LMFDB - Embedded newform 63.4.f.b.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.6
Root			$-1.46974 - 2.54566i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.b.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46974 + 2.54566i) q^{2} +(3.48146 - 3.85739i) q^{3} +(-0.320267 + 0.554718i) q^{4} +(1.28443 - 2.22469i) q^{5} +(14.9364 + 3.19326i) q^{6} +(3.50000 + 6.06218i) q^{7} +21.6330 q^{8} +(-2.75892 - 26.8587i) q^{9} +O(q^{10})$	\(q+(1.46974 + 2.54566i) q^{2} +(3.48146 - 3.85739i) q^{3} +(-0.320267 + 0.554718i) q^{4} +(1.28443 - 2.22469i) q^{5} +(14.9364 + 3.19326i) q^{6} +(3.50000 + 6.06218i) q^{7} +21.6330 q^{8} +(-2.75892 - 26.8587i) q^{9} +7.55109 q^{10} +(0.257136 + 0.445373i) q^{11} +(1.02477 + 3.16662i) q^{12} +(-32.7217 + 56.6756i) q^{13} +(-10.2882 + 17.8196i) q^{14} +(-4.10983 - 12.6997i) q^{15} +(34.3570 + 59.5081i) q^{16} -3.37738 q^{17} +(64.3182 - 46.4985i) q^{18} -123.871 q^{19} +(0.822718 + 1.42499i) q^{20} +(35.5693 + 7.60435i) q^{21} +(-0.755846 + 1.30916i) q^{22} +(12.5592 - 21.7531i) q^{23} +(75.3143 - 83.4469i) q^{24} +(59.2005 + 102.538i) q^{25} -192.369 q^{26} +(-113.209 - 82.8651i) q^{27} -4.48373 q^{28} +(-118.731 - 205.649i) q^{29} +(26.2888 - 29.1275i) q^{30} +(44.9570 - 77.8677i) q^{31} +(-14.4597 + 25.0449i) q^{32} +(2.61319 + 0.558672i) q^{33} +(-4.96386 - 8.59766i) q^{34} +17.9820 q^{35} +(15.7826 + 7.07151i) q^{36} -67.4721 q^{37} +(-182.057 - 315.333i) q^{38} +(104.701 + 323.534i) q^{39} +(27.7860 - 48.1267i) q^{40} +(-143.658 + 248.823i) q^{41} +(32.9195 + 101.724i) q^{42} +(217.750 + 377.154i) q^{43} -0.329409 q^{44} +(-63.2959 - 28.3602i) q^{45} +73.8349 q^{46} +(-27.0274 - 46.8128i) q^{47} +(349.158 + 74.6464i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-174.019 + 301.409i) q^{50} +(-11.7582 + 13.0279i) q^{51} +(-20.9593 - 36.3026i) q^{52} +272.147 q^{53} +(44.5583 - 409.983i) q^{54} +1.32109 q^{55} +(75.7155 + 131.143i) q^{56} +(-431.250 + 477.817i) q^{57} +(349.008 - 604.500i) q^{58} +(258.248 - 447.299i) q^{59} +(8.36099 + 1.78749i) q^{60} +(-125.855 - 217.988i) q^{61} +264.300 q^{62} +(153.166 - 110.730i) q^{63} +464.704 q^{64} +(84.0572 + 145.591i) q^{65} +(2.41851 + 7.47339i) q^{66} +(-230.875 + 399.888i) q^{67} +(1.08166 - 1.87349i) q^{68} +(-40.1861 - 124.178i) q^{69} +(26.4288 + 45.7760i) q^{70} +532.933 q^{71} +(-59.6836 - 581.034i) q^{72} -360.888 q^{73} +(-99.1664 - 171.761i) q^{74} +(601.634 + 128.623i) q^{75} +(39.6716 - 68.7132i) q^{76} +(-1.79995 + 3.11761i) q^{77} +(-669.726 + 742.044i) q^{78} +(-381.337 - 660.495i) q^{79} +176.516 q^{80} +(-713.777 + 148.202i) q^{81} -844.559 q^{82} +(472.421 + 818.258i) q^{83} +(-15.6099 + 17.2955i) q^{84} +(-4.33799 + 7.51362i) q^{85} +(-640.071 + 1108.64i) q^{86} +(-1206.63 - 257.964i) q^{87} +(5.56263 + 9.63475i) q^{88} +1494.37 q^{89} +(-20.8328 - 202.812i) q^{90} -458.104 q^{91} +(8.04457 + 13.9336i) q^{92} +(-143.851 - 444.510i) q^{93} +(79.4464 - 137.605i) q^{94} +(-159.103 + 275.574i) q^{95} +(46.2671 + 142.969i) q^{96} +(-672.791 - 1165.31i) q^{97} -144.034 q^{98} +(11.2527 - 8.13509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.46974	+	2.54566i	0.519631	+	0.900028i	0.999740	+	0.0228186i	$0.00726401\pi$
$2$	1.46974	+	2.54566i	0.519631	+	0.900028i	−0.480108	+	0.877209i	$0.659403\pi$
$3$	3.48146	−	3.85739i	0.670007	−	0.742355i
$3$	3.48146	−	3.85739i	0.670007	−	0.742355i
$4$	−0.320267	+	0.554718i	−0.0400333	+	0.0693397i
$5$	1.28443	−	2.22469i	0.114883	−	0.198982i	−0.802850	−	0.596181i	$-0.796684\pi$
$5$	1.28443	−	2.22469i	0.114883	−	0.198982i	0.917733	+	0.397198i	$0.130017\pi$
$6$	14.9364	+	3.19326i	1.01630	+	0.217274i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	21.6330			0.956052
$9$	−2.75892	−	26.8587i	−0.102182	−	0.994766i
$10$	7.55109			0.238786
$11$	0.257136	+	0.445373i	0.00704814	+	0.0122077i	0.869528	−	0.493884i	$-0.164423\pi$
$11$	0.257136	+	0.445373i	0.00704814	+	0.0122077i	−0.862480	+	0.506091i	$0.831090\pi$
$12$	1.02477	+	3.16662i	0.0246521	+	0.0761770i
$13$	−32.7217	+	56.6756i	−0.698105	+	1.20915i	0.271018	+	0.962574i	$0.412640\pi$
$13$	−32.7217	+	56.6756i	−0.698105	+	1.20915i	−0.969123	+	0.246579i	$0.920694\pi$
$14$	−10.2882	+	17.8196i	−0.196402	+	0.340179i
$15$	−4.10983	−	12.6997i	−0.0707435	−	0.218603i
$16$	34.3570	+	59.5081i	0.536828	+	0.929813i
$17$	−3.37738			−0.0481843			−0.0240922	−	0.999710i	$-0.507670\pi$
$17$	−3.37738			−0.0481843			−0.0240922	+	0.999710i	$0.507670\pi$
$18$	64.3182	−	46.4985i	0.842220	−	0.608878i
$19$	−123.871			−1.49568			−0.747838	−	0.663881i	$-0.768908\pi$
$19$	−123.871			−1.49568			−0.747838	+	0.663881i	$0.768908\pi$
$20$	0.822718	+	1.42499i	0.00919826	+	0.0159319i
$21$	35.5693	+	7.60435i	0.369612	+	0.0790192i
$22$	−0.755846	+	1.30916i	−0.00732486	+	0.0126870i
$23$	12.5592	−	21.7531i	0.113860	−	0.197211i	−0.803464	−	0.595354i	$-0.797012\pi$
$23$	12.5592	−	21.7531i	0.113860	−	0.197211i	0.917323	+	0.398143i	$0.130345\pi$
$24$	75.3143	−	83.4469i	0.640561	−	0.709730i
$25$	59.2005	+	102.538i	0.473604	+	0.820306i
$26$	−192.369			−1.45103
$27$	−113.209	−	82.8651i	−0.806932	−	0.590644i
$28$	−4.48373			−0.0302623
$29$	−118.731	−	205.649i	−0.760272	−	1.31683i	−0.942711	−	0.333612i	$-0.891733\pi$
$29$	−118.731	−	205.649i	−0.760272	−	1.31683i	0.182439	−	0.983217i	$-0.441601\pi$
$30$	26.2888	−	29.1275i	0.159988	−	0.177264i
$31$	44.9570	−	77.8677i	0.260468	−	0.451144i	−0.705898	−	0.708313i	$-0.749456\pi$
$31$	44.9570	−	77.8677i	0.260468	−	0.451144i	0.966366	+	0.257169i	$0.0827898\pi$
$32$	−14.4597	+	25.0449i	−0.0798791	+	0.138355i
$33$	2.61319	+	0.558672i	0.0137848	+	0.00294704i
$34$	−4.96386	−	8.59766i	−0.0250381	−	0.0433673i
$35$	17.9820			0.0868431
$36$	15.7826	+	7.07151i	0.0730675	+	0.0327385i
$37$	−67.4721			−0.299793			−0.149897	−	0.988702i	$-0.547894\pi$
$37$	−67.4721			−0.299793			−0.149897	+	0.988702i	$0.547894\pi$
$38$	−182.057	−	315.333i	−0.777200	−	1.34615i
$39$	104.701	+	323.534i	0.429886	+	1.32838i
$40$	27.7860	−	48.1267i	0.109834	−	0.190238i
$41$	−143.658	+	248.823i	−0.547210	+	0.947796i	0.451254	+	0.892396i	$0.350977\pi$
$41$	−143.658	+	248.823i	−0.547210	+	0.947796i	−0.998464	+	0.0554003i	$0.982357\pi$
$42$	32.9195	+	101.724i	0.120942	+	0.373722i
$43$	217.750	+	377.154i	0.772245	+	1.33757i	0.936330	+	0.351122i	$0.114200\pi$
$43$	217.750	+	377.154i	0.772245	+	1.33757i	−0.164085	+	0.986446i	$0.552467\pi$
$44$	−0.329409			−0.00112864
$45$	−63.2959	−	28.3602i	−0.209680	−	0.0939488i
$46$	73.8349			0.236660
$47$	−27.0274	−	46.8128i	−0.0838797	−	0.145284i	0.821034	−	0.570880i	$-0.193398\pi$
$47$	−27.0274	−	46.8128i	−0.0838797	−	0.145284i	−0.904913	+	0.425596i	$0.860064\pi$
$48$	349.158	+	74.6464i	1.04993	+	0.224464i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−174.019	+	301.409i	−0.492199	+	0.852513i
$51$	−11.7582	+	13.0279i	−0.0322838	+	0.0357699i
$52$	−20.9593	−	36.3026i	−0.0558949	−	0.0968128i
$53$	272.147			0.705325			0.352662	−	0.935751i	$-0.385276\pi$
$53$	272.147			0.705325			0.352662	+	0.935751i	$0.385276\pi$
$54$	44.5583	−	409.983i	0.112289	−	1.03318i
$55$	1.32109			0.00323883
$56$	75.7155	+	131.143i	0.180677	+	0.312942i
$57$	−431.250	+	477.817i	−1.00211	+	1.11032i
$58$	349.008	−	604.500i	0.790122	−	1.36853i
$59$	258.248	−	447.299i	0.569848	−	0.987005i	−0.426733	−	0.904378i	$-0.640335\pi$
$59$	258.248	−	447.299i	0.569848	−	0.987005i	0.996580	−	0.0826276i	$-0.0263312\pi$
$60$	8.36099	+	1.78749i	0.0179900	+	0.00384607i
$61$	−125.855	−	217.988i	−0.264166	−	0.457549i	0.703179	−	0.711013i	$-0.251763\pi$
$61$	−125.855	−	217.988i	−0.264166	−	0.457549i	−0.967345	+	0.253464i	$0.918430\pi$
$62$	264.300			0.541389
$63$	153.166	−	110.730i	0.306303	−	0.221440i
$64$	464.704			0.907625
$65$	84.0572	+	145.591i	0.160400	+	0.277821i
$66$	2.41851	+	7.47339i	0.00451058	+	0.0139380i
$67$	−230.875	+	399.888i	−0.420984	+	0.729165i	−0.996036	−	0.0889517i	$-0.971648\pi$
$67$	−230.875	+	399.888i	−0.420984	+	0.729165i	0.575052	+	0.818117i	$0.304982\pi$
$68$	1.08166	−	1.87349i	0.00192898	−	0.00334109i
$69$	−40.1861	−	124.178i	−0.0701136	−	0.216657i
$70$	26.4288	+	45.7760i	0.0451264	+	0.0781612i
$71$	532.933			0.890809			0.445405	−	0.895329i	$-0.353060\pi$
$71$	532.933			0.890809			0.445405	+	0.895329i	$0.353060\pi$
$72$	−59.6836	−	581.034i	−0.0976914	−	0.951048i
$73$	−360.888			−0.578613			−0.289306	−	0.957237i	$-0.593425\pi$
$73$	−360.888			−0.578613			−0.289306	+	0.957237i	$0.593425\pi$
$74$	−99.1664	−	171.761i	−0.155782	−	0.269822i
$75$	601.634	+	128.623i	0.926276	+	0.198028i
$76$	39.6716	−	68.7132i	0.0598769	−	0.103710i
$77$	−1.79995	+	3.11761i	−0.00266395	+	0.00461409i
$78$	−669.726	+	742.044i	−0.972199	+	1.07718i
$79$	−381.337	−	660.495i	−0.543086	−	0.940652i	−0.998725	−	0.0504873i	$-0.983923\pi$
$79$	−381.337	−	660.495i	−0.543086	−	0.940652i	0.455639	−	0.890165i	$-0.349411\pi$
$80$	176.516			0.246689
$81$	−713.777	+	148.202i	−0.979118	+	0.203294i
$82$	−844.559			−1.13739
$83$	472.421	+	818.258i	0.624759	+	1.08211i	0.988587	+	0.150648i	$0.0481361\pi$
$83$	472.421	+	818.258i	0.624759	+	1.08211i	−0.363829	+	0.931466i	$0.618531\pi$
$84$	−15.6099	+	17.2955i	−0.0202760	+	0.0224654i
$85$	−4.33799	+	7.51362i	−0.00553554	+	0.00958784i
$86$	−640.071	+	1108.64i	−0.802566	+	1.39008i
$87$	−1206.63	−	257.964i	−1.48694	−	0.317893i
$88$	5.56263	+	9.63475i	0.00673839	+	0.0116712i
$89$	1494.37			1.77981			0.889906	−	0.456145i	$-0.150770\pi$
$89$	1494.37			1.77981			0.889906	+	0.456145i	$0.150770\pi$
$90$	−20.8328	−	202.812i	−0.0243997	−	0.237536i
$91$	−458.104			−0.527718
$92$	8.04457	+	13.9336i	0.00911635	+	0.0157900i
$93$	−143.851	−	444.510i	−0.160394	−	0.495629i
$94$	79.4464	−	137.605i	0.0871731	−	0.150988i
$95$	−159.103	+	275.574i	−0.171827	+	0.297613i
$96$	46.2671	+	142.969i	0.0491887	+	0.151997i
$97$	−672.791	−	1165.31i	−0.704243	−	1.21978i	−0.966964	−	0.254912i	$-0.917953\pi$
$97$	−672.791	−	1165.31i	−0.704243	−	1.21978i	0.262722	−	0.964872i	$-0.415380\pi$
$98$	−144.034			−0.148466
$99$	11.2527	−	8.13509i	0.0114236	−	0.00825866i
$100$	−75.8398			−0.0758398
$101$	−889.853	−	1541.27i	−0.876670	−	1.51844i	−0.854973	−	0.518672i	$-0.826427\pi$
$101$	−889.853	−	1541.27i	−0.876670	−	1.51844i	−0.0216967	−	0.999765i	$-0.506907\pi$
$102$	−50.4460	−	10.7848i	−0.0489696	−	0.0104692i
$103$	18.6509	−	32.3042i	0.0178420	−	0.0309032i	−0.856967	−	0.515372i	$-0.827654\pi$
$103$	18.6509	−	32.3042i	0.0178420	−	0.0309032i	0.874809	+	0.484469i	$0.160987\pi$
$104$	−707.868	+	1226.06i	−0.667425	+	1.15601i
$105$	62.6034	−	69.3635i	0.0581854	−	0.0644684i
$106$	399.985	+	692.794i	0.366509	+	0.634812i
$107$	389.494			0.351905			0.175953	−	0.984399i	$-0.443699\pi$
$107$	389.494			0.351905			0.175953	+	0.984399i	$0.443699\pi$
$108$	82.2240	−	36.2604i	0.0732593	−	0.0323070i
$109$	115.830			0.101784			0.0508922	−	0.998704i	$-0.483794\pi$
$109$	115.830			0.101784			0.0508922	+	0.998704i	$0.483794\pi$
$110$	1.94166	+	3.36305i	0.00168300	+	0.00291504i
$111$	−234.901	+	260.266i	−0.200863	+	0.222553i
$112$	−240.499	+	416.556i	−0.202902	+	0.351436i
$113$	960.089	−	1662.92i	0.799270	−	1.38438i	−0.120821	−	0.992674i	$-0.538553\pi$
$113$	960.089	−	1662.92i	0.799270	−	1.38438i	0.920092	−	0.391703i	$-0.128114\pi$
$114$	−1850.19	−	395.551i	−1.52005	−	0.324971i
$115$	−32.2627	−	55.8806i	−0.0261610	−	0.0453121i
$116$	152.103			0.121745
$117$	1612.51	+	722.498i	1.27416	+	0.570897i
$118$	1518.23			1.18444
$119$	−11.8208	−	20.4743i	−0.00910599	−	0.0157720i
$120$	−88.9079	−	274.733i	−0.0676345	−	0.208996i
$121$	665.368	−	1152.45i	0.499901	−	0.865853i
$122$	369.949	−	640.771i	0.274538	−	0.475513i
$123$	459.668	+	1420.41i	0.336967	+	1.04125i
$124$	28.7964	+	49.8769i	0.0208548	+	0.0361216i
$125$	625.261			0.447401
$126$	506.996	+	227.164i	0.358467	+	0.160614i
$127$	2674.36			1.86859			0.934295	−	0.356502i	$-0.116031\pi$
$127$	2674.36			1.86859			0.934295	+	0.356502i	$0.116031\pi$
$128$	798.671	+	1383.34i	0.551510	+	0.955243i
$129$	2212.92	+	473.099i	1.51036	+	0.322899i
$130$	−247.084	+	427.962i	−0.166698	+	0.288729i
$131$	−618.749	+	1071.70i	−0.412674	+	0.714773i	−0.995181	−	0.0980531i	$-0.968738\pi$
$131$	−618.749	+	1071.70i	−0.412674	+	0.714773i	0.582507	+	0.812826i	$0.302072\pi$
$132$	−1.14682	+	1.27066i	−0.000756197	+	0.000837852i
$133$	−433.547	−	750.925i	−0.282656	−	0.489575i
$134$	−1357.31			−0.875025
$135$	−329.758	+	145.422i	−0.210230	+	0.0927106i
$136$	−73.0627			−0.0460668
$137$	−1189.17	−	2059.69i	−0.741586	−	1.28446i	−0.951773	−	0.306803i	$-0.900741\pi$
$137$	−1189.17	−	2059.69i	−0.741586	−	1.28446i	0.210187	−	0.977661i	$-0.432593\pi$
$138$	257.053	−	284.810i	0.158564	−	0.175686i
$139$	−582.235	+	1008.46i	−0.355284	+	0.615371i	−0.987167	−	0.159694i	$-0.948949\pi$
$139$	−582.235	+	1008.46i	−0.355284	+	0.615371i	0.631882	+	0.775064i	$0.282283\pi$
$140$	−5.75902	+	9.97492i	−0.00347662	+	0.00602168i
$141$	−274.670	−	58.7216i	−0.164052	−	0.0350727i
$142$	783.272	+	1356.67i	0.462892	+	0.801753i
$143$	−33.6557			−0.0196814
$144$	1503.52	−	1086.96i	0.870092	−	0.629028i
$145$	−610.007			−0.349368
$146$	−530.411	−	918.699i	−0.300665	−	0.520768i
$147$	78.3936	+	242.243i	0.0439850	+	0.135917i
$148$	21.6091	−	37.4280i	0.0120017	−	0.0207876i
$149$	−839.695	+	1454.39i	−0.461681	+	0.799655i	−0.999045	−	0.0436954i	$-0.986087\pi$
$149$	−839.695	+	1454.39i	−0.461681	+	0.799655i	0.537364	+	0.843351i	$0.319420\pi$
$150$	556.814	+	1720.60i	0.303091	+	0.936576i
$151$	−432.249	−	748.678i	−0.232953	−	0.403487i	0.725723	−	0.687988i	$-0.241506\pi$
$151$	−432.249	−	748.678i	−0.232953	−	0.403487i	−0.958676	+	0.284500i	$0.908172\pi$
$152$	−2679.69			−1.42995
$153$	9.31790	+	90.7118i	0.00492358	+	0.0479321i
$154$	−10.5819			−0.00553708
$155$	−115.488	−	200.031i	−0.0598465	−	0.103657i
$156$	−213.002	−	45.5377i	−0.109319	−	0.0233714i
$157$	−861.709	+	1492.52i	−0.438037	+	0.758703i	−0.997538	−	0.0701271i	$-0.977659\pi$
$157$	−861.709	+	1492.52i	−0.438037	+	0.758703i	0.559501	+	0.828830i	$0.310993\pi$
$158$	1120.93	−	1941.51i	0.564409	−	0.977584i
$159$	947.467	−	1049.78i	0.472572	−	0.523602i
$160$	37.1447	+	64.3366i	0.0183534	+	0.0317891i
$161$	175.828			0.0860697
$162$	−1426.34	−	1599.22i	−0.691751	−	0.775595i
$163$	2035.48			0.978105			0.489052	−	0.872254i	$-0.337343\pi$
$163$	2035.48			0.978105			0.489052	+	0.872254i	$0.337343\pi$
$164$	−92.0177	−	159.379i	−0.0438133	−	0.0758868i
$165$	4.59932	−	5.09596i	0.00217004	−	0.00240436i
$166$	−1388.67	+	2405.25i	−0.649288	+	1.12460i
$167$	−805.356	+	1394.92i	−0.373175	+	0.646359i	−0.990052	−	0.140701i	$-0.955064\pi$
$167$	−805.356	+	1394.92i	−0.373175	+	0.646359i	0.616877	+	0.787060i	$0.288398\pi$
$168$	769.470	+	164.505i	0.353368	+	0.0755465i
$169$	−1042.92	−	1806.39i	−0.474701	−	0.822206i
$170$	−25.5029			−0.0115058
$171$	341.749	+	3327.00i	0.152831	+	1.48785i
$172$	−278.952			−0.123662
$173$	−1005.85	−	1742.19i	−0.442045	−	0.765644i	0.555797	−	0.831318i	$-0.312413\pi$
$173$	−1005.85	−	1742.19i	−0.442045	−	0.765644i	−0.997841	+	0.0656748i	$0.979080\pi$
$174$	−1116.74	−	3450.80i	−0.486549	−	1.50348i
$175$	−414.403	+	717.768i	−0.179005	+	0.310047i
$176$	−17.6689	+	30.6034i	−0.00756727	+	0.0131069i
$177$	−826.326	−	2553.41i	−0.350907	−	1.08433i
$178$	2196.34	+	3804.17i	0.924846	+	1.60188i
$179$	−1778.67			−0.742704			−0.371352	−	0.928492i	$-0.621106\pi$
$179$	−1778.67			−0.742704			−0.371352	+	0.928492i	$0.621106\pi$
$180$	36.0035	−	26.0285i	0.0149086	−	0.0107781i
$181$	−608.294			−0.249802			−0.124901	−	0.992169i	$-0.539861\pi$
$181$	−608.294			−0.249802			−0.124901	+	0.992169i	$0.539861\pi$
$182$	−673.293	−	1166.18i	−0.274219	−	0.474961i
$183$	−1279.02	−	273.442i	−0.516657	−	0.110456i
$184$	271.693	−	470.585i	0.108856	−	0.188544i
$185$	−86.6630	+	150.105i	−0.0344410	+	0.0596536i
$186$	920.149	−	1019.51i	0.362734	−	0.401903i
$187$	−0.868446	−	1.50419i	−0.000339610	−	0.000588222i
$188$	34.6239			0.0134319
$189$	106.110	−	976.324i	0.0408379	−	0.375752i
$190$	−935.357			−0.357147
$191$	2197.42	+	3806.04i	0.832459	+	1.44186i	0.896082	+	0.443888i	$0.146401\pi$
$191$	2197.42	+	3806.04i	0.832459	+	1.44186i	−0.0636229	+	0.997974i	$0.520265\pi$
$192$	1617.85	−	1792.55i	0.608115	−	0.673780i
$193$	−593.459	+	1027.90i	−0.221337	+	0.383367i	−0.955214	−	0.295915i	$-0.904376\pi$
$193$	−593.459	+	1027.90i	−0.221337	+	0.383367i	0.733877	+	0.679282i	$0.237709\pi$
$194$	1977.65	−	3425.40i	0.731893	−	1.26768i
$195$	854.244	+	182.629i	0.313711	+	0.0670682i
$196$	−15.6931	−	27.1812i	−0.00571905	−	0.00990568i
$197$	−816.364			−0.295246			−0.147623	−	0.989044i	$-0.547162\pi$
$197$	−816.364			−0.295246			−0.147623	+	0.989044i	$0.547162\pi$
$198$	37.2477	+	16.6892i	0.0133691	+	0.00599014i
$199$	−5392.46			−1.92091			−0.960455	−	0.278434i	$-0.910185\pi$
$199$	−5392.46			−1.92091			−0.960455	+	0.278434i	$0.910185\pi$
$200$	1280.68	+	2218.21i	0.452790	+	0.784256i
$201$	738.740	+	2282.77i	0.259237	+	0.801065i
$202$	2615.70	−	4530.53i	0.911090	−	1.57805i
$203$	831.120	−	1439.54i	0.287356	−	0.497715i
$204$	−3.46103	−	10.6949i	−0.00118785	−	0.00367054i
$205$	369.036	+	639.190i	0.125730	+	0.217770i
$206$	109.648			0.0370850
$207$	−618.910	−	277.308i	−0.207813	−	0.0931122i
$208$	−4496.87			−1.49905
$209$	−31.8516	−	55.1686i	−0.0105417	−	0.0182588i
$210$	268.587	+	57.4211i	0.0882583	+	0.0188687i
$211$	−1308.19	+	2265.85i	−0.426822	+	0.739277i	−0.996589	−	0.0825297i	$-0.973700\pi$
$211$	−1308.19	+	2265.85i	−0.426822	+	0.739277i	0.569767	+	0.821806i	$0.307033\pi$
$212$	−87.1595	+	150.965i	−0.0282365	+	0.0489070i
$213$	1855.38	−	2055.73i	0.596848	−	0.661297i
$214$	572.455	+	991.522i	0.182861	+	0.316724i
$215$	1118.73			0.354870
$216$	−2449.06	−	1792.62i	−0.771469	−	0.564687i
$217$	629.397			0.196895
$218$	170.240	+	294.864i	0.0528903	+	0.0916087i
$219$	−1256.42	+	1392.09i	−0.387674	+	0.429536i
$220$	−0.423101	+	0.732832i	−0.000129661	+	0.000224580i
$221$	110.513	−	191.415i	0.0336377	−	0.0582622i
$222$	−1007.79	−	215.456i	−0.304679	−	0.0651372i
$223$	421.949	+	730.837i	0.126708	+	0.219464i	0.922399	−	0.386238i	$-0.126226\pi$
$223$	421.949	+	730.837i	0.126708	+	0.219464i	−0.795692	+	0.605702i	$0.792892\pi$
$224$	−202.435			−0.0603829
$225$	2590.71	−	1872.94i	0.767619	−	0.554946i
$226$	5644.32			1.66130
$227$	1674.64	+	2900.56i	0.489646	+	0.848092i	0.999929	−	0.0119145i	$-0.00379261\pi$
$227$	1674.64	+	2900.56i	0.489646	+	0.848092i	−0.510283	+	0.860007i	$0.670459\pi$
$228$	−126.939	−	392.251i	−0.0368716	−	0.113936i
$229$	345.311	−	598.097i	0.0996455	−	0.172591i	−0.811892	−	0.583807i	$-0.801562\pi$
$229$	345.311	−	598.097i	0.0996455	−	0.172591i	0.911538	+	0.411216i	$0.134896\pi$
$230$	94.8354	−	164.260i	0.0271881	−	0.0470912i
$231$	5.75938	+	17.7970i	0.00164043	+	0.00506906i
$232$	−2568.52	−	4448.80i	−0.726859	−	1.25896i
$233$	−4203.93			−1.18201			−0.591005	−	0.806668i	$-0.701269\pi$
$233$	−4203.93			−1.18201			−0.591005	+	0.806668i	$0.701269\pi$
$234$	530.731	+	5166.79i	0.148269	+	1.44343i
$235$	−138.859			−0.0385453
$236$	165.416	+	286.510i	0.0456258	+	0.0790262i
$237$	−3875.40	−	828.519i	−1.06217	−	0.227081i
$238$	34.7470	−	60.1836i	0.00946351	−	0.0163913i
$239$	−2153.66	+	3730.24i	−0.582881	+	1.00958i	0.412255	+	0.911068i	$0.364741\pi$
$239$	−2153.66	+	3730.24i	−0.582881	+	1.00958i	−0.995136	+	0.0985105i	$0.968592\pi$
$240$	614.533	−	680.891i	0.165283	−	0.183131i
$241$	2669.25	+	4623.27i	0.713450	+	1.23573i	0.963554	+	0.267512i	$0.0862016\pi$
$241$	2669.25	+	4623.27i	0.713450	+	1.23573i	−0.250105	+	0.968219i	$0.580465\pi$
$242$	3911.67			1.03906
$243$	−1913.31	+	3269.27i	−0.505099	+	0.863062i
$244$	161.229			0.0423018
$245$	62.9369	+	109.010i	0.0164118	+	0.0284261i
$246$	−2940.30	+	3257.80i	−0.762059	+	0.844347i
$247$	4053.25	−	7020.44i	1.04414	−	1.80850i
$248$	972.554	−	1684.51i	0.249021	−	0.431317i
$249$	4801.05	+	1026.42i	1.22191	+	0.261231i
$250$	918.971	+	1591.70i	0.232483	+	0.402673i
$251$	2972.68			0.747546			0.373773	−	0.927520i	$-0.378064\pi$
$251$	2972.68			0.747546			0.373773	+	0.927520i	$0.378064\pi$
$252$	12.3702	+	120.427i	0.00309227	+	0.0301039i
$253$	12.9177			0.00320999
$254$	3930.61	+	6808.01i	0.970977	+	1.68178i
$255$	13.8804	+	42.8917i	0.00340873	+	0.0105333i
$256$	−488.860	+	846.730i	−0.119351	+	0.206721i
$257$	2557.91	−	4430.43i	0.620848	−	1.07534i	−0.368480	−	0.929636i	$-0.620122\pi$
$257$	2557.91	−	4430.43i	0.620848	−	1.07534i	0.989328	−	0.145705i	$-0.0465449\pi$
$258$	2048.06	+	6328.67i	0.494212	+	1.52715i
$259$	−236.152	−	409.028i	−0.0566556	−	0.0981304i
$260$	−107.683			−0.0256854
$261$	−5195.89	+	3756.34i	−1.23225	+	0.890848i
$262$	−3637.60			−0.857753
$263$	−3635.02	−	6296.03i	−0.852261	−	1.47616i	−0.879163	−	0.476522i	$-0.841897\pi$
$263$	−3635.02	−	6296.03i	−0.852261	−	1.47616i	0.0269012	−	0.999638i	$-0.491436\pi$
$264$	56.5310	+	12.0858i	0.0131790	+	0.00281753i
$265$	349.552	−	605.442i	0.0810295	−	0.140347i
$266$	1274.40	−	2207.33i	0.293754	−	0.508797i
$267$	5202.59	−	5764.38i	1.19249	−	1.32125i
$268$	−147.883	−	256.141i	−0.0337067	−	0.0583818i
$269$	793.367			0.179823			0.0899116	−	0.995950i	$-0.471342\pi$
$269$	793.367			0.179823			0.0899116	+	0.995950i	$0.471342\pi$
$270$	−854.854	−	625.722i	−0.192684	−	0.141038i
$271$	7063.92			1.58340			0.791702	−	0.610907i	$-0.209195\pi$
$271$	7063.92			1.58340			0.791702	+	0.610907i	$0.209195\pi$
$272$	−116.036	−	200.981i	−0.0258667	−	0.0448025i
$273$	−1594.87	+	1767.08i	−0.353574	+	0.391754i
$274$	3495.53	−	6054.43i	0.770702	−	1.33490i
$275$	−30.4452	+	52.7326i	−0.00667605	+	0.0115633i
$276$	81.7542	+	17.4782i	0.0178298	+	0.00381182i
$277$	−3579.28	−	6199.49i	−0.776383	−	1.34473i	−0.934014	−	0.357237i	$-0.883719\pi$
$277$	−3579.28	−	6199.49i	−0.776383	−	1.34473i	0.157631	−	0.987498i	$-0.449614\pi$
$278$	−3422.94			−0.738468
$279$	−2215.46	−	992.654i	−0.475398	−	0.213006i
$280$	389.004			0.0830265
$281$	3779.92	+	6547.02i	0.802461	+	1.38990i	0.917992	+	0.396599i	$0.129810\pi$
$281$	3779.92	+	6547.02i	0.802461	+	1.38990i	−0.115532	+	0.993304i	$0.536857\pi$
$282$	−254.208	−	785.522i	−0.0536803	−	0.165876i
$283$	1898.23	−	3287.84i	0.398722	−	0.690606i	−0.594847	−	0.803839i	$-0.702787\pi$
$283$	1898.23	−	3287.84i	0.398722	−	0.690606i	0.993568	+	0.113233i	$0.0361206\pi$
$284$	−170.680	+	295.627i	−0.0356621	+	0.0617685i
$285$	509.087	+	1573.12i	0.105809	+	0.326960i
$286$	−49.4651	−	85.6761i	−0.0102270	−	0.0177138i
$287$	−2011.21			−0.413652
$288$	712.565	+	319.271i	0.145793	+	0.0653236i
$289$	−4901.59			−0.997678
$290$	−896.551	−	1552.87i	−0.181542	−	0.314441i
$291$	−6837.34	−	1461.75i	−1.37736	−	0.294465i
$292$	115.580	−	200.191i	0.0231638	−	0.0401209i
$293$	−301.402	+	522.043i	−0.0600958	+	0.104089i	−0.894508	−	0.447052i	$-0.852474\pi$
$293$	−301.402	+	522.043i	−0.0600958	+	0.104089i	0.834412	+	0.551141i	$0.185807\pi$
$294$	−501.450	+	555.597i	−0.0994733	+	0.110215i
$295$	−663.401	−	1149.04i	−0.130931	−	0.226779i
$296$	−1459.62			−0.286618
$297$	7.79563	−	71.7280i	0.00152306	−	0.0140137i
$298$	−4936.53			−0.959616
$299$	821.915	+	1423.60i	0.158972	+	0.275347i
$300$	−264.033	+	292.544i	−0.0508131	+	0.0563000i
$301$	−1524.25	+	2640.08i	−0.291881	+	0.505553i
$302$	1270.59	−	2200.72i	0.242100	−	0.419329i
$303$	−9043.26	−	1933.36i	−1.71459	−	0.366562i
$304$	−4255.82	−	7371.30i	−0.802921	−	1.39070i
$305$	−646.608			−0.121392
$306$	−217.227	+	157.043i	−0.0405818	+	0.0293384i
$307$	9215.96			1.71330			0.856649	−	0.515900i	$-0.172542\pi$
$307$	9215.96			1.71330			0.856649	+	0.515900i	$0.172542\pi$
$308$	−1.15293	−	1.99693i	−0.000213293	−	0.000369435i
$309$	−59.6779	−	184.409i	−0.0109869	−	0.0339504i
$310$	339.474	−	587.986i	0.0621962	−	0.107727i
$311$	−1096.79	+	1899.69i	−0.199977	+	0.346371i	−0.948521	−	0.316715i	$-0.897420\pi$
$311$	−1096.79	+	1899.69i	−0.199977	+	0.346371i	0.748543	+	0.663086i	$0.230754\pi$
$312$	2264.99	+	6999.01i	0.410993	+	1.27000i
$313$	3104.10	+	5376.46i	0.560556	+	0.970912i	0.997448	+	0.0713977i	$0.0227459\pi$
$313$	3104.10	+	5376.46i	0.560556	+	0.970912i	−0.436892	+	0.899514i	$0.643921\pi$
$314$	−5065.95			−0.910471
$315$	−49.6107	−	482.972i	−0.00887381	−	0.0863885i
$316$	488.518			0.0869661
$317$	−3378.09	−	5851.03i	−0.598526	−	1.03668i	−0.993039	−	0.117787i	$-0.962420\pi$
$317$	−3378.09	−	5851.03i	−0.598526	−	1.03668i	0.394513	−	0.918890i	$-0.370913\pi$
$318$	4064.90	+	869.035i	0.716819	+	0.153249i
$319$	61.0603	−	105.760i	0.0107170	−	0.0185624i
$320$	596.878	−	1033.82i	0.104270	−	0.180602i
$321$	1356.01	−	1502.43i	0.235779	−	0.261239i
$322$	258.422	+	447.600i	0.0447245	+	0.0774651i
$323$	418.357			0.0720682
$324$	146.389	−	443.409i	0.0251009	−	0.0760303i
$325$	−7748.56			−1.32250
$326$	2991.62	+	5181.64i	0.508254	+	0.880321i
$327$	403.257	−	446.801i	0.0681962	−	0.0755601i
$328$	−3107.75	+	5382.79i	−0.523162	+	0.906142i
$329$	189.192	−	327.689i	0.0317036	−	0.0549122i
$330$	19.7324	+	4.21858i	0.00329161	+	0.000703713i
$331$	2846.09	+	4929.58i	0.472615	+	0.818592i	0.999509	−	0.0313384i	$-0.00997695\pi$
$331$	2846.09	+	4929.58i	0.472615	+	0.818592i	−0.526894	+	0.849931i	$0.676644\pi$
$332$	−605.203			−0.100045
$333$	186.150	+	1812.21i	0.0306335	+	0.298224i
$334$	−4734.65			−0.775655
$335$	593.084	+	1027.25i	0.0967273	+	0.167537i
$336$	769.534	+	2377.92i	0.124945	+	0.386090i
$337$	−4764.00	+	8251.49i	−0.770064	+	1.33379i	0.167463	+	0.985878i	$0.446442\pi$
$337$	−4764.00	+	8251.49i	−0.770064	+	1.33379i	−0.937527	+	0.347912i	$0.886891\pi$
$338$	3065.63	−	5309.83i	0.493339	−	0.854487i
$339$	−3072.03	−	9492.83i	−0.492183	−	1.52088i
$340$	−2.77863	−	4.81272i	−0.000443212	−	0.000767666i
$341$	46.2403			0.00734326
$342$	−7967.14	+	5759.80i	−1.25969	+	0.910685i
$343$	−343.000			−0.0539949
$344$	4710.58	+	8158.97i	0.738307	+	1.27878i
$345$	−327.874	−	70.0961i	−0.0511657	−	0.0109387i
$346$	2956.69	−	5121.13i	0.459400	−	0.795705i
$347$	−3361.54	+	5822.36i	−0.520049	+	0.900751i	0.479679	+	0.877444i	$0.340753\pi$
$347$	−3361.54	+	5822.36i	−0.520049	+	0.900751i	−0.999728	+	0.0233073i	$0.992580\pi$
$348$	529.539	−	586.720i	0.0815698	−	0.0903778i
$349$	1612.48	+	2792.90i	0.247319	+	0.428368i	0.962781	−	0.270283i	$-0.0871173\pi$
$349$	1612.48	+	2792.90i	0.247319	+	0.428368i	−0.715462	+	0.698651i	$0.753784\pi$
$350$	−2436.26			−0.372067
$351$	8400.83	−	3704.73i	1.27750	−	0.563373i
$352$	−14.8724			−0.00225199
$353$	−3600.05	−	6235.47i	−0.542809	−	0.940172i	−0.998741	−	0.0501580i	$-0.984028\pi$
$353$	−3600.05	−	6235.47i	−0.542809	−	0.940172i	0.455933	−	0.890014i	$-0.349306\pi$
$354$	5285.65	−	5856.40i	0.793585	−	0.879277i
$355$	684.513	−	1185.61i	0.102338	−	0.177255i
$356$	−478.598	+	828.955i	−0.0712518	+	0.123412i
$357$	−120.131	−	25.6827i	−0.0178095	−	0.00380749i
$358$	−2614.18	−	4527.89i	−0.385932	−	0.668454i
$359$	3642.82			0.535545			0.267772	−	0.963482i	$-0.413712\pi$
$359$	3642.82			0.535545			0.267772	+	0.963482i	$0.413712\pi$
$360$	−1369.28	−	613.517i	−0.200465	−	0.0898200i
$361$	8484.92			1.23705
$362$	−894.033	−	1548.51i	−0.129805	−	0.224829i
$363$	−2129.00	−	6578.79i	−0.307834	−	0.951231i
$364$	146.715	−	254.118i	0.0211263	−	0.0365918i
$365$	−463.534	+	802.864i	−0.0664725	+	0.115134i
$366$	−1183.74	−	3657.85i	−0.169058	−	0.522402i
$367$	1416.38	+	2453.25i	0.201457	+	0.348933i	0.948998	−	0.315282i	$-0.102099\pi$
$367$	1416.38	+	2453.25i	0.201457	+	0.348933i	−0.747541	+	0.664215i	$0.768766\pi$
$368$	1725.98			0.244492
$369$	7079.40	+	3171.98i	0.998750	+	0.447498i
$370$	−509.488			−0.0715865
$371$	952.513	+	1649.80i	0.133294	+	0.230872i
$372$	292.648	+	62.5651i	0.0407879	+	0.00872003i
$373$	−2583.17	+	4474.18i	−0.358583	+	0.621084i	−0.987724	−	0.156207i	$-0.950073\pi$
$373$	−2583.17	+	4474.18i	−0.358583	+	0.621084i	0.629141	+	0.777291i	$0.283407\pi$
$374$	2.55278	−	4.42154i	0.000352944	−	0.000611317i
$375$	2176.82	−	2411.88i	0.299761	−	0.332130i
$376$	−584.683	−	1012.70i	−0.0801934	−	0.138899i
$377$	15540.4			2.12300
$378$	2641.34	−	1164.82i	0.359408	−	0.158497i
$379$	56.3096			0.00763174			0.00381587	−	0.999993i	$-0.498785\pi$
$379$	56.3096			0.00763174			0.00381587	+	0.999993i	$0.498785\pi$
$380$	−101.910	−	176.514i	−0.0137576	−	0.0238289i
$381$	9310.66	−	10316.0i	1.25197	−	1.38716i
$382$	−6459.27	+	11187.8i	−0.865144	+	1.49847i
$383$	2527.70	−	4378.10i	0.337230	−	0.584100i	−0.646680	−	0.762761i	$-0.723843\pi$
$383$	2527.70	−	4378.10i	0.337230	−	0.584100i	0.983911	+	0.178661i	$0.0571765\pi$
$384$	8116.62	+	1735.25i	1.07864	+	0.230603i
$385$	4.62382	+	8.00868i	0.000612082	+	0.00106016i
$386$	−3488.92			−0.460055
$387$	9529.10	−	6889.01i	1.25166	−	0.904879i
$388$	861.889			0.112773
$389$	−1267.99	−	2196.23i	−0.165269	−	0.286255i	0.771482	−	0.636252i	$-0.219516\pi$
$389$	−1267.99	−	2196.23i	−0.165269	−	0.286255i	−0.936751	+	0.349997i	$0.886183\pi$
$390$	790.605	+	2443.03i	0.102651	+	0.317199i
$391$	−42.4171	+	73.4685i	−0.00548625	+	0.00950246i
$392$	−530.008	+	918.001i	−0.0682894	+	0.118281i
$393$	1979.83	+	6117.85i	0.254121	+	0.785253i
$394$	−1199.84	−	2078.19i	−0.153419	−	0.265730i
$395$	−1959.20			−0.249564
$396$	0.908811	+	8.84748i	0.000115327	+	0.00112273i
$397$	3204.52			0.405114			0.202557	−	0.979270i	$-0.435075\pi$
$397$	3204.52			0.405114			0.202557	+	0.979270i	$0.435075\pi$
$398$	−7925.51	−	13727.4i	−0.998165	−	1.72887i
$399$	−4405.99	−	941.955i	−0.552820	−	0.118187i
$400$	−4067.90	+	7045.81i	−0.508488	+	0.880727i
$401$	−775.959	+	1344.00i	−0.0966323	+	0.167372i	−0.910289	−	0.413974i	$-0.864140\pi$
$401$	−775.959	+	1344.00i	−0.0966323	+	0.167372i	0.813656	+	0.581346i	$0.197474\pi$
$402$	−4725.40	+	5235.66i	−0.586272	+	0.649579i
$403$	2942.13	+	5095.93i	0.363668	+	0.629891i
$404$	1139.96			0.140384
$405$	−587.091	+	1778.29i	−0.0720315	+	0.218182i
$406$	4886.12			0.597276
$407$	−17.3495	−	30.0503i	−0.00211298	−	0.00365980i
$408$	−254.365	+	281.832i	−0.0308650	+	0.0341979i
$409$	−283.105	+	490.353i	−0.0342265	+	0.0592821i	−0.882631	−	0.470066i	$-0.844230\pi$
$409$	−283.105	+	490.353i	−0.0342265	+	0.0592821i	0.848405	+	0.529348i	$0.177563\pi$
$410$	−1084.77	+	1878.88i	−0.130666	+	0.226321i
$411$	−12085.1	−	2583.66i	−1.45040	−	0.310080i
$412$	11.9465	+	20.6919i	0.00142855	+	0.00247432i
$413$	3615.47			0.430764
$414$	−203.704	−	1983.11i	−0.0241824	−	0.235421i
$415$	2427.16			0.287096
$416$	−946.289	−	1639.02i	−0.111528	−	0.193172i
$417$	1863.00	+	5756.82i	0.218781	+	0.676050i
$418$	93.6271	−	162.167i	0.0109556	−	0.0189757i
$419$	−5322.92	+	9219.56i	−0.620624	+	1.07495i	0.368746	+	0.929530i	$0.379787\pi$
$419$	−5322.92	+	9219.56i	−0.620624	+	1.07495i	−0.989370	+	0.145422i	$0.953546\pi$
$420$	18.4274	+	56.9420i	0.00214087	+	0.00661545i
$421$	4641.80	+	8039.83i	0.537357	+	0.930730i	0.999045	+	0.0436879i	$0.0139107\pi$
$421$	4641.80	+	8039.83i	0.537357	+	0.930730i	−0.461688	+	0.887042i	$0.652756\pi$
$422$	−7690.78			−0.887159
$423$	−1182.76	+	855.072i	−0.135952	+	0.0982861i
$424$	5887.35			0.674328
$425$	−199.942	−	346.310i	−0.0228203	−	0.0395259i
$426$	7960.12	+	1701.79i	0.905326	+	0.193549i
$427$	880.987	−	1525.91i	0.0998454	−	0.172937i
$428$	−124.742	+	216.060i	−0.0140879	+	0.0244010i
$429$	−117.171	+	129.823i	−0.0131866	+	0.0146105i
$430$	1644.25	+	2847.92i	0.184402	+	0.319393i
$431$	−7494.55			−0.837587			−0.418793	−	0.908082i	$-0.637547\pi$
$431$	−7494.55			−0.837587			−0.418793	+	0.908082i	$0.637547\pi$
$432$	1041.61	−	9583.87i	0.116005	−	1.06737i
$433$	−1564.51			−0.173639			−0.0868195	−	0.996224i	$-0.527670\pi$
$433$	−1564.51			−0.173639			−0.0868195	+	0.996224i	$0.527670\pi$
$434$	925.050	+	1602.23i	0.102313	+	0.177211i
$435$	−2123.71	+	2353.04i	−0.234079	+	0.259355i
$436$	−37.0964	+	64.2529i	−0.00407476	+	0.00705770i
$437$	−1555.71	+	2694.57i	−0.170297	+	0.294963i
$438$	−5390.38	−	1152.41i	−0.588042	−	0.125717i
$439$	−5698.55	−	9870.17i	−0.619537	−	1.07307i	−0.989570	−	0.144051i	$-0.953987\pi$
$439$	−5698.55	−	9870.17i	−0.619537	−	1.07307i	0.370033	−	0.929019i	$-0.379346\pi$
$440$	28.5791			0.00309649
$441$	1207.35	+	540.962i	0.130369	+	0.0584129i
$442$	649.704			0.0699169
$443$	−2167.76	−	3754.67i	−0.232491	−	0.402686i	0.726050	−	0.687642i	$-0.241354\pi$
$443$	−2167.76	−	3754.67i	−0.232491	−	0.402686i	−0.958541	+	0.284956i	$0.908021\pi$
$444$	−69.1434	−	213.659i	−0.00739054	−	0.0228374i
$445$	1919.41	−	3324.52i	0.204469	−	0.354151i
$446$	−1240.31	+	2148.28i	−0.131682	+	0.228081i
$447$	2686.80	+	8302.44i	0.284299	+	0.878506i
$448$	1626.46	+	2817.12i	0.171525	+	0.297090i
$449$	−14016.9			−1.47327			−0.736634	−	0.676291i	$-0.763586\pi$
$449$	−14016.9			−1.47327			−0.736634	+	0.676291i	$0.763586\pi$
$450$	8575.55	+	3842.35i	0.898345	+	0.402511i
$451$	−147.759			−0.0154272
$452$	614.969	+	1065.16i	0.0639949	+	0.110842i
$453$	−4392.80	−	939.136i	−0.455611	−	0.0974049i
$454$	−4922.56	+	8526.13i	−0.508871	+	0.881390i
$455$	−588.400	+	1019.14i	−0.0606256	+	0.105007i
$456$	−9329.23	+	10336.6i	−0.958073	+	1.06153i
$457$	−1253.03	−	2170.31i	−0.128259	−	0.222151i	0.794743	−	0.606946i	$-0.207606\pi$
$457$	−1253.03	−	2170.31i	−0.128259	−	0.222151i	−0.923002	+	0.384795i	$0.874272\pi$
$458$	2030.07			0.207116
$459$	382.351	+	279.867i	0.0388815	+	0.0284598i
$460$	41.3306			0.00418924
$461$	−6832.01	−	11833.4i	−0.690235	−	1.19552i	−0.971761	−	0.235968i	$-0.924174\pi$
$461$	−6832.01	−	11833.4i	−0.690235	−	1.19552i	0.281526	−	0.959554i	$-0.409160\pi$
$462$	−36.8403	+	40.8183i	−0.00370988	+	0.00411048i
$463$	−795.181	+	1377.29i	−0.0798168	+	0.138247i	−0.903171	−	0.429281i	$-0.858767\pi$
$463$	−795.181	+	1377.29i	−0.0798168	+	0.138247i	0.823354	+	0.567528i	$0.192100\pi$
$464$	8158.51	−	14131.0i	0.816270	−	1.41382i
$465$	−1173.66	−	250.917i	−0.117048	−	0.0250236i
$466$	−6178.68	−	10701.8i	−0.614210	−	1.06384i
$467$	−8980.42			−0.889859			−0.444930	−	0.895566i	$-0.646771\pi$
$467$	−8980.42			−0.889859			−0.444930	+	0.895566i	$0.646771\pi$
$468$	−917.215	+	663.095i	−0.0905946	+	0.0654949i
$469$	−3232.25			−0.318234
$470$	−204.086	−	353.487i	−0.0200293	−	0.0346918i
$471$	2757.24	+	8520.10i	0.269739	+	0.833515i
$472$	5586.68	−	9676.41i	0.544804	−	0.943629i
$473$	−111.983	+	193.960i	−0.0108858	+	0.0188547i
$474$	−3586.69	−	11083.2i	−0.347557	−	1.07398i
$475$	−7333.20	−	12701.5i	−0.708358	−	1.22691i
$476$	15.1432			0.00145817
$477$	−750.830	−	7309.50i	−0.0720716	−	0.701633i
$478$	−12661.3			−1.21153
$479$	−2195.90	−	3803.40i	−0.209464	−	0.362801i	0.742082	−	0.670309i	$-0.233838\pi$
$479$	−2195.90	−	3803.40i	−0.209464	−	0.362801i	−0.951546	+	0.307508i	$0.900505\pi$
$480$	377.489	+	80.7032i	0.0358957	+	0.00767413i
$481$	2207.80	−	3824.03i	0.209287	−	0.362496i
$482$	−7846.20	+	13590.0i	−0.741461	+	1.28425i
$483$	612.139	−	678.239i	0.0576673	−	0.0638943i
$484$	426.190	+	738.183i	0.0400254	+	0.0693260i
$485$	−3456.60			−0.323621
$486$	−11134.5	−	65.6670i	−1.03924	−	0.00612904i
$487$	9440.93			0.878458			0.439229	−	0.898375i	$-0.355252\pi$
$487$	9440.93			0.878458			0.439229	+	0.898375i	$0.355252\pi$
$488$	−2722.63	−	4715.73i	−0.252556	−	0.437441i
$489$	7086.43	−	7851.64i	0.655337	−	0.726101i
$490$	−185.002	+	320.432i	−0.0170562	+	0.0295421i
$491$	3654.61	−	6329.98i	0.335907	−	0.581808i	−0.647751	−	0.761852i	$-0.724290\pi$
$491$	3654.61	−	6329.98i	0.335907	−	0.581808i	0.983659	+	0.180043i	$0.0576238\pi$
$492$	−935.144	−	199.924i	−0.0856902	−	0.0183197i
$493$	401.001	+	694.554i	0.0366332	+	0.0634505i
$494$	23828.9			2.17027
$495$	−3.64478	−	35.4827i	−0.000330951	−	0.00322188i
$496$	6178.34			0.559306
$497$	1865.26	+	3230.73i	0.168347	+	0.291586i
$498$	4443.39	+	13730.4i	0.399825	+	1.23549i
$499$	4297.36	−	7443.25i	0.385524	−	0.667746i	−0.606318	−	0.795222i	$-0.707354\pi$
$499$	4297.36	−	7443.25i	0.385524	−	0.667746i	0.991842	+	0.127476i	$0.0406875\pi$
$500$	−200.250	+	346.844i	−0.0179109	+	0.0310226i
$501$	2576.93	+	7962.91i	0.229798	+	0.710093i
$502$	4369.07	+	7567.45i	0.388448	+	0.672812i
$503$	13124.1			1.16337			0.581684	−	0.813415i	$-0.302394\pi$
$503$	13124.1			1.16337			0.581684	+	0.813415i	$0.302394\pi$
$504$	3313.44	−	2395.43i	0.292842	−	0.211708i
$505$	−4571.80			−0.402856
$506$	18.9856	+	32.8841i	0.00166801	+	0.00288908i
$507$	−10598.8	−	2265.92i	−0.928421	−	0.198487i
$508$	−856.507	+	1483.51i	−0.0748058	+	0.129568i
$509$	−10630.6	+	18412.8i	−0.925725	+	1.60340i	−0.135333	+	0.990800i	$0.543211\pi$
$509$	−10630.6	+	18412.8i	−0.925725	+	1.60340i	−0.790391	+	0.612602i	$0.790123\pi$
$510$	−88.7871	+	98.3745i	−0.00770894	+	0.00854136i
$511$	−1263.11	−	2187.77i	−0.109348	−	0.189395i
$512$	9904.75			0.854946
$513$	14023.3	+	10264.5i	1.20691	+	0.883413i
$514$	15037.8			1.29045
$515$	−47.9113	−	82.9848i	−0.00409946	−	0.00710048i
$516$	−971.159	+	1076.03i	−0.0828545	+	0.0918012i
$517$	13.8994	−	24.0745i	0.00118239	−	0.00204796i
$518$	694.165	−	1202.33i	0.0588800	−	0.101983i
$519$	−10222.2	−	2185.39i	−0.864552	−	0.184832i
$520$	1818.41	+	3149.58i	0.153351	+	0.265612i
$521$	18918.3			1.59084			0.795419	−	0.606059i	$-0.207251\pi$
$521$	18918.3			1.59084			0.795419	+	0.606059i	$0.207251\pi$
$522$	−17199.0	−	7706.14i	−1.44210	−	0.646147i
$523$	−3728.42			−0.311725			−0.155863	−	0.987779i	$-0.549816\pi$
$523$	−3728.42			−0.311725			−0.155863	+	0.987779i	$0.549816\pi$
$524$	−396.329	−	686.462i	−0.0330414	−	0.0572294i
$525$	1325.98	+	4097.39i	0.110230	+	0.340619i
$526$	10685.1	−	18507.1i	0.885723	−	1.53412i
$527$	−151.837	+	262.989i	−0.0125505	+	0.0217381i
$528$	56.5357	+	174.700i	0.00465985	+	0.0143993i
$529$	5768.03	+	9990.53i	0.474072	+	0.821117i
$530$	2055.00			0.168422
$531$	−12726.3	−	5702.14i	−1.04007	−	0.466011i
$532$	555.402			0.0452627
$533$	−9401.47	−	16283.8i	−0.764020	−	1.32332i
$534$	22320.6	+	4771.92i	1.80882	+	0.386706i
$535$	500.277	−	866.505i	0.0404278	−	0.0700229i
$536$	−4994.52	+	8650.77i	−0.402482	+	0.697120i
$537$	−6192.36	+	6861.02i	−0.497616	+	0.551350i
$538$	1166.04	+	2019.65i	0.0934418	+	0.161846i
$539$	−25.1994			−0.00201375
$540$	24.9424	−	229.497i	0.00198769	−	0.0182888i
$541$	−20984.0			−1.66761			−0.833803	−	0.552062i	$-0.813841\pi$
$541$	−20984.0			−1.66761			−0.833803	+	0.552062i	$0.813841\pi$
$542$	10382.1	+	17982.4i	0.822786	+	1.42511i
$543$	−2117.75	+	2346.43i	−0.167369	+	0.185442i
$544$	48.8357	−	84.5859i	0.00384892	−	0.00666653i
$545$	148.775	−	257.686i	0.0116932	−	0.0202533i
$546$	−6842.44	−	1462.84i	−0.536318	−	0.114659i
$547$	1420.25	+	2459.94i	0.111015	+	0.192284i	0.916180	−	0.400767i	$-0.131256\pi$
$547$	1420.25	+	2459.94i	0.111015	+	0.192284i	−0.805165	+	0.593051i	$0.797923\pi$
$548$	1523.40			0.118753
$549$	−5507.64	+	3981.72i	−0.428161	+	0.309537i
$550$	−178.986			−0.0138763
$551$	14707.3	+	25473.8i	1.13712	+	1.96955i
$552$	−869.345	−	2686.35i	−0.0670322	−	0.207135i
$553$	2669.36	−	4623.47i	0.205267	−	0.355533i
$554$	10521.2	−	18223.3i	0.806866	−	1.39753i
$555$	277.299	+	856.876i	0.0212084	+	0.0655358i
$556$	−372.941	−	645.953i	−0.0284464	−	0.0492707i
$557$	5824.36			0.443063			0.221532	−	0.975153i	$-0.428894\pi$
$557$	5824.36			0.443063			0.221532	+	0.975153i	$0.428894\pi$
$558$	−729.182	−	7098.75i	−0.0553203	−	0.538555i
$559$	−28500.6			−2.15643
$560$	617.806	+	1070.07i	0.0466198	+	0.0807478i
$561$	−8.82571	−	1.88685i	−0.000664210	−	0.000142001i
$562$	−11111.0	+	19244.8i	−0.833967	+	1.44447i
$563$	−3690.44	+	6392.02i	−0.276258	+	0.478493i	−0.970452	−	0.241295i	$-0.922428\pi$
$563$	−3690.44	+	6392.02i	−0.276258	+	0.478493i	0.694194	+	0.719788i	$0.255761\pi$
$564$	120.541	−	133.558i	0.00899949	−	0.00997127i
$565$	−2466.33	−	4271.80i	−0.183645	−	0.318082i
$566$	11159.6			0.828753
$567$	−3396.64	−	3808.34i	−0.251580	−	0.282072i
$568$	11528.9			0.851660
$569$	6025.58	+	10436.6i	0.443946	+	0.768937i	0.997978	−	0.0635582i	$-0.0202448\pi$
$569$	6025.58	+	10436.6i	0.443946	+	0.768937i	−0.554032	+	0.832495i	$0.686912\pi$
$570$	−3256.41	+	3608.04i	−0.239291	+	0.265130i
$571$	9135.44	−	15823.0i	0.669538	−	1.15967i	−0.308495	−	0.951226i	$-0.599825\pi$
$571$	9135.44	−	15823.0i	0.669538	−	1.15967i	0.978033	−	0.208448i	$-0.0668412\pi$
$572$	10.7788	−	18.6694i	0.000787910	−	0.00136470i
$573$	22331.6	+	4774.27i	1.62813	+	0.348077i
$574$	−2955.96	−	5119.87i	−0.214947	−	0.372298i
$575$	2974.04			0.215697
$576$	−1282.08	−	12481.3i	−0.0927430	−	0.902875i
$577$	10165.1			0.733413			0.366707	−	0.930337i	$-0.380485\pi$
$577$	10165.1			0.733413			0.366707	+	0.930337i	$0.380485\pi$
$578$	−7204.06	−	12477.8i	−0.518425	−	0.897938i
$579$	1898.91	+	5867.79i	0.136297	+	0.421170i
$580$	195.365	−	338.382i	0.0139864	−	0.0242251i
$581$	−3306.95	+	5727.81i	−0.236137	+	0.409001i
$582$	−6327.97	−	19554.0i	−0.450692	−	1.39268i
$583$	69.9788	+	121.207i	0.00497123	+	0.00861042i
$584$	−7807.08			−0.553184
$585$	3678.48	−	2659.34i	0.259977	−	0.187949i
$586$	−1771.93			−0.124911
$587$	2317.67	+	4014.32i	0.162965	+	0.282264i	0.935931	−	0.352184i	$-0.114561\pi$
$587$	2317.67	+	4014.32i	0.162965	+	0.282264i	−0.772966	+	0.634448i	$0.781228\pi$
$588$	−159.483	−	34.0958i	−0.0111853	−	0.00239131i
$589$	−5568.84	+	9645.52i	−0.389576	+	0.674765i
$590$	1950.05	−	3377.59i	0.136072	−	0.235683i
$591$	−2842.13	+	3149.03i	−0.197817	+	0.219177i
$592$	−2318.14	−	4015.14i	−0.160937	−	0.278752i
$593$	16282.3			1.12755			0.563773	−	0.825930i	$-0.309349\pi$
$593$	16282.3			1.12755			0.563773	+	0.825930i	$0.309349\pi$
$594$	194.053	−	85.5765i	0.0134042	−	0.00591119i
$595$	−60.7319			−0.00418448
$596$	−537.852	−	931.588i	−0.0369653	−	0.0640257i
$597$	−18773.6	+	20800.8i	−1.28702	+	1.42600i
$598$	−2416.00	+	4184.64i	−0.165213	+	0.286158i
$599$	−4879.82	+	8452.09i	−0.332861	+	0.576532i	−0.983072	−	0.183222i	$-0.941347\pi$
$599$	−4879.82	+	8452.09i	−0.332861	+	0.576532i	0.650210	+	0.759754i	$0.274681\pi$
$600$	13015.1	+	2782.50i	0.885569	+	0.189325i
$601$	−5922.17	−	10257.5i	−0.401947	−	0.696193i	0.592014	−	0.805928i	$-0.298333\pi$
$601$	−5922.17	−	10257.5i	−0.401947	−	0.696193i	−0.993961	+	0.109735i	$0.965000\pi$
$602$	−8960.99			−0.606683
$603$	11377.4	+	5097.75i	0.768365	+	0.344272i
$604$	553.740			0.0373036
$605$	−1709.23	−	2960.48i	−0.114860	−	0.198943i
$606$	−8369.57	−	25862.6i	−0.561040	−	1.73366i
$607$	11103.1	−	19231.1i	0.742438	−	1.28594i	−0.208944	−	0.977928i	$-0.567003\pi$
$607$	11103.1	−	19231.1i	0.742438	−	1.28594i	0.951382	−	0.308013i	$-0.0996639\pi$
$608$	1791.13	−	3102.32i	0.119473	−	0.206934i
$609$	−2659.37	−	8217.66i	−0.176951	−	0.546792i
$610$	−950.345	−	1646.04i	−0.0630792	−	0.109256i
$611$	3537.52			0.234227
$612$	−53.3037	−	23.8832i	−0.00352071	−	0.00157748i
$613$	−19461.8			−1.28231			−0.641154	−	0.767412i	$-0.721544\pi$
$613$	−19461.8			−1.28231			−0.641154	+	0.767412i	$0.721544\pi$
$614$	13545.1	+	23460.7i	0.890283	+	1.54202i
$615$	3750.39	+	801.794i	0.245903	+	0.0525715i
$616$	−38.9384	+	67.4433i	−0.00254687	+	0.00441131i
$617$	7910.09	−	13700.7i	0.516124	−	0.893952i	−0.483701	−	0.875233i	$-0.660708\pi$
$617$	7910.09	−	13700.7i	0.516124	−	0.893952i	0.999825	−	0.0187190i	$-0.00595881\pi$
$618$	381.733	−	422.953i	0.0248472	−	0.0275302i
$619$	7699.02	+	13335.1i	0.499919	+	0.865885i	1.00000		9.34445e-5i	$-2.97443e-5\pi$
$619$	7699.02	+	13335.1i	0.499919	+	0.865885i	−0.500081	+	0.865979i	$0.666696\pi$
$620$	147.948			0.00958341
$621$	−3224.39	+	1421.94i	−0.208358	+	0.0918850i
$622$	−6447.95			−0.415658
$623$	5230.30	+	9059.15i	0.336353	+	0.582580i
$624$	−15655.7	+	17346.2i	−1.00437	+	1.11283i
$625$	−6596.96	+	11426.3i	−0.422205	+	0.731281i
$626$	−9124.43	+	15804.0i	−0.582565	+	1.00903i
$627$	−323.697	−	69.2030i	−0.0206176	−	0.00440782i
$628$	−551.953	−	956.010i	−0.0350722	−	0.0607468i
$629$	227.879			0.0144453
$630$	1156.57	−	836.135i	0.0731409	−	0.0528768i
$631$	15072.8			0.950930			0.475465	−	0.879735i	$-0.342280\pi$
$631$	15072.8			0.950930			0.475465	+	0.879735i	$0.342280\pi$
$632$	−8249.46	−	14288.5i	−0.519218	−	0.899312i
$633$	4185.86	+	12934.6i	0.262832	+	0.812173i
$634$	9929.84	−	17199.0i	0.622025	−	1.07738i
$635$	3435.01	−	5949.62i	0.214668	−	0.371817i
$636$	278.888	+	861.785i	0.0173878	+	0.0537296i
$637$	−1603.36	−	2777.11i	−0.0997293	−	0.172736i
$638$	358.971			0.0222755
$639$	−1470.32	−	14313.9i	−0.0910248	−	0.886147i
$640$	4103.34			0.253435
$641$	−10224.1	−	17708.7i	−0.629996	−	1.09119i	−0.987552	−	0.157293i	$-0.949723\pi$
$641$	−10224.1	−	17708.7i	−0.629996	−	1.09119i	0.357556	−	0.933892i	$-0.383610\pi$
$642$	5817.66	+	1243.76i	0.357640	+	0.0764597i
$643$	−4171.56	+	7225.36i	−0.255848	+	0.443142i	−0.965126	−	0.261787i	$-0.915688\pi$
$643$	−4171.56	+	7225.36i	−0.255848	+	0.443142i	0.709277	+	0.704929i	$0.249021\pi$
$644$	−56.3120	+	97.5352i	−0.00344566	+	0.00596805i
$645$	3894.83	−	4315.40i	0.237765	−	0.263440i
$646$	614.876	+	1065.00i	0.0374489	+	0.0648634i
$647$	−2134.15			−0.129679			−0.0648394	−	0.997896i	$-0.520653\pi$
$647$	−2134.15			−0.129679			−0.0648394	+	0.997896i	$0.520653\pi$
$648$	−15441.1	+	3206.05i	−0.936088	+	0.194360i
$649$	265.620			0.0160655
$650$	−11388.4	−	19725.2i	−0.687213	−	1.19029i
$651$	2191.22	−	2427.83i	0.131921	−	0.146166i
$652$	−651.896	+	1129.12i	−0.0391568	+	0.0678215i
$653$	12547.6	−	21733.2i	0.751956	−	1.30243i	−0.194917	−	0.980820i	$-0.562444\pi$
$653$	12547.6	−	21733.2i	0.751956	−	1.30243i	0.946873	−	0.321607i	$-0.104223\pi$
$654$	1730.09	+	369.875i	0.103443	+	0.0221151i
$655$	1589.47	+	2753.05i	0.0948181	+	0.164230i
$656$	−19742.6			−1.17503
$657$	995.659	+	9692.97i	0.0591239	+	0.575584i
$658$	1112.25			0.0658966
$659$	−10513.7	−	18210.3i	−0.621481	−	1.07644i	−0.989210	−	0.146504i	$-0.953198\pi$
$659$	−10513.7	−	18210.3i	−0.621481	−	1.07644i	0.367729	−	0.929933i	$-0.380136\pi$
$660$	1.35381	+	4.18339i	7.98441e−5	+	0.000246725i
$661$	1328.17	−	2300.46i	0.0781541	−	0.135367i	−0.824299	−	0.566154i	$-0.808431\pi$
$661$	1328.17	−	2300.46i	0.0781541	−	0.135367i	0.902454	+	0.430787i	$0.141764\pi$
$662$	−8366.03	+	14490.4i	−0.491171	+	0.850732i
$663$	−353.614	−	1092.70i	−0.0207138	−	0.0640072i
$664$	10219.9	+	17701.4i	0.597302	+	1.03456i
$665$	−2227.44			−0.129889
$666$	−4339.69	+	3137.35i	−0.252492	+	0.182538i
$667$	−5964.68			−0.346257
$668$	−515.857	−	893.491i	−0.0298789	−	0.0517518i
$669$	4288.12	+	916.756i	0.247815	+	0.0529803i
$670$	−1743.36	+	3019.59i	−0.100525	+	0.174115i
$671$	64.7239	−	112.105i	0.00372376	−	0.00644973i
$672$	−704.769	+	780.872i	−0.0404570	+	0.0448256i
$673$	7895.64	+	13675.6i	0.452235	+	0.783295i	0.998525	−	0.0543020i	$-0.0172934\pi$
$673$	7895.64	+	13675.6i	0.452235	+	0.783295i	−0.546289	+	0.837597i	$0.683960\pi$
$674$	−28007.3			−1.60060
$675$	1794.79	−	16514.0i	0.102343	−	0.941663i
$676$	1336.05			0.0760154
$677$	−2006.04	−	3474.56i	−0.113882	−	0.197250i	0.803450	−	0.595372i	$-0.202995\pi$
$677$	−2006.04	−	3474.56i	−0.113882	−	0.197250i	−0.917332	+	0.398122i	$0.869662\pi$
$678$	19650.5	−	21772.3i	1.11308	−	1.23328i
$679$	4709.53	−	8157.15i	0.266179	−	0.461035i
$680$	−93.8437	+	162.542i	−0.00529227	+	0.00916648i
$681$	17018.8	+	3638.44i	0.957652	+	0.204736i
$682$	67.9611	+	117.712i	0.00381579	+	0.00660913i
$683$	−7438.45			−0.416727			−0.208363	−	0.978051i	$-0.566814\pi$
$683$	−7438.45			−0.416727			−0.208363	+	0.978051i	$0.566814\pi$
$684$	−1955.00	−	875.952i	−0.109285	−	0.0489662i
$685$	−6109.58			−0.340781
$686$	−504.121	−	873.162i	−0.0280575	−	0.0485969i
$687$	−1104.91	−	3414.25i	−0.0613607	−	0.189609i
$688$	−14962.5	+	25915.7i	−0.829126	+	1.43609i
$689$	−8905.10	+	15424.1i	−0.492391	+	0.852846i
$690$	−303.449	−	937.681i	−0.0167422	−	0.0517346i
$691$	−8035.53	−	13918.0i	−0.442382	−	0.766228i	0.555484	−	0.831527i	$-0.312533\pi$
$691$	−8035.53	−	13918.0i	−0.442382	−	0.766228i	−0.997866	+	0.0652991i	$0.979200\pi$
$692$	1288.57			0.0707860
$693$	88.7008	+	39.7431i	0.00486214	+	0.00217852i
$694$	−19762.4			−1.08093
$695$	1495.68	+	2590.59i	0.0816320	+	0.141391i
$696$	−26102.9	−	5580.54i	−1.42159	−	0.303922i
$697$	485.187	−	840.369i	0.0263670	−	0.0456689i
$698$	−4739.86	+	8209.67i	−0.257029	+	0.445187i
$699$	−14635.8	+	16216.2i	−0.791955	+	0.877472i
$700$	−265.439	−	459.754i	−0.0143324	−	0.0248244i
$701$	−27269.4			−1.46926			−0.734630	−	0.678467i	$-0.762644\pi$
$701$	−27269.4			−1.46926			−0.734630	+	0.678467i	$0.762644\pi$
$702$	21778.0	+	15940.7i	1.17088	+	0.857042i
$703$	8357.81			0.448394
$704$	119.492	+	206.967i	0.00639707	+	0.0110800i
$705$	−483.430	+	535.632i	−0.0258256	+	0.0286143i
$706$	10582.3	−	18329.0i	0.564121	−	0.977086i
$707$	6228.97	−	10788.9i	0.331350	−	0.573915i
$708$	1681.07	+	359.395i	0.0892351	+	0.0190775i
$709$	−6412.84	−	11107.4i	−0.339689	−	0.588358i	0.644686	−	0.764448i	$-0.276988\pi$
$709$	−6412.84	−	11107.4i	−0.339689	−	0.588358i	−0.984374	+	0.176090i	$0.943655\pi$
$710$	4024.22			0.212713
$711$	−16687.9	+	12064.5i	−0.880235	+	0.636361i
$712$	32327.8			1.70159
$713$	−1129.24	−	1955.91i	−0.0593135	−	0.102734i
$714$	−111.181	−	343.560i	−0.00582754	−	0.0180076i
$715$	−43.2283	+	74.8736i	−0.00226104	+	0.00391624i
$716$	569.648	−	986.659i	0.0297329	−	0.0514989i
$717$	6891.14	+	21294.2i	0.358932	+	1.10913i
$718$	5353.99	+	9273.39i	0.278286	+	0.482005i
$719$	−9140.58			−0.474111			−0.237056	−	0.971496i	$-0.576182\pi$
$719$	−9140.58			−0.474111			−0.237056	+	0.971496i	$0.576182\pi$
$720$	−486.993	−	4740.99i	−0.0252072	−	0.245397i
$721$	261.112			0.0134873
$722$	12470.6	+	21599.7i	0.642809	+	1.11338i
$723$	27126.6	+	5799.39i	1.39537	+	0.298315i
$724$	194.816	−	337.432i	0.0100004	−	0.0173212i
$725$	14057.9	−	24349.0i	0.720135	−	1.24731i
$726$	13618.3	−	15088.8i	0.696174	−	0.771349i
$727$	5825.85	+	10090.7i	0.297206	+	0.514776i	0.975496	−	0.220019i	$-0.0706119\pi$
$727$	5825.85	+	10090.7i	0.297206	+	0.514776i	−0.678290	+	0.734795i	$0.737279\pi$
$728$	−9910.15			−0.504526
$729$	5949.75	+	18762.2i	0.302279	+	0.953220i
$730$	−2725.10			−0.138165
$731$	−735.423	−	1273.79i	−0.0372101	−	0.0644498i
$732$	561.312	−	621.923i	0.0283425	−	0.0314029i
$733$	−9415.51	+	16308.1i	−0.474447	+	0.821766i	−0.999572	−	0.0292588i	$-0.990685\pi$
$733$	−9415.51	+	16308.1i	−0.474447	+	0.821766i	0.525125	+	0.851025i	$0.324019\pi$
$734$	−4163.43	+	7211.27i	−0.209366	+	0.362633i
$735$	639.606	+	136.741i	0.0320982	+	0.00686227i
$736$	363.203	+	629.086i	0.0181900	+	0.0315060i
$737$	−237.466			−0.0118686
$738$	2330.07	+	22683.7i	0.116221	+	1.13144i
$739$	7467.51			0.371714			0.185857	−	0.982577i	$-0.440494\pi$
$739$	7467.51			0.371714			0.185857	+	0.982577i	$0.440494\pi$
$740$	−55.5105	−	96.1470i	−0.00275758	−	0.00477626i
$741$	−12969.4	−	40076.3i	−0.642970	−	1.98683i
$742$	−2799.89	+	4849.56i	−0.138527	+	0.239936i
$743$	6233.54	−	10796.8i	0.307788	−	0.533104i	−0.670090	−	0.742280i	$-0.733745\pi$
$743$	6233.54	−	10796.8i	0.307788	−	0.533104i	0.977878	+	0.209175i	$0.0670779\pi$
$744$	−3111.92	−	9616.07i	−0.153345	−	0.473847i
$745$	2157.05	+	3736.12i	0.106078	+	0.183733i
$746$	−15186.3			−0.745324
$747$	20674.0	−	14946.1i	1.01261	−	0.732061i
$748$	1.11254			5.43828e−5
$749$	1363.23	+	2361.18i	0.0665038	+	0.115188i
$750$	9339.18	+	1996.62i	0.454692	+	0.0972084i
$751$	1228.34	−	2127.55i	0.0596842	−	0.103376i	−0.834639	−	0.550797i	$-0.814324\pi$
$751$	1228.34	−	2127.55i	0.0596842	−	0.103376i	0.894324	+	0.447421i	$0.147657\pi$
$752$	1857.16	−	3216.69i	0.0900580	−	0.155985i
$753$	10349.3	−	11466.8i	0.500861	−	0.554945i
$754$	22840.3	+	39560.5i	1.10318	+	1.91076i
$755$	−2220.77			−0.107049
$756$	507.601	+	371.545i	0.0244197	+	0.0178743i
$757$	−7246.72			−0.347935			−0.173967	−	0.984751i	$-0.555659\pi$
$757$	−7246.72			−0.347935			−0.173967	+	0.984751i	$0.555659\pi$
$758$	82.7604	+	143.345i	0.00396569	+	0.00686878i
$759$	44.9723	−	49.8285i	0.00215071	−	0.00238295i
$760$	−3441.87	+	5961.49i	−0.164276	+	0.284534i
$761$	6341.49	−	10983.8i	0.302075	−	0.523209i	−0.674531	−	0.738246i	$-0.735654\pi$
$761$	6341.49	−	10983.8i	0.302075	−	0.523209i	0.976606	+	0.215038i	$0.0689875\pi$
$762$	39945.4	+	8539.91i	1.89904	+	0.405995i
$763$	405.405	+	702.181i	0.0192354	+	0.0333167i
$764$	−2815.04			−0.133304
$765$	213.774	+	95.7832i	0.0101033	+	0.00452686i
$766$	14860.2			0.700942
$767$	16900.6	+	29272.7i	0.795627	+	1.37807i
$768$	1564.22	+	4833.58i	0.0734949	+	0.227105i
$769$	7148.72	−	12381.9i	0.335227	−	0.580630i	−0.648302	−	0.761384i	$-0.724520\pi$
$769$	7148.72	−	12381.9i	0.335227	−	0.580630i	0.983528	+	0.180754i	$0.0578537\pi$
$770$	−13.5916	+	23.5414i	−0.000636114	+	0.00110178i
$771$	−8184.64	−	25291.2i	−0.382312	−	1.18137i
$772$	−380.130	−	658.405i	−0.0177217	−	0.0306949i
$773$	6703.00			0.311889			0.155944	−	0.987766i	$-0.450158\pi$
$773$	6703.00			0.311889			0.155944	+	0.987766i	$0.450158\pi$
$774$	31542.4	+	14132.8i	1.46482	+	0.656323i
$775$	10645.9			0.493435
$776$	−14554.5	−	25209.1i	−0.673293	−	1.16618i
$777$	−2399.94	−	513.081i	−0.110807	−	0.0236894i
$778$	3727.24	−	6455.76i	0.171758	−	0.297494i
$779$	17795.0	−	30821.8i	0.818449	−	1.41760i
$780$	−374.893	+	415.375i	−0.0172094	+	0.0190677i
$781$	137.036	+	237.354i	0.00627854	+	0.0108748i
$782$	−249.368			−0.0114033
$783$	−3599.60	+	33120.1i	−0.164290	+	1.51164i
$784$	−3366.99			−0.153379
$785$	2213.60	+	3834.07i	0.100646	+	0.174323i
$786$	−12664.1	+	14031.6i	−0.574701	+	0.636758i
$787$	−17467.5	+	30254.6i	−0.791167	+	1.37034i	0.134078	+	0.990971i	$0.457193\pi$
$787$	−17467.5	+	30254.6i	−0.791167	+	1.37034i	−0.925245	+	0.379371i	$0.876141\pi$
$788$	261.454	−	452.852i	0.0118197	−	0.0204723i
$789$	−36941.4	−	7897.69i	−1.66686	−	0.356357i
$790$	−2879.51	−	4987.45i	−0.129681	−	0.224615i
$791$	13441.2			0.604192
$792$	243.430	−	175.986i	0.0109216	−	0.00789571i
$793$	16472.8			0.737662
$794$	4709.81	+	8157.63i	0.210510	+	0.364614i
$795$	−1118.48	−	3456.18i	−0.0498972	−	0.154186i
$796$	1727.02	−	2991.29i	0.0769004	−	0.133195i
$797$	−1307.08	+	2263.93i	−0.0580918	+	0.100618i	−0.893609	−	0.448847i	$-0.851835\pi$
$797$	−1307.08	+	2263.93i	−0.0580918	+	0.100618i	0.835517	+	0.549465i	$0.185168\pi$
$798$	−4077.75	−	12600.6i	−0.180891	−	0.558967i
$799$	91.2816	+	158.104i	0.00404169	+	0.00700041i
$800$	−3424.08			−0.151324
$801$	−4122.85	−	40136.9i	−0.181865	−	1.77050i
$802$	−4561.83			−0.200853
$803$	−92.7973	−	160.730i	−0.00407814	−	0.00706355i
$804$	−1502.89	−	321.301i	−0.0659237	−	0.0140938i
$805$	225.839	−	391.164i	0.00988791	−	0.0171264i
$806$	−8648.34	+	14979.4i	−0.377946	+	0.654622i
$807$	2762.07	−	3060.33i	0.120483	−	0.133493i
$808$	−19250.2	−	33342.3i	−0.838142	−	1.45170i
$809$	14079.7			0.611885			0.305942	−	0.952050i	$-0.401029\pi$
$809$	14079.7			0.611885			0.305942	+	0.952050i	$0.401029\pi$
$810$	−5389.79	+	1119.08i	−0.233800	+	0.0485439i
$811$	360.517			0.0156097			0.00780485	−	0.999970i	$-0.497516\pi$
$811$	360.517			0.0156097			0.00780485	+	0.999970i	$0.497516\pi$
$812$	532.360	+	922.074i	0.0230076	+	0.0398503i
$813$	24592.7	−	27248.3i	1.06089	−	1.17545i
$814$	50.9986	−	88.3321i	0.00219594	−	0.00380349i
$815$	2614.42	−	4528.31i	0.112367	−	0.194626i
$816$	−1179.24	−	252.109i	−0.0505902	−	0.0108157i
$817$	−26972.8	−	46718.3i	−1.15503	−	2.00057i
$818$	−1664.36			−0.0711407
$819$	1263.87	+	12304.1i	0.0539233	+	0.524955i
$820$	−472.760			−0.0201335
$821$	10003.0	+	17325.6i	0.425220	+	0.736502i	0.996441	−	0.0842940i	$-0.0268635\pi$
$821$	10003.0	+	17325.6i	0.425220	+	0.736502i	−0.571221	+	0.820796i	$0.693530\pi$
$822$	−11184.8	−	34561.8i	−0.474591	−	1.46652i
$823$	−5593.59	+	9688.38i	−0.236914	+	0.410347i	−0.959827	−	0.280592i	$-0.909469\pi$
$823$	−5593.59	+	9688.38i	−0.236914	+	0.410347i	0.722913	+	0.690939i	$0.242803\pi$
$824$	403.474	−	698.837i	0.0170579	−	0.0295451i
$825$	97.4166	+	301.025i	0.00411105	+	0.0127035i
$826$	5313.80	+	9203.77i	0.223839	+	0.387700i
$827$	−10206.8			−0.429172			−0.214586	−	0.976705i	$-0.568840\pi$
$827$	−10206.8			−0.429172			−0.214586	+	0.976705i	$0.568840\pi$
$828$	352.044	−	254.508i	0.0147758	−	0.0106821i
$829$	12084.0			0.506267			0.253134	−	0.967431i	$-0.418539\pi$
$829$	12084.0			0.506267			0.253134	+	0.967431i	$0.418539\pi$
$830$	3567.29	+	6178.74i	0.149184	+	0.258394i
$831$	−36375.0	−	7776.59i	−1.51845	−	0.324629i
$832$	−15205.9	+	26337.4i	−0.633618	+	1.09746i
$833$	82.7457	−	143.320i	0.00344174	−	0.00596127i
$834$	−11916.8	+	13203.6i	−0.494778	+	0.548205i
$835$	2068.84	+	3583.34i	0.0857427	+	0.148511i
$836$	40.8040			0.00168808
$837$	−11542.1	+	5090.00i	−0.476645	+	0.210198i
$838$	−31293.2			−1.28998
$839$	2735.13	+	4737.38i	0.112547	+	0.194937i	0.916797	−	0.399354i	$-0.130766\pi$
$839$	2735.13	+	4737.38i	0.112547	+	0.194937i	−0.804249	+	0.594292i	$0.797432\pi$
$840$	1354.30	−	1500.54i	0.0556283	−	0.0616351i
$841$	−15999.8	+	27712.5i	−0.656026	+	1.13627i
$842$	−13644.5	+	23632.9i	−0.558455	+	0.967273i
$843$	38414.1	+	8212.53i	1.56946	+	0.335533i
$844$	−837.937	−	1451.35i	−0.0341742	−	0.0591914i
$845$	−5358.20			−0.218139
$846$	−3915.08	−	1754.18i	−0.159105	−	0.0712885i
$847$	9315.15			0.377889
$848$	9350.14	+	16194.9i	0.378638	+	0.655821i
$849$	−6073.85	−	18768.7i	−0.245529	−	0.758704i
$850$	587.726	−	1017.97i	0.0237163	−	0.0410778i
$851$	−847.394	+	1467.73i	−0.0341343	+	0.0591224i
$852$	546.133	+	1687.59i	0.0219603	+	0.0678592i
$853$	1202.54	+	2082.86i	0.0482699	+	0.0836060i	0.889151	−	0.457614i	$-0.151296\pi$
$853$	1202.54	+	2082.86i	0.0482699	+	0.0836060i	−0.840881	+	0.541220i	$0.817963\pi$
$854$	5179.29			0.207531
$855$	7840.50	+	3513.00i	0.313613	+	0.140517i
$856$	8425.93			0.336440
$857$	33.0440	+	57.2339i	0.00131711	+	0.00228130i	0.866683	−	0.498859i	$-0.166247\pi$
$857$	33.0440	+	57.2339i	0.00131711	+	0.00228130i	−0.865366	+	0.501140i	$0.832914\pi$
$858$	−502.697	−	107.471i	−0.0200021	−	0.00427624i
$859$	−15282.9	+	26470.7i	−0.607037	+	1.05142i	0.384689	+	0.923046i	$0.374309\pi$
$859$	−15282.9	+	26470.7i	−0.607037	+	1.05142i	−0.991726	+	0.128373i	$0.959025\pi$
$860$	−358.293	+	620.582i	−0.0142066	+	0.0246066i
$861$	−7001.95	+	7758.03i	−0.277150	+	0.307077i
$862$	−11015.0	−	19078.6i	−0.435236	−	0.753851i
$863$	−3384.92			−0.133516			−0.0667579	−	0.997769i	$-0.521266\pi$
$863$	−3384.92			−0.133516			−0.0667579	+	0.997769i	$0.521266\pi$
$864$	3712.31	−	1637.11i	0.146175	−	0.0644627i
$865$	−5167.78			−0.203133
$866$	−2299.42	−	3982.72i	−0.0902282	−	0.156280i
$867$	−17064.7	+	18907.4i	−0.668451	+	0.740632i
$868$	−201.575	+	349.138i	−0.00788237	+	0.0136527i
$869$	196.111	−	339.674i	0.00765548	−	0.0132597i
$870$	−9111.34	−	1947.91i	−0.355061	−	0.0759084i
$871$	−15109.3	−	26170.0i	−0.587781	−	1.01807i
$872$	2505.75			0.0973111
$873$	−29442.4	+	21285.3i	−1.14144	+	0.825197i
$874$	−9145.97			−0.353967
$875$	2188.41	+	3790.44i	0.0845508	+	0.146446i
$876$	−369.827	−	1142.79i	−0.0142640	−	0.0440770i
$877$	10670.0	−	18480.9i	0.410832	−	0.711582i	−0.584149	−	0.811646i	$-0.698572\pi$
$877$	10670.0	−	18480.9i	0.410832	−	0.711582i	0.994981	+	0.100065i	$0.0319050\pi$
$878$	16750.8	−	29013.2i	0.643862	−	1.11520i
$879$	964.406	+	2980.09i	0.0370064	+	0.114353i
$880$	45.3887	+	78.6155i	0.00173870	+	0.00301151i
$881$	24424.6			0.934037			0.467019	−	0.884247i	$-0.345328\pi$
$881$	24424.6			0.934037			0.467019	+	0.884247i	$0.345328\pi$
$882$	397.379	+	3868.57i	0.0151706	+	0.147689i
$883$	−39237.6			−1.49541			−0.747707	−	0.664029i	$-0.768845\pi$
$883$	−39237.6			−1.49541			−0.747707	+	0.664029i	$0.768845\pi$
$884$	70.7875	+	122.608i	0.00269326	+	0.00466486i
$885$	−6741.91	−	1441.35i	−0.256076	−	0.0547463i
$886$	6372.09	−	11036.8i	0.241619	−	0.418497i
$887$	8290.31	−	14359.2i	0.313823	−	0.543558i	−0.665363	−	0.746520i	$-0.731723\pi$
$887$	8290.31	−	14359.2i	0.313823	−	0.543558i	0.979187	+	0.202962i	$0.0650567\pi$
$888$	−5081.62	+	5630.34i	−0.192036	+	0.212772i
$889$	9360.25	+	16212.4i	0.353130	+	0.611639i
$890$	11284.1			0.424995
$891$	−249.543	−	279.789i	−0.00938272	−	0.0105200i
$892$	−540.545			−0.0202901
$893$	3347.90	+	5798.73i	0.125457	+	0.217298i
$894$	−17186.3	+	19042.1i	−0.642949	+	0.712376i
$895$	−2284.57	+	3956.99i	−0.0853237	+	0.147785i
$896$	−5590.70	+	9683.37i	−0.208451	+	0.361048i
$897$	8352.83	+	1785.75i	0.310918	+	0.0664710i
$898$	−20601.2	−	35682.3i	−0.765557	−	1.32598i
$899$	−21351.2			−0.792106
$900$	209.236	+	2036.96i	0.00774946	+	0.0754428i
$901$	−919.142			−0.0339856
$902$	−217.167	−	376.144i	−0.00801648	−	0.0138850i
$903$	4877.20	+	15070.9i	0.179738	+	0.555404i
$904$	20769.6	−	35974.0i	0.764144	−	1.32354i
$905$	−781.309	+	1353.27i	−0.0286979	+	0.0497062i
$906$	−4065.55	−	12562.9i	−0.149083	−	0.460677i
$907$	15696.1	+	27186.4i	0.574619	+	0.995270i	0.996083	+	0.0884245i	$0.0281832\pi$
$907$	15696.1	+	27186.4i	0.574619	+	0.995270i	−0.421464	+	0.906845i	$0.638483\pi$
$908$	−2145.32			−0.0784087
$909$	−38941.4	+	28152.5i	−1.42091	+	1.02724i
$910$	−3459.18			−0.126012
$911$	25767.8	+	44631.2i	0.937131	+	1.62316i	0.770789	+	0.637091i	$0.219862\pi$
$911$	25767.8	+	44631.2i	0.937131	+	1.62316i	0.166343	+	0.986068i	$0.446804\pi$
$912$	−43250.4	−	9246.49i	−1.57036	−	0.335726i
$913$	−242.953	+	420.808i	−0.00880677	+	0.0152538i
$914$	3683.26	−	6379.59i	0.133295	−	0.230873i
$915$	−2251.14	+	2494.22i	−0.0813336	+	0.0901162i
$916$	221.183	+	383.101i	0.00797828	+	0.0138188i
$917$	−8662.48			−0.311952
$918$	−150.490	+	1384.67i	−0.00541058	+	0.0497830i
$919$	27365.1			0.982253			0.491127	−	0.871088i	$-0.336585\pi$
$919$	27365.1			0.982253			0.491127	+	0.871088i	$0.336585\pi$
$920$	−697.938	−	1208.86i	−0.0250112	−	0.0433207i
$921$	32085.0	−	35549.5i	1.14792	−	1.27188i
$922$	20082.5	−	34784.0i	0.717335	−	1.24246i
$923$	−17438.5	+	30204.3i	−0.621878	+	1.07712i
$924$	−11.7168	−	2.50494i	−0.000417159	−	8.91844e-5i
$925$	−3994.38	−	6918.48i	−0.141983	−	0.245922i
$926$	−4674.83			−0.165901
$927$	−919.105	−	411.813i	−0.0325646	−	0.0145908i
$928$	6867.26			0.242919
$929$	−16662.2	−	28859.8i	−0.588450	−	1.01922i	−0.994436	−	0.105345i	$-0.966405\pi$
$929$	−16662.2	−	28859.8i	−0.588450	−	1.01922i	0.405986	−	0.913879i	$-0.366928\pi$
$930$	−1086.23	−	3356.53i	−0.0382998	−	0.118349i
$931$	3034.83	−	5256.48i	0.106834	−	0.185042i
$932$	1346.38	−	2331.99i	0.0473198	−	0.0819603i
$933$	3509.43	+	10844.4i	0.123144	+	0.380525i
$934$	−13198.9	−	22861.1i	−0.462399	−	0.800898i
$935$	−4.46182			−0.000156061
$936$	34883.4	+	15629.8i	1.21816	+	0.545807i
$937$	49600.6			1.72933			0.864664	−	0.502351i	$-0.167531\pi$
$937$	49600.6			1.72933			0.864664	+	0.502351i	$0.167531\pi$
$938$	−4750.57	−	8228.23i	−0.165364	−	0.286419i
$939$	31545.9	+	6744.18i	1.09634	+	0.234386i
$940$	44.4718	−	77.0274i	0.00154310	−	0.00267272i
$941$	6074.50	−	10521.3i	0.210439	−	0.364491i	−0.741413	−	0.671049i	$-0.765844\pi$
$941$	6074.50	−	10521.3i	0.210439	−	0.364491i	0.951852	+	0.306558i	$0.0991773\pi$
$942$	−17636.9	+	19541.3i	−0.610022	+	0.675893i
$943$	3608.45	+	6250.02i	0.124610	+	0.215831i
$944$	35490.5			1.22364
$945$	−2035.73	−	1490.08i	−0.0700765	−	0.0512934i
$946$	−658.342			−0.0226264
$947$	1818.92	+	3150.47i	0.0624151	+	0.108106i	0.895544	−	0.444972i	$-0.146786\pi$
$947$	1818.92	+	3150.47i	0.0624151	+	0.108106i	−0.833129	+	0.553078i	$0.813453\pi$
$948$	1700.75	−	1884.40i	0.0582679	−	0.0645597i
$949$	11808.9	−	20453.5i	0.403932	−	0.699631i
$950$	21555.8	−	37335.7i	0.736170	−	1.27508i
$951$	−34330.4	−	7339.48i	−1.17060	−	0.250262i
$952$	−255.720	−	442.919i	−0.00870580	−	0.0150789i
$953$	−26019.5			−0.884421			−0.442210	−	0.896911i	$-0.645806\pi$
$953$	−26019.5			−0.884421			−0.442210	+	0.896911i	$0.645806\pi$
$954$	17504.0	−	12654.4i	0.594039	−	0.429457i
$955$	11289.7			0.382540
$956$	−1379.49	−	2389.34i	−0.0466693	−	0.0808336i
$957$	−195.377	−	603.731i	−0.00659942	−	0.0203927i
$958$	6454.79	−	11180.0i	0.217688	−	0.377046i
$959$	8324.16	−	14417.9i	0.280293	−	0.485482i
$960$	−1909.85	−	5901.60i	−0.0642086	−	0.198410i
$961$	10853.2	+	18798.4i	0.364313	+	0.631008i
$962$	12979.6			0.435009
$963$	−1074.58	−	10461.3i	−0.0359584	−	0.350063i
$964$	−3419.48			−0.114247
$965$	1524.51	+	2640.53i	0.0508556	+	0.0880845i
$966$	2626.25	+	561.466i	0.0874724	+	0.0187007i
$967$	10957.4	−	18978.7i	0.364390	−	0.631141i	−0.624288	−	0.781194i	$-0.714611\pi$
$967$	10957.4	−	18978.7i	0.364390	−	0.631141i	0.988678	+	0.150053i	$0.0479443\pi$
$968$	14393.9	−	24931.0i	0.477931	−	0.827801i
$969$	1456.49	−	1613.77i	0.0482862	−	0.0535002i
$970$	−5080.30	−	8799.34i	−0.168164	−	0.291268i
$971$	−11091.9			−0.366587			−0.183293	−	0.983058i	$-0.558676\pi$
$971$	−11091.9			−0.366587			−0.183293	+	0.983058i	$0.558676\pi$
$972$	−1200.75	−	2108.39i	−0.0396237	−	0.0695746i
$973$	−8151.29			−0.268570
$974$	13875.7	+	24033.4i	0.456474	+	0.790637i
$975$	−26976.3	+	29889.2i	−0.886084	+	0.981765i
$976$	8648.02	−	14978.8i	0.283623	−	0.491250i
$977$	−28160.4	+	48775.3i	−0.922142	+	1.59720i	−0.126047	+	0.992024i	$0.540229\pi$
$977$	−28160.4	+	48775.3i	−0.922142	+	1.59720i	−0.796095	+	0.605172i	$0.793104\pi$
$978$	30402.8	+	6499.81i	0.994044	+	0.212516i
$979$	384.257	+	665.553i	0.0125444	+	0.0217275i
$980$	−80.6263			−0.00262807
$981$	−319.565	−	3111.04i	−0.0104005	−	0.101252i
$982$	21485.3			0.698192
$983$	70.5955	+	122.275i	0.00229059	+	0.00396741i	0.867168	−	0.498015i	$-0.165938\pi$
$983$	70.5955	+	122.275i	0.00229059	+	0.00396741i	−0.864878	+	0.501982i	$0.832604\pi$
$984$	9944.00	+	30727.8i	0.322158	+	0.995493i
$985$	−1048.56	+	1816.16i	−0.0339186	+	0.0587488i
$986$	−1178.73	+	2041.63i	−0.0380715	+	0.0659418i
$987$	−605.364	−	1870.62i	−0.0195227	−	0.0603268i
$988$	2596.24	+	4496.82i	0.0836007	+	0.144801i
$989$	10939.0			0.351710
$990$	84.9702	−	61.4287i	0.00272781	−	0.00197205i
$991$	−43398.1			−1.39111			−0.695553	−	0.718475i	$-0.744840\pi$
$991$	−43398.1			−1.39111			−0.695553	+	0.718475i	$0.744840\pi$
$992$	1300.12	+	2251.88i	0.0416119	+	0.0720739i
$993$	28923.9	+	6183.62i	0.924341	+	0.197615i
$994$	−5482.90	+	9496.67i	−0.174957	+	0.303034i
$995$	−6926.21	+	11996.6i	−0.220679	+	0.382227i
$996$	−2106.99	+	2334.50i	−0.0670306	+	0.0742687i
$997$	−19503.1	−	33780.3i	−0.619527	−	1.07305i	−0.989572	−	0.144038i	$-0.953991\pi$
$997$	−19503.1	−	33780.3i	−0.619527	−	1.07305i	0.370046	−	0.929014i	$-0.379342\pi$
$998$	25264.0			0.801320
$999$	7638.48	+	5591.09i	0.241913	+	0.177071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.b.22.6	✓	16
3.2	odd	2		189.4.f.b.64.3		16
9.2	odd	6		189.4.f.b.127.3		16
9.4	even	3		567.4.a.i.1.3		8
9.5	odd	6		567.4.a.g.1.6		8
9.7	even	3	inner	63.4.f.b.43.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.6	✓	16	1.1	even	1	trivial
63.4.f.b.43.6	yes	16	9.7	even	3	inner
189.4.f.b.64.3		16	3.2	odd	2
189.4.f.b.127.3		16	9.2	odd	6
567.4.a.g.1.6		8	9.5	odd	6
567.4.a.i.1.3		8	9.4	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46974 + 2.54566i) q^{2} +(3.48146 - 3.85739i) q^{3} +(-0.320267 + 0.554718i) q^{4} +(1.28443 - 2.22469i) q^{5} +(14.9364 + 3.19326i) q^{6} +(3.50000 + 6.06218i) q^{7} +21.6330 q^{8} +(-2.75892 - 26.8587i) q^{9} +O(q^{10})\)	\(q+(1.46974 + 2.54566i) q^{2} +(3.48146 - 3.85739i) q^{3} +(-0.320267 + 0.554718i) q^{4} +(1.28443 - 2.22469i) q^{5} +(14.9364 + 3.19326i) q^{6} +(3.50000 + 6.06218i) q^{7} +21.6330 q^{8} +(-2.75892 - 26.8587i) q^{9} +7.55109 q^{10} +(0.257136 + 0.445373i) q^{11} +(1.02477 + 3.16662i) q^{12} +(-32.7217 + 56.6756i) q^{13} +(-10.2882 + 17.8196i) q^{14} +(-4.10983 - 12.6997i) q^{15} +(34.3570 + 59.5081i) q^{16} -3.37738 q^{17} +(64.3182 - 46.4985i) q^{18} -123.871 q^{19} +(0.822718 + 1.42499i) q^{20} +(35.5693 + 7.60435i) q^{21} +(-0.755846 + 1.30916i) q^{22} +(12.5592 - 21.7531i) q^{23} +(75.3143 - 83.4469i) q^{24} +(59.2005 + 102.538i) q^{25} -192.369 q^{26} +(-113.209 - 82.8651i) q^{27} -4.48373 q^{28} +(-118.731 - 205.649i) q^{29} +(26.2888 - 29.1275i) q^{30} +(44.9570 - 77.8677i) q^{31} +(-14.4597 + 25.0449i) q^{32} +(2.61319 + 0.558672i) q^{33} +(-4.96386 - 8.59766i) q^{34} +17.9820 q^{35} +(15.7826 + 7.07151i) q^{36} -67.4721 q^{37} +(-182.057 - 315.333i) q^{38} +(104.701 + 323.534i) q^{39} +(27.7860 - 48.1267i) q^{40} +(-143.658 + 248.823i) q^{41} +(32.9195 + 101.724i) q^{42} +(217.750 + 377.154i) q^{43} -0.329409 q^{44} +(-63.2959 - 28.3602i) q^{45} +73.8349 q^{46} +(-27.0274 - 46.8128i) q^{47} +(349.158 + 74.6464i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-174.019 + 301.409i) q^{50} +(-11.7582 + 13.0279i) q^{51} +(-20.9593 - 36.3026i) q^{52} +272.147 q^{53} +(44.5583 - 409.983i) q^{54} +1.32109 q^{55} +(75.7155 + 131.143i) q^{56} +(-431.250 + 477.817i) q^{57} +(349.008 - 604.500i) q^{58} +(258.248 - 447.299i) q^{59} +(8.36099 + 1.78749i) q^{60} +(-125.855 - 217.988i) q^{61} +264.300 q^{62} +(153.166 - 110.730i) q^{63} +464.704 q^{64} +(84.0572 + 145.591i) q^{65} +(2.41851 + 7.47339i) q^{66} +(-230.875 + 399.888i) q^{67} +(1.08166 - 1.87349i) q^{68} +(-40.1861 - 124.178i) q^{69} +(26.4288 + 45.7760i) q^{70} +532.933 q^{71} +(-59.6836 - 581.034i) q^{72} -360.888 q^{73} +(-99.1664 - 171.761i) q^{74} +(601.634 + 128.623i) q^{75} +(39.6716 - 68.7132i) q^{76} +(-1.79995 + 3.11761i) q^{77} +(-669.726 + 742.044i) q^{78} +(-381.337 - 660.495i) q^{79} +176.516 q^{80} +(-713.777 + 148.202i) q^{81} -844.559 q^{82} +(472.421 + 818.258i) q^{83} +(-15.6099 + 17.2955i) q^{84} +(-4.33799 + 7.51362i) q^{85} +(-640.071 + 1108.64i) q^{86} +(-1206.63 - 257.964i) q^{87} +(5.56263 + 9.63475i) q^{88} +1494.37 q^{89} +(-20.8328 - 202.812i) q^{90} -458.104 q^{91} +(8.04457 + 13.9336i) q^{92} +(-143.851 - 444.510i) q^{93} +(79.4464 - 137.605i) q^{94} +(-159.103 + 275.574i) q^{95} +(46.2671 + 142.969i) q^{96} +(-672.791 - 1165.31i) q^{97} -144.034 q^{98} +(11.2527 - 8.13509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

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