LMFDB - Embedded newform 189.3.j.b.116.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("189.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.5
Character	$\chi$	$=$	189.116
Dual form			189.3.j.b.44.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0767494i q^{2} +3.99411 q^{4} +(3.53076 + 2.03848i) q^{5} +(2.97142 + 6.33803i) q^{7} -0.613543i q^{8} +O(q^{10})$	\(q-0.0767494i q^{2} +3.99411 q^{4} +(3.53076 + 2.03848i) q^{5} +(2.97142 + 6.33803i) q^{7} -0.613543i q^{8} +(0.156452 - 0.270983i) q^{10} +(-10.7907 + 6.23001i) q^{11} +(-5.97803 - 10.3542i) q^{13} +(0.486440 - 0.228055i) q^{14} +15.9293 q^{16} +(14.2872 + 8.24873i) q^{17} +(-3.69254 - 6.39566i) q^{19} +(14.1022 + 8.14193i) q^{20} +(0.478149 + 0.828179i) q^{22} +(24.1805 + 13.9606i) q^{23} +(-4.18917 - 7.25586i) q^{25} +(-0.794682 + 0.458810i) q^{26} +(11.8682 + 25.3148i) q^{28} +(-32.2098 - 18.5963i) q^{29} +32.5589 q^{31} -3.67674i q^{32} +(0.633085 - 1.09653i) q^{34} +(-2.42859 + 28.4352i) q^{35} +(-10.3724 - 17.9656i) q^{37} +(-0.490863 + 0.283400i) q^{38} +(1.25070 - 2.16627i) q^{40} +(26.1324 - 15.0876i) q^{41} +(-12.7866 + 22.1470i) q^{43} +(-43.0992 + 24.8833i) q^{44} +(1.07147 - 1.85584i) q^{46} -79.0168i q^{47} +(-31.3413 + 37.6660i) q^{49} +(-0.556883 + 0.321516i) q^{50} +(-23.8769 - 41.3560i) q^{52} +(-61.5964 - 35.5627i) q^{53} -50.7991 q^{55} +(3.88865 - 1.82310i) q^{56} +(-1.42726 + 2.47208i) q^{58} -43.1097i q^{59} -22.4723 q^{61} -2.49887i q^{62} +63.4352 q^{64} -48.7444i q^{65} -86.1477 q^{67} +(57.0647 + 32.9463i) q^{68} +(2.18239 + 0.186393i) q^{70} +102.757i q^{71} +(0.403723 - 0.699268i) q^{73} +(-1.37885 + 0.796079i) q^{74} +(-14.7484 - 25.5450i) q^{76} +(-71.5497 - 49.8797i) q^{77} -27.0511 q^{79} +(56.2427 + 32.4717i) q^{80} +(-1.15796 - 2.00565i) q^{82} +(-36.4392 - 21.0382i) q^{83} +(33.6298 + 58.2485i) q^{85} +(1.69977 + 0.981361i) q^{86} +(3.82238 + 6.62055i) q^{88} +(36.1770 - 20.8868i) q^{89} +(47.8623 - 68.6558i) q^{91} +(96.5795 + 55.7602i) q^{92} -6.06449 q^{94} -30.1087i q^{95} +(6.66199 - 11.5389i) q^{97} +(2.89084 + 2.40542i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) $ 22 * q - 24 * q^4 - 12 * q^5	$ 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) $ 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.0767494i		−	0.0383747i	−0.999816	−	0.0191873i	$-0.993892\pi$
$2$		−	0.0767494i		−	0.0383747i	0.999816	−	0.0191873i	$-0.00610790\pi$
$3$		0			0
$3$		0			0
$4$	3.99411			0.998527
$5$	3.53076	+	2.03848i	0.706151	+	0.407697i	0.809634	−	0.586935i	$-0.199665\pi$
$5$	3.53076	+	2.03848i	0.706151	+	0.407697i	−0.103483	+	0.994631i	$0.532999\pi$
$6$		0			0
$7$	2.97142	+	6.33803i	0.424489	+	0.905433i
$7$	2.97142	+	6.33803i	0.424489	+	0.905433i
$8$		−	0.613543i		−	0.0766929i
$9$		0			0
$10$	0.156452	−	0.270983i	0.0156452	−	0.0270983i
$11$	−10.7907	+	6.23001i	−0.980972	+	0.566365i	−0.902564	−	0.430557i	$-0.858317\pi$
$11$	−10.7907	+	6.23001i	−0.980972	+	0.566365i	−0.0784087	+	0.996921i	$0.524984\pi$
$12$		0			0
$13$	−5.97803	−	10.3542i	−0.459848	−	0.796480i	0.539104	−	0.842239i	$-0.318763\pi$
$13$	−5.97803	−	10.3542i	−0.459848	−	0.796480i	−0.998953	+	0.0457586i	$0.985429\pi$
$14$	0.486440	−	0.228055i	0.0347457	−	0.0162896i
$15$		0			0
$16$	15.9293			0.995584
$17$	14.2872	+	8.24873i	0.840424	+	0.485219i	0.857408	−	0.514637i	$-0.172073\pi$
$17$	14.2872	+	8.24873i	0.840424	+	0.485219i	−0.0169841	+	0.999856i	$0.505406\pi$
$18$		0			0
$19$	−3.69254	−	6.39566i	−0.194344	−	0.336614i	0.752341	−	0.658774i	$-0.228924\pi$
$19$	−3.69254	−	6.39566i	−0.194344	−	0.336614i	−0.946685	+	0.322160i	$0.895591\pi$
$20$	14.1022	+	8.14193i	0.705111	+	0.407096i
$21$		0			0
$22$	0.478149	+	0.828179i	0.0217341	+	0.0376445i
$23$	24.1805	+	13.9606i	1.05133	+	0.606983i	0.923020	−	0.384752i	$-0.125713\pi$
$23$	24.1805	+	13.9606i	1.05133	+	0.606983i	0.128305	+	0.991735i	$0.459046\pi$
$24$		0			0
$25$	−4.18917	−	7.25586i	−0.167567	−	0.290234i
$26$	−0.794682	+	0.458810i	−0.0305647	+	0.0176465i
$27$		0			0
$28$	11.8682	+	25.3148i	0.423864	+	0.904100i
$29$	−32.2098	−	18.5963i	−1.11068	−	0.641253i	−0.171676	−	0.985153i	$-0.554918\pi$
$29$	−32.2098	−	18.5963i	−1.11068	−	0.641253i	−0.939006	+	0.343901i	$0.888252\pi$
$30$		0			0
$31$	32.5589			1.05029			0.525143	−	0.851014i	$-0.324012\pi$
$31$	32.5589			1.05029			0.525143	+	0.851014i	$0.324012\pi$
$32$		−	3.67674i		−	0.114898i
$33$		0			0
$34$	0.633085	−	1.09653i	0.0186201	−	0.0322510i
$35$	−2.42859	+	28.4352i	−0.0693884	+	0.812436i
$36$		0			0
$37$	−10.3724	−	17.9656i	−0.280336	−	0.485557i	0.691131	−	0.722729i	$-0.257113\pi$
$37$	−10.3724	−	17.9656i	−0.280336	−	0.485557i	−0.971468	+	0.237172i	$0.923779\pi$
$38$	−0.490863	+	0.283400i	−0.0129175	+	0.00745789i
$39$		0			0
$40$	1.25070	−	2.16627i	0.0312674	−	0.0541568i
$41$	26.1324	−	15.0876i	0.637376	−	0.367989i	−0.146227	−	0.989251i	$-0.546713\pi$
$41$	26.1324	−	15.0876i	0.637376	−	0.367989i	0.783603	+	0.621262i	$0.213380\pi$
$42$		0			0
$43$	−12.7866	+	22.1470i	−0.297362	+	0.515046i	−0.975532	−	0.219859i	$-0.929440\pi$
$43$	−12.7866	+	22.1470i	−0.297362	+	0.515046i	0.678170	+	0.734906i	$0.262774\pi$
$44$	−43.0992	+	24.8833i	−0.979528	+	0.565531i
$45$		0			0
$46$	1.07147	−	1.85584i	0.0232928	−	0.0403443i
$47$		−	79.0168i		−	1.68121i	−0.541649	−	0.840604i	$-0.682200\pi$
$47$		−	79.0168i		−	1.68121i	0.541649	−	0.840604i	$-0.317800\pi$
$48$		0			0
$49$	−31.3413	+	37.6660i	−0.639618	+	0.768693i
$50$	−0.556883	+	0.321516i	−0.0111377	+	0.00643033i
$51$		0			0
$52$	−23.8769	−	41.3560i	−0.459171	−	0.795307i
$53$	−61.5964	−	35.5627i	−1.16220	−	0.670995i	−0.210367	−	0.977622i	$-0.567466\pi$
$53$	−61.5964	−	35.5627i	−1.16220	−	0.670995i	−0.951830	+	0.306628i	$0.900799\pi$
$54$		0			0
$55$	−50.7991			−0.923620
$56$	3.88865	−	1.82310i	0.0694403	−	0.0325553i
$57$		0			0
$58$	−1.42726	+	2.47208i	−0.0246079	+	0.0426221i
$59$		−	43.1097i		−	0.730673i	−0.930876	−	0.365336i	$-0.880954\pi$
$59$		−	43.1097i		−	0.730673i	0.930876	−	0.365336i	$-0.119046\pi$
$60$		0			0
$61$	−22.4723			−0.368398			−0.184199	−	0.982889i	$-0.558969\pi$
$61$	−22.4723			−0.368398			−0.184199	+	0.982889i	$0.558969\pi$
$62$		−	2.49887i		−	0.0403044i
$63$		0			0
$64$	63.4352			0.991175
$65$		−	48.7444i		−	0.749914i
$66$		0			0
$67$	−86.1477			−1.28579			−0.642893	−	0.765956i	$-0.722266\pi$
$67$	−86.1477			−1.28579			−0.642893	+	0.765956i	$0.722266\pi$
$68$	57.0647	+	32.9463i	0.839187	+	0.484505i
$69$		0			0
$70$	2.18239	+	0.186393i	0.0311770	+	0.00266276i
$71$			102.757i			1.44728i	0.690179	+	0.723639i	$0.257532\pi$
$71$			102.757i			1.44728i	−0.690179	+	0.723639i	$0.742468\pi$
$72$		0			0
$73$	0.403723	−	0.699268i	0.00553045	−	0.00957902i	−0.863247	−	0.504782i	$-0.831573\pi$
$73$	0.403723	−	0.699268i	0.00553045	−	0.00957902i	0.868777	+	0.495203i	$0.164906\pi$
$74$	−1.37885	+	0.796079i	−0.0186331	+	0.0107578i
$75$		0			0
$76$	−14.7484	−	25.5450i	−0.194058	−	0.336118i
$77$	−71.5497	−	49.8797i	−0.929217	−	0.647789i
$78$		0			0
$79$	−27.0511			−0.342419			−0.171210	−	0.985235i	$-0.554768\pi$
$79$	−27.0511			−0.342419			−0.171210	+	0.985235i	$0.554768\pi$
$80$	56.2427	+	32.4717i	0.703033	+	0.405896i
$81$		0			0
$82$	−1.15796	−	2.00565i	−0.0141215	−	0.0244591i
$83$	−36.4392	−	21.0382i	−0.439027	−	0.253472i	0.264158	−	0.964479i	$-0.414906\pi$
$83$	−36.4392	−	21.0382i	−0.439027	−	0.253472i	−0.703185	+	0.711007i	$0.748239\pi$
$84$		0			0
$85$	33.6298	+	58.2485i	0.395644	+	0.685276i
$86$	1.69977	+	0.981361i	0.0197647	+	0.0114112i
$87$		0			0
$88$	3.82238	+	6.62055i	0.0434361	+	0.0752336i
$89$	36.1770	−	20.8868i	0.406483	−	0.234683i	−0.282795	−	0.959180i	$-0.591261\pi$
$89$	36.1770	−	20.8868i	0.406483	−	0.234683i	0.689277	+	0.724498i	$0.257928\pi$
$90$		0			0
$91$	47.8623	−	68.6558i	0.525959	−	0.754459i
$92$	96.5795	+	55.7602i	1.04978	+	0.606089i
$93$		0			0
$94$	−6.06449			−0.0645159
$95$		−	30.1087i		−	0.316934i
$96$		0			0
$97$	6.66199	−	11.5389i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$97$	6.66199	−	11.5389i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$98$	2.89084	+	2.40542i	0.0294984	+	0.0245451i
$99$		0			0
$100$	−16.7320	−	28.9807i	−0.167320	−	0.289807i
$101$	−138.166	+	79.7700i	−1.36798	+	0.789802i	−0.990669	−	0.136286i	$-0.956483\pi$
$101$	−138.166	+	79.7700i	−1.36798	+	0.789802i	−0.377307	+	0.926088i	$0.623150\pi$
$102$		0			0
$103$	89.1233	−	154.366i	0.865274	−	1.49870i	−0.00150025	−	0.999999i	$-0.500478\pi$
$103$	89.1233	−	154.366i	0.865274	−	1.49870i	0.866775	−	0.498700i	$-0.166189\pi$
$104$	−6.35277	+	3.66778i	−0.0610844	+	0.0352671i
$105$		0			0
$106$	−2.72942	+	4.72749i	−0.0257492	+	0.0445989i
$107$	97.7058	−	56.4105i	0.913138	−	0.527201i	0.0316986	−	0.999497i	$-0.489908\pi$
$107$	97.7058	−	56.4105i	0.913138	−	0.527201i	0.881439	+	0.472297i	$0.156575\pi$
$108$		0			0
$109$	−101.056	+	175.034i	−0.927120	+	1.60582i	−0.139004	+	0.990292i	$0.544390\pi$
$109$	−101.056	+	175.034i	−0.927120	+	1.60582i	−0.788116	+	0.615527i	$0.788943\pi$
$110$			3.89880i			0.0354436i
$111$		0			0
$112$	47.3329	+	100.961i	0.422615	+	0.901435i
$113$	−36.2418	+	20.9242i	−0.320724	+	0.185170i	−0.651715	−	0.758464i	$-0.725950\pi$
$113$	−36.2418	+	20.9242i	−0.320724	+	0.185170i	0.330991	+	0.943634i	$0.392617\pi$
$114$		0			0
$115$	56.9169	+	98.5830i	0.494930	+	0.857243i
$116$	−128.649	−	74.2758i	−1.10905	−	0.640308i
$117$		0			0
$118$	−3.30864			−0.0280393
$119$	−9.82731	+	115.063i	−0.0825824	+	0.966918i
$120$		0			0
$121$	17.1261	−	29.6632i	0.141538	−	0.245150i
$122$			1.72473i			0.0141372i
$123$		0			0
$124$	130.044			1.04874
$125$		−	136.082i		−	1.08866i
$126$		0			0
$127$	84.6221			0.666316			0.333158	−	0.942871i	$-0.391886\pi$
$127$	84.6221			0.666316			0.333158	+	0.942871i	$0.391886\pi$
$128$		−	19.5756i		−	0.152934i
$129$		0			0
$130$	−3.74110			−0.0287777
$131$	162.040	+	93.5536i	1.23694	+	0.714149i	0.968468	−	0.249137i	$-0.0801470\pi$
$131$	162.040	+	93.5536i	1.23694	+	0.714149i	0.268475	+	0.963287i	$0.413480\pi$
$132$		0			0
$133$	29.5638	−	42.4076i	0.222284	−	0.318854i
$134$			6.61178i			0.0493416i
$135$		0			0
$136$	5.06095	−	8.76582i	0.0372129	−	0.0644546i
$137$	50.2755	−	29.0266i	0.366975	−	0.211873i	−0.305161	−	0.952301i	$-0.598710\pi$
$137$	50.2755	−	29.0266i	0.366975	−	0.211873i	0.672136	+	0.740428i	$0.265377\pi$
$138$		0			0
$139$	18.1886	+	31.5036i	0.130853	+	0.226645i	0.924006	−	0.382379i	$-0.124895\pi$
$139$	18.1886	+	31.5036i	0.130853	+	0.226645i	−0.793152	+	0.609023i	$0.791562\pi$
$140$	−9.70007	+	113.573i	−0.0692862	+	0.811239i
$141$		0			0
$142$	7.88651			0.0555388
$143$	129.014	+	74.4863i	0.902196	+	0.520883i
$144$		0			0
$145$	−75.8166	−	131.318i	−0.522873	−	0.905643i
$146$	−0.0536684	−	0.0309855i	−0.000367592	−	0.000212229i
$147$		0			0
$148$	−41.4287	−	71.7566i	−0.279924	−	0.484842i
$149$	20.1499	+	11.6336i	0.135234	+	0.0780776i	0.566091	−	0.824343i	$-0.308455\pi$
$149$	20.1499	+	11.6336i	0.135234	+	0.0780776i	−0.430856	+	0.902420i	$0.641788\pi$
$150$		0			0
$151$	−29.6369	−	51.3327i	−0.196271	−	0.339952i	0.751045	−	0.660251i	$-0.229550\pi$
$151$	−29.6369	−	51.3327i	−0.196271	−	0.339952i	−0.947316	+	0.320299i	$0.896217\pi$
$152$	−3.92401	+	2.26553i	−0.0258159	+	0.0149048i
$153$		0			0
$154$	−3.82824	+	5.49140i	−0.0248587	+	0.0356584i
$155$	114.957	+	66.3707i	0.741661	+	0.428198i
$156$		0			0
$157$	94.3925			0.601226			0.300613	−	0.953746i	$-0.402809\pi$
$157$	94.3925			0.601226			0.300613	+	0.953746i	$0.402809\pi$
$158$			2.07616i			0.0131402i
$159$		0			0
$160$	7.49497	−	12.9817i	0.0468436	−	0.0811355i
$161$	−16.6323	+	194.740i	−0.103306	+	1.20956i
$162$		0			0
$163$	38.8629	+	67.3124i	0.238422	+	0.412960i	0.960262	−	0.279101i	$-0.0900364\pi$
$163$	38.8629	+	67.3124i	0.238422	+	0.412960i	−0.721839	+	0.692061i	$0.756703\pi$
$164$	104.376	−	60.2614i	0.636438	−	0.367447i
$165$		0			0
$166$	−1.61467	+	2.79669i	−0.00972692	+	0.0168475i
$167$	−165.547	+	95.5786i	−0.991300	+	0.572327i	−0.905662	−	0.423999i	$-0.860626\pi$
$167$	−165.547	+	95.5786i	−0.991300	+	0.572327i	−0.0856370	+	0.996326i	$0.527293\pi$
$168$		0			0
$169$	13.0264	−	22.5624i	0.0770794	−	0.133505i
$170$	4.47054	−	2.58106i	0.0262973	−	0.0151827i
$171$		0			0
$172$	−51.0710	+	88.4575i	−0.296924	+	0.514288i
$173$		−	27.9268i		−	0.161427i	−0.996737	−	0.0807134i	$-0.974280\pi$
$173$		−	27.9268i		−	0.161427i	0.996737	−	0.0807134i	$-0.0257198\pi$
$174$		0			0
$175$	33.5401	−	48.1113i	0.191657	−	0.274922i
$176$	−171.889	+	99.2400i	−0.976641	+	0.563864i
$177$		0			0
$178$	−1.60305	−	2.77656i	−0.00900589	−	0.0155987i
$179$	−49.1073	−	28.3521i	−0.274342	−	0.158392i	0.356517	−	0.934289i	$-0.383964\pi$
$179$	−49.1073	−	28.3521i	−0.274342	−	0.158392i	−0.630859	+	0.775897i	$0.717297\pi$
$180$		0			0
$181$	81.8315			0.452108			0.226054	−	0.974115i	$-0.427417\pi$
$181$	81.8315			0.452108			0.226054	+	0.974115i	$0.427417\pi$
$182$	−5.26929	−	3.67340i	−0.0289521	−	0.0201835i
$183$		0			0
$184$	8.56543	−	14.8358i	0.0465513	−	0.0806291i
$185$		−	84.5763i		−	0.457169i
$186$		0			0
$187$	−205.559			−1.09924
$188$		−	315.602i		−	1.67873i
$189$		0			0
$190$	−2.31082			−0.0121622
$191$			163.400i			0.855499i	0.903897	+	0.427750i	$0.140693\pi$
$191$			163.400i			0.855499i	−0.903897	+	0.427750i	$0.859307\pi$
$192$		0			0
$193$	−326.842			−1.69348			−0.846740	−	0.532007i	$-0.821438\pi$
$193$	−326.842			−1.69348			−0.846740	+	0.532007i	$0.821438\pi$
$194$	−0.885604	−	0.511304i	−0.00456497	−	0.00263559i
$195$		0			0
$196$	−125.180	+	150.442i	−0.638676	+	0.767561i
$197$		−	262.028i		−	1.33009i	−0.746802	−	0.665046i	$-0.768412\pi$
$197$		−	262.028i		−	1.33009i	0.746802	−	0.665046i	$-0.231588\pi$
$198$		0			0
$199$	50.0375	−	86.6676i	0.251445	−	0.435515i	−0.712479	−	0.701694i	$-0.752428\pi$
$199$	50.0375	−	86.6676i	0.251445	−	0.435515i	0.963924	+	0.266178i	$0.0857609\pi$
$200$	−4.45178	+	2.57024i	−0.0222589	+	0.0128512i
$201$		0			0
$202$	6.12230	+	10.6041i	0.0303084	+	0.0524957i
$203$	22.1552	−	259.404i	0.109139	−	1.27785i
$204$		0			0
$205$	123.023			0.600112
$206$	−11.8475	−	6.84015i	−0.0575121	−	0.0332046i
$207$		0			0
$208$	−95.2261	−	164.936i	−0.457818	−	0.792963i
$209$	79.6901	+	46.0091i	0.381292	+	0.220139i
$210$		0			0
$211$	124.345	+	215.372i	0.589312	+	1.02072i	0.994323	+	0.106407i	$0.0339345\pi$
$211$	124.345	+	215.372i	0.589312	+	1.02072i	−0.405010	+	0.914312i	$0.632732\pi$
$212$	−246.023	−	142.041i	−1.16049	−	0.670007i
$213$		0			0
$214$	−4.32947	−	7.49886i	−0.0202312	−	0.0350414i
$215$	−90.2925	+	52.1304i	−0.419965	+	0.242467i
$216$		0			0
$217$	96.7462	+	206.359i	0.445835	+	0.950963i
$218$	13.4338	+	7.75599i	0.0616228	+	0.0355779i
$219$		0			0
$220$	−202.897			−0.922260
$221$		−	197.244i		−	0.892509i
$222$		0			0
$223$	−6.13684	+	10.6293i	−0.0275195	+	0.0476651i	−0.879457	−	0.475978i	$-0.842094\pi$
$223$	−6.13684	+	10.6293i	−0.0275195	+	0.0476651i	0.851938	+	0.523643i	$0.175427\pi$
$224$	23.3033	−	10.9252i	0.104033	−	0.0487730i
$225$		0			0
$226$	1.60592	+	2.78153i	0.00710584	+	0.0123077i
$227$	14.5927	−	8.42508i	0.0642849	−	0.0371149i	−0.467513	−	0.883986i	$-0.654850\pi$
$227$	14.5927	−	8.42508i	0.0642849	−	0.0371149i	0.531798	+	0.846871i	$0.321517\pi$
$228$		0			0
$229$	−56.1460	+	97.2478i	−0.245179	+	0.424663i	−0.962182	−	0.272408i	$-0.912180\pi$
$229$	−56.1460	+	97.2478i	−0.245179	+	0.424663i	0.717003	+	0.697070i	$0.245513\pi$
$230$	7.56618	−	4.36834i	0.0328965	−	0.0189928i
$231$		0			0
$232$	−11.4096	+	19.7621i	−0.0491795	+	0.0851814i
$233$	123.161	−	71.1068i	0.528586	−	0.305179i	−0.211855	−	0.977301i	$-0.567950\pi$
$233$	123.161	−	71.1068i	0.528586	−	0.305179i	0.740440	+	0.672122i	$0.234617\pi$
$234$		0			0
$235$	161.074	−	278.989i	0.685423	−	1.18719i
$236$		−	172.185i		−	0.729597i
$237$		0			0
$238$	8.83103	+	0.754240i	0.0371052	+	0.00316907i
$239$	−205.534	+	118.665i	−0.859975	+	0.496507i	−0.864004	−	0.503485i	$-0.832051\pi$
$239$	−205.534	+	118.665i	−0.859975	+	0.496507i	0.00402865	+	0.999992i	$0.498718\pi$
$240$		0			0
$241$	−79.0467	−	136.913i	−0.327995	−	0.568103i	0.654119	−	0.756391i	$-0.273039\pi$
$241$	−79.0467	−	136.913i	−0.327995	−	0.568103i	−0.982114	+	0.188288i	$0.939706\pi$
$242$	−2.27663	−	1.31441i	−0.00940757	−	0.00543146i
$243$		0			0
$244$	−89.7568			−0.367856
$245$	−187.440	+	69.1007i	−0.765061	+	0.282044i
$246$		0			0
$247$	−44.1482	+	76.4669i	−0.178738	+	0.309582i
$248$		−	19.9763i		−	0.0805494i
$249$		0			0
$250$	−10.4442			−0.0417770
$251$			462.619i			1.84310i	0.388254	+	0.921552i	$0.373078\pi$
$251$			462.619i			1.84310i	−0.388254	+	0.921552i	$0.626922\pi$
$252$		0			0
$253$	−347.899			−1.37509
$254$		−	6.49470i		−	0.0255697i
$255$		0			0
$256$	252.238			0.985306
$257$	−99.4583	−	57.4223i	−0.386997	−	0.223433i	0.293861	−	0.955848i	$-0.405060\pi$
$257$	−99.4583	−	57.4223i	−0.386997	−	0.223433i	−0.680858	+	0.732415i	$0.738393\pi$
$258$		0			0
$259$	83.0456	−	119.124i	0.320640	−	0.459940i
$260$		−	194.691i		−	0.748810i
$261$		0			0
$262$	7.18018	−	12.4364i	0.0274053	−	0.0474673i
$263$	29.2952	−	16.9136i	0.111389	−	0.0643102i	−0.443271	−	0.896388i	$-0.646182\pi$
$263$	29.2952	−	16.9136i	0.111389	−	0.0643102i	0.554659	+	0.832078i	$0.312849\pi$
$264$		0			0
$265$	−144.988	−	251.127i	−0.547125	−	0.947648i
$266$	−3.25476	−	2.26900i	−0.0122359	−	0.00853009i
$267$		0			0
$268$	−344.083			−1.28389
$269$	43.6851	+	25.2216i	0.162398	+	0.0937605i	0.578996	−	0.815330i	$-0.303445\pi$
$269$	43.6851	+	25.2216i	0.162398	+	0.0937605i	−0.416598	+	0.909091i	$0.636778\pi$
$270$		0			0
$271$	203.410	+	352.317i	0.750591	+	1.30006i	0.947537	+	0.319647i	$0.103564\pi$
$271$	203.410	+	352.317i	0.750591	+	1.30006i	−0.196946	+	0.980414i	$0.563102\pi$
$272$	227.586	+	131.397i	0.836713	+	0.483077i
$273$		0			0
$274$	−2.22777	−	3.85861i	−0.00813056	−	0.0140825i
$275$	90.4082	+	52.1972i	0.328757	+	0.189808i
$276$		0			0
$277$	39.2392	+	67.9644i	0.141658	+	0.245359i	0.928121	−	0.372278i	$-0.121423\pi$
$277$	39.2392	+	67.9644i	0.141658	+	0.245359i	−0.786463	+	0.617637i	$0.788090\pi$
$278$	2.41788	−	1.39597i	0.00869742	−	0.00502146i
$279$		0			0
$280$	17.4462	+	1.49005i	0.0623080	+	0.00532159i
$281$	124.764	+	72.0327i	0.444001	+	0.256344i	0.705293	−	0.708916i	$-0.250815\pi$
$281$	124.764	+	72.0327i	0.444001	+	0.256344i	−0.261292	+	0.965260i	$0.584149\pi$
$282$		0			0
$283$	197.954			0.699485			0.349743	−	0.936846i	$-0.386269\pi$
$283$	197.954			0.699485			0.349743	+	0.936846i	$0.386269\pi$
$284$			410.421i			1.44515i
$285$		0			0
$286$	5.71678	−	9.90175i	0.0199887	−	0.0346215i
$287$	173.276	+	120.797i	0.603749	+	0.420894i
$288$		0			0
$289$	−8.41704	−	14.5787i	−0.0291247	−	0.0504455i
$290$	−10.0786	+	5.81888i	−0.0347538	+	0.0200651i
$291$		0			0
$292$	1.61251	−	2.79295i	0.00552230	−	0.00956491i
$293$	248.893	−	143.698i	0.849463	−	0.490438i	−0.0110067	−	0.999939i	$-0.503504\pi$
$293$	248.893	−	143.698i	0.849463	−	0.490438i	0.860470	+	0.509502i	$0.170170\pi$
$294$		0			0
$295$	87.8784	−	152.210i	0.297893	−	0.515966i
$296$	−11.0227	+	6.36394i	−0.0372388	+	0.0214998i
$297$		0			0
$298$	0.892869	−	1.54649i	0.00299620	−	0.00518958i
$299$		−	333.827i		−	1.11648i
$300$		0			0
$301$	−178.363	−	15.2336i	−0.592567	−	0.0506099i
$302$	−3.93975	+	2.27462i	−0.0130455	+	0.00753185i
$303$		0			0
$304$	−58.8197	−	101.879i	−0.193486	−	0.335127i
$305$	−79.3442	−	45.8094i	−0.260145	−	0.150195i
$306$		0			0
$307$	93.1935			0.303562			0.151781	−	0.988414i	$-0.451499\pi$
$307$	93.1935			0.303562			0.151781	+	0.988414i	$0.451499\pi$
$308$	−285.777	−	199.225i	−0.927849	−	0.646835i
$309$		0			0
$310$	5.09391	−	8.82291i	0.0164320	−	0.0284610i
$311$		−	6.34935i		−	0.0204159i	−0.999948	−	0.0102080i	$-0.996751\pi$
$311$		−	6.34935i		−	0.0204159i	0.999948	−	0.0102080i	$-0.00324935\pi$
$312$		0			0
$313$	457.917			1.46299			0.731497	−	0.681845i	$-0.238822\pi$
$313$	457.917			1.46299			0.731497	+	0.681845i	$0.238822\pi$
$314$		−	7.24457i		−	0.0230719i
$315$		0			0
$316$	−108.045			−0.341915
$317$			515.586i			1.62645i	0.581946	+	0.813227i	$0.302291\pi$
$317$			515.586i			1.62645i	−0.581946	+	0.813227i	$0.697709\pi$
$318$		0			0
$319$	463.421			1.45273
$320$	223.974	+	129.312i	0.699920	+	0.404099i
$321$		0			0
$322$	14.9461	+	1.27652i	0.0464166	+	0.00396434i
$323$		−	121.835i		−	0.377198i
$324$		0			0
$325$	−50.0860	+	86.7514i	−0.154111	+	0.266927i
$326$	5.16619	−	2.98270i	0.0158472	−	0.00914939i
$327$		0			0
$328$	−9.25687	−	16.0334i	−0.0282222	−	0.0488822i
$329$	500.811	−	234.793i	1.52222	−	0.713655i
$330$		0			0
$331$	297.255			0.898051			0.449026	−	0.893519i	$-0.351771\pi$
$331$	297.255			0.898051			0.449026	+	0.893519i	$0.351771\pi$
$332$	−145.542	−	84.0289i	−0.438380	−	0.253099i
$333$		0			0
$334$	7.33560	+	12.7056i	0.0219629	+	0.0380408i
$335$	−304.166	−	175.611i	−0.907959	−	0.524211i
$336$		0			0
$337$	−57.4915	−	99.5781i	−0.170598	−	0.295484i	0.768031	−	0.640412i	$-0.221237\pi$
$337$	−57.4915	−	99.5781i	−0.170598	−	0.295484i	−0.938629	+	0.344928i	$0.887903\pi$
$338$	−1.73165	−	0.999769i	−0.00512323	−	0.00295790i
$339$		0			0
$340$	134.321	+	232.651i	0.395062	+	0.684267i
$341$	−351.333	+	202.842i	−1.03030	+	0.594845i
$342$		0			0
$343$	−331.856	−	86.7204i	−0.967511	−	0.252829i
$344$	13.5881	+	7.84511i	0.0395004	+	0.0228056i
$345$		0			0
$346$	−2.14337			−0.00619470
$347$			453.649i			1.30734i	0.756778	+	0.653672i	$0.226772\pi$
$347$			453.649i			1.30734i	−0.756778	+	0.653672i	$0.773228\pi$
$348$		0			0
$349$	−262.257	+	454.242i	−0.751452	+	1.30155i	0.195668	+	0.980670i	$0.437313\pi$
$349$	−262.257	+	454.242i	−0.751452	+	1.30155i	−0.947119	+	0.320882i	$0.896021\pi$
$350$	−3.69252	−	2.57418i	−0.0105500	−	0.00735480i
$351$		0			0
$352$	22.9061	+	39.6746i	0.0650742	+	0.112712i
$353$	−437.801	+	252.765i	−1.24023	+	0.716047i	−0.969141	−	0.246507i	$-0.920717\pi$
$353$	−437.801	+	252.765i	−1.24023	+	0.716047i	−0.271089	+	0.962554i	$0.587384\pi$
$354$		0			0
$355$	−209.468	+	362.809i	−0.590050	+	1.02200i
$356$	144.495	−	83.4241i	0.405884	−	0.234337i
$357$		0			0
$358$	−2.17601	+	3.76895i	−0.00607823	+	0.0105278i
$359$	43.4754	−	25.1005i	0.121101	−	0.0699179i	−0.438226	−	0.898865i	$-0.644393\pi$
$359$	43.4754	−	25.1005i	0.121101	−	0.0699179i	0.559327	+	0.828947i	$0.311060\pi$
$360$		0			0
$361$	153.230	−	265.403i	0.424461	−	0.735188i
$362$		−	6.28052i		−	0.0173495i
$363$		0			0
$364$	191.167	−	274.219i	0.525184	−	0.753348i
$365$	2.85089	−	1.64596i	0.00781067	−	0.00450949i
$366$		0			0
$367$	297.239	+	514.834i	0.809917	+	1.40282i	0.912921	+	0.408136i	$0.133821\pi$
$367$	297.239	+	514.834i	0.809917	+	1.40282i	−0.103005	+	0.994681i	$0.532846\pi$
$368$	385.179	+	222.383i	1.04668	+	0.604303i
$369$		0			0
$370$	−6.49118			−0.0175437
$371$	42.3684	−	496.072i	0.114201	−	1.33712i
$372$		0			0
$373$	304.636	−	527.644i	0.816718	−	1.41460i	−0.0913705	−	0.995817i	$-0.529125\pi$
$373$	304.636	−	527.644i	0.816718	−	1.41460i	0.908088	−	0.418779i	$-0.137542\pi$
$374$			15.7765i			0.0421831i
$375$		0			0
$376$	−48.4802			−0.128937
$377$			444.677i			1.17952i
$378$		0			0
$379$	468.439			1.23599			0.617994	−	0.786183i	$-0.287946\pi$
$379$	468.439			1.23599			0.617994	+	0.786183i	$0.287946\pi$
$380$		−	120.257i		−	0.316467i
$381$		0			0
$382$	12.5409			0.0328295
$383$	380.512	+	219.689i	0.993504	+	0.573600i	0.906320	−	0.422592i	$-0.138880\pi$
$383$	380.512	+	219.689i	0.993504	+	0.573600i	0.0871844	+	0.996192i	$0.472213\pi$
$384$		0			0
$385$	−150.946	−	321.966i	−0.392067	−	0.836276i
$386$			25.0849i			0.0649868i
$387$		0			0
$388$	26.6087	−	46.0877i	0.0685792	−	0.118783i
$389$	230.033	−	132.809i	0.591343	−	0.341412i	−0.174285	−	0.984695i	$-0.555761\pi$
$389$	230.033	−	132.809i	0.591343	−	0.341412i	0.765629	+	0.643283i	$0.222428\pi$
$390$		0			0
$391$	230.314	+	398.916i	0.589039	+	1.02025i
$392$	23.1097	+	19.2292i	0.0589533	+	0.0490541i
$393$		0			0
$394$	−20.1105			−0.0510419
$395$	−95.5109	−	55.1432i	−0.241800	−	0.139603i
$396$		0			0
$397$	98.4268	+	170.480i	0.247926	+	0.429421i	0.962950	−	0.269679i	$-0.0869176\pi$
$397$	98.4268	+	170.480i	0.247926	+	0.429421i	−0.715024	+	0.699100i	$0.753584\pi$
$398$	−6.65168	−	3.84035i	−0.0167128	−	0.00964912i
$399$		0			0
$400$	−66.7308	−	115.581i	−0.166827	−	0.288953i
$401$	−160.126	−	92.4488i	−0.399317	−	0.230546i	0.286872	−	0.957969i	$-0.407384\pi$
$401$	−160.126	−	92.4488i	−0.399317	−	0.230546i	−0.686189	+	0.727423i	$0.740718\pi$
$402$		0			0
$403$	−194.638	−	337.122i	−0.482972	−	0.836532i
$404$	−551.849	+	318.610i	−1.36596	+	0.788639i
$405$		0			0
$406$	−19.9091	−	1.70039i	−0.0490372	−	0.00418816i
$407$	223.852	+	129.241i	0.550005	+	0.317545i
$408$		0			0
$409$	−598.664			−1.46373			−0.731863	−	0.681452i	$-0.761349\pi$
$409$	−598.664			−1.46373			−0.731863	+	0.681452i	$0.761349\pi$
$410$		−	9.44194i		−	0.0230291i
$411$		0			0
$412$	355.968	−	616.555i	0.864000	−	1.49649i
$413$	273.231	−	128.097i	0.661575	−	0.310163i
$414$		0			0
$415$	−85.7720	−	148.562i	−0.206680	−	0.357980i
$416$	−38.0699	+	21.9796i	−0.0915141	+	0.0528357i
$417$		0			0
$418$	3.53117	−	6.11616i	0.00844777	−	0.0146320i
$419$	−249.386	+	143.983i	−0.595194	+	0.343635i	−0.767148	−	0.641470i	$-0.778325\pi$
$419$	−249.386	+	143.983i	−0.595194	+	0.343635i	0.171955	+	0.985105i	$0.444992\pi$
$420$		0			0
$421$	−52.7568	+	91.3775i	−0.125313	+	0.217049i	−0.921855	−	0.387534i	$-0.873327\pi$
$421$	−52.7568	+	91.3775i	−0.125313	+	0.217049i	0.796542	+	0.604583i	$0.206660\pi$
$422$	16.5296	−	9.54339i	0.0391698	−	0.0226147i
$423$		0			0
$424$	−21.8193	+	37.7921i	−0.0514605	+	0.0891322i
$425$		−	138.221i		−	0.325227i
$426$		0			0
$427$	−66.7747	−	142.430i	−0.156381	−	0.333560i
$428$	390.248	−	225.310i	0.911793	−	0.526424i
$429$		0			0
$430$	4.00098	+	6.92990i	0.00930460	+	0.0161160i
$431$	230.505	+	133.082i	0.534815	+	0.308775i	0.742975	−	0.669319i	$-0.233414\pi$
$431$	230.505	+	133.082i	0.534815	+	0.308775i	−0.208160	+	0.978095i	$0.566748\pi$
$432$		0			0
$433$	−235.623			−0.544164			−0.272082	−	0.962274i	$-0.587712\pi$
$433$	−235.623			−0.544164			−0.272082	+	0.962274i	$0.587712\pi$
$434$	15.8379	−	7.42521i	0.0364929	−	0.0171088i
$435$		0			0
$436$	−403.629	+	699.106i	−0.925755	+	1.60345i
$437$		−	206.200i		−	0.471854i
$438$		0			0
$439$	−627.412			−1.42918			−0.714592	−	0.699542i	$-0.753388\pi$
$439$	−627.412			−1.42918			−0.714592	+	0.699542i	$0.753388\pi$
$440$			31.1674i			0.0708350i
$441$		0			0
$442$	−15.1384			−0.0342497
$443$		−	463.543i		−	1.04637i	−0.852218	−	0.523187i	$-0.824743\pi$
$443$		−	463.543i		−	1.04637i	0.852218	−	0.523187i	$-0.175257\pi$
$444$		0			0
$445$	170.309			0.382718
$446$	0.815794	+	0.470999i	0.00182913	+	0.00105605i
$447$		0			0
$448$	188.493	+	402.054i	0.420743	+	0.897443i
$449$		−	584.536i		−	1.30186i	−0.759137	−	0.650931i	$-0.774379\pi$
$449$		−	584.536i		−	1.30186i	0.759137	−	0.650931i	$-0.225621\pi$
$450$		0			0
$451$	−187.991	+	325.611i	−0.416832	+	0.721975i
$452$	−144.754	+	83.5736i	−0.320251	+	0.184897i
$453$		0			0
$454$	−0.646619	−	1.11998i	−0.00142427	−	0.00246691i
$455$	308.944	−	144.840i	0.678997	−	0.318330i
$456$		0			0
$457$	−414.033			−0.905981			−0.452991	−	0.891515i	$-0.649643\pi$
$457$	−414.033			−0.905981			−0.452991	+	0.891515i	$0.649643\pi$
$458$	7.46371	+	4.30917i	0.0162963	+	0.00940867i
$459$		0			0
$460$	227.332	+	393.751i	0.494201	+	0.855981i
$461$	−335.821	−	193.886i	−0.728462	−	0.420578i	0.0893972	−	0.995996i	$-0.471506\pi$
$461$	−335.821	−	193.886i	−0.728462	−	0.420578i	−0.817859	+	0.575418i	$0.804839\pi$
$462$		0			0
$463$	−330.230	−	571.974i	−0.713239	−	1.23537i	−0.963635	−	0.267222i	$-0.913894\pi$
$463$	−330.230	−	571.974i	−0.713239	−	1.23537i	0.250396	−	0.968143i	$-0.419439\pi$
$464$	−513.081	−	296.227i	−1.10578	−	0.638421i
$465$		0			0
$466$	−5.45740	−	9.45249i	−0.0117112	−	0.0202843i
$467$	−752.865	+	434.667i	−1.61213	+	0.930764i	−0.623255	+	0.782019i	$0.714190\pi$
$467$	−752.865	+	434.667i	−1.61213	+	0.930764i	−0.988876	+	0.148746i	$0.952476\pi$
$468$		0			0
$469$	−255.981	−	546.007i	−0.545802	−	1.16419i
$470$	−21.4122	−	12.3624i	−0.0455580	−	0.0263029i
$471$		0			0
$472$	−26.4496			−0.0560374
$473$		−	318.642i		−	0.673661i
$474$		0			0
$475$	−30.9373	+	53.5851i	−0.0651313	+	0.112811i
$476$	−39.2513	+	459.575i	−0.0824608	+	0.965494i
$477$		0			0
$478$	9.10748	+	15.7746i	0.0190533	+	0.0330013i
$479$	128.334	−	74.0939i	0.267922	−	0.154685i	−0.360021	−	0.932944i	$-0.617231\pi$
$479$	128.334	−	74.0939i	0.267922	−	0.154685i	0.627943	+	0.778260i	$0.283897\pi$
$480$		0			0
$481$	−124.014	+	214.798i	−0.257824	+	0.446565i
$482$	−10.5080	+	6.06678i	−0.0218008	+	0.0125867i
$483$		0			0
$484$	68.4033	−	118.478i	0.141329	−	0.244789i
$485$	47.0437	−	27.1607i	0.0969974	−	0.0560015i
$486$		0			0
$487$	66.1378	−	114.554i	0.135807	−	0.235224i	−0.790099	−	0.612980i	$-0.789971\pi$
$487$	66.1378	−	114.554i	0.135807	−	0.235224i	0.925905	+	0.377756i	$0.123304\pi$
$488$			13.7877i			0.0282535i
$489$		0			0
$490$	5.30343	+	14.3859i	0.0108233	+	0.0293590i
$491$	−293.673	+	169.552i	−0.598111	+	0.345320i	−0.768298	−	0.640092i	$-0.778896\pi$
$491$	−293.673	+	169.552i	−0.598111	+	0.345320i	0.170187	+	0.985412i	$0.445563\pi$
$492$		0			0
$493$	−306.792	−	531.379i	−0.622296	−	1.07785i
$494$	5.86878	+	3.38834i	0.0118801	+	0.00685900i
$495$		0			0
$496$	518.641			1.04565
$497$	−651.275	+	305.334i	−1.31041	+	0.614354i
$498$		0			0
$499$	−94.3477	+	163.415i	−0.189074	+	0.327485i	−0.944942	−	0.327239i	$-0.893882\pi$
$499$	−94.3477	+	163.415i	−0.189074	+	0.327485i	0.755868	+	0.654724i	$0.227215\pi$
$500$		−	543.528i		−	1.08706i
$501$		0			0
$502$	35.5057			0.0707286
$503$		−	400.956i		−	0.797130i	−0.917140	−	0.398565i	$-0.869508\pi$
$503$		−	400.956i		−	0.797130i	0.917140	−	0.398565i	$-0.130492\pi$
$504$		0			0
$505$	−650.439			−1.28800
$506$			26.7010i			0.0527688i
$507$		0			0
$508$	337.990			0.665335
$509$	−607.233	−	350.586i	−1.19299	−	0.688775i	−0.234009	−	0.972234i	$-0.575184\pi$
$509$	−607.233	−	350.586i	−1.19299	−	0.688775i	−0.958984	+	0.283460i	$0.908518\pi$
$510$		0			0
$511$	5.63162	+	0.480984i	0.0110208	+	0.000941261i
$512$		−	97.6614i		−	0.190745i
$513$		0			0
$514$	−4.40712	+	7.63336i	−0.00857417	+	0.0148509i
$515$	629.345	−	363.353i	1.22203	−	0.705539i
$516$		0			0
$517$	492.276	+	852.646i	0.952177	+	1.64922i
$518$	−9.14272	−	6.37370i	−0.0176500	−	0.0123044i
$519$		0			0
$520$	−29.9068			−0.0575131
$521$	520.208	+	300.342i	0.998480	+	0.576472i	0.907798	−	0.419407i	$-0.137762\pi$
$521$	520.208	+	300.342i	0.998480	+	0.576472i	0.0906815	+	0.995880i	$0.471095\pi$
$522$		0			0
$523$	−313.375	−	542.781i	−0.599187	−	1.03782i	−0.992941	−	0.118607i	$-0.962157\pi$
$523$	−313.375	−	542.781i	−0.599187	−	1.03782i	0.393754	−	0.919216i	$-0.371176\pi$
$524$	647.204	+	373.663i	1.23512	+	0.713098i
$525$		0			0
$526$	−1.29811	−	2.24839i	−0.00246789	−	0.00427450i
$527$	465.175	+	268.569i	0.882686	+	0.509619i
$528$		0			0
$529$	125.297	+	217.021i	0.236856	+	0.410247i
$530$	−19.2738	+	11.1277i	−0.0363657	+	0.0209957i
$531$		0			0
$532$	118.081	−	169.381i	0.221957	−	0.318385i
$533$	−312.441	−	180.388i	−0.586193	−	0.338438i
$534$		0			0
$535$	459.967			0.859751
$536$			52.8553i			0.0986106i
$537$		0			0
$538$	1.93574	−	3.35280i	0.00359803	−	0.00623197i
$539$	103.535	−	601.698i	0.192087	−	1.11632i
$540$		0			0
$541$	413.819	+	716.755i	0.764915	+	1.32487i	0.940292	+	0.340370i	$0.110552\pi$
$541$	413.819	+	716.755i	0.764915	+	1.32487i	−0.175377	+	0.984501i	$0.556114\pi$
$542$	27.0401	−	15.6116i	0.0498895	−	0.0288037i
$543$		0			0
$544$	30.3284	−	52.5304i	0.0557508	−	0.0965632i
$545$	−713.609	+	412.002i	−1.30937	+	0.755967i
$546$		0			0
$547$	−131.228	+	227.294i	−0.239905	+	0.415528i	−0.960687	−	0.277634i	$-0.910450\pi$
$547$	−131.228	+	227.294i	−0.239905	+	0.415528i	0.720782	+	0.693162i	$0.243783\pi$
$548$	200.806	−	115.935i	0.366434	−	0.211561i
$549$		0			0
$550$	4.00610	−	6.93877i	0.00728382	−	0.0126159i
$551$			274.671i			0.498495i
$552$		0			0
$553$	−80.3803	−	171.451i	−0.145353	−	0.310038i
$554$	5.21622	−	3.01159i	0.00941556	−	0.00543608i
$555$		0			0
$556$	72.6473	+	125.829i	0.130661	+	0.226311i
$557$	−65.3868	−	37.7511i	−0.117391	−	0.0677757i	0.440155	−	0.897922i	$-0.354924\pi$
$557$	−65.3868	−	37.7511i	−0.117391	−	0.0677757i	−0.557546	+	0.830146i	$0.688257\pi$
$558$		0			0
$559$	305.754			0.546966
$560$	−38.6859	+	452.955i	−0.0690820	+	0.808848i
$561$		0			0
$562$	5.52847	−	9.57559i	0.00983713	−	0.0170384i
$563$		−	123.229i		−	0.218880i	−0.993993	−	0.109440i	$-0.965094\pi$
$563$		−	123.229i		−	0.218880i	0.993993	−	0.109440i	$-0.0349057\pi$
$564$		0			0
$565$	−170.615			−0.301973
$566$		−	15.1929i		−	0.0268425i
$567$		0			0
$568$	63.0456			0.110996
$569$			327.476i			0.575529i	0.957701	+	0.287764i	$0.0929120\pi$
$569$			327.476i			0.575529i	−0.957701	+	0.287764i	$0.907088\pi$
$570$		0			0
$571$	−609.711			−1.06780			−0.533898	−	0.845549i	$-0.679273\pi$
$571$	−609.711			−1.06780			−0.533898	+	0.845549i	$0.679273\pi$
$572$	515.296	+	297.507i	0.900868	+	0.520116i
$573$		0			0
$574$	9.27106	−	13.2988i	0.0161517	−	0.0231687i
$575$		−	233.934i		−	0.406841i
$576$		0			0
$577$	−27.1341	+	46.9976i	−0.0470261	+	0.0814517i	−0.888580	−	0.458721i	$-0.848308\pi$
$577$	−27.1341	+	46.9976i	−0.0470261	+	0.0814517i	0.841554	+	0.540173i	$0.181641\pi$
$578$	−1.11891	+	0.646003i	−0.00193583	+	0.00111765i
$579$		0			0
$580$	−302.820	−	524.499i	−0.522103	−	0.904309i
$581$	25.0643	−	293.466i	0.0431400	−	0.505106i
$582$		0			0
$583$	886.224			1.52011
$584$	−0.429031	−	0.247701i	−0.000734642	−	0.000424146i
$585$		0			0
$586$	−11.0288	−	19.1024i	−0.0188204	−	0.0325979i
$587$	−134.422	−	77.6088i	−0.228999	−	0.132213i	0.381111	−	0.924529i	$-0.375541\pi$
$587$	−134.422	−	77.6088i	−0.228999	−	0.132213i	−0.610110	+	0.792317i	$0.708875\pi$
$588$		0			0
$589$	−120.225	−	208.235i	−0.204117	−	0.353541i
$590$	−11.6820	−	6.74461i	−0.0198000	−	0.0114315i
$591$		0			0
$592$	−165.226	−	286.180i	−0.279099	−	0.483413i
$593$	411.343	−	237.489i	0.693665	−	0.400488i	−0.111318	−	0.993785i	$-0.535507\pi$
$593$	411.343	−	237.489i	0.693665	−	0.400488i	0.804984	+	0.593297i	$0.202174\pi$
$594$		0			0
$595$	−269.252	+	386.228i	−0.452525	+	0.649122i
$596$	80.4810	+	46.4657i	0.135035	+	0.0779626i
$597$		0			0
$598$	−25.6211			−0.0428446
$599$			755.537i			1.26133i	0.776055	+	0.630666i	$0.217218\pi$
$599$			755.537i			1.26133i	−0.776055	+	0.630666i	$0.782782\pi$
$600$		0			0
$601$	−118.651	+	205.509i	−0.197422	+	0.341945i	−0.947692	−	0.319187i	$-0.896590\pi$
$601$	−118.651	+	205.509i	−0.197422	+	0.341945i	0.750270	+	0.661132i	$0.229924\pi$
$602$	−1.16917	+	13.6892i	−0.00194214	+	0.0227396i
$603$		0			0
$604$	−118.373	−	205.028i	−0.195982	−	0.339451i
$605$	120.936	−	69.8223i	0.199894	−	0.115409i
$606$		0			0
$607$	241.547	−	418.371i	0.397935	−	0.689244i	−0.595536	−	0.803329i	$-0.703060\pi$
$607$	241.547	−	418.371i	0.397935	−	0.689244i	0.993471	+	0.114084i	$0.0363935\pi$
$608$	−23.5152	+	13.5765i	−0.0386763	+	0.0223298i
$609$		0			0
$610$	−3.51584	+	6.08962i	−0.00576368	+	0.00998298i
$611$	−818.159	+	472.365i	−1.33905	+	0.773101i
$612$		0			0
$613$	27.9363	−	48.3870i	0.0455730	−	0.0789348i	−0.842339	−	0.538948i	$-0.818822\pi$
$613$	27.9363	−	48.3870i	0.0455730	−	0.0789348i	0.887912	+	0.460013i	$0.152155\pi$
$614$		−	7.15254i		−	0.0116491i
$615$		0			0
$616$	−30.6034	+	43.8988i	−0.0496808	+	0.0712643i
$617$	−356.111	+	205.601i	−0.577165	+	0.333226i	−0.760006	−	0.649916i	$-0.774804\pi$
$617$	−356.111	+	205.601i	−0.577165	+	0.333226i	0.182841	+	0.983143i	$0.441471\pi$
$618$		0			0
$619$	−234.485	−	406.139i	−0.378812	−	0.656122i	0.612078	−	0.790798i	$-0.290334\pi$
$619$	−234.485	−	406.139i	−0.378812	−	0.656122i	−0.990890	+	0.134676i	$0.957001\pi$
$620$	459.152	+	265.092i	0.740568	+	0.427567i
$621$		0			0
$622$	−0.487308			−0.000783454
$623$	239.878	+	167.227i	0.385037	+	0.268423i
$624$		0			0
$625$	172.672	−	299.077i	0.276276	−	0.478524i
$626$		−	35.1449i		−	0.0561419i
$627$		0			0
$628$	377.014			0.600341
$629$		−	342.238i		−	0.544099i
$630$		0			0
$631$	7.39326			0.0117167			0.00585836	−	0.999983i	$-0.498135\pi$
$631$	7.39326			0.0117167			0.00585836	+	0.999983i	$0.498135\pi$
$632$			16.5970i			0.0262611i
$633$		0			0
$634$	39.5709			0.0624147
$635$	298.780	+	172.501i	0.470520	+	0.271655i
$636$		0			0
$637$	577.362	+	99.3471i	0.906376	+	0.155961i
$638$		−	35.5673i		−	0.0557481i
$639$		0			0
$640$	39.9045	−	69.1166i	0.0623507	−	0.107995i
$641$	547.775	−	316.258i	0.854564	−	0.493383i	−0.00762424	−	0.999971i	$-0.502427\pi$
$641$	547.775	−	316.258i	0.854564	−	0.493383i	0.862188	+	0.506588i	$0.169094\pi$
$642$		0			0
$643$	−203.977	−	353.299i	−0.317227	−	0.549454i	0.662681	−	0.748902i	$-0.269419\pi$
$643$	−203.977	−	353.299i	−0.317227	−	0.549454i	−0.979908	+	0.199448i	$0.936085\pi$
$644$	−66.4312	+	777.811i	−0.103154	+	1.20778i
$645$		0			0
$646$	−9.35075			−0.0144749
$647$	−134.044	−	77.3904i	−0.207178	−	0.119614i	0.392821	−	0.919615i	$-0.371499\pi$
$647$	−134.044	−	77.3904i	−0.207178	−	0.119614i	−0.599999	+	0.800001i	$0.704832\pi$
$648$		0			0
$649$	268.574	+	465.184i	0.413827	+	0.716770i
$650$	6.65812	+	3.84407i	0.0102433	+	0.00591395i
$651$		0			0
$652$	155.223	+	268.853i	0.238071	+	0.412352i
$653$	361.551	+	208.742i	0.553677	+	0.319666i	0.750604	−	0.660753i	$-0.229763\pi$
$653$	361.551	+	208.742i	0.553677	+	0.319666i	−0.196927	+	0.980418i	$0.563096\pi$
$654$		0			0
$655$	381.415	+	660.630i	0.582313	+	1.00860i
$656$	416.273	−	240.335i	0.634562	−	0.366364i
$657$		0			0
$658$	−18.0202	−	38.4369i	−0.0273863	−	0.0584148i
$659$	553.079	+	319.320i	0.839270	+	0.484553i	0.857016	−	0.515290i	$-0.172316\pi$
$659$	553.079	+	319.320i	0.839270	+	0.484553i	−0.0177460	+	0.999843i	$0.505649\pi$
$660$		0			0
$661$	395.587			0.598468			0.299234	−	0.954180i	$-0.403269\pi$
$661$	395.587			0.598468			0.299234	+	0.954180i	$0.403269\pi$
$662$		−	22.8141i		−	0.0344624i
$663$		0			0
$664$	−12.9078	+	22.3570i	−0.0194395	+	0.0336702i
$665$	190.830	−	89.4657i	0.286962	−	0.134535i
$666$		0			0
$667$	−519.232	−	899.336i	−0.778459	−	1.34833i
$668$	−661.213	+	381.751i	−0.989840	+	0.571484i
$669$		0			0
$670$	−13.4780	+	23.3446i	−0.0201164	+	0.0348427i
$671$	242.492	−	140.003i	0.361388	−	0.208648i
$672$		0			0
$673$	−367.518	+	636.559i	−0.546089	+	0.945854i	0.452449	+	0.891790i	$0.350551\pi$
$673$	−367.518	+	636.559i	−0.546089	+	0.945854i	−0.998538	+	0.0540632i	$0.982783\pi$
$674$	−7.64256	+	4.41243i	−0.0113391	+	0.00654664i
$675$		0			0
$676$	52.0289	−	90.1167i	0.0769659	−	0.133309i
$677$		−	249.213i		−	0.368113i	−0.982916	−	0.184057i	$-0.941077\pi$
$677$		−	249.213i		−	0.368113i	0.982916	−	0.184057i	$-0.0589229\pi$
$678$		0			0
$679$	92.9296	+	7.93692i	0.136862	+	0.0116891i
$680$	35.7379	−	20.6333i	0.0525558	−	0.0303431i
$681$		0			0
$682$	15.5680	+	26.9646i	0.0228270	+	0.0395375i
$683$	−863.031	−	498.271i	−1.26359	−	0.729533i	−0.289821	−	0.957081i	$-0.593596\pi$
$683$	−863.031	−	498.271i	−1.26359	−	0.729533i	−0.973767	+	0.227548i	$0.926929\pi$
$684$		0			0
$685$	236.681			0.345519
$686$	−6.65574	+	25.4698i	−0.00970224	+	0.0371279i
$687$		0			0
$688$	−203.682	+	352.787i	−0.296049	+	0.512772i
$689$			850.379i			1.23422i
$690$		0			0
$691$	168.185			0.243394			0.121697	−	0.992567i	$-0.461166\pi$
$691$	168.185			0.243394			0.121697	+	0.992567i	$0.461166\pi$
$692$		−	111.543i		−	0.161189i
$693$		0			0
$694$	34.8172			0.0501689
$695$			148.309i			0.213394i
$696$		0			0
$697$	497.813			0.714222
$698$	34.8628	+	20.1280i	0.0499467	+	0.0288367i
$699$		0			0
$700$	133.963	−	192.162i	0.191375	−	0.274517i
$701$		−	240.389i		−	0.342923i	−0.985191	−	0.171462i	$-0.945151\pi$
$701$		−	240.389i		−	0.342923i	0.985191	−	0.171462i	$-0.0548489\pi$
$702$		0			0
$703$	−76.6013	+	132.677i	−0.108963	+	0.188730i
$704$	−684.510	+	395.202i	−0.972315	+	0.561366i
$705$		0			0
$706$	19.3995	+	33.6010i	0.0274781	+	0.0475935i
$707$	−916.133	−	638.668i	−1.29580	−	0.903349i
$708$		0			0
$709$	730.648			1.03053			0.515267	−	0.857030i	$-0.327693\pi$
$709$	730.648			1.03053			0.515267	+	0.857030i	$0.327693\pi$
$710$	27.8454	+	16.0765i	0.0392188	+	0.0226430i
$711$		0			0
$712$	−12.8149	−	22.1961i	−0.0179985	−	0.0311743i
$713$	787.289	+	454.541i	1.10419	+	0.637505i
$714$		0			0
$715$	303.678	+	525.986i	0.424725	+	0.735645i
$716$	−196.140	−	113.241i	−0.273938	−	0.158158i
$717$		0			0
$718$	−1.92645	−	3.33671i	−0.00268308	−	0.00464723i
$719$	474.766	−	274.106i	0.660315	−	0.381233i	−0.132082	−	0.991239i	$-0.542166\pi$
$719$	474.766	−	274.106i	0.660315	−	0.381233i	0.792397	+	0.610006i	$0.208833\pi$
$720$		0			0
$721$	1243.20	+	106.179i	1.72427	+	0.147266i
$722$	−20.3695	−	11.7603i	−0.0282126	−	0.0162886i
$723$		0			0
$724$	326.844			0.451442
$725$			311.613i			0.429811i
$726$		0			0
$727$	22.9974	−	39.8326i	0.0316333	−	0.0547904i	−0.849775	−	0.527145i	$-0.823262\pi$
$727$	22.9974	−	39.8326i	0.0316333	−	0.0547904i	0.881409	+	0.472355i	$0.156596\pi$
$728$	−42.1233	−	29.3656i	−0.0578616	−	0.0403373i
$729$		0			0
$730$	−0.126327	−	0.218804i	−0.000173050	−	0.000299732i
$731$	−365.369	+	210.946i	−0.499821	+	0.288572i
$732$		0			0
$733$	32.1883	−	55.7518i	0.0439131	−	0.0760598i	−0.843233	−	0.537548i	$-0.819351\pi$
$733$	32.1883	−	55.7518i	0.0439131	−	0.0760598i	0.887147	+	0.461488i	$0.152684\pi$
$734$	39.5132	−	22.8129i	0.0538327	−	0.0310803i
$735$		0			0
$736$	51.3295	−	88.9053i	0.0697412	−	0.120795i
$737$	929.593	−	536.701i	1.26132	−	0.728224i
$738$		0			0
$739$	−329.883	+	571.374i	−0.446391	+	0.773172i	−0.998148	−	0.0608329i	$-0.980624\pi$
$739$	−329.883	+	571.374i	−0.446391	+	0.773172i	0.551757	+	0.834005i	$0.313958\pi$
$740$		−	337.807i		−	0.456496i
$741$		0			0
$742$	−38.0732	−	3.25175i	−0.0513116	−	0.00438242i
$743$	−267.309	+	154.331i	−0.359769	+	0.207713i	−0.668980	−	0.743281i	$-0.733269\pi$
$743$	−267.309	+	154.331i	−0.359769	+	0.207713i	0.309210	+	0.950994i	$0.399935\pi$
$744$		0			0
$745$	47.4297	+	82.1506i	0.0636640	+	0.110269i
$746$	−40.4964	−	23.3806i	−0.0542847	−	0.0313413i
$747$		0			0
$748$	−821.024			−1.09763
$749$	647.857	+	451.643i	0.864962	+	0.602994i
$750$		0			0
$751$	122.235	−	211.718i	0.162763	−	0.281914i	−0.773095	−	0.634290i	$-0.781293\pi$
$751$	122.235	−	211.718i	0.162763	−	0.281914i	0.935859	+	0.352375i	$0.114626\pi$
$752$		−	1258.69i		−	1.67379i
$753$		0			0
$754$	34.1287			0.0452635
$755$		−	241.658i		−	0.320076i
$756$		0			0
$757$	159.987			0.211343			0.105671	−	0.994401i	$-0.466301\pi$
$757$	159.987			0.211343			0.105671	+	0.994401i	$0.466301\pi$
$758$		−	35.9524i		−	0.0474306i
$759$		0			0
$760$	−18.4730			−0.0243066
$761$	−971.609	−	560.959i	−1.27675	−	0.737134i	−0.300503	−	0.953781i	$-0.597155\pi$
$761$	−971.609	−	560.959i	−1.27675	−	0.737134i	−0.976250	+	0.216647i	$0.930488\pi$
$762$		0			0
$763$	−1409.65	−	120.395i	−1.84751	−	0.157792i
$764$			652.639i			0.854239i
$765$		0			0
$766$	16.8610	−	29.2041i	0.0220117	−	0.0381254i
$767$	−446.368	+	257.711i	−0.581966	+	0.335999i
$768$		0			0
$769$	−20.2793	−	35.1248i	−0.0263710	−	0.0456760i	0.852539	−	0.522664i	$-0.175062\pi$
$769$	−20.2793	−	35.1248i	−0.0263710	−	0.0456760i	−0.878910	+	0.476988i	$0.841728\pi$
$770$	−24.7107	+	11.5850i	−0.0320918	+	0.0150454i
$771$		0			0
$772$	−1305.44			−1.69099
$773$	720.499	+	415.980i	0.932082	+	0.538138i	0.887469	−	0.460867i	$-0.152461\pi$
$773$	720.499	+	415.980i	0.932082	+	0.538138i	0.0446123	+	0.999004i	$0.485795\pi$
$774$		0			0
$775$	−136.395	−	236.242i	−0.175993	−	0.304829i
$776$	−7.07962	−	4.08742i	−0.00912322	−	0.00526729i
$777$		0			0
$778$	−10.1930	−	17.6549i	−0.0131016	−	0.0226926i
$779$	−192.990	−	111.423i	−0.247741	−	0.143033i
$780$		0			0
$781$	−640.175	−	1108.82i	−0.819686	−	1.41974i
$782$	30.6166	−	17.6765i	0.0391516	−	0.0226042i
$783$		0			0
$784$	−499.246	+	599.994i	−0.636793	+	0.765299i
$785$	333.277	+	192.418i	0.424557	+	0.245118i
$786$		0			0
$787$	−897.749			−1.14072			−0.570361	−	0.821394i	$-0.693197\pi$
$787$	−897.749			−1.14072			−0.570361	+	0.821394i	$0.693197\pi$
$788$		−	1046.57i		−	1.32813i
$789$		0			0
$790$	−4.23221	+	7.33040i	−0.00535723	+	0.00927899i
$791$	−240.308	−	167.527i	−0.303803	−	0.211791i
$792$		0			0
$793$	134.340	+	232.684i	0.169407	+	0.293422i
$794$	13.0842	−	7.55419i	0.0164789	−	0.00951410i
$795$		0			0
$796$	199.855	−	346.160i	0.251075	−	0.434874i
$797$	83.2647	−	48.0729i	0.104473	−	0.0603173i	−0.446853	−	0.894607i	$-0.647455\pi$
$797$	83.2647	−	48.0729i	0.104473	−	0.0603173i	0.551326	+	0.834290i	$0.314122\pi$
$798$		0			0
$799$	651.788	−	1128.93i	0.815755	−	1.41293i
$800$	−26.6779	+	15.4025i	−0.0333474	+	0.0192531i
$801$		0			0
$802$	−7.09539	+	12.2896i	−0.00884712	+	0.0153237i
$803$			10.0608i			0.0125290i
$804$		0			0
$805$	−455.698	+	653.673i	−0.566084	+	0.812016i
$806$	−25.8739	+	14.9383i	−0.0321017	+	0.0185339i
$807$		0			0
$808$	48.9423	+	84.7706i	0.0605722	+	0.104914i
$809$	−1082.54	−	625.002i	−1.33812	−	0.772561i	−0.351588	−	0.936155i	$-0.614358\pi$
$809$	−1082.54	−	625.002i	−1.33812	−	0.772561i	−0.986528	+	0.163594i	$0.947691\pi$
$810$		0			0
$811$	−1588.72			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$811$	−1588.72			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$812$	88.4901	−	1036.09i	0.108978	−	1.27597i
$813$		0			0
$814$	9.91916	−	17.1805i	0.0121857	−	0.0211063i
$815$			316.885i			0.388816i
$816$		0			0
$817$	188.860			0.231162
$818$			45.9471i			0.0561700i
$819$		0			0
$820$	491.367			0.599228
$821$			295.206i			0.359569i	0.983706	+	0.179784i	$0.0575400\pi$
$821$			295.206i			0.359569i	−0.983706	+	0.179784i	$0.942460\pi$
$822$		0			0
$823$	−1346.83			−1.63648			−0.818241	−	0.574875i	$-0.805051\pi$
$823$	−1346.83			−1.63648			−0.818241	+	0.574875i	$0.805051\pi$
$824$	−94.7102	−	54.6809i	−0.114940	−	0.0663604i
$825$		0			0
$826$	−9.83138	−	20.9703i	−0.0119024	−	0.0253877i
$827$			1226.89i			1.48354i	0.670653	+	0.741772i	$0.266014\pi$
$827$			1226.89i			1.48354i	−0.670653	+	0.741772i	$0.733986\pi$
$828$		0			0
$829$	529.304	−	916.782i	0.638485	−	1.10589i	−0.347280	−	0.937761i	$-0.612895\pi$
$829$	529.304	−	916.782i	0.638485	−	1.10589i	0.985765	−	0.168127i	$-0.0537720\pi$
$830$	−11.4020	+	6.58295i	−0.0137374	+	0.00793127i
$831$		0			0
$832$	−379.217	−	656.824i	−0.455790	−	0.789452i
$833$	−758.476	+	279.616i	−0.910535	+	0.335674i
$834$		0			0
$835$	−779.342			−0.933343
$836$	318.291	+	183.765i	0.380731	+	0.219815i
$837$		0			0
$838$	11.0506	+	19.1402i	0.0131869	+	0.0228404i
$839$	−36.0995	−	20.8420i	−0.0430268	−	0.0248415i	0.478332	−	0.878179i	$-0.341241\pi$
$839$	−36.0995	−	20.8420i	−0.0430268	−	0.0248415i	−0.521359	+	0.853337i	$0.674575\pi$
$840$		0			0
$841$	271.147	+	469.640i	0.322410	+	0.558431i
$842$	7.01316	+	4.04905i	0.00832917	+	0.00480885i
$843$		0			0
$844$	496.647	+	860.218i	0.588444	+	1.01922i
$845$	91.9862	−	53.1082i	0.108859	−	0.0628500i
$846$		0			0
$847$	238.895	+	20.4035i	0.282048	+	0.0240891i
$848$	−981.191	−	566.491i	−1.15707	−	0.668032i
$849$		0			0
$850$	−10.6084			−0.0124805
$851$		−	579.223i		−	0.680638i
$852$		0			0
$853$	309.770	−	536.537i	0.363153	−	0.629000i	−0.625325	−	0.780365i	$-0.715033\pi$
$853$	309.770	−	536.537i	0.363153	−	0.629000i	0.988478	+	0.151365i	$0.0483667\pi$
$854$	−10.9314	+	5.12492i	−0.0128003	+	0.00600108i
$855$		0			0
$856$	−34.6102	−	59.9467i	−0.0404325	−	0.0700312i
$857$	705.896	−	407.550i	0.823683	−	0.475554i	−0.0280018	−	0.999608i	$-0.508914\pi$
$857$	705.896	−	407.550i	0.823683	−	0.475554i	0.851685	+	0.524054i	$0.175581\pi$
$858$		0			0
$859$	−343.813	+	595.501i	−0.400248	+	0.693250i	−0.993756	−	0.111579i	$-0.964409\pi$
$859$	−343.813	+	595.501i	−0.400248	+	0.693250i	0.593508	+	0.804828i	$0.297743\pi$
$860$	−360.638	+	208.215i	−0.419347	+	0.242110i
$861$		0			0
$862$	10.2140	−	17.6911i	0.0118492	−	0.0205233i
$863$	−261.740	+	151.116i	−0.303291	+	0.175105i	−0.643921	−	0.765092i	$-0.722693\pi$
$863$	−261.740	+	151.116i	−0.303291	+	0.175105i	0.340629	+	0.940198i	$0.389360\pi$
$864$		0			0
$865$	56.9284	−	98.6028i	0.0658131	−	0.113992i
$866$			18.0839i			0.0208821i
$867$		0			0
$868$	386.415	+	824.221i	0.445178	+	0.949563i
$869$	291.900	−	168.529i	0.335904	−	0.193934i
$870$		0			0
$871$	514.993	+	891.994i	0.591266	+	1.02410i
$872$	107.391	+	62.0022i	0.123155	+	0.0711035i
$873$		0			0
$874$	−15.8257			−0.0181073
$875$	862.494	−	404.359i	0.985708	−	0.462124i
$876$		0			0
$877$	−2.01936	+	3.49764i	−0.00230258	+	0.00398819i	−0.867174	−	0.498005i	$-0.834066\pi$
$877$	−2.01936	+	3.49764i	−0.00230258	+	0.00398819i	0.864872	+	0.501993i	$0.167400\pi$
$878$			48.1535i			0.0548445i
$879$		0			0
$880$	−809.196			−0.919541
$881$			34.5348i			0.0391996i	0.999808	+	0.0195998i	$0.00623920\pi$
$881$			34.5348i			0.0391996i	−0.999808	+	0.0195998i	$0.993761\pi$
$882$		0			0
$883$	1539.71			1.74373			0.871863	−	0.489750i	$-0.162912\pi$
$883$	1539.71			1.74373			0.871863	+	0.489750i	$0.162912\pi$
$884$		−	787.816i		−	0.891194i
$885$		0			0
$886$	−35.5767			−0.0401542
$887$	1153.03	+	665.702i	1.29992	+	0.750510i	0.980390	−	0.197066i	$-0.0631412\pi$
$887$	1153.03	+	665.702i	1.29992	+	0.750510i	0.319531	+	0.947576i	$0.396475\pi$
$888$		0			0
$889$	251.448	+	536.338i	0.282844	+	0.603304i
$890$		−	13.0711i		−	0.0146867i
$891$		0			0
$892$	−24.5112	+	42.4547i	−0.0274789	+	0.0475949i
$893$	−505.365	+	291.773i	−0.565918	+	0.326733i
$894$		0			0
$895$	−115.591	−	200.209i	−0.129151	−	0.223697i
$896$	124.071	−	58.1673i	0.138472	−	0.0649189i
$897$		0			0
$898$	−44.8628			−0.0499586
$899$	−1048.71	−	605.475i	−1.16653	−	0.673499i
$900$		0			0
$901$	−586.694	−	1016.18i	−0.651159	−	1.12784i
$902$	24.9904	+	14.4282i	0.0277056	+	0.0159958i
$903$		0			0
$904$	12.8379	+	22.2359i	0.0142012	+	0.0245972i
$905$	288.927	+	166.812i	0.319256	+	0.184323i
$906$		0			0
$907$	−418.678	−	725.171i	−0.461607	−	0.799527i	0.537434	−	0.843306i	$-0.319394\pi$
$907$	−418.678	−	725.171i	−0.461607	−	0.799527i	−0.999041	+	0.0437787i	$0.986060\pi$
$908$	58.2847	−	33.6507i	0.0641902	−	0.0370602i
$909$		0			0
$910$	−11.1164	−	23.7112i	−0.0122158	−	0.0260563i
$911$	−50.4341	−	29.1181i	−0.0553612	−	0.0319628i	0.472064	−	0.881564i	$-0.343509\pi$
$911$	−50.4341	−	29.1181i	−0.0553612	−	0.0319628i	−0.527425	+	0.849602i	$0.676842\pi$
$912$		0			0
$913$	524.273			0.574231
$914$			31.7768i			0.0347668i
$915$		0			0
$916$	−224.253	+	388.418i	−0.244818	+	0.424037i
$917$	−111.457	+	1305.00i	−0.121545	+	1.42312i
$918$		0			0
$919$	140.456	+	243.278i	0.152836	+	0.264720i	0.932269	−	0.361766i	$-0.117826\pi$
$919$	140.456	+	243.278i	0.152836	+	0.264720i	−0.779433	+	0.626486i	$0.784493\pi$
$920$	60.4849	−	34.9210i	0.0657445	−	0.0379576i
$921$		0			0
$922$	−14.8807	+	25.7741i	−0.0161395	+	0.0279545i
$923$	1063.97	−	614.282i	1.15273	−	0.665528i
$924$		0			0
$925$	−86.9040	+	150.522i	−0.0939502	+	0.162727i
$926$	−43.8987	+	25.3449i	−0.0474068	+	0.0273703i
$927$		0			0
$928$	−68.3739	+	118.427i	−0.0736787	+	0.127615i
$929$			163.376i			0.175862i	0.996127	+	0.0879310i	$0.0280255\pi$
$929$			163.376i			0.175862i	−0.996127	+	0.0879310i	$0.971974\pi$
$930$		0			0
$931$	356.628	+	61.3652i	0.383059	+	0.0659132i
$932$	491.917	−	284.008i	0.527808	−	0.304730i
$933$		0			0
$934$	33.3604	+	57.7819i	0.0357178	+	0.0618650i
$935$	−725.777	−	419.028i	−0.776232	−	0.448158i
$936$		0			0
$937$	1117.03			1.19213			0.596066	−	0.802935i	$-0.296730\pi$
$937$	1117.03			1.19213			0.596066	+	0.802935i	$0.296730\pi$
$938$	−41.9057	+	19.6464i	−0.0446755	+	0.0209450i
$939$		0			0
$940$	643.349	−	1114.31i	0.684414	−	1.18544i
$941$			643.914i			0.684287i	0.939648	+	0.342144i	$0.111153\pi$
$941$			643.914i			0.684287i	−0.939648	+	0.342144i	$0.888847\pi$
$942$		0			0
$943$	842.526			0.893453
$944$		−	686.709i		−	0.727446i
$945$		0			0
$946$	−24.4556			−0.0258515
$947$		−	1321.22i		−	1.39517i	−0.716504	−	0.697583i	$-0.754259\pi$
$947$		−	1321.22i		−	1.39517i	0.716504	−	0.697583i	$-0.245741\pi$
$948$		0			0
$949$	−9.65386			−0.0101727
$950$	4.11262	+	2.37442i	0.00432907	+	0.00249939i
$951$		0			0
$952$	70.5963	+	6.02947i	0.0741557	+	0.00633348i
$953$			1182.43i			1.24075i	0.784307	+	0.620373i	$0.213019\pi$
$953$			1182.43i			1.24075i	−0.784307	+	0.620373i	$0.786981\pi$
$954$		0			0
$955$	−333.089	+	576.927i	−0.348784	+	0.604112i
$956$	−820.926	+	473.962i	−0.858709	+	0.495776i
$957$		0			0
$958$	−5.68666	−	9.84959i	−0.00593598	−	0.0102814i
$959$	333.361	+	232.397i	0.347613	+	0.242333i
$960$		0			0
$961$	99.0791			0.103100
$962$	16.4856	+	9.51796i	0.0171368	+	0.00989393i
$963$		0			0
$964$	−315.721	−	546.845i	−0.327512	−	0.567267i
$965$	−1154.00	−	666.261i	−1.19585	−	0.690426i
$966$		0			0
$967$	345.416	+	598.278i	0.357203	+	0.618694i	0.987492	−	0.157666i	$-0.0503970\pi$
$967$	345.416	+	598.278i	0.357203	+	0.618694i	−0.630289	+	0.776361i	$0.717064\pi$
$968$	−18.1996	−	10.5076i	−0.0188013	−	0.0108549i
$969$		0			0
$970$	−2.08457	−	3.61058i	−0.00214904	−	0.00372225i
$971$	760.475	−	439.061i	0.783188	−	0.452174i	−0.0543710	−	0.998521i	$-0.517315\pi$
$971$	760.475	−	439.061i	0.783188	−	0.452174i	0.837559	+	0.546347i	$0.183982\pi$
$972$		0			0
$973$	−145.625	+	208.891i	−0.149666	+	0.214687i
$974$	−8.79195	−	5.07604i	−0.00902665	−	0.00521154i
$975$		0			0
$976$	−357.969			−0.366771
$977$		−	58.7407i		−	0.0601235i	−0.999548	−	0.0300618i	$-0.990430\pi$
$977$		−	58.7407i		−	0.0601235i	0.999548	−	0.0300618i	$-0.00957039\pi$
$978$		0			0
$979$	−260.250	+	450.766i	−0.265832	+	0.460435i
$980$	−748.655	+	275.996i	−0.763934	+	0.281628i
$981$		0			0
$982$	13.0130	+	22.5392i	0.0132515	+	0.0229523i
$983$	145.143	−	83.7982i	0.147653	−	0.0852474i	−0.424353	−	0.905497i	$-0.639499\pi$
$983$	145.143	−	83.7982i	0.147653	−	0.0852474i	0.572006	+	0.820249i	$0.306165\pi$
$984$		0			0
$985$	534.140	−	925.158i	0.542274	−	0.939247i
$986$	−40.7830	+	23.5461i	−0.0413621	+	0.0238804i
$987$		0			0
$988$	−176.333	+	305.417i	−0.178474	+	0.309127i
$989$	−618.371	+	357.017i	−0.625248	+	0.360987i
$990$		0			0
$991$	−646.870	+	1120.41i	−0.652745	+	1.13059i	0.329709	+	0.944083i	$0.393049\pi$
$991$	−646.870	+	1120.41i	−0.652745	+	1.13059i	−0.982454	+	0.186505i	$0.940284\pi$
$992$		−	119.710i		−	0.120676i
$993$		0			0
$994$	23.4342	+	49.9850i	0.0235756	+	0.0502867i
$995$	353.341	−	204.001i	0.355116	−	0.205027i
$996$		0			0
$997$	350.385	+	606.885i	0.351439	+	0.608711i	0.986502	−	0.163750i	$-0.0523590\pi$
$997$	350.385	+	606.885i	0.351439	+	0.608711i	−0.635062	+	0.772461i	$0.719026\pi$
$998$	12.5420	+	7.24113i	0.0125671	+	0.00725564i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.b.116.5		22
3.2	odd	2		63.3.j.b.11.7	✓	22
7.2	even	3		189.3.n.b.170.5		22
9.4	even	3		63.3.n.b.32.7	yes	22
9.5	odd	6		189.3.n.b.179.5		22
21.2	odd	6		63.3.n.b.2.7	yes	22
21.5	even	6		441.3.n.f.128.7		22
21.11	odd	6		441.3.r.g.344.5		22
21.17	even	6		441.3.r.f.344.5		22
21.20	even	2		441.3.j.f.263.7		22
63.4	even	3		441.3.r.g.50.5		22
63.13	odd	6		441.3.n.f.410.7		22
63.23	odd	6	inner	189.3.j.b.44.7		22
63.31	odd	6		441.3.r.f.50.5		22
63.40	odd	6		441.3.j.f.275.5		22
63.58	even	3		63.3.j.b.23.5	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.7	✓	22	3.2	odd	2
63.3.j.b.23.5	yes	22	63.58	even	3
63.3.n.b.2.7	yes	22	21.2	odd	6
63.3.n.b.32.7	yes	22	9.4	even	3
189.3.j.b.44.7		22	63.23	odd	6	inner
189.3.j.b.116.5		22	1.1	even	1	trivial
189.3.n.b.170.5		22	7.2	even	3
189.3.n.b.179.5		22	9.5	odd	6
441.3.j.f.263.7		22	21.20	even	2
441.3.j.f.275.5		22	63.40	odd	6
441.3.n.f.128.7		22	21.5	even	6
441.3.n.f.410.7		22	63.13	odd	6
441.3.r.f.50.5		22	63.31	odd	6
441.3.r.f.344.5		22	21.17	even	6
441.3.r.g.50.5		22	63.4	even	3
441.3.r.g.344.5		22	21.11	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.0767494i q^{2} +3.99411 q^{4} +(3.53076 + 2.03848i) q^{5} +(2.97142 + 6.33803i) q^{7} -0.613543i q^{8} +O(q^{10})\)	\(q-0.0767494i q^{2} +3.99411 q^{4} +(3.53076 + 2.03848i) q^{5} +(2.97142 + 6.33803i) q^{7} -0.613543i q^{8} +(0.156452 - 0.270983i) q^{10} +(-10.7907 + 6.23001i) q^{11} +(-5.97803 - 10.3542i) q^{13} +(0.486440 - 0.228055i) q^{14} +15.9293 q^{16} +(14.2872 + 8.24873i) q^{17} +(-3.69254 - 6.39566i) q^{19} +(14.1022 + 8.14193i) q^{20} +(0.478149 + 0.828179i) q^{22} +(24.1805 + 13.9606i) q^{23} +(-4.18917 - 7.25586i) q^{25} +(-0.794682 + 0.458810i) q^{26} +(11.8682 + 25.3148i) q^{28} +(-32.2098 - 18.5963i) q^{29} +32.5589 q^{31} -3.67674i q^{32} +(0.633085 - 1.09653i) q^{34} +(-2.42859 + 28.4352i) q^{35} +(-10.3724 - 17.9656i) q^{37} +(-0.490863 + 0.283400i) q^{38} +(1.25070 - 2.16627i) q^{40} +(26.1324 - 15.0876i) q^{41} +(-12.7866 + 22.1470i) q^{43} +(-43.0992 + 24.8833i) q^{44} +(1.07147 - 1.85584i) q^{46} -79.0168i q^{47} +(-31.3413 + 37.6660i) q^{49} +(-0.556883 + 0.321516i) q^{50} +(-23.8769 - 41.3560i) q^{52} +(-61.5964 - 35.5627i) q^{53} -50.7991 q^{55} +(3.88865 - 1.82310i) q^{56} +(-1.42726 + 2.47208i) q^{58} -43.1097i q^{59} -22.4723 q^{61} -2.49887i q^{62} +63.4352 q^{64} -48.7444i q^{65} -86.1477 q^{67} +(57.0647 + 32.9463i) q^{68} +(2.18239 + 0.186393i) q^{70} +102.757i q^{71} +(0.403723 - 0.699268i) q^{73} +(-1.37885 + 0.796079i) q^{74} +(-14.7484 - 25.5450i) q^{76} +(-71.5497 - 49.8797i) q^{77} -27.0511 q^{79} +(56.2427 + 32.4717i) q^{80} +(-1.15796 - 2.00565i) q^{82} +(-36.4392 - 21.0382i) q^{83} +(33.6298 + 58.2485i) q^{85} +(1.69977 + 0.981361i) q^{86} +(3.82238 + 6.62055i) q^{88} +(36.1770 - 20.8868i) q^{89} +(47.8623 - 68.6558i) q^{91} +(96.5795 + 55.7602i) q^{92} -6.06449 q^{94} -30.1087i q^{95} +(6.66199 - 11.5389i) q^{97} +(2.89084 + 2.40542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) 22 * q - 24 * q^4 - 12 * q^5	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

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