LMFDB - Embedded newform 63.4.o.a.20.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.14
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.628557 + 0.362898i) q^{2} +(2.99138 - 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(3.42210 - 1.58500i) q^{6} +(4.49570 - 17.9663i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +O(q^{10})$	\(q+(0.628557 + 0.362898i) q^{2} +(2.99138 - 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(3.42210 - 1.58500i) q^{6} +(4.49570 - 17.9663i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +8.03191i q^{10} +(0.219645 + 0.126812i) q^{11} +(-38.6754 - 3.48437i) q^{12} +(12.3956 - 7.15663i) q^{13} +(9.34574 - 9.66138i) q^{14} +(57.2705 + 5.15965i) q^{15} +(-25.8174 + 44.7170i) q^{16} +92.5854 q^{17} +(3.50257 - 19.2809i) q^{18} +130.104i q^{19} +(41.3506 - 71.6214i) q^{20} +(-62.8856 - 72.8450i) q^{21} +(0.0920395 + 0.159417i) q^{22} +(-102.797 + 59.3500i) q^{23} +(-47.7148 - 33.5944i) q^{24} +(1.26793 - 2.19612i) q^{25} +10.3885 q^{26} +(-135.230 - 37.3606i) q^{27} +(-133.077 + 38.0370i) q^{28} +(248.320 + 143.368i) q^{29} +(34.1254 + 24.0265i) q^{30} +(-214.225 + 123.683i) q^{31} +(-110.262 + 63.6597i) q^{32} +(1.19583 - 0.553867i) q^{33} +(58.1952 + 33.5990i) q^{34} +(197.060 - 56.3252i) q^{35} +(-130.497 + 153.898i) q^{36} +188.615 q^{37} +(-47.2144 + 81.7777i) q^{38} +(6.67351 - 74.0738i) q^{39} +(107.629 - 62.1397i) q^{40} +(-53.2437 - 92.2207i) q^{41} +(-13.0919 - 68.6083i) q^{42} +(-21.5586 + 37.3406i) q^{43} -1.89539i q^{44} +(193.240 - 227.892i) q^{45} -86.1520 q^{46} +(68.8818 - 119.307i) q^{47} +(112.761 + 243.457i) q^{48} +(-302.577 - 161.542i) q^{49} +(1.59393 - 0.920258i) q^{50} +(276.958 - 393.370i) q^{51} +(-92.6354 - 53.4830i) q^{52} -419.280i q^{53} +(-71.4418 - 72.5580i) q^{54} +2.80669i q^{55} +(-201.769 - 50.4884i) q^{56} +(552.775 + 389.190i) q^{57} +(104.056 + 180.230i) q^{58} +(217.560 + 376.825i) q^{59} +(-180.604 - 389.934i) q^{60} +(163.504 + 94.3989i) q^{61} -179.537 q^{62} +(-497.613 + 49.2767i) q^{63} +320.670 q^{64} +(137.175 + 79.1977i) q^{65} +(0.952645 + 0.0858263i) q^{66} +(-185.350 - 321.035i) q^{67} +(-345.956 - 599.213i) q^{68} +(-55.3435 + 614.296i) q^{69} +(144.304 + 36.1090i) q^{70} -26.1630i q^{71} +(-285.466 + 102.234i) q^{72} -728.545i q^{73} +(118.555 + 68.4480i) q^{74} +(-5.53785 - 11.9565i) q^{75} +(842.032 - 486.147i) q^{76} +(3.26580 - 3.37610i) q^{77} +(31.0759 - 44.1378i) q^{78} +(-48.6779 + 84.3125i) q^{79} -571.409 q^{80} +(-563.259 + 462.796i) q^{81} -77.2880i q^{82} +(-401.359 + 695.174i) q^{83} +(-236.474 + 679.189i) q^{84} +(512.291 + 887.315i) q^{85} +(-27.1017 + 15.6471i) q^{86} +(1351.95 - 626.177i) q^{87} +(1.42415 - 2.46670i) q^{88} -236.618 q^{89} +(204.164 - 73.1170i) q^{90} +(-72.8512 - 254.878i) q^{91} +(768.227 + 443.536i) q^{92} +(-115.333 + 1280.16i) q^{93} +(86.5924 - 49.9941i) q^{94} +(-1246.88 + 719.887i) q^{95} +(-59.3623 + 658.903i) q^{96} +(-1268.09 - 732.133i) q^{97} +(-131.564 - 211.343i) q^{98} +(1.22395 - 6.73758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.628557	+	0.362898i	0.222229	+	0.128304i	0.606982	−	0.794716i	$-0.292380\pi$
$2$	0.628557	+	0.362898i	0.222229	+	0.128304i	−0.384753	+	0.923019i	$0.625713\pi$
$3$	2.99138	−	4.24872i	0.575691	−	0.817667i
$3$	2.99138	−	4.24872i	0.575691	−	0.817667i
$4$	−3.73661	−	6.47200i	−0.467076	−	0.809000i
$5$	5.53318	+	9.58374i	0.494902	+	0.857196i	0.999983	−	0.00587635i	$-0.00187051\pi$
$5$	5.53318	+	9.58374i	0.494902	+	0.857196i	−0.505080	+	0.863072i	$0.668537\pi$
$6$	3.42210	−	1.58500i	0.232845	−	0.107846i
$7$	4.49570	−	17.9663i	0.242745	−	0.970090i
$7$	4.49570	−	17.9663i	0.242745	−	0.970090i
$8$		−	11.2304i		−	0.496318i
$9$	−9.10332	−	25.4191i	−0.337160	−	0.941447i
$10$			8.03191i			0.253991i
$11$	0.219645	+	0.126812i	0.00602049	+	0.00347593i	0.503007	−	0.864282i	$-0.332227\pi$
$11$	0.219645	+	0.126812i	0.00602049	+	0.00347593i	−0.496987	+	0.867758i	$0.665560\pi$
$12$	−38.6754	−	3.48437i	−0.930384	−	0.0838208i
$13$	12.3956	−	7.15663i	0.264456	−	0.152684i	−0.361909	−	0.932213i	$-0.617875\pi$
$13$	12.3956	−	7.15663i	0.264456	−	0.152684i	0.626366	+	0.779529i	$0.284542\pi$
$14$	9.34574	−	9.66138i	0.178411	−	0.184437i
$15$	57.2705	+	5.15965i	0.985812	+	0.0888145i
$16$	−25.8174	+	44.7170i	−0.403397	+	0.698704i
$17$	92.5854			1.32090			0.660449	−	0.750871i	$-0.270366\pi$
$17$	92.5854			1.32090			0.660449	+	0.750871i	$0.270366\pi$
$18$	3.50257	−	19.2809i	0.0458646	−	0.252475i
$19$			130.104i			1.57094i	0.618899	+	0.785470i	$0.287579\pi$
$19$			130.104i			1.57094i	−0.618899	+	0.785470i	$0.712421\pi$
$20$	41.3506	−	71.6214i	0.462314	−	0.800752i
$21$	−62.8856	−	72.8450i	−0.653465	−	0.756957i
$22$	0.0920395	+	0.159417i	0.000891950	+	0.00154490i
$23$	−102.797	+	59.3500i	−0.931944	+	0.538058i	−0.887426	−	0.460951i	$-0.847509\pi$
$23$	−102.797	+	59.3500i	−0.931944	+	0.538058i	−0.0445181	+	0.999009i	$0.514175\pi$
$24$	−47.7148	−	33.5944i	−0.405823	−	0.285726i
$25$	1.26793	−	2.19612i	0.0101434	−	0.0175689i
$26$	10.3885			0.0783597
$27$	−135.230	−	37.3606i	−0.963891	−	0.266298i
$28$	−133.077	+	38.0370i	−0.898183	+	0.256726i
$29$	248.320	+	143.368i	1.59007	+	0.918025i	0.993294	+	0.115615i	$0.0368837\pi$
$29$	248.320	+	143.368i	1.59007	+	0.918025i	0.596772	+	0.802411i	$0.296450\pi$
$30$	34.1254	+	24.0265i	0.207680	+	0.146220i
$31$	−214.225	+	123.683i	−1.24116	+	0.716582i	−0.969330	−	0.245764i	$-0.920961\pi$
$31$	−214.225	+	123.683i	−1.24116	+	0.716582i	−0.271827	+	0.962346i	$0.587628\pi$
$32$	−110.262	+	63.6597i	−0.609117	+	0.351674i
$33$	1.19583	−	0.553867i	0.00630810	−	0.00292170i
$34$	58.1952	+	33.5990i	0.293541	+	0.169476i
$35$	197.060	−	56.3252i	0.951692	−	0.272020i
$36$	−130.497	+	153.898i	−0.604151	+	0.712490i
$37$	188.615			0.838058			0.419029	−	0.907973i	$-0.362371\pi$
$37$	188.615			0.838058			0.419029	+	0.907973i	$0.362371\pi$
$38$	−47.2144	+	81.7777i	−0.201558	+	0.349108i
$39$	6.67351	−	74.0738i	0.0274004	−	0.304136i
$40$	107.629	−	62.1397i	0.425442	−	0.245629i
$41$	−53.2437	−	92.2207i	−0.202811	−	0.351279i	0.746622	−	0.665249i	$-0.231674\pi$
$41$	−53.2437	−	92.2207i	−0.202811	−	0.351279i	−0.949433	+	0.313969i	$0.898341\pi$
$42$	−13.0919	−	68.6083i	−0.0480983	−	0.252059i
$43$	−21.5586	+	37.3406i	−0.0764572	+	0.132428i	−0.901719	−	0.432323i	$-0.857694\pi$
$43$	−21.5586	+	37.3406i	−0.0764572	+	0.132428i	0.825262	+	0.564750i	$0.191028\pi$
$44$		−	1.89539i		−	0.00649410i
$45$	193.240	−	227.892i	0.640144	−	0.754937i
$46$	−86.1520			−0.276139
$47$	68.8818	−	119.307i	0.213776	−	0.370270i	−0.739118	−	0.673576i	$-0.764757\pi$
$47$	68.8818	−	119.307i	0.213776	−	0.370270i	0.952893	+	0.303306i	$0.0980906\pi$
$48$	112.761	+	243.457i	0.339075	+	0.732082i
$49$	−302.577	−	161.542i	−0.882150	−	0.470969i
$50$	1.59393	−	0.920258i	0.00450832	−	0.00260288i
$51$	276.958	−	393.370i	0.760429	−	1.08006i
$52$	−92.6354	−	53.4830i	−0.247043	−	0.142630i
$53$		−	419.280i		−	1.08665i	−0.839522	−	0.543325i	$-0.817165\pi$
$53$		−	419.280i		−	1.08665i	0.839522	−	0.543325i	$-0.182835\pi$
$54$	−71.4418	−	72.5580i	−0.180037	−	0.182850i
$55$			2.80669i			0.00688098i
$56$	−201.769	−	50.4884i	−0.481473	−	0.120479i
$57$	552.775	+	389.190i	1.28451	+	0.904376i
$58$	104.056	+	180.230i	0.235572	+	0.408023i
$59$	217.560	+	376.825i	0.480066	+	0.831498i	0.999739	−	0.0228670i	$-0.00727943\pi$
$59$	217.560	+	376.825i	0.480066	+	0.831498i	−0.519673	+	0.854365i	$0.673946\pi$
$60$	−180.604	−	389.934i	−0.388599	−	0.839005i
$61$	163.504	+	94.3989i	0.343189	+	0.198140i	0.661681	−	0.749785i	$-0.269843\pi$
$61$	163.504	+	94.3989i	0.343189	+	0.198140i	−0.318493	+	0.947925i	$0.603177\pi$
$62$	−179.537			−0.367761
$63$	−497.613	+	49.2767i	−0.995133	+	0.0985440i
$64$	320.670			0.626310
$65$	137.175	+	79.1977i	0.261760	+	0.151127i
$66$	0.952645	+	0.0858263i	0.00177670	+	0.000160068i
$67$	−185.350	−	321.035i	−0.337971	−	0.585383i	0.646080	−	0.763270i	$-0.276407\pi$
$67$	−185.350	−	321.035i	−0.337971	−	0.585383i	−0.984051	+	0.177887i	$0.943074\pi$
$68$	−345.956	−	599.213i	−0.616960	−	1.06861i
$69$	−55.3435	+	614.296i	−0.0965591	+	1.07178i
$70$	144.304	+	36.1090i	0.246394	+	0.0616551i
$71$		−	26.1630i		−	0.0437321i	−0.999761	−	0.0218661i	$-0.993039\pi$
$71$		−	26.1630i		−	0.0437321i	0.999761	−	0.0218661i	$-0.00696074\pi$
$72$	−285.466	+	102.234i	−0.467257	+	0.167339i
$73$		−	728.545i		−	1.16808i	−0.811725	−	0.584039i	$-0.801471\pi$
$73$		−	728.545i		−	1.16808i	0.811725	−	0.584039i	$-0.198529\pi$
$74$	118.555	+	68.4480i	0.186240	+	0.107526i
$75$	−5.53785	−	11.9565i	−0.00852607	−	0.0184082i
$76$	842.032	−	486.147i	1.27089	−	0.733749i
$77$	3.26580	−	3.37610i	0.00483341	−	0.00499665i
$78$	31.0759	−	44.1378i	0.0451109	−	0.0640721i
$79$	−48.6779	+	84.3125i	−0.0693251	+	0.120075i	−0.898604	−	0.438760i	$-0.855418\pi$
$79$	−48.6779	+	84.3125i	−0.0693251	+	0.120075i	0.829279	+	0.558834i	$0.188751\pi$
$80$	−571.409			−0.798568
$81$	−563.259	+	462.796i	−0.772646	+	0.634837i
$82$		−	77.2880i		−	0.104086i
$83$	−401.359	+	695.174i	−0.530781	+	0.919340i	0.468573	+	0.883425i	$0.344768\pi$
$83$	−401.359	+	695.174i	−0.530781	+	0.919340i	−0.999355	+	0.0359157i	$0.988565\pi$
$84$	−236.474	+	679.189i	−0.307160	+	0.882210i
$85$	512.291	+	887.315i	0.653715	+	1.13227i
$86$	−27.1017	+	15.6471i	−0.0339819	+	0.0196195i
$87$	1351.95	−	626.177i	1.66603	−	0.771647i
$88$	1.42415	−	2.46670i	0.00172517	−	0.00298808i
$89$	−236.618			−0.281814			−0.140907	−	0.990023i	$-0.545002\pi$
$89$	−236.618			−0.281814			−0.140907	+	0.990023i	$0.545002\pi$
$90$	204.164	−	73.1170i	0.239119	−	0.0856357i
$91$	−72.8512	−	254.878i	−0.0839218	−	0.293610i
$92$	768.227	+	443.536i	0.870578	+	0.502628i
$93$	−115.333	+	1280.16i	−0.128597	+	1.42738i
$94$	86.5924	−	49.9941i	0.0950141	−	0.0548564i
$95$	−1246.88	+	719.887i	−1.34660	+	0.777462i
$96$	−59.3623	+	658.903i	−0.0631108	+	0.700510i
$97$	−1268.09	−	732.133i	−1.32737	−	0.766360i	−0.342481	−	0.939525i	$-0.611267\pi$
$97$	−1268.09	−	732.133i	−1.32737	−	0.766360i	−0.984893	+	0.173165i	$0.944601\pi$
$98$	−131.564	−	211.343i	−0.135612	−	0.217846i
$99$	1.22395	−	6.73758i	0.00124254	−	0.00683992i
$100$	−18.9510			−0.0189510
$101$	−783.722	+	1357.45i	−0.772112	+	1.33734i	0.164292	+	0.986412i	$0.447466\pi$
$101$	−783.722	+	1357.45i	−0.772112	+	1.33734i	−0.936404	+	0.350925i	$0.885867\pi$
$102$	316.837	−	146.748i	0.307564	−	0.142453i
$103$	86.8588	−	50.1479i	0.0830918	−	0.0479730i	−0.457878	−	0.889015i	$-0.651391\pi$
$103$	86.8588	−	50.1479i	0.0830918	−	0.0479730i	0.540970	+	0.841042i	$0.318057\pi$
$104$	−80.3717	−	139.208i	−0.0757798	−	0.131254i
$105$	350.171	−	1005.74i	0.325459	−	0.934767i
$106$	152.156	−	263.541i	0.139421	−	0.241485i
$107$		−	553.381i		−	0.499976i	−0.968249	−	0.249988i	$-0.919573\pi$
$107$		−	553.381i		−	0.499976i	0.968249	−	0.249988i	$-0.0804266\pi$
$108$	263.505	+	1014.81i	0.234775	+	0.904169i
$109$	−400.600			−0.352023			−0.176012	−	0.984388i	$-0.556320\pi$
$109$	−400.600			−0.352023			−0.176012	+	0.984388i	$0.556320\pi$
$110$	−1.01854	+	1.76417i	−0.000882856	+	0.00152915i
$111$	564.219	−	801.374i	0.482462	−	0.685253i
$112$	687.334	+	664.878i	0.579883	+	0.560938i
$113$	−617.417	+	356.466i	−0.513997	+	0.296756i	−0.734475	−	0.678635i	$-0.762572\pi$
$113$	−617.417	+	356.466i	−0.513997	+	0.296756i	0.220478	+	0.975392i	$0.429238\pi$
$114$	206.215	+	445.229i	0.169419	+	0.365785i
$115$	−1137.59	−	656.788i	−0.922442	−	0.532572i
$116$		−	2142.84i		−	1.71515i
$117$	−294.756	−	249.937i	−0.232908	−	0.197493i
$118$			315.808i			0.246377i
$119$	416.236	−	1663.42i	0.320641	−	1.28139i
$120$	57.9449	−	643.170i	0.0440802	−	0.489276i
$121$	−665.468	−	1152.62i	−0.499976	−	0.865984i
$122$	68.5143	+	118.670i	0.0508442	+	0.0880648i
$123$	−551.092	−	49.6494i	−0.403986	−	0.0363962i
$124$	1600.95	+	924.307i	1.15943	+	0.669397i
$125$	1411.36			1.00988
$126$	−330.661	−	149.609i	−0.233790	−	0.105780i
$127$	102.170			0.0713865			0.0356932	−	0.999363i	$-0.488636\pi$
$127$	102.170			0.0713865			0.0356932	+	0.999363i	$0.488636\pi$
$128$	1083.65	+	625.648i	0.748300	+	0.432031i
$129$	94.1600	+	203.297i	0.0642661	+	0.138754i
$130$	57.4814	+	99.5606i	0.0387804	+	0.0671696i
$131$	−236.423	−	409.496i	−0.157682	−	0.273113i	0.776350	−	0.630302i	$-0.217069\pi$
$131$	−236.423	−	409.496i	−0.157682	−	0.273113i	−0.934032	+	0.357188i	$0.883735\pi$
$132$	−8.05298	−	5.66982i	−0.00531001	−	0.00373859i
$133$	2337.49	+	584.907i	1.52395	+	0.381338i
$134$		−	269.052i		−	0.173452i
$135$	−390.198	−	1502.73i	−0.248762	−	0.958035i
$136$		−	1039.77i		−	0.655585i
$137$	2268.47	+	1309.70i	1.41466	+	0.816756i	0.995823	−	0.0913039i	$-0.0291035\pi$
$137$	2268.47	+	1309.70i	1.41466	+	0.816756i	0.418840	+	0.908060i	$0.362437\pi$
$138$	−257.713	+	366.036i	−0.158971	+	0.225790i
$139$	−1075.92	+	621.185i	−0.656537	+	0.379052i	−0.790956	−	0.611873i	$-0.790417\pi$
$139$	−1075.92	+	621.185i	−0.656537	+	0.379052i	0.134419	+	0.990925i	$0.457083\pi$
$140$	−1100.87	−	1064.91i	−0.664577	−	0.642865i
$141$	−300.850	−	649.552i	−0.179689	−	0.387958i
$142$	9.49451	−	16.4450i	0.00561100	−	0.00971853i
$143$	3.63018			0.00212287
$144$	1371.69	+	249.181i	0.793802	+	0.144202i
$145$			3173.12i			1.81733i
$146$	264.387	−	457.932i	0.149869	−	0.259581i
$147$	−1591.47	+	802.334i	−0.892941	+	0.450173i
$148$	−704.781	−	1220.72i	−0.391437	−	0.677989i
$149$	973.891	−	562.276i	0.535465	−	0.309151i	−0.207774	−	0.978177i	$-0.566622\pi$
$149$	973.891	−	562.276i	0.535465	−	0.309151i	0.743239	+	0.669026i	$0.233289\pi$
$150$	0.858135	−	9.52502i	0.000467109	−	0.00518476i
$151$	237.798	−	411.879i	0.128157	−	0.221975i	−0.794805	−	0.606864i	$-0.792427\pi$
$151$	237.798	−	411.879i	0.128157	−	0.221975i	0.922963	+	0.384889i	$0.125760\pi$
$152$	1461.12			0.779686
$153$	−842.835	−	2353.44i	−0.445354	−	1.24356i
$154$	3.27792	−	0.936921i	0.00171521	−	0.000490255i
$155$	−2370.68	−	1368.71i	−1.22850	−	0.709276i
$156$	−504.342	+	233.594i	−0.258844	+	0.119888i
$157$	−1674.30	+	966.660i	−0.851108	+	0.491388i	−0.861025	−	0.508563i	$-0.830177\pi$
$157$	−1674.30	+	966.660i	−0.851108	+	0.491388i	0.00991644	+	0.999951i	$0.496843\pi$
$158$	−61.1936	+	35.3302i	−0.0308121	+	0.0177893i
$159$	−1781.40	−	1254.22i	−0.888519	−	0.625575i
$160$	−1220.20	−	704.481i	−0.602906	−	0.348088i
$161$	604.156	+	2113.71i	0.295740	+	1.03468i
$162$	−521.988	+	86.4882i	−0.253156	+	0.0419454i
$163$	−743.323			−0.357187			−0.178594	−	0.983923i	$-0.557155\pi$
$163$	−743.323			−0.357187			−0.178594	+	0.983923i	$0.557155\pi$
$164$	−397.902	+	689.186i	−0.189457	+	0.328149i
$165$	11.9249	+	8.39587i	0.00562636	+	0.00396132i
$166$	−504.554	+	291.304i	−0.235910	+	0.136202i
$167$	1811.60	+	3137.78i	0.839435	+	1.45394i	0.890368	+	0.455242i	$0.150447\pi$
$167$	1811.60	+	3137.78i	0.839435	+	1.45394i	−0.0509327	+	0.998702i	$0.516219\pi$
$168$	−818.078	+	706.230i	−0.375691	+	0.324326i
$169$	−996.065	+	1725.24i	−0.453375	+	0.785269i
$170$			743.638i			0.335496i
$171$	3307.12	−	1184.38i	1.47896	−	0.529658i
$172$	322.225			0.142845
$173$	1648.50	−	2855.29i	0.724470	−	1.25482i	−0.234722	−	0.972063i	$-0.575418\pi$
$173$	1648.50	−	2855.29i	0.724470	−	1.25482i	0.959192	−	0.282756i	$-0.0912488\pi$
$174$	1077.02	+	97.0313i	0.469244	+	0.0422754i
$175$	−33.7559	−	32.6531i	−0.0145812	−	0.0141048i
$176$	−11.3413	+	6.54791i	−0.00485729	+	0.00280436i
$177$	2251.83	+	202.873i	0.956259	+	0.0861519i
$178$	−148.728	−	85.8680i	−0.0626270	−	0.0361577i
$179$			2746.77i			1.14695i	0.819225	+	0.573473i	$0.194404\pi$
$179$			2746.77i			1.14695i	−0.819225	+	0.573473i	$0.805596\pi$
$180$	−2196.98	−	399.103i	−0.909740	−	0.165263i
$181$			738.434i			0.303245i	0.988438	+	0.151622i	$0.0484498\pi$
$181$			738.434i			0.303245i	−0.988438	+	0.151622i	$0.951550\pi$
$182$	46.7035	−	186.643i	0.0190214	−	0.0760159i
$183$	890.177	−	412.299i	0.359583	−	0.166547i
$184$	666.524	+	1154.45i	0.267048	+	0.462541i
$185$	1043.64	+	1807.64i	0.414757	+	0.718380i
$186$	−537.062	+	762.801i	−0.211716	+	0.300706i
$187$	20.3359	+	11.7409i	0.00795245	+	0.00459135i
$188$	−1029.54			−0.399398
$189$	−1279.19	+	2261.63i	−0.492313	+	0.870418i
$190$	−1044.98			−0.399005
$191$	−2879.69	−	1662.59i	−1.09093	−	0.629848i	−0.157105	−	0.987582i	$-0.550216\pi$
$191$	−2879.69	−	1662.59i	−1.09093	−	0.629848i	−0.933823	+	0.357734i	$0.883549\pi$
$192$	959.247	−	1362.44i	0.360561	−	0.512113i
$193$	1660.75	+	2876.50i	0.619394	+	1.07282i	0.989596	+	0.143871i	$0.0459550\pi$
$193$	1660.75	+	2876.50i	0.619394	+	1.07282i	−0.370202	+	0.928951i	$0.620712\pi$
$194$	−531.379	−	920.376i	−0.196654	−	0.340614i
$195$	746.830	−	345.906i	0.274265	−	0.127030i
$196$	85.1126	+	2561.90i	0.0310177	+	0.933638i
$197$			501.482i			0.181366i	0.995880	+	0.0906830i	$0.0289050\pi$
$197$			501.482i			0.181366i	−0.995880	+	0.0906830i	$0.971095\pi$
$198$	3.21437	−	3.79079i	0.00115371	−	0.00136060i
$199$		−	4067.59i		−	1.44896i	−0.689294	−	0.724482i	$-0.742079\pi$
$199$		−	4067.59i		−	1.44896i	0.689294	−	0.724482i	$-0.257921\pi$
$200$	−24.6633	−	14.2393i	−0.00871978	−	0.00503437i
$201$	−1918.44	−	172.837i	−0.673215	−	0.0606518i
$202$	−985.229	+	568.822i	−0.343171	+	0.198130i
$203$	3692.16	−	3816.86i	1.27655	−	1.31966i
$204$	−3580.77	−	322.602i	−1.22894	−	0.110719i
$205$	589.213	−	1020.55i	0.200744	−	0.347698i
$206$	72.7943			0.0246205
$207$	2444.42	+	2072.73i	0.820767	+	0.695965i
$208$			739.062i			0.246369i
$209$	−16.4987	+	28.5766i	−0.00546048	+	0.00945783i
$210$	585.085	−	505.092i	0.192260	−	0.165974i
$211$	−2456.95	−	4255.56i	−0.801628	−	1.38846i	−0.918544	−	0.395319i	$-0.870634\pi$
$211$	−2456.95	−	4255.56i	−0.801628	−	1.38846i	0.116916	−	0.993142i	$-0.462699\pi$
$212$	−2713.58	+	1566.68i	−0.879100	+	0.507549i
$213$	−111.160	−	78.2635i	−0.0357583	−	0.0251762i
$214$	200.821	−	347.832i	0.0641487	−	0.111109i
$215$	−477.150			−0.151355
$216$	−419.574	+	1518.69i	−0.132169	+	0.478396i
$217$	1259.03	+	4404.87i	0.393865	+	1.37798i
$218$	−251.800	−	145.377i	−0.0782296	−	0.0451659i
$219$	−3095.39	−	2179.35i	−0.955100	−	0.672452i
$220$	18.1649	−	10.4875i	0.00556672	−	0.00321394i
$221$	1147.66	−	662.599i	0.349320	−	0.201680i
$222$	645.461	−	298.956i	0.195137	−	0.0903810i
$223$	1033.31	+	596.580i	0.310293	+	0.179148i	0.647058	−	0.762441i	$-0.275999\pi$
$223$	1033.31	+	596.580i	0.310293	+	0.179148i	−0.336765	+	0.941589i	$0.609333\pi$
$224$	648.027	+	2267.20i	0.193295	+	0.676265i
$225$	−67.3657	−	12.2376i	−0.0199602	−	0.00362597i
$226$	−517.443			−0.152300
$227$	−2804.31	+	4857.22i	−0.819951	+	1.42020i	0.0857665	+	0.996315i	$0.472666\pi$
$227$	−2804.31	+	4857.22i	−0.819951	+	1.42020i	−0.905718	+	0.423882i	$0.860667\pi$
$228$	453.330	−	5031.81i	0.131678	−	1.46158i
$229$	4618.56	−	2666.53i	1.33276	−	0.769472i	0.347042	−	0.937850i	$-0.387186\pi$
$229$	4618.56	−	2666.53i	1.33276	−	0.769472i	0.985722	+	0.168378i	$0.0538530\pi$
$230$	−476.694	−	825.658i	−0.136662	−	0.236706i
$231$	−4.57487	−	23.9747i	−0.00130305	−	0.00682865i
$232$	1610.08	−	2788.73i	0.455632	−	0.789179i
$233$		−	111.828i		−	0.0314424i	−0.999876	−	0.0157212i	$-0.994996\pi$
$233$		−	111.828i		−	0.0314424i	0.999876	−	0.0157212i	$-0.00500442\pi$
$234$	−94.5698	−	264.066i	−0.0264197	−	0.0737715i
$235$	1524.54			0.423192
$236$	1625.87	−	2816.09i	0.448455	−	0.776746i
$237$	212.607	+	459.029i	0.0582713	+	0.125811i
$238$	865.279	−	894.503i	0.235663	−	0.243622i
$239$	4132.66	−	2385.99i	1.11849	−	0.645762i	0.177477	−	0.984125i	$-0.443206\pi$
$239$	4132.66	−	2385.99i	1.11849	−	0.645762i	0.941016	+	0.338363i	$0.109873\pi$
$240$	−1709.30	+	2427.76i	−0.459728	+	0.652963i
$241$	−4621.37	−	2668.15i	−1.23522	−	0.713156i	−0.267109	−	0.963666i	$-0.586068\pi$
$241$	−4621.37	−	2668.15i	−1.23522	−	0.713156i	−0.968114	+	0.250510i	$0.919402\pi$
$242$		−	965.987i		−	0.256595i
$243$	281.371	+	3777.53i	0.0742797	+	0.997237i
$244$		−	1410.93i		−	0.370186i
$245$	−126.035	−	3793.67i	−0.0328656	−	0.989259i
$246$	−328.375	−	231.198i	−0.0851075	−	0.0599212i
$247$	931.104	+	1612.72i	0.239857	+	0.415445i
$248$	1389.00	+	2405.83i	0.355653	+	0.616008i
$249$	1752.99	+	3784.79i	0.446149	+	0.963258i
$250$	887.119	+	512.178i	0.224425	+	0.129572i
$251$	−3081.73			−0.774970			−0.387485	−	0.921876i	$-0.626656\pi$
$251$	−3081.73			−0.774970			−0.387485	+	0.921876i	$0.626656\pi$
$252$	2178.30	+	3036.42i	0.544525	+	0.759035i
$253$	−30.1052			−0.00748101
$254$	64.2194	+	37.0771i	0.0158641	+	0.00915915i
$255$	5302.41	+	477.709i	1.30216	+	0.117315i
$256$	−828.589	−	1435.16i	−0.202292	−	0.350381i
$257$	−1067.55	−	1849.05i	−0.259113	−	0.448797i	0.706892	−	0.707322i	$-0.250097\pi$
$257$	−1067.55	−	1849.05i	−0.259113	−	0.448797i	−0.966005	+	0.258525i	$0.916764\pi$
$258$	−14.5909	+	161.954i	−0.00352088	+	0.0390807i
$259$	847.957	−	3388.72i	0.203434	−	0.812992i
$260$		−	1183.72i		−	0.282352i
$261$	1383.74	−	7617.20i	0.328166	−	1.80649i
$262$		−	343.189i		−	0.0809248i
$263$	−1429.14	−	825.115i	−0.335075	−	0.193455i	0.323017	−	0.946393i	$-0.395303\pi$
$263$	−1429.14	−	825.115i	−0.335075	−	0.193455i	−0.658092	+	0.752938i	$0.728636\pi$
$264$	−6.22015	−	13.4296i	−0.00145009	−	0.00313082i
$265$	4018.27	−	2319.95i	0.931473	−	0.537786i
$266$	1256.98	+	1215.92i	0.289739	+	0.280273i
$267$	−707.812	+	1005.32i	−0.162238	+	0.230430i
$268$	−1385.16	+	2399.16i	−0.315716	+	0.546837i
$269$	−5477.73			−1.24157			−0.620787	−	0.783979i	$-0.713187\pi$
$269$	−5477.73			−1.24157			−0.620787	+	0.783979i	$0.713187\pi$
$270$	300.077	−	1086.16i	0.0676374	−	0.244820i
$271$		−	3607.16i		−	0.808558i	−0.914636	−	0.404279i	$-0.867523\pi$
$271$		−	3607.16i		−	0.808558i	0.914636	−	0.404279i	$-0.132477\pi$
$272$	−2390.31	+	4140.15i	−0.532846	+	0.922916i
$273$	−1300.83	−	452.912i	−0.288388	−	0.100408i
$274$	950.577	+	1646.45i	0.209586	+	0.363013i
$275$	0.556988	−	0.321577i	0.000122137	−	7.05158e-5i
$276$	4182.52	−	1937.20i	0.912167	−	0.422485i
$277$	−1488.99	+	2579.00i	−0.322977	+	0.559413i	−0.981101	−	0.193497i	$-0.938017\pi$
$277$	−1488.99	+	2579.00i	−0.322977	+	0.559413i	0.658124	+	0.752910i	$0.271350\pi$
$278$	−901.707			−0.194535
$279$	5094.05	+	4319.47i	1.09309	+	0.926881i
$280$	−632.554	−	2213.06i	−0.135008	−	0.472342i
$281$	−4936.36	−	2850.01i	−1.04797	−	0.605043i	−0.125886	−	0.992045i	$-0.540177\pi$
$281$	−4936.36	−	2850.01i	−1.04797	−	0.605043i	−0.922079	+	0.387002i	$0.873511\pi$
$282$	46.6192	−	517.458i	0.00984445	−	0.109270i
$283$	−476.719	+	275.234i	−0.100134	+	0.0578125i	−0.549231	−	0.835671i	$-0.685079\pi$
$283$	−476.719	+	275.234i	−0.100134	+	0.0578125i	0.449097	+	0.893483i	$0.351746\pi$
$284$	−169.327	+	97.7611i	−0.0353793	+	0.0204262i
$285$	−671.291	+	7451.11i	−0.139522	+	1.54865i
$286$	2.28178	+	1.31739i	0.000471763	+	0.000272373i
$287$	−1896.23	+	541.996i	−0.390004	+	0.111474i
$288$	2621.92	+	2223.24i	0.536452	+	0.454881i
$289$	3659.06			0.744771
$290$	−1151.52	+	1994.49i	−0.233170	+	0.403863i
$291$	−6903.98	+	3197.69i	−1.39078	+	0.644164i
$292$	−4715.14	+	2722.29i	−0.944976	+	0.545582i
$293$	−3915.00	−	6780.98i	−0.780603	−	1.35204i	−0.931591	−	0.363508i	$-0.881579\pi$
$293$	−3915.00	−	6780.98i	−0.780603	−	1.35204i	0.150988	−	0.988536i	$-0.451754\pi$
$294$	−1291.50	−	73.2286i	−0.256196	−	0.0145265i
$295$	−2407.59	+	4170.08i	−0.475171	+	0.823021i
$296$		−	2118.22i		−	0.415943i
$297$	−24.9648	−	25.3548i	−0.00487746	−	0.00495366i
$298$	816.195			0.158661
$299$	−849.492	+	1471.36i	−0.164306	+	0.284586i
$300$	−56.6897	+	80.5177i	−0.0109099	+	0.0154956i
$301$	573.953	+	555.201i	0.109907	+	0.106316i
$302$	298.940	−	172.593i	0.0569604	−	0.0328861i
$303$	3423.01	+	7390.46i	0.648999	+	1.40122i
$304$	−5817.86	−	3358.94i	−1.09762	−	0.633712i
$305$			2089.30i			0.392240i
$306$	324.287	−	1785.13i	0.0605825	−	0.333494i
$307$		−	5845.06i		−	1.08663i	−0.839529	−	0.543315i	$-0.817169\pi$
$307$		−	5845.06i		−	1.08663i	0.839529	−	0.543315i	$-0.182831\pi$
$308$	−34.0531	−	8.52109i	−0.00629986	−	0.00157641i
$309$	46.7627	−	519.050i	0.00860917	−	0.0955591i
$310$	−993.407	−	1720.63i	−0.182006	−	0.315243i
$311$	2909.85	+	5040.01i	0.530554	+	0.918947i	0.999364	+	0.0356482i	$0.0113496\pi$
$311$	2909.85	+	5040.01i	0.530554	+	0.918947i	−0.468810	+	0.883299i	$0.655317\pi$
$312$	−831.878	−	74.9462i	−0.150948	−	0.0135993i
$313$	5754.23	+	3322.21i	1.03913	+	0.599943i	0.919587	−	0.392886i	$-0.128523\pi$
$313$	5754.23	+	3322.21i	1.03913	+	0.599943i	0.119545	+	0.992829i	$0.461857\pi$
$314$	−1403.19			−0.252187
$315$	−3225.64	−	4496.34i	−0.576965	−	0.804254i
$316$	727.561			0.129521
$317$	5206.82	+	3006.16i	0.922536	+	0.532626i	0.884443	−	0.466648i	$-0.154538\pi$
$317$	5206.82	+	3006.16i	0.922536	+	0.532626i	0.0380927	+	0.999274i	$0.487872\pi$
$318$	−664.559	−	1434.82i	−0.117191	−	0.253021i
$319$	36.3615	+	62.9800i	0.00638198	+	0.0110539i
$320$	1774.33	+	3073.22i	0.309962	+	0.536870i
$321$	−2351.16	−	1655.37i	−0.408814	−	0.287831i
$322$	−387.313	+	1547.83i	−0.0670314	+	0.267880i
$323$			12045.7i			2.07505i
$324$	5099.89	+	1916.13i	0.874468	+	0.328554i
$325$		−	36.2964i		−	0.00619496i
$326$	−467.221	−	269.750i	−0.0793772	−	0.0458285i
$327$	−1198.35	+	1702.04i	−0.202657	+	0.287838i
$328$	−1035.68	+	597.947i	−0.174346	+	0.100659i
$329$	−1833.83	−	1773.92i	−0.307302	−	0.297263i
$330$	4.44861	+	9.60479i	0.000742085	+	0.00160220i
$331$	1371.24	−	2375.06i	0.227705	−	0.394397i	−0.729422	−	0.684064i	$-0.760211\pi$
$331$	1371.24	−	2375.06i	0.227705	−	0.394397i	0.957128	+	0.289667i	$0.0935444\pi$
$332$	5998.89			0.991662
$333$	−1717.02	−	4794.42i	−0.282560	−	0.788988i
$334$			2629.70i			0.430811i
$335$	2051.14	−	3552.68i	0.334525	−	0.579414i
$336$	4880.96	−	931.390i	0.792494	−	0.151225i
$337$	1953.27	+	3383.16i	0.315731	+	0.546862i	0.979593	−	0.200993i	$-0.0644169\pi$
$337$	1953.27	+	3383.16i	0.315731	+	0.546862i	−0.663862	+	0.747856i	$0.731084\pi$
$338$	−1252.17	+	722.940i	−0.201506	+	0.116339i
$339$	−332.402	+	3689.56i	−0.0532555	+	0.591119i
$340$	3828.47	−	6631.10i	0.610670	−	1.05771i
$341$	−62.7377			−0.00996316
$342$	2508.52	+	455.698i	0.396624	+	0.0720506i
$343$	−4262.62	+	4709.96i	−0.671019	+	0.741440i
$344$	419.350	+	242.112i	0.0657262	+	0.0379471i
$345$	−6193.48	+	2868.61i	−0.966509	+	0.447654i
$346$	2072.36	−	1196.48i	0.321996	−	0.185904i
$347$	−509.871	+	294.374i	−0.0788799	+	0.0455413i	−0.538921	−	0.842356i	$-0.681168\pi$
$347$	−509.871	+	294.374i	−0.0788799	+	0.0455413i	0.460041	+	0.887898i	$0.347835\pi$
$348$	−9104.33	−	6410.04i	−1.40242	−	0.987397i
$349$	6360.33	+	3672.14i	0.975532	+	0.563224i	0.900918	−	0.433989i	$-0.142894\pi$
$349$	6360.33	+	3672.14i	0.975532	+	0.563224i	0.0746138	+	0.997213i	$0.476228\pi$
$350$	−9.36780	−	32.7743i	−0.00143066	−	0.00500532i
$351$	−1943.64	+	504.683i	−0.295566	+	0.0767464i
$352$	−32.2913			−0.00488957
$353$	4370.77	−	7570.40i	0.659016	−	1.14145i	−0.321855	−	0.946789i	$-0.604306\pi$
$353$	4370.77	−	7570.40i	0.659016	−	1.14145i	0.980871	−	0.194660i	$-0.0623604\pi$
$354$	1341.78	+	944.701i	0.201454	+	0.141837i
$355$	250.740	−	144.765i	0.0374870	−	0.0216431i
$356$	884.148	+	1531.39i	0.131628	+	0.227987i
$357$	−5822.29	−	6744.39i	−0.863161	−	0.999862i
$358$	−996.797	+	1726.50i	−0.147157	+	0.254884i
$359$		−	7817.81i		−	1.14933i	−0.818390	−	0.574663i	$-0.805133\pi$
$359$		−	7817.81i		−	1.14933i	0.818390	−	0.574663i	$-0.194867\pi$
$360$	−2559.32	−	2170.16i	−0.374689	−	0.317715i
$361$	−10068.0			−1.46785
$362$	−267.976	+	464.148i	−0.0389075	+	0.0673897i
$363$	−6887.85	−	620.545i	−0.995918	−	0.0897249i
$364$	−1377.35	+	1423.87i	−0.198332	+	0.205031i
$365$	6982.19	−	4031.17i	1.00127	−	0.578085i
$366$	709.150	+	63.8892i	0.101278	+	0.00912443i
$367$	2084.12	+	1203.27i	0.296431	+	0.171145i	0.640839	−	0.767676i	$-0.278587\pi$
$367$	2084.12	+	1203.27i	0.296431	+	0.171145i	−0.344407	+	0.938820i	$0.611920\pi$
$368$		−	6129.05i		−	0.868204i
$369$	−1859.47	+	2192.92i	−0.262331	+	0.309374i
$370$			1514.94i			0.212859i
$371$	−7532.91	−	1884.95i	−1.05415	−	0.263779i
$372$	8716.16	−	4037.03i	1.21482	−	0.562662i
$373$	−2185.08	−	3784.67i	−0.303322	−	0.525370i	0.673564	−	0.739129i	$-0.264763\pi$
$373$	−2185.08	−	3784.67i	−0.303322	−	0.525370i	−0.976886	+	0.213759i	$0.931429\pi$
$374$	8.52152	+	14.7597i	0.00117817	+	0.00204066i
$375$	4221.90	−	5996.47i	0.581381	−	0.825750i
$376$	−1339.86	−	773.570i	−0.183772	−	0.106101i
$377$	4104.12			0.560671
$378$	−1624.78	+	957.348i	−0.221084	+	0.130266i
$379$	11260.9			1.52620			0.763102	−	0.646278i	$-0.223675\pi$
$379$	11260.9			1.52620			0.763102	+	0.646278i	$0.223675\pi$
$380$	9318.22	+	5379.88i	1.25793	+	0.726268i
$381$	305.628	−	434.090i	0.0410965	−	0.0583704i
$382$	−1206.70	−	2090.07i	−0.161624	−	0.279940i
$383$	−1486.57	−	2574.82i	−0.198330	−	0.343517i	0.749657	−	0.661826i	$-0.230218\pi$
$383$	−1486.57	−	2574.82i	−0.198330	−	0.343517i	−0.947987	+	0.318309i	$0.896885\pi$
$384$	5899.83	−	2732.60i	0.784048	−	0.363144i
$385$	50.4259	+	12.6180i	0.00667518	+	0.00167032i
$386$			2410.72i			0.317882i
$387$	1145.42	+	208.077i	0.150452	+	0.0273311i
$388$			10942.8i			1.43179i
$389$	−5714.27	−	3299.13i	−0.744794	−	0.430007i	0.0790159	−	0.996873i	$-0.474822\pi$
$389$	−5714.27	−	3299.13i	−0.744794	−	0.430007i	−0.823810	+	0.566866i	$0.808156\pi$
$390$	594.954	+	53.6010i	0.0772479	+	0.00695947i
$391$	−9517.53	+	5494.95i	−1.23100	+	0.710720i
$392$	−1814.18	+	3398.06i	−0.233750	+	0.437827i
$393$	−2447.07	−	220.463i	−0.314092	−	0.0282974i
$394$	−181.987	+	315.210i	−0.0232699	+	0.0403047i
$395$	−1077.37			−0.137237
$396$	−48.1790	+	17.2543i	−0.00611385	+	0.00218955i
$397$		−	5908.48i		−	0.746947i	−0.927641	−	0.373474i	$-0.878167\pi$
$397$		−	5908.48i		−	0.746947i	0.927641	−	0.373474i	$-0.121833\pi$
$398$	1476.12	−	2556.71i	0.185907	−	0.322001i
$399$	9477.42	−	8181.66i	1.18913	−	1.02655i
$400$	65.4693	+	113.396i	0.00818366	+	0.0141745i
$401$	−4847.53	+	2798.72i	−0.603676	+	0.348532i	−0.770486	−	0.637457i	$-0.779986\pi$
$401$	−4847.53	+	2798.72i	−0.603676	+	0.348532i	0.166811	+	0.985989i	$0.446653\pi$
$402$	−1143.13	−	804.835i	−0.141826	−	0.0998546i
$403$	−1770.30	+	3066.25i	−0.218821	+	0.379009i
$404$	11713.9			1.44254
$405$	−7551.93	−	2837.40i	−0.926564	−	0.348127i
$406$	3705.87	−	1059.24i	0.453003	−	0.129481i
$407$	41.4283	+	23.9187i	0.00504552	+	0.00291303i
$408$	−4417.70	−	3110.35i	−0.536051	−	0.377415i
$409$	948.568	−	547.656i	0.114679	−	0.0662099i	−0.441563	−	0.897230i	$-0.645576\pi$
$409$	948.568	−	547.656i	0.114679	−	0.0662099i	0.556242	+	0.831020i	$0.312243\pi$
$410$	740.708	−	427.648i	0.0892219	−	0.0515123i
$411$	12350.4	−	5720.30i	1.48224	−	0.686525i
$412$	−649.115	−	374.767i	−0.0776204	−	0.0448141i
$413$	7748.24	−	2214.66i	0.923162	−	0.263865i
$414$	784.269	+	2189.90i	0.0931031	+	0.259971i
$415$	−8883.16			−1.05074
$416$	−911.178	+	1578.21i	−0.107390	+	0.186005i
$417$	−579.251	+	6429.50i	−0.0680241	+	0.755046i
$418$	−20.7408	+	11.9747i	−0.00242695	+	0.00140120i
$419$	6796.78	+	11772.4i	0.792468	+	1.37260i	0.924434	+	0.381341i	$0.124538\pi$
$419$	6796.78	+	11772.4i	0.792468	+	1.37260i	−0.131966	+	0.991254i	$0.542129\pi$
$420$	−7817.63	+	1491.77i	−0.908241	+	0.173312i
$421$	2842.13	−	4922.72i	0.329019	−	0.569878i	−0.653298	−	0.757101i	$-0.726615\pi$
$421$	2842.13	−	4922.72i	0.329019	−	0.569878i	0.982318	+	0.187222i	$0.0599485\pi$
$422$		−	3566.49i		−	0.411407i
$423$	−3659.72	−	664.825i	−0.420666	−	0.0764182i
$424$	−4708.68			−0.539324
$425$	117.392	−	203.329i	0.0133984	−	0.0232068i
$426$	−41.4685	−	89.5327i	−0.00471633	−	0.0101828i
$427$	2431.06	−	2513.17i	0.275521	−	0.284826i
$428$	−3581.48	+	2067.77i	−0.404480	+	0.233527i
$429$	10.8592	−	15.4236i	0.00122212	−	0.00173581i
$430$	−299.916	−	173.157i	−0.0336355	−	0.0194194i
$431$			4806.22i			0.537140i	0.963260	+	0.268570i	$0.0865511\pi$
$431$			4806.22i			0.537140i	−0.963260	+	0.268570i	$0.913449\pi$
$432$	5161.95	−	5082.54i	0.574894	−	0.566050i
$433$			9621.49i			1.06785i	0.845532	+	0.533925i	$0.179284\pi$
$433$			9621.49i			1.06785i	−0.845532	+	0.533925i	$0.820716\pi$
$434$	−807.142	+	3225.61i	−0.0892720	+	0.356761i
$435$	13481.7	+	9491.99i	1.48597	+	1.04622i
$436$	1496.89	+	2592.68i	0.164422	+	0.284787i
$437$	−7721.67	−	13374.3i	−0.845257	−	1.46403i
$438$	−1154.75	−	2493.16i	−0.125972	−	0.271981i
$439$	−11200.0	−	6466.31i	−1.21764	−	0.703007i	−0.253230	−	0.967406i	$-0.581493\pi$
$439$	−11200.0	−	6466.31i	−1.21764	−	0.703007i	−0.964413	+	0.264399i	$0.914826\pi$
$440$	31.5202			0.00341516
$441$	−1351.80	+	9161.81i	−0.145967	+	0.989290i
$442$	961.823			0.103505
$443$	11401.0	+	6582.35i	1.22275	+	0.705953i	0.965502	−	0.260394i	$-0.0838524\pi$
$443$	11401.0	+	6582.35i	1.22275	+	0.705953i	0.257244	+	0.966347i	$0.417186\pi$
$444$	−7294.76	−	657.205i	−0.779716	−	0.0702467i
$445$	−1309.25	−	2267.68i	−0.139470	−	0.241569i
$446$	432.995	+	749.969i	0.0459706	+	0.0796235i
$447$	524.319	−	5819.78i	0.0554798	−	0.615807i
$448$	1441.64	−	5761.27i	0.152033	−	0.607577i
$449$			7787.86i			0.818557i	0.912410	+	0.409278i	$0.134219\pi$
$449$			7787.86i			0.818557i	−0.912410	+	0.409278i	$0.865781\pi$
$450$	−37.9022	−	32.1389i	−0.00397050	−	0.00336676i
$451$		−	27.0077i		−	0.00281983i
$452$	4614.09	+	2663.95i	0.480152	+	0.277216i
$453$	−1038.61	−	2242.42i	−0.107723	−	0.232579i
$454$	−3525.34	+	2035.36i	−0.364433	+	0.210406i
$455$	2039.59	−	2108.47i	0.210148	−	0.217246i
$456$	4370.75	−	6207.88i	0.448858	−	0.637524i
$457$	−2408.56	+	4171.76i	−0.246538	+	0.427017i	−0.962563	−	0.271058i	$-0.912626\pi$
$457$	−2408.56	+	4171.76i	−0.246538	+	0.427017i	0.716025	+	0.698075i	$0.245960\pi$
$458$	3870.71			0.394904
$459$	−12520.3	−	3459.05i	−1.27320	−	0.351753i
$460$			9816.65i			0.995008i
$461$	25.6446	−	44.4177i	0.00259086	−	0.00448750i	−0.864727	−	0.502242i	$-0.832509\pi$
$461$	25.6446	−	44.4177i	0.00259086	−	0.00448750i	0.867318	+	0.497755i	$0.165842\pi$
$462$	5.82478	−	16.7297i	0.000586566	−	0.00168471i
$463$	4787.43	+	8292.07i	0.480542	+	0.832322i	0.999751	−	0.0223247i	$-0.00710677\pi$
$463$	4787.43	+	8292.07i	0.480542	+	0.832322i	−0.519209	+	0.854647i	$0.673773\pi$
$464$	−12822.0	+	7402.77i	−1.28286	+	0.740657i
$465$	−12906.9	+	5978.04i	−1.28719	+	0.596183i
$466$	40.5820	−	70.2901i	0.00403418	−	0.00698740i
$467$	−12806.5			−1.26898			−0.634492	−	0.772929i	$-0.718791\pi$
$467$	−12806.5			−1.26898			−0.634492	+	0.772929i	$0.718791\pi$
$468$	−516.201	+	2841.58i	−0.0509859	+	0.280667i
$469$	−6601.09	+	1886.77i	−0.649915	+	0.185764i
$470$	958.262	+	553.253i	0.0940453	+	0.0542971i
$471$	−901.404	+	10005.3i	−0.0881837	+	0.978811i
$472$	4231.89	−	2443.28i	0.412688	−	0.238265i
$473$	−9.47047	+	5.46778i	−0.000920619	+	0.000531520i
$474$	−32.9452	+	365.681i	−0.00319245	+	0.0354352i
$475$	285.723	+	164.962i	0.0275998	+	0.0159347i
$476$	−12321.0	+	3521.67i	−1.18641	+	0.339108i
$477$	−10657.7	+	3816.84i	−1.02302	+	0.366375i
$478$	3463.49			0.331415
$479$	2542.79	−	4404.24i	0.242553	−	0.420114i	−0.718888	−	0.695126i	$-0.755348\pi$
$479$	2542.79	−	4404.24i	0.242553	−	0.420114i	0.961441	+	0.275012i	$0.0886818\pi$
$480$	−6643.21	+	3076.91i	−0.631708	+	0.292586i
$481$	2338.01	−	1349.85i	0.221630	−	0.127958i
$482$	−1936.53	−	3354.17i	−0.183001	−	0.316967i
$483$	10787.8	+	3756.01i	1.01628	+	0.353839i
$484$	−4973.19	+	8613.81i	−0.467054	+	0.808961i
$485$		−	16204.1i		−	1.51709i
$486$	−1194.00	+	2476.50i	−0.111442	+	0.231145i
$487$	16991.3			1.58100			0.790501	−	0.612461i	$-0.209820\pi$
$487$	16991.3			1.58100			0.790501	+	0.612461i	$0.209820\pi$
$488$	1060.14	−	1836.21i	0.0983405	−	0.170331i
$489$	−2223.56	+	3158.17i	−0.205629	+	0.292060i
$490$	1297.49	−	2430.27i	0.119622	−	0.224058i
$491$	8055.59	−	4650.90i	0.740415	−	0.427479i	−0.0818052	−	0.996648i	$-0.526069\pi$
$491$	8055.59	−	4650.90i	0.740415	−	0.427479i	0.822220	+	0.569170i	$0.192735\pi$
$492$	1737.89	+	3752.19i	0.159248	+	0.343825i
$493$	22990.8	+	13273.8i	2.10032	+	1.21262i
$494$			1351.58i			0.123098i
$495$	71.3435	−	25.5502i	0.00647808	−	0.00231999i
$496$		−	12772.6i		−	1.15627i
$497$	−470.054	−	117.621i	−0.0424241	−	0.0106157i
$498$	−271.640	+	3015.11i	−0.0244427	+	0.271306i
$499$	250.332	+	433.588i	0.0224577	+	0.0388979i	0.877036	−	0.480425i	$-0.159518\pi$
$499$	250.332	+	433.588i	0.0224577	+	0.0388979i	−0.854578	+	0.519323i	$0.826184\pi$
$500$	−5273.69	−	9134.30i	−0.471693	−	0.816997i
$501$	18750.7	+	1689.30i	1.67210	+	0.150644i
$502$	−1937.05	−	1118.35i	−0.172220	−	0.0994315i
$503$	3581.09			0.317441			0.158721	−	0.987324i	$-0.449263\pi$
$503$	3581.09			0.317441			0.158721	+	0.987324i	$0.449263\pi$
$504$	553.396	+	5588.39i	0.0489092	+	0.493902i
$505$	−17345.9			−1.52848
$506$	−18.9228	−	10.9251i	−0.00166249	−	0.000959842i
$507$	4350.44	+	9392.84i	0.381085	+	0.822782i
$508$	−381.768	−	661.241i	−0.0333429	−	0.0577516i
$509$	5085.37	+	8808.13i	0.442839	+	0.767020i	0.997899	−	0.0647904i	$-0.0206379\pi$
$509$	5085.37	+	8808.13i	0.442839	+	0.767020i	−0.555060	+	0.831811i	$0.687305\pi$
$510$	3159.51	+	2224.50i	0.274325	+	0.193142i
$511$	−13089.3	−	3275.32i	−1.13314	−	0.283545i
$512$		−	11213.1i		−	0.967882i
$513$	4860.76	−	17594.0i	0.418338	−	1.51421i
$514$		−	1549.65i		−	0.132981i
$515$	961.210	+	554.955i	0.0822446	+	0.0474839i
$516$	963.895	−	1369.04i	0.0822348	−	0.116800i
$517$	30.2591	−	17.4701i	0.00257407	−	0.00148614i
$518$	1762.75	−	1822.28i	0.149519	−	0.154569i
$519$	−7200.05	−	15545.3i	−0.608954	−	1.31476i
$520$	889.422	−	1540.52i	0.0750072	−	0.129916i
$521$	389.899			0.0327865			0.0163933	−	0.999866i	$-0.494782\pi$
$521$	389.899			0.0327865			0.0163933	+	0.999866i	$0.494782\pi$
$522$	3634.02	−	4285.69i	0.304707	−	0.359348i
$523$		−	14306.4i		−	1.19613i	−0.801448	−	0.598065i	$-0.795937\pi$
$523$		−	14306.4i		−	1.19613i	0.801448	−	0.598065i	$-0.204063\pi$
$524$	−1766.84	+	3060.25i	−0.147299	+	0.255130i
$525$	−239.711	+	45.7419i	−0.0199273	+	0.00380255i
$526$	−598.865	−	1037.26i	−0.0496421	−	0.0859827i
$527$	−19834.1	+	11451.2i	−1.63944	+	0.946532i
$528$	−6.10589	+	67.7734i	−0.000503266	+	0.00558609i
$529$	961.351	−	1665.11i	0.0790130	−	0.136854i
$530$	3367.62			0.276000
$531$	7598.02	−	8960.53i	0.620953	−	0.732305i
$532$	−4948.76	−	17313.8i	−0.403301	−	1.41099i
$533$	−1319.98	−	762.090i	−0.107269	−	0.0619320i
$534$	−809.730	+	375.039i	−0.0656188	+	0.0303924i
$535$	5303.46	−	3061.96i	0.428577	−	0.247439i
$536$	−3605.35	+	2081.55i	−0.290536	+	0.167741i
$537$	11670.3	+	8216.63i	0.937820	+	0.660286i
$538$	−3443.07	−	1987.86i	−0.275913	−	0.159299i
$539$	−45.9740	−	73.8523i	−0.00367392	−	0.00590175i
$540$	−8267.67	+	8140.49i	−0.658859	+	0.648724i
$541$	21775.6			1.73051			0.865257	−	0.501328i	$-0.167155\pi$
$541$	21775.6			1.73051			0.865257	+	0.501328i	$0.167155\pi$
$542$	1309.03	−	2267.30i	0.103741	−	0.179685i
$543$	3137.40	+	2208.93i	0.247954	+	0.174575i
$544$	−10208.6	+	5893.96i	−0.804581	+	0.464525i
$545$	−2216.59	−	3839.25i	−0.174217	−	0.301753i
$546$	−653.287	−	756.750i	−0.0512053	−	0.0593149i
$547$	8960.85	−	15520.7i	0.700436	−	1.21319i	−0.267878	−	0.963453i	$-0.586322\pi$
$547$	8960.85	−	15520.7i	0.700436	−	1.21319i	0.968314	−	0.249738i	$-0.0803444\pi$
$548$		−	19575.4i		−	1.52595i
$549$	911.107	−	5015.46i	0.0708290	−	0.389899i
$550$	0.466799			3.61897e−5
$551$	−18652.7	+	32307.4i	−1.44216	+	2.49790i
$552$	6898.78	+	621.530i	0.531941	+	0.0479240i
$553$	1295.94	+	1253.61i	0.0996549	+	0.0963991i
$554$	−1871.83	+	1080.70i	−0.143550	+	0.0828783i
$555$	10802.1	+	973.189i	0.826168	+	0.0744317i
$556$	8040.62	+	4642.25i	0.613306	+	0.354092i
$557$		−	19309.8i		−	1.46891i	−0.678657	−	0.734455i	$-0.737438\pi$
$557$		−	19309.8i		−	1.46891i	0.678657	−	0.734455i	$-0.262562\pi$
$558$	1634.38	+	4563.65i	0.123994	+	0.346227i
$559$			617.148i			0.0466951i
$560$	−2568.88	+	10266.1i	−0.193848	+	0.774683i
$561$	110.716	−	51.2801i	0.00833235	−	0.00385926i
$562$	−2068.52	−	3582.78i	−0.155259	−	0.268916i
$563$	−3232.24	−	5598.41i	−0.241959	−	0.419085i	0.719313	−	0.694686i	$-0.244457\pi$
$563$	−3232.24	−	5598.41i	−0.241959	−	0.419085i	−0.961272	+	0.275601i	$0.911123\pi$
$564$	−3079.74	+	4374.23i	−0.229930	+	0.326575i
$565$	−6832.55	−	3944.78i	−0.508757	−	0.293731i
$566$	−399.527			−0.0296702
$567$	5782.50	+	12200.3i	0.428293	+	0.903640i
$568$	−293.821			−0.0217050
$569$	17286.9	+	9980.61i	1.27365	+	0.735341i	0.975673	−	0.219233i	$-0.0703555\pi$
$569$	17286.9	+	9980.61i	1.27365	+	0.735341i	0.297975	+	0.954574i	$0.403689\pi$
$570$	−3125.94	+	4439.84i	−0.229704	+	0.326253i
$571$	6257.56	+	10838.4i	0.458617	+	0.794349i	0.998888	−	0.0471426i	$-0.0150115\pi$
$571$	6257.56	+	10838.4i	0.458617	+	0.794349i	−0.540271	+	0.841491i	$0.681678\pi$
$572$	−13.5646	−	23.4945i	−0.000991545	−	0.00171741i
$573$	−15678.1	+	7261.58i	−1.14304	+	0.529419i
$574$	−1388.58	−	347.463i	−0.100973	−	0.0252663i
$575$			301.007i			0.0218310i
$576$	−2919.17	−	8151.15i	−0.211166	−	0.589638i
$577$			547.118i			0.0394746i	0.999805	+	0.0197373i	$0.00628298\pi$
$577$			547.118i			0.0394746i	−0.999805	+	0.0197373i	$0.993717\pi$
$578$	2299.93	+	1327.87i	0.165509	+	0.0955569i
$579$	17189.4	+	1548.64i	1.23379	+	0.111156i
$580$	20536.4	−	11856.7i	1.47022	−	0.848832i
$581$	10685.3	+	10336.2i	0.762999	+	0.738071i
$582$	−5499.98	−	495.508i	−0.391721	−	0.0352912i
$583$	53.1697	−	92.0926i	0.00377712	−	0.00654217i
$584$	−8181.85			−0.579739
$585$	764.391	−	4207.81i	0.0540234	−	0.297387i
$586$		−	5682.98i		−	0.400617i
$587$	−902.414	+	1563.03i	−0.0634525	+	0.109903i	−0.896006	−	0.444041i	$-0.853544\pi$
$587$	−902.414	+	1563.03i	−0.0634525	+	0.109903i	0.832554	+	0.553944i	$0.186878\pi$
$588$	11139.4	+	7302.00i	0.781262	+	0.512124i
$589$	−16091.6	−	27871.4i	−1.12571	−	1.94978i
$590$	−3026.62	+	1747.42i	−0.211193	+	0.121933i
$591$	2130.66	+	1500.12i	0.148297	+	0.104411i
$592$	−4869.55	+	8434.31i	−0.338070	+	0.585554i
$593$	−20359.7			−1.40990			−0.704951	−	0.709256i	$-0.749031\pi$
$593$	−20359.7			−1.40990			−0.704951	+	0.709256i	$0.749031\pi$
$594$	−6.49060	−	24.9967i	−0.000448338	−	0.00172664i
$595$	18244.9	−	5214.89i	1.25709	−	0.359311i
$596$	−7278.10	−	4202.01i	−0.500206	−	0.288794i
$597$	−17282.1	−	12167.7i	−1.18477	−	0.834155i
$598$	−1067.91	+	616.557i	−0.0730268	+	0.0421620i
$599$	−3739.33	+	2158.90i	−0.255067	+	0.147263i	−0.622082	−	0.782952i	$-0.713713\pi$
$599$	−3739.33	+	2158.90i	−0.255067	+	0.147263i	0.367015	+	0.930215i	$0.380380\pi$
$600$	−134.276	+	62.1922i	−0.00913634	+	0.00423164i
$601$	−6928.17	−	3999.98i	−0.470227	−	0.271485i	0.246108	−	0.969242i	$-0.420848\pi$
$601$	−6928.17	−	3999.98i	−0.470227	−	0.271485i	−0.716335	+	0.697757i	$0.754182\pi$
$602$	159.281	+	557.262i	0.0107837	+	0.0377281i
$603$	−6473.11	+	7633.90i	−0.437157	+	0.515549i
$604$	−3554.24			−0.239437
$605$	7364.30	−	12755.3i	0.494878	−	0.857154i
$606$	−530.423	+	5887.53i	−0.0355561	+	0.394661i
$607$	3079.67	−	1778.05i	0.205931	−	0.118894i	−0.393488	−	0.919330i	$-0.628732\pi$
$607$	3079.67	−	1778.05i	0.205931	−	0.118894i	0.599419	+	0.800435i	$0.295398\pi$
$608$	−8282.37	−	14345.5i	−0.552458	−	0.956886i
$609$	−5172.14	−	27104.7i	−0.344148	−	1.80351i
$610$	−758.204	+	1313.25i	−0.0503258	+	0.0871669i
$611$		−	1971.85i		−	0.130560i
$612$	−12082.1	+	14248.7i	−0.798022	+	0.941127i
$613$	−7113.75			−0.468714			−0.234357	−	0.972151i	$-0.575298\pi$
$613$	−7113.75			−0.468714			−0.234357	+	0.972151i	$0.575298\pi$
$614$	2121.16	−	3673.96i	0.139419	−	0.241480i
$615$	−2573.46	−	5556.25i	−0.168735	−	0.364308i
$616$	−37.9149	−	36.6762i	−0.00247993	−	0.00239891i
$617$	790.942	−	456.650i	0.0516080	−	0.0297959i	−0.473974	−	0.880539i	$-0.657181\pi$
$617$	790.942	−	456.650i	0.0516080	−	0.0297959i	0.525582	+	0.850743i	$0.323848\pi$
$618$	217.755	−	309.283i	0.0141738	−	0.0201314i
$619$	819.836	+	473.333i	0.0532342	+	0.0307348i	0.526381	−	0.850249i	$-0.323549\pi$
$619$	819.836	+	473.333i	0.0532342	+	0.0307348i	−0.473147	+	0.880984i	$0.656882\pi$
$620$			20457.4i			1.32514i
$621$	16118.6	−	4185.35i	1.04158	−	0.270454i
$622$			4223.91i			0.272288i
$623$	−1063.76	+	4251.15i	−0.0684088	+	0.273385i
$624$	3140.07	+	2210.81i	0.201448	+	0.141832i
$625$	7650.79	+	13251.6i	0.489651	+	0.848100i
$626$	2411.24	+	4176.39i	0.153950	+	0.266649i
$627$	72.0603	+	155.582i	0.00458981	+	0.00990964i
$628$	12512.4	+	7224.06i	0.795065	+	0.459031i
$629$	17463.0			1.10699
$630$	−395.786	−	3996.78i	−0.0250293	−	0.252755i
$631$	3209.46			0.202482			0.101241	−	0.994862i	$-0.467719\pi$
$631$	3209.46			0.202482			0.101241	+	0.994862i	$0.467719\pi$
$632$	946.863	+	546.671i	0.0595952	+	0.0344073i
$633$	−25430.4	−	2291.09i	−1.59679	−	0.143859i
$634$	2181.85	+	3779.08i	0.136676	+	0.236730i
$635$	565.322	+	979.167i	0.0353293	+	0.0611922i
$636$	−1460.92	+	16215.8i	−0.0910840	+	1.01100i
$637$	−4906.74	+	163.014i	−0.305199	+	0.0101395i
$638$			52.7820i			0.00327533i
$639$	−665.040	+	238.170i	−0.0411715	+	0.0147447i
$640$			13847.3i			0.855253i
$641$	12387.1	+	7151.71i	0.763279	+	0.440679i	0.830472	−	0.557061i	$-0.188071\pi$
$641$	12387.1	+	7151.71i	0.763279	+	0.440679i	−0.0671928	+	0.997740i	$0.521404\pi$
$642$	−877.111	−	1893.73i	−0.0539202	−	0.116417i
$643$	844.276	−	487.443i	0.0517807	−	0.0298956i	−0.473886	−	0.880586i	$-0.657149\pi$
$643$	844.276	−	487.443i	0.0517807	−	0.0298956i	0.525667	+	0.850691i	$0.323816\pi$
$644$	11422.4	−	11808.2i	0.698923	−	0.722529i
$645$	−1427.34	+	2027.28i	−0.0871339	+	0.123758i
$646$	−4371.36	+	7571.43i	−0.266237	+	0.461136i
$647$	12668.5			0.769783			0.384891	−	0.922962i	$-0.374239\pi$
$647$	12668.5			0.769783			0.384891	+	0.922962i	$0.374239\pi$
$648$	5197.38	+	6325.62i	0.315081	+	0.383478i
$649$			110.357i			0.00667470i
$650$	13.1719	−	22.8144i	0.000794836	−	0.00137670i
$651$	22481.3	+	7827.34i	1.35347	+	0.471240i
$652$	2777.51	+	4810.78i	0.166834	+	0.288964i
$653$	−13746.7	+	7936.65i	−0.823812	+	0.475628i	−0.851729	−	0.523982i	$-0.824446\pi$
$653$	−13746.7	+	7936.65i	−0.823812	+	0.475628i	0.0279172	+	0.999610i	$0.491113\pi$
$654$	−1370.90	+	634.952i	−0.0819668	+	0.0379642i
$655$	2616.34	−	4531.63i	0.156074	−	0.270329i
$656$	5498.45			0.327254
$657$	−18518.9	+	6632.18i	−1.09968	+	0.393829i
$658$	−508.918	−	1780.50i	−0.0301515	−	0.105488i
$659$	−26410.9	−	15248.4i	−1.56119	−	0.901353i	−0.997137	−	0.0756145i	$-0.975908\pi$
$659$	−26410.9	−	15248.4i	−1.56119	−	0.901353i	−0.564053	−	0.825739i	$-0.690759\pi$
$660$	9.77954	−	108.550i	0.000576770	−	0.00640196i
$661$	−14464.7	+	8351.23i	−0.851155	+	0.491415i	−0.861040	−	0.508536i	$-0.830187\pi$
$661$	−14464.7	+	8351.23i	−0.851155	+	0.491415i	0.00988528	+	0.999951i	$0.496853\pi$
$662$	1723.81	−	995.243i	0.101205	−	0.0584308i
$663$	617.870	−	6858.16i	0.0361932	−	0.401733i
$664$	7807.08	+	4507.42i	0.456285	+	0.263436i
$665$	7328.13	+	25638.3i	0.427327	+	1.49505i
$666$	660.638	−	3636.67i	0.0384372	−	0.211589i
$667$	−34035.5			−1.97580
$668$	13538.5	−	23449.3i	0.784160	−	1.35821i
$669$	5625.71	−	2605.64i	0.325116	−	0.150583i
$670$	2578.52	−	1488.71i	0.148682	−	0.0858416i
$671$	23.9418	+	41.4685i	0.00137744	+	0.00238580i
$672$	11571.2	+	4028.75i	0.664238	+	0.231268i
$673$	−12445.2	+	21555.7i	−0.712820	+	1.23464i	0.250975	+	0.967994i	$0.419249\pi$
$673$	−12445.2	+	21555.7i	−0.712820	+	1.23464i	−0.963794	+	0.266646i	$0.914084\pi$
$674$			2835.35i			0.162038i
$675$	−253.511	+	249.611i	−0.0144557	+	0.0142334i
$676$	14887.6			0.847043
$677$	756.276	−	1309.91i	0.0429336	−	0.0743632i	−0.843760	−	0.536721i	$-0.819663\pi$
$677$	756.276	−	1309.91i	0.0429336	−	0.0743632i	0.886694	+	0.462357i	$0.152996\pi$
$678$	−1547.87	+	2198.47i	−0.0876776	+	0.124531i
$679$	−18854.7	+	19491.5i	−1.06565	+	1.10164i
$680$	9964.90	−	5753.23i	0.561965	−	0.324451i
$681$	12248.2	+	26444.5i	0.689210	+	1.48804i
$682$	−39.4342	−	22.7674i	−0.00221410	−	0.00127831i
$683$			2180.44i			0.122156i	0.998133	+	0.0610778i	$0.0194538\pi$
$683$			2180.44i			0.122156i	−0.998133	+	0.0610778i	$0.980546\pi$
$684$	−20022.7	−	16978.1i	−1.11928	−	0.949086i
$685$			28987.3i			1.61686i
$686$	−4388.53	+	1413.58i	−0.244249	+	0.0786748i
$687$	2486.52	−	27599.6i	0.138088	−	1.53274i
$688$	−1113.17	−	1928.08i	−0.0616852	−	0.106842i
$689$	−3000.63	−	5197.24i	−0.165914	−	0.287372i
$690$	−4933.97	−	444.514i	−0.272222	−	0.0245252i
$691$	−24166.2	−	13952.4i	−1.33043	−	0.768124i	−0.345064	−	0.938579i	$-0.612143\pi$
$691$	−24166.2	−	13952.4i	−1.33043	−	0.768124i	−0.985365	+	0.170455i	$0.945476\pi$
$692$	−24639.2			−1.35353
$693$	−115.547	−	52.2799i	−0.00633372	−	0.00286573i
$694$	−427.311			−0.0233725
$695$	−11906.6	−	6874.25i	−0.649844	−	0.375187i
$696$	−7032.22	−	15182.9i	−0.382982	−	0.826879i
$697$	−4929.59	−	8538.30i	−0.267893	−	0.464004i
$698$	2665.22	+	4616.30i	0.144527	+	0.250329i
$699$	−475.125	−	334.519i	−0.0257094	−	0.0181011i
$700$	−85.1981	+	340.480i	−0.00460027	+	0.0183842i
$701$			15696.6i			0.845722i	0.906195	+	0.422861i	$0.138974\pi$
$701$			15696.6i			0.845722i	−0.906195	+	0.422861i	$0.861026\pi$
$702$	−1404.84	−	388.120i	−0.0755302	−	0.0208670i
$703$			24539.6i			1.31654i
$704$	70.4336	+	40.6648i	0.00377069	+	0.00217701i
$705$	4560.48	−	6477.36i	0.243628	−	0.346030i
$706$	5494.56	−	3172.29i	0.292904	−	0.169108i
$707$	20864.9	+	20183.3i	1.10991	+	1.07365i
$708$	−7101.21	−	15331.9i	−0.376949	−	0.813853i
$709$	9253.46	−	16027.5i	0.490157	−	0.848976i	−0.509779	−	0.860305i	$-0.670273\pi$
$709$	9253.46	−	16027.5i	0.490157	−	0.848976i	0.999936	+	0.0113291i	$0.00360624\pi$
$710$	210.139			0.0111076
$711$	2586.28	+	469.823i	0.136418	+	0.0247816i
$712$			2657.31i			0.139869i
$713$	14681.1	−	25428.5i	0.771126	−	1.33563i
$714$	−1212.12	−	6352.13i	−0.0635329	−	0.332945i
$715$	20.0864	+	34.7907i	0.00105062	+	0.00181972i
$716$	17777.1	−	10263.6i	0.927879	−	0.535711i
$717$	2224.93	−	24696.0i	0.115888	−	1.28631i
$718$	2837.06	−	4913.94i	0.147463	−	0.255413i
$719$	12998.8			0.674232			0.337116	−	0.941463i	$-0.390549\pi$
$719$	12998.8			0.674232			0.337116	+	0.941463i	$0.390549\pi$
$720$	5201.72	+	14524.7i	0.269245	+	0.751810i
$721$	−510.483	−	1785.98i	−0.0263681	−	0.0922517i
$722$	−6328.32	−	3653.66i	−0.326199	−	0.188331i
$723$	−25160.5	+	11653.5i	−1.29423	+	0.599444i
$724$	4779.14	−	2759.24i	0.245325	−	0.141639i
$725$	629.705	−	363.561i	0.0322575	−	0.0186239i
$726$	−4104.21	−	2889.63i	−0.209809	−	0.147719i
$727$	1646.14	+	950.399i	0.0839779	+	0.0484846i	0.541401	−	0.840765i	$-0.317894\pi$
$727$	1646.14	+	950.399i	0.0839779	+	0.0484846i	−0.457423	+	0.889249i	$0.651227\pi$
$728$	−2862.38	+	818.148i	−0.145724	+	0.0416519i
$729$	16891.4	+	10104.6i	0.858171	+	0.513364i
$730$	5851.61			0.296682
$731$	−1996.01	+	3457.20i	−0.100992	+	0.174923i
$732$	−5994.64	−	4220.62i	−0.302689	−	0.213113i
$733$	4804.26	−	2773.74i	0.242087	−	0.139769i	−0.374049	−	0.927409i	$-0.622031\pi$
$733$	4804.26	−	2773.74i	0.242087	−	0.139769i	0.616135	+	0.787640i	$0.288697\pi$
$734$	873.327	+	1512.65i	0.0439170	+	0.0760665i
$735$	−16495.3	−	10812.8i	−0.827805	−	0.542634i
$736$	7556.41	−	13088.1i	0.378442	−	0.655480i
$737$		−	94.0181i		−	0.00469905i
$738$	−1964.59	+	703.577i	−0.0979913	+	0.0350936i
$739$	−15681.5			−0.780586			−0.390293	−	0.920691i	$-0.627626\pi$
$739$	−15681.5			−0.780586			−0.390293	+	0.920691i	$0.627626\pi$
$740$	7799.36	−	13508.9i	0.387446	−	0.671076i
$741$	9637.29	+	868.249i	0.477780	+	0.0430445i
$742$	−4050.82	−	3918.48i	−0.200418	−	0.193870i
$743$	15659.4	−	9040.97i	0.773201	−	0.446408i	−0.0608145	−	0.998149i	$-0.519370\pi$
$743$	15659.4	−	9040.97i	0.773201	−	0.446408i	0.834015	+	0.551741i	$0.186036\pi$
$744$	14376.7	+	1295.24i	0.708436	+	0.0638249i
$745$	10777.4	+	6222.35i	0.530006	+	0.305999i
$746$		−	3171.84i		−	0.155669i
$747$	21324.4	+	3873.78i	1.04447	+	0.189738i
$748$		−	175.485i		−	0.00857804i
$749$	−9942.23	−	2487.83i	−0.485021	−	0.121366i
$750$	4829.81	−	2237.00i	0.235146	−	0.108912i
$751$	−11091.4	−	19210.8i	−0.538921	−	0.933438i	−0.998962	−	0.0455407i	$-0.985499\pi$
$751$	−11091.4	−	19210.8i	−0.538921	−	0.933438i	0.460042	−	0.887897i	$-0.347834\pi$
$752$	3556.70	+	6160.39i	0.172473	+	0.298732i
$753$	−9218.63	+	13093.4i	−0.446143	+	0.633667i
$754$	2579.67	+	1489.38i	0.124597	+	0.0719361i
$755$	5263.12			0.253701
$756$	19417.1	−	171.925i	0.934116	−	0.00827098i
$757$	−2531.12			−0.121526			−0.0607630	−	0.998152i	$-0.519353\pi$
$757$	−2531.12			−0.121526			−0.0607630	+	0.998152i	$0.519353\pi$
$758$	7078.10	+	4086.54i	0.339166	+	0.195818i
$759$	−90.0559	+	127.909i	−0.00430675	+	0.00611698i
$760$	8084.62	+	14003.0i	0.385868	+	0.668344i
$761$	1897.02	+	3285.73i	0.0903637	+	0.156514i	0.907664	−	0.419697i	$-0.137864\pi$
$761$	1897.02	+	3285.73i	0.0903637	+	0.156514i	−0.817301	+	0.576212i	$0.804530\pi$
$762$	349.635	−	161.939i	0.0166220	−	0.00769873i
$763$	−1800.98	+	7197.31i	−0.0854518	+	0.341494i
$764$			24849.8i			1.17675i
$765$	17891.2	−	21099.5i	0.845564	−	0.997194i
$766$		−	2157.89i		−	0.101786i
$767$	5393.59	+	3113.99i	0.253913	+	0.146597i
$768$	−8576.22	−	772.654i	−0.402953	−	0.0363031i
$769$	5524.12	−	3189.35i	0.259044	−	0.149559i	−0.364854	−	0.931065i	$-0.618881\pi$
$769$	5524.12	−	3189.35i	0.259044	−	0.149559i	0.623898	+	0.781506i	$0.285548\pi$
$770$	27.1165	+	26.2306i	0.00126911	+	0.00122764i
$771$	−11049.6	−	995.485i	−0.516135	−	0.0465000i
$772$	12411.1	−	21496.7i	0.578609	−	1.00218i
$773$	29728.9			1.38328			0.691638	−	0.722244i	$-0.256889\pi$
$773$	29728.9			1.38328			0.691638	+	0.722244i	$0.256889\pi$
$774$	644.451	+	546.458i	0.0299281	+	0.0253773i
$775$			627.283i			0.0290744i
$776$	−8222.15	+	14241.2i	−0.380358	+	0.658799i
$777$	−11861.2	−	13739.7i	−0.547642	−	0.634374i
$778$	−2394.50	−	4147.39i	−0.110343	−	0.191120i
$779$	11998.3	−	6927.20i	0.551839	−	0.318604i
$780$	−5029.32	−	3540.97i	−0.230870	−	0.162547i
$781$	3.31779	−	5.74657i	0.000152010	−	0.000263289i
$782$	−7976.42			−0.364752
$783$	−28224.1	−	28665.0i	−1.28818	−	1.30831i
$784$	15035.5	−	9359.77i	0.684924	−	0.426374i
$785$	−18528.4	−	10697.4i	−0.842431	−	0.486378i
$786$	−1458.12	−	1026.61i	−0.0661695	−	0.0465877i
$787$	−3237.27	+	1869.04i	−0.146628	+	0.0846556i	−0.571519	−	0.820589i	$-0.693646\pi$
$787$	−3237.27	+	1869.04i	−0.146628	+	0.0846556i	0.424891	+	0.905244i	$0.360312\pi$
$788$	3245.59	−	1873.84i	0.146725	−	0.0847117i
$789$	−7780.79	+	3603.80i	−0.351082	+	0.162609i
$790$	−677.190	−	390.976i	−0.0304979	−	0.0176080i
$791$	3628.66	+	12695.3i	0.163110	+	0.570660i
$792$	−75.6656	−	13.7454i	−0.00339477	−	0.000616694i
$793$	2702.31			0.121011
$794$	2144.17	−	3713.82i	0.0958361	−	0.165993i
$795$	2163.34	−	24012.4i	0.0965103	−	1.07123i
$796$	−26325.4	+	15199.0i	−1.17221	+	0.676776i
$797$	5377.39	+	9313.91i	0.238992	+	0.413947i	0.960425	−	0.278537i	$-0.0898496\pi$
$797$	5377.39	+	9313.91i	0.238992	+	0.413947i	−0.721433	+	0.692484i	$0.756516\pi$
$798$	8926.21	−	1703.31i	0.395970	−	0.0755595i
$799$	6377.45	−	11046.1i	0.282376	−	0.489089i
$800$			322.864i			0.0142687i
$801$	2154.00	+	6014.60i	0.0950162	+	0.265313i
$802$	−4062.60			−0.178872
$803$	92.3882	−	160.021i	0.00406016	−	0.00703241i
$804$	6049.86	+	13062.0i	0.265376	+	0.572960i
$805$	−16914.3	+	17485.6i	−0.740561	+	0.765573i
$806$	−2225.47	+	1284.88i	−0.0972566	+	0.0561511i
$807$	−16386.0	+	23273.4i	−0.714763	+	1.01519i
$808$	15244.7	+	8801.51i	0.663744	+	0.383213i
$809$		−	31037.7i		−	1.34886i	−0.738340	−	0.674429i	$-0.764390\pi$
$809$		−	31037.7i		−	1.34886i	0.738340	−	0.674429i	$-0.235610\pi$
$810$	−3717.13	−	4524.05i	−0.161243	−	0.196245i
$811$		−	3943.22i		−	0.170734i	−0.996350	−	0.0853669i	$-0.972794\pi$
$811$		−	3943.22i		−	0.170734i	0.996350	−	0.0853669i	$-0.0272062\pi$
$812$	−38498.9	−	9633.55i	−1.66385	−	0.416344i
$813$	−15325.8	−	10790.4i	−0.661131	−	0.465479i
$814$	17.3601	+	30.0685i	0.000747506	+	0.00129472i
$815$	−4112.93	−	7123.81i	−0.176773	−	0.306179i
$816$	10440.0	+	22540.5i	0.447884	+	0.967006i
$817$	−4858.16	−	2804.86i	−0.208036	−	0.120110i
$818$	794.973			0.0339799
$819$	−5815.58	+	4172.05i	−0.248123	+	0.178001i
$820$	−8806.64			−0.375050
$821$	25087.6	+	14484.3i	1.06646	+	0.615720i	0.927212	−	0.374537i	$-0.122198\pi$
$821$	25087.6	+	14484.3i	1.06646	+	0.615720i	0.139247	+	0.990258i	$0.455532\pi$
$822$	9838.84	+	886.408i	0.417481	+	0.0376120i
$823$	−18643.1	−	32290.8i	−0.789622	−	1.36766i	−0.926199	−	0.377035i	$-0.876944\pi$
$823$	−18643.1	−	32290.8i	−0.789622	−	1.36766i	0.136577	−	0.990629i	$-0.456390\pi$
$824$	−563.181	−	975.458i	−0.0238099	−	0.0412399i
$825$	0.299869	−	3.32845i	1.26547e−5	−	0.000140463i
$826$	5673.91	+	1419.78i	0.239008	+	0.0598067i
$827$			13151.6i			0.552992i	0.961015	+	0.276496i	$0.0891732\pi$
$827$			13151.6i			0.552992i	−0.961015	+	0.276496i	$0.910827\pi$
$828$	4280.86	−	23565.3i	0.179674	−	0.989069i
$829$		−	27671.1i		−	1.15929i	−0.814867	−	0.579647i	$-0.803190\pi$
$829$		−	27671.1i		−	1.15929i	0.814867	−	0.579647i	$-0.196810\pi$
$830$	−5583.57	−	3223.68i	−0.233504	−	0.134814i
$831$	6503.35	+	14041.1i	0.271479	+	0.586137i
$832$	3974.92	−	2294.92i	0.165632	−	0.0956274i
$833$	−28014.3	−	14956.5i	−1.16523	−	0.622102i
$834$	−2697.34	+	3831.10i	−0.111992	+	0.159065i
$835$	−20047.8	+	34723.8i	−0.830877	+	1.43912i
$836$	246.597			0.0102018
$837$	33590.5	−	8722.06i	1.38716	−	0.360189i
$838$			9866.14i			0.406707i
$839$	8498.72	−	14720.2i	0.349712	−	0.605719i	−0.636486	−	0.771288i	$-0.719613\pi$
$839$	8498.72	−	14720.2i	0.349712	−	0.605719i	0.986198	+	0.165569i	$0.0529461\pi$
$840$	−11294.9	−	3932.56i	−0.463942	−	0.161531i
$841$	28914.2	+	50080.8i	1.18554	+	2.05342i
$842$	3572.89	−	2062.81i	0.146235	−	0.0844288i
$843$	−26875.4	+	12447.8i	−1.09803	+	0.508569i
$844$	−18361.3	+	31802.8i	−0.748843	+	1.29703i
$845$	−22045.6			−0.897506
$846$	−2059.08	−	1745.99i	−0.0836793	−	0.0709554i
$847$	−23700.2	+	6774.16i	−0.961449	+	0.274809i
$848$	18748.9	+	10824.7i	0.759247	+	0.438351i
$849$	−256.654	+	2848.77i	−0.0103750	+	0.115159i
$850$	147.575	−	85.2024i	0.00595503	−	0.00343814i
$851$	−19389.1	+	11194.3i	−0.781023	+	0.450924i
$852$	−91.1616	+	1011.86i	−0.00366566	+	0.0406877i
$853$	13130.3	+	7580.75i	0.527047	+	0.304291i	0.739813	−	0.672812i	$-0.234914\pi$
$853$	13130.3	+	7580.75i	0.527047	+	0.304291i	−0.212766	+	0.977103i	$0.568247\pi$
$854$	2440.09	−	697.445i	0.0977729	−	0.0279462i
$855$	29649.6	+	25141.2i	1.18596	+	1.00563i
$856$	−6214.69			−0.248147
$857$	−14186.9	+	24572.4i	−0.565477	+	0.979436i	0.431528	+	0.902100i	$0.357975\pi$
$857$	−14186.9	+	24572.4i	−0.565477	+	0.979436i	−0.997005	+	0.0773360i	$0.975359\pi$
$858$	12.4229	−	5.75385i	0.000494300	−	0.000228943i
$859$	33411.7	−	19290.2i	1.32712	−	0.766210i	0.342263	−	0.939604i	$-0.388807\pi$
$859$	33411.7	−	19290.2i	1.32712	−	0.766210i	0.984853	+	0.173394i	$0.0554734\pi$
$860$	1782.93	+	3088.12i	0.0706945	+	0.122446i
$861$	−3369.56	+	9677.89i	−0.133373	+	0.383068i
$862$	−1744.17	+	3020.98i	−0.0689171	+	0.119368i
$863$		−	112.649i		−	0.00444337i	−0.999998	−	0.00222168i	$-0.999293\pi$
$863$		−	112.649i		−	0.00444337i	0.999998	−	0.00222168i	$-0.000707185\pi$
$864$	17289.1	−	4489.26i	0.680772	−	0.176768i
$865$	36485.8			1.43417
$866$	−3491.62	+	6047.66i	−0.137009	+	0.237307i
$867$	10945.6	−	15546.3i	0.428758	−	0.608975i
$868$	23803.8	−	24607.7i	0.930821	−	0.962259i
$869$	−21.3837	+	12.3459i	−0.000834742	+	0.000481939i
$870$	5029.40	+	10858.7i	0.195991	+	0.423156i
$871$	−4595.05	−	2652.95i	−0.178757	−	0.103205i
$872$			4498.90i			0.174716i
$873$	−7066.31	+	38898.6i	−0.273950	+	1.50804i
$874$		−	11208.7i		−	0.433799i
$875$	6345.03	−	25356.9i	0.245144	−	0.979679i
$876$	−2538.52	+	28176.7i	−0.0979094	+	1.08676i
$877$	10379.3	+	17977.5i	0.399639	+	0.692196i	0.993681	−	0.112238i	$-0.0358020\pi$
$877$	10379.3	+	17977.5i	0.399639	+	0.692196i	−0.594042	+	0.804434i	$0.702469\pi$
$878$	−4693.22	−	8128.89i	−0.180397	−	0.312456i
$879$	−40521.7	−	3650.71i	−1.55491	−	0.140086i
$880$	−125.507	−	72.4615i	−0.00480777	−	0.00277577i
$881$	−18603.4			−0.711425			−0.355712	−	0.934595i	$-0.615762\pi$
$881$	−18603.4			−0.711425			−0.355712	+	0.934595i	$0.615762\pi$
$882$	−4174.48	+	5268.16i	−0.159367	+	0.201120i
$883$	17188.8			0.655096			0.327548	−	0.944835i	$-0.393778\pi$
$883$	17188.8			0.655096			0.327548	+	0.944835i	$0.393778\pi$
$884$	−8576.68	−	4951.75i	−0.326318	−	0.188400i
$885$	10515.5	+	22703.5i	0.399406	+	0.862338i
$886$	4777.44	+	8274.77i	0.181153	+	0.313766i
$887$	6615.31	+	11458.1i	0.250417	+	0.433736i	0.963641	−	0.267201i	$-0.0860988\pi$
$887$	6615.31	+	11458.1i	0.250417	+	0.433736i	−0.713223	+	0.700937i	$0.752765\pi$
$888$	−8999.74	−	6336.40i	−0.340103	−	0.239455i
$889$	459.323	−	1835.61i	0.0173287	−	0.0692513i
$890$		−	1900.49i		−	0.0715782i
$891$	−182.405	+	30.2227i	−0.00685836	+	0.00113636i
$892$		−	8916.74i		−	0.334703i
$893$	15522.3	+	8961.79i	0.581672	+	0.335829i
$894$	2441.55	−	3467.79i	0.0913396	−	0.129732i
$895$	−26324.3	+	15198.4i	−0.983157	+	0.567626i
$896$	16112.4	−	16656.6i	0.600756	−	0.621046i
$897$	3710.26	+	8010.66i	0.138107	+	0.298181i
$898$	−2826.20	+	4895.12i	−0.105024	+	0.181907i
$899$	−70928.4			−2.63136
$900$	172.517	+	481.718i	0.00638953	+	0.0178414i
$901$		−	38819.2i		−	1.43535i
$902$	9.80104	−	16.9759i	0.000361795	−	0.000626647i
$903$	4075.81	−	777.750i	0.150204	−	0.0286621i
$904$	4003.25	+	6933.83i	0.147286	+	0.255106i
$905$	−7076.96	+	4085.88i	−0.259940	+	0.150077i
$906$	160.942	−	1786.40i	0.00590169	−	0.0655069i
$907$	21753.0	−	37677.2i	0.796356	−	1.37933i	−0.125618	−	0.992079i	$-0.540091\pi$
$907$	21753.0	−	37677.2i	0.796356	−	1.37933i	0.921975	−	0.387251i	$-0.126575\pi$
$908$	41914.5			1.53192
$909$	41639.5	+	7564.23i	1.51936	+	0.276006i
$910$	2047.16	−	585.134i	0.0745743	−	0.0213154i
$911$	14899.7	+	8602.33i	0.541875	+	0.312852i	0.745838	−	0.666127i	$-0.232049\pi$
$911$	14899.7	+	8602.33i	0.541875	+	0.312852i	−0.203964	+	0.978978i	$0.565382\pi$
$912$	−31674.6	+	14670.6i	−1.15006	+	0.532667i
$913$	−176.313	+	101.794i	−0.00639113	+	0.00368992i
$914$	−3027.84	+	1748.13i	−0.109576	+	0.0632635i
$915$	8876.87	+	6249.90i	0.320722	+	0.225809i
$916$	−34515.5	−	19927.5i	−1.24500	−	0.718804i
$917$	−8420.02	+	2406.68i	−0.303221	+	0.0866690i
$918$	−6614.47	−	6717.81i	−0.237811	−	0.241526i
$919$	18441.8			0.661956			0.330978	−	0.943639i	$-0.392621\pi$
$919$	18441.8			0.661956			0.330978	+	0.943639i	$0.392621\pi$
$920$	−7375.99	+	12775.6i	−0.264325	+	0.457825i
$921$	−24834.1	−	17484.8i	−0.888502	−	0.625563i
$922$	32.2382	−	18.6127i	0.00115153	−	0.000664834i
$923$	−187.239	−	324.308i	−0.00667719	−	0.0115652i
$924$	−138.070	+	119.193i	−0.00491575	+	0.00424367i
$925$	239.151	−	414.221i	0.00850079	−	0.0147238i
$926$			6949.39i			0.246621i
$927$	−2065.42	−	1751.36i	−0.0731793	−	0.0620519i
$928$	−36507.0			−1.29138
$929$	−17234.7	+	29851.4i	−0.608668	+	1.05424i	0.382792	+	0.923835i	$0.374963\pi$
$929$	−17234.7	+	29851.4i	−0.608668	+	1.05424i	−0.991460	+	0.130410i	$0.958371\pi$
$930$	−10282.1	−	926.346i	−0.362543	−	0.0326625i
$931$	21017.3	−	39366.5i	0.739864	−	1.38580i
$932$	−723.749	+	417.857i	−0.0254369	+	0.0146860i
$933$	30118.1	+	2713.42i	1.05683	+	0.0952125i
$934$	−8049.64	−	4647.46i	−0.282005	−	0.162815i
$935$			259.859i			0.00908908i
$936$	−2806.89	+	3310.23i	−0.0980192	+	0.115596i
$937$		−	8204.91i		−	0.286065i	−0.989718	−	0.143032i	$-0.954315\pi$
$937$		−	8204.91i		−	0.286065i	0.989718	−	0.143032i	$-0.0456853\pi$
$938$	−4833.87	−	1209.57i	−0.168264	−	0.0421045i
$939$	31328.2	−	14510.2i	1.08877	−	0.504282i
$940$	−5696.62	−	9866.83i	−0.197663	−	0.342362i
$941$	11955.6	+	20707.8i	0.414179	+	0.717380i	0.995342	−	0.0964079i	$-0.0307353\pi$
$941$	11955.6	+	20707.8i	0.414179	+	0.717380i	−0.581163	+	0.813787i	$0.697402\pi$
$942$	−4197.48	+	5961.79i	−0.145182	+	0.206205i
$943$	10946.6	+	6320.03i	0.378017	+	0.218249i
$944$	−22467.3			−0.774628
$945$	−28752.8	+	254.587i	−0.989766	+	0.00876373i
$946$	−7.93698			−0.000272784
$947$	−34519.4	−	19929.8i	−1.18451	−	0.683877i	−0.227456	−	0.973788i	$-0.573041\pi$
$947$	−34519.4	−	19929.8i	−1.18451	−	0.683877i	−0.957054	+	0.289911i	$0.906374\pi$
$948$	2176.41	−	3091.20i	0.0745638	−	0.105905i
$949$	−5213.93	−	9030.78i	−0.178347	−	0.308906i
$950$	119.729	+	207.377i	0.00408897	+	0.00708231i
$951$	28347.9	−	13129.8i	0.966607	−	0.447699i
$952$	−18680.9	−	4674.49i	−0.635977	−	0.159140i
$953$		−	10983.4i		−	0.373334i	−0.982423	−	0.186667i	$-0.940232\pi$
$953$		−	10983.4i		−	0.373334i	0.982423	−	0.186667i	$-0.0597685\pi$
$954$	−8084.10	−	1468.56i	−0.274353	−	0.0498389i
$955$		−	36797.6i		−	1.24685i
$956$	−30884.3	−	17831.1i	−1.04484	−	0.603240i
$957$	376.355	+	33.9069i	0.0127125	+	0.00114530i
$958$	3196.58	−	1845.54i	0.107804	−	0.0622409i
$959$	33728.9	−	34868.1i	1.13573	−	1.17409i
$960$	18365.0	+	1654.55i	0.617423	+	0.0556253i
$961$	15699.3	−	27191.9i	0.526980	−	0.912756i
$962$	1959.43			0.0656699
$963$	−14066.4	+	5037.61i	−0.470701	+	0.168572i
$964$			39879.3i			1.33239i
$965$	−18378.4	+	31832.3i	−0.613079	+	1.06188i
$966$	5417.72	+	6275.74i	0.180447	+	0.209026i
$967$	−7413.81	−	12841.1i	−0.246548	−	0.427034i	0.716018	−	0.698082i	$-0.245963\pi$
$967$	−7413.81	−	12841.1i	−0.246548	−	0.427034i	−0.962566	+	0.271048i	$0.912630\pi$
$968$	−12944.4	+	7473.47i	−0.429803	+	0.248147i
$969$	51178.9	+	36033.3i	1.69670	+	1.19459i
$970$	5880.43	−	10185.2i	0.194649	−	0.337141i
$971$	−8249.56			−0.272648			−0.136324	−	0.990664i	$-0.543529\pi$
$971$	−8249.56			−0.272648			−0.136324	+	0.990664i	$0.543529\pi$
$972$	23396.8	−	15936.2i	0.772071	−	0.525878i
$973$	6323.38	+	22123.1i	0.208344	+	0.728913i
$974$	10680.0	+	6166.09i	0.351344	+	0.202848i
$975$	−154.213	−	108.576i	−0.00506542	−	0.00356638i
$976$	−8442.48	+	4874.27i	−0.276882	+	0.159858i
$977$	4134.88	−	2387.28i	0.135401	−	0.0781737i	−0.430769	−	0.902462i	$-0.641758\pi$
$977$	4134.88	−	2387.28i	0.135401	−	0.0781737i	0.566170	+	0.824288i	$0.308424\pi$
$978$	−2543.73	+	1178.17i	−0.0831692	+	0.0385211i
$979$	−51.9718	−	30.0059i	−0.00169666	−	0.000979564i
$980$	−24081.7	+	14991.1i	−0.784960	+	0.488648i
$981$	3646.79	+	10182.9i	0.118688	+	0.331411i
$982$	6751.20			0.219389
$983$	8970.02	−	15536.5i	0.291047	−	0.504108i	−0.683011	−	0.730409i	$-0.739330\pi$
$983$	8970.02	−	15536.5i	0.291047	−	0.504108i	0.974058	+	0.226300i	$0.0726630\pi$
$984$	−557.582	+	6188.98i	−0.0180641	+	0.200506i
$985$	−4806.07	+	2774.79i	−0.155466	+	0.0897584i
$986$	9634.04	+	16686.6i	0.311167	+	0.538957i
$987$	−13022.6	+	2484.99i	−0.419973	+	0.0801398i
$988$	6958.35	−	12052.2i	0.224063	−	0.388089i
$989$		−	5118.02i		−	0.164554i
$990$	54.1156	+	9.83063i	0.00173728	+	0.000315594i
$991$	1714.50			0.0549574			0.0274787	−	0.999622i	$-0.491252\pi$
$991$	1714.50			0.0549574			0.0274787	+	0.999622i	$0.491252\pi$
$992$	15747.2	−	27274.9i	0.504006	−	0.872964i
$993$	−5989.09	−	12930.8i	−0.191398	−	0.413238i
$994$	−252.771	−	244.513i	−0.00806581	−	0.00780229i
$995$	38982.7	−	22506.7i	1.24205	−	0.717095i
$996$	17944.9	−	25487.6i	0.570891	−	0.810849i
$997$	−29996.8	−	17318.7i	−0.952867	−	0.550138i	−0.0588968	−	0.998264i	$-0.518758\pi$
$997$	−29996.8	−	17318.7i	−0.952867	−	0.550138i	−0.893970	+	0.448126i	$0.852092\pi$
$998$			363.380i			0.0115256i
$999$	−25506.5	−	7046.77i	−0.807796	−	0.223173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.14	yes	44
3.2	odd	2		189.4.o.a.62.9		44
7.6	odd	2	inner	63.4.o.a.20.13	✓	44
9.2	odd	6		567.4.c.c.566.12		44
9.4	even	3		189.4.o.a.125.10		44
9.5	odd	6	inner	63.4.o.a.41.13	yes	44
9.7	even	3		567.4.c.c.566.33		44
21.20	even	2		189.4.o.a.62.10		44
63.13	odd	6		189.4.o.a.125.9		44
63.20	even	6		567.4.c.c.566.34		44
63.34	odd	6		567.4.c.c.566.11		44
63.41	even	6	inner	63.4.o.a.41.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.13	✓	44	7.6	odd	2	inner
63.4.o.a.20.14	yes	44	1.1	even	1	trivial
63.4.o.a.41.13	yes	44	9.5	odd	6	inner
63.4.o.a.41.14	yes	44	63.41	even	6	inner
189.4.o.a.62.9		44	3.2	odd	2
189.4.o.a.62.10		44	21.20	even	2
189.4.o.a.125.9		44	63.13	odd	6
189.4.o.a.125.10		44	9.4	even	3
567.4.c.c.566.11		44	63.34	odd	6
567.4.c.c.566.12		44	9.2	odd	6
567.4.c.c.566.33		44	9.7	even	3
567.4.c.c.566.34		44	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.628557 + 0.362898i) q^{2} +(2.99138 - 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(3.42210 - 1.58500i) q^{6} +(4.49570 - 17.9663i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +O(q^{10})\)	\(q+(0.628557 + 0.362898i) q^{2} +(2.99138 - 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(3.42210 - 1.58500i) q^{6} +(4.49570 - 17.9663i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +8.03191i q^{10} +(0.219645 + 0.126812i) q^{11} +(-38.6754 - 3.48437i) q^{12} +(12.3956 - 7.15663i) q^{13} +(9.34574 - 9.66138i) q^{14} +(57.2705 + 5.15965i) q^{15} +(-25.8174 + 44.7170i) q^{16} +92.5854 q^{17} +(3.50257 - 19.2809i) q^{18} +130.104i q^{19} +(41.3506 - 71.6214i) q^{20} +(-62.8856 - 72.8450i) q^{21} +(0.0920395 + 0.159417i) q^{22} +(-102.797 + 59.3500i) q^{23} +(-47.7148 - 33.5944i) q^{24} +(1.26793 - 2.19612i) q^{25} +10.3885 q^{26} +(-135.230 - 37.3606i) q^{27} +(-133.077 + 38.0370i) q^{28} +(248.320 + 143.368i) q^{29} +(34.1254 + 24.0265i) q^{30} +(-214.225 + 123.683i) q^{31} +(-110.262 + 63.6597i) q^{32} +(1.19583 - 0.553867i) q^{33} +(58.1952 + 33.5990i) q^{34} +(197.060 - 56.3252i) q^{35} +(-130.497 + 153.898i) q^{36} +188.615 q^{37} +(-47.2144 + 81.7777i) q^{38} +(6.67351 - 74.0738i) q^{39} +(107.629 - 62.1397i) q^{40} +(-53.2437 - 92.2207i) q^{41} +(-13.0919 - 68.6083i) q^{42} +(-21.5586 + 37.3406i) q^{43} -1.89539i q^{44} +(193.240 - 227.892i) q^{45} -86.1520 q^{46} +(68.8818 - 119.307i) q^{47} +(112.761 + 243.457i) q^{48} +(-302.577 - 161.542i) q^{49} +(1.59393 - 0.920258i) q^{50} +(276.958 - 393.370i) q^{51} +(-92.6354 - 53.4830i) q^{52} -419.280i q^{53} +(-71.4418 - 72.5580i) q^{54} +2.80669i q^{55} +(-201.769 - 50.4884i) q^{56} +(552.775 + 389.190i) q^{57} +(104.056 + 180.230i) q^{58} +(217.560 + 376.825i) q^{59} +(-180.604 - 389.934i) q^{60} +(163.504 + 94.3989i) q^{61} -179.537 q^{62} +(-497.613 + 49.2767i) q^{63} +320.670 q^{64} +(137.175 + 79.1977i) q^{65} +(0.952645 + 0.0858263i) q^{66} +(-185.350 - 321.035i) q^{67} +(-345.956 - 599.213i) q^{68} +(-55.3435 + 614.296i) q^{69} +(144.304 + 36.1090i) q^{70} -26.1630i q^{71} +(-285.466 + 102.234i) q^{72} -728.545i q^{73} +(118.555 + 68.4480i) q^{74} +(-5.53785 - 11.9565i) q^{75} +(842.032 - 486.147i) q^{76} +(3.26580 - 3.37610i) q^{77} +(31.0759 - 44.1378i) q^{78} +(-48.6779 + 84.3125i) q^{79} -571.409 q^{80} +(-563.259 + 462.796i) q^{81} -77.2880i q^{82} +(-401.359 + 695.174i) q^{83} +(-236.474 + 679.189i) q^{84} +(512.291 + 887.315i) q^{85} +(-27.1017 + 15.6471i) q^{86} +(1351.95 - 626.177i) q^{87} +(1.42415 - 2.46670i) q^{88} -236.618 q^{89} +(204.164 - 73.1170i) q^{90} +(-72.8512 - 254.878i) q^{91} +(768.227 + 443.536i) q^{92} +(-115.333 + 1280.16i) q^{93} +(86.5924 - 49.9941i) q^{94} +(-1246.88 + 719.887i) q^{95} +(-59.3623 + 658.903i) q^{96} +(-1268.09 - 732.133i) q^{97} +(-131.564 - 211.343i) q^{98} +(1.22395 - 6.73758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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