LMFDB - Embedded newform 63.4.s.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(47,63)]

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, 5]))

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

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

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.s (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			47.7
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65116 + 1.53065i) q^{2} +(1.23858 - 5.04638i) q^{3} +(0.685763 - 1.18778i) q^{4} +5.50223 q^{5} +(4.44054 + 15.2746i) q^{6} +(-18.4916 + 1.02989i) q^{7} -20.2917i q^{8} +(-23.9318 - 12.5007i) q^{9} +O(q^{10})$	\(q+(-2.65116 + 1.53065i) q^{2} +(1.23858 - 5.04638i) q^{3} +(0.685763 - 1.18778i) q^{4} +5.50223 q^{5} +(4.44054 + 15.2746i) q^{6} +(-18.4916 + 1.02989i) q^{7} -20.2917i q^{8} +(-23.9318 - 12.5007i) q^{9} +(-14.5873 + 8.42197i) q^{10} -59.4170i q^{11} +(-5.14459 - 4.93177i) q^{12} +(12.7466 - 7.35927i) q^{13} +(47.4478 - 31.0345i) q^{14} +(6.81496 - 27.7663i) q^{15} +(36.5456 + 63.2988i) q^{16} +(-29.3070 - 50.7613i) q^{17} +(82.5813 - 3.48984i) q^{18} +(-66.1714 - 38.2041i) q^{19} +(3.77322 - 6.53541i) q^{20} +(-17.7062 + 94.5912i) q^{21} +(90.9465 + 157.524i) q^{22} -26.0925i q^{23} +(-102.400 - 25.1330i) q^{24} -94.7255 q^{25} +(-22.5289 + 39.0212i) q^{26} +(-92.7248 + 105.286i) q^{27} +(-11.4576 + 22.6701i) q^{28} +(217.541 + 125.597i) q^{29} +(24.4329 + 84.0442i) q^{30} +(190.447 + 109.955i) q^{31} +(-53.1911 - 30.7099i) q^{32} +(-299.841 - 73.5929i) q^{33} +(155.395 + 89.7174i) q^{34} +(-101.745 + 5.66667i) q^{35} +(-31.2596 + 19.8531i) q^{36} +(-97.2240 + 168.397i) q^{37} +233.908 q^{38} +(-21.3499 - 73.4394i) q^{39} -111.650i q^{40} +(37.6465 + 65.2056i) q^{41} +(-97.8439 - 277.878i) q^{42} +(210.991 - 365.447i) q^{43} +(-70.5741 - 40.7460i) q^{44} +(-131.678 - 68.7817i) q^{45} +(39.9385 + 69.1755i) q^{46} +(-191.626 - 331.907i) q^{47} +(364.694 - 106.022i) q^{48} +(340.879 - 38.0885i) q^{49} +(251.132 - 144.991i) q^{50} +(-292.460 + 85.0223i) q^{51} -20.1869i q^{52} +(92.7384 - 53.5426i) q^{53} +(84.6726 - 421.059i) q^{54} -326.926i q^{55} +(20.8982 + 375.226i) q^{56} +(-274.751 + 286.607i) q^{57} -768.979 q^{58} +(-266.985 + 462.431i) q^{59} +(-28.3067 - 27.1357i) q^{60} +(35.7367 - 20.6326i) q^{61} -673.209 q^{62} +(455.412 + 206.511i) q^{63} -396.705 q^{64} +(70.1349 - 40.4924i) q^{65} +(907.570 - 263.844i) q^{66} +(-166.519 + 288.420i) q^{67} -80.3906 q^{68} +(-131.673 - 32.3178i) q^{69} +(261.069 - 170.759i) q^{70} -500.325i q^{71} +(-253.661 + 485.618i) q^{72} +(351.906 - 203.173i) q^{73} -595.262i q^{74} +(-117.325 + 478.020i) q^{75} +(-90.7557 + 52.3978i) q^{76} +(61.1928 + 1098.72i) q^{77} +(169.012 + 162.020i) q^{78} +(-75.1067 - 130.089i) q^{79} +(201.082 + 348.284i) q^{80} +(416.465 + 598.329i) q^{81} +(-199.614 - 115.247i) q^{82} +(493.101 - 854.077i) q^{83} +(100.211 + 85.8981i) q^{84} +(-161.254 - 279.300i) q^{85} +1291.81i q^{86} +(903.252 - 942.229i) q^{87} -1205.67 q^{88} +(311.609 - 539.722i) q^{89} +(454.381 - 19.2019i) q^{90} +(-228.126 + 149.212i) q^{91} +(-30.9921 - 17.8933i) q^{92} +(790.758 - 824.881i) q^{93} +(1016.06 + 586.625i) q^{94} +(-364.090 - 210.208i) q^{95} +(-220.855 + 230.385i) q^{96} +(-407.846 - 235.470i) q^{97} +(-845.423 + 622.744i) q^{98} +(-742.754 + 1421.96i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.65116	+	1.53065i	−0.937326	+	0.541166i	−0.889121	−	0.457672i	$-0.848683\pi$
$2$	−2.65116	+	1.53065i	−0.937326	+	0.541166i	−0.0482051	+	0.998837i	$0.515350\pi$
$3$	1.23858	−	5.04638i	0.238365	−	0.971176i
$3$	1.23858	−	5.04638i	0.238365	−	0.971176i
$4$	0.685763	−	1.18778i	0.0857203	−	0.148472i
$5$	5.50223			0.492134			0.246067	−	0.969253i	$-0.420862\pi$
$5$	5.50223			0.492134			0.246067	+	0.969253i	$0.420862\pi$
$6$	4.44054	+	15.2746i	0.302141	+	1.03930i
$7$	−18.4916	+	1.02989i	−0.998453	+	0.0556087i
$7$	−18.4916	+	1.02989i	−0.998453	+	0.0556087i
$8$		−	20.2917i		−	0.896776i
$9$	−23.9318	−	12.5007i	−0.886364	−	0.462989i
$10$	−14.5873	+	8.42197i	−0.461290	+	0.266326i
$11$		−	59.4170i		−	1.62863i	−0.580425	−	0.814314i	$-0.697114\pi$
$11$		−	59.4170i		−	1.62863i	0.580425	−	0.814314i	$-0.302886\pi$
$12$	−5.14459	−	4.93177i	−0.123760	−	0.118640i
$13$	12.7466	−	7.35927i	0.271945	−	0.157007i	−0.357826	−	0.933788i	$-0.616482\pi$
$13$	12.7466	−	7.35927i	0.271945	−	0.157007i	0.629771	+	0.776781i	$0.283149\pi$
$14$	47.4478	−	31.0345i	0.905782	−	0.592452i
$15$	6.81496	−	27.7663i	0.117308	−	0.477949i
$16$	36.5456	+	63.2988i	0.571024	+	0.989043i
$17$	−29.3070	−	50.7613i	−0.418117	−	0.724201i	0.577633	−	0.816297i	$-0.303977\pi$
$17$	−29.3070	−	50.7613i	−0.418117	−	0.724201i	−0.995750	+	0.0920961i	$0.970643\pi$
$18$	82.5813	−	3.48984i	1.08137	−	0.0456979i
$19$	−66.1714	−	38.2041i	−0.798987	−	0.461296i	0.0441297	−	0.999026i	$-0.485949\pi$
$19$	−66.1714	−	38.2041i	−0.798987	−	0.461296i	−0.843117	+	0.537730i	$0.819282\pi$
$20$	3.77322	−	6.53541i	0.0421859	−	0.0730681i
$21$	−17.7062	+	94.5912i	−0.183991	+	0.982928i
$22$	90.9465	+	157.524i	0.881357	+	1.52656i
$23$		−	26.0925i		−	0.236551i	−0.992981	−	0.118275i	$-0.962263\pi$
$23$		−	26.0925i		−	0.236551i	0.992981	−	0.118275i	$-0.0377366\pi$
$24$	−102.400	−	25.1330i	−0.870927	−	0.213760i
$25$	−94.7255			−0.757804
$26$	−22.5289	+	39.0212i	−0.169934	+	0.294334i
$27$	−92.7248	+	105.286i	−0.660922	+	0.750455i
$28$	−11.4576	+	22.6701i	−0.0773314	+	0.153009i
$29$	217.541	+	125.597i	1.39297	+	0.804234i	0.993643	−	0.112573i	$-0.0359091\pi$
$29$	217.541	+	125.597i	1.39297	+	0.804234i	0.399331	+	0.916807i	$0.369242\pi$
$30$	24.4329	+	84.0442i	0.148694	+	0.511477i
$31$	190.447	+	109.955i	1.10340	+	0.637048i	0.937112	−	0.349030i	$-0.113489\pi$
$31$	190.447	+	109.955i	1.10340	+	0.637048i	0.166287	+	0.986077i	$0.446822\pi$
$32$	−53.1911	−	30.7099i	−0.293842	−	0.169650i
$33$	−299.841	−	73.5929i	−1.58168	−	0.388208i
$34$	155.395	+	89.7174i	0.783825	+	0.452542i
$35$	−101.745	+	5.66667i	−0.491373	+	0.0273669i
$36$	−31.2596	+	19.8531i	−0.144720	+	0.0919126i
$37$	−97.2240	+	168.397i	−0.431987	+	0.748223i	−0.997044	−	0.0768282i	$-0.975521\pi$
$37$	−97.2240	+	168.397i	−0.431987	+	0.748223i	0.565057	+	0.825052i	$0.308854\pi$
$38$	233.908			0.998549
$39$	−21.3499	−	73.4394i	−0.0876595	−	0.301531i
$40$		−	111.650i		−	0.441334i
$41$	37.6465	+	65.2056i	0.143400	+	0.248376i	0.928775	−	0.370645i	$-0.120863\pi$
$41$	37.6465	+	65.2056i	0.143400	+	0.248376i	−0.785375	+	0.619020i	$0.787530\pi$
$42$	−97.8439	−	277.878i	−0.359468	−	1.02089i
$43$	210.991	−	365.447i	0.748275	−	1.29605i	−0.200375	−	0.979719i	$-0.564216\pi$
$43$	210.991	−	365.447i	0.748275	−	1.29605i	0.948649	−	0.316330i	$-0.102451\pi$
$44$	−70.5741	−	40.7460i	−0.241806	−	0.139606i
$45$	−131.678	−	68.7817i	−0.436210	−	0.227853i
$46$	39.9385	+	69.1755i	0.128013	+	0.221725i
$47$	−191.626	−	331.907i	−0.594715	−	1.03008i	−0.993587	−	0.113070i	$-0.963932\pi$
$47$	−191.626	−	331.907i	−0.594715	−	1.03008i	0.398872	−	0.917006i	$-0.369402\pi$
$48$	364.694	−	106.022i	1.09665	−	0.318811i
$49$	340.879	−	38.0885i	0.993815	−	0.111045i
$50$	251.132	−	144.991i	0.710309	−	0.410097i
$51$	−292.460	+	85.0223i	−0.802991	+	0.233441i
$52$		−	20.1869i		−	0.0538349i
$53$	92.7384	−	53.5426i	0.240351	−	0.138767i	−0.374987	−	0.927030i	$-0.622353\pi$
$53$	92.7384	−	53.5426i	0.240351	−	0.138767i	0.615338	+	0.788263i	$0.289020\pi$
$54$	84.6726	−	421.059i	0.213379	−	1.06109i
$55$		−	326.926i		−	0.801503i
$56$	20.8982	+	375.226i	0.0498685	+	0.895388i
$57$	−274.751	+	286.607i	−0.638450	+	0.666000i
$58$	−768.979			−1.74090
$59$	−266.985	+	462.431i	−0.589126	+	1.02040i	0.405221	+	0.914219i	$0.367194\pi$
$59$	−266.985	+	462.431i	−0.589126	+	1.02040i	−0.994347	+	0.106177i	$0.966139\pi$
$60$	−28.3067	−	27.1357i	−0.0609063	−	0.0583868i
$61$	35.7367	−	20.6326i	0.0750101	−	0.0433071i	−0.462026	−	0.886866i	$-0.652877\pi$
$61$	35.7367	−	20.6326i	0.0750101	−	0.0433071i	0.537036	+	0.843559i	$0.319544\pi$
$62$	−673.209			−1.37899
$63$	455.412	+	206.511i	0.910739	+	0.412983i
$64$	−396.705			−0.774815
$65$	70.1349	−	40.4924i	0.133833	−	0.0772687i
$66$	907.570	−	263.844i	1.69264	−	0.492075i
$67$	−166.519	+	288.420i	−0.303636	+	0.525912i	−0.976957	−	0.213438i	$-0.931534\pi$
$67$	−166.519	+	288.420i	−0.303636	+	0.525912i	0.673321	+	0.739350i	$0.264867\pi$
$68$	−80.3906			−0.143365
$69$	−131.673	−	32.3178i	−0.229732	−	0.0563855i
$70$	261.069	−	170.759i	0.445767	−	0.291566i
$71$		−	500.325i		−	0.836305i	−0.908377	−	0.418153i	$-0.862678\pi$
$71$		−	500.325i		−	0.836305i	0.908377	−	0.418153i	$-0.137322\pi$
$72$	−253.661	+	485.618i	−0.415197	+	0.794870i
$73$	351.906	−	203.173i	0.564213	−	0.325748i	−0.190622	−	0.981664i	$-0.561050\pi$
$73$	351.906	−	203.173i	0.564213	−	0.325748i	0.754835	+	0.655915i	$0.227717\pi$
$74$		−	595.262i		−	0.935106i
$75$	−117.325	+	478.020i	−0.180634	+	0.735961i
$76$	−90.7557	+	52.3978i	−0.136979	+	0.0790848i
$77$	61.1928	+	1098.72i	0.0905658	+	1.62611i
$78$	169.012	+	162.020i	0.245344	+	0.235195i
$79$	−75.1067	−	130.089i	−0.106964	−	0.185267i	0.807575	−	0.589765i	$-0.200780\pi$
$79$	−75.1067	−	130.089i	−0.106964	−	0.185267i	−0.914539	+	0.404498i	$0.867446\pi$
$80$	201.082	+	348.284i	0.281021	+	0.486742i
$81$	416.465	+	598.329i	0.571282	+	0.820754i
$82$	−199.614	−	115.247i	−0.268825	−	0.155206i
$83$	493.101	−	854.077i	0.652107	−	1.12948i	−0.330503	−	0.943805i	$-0.607218\pi$
$83$	493.101	−	854.077i	0.652107	−	1.12948i	0.982611	−	0.185678i	$-0.0594482\pi$
$84$	100.211	+	85.8981i	0.130166	+	0.111574i
$85$	−161.254	−	279.300i	−0.205770	−	0.356404i
$86$			1291.81i			1.61976i
$87$	903.252	−	942.229i	1.11309	−	1.16112i
$88$	−1205.67			−1.46051
$89$	311.609	−	539.722i	0.371129	−	0.642814i	−0.618611	−	0.785698i	$-0.712304\pi$
$89$	311.609	−	539.722i	0.371129	−	0.642814i	0.989739	+	0.142884i	$0.0456375\pi$
$90$	454.381	−	19.2019i	0.532177	−	0.0224895i
$91$	−228.126	+	149.212i	−0.262793	+	0.171887i
$92$	−30.9921	−	17.8933i	−0.0351212	−	0.0202772i
$93$	790.758	−	824.881i	0.881697	−	0.919744i
$94$	1016.06	+	586.625i	1.11488	+	0.643678i
$95$	−364.090	−	210.208i	−0.393209	−	0.227019i
$96$	−220.855	+	230.385i	−0.234801	+	0.244933i
$97$	−407.846	−	235.470i	−0.426912	−	0.246478i	0.271118	−	0.962546i	$-0.412607\pi$
$97$	−407.846	−	235.470i	−0.426912	−	0.246478i	−0.698030	+	0.716068i	$0.745940\pi$
$98$	−845.423	+	622.744i	−0.871435	+	0.641904i
$99$	−742.754	+	1421.96i	−0.754037	+	1.44356i
$100$	−64.9592	+	112.513i	−0.0649592	+	0.112513i
$101$	−1201.60			−1.18380			−0.591898	−	0.806013i	$-0.701621\pi$
$101$	−1201.60			−1.18380			−0.591898	+	0.806013i	$0.701621\pi$
$102$	645.218	−	673.060i	0.626334	−	0.653361i
$103$		−	1020.81i		−	0.976539i	−0.872693	−	0.488269i	$-0.837628\pi$
$103$		−	1020.81i		−	0.976539i	0.872693	−	0.488269i	$-0.162372\pi$
$104$	−149.332	−	258.651i	−0.140800	−	0.243873i
$105$	−97.4234	+	520.462i	−0.0905481	+	0.483733i
$106$	−163.910	+	283.900i	−0.150192	+	0.260139i
$107$	225.733	+	130.327i	0.203948	+	0.117750i	0.598496	−	0.801126i	$-0.295765\pi$
$107$	225.733	+	130.327i	0.203948	+	0.117750i	−0.394548	+	0.918876i	$0.629099\pi$
$108$	61.4688	+	182.337i	0.0547670	+	0.162458i
$109$	1029.70	+	1783.50i	0.904840	+	1.56723i	0.821131	+	0.570739i	$0.193343\pi$
$109$	1029.70	+	1783.50i	0.904840	+	1.56723i	0.0837089	+	0.996490i	$0.473323\pi$
$110$	500.408	+	866.733i	0.433746	+	0.751270i
$111$	729.374	+	699.202i	0.623686	+	0.597886i
$112$	−740.977	−	1132.86i	−0.625140	−	0.955759i
$113$	−141.454	+	81.6684i	−0.117760	+	0.0679886i	−0.557723	−	0.830027i	$-0.688325\pi$
$113$	−141.454	+	81.6684i	−0.117760	+	0.0679886i	0.439963	+	0.898016i	$0.354991\pi$
$114$	289.714	−	1180.39i	0.238019	−	0.969766i
$115$		−	143.567i		−	0.116415i
$116$	298.362	−	172.260i	0.238812	−	0.137878i
$117$	−397.046	+	16.7789i	−0.313735	+	0.0132582i
$118$		−	1634.64i		−	1.27526i
$119$	594.212	+	908.474i	0.457742	+	0.699829i
$120$	−563.426	−	138.287i	−0.428613	−	0.105199i
$121$	−2199.38			−1.65243
$122$	−63.1625	+	109.401i	−0.0468726	+	0.0811858i
$123$	375.680	−	109.216i	0.275398	−	0.0800622i
$124$	261.203	−	150.806i	0.189167	−	0.109216i
$125$	−1208.98			−0.865075
$126$	−1523.47	+	149.582i	−1.07715	+	0.105761i
$127$	2368.78			1.65508			0.827539	−	0.561408i	$-0.189740\pi$
$127$	2368.78			1.65508			0.827539	+	0.561408i	$0.189740\pi$
$128$	1477.26	−	852.894i	1.02010	−	0.588953i
$129$	−1582.85	−	1517.38i	−1.08033	−	1.03564i
$130$	−123.959	+	214.704i	−0.0836303	+	0.144852i
$131$	881.350			0.587816			0.293908	−	0.955834i	$-0.405044\pi$
$131$	881.350			0.587816			0.293908	+	0.955834i	$0.405044\pi$
$132$	−293.031	+	305.676i	−0.193220	+	0.201558i
$133$	1262.96	+	638.305i	0.823403	+	0.416151i
$134$		−	1019.53i		−	0.657269i
$135$	−510.193	+	579.307i	−0.325262	+	0.369324i
$136$	−1030.03	+	594.690i	−0.649446	+	0.374958i
$137$		−	1216.43i		−	0.758588i	−0.925276	−	0.379294i	$-0.876167\pi$
$137$		−	1216.43i		−	0.758588i	0.925276	−	0.379294i	$-0.123833\pi$
$138$	398.553	−	115.865i	0.245848	−	0.0714717i
$139$	2303.79	−	1330.09i	1.40579	−	0.811634i	0.410812	−	0.911720i	$-0.365245\pi$
$139$	2303.79	−	1330.09i	1.40579	−	0.811634i	0.994979	+	0.100086i	$0.0319119\pi$
$140$	−63.0422	+	124.736i	−0.0380574	+	0.0753010i
$141$	−1912.27	+	555.925i	−1.14214	+	0.332038i
$142$	765.821	+	1326.44i	0.452580	+	0.783891i
$143$	−437.266	−	757.367i	−0.255706	−	0.442896i
$144$	−83.3229	−	1971.70i	−0.0482193	−	1.14103i
$145$	1196.96	+	691.064i	0.685530	+	0.395791i
$146$	−621.973	+	1077.29i	−0.352568	+	0.610665i
$147$	229.997	−	1767.38i	0.129047	−	0.991639i
$148$	133.345	+	230.961i	0.0740601	+	0.128276i
$149$		−	989.826i		−	0.544226i	−0.962265	−	0.272113i	$-0.912277\pi$
$149$		−	989.826i		−	0.544226i	0.962265	−	0.272113i	$-0.0877225\pi$
$150$	−420.633	−	1446.89i	−0.228963	−	0.787588i
$151$	982.760			0.529641			0.264821	−	0.964298i	$-0.414687\pi$
$151$	982.760			0.529641			0.264821	+	0.964298i	$0.414687\pi$
$152$	−775.226	+	1342.73i	−0.413679	+	0.716512i
$153$	66.8192	+	1581.17i	0.0353073	+	0.835489i
$154$	−1843.98	−	2819.21i	−0.964883	−	1.47518i
$155$	1047.89	+	604.997i	0.543020	+	0.313513i
$156$	−101.870	−	25.0031i	−0.0522831	−	0.0128324i
$157$	−576.402	−	332.786i	−0.293006	−	0.169167i	0.346291	−	0.938127i	$-0.387441\pi$
$157$	−576.402	−	332.786i	−0.293006	−	0.169167i	−0.639297	+	0.768960i	$0.720774\pi$
$158$	398.240	+	229.924i	0.200520	+	0.115771i
$159$	−155.332	−	534.310i	−0.0774755	−	0.266500i
$160$	−292.669	−	168.973i	−0.144610	−	0.0834904i
$161$	26.8724	+	482.493i	0.0131543	+	0.236185i
$162$	−2019.95	−	948.806i	−0.979641	−	0.460156i
$163$	462.170	−	800.502i	0.222086	−	0.384663i	−0.733356	−	0.679845i	$-0.762047\pi$
$163$	462.170	−	800.502i	0.222086	−	0.384663i	0.955441	+	0.295182i	$0.0953803\pi$
$164$	103.266			0.0491691
$165$	−1649.79	−	404.925i	−0.778401	−	0.191051i
$166$			3019.06i			1.41159i
$167$	−925.982	−	1603.85i	−0.429070	−	0.743171i	0.567721	−	0.823221i	$-0.307825\pi$
$167$	−925.982	−	1603.85i	−0.429070	−	0.743171i	−0.996791	+	0.0800504i	$0.974492\pi$
$168$	1919.42	+	359.289i	0.881466	+	0.164998i
$169$	−990.182	+	1715.05i	−0.450697	+	0.780631i
$170$	855.020	+	493.646i	0.385747	+	0.222711i
$171$	1106.02	+	1741.48i	0.494619	+	0.778798i
$172$	−289.379	−	501.220i	−0.128285	−	0.222196i
$173$	−738.631	−	1279.35i	−0.324607	−	0.562236i	0.656825	−	0.754043i	$-0.271899\pi$
$173$	−738.631	−	1279.35i	−0.324607	−	0.562236i	−0.981433	+	0.191806i	$0.938565\pi$
$174$	−952.444	+	3880.56i	−0.414969	+	1.69072i
$175$	1751.63	−	97.5565i	0.756631	−	0.0421405i
$176$	3761.02	−	2171.43i	1.61078	−	0.929986i
$177$	2002.92	+	1920.06i	0.850557	+	0.815372i
$178$			1907.85i			0.803368i
$179$	452.182	−	261.067i	0.188814	−	0.109012i	−0.402613	−	0.915370i	$-0.631898\pi$
$179$	452.182	−	261.067i	0.188814	−	0.109012i	0.591427	+	0.806358i	$0.298565\pi$
$180$	−171.997	+	109.236i	−0.0712218	+	0.0452334i
$181$			3401.17i			1.39672i	0.715745	+	0.698362i	$0.246087\pi$
$181$			3401.17i			1.39672i	−0.715745	+	0.698362i	$0.753913\pi$
$182$	376.408	−	744.767i	0.153303	−	0.303328i
$183$	−59.8570	−	205.896i	−0.0241790	−	0.0831709i
$184$	−529.462			−0.212133
$185$	−534.948	+	926.558i	−0.212596	+	0.368226i
$186$	−833.824	+	3397.26i	−0.328704	+	1.33924i
$187$	−3016.08	+	1741.34i	−1.17945	+	0.680958i
$188$	−525.641			−0.203917
$189$	1606.20	−	2042.40i	0.618168	−	0.786046i
$190$	1287.01			0.491420
$191$	2367.55	−	1366.91i	0.896911	−	0.517832i	0.0207146	−	0.999785i	$-0.493406\pi$
$191$	2367.55	−	1366.91i	0.896911	−	0.517832i	0.876197	+	0.481953i	$0.160073\pi$
$192$	−491.352	+	2001.92i	−0.184689	+	0.752481i
$193$	−1114.05	+	1929.59i	−0.415498	+	0.719663i	−0.995481	−	0.0949654i	$-0.969726\pi$
$193$	−1114.05	+	1929.59i	−0.415498	+	0.719663i	0.579983	+	0.814629i	$0.303059\pi$
$194$	1441.68			0.533541
$195$	−117.472	−	404.080i	−0.0431402	−	0.148394i
$196$	188.521	−	431.007i	0.0687031	−	0.157073i
$197$		−	3184.20i		−	1.15160i	−0.817591	−	0.575800i	$-0.804691\pi$
$197$		−	3184.20i		−	1.15160i	0.817591	−	0.575800i	$-0.195309\pi$
$198$	−207.356	−	4906.73i	−0.0744248	−	1.76114i
$199$	−2236.98	+	1291.52i	−0.796860	+	0.460068i	−0.842372	−	0.538896i	$-0.818841\pi$
$199$	−2236.98	+	1291.52i	−0.796860	+	0.460068i	0.0455118	+	0.998964i	$0.485508\pi$
$200$			1922.14i			0.679580i
$201$	1249.23	+	1197.55i	0.438377	+	0.420243i
$202$	3185.62	−	1839.22i	1.10960	−	0.640629i
$203$	−4152.02	−	2098.45i	−1.43554	−	0.725528i
$204$	−99.5704	+	405.681i	−0.0341732	+	0.139232i
$205$	207.139	+	358.776i	0.0705719	+	0.122234i
$206$	1562.50	+	2706.33i	0.528469	+	0.915335i
$207$	−326.175	+	624.442i	−0.109520	+	0.209670i
$208$	931.666	+	537.897i	0.310574	+	0.179310i
$209$	−2269.97	+	3931.71i	−0.751279	+	1.30125i
$210$	−538.359	−	1528.95i	−0.176906	−	0.502417i
$211$	2235.20	+	3871.49i	0.729278	+	1.26315i	0.957189	+	0.289465i	$0.0934775\pi$
$211$	2235.20	+	3871.49i	0.729278	+	1.26315i	−0.227910	+	0.973682i	$0.573189\pi$
$212$		−	146.870i		−	0.0475805i
$213$	−2524.83	−	619.694i	−0.812199	−	0.199346i
$214$	−797.940			−0.254888
$215$	1160.92	−	2010.77i	0.368252	−	0.637830i
$216$	2136.43	+	1881.55i	0.672989	+	0.592699i
$217$	−3634.92	−	1837.10i	−1.13712	−	0.574703i
$218$	−5459.81	−	3152.22i	−1.69626	−	0.979337i
$219$	−589.424	−	2027.50i	−0.181870	−	0.625597i
$220$	−388.315	−	224.194i	−0.119001	−	0.0687051i
$221$	−747.132	−	431.357i	−0.227410	−	0.131295i
$222$	−3003.92	−	737.281i	−0.908152	−	0.222897i
$223$	−1671.62	−	965.108i	−0.501972	−	0.289813i	0.227556	−	0.973765i	$-0.426927\pi$
$223$	−1671.62	−	965.108i	−0.501972	−	0.289813i	−0.729527	+	0.683952i	$0.760260\pi$
$224$	1015.22	+	513.094i	0.302821	+	0.153047i
$225$	2266.95	+	1184.14i	0.671690	+	0.350855i
$226$	250.011	−	433.032i	0.0735862	−	0.127455i
$227$	−1092.70			−0.319494			−0.159747	−	0.987158i	$-0.551068\pi$
$227$	−1092.70			−0.319494			−0.159747	+	0.987158i	$0.551068\pi$
$228$	152.011	+	522.887i	0.0441542	+	0.151882i
$229$		−	3841.90i		−	1.10865i	−0.832301	−	0.554324i	$-0.812977\pi$
$229$		−	3841.90i		−	1.10865i	0.832301	−	0.554324i	$-0.187023\pi$
$230$	219.751	+	380.619i	0.0629997	+	0.109119i
$231$	5620.33	+	1052.05i	1.60082	+	0.299652i
$232$	2548.58	−	4414.27i	0.721218	−	1.24919i
$233$	4219.38	+	2436.06i	1.18636	+	0.684943i	0.957476	−	0.288512i	$-0.0931604\pi$
$233$	4219.38	+	2436.06i	1.18636	+	0.684943i	0.228880	+	0.973455i	$0.426494\pi$
$234$	1026.95	−	652.221i	0.286897	−	0.182210i
$235$	−1054.37	−	1826.23i	−0.292679	−	0.506936i
$236$	366.176	+	634.236i	0.101000	+	0.174937i
$237$	−749.502	+	217.891i	−0.205424	+	0.0597196i
$238$	−2965.90	−	1498.98i	−0.807777	−	0.408254i
$239$	−1383.42	+	798.720i	−0.374419	+	0.216171i	−0.675387	−	0.737463i	$-0.736024\pi$
$239$	−1383.42	+	798.720i	−0.374419	+	0.216171i	0.300968	+	0.953634i	$0.402690\pi$
$240$	2006.63	−	583.357i	0.539698	−	0.156898i
$241$		−	6885.74i		−	1.84045i	−0.391385	−	0.920227i	$-0.628004\pi$
$241$		−	6885.74i		−	1.84045i	0.391385	−	0.920227i	$-0.371996\pi$
$242$	5830.91	−	3366.48i	1.54886	−	0.894237i
$243$	3535.22	−	1360.56i	0.933270	−	0.359176i
$244$		−	56.5963i		−	0.0148492i
$245$	1875.59	−	209.572i	0.489091	−	0.0546492i
$246$	−828.817	+	864.582i	−0.214811	+	0.224080i
$247$	−1124.62			−0.289707
$248$	2231.17	−	3864.50i	0.571289	−	0.989501i
$249$	−3699.25	−	3546.22i	−0.941487	−	0.902540i
$250$	3205.20	−	1850.52i	0.810858	−	0.468149i
$251$	−7468.24			−1.87805			−0.939026	−	0.343846i	$-0.888270\pi$
$251$	−7468.24			−1.87805			−0.939026	+	0.343846i	$0.888270\pi$
$252$	557.593	−	399.310i	0.139385	−	0.0998181i
$253$	−1550.34			−0.385253
$254$	−6280.00	+	3625.76i	−1.55135	+	0.895671i
$255$	−1609.18	+	467.812i	−0.395179	+	0.114884i
$256$	−1024.14	+	1773.86i	−0.250034	+	0.433072i
$257$	892.599			0.216649			0.108324	−	0.994116i	$-0.465451\pi$
$257$	892.599			0.216649			0.108324	+	0.994116i	$0.465451\pi$
$258$	6518.96	+	1600.01i	1.57307	+	0.386095i
$259$	1624.40	−	3214.06i	0.389711	−	0.771088i
$260$		−	111.073i		−	0.0264940i
$261$	−3636.09	−	5725.18i	−0.862331	−	1.35778i
$262$	−2336.60	+	1349.04i	−0.550975	+	0.318106i
$263$			6421.39i			1.50555i	0.658277	+	0.752775i	$0.271285\pi$
$263$			6421.39i			1.50555i	−0.658277	+	0.752775i	$0.728715\pi$
$264$	−1493.33	+	6084.28i	−0.348136	+	1.41841i
$265$	510.268	−	294.603i	0.118285	−	0.0682918i
$266$	−4325.33	+	240.899i	−0.997004	+	0.0555280i
$267$	−2337.69	−	2240.98i	−0.535821	−	0.513656i
$268$	228.386	+	395.575i	0.0520555	+	0.0901628i
$269$	3574.44	+	6191.12i	0.810177	+	1.40327i	0.912740	+	0.408542i	$0.133963\pi$
$269$	3574.44	+	6191.12i	0.810177	+	1.40327i	−0.102562	+	0.994727i	$0.532704\pi$
$270$	465.888	−	2316.76i	0.105011	−	0.522198i
$271$	4716.19	+	2722.90i	1.05715	+	0.610347i	0.924643	−	0.380835i	$-0.124363\pi$
$271$	4716.19	+	2722.90i	1.05715	+	0.610347i	0.132509	+	0.991182i	$0.457697\pi$
$272$	2142.08	−	3710.20i	0.477511	−	0.827073i
$273$	470.428	+	1336.02i	0.104292	+	0.296190i
$274$	1861.92	+	3224.95i	0.410522	+	0.711044i
$275$			5628.31i			1.23418i
$276$	−128.683	+	134.235i	−0.0280644	+	0.0292754i
$277$	3155.80			0.684525			0.342262	−	0.939604i	$-0.388807\pi$
$277$	3155.80			0.684525			0.342262	+	0.939604i	$0.388807\pi$
$278$	−4071.81	+	7052.58i	−0.878456	+	1.52153i
$279$	−3183.24	−	5012.15i	−0.683067	−	1.07552i
$280$	114.987	+	2064.58i	0.0245420	+	0.440651i
$281$	27.5066	+	15.8809i	0.00583951	+	0.00337145i	0.502917	−	0.864335i	$-0.332260\pi$
$281$	27.5066	+	15.8809i	0.00583951	+	0.00337145i	−0.497077	+	0.867706i	$0.665594\pi$
$282$	4218.81	−	4400.86i	0.890874	−	0.929317i
$283$	−5043.64	−	2911.94i	−1.05941	−	0.611651i	−0.134141	−	0.990962i	$-0.542827\pi$
$283$	−5043.64	−	2911.94i	−1.05941	−	0.611651i	−0.925269	+	0.379312i	$0.876161\pi$
$284$	−594.274	−	343.104i	−0.124168	−	0.0716884i
$285$	−1511.74	+	1576.98i	−0.314203	+	0.327761i
$286$	2318.52	+	1338.60i	0.479361	+	0.276759i
$287$	−763.298	−	1166.98i	−0.156990	−	0.240017i
$288$	889.064	+	1399.87i	0.181905	+	0.286417i
$289$	738.697	−	1279.46i	0.150356	−	0.260423i
$290$	−4231.10			−0.856754
$291$	−1693.42	+	1766.49i	−0.341134	+	0.355855i
$292$		−	557.314i		−	0.111693i
$293$	177.914	+	308.157i	0.0354739	+	0.0614427i	0.883217	−	0.468964i	$-0.155373\pi$
$293$	177.914	+	308.157i	0.0354739	+	0.0614427i	−0.847743	+	0.530407i	$0.822039\pi$
$294$	2095.47	+	5037.64i	0.415682	+	0.999324i
$295$	−1469.01	+	2544.40i	−0.289929	+	0.502172i
$296$	3417.06	+	1972.84i	0.670988	+	0.387395i
$297$	6255.77	+	5509.43i	1.22221	+	1.07640i
$298$	1515.08	+	2624.19i	0.294517	+	0.510118i
$299$	−192.022	−	332.592i	−0.0371402	−	0.0643287i
$300$	487.324	+	467.165i	0.0937855	+	0.0899059i
$301$	−3525.19	+	6975.00i	−0.675045	+	1.33565i
$302$	−2605.45	+	1504.26i	−0.496447	+	0.286624i
$303$	−1488.28	+	6063.71i	−0.282176	+	1.14967i
$304$		−	5584.76i		−	1.05364i
$305$	196.632	−	113.525i	0.0369150	−	0.0213129i
$306$	−2597.36	−	4089.65i	−0.485232	−	0.764019i
$307$		−	10085.9i		−	1.87502i	−0.347955	−	0.937511i	$-0.613124\pi$
$307$		−	10085.9i		−	1.87502i	0.347955	−	0.937511i	$-0.386876\pi$
$308$	1346.99	+	680.775i	0.249195	+	0.125944i
$309$	−5151.40	−	1264.36i	−0.948390	−	0.232773i
$310$	−3704.15			−0.678650
$311$	2633.24	−	4560.90i	0.480119	−	0.831591i	−0.519621	−	0.854397i	$-0.673927\pi$
$311$	2633.24	−	4560.90i	0.480119	−	0.831591i	0.999740	+	0.0228062i	$0.00726008\pi$
$312$	−1490.21	+	433.226i	−0.270406	+	0.0786109i
$313$	−7509.58	+	4335.66i	−1.35612	+	0.782958i	−0.989099	−	0.147253i	$-0.952957\pi$
$313$	−7509.58	+	4335.66i	−1.35612	+	0.782958i	−0.367024	+	0.930211i	$0.619623\pi$
$314$	2037.51			0.366189
$315$	2505.78	+	1136.27i	0.448206	+	0.203243i
$316$	−206.021			−0.0366760
$317$	3074.94	−	1775.32i	0.544814	−	0.314548i	−0.202214	−	0.979341i	$-0.564814\pi$
$317$	3074.94	−	1775.32i	0.544814	−	0.314548i	0.747028	+	0.664793i	$0.231480\pi$
$318$	1229.65	+	1178.78i	0.216841	+	0.207871i
$319$	7462.60	−	12925.6i	1.30980	−	2.26864i
$320$	−2182.76			−0.381313
$321$	937.269	−	977.714i	0.162970	−	0.170002i
$322$	−809.769	−	1238.03i	−0.140145	−	0.214264i
$323$			4478.59i			0.771503i
$324$	996.277	−	84.3548i	0.170829	−	0.0144641i
$325$	−1207.43	+	697.111i	−0.206081	+	0.118981i
$326$			2829.68i			0.480740i
$327$	10275.6	−	2987.26i	1.73774	−	0.505186i
$328$	1323.13	−	763.911i	0.222737	−	0.128597i
$329$	3885.31	+	5940.13i	0.651076	+	0.995411i
$330$	4993.66	−	1451.73i	0.833005	−	0.242167i
$331$	1383.92	+	2397.03i	0.229811	+	0.398044i	0.957752	−	0.287596i	$-0.0928560\pi$
$331$	1383.92	+	2397.03i	0.229811	+	0.398044i	−0.727941	+	0.685640i	$0.759523\pi$
$332$	−676.301	−	1171.39i	−0.111798	−	0.193639i
$333$	4431.83	−	2814.68i	0.729317	−	0.463193i
$334$	4909.85	+	2834.70i	0.804357	+	0.464396i
$335$	−916.228	+	1586.95i	−0.149429	+	0.258819i
$336$	−6634.59	+	2336.11i	−1.07722	+	0.379301i
$337$	4541.71	+	7866.48i	0.734133	+	1.27156i	0.955102	+	0.296276i	$0.0957447\pi$
$337$	4541.71	+	7866.48i	0.734133	+	1.27156i	−0.220969	+	0.975281i	$0.570922\pi$
$338$		−	6062.48i		−	0.975608i
$339$	236.927	+	814.982i	0.0379590	+	0.130571i
$340$	−442.328			−0.0705547
$341$	6533.19	−	11315.8i	1.03751	−	1.79703i
$342$	−5597.84	−	2924.01i	−0.885078	−	0.462317i
$343$	−6264.17	+	1055.38i	−0.986102	+	0.166138i
$344$	−7415.54	−	4281.37i	−1.16227	−	0.671034i
$345$	−724.494	−	177.820i	−0.113059	−	0.0277492i
$346$	3916.46	+	2261.17i	0.608526	+	0.351333i
$347$	1411.92	+	815.173i	0.218432	+	0.126112i	0.605224	−	0.796055i	$-0.293084\pi$
$347$	1411.92	+	815.173i	0.218432	+	0.126112i	−0.386792	+	0.922167i	$0.626417\pi$
$348$	−499.740	−	1719.01i	−0.0769796	−	0.264794i
$349$	−621.203	−	358.652i	−0.0952787	−	0.0550092i	0.451604	−	0.892219i	$-0.350852\pi$
$349$	−621.203	−	358.652i	−0.0952787	−	0.0550092i	−0.546882	+	0.837210i	$0.684185\pi$
$350$	−4494.51	+	2939.76i	−0.686405	+	0.448962i
$351$	−407.102	+	2024.43i	−0.0619073	+	0.307852i
$352$	−1824.69	+	3160.45i	−0.276296	+	0.478559i
$353$	8387.64			1.26467			0.632336	−	0.774694i	$-0.282096\pi$
$353$	8387.64			1.26467			0.632336	+	0.774694i	$0.282096\pi$
$354$	−8248.99	−	2024.63i	−1.23850	−	0.303977i
$355$		−	2752.90i		−	0.411574i
$356$	−427.379	−	740.242i	−0.0636265	−	0.110204i
$357$	5320.48	−	1873.40i	0.788767	−	0.277733i
$358$	−799.204	+	1384.26i	−0.117987	+	0.204359i
$359$	−6043.86	−	3489.42i	−0.888531	−	0.512994i	−0.0150696	−	0.999886i	$-0.504797\pi$
$359$	−6043.86	−	3489.42i	−0.888531	−	0.512994i	−0.873462	+	0.486893i	$0.838130\pi$
$360$	−1395.70	+	2671.98i	−0.204333	+	0.391183i
$361$	−510.398	−	884.036i	−0.0744129	−	0.128887i
$362$	−5205.99	−	9017.04i	−0.755858	−	1.30919i
$363$	−2724.11	+	11098.9i	−0.393881	+	1.60480i
$364$	20.7902	+	373.287i	0.00299369	+	0.0537516i
$365$	1936.27	−	1117.91i	0.277668	−	0.160312i
$366$	473.845	+	454.243i	0.0676728	+	0.0648734i
$367$			4329.87i			0.615851i	0.951410	+	0.307926i	$0.0996348\pi$
$367$			4329.87i			0.615851i	−0.951410	+	0.307926i	$0.900365\pi$
$368$	1651.63	−	953.567i	0.233959	−	0.135076i
$369$	−85.8329	−	2031.10i	−0.0121092	−	0.286544i
$370$		−	3275.27i		−	0.460198i
$371$	−1659.74	+	1085.60i	−0.232262	+	0.151918i
$372$	−437.501	−	1504.92i	−0.0609768	−	0.209748i
$373$	−4667.41			−0.647907			−0.323954	−	0.946073i	$-0.605012\pi$
$373$	−4667.41			−0.647907			−0.323954	+	0.946073i	$0.605012\pi$
$374$	5330.74	−	9233.12i	0.737022	−	1.27656i
$375$	−1497.42	+	6100.97i	−0.206204	+	0.840140i
$376$	−6734.96	+	3888.43i	−0.923747	+	0.533326i
$377$	3697.21			0.505082
$378$	−1132.09	+	7873.25i	−0.154043	+	1.07131i
$379$	57.5316			0.00779736			0.00389868	−	0.999992i	$-0.498759\pi$
$379$	57.5316			0.00779736			0.00389868	+	0.999992i	$0.498759\pi$
$380$	−499.359	+	288.305i	−0.0674120	+	0.0389203i
$381$	2933.92	−	11953.7i	0.394513	−	1.60737i
$382$	−4184.51	+	7247.78i	−0.560466	+	0.970755i
$383$	−3880.55			−0.517720			−0.258860	−	0.965915i	$-0.583347\pi$
$383$	−3880.55			−0.517720			−0.258860	+	0.965915i	$0.583347\pi$
$384$	−2474.32	−	8511.17i	−0.328821	−	1.13108i
$385$	336.697	+	6045.38i	0.0445705	+	0.800263i
$386$		−	6820.87i		−	0.899412i
$387$	−9617.74	+	6108.28i	−1.26330	+	0.802329i
$388$	−559.370	+	322.953i	−0.0731900	+	0.0422563i
$389$			5277.43i			0.687856i	0.938996	+	0.343928i	$0.111758\pi$
$389$			5277.43i			0.687856i	−0.938996	+	0.343928i	$0.888242\pi$
$390$	929.941	+	891.472i	0.120742	+	0.115747i
$391$	−1324.49	+	764.695i	−0.171310	+	0.0989061i
$392$	−772.881	−	6917.01i	−0.0995827	−	0.891229i
$393$	1091.62	−	4447.62i	0.140115	−	0.570872i
$394$	4873.89	+	8441.83i	0.623206	+	1.07942i
$395$	−413.254	−	715.777i	−0.0526407	−	0.0911763i
$396$	1179.61	+	1857.35i	0.149691	+	0.235695i
$397$	−3252.23	−	1877.68i	−0.411146	−	0.237375i	0.280136	−	0.959960i	$-0.409620\pi$
$397$	−3252.23	−	1877.68i	−0.411146	−	0.237375i	−0.691282	+	0.722585i	$0.742954\pi$
$398$	3953.72	−	6848.05i	0.497945	−	0.862467i
$399$	4785.41	−	5582.78i	0.600426	−	0.700473i
$400$	−3461.80	−	5996.01i	−0.432724	−	0.749501i
$401$			3917.75i			0.487887i	0.969789	+	0.243944i	$0.0784412\pi$
$401$			3917.75i			0.487887i	−0.969789	+	0.243944i	$0.921559\pi$
$402$	−5144.93	−	1262.77i	−0.638323	−	0.156670i
$403$	3236.75			0.400084
$404$	−824.010	+	1427.23i	−0.101475	+	0.175760i
$405$	2291.48	+	3292.14i	0.281148	+	0.403921i
$406$	14219.7	−	791.962i	1.73820	−	0.0968089i
$407$	10005.6	+	5776.76i	1.21858	+	0.703546i
$408$	1725.25	+	5934.51i	0.209344	+	0.720102i
$409$	5560.57	+	3210.40i	0.672256	+	0.388127i	0.796931	−	0.604071i	$-0.206456\pi$
$409$	5560.57	+	3210.40i	0.672256	+	0.388127i	−0.124675	+	0.992198i	$0.539789\pi$
$410$	−1098.32	−	634.115i	−0.132298	−	0.0763822i
$411$	−6138.56	−	1506.65i	−0.736722	−	0.180821i
$412$	−1212.49	−	700.034i	−0.144989	−	0.0837092i
$413$	4460.72	−	8826.05i	0.531471	−	1.05158i
$414$	−91.0587	−	2154.75i	−0.0108099	−	0.255798i
$415$	2713.16	−	4699.32i	0.320924	−	0.555857i
$416$	−904.009			−0.106545
$417$	−3858.72	−	13273.2i	−0.453147	−	1.55873i
$418$		−	13898.1i		−	1.62626i
$419$	2427.93	+	4205.30i	0.283084	+	0.490316i	0.972143	−	0.234390i	$-0.0753092\pi$
$419$	2427.93	+	4205.30i	0.283084	+	0.490316i	−0.689059	+	0.724705i	$0.741976\pi$
$420$	551.383	+	472.631i	0.0640589	+	0.0549096i
$421$	1333.50	−	2309.69i	0.154372	−	0.267381i	−0.778458	−	0.627697i	$-0.783998\pi$
$421$	1333.50	−	2309.69i	0.154372	−	0.267381i	0.932830	+	0.360316i	$0.117331\pi$
$422$	−11851.8	−	6842.62i	−1.36714	−	0.789321i
$423$	436.903	+	10338.6i	0.0502198	+	1.18837i
$424$	−1086.47	−	1881.82i	−0.124443	−	0.215541i
$425$	2776.12	+	4808.38i	0.316851	+	0.548802i
$426$	7642.26	−	2221.72i	0.869175	−	0.252682i
$427$	−639.580	+	418.335i	−0.0724858	+	0.0474113i
$428$	309.599	−	178.747i	0.0349650	−	0.0201871i
$429$	−4363.55	+	1268.55i	−0.491082	+	0.142765i
$430$			7107.84i			0.797140i
$431$	−1671.85	+	965.244i	−0.186845	+	0.107875i	−0.590505	−	0.807034i	$-0.701071\pi$
$431$	−1671.85	+	965.244i	−0.186845	+	0.107875i	0.403660	+	0.914909i	$0.367738\pi$
$432$	−10053.1	−	2021.63i	−1.11963	−	0.225153i
$433$			14198.8i			1.57587i	0.615761	+	0.787933i	$0.288849\pi$
$433$			14198.8i			1.57587i	−0.615761	+	0.787933i	$0.711151\pi$
$434$	12448.7	−	693.329i	1.37686	−	0.0766840i
$435$	4969.90	−	5184.36i	0.547789	−	0.571428i
$436$	2824.53			0.310253
$437$	−996.841	+	1726.58i	−0.109120	+	0.189001i
$438$	4666.04	+	4473.02i	0.509023	+	0.487966i
$439$	−5176.07	+	2988.40i	−0.562734	+	0.324895i	−0.754242	−	0.656596i	$-0.771995\pi$
$439$	−5176.07	+	2988.40i	−0.562734	+	0.324895i	0.191508	+	0.981491i	$0.438662\pi$
$440$	−6633.89			−0.718769
$441$	−8633.98	−	3349.70i	−0.932295	−	0.361699i
$442$	2641.02			0.284209
$443$	−1832.30	+	1057.88i	−0.196513	+	0.113457i	−0.595028	−	0.803705i	$-0.702859\pi$
$443$	−1832.30	+	1057.88i	−0.196513	+	0.113457i	0.398515	+	0.917162i	$0.369526\pi$
$444$	1330.67	−	386.846i	0.142232	−	0.0413489i
$445$	1714.54	−	2969.67i	0.182645	−	0.316351i
$446$	5908.96			0.627348
$447$	−4995.04	−	1225.98i	−0.528539	−	0.129725i
$448$	7335.71	−	408.561i	0.773616	−	0.0430864i
$449$			7685.78i			0.807827i	0.914797	+	0.403913i	$0.132350\pi$
$449$			7685.78i			0.807827i	−0.914797	+	0.403913i	$0.867650\pi$
$450$	−7822.55	+	330.576i	−0.819463	+	0.0346300i
$451$	3874.32	−	2236.84i	0.404511	−	0.233545i
$452$			224.020i			0.0233120i
$453$	1217.23	−	4959.38i	0.126248	−	0.514375i
$454$	2896.92	−	1672.54i	0.299470	−	0.172899i
$455$	−1255.20	+	821.000i	−0.129329	+	0.0845914i
$456$	5815.74	+	5575.17i	0.597253	+	0.572546i
$457$	−2262.72	−	3919.14i	−0.231609	−	0.401159i	0.726672	−	0.686984i	$-0.241066\pi$
$457$	−2262.72	−	3919.14i	−0.231609	−	0.401159i	−0.958282	+	0.285825i	$0.907732\pi$
$458$	5880.60	+	10185.5i	0.599962	+	1.03916i
$459$	8061.93	+	1621.21i	0.819823	+	0.164862i
$460$	−170.526	−	98.4530i	−0.0172843	−	0.00997912i
$461$	8067.99	−	13974.2i	0.815106	−	1.41181i	−0.0941454	−	0.995558i	$-0.530012\pi$
$461$	8067.99	−	13974.2i	0.815106	−	1.41181i	0.909252	−	0.416247i	$-0.136655\pi$
$462$	−16510.7	+	5813.59i	−1.66266	+	0.585439i
$463$	−1572.22	−	2723.17i	−0.157813	−	0.273340i	0.776267	−	0.630405i	$-0.217111\pi$
$463$	−1572.22	−	2723.17i	−0.157813	−	0.273340i	−0.934080	+	0.357065i	$0.883778\pi$
$464$			18360.1i			1.83695i
$465$	4350.93	−	4538.68i	0.433913	−	0.452638i
$466$	−14915.0			−1.48267
$467$	−7929.49	+	13734.3i	−0.785724	+	1.36091i	0.142842	+	0.989746i	$0.454376\pi$
$467$	−7929.49	+	13734.3i	−0.785724	+	1.36091i	−0.928566	+	0.371168i	$0.878957\pi$
$468$	−252.350	+	483.108i	−0.0249250	+	0.0477173i
$469$	2782.17	−	5504.85i	0.273921	−	0.541983i
$470$	5590.62	+	3227.75i	0.548672	+	0.316776i
$471$	−2393.28	+	2496.56i	−0.234133	+	0.244236i
$472$	9383.51	+	5417.57i	0.915066	+	0.528314i
$473$	−21713.8	−	12536.4i	−2.11078	−	1.21866i
$474$	1653.53	−	1724.89i	0.160231	−	0.167145i
$475$	6268.12	+	3618.90i	0.605476	+	0.349572i
$476$	1486.55	−	82.7933i	0.143143	−	0.00797232i
$477$	−2888.72	+	122.076i	−0.277286	+	0.0117179i
$478$	2445.12	−	4235.07i	0.233969	−	0.405246i
$479$	−10563.1			−1.00760			−0.503798	−	0.863821i	$-0.668065\pi$
$479$	−10563.1			−1.00760			−0.503798	+	0.863821i	$0.668065\pi$
$480$	−1215.19	+	1267.63i	−0.115554	+	0.120540i
$481$			2861.99i			0.271300i
$482$	10539.6	+	18255.2i	0.995990	+	1.72511i
$483$	2468.12	+	461.999i	0.232513	+	0.0435232i
$484$	−1508.25	+	2612.37i	−0.141647	+	0.245339i
$485$	−2244.06	−	1295.61i	−0.210098	−	0.121300i
$486$	−7289.90	+	9018.23i	−0.680404	+	0.841719i
$487$	4915.35	+	8513.63i	0.457363	+	0.792175i	0.998821	−	0.0485525i	$-0.0154608\pi$
$487$	4915.35	+	8513.63i	0.457363	+	0.792175i	−0.541458	+	0.840728i	$0.682127\pi$
$488$	−418.671	−	725.159i	−0.0388368	−	0.0672672i
$489$	−3467.20	−	3323.77i	−0.320638	−	0.307374i
$490$	−4651.71	+	3426.48i	−0.428863	+	0.315903i
$491$	4775.18	−	2756.95i	0.438902	−	0.253400i	−0.264230	−	0.964460i	$-0.585118\pi$
$491$	4775.18	−	2756.95i	0.438902	−	0.253400i	0.703132	+	0.711060i	$0.251784\pi$
$492$	127.904	−	521.120i	0.0117202	−	0.0477518i
$493$		−	14723.5i		−	1.34506i
$494$	2981.54	−	1721.39i	0.271550	−	0.156779i
$495$	−4086.80	+	7823.94i	−0.371087	+	0.710424i
$496$			16073.4i			1.45508i
$497$	515.278	+	9251.81i	0.0465058	+	0.835011i
$498$	15235.3	+	3739.35i	1.37090	+	0.336475i
$499$	3718.10			0.333557			0.166779	−	0.985994i	$-0.446663\pi$
$499$	3718.10			0.333557			0.166779	+	0.985994i	$0.446663\pi$
$500$	−829.073	+	1436.00i	−0.0741546	+	0.128439i
$501$	−9240.53	+	2686.36i	−0.824024	+	0.239556i
$502$	19799.5	−	11431.2i	1.76035	−	1.01634i
$503$	−16413.0			−1.45491			−0.727453	−	0.686158i	$-0.759296\pi$
$503$	−16413.0			−1.45491			−0.727453	+	0.686158i	$0.759296\pi$
$504$	4190.46	−	9241.09i	0.370353	−	0.816728i
$505$	−6611.46			−0.582586
$506$	4110.20	−	2373.03i	0.361108	−	0.208486i
$507$	7428.35	+	7121.06i	0.650699	+	0.623782i
$508$	1624.42	−	2813.58i	0.141874	−	0.245733i
$509$	5482.62			0.477432			0.238716	−	0.971089i	$-0.423274\pi$
$509$	5482.62			0.477432			0.238716	+	0.971089i	$0.423274\pi$
$510$	3550.13	−	3703.33i	0.308240	−	0.321542i
$511$	−6298.07	+	4119.42i	−0.545225	+	0.356619i
$512$			7375.92i			0.636665i
$513$	10158.1	−	3424.45i	0.874250	−	0.294723i
$514$	−2366.42	+	1366.25i	−0.203071	+	0.117243i
$515$		−	5616.73i		−	0.480588i
$516$	−2887.76	+	839.515i	−0.246370	+	0.0716232i
$517$	−19720.9	+	11385.9i	−1.67761	+	0.968569i
$518$	613.053	+	11007.4i	0.0520000	+	0.933659i
$519$	−7370.92	+	2142.83i	−0.623405	+	0.181233i
$520$	−821.660	−	1423.16i	−0.0692926	−	0.120018i
$521$	−4450.46	−	7708.43i	−0.374238	−	0.648200i	0.615974	−	0.787766i	$-0.288763\pi$
$521$	−4450.46	−	7708.43i	−0.374238	−	0.648200i	−0.990213	+	0.139566i	$0.955429\pi$
$522$	18403.1	+	9612.78i	1.54307	+	0.806015i
$523$	−15123.5	−	8731.55i	−1.26444	−	0.730026i	−0.290512	−	0.956871i	$-0.593826\pi$
$523$	−15123.5	−	8731.55i	−1.26444	−	0.730026i	−0.973931	+	0.226845i	$0.927159\pi$
$524$	604.397	−	1046.85i	0.0503878	−	0.0872742i
$525$	1677.23	−	8960.20i	0.139429	−	0.744867i
$526$	−9828.88	−	17024.1i	−0.814752	−	1.41119i
$527$		−	12889.8i		−	1.06544i
$528$	−6299.51	−	21669.0i	−0.519225	−	1.78603i
$529$	11486.2			0.944044
$530$	−901.868	+	1562.08i	−0.0739144	+	0.128023i
$531$	12170.1	−	7729.32i	0.994612	−	0.631683i
$532$	1624.26	−	1062.39i	0.132369	−	0.0865796i
$533$	959.731	+	554.101i	0.0779936	+	0.0450296i
$534$	9627.74	+	2363.03i	0.780212	+	0.191495i
$535$	1242.04	+	717.090i	0.100370	+	0.0579486i
$536$	5852.54	+	3378.96i	0.471625	+	0.272293i
$537$	−757.380	−	2605.23i	−0.0608628	−	0.209356i
$538$	−18952.8	−	10942.4i	−1.51880	−	0.876880i
$539$	−2263.11	−	20254.0i	−0.180851	−	1.61856i
$540$	338.215	+	1003.26i	0.0269527	+	0.0799510i
$541$	3242.17	−	5615.60i	0.257656	−	0.446273i	−0.707958	−	0.706255i	$-0.750383\pi$
$541$	3242.17	−	5615.60i	0.257656	−	0.446273i	0.965613	+	0.259982i	$0.0837167\pi$
$542$	−16671.2			−1.32120
$543$	17163.6	+	4212.63i	1.35646	+	0.332930i
$544$			3600.06i			0.283734i
$545$	5665.66	+	9813.21i	0.445303	+	0.771287i
$546$	−3292.16	−	2821.95i	−0.258043	−	0.221187i
$547$	7429.77	−	12868.7i	0.580757	−	1.00590i	−0.414633	−	0.909989i	$-0.636090\pi$
$547$	7429.77	−	12868.7i	0.580757	−	1.00590i	0.995390	−	0.0959117i	$-0.0305766\pi$
$548$	−1444.84	−	834.181i	−0.112629	−	0.0650264i
$549$	−1113.17	+	47.0418i	−0.0865370	+	0.00365700i
$550$	−8614.95	−	14921.5i	−0.667896	−	1.15683i
$551$	−9596.64	−	16621.9i	−0.741979	−	1.28515i
$552$	−655.783	+	2671.87i	−0.0505652	+	0.206018i
$553$	1522.82	+	2328.20i	0.117101	+	0.179032i
$554$	−8366.52	+	4830.41i	−0.641623	+	0.370441i
$555$	4013.18	+	3847.17i	0.306937	+	0.294240i
$556$		−	3648.51i		−	0.278294i
$557$	10822.7	−	6248.49i	0.823290	−	0.475327i	−0.0282599	−	0.999601i	$-0.508997\pi$
$557$	10822.7	−	6248.49i	0.823290	−	0.475327i	0.851550	+	0.524274i	$0.175663\pi$
$558$	16111.1	+	8415.58i	1.22229	+	0.638459i
$559$		−	6210.96i		−	0.469938i
$560$	−4077.02	−	6233.24i	−0.307653	−	0.470362i
$561$	5051.77	+	17377.1i	0.380189	+	1.30777i
$562$	−97.2323			−0.00729804
$563$	−12205.3	+	21140.2i	−0.913664	+	1.58251i	−0.104818	+	0.994491i	$0.533426\pi$
$563$	−12205.3	+	21140.2i	−0.913664	+	1.58251i	−0.808846	+	0.588021i	$0.799907\pi$
$564$	−651.050	+	2652.58i	−0.0486066	+	0.198039i
$565$	−778.311	+	449.358i	−0.0579536	+	0.0334595i
$566$	17828.6			1.32402
$567$	−8317.31	−	10635.2i	−0.616039	−	0.787715i
$568$	−10152.5			−0.749978
$569$	13128.1	−	7579.50i	0.967237	−	0.558434i	0.0688439	−	0.997627i	$-0.478069\pi$
$569$	13128.1	−	7579.50i	0.967237	−	0.558434i	0.898393	+	0.439193i	$0.144736\pi$
$570$	1594.07	−	6494.76i	0.117137	−	0.477255i
$571$	−5144.94	+	8911.30i	−0.377074	+	0.653111i	−0.990635	−	0.136536i	$-0.956403\pi$
$571$	−5144.94	+	8911.30i	−0.377074	+	0.653111i	0.613562	+	0.789647i	$0.289736\pi$
$572$	−1199.44			−0.0876769
$573$	−3965.52	−	13640.6i	−0.289113	−	0.994492i
$574$	3809.87	+	1925.52i	0.277040	+	0.140017i
$575$			2471.63i			0.179259i
$576$	9493.88	+	4959.09i	0.686768	+	0.358731i
$577$	−3545.65	+	2047.08i	−0.255818	+	0.147697i	−0.622426	−	0.782679i	$-0.713853\pi$
$577$	−3545.65	+	2047.08i	−0.255818	+	0.147697i	0.366607	+	0.930376i	$0.380519\pi$
$578$			4522.74i			0.325469i
$579$	8357.60	+	8011.87i	0.599879	+	0.575064i
$580$	1641.66	−	947.811i	0.117528	−	0.0678547i
$581$	−8238.63	+	16301.1i	−0.588289	+	1.16400i
$582$	1785.64	−	7275.28i	0.127178	−	0.518162i
$583$	−3181.34	−	5510.24i	−0.225999	−	0.391442i
$584$	−4122.73	−	7140.78i	−0.292123	−	0.505972i
$585$	−2184.64	+	92.3216i	−0.154400	+	0.00652483i
$586$	−943.358	−	544.648i	−0.0665013	−	0.0383945i
$587$	4131.33	−	7155.67i	0.290491	−	0.503145i	−0.683435	−	0.730011i	$-0.739515\pi$
$587$	4131.33	−	7155.67i	0.290491	−	0.503145i	0.973926	+	0.226866i	$0.0728481\pi$
$588$	−1941.52	−	1485.19i	−0.136169	−	0.104163i
$589$	−8401.45	−	14551.7i	−0.587734	−	1.01799i
$590$		−	8994.14i		−	0.627598i
$591$	−16068.7	−	3943.90i	−1.11840	−	0.274501i
$592$	−14212.4			−0.986700
$593$	−2857.34	+	4949.05i	−0.197870	+	0.342721i	−0.947838	−	0.318754i	$-0.896736\pi$
$593$	−2857.34	+	4949.05i	−0.197870	+	0.342721i	0.749968	+	0.661474i	$0.230069\pi$
$594$	−25018.0	−	5031.00i	−1.72812	−	0.347516i
$595$	3269.49	+	4998.63i	0.225271	+	0.344410i
$596$	−1175.69	−	678.786i	−0.0808024	−	0.0466513i
$597$	3746.82	+	12888.3i	0.256863	+	0.883555i
$598$	1018.16	+	587.836i	0.0696250	+	0.0401980i
$599$	−9639.02	−	5565.09i	−0.657495	−	0.379605i	0.133827	−	0.991005i	$-0.457273\pi$
$599$	−9639.02	−	5565.09i	−0.657495	−	0.379605i	−0.791322	+	0.611400i	$0.790607\pi$
$600$	9699.85	+	2380.73i	0.659992	+	0.161988i
$601$	12690.8	+	7327.05i	0.861347	+	0.497299i	0.864463	−	0.502696i	$-0.167658\pi$
$601$	12690.8	+	7327.05i	0.861347	+	0.497299i	−0.00311588	+	0.999995i	$0.500992\pi$
$602$	−1330.42	−	23887.6i	−0.0900728	−	1.61726i
$603$	7590.57	−	4820.81i	0.512623	−	0.325570i
$604$	673.940	−	1167.30i	0.0454010	−	0.0786369i
$605$	−12101.5			−0.813216
$606$	−5335.74	−	18353.9i	−0.357673	−	1.23032i
$607$			23920.2i			1.59949i	0.600340	+	0.799745i	$0.295032\pi$
$607$			23920.2i			1.59949i	−0.600340	+	0.799745i	$0.704968\pi$
$608$	2346.48	+	4064.23i	0.156517	+	0.271096i
$609$	−15732.2	+	18353.6i	−1.04680	+	1.22122i
$610$	−347.534	+	601.947i	−0.0230676	+	0.0399543i
$611$	−4885.18	−	2820.46i	−0.323459	−	0.186749i
$612$	1923.90	+	1004.94i	0.127073	+	0.0663763i
$613$	2063.73	+	3574.48i	0.135976	+	0.235517i	0.925970	−	0.377598i	$-0.123250\pi$
$613$	2063.73	+	3574.48i	0.135976	+	0.235517i	−0.789994	+	0.613115i	$0.789916\pi$
$614$	15437.9	+	26739.3i	1.01470	+	1.75751i
$615$	2067.08	−	600.930i	0.135533	−	0.0394014i
$616$	22294.8	−	1241.71i	1.45825	−	0.0812172i
$617$	−3577.34	+	2065.38i	−0.233417	+	0.134763i	−0.612147	−	0.790744i	$-0.709694\pi$
$617$	−3577.34	+	2065.38i	−0.233417	+	0.134763i	0.378731	+	0.925507i	$0.376361\pi$
$618$	15592.5	−	4532.96i	1.01492	−	0.295052i
$619$			4035.79i			0.262055i	0.991379	+	0.131028i	$0.0418276\pi$
$619$			4035.79i			0.262055i	−0.991379	+	0.131028i	$0.958172\pi$
$620$	1437.20	−	829.768i	0.0930958	−	0.0537489i
$621$	2747.18	+	2419.43i	0.177521	+	0.156342i
$622$			16122.2i			1.03930i
$623$	−5206.29	+	10301.2i	−0.334808	+	0.662457i
$624$	3868.38	−	4035.31i	0.248172	−	0.258881i
$625$	5188.60			0.332071
$626$	13272.7	−	22989.0i	0.847420	−	1.46777i
$627$	17029.3	+	16324.9i	1.08467	+	1.03980i
$628$	−790.550	+	456.424i	−0.0502331	+	0.0290021i
$629$	11397.4			0.722485
$630$	−8382.45	+	823.034i	−0.530103	+	0.0520484i
$631$	−19836.6			−1.25147			−0.625737	−	0.780034i	$-0.715202\pi$
$631$	−19836.6			−1.25147			−0.625737	+	0.780034i	$0.715202\pi$
$632$	−2639.72	+	1524.04i	−0.166143	+	0.0959228i
$633$	22305.5	−	6484.52i	1.40057	−	0.407167i
$634$	−5434.77	+	9413.30i	−0.340445	+	0.589669i
$635$	13033.5			0.814521
$636$	−741.161	−	181.910i	−0.0462090	−	0.0113415i
$637$	4064.75	−	2994.12i	0.252828	−	0.186234i
$638$			45690.5i			2.83527i
$639$	−6254.42	+	11973.7i	−0.387200	+	0.741271i
$640$	8128.20	−	4692.82i	0.502024	−	0.289844i
$641$		−	1990.63i		−	0.122660i	−0.998118	−	0.0613302i	$-0.980466\pi$
$641$		−	1990.63i		−	0.122660i	0.998118	−	0.0613302i	$-0.0195343\pi$
$642$	−988.314	+	4026.70i	−0.0607564	+	0.247541i
$643$	3590.95	−	2073.23i	0.220238	−	0.127155i	−0.385822	−	0.922573i	$-0.626082\pi$
$643$	3590.95	−	2073.23i	0.220238	−	0.127155i	0.606061	+	0.795419i	$0.292749\pi$
$644$	591.521	+	298.957i	0.0361944	+	0.0182928i
$645$	−8709.22	−	8348.94i	−0.531667	−	0.509673i
$646$	−6855.14	−	11873.5i	−0.417511	−	0.723150i
$647$	7896.88	+	13677.8i	0.479843	+	0.831112i	0.999733	−	0.0231210i	$-0.00736030\pi$
$647$	7896.88	+	13677.8i	0.479843	+	0.831112i	−0.519890	+	0.854233i	$0.674027\pi$
$648$	12141.1	−	8450.78i	0.736032	−	0.512312i
$649$	27476.3	+	15863.4i	1.66185	+	0.959467i
$650$	2134.06	−	3696.30i	0.128777	−	0.223048i
$651$	−13772.9	+	16067.8i	−0.829187	+	0.967351i
$652$	−633.878	−	1097.91i	−0.0380745	−	0.0659469i
$653$		−	13416.5i		−	0.804023i	−0.915635	−	0.402012i	$-0.868311\pi$
$653$		−	13416.5i		−	0.804023i	0.915635	−	0.402012i	$-0.131689\pi$
$654$	−22669.7	+	23648.0i	−1.35544	+	1.41393i
$655$	4849.39			0.289284
$656$	−2751.62	+	4765.95i	−0.163770	+	0.283657i
$657$	−10961.6	+	463.230i	−0.650916	+	0.0275073i
$658$	−19392.8	−	9801.21i	−1.14895	−	0.580685i
$659$	382.577	+	220.881i	0.0226147	+	0.0130566i	0.511265	−	0.859423i	$-0.329177\pi$
$659$	382.577	+	220.881i	0.0226147	+	0.0130566i	−0.488650	+	0.872480i	$0.662511\pi$
$660$	−1612.32	+	1681.90i	−0.0950904	+	0.0991937i
$661$	−3170.86	−	1830.70i	−0.186584	−	0.107724i	0.403798	−	0.914848i	$-0.367690\pi$
$661$	−3170.86	−	1830.70i	−0.186584	−	0.107724i	−0.590383	+	0.807124i	$0.701023\pi$
$662$	−7338.00	−	4236.60i	−0.430815	−	0.248731i
$663$	−3102.17	+	3236.04i	−0.181717	+	0.189558i
$664$	−17330.7	−	10005.9i	−1.01289	−	0.584794i
$665$	6949.10	+	3512.10i	0.405225	+	0.204802i
$666$	−7441.20	+	14245.7i	−0.432944	+	0.828844i
$667$	3277.15	−	5676.19i	0.190242	−	0.329509i
$668$	−2540.02			−0.147120
$669$	−6940.73	+	7240.24i	−0.401112	+	0.418421i
$670$		−	5609.69i		−	0.323464i
$671$	−1225.93	−	2123.37i	−0.0705312	−	0.122164i
$672$	3846.69	−	4487.65i	0.220818	−	0.257611i
$673$	−2370.91	+	4106.54i	−0.135798	+	0.235209i	−0.925902	−	0.377764i	$-0.876693\pi$
$673$	−2370.91	+	4106.54i	−0.135798	+	0.235209i	0.790104	+	0.612973i	$0.210026\pi$
$674$	−24081.6	−	13903.5i	−1.37625	−	0.794575i
$675$	8783.40	−	9973.25i	0.500849	−	0.568697i
$676$	1358.06	+	2352.23i	0.0772679	+	0.133832i
$677$	4086.07	+	7077.29i	0.231965	+	0.401776i	0.958386	−	0.285474i	$-0.0921510\pi$
$677$	4086.07	+	7077.29i	0.231965	+	0.401776i	−0.726421	+	0.687250i	$0.758818\pi$
$678$	−1875.58	−	1797.99i	−0.106241	−	0.101846i
$679$	7784.22	+	3934.18i	0.439957	+	0.222356i
$680$	−5667.48	+	3272.12i	−0.319614	+	0.184529i
$681$	−1353.40	+	5514.18i	−0.0761562	+	0.310284i
$682$			40000.0i			2.24587i
$683$	−18929.2	+	10928.8i	−1.06048	+	0.612266i	−0.925564	−	0.378592i	$-0.876408\pi$
$683$	−18929.2	+	10928.8i	−1.06048	+	0.612266i	−0.134912	+	0.990858i	$0.543075\pi$
$684$	2826.96	−	119.466i	0.158029	−	0.00667819i
$685$		−	6693.07i		−	0.373327i
$686$	14991.9	−	12386.2i	0.834391	−	0.689370i
$687$	−19387.7	−	4758.51i	−1.07669	−	0.264263i
$688$	30843.1			1.70913
$689$	788.068	−	1364.97i	0.0435748	−	0.0754737i
$690$	2192.93	−	637.516i	0.120990	−	0.0351737i
$691$	22416.7	−	12942.3i	1.23411	−	0.712516i	0.266228	−	0.963910i	$-0.414222\pi$
$691$	22416.7	−	12942.3i	1.23411	−	0.712516i	0.967885	+	0.251394i	$0.0808891\pi$
$692$	−2026.10			−0.111302
$693$	12270.3	−	27059.2i	0.672596	−	1.48325i
$694$	−4990.97			−0.272989
$695$	12676.0	−	7318.48i	0.691838	−	0.399433i
$696$	−19119.4	−	18328.5i	−1.04127	−	0.998191i
$697$	2206.61	−	3821.96i	0.119916	−	0.207700i
$698$	2195.88			0.119076
$699$	17519.3	−	18275.3i	0.947986	−	0.988894i
$700$	1085.32	−	2147.44i	0.0586020	−	0.115951i
$701$		−	24745.4i		−	1.33327i	−0.745385	−	0.666634i	$-0.767734\pi$
$701$		−	24745.4i		−	1.33327i	0.745385	−	0.666634i	$-0.232266\pi$
$702$	−2019.39	−	5990.21i	−0.108571	−	0.322060i
$703$	12866.9	−	7428.70i	0.690304	−	0.398547i
$704$			23571.0i			1.26188i
$705$	−10521.8	+	3058.83i	−0.562088	+	0.163407i
$706$	−22237.0	+	12838.5i	−1.18541	+	0.684397i
$707$	22219.4	−	1237.51i	1.18196	−	0.0658293i
$708$	3654.13	−	1062.31i	0.193970	−	0.0563899i
$709$	7953.44	+	13775.8i	0.421294	+	0.729703i	0.996066	−	0.0886105i	$-0.0282426\pi$
$709$	7953.44	+	13775.8i	0.421294	+	0.729703i	−0.574772	+	0.818314i	$0.694909\pi$
$710$	4213.72	+	7298.38i	0.222730	+	0.385780i
$711$	171.241	+	4052.14i	0.00903242	+	0.213737i
$712$	−10951.9	−	6323.07i	−0.576460	−	0.332819i
$713$	2869.00	−	4969.26i	0.150694	−	0.261010i
$714$	−11237.9	+	13110.5i	−0.589032	+	0.687180i
$715$	−2405.94	−	4167.20i	−0.125842	−	0.217965i
$716$		−	716.121i		−	0.0373781i
$717$	2317.16	+	7970.55i	0.120692	+	0.415155i
$718$	21364.3			1.11046
$719$	3347.21	−	5797.53i	0.173616	−	0.300711i	−0.766066	−	0.642762i	$-0.777788\pi$
$719$	3347.21	−	5797.53i	0.173616	−	0.300711i	0.939681	+	0.342051i	$0.111122\pi$
$720$	−458.462	−	10848.7i	−0.0237304	−	0.561540i
$721$	1051.32	+	18876.4i	0.0543040	+	0.975028i
$722$	2706.29	+	1562.48i	0.139498	+	0.0805394i
$723$	−34748.0	−	8528.55i	−1.78740	−	0.438700i
$724$	4039.83	+	2332.39i	0.207374	+	0.119728i
$725$	−20606.6	−	11897.2i	−1.05560	−	0.609452i
$726$	−9766.45	−	33594.6i	−0.499266	−	1.71737i
$727$	17642.6	+	10186.0i	0.900041	+	0.519639i	0.877213	−	0.480101i	$-0.159400\pi$
$727$	17642.6	+	10186.0i	0.900041	+	0.519639i	0.0228273	+	0.999739i	$0.492733\pi$
$728$	3027.77	+	4629.08i	0.154144	+	0.235666i
$729$	−2487.22	−	19525.2i	−0.126364	−	0.991984i
$730$	−3422.24	+	5927.49i	−0.173511	+	0.300529i
$731$	−24734.1			−1.25147
$732$	−285.606	−	70.0991i	−0.0144212	−	0.00353953i
$733$		−	12531.3i		−	0.631453i	−0.948850	−	0.315727i	$-0.897752\pi$
$733$		−	12531.3i		−	0.631453i	0.948850	−	0.315727i	$-0.102248\pi$
$734$	−6627.51	−	11479.2i	−0.333278	−	0.577254i
$735$	1265.50	−	9724.52i	0.0635083	−	0.488019i
$736$	−801.299	+	1387.89i	−0.0401308	+	0.0695086i
$737$	17137.1	+	9894.09i	0.856515	+	0.494509i
$738$	3336.45	+	5253.38i	0.166418	+	0.262032i
$739$	3311.99	+	5736.53i	0.164863	+	0.285550i	0.936606	−	0.350383i	$-0.113949\pi$
$739$	3311.99	+	5736.53i	0.164863	+	0.285550i	−0.771744	+	0.635933i	$0.780615\pi$
$740$	733.695	+	1270.80i	0.0364475	+	0.0631290i
$741$	−1392.93	+	5675.24i	−0.0690561	+	0.281356i
$742$	2738.57	−	5418.57i	0.135493	−	0.268089i
$743$	23846.9	−	13768.0i	1.17747	−	0.679811i	0.222039	−	0.975038i	$-0.428729\pi$
$743$	23846.9	−	13768.0i	1.17747	−	0.679811i	0.955427	+	0.295227i	$0.0953953\pi$
$744$	−16738.3	−	16045.8i	−0.824804	−	0.790684i
$745$		−	5446.25i		−	0.267832i
$746$	12374.1	−	7144.16i	0.607301	−	0.350625i
$747$	−22477.4	+	14275.5i	−1.10094	+	0.699215i
$748$			4776.57i			0.233488i
$749$	−4308.39	−	2177.48i	−0.210180	−	0.106226i
$750$	−5368.53	−	18466.7i	−0.261375	−	0.899076i
$751$	27525.1			1.33742			0.668712	−	0.743522i	$-0.266846\pi$
$751$	27525.1			1.33742			0.668712	+	0.743522i	$0.266846\pi$
$752$	14006.2	−	24259.4i	0.679193	−	1.17640i
$753$	−9250.03	+	37687.5i	−0.447662	+	1.82392i
$754$	−9801.90	+	5659.13i	−0.473427	+	0.273333i
$755$	5407.37			0.260655
$756$	−1324.44	−	3308.40i	−0.0637163	−	0.159161i
$757$	15056.0			0.722877			0.361439	−	0.932396i	$-0.382286\pi$
$757$	15056.0			0.722877			0.361439	+	0.932396i	$0.382286\pi$
$758$	−152.525	+	88.0605i	−0.00730867	+	0.00421966i
$759$	−1920.22	+	7823.60i	−0.0918310	+	0.374149i
$760$	−4265.47	+	7388.01i	−0.203585	+	0.352620i
$761$	9883.03			0.470775			0.235387	−	0.971902i	$-0.424364\pi$
$761$	9883.03			0.470775			0.235387	+	0.971902i	$0.424364\pi$
$762$	10518.7	+	36182.1i	0.500067	+	1.72013i
$763$	−20877.6	−	31919.2i	−0.990592	−	1.51449i
$764$		−	3749.50i		−	0.177555i
$765$	367.655	+	8699.95i	0.0173759	+	0.411173i
$766$	10287.9	−	5939.75i	0.485272	−	0.280172i
$767$			7859.25i			0.369988i
$768$	7683.11	+	7365.28i	0.360990	+	0.346057i
$769$	−6460.28	+	3729.84i	−0.302944	+	0.174905i	−0.643765	−	0.765224i	$-0.722628\pi$
$769$	−6460.28	+	3729.84i	−0.302944	+	0.174905i	0.340821	+	0.940128i	$0.389295\pi$
$770$	−10146.0	−	15511.9i	−0.474852	−	0.725988i
$771$	1105.56	−	4504.39i	0.0516416	−	0.210404i
$772$	1527.95	+	2646.48i	0.0712332	+	0.123380i
$773$	−1435.39	−	2486.18i	−0.0667886	−	0.115681i	0.830697	−	0.556724i	$-0.187942\pi$
$773$	−1435.39	−	2486.18i	−0.0667886	−	0.115681i	−0.897486	+	0.441043i	$0.854609\pi$
$774$	16148.5	−	30915.4i	0.749932	−	1.43570i
$775$	−18040.2	−	10415.5i	−0.836160	−	0.482757i
$776$	−4778.08	+	8275.88i	−0.221035	+	0.382844i
$777$	−14207.4	−	12178.2i	−0.655968	−	0.562278i
$778$	−8077.88	−	13991.3i	−0.372244	−	0.644746i
$779$		−	5752.99i		−	0.264599i
$780$	−560.515	−	137.573i	−0.0257303	−	0.00631524i
$781$	−29727.8			−1.36203
$782$	2340.96	−	4054.65i	0.107049	−	0.185415i
$783$	−33395.0	+	11258.0i	−1.52419	+	0.513828i
$784$	14868.6	+	20185.2i	0.677321	+	0.919517i
$785$	−3171.50	−	1831.06i	−0.144198	−	0.0832528i
$786$	3913.67	+	13462.2i	0.177603	+	0.610919i
$787$	−11631.6	−	6715.53i	−0.526840	−	0.304171i	0.212889	−	0.977076i	$-0.431713\pi$
$787$	−11631.6	−	6715.53i	−0.526840	−	0.304171i	−0.739729	+	0.672905i	$0.765046\pi$
$788$	−3782.12	−	2183.61i	−0.170980	−	0.0987155i
$789$	32404.8	+	7953.42i	1.46215	+	0.358871i
$790$	2191.20	+	1265.09i	0.0986830	+	0.0569747i
$791$	2531.60	−	1655.86i	0.113797	−	0.0744319i
$792$	28854.0	+	15071.8i	1.29455	+	0.676202i
$793$	303.682	−	525.992i	0.0135991	−	0.0235543i
$794$	11496.2			0.513837
$795$	−854.670	−	2939.89i	−0.0381284	−	0.131154i
$796$			3542.71i			0.157749i
$797$	12211.0	+	21150.1i	0.542707	+	0.939996i	0.998747	+	0.0500368i	$0.0159339\pi$
$797$	12211.0	+	21150.1i	0.542707	+	0.939996i	−0.456041	+	0.889959i	$0.650733\pi$
$798$	−4141.61	+	22125.6i	−0.183724	+	0.981502i
$799$	−11232.0	+	19454.4i	−0.497321	+	0.861386i
$800$	5038.55	+	2909.01i	0.222675	+	0.128561i
$801$	−14204.3	+	9021.21i	−0.626571	+	0.397938i
$802$	−5996.69	−	10386.6i	−0.264028	−	0.457310i
$803$	−12071.9	−	20909.2i	−0.530523	−	0.918892i
$804$	2279.10	−	662.567i	0.0999721	−	0.0290634i
$805$	147.858	+	2654.79i	0.00647367	+	0.116235i
$806$	−8581.14	+	4954.32i	−0.375010	+	0.216512i
$807$	35670.0	−	10369.8i	1.55594	−	0.452334i
$808$			24382.5i			1.06160i
$809$	15783.5	−	9112.60i	0.685931	−	0.396022i	−0.116155	−	0.993231i	$-0.537057\pi$
$809$	15783.5	−	9112.60i	0.685931	−	0.396022i	0.802086	+	0.597209i	$0.203724\pi$
$810$	−11114.2	−	5220.55i	−0.482115	−	0.226458i
$811$		−	9023.87i		−	0.390716i	−0.980732	−	0.195358i	$-0.937413\pi$
$811$		−	9023.87i		−	0.390716i	0.980732	−	0.195358i	$-0.0625870\pi$
$812$	−5339.79	+	3492.63i	−0.230776	+	0.150945i
$813$	19582.1	−	20427.2i	0.844743	−	0.881195i
$814$	−35368.7			−1.52294
$815$	2542.96	−	4404.54i	0.109296	−	0.189306i
$816$	−16069.9	−	15405.1i	−0.689411	−	0.660892i
$817$	−27923.1	+	16121.4i	−1.19572	+	0.690351i
$818$	−19655.9			−0.840164
$819$	7324.74	−	719.182i	0.312512	−	0.0306841i
$820$	568.194			0.0241978
$821$	−37336.3	+	21556.1i	−1.58714	+	0.916337i	−0.593368	+	0.804931i	$0.702202\pi$
$821$	−37336.3	+	21556.1i	−1.58714	+	0.916337i	−0.993775	+	0.111406i	$0.964465\pi$
$822$	18580.4	−	5401.60i	0.788403	−	0.229200i
$823$	20544.3	−	35583.8i	0.870146	−	1.50714i	0.00830039	−	0.999966i	$-0.497358\pi$
$823$	20544.3	−	35583.8i	0.870146	−	1.50714i	0.861845	−	0.507171i	$-0.169309\pi$
$824$	−20714.0			−0.875736
$825$	28402.5	+	6971.12i	1.19861	+	0.294186i
$826$	1683.49	+	30227.1i	0.0709154	+	1.27329i
$827$		−	5668.45i		−	0.238345i	−0.992874	−	0.119173i	$-0.961976\pi$
$827$		−	5668.45i		−	0.238345i	0.992874	−	0.119173i	$-0.0380242\pi$
$828$	518.019	+	815.642i	0.0217420	+	0.0342337i
$829$	3922.78	−	2264.82i	0.164347	−	0.0948858i	−0.415571	−	0.909561i	$-0.636418\pi$
$829$	3922.78	−	2264.82i	0.164347	−	0.0948858i	0.579918	+	0.814675i	$0.303085\pi$
$830$			16611.5i			0.694693i
$831$	3908.71	−	15925.3i	0.163167	−	0.664794i
$832$	−5056.65	+	2919.46i	−0.210707	+	0.121652i
$833$	−11923.6	−	16187.2i	−0.495951	−	0.673292i
$834$	30546.7	+	29283.1i	1.26828	+	1.21582i
$835$	−5094.96	−	8824.74i	−0.211160	−	0.365740i
$836$	3113.32	+	5392.43i	0.128800	+	0.223088i
$837$	−29235.9	+	9855.88i	−1.20734	+	0.407012i
$838$	−12873.7	−	7432.61i	−0.530684	−	0.306390i
$839$	7887.26	−	13661.1i	0.324551	−	0.562139i	−0.656870	−	0.754004i	$-0.728120\pi$
$839$	7887.26	−	13661.1i	0.324551	−	0.562139i	0.981421	+	0.191865i	$0.0614535\pi$
$840$	10561.1	+	1976.89i	0.433799	+	0.0812013i
$841$	19354.7	+	33523.4i	0.793585	+	1.37453i
$842$			8164.47i			0.334164i
$843$	114.210	−	119.139i	0.00466620	−	0.00486756i
$844$	6131.28			0.250056
$845$	−5448.21	+	9436.57i	−0.221804	+	0.384175i
$846$	−16983.1	−	26740.5i	−0.690177	−	1.08671i
$847$	40670.1	−	2265.11i	1.64987	−	0.0918893i
$848$	6778.36	+	3913.49i	0.274493	+	0.158478i
$849$	−20941.7	+	21845.4i	−0.846547	+	0.883077i
$850$	−14719.9	−	8498.53i	−0.593986	−	0.342938i
$851$	4393.90	+	2536.82i	0.176993	+	0.102187i
$852$	−2467.49	+	2573.97i	−0.0992193	+	0.103501i
$853$	23201.4	+	13395.3i	0.931301	+	0.537687i	0.887223	−	0.461341i	$-0.152632\pi$
$853$	23201.4	+	13395.3i	0.931301	+	0.537687i	0.0440783	+	0.999028i	$0.485965\pi$
$854$	1055.30	−	2088.04i	0.0422855	−	0.0836667i
$855$	6085.60	+	9582.03i	0.243419	+	0.383273i
$856$	2644.56	−	4580.51i	0.105595	−	0.182896i
$857$	−13696.0			−0.545914			−0.272957	−	0.962026i	$-0.588002\pi$
$857$	−13696.0			−0.545914			−0.272957	+	0.962026i	$0.588002\pi$
$858$	9626.76	−	10042.2i	0.383044	−	0.399574i
$859$		−	3353.32i		−	0.133194i	−0.997780	−	0.0665970i	$-0.978786\pi$
$859$		−	3353.32i		−	0.133194i	0.997780	−	0.0665970i	$-0.0212142\pi$
$860$	−1592.23	−	2757.82i	−0.0631333	−	0.109350i
$861$	−6834.45	+	2406.48i	−0.270520	+	0.0952528i
$862$	2954.90	−	5118.03i	0.116757	−	0.202228i
$863$	7661.03	+	4423.10i	0.302184	+	0.174466i	0.643423	−	0.765510i	$-0.277513\pi$
$863$	7661.03	+	4423.10i	0.302184	+	0.174466i	−0.341240	+	0.939976i	$0.610847\pi$
$864$	8165.45	−	2752.70i	0.321521	−	0.108390i
$865$	−4064.12	−	7039.26i	−0.159750	−	0.276696i
$866$	−21733.3	−	37643.2i	−0.852805	−	1.47710i
$867$	−5541.70	−	5312.46i	−0.217077	−	0.208098i
$868$	−4674.76	+	3057.65i	−0.182801	+	0.119566i
$869$	−7729.48	+	4462.62i	−0.301731	+	0.174205i
$870$	−5240.56	+	21351.7i	−0.204220	+	0.832059i
$871$			4901.85i			0.190692i
$872$	36190.2	−	20894.4i	1.40545	−	0.811439i
$873$	6816.95	+	10733.6i	0.264283	+	0.416124i
$874$		−	6103.25i		−	0.236208i
$875$	22356.0	−	1245.11i	0.863737	−	0.0481057i
$876$	−2812.42	−	690.280i	−0.108474	−	0.0266237i
$877$	−14339.3			−0.552115			−0.276057	−	0.961141i	$-0.589028\pi$
$877$	−14339.3			−0.552115			−0.276057	+	0.961141i	$0.589028\pi$
$878$	9148.38	−	15845.5i	0.351643	−	0.609064i
$879$	1775.44	−	516.145i	0.0681274	−	0.0198056i
$880$	20694.0	−	11947.7i	0.792721	−	0.457678i
$881$	31099.9			1.18931			0.594654	−	0.803982i	$-0.297289\pi$
$881$	31099.9			1.18931			0.594654	+	0.803982i	$0.297289\pi$
$882$	28017.3	−	4335.01i	1.06960	−	0.165496i
$883$	−3877.74			−0.147788			−0.0738938	−	0.997266i	$-0.523543\pi$
$883$	−3877.74			−0.147788			−0.0738938	+	0.997266i	$0.523543\pi$
$884$	−1024.71	+	591.617i	−0.0389872	+	0.0225093i
$885$	11020.5	+	10564.6i	0.418588	+	0.401272i
$886$	3238.48	−	5609.21i	0.122798	−	0.212692i
$887$	−6654.64			−0.251906			−0.125953	−	0.992036i	$-0.540199\pi$
$887$	−6654.64			−0.251906			−0.125953	+	0.992036i	$0.540199\pi$
$888$	14188.0	−	14800.2i	0.536169	−	0.559306i
$889$	−43802.5	+	2439.57i	−1.65252	+	0.0920367i
$890$			10497.4i			0.395365i
$891$	35550.9	−	24745.1i	1.33670	−	0.930406i
$892$	−2292.66	+	1323.67i	−0.0860584	+	0.0496858i
$893$			29283.6i			1.09736i
$894$	15119.2	−	4395.37i	0.565616	−	0.164433i
$895$	2488.01	−	1436.45i	0.0929217	−	0.0536484i
$896$	−26438.5	+	17292.8i	−0.985767	+	0.644767i
$897$	−1916.22	+	557.073i	−0.0713274	+	0.0207359i
$898$	−11764.2	−	20376.2i	−0.437168	−	0.757197i
$899$	27620.0	+	47839.3i	1.02467	+	1.77478i
$900$	2961.08	−	1880.60i	0.109670	−	0.0696518i
$901$	−5435.77	−	3138.35i	−0.200990	−	0.116042i
$902$	−6847.63	+	11860.4i	−0.252773	+	0.437815i
$903$	30832.2	+	26428.5i	1.13625	+	0.973961i
$904$	1657.19	+	2870.34i	0.0609705	+	0.105604i
$905$			18714.0i			0.687375i
$906$	4363.99	+	15011.2i	0.160026	+	0.550458i
$907$	31281.4			1.14519			0.572593	−	0.819840i	$-0.305938\pi$
$907$	31281.4			1.14519			0.572593	+	0.819840i	$0.305938\pi$
$908$	−749.333	+	1297.88i	−0.0273871	+	0.0474359i
$909$	28756.4	+	15020.8i	1.04927	+	0.548084i
$910$	2071.08	−	4097.88i	0.0754458	−	0.149278i
$911$	−11285.5	−	6515.71i	−0.410436	−	0.236965i	0.280541	−	0.959842i	$-0.409486\pi$
$911$	−11285.5	−	6515.71i	−0.410436	−	0.236965i	−0.690977	+	0.722877i	$0.742819\pi$
$912$	−28182.8	−	6917.18i	−1.02327	−	0.251152i
$913$	−50746.7	−	29298.6i	−1.83951	−	1.06204i
$914$	11997.7	+	6926.85i	0.434187	+	0.250678i
$915$	−329.347	−	1132.89i	−0.0118993	−	0.0409312i
$916$	−4563.32	−	2634.63i	−0.164603	−	0.0950336i
$917$	−16297.6	+	907.691i	−0.586906	+	0.0326877i
$918$	−23855.0	+	8041.88i	−0.857659	+	0.289130i
$919$	−23820.0	+	41257.4i	−0.855003	+	1.48091i	0.0216393	+	0.999766i	$0.493111\pi$
$919$	−23820.0	+	41257.4i	−0.855003	+	1.48091i	−0.876642	+	0.481143i	$0.840222\pi$
$920$	−2913.22			−0.104398
$921$	−50897.2	−	12492.2i	−1.82098	−	0.446940i
$922$			49397.0i			1.76443i
$923$	−3682.03	−	6377.46i	−0.131306	−	0.227429i
$924$	5103.81	−	5954.23i	0.181713	−	0.211991i
$925$	9209.59	−	15951.5i	0.327361	−	0.567007i
$926$	8336.42	+	4813.04i	0.295844	+	0.170806i
$927$	−12760.9	+	24429.9i	−0.452127	+	0.865569i
$928$	−7714.14	−	13361.3i	−0.272876	−	0.472635i
$929$	375.384	+	650.184i	0.0132572	+	0.0229622i	0.872578	−	0.488475i	$-0.162447\pi$
$929$	375.384	+	650.184i	0.0132572	+	0.0229622i	−0.859321	+	0.511437i	$0.829113\pi$
$930$	−4587.89	+	18692.5i	−0.161767	+	0.659088i
$931$	−24011.6	−	10502.6i	−0.845270	−	0.369719i
$932$	5786.99	−	3341.12i	0.203390	−	0.117427i
$933$	−19754.5	−	18937.3i	−0.693177	−	0.664502i
$934$		−	48549.0i		−	1.70083i
$935$	−16595.2	+	9581.23i	−0.580449	+	0.335123i
$936$	340.474	+	8056.75i	0.0118897	+	0.281349i
$937$		−	27064.0i		−	0.943589i	−0.881709	−	0.471794i	$-0.843606\pi$
$937$		−	27064.0i		−	0.943589i	0.881709	−	0.471794i	$-0.156394\pi$
$938$	1050.00	+	18852.7i	0.0365498	+	0.656252i
$939$	12578.1	+	43266.2i	0.437137	+	1.50366i
$940$	−2892.20			−0.100354
$941$	14965.8	−	25921.5i	0.518459	−	0.897998i	−0.481311	−	0.876550i	$-0.659839\pi$
$941$	14965.8	−	25921.5i	0.518459	−	0.897998i	0.999770	−	0.0214477i	$-0.00682753\pi$
$942$	2523.63	−	10282.0i	0.0872868	−	0.355634i
$943$	1701.38	−	982.292i	0.0587535	−	0.0339213i
$944$	−39028.4			−1.34562
$945$	8837.66	−	11237.8i	0.304221	−	0.386840i
$946$	76755.5			2.63799
$947$	−20049.8	+	11575.8i	−0.687995	+	0.397214i	−0.802861	−	0.596167i	$-0.796690\pi$
$947$	−20049.8	+	11575.8i	−0.687995	+	0.397214i	0.114865	+	0.993381i	$0.463356\pi$
$948$	−255.175	+	1039.66i	−0.00874228	+	0.0356188i
$949$	2990.41	−	5179.55i	0.102290	−	0.177171i
$950$	−22157.0			−0.756704
$951$	−5150.36	−	17716.2i	−0.175617	−	0.604087i
$952$	18434.5	−	12057.6i	0.627590	−	0.410492i
$953$			16312.5i			0.554472i	0.960802	+	0.277236i	$0.0894184\pi$
$953$			16312.5i			0.554472i	−0.960802	+	0.277236i	$0.910582\pi$
$954$	7471.60	−	4745.25i	0.253566	−	0.161041i
$955$	13026.8	−	7521.03i	0.441401	−	0.254843i
$956$			2190.93i			0.0741210i
$957$	−55984.4	−	53668.5i	−1.89103	−	1.81281i
$958$	28004.4	−	16168.3i	0.944447	−	0.545277i
$959$	1252.78	+	22493.7i	0.0421841	+	0.757414i
$960$	−2703.53	+	11015.0i	−0.0908917	+	0.370322i
$961$	9284.65	+	16081.5i	0.311659	+	0.539810i
$962$	−4380.70	−	7587.59i	−0.146818	−	0.254297i
$963$	−3773.03	−	5940.79i	−0.126256	−	0.198795i
$964$	−8178.71	−	4721.98i	−0.273256	−	0.157764i
$965$	−6129.76	+	10617.1i	−0.204481	+	0.354171i
$966$	−7250.55	+	2553.00i	−0.241493	+	0.0850324i
$967$	2542.55	+	4403.83i	0.0845533	+	0.146451i	0.905201	−	0.424984i	$-0.139720\pi$
$967$	2542.55	+	4403.83i	0.0845533	+	0.146451i	−0.820647	+	0.571435i	$0.806387\pi$
$968$			44629.2i			1.48186i
$969$	22600.7	+	5547.10i	0.749265	+	0.183899i
$970$	7932.48			0.262574
$971$	−18128.7	+	31399.9i	−0.599155	+	1.03777i	0.393791	+	0.919200i	$0.371163\pi$
$971$	−18128.7	+	31399.9i	−0.599155	+	1.03777i	−0.992946	+	0.118567i	$0.962170\pi$
$972$	808.285	−	5132.07i	0.0266726	−	0.169353i
$973$	−41230.9	+	26968.2i	−1.35848	+	0.888552i
$974$	−26062.7	−	15047.3i	−0.857396	−	0.495018i
$975$	2022.38	+	6956.58i	0.0664287	+	0.228501i
$976$	2612.04	+	1508.06i	0.0856652	+	0.0494588i
$977$	−1344.95	−	776.507i	−0.0440417	−	0.0254275i	0.477817	−	0.878459i	$-0.341428\pi$
$977$	−1344.95	−	776.507i	−0.0440417	−	0.0254275i	−0.521859	+	0.853032i	$0.674761\pi$
$978$	14279.6	+	3504.79i	0.466883	+	0.114592i
$979$	−32068.7	−	18514.9i	−1.04690	−	0.604430i
$980$	1037.29	−	2371.50i	0.0338111	−	0.0773008i
$981$	−2347.69	−	55554.3i	−0.0764078	−	1.80807i
$982$	−8439.84	+	14618.2i	−0.274263	+	0.475037i
$983$	29218.9			0.948054			0.474027	−	0.880510i	$-0.342800\pi$
$983$	29218.9			0.948054			0.474027	+	0.880510i	$0.342800\pi$
$984$	−2216.17	−	7623.20i	−0.0717978	−	0.246970i
$985$		−	17520.2i		−	0.566741i
$986$	22536.5	+	39034.4i	0.727899	+	1.26076i
$987$	34788.4	−	12249.4i	1.12191	−	0.395037i
$988$	−771.220	+	1335.79i	−0.0248338	+	0.0430134i
$989$	−9535.44	−	5505.29i	−0.306582	−	0.177005i
$990$	−1140.92	−	26998.0i	−0.0366270	−	0.866718i
$991$	2491.34	+	4315.12i	0.0798586	+	0.138319i	0.903189	−	0.429244i	$-0.141220\pi$
$991$	2491.34	+	4315.12i	0.0798586	+	0.138319i	−0.823330	+	0.567563i	$0.807886\pi$
$992$	−6753.40	−	11697.2i	−0.216150	−	0.374383i
$993$	13810.4	−	4014.89i	0.441349	−	0.128307i
$994$	−15527.4	−	23739.3i	−0.495470	−	0.757511i
$995$	−12308.4	+	7106.24i	−0.392162	+	0.226415i
$996$	−6748.92	+	1962.01i	−0.214706	+	0.0624183i
$997$		−	32768.7i		−	1.04092i	−0.853887	−	0.520459i	$-0.825761\pi$
$997$		−	32768.7i		−	1.04092i	0.853887	−	0.520459i	$-0.174239\pi$
$998$	−9857.28	+	5691.11i	−0.312652	+	0.180510i
$999$	−8714.73	−	25850.9i	−0.275998	−	0.818704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.47.7	yes	44
3.2	odd	2		189.4.s.a.89.16		44
7.3	odd	6		63.4.i.a.38.7	yes	44
9.4	even	3		189.4.i.a.152.7		44
9.5	odd	6		63.4.i.a.5.16	✓	44
21.17	even	6		189.4.i.a.143.16		44
63.31	odd	6		189.4.s.a.17.16		44
63.59	even	6	inner	63.4.s.a.59.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.16	✓	44	9.5	odd	6
63.4.i.a.38.7	yes	44	7.3	odd	6
63.4.s.a.47.7	yes	44	1.1	even	1	trivial
63.4.s.a.59.7	yes	44	63.59	even	6	inner
189.4.i.a.143.16		44	21.17	even	6
189.4.i.a.152.7		44	9.4	even	3
189.4.s.a.17.16		44	63.31	odd	6
189.4.s.a.89.16		44	3.2	odd	2

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65116 + 1.53065i) q^{2} +(1.23858 - 5.04638i) q^{3} +(0.685763 - 1.18778i) q^{4} +5.50223 q^{5} +(4.44054 + 15.2746i) q^{6} +(-18.4916 + 1.02989i) q^{7} -20.2917i q^{8} +(-23.9318 - 12.5007i) q^{9} +O(q^{10})\)	\(q+(-2.65116 + 1.53065i) q^{2} +(1.23858 - 5.04638i) q^{3} +(0.685763 - 1.18778i) q^{4} +5.50223 q^{5} +(4.44054 + 15.2746i) q^{6} +(-18.4916 + 1.02989i) q^{7} -20.2917i q^{8} +(-23.9318 - 12.5007i) q^{9} +(-14.5873 + 8.42197i) q^{10} -59.4170i q^{11} +(-5.14459 - 4.93177i) q^{12} +(12.7466 - 7.35927i) q^{13} +(47.4478 - 31.0345i) q^{14} +(6.81496 - 27.7663i) q^{15} +(36.5456 + 63.2988i) q^{16} +(-29.3070 - 50.7613i) q^{17} +(82.5813 - 3.48984i) q^{18} +(-66.1714 - 38.2041i) q^{19} +(3.77322 - 6.53541i) q^{20} +(-17.7062 + 94.5912i) q^{21} +(90.9465 + 157.524i) q^{22} -26.0925i q^{23} +(-102.400 - 25.1330i) q^{24} -94.7255 q^{25} +(-22.5289 + 39.0212i) q^{26} +(-92.7248 + 105.286i) q^{27} +(-11.4576 + 22.6701i) q^{28} +(217.541 + 125.597i) q^{29} +(24.4329 + 84.0442i) q^{30} +(190.447 + 109.955i) q^{31} +(-53.1911 - 30.7099i) q^{32} +(-299.841 - 73.5929i) q^{33} +(155.395 + 89.7174i) q^{34} +(-101.745 + 5.66667i) q^{35} +(-31.2596 + 19.8531i) q^{36} +(-97.2240 + 168.397i) q^{37} +233.908 q^{38} +(-21.3499 - 73.4394i) q^{39} -111.650i q^{40} +(37.6465 + 65.2056i) q^{41} +(-97.8439 - 277.878i) q^{42} +(210.991 - 365.447i) q^{43} +(-70.5741 - 40.7460i) q^{44} +(-131.678 - 68.7817i) q^{45} +(39.9385 + 69.1755i) q^{46} +(-191.626 - 331.907i) q^{47} +(364.694 - 106.022i) q^{48} +(340.879 - 38.0885i) q^{49} +(251.132 - 144.991i) q^{50} +(-292.460 + 85.0223i) q^{51} -20.1869i q^{52} +(92.7384 - 53.5426i) q^{53} +(84.6726 - 421.059i) q^{54} -326.926i q^{55} +(20.8982 + 375.226i) q^{56} +(-274.751 + 286.607i) q^{57} -768.979 q^{58} +(-266.985 + 462.431i) q^{59} +(-28.3067 - 27.1357i) q^{60} +(35.7367 - 20.6326i) q^{61} -673.209 q^{62} +(455.412 + 206.511i) q^{63} -396.705 q^{64} +(70.1349 - 40.4924i) q^{65} +(907.570 - 263.844i) q^{66} +(-166.519 + 288.420i) q^{67} -80.3906 q^{68} +(-131.673 - 32.3178i) q^{69} +(261.069 - 170.759i) q^{70} -500.325i q^{71} +(-253.661 + 485.618i) q^{72} +(351.906 - 203.173i) q^{73} -595.262i q^{74} +(-117.325 + 478.020i) q^{75} +(-90.7557 + 52.3978i) q^{76} +(61.1928 + 1098.72i) q^{77} +(169.012 + 162.020i) q^{78} +(-75.1067 - 130.089i) q^{79} +(201.082 + 348.284i) q^{80} +(416.465 + 598.329i) q^{81} +(-199.614 - 115.247i) q^{82} +(493.101 - 854.077i) q^{83} +(100.211 + 85.8981i) q^{84} +(-161.254 - 279.300i) q^{85} +1291.81i q^{86} +(903.252 - 942.229i) q^{87} -1205.67 q^{88} +(311.609 - 539.722i) q^{89} +(454.381 - 19.2019i) q^{90} +(-228.126 + 149.212i) q^{91} +(-30.9921 - 17.8933i) q^{92} +(790.758 - 824.881i) q^{93} +(1016.06 + 586.625i) q^{94} +(-364.090 - 210.208i) q^{95} +(-220.855 + 230.385i) q^{96} +(-407.846 - 235.470i) q^{97} +(-845.423 + 622.744i) q^{98} +(-742.754 + 1421.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Introduction

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