LMFDB - Embedded newform 63.4.s.a.47.1

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			47.1
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.53659 + 2.61920i) q^{2} +(2.85276 + 4.34301i) q^{3} +(9.72046 - 16.8363i) q^{4} -12.2114 q^{5} +(-24.3171 - 12.2305i) q^{6} +(-10.8477 - 15.0109i) q^{7} +59.9322i q^{8} +(-10.7235 + 24.7791i) q^{9} +O(q^{10})$	\(q+(-4.53659 + 2.61920i) q^{2} +(2.85276 + 4.34301i) q^{3} +(9.72046 - 16.8363i) q^{4} -12.2114 q^{5} +(-24.3171 - 12.2305i) q^{6} +(-10.8477 - 15.0109i) q^{7} +59.9322i q^{8} +(-10.7235 + 24.7791i) q^{9} +(55.3983 - 31.9842i) q^{10} -63.6103i q^{11} +(100.851 - 5.81394i) q^{12} +(13.7938 - 7.96386i) q^{13} +(88.5281 + 39.6863i) q^{14} +(-34.8363 - 53.0344i) q^{15} +(-79.2109 - 137.197i) q^{16} +(17.9283 + 31.0528i) q^{17} +(-16.2534 - 140.500i) q^{18} +(-13.8136 - 7.97531i) q^{19} +(-118.701 + 205.596i) q^{20} +(34.2469 - 89.9341i) q^{21} +(166.608 + 288.574i) q^{22} -45.6368i q^{23} +(-260.286 + 170.972i) q^{24} +24.1192 q^{25} +(-41.7179 + 72.2576i) q^{26} +(-138.208 + 24.1166i) q^{27} +(-358.173 + 36.7217i) q^{28} +(-206.656 - 119.313i) q^{29} +(296.946 + 149.352i) q^{30} +(-117.170 - 67.6480i) q^{31} +(303.473 + 175.210i) q^{32} +(276.260 - 181.465i) q^{33} +(-162.667 - 93.9160i) q^{34} +(132.466 + 183.305i) q^{35} +(312.952 + 421.409i) q^{36} +(18.0766 - 31.3095i) q^{37} +83.5558 q^{38} +(73.9376 + 37.1877i) q^{39} -731.858i q^{40} +(-84.5046 - 146.366i) q^{41} +(80.1916 + 497.694i) q^{42} +(-37.8895 + 65.6266i) q^{43} +(-1070.96 - 618.321i) q^{44} +(130.950 - 302.589i) q^{45} +(119.532 + 207.036i) q^{46} +(3.46782 + 6.00643i) q^{47} +(369.880 - 735.405i) q^{48} +(-107.656 + 325.667i) q^{49} +(-109.419 + 63.1731i) q^{50} +(-83.7175 + 166.449i) q^{51} -309.649i q^{52} +(-33.2929 + 19.2216i) q^{53} +(563.826 - 471.402i) q^{54} +776.773i q^{55} +(899.638 - 650.124i) q^{56} +(-4.77014 - 82.7444i) q^{57} +1250.02 q^{58} +(-62.2422 + 107.807i) q^{59} +(-1231.53 + 70.9965i) q^{60} +(-445.858 + 257.416i) q^{61} +708.735 q^{62} +(488.283 - 107.826i) q^{63} -568.272 q^{64} +(-168.442 + 97.2502i) q^{65} +(-777.987 + 1546.81i) q^{66} +(-167.966 + 290.926i) q^{67} +697.087 q^{68} +(198.201 - 130.191i) q^{69} +(-1081.06 - 484.626i) q^{70} -716.432i q^{71} +(-1485.07 - 642.684i) q^{72} +(725.427 - 418.826i) q^{73} +189.385i q^{74} +(68.8063 + 104.750i) q^{75} +(-268.550 + 155.047i) q^{76} +(-954.850 + 690.023i) q^{77} +(-432.827 + 24.9521i) q^{78} +(204.927 + 354.944i) q^{79} +(967.279 + 1675.38i) q^{80} +(-499.012 - 531.439i) q^{81} +(766.726 + 442.670i) q^{82} +(135.674 - 234.994i) q^{83} +(-1181.27 - 1450.79i) q^{84} +(-218.931 - 379.199i) q^{85} -396.962i q^{86} +(-71.3628 - 1237.88i) q^{87} +3812.30 q^{88} +(-717.489 + 1242.73i) q^{89} +(198.477 + 1715.71i) q^{90} +(-269.176 - 120.669i) q^{91} +(-768.356 - 443.611i) q^{92} +(-40.4612 - 701.853i) q^{93} +(-31.4641 - 18.1658i) q^{94} +(168.684 + 97.3899i) q^{95} +(104.796 + 1817.82i) q^{96} +(433.147 + 250.077i) q^{97} +(-364.596 - 1759.39i) q^{98} +(1576.21 + 682.126i) 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 $

$2$	−4.53659	+	2.61920i	−1.60393	+	0.926028i	−0.613237	+	0.789899i	$0.710133\pi$
$2$	−4.53659	+	2.61920i	−1.60393	+	0.926028i	−0.990691	+	0.136130i	$0.956534\pi$
$3$	2.85276	+	4.34301i	0.549014	+	0.835813i
$3$	2.85276	+	4.34301i	0.549014	+	0.835813i
$4$	9.72046	−	16.8363i	1.21506	−	2.10454i
$5$	−12.2114			−1.09222			−0.546112	−	0.837712i	$-0.683893\pi$
$5$	−12.2114			−1.09222			−0.546112	+	0.837712i	$0.683893\pi$
$6$	−24.3171	−	12.2305i	−1.65457	−	0.832182i
$7$	−10.8477	−	15.0109i	−0.585719	−	0.810514i
$7$	−10.8477	−	15.0109i	−0.585719	−	0.810514i
$8$			59.9322i			2.64865i
$9$	−10.7235	+	24.7791i	−0.397167	+	0.917746i
$10$	55.3983	−	31.9842i	1.75185	−	1.01143i
$11$		−	63.6103i		−	1.74357i	−0.489892	−	0.871783i	$-0.662964\pi$
$11$		−	63.6103i		−	1.74357i	0.489892	−	0.871783i	$-0.337036\pi$
$12$	100.851	−	5.81394i	2.42609	−	0.139862i
$13$	13.7938	−	7.96386i	0.294286	−	0.169906i	−0.345587	−	0.938387i	$-0.612320\pi$
$13$	13.7938	−	7.96386i	0.294286	−	0.169906i	0.639873	+	0.768481i	$0.278987\pi$
$14$	88.5281	+	39.6863i	1.69001	+	0.757614i
$15$	−34.8363	−	53.0344i	−0.599646	−	0.912895i
$16$	−79.2109	−	137.197i	−1.23767	−	2.14371i
$17$	17.9283	+	31.0528i	0.255780	+	0.443024i	0.965107	−	0.261855i	$-0.0843343\pi$
$17$	17.9283	+	31.0528i	0.255780	+	0.443024i	−0.709327	+	0.704880i	$0.751001\pi$
$18$	−16.2534	−	140.500i	−0.212831	−	1.83979i
$19$	−13.8136	−	7.97531i	−0.166793	−	0.0962979i	0.414280	−	0.910150i	$-0.364033\pi$
$19$	−13.8136	−	7.97531i	−0.166793	−	0.0962979i	−0.581073	+	0.813852i	$0.697367\pi$
$20$	−118.701	+	205.596i	−1.32711	+	2.29863i
$21$	34.2469	−	89.9341i	0.355871	−	0.934535i
$22$	166.608	+	288.574i	1.61459	+	2.79655i
$23$		−	45.6368i		−	0.413736i	−0.978369	−	0.206868i	$-0.933673\pi$
$23$		−	45.6368i		−	0.413736i	0.978369	−	0.206868i	$-0.0663271\pi$
$24$	−260.286	+	170.972i	−2.21378	+	1.45415i
$25$	24.1192			0.192953
$26$	−41.7179	+	72.2576i	−0.314675	+	0.545034i
$27$	−138.208	+	24.1166i	−0.985115	+	0.171898i
$28$	−358.173	+	36.7217i	−2.41744	+	0.247848i
$29$	−206.656	−	119.313i	−1.32328	−	0.763996i	−0.339030	−	0.940776i	$-0.610099\pi$
$29$	−206.656	−	119.313i	−1.32328	−	0.763996i	−0.984251	+	0.176779i	$0.943432\pi$
$30$	296.946	+	149.352i	1.80716	+	0.908929i
$31$	−117.170	−	67.6480i	−0.678848	−	0.391933i	0.120573	−	0.992705i	$-0.461527\pi$
$31$	−117.170	−	67.6480i	−0.678848	−	0.391933i	−0.799421	+	0.600771i	$0.794860\pi$
$32$	303.473	+	175.210i	1.67647	+	0.967909i
$33$	276.260	−	181.465i	1.45730	−	0.957242i
$34$	−162.667	−	93.9160i	−0.820506	−	0.473719i
$35$	132.466	+	183.305i	0.639736	+	0.885263i
$36$	312.952	+	421.409i	1.44885	+	1.95097i
$37$	18.0766	−	31.3095i	0.0803180	−	0.139115i	−0.823069	−	0.567942i	$-0.807740\pi$
$37$	18.0766	−	31.3095i	0.0803180	−	0.139115i	0.903387	+	0.428827i	$0.141073\pi$
$38$	83.5558			0.356698
$39$	73.9376	+	37.1877i	0.303577	+	0.152687i
$40$		−	731.858i		−	2.89292i
$41$	−84.5046	−	146.366i	−0.321888	−	0.557526i	0.658990	−	0.752152i	$-0.270984\pi$
$41$	−84.5046	−	146.366i	−0.321888	−	0.557526i	−0.980878	+	0.194626i	$0.937651\pi$
$42$	80.1916	+	497.694i	0.294615	+	1.82847i
$43$	−37.8895	+	65.6266i	−0.134374	+	0.232743i	−0.925358	−	0.379094i	$-0.876236\pi$
$43$	−37.8895	+	65.6266i	−0.134374	+	0.232743i	0.790984	+	0.611837i	$0.209569\pi$
$44$	−1070.96	−	618.321i	−3.66941	−	2.11853i
$45$	130.950	−	302.589i	0.433796	−	1.00238i
$46$	119.532	+	207.036i	0.383131	+	0.663603i
$47$	3.46782	+	6.00643i	0.0107624	+	0.0186410i	0.871356	−	0.490651i	$-0.163241\pi$
$47$	3.46782	+	6.00643i	0.0107624	+	0.0186410i	−0.860594	+	0.509292i	$0.829907\pi$
$48$	369.880	−	735.405i	1.11224	−	2.21139i
$49$	−107.656	+	325.667i	−0.313867	+	0.949467i
$50$	−109.419	+	63.1731i	−0.309484	+	0.178680i
$51$	−83.7175	+	166.449i	−0.229859	+	0.457011i
$52$		−	309.649i		−	0.825782i
$53$	−33.2929	+	19.2216i	−0.0862854	+	0.0498169i	−0.542522	−	0.840042i	$-0.682530\pi$
$53$	−33.2929	+	19.2216i	−0.0862854	+	0.0498169i	0.456236	+	0.889859i	$0.349197\pi$
$54$	563.826	−	471.402i	1.42087	−	1.18796i
$55$			776.773i			1.90436i
$56$	899.638	−	650.124i	2.14677	−	1.55137i
$57$	−4.77014	−	82.7444i	−0.0110846	−	0.192277i
$58$	1250.02			2.82993
$59$	−62.2422	+	107.807i	−0.137343	+	0.237885i	−0.926490	−	0.376319i	$-0.877190\pi$
$59$	−62.2422	+	107.807i	−0.137343	+	0.237885i	0.789147	+	0.614204i	$0.210523\pi$
$60$	−1231.53	+	70.9965i	−2.64983	+	0.152760i
$61$	−445.858	+	257.416i	−0.935841	+	0.540308i	−0.888654	−	0.458578i	$-0.848359\pi$
$61$	−445.858	+	257.416i	−0.935841	+	0.540308i	−0.0471866	+	0.998886i	$0.515026\pi$
$62$	708.735			1.45177
$63$	488.283	−	107.826i	0.976475	−	0.215632i
$64$	−568.272			−1.10991
$65$	−168.442	+	97.2502i	−0.321426	+	0.185575i
$66$	−777.987	+	1546.81i	−1.45096	+	2.88484i
$67$	−167.966	+	290.926i	−0.306273	+	0.530481i	−0.977544	−	0.210731i	$-0.932415\pi$
$67$	−167.966	+	290.926i	−0.306273	+	0.530481i	0.671271	+	0.741212i	$0.265749\pi$
$68$	697.087			1.24315
$69$	198.201	−	130.191i	0.345806	−	0.227147i
$70$	−1081.06	−	484.626i	−1.84587	−	0.827485i
$71$		−	716.432i		−	1.19753i	−0.800924	−	0.598767i	$-0.795658\pi$
$71$		−	716.432i		−	1.19753i	0.800924	−	0.598767i	$-0.204342\pi$
$72$	−1485.07	−	642.684i	−2.43079	−	1.05196i
$73$	725.427	−	418.826i	1.16308	−	0.671504i	0.211040	−	0.977478i	$-0.432315\pi$
$73$	725.427	−	418.826i	1.16308	−	0.671504i	0.952040	+	0.305973i	$0.0989818\pi$
$74$			189.385i			0.297507i
$75$	68.8063	+	104.750i	0.105934	+	0.161273i
$76$	−268.550	+	155.047i	−0.405326	+	0.234015i
$77$	−954.850	+	690.023i	−1.41319	+	1.02124i
$78$	−432.827	+	24.9521i	−0.628308	+	0.0362213i
$79$	204.927	+	354.944i	0.291849	+	0.505498i	0.974247	−	0.225483i	$-0.0723960\pi$
$79$	204.927	+	354.944i	0.291849	+	0.505498i	−0.682398	+	0.730981i	$0.739063\pi$
$80$	967.279	+	1675.38i	1.35181	+	2.34141i
$81$	−499.012	−	531.439i	−0.684516	−	0.728998i
$82$	766.726	+	442.670i	1.03257	+	0.596155i
$83$	135.674	−	234.994i	0.179423	−	0.310770i	−0.762260	−	0.647271i	$-0.775910\pi$
$83$	135.674	−	234.994i	0.179423	−	0.310770i	0.941683	+	0.336501i	$0.109243\pi$
$84$	−1181.27	−	1450.79i	−1.53436	−	1.88446i
$85$	−218.931	−	379.199i	−0.279369	−	0.483882i
$86$		−	396.962i		−	0.497738i
$87$	−71.3628	−	1237.88i	−0.0879413	−	1.52546i
$88$	3812.30			4.61810
$89$	−717.489	+	1242.73i	−0.854535	+	1.48010i	0.0225404	+	0.999746i	$0.492825\pi$
$89$	−717.489	+	1242.73i	−0.854535	+	1.48010i	−0.877076	+	0.480352i	$0.840509\pi$
$90$	198.477	+	1715.71i	0.232459	+	2.00946i
$91$	−269.176	−	120.669i	−0.310080	−	0.139006i
$92$	−768.356	−	443.611i	−0.870725	−	0.502713i
$93$	−40.4612	−	701.853i	−0.0451143	−	0.782567i
$94$	−31.4641	−	18.1658i	−0.0345242	−	0.0199326i
$95$	168.684	+	97.3899i	0.182175	+	0.105179i
$96$	104.796	+	1817.82i	0.111413	+	1.93261i
$97$	433.147	+	250.077i	0.453396	+	0.261768i	0.709263	−	0.704944i	$-0.249028\pi$
$97$	433.147	+	250.077i	0.453396	+	0.261768i	−0.255868	+	0.966712i	$0.582361\pi$
$98$	−364.596	−	1759.39i	−0.375813	−	1.81353i
$99$	1576.21	+	682.126i	1.60015	+	0.692487i
$100$	234.450	−	406.078i	0.234450	−	0.406078i
$101$	1837.11			1.80989			0.904945	−	0.425529i	$-0.139912\pi$
$101$	1837.11			1.80989			0.904945	+	0.425529i	$0.139912\pi$
$102$	−56.1724	−	974.386i	−0.0545284	−	0.945868i
$103$		−	672.703i		−	0.643528i	−0.946820	−	0.321764i	$-0.895724\pi$
$103$		−	672.703i		−	0.643528i	0.946820	−	0.321764i	$-0.104276\pi$
$104$	477.291	+	826.693i	0.450022	+	0.779461i
$105$	−418.204	+	1098.23i	−0.388691	+	1.02072i
$106$	100.691	−	174.402i	0.0922637	−	0.159805i
$107$	837.754	+	483.678i	0.756904	+	0.436999i	0.828183	−	0.560457i	$-0.189375\pi$
$107$	837.754	+	483.678i	0.756904	+	0.436999i	−0.0712787	+	0.997456i	$0.522708\pi$
$108$	−937.408	+	2561.34i	−0.835204	+	2.28208i
$109$	−749.801	−	1298.69i	−0.658880	−	1.14121i	−0.980906	−	0.194483i	$-0.937697\pi$
$109$	−749.801	−	1298.69i	−0.658880	−	1.14121i	0.322026	−	0.946731i	$-0.395636\pi$
$110$	−2034.53	−	3523.90i	−1.76350	−	3.05446i
$111$	187.546	−	10.8118i	0.160370	−	0.00924517i
$112$	−1200.21	+	2677.30i	−1.01258	+	2.25876i
$113$	−1202.80	+	694.434i	−1.00132	+	0.578114i	−0.908639	−	0.417582i	$-0.862878\pi$
$113$	−1202.80	+	694.434i	−1.00132	+	0.578114i	−0.0926834	+	0.995696i	$0.529544\pi$
$114$	238.365	+	362.884i	0.195832	+	0.298133i
$115$			557.291i			0.451893i
$116$	−4017.59	+	2319.56i	−3.21572	+	1.85660i
$117$	49.4195	+	427.199i	0.0390499	+	0.337561i
$118$		−	652.100i		−	0.508734i
$119$	271.651	−	605.972i	0.209262	−	0.466801i
$120$	3178.47	−	2087.82i	2.41794	−	1.58825i
$121$	−2715.27			−2.04002
$122$	1348.45	−	2335.59i	1.00068	−	1.73323i
$123$	394.599	−	784.552i	0.289267	−	0.575128i
$124$	−2277.89	+	1315.14i	−1.64968	+	0.952443i
$125$	1231.90			0.881476
$126$	−1932.73	+	1768.08i	−1.36651	+	1.25010i
$127$	−404.036			−0.282302			−0.141151	−	0.989988i	$-0.545080\pi$
$127$	−404.036			−0.282302			−0.141151	+	0.989988i	$0.545080\pi$
$128$	150.232	−	86.7367i	0.103741	−	0.0598946i
$129$	−393.107	+	22.6622i	−0.268303	+	0.0154674i
$130$	509.436	−	882.369i	0.343696	−	0.595299i
$131$	2734.20			1.82357			0.911786	−	0.410666i	$-0.134704\pi$
$131$	2734.20			1.82357			0.911786	+	0.410666i	$0.134704\pi$
$132$	−369.826	−	6415.13i	−0.243858	−	4.23004i
$133$	30.1289	+	293.869i	0.0196429	+	0.191592i
$134$		−	1759.75i		−	1.13447i
$135$	1687.72	−	294.498i	1.07597	−	0.187751i
$136$	−1861.06	+	1074.48i	−1.17342	+	0.677473i
$137$			857.985i			0.535056i	0.963550	+	0.267528i	$0.0862068\pi$
$137$			857.985i			0.535056i	−0.963550	+	0.267528i	$0.913793\pi$
$138$	−558.162	+	1109.75i	−0.344304	+	0.684554i
$139$	2002.26	−	1156.01i	1.22180	−	0.705404i	0.256496	−	0.966545i	$-0.417432\pi$
$139$	2002.26	−	1156.01i	1.22180	−	0.705404i	0.965301	+	0.261141i	$0.0840987\pi$
$140$	4373.81	−	448.424i	2.64039	−	0.270705i
$141$	−16.1932	+	32.1957i	−0.00967171	+	0.0192295i
$142$	1876.48	+	3250.16i	1.10895	+	1.92076i
$143$	−506.583	−	877.428i	−0.296242	−	0.513107i
$144$	4249.05	−	491.541i	2.45894	−	0.284457i
$145$	2523.57	+	1456.98i	1.44532	+	0.834455i
$146$	−2193.98	+	3800.08i	−1.24366	+	2.15409i
$147$	−1721.49	+	461.498i	−0.965894	+	0.258937i
$148$	−351.425	−	608.685i	−0.195182	−	0.338065i
$149$		−	1902.25i		−	1.04590i	−0.852365	−	0.522948i	$-0.824832\pi$
$149$		−	1902.25i		−	1.04590i	0.852365	−	0.522948i	$-0.175168\pi$
$150$	−586.507	−	294.990i	−0.319254	−	0.160572i
$151$	−1537.96			−0.828856			−0.414428	−	0.910082i	$-0.636018\pi$
$151$	−1537.96			−0.828856			−0.414428	+	0.910082i	$0.636018\pi$
$152$	477.977	−	827.881i	0.255060	−	0.441776i
$153$	−961.717	+	111.254i	−0.508171	+	0.0587866i
$154$	2524.46	−	5631.30i	1.32095	−	2.94664i
$155$	1430.81	+	826.079i	0.741455	+	0.428079i
$156$	1344.81	−	883.356i	0.690199	−	0.453366i
$157$	−2520.20	−	1455.04i	−1.28111	−	0.739647i	−0.304055	−	0.952654i	$-0.598341\pi$
$157$	−2520.20	−	1455.04i	−1.28111	−	0.739647i	−0.977051	+	0.213007i	$0.931674\pi$
$158$	−1859.34	−	1073.49i	−0.936211	−	0.540522i
$159$	−178.456	−	89.7566i	−0.0890095	−	0.0447683i
$160$	−3705.84	−	2139.57i	−1.83108	−	1.05717i
$161$	−685.051	+	495.053i	−0.335339	+	0.242333i
$162$	3655.76	+	1103.91i	1.77299	+	0.535378i
$163$	−1133.65	+	1963.54i	−0.544751	+	0.943536i	0.453872	+	0.891067i	$0.350042\pi$
$163$	−1133.65	+	1963.54i	−0.544751	+	0.943536i	−0.998623	+	0.0524693i	$0.983291\pi$
$164$	−3285.69			−1.56445
$165$	−3373.54	+	2215.95i	−1.59169	+	1.04552i
$166$			1421.43i			0.664604i
$167$	671.601	+	1163.25i	0.311198	+	0.539011i	0.978622	−	0.205667i	$-0.0659364\pi$
$167$	671.601	+	1163.25i	0.311198	+	0.539011i	−0.667424	+	0.744678i	$0.732603\pi$
$168$	5389.95	+	2052.49i	2.47526	+	0.942578i
$169$	−971.654	+	1682.95i	−0.442264	+	0.766024i
$170$	1986.40	+	1146.85i	0.896177	+	0.517408i
$171$	345.752	−	256.767i	0.154622	−	0.114827i
$172$	736.607	+	1275.84i	0.326545	+	0.565593i
$173$	471.258	+	816.242i	0.207104	+	0.358715i	0.950801	−	0.309802i	$-0.100263\pi$
$173$	471.258	+	816.242i	0.207104	+	0.358715i	−0.743697	+	0.668517i	$0.766929\pi$
$174$	3566.01	+	5428.86i	1.55367	+	2.36529i
$175$	−261.637	−	362.052i	−0.113016	−	0.156392i
$176$	−8727.16	+	5038.63i	−3.73770	+	2.15796i
$177$	−645.767	+	37.2279i	−0.274231	+	0.0158091i
$178$		−	7516.99i		−	3.16530i
$179$	−62.9841	+	36.3639i	−0.0262997	+	0.0151842i	−0.513092	−	0.858333i	$-0.671500\pi$
$179$	−62.9841	+	36.3639i	−0.0262997	+	0.0151842i	0.486792	+	0.873518i	$0.338167\pi$
$180$	−3821.60	−	5146.01i	−1.58247	−	2.13090i
$181$		−	1860.29i		−	0.763944i	−0.924174	−	0.381972i	$-0.875245\pi$
$181$		−	1860.29i		−	0.763944i	0.924174	−	0.381972i	$-0.124755\pi$
$182$	1537.20	−	157.601i	0.626069	−	0.0641876i
$183$	−2389.89	−	1202.02i	−0.965386	−	0.485551i
$184$	2735.11			1.09584
$185$	−220.741	+	382.334i	−0.0877253	+	0.151945i
$186$	2021.85	+	3078.05i	0.797039	+	1.21340i
$187$	1975.28	−	1140.43i	0.772442	−	0.445970i
$188$	134.835			0.0523077
$189$	1861.24	+	1813.02i	0.716326	+	0.697766i
$190$	−1020.34			−0.389595
$191$	3.53484	−	2.04084i	0.00133912	−	0.000773141i	−0.499330	−	0.866412i	$-0.666421\pi$
$191$	3.53484	−	2.04084i	0.00133912	−	0.000773141i	0.500669	+	0.865639i	$0.333087\pi$
$192$	−1621.14	−	2468.01i	−0.609354	−	0.927674i
$193$	2201.44	−	3813.01i	0.821053	−	1.42210i	−0.0838467	−	0.996479i	$-0.526721\pi$
$193$	2201.44	−	3813.01i	0.821053	−	1.42210i	0.904899	−	0.425626i	$-0.139946\pi$
$194$	−2620.01			−0.969619
$195$	−902.884	−	454.115i	−0.331574	−	0.166769i
$196$	4436.57	+	4978.17i	1.61683	+	1.81420i
$197$			389.909i			0.141014i	0.997511	+	0.0705072i	$0.0224618\pi$
$197$			389.909i			0.141014i	−0.997511	+	0.0705072i	$0.977538\pi$
$198$	−8937.25	+	1033.88i	−3.20779	+	0.371085i
$199$	912.641	−	526.914i	0.325103	−	0.187698i	−0.328562	−	0.944482i	$-0.606564\pi$
$199$	912.641	−	526.914i	0.325103	−	0.187698i	0.653665	+	0.756784i	$0.273231\pi$
$200$			1445.52i			0.511067i
$201$	−1742.66	+	100.463i	−0.611531	+	0.0352542i
$202$	−8334.20	+	4811.75i	−2.90293	+	1.67601i
$203$	450.738	+	4396.38i	0.155840	+	1.52002i
$204$	1988.62	+	3027.46i	0.682507	+	1.03904i
$205$	1031.92	+	1787.34i	0.351574	+	0.608943i
$206$	1761.95	+	3051.78i	0.595925	+	1.03217i
$207$	1130.84	+	489.387i	0.379705	+	0.164322i
$208$	−2185.24	−	1261.65i	−0.728457	−	0.420575i
$209$	−507.312	+	878.689i	−0.167902	+	0.290814i
$210$	−979.255	−	6077.56i	−0.321786	−	1.99710i
$211$	−561.416	−	972.401i	−0.183173	−	0.317265i	0.759786	−	0.650173i	$-0.225303\pi$
$211$	−561.416	−	972.401i	−0.183173	−	0.317265i	−0.942959	+	0.332908i	$0.891970\pi$
$212$			747.372i			0.242121i
$213$	3111.47	−	2043.81i	1.00091	−	0.657463i
$214$	−5067.40			−1.61869
$215$	462.686	−	801.395i	0.146767	−	0.254208i
$216$	−1445.36	−	8283.09i	−0.455298	−	2.60923i
$217$	255.558	+	2492.65i	0.0799467	+	0.779779i
$218$	6803.09	+	3927.77i	2.11359	+	1.22028i
$219$	3888.43	+	1955.73i	1.19980	+	0.603452i
$220$	13078.0	+	7550.59i	4.00781	+	2.31391i
$221$	494.601	+	285.558i	0.150545	+	0.0869172i
$222$	−822.500	+	540.269i	−0.248660	+	0.163336i
$223$	−3850.81	−	2223.27i	−1.15637	−	0.667628i	−0.205935	−	0.978566i	$-0.566024\pi$
$223$	−3850.81	−	2223.27i	−1.15637	−	0.667628i	−0.950430	+	0.310937i	$0.899357\pi$
$224$	−661.904	−	6456.04i	−0.197435	−	1.92572i
$225$	−258.642	+	597.653i	−0.0766348	+	0.177082i
$226$	3637.73	−	6300.73i	1.07070	−	1.85451i
$227$	−47.2354			−0.0138111			−0.00690556	−	0.999976i	$-0.502198\pi$
$227$	−47.2354			−0.0138111			−0.00690556	+	0.999976i	$0.502198\pi$
$228$	−1439.48	−	724.002i	−0.418122	−	0.210299i
$229$		−	3303.18i		−	0.953188i	−0.879124	−	0.476594i	$-0.841871\pi$
$229$		−	3303.18i		−	0.953188i	0.879124	−	0.476594i	$-0.158129\pi$
$230$	−1459.66	−	2528.20i	−0.418465	−	0.724803i
$231$	−5720.74	−	2178.45i	−1.62942	−	0.620484i
$232$	7150.70	−	12385.4i	2.02356	−	3.50491i
$233$	−4018.91	−	2320.32i	−1.12999	−	0.652400i	−0.186057	−	0.982539i	$-0.559571\pi$
$233$	−4018.91	−	2320.32i	−1.12999	−	0.652400i	−0.943932	+	0.330139i	$0.892904\pi$
$234$	−1343.12	−	1808.59i	−0.375224	−	0.505262i
$235$	−42.3470	−	73.3472i	−0.0117550	−	0.0203602i
$236$	1210.04	+	2095.86i	0.333759	+	0.578088i
$237$	−956.919	+	1902.57i	−0.262273	+	0.521457i
$238$	354.793	+	3460.56i	0.0966295	+	0.942498i
$239$	3801.25	−	2194.65i	1.02880	−	0.593976i	0.112157	−	0.993691i	$-0.464224\pi$
$239$	3801.25	−	2194.65i	1.02880	−	0.593976i	0.916640	+	0.399715i	$0.130891\pi$
$240$	−4516.76	+	8980.35i	−1.21482	+	2.41533i
$241$			1111.32i			0.297040i	0.988909	+	0.148520i	$0.0474509\pi$
$241$			1111.32i			0.297040i	−0.988909	+	0.148520i	$0.952549\pi$
$242$	12318.1	−	7111.84i	3.27205	−	1.88912i
$243$	884.484	−	3683.29i	0.233497	−	0.972358i
$244$			10008.8i			2.62602i
$245$	1314.64	−	3976.86i	0.342813	−	1.03703i
$246$	264.767	+	4592.73i	0.0686216	+	1.19033i
$247$	−254.057			−0.0654464
$248$	4054.29	−	7022.23i	1.03810	−	1.79803i
$249$	1407.63	−	81.1483i	0.358252	−	0.0206529i
$250$	−5588.63	+	3226.60i	−1.41382	+	0.816271i
$251$	−1262.49			−0.317480			−0.158740	−	0.987320i	$-0.550743\pi$
$251$	−1262.49			−0.317480			−0.158740	+	0.987320i	$0.550743\pi$
$252$	2930.94	−	9269.01i	0.732667	−	2.31704i
$253$	−2902.97			−0.721376
$254$	1832.95	−	1058.25i	0.452792	−	0.261420i
$255$	1022.31	−	2032.58i	0.251057	−	0.499158i
$256$	1818.72	−	3150.12i	0.444025	−	0.769073i
$257$	−5341.95			−1.29658			−0.648291	−	0.761392i	$-0.724516\pi$
$257$	−5341.95			−1.29658			−0.648291	+	0.761392i	$0.724516\pi$
$258$	1724.01	−	1132.44i	0.416016	−	0.273265i
$259$	−666.073	+	68.2891i	−0.159798	+	0.0163833i
$260$			3781.26i			0.901939i
$261$	5172.56	−	3841.31i	1.22672	−	0.911001i
$262$	−12403.9	+	7161.42i	−2.92488	+	1.68868i
$263$		−	1039.28i		−	0.243669i	−0.992550	−	0.121835i	$-0.961122\pi$
$263$		−	1039.28i		−	0.243669i	0.992550	−	0.121835i	$-0.0388777\pi$
$264$	10875.6	+	16556.9i	2.53540	+	3.85987i
$265$	406.554	−	234.724i	0.0942430	−	0.0544112i
$266$	−906.385	−	1254.25i	−0.208925	−	0.289109i
$267$	−7444.00	+	429.140i	−1.70624	+	0.0983630i
$268$	3265.41	+	5655.86i	0.744279	+	1.28913i
$269$	−2118.62	−	3669.55i	−0.480202	−	0.831735i	0.519540	−	0.854446i	$-0.326103\pi$
$269$	−2118.62	−	3669.55i	−0.480202	−	0.831735i	−0.999742	+	0.0227115i	$0.992770\pi$
$270$	−6885.13	+	5756.49i	−1.55191	+	1.29751i
$271$	5981.42	+	3453.38i	1.34076	+	0.774087i	0.986919	−	0.161219i	$-0.0515425\pi$
$271$	5981.42	+	3453.38i	1.34076	+	0.774087i	0.353840	+	0.935306i	$0.384876\pi$
$272$	2840.24	−	4919.44i	0.633143	−	1.09664i
$273$	−243.828	−	1513.27i	−0.0540554	−	0.335485i
$274$	−2247.24	−	3892.33i	−0.495477	−	0.858191i
$275$		−	1534.23i		−	0.336427i
$276$	−265.330	−	4602.50i	−0.0578658	−	1.00376i
$277$	−2452.47			−0.531966			−0.265983	−	0.963978i	$-0.585696\pi$
$277$	−2452.47			−0.531966			−0.265983	+	0.963978i	$0.585696\pi$
$278$	−6055.63	+	10488.7i	−1.30645	+	2.26284i
$279$	2932.73	−	2177.94i	0.629312	−	0.467347i
$280$	−10985.9	+	7938.95i	−2.34475	+	1.69444i
$281$	−7204.13	−	4159.31i	−1.52940	−	0.883002i	−0.999387	−	0.0350152i	$-0.988852\pi$
$281$	−7204.13	−	4159.31i	−1.52940	−	0.883002i	−0.530017	−	0.847987i	$-0.677815\pi$
$282$	−10.8652	−	188.472i	−0.00229438	−	0.0397991i
$283$	5933.84	+	3425.91i	1.24640	+	0.719608i	0.970389	−	0.241548i	$-0.0776550\pi$
$283$	5933.84	+	3425.91i	1.24640	+	0.719608i	0.276008	+	0.961155i	$0.410988\pi$
$284$	−12062.1	−	6964.05i	−2.52026	−	1.45507i
$285$	58.2502	+	1010.43i	0.0121068	+	0.210009i
$286$	4596.33	+	2653.69i	0.950302	+	0.548657i
$287$	−1280.42	+	2856.23i	−0.263347	+	0.587448i
$288$	−7595.86	+	5640.94i	−1.55413	+	1.15415i
$289$	1813.65	−	3141.33i	0.369153	−	0.639392i
$290$	−15264.6			−3.09092
$291$	149.575	+	2594.57i	0.0301313	+	0.522668i
$292$		−	16284.7i		−	3.26366i
$293$	−388.740	−	673.317i	−0.0775100	−	0.134251i	0.824665	−	0.565621i	$-0.191364\pi$
$293$	−388.740	−	673.317i	−0.0775100	−	0.134251i	−0.902175	+	0.431370i	$0.858030\pi$
$294$	6600.96	−	6602.57i	1.30944	−	1.30976i
$295$	760.066	−	1316.47i	0.150009	−	0.259824i
$296$	1876.45	+	1083.37i	0.368467	+	0.212735i
$297$	1534.06	+	8791.44i	0.299715	+	1.71761i
$298$	4982.38	+	8629.74i	0.968529	+	1.67754i
$299$	−363.445	−	629.506i	−0.0702962	−	0.121757i
$300$	2432.43	−	140.227i	0.468122	−	0.0269868i
$301$	1396.13	−	143.138i	0.267347	−	0.0274098i
$302$	6977.09	−	4028.23i	1.32943	−	0.767544i
$303$	5240.82	+	7978.57i	0.993655	+	1.51273i
$304$			2526.92i			0.476740i
$305$	5444.57	−	3143.42i	1.02215	−	0.590137i
$306$	4071.52	−	3023.65i	0.760632	−	0.564871i
$307$		−	5502.32i		−	1.02291i	−0.859309	−	0.511456i	$-0.829106\pi$
$307$		−	5502.32i		−	1.02291i	0.859309	−	0.511456i	$-0.170894\pi$
$308$	2335.88	+	22783.5i	0.432139	+	4.21497i
$309$	2921.56	−	1919.06i	0.537869	−	0.353306i
$310$	−8654.67			−1.58565
$311$	−1073.75	+	1859.79i	−0.195777	+	0.339096i	−0.947155	−	0.320776i	$-0.896056\pi$
$311$	−1073.75	+	1859.79i	−0.195777	+	0.339096i	0.751378	+	0.659872i	$0.229390\pi$
$312$	−2228.74	+	4431.24i	−0.404415	+	0.804069i
$313$	1705.95	−	984.930i	0.308070	−	0.177864i	−0.337992	−	0.941149i	$-0.609748\pi$
$313$	1705.95	−	984.930i	0.308070	−	0.177864i	0.646063	+	0.763284i	$0.276414\pi$
$314$	15244.1			2.73974
$315$	−5962.64	+	1316.71i	−1.06653	+	0.235518i
$316$	7967.94			1.41846
$317$	1256.62	−	725.513i	0.222647	−	0.128545i	−0.384528	−	0.923113i	$-0.625636\pi$
$317$	1256.62	−	725.513i	0.222647	−	0.128545i	0.607175	+	0.794568i	$0.292303\pi$
$318$	1044.67	−	60.2245i	0.184222	−	0.0106202i
$319$	−7589.54	+	13145.5i	−1.33208	+	2.30723i
$320$	6939.41			1.21227
$321$	289.294	+	5018.19i	0.0503016	+	0.872549i
$322$	1811.16	−	4040.14i	0.313453	−	0.699218i
$323$		−	571.936i		−	0.0985244i
$324$	−13798.1	+	3235.70i	−2.36593	+	0.554819i
$325$	332.695	−	192.082i	0.0567835	−	0.0327839i
$326$		−	11877.1i		−	2.01782i
$327$	3501.24	−	6961.26i	0.592107	−	1.17724i
$328$	8772.05	−	5064.54i	1.47669	−	0.852569i
$329$	52.5445	−	117.211i	0.00880508	−	0.0196415i
$330$	9500.34	−	18888.8i	1.58478	−	3.15090i
$331$	594.425	+	1029.57i	0.0987086	+	0.170968i	0.911150	−	0.412074i	$-0.135195\pi$
$331$	594.425	+	1029.57i	0.0987086	+	0.170968i	−0.812442	+	0.583042i	$0.801862\pi$
$332$	−2637.62	−	4568.50i	−0.436019	−	0.755207i
$333$	581.979	+	783.670i	0.0957725	+	0.128963i
$334$	−6093.56	−	3518.12i	−0.998279	−	0.576356i
$335$	2051.11	−	3552.62i	0.334519	−	0.579404i
$336$	−15051.4	+	2425.18i	−2.44382	+	0.393764i
$337$	3178.71	+	5505.69i	0.513814	+	0.889952i	0.999872	+	0.0160253i	$0.00510122\pi$
$337$	3178.71	+	5505.69i	0.513814	+	0.889952i	−0.486058	+	0.873927i	$0.661565\pi$
$338$		−	10179.8i		−	1.63820i
$339$	−6447.22	−	3242.70i	−1.03294	−	0.519526i
$340$	−8512.43			−1.35780
$341$	−4303.11	+	7453.20i	−0.683361	+	1.18362i
$342$	−896.012	+	2070.44i	−0.141669	+	0.327359i
$343$	6056.39	−	1916.71i	0.953394	−	0.301727i
$344$	−3933.15	−	2270.80i	−0.616456	−	0.355911i
$345$	−2420.32	+	1589.82i	−0.377698	+	0.248095i
$346$	−4275.81	−	2468.64i	−0.664361	−	0.383569i
$347$	9636.20	+	5563.46i	1.49077	+	0.860698i	0.999944	−	0.0105578i	$-0.00336073\pi$
$347$	9636.20	+	5563.46i	1.49077	+	0.860698i	0.490829	+	0.871256i	$0.336694\pi$
$348$	−21535.1	−	10831.3i	−3.31725	−	1.66844i
$349$	−2318.23	−	1338.43i	−0.355564	−	0.205285i	0.311569	−	0.950224i	$-0.399145\pi$
$349$	−2318.23	−	1338.43i	−0.355564	−	0.205285i	−0.667133	+	0.744938i	$0.732479\pi$
$350$	2135.23	+	957.201i	0.326093	+	0.146184i
$351$	−1714.35	+	1433.33i	−0.260699	+	0.217964i
$352$	11145.2	−	19304.0i	1.68761	−	2.92303i
$353$	7528.80			1.13518			0.567589	−	0.823312i	$-0.307876\pi$
$353$	7528.80			1.13518			0.567589	+	0.823312i	$0.307876\pi$
$354$	2832.08	−	1860.28i	0.425207	−	0.279302i
$355$			8748.67i			1.30797i
$356$	13948.6	+	24159.7i	2.07662	+	3.59681i
$357$	3406.70	−	548.909i	0.505046	−	0.0813762i
$358$	190.489	−	329.936i	0.0281219	−	0.0487086i
$359$	−9009.61	−	5201.70i	−1.32454	−	0.764722i	−0.340089	−	0.940393i	$-0.610457\pi$
$359$	−9009.61	−	5201.70i	−1.32454	−	0.764722i	−0.984449	+	0.175671i	$0.943791\pi$
$360$	18134.8	+	7848.09i	2.65497	+	1.14897i
$361$	−3302.29	−	5719.73i	−0.481453	−	0.833902i
$362$	4872.47	+	8439.36i	0.707434	+	1.22531i
$363$	−7746.01	−	11792.4i	−1.12000	−	1.70508i
$364$	−4648.13	+	3358.97i	−0.669308	+	0.483676i
$365$	−8858.51	+	5114.46i	−1.27034	+	0.733433i
$366$	13990.3	−	806.527i	1.99804	−	0.115185i
$367$			12167.3i			1.73060i	0.501256	+	0.865299i	$0.332872\pi$
$367$			12167.3i			1.73060i	−0.501256	+	0.865299i	$0.667128\pi$
$368$	−6261.25	+	3614.93i	−0.886930	+	0.512069i
$369$	4533.02	−	524.391i	0.639511	−	0.0739803i
$370$		−	2312.66i		−	0.324944i
$371$	649.684	+	291.247i	0.0909163	+	0.0407568i
$372$	−12209.9	−	6141.11i	−1.70176	−	0.855919i
$373$	−2216.79			−0.307724			−0.153862	−	0.988092i	$-0.549171\pi$
$373$	−2216.79			−0.307724			−0.153862	+	0.988092i	$0.549171\pi$
$374$	−5974.02	+	10347.3i	−0.825961	+	1.43061i
$375$	3514.31	+	5350.16i	0.483942	+	0.736749i
$376$	−359.979	+	207.834i	−0.0493736	+	0.0285059i
$377$	−3800.77			−0.519230
$378$	−13192.4	−	3349.95i	−1.79509	−	0.455828i
$379$	−2955.89			−0.400617			−0.200308	−	0.979733i	$-0.564194\pi$
$379$	−2955.89			−0.400617			−0.200308	+	0.979733i	$0.564194\pi$
$380$	3279.38	−	1893.35i	0.442707	−	0.255597i
$381$	−1152.62	−	1754.73i	−0.154988	−	0.235952i
$382$	−10.6907	+	18.5169i	−0.00143190	+	0.00248013i
$383$	−7449.29			−0.993840			−0.496920	−	0.867796i	$-0.665536\pi$
$383$	−7449.29			−0.993840			−0.496920	+	0.867796i	$0.665536\pi$
$384$	805.276	+	405.022i	0.107016	+	0.0538247i
$385$	11660.1	−	8426.17i	1.54351	−	1.11542i
$386$			23064.1i			3.04127i
$387$	−1219.86	−	1642.62i	−0.160230	−	0.215760i
$388$	8420.76	−	4861.73i	1.10180	−	0.636126i
$389$			6028.72i			0.785779i	0.919586	+	0.392890i	$0.128525\pi$
$389$			6028.72i			0.785779i	−0.919586	+	0.392890i	$0.871475\pi$
$390$	5285.44	−	304.701i	0.686253	−	0.0395618i
$391$	1417.15	−	818.193i	0.183295	−	0.105826i
$392$	−19517.9	−	6452.08i	−2.51481	−	0.831324i
$393$	7800.01	+	11874.7i	1.00117	+	1.52417i
$394$	−1021.25	−	1768.86i	−0.130583	−	0.226177i
$395$	−2502.46	−	4334.38i	−0.318765	−	0.552117i
$396$	26806.0	−	19907.0i	3.40164	−	2.52617i
$397$	12778.7	+	7377.79i	1.61548	+	0.932696i	0.988070	+	0.154005i	$0.0492172\pi$
$397$	12778.7	+	7377.79i	1.61548	+	0.932696i	0.627407	+	0.778691i	$0.284116\pi$
$398$	−2760.19	+	4780.79i	−0.347628	+	0.602109i
$399$	−1190.33	+	969.188i	−0.149351	+	0.121604i
$400$	−1910.50	−	3309.09i	−0.238813	−	0.413636i
$401$			3802.58i			0.473546i	0.971565	+	0.236773i	$0.0760898\pi$
$401$			3802.58i			0.473546i	−0.971565	+	0.236773i	$0.923910\pi$
$402$	7642.61	−	5020.14i	0.948206	−	0.622841i
$403$	−2154.96			−0.266367
$404$	17857.5	−	30930.1i	2.19912	−	3.80899i
$405$	6093.66	+	6489.64i	0.747645	+	0.796229i
$406$	−13559.8	−	18764.0i	−1.65754	−	2.29370i
$407$	−1991.61	−	1149.85i	−0.242556	−	0.140040i
$408$	−9975.67	−	5017.37i	−1.21046	−	0.608816i
$409$	−3772.89	−	2178.28i	−0.456130	−	0.263347i	0.254285	−	0.967129i	$-0.418160\pi$
$409$	−3772.89	−	2178.28i	−0.456130	−	0.263347i	−0.710416	+	0.703782i	$0.751493\pi$
$410$	−9362.83	−	5405.63i	−1.12780	−	0.651134i
$411$	−3726.24	+	2447.63i	−0.447207	+	0.293753i
$412$	−11325.8	−	6538.98i	−1.35433	−	0.781923i
$413$	2293.46	−	235.137i	0.273254	−	0.0280153i
$414$	−6411.97	+	741.753i	−0.761187	+	0.0880560i
$415$	−1656.77	+	2869.61i	−0.195970	+	0.339431i
$416$	5581.40			0.657814
$417$	10732.5	+	5398.04i	1.26037	+	0.633917i
$418$		−	5315.01i		−	0.621927i
$419$	−4875.07	−	8443.88i	−0.568408	−	0.984512i	−0.996724	−	0.0808824i	$-0.974226\pi$
$419$	−4875.07	−	8443.88i	−0.568408	−	0.984512i	0.428316	−	0.903629i	$-0.359107\pi$
$420$	14424.9	+	17716.3i	1.67587	+	2.05825i
$421$	4245.69	−	7353.75i	0.491502	−	0.851306i	−0.508450	−	0.861091i	$-0.669781\pi$
$421$	4245.69	−	7353.75i	0.491502	−	0.851306i	0.999952	+	0.00978535i	$0.00311482\pi$
$422$	5093.83	+	2940.93i	0.587592	+	0.339246i
$423$	−186.021	+	21.5194i	−0.0213822	+	0.00247355i
$424$	−1151.99	−	1995.31i	−0.131948	−	0.228540i
$425$	432.417	+	748.969i	0.0493537	+	0.0854831i
$426$	−8762.34	+	17421.5i	−0.996565	+	1.98140i
$427$	8700.58	+	3900.38i	0.986067	+	0.442044i
$428$	16286.7	−	9403.14i	1.83936	−	1.06196i
$429$	2365.52	−	4703.19i	0.266220	−	0.529306i
$430$			4847.47i			0.543642i
$431$	3582.61	−	2068.42i	0.400390	−	0.231166i	−0.286262	−	0.958151i	$-0.592413\pi$
$431$	3582.61	−	2068.42i	0.400390	−	0.231166i	0.686652	+	0.726986i	$0.259079\pi$
$432$	14256.3	+	17051.4i	1.58775	+	1.89905i
$433$			1005.45i			0.111591i	0.998442	+	0.0557953i	$0.0177694\pi$
$433$			1005.45i			0.111591i	−0.998442	+	0.0557953i	$0.982231\pi$
$434$	−7688.12	−	10638.8i	−0.850326	−	1.17668i
$435$	871.442	+	15116.3i	0.0960516	+	1.66614i
$436$	−29153.6			−3.20231
$437$	−363.968	+	630.410i	−0.0398419	+	0.0690083i
$438$	−22762.7	+	1312.25i	−2.48321	+	0.143154i
$439$	−7127.88	+	4115.28i	−0.774932	+	0.447407i	−0.834631	−	0.550809i	$-0.814319\pi$
$439$	−7127.88	+	4115.28i	−0.774932	+	0.447407i	0.0596993	+	0.998216i	$0.480986\pi$
$440$	−46553.7			−5.04400
$441$	−6915.30	−	6159.93i	−0.746712	−	0.665147i
$442$	−2991.74			−0.321951
$443$	−1172.25	+	676.800i	−0.125723	+	0.0725863i	−0.561543	−	0.827448i	$-0.689792\pi$
$443$	−1172.25	+	676.800i	−0.125723	+	0.0725863i	0.435820	+	0.900034i	$0.356459\pi$
$444$	1641.00	−	3262.68i	0.175402	−	0.348738i
$445$	8761.57	−	15175.5i	0.933344	−	1.61660i
$446$	23292.8			2.47297
$447$	8261.50	−	5426.67i	0.874174	−	0.574212i
$448$	6164.42	+	8530.29i	0.650093	+	0.899594i
$449$		−	11342.5i		−	1.19217i	−0.802922	−	0.596084i	$-0.796722\pi$
$449$		−	11342.5i		−	1.19217i	0.802922	−	0.596084i	$-0.203278\pi$
$450$	−392.019	−	3388.75i	−0.0410665	−	0.354993i
$451$	−9310.40	+	5375.36i	−0.972084	+	0.561233i
$452$			27000.9i			2.80977i
$453$	−4387.43	−	6679.37i	−0.455054	−	0.692769i
$454$	214.288	−	123.719i	0.0221520	−	0.0127895i
$455$	3287.02	+	1473.54i	0.338677	+	0.151825i
$456$	4959.05	−	285.885i	0.509274	−	0.0293592i
$457$	3633.76	+	6293.85i	0.371948	+	0.644232i	0.989865	−	0.142011i	$-0.0453568\pi$
$457$	3633.76	+	6293.85i	0.371948	+	0.644232i	−0.617918	+	0.786243i	$0.712023\pi$
$458$	8651.69	+	14985.2i	0.882679	+	1.52884i
$459$	−3226.73	−	3859.37i	−0.328128	−	0.392462i
$460$	9382.73	+	5417.12i	0.951027	+	0.549075i
$461$	6216.19	−	10766.8i	0.628019	−	1.08776i	−0.359930	−	0.932979i	$-0.617199\pi$
$461$	6216.19	−	10766.8i	0.628019	−	1.08776i	0.987949	−	0.154782i	$-0.0494674\pi$
$462$	31658.5	−	5101.01i	3.18806	−	0.513681i
$463$	1444.49	+	2501.94i	0.144992	+	0.251134i	0.929370	−	0.369150i	$-0.120351\pi$
$463$	1444.49	+	2501.94i	0.144992	+	0.251134i	−0.784378	+	0.620283i	$0.787018\pi$
$464$			37803.6i			3.78230i
$465$	494.089	+	8570.63i	0.0492749	+	0.854739i
$466$	24309.6			2.41656
$467$	1313.23	−	2274.59i	0.130127	−	0.225386i	−0.793598	−	0.608442i	$-0.791795\pi$
$467$	1313.23	−	2274.59i	0.130127	−	0.225386i	0.923725	+	0.383055i	$0.125128\pi$
$468$	7672.85	+	3320.53i	0.757858	+	0.327973i
$469$	6189.11	−	634.537i	0.609353	−	0.0624738i
$470$	384.222	+	221.831i	0.0377082	+	0.0217708i
$471$	−870.277	−	15096.1i	−0.0851385	−	1.47684i
$472$	−6461.08	−	3730.31i	−0.630075	−	0.363774i
$473$	4174.53	+	2410.17i	0.405803	+	0.234291i
$474$	−642.070	−	11137.6i	−0.0622178	−	1.07925i
$475$	−333.174	−	192.358i	−0.0321833	−	0.0185810i
$476$	−7561.77	−	10463.9i	−0.728136	−	1.00759i
$477$	−119.279	−	1031.09i	−0.0114495	−	0.0989737i
$478$	−11496.5	+	19912.5i	−1.10008	+	1.90539i
$479$	761.663			0.0726540			0.0363270	−	0.999340i	$-0.488434\pi$
$479$	761.663			0.0726540			0.0363270	+	0.999340i	$0.488434\pi$
$480$	−1279.71	−	22198.2i	−0.121688	−	2.11084i
$481$		−	575.837i		−	0.0545860i
$482$	−2910.78	−	5041.62i	−0.275068	−	0.476431i
$483$	−4104.31	−	1562.92i	−0.386651	−	0.147237i
$484$	−26393.7	+	45715.2i	−2.47874	+	4.29331i
$485$	−5289.34	−	3053.80i	−0.495210	−	0.285909i
$486$	5634.73	+	19026.2i	0.525919	+	1.77582i
$487$	−8677.57	−	15030.0i	−0.807430	−	1.39851i	−0.914639	−	0.404273i	$-0.867525\pi$
$487$	−8677.57	−	15030.0i	−0.807430	−	1.39851i	0.107209	−	0.994237i	$-0.465809\pi$
$488$	−15427.5	−	26721.2i	−1.43109	−	2.47872i
$489$	−11761.7	+	678.052i	−1.08770	+	0.0627046i
$490$	4452.24	+	21484.7i	0.410472	+	1.98078i
$491$	17290.8	−	9982.86i	1.58925	−	0.917557i	0.595825	−	0.803114i	$-0.296825\pi$
$491$	17290.8	−	9982.86i	1.58925	−	0.917557i	0.993430	−	0.114442i	$-0.0365081\pi$
$492$	−9373.30	−	14269.8i	−0.858904	−	1.30759i
$493$		−	8556.35i		−	0.781661i
$494$	1152.55	−	665.427i	0.104971	−	0.0606052i
$495$	−19247.8	−	8329.74i	−1.74772	−	0.756351i
$496$			21433.8i			1.94034i
$497$	−10754.3	+	7771.62i	−0.970618	+	0.701418i
$498$	−6173.29	+	4055.00i	−0.555485	+	0.364877i
$499$	−1541.61			−0.138300			−0.0691500	−	0.997606i	$-0.522029\pi$
$499$	−1541.61			−0.138300			−0.0691500	+	0.997606i	$0.522029\pi$
$500$	11974.6	−	20740.7i	1.07104	−	1.85510i
$501$	−3136.08	+	6235.24i	−0.279660	+	0.556028i
$502$	5727.40	−	3306.71i	0.509216	−	0.293996i
$503$	−578.894			−0.0513153			−0.0256577	−	0.999671i	$-0.508168\pi$
$503$	−578.894			−0.0513153			−0.0256577	+	0.999671i	$0.508168\pi$
$504$	6462.24	+	29263.9i	0.571133	+	2.58634i
$505$	−22433.7			−1.97681
$506$	13169.6	−	7603.47i	1.15704	−	0.668015i
$507$	−10081.0	+	581.159i	−0.883062	+	0.0509077i
$508$	−3927.41	+	6802.47i	−0.343013	+	0.594116i
$509$	−9161.99			−0.797835			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−9161.99			−0.797835			−0.398918	+	0.916987i	$0.630614\pi$
$510$	685.946	+	11898.7i	0.0595573	+	1.03310i
$511$	−14156.2	−	6346.06i	−1.22550	−	0.549380i
$512$			20442.2i			1.76451i
$513$	2101.49	+	769.111i	0.180864	+	0.0661932i
$514$	24234.3	−	13991.7i	2.07963	−	1.20067i
$515$			8214.66i			0.702876i
$516$	−3439.63	+	6838.76i	−0.293452	+	0.583449i
$517$	382.071	−	220.589i	0.0325019	−	0.0187650i
$518$	2842.84	−	2054.38i	0.241134	−	0.174255i
$519$	−2200.57	+	4375.22i	−0.186116	+	0.370040i
$520$	−5828.41	−	10095.1i	−0.491525	−	0.851346i
$521$	6093.28	+	10553.9i	0.512382	+	0.887473i	0.999897	+	0.0143576i	$0.00457032\pi$
$521$	6093.28	+	10553.9i	0.512382	+	0.887473i	−0.487514	+	0.873115i	$0.662096\pi$
$522$	−13404.6	+	30974.5i	−1.12396	+	2.59716i
$523$	−8988.68	−	5189.62i	−0.751525	−	0.433893i	0.0747195	−	0.997205i	$-0.476194\pi$
$523$	−8988.68	−	5189.62i	−0.751525	−	0.433893i	−0.826245	+	0.563311i	$0.809527\pi$
$524$	26577.6	−	46033.8i	2.21574	−	3.83778i
$525$	826.007	−	2169.14i	0.0686665	−	0.180322i
$526$	2722.10	+	4714.81i	0.225644	+	0.390828i
$527$		−	4851.26i		−	0.400995i
$528$	−46779.3	−	23528.2i	−3.85570	−	1.93927i
$529$	10084.3			0.828822
$530$	−1229.58	+	2129.69i	−0.100773	+	0.174543i
$531$	−2003.90	−	2698.37i	−0.163770	−	0.220526i
$532$	5240.54	+	2349.28i	0.427079	+	0.191455i
$533$	−2331.28	−	1345.97i	−0.189454	−	0.109381i
$534$	32646.4	−	21444.2i	2.64560	−	1.73779i
$535$	−10230.2	−	5906.40i	−0.826709	−	0.477301i
$536$	−17435.8	−	10066.6i	−1.40506	−	0.811212i
$537$	−337.607	−	169.803i	−0.0271300	−	0.0136453i
$538$	19222.6	+	11098.2i	1.54042	+	0.889362i
$539$	20715.8	+	6848.05i	1.65546	+	0.547248i
$540$	11447.1	−	31277.6i	0.912230	−	2.49254i
$541$	2598.10	−	4500.05i	0.206472	−	0.357619i	−0.744129	−	0.668036i	$-0.767135\pi$
$541$	2598.10	−	4500.05i	0.206472	−	0.357619i	0.950601	+	0.310417i	$0.100469\pi$
$542$	−36180.4			−2.86731
$543$	8079.24	−	5306.95i	0.638515	−	0.419416i
$544$			12564.9i			0.990288i
$545$	9156.15	+	15858.9i	0.719645	+	1.24646i
$546$	5069.72	+	6226.47i	0.397370	+	0.488037i
$547$	10154.0	−	17587.3i	0.793703	−	1.37473i	−0.129957	−	0.991520i	$-0.541484\pi$
$547$	10154.0	−	17587.3i	0.793703	−	1.37473i	0.923660	−	0.383214i	$-0.125183\pi$
$548$	14445.3	+	8340.01i	1.12605	+	0.650123i
$549$	−1597.39	−	13808.4i	−0.124180	−	1.07346i
$550$	4018.46	+	6960.17i	0.311541	+	0.539605i
$551$	1903.12	+	3296.30i	0.147143	+	0.254858i
$552$	7802.62	+	11878.6i	0.601633	+	0.915920i
$553$	3105.06	−	6926.47i	0.238772	−	0.532628i
$554$	11125.8	−	6423.51i	0.853235	−	0.492615i
$555$	−2290.20	+	132.028i	−0.175160	+	0.0100978i
$556$		−	44947.7i		−	3.42843i
$557$	−8891.43	+	5133.47i	−0.676377	+	0.390507i	−0.798489	−	0.602010i	$-0.794367\pi$
$557$	−8891.43	+	5133.47i	−0.676377	+	0.390507i	0.122111	+	0.992516i	$0.461033\pi$
$558$	−7600.13	+	17561.9i	−0.576594	+	1.33235i
$559$			1206.99i			0.0913241i
$560$	14656.2	−	32693.7i	1.10596	−	2.46707i
$561$	10587.9	+	5325.29i	0.796829	+	0.400774i
$562$	43576.3			3.27074
$563$	4175.18	−	7231.63i	0.312545	−	0.541344i	−0.666367	−	0.745624i	$-0.732152\pi$
$563$	4175.18	−	7231.63i	0.312545	−	0.541344i	0.978913	+	0.204279i	$0.0654851\pi$
$564$	384.652	+	585.590i	0.0287177	+	0.0437195i
$565$	14687.9	−	8480.04i	1.09367	−	0.631430i
$566$	−35892.6			−2.66551
$567$	−2564.28	+	13255.5i	−0.189929	+	0.981798i
$568$	42937.3			3.17185
$569$	−2740.97	+	1582.50i	−0.201946	+	0.116594i	−0.597563	−	0.801822i	$-0.703864\pi$
$569$	−2740.97	+	1582.50i	−0.201946	+	0.116594i	0.395617	+	0.918416i	$0.370531\pi$
$570$	−2910.78	−	4431.33i	−0.213893	−	0.325628i
$571$	1478.65	−	2561.10i	0.108371	−	0.187703i	−0.806740	−	0.590907i	$-0.798770\pi$
$571$	1478.65	−	2561.10i	0.108371	−	0.187703i	0.915110	+	0.403204i	$0.132103\pi$
$572$	−19696.9			−1.43980
$573$	18.9474	+	9.52982i	0.00138140	+	0.000694788i
$574$	−1672.30	−	16311.2i	−0.121604	−	1.18609i
$575$		−	1100.72i		−	0.0798319i
$576$	6093.87	−	14081.3i	0.440818	−	1.01861i
$577$	−21694.0	+	12525.0i	−1.56522	+	0.903681i	−0.568507	+	0.822678i	$0.692479\pi$
$577$	−21694.0	+	12525.0i	−1.56522	+	0.903681i	−0.996714	+	0.0810022i	$0.974188\pi$
$578$			19001.3i			1.36738i
$579$	22840.1	−	1316.71i	1.63938	−	0.0945089i
$580$	49060.5	−	28325.1i	3.51229	−	2.02782i
$581$	−4999.22	+	512.545i	−0.356975	+	0.0365989i
$582$	−7474.27	−	11378.8i	−0.532334	−	0.810420i
$583$	1222.69	+	2117.77i	0.0868590	+	0.150444i
$584$	25101.1	+	43476.4i	1.77858	+	3.08059i
$585$	−603.483	−	5216.72i	−0.0426512	−	0.368692i
$586$	3527.11	+	2036.38i	0.248641	+	0.143553i
$587$	−6544.89	+	11336.1i	−0.460198	+	0.797087i	−0.998970	−	0.0453646i	$-0.985555\pi$
$587$	−6544.89	+	11336.1i	−0.460198	+	0.797087i	0.538772	+	0.842452i	$0.318888\pi$
$588$	−8963.79	+	33469.6i	−0.628674	+	2.34739i
$589$	1079.03	+	1868.93i	0.0754847	+	0.130743i
$590$			7963.07i			0.555652i
$591$	−1693.38	+	1112.32i	−0.117862	+	0.0774189i
$592$	−5727.44			−0.397629
$593$	−3549.51	+	6147.93i	−0.245803	+	0.425743i	−0.962357	−	0.271789i	$-0.912385\pi$
$593$	−3549.51	+	6147.93i	−0.245803	+	0.425743i	0.716554	+	0.697531i	$0.245718\pi$
$594$	−29986.0	−	35865.2i	−2.07128	−	2.47738i
$595$	−3317.25	+	7399.79i	−0.228561	+	0.509852i
$596$	−32026.9	−	18490.8i	−2.20113	−	1.27082i
$597$	4891.94	+	2460.45i	0.335366	+	0.168676i
$598$	3297.61	+	1903.87i	0.225500	+	0.130193i
$599$	14190.2	+	8192.71i	0.967939	+	0.558840i	0.898607	−	0.438754i	$-0.144580\pi$
$599$	14190.2	+	8192.71i	0.967939	+	0.558840i	0.0693315	+	0.997594i	$0.477913\pi$
$600$	−6277.89	+	4123.71i	−0.427156	+	0.280583i
$601$	−1449.23	−	836.712i	−0.0983615	−	0.0567890i	0.450012	−	0.893022i	$-0.351420\pi$
$601$	−1449.23	−	836.712i	−0.0983615	−	0.0567890i	−0.548374	+	0.836233i	$0.684753\pi$
$602$	−5958.77	+	4306.11i	−0.403424	+	0.291535i
$603$	−5407.70	−	7281.80i	−0.365205	−	0.491771i
$604$	−14949.7	+	25893.6i	−1.00711	+	1.74436i
$605$	33157.3			2.22816
$606$	−44673.0	−	22468.8i	−2.99458	−	1.50616i
$607$			9484.81i			0.634228i	0.948387	+	0.317114i	$0.102714\pi$
$607$			9484.81i			0.634228i	−0.948387	+	0.317114i	$0.897286\pi$
$608$	−2794.71	−	4840.58i	−0.186415	−	0.322881i
$609$	−17807.7	+	14499.4i	−1.18490	+	0.964768i
$610$	−16466.5	+	28520.9i	−1.09297	+	1.89308i
$611$	95.6688	+	55.2344i	0.00633444	+	0.00365719i
$612$	−7475.22	+	17273.2i	−0.493739	+	1.14090i
$613$	791.346	+	1370.65i	0.0521405	+	0.0903100i	0.890918	−	0.454165i	$-0.150062\pi$
$613$	791.346	+	1370.65i	0.0521405	+	0.0903100i	−0.838777	+	0.544475i	$0.816729\pi$
$614$	14411.7	+	24961.8i	0.947246	+	1.64068i
$615$	−4818.62	+	9580.51i	−0.315944	+	0.628168i
$616$	−41354.6	−	57226.2i	−2.70491	−	3.74304i
$617$	−19948.8	+	11517.5i	−1.30164	+	0.751500i	−0.980685	−	0.195595i	$-0.937336\pi$
$617$	−19948.8	+	11517.5i	−1.30164	+	0.751500i	−0.320952	+	0.947095i	$0.604003\pi$
$618$	−8227.50	+	16358.1i	−0.535532	+	1.06476i
$619$		−	1130.29i		−	0.0733928i	−0.999326	−	0.0366964i	$-0.988317\pi$
$619$		−	1130.29i		−	0.0733928i	0.999326	−	0.0366964i	$-0.0116835\pi$
$620$	27816.3	−	16059.7i	1.80182	−	1.04028i
$621$	1100.61	+	6307.36i	0.0711204	+	0.407578i
$622$		−	11249.5i		−	0.725180i
$623$	26437.6	−	2710.51i	1.70016	−	0.174308i
$624$	−754.609	−	13089.7i	−0.0484111	−	0.839756i
$625$	−18058.2			−1.15572
$626$	−5159.47	+	8936.46i	−0.329415	+	0.570563i
$627$	−5263.40	+	303.430i	−0.335247	+	0.0193267i
$628$	−48994.9	+	28287.2i	−3.11323	+	1.79743i
$629$	1296.33			0.0821750
$630$	23601.3	−	21590.7i	1.49254	−	1.36539i
$631$	6214.42			0.392064			0.196032	−	0.980598i	$-0.437194\pi$
$631$	6214.42			0.392064			0.196032	+	0.980598i	$0.437194\pi$
$632$	−21272.6	+	12281.7i	−1.33889	+	0.773008i
$633$	2621.56	−	5212.26i	0.164610	−	0.327281i
$634$	−3800.53	+	6582.71i	−0.238073	+	0.412355i
$635$	4933.86			0.308337
$636$	−3245.85	+	2132.07i	−0.202368	+	0.132928i
$637$	1108.58	+	5349.55i	0.0689535	+	0.332742i
$638$		−	79514.3i		−	4.93417i
$639$	17752.6	+	7682.67i	1.09903	+	0.475621i
$640$	−1834.55	+	1059.18i	−0.113308	+	0.0654184i
$641$		−	16495.0i		−	1.01640i	−0.861239	−	0.508200i	$-0.830311\pi$
$641$		−	16495.0i		−	1.01640i	0.861239	−	0.508200i	$-0.169689\pi$
$642$	−14456.1	−	22007.8i	−0.888686	−	1.35293i
$643$	−11470.6	+	6622.54i	−0.703507	+	0.406170i	−0.808652	−	0.588287i	$-0.799803\pi$
$643$	−11470.6	+	6622.54i	−0.703507	+	0.406170i	0.105145	+	0.994457i	$0.466469\pi$
$644$	1675.86	+	16345.9i	0.102544	+	1.00018i
$645$	4800.40	−	276.739i	0.293047	−	0.0168939i
$646$	1498.02	+	2594.64i	0.0912364	+	0.158026i
$647$	−5765.87	−	9986.78i	−0.350355	−	0.606833i	0.635956	−	0.771725i	$-0.280606\pi$
$647$	−5765.87	−	9986.78i	−0.350355	−	0.606833i	−0.986312	+	0.164892i	$0.947272\pi$
$648$	31850.3	−	29906.9i	1.93086	−	1.81305i
$649$	6857.61	+	3959.24i	0.414768	+	0.239467i
$650$	−1006.20	+	1742.79i	−0.0607177	+	0.105166i
$651$	−10096.6	+	8220.82i	−0.607858	+	0.494930i
$652$	22039.2	+	38173.0i	1.32381	+	2.29290i
$653$		−	13728.4i		−	0.822719i	−0.911473	−	0.411359i	$-0.865054\pi$
$653$		−	13728.4i		−	0.822719i	0.911473	−	0.411359i	$-0.134946\pi$
$654$	2349.25	+	40750.9i	0.140463	+	2.43652i
$655$	−33388.5			−1.99175
$656$	−13387.4	+	23187.6i	−0.796782	+	1.38007i
$657$	2599.01	+	22466.7i	0.154333	+	1.33411i
$658$	68.6264	+	669.363i	0.00406586	+	0.0396573i
$659$	−104.852	−	60.5365i	−0.00619797	−	0.00357840i	0.496898	−	0.867809i	$-0.334472\pi$
$659$	−104.852	−	60.5365i	−0.00619797	−	0.00357840i	−0.503096	+	0.864231i	$0.667806\pi$
$660$	4516.11	+	78338.0i	0.266347	+	4.62015i
$661$	24111.8	+	13920.9i	1.41882	+	0.819156i	0.996195	−	0.0871490i	$-0.0277756\pi$
$661$	24111.8	+	13920.9i	1.41882	+	0.819156i	0.422624	+	0.906305i	$0.361109\pi$
$662$	−5393.33	−	3113.84i	−0.316643	−	0.182814i
$663$	170.796	+	2962.68i	0.0100048	+	0.173546i
$664$	14083.7	+	8131.23i	0.823123	+	0.475230i
$665$	−367.917	−	3588.56i	−0.0214544	−	0.209261i
$666$	−4692.79	−	2030.87i	−0.273036	−	0.118160i
$667$	−5445.07	+	9431.14i	−0.316093	+	0.547489i
$668$	26113.1			1.51249
$669$	−1329.77	−	23066.6i	−0.0768487	−	1.33304i
$670$			21489.1i			1.23910i
$671$	16374.3	+	28361.2i	0.942062	+	1.63170i
$672$	26150.4	−	21292.2i	1.50115	−	1.22227i
$673$	10610.3	−	18377.6i	0.607724	−	1.05261i	−0.383890	−	0.923379i	$-0.625416\pi$
$673$	10610.3	−	18377.6i	0.607724	−	1.05261i	0.991615	−	0.129230i	$-0.0412507\pi$
$674$	−28841.0	−	16651.4i	−1.64824	−	0.951613i
$675$	−3333.46	+	581.673i	−0.190081	+	0.0331683i
$676$	18889.8	+	32718.2i	1.07475	+	1.86152i
$677$	−5178.79	−	8969.93i	−0.293999	−	0.509221i	0.680753	−	0.732513i	$-0.261653\pi$
$677$	−5178.79	−	8969.93i	−0.293999	−	0.509221i	−0.974751	+	0.223293i	$0.928319\pi$
$678$	37741.7	−	2175.78i	2.13785	−	0.123245i
$679$	−944.735	−	9214.69i	−0.0533956	−	0.520806i
$680$	22726.2	−	13121.0i	1.28163	−	0.739952i
$681$	−134.751	−	205.144i	−0.00758250	−	0.0115435i
$682$		−	45082.8i		−	2.53125i
$683$	−5821.72	+	3361.17i	−0.326152	+	0.188304i	−0.654131	−	0.756381i	$-0.726966\pi$
$683$	−5821.72	+	3361.17i	−0.326152	+	0.188304i	0.327979	+	0.944685i	$0.393632\pi$
$684$	−962.142	−	8317.08i	−0.0537842	−	0.464929i
$685$		−	10477.2i		−	0.584401i
$686$	−22455.1	+	24558.2i	−1.24977	+	1.36682i
$687$	14345.7	−	9423.17i	0.796687	−	0.523314i
$688$	12005.1			0.665245
$689$	−306.157	+	530.279i	−0.0169284	+	0.0293208i
$690$	6815.96	−	13551.7i	0.376057	−	0.747686i
$691$	860.287	−	496.687i	0.0473616	−	0.0273442i	−0.476132	−	0.879374i	$-0.657962\pi$
$691$	860.287	−	496.687i	0.0473616	−	0.0273442i	0.523494	+	0.852029i	$0.324628\pi$
$692$	18323.4			1.00657
$693$	−6858.84	−	31059.8i	−0.375968	−	1.70255i
$694$	−58287.4			−3.18812
$695$	−24450.5	+	14116.5i	−1.33448	+	0.770460i
$696$	74189.0	−	4276.93i	4.04041	−	0.232926i
$697$	3030.06	−	5248.21i	0.164665	−	0.285208i
$698$	14022.5			0.760399
$699$	−1387.81	−	24073.5i	−0.0750958	−	1.30264i
$700$	−8638.85	+	885.697i	−0.466454	+	0.0478231i
$701$		−	3345.02i		−	0.180228i	−0.995931	−	0.0901138i	$-0.971277\pi$
$701$		−	3345.02i		−	0.180228i	0.995931	−	0.0901138i	$-0.0287231\pi$
$702$	4023.14	−	10992.7i	0.216301	−	0.591013i
$703$	−499.406	+	288.332i	−0.0267930	+	0.0154689i
$704$			36147.9i			1.93519i
$705$	197.742	−	393.156i	0.0105637	−	0.0210030i
$706$	−34155.1	+	19719.5i	−1.82074	+	1.05121i
$707$	−19928.3	−	27576.7i	−1.06009	−	1.46694i
$708$	−5650.37	+	11234.2i	−0.299935	+	0.596339i
$709$	2778.33	+	4812.22i	0.147169	+	0.254903i	0.930180	−	0.367104i	$-0.119651\pi$
$709$	2778.33	+	4812.22i	0.147169	+	0.254903i	−0.783011	+	0.622007i	$0.786317\pi$
$710$	−22914.5	−	39689.2i	−1.21122	−	2.09790i
$711$	−10992.8	+	1271.67i	−0.579832	+	0.0670765i
$712$	−74479.3	−	43000.6i	−3.92027	−	2.26337i
$713$	−3087.24	+	5347.25i	−0.162157	+	0.280864i
$714$	−14017.1	+	11413.0i	−0.734702	+	0.598209i
$715$	6186.11	+	10714.7i	0.323563	+	0.560427i
$716$			1413.89i			0.0737984i
$717$	20375.5	+	10248.1i	1.06128	+	0.533781i
$718$	54497.3			2.83262
$719$	−11984.2	+	20757.2i	−0.621605	+	1.07665i	0.367582	+	0.929991i	$0.380186\pi$
$719$	−11984.2	+	20757.2i	−0.621605	+	1.07665i	−0.989187	+	0.146660i	$0.953148\pi$
$720$	−51887.0	+	6002.42i	−2.68572	+	0.310690i
$721$	−10097.9	+	7297.25i	−0.521588	+	0.376926i
$722$	29962.3	+	17298.7i	1.54443	+	0.891679i
$723$	−4826.49	+	3170.34i	−0.248270	+	0.163079i
$724$	−31320.4	−	18082.8i	−1.60775	−	0.928236i
$725$	−4984.39	−	2877.74i	−0.255332	−	0.147416i
$726$	66027.3	+	33209.2i	3.37535	+	1.69767i
$727$	28778.8	+	16615.4i	1.46815	+	0.847637i	0.999363	−	0.0356749i	$-0.0113581\pi$
$727$	28778.8	+	16615.4i	1.46815	+	0.847637i	0.468786	+	0.883312i	$0.344691\pi$
$728$	7231.94	−	16132.3i	0.368178	−	0.821294i
$729$	18519.8	−	6666.21i	0.940902	−	0.338678i
$730$	26791.6	−	46404.5i	1.35836	−	2.35275i
$731$	−2717.19			−0.137481
$732$	−43468.4	+	28552.8i	−2.19486	+	1.44172i
$733$		−	22547.5i		−	1.13617i	−0.822971	−	0.568084i	$-0.807685\pi$
$733$		−	22547.5i		−	1.13617i	0.822971	−	0.568084i	$-0.192315\pi$
$734$	−31868.7	−	55198.2i	−1.60258	−	2.77576i
$735$	21021.9	−	5635.55i	1.05497	−	0.282817i
$736$	7996.04	−	13849.5i	0.400459	−	0.693616i
$737$	18505.9	+	10684.4i	0.924929	+	0.534008i
$738$	−19191.0	+	14251.8i	−0.957222	+	0.710864i
$739$	10873.2	+	18833.0i	0.541242	+	0.937458i	0.998833	+	0.0482957i	$0.0153790\pi$
$739$	10873.2	+	18833.0i	0.541242	+	0.937458i	−0.457591	+	0.889163i	$0.651288\pi$
$740$	4291.40	+	7432.92i	0.213182	+	0.369243i
$741$	−724.763	−	1103.37i	−0.0359310	−	0.0547009i
$742$	−3710.19	+	380.387i	−0.183565	+	0.0188200i
$743$	−22091.4	+	12754.5i	−1.09079	+	0.629766i	−0.933786	−	0.357833i	$-0.883516\pi$
$743$	−22091.4	+	12754.5i	−1.09079	+	0.629766i	−0.157000	+	0.987599i	$0.550182\pi$
$744$	42063.6	−	2424.92i	2.07275	−	0.119492i
$745$			23229.2i			1.14235i
$746$	10056.7	−	5806.22i	0.493567	−	0.284961i
$747$	4368.05	+	5881.84i	0.213947	+	0.288093i
$748$		−	44341.9i		−	2.16751i
$749$	−1827.22	−	17822.3i	−0.0891393	−	0.869440i
$750$	−29956.2	−	15066.8i	−1.45846	−	0.733548i
$751$	32562.1			1.58217			0.791084	−	0.611707i	$-0.209517\pi$
$751$	32562.1			1.58217			0.791084	+	0.611707i	$0.209517\pi$
$752$	549.378	−	951.550i	0.0266406	−	0.0461429i
$753$	−3601.58	−	5483.00i	−0.174301	−	0.265354i
$754$	17242.6	−	9955.00i	0.832808	−	0.480822i
$755$	18780.7			0.905297
$756$	48616.7	−	13713.1i	2.33885	−	0.659712i
$757$	−922.082			−0.0442717			−0.0221358	−	0.999755i	$-0.507047\pi$
$757$	−922.082			−0.0442717			−0.0221358	+	0.999755i	$0.507047\pi$
$758$	13409.7	−	7742.07i	0.642561	−	0.370983i
$759$	−8281.48	−	12607.6i	−0.396046	−	0.602936i
$760$	−5836.79	+	10109.6i	−0.278582	+	0.482519i
$761$	−10276.7			−0.489529			−0.244764	−	0.969583i	$-0.578711\pi$
$761$	−10276.7			−0.489529			−0.244764	+	0.969583i	$0.578711\pi$
$762$	9824.95	+	4941.57i	0.467087	+	0.234927i
$763$	−11361.0	+	25343.0i	−0.539052	+	1.20246i
$764$		−	79.3516i		−	0.00375764i
$765$	11743.9	−	1358.57i	0.555037	−	0.0642081i
$766$	33794.4	−	19511.2i	1.59405	−	0.920324i
$767$			1982.75i			0.0933416i
$768$	18869.4	−	1087.80i	0.886577	−	0.0511103i
$769$	−30344.0	+	17519.1i	−1.42293	+	0.821528i	−0.996548	−	0.0830156i	$-0.973545\pi$
$769$	−30344.0	+	17519.1i	−1.42293	+	0.821528i	−0.426380	+	0.904544i	$0.640212\pi$
$770$	−30827.2	+	68766.3i	−1.44277	+	3.21840i
$771$	−15239.3	−	23200.2i	−0.711842	−	1.08370i
$772$	−42798.0	−	74128.3i	−1.99525	−	3.45588i
$773$	4927.07	+	8533.94i	0.229256	+	0.397082i	0.957588	−	0.288142i	$-0.0930375\pi$
$773$	4927.07	+	8533.94i	0.229256	+	0.397082i	−0.728332	+	0.685224i	$0.759704\pi$
$774$	9836.37	+	4256.83i	0.456797	+	0.197685i
$775$	−2826.04	−	1631.61i	−0.130986	−	0.0756249i
$776$	−14987.7	+	25959.4i	−0.693333	+	1.20089i
$777$	−2196.73	−	2697.95i	−0.101425	−	0.124567i
$778$	−15790.4	−	27349.9i	−0.727654	−	1.26033i
$779$			2695.80i			0.123989i
$780$	−16422.1	+	10787.0i	−0.753852	+	0.495177i
$781$	−45572.5			−2.08798
$782$	−4286.03	+	7423.62i	−0.195995	+	0.339473i
$783$	31439.0	+	11506.2i	1.43491	+	0.525155i
$784$	53208.2	−	11026.2i	2.42384	−	0.502288i
$785$	30775.2	+	17768.1i	1.39925	+	0.807860i
$786$	−66487.6	−	33440.7i	−3.01722	−	1.51754i
$787$	−18307.3	−	10569.7i	−0.829206	−	0.478742i	0.0243745	−	0.999703i	$-0.492241\pi$
$787$	−18307.3	−	10569.7i	−0.829206	−	0.478742i	−0.853581	+	0.520960i	$0.825574\pi$
$788$	6564.63	+	3790.09i	0.296771	+	0.171341i
$789$	4513.62	−	2964.83i	0.203662	−	0.133778i
$790$	22705.2	+	13108.9i	1.02255	+	0.590371i
$791$	23471.6	+	10522.1i	1.05506	+	0.472974i
$792$	−40881.3	+	94465.6i	−1.83416	+	4.23824i
$793$	−4100.05	+	7101.50i	−0.183603	+	0.318010i
$794$	−77295.7			−3.45481
$795$	2179.21	+	1096.06i	0.0972183	+	0.0488970i
$796$		−	20487.4i		−	0.912256i
$797$	−10049.6	−	17406.5i	−0.446645	−	0.773612i	0.551520	−	0.834161i	$-0.314048\pi$
$797$	−10049.6	−	17406.5i	−0.446645	−	0.773612i	−0.998165	+	0.0605498i	$0.980715\pi$
$798$	2861.53	−	7514.52i	0.126939	−	0.333347i
$799$	−124.344	+	215.371i	−0.00550562	+	0.00953601i
$800$	7319.53	+	4225.93i	0.323480	+	0.186761i
$801$	−23099.7	−	31105.2i	−1.01896	−	1.37209i
$802$	−9959.74	−	17250.8i	−0.438517	−	0.759534i
$803$	−26641.6	−	46144.6i	−1.17081	−	2.02791i
$804$	−15248.0	+	30316.5i	−0.668852	+	1.32983i
$805$	8365.46	−	6045.31i	0.366265	−	0.264682i
$806$	9776.16	−	5644.27i	0.427234	−	0.246664i
$807$	9893.01	−	19669.5i	0.431537	−	0.857993i
$808$			110102.i			4.79377i
$809$	−25583.5	+	14770.7i	−1.11183	+	0.641914i	−0.939302	−	0.343091i	$-0.888526\pi$
$809$	−25583.5	+	14770.7i	−1.11183	+	0.641914i	−0.172525	+	0.985005i	$0.555193\pi$
$810$	−44642.1	−	13480.3i	−1.93650	−	0.584753i
$811$		−	13234.7i		−	0.573036i	−0.958075	−	0.286518i	$-0.907502\pi$
$811$		−	13234.7i		−	0.573036i	0.958075	−	0.286518i	$-0.0924978\pi$
$812$	78400.2	+	35146.0i	3.38831	+	1.51894i
$813$	2065.51	+	35829.0i	0.0891029	+	1.54561i
$814$	12046.8			0.518723
$815$	13843.5	−	23977.7i	0.594990	−	1.03055i
$816$	29467.7	−	1698.79i	1.26419	−	0.0728792i
$817$	1046.78	−	604.361i	0.0448254	−	0.0258800i
$818$	22821.4			0.975467
$819$	5876.58	−	5375.95i	0.250726	−	0.229366i
$820$	40123.0			1.70873
$821$	−5614.55	+	3241.56i	−0.238671	+	0.137797i	−0.614566	−	0.788866i	$-0.710669\pi$
$821$	−5614.55	+	3241.56i	−0.238671	+	0.137797i	0.375895	+	0.926662i	$0.377335\pi$
$822$	10493.6	−	20863.7i	0.445264	−	0.885285i
$823$	−7749.57	+	13422.6i	−0.328230	+	0.568510i	−0.982161	−	0.188044i	$-0.939785\pi$
$823$	−7749.57	+	13422.6i	−0.328230	+	0.568510i	0.653931	+	0.756554i	$0.273119\pi$
$824$	40316.5			1.70448
$825$	6663.17	−	4376.79i	0.281190	−	0.184703i
$826$	−9788.63	+	7073.76i	−0.412336	+	0.297975i
$827$			7987.02i			0.335835i	0.985801	+	0.167918i	$0.0537043\pi$
$827$			7987.02i			0.335835i	−0.985801	+	0.167918i	$0.946296\pi$
$828$	19231.8	−	14282.1i	0.807186	−	0.599443i
$829$	38491.6	−	22223.1i	1.61263	−	0.931051i	0.623870	−	0.781528i	$-0.285559\pi$
$829$	38491.6	−	22223.1i	1.61263	−	0.931051i	0.988758	−	0.149524i	$-0.0477740\pi$
$830$		−	17357.7i		−	0.725897i
$831$	−6996.30	−	10651.1i	−0.292057	−	0.444624i
$832$	−7838.63	+	4525.64i	−0.326629	+	0.188580i
$833$	−12043.0	+	2495.64i	−0.500918	+	0.103804i
$834$	−62827.7	+	3621.96i	−2.60857	+	0.150381i
$835$	−8201.22	−	14204.9i	−0.339898	−	0.588721i
$836$	9862.60	+	17082.5i	0.408021	+	0.706712i
$837$	17825.2	+	6523.74i	0.736116	+	0.269407i
$838$	44232.5	+	25537.6i	1.82337	+	1.05272i
$839$	−8987.71	+	15567.2i	−0.369833	+	0.640570i	−0.989539	−	0.144264i	$-0.953918\pi$
$839$	−8987.71	+	15567.2i	−0.369833	+	0.640570i	0.619706	+	0.784834i	$0.287252\pi$
$840$	−65819.0	−	25063.9i	−2.70354	−	1.02951i
$841$	16276.8	+	28192.2i	0.667381	+	1.15594i
$842$			44481.3i			1.82058i
$843$	−2487.74	−	43153.2i	−0.101640	−	1.76308i
$844$	−21828.9			−0.890262
$845$	11865.3	−	20551.3i	0.483051	−	0.836669i
$846$	787.540	−	584.853i	0.0320049	−	0.0237679i
$847$	29454.3	+	40758.7i	1.19488	+	1.65347i
$848$	5274.31	+	3045.13i	0.213586	+	0.123314i
$849$	2049.08	+	35544.0i	0.0828319	+	1.43683i
$850$	−3923.40	−	2265.18i	−0.158320	−	0.0914058i
$851$	−1428.87	−	824.956i	−0.0575569	−	0.0332305i
$852$	−4165.29	−	72252.6i	−0.167489	−	2.90532i
$853$	−21062.1	−	12160.2i	−0.845431	−	0.488110i	0.0136759	−	0.999906i	$-0.495647\pi$
$853$	−21062.1	−	12160.2i	−0.845431	−	0.488110i	−0.859106	+	0.511797i	$0.828980\pi$
$854$	−49686.9	+	5094.14i	−1.99093	+	0.204119i
$855$	−4222.13	+	3135.49i	−0.168882	+	0.125417i
$856$	−28987.9	+	50208.4i	−1.15746	+	2.00478i
$857$	−22896.8			−0.912648			−0.456324	−	0.889814i	$-0.650834\pi$
$857$	−22896.8			−0.912648			−0.456324	+	0.889814i	$0.650834\pi$
$858$	1587.21	+	27532.2i	0.0631543	+	1.09550i
$859$		−	8766.61i		−	0.348210i	−0.984727	−	0.174105i	$-0.944297\pi$
$859$		−	8766.61i		−	0.348210i	0.984727	−	0.174105i	$-0.0557033\pi$
$860$	−8995.03	−	15579.9i	−0.356661	−	0.617754i
$861$	−16057.3	+	2587.26i	−0.635578	+	0.102408i
$862$	−10835.2	+	18767.2i	−0.428132	+	0.741546i
$863$	6585.65	+	3802.22i	0.259766	+	0.149976i	0.624228	−	0.781242i	$-0.285414\pi$
$863$	6585.65	+	3802.22i	0.259766	+	0.149976i	−0.364462	+	0.931218i	$0.618747\pi$
$864$	−46167.8	−	16896.7i	−1.81790	−	0.665320i
$865$	−5754.73	−	9967.49i	−0.226204	−	0.391798i
$866$	−2633.47	−	4561.31i	−0.103336	−	0.178983i
$867$	18816.7	−	1084.77i	0.737082	−	0.0424921i
$868$	44451.2	+	19927.0i	1.73822	+	0.779225i
$869$	22578.1	−	13035.5i	0.881369	−	0.508859i
$870$	−43546.1	−	66294.2i	−1.69696	−	2.58343i
$871$			5350.63i			0.208151i
$872$	77833.6	−	44937.2i	3.02268	−	1.74514i
$873$	−10841.6	+	8051.29i	−0.420310	+	0.312136i
$874$		−	3813.22i		−	0.147579i
$875$	−13363.2	−	18492.0i	−0.516297	−	0.714449i
$876$	70724.7	−	46456.4i	2.72781	−	1.79180i
$877$	−37256.0			−1.43449			−0.717244	−	0.696822i	$-0.754597\pi$
$877$	−37256.0			−1.43449			−0.717244	+	0.696822i	$0.754597\pi$
$878$	21557.5	−	37338.7i	0.828623	−	1.43522i
$879$	1815.24	−	3609.11i	0.0696549	−	0.138490i
$880$	106571.	−	61528.9i	4.08240	−	2.35698i
$881$	1271.30			0.0486164			0.0243082	−	0.999705i	$-0.492262\pi$
$881$	1271.30			0.0486164			0.0243082	+	0.999705i	$0.492262\pi$
$882$	47506.0	+	9832.52i	1.81362	+	0.375372i
$883$	29075.5			1.10812			0.554060	−	0.832477i	$-0.313078\pi$
$883$	29075.5			1.10812			0.554060	+	0.832477i	$0.313078\pi$
$884$	9615.49	−	5551.50i	0.365841	−	0.211219i
$885$	7885.75	−	454.606i	0.299521	−	0.0172671i
$886$	3545.35	−	6140.73i	0.134434	−	0.232846i
$887$	28507.3			1.07912			0.539560	−	0.841947i	$-0.318590\pi$
$887$	28507.3			1.07912			0.539560	+	0.841947i	$0.318590\pi$
$888$	647.976	+	11240.0i	0.0244872	+	0.424764i
$889$	4382.84	+	6064.95i	0.165350	+	0.228810i
$890$			91793.3i			3.45721i
$891$	−33805.0	+	31742.3i	−1.27106	+	1.19350i
$892$	−74863.3	+	43222.4i	−2.81010	+	1.62241i
$893$		−	110.628i		−	0.00414559i
$894$	−23265.5	+	46257.1i	−0.870376	+	1.73050i
$895$	769.126	−	444.055i	0.0287252	−	0.0165845i
$896$	−2931.67	−	1314.24i	−0.109308	−	0.0490018i
$897$	1697.13	−	3374.28i	0.0631722	−	0.125601i
$898$	29708.2	+	51456.1i	1.10398	+	1.91215i
$899$	16142.6	+	27959.8i	0.598871	+	1.03728i
$900$	7548.16	+	10164.0i	0.279561	+	0.376446i
$901$	−1193.77	−	689.224i	−0.0441402	−	0.0254843i
$902$	28158.3	−	48771.7i	1.03943	−	1.80035i
$903$	4604.47	+	5655.07i	0.169687	+	0.208404i
$904$	−41619.0	−	72086.1i	−1.53122	−	2.65216i
$905$			22716.8i			0.834398i
$906$	37398.6	+	18810.0i	1.37140	+	0.689759i
$907$	26310.6			0.963208			0.481604	−	0.876389i	$-0.340054\pi$
$907$	26310.6			0.963208			0.481604	+	0.876389i	$0.340054\pi$
$908$	−459.150	+	795.271i	−0.0167813	+	0.0290661i
$909$	−19700.2	+	45521.9i	−0.718829	+	1.66102i
$910$	−18771.4	+	1924.53i	−0.683808	+	0.0701073i
$911$	−12914.3	−	7456.08i	−0.469671	−	0.271164i	0.246431	−	0.969160i	$-0.420742\pi$
$911$	−12914.3	−	7456.08i	−0.469671	−	0.271164i	−0.716102	+	0.697996i	$0.754075\pi$
$912$	−10974.5	+	7208.71i	−0.398466	+	0.261737i
$913$	−14948.0	−	8630.25i	−0.541848	−	0.312836i
$914$	−32969.8	−	19035.1i	−1.19315	−	0.688868i
$915$	29184.0	+	14678.4i	1.05442	+	0.530331i
$916$	−55613.3	−	32108.4i	−2.00602	−	1.15818i
$917$	−29659.7	−	41042.9i	−1.06810	−	1.47803i
$918$	24746.8	+	9056.94i	0.889724	+	0.325625i
$919$	17879.8	−	30968.8i	0.641786	−	1.11161i	−0.343248	−	0.939245i	$-0.611527\pi$
$919$	17879.8	−	30968.8i	0.641786	−	1.11161i	0.985034	−	0.172361i	$-0.0551396\pi$
$920$	−33399.7			−1.19691
$921$	23896.7	−	15696.8i	0.854964	−	0.561593i
$922$			65125.9i			2.32625i
$923$	−5705.57	−	9882.33i	−0.203468	−	0.352417i
$924$	−92285.3	+	75140.6i	−3.28568	+	2.67526i
$925$	435.992	−	755.160i	0.0154976	−	0.0268427i
$926$	−13106.2	−	7566.85i	−0.465114	−	0.268534i
$927$	16669.0	+	7213.74i	0.590595	+	0.255588i
$928$	−41809.8	−	72416.7i	−1.47896	−	2.56163i
$929$	17162.8	+	29726.8i	0.606127	+	1.04984i	0.991872	+	0.127238i	$0.0406111\pi$
$929$	17162.8	+	29726.8i	0.606127	+	1.04984i	−0.385745	+	0.922605i	$0.626056\pi$
$930$	−24689.7	−	37587.4i	−0.870546	−	1.32531i
$931$	4084.42	−	3640.06i	0.143782	−	0.128140i
$932$	−78131.3	+	45109.1i	−2.74600	+	1.58541i
$933$	−11140.2	+	642.223i	−0.390905	+	0.0225353i
$934$			13758.5i			0.482005i
$935$	−24121.0	+	13926.3i	−0.843680	+	0.487099i
$936$	−25603.0	+	2961.82i	−0.894081	+	0.103430i
$937$			14515.1i			0.506071i	0.967457	+	0.253036i	$0.0814289\pi$
$937$			14515.1i			0.506071i	−0.967457	+	0.253036i	$0.918571\pi$
$938$	−26415.5	+	19089.2i	−0.919505	+	0.664481i
$939$	9144.23	+	4599.19i	0.317796	+	0.159839i
$940$	−1646.53			−0.0571318
$941$	−11926.3	+	20656.9i	−0.413162	+	0.715617i	−0.995234	−	0.0975205i	$-0.968909\pi$
$941$	−11926.3	+	20656.9i	−0.413162	+	0.715617i	0.582072	+	0.813137i	$0.302242\pi$
$942$	43487.9	+	66205.5i	1.50415	+	2.28991i
$943$	−6679.69	+	3856.52i	−0.230669	+	0.133177i
$944$	19721.0			0.679942
$945$	−22728.5	−	22139.6i	−0.782389	−	0.762117i
$946$	−25250.9			−0.867839
$947$	36030.5	−	20802.2i	1.23636	−	0.713814i	0.268014	−	0.963415i	$-0.413633\pi$
$947$	36030.5	−	20802.2i	1.23636	−	0.713814i	0.968349	+	0.249601i	$0.0802994\pi$
$948$	22730.6	+	34604.9i	0.778752	+	1.18556i
$949$	6670.94	−	11554.4i	0.228185	−	0.395228i
$950$	2015.30			0.0688262
$951$	6735.76	+	3387.82i	0.229676	+	0.115518i
$952$	36317.2	+	16280.6i	1.23639	+	0.554263i
$953$		−	21486.0i		−	0.730326i	−0.930944	−	0.365163i	$-0.881013\pi$
$953$		−	21486.0i		−	0.730326i	0.930944	−	0.365163i	$-0.118987\pi$
$954$	3241.76	+	4365.23i	0.110017	+	0.148144i
$955$	−43.1654	+	24.9216i	−0.00146262	+	0.000844443i
$956$		−	85332.1i		−	2.88686i
$957$	−78742.1	+	4539.41i	−2.65974	+	0.153332i
$958$	−3455.36	+	1994.95i	−0.116532	+	0.0672797i
$959$	12879.2	−	9307.14i	0.433670	−	0.313392i
$960$	19796.5	+	30138.0i	0.665551	+	1.01323i
$961$	−5743.01	−	9947.18i	−0.192777	−	0.333899i
$962$	1508.23	+	2612.34i	0.0505482	+	0.0875521i
$963$	−20968.8	+	15572.1i	−0.701672	+	0.521085i
$964$	18710.6	+	10802.6i	0.625133	+	0.360921i
$965$	−26882.7	+	46562.3i	−0.896773	+	1.55326i
$966$	22713.2	−	3659.69i	0.756506	−	0.121893i
$967$	−8872.69	−	15367.9i	−0.295064	−	0.511065i	0.679936	−	0.733271i	$-0.262007\pi$
$967$	−8872.69	−	15367.9i	−0.295064	−	0.511065i	−0.975000	+	0.222206i	$0.928674\pi$
$968$		−	162732.i		−	5.40331i
$969$	2483.93	−	1631.60i	0.0823480	−	0.0540913i
$970$	31994.1			1.05904
$971$	17856.1	−	30927.8i	0.590145	−	1.02216i	−0.404067	−	0.914729i	$-0.632404\pi$
$971$	17856.1	−	30927.8i	0.590145	−	1.02216i	0.994212	−	0.107432i	$-0.0342629\pi$
$972$	−53415.4	−	50694.7i	−1.76265	−	1.67287i
$973$	−39072.6	−	17515.9i	−1.28737	−	0.577115i
$974$	78733.2	+	45456.6i	2.59012	+	1.49541i
$975$	1783.31	+	896.937i	0.0585762	+	0.0294615i
$976$	70633.6	+	40780.4i	2.31652	+	1.33745i
$977$	−35362.2	−	20416.4i	−1.15797	−	0.668555i	−0.207155	−	0.978308i	$-0.566420\pi$
$977$	−35362.2	−	20416.4i	−1.15797	−	0.668555i	−0.950817	+	0.309753i	$0.899754\pi$
$978$	51582.2	−	33882.4i	1.68652	−	1.10781i
$979$	79050.2	+	45639.7i	2.58065	+	1.48994i
$980$	−54176.9	−	60790.6i	−1.76594	−	1.98152i
$981$	40221.0	−	4652.87i	1.30903	−	0.151432i
$982$	−52294.3	+	90576.4i	−1.69937	+	2.94339i
$983$	−29591.4			−0.960141			−0.480070	−	0.877230i	$-0.659389\pi$
$983$	−29591.4			−0.960141			−0.480070	+	0.877230i	$0.659389\pi$
$984$	47019.9	+	23649.2i	1.52331	+	0.766167i
$985$		−	4761.34i		−	0.154019i
$986$	22410.8	+	38816.7i	0.723840	+	1.25373i
$987$	658.945	−	106.173i	0.0212507	−	0.00342405i
$988$	−2469.55	+	4277.38i	−0.0795211	+	0.137735i
$989$	2994.99	+	1729.16i	0.0962944	+	0.0555956i
$990$	109137.	−	12625.2i	3.50363	−	0.405308i
$991$	−21470.6	−	37188.1i	−0.688230	−	1.19205i	−0.972410	−	0.233278i	$-0.925055\pi$
$991$	−21470.6	−	37188.1i	−0.688230	−	1.19205i	0.284181	−	0.958771i	$-0.408278\pi$
$992$	−23705.2	−	41058.7i	−0.758712	−	1.31413i
$993$	−2775.70	+	5518.72i	−0.0887052	+	0.176366i
$994$	28432.5	−	63424.4i	0.907269	−	2.02384i
$995$	−11144.7	+	6434.37i	−0.355085	+	0.205008i
$996$	12316.5	−	24488.1i	0.391832	−	0.779050i
$997$			43491.5i			1.38153i	0.723077	+	0.690767i	$0.242727\pi$
$997$			43491.5i			1.38153i	−0.723077	+	0.690767i	$0.757273\pi$
$998$	6993.64	−	4037.78i	0.221823	−	0.128070i
$999$	−1743.24	+	4763.16i	−0.0552089	+	0.150851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.47.1	yes	44
3.2	odd	2		189.4.s.a.89.22		44
7.3	odd	6		63.4.i.a.38.1	yes	44
9.4	even	3		189.4.i.a.152.1		44
9.5	odd	6		63.4.i.a.5.22	✓	44
21.17	even	6		189.4.i.a.143.22		44
63.31	odd	6		189.4.s.a.17.22		44
63.59	even	6	inner	63.4.s.a.59.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.22	✓	44	9.5	odd	6
63.4.i.a.38.1	yes	44	7.3	odd	6
63.4.s.a.47.1	yes	44	1.1	even	1	trivial
63.4.s.a.59.1	yes	44	63.59	even	6	inner
189.4.i.a.143.22		44	21.17	even	6
189.4.i.a.152.1		44	9.4	even	3
189.4.s.a.17.22		44	63.31	odd	6
189.4.s.a.89.22		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)

\(f(q)\)	\(=\)	\(q+(-4.53659 + 2.61920i) q^{2} +(2.85276 + 4.34301i) q^{3} +(9.72046 - 16.8363i) q^{4} -12.2114 q^{5} +(-24.3171 - 12.2305i) q^{6} +(-10.8477 - 15.0109i) q^{7} +59.9322i q^{8} +(-10.7235 + 24.7791i) q^{9} +O(q^{10})\)	\(q+(-4.53659 + 2.61920i) q^{2} +(2.85276 + 4.34301i) q^{3} +(9.72046 - 16.8363i) q^{4} -12.2114 q^{5} +(-24.3171 - 12.2305i) q^{6} +(-10.8477 - 15.0109i) q^{7} +59.9322i q^{8} +(-10.7235 + 24.7791i) q^{9} +(55.3983 - 31.9842i) q^{10} -63.6103i q^{11} +(100.851 - 5.81394i) q^{12} +(13.7938 - 7.96386i) q^{13} +(88.5281 + 39.6863i) q^{14} +(-34.8363 - 53.0344i) q^{15} +(-79.2109 - 137.197i) q^{16} +(17.9283 + 31.0528i) q^{17} +(-16.2534 - 140.500i) q^{18} +(-13.8136 - 7.97531i) q^{19} +(-118.701 + 205.596i) q^{20} +(34.2469 - 89.9341i) q^{21} +(166.608 + 288.574i) q^{22} -45.6368i q^{23} +(-260.286 + 170.972i) q^{24} +24.1192 q^{25} +(-41.7179 + 72.2576i) q^{26} +(-138.208 + 24.1166i) q^{27} +(-358.173 + 36.7217i) q^{28} +(-206.656 - 119.313i) q^{29} +(296.946 + 149.352i) q^{30} +(-117.170 - 67.6480i) q^{31} +(303.473 + 175.210i) q^{32} +(276.260 - 181.465i) q^{33} +(-162.667 - 93.9160i) q^{34} +(132.466 + 183.305i) q^{35} +(312.952 + 421.409i) q^{36} +(18.0766 - 31.3095i) q^{37} +83.5558 q^{38} +(73.9376 + 37.1877i) q^{39} -731.858i q^{40} +(-84.5046 - 146.366i) q^{41} +(80.1916 + 497.694i) q^{42} +(-37.8895 + 65.6266i) q^{43} +(-1070.96 - 618.321i) q^{44} +(130.950 - 302.589i) q^{45} +(119.532 + 207.036i) q^{46} +(3.46782 + 6.00643i) q^{47} +(369.880 - 735.405i) q^{48} +(-107.656 + 325.667i) q^{49} +(-109.419 + 63.1731i) q^{50} +(-83.7175 + 166.449i) q^{51} -309.649i q^{52} +(-33.2929 + 19.2216i) q^{53} +(563.826 - 471.402i) q^{54} +776.773i q^{55} +(899.638 - 650.124i) q^{56} +(-4.77014 - 82.7444i) q^{57} +1250.02 q^{58} +(-62.2422 + 107.807i) q^{59} +(-1231.53 + 70.9965i) q^{60} +(-445.858 + 257.416i) q^{61} +708.735 q^{62} +(488.283 - 107.826i) q^{63} -568.272 q^{64} +(-168.442 + 97.2502i) q^{65} +(-777.987 + 1546.81i) q^{66} +(-167.966 + 290.926i) q^{67} +697.087 q^{68} +(198.201 - 130.191i) q^{69} +(-1081.06 - 484.626i) q^{70} -716.432i q^{71} +(-1485.07 - 642.684i) q^{72} +(725.427 - 418.826i) q^{73} +189.385i q^{74} +(68.8063 + 104.750i) q^{75} +(-268.550 + 155.047i) q^{76} +(-954.850 + 690.023i) q^{77} +(-432.827 + 24.9521i) q^{78} +(204.927 + 354.944i) q^{79} +(967.279 + 1675.38i) q^{80} +(-499.012 - 531.439i) q^{81} +(766.726 + 442.670i) q^{82} +(135.674 - 234.994i) q^{83} +(-1181.27 - 1450.79i) q^{84} +(-218.931 - 379.199i) q^{85} -396.962i q^{86} +(-71.3628 - 1237.88i) q^{87} +3812.30 q^{88} +(-717.489 + 1242.73i) q^{89} +(198.477 + 1715.71i) q^{90} +(-269.176 - 120.669i) q^{91} +(-768.356 - 443.611i) q^{92} +(-40.4612 - 701.853i) q^{93} +(-31.4641 - 18.1658i) q^{94} +(168.684 + 97.3899i) q^{95} +(104.796 + 1817.82i) q^{96} +(433.147 + 250.077i) q^{97} +(-364.596 - 1759.39i) q^{98} +(1576.21 + 682.126i) 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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