LMFDB - Embedded newform 108.3.k.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	108.5
Dual form			108.3.k.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +O(q^{10})$	\(q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +(-1.69236 + 4.64973i) q^{11} +(3.65864 + 3.06996i) q^{13} +(-8.52437 + 7.12360i) q^{15} +(20.4937 + 11.8321i) q^{17} +(-13.5371 - 23.4469i) q^{19} +(1.09075 - 0.626820i) q^{21} +(20.7690 + 3.66213i) q^{23} +(8.64689 - 7.25561i) q^{25} +(-23.3007 - 13.6409i) q^{27} +(-2.12470 - 2.53212i) q^{29} +(3.01492 - 17.0984i) q^{31} +(-14.8444 - 0.0298779i) q^{33} +(1.34479 - 0.776415i) q^{35} +(24.9593 - 43.2309i) q^{37} +(-4.92757 + 13.4541i) q^{39} +(26.0603 - 31.0575i) q^{41} +(-61.2373 - 22.2885i) q^{43} +(-28.7948 - 16.7796i) q^{45} +(-26.9440 + 4.75095i) q^{47} +(45.8797 - 16.6988i) q^{49} +(-12.4684 + 69.8889i) q^{51} +59.1590i q^{53} -18.3230 q^{55} +(52.3339 - 62.1148i) q^{57} +(-16.8092 - 46.1828i) q^{59} +(11.9824 + 67.9556i) q^{61} +(2.88133 + 2.43755i) q^{63} +(-6.04884 + 16.6191i) q^{65} +(56.4874 + 47.3986i) q^{67} +(10.8610 + 62.3289i) q^{69} +(88.6346 + 51.1732i) q^{71} +(-3.81627 - 6.60997i) q^{73} +(29.2922 + 16.9906i) q^{75} +(2.04344 + 0.360314i) q^{77} +(-99.5742 + 83.5527i) q^{79} +(14.7073 - 79.6536i) q^{81} +(-44.1227 - 52.5834i) q^{83} +(-15.2165 + 86.2972i) q^{85} +(4.97544 - 8.57780i) q^{87} +(-137.829 + 79.5758i) q^{89} +(1.00139 - 1.73447i) q^{91} +(51.3134 - 8.94149i) q^{93} +(64.4432 - 76.8005i) q^{95} +(-8.07251 - 2.93815i) q^{97} +(-15.0627 - 41.9085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	1.02038	+	2.82114i	0.340128	+	0.940379i
$3$	1.02038	+	2.82114i	0.340128	+	0.940379i
$4$		0			0
$5$	1.26650	+	3.47969i	0.253301	+	0.695938i	0.999542	+	0.0302625i	$0.00963434\pi$
$5$	1.26650	+	3.47969i	0.253301	+	0.695938i	−0.746241	+	0.665676i	$0.768143\pi$
$6$		0			0
$7$	−0.0728181	−	0.412972i	−0.0104026	−	0.0589960i	0.979165	−	0.203068i	$-0.0650913\pi$
$7$	−0.0728181	−	0.412972i	−0.0104026	−	0.0589960i	−0.989567	+	0.144072i	$0.953980\pi$
$8$		0			0
$9$	−6.91763	+	5.75729i	−0.768626	+	0.639699i
$10$		0			0
$11$	−1.69236	+	4.64973i	−0.153851	+	0.422703i	−0.992542	−	0.121906i	$-0.961099\pi$
$11$	−1.69236	+	4.64973i	−0.153851	+	0.422703i	0.838691	+	0.544608i	$0.183322\pi$
$12$		0			0
$13$	3.65864	+	3.06996i	0.281434	+	0.236151i	0.772567	−	0.634934i	$-0.218973\pi$
$13$	3.65864	+	3.06996i	0.281434	+	0.236151i	−0.491133	+	0.871085i	$0.663417\pi$
$14$		0			0
$15$	−8.52437	+	7.12360i	−0.568291	+	0.474907i
$16$		0			0
$17$	20.4937	+	11.8321i	1.20551	+	0.696004i	0.961776	−	0.273838i	$-0.0882931\pi$
$17$	20.4937	+	11.8321i	1.20551	+	0.696004i	0.243738	+	0.969841i	$0.421626\pi$
$18$		0			0
$19$	−13.5371	−	23.4469i	−0.712478	−	1.23405i	−0.963924	−	0.266177i	$-0.914240\pi$
$19$	−13.5371	−	23.4469i	−0.712478	−	1.23405i	0.251446	−	0.967871i	$-0.419094\pi$
$20$		0			0
$21$	1.09075	−	0.626820i	0.0519404	−	0.0298486i
$22$		0			0
$23$	20.7690	+	3.66213i	0.902998	+	0.159223i	0.605822	−	0.795600i	$-0.292844\pi$
$23$	20.7690	+	3.66213i	0.902998	+	0.159223i	0.297176	+	0.954823i	$0.403955\pi$
$24$		0			0
$25$	8.64689	−	7.25561i	0.345876	−	0.290224i
$26$		0			0
$27$	−23.3007	−	13.6409i	−0.862991	−	0.505220i
$28$		0			0
$29$	−2.12470	−	2.53212i	−0.0732655	−	0.0873144i	0.728167	−	0.685400i	$-0.240373\pi$
$29$	−2.12470	−	2.53212i	−0.0732655	−	0.0873144i	−0.801432	+	0.598086i	$0.795928\pi$
$30$		0			0
$31$	3.01492	−	17.0984i	0.0972554	−	0.551563i	−0.896777	−	0.442482i	$-0.854098\pi$
$31$	3.01492	−	17.0984i	0.0972554	−	0.551563i	0.994033	−	0.109081i	$-0.0347908\pi$
$32$		0			0
$33$	−14.8444	−	0.0298779i	−0.449830	−	0.000905391i
$34$		0			0
$35$	1.34479	−	0.776415i	0.0384226	−	0.0221833i
$36$		0			0
$37$	24.9593	−	43.2309i	0.674577	−	1.16840i	−0.302016	−	0.953303i	$-0.597659\pi$
$37$	24.9593	−	43.2309i	0.674577	−	1.16840i	0.976592	−	0.215098i	$-0.0690072\pi$
$38$		0			0
$39$	−4.92757	+	13.4541i	−0.126348	+	0.344976i
$40$		0			0
$41$	26.0603	−	31.0575i	0.635618	−	0.757500i	−0.348053	−	0.937475i	$-0.613157\pi$
$41$	26.0603	−	31.0575i	0.635618	−	0.757500i	0.983671	+	0.179975i	$0.0576015\pi$
$42$		0			0
$43$	−61.2373	−	22.2885i	−1.42412	−	0.518338i	−0.488881	−	0.872350i	$-0.662595\pi$
$43$	−61.2373	−	22.2885i	−1.42412	−	0.518338i	−0.935241	+	0.354012i	$0.884817\pi$
$44$		0			0
$45$	−28.7948	−	16.7796i	−0.639884	−	0.372880i
$46$		0			0
$47$	−26.9440	+	4.75095i	−0.573276	+	0.101084i	−0.452768	−	0.891628i	$-0.649564\pi$
$47$	−26.9440	+	4.75095i	−0.573276	+	0.101084i	−0.120508	+	0.992712i	$0.538452\pi$
$48$		0			0
$49$	45.8797	−	16.6988i	0.936320	−	0.340793i
$50$		0			0
$51$	−12.4684	+	69.8889i	−0.244478	+	1.37037i
$52$		0			0
$53$			59.1590i			1.11621i	0.829771	+	0.558104i	$0.188471\pi$
$53$			59.1590i			1.11621i	−0.829771	+	0.558104i	$0.811529\pi$
$54$		0			0
$55$	−18.3230			−0.333145
$56$		0			0
$57$	52.3339	−	62.1148i	0.918139	−	1.08973i
$58$		0			0
$59$	−16.8092	−	46.1828i	−0.284901	−	0.782760i	−0.996760	−	0.0804369i	$-0.974368\pi$
$59$	−16.8092	−	46.1828i	−0.284901	−	0.782760i	0.711858	−	0.702323i	$-0.247854\pi$
$60$		0			0
$61$	11.9824	+	67.9556i	0.196433	+	1.11403i	0.910364	+	0.413809i	$0.135802\pi$
$61$	11.9824	+	67.9556i	0.196433	+	1.11403i	−0.713931	+	0.700216i	$0.753087\pi$
$62$		0			0
$63$	2.88133	+	2.43755i	0.0457354	+	0.0386913i
$64$		0			0
$65$	−6.04884	+	16.6191i	−0.0930591	+	0.255678i
$66$		0			0
$67$	56.4874	+	47.3986i	0.843096	+	0.707441i	0.958258	−	0.285905i	$-0.0922943\pi$
$67$	56.4874	+	47.3986i	0.843096	+	0.707441i	−0.115162	+	0.993347i	$0.536739\pi$
$68$		0			0
$69$	10.8610	+	62.3289i	0.157405	+	0.903317i
$70$		0			0
$71$	88.6346	+	51.1732i	1.24837	+	0.720749i	0.970785	−	0.239951i	$-0.0771313\pi$
$71$	88.6346	+	51.1732i	1.24837	+	0.720749i	0.277589	+	0.960700i	$0.410465\pi$
$72$		0			0
$73$	−3.81627	−	6.60997i	−0.0522776	−	0.0905475i	0.838702	−	0.544590i	$-0.183315\pi$
$73$	−3.81627	−	6.60997i	−0.0522776	−	0.0905475i	−0.890980	+	0.454043i	$0.849981\pi$
$74$		0			0
$75$	29.2922	+	16.9906i	0.390563	+	0.226541i
$76$		0			0
$77$	2.04344	+	0.360314i	0.0265382	+	0.00467940i
$78$		0			0
$79$	−99.5742	+	83.5527i	−1.26043	+	1.05763i	−0.264797	+	0.964304i	$0.585305\pi$
$79$	−99.5742	+	83.5527i	−1.26043	+	1.05763i	−0.995636	+	0.0933246i	$0.970251\pi$
$80$		0			0
$81$	14.7073	−	79.6536i	0.181571	−	0.983378i
$82$		0			0
$83$	−44.1227	−	52.5834i	−0.531598	−	0.633534i	0.431684	−	0.902025i	$-0.357920\pi$
$83$	−44.1227	−	52.5834i	−0.531598	−	0.633534i	−0.963282	+	0.268491i	$0.913475\pi$
$84$		0			0
$85$	−15.2165	+	86.2972i	−0.179018	+	1.01526i
$86$		0			0
$87$	4.97544	−	8.57780i	0.0571890	−	0.0985954i
$88$		0			0
$89$	−137.829	+	79.5758i	−1.54864	+	0.894110i	−0.550399	+	0.834902i	$0.685524\pi$
$89$	−137.829	+	79.5758i	−1.54864	+	0.894110i	−0.998246	+	0.0592087i	$0.981142\pi$
$90$		0			0
$91$	1.00139	−	1.73447i	0.0110043	−	0.0190601i
$92$		0			0
$93$	51.3134	−	8.94149i	0.551757	−	0.0961450i
$94$		0			0
$95$	64.4432	−	76.8005i	0.678350	−	0.808426i
$96$		0			0
$97$	−8.07251	−	2.93815i	−0.0832217	−	0.0302902i	0.300074	−	0.953916i	$-0.402989\pi$
$97$	−8.07251	−	2.93815i	−0.0832217	−	0.0302902i	−0.383296	+	0.923626i	$0.625211\pi$
$98$		0			0
$99$	−15.0627	−	41.9085i	−0.152148	−	0.423318i
$100$		0			0
$101$	−177.614	+	31.3181i	−1.75855	+	0.310080i	−0.957483	−	0.288491i	$-0.906846\pi$
$101$	−177.614	+	31.3181i	−1.75855	+	0.310080i	−0.801070	+	0.598571i	$0.795735\pi$
$102$		0			0
$103$	53.4283	−	19.4463i	0.518721	−	0.188799i	−0.0693741	−	0.997591i	$-0.522100\pi$
$103$	53.4283	−	19.4463i	0.518721	−	0.188799i	0.588095	+	0.808792i	$0.299878\pi$
$104$		0			0
$105$	3.56258	+	3.00160i	0.0339293	+	0.0285866i
$106$		0			0
$107$		−	165.438i		−	1.54615i	−0.634315	−	0.773074i	$-0.718718\pi$
$107$		−	165.438i		−	1.54615i	0.634315	−	0.773074i	$-0.281282\pi$
$108$		0			0
$109$	29.6226			0.271767			0.135883	−	0.990725i	$-0.456613\pi$
$109$	29.6226			0.271767			0.135883	+	0.990725i	$0.456613\pi$
$110$		0			0
$111$	147.428	+	26.3017i	1.32818	+	0.236952i
$112$		0			0
$113$	−33.8000	−	92.8649i	−0.299115	−	0.821813i	−0.994648	−	0.103319i	$-0.967054\pi$
$113$	−33.8000	−	92.8649i	−0.299115	−	0.821813i	0.695533	−	0.718494i	$-0.255168\pi$
$114$		0			0
$115$	13.5609	+	76.9077i	0.117921	+	0.668762i
$116$		0			0
$117$	−42.9838	−	0.173031i	−0.367383	−	0.00147890i
$118$		0			0
$119$	3.39400	−	9.32493i	0.0285210	−	0.0783607i
$120$		0			0
$121$	73.9355	+	62.0392i	0.611037	+	0.512721i
$122$		0			0
$123$	114.209	+	41.8292i	0.928529	+	0.340075i
$124$		0			0
$125$	116.371	+	67.1869i	0.930969	+	0.537495i
$126$		0			0
$127$	−97.3125	−	168.550i	−0.766240	−	1.32717i	−0.939588	−	0.342306i	$-0.888792\pi$
$127$	−97.3125	−	168.550i	−0.766240	−	1.32717i	0.173348	−	0.984861i	$-0.444541\pi$
$128$		0			0
$129$	0.393494	−	195.502i	0.00305034	−	1.51552i
$130$		0			0
$131$	−39.4243	−	6.95157i	−0.300949	−	0.0530654i	0.0211346	−	0.999777i	$-0.493272\pi$
$131$	−39.4243	−	6.95157i	−0.300949	−	0.0530654i	−0.322084	+	0.946711i	$0.604383\pi$
$132$		0			0
$133$	−8.69718	+	7.29780i	−0.0653923	+	0.0548707i
$134$		0			0
$135$	17.9558	−	98.3557i	0.133006	−	0.728561i
$136$		0			0
$137$	−122.095	−	145.507i	−0.891201	−	1.06209i	−0.997700	−	0.0677791i	$-0.978409\pi$
$137$	−122.095	−	145.507i	−0.891201	−	1.06209i	0.106499	−	0.994313i	$-0.466036\pi$
$138$		0			0
$139$	−9.40172	+	53.3198i	−0.0676383	+	0.383596i	0.932131	+	0.362121i	$0.117947\pi$
$139$	−9.40172	+	53.3198i	−0.0676383	+	0.383596i	−0.999769	+	0.0214748i	$0.993164\pi$
$140$		0			0
$141$	−40.8963	−	71.1649i	−0.290045	−	0.504716i
$142$		0			0
$143$	−20.4662	+	11.8162i	−0.143121	+	0.0826307i
$144$		0			0
$145$	6.12004	−	10.6002i	0.0422072	−	0.0731050i
$146$		0			0
$147$	93.9247	+	112.394i	0.638943	+	0.764583i
$148$		0			0
$149$	−20.0605	+	23.9072i	−0.134634	+	0.160451i	−0.829149	−	0.559028i	$-0.811175\pi$
$149$	−20.0605	+	23.9072i	−0.134634	+	0.160451i	0.694515	+	0.719478i	$0.255619\pi$
$150$		0			0
$151$	23.7123	+	8.63059i	0.157035	+	0.0571562i	0.419342	−	0.907828i	$-0.362261\pi$
$151$	23.7123	+	8.63059i	0.157035	+	0.0571562i	−0.262306	+	0.964985i	$0.584483\pi$
$152$		0			0
$153$	−209.889	+	36.1385i	−1.37182	+	0.236199i
$154$		0			0
$155$	63.3157	−	11.1643i	0.408488	−	0.0720275i
$156$		0			0
$157$	−74.4482	+	27.0969i	−0.474192	+	0.172592i	−0.568050	−	0.822994i	$-0.692302\pi$
$157$	−74.4482	+	27.0969i	−0.474192	+	0.172592i	0.0938584	+	0.995586i	$0.470080\pi$
$158$		0			0
$159$	−166.896	+	60.3649i	−1.04966	+	0.379653i
$160$		0			0
$161$		−	8.84367i		−	0.0549296i
$162$		0			0
$163$	−57.7099			−0.354049			−0.177024	−	0.984206i	$-0.556647\pi$
$163$	−57.7099			−0.354049			−0.177024	+	0.984206i	$0.556647\pi$
$164$		0			0
$165$	−18.6965	−	51.6917i	−0.113312	−	0.313283i
$166$		0			0
$167$	33.8026	+	92.8720i	0.202411	+	0.556120i	0.998816	−	0.0486438i	$-0.0154899\pi$
$167$	33.8026	+	92.8720i	0.202411	+	0.556120i	−0.796405	+	0.604763i	$0.793268\pi$
$168$		0			0
$169$	−25.3856	−	143.969i	−0.150210	−	0.851886i
$170$		0			0
$171$	228.635	+	84.2602i	1.33705	+	0.492750i
$172$		0			0
$173$	−25.1544	+	69.1111i	−0.145401	+	0.399486i	−0.990919	−	0.134461i	$-0.957070\pi$
$173$	−25.1544	+	69.1111i	−0.145401	+	0.399486i	0.845518	+	0.533947i	$0.179292\pi$
$174$		0			0
$175$	−3.62601	−	3.04259i	−0.0207201	−	0.0173862i
$176$		0			0
$177$	113.136	−	94.5452i	0.639188	−	0.534154i
$178$		0			0
$179$	149.606	+	86.3751i	0.835788	+	0.482542i	0.855830	−	0.517257i	$-0.173047\pi$
$179$	149.606	+	86.3751i	0.835788	+	0.482542i	−0.0200423	+	0.999799i	$0.506380\pi$
$180$		0			0
$181$	126.841	+	219.695i	0.700778	+	1.21378i	0.968194	+	0.250201i	$0.0804968\pi$
$181$	126.841	+	219.695i	0.700778	+	1.21378i	−0.267416	+	0.963581i	$0.586170\pi$
$182$		0			0
$183$	−179.485	+	103.145i	−0.980794	+	0.563633i
$184$		0			0
$185$	182.041	+	32.0988i	0.984006	+	0.173507i
$186$		0			0
$187$	−89.6987	+	75.2661i	−0.479672	+	0.402493i
$188$		0			0
$189$	−3.93661	+	10.6159i	−0.0208286	+	0.0561686i
$190$		0			0
$191$	197.779	+	235.704i	1.03549	+	1.23405i	0.971732	+	0.236088i	$0.0758655\pi$
$191$	197.779	+	235.704i	1.03549	+	1.23405i	0.0637623	+	0.997965i	$0.479690\pi$
$192$		0			0
$193$	35.8393	−	203.255i	0.185696	−	1.05313i	−0.739363	−	0.673307i	$-0.764873\pi$
$193$	35.8393	−	203.255i	0.185696	−	1.05313i	0.925058	−	0.379825i	$-0.124016\pi$
$194$		0			0
$195$	−53.0568	−	0.106790i	−0.272086	−	0.000547639i
$196$		0			0
$197$	−211.002	+	121.822i	−1.07108	+	0.618386i	−0.928475	−	0.371394i	$-0.878880\pi$
$197$	−211.002	+	121.822i	−1.07108	+	0.618386i	−0.142601	+	0.989780i	$0.545546\pi$
$198$		0			0
$199$	57.5016	−	99.5957i	0.288953	−	0.500481i	−0.684607	−	0.728912i	$-0.740026\pi$
$199$	57.5016	−	99.5957i	0.288953	−	0.500481i	0.973560	+	0.228431i	$0.0733596\pi$
$200$		0			0
$201$	−76.0790	+	207.724i	−0.378503	+	1.03345i
$202$		0			0
$203$	−0.890977	+	1.06183i	−0.00438905	+	0.00523067i
$204$		0			0
$205$	141.076	+	51.3475i	0.688176	+	0.250476i
$206$		0			0
$207$	−164.756	+	94.2396i	−0.795922	+	0.455264i
$208$		0			0
$209$	131.931	−	23.2631i	0.631251	−	0.111307i
$210$		0			0
$211$	84.7742	−	30.8553i	0.401773	−	0.146234i	−0.133227	−	0.991086i	$-0.542534\pi$
$211$	84.7742	−	30.8553i	0.401773	−	0.146234i	0.535000	+	0.844852i	$0.320312\pi$
$212$		0			0
$213$	−53.9253	+	302.267i	−0.253170	+	1.41909i
$214$		0			0
$215$		−	241.315i		−	1.12240i
$216$		0			0
$217$	−7.28072			−0.0335517
$218$		0			0
$219$	14.7536	−	17.5109i	0.0673679	−	0.0799585i
$220$		0			0
$221$	38.6552	+	106.204i	0.174910	+	0.480562i
$222$		0			0
$223$	−33.8615	−	192.038i	−0.151845	−	0.861156i	−0.961614	−	0.274407i	$-0.911518\pi$
$223$	−33.8615	−	192.038i	−0.151845	−	0.861156i	0.809769	−	0.586749i	$-0.199593\pi$
$224$		0			0
$225$	−18.0434	+	99.9743i	−0.0801930	+	0.444330i
$226$		0			0
$227$	11.5741	−	31.7996i	0.0509873	−	0.140086i	−0.911585	−	0.411112i	$-0.865141\pi$
$227$	11.5741	−	31.7996i	0.0509873	−	0.140086i	0.962572	+	0.271026i	$0.0873628\pi$
$228$		0			0
$229$	−198.049	−	166.183i	−0.864842	−	0.725689i	0.0981633	−	0.995170i	$-0.468703\pi$
$229$	−198.049	−	166.183i	−0.864842	−	0.725689i	−0.963006	+	0.269481i	$0.913148\pi$
$230$		0			0
$231$	1.06860	+	6.13249i	0.00462598	+	0.0265476i
$232$		0			0
$233$	232.807	+	134.411i	0.999172	+	0.576872i	0.908003	−	0.418963i	$-0.137606\pi$
$233$	232.807	+	134.411i	0.999172	+	0.576872i	0.0911690	+	0.995835i	$0.470940\pi$
$234$		0			0
$235$	−50.6565	−	87.7397i	−0.215560	−	0.373360i
$236$		0			0
$237$	−337.318	−	195.657i	−1.42328	−	0.825556i
$238$		0			0
$239$	−281.988	−	49.7222i	−1.17987	−	0.208043i	−0.450890	−	0.892580i	$-0.648893\pi$
$239$	−281.988	−	49.7222i	−1.17987	−	0.208043i	−0.728978	+	0.684537i	$0.760004\pi$
$240$		0			0
$241$	203.574	−	170.819i	0.844707	−	0.708793i	−0.113910	−	0.993491i	$-0.536338\pi$
$241$	203.574	−	170.819i	0.844707	−	0.708793i	0.958617	+	0.284698i	$0.0918932\pi$
$242$		0			0
$243$	239.721	−	39.7861i	0.986505	−	0.163729i
$244$		0			0
$245$	116.214	+	138.498i	0.474341	+	0.565298i
$246$		0			0
$247$	22.4539	−	127.342i	0.0909063	−	0.515555i
$248$		0			0
$249$	103.323	−	178.131i	0.414951	−	0.715387i
$250$		0			0
$251$	−191.060	+	110.308i	−0.761195	+	0.439476i	−0.829725	−	0.558173i	$-0.811502\pi$
$251$	−191.060	+	110.308i	−0.761195	+	0.439476i	0.0685298	+	0.997649i	$0.478169\pi$
$252$		0			0
$253$	−52.1765	+	90.3724i	−0.206231	+	0.357203i
$254$		0			0
$255$	−258.983	+	45.1284i	−1.01562	+	0.176974i
$256$		0			0
$257$	−83.9405	+	100.036i	−0.326617	+	0.389246i	−0.904217	−	0.427073i	$-0.859545\pi$
$257$	−83.9405	+	100.036i	−0.326617	+	0.389246i	0.577601	+	0.816320i	$0.303989\pi$
$258$		0			0
$259$	−19.6706	−	7.15952i	−0.0759484	−	0.0276429i
$260$		0			0
$261$	29.2760	+	5.28375i	0.112169	+	0.0202443i
$262$		0			0
$263$	367.106	−	64.7307i	1.39584	−	0.246124i	0.575408	−	0.817867i	$-0.304843\pi$
$263$	367.106	−	64.7307i	1.39584	−	0.246124i	0.820433	+	0.571742i	$0.193732\pi$
$264$		0			0
$265$	−205.855	+	74.9251i	−0.776811	+	0.282736i
$266$		0			0
$267$	−365.133	−	307.638i	−1.36754	−	1.15220i
$268$		0			0
$269$		−	494.470i		−	1.83818i	−0.394050	−	0.919089i	$-0.628926\pi$
$269$		−	494.470i		−	1.83818i	0.394050	−	0.919089i	$-0.371074\pi$
$270$		0			0
$271$	142.570			0.526089			0.263044	−	0.964784i	$-0.415273\pi$
$271$	142.570			0.526089			0.263044	+	0.964784i	$0.415273\pi$
$272$		0			0
$273$	5.91497	+	1.05525i	0.0216666	+	0.00386538i
$274$		0			0
$275$	19.1029	+	52.4848i	0.0694651	+	0.190854i
$276$		0			0
$277$	−55.8824	−	316.925i	−0.201742	−	1.14413i	−0.902485	−	0.430721i	$-0.858259\pi$
$277$	−55.8824	−	316.925i	−0.201742	−	1.14413i	0.700744	−	0.713413i	$-0.252852\pi$
$278$		0			0
$279$	77.5846	+	135.638i	0.278081	+	0.486159i
$280$		0			0
$281$	99.5636	−	273.549i	0.354319	−	0.973483i	−0.626647	−	0.779303i	$-0.715573\pi$
$281$	99.5636	−	273.549i	0.354319	−	0.973483i	0.980966	−	0.194180i	$-0.0622046\pi$
$282$		0			0
$283$	−176.969	−	148.495i	−0.625333	−	0.524717i	0.274142	−	0.961689i	$-0.411606\pi$
$283$	−176.969	−	148.495i	−0.625333	−	0.524717i	−0.899475	+	0.436972i	$0.856051\pi$
$284$		0			0
$285$	282.422	+	103.437i	0.990953	+	0.362938i
$286$		0			0
$287$	−14.7236	−	8.50065i	−0.0513016	−	0.0296190i
$288$		0			0
$289$	135.495	+	234.685i	0.468842	+	0.812058i
$290$		0			0
$291$	0.0518718	−	25.7717i	0.000178254	−	0.0885625i
$292$		0			0
$293$	362.264	+	63.8769i	1.23640	+	0.218010i	0.753371	−	0.657596i	$-0.228427\pi$
$293$	362.264	+	63.8769i	1.23640	+	0.218010i	0.483026	+	0.875606i	$0.339538\pi$
$294$		0			0
$295$	139.413	−	116.981i	0.472587	−	0.396547i
$296$		0			0
$297$	102.860	−	85.2567i	0.346330	−	0.287060i
$298$		0			0
$299$	64.7436	+	77.1584i	0.216534	+	0.258055i
$300$		0			0
$301$	−4.74536	+	26.9123i	−0.0157653	+	0.0894096i
$302$		0			0
$303$	−269.587	−	469.116i	−0.889726	−	1.54824i
$304$		0			0
$305$	−221.289	+	127.761i	−0.725536	+	0.418889i
$306$		0			0
$307$	−194.279	+	336.501i	−0.632831	+	1.09610i	0.354139	+	0.935193i	$0.384774\pi$
$307$	−194.279	+	336.501i	−0.632831	+	1.09610i	−0.986970	+	0.160903i	$0.948559\pi$
$308$		0			0
$309$	109.378	+	130.886i	0.353974	+	0.423579i
$310$		0			0
$311$	−298.220	+	355.405i	−0.958907	+	1.14278i	0.0307784	+	0.999526i	$0.490201\pi$
$311$	−298.220	+	355.405i	−0.958907	+	1.14278i	−0.989686	+	0.143255i	$0.954243\pi$
$312$		0			0
$313$	46.6231	+	16.9694i	0.148956	+	0.0542154i	0.415422	−	0.909629i	$-0.363634\pi$
$313$	46.6231	+	16.9694i	0.148956	+	0.0542154i	−0.266466	+	0.963844i	$0.585856\pi$
$314$		0			0
$315$	−4.83272	+	13.1133i	−0.0153420	+	0.0416295i
$316$		0			0
$317$	−125.557	+	22.1392i	−0.396080	+	0.0698396i	−0.368141	−	0.929770i	$-0.620006\pi$
$317$	−125.557	+	22.1392i	−0.396080	+	0.0698396i	−0.0279392	+	0.999610i	$0.508894\pi$
$318$		0			0
$319$	15.3694	−	5.59401i	0.0481800	−	0.0175361i
$320$		0			0
$321$	466.723	−	168.810i	1.45397	−	0.525889i
$322$		0			0
$323$		−	640.686i		−	1.98355i
$324$		0			0
$325$	53.9103			0.165878
$326$		0			0
$327$	30.2264	+	83.5693i	0.0924355	+	0.255564i
$328$		0			0
$329$	3.92402	+	10.7812i	0.0119271	+	0.0327695i
$330$		0			0
$331$	108.947	+	617.872i	0.329146	+	1.86668i	0.478773	+	0.877939i	$0.341082\pi$
$331$	108.947	+	617.872i	0.329146	+	1.86668i	−0.149626	+	0.988743i	$0.547807\pi$
$332$		0			0
$333$	76.2329	+	442.753i	0.228928	+	1.32959i
$334$		0			0
$335$	−93.3909	+	256.589i	−0.278779	+	0.765938i
$336$		0			0
$337$	−180.611	−	151.551i	−0.535938	−	0.449705i	0.334208	−	0.942499i	$-0.391531\pi$
$337$	−180.611	−	151.551i	−0.535938	−	0.449705i	−0.870146	+	0.492794i	$0.835976\pi$
$338$		0			0
$339$	227.496	−	190.112i	0.671078	−	0.560804i
$340$		0			0
$341$	74.4008	+	42.9553i	0.218184	+	0.125969i
$342$		0			0
$343$	−20.5109	−	35.5260i	−0.0597986	−	0.103574i
$344$		0			0
$345$	−203.130	+	116.733i	−0.588782	+	0.338355i
$346$		0			0
$347$	−669.149	−	117.989i	−1.92838	−	0.340026i	−0.928847	−	0.370464i	$-0.879199\pi$
$347$	−669.149	−	117.989i	−1.92838	−	0.340026i	−0.999537	+	0.0304385i	$0.990310\pi$
$348$		0			0
$349$	330.676	−	277.470i	0.947496	−	0.795043i	−0.0313783	−	0.999508i	$-0.509990\pi$
$349$	330.676	−	277.470i	0.947496	−	0.795043i	0.978874	+	0.204464i	$0.0655452\pi$
$350$		0			0
$351$	−43.3719	−	121.440i	−0.123567	−	0.345982i
$352$		0			0
$353$	−198.688	−	236.787i	−0.562856	−	0.670786i	0.407292	−	0.913298i	$-0.366473\pi$
$353$	−198.688	−	236.787i	−0.562856	−	0.670786i	−0.970148	+	0.242512i	$0.922029\pi$
$354$		0			0
$355$	−65.8109	+	373.232i	−0.185383	+	1.05136i
$356$		0			0
$357$	29.7701	+	0.0599195i	0.0833896	+	0.000167842i
$358$		0			0
$359$	−110.775	+	63.9560i	−0.308566	+	0.178150i	−0.646284	−	0.763097i	$-0.723678\pi$
$359$	−110.775	+	63.9560i	−0.308566	+	0.178150i	0.337719	+	0.941247i	$0.390345\pi$
$360$		0			0
$361$	−186.005	+	322.170i	−0.515250	+	0.892438i
$362$		0			0
$363$	−99.5786	+	271.886i	−0.274321	+	0.748997i
$364$		0			0
$365$	18.1673	−	21.6510i	0.0497735	−	0.0593177i
$366$		0			0
$367$	277.830	+	101.122i	0.757030	+	0.275537i	0.691561	−	0.722318i	$-0.256923\pi$
$367$	277.830	+	101.122i	0.757030	+	0.275537i	0.0654694	+	0.997855i	$0.479146\pi$
$368$		0			0
$369$	−1.46883	+	364.881i	−0.00398057	+	0.988838i
$370$		0			0
$371$	24.4310	−	4.30785i	0.0658518	−	0.0116114i
$372$		0			0
$373$	−486.381	+	177.028i	−1.30397	+	0.474607i	−0.898288	−	0.439407i	$-0.855189\pi$
$373$	−486.381	+	177.028i	−1.30397	+	0.474607i	−0.405683	+	0.914014i	$0.632966\pi$
$374$		0			0
$375$	−70.8002	+	396.855i	−0.188801	+	1.05828i
$376$		0			0
$377$		−	15.7869i		−	0.0418749i
$378$		0			0
$379$	−85.3566			−0.225215			−0.112608	−	0.993640i	$-0.535920\pi$
$379$	−85.3566			−0.225215			−0.112608	+	0.993640i	$0.535920\pi$
$380$		0			0
$381$	376.207	−	446.518i	0.987420	−	1.17196i
$382$		0			0
$383$	154.048	+	423.243i	0.402214	+	1.10507i	0.961189	+	0.275889i	$0.0889722\pi$
$383$	154.048	+	423.243i	0.402214	+	1.10507i	−0.558976	+	0.829184i	$0.688806\pi$
$384$		0			0
$385$	1.33425	+	7.56689i	0.00346558	+	0.0196543i
$386$		0			0
$387$	551.938	−	198.377i	1.42620	−	0.512601i
$388$		0			0
$389$	77.8458	−	213.880i	0.200118	−	0.549819i	−0.798522	−	0.601966i	$-0.794384\pi$
$389$	77.8458	−	213.880i	0.200118	−	0.549819i	0.998639	+	0.0521470i	$0.0166064\pi$
$390$		0			0
$391$	382.303	+	320.790i	0.977757	+	0.820435i
$392$		0			0
$393$	−20.6166	−	118.315i	−0.0524596	−	0.301055i
$394$		0			0
$395$	−416.849	−	240.668i	−1.05531	−	0.609285i
$396$		0			0
$397$	310.195	+	537.274i	0.781349	+	1.35334i	0.931156	+	0.364620i	$0.118801\pi$
$397$	310.195	+	537.274i	0.781349	+	1.35334i	−0.149808	+	0.988715i	$0.547865\pi$
$398$		0			0
$399$	−29.4625	−	17.0894i	−0.0738410	−	0.0428305i
$400$		0			0
$401$	78.5688	+	13.8538i	0.195932	+	0.0345481i	0.270753	−	0.962649i	$-0.412727\pi$
$401$	78.5688	+	13.8538i	0.195932	+	0.0345481i	−0.0748208	+	0.997197i	$0.523838\pi$
$402$		0			0
$403$	63.5221	−	53.3014i	0.157623	−	0.132262i
$404$		0			0
$405$	295.797	−	49.7049i	0.730362	−	0.122728i
$406$		0			0
$407$	158.771	+	189.216i	0.390102	+	0.464905i
$408$		0			0
$409$	−50.6875	+	287.463i	−0.123930	+	0.702844i	0.858007	+	0.513638i	$0.171703\pi$
$409$	−50.6875	+	287.463i	−0.123930	+	0.702844i	−0.981937	+	0.189206i	$0.939409\pi$
$410$		0			0
$411$	285.911	−	492.918i	0.695647	−	1.19931i
$412$		0			0
$413$	−17.8482	+	10.3047i	−0.0432160	+	0.0249508i
$414$		0			0
$415$	127.092	−	220.130i	0.306246	−	0.530434i
$416$		0			0
$417$	−160.016	+	27.8832i	−0.383731	+	0.0668661i
$418$		0			0
$419$	−155.180	+	184.937i	−0.370359	+	0.441376i	−0.918747	−	0.394848i	$-0.870797\pi$
$419$	−155.180	+	184.937i	−0.370359	+	0.441376i	0.548388	+	0.836224i	$0.315242\pi$
$420$		0			0
$421$	−227.236	−	82.7073i	−0.539754	−	0.196454i	0.0577343	−	0.998332i	$-0.481612\pi$
$421$	−227.236	−	82.7073i	−0.539754	−	0.196454i	−0.597488	+	0.801878i	$0.703835\pi$
$422$		0			0
$423$	159.036	−	187.990i	0.375972	−	0.444420i
$424$		0			0
$425$	263.056	−	46.3838i	0.618955	−	0.109138i
$426$		0			0
$427$	27.1912	−	9.89679i	0.0636797	−	0.0231775i
$428$		0			0
$429$	−54.2185	−	45.6810i	−0.126384	−	0.106483i
$430$		0			0
$431$		−	173.287i		−	0.402059i	−0.979585	−	0.201029i	$-0.935571\pi$
$431$		−	173.287i		−	0.402059i	0.979585	−	0.201029i	$-0.0644287\pi$
$432$		0			0
$433$	−277.794			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$433$	−277.794			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$434$		0			0
$435$	36.1495	+	6.44918i	0.0831023	+	0.0148257i
$436$		0			0
$437$	−195.285	−	536.542i	−0.446878	−	1.22779i
$438$		0			0
$439$	8.10666	+	45.9751i	0.0184662	+	0.104727i	0.992648	−	0.121039i	$-0.0386226\pi$
$439$	8.10666	+	45.9751i	0.0184662	+	0.104727i	−0.974182	+	0.225766i	$0.927512\pi$
$440$		0			0
$441$	−221.239	+	379.659i	−0.501675	+	0.860905i
$442$		0			0
$443$	−13.9231	+	38.2535i	−0.0314292	+	0.0863511i	−0.954415	−	0.298483i	$-0.903519\pi$
$443$	−13.9231	+	38.2535i	−0.0314292	+	0.0863511i	0.922986	+	0.384834i	$0.125741\pi$
$444$		0			0
$445$	−451.461	−	378.821i	−1.01452	−	0.851282i
$446$		0			0
$447$	−87.9148	−	32.1989i	−0.196677	−	0.0720333i
$448$		0			0
$449$	−59.6506	−	34.4393i	−0.132852	−	0.0767022i	0.432101	−	0.901825i	$-0.357772\pi$
$449$	−59.6506	−	34.4393i	−0.132852	−	0.0767022i	−0.564953	+	0.825123i	$0.691106\pi$
$450$		0			0
$451$	100.305	+	173.734i	0.222407	+	0.385220i
$452$		0			0
$453$	−0.152369	+	75.7023i	−0.000336356	+	0.167113i
$454$		0			0
$455$	7.30368	+	1.28784i	0.0160520	+	0.00283041i
$456$		0			0
$457$	−285.792	+	239.808i	−0.625365	+	0.524744i	−0.899485	−	0.436952i	$-0.856058\pi$
$457$	−285.792	+	239.808i	−0.625365	+	0.524744i	0.274120	+	0.961696i	$0.411614\pi$
$458$		0			0
$459$	−316.119	−	555.250i	−0.688712	−	1.20969i
$460$		0			0
$461$	−167.368	−	199.462i	−0.363055	−	0.432672i	0.553335	−	0.832959i	$-0.313355\pi$
$461$	−167.368	−	199.462i	−0.363055	−	0.432672i	−0.916390	+	0.400287i	$0.868910\pi$
$462$		0			0
$463$	146.176	−	829.003i	0.315714	−	1.79050i	−0.252474	−	0.967604i	$-0.581244\pi$
$463$	146.176	−	829.003i	0.315714	−	1.79050i	0.568188	−	0.822899i	$-0.307645\pi$
$464$		0			0
$465$	96.1023	+	167.230i	0.206672	+	0.359635i
$466$		0			0
$467$	−43.5511	+	25.1442i	−0.0932572	+	0.0538421i	−0.545903	−	0.837848i	$-0.683813\pi$
$467$	−43.5511	+	25.1442i	−0.0932572	+	0.0538421i	0.452646	+	0.891690i	$0.350480\pi$
$468$		0			0
$469$	15.4610	−	26.7792i	0.0329658	−	0.0570985i
$470$		0			0
$471$	−152.410	−	182.379i	−0.323588	−	0.387217i
$472$		0			0
$473$	207.271	−	247.016i	0.438206	−	0.522233i
$474$		0			0
$475$	−287.175	−	104.523i	−0.604579	−	0.220049i
$476$		0			0
$477$	−340.595	−	409.240i	−0.714036	−	0.857946i
$478$		0			0
$479$	−285.923	+	50.4159i	−0.596917	+	0.105252i	−0.463940	−	0.885867i	$-0.653565\pi$
$479$	−285.923	+	50.4159i	−0.596917	+	0.105252i	−0.132977	+	0.991119i	$0.542454\pi$
$480$		0			0
$481$	224.034	−	81.5419i	0.465768	−	0.169526i
$482$		0			0
$483$	24.9492	−	9.02394i	0.0516547	−	0.0186831i
$484$		0			0
$485$		−	31.8110i		−	0.0655897i
$486$		0			0
$487$	211.322			0.433925			0.216963	−	0.976180i	$-0.430385\pi$
$487$	211.322			0.433925			0.216963	+	0.976180i	$0.430385\pi$
$488$		0			0
$489$	−58.8863	−	162.808i	−0.120422	−	0.332940i
$490$		0			0
$491$	−67.3176	−	184.954i	−0.137103	−	0.376688i	0.852073	−	0.523424i	$-0.175345\pi$
$491$	−67.3176	−	184.954i	−0.137103	−	0.376688i	−0.989176	+	0.146736i	$0.953123\pi$
$492$		0			0
$493$	−13.5828	−	77.0321i	−0.0275514	−	0.156252i
$494$		0			0
$495$	126.752	−	105.491i	0.256064	−	0.213113i
$496$		0			0
$497$	14.6789	−	40.3299i	0.0295350	−	0.0811468i
$498$		0			0
$499$	373.550	+	313.445i	0.748596	+	0.628147i	0.935131	−	0.354301i	$-0.115281\pi$
$499$	373.550	+	313.445i	0.748596	+	0.628147i	−0.186535	+	0.982448i	$0.559726\pi$
$500$		0			0
$501$	−227.513	+	190.127i	−0.454118	+	0.379495i
$502$		0			0
$503$	829.430	+	478.871i	1.64897	+	0.952031i	0.977484	+	0.211009i	$0.0676749\pi$
$503$	829.430	+	478.871i	1.64897	+	0.952031i	0.671481	+	0.741022i	$0.265658\pi$
$504$		0			0
$505$	−333.926	−	578.377i	−0.661239	−	1.14530i
$506$		0			0
$507$	380.252	−	218.520i	0.750005	−	0.431005i
$508$		0			0
$509$	92.3684	+	16.2870i	0.181470	+	0.0319981i	0.263645	−	0.964620i	$-0.415075\pi$
$509$	92.3684	+	16.2870i	0.181470	+	0.0319981i	−0.0821744	+	0.996618i	$0.526186\pi$
$510$		0			0
$511$	−2.45184	+	2.05734i	−0.00479812	+	0.00402610i
$512$		0			0
$513$	−4.41392	+	730.989i	−0.00860414	+	1.42493i
$514$		0			0
$515$	135.334	+	161.285i	0.262785	+	0.313175i
$516$		0			0
$517$	23.5084	−	133.323i	0.0454707	−	0.257877i
$518$		0			0
$519$	−220.639	−	0.444089i	−0.425123	−	0.000855663i
$520$		0			0
$521$	−463.569	+	267.642i	−0.889767	+	0.513707i	−0.873866	−	0.486166i	$-0.838395\pi$
$521$	−463.569	+	267.642i	−0.889767	+	0.513707i	−0.0159010	+	0.999874i	$0.505062\pi$
$522$		0			0
$523$	182.495	−	316.090i	0.348939	−	0.604379i	−0.637123	−	0.770763i	$-0.719875\pi$
$523$	182.495	−	316.090i	0.348939	−	0.604379i	0.986061	+	0.166383i	$0.0532088\pi$
$524$		0			0
$525$	4.88363	−	13.3341i	0.00930215	−	0.0253983i
$526$		0			0
$527$	264.097	−	314.738i	0.501132	−	0.597226i
$528$		0			0
$529$	−79.1589	−	28.8115i	−0.149639	−	0.0544641i
$530$		0			0
$531$	382.168	+	222.701i	0.719713	+	0.419398i
$532$		0			0
$533$	190.691	−	33.6240i	0.357769	−	0.0630843i
$534$		0			0
$535$	575.673	−	209.528i	1.07602	−	0.391641i
$536$		0			0
$537$	−91.0203	+	510.195i	−0.169498	+	0.950084i
$538$		0			0
$539$			241.589i			0.448216i
$540$		0			0
$541$	177.907			0.328848			0.164424	−	0.986390i	$-0.447423\pi$
$541$	177.907			0.328848			0.164424	+	0.986390i	$0.447423\pi$
$542$		0			0
$543$	−490.362	+	582.008i	−0.903062	+	1.07184i
$544$		0			0
$545$	37.5171	+	103.077i	0.0688387	+	0.189133i
$546$		0			0
$547$	−25.3653	−	143.854i	−0.0463717	−	0.262987i	0.952804	−	0.303587i	$-0.0981842\pi$
$547$	−25.3653	−	143.854i	−0.0463717	−	0.262987i	−0.999175	+	0.0405999i	$0.987073\pi$
$548$		0			0
$549$	−474.130	−	401.105i	−0.863624	−	0.730611i
$550$		0			0
$551$	−30.6081	+	84.0951i	−0.0555501	+	0.152623i
$552$		0			0
$553$	41.7557	+	35.0372i	0.0755077	+	0.0633584i
$554$		0			0
$555$	95.1969	+	546.316i	0.171526	+	0.984353i
$556$		0			0
$557$	310.962	+	179.534i	0.558280	+	0.322323i	0.752455	−	0.658644i	$-0.228870\pi$
$557$	310.962	+	179.534i	0.558280	+	0.322323i	−0.194175	+	0.980967i	$0.562203\pi$
$558$		0			0
$559$	−155.620	−	269.542i	−0.278390	−	0.482186i
$560$		0			0
$561$	−303.863	−	176.252i	−0.541646	−	0.314175i
$562$		0			0
$563$	88.7692	+	15.6524i	0.157672	+	0.0278018i	0.251927	−	0.967746i	$-0.418936\pi$
$563$	88.7692	+	15.6524i	0.157672	+	0.0278018i	−0.0942550	+	0.995548i	$0.530047\pi$
$564$		0			0
$565$	280.333	−	235.227i	0.496165	−	0.416332i
$566$		0			0
$567$	−33.9657	−	0.273462i	−0.0599042	−	0.000482296i
$568$		0			0
$569$	55.8825	+	66.5981i	0.0982117	+	0.117044i	0.812912	−	0.582387i	$-0.197881\pi$
$569$	55.8825	+	66.5981i	0.0982117	+	0.117044i	−0.714700	+	0.699431i	$0.753437\pi$
$570$		0			0
$571$	−53.7562	+	304.867i	−0.0941440	+	0.533917i	0.900862	+	0.434105i	$0.142935\pi$
$571$	−53.7562	+	304.867i	−0.0941440	+	0.533917i	−0.995006	+	0.0998121i	$0.968176\pi$
$572$		0			0
$573$	−463.143	+	798.472i	−0.808278	+	1.39349i
$574$		0			0
$575$	206.158	−	119.025i	0.358536	−	0.207001i
$576$		0			0
$577$	−0.428109	+	0.741507i	−0.000741957	+	0.00128511i	−0.866396	−	0.499357i	$-0.833570\pi$
$577$	−0.428109	+	0.741507i	−0.000741957	+	0.00128511i	0.865654	+	0.500642i	$0.166903\pi$
$578$		0			0
$579$	609.979	−	106.290i	1.05350	−	0.183576i
$580$		0			0
$581$	−18.5025	+	22.0505i	−0.0318460	+	0.0379526i
$582$		0			0
$583$	−275.073	−	100.118i	−0.471824	−	0.171730i
$584$		0			0
$585$	−53.8371	−	149.789i	−0.0920292	−	0.256050i
$586$		0			0
$587$	−145.579	+	25.6695i	−0.248005	+	0.0437300i	−0.296269	−	0.955105i	$-0.595742\pi$
$587$	−145.579	+	25.6695i	−0.248005	+	0.0437300i	0.0482634	+	0.998835i	$0.484631\pi$
$588$		0			0
$589$	−441.719	+	160.773i	−0.749947	+	0.272958i
$590$		0			0
$591$	−558.980	−	470.960i	−0.945820	−	0.796887i
$592$		0			0
$593$			1100.38i			1.85562i	0.373053	+	0.927810i	$0.378311\pi$
$593$			1100.38i			1.85562i	−0.373053	+	0.927810i	$0.621689\pi$
$594$		0			0
$595$	36.7464			0.0617586
$596$		0			0
$597$	339.647	+	60.5940i	0.568923	+	0.101498i
$598$		0			0
$599$	278.390	+	764.871i	0.464758	+	1.27691i	0.921869	+	0.387503i	$0.126662\pi$
$599$	278.390	+	764.871i	0.464758	+	1.27691i	−0.457110	+	0.889410i	$0.651116\pi$
$600$		0			0
$601$	29.8172	+	169.102i	0.0496127	+	0.281367i	0.999514	−	0.0311835i	$-0.00992763\pi$
$601$	29.8172	+	169.102i	0.0496127	+	0.281367i	−0.949901	+	0.312551i	$0.898817\pi$
$602$		0			0
$603$	−663.646	−	2.67151i	−1.10057	−	0.00443036i
$604$		0			0
$605$	−122.238	+	335.846i	−0.202046	+	0.555117i
$606$		0			0
$607$	228.821	+	192.003i	0.376970	+	0.316315i	0.811512	−	0.584336i	$-0.198645\pi$
$607$	228.821	+	192.003i	0.376970	+	0.316315i	−0.434542	+	0.900652i	$0.643090\pi$
$608$		0			0
$609$	−3.90469	−	1.43010i	−0.00641165	−	0.00234827i
$610$		0			0
$611$	−113.164	−	65.3351i	−0.185211	−	0.106931i
$612$		0			0
$613$	−531.261	−	920.171i	−0.866657	−	1.50109i	−0.865392	−	0.501096i	$-0.832931\pi$
$613$	−531.261	−	920.171i	−0.866657	−	1.50109i	−0.00126544	−	0.999999i	$-0.500403\pi$
$614$		0			0
$615$	−0.906517	+	450.389i	−0.00147401	+	0.732340i
$616$		0			0
$617$	1155.37	+	203.722i	1.87255	+	0.330182i	0.990116	−	0.140248i	$-0.0447900\pi$
$617$	1155.37	+	203.722i	1.87255	+	0.330182i	0.882437	+	0.470430i	$0.155901\pi$
$618$		0			0
$619$	−830.742	+	697.075i	−1.34207	+	1.12613i	−0.360983	+	0.932572i	$0.617559\pi$
$619$	−830.742	+	697.075i	−1.34207	+	1.12613i	−0.981089	+	0.193559i	$0.937997\pi$
$620$		0			0
$621$	−433.977	−	368.638i	−0.698836	−	0.593621i
$622$		0			0
$623$	42.8991	+	51.1251i	0.0688589	+	0.0820628i
$624$		0			0
$625$	−37.4029	+	212.122i	−0.0598446	+	0.339395i
$626$		0			0
$627$	200.249	+	348.459i	0.319376	+	0.555757i
$628$		0			0
$629$	1023.02	−	590.641i	1.62642	−	0.939016i
$630$		0			0
$631$	224.052	−	388.070i	0.355075	−	0.615008i	−0.632056	−	0.774923i	$-0.717789\pi$
$631$	224.052	−	388.070i	0.355075	−	0.615008i	0.987131	+	0.159915i	$0.0511220\pi$
$632$		0			0
$633$	173.549	+	207.675i	0.274169	+	0.328081i
$634$		0			0
$635$	463.256	−	552.087i	0.729537	−	0.869428i
$636$		0			0
$637$	219.122	+	79.7540i	0.343991	+	0.125202i
$638$		0			0
$639$	−907.760	+	156.297i	−1.42059	+	0.244597i
$640$		0			0
$641$	−1055.80	+	186.166i	−1.64711	+	0.290430i	−0.918773	−	0.394787i	$-0.870818\pi$
$641$	−1055.80	+	186.166i	−1.64711	+	0.290430i	−0.728339	+	0.685217i	$0.759707\pi$
$642$		0			0
$643$	567.428	−	206.527i	0.882469	−	0.321193i	0.139263	−	0.990255i	$-0.455527\pi$
$643$	567.428	−	206.527i	0.882469	−	0.321193i	0.743206	+	0.669063i	$0.233304\pi$
$644$		0			0
$645$	680.784	−	246.234i	1.05548	−	0.381759i
$646$		0			0
$647$			666.631i			1.03034i	0.857087	+	0.515171i	$0.172272\pi$
$647$			666.631i			1.03034i	−0.857087	+	0.515171i	$0.827728\pi$
$648$		0			0
$649$	243.185			0.374707
$650$		0			0
$651$	−7.42913	−	20.5399i	−0.0114119	−	0.0315513i
$652$		0			0
$653$	−331.003	−	909.424i	−0.506896	−	1.39269i	−0.884422	−	0.466687i	$-0.845447\pi$
$653$	−331.003	−	909.424i	−0.506896	−	1.39269i	0.377526	−	0.925999i	$-0.376775\pi$
$654$		0			0
$655$	−25.7417	−	145.989i	−0.0393004	−	0.222883i
$656$		0			0
$657$	64.4550	+	23.7540i	0.0981050	+	0.0361552i
$658$		0			0
$659$	−80.4022	+	220.903i	−0.122006	+	0.335210i	−0.985628	−	0.168931i	$-0.945969\pi$
$659$	−80.4022	+	220.903i	−0.122006	+	0.335210i	0.863621	+	0.504141i	$0.168191\pi$
$660$		0			0
$661$	217.996	+	182.920i	0.329797	+	0.276732i	0.792617	−	0.609720i	$-0.208718\pi$
$661$	217.996	+	182.920i	0.329797	+	0.276732i	−0.462820	+	0.886452i	$0.653162\pi$
$662$		0			0
$663$	−260.174	+	217.421i	−0.392419	+	0.327935i
$664$		0			0
$665$	−36.4091	−	21.0208i	−0.0547505	−	0.0316102i
$666$		0			0
$667$	−34.8548	−	60.3703i	−0.0522561	−	0.0905103i
$668$		0			0
$669$	507.213	−	291.480i	0.758167	−	0.435695i
$670$		0			0
$671$	−336.253	−	59.2906i	−0.501123	−	0.0883615i
$672$		0			0
$673$	−456.711	+	383.226i	−0.678620	+	0.569430i	−0.915603	−	0.402084i	$-0.868286\pi$
$673$	−456.711	+	383.226i	−0.678620	+	0.569430i	0.236983	+	0.971514i	$0.423841\pi$
$674$		0			0
$675$	−300.452	+	51.1092i	−0.445115	+	0.0757174i
$676$		0			0
$677$	−193.259	−	230.317i	−0.285464	−	0.340203i	0.604188	−	0.796842i	$-0.293498\pi$
$677$	−193.259	−	230.317i	−0.285464	−	0.340203i	−0.889652	+	0.456639i	$0.849053\pi$
$678$		0			0
$679$	−0.625550	+	3.54767i	−0.000921282	+	0.00522485i
$680$		0			0
$681$	101.521	+	0.204336i	0.149076	+	0.000300052i
$682$		0			0
$683$	690.441	−	398.626i	1.01089	−	0.583640i	0.0994413	−	0.995043i	$-0.468294\pi$
$683$	690.441	−	398.626i	1.01089	−	0.583640i	0.911454	+	0.411403i	$0.134961\pi$
$684$		0			0
$685$	351.685	−	609.136i	0.513408	−	0.889249i
$686$		0			0
$687$	266.738	−	728.293i	0.388265	−	1.06011i
$688$		0			0
$689$	−181.616	+	216.442i	−0.263594	+	0.314139i
$690$		0			0
$691$	571.492	+	208.006i	0.827050	+	0.301022i	0.720648	−	0.693301i	$-0.243845\pi$
$691$	571.492	+	208.006i	0.827050	+	0.301022i	0.106403	+	0.994323i	$0.466067\pi$
$692$		0			0
$693$	−16.2102	+	9.27217i	−0.0233914	+	0.0133798i
$694$		0			0
$695$	−197.444	+	34.8147i	−0.284092	+	0.0500931i
$696$		0			0
$697$	901.548	−	328.137i	1.29347	−	0.470784i
$698$		0			0
$699$	−141.640	+	793.932i	−0.202632	+	1.13581i
$700$		0			0
$701$			722.930i			1.03128i	0.856804	+	0.515642i	$0.172446\pi$
$701$			722.930i			1.03128i	−0.856804	+	0.515642i	$0.827554\pi$
$702$		0			0
$703$	−1351.51			−1.92248
$704$		0			0
$705$	195.837	−	232.437i	0.277782	−	0.329698i
$706$		0			0
$707$	25.8670	+	71.0690i	0.0365870	+	0.100522i
$708$		0			0
$709$	−109.152	−	619.033i	−0.153952	−	0.873108i	−0.959737	−	0.280899i	$-0.909367\pi$
$709$	−109.152	−	619.033i	−0.153952	−	0.873108i	0.805785	−	0.592208i	$-0.201744\pi$
$710$		0			0
$711$	207.781	−	1151.26i	0.292237	−	1.61922i
$712$		0			0
$713$	125.233	−	344.076i	0.175643	−	0.482575i
$714$		0			0
$715$	−67.0373	−	56.2510i	−0.0937584	−	0.0786727i
$716$		0			0
$717$	−147.463	−	846.264i	−0.205667	−	1.18028i
$718$		0			0
$719$	−594.383	−	343.167i	−0.826680	−	0.477284i	0.0260347	−	0.999661i	$-0.491712\pi$
$719$	−594.383	−	343.167i	−0.826680	−	0.477284i	−0.852714	+	0.522377i	$0.825045\pi$
$720$		0			0
$721$	−11.9213	−	20.6484i	−0.0165344	−	0.0286385i
$722$		0			0
$723$	689.629	+	400.010i	0.953843	+	0.553264i
$724$		0			0
$725$	−36.7441	−	6.47897i	−0.0506815	−	0.00893651i
$726$		0			0
$727$	−178.673	+	149.924i	−0.245767	+	0.206223i	−0.757347	−	0.653012i	$-0.773505\pi$
$727$	−178.673	+	149.924i	−0.245767	+	0.206223i	0.511580	+	0.859236i	$0.329060\pi$
$728$		0			0
$729$	356.849	+	635.688i	0.489505	+	0.872000i
$730$		0			0
$731$	−991.261	−	1181.34i	−1.35603	−	1.61606i
$732$		0			0
$733$	−32.0772	+	181.919i	−0.0437615	+	0.248184i	−0.998839	−	0.0481722i	$-0.984660\pi$
$733$	−32.0772	+	181.919i	−0.0437615	+	0.248184i	0.955078	+	0.296356i	$0.0957715\pi$
$734$		0			0
$735$	−272.139	+	469.176i	−0.370258	+	0.638334i
$736$		0			0
$737$	−315.988	+	182.436i	−0.428749	+	0.247538i
$738$		0			0
$739$	117.640	−	203.758i	0.159188	−	0.275721i	−0.775388	−	0.631485i	$-0.782446\pi$
$739$	117.640	−	203.758i	0.159188	−	0.275721i	0.934576	+	0.355763i	$0.115779\pi$
$740$		0			0
$741$	382.161	−	66.5925i	0.515737	−	0.0898685i
$742$		0			0
$743$	808.583	−	963.631i	1.08827	−	1.29695i	0.136327	−	0.990664i	$-0.456470\pi$
$743$	808.583	−	963.631i	1.08827	−	1.29695i	0.951941	−	0.306283i	$-0.0990853\pi$
$744$		0			0
$745$	−108.596	−	39.5258i	−0.145767	−	0.0530547i
$746$		0			0
$747$	607.962	+	109.725i	0.813871	+	0.146888i
$748$		0			0
$749$	−68.3213	+	12.0469i	−0.0912166	+	0.0160840i
$750$		0			0
$751$	−611.586	+	222.599i	−0.814363	+	0.296404i	−0.715425	−	0.698690i	$-0.753767\pi$
$751$	−611.586	+	222.599i	−0.814363	+	0.296404i	−0.0989379	+	0.995094i	$0.531545\pi$
$752$		0			0
$753$	−506.150	−	426.449i	−0.672178	−	0.566333i
$754$		0			0
$755$			93.4423i			0.123765i
$756$		0			0
$757$	802.442			1.06003			0.530015	−	0.847988i	$-0.322186\pi$
$757$	802.442			1.06003			0.530015	+	0.847988i	$0.322186\pi$
$758$		0			0
$759$	−308.193	−	54.9826i	−0.406051	−	0.0724408i
$760$		0			0
$761$	−242.179	−	665.380i	−0.318237	−	0.874350i	−0.990924	−	0.134422i	$-0.957082\pi$
$761$	−242.179	−	665.380i	−0.318237	−	0.874350i	0.672687	−	0.739927i	$-0.265140\pi$
$762$		0			0
$763$	−2.15706	−	12.2333i	−0.00282708	−	0.0160332i
$764$		0			0
$765$	−391.576	−	684.578i	−0.511863	−	0.894873i
$766$		0			0
$767$	80.2809	−	220.570i	0.104669	−	0.287575i
$768$		0			0
$769$	840.006	+	704.848i	1.09233	+	0.916578i	0.996886	−	0.0788564i	$-0.0251269\pi$
$769$	840.006	+	704.848i	1.09233	+	0.916578i	0.0954490	+	0.995434i	$0.469571\pi$
$770$		0			0
$771$	−367.868	−	134.732i	−0.477131	−	0.174750i
$772$		0			0
$773$	−218.368	−	126.075i	−0.282495	−	0.163098i	0.352058	−	0.935978i	$-0.385482\pi$
$773$	−218.368	−	126.075i	−0.282495	−	0.163098i	−0.634552	+	0.772880i	$0.718815\pi$
$774$		0			0
$775$	−97.9899	−	169.723i	−0.126439	−	0.218998i
$776$		0			0
$777$	0.126398	−	62.7990i	0.000162675	−	0.0808224i
$778$		0			0
$779$	−1080.98	−	190.607i	−1.38766	−	0.244681i
$780$		0			0
$781$	−387.943	+	325.523i	−0.496726	+	0.416803i
$782$		0			0
$783$	14.9666	+	87.9831i	0.0191144	+	0.112367i
$784$		0			0
$785$	−188.578	−	224.738i	−0.240226	−	0.286291i
$786$		0			0
$787$	−126.861	+	719.465i	−0.161196	+	0.914187i	0.791705	+	0.610904i	$0.209194\pi$
$787$	−126.861	+	719.465i	−0.161196	+	0.914187i	−0.952901	+	0.303283i	$0.901917\pi$
$788$		0			0
$789$	557.204	+	969.607i	0.706215	+	1.22891i
$790$		0			0
$791$	−35.8893	+	20.7207i	−0.0453721	+	0.0261956i
$792$		0			0
$793$	−164.782	+	285.411i	−0.207796	+	0.359912i
$794$		0			0
$795$	−421.425	−	504.293i	−0.530095	−	0.634331i
$796$		0			0
$797$	−749.785	+	893.559i	−0.940759	+	1.12115i	0.0517109	+	0.998662i	$0.483533\pi$
$797$	−749.785	+	893.559i	−0.940759	+	1.12115i	−0.992470	+	0.122491i	$0.960912\pi$
$798$		0			0
$799$	−608.396	−	221.438i	−0.761447	−	0.277144i
$800$		0			0
$801$	495.312	−	1344.00i	0.618367	−	1.67790i
$802$		0			0
$803$	37.1930	−	6.55814i	0.0463176	−	0.00816705i
$804$		0			0
$805$	30.7732	−	11.2005i	0.0382276	−	0.0139137i
$806$		0			0
$807$	1394.97	−	504.549i	1.72858	−	0.625216i
$808$		0			0
$809$			114.072i			0.141004i	0.997512	+	0.0705020i	$0.0224601\pi$
$809$			114.072i			0.141004i	−0.997512	+	0.0705020i	$0.977540\pi$
$810$		0			0
$811$	−342.119			−0.421849			−0.210924	−	0.977502i	$-0.567647\pi$
$811$	−342.119			−0.421849			−0.210924	+	0.977502i	$0.567647\pi$
$812$		0			0
$813$	145.476	+	402.210i	0.178938	+	0.494723i
$814$		0			0
$815$	−73.0898	−	200.813i	−0.0896808	−	0.246396i
$816$		0			0
$817$	306.376	+	1737.55i	0.375002	+	2.12674i
$818$		0			0
$819$	3.05854	+	17.7637i	0.00373448	+	0.0216895i
$820$		0			0
$821$	−313.702	+	861.889i	−0.382098	+	1.04980i	0.588374	+	0.808589i	$0.299768\pi$
$821$	−313.702	+	861.889i	−0.382098	+	1.04980i	−0.970472	+	0.241216i	$0.922454\pi$
$822$		0			0
$823$	−555.765	−	466.342i	−0.675292	−	0.566637i	0.239335	−	0.970937i	$-0.423071\pi$
$823$	−555.765	−	466.342i	−0.675292	−	0.566637i	−0.914626	+	0.404300i	$0.867515\pi$
$824$		0			0
$825$	−128.575	+	107.447i	−0.155848	+	0.130238i
$826$		0			0
$827$	−407.878	−	235.488i	−0.493202	−	0.284750i	0.232700	−	0.972549i	$-0.425244\pi$
$827$	−407.878	−	235.488i	−0.493202	−	0.284750i	−0.725902	+	0.687798i	$0.758577\pi$
$828$		0			0
$829$	781.648	+	1353.85i	0.942881	+	1.63312i	0.759940	+	0.649993i	$0.225228\pi$
$829$	781.648	+	1353.85i	0.942881	+	1.63312i	0.182940	+	0.983124i	$0.441438\pi$
$830$		0			0
$831$	837.068	−	481.037i	1.00730	−	0.578866i
$832$		0			0
$833$	1137.83	+	200.630i	1.36594	+	0.240852i
$834$		0			0
$835$	−280.355	+	235.245i	−0.335754	+	0.281731i
$836$		0			0
$837$	−303.489	+	357.280i	−0.362591	+	0.426858i
$838$		0			0
$839$	546.909	+	651.781i	0.651858	+	0.776854i	0.986193	−	0.165600i	$-0.0529561\pi$
$839$	546.909	+	651.781i	0.651858	+	0.776854i	−0.334335	+	0.942454i	$0.608512\pi$
$840$		0			0
$841$	144.141	−	817.463i	0.171392	−	0.972014i
$842$		0			0
$843$	873.312	+	1.75775i	1.03596	+	0.00208511i
$844$		0			0
$845$	468.816	−	270.671i	0.554811	−	0.320321i
$846$		0			0
$847$	20.2366	−	35.0509i	0.0238921	−	0.0413824i
$848$		0			0
$849$	238.348	−	650.776i	0.280739	−	0.766521i
$850$		0			0
$851$	676.696	−	806.455i	0.795178	−	0.947656i
$852$		0			0
$853$	−59.6797	−	21.7216i	−0.0699644	−	0.0254650i	0.306801	−	0.951774i	$-0.400741\pi$
$853$	−59.6797	−	21.7216i	−0.0699644	−	0.0254650i	−0.376765	+	0.926309i	$0.622964\pi$
$854$		0			0
$855$	−3.63219	+	902.296i	−0.00424818	+	1.05532i
$856$		0			0
$857$	−134.075	+	23.6410i	−0.156447	+	0.0275858i	−0.251323	−	0.967903i	$-0.580866\pi$
$857$	−134.075	+	23.6410i	−0.156447	+	0.0275858i	0.0948762	+	0.995489i	$0.469754\pi$
$858$		0			0
$859$	−228.573	+	83.1938i	−0.266092	+	0.0968496i	−0.471621	−	0.881802i	$-0.656331\pi$
$859$	−228.573	+	83.1938i	−0.266092	+	0.0968496i	0.205529	+	0.978651i	$0.434109\pi$
$860$		0			0
$861$	8.95781	−	50.2111i	0.0104040	−	0.0583172i
$862$		0			0
$863$			1043.35i			1.20898i	0.796612	+	0.604490i	$0.206623\pi$
$863$			1043.35i			1.20898i	−0.796612	+	0.604490i	$0.793377\pi$
$864$		0			0
$865$	−272.343			−0.314848
$866$		0			0
$867$	−523.821	+	621.719i	−0.604176	+	0.717093i
$868$		0			0
$869$	−219.982	−	604.394i	−0.253143	−	0.695506i
$870$		0			0
$871$	61.1553	+	346.829i	0.0702127	+	0.398196i
$872$		0			0
$873$	72.7584	−	26.1507i	0.0833430	−	0.0299550i
$874$		0			0
$875$	19.2724	−	52.9504i	0.0220256	−	0.0605148i
$876$		0			0
$877$	1205.65	+	1011.66i	1.37475	+	1.15355i	0.971110	+	0.238631i	$0.0766986\pi$
$877$	1205.65	+	1011.66i	1.37475	+	1.15355i	0.403637	+	0.914919i	$0.367746\pi$
$878$		0			0
$879$	189.443	+	1087.18i	0.215521	+	1.23683i
$880$		0			0
$881$	−1033.74	−	596.831i	−1.17337	−	0.677447i	−0.218901	−	0.975747i	$-0.570247\pi$
$881$	−1033.74	−	596.831i	−1.17337	−	0.677447i	−0.954472	+	0.298300i	$0.903581\pi$
$882$		0			0
$883$	139.976	+	242.446i	0.158523	+	0.274570i	0.934336	−	0.356392i	$-0.115993\pi$
$883$	139.976	+	242.446i	0.158523	+	0.274570i	−0.775813	+	0.630963i	$0.782660\pi$
$884$		0			0
$885$	472.276	+	273.937i	0.533645	+	0.309534i
$886$		0			0
$887$	−279.453	−	49.2751i	−0.315054	−	0.0555526i	0.0138851	−	0.999904i	$-0.495580\pi$
$887$	−279.453	−	49.2751i	−0.315054	−	0.0555526i	−0.328939	+	0.944351i	$0.606691\pi$
$888$		0			0
$889$	−62.5204	+	52.4609i	−0.0703267	+	0.0590111i
$890$		0			0
$891$	345.478	+	203.188i	0.387741	+	0.228044i
$892$		0			0
$893$	476.138	+	567.439i	0.533189	+	0.635430i
$894$		0			0
$895$	−111.082	+	629.977i	−0.124114	+	0.703885i
$896$		0			0
$897$	−151.611	+	261.382i	−0.169020	+	0.291395i
$898$		0			0
$899$	−49.7010	+	28.6949i	−0.0552848	+	0.0319187i
$900$		0			0
$901$	−699.973	+	1212.39i	−0.776884	+	1.34560i
$902$		0			0
$903$	−80.7654	+	14.0736i	−0.0894412	+	0.0155853i
$904$		0			0
$905$	−603.825	+	719.611i	−0.667210	+	0.795150i
$906$		0			0
$907$	−92.0530	−	33.5046i	−0.101492	−	0.0369400i	0.290775	−	0.956791i	$-0.406087\pi$
$907$	−92.0530	−	33.5046i	−0.101492	−	0.0369400i	−0.392267	+	0.919851i	$0.628309\pi$
$908$		0			0
$909$	1048.36	−	1239.22i	1.15331	−	1.36328i
$910$		0			0
$911$	−400.721	+	70.6580i	−0.439870	+	0.0775609i	−0.389197	−	0.921154i	$-0.627248\pi$
$911$	−400.721	+	70.6580i	−0.439870	+	0.0775609i	−0.0506725	+	0.998715i	$0.516136\pi$
$912$		0			0
$913$	319.170	−	116.168i	0.349584	−	0.127238i
$914$		0			0
$915$	−586.231	−	493.920i	−0.640689	−	0.539804i
$916$		0			0
$917$			16.7873i			0.0183068i
$918$		0			0
$919$	1484.71			1.61557			0.807784	−	0.589479i	$-0.200667\pi$
$919$	1484.71			1.61557			0.807784	+	0.589479i	$0.200667\pi$
$920$		0			0
$921$	−1147.56	−	204.727i	−1.24599	−	0.222288i
$922$		0			0
$923$	167.182	+	459.329i	0.181129	+	0.497648i
$924$		0			0
$925$	−97.8452	−	554.908i	−0.105779	−	0.599900i
$926$		0			0
$927$	−257.639	+	442.124i	−0.277928	+	0.476941i
$928$		0			0
$929$	186.754	−	513.101i	0.201026	−	0.552316i	−0.797684	−	0.603075i	$-0.793942\pi$
$929$	186.754	−	513.101i	0.201026	−	0.552316i	0.998711	+	0.0507594i	$0.0161642\pi$
$930$		0			0
$931$	−1012.61	−	849.684i	−1.08766	−	0.912657i
$932$		0			0
$933$	−1306.95	−	478.670i	−1.40080	−	0.513044i
$934$		0			0
$935$	−375.507	−	216.799i	−0.401611	−	0.231870i
$936$		0			0
$937$	−730.836	−	1265.84i	−0.779974	−	1.35095i	−0.931956	−	0.362572i	$-0.881899\pi$
$937$	−730.836	−	1265.84i	−0.779974	−	1.35095i	0.151982	−	0.988383i	$-0.451435\pi$
$938$		0			0
$939$	−0.299587	+	148.845i	−0.000319049	+	0.158515i
$940$		0			0
$941$	−1339.88	−	236.256i	−1.42388	−	0.251069i	−0.591964	−	0.805964i	$-0.701647\pi$
$941$	−1339.88	−	236.256i	−1.42388	−	0.251069i	−0.831921	+	0.554895i	$0.812759\pi$
$942$		0			0
$943$	654.983	−	549.596i	0.694574	−	0.582816i
$944$		0			0
$945$	−41.9257	−	0.253159i	−0.0443658	−	0.000267893i
$946$		0			0
$947$	−339.126	−	404.154i	−0.358105	−	0.426773i	0.556672	−	0.830733i	$-0.312078\pi$
$947$	−339.126	−	404.154i	−0.358105	−	0.426773i	−0.914777	+	0.403959i	$0.867634\pi$
$948$		0			0
$949$	6.33001	−	35.8993i	0.00667019	−	0.0378285i
$950$		0			0
$951$	−190.574	−	331.624i	−0.200394	−	0.348711i
$952$		0			0
$953$	671.482	−	387.680i	0.704598	−	0.406800i	−0.104460	−	0.994529i	$-0.533311\pi$
$953$	671.482	−	387.680i	0.704598	−	0.406800i	0.809058	+	0.587729i	$0.199978\pi$
$954$		0			0
$955$	−569.690	+	986.731i	−0.596534	+	1.03323i
$956$		0			0
$957$	31.4642	+	37.6512i	0.0328779	+	0.0393429i
$958$		0			0
$959$	−51.1995	+	61.0172i	−0.0533884	+	0.0636258i
$960$		0			0
$961$	619.778	+	225.581i	0.644930	+	0.234735i
$962$		0			0
$963$	952.474	+	1144.44i	0.989069	+	1.18841i
$964$		0			0
$965$	752.654	−	132.713i	0.779952	−	0.137527i
$966$		0			0
$967$	−1178.44	+	428.916i	−1.21865	+	0.443553i	−0.869697	−	0.493586i	$-0.835686\pi$
$967$	−1178.44	+	428.916i	−1.21865	+	0.443553i	−0.348956	+	0.937139i	$0.613464\pi$
$968$		0			0
$969$	1807.46	−	653.746i	1.86529	−	0.674661i
$970$		0			0
$971$			1101.11i			1.13400i	0.823719	+	0.566998i	$0.191895\pi$
$971$			1101.11i			1.13400i	−0.823719	+	0.566998i	$0.808105\pi$
$972$		0			0
$973$	22.7042			0.0233342
$974$		0			0
$975$	55.0093	+	152.088i	0.0564198	+	0.155988i
$976$		0			0
$977$	450.997	+	1239.11i	0.461615	+	1.26828i	0.924271	+	0.381738i	$0.124674\pi$
$977$	450.997	+	1239.11i	0.461615	+	1.26828i	−0.462656	+	0.886538i	$0.653104\pi$
$978$		0			0
$979$	−136.749	−	775.540i	−0.139682	−	0.792176i
$980$		0			0
$981$	−204.918	+	170.546i	−0.208887	+	0.173849i
$982$		0			0
$983$	545.281	−	1498.15i	0.554711	−	1.52406i	−0.272496	−	0.962157i	$-0.587849\pi$
$983$	545.281	−	1498.15i	0.554711	−	1.52406i	0.827206	−	0.561898i	$-0.189929\pi$
$984$		0			0
$985$	−691.138	−	579.934i	−0.701663	−	0.588765i
$986$		0			0
$987$	−26.4111	+	22.0711i	−0.0267590	+	0.0223618i
$988$		0			0
$989$	−1190.21	−	687.168i	−1.20345	−	0.694811i
$990$		0			0
$991$	216.060	+	374.228i	0.218023	+	0.377626i	0.954203	−	0.299159i	$-0.0967060\pi$
$991$	216.060	+	374.228i	0.218023	+	0.377626i	−0.736181	+	0.676785i	$0.763373\pi$
$992$		0			0
$993$	−1631.93	+	937.822i	−1.64344	+	0.944433i
$994$		0			0
$995$	419.388	+	73.9495i	0.421496	+	0.0743211i
$996$		0			0
$997$	1122.30	−	941.723i	1.12568	−	0.944556i	0.126801	−	0.991928i	$-0.459529\pi$
$997$	1122.30	−	941.723i	1.12568	−	0.944556i	0.998877	+	0.0473719i	$0.0150846\pi$
$998$		0			0
$999$	−1171.28	+	666.842i	−1.17245	+	0.667510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.5.4	✓	36
3.2	odd	2		324.3.k.a.125.2		36
4.3	odd	2		432.3.bc.b.113.3		36
27.4	even	9		2916.3.c.b.1457.12		36
27.11	odd	18	inner	108.3.k.a.65.4	yes	36
27.16	even	9		324.3.k.a.197.2		36
27.23	odd	18		2916.3.c.b.1457.25		36
108.11	even	18		432.3.bc.b.65.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.4	✓	36	1.1	even	1	trivial
108.3.k.a.65.4	yes	36	27.11	odd	18	inner
324.3.k.a.125.2		36	3.2	odd	2
324.3.k.a.197.2		36	27.16	even	9
432.3.bc.b.65.3		36	108.11	even	18
432.3.bc.b.113.3		36	4.3	odd	2
2916.3.c.b.1457.12		36	27.4	even	9
2916.3.c.b.1457.25		36	27.23	odd	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +O(q^{10})\)	\(q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +(-1.69236 + 4.64973i) q^{11} +(3.65864 + 3.06996i) q^{13} +(-8.52437 + 7.12360i) q^{15} +(20.4937 + 11.8321i) q^{17} +(-13.5371 - 23.4469i) q^{19} +(1.09075 - 0.626820i) q^{21} +(20.7690 + 3.66213i) q^{23} +(8.64689 - 7.25561i) q^{25} +(-23.3007 - 13.6409i) q^{27} +(-2.12470 - 2.53212i) q^{29} +(3.01492 - 17.0984i) q^{31} +(-14.8444 - 0.0298779i) q^{33} +(1.34479 - 0.776415i) q^{35} +(24.9593 - 43.2309i) q^{37} +(-4.92757 + 13.4541i) q^{39} +(26.0603 - 31.0575i) q^{41} +(-61.2373 - 22.2885i) q^{43} +(-28.7948 - 16.7796i) q^{45} +(-26.9440 + 4.75095i) q^{47} +(45.8797 - 16.6988i) q^{49} +(-12.4684 + 69.8889i) q^{51} +59.1590i q^{53} -18.3230 q^{55} +(52.3339 - 62.1148i) q^{57} +(-16.8092 - 46.1828i) q^{59} +(11.9824 + 67.9556i) q^{61} +(2.88133 + 2.43755i) q^{63} +(-6.04884 + 16.6191i) q^{65} +(56.4874 + 47.3986i) q^{67} +(10.8610 + 62.3289i) q^{69} +(88.6346 + 51.1732i) q^{71} +(-3.81627 - 6.60997i) q^{73} +(29.2922 + 16.9906i) q^{75} +(2.04344 + 0.360314i) q^{77} +(-99.5742 + 83.5527i) q^{79} +(14.7073 - 79.6536i) q^{81} +(-44.1227 - 52.5834i) q^{83} +(-15.2165 + 86.2972i) q^{85} +(4.97544 - 8.57780i) q^{87} +(-137.829 + 79.5758i) q^{89} +(1.00139 - 1.73447i) q^{91} +(51.3134 - 8.94149i) q^{93} +(64.4432 - 76.8005i) q^{95} +(-8.07251 - 2.93815i) q^{97} +(-15.0627 - 41.9085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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