LMFDB - Embedded newform 216.3.u.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, degree $6$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42216 - 2.64149i) q^{3} +(3.87609 - 4.61934i) q^{5} +(8.68461 + 3.16094i) q^{7} +(-4.95492 - 7.51324i) q^{9} +O(q^{10})$	\(q+(1.42216 - 2.64149i) q^{3} +(3.87609 - 4.61934i) q^{5} +(8.68461 + 3.16094i) q^{7} +(-4.95492 - 7.51324i) q^{9} +(-3.73812 - 4.45492i) q^{11} +(-3.03632 + 17.2198i) q^{13} +(-6.68952 - 16.8081i) q^{15} +(12.6699 + 7.31497i) q^{17} +(-13.4872 - 23.3604i) q^{19} +(20.7005 - 18.4449i) q^{21} +(-4.13623 - 11.3642i) q^{23} +(-1.97306 - 11.1898i) q^{25} +(-26.8928 + 2.40332i) q^{27} +(-13.1052 + 2.31081i) q^{29} +(31.1665 - 11.3437i) q^{31} +(-17.0838 + 3.53859i) q^{33} +(48.2638 - 27.8651i) q^{35} +(-18.9955 + 32.9011i) q^{37} +(41.1678 + 32.5098i) q^{39} +(45.8030 + 8.07631i) q^{41} +(-56.7271 + 47.5997i) q^{43} +(-53.9120 - 6.23352i) q^{45} +(22.0464 - 60.5721i) q^{47} +(27.8948 + 23.4065i) q^{49} +(37.3410 - 23.0643i) q^{51} +58.2853i q^{53} -35.0681 q^{55} +(-80.8873 + 2.40387i) q^{57} +(13.9389 - 16.6118i) q^{59} +(-35.0222 - 12.7470i) q^{61} +(-19.2826 - 80.9118i) q^{63} +(67.7753 + 80.7714i) q^{65} +(-19.0195 + 107.865i) q^{67} +(-35.9008 - 5.23591i) q^{69} +(45.4591 + 26.2458i) q^{71} +(58.0979 + 100.629i) q^{73} +(-32.3637 - 10.7019i) q^{75} +(-18.3824 - 50.5053i) q^{77} +(4.90201 + 27.8007i) q^{79} +(-31.8976 + 74.4550i) q^{81} +(57.8743 - 10.2048i) q^{83} +(82.9001 - 30.1732i) q^{85} +(-12.5338 + 37.9037i) q^{87} +(-150.590 + 86.9433i) q^{89} +(-80.8001 + 139.950i) q^{91} +(14.3596 - 98.4583i) q^{93} +(-160.187 - 28.2454i) q^{95} +(55.2376 - 46.3499i) q^{97} +(-14.9488 + 50.1592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.42216	−	2.64149i	0.474054	−	0.880496i
$3$	1.42216	−	2.64149i	0.474054	−	0.880496i
$4$		0			0
$5$	3.87609	−	4.61934i	0.775218	−	0.923869i	−0.223489	−	0.974706i	$-0.571745\pi$
$5$	3.87609	−	4.61934i	0.775218	−	0.923869i	0.998707	+	0.0508376i	$0.0161891\pi$
$6$		0			0
$7$	8.68461	+	3.16094i	1.24066	+	0.451563i	0.877235	−	0.480061i	$-0.159385\pi$
$7$	8.68461	+	3.16094i	1.24066	+	0.451563i	0.363424	+	0.931624i	$0.381608\pi$
$8$		0			0
$9$	−4.95492	−	7.51324i	−0.550547	−	0.834804i
$10$		0			0
$11$	−3.73812	−	4.45492i	−0.339829	−	0.404993i	0.568881	−	0.822420i	$-0.307376\pi$
$11$	−3.73812	−	4.45492i	−0.339829	−	0.404993i	−0.908711	+	0.417427i	$0.862932\pi$
$12$		0			0
$13$	−3.03632	+	17.2198i	−0.233563	+	1.32460i	0.612056	+	0.790815i	$0.290343\pi$
$13$	−3.03632	+	17.2198i	−0.233563	+	1.32460i	−0.845619	+	0.533787i	$0.820768\pi$
$14$		0			0
$15$	−6.68952	−	16.8081i	−0.445968	−	1.12054i
$16$		0			0
$17$	12.6699	+	7.31497i	0.745288	+	0.430292i	0.823989	−	0.566606i	$-0.191744\pi$
$17$	12.6699	+	7.31497i	0.745288	+	0.430292i	−0.0787006	+	0.996898i	$0.525077\pi$
$18$		0			0
$19$	−13.4872	−	23.3604i	−0.709851	−	1.22950i	−0.964912	−	0.262573i	$-0.915429\pi$
$19$	−13.4872	−	23.3604i	−0.709851	−	1.22950i	0.255062	−	0.966925i	$-0.417904\pi$
$20$		0			0
$21$	20.7005	−	18.4449i	0.985738	−	0.878330i
$22$		0			0
$23$	−4.13623	−	11.3642i	−0.179836	−	0.494095i	0.816718	−	0.577036i	$-0.195791\pi$
$23$	−4.13623	−	11.3642i	−0.179836	−	0.494095i	−0.996554	+	0.0829410i	$0.973569\pi$
$24$		0			0
$25$	−1.97306	−	11.1898i	−0.0789225	−	0.447592i
$26$		0			0
$27$	−26.8928	+	2.40332i	−0.996031	+	0.0890120i
$28$		0			0
$29$	−13.1052	+	2.31081i	−0.451905	+	0.0796830i	−0.394968	−	0.918695i	$-0.629244\pi$
$29$	−13.1052	+	2.31081i	−0.451905	+	0.0796830i	−0.0569365	+	0.998378i	$0.518133\pi$
$30$		0			0
$31$	31.1665	−	11.3437i	1.00537	−	0.365925i	0.213717	−	0.976896i	$-0.431443\pi$
$31$	31.1665	−	11.3437i	1.00537	−	0.365925i	0.791653	+	0.610971i	$0.209221\pi$
$32$		0			0
$33$	−17.0838	+	3.53859i	−0.517692	+	0.107230i
$34$		0			0
$35$	48.2638	−	27.8651i	1.37897	−	0.796147i
$36$		0			0
$37$	−18.9955	+	32.9011i	−0.513391	+	0.889219i	0.486488	+	0.873687i	$0.338278\pi$
$37$	−18.9955	+	32.9011i	−0.513391	+	0.889219i	−0.999879	+	0.0155324i	$0.995056\pi$
$38$		0			0
$39$	41.1678	+	32.5098i	1.05559	+	0.833584i
$40$		0			0
$41$	45.8030	+	8.07631i	1.11715	+	0.196983i	0.701588	−	0.712583i	$-0.252475\pi$
$41$	45.8030	+	8.07631i	1.11715	+	0.196983i	0.415559	+	0.909566i	$0.363586\pi$
$42$		0			0
$43$	−56.7271	+	47.5997i	−1.31924	+	1.10697i	−0.332769	+	0.943008i	$0.607983\pi$
$43$	−56.7271	+	47.5997i	−1.31924	+	1.10697i	−0.986467	+	0.163962i	$0.947573\pi$
$44$		0			0
$45$	−53.9120	−	6.23352i	−1.19804	−	0.138523i
$46$		0			0
$47$	22.0464	−	60.5721i	0.469073	−	1.28877i	−0.449417	−	0.893322i	$-0.648368\pi$
$47$	22.0464	−	60.5721i	0.469073	−	1.28877i	0.918490	−	0.395445i	$-0.129410\pi$
$48$		0			0
$49$	27.8948	+	23.4065i	0.569281	+	0.477684i
$50$		0			0
$51$	37.3410	−	23.0643i	0.732177	−	0.452242i
$52$		0			0
$53$			58.2853i			1.09972i	0.835256	+	0.549861i	$0.185319\pi$
$53$			58.2853i			1.09972i	−0.835256	+	0.549861i	$0.814681\pi$
$54$		0			0
$55$	−35.0681			−0.637602
$56$		0			0
$57$	−80.8873	+	2.40387i	−1.41907	+	0.0421731i
$58$		0			0
$59$	13.9389	−	16.6118i	0.236253	−	0.281556i	−0.634871	−	0.772618i	$-0.718947\pi$
$59$	13.9389	−	16.6118i	0.236253	−	0.281556i	0.871124	+	0.491062i	$0.163391\pi$
$60$		0			0
$61$	−35.0222	−	12.7470i	−0.574134	−	0.208968i	0.0386029	−	0.999255i	$-0.487709\pi$
$61$	−35.0222	−	12.7470i	−0.574134	−	0.208968i	−0.612737	+	0.790287i	$0.709931\pi$
$62$		0			0
$63$	−19.2826	−	80.9118i	−0.306074	−	1.28431i
$64$		0			0
$65$	67.7753	+	80.7714i	1.04270	+	1.24264i
$66$		0			0
$67$	−19.0195	+	107.865i	−0.283873	+	1.60993i	0.425408	+	0.905002i	$0.360130\pi$
$67$	−19.0195	+	107.865i	−0.283873	+	1.60993i	−0.709282	+	0.704925i	$0.750981\pi$
$68$		0			0
$69$	−35.9008	−	5.23591i	−0.520301	−	0.0758828i
$70$		0			0
$71$	45.4591	+	26.2458i	0.640269	+	0.369659i	0.784718	−	0.619853i	$-0.212808\pi$
$71$	45.4591	+	26.2458i	0.640269	+	0.369659i	−0.144449	+	0.989512i	$0.546141\pi$
$72$		0			0
$73$	58.0979	+	100.629i	0.795862	+	1.37847i	0.922290	+	0.386498i	$0.126315\pi$
$73$	58.0979	+	100.629i	0.795862	+	1.37847i	−0.126428	+	0.991976i	$0.540351\pi$
$74$		0			0
$75$	−32.3637	−	10.7019i	−0.431516	−	0.142692i
$76$		0			0
$77$	−18.3824	−	50.5053i	−0.238733	−	0.655912i
$78$		0			0
$79$	4.90201	+	27.8007i	0.0620508	+	0.351907i	0.999987	+	0.00509958i	$0.00162325\pi$
$79$	4.90201	+	27.8007i	0.0620508	+	0.351907i	−0.937936	+	0.346808i	$0.887266\pi$
$80$		0			0
$81$	−31.8976	+	74.4550i	−0.393797	+	0.919197i
$82$		0			0
$83$	57.8743	−	10.2048i	0.697280	−	0.122949i	0.186238	−	0.982505i	$-0.440371\pi$
$83$	57.8743	−	10.2048i	0.697280	−	0.122949i	0.511043	+	0.859555i	$0.329259\pi$
$84$		0			0
$85$	82.9001	−	30.1732i	0.975295	−	0.354978i
$86$		0			0
$87$	−12.5338	+	37.9037i	−0.144066	+	0.435674i
$88$		0			0
$89$	−150.590	+	86.9433i	−1.69203	+	0.976891i	−0.739145	+	0.673547i	$0.764770\pi$
$89$	−150.590	+	86.9433i	−1.69203	+	0.976891i	−0.952881	+	0.303345i	$0.901897\pi$
$90$		0			0
$91$	−80.8001	+	139.950i	−0.887913	+	1.53791i
$92$		0			0
$93$	14.3596	−	98.4583i	0.154404	−	1.05869i
$94$		0			0
$95$	−160.187	−	28.2454i	−1.68618	−	0.297320i
$96$		0			0
$97$	55.2376	−	46.3499i	0.569460	−	0.477834i	−0.312007	−	0.950080i	$-0.601001\pi$
$97$	55.2376	−	46.3499i	0.569460	−	0.477834i	0.881467	+	0.472246i	$0.156557\pi$
$98$		0			0
$99$	−14.9488	+	50.1592i	−0.150998	+	0.506659i
$100$		0			0
$101$	60.7064	−	166.789i	0.601053	−	1.65138i	−0.148092	−	0.988974i	$-0.547313\pi$
$101$	60.7064	−	166.789i	0.601053	−	1.65138i	0.749145	−	0.662406i	$-0.230465\pi$
$102$		0			0
$103$	−87.2408	−	73.2037i	−0.846998	−	0.710716i	0.112128	−	0.993694i	$-0.464233\pi$
$103$	−87.2408	−	73.2037i	−0.846998	−	0.710716i	−0.959126	+	0.282978i	$0.908678\pi$
$104$		0			0
$105$	−4.96651	−	167.117i	−0.0473001	−	1.59159i
$106$		0			0
$107$			53.6016i			0.500950i	0.968123	+	0.250475i	$0.0805868\pi$
$107$			53.6016i			0.500950i	−0.968123	+	0.250475i	$0.919413\pi$
$108$		0			0
$109$	51.1559			0.469320			0.234660	−	0.972078i	$-0.424602\pi$
$109$	51.1559			0.469320			0.234660	+	0.972078i	$0.424602\pi$
$110$		0			0
$111$	59.8933	+	96.9670i	0.539579	+	0.873576i
$112$		0			0
$113$	−65.0619	+	77.5377i	−0.575769	+	0.686175i	−0.972804	−	0.231629i	$-0.925595\pi$
$113$	−65.0619	+	77.5377i	−0.575769	+	0.686175i	0.397035	+	0.917803i	$0.370039\pi$
$114$		0			0
$115$	−68.5275	−	24.9420i	−0.595892	−	0.216887i
$116$		0			0
$117$	144.421	−	62.5102i	1.23437	−	0.534276i
$118$		0			0
$119$	86.9110	+	103.577i	0.730345	+	0.870391i
$120$		0			0
$121$	15.1387	−	85.8556i	0.125113	−	0.709551i
$122$		0			0
$123$	86.4728	−	109.502i	0.703031	−	0.890263i
$124$		0			0
$125$	71.2188	+	41.1182i	0.569750	+	0.328945i
$126$		0			0
$127$	5.92923	+	10.2697i	0.0466869	+	0.0808640i	0.888424	−	0.459023i	$-0.151800\pi$
$127$	5.92923	+	10.2697i	0.0466869	+	0.0808640i	−0.841738	+	0.539887i	$0.818467\pi$
$128$		0			0
$129$	45.0590	+	217.538i	0.349295	+	1.68634i
$130$		0			0
$131$	−32.4567	−	89.1740i	−0.247761	−	0.680718i	−0.999768	−	0.0215619i	$-0.993136\pi$
$131$	−32.4567	−	89.1740i	−0.247761	−	0.680718i	0.752007	−	0.659156i	$-0.229086\pi$
$132$		0			0
$133$	−43.2898	−	245.509i	−0.325487	−	1.84593i
$134$		0			0
$135$	−93.1372	+	133.543i	−0.689905	+	0.989205i
$136$		0			0
$137$	155.029	−	27.3358i	1.13160	−	0.199531i	0.423671	−	0.905816i	$-0.360741\pi$
$137$	155.029	−	27.3358i	1.13160	−	0.199531i	0.707928	+	0.706285i	$0.249630\pi$
$138$		0			0
$139$	114.933	−	41.8322i	0.826856	−	0.300951i	0.106288	−	0.994335i	$-0.466103\pi$
$139$	114.933	−	41.8322i	0.826856	−	0.300951i	0.720568	+	0.693384i	$0.243881\pi$
$140$		0			0
$141$	−128.647	−	144.379i	−0.912389	−	1.02396i
$142$		0			0
$143$	88.0631	−	50.8433i	0.615826	−	0.355547i
$144$		0			0
$145$	−40.1227	+	69.4945i	−0.276708	+	0.479272i
$146$		0			0
$147$	101.499	−	40.3959i	0.690469	−	0.274802i
$148$		0			0
$149$	−111.780	−	19.7098i	−0.750199	−	0.132280i	−0.214541	−	0.976715i	$-0.568825\pi$
$149$	−111.780	−	19.7098i	−0.750199	−	0.132280i	−0.535658	+	0.844435i	$0.679937\pi$
$150$		0			0
$151$	154.165	−	129.360i	1.02096	−	0.856689i	0.0312141	−	0.999513i	$-0.490063\pi$
$151$	154.165	−	129.360i	1.02096	−	0.856689i	0.989748	+	0.142824i	$0.0456182\pi$
$152$		0			0
$153$	−7.81920	−	131.437i	−0.0511059	−	0.859066i
$154$		0			0
$155$	68.4037	−	187.938i	0.441314	−	1.21250i
$156$		0			0
$157$	124.129	+	104.156i	0.790627	+	0.663415i	0.945901	−	0.324456i	$-0.105181\pi$
$157$	124.129	+	104.156i	0.790627	+	0.663415i	−0.155273	+	0.987872i	$0.549626\pi$
$158$		0			0
$159$	153.960	+	82.8910i	0.968301	+	0.521327i
$160$		0			0
$161$		−	111.768i		−	0.694211i
$162$		0			0
$163$	−90.9539			−0.558000			−0.279000	−	0.960291i	$-0.590003\pi$
$163$	−90.9539			−0.558000			−0.279000	+	0.960291i	$0.590003\pi$
$164$		0			0
$165$	−49.8725	+	92.6320i	−0.302258	+	0.561406i
$166$		0			0
$167$	40.9931	−	48.8537i	0.245468	−	0.292537i	−0.629217	−	0.777230i	$-0.716624\pi$
$167$	40.9931	−	48.8537i	0.245468	−	0.292537i	0.874684	+	0.484693i	$0.161069\pi$
$168$		0			0
$169$	−128.495	−	46.7684i	−0.760326	−	0.276736i
$170$		0			0
$171$	−108.685	+	217.081i	−0.635584	+	1.26948i
$172$		0			0
$173$	−76.1711	−	90.7772i	−0.440295	−	0.524723i	0.499568	−	0.866275i	$-0.333492\pi$
$173$	−76.1711	−	90.7772i	−0.440295	−	0.524723i	−0.939863	+	0.341551i	$0.889048\pi$
$174$		0			0
$175$	18.2350	−	103.416i	0.104200	−	0.590947i
$176$		0			0
$177$	−24.0564	−	60.4442i	−0.135912	−	0.341492i
$178$		0			0
$179$	−137.341	−	79.2939i	−0.767268	−	0.442983i	0.0646309	−	0.997909i	$-0.479413\pi$
$179$	−137.341	−	79.2939i	−0.767268	−	0.442983i	−0.831899	+	0.554927i	$0.812746\pi$
$180$		0			0
$181$	−122.997	−	213.037i	−0.679542	−	1.17700i	−0.975119	−	0.221683i	$-0.928845\pi$
$181$	−122.997	−	213.037i	−0.679542	−	1.17700i	0.295577	−	0.955319i	$-0.404488\pi$
$182$		0			0
$183$	−83.4783	+	74.3823i	−0.456165	+	0.406461i
$184$		0			0
$185$	78.3534	+	215.274i	0.423532	+	1.16365i
$186$		0			0
$187$	−14.7740	−	83.7877i	−0.0790055	−	0.448062i
$188$		0			0
$189$	−241.151	−	64.1347i	−1.27593	−	0.339337i
$190$		0			0
$191$	−347.302	+	61.2388i	−1.81834	+	0.320622i	−0.975908	−	0.218184i	$-0.929987\pi$
$191$	−347.302	+	61.2388i	−1.81834	+	0.320622i	−0.842430	+	0.538806i	$0.818876\pi$
$192$		0			0
$193$	−72.1123	+	26.2467i	−0.373639	+	0.135993i	−0.522012	−	0.852938i	$-0.674818\pi$
$193$	−72.1123	+	26.2467i	−0.373639	+	0.135993i	0.148373	+	0.988931i	$0.452596\pi$
$194$		0			0
$195$	309.744	−	64.1576i	1.58843	−	0.329013i
$196$		0			0
$197$	−119.056	+	68.7370i	−0.604345	+	0.348919i	−0.770749	−	0.637139i	$-0.780118\pi$
$197$	−119.056	+	68.7370i	−0.604345	+	0.348919i	0.166404	+	0.986058i	$0.446784\pi$
$198$		0			0
$199$	−141.055	+	244.314i	−0.708818	+	1.22771i	0.256478	+	0.966550i	$0.417438\pi$
$199$	−141.055	+	244.314i	−0.708818	+	1.22771i	−0.965296	+	0.261159i	$0.915895\pi$
$200$		0			0
$201$	257.876	+	203.641i	1.28296	+	1.01314i
$202$		0			0
$203$	−121.118	−	21.3564i	−0.596642	−	0.105204i
$204$		0			0
$205$	214.844	−	180.276i	1.04802	−	0.879393i
$206$		0			0
$207$	−64.8873	+	87.3851i	−0.313465	+	0.422150i
$208$		0			0
$209$	−53.6523	+	147.408i	−0.256710	+	0.705304i
$210$		0			0
$211$	175.868	+	147.571i	0.833499	+	0.699388i	0.956091	−	0.293069i	$-0.0946765\pi$
$211$	175.868	+	147.571i	0.833499	+	0.699388i	−0.122593	+	0.992457i	$0.539121\pi$
$212$		0			0
$213$	133.978	−	82.7539i	0.629005	−	0.388516i
$214$		0			0
$215$			446.543i			2.07694i
$216$		0			0
$217$	306.525			1.41256
$218$		0			0
$219$	348.434	−	10.3550i	1.59102	−	0.0472832i
$220$		0			0
$221$	−164.432	+	195.963i	−0.744038	+	0.886710i
$222$		0			0
$223$	−108.648	−	39.5446i	−0.487210	−	0.177330i	0.0867224	−	0.996233i	$-0.472361\pi$
$223$	−108.648	−	39.5446i	−0.487210	−	0.177330i	−0.573933	+	0.818902i	$0.694583\pi$
$224$		0			0
$225$	−74.2953	+	70.2686i	−0.330201	+	0.312305i
$226$		0			0
$227$	−51.4335	−	61.2961i	−0.226579	−	0.270027i	0.640763	−	0.767739i	$-0.278618\pi$
$227$	−51.4335	−	61.2961i	−0.226579	−	0.270027i	−0.867342	+	0.497712i	$0.834174\pi$
$228$		0			0
$229$	3.71480	−	21.0677i	0.0162218	−	0.0919986i	−0.975622	−	0.219458i	$-0.929571\pi$
$229$	3.71480	−	21.0677i	0.0162218	−	0.0919986i	0.991844	+	0.127459i	$0.0406822\pi$
$230$		0			0
$231$	−159.552	−	23.2697i	−0.690700	−	0.100734i
$232$		0			0
$233$	14.0254	+	8.09754i	0.0601946	+	0.0347534i	0.529795	−	0.848126i	$-0.322269\pi$
$233$	14.0254	+	8.09754i	0.0601946	+	0.0347534i	−0.469601	+	0.882879i	$0.655602\pi$
$234$		0			0
$235$	−194.349	−	336.623i	−0.827018	−	1.43244i
$236$		0			0
$237$	80.4066	+	26.5884i	0.339268	+	0.112187i
$238$		0			0
$239$	−137.014	−	376.442i	−0.573278	−	1.57507i	−0.799291	−	0.600945i	$-0.794791\pi$
$239$	−137.014	−	376.442i	−0.573278	−	1.57507i	0.226012	−	0.974124i	$-0.427431\pi$
$240$		0			0
$241$	−5.14417	−	29.1740i	−0.0213451	−	0.121054i	0.972273	−	0.233847i	$-0.0751315\pi$
$241$	−5.14417	−	29.1740i	−0.0213451	−	0.121054i	−0.993619	+	0.112793i	$0.964020\pi$
$242$		0			0
$243$	151.309	+	190.144i	0.622669	+	0.782486i
$244$		0			0
$245$	216.245	−	38.1299i	0.882635	−	0.155632i
$246$		0			0
$247$	443.214	−	161.317i	1.79439	−	0.653104i
$248$		0			0
$249$	55.3506	−	167.387i	0.222292	−	0.672237i
$250$		0			0
$251$	−90.4985	+	52.2493i	−0.360552	+	0.208165i	−0.669323	−	0.742972i	$-0.733416\pi$
$251$	−90.4985	+	52.2493i	−0.360552	+	0.208165i	0.308771	+	0.951136i	$0.400082\pi$
$252$		0			0
$253$	−35.1649	+	60.9073i	−0.138992	+	0.240740i
$254$		0			0
$255$	38.1952	−	261.891i	0.149785	−	1.02702i
$256$		0			0
$257$	−348.422	−	61.4362i	−1.35573	−	0.239051i	−0.551898	−	0.833911i	$-0.686096\pi$
$257$	−348.422	−	61.4362i	−1.35573	−	0.239051i	−0.803829	+	0.594860i	$0.797208\pi$
$258$		0			0
$259$	−268.967	+	225.690i	−1.03848	+	0.871390i
$260$		0			0
$261$	82.2970	+	87.0129i	0.315314	+	0.333383i
$262$		0			0
$263$	−75.3516	+	207.027i	−0.286508	+	0.787174i	0.710041	+	0.704161i	$0.248677\pi$
$263$	−75.3516	+	207.027i	−0.286508	+	0.787174i	−0.996548	+	0.0830132i	$0.973546\pi$
$264$		0			0
$265$	269.240	+	225.919i	1.01600	+	0.852524i
$266$		0			0
$267$	15.4962	+	521.430i	0.0580383	+	1.95292i
$268$		0			0
$269$			455.087i			1.69177i	0.533362	+	0.845887i	$0.320928\pi$
$269$			455.087i			1.69177i	−0.533362	+	0.845887i	$0.679072\pi$
$270$		0			0
$271$	62.9950			0.232454			0.116227	−	0.993223i	$-0.462920\pi$
$271$	62.9950			0.232454			0.116227	+	0.993223i	$0.462920\pi$
$272$		0			0
$273$	254.765	+	412.464i	0.933206	+	1.51086i
$274$		0			0
$275$	−42.4741	+	50.6187i	−0.154451	+	0.184068i
$276$		0			0
$277$	102.784	+	37.4101i	0.371060	+	0.135055i	0.520818	−	0.853668i	$-0.325627\pi$
$277$	102.784	+	37.4101i	0.371060	+	0.135055i	−0.149758	+	0.988723i	$0.547849\pi$
$278$		0			0
$279$	−239.655	−	177.954i	−0.858978	−	0.637829i
$280$		0			0
$281$	−234.849	−	279.883i	−0.835763	−	0.996024i	−0.999954	−	0.00959494i	$-0.996946\pi$
$281$	−234.849	−	279.883i	−0.835763	−	0.996024i	0.164191	−	0.986429i	$-0.447499\pi$
$282$		0			0
$283$	54.3675	−	308.333i	0.192111	−	1.08952i	−0.724362	−	0.689420i	$-0.757865\pi$
$283$	54.3675	−	308.333i	0.192111	−	1.08952i	0.916473	−	0.400097i	$-0.131023\pi$
$284$		0			0
$285$	−302.422	+	382.964i	−1.06113	+	1.34373i
$286$		0			0
$287$	372.253	+	214.920i	1.29705	+	0.748851i
$288$		0			0
$289$	−37.4824	−	64.9214i	−0.129697	−	0.224642i
$290$		0			0
$291$	−43.8759	−	211.826i	−0.150776	−	0.727926i
$292$		0			0
$293$	−16.2869	−	44.7480i	−0.0555868	−	0.152724i	0.908791	−	0.417251i	$-0.137006\pi$
$293$	−16.2869	−	44.7480i	−0.0555868	−	0.152724i	−0.964378	+	0.264527i	$0.914784\pi$
$294$		0			0
$295$	−22.7070	−	128.778i	−0.0769727	−	0.436534i
$296$		0			0
$297$	111.235	+	110.822i	0.374530	+	0.373136i
$298$		0			0
$299$	208.248	−	36.7198i	0.696483	−	0.122809i
$300$		0			0
$301$	−643.113	+	234.074i	−2.13659	+	0.777655i
$302$		0			0
$303$	−354.238	−	397.556i	−1.16910	−	1.31207i
$304$		0			0
$305$	−194.632	+	112.371i	−0.638138	+	0.368429i
$306$		0			0
$307$	−146.548	+	253.828i	−0.477354	+	0.826801i	−0.999663	−	0.0259552i	$-0.991737\pi$
$307$	−146.548	+	253.828i	−0.477354	+	0.826801i	0.522309	+	0.852756i	$0.325071\pi$
$308$		0			0
$309$	−317.437	+	126.338i	−1.02731	+	0.408861i
$310$		0			0
$311$	68.8635	+	12.1425i	0.221426	+	0.0390434i	0.283260	−	0.959043i	$-0.408584\pi$
$311$	68.8635	+	12.1425i	0.221426	+	0.0390434i	−0.0618344	+	0.998086i	$0.519695\pi$
$312$		0			0
$313$	−477.289	+	400.493i	−1.52488	+	1.27953i	−0.700179	+	0.713967i	$0.746897\pi$
$313$	−477.289	+	400.493i	−1.52488	+	1.27953i	−0.824705	+	0.565563i	$0.808659\pi$
$314$		0			0
$315$	−448.501	−	224.548i	−1.42381	−	0.712852i
$316$		0			0
$317$	105.608	−	290.156i	0.333148	−	0.915317i	−0.654139	−	0.756374i	$-0.726969\pi$
$317$	105.608	−	290.156i	0.333148	−	0.915317i	0.987288	−	0.158943i	$-0.0508087\pi$
$318$		0			0
$319$	59.2835	+	49.7447i	0.185842	+	0.155940i
$320$		0			0
$321$	141.588	+	76.2301i	0.441084	+	0.237477i
$322$		0			0
$323$		−	394.633i		−	1.22177i
$324$		0			0
$325$	198.677			0.611315
$326$		0			0
$327$	72.7518	−	135.128i	0.222483	−	0.413234i
$328$		0			0
$329$	382.929	−	456.358i	1.16392	−	1.38711i
$330$		0			0
$331$	144.865	+	52.7264i	0.437657	+	0.159294i	0.551446	−	0.834211i	$-0.314076\pi$
$331$	144.865	+	52.7264i	0.437657	+	0.159294i	−0.113788	+	0.993505i	$0.536299\pi$
$332$		0			0
$333$	341.315	−	20.3048i	1.02497	−	0.0609755i
$334$		0			0
$335$	424.545	+	505.953i	1.26730	+	1.51031i
$336$		0			0
$337$	38.0585	−	215.840i	0.112933	−	0.640476i	−0.874820	−	0.484449i	$-0.839020\pi$
$337$	38.0585	−	215.840i	0.112933	−	0.640476i	0.987753	−	0.156027i	$-0.0498687\pi$
$338$		0			0
$339$	112.287	+	282.131i	0.331229	+	0.832246i
$340$		0			0
$341$	−167.039	−	96.4401i	−0.489851	−	0.282816i
$342$		0			0
$343$	−58.1594	−	100.735i	−0.169561	−	0.293688i
$344$		0			0
$345$	−163.341	+	145.543i	−0.473452	+	0.421864i
$346$		0			0
$347$	−155.746	−	427.908i	−0.448835	−	1.23316i	−0.933536	−	0.358483i	$-0.883294\pi$
$347$	−155.746	−	427.908i	−0.448835	−	1.23316i	0.484701	−	0.874680i	$-0.338928\pi$
$348$		0			0
$349$	−74.8696	−	424.606i	−0.214526	−	1.21664i	−0.881727	−	0.471760i	$-0.843619\pi$
$349$	−74.8696	−	424.606i	−0.214526	−	1.21664i	0.667201	−	0.744878i	$-0.267492\pi$
$350$		0			0
$351$	40.2704	−	470.387i	0.114730	−	1.34013i
$352$		0			0
$353$	232.711	−	41.0332i	0.659238	−	0.116241i	0.165986	−	0.986128i	$-0.446919\pi$
$353$	232.711	−	41.0332i	0.659238	−	0.116241i	0.493252	+	0.869887i	$0.335808\pi$
$354$		0			0
$355$	297.442	−	108.260i	0.837865	−	0.304958i
$356$		0			0
$357$	397.198	−	82.2720i	1.11260	−	0.230454i
$358$		0			0
$359$	237.859	−	137.328i	0.662560	−	0.382529i	−0.130692	−	0.991423i	$-0.541720\pi$
$359$	237.859	−	137.328i	0.662560	−	0.382529i	0.793252	+	0.608894i	$0.208386\pi$
$360$		0			0
$361$	−183.307	+	317.497i	−0.507776	+	0.879494i
$362$		0			0
$363$	−205.257	−	162.089i	−0.565446	−	0.446527i
$364$		0			0
$365$	690.031	+	121.671i	1.89050	+	0.333345i
$366$		0			0
$367$	189.204	−	158.761i	0.515543	−	0.432592i	−0.347532	−	0.937668i	$-0.612980\pi$
$367$	189.204	−	158.761i	0.515543	−	0.432592i	0.863075	+	0.505076i	$0.168536\pi$
$368$		0			0
$369$	−166.271	−	384.147i	−0.450599	−	1.04105i
$370$		0			0
$371$	−184.236	+	506.185i	−0.496594	+	1.36438i
$372$		0			0
$373$	−101.990	−	85.5794i	−0.273431	−	0.229435i	0.495753	−	0.868464i	$-0.334892\pi$
$373$	−101.990	−	85.5794i	−0.273431	−	0.229435i	−0.769183	+	0.639028i	$0.779337\pi$
$374$		0			0
$375$	209.898	−	129.647i	0.559727	−	0.345725i
$376$		0			0
$377$		−	232.686i		−	0.617205i
$378$		0			0
$379$	69.1281			0.182396			0.0911980	−	0.995833i	$-0.470930\pi$
$379$	69.1281			0.182396			0.0911980	+	0.995833i	$0.470930\pi$
$380$		0			0
$381$	35.5597	−	1.05679i	0.0933325	−	0.00277372i
$382$		0			0
$383$	−118.774	+	141.549i	−0.310114	+	0.369580i	−0.898479	−	0.439016i	$-0.855327\pi$
$383$	−118.774	+	141.549i	−0.310114	+	0.369580i	0.588365	+	0.808595i	$0.299772\pi$
$384$		0			0
$385$	−304.553	−	110.848i	−0.791047	−	0.287918i
$386$		0			0
$387$	638.706	+	190.352i	1.65040	+	0.491865i
$388$		0			0
$389$	−474.288	−	565.234i	−1.21925	−	1.45304i	−0.852502	−	0.522723i	$-0.824916\pi$
$389$	−474.288	−	565.234i	−1.21925	−	1.45304i	−0.366746	−	0.930321i	$-0.619528\pi$
$390$		0			0
$391$	30.7231	−	174.240i	0.0785758	−	0.445626i
$392$		0			0
$393$	−281.711	−	41.0858i	−0.716821	−	0.104544i
$394$		0			0
$395$	147.422	+	85.1139i	0.373219	+	0.215478i
$396$		0			0
$397$	188.882	+	327.153i	0.475774	+	0.824064i	0.999615	−	0.0277519i	$-0.00883483\pi$
$397$	188.882	+	327.153i	0.475774	+	0.824064i	−0.523841	+	0.851816i	$0.675501\pi$
$398$		0			0
$399$	−710.073	−	234.803i	−1.77963	−	0.588479i
$400$		0			0
$401$	139.300	+	382.724i	0.347382	+	0.954425i	0.983191	+	0.182578i	$0.0584443\pi$
$401$	139.300	+	382.724i	0.347382	+	0.954425i	−0.635809	+	0.771846i	$0.719333\pi$
$402$		0			0
$403$	100.705	+	571.124i	0.249887	+	1.41718i
$404$		0			0
$405$	220.295	+	435.940i	0.543939	+	1.07640i
$406$		0			0
$407$	217.579	−	38.3651i	0.534593	−	0.0942632i
$408$		0			0
$409$	−157.151	+	57.1982i	−0.384232	+	0.139849i	−0.526912	−	0.849920i	$-0.676650\pi$
$409$	−157.151	+	57.1982i	−0.384232	+	0.139849i	0.142680	+	0.989769i	$0.454428\pi$
$410$		0			0
$411$	148.269	−	448.383i	0.360752	−	1.09096i
$412$		0			0
$413$	173.563	−	100.207i	0.420250	−	0.242631i
$414$		0			0
$415$	177.186	−	306.896i	0.426955	−	0.739508i
$416$		0			0
$417$	52.9540	−	363.086i	0.126988	−	0.870711i
$418$		0			0
$419$	−293.175	−	51.6947i	−0.699702	−	0.123376i	−0.187530	−	0.982259i	$-0.560048\pi$
$419$	−293.175	−	51.6947i	−0.699702	−	0.123376i	−0.512172	+	0.858883i	$0.671159\pi$
$420$		0			0
$421$	352.567	−	295.839i	0.837452	−	0.702705i	−0.119537	−	0.992830i	$-0.538141\pi$
$421$	352.567	−	295.839i	0.837452	−	0.702705i	0.956989	+	0.290124i	$0.0936967\pi$
$422$		0			0
$423$	−564.331	+	134.490i	−1.33412	+	0.317942i
$424$		0			0
$425$	56.8545	−	156.207i	0.133775	−	0.367545i
$426$		0			0
$427$	−263.861	−	221.406i	−0.617942	−	0.518515i
$428$		0			0
$429$	−9.06199	−	304.925i	−0.0211235	−	0.710781i
$430$		0			0
$431$		−	305.110i		−	0.707911i	−0.935262	−	0.353956i	$-0.884836\pi$
$431$		−	305.110i		−	0.707911i	0.935262	−	0.353956i	$-0.115164\pi$
$432$		0			0
$433$	599.971			1.38562			0.692808	−	0.721123i	$-0.256374\pi$
$433$	599.971			1.38562			0.692808	+	0.721123i	$0.256374\pi$
$434$		0			0
$435$	126.508	+	204.816i	0.290823	+	0.470841i
$436$		0			0
$437$	−209.687	+	249.895i	−0.479832	+	0.571842i
$438$		0			0
$439$	512.437	+	186.512i	1.16728	+	0.424856i	0.851694	−	0.524039i	$-0.175576\pi$
$439$	512.437	+	186.512i	1.16728	+	0.424856i	0.315589	+	0.948896i	$0.397798\pi$
$440$		0			0
$441$	37.6423	−	325.558i	0.0853567	−	0.738226i
$442$		0			0
$443$	−269.567	−	321.258i	−0.608504	−	0.725187i	0.370544	−	0.928815i	$-0.379171\pi$
$443$	−269.567	−	321.258i	−0.608504	−	0.725187i	−0.979048	+	0.203628i	$0.934727\pi$
$444$		0			0
$445$	−182.080	+	1032.63i	−0.409169	+	2.32051i
$446$		0			0
$447$	−211.032	+	267.234i	−0.472107	+	0.597839i
$448$		0			0
$449$	−417.792	−	241.212i	−0.930494	−	0.537221i	−0.0435263	−	0.999052i	$-0.513859\pi$
$449$	−417.792	−	241.212i	−0.930494	−	0.537221i	−0.886968	+	0.461831i	$0.847193\pi$
$450$		0			0
$451$	−135.238	−	234.239i	−0.299863	−	0.519377i
$452$		0			0
$453$	−122.455	−	591.197i	−0.270321	−	1.30507i
$454$		0			0
$455$	333.288	+	915.702i	0.732502	+	2.01253i
$456$		0			0
$457$	34.8091	+	197.412i	0.0761687	+	0.431974i	0.998915	+	0.0465666i	$0.0148280\pi$
$457$	34.8091	+	197.412i	0.0761687	+	0.431974i	−0.922747	+	0.385407i	$0.874061\pi$
$458$		0			0
$459$	−358.310	−	166.270i	−0.780631	−	0.362245i
$460$		0			0
$461$	758.666	−	133.773i	1.64570	−	0.290181i	0.727441	−	0.686170i	$-0.240710\pi$
$461$	758.666	−	133.773i	1.64570	−	0.290181i	0.918255	+	0.395990i	$0.129598\pi$
$462$		0			0
$463$	−200.378	+	72.9318i	−0.432783	+	0.157520i	−0.549220	−	0.835678i	$-0.685075\pi$
$463$	−200.378	+	72.9318i	−0.432783	+	0.157520i	0.116437	+	0.993198i	$0.462853\pi$
$464$		0			0
$465$	−399.154	−	447.965i	−0.858396	−	0.963366i
$466$		0			0
$467$	116.214	−	67.0964i	0.248853	−	0.143675i	−0.370386	−	0.928878i	$-0.620775\pi$
$467$	116.214	−	67.0964i	0.248853	−	0.143675i	0.619239	+	0.785203i	$0.287441\pi$
$468$		0			0
$469$	−506.132	+	876.647i	−1.07917	+	1.86918i
$470$		0			0
$471$	451.658	−	179.757i	0.958934	−	0.381650i
$472$		0			0
$473$	424.106	+	74.7813i	0.896630	+	0.158100i
$474$		0			0
$475$	−234.788	+	197.010i	−0.494290	+	0.414758i
$476$		0			0
$477$	437.911	−	288.799i	0.918053	−	0.605448i
$478$		0			0
$479$	−68.5664	+	188.385i	−0.143145	+	0.393288i	−0.990460	−	0.137804i	$-0.955996\pi$
$479$	−68.5664	+	188.385i	−0.143145	+	0.393288i	0.847315	+	0.531091i	$0.178218\pi$
$480$		0			0
$481$	−508.875	−	426.997i	−1.05795	−	0.887728i
$482$		0			0
$483$	−295.234	−	158.952i	−0.611250	−	0.329093i
$484$		0			0
$485$		−	434.818i		−	0.896532i
$486$		0			0
$487$	311.041			0.638689			0.319344	−	0.947639i	$-0.396537\pi$
$487$	311.041			0.638689			0.319344	+	0.947639i	$0.396537\pi$
$488$		0			0
$489$	−129.351	+	240.254i	−0.264522	+	0.491316i
$490$		0			0
$491$	27.8644	−	33.2075i	0.0567503	−	0.0676324i	−0.736923	−	0.675977i	$-0.763722\pi$
$491$	27.8644	−	33.2075i	0.0567503	−	0.0676324i	0.793673	+	0.608345i	$0.208166\pi$
$492$		0			0
$493$	−182.946	−	66.5867i	−0.371086	−	0.135064i
$494$		0			0
$495$	173.760	+	263.475i	0.351030	+	0.532273i
$496$		0			0
$497$	311.833	+	371.628i	0.627431	+	0.747743i
$498$		0			0
$499$	−145.428	+	824.765i	−0.291440	+	1.65284i	0.389891	+	0.920861i	$0.372513\pi$
$499$	−145.428	+	824.765i	−0.291440	+	1.65284i	−0.681331	+	0.731976i	$0.738598\pi$
$500$		0			0
$501$	−70.7477	−	177.761i	−0.141213	−	0.354812i
$502$		0			0
$503$	−10.3018	−	5.94777i	−0.0204808	−	0.0118246i	0.489725	−	0.871877i	$-0.337097\pi$
$503$	−10.3018	−	5.94777i	−0.0204808	−	0.0118246i	−0.510205	+	0.860053i	$0.670431\pi$
$504$		0			0
$505$	−535.154	−	926.914i	−1.05971	−	1.83547i
$506$		0			0
$507$	−306.279	+	272.906i	−0.604100	+	0.538277i
$508$		0			0
$509$	−90.9444	−	249.868i	−0.178673	−	0.490899i	0.817734	−	0.575596i	$-0.195230\pi$
$509$	−90.9444	−	249.868i	−0.178673	−	0.490899i	−0.996407	+	0.0846971i	$0.973008\pi$
$510$		0			0
$511$	186.477	+	1057.56i	0.364926	+	2.06960i
$512$		0			0
$513$	418.851	+	595.814i	0.816473	+	1.16143i
$514$		0			0
$515$	−676.307	+	119.251i	−1.31322	+	0.231556i
$516$		0			0
$517$	−352.256	+	128.211i	−0.681346	+	0.247990i
$518$		0			0
$519$	−348.114	+	72.1053i	−0.670740	+	0.138931i
$520$		0			0
$521$	578.313	−	333.889i	1.11001	−	0.640863i	0.171175	−	0.985241i	$-0.445244\pi$
$521$	578.313	−	333.889i	1.11001	−	0.640863i	0.938831	+	0.344378i	$0.111910\pi$
$522$		0			0
$523$	−313.577	+	543.132i	−0.599574	+	1.03849i	0.393310	+	0.919406i	$0.371330\pi$
$523$	−313.577	+	543.132i	−0.599574	+	1.03849i	−0.992884	+	0.119087i	$0.962003\pi$
$524$		0			0
$525$	−247.239	−	195.241i	−0.470931	−	0.371888i
$526$		0			0
$527$	477.855	+	84.2587i	0.906745	+	0.159884i
$528$		0			0
$529$	293.201	−	246.025i	0.554255	−	0.465075i
$530$		0			0
$531$	−193.875	−	22.4166i	−0.365112	−	0.0422158i
$532$		0			0
$533$	−278.145	+	764.198i	−0.521849	+	1.43377i
$534$		0			0
$535$	247.604	+	207.765i	0.462812	+	0.388345i
$536$		0			0
$537$	−404.775	+	250.016i	−0.753771	+	0.465579i
$538$		0			0
$539$		−	211.766i		−	0.392886i
$540$		0			0
$541$	604.640			1.11763			0.558817	−	0.829291i	$-0.311255\pi$
$541$	604.640			1.11763			0.558817	+	0.829291i	$0.311255\pi$
$542$		0			0
$543$	−737.657	+	21.9222i	−1.35848	+	0.0403725i
$544$		0			0
$545$	198.285	−	236.307i	0.363825	−	0.433590i
$546$		0			0
$547$	668.376	+	243.269i	1.22189	+	0.444733i	0.870814	−	0.491613i	$-0.163592\pi$
$547$	668.376	+	243.269i	1.22189	+	0.444733i	0.351080	+	0.936346i	$0.385815\pi$
$548$		0			0
$549$	77.7605	+	326.290i	0.141640	+	0.594336i
$550$		0			0
$551$	230.734	+	274.978i	0.418755	+	0.499053i
$552$		0			0
$553$	−45.3042	+	256.933i	−0.0819245	+	0.464617i
$554$		0			0
$555$	680.076	+	99.1850i	1.22536	+	0.178712i
$556$		0			0
$557$	−260.694	−	150.512i	−0.468032	−	0.270218i	0.247384	−	0.968918i	$-0.420429\pi$
$557$	−260.694	−	150.512i	−0.468032	−	0.270218i	−0.715415	+	0.698699i	$0.753763\pi$
$558$		0			0
$559$	−647.417	−	1121.36i	−1.15817	−	2.00601i
$560$		0			0
$561$	−242.335	−	80.1341i	−0.431970	−	0.142842i
$562$		0			0
$563$	114.803	+	315.419i	0.203913	+	0.560247i	0.998925	−	0.0463465i	$-0.0147578\pi$
$563$	114.803	+	315.419i	0.203913	+	0.560247i	−0.795012	+	0.606593i	$0.792536\pi$
$564$		0			0
$565$	105.988	+	601.087i	0.187589	+	1.06387i
$566$		0			0
$567$	−512.366	+	545.787i	−0.903643	+	0.962586i
$568$		0			0
$569$	31.4620	−	5.54760i	0.0552935	−	0.00974973i	−0.145933	−	0.989294i	$-0.546618\pi$
$569$	31.4620	−	5.54760i	0.0552935	−	0.00974973i	0.201226	+	0.979545i	$0.435507\pi$
$570$		0			0
$571$	−839.737	+	305.639i	−1.47064	+	0.535270i	−0.948275	−	0.317450i	$-0.897173\pi$
$571$	−839.737	+	305.639i	−1.47064	+	0.535270i	−0.522368	+	0.852720i	$0.674951\pi$
$572$		0			0
$573$	−332.158	+	1004.49i	−0.579683	+	1.75303i
$574$		0			0
$575$	−119.002	+	68.7058i	−0.206960	+	0.119488i
$576$		0			0
$577$	188.273	−	326.099i	0.326297	−	0.565162i	−0.655477	−	0.755215i	$-0.727532\pi$
$577$	188.273	−	326.099i	0.326297	−	0.565162i	0.981774	+	0.190052i	$0.0608658\pi$
$578$		0			0
$579$	−33.2248	+	227.811i	−0.0573831	+	0.393455i
$580$		0			0
$581$	534.872	+	94.3124i	0.920606	+	0.162328i
$582$		0			0
$583$	259.656	−	217.878i	0.445380	−	0.373718i
$584$		0			0
$585$	271.034	−	909.428i	0.463306	−	1.55458i
$586$		0			0
$587$	151.825	−	417.135i	0.258645	−	0.710622i	−0.740606	−	0.671939i	$-0.765462\pi$
$587$	151.825	−	417.135i	0.258645	−	0.710622i	0.999252	−	0.0386825i	$-0.0123161\pi$
$588$		0			0
$589$	−685.340	−	575.069i	−1.16357	−	0.976348i
$590$		0			0
$591$	12.2513	+	412.240i	0.0207297	+	0.697530i
$592$		0			0
$593$		−	575.982i		−	0.971302i	−0.874153	−	0.485651i	$-0.838583\pi$
$593$		−	575.982i		−	0.971302i	0.874153	−	0.485651i	$-0.161417\pi$
$594$		0			0
$595$	815.331			1.37030
$596$		0			0
$597$	444.750	+	720.048i	0.744975	+	1.20611i
$598$		0			0
$599$	−89.9369	+	107.183i	−0.150145	+	0.178936i	−0.835874	−	0.548921i	$-0.815039\pi$
$599$	−89.9369	+	107.183i	−0.150145	+	0.178936i	0.685729	+	0.727857i	$0.259483\pi$
$600$		0			0
$601$	−145.813	−	53.0714i	−0.242617	−	0.0883052i	0.217850	−	0.975982i	$-0.430096\pi$
$601$	−145.813	−	53.0714i	−0.242617	−	0.0883052i	−0.460467	+	0.887677i	$0.652318\pi$
$602$		0			0
$603$	904.656	−	391.564i	1.50026	−	0.649361i
$604$		0			0
$605$	−337.918	−	402.715i	−0.558542	−	0.665645i
$606$		0			0
$607$	137.119	−	777.641i	0.225896	−	1.28112i	−0.635068	−	0.772456i	$-0.719028\pi$
$607$	137.119	−	777.641i	0.225896	−	1.28112i	0.860964	−	0.508666i	$-0.169861\pi$
$608$		0			0
$609$	−228.662	+	289.560i	−0.375472	+	0.475468i
$610$		0			0
$611$	976.100	+	563.552i	1.59755	+	0.922343i
$612$		0			0
$613$	177.178	+	306.881i	0.289034	+	0.500622i	0.973580	−	0.228348i	$-0.0733325\pi$
$613$	177.178	+	306.881i	0.289034	+	0.500622i	−0.684545	+	0.728971i	$0.739999\pi$
$614$		0			0
$615$	−170.653	−	823.889i	−0.277485	−	1.33966i
$616$		0			0
$617$	44.4149	+	122.029i	0.0719853	+	0.197778i	0.970467	−	0.241232i	$-0.0775515\pi$
$617$	44.4149	+	122.029i	0.0719853	+	0.197778i	−0.898482	+	0.439010i	$0.855329\pi$
$618$		0			0
$619$	−121.841	−	690.992i	−0.196834	−	1.11630i	−0.909782	−	0.415086i	$-0.863751\pi$
$619$	−121.841	−	690.992i	−0.196834	−	1.11630i	0.712948	−	0.701217i	$-0.247360\pi$
$620$		0			0
$621$	138.547	+	295.675i	0.223103	+	0.476127i
$622$		0			0
$623$	−1582.64	+	279.062i	−2.54035	+	0.447933i
$624$		0			0
$625$	732.919	−	266.761i	1.17267	−	0.426817i
$626$		0			0
$627$	313.076	+	351.360i	0.499323	+	0.560383i
$628$		0			0
$629$	−481.341	+	277.903i	−0.765249	+	0.441817i
$630$		0			0
$631$	−57.0965	+	98.8940i	−0.0904857	+	0.156726i	−0.907716	−	0.419586i	$-0.862175\pi$
$631$	−57.0965	+	98.8940i	−0.0904857	+	0.156726i	0.817230	+	0.576312i	$0.195509\pi$
$632$		0			0
$633$	639.920	−	254.684i	1.01093	−	0.402345i
$634$		0			0
$635$	70.4216	+	12.4172i	0.110900	+	0.0195547i
$636$		0			0
$637$	−487.754	+	409.274i	−0.765704	+	0.642502i
$638$		0			0
$639$	−28.0550	−	471.591i	−0.0439045	−	0.738014i
$640$		0			0
$641$	−243.212	+	668.219i	−0.379426	+	1.04246i	0.592169	+	0.805814i	$0.298272\pi$
$641$	−243.212	+	668.219i	−0.379426	+	1.04246i	−0.971595	+	0.236650i	$0.923950\pi$
$642$		0			0
$643$	−612.615	−	514.045i	−0.952745	−	0.799448i	0.0270123	−	0.999635i	$-0.491401\pi$
$643$	−612.615	−	514.045i	−0.952745	−	0.799448i	−0.979758	+	0.200187i	$0.935845\pi$
$644$		0			0
$645$	1179.54	+	635.056i	1.82874	+	0.984583i
$646$		0			0
$647$			410.339i			0.634217i	0.948389	+	0.317109i	$0.102712\pi$
$647$			410.339i			0.634217i	−0.948389	+	0.317109i	$0.897288\pi$
$648$		0			0
$649$	−126.110			−0.194314
$650$		0			0
$651$	435.928	−	809.683i	0.669629	−	1.24375i
$652$		0			0
$653$	253.205	−	301.758i	0.387756	−	0.462110i	−0.536490	−	0.843906i	$-0.680250\pi$
$653$	253.205	−	301.758i	0.387756	−	0.462110i	0.924246	+	0.381797i	$0.124695\pi$
$654$		0			0
$655$	−537.730	−	195.718i	−0.820962	−	0.298806i
$656$		0			0
$657$	468.176	−	935.110i	0.712597	−	1.42330i
$658$		0			0
$659$	406.721	+	484.712i	0.617180	+	0.735526i	0.980583	−	0.196106i	$-0.0628297\pi$
$659$	406.721	+	484.712i	0.617180	+	0.735526i	−0.363403	+	0.931632i	$0.618385\pi$
$660$		0			0
$661$	−7.91879	+	44.9097i	−0.0119800	+	0.0679420i	−0.990212	−	0.139574i	$-0.955427\pi$
$661$	−7.91879	+	44.9097i	−0.0119800	+	0.0679420i	0.978232	+	0.207516i	$0.0665379\pi$
$662$		0			0
$663$	283.784	+	713.037i	0.428031	+	1.07547i
$664$		0			0
$665$	−1301.88	−	751.643i	−1.95772	−	1.13029i
$666$		0			0
$667$	80.4667	+	139.372i	0.120640	+	0.208954i
$668$		0			0
$669$	−258.971	+	230.753i	−0.387102	+	0.344923i
$670$		0			0
$671$	74.1302	+	203.671i	0.110477	+	0.303534i
$672$		0			0
$673$	18.1549	+	102.962i	0.0269761	+	0.152989i	0.995320	−	0.0966289i	$-0.0308060\pi$
$673$	18.1549	+	102.962i	0.0269761	+	0.152989i	−0.968344	+	0.249618i	$0.919695\pi$
$674$		0			0
$675$	79.9540	+	296.183i	0.118450	+	0.438790i
$676$		0			0
$677$	−963.897	+	169.961i	−1.42378	+	0.251050i	−0.831877	−	0.554961i	$-0.812733\pi$
$677$	−963.897	+	169.961i	−1.42378	+	0.251050i	−0.591901	+	0.806011i	$0.701622\pi$
$678$		0			0
$679$	626.227	−	227.928i	0.922278	−	0.335682i
$680$		0			0
$681$	−235.060	+	48.6882i	−0.345168	+	0.0714951i
$682$		0			0
$683$	364.964	−	210.712i	0.534354	−	0.308509i	−0.208434	−	0.978037i	$-0.566837\pi$
$683$	364.964	−	210.712i	0.534354	−	0.308509i	0.742788	+	0.669527i	$0.233503\pi$
$684$		0			0
$685$	474.633	−	822.088i	0.692895	−	1.20013i
$686$		0			0
$687$	−50.3670	−	39.7742i	−0.0733144	−	0.0578955i
$688$		0			0
$689$	−1003.66	−	176.973i	−1.45669	−	0.256855i
$690$		0			0
$691$	−703.882	+	590.627i	−1.01864	+	0.854743i	−0.989456	−	0.144831i	$-0.953736\pi$
$691$	−703.882	+	590.627i	−1.01864	+	0.854743i	−0.0291866	+	0.999574i	$0.509292\pi$
$692$		0			0
$693$	−288.375	+	388.361i	−0.416125	+	0.560405i
$694$		0			0
$695$	252.253	−	693.061i	0.362955	−	0.997210i
$696$		0			0
$697$	521.242	+	437.374i	0.747837	+	0.627509i
$698$		0			0
$699$	41.3359	−	25.5318i	0.0591357	−	0.0365262i
$700$		0			0
$701$			1172.26i			1.67227i	0.548523	+	0.836136i	$0.315190\pi$
$701$			1172.26i			1.67227i	−0.548523	+	0.836136i	$0.684810\pi$
$702$		0			0
$703$	1024.78			1.45772
$704$		0			0
$705$	−1165.58	+	34.6396i	−1.65331	+	0.0491342i
$706$		0			0
$707$	1054.42	−	1256.61i	1.49140	−	1.77739i
$708$		0			0
$709$	180.154	+	65.5708i	0.254096	+	0.0924835i	0.465928	−	0.884823i	$-0.345721\pi$
$709$	180.154	+	65.5708i	0.254096	+	0.0924835i	−0.211832	+	0.977306i	$0.567943\pi$
$710$		0			0
$711$	184.584	−	174.580i	0.259612	−	0.245542i
$712$		0			0
$713$	−257.823	−	307.262i	−0.361603	−	0.430942i
$714$		0			0
$715$	106.478	−	603.867i	0.148920	−	0.844569i
$716$		0			0
$717$	−1189.22	−	173.441i	−1.65861	−	0.241898i
$718$		0			0
$719$	−825.555	−	476.635i	−1.14820	−	0.662913i	−0.199752	−	0.979847i	$-0.564014\pi$
$719$	−825.555	−	476.635i	−1.14820	−	0.662913i	−0.948448	+	0.316933i	$0.897347\pi$
$720$		0			0
$721$	−526.260	−	911.509i	−0.729903	−	1.26423i
$722$		0			0
$723$	−84.3787	−	27.9019i	−0.116706	−	0.0385918i
$724$		0			0
$725$	51.7149	+	142.086i	0.0713309	+	0.195980i
$726$		0			0
$727$	59.7401	+	338.803i	0.0821734	+	0.466028i	0.997931	+	0.0642968i	$0.0204804\pi$
$727$	59.7401	+	338.803i	0.0821734	+	0.466028i	−0.915757	+	0.401732i	$0.868408\pi$
$728$		0			0
$729$	717.448	−	129.264i	0.984154	−	0.177317i
$730$		0			0
$731$	−1066.92	+	188.126i	−1.45953	+	0.257355i
$732$		0			0
$733$	1369.05	−	498.295i	1.86774	−	0.679802i	0.895857	−	0.444342i	$-0.146562\pi$
$733$	1369.05	−	498.295i	1.86774	−	0.679802i	0.971884	−	0.235460i	$-0.0756597\pi$
$734$		0			0
$735$	206.816	−	625.437i	0.281382	−	0.850934i
$736$		0			0
$737$	551.628	−	318.482i	0.748477	−	0.432134i
$738$		0			0
$739$	202.396	−	350.561i	0.273879	−	0.474372i	−0.695973	−	0.718068i	$-0.745027\pi$
$739$	202.396	−	350.561i	0.273879	−	0.474372i	0.969852	+	0.243696i	$0.0783600\pi$
$740$		0			0
$741$	204.205	−	1400.16i	0.275581	−	1.88956i
$742$		0			0
$743$	−542.989	−	95.7437i	−0.730807	−	0.128861i	−0.204151	−	0.978939i	$-0.565443\pi$
$743$	−542.989	−	95.7437i	−0.730807	−	0.128861i	−0.526656	+	0.850079i	$0.676554\pi$
$744$		0			0
$745$	−524.314	+	439.952i	−0.703777	+	0.590539i
$746$		0			0
$747$	−363.433	−	384.259i	−0.486524	−	0.514403i
$748$		0			0
$749$	−169.432	+	465.510i	−0.226210	+	0.621508i
$750$		0			0
$751$	−303.441	−	254.618i	−0.404050	−	0.339038i	0.418007	−	0.908444i	$-0.362729\pi$
$751$	−303.441	−	254.618i	−0.404050	−	0.339038i	−0.822057	+	0.569406i	$0.807173\pi$
$752$		0			0
$753$	9.31259	+	313.358i	0.0123673	+	0.416146i
$754$		0			0
$755$		−	1213.55i		−	1.60736i
$756$		0			0
$757$	945.427			1.24891			0.624456	−	0.781060i	$-0.285321\pi$
$757$	945.427			1.24891			0.624456	+	0.781060i	$0.285321\pi$
$758$		0			0
$759$	110.876	+	179.508i	0.146082	+	0.236505i
$760$		0			0
$761$	−819.840	+	977.048i	−1.07732	+	1.28390i	−0.120660	+	0.992694i	$0.538501\pi$
$761$	−819.840	+	977.048i	−1.07732	+	1.28390i	−0.956660	+	0.291206i	$0.905943\pi$
$762$		0			0
$763$	444.269	+	161.701i	0.582266	+	0.211927i
$764$		0			0
$765$	−637.461	−	473.343i	−0.833283	−	0.618748i
$766$		0			0
$767$	243.729	+	290.465i	0.317769	+	0.378702i
$768$		0			0
$769$	34.4167	−	195.187i	0.0447551	−	0.253819i	−0.954219	−	0.299110i	$-0.903310\pi$
$769$	34.4167	−	195.187i	0.0447551	−	0.253819i	0.998974	+	0.0452908i	$0.0144214\pi$
$770$		0			0
$771$	−657.795	+	832.981i	−0.853171	+	1.08039i
$772$		0			0
$773$	857.130	+	494.864i	1.10884	+	0.640186i	0.938528	−	0.345204i	$-0.112190\pi$
$773$	857.130	+	494.864i	1.10884	+	0.640186i	0.170308	+	0.985391i	$0.445524\pi$
$774$		0			0
$775$	−188.427	−	326.365i	−0.243131	−	0.421116i
$776$		0			0
$777$	213.643	+	1031.44i	0.274959	+	1.32746i
$778$		0			0
$779$	−429.087	−	1178.91i	−0.550817	−	1.51336i
$780$		0			0
$781$	−53.0086	−	300.627i	−0.0678728	−	0.384926i
$782$		0			0
$783$	346.883	−	93.6403i	0.443018	−	0.119592i
$784$		0			0
$785$	962.267	−	169.674i	1.22582	−	0.216145i
$786$		0			0
$787$	−1205.66	+	438.825i	−1.53197	+	0.557592i	−0.964104	−	0.265526i	$-0.914454\pi$
$787$	−1205.66	+	438.825i	−1.53197	+	0.557592i	−0.567869	+	0.823119i	$0.692232\pi$
$788$		0			0
$789$	439.697	+	493.466i	0.557283	+	0.625432i
$790$		0			0
$791$	−810.130	+	467.729i	−1.02418	+	0.591313i
$792$		0			0
$793$	325.840	−	564.372i	0.410896	−	0.711692i
$794$		0			0
$795$	979.664	−	389.901i	1.23228	−	0.490441i
$796$		0			0
$797$	1524.03	+	268.727i	1.91220	+	0.337173i	0.997722	−	0.0674584i	$-0.0214890\pi$
$797$	1524.03	+	268.727i	1.91220	+	0.337173i	0.914480	+	0.404631i	$0.132600\pi$
$798$		0			0
$799$	722.409	−	606.173i	0.904141	−	0.758665i
$800$		0			0
$801$	1399.39	+	700.624i	1.74705	+	0.874686i
$802$		0			0
$803$	231.115	−	634.984i	0.287815	−	0.790764i
$804$		0			0
$805$	−516.295	−	433.223i	−0.641360	−	0.538165i
$806$		0			0
$807$	1202.11	+	647.207i	1.48960	+	0.801992i
$808$		0			0
$809$			154.179i			0.190579i	0.995450	+	0.0952896i	$0.0303777\pi$
$809$			154.179i			0.190579i	−0.995450	+	0.0952896i	$0.969622\pi$
$810$		0			0
$811$	−867.983			−1.07026			−0.535131	−	0.844769i	$-0.679738\pi$
$811$	−867.983			−1.07026			−0.535131	+	0.844769i	$0.679738\pi$
$812$		0			0
$813$	89.5890	−	166.401i	0.110196	−	0.204675i
$814$		0			0
$815$	−352.546	+	420.148i	−0.432571	+	0.515519i
$816$		0			0
$817$	1877.04	+	683.186i	2.29748	+	0.836213i
$818$		0			0
$819$	1451.84	−	86.3697i	1.77269	−	0.105458i
$820$		0			0
$821$	16.2664	+	19.3855i	0.0198129	+	0.0236121i	0.775860	−	0.630905i	$-0.217316\pi$
$821$	16.2664	+	19.3855i	0.0198129	+	0.0236121i	−0.756047	+	0.654517i	$0.772872\pi$
$822$		0			0
$823$	−98.5982	+	559.178i	−0.119803	+	0.679439i	0.864456	+	0.502709i	$0.167663\pi$
$823$	−98.5982	+	559.178i	−0.119803	+	0.679439i	−0.984259	+	0.176730i	$0.943448\pi$
$824$		0			0
$825$	73.3036	+	184.183i	0.0888529	+	0.223252i
$826$		0			0
$827$	−862.945	−	498.221i	−1.04346	−	0.602444i	−0.122651	−	0.992450i	$-0.539140\pi$
$827$	−862.945	−	498.221i	−1.04346	−	0.602444i	−0.920812	+	0.390006i	$0.872473\pi$
$828$		0			0
$829$	−471.558	−	816.762i	−0.568827	−	0.985238i	−0.996682	−	0.0813903i	$-0.974064\pi$
$829$	−471.558	−	816.762i	−0.568827	−	0.985238i	0.427855	−	0.903847i	$-0.359269\pi$
$830$		0			0
$831$	244.993	−	218.298i	0.294817	−	0.262693i
$832$		0			0
$833$	182.206	+	500.608i	0.218735	+	0.600970i
$834$		0			0
$835$	−66.7790	−	378.723i	−0.0799749	−	0.453560i
$836$		0			0
$837$	−810.892	+	379.966i	−0.968807	+	0.453962i
$838$		0			0
$839$	267.551	−	47.1764i	0.318892	−	0.0562293i	−0.0119110	−	0.999929i	$-0.503791\pi$
$839$	267.551	−	47.1764i	0.318892	−	0.0562293i	0.330803	+	0.943700i	$0.392680\pi$
$840$		0			0
$841$	−623.874	+	227.072i	−0.741824	+	0.270002i
$842$		0			0
$843$	−1073.30	+	222.314i	−1.27319	+	0.263718i
$844$		0			0
$845$	−714.098	+	412.285i	−0.845087	+	0.487911i
$846$		0			0
$847$	402.858	−	697.771i	0.475629	−	0.823814i
$848$		0			0
$849$	−737.139	−	582.110i	−0.868244	−	0.685642i
$850$		0			0
$851$	452.464	+	79.7817i	0.531686	+	0.0937505i
$852$		0			0
$853$	453.287	−	380.353i	0.531403	−	0.445900i	−0.337182	−	0.941439i	$-0.609474\pi$
$853$	453.287	−	380.353i	0.531403	−	0.445900i	0.868586	+	0.495539i	$0.165029\pi$
$854$		0			0
$855$	581.501	+	1343.48i	0.680119	+	1.57132i
$856$		0			0
$857$	−246.495	+	677.239i	−0.287625	+	0.790244i	0.708772	+	0.705438i	$0.249249\pi$
$857$	−246.495	+	677.239i	−0.287625	+	0.790244i	−0.996397	+	0.0848065i	$0.972973\pi$
$858$		0			0
$859$	639.659	+	536.737i	0.744655	+	0.624840i	0.934083	−	0.357055i	$-0.116219\pi$
$859$	639.659	+	536.737i	0.744655	+	0.624840i	−0.189428	+	0.981895i	$0.560664\pi$
$860$		0			0
$861$	1097.11	−	677.651i	1.27423	−	0.787051i
$862$		0			0
$863$		−	695.905i		−	0.806379i	−0.915117	−	0.403189i	$-0.867902\pi$
$863$		−	695.905i		−	0.806379i	0.915117	−	0.403189i	$-0.132098\pi$
$864$		0			0
$865$	−714.577			−0.826101
$866$		0			0
$867$	−224.795	+	6.68063i	−0.259279	+	0.00770545i
$868$		0			0
$869$	105.526	−	125.760i	0.121433	−	0.144719i
$870$		0			0
$871$	−1799.67	−	655.026i	−2.06621	−	0.752039i
$872$		0			0
$873$	−621.936	−	185.354i	−0.712412	−	0.212318i
$874$		0			0
$875$	488.535	+	582.214i	0.558326	+	0.665387i
$876$		0			0
$877$	136.129	−	772.026i	0.155221	−	0.880304i	−0.803362	−	0.595491i	$-0.796958\pi$
$877$	136.129	−	772.026i	0.155221	−	0.880304i	0.958583	−	0.284813i	$-0.0919314\pi$
$878$		0			0
$879$	−141.364	−	20.6171i	−0.160824	−	0.0234552i
$880$		0			0
$881$	1180.38	+	681.491i	1.33982	+	0.773543i	0.986780	−	0.162067i	$-0.0518160\pi$
$881$	1180.38	+	681.491i	1.33982	+	0.773543i	0.353036	+	0.935610i	$0.385149\pi$
$882$		0			0
$883$	−186.082	−	322.304i	−0.210739	−	0.365010i	0.741207	−	0.671276i	$-0.234254\pi$
$883$	−186.082	−	322.304i	−0.210739	−	0.365010i	−0.951946	+	0.306266i	$0.900920\pi$
$884$		0			0
$885$	−372.457	−	123.162i	−0.420856	−	0.139166i
$886$		0			0
$887$	−30.4466	−	83.6514i	−0.0343254	−	0.0943083i	0.921346	−	0.388743i	$-0.127091\pi$
$887$	−30.4466	−	83.6514i	−0.0343254	−	0.0943083i	−0.955671	+	0.294435i	$0.904869\pi$
$888$		0			0
$889$	19.0311	+	107.931i	0.0214073	+	0.121407i
$890$		0			0
$891$	450.928	−	136.221i	0.506092	−	0.152885i
$892$		0			0
$893$	−1712.33	+	301.931i	−1.91751	+	0.338108i
$894$		0			0
$895$	−898.632	+	327.075i	−1.00406	+	0.365447i
$896$		0			0
$897$	199.168	−	602.307i	0.222038	−	0.671468i
$898$		0			0
$899$	−382.231	+	220.681i	−0.425173	+	0.245474i
$900$		0			0
$901$	−426.355	+	738.469i	−0.473202	+	0.819610i
$902$		0			0
$903$	−296.306	+	2031.67i	−0.328135	+	2.24991i
$904$		0			0
$905$	−1460.84	−	257.586i	−1.61419	−	0.284625i
$906$		0			0
$907$	198.330	−	166.419i	0.218666	−	0.183483i	−0.526874	−	0.849943i	$-0.676636\pi$
$907$	198.330	−	166.419i	0.218666	−	0.183483i	0.745540	+	0.666461i	$0.232192\pi$
$908$		0			0
$909$	−1553.92	+	370.326i	−1.70949	+	0.407400i
$910$		0			0
$911$	314.425	−	863.876i	0.345143	−	0.948272i	−0.638735	−	0.769427i	$-0.720542\pi$
$911$	314.425	−	863.876i	0.345143	−	0.948272i	0.983877	−	0.178845i	$-0.0572359\pi$
$912$		0			0
$913$	−261.803	−	219.678i	−0.286750	−	0.240612i
$914$		0			0
$915$	20.0283	+	673.928i	0.0218888	+	0.736533i
$916$		0			0
$917$		−	877.035i		−	0.956418i
$918$		0			0
$919$	638.156			0.694403			0.347201	−	0.937791i	$-0.387132\pi$
$919$	638.156			0.694403			0.347201	+	0.937791i	$0.387132\pi$
$920$		0			0
$921$	462.069	+	748.088i	0.501704	+	0.812256i
$922$		0			0
$923$	−589.977	+	703.107i	−0.639195	+	0.761763i
$924$		0			0
$925$	405.636	+	147.639i	0.438526	+	0.159610i
$926$		0			0
$927$	−117.726	+	1018.18i	−0.126997	+	1.09836i
$928$		0			0
$929$	31.0811	+	37.0410i	0.0334565	+	0.0398719i	0.782513	−	0.622634i	$-0.213937\pi$
$929$	31.0811	+	37.0410i	0.0334565	+	0.0398719i	−0.749057	+	0.662506i	$0.769493\pi$
$930$		0			0
$931$	170.565	−	967.322i	0.183206	−	1.03901i
$932$		0			0
$933$	130.009	−	164.633i	0.139345	−	0.176456i
$934$		0			0
$935$	−444.310	−	256.522i	−0.475197	−	0.274355i
$936$		0			0
$937$	459.852	+	796.488i	0.490771	+	0.850040i	0.999944	−	0.0106242i	$-0.00338187\pi$
$937$	459.852	+	796.488i	0.490771	+	0.850040i	−0.509173	+	0.860664i	$0.670049\pi$
$938$		0			0
$939$	379.116	+	1830.32i	0.403744	+	1.94922i
$940$		0			0
$941$	136.620	+	375.361i	0.145186	+	0.398896i	0.990876	−	0.134780i	$-0.0430327\pi$
$941$	136.620	+	375.361i	0.145186	+	0.398896i	−0.845689	+	0.533675i	$0.820810\pi$
$942$		0			0
$943$	−97.6711	−	553.920i	−0.103575	−	0.587402i
$944$		0			0
$945$	−1230.98	+	865.366i	−1.30263	+	0.915731i
$946$		0			0
$947$	−938.217	+	165.433i	−0.990726	+	0.174692i	−0.645444	−	0.763807i	$-0.723328\pi$
$947$	−938.217	+	165.433i	−0.990726	+	0.174692i	−0.345282	+	0.938499i	$0.612217\pi$
$948$		0			0
$949$	−1909.21	+	694.896i	−2.01181	+	0.732240i
$950$		0			0
$951$	−616.251	−	691.610i	−0.648003	−	0.727245i
$952$		0			0
$953$	298.910	−	172.576i	0.313652	−	0.181087i	−0.334908	−	0.942251i	$-0.608705\pi$
$953$	298.910	−	172.576i	0.313652	−	0.181087i	0.648560	+	0.761164i	$0.275372\pi$
$954$		0			0
$955$	−1063.29	+	1841.68i	−1.11340	+	1.92846i
$956$		0			0
$957$	215.711	−	85.8515i	0.225403	−	0.0897090i
$958$		0			0
$959$	1432.77	+	252.637i	1.49403	+	0.263438i
$960$		0			0
$961$	106.501	−	89.3648i	0.110823	−	0.0929915i
$962$		0			0
$963$	402.722	−	265.592i	0.418195	−	0.275796i
$964$		0			0
$965$	−158.271	+	434.846i	−0.164011	+	0.450618i
$966$		0			0
$967$	1055.08	+	885.319i	1.09109	+	0.915531i	0.996794	−	0.0800132i	$-0.0254962\pi$
$967$	1055.08	+	885.319i	1.09109	+	0.915531i	0.0942939	+	0.995544i	$0.469941\pi$
$968$		0			0
$969$	−1042.42	−	561.231i	−1.07577	−	0.579186i
$970$		0			0
$971$			481.713i			0.496100i	0.968747	+	0.248050i	$0.0797897\pi$
$971$			481.713i			0.496100i	−0.968747	+	0.248050i	$0.920210\pi$
$972$		0			0
$973$	1130.38			1.16175
$974$		0			0
$975$	282.551	−	524.804i	0.289796	−	0.538260i
$976$		0			0
$977$	−886.249	+	1056.19i	−0.907112	+	1.08105i	0.0892648	+	0.996008i	$0.471548\pi$
$977$	−886.249	+	1056.19i	−0.907112	+	1.08105i	−0.996377	+	0.0850463i	$0.972896\pi$
$978$		0			0
$979$	950.251	+	345.863i	0.970634	+	0.353282i
$980$		0			0
$981$	−253.473	−	384.346i	−0.258382	−	0.391790i
$982$		0			0
$983$	−131.464	−	156.673i	−0.133737	−	0.159382i	0.695019	−	0.718991i	$-0.255396\pi$
$983$	−131.464	−	156.673i	−0.133737	−	0.159382i	−0.828757	+	0.559609i	$0.810951\pi$
$984$		0			0
$985$	−143.952	+	816.392i	−0.146144	+	0.828824i
$986$		0			0
$987$	−660.876	−	1660.52i	−0.669580	−	1.68239i
$988$		0			0
$989$	775.569	+	447.775i	0.784195	+	0.452755i
$990$		0			0
$991$	196.402	+	340.178i	0.198185	+	0.343267i	0.947940	−	0.318449i	$-0.103162\pi$
$991$	196.402	+	340.178i	0.198185	+	0.343267i	−0.749755	+	0.661716i	$0.769829\pi$
$992$		0			0
$993$	345.297	−	307.673i	0.347731	−	0.309841i
$994$		0			0
$995$	581.830	+	1598.56i	0.584753	+	1.60660i
$996$		0			0
$997$	−37.7003	−	213.809i	−0.0378138	−	0.214452i	0.960046	−	0.279842i	$-0.0902821\pi$
$997$	−37.7003	−	213.809i	−0.0378138	−	0.214452i	−0.997860	+	0.0653896i	$0.979171\pi$
$998$		0			0
$999$	431.770	−	930.456i	0.432202	−	0.931388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.12	✓	108
4.3	odd	2		432.3.bc.d.257.7		108
27.2	odd	18	inner	216.3.u.a.137.12	yes	108
108.83	even	18		432.3.bc.d.353.7		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.12	✓	108	1.1	even	1	trivial
216.3.u.a.137.12	yes	108	27.2	odd	18	inner
432.3.bc.d.257.7		108	4.3	odd	2
432.3.bc.d.353.7		108	108.83	even	18

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42216 - 2.64149i) q^{3} +(3.87609 - 4.61934i) q^{5} +(8.68461 + 3.16094i) q^{7} +(-4.95492 - 7.51324i) q^{9} +O(q^{10})\)	\(q+(1.42216 - 2.64149i) q^{3} +(3.87609 - 4.61934i) q^{5} +(8.68461 + 3.16094i) q^{7} +(-4.95492 - 7.51324i) q^{9} +(-3.73812 - 4.45492i) q^{11} +(-3.03632 + 17.2198i) q^{13} +(-6.68952 - 16.8081i) q^{15} +(12.6699 + 7.31497i) q^{17} +(-13.4872 - 23.3604i) q^{19} +(20.7005 - 18.4449i) q^{21} +(-4.13623 - 11.3642i) q^{23} +(-1.97306 - 11.1898i) q^{25} +(-26.8928 + 2.40332i) q^{27} +(-13.1052 + 2.31081i) q^{29} +(31.1665 - 11.3437i) q^{31} +(-17.0838 + 3.53859i) q^{33} +(48.2638 - 27.8651i) q^{35} +(-18.9955 + 32.9011i) q^{37} +(41.1678 + 32.5098i) q^{39} +(45.8030 + 8.07631i) q^{41} +(-56.7271 + 47.5997i) q^{43} +(-53.9120 - 6.23352i) q^{45} +(22.0464 - 60.5721i) q^{47} +(27.8948 + 23.4065i) q^{49} +(37.3410 - 23.0643i) q^{51} +58.2853i q^{53} -35.0681 q^{55} +(-80.8873 + 2.40387i) q^{57} +(13.9389 - 16.6118i) q^{59} +(-35.0222 - 12.7470i) q^{61} +(-19.2826 - 80.9118i) q^{63} +(67.7753 + 80.7714i) q^{65} +(-19.0195 + 107.865i) q^{67} +(-35.9008 - 5.23591i) q^{69} +(45.4591 + 26.2458i) q^{71} +(58.0979 + 100.629i) q^{73} +(-32.3637 - 10.7019i) q^{75} +(-18.3824 - 50.5053i) q^{77} +(4.90201 + 27.8007i) q^{79} +(-31.8976 + 74.4550i) q^{81} +(57.8743 - 10.2048i) q^{83} +(82.9001 - 30.1732i) q^{85} +(-12.5338 + 37.9037i) q^{87} +(-150.590 + 86.9433i) q^{89} +(-80.8001 + 139.950i) q^{91} +(14.3596 - 98.4583i) q^{93} +(-160.187 - 28.2454i) q^{95} +(55.2376 - 46.3499i) q^{97} +(-14.9488 + 50.1592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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