LMFDB - Embedded newform 216.3.j.a.125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(125,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("216.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.3
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86434 + 0.724045i) q^{2} +(2.95152 - 2.69973i) q^{4} +(-0.693019 + 1.20034i) q^{5} +(-0.562989 - 0.975125i) q^{7} +(-3.54790 + 7.17024i) q^{8} +O(q^{10})$	\(q+(-1.86434 + 0.724045i) q^{2} +(2.95152 - 2.69973i) q^{4} +(-0.693019 + 1.20034i) q^{5} +(-0.562989 - 0.975125i) q^{7} +(-3.54790 + 7.17024i) q^{8} +(0.422919 - 2.73963i) q^{10} +(1.11157 + 1.92529i) q^{11} +(14.4573 + 8.34694i) q^{13} +(1.75564 + 1.41033i) q^{14} +(1.42291 - 15.9366i) q^{16} -20.2816i q^{17} +21.0174i q^{19} +(1.19515 + 5.41380i) q^{20} +(-3.46633 - 2.78457i) q^{22} +(18.0360 + 10.4131i) q^{23} +(11.5394 + 19.9869i) q^{25} +(-32.9969 - 5.09377i) q^{26} +(-4.29425 - 1.35818i) q^{28} +(26.9695 + 46.7126i) q^{29} +(9.19365 - 15.9239i) q^{31} +(8.88603 + 30.7415i) q^{32} +(14.6848 + 37.8118i) q^{34} +1.56065 q^{35} +34.8194i q^{37} +(-15.2175 - 39.1835i) q^{38} +(-6.14800 - 9.22782i) q^{40} +(15.1169 + 8.72774i) q^{41} +(-44.2282 + 25.5352i) q^{43} +(8.47857 + 2.68160i) q^{44} +(-41.1649 - 6.35467i) q^{46} +(-32.4750 + 18.7494i) q^{47} +(23.8661 - 41.3373i) q^{49} +(-35.9849 - 28.9073i) q^{50} +(65.2055 - 14.3947i) q^{52} +52.6541 q^{53} -3.08135 q^{55} +(8.98931 - 0.577118i) q^{56} +(-84.1024 - 67.5609i) q^{58} +(27.1346 - 46.9986i) q^{59} +(76.5667 - 44.2058i) q^{61} +(-5.61048 + 36.3441i) q^{62} +(-38.8248 - 50.8786i) q^{64} +(-20.0384 + 11.5692i) q^{65} +(-66.0909 - 38.1576i) q^{67} +(-54.7549 - 59.8615i) q^{68} +(-2.90958 + 1.12998i) q^{70} -69.4903i q^{71} -82.6983 q^{73} +(-25.2108 - 64.9151i) q^{74} +(56.7412 + 62.0331i) q^{76} +(1.25160 - 2.16783i) q^{77} +(19.8580 + 34.3950i) q^{79} +(18.1433 + 12.7524i) q^{80} +(-34.5023 - 5.32616i) q^{82} +(-56.9488 - 98.6383i) q^{83} +(24.3449 + 14.0555i) q^{85} +(63.9677 - 79.6294i) q^{86} +(-17.7485 + 1.13946i) q^{88} -25.3593i q^{89} -18.7969i q^{91} +(81.3463 - 17.9580i) q^{92} +(46.9689 - 58.4686i) q^{94} +(-25.2281 - 14.5654i) q^{95} +(10.4267 + 18.0596i) q^{97} +(-14.5644 + 94.3468i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.86434	+	0.724045i	−0.932169	+	0.362023i
$2$	−1.86434	+	0.724045i	−0.932169	+	0.362023i
$3$		0			0
$3$		0			0
$4$	2.95152	−	2.69973i	0.737879	−	0.674933i
$5$	−0.693019	+	1.20034i	−0.138604	+	0.240069i	−0.926968	−	0.375139i	$-0.877595\pi$
$5$	−0.693019	+	1.20034i	−0.138604	+	0.240069i	0.788365	+	0.615208i	$0.210928\pi$
$6$		0			0
$7$	−0.562989	−	0.975125i	−0.0804270	−	0.139304i	0.823006	−	0.568032i	$-0.192295\pi$
$7$	−0.562989	−	0.975125i	−0.0804270	−	0.139304i	−0.903433	+	0.428728i	$0.858962\pi$
$8$	−3.54790	+	7.17024i	−0.443488	+	0.896280i
$9$		0			0
$10$	0.422919	−	2.73963i	0.0422919	−	0.273963i
$11$	1.11157	+	1.92529i	0.101052	+	0.175026i	0.912118	−	0.409927i	$-0.134446\pi$
$11$	1.11157	+	1.92529i	0.101052	+	0.175026i	−0.811067	+	0.584954i	$0.801113\pi$
$12$		0			0
$13$	14.4573	+	8.34694i	1.11210	+	0.642072i	0.939373	−	0.342897i	$-0.111408\pi$
$13$	14.4573	+	8.34694i	1.11210	+	0.642072i	0.172729	+	0.984969i	$0.444742\pi$
$14$	1.75564	+	1.41033i	0.125403	+	0.100738i
$15$		0			0
$16$	1.42291	−	15.9366i	0.0889319	−	0.996038i
$17$		−	20.2816i		−	1.19304i	−0.802600	−	0.596518i	$-0.796550\pi$
$17$		−	20.2816i		−	1.19304i	0.802600	−	0.596518i	$-0.203450\pi$
$18$		0			0
$19$			21.0174i			1.10618i	0.833122	+	0.553089i	$0.186551\pi$
$19$			21.0174i			1.10618i	−0.833122	+	0.553089i	$0.813449\pi$
$20$	1.19515	+	5.41380i	0.0597574	+	0.270690i
$21$		0			0
$22$	−3.46633	−	2.78457i	−0.157561	−	0.126571i
$23$	18.0360	+	10.4131i	0.784176	+	0.452744i	0.837908	−	0.545811i	$-0.183778\pi$
$23$	18.0360	+	10.4131i	0.784176	+	0.452744i	−0.0537322	+	0.998555i	$0.517112\pi$
$24$		0			0
$25$	11.5394	+	19.9869i	0.461578	+	0.799476i
$26$	−32.9969	−	5.09377i	−1.26911	−	0.195914i
$27$		0			0
$28$	−4.29425	−	1.35818i	−0.153366	−	0.0485065i
$29$	26.9695	+	46.7126i	0.929984	+	1.61078i	0.783343	+	0.621589i	$0.213513\pi$
$29$	26.9695	+	46.7126i	0.929984	+	1.61078i	0.146640	+	0.989190i	$0.453154\pi$
$30$		0			0
$31$	9.19365	−	15.9239i	0.296569	−	0.513673i	−0.678779	−	0.734342i	$-0.737491\pi$
$31$	9.19365	−	15.9239i	0.296569	−	0.513673i	0.975349	+	0.220669i	$0.0708241\pi$
$32$	8.88603	+	30.7415i	0.277688	+	0.960671i
$33$		0			0
$34$	14.6848	+	37.8118i	0.431906	+	1.11211i
$35$	1.56065			0.0445899
$36$		0			0
$37$			34.8194i			0.941065i	0.882383	+	0.470532i	$0.155938\pi$
$37$			34.8194i			0.941065i	−0.882383	+	0.470532i	$0.844062\pi$
$38$	−15.2175	−	39.1835i	−0.400461	−	1.03114i
$39$		0			0
$40$	−6.14800	−	9.22782i	−0.153700	−	0.230696i
$41$	15.1169	+	8.72774i	0.368705	+	0.212872i	0.672892	−	0.739740i	$-0.265052\pi$
$41$	15.1169	+	8.72774i	0.368705	+	0.212872i	−0.304188	+	0.952612i	$0.598385\pi$
$42$		0			0
$43$	−44.2282	+	25.5352i	−1.02856	+	0.593841i	−0.916573	−	0.399868i	$-0.869056\pi$
$43$	−44.2282	+	25.5352i	−1.02856	+	0.593841i	−0.111990	+	0.993709i	$0.535722\pi$
$44$	8.47857	+	2.68160i	0.192695	+	0.0609454i
$45$		0			0
$46$	−41.1649	−	6.35467i	−0.894888	−	0.138145i
$47$	−32.4750	+	18.7494i	−0.690957	+	0.398924i	−0.803970	−	0.594669i	$-0.797283\pi$
$47$	−32.4750	+	18.7494i	−0.690957	+	0.398924i	0.113014	+	0.993593i	$0.463950\pi$
$48$		0			0
$49$	23.8661	−	41.3373i	0.487063	−	0.843618i
$50$	−35.9849	−	28.9073i	−0.719697	−	0.578146i
$51$		0			0
$52$	65.2055	−	14.3947i	1.25395	−	0.276822i
$53$	52.6541			0.993473			0.496736	−	0.867901i	$-0.334532\pi$
$53$	52.6541			0.993473			0.496736	+	0.867901i	$0.334532\pi$
$54$		0			0
$55$	−3.08135			−0.0560245
$56$	8.98931	−	0.577118i	0.160523	−	0.0103057i
$57$		0			0
$58$	−84.1024	−	67.5609i	−1.45004	−	1.16484i
$59$	27.1346	−	46.9986i	0.459909	−	0.796586i	−0.539047	−	0.842276i	$-0.681215\pi$
$59$	27.1346	−	46.9986i	0.459909	−	0.796586i	0.998956	+	0.0456902i	$0.0145487\pi$
$60$		0			0
$61$	76.5667	−	44.2058i	1.25519	−	0.724686i	0.283056	−	0.959103i	$-0.408652\pi$
$61$	76.5667	−	44.2058i	1.25519	−	0.724686i	0.972136	+	0.234418i	$0.0753184\pi$
$62$	−5.61048	+	36.3441i	−0.0904915	+	0.586195i
$63$		0			0
$64$	−38.8248	−	50.8786i	−0.606637	−	0.794979i
$65$	−20.0384	+	11.5692i	−0.308283	+	0.177987i
$66$		0			0
$67$	−66.0909	−	38.1576i	−0.986432	−	0.569517i	−0.0822260	−	0.996614i	$-0.526203\pi$
$67$	−66.0909	−	38.1576i	−0.986432	−	0.569517i	−0.904206	+	0.427097i	$0.859536\pi$
$68$	−54.7549	−	59.8615i	−0.805219	−	0.880317i
$69$		0			0
$70$	−2.90958	+	1.12998i	−0.0415654	+	0.0161426i
$71$		−	69.4903i		−	0.978736i	−0.872077	−	0.489368i	$-0.837227\pi$
$71$		−	69.4903i		−	0.978736i	0.872077	−	0.489368i	$-0.162773\pi$
$72$		0			0
$73$	−82.6983			−1.13285			−0.566427	−	0.824112i	$-0.691675\pi$
$73$	−82.6983			−1.13285			−0.566427	+	0.824112i	$0.691675\pi$
$74$	−25.2108	−	64.9151i	−0.340687	−	0.877232i
$75$		0			0
$76$	56.7412	+	62.0331i	0.746595	+	0.816225i
$77$	1.25160	−	2.16783i	0.0162545	−	0.0281537i
$78$		0			0
$79$	19.8580	+	34.3950i	0.251366	+	0.435380i	0.963902	−	0.266256i	$-0.0857867\pi$
$79$	19.8580	+	34.3950i	0.251366	+	0.435380i	−0.712536	+	0.701636i	$0.752453\pi$
$80$	18.1433	+	12.7524i	0.226791	+	0.159404i
$81$		0			0
$82$	−34.5023	−	5.32616i	−0.420760	−	0.0649531i
$83$	−56.9488	−	98.6383i	−0.686131	−	1.18841i	−0.973080	−	0.230467i	$-0.925975\pi$
$83$	−56.9488	−	98.6383i	−0.686131	−	1.18841i	0.286949	−	0.957946i	$-0.407359\pi$
$84$		0			0
$85$	24.3449	+	14.0555i	0.286411	+	0.165359i
$86$	63.9677	−	79.6294i	0.743811	−	0.925923i
$87$		0			0
$88$	−17.7485	+	1.13946i	−0.201688	+	0.0129485i
$89$		−	25.3593i		−	0.284936i	−0.989799	−	0.142468i	$-0.954496\pi$
$89$		−	25.3593i		−	0.284936i	0.989799	−	0.142468i	$-0.0455038\pi$
$90$		0			0
$91$		−	18.7969i		−	0.206560i
$92$	81.3463	−	17.9580i	0.884199	−	0.195195i
$93$		0			0
$94$	46.9689	−	58.4686i	0.499669	−	0.622007i
$95$	−25.2281	−	14.5654i	−0.265559	−	0.153320i
$96$		0			0
$97$	10.4267	+	18.0596i	0.107492	+	0.186182i	0.914754	−	0.404012i	$-0.132385\pi$
$97$	10.4267	+	18.0596i	0.107492	+	0.186182i	−0.807262	+	0.590194i	$0.799051\pi$
$98$	−14.5644	+	94.3468i	−0.148617	+	0.962723i
$99$		0			0
$100$	88.0182	+	27.8383i	0.880182	+	0.278383i
$101$	37.6168	+	65.1543i	0.372444	+	0.645092i	0.989941	−	0.141481i	$-0.0451865\pi$
$101$	37.6168	+	65.1543i	0.372444	+	0.645092i	−0.617497	+	0.786573i	$0.711853\pi$
$102$		0			0
$103$	−82.1673	+	142.318i	−0.797741	+	1.38173i	0.123343	+	0.992364i	$0.460638\pi$
$103$	−82.1673	+	142.318i	−0.797741	+	1.38173i	−0.921084	+	0.389364i	$0.872695\pi$
$104$	−111.143	+	74.0484i	−1.06868	+	0.712004i
$105$		0			0
$106$	−98.1650	+	38.1239i	−0.926085	+	0.359660i
$107$	−136.212			−1.27301			−0.636504	−	0.771273i	$-0.719620\pi$
$107$	−136.212			−1.27301			−0.636504	+	0.771273i	$0.719620\pi$
$108$		0			0
$109$		−	75.3671i		−	0.691441i	−0.938337	−	0.345721i	$-0.887634\pi$
$109$		−	75.3671i		−	0.691441i	0.938337	−	0.345721i	$-0.112366\pi$
$110$	5.74468	−	2.23104i	0.0522243	−	0.0202821i
$111$		0			0
$112$	−16.3413	+	7.58461i	−0.145904	+	0.0677197i
$113$	95.2511	+	54.9933i	0.842930	+	0.486666i	0.858259	−	0.513217i	$-0.171546\pi$
$113$	95.2511	+	54.9933i	0.842930	+	0.486666i	−0.0153290	+	0.999883i	$0.504880\pi$
$114$		0			0
$115$	−24.9987	+	14.4330i	−0.217380	+	0.125504i
$116$	205.712	+	65.0626i	1.77338	+	0.560884i
$117$		0			0
$118$	−16.5591	+	107.268i	−0.140331	+	0.909050i
$119$	−19.7771	+	11.4183i	−0.166194	+	0.0959523i
$120$		0			0
$121$	58.0288	−	100.509i	0.479577	−	0.830652i
$122$	−110.739	+	137.852i	−0.907699	+	1.12994i
$123$		0			0
$124$	−15.8549	−	71.8199i	−0.127862	−	0.579193i
$125$	−66.6392			−0.533114
$126$		0			0
$127$	139.760			1.10048			0.550238	−	0.835008i	$-0.314537\pi$
$127$	139.760			1.10048			0.550238	+	0.835008i	$0.314537\pi$
$128$	109.221	+	66.7441i	0.853289	+	0.521438i
$129$		0			0
$130$	28.9818	−	36.0776i	0.222937	−	0.277520i
$131$	−15.9691	+	27.6593i	−0.121902	+	0.211140i	−0.920518	−	0.390701i	$-0.872233\pi$
$131$	−15.9691	+	27.6593i	−0.121902	+	0.211140i	0.798616	+	0.601841i	$0.205566\pi$
$132$		0			0
$133$	20.4946	−	11.8325i	0.154094	−	0.0889665i
$134$	150.844	+	23.2859i	1.12570	+	0.173775i
$135$		0			0
$136$	145.424	+	71.9572i	1.06929	+	0.529097i
$137$	−67.6082	+	39.0336i	−0.493491	+	0.284917i	−0.726021	−	0.687672i	$-0.758633\pi$
$137$	−67.6082	+	39.0336i	−0.493491	+	0.284917i	0.232531	+	0.972589i	$0.425299\pi$
$138$		0			0
$139$	−22.9132	−	13.2289i	−0.164843	−	0.0951723i	0.415309	−	0.909680i	$-0.363674\pi$
$139$	−22.9132	−	13.2289i	−0.164843	−	0.0951723i	−0.580152	+	0.814508i	$0.697007\pi$
$140$	4.60628	−	4.21333i	0.0329020	−	0.0300952i
$141$		0			0
$142$	50.3141	+	129.553i	0.354325	+	0.912348i
$143$			37.1127i			0.259529i
$144$		0			0
$145$	−74.7616			−0.515597
$146$	154.178	−	59.8773i	1.05601	−	0.410119i
$147$		0			0
$148$	94.0030	+	102.770i	0.635155	+	0.694392i
$149$	−60.9394	+	105.550i	−0.408989	+	0.708390i	−0.994777	−	0.102075i	$-0.967452\pi$
$149$	−60.9394	+	105.550i	−0.408989	+	0.708390i	0.585788	+	0.810465i	$0.300785\pi$
$150$		0			0
$151$	−123.778	−	214.390i	−0.819724	−	1.41980i	−0.905886	−	0.423522i	$-0.860794\pi$
$151$	−123.778	−	214.390i	−0.819724	−	1.41980i	0.0861624	−	0.996281i	$-0.472540\pi$
$152$	−150.700	−	74.5676i	−0.991445	−	0.490576i
$153$		0			0
$154$	−0.763796	+	4.94779i	−0.00495971	+	0.0321285i
$155$	12.7427	+	22.0711i	0.0822113	+	0.142394i
$156$		0			0
$157$	25.8090	+	14.9009i	0.164389	+	0.0949099i	0.579937	−	0.814661i	$-0.303077\pi$
$157$	25.8090	+	14.9009i	0.164389	+	0.0949099i	−0.415549	+	0.909571i	$0.636410\pi$
$158$	−61.9255	−	49.7458i	−0.391933	−	0.314847i
$159$		0			0
$160$	−43.0586	−	10.6381i	−0.269116	−	0.0664883i
$161$		−	23.4499i		−	0.145651i
$162$		0			0
$163$		−	107.162i		−	0.657434i	−0.944428	−	0.328717i	$-0.893384\pi$
$163$		−	107.162i		−	0.657434i	0.944428	−	0.328717i	$-0.106616\pi$
$164$	68.1803	−	15.0515i	0.415734	−	0.0917772i
$165$		0			0
$166$	177.590	+	142.662i	1.06982	+	0.859407i
$167$	213.521	+	123.276i	1.27857	+	0.738182i	0.976585	−	0.215131i	$-0.0690178\pi$
$167$	213.521	+	123.276i	1.27857	+	0.738182i	0.301984	+	0.953313i	$0.402351\pi$
$168$		0			0
$169$	54.8427	+	94.9904i	0.324513	+	0.562074i
$170$	−55.5640	−	8.57748i	−0.326847	−	0.0504558i
$171$		0			0
$172$	−61.6022	+	194.772i	−0.358153	+	1.13239i
$173$	−92.5883	−	160.368i	−0.535192	−	0.926981i	−0.999154	−	0.0411252i	$-0.986906\pi$
$173$	−92.5883	−	160.368i	−0.535192	−	0.926981i	0.463962	−	0.885855i	$-0.346428\pi$
$174$		0			0
$175$	12.9932	−	22.5048i	0.0742466	−	0.128599i
$176$	32.2642	−	14.9751i	0.183320	−	0.0850857i
$177$		0			0
$178$	18.3613	+	47.2783i	0.103153	+	0.265609i
$179$	−15.9626			−0.0891768			−0.0445884	−	0.999005i	$-0.514198\pi$
$179$	−15.9626			−0.0891768			−0.0445884	+	0.999005i	$0.514198\pi$
$180$		0			0
$181$		−	6.32493i		−	0.0349443i	−0.999847	−	0.0174722i	$-0.994438\pi$
$181$		−	6.32493i		−	0.0349443i	0.999847	−	0.0174722i	$-0.00556185\pi$
$182$	13.6098	+	35.0438i	0.0747792	+	0.192549i
$183$		0			0
$184$	−138.655	+	92.3781i	−0.753558	+	0.502055i
$185$	−41.7953	−	24.1305i	−0.225920	−	0.130435i
$186$		0			0
$187$	39.0480	−	22.5444i	0.208813	−	0.120558i
$188$	−45.2320	+	143.013i	−0.240596	+	0.760707i
$189$		0			0
$190$	57.5797	+	8.88865i	0.303051	+	0.0467823i
$191$	−196.282	+	113.324i	−1.02766	+	0.593317i	−0.916312	−	0.400465i	$-0.868849\pi$
$191$	−196.282	+	113.324i	−1.02766	+	0.593317i	−0.111343	+	0.993782i	$0.535515\pi$
$192$		0			0
$193$	−15.0900	+	26.1366i	−0.0781865	+	0.135423i	−0.902468	−	0.430758i	$-0.858246\pi$
$193$	−15.0900	+	26.1366i	−0.0781865	+	0.135423i	0.824281	+	0.566181i	$0.191580\pi$
$194$	−32.5150	−	26.1199i	−0.167603	−	0.134638i
$195$		0			0
$196$	−41.1583	−	186.440i	−0.209991	−	0.951223i
$197$	−133.378			−0.677046			−0.338523	−	0.940958i	$-0.609927\pi$
$197$	−133.378			−0.677046			−0.338523	+	0.940958i	$0.609927\pi$
$198$		0			0
$199$	57.6075			0.289485			0.144743	−	0.989469i	$-0.453765\pi$
$199$	57.6075			0.289485			0.144743	+	0.989469i	$0.453765\pi$
$200$	−184.252	+	11.8291i	−0.921259	+	0.0591453i
$201$		0			0
$202$	−117.305	−	94.2334i	−0.580719	−	0.466502i
$203$	30.3671	−	52.5973i	0.149592	−	0.259100i
$204$		0			0
$205$	−20.9526	+	12.0970i	−0.102208	+	0.0590097i
$206$	50.1431	−	324.822i	0.243413	−	1.57680i
$207$		0			0
$208$	153.593	−	218.524i	0.738429	−	1.05059i
$209$	−40.4645	+	23.3622i	−0.193610	+	0.111781i
$210$		0			0
$211$	193.714	+	111.841i	0.918077	+	0.530052i	0.883021	−	0.469333i	$-0.155506\pi$
$211$	193.714	+	111.841i	0.918077	+	0.530052i	0.0350558	+	0.999385i	$0.488839\pi$
$212$	155.409	−	142.152i	0.733063	−	0.670527i
$213$		0			0
$214$	253.945	−	98.6236i	1.18666	−	0.460858i
$215$		−	70.7854i		−	0.329235i
$216$		0			0
$217$	−20.7037			−0.0954086
$218$	54.5692	+	140.510i	0.250317	+	0.644540i
$219$		0			0
$220$	−9.09465	+	8.31881i	−0.0413393	+	0.0378128i
$221$	169.289	−	293.218i	0.766015	−	1.32678i
$222$		0			0
$223$	−143.560	−	248.653i	−0.643766	−	1.11503i	−0.984585	−	0.174906i	$-0.944038\pi$
$223$	−143.560	−	248.653i	−0.643766	−	1.11503i	0.340819	−	0.940129i	$-0.389296\pi$
$224$	24.9740	−	25.9721i	0.111491	−	0.115947i
$225$		0			0
$226$	−217.398	−	33.5600i	−0.961938	−	0.148495i
$227$	124.089	+	214.928i	0.546647	+	0.946820i	0.998501	+	0.0547284i	$0.0174293\pi$
$227$	124.089	+	214.928i	0.546647	+	0.946820i	−0.451854	+	0.892092i	$0.649237\pi$
$228$		0			0
$229$	−263.023	−	151.856i	−1.14857	−	0.663128i	−0.200033	−	0.979789i	$-0.564105\pi$
$229$	−263.023	−	151.856i	−1.14857	−	0.663128i	−0.948539	+	0.316661i	$0.897438\pi$
$230$	36.1558	−	45.0081i	0.157199	−	0.195687i
$231$		0			0
$232$	−430.626	+	27.6464i	−1.85615	+	0.119166i
$233$		−	191.277i		−	0.820933i	−0.911876	−	0.410466i	$-0.865366\pi$
$233$		−	191.277i		−	0.820933i	0.911876	−	0.410466i	$-0.134634\pi$
$234$		0			0
$235$		−	51.9749i		−	0.221170i
$236$	−46.7951	−	211.973i	−0.198284	−	0.898192i
$237$		0			0
$238$	28.6038	−	35.6071i	0.120184	−	0.149610i
$239$	−114.707	−	66.2261i	−0.479946	−	0.277097i	0.240448	−	0.970662i	$-0.422706\pi$
$239$	−114.707	−	66.2261i	−0.479946	−	0.277097i	−0.720394	+	0.693565i	$0.756039\pi$
$240$		0			0
$241$	124.111	+	214.967i	0.514983	+	0.891978i	0.999849	+	0.0173887i	$0.00553528\pi$
$241$	124.111	+	214.967i	0.514983	+	0.891978i	−0.484865	+	0.874589i	$0.661131\pi$
$242$	−35.4124	+	229.398i	−0.146332	+	0.947926i
$243$		0			0
$244$	106.644	−	337.184i	0.437066	−	1.38190i
$245$	33.0793	+	57.2951i	0.135018	+	0.233857i
$246$		0			0
$247$	−175.431	+	303.855i	−0.710246	+	1.23018i
$248$	81.5598	+	122.417i	0.328870	+	0.493617i
$249$		0			0
$250$	124.238	−	48.2498i	0.496952	−	0.192999i
$251$	238.739			0.951150			0.475575	−	0.879675i	$-0.342240\pi$
$251$	238.739			0.951150			0.475575	+	0.879675i	$0.342240\pi$
$252$		0			0
$253$			46.2995i			0.183002i
$254$	−260.561	+	101.193i	−1.02583	+	0.398397i
$255$		0			0
$256$	−251.951	−	45.3527i	−0.984182	−	0.177159i
$257$	−41.8437	−	24.1585i	−0.162816	−	0.0940018i	0.416378	−	0.909192i	$-0.363299\pi$
$257$	−41.8437	−	24.1585i	−0.162816	−	0.0940018i	−0.579194	+	0.815190i	$0.696633\pi$
$258$		0			0
$259$	33.9533	−	19.6029i	0.131094	−	0.0756870i
$260$	−27.9100	+	88.2449i	−0.107346	+	0.339404i
$261$		0			0
$262$	9.74524	−	63.1287i	0.0371956	−	0.240949i
$263$	332.934	−	192.220i	1.26591	−	0.730873i	0.291698	−	0.956510i	$-0.405780\pi$
$263$	332.934	−	192.220i	1.26591	−	0.730873i	0.974211	+	0.225637i	$0.0724464\pi$
$264$		0			0
$265$	−36.4903	+	63.2030i	−0.137699	+	0.238502i
$266$	−29.6415	+	36.8989i	−0.111434	+	0.138717i
$267$		0			0
$268$	−298.084	+	65.8048i	−1.11225	+	0.245540i
$269$	113.224			0.420909			0.210454	−	0.977604i	$-0.432506\pi$
$269$	113.224			0.420909			0.210454	+	0.977604i	$0.432506\pi$
$270$		0			0
$271$	399.534			1.47429			0.737147	−	0.675732i	$-0.236172\pi$
$271$	399.534			1.47429			0.737147	+	0.675732i	$0.236172\pi$
$272$	−323.220	−	28.8589i	−1.18831	−	0.106099i
$273$		0			0
$274$	97.7825	−	121.723i	0.356871	−	0.444246i
$275$	−25.6537	+	44.4336i	−0.0932863	+	0.161577i
$276$		0			0
$277$	−464.208	+	268.010i	−1.67584	+	0.967546i	−0.711573	+	0.702612i	$0.752017\pi$
$277$	−464.208	+	268.010i	−1.67584	+	0.967546i	−0.964267	+	0.264934i	$0.914650\pi$
$278$	52.2963	+	8.07304i	0.188116	+	0.0290397i
$279$		0			0
$280$	−5.53703	+	11.1902i	−0.0197751	+	0.0399651i
$281$	41.0005	−	23.6717i	0.145909	−	0.0842407i	−0.425268	−	0.905067i	$-0.639820\pi$
$281$	41.0005	−	23.6717i	0.145909	−	0.0842407i	0.571177	+	0.820827i	$0.306487\pi$
$282$		0			0
$283$	247.514	+	142.902i	0.874608	+	0.504955i	0.868877	−	0.495028i	$-0.164842\pi$
$283$	247.514	+	142.902i	0.874608	+	0.504955i	0.00573140	+	0.999984i	$0.498176\pi$
$284$	−187.605	−	205.102i	−0.660581	−	0.722189i
$285$		0			0
$286$	−26.8713	−	69.1907i	−0.0939555	−	0.241925i
$287$		−	19.6545i		−	0.0684825i
$288$		0			0
$289$	−122.344			−0.423335
$290$	139.381	−	54.1308i	0.480624	−	0.186658i
$291$		0			0
$292$	−244.086	+	223.263i	−0.835909	+	0.764600i
$293$	−57.0269	+	98.7736i	−0.194631	+	0.337111i	−0.946780	−	0.321883i	$-0.895684\pi$
$293$	−57.0269	+	98.7736i	−0.194631	+	0.337111i	0.752148	+	0.658994i	$0.229018\pi$
$294$		0			0
$295$	37.6096	+	65.1418i	0.127490	+	0.220820i
$296$	−249.664	−	123.536i	−0.843458	−	0.417351i
$297$		0			0
$298$	37.1886	−	240.904i	0.124794	−	0.808402i
$299$	173.835	+	301.092i	0.581389	+	1.00700i
$300$		0			0
$301$	49.7999	+	28.7520i	0.165448	+	0.0955216i
$302$	385.993	+	310.075i	1.27812	+	1.02674i
$303$		0			0
$304$	334.946	+	29.9058i	1.10179	+	0.0983745i
$305$			122.542i			0.401777i
$306$		0			0
$307$			178.258i			0.580644i	0.956929	+	0.290322i	$0.0937624\pi$
$307$			178.258i			0.580644i	−0.956929	+	0.290322i	$0.906238\pi$
$308$	−2.15845	−	9.77738i	−0.00700795	−	0.0317447i
$309$		0			0
$310$	−39.7373	−	31.9217i	−0.128185	−	0.102973i
$311$	−148.082	−	85.4953i	−0.476148	−	0.274904i	0.242662	−	0.970111i	$-0.421980\pi$
$311$	−148.082	−	85.4953i	−0.476148	−	0.274904i	−0.718810	+	0.695207i	$0.755313\pi$
$312$		0			0
$313$	−51.7235	−	89.5878i	−0.165251	−	0.286223i	0.771493	−	0.636237i	$-0.219510\pi$
$313$	−51.7235	−	89.5878i	−0.165251	−	0.286223i	−0.936744	+	0.350014i	$0.886177\pi$
$314$	−58.9057	−	9.09333i	−0.187598	−	0.0289597i
$315$		0			0
$316$	151.468	+	47.9063i	0.479330	+	0.151602i
$317$	−238.433	−	412.979i	−0.752156	−	1.30277i	−0.946776	−	0.321893i	$-0.895681\pi$
$317$	−238.433	−	412.979i	−0.752156	−	1.30277i	0.194620	−	0.980879i	$-0.437653\pi$
$318$		0			0
$319$	−59.9569	+	103.848i	−0.187953	+	0.325543i
$320$	87.9782	−	11.3432i	0.274932	−	0.0354476i
$321$		0			0
$322$	16.9788	+	43.7185i	0.0527291	+	0.135772i
$323$	426.266			1.31971
$324$		0			0
$325$			385.276i			1.18547i
$326$	77.5899	+	199.786i	0.238006	+	0.612840i
$327$		0			0
$328$	−116.213	+	77.4267i	−0.354309	+	0.236057i
$329$	36.5661	+	21.1114i	0.111143	+	0.0641685i
$330$		0			0
$331$	146.687	−	84.6897i	0.443163	−	0.255860i	−0.261775	−	0.965129i	$-0.584308\pi$
$331$	146.687	−	84.6897i	0.443163	−	0.255860i	0.704938	+	0.709269i	$0.250975\pi$
$332$	−434.382	−	137.386i	−1.30838	−	0.413814i
$333$		0			0
$334$	−487.333	−	75.2302i	−1.45908	−	0.225240i
$335$	91.6046	−	52.8879i	0.273446	−	0.157874i
$336$		0			0
$337$	296.462	−	513.487i	0.879709	−	1.52370i	0.0280486	−	0.999607i	$-0.491071\pi$
$337$	296.462	−	513.487i	0.879709	−	1.52370i	0.851660	−	0.524094i	$-0.175596\pi$
$338$	−171.023	−	137.386i	−0.505985	−	0.406467i
$339$		0			0
$340$	109.801	−	24.2395i	0.322943	−	0.0712927i
$341$	40.8774			0.119875
$342$		0			0
$343$	−108.918			−0.317546
$344$	−26.1760	−	407.723i	−0.0760931	−	1.18524i
$345$		0			0
$346$	288.729	+	231.941i	0.834478	+	0.670351i
$347$	−173.414	+	300.362i	−0.499752	+	0.865595i	−1.00000		0.000286796i	$-0.999909\pi$
$347$	−173.414	+	300.362i	−0.499752	+	0.865595i	0.500248	+	0.865882i	$0.333242\pi$
$348$		0			0
$349$	197.166	−	113.834i	0.564945	−	0.326171i	−0.190183	−	0.981749i	$-0.560908\pi$
$349$	197.166	−	113.834i	0.564945	−	0.326171i	0.755128	+	0.655578i	$0.227575\pi$
$350$	−7.92915	+	51.3642i	−0.0226547	+	0.146755i
$351$		0			0
$352$	−49.3088	+	51.2794i	−0.140082	+	0.145680i
$353$	133.728	−	77.2082i	0.378834	−	0.218720i	−0.298477	−	0.954417i	$-0.596479\pi$
$353$	133.728	−	77.2082i	0.378834	−	0.218720i	0.677311	+	0.735697i	$0.263145\pi$
$354$		0			0
$355$	83.4123	+	48.1581i	0.234964	+	0.135657i
$356$	−68.4633	−	74.8484i	−0.192313	−	0.210248i
$357$		0			0
$358$	29.7598	−	11.5577i	0.0831279	−	0.0322840i
$359$			10.6646i			0.0297064i	0.999890	+	0.0148532i	$0.00472809\pi$
$359$			10.6646i			0.0297064i	−0.999890	+	0.0148532i	$0.995272\pi$
$360$		0			0
$361$	−80.7299			−0.223628
$362$	4.57953	+	11.7918i	0.0126506	+	0.0325740i
$363$		0			0
$364$	−50.7466	−	55.4795i	−0.139414	−	0.152416i
$365$	57.3115	−	99.2665i	0.157018	−	0.271963i
$366$		0			0
$367$	9.10814	+	15.7758i	0.0248178	+	0.0429857i	0.878168	−	0.478353i	$-0.158766\pi$
$367$	9.10814	+	15.7758i	0.0248178	+	0.0429857i	−0.853350	+	0.521339i	$0.825433\pi$
$368$	191.613	−	272.616i	0.520689	−	0.740805i
$369$		0			0
$370$	95.3921	+	14.7258i	0.257816	+	0.0397994i
$371$	−29.6436	−	51.3443i	−0.0799020	−	0.138394i
$372$		0			0
$373$	−88.6255	−	51.1680i	−0.237602	−	0.137180i	0.376472	−	0.926428i	$-0.377137\pi$
$373$	−88.6255	−	51.1680i	−0.237602	−	0.137180i	−0.614074	+	0.789248i	$0.710470\pi$
$374$	−56.4755	+	70.3028i	−0.151004	+	0.187975i
$375$		0			0
$376$	−19.2200	−	299.375i	−0.0511170	−	0.796209i
$377$			900.452i			2.38847i
$378$		0			0
$379$			161.449i			0.425986i	0.977054	+	0.212993i	$0.0683211\pi$
$379$			161.449i			0.425986i	−0.977054	+	0.212993i	$0.931679\pi$
$380$	−113.784	+	25.1189i	−0.299431	+	0.0661023i
$381$		0			0
$382$	283.885	−	353.391i	0.743155	−	0.925106i
$383$	−184.025	−	106.247i	−0.480483	−	0.277407i	0.240135	−	0.970740i	$-0.422808\pi$
$383$	−184.025	−	106.247i	−0.480483	−	0.277407i	−0.720618	+	0.693333i	$0.756142\pi$
$384$		0			0
$385$	1.73476	+	3.00470i	0.00450588	+	0.00780442i
$386$	9.20876	−	59.6534i	0.0238569	−	0.154543i
$387$		0			0
$388$	79.5309	+	25.1540i	0.204976	+	0.0648298i
$389$	255.814	+	443.083i	0.657620	+	1.13903i	0.981230	+	0.192840i	$0.0617699\pi$
$389$	255.814	+	443.083i	0.657620	+	1.13903i	−0.323611	+	0.946190i	$0.604897\pi$
$390$		0			0
$391$	211.195	−	365.800i	0.540140	−	0.935550i
$392$	211.724	+	317.786i	0.540112	+	0.810679i
$393$		0			0
$394$	248.662	−	96.5717i	0.631121	−	0.245106i
$395$	−55.0478			−0.139361
$396$		0			0
$397$		−	198.582i		−	0.500206i	−0.968219	−	0.250103i	$-0.919536\pi$
$397$		−	198.582i		−	0.500206i	0.968219	−	0.250103i	$-0.0804644\pi$
$398$	−107.400	+	41.7105i	−0.269849	+	0.104800i
$399$		0			0
$400$	334.943	−	155.460i	0.837358	−	0.388650i
$401$	−357.504	−	206.405i	−0.891532	−	0.514726i	−0.0170888	−	0.999854i	$-0.505440\pi$
$401$	−357.504	−	206.405i	−0.891532	−	0.514726i	−0.874443	+	0.485128i	$0.838773\pi$
$402$		0			0
$403$	265.831	−	153.478i	0.659630	−	0.380838i
$404$	286.926	+	90.7487i	0.710212	+	0.224625i
$405$		0			0
$406$	−18.5317	+	120.046i	−0.0456445	+	0.295681i
$407$	−67.0374	+	38.7041i	−0.164711	+	0.0950960i
$408$		0			0
$409$	104.695	−	181.337i	0.255978	−	0.443368i	−0.709182	−	0.705025i	$-0.750936\pi$
$409$	104.695	−	181.337i	0.255978	−	0.443368i	0.965161	+	0.261657i	$0.0842691\pi$
$410$	30.3040	−	37.7235i	0.0739121	−	0.0920086i
$411$		0			0
$412$	141.702	+	641.884i	0.343937	+	1.55797i
$413$	−61.1060			−0.147956
$414$		0			0
$415$	157.867			0.380401
$416$	−128.129	+	518.611i	−0.308002	+	1.24666i
$417$		0			0
$418$	58.5243	−	72.8532i	0.140010	−	0.174290i
$419$	−79.4861	+	137.674i	−0.189704	+	0.328577i	−0.945152	−	0.326632i	$-0.894086\pi$
$419$	−79.4861	+	137.674i	−0.189704	+	0.328577i	0.755447	+	0.655209i	$0.227420\pi$
$420$		0			0
$421$	−186.964	+	107.944i	−0.444095	+	0.256399i	−0.705333	−	0.708876i	$-0.749203\pi$
$421$	−186.964	+	107.944i	−0.444095	+	0.256399i	0.261238	+	0.965274i	$0.415869\pi$
$422$	−442.127	−	68.2516i	−1.04769	−	0.161734i
$423$		0			0
$424$	−186.811	+	377.542i	−0.440593	+	0.890430i
$425$	405.367	−	234.039i	0.953804	−	0.550679i
$426$		0			0
$427$	−86.2124	−	49.7747i	−0.201903	−	0.116568i
$428$	−402.032	+	367.736i	−0.939327	+	0.859195i
$429$		0			0
$430$	51.2518	+	131.968i	0.119190	+	0.306902i
$431$			529.918i			1.22951i	0.788719	+	0.614754i	$0.210745\pi$
$431$			529.918i			1.22951i	−0.788719	+	0.614754i	$0.789255\pi$
$432$		0			0
$433$	−359.670			−0.830646			−0.415323	−	0.909674i	$-0.636332\pi$
$433$	−359.670			−0.830646			−0.415323	+	0.909674i	$0.636332\pi$
$434$	38.5987	−	14.9904i	0.0889370	−	0.0345401i
$435$		0			0
$436$	−203.471	−	222.447i	−0.466676	−	0.510200i
$437$	−218.856	+	379.070i	−0.500815	+	0.867438i
$438$		0			0
$439$	9.93781	+	17.2128i	0.0226374	+	0.0392091i	0.877122	−	0.480267i	$-0.159460\pi$
$439$	9.93781	+	17.2128i	0.0226374	+	0.0392091i	−0.854485	+	0.519476i	$0.826127\pi$
$440$	10.9323	−	22.0940i	0.0248462	−	0.0502137i
$441$		0			0
$442$	−103.310	+	669.230i	−0.233733	+	1.51410i
$443$	−278.188	−	481.835i	−0.627963	−	1.08766i	−0.987960	−	0.154710i	$-0.950556\pi$
$443$	−278.188	−	481.835i	−0.627963	−	1.08766i	0.359997	−	0.932954i	$-0.382778\pi$
$444$		0			0
$445$	30.4399	+	17.5745i	0.0684043	+	0.0394932i
$446$	447.680	+	359.629i	1.00377	+	0.806344i
$447$		0			0
$448$	−27.7551	+	66.5031i	−0.0619534	+	0.148444i
$449$		−	277.873i		−	0.618870i	−0.950921	−	0.309435i	$-0.899860\pi$
$449$		−	277.873i		−	0.618870i	0.950921	−	0.309435i	$-0.100140\pi$
$450$		0			0
$451$			38.8059i			0.0860441i
$452$	429.602	−	94.8388i	0.950447	−	0.209820i
$453$		0			0
$454$	−386.961	−	310.853i	−0.852338	−	0.684698i
$455$	22.5628	+	13.0266i	0.0495885	+	0.0286300i
$456$		0			0
$457$	354.954	+	614.799i	0.776705	+	1.34529i	0.933831	+	0.357715i	$0.116444\pi$
$457$	354.954	+	614.799i	0.776705	+	1.34529i	−0.157125	+	0.987579i	$0.550223\pi$
$458$	600.315	+	92.6712i	1.31073	+	0.202339i
$459$		0			0
$460$	−34.8188	+	110.089i	−0.0756931	+	0.239324i
$461$	−266.139	−	460.966i	−0.577308	−	0.999927i	−0.995787	−	0.0917001i	$-0.970770\pi$
$461$	−266.139	−	460.966i	−0.577308	−	0.999927i	0.418479	−	0.908227i	$-0.362563\pi$
$462$		0			0
$463$	−116.898	+	202.473i	−0.252479	+	0.437306i	−0.964208	−	0.265148i	$-0.914579\pi$
$463$	−116.898	+	202.473i	−0.252479	+	0.437306i	0.711729	+	0.702454i	$0.247912\pi$
$464$	782.815	−	363.335i	1.68710	−	0.783049i
$465$		0			0
$466$	138.493	+	356.606i	0.297196	+	0.765249i
$467$	−602.162			−1.28943			−0.644713	−	0.764425i	$-0.723023\pi$
$467$	−602.162			−1.28943			−0.644713	+	0.764425i	$0.723023\pi$
$468$		0			0
$469$			85.9292i			0.183218i
$470$	37.6322	+	96.8988i	0.0800684	+	0.206168i
$471$		0			0
$472$	240.720	+	361.308i	0.510000	+	0.765483i
$473$	−98.3252	−	56.7681i	−0.207876	−	0.120017i
$474$		0			0
$475$	−420.072	+	242.529i	−0.884363	+	0.510587i
$476$	−27.5461	+	87.0942i	−0.0578699	+	0.182971i
$477$		0			0
$478$	261.803	+	40.4149i	0.547706	+	0.0845500i
$479$	728.715	−	420.724i	1.52133	−	0.878337i	0.521642	−	0.853165i	$-0.325320\pi$
$479$	728.715	−	420.724i	1.52133	−	0.878337i	0.999683	−	0.0251729i	$-0.00801363\pi$
$480$		0			0
$481$	−290.635	+	503.395i	−0.604231	+	1.04656i
$482$	−387.030	−	310.909i	−0.802968	−	0.645038i
$483$		0			0
$484$	−100.074	−	453.316i	−0.206764	−	0.936603i
$485$	−28.9037			−0.0595953
$486$		0			0
$487$	−475.714			−0.976826			−0.488413	−	0.872613i	$-0.662424\pi$
$487$	−475.714			−0.976826			−0.488413	+	0.872613i	$0.662424\pi$
$488$	45.3153	+	705.840i	0.0928592	+	1.44639i
$489$		0			0
$490$	−103.155	−	82.8665i	−0.210521	−	0.169115i
$491$	110.548	−	191.474i	0.225148	−	0.389968i	−0.731216	−	0.682146i	$-0.761047\pi$
$491$	110.548	−	191.474i	0.225148	−	0.389968i	0.956364	+	0.292178i	$0.0943801\pi$
$492$		0			0
$493$	947.407	−	546.985i	1.92172	−	1.10950i
$494$	107.058	−	693.508i	0.216716	−	1.40386i
$495$		0			0
$496$	−240.691	−	169.174i	−0.485263	−	0.341076i
$497$	−67.7617	+	39.1222i	−0.136341	+	0.0787168i
$498$		0			0
$499$	−687.365	−	396.850i	−1.37748	−	0.795291i	−0.385628	−	0.922654i	$-0.626015\pi$
$499$	−687.365	−	396.850i	−1.37748	−	0.795291i	−0.991856	+	0.127363i	$0.959349\pi$
$500$	−196.687	+	179.908i	−0.393374	+	0.359816i
$501$		0			0
$502$	−445.090	+	172.858i	−0.886633	+	0.344338i
$503$			60.2823i			0.119845i	0.998203	+	0.0599227i	$0.0190854\pi$
$503$			60.2823i			0.119845i	−0.998203	+	0.0599227i	$0.980915\pi$
$504$		0			0
$505$	−104.277			−0.206489
$506$	−33.5229	−	86.3179i	−0.0662508	−	0.170589i
$507$		0			0
$508$	412.505	−	377.315i	0.812018	−	0.742747i
$509$	43.3811	−	75.1383i	0.0852282	−	0.147619i	−0.820260	−	0.571990i	$-0.806171\pi$
$509$	43.3811	−	75.1383i	0.0852282	−	0.147619i	0.905488	+	0.424371i	$0.139505\pi$
$510$		0			0
$511$	46.5582	+	80.6412i	0.0911120	+	0.157811i
$512$	502.559	−	97.8708i	0.981560	−	0.191154i
$513$		0			0
$514$	95.5026	+	14.7428i	0.185803	+	0.0286826i
$515$	−113.887	−	197.258i	−0.221140	−	0.383026i
$516$		0			0
$517$	−72.1962	−	41.6825i	−0.139644	−	0.0806238i
$518$	−49.1070	+	61.1302i	−0.0948011	+	0.118012i
$519$		0			0
$520$	−11.8595	−	184.727i	−0.0228068	−	0.355243i
$521$		−	762.810i		−	1.46413i	−0.681237	−	0.732063i	$-0.738558\pi$
$521$		−	762.810i		−	1.46413i	0.681237	−	0.732063i	$-0.261442\pi$
$522$		0			0
$523$		−	921.604i		−	1.76215i	−0.472978	−	0.881074i	$-0.656821\pi$
$523$		−	921.604i		−	1.76215i	0.472978	−	0.881074i	$-0.343179\pi$
$524$	27.5396	+	124.749i	0.0525564	+	0.238071i
$525$		0			0
$526$	−481.526	+	599.422i	−0.915450	+	1.13959i
$527$	−322.962	−	186.462i	−0.612830	−	0.353818i
$528$		0			0
$529$	−47.6340	−	82.5045i	−0.0900454	−	0.155963i
$530$	22.2684	−	144.252i	0.0420159	−	0.272174i
$531$		0			0
$532$	28.5454	−	90.2538i	0.0536567	−	0.169650i
$533$	145.700	+	252.360i	0.273358	+	0.473470i
$534$		0			0
$535$	94.3975	−	163.501i	0.176444	−	0.305610i
$536$	508.083	−	338.509i	0.947917	−	0.631546i
$537$		0			0
$538$	−211.089	+	81.9796i	−0.392358	+	0.152378i
$539$	106.115			0.196874
$540$		0			0
$541$		−	841.319i		−	1.55512i	−0.628810	−	0.777559i	$-0.716458\pi$
$541$		−	841.319i		−	1.55512i	0.628810	−	0.777559i	$-0.283542\pi$
$542$	−744.866	+	289.280i	−1.37429	+	0.533728i
$543$		0			0
$544$	623.487	−	180.223i	1.14612	−	0.331292i
$545$	90.4665	+	52.2309i	0.165994	+	0.0958364i
$546$		0			0
$547$	−282.340	+	163.009i	−0.516161	+	0.298006i	−0.735363	−	0.677674i	$-0.762988\pi$
$547$	−282.340	+	163.009i	−0.516161	+	0.298006i	0.219201	+	0.975680i	$0.429655\pi$
$548$	−94.1666	+	297.732i	−0.171837	+	0.543307i
$549$		0			0
$550$	15.6553	−	101.414i	0.0284643	−	0.184389i
$551$	−981.776	+	566.829i	−1.78181	+	1.02873i
$552$		0			0
$553$	22.3596	−	38.7280i	0.0404333	−	0.0700325i
$554$	671.388	−	835.769i	1.21189	−	1.50861i
$555$		0			0
$556$	−103.343	+	22.8140i	−0.185869	+	0.0410324i
$557$	−108.173			−0.194206			−0.0971029	−	0.995274i	$-0.530958\pi$
$557$	−108.173			−0.194206			−0.0971029	+	0.995274i	$0.530958\pi$
$558$		0			0
$559$	−852.562			−1.52515
$560$	2.22066	−	24.8714i	0.00396547	−	0.0444133i
$561$		0			0
$562$	−59.2995	+	73.8182i	−0.105515	+	0.131349i
$563$	408.191	−	707.008i	0.725029	−	1.25579i	−0.233933	−	0.972253i	$-0.575160\pi$
$563$	408.191	−	707.008i	0.725029	−	1.25579i	0.958962	−	0.283535i	$-0.0915071\pi$
$564$		0			0
$565$	−132.022	+	76.2228i	−0.233667	+	0.134908i
$566$	−564.918	−	87.2070i	−0.998088	−	0.154076i
$567$		0			0
$568$	498.262	+	246.545i	0.877222	+	0.434058i
$569$	−339.011	+	195.728i	−0.595801	+	0.343986i	−0.767388	−	0.641183i	$-0.778444\pi$
$569$	−339.011	+	195.728i	−0.595801	+	0.343986i	0.171587	+	0.985169i	$0.445111\pi$
$570$		0			0
$571$	−207.111	−	119.576i	−0.362717	−	0.209415i	0.307555	−	0.951530i	$-0.400489\pi$
$571$	−207.111	−	119.576i	−0.362717	−	0.209415i	−0.670272	+	0.742116i	$0.733823\pi$
$572$	100.194	+	109.539i	0.175165	+	0.191501i
$573$		0			0
$574$	14.2307	+	36.6426i	0.0247922	+	0.0638373i
$575$			480.647i			0.835907i
$576$		0			0
$577$	684.269			1.18591			0.592954	−	0.805236i	$-0.297961\pi$
$577$	684.269			1.18591			0.592954	+	0.805236i	$0.297961\pi$
$578$	228.090	−	88.5824i	0.394620	−	0.153257i
$579$		0			0
$580$	−220.660	+	201.836i	−0.380449	+	0.347993i
$581$	−64.1231	+	111.064i	−0.110367	+	0.191161i
$582$		0			0
$583$	58.5285	+	101.374i	0.100392	+	0.173884i
$584$	293.406	−	592.967i	0.502407	−	1.01535i
$585$		0			0
$586$	34.8010	−	225.437i	0.0593874	−	0.384706i
$587$	−483.688	−	837.773i	−0.824001	−	1.42721i	−0.902681	−	0.430311i	$-0.858404\pi$
$587$	−483.688	−	837.773i	−0.824001	−	1.42721i	0.0786797	−	0.996900i	$-0.474930\pi$
$588$		0			0
$589$	334.678	+	193.226i	0.568213	+	0.328058i
$590$	−117.283	−	94.2153i	−0.198784	−	0.159687i
$591$		0			0
$592$	554.903	+	49.5449i	0.937336	+	0.0836907i
$593$			600.206i			1.01215i	0.862489	+	0.506076i	$0.168905\pi$
$593$			600.206i			1.01215i	−0.862489	+	0.506076i	$0.831095\pi$
$594$		0			0
$595$		−	31.6525i		−	0.0531974i
$596$	105.093	+	476.053i	0.176331	+	0.798746i
$597$		0			0
$598$	−542.092	−	435.472i	−0.906508	−	0.728214i
$599$	509.888	+	294.384i	0.851231	+	0.491459i	0.861066	−	0.508493i	$-0.169797\pi$
$599$	509.888	+	294.384i	0.851231	+	0.491459i	−0.00983473	+	0.999952i	$0.503131\pi$
$600$		0			0
$601$	−542.913	−	940.353i	−0.903349	−	1.56465i	−0.823118	−	0.567870i	$-0.807768\pi$
$601$	−542.913	−	940.353i	−0.903349	−	1.56465i	−0.0802311	−	0.996776i	$-0.525566\pi$
$602$	−113.662	−	17.5461i	−0.188807	−	0.0291463i
$603$		0			0
$604$	−944.129	−	298.609i	−1.56313	−	0.494385i
$605$	80.4302	+	139.309i	0.132942	+	0.230263i
$606$		0			0
$607$	150.149	−	260.065i	0.247362	−	0.428444i	−0.715431	−	0.698684i	$-0.753770\pi$
$607$	150.149	−	260.065i	0.247362	−	0.428444i	0.962793	+	0.270240i	$0.0871029\pi$
$608$	−646.105	+	186.761i	−1.06267	+	0.307173i
$609$		0			0
$610$	−88.7259	−	228.460i	−0.145452	−	0.374524i
$611$	−626.001			−1.02455
$612$		0			0
$613$			310.763i			0.506955i	0.967341	+	0.253477i	$0.0815743\pi$
$613$			310.763i			0.506955i	−0.967341	+	0.253477i	$0.918426\pi$
$614$	−129.067	−	332.333i	−0.210206	−	0.541258i
$615$		0			0
$616$	11.1033	+	16.6655i	0.0180249	+	0.0270544i
$617$	−378.986	−	218.808i	−0.614240	−	0.354631i	0.160383	−	0.987055i	$-0.448727\pi$
$617$	−378.986	−	218.808i	−0.614240	−	0.354631i	−0.774623	+	0.632423i	$0.782060\pi$
$618$		0			0
$619$	−149.702	+	86.4306i	−0.241845	+	0.139629i	−0.616025	−	0.787727i	$-0.711258\pi$
$619$	−149.702	+	86.4306i	−0.241845	+	0.139629i	0.374179	+	0.927356i	$0.377924\pi$
$620$	97.1964	+	30.7412i	0.156768	+	0.0495826i
$621$		0			0
$622$	337.978	+	52.1740i	0.543373	+	0.0838810i
$623$	−24.7285	+	14.2770i	−0.0396926	+	0.0229165i
$624$		0			0
$625$	−242.304	+	419.683i	−0.387686	+	0.671492i
$626$	161.296	+	129.572i	0.257661	+	0.206984i
$627$		0			0
$628$	116.404	−	25.6973i	0.185357	−	0.0409193i
$629$	706.193			1.12272
$630$		0			0
$631$	1044.76			1.65572			0.827858	−	0.560937i	$-0.189559\pi$
$631$	1044.76			1.65572			0.827858	+	0.560937i	$0.189559\pi$
$632$	−317.074	+	20.3563i	−0.501700	+	0.0322094i
$633$		0			0
$634$	743.536	+	597.296i	1.17277	+	0.942107i
$635$	−96.8566	+	167.761i	−0.152530	+	0.264190i
$636$		0			0
$637$	690.079	−	398.418i	1.08333	−	0.625459i
$638$	36.5890	−	237.020i	0.0573496	−	0.371505i
$639$		0			0
$640$	−155.808	+	84.8479i	−0.243450	+	0.132575i
$641$	66.0620	−	38.1409i	0.103061	−	0.0595022i	−0.447584	−	0.894242i	$-0.647715\pi$
$641$	66.0620	−	38.1409i	0.103061	−	0.0595022i	0.550644	+	0.834740i	$0.314382\pi$
$642$		0			0
$643$	−195.821	−	113.057i	−0.304543	−	0.175828i	0.339939	−	0.940447i	$-0.389594\pi$
$643$	−195.821	−	113.057i	−0.304543	−	0.175828i	−0.644482	+	0.764620i	$0.722927\pi$
$644$	−63.3083	−	69.2127i	−0.0983048	−	0.107473i
$645$		0			0
$646$	−794.704	+	308.636i	−1.23019	+	0.477765i
$647$		−	619.832i		−	0.958010i	−0.877812	−	0.479005i	$-0.840998\pi$
$647$		−	619.832i		−	0.958010i	0.877812	−	0.479005i	$-0.159002\pi$
$648$		0			0
$649$	120.648			0.185898
$650$	−278.957	−	718.285i	−0.429165	−	1.10505i
$651$		0			0
$652$	−289.308	−	316.290i	−0.443724	−	0.485107i
$653$	135.140	−	234.070i	0.206953	−	0.358453i	−0.743800	−	0.668402i	$-0.766979\pi$
$653$	135.140	−	234.070i	0.206953	−	0.358453i	0.950753	+	0.309949i	$0.100312\pi$
$654$		0			0
$655$	−22.1338	−	38.3369i	−0.0337921	−	0.0585296i
$656$	160.601	−	228.493i	0.244818	−	0.348313i
$657$		0			0
$658$	−83.4572	−	12.8834i	−0.126835	−	0.0195796i
$659$	171.355	+	296.796i	0.260023	+	0.450373i	0.966248	−	0.257615i	$-0.0829365\pi$
$659$	171.355	+	296.796i	0.260023	+	0.450373i	−0.706225	+	0.707988i	$0.749603\pi$
$660$		0			0
$661$	165.843	+	95.7496i	0.250897	+	0.144856i	0.620175	−	0.784463i	$-0.287062\pi$
$661$	165.843	+	95.7496i	0.250897	+	0.144856i	−0.369278	+	0.929319i	$0.620395\pi$
$662$	−212.155	+	264.098i	−0.320476	+	0.398940i
$663$		0			0
$664$	909.309	−	58.3781i	1.36944	−	0.0879189i
$665$			32.8007i			0.0493244i
$666$		0			0
$667$			1123.35i			1.68418i
$668$	963.024	−	212.597i	1.44165	−	0.318259i
$669$		0			0
$670$	−132.489	+	164.927i	−0.197744	+	0.246159i
$671$	170.218	+	98.2754i	0.253678	+	0.146461i
$672$		0			0
$673$	−163.581	−	283.331i	−0.243063	−	0.420997i	0.718522	−	0.695504i	$-0.244819\pi$
$673$	−163.581	−	283.331i	−0.243063	−	0.420997i	−0.961585	+	0.274507i	$0.911485\pi$
$674$	−180.918	+	1171.97i	−0.268424	+	1.73882i
$675$		0			0
$676$	418.318	+	132.305i	0.618813	+	0.195718i
$677$	554.307	+	960.088i	0.818770	+	1.41815i	0.906589	+	0.422014i	$0.138677\pi$
$677$	554.307	+	960.088i	0.818770	+	1.41815i	−0.0878198	+	0.996136i	$0.527990\pi$
$678$		0			0
$679$	11.7403	−	20.3347i	0.0172905	−	0.0299481i
$680$	−187.155	+	124.691i	−0.275228	+	0.183370i
$681$		0			0
$682$	−76.2093	+	29.5971i	−0.111744	+	0.0433975i
$683$	−168.798			−0.247142			−0.123571	−	0.992336i	$-0.539435\pi$
$683$	−168.798			−0.247142			−0.123571	+	0.992336i	$0.539435\pi$
$684$		0			0
$685$		−	108.204i		−	0.157962i
$686$	203.060	−	78.8617i	0.296007	−	0.114959i
$687$		0			0
$688$	344.011	+	741.181i	0.500016	+	1.07730i
$689$	761.237	+	439.500i	1.10484	+	0.637881i
$690$		0			0
$691$	−11.1188	+	6.41947i	−0.0160910	+	0.00929012i	−0.508024	−	0.861343i	$-0.669624\pi$
$691$	−11.1188	+	6.41947i	−0.0160910	+	0.00929012i	0.491933	+	0.870633i	$0.336291\pi$
$692$	−706.225	−	223.364i	−1.02056	−	0.322781i
$693$		0			0
$694$	105.827	−	685.535i	0.152488	−	0.987803i
$695$	31.7586	−	18.3358i	0.0456958	−	0.0263825i
$696$		0			0
$697$	177.013	−	306.595i	0.253964	−	0.439878i
$698$	−285.163	+	354.982i	−0.408543	+	0.508570i
$699$		0			0
$700$	−22.4074	−	101.501i	−0.0320106	−	0.145002i
$701$	275.178			0.392551			0.196275	−	0.980549i	$-0.437115\pi$
$701$	275.178			0.392551			0.196275	+	0.980549i	$0.437115\pi$
$702$		0			0
$703$	−731.812			−1.04098
$704$	54.7998	−	131.304i	0.0778406	−	0.186511i
$705$		0			0
$706$	−193.413	+	240.768i	−0.273956	+	0.341031i
$707$	42.3557	−	73.3623i	0.0599091	−	0.103766i
$708$		0			0
$709$	−1131.99	+	653.558i	−1.59661	+	0.921802i	−0.604473	+	0.796625i	$0.706616\pi$
$709$	−1131.99	+	653.558i	−1.59661	+	0.921802i	−0.992134	+	0.125176i	$0.960050\pi$
$710$	−190.377	−	29.3888i	−0.268137	−	0.0413926i
$711$		0			0
$712$	181.832	+	89.9723i	0.255383	+	0.126366i
$713$	331.634	−	191.469i	0.465125	−	0.268540i
$714$		0			0
$715$	−44.5480	−	25.7198i	−0.0623050	−	0.0359718i
$716$	−47.1140	+	43.0949i	−0.0658017	+	0.0601883i
$717$		0			0
$718$	−7.72164	−	19.8824i	−0.0107544	−	0.0276914i
$719$		−	697.960i		−	0.970737i	−0.874310	−	0.485368i	$-0.838686\pi$
$719$		−	697.960i		−	0.970737i	0.874310	−	0.485368i	$-0.161314\pi$
$720$		0			0
$721$	185.037			0.256640
$722$	150.508	−	58.4521i	0.208460	−	0.0809586i
$723$		0			0
$724$	−17.0756	−	18.6681i	−0.0235851	−	0.0257847i
$725$	−622.427	+	1078.08i	−0.858520	+	1.48700i
$726$		0			0
$727$	557.371	+	965.394i	0.766672	+	1.32791i	0.939358	+	0.342938i	$0.111422\pi$
$727$	557.371	+	965.394i	0.766672	+	1.32791i	−0.172686	+	0.984977i	$0.555245\pi$
$728$	134.779	+	66.6896i	0.185135	+	0.0916067i
$729$		0			0
$730$	−34.9747	+	226.562i	−0.0479105	+	0.310360i
$731$	517.894	+	897.019i	0.708474	+	1.22711i
$732$		0			0
$733$	1144.81	+	660.955i	1.56181	+	0.901712i	0.997074	+	0.0764405i	$0.0243555\pi$
$733$	1144.81	+	660.955i	1.56181	+	0.901712i	0.564736	+	0.825271i	$0.308978\pi$
$734$	−28.4030	−	22.8166i	−0.0386962	−	0.0310854i
$735$		0			0
$736$	−159.846	+	646.986i	−0.217182	+	0.879057i
$737$		−	169.659i		−	0.230202i
$738$		0			0
$739$			514.111i			0.695685i	0.937553	+	0.347842i	$0.113086\pi$
$739$			514.111i			0.695685i	−0.937553	+	0.347842i	$0.886914\pi$
$740$	−188.505	+	41.6143i	−0.254737	+	0.0562356i
$741$		0			0
$742$	92.4414	+	74.2598i	0.124584	+	0.100081i
$743$	−622.933	−	359.650i	−0.838402	−	0.484052i	0.0183187	−	0.999832i	$-0.494169\pi$
$743$	−622.933	−	359.650i	−0.838402	−	0.484052i	−0.856721	+	0.515781i	$0.827502\pi$
$744$		0			0
$745$	−84.4643	−	146.296i	−0.113375	−	0.196371i
$746$	202.276	+	31.2255i	0.271147	+	0.0418573i
$747$		0			0
$748$	54.3871	−	171.959i	0.0727100	−	0.229892i
$749$	76.6858	+	132.824i	0.102384	+	0.177335i
$750$		0			0
$751$	−125.288	+	217.005i	−0.166828	+	0.288955i	−0.937303	−	0.348516i	$-0.886686\pi$
$751$	−125.288	+	217.005i	−0.166828	+	0.288955i	0.770475	+	0.637470i	$0.220019\pi$
$752$	252.593	+	544.220i	0.335895	+	0.723696i
$753$		0			0
$754$	−651.968	−	1678.75i	−0.864679	−	2.22646i
$755$	343.123			0.454467
$756$		0			0
$757$			792.168i			1.04646i	0.852192	+	0.523229i	$0.175273\pi$
$757$			792.168i			1.04646i	−0.852192	+	0.523229i	$0.824727\pi$
$758$	−116.896	−	300.995i	−0.154216	−	0.397091i
$759$		0			0
$760$	193.945	−	129.215i	0.255190	−	0.170019i
$761$	896.813	+	517.775i	1.17847	+	0.680388i	0.955659	−	0.294474i	$-0.0951446\pi$
$761$	896.813	+	517.775i	1.17847	+	0.680388i	0.222807	+	0.974863i	$0.428478\pi$
$762$		0			0
$763$	−73.4923	+	42.4308i	−0.0963202	+	0.0556105i
$764$	−273.387	+	864.385i	−0.357837	+	1.13139i
$765$		0			0
$766$	420.012	+	64.8378i	0.548319	+	0.0846446i
$767$	784.588	−	452.982i	1.02293	−	0.590589i
$768$		0			0
$769$	−75.7290	+	131.167i	−0.0984773	+	0.170568i	−0.911055	−	0.412286i	$-0.864731\pi$
$769$	−75.7290	+	131.167i	−0.0984773	+	0.170568i	0.812577	+	0.582853i	$0.198064\pi$
$770$	−5.40973	−	4.34573i	−0.00702562	−	0.00564381i
$771$		0			0
$772$	26.0235	+	117.882i	0.0337092	+	0.152697i
$773$	−135.306			−0.175040			−0.0875199	−	0.996163i	$-0.527894\pi$
$773$	−135.306			−0.175040			−0.0875199	+	0.996163i	$0.527894\pi$
$774$		0			0
$775$	424.358			0.547559
$776$	−166.485	+	10.6884i	−0.214543	+	0.0137737i
$777$		0			0
$778$	−797.736	−	640.836i	−1.02537	−	0.823696i
$779$	−183.434	+	317.717i	−0.235474	+	0.407853i
$780$		0			0
$781$	133.789	−	77.2431i	0.171305	−	0.0989028i
$782$	−128.883	+	834.890i	−0.164812	+	1.06763i
$783$		0			0
$784$	−624.816	−	439.164i	−0.796960	−	0.560158i
$785$	−35.7723	+	20.6532i	−0.0455698	+	0.0263098i
$786$		0			0
$787$	682.754	+	394.188i	0.867541	+	0.500875i	0.866530	−	0.499125i	$-0.166345\pi$
$787$	682.754	+	394.188i	0.867541	+	0.500875i	0.00101045	+	0.999999i	$0.499678\pi$
$788$	−393.667	+	360.085i	−0.499578	+	0.456960i
$789$		0			0
$790$	102.628	−	39.8571i	0.129908	−	0.0504520i
$791$		−	123.842i		−	0.156564i
$792$		0			0
$793$	1475.93			1.86120
$794$	143.782	+	370.223i	0.181086	+	0.466276i
$795$		0			0
$796$	170.030	−	155.525i	0.213605	−	0.195383i
$797$	539.944	−	935.210i	0.677470	−	1.17341i	−0.298270	−	0.954482i	$-0.596410\pi$
$797$	539.944	−	935.210i	0.677470	−	1.17341i	0.975740	−	0.218931i	$-0.0702571\pi$
$798$		0			0
$799$	380.269	+	658.645i	0.475931	+	0.824336i
$800$	−511.887	+	532.344i	−0.639859	+	0.665430i
$801$		0			0
$802$	815.956	+	125.960i	1.01740	+	0.157057i
$803$	−91.9247	−	159.218i	−0.114477	−	0.198279i
$804$		0			0
$805$	28.1479	+	16.2512i	0.0349664	+	0.0201878i
$806$	−384.474	+	478.608i	−0.477015	+	0.593806i
$807$		0			0
$808$	−600.633	+	38.5609i	−0.743358	+	0.0477239i
$809$		−	81.1370i		−	0.100293i	−0.998742	−	0.0501465i	$-0.984031\pi$
$809$		−	81.1370i		−	0.100293i	0.998742	−	0.0501465i	$-0.0159688\pi$
$810$		0			0
$811$			129.860i			0.160124i	0.996790	+	0.0800618i	$0.0255118\pi$
$811$			129.860i			0.160124i	−0.996790	+	0.0800618i	$0.974488\pi$
$812$	−52.3696	−	237.225i	−0.0644946	−	0.292149i
$813$		0			0
$814$	96.9570	−	120.696i	0.119112	−	0.148275i
$815$	128.631	+	74.2651i	0.157829	+	0.0911229i
$816$		0			0
$817$	−536.682	−	929.560i	−0.656893	−	1.13777i
$818$	−63.8908	+	413.878i	−0.0781062	+	0.505964i
$819$		0			0
$820$	−29.1834	+	92.2709i	−0.0355895	+	0.112525i
$821$	−98.1901	−	170.070i	−0.119598	−	0.207150i	0.800010	−	0.599986i	$-0.204827\pi$
$821$	−98.1901	−	170.070i	−0.119598	−	0.207150i	−0.919608	+	0.392836i	$0.871494\pi$
$822$		0			0
$823$	404.339	−	700.336i	0.491299	−	0.850955i	−0.508651	−	0.860973i	$-0.669856\pi$
$823$	404.339	−	700.336i	0.491299	−	0.850955i	0.999950	+	0.0100182i	$0.00318895\pi$
$824$	−728.933	−	1094.09i	−0.884627	−	1.32778i
$825$		0			0
$826$	113.922	−	44.2435i	0.137920	−	0.0535635i
$827$	832.552			1.00671			0.503357	−	0.864079i	$-0.332098\pi$
$827$	832.552			1.00671			0.503357	+	0.864079i	$0.332098\pi$
$828$		0			0
$829$			316.550i			0.381845i	0.981605	+	0.190923i	$0.0611479\pi$
$829$			316.550i			0.381845i	−0.981605	+	0.190923i	$0.938852\pi$
$830$	−294.317	+	114.303i	−0.354598	+	0.137714i
$831$		0			0
$832$	−136.622	−	1059.64i	−0.164209	−	1.27360i
$833$	−838.387	−	484.043i	−1.00647	−	0.581084i
$834$		0			0
$835$	−295.948	+	170.866i	−0.354429	+	0.204630i
$836$	−56.3601	+	178.197i	−0.0674164	+	0.213155i
$837$		0			0
$838$	48.5068	−	314.222i	0.0578840	−	0.374967i
$839$	−1011.15	+	583.790i	−1.20519	+	0.695816i	−0.961704	−	0.274089i	$-0.911624\pi$
$839$	−1011.15	+	583.790i	−1.20519	+	0.695816i	−0.243484	+	0.969905i	$0.578290\pi$
$840$		0			0
$841$	−1034.21	+	1791.31i	−1.22974	+	2.12997i
$842$	270.408	−	336.614i	0.321150	−	0.399780i
$843$		0			0
$844$	873.691	−	192.876i	1.03518	−	0.228526i
$845$	−152.028			−0.179915
$846$		0			0
$847$	−130.678			−0.154284
$848$	74.9220	−	839.127i	0.0883515	−	0.989537i
$849$		0			0
$850$	−586.286	+	729.831i	−0.689749	+	0.858625i
$851$	−362.578	+	628.004i	−0.426062	+	0.737960i
$852$		0			0
$853$	−152.565	+	88.0833i	−0.178857	+	0.103263i	−0.586755	−	0.809764i	$-0.699595\pi$
$853$	−152.565	+	88.0833i	−0.178857	+	0.103263i	0.407899	+	0.913027i	$0.366262\pi$
$854$	196.768	+	30.3753i	0.230408	+	0.0355683i
$855$		0			0
$856$	483.267	−	976.673i	0.564564	−	1.14097i
$857$	−1034.77	+	597.426i	−1.20744	+	0.697114i	−0.962198	−	0.272349i	$-0.912199\pi$
$857$	−1034.77	+	597.426i	−1.20744	+	0.697114i	−0.245238	+	0.969463i	$0.578866\pi$
$858$		0			0
$859$	438.348	+	253.080i	0.510300	+	0.294622i	0.732957	−	0.680275i	$-0.238140\pi$
$859$	438.348	+	253.080i	0.510300	+	0.294622i	−0.222657	+	0.974897i	$0.571473\pi$
$860$	−191.102	−	208.924i	−0.222211	−	0.242935i
$861$		0			0
$862$	−383.685	−	987.947i	−0.445110	−	1.14611i
$863$		−	214.021i		−	0.247997i	−0.992282	−	0.123998i	$-0.960428\pi$
$863$		−	214.021i		−	0.247997i	0.992282	−	0.123998i	$-0.0395718\pi$
$864$		0			0
$865$	256.662			0.296719
$866$	670.547	−	260.417i	0.774303	−	0.300713i
$867$		0			0
$868$	−61.1073	+	55.8943i	−0.0704001	+	0.0643944i
$869$	−44.1469	+	76.4646i	−0.0508019	+	0.0879915i
$870$		0			0
$871$	−636.998	−	1103.31i	−0.731342	−	1.26672i
$872$	540.401	+	267.395i	0.619725	+	0.306646i
$873$		0			0
$874$	133.558	−	865.177i	0.152813	−	0.989905i
$875$	37.5171	+	64.9816i	0.0428767	+	0.0742646i
$876$		0			0
$877$	−720.576	−	416.025i	−0.821638	−	0.474373i	0.0293431	−	0.999569i	$-0.490658\pi$
$877$	−720.576	−	416.025i	−0.821638	−	0.474373i	−0.850981	+	0.525197i	$0.823992\pi$
$878$	−30.9903	−	24.8950i	−0.0352964	−	0.0283543i
$879$		0			0
$880$	−4.38448	+	49.1062i	−0.00498237	+	0.0558025i
$881$		−	902.400i		−	1.02429i	−0.858899	−	0.512145i	$-0.828851\pi$
$881$		−	902.400i		−	1.02429i	0.858899	−	0.512145i	$-0.171149\pi$
$882$		0			0
$883$		−	1309.72i		−	1.48326i	−0.670810	−	0.741630i	$-0.734053\pi$
$883$		−	1309.72i		−	1.48326i	0.670810	−	0.741630i	$-0.265947\pi$
$884$	−291.948	−	1322.47i	−0.330258	−	1.49601i
$885$		0			0
$886$	867.506	+	696.883i	0.979127	+	0.786550i
$887$	731.925	+	422.577i	0.825169	+	0.476412i	0.852196	−	0.523223i	$-0.175271\pi$
$887$	731.925	+	422.577i	0.825169	+	0.476412i	−0.0270266	+	0.999635i	$0.508604\pi$
$888$		0			0
$889$	−78.6835	−	136.284i	−0.0885079	−	0.153300i
$890$	−69.4750	−	10.7249i	−0.0780618	−	0.0120505i
$891$		0			0
$892$	−1095.01	−	346.330i	−1.22759	−	0.388263i
$893$	−394.064	−	682.539i	−0.441281	−	0.764321i
$894$		0			0
$895$	11.0624	−	19.1607i	0.0123602	−	0.0214086i
$896$	3.59368	−	144.080i	0.00401080	−	0.160804i
$897$		0			0
$898$	201.192	+	518.049i	0.224045	+	0.576892i
$899$	991.793			1.10322
$900$		0			0
$901$		−	1067.91i		−	1.18525i
$902$	−28.0972	−	72.3473i	−0.0311499	−	0.0802077i
$903$		0			0
$904$	−732.257	+	487.863i	−0.810018	+	0.539671i
$905$	7.59209	+	4.38330i	0.00838905	+	0.00484342i
$906$		0			0
$907$	757.357	−	437.260i	0.835013	−	0.482095i	−0.0205528	−	0.999789i	$-0.506543\pi$
$907$	757.357	−	437.260i	0.835013	−	0.482095i	0.855566	+	0.517694i	$0.173209\pi$
$908$	946.499	+	299.358i	1.04240	+	0.329689i
$909$		0			0
$910$	−51.4965	−	7.94958i	−0.0565896	−	0.00873580i
$911$	669.345	−	386.447i	0.734737	−	0.424201i	−0.0854156	−	0.996345i	$-0.527222\pi$
$911$	669.345	−	386.447i	0.734737	−	0.424201i	0.820153	+	0.572145i	$0.193888\pi$
$912$		0			0
$913$	126.605	−	219.286i	0.138669	−	0.240182i
$914$	−1106.90	−	889.191i	−1.21105	−	0.972856i
$915$		0			0
$916$	−1186.29	+	261.884i	−1.29507	+	0.285900i
$917$	35.9617			0.0392167
$918$		0			0
$919$	−827.783			−0.900743			−0.450371	−	0.892841i	$-0.648708\pi$
$919$	−827.783			−0.900743			−0.450371	+	0.892841i	$0.648708\pi$
$920$	−14.7952	−	230.453i	−0.0160818	−	0.250493i
$921$		0			0
$922$	829.933	+	666.701i	0.900145	+	0.723103i
$923$	580.031	−	1004.64i	0.628419	−	1.08845i
$924$		0			0
$925$	−695.932	+	401.797i	−0.752359	+	0.434375i
$926$	71.3375	−	462.117i	0.0770383	−	0.499046i
$927$		0			0
$928$	−1196.36	+	1244.17i	−1.28918	+	1.34070i
$929$	318.846	−	184.086i	0.343214	−	0.198155i	−0.318478	−	0.947930i	$-0.603172\pi$
$929$	318.846	−	184.086i	0.343214	−	0.198155i	0.661692	+	0.749775i	$0.269838\pi$
$930$		0			0
$931$	868.801	+	501.602i	0.933191	+	0.538778i
$932$	−516.397	−	564.559i	−0.554074	−	0.605749i
$933$		0			0
$934$	1122.63	−	435.992i	1.20196	−	0.466801i
$935$			62.4947i			0.0668393i
$936$		0			0
$937$	−733.051			−0.782339			−0.391169	−	0.920319i	$-0.627929\pi$
$937$	−733.051			−0.782339			−0.391169	+	0.920319i	$0.627929\pi$
$938$	−62.2166	−	160.201i	−0.0663290	−	0.170790i
$939$		0			0
$940$	−140.318	−	153.405i	−0.149275	−	0.163197i
$941$	751.175	−	1301.07i	0.798273	−	1.38265i	−0.122467	−	0.992473i	$-0.539080\pi$
$941$	751.175	−	1301.07i	0.798273	−	1.38265i	0.920740	−	0.390177i	$-0.127586\pi$
$942$		0			0
$943$	181.766	+	314.828i	0.192753	+	0.333858i
$944$	−710.387	−	499.309i	−0.752529	−	0.528929i
$945$		0			0
$946$	224.414	+	34.6430i	0.237224	+	0.0366206i
$947$	−15.4857	−	26.8220i	−0.0163524	−	0.0283232i	0.857733	−	0.514095i	$-0.171872\pi$
$947$	−15.4857	−	26.8220i	−0.0163524	−	0.0283232i	−0.874086	+	0.485772i	$0.838539\pi$
$948$		0			0
$949$	−1195.60	−	690.278i	−1.25985	−	0.727374i
$950$	607.555	−	756.307i	0.639532	−	0.796113i
$951$		0			0
$952$	−11.7049	−	182.318i	−0.0122951	−	0.191510i
$953$		−	273.313i		−	0.286792i	−0.989665	−	0.143396i	$-0.954198\pi$
$953$		−	273.313i		−	0.286792i	0.989665	−	0.143396i	$-0.0458022\pi$
$954$		0			0
$955$		−	314.142i		−	0.328944i
$956$	−517.352	+	114.210i	−0.541164	+	0.119467i
$957$		0			0
$958$	−1053.95	+	1311.99i	−1.10015	+	1.36951i
$959$	76.1253	+	43.9510i	0.0793799	+	0.0458300i
$960$		0			0
$961$	311.454	+	539.454i	0.324093	+	0.561346i
$962$	177.362	−	1148.93i	0.184368	−	1.19432i
$963$		0			0
$964$	946.668	+	299.411i	0.982020	+	0.310593i
$965$	−20.9153	−	36.2264i	−0.0216739	−	0.0375403i
$966$		0			0
$967$	276.224	−	478.433i	0.285650	−	0.494760i	−0.687117	−	0.726547i	$-0.741124\pi$
$967$	276.224	−	478.433i	0.285650	−	0.494760i	0.972767	+	0.231787i	$0.0744572\pi$
$968$	514.793	+	772.677i	0.531811	+	0.798220i
$969$		0			0
$970$	53.8863	−	20.9276i	0.0555529	−	0.0215748i
$971$	−1433.59			−1.47641			−0.738203	−	0.674579i	$-0.764325\pi$
$971$	−1433.59			−1.47641			−0.738203	+	0.674579i	$0.764325\pi$
$972$		0			0
$973$			29.7910i			0.0306177i
$974$	886.893	−	344.439i	0.910568	−	0.353633i
$975$		0			0
$976$	−595.543	−	1283.11i	−0.610187	−	1.31467i
$977$	125.056	+	72.2010i	0.128000	+	0.0739007i	0.562633	−	0.826707i	$-0.309789\pi$
$977$	125.056	+	72.2010i	0.128000	+	0.0739007i	−0.434633	+	0.900608i	$0.643122\pi$
$978$		0			0
$979$	48.8240	−	28.1886i	0.0498713	−	0.0287932i
$980$	252.315	+	79.8021i	0.257465	+	0.0814307i
$981$		0			0
$982$	−67.4623	+	437.014i	−0.0686989	+	0.445024i
$983$	−1567.87	+	905.210i	−1.59498	+	0.920865i	−0.602551	+	0.798080i	$0.705849\pi$
$983$	−1567.87	+	905.210i	−1.59498	+	0.920865i	−0.992433	+	0.122785i	$0.960818\pi$
$984$		0			0
$985$	92.4335	−	160.100i	0.0938411	−	0.162538i
$986$	−1370.24	+	1705.73i	−1.38970	+	1.72995i
$987$		0			0
$988$	302.540	+	1370.45i	0.306214	+	1.38709i
$989$	−1063.60			−1.07543
$990$		0			0
$991$	−1230.50			−1.24167			−0.620836	−	0.783940i	$-0.713207\pi$
$991$	−1230.50			−1.24167			−0.620836	+	0.783940i	$0.713207\pi$
$992$	571.218	+	141.126i	0.575825	+	0.142264i
$993$		0			0
$994$	98.0045	−	122.000i	0.0985961	−	0.122736i
$995$	−39.9231	+	69.1489i	−0.0401238	+	0.0694964i
$996$		0			0
$997$	−171.763	+	99.1676i	−0.172280	+	0.0994660i	−0.583661	−	0.811998i	$-0.698380\pi$
$997$	−171.763	+	99.1676i	−0.172280	+	0.0994660i	0.411380	+	0.911464i	$0.365047\pi$
$998$	1568.82	+	242.180i	1.57196	+	0.242666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.3		44
3.2	odd	2		72.3.j.a.5.20	yes	44
4.3	odd	2		864.3.n.a.17.9		44
8.3	odd	2		864.3.n.a.17.14		44
8.5	even	2	inner	216.3.j.a.125.4		44
9.2	odd	6	inner	216.3.j.a.197.4		44
9.4	even	3		648.3.h.a.485.23		44
9.5	odd	6		648.3.h.a.485.22		44
9.7	even	3		72.3.j.a.29.19	yes	44
12.11	even	2		288.3.n.a.113.17		44
24.5	odd	2		72.3.j.a.5.19	✓	44
24.11	even	2		288.3.n.a.113.6		44
36.7	odd	6		288.3.n.a.209.6		44
36.11	even	6		864.3.n.a.305.14		44
36.23	even	6		2592.3.h.a.1457.17		44
36.31	odd	6		2592.3.h.a.1457.28		44
72.5	odd	6		648.3.h.a.485.24		44
72.11	even	6		864.3.n.a.305.9		44
72.13	even	6		648.3.h.a.485.21		44
72.29	odd	6	inner	216.3.j.a.197.3		44
72.43	odd	6		288.3.n.a.209.17		44
72.59	even	6		2592.3.h.a.1457.27		44
72.61	even	6		72.3.j.a.29.20	yes	44
72.67	odd	6		2592.3.h.a.1457.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.19	✓	44	24.5	odd	2
72.3.j.a.5.20	yes	44	3.2	odd	2
72.3.j.a.29.19	yes	44	9.7	even	3
72.3.j.a.29.20	yes	44	72.61	even	6
216.3.j.a.125.3		44	1.1	even	1	trivial
216.3.j.a.125.4		44	8.5	even	2	inner
216.3.j.a.197.3		44	72.29	odd	6	inner
216.3.j.a.197.4		44	9.2	odd	6	inner
288.3.n.a.113.6		44	24.11	even	2
288.3.n.a.113.17		44	12.11	even	2
288.3.n.a.209.6		44	36.7	odd	6
288.3.n.a.209.17		44	72.43	odd	6
648.3.h.a.485.21		44	72.13	even	6
648.3.h.a.485.22		44	9.5	odd	6
648.3.h.a.485.23		44	9.4	even	3
648.3.h.a.485.24		44	72.5	odd	6
864.3.n.a.17.9		44	4.3	odd	2
864.3.n.a.17.14		44	8.3	odd	2
864.3.n.a.305.9		44	72.11	even	6
864.3.n.a.305.14		44	36.11	even	6
2592.3.h.a.1457.17		44	36.23	even	6
2592.3.h.a.1457.18		44	72.67	odd	6
2592.3.h.a.1457.27		44	72.59	even	6
2592.3.h.a.1457.28		44	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.86434 + 0.724045i) q^{2} +(2.95152 - 2.69973i) q^{4} +(-0.693019 + 1.20034i) q^{5} +(-0.562989 - 0.975125i) q^{7} +(-3.54790 + 7.17024i) q^{8} +O(q^{10})\)	\(q+(-1.86434 + 0.724045i) q^{2} +(2.95152 - 2.69973i) q^{4} +(-0.693019 + 1.20034i) q^{5} +(-0.562989 - 0.975125i) q^{7} +(-3.54790 + 7.17024i) q^{8} +(0.422919 - 2.73963i) q^{10} +(1.11157 + 1.92529i) q^{11} +(14.4573 + 8.34694i) q^{13} +(1.75564 + 1.41033i) q^{14} +(1.42291 - 15.9366i) q^{16} -20.2816i q^{17} +21.0174i q^{19} +(1.19515 + 5.41380i) q^{20} +(-3.46633 - 2.78457i) q^{22} +(18.0360 + 10.4131i) q^{23} +(11.5394 + 19.9869i) q^{25} +(-32.9969 - 5.09377i) q^{26} +(-4.29425 - 1.35818i) q^{28} +(26.9695 + 46.7126i) q^{29} +(9.19365 - 15.9239i) q^{31} +(8.88603 + 30.7415i) q^{32} +(14.6848 + 37.8118i) q^{34} +1.56065 q^{35} +34.8194i q^{37} +(-15.2175 - 39.1835i) q^{38} +(-6.14800 - 9.22782i) q^{40} +(15.1169 + 8.72774i) q^{41} +(-44.2282 + 25.5352i) q^{43} +(8.47857 + 2.68160i) q^{44} +(-41.1649 - 6.35467i) q^{46} +(-32.4750 + 18.7494i) q^{47} +(23.8661 - 41.3373i) q^{49} +(-35.9849 - 28.9073i) q^{50} +(65.2055 - 14.3947i) q^{52} +52.6541 q^{53} -3.08135 q^{55} +(8.98931 - 0.577118i) q^{56} +(-84.1024 - 67.5609i) q^{58} +(27.1346 - 46.9986i) q^{59} +(76.5667 - 44.2058i) q^{61} +(-5.61048 + 36.3441i) q^{62} +(-38.8248 - 50.8786i) q^{64} +(-20.0384 + 11.5692i) q^{65} +(-66.0909 - 38.1576i) q^{67} +(-54.7549 - 59.8615i) q^{68} +(-2.90958 + 1.12998i) q^{70} -69.4903i q^{71} -82.6983 q^{73} +(-25.2108 - 64.9151i) q^{74} +(56.7412 + 62.0331i) q^{76} +(1.25160 - 2.16783i) q^{77} +(19.8580 + 34.3950i) q^{79} +(18.1433 + 12.7524i) q^{80} +(-34.5023 - 5.32616i) q^{82} +(-56.9488 - 98.6383i) q^{83} +(24.3449 + 14.0555i) q^{85} +(63.9677 - 79.6294i) q^{86} +(-17.7485 + 1.13946i) q^{88} -25.3593i q^{89} -18.7969i q^{91} +(81.3463 - 17.9580i) q^{92} +(46.9689 - 58.4686i) q^{94} +(-25.2281 - 14.5654i) q^{95} +(10.4267 + 18.0596i) q^{97} +(-14.5644 + 94.3468i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

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