LMFDB - Embedded newform 63.3.n.b.32.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (of order $6$, degree $2$, 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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.7
Character	$\chi$	$=$	63.32
Dual form			63.3.n.b.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0664669 + 0.0383747i) q^{2} +(-2.92647 + 0.660129i) q^{3} +(-1.99705 - 3.45900i) q^{4} -4.07697i q^{5} +(-0.219846 - 0.0684257i) q^{6} +(-6.97461 - 0.595686i) q^{7} -0.613543i q^{8} +(8.12846 - 3.86370i) q^{9} +O(q^{10})$	\(q+(0.0664669 + 0.0383747i) q^{2} +(-2.92647 + 0.660129i) q^{3} +(-1.99705 - 3.45900i) q^{4} -4.07697i q^{5} +(-0.219846 - 0.0684257i) q^{6} +(-6.97461 - 0.595686i) q^{7} -0.613543i q^{8} +(8.12846 - 3.86370i) q^{9} +(0.156452 - 0.270983i) q^{10} -12.4600i q^{11} +(8.12771 + 8.80435i) q^{12} +(-5.97803 + 10.3542i) q^{13} +(-0.440721 - 0.307242i) q^{14} +(2.69132 + 11.9311i) q^{15} +(-7.96467 + 13.7952i) q^{16} +(14.2872 + 8.24873i) q^{17} +(0.688542 + 0.0551192i) q^{18} +(-3.69254 - 6.39566i) q^{19} +(-14.1022 + 8.14193i) q^{20} +(20.8042 - 2.86088i) q^{21} +(0.478149 - 0.828179i) q^{22} -27.9212i q^{23} +(0.405017 + 1.79552i) q^{24} +8.37834 q^{25} +(-0.794682 + 0.458810i) q^{26} +(-21.2372 + 16.6728i) q^{27} +(11.8682 + 25.3148i) q^{28} +(32.2098 - 18.5963i) q^{29} +(-0.278969 + 0.896304i) q^{30} +(-16.2794 - 28.1968i) q^{31} +(-3.18415 + 1.83837i) q^{32} +(8.22522 + 36.4639i) q^{33} +(0.633085 + 1.09653i) q^{34} +(-2.42859 + 28.4352i) q^{35} +(-29.5975 - 20.4003i) q^{36} +(-10.3724 - 17.9656i) q^{37} -0.566800i q^{38} +(10.6594 - 34.2477i) q^{39} -2.50139 q^{40} +(-26.1324 - 15.0876i) q^{41} +(1.49258 + 0.608201i) q^{42} +(-12.7866 - 22.1470i) q^{43} +(-43.0992 + 24.8833i) q^{44} +(-15.7522 - 33.1395i) q^{45} +(1.07147 - 1.85584i) q^{46} +(68.4306 + 39.5084i) q^{47} +(14.2018 - 45.6290i) q^{48} +(48.2903 + 8.30936i) q^{49} +(0.556883 + 0.321516i) q^{50} +(-47.2563 - 14.7083i) q^{51} +47.7538 q^{52} +(-61.5964 - 35.5627i) q^{53} +(-2.05138 + 0.293222i) q^{54} -50.7991 q^{55} +(-0.365479 + 4.27922i) q^{56} +(15.0281 + 16.2792i) q^{57} +2.85451 q^{58} +(-37.3341 + 21.5548i) q^{59} +(35.8950 - 33.1364i) q^{60} +(11.2361 - 19.4616i) q^{61} -2.49887i q^{62} +(-58.9944 + 22.1058i) q^{63} +63.4352 q^{64} +(42.2139 + 24.3722i) q^{65} +(-0.852585 + 2.73928i) q^{66} +(43.0738 + 74.6061i) q^{67} -65.8926i q^{68} +(18.4316 + 81.7106i) q^{69} +(-1.25261 + 1.79681i) q^{70} +102.757i q^{71} +(-2.37054 - 4.98716i) q^{72} +(0.403723 - 0.699268i) q^{73} -1.59216i q^{74} +(-24.5190 + 5.53079i) q^{75} +(-14.7484 + 25.5450i) q^{76} +(-7.42226 + 86.9038i) q^{77} +(2.02274 - 1.86729i) q^{78} +(13.5256 - 23.4270i) q^{79} +(56.2427 + 32.4717i) q^{80} +(51.1437 - 62.8118i) q^{81} +(-1.15796 - 2.00565i) q^{82} +(36.4392 - 21.0382i) q^{83} +(-51.4429 - 66.2484i) q^{84} +(33.6298 - 58.2485i) q^{85} -1.96272i q^{86} +(-81.9850 + 75.6842i) q^{87} -7.64476 q^{88} +(36.1770 - 20.8868i) q^{89} +(0.224719 - 2.80716i) q^{90} +(47.8623 - 68.6558i) q^{91} +(-96.5795 + 55.7602i) q^{92} +(66.2548 + 71.7706i) q^{93} +(3.03225 + 5.25200i) q^{94} +(-26.0749 + 15.0543i) q^{95} +(8.10476 - 7.48188i) q^{96} +(6.66199 + 11.5389i) q^{97} +(2.89084 + 2.40542i) q^{98} +(-48.1417 - 101.281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.0664669	+	0.0383747i	0.0332335	+	0.0191873i	0.516525	−	0.856272i	$-0.327225\pi$
$2$	0.0664669	+	0.0383747i	0.0332335	+	0.0191873i	−0.483291	+	0.875460i	$0.660559\pi$
$3$	−2.92647	+	0.660129i	−0.975490	+	0.220043i
$3$	−2.92647	+	0.660129i	−0.975490	+	0.220043i
$4$	−1.99705	−	3.45900i	−0.499264	−	0.864750i
$5$		−	4.07697i		−	0.815393i	−0.913117	−	0.407697i	$-0.866332\pi$
$5$		−	4.07697i		−	0.815393i	0.913117	−	0.407697i	$-0.133668\pi$
$6$	−0.219846	−	0.0684257i	−0.0366410	−	0.0114043i
$7$	−6.97461	−	0.595686i	−0.996373	−	0.0850980i
$7$	−6.97461	−	0.595686i	−0.996373	−	0.0850980i
$8$		−	0.613543i		−	0.0766929i
$9$	8.12846	−	3.86370i	0.903162	−	0.429300i
$10$	0.156452	−	0.270983i	0.0156452	−	0.0270983i
$11$		−	12.4600i		−	1.13273i	−0.824155	−	0.566365i	$-0.808349\pi$
$11$		−	12.4600i		−	1.13273i	0.824155	−	0.566365i	$-0.191651\pi$
$12$	8.12771	+	8.80435i	0.677309	+	0.733696i
$13$	−5.97803	+	10.3542i	−0.459848	+	0.796480i	−0.998953	−	0.0457586i	$-0.985429\pi$
$13$	−5.97803	+	10.3542i	−0.459848	+	0.796480i	0.539104	+	0.842239i	$0.318763\pi$
$14$	−0.440721	−	0.307242i	−0.0314801	−	0.0219458i
$15$	2.69132	+	11.9311i	0.179422	+	0.795408i
$16$	−7.96467	+	13.7952i	−0.497792	+	0.862201i
$17$	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	$0.505406\pi$
$18$	0.688542	+	0.0551192i	0.0382523	+	0.00306218i
$19$	−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
$21$	20.8042	−	2.86088i	0.990677	−	0.136232i
$22$	0.478149	−	0.828179i	0.0217341	−	0.0376445i
$23$		−	27.9212i		−	1.21397i	−0.794715	−	0.606983i	$-0.792380\pi$
$23$		−	27.9212i		−	1.21397i	0.794715	−	0.606983i	$-0.207620\pi$
$24$	0.405017	+	1.79552i	0.0168757	+	0.0748131i
$25$	8.37834			0.335134
$26$	−0.794682	+	0.458810i	−0.0305647	+	0.0176465i
$27$	−21.2372	+	16.6728i	−0.786561	+	0.617512i
$28$	11.8682	+	25.3148i	0.423864	+	0.904100i
$29$	32.2098	−	18.5963i	1.11068	−	0.641253i	0.171676	−	0.985153i	$-0.445082\pi$
$29$	32.2098	−	18.5963i	1.11068	−	0.641253i	0.939006	+	0.343901i	$0.111748\pi$
$30$	−0.278969	+	0.896304i	−0.00929897	+	0.0298768i
$31$	−16.2794	−	28.1968i	−0.525143	−	0.909574i	−0.999571	−	0.0292800i	$-0.990679\pi$
$31$	−16.2794	−	28.1968i	−0.525143	−	0.909574i	0.474428	−	0.880294i	$-0.342655\pi$
$32$	−3.18415	+	1.83837i	−0.0995047	+	0.0574491i
$33$	8.22522	+	36.4639i	0.249249	+	1.10497i
$34$	0.633085	+	1.09653i	0.0186201	+	0.0322510i
$35$	−2.42859	+	28.4352i	−0.0693884	+	0.812436i
$36$	−29.5975	−	20.4003i	−0.822153	−	0.566676i
$37$	−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	$0.923779\pi$
$38$		−	0.566800i		−	0.0149158i
$39$	10.6594	−	34.2477i	0.273317	−	0.878145i
$40$	−2.50139			−0.0625349
$41$	−26.1324	−	15.0876i	−0.637376	−	0.367989i	0.146227	−	0.989251i	$-0.453287\pi$
$41$	−26.1324	−	15.0876i	−0.637376	−	0.367989i	−0.783603	+	0.621262i	$0.786620\pi$
$42$	1.49258	+	0.608201i	0.0355376	+	0.0144810i
$43$	−12.7866	−	22.1470i	−0.297362	−	0.515046i	0.678170	−	0.734906i	$-0.262774\pi$
$43$	−12.7866	−	22.1470i	−0.297362	−	0.515046i	−0.975532	+	0.219859i	$0.929440\pi$
$44$	−43.0992	+	24.8833i	−0.979528	+	0.565531i
$45$	−15.7522	−	33.1395i	−0.350048	−	0.736432i
$46$	1.07147	−	1.85584i	0.0232928	−	0.0403443i
$47$	68.4306	+	39.5084i	1.45597	+	0.840604i	0.998810	−	0.0487800i	$-0.0155333\pi$
$47$	68.4306	+	39.5084i	1.45597	+	0.840604i	0.457160	+	0.889384i	$0.348867\pi$
$48$	14.2018	−	45.6290i	0.295870	−	0.950605i
$49$	48.2903	+	8.30936i	0.985517	+	0.169579i
$50$	0.556883	+	0.321516i	0.0111377	+	0.00643033i
$51$	−47.2563	−	14.7083i	−0.926595	−	0.288397i
$52$	47.7538			0.918342
$53$	−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	$0.900799\pi$
$54$	−2.05138	+	0.293222i	−0.0379886	+	0.00543003i
$55$	−50.7991			−0.923620
$56$	−0.365479	+	4.27922i	−0.00652641	+	0.0764147i
$57$	15.0281	+	16.2792i	0.263650	+	0.285599i
$58$	2.85451			0.0492158
$59$	−37.3341	+	21.5548i	−0.632781	+	0.365336i	−0.781828	−	0.623494i	$-0.785713\pi$
$59$	−37.3341	+	21.5548i	−0.632781	+	0.365336i	0.149047	+	0.988830i	$0.452379\pi$
$60$	35.8950	−	33.1364i	0.598251	−	0.552273i
$61$	11.2361	−	19.4616i	0.184199	−	0.319042i	−0.759107	−	0.650966i	$-0.774364\pi$
$61$	11.2361	−	19.4616i	0.184199	−	0.319042i	0.943306	+	0.331923i	$0.107698\pi$
$62$		−	2.49887i		−	0.0403044i
$63$	−58.9944	+	22.1058i	−0.936419	+	0.350885i
$64$	63.4352			0.991175
$65$	42.2139	+	24.3722i	0.649445	+	0.374957i
$66$	−0.852585	+	2.73928i	−0.0129180	+	0.0415043i
$67$	43.0738	+	74.6061i	0.642893	+	1.11352i	0.984784	+	0.173784i	$0.0555993\pi$
$67$	43.0738	+	74.6061i	0.642893	+	1.11352i	−0.341891	+	0.939740i	$0.611067\pi$
$68$		−	65.8926i		−	0.969009i
$69$	18.4316	+	81.7106i	0.267125	+	1.18421i
$70$	−1.25261	+	1.79681i	−0.0178945	+	0.0256687i
$71$			102.757i			1.44728i	0.690179	+	0.723639i	$0.257532\pi$
$71$			102.757i			1.44728i	−0.690179	+	0.723639i	$0.742468\pi$
$72$	−2.37054	−	4.98716i	−0.0329242	−	0.0692661i
$73$	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	$0.164906\pi$
$74$		−	1.59216i		−	0.0215157i
$75$	−24.5190	+	5.53079i	−0.326920	+	0.0737438i
$76$	−14.7484	+	25.5450i	−0.194058	+	0.336118i
$77$	−7.42226	+	86.9038i	−0.0963930	+	1.12862i
$78$	2.02274	−	1.86729i	0.0259326	−	0.0239396i
$79$	13.5256	−	23.4270i	0.171210	−	0.296544i	−0.767633	−	0.640889i	$-0.778566\pi$
$79$	13.5256	−	23.4270i	0.171210	−	0.296544i	0.938843	+	0.344345i	$0.111899\pi$
$80$	56.2427	+	32.4717i	0.703033	+	0.405896i
$81$	51.1437	−	62.8118i	0.631404	−	0.775454i
$82$	−1.15796	−	2.00565i	−0.0141215	−	0.0244591i
$83$	36.4392	−	21.0382i	0.439027	−	0.253472i	−0.264158	−	0.964479i	$-0.585094\pi$
$83$	36.4392	−	21.0382i	0.439027	−	0.253472i	0.703185	+	0.711007i	$0.251761\pi$
$84$	−51.4429	−	66.2484i	−0.612416	−	0.788672i
$85$	33.6298	−	58.2485i	0.395644	−	0.685276i
$86$		−	1.96272i		−	0.0228224i
$87$	−81.9850	+	75.6842i	−0.942356	+	0.869934i
$88$	−7.64476			−0.0868723
$89$	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	$0.257928\pi$
$90$	0.224719	−	2.80716i	0.00249688	−	0.0311907i
$91$	47.8623	−	68.6558i	0.525959	−	0.754459i
$92$	−96.5795	+	55.7602i	−1.04978	+	0.606089i
$93$	66.2548	+	71.7706i	0.712417	+	0.771727i
$94$	3.03225	+	5.25200i	0.0322579	+	0.0558724i
$95$	−26.0749	+	15.0543i	−0.274473	+	0.158467i
$96$	8.10476	−	7.48188i	0.0844246	−	0.0779363i
$97$	6.66199	+	11.5389i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$97$	6.66199	+	11.5389i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$98$	2.89084	+	2.40542i	0.0294984	+	0.0245451i
$99$	−48.1417	−	101.281i	−0.486280	−	1.02304i
$100$	−16.7320	−	28.9807i	−0.167320	−	0.289807i
$101$		−	159.540i		−	1.57960i	−0.613362	−	0.789802i	$-0.710183\pi$
$101$		−	159.540i		−	1.57960i	0.613362	−	0.789802i	$-0.289817\pi$
$102$	−2.57656	−	2.79106i	−0.0252604	−	0.0273633i
$103$	−178.247			−1.73055			−0.865274	−	0.501299i	$-0.832856\pi$
$103$	−178.247			−1.73055			−0.865274	+	0.501299i	$0.832856\pi$
$104$	6.35277	+	3.66778i	0.0610844	+	0.0352671i
$105$	−11.6637	−	84.8181i	−0.111083	−	0.807791i
$106$	−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	$0.156575\pi$
$108$	100.083	+	40.1628i	0.926695	+	0.371878i
$109$	−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	$0.788943\pi$
$110$	−3.37646	−	1.94940i	−0.0306951	−	0.0177218i
$111$	42.2143	+	45.7287i	0.380309	+	0.411970i
$112$	63.7681	−	91.4718i	0.569358	−	0.816713i
$113$	36.2418	+	20.9242i	0.320724	+	0.185170i	0.651715	−	0.758464i	$-0.274050\pi$
$113$	36.2418	+	20.9242i	0.320724	+	0.185170i	−0.330991	+	0.943634i	$0.607383\pi$
$114$	0.374161	+	1.65872i	0.00328211	+	0.0145502i
$115$	−113.834			−0.989860
$116$	−128.649	−	74.2758i	−1.10905	−	0.640308i
$117$	−8.58649	+	107.261i	−0.0733888	+	0.916764i
$118$	−3.30864			−0.0280393
$119$	−94.7341	−	66.0423i	−0.796084	−	0.554978i
$120$	7.32026	−	1.65124i	0.0610021	−	0.0137604i
$121$	−34.2521			−0.283075
$122$	1.49366	−	0.862367i	0.0122431	−	0.00706858i
$123$	86.4355	+	26.9025i	0.702728	+	0.218720i
$124$	−65.0218	+	112.621i	−0.524369	+	0.908235i
$125$		−	136.082i		−	1.08866i
$126$	−4.76948	−	0.794590i	−0.0378530	−	0.00630627i
$127$	84.6221			0.666316			0.333158	−	0.942871i	$-0.391886\pi$
$127$	84.6221			0.666316			0.333158	+	0.942871i	$0.391886\pi$
$128$	16.9529	+	9.78779i	0.132445	+	0.0764671i
$129$	52.0394	+	56.3717i	0.403406	+	0.436990i
$130$	1.87055	+	3.23989i	0.0143889	+	0.0249222i
$131$		−	187.107i		−	1.42830i	−0.699993	−	0.714149i	$-0.746814\pi$
$131$		−	187.107i		−	1.42830i	0.699993	−	0.714149i	$-0.253186\pi$
$132$	109.702	−	101.271i	0.831079	−	0.767208i
$133$	21.9442	+	46.8068i	0.164994	+	0.351931i
$134$			6.61178i			0.0493416i
$135$	67.9745	+	86.5832i	0.503515	+	0.641357i
$136$	5.06095	−	8.76582i	0.0372129	−	0.0644546i
$137$			58.0532i			0.423746i	0.977297	+	0.211873i	$0.0679563\pi$
$137$			58.0532i			0.423746i	−0.977297	+	0.211873i	$0.932044\pi$
$138$	−1.91053	+	6.13836i	−0.0138444	+	0.0444809i
$139$	18.1886	−	31.5036i	0.130853	−	0.226645i	−0.793152	−	0.609023i	$-0.791562\pi$
$139$	18.1886	−	31.5036i	0.130853	−	0.226645i	0.924006	+	0.382379i	$0.124895\pi$
$140$	103.208	−	48.3862i	0.737197	−	0.345616i
$141$	−226.341	−	70.4472i	−1.60525	−	0.499625i
$142$	−3.94326	+	6.82992i	−0.0277694	+	0.0480980i
$143$	129.014	+	74.4863i	0.902196	+	0.520883i
$144$	−11.4400	+	142.907i	−0.0794444	+	0.992410i
$145$	−75.8166	−	131.318i	−0.522873	−	0.905643i
$146$	0.0536684	−	0.0309855i	0.000367592	−	0.000212229i
$147$	−146.805	+	7.56075i	−0.998676	+	0.0514337i
$148$	−41.4287	+	71.7566i	−0.279924	+	0.484842i
$149$		−	23.2671i		−	0.156155i	−0.996947	−	0.0780776i	$-0.975122\pi$
$149$		−	23.2671i		−	0.156155i	0.996947	−	0.0780776i	$-0.0248782\pi$
$150$	−1.84194	−	0.573294i	−0.0122796	−	0.00382196i
$151$	59.2739			0.392542			0.196271	−	0.980550i	$-0.437117\pi$
$151$	59.2739			0.392542			0.196271	+	0.980550i	$0.437117\pi$
$152$	−3.92401	+	2.26553i	−0.0258159	+	0.0149048i
$153$	148.004	+	11.8480i	0.967344	+	0.0774378i
$154$	−3.82824	+	5.49140i	−0.0248587	+	0.0356584i
$155$	−114.957	+	66.3707i	−0.741661	+	0.428198i
$156$	−139.750	+	31.5237i	−0.895834	+	0.202075i
$157$	−47.1962	−	81.7463i	−0.300613	−	0.520677i	0.675662	−	0.737212i	$-0.263858\pi$
$157$	−47.1962	−	81.7463i	−0.300613	−	0.520677i	−0.976275	+	0.216535i	$0.930525\pi$
$158$	1.79800	−	1.03808i	0.0113798	−	0.00657011i
$159$	203.736	+	63.4117i	1.28136	+	0.398815i
$160$	7.49497	+	12.9817i	0.0468436	+	0.0811355i
$161$	−16.6323	+	194.740i	−0.103306	+	1.20956i
$162$	5.80975	−	2.21228i	0.0358626	−	0.0136561i
$163$	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	$0.756703\pi$
$164$			120.523i			0.734895i
$165$	148.662	−	33.5339i	0.900982	−	0.203236i
$166$	3.22934			0.0194538
$167$	165.547	+	95.5786i	0.991300	+	0.572327i	0.905662	−	0.423999i	$-0.139374\pi$
$167$	165.547	+	95.5786i	0.991300	+	0.572327i	0.0856370	+	0.996326i	$0.472707\pi$
$168$	−1.75527	−	12.7643i	−0.0104481	−	0.0759779i
$169$	13.0264	+	22.5624i	0.0770794	+	0.133505i
$170$	4.47054	−	2.58106i	0.0262973	−	0.0151827i
$171$	−54.7255	−	37.7200i	−0.320032	−	0.220585i
$172$	−51.0710	+	88.4575i	−0.296924	+	0.514288i
$173$	24.1853	+	13.9634i	0.139800	+	0.0807134i	0.568269	−	0.822843i	$-0.307613\pi$
$173$	24.1853	+	13.9634i	0.139800	+	0.0807134i	−0.428469	+	0.903557i	$0.640947\pi$
$174$	−8.35365	+	1.88435i	−0.0480095	+	0.0108296i
$175$	−58.4357	−	4.99087i	−0.333918	−	0.0285192i
$176$	171.889	+	99.2400i	0.976641	+	0.563864i
$177$	95.0281	−	87.7249i	0.536882	−	0.495621i
$178$	3.20610			0.0180118
$179$	−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	$0.717297\pi$
$180$	−83.1715	+	120.668i	−0.462064	+	0.670378i
$181$	81.8315			0.452108			0.226054	−	0.974115i	$-0.427417\pi$
$181$	81.8315			0.452108			0.226054	+	0.974115i	$0.427417\pi$
$182$	5.81590	−	2.72664i	0.0319555	−	0.0149815i
$183$	−20.0351	+	64.3710i	−0.109481	+	0.351754i
$184$	−17.1309			−0.0931025
$185$	−73.2452	+	42.2881i	−0.395920	+	0.228584i
$186$	1.64958	+	7.31288i	0.00886870	+	0.0393165i
$187$	102.779	−	178.019i	0.549622	−	0.951973i
$188$		−	315.602i		−	1.67873i
$189$	158.053	−	103.636i	0.836257	−	0.548337i
$190$	−2.31082			−0.0121622
$191$	−141.509	−	81.7002i	−0.740884	−	0.427750i	0.0815066	−	0.996673i	$-0.474027\pi$
$191$	−141.509	−	81.7002i	−0.740884	−	0.427750i	−0.822391	+	0.568923i	$0.807360\pi$
$192$	−185.641	+	41.8754i	−0.966882	+	0.218101i
$193$	163.421	+	283.053i	0.846740	+	1.46660i	0.884102	+	0.467295i	$0.154771\pi$
$193$	163.421	+	283.053i	0.846740	+	1.46660i	−0.0373615	+	0.999302i	$0.511895\pi$
$194$			1.02261i			0.00527117i
$195$	−139.627	−	43.4579i	−0.716034	−	0.222861i
$196$	−67.6963	−	183.630i	−0.345389	−	0.936890i
$197$		−	262.028i		−	1.33009i	−0.746802	−	0.665046i	$-0.768412\pi$
$197$		−	262.028i		−	1.33009i	0.746802	−	0.665046i	$-0.231588\pi$
$198$	0.686786	−	8.57924i	0.00346862	−	0.0433295i
$199$	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	$0.0857609\pi$
$200$		−	5.14047i		−	0.0257024i
$201$	−175.304	−	189.898i	−0.872159	−	0.944767i
$202$	6.12230	−	10.6041i	0.0303084	−	0.0524957i
$203$	−235.728	+	110.515i	−1.16122	+	0.544410i
$204$	43.4976	+	192.833i	0.213224	+	0.945259i
$205$	−61.5115	+	106.541i	−0.300056	+	0.519712i
$206$	−11.8475	−	6.84015i	−0.0575121	−	0.0332046i
$207$	−107.879	−	226.956i	−0.521155	−	1.09641i
$208$	−95.2261	−	164.936i	−0.457818	−	0.792963i
$209$	−79.6901	+	46.0091i	−0.381292	+	0.220139i
$210$	2.47962	−	6.08519i	0.0118077	−	0.0289771i
$211$	124.345	−	215.372i	0.589312	−	1.02072i	−0.405010	−	0.914312i	$-0.632732\pi$
$211$	124.345	−	215.372i	0.589312	−	1.02072i	0.994323	−	0.106407i	$-0.0339345\pi$
$212$			284.083i			1.34001i
$213$	−67.8327	−	300.714i	−0.318463	−	1.41180i
$214$	8.65894			0.0404623
$215$	−90.2925	+	52.1304i	−0.419965	+	0.242467i
$216$	10.2295	+	13.0299i	0.0473588	+	0.0603237i
$217$	96.7462	+	206.359i	0.445835	+	0.950963i
$218$	−13.4338	+	7.75599i	−0.0616228	+	0.0355779i
$219$	−0.719876	+	2.31290i	−0.00328710	+	0.0105612i
$220$	101.449	+	175.714i	0.461130	+	0.798700i
$221$	−170.819	+	98.6222i	−0.772935	+	0.446254i
$222$	1.05103	+	4.65940i	0.00473437	+	0.0209883i
$223$	−6.13684	−	10.6293i	−0.0275195	−	0.0476651i	0.851938	−	0.523643i	$-0.175427\pi$
$223$	−6.13684	−	10.6293i	−0.0275195	−	0.0476651i	−0.879457	+	0.475978i	$0.842094\pi$
$224$	23.3033	−	10.9252i	0.104033	−	0.0487730i
$225$	68.1030	−	32.3714i	0.302680	−	0.143873i
$226$	1.60592	+	2.78153i	0.00710584	+	0.0123077i
$227$			16.8502i			0.0742298i	0.999311	+	0.0371149i	$0.0118167\pi$
$227$			16.8502i			0.0742298i	−0.999311	+	0.0371149i	$0.988183\pi$
$228$	26.2978	−	84.4925i	0.115341	−	0.370581i
$229$	112.292			0.490358			0.245179	−	0.969478i	$-0.421153\pi$
$229$	112.292			0.490358			0.245179	+	0.969478i	$0.421153\pi$
$230$	−7.56618	−	4.36834i	−0.0328965	−	0.0189928i
$231$	−35.6467	−	259.221i	−0.154315	−	1.12217i
$232$	−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	$0.234617\pi$
$234$	−4.68684	+	6.79983i	−0.0200292	+	0.0290591i
$235$	161.074	−	278.989i	0.685423	−	1.18719i
$236$	149.116	+	86.0924i	0.631849	+	0.364798i
$237$	−24.1173	+	77.4869i	−0.101761	+	0.326949i
$238$	−3.76233	−	8.02502i	−0.0158081	−	0.0337186i
$239$	205.534	+	118.665i	0.859975	+	0.496507i	0.864004	−	0.503485i	$-0.167949\pi$
$239$	205.534	+	118.665i	0.859975	+	0.496507i	−0.00402865	+	0.999992i	$0.501282\pi$
$240$	−186.028	−	57.9001i	−0.775117	−	0.241250i
$241$	158.093			0.655989			0.327995	−	0.944680i	$-0.393627\pi$
$241$	158.093			0.655989			0.327995	+	0.944680i	$0.393627\pi$
$242$	−2.27663	−	1.31441i	−0.00940757	−	0.00543146i
$243$	−108.207	+	217.578i	−0.445295	+	0.895384i
$244$	−89.7568			−0.367856
$245$	33.8770	−	196.878i	0.138273	−	0.803584i
$246$	4.71273	+	5.10507i	0.0191574	+	0.0207523i
$247$	88.2963			0.357475
$248$	−17.2999	+	9.98813i	−0.0697578	+	0.0402747i
$249$	−92.7504	+	85.6223i	−0.372492	+	0.343864i
$250$	5.22212	−	9.04498i	0.0208885	−	0.0361799i
$251$			462.619i			1.84310i	0.388254	+	0.921552i	$0.373078\pi$
$251$			462.619i			1.84310i	−0.388254	+	0.921552i	$0.626922\pi$
$252$	194.279	+	159.915i	0.770948	+	0.634584i
$253$	−347.899			−1.37509
$254$	5.62457	+	3.24735i	0.0221440	+	0.0127848i
$255$	−59.9650	+	192.662i	−0.235157	+	0.755539i
$256$	−126.119	−	218.445i	−0.492653	−	0.853300i
$257$			114.845i			0.446866i	0.974719	+	0.223433i	$0.0717264\pi$
$257$			114.845i			0.446866i	−0.974719	+	0.223433i	$0.928274\pi$
$258$	1.29565	+	5.74385i	0.00502190	+	0.0222630i
$259$	61.6419	+	131.482i	0.238000	+	0.507652i
$260$		−	194.691i		−	0.748810i
$261$	189.965	−	275.608i	0.727837	−	1.05597i
$262$	7.18018	−	12.4364i	0.0274053	−	0.0474673i
$263$			33.8272i			0.128620i	0.997930	+	0.0643102i	$0.0204847\pi$
$263$			33.8272i			0.128620i	−0.997930	+	0.0643102i	$0.979515\pi$
$264$	22.3722	−	5.04653i	0.0847430	−	0.0191156i
$265$	−144.988	+	251.127i	−0.547125	+	0.947648i
$266$	−0.337635	+	3.95321i	−0.00126930	+	0.0148617i
$267$	−92.0829	+	85.0060i	−0.344880	+	0.318375i
$268$	172.042	−	297.985i	0.641946	−	1.11188i
$269$	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	$0.636778\pi$
$270$	1.19546	+	8.36342i	0.00442761	+	0.0309756i
$271$	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
$273$	−94.7459	+	232.514i	−0.347054	+	0.851701i
$274$	−2.22777	+	3.85861i	−0.00813056	+	0.0140825i
$275$		−	104.394i		−	0.379616i
$276$	245.828	−	226.935i	0.890681	−	0.822230i
$277$	−78.4785			−0.283316			−0.141658	−	0.989916i	$-0.545243\pi$
$277$	−78.4785			−0.283316			−0.141658	+	0.989916i	$0.545243\pi$
$278$	2.41788	−	1.39597i	0.00869742	−	0.00502146i
$279$	−241.271	−	166.298i	−0.864769	−	0.596049i
$280$	17.4462	+	1.49005i	0.0623080	+	0.00532159i
$281$	−124.764	+	72.0327i	−0.444001	+	0.256344i	−0.705293	−	0.708916i	$-0.749185\pi$
$281$	−124.764	+	72.0327i	−0.444001	+	0.256344i	0.261292	+	0.965260i	$0.415851\pi$
$282$	−12.3408	−	13.3682i	−0.0437616	−	0.0474048i
$283$	−98.9771	−	171.433i	−0.349743	−	0.605772i	0.636461	−	0.771309i	$-0.280398\pi$
$283$	−98.9771	−	171.433i	−0.349743	−	0.605772i	−0.986204	+	0.165537i	$0.947064\pi$
$284$	355.435	−	205.211i	1.25153	−	0.722573i
$285$	66.3696	−	61.2689i	0.232876	−	0.214979i
$286$	5.71678	+	9.90175i	0.0199887	+	0.0346215i
$287$	173.276	+	120.797i	0.603749	+	0.420894i
$288$	−18.7793	+	27.2457i	−0.0652060	+	0.0946031i
$289$	−8.41704	−	14.5787i	−0.0291247	−	0.0504455i
$290$		−	11.6378i		−	0.0401302i
$291$	−27.1133	−	29.3705i	−0.0931728	−	0.100930i
$292$	−3.22503			−0.0110446
$293$	−248.893	−	143.698i	−0.849463	−	0.490438i	0.0110067	−	0.999939i	$-0.496496\pi$
$293$	−248.893	−	143.698i	−0.849463	−	0.490438i	−0.860470	+	0.509502i	$0.829830\pi$
$294$	−10.0478	−	5.13107i	−0.0341763	−	0.0174526i
$295$	87.8784	+	152.210i	0.297893	+	0.515966i
$296$	−11.0227	+	6.36394i	−0.0372388	+	0.0214998i
$297$	207.744	+	264.615i	0.699474	+	0.890961i
$298$	0.892869	−	1.54649i	0.00299620	−	0.00518958i
$299$	289.103	+	166.914i	0.966900	+	0.558240i
$300$	68.0967	+	73.7659i	0.226989	+	0.245886i
$301$	75.9887	+	162.083i	0.252454	+	0.538483i
$302$	3.93975	+	2.27462i	0.0130455	+	0.00753185i
$303$	105.317	+	466.889i	0.347581	+	1.54089i
$304$	117.639			0.386972
$305$	−79.3442	−	45.8094i	−0.260145	−	0.150195i
$306$	9.38268	+	6.46709i	0.0306624	+	0.0211343i
$307$	93.1935			0.303562			0.151781	−	0.988414i	$-0.451499\pi$
$307$	93.1935			0.303562			0.151781	+	0.988414i	$0.451499\pi$
$308$	315.423	−	147.878i	1.02410	−	0.480123i
$309$	521.633	−	117.666i	1.68813	−	0.380795i
$310$	−10.1878			−0.0328639
$311$	−5.49869	+	3.17467i	−0.0176807	+	0.0102080i	−0.508814	−	0.860876i	$-0.669916\pi$
$311$	−5.49869	+	3.17467i	−0.0176807	+	0.0102080i	0.491134	+	0.871084i	$0.336583\pi$
$312$	−21.0124	−	6.53999i	−0.0673475	−	0.0209615i
$313$	−228.959	+	396.568i	−0.731497	+	1.26699i	0.224746	+	0.974417i	$0.427845\pi$
$313$	−228.959	+	396.568i	−0.731497	+	1.26699i	−0.956243	+	0.292572i	$0.905489\pi$
$314$		−	7.24457i		−	0.0230719i
$315$	90.1244	+	240.518i	0.286109	+	0.763549i
$316$	−108.045			−0.341915
$317$	−446.511	−	257.793i	−1.40855	−	0.813227i	−0.413303	−	0.910594i	$-0.635625\pi$
$317$	−446.511	−	257.793i	−1.40855	−	0.813227i	−0.995249	+	0.0973664i	$0.968958\pi$
$318$	11.1083	+	12.0331i	0.0349318	+	0.0378399i
$319$	−231.711	−	401.335i	−0.726366	−	1.25810i
$320$		−	258.623i		−	0.808198i
$321$	−248.695	+	229.582i	−0.774750	+	0.715209i
$322$	−8.57857	+	12.3055i	−0.0266415	+	0.0382158i
$323$		−	121.835i		−	0.377198i
$324$	−319.403	−	51.4675i	−0.985811	−	0.158850i
$325$	−50.0860	+	86.7514i	−0.154111	+	0.266927i
$326$			5.96540i			0.0182988i
$327$	180.192	−	578.943i	0.551047	−	1.77047i
$328$	−9.25687	+	16.0334i	−0.0282222	+	0.0488822i
$329$	−453.742	−	316.319i	−1.37915	−	0.961455i
$330$	11.1680	+	3.47596i	0.0338423	+	0.0105332i
$331$	−148.627	+	257.430i	−0.449026	+	0.777735i	−0.998323	−	0.0578919i	$-0.981562\pi$
$331$	−148.627	+	257.430i	−0.449026	+	0.777735i	0.549297	+	0.835627i	$0.314895\pi$
$332$	−145.542	−	84.0289i	−0.438380	−	0.253099i
$333$	−153.726	−	105.957i	−0.461639	−	0.318188i
$334$	7.33560	+	12.7056i	0.0219629	+	0.0380408i
$335$	304.166	−	175.611i	0.907959	−	0.524211i
$336$	−126.232	+	309.785i	−0.375691	+	0.921978i
$337$	−57.4915	+	99.5781i	−0.170598	+	0.295484i	−0.938629	−	0.344928i	$-0.887903\pi$
$337$	−57.4915	+	99.5781i	−0.170598	+	0.295484i	0.768031	+	0.640412i	$0.221237\pi$
$338$			1.99954i			0.00591579i
$339$	−119.873	−	37.3098i	−0.353608	−	0.110058i
$340$	−268.642			−0.790124
$341$	−351.333	+	202.842i	−1.03030	+	0.594845i
$342$	−2.18994	−	4.60721i	−0.00640334	−	0.0134714i
$343$	−331.856	−	86.7204i	−0.967511	−	0.252829i
$344$	−13.5881	+	7.84511i	−0.0395004	+	0.0228056i
$345$	333.131	−	75.1450i	0.965598	−	0.217812i
$346$	1.07168	+	1.85621i	0.00309735	+	0.00536477i
$347$	392.871	−	226.824i	1.13219	−	0.653672i	0.187708	−	0.982225i	$-0.439894\pi$
$347$	392.871	−	226.824i	1.13219	−	0.653672i	0.944486	+	0.328553i	$0.106561\pi$
$348$	425.520	+	132.441i	1.22276	+	0.380577i
$349$	−262.257	−	454.242i	−0.751452	−	1.30155i	−0.947119	−	0.320882i	$-0.896021\pi$
$349$	−262.257	−	454.242i	−0.751452	−	1.30155i	0.195668	−	0.980670i	$-0.437313\pi$
$350$	−3.69252	−	2.57418i	−0.0105500	−	0.00735480i
$351$	−45.6782	−	319.565i	−0.130137	−	0.910443i
$352$	22.9061	+	39.6746i	0.0650742	+	0.112712i
$353$		−	505.529i		−	1.43209i	−0.698052	−	0.716047i	$-0.745949\pi$
$353$		−	505.529i		−	1.43209i	0.698052	−	0.716047i	$-0.254051\pi$
$354$	9.68264	−	2.18413i	0.0273521	−	0.00616986i
$355$	418.935			1.18010
$356$	−144.495	−	83.4241i	−0.405884	−	0.234337i
$357$	320.833	+	130.734i	0.898692	+	0.366202i
$358$	−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	$0.311060\pi$
$360$	−20.3325	+	9.66463i	−0.0564791	+	0.0268462i
$361$	153.230	−	265.403i	0.424461	−	0.735188i
$362$	5.43909	+	3.14026i	0.0150251	+	0.00867475i
$363$	100.238	−	22.6108i	0.276137	−	0.0622887i
$364$	−333.064	−	28.4463i	−0.915011	−	0.0781491i
$365$	−2.85089	−	1.64596i	−0.00781067	−	0.00450949i
$366$	−3.80189	+	3.50970i	−0.0103877	+	0.00958935i
$367$	−594.479			−1.61983			−0.809917	−	0.586545i	$-0.800488\pi$
$367$	−594.479			−1.61983			−0.809917	+	0.586545i	$0.800488\pi$
$368$	385.179	+	222.383i	1.04668	+	0.604303i
$369$	−270.710	−	21.6709i	−0.733632	−	0.0587287i
$370$	−6.49118			−0.0175437
$371$	408.427	+	284.728i	1.10088	+	0.767461i
$372$	115.940	−	372.505i	0.311667	−	1.00136i
$373$	−609.271			−1.63344			−0.816718	−	0.577038i	$-0.804209\pi$
$373$	−609.271			−1.63344			−0.816718	+	0.577038i	$0.804209\pi$
$374$	13.6628	−	7.88825i	0.0365317	−	0.0210916i
$375$	89.8319	+	398.241i	0.239552	+	1.06198i
$376$	24.2401	−	41.9851i	0.0644684	−	0.111662i
$377$			444.677i			1.17952i
$378$	14.4823	−	0.823126i	0.0383129	−	0.00217758i
$379$	468.439			1.23599			0.617994	−	0.786183i	$-0.287946\pi$
$379$	468.439			1.23599			0.617994	+	0.786183i	$0.287946\pi$
$380$	104.146	+	60.1287i	0.274068	+	0.158233i
$381$	−247.644	+	55.8615i	−0.649985	+	0.146618i
$382$	−6.27044	−	10.8607i	−0.0164148	−	0.0284312i
$383$		−	439.378i		−	1.14720i	−0.819136	−	0.573600i	$-0.805546\pi$
$383$		−	439.378i		−	1.14720i	0.819136	−	0.573600i	$-0.194454\pi$
$384$	−56.0735	−	17.4525i	−0.146025	−	0.0454493i
$385$	354.304	+	30.2603i	0.920269	+	0.0785982i
$386$			25.0849i			0.0649868i
$387$	−189.504	−	130.617i	−0.489675	−	0.337513i
$388$	26.6087	−	46.0877i	0.0685792	−	0.118783i
$389$			265.619i			0.682825i	0.939914	+	0.341412i	$0.110905\pi$
$389$			265.619i			0.682825i	−0.939914	+	0.341412i	$0.889095\pi$
$390$	−7.61286	−	8.24664i	−0.0195202	−	0.0211452i
$391$	230.314	−	398.916i	0.589039	−	1.02025i
$392$	5.09815	−	29.6282i	0.0130055	−	0.0755821i
$393$	123.515	+	547.564i	0.314287	+	1.39329i
$394$	10.0553	−	17.4162i	0.0255209	−	0.0442036i
$395$	−95.5109	−	55.1432i	−0.241800	−	0.139603i
$396$	−254.189	+	368.786i	−0.641890	+	0.931277i
$397$	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
$399$	−95.1176	−	122.493i	−0.238390	−	0.307000i
$400$	−66.7308	+	115.581i	−0.166827	+	0.288953i
$401$			184.898i			0.461091i	0.973062	+	0.230546i	$0.0740511\pi$
$401$			184.898i			0.461091i	−0.973062	+	0.230546i	$0.925949\pi$
$402$	−4.36463	−	19.3492i	−0.0108573	−	0.0481323i
$403$	389.275			0.965944
$404$	−551.849	+	318.610i	−1.36596	+	0.788639i
$405$	−256.082	−	208.511i	−0.632300	−	0.514842i
$406$	−19.9091	−	1.70039i	−0.0490372	−	0.00418816i
$407$	−223.852	+	129.241i	−0.550005	+	0.317545i
$408$	−9.02414	+	28.9938i	−0.0221180	+	0.0710632i
$409$	299.332	+	518.458i	0.731863	+	1.26762i	0.956086	+	0.293085i	$0.0946820\pi$
$409$	299.332	+	518.458i	0.731863	+	1.26762i	−0.224224	+	0.974538i	$0.571985\pi$
$410$	−8.17696	+	4.72097i	−0.0199438	+	0.0115146i
$411$	−38.3226	−	169.891i	−0.0932423	−	0.413360i
$412$	355.968	+	616.555i	0.864000	+	1.49649i
$413$	273.231	−	128.097i	0.661575	−	0.310163i
$414$	1.53899	−	19.2249i	0.00371738	−	0.0464370i
$415$	−85.7720	−	148.562i	−0.206680	−	0.357980i
$416$		−	43.9593i		−	0.105671i
$417$	−32.4320	+	104.201i	−0.0777746	+	0.249883i
$418$	−7.06234			−0.0168955
$419$	249.386	+	143.983i	0.595194	+	0.343635i	0.767148	−	0.641470i	$-0.221675\pi$
$419$	249.386	+	143.983i	0.595194	+	0.343635i	−0.171955	+	0.985105i	$0.555008\pi$
$420$	−270.093	+	209.731i	−0.643078	+	0.499360i
$421$	−52.7568	−	91.3775i	−0.125313	−	0.217049i	0.796542	−	0.604583i	$-0.206660\pi$
$421$	−52.7568	−	91.3775i	−0.125313	−	0.217049i	−0.921855	+	0.387534i	$0.873327\pi$
$422$	16.5296	−	9.54339i	0.0391698	−	0.0226147i
$423$	708.884	+	56.7476i	1.67585	+	0.134155i
$424$	−21.8193	+	37.7921i	−0.0514605	+	0.0891322i
$425$	119.703	+	69.1107i	0.281655	+	0.162613i
$426$	7.03119	−	22.5906i	0.0165051	−	0.0530296i
$427$	−89.9607	+	129.044i	−0.210681	+	0.302210i
$428$	−390.248	−	225.310i	−0.911793	−	0.526424i
$429$	−426.727	−	132.816i	−0.994701	−	0.309595i
$430$	−8.00195			−0.0186092
$431$	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	$0.566748\pi$
$432$	−60.8582	−	425.765i	−0.140876	−	0.985567i
$433$	−235.623			−0.544164			−0.272082	−	0.962274i	$-0.587712\pi$
$433$	−235.623			−0.544164			−0.272082	+	0.962274i	$0.587712\pi$
$434$	−1.48854	+	17.4287i	−0.00342982	+	0.0401582i
$435$	308.562	+	334.250i	0.709338	+	0.768391i
$436$	807.258			1.85151
$437$	−178.575	+	103.100i	−0.408638	+	0.235927i
$438$	−0.136605	+	0.126106i	−0.000311883	+	0.000287914i
$439$	313.706	−	543.354i	0.714592	−	1.23771i	−0.248525	−	0.968626i	$-0.579946\pi$
$439$	313.706	−	543.354i	0.714592	−	1.23771i	0.963117	−	0.269084i	$-0.0867209\pi$
$440$			31.1674i			0.0708350i
$441$	424.631	−	119.037i	0.962881	−	0.269925i
$442$	−15.1384			−0.0342497
$443$	401.440	+	231.772i	0.906186	+	0.523187i	0.879202	−	0.476449i	$-0.158076\pi$
$443$	401.440	+	231.772i	0.906186	+	0.523187i	0.0269838	+	0.999636i	$0.491410\pi$
$444$	73.8713	−	237.342i	0.166377	−	0.534554i
$445$	−85.1547	−	147.492i	−0.191359	−	0.331443i
$446$		−	0.941998i		−	0.00211210i
$447$	15.3593	+	68.0906i	0.0343609	+	0.152328i
$448$	−442.436	−	37.7875i	−0.987580	−	0.0843471i
$449$		−	584.536i		−	1.30186i	−0.759137	−	0.650931i	$-0.774379\pi$
$449$		−	584.536i		−	1.30186i	0.759137	−	0.650931i	$-0.225621\pi$
$450$	5.76884	+	0.461807i	0.0128196	+	0.00102624i
$451$	−187.991	+	325.611i	−0.416832	+	0.721975i
$452$		−	167.147i		−	0.369795i
$453$	−173.463	+	39.1284i	−0.382921	+	0.0863762i
$454$	−0.646619	+	1.11998i	−0.00142427	+	0.00246691i
$455$	−279.907	−	195.133i	−0.615181	−	0.428863i
$456$	9.98797	−	9.22036i	0.0219034	−	0.0202201i
$457$	207.017	−	358.563i	0.452991	−	0.784603i	−0.545580	−	0.838059i	$-0.683690\pi$
$457$	207.017	−	358.563i	0.452991	−	0.784603i	0.998570	+	0.0534563i	$0.0170238\pi$
$458$	7.46371	+	4.30917i	0.0162963	+	0.00940867i
$459$	−440.949	+	63.0287i	−0.960674	+	0.137317i
$460$	227.332	+	393.751i	0.494201	+	0.855981i
$461$	335.821	−	193.886i	0.728462	−	0.420578i	−0.0893972	−	0.995996i	$-0.528494\pi$
$461$	335.821	−	193.886i	0.728462	−	0.420578i	0.817859	+	0.575418i	$0.195161\pi$
$462$	7.57820	−	18.5975i	0.0164030	−	0.0402544i
$463$	−330.230	+	571.974i	−0.713239	+	1.23537i	0.250396	+	0.968143i	$0.419439\pi$
$463$	−330.230	+	571.974i	−0.713239	+	1.23537i	−0.963635	+	0.267222i	$0.913894\pi$
$464$			592.455i			1.27684i
$465$	292.606	−	270.119i	0.629261	−	0.580900i
$466$	10.9148			0.0234223
$467$	−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	$0.952476\pi$
$468$	388.165	−	184.506i	0.829412	−	0.394244i
$469$	−255.981	−	546.007i	−0.545802	−	1.16419i
$470$	21.4122	−	12.3624i	0.0455580	−	0.0263029i
$471$	192.082	+	208.073i	0.407816	+	0.441768i
$472$	13.2248	+	22.9061i	0.0280187	+	0.0485298i
$473$	−275.952	+	159.321i	−0.583408	+	0.336831i
$474$	−4.57654	+	4.22482i	−0.00965515	+	0.00891312i
$475$	−30.9373	−	53.5851i	−0.0651313	−	0.112811i
$476$	−39.2513	+	459.575i	−0.0824608	+	0.965494i
$477$	−638.088	−	51.0802i	−1.33771	−	0.107086i
$478$	9.10748	+	15.7746i	0.0190533	+	0.0330013i
$479$			148.188i			0.309369i	0.987964	+	0.154685i	$0.0494361\pi$
$479$			148.188i			0.309369i	−0.987964	+	0.154685i	$0.950564\pi$
$480$	−30.5034	−	33.0428i	−0.0635487	−	0.0688392i
$481$	248.027			0.515649
$482$	10.5080	+	6.06678i	0.0218008	+	0.0125867i
$483$	−79.8793	−	580.879i	−0.165382	−	1.20265i
$484$	68.4033	+	118.478i	0.141329	+	0.244789i
$485$	47.0437	−	27.1607i	0.0969974	−	0.0560015i
$486$	−15.5417	+	10.3094i	−0.0319787	+	0.0212127i
$487$	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	$0.123304\pi$
$488$	−11.9405	−	6.89386i	−0.0244683	−	0.0141268i
$489$	−158.166	−	171.333i	−0.323448	−	0.350375i
$490$	9.80683	−	11.7859i	0.0200139	−	0.0240528i
$491$	293.673	+	169.552i	0.598111	+	0.345320i	0.768298	−	0.640092i	$-0.221104\pi$
$491$	293.673	+	169.552i	0.598111	+	0.345320i	−0.170187	+	0.985412i	$0.554437\pi$
$492$	−79.5606	−	352.706i	−0.161708	−	0.716883i
$493$	613.584			1.24459
$494$	5.86878	+	3.38834i	0.0118801	+	0.00685900i
$495$	−412.918	+	196.272i	−0.834178	+	0.396510i
$496$	518.641			1.04565
$497$	61.2107	−	716.687i	0.123160	−	1.44203i
$498$	−9.45056	+	2.13178i	−0.0189770	+	0.00428068i
$499$	188.695			0.378147			0.189074	−	0.981963i	$-0.439452\pi$
$499$	188.695			0.378147			0.189074	+	0.981963i	$0.439452\pi$
$500$	−470.709	+	271.764i	−0.941418	+	0.543528i
$501$	−547.563	−	170.426i	−1.09294	−	0.340171i
$502$	−17.7529	+	30.7489i	−0.0353643	+	0.0612527i
$503$		−	400.956i		−	0.797130i	−0.917140	−	0.398565i	$-0.869508\pi$
$503$		−	400.956i		−	0.797130i	0.917140	−	0.398565i	$-0.130492\pi$
$504$	13.5628	+	36.1956i	0.0269104	+	0.0718166i
$505$	−650.439			−1.28800
$506$	−23.1238	−	13.3505i	−0.0456991	−	0.0263844i
$507$	−53.0155	−	57.4291i	−0.104567	−	0.113272i
$508$	−168.995	−	292.708i	−0.332667	−	0.576197i
$509$			701.173i			1.37755i	0.724975	+	0.688775i	$0.241851\pi$
$509$			701.173i			1.37755i	−0.724975	+	0.688775i	$0.758149\pi$
$510$	−11.3791	+	10.5045i	−0.0223119	+	0.0205971i
$511$	−3.23235	+	4.63663i	−0.00632554	+	0.00907364i
$512$		−	97.6614i		−	0.190745i
$513$	185.053	+	74.2607i	0.360727	+	0.144758i
$514$	−4.40712	+	7.63336i	−0.00857417	+	0.0148509i
$515$			726.705i			1.41108i
$516$	91.0643	−	292.582i	0.176481	−	0.567019i
$517$	492.276	−	852.646i	0.952177	−	1.64922i
$518$	−0.948427	+	11.1047i	−0.00183094	+	0.0214376i
$519$	−79.9953	−	24.8981i	−0.154134	−	0.0479732i
$520$	14.9534	−	25.9000i	0.0287565	−	0.0498078i
$521$	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	$0.471095\pi$
$522$	23.2028	−	11.0290i	0.0444498	−	0.0211283i
$523$	−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
$525$	174.305	−	23.9695i	0.332009	−	0.0456561i
$526$	−1.29811	+	2.24839i	−0.00246789	+	0.00427450i
$527$		−	537.138i		−	1.01924i
$528$	−568.539	−	176.954i	−1.07678	−	0.335141i
$529$	−250.594			−0.473713
$530$	−19.2738	+	11.1277i	−0.0363657	+	0.0209957i
$531$	−220.187	+	319.455i	−0.414665	+	0.601611i
$532$	118.081	−	169.381i	0.221957	−	0.318385i
$533$	312.441	−	180.388i	0.586193	−	0.338438i
$534$	−9.38254	+	2.11644i	−0.0175703	+	0.00396336i
$535$	−229.984	−	398.343i	−0.429876	−	0.744567i
$536$	45.7740	−	26.4276i	0.0853993	−	0.0493053i
$537$	162.427	+	50.5544i	0.302471	+	0.0941423i
$538$	1.93574	+	3.35280i	0.00359803	+	0.00623197i
$539$	103.535	−	601.698i	0.192087	−	1.11632i
$540$	163.742	−	408.035i	0.303227	−	0.755621i
$541$	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	$0.556114\pi$
$542$			31.2232i			0.0576074i
$543$	−239.477	+	54.0193i	−0.441027	+	0.0994831i
$544$	−60.6568			−0.111502
$545$	713.609	+	412.002i	1.30937	+	0.755967i
$546$	−15.2201	+	11.8187i	−0.0278757	+	0.0216459i
$547$	−131.228	−	227.294i	−0.239905	−	0.415528i	0.720782	−	0.693162i	$-0.243783\pi$
$547$	−131.228	−	227.294i	−0.239905	−	0.415528i	−0.960687	+	0.277634i	$0.910450\pi$
$548$	200.806	−	115.935i	0.366434	−	0.211561i
$549$	16.1389	−	201.606i	0.0293970	−	0.367223i
$550$	4.00610	−	6.93877i	0.00728382	−	0.0126159i
$551$	−237.872	−	137.335i	−0.431709	−	0.249247i
$552$	50.1330	−	11.3086i	0.0908206	−	0.0204866i
$553$	−108.291	+	155.337i	−0.195824	+	0.280898i
$554$	−5.21622	−	3.01159i	−0.00941556	−	0.00543608i
$555$	186.434	−	172.106i	0.335918	−	0.310101i
$556$	−145.295			−0.261321
$557$	−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	$0.688257\pi$
$558$	−9.65488	−	20.3120i	−0.0173027	−	0.0364014i
$559$	305.754			0.546966
$560$	−372.928	−	259.980i	−0.665942	−	0.464251i
$561$	−183.265	+	588.815i	−0.326676	+	1.04958i
$562$	−11.0569			−0.0196743
$563$	−106.720	+	61.6147i	−0.189556	+	0.109440i	−0.591775	−	0.806104i	$-0.701572\pi$
$563$	−106.720	+	61.6147i	−0.189556	+	0.109440i	0.402219	+	0.915544i	$0.368239\pi$
$564$	208.338	+	923.599i	0.369393	+	1.63759i
$565$	85.3073	−	147.757i	0.150986	−	0.261516i
$566$		−	15.1929i		−	0.0268425i
$567$	−394.123	+	407.622i	−0.695103	+	0.718910i
$568$	63.0456			0.110996
$569$	−283.603	−	163.738i	−0.498423	−	0.287764i	0.229639	−	0.973276i	$-0.426245\pi$
$569$	−283.603	−	163.738i	−0.498423	−	0.287764i	−0.728062	+	0.685511i	$0.759579\pi$
$570$	6.76256	−	1.52544i	0.0118641	−	0.00267621i
$571$	304.856	+	528.025i	0.533898	+	0.924738i	0.999216	+	0.0395945i	$0.0126066\pi$
$571$	304.856	+	528.025i	0.533898	+	0.924738i	−0.465318	+	0.885144i	$0.654060\pi$
$572$		−	595.013i		−	1.04023i
$573$	468.054	+	145.679i	0.816848	+	0.254239i
$574$	6.88159	+	14.6784i	0.0119888	+	0.0255721i
$575$		−	233.934i		−	0.406841i
$576$	515.631	−	245.094i	0.895192	−	0.425511i
$577$	−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	$0.181641\pi$
$578$		−	1.29201i		−	0.00223530i
$579$	−665.098	−	720.468i	−1.14870	−	1.24433i
$580$	−302.820	+	524.499i	−0.522103	+	0.904309i
$581$	−266.682	+	125.027i	−0.459004	+	0.215192i
$582$	−0.675053	−	2.99263i	−0.00115988	−	0.00514198i
$583$	−443.112	+	767.493i	−0.760055	+	1.31645i
$584$	−0.429031	−	0.247701i	−0.000734642	−	0.000424146i
$585$	437.301	+	35.0068i	0.747523	+	0.0598407i
$586$	−11.0288	−	19.1024i	−0.0188204	−	0.0325979i
$587$	134.422	−	77.6088i	0.228999	−	0.132213i	−0.381111	−	0.924529i	$-0.624459\pi$
$587$	134.422	−	77.6088i	0.228999	−	0.132213i	0.610110	+	0.792317i	$0.291125\pi$
$588$	319.331	+	492.701i	0.543080	+	0.837927i
$589$	−120.225	+	208.235i	−0.204117	+	0.353541i
$590$			13.4892i			0.0228631i
$591$	172.972	+	766.818i	0.292678	+	1.29749i
$592$	330.453			0.558197
$593$	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	$0.202174\pi$
$594$	3.65355	+	25.5603i	0.00615076	+	0.0430308i
$595$	−269.252	+	386.228i	−0.452525	+	0.649122i
$596$	−80.4810	+	46.4657i	−0.135035	+	0.0779626i
$597$	−89.2216	+	286.661i	−0.149450	+	0.480170i
$598$	12.8105	+	22.1885i	0.0214223	+	0.0371045i
$599$	654.315	−	377.769i	1.09234	−	0.630666i	0.158145	−	0.987416i	$-0.449449\pi$
$599$	654.315	−	377.769i	1.09234	−	0.630666i	0.934200	+	0.356750i	$0.116115\pi$
$600$	3.39338	+	15.0434i	0.00565563	+	0.0250724i
$601$	−118.651	−	205.509i	−0.197422	−	0.341945i	0.750270	−	0.661132i	$-0.229924\pi$
$601$	−118.651	−	205.509i	−0.197422	−	0.341945i	−0.947692	+	0.319187i	$0.896590\pi$
$602$	−1.16917	+	13.6892i	−0.00194214	+	0.0227396i
$603$	638.379	+	440.008i	1.05867	+	0.729698i
$604$	−118.373	−	205.028i	−0.195982	−	0.339451i
$605$			139.645i			0.230818i
$606$	−10.9166	+	35.0742i	−0.0180142	+	0.0578782i
$607$	−483.094			−0.795871			−0.397935	−	0.917413i	$-0.630273\pi$
$607$	−483.094			−0.795871			−0.397935	+	0.917413i	$0.630273\pi$
$608$	23.5152	+	13.5765i	0.0386763	+	0.0223298i
$609$	616.897	−	479.030i	1.01297	−	0.786585i
$610$	−3.51584	−	6.08962i	−0.00576368	−	0.00998298i
$611$	−818.159	+	472.365i	−1.33905	+	0.773101i
$612$	−254.589	−	535.606i	−0.415995	−	0.875173i
$613$	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	$0.152155\pi$
$614$	6.19428	+	3.57627i	0.0100884	+	0.00582454i
$615$	109.681	−	352.395i	0.178343	−	0.573000i
$616$	53.3192	+	4.55388i	0.0865571	+	0.00739266i
$617$	356.111	+	205.601i	0.577165	+	0.333226i	0.760006	−	0.649916i	$-0.225196\pi$
$617$	356.111	+	205.601i	0.577165	+	0.333226i	−0.182841	+	0.983143i	$0.558529\pi$
$618$	39.1867	+	12.1966i	0.0634090	+	0.0197357i
$619$	468.969			0.757624			0.378812	−	0.925474i	$-0.376333\pi$
$619$	468.969			0.757624			0.378812	+	0.925474i	$0.376333\pi$
$620$	459.152	+	265.092i	0.740568	+	0.427567i
$621$	465.525	+	592.967i	0.749638	+	0.954859i
$622$	−0.487308			−0.000783454
$623$	−264.762	+	124.127i	−0.424979	+	0.199241i
$624$	387.556	+	419.820i	0.621083	+	0.672788i
$625$	−345.345			−0.552552
$626$	−30.4363	+	17.5724i	−0.0486203	+	0.0280710i
$627$	202.839	−	187.250i	0.323507	−	0.298644i
$628$	−188.507	+	326.504i	−0.300170	+	0.519910i
$629$		−	342.238i		−	0.544099i
$630$	−3.23951	+	19.4450i	−0.00514209	+	0.0308651i
$631$	7.39326			0.0117167			0.00585836	−	0.999983i	$-0.498135\pi$
$631$	7.39326			0.0117167			0.00585836	+	0.999983i	$0.498135\pi$
$632$	−14.3734	−	8.29851i	−0.0227428	−	0.0131306i
$633$	−221.719	+	712.362i	−0.350266	+	1.12538i
$634$	−19.7855	−	34.2694i	−0.0312073	−	0.0540527i
$635$		−	345.002i		−	0.543310i
$636$	−187.531	−	831.360i	−0.294861	−	1.30717i
$637$	−374.718	+	450.336i	−0.588254	+	0.706964i
$638$		−	35.5673i		−	0.0557481i
$639$	397.021	+	835.253i	0.621315	+	1.30713i
$640$	39.9045	−	69.1166i	0.0623507	−	0.107995i
$641$			632.517i			0.986765i	0.869812	+	0.493383i	$0.164240\pi$
$641$			632.517i			0.986765i	−0.869812	+	0.493383i	$0.835760\pi$
$642$	−25.3401	+	5.71601i	−0.0394706	+	0.00890345i
$643$	−203.977	+	353.299i	−0.317227	+	0.549454i	−0.979908	−	0.199448i	$-0.936085\pi$
$643$	−203.977	+	353.299i	−0.317227	+	0.549454i	0.662681	+	0.748902i	$0.269419\pi$
$644$	706.820	−	331.374i	1.09755	−	0.514557i
$645$	229.826	−	212.163i	0.356319	−	0.328935i
$646$	4.67538	−	8.09799i	0.00723743	−	0.0125356i
$647$	−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	$0.704832\pi$
$648$	−38.5377	−	31.3789i	−0.0594718	−	0.0484242i
$649$	268.574	+	465.184i	0.413827	+	0.716770i
$650$	−6.65812	+	3.84407i	−0.0102433	+	0.00591395i
$651$	−419.348	−	540.039i	−0.644160	−	0.829552i
$652$	155.223	−	268.853i	0.238071	−	0.412352i
$653$		−	417.483i		−	0.639331i	−0.947530	−	0.319666i	$-0.896429\pi$
$653$		−	417.483i		−	0.639331i	0.947530	−	0.319666i	$-0.103571\pi$
$654$	34.1936	−	31.5657i	0.0522838	−	0.0482656i
$655$	−762.830			−1.16463
$656$	416.273	−	240.335i	0.634562	−	0.366364i
$657$	0.579884	−	7.24384i	0.000882624	−	0.0110256i
$658$	−18.0202	−	38.4369i	−0.0273863	−	0.0584148i
$659$	−553.079	+	319.320i	−0.839270	+	0.484553i	−0.857016	−	0.515290i	$-0.827684\pi$
$659$	−553.079	+	319.320i	−0.839270	+	0.484553i	0.0177460	+	0.999843i	$0.494351\pi$
$660$	−412.880	−	447.253i	−0.625576	−	0.677656i
$661$	−197.794	−	342.589i	−0.299234	−	0.518289i	0.676727	−	0.736234i	$-0.263398\pi$
$661$	−197.794	−	342.589i	−0.299234	−	0.518289i	−0.975961	+	0.217946i	$0.930064\pi$
$662$	−19.7576	+	11.4071i	−0.0298453	+	0.0172312i
$663$	434.792	−	401.377i	0.655795	−	0.605396i
$664$	−12.9078	−	22.3570i	−0.0194395	−	0.0336702i
$665$	190.830	−	89.4657i	0.286962	−	0.134535i
$666$	−6.15162	−	12.9418i	−0.00923666	−	0.0194321i
$667$	−519.232	−	899.336i	−0.778459	−	1.34833i
$668$		−	763.503i		−	1.14297i
$669$	24.9760	+	27.0553i	0.0373333	+	0.0404414i
$670$	26.9560			0.0402328
$671$	−242.492	−	140.003i	−0.361388	−	0.208648i
$672$	−60.9844	+	47.3553i	−0.0907506	+	0.0704692i
$673$	−367.518	−	636.559i	−0.546089	−	0.945854i	−0.998538	−	0.0540632i	$-0.982783\pi$
$673$	−367.518	−	636.559i	−0.546089	−	0.945854i	0.452449	−	0.891790i	$-0.350551\pi$
$674$	−7.64256	+	4.41243i	−0.0113391	+	0.00654664i
$675$	−177.932	+	139.691i	−0.263603	+	0.206949i
$676$	52.0289	−	90.1167i	0.0769659	−	0.133309i
$677$	215.824	+	124.606i	0.318795	+	0.184057i	0.650855	−	0.759202i	$-0.274410\pi$
$677$	215.824	+	124.606i	0.318795	+	0.184057i	−0.332060	+	0.943258i	$0.607744\pi$
$678$	−6.53585	−	7.07996i	−0.00963989	−	0.0104424i
$679$	−39.5912	−	84.4478i	−0.0583081	−	0.124371i
$680$	−35.7379	−	20.6333i	−0.0525558	−	0.0303431i
$681$	−11.1233	−	49.3115i	−0.0163337	−	0.0724104i
$682$	−31.1360			−0.0456540
$683$	−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	$0.926929\pi$
$684$	−21.1837	+	264.625i	−0.0309704	+	0.386878i
$685$	236.681			0.345519
$686$	−18.7296	−	18.4989i	−0.0273026	−	0.0269664i
$687$	−328.619	+	74.1272i	−0.478340	+	0.107900i
$688$	407.363			0.592098
$689$	736.450	−	425.190i	1.06887	−	0.617111i
$690$	25.0259	+	7.78916i	0.0362694	+	0.0112886i
$691$	−84.0927	+	145.653i	−0.121697	+	0.210786i	−0.920437	−	0.390891i	$-0.872167\pi$
$691$	−84.0927	+	145.653i	−0.121697	+	0.210786i	0.798740	+	0.601676i	$0.205500\pi$
$692$		−	111.543i		−	0.161189i
$693$	275.438	+	735.071i	0.397458	+	1.06071i
$694$	34.8172			0.0501689
$695$	−128.439	−	74.1544i	−0.184805	−	0.106697i
$696$	46.4355	+	50.3013i	0.0667177	+	0.0722720i
$697$	−248.906	−	431.118i	−0.357111	−	0.618534i
$698$		−	40.2561i		−	0.0576734i
$699$	−313.486	+	289.394i	−0.448478	+	0.414011i
$700$	99.4358	+	212.096i	0.142051	+	0.302994i
$701$		−	240.389i		−	0.342923i	−0.985191	−	0.171462i	$-0.945151\pi$
$701$		−	240.389i		−	0.342923i	0.985191	−	0.171462i	$-0.0548489\pi$
$702$	9.22713	−	22.9934i	0.0131441	−	0.0327541i
$703$	−76.6013	+	132.677i	−0.108963	+	0.188730i
$704$		−	790.404i		−	1.12273i
$705$	−287.211	+	922.783i	−0.407391	+	1.30891i
$706$	19.3995	−	33.6010i	0.0274781	−	0.0475935i
$707$	−95.0358	+	1112.73i	−0.134421	+	1.57387i
$708$	−493.217	−	153.511i	−0.696634	−	0.216823i
$709$	−365.324	+	632.760i	−0.515267	+	0.892468i	0.484576	+	0.874749i	$0.338974\pi$
$709$	−365.324	+	632.760i	−0.515267	+	0.892468i	−0.999843	+	0.0177190i	$0.994360\pi$
$710$	27.8454	+	16.0765i	0.0392188	+	0.0226430i
$711$	19.4273	−	242.684i	0.0273239	−	0.341327i
$712$	−12.8149	−	22.1961i	−0.0179985	−	0.0311743i
$713$	−787.289	+	454.541i	−1.10419	+	0.637505i
$714$	16.3079	+	21.0014i	0.0228402	+	0.0294137i
$715$	303.678	−	525.986i	0.424725	−	0.735645i
$716$			226.483i			0.316317i
$717$	−679.824	−	211.591i	−0.948150	−	0.295106i
$718$	3.85290			0.00536615
$719$	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	$0.208833\pi$
$720$	582.627	+	46.6405i	0.809204	+	0.0647784i
$721$	1243.20	+	106.179i	1.72427	+	0.147266i
$722$	20.3695	−	11.7603i	0.0282126	−	0.0162886i
$723$	−462.656	+	104.362i	−0.639911	+	0.144346i
$724$	−163.422	−	283.055i	−0.225721	−	0.390960i
$725$	269.865	−	155.806i	0.372227	−	0.214905i
$726$	7.53018	+	2.34372i	0.0103721	+	0.00322827i
$727$	22.9974	+	39.8326i	0.0316333	+	0.0547904i	0.881409	−	0.472355i	$-0.156596\pi$
$727$	22.9974	+	39.8326i	0.0316333	+	0.0547904i	−0.849775	+	0.527145i	$0.823262\pi$
$728$	−42.1233	−	29.3656i	−0.0578616	−	0.0403373i
$729$	173.034	−	708.167i	0.237358	−	0.971422i
$730$	−0.126327	−	0.218804i	−0.000173050	−	0.000299732i
$731$		−	421.892i		−	0.577143i
$732$	262.671	−	59.2511i	0.358840	−	0.0809441i
$733$	−64.3767			−0.0878263			−0.0439131	−	0.999035i	$-0.513982\pi$
$733$	−64.3767			−0.0878263			−0.0439131	+	0.999035i	$0.513982\pi$
$734$	−39.5132	−	22.8129i	−0.0538327	−	0.0310803i
$735$	30.8249	+	598.521i	0.0419387	+	0.814314i
$736$	51.3295	+	88.9053i	0.0697412	+	0.120795i
$737$	929.593	−	536.701i	1.26132	−	0.728224i
$738$	−17.1617	−	11.8288i	−0.0232543	−	0.0160282i
$739$	−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	$0.313958\pi$
$740$	292.549	+	168.903i	0.395337	+	0.228248i
$741$	−258.397	+	58.2870i	−0.348713	+	0.0786599i
$742$	16.2205	+	34.5983i	0.0218605	+	0.0466284i
$743$	267.309	+	154.331i	0.359769	+	0.207713i	0.668980	−	0.743281i	$-0.266731\pi$
$743$	267.309	+	154.331i	0.359769	+	0.207713i	−0.309210	+	0.950994i	$0.600065\pi$
$744$	44.0343	−	40.6502i	0.0591859	−	0.0546373i
$745$	−94.8593			−0.127328
$746$	−40.4964	−	23.3806i	−0.0542847	−	0.0313413i
$747$	214.910	−	311.798i	0.287697	−	0.417401i
$748$	−821.024			−1.09763
$749$	−715.062	+	335.239i	−0.954689	+	0.447582i
$750$	−9.31153	+	29.9171i	−0.0124154	+	0.0398895i
$751$	−244.470			−0.325526			−0.162763	−	0.986665i	$-0.552041\pi$
$751$	−244.470			−0.325526			−0.162763	+	0.986665i	$0.552041\pi$
$752$	−1090.05	+	629.343i	−1.44954	+	0.836893i
$753$	−305.388	−	1353.84i	−0.405562	−	1.79793i
$754$	−17.0644	+	29.5563i	−0.0226318	+	0.0391994i
$755$		−	241.658i		−	0.320076i
$756$	−674.116	−	339.738i	−0.891688	−	0.449389i
$757$	159.987			0.211343			0.105671	−	0.994401i	$-0.466301\pi$
$757$	159.987			0.211343			0.105671	+	0.994401i	$0.466301\pi$
$758$	31.1357	+	17.9762i	0.0410761	+	0.0237153i
$759$	1018.12	−	229.658i	1.34139	−	0.302580i
$760$	9.23649	+	15.9981i	0.0121533	+	0.0210501i
$761$			1121.92i			1.47427i	0.675747	+	0.737134i	$0.263821\pi$
$761$			1121.92i			1.47427i	−0.675747	+	0.737134i	$0.736179\pi$
$762$	−18.6038	−	5.79033i	−0.0244145	−	0.00759885i
$763$	809.092	−	1160.60i	1.06041	−	1.52110i
$764$			652.639i			0.854239i
$765$	48.3039	−	603.406i	0.0631423	−	0.788766i
$766$	16.8610	−	29.2041i	0.0220117	−	0.0381254i
$767$		−	515.422i		−	0.671997i
$768$	513.286	+	556.018i	0.668341	+	0.723981i
$769$	−20.2793	+	35.1248i	−0.0263710	+	0.0456760i	−0.878910	−	0.476988i	$-0.841728\pi$
$769$	−20.2793	+	35.1248i	−0.0263710	+	0.0456760i	0.852539	+	0.522664i	$0.175062\pi$
$770$	22.3882	+	15.6076i	0.0290756	+	0.0202696i
$771$	−75.8122	−	336.089i	−0.0983297	−	0.435913i
$772$	652.721	−	1130.55i	0.845493	−	1.46444i
$773$	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	$0.485795\pi$
$774$	−7.58336	−	15.9539i	−0.00979763	−	0.0206123i
$775$	−136.395	−	236.242i	−0.175993	−	0.304829i
$776$	7.07962	−	4.08742i	0.00912322	−	0.00526729i
$777$	−267.188	−	344.086i	−0.343872	−	0.442839i
$778$	−10.1930	+	17.6549i	−0.0131016	+	0.0226926i
$779$			222.846i			0.286066i
$780$	128.521	+	569.756i	0.164770	+	0.730457i
$781$	1280.35			1.63937
$782$	30.6166	−	17.6765i	0.0391516	−	0.0226042i
$783$	−373.991	+	931.961i	−0.477639	+	1.19024i
$784$	−499.246	+	599.994i	−0.636793	+	0.765299i
$785$	−333.277	+	192.418i	−0.424557	+	0.245118i
$786$	−12.8029	+	41.1347i	−0.0162887	+	0.0523342i
$787$	448.874	+	777.473i	0.570361	+	0.987895i	0.996529	+	0.0832506i	$0.0265302\pi$
$787$	448.874	+	777.473i	0.570361	+	0.987895i	−0.426167	+	0.904644i	$0.640136\pi$
$788$	−906.356	+	523.285i	−1.15020	+	0.664067i
$789$	−22.3303	−	98.9943i	−0.0283020	−	0.125468i
$790$	−4.23221	−	7.33040i	−0.00535723	−	0.00927899i
$791$	−240.308	−	167.527i	−0.303803	−	0.211791i
$792$	−62.1401	+	29.5370i	−0.0784597	+	0.0372942i
$793$	134.340	+	232.684i	0.169407	+	0.293422i
$794$			15.1084i			0.0190282i
$795$	258.527	−	830.625i	0.325191	−	1.04481i
$796$	−399.711			−0.502149
$797$	−83.2647	−	48.0729i	−0.104473	−	0.0603173i	0.446853	−	0.894607i	$-0.352545\pi$
$797$	−83.2647	−	48.0729i	−0.104473	−	0.0603173i	−0.551326	+	0.834290i	$0.685878\pi$
$798$	−1.62155	−	11.7918i	−0.00203201	−	0.0147767i
$799$	651.788	+	1128.93i	0.815755	+	1.41293i
$800$	−26.6779	+	15.4025i	−0.0333474	+	0.0192531i
$801$	213.363	−	309.554i	0.266371	−	0.386460i
$802$	−7.09539	+	12.2896i	−0.00884712	+	0.0153237i
$803$	−8.71290	−	5.03039i	−0.0108504	−	0.00626450i
$804$	−306.766	+	985.613i	−0.381550	+	1.22589i
$805$	793.946	+	67.8093i	0.986269	+	0.0842351i
$806$	25.8739	+	14.9383i	0.0321017	+	0.0185339i
$807$	−144.493	−	44.9724i	−0.179049	−	0.0557279i
$808$	−97.8846			−0.121144
$809$	−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	$0.947691\pi$
$810$	−9.01940	−	23.6861i	−0.0111351	−	0.0292422i
$811$	−1588.72			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$811$	−1588.72			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$812$	853.034	+	594.679i	1.05053	+	0.732363i
$813$	−827.848	−	896.768i	−1.01826	−	1.10304i
$814$	−19.8383			−0.0243714
$815$	274.431	−	158.443i	0.336725	−	0.194408i
$816$	579.285	−	534.765i	0.709908	−	0.655349i
$817$	−94.4298	+	163.557i	−0.115581	+	0.200192i
$818$			45.9471i			0.0561700i
$819$	123.781	−	742.991i	0.151137	−	0.907193i
$820$	491.367			0.599228
$821$	−255.656	−	147.603i	−0.311396	−	0.179784i	0.336155	−	0.941807i	$-0.390873\pi$
$821$	−255.656	−	147.603i	−0.311396	−	0.179784i	−0.647551	+	0.762022i	$0.724207\pi$
$822$	3.97233	−	12.7627i	0.00483251	−	0.0155264i
$823$	673.413	+	1166.38i	0.818241	+	1.41724i	0.906977	+	0.421180i	$0.138384\pi$
$823$	673.413	+	1166.38i	0.818241	+	1.41724i	−0.0887357	+	0.996055i	$0.528283\pi$
$824$			109.362i			0.132721i
$825$	68.9137	+	305.507i	0.0835318	+	0.370311i
$826$	23.0765	+	1.97091i	0.0279376	+	0.00238609i
$827$			1226.89i			1.48354i	0.670653	+	0.741772i	$0.266014\pi$
$827$			1226.89i			1.48354i	−0.670653	+	0.741772i	$0.733986\pi$
$828$	−569.602	+	826.398i	−0.687925	+	0.998065i
$829$	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	$-0.0537720\pi$
$830$		−	13.1659i		−	0.0158625i
$831$	229.665	−	51.8059i	0.276372	−	0.0623417i
$832$	−379.217	+	656.824i	−0.455790	+	0.789452i
$833$	621.392	+	517.051i	0.745969	+	0.620710i
$834$	−6.15435	+	5.68137i	−0.00737931	+	0.00681219i
$835$	389.671	−	674.930i	0.466672	−	0.808299i
$836$	318.291	+	183.765i	0.380731	+	0.219815i
$837$	815.849	+	327.396i	0.974730	+	0.391154i
$838$	11.0506	+	19.1402i	0.0131869	+	0.0228404i
$839$	36.0995	−	20.8420i	0.0430268	−	0.0248415i	−0.478332	−	0.878179i	$-0.658759\pi$
$839$	36.0995	−	20.8420i	0.0430268	−	0.0248415i	0.521359	+	0.853337i	$0.325425\pi$
$840$	−52.0395	+	7.15619i	−0.0619518	+	0.00851928i
$841$	271.147	−	469.640i	0.322410	−	0.558431i
$842$		−	8.09810i		−	0.00961770i
$843$	317.568	−	293.162i	0.376712	−	0.347761i
$844$	−993.294			−1.17689
$845$	91.9862	−	53.1082i	0.108859	−	0.0628500i
$846$	44.9396	+	30.9750i	0.0531201	+	0.0366135i
$847$	238.895	+	20.4035i	0.282048	+	0.0240891i
$848$	981.191	−	566.491i	1.15707	−	0.668032i
$849$	402.822	+	436.357i	0.474466	+	0.513966i
$850$	5.30420	+	9.18715i	0.00624024	+	0.0108084i
$851$	−501.622	+	289.611i	−0.589450	+	0.340319i
$852$	−904.706	+	835.176i	−1.06186	+	0.980254i
$853$	309.770	+	536.537i	0.363153	+	0.629000i	0.988478	−	0.151365i	$-0.0483667\pi$
$853$	309.770	+	536.537i	0.363153	+	0.629000i	−0.625325	+	0.780365i	$0.715033\pi$
$854$	−10.9314	+	5.12492i	−0.0128003	+	0.00600108i
$855$	−153.783	+	223.114i	−0.179864	+	0.260952i
$856$	−34.6102	−	59.9467i	−0.0404325	−	0.0700312i
$857$			815.099i			0.951107i	0.879687	+	0.475554i	$0.157752\pi$
$857$			815.099i			0.951107i	−0.879687	+	0.475554i	$0.842248\pi$
$858$	−23.2664	−	25.2034i	−0.0271170	−	0.0293746i
$859$	687.626			0.800496			0.400248	−	0.916407i	$-0.368924\pi$
$859$	687.626			0.800496			0.400248	+	0.916407i	$0.368924\pi$
$860$	360.638	+	208.215i	0.419347	+	0.242110i
$861$	−586.828	−	239.123i	−0.681566	−	0.277727i
$862$	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	$0.389360\pi$
$864$	36.9715	−	92.1305i	0.0427911	−	0.106633i
$865$	56.9284	−	98.6028i	0.0658131	−	0.113992i
$866$	−15.6611	−	9.04197i	−0.0180845	−	0.0104411i
$867$	34.2561	+	37.1079i	0.0395110	+	0.0428004i
$868$	520.589	−	746.755i	0.599756	−	0.860317i
$869$	−291.900	−	168.529i	−0.335904	−	0.193934i
$870$	7.68242	+	34.0575i	0.00883037	+	0.0391466i
$871$	−1029.99			−1.18253
$872$	107.391	+	62.0022i	0.123155	+	0.0711035i
$873$	98.7346	+	68.0536i	0.113098	+	0.0779538i
$874$	−15.8257			−0.0181073
$875$	−81.0624	+	949.121i	−0.0926428	+	1.08471i
$876$	9.43794	−	2.12893i	0.0107739	−	0.00243029i
$877$	4.03873			0.00460516			0.00230258	−	0.999997i	$-0.499267\pi$
$877$	4.03873			0.00460516			0.00230258	+	0.999997i	$0.499267\pi$
$878$	41.7021	−	24.0767i	0.0474967	−	0.0274222i
$879$	823.236	+	256.227i	0.936560	+	0.291499i
$880$	404.598	−	700.785i	0.459771	−	0.796346i
$881$			34.5348i			0.0391996i	0.999808	+	0.0195998i	$0.00623920\pi$
$881$			34.5348i			0.0391996i	−0.999808	+	0.0195998i	$0.993761\pi$
$882$	32.7919	+	8.38306i	0.0371790	+	0.00950461i
$883$	1539.71			1.74373			0.871863	−	0.489750i	$-0.162912\pi$
$883$	1539.71			1.74373			0.871863	+	0.489750i	$0.162912\pi$
$884$	682.268	+	393.908i	0.771797	+	0.445597i
$885$	−357.652	−	387.427i	−0.404126	−	0.437770i
$886$	17.7883	+	30.8103i	0.0200771	+	0.0347746i
$887$		−	1331.40i		−	1.50102i	−0.660859	−	0.750510i	$-0.729808\pi$
$887$		−	1331.40i		−	1.50102i	0.660859	−	0.750510i	$-0.270192\pi$
$888$	28.0565	−	25.9003i	0.0315952	−	0.0291670i
$889$	−590.206	−	50.4082i	−0.663899	−	0.0567022i
$890$		−	13.0711i		−	0.0146867i
$891$	−782.636	−	637.252i	−0.878380	−	0.715209i
$892$	−24.5112	+	42.4547i	−0.0274789	+	0.0475949i
$893$		−	583.545i		−	0.653466i
$894$	−1.59207	+	5.11518i	−0.00178084	+	0.00572168i
$895$	−115.591	+	200.209i	−0.129151	+	0.223697i
$896$	−112.410	−	78.3646i	−0.125457	−	0.0874605i
$897$	−956.236	−	297.623i	−1.06604	−	0.331798i
$898$	22.4314	−	38.8523i	0.0249793	−	0.0432654i
$899$	−1048.71	−	605.475i	−1.16653	−	0.673499i
$900$	−247.978	−	170.921i	−0.275531	−	0.189912i
$901$	−586.694	−	1016.18i	−0.651159	−	1.12784i
$902$	−24.9904	+	14.4282i	−0.0277056	+	0.0159958i
$903$	−329.374	−	424.170i	−0.364756	−	0.469734i
$904$	12.8379	−	22.2359i	0.0142012	−	0.0245972i
$905$		−	333.624i		−	0.368646i
$906$	−13.0311	−	4.05586i	−0.0143831	−	0.00447666i
$907$	837.355			0.923214			0.461607	−	0.887084i	$-0.347273\pi$
$907$	837.355			0.923214			0.461607	+	0.887084i	$0.347273\pi$
$908$	58.2847	−	33.6507i	0.0641902	−	0.0370602i
$909$	−616.414	−	1296.81i	−0.678123	−	1.42664i
$910$	−11.1164	−	23.7112i	−0.0122158	−	0.0260563i
$911$	50.4341	−	29.1181i	0.0553612	−	0.0319628i	−0.472064	−	0.881564i	$-0.656491\pi$
$911$	50.4341	−	29.1181i	0.0553612	−	0.0319628i	0.527425	+	0.849602i	$0.323158\pi$
$912$	−344.268	+	77.6572i	−0.377487	+	0.0851504i
$913$	−262.136	−	454.034i	−0.287115	−	0.497298i
$914$	27.5195	−	15.8884i	0.0301089	−	0.0173834i
$915$	262.439	+	81.6824i	0.286818	+	0.0892704i
$916$	−224.253	−	388.418i	−0.244818	−	0.424037i
$917$	−111.457	+	1305.00i	−0.121545	+	1.42312i
$918$	−31.7273	−	12.7320i	−0.0345613	−	0.0138693i
$919$	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	$0.784493\pi$
$920$			69.8420i			0.0759152i
$921$	−272.728	+	61.5197i	−0.296122	+	0.0667966i
$922$	29.7613			0.0322791
$923$	−1063.97	−	614.282i	−1.15273	−	0.665528i
$924$	−825.457	+	640.980i	−0.893352	+	0.693702i
$925$	−86.9040	−	150.522i	−0.0939502	−	0.162727i
$926$	−43.8987	+	25.3449i	−0.0474068	+	0.0273703i
$927$	−1448.87	+	688.690i	−1.56297	+	0.742924i
$928$	−68.3739	+	118.427i	−0.0736787	+	0.127615i
$929$	−141.488	−	81.6879i	−0.152301	−	0.0879310i	0.421913	−	0.906636i	$-0.361359\pi$
$929$	−141.488	−	81.6879i	−0.152301	−	0.0879310i	−0.574214	+	0.818705i	$0.694692\pi$
$930$	29.8143	−	6.72527i	0.0320584	−	0.00723148i
$931$	−125.170	−	339.531i	−0.134447	−	0.364695i
$932$	−491.917	−	284.008i	−0.527808	−	0.304730i
$933$	13.9961	−	12.9204i	0.0150012	−	0.0138483i
$934$	−66.7208			−0.0714356
$935$	−725.777	−	419.028i	−0.776232	−	0.448158i
$936$	65.8094	+	5.26818i	0.0703092	+	0.00562840i
$937$	1117.03			1.19213			0.596066	−	0.802935i	$-0.296730\pi$
$937$	1117.03			1.19213			0.596066	+	0.802935i	$0.296730\pi$
$938$	3.93855	−	46.1146i	0.00419888	−	0.0491627i
$939$	408.254	−	1311.69i	0.434776	−	1.39690i
$940$	−1286.70			−1.36883
$941$	557.646	−	321.957i	0.592610	−	0.342144i	−0.173519	−	0.984831i	$-0.555514\pi$
$941$	557.646	−	321.957i	0.592610	−	0.342144i	0.766129	+	0.642687i	$0.222180\pi$
$942$	4.78235	+	21.2010i	0.00507680	+	0.0225064i
$943$	−421.263	+	729.649i	−0.446727	+	0.773753i
$944$		−	686.709i		−	0.727446i
$945$	−422.519	−	644.375i	−0.447110	−	0.681879i
$946$	−24.4556			−0.0258515
$947$	1144.21	+	660.611i	1.20825	+	0.697583i	0.962377	−	0.271719i	$-0.0875922\pi$
$947$	1144.21	+	660.611i	1.20825	+	0.697583i	0.245873	+	0.969302i	$0.420925\pi$
$948$	316.191	−	71.3237i	0.333535	−	0.0752360i
$949$	4.82693	+	8.36049i	0.00508633	+	0.00880979i
$950$		−	4.74884i		−	0.00499878i
$951$	1476.88	+	459.669i	1.55297	+	0.483354i
$952$	−40.5198	+	58.1234i	−0.0425628	+	0.0610540i
$953$			1182.43i			1.24075i	0.784307	+	0.620373i	$0.213019\pi$
$953$			1182.43i			1.24075i	−0.784307	+	0.620373i	$0.786981\pi$
$954$	−40.4515	−	27.8816i	−0.0424020	−	0.0292260i
$955$	−333.089	+	576.927i	−0.348784	+	0.604112i
$956$		−	947.923i		−	0.991552i
$957$	943.027	+	1021.53i	0.985399	+	1.06743i
$958$	−5.68666	+	9.84959i	−0.00593598	+	0.0102814i
$959$	34.5815	−	404.898i	0.0360599	−	0.422209i
$960$	170.725	+	756.853i	0.177838	+	0.788389i
$961$	−49.5395	+	85.8050i	−0.0515500	+	0.0892872i
$962$	16.4856	+	9.51796i	0.0171368	+	0.00989393i
$963$	576.245	−	836.035i	0.598385	−	0.868157i
$964$	−315.721	−	546.845i	−0.327512	−	0.567267i
$965$	1154.00	−	666.261i	1.19585	−	0.690426i
$966$	16.9817	−	41.6746i	0.0175794	−	0.0431414i
$967$	345.416	−	598.278i	0.357203	−	0.618694i	−0.630289	−	0.776361i	$-0.717064\pi$
$967$	345.416	−	598.278i	0.357203	−	0.618694i	0.987492	+	0.157666i	$0.0503970\pi$
$968$			21.0151i			0.0217099i
$969$	80.4268	+	356.546i	0.0829997	+	0.367953i
$970$	4.16914			0.00429808
$971$	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	$0.183982\pi$
$972$	968.698	−	60.2289i	0.996603	−	0.0619639i
$973$	−145.625	+	208.891i	−0.149666	+	0.214687i
$974$	8.79195	−	5.07604i	0.00902665	−	0.00521154i
$975$	89.3080	−	286.939i	0.0915979	−	0.294296i
$976$	178.984	+	310.010i	0.183386	+	0.317633i
$977$	−50.8709	+	29.3703i	−0.0520685	+	0.0300618i	−0.525808	−	0.850603i	$-0.676237\pi$
$977$	−50.8709	+	29.3703i	−0.0520685	+	0.0300618i	0.473740	+	0.880665i	$0.342904\pi$
$978$	−3.93793	−	17.4576i	−0.00402652	−	0.0178503i
$979$	−260.250	−	450.766i	−0.265832	−	0.460435i
$980$	−748.655	+	275.996i	−0.763934	+	0.281628i
$981$	−145.151	+	1813.21i	−0.147962	+	1.84833i
$982$	13.0130	+	22.5392i	0.0132515	+	0.0229523i
$983$			167.596i			0.170495i	0.996360	+	0.0852474i	$0.0271681\pi$
$983$			167.596i			0.170495i	−0.996360	+	0.0852474i	$0.972832\pi$
$984$	16.5059	−	53.0319i	0.0167743	−	0.0538942i
$985$	−1068.28			−1.08455
$986$	40.7830	+	23.5461i	0.0413621	+	0.0238804i
$987$	1536.67	+	626.170i	1.55691	+	0.634417i
$988$	−176.333	−	305.417i	−0.178474	−	0.309127i
$989$	−618.371	+	357.017i	−0.625248	+	0.360987i
$990$	−34.9773	−	2.80000i	−0.0353306	−	0.00282829i
$991$	−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	$0.940284\pi$
$992$	103.672	+	59.8552i	0.104508	+	0.0603379i
$993$	265.017	−	851.476i	0.266885	−	0.857478i
$994$	31.5712	−	45.2871i	0.0317617	−	0.0455604i
$995$	−353.341	−	204.001i	−0.355116	−	0.205027i
$996$	481.395	+	149.831i	0.483328	+	0.150433i
$997$	−700.770			−0.702879			−0.351439	−	0.936211i	$-0.614308\pi$
$997$	−700.770			−0.702879			−0.351439	+	0.936211i	$0.614308\pi$
$998$	12.5420	+	7.24113i	0.0125671	+	0.00725564i
$999$	519.819	+	208.600i	0.520339	+	0.208809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.32.7	yes	22
3.2	odd	2		189.3.n.b.179.5		22
7.2	even	3		63.3.j.b.23.5	yes	22
7.3	odd	6		441.3.r.f.50.5		22
7.4	even	3		441.3.r.g.50.5		22
7.5	odd	6		441.3.j.f.275.5		22
7.6	odd	2		441.3.n.f.410.7		22
9.2	odd	6		63.3.j.b.11.7	✓	22
9.7	even	3		189.3.j.b.116.5		22
21.2	odd	6		189.3.j.b.44.7		22
63.2	odd	6	inner	63.3.n.b.2.7	yes	22
63.11	odd	6		441.3.r.g.344.5		22
63.16	even	3		189.3.n.b.170.5		22
63.20	even	6		441.3.j.f.263.7		22
63.38	even	6		441.3.r.f.344.5		22
63.47	even	6		441.3.n.f.128.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.7	✓	22	9.2	odd	6
63.3.j.b.23.5	yes	22	7.2	even	3
63.3.n.b.2.7	yes	22	63.2	odd	6	inner
63.3.n.b.32.7	yes	22	1.1	even	1	trivial
189.3.j.b.44.7		22	21.2	odd	6
189.3.j.b.116.5		22	9.7	even	3
189.3.n.b.170.5		22	63.16	even	3
189.3.n.b.179.5		22	3.2	odd	2
441.3.j.f.263.7		22	63.20	even	6
441.3.j.f.275.5		22	7.5	odd	6
441.3.n.f.128.7		22	63.47	even	6
441.3.n.f.410.7		22	7.6	odd	2
441.3.r.f.50.5		22	7.3	odd	6
441.3.r.f.344.5		22	63.38	even	6
441.3.r.g.50.5		22	7.4	even	3
441.3.r.g.344.5		22	63.11	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0664669 + 0.0383747i) q^{2} +(-2.92647 + 0.660129i) q^{3} +(-1.99705 - 3.45900i) q^{4} -4.07697i q^{5} +(-0.219846 - 0.0684257i) q^{6} +(-6.97461 - 0.595686i) q^{7} -0.613543i q^{8} +(8.12846 - 3.86370i) q^{9} +O(q^{10})\)	\(q+(0.0664669 + 0.0383747i) q^{2} +(-2.92647 + 0.660129i) q^{3} +(-1.99705 - 3.45900i) q^{4} -4.07697i q^{5} +(-0.219846 - 0.0684257i) q^{6} +(-6.97461 - 0.595686i) q^{7} -0.613543i q^{8} +(8.12846 - 3.86370i) q^{9} +(0.156452 - 0.270983i) q^{10} -12.4600i q^{11} +(8.12771 + 8.80435i) q^{12} +(-5.97803 + 10.3542i) q^{13} +(-0.440721 - 0.307242i) q^{14} +(2.69132 + 11.9311i) q^{15} +(-7.96467 + 13.7952i) q^{16} +(14.2872 + 8.24873i) q^{17} +(0.688542 + 0.0551192i) q^{18} +(-3.69254 - 6.39566i) q^{19} +(-14.1022 + 8.14193i) q^{20} +(20.8042 - 2.86088i) q^{21} +(0.478149 - 0.828179i) q^{22} -27.9212i q^{23} +(0.405017 + 1.79552i) q^{24} +8.37834 q^{25} +(-0.794682 + 0.458810i) q^{26} +(-21.2372 + 16.6728i) q^{27} +(11.8682 + 25.3148i) q^{28} +(32.2098 - 18.5963i) q^{29} +(-0.278969 + 0.896304i) q^{30} +(-16.2794 - 28.1968i) q^{31} +(-3.18415 + 1.83837i) q^{32} +(8.22522 + 36.4639i) q^{33} +(0.633085 + 1.09653i) q^{34} +(-2.42859 + 28.4352i) q^{35} +(-29.5975 - 20.4003i) q^{36} +(-10.3724 - 17.9656i) q^{37} -0.566800i q^{38} +(10.6594 - 34.2477i) q^{39} -2.50139 q^{40} +(-26.1324 - 15.0876i) q^{41} +(1.49258 + 0.608201i) q^{42} +(-12.7866 - 22.1470i) q^{43} +(-43.0992 + 24.8833i) q^{44} +(-15.7522 - 33.1395i) q^{45} +(1.07147 - 1.85584i) q^{46} +(68.4306 + 39.5084i) q^{47} +(14.2018 - 45.6290i) q^{48} +(48.2903 + 8.30936i) q^{49} +(0.556883 + 0.321516i) q^{50} +(-47.2563 - 14.7083i) q^{51} +47.7538 q^{52} +(-61.5964 - 35.5627i) q^{53} +(-2.05138 + 0.293222i) q^{54} -50.7991 q^{55} +(-0.365479 + 4.27922i) q^{56} +(15.0281 + 16.2792i) q^{57} +2.85451 q^{58} +(-37.3341 + 21.5548i) q^{59} +(35.8950 - 33.1364i) q^{60} +(11.2361 - 19.4616i) q^{61} -2.49887i q^{62} +(-58.9944 + 22.1058i) q^{63} +63.4352 q^{64} +(42.2139 + 24.3722i) q^{65} +(-0.852585 + 2.73928i) q^{66} +(43.0738 + 74.6061i) q^{67} -65.8926i q^{68} +(18.4316 + 81.7106i) q^{69} +(-1.25261 + 1.79681i) q^{70} +102.757i q^{71} +(-2.37054 - 4.98716i) q^{72} +(0.403723 - 0.699268i) q^{73} -1.59216i q^{74} +(-24.5190 + 5.53079i) q^{75} +(-14.7484 + 25.5450i) q^{76} +(-7.42226 + 86.9038i) q^{77} +(2.02274 - 1.86729i) q^{78} +(13.5256 - 23.4270i) q^{79} +(56.2427 + 32.4717i) q^{80} +(51.1437 - 62.8118i) q^{81} +(-1.15796 - 2.00565i) q^{82} +(36.4392 - 21.0382i) q^{83} +(-51.4429 - 66.2484i) q^{84} +(33.6298 - 58.2485i) q^{85} -1.96272i q^{86} +(-81.9850 + 75.6842i) q^{87} -7.64476 q^{88} +(36.1770 - 20.8868i) q^{89} +(0.224719 - 2.80716i) q^{90} +(47.8623 - 68.6558i) q^{91} +(-96.5795 + 55.7602i) q^{92} +(66.2548 + 71.7706i) q^{93} +(3.03225 + 5.25200i) q^{94} +(-26.0749 + 15.0543i) q^{95} +(8.10476 - 7.48188i) q^{96} +(6.66199 + 11.5389i) q^{97} +(2.89084 + 2.40542i) q^{98} +(-48.1417 - 101.281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Introduction

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