LMFDB - Embedded newform 108.3.k.a.41.4

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			41.4
Character	$\chi$	$=$	108.41
Dual form			108.3.k.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +O(q^{10})$	\(q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +(12.6606 + 15.0883i) q^{11} +(-1.31536 + 7.45976i) q^{13} +(20.5507 + 16.5161i) q^{15} +(-3.16520 - 1.82743i) q^{17} +(-16.8333 - 29.1562i) q^{19} +(-4.16730 + 12.2498i) q^{21} +(1.05125 + 2.88830i) q^{23} +(-9.07052 - 51.4415i) q^{25} +(-1.71228 - 26.9457i) q^{27} +(23.9443 - 4.22203i) q^{29} +(-27.1255 + 9.87288i) q^{31} +(-44.4514 + 38.9307i) q^{33} +(32.8265 - 18.9524i) q^{35} +(-14.9004 + 25.8083i) q^{37} +(-22.4577 - 3.47182i) q^{39} +(-22.6547 - 3.99463i) q^{41} +(-6.85241 + 5.74986i) q^{43} +(-48.2333 + 62.6865i) q^{45} +(3.60489 - 9.90435i) q^{47} +(-23.2857 - 19.5391i) q^{49} +(5.28021 - 9.60944i) q^{51} -70.8948i q^{53} +173.099 q^{55} +(86.3808 - 52.3388i) q^{57} +(-43.8902 + 52.3064i) q^{59} +(-99.7950 - 36.3224i) q^{61} +(-37.0056 - 11.7218i) q^{63} +(42.7906 + 50.9958i) q^{65} +(-4.27685 + 24.2552i) q^{67} +(-8.59625 + 3.33634i) q^{69} +(29.9139 + 17.2708i) q^{71} +(20.9190 + 36.2328i) q^{73} +(153.714 - 30.4697i) q^{75} +(29.0553 + 79.8287i) q^{77} +(8.78445 + 49.8191i) q^{79} +(80.7102 - 6.84554i) q^{81} +(-30.9208 + 5.45218i) q^{83} +(-30.1831 + 10.9857i) q^{85} +(14.1827 + 71.5490i) q^{87} +(40.0231 - 23.1073i) q^{89} +(-16.3354 + 28.2938i) q^{91} +(-31.3333 - 80.7318i) q^{93} +(-291.379 - 51.3780i) q^{95} +(84.8132 - 71.1668i) q^{97} +(-119.587 - 130.854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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
$3$	0.0634556	+	2.99933i	0.0211519	+	0.999776i
$3$	0.0634556	+	2.99933i	0.0211519	+	0.999776i
$4$		0			0
$5$	5.64904	−	6.73227i	1.12981	−	1.34645i	0.199404	−	0.979917i	$-0.436099\pi$
$5$	5.64904	−	6.73227i	1.12981	−	1.34645i	0.930404	−	0.366536i	$-0.119456\pi$
$6$		0			0
$7$	4.05297	+	1.47516i	0.578995	+	0.210737i	0.614882	−	0.788619i	$-0.289204\pi$
$7$	4.05297	+	1.47516i	0.578995	+	0.210737i	−0.0358873	+	0.999356i	$0.511426\pi$
$8$		0			0
$9$	−8.99195	+	0.380648i	−0.999105	+	0.0422943i
$10$		0			0
$11$	12.6606	+	15.0883i	1.15096	+	1.37166i	0.916742	+	0.399479i	$0.130809\pi$
$11$	12.6606	+	15.0883i	1.15096	+	1.37166i	0.234219	+	0.972184i	$0.424747\pi$
$12$		0			0
$13$	−1.31536	+	7.45976i	−0.101181	+	0.573828i	0.891496	+	0.453029i	$0.149657\pi$
$13$	−1.31536	+	7.45976i	−0.101181	+	0.573828i	−0.992677	+	0.120799i	$0.961454\pi$
$14$		0			0
$15$	20.5507	+	16.5161i	1.37005	+	1.10108i
$16$		0			0
$17$	−3.16520	−	1.82743i	−0.186188	−	0.107496i	0.404009	−	0.914755i	$-0.367617\pi$
$17$	−3.16520	−	1.82743i	−0.186188	−	0.107496i	−0.590197	+	0.807259i	$0.700950\pi$
$18$		0			0
$19$	−16.8333	−	29.1562i	−0.885964	−	1.53453i	−0.844605	−	0.535391i	$-0.820164\pi$
$19$	−16.8333	−	29.1562i	−0.885964	−	1.53453i	−0.0413596	−	0.999144i	$-0.513169\pi$
$20$		0			0
$21$	−4.16730	+	12.2498i	−0.198443	+	0.583323i
$22$		0			0
$23$	1.05125	+	2.88830i	0.0457067	+	0.125578i	0.960446	−	0.278467i	$-0.0898262\pi$
$23$	1.05125	+	2.88830i	0.0457067	+	0.125578i	−0.914739	+	0.404045i	$0.867604\pi$
$24$		0			0
$25$	−9.07052	−	51.4415i	−0.362821	−	2.05766i
$26$		0			0
$27$	−1.71228	−	26.9457i	−0.0634178	−	0.997987i
$28$		0			0
$29$	23.9443	−	4.22203i	0.825667	−	0.145587i	0.255179	−	0.966894i	$-0.417865\pi$
$29$	23.9443	−	4.22203i	0.825667	−	0.145587i	0.570487	+	0.821306i	$0.306754\pi$
$30$		0			0
$31$	−27.1255	+	9.87288i	−0.875016	+	0.318480i	−0.740197	−	0.672390i	$-0.765268\pi$
$31$	−27.1255	+	9.87288i	−0.875016	+	0.318480i	−0.134820	+	0.990870i	$0.543045\pi$
$32$		0			0
$33$	−44.4514	+	38.9307i	−1.34701	+	1.17972i
$34$		0			0
$35$	32.8265	−	18.9524i	0.937901	−	0.541497i
$36$		0			0
$37$	−14.9004	+	25.8083i	−0.402714	+	0.697522i	−0.994052	−	0.108902i	$-0.965267\pi$
$37$	−14.9004	+	25.8083i	−0.402714	+	0.697522i	0.591338	+	0.806424i	$0.298600\pi$
$38$		0			0
$39$	−22.4577	−	3.47182i	−0.575839	−	0.0890211i
$40$		0			0
$41$	−22.6547	−	3.99463i	−0.552552	−	0.0974299i	−0.109601	−	0.993976i	$-0.534957\pi$
$41$	−22.6547	−	3.99463i	−0.552552	−	0.0974299i	−0.442951	+	0.896546i	$0.646069\pi$
$42$		0			0
$43$	−6.85241	+	5.74986i	−0.159358	+	0.133718i	−0.718980	−	0.695031i	$-0.755391\pi$
$43$	−6.85241	+	5.74986i	−0.159358	+	0.133718i	0.559622	+	0.828748i	$0.310946\pi$
$44$		0			0
$45$	−48.2333	+	62.6865i	−1.07185	+	1.39303i
$46$		0			0
$47$	3.60489	−	9.90435i	0.0766997	−	0.210731i	−0.895417	−	0.445229i	$-0.853122\pi$
$47$	3.60489	−	9.90435i	0.0766997	−	0.210731i	0.972117	+	0.234498i	$0.0753446\pi$
$48$		0			0
$49$	−23.2857	−	19.5391i	−0.475219	−	0.398756i
$50$		0			0
$51$	5.28021	−	9.60944i	0.103534	−	0.188420i
$52$		0			0
$53$		−	70.8948i		−	1.33764i	−0.743426	−	0.668818i	$-0.766800\pi$
$53$		−	70.8948i		−	1.33764i	0.743426	−	0.668818i	$-0.233200\pi$
$54$		0			0
$55$	173.099			3.14725
$56$		0			0
$57$	86.3808	−	52.3388i	1.51545	−	0.918224i
$58$		0			0
$59$	−43.8902	+	52.3064i	−0.743903	+	0.886549i	−0.996717	−	0.0809663i	$-0.974199\pi$
$59$	−43.8902	+	52.3064i	−0.743903	+	0.886549i	0.252814	+	0.967515i	$0.418644\pi$
$60$		0			0
$61$	−99.7950	−	36.3224i	−1.63598	−	0.595449i	−0.649653	−	0.760231i	$-0.725086\pi$
$61$	−99.7950	−	36.3224i	−1.63598	−	0.595449i	−0.986330	+	0.164781i	$0.947308\pi$
$62$		0			0
$63$	−37.0056	−	11.7218i	−0.587390	−	0.186060i
$64$		0			0
$65$	42.7906	+	50.9958i	0.658317	+	0.784551i
$66$		0			0
$67$	−4.27685	+	24.2552i	−0.0638336	+	0.362018i	0.936113	+	0.351699i	$0.114396\pi$
$67$	−4.27685	+	24.2552i	−0.0638336	+	0.362018i	−0.999947	+	0.0103194i	$0.996715\pi$
$68$		0			0
$69$	−8.59625	+	3.33634i	−0.124583	+	0.0483527i
$70$		0			0
$71$	29.9139	+	17.2708i	0.421323	+	0.243251i	0.695643	−	0.718387i	$-0.255119\pi$
$71$	29.9139	+	17.2708i	0.421323	+	0.243251i	−0.274320	+	0.961638i	$0.588453\pi$
$72$		0			0
$73$	20.9190	+	36.2328i	0.286562	+	0.496340i	0.972987	−	0.230861i	$-0.0741542\pi$
$73$	20.9190	+	36.2328i	0.286562	+	0.496340i	−0.686425	+	0.727201i	$0.740821\pi$
$74$		0			0
$75$	153.714	−	30.4697i	2.04953	−	0.406263i
$76$		0			0
$77$	29.0553	+	79.8287i	0.377341	+	1.03674i
$78$		0			0
$79$	8.78445	+	49.8191i	0.111196	+	0.630621i	0.988564	+	0.150804i	$0.0481861\pi$
$79$	8.78445	+	49.8191i	0.111196	+	0.630621i	−0.877368	+	0.479818i	$0.840703\pi$
$80$		0			0
$81$	80.7102	−	6.84554i	0.996422	−	0.0845129i
$82$		0			0
$83$	−30.9208	+	5.45218i	−0.372540	+	0.0656889i	−0.356784	−	0.934187i	$-0.616127\pi$
$83$	−30.9208	+	5.45218i	−0.372540	+	0.0656889i	−0.0157564	+	0.999876i	$0.505016\pi$
$84$		0			0
$85$	−30.1831	+	10.9857i	−0.355095	+	0.129244i
$86$		0			0
$87$	14.1827	+	71.5490i	0.163019	+	0.822403i
$88$		0			0
$89$	40.0231	−	23.1073i	0.449697	−	0.259633i	−0.258005	−	0.966144i	$-0.583065\pi$
$89$	40.0231	−	23.1073i	0.449697	−	0.259633i	0.707702	+	0.706511i	$0.249732\pi$
$90$		0			0
$91$	−16.3354	+	28.2938i	−0.179510	+	0.310921i
$92$		0			0
$93$	−31.3333	−	80.7318i	−0.336917	−	0.868084i
$94$		0			0
$95$	−291.379	−	51.3780i	−3.06715	−	0.540821i
$96$		0			0
$97$	84.8132	−	71.1668i	0.874363	−	0.733678i	−0.0906489	−	0.995883i	$-0.528894\pi$
$97$	84.8132	−	71.1668i	0.874363	−	0.733678i	0.965012	+	0.262205i	$0.0844497\pi$
$98$		0			0
$99$	−119.587	−	130.854i	−1.20795	−	1.32176i
$100$		0			0
$101$	−27.7555	+	76.2576i	−0.274807	+	0.755026i	0.723123	+	0.690719i	$0.242706\pi$
$101$	−27.7555	+	76.2576i	−0.274807	+	0.755026i	−0.997930	+	0.0643070i	$0.979516\pi$
$102$		0			0
$103$	120.693	+	101.273i	1.17177	+	0.983234i	0.999998	−	0.00190171i	$-0.000605335\pi$
$103$	120.693	+	101.273i	1.17177	+	0.983234i	0.171775	+	0.985136i	$0.445050\pi$
$104$		0			0
$105$	58.9275	+	97.2549i	0.561214	+	0.926237i
$106$		0			0
$107$		−	60.6265i		−	0.566603i	−0.959031	−	0.283301i	$-0.908570\pi$
$107$		−	60.6265i		−	0.566603i	0.959031	−	0.283301i	$-0.0914297\pi$
$108$		0			0
$109$	13.0119			0.119375			0.0596876	−	0.998217i	$-0.480990\pi$
$109$	13.0119			0.119375			0.0596876	+	0.998217i	$0.480990\pi$
$110$		0			0
$111$	−78.3531	−	43.0536i	−0.705884	−	0.387870i
$112$		0			0
$113$	72.3782	−	86.2570i	0.640515	−	0.763336i	−0.343936	−	0.938993i	$-0.611760\pi$
$113$	72.3782	−	86.2570i	0.640515	−	0.763336i	0.984452	+	0.175657i	$0.0562048\pi$
$114$		0			0
$115$	25.3834	+	9.23879i	0.220725	+	0.0803373i
$116$		0			0
$117$	8.98807	−	67.5785i	0.0768211	−	0.577594i
$118$		0			0
$119$	−10.1327	−	12.0757i	−0.0851487	−	0.101476i
$120$		0			0
$121$	−46.3548	+	262.891i	−0.383098	+	2.17265i
$122$		0			0
$123$	10.5436	−	68.2022i	0.0857206	−	0.554490i
$124$		0			0
$125$	−207.284	−	119.676i	−1.65827	−	0.957405i
$126$		0			0
$127$	28.4023	+	49.1942i	0.223640	+	0.387356i	0.955911	−	0.293658i	$-0.0948726\pi$
$127$	28.4023	+	49.1942i	0.223640	+	0.387356i	−0.732270	+	0.681014i	$0.761539\pi$
$128$		0			0
$129$	−17.6805	−	20.1878i	−0.137058	−	0.156494i
$130$		0			0
$131$	4.65602	+	12.7923i	0.0355421	+	0.0976511i	0.956194	−	0.292733i	$-0.0945646\pi$
$131$	4.65602	+	12.7923i	0.0355421	+	0.0976511i	−0.920652	+	0.390384i	$0.872342\pi$
$132$		0			0
$133$	−25.2149	−	143.001i	−0.189586	−	1.07519i
$134$		0			0
$135$	−191.078	−	140.690i	−1.41539	−	1.04215i
$136$		0			0
$137$	176.617	−	31.1423i	1.28917	−	0.227316i	0.513302	−	0.858208i	$-0.328422\pi$
$137$	176.617	−	31.1423i	1.28917	−	0.227316i	0.775871	+	0.630892i	$0.217311\pi$
$138$		0			0
$139$	−108.775	+	39.5907i	−0.782551	+	0.284825i	−0.702236	−	0.711944i	$-0.747815\pi$
$139$	−108.775	+	39.5907i	−0.782551	+	0.284825i	−0.0803153	+	0.996770i	$0.525593\pi$
$140$		0			0
$141$	29.9351	+	10.1838i	0.212306	+	0.0722252i
$142$		0			0
$143$	−129.208	+	74.5984i	−0.903554	+	0.521667i
$144$		0			0
$145$	106.839	−	185.050i	0.736819	−	1.27621i
$146$		0			0
$147$	57.1265	−	71.0815i	0.388615	−	0.483547i
$148$		0			0
$149$	−77.5851	−	13.6804i	−0.520706	−	0.0918145i	−0.0928828	−	0.995677i	$-0.529608\pi$
$149$	−77.5851	−	13.6804i	−0.520706	−	0.0918145i	−0.427823	+	0.903863i	$0.640719\pi$
$150$		0			0
$151$	−31.2173	+	26.1944i	−0.206737	+	0.173473i	−0.740277	−	0.672302i	$-0.765306\pi$
$151$	−31.2173	+	26.1944i	−0.206737	+	0.173473i	0.533540	+	0.845775i	$0.320861\pi$
$152$		0			0
$153$	29.1569	+	15.2273i	0.190568	+	0.0995250i
$154$		0			0
$155$	−86.7663	+	238.388i	−0.559783	+	1.53799i
$156$		0			0
$157$	−140.499	−	117.893i	−0.894901	−	0.750911i	0.0742864	−	0.997237i	$-0.476332\pi$
$157$	−140.499	−	117.893i	−0.894901	−	0.750911i	−0.969187	+	0.246326i	$0.920777\pi$
$158$		0			0
$159$	212.637	−	4.49867i	1.33734	−	0.0282935i
$160$		0			0
$161$			13.2569i			0.0823413i
$162$		0			0
$163$	−225.642			−1.38431			−0.692154	−	0.721750i	$-0.743338\pi$
$163$	−225.642			−1.38431			−0.692154	+	0.721750i	$0.743338\pi$
$164$		0			0
$165$	10.9841	+	519.179i	0.0665701	+	3.14654i
$166$		0			0
$167$	119.618	−	142.556i	0.716278	−	0.853627i	−0.277986	−	0.960585i	$-0.589667\pi$
$167$	119.618	−	142.556i	0.716278	−	0.853627i	0.994263	+	0.106959i	$0.0341112\pi$
$168$		0			0
$169$	104.890	+	38.1769i	0.620652	+	0.225899i
$170$		0			0
$171$	162.463	+	255.763i	0.950073	+	1.49569i
$172$		0			0
$173$	89.4213	+	106.568i	0.516886	+	0.616001i	0.959841	−	0.280543i	$-0.0905145\pi$
$173$	89.4213	+	106.568i	0.516886	+	0.616001i	−0.442956	+	0.896544i	$0.646070\pi$
$174$		0			0
$175$	39.1219	−	221.871i	0.223553	−	1.26783i
$176$		0			0
$177$	−159.669	−	128.322i	−0.902085	−	0.724984i
$178$		0			0
$179$	125.967	+	72.7273i	0.703728	+	0.406298i	0.808735	−	0.588174i	$-0.200153\pi$
$179$	125.967	+	72.7273i	0.703728	+	0.406298i	−0.105006	+	0.994472i	$0.533486\pi$
$180$		0			0
$181$	125.541	+	217.444i	0.693599	+	1.20135i	0.970651	+	0.240494i	$0.0773094\pi$
$181$	125.541	+	217.444i	0.693599	+	1.20135i	−0.277052	+	0.960855i	$0.589357\pi$
$182$		0			0
$183$	102.610	−	301.623i	0.560712	−	1.64821i
$184$		0			0
$185$	89.5752	+	246.106i	0.484190	+	1.33030i
$186$		0			0
$187$	−12.5005	−	70.8938i	−0.0668475	−	0.379111i
$188$		0			0
$189$	32.8093	−	111.736i	0.173594	−	0.591194i
$190$		0			0
$191$	−28.3584	+	5.00035i	−0.148473	+	0.0261798i	−0.247391	−	0.968916i	$-0.579573\pi$
$191$	−28.3584	+	5.00035i	−0.148473	+	0.0261798i	0.0989175	+	0.995096i	$0.468462\pi$
$192$		0			0
$193$	84.8880	−	30.8967i	0.439834	−	0.160087i	−0.112605	−	0.993640i	$-0.535919\pi$
$193$	84.8880	−	30.8967i	0.439834	−	0.160087i	0.552439	+	0.833553i	$0.313697\pi$
$194$		0			0
$195$	−150.238	+	131.579i	−0.770451	+	0.674764i
$196$		0			0
$197$	246.767	−	142.471i	1.25263	−	0.723204i	0.280996	−	0.959709i	$-0.409335\pi$
$197$	246.767	−	142.471i	1.25263	−	0.723204i	0.971630	+	0.236505i	$0.0760020\pi$
$198$		0			0
$199$	78.3479	−	135.703i	0.393708	−	0.681922i	−0.599227	−	0.800579i	$-0.704525\pi$
$199$	78.3479	−	135.703i	0.393708	−	0.681922i	0.992935	+	0.118657i	$0.0378588\pi$
$200$		0			0
$201$	−73.0208	−	11.2886i	−0.363288	−	0.0561620i
$202$		0			0
$203$	103.274	+	18.2099i	0.508738	+	0.0897042i
$204$		0			0
$205$	−154.870	+	129.951i	−0.755463	+	0.633909i
$206$		0			0
$207$	−10.5523	−	25.5713i	−0.0509771	−	0.123533i
$208$		0			0
$209$	226.797	−	623.120i	1.08515	−	2.98143i
$210$		0			0
$211$	142.593	+	119.650i	0.675795	+	0.567060i	0.914774	−	0.403965i	$-0.132368\pi$
$211$	142.593	+	119.650i	0.675795	+	0.567060i	−0.238979	+	0.971025i	$0.576813\pi$
$212$		0			0
$213$	−49.9027	+	90.8177i	−0.234285	+	0.426374i
$214$		0			0
$215$			78.6134i			0.365644i
$216$		0			0
$217$	−124.503			−0.573746
$218$		0			0
$219$	−107.347	+	65.0422i	−0.490168	+	0.296996i
$220$		0			0
$221$	17.7956	−	21.2079i	0.0805229	−	0.0959634i
$222$		0			0
$223$	−50.7592	−	18.4748i	−0.227620	−	0.0828468i	0.225693	−	0.974199i	$-0.427536\pi$
$223$	−50.7592	−	18.4748i	−0.227620	−	0.0828468i	−0.453312	+	0.891352i	$0.649758\pi$
$224$		0			0
$225$	101.143	+	459.107i	0.449524	+	2.04047i
$226$		0			0
$227$	−184.955	−	220.421i	−0.814781	−	0.971018i	0.185150	−	0.982710i	$-0.440723\pi$
$227$	−184.955	−	220.421i	−0.814781	−	0.971018i	−0.999932	+	0.0116918i	$0.996278\pi$
$228$		0			0
$229$	38.3441	−	217.460i	0.167441	−	0.949608i	−0.779070	−	0.626937i	$-0.784308\pi$
$229$	38.3441	−	217.460i	0.167441	−	0.949608i	0.946511	−	0.322671i	$-0.104581\pi$
$230$		0			0
$231$	−237.589	+	92.2119i	−1.02852	+	0.399186i
$232$		0			0
$233$	351.012	+	202.657i	1.50649	+	0.869772i	0.999972	+	0.00754192i	$0.00240069\pi$
$233$	351.012	+	202.657i	1.50649	+	0.869772i	0.506517	+	0.862230i	$0.330933\pi$
$234$		0			0
$235$	−46.3145	−	80.2191i	−0.197083	−	0.341358i
$236$		0			0
$237$	−148.866	+	29.5087i	−0.628128	+	0.124509i
$238$		0			0
$239$	113.967	+	313.121i	0.476848	+	1.31013i	0.912154	+	0.409847i	$0.134418\pi$
$239$	113.967	+	313.121i	0.476848	+	1.31013i	−0.435306	+	0.900283i	$0.643360\pi$
$240$		0			0
$241$	5.43972	+	30.8502i	0.0225714	+	0.128009i	0.994011	−	0.109277i	$-0.0348534\pi$
$241$	5.43972	+	30.8502i	0.0225714	+	0.128009i	−0.971440	+	0.237286i	$0.923742\pi$
$242$		0			0
$243$	25.6535	+	241.642i	0.105570	+	0.994412i
$244$		0			0
$245$	−263.084	+	46.3889i	−1.07381	+	0.189342i
$246$		0			0
$247$	239.640	−	87.2218i	0.970202	−	0.353125i
$248$		0			0
$249$	−18.3150	−	92.3958i	−0.0735541	−	0.371068i
$250$		0			0
$251$	86.8677	−	50.1531i	0.346086	−	0.199813i	−0.316874	−	0.948468i	$-0.602633\pi$
$251$	86.8677	−	50.1531i	0.346086	−	0.199813i	0.662960	+	0.748655i	$0.269300\pi$
$252$		0			0
$253$	−30.2700	+	52.4292i	−0.119644	+	0.207230i
$254$		0			0
$255$	−34.8652	−	89.8319i	−0.136726	−	0.352282i
$256$		0			0
$257$	−389.385	−	68.6591i	−1.51512	−	0.267156i	−0.646605	−	0.762825i	$-0.723812\pi$
$257$	−389.385	−	68.6591i	−1.51512	−	0.267156i	−0.868512	+	0.495669i	$0.834923\pi$
$258$		0			0
$259$	−98.4623	+	82.6197i	−0.380163	+	0.318995i
$260$		0			0
$261$	−213.699	+	47.0787i	−0.818770	+	0.180378i
$262$		0			0
$263$	−107.565	+	295.532i	−0.408992	+	1.12370i	0.548729	+	0.836000i	$0.315112\pi$
$263$	−107.565	+	295.532i	−0.408992	+	1.12370i	−0.957721	+	0.287697i	$0.907110\pi$
$264$		0			0
$265$	−477.282	−	400.487i	−1.80107	−	1.51127i
$266$		0			0
$267$	71.8461	+	118.576i	0.269087	+	0.444105i
$268$		0			0
$269$			182.669i			0.679069i	0.940594	+	0.339534i	$0.110269\pi$
$269$			182.669i			0.679069i	−0.940594	+	0.339534i	$0.889731\pi$
$270$		0			0
$271$	−461.198			−1.70184			−0.850919	−	0.525297i	$-0.823954\pi$
$271$	−461.198			−1.70184			−0.850919	+	0.525297i	$0.823954\pi$
$272$		0			0
$273$	−85.8989	−	47.1999i	−0.314648	−	0.172893i
$274$		0			0
$275$	661.326	−	788.138i	2.40482	−	2.86596i
$276$		0			0
$277$	−148.424	−	54.0220i	−0.535827	−	0.195025i	0.0599111	−	0.998204i	$-0.480918\pi$
$277$	−148.424	−	54.0220i	−0.535827	−	0.195025i	−0.595738	+	0.803179i	$0.703141\pi$
$278$		0			0
$279$	240.153	−	99.1017i	0.860764	−	0.355203i
$280$		0			0
$281$	−131.821	−	157.098i	−0.469113	−	0.559067i	0.478665	−	0.877998i	$-0.341121\pi$
$281$	−131.821	−	157.098i	−0.469113	−	0.559067i	−0.947778	+	0.318930i	$0.896676\pi$
$282$		0			0
$283$	70.6906	−	400.906i	0.249790	−	1.41663i	−0.559310	−	0.828959i	$-0.688934\pi$
$283$	70.6906	−	400.906i	0.249790	−	1.41663i	0.809100	−	0.587671i	$-0.199955\pi$
$284$		0			0
$285$	135.610	−	877.202i	0.475824	−	3.07790i
$286$		0			0
$287$	−85.9258	−	49.6093i	−0.299393	−	0.172855i
$288$		0			0
$289$	−137.821	−	238.713i	−0.476889	−	0.825996i
$290$		0			0
$291$	218.834	+	249.867i	0.752008	+	0.858649i
$292$		0			0
$293$	146.516	+	402.550i	0.500055	+	1.37389i	0.891221	+	0.453570i	$0.149850\pi$
$293$	146.516	+	402.550i	0.500055	+	1.37389i	−0.391166	+	0.920320i	$0.627928\pi$
$294$		0			0
$295$	104.202	+	590.962i	0.353229	+	2.00326i
$296$		0			0
$297$	384.885	−	366.983i	1.29591	−	1.23563i
$298$		0			0
$299$	−22.9288	+	4.04297i	−0.0766849	+	0.0135216i
$300$		0			0
$301$	−36.2545	+	13.1956i	−0.120447	+	0.0438391i
$302$		0			0
$303$	−230.483	−	78.4089i	−0.760670	−	0.258775i
$304$		0			0
$305$	−808.278	+	466.660i	−2.65009	+	1.53003i
$306$		0			0
$307$	−50.5433	+	87.5435i	−0.164636	+	0.285158i	−0.936526	−	0.350598i	$-0.885978\pi$
$307$	−50.5433	+	87.5435i	−0.164636	+	0.285158i	0.771890	+	0.635756i	$0.219312\pi$
$308$		0			0
$309$	−296.093	+	368.423i	−0.958229	+	1.19231i
$310$		0			0
$311$	7.38442	+	1.30207i	0.0237441	+	0.00418673i	0.185508	−	0.982643i	$-0.440607\pi$
$311$	7.38442	+	1.30207i	0.0237441	+	0.00418673i	−0.161764	+	0.986830i	$0.551718\pi$
$312$		0			0
$313$	353.344	−	296.491i	1.12889	−	0.947254i	0.129875	−	0.991530i	$-0.458543\pi$
$313$	353.344	−	296.491i	1.12889	−	0.947254i	0.999019	+	0.0442760i	$0.0140981\pi$
$314$		0			0
$315$	−287.960	+	182.914i	−0.914159	+	0.580681i
$316$		0			0
$317$	22.7695	−	62.5587i	0.0718281	−	0.197346i	−0.898584	−	0.438802i	$-0.855403\pi$
$317$	22.7695	−	62.5587i	0.0718281	−	0.197346i	0.970412	+	0.241456i	$0.0776250\pi$
$318$		0			0
$319$	366.852	+	307.826i	1.15001	+	0.964971i
$320$		0			0
$321$	181.839	−	3.84709i	0.566476	−	0.0119847i
$322$		0			0
$323$			123.047i			0.380950i
$324$		0			0
$325$	395.672			1.21745
$326$		0			0
$327$	0.825677	+	39.0269i	0.00252501	+	0.119348i
$328$		0			0
$329$	29.2210	−	34.8242i	0.0888175	−	0.105849i
$330$		0			0
$331$	250.644	+	91.2269i	0.757233	+	0.275610i	0.691646	−	0.722237i	$-0.256886\pi$
$331$	250.644	+	91.2269i	0.757233	+	0.275610i	0.0655866	+	0.997847i	$0.479108\pi$
$332$		0			0
$333$	124.160	−	237.739i	0.372853	−	0.713930i
$334$		0			0
$335$	139.133	+	165.812i	0.415321	+	0.494960i
$336$		0			0
$337$	−94.3310	+	534.978i	−0.279914	+	1.58747i	0.442993	+	0.896525i	$0.353917\pi$
$337$	−94.3310	+	534.978i	−0.279914	+	1.58747i	−0.722907	+	0.690945i	$0.757194\pi$
$338$		0			0
$339$	263.306	+	211.613i	0.776714	+	0.624226i
$340$		0			0
$341$	−492.390	−	284.281i	−1.44396	−	0.833669i
$342$		0			0
$343$	−171.223	−	296.568i	−0.499194	−	0.864629i
$344$		0			0
$345$	−26.0995	+	76.7194i	−0.0756506	+	0.222375i
$346$		0			0
$347$	−142.664	−	391.967i	−0.411136	−	1.12959i	−0.956588	−	0.291445i	$-0.905864\pi$
$347$	−142.664	−	391.967i	−0.411136	−	1.12959i	0.545452	−	0.838142i	$-0.316358\pi$
$348$		0			0
$349$	76.3391	+	432.940i	0.218737	+	1.24052i	0.874304	+	0.485380i	$0.161319\pi$
$349$	76.3391	+	432.940i	0.218737	+	1.24052i	−0.655567	+	0.755137i	$0.727570\pi$
$350$		0			0
$351$	203.260	+	22.6700i	0.579089	+	0.0645868i
$352$		0			0
$353$	−11.4788	+	2.02403i	−0.0325180	+	0.00573380i	−0.189883	−	0.981807i	$-0.560811\pi$
$353$	−11.4788	+	2.02403i	−0.0325180	+	0.00573380i	0.157366	+	0.987540i	$0.449700\pi$
$354$		0			0
$355$	285.257	−	103.825i	0.803540	−	0.292465i
$356$		0			0
$357$	35.5760	−	31.1576i	0.0996526	−	0.0872761i
$358$		0			0
$359$	192.363	−	111.061i	0.535831	−	0.309362i	−0.207557	−	0.978223i	$-0.566551\pi$
$359$	192.363	−	111.061i	0.535831	−	0.309362i	0.743387	+	0.668861i	$0.233218\pi$
$360$		0			0
$361$	−386.221	+	668.955i	−1.06986	+	1.85306i
$362$		0			0
$363$	−791.439	−	122.351i	−2.18027	−	0.337056i
$364$		0			0
$365$	362.101	+	63.8483i	0.992059	+	0.174927i
$366$		0			0
$367$	185.653	−	155.782i	0.505868	−	0.424473i	−0.353805	−	0.935319i	$-0.615112\pi$
$367$	185.653	−	155.782i	0.505868	−	0.424473i	0.859672	+	0.510846i	$0.170668\pi$
$368$		0			0
$369$	205.230	+	27.2960i	0.556179	+	0.0739729i
$370$		0			0
$371$	104.581	−	287.334i	0.281890	−	0.774485i
$372$		0			0
$373$	445.391	+	373.728i	1.19408	+	1.00195i	0.999779	+	0.0210080i	$0.00668756\pi$
$373$	445.391	+	373.728i	1.19408	+	1.00195i	0.194299	+	0.980942i	$0.437757\pi$
$374$		0			0
$375$	345.793	−	629.308i	0.922115	−	1.67815i
$376$		0			0
$377$			184.172i			0.488521i
$378$		0			0
$379$	−225.207			−0.594213			−0.297107	−	0.954844i	$-0.596022\pi$
$379$	−225.207			−0.594213			−0.297107	+	0.954844i	$0.596022\pi$
$380$		0			0
$381$	−145.747	+	88.3095i	−0.382539	+	0.231783i
$382$		0			0
$383$	25.3855	−	30.2532i	0.0662806	−	0.0789902i	−0.731885	−	0.681428i	$-0.761359\pi$
$383$	25.3855	−	30.2532i	0.0662806	−	0.0789902i	0.798166	+	0.602438i	$0.205804\pi$
$384$		0			0
$385$	701.562	+	255.348i	1.82224	+	0.663241i
$386$		0			0
$387$	59.4278	−	54.3108i	0.153560	−	0.140338i
$388$		0			0
$389$	−143.473	−	170.984i	−0.368824	−	0.439548i	0.549429	−	0.835540i	$-0.314845\pi$
$389$	−143.473	−	170.984i	−0.368824	−	0.439548i	−0.918254	+	0.395992i	$0.870401\pi$
$390$		0			0
$391$	1.95073	−	11.0631i	0.00498908	−	0.0282945i
$392$		0			0
$393$	−38.0729	+	14.7767i	−0.0968775	+	0.0375997i
$394$		0			0
$395$	385.019	+	222.291i	0.974732	+	0.562762i
$396$		0			0
$397$	−81.7197	−	141.543i	−0.205843	−	0.356531i	0.744558	−	0.667558i	$-0.232660\pi$
$397$	−81.7197	−	141.543i	−0.205843	−	0.356531i	−0.950401	+	0.311027i	$0.899327\pi$
$398$		0			0
$399$	427.306	−	84.7019i	1.07094	−	0.212286i
$400$		0			0
$401$	98.9356	+	271.823i	0.246722	+	0.677864i	0.999801	+	0.0199338i	$0.00634555\pi$
$401$	98.9356	+	271.823i	0.246722	+	0.677864i	−0.753079	+	0.657930i	$0.771432\pi$
$402$		0			0
$403$	−37.9696	−	215.336i	−0.0942173	−	0.534333i
$404$		0			0
$405$	409.849	−	582.033i	1.01197	−	1.43712i
$406$		0			0
$407$	−578.051	+	101.926i	−1.42027	+	0.250433i
$408$		0			0
$409$	−85.1579	+	30.9950i	−0.208210	+	0.0757823i	−0.444020	−	0.896017i	$-0.646448\pi$
$409$	−85.1579	+	30.9950i	−0.208210	+	0.0757823i	0.235810	+	0.971799i	$0.424226\pi$
$410$		0			0
$411$	104.613	+	527.756i	0.254534	+	1.28408i
$412$		0			0
$413$	−255.046	+	147.251i	−0.617544	+	0.356539i
$414$		0			0
$415$	−137.968	+	238.967i	−0.332452	+	0.575824i
$416$		0			0
$417$	−125.648	−	323.739i	−0.301314	−	0.776352i
$418$		0			0
$419$	−636.775	−	112.281i	−1.51975	−	0.267973i	−0.649415	−	0.760434i	$-0.724986\pi$
$419$	−636.775	−	112.281i	−1.51975	−	0.267973i	−0.870334	+	0.492462i	$0.836097\pi$
$420$		0			0
$421$	−94.6516	+	79.4221i	−0.224826	+	0.188651i	−0.748242	−	0.663426i	$-0.769102\pi$
$421$	−94.6516	+	79.4221i	−0.224826	+	0.188651i	0.523416	+	0.852077i	$0.324657\pi$
$422$		0			0
$423$	−28.6449	+	90.4315i	−0.0677184	+	0.213786i
$424$		0			0
$425$	−65.2957	+	179.398i	−0.153637	+	0.422114i
$426$		0			0
$427$	−350.884	−	294.427i	−0.821743	−	0.689524i
$428$		0			0
$429$	−231.944	−	382.804i	−0.540662	−	0.892317i
$430$		0			0
$431$			679.383i			1.57629i	0.615487	+	0.788147i	$0.288959\pi$
$431$			679.383i			1.57629i	−0.615487	+	0.788147i	$0.711041\pi$
$432$		0			0
$433$	738.981			1.70665			0.853327	−	0.521376i	$-0.174581\pi$
$433$	738.981			1.70665			0.853327	+	0.521376i	$0.174581\pi$
$434$		0			0
$435$	561.805	+	308.702i	1.29151	+	0.709660i
$436$		0			0
$437$	66.5156	−	79.2702i	0.152210	−	0.181396i
$438$		0			0
$439$	−294.308	−	107.120i	−0.670407	−	0.244008i	−0.0156837	−	0.999877i	$-0.504992\pi$
$439$	−294.308	−	107.120i	−0.670407	−	0.244008i	−0.654723	+	0.755869i	$0.727215\pi$
$440$		0			0
$441$	216.822	+	166.831i	0.491659	+	0.378300i
$442$		0			0
$443$	−316.952	−	377.729i	−0.715467	−	0.852661i	0.278715	−	0.960374i	$-0.410092\pi$
$443$	−316.952	−	377.729i	−0.715467	−	0.852661i	−0.994182	+	0.107713i	$0.965647\pi$
$444$		0			0
$445$	70.5273	−	399.980i	0.158488	−	0.898832i
$446$		0			0
$447$	36.1087	−	233.571i	0.0807800	−	0.522531i
$448$		0			0
$449$	−403.766	−	233.114i	−0.899255	−	0.519185i	−0.0222969	−	0.999751i	$-0.507098\pi$
$449$	−403.766	−	233.114i	−0.899255	−	0.519185i	−0.876959	+	0.480566i	$0.840431\pi$
$450$		0			0
$451$	−226.549	−	392.394i	−0.502326	−	0.870054i
$452$		0			0
$453$	−80.5466	−	91.9688i	−0.177807	−	0.203022i
$454$		0			0
$455$	98.2018	+	269.807i	0.215828	+	0.592983i
$456$		0			0
$457$	−65.2077	−	369.811i	−0.142687	−	0.809216i	−0.969196	−	0.246292i	$-0.920788\pi$
$457$	−65.2077	−	369.811i	−0.142687	−	0.809216i	0.826509	−	0.562923i	$-0.190323\pi$
$458$		0			0
$459$	−43.8216	+	88.4175i	−0.0954718	+	0.192631i
$460$		0			0
$461$	−116.143	+	20.4791i	−0.251937	+	0.0444232i	−0.298190	−	0.954507i	$-0.596383\pi$
$461$	−116.143	+	20.4791i	−0.251937	+	0.0444232i	0.0462535	+	0.998930i	$0.485272\pi$
$462$		0			0
$463$	82.8187	−	30.1435i	0.178874	−	0.0651048i	−0.251030	−	0.967979i	$-0.580769\pi$
$463$	82.8187	−	30.1435i	0.178874	−	0.0651048i	0.429905	+	0.902874i	$0.358547\pi$
$464$		0			0
$465$	−720.511	−	245.114i	−1.54949	−	0.527126i
$466$		0			0
$467$	288.366	−	166.488i	0.617486	−	0.356506i	−0.158403	−	0.987374i	$-0.550635\pi$
$467$	288.366	−	166.488i	0.617486	−	0.356506i	0.775890	+	0.630869i	$0.217301\pi$
$468$		0			0
$469$	−53.1143	+	91.9966i	−0.113250	+	0.196155i
$470$		0			0
$471$	344.684	−	428.885i	0.731814	−	0.910584i
$472$		0			0
$473$	−173.511	−	30.5947i	−0.366831	−	0.0646822i
$474$		0			0
$475$	−1347.15	+	1130.39i	−2.83610	+	2.37977i
$476$		0			0
$477$	26.9860	+	637.482i	0.0565744	+	1.33644i
$478$		0			0
$479$	−143.904	+	395.374i	−0.300427	+	0.825416i	0.693999	+	0.719976i	$0.255847\pi$
$479$	−143.904	+	395.374i	−0.300427	+	0.825416i	−0.994426	+	0.105440i	$0.966375\pi$
$480$		0			0
$481$	−172.924	−	145.101i	−0.359510	−	0.301665i
$482$		0			0
$483$	−39.7619	+	0.841227i	−0.0823228	+	0.00174167i
$484$		0			0
$485$		−	973.009i		−	2.00620i
$486$		0			0
$487$	212.098			0.435519			0.217760	−	0.976002i	$-0.430125\pi$
$487$	212.098			0.435519			0.217760	+	0.976002i	$0.430125\pi$
$488$		0			0
$489$	−14.3183	−	676.775i	−0.0292807	−	1.38400i
$490$		0			0
$491$	−173.315	+	206.549i	−0.352983	+	0.420669i	−0.913094	−	0.407748i	$-0.866314\pi$
$491$	−173.315	+	206.549i	−0.352983	+	0.420669i	0.560111	+	0.828418i	$0.310758\pi$
$492$		0			0
$493$	−83.5041	−	30.3930i	−0.169380	−	0.0616491i
$494$		0			0
$495$	−1556.49	+	65.8897i	−3.14443	+	0.133110i
$496$		0			0
$497$	95.7630	+	114.126i	0.192682	+	0.229629i
$498$		0			0
$499$	61.6379	−	349.566i	0.123523	−	0.700533i	−0.858651	−	0.512560i	$-0.828697\pi$
$499$	61.6379	−	349.566i	0.123523	−	0.700533i	0.982174	−	0.187973i	$-0.0601918\pi$
$500$		0			0
$501$	435.162	+	349.729i	0.868586	+	0.698062i
$502$		0			0
$503$	410.636	+	237.081i	0.816374	+	0.471333i	0.849164	−	0.528129i	$-0.177106\pi$
$503$	410.636	+	237.081i	0.816374	+	0.471333i	−0.0327908	+	0.999462i	$0.510439\pi$
$504$		0			0
$505$	356.595	+	617.640i	0.706128	+	1.22305i
$506$		0			0
$507$	−107.849	+	317.023i	−0.212720	+	0.625291i
$508$		0			0
$509$	−28.2600	−	77.6437i	−0.0555206	−	0.152542i	0.908832	−	0.417163i	$-0.136975\pi$
$509$	−28.2600	−	77.6437i	−0.0555206	−	0.152542i	−0.964353	+	0.264621i	$0.914753\pi$
$510$		0			0
$511$	31.3349	+	177.709i	0.0613208	+	0.347768i
$512$		0			0
$513$	−756.808	+	503.508i	−1.47526	+	0.981498i
$514$		0			0
$515$	1363.60	−	240.439i	2.64776	−	0.466871i
$516$		0			0
$517$	195.080	−	71.0032i	0.377330	−	0.137337i
$518$		0			0
$519$	−313.959	+	274.966i	−0.604930	+	0.529800i
$520$		0			0
$521$	489.450	−	282.584i	0.939444	−	0.542388i	0.0496582	−	0.998766i	$-0.484187\pi$
$521$	489.450	−	282.584i	0.939444	−	0.542388i	0.889786	+	0.456378i	$0.150853\pi$
$522$		0			0
$523$	340.114	−	589.095i	0.650314	−	1.12638i	−0.332733	−	0.943021i	$-0.607971\pi$
$523$	340.114	−	589.095i	0.650314	−	1.12638i	0.983047	−	0.183356i	$-0.0586960\pi$
$524$		0			0
$525$	667.947	+	103.260i	1.27228	+	0.196686i
$526$		0			0
$527$	103.900	+	18.3203i	0.197153	+	0.0347634i
$528$		0			0
$529$	398.000	−	333.962i	0.752364	−	0.631308i
$530$		0			0
$531$	374.748	−	487.043i	0.705741	−	0.917218i
$532$		0			0
$533$	59.5979	−	163.744i	0.111816	−	0.307212i
$534$		0			0
$535$	−408.154	−	342.482i	−0.762904	−	0.640153i
$536$		0			0
$537$	−210.140	+	382.433i	−0.391322	+	0.712165i
$538$		0			0
$539$		−	598.718i		−	1.11079i
$540$		0			0
$541$	53.2254			0.0983833			0.0491916	−	0.998789i	$-0.484335\pi$
$541$	53.2254			0.0983833			0.0491916	+	0.998789i	$0.484335\pi$
$542$		0			0
$543$	−644.220	+	390.338i	−1.18641	+	0.718855i
$544$		0			0
$545$	73.5047	−	87.5995i	0.134871	−	0.160733i
$546$		0			0
$547$	−128.793	−	46.8768i	−0.235453	−	0.0856981i	0.221599	−	0.975138i	$-0.428873\pi$
$547$	−128.793	−	46.8768i	−0.235453	−	0.0856981i	−0.457052	+	0.889440i	$0.651095\pi$
$548$		0			0
$549$	911.177	+	288.622i	1.65970	+	0.525724i
$550$		0			0
$551$	−526.161	−	627.054i	−0.954920	−	1.13803i
$552$		0			0
$553$	−37.8880	+	214.873i	−0.0685135	+	0.388560i
$554$		0			0
$555$	−732.468	+	284.282i	−1.31976	+	0.512220i
$556$		0			0
$557$	519.540	+	299.956i	0.932746	+	0.538521i	0.887679	−	0.460463i	$-0.152317\pi$
$557$	519.540	+	299.956i	0.932746	+	0.538521i	0.0450671	+	0.998984i	$0.485650\pi$
$558$		0			0
$559$	−33.8792	−	58.6805i	−0.0606068	−	0.104974i
$560$		0			0
$561$	211.841	−	41.9917i	0.377612	−	0.0748515i
$562$		0			0
$563$	75.8301	+	208.342i	0.134689	+	0.370056i	0.988641	−	0.150296i	$-0.0480228\pi$
$563$	75.8301	+	208.342i	0.134689	+	0.370056i	−0.853952	+	0.520352i	$0.825801\pi$
$564$		0			0
$565$	−171.838	−	974.539i	−0.304137	−	1.72485i
$566$		0			0
$567$	337.214	+	91.3156i	0.594734	+	0.161050i
$568$		0			0
$569$	−121.585	+	21.4387i	−0.213681	+	0.0376778i	−0.279464	−	0.960156i	$-0.590157\pi$
$569$	−121.585	+	21.4387i	−0.213681	+	0.0376778i	0.0657826	+	0.997834i	$0.479046\pi$
$570$		0			0
$571$	−704.732	+	256.501i	−1.23421	+	0.449215i	−0.875036	−	0.484057i	$-0.839163\pi$
$571$	−704.732	+	256.501i	−1.23421	+	0.449215i	−0.359171	+	0.933272i	$0.616940\pi$
$572$		0			0
$573$	−16.7972	−	84.7388i	−0.0293145	−	0.147886i
$574$		0			0
$575$	139.043	−	80.2765i	0.241814	−	0.139611i
$576$		0			0
$577$	−15.9521	+	27.6299i	−0.0276467	+	0.0478855i	−0.879518	−	0.475866i	$-0.842135\pi$
$577$	−15.9521	+	27.6299i	−0.0276467	+	0.0478855i	0.851871	+	0.523752i	$0.175468\pi$
$578$		0			0
$579$	98.0560	+	252.647i	0.169354	+	0.436350i
$580$		0			0
$581$	−133.364	−	23.5157i	−0.229542	−	0.0404745i
$582$		0			0
$583$	1069.68	−	897.569i	1.83479	−	1.53957i
$584$		0			0
$585$	−404.182	−	442.264i	−0.690910	−	0.756006i
$586$		0			0
$587$	−43.4593	+	119.403i	−0.0740363	+	0.203413i	−0.971190	−	0.238304i	$-0.923408\pi$
$587$	−43.4593	+	119.403i	−0.0740363	+	0.203413i	0.897154	+	0.441717i	$0.145631\pi$
$588$		0			0
$589$	744.468	+	624.683i	1.26395	+	1.06058i
$590$		0			0
$591$	442.977	+	731.096i	0.749538	+	1.23705i
$592$		0			0
$593$			606.986i			1.02359i	0.859109	+	0.511793i	$0.171019\pi$
$593$			606.986i			1.02359i	−0.859109	+	0.511793i	$0.828981\pi$
$594$		0			0
$595$	−138.537			−0.232835
$596$		0			0
$597$	411.988	+	226.380i	0.690097	+	0.379196i
$598$		0			0
$599$	−168.791	+	201.157i	−0.281787	+	0.335821i	−0.888309	−	0.459246i	$-0.848120\pi$
$599$	−168.791	+	201.157i	−0.281787	+	0.335821i	0.606522	+	0.795067i	$0.292564\pi$
$600$		0			0
$601$	−998.384	−	363.382i	−1.66120	−	0.604629i	−0.670653	−	0.741771i	$-0.733986\pi$
$601$	−998.384	−	363.382i	−1.66120	−	0.604629i	−0.990551	+	0.137142i	$0.956208\pi$
$602$		0			0
$603$	29.2245	−	219.730i	0.0484652	−	0.364394i
$604$		0			0
$605$	1507.99	+	1797.16i	2.49255	+	2.97051i
$606$		0			0
$607$	−180.588	+	1024.16i	−0.297509	+	1.68725i	0.359320	+	0.933215i	$0.383009\pi$
$607$	−180.588	+	1024.16i	−0.297509	+	1.68725i	−0.656828	+	0.754040i	$0.728102\pi$
$608$		0			0
$609$	−48.0643	+	310.907i	−0.0789233	+	0.510521i
$610$		0			0
$611$	69.1423	+	39.9193i	0.113163	+	0.0653344i
$612$		0			0
$613$	244.419	+	423.347i	0.398726	+	0.690614i	0.993569	−	0.113228i	$-0.0361190\pi$
$613$	244.419	+	423.347i	0.398726	+	0.690614i	−0.594843	+	0.803842i	$0.702786\pi$
$614$		0			0
$615$	−399.594	−	456.260i	−0.649746	−	0.741886i
$616$		0			0
$617$	122.120	+	335.523i	0.197926	+	0.543797i	0.998459	−	0.0554913i	$-0.0176725\pi$
$617$	122.120	+	335.523i	0.197926	+	0.543797i	−0.800533	+	0.599288i	$0.795450\pi$
$618$		0			0
$619$	−53.2686	−	302.101i	−0.0860559	−	0.488047i	−0.997124	−	0.0757908i	$-0.975852\pi$
$619$	−53.2686	−	302.101i	−0.0860559	−	0.488047i	0.911068	−	0.412257i	$-0.135259\pi$
$620$		0			0
$621$	76.0271	−	33.2723i	0.122427	−	0.0535786i
$622$		0			0
$623$	196.299	−	34.6128i	0.315087	−	0.0555583i
$624$		0			0
$625$	−749.523	+	272.804i	−1.19924	+	0.436486i
$626$		0			0
$627$	1883.33	+	640.699i	3.00372	+	1.02185i
$628$		0			0
$629$	94.3257	−	54.4590i	0.149961	−	0.0865803i
$630$		0			0
$631$	403.300	−	698.535i	0.639144	−	1.10703i	−0.346477	−	0.938058i	$-0.612622\pi$
$631$	403.300	−	698.535i	0.639144	−	1.10703i	0.985621	−	0.168971i	$-0.0540444\pi$
$632$		0			0
$633$	−349.820	+	435.275i	−0.552638	+	0.687638i
$634$		0			0
$635$	491.634	+	86.6884i	0.774227	+	0.136517i
$636$		0			0
$637$	176.386	−	148.005i	0.276901	−	0.232347i
$638$		0			0
$639$	−275.559	−	143.912i	−0.431234	−	0.225214i
$640$		0			0
$641$	196.557	−	540.037i	0.306642	−	0.842492i	−0.686664	−	0.726975i	$-0.740925\pi$
$641$	196.557	−	540.037i	0.306642	−	0.842492i	0.993306	−	0.115516i	$-0.0368523\pi$
$642$		0			0
$643$	−499.279	−	418.945i	−0.776484	−	0.651548i	0.165876	−	0.986147i	$-0.446955\pi$
$643$	−499.279	−	418.945i	−0.776484	−	0.651548i	−0.942361	+	0.334599i	$0.891399\pi$
$644$		0			0
$645$	−235.788	+	4.98846i	−0.365562	+	0.00773405i
$646$		0			0
$647$		−	653.900i		−	1.01066i	−0.862925	−	0.505332i	$-0.831370\pi$
$647$		−	653.900i		−	1.01066i	0.862925	−	0.505332i	$-0.168630\pi$
$648$		0			0
$649$	−1344.89			−2.07225
$650$		0			0
$651$	−7.90040	−	373.425i	−0.0121358	−	0.573617i
$652$		0			0
$653$	−691.419	+	824.001i	−1.05883	+	1.26187i	−0.0949693	+	0.995480i	$0.530275\pi$
$653$	−691.419	+	824.001i	−1.05883	+	1.26187i	−0.963865	+	0.266390i	$0.914169\pi$
$654$		0			0
$655$	112.423	+	40.9187i	0.171638	+	0.0624713i
$656$		0			0
$657$	−201.895	−	317.841i	−0.307298	−	0.483776i
$658$		0			0
$659$	624.556	+	744.317i	0.947733	+	1.12946i	0.991459	+	0.130421i	$0.0416329\pi$
$659$	624.556	+	744.317i	0.947733	+	1.12946i	−0.0437255	+	0.999044i	$0.513923\pi$
$660$		0			0
$661$	−9.91401	+	56.2251i	−0.0149985	+	0.0850607i	−0.991388	−	0.130956i	$-0.958195\pi$
$661$	−9.91401	+	56.2251i	−0.0149985	+	0.0850607i	0.976390	+	0.216017i	$0.0693065\pi$
$662$		0			0
$663$	64.7387	+	52.0290i	0.0976452	+	0.0784751i
$664$		0			0
$665$	−1105.16	−	638.064i	−1.66189	−	0.959494i
$666$		0			0
$667$	37.3661	+	64.7200i	0.0560211	+	0.0970314i
$668$		0			0
$669$	52.1912	−	153.416i	0.0780137	−	0.229321i
$670$		0			0
$671$	−715.419	−	1965.60i	−1.06620	−	2.92936i
$672$		0			0
$673$	−57.6515	−	326.958i	−0.0856634	−	0.485821i	−0.997211	−	0.0746277i	$-0.976223\pi$
$673$	−57.6515	−	326.958i	−0.0856634	−	0.485821i	0.911548	−	0.411194i	$-0.134888\pi$
$674$		0			0
$675$	−1370.59	+	332.493i	−2.03051	+	0.492583i
$676$		0			0
$677$	389.350	−	68.6529i	0.575111	−	0.101408i	0.121475	−	0.992595i	$-0.461238\pi$
$677$	389.350	−	68.6529i	0.575111	−	0.101408i	0.453636	+	0.891187i	$0.350127\pi$
$678$		0			0
$679$	448.727	−	163.323i	0.660865	−	0.240535i
$680$		0			0
$681$	649.379	−	568.729i	0.953567	−	0.835138i
$682$		0			0
$683$	74.8054	−	43.1889i	0.109525	−	0.0632341i	−0.444237	−	0.895909i	$-0.646525\pi$
$683$	74.8054	−	43.1889i	0.109525	−	0.0632341i	0.553762	+	0.832675i	$0.313192\pi$
$684$		0			0
$685$	788.057	−	1364.95i	1.15045	−	1.99263i
$686$		0			0
$687$	654.668	+	101.207i	0.952937	+	0.147318i
$688$		0			0
$689$	528.858	+	93.2519i	0.767573	+	0.135344i
$690$		0			0
$691$	460.719	−	386.589i	0.666742	−	0.559463i	−0.245357	−	0.969433i	$-0.578905\pi$
$691$	460.719	−	386.589i	0.666742	−	0.559463i	0.912099	+	0.409970i	$0.134461\pi$
$692$		0			0
$693$	−291.650	−	706.755i	−0.420851	−	1.01985i
$694$		0			0
$695$	−347.937	+	955.949i	−0.500629	+	1.37547i
$696$		0			0
$697$	64.4066	+	54.0436i	0.0924055	+	0.0775374i
$698$		0			0
$699$	−585.561	+	1065.66i	−0.837712	+	1.52455i
$700$		0			0
$701$		−	839.245i		−	1.19721i	−0.801044	−	0.598606i	$-0.795722\pi$
$701$		−	839.245i		−	1.19721i	0.801044	−	0.598606i	$-0.204278\pi$
$702$		0			0
$703$	1003.29			1.42716
$704$		0			0
$705$	237.665	−	144.003i	0.337113	−	0.204259i
$706$		0			0
$707$	−224.984	+	268.126i	−0.318224	+	0.379244i
$708$		0			0
$709$	−500.860	−	182.298i	−0.706432	−	0.257120i	−0.0362774	−	0.999342i	$-0.511550\pi$
$709$	−500.860	−	182.298i	−0.706432	−	0.257120i	−0.670155	+	0.742222i	$0.733772\pi$
$710$		0			0
$711$	−97.9529	−	444.627i	−0.137768	−	0.625354i
$712$		0			0
$713$	−57.0317	−	67.9677i	−0.0799883	−	0.0953263i
$714$		0			0
$715$	−227.686	+	1291.27i	−0.318442	+	1.80598i
$716$		0			0
$717$	−931.921	+	361.693i	−1.29975	+	0.504453i
$718$		0			0
$719$	−903.864	−	521.846i	−1.25711	−	0.725794i	−0.284600	−	0.958646i	$-0.591861\pi$
$719$	−903.864	−	521.846i	−1.25711	−	0.725794i	−0.972512	+	0.232852i	$0.925194\pi$
$720$		0			0
$721$	339.769	+	588.497i	0.471247	+	0.816224i
$722$		0			0
$723$	−92.1846	+	18.2731i	−0.127503	+	0.0252740i
$724$		0			0
$725$	−434.375	−	1193.44i	−0.599138	−	1.64612i
$726$		0			0
$727$	144.189	+	817.738i	0.198335	+	1.12481i	0.907589	+	0.419859i	$0.137921\pi$
$727$	144.189	+	817.738i	0.198335	+	1.12481i	−0.709255	+	0.704952i	$0.750968\pi$
$728$		0			0
$729$	−723.136	+	92.2770i	−0.991956	+	0.126580i
$730$		0			0
$731$	32.1967	−	5.67715i	0.0440448	−	0.00776628i
$732$		0			0
$733$	−948.261	+	345.139i	−1.29367	+	0.470858i	−0.894930	−	0.446206i	$-0.852775\pi$
$733$	−948.261	+	345.139i	−1.29367	+	0.470858i	−0.398741	+	0.917064i	$0.630553\pi$
$734$		0			0
$735$	−155.830	−	786.133i	−0.212013	−	1.06957i
$736$		0			0
$737$	−420.117	+	242.555i	−0.570037	+	0.329111i
$738$		0			0
$739$	−397.795	+	689.001i	−0.538288	+	0.932342i	0.460708	+	0.887552i	$0.347595\pi$
$739$	−397.795	+	689.001i	−0.538288	+	0.932342i	−0.998996	+	0.0447908i	$0.985738\pi$
$740$		0			0
$741$	276.813	+	713.224i	0.373567	+	0.962515i
$742$		0			0
$743$	82.1407	+	14.4836i	0.110553	+	0.0194934i	0.228651	−	0.973509i	$-0.426569\pi$
$743$	82.1407	+	14.4836i	0.110553	+	0.0194934i	−0.118098	+	0.993002i	$0.537680\pi$
$744$		0			0
$745$	−530.381	+	445.043i	−0.711921	+	0.597373i
$746$		0			0
$747$	275.963	−	60.7957i	0.369429	−	0.0813865i
$748$		0			0
$749$	89.4337	−	245.717i	0.119404	−	0.328060i
$750$		0			0
$751$	378.125	+	317.285i	0.503496	+	0.422483i	0.858833	−	0.512255i	$-0.171190\pi$
$751$	378.125	+	317.285i	0.503496	+	0.422483i	−0.355338	+	0.934738i	$0.615634\pi$
$752$		0			0
$753$	155.938	+	257.362i	0.207089	+	0.341783i
$754$		0			0
$755$			358.137i			0.474353i
$756$		0			0
$757$	−488.264			−0.644998			−0.322499	−	0.946570i	$-0.604523\pi$
$757$	−488.264			−0.644998			−0.322499	+	0.946570i	$0.604523\pi$
$758$		0			0
$759$	−159.173	−	87.4628i	−0.209714	−	0.115234i
$760$		0			0
$761$	−54.9049	+	65.4331i	−0.0721483	+	0.0859830i	−0.800911	−	0.598783i	$-0.795651\pi$
$761$	−54.9049	+	65.4331i	−0.0721483	+	0.0859830i	0.728763	+	0.684766i	$0.240096\pi$
$762$		0			0
$763$	52.7367	+	19.1946i	0.0691176	+	0.0251567i
$764$		0			0
$765$	267.223	−	110.272i	0.349311	−	0.144147i
$766$		0			0
$767$	−332.462	−	396.212i	−0.433457	−	0.516574i
$768$		0			0
$769$	158.722	−	900.158i	0.206401	−	1.17056i	−0.688819	−	0.724933i	$-0.741871\pi$
$769$	158.722	−	900.158i	0.206401	−	1.17056i	0.895220	−	0.445624i	$-0.147018\pi$
$770$		0			0
$771$	181.223	−	1172.25i	0.235049	−	1.52043i
$772$		0			0
$773$	1171.92	+	676.608i	1.51607	+	0.875301i	0.999822	+	0.0188590i	$0.00600335\pi$
$773$	1171.92	+	676.608i	1.51607	+	0.875301i	0.516243	+	0.856442i	$0.327330\pi$
$774$		0			0
$775$	753.918	+	1305.82i	0.972798	+	1.68494i
$776$		0			0
$777$	−254.052	−	290.078i	−0.326965	−	0.373331i
$778$		0			0
$779$	264.885	+	727.766i	0.340032	+	0.934230i
$780$		0			0
$781$	118.141	+	670.009i	0.151268	+	0.857886i
$782$		0			0
$783$	−154.765	−	637.966i	−0.197656	−	0.814772i
$784$		0			0
$785$	−1587.37	+	279.897i	−2.02213	+	0.356556i
$786$		0			0
$787$	571.286	−	207.931i	0.725903	−	0.264207i	0.0474733	−	0.998873i	$-0.484883\pi$
$787$	571.286	−	207.931i	0.725903	−	0.264207i	0.678430	+	0.734665i	$0.262661\pi$
$788$		0			0
$789$	−893.225	−	303.870i	−1.13210	−	0.385133i
$790$		0			0
$791$	420.589	−	242.827i	0.531718	−	0.306988i
$792$		0			0
$793$	402.222	−	696.670i	0.507216	−	0.878524i
$794$		0			0
$795$	1170.91	−	1456.94i	1.47284	−	1.83263i
$796$		0			0
$797$	−1368.77	−	241.352i	−1.71741	−	0.302825i	−0.773687	−	0.633569i	$-0.781589\pi$
$797$	−1368.77	−	241.352i	−1.71741	−	0.302825i	−0.943721	+	0.330743i	$0.892701\pi$
$798$		0			0
$799$	−29.5097	+	24.7616i	−0.0369333	+	0.0309907i
$800$		0			0
$801$	−351.089	+	223.015i	−0.438314	+	0.278420i
$802$		0			0
$803$	−281.844	+	774.361i	−0.350989	+	0.964335i
$804$		0			0
$805$	89.2493	+	74.8890i	0.110869	+	0.0930298i
$806$		0			0
$807$	−547.886	+	11.5914i	−0.678917	+	0.0143636i
$808$		0			0
$809$		−	422.581i		−	0.522350i	−0.965291	−	0.261175i	$-0.915890\pi$
$809$		−	422.581i		−	0.522350i	0.965291	−	0.261175i	$-0.0841100\pi$
$810$		0			0
$811$	336.669			0.415129			0.207564	−	0.978221i	$-0.433446\pi$
$811$	336.669			0.415129			0.207564	+	0.978221i	$0.433446\pi$
$812$		0			0
$813$	−29.2656	−	1383.28i	−0.0359971	−	1.70146i
$814$		0			0
$815$	−1274.66	+	1519.08i	−1.56400	+	1.86391i
$816$		0			0
$817$	282.993	+	103.001i	0.346380	+	0.126072i
$818$		0			0
$819$	136.117	−	260.634i	0.166199	−	0.318235i
$820$		0			0
$821$	−275.130	−	327.887i	−0.335116	−	0.399375i	0.572002	−	0.820252i	$-0.306167\pi$
$821$	−275.130	−	327.887i	−0.335116	−	0.399375i	−0.907118	+	0.420877i	$0.861722\pi$
$822$		0			0
$823$	94.1304	−	533.840i	0.114375	−	0.648651i	−0.872683	−	0.488287i	$-0.837622\pi$
$823$	94.1304	−	533.840i	0.114375	−	0.648651i	0.987058	−	0.160364i	$-0.0512669\pi$
$824$		0			0
$825$	2405.85	+	1933.52i	2.91618	+	2.34366i
$826$		0			0
$827$	−266.300	−	153.748i	−0.322008	−	0.185911i	0.330280	−	0.943883i	$-0.392857\pi$
$827$	−266.300	−	153.748i	−0.322008	−	0.185911i	−0.652287	+	0.757972i	$0.726190\pi$
$828$		0			0
$829$	−165.593	−	286.816i	−0.199751	−	0.345978i	0.748697	−	0.662912i	$-0.230680\pi$
$829$	−165.593	−	286.816i	−0.199751	−	0.345978i	−0.948447	+	0.316934i	$0.897347\pi$
$830$		0			0
$831$	152.611	−	448.601i	0.183648	−	0.539833i
$832$		0			0
$833$	37.9978	+	104.398i	0.0456156	+	0.125328i
$834$		0			0
$835$	−283.993	−	1610.61i	−0.340112	−	1.92887i
$836$		0			0
$837$	312.478	+	714.009i	0.373330	+	0.853058i
$838$		0			0
$839$	747.773	−	131.853i	0.891267	−	0.157154i	0.290781	−	0.956790i	$-0.406085\pi$
$839$	747.773	−	131.853i	0.891267	−	0.157154i	0.600486	+	0.799635i	$0.294974\pi$
$840$		0			0
$841$	−234.776	+	85.4514i	−0.279163	+	0.101607i
$842$		0			0
$843$	462.823	−	405.343i	0.549019	−	0.480833i
$844$		0			0
$845$	849.546	−	490.486i	1.00538	−	0.580456i
$846$		0			0
$847$	−575.681	+	997.108i	−0.679670	+	1.17722i
$848$		0			0
$849$	1206.94	+	186.585i	1.42160	+	0.219770i
$850$		0			0
$851$	−90.2063	−	15.9058i	−0.106000	−	0.0186907i
$852$		0			0
$853$	−398.713	+	334.560i	−0.467424	+	0.392216i	−0.845854	−	0.533414i	$-0.820909\pi$
$853$	−398.713	+	334.560i	−0.467424	+	0.392216i	0.378430	+	0.925630i	$0.376464\pi$
$854$		0			0
$855$	2639.62	+	351.075i	3.08728	+	0.410614i
$856$		0			0
$857$	386.012	−	1060.56i	0.450422	−	1.23752i	−0.482006	−	0.876168i	$-0.660092\pi$
$857$	386.012	−	1060.56i	0.450422	−	1.23752i	0.932428	−	0.361356i	$-0.117686\pi$
$858$		0			0
$859$	596.284	+	500.341i	0.694160	+	0.582470i	0.920106	−	0.391670i	$-0.128103\pi$
$859$	596.284	+	500.341i	0.694160	+	0.582470i	−0.225945	+	0.974140i	$0.572547\pi$
$860$		0			0
$861$	143.342	−	260.868i	0.166483	−	0.302982i
$862$		0			0
$863$			1131.63i			1.31127i	0.755078	+	0.655635i	$0.227599\pi$
$863$			1131.63i			1.31127i	−0.755078	+	0.655635i	$0.772401\pi$
$864$		0			0
$865$	1222.59			1.41340
$866$		0			0
$867$	707.233	−	428.518i	0.815725	−	0.494254i
$868$		0			0
$869$	−640.469	+	763.281i	−0.737018	+	0.878344i
$870$		0			0
$871$	−175.313	−	63.8086i	−0.201277	−	0.0732590i
$872$		0			0
$873$	−735.547	+	672.212i	−0.842551	+	0.770002i
$874$		0			0
$875$	−663.575	−	790.818i	−0.758372	−	0.903792i
$876$		0			0
$877$	−104.520	+	592.762i	−0.119179	+	0.675898i	0.865417	+	0.501052i	$0.167054\pi$
$877$	−104.520	+	592.762i	−0.119179	+	0.675898i	−0.984596	+	0.174845i	$0.944057\pi$
$878$		0			0
$879$	−1198.08	+	464.994i	−1.36301	+	0.529004i
$880$		0			0
$881$	661.931	+	382.166i	0.751340	+	0.433786i	0.826178	−	0.563409i	$-0.190511\pi$
$881$	661.931	+	382.166i	0.751340	+	0.433786i	−0.0748378	+	0.997196i	$0.523844\pi$
$882$		0			0
$883$	3.19534	+	5.53449i	0.00361873	+	0.00626782i	0.867829	−	0.496863i	$-0.165515\pi$
$883$	3.19534	+	5.53449i	0.00361873	+	0.00626782i	−0.864210	+	0.503131i	$0.832181\pi$
$884$		0			0
$885$	−1765.88	+	350.037i	−1.99534	+	0.395522i
$886$		0			0
$887$	246.492	+	677.231i	0.277894	+	0.763507i	0.997601	+	0.0692290i	$0.0220539\pi$
$887$	246.492	+	677.231i	0.277894	+	0.763507i	−0.719707	+	0.694278i	$0.755724\pi$
$888$		0			0
$889$	42.5442	+	241.280i	0.0478563	+	0.271407i
$890$		0			0
$891$	1125.13	+	1131.11i	1.26277	+	1.26948i
$892$		0			0
$893$	−349.455	+	61.6183i	−0.391327	+	0.0690015i
$894$		0			0
$895$	1201.21	−	437.206i	1.34214	−	0.488499i
$896$		0			0
$897$	−13.5811	−	68.5144i	−0.0151406	−	0.0763818i
$898$		0			0
$899$	−607.819	+	350.924i	−0.676105	+	0.390350i
$900$		0			0
$901$	−129.555	+	224.396i	−0.143790	+	0.249052i
$902$		0			0
$903$	−41.8784	−	107.902i	−0.0463770	−	0.119493i
$904$		0			0
$905$	2173.08	+	383.173i	2.40119	+	0.423395i
$906$		0			0
$907$	−982.519	+	824.431i	−1.08326	+	0.908965i	−0.996188	−	0.0872369i	$-0.972196\pi$
$907$	−982.519	+	824.431i	−1.08326	+	0.908965i	−0.0870746	+	0.996202i	$0.527752\pi$
$908$		0			0
$909$	220.549	−	696.270i	0.242628	−	0.765973i
$910$		0			0
$911$	76.4002	−	209.908i	0.0838641	−	0.230415i	−0.890672	−	0.454647i	$-0.849765\pi$
$911$	76.4002	−	209.908i	0.0838641	−	0.230415i	0.974536	+	0.224233i	$0.0719875\pi$
$912$		0			0
$913$	−473.740	−	397.515i	−0.518883	−	0.435394i
$914$		0			0
$915$	−1450.96	−	2394.68i	−1.58574	−	2.61714i
$916$		0			0
$917$			58.7151i			0.0640296i
$918$		0			0
$919$	606.971			0.660469			0.330235	−	0.943899i	$-0.392872\pi$
$919$	606.971			0.660469			0.330235	+	0.943899i	$0.392872\pi$
$920$		0			0
$921$	−265.779	−	146.041i	−0.288577	−	0.158568i
$922$		0			0
$923$	−168.184	+	200.434i	−0.182214	+	0.217154i
$924$		0			0
$925$	1462.77	+	532.406i	1.58138	+	0.575574i
$926$		0			0
$927$	−1123.81	−	864.701i	−1.21231	−	0.932795i
$928$		0			0
$929$	363.623	+	433.349i	0.391413	+	0.466468i	0.925382	−	0.379036i	$-0.123744\pi$
$929$	363.623	+	433.349i	0.391413	+	0.466468i	−0.533969	+	0.845504i	$0.679300\pi$
$930$		0			0
$931$	−177.708	+	1007.83i	−0.190878	+	1.08252i
$932$		0			0
$933$	−3.43676	+	22.2309i	−0.00368356	+	0.0238273i
$934$		0			0
$935$	−547.892	−	316.325i	−0.585980	−	0.338316i
$936$		0			0
$937$	174.168	+	301.667i	0.185878	+	0.321950i	0.943872	−	0.330311i	$-0.107154\pi$
$937$	174.168	+	301.667i	0.185878	+	0.321950i	−0.757994	+	0.652262i	$0.773820\pi$
$938$		0			0
$939$	911.695	+	1040.98i	0.970921	+	1.10861i
$940$		0			0
$941$	−591.614	−	1625.45i	−0.628708	−	1.72736i	−0.684595	−	0.728924i	$-0.740021\pi$
$941$	−591.614	−	1625.45i	−0.628708	−	1.72736i	0.0558865	−	0.998437i	$-0.482202\pi$
$942$		0			0
$943$	−12.2781	−	69.6328i	−0.0130203	−	0.0738418i
$944$		0			0
$945$	−566.893	−	852.080i	−0.599887	−	0.901672i
$946$		0			0
$947$	−200.007	+	35.2667i	−0.211201	+	0.0372404i	−0.278247	−	0.960509i	$-0.589754\pi$
$947$	−200.007	+	35.2667i	−0.211201	+	0.0372404i	0.0670465	+	0.997750i	$0.478642\pi$
$948$		0			0
$949$	−297.804	+	108.392i	−0.313808	+	0.114217i
$950$		0			0
$951$	189.079	+	64.3236i	0.198821	+	0.0676378i
$952$		0			0
$953$	223.234	−	128.884i	0.234243	−	0.135241i	−0.378285	−	0.925689i	$-0.623486\pi$
$953$	223.234	−	128.884i	0.234243	−	0.135241i	0.612528	+	0.790449i	$0.290153\pi$
$954$		0			0
$955$	−126.534	+	219.163i	−0.132496	+	0.229490i
$956$		0			0
$957$	−899.992	+	1119.84i	−0.940430	+	1.17016i
$958$		0			0
$959$	761.761	+	134.319i	0.794329	+	0.140062i
$960$		0			0
$961$	−97.8491	+	82.1051i	−0.101820	+	0.0854372i
$962$		0			0
$963$	23.0774	+	545.150i	0.0239641	+	0.566096i
$964$		0			0
$965$	271.531	−	746.026i	0.281379	−	0.773084i
$966$		0			0
$967$	−940.814	−	789.437i	−0.972921	−	0.816377i	0.0100857	−	0.999949i	$-0.496790\pi$
$967$	−940.814	−	789.437i	−0.972921	−	0.816377i	−0.983006	+	0.183572i	$0.941234\pi$
$968$		0			0
$969$	−369.058	+	7.80801i	−0.380865	+	0.00805780i
$970$		0			0
$971$		−	1295.87i		−	1.33458i	−0.744800	−	0.667288i	$-0.767455\pi$
$971$		−	1295.87i		−	1.33458i	0.744800	−	0.667288i	$-0.232545\pi$
$972$		0			0
$973$	−499.262			−0.513117
$974$		0			0
$975$	25.1076	+	1186.75i	0.0257514	+	1.21718i
$976$		0			0
$977$	480.625	−	572.787i	0.491940	−	0.586271i	−0.461770	−	0.887000i	$-0.652785\pi$
$977$	480.625	−	572.787i	0.491940	−	0.586271i	0.953710	+	0.300729i	$0.0972299\pi$
$978$		0			0
$979$	855.365	+	311.327i	0.873713	+	0.318005i
$980$		0			0
$981$	−117.002	+	4.95296i	−0.119268	+	0.00504888i
$982$		0			0
$983$	95.9650	+	114.367i	0.0976246	+	0.116344i	0.812645	−	0.582759i	$-0.198027\pi$
$983$	95.9650	+	114.367i	0.0976246	+	0.116344i	−0.715020	+	0.699104i	$0.753583\pi$
$984$		0			0
$985$	434.845	−	2466.13i	0.441467	−	2.50368i
$986$		0			0
$987$	106.303	+	85.4335i	0.107704	+	0.0865588i
$988$		0			0
$989$	−23.8109	−	13.7472i	−0.0240758	−	0.0139002i
$990$		0			0
$991$	−289.456	−	501.353i	−0.292085	−	0.505906i	0.682217	−	0.731149i	$-0.261016\pi$
$991$	−289.456	−	501.353i	−0.292085	−	0.505906i	−0.974303	+	0.225243i	$0.927682\pi$
$992$		0			0
$993$	−257.715	+	757.553i	−0.259532	+	0.762893i
$994$		0			0
$995$	−470.995	−	1294.05i	−0.473362	−	1.30055i
$996$		0			0
$997$	262.672	+	1489.69i	0.263463	+	1.49417i	0.773377	+	0.633947i	$0.218566\pi$
$997$	262.672	+	1489.69i	0.263463	+	1.49417i	−0.509914	+	0.860225i	$0.670323\pi$
$998$		0			0
$999$	720.935	+	357.311i	0.721657	+	0.357669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.41.4	yes	36
3.2	odd	2		324.3.k.a.233.1		36
4.3	odd	2		432.3.bc.b.257.3		36
27.2	odd	18	inner	108.3.k.a.29.4	✓	36
27.5	odd	18		2916.3.c.b.1457.35		36
27.22	even	9		2916.3.c.b.1457.2		36
27.25	even	9		324.3.k.a.89.1		36
108.83	even	18		432.3.bc.b.353.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.4	✓	36	27.2	odd	18	inner
108.3.k.a.41.4	yes	36	1.1	even	1	trivial
324.3.k.a.89.1		36	27.25	even	9
324.3.k.a.233.1		36	3.2	odd	2
432.3.bc.b.257.3		36	4.3	odd	2
432.3.bc.b.353.3		36	108.83	even	18
2916.3.c.b.1457.2		36	27.22	even	9
2916.3.c.b.1457.35		36	27.5	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)

\(f(q)\)	\(=\)	\(q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +O(q^{10})\)	\(q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +(12.6606 + 15.0883i) q^{11} +(-1.31536 + 7.45976i) q^{13} +(20.5507 + 16.5161i) q^{15} +(-3.16520 - 1.82743i) q^{17} +(-16.8333 - 29.1562i) q^{19} +(-4.16730 + 12.2498i) q^{21} +(1.05125 + 2.88830i) q^{23} +(-9.07052 - 51.4415i) q^{25} +(-1.71228 - 26.9457i) q^{27} +(23.9443 - 4.22203i) q^{29} +(-27.1255 + 9.87288i) q^{31} +(-44.4514 + 38.9307i) q^{33} +(32.8265 - 18.9524i) q^{35} +(-14.9004 + 25.8083i) q^{37} +(-22.4577 - 3.47182i) q^{39} +(-22.6547 - 3.99463i) q^{41} +(-6.85241 + 5.74986i) q^{43} +(-48.2333 + 62.6865i) q^{45} +(3.60489 - 9.90435i) q^{47} +(-23.2857 - 19.5391i) q^{49} +(5.28021 - 9.60944i) q^{51} -70.8948i q^{53} +173.099 q^{55} +(86.3808 - 52.3388i) q^{57} +(-43.8902 + 52.3064i) q^{59} +(-99.7950 - 36.3224i) q^{61} +(-37.0056 - 11.7218i) q^{63} +(42.7906 + 50.9958i) q^{65} +(-4.27685 + 24.2552i) q^{67} +(-8.59625 + 3.33634i) q^{69} +(29.9139 + 17.2708i) q^{71} +(20.9190 + 36.2328i) q^{73} +(153.714 - 30.4697i) q^{75} +(29.0553 + 79.8287i) q^{77} +(8.78445 + 49.8191i) q^{79} +(80.7102 - 6.84554i) q^{81} +(-30.9208 + 5.45218i) q^{83} +(-30.1831 + 10.9857i) q^{85} +(14.1827 + 71.5490i) q^{87} +(40.0231 - 23.1073i) q^{89} +(-16.3354 + 28.2938i) q^{91} +(-31.3333 - 80.7318i) q^{93} +(-291.379 - 51.3780i) q^{95} +(84.8132 - 71.1668i) q^{97} +(-119.587 - 130.854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 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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