LMFDB - Embedded newform 63.4.g.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([2, 4]))

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

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

chi := DirichletCharacter("63.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.g (of order $3$, 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 $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	63.4
Dual form			63.4.g.a.16.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.267129 + 0.462682i) q^{2} +(3.78900 - 3.55577i) q^{3} +(3.85728 + 6.68101i) q^{4} -1.39324 q^{5} +(0.633036 + 2.70295i) q^{6} +(16.9882 + 7.37568i) q^{7} -8.39564 q^{8} +(1.71302 - 26.9456i) q^{9} +O(q^{10})$	\(q+(-0.267129 + 0.462682i) q^{2} +(3.78900 - 3.55577i) q^{3} +(3.85728 + 6.68101i) q^{4} -1.39324 q^{5} +(0.633036 + 2.70295i) q^{6} +(16.9882 + 7.37568i) q^{7} -8.39564 q^{8} +(1.71302 - 26.9456i) q^{9} +(0.372176 - 0.644627i) q^{10} +19.3952 q^{11} +(38.3714 + 11.5987i) q^{12} +(4.05999 - 7.03211i) q^{13} +(-7.95064 + 5.88988i) q^{14} +(-5.27899 + 4.95404i) q^{15} +(-28.6155 + 49.5636i) q^{16} +(28.8598 - 49.9867i) q^{17} +(12.0096 + 7.99055i) q^{18} +(35.7871 + 61.9851i) q^{19} +(-5.37413 - 9.30826i) q^{20} +(90.5945 - 32.4597i) q^{21} +(-5.18104 + 8.97382i) q^{22} -210.330 q^{23} +(-31.8111 + 29.8530i) q^{24} -123.059 q^{25} +(2.16909 + 3.75697i) q^{26} +(-89.3217 - 108.188i) q^{27} +(16.2514 + 141.949i) q^{28} +(-78.1687 - 135.392i) q^{29} +(-0.881972 - 3.76586i) q^{30} +(-55.5662 - 96.2435i) q^{31} +(-48.8707 - 84.6465i) q^{32} +(73.4886 - 68.9650i) q^{33} +(15.4186 + 26.7058i) q^{34} +(-23.6687 - 10.2761i) q^{35} +(186.632 - 92.4921i) q^{36} +(26.2246 + 45.4224i) q^{37} -38.2391 q^{38} +(-9.62125 - 41.0810i) q^{39} +11.6972 q^{40} +(-201.952 + 349.790i) q^{41} +(-9.18193 + 50.5874i) q^{42} +(89.7250 + 155.408i) q^{43} +(74.8130 + 129.580i) q^{44} +(-2.38666 + 37.5417i) q^{45} +(56.1854 - 97.3160i) q^{46} +(46.4100 - 80.3846i) q^{47} +(67.8123 + 289.547i) q^{48} +(234.199 + 250.599i) q^{49} +(32.8726 - 56.9371i) q^{50} +(-68.3912 - 292.018i) q^{51} +62.6421 q^{52} +(214.618 - 371.730i) q^{53} +(73.9170 - 12.4273i) q^{54} -27.0223 q^{55} +(-142.627 - 61.9235i) q^{56} +(356.002 + 107.611i) q^{57} +83.5246 q^{58} +(194.873 + 337.530i) q^{59} +(-53.4606 - 16.1598i) q^{60} +(176.158 - 305.114i) q^{61} +59.3735 q^{62} +(227.843 - 445.123i) q^{63} -405.630 q^{64} +(-5.65655 + 9.79743i) q^{65} +(12.2779 + 52.4244i) q^{66} +(-431.235 - 746.921i) q^{67} +445.282 q^{68} +(-796.942 + 747.886i) q^{69} +(11.0772 - 8.20602i) q^{70} +377.064 q^{71} +(-14.3819 + 226.226i) q^{72} +(183.741 - 318.248i) q^{73} -28.0215 q^{74} +(-466.270 + 437.569i) q^{75} +(-276.082 + 478.188i) q^{76} +(329.491 + 143.053i) q^{77} +(21.5776 + 6.52237i) q^{78} +(154.998 - 268.465i) q^{79} +(39.8684 - 69.0540i) q^{80} +(-723.131 - 92.3169i) q^{81} +(-107.894 - 186.879i) q^{82} +(110.580 + 191.530i) q^{83} +(566.313 + 480.057i) q^{84} +(-40.2087 + 69.6435i) q^{85} -95.8727 q^{86} +(-777.604 - 235.051i) q^{87} -162.836 q^{88} +(712.416 + 1233.94i) q^{89} +(-16.7323 - 11.1328i) q^{90} +(120.839 - 89.5178i) q^{91} +(-811.304 - 1405.22i) q^{92} +(-552.760 - 167.086i) q^{93} +(24.7950 + 42.9461i) q^{94} +(-49.8601 - 86.3602i) q^{95} +(-486.154 - 146.953i) q^{96} +(-288.900 - 500.389i) q^{97} +(-178.509 + 41.4171i) q^{98} +(33.2245 - 522.617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9}+O(q^{10}) $ 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9	\( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9} - 18 q^{10} - 10 q^{11} - 41 q^{12} - 14 q^{13} - 79 q^{14} + 119 q^{15} - 247 q^{16} - 162 q^{17} + 157 q^{18} + 58 q^{19} - 362 q^{20} + 166 q^{21} - 18 q^{22} + 186 q^{23} + 414 q^{24} + 698 q^{25} - 266 q^{26} + 272 q^{27} - 172 q^{28} + 248 q^{29} + 616 q^{30} + 61 q^{31} - 163 q^{32} + 23 q^{33} + 6 q^{34} + 289 q^{35} - 806 q^{36} - 86 q^{37} + 1522 q^{38} - 565 q^{39} + 36 q^{40} - 692 q^{41} + 395 q^{42} - 86 q^{43} - 443 q^{44} - 1483 q^{45} - 270 q^{46} - 1005 q^{47} - 1013 q^{48} - 277 q^{49} + 239 q^{50} - 1719 q^{51} + 670 q^{52} + 258 q^{53} + 910 q^{54} - 870 q^{55} + 714 q^{56} + 566 q^{57} - 474 q^{58} - 1665 q^{59} + 4 q^{60} + 439 q^{61} + 1812 q^{62} + 493 q^{63} + 872 q^{64} - 613 q^{65} + 3073 q^{66} + 295 q^{67} + 2748 q^{68} + 1389 q^{69} - 1044 q^{70} + 636 q^{71} + 981 q^{72} - 338 q^{73} - 2238 q^{74} - 1064 q^{75} + 1006 q^{76} - 2909 q^{77} + 157 q^{78} + 133 q^{79} - 4817 q^{80} + 1325 q^{81} + 6 q^{82} - 1356 q^{83} - 7081 q^{84} + 483 q^{85} + 6686 q^{86} + 2774 q^{87} - 738 q^{88} - 2200 q^{89} + 2665 q^{90} + 1552 q^{91} - 396 q^{92} + 4365 q^{93} - 1191 q^{94} + 3083 q^{95} - 1468 q^{96} - 266 q^{97} + 3601 q^{98} - 5395 q^{99}+O(q^{100}) \) 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9 - 18 * q^10 - 10 * q^11 - 41 * q^12 - 14 * q^13 - 79 * q^14 + 119 * q^15 - 247 * q^16 - 162 * q^17 + 157 * q^18 + 58 * q^19 - 362 * q^20 + 166 * q^21 - 18 * q^22 + 186 * q^23 + 414 * q^24 + 698 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 616 * q^30 + 61 * q^31 - 163 * q^32 + 23 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 + 1522 * q^38 - 565 * q^39 + 36 * q^40 - 692 * q^41 + 395 * q^42 - 86 * q^43 - 443 * q^44 - 1483 * q^45 - 270 * q^46 - 1005 * q^47 - 1013 * q^48 - 277 * q^49 + 239 * q^50 - 1719 * q^51 + 670 * q^52 + 258 * q^53 + 910 * q^54 - 870 * q^55 + 714 * q^56 + 566 * q^57 - 474 * q^58 - 1665 * q^59 + 4 * q^60 + 439 * q^61 + 1812 * q^62 + 493 * q^63 + 872 * q^64 - 613 * q^65 + 3073 * q^66 + 295 * q^67 + 2748 * q^68 + 1389 * q^69 - 1044 * q^70 + 636 * q^71 + 981 * q^72 - 338 * q^73 - 2238 * q^74 - 1064 * q^75 + 1006 * q^76 - 2909 * q^77 + 157 * q^78 + 133 * q^79 - 4817 * q^80 + 1325 * q^81 + 6 * q^82 - 1356 * q^83 - 7081 * q^84 + 483 * q^85 + 6686 * q^86 + 2774 * q^87 - 738 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 + 4365 * q^93 - 1191 * q^94 + 3083 * q^95 - 1468 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.267129	+	0.462682i	−0.0944445	+	0.163583i	−0.909377	−	0.415974i	$-0.863441\pi$
$2$	−0.267129	+	0.462682i	−0.0944445	+	0.163583i	0.814932	+	0.579556i	$0.196774\pi$
$3$	3.78900	−	3.55577i	0.729193	−	0.684308i
$3$	3.78900	−	3.55577i	0.729193	−	0.684308i
$4$	3.85728	+	6.68101i	0.482160	+	0.835126i
$5$	−1.39324			−0.124615			−0.0623077	−	0.998057i	$-0.519846\pi$
$5$	−1.39324			−0.124615			−0.0623077	+	0.998057i	$0.519846\pi$
$6$	0.633036	+	2.70295i	0.0430726	+	0.183912i
$7$	16.9882	+	7.37568i	0.917277	+	0.398249i
$7$	16.9882	+	7.37568i	0.917277	+	0.398249i
$8$	−8.39564			−0.371039
$9$	1.71302	−	26.9456i	0.0634453	−	0.997985i
$10$	0.372176	−	0.644627i	0.0117692	−	0.0203849i
$11$	19.3952			0.531626			0.265813	−	0.964025i	$-0.414360\pi$
$11$	19.3952			0.531626			0.265813	+	0.964025i	$0.414360\pi$
$12$	38.3714	+	11.5987i	0.923072	+	0.279022i
$13$	4.05999	−	7.03211i	0.0866184	−	0.150027i	−0.819461	−	0.573134i	$-0.805727\pi$
$13$	4.05999	−	7.03211i	0.0866184	−	0.150027i	0.906080	+	0.423107i	$0.139061\pi$
$14$	−7.95064	+	5.88988i	−0.151778	+	0.112438i
$15$	−5.27899	+	4.95404i	−0.0908686	+	0.0852752i
$16$	−28.6155	+	49.5636i	−0.447118	+	0.774431i
$17$	28.8598	−	49.9867i	0.411737	−	0.713150i	−0.583342	−	0.812226i	$-0.698255\pi$
$17$	28.8598	−	49.9867i	0.411737	−	0.713150i	0.995080	+	0.0990761i	$0.0315887\pi$
$18$	12.0096	+	7.99055i	0.157261	+	0.104633i
$19$	35.7871	+	61.9851i	0.432112	+	0.748440i	0.997055	−	0.0766902i	$-0.0244352\pi$
$19$	35.7871	+	61.9851i	0.432112	+	0.748440i	−0.564943	+	0.825130i	$0.691102\pi$
$20$	−5.37413	−	9.30826i	−0.0600846	−	0.104070i
$21$	90.5945	−	32.4597i	0.941397	−	0.337300i
$22$	−5.18104	+	8.97382i	−0.0502092	+	0.0869648i
$23$	−210.330			−1.90682			−0.953411	−	0.301673i	$-0.902455\pi$
$23$	−210.330			−1.90682			−0.953411	+	0.301673i	$0.902455\pi$
$24$	−31.8111	+	29.8530i	−0.270559	+	0.253905i
$25$	−123.059			−0.984471
$26$	2.16909	+	3.75697i	0.0163613	+	0.0283385i
$27$	−89.3217	−	108.188i	−0.636665	−	0.771140i
$28$	16.2514	+	141.949i	0.109687	+	0.958062i
$29$	−78.1687	−	135.392i	−0.500537	−	0.866955i	−1.00000		0.000619685i	$-0.999803\pi$
$29$	−78.1687	−	135.392i	−0.500537	−	0.866955i	0.499463	−	0.866335i	$-0.333531\pi$
$30$	−0.881972	−	3.76586i	−0.00536751	−	0.0229183i
$31$	−55.5662	−	96.2435i	−0.321935	−	0.557608i	0.658952	−	0.752185i	$-0.271000\pi$
$31$	−55.5662	−	96.2435i	−0.321935	−	0.557608i	−0.980887	+	0.194577i	$0.937667\pi$
$32$	−48.8707	−	84.6465i	−0.269975	−	0.467610i
$33$	73.4886	−	68.9650i	0.387658	−	0.363796i
$34$	15.4186	+	26.7058i	0.0777727	+	0.134706i
$35$	−23.6687	−	10.2761i	−0.114307	−	0.0496279i
$36$	186.632	−	92.4921i	0.864035	−	0.428204i
$37$	26.2246	+	45.4224i	0.116522	+	0.201821i	0.918387	−	0.395683i	$-0.129492\pi$
$37$	26.2246	+	45.4224i	0.116522	+	0.201821i	−0.801865	+	0.597505i	$0.796159\pi$
$38$	−38.2391			−0.163242
$39$	−9.62125	−	41.0810i	−0.0395034	−	0.168673i
$40$	11.6972			0.0462371
$41$	−201.952	+	349.790i	−0.769257	+	1.33239i	0.168709	+	0.985666i	$0.446040\pi$
$41$	−201.952	+	349.790i	−0.769257	+	1.33239i	−0.937966	+	0.346726i	$0.887293\pi$
$42$	−9.18193	+	50.5874i	−0.0337334	+	0.185852i
$43$	89.7250	+	155.408i	0.318208	+	0.551152i	0.980114	−	0.198435i	$-0.0635857\pi$
$43$	89.7250	+	155.408i	0.318208	+	0.551152i	−0.661906	+	0.749586i	$0.730252\pi$
$44$	74.8130	+	129.580i	0.256329	+	0.443975i
$45$	−2.38666	+	37.5417i	−0.00790626	+	0.124364i
$46$	56.1854	−	97.3160i	0.180089	−	0.311923i
$47$	46.4100	−	80.3846i	0.144034	−	0.249474i	−0.784978	−	0.619524i	$-0.787326\pi$
$47$	46.4100	−	80.3846i	0.144034	−	0.249474i	0.929012	+	0.370049i	$0.120659\pi$
$48$	67.8123	+	289.547i	0.203914	+	0.870676i
$49$	234.199	+	250.599i	0.682795	+	0.730610i
$50$	32.8726	−	56.9371i	0.0929779	−	0.161042i
$51$	−68.3912	−	292.018i	−0.187778	−	0.801780i
$52$	62.6421			0.167056
$53$	214.618	−	371.730i	0.556229	−	0.963416i	−0.441578	−	0.897223i	$-0.645581\pi$
$53$	214.618	−	371.730i	0.556229	−	0.963416i	0.997807	−	0.0661934i	$-0.0210854\pi$
$54$	73.9170	−	12.4273i	0.186275	−	0.0313175i
$55$	−27.0223			−0.0662488
$56$	−142.627	−	61.9235i	−0.340345	−	0.147766i
$57$	356.002	+	107.611i	0.827256	+	0.250060i
$58$	83.5246			0.189092
$59$	194.873	+	337.530i	0.430005	+	0.744790i	0.996873	−	0.0790180i	$-0.0251785\pi$
$59$	194.873	+	337.530i	0.430005	+	0.744790i	−0.566868	+	0.823809i	$0.691845\pi$
$60$	−53.4606	−	16.1598i	−0.115029	−	0.0347704i
$61$	176.158	−	305.114i	0.369749	−	0.640424i	−0.619777	−	0.784778i	$-0.712777\pi$
$61$	176.158	−	305.114i	0.369749	−	0.640424i	0.989526	+	0.144354i	$0.0461104\pi$
$62$	59.3735			0.121620
$63$	227.843	−	445.123i	0.455644	−	0.890162i
$64$	−405.630			−0.792245
$65$	−5.65655	+	9.79743i	−0.0107940	+	0.0186957i
$66$	12.2779	+	52.4244i	0.0228985	+	0.0977727i
$67$	−431.235	−	746.921i	−0.786325	−	1.36195i	−0.928204	−	0.372071i	$-0.878648\pi$
$67$	−431.235	−	746.921i	−0.786325	−	1.36195i	0.141879	−	0.989884i	$-0.454686\pi$
$68$	445.282			0.794094
$69$	−796.942	+	747.886i	−1.39044	+	1.30485i
$70$	11.0772	−	8.20602i	0.0189139	−	0.0140115i
$71$	377.064			0.630272			0.315136	−	0.949047i	$-0.397950\pi$
$71$	377.064			0.630272			0.315136	+	0.949047i	$0.397950\pi$
$72$	−14.3819	+	226.226i	−0.0235407	+	0.370291i
$73$	183.741	−	318.248i	0.294592	−	0.510248i	−0.680298	−	0.732936i	$-0.738150\pi$
$73$	183.741	−	318.248i	0.294592	−	0.510248i	0.974890	+	0.222688i	$0.0714830\pi$
$74$	−28.0215			−0.0440193
$75$	−466.270	+	437.569i	−0.717870	+	0.673681i
$76$	−276.082	+	478.188i	−0.416694	+	0.721736i
$77$	329.491	+	143.053i	0.487649	+	0.211720i
$78$	21.5776	+	6.52237i	0.0313228	+	0.00946812i
$79$	154.998	−	268.465i	0.220742	−	0.382337i	−0.734291	−	0.678835i	$-0.762485\pi$
$79$	154.998	−	268.465i	0.220742	−	0.382337i	0.955034	+	0.296497i	$0.0958186\pi$
$80$	39.8684	−	69.0540i	0.0557177	−	0.0965060i
$81$	−723.131	−	92.3169i	−0.991949	−	0.126635i
$82$	−107.894	−	186.879i	−0.145304	−	0.251674i
$83$	110.580	+	191.530i	0.146237	+	0.253291i	0.929834	−	0.367980i	$-0.119950\pi$
$83$	110.580	+	191.530i	0.146237	+	0.253291i	−0.783597	+	0.621270i	$0.786617\pi$
$84$	566.313	+	480.057i	0.735592	+	0.623553i
$85$	−40.2087	+	69.6435i	−0.0513088	+	0.0888694i
$86$	−95.8727			−0.120212
$87$	−777.604	−	235.051i	−0.958252	−	0.289656i
$88$	−162.836			−0.197254
$89$	712.416	+	1233.94i	0.848494	+	1.46963i	0.882552	+	0.470215i	$0.155824\pi$
$89$	712.416	+	1233.94i	0.848494	+	1.46963i	−0.0340580	+	0.999420i	$0.510843\pi$
$90$	−16.7323	−	11.1328i	−0.0195971	−	0.0130388i
$91$	120.839	−	89.5178i	0.139201	−	0.103121i
$92$	−811.304	−	1405.22i	−0.919395	−	1.59244i
$93$	−552.760	−	167.086i	−0.616328	−	0.186301i
$94$	24.7950	+	42.9461i	0.0272064	+	0.0471229i
$95$	−49.8601	−	86.3602i	−0.0538478	−	0.0932670i
$96$	−486.154	−	146.953i	−0.516853	−	0.156232i
$97$	−288.900	−	500.389i	−0.302406	−	0.523782i	0.674275	−	0.738481i	$-0.264456\pi$
$97$	−288.900	−	500.389i	−0.302406	−	0.523782i	−0.976680	+	0.214699i	$0.931123\pi$
$98$	−178.509	+	41.4171i	−0.184001	+	0.0426914i
$99$	33.2245	−	522.617i	0.0337292	−	0.530555i
$100$	−474.673	−	822.158i	−0.474673	−	0.822158i
$101$	−860.836			−0.848083			−0.424042	−	0.905643i	$-0.639389\pi$
$101$	−860.836			−0.848083			−0.424042	+	0.905643i	$0.639389\pi$
$102$	153.381	+	46.3633i	0.148892	+	0.0450064i
$103$	1516.22			1.45046			0.725229	−	0.688508i	$-0.241734\pi$
$103$	1516.22			1.45046			0.725229	+	0.688508i	$0.241734\pi$
$104$	−34.0862	+	59.0391i	−0.0321388	+	0.0556660i
$105$	−126.220	+	45.2242i	−0.117313	+	0.0420327i
$106$	114.662	+	198.600i	0.105065	+	0.181979i
$107$	636.666	+	1102.74i	0.575223	+	0.996315i	0.996017	+	0.0891594i	$0.0284180\pi$
$107$	636.666	+	1102.74i	0.575223	+	0.996315i	−0.420794	+	0.907156i	$0.638249\pi$
$108$	378.266	−	1014.07i	0.337025	−	0.903509i
$109$	−148.428	+	257.085i	−0.130430	+	0.225911i	−0.923842	−	0.382773i	$-0.874969\pi$
$109$	−148.428	+	257.085i	−0.130430	+	0.225911i	0.793413	+	0.608684i	$0.208302\pi$
$110$	7.21844	−	12.5027i	0.00625683	−	0.0108371i
$111$	260.877	+	78.8567i	0.223075	+	0.0674301i
$112$	−851.692	+	630.938i	−0.718548	+	0.532304i
$113$	−834.841	+	1445.99i	−0.695002	+	1.20378i	0.275178	+	0.961393i	$0.411263\pi$
$113$	−834.841	+	1445.99i	−0.695002	+	1.20378i	−0.970180	+	0.242386i	$0.922070\pi$
$114$	−144.888	+	135.970i	−0.119035	+	0.111708i
$115$	293.041			0.237619
$116$	603.038	−	1044.49i	0.482678	−	0.836023i
$117$	−182.530	−	121.445i	−0.144230	−	0.0959624i
$118$	−208.225			−0.162446
$119$	858.963	−	636.324i	0.661689	−	0.490183i
$120$	44.3205	−	41.5924i	0.0337158	−	0.0316404i
$121$	−954.824			−0.717374
$122$	94.1138	+	163.010i	0.0698415	+	0.120969i
$123$	478.579	+	2043.45i	0.350830	+	1.49798i
$124$	428.669	−	742.477i	0.310449	−	0.537713i
$125$	345.606			0.247295
$126$	145.087	+	224.324i	0.102582	+	0.158606i
$127$	1419.40			0.991745			0.495873	−	0.868395i	$-0.334848\pi$
$127$	1419.40			0.991745			0.495873	+	0.868395i	$0.334848\pi$
$128$	499.321	−	864.849i	0.344798	−	0.597208i
$129$	892.564	+	269.800i	0.609193	+	0.184144i
$130$	−3.02206	−	5.23436i	−0.00203886	−	0.00353141i
$131$	−1257.63			−0.838779			−0.419389	−	0.907806i	$-0.637756\pi$
$131$	−1257.63			−0.838779			−0.419389	+	0.907806i	$0.637756\pi$
$132$	744.222	+	224.960i	0.490729	+	0.148336i
$133$	150.777	+	1316.97i	0.0983010	+	0.858615i
$134$	460.782			0.297056
$135$	124.447	+	150.732i	0.0793383	+	0.0960959i
$136$	−242.297	+	419.671i	−0.152770	+	0.264606i
$137$	2134.03			1.33082			0.665410	−	0.746478i	$-0.268257\pi$
$137$	2134.03			1.33082			0.665410	+	0.746478i	$0.268257\pi$
$138$	−133.147	−	568.513i	−0.0821319	−	0.350688i
$139$	1103.28	−	1910.93i	0.673229	−	1.16607i	−0.303754	−	0.952751i	$-0.598240\pi$
$139$	1103.28	−	1910.93i	0.673229	−	1.16607i	0.976983	−	0.213317i	$-0.0684266\pi$
$140$	−22.6421	−	197.769i	−0.0136686	−	0.119389i
$141$	−109.981	−	469.600i	−0.0656886	−	0.280479i
$142$	−100.725	+	174.461i	−0.0595257	+	0.103102i
$143$	78.7445	−	136.389i	0.0460486	−	0.0797585i
$144$	1286.50	+	855.967i	0.744503	+	0.495351i
$145$	108.908	+	188.634i	0.0623745	+	0.108036i
$146$	98.1650	+	170.027i	0.0556452	+	0.0963802i
$147$	1778.45	+	116.763i	0.997852	+	0.0655132i
$148$	−202.312	+	350.414i	−0.112364	+	0.194621i
$149$	−1765.77			−0.970854			−0.485427	−	0.874277i	$-0.661336\pi$
$149$	−1765.77			−0.970854			−0.485427	+	0.874277i	$0.661336\pi$
$150$	−77.9007	−	332.622i	−0.0424038	−	0.181056i
$151$	−2588.65			−1.39511			−0.697555	−	0.716532i	$-0.745729\pi$
$151$	−2588.65			−1.39511			−0.697555	+	0.716532i	$0.745729\pi$
$152$	−300.456	−	520.405i	−0.160330	−	0.277700i
$153$	−1297.48	−	863.274i	−0.685591	−	0.456154i
$154$	−154.205	+	114.236i	−0.0806894	+	0.0597751i
$155$	77.4172	+	134.090i	0.0401180	+	0.0694865i
$156$	237.351	−	222.741i	0.121816	−	0.114318i
$157$	1199.76	+	2078.05i	0.609882	+	1.05635i	0.991259	+	0.131927i	$0.0421166\pi$
$157$	1199.76	+	2078.05i	0.609882	+	1.05635i	−0.381377	+	0.924420i	$0.624550\pi$
$158$	82.8091	+	143.430i	0.0416958	+	0.0722193i
$159$	−508.597	−	2171.62i	−0.253675	−	1.08315i
$160$	68.0887	+	117.933i	0.0336430	+	0.0582714i
$161$	−3573.14	−	1551.33i	−1.74909	−	0.759390i
$162$	235.883	−	309.919i	0.114399	−	0.150306i
$163$	1023.61	+	1772.94i	0.491872	+	0.851947i	0.999956	−	0.00936052i	$-0.00297959\pi$
$163$	1023.61	+	1772.94i	0.491872	+	0.851947i	−0.508085	+	0.861307i	$0.669646\pi$
$164$	−3115.94			−1.48362
$165$	−102.387	+	96.0849i	−0.0483081	+	0.0453345i
$166$	−118.156			−0.0552452
$167$	1270.89	−	2201.24i	0.588887	−	1.01998i	−0.405491	−	0.914099i	$-0.632900\pi$
$167$	1270.89	−	2201.24i	0.588887	−	1.01998i	0.994379	−	0.105884i	$-0.0337672\pi$
$168$	−760.599	+	272.520i	−0.349295	+	0.125151i
$169$	1065.53	+	1845.56i	0.484995	+	0.840035i
$170$	−21.4819	−	37.2077i	−0.00969167	−	0.0167865i
$171$	1731.53	−	858.123i	0.774347	−	0.383756i
$172$	−692.190	+	1198.91i	−0.306854	+	0.531487i
$173$	−2151.40	+	3726.33i	−0.945479	+	1.63762i	−0.190690	+	0.981650i	$0.561073\pi$
$173$	−2151.40	+	3726.33i	−0.945479	+	1.63762i	−0.754789	+	0.655967i	$0.772261\pi$
$174$	316.475	−	296.994i	0.137884	−	0.129397i
$175$	−2090.55	−	907.642i	−0.903033	−	0.392065i
$176$	−555.006	+	961.298i	−0.237700	+	0.411708i
$177$	1938.55	+	585.977i	0.823223	+	0.248840i
$178$	−761.229			−0.320542
$179$	783.675	−	1357.37i	0.327233	−	0.566783i	−0.654729	−	0.755864i	$-0.727217\pi$
$179$	783.675	−	1357.37i	0.327233	−	0.566783i	0.981962	+	0.189080i	$0.0605506\pi$
$180$	−260.023	+	128.864i	−0.107672	+	0.0533608i
$181$	642.368			0.263795			0.131897	−	0.991263i	$-0.457893\pi$
$181$	642.368			0.263795			0.131897	+	0.991263i	$0.457893\pi$
$182$	9.13872	+	79.8226i	0.00372202	+	0.0325101i
$183$	−417.454	−	1782.45i	−0.168629	−	0.720015i
$184$	1765.86			0.707505
$185$	−36.5372	−	63.2844i	−0.0145204	−	0.0251501i
$186$	224.966	−	211.118i	0.0886845	−	0.0832255i
$187$	559.744	−	969.504i	0.218890	−	0.379129i
$188$	716.067			0.277790
$189$	−719.456	−	2496.73i	−0.276893	−	0.960901i
$190$	53.2764			0.0203425
$191$	265.514	−	459.884i	0.100586	−	0.174220i	−0.811340	−	0.584574i	$-0.801262\pi$
$191$	265.514	−	459.884i	0.100586	−	0.174220i	0.911926	+	0.410354i	$0.134595\pi$
$192$	−1536.93	+	1442.32i	−0.577700	+	0.542140i
$193$	−708.896	−	1227.84i	−0.264391	−	0.457939i	0.703013	−	0.711177i	$-0.251838\pi$
$193$	−708.896	−	1227.84i	−0.264391	−	0.457939i	−0.967404	+	0.253238i	$0.918504\pi$
$194$	308.695			0.114242
$195$	13.4047	+	57.2358i	0.00492273	+	0.0210192i
$196$	−770.884	+	2531.32i	−0.280934	+	0.922492i
$197$	−4070.58			−1.47217			−0.736084	−	0.676891i	$-0.763327\pi$
$197$	−4070.58			−1.47217			−0.736084	+	0.676891i	$0.763327\pi$
$198$	232.930	+	154.979i	0.0836041	+	0.0556255i
$199$	−154.635	+	267.836i	−0.0550844	+	0.0954090i	−0.892253	−	0.451536i	$-0.850876\pi$
$199$	−154.635	+	267.836i	−0.0550844	+	0.0954090i	0.837168	+	0.546945i	$0.184209\pi$
$200$	1033.16			0.365277
$201$	−4289.83	−	1296.71i	−1.50538	−	0.455040i
$202$	229.955	−	398.293i	0.0800968	−	0.138732i
$203$	−329.338	−	2876.62i	−0.113867	−	0.994576i
$204$	1687.17	−	1583.32i	0.579048	−	0.543405i
$205$	281.367	−	487.342i	0.0958612	−	0.166036i
$206$	−405.026	+	701.525i	−0.136988	+	0.237270i
$207$	−360.301	+	5667.48i	−0.120979	+	1.90298i
$208$	232.358	+	402.455i	0.0774572	+	0.134160i
$209$	694.100	+	1202.22i	0.229722	+	0.397890i
$210$	12.7927	−	70.4804i	0.00420370	−	0.0231601i
$211$	−1225.67	+	2122.93i	−0.399899	+	0.692646i	−0.993713	−	0.111957i	$-0.964288\pi$
$211$	−1225.67	+	2122.93i	−0.399899	+	0.692646i	0.593814	+	0.804602i	$0.297622\pi$
$212$	3311.38			1.07277
$213$	1428.70	−	1340.75i	0.459590	−	0.431300i
$214$	−680.289			−0.217307
$215$	−125.009	−	216.521i	−0.0396536	−	0.0686820i
$216$	749.913	+	908.308i	0.236227	+	0.286123i
$217$	−234.110	−	2044.84i	−0.0732369	−	0.639691i
$218$	−79.2990	−	137.350i	−0.0246367	−	0.0426721i
$219$	−435.423	−	1859.18i	−0.134352	−	0.573661i
$220$	−104.233	−	180.536i	−0.0319425	−	0.0553261i
$221$	−234.341	−	405.891i	−0.0713280	−	0.123544i
$222$	−106.173	+	99.6379i	−0.0320986	+	0.0301228i
$223$	−2312.36	−	4005.13i	−0.694383	−	1.20271i	−0.970388	−	0.241550i	$-0.922344\pi$
$223$	−2312.36	−	4005.13i	−0.694383	−	1.20271i	0.276005	−	0.961156i	$-0.410989\pi$
$224$	−205.901	−	1798.45i	−0.0614165	−	0.536446i
$225$	−210.803	+	3315.90i	−0.0624601	+	0.982488i
$226$	−446.021	−	772.531i	−0.131278	−	0.227381i
$227$	5235.73			1.53087			0.765436	−	0.643512i	$-0.222523\pi$
$227$	5235.73			1.53087			0.765436	+	0.643512i	$0.222523\pi$
$228$	654.252	+	2793.54i	0.190039	+	0.811432i
$229$	1249.35			0.360522			0.180261	−	0.983619i	$-0.442306\pi$
$229$	1249.35			0.360522			0.180261	+	0.983619i	$0.442306\pi$
$230$	−78.2799	+	135.585i	−0.0224418	+	0.0388704i
$231$	1757.10	−	629.564i	0.500471	−	0.179317i
$232$	656.277	+	1136.70i	0.185718	+	0.321674i
$233$	1274.52	+	2207.54i	0.358355	+	0.620689i	0.987686	−	0.156448i	$-0.0500044\pi$
$233$	1274.52	+	2207.54i	0.358355	+	0.620689i	−0.629331	+	0.777137i	$0.716671\pi$
$234$	104.949	−	52.0115i	0.0293195	−	0.0145303i
$235$	−64.6604	+	111.995i	−0.0179489	+	0.0310883i
$236$	−1503.36	+	2603.90i	−0.414663	+	0.718217i
$237$	−367.310	−	1568.35i	−0.100672	−	0.429854i
$238$	64.9613	+	567.407i	0.0176925	+	0.154536i
$239$	565.969	−	980.288i	0.153178	−	0.265312i	−0.779216	−	0.626755i	$-0.784383\pi$
$239$	565.969	−	980.288i	0.153178	−	0.265312i	0.932394	+	0.361443i	$0.117716\pi$
$240$	−94.4790	−	403.408i	−0.0254108	−	0.108500i
$241$	6320.93			1.68949			0.844745	−	0.535170i	$-0.179752\pi$
$241$	6320.93			1.68949			0.844745	+	0.535170i	$0.179752\pi$
$242$	255.062	−	441.780i	0.0677520	−	0.117350i
$243$	−3068.20	+	2221.50i	−0.809980	+	0.586457i
$244$	2717.96			0.713113
$245$	−326.296	−	349.145i	−0.0850868	−	0.0910451i
$246$	−1073.31	−	324.435i	−0.278177	−	0.0840863i
$247$	581.181			0.149715
$248$	466.514	+	808.026i	0.119450	+	0.206894i
$249$	1100.02	+	332.510i	0.279964	+	0.0846263i
$250$	−92.3215	+	159.906i	−0.0233557	+	0.0404533i
$251$	1739.84			0.437521			0.218761	−	0.975779i	$-0.429799\pi$
$251$	1739.84			0.437521			0.218761	+	0.975779i	$0.429799\pi$
$252$	3852.73	−	194.742i	0.963091	−	0.0486810i
$253$	−4079.41			−1.01372
$254$	−379.164	+	656.732i	−0.0936649	+	0.162232i
$255$	95.2855	+	406.852i	0.0234000	+	0.0999140i
$256$	−1355.75	−	2348.23i	−0.330994	−	0.573299i
$257$	7330.49			1.77924			0.889618	−	0.456706i	$-0.150971\pi$
$257$	7330.49			1.77924			0.889618	+	0.456706i	$0.150971\pi$
$258$	−363.262	+	340.901i	−0.0876577	+	0.0822619i
$259$	110.489	+	965.070i	0.0265075	+	0.231531i
$260$	−87.2756			−0.0208177
$261$	−3782.13	+	1874.37i	−0.896965	+	0.444524i
$262$	335.951	−	581.884i	0.0792180	−	0.137210i
$263$	4033.27			0.945636			0.472818	−	0.881160i	$-0.343237\pi$
$263$	4033.27			0.945636			0.472818	+	0.881160i	$0.343237\pi$
$264$	−616.984	+	579.006i	−0.143836	+	0.134982i
$265$	−299.015	+	517.910i	−0.0693146	+	0.120056i
$266$	−649.615	−	282.040i	−0.149738	−	0.0650111i
$267$	7086.95	+	2142.21i	1.62440	+	0.491016i
$268$	3326.79	−	5762.18i	0.758270	−	1.31336i
$269$	−2562.84	+	4438.97i	−0.580890	+	1.00613i	0.414485	+	0.910056i	$0.363962\pi$
$269$	−2562.84	+	4438.97i	−0.580890	+	1.00613i	−0.995374	+	0.0960740i	$0.969371\pi$
$270$	−102.984	+	17.3142i	−0.0232127	+	0.00390264i
$271$	−3560.18	−	6166.40i	−0.798027	−	1.38222i	−0.920899	−	0.389800i	$-0.872544\pi$
$271$	−3560.18	−	6166.40i	−0.798027	−	1.38222i	0.122873	−	0.992422i	$-0.460789\pi$
$272$	1651.68	+	2860.79i	0.368190	+	0.637725i
$273$	139.552	−	768.857i	0.0309381	−	0.170452i
$274$	−570.062	+	987.376i	−0.125689	+	0.217699i
$275$	−2386.76			−0.523370
$276$	−8070.67	−	2439.57i	−1.76013	−	0.532046i
$277$	−867.110			−0.188085			−0.0940426	−	0.995568i	$-0.529979\pi$
$277$	−867.110			−0.188085			−0.0940426	+	0.995568i	$0.529979\pi$
$278$	589.436	+	1020.93i	0.127166	+	0.220257i
$279$	−2688.53	+	1332.40i	−0.576910	+	0.285909i
$280$	198.714	+	86.2745i	0.0424122	+	0.0184139i
$281$	−3122.11	−	5407.66i	−0.662811	−	1.14802i	−0.979874	−	0.199617i	$-0.936030\pi$
$281$	−3122.11	−	5407.66i	−0.662811	−	1.14802i	0.317063	−	0.948404i	$-0.397303\pi$
$282$	246.655	+	74.5577i	0.0520854	+	0.0157441i
$283$	−1463.30	−	2534.50i	−0.307364	−	0.532370i	0.670421	−	0.741981i	$-0.266114\pi$
$283$	−1463.30	−	2534.50i	−0.307364	−	0.532370i	−0.977785	+	0.209611i	$0.932780\pi$
$284$	1454.44	+	2519.17i	0.303892	+	0.526357i
$285$	−495.997	−	149.928i	−0.103089	−	0.0311612i
$286$	42.0699	+	72.8673i	0.00869807	+	0.0150655i
$287$	−6010.74	+	4452.78i	−1.23625	+	0.915817i
$288$	−2364.57	+	1171.85i	−0.483797	+	0.239763i
$289$	790.720	+	1369.57i	0.160944	+	0.278764i
$290$	−116.370			−0.0235637
$291$	−2873.91	−	868.713i	−0.578940	−	0.175000i
$292$	2834.96			0.568162
$293$	2992.94	−	5183.92i	0.596755	−	1.03361i	−0.396542	−	0.918017i	$-0.629790\pi$
$293$	2992.94	−	5183.92i	0.596755	−	1.03361i	0.993297	−	0.115593i	$-0.0368769\pi$
$294$	−529.101	+	791.666i	−0.104958	+	0.157044i
$295$	−271.505	−	470.261i	−0.0535852	−	0.0928123i
$296$	−220.173	−	381.350i	−0.0432340	−	0.0748836i
$297$	−1732.42	−	2098.33i	−0.338468	−	0.409958i
$298$	471.688	−	816.987i	0.0916918	−	0.158815i
$299$	−853.939	+	1479.07i	−0.165166	+	0.286076i
$300$	−4721.94	−	1427.33i	−0.908737	−	0.274689i
$301$	378.027	+	3301.89i	0.0723890	+	0.632285i
$302$	691.505	−	1197.72i	0.131760	−	0.228216i
$303$	−3261.71	+	3060.93i	−0.618417	+	0.580350i
$304$	−4096.27			−0.772820
$305$	−245.430	+	425.098i	−0.0460764	+	0.0798066i
$306$	746.017	−	369.716i	0.139369	−	0.0690695i
$307$	−3568.44			−0.663394			−0.331697	−	0.943386i	$-0.607621\pi$
$307$	−3568.44			−0.663394			−0.331697	+	0.943386i	$0.607621\pi$
$308$	315.200	+	2753.13i	0.0583123	+	0.509331i
$309$	5744.94	−	5391.31i	1.05766	−	0.992560i
$310$	−82.7216			−0.0151557
$311$	−2921.58	−	5060.33i	−0.532694	−	0.922653i	−0.999271	−	0.0381722i	$-0.987846\pi$
$311$	−2921.58	−	5060.33i	−0.532694	−	0.922653i	0.466578	−	0.884480i	$-0.345487\pi$
$312$	80.7766	+	344.902i	0.0146573	+	0.0625840i
$313$	1950.29	−	3378.00i	0.352194	−	0.610018i	−0.634440	−	0.772972i	$-0.718769\pi$
$313$	1950.29	−	3378.00i	0.352194	−	0.610018i	0.986634	+	0.162955i	$0.0521024\pi$
$314$	−1281.97			−0.230400
$315$	−317.441	+	620.164i	−0.0567802	+	0.110928i
$316$	2391.49			0.425733
$317$	−1269.40	+	2198.66i	−0.224910	+	0.389555i	−0.956292	−	0.292412i	$-0.905542\pi$
$317$	−1269.40	+	2198.66i	−0.224910	+	0.389555i	0.731383	+	0.681967i	$0.238875\pi$
$318$	1140.63	+	344.785i	0.201142	+	0.0608005i
$319$	−1516.10	−	2625.96i	−0.266098	−	0.460896i
$320$	565.140			0.0987259
$321$	6333.41	+	1914.44i	1.10124	+	0.332877i
$322$	1672.26	−	1238.82i	0.289415	−	0.214400i
$323$	4131.24			0.711667
$324$	−2172.55	−	5187.34i	−0.372523	−	0.889462i
$325$	−499.618	+	865.363i	−0.0852733	+	0.147698i
$326$	−1093.74			−0.185818
$327$	351.741	+	1501.87i	0.0594842	+	0.253987i
$328$	1695.51	−	2936.72i	0.285424	−	0.494369i
$329$	1381.31	−	1023.28i	0.231472	−	0.171476i
$330$	−17.1061	−	73.0398i	−0.00285351	−	0.0121840i
$331$	−5220.61	+	9042.37i	−0.866921	+	1.50155i	−0.00179387	+	0.999998i	$0.500571\pi$
$331$	−5220.61	+	9042.37i	−0.866921	+	1.50155i	−0.865127	+	0.501553i	$0.832762\pi$
$332$	−853.075	+	1477.57i	−0.141020	+	0.244253i
$333$	1268.86	−	628.829i	0.208808	−	0.103482i
$334$	678.982	+	1176.03i	0.111234	+	0.192663i
$335$	600.815	+	1040.64i	0.0979881	+	0.169720i
$336$	−983.591	+	5419.04i	−0.159700	+	0.879860i
$337$	−2095.75	+	3629.94i	−0.338762	+	0.586753i	−0.984200	−	0.177060i	$-0.943341\pi$
$337$	−2095.75	+	3629.94i	−0.338762	+	0.586753i	0.645438	+	0.763812i	$0.276675\pi$
$338$	−1138.54			−0.183220
$339$	1978.38	+	8447.35i	0.316965	+	1.35338i
$340$	−620.386			−0.0989563
$341$	−1077.72	−	1866.67i	−0.171149	−	0.296439i
$342$	−65.5046	+	1030.38i	−0.0103570	+	0.162913i
$343$	2130.28	+	5984.61i	0.335348	+	0.942094i
$344$	−753.299	−	1304.75i	−0.118067	−	0.204499i
$345$	1110.33	−	1041.99i	0.173270	−	0.162605i
$346$	−1149.40	−	1990.83i	−0.178591	−	0.309328i
$347$	−954.259	−	1652.83i	−0.147629	−	0.255701i	0.782722	−	0.622372i	$-0.213831\pi$
$347$	−954.259	−	1652.83i	−0.147629	−	0.255701i	−0.930351	+	0.366671i	$0.880498\pi$
$348$	−1429.06	−	6101.84i	−0.220131	−	0.939922i
$349$	130.338	+	225.753i	0.0199910	+	0.0346254i	0.875848	−	0.482587i	$-0.160303\pi$
$349$	130.338	+	225.753i	0.0199910	+	0.0346254i	−0.855857	+	0.517213i	$0.826970\pi$
$350$	978.397	−	724.801i	0.149421	−	0.110692i
$351$	−1123.43	+	188.878i	−0.170839	+	0.0287223i
$352$	−947.859	−	1641.74i	−0.143526	−	0.248594i
$353$	5751.12			0.867143			0.433571	−	0.901119i	$-0.357253\pi$
$353$	5751.12			0.867143			0.433571	+	0.901119i	$0.357253\pi$
$354$	−788.965	+	740.400i	−0.118455	+	0.111163i
$355$	−525.342			−0.0785415
$356$	−5495.98	+	9519.32i	−0.818221	+	1.41720i
$357$	991.988	−	5465.30i	0.147063	−	0.810237i
$358$	418.685	+	725.184i	0.0618106	+	0.107059i
$359$	−2533.53	−	4388.20i	−0.372464	−	0.645126i	0.617480	−	0.786586i	$-0.288153\pi$
$359$	−2533.53	−	4388.20i	−0.372464	−	0.645126i	−0.989944	+	0.141461i	$0.954820\pi$
$360$	20.0375	−	315.187i	0.00293353	−	0.0461439i
$361$	868.066	−	1503.53i	0.126559	−	0.219206i
$362$	−171.595	+	297.212i	−0.0249139	+	0.0431522i
$363$	−3617.83	+	3395.13i	−0.523104	+	0.490905i
$364$	1064.18	+	462.028i	0.153236	+	0.0665298i
$365$	−255.995	+	443.396i	−0.0367107	+	0.0635847i
$366$	936.222	+	282.997i	0.133708	+	0.0404167i
$367$	−584.287			−0.0831050			−0.0415525	−	0.999136i	$-0.513230\pi$
$367$	−584.287			−0.0831050			−0.0415525	+	0.999136i	$0.513230\pi$
$368$	6018.72	−	10424.7i	0.852575	−	1.47670i
$369$	9079.36	+	6040.91i	1.28090	+	0.852241i
$370$	39.0407			0.00548548
$371$	6387.74	−	4732.07i	0.893895	−	0.662202i
$372$	−1015.85	−	4337.49i	−0.141584	−	0.604539i
$373$	3082.79			0.427937			0.213969	−	0.976841i	$-0.431361\pi$
$373$	3082.79			0.427937			0.213969	+	0.976841i	$0.431361\pi$
$374$	299.048	+	517.966i	0.0413460	+	0.0716133i
$375$	1309.50	−	1228.89i	0.180326	−	0.169226i
$376$	−389.642	+	674.880i	−0.0534422	+	0.0925646i
$377$	−1269.46			−0.173423
$378$	1347.38	+	334.070i	0.183338	+	0.0454569i
$379$	2231.91			0.302495			0.151247	−	0.988496i	$-0.451671\pi$
$379$	2231.91			0.302495			0.151247	+	0.988496i	$0.451671\pi$
$380$	384.649	−	666.232i	0.0519265	−	0.0899394i
$381$	5378.12	−	5047.07i	0.723174	−	0.678659i
$382$	141.853	+	245.697i	0.0189996	+	0.0329083i
$383$	3193.32			0.426034			0.213017	−	0.977049i	$-0.431671\pi$
$383$	3193.32			0.426034			0.213017	+	0.977049i	$0.431671\pi$
$384$	−1183.28	−	5052.38i	−0.157250	−	0.671428i
$385$	−459.060	−	199.307i	−0.0607685	−	0.0263835i
$386$	757.468			0.0998811
$387$	4341.27	−	2151.48i	0.570230	−	0.282599i
$388$	2228.74	−	3860.29i	0.291616	−	0.505094i
$389$	−10299.8			−1.34247			−0.671237	−	0.741242i	$-0.734237\pi$
$389$	−10299.8			−1.34247			−0.671237	+	0.741242i	$0.734237\pi$
$390$	−30.0628	−	9.08724i	−0.00390330	−	0.00117987i
$391$	−6070.10	+	10513.7i	−0.785110	+	1.35985i
$392$	−1966.25	−	2103.94i	−0.253343	−	0.271084i
$393$	−4765.17	+	4471.86i	−0.611632	+	0.573983i
$394$	1087.37	−	1883.38i	0.139038	−	0.240821i
$395$	−215.950	+	374.036i	−0.0275079	+	0.0476451i
$396$	3619.76	−	1793.91i	0.459343	−	0.227645i
$397$	6193.80	+	10728.0i	0.783018	+	1.35623i	0.930176	+	0.367114i	$0.119654\pi$
$397$	6193.80	+	10728.0i	0.783018	+	1.35623i	−0.147158	+	0.989113i	$0.547013\pi$
$398$	−82.6152	−	143.094i	−0.0104048	−	0.0180217i
$399$	5254.13	+	4453.87i	0.659237	+	0.558828i
$400$	3521.40	−	6099.24i	0.440175	−	0.762405i
$401$	−4998.69			−0.622501			−0.311250	−	0.950328i	$-0.600748\pi$
$401$	−4998.69			−0.622501			−0.311250	+	0.950328i	$0.600748\pi$
$402$	1745.90	−	1638.44i	0.216611	−	0.203278i
$403$	−902.393			−0.111542
$404$	−3320.49	−	5751.26i	−0.408912	−	0.708257i
$405$	1007.50	+	128.620i	0.123612	+	0.0157807i
$406$	1418.93	+	616.050i	0.173450	+	0.0753056i
$407$	508.633	+	880.978i	0.0619460	+	0.107294i
$408$	574.188	+	2451.68i	0.0696730	+	0.297491i
$409$	3949.37	+	6840.51i	0.477467	+	0.826997i	0.999666	−	0.0258265i	$-0.00822175\pi$
$409$	3949.37	+	6840.51i	0.477467	+	0.826997i	−0.522200	+	0.852823i	$0.674888\pi$
$410$	150.323	+	260.367i	0.0181071	+	0.0313625i
$411$	8085.84	−	7588.11i	0.970425	−	0.910691i
$412$	5848.47	+	10129.9i	0.699354	+	1.21132i
$413$	821.033	+	7171.35i	0.0978217	+	0.854429i
$414$	−2525.99	−	1680.66i	−0.299869	−	0.199516i
$415$	−154.064	−	266.847i	−0.0182234	−	0.0315639i
$416$	−793.658			−0.0935391
$417$	−2614.52	−	11163.5i	−0.307035	−	1.31098i
$418$	−741.658			−0.0867839
$419$	−5022.29	+	8698.86i	−0.585572	+	1.01424i	0.409231	+	0.912431i	$0.365797\pi$
$419$	−5022.29	+	8698.86i	−0.585572	+	1.01424i	−0.994804	+	0.101810i	$0.967536\pi$
$420$	−789.010	−	668.835i	−0.0916661	−	0.0777043i
$421$	−5.00064	−	8.66136i	−0.000578899	−	0.00100268i	0.865736	−	0.500501i	$-0.166851\pi$
$421$	−5.00064	−	8.66136i	−0.000578899	−	0.00100268i	−0.866315	+	0.499499i	$0.833518\pi$
$422$	−654.826	−	1134.19i	−0.0755366	−	0.130833i
$423$	−2086.51	−	1388.25i	−0.239833	−	0.159572i
$424$	−1801.86	+	3120.91i	−0.206382	+	0.357465i
$425$	−3551.46	+	6151.31i	−0.405344	+	0.702076i
$426$	238.695	+	1019.19i	0.0271475	+	0.115915i
$427$	5243.03	−	3884.06i	0.594210	−	0.440194i
$428$	−4911.61	+	8507.15i	−0.554700	+	0.960768i
$429$	−186.607	−	796.777i	−0.0210010	−	0.0896707i
$430$	133.574			0.0149802
$431$	−1362.41	+	2359.77i	−0.152262	+	0.263726i	−0.932059	−	0.362307i	$-0.881989\pi$
$431$	−1362.41	+	2359.77i	−0.152262	+	0.263726i	0.779796	+	0.626033i	$0.215323\pi$
$432$	7918.17	−	1331.24i	0.881859	−	0.148263i
$433$	−4356.92			−0.483557			−0.241779	−	0.970331i	$-0.577731\pi$
$433$	−4356.92			−0.483557			−0.241779	+	0.970331i	$0.577731\pi$
$434$	1008.65	+	437.919i	0.111559	+	0.0484350i
$435$	1083.39	+	327.483i	0.119413	+	0.0360956i
$436$	−2290.12			−0.251552
$437$	−7527.12	−	13037.3i	−0.823961	−	1.42714i
$438$	976.523	+	295.179i	0.106530	+	0.0322014i
$439$	−3938.22	+	6821.20i	−0.428157	+	0.741590i	−0.996709	−	0.0810570i	$-0.974170\pi$
$439$	−3938.22	+	6821.20i	−0.428157	+	0.741590i	0.568552	+	0.822647i	$0.307504\pi$
$440$	226.869			0.0245808
$441$	7153.73	−	5881.35i	0.772458	−	0.635066i
$442$	250.398			0.0269462
$443$	2103.06	−	3642.62i	0.225552	−	0.390668i	−0.730933	−	0.682449i	$-0.760915\pi$
$443$	2103.06	−	3642.62i	0.225552	−	0.390668i	0.956485	+	0.291782i	$0.0942480\pi$
$444$	479.433	+	2047.09i	0.0512452	+	0.218808i
$445$	−992.568	−	1719.18i	−0.105735	−	0.183139i
$446$	2470.80			0.262323
$447$	−6690.48	+	6278.65i	−0.707940	+	0.664363i
$448$	−6890.92	−	2991.79i	−0.726709	−	0.315511i
$449$	8229.28			0.864952			0.432476	−	0.901645i	$-0.357640\pi$
$449$	8229.28			0.864952			0.432476	+	0.901645i	$0.357640\pi$
$450$	−1477.89	−	983.308i	−0.154819	−	0.103008i
$451$	−3916.90	+	6784.27i	−0.408957	+	0.708334i
$452$	−12880.9			−1.34041
$453$	−9808.40	+	9204.65i	−1.01730	+	0.954684i
$454$	−1398.62	+	2422.48i	−0.144582	+	0.250424i
$455$	−168.357	+	124.720i	−0.0173466	+	0.0128505i
$456$	−2988.87	−	903.462i	−0.306944	−	0.0927817i
$457$	−393.339	+	681.284i	−0.0402618	+	0.0697355i	−0.885454	−	0.464727i	$-0.846153\pi$
$457$	−393.339	+	681.284i	−0.0402618	+	0.0697355i	0.845192	+	0.534462i	$0.179486\pi$
$458$	−333.738	+	578.052i	−0.0340493	+	0.0589751i
$459$	−7985.77	+	1342.61i	−0.812078	+	0.136531i
$460$	1130.34	+	1957.81i	0.114571	+	0.198442i
$461$	−9476.59	−	16413.9i	−0.957416	−	1.65829i	−0.728739	−	0.684791i	$-0.759893\pi$
$461$	−9476.59	−	16413.9i	−0.957416	−	1.65829i	−0.228677	−	0.973502i	$-0.573440\pi$
$462$	−178.086	+	981.154i	−0.0179336	+	0.0988040i
$463$	6255.13	−	10834.2i	0.627863	−	1.08749i	−0.360117	−	0.932907i	$-0.617263\pi$
$463$	6255.13	−	10834.2i	0.627863	−	1.08749i	0.987980	−	0.154583i	$-0.0494036\pi$
$464$	8947.36			0.895195
$465$	770.128	+	232.791i	0.0768040	+	0.0232160i
$466$	−1361.85			−0.135379
$467$	−6997.28	−	12119.6i	−0.693352	−	1.20092i	−0.970733	−	0.240161i	$-0.922800\pi$
$467$	−6997.28	−	12119.6i	−0.693352	−	1.20092i	0.277381	−	0.960760i	$-0.410534\pi$
$468$	107.307	−	1687.93i	0.0105989	−	0.166719i
$469$	−1816.87	−	15869.5i	−0.178881	−	1.56244i
$470$	−34.5454	−	59.8344i	−0.00339034	−	0.00587224i
$471$	11935.0	+	3607.65i	1.16759	+	0.352934i
$472$	−1636.08	−	2833.78i	−0.159548	−	0.276346i
$473$	1740.24	+	3014.18i	0.169168	+	0.293007i
$474$	823.766	+	249.005i	0.0798245	+	0.0241290i
$475$	−4403.92	−	7627.81i	−0.425402	−	0.736817i
$476$	7564.55	+	3284.26i	0.728405	+	0.316247i
$477$	−9648.85	−	6419.81i	−0.926185	−	0.616232i
$478$	302.374	+	523.727i	0.0289336	+	0.0501145i
$479$	9277.18			0.884937			0.442469	−	0.896784i	$-0.354103\pi$
$479$	9277.18			0.884937			0.442469	+	0.896784i	$0.354103\pi$
$480$	677.330	+	204.741i	0.0644078	+	0.0194689i
$481$	425.887			0.0403717
$482$	−1688.51	+	2924.58i	−0.159563	+	0.276371i
$483$	−19054.8	+	6827.27i	−1.79508	+	0.643171i
$484$	−3683.03	−	6379.19i	−0.345889	−	0.599098i
$485$	402.507	+	697.163i	0.0376844	+	0.0652712i
$486$	−208.240	−	2013.03i	−0.0194361	−	0.187886i
$487$	1909.97	−	3308.17i	0.177719	−	0.307819i	−0.763380	−	0.645950i	$-0.776461\pi$
$487$	1909.97	−	3308.17i	0.177719	−	0.307819i	0.941099	+	0.338131i	$0.109795\pi$
$488$	−1478.96	+	2561.63i	−0.137191	+	0.237622i
$489$	10182.6	+	3077.96i	0.941663	+	0.284642i
$490$	248.706	−	57.7041i	0.0229294	−	0.00532001i
$491$	−4413.32	+	7644.10i	−0.405643	+	0.702594i	−0.994396	−	0.105719i	$-0.966286\pi$
$491$	−4413.32	+	7644.10i	−0.405643	+	0.702594i	0.588753	+	0.808313i	$0.299619\pi$
$492$	−11806.3	+	11079.6i	−1.08185	+	1.01525i
$493$	−9023.74			−0.824359
$494$	−155.251	+	268.902i	−0.0141398	+	0.0244908i
$495$	−46.2898	+	728.131i	−0.00420317	+	0.0661153i
$496$	6360.23			0.575772
$497$	6405.65	+	2781.10i	0.578134	+	0.251005i
$498$	−447.694	+	420.137i	−0.0402845	+	0.0378048i
$499$	−17211.8			−1.54410			−0.772052	−	0.635559i	$-0.780770\pi$
$499$	−17211.8			−1.54410			−0.772052	+	0.635559i	$0.780770\pi$
$500$	1333.10	+	2309.00i	0.119236	+	0.206523i
$501$	−3011.71	−	12859.5i	−0.268570	−	1.14674i
$502$	−464.763	+	804.992i	−0.0413215	+	0.0715709i
$503$	13600.4			1.20559			0.602797	−	0.797895i	$-0.294053\pi$
$503$	13600.4			1.20559			0.602797	+	0.797895i	$0.294053\pi$
$504$	−1912.89	+	3737.09i	−0.169061	+	0.330285i
$505$	1199.35			0.105684
$506$	1089.73	−	1887.47i	0.0957400	−	0.165826i
$507$	10599.7	+	3204.03i	0.928497	+	0.280662i
$508$	5475.04	+	9483.05i	0.478180	+	0.828233i
$509$	9610.37			0.836881			0.418440	−	0.908244i	$-0.362577\pi$
$509$	9610.37			0.836881			0.418440	+	0.908244i	$0.362577\pi$
$510$	−213.697	−	64.5953i	−0.0185542	−	0.00560849i
$511$	5468.72	−	4051.25i	0.473428	−	0.350718i
$512$	9437.78			0.814639
$513$	3509.48	−	9408.35i	0.302041	−	0.809724i
$514$	−1958.19	+	3391.68i	−0.168039	+	0.291052i
$515$	−2112.45			−0.180749
$516$	1640.33	+	7003.92i	0.139945	+	0.597540i
$517$	900.134	−	1559.08i	0.0765723	−	0.132627i
$518$	−476.035	−	206.677i	−0.0403779	−	0.0175307i
$519$	5098.33	+	21769.0i	0.431198	+	1.84114i
$520$	47.4904	−	82.2557i	0.00400498	−	0.00693683i
$521$	−5228.57	+	9056.15i	−0.439670	+	0.761530i	−0.997664	−	0.0683147i	$-0.978238\pi$
$521$	−5228.57	+	9056.15i	−0.439670	+	0.761530i	0.557994	+	0.829845i	$0.311571\pi$
$522$	143.080	−	2250.62i	0.0119970	−	0.188711i
$523$	−7878.59	−	13646.1i	−0.658713	−	1.14092i	−0.980949	−	0.194265i	$-0.937768\pi$
$523$	−7878.59	−	13646.1i	−0.658713	−	1.14092i	0.322236	−	0.946659i	$-0.395565\pi$
$524$	−4851.05	−	8402.27i	−0.404426	−	0.700486i
$525$	−11148.5	+	3994.46i	−0.926778	+	0.332062i
$526$	−1077.41	+	1866.12i	−0.0893101	+	0.154690i
$527$	−6414.53			−0.530211
$528$	1315.24	+	5615.83i	0.108406	+	0.462874i
$529$	32071.9			2.63597
$530$	−159.752	−	276.698i	−0.0130928	−	0.0226773i
$531$	9428.77	−	4672.77i	0.770572	−	0.381885i
$532$	−8217.10	+	6087.27i	−0.669655	+	0.496084i
$533$	1639.84	+	2840.29i	0.133264	+	0.230819i
$534$	−2884.30	+	2706.75i	−0.233737	+	0.219350i
$535$	−887.030	−	1536.38i	−0.0716816	−	0.124156i
$536$	3620.50	+	6270.89i	0.291757	+	0.505338i
$537$	−1857.13	−	7929.62i	−0.149239	−	0.637222i
$538$	−1369.22	−	2371.56i	−0.109724	−	0.190047i
$539$	4542.34	+	4860.43i	0.362992	+	0.388411i
$540$	−527.016	+	1412.85i	−0.0419984	+	0.112591i
$541$	592.613	+	1026.44i	0.0470950	+	0.0815710i	0.888612	−	0.458660i	$-0.151670\pi$
$541$	592.613	+	1026.44i	0.0470950	+	0.0815710i	−0.841517	+	0.540231i	$0.818337\pi$
$542$	3804.11			0.301477
$543$	2433.93	−	2284.11i	0.192357	−	0.180517i
$544$	−5641.60			−0.444635
$545$	206.796	−	358.182i	0.0162535	−	0.0281520i
$546$	318.457	+	269.953i	0.0249610	+	0.0211592i
$547$	−2260.79	−	3915.81i	−0.176718	−	0.306084i	0.764037	−	0.645173i	$-0.223215\pi$
$547$	−2260.79	−	3915.81i	−0.176718	−	0.306084i	−0.940754	+	0.339089i	$0.889881\pi$
$548$	8231.56	+	14257.5i	0.641669	+	1.11140i
$549$	−7919.72	−	5269.34i	−0.615675	−	0.409636i
$550$	637.573	−	1104.31i	0.0494295	−	0.0856143i
$551$	5594.86	−	9690.58i	0.432576	−	0.749243i
$552$	6690.84	−	6278.99i	0.515908	−	0.484151i
$553$	4613.25	−	3417.52i	0.354747	−	0.262799i
$554$	231.631	−	401.196i	0.0177636	−	0.0307675i
$555$	−363.464	−	109.866i	−0.0277985	−	0.00840283i
$556$	17022.6			1.29842
$557$	−9190.20	+	15917.9i	−0.699104	+	1.21088i	0.269673	+	0.962952i	$0.413084\pi$
$557$	−9190.20	+	15917.9i	−0.699104	+	1.21088i	−0.968777	+	0.247932i	$0.920249\pi$
$558$	101.708	−	1599.85i	0.00771622	−	0.121375i
$559$	1457.13			0.110251
$560$	1186.61	−	879.049i	0.0895420	−	0.0663332i
$561$	−1326.46	−	5663.77i	−0.0998278	−	0.426247i
$562$	3336.03			0.250395
$563$	−4074.42	−	7057.11i	−0.305003	−	0.528280i	0.672259	−	0.740316i	$-0.265324\pi$
$563$	−4074.42	−	7057.11i	−0.305003	−	0.528280i	−0.977262	+	0.212036i	$0.931991\pi$
$564$	2713.18	−	2546.17i	0.202563	−	0.190094i
$565$	1163.14	−	2014.61i	0.0866079	−	0.150009i
$566$	1563.56			0.116115
$567$	−11603.8	−	6901.88i	−0.859460	−	0.511202i
$568$	−3165.70			−0.233855
$569$	5022.88	−	8699.88i	0.370070	−	0.640981i	−0.619506	−	0.784992i	$-0.712667\pi$
$569$	5022.88	−	8699.88i	0.370070	−	0.640981i	0.989576	+	0.144012i	$0.0460002\pi$
$570$	201.864	−	189.438i	0.0148336	−	0.0139205i
$571$	9189.19	+	15916.1i	0.673478	+	1.16650i	0.976911	+	0.213645i	$0.0685335\pi$
$571$	9189.19	+	15916.1i	0.673478	+	1.16650i	−0.303434	+	0.952853i	$0.598133\pi$
$572$	1214.96			0.0888112
$573$	−629.208	−	2686.61i	−0.0458735	−	0.195872i
$574$	−454.577	−	3970.53i	−0.0330552	−	0.288722i
$575$	25883.0			1.87721
$576$	−694.853	+	10929.9i	−0.0502643	+	0.790649i
$577$	7295.68	−	12636.5i	0.526383	−	0.911722i	−0.473145	−	0.880985i	$-0.656881\pi$
$577$	7295.68	−	12636.5i	0.526383	−	0.911722i	0.999527	−	0.0307372i	$-0.00978551\pi$
$578$	−844.898			−0.0608013
$579$	−7051.94	−	2131.63i	−0.506163	−	0.153001i
$580$	−840.177	+	1455.23i	−0.0601491	+	0.104181i
$581$	465.891	+	4069.35i	0.0332675	+	0.290577i
$582$	1169.64	−	1097.65i	0.0833046	−	0.0781768i
$583$	4162.58	−	7209.80i	0.295706	−	0.512177i
$584$	−1542.62	+	2671.90i	−0.109305	+	0.189322i
$585$	254.308	+	169.202i	0.0179732	+	0.0119584i
$586$	1599.00	+	2769.55i	0.112720	+	0.195238i
$587$	−4804.17	−	8321.07i	−0.337801	−	0.585089i	0.646218	−	0.763153i	$-0.276350\pi$
$587$	−4804.17	−	8321.07i	−0.337801	−	0.585089i	−0.984019	+	0.178064i	$0.943017\pi$
$588$	6079.90	+	12332.2i	0.426413	+	0.864920i
$589$	3977.11	−	6888.55i	0.278224	−	0.481898i
$590$	290.108			0.0202433
$591$	−15423.4	+	14474.0i	−1.07349	+	1.00742i
$592$	−3001.73			−0.208396
$593$	−5093.51	−	8822.22i	−0.352724	−	0.610936i	0.634001	−	0.773332i	$-0.281411\pi$
$593$	−5093.51	−	8822.22i	−0.352724	−	0.610936i	−0.986726	+	0.162395i	$0.948078\pi$
$594$	1433.64	−	241.031i	0.0990285	−	0.0166492i
$595$	−1196.74	+	886.553i	−0.0824566	+	0.0610842i
$596$	−6811.06	−	11797.1i	−0.468107	−	0.810785i
$597$	366.450	+	1564.68i	0.0251220	+	0.107266i
$598$	−456.225	−	790.204i	−0.0311980	−	0.0540365i
$599$	10640.4	+	18429.8i	0.725804	+	1.25713i	0.958642	+	0.284614i	$0.0918654\pi$
$599$	10640.4	+	18429.8i	0.725804	+	1.25713i	−0.232838	+	0.972515i	$0.574801\pi$
$600$	3914.64	−	3673.67i	0.266357	−	0.249962i
$601$	5973.18	+	10345.9i	0.405410	+	0.702190i	0.994369	−	0.105973i	$-0.0337956\pi$
$601$	5973.18	+	10345.9i	0.405410	+	0.702190i	−0.588959	+	0.808163i	$0.700462\pi$
$602$	−1628.71	−	707.126i	−0.110268	−	0.0478743i
$603$	−20865.0	+	10340.4i	−1.40910	+	0.698331i
$604$	−9985.16	−	17294.8i	−0.672667	−	1.16509i
$605$	1330.30			0.0893958
$606$	−544.940	−	2326.80i	−0.0365292	−	0.155973i
$607$	−24082.0			−1.61031			−0.805155	−	0.593064i	$-0.797918\pi$
$607$	−24082.0			−1.61031			−0.805155	+	0.593064i	$0.797918\pi$
$608$	3497.88	−	6058.51i	0.233319	−	0.404120i
$609$	−11476.4	−	9728.45i	−0.763627	−	0.647318i
$610$	−131.123	−	227.112i	−0.00870332	−	0.0150746i
$611$	−376.849	−	652.721i	−0.0249520	−	0.0432181i
$612$	762.779	−	11998.4i	0.0503816	−	0.792494i
$613$	−1910.99	+	3309.93i	−0.125912	+	0.218086i	−0.922089	−	0.386978i	$-0.873519\pi$
$613$	−1910.99	+	3309.93i	−0.125912	+	0.218086i	0.796177	+	0.605064i	$0.206852\pi$
$614$	953.236	−	1651.05i	0.0626539	−	0.108520i
$615$	−666.777	−	2847.02i	−0.0437187	−	0.186671i
$616$	−2766.29	−	1201.02i	−0.180936	−	0.0785561i
$617$	−7038.79	+	12191.5i	−0.459272	+	0.795483i	−0.998923	−	0.0464064i	$-0.985223\pi$
$617$	−7038.79	+	12191.5i	−0.459272	+	0.795483i	0.539650	+	0.841889i	$0.318556\pi$
$618$	959.819	+	4098.26i	0.0624750	+	0.266757i
$619$	−24244.5			−1.57426			−0.787132	−	0.616784i	$-0.788435\pi$
$619$	−24244.5			−1.57426			−0.787132	+	0.616784i	$0.788435\pi$
$620$	−597.240	+	1034.45i	−0.0386867	+	0.0670073i
$621$	18787.1	+	22755.2i	1.21401	+	1.47043i
$622$	3121.76			0.201240
$623$	3001.53	+	26217.0i	0.193024	+	1.68597i
$624$	2311.44	+	698.693i	0.148288	+	0.0448239i
$625$	14900.8			0.953654
$626$	1041.96	+	1804.72i	0.0665256	+	0.115226i
$627$	6904.74	+	2087.14i	0.439791	+	0.132938i
$628$	−9255.65	+	16031.3i	−0.588122	+	1.01866i
$629$	3027.35			0.191905
$630$	−202.141	−	312.538i	−0.0127833	−	0.0197648i
$631$	−7470.58			−0.471314			−0.235657	−	0.971836i	$-0.575724\pi$
$631$	−7470.58			−0.471314			−0.235657	+	0.971836i	$0.575724\pi$
$632$	−1301.31	+	2253.93i	−0.0819040	+	0.141862i
$633$	2904.56	+	12402.0i	0.182379	+	0.778727i
$634$	−678.186	−	1174.65i	−0.0424829	−	0.0735826i
$635$	−1977.57			−0.123587
$636$	12546.8	−	11774.5i	0.782253	−	0.734102i
$637$	2713.09	−	629.482i	0.168754	−	0.0391538i
$638$	1619.98			0.100526
$639$	645.920	−	10160.2i	0.0399878	−	0.629002i
$640$	−695.675	+	1204.94i	−0.0429671	+	0.0744213i
$641$	−15596.3			−0.961022			−0.480511	−	0.876989i	$-0.659549\pi$
$641$	−15596.3			−0.961022			−0.480511	+	0.876989i	$0.659549\pi$
$642$	−2577.61	+	2418.95i	−0.158458	+	0.148705i
$643$	13714.2	−	23753.6i	0.841109	−	1.45684i	−0.0478482	−	0.998855i	$-0.515236\pi$
$643$	13714.2	−	23753.6i	0.841109	−	1.45684i	0.888958	−	0.457990i	$-0.151430\pi$
$644$	−3418.16	−	29856.1i	−0.209153	−	1.82686i
$645$	−1243.56	−	375.897i	−0.0759147	−	0.0229472i
$646$	−1103.58	+	1911.45i	−0.0672130	+	0.116416i
$647$	1413.31	−	2447.93i	0.0858780	−	0.148745i	−0.819887	−	0.572525i	$-0.805964\pi$
$647$	1413.31	−	2447.93i	0.0858780	−	0.148745i	0.905765	+	0.423780i	$0.139297\pi$
$648$	6071.15	+	775.060i	0.368051	+	0.0469865i
$649$	3779.61	+	6546.47i	0.228602	+	0.395950i
$650$	−266.925	−	462.328i	−0.0161072	−	0.0278985i
$651$	−8158.03	−	6915.47i	−0.491150	−	0.416342i
$652$	−7896.68	+	13677.5i	−0.474322	+	0.821550i
$653$	−6833.39			−0.409512			−0.204756	−	0.978813i	$-0.565640\pi$
$653$	−6833.39			−0.409512			−0.204756	+	0.978813i	$0.565640\pi$
$654$	−788.849	−	238.450i	−0.0471658	−	0.0142571i
$655$	1752.19			0.104525
$656$	−11557.9	−	20018.9i	−0.687897	−	1.19147i
$657$	−8260.63	−	5496.17i	−0.490530	−	0.326371i
$658$	104.465	+	912.458i	0.00618919	+	0.0540598i
$659$	−2394.72	−	4147.77i	−0.141555	−	0.245181i	0.786527	−	0.617556i	$-0.211877\pi$
$659$	−2394.72	−	4147.77i	−0.141555	−	0.245181i	−0.928082	+	0.372375i	$0.878544\pi$
$660$	−1036.88	−	313.424i	−0.0611524	−	0.0184849i
$661$	−6881.85	−	11919.7i	−0.404952	−	0.701397i	0.589364	−	0.807867i	$-0.299378\pi$
$661$	−6881.85	−	11919.7i	−0.404952	−	0.701397i	−0.994316	+	0.106471i	$0.966045\pi$
$662$	−2789.16	−	4830.96i	−0.163752	−	0.283626i
$663$	−2331.17	−	704.657i	−0.136554	−	0.0412769i
$664$	−928.388	−	1608.02i	−0.0542597	−	0.0939806i
$665$	−210.069	−	1834.86i	−0.0122498	−	0.106997i
$666$	−48.0015	+	755.056i	−0.00279282	+	0.0439306i
$667$	16441.3	+	28477.1i	0.954435	+	1.65313i
$668$	19608.7			1.13575
$669$	−23002.9	−	6953.21i	−1.32936	−	0.401834i
$670$	−641.981			−0.0370178
$671$	3416.62	−	5917.76i	0.196568	−	0.340466i
$672$	−7175.02	−	6082.18i	−0.411878	−	0.349145i
$673$	−10042.1	−	17393.4i	−0.575176	−	0.996233i	−0.996023	−	0.0891016i	$-0.971600\pi$
$673$	−10042.1	−	17393.4i	−0.575176	−	0.996233i	0.420847	−	0.907132i	$-0.361733\pi$
$674$	−1119.67	−	1939.33i	−0.0639884	−	0.110831i
$675$	10991.8	+	13313.5i	0.626779	+	0.759165i
$676$	−8220.13	+	14237.7i	−0.467690	+	0.810063i
$677$	−11556.5	+	20016.5i	−0.656060	+	1.13633i	0.325567	+	0.945519i	$0.394445\pi$
$677$	−11556.5	+	20016.5i	−0.656060	+	1.13633i	−0.981627	+	0.190810i	$0.938889\pi$
$678$	−4436.92	−	1341.17i	−0.251326	−	0.0759696i
$679$	−1217.18	−	10631.5i	−0.0687942	−	0.600886i
$680$	337.578	−	584.702i	0.0190375	−	0.0329740i
$681$	19838.2	−	18617.1i	1.11630	−	1.04759i
$682$	1151.56			0.0646564
$683$	1185.46	−	2053.27i	0.0664132	−	0.115031i	−0.830907	−	0.556412i	$-0.812178\pi$
$683$	1185.46	−	2053.27i	0.0664132	−	0.115031i	0.897320	+	0.441381i	$0.145511\pi$
$684$	12412.1	+	8258.34i	0.693845	+	0.461646i
$685$	−2973.22			−0.165841
$686$	−3338.03	−	613.021i	−0.185782	−	0.0341185i
$687$	4733.79	−	4442.40i	0.262890	−	0.246708i
$688$	−10270.1			−0.569106
$689$	−1742.70	−	3018.44i	−0.0963592	−	0.166899i
$690$	185.506	+	792.076i	0.0102349	+	0.0437012i
$691$	−5314.04	+	9204.19i	−0.292555	+	0.506721i	−0.974413	−	0.224764i	$-0.927839\pi$
$691$	−5314.04	+	9204.19i	−0.292555	+	0.506721i	0.681858	+	0.731485i	$0.261172\pi$
$692$	−33194.2			−1.82349
$693$	4419.08	−	8633.27i	0.242232	−	0.473233i
$694$	1019.64			0.0557710
$695$	−1537.13	+	2662.39i	−0.0838947	+	0.145310i
$696$	6528.49	+	1973.40i	0.355548	+	0.107474i
$697$	11656.6	+	20189.8i	0.633464	+	1.09719i
$698$	−139.269			−0.00755216
$699$	12678.7	+	3832.45i	0.686052	+	0.207377i
$700$	−1999.88	−	17468.0i	−0.107983	−	0.943185i
$701$	−13584.8			−0.731942			−0.365971	−	0.930626i	$-0.619263\pi$
$701$	−13584.8			−0.731942			−0.365971	+	0.930626i	$0.619263\pi$
$702$	212.712	−	570.247i	0.0114363	−	0.0306590i
$703$	−1877.01	+	3251.07i	−0.100701	+	0.174419i
$704$	−7867.29			−0.421178
$705$	153.230	+	654.267i	0.00818581	+	0.0349519i
$706$	−1536.29	+	2660.94i	−0.0818969	+	0.141850i
$707$	−14624.1	−	6349.25i	−0.777928	−	0.337748i
$708$	3562.62	+	15211.8i	0.189112	+	0.807476i
$709$	−10642.0	+	18432.5i	−0.563707	+	0.976369i	0.433462	+	0.901172i	$0.357292\pi$
$709$	−10642.0	+	18432.5i	−0.563707	+	0.976369i	−0.997169	+	0.0751969i	$0.976041\pi$
$710$	140.334	−	243.066i	0.00741781	−	0.0128480i
$711$	−6968.43	−	4636.41i	−0.367562	−	0.244555i
$712$	−5981.19	−	10359.7i	−0.314824	−	0.545291i
$713$	11687.3	+	20242.9i	0.613873	+	1.06326i
$714$	2263.71	+	1918.92i	0.118651	+	0.100579i
$715$	−109.710	+	190.024i	−0.00573836	+	0.00993913i
$716$	12091.4			0.631114
$717$	−1341.22	−	5726.77i	−0.0698588	−	0.298284i
$718$	2707.12			0.140709
$719$	−13420.8	−	23245.5i	−0.696120	−	1.20572i	−0.969802	−	0.243895i	$-0.921575\pi$
$719$	−13420.8	−	23245.5i	−0.696120	−	1.20572i	0.273681	−	0.961820i	$-0.411759\pi$
$720$	−1792.41	−	1192.57i	−0.0927765	−	0.0617283i
$721$	25757.8	+	11183.1i	1.33047	+	0.577643i
$722$	463.772	+	803.277i	0.0239055	+	0.0414056i
$723$	23950.0	−	22475.8i	1.23196	−	1.15613i
$724$	2477.79	+	4291.67i	0.127191	+	0.220302i
$725$	9619.35	+	16661.2i	0.492764	+	0.853492i
$726$	−604.438	−	2580.84i	−0.0308992	−	0.131934i
$727$	8514.96	+	14748.3i	0.434391	+	0.752387i	0.997246	−	0.0741684i	$-0.0236302\pi$
$727$	8514.96	+	14748.3i	0.434391	+	0.752387i	−0.562855	+	0.826556i	$0.690297\pi$
$728$	−1014.52	+	751.560i	−0.0516491	+	0.0382619i
$729$	−3726.28	+	19327.1i	−0.189314	+	0.981917i
$730$	−136.768	−	236.888i	−0.00693424	−	0.0120105i
$731$	10357.8			0.524072
$732$	10298.3	−	9664.44i	0.519997	−	0.487989i
$733$	1421.58			0.0716335			0.0358168	−	0.999358i	$-0.488597\pi$
$733$	1421.58			0.0716335			0.0358168	+	0.999358i	$0.488597\pi$
$734$	156.080	−	270.339i	0.00784881	−	0.0135945i
$735$	−2477.81	−	162.679i	−0.124348	−	0.00816395i
$736$	10279.0	+	17803.7i	0.514794	+	0.891650i
$737$	−8363.91	−	14486.7i	−0.418031	−	0.724051i
$738$	−5220.38	+	2587.15i	−0.260386	+	0.129044i
$739$	12068.5	−	20903.3i	0.600742	−	1.04052i	−0.391967	−	0.919979i	$-0.628205\pi$
$739$	12068.5	−	20903.3i	0.600742	−	1.04052i	0.992709	−	0.120537i	$-0.0384616\pi$
$740$	281.869	−	488.212i	0.0140023	−	0.0242527i
$741$	2202.09	−	2066.55i	0.109171	−	0.102451i
$742$	483.090	+	4219.57i	0.0239013	+	0.208767i
$743$	3732.57	−	6465.00i	0.184300	−	0.319216i	−0.759041	−	0.651043i	$-0.774332\pi$
$743$	3732.57	−	6465.00i	0.184300	−	0.319216i	0.943340	+	0.331827i	$0.107665\pi$
$744$	4640.78	+	1402.79i	0.228682	+	0.0691249i
$745$	2460.14			0.120983
$746$	−823.503	+	1426.35i	−0.0404163	+	0.0700031i
$747$	5350.31	−	2651.54i	0.262058	−	0.129873i
$748$	8636.36			0.422161
$749$	2682.38	+	23429.4i	0.130857	+	1.14298i
$750$	218.781	+	934.156i	0.0106517	+	0.0454807i
$751$	25390.9			1.23373			0.616863	−	0.787070i	$-0.288403\pi$
$751$	25390.9			1.23373			0.616863	+	0.787070i	$0.288403\pi$
$752$	2656.10	+	4600.50i	0.128800	+	0.223089i
$753$	6592.25	−	6186.47i	0.319037	−	0.299399i
$754$	339.109	−	587.354i	0.0163788	−	0.0283689i
$755$	3606.62			0.173852
$756$	13905.5	−	14437.3i	0.668967	−	0.694549i
$757$	−1908.73			−0.0916434			−0.0458217	−	0.998950i	$-0.514591\pi$
$757$	−1908.73			−0.0916434			−0.0458217	+	0.998950i	$0.514591\pi$
$758$	−596.208	+	1032.66i	−0.0285689	+	0.0494829i
$759$	−15456.9	+	14505.4i	−0.739195	+	0.693694i
$760$	418.608	+	725.050i	0.0199796	+	0.0346057i
$761$	23233.7			1.10673			0.553365	−	0.832939i	$-0.313343\pi$
$761$	23233.7			1.10673			0.553365	+	0.832939i	$0.313343\pi$
$762$	898.533	+	3836.58i	0.0427171	+	0.182394i
$763$	−4417.71	+	3272.66i	−0.209609	+	0.155279i
$764$	4096.65			0.193994
$765$	1807.71	+	1202.75i	0.0854351	+	0.0568438i
$766$	−853.029	+	1477.49i	−0.0402365	+	0.0696917i
$767$	3164.73			0.148985
$768$	−13486.7	−	4076.70i	−0.633671	−	0.191544i
$769$	−13166.1	+	22804.4i	−0.617403	+	1.06937i	0.372555	+	0.928010i	$0.378482\pi$
$769$	−13166.1	+	22804.4i	−0.617403	+	1.06937i	−0.989958	+	0.141363i	$0.954852\pi$
$770$	214.844	−	159.158i	0.0100551	−	0.00744889i
$771$	27775.2	−	26065.5i	1.29741	−	1.21754i
$772$	5468.83	−	9472.29i	0.254958	−	0.441600i
$773$	6385.60	−	11060.2i	0.297120	−	0.514628i	−0.678356	−	0.734734i	$-0.737307\pi$
$773$	6385.60	−	11060.2i	0.297120	−	0.514628i	0.975476	+	0.220106i	$0.0706404\pi$
$774$	−164.232	+	2583.35i	−0.00762688	+	0.119970i
$775$	6837.92	+	11843.6i	0.316936	+	0.548949i
$776$	2425.50	+	4201.09i	0.112204	+	0.194343i
$777$	3850.21	+	3263.78i	0.177768	+	0.150691i
$778$	2751.39	−	4765.55i	0.126789	−	0.219606i
$779$	−28909.0			−1.32962
$780$	−330.687	+	310.332i	−0.0151801	+	0.0142457i
$781$	7313.26			0.335069
$782$	−3243.00	−	5617.05i	−0.148299	−	0.256861i
$783$	−7665.64	+	20550.4i	−0.349869	+	0.937944i
$784$	−19122.3	+	4436.70i	−0.871097	+	0.202109i
$785$	−1671.56	−	2895.23i	−0.0760007	−	0.131637i
$786$	−796.127	−	3399.32i	−0.0361284	−	0.154262i
$787$	−2367.12	−	4099.97i	−0.107215	−	0.185703i	0.807426	−	0.589969i	$-0.200860\pi$
$787$	−2367.12	−	4099.97i	−0.107215	−	0.185703i	−0.914641	+	0.404267i	$0.867527\pi$
$788$	−15701.4	−	27195.6i	−0.709821	−	1.22945i
$789$	15282.1	−	14341.4i	0.689551	−	0.647106i
$790$	−115.373	−	199.832i	−0.00519594	−	0.00899963i
$791$	−24847.6	+	18407.2i	−1.11691	+	0.827415i
$792$	−278.941	+	4387.70i	−0.0125148	+	0.196856i
$793$	−1430.40	−	2477.52i	−0.0640541	−	0.110945i
$794$	−6618.19			−0.295807
$795$	708.598	+	3025.59i	0.0316118	+	0.134977i
$796$	−2385.89			−0.106238
$797$	1883.34	−	3262.04i	0.0837031	−	0.144978i	−0.821135	−	0.570734i	$-0.806659\pi$
$797$	1883.34	−	3262.04i	0.0837031	−	0.144978i	0.904838	+	0.425756i	$0.139992\pi$
$798$	−3464.26	+	1241.23i	−0.153676	+	0.0550616i
$799$	−2678.77	−	4639.77i	−0.118608	−	0.205436i
$800$	6013.97	+	10416.5i	0.265783	+	0.460349i
$801$	34469.7	−	17082.7i	1.52051	−	0.753543i
$802$	1335.30	−	2312.80i	0.0587918	−	0.101830i
$803$	3563.69	−	6172.50i	0.156613	−	0.271261i
$804$	−7883.74	−	33662.2i	−0.345819	−	1.47658i
$805$	4978.24	+	2161.38i	0.217963	+	0.0946317i
$806$	241.056	−	417.521i	0.0105345	−	0.0182463i
$807$	6073.35	+	25932.1i	0.264922	+	1.13117i
$808$	7227.28			0.314672
$809$	−2426.99	+	4203.67i	−0.105474	+	0.182686i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−2426.99	+	4203.67i	−0.105474	+	0.182686i	0.808458	+	0.588554i	$0.200303\pi$
$810$	−328.642	+	431.792i	−0.0142559	+	0.0187304i
$811$	3204.85			0.138764			0.0693820	−	0.997590i	$-0.477897\pi$
$811$	3204.85			0.138764			0.0693820	+	0.997590i	$0.477897\pi$
$812$	17948.4	−	13296.2i	0.775695	−	0.574639i
$813$	−35415.8	−	10705.3i	−1.52778	−	0.461811i
$814$	−543.483			−0.0234018
$815$	−1426.13	−	2470.13i	−0.0612947	−	0.106166i
$816$	16430.5	+	4966.55i	0.704882	+	0.213069i
$817$	−6422.00	+	11123.2i	−0.275003	+	0.476319i
$818$	−4219.97			−0.180376
$819$	−2205.11	−	3409.41i	−0.0940816	−	0.145463i
$820$	4341.25			0.184882
$821$	5748.65	−	9956.96i	0.244372	−	0.423265i	−0.717583	−	0.696473i	$-0.754752\pi$
$821$	5748.65	−	9956.96i	0.244372	−	0.423265i	0.961955	+	0.273208i	$0.0880849\pi$
$822$	1350.92	+	5768.18i	0.0573219	+	0.244755i
$823$	−13262.3	−	22970.9i	−0.561717	−	0.972923i	−0.997347	−	0.0727968i	$-0.976808\pi$
$823$	−13262.3	−	22970.9i	−0.561717	−	0.972923i	0.435630	−	0.900126i	$-0.356526\pi$
$824$	−12729.6			−0.538176
$825$	−9043.42	+	8486.76i	−0.381638	+	0.358147i
$826$	−3537.37	−	1535.80i	−0.149008	−	0.0646941i
$827$	18948.7			0.796750			0.398375	−	0.917223i	$-0.369574\pi$
$827$	18948.7			0.796750			0.398375	+	0.917223i	$0.369574\pi$
$828$	−39254.3	+	19453.9i	−1.64756	+	0.816510i
$829$	−11676.6	+	20224.5i	−0.489198	+	0.847316i	−0.999923	−	0.0124282i	$-0.996044\pi$
$829$	−11676.6	+	20224.5i	−0.489198	+	0.847316i	0.510725	+	0.859744i	$0.329377\pi$
$830$	164.620			0.00688440
$831$	−3285.48	+	3083.24i	−0.137150	+	0.128708i
$832$	−1646.85	+	2852.43i	−0.0686230	+	0.118858i
$833$	19285.6	−	4474.58i	0.802167	−	0.186116i
$834$	5863.58	+	1772.42i	0.243452	+	0.0735897i
$835$	−1770.65	+	3066.86i	−0.0733844	+	0.127105i
$836$	−5354.68	+	9274.58i	−0.221526	+	0.383694i
$837$	−5449.12	+	14608.2i	−0.225029	+	0.603267i
$838$	−2683.20	−	4647.44i	−0.110608	−	0.191579i
$839$	1451.60	+	2514.25i	0.0597316	+	0.103458i	0.894345	−	0.447378i	$-0.147642\pi$
$839$	1451.60	+	2514.25i	0.0597316	+	0.103458i	−0.834613	+	0.550836i	$0.814309\pi$
$840$	1059.70	−	379.687i	0.0435275	−	0.0155958i
$841$	−26.1867	+	45.3567i	−0.00107371	+	0.00185972i
$842$	5.34327			0.000218695
$843$	−31058.1	−	9388.11i	−1.26892	−	0.383563i
$844$	−18911.1			−0.771262
$845$	−1484.54	−	2571.31i	−0.0604377	−	0.104681i
$846$	1199.68	−	594.548i	0.0487541	−	0.0241619i
$847$	−16220.8	−	7042.47i	−0.658031	−	0.285693i
$848$	12282.8	+	21274.5i	0.497400	+	0.861521i
$849$	−14556.5	−	4400.09i	−0.588433	−	0.177869i
$850$	−1897.40	−	3286.39i	−0.0765649	−	0.132614i
$851$	−5515.84	−	9553.71i	−0.222186	−	0.384838i
$852$	14468.5	+	4373.47i	0.581786	+	0.175860i
$853$	−17856.2	−	30927.9i	−0.716747	−	1.24144i	−0.962282	−	0.272054i	$-0.912297\pi$
$853$	−17856.2	−	30927.9i	−0.716747	−	1.24144i	0.245535	−	0.969388i	$-0.421036\pi$
$854$	396.517	+	3463.40i	0.0158882	+	0.138776i
$855$	−2412.44	+	1195.57i	−0.0964955	+	0.0478219i
$856$	−5345.22	−	9258.20i	−0.213430	−	0.369671i
$857$	−10068.6			−0.401328			−0.200664	−	0.979660i	$-0.564310\pi$
$857$	−10068.6			−0.401328			−0.200664	+	0.979660i	$0.564310\pi$
$858$	418.502	+	126.503i	0.0166520	+	0.00503350i
$859$	18203.2			0.723033			0.361517	−	0.932366i	$-0.382259\pi$
$859$	18203.2			0.723033			0.361517	+	0.932366i	$0.382259\pi$
$860$	964.387	−	1670.37i	0.0382388	−	0.0662315i
$861$	−6941.60	+	38244.4i	−0.274761	+	1.51378i
$862$	−727.881	−	1260.73i	−0.0287607	−	0.0498150i
$863$	11358.5	+	19673.5i	0.448028	+	0.776008i	0.998258	−	0.0590059i	$-0.0187931\pi$
$863$	11358.5	+	19673.5i	0.448028	+	0.776008i	−0.550229	+	0.835014i	$0.685460\pi$
$864$	−4792.52	+	12848.0i	−0.188709	+	0.505900i
$865$	2997.42	−	5191.68i	0.117821	−	0.204072i
$866$	1163.86	−	2015.87i	0.0456693	−	0.0791016i
$867$	7865.90	+	2377.67i	0.308120	+	0.0931372i
$868$	12758.6	−	9451.63i	0.498911	−	0.369596i
$869$	3006.23	−	5206.94i	0.117352	−	0.203260i
$870$	−440.926	+	413.785i	−0.0171825	+	0.0161248i
$871$	−7003.24			−0.272441
$872$	1246.15	−	2158.40i	0.0483945	−	0.0838217i
$873$	−13978.2	+	6927.40i	−0.541913	+	0.268565i
$874$	8042.86			0.311274
$875$	5871.23	+	2549.08i	0.226839	+	0.0984852i
$876$	10741.7	−	10080.5i	0.414300	−	0.388798i
$877$	−44413.4			−1.71007			−0.855037	−	0.518568i	$-0.826465\pi$
$877$	−44413.4			−1.71007			−0.855037	+	0.518568i	$0.826465\pi$
$878$	−2104.03	−	3644.29i	−0.0808742	−	0.140078i
$879$	−7092.58	−	30284.1i	−0.272158	−	1.16207i
$880$	773.257	−	1339.32i	0.0296210	−	0.0513051i
$881$	372.284			0.0142367			0.00711837	−	0.999975i	$-0.497734\pi$
$881$	372.284			0.0142367			0.00711837	+	0.999975i	$0.497734\pi$
$882$	810.219	+	4880.98i	0.0309314	+	0.186339i
$883$	6638.71			0.253013			0.126507	−	0.991966i	$-0.459624\pi$
$883$	6638.71			0.253013			0.126507	+	0.991966i	$0.459624\pi$
$884$	1807.84	−	3131.27i	0.0687831	−	0.119136i
$885$	−2700.87	−	816.408i	−0.102586	−	0.0310093i
$886$	1123.58	+	1946.10i	0.0426043	+	0.0737929i
$887$	38202.3			1.44612			0.723059	−	0.690786i	$-0.242736\pi$
$887$	38202.3			1.44612			0.723059	+	0.690786i	$0.242736\pi$
$888$	−2190.23	−	662.053i	−0.0827694	−	0.0250192i
$889$	24113.1	+	10469.1i	0.909705	+	0.394962i
$890$	1060.58			0.0399445
$891$	−14025.3	−	1790.51i	−0.527346	−	0.0673225i
$892$	17838.9	−	30897.9i	0.669608	−	1.15980i
$893$	6643.52			0.248955
$894$	−1117.79	−	4772.78i	−0.0418172	−	0.178552i
$895$	−1091.85	+	1891.14i	−0.0407782	+	0.0706299i
$896$	14861.4	−	11009.4i	0.554113	−	0.410490i
$897$	2023.64	+	8640.59i	0.0753260	+	0.321629i
$898$	−2198.28	+	3807.54i	−0.0816900	+	0.141491i
$899$	−8687.08	+	15046.5i	−0.322281	+	0.558206i
$900$	−22966.7	+	11382.0i	−0.850617	+	0.421555i
$901$	−12387.7	−	21456.1i	−0.458040	−	0.793349i
$902$	−2092.64	−	3624.56i	−0.0772475	−	0.133797i
$903$	13173.1	+	11166.7i	0.485463	+	0.411522i
$904$	7009.03	−	12140.0i	0.257873	−	0.446649i
$905$	−894.973			−0.0328728
$906$	−1638.71	−	6997.00i	−0.0600910	−	0.256578i
$907$	3048.95			0.111619			0.0558097	−	0.998441i	$-0.482226\pi$
$907$	3048.95			0.111619			0.0558097	+	0.998441i	$0.482226\pi$
$908$	20195.7	+	34980.0i	0.738126	+	1.27847i
$909$	−1474.63	+	23195.8i	−0.0538069	+	0.846375i
$910$	−12.7325	−	111.212i	−0.000463820	−	0.00405126i
$911$	−12782.5	−	22139.9i	−0.464876	−	0.805189i	0.534320	−	0.845282i	$-0.320568\pi$
$911$	−12782.5	−	22139.9i	−0.464876	−	0.805189i	−0.999196	+	0.0400933i	$0.987234\pi$
$912$	−15520.8	+	14565.4i	−0.563535	+	0.528847i
$913$	2144.72	+	3714.77i	0.0777436	+	0.134656i
$914$	−210.145	−	363.982i	−0.00760501	−	0.0131723i
$915$	581.614	+	2483.39i	0.0210137	+	0.0897248i
$916$	4819.10	+	8346.93i	0.173829	+	0.301081i
$917$	−21365.0	−	9275.90i	−0.769393	−	0.334043i
$918$	1512.03	−	4053.52i	0.0543622	−	0.145736i
$919$	−7508.94	−	13005.9i	−0.269529	−	0.466838i	0.699211	−	0.714915i	$-0.253535\pi$
$919$	−7508.94	−	13005.9i	−0.269529	−	0.466838i	−0.968740	+	0.248077i	$0.920201\pi$
$920$	−2460.27			−0.0881659
$921$	−13520.8	+	12688.6i	−0.483742	+	0.453966i
$922$	10125.9			0.361691
$923$	1530.88	−	2651.56i	0.0545931	−	0.0945580i
$924$	10983.8	+	9310.82i	0.391060	+	0.331497i
$925$	−3227.17	−	5589.63i	−0.114712	−	0.198687i
$926$	3341.86	+	5788.27i	0.118596	+	0.205415i
$927$	2597.31	−	40855.3i	0.0920248	−	1.44754i
$928$	−7640.31	+	13233.4i	−0.270265	+	0.468112i
$929$	−21120.3	+	36581.5i	−0.745894	+	1.29193i	0.203883	+	0.978995i	$0.434644\pi$
$929$	−21120.3	+	36581.5i	−0.745894	+	1.29193i	−0.949776	+	0.312930i	$0.898689\pi$
$930$	−313.432	+	294.139i	−0.0110514	+	0.0103712i
$931$	−7152.11	+	23485.1i	−0.251773	+	0.826736i
$932$	−9832.39	+	17030.2i	−0.345569	+	0.598544i
$933$	−29063.2	−	8785.11i	−1.01981	−	0.308265i
$934$	7476.72			0.261933
$935$	−779.858	+	1350.75i	−0.0272771	+	0.0472453i
$936$	1532.45	+	1019.61i	0.0535147	+	0.0356057i
$937$	−53310.0			−1.85866			−0.929328	−	0.369255i	$-0.879613\pi$
$937$	−53310.0			−1.85866			−0.929328	+	0.369255i	$0.879613\pi$
$938$	7827.87	+	3398.58i	0.272483	+	0.118302i
$939$	−4621.73	−	19734.0i	−0.160623	−	0.685830i
$940$	−997.654			−0.0346169
$941$	−4774.02	−	8268.84i	−0.165386	−	0.286457i	0.771406	−	0.636343i	$-0.219554\pi$
$941$	−4774.02	−	8268.84i	−0.165386	−	0.286457i	−0.936792	+	0.349886i	$0.886220\pi$
$942$	−4857.37	+	4558.38i	−0.168006	+	0.157665i
$943$	42476.6	−	73571.6i	1.46684	−	2.54064i
$944$	−22305.6			−0.769052
$945$	1002.38	+	3478.55i	0.0345051	+	0.119743i
$946$	−1859.47			−0.0639078
$947$	8890.66	−	15399.1i	0.305077	−	0.528409i	−0.672202	−	0.740368i	$-0.734651\pi$
$947$	8890.66	−	15399.1i	0.305077	−	0.528409i	0.977278	+	0.211960i	$0.0679845\pi$
$948$	9061.34	−	8503.58i	0.310442	−	0.291333i
$949$	−1491.97	−	2584.17i	−0.0510341	−	0.0883937i
$950$	4705.67			0.160707
$951$	3008.18	+	12844.4i	0.102573	+	0.437968i
$952$	−7211.54	+	5342.35i	−0.245512	+	0.181877i
$953$	−3414.93			−0.116076			−0.0580380	−	0.998314i	$-0.518484\pi$
$953$	−3414.93			−0.116076			−0.0580380	+	0.998314i	$0.518484\pi$
$954$	5547.82	−	2749.42i	0.188278	−	0.0933081i
$955$	−369.925	+	640.729i	−0.0125346	+	0.0217105i
$956$	8732.42			0.295425
$957$	−15081.8	−	4558.87i	−0.509432	−	0.153989i
$958$	−2478.21	+	4292.38i	−0.0835775	+	0.144760i
$959$	36253.3	+	15739.9i	1.22073	+	0.529998i
$960$	2141.31	−	2009.51i	0.0719902	−	0.0675589i
$961$	8720.29	−	15104.0i	0.292716	−	0.506998i
$962$	−113.767	+	197.050i	−0.00381288	+	0.00660411i
$963$	30804.6	−	15266.3i	1.03080	−	0.510852i
$964$	24381.6	+	42230.2i	0.814605	+	1.41094i
$965$	987.664	+	1710.68i	0.0329472	+	0.0570662i
$966$	1931.24	−	10640.1i	0.0643236	−	0.354388i
$967$	372.673	−	645.489i	0.0123933	−	0.0214659i	−0.859762	−	0.510695i	$-0.829388\pi$
$967$	372.673	−	645.489i	0.0123933	−	0.0214659i	0.872156	+	0.489229i	$0.162722\pi$
$968$	8016.37			0.266173
$969$	15653.3	−	14689.7i	0.518942	−	0.486999i
$970$	−430.086			−0.0142363
$971$	10867.8	+	18823.6i	0.359180	+	0.622118i	0.987824	−	0.155575i	$-0.0497231\pi$
$971$	10867.8	+	18823.6i	0.359180	+	0.622118i	−0.628644	+	0.777693i	$0.716390\pi$
$972$	−26676.8	−	11929.7i	−0.880306	−	0.393669i
$973$	32837.2	−	24325.9i	1.08192	−	0.801494i
$974$	1020.42	+	1767.42i	0.0335692	+	0.0581435i
$975$	1183.98	+	5055.39i	0.0388900	+	0.166053i
$976$	10081.7	+	17462.0i	0.330643	+	0.572690i
$977$	3494.69	+	6052.98i	0.114437	+	0.198211i	0.917555	−	0.397610i	$-0.130160\pi$
$977$	3494.69	+	6052.98i	0.114437	+	0.198211i	−0.803118	+	0.595821i	$0.796827\pi$
$978$	−4144.19	+	3889.09i	−0.135497	+	0.127157i
$979$	13817.5	+	23932.6i	0.451082	+	0.781296i
$980$	1074.03	−	3526.74i	0.0350087	−	0.114957i
$981$	6673.05	+	4439.88i	0.217181	+	0.144500i
$982$	−2357.86	−	4083.93i	−0.0766214	−	0.132712i
$983$	−23393.6			−0.759045			−0.379522	−	0.925183i	$-0.623912\pi$
$983$	−23393.6			−0.759045			−0.379522	+	0.925183i	$0.623912\pi$
$984$	−4017.98	−	17156.1i	−0.130171	−	0.555808i
$985$	5671.30			0.183455
$986$	2410.51	−	4175.12i	0.0778561	−	0.134851i
$987$	1595.23	−	8788.86i	0.0514457	−	0.283437i
$988$	2241.78	+	3882.88i	0.0721868	+	0.125031i
$989$	−18871.9	−	32687.1i	−0.606766	−	1.05095i
$990$	−324.528	−	215.923i	−0.0104183	−	0.00693179i
$991$	18122.6	−	31389.3i	0.580912	−	1.00617i	−0.414460	−	0.910068i	$-0.636029\pi$
$991$	18122.6	−	31389.3i	0.580912	−	1.00617i	0.995372	−	0.0961013i	$-0.0306373\pi$
$992$	−5431.12	+	9406.97i	−0.173829	+	0.301080i
$993$	12371.7	+	52824.8i	0.395371	+	1.68816i
$994$	−2997.90	+	2220.86i	−0.0956617	+	0.0708667i
$995$	215.444	−	373.160i	0.00686436	−	0.0118894i
$996$	2021.59	+	8631.84i	0.0643139	+	0.274609i
$997$	12741.4			0.404740			0.202370	−	0.979309i	$-0.435136\pi$
$997$	12741.4			0.404740			0.202370	+	0.979309i	$0.435136\pi$
$998$	4597.79	−	7963.60i	0.145832	−	0.252589i
$999$	2571.73	−	6894.39i	0.0814473	−	0.218347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.g.a.4.11	✓	44
3.2	odd	2		189.4.g.a.172.12		44
7.2	even	3		63.4.h.a.58.12	yes	44
9.2	odd	6		189.4.h.a.46.11		44
9.7	even	3		63.4.h.a.25.12	yes	44
21.2	odd	6		189.4.h.a.37.11		44
63.2	odd	6		189.4.g.a.100.12		44
63.16	even	3	inner	63.4.g.a.16.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.11	✓	44	1.1	even	1	trivial
63.4.g.a.16.11	yes	44	63.16	even	3	inner
63.4.h.a.25.12	yes	44	9.7	even	3
63.4.h.a.58.12	yes	44	7.2	even	3
189.4.g.a.100.12		44	63.2	odd	6
189.4.g.a.172.12		44	3.2	odd	2
189.4.h.a.37.11		44	21.2	odd	6
189.4.h.a.46.11		44	9.2	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.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.267129 + 0.462682i) q^{2} +(3.78900 - 3.55577i) q^{3} +(3.85728 + 6.68101i) q^{4} -1.39324 q^{5} +(0.633036 + 2.70295i) q^{6} +(16.9882 + 7.37568i) q^{7} -8.39564 q^{8} +(1.71302 - 26.9456i) q^{9} +O(q^{10})\)	\(q+(-0.267129 + 0.462682i) q^{2} +(3.78900 - 3.55577i) q^{3} +(3.85728 + 6.68101i) q^{4} -1.39324 q^{5} +(0.633036 + 2.70295i) q^{6} +(16.9882 + 7.37568i) q^{7} -8.39564 q^{8} +(1.71302 - 26.9456i) q^{9} +(0.372176 - 0.644627i) q^{10} +19.3952 q^{11} +(38.3714 + 11.5987i) q^{12} +(4.05999 - 7.03211i) q^{13} +(-7.95064 + 5.88988i) q^{14} +(-5.27899 + 4.95404i) q^{15} +(-28.6155 + 49.5636i) q^{16} +(28.8598 - 49.9867i) q^{17} +(12.0096 + 7.99055i) q^{18} +(35.7871 + 61.9851i) q^{19} +(-5.37413 - 9.30826i) q^{20} +(90.5945 - 32.4597i) q^{21} +(-5.18104 + 8.97382i) q^{22} -210.330 q^{23} +(-31.8111 + 29.8530i) q^{24} -123.059 q^{25} +(2.16909 + 3.75697i) q^{26} +(-89.3217 - 108.188i) q^{27} +(16.2514 + 141.949i) q^{28} +(-78.1687 - 135.392i) q^{29} +(-0.881972 - 3.76586i) q^{30} +(-55.5662 - 96.2435i) q^{31} +(-48.8707 - 84.6465i) q^{32} +(73.4886 - 68.9650i) q^{33} +(15.4186 + 26.7058i) q^{34} +(-23.6687 - 10.2761i) q^{35} +(186.632 - 92.4921i) q^{36} +(26.2246 + 45.4224i) q^{37} -38.2391 q^{38} +(-9.62125 - 41.0810i) q^{39} +11.6972 q^{40} +(-201.952 + 349.790i) q^{41} +(-9.18193 + 50.5874i) q^{42} +(89.7250 + 155.408i) q^{43} +(74.8130 + 129.580i) q^{44} +(-2.38666 + 37.5417i) q^{45} +(56.1854 - 97.3160i) q^{46} +(46.4100 - 80.3846i) q^{47} +(67.8123 + 289.547i) q^{48} +(234.199 + 250.599i) q^{49} +(32.8726 - 56.9371i) q^{50} +(-68.3912 - 292.018i) q^{51} +62.6421 q^{52} +(214.618 - 371.730i) q^{53} +(73.9170 - 12.4273i) q^{54} -27.0223 q^{55} +(-142.627 - 61.9235i) q^{56} +(356.002 + 107.611i) q^{57} +83.5246 q^{58} +(194.873 + 337.530i) q^{59} +(-53.4606 - 16.1598i) q^{60} +(176.158 - 305.114i) q^{61} +59.3735 q^{62} +(227.843 - 445.123i) q^{63} -405.630 q^{64} +(-5.65655 + 9.79743i) q^{65} +(12.2779 + 52.4244i) q^{66} +(-431.235 - 746.921i) q^{67} +445.282 q^{68} +(-796.942 + 747.886i) q^{69} +(11.0772 - 8.20602i) q^{70} +377.064 q^{71} +(-14.3819 + 226.226i) q^{72} +(183.741 - 318.248i) q^{73} -28.0215 q^{74} +(-466.270 + 437.569i) q^{75} +(-276.082 + 478.188i) q^{76} +(329.491 + 143.053i) q^{77} +(21.5776 + 6.52237i) q^{78} +(154.998 - 268.465i) q^{79} +(39.8684 - 69.0540i) q^{80} +(-723.131 - 92.3169i) q^{81} +(-107.894 - 186.879i) q^{82} +(110.580 + 191.530i) q^{83} +(566.313 + 480.057i) q^{84} +(-40.2087 + 69.6435i) q^{85} -95.8727 q^{86} +(-777.604 - 235.051i) q^{87} -162.836 q^{88} +(712.416 + 1233.94i) q^{89} +(-16.7323 - 11.1328i) q^{90} +(120.839 - 89.5178i) q^{91} +(-811.304 - 1405.22i) q^{92} +(-552.760 - 167.086i) q^{93} +(24.7950 + 42.9461i) q^{94} +(-49.8601 - 86.3602i) q^{95} +(-486.154 - 146.953i) q^{96} +(-288.900 - 500.389i) q^{97} +(-178.509 + 41.4171i) q^{98} +(33.2245 - 522.617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9}+O(q^{10}) \) 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9	\( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9} - 18 q^{10} - 10 q^{11} - 41 q^{12} - 14 q^{13} - 79 q^{14} + 119 q^{15} - 247 q^{16} - 162 q^{17} + 157 q^{18} + 58 q^{19} - 362 q^{20} + 166 q^{21} - 18 q^{22} + 186 q^{23} + 414 q^{24} + 698 q^{25} - 266 q^{26} + 272 q^{27} - 172 q^{28} + 248 q^{29} + 616 q^{30} + 61 q^{31} - 163 q^{32} + 23 q^{33} + 6 q^{34} + 289 q^{35} - 806 q^{36} - 86 q^{37} + 1522 q^{38} - 565 q^{39} + 36 q^{40} - 692 q^{41} + 395 q^{42} - 86 q^{43} - 443 q^{44} - 1483 q^{45} - 270 q^{46} - 1005 q^{47} - 1013 q^{48} - 277 q^{49} + 239 q^{50} - 1719 q^{51} + 670 q^{52} + 258 q^{53} + 910 q^{54} - 870 q^{55} + 714 q^{56} + 566 q^{57} - 474 q^{58} - 1665 q^{59} + 4 q^{60} + 439 q^{61} + 1812 q^{62} + 493 q^{63} + 872 q^{64} - 613 q^{65} + 3073 q^{66} + 295 q^{67} + 2748 q^{68} + 1389 q^{69} - 1044 q^{70} + 636 q^{71} + 981 q^{72} - 338 q^{73} - 2238 q^{74} - 1064 q^{75} + 1006 q^{76} - 2909 q^{77} + 157 q^{78} + 133 q^{79} - 4817 q^{80} + 1325 q^{81} + 6 q^{82} - 1356 q^{83} - 7081 q^{84} + 483 q^{85} + 6686 q^{86} + 2774 q^{87} - 738 q^{88} - 2200 q^{89} + 2665 q^{90} + 1552 q^{91} - 396 q^{92} + 4365 q^{93} - 1191 q^{94} + 3083 q^{95} - 1468 q^{96} - 266 q^{97} + 3601 q^{98} - 5395 q^{99}+O(q^{100}) \) 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9 - 18 * q^10 - 10 * q^11 - 41 * q^12 - 14 * q^13 - 79 * q^14 + 119 * q^15 - 247 * q^16 - 162 * q^17 + 157 * q^18 + 58 * q^19 - 362 * q^20 + 166 * q^21 - 18 * q^22 + 186 * q^23 + 414 * q^24 + 698 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 616 * q^30 + 61 * q^31 - 163 * q^32 + 23 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 + 1522 * q^38 - 565 * q^39 + 36 * q^40 - 692 * q^41 + 395 * q^42 - 86 * q^43 - 443 * q^44 - 1483 * q^45 - 270 * q^46 - 1005 * q^47 - 1013 * q^48 - 277 * q^49 + 239 * q^50 - 1719 * q^51 + 670 * q^52 + 258 * q^53 + 910 * q^54 - 870 * q^55 + 714 * q^56 + 566 * q^57 - 474 * q^58 - 1665 * q^59 + 4 * q^60 + 439 * q^61 + 1812 * q^62 + 493 * q^63 + 872 * q^64 - 613 * q^65 + 3073 * q^66 + 295 * q^67 + 2748 * q^68 + 1389 * q^69 - 1044 * q^70 + 636 * q^71 + 981 * q^72 - 338 * q^73 - 2238 * q^74 - 1064 * q^75 + 1006 * q^76 - 2909 * q^77 + 157 * q^78 + 133 * q^79 - 4817 * q^80 + 1325 * q^81 + 6 * q^82 - 1356 * q^83 - 7081 * q^84 + 483 * q^85 + 6686 * q^86 + 2774 * q^87 - 738 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 + 4365 * q^93 - 1191 * q^94 + 3083 * q^95 - 1468 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Introduction

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