LMFDB - Embedded newform 63.4.s.a.59.5

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			59.5
Character	$\chi$	$=$	63.59
Dual form			63.4.s.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.16085 - 1.82492i) q^{2} +(-3.78544 - 3.55956i) q^{3} +(2.66064 + 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 + 18.1593i) q^{6} +(4.78838 - 17.8905i) q^{7} +9.77690i q^{8} +(1.65907 + 26.9490i) q^{9} +O(q^{10})$	\(q+(-3.16085 - 1.82492i) q^{2} +(-3.78544 - 3.55956i) q^{3} +(2.66064 + 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 + 18.1593i) q^{6} +(4.78838 - 17.8905i) q^{7} +9.77690i q^{8} +(1.65907 + 26.9490i) q^{9} +(38.6615 + 22.3212i) q^{10} -10.0114i q^{11} +(6.33205 - 26.9153i) q^{12} +(57.0263 + 32.9241i) q^{13} +(-47.7841 + 47.8109i) q^{14} +(46.3010 + 43.5383i) q^{15} +(39.1271 - 67.7702i) q^{16} +(-38.6818 + 66.9989i) q^{17} +(43.9356 - 88.2093i) q^{18} +(-104.262 + 60.1959i) q^{19} +(-32.5432 - 56.3665i) q^{20} +(-81.8086 + 50.6790i) q^{21} +(-18.2699 + 31.6444i) q^{22} -122.606i q^{23} +(34.8015 - 37.0098i) q^{24} +24.6062 q^{25} +(-120.168 - 208.136i) q^{26} +(89.6462 - 107.919i) q^{27} +(95.1861 - 25.5337i) q^{28} +(-50.3417 + 29.0648i) q^{29} +(-66.8969 - 222.113i) q^{30} +(-174.476 + 100.734i) q^{31} +(-179.613 + 103.700i) q^{32} +(-35.6361 + 37.8974i) q^{33} +(244.535 - 141.182i) q^{34} +(-58.5684 + 218.826i) q^{35} +(-119.776 + 79.3470i) q^{36} +(82.9121 + 143.608i) q^{37} +439.410 q^{38} +(-98.6739 - 327.621i) q^{39} -119.585i q^{40} +(-112.422 + 194.721i) q^{41} +(351.069 - 10.8948i) q^{42} +(152.402 + 263.969i) q^{43} +(46.1360 - 26.6366i) q^{44} +(-20.2926 - 329.623i) q^{45} +(-223.746 + 387.539i) q^{46} +(11.2933 - 19.5606i) q^{47} +(-389.345 + 117.264i) q^{48} +(-297.143 - 171.333i) q^{49} +(-77.7763 - 44.9042i) q^{50} +(384.914 - 115.930i) q^{51} +350.397i q^{52} +(360.132 + 207.922i) q^{53} +(-480.301 + 177.519i) q^{54} +122.453i q^{55} +(174.914 + 46.8155i) q^{56} +(608.949 + 143.260i) q^{57} +212.163 q^{58} +(180.334 + 312.348i) q^{59} +(-77.4496 + 329.211i) q^{60} +(-635.689 - 367.015i) q^{61} +735.324 q^{62} +(490.076 + 99.3604i) q^{63} +130.940 q^{64} +(-697.509 - 402.707i) q^{65} +(181.800 - 54.7551i) q^{66} +(55.6457 + 96.3811i) q^{67} -411.673 q^{68} +(-436.423 + 464.117i) q^{69} +(584.464 - 584.792i) q^{70} -455.487i q^{71} +(-263.478 + 16.2205i) q^{72} +(-662.747 - 382.637i) q^{73} -605.230i q^{74} +(-93.1451 - 87.5871i) q^{75} +(-554.808 - 320.319i) q^{76} +(-179.109 - 47.9383i) q^{77} +(-285.987 + 1215.63i) q^{78} +(21.5683 - 37.3573i) q^{79} +(-478.578 + 828.921i) q^{80} +(-723.495 + 89.4203i) q^{81} +(710.697 - 410.321i) q^{82} +(-200.064 - 346.522i) q^{83} +(-451.210 - 242.165i) q^{84} +(473.131 - 819.488i) q^{85} -1112.49i q^{86} +(294.023 + 69.1714i) q^{87} +97.8802 q^{88} +(347.632 + 602.117i) q^{89} +(-537.392 + 1078.92i) q^{90} +(862.094 - 862.577i) q^{91} +(565.012 - 326.210i) q^{92} +(1019.04 + 239.737i) q^{93} +(-71.3928 + 41.2186i) q^{94} +(1275.27 - 736.277i) q^{95} +(1049.04 + 246.795i) q^{96} +(-955.178 + 551.472i) q^{97} +(626.554 + 1083.82i) q^{98} +(269.796 - 16.6095i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−3.16085	−	1.82492i	−1.11753	−	0.645205i	−0.176759	−	0.984254i	$-0.556561\pi$
$2$	−3.16085	−	1.82492i	−1.11753	−	0.645205i	−0.940769	+	0.339049i	$0.889895\pi$
$3$	−3.78544	−	3.55956i	−0.728508	−	0.685038i
$3$	−3.78544	−	3.55956i	−0.728508	−	0.685038i
$4$	2.66064	+	4.60836i	0.332580	+	0.576045i
$5$	−12.2314			−1.09401			−0.547003	−	0.837131i	$-0.684231\pi$
$5$	−12.2314			−1.09401			−0.547003	+	0.837131i	$0.684231\pi$
$6$	5.46929	+	18.1593i	0.372138	+	1.23559i
$7$	4.78838	−	17.8905i	0.258548	−	0.965998i
$7$	4.78838	−	17.8905i	0.258548	−	0.965998i
$8$			9.77690i			0.432082i
$9$	1.65907	+	26.9490i	0.0614469	+	0.998110i
$10$	38.6615	+	22.3212i	1.22258	+	0.705858i
$11$		−	10.0114i		−	0.274413i	−0.990542	−	0.137206i	$-0.956188\pi$
$11$		−	10.0114i		−	0.274413i	0.990542	−	0.137206i	$-0.0438124\pi$
$12$	6.33205	−	26.9153i	0.152326	−	0.647483i
$13$	57.0263	+	32.9241i	1.21663	+	0.702424i	0.964196	−	0.265189i	$-0.0854345\pi$
$13$	57.0263	+	32.9241i	1.21663	+	0.702424i	0.252437	+	0.967613i	$0.418768\pi$
$14$	−47.7841	+	47.8109i	−0.912202	+	0.912714i
$15$	46.3010	+	43.5383i	0.796992	+	0.749435i
$16$	39.1271	−	67.7702i	0.611361	−	1.05891i
$17$	−38.6818	+	66.9989i	−0.551866	+	0.955860i	0.446274	+	0.894896i	$0.352751\pi$
$17$	−38.6818	+	66.9989i	−0.551866	+	0.955860i	−0.998140	+	0.0609637i	$0.980583\pi$
$18$	43.9356	−	88.2093i	0.575317	−	1.15506i
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.972864	−	0.231378i	$-0.925677\pi$
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.286053	+	0.958214i	$0.592343\pi$
$20$	−32.5432	−	56.3665i	−0.363844	−	0.630196i
$21$	−81.8086	+	50.6790i	−0.850100	+	0.526622i
$22$	−18.2699	+	31.6444i	−0.177053	+	0.306664i
$23$		−	122.606i		−	1.11153i	−0.831341	−	0.555763i	$-0.812426\pi$
$23$		−	122.606i		−	1.11153i	0.831341	−	0.555763i	$-0.187574\pi$
$24$	34.8015	−	37.0098i	0.295993	−	0.314775i
$25$	24.6062			0.196849
$26$	−120.168	−	208.136i	−0.906415	−	1.56996i
$27$	89.6462	−	107.919i	0.638979	−	0.769225i
$28$	95.1861	−	25.5337i	0.642446	−	0.172336i
$29$	−50.3417	+	29.0648i	−0.322352	+	0.186110i	−0.652441	−	0.757840i	$-0.726255\pi$
$29$	−50.3417	+	29.0648i	−0.322352	+	0.186110i	0.330088	+	0.943950i	$0.392922\pi$
$30$	−66.8969	−	222.113i	−0.407121	−	1.35174i
$31$	−174.476	+	100.734i	−1.01087	+	0.583624i	−0.911445	−	0.411421i	$-0.865033\pi$
$31$	−174.476	+	100.734i	−1.01087	+	0.583624i	−0.0994218	+	0.995045i	$0.531699\pi$
$32$	−179.613	+	103.700i	−0.992233	+	0.572866i
$33$	−35.6361	+	37.8974i	−0.187983	+	0.199912i
$34$	244.535	−	141.182i	1.23345	−	0.712134i
$35$	−58.5684	+	218.826i	−0.282853	+	1.05681i
$36$	−119.776	+	79.3470i	−0.554520	+	0.367347i
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	0.989315	−	0.145794i	$-0.0465737\pi$
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	−0.620919	+	0.783875i	$0.713240\pi$
$38$	439.410			1.87583
$39$	−98.6739	−	327.621i	−0.405140	−	1.34516i
$40$		−	119.585i		−	0.472700i
$41$	−112.422	+	194.721i	−0.428228	+	0.741713i	−0.996716	−	0.0809786i	$-0.974195\pi$
$41$	−112.422	+	194.721i	−0.428228	+	0.741713i	0.568487	+	0.822692i	$0.307529\pi$
$42$	351.069	−	10.8948i	1.28979	−	0.0400262i
$43$	152.402	+	263.969i	0.540492	+	0.936159i	0.998876	+	0.0474048i	$0.0150951\pi$
$43$	152.402	+	263.969i	0.540492	+	0.936159i	−0.458384	+	0.888754i	$0.651572\pi$
$44$	46.1360	−	26.6366i	0.158074	−	0.0912641i
$45$	−20.2926	−	329.623i	−0.0672233	−	1.09194i
$46$	−223.746	+	387.539i	−0.717163	+	1.24216i
$47$	11.2933	−	19.5606i	0.0350489	−	0.0607064i	−0.847969	−	0.530046i	$-0.822175\pi$
$47$	11.2933	−	19.5606i	0.0350489	−	0.0607064i	0.883018	+	0.469340i	$0.155508\pi$
$48$	−389.345	+	117.264i	−1.17077	+	0.352618i
$49$	−297.143	−	171.333i	−0.866306	−	0.499514i
$50$	−77.7763	−	44.9042i	−0.219985	−	0.127008i
$51$	384.914	−	115.930i	1.05684	−	0.318302i
$52$			350.397i			0.934447i
$53$	360.132	+	207.922i	0.933358	+	0.538875i	0.887872	−	0.460090i	$-0.152183\pi$
$53$	360.132	+	207.922i	0.933358	+	0.538875i	0.0454860	+	0.998965i	$0.485516\pi$
$54$	−480.301	+	177.519i	−1.21038	+	0.447358i
$55$			122.453i			0.300209i
$56$	174.914	+	46.8155i	0.417391	+	0.111714i
$57$	608.949	+	143.260i	1.41504	+	0.332900i
$58$	212.163			0.480317
$59$	180.334	+	312.348i	0.397924	+	0.689225i	0.993470	−	0.114096i	$-0.0363973\pi$
$59$	180.334	+	312.348i	0.397924	+	0.689225i	−0.595545	+	0.803322i	$0.703064\pi$
$60$	−77.4496	+	329.211i	−0.166645	+	0.708350i
$61$	−635.689	−	367.015i	−1.33429	−	0.770353i	−0.348336	−	0.937370i	$-0.613253\pi$
$61$	−635.689	−	367.015i	−1.33429	−	0.770353i	−0.985954	+	0.167017i	$0.946586\pi$
$62$	735.324			1.50623
$63$	490.076	+	99.3604i	0.980060	+	0.198702i
$64$	130.940			0.255742
$65$	−697.509	−	402.707i	−1.33100	−	0.768456i
$66$	181.800	−	54.7551i	0.339061	−	0.102120i
$67$	55.6457	+	96.3811i	0.101466	+	0.175744i	0.912289	−	0.409548i	$-0.134313\pi$
$67$	55.6457	+	96.3811i	0.101466	+	0.175744i	−0.810823	+	0.585291i	$0.800980\pi$
$68$	−411.673			−0.734158
$69$	−436.423	+	464.117i	−0.761437	+	0.809755i
$70$	584.464	−	584.792i	0.997955	−	0.998514i
$71$		−	455.487i		−	0.761358i	−0.924707	−	0.380679i	$-0.875690\pi$
$71$		−	455.487i		−	0.761358i	0.924707	−	0.380679i	$-0.124310\pi$
$72$	−263.478	+	16.2205i	−0.431266	+	0.0265501i
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.136438	−	0.990649i	$-0.543565\pi$
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.926146	+	0.377166i	$0.876899\pi$
$74$		−	605.230i		−	0.950765i
$75$	−93.1451	−	87.5871i	−0.143406	−	0.134849i
$76$	−554.808	−	320.319i	−0.837380	−	0.483462i
$77$	−179.109	−	47.9383i	−0.265082	−	0.0709490i
$78$	−285.987	+	1215.63i	−0.415149	+	1.76465i
$79$	21.5683	−	37.3573i	0.0307167	−	0.0532029i	−0.850258	−	0.526366i	$-0.823554\pi$
$79$	21.5683	−	37.3573i	0.0307167	−	0.0532029i	0.880975	+	0.473163i	$0.156888\pi$
$80$	−478.578	+	828.921i	−0.668833	+	1.15845i
$81$	−723.495	+	89.4203i	−0.992449	+	0.122662i
$82$	710.697	−	410.321i	0.957115	−	0.552590i
$83$	−200.064	−	346.522i	−0.264577	−	0.458262i	0.702875	−	0.711313i	$-0.251899\pi$
$83$	−200.064	−	346.522i	−0.264577	−	0.458262i	−0.967453	+	0.253051i	$0.918566\pi$
$84$	−451.210	−	242.165i	−0.586084	−	0.314552i
$85$	473.131	−	819.488i	0.603745	−	1.04572i
$86$		−	1112.49i		−	1.39491i
$87$	294.023	+	69.1714i	0.362329	+	0.0852408i
$88$	97.8802			0.118569
$89$	347.632	+	602.117i	0.414033	+	0.717127i	0.995326	−	0.0965674i	$-0.0307863\pi$
$89$	347.632	+	602.117i	0.414033	+	0.717127i	−0.581293	+	0.813694i	$0.697453\pi$
$90$	−537.392	+	1078.92i	−0.629401	+	1.26365i
$91$	862.094	−	862.577i	0.993099	−	0.993656i
$92$	565.012	−	326.210i	0.640289	−	0.369671i
$93$	1019.04	+	239.737i	1.13623	+	0.267307i
$94$	−71.3928	+	41.2186i	−0.0783362	+	0.0452274i
$95$	1275.27	−	736.277i	1.37726	−	0.795163i
$96$	1049.04	+	246.795i	1.11528	+	0.262380i
$97$	−955.178	+	551.472i	−0.999831	+	0.577253i	−0.908198	−	0.418540i	$-0.862542\pi$
$97$	−955.178	+	551.472i	−0.999831	+	0.577253i	−0.0916328	+	0.995793i	$0.529209\pi$
$98$	626.554	+	1083.82i	0.645832	+	1.11717i
$99$	269.796	−	16.6095i	0.273894	−	0.0168618i
$100$	65.4681	+	113.394i	0.0654681	+	0.113394i
$101$	−704.387			−0.693951			−0.346976	−	0.937874i	$-0.612791\pi$
$101$	−704.387			−0.693951			−0.346976	+	0.937874i	$0.612791\pi$
$102$	−1428.22	−	336.000i	−1.38642	−	0.326166i
$103$			1038.72i			0.993672i	0.867845	+	0.496836i	$0.165505\pi$
$103$			1038.72i			0.993672i	−0.867845	+	0.496836i	$0.834495\pi$
$104$	−321.896	+	557.540i	−0.303505	+	0.525686i
$105$	1000.63	−	619.873i	0.930014	−	0.576128i
$106$	−758.882	−	1314.42i	−0.695369	−	1.20442i
$107$	50.4942	−	29.1528i	0.0456211	−	0.0263394i	−0.477016	−	0.878895i	$-0.658282\pi$
$107$	50.4942	−	29.1528i	0.0456211	−	0.0263394i	0.522637	+	0.852555i	$0.324948\pi$
$108$	735.846	+	125.988i	0.655619	+	0.112252i
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	−0.992551	−	0.121827i	$-0.961125\pi$
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	0.601781	+	0.798661i	$0.294458\pi$
$110$	223.466	−	387.054i	0.193697	−	0.335493i
$111$	197.323	−	838.749i	0.168730	−	0.717212i
$112$	−1025.09	−	1024.51i	−0.864838	−	0.864353i
$113$	−2032.03	−	1173.20i	−1.69166	−	0.976681i	−0.953179	−	0.302407i	$-0.902210\pi$
$113$	−2032.03	−	1173.20i	−1.69166	−	0.976681i	−0.738481	−	0.674274i	$-0.764457\pi$
$114$	−1663.36	−	1564.11i	−1.36656	−	1.28502i
$115$			1499.64i			1.21602i
$116$	−267.882	−	154.662i	−0.214416	−	0.123793i
$117$	−792.661	+	1591.42i	−0.626338	+	1.25750i
$118$		−	1316.38i		−	1.02697i
$119$	1013.42	+	1012.86i	0.780675	+	0.780238i
$120$	−425.669	+	452.681i	−0.323818	+	0.344366i
$121$	1230.77			0.924698
$122$	1339.54	+	2320.16i	0.994071	+	1.72178i
$123$	1118.69	−	336.930i	0.820069	−	0.246991i
$124$	−928.437	−	536.033i	−0.672388	−	0.388203i
$125$	1227.95			0.878652
$126$	−1367.73	−	1208.41i	−0.967041	−	0.854395i
$127$	−1026.54			−0.717251			−0.358625	−	0.933482i	$-0.616754\pi$
$127$	−1026.54			−0.717251			−0.358625	+	0.933482i	$0.616754\pi$
$128$	1023.03	+	590.644i	0.706434	+	0.407860i
$129$	362.703	−	1541.72i	0.247552	−	1.05226i
$130$	1469.81	+	2545.79i	0.991624	+	1.71754i
$131$	−1431.15			−0.954506			−0.477253	−	0.878766i	$-0.658368\pi$
$131$	−1431.15			−0.954506			−0.477253	+	0.878766i	$0.658368\pi$
$132$	−269.460	−	63.3925i	−0.177678	−	0.0418001i
$133$	577.689	+	2153.55i	0.376632	+	1.40403i
$134$		−	406.195i		−	0.261865i
$135$	−1096.50	+	1320.00i	−0.699046	+	0.841536i
$136$	−655.042	−	378.189i	−0.413010	−	0.238451i
$137$		−	2527.45i		−	1.57616i	−0.615571	−	0.788081i	$-0.711075\pi$
$137$		−	2527.45i		−	1.57616i	0.615571	−	0.788081i	$-0.288925\pi$
$138$	2226.44	−	670.567i	1.37339	−	0.413641i
$139$	−247.028	−	142.622i	−0.150739	−	0.0870290i	0.422734	−	0.906254i	$-0.361071\pi$
$139$	−247.028	−	142.622i	−0.150739	−	0.0870290i	−0.573472	+	0.819225i	$0.694404\pi$
$140$	−1164.26	+	312.311i	−0.702840	+	0.188537i
$141$	−112.377	+	33.8461i	−0.0671195	+	0.0202153i
$142$	−831.226	+	1439.73i	−0.491232	+	0.850839i
$143$	329.616	−	570.911i	0.192754	−	0.333860i
$144$	1891.25	+	942.001i	1.09447	+	0.545139i
$145$	615.748	−	355.502i	0.352656	−	0.203606i
$146$	1396.56	+	2418.91i	0.791645	+	1.37117i
$147$	514.944	+	1706.27i	0.288924	+	0.957352i
$148$	−441.198	+	764.177i	−0.245042	+	0.424425i
$149$			1884.28i			1.03601i	0.855376	+	0.518007i	$0.173326\pi$
$149$			1884.28i			1.03601i	−0.855376	+	0.518007i	$0.826674\pi$
$150$	134.578	+	446.831i	0.0732551	+	0.243224i
$151$	−400.447			−0.215814			−0.107907	−	0.994161i	$-0.534415\pi$
$151$	−400.447			−0.215814			−0.107907	+	0.994161i	$0.534415\pi$
$152$	−588.529	−	1019.36i	−0.314053	−	0.543955i
$153$	−1869.73	−	931.280i	−0.987964	−	0.492089i
$154$	478.652	+	478.384i	0.250460	+	0.250320i
$155$	2134.08	−	1232.11i	1.10589	−	0.638489i
$156$	1247.26	−	1326.40i	0.640132	−	0.680752i
$157$	1698.99	−	980.915i	0.863659	−	0.498634i	−0.00157672	−	0.999999i	$-0.500502\pi$
$157$	1698.99	−	980.915i	0.863659	−	0.498634i	0.865236	+	0.501365i	$0.167169\pi$
$158$	−136.348	+	78.7205i	−0.0686536	+	0.0396372i
$159$	−623.146	−	2068.99i	−0.310809	−	1.03196i
$160$	2196.92	−	1268.39i	1.08551	−	0.626719i
$161$	−2193.49	−	587.084i	−1.07373	−	0.287383i
$162$	2450.04	+	1037.67i	1.18823	+	0.503255i
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	0.999575	+	0.0291623i	$0.00928395\pi$
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	−0.474532	+	0.880238i	$0.657383\pi$
$164$	−1196.46			−0.569680
$165$	435.878	−	463.537i	0.205655	−	0.218705i
$166$			1460.40i			0.682827i
$167$	724.771	−	1255.34i	0.335835	−	0.581683i	−0.647810	−	0.761802i	$-0.724315\pi$
$167$	724.771	−	1255.34i	0.335835	−	0.581683i	0.983645	+	0.180119i	$0.0576482\pi$
$168$	−495.483	−	799.834i	−0.227544	−	0.367313i
$169$	1069.50	+	1852.42i	0.486798	+	0.843160i
$170$	−2990.99	+	1726.85i	−1.34940	+	0.779079i
$171$	−1795.20	−	2709.89i	−0.802819	−	1.21188i
$172$	−810.975	+	1404.65i	−0.359513	+	0.622695i
$173$	−922.964	+	1598.62i	−0.405617	+	0.702549i	−0.994393	−	0.105747i	$-0.966277\pi$
$173$	−922.964	+	1598.62i	−0.405617	+	0.702549i	0.588776	+	0.808296i	$0.299610\pi$
$174$	−803.131	−	755.208i	−0.349915	−	0.329035i
$175$	117.824	−	440.218i	0.0508951	−	0.190156i
$176$	−678.472	−	391.716i	−0.290578	−	0.167765i
$177$	429.178	−	1824.29i	0.182254	−	0.774699i
$178$		−	2537.60i		−	1.06855i
$179$	389.538	+	224.900i	0.162656	+	0.0939096i	0.579118	−	0.815243i	$-0.303397\pi$
$179$	389.538	+	224.900i	0.162656	+	0.0939096i	−0.416462	+	0.909153i	$0.636730\pi$
$180$	1465.03	−	970.522i	0.606648	−	0.401880i
$181$		−	3067.12i		−	1.25954i	−0.776781	−	0.629771i	$-0.783149\pi$
$181$		−	3067.12i		−	1.25954i	0.776781	−	0.629771i	$-0.216851\pi$
$182$	−4299.08	+	1153.23i	−1.75093	+	0.469686i
$183$	1099.95	+	3652.09i	0.444320	+	1.47525i
$184$	1198.71			0.480271
$185$	−1014.13	−	1756.52i	−0.403028	−	0.698064i
$186$	−2783.52	−	2617.43i	−1.09730	−	1.03182i
$187$	670.751	+	387.258i	0.262300	+	0.151439i
$188$	120.189			0.0466261
$189$	−1501.47	−	2120.58i	−0.577863	−	0.816134i
$190$	−5374.58			−2.05217
$191$	−4503.79	−	2600.27i	−1.70619	−	0.985071i	−0.939170	−	0.343452i	$-0.888404\pi$
$191$	−4503.79	−	2600.27i	−1.70619	−	0.985071i	−0.767023	−	0.641619i	$-0.778263\pi$
$192$	−495.664	−	466.088i	−0.186310	−	0.175193i
$193$	−1188.11	−	2057.87i	−0.443119	−	0.767505i	0.554800	−	0.831984i	$-0.312795\pi$
$193$	−1188.11	−	2057.87i	−0.443119	−	0.767505i	−0.997919	+	0.0644786i	$0.979462\pi$
$194$	4025.56			1.48979
$195$	1206.92	+	4007.25i	0.443226	+	1.47161i
$196$	−1.02330	−	1825.20i	−0.000372923	−	0.665159i
$197$		−	148.115i		−	0.0535672i	−0.999641	−	0.0267836i	$-0.991473\pi$
$197$		−	148.115i		−	0.0535672i	0.999641	−	0.0267836i	$-0.00852651\pi$
$198$	−883.096	−	439.855i	−0.316964	−	0.157875i
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	0.212803	−	0.977095i	$-0.431741\pi$
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	−0.739788	+	0.672840i	$0.765074\pi$
$200$			240.572i			0.0850551i
$201$	132.431	−	562.919i	0.0464725	−	0.197538i
$202$	2226.46	+	1285.45i	0.775510	+	0.447741i
$203$	278.930	+	1039.81i	0.0964386	+	0.359510i
$204$	1558.36	+	1465.38i	0.534839	+	0.502926i
$205$	1375.07	−	2381.70i	0.468484	−	0.811439i
$206$	1895.58	−	3283.24i	0.641122	−	1.11046i
$207$	3304.10	−	203.411i	1.10943	−	0.0682999i
$208$	4462.55	−	2576.45i	1.48761	−	0.858869i
$209$	602.643	+	1043.81i	0.199453	+	0.345463i
$210$	−4294.05	+	133.258i	−1.41104	+	0.0437889i
$211$	545.976	−	945.659i	0.178135	−	0.308540i	−0.763106	−	0.646273i	$-0.776327\pi$
$211$	545.976	−	945.659i	0.178135	−	0.308540i	0.941242	+	0.337733i	$0.109660\pi$
$212$			2212.82i			0.716875i
$213$	−1621.33	+	1724.22i	−0.521559	+	0.554655i
$214$	−212.806			−0.0679772
$215$	−1864.09	−	3228.70i	−0.591301	−	1.02416i
$216$	1055.12	+	876.462i	0.332368	+	0.276091i
$217$	966.726	+	3603.83i	0.302422	+	1.12739i
$218$	2811.22	−	1623.06i	0.873393	−	0.504254i
$219$	1146.77	+	3807.53i	0.353841	+	1.17484i
$220$	−564.306	+	325.802i	−0.172934	+	0.0998435i
$221$	−4411.76	+	2547.13i	−1.34284	+	0.775288i
$222$	−2154.35	+	2291.06i	−0.651310	+	0.692639i
$223$	1063.36	−	613.931i	0.319317	−	0.184358i	−0.331771	−	0.943360i	$-0.607646\pi$
$223$	1063.36	−	613.931i	0.319317	−	0.184358i	0.651088	+	0.759002i	$0.274313\pi$
$224$	995.188	+	3709.93i	0.296847	+	1.10661i
$225$	40.8233	+	663.111i	0.0120958	+	0.196477i
$226$	4281.96	+	7416.58i	1.26032	+	2.18294i
$227$	−2263.45			−0.661809			−0.330905	−	0.943664i	$-0.607354\pi$
$227$	−2263.45			−0.661809			−0.330905	+	0.943664i	$0.607354\pi$
$228$	959.998	+	3187.42i	0.278848	+	0.925842i
$229$			5152.41i			1.48682i	0.668839	+	0.743408i	$0.266792\pi$
$229$			5152.41i			1.48682i	−0.668839	+	0.743408i	$0.733208\pi$
$230$	2736.71	−	4740.12i	0.784580	−	1.35893i
$231$	507.366	+	819.016i	0.144512	+	0.233278i
$232$	−284.164	−	492.186i	−0.0804149	−	0.139283i
$233$	−361.488	+	208.705i	−0.101639	+	0.0586812i	−0.549958	−	0.835192i	$-0.685356\pi$
$233$	−361.488	+	208.705i	−0.101639	+	0.0586812i	0.448319	+	0.893874i	$0.352023\pi$
$234$	5409.69	−	3583.70i	1.51129	−	1.00117i
$235$	−138.132	+	239.252i	−0.0383437	+	0.0664132i
$236$	−959.609	+	1662.09i	−0.264683	+	0.458445i
$237$	−214.621	+	64.6403i	−0.0588233	+	0.0177166i
$238$	−1354.90	−	5050.89i	−0.369013	−	1.37563i
$239$	4832.69	+	2790.15i	1.30795	+	0.755146i	0.981754	−	0.190155i	$-0.0608992\pi$
$239$	4832.69	+	2790.15i	1.30795	+	0.755146i	0.326198	+	0.945302i	$0.394233\pi$
$240$	4762.22	−	1434.30i	1.28083	−	0.385766i
$241$			2773.85i			0.741409i	0.928751	+	0.370704i	$0.120884\pi$
$241$			2773.85i			0.741409i	−0.928751	+	0.370704i	$0.879116\pi$
$242$	−3890.28	−	2246.06i	−1.03338	−	0.596620i
$243$	3057.04	+	2236.83i	0.807034	+	0.590505i
$244$		−	3905.98i		−	1.02481i
$245$	3634.46	+	2095.64i	0.947744	+	0.546472i
$246$	−4150.86	−	976.524i	−1.07581	−	0.253093i
$247$	−7927.59			−2.04219
$248$	−984.866	−	1705.84i	−0.252174	−	0.436778i
$249$	−476.134	+	2023.88i	−0.121180	+	0.515093i
$250$	−3881.37	−	2240.91i	−0.981918	−	0.566911i
$251$	3751.34			0.943357			0.471678	−	0.881771i	$-0.343648\pi$
$251$	3751.34			0.943357			0.471678	+	0.881771i	$0.343648\pi$
$252$	846.026	+	2522.81i	0.211487	+	0.630643i
$253$	−1227.45			−0.305017
$254$	3244.74	+	1873.35i	0.801548	+	0.462774i
$255$	−4708.03	+	1417.98i	−1.15619	+	0.348225i
$256$	−2679.51	−	4641.05i	−0.654178	−	1.13307i
$257$	7511.72			1.82322			0.911612	−	0.411052i	$-0.134839\pi$
$257$	7511.72			1.82322			0.911612	+	0.411052i	$0.134839\pi$
$258$	−3959.96	+	4211.25i	−0.955567	+	1.01620i
$259$	2966.24	−	795.692i	0.711633	−	0.190895i
$260$		−	4285.83i		−	1.02229i
$261$	−866.787	−	1308.44i	−0.205566	−	0.310307i
$262$	4523.65	+	2611.73i	1.06669	+	0.615852i
$263$			5534.91i			1.29771i	0.760913	+	0.648854i	$0.224752\pi$
$263$			5534.91i			1.29771i	−0.760913	+	0.648854i	$0.775248\pi$
$264$	−370.519	−	348.410i	−0.0863784	−	0.0812242i
$265$	−4404.91	−	2543.17i	−1.02110	−	0.589532i
$266$	2104.06	−	7861.28i	0.484993	−	1.81205i
$267$	827.331	−	3516.70i	0.189632	−	0.806061i
$268$	−296.106	+	512.870i	−0.0674908	+	0.116898i
$269$	−411.958	+	713.532i	−0.0933737	+	0.161728i	−0.908929	−	0.416952i	$-0.863098\pi$
$269$	−411.958	+	713.532i	−0.0933737	+	0.161728i	0.815555	+	0.578680i	$0.196432\pi$
$270$	5874.74	−	2171.30i	1.32417	−	0.489412i
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	−0.858043	−	0.513577i	$-0.828320\pi$
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	0.0157492	+	0.999876i	$0.494987\pi$
$272$	3027.02	+	5242.95i	0.674779	+	1.16875i
$273$	−6333.80	+	196.557i	−1.40417	+	0.0435758i
$274$	−4612.38	+	7988.87i	−1.01695	+	1.76141i
$275$		−	246.341i		−	0.0540180i
$276$	−3299.98	−	776.347i	−0.719694	−	0.169314i
$277$	−2642.56			−0.573199			−0.286599	−	0.958051i	$-0.592525\pi$
$277$	−2642.56			−0.573199			−0.286599	+	0.958051i	$0.592525\pi$
$278$	520.546	+	901.612i	0.112303	+	0.194515i
$279$	−3004.15	−	4534.84i	−0.644636	−	0.973095i
$280$	−2139.44	−	572.618i	−0.456628	−	0.122216i
$281$	−3315.71	+	1914.33i	−0.703910	+	0.406403i	−0.808802	−	0.588081i	$-0.799884\pi$
$281$	−3315.71	+	1914.33i	−0.703910	+	0.406403i	0.104892	+	0.994484i	$0.466550\pi$
$282$	416.973	+	98.0963i	0.0880510	+	0.0207147i
$283$	6229.03	−	3596.33i	1.30840	−	0.755406i	0.326572	−	0.945172i	$-0.394106\pi$
$283$	6229.03	−	3596.33i	1.30840	−	0.755406i	0.981829	+	0.189766i	$0.0607731\pi$
$284$	2099.05	−	1211.89i	0.438576	−	0.253212i
$285$	−7448.28	−	1752.27i	−1.54806	−	0.364194i
$286$	−2083.73	+	1203.04i	−0.430816	+	0.248732i
$287$	2945.34	+	2943.69i	0.605776	+	0.605437i
$288$	−3092.59	−	4668.35i	−0.632753	−	0.955157i
$289$	−536.069	−	928.499i	−0.109112	−	0.188988i
$290$	−2595.05			−0.525470
$291$	5578.76	+	1312.45i	1.12382	+	0.264389i
$292$		−	4072.23i		−	0.816128i
$293$	−1871.73	+	3241.93i	−0.373199	+	0.646400i	−0.990056	−	0.140675i	$-0.955073\pi$
$293$	−1871.73	+	3241.93i	−0.373199	+	0.646400i	0.616856	+	0.787076i	$0.288406\pi$
$294$	1486.14	−	6332.99i	0.294808	−	1.25628i
$295$	−2205.74	−	3820.45i	−0.435332	−	0.754017i
$296$	−1404.04	+	810.623i	−0.275703	+	0.159177i
$297$	−1080.42	−	897.482i	−0.211085	−	0.175344i
$298$	3438.65	−	5955.92i	0.668442	−	1.15778i
$299$	4036.69	−	6991.76i	0.780763	−	1.35232i
$300$	155.808	−	662.283i	0.0299852	−	0.127457i
$301$	5452.30	−	1462.58i	1.04407	−	0.280072i
$302$	1265.75	+	730.781i	0.241178	+	0.139244i
$303$	2666.41	+	2507.31i	0.505549	+	0.475383i
$304$			9421.17i			1.77744i
$305$	7775.35	+	4489.10i	1.45972	+	0.842771i
$306$	4210.42	+	6355.73i	0.786580	+	1.18736i
$307$		−	4199.35i		−	0.780682i	−0.920670	−	0.390341i	$-0.872357\pi$
$307$		−	4199.35i		−	0.780682i	0.920670	−	0.390341i	$-0.127643\pi$
$308$	−255.627	−	952.944i	−0.0472912	−	0.176296i
$309$	3697.39	−	3932.01i	0.680703	−	0.723898i
$310$	−8994.02			−1.64783
$311$	1241.68	+	2150.64i	0.226395	+	0.392128i	0.956737	−	0.290954i	$-0.0939725\pi$
$311$	1241.68	+	2150.64i	0.226395	+	0.392128i	−0.730342	+	0.683082i	$0.760639\pi$
$312$	3203.11	−	964.725i	0.581220	−	0.175054i
$313$	−710.623	−	410.278i	−0.128328	−	0.0740904i	0.434462	−	0.900690i	$-0.356939\pi$
$313$	−710.623	−	410.278i	−0.128328	−	0.0740904i	−0.562790	+	0.826600i	$0.690272\pi$
$314$	−7160.35			−1.28688
$315$	−5994.30	−	1215.31i	−1.07219	−	0.217381i
$316$	229.541			0.0408630
$317$	−3579.71	−	2066.74i	−0.634247	−	0.366183i	0.148148	−	0.988965i	$-0.452669\pi$
$317$	−3579.71	−	2066.74i	−0.634247	−	0.366183i	−0.782395	+	0.622782i	$0.786002\pi$
$318$	−1806.06	+	7676.95i	−0.318488	+	1.35378i
$319$	290.979	+	503.990i	0.0510711	+	0.0884577i
$320$	−1601.57			−0.279783
$321$	−294.914	−	69.3809i	−0.0512788	−	0.0120638i
$322$	5861.90	+	5858.61i	1.01451	+	1.01394i
$323$		−	9313.95i		−	1.60446i
$324$	−2337.04	−	3096.21i	−0.400727	−	0.530900i
$325$	1403.20	+	810.137i	0.239494	+	0.138272i
$326$		−	7975.88i		−	1.35504i
$327$	4425.05	−	1332.75i	0.748336	−	0.225386i
$328$	−1903.76	−	1099.14i	−0.320481	−	0.185030i
$329$	−295.872	−	295.707i	−0.0495805	−	0.0495527i
$330$	−2223.66	+	669.729i	−0.370935	+	0.111719i
$331$	4444.19	−	7697.57i	0.737991	−	1.27824i	−0.215408	−	0.976524i	$-0.569108\pi$
$331$	4444.19	−	7697.57i	0.737991	−	1.27824i	0.953399	−	0.301713i	$-0.0975584\pi$
$332$	1064.60	−	1843.94i	0.175986	−	0.304817i
$333$	−3732.53	+	2472.65i	−0.614238	+	0.406908i
$334$	−4581.78	+	2645.29i	−0.750610	+	0.433365i
$335$	−680.622	−	1178.87i	−0.111004	−	0.192265i
$336$	233.589	+	7527.10i	0.0379266	+	1.22213i
$337$	1800.32	−	3118.24i	0.291007	−	0.504040i	−0.683041	−	0.730380i	$-0.739343\pi$
$337$	1800.32	−	3118.24i	0.291007	−	0.504040i	0.974048	+	0.226341i	$0.0726763\pi$
$338$		−	7806.96i		−	1.25634i
$339$	3516.08	+	11674.2i	0.563325	+	1.87037i
$340$	5035.32			0.803173
$341$	1008.49	+	1746.75i	0.160154	+	0.277395i
$342$	729.010	+	11841.6i	0.115264	+	1.87229i
$343$	−4488.08	+	4495.64i	−0.706512	+	0.707701i
$344$	−2580.80	+	1490.02i	−0.404498	+	0.233537i
$345$	5338.05	−	5676.78i	0.833017	−	0.885877i
$346$	5834.70	−	3368.66i	0.906576	−	0.523412i
$347$	−8104.74	+	4679.27i	−1.25385	+	0.723909i	−0.971871	−	0.235512i	$-0.924323\pi$
$347$	−8104.74	+	4679.27i	−1.25385	+	0.723909i	−0.281976	+	0.959421i	$0.590990\pi$
$348$	463.523	+	1539.00i	0.0714006	+	0.237067i
$349$	−3496.96	+	2018.97i	−0.536355	+	0.309665i	−0.743601	−	0.668624i	$-0.766884\pi$
$349$	−3496.96	+	2018.97i	−0.536355	+	0.309665i	0.207245	+	0.978289i	$0.433550\pi$
$350$	−1175.78	+	1176.44i	−0.179566	+	0.179667i
$351$	8665.33	−	3202.71i	1.31772	−	0.487031i
$352$	1038.18	+	1798.18i	0.157202	+	0.272282i
$353$	−4358.17			−0.657117			−0.328558	−	0.944484i	$-0.606563\pi$
$353$	−4358.17			−0.657117			−0.328558	+	0.944484i	$0.606563\pi$
$354$	−4685.74	+	4983.08i	−0.703514	+	0.748157i
$355$			5571.23i			0.832930i
$356$	−1849.85	+	3204.03i	−0.275398	+	0.477003i
$357$	−230.931	−	7441.44i	−0.0342358	−	1.10320i
$358$	−820.847	−	1421.75i	−0.121182	−	0.209893i
$359$	−3099.17	+	1789.31i	−0.455621	+	0.263053i	−0.710201	−	0.703999i	$-0.751396\pi$
$359$	−3099.17	+	1789.31i	−0.455621	+	0.263053i	0.254580	+	0.967052i	$0.418063\pi$
$360$	3222.69	−	198.399i	0.471807	−	0.0290460i
$361$	3817.59	−	6612.26i	0.556581	−	0.964026i
$362$	−5597.23	+	9694.68i	−0.812662	+	1.40757i
$363$	−4659.01	−	4381.01i	−0.673649	−	0.633453i
$364$	6268.78	+	1677.83i	0.902675	+	0.241600i
$365$	8106.29	+	4680.17i	1.16247	+	0.671154i
$366$	3187.98	−	13551.0i	0.455297	−	1.93531i
$367$		−	10258.5i		−	1.45910i	−0.683926	−	0.729551i	$-0.739729\pi$
$367$		−	10258.5i		−	1.45910i	0.683926	−	0.729551i	$-0.260271\pi$
$368$	−8309.02	−	4797.22i	−1.17700	−	0.679544i
$369$	−5434.04	−	2706.60i	−0.766625	−	0.381843i
$370$			7402.79i			1.04014i
$371$	5444.30	−	5447.35i	0.761870	−	0.762297i
$372$	1606.50	+	5333.94i	0.223906	+	0.743420i
$373$	9853.78			1.36785			0.683927	−	0.729551i	$-0.260271\pi$
$373$	9853.78			1.36785			0.683927	+	0.729551i	$0.260271\pi$
$374$	−1413.43	−	2448.13i	−0.195419	−	0.338475i
$375$	−4648.34	−	4370.97i	−0.640105	−	0.601909i
$376$	191.242	+	110.413i	0.0262302	+	0.0151440i
$377$	−3827.73			−0.522913
$378$	876.050	+	9442.88i	0.119204	+	1.28489i
$379$	−11181.0			−1.51538			−0.757688	−	0.652617i	$-0.773671\pi$
$379$	−11181.0			−1.51538			−0.757688	+	0.652617i	$0.773671\pi$
$380$	6786.06	+	3917.93i	0.916099	+	0.528910i
$381$	3885.91	+	3654.04i	0.522523	+	0.491344i
$382$	9490.53	+	16438.1i	1.27115	+	2.20169i
$383$	−8990.60			−1.19947			−0.599737	−	0.800198i	$-0.704728\pi$
$383$	−8990.60			−1.19947			−0.599737	+	0.800198i	$0.704728\pi$
$384$	−1770.17	−	5877.37i	−0.235243	−	0.781063i
$385$	2190.74	+	586.350i	0.290002	+	0.0776186i
$386$			8672.81i			1.14361i
$387$	−6860.84	+	4545.03i	−0.901178	+	0.596994i
$388$	−5082.76	−	2934.53i	−0.665047	−	0.383965i
$389$			1888.31i			0.246121i	0.992399	+	0.123061i	$0.0392709\pi$
$389$			1888.31i			0.246121i	−0.992399	+	0.123061i	$0.960729\pi$
$390$	3498.01	−	14868.8i	0.454176	−	1.93054i
$391$	8214.46	+	4742.62i	1.06246	+	0.613414i
$392$	1675.11	−	2905.14i	0.215831	−	0.374315i
$393$	5417.54	+	5094.27i	0.695365	+	0.653873i
$394$	−270.297	+	468.168i	−0.0345618	+	0.0598629i
$395$	−263.809	+	456.931i	−0.0336043	+	0.0582043i
$396$	794.373	+	1199.13i	0.100805	+	0.152168i
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.204984	−	0.978765i	$-0.434286\pi$
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.950128	+	0.311861i	$0.100952\pi$
$398$	3117.38	+	5399.47i	0.392614	+	0.680027i
$399$	5478.88	−	10208.4i	0.687437	−	1.28086i
$400$	962.768	−	1667.56i	0.120346	−	0.208445i
$401$		−	2064.71i		−	0.257124i	−0.991701	−	0.128562i	$-0.958964\pi$
$401$		−	2064.71i		−	0.257124i	0.991701	−	0.128562i	$-0.0410361\pi$
$402$	−1445.87	+	1537.62i	−0.179387	+	0.190770i
$403$	−13266.3			−1.63981
$404$	−1874.12	−	3246.07i	−0.230794	−	0.399747i
$405$	8849.33	−	1093.73i	1.08574	−	0.134193i
$406$	1015.92	−	3795.72i	0.124185	−	0.463986i
$407$	1437.71	−	830.064i	0.175098	−	0.101093i
$408$	1133.43	+	3763.27i	0.137533	+	0.456641i
$409$	−124.596	+	71.9353i	−0.0150632	+	0.00869676i	−0.507513	−	0.861644i	$-0.669435\pi$
$409$	−124.596	+	71.9353i	−0.0150632	+	0.00869676i	0.492449	+	0.870341i	$0.336102\pi$
$410$	−8692.80	+	5018.79i	−1.04709	+	0.604537i
$411$	−8996.59	+	9567.49i	−1.07973	+	1.14825i
$412$	−4786.80	+	2763.66i	−0.572399	+	0.330475i
$413$	6451.59	−	1730.64i	0.768673	−	0.206196i
$414$	−10815.0	−	5386.76i	−1.28388	−	0.639480i
$415$	2447.06	+	4238.43i	0.289449	+	0.501341i
$416$	−13656.9			−1.60958
$417$	427.439	+	1419.20i	0.0501961	+	0.166663i
$418$		−	4399.09i		−	0.514753i
$419$	1974.15	−	3419.34i	0.230176	−	0.398677i	−0.727684	−	0.685913i	$-0.759403\pi$
$419$	1974.15	−	3419.34i	0.230176	−	0.398677i	0.957860	+	0.287236i	$0.0927365\pi$
$420$	5518.91	+	2962.00i	0.641179	+	0.344121i
$421$	5518.29	+	9557.95i	0.638824	+	1.10648i	0.985691	+	0.168561i	$0.0539120\pi$
$421$	5518.29	+	9557.95i	0.638824	+	1.10648i	−0.346868	+	0.937914i	$0.612755\pi$
$422$	−3451.50	+	1992.72i	−0.398143	+	0.229868i
$423$	545.874	+	271.891i	0.0627453	+	0.0312524i
$424$	−2032.84	+	3520.98i	−0.232838	+	0.403287i
$425$	−951.812	+	1648.59i	−0.108634	+	0.188160i
$426$	8271.34	−	2491.19i	0.940723	−	0.283330i
$427$	−9610.03	+	9615.42i	−1.08914	+	1.08975i
$428$	268.694	+	155.130i	0.0303453	+	0.0175199i
$429$	−3279.93	+	987.861i	−0.369130	+	0.111176i
$430$			13607.2i			1.52604i
$431$	1481.18	+	855.162i	0.165536	+	0.0955724i	0.580479	−	0.814275i	$-0.302865\pi$
$431$	1481.18	+	855.162i	0.165536	+	0.0955724i	−0.414943	+	0.909847i	$0.636199\pi$
$432$	−3806.10	−	10297.9i	−0.423892	−	1.14689i
$433$		−	11599.1i		−	1.28734i	−0.765303	−	0.643670i	$-0.777411\pi$
$433$		−	11599.1i		−	1.28734i	0.765303	−	0.643670i	$-0.222589\pi$
$434$	3521.01	−	13155.3i	0.389433	−	1.45502i
$435$	−3596.30	−	846.060i	−0.396390	−	0.0932539i
$436$	−4732.67			−0.519849
$437$	7380.37	+	12783.2i	0.807897	+	1.39932i
$438$	3323.68	−	14127.8i	0.362583	−	1.54121i
$439$	−3706.44	−	2139.92i	−0.402959	−	0.232648i	0.284801	−	0.958587i	$-0.408072\pi$
$439$	−3706.44	−	2139.92i	−0.402959	−	0.232648i	−0.687760	+	0.725938i	$0.741406\pi$
$440$	−1197.21			−0.129715
$441$	4124.28	−	8291.95i	0.445339	−	0.895362i
$442$	18593.2			2.00088
$443$	8038.03	+	4640.76i	0.862073	+	0.497718i	0.864706	−	0.502278i	$-0.167505\pi$
$443$	8038.03	+	4640.76i	0.862073	+	0.497718i	−0.00263274	+	0.999997i	$0.500838\pi$
$444$	4390.26	−	1322.27i	0.469262	−	0.141334i
$445$	−4252.02	−	7364.71i	−0.452955	−	0.784541i
$446$	−4481.49			−0.475795
$447$	6707.20	−	7132.82i	0.709709	−	0.754744i
$448$	626.989	−	2342.58i	0.0661216	−	0.247046i
$449$			6876.47i			0.722763i	0.932418	+	0.361382i	$0.117695\pi$
$449$			6876.47i			0.722763i	−0.932418	+	0.361382i	$0.882305\pi$
$450$	1081.09	−	2170.49i	0.113251	−	0.227373i
$451$	1949.42	+	1125.50i	0.203536	+	0.117511i
$452$		−	12485.8i		−	1.29930i
$453$	1515.87	+	1425.41i	0.157222	+	0.147841i
$454$	7154.43	+	4130.61i	0.739590	+	0.427003i
$455$	−10544.6	+	10550.5i	−1.08646	+	1.08707i
$456$	−1400.64	+	5953.64i	−0.143840	+	0.611414i
$457$	5580.75	−	9666.14i	0.571239	−	0.989416i	−0.425200	−	0.905100i	$-0.639796\pi$
$457$	5580.75	−	9666.14i	0.571239	−	0.989416i	0.996439	−	0.0843160i	$-0.0268705\pi$
$458$	9402.71	−	16286.0i	0.959301	−	1.66156i
$459$	3762.79	+	10180.7i	0.382640	+	1.03528i
$460$	−6910.87	+	3989.99i	−0.700480	+	0.404422i
$461$	193.554	+	335.245i	0.0195547	+	0.0338697i	0.875637	−	0.482970i	$-0.160442\pi$
$461$	193.554	+	335.245i	0.0195547	+	0.0338697i	−0.856082	+	0.516839i	$0.827108\pi$
$462$	−109.072	−	3514.68i	−0.0109837	−	0.353935i
$463$	−2485.01	+	4304.16i	−0.249435	+	0.432033i	−0.963369	−	0.268179i	$-0.913578\pi$
$463$	−2485.01	+	4304.16i	−0.249435	+	0.432033i	0.713934	+	0.700213i	$0.246911\pi$
$464$			4548.89i			0.455122i
$465$	−12464.2	−	2932.31i	−1.24304	−	0.292436i
$466$	1523.48			0.151446
$467$	−4548.20	−	7877.72i	−0.450676	−	0.780594i	0.547752	−	0.836641i	$-0.315484\pi$
$467$	−4548.20	−	7877.72i	−0.450676	−	0.780594i	−0.998428	+	0.0560470i	$0.982150\pi$
$468$	−9442.83	+	581.331i	−0.932681	+	0.0574189i
$469$	1990.76	−	534.021i	0.196002	−	0.0525774i
$470$	873.231	−	504.160i	0.0857003	−	0.0494791i
$471$	−9923.06	−	2334.48i	−0.970765	−	0.228380i
$472$	−3053.80	+	1763.11i	−0.297802	+	0.171936i
$473$	2642.69	−	1525.76i	0.256894	−	0.148318i
$474$	796.347	+	187.347i	0.0771676	+	0.0181543i
$475$	−2565.50	+	1481.19i	−0.247817	+	0.143077i
$476$	−1971.25	+	7365.06i	−0.189815	+	0.709195i
$477$	−5005.82	+	10050.2i	−0.480504	+	0.964707i
$478$	−10183.6	−	17638.5i	−0.974449	−	1.68779i
$479$	13858.1			1.32191			0.660953	−	0.750427i	$-0.270152\pi$
$479$	13858.1			1.32191			0.660953	+	0.750427i	$0.270152\pi$
$480$	−12831.2	−	3018.64i	−1.22013	−	0.287045i
$481$			10919.2i			1.03508i
$482$	5062.05	−	8767.72i	0.478361	−	0.828545i
$483$	6213.54	+	10030.2i	0.585354	+	0.944908i
$484$	3274.64	+	5671.84i	0.307536	+	0.532667i
$485$	11683.1	−	6745.26i	1.09382	−	0.631518i
$486$	−5580.82	−	12649.1i	−0.520887	−	1.18061i
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	−0.895980	−	0.444094i	$-0.853526\pi$
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	0.832587	+	0.553894i	$0.186859\pi$
$488$	3588.27	−	6215.07i	0.332856	−	0.576523i
$489$	2600.37	−	11053.3i	0.240476	−	1.02218i
$490$	−7663.61	−	13256.6i	−0.706544	−	1.22219i
$491$	−15324.0	−	8847.30i	−1.40847	−	0.813183i	−0.413233	−	0.910625i	$-0.635601\pi$
$491$	−15324.0	−	8847.30i	−1.40847	−	0.813183i	−0.995241	+	0.0974422i	$0.968934\pi$
$492$	4529.11	+	4258.86i	0.415016	+	0.390252i
$493$		−	4497.12i		−	0.410832i
$494$	25057.9	+	14467.2i	2.28220	+	1.31763i
$495$	−3299.98	+	203.157i	−0.299642	+	0.0184469i
$496$			15765.7i			1.42722i
$497$	−8148.91	−	2181.05i	−0.735470	−	0.196848i
$498$	5198.39	−	5528.26i	0.467762	−	0.497445i
$499$	−14157.8			−1.27012			−0.635059	−	0.772464i	$-0.719024\pi$
$499$	−14157.8			−1.27012			−0.635059	+	0.772464i	$0.719024\pi$
$500$	3267.14	+	5658.85i	0.292222	+	0.506143i
$501$	−7212.03	+	2172.15i	−0.643133	+	0.193701i
$502$	−11857.4	−	6845.88i	−1.05423	−	0.608659i
$503$	−5337.01			−0.473093			−0.236546	−	0.971620i	$-0.576015\pi$
$503$	−5337.01			−0.473093			−0.236546	+	0.971620i	$0.576015\pi$
$504$	−971.437	+	4791.43i	−0.0858556	+	0.423466i
$505$	8615.60			0.759187
$506$	3879.79	+	2240.00i	0.340865	+	0.196799i
$507$	2545.30	−	10819.2i	0.222960	−	0.947724i
$508$	−2731.25	−	4730.67i	−0.238543	−	0.413169i
$509$	−1521.38			−0.132483			−0.0662417	−	0.997804i	$-0.521101\pi$
$509$	−1521.38			−0.132483			−0.0662417	+	0.997804i	$0.521101\pi$
$510$	17469.0	+	4109.73i	1.51675	+	0.356828i
$511$	−10019.1	+	10024.7i	−0.867353	+	0.867839i
$512$			10109.2i			0.872595i
$513$	−2850.43	+	16648.2i	−0.245321	+	1.43282i
$514$	−23743.4	−	13708.3i	−2.03750	−	1.17635i
$515$		−	12705.0i		−	1.08708i
$516$	8069.83	−	2430.50i	0.688477	−	0.207358i
$517$	−195.828	−	113.061i	−0.0166586	−	0.00961786i
$518$	−10827.9	−	2898.07i	−0.918437	−	0.245819i
$519$	9184.21	−	2766.13i	0.776767	−	0.233949i
$520$	3937.23	−	6819.47i	0.332036	−	0.575103i
$521$	−8290.88	+	14360.2i	−0.697178	+	1.20755i	0.272262	+	0.962223i	$0.412228\pi$
$521$	−8290.88	+	14360.2i	−0.697178	+	1.20755i	−0.969441	+	0.245325i	$0.921105\pi$
$522$	351.993	+	5717.58i	0.0295140	+	0.479410i
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	−0.125009	−	0.992156i	$-0.539896\pi$
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	0.796727	+	0.604339i	$0.206563\pi$
$524$	−3807.78	−	6595.26i	−0.317449	−	0.549838i
$525$	−2013.00	+	1247.02i	−0.167342	+	0.103665i
$526$	10100.8	−	17495.0i	0.837288	−	1.45023i
$527$		−	15586.3i		−	1.28833i
$528$	1173.98	+	3897.88i	0.0967629	+	0.321275i
$529$	−2865.21			−0.235491
$530$	9282.16	+	16077.2i	0.760738	+	1.31764i
$531$	−8118.28	+	5378.04i	−0.663472	+	0.439523i
$532$	−8387.31	+	8392.01i	−0.683526	+	0.683910i
$533$	−12822.0	+	7402.79i	−1.04199	+	0.601596i
$534$	−9032.74	+	9605.93i	−0.731994	+	0.778444i
$535$	−617.613	+	356.579i	−0.0499098	+	0.0288154i
$536$	−942.309	+	544.042i	−0.0759357	+	0.0438415i
$537$	−674.028	−	2237.93i	−0.0541647	−	0.179839i
$538$	2604.27	−	1503.58i	0.208695	−	0.120490i
$539$	−1715.28	+	2974.81i	−0.137073	+	0.237725i
$540$	−9000.40	−	1541.00i	−0.717251	−	0.122804i
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	0.999995	−	0.00324160i	$-0.00103183\pi$
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	−0.502805	+	0.864400i	$0.667699\pi$
$542$	15836.5			1.25505
$543$	−10917.6	+	11610.4i	−0.862833	+	0.917585i
$544$		−	16045.2i		−	1.26458i
$545$	5439.21	−	9420.99i	0.427505	−	0.740460i
$546$	20378.9	+	10937.4i	1.59732	+	0.857282i
$547$	4213.76	+	7298.44i	0.329373	+	0.570491i	0.982388	−	0.186854i	$-0.0598292\pi$
$547$	4213.76	+	7298.44i	0.329373	+	0.570491i	−0.653014	+	0.757346i	$0.726496\pi$
$548$	11647.4	−	6724.61i	0.907940	−	0.524199i
$549$	8836.04	−	17740.1i	0.686909	−	1.37910i
$550$	−449.553	+	778.648i	−0.0348527	+	0.0603666i
$551$	3499.16	−	6060.73i	0.270543	−	0.468595i
$552$	−4537.63	−	4266.87i	−0.349881	−	0.329003i
$553$	−565.066	−	564.749i	−0.0434522	−	0.0434278i
$554$	8352.73	+	4822.45i	0.640566	+	0.369831i
$555$	−2413.52	+	10259.0i	−0.184592	+	0.784634i
$556$		−	1517.86i		−	0.115776i
$557$	17760.6	+	10254.1i	1.35106	+	0.780035i	0.988398	−	0.151886i	$-0.0485347\pi$
$557$	17760.6	+	10254.1i	1.35106	+	0.780035i	0.362662	+	0.931921i	$0.381868\pi$
$558$	1219.95	+	19816.2i	0.0925532	+	1.50338i
$559$			20070.9i			1.51862i
$560$	12538.2	+	12531.2i	0.946138	+	0.945607i
$561$	−1160.62	−	3853.52i	−0.0873463	−	0.290010i
$562$	13973.9			1.04885
$563$	2255.95	+	3907.43i	0.168876	+	0.292502i	0.938025	−	0.346568i	$-0.112653\pi$
$563$	2255.95	+	3907.43i	0.168876	+	0.292502i	−0.769149	+	0.639069i	$0.779320\pi$
$564$	−454.970	−	427.821i	−0.0339675	−	0.0319407i
$565$	24854.5	+	14349.8i	1.85069	+	1.06849i
$566$	−26252.0			−1.94957
$567$	−1864.59	+	13371.9i	−0.138105	+	0.990418i
$568$	4453.25			0.328969
$569$	−11133.3	−	6427.82i	−0.820268	−	0.473582i	0.0302406	−	0.999543i	$-0.490373\pi$
$569$	−11133.3	−	6427.82i	−0.820268	−	0.473582i	−0.850509	+	0.525960i	$0.823706\pi$
$570$	20345.1	+	19131.1i	1.49502	+	1.40582i
$571$	−3099.39	−	5368.30i	−0.227155	−	0.393444i	0.729809	−	0.683651i	$-0.239609\pi$
$571$	−3099.39	−	5368.30i	−0.227155	−	0.393444i	−0.956964	+	0.290208i	$0.906276\pi$
$572$	3507.95			0.256424
$573$	7793.02	+	25874.7i	0.568164	+	1.88644i
$574$	−3937.78	−	14679.5i	−0.286341	−	1.06744i
$575$		−	3016.86i		−	0.218803i
$576$	217.238	+	3528.69i	0.0157145	+	0.255258i
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.943908	−	0.330209i	$-0.107119\pi$
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.185985	+	0.982553i	$0.440452\pi$
$578$			3913.12i			0.281599i
$579$	−2827.59	+	12019.1i	−0.202954	+	0.862687i
$580$	3276.56	+	1891.72i	0.234572	+	0.135430i
$581$	−7157.45	+	1919.98i	−0.511086	+	0.137099i
$582$	−15238.5	−	14329.2i	−1.08532	−	1.02056i
$583$	2081.59	−	3605.42i	0.147874	−	0.256126i
$584$	3741.00	−	6479.61i	0.265075	−	0.459123i
$585$	9695.32	−	19465.3i	0.685218	−	1.37571i
$586$	11832.5	−	6831.49i	0.834122	−	0.481580i
$587$	−2442.51	−	4230.56i	−0.171743	−	0.297468i	0.767286	−	0.641305i	$-0.221607\pi$
$587$	−2442.51	−	4230.56i	−0.171743	−	0.297468i	−0.939029	+	0.343837i	$0.888273\pi$
$588$	−6493.02	+	6912.81i	−0.455387	+	0.484829i
$589$	12127.5	−	21005.5i	0.848398	−	1.46947i
$590$			16101.1i			1.12351i
$591$	−527.223	+	560.679i	−0.0366956	+	0.0390241i
$592$	12976.4			0.900893
$593$	−1304.78	−	2259.95i	−0.0903557	−	0.156501i	0.817305	−	0.576205i	$-0.195467\pi$
$593$	−1304.78	−	2259.95i	−0.0903557	−	0.156501i	−0.907661	+	0.419704i	$0.862134\pi$
$594$	1777.21	+	4808.48i	0.122761	+	0.332145i
$595$	−12395.5	−	12388.6i	−0.854063	−	0.853585i
$596$	−8683.43	+	5013.38i	−0.596791	+	0.344557i
$597$	2559.80	+	8499.13i	0.175487	+	0.582657i
$598$	−25518.7	+	14733.3i	−1.74505	+	1.00750i
$599$	13896.7	−	8023.27i	0.947920	−	0.547282i	0.0554860	−	0.998459i	$-0.482329\pi$
$599$	13896.7	−	8023.27i	0.947920	−	0.547282i	0.892434	+	0.451177i	$0.148996\pi$
$600$	856.331	−	910.670i	0.0582659	−	0.0619633i
$601$	6848.07	−	3953.74i	0.464790	−	0.268347i	−0.249266	−	0.968435i	$-0.580189\pi$
$601$	6848.07	−	3953.74i	0.464790	−	0.268347i	0.714056	+	0.700088i	$0.246856\pi$
$602$	−19903.0	−	5327.01i	−1.34748	−	0.360652i
$603$	−2505.05	+	1659.50i	−0.169177	+	0.112073i
$604$	−1065.44	−	1845.40i	−0.0717753	−	0.124318i
$605$	−15054.0			−1.01162
$606$	−3852.49	−	12791.2i	−0.258246	−	0.857436i
$607$		−	3703.30i		−	0.247632i	−0.992305	−	0.123816i	$-0.960487\pi$
$607$		−	3703.30i		−	0.247632i	0.992305	−	0.123816i	$-0.0395132\pi$
$608$	12484.6	−	21624.0i	0.832759	−	1.44238i
$609$	2645.41	−	4929.02i	0.176022	−	0.327970i
$610$	−16384.5	−	28378.7i	−1.08752	−	1.88364i
$611$	1288.03	−	743.644i	0.0852833	−	0.0492383i
$612$	−682.993	−	11094.2i	−0.0451117	−	0.732770i
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	−0.980704	−	0.195498i	$-0.937368\pi$
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	0.659658	+	0.751566i	$0.270701\pi$
$614$	−7663.46	+	13273.5i	−0.503700	+	0.872435i
$615$	−13683.0	+	4121.11i	−0.897161	+	0.270210i
$616$	468.688	−	1751.13i	0.0306558	−	0.114537i
$617$	−22722.4	−	13118.8i	−1.48261	−	0.855985i	−0.482804	−	0.875729i	$-0.660382\pi$
$617$	−22722.4	−	13118.8i	−1.48261	−	0.855985i	−0.999805	+	0.0197440i	$0.993715\pi$
$618$	−18862.5	+	5681.06i	−1.22777	+	0.369783i
$619$		−	5165.08i		−	0.335383i	−0.985839	−	0.167692i	$-0.946369\pi$
$619$		−	5165.08i		−	0.335383i	0.985839	−	0.167692i	$-0.0536313\pi$
$620$	11356.0	+	6556.41i	0.735596	+	0.424697i
$621$	−13231.5	−	10991.2i	−0.855013	−	0.710241i
$622$		−	9063.81i		−	0.584286i
$623$	12436.8	−	3336.17i	0.799791	−	0.214544i
$624$	−26063.7	−	6131.70i	−1.67209	−	0.393373i
$625$	−18095.3			−1.15810
$626$	1497.45	+	2593.65i	0.0956070	+	0.165596i
$627$	1434.23	−	6096.42i	0.0913520	−	0.388305i
$628$	9040.81	+	5219.72i	0.574471	+	0.331671i
$629$	−12828.8			−0.813221
$630$	16729.2	+	14780.5i	1.05795	+	0.934713i
$631$	1350.06			0.0851743			0.0425871	−	0.999093i	$-0.486440\pi$
$631$	1350.06			0.0851743			0.0425871	+	0.999093i	$0.486440\pi$
$632$	365.239	+	210.871i	0.0229880	+	0.0132721i
$633$	−5432.89	+	1636.30i	−0.341134	+	0.102744i
$634$	7543.27	+	13065.3i	0.472526	+	0.818439i
$635$	12556.0			0.784677
$636$	7876.68	−	8376.51i	0.491086	−	0.522249i
$637$	−11303.9	−	19553.7i	−0.703106	−	1.21624i
$638$		−	2124.05i		−	0.131805i
$639$	12274.9	−	755.684i	0.759919	−	0.0467831i
$640$	−12513.0	−	7224.38i	−0.772843	−	0.446201i
$641$		−	18082.9i		−	1.11424i	−0.830431	−	0.557122i	$-0.811906\pi$
$641$		−	18082.9i		−	1.11424i	0.830431	−	0.557122i	$-0.188094\pi$
$642$	805.564	+	757.496i	0.0495219	+	0.0465669i
$643$	−16884.0	−	9748.00i	−1.03552	−	0.597859i	−0.116961	−	0.993137i	$-0.537315\pi$
$643$	−16884.0	−	9748.00i	−1.03552	−	0.597859i	−0.918562	+	0.395277i	$0.870649\pi$
$644$	−3130.58	−	11670.4i	−0.191556	−	0.714096i
$645$	−4436.35	+	18857.4i	−0.270823	+	1.15117i
$646$	−16997.2	+	29440.0i	−1.03521	+	1.79303i
$647$	8503.93	−	14729.2i	0.516730	−	0.895002i	−0.483082	−	0.875575i	$-0.660483\pi$
$647$	8503.93	−	14729.2i	0.516730	−	0.895002i	0.999811	−	0.0194267i	$-0.00618409\pi$
$648$	−874.254	−	7073.54i	−0.0529999	−	0.428819i
$649$	3127.04	−	1805.40i	0.189132	−	0.109196i
$650$	−2956.86	−	5121.44i	−0.178427	−	0.309045i
$651$	9168.57	−	17083.2i	0.551988	−	1.02848i
$652$	−5814.22	+	10070.5i	−0.349237	+	0.604896i
$653$			4331.50i			0.259578i	0.991542	+	0.129789i	$0.0414301\pi$
$653$			4331.50i			0.259578i	−0.991542	+	0.129789i	$0.958570\pi$
$654$	−16419.1	−	3862.72i	−0.981707	−	0.230954i
$655$	17504.9			1.04424
$656$	8797.50	+	15237.7i	0.523604	+	0.906909i
$657$	9212.13	−	18495.2i	0.547031	−	1.09827i
$658$	395.568	+	1474.63i	0.0234359	+	0.0873661i
$659$	2674.86	−	1544.33i	0.158115	−	0.0912875i	−0.418855	−	0.908053i	$-0.637568\pi$
$659$	2674.86	−	1544.33i	0.158115	−	0.0912875i	0.576970	+	0.816766i	$0.304235\pi$
$660$	3295.86	+	775.377i	0.194380	+	0.0457296i
$661$	−19561.4	+	11293.8i	−1.15106	+	0.664564i	−0.949145	−	0.314839i	$-0.898050\pi$
$661$	−19561.4	+	11293.8i	−1.15106	+	0.664564i	−0.201914	+	0.979403i	$0.564716\pi$
$662$	−28094.8	+	16220.6i	−1.64945	+	0.952311i
$663$	25767.1	+	6061.92i	1.50937	+	0.355091i
$664$	3387.91	−	1956.01i	0.198007	−	0.114319i
$665$	−7065.92	−	26340.8i	−0.412037	−	1.53602i
$666$	16310.3	−	1004.12i	0.948968	−	0.0584216i
$667$	3563.52	+	6172.19i	0.206866	+	0.358303i
$668$	7713.41			0.446768
$669$	−6210.60	−	1461.09i	−0.358917	−	0.0844382i
$670$			4968.31i			0.286482i
$671$	−3674.33	+	6364.12i	−0.211395	+	0.366146i
$672$	9438.51	−	17586.2i	0.541813	−	1.00952i
$673$	3978.45	+	6890.88i	0.227872	+	0.394686i	0.957177	−	0.289502i	$-0.0934898\pi$
$673$	3978.45	+	6890.88i	0.227872	+	0.394686i	−0.729305	+	0.684189i	$0.760156\pi$
$674$	−11381.0	+	6570.85i	−0.650418	+	0.375519i
$675$	2205.85	−	2655.48i	0.125783	−	0.151421i
$676$	−5691.08	+	9857.24i	−0.323798	+	0.560835i
$677$	−5552.77	+	9617.67i	−0.315229	+	0.545993i	−0.979486	−	0.201511i	$-0.935415\pi$
$677$	−5552.77	+	9617.67i	−0.315229	+	0.545993i	0.664257	+	0.747504i	$0.268748\pi$
$678$	10190.7	−	43316.9i	0.577241	−	2.45365i
$679$	5292.38	+	19729.3i	0.299121	+	1.11508i
$680$	8012.05	+	4625.76i	0.451836	+	0.260867i
$681$	8568.16	+	8056.90i	0.482133	+	0.453364i
$682$		−	7361.60i		−	0.413329i
$683$	16295.7	+	9408.31i	0.912938	+	0.527085i	0.881375	−	0.472417i	$-0.156618\pi$
$683$	16295.7	+	9408.31i	0.912938	+	0.527085i	0.0315626	+	0.999502i	$0.489952\pi$
$684$	7711.80	−	15482.9i	0.431094	−	0.865505i
$685$			30914.1i			1.72433i
$686$	22390.3	−	6019.65i	1.24616	−	0.335031i
$687$	18340.3	−	19504.1i	1.01852	−	1.08316i
$688$	23852.3			1.32174
$689$	13691.3	+	23714.1i	0.757037	+	1.31123i
$690$	−27232.4	+	8201.95i	−1.50249	+	0.452526i
$691$	−12726.4	−	7347.58i	−0.700629	−	0.404508i	0.106953	−	0.994264i	$-0.465891\pi$
$691$	−12726.4	−	7347.58i	−0.700629	−	0.404508i	−0.807582	+	0.589756i	$0.799224\pi$
$692$	−9822.69			−0.539599
$693$	994.734	−	4906.33i	0.0545264	−	0.268941i
$694$	34157.1			1.86828
$695$	3021.49	+	1744.46i	0.164909	+	0.0952103i
$696$	−676.282	+	2874.64i	−0.0368310	+	0.156556i
$697$	−8697.38	−	15064.3i	−0.472649	−	0.818653i
$698$	14737.8			0.799190
$699$	2111.29	+	496.697i	0.114243	+	0.0268767i
$700$	2342.17	−	628.285i	0.126465	−	0.0339242i
$701$		−	2167.47i		−	0.116782i	−0.998294	−	0.0583910i	$-0.981403\pi$
$701$		−	2167.47i		−	0.116782i	0.998294	−	0.0583910i	$-0.0185970\pi$
$702$	−33234.5	−	5690.24i	−1.78683	−	0.305932i
$703$	−17289.2	−	9981.93i	−0.927560	−	0.535527i
$704$		−	1310.89i		−	0.0701788i
$705$	1374.52	−	413.984i	0.0734292	−	0.0221157i
$706$	13775.5	+	7953.30i	0.734346	+	0.423975i
$707$	−3372.87	+	12601.9i	−0.179420	+	0.670356i
$708$	9548.85	−	2875.96i	0.506875	−	0.152663i
$709$	−17149.1	+	29703.1i	−0.908388	+	1.57337i	−0.0920850	+	0.995751i	$0.529353\pi$
$709$	−17149.1	+	29703.1i	−0.908388	+	1.57337i	−0.816303	+	0.577623i	$0.803980\pi$
$710$	10167.0	−	17609.8i	0.537411	−	0.930823i
$711$	1042.53	+	519.264i	0.0549898	+	0.0273895i
$712$	−5886.84	+	3398.77i	−0.309858	+	0.178896i
$713$	12350.6	+	21391.8i	0.648714	+	1.12361i
$714$	−12850.1	+	23942.7i	−0.673532	+	1.25495i
$715$	−4031.65	+	6983.02i	−0.210874	+	0.365245i
$716$			2393.51i			0.124930i
$717$	−8362.11	−	27764.2i	−0.435549	−	1.44613i
$718$	13061.3			0.678893
$719$	−7330.37	−	12696.6i	−0.380218	−	0.658557i	0.610875	−	0.791727i	$-0.290818\pi$
$719$	−7330.37	−	12696.6i	−0.380218	−	0.658557i	−0.991093	+	0.133170i	$0.957484\pi$
$720$	−23132.6	−	11521.9i	−1.19736	−	0.596386i
$721$	18583.3	+	4973.79i	0.959885	+	0.256912i
$722$	−24133.6	+	13933.6i	−1.24399	+	0.718218i
$723$	9873.69	−	10500.2i	0.507893	−	0.540122i
$724$	14134.4	−	8160.48i	0.725552	−	0.418898i
$725$	−1238.72	+	715.173i	−0.0634549	+	0.0366357i
$726$	6731.45	+	22350.0i	0.344115	+	1.14254i
$727$	−9274.34	+	5354.55i	−0.473131	+	0.273162i	−0.717550	−	0.696507i	$-0.754736\pi$
$727$	−9274.34	+	5354.55i	−0.473131	+	0.273162i	0.244418	+	0.969670i	$0.421403\pi$
$728$	8433.33	+	8428.61i	0.429341	+	0.429100i
$729$	−3610.11	−	19349.1i	−0.183413	−	0.983036i
$730$	−17081.8	−	29586.6i	−0.866064	−	1.50007i
$731$	−23580.8			−1.19312
$732$	−13903.6	+	14785.8i	−0.702036	+	0.746585i
$733$			15214.2i			0.766644i	0.923615	+	0.383322i	$0.125220\pi$
$733$			15214.2i			0.766644i	−0.923615	+	0.383322i	$0.874780\pi$
$734$	−18720.9	+	32425.6i	−0.941421	+	1.63059i
$735$	−6298.46	−	20870.0i	−0.316085	−	1.04735i
$736$	12714.2	+	22021.7i	0.636755	+	1.10289i
$737$	964.907	−	557.089i	0.0482263	−	0.0278435i
$738$	12236.8	+	18471.8i	0.610358	+	0.921351i
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	−0.720462	−	0.693495i	$-0.756070\pi$
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	0.960815	+	0.277191i	$0.0894035\pi$
$740$	5396.45	−	9346.92i	0.268078	−	0.464324i
$741$	30009.4	+	28218.7i	1.48775	+	1.39898i
$742$	−27149.5	+	7282.86i	−1.34325	+	0.360326i
$743$	−4935.72	−	2849.64i	−0.243706	−	0.140704i	0.373173	−	0.927762i	$-0.378270\pi$
$743$	−4935.72	−	2849.64i	−0.243706	−	0.140704i	−0.616879	+	0.787058i	$0.711603\pi$
$744$	−2343.89	+	9963.04i	−0.115499	+	0.490944i
$745$		−	23047.3i		−	1.13341i
$746$	−31146.3	−	17982.3i	−1.52861	−	0.882546i
$747$	9006.49	−	5966.44i	0.441138	−	0.292236i
$748$			4121.41i			0.201462i
$749$	−279.775	−	1042.96i	−0.0136485	−	0.0508799i
$750$	6716.03	+	22298.8i	0.326980	+	1.08565i
$751$	34815.7			1.69167			0.845833	−	0.533448i	$-0.179104\pi$
$751$	34815.7			1.69167			0.845833	+	0.533448i	$0.179104\pi$
$752$	−883.748	−	1530.70i	−0.0428550	−	0.0742271i
$753$	−14200.5	−	13353.1i	−0.687243	−	0.646235i
$754$	12098.9	+	6985.29i	0.584370	+	0.337386i
$755$	4898.01			0.236102
$756$	5777.51	−	12561.4i	0.277944	−	0.604304i
$757$	−12225.4			−0.586976			−0.293488	−	0.955963i	$-0.594816\pi$
$757$	−12225.4			−0.586976			−0.293488	+	0.955963i	$0.594816\pi$
$758$	35341.3	+	20404.3i	1.69348	+	0.977728i
$759$	4646.45	+	4369.19i	0.222207	+	0.208948i
$760$	7198.51	+	12468.2i	0.343576	+	0.595091i
$761$	11388.4			0.542482			0.271241	−	0.962512i	$-0.412566\pi$
$761$	11388.4			0.542482			0.271241	+	0.962512i	$0.412566\pi$
$762$	−5614.45	−	18641.3i	−0.266916	−	0.886225i
$763$	11650.5	+	11644.0i	0.552787	+	0.552477i
$764$		−	27673.4i		−	1.31046i
$765$	22869.3	+	11390.8i	1.08084	+	0.538348i
$766$	28417.9	+	16407.1i	1.34045	+	0.773906i
$767$			23749.4i			1.11805i
$768$	−6376.97	+	27106.3i	−0.299621	+	1.27359i
$769$	5063.88	+	2923.63i	0.237462	+	0.137099i	0.614010	−	0.789299i	$-0.289556\pi$
$769$	5063.88	+	2923.63i	0.237462	+	0.137099i	−0.376548	+	0.926397i	$0.622889\pi$
$770$	−5854.57	−	5851.29i	−0.274005	−	0.273852i
$771$	−28435.2	−	26738.4i	−1.32823	−	1.24898i
$772$	6322.26	−	10950.5i	0.294745	−	0.510513i
$773$	−2151.82	+	3727.06i	−0.100124	+	0.173419i	−0.911735	−	0.410778i	$-0.865257\pi$
$773$	−2151.82	+	3727.06i	−0.100124	+	0.173419i	0.811612	+	0.584197i	$0.198590\pi$
$774$	29980.4	−	1845.69i	1.39228	−	0.0857131i
$775$	−4293.20	+	2478.68i	−0.198989	+	0.114886i
$776$	−5391.69	−	9338.68i	−0.249421	−	0.432009i
$777$	−14060.8	−	7546.46i	−0.649201	−	0.348427i
$778$	3446.01	−	5968.66i	0.158799	−	0.275047i
$779$		−	27069.4i		−	1.24501i
$780$	−15255.7	+	16223.7i	−0.700308	+	0.744747i
$781$	−4560.05			−0.208926
$782$	−17309.8	−	29981.4i	−0.791555	−	1.37101i
$783$	−1376.29	+	8038.39i	−0.0628157	+	0.366882i
$784$	−23237.6	+	13433.6i	−1.05857	+	0.611955i
$785$	−20781.0	+	11997.9i	−0.944848	+	0.545509i
$786$	−7827.39	−	25988.8i	−0.355208	−	1.17937i
$787$	24548.4	−	14173.0i	1.11189	−	0.641949i	0.172571	−	0.984997i	$-0.444793\pi$
$787$	24548.4	−	14173.0i	1.11189	−	0.641949i	0.939318	+	0.343048i	$0.111459\pi$
$788$	682.566	−	394.080i	0.0308571	−	0.0178154i
$789$	19701.9	−	20952.1i	0.888979	−	0.945391i
$790$	1667.72	−	962.859i	0.0751074	−	0.0433633i
$791$	−30719.2	+	30736.5i	−1.38085	+	1.38162i
$792$	162.390	+	2637.77i	0.00728570	+	0.118345i
$793$	−24167.3	−	41859.0i	−1.08223	−	1.87447i
$794$	−38508.1			−1.72116
$795$	7621.92	+	25306.6i	0.340027	+	1.12897i
$796$		−	9089.98i		−	0.404756i
$797$	4002.70	−	6932.88i	0.177896	−	0.308124i	−0.763264	−	0.646087i	$-0.776404\pi$
$797$	4002.70	−	6932.88i	0.177896	−	0.308124i	0.941160	+	0.337963i	$0.109738\pi$
$798$	−35947.5	+	22268.8i	−1.59465	+	0.987855i
$799$	873.691	+	1513.28i	0.0386846	+	0.0670036i
$800$	−4419.60	+	2551.65i	−0.195320	+	0.112768i
$801$	−15649.7	+	10367.3i	−0.690331	+	0.457316i
$802$	−3767.92	+	6526.23i	−0.165898	+	0.287343i
$803$	−3830.72	+	6635.00i	−0.168348	+	0.291587i
$804$	2946.48	−	887.432i	0.129247	−	0.0389270i
$805$	26829.3	+	7180.83i	1.17467	+	0.314399i
$806$	41932.8	+	24209.9i	1.83253	+	1.05801i
$807$	4099.30	−	1234.64i	0.178813	−	0.0538556i
$808$		−	6886.72i		−	0.299844i
$809$	−9857.91	−	5691.47i	−0.428412	−	0.247344i	0.270258	−	0.962788i	$-0.412891\pi$
$809$	−9857.91	−	5691.47i	−0.428412	−	0.247344i	−0.698670	+	0.715444i	$0.746224\pi$
$810$	−29967.3	−	12692.2i	−1.29993	−	0.550564i
$811$			3510.72i			0.152008i	0.997108	+	0.0760038i	$0.0242161\pi$
$811$			3510.72i			0.152008i	−0.997108	+	0.0760038i	$0.975784\pi$
$812$	−4049.70	+	4051.97i	−0.175021	+	0.175119i
$813$	21946.8	+	5163.17i	0.946751	+	0.222731i
$814$	−6059.18			−0.260902
$815$	−13364.4	−	23147.9i	−0.574400	−	0.994890i
$816$	7204.00	−	30621.7i	0.309057	−	1.31369i
$817$	−31779.6	−	18348.0i	−1.36087	−	0.785697i
$818$	525.104			0.0224448
$819$	24675.8	+	21801.5i	1.05280	+	0.930165i
$820$	14634.3			0.623233
$821$	11046.2	+	6377.52i	0.469567	+	0.271105i	0.716058	−	0.698040i	$-0.245944\pi$
$821$	11046.2	+	6377.52i	0.469567	+	0.271105i	−0.246491	+	0.969145i	$0.579278\pi$
$822$	45896.7	−	13823.3i	1.94748	−	0.586550i
$823$	4835.76	+	8375.78i	0.204817	+	0.354753i	0.950074	−	0.312024i	$-0.101007\pi$
$823$	4835.76	+	8375.78i	0.204817	+	0.354753i	−0.745258	+	0.666777i	$0.767674\pi$
$824$	−10155.5			−0.429348
$825$	−876.867	+	932.510i	−0.0370044	+	0.0393525i
$826$	−23550.8	−	6303.33i	−0.992053	−	0.265522i
$827$			41804.8i			1.75779i	0.477011	+	0.878897i	$0.341720\pi$
$827$			41804.8i			1.75779i	−0.477011	+	0.878897i	$0.658280\pi$
$828$	9728.41	+	14685.3i	0.408316	+	0.616364i
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	0.743465	−	0.668775i	$-0.233181\pi$
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	−0.207444	+	0.978247i	$0.566515\pi$
$830$		−	17862.7i		−	0.747017i
$831$	10003.2	+	9406.35i	0.417580	+	0.392663i
$832$	7467.01	+	4311.08i	0.311144	+	0.179639i
$833$	22973.2	−	13280.8i	0.955551	−	0.552402i
$834$	1238.85	−	5265.91i	0.0514362	−	0.218637i
$835$	−8864.93	+	15354.5i	−0.367406	+	0.636365i
$836$	−3206.83	+	5554.39i	−0.132668	+	0.229788i
$837$	−4770.01	+	27859.8i	−0.196984	+	1.15051i
$838$	−12480.0	+	7205.33i	−0.514457	+	0.297022i
$839$	−746.315	−	1292.66i	−0.0307100	−	0.0531912i	0.850262	−	0.526360i	$-0.176443\pi$
$839$	−746.315	−	1292.66i	−0.0307100	−	0.0531912i	−0.880972	+	0.473169i	$0.843110\pi$
$840$	6060.44	+	9783.06i	0.248934	+	0.401842i
$841$	−10505.0	+	18195.1i	−0.430726	+	0.746039i
$842$		−	40281.6i		−	1.64869i
$843$	19365.6	+	4555.91i	0.791205	+	0.186137i
$844$	5810.58			0.236977
$845$	−13081.4	−	22657.6i	−0.532560	−	0.922422i
$846$	−1229.25	−	1855.58i	−0.0499555	−	0.0754091i
$847$	5893.41	−	22019.2i	0.239079	−	0.893256i
$848$	28181.9	−	16270.8i	1.14124	−	0.658894i
$849$	−36381.0	−	8558.92i	−1.47066	−	0.345985i
$850$	6017.06	−	3473.95i	0.242804	−	0.140183i
$851$	17607.2	−	10165.5i	0.709244	−	0.409482i
$852$	−12259.6	−	2884.17i	−0.492966	−	0.115974i
$853$	3660.40	−	2113.34i	0.146928	−	0.0848291i	−0.424734	−	0.905318i	$-0.639632\pi$
$853$	3660.40	−	2113.34i	0.146928	−	0.0848291i	0.571662	+	0.820489i	$0.306299\pi$
$854$	47923.2	−	12855.4i	1.92025	−	0.515107i
$855$	21957.7	+	33145.7i	0.878289	+	1.32580i
$856$	285.025	+	493.677i	0.0113808	+	0.0197121i
$857$	6728.80			0.268205			0.134102	−	0.990967i	$-0.457185\pi$
$857$	6728.80			0.268205			0.134102	+	0.990967i	$0.457185\pi$
$858$	12170.1	+	2863.12i	0.484244	+	0.113922i
$859$		−	39541.8i		−	1.57060i	−0.619113	−	0.785302i	$-0.712508\pi$
$859$		−	39541.8i		−	1.57060i	0.619113	−	0.785302i	$-0.287492\pi$
$860$	9919.32	−	17180.8i	0.393309	−	0.681232i
$861$	−671.161	−	21627.2i	−0.0265657	−	0.856045i
$862$	−3121.20	−	5406.07i	−0.123328	−	0.213610i
$863$	−22905.9	+	13224.7i	−0.903508	+	0.521640i	−0.878337	−	0.478043i	$-0.841346\pi$
$863$	−22905.9	+	13224.7i	−0.903508	+	0.521640i	−0.0251711	+	0.999683i	$0.508013\pi$
$864$	−4910.45	+	28680.0i	−0.193353	+	1.12930i
$865$	11289.1	−	19553.3i	0.443747	−	0.768592i
$866$	−21167.4	+	36663.1i	−0.830599	+	1.43864i
$867$	−1275.79	+	5422.94i	−0.0499748	+	0.212425i
$868$	−14035.6	+	14043.5i	−0.548848	+	0.549156i
$869$	−373.998	−	215.928i	−0.0145996	−	0.00842906i
$870$	9823.38	+	9237.22i	0.382809	+	0.359967i
$871$			7328.34i			0.285088i
$872$	−7530.49	−	4347.73i	−0.292448	−	0.168845i
$873$	−16446.3	−	24826.1i	−0.637599	−	0.962471i
$874$		−	53874.2i		−	2.08504i
$875$	5879.91	−	21968.7i	0.227174	−	0.848776i
$876$	−14495.3	+	15415.2i	−0.559078	+	0.594555i
$877$	2426.36			0.0934234			0.0467117	−	0.998908i	$-0.485126\pi$
$877$	2426.36			0.0934234			0.0467117	+	0.998908i	$0.485126\pi$
$878$	7810.34	+	13527.9i	0.300212	+	0.519982i
$879$	18625.1	−	5609.58i	0.714687	−	0.215252i
$880$	8298.64	+	4791.22i	0.317894	+	0.183536i
$881$	22112.5			0.845616			0.422808	−	0.906219i	$-0.361044\pi$
$881$	22112.5			0.845616			0.422808	+	0.906219i	$0.361044\pi$
$882$	−28168.3	+	18683.1i	−1.07537	+	0.713258i
$883$	−50385.7			−1.92029			−0.960144	−	0.279506i	$-0.909829\pi$
$883$	−50385.7			−1.92029			−0.960144	+	0.279506i	$0.909829\pi$
$884$	−23476.2	−	13554.0i	−0.893201	−	0.515690i
$885$	−5249.43	+	22313.5i	−0.199387	+	0.847526i
$886$	−16938.0	−	29337.5i	−0.642261	−	1.11243i
$887$	10325.0			0.390845			0.195422	−	0.980719i	$-0.437392\pi$
$887$	10325.0			0.390845			0.195422	+	0.980719i	$0.437392\pi$
$888$	8200.37	+	1929.20i	0.309895	+	0.0729052i
$889$	−4915.47	+	18365.4i	−0.185444	+	0.692863i
$890$			31038.3i			1.16900i
$891$	895.220	+	7243.18i	0.0336599	+	0.272341i
$892$	5658.42	+	3266.89i	0.212397	+	0.122627i
$893$			2719.24i			0.101899i
$894$	−34217.2	+	10305.7i	−1.28008	+	0.385540i
$895$	−4764.58	−	2750.83i	−0.177947	−	0.102738i
$896$	15465.6	−	15474.3i	0.576639	−	0.576963i
$897$	−40168.2	+	12098.0i	−1.49518	+	0.450324i
$898$	12549.0	−	21735.5i	0.466331	−	0.807708i
$899$	5855.63	−	10142.2i	0.217237	−	0.376266i
$900$	−2947.24	+	1952.43i	−0.109157	+	0.0723121i
$901$	−27861.2	+	16085.6i	−1.03018	+	0.594773i
$902$	−4107.88	−	7115.06i	−0.151638	−	0.262645i
$903$	−25845.5	−	13871.3i	−0.952474	−	0.511194i
$904$	11470.2	−	19867.0i	0.422006	−	0.730936i
$905$			37515.0i			1.37795i
$906$	−2190.16	−	7271.84i	−0.0803125	−	0.266656i
$907$	−4878.45			−0.178596			−0.0892979	−	0.996005i	$-0.528462\pi$
$907$	−4878.45			−0.178596			−0.0892979	+	0.996005i	$0.528462\pi$
$908$	−6022.23	−	10430.8i	−0.220104	−	0.381232i
$909$	−1168.62	−	18982.5i	−0.0426412	−	0.692640i
$910$	52583.6	−	14105.5i	1.91553	−	0.513839i
$911$	26279.5	−	15172.5i	0.955741	−	0.551797i	0.0608814	−	0.998145i	$-0.480609\pi$
$911$	26279.5	−	15172.5i	0.955741	−	0.551797i	0.894860	+	0.446348i	$0.147276\pi$
$912$	33535.2	−	35663.2i	1.21761	−	1.29488i
$913$	−3469.16	+	2002.92i	−0.125753	+	0.0726035i
$914$	−35279.8	+	20368.8i	−1.27675	+	0.737133i
$915$	−13453.9	−	44670.0i	−0.486089	−	1.61393i
$916$	−23744.1	+	13708.7i	−0.856472	+	0.494484i
$917$	−6852.90	+	25604.1i	−0.246786	+	0.922052i
$918$	6685.34	−	39046.4i	0.240359	−	1.40384i
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	−0.999961	−	0.00880146i	$-0.997198\pi$
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	0.492358	−	0.870393i	$-0.336135\pi$
$920$	−14661.8			−0.525419
$921$	−14947.8	+	15896.4i	−0.534797	+	0.568733i
$922$		−	1412.88i		−	0.0504671i
$923$	14996.5	−	25974.7i	0.534796	−	0.926293i
$924$	−2424.40	+	4517.23i	−0.0863171	+	0.160829i
$925$	2040.15	+	3533.64i	0.0725185	+	0.125606i
$926$	15709.5	−	9069.87i	0.557500	−	0.321873i
$927$	−27992.5	+	1723.31i	−0.991794	+	0.0610581i
$928$	6028.03	−	10440.9i	0.213232	−	0.369329i
$929$	−10855.5	+	18802.2i	−0.383376	+	0.664026i	−0.991542	−	0.129783i	$-0.958572\pi$
$929$	−10855.5	+	18802.2i	−0.383376	+	0.664026i	0.608167	+	0.793809i	$0.291905\pi$
$930$	34046.3	+	32014.7i	1.20045	+	1.12882i
$931$	41294.4	−	23.1518i	1.45367	−	0.000815004i
$932$	−1923.57	−	1110.58i	−0.0676060	−	0.0390323i
$933$	2955.06	−	12560.9i	0.103692	−	0.440758i
$934$			33200.3i			1.16311i
$935$	−8204.20	−	4736.70i	−0.286958	−	0.165675i
$936$	−15559.2	−	7749.77i	−0.543342	−	0.270629i
$937$			6528.34i			0.227611i	0.993503	+	0.113805i	$0.0363041\pi$
$937$			6528.34i			0.227611i	−0.993503	+	0.113805i	$0.963696\pi$
$938$	−7267.04	−	1945.01i	−0.252961	−	0.0677047i
$939$	1229.61	+	4082.59i	0.0427335	+	0.141885i
$940$	−1470.08			−0.0510093
$941$	1498.33	+	2595.18i	0.0519066	+	0.0899049i	0.890811	−	0.454374i	$-0.150137\pi$
$941$	1498.33	+	2595.18i	0.0519066	+	0.0899049i	−0.838905	+	0.544278i	$0.816804\pi$
$942$	27105.0	+	25487.7i	0.937505	+	0.881564i
$943$	23873.9	+	13783.6i	0.824434	+	0.475987i
$944$	28223.9			0.973102
$945$	18365.1	+	25937.5i	0.632185	+	0.892855i
$946$	−11137.5			−0.382782
$947$	4997.80	+	2885.48i	0.171496	+	0.0990133i	0.583291	−	0.812263i	$-0.301765\pi$
$947$	4997.80	+	2885.48i	0.171496	+	0.0990133i	−0.411795	+	0.911277i	$0.635098\pi$
$948$	−868.914	−	817.066i	−0.0297690	−	0.0279927i
$949$	−25196.0	−	43640.7i	−0.861850	−	1.49277i
$950$	10812.2			0.369257
$951$	6194.05	+	20565.7i	0.211205	+	0.701250i
$952$	−9902.59	+	9908.14i	−0.337127	+	0.337316i
$953$		−	38807.0i		−	1.31908i	−0.751670	−	0.659540i	$-0.770751\pi$
$953$		−	38807.0i		−	1.31908i	0.751670	−	0.659540i	$-0.229249\pi$
$954$	34163.3	−	22631.8i	1.15941	−	0.768063i
$955$	55087.5	+	31804.8i	1.86659	+	1.07767i
$956$			29694.3i			1.00458i
$957$	692.500	−	2943.58i	0.0233912	−	0.0994277i
$958$	−43803.3	−	25289.9i	−1.47727	−	0.852900i
$959$	−45217.4	−	12102.4i	−1.52257	−	0.407514i
$960$	6062.65	+	5700.89i	0.203824	+	0.191662i
$961$	5399.17	−	9351.64i	0.181235	−	0.313908i
$962$	19926.7	−	34514.0i	0.667840	−	1.15673i
$963$	869.413	+	1312.40i	0.0290929	+	0.0439164i
$964$	−12782.9	+	7380.21i	−0.427085	+	0.246577i
$965$	14532.2	+	25170.5i	0.484775	+	0.839656i
$966$	−1335.76	−	43043.2i	−0.0444902	−	1.43363i
$967$	−27150.0	+	47025.2i	−0.902880	+	1.56383i	−0.0791416	+	0.996863i	$0.525218\pi$
$967$	−27150.0	+	47025.2i	−0.902880	+	1.56383i	−0.823738	+	0.566970i	$0.808115\pi$
$968$			12033.1i			0.399545i
$969$	−33153.6	+	35257.4i	−1.09912	+	1.16886i
$970$	−49238.1			−1.62984
$971$	17624.4	+	30526.3i	0.582485	+	1.00889i	0.995184	+	0.0980262i	$0.0312529\pi$
$971$	17624.4	+	30526.3i	0.582485	+	1.00889i	−0.412699	+	0.910868i	$0.635414\pi$
$972$	−2174.43	+	20039.3i	−0.0717540	+	0.661278i
$973$	−3734.45	+	3736.54i	−0.123043	+	0.123112i
$974$	4306.94	−	2486.61i	0.141687	−	0.0818031i
$975$	−2427.99	−	8061.49i	−0.0797516	−	0.264794i
$976$	−49745.4	+	28720.5i	−1.63147	+	0.941928i
$977$	42809.1	−	24715.8i	1.40183	−	0.809344i	0.407245	−	0.913319i	$-0.366489\pi$
$977$	42809.1	−	24715.8i	1.40183	−	0.809344i	0.994580	+	0.103975i	$0.0331562\pi$
$978$	−28390.6	+	30192.2i	−0.928254	+	0.987158i
$979$	6028.02	−	3480.28i	0.196789	−	0.113616i
$980$	12.5163	+	22324.6i	0.000407980	+	0.727688i
$981$	−21494.8	−	10706.2i	−0.699566	−	0.348442i
$982$	32291.1	+	55929.9i	1.04934	+	1.81751i
$983$	42847.4			1.39026			0.695128	−	0.718886i	$-0.255348\pi$
$983$	42847.4			1.39026			0.695128	+	0.718886i	$0.255348\pi$
$984$	3294.13	+	10937.3i	0.106721	+	0.354337i
$985$			1811.64i			0.0586029i
$986$	−8206.87	+	14214.7i	−0.265071	+	0.459116i
$987$	67.4211	+	2172.55i	0.00217430	+	0.0700640i
$988$	−21092.4	−	36533.2i	−0.679190	−	1.17639i
$989$	32364.1	−	18685.4i	1.04057	−	0.600771i
$990$	10801.5	+	5380.03i	0.346761	+	0.172716i
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	−0.517178	−	0.855878i	$-0.673018\pi$
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	0.999801	+	0.0199505i	$0.00635086\pi$
$992$	20892.2	−	36186.3i	0.668677	−	1.15818i
$993$	−44223.2	+	13319.3i	−1.41327	+	0.425654i
$994$	21777.2	+	21765.0i	0.694901	+	0.694512i
$995$	18094.8	+	10447.0i	0.576525	+	0.332857i
$996$	−10593.6	+	3190.61i	−0.337018	+	0.101504i
$997$		−	7200.82i		−	0.228738i	−0.993438	−	0.114369i	$-0.963515\pi$
$997$		−	7200.82i		−	0.228738i	0.993438	−	0.114369i	$-0.0364847\pi$
$998$	44750.5	+	25836.7i	1.41939	+	0.819487i
$999$	22930.8	+	3926.10i	0.726225	+	0.124341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.59.5	yes	44
3.2	odd	2		189.4.s.a.17.18		44
7.5	odd	6		63.4.i.a.5.18	✓	44
9.2	odd	6		63.4.i.a.38.5	yes	44
9.7	even	3		189.4.i.a.143.18		44
21.5	even	6		189.4.i.a.152.5		44
63.47	even	6	inner	63.4.s.a.47.5	yes	44
63.61	odd	6		189.4.s.a.89.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.18	✓	44	7.5	odd	6
63.4.i.a.38.5	yes	44	9.2	odd	6
63.4.s.a.47.5	yes	44	63.47	even	6	inner
63.4.s.a.59.5	yes	44	1.1	even	1	trivial
189.4.i.a.143.18		44	9.7	even	3
189.4.i.a.152.5		44	21.5	even	6
189.4.s.a.17.18		44	3.2	odd	2
189.4.s.a.89.18		44	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.16085 - 1.82492i) q^{2} +(-3.78544 - 3.55956i) q^{3} +(2.66064 + 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 + 18.1593i) q^{6} +(4.78838 - 17.8905i) q^{7} +9.77690i q^{8} +(1.65907 + 26.9490i) q^{9} +O(q^{10})\)	\(q+(-3.16085 - 1.82492i) q^{2} +(-3.78544 - 3.55956i) q^{3} +(2.66064 + 4.60836i) q^{4} -12.2314 q^{5} +(5.46929 + 18.1593i) q^{6} +(4.78838 - 17.8905i) q^{7} +9.77690i q^{8} +(1.65907 + 26.9490i) q^{9} +(38.6615 + 22.3212i) q^{10} -10.0114i q^{11} +(6.33205 - 26.9153i) q^{12} +(57.0263 + 32.9241i) q^{13} +(-47.7841 + 47.8109i) q^{14} +(46.3010 + 43.5383i) q^{15} +(39.1271 - 67.7702i) q^{16} +(-38.6818 + 66.9989i) q^{17} +(43.9356 - 88.2093i) q^{18} +(-104.262 + 60.1959i) q^{19} +(-32.5432 - 56.3665i) q^{20} +(-81.8086 + 50.6790i) q^{21} +(-18.2699 + 31.6444i) q^{22} -122.606i q^{23} +(34.8015 - 37.0098i) q^{24} +24.6062 q^{25} +(-120.168 - 208.136i) q^{26} +(89.6462 - 107.919i) q^{27} +(95.1861 - 25.5337i) q^{28} +(-50.3417 + 29.0648i) q^{29} +(-66.8969 - 222.113i) q^{30} +(-174.476 + 100.734i) q^{31} +(-179.613 + 103.700i) q^{32} +(-35.6361 + 37.8974i) q^{33} +(244.535 - 141.182i) q^{34} +(-58.5684 + 218.826i) q^{35} +(-119.776 + 79.3470i) q^{36} +(82.9121 + 143.608i) q^{37} +439.410 q^{38} +(-98.6739 - 327.621i) q^{39} -119.585i q^{40} +(-112.422 + 194.721i) q^{41} +(351.069 - 10.8948i) q^{42} +(152.402 + 263.969i) q^{43} +(46.1360 - 26.6366i) q^{44} +(-20.2926 - 329.623i) q^{45} +(-223.746 + 387.539i) q^{46} +(11.2933 - 19.5606i) q^{47} +(-389.345 + 117.264i) q^{48} +(-297.143 - 171.333i) q^{49} +(-77.7763 - 44.9042i) q^{50} +(384.914 - 115.930i) q^{51} +350.397i q^{52} +(360.132 + 207.922i) q^{53} +(-480.301 + 177.519i) q^{54} +122.453i q^{55} +(174.914 + 46.8155i) q^{56} +(608.949 + 143.260i) q^{57} +212.163 q^{58} +(180.334 + 312.348i) q^{59} +(-77.4496 + 329.211i) q^{60} +(-635.689 - 367.015i) q^{61} +735.324 q^{62} +(490.076 + 99.3604i) q^{63} +130.940 q^{64} +(-697.509 - 402.707i) q^{65} +(181.800 - 54.7551i) q^{66} +(55.6457 + 96.3811i) q^{67} -411.673 q^{68} +(-436.423 + 464.117i) q^{69} +(584.464 - 584.792i) q^{70} -455.487i q^{71} +(-263.478 + 16.2205i) q^{72} +(-662.747 - 382.637i) q^{73} -605.230i q^{74} +(-93.1451 - 87.5871i) q^{75} +(-554.808 - 320.319i) q^{76} +(-179.109 - 47.9383i) q^{77} +(-285.987 + 1215.63i) q^{78} +(21.5683 - 37.3573i) q^{79} +(-478.578 + 828.921i) q^{80} +(-723.495 + 89.4203i) q^{81} +(710.697 - 410.321i) q^{82} +(-200.064 - 346.522i) q^{83} +(-451.210 - 242.165i) q^{84} +(473.131 - 819.488i) q^{85} -1112.49i q^{86} +(294.023 + 69.1714i) q^{87} +97.8802 q^{88} +(347.632 + 602.117i) q^{89} +(-537.392 + 1078.92i) q^{90} +(862.094 - 862.577i) q^{91} +(565.012 - 326.210i) q^{92} +(1019.04 + 239.737i) q^{93} +(-71.3928 + 41.2186i) q^{94} +(1275.27 - 736.277i) q^{95} +(1049.04 + 246.795i) q^{96} +(-955.178 + 551.472i) q^{97} +(626.554 + 1083.82i) q^{98} +(269.796 - 16.6095i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more