LMFDB - Embedded newform 216.3.j.a.197.3

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			197.3
Character	$\chi$	$=$	216.197
Dual form			216.3.j.a.125.3

$q$-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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

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

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	0.788365	−	0.615208i	$-0.210928\pi$
$5$	−0.693019	−	1.20034i	−0.138604	−	0.240069i	−0.926968	+	0.375139i	$0.877595\pi$
$6$		0			0
$7$	−0.562989	+	0.975125i	−0.0804270	+	0.139304i	−0.903433	−	0.428728i	$-0.858962\pi$
$7$	−0.562989	+	0.975125i	−0.0804270	+	0.139304i	0.823006	+	0.568032i	$0.192295\pi$
$8$	−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	−0.811067	−	0.584954i	$-0.801113\pi$
$11$	1.11157	−	1.92529i	0.101052	−	0.175026i	0.912118	+	0.409927i	$0.134446\pi$
$12$		0			0
$13$	14.4573	−	8.34694i	1.11210	−	0.642072i	0.172729	−	0.984969i	$-0.444742\pi$
$13$	14.4573	−	8.34694i	1.11210	−	0.642072i	0.939373	+	0.342897i	$0.111408\pi$
$14$	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	$0.203450\pi$
$17$			20.2816i			1.19304i	−0.802600	+	0.596518i	$0.796550\pi$
$18$		0			0
$19$		−	21.0174i		−	1.10618i	−0.833122	−	0.553089i	$-0.813449\pi$
$19$		−	21.0174i		−	1.10618i	0.833122	−	0.553089i	$-0.186551\pi$
$20$	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	−0.0537322	−	0.998555i	$-0.517112\pi$
$23$	18.0360	−	10.4131i	0.784176	−	0.452744i	0.837908	+	0.545811i	$0.183778\pi$
$24$		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	0.146640	−	0.989190i	$-0.453154\pi$
$29$	26.9695	−	46.7126i	0.929984	−	1.61078i	0.783343	−	0.621589i	$-0.213513\pi$
$30$		0			0
$31$	9.19365	+	15.9239i	0.296569	+	0.513673i	0.975349	−	0.220669i	$-0.0708241\pi$
$31$	9.19365	+	15.9239i	0.296569	+	0.513673i	−0.678779	+	0.734342i	$0.737491\pi$
$32$	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	$-0.844062\pi$
$37$		−	34.8194i		−	0.941065i	0.882383	−	0.470532i	$-0.155938\pi$
$38$	−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	−0.304188	−	0.952612i	$-0.598385\pi$
$41$	15.1169	−	8.72774i	0.368705	−	0.212872i	0.672892	+	0.739740i	$0.265052\pi$
$42$		0			0
$43$	−44.2282	−	25.5352i	−1.02856	−	0.593841i	−0.111990	−	0.993709i	$-0.535722\pi$
$43$	−44.2282	−	25.5352i	−1.02856	−	0.593841i	−0.916573	+	0.399868i	$0.869056\pi$
$44$	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	0.113014	−	0.993593i	$-0.463950\pi$
$47$	−32.4750	−	18.7494i	−0.690957	−	0.398924i	−0.803970	+	0.594669i	$0.797283\pi$
$48$		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	0.998956	−	0.0456902i	$-0.0145487\pi$
$59$	27.1346	+	46.9986i	0.459909	+	0.796586i	−0.539047	+	0.842276i	$0.681215\pi$
$60$		0			0
$61$	76.5667	+	44.2058i	1.25519	+	0.724686i	0.972136	−	0.234418i	$-0.0753184\pi$
$61$	76.5667	+	44.2058i	1.25519	+	0.724686i	0.283056	+	0.959103i	$0.408652\pi$
$62$	−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	−0.904206	−	0.427097i	$-0.859536\pi$
$67$	−66.0909	+	38.1576i	−0.986432	+	0.569517i	−0.0822260	+	0.996614i	$0.526203\pi$
$68$	−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	$0.162773\pi$
$71$			69.4903i			0.978736i	−0.872077	+	0.489368i	$0.837227\pi$
$72$		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	−0.712536	−	0.701636i	$-0.752453\pi$
$79$	19.8580	−	34.3950i	0.251366	−	0.435380i	0.963902	+	0.266256i	$0.0857867\pi$
$80$	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	0.286949	+	0.957946i	$0.407359\pi$
$83$	−56.9488	+	98.6383i	−0.686131	+	1.18841i	−0.973080	+	0.230467i	$0.925975\pi$
$84$		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	$0.0455038\pi$
$89$			25.3593i			0.284936i	−0.989799	+	0.142468i	$0.954496\pi$
$90$		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	−0.807262	−	0.590194i	$-0.799051\pi$
$97$	10.4267	−	18.0596i	0.107492	−	0.186182i	0.914754	+	0.404012i	$0.132385\pi$
$98$	−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	−0.617497	−	0.786573i	$-0.711853\pi$
$101$	37.6168	−	65.1543i	0.372444	−	0.645092i	0.989941	+	0.141481i	$0.0451865\pi$
$102$		0			0
$103$	−82.1673	−	142.318i	−0.797741	−	1.38173i	−0.921084	−	0.389364i	$-0.872695\pi$
$103$	−82.1673	−	142.318i	−0.797741	−	1.38173i	0.123343	−	0.992364i	$-0.460638\pi$
$104$	−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	$0.112366\pi$
$109$			75.3671i			0.691441i	−0.938337	+	0.345721i	$0.887634\pi$
$110$	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	−0.0153290	−	0.999883i	$-0.504880\pi$
$113$	95.2511	−	54.9933i	0.842930	−	0.486666i	0.858259	+	0.513217i	$0.171546\pi$
$114$		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	0.798616	−	0.601841i	$-0.205566\pi$
$131$	−15.9691	−	27.6593i	−0.121902	−	0.211140i	−0.920518	+	0.390701i	$0.872233\pi$
$132$		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	0.232531	−	0.972589i	$-0.425299\pi$
$137$	−67.6082	−	39.0336i	−0.493491	−	0.284917i	−0.726021	+	0.687672i	$0.758633\pi$
$138$		0			0
$139$	−22.9132	+	13.2289i	−0.164843	+	0.0951723i	−0.580152	−	0.814508i	$-0.697007\pi$
$139$	−22.9132	+	13.2289i	−0.164843	+	0.0951723i	0.415309	+	0.909680i	$0.363674\pi$
$140$	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	0.585788	−	0.810465i	$-0.300785\pi$
$149$	−60.9394	−	105.550i	−0.408989	−	0.708390i	−0.994777	+	0.102075i	$0.967452\pi$
$150$		0			0
$151$	−123.778	+	214.390i	−0.819724	+	1.41980i	0.0861624	+	0.996281i	$0.472540\pi$
$151$	−123.778	+	214.390i	−0.819724	+	1.41980i	−0.905886	+	0.423522i	$0.860794\pi$
$152$	−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	−0.415549	−	0.909571i	$-0.636410\pi$
$157$	25.8090	−	14.9009i	0.164389	−	0.0949099i	0.579937	+	0.814661i	$0.303077\pi$
$158$	−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	$0.106616\pi$
$163$			107.162i			0.657434i	−0.944428	+	0.328717i	$0.893384\pi$
$164$	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	0.301984	−	0.953313i	$-0.402351\pi$
$167$	213.521	−	123.276i	1.27857	−	0.738182i	0.976585	+	0.215131i	$0.0690178\pi$
$168$		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	0.463962	+	0.885855i	$0.346428\pi$
$173$	−92.5883	+	160.368i	−0.535192	+	0.926981i	−0.999154	+	0.0411252i	$0.986906\pi$
$174$		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	$0.00556185\pi$
$181$			6.32493i			0.0349443i	−0.999847	+	0.0174722i	$0.994438\pi$
$182$	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	−0.111343	−	0.993782i	$-0.535515\pi$
$191$	−196.282	−	113.324i	−1.02766	−	0.593317i	−0.916312	+	0.400465i	$0.868849\pi$
$192$		0			0
$193$	−15.0900	−	26.1366i	−0.0781865	−	0.135423i	0.824281	−	0.566181i	$-0.191580\pi$
$193$	−15.0900	−	26.1366i	−0.0781865	−	0.135423i	−0.902468	+	0.430758i	$0.858246\pi$
$194$	−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	0.0350558	−	0.999385i	$-0.488839\pi$
$211$	193.714	−	111.841i	0.918077	−	0.530052i	0.883021	+	0.469333i	$0.155506\pi$
$212$	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	0.340819	+	0.940129i	$0.389296\pi$
$223$	−143.560	+	248.653i	−0.643766	+	1.11503i	−0.984585	+	0.174906i	$0.944038\pi$
$224$	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	−0.451854	−	0.892092i	$-0.649237\pi$
$227$	124.089	−	214.928i	0.546647	−	0.946820i	0.998501	−	0.0547284i	$-0.0174293\pi$
$228$		0			0
$229$	−263.023	+	151.856i	−1.14857	+	0.663128i	−0.948539	−	0.316661i	$-0.897438\pi$
$229$	−263.023	+	151.856i	−1.14857	+	0.663128i	−0.200033	+	0.979789i	$0.564105\pi$
$230$	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	$0.134634\pi$
$233$			191.277i			0.820933i	−0.911876	+	0.410466i	$0.865366\pi$
$234$		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	−0.720394	−	0.693565i	$-0.756039\pi$
$239$	−114.707	+	66.2261i	−0.479946	+	0.277097i	0.240448	+	0.970662i	$0.422706\pi$
$240$		0			0
$241$	124.111	−	214.967i	0.514983	−	0.891978i	−0.484865	−	0.874589i	$-0.661131\pi$
$241$	124.111	−	214.967i	0.514983	−	0.891978i	0.999849	−	0.0173887i	$-0.00553528\pi$
$242$	−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	−0.579194	−	0.815190i	$-0.696633\pi$
$257$	−41.8437	+	24.1585i	−0.162816	+	0.0940018i	0.416378	+	0.909192i	$0.363299\pi$
$258$		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	0.974211	−	0.225637i	$-0.0724464\pi$
$263$	332.934	+	192.220i	1.26591	+	0.730873i	0.291698	+	0.956510i	$0.405780\pi$
$264$		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	−0.964267	−	0.264934i	$-0.914650\pi$
$277$	−464.208	−	268.010i	−1.67584	−	0.967546i	−0.711573	−	0.702612i	$-0.752017\pi$
$278$	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	0.571177	−	0.820827i	$-0.306487\pi$
$281$	41.0005	+	23.6717i	0.145909	+	0.0842407i	−0.425268	+	0.905067i	$0.639820\pi$
$282$		0			0
$283$	247.514	−	142.902i	0.874608	−	0.504955i	0.00573140	−	0.999984i	$-0.498176\pi$
$283$	247.514	−	142.902i	0.874608	−	0.504955i	0.868877	+	0.495028i	$0.164842\pi$
$284$	−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	0.752148	−	0.658994i	$-0.229018\pi$
$293$	−57.0269	−	98.7736i	−0.194631	−	0.337111i	−0.946780	+	0.321883i	$0.895684\pi$
$294$		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	$-0.906238\pi$
$307$		−	178.258i		−	0.580644i	0.956929	−	0.290322i	$-0.0937624\pi$
$308$	−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	−0.718810	−	0.695207i	$-0.755313\pi$
$311$	−148.082	+	85.4953i	−0.476148	+	0.274904i	0.242662	+	0.970111i	$0.421980\pi$
$312$		0			0
$313$	−51.7235	+	89.5878i	−0.165251	+	0.286223i	−0.936744	−	0.350014i	$-0.886177\pi$
$313$	−51.7235	+	89.5878i	−0.165251	+	0.286223i	0.771493	+	0.636237i	$0.219510\pi$
$314$	−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	0.194620	+	0.980879i	$0.437653\pi$
$317$	−238.433	+	412.979i	−0.752156	+	1.30277i	−0.946776	+	0.321893i	$0.895681\pi$
$318$		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	0.704938	−	0.709269i	$-0.250975\pi$
$331$	146.687	+	84.6897i	0.443163	+	0.255860i	−0.261775	+	0.965129i	$0.584308\pi$
$332$	−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	0.851660	+	0.524094i	$0.175596\pi$
$337$	296.462	+	513.487i	0.879709	+	1.52370i	0.0280486	+	0.999607i	$0.491071\pi$
$338$	−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	0.500248	−	0.865882i	$-0.333242\pi$
$347$	−173.414	−	300.362i	−0.499752	−	0.865595i	−1.00000		0.000286796i	$0.999909\pi$
$348$		0			0
$349$	197.166	+	113.834i	0.564945	+	0.326171i	0.755128	−	0.655578i	$-0.227575\pi$
$349$	197.166	+	113.834i	0.564945	+	0.326171i	−0.190183	+	0.981749i	$0.560908\pi$
$350$	−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	0.677311	−	0.735697i	$-0.263145\pi$
$353$	133.728	+	77.2082i	0.378834	+	0.218720i	−0.298477	+	0.954417i	$0.596479\pi$
$354$		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	$-0.995272\pi$
$359$		−	10.6646i		−	0.0297064i	0.999890	−	0.0148532i	$-0.00472809\pi$
$360$		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	−0.853350	−	0.521339i	$-0.825433\pi$
$367$	9.10814	−	15.7758i	0.0248178	−	0.0429857i	0.878168	+	0.478353i	$0.158766\pi$
$368$	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	−0.614074	−	0.789248i	$-0.710470\pi$
$373$	−88.6255	+	51.1680i	−0.237602	+	0.137180i	0.376472	+	0.926428i	$0.377137\pi$
$374$	−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	$-0.931679\pi$
$379$		−	161.449i		−	0.425986i	0.977054	−	0.212993i	$-0.0683211\pi$
$380$	−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	−0.720618	−	0.693333i	$-0.756142\pi$
$383$	−184.025	+	106.247i	−0.480483	+	0.277407i	0.240135	+	0.970740i	$0.422808\pi$
$384$		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	−0.323611	−	0.946190i	$-0.604897\pi$
$389$	255.814	−	443.083i	0.657620	−	1.13903i	0.981230	−	0.192840i	$-0.0617699\pi$
$390$		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	$0.0804644\pi$
$397$			198.582i			0.500206i	−0.968219	+	0.250103i	$0.919536\pi$
$398$	−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	−0.874443	−	0.485128i	$-0.838773\pi$
$401$	−357.504	+	206.405i	−0.891532	+	0.514726i	−0.0170888	+	0.999854i	$0.505440\pi$
$402$		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	0.965161	−	0.261657i	$-0.0842691\pi$
$409$	104.695	+	181.337i	0.255978	+	0.443368i	−0.709182	+	0.705025i	$0.750936\pi$
$410$	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	0.755447	−	0.655209i	$-0.227420\pi$
$419$	−79.4861	−	137.674i	−0.189704	−	0.328577i	−0.945152	+	0.326632i	$0.894086\pi$
$420$		0			0
$421$	−186.964	−	107.944i	−0.444095	−	0.256399i	0.261238	−	0.965274i	$-0.415869\pi$
$421$	−186.964	−	107.944i	−0.444095	−	0.256399i	−0.705333	+	0.708876i	$0.749203\pi$
$422$	−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	$-0.789255\pi$
$431$		−	529.918i		−	1.22951i	0.788719	−	0.614754i	$-0.210745\pi$
$432$		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	−0.854485	−	0.519476i	$-0.826127\pi$
$439$	9.93781	−	17.2128i	0.0226374	−	0.0392091i	0.877122	+	0.480267i	$0.159460\pi$
$440$	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	0.359997	+	0.932954i	$0.382778\pi$
$443$	−278.188	+	481.835i	−0.627963	+	1.08766i	−0.987960	+	0.154710i	$0.950556\pi$
$444$		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	$0.100140\pi$
$449$			277.873i			0.618870i	−0.950921	+	0.309435i	$0.899860\pi$
$450$		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	−0.157125	−	0.987579i	$-0.550223\pi$
$457$	354.954	−	614.799i	0.776705	−	1.34529i	0.933831	−	0.357715i	$-0.116444\pi$
$458$	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	0.418479	+	0.908227i	$0.362563\pi$
$461$	−266.139	+	460.966i	−0.577308	+	0.999927i	−0.995787	+	0.0917001i	$0.970770\pi$
$462$		0			0
$463$	−116.898	−	202.473i	−0.252479	−	0.437306i	0.711729	−	0.702454i	$-0.247912\pi$
$463$	−116.898	−	202.473i	−0.252479	−	0.437306i	−0.964208	+	0.265148i	$0.914579\pi$
$464$	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	0.999683	+	0.0251729i	$0.00801363\pi$
$479$	728.715	+	420.724i	1.52133	+	0.878337i	0.521642	+	0.853165i	$0.325320\pi$
$480$		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	0.956364	−	0.292178i	$-0.0943801\pi$
$491$	110.548	+	191.474i	0.225148	+	0.389968i	−0.731216	+	0.682146i	$0.761047\pi$
$492$		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	−0.991856	−	0.127363i	$-0.959349\pi$
$499$	−687.365	+	396.850i	−1.37748	+	0.795291i	−0.385628	+	0.922654i	$0.626015\pi$
$500$	−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	$-0.980915\pi$
$503$		−	60.2823i		−	0.119845i	0.998203	−	0.0599227i	$-0.0190854\pi$
$504$		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	0.905488	−	0.424371i	$-0.139505\pi$
$509$	43.3811	+	75.1383i	0.0852282	+	0.147619i	−0.820260	+	0.571990i	$0.806171\pi$
$510$		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	$0.261442\pi$
$521$			762.810i			1.46413i	−0.681237	+	0.732063i	$0.738558\pi$
$522$		0			0
$523$			921.604i			1.76215i	0.472978	+	0.881074i	$0.343179\pi$
$523$			921.604i			1.76215i	−0.472978	+	0.881074i	$0.656821\pi$
$524$	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	$0.283542\pi$
$541$			841.319i			1.55512i	−0.628810	+	0.777559i	$0.716458\pi$
$542$	−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	0.219201	−	0.975680i	$-0.429655\pi$
$547$	−282.340	−	163.009i	−0.516161	−	0.298006i	−0.735363	+	0.677674i	$0.762988\pi$
$548$	−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	0.958962	+	0.283535i	$0.0915071\pi$
$563$	408.191	+	707.008i	0.725029	+	1.25579i	−0.233933	+	0.972253i	$0.575160\pi$
$564$		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	0.171587	−	0.985169i	$-0.445111\pi$
$569$	−339.011	−	195.728i	−0.595801	−	0.343986i	−0.767388	+	0.641183i	$0.778444\pi$
$570$		0			0
$571$	−207.111	+	119.576i	−0.362717	+	0.209415i	−0.670272	−	0.742116i	$-0.733823\pi$
$571$	−207.111	+	119.576i	−0.362717	+	0.209415i	0.307555	+	0.951530i	$0.400489\pi$
$572$	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	0.0786797	+	0.996900i	$0.474930\pi$
$587$	−483.688	+	837.773i	−0.824001	+	1.42721i	−0.902681	+	0.430311i	$0.858404\pi$
$588$		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	$-0.831095\pi$
$593$		−	600.206i		−	1.01215i	0.862489	−	0.506076i	$-0.168905\pi$
$594$		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	−0.00983473	−	0.999952i	$-0.503131\pi$
$599$	509.888	−	294.384i	0.851231	−	0.491459i	0.861066	+	0.508493i	$0.169797\pi$
$600$		0			0
$601$	−542.913	+	940.353i	−0.903349	+	1.56465i	−0.0802311	+	0.996776i	$0.525566\pi$
$601$	−542.913	+	940.353i	−0.903349	+	1.56465i	−0.823118	+	0.567870i	$0.807768\pi$
$602$	−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	0.962793	−	0.270240i	$-0.0871029\pi$
$607$	150.149	+	260.065i	0.247362	+	0.428444i	−0.715431	+	0.698684i	$0.753770\pi$
$608$	−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	$-0.918426\pi$
$613$		−	310.763i		−	0.506955i	0.967341	−	0.253477i	$-0.0815743\pi$
$614$	−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	−0.774623	−	0.632423i	$-0.782060\pi$
$617$	−378.986	+	218.808i	−0.614240	+	0.354631i	0.160383	+	0.987055i	$0.448727\pi$
$618$		0			0
$619$	−149.702	−	86.4306i	−0.241845	−	0.139629i	0.374179	−	0.927356i	$-0.377924\pi$
$619$	−149.702	−	86.4306i	−0.241845	−	0.139629i	−0.616025	+	0.787727i	$0.711258\pi$
$620$	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	0.550644	−	0.834740i	$-0.314382\pi$
$641$	66.0620	+	38.1409i	0.103061	+	0.0595022i	−0.447584	+	0.894242i	$0.647715\pi$
$642$		0			0
$643$	−195.821	+	113.057i	−0.304543	+	0.175828i	−0.644482	−	0.764620i	$-0.722927\pi$
$643$	−195.821	+	113.057i	−0.304543	+	0.175828i	0.339939	+	0.940447i	$0.389594\pi$
$644$	−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	$0.159002\pi$
$647$			619.832i			0.958010i	−0.877812	+	0.479005i	$0.840998\pi$
$648$		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	0.950753	−	0.309949i	$-0.100312\pi$
$653$	135.140	+	234.070i	0.206953	+	0.358453i	−0.743800	+	0.668402i	$0.766979\pi$
$654$		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	−0.706225	−	0.707988i	$-0.749603\pi$
$659$	171.355	−	296.796i	0.260023	−	0.450373i	0.966248	+	0.257615i	$0.0829365\pi$
$660$		0			0
$661$	165.843	−	95.7496i	0.250897	−	0.144856i	−0.369278	−	0.929319i	$-0.620395\pi$
$661$	165.843	−	95.7496i	0.250897	−	0.144856i	0.620175	+	0.784463i	$0.287062\pi$
$662$	−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	−0.961585	−	0.274507i	$-0.911485\pi$
$673$	−163.581	+	283.331i	−0.243063	+	0.420997i	0.718522	+	0.695504i	$0.244819\pi$
$674$	−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	−0.0878198	−	0.996136i	$-0.527990\pi$
$677$	554.307	−	960.088i	0.818770	−	1.41815i	0.906589	−	0.422014i	$-0.138677\pi$
$678$		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	0.491933	−	0.870633i	$-0.336291\pi$
$691$	−11.1188	−	6.41947i	−0.0160910	−	0.00929012i	−0.508024	+	0.861343i	$0.669624\pi$
$692$	−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	−0.992134	−	0.125176i	$-0.960050\pi$
$709$	−1131.99	−	653.558i	−1.59661	−	0.921802i	−0.604473	−	0.796625i	$-0.706616\pi$
$710$	−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	$0.161314\pi$
$719$			697.960i			0.970737i	−0.874310	+	0.485368i	$0.838686\pi$
$720$		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	−0.172686	−	0.984977i	$-0.555245\pi$
$727$	557.371	−	965.394i	0.766672	−	1.32791i	0.939358	−	0.342938i	$-0.111422\pi$
$728$	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	0.564736	−	0.825271i	$-0.308978\pi$
$733$	1144.81	−	660.955i	1.56181	−	0.901712i	0.997074	−	0.0764405i	$-0.0243555\pi$
$734$	−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	$-0.886914\pi$
$739$		−	514.111i		−	0.695685i	0.937553	−	0.347842i	$-0.113086\pi$
$740$	−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	−0.856721	−	0.515781i	$-0.827502\pi$
$743$	−622.933	+	359.650i	−0.838402	+	0.484052i	0.0183187	+	0.999832i	$0.494169\pi$
$744$		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	0.770475	−	0.637470i	$-0.220019\pi$
$751$	−125.288	−	217.005i	−0.166828	−	0.288955i	−0.937303	+	0.348516i	$0.886686\pi$
$752$	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	$-0.824727\pi$
$757$		−	792.168i		−	1.04646i	0.852192	−	0.523229i	$-0.175273\pi$
$758$	−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	0.222807	−	0.974863i	$-0.428478\pi$
$761$	896.813	−	517.775i	1.17847	−	0.680388i	0.955659	+	0.294474i	$0.0951446\pi$
$762$		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	0.812577	−	0.582853i	$-0.198064\pi$
$769$	−75.7290	−	131.167i	−0.0984773	−	0.170568i	−0.911055	+	0.412286i	$0.864731\pi$
$770$	−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	0.00101045	−	0.999999i	$-0.499678\pi$
$787$	682.754	−	394.188i	0.867541	−	0.500875i	0.866530	+	0.499125i	$0.166345\pi$
$788$	−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	0.975740	+	0.218931i	$0.0702571\pi$
$797$	539.944	+	935.210i	0.677470	+	1.17341i	−0.298270	+	0.954482i	$0.596410\pi$
$798$		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	$0.0159688\pi$
$809$			81.1370i			0.100293i	−0.998742	+	0.0501465i	$0.984031\pi$
$810$		0			0
$811$		−	129.860i		−	0.160124i	−0.996790	−	0.0800618i	$-0.974488\pi$
$811$		−	129.860i		−	0.160124i	0.996790	−	0.0800618i	$-0.0255118\pi$
$812$	−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	−0.919608	−	0.392836i	$-0.871494\pi$
$821$	−98.1901	+	170.070i	−0.119598	+	0.207150i	0.800010	+	0.599986i	$0.204827\pi$
$822$		0			0
$823$	404.339	+	700.336i	0.491299	+	0.850955i	0.999950	−	0.0100182i	$-0.00318895\pi$
$823$	404.339	+	700.336i	0.491299	+	0.850955i	−0.508651	+	0.860973i	$0.669856\pi$
$824$	−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	$-0.938852\pi$
$829$		−	316.550i		−	0.381845i	0.981605	−	0.190923i	$-0.0611479\pi$
$830$	−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	−0.243484	−	0.969905i	$-0.578290\pi$
$839$	−1011.15	−	583.790i	−1.20519	−	0.695816i	−0.961704	+	0.274089i	$0.911624\pi$
$840$		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	0.407899	−	0.913027i	$-0.366262\pi$
$853$	−152.565	−	88.0833i	−0.178857	−	0.103263i	−0.586755	+	0.809764i	$0.699595\pi$
$854$	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	−0.245238	−	0.969463i	$-0.578866\pi$
$857$	−1034.77	−	597.426i	−1.20744	−	0.697114i	−0.962198	+	0.272349i	$0.912199\pi$
$858$		0			0
$859$	438.348	−	253.080i	0.510300	−	0.294622i	−0.222657	−	0.974897i	$-0.571473\pi$
$859$	438.348	−	253.080i	0.510300	−	0.294622i	0.732957	+	0.680275i	$0.238140\pi$
$860$	−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	$0.0395718\pi$
$863$			214.021i			0.247997i	−0.992282	+	0.123998i	$0.960428\pi$
$864$		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	−0.850981	−	0.525197i	$-0.823992\pi$
$877$	−720.576	+	416.025i	−0.821638	+	0.474373i	0.0293431	+	0.999569i	$0.490658\pi$
$878$	−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	$0.171149\pi$
$881$			902.400i			1.02429i	−0.858899	+	0.512145i	$0.828851\pi$
$882$		0			0
$883$			1309.72i			1.48326i	0.670810	+	0.741630i	$0.265947\pi$
$883$			1309.72i			1.48326i	−0.670810	+	0.741630i	$0.734053\pi$
$884$	−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	−0.0270266	−	0.999635i	$-0.508604\pi$
$887$	731.925	−	422.577i	0.825169	−	0.476412i	0.852196	+	0.523223i	$0.175271\pi$
$888$		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	0.855566	−	0.517694i	$-0.173209\pi$
$907$	757.357	+	437.260i	0.835013	+	0.482095i	−0.0205528	+	0.999789i	$0.506543\pi$
$908$	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	0.820153	−	0.572145i	$-0.193888\pi$
$911$	669.345	+	386.447i	0.734737	+	0.424201i	−0.0854156	+	0.996345i	$0.527222\pi$
$912$		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	0.661692	−	0.749775i	$-0.269838\pi$
$929$	318.846	+	184.086i	0.343214	+	0.198155i	−0.318478	+	0.947930i	$0.603172\pi$
$930$		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	0.920740	+	0.390177i	$0.127586\pi$
$941$	751.175	+	1301.07i	0.798273	+	1.38265i	−0.122467	+	0.992473i	$0.539080\pi$
$942$		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	−0.874086	−	0.485772i	$-0.838539\pi$
$947$	−15.4857	+	26.8220i	−0.0163524	+	0.0283232i	0.857733	+	0.514095i	$0.171872\pi$
$948$		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	$0.0458022\pi$
$953$			273.313i			0.286792i	−0.989665	+	0.143396i	$0.954198\pi$
$954$		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	0.972767	−	0.231787i	$-0.0744572\pi$
$967$	276.224	+	478.433i	0.285650	+	0.494760i	−0.687117	+	0.726547i	$0.741124\pi$
$968$	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	−0.434633	−	0.900608i	$-0.643122\pi$
$977$	125.056	−	72.2010i	0.128000	−	0.0739007i	0.562633	+	0.826707i	$0.309789\pi$
$978$		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	−0.992433	−	0.122785i	$-0.960818\pi$
$983$	−1567.87	−	905.210i	−1.59498	−	0.920865i	−0.602551	−	0.798080i	$-0.705849\pi$
$984$		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	0.411380	−	0.911464i	$-0.365047\pi$
$997$	−171.763	−	99.1676i	−0.172280	−	0.0994660i	−0.583661	+	0.811998i	$0.698380\pi$
$998$	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.197.3		44
3.2	odd	2		72.3.j.a.29.20	yes	44
4.3	odd	2		864.3.n.a.305.9		44
8.3	odd	2		864.3.n.a.305.14		44
8.5	even	2	inner	216.3.j.a.197.4		44
9.2	odd	6		648.3.h.a.485.21		44
9.4	even	3		72.3.j.a.5.19	✓	44
9.5	odd	6	inner	216.3.j.a.125.4		44
9.7	even	3		648.3.h.a.485.24		44
12.11	even	2		288.3.n.a.209.17		44
24.5	odd	2		72.3.j.a.29.19	yes	44
24.11	even	2		288.3.n.a.209.6		44
36.7	odd	6		2592.3.h.a.1457.27		44
36.11	even	6		2592.3.h.a.1457.18		44
36.23	even	6		864.3.n.a.17.14		44
36.31	odd	6		288.3.n.a.113.6		44
72.5	odd	6	inner	216.3.j.a.125.3		44
72.11	even	6		2592.3.h.a.1457.28		44
72.13	even	6		72.3.j.a.5.20	yes	44
72.29	odd	6		648.3.h.a.485.23		44
72.43	odd	6		2592.3.h.a.1457.17		44
72.59	even	6		864.3.n.a.17.9		44
72.61	even	6		648.3.h.a.485.22		44
72.67	odd	6		288.3.n.a.113.17		44

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