.6i	−0.814645	+	1.17455i
$705$		0			0
$706$	14645.7	−	30308.6i	0.780735	−	1.61569i
$707$	13703.4	+	7911.65i	0.728951	+	0.420860i
$708$		0			0
$709$	−15227.8	+	8791.76i	−0.806616	+	0.465700i	−0.845779	−	0.533533i	$-0.820864\pi$
$709$	−15227.8	+	8791.76i	−0.806616	+	0.465700i	0.0391631	+	0.999233i	$0.487531\pi$
$710$	−164.642	−	2237.05i	−0.00870267	−	0.118246i
$711$		0			0
$712$	20969.7	−	4697.95i	1.10375	−	0.247279i
$713$	−1481.52	−	2566.07i	−0.0778168	−	0.134783i
$714$		0			0
$715$	18144.6	+	10475.8i	0.949047	+	0.547933i
$716$	−19412.3	−	7678.64i	−1.01323	−	0.400788i
$717$		0			0
$718$	5017.09	+	7379.86i	0.260775	+	0.383585i
$719$	−22304.9			−1.15693			−0.578465	−	0.815707i	$-0.696348\pi$
$719$	−22304.9			−1.15693			−0.578465	+	0.815707i	$0.696348\pi$
$720$		0			0
$721$	18136.4			0.936801
$722$	−2660.82	−	3913.92i	−0.137154	−	0.201747i
$723$		0			0
$724$	−8658.89	−	3425.06i	−0.444482	−	0.175817i
$725$	−5214.80	−	3010.77i	−0.267135	−	0.154230i
$726$		0			0
$727$	4043.69	+	7003.88i	0.206289	+	0.357303i	0.950543	−	0.310594i	$-0.100528\pi$
$727$	4043.69	+	7003.88i	0.206289	+	0.357303i	−0.744254	+	0.667897i	$0.767195\pi$
$728$	−3421.05	−	15270.1i	−0.174166	−	0.777403i
$729$		0			0
$730$	−726.327	−	9868.87i	−0.0368254	−	0.500361i
$731$	−5270.75	+	3043.07i	−0.266684	+	0.153970i
$732$		0			0
$733$	13603.1	+	7853.73i	0.685457	+	0.395749i	0.801908	−	0.597447i	$-0.203818\pi$
$733$	13603.1	+	7853.73i	0.685457	+	0.395749i	−0.116451	+	0.993196i	$0.537152\pi$
$734$	3799.46	−	7862.80i	0.191063	−	0.395397i
$735$		0			0
$736$	1874.84	+	1515.71i	0.0938959	+	0.0759100i
$737$	−288.002			−0.0143944
$738$		0			0
$739$			19955.2i			0.993320i	0.867945	+	0.496660i	$0.165440\pi$
$739$			19955.2i			0.993320i	−0.867945	+	0.496660i	$0.834560\pi$
$740$	−10964.1	−	13824.1i	−0.544659	−	0.686734i
$741$		0			0
$742$	17425.1	+	8420.15i	0.862123	+	0.416595i
$743$	−11136.7	+	19289.3i	−0.549886	+	0.952431i	0.448395	+	0.893835i	$0.351996\pi$
$743$	−11136.7	+	19289.3i	−0.549886	+	0.952431i	−0.998282	+	0.0585958i	$0.981338\pi$
$744$		0			0
$745$	−15986.6	−	27689.6i	−0.786181	−	1.36170i
$746$	−267.376	−	3632.94i	−0.0131224	−	0.178300i
$747$		0			0
$748$	7276.90	+	49169.2i	0.355708	+	2.40348i
$749$	−2236.89	+	1291.47i	−0.109124	+	0.0630029i
$750$		0			0
$751$	−7736.20	+	13399.5i	−0.375896	+	0.651071i	−0.990461	−	0.137795i	$-0.955998\pi$
$751$	−7736.20	+	13399.5i	−0.375896	+	0.651071i	0.614565	+	0.788867i	$0.289332\pi$
$752$	3405.56	−	14562.0i	0.165144	−	0.706145i
$753$		0			0
$754$	−7708.01	−	11338.1i	−0.372293	−	0.547623i
$755$			44111.8i			2.12635i
$756$		0			0
$757$		−	8860.07i		−	0.425396i	−0.977118	−	0.212698i	$-0.931775\pi$
$757$		−	8860.07i		−	0.425396i	0.977118	−	0.212698i	$-0.0682250\pi$
$758$	7041.79	−	4787.26i	0.337426	−	0.229394i
$759$		0			0
$760$	−6230.00	+	19913.8i	−0.297350	+	0.950458i
$761$	−12156.9	+	21056.3i	−0.579088	+	1.00301i	0.416496	+	0.909137i	$0.363258\pi$
$761$	−12156.9	+	21056.3i	−0.579088	+	1.00301i	−0.995584	+	0.0938723i	$0.970075\pi$
$762$		0			0
$763$	8851.27	−	5110.28i	0.419970	−	0.242470i
$764$	−8060.49	+	1192.93i	−0.381699	+	0.0564904i
$765$		0			0
$766$	−25867.6	+	1903.80i	−1.22015	+	0.0898004i
$767$	−11121.4	−	19262.8i	−0.523558	−	0.906830i
$768$		0			0
$769$	−7978.69	+	13819.5i	−0.374147	+	0.648042i	−0.990199	−	0.139664i	$-0.955398\pi$
$769$	−7978.69	+	13819.5i	−0.374147	+	0.648042i	0.616052	+	0.787706i	$0.288731\pi$
$770$	−18114.1	+	37486.2i	−0.847773	+	1.75443i
$771$		0			0
$772$	−16958.5	−	21382.1i	−0.790607	−	0.996836i
$773$			4145.20i			0.192875i	0.995339	+	0.0964375i	$0.0307448\pi$
$773$			4145.20i			0.192875i	−0.995339	+	0.0964375i	$0.969255\pi$
$774$		0			0
$775$	8671.24			0.401910
$776$	−2632.36	−	2859.89i	−0.121773	−	0.132299i
$777$		0			0
$778$	24332.3	+	11757.8i	1.12128	+	0.541823i
$779$	7620.13	+	4399.48i	0.350474	+	0.202346i
$780$		0			0
$781$	−2796.98	+	1614.84i	−0.128148	+	0.0739864i
$782$	4475.97	−	329.421i	0.204681	−	0.0150640i
$783$		0			0
$784$	8751.85	−	2648.51i	0.398681	−	0.120650i
$785$	13263.6	+	22973.3i	0.603057	+	1.04453i
$786$		0			0
$787$	13750.5	+	7938.85i	0.622811	+	0.359580i	0.777963	−	0.628311i	$-0.216253\pi$
$787$	13750.5	+	7938.85i	0.622811	+	0.359580i	−0.155152	+	0.987891i	$0.549587\pi$
$788$	22234.1	+	8794.81i	1.00515	+	0.397592i
$789$		0			0
$790$	11621.8	−	7900.88i	0.523397	−	0.355824i
$791$	−25468.2			−1.14481
$792$		0			0
$793$	27091.2			1.21316
$794$	−7665.18	+	5211.06i	−0.342603	+	0.232914i
$795$		0			0
$796$	3751.70	−	9484.67i	0.167055	−	0.422331i
$797$	20181.7	+	11651.9i	0.896954	+	0.517857i	0.876211	−	0.481928i	$-0.160063\pi$
$797$	20181.7	+	11651.9i	0.896954	+	0.517857i	0.0207434	+	0.999785i	$0.493397\pi$
$798$		0			0
$799$	−13919.9	−	24110.0i	−0.616334	−	1.06752i
$800$	−6584.72	+	2533.74i	−0.291006	+	0.111976i
$801$		0			0
$802$	−10484.4	+	771.625i	−0.461615	+	0.0339739i
$803$	−12339.0	+	7123.94i	−0.542260	+	0.313074i
$804$		0			0
$805$	3255.62	+	1879.63i	0.142541	+	0.0822961i
$806$	17776.3	+	8589.88i	0.776855	+	0.375392i
$807$		0			0
$808$	11951.2	−	11000.4i	0.520350	−	0.478952i
$809$	31273.0			1.35909			0.679543	−	0.733636i	$-0.262178\pi$
$809$	31273.0			1.35909			0.679543	+	0.733636i	$0.262178\pi$
$810$		0			0
$811$		−	7848.52i		−	0.339826i	−0.985459	−	0.169913i	$-0.945651\pi$
$811$		−	7848.52i		−	0.339826i	0.985459	−	0.169913i	$-0.0543486\pi$
$812$	21345.1	−	16929.1i	0.922495	−	0.731646i
$813$		0			0
$814$	−11053.1	+	22873.9i	−0.475937	+	0.984928i
$815$	2760.38	−	4781.12i	0.118641	−	0.205491i
$816$		0			0
$817$	1839.30	+	3185.77i	0.0787627	+	0.136421i
$818$	5145.17	−	378.673i	0.219923	−	0.0161858i
$819$		0			0
$820$	1832.55	+	12382.3i	0.0780431	+	0.527328i
$821$	−19974.4	+	11532.2i	−0.849101	+	0.490229i	−0.860347	−	0.509708i	$-0.829753\pi$
$821$	−19974.4	+	11532.2i	−0.849101	+	0.490229i	0.0112464	+	0.999937i	$0.496420\pi$
$822$		0			0
$823$	−7822.69	+	13549.3i	−0.331327	+	0.573875i	−0.982772	−	0.184821i	$-0.940830\pi$
$823$	−7822.69	+	13549.3i	−0.331327	+	0.573875i	0.651446	+	0.758695i	$0.274163\pi$
$824$	5558.82	−	17768.4i	0.235013	−	0.751202i
$825$		0			0
$826$	36552.2	−	24849.4i	1.53972	−	1.04676i
$827$			8604.49i			0.361799i	0.983502	+	0.180899i	$0.0579008\pi$
$827$			8604.49i			0.361799i	−0.983502	+	0.180899i	$0.942099\pi$
$828$		0			0
$829$			45496.6i			1.90610i	0.302806	+	0.953052i	$0.402077\pi$
$829$			45496.6i			1.90610i	−0.302806	+	0.953052i	$0.597923\pi$
$830$	15926.7	+	23427.3i	0.666053	+	0.979726i
$831$		0			0
$832$	−16008.9	−	1328.68i	−0.667077	−	0.0553652i
$833$	8511.00	−	14741.5i	0.354008	−	0.613160i
$834$		0			0
$835$	−3875.11	+	2237.30i	−0.160603	+	0.0927244i
$836$	29719.1	−	4398.34i	1.22949	−	0.181961i
$837$		0			0
$838$	1238.72	+	16830.9i	0.0510630	+	0.693812i
$839$	−11036.2	−	19115.3i	−0.454126	−	0.786570i	0.544511	−	0.838754i	$-0.316715\pi$
$839$	−11036.2	−	19115.3i	−0.454126	−	0.786570i	−0.998638	+	0.0521835i	$0.983382\pi$
$840$		0			0
$841$	−260.281	+	450.821i	−0.0106721	+	0.0184846i
$842$	−18422.2	−	8901.98i	−0.754005	−	0.364350i
$843$		0			0
$844$	−6530.24	+	5179.24i	−0.266327	+	0.211228i
$845$		−	15528.0i		−	0.632164i
$846$		0			0
$847$	30606.2			1.24161
$848$	13590.1	−	14490.7i	0.550338	−	0.586809i
$849$		0			0
$850$	−5714.49	+	11825.9i	−0.230595	+	0.477205i
$851$	1986.57	+	1146.95i	0.0800220	+	0.0462007i
$852$		0			0
$853$	−37005.7	+	21365.3i	−1.48541	+	0.857600i	−0.999862	−	0.0166119i	$-0.994712\pi$
$853$	−37005.7	+	21365.3i	−1.48541	+	0.857600i	−0.485545	+	0.874212i	$0.661379\pi$
$854$	3951.34	+	53688.3i	0.158328	+	2.15126i
$855$		0			0
$856$	579.654	+	2587.34i	0.0231451	+	0.103310i
$857$	−10344.5	−	17917.1i	−0.412322	−	0.714164i	0.582821	−	0.812601i	$-0.301949\pi$
$857$	−10344.5	−	17917.1i	−0.412322	−	0.714164i	−0.995143	+	0.0984372i	$0.968616\pi$
$858$		0			0
$859$	6732.86	+	3887.22i	0.267430	+	0.154401i	0.627719	−	0.778440i	$-0.283989\pi$
$859$	6732.86	+	3887.22i	0.267430	+	0.154401i	−0.360289	+	0.932841i	$0.617322\pi$
$860$	−1924.86	+	4866.23i	−0.0763223	+	0.192950i
$861$		0			0
$862$	1870.54	+	2751.46i	0.0739106	+	0.108718i
$863$	−10537.9			−0.415659			−0.207830	−	0.978165i	$-0.566640\pi$
$863$	−10537.9			−0.415659			−0.207830	+	0.978165i	$0.566640\pi$
$864$		0			0
$865$	−10920.3			−0.429248
$866$	9197.57	+	13529.1i	0.360908	+	0.530875i
$867$		0			0
$868$	−14430.4	+	36481.4i	−0.564284	+	1.42656i
$869$	−17523.2	−	10117.0i	−0.684042	−	0.394932i
$870$		0			0
$871$	−86.6366	−	150.059i	−0.00337034	−	0.00583761i
$872$	−2293.67	−	10238.0i	−0.0890750	−	0.397594i
$873$		0			0
$874$	−199.110	−	2705.38i	−0.00770595	−	0.104704i
$875$	21028.2	−	12140.6i	0.812438	−	0.469061i
$876$		0			0
$877$	−35725.0	−	20625.8i	−1.37554	−	0.794168i	−0.383920	−	0.923366i	$-0.625426\pi$
$877$	−35725.0	−	20625.8i	−1.37554	−	0.794168i	−0.991619	+	0.129199i	$0.958760\pi$
$878$	7710.45	−	15956.4i	0.296373	−	0.613329i
$879$		0			0
$880$	31173.6	+	29236.1i	1.19416	+	1.11994i
$881$	11507.8			0.440075			0.220038	−	0.975491i	$-0.429382\pi$
$881$	11507.8			0.440075			0.220038	+	0.975491i	$0.429382\pi$
$882$		0			0
$883$		−	5036.66i		−	0.191956i	−0.995383	−	0.0959779i	$-0.969402\pi$
$883$		−	5036.66i		−	0.191956i	0.995383	−	0.0959779i	$-0.0305978\pi$
$884$	−23429.8	+	18582.6i	−0.891437	+	0.707013i
$885$		0			0
$886$	32977.8	+	15935.5i	1.25046	+	0.604249i
$887$	−20559.2	+	35609.6i	−0.778253	+	1.34797i	0.154695	+	0.987962i	$0.450560\pi$
$887$	−20559.2	+	35609.6i	−0.778253	+	1.34797i	−0.932948	+	0.360011i	$0.882773\pi$
$888$		0			0
$889$	5105.38	+	8842.78i	0.192609	+	0.333608i
$890$	−2524.75	−	34304.6i	−0.0950895	−	1.29202i
$891$		0			0
$892$	49458.3	−	7319.68i	1.85649	−	0.274755i
$893$	−14572.7	+	8413.53i	−0.546087	+	0.315284i
$894$		0			0
$895$	−16707.6	+	28938.4i	−0.623992	+	1.08079i
$896$	298.189	−	31919.6i	0.0111181	−	1.19013i
$897$		0			0
$898$	−10731.6	−	15785.6i	−0.398794	−	0.586604i
$899$			34371.4i			1.27514i
$900$		0			0
$901$		−	36983.0i		−	1.36746i
$902$	14904.5	−	10132.6i	0.550183	−	0.374034i
$903$		0			0
$904$	−7806.04	+	24951.4i	−0.287196	+	0.918001i
$905$	−7452.43	+	12908.0i	−0.273732	+	0.474117i
$906$		0			0
$907$	19167.0	−	11066.1i	0.701685	−	0.405118i	−0.106290	−	0.994335i	$-0.533897\pi$
$907$	19167.0	−	11066.1i	0.701685	−	0.405118i	0.807975	+	0.589217i	$0.200564\pi$
$908$	1770.88	+	11965.6i	0.0647233	+	0.437328i
$909$		0			0
$910$	−24980.7	+	1838.52i	−0.910002	+	0.0669741i
$911$	−24001.4	−	41571.6i	−0.872889	−	1.51189i	−0.858995	−	0.511984i	$-0.828911\pi$
$911$	−24001.4	−	41571.6i	−0.872889	−	1.51189i	−0.0138941	−	0.999903i	$-0.504423\pi$
$912$		0			0
$913$	20394.0	−	35323.4i	0.739258	−	1.28043i
$914$	4179.94	−	8650.19i	0.151269	−	0.313045i
$915$		0			0
$916$	17551.3	−	13920.2i	0.633092	−	0.502115i
$917$			46728.0i			1.68276i
$918$		0			0
$919$	−1607.53			−0.0577014			−0.0288507	−	0.999584i	$-0.509185\pi$
$919$	−1607.53			−0.0577014			−0.0288507	+	0.999584i	$0.509185\pi$
$920$	2839.35	−	2613.45i	0.101751	−	0.0936554i
$921$		0			0
$922$	−20691.7	−	9998.63i	−0.739094	−	0.357145i
$923$	−1682.77	−	971.549i	−0.0600099	−	0.0346467i
$924$		0			0
$925$	−5813.62	+	3356.50i	−0.206649	+	0.119309i
$926$	−18418.7	+	1355.58i	−0.653647	+	0.0481069i
$927$		0			0
$928$	−10043.3	−	26100.8i	−0.355268	−	0.923277i
$929$	−22681.7	−	39285.9i	−0.801037	−	1.38744i	−0.918934	−	0.394412i	$-0.870948\pi$
$929$	−22681.7	−	39285.9i	−0.801037	−	1.38744i	0.117896	−	0.993026i	$-0.462385\pi$
$930$		0			0
$931$	−8910.12	−	5144.26i	−0.313660	−	0.181092i
$932$	−18826.9	+	47596.3i	−0.661691	+	1.67282i
$933$		0			0
$934$	−7544.00	+	5128.68i	−0.264291	+	0.179674i
$935$	79560.5			2.78279
$936$		0			0
$937$	−14743.9			−0.514047			−0.257024	−	0.966405i	$-0.582742\pi$
$937$	−14743.9			−0.514047			−0.257024	+	0.966405i	$0.582742\pi$
$938$	284.745	−	193.580i	0.00991179	−	0.00673839i
$939$		0			0
$940$	−22259.6	−	8804.89i	−0.772371	−	0.305515i
$941$	2624.92	+	1515.50i	0.0909350	+	0.0525014i	0.544778	−	0.838580i	$-0.316614\pi$
$941$	2624.92	+	1515.50i	0.0909350	+	0.0525014i	−0.453843	+	0.891082i	$0.649947\pi$
$942$		0			0
$943$	−813.671	−	1409.32i	−0.0280984	−	0.0486678i
$944$	−13142.0	−	43426.9i	−0.453109	−	1.49727i
$945$		0			0
$946$	7514.43	−	553.045i	0.258261	−	0.0190074i
$947$	−14456.6	+	8346.53i	−0.496069	+	0.286405i	−0.727089	−	0.686544i	$-0.759127\pi$
$947$	−14456.6	+	8346.53i	−0.496069	+	0.286405i	0.231020	+	0.972949i	$0.425794\pi$
$948$		0			0
$949$	−7423.65	−	4286.05i	−0.253932	−	0.146608i
$950$	7147.85	+	3453.98i	0.244112	+	0.117960i
$951$		0			0
$952$	−40243.6	−	43722.0i	−1.37007	−	1.48849i
$953$	−20510.3			−0.697160			−0.348580	−	0.937279i	$-0.613336\pi$
$953$	−20510.3			−0.697160			−0.348580	+	0.937279i	$0.613336\pi$
$954$		0			0
$955$			13042.7i			0.441938i
$956$	−14777.1	−	18631.7i	−0.499923	−	0.630328i
$957$		0			0
$958$	19900.1	−	41182.2i	0.671129	−	1.38887i
$959$	−2536.03	+	4392.53i	−0.0853937	+	0.147906i
$960$		0			0
$961$	−9852.59	−	17065.2i	−0.330724	−	0.572830i
$962$	−15243.1	+	1121.86i	−0.510871	+	0.0375990i
$963$		0			0
$964$	−1348.25	+	199.536i	−0.0450457	+	0.00666664i
$965$	−37830.8	+	21841.6i	−1.26198	+	0.728607i
$966$		0			0
$967$	21065.6	−	36486.6i	0.700541	−	1.21337i	−0.267736	−	0.963492i	$-0.586275\pi$
$967$	21065.6	−	36486.6i	0.700541	−	1.21337i	0.968277	−	0.249880i	$-0.0803912\pi$
$968$	9380.83	−	29985.2i	0.311479	−	0.995620i
$969$		0			0
$970$	−5145.26	+	3497.93i	−0.170314	+	0.115785i
$971$			22531.9i			0.744680i	0.928096	+	0.372340i	$0.121444\pi$
$971$			22531.9i			0.744680i	−0.928096	+	0.372340i	$0.878556\pi$
$972$		0			0
$973$			60202.3i			1.98355i
$974$	9839.94	+	14474.0i	0.323708	+	0.476157i
$975$		0			0
$976$	53810.0	+	12584.4i	1.76477	+	0.412721i
$977$	−16527.4	+	28626.3i	−0.541206	+	0.937397i	0.457629	+	0.889143i	$0.348699\pi$
$977$	−16527.4	+	28626.3i	−0.541206	+	0.937397i	−0.998835	+	0.0482533i	$0.984635\pi$
$978$		0			0
$979$	−42891.1	+	24763.2i	−1.40021	+	0.808411i
$980$	−2142.77	−	14478.5i	−0.0698453	−	0.471937i
$981$		0			0
$982$	−121.969	−	1657.24i	−0.00396353	−	0.0538539i
$983$	10231.8	+	17722.1i	0.331989	+	0.575022i	0.982902	−	0.184131i	$-0.0589470\pi$
$983$	10231.8	+	17722.1i	0.331989	+	0.575022i	−0.650913	+	0.759152i	$0.725614\pi$
$984$		0			0
$985$	19136.2	−	33144.9i	0.619016	−	1.07217i
$986$	−46875.9	−	22651.4i	−1.51403	−	0.731609i
$987$		0			0
$988$	11231.8	+	14161.6i	0.361670	+	0.456011i
$989$		−	680.348i		−	0.0218744i
$990$		0			0
$991$	37176.3			1.19167			0.595835	−	0.803107i	$-0.296821\pi$
$991$	37176.3			1.19167			0.595835	+	0.803107i	$0.296821\pi$
$992$	31318.2	+	25319.2i	1.00237	+	0.810367i
$993$		0			0
$994$	1679.94	−	3476.56i	0.0536062	−	0.110935i
$995$	−14139.0	−	8163.15i	−0.450489	−	0.260090i
$996$		0			0
$997$	17012.3	−	9822.05i	0.540406	−	0.312004i	−0.204837	−	0.978796i	$-0.565667\pi$
$997$	17012.3	−	9822.05i	0.540406	−	0.312004i	0.745243	+	0.666792i	$0.232333\pi$
$998$	−3637.72	−	49427.0i	−0.115381	−	1.56772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.n.a.37.11		68
3.2	odd	2		72.4.n.a.13.24	yes	68
4.3	odd	2		864.4.r.a.145.28		68
8.3	odd	2		864.4.r.a.145.7		68
8.5	even	2	inner	216.4.n.a.37.12		68
9.2	odd	6		72.4.n.a.61.23	yes	68
9.7	even	3	inner	216.4.n.a.181.12		68
12.11	even	2		288.4.r.a.49.10		68
24.5	odd	2		72.4.n.a.13.23	✓	68
24.11	even	2		288.4.r.a.49.25		68
36.7	odd	6		864.4.r.a.721.7		68
36.11	even	6		288.4.r.a.241.25		68
72.11	even	6		288.4.r.a.241.10		68
72.29	odd	6		72.4.n.a.61.24	yes	68
72.43	odd	6		864.4.r.a.721.28		68
72.61	even	6	inner	216.4.n.a.181.11		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.n.a.13.23	✓	68	24.5	odd	2
72.4.n.a.13.24	yes	68	3.2	odd	2
72.4.n.a.61.23	yes	68	9.2	odd	6
72.4.n.a.61.24	yes	68	72.29	odd	6
216.4.n.a.37.11		68	1.1	even	1	trivial
216.4.n.a.37.12		68	8.5	even	2	inner
216.4.n.a.181.11		68	72.61	even	6	inner
216.4.n.a.181.12		68	9.7	even	3	inner
288.4.r.a.49.10		68	12.11	even	2
288.4.r.a.49.25		68	24.11	even	2
288.4.r.a.241.10		68	72.11	even	6
288.4.r.a.241.25		68	36.11	even	6
864.4.r.a.145.7		68	8.3	odd	2
864.4.r.a.145.28		68	4.3	odd	2
864.4.r.a.721.7		68	36.7	odd	6
864.4.r.a.721.28		68	72.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59019 - 2.33908i) q^{2} +(-2.94259 + 7.43916i) q^{4} +(11.0897 + 6.40265i) q^{5} +(11.0213 + 19.0894i) q^{7} +(22.0801 - 4.94672i) q^{8} +O(q^{10})\)	\(q+(-1.59019 - 2.33908i) q^{2} +(-2.94259 + 7.43916i) q^{4} +(11.0897 + 6.40265i) q^{5} +(11.0213 + 19.0894i) q^{7} +(22.0801 - 4.94672i) q^{8} +(-2.65844 - 36.1212i) q^{10} +(-45.1623 + 26.0744i) q^{11} +(-27.1714 - 15.6874i) q^{13} +(27.1257 - 56.1353i) q^{14} +(-46.6823 - 43.7809i) q^{16} -119.141 q^{17} +72.0120i q^{19} +(-80.2629 + 63.6578i) q^{20} +(132.807 + 64.1748i) q^{22} +(6.65920 - 11.5341i) q^{23} +(19.4879 + 33.7540i) q^{25} +(6.51355 + 88.5020i) q^{26} +(-174.440 + 25.8166i) q^{28} +(-133.796 + 77.2471i) q^{29} +(111.239 - 192.671i) q^{31} +(-28.1733 + 178.813i) q^{32} +(189.457 + 278.681i) q^{34} +282.261i q^{35} +172.235i q^{37} +(168.442 - 114.513i) q^{38} +(276.534 + 86.5134i) q^{40} +(61.0938 - 105.818i) q^{41} +(44.2394 - 25.5416i) q^{43} +(-61.0778 - 412.696i) q^{44} +(-37.5685 + 2.76496i) q^{46} +(116.835 + 202.364i) q^{47} +(-71.4361 + 123.731i) q^{49} +(47.9640 - 99.2591i) q^{50} +(196.656 - 155.971i) q^{52} +310.412i q^{53} -667.782 q^{55} +(337.780 + 366.976i) q^{56} +(393.448 + 190.122i) q^{58} +(613.956 + 354.468i) q^{59} +(-747.786 + 431.734i) q^{61} +(-627.564 + 46.1873i) q^{62} +(463.060 - 218.448i) q^{64} +(-200.882 - 347.938i) q^{65} +(4.78278 + 2.76134i) q^{67} +(350.585 - 886.313i) q^{68} +(660.231 - 448.849i) q^{70} +61.9318 q^{71} +273.216 q^{73} +(402.871 - 273.886i) q^{74} +(-535.709 - 211.902i) q^{76} +(-995.490 - 574.746i) q^{77} +(194.002 + 336.022i) q^{79} +(-237.380 - 784.408i) q^{80} +(-344.666 + 25.3667i) q^{82} +(-677.357 + 391.072i) q^{83} +(-1321.25 - 762.821i) q^{85} +(-130.093 - 62.8635i) q^{86} +(-868.204 + 799.131i) q^{88} +949.710 q^{89} -691.580i q^{91} +(66.2085 + 83.4790i) q^{92} +(287.557 - 595.085i) q^{94} +(-461.068 + 798.593i) q^{95} +(-85.8899 - 148.766i) q^{97} +(403.014 - 29.6609i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8	\( 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 20 q^{10} + 10 q^{14} - q^{16} + 8 q^{17} + 52 q^{20} - 17 q^{22} - 274 q^{23} + 648 q^{25} - 368 q^{26} + 124 q^{28} - 2 q^{31} - 259 q^{32} + 189 q^{34} - 319 q^{38} + 214 q^{40} + 22 q^{41} - 282 q^{44} - 24 q^{46} + 942 q^{47} - 1080 q^{49} - 53 q^{50} - 588 q^{52} - 508 q^{55} + 502 q^{56} + 280 q^{58} - 1744 q^{62} + 410 q^{64} + 502 q^{65} - 1149 q^{68} - 586 q^{70} + 3984 q^{71} - 8 q^{73} - 1778 q^{74} + 621 q^{76} - 2 q^{79} - 4704 q^{80} + 714 q^{82} + 2923 q^{86} - 533 q^{88} + 856 q^{89} - 3342 q^{92} + 1518 q^{94} + 2792 q^{95} - 2 q^{97} + 6414 q^{98}+O(q^{100}) \) 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 20 * q^10 + 10 * q^14 - q^16 + 8 * q^17 + 52 * q^20 - 17 * q^22 - 274 * q^23 + 648 * q^25 - 368 * q^26 + 124 * q^28 - 2 * q^31 - 259 * q^32 + 189 * q^34 - 319 * q^38 + 214 * q^40 + 22 * q^41 - 282 * q^44 - 24 * q^46 + 942 * q^47 - 1080 * q^49 - 53 * q^50 - 588 * q^52 - 508 * q^55 + 502 * q^56 + 280 * q^58 - 1744 * q^62 + 410 * q^64 + 502 * q^65 - 1149 * q^68 - 586 * q^70 + 3984 * q^71 - 8 * q^73 - 1778 * q^74 + 621 * q^76 - 2 * q^79 - 4704 * q^80 + 714 * q^82 + 2923 * q^86 - 533 * q^88 + 856 * q^89 - 3342 * q^92 + 1518 * q^94 + 2792 * q^95 - 2 * q^97 + 6414 * q^98

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