LMFDB - Embedded newform 63.4.f.a.22.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-4.50000 + 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +(7.00000 - 12.1244i) q^{5} +(-4.50000 - 2.59808i) q^{6} +(3.50000 + 6.06218i) q^{7} +15.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-4.50000 + 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +(7.00000 - 12.1244i) q^{5} +(-4.50000 - 2.59808i) q^{6} +(3.50000 + 6.06218i) q^{7} +15.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +14.0000 q^{10} +(23.5000 + 40.7032i) q^{11} +36.3731i q^{12} +(43.0000 - 74.4782i) q^{13} +(-3.50000 + 6.06218i) q^{14} +72.7461i q^{15} +(-20.5000 - 35.5070i) q^{16} -9.00000 q^{17} +27.0000 q^{18} -131.000 q^{19} +(-49.0000 - 84.8705i) q^{20} +(-31.5000 - 18.1865i) q^{21} +(-23.5000 + 40.7032i) q^{22} +(6.00000 - 10.3923i) q^{23} +(-67.5000 + 38.9711i) q^{24} +(-35.5000 - 61.4878i) q^{25} +86.0000 q^{26} +140.296i q^{27} +49.0000 q^{28} +(130.000 + 225.167i) q^{29} +(-63.0000 + 36.3731i) q^{30} +(27.0000 - 46.7654i) q^{31} +(80.5000 - 139.430i) q^{32} +(-211.500 - 122.110i) q^{33} +(-4.50000 - 7.79423i) q^{34} +98.0000 q^{35} +(-94.5000 - 163.679i) q^{36} -246.000 q^{37} +(-65.5000 - 113.449i) q^{38} +446.869i q^{39} +(105.000 - 181.865i) q^{40} +(-191.500 + 331.688i) q^{41} -36.3731i q^{42} +(84.5000 + 146.358i) q^{43} +329.000 q^{44} +(-189.000 - 327.358i) q^{45} +12.0000 q^{46} +(-48.0000 - 83.1384i) q^{47} +(184.500 + 106.521i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(35.5000 - 61.4878i) q^{50} +(40.5000 - 23.3827i) q^{51} +(-301.000 - 521.347i) q^{52} +300.000 q^{53} +(-121.500 + 70.1481i) q^{54} +658.000 q^{55} +(52.5000 + 90.9327i) q^{56} +(589.500 - 340.348i) q^{57} +(-130.000 + 225.167i) q^{58} +(-214.500 + 371.525i) q^{59} +(441.000 + 254.611i) q^{60} +(190.000 + 329.090i) q^{61} +54.0000 q^{62} +189.000 q^{63} -167.000 q^{64} +(-602.000 - 1042.69i) q^{65} -244.219i q^{66} +(77.5000 - 134.234i) q^{67} +(-31.5000 + 54.5596i) q^{68} +62.3538i q^{69} +(49.0000 + 84.8705i) q^{70} +72.0000 q^{71} +(202.500 - 350.740i) q^{72} +117.000 q^{73} +(-123.000 - 213.042i) q^{74} +(319.500 + 184.463i) q^{75} +(-458.500 + 794.145i) q^{76} +(-164.500 + 284.922i) q^{77} +(-387.000 + 223.435i) q^{78} +(263.000 + 455.529i) q^{79} -574.000 q^{80} +(-364.500 - 631.333i) q^{81} -383.000 q^{82} +(-288.000 - 498.831i) q^{83} +(-220.500 + 127.306i) q^{84} +(-63.0000 + 109.119i) q^{85} +(-84.5000 + 146.358i) q^{86} +(-1170.00 - 675.500i) q^{87} +(352.500 + 610.548i) q^{88} -278.000 q^{89} +(189.000 - 327.358i) q^{90} +602.000 q^{91} +(-42.0000 - 72.7461i) q^{92} +280.592i q^{93} +(48.0000 - 83.1384i) q^{94} +(-917.000 + 1588.29i) q^{95} +836.581i q^{96} +(100.500 + 174.071i) q^{97} -49.0000 q^{98} +1269.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 9 q^{3} + 7 q^{4} + 14 q^{5} - 9 q^{6} + 7 q^{7} + 30 q^{8} + 27 q^{9}+O(q^{10}) $ 2 * q + q^2 - 9 * q^3 + 7 * q^4 + 14 * q^5 - 9 * q^6 + 7 * q^7 + 30 * q^8 + 27 * q^9	\( 2 q + q^{2} - 9 q^{3} + 7 q^{4} + 14 q^{5} - 9 q^{6} + 7 q^{7} + 30 q^{8} + 27 q^{9} + 28 q^{10} + 47 q^{11} + 86 q^{13} - 7 q^{14} - 41 q^{16} - 18 q^{17} + 54 q^{18} - 262 q^{19} - 98 q^{20} - 63 q^{21} - 47 q^{22} + 12 q^{23} - 135 q^{24} - 71 q^{25} + 172 q^{26} + 98 q^{28} + 260 q^{29} - 126 q^{30} + 54 q^{31} + 161 q^{32} - 423 q^{33} - 9 q^{34} + 196 q^{35} - 189 q^{36} - 492 q^{37} - 131 q^{38} + 210 q^{40} - 383 q^{41} + 169 q^{43} + 658 q^{44} - 378 q^{45} + 24 q^{46} - 96 q^{47} + 369 q^{48} - 49 q^{49} + 71 q^{50} + 81 q^{51} - 602 q^{52} + 600 q^{53} - 243 q^{54} + 1316 q^{55} + 105 q^{56} + 1179 q^{57} - 260 q^{58} - 429 q^{59} + 882 q^{60} + 380 q^{61} + 108 q^{62} + 378 q^{63} - 334 q^{64} - 1204 q^{65} + 155 q^{67} - 63 q^{68} + 98 q^{70} + 144 q^{71} + 405 q^{72} + 234 q^{73} - 246 q^{74} + 639 q^{75} - 917 q^{76} - 329 q^{77} - 774 q^{78} + 526 q^{79} - 1148 q^{80} - 729 q^{81} - 766 q^{82} - 576 q^{83} - 441 q^{84} - 126 q^{85} - 169 q^{86} - 2340 q^{87} + 705 q^{88} - 556 q^{89} + 378 q^{90} + 1204 q^{91} - 84 q^{92} + 96 q^{94} - 1834 q^{95} + 201 q^{97} - 98 q^{98} + 2538 q^{99}+O(q^{100}) \) 2 * q + q^2 - 9 * q^3 + 7 * q^4 + 14 * q^5 - 9 * q^6 + 7 * q^7 + 30 * q^8 + 27 * q^9 + 28 * q^10 + 47 * q^11 + 86 * q^13 - 7 * q^14 - 41 * q^16 - 18 * q^17 + 54 * q^18 - 262 * q^19 - 98 * q^20 - 63 * q^21 - 47 * q^22 + 12 * q^23 - 135 * q^24 - 71 * q^25 + 172 * q^26 + 98 * q^28 + 260 * q^29 - 126 * q^30 + 54 * q^31 + 161 * q^32 - 423 * q^33 - 9 * q^34 + 196 * q^35 - 189 * q^36 - 492 * q^37 - 131 * q^38 + 210 * q^40 - 383 * q^41 + 169 * q^43 + 658 * q^44 - 378 * q^45 + 24 * q^46 - 96 * q^47 + 369 * q^48 - 49 * q^49 + 71 * q^50 + 81 * q^51 - 602 * q^52 + 600 * q^53 - 243 * q^54 + 1316 * q^55 + 105 * q^56 + 1179 * q^57 - 260 * q^58 - 429 * q^59 + 882 * q^60 + 380 * q^61 + 108 * q^62 + 378 * q^63 - 334 * q^64 - 1204 * q^65 + 155 * q^67 - 63 * q^68 + 98 * q^70 + 144 * q^71 + 405 * q^72 + 234 * q^73 - 246 * q^74 + 639 * q^75 - 917 * q^76 - 329 * q^77 - 774 * q^78 + 526 * q^79 - 1148 * q^80 - 729 * q^81 - 766 * q^82 - 576 * q^83 - 441 * q^84 - 126 * q^85 - 169 * q^86 - 2340 * q^87 + 705 * q^88 - 556 * q^89 + 378 * q^90 + 1204 * q^91 - 84 * q^92 + 96 * q^94 - 1834 * q^95 + 201 * q^97 - 98 * q^98 + 2538 * 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 $

$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$3$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$4$	3.50000	−	6.06218i	0.437500	−	0.757772i
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	−0.362228	−	0.932089i	$-0.617984\pi$
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	0.988327	−	0.152346i	$-0.0486828\pi$
$6$	−4.50000	−	2.59808i	−0.306186	−	0.176777i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	15.0000			0.662913
$9$	13.5000	−	23.3827i	0.500000	−	0.866025i
$10$	14.0000			0.442719
$11$	23.5000	+	40.7032i	0.644138	+	1.11568i	0.984500	+	0.175385i	$0.0561170\pi$
$11$	23.5000	+	40.7032i	0.644138	+	1.11568i	−0.340362	+	0.940294i	$0.610550\pi$
$12$			36.3731i			0.875000i
$13$	43.0000	−	74.4782i	0.917389	−	1.58896i	0.114023	−	0.993478i	$-0.463626\pi$
$13$	43.0000	−	74.4782i	0.917389	−	1.58896i	0.803366	−	0.595486i	$-0.203040\pi$
$14$	−3.50000	+	6.06218i	−0.0668153	+	0.115728i
$15$			72.7461i			1.25220i
$16$	−20.5000	−	35.5070i	−0.320312	−	0.554798i
$17$	−9.00000			−0.128401			−0.0642006	−	0.997937i	$-0.520450\pi$
$17$	−9.00000			−0.128401			−0.0642006	+	0.997937i	$0.520450\pi$
$18$	27.0000			0.353553
$19$	−131.000			−1.58176			−0.790881	−	0.611971i	$-0.790377\pi$
$19$	−131.000			−1.58176			−0.790881	+	0.611971i	$0.790377\pi$
$20$	−49.0000	−	84.8705i	−0.547837	−	0.948881i
$21$	−31.5000	−	18.1865i	−0.327327	−	0.188982i
$22$	−23.5000	+	40.7032i	−0.227737	+	0.394452i
$23$	6.00000	−	10.3923i	0.0543951	−	0.0942150i	−0.837546	−	0.546367i	$-0.816010\pi$
$23$	6.00000	−	10.3923i	0.0543951	−	0.0942150i	0.891941	+	0.452152i	$0.149344\pi$
$24$	−67.5000	+	38.9711i	−0.574099	+	0.331456i
$25$	−35.5000	−	61.4878i	−0.284000	−	0.491902i
$26$	86.0000			0.648692
$27$			140.296i			1.00000i
$28$	49.0000			0.330719
$29$	130.000	+	225.167i	0.832427	+	1.44181i	0.896108	+	0.443836i	$0.146383\pi$
$29$	130.000	+	225.167i	0.832427	+	1.44181i	−0.0636806	+	0.997970i	$0.520284\pi$
$30$	−63.0000	+	36.3731i	−0.383406	+	0.221359i
$31$	27.0000	−	46.7654i	0.156430	−	0.270945i	−0.777149	−	0.629317i	$-0.783335\pi$
$31$	27.0000	−	46.7654i	0.156430	−	0.270945i	0.933579	+	0.358372i	$0.116668\pi$
$32$	80.5000	−	139.430i	0.444704	−	0.770250i
$33$	−211.500	−	122.110i	−1.11568	−	0.644138i
$34$	−4.50000	−	7.79423i	−0.0226983	−	0.0393147i
$35$	98.0000			0.473286
$36$	−94.5000	−	163.679i	−0.437500	−	0.757772i
$37$	−246.000			−1.09303			−0.546516	−	0.837449i	$-0.684046\pi$
$37$	−246.000			−1.09303			−0.546516	+	0.837449i	$0.684046\pi$
$38$	−65.5000	−	113.449i	−0.279619	−	0.484313i
$39$			446.869i			1.83478i
$40$	105.000	−	181.865i	0.415049	−	0.718886i
$41$	−191.500	+	331.688i	−0.729446	+	1.26344i	0.227672	+	0.973738i	$0.426889\pi$
$41$	−191.500	+	331.688i	−0.729446	+	1.26344i	−0.957118	+	0.289699i	$0.906445\pi$
$42$		−	36.3731i		−	0.133631i
$43$	84.5000	+	146.358i	0.299677	+	0.519057i	0.976062	−	0.217492i	$-0.0697876\pi$
$43$	84.5000	+	146.358i	0.299677	+	0.519057i	−0.676385	+	0.736549i	$0.736454\pi$
$44$	329.000			1.12724
$45$	−189.000	−	327.358i	−0.626099	−	1.08444i
$46$	12.0000			0.0384631
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	0.781878	−	0.623431i	$-0.214262\pi$
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	−0.930846	+	0.365410i	$0.880929\pi$
$48$	184.500	+	106.521i	0.554798	+	0.320312i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	35.5000	−	61.4878i	0.100409	−	0.173914i
$51$	40.5000	−	23.3827i	0.111199	−	0.0642006i
$52$	−301.000	−	521.347i	−0.802715	−	1.39034i
$53$	300.000			0.777513			0.388756	−	0.921341i	$-0.372905\pi$
$53$	300.000			0.777513			0.388756	+	0.921341i	$0.372905\pi$
$54$	−121.500	+	70.1481i	−0.306186	+	0.176777i
$55$	658.000			1.61318
$56$	52.5000	+	90.9327i	0.125279	+	0.216989i
$57$	589.500	−	340.348i	1.36985	−	0.790881i
$58$	−130.000	+	225.167i	−0.294308	+	0.509756i
$59$	−214.500	+	371.525i	−0.473314	+	0.819804i	−0.999533	−	0.0305450i	$-0.990276\pi$
$59$	−214.500	+	371.525i	−0.473314	+	0.819804i	0.526219	+	0.850349i	$0.323609\pi$
$60$	441.000	+	254.611i	0.948881	+	0.547837i
$61$	190.000	+	329.090i	0.398803	+	0.690748i	0.993579	−	0.113144i	$-0.0360923\pi$
$61$	190.000	+	329.090i	0.398803	+	0.690748i	−0.594775	+	0.803892i	$0.702759\pi$
$62$	54.0000			0.110613
$63$	189.000			0.377964
$64$	−167.000			−0.326172
$65$	−602.000	−	1042.69i	−1.14875	−	1.98970i
$66$		−	244.219i		−	0.455474i
$67$	77.5000	−	134.234i	0.141315	−	0.244765i	−0.786677	−	0.617365i	$-0.788200\pi$
$67$	77.5000	−	134.234i	0.141315	−	0.244765i	0.927992	+	0.372600i	$0.121533\pi$
$68$	−31.5000	+	54.5596i	−0.0561755	+	0.0972989i
$69$			62.3538i			0.108790i
$70$	49.0000	+	84.8705i	0.0836660	+	0.144914i
$71$	72.0000			0.120350			0.0601748	−	0.998188i	$-0.480834\pi$
$71$	72.0000			0.120350			0.0601748	+	0.998188i	$0.480834\pi$
$72$	202.500	−	350.740i	0.331456	−	0.574099i
$73$	117.000			0.187586			0.0937932	−	0.995592i	$-0.470101\pi$
$73$	117.000			0.187586			0.0937932	+	0.995592i	$0.470101\pi$
$74$	−123.000	−	213.042i	−0.193222	−	0.334671i
$75$	319.500	+	184.463i	0.491902	+	0.284000i
$76$	−458.500	+	794.145i	−0.692020	+	1.19861i
$77$	−164.500	+	284.922i	−0.243461	+	0.421687i
$78$	−387.000	+	223.435i	−0.561784	+	0.324346i
$79$	263.000	+	455.529i	0.374555	+	0.648748i	0.990260	−	0.139229i	$-0.0444623\pi$
$79$	263.000	+	455.529i	0.374555	+	0.648748i	−0.615706	+	0.787976i	$0.711129\pi$
$80$	−574.000			−0.802189
$81$	−364.500	−	631.333i	−0.500000	−	0.866025i
$82$	−383.000			−0.515796
$83$	−288.000	−	498.831i	−0.380869	−	0.659684i	0.610318	−	0.792157i	$-0.291042\pi$
$83$	−288.000	−	498.831i	−0.380869	−	0.659684i	−0.991187	+	0.132473i	$0.957708\pi$
$84$	−220.500	+	127.306i	−0.286411	+	0.165359i
$85$	−63.0000	+	109.119i	−0.0803919	+	0.139243i
$86$	−84.5000	+	146.358i	−0.105952	+	0.183514i
$87$	−1170.00	−	675.500i	−1.44181	−	0.832427i
$88$	352.500	+	610.548i	0.427007	+	0.739598i
$89$	−278.000			−0.331100			−0.165550	−	0.986201i	$-0.552940\pi$
$89$	−278.000			−0.331100			−0.165550	+	0.986201i	$0.552940\pi$
$90$	189.000	−	327.358i	0.221359	−	0.383406i
$91$	602.000			0.693481
$92$	−42.0000	−	72.7461i	−0.0475957	−	0.0824381i
$93$			280.592i			0.312861i
$94$	48.0000	−	83.1384i	0.0526683	−	0.0912242i
$95$	−917.000	+	1588.29i	−0.990339	+	1.71532i
$96$			836.581i			0.889408i
$97$	100.500	+	174.071i	0.105198	+	0.182209i	0.913819	−	0.406121i	$-0.133119\pi$
$97$	100.500	+	174.071i	0.105198	+	0.182209i	−0.808621	+	0.588330i	$0.799786\pi$
$98$	−49.0000			−0.0505076
$99$	1269.00			1.28828
$100$	−497.000			−0.497000
$101$	−70.0000	−	121.244i	−0.0689630	−	0.119447i	0.829482	−	0.558533i	$-0.188636\pi$
$101$	−70.0000	−	121.244i	−0.0689630	−	0.119447i	−0.898445	+	0.439086i	$0.855302\pi$
$102$	40.5000	+	23.3827i	0.0393147	+	0.0226983i
$103$	665.000	−	1151.81i	0.636159	−	1.10186i	−0.350109	−	0.936709i	$-0.613855\pi$
$103$	665.000	−	1151.81i	0.636159	−	1.10186i	0.986268	−	0.165151i	$-0.0528112\pi$
$104$	645.000	−	1117.17i	0.608149	−	1.05334i
$105$	−441.000	+	254.611i	−0.409878	+	0.236643i
$106$	150.000	+	259.808i	0.137446	+	0.238064i
$107$	−1373.00			−1.24049			−0.620247	−	0.784406i	$-0.712968\pi$
$107$	−1373.00			−1.24049			−0.620247	+	0.784406i	$0.712968\pi$
$108$	850.500	+	491.036i	0.757772	+	0.437500i
$109$	−666.000			−0.585241			−0.292620	−	0.956229i	$-0.594527\pi$
$109$	−666.000			−0.585241			−0.292620	+	0.956229i	$0.594527\pi$
$110$	329.000	+	569.845i	0.285172	+	0.493932i
$111$	1107.00	−	639.127i	0.946593	−	0.546516i
$112$	143.500	−	248.549i	0.121067	−	0.209694i
$113$	−395.000	+	684.160i	−0.328836	+	0.569561i	−0.982281	−	0.187413i	$-0.939990\pi$
$113$	−395.000	+	684.160i	−0.328836	+	0.569561i	0.653445	+	0.756974i	$0.273323\pi$
$114$	589.500	+	340.348i	0.484313	+	0.279619i
$115$	−84.0000	−	145.492i	−0.0681134	−	0.117976i
$116$	1820.00			1.45675
$117$	−1161.00	−	2010.91i	−0.917389	−	1.58896i
$118$	−429.000			−0.334683
$119$	−31.5000	−	54.5596i	−0.0242655	−	0.0420292i
$120$			1091.19i			0.830098i
$121$	−439.000	+	760.370i	−0.329827	+	0.571277i
$122$	−190.000	+	329.090i	−0.140998	+	0.244216i
$123$		−	1990.13i		−	1.45889i
$124$	−189.000	−	327.358i	−0.136877	−	0.237077i
$125$	756.000			0.540950
$126$	94.5000	+	163.679i	0.0668153	+	0.115728i
$127$	660.000			0.461146			0.230573	−	0.973055i	$-0.425940\pi$
$127$	660.000			0.461146			0.230573	+	0.973055i	$0.425940\pi$
$128$	−727.500	−	1260.07i	−0.502363	−	0.870119i
$129$	−760.500	−	439.075i	−0.519057	−	0.299677i
$130$	602.000	−	1042.69i	0.406145	−	0.703464i
$131$	322.000	−	557.720i	0.214758	−	0.371971i	−0.738440	−	0.674319i	$-0.764437\pi$
$131$	322.000	−	557.720i	0.214758	−	0.371971i	0.953198	+	0.302348i	$0.0977705\pi$
$132$	−1480.50	+	854.767i	−0.976220	+	0.563621i
$133$	−458.500	−	794.145i	−0.298925	−	0.517753i
$134$	155.000			0.0999251
$135$	1701.00	+	982.073i	1.08444	+	0.626099i
$136$	−135.000			−0.0851188
$137$	289.500	+	501.429i	0.180538	+	0.312700i	0.942064	−	0.335434i	$-0.108883\pi$
$137$	289.500	+	501.429i	0.180538	+	0.312700i	−0.761526	+	0.648134i	$0.775550\pi$
$138$	−54.0000	+	31.1769i	−0.0333100	+	0.0192316i
$139$	−1087.50	+	1883.61i	−0.663601	+	1.14939i	0.316062	+	0.948739i	$0.397639\pi$
$139$	−1087.50	+	1883.61i	−0.663601	+	1.14939i	−0.979663	+	0.200652i	$0.935694\pi$
$140$	343.000	−	594.093i	0.207063	−	0.358643i
$141$	432.000	+	249.415i	0.258021	+	0.148969i
$142$	36.0000	+	62.3538i	0.0212750	+	0.0368494i
$143$	4042.00			2.36370
$144$	−1107.00			−0.640625
$145$	3640.00			2.08473
$146$	58.5000	+	101.325i	0.0331609	+	0.0574364i
$147$		−	254.611i		−	0.142857i
$148$	−861.000	+	1491.30i	−0.478201	+	0.828269i
$149$	1140.00	−	1974.54i	0.626795	−	1.08564i	−0.361396	−	0.932412i	$-0.617700\pi$
$149$	1140.00	−	1974.54i	0.626795	−	1.08564i	0.988191	−	0.153228i	$-0.0489669\pi$
$150$			368.927i			0.200818i
$151$	335.000	+	580.237i	0.180542	+	0.312709i	0.942065	−	0.335429i	$-0.108881\pi$
$151$	335.000	+	580.237i	0.180542	+	0.312709i	−0.761523	+	0.648138i	$0.775548\pi$
$152$	−1965.00			−1.04857
$153$	−121.500	+	210.444i	−0.0642006	+	0.111199i
$154$	−329.000			−0.172153
$155$	−378.000	−	654.715i	−0.195882	−	0.339277i
$156$	2709.00	+	1564.04i	1.39034	+	0.802715i
$157$	391.000	−	677.232i	0.198759	−	0.344261i	−0.749367	−	0.662155i	$-0.769642\pi$
$157$	391.000	−	677.232i	0.198759	−	0.344261i	0.948126	+	0.317894i	$0.102975\pi$
$158$	−263.000	+	455.529i	−0.132425	+	0.229367i
$159$	−1350.00	+	779.423i	−0.673346	+	0.388756i
$160$	−1127.00	−	1952.02i	−0.556857	−	0.964505i
$161$	84.0000			0.0411188
$162$	364.500	−	631.333i	0.176777	−	0.306186i
$163$	−2108.00			−1.01295			−0.506476	−	0.862254i	$-0.669052\pi$
$163$	−2108.00			−1.01295			−0.506476	+	0.862254i	$0.669052\pi$
$164$	1340.50	+	2321.81i	0.638265	+	1.10551i
$165$	−2961.00	+	1709.53i	−1.39705	+	0.806588i
$166$	288.000	−	498.831i	0.134657	−	0.233234i
$167$	22.0000	−	38.1051i	0.0101941	−	0.0176567i	−0.860883	−	0.508802i	$-0.830088\pi$
$167$	22.0000	−	38.1051i	0.0101941	−	0.0176567i	0.871077	+	0.491146i	$0.163422\pi$
$168$	−472.500	−	272.798i	−0.216989	−	0.125279i
$169$	−2599.50	−	4502.47i	−1.18320	−	2.04937i
$170$	−126.000			−0.0568456
$171$	−1768.50	+	3063.13i	−0.790881	+	1.36985i
$172$	1183.00			0.524435
$173$	2255.00	+	3905.77i	0.991009	+	1.71648i	0.611377	+	0.791339i	$0.290616\pi$
$173$	2255.00	+	3905.77i	0.991009	+	1.71648i	0.379631	+	0.925138i	$0.376051\pi$
$174$		−	1351.00i		−	0.588615i
$175$	248.500	−	430.415i	0.107342	−	0.185922i
$176$	963.500	−	1668.83i	0.412651	−	0.714732i
$177$		−	2229.15i		−	0.946628i
$178$	−139.000	−	240.755i	−0.0585308	−	0.101378i
$179$	−1744.00			−0.728227			−0.364114	−	0.931355i	$-0.618628\pi$
$179$	−1744.00			−0.728227			−0.364114	+	0.931355i	$0.618628\pi$
$180$	−2646.00			−1.09567
$181$	−2240.00			−0.919878			−0.459939	−	0.887951i	$-0.652129\pi$
$181$	−2240.00			−0.919878			−0.459939	+	0.887951i	$0.652129\pi$
$182$	301.000	+	521.347i	0.122591	+	0.212334i
$183$	−1710.00	−	987.269i	−0.690748	−	0.398803i
$184$	90.0000	−	155.885i	0.0360592	−	0.0624563i
$185$	−1722.00	+	2982.59i	−0.684346	+	1.18532i
$186$	−243.000	+	140.296i	−0.0957937	+	0.0553065i
$187$	−211.500	−	366.329i	−0.0827081	−	0.143255i
$188$	−672.000			−0.260695
$189$	−850.500	+	491.036i	−0.327327	+	0.188982i
$190$	−1834.00			−0.700275
$191$	−206.000	−	356.802i	−0.0780400	−	0.135169i	0.824364	−	0.566060i	$-0.191533\pi$
$191$	−206.000	−	356.802i	−0.0780400	−	0.135169i	−0.902404	+	0.430891i	$0.858200\pi$
$192$	751.500	−	433.879i	0.282473	−	0.163086i
$193$	1743.50	−	3019.83i	0.650258	−	1.12628i	−0.332802	−	0.942997i	$-0.607994\pi$
$193$	1743.50	−	3019.83i	0.650258	−	1.12628i	0.983060	−	0.183284i	$-0.0586727\pi$
$194$	−100.500	+	174.071i	−0.0371932	+	0.0644205i
$195$	5418.00	+	3128.08i	1.98970	+	1.14875i
$196$	171.500	+	297.047i	0.0625000	+	0.108253i
$197$	−1454.00			−0.525854			−0.262927	−	0.964816i	$-0.584688\pi$
$197$	−1454.00			−0.525854			−0.262927	+	0.964816i	$0.584688\pi$
$198$	634.500	+	1098.99i	0.227737	+	0.394452i
$199$	3582.00			1.27599			0.637993	−	0.770042i	$-0.279765\pi$
$199$	3582.00			1.27599			0.637993	+	0.770042i	$0.279765\pi$
$200$	−532.500	−	922.317i	−0.188267	−	0.326088i
$201$			805.404i			0.282631i
$202$	70.0000	−	121.244i	0.0243821	−	0.0422310i
$203$	−910.000	+	1576.17i	−0.314628	+	0.544952i
$204$		−	327.358i		−	0.112351i
$205$	2681.00	+	4643.63i	0.913411	+	1.58207i
$206$	1330.00			0.449832
$207$	−162.000	−	280.592i	−0.0543951	−	0.0942150i
$208$	−3526.00			−1.17540
$209$	−3078.50	−	5332.12i	−1.01887	−	1.76474i
$210$	−441.000	−	254.611i	−0.144914	−	0.0836660i
$211$	−836.000	+	1447.99i	−0.272761	+	0.472436i	−0.969568	−	0.244823i	$-0.921270\pi$
$211$	−836.000	+	1447.99i	−0.272761	+	0.472436i	0.696807	+	0.717259i	$0.254604\pi$
$212$	1050.00	−	1818.65i	0.340162	−	0.589177i
$213$	−324.000	+	187.061i	−0.104226	+	0.0601748i
$214$	−686.500	−	1189.05i	−0.219291	−	0.379822i
$215$	2366.00			0.750511
$216$			2104.44i			0.662913i
$217$	378.000			0.118250
$218$	−333.000	−	576.773i	−0.103457	−	0.179193i
$219$	−526.500	+	303.975i	−0.162455	+	0.0937932i
$220$	2303.00	−	3988.91i	0.705765	−	1.22242i
$221$	−387.000	+	670.304i	−0.117794	+	0.204025i
$222$	1107.00	+	639.127i	0.334671	+	0.193222i
$223$	874.000	+	1513.81i	0.262455	+	0.454585i	0.966894	−	0.255180i	$-0.0821347\pi$
$223$	874.000	+	1513.81i	0.262455	+	0.454585i	−0.704439	+	0.709764i	$0.748801\pi$
$224$	1127.00			0.336165
$225$	−1917.00			−0.568000
$226$	−790.000			−0.232522
$227$	472.500	+	818.394i	0.138154	+	0.239290i	0.926798	−	0.375561i	$-0.122550\pi$
$227$	472.500	+	818.394i	0.138154	+	0.239290i	−0.788644	+	0.614850i	$0.789216\pi$
$228$		−	4764.87i		−	1.38404i
$229$	245.000	−	424.352i	0.0706989	−	0.122454i	−0.828509	−	0.559976i	$-0.810810\pi$
$229$	245.000	−	424.352i	0.0706989	−	0.122454i	0.899208	+	0.437522i	$0.144144\pi$
$230$	84.0000	−	145.492i	0.0240817	−	0.0417108i
$231$		−	1709.53i		−	0.486922i
$232$	1950.00	+	3377.50i	0.551827	+	0.955792i
$233$	363.000			0.102064			0.0510320	−	0.998697i	$-0.483749\pi$
$233$	363.000			0.102064			0.0510320	+	0.998697i	$0.483749\pi$
$234$	1161.00	−	2010.91i	0.324346	−	0.561784i
$235$	−1344.00			−0.373076
$236$	1501.50	+	2600.67i	0.414150	+	0.717328i
$237$	−2367.00	−	1366.59i	−0.648748	−	0.374555i
$238$	31.5000	−	54.5596i	0.00857917	−	0.0148596i
$239$	3273.00	−	5669.00i	0.885827	−	1.53430i	0.0410652	−	0.999156i	$-0.486925\pi$
$239$	3273.00	−	5669.00i	0.885827	−	1.53430i	0.844762	−	0.535142i	$-0.179742\pi$
$240$	2583.00	−	1491.30i	0.694716	−	0.401095i
$241$	1830.50	+	3170.52i	0.489265	+	0.847432i	0.999924	−	0.0123516i	$-0.00393175\pi$
$241$	1830.50	+	3170.52i	0.489265	+	0.847432i	−0.510659	+	0.859784i	$0.670598\pi$
$242$	−878.000			−0.233223
$243$	3280.50	+	1894.00i	0.866025	+	0.500000i
$244$	2660.00			0.697906
$245$	343.000	+	594.093i	0.0894427	+	0.154919i
$246$	1723.50	−	995.063i	0.446692	−	0.257898i
$247$	−5633.00	+	9756.64i	−1.45109	+	2.51336i
$248$	405.000	−	701.481i	0.103700	−	0.179613i
$249$	2592.00	+	1496.49i	0.659684	+	0.380869i
$250$	378.000	+	654.715i	0.0956273	+	0.165631i
$251$	−3017.00			−0.758691			−0.379345	−	0.925255i	$-0.623851\pi$
$251$	−3017.00			−0.758691			−0.379345	+	0.925255i	$0.623851\pi$
$252$	661.500	−	1145.75i	0.165359	−	0.286411i
$253$	564.000			0.140152
$254$	330.000	+	571.577i	0.0815198	+	0.141197i
$255$		−	654.715i		−	0.160784i
$256$	59.5000	−	103.057i	0.0145264	−	0.0251604i
$257$	45.5000	−	78.8083i	0.0110436	−	0.0191281i	−0.860451	−	0.509534i	$-0.829818\pi$
$257$	45.5000	−	78.8083i	0.0110436	−	0.0191281i	0.871494	+	0.490405i	$0.163151\pi$
$258$		−	878.150i		−	0.211904i
$259$	−861.000	−	1491.30i	−0.206563	−	0.357778i
$260$	−8428.00			−2.01032
$261$	7020.00			1.66485
$262$	644.000			0.151857
$263$	475.000	+	822.724i	0.111368	+	0.192895i	0.916322	−	0.400442i	$-0.131143\pi$
$263$	475.000	+	822.724i	0.111368	+	0.192895i	−0.804954	+	0.593337i	$0.797810\pi$
$264$	−3172.50	−	1831.64i	−0.739598	−	0.427007i
$265$	2100.00	−	3637.31i	0.486800	−	0.843162i
$266$	458.500	−	794.145i	0.105686	−	0.183053i
$267$	1251.00	−	722.265i	0.286741	−	0.165550i
$268$	−542.500	−	939.638i	−0.123651	−	0.214170i
$269$	−5196.00			−1.17772			−0.588858	−	0.808236i	$-0.700422\pi$
$269$	−5196.00			−1.17772			−0.588858	+	0.808236i	$0.700422\pi$
$270$			1964.15i			0.442719i
$271$	2746.00			0.615526			0.307763	−	0.951463i	$-0.400420\pi$
$271$	2746.00			0.615526			0.307763	+	0.951463i	$0.400420\pi$
$272$	184.500	+	319.563i	0.0411285	+	0.0712367i
$273$	−2709.00	+	1564.04i	−0.600572	+	0.346740i
$274$	−289.500	+	501.429i	−0.0638297	+	0.110556i
$275$	1668.50	−	2889.93i	0.365870	−	0.633706i
$276$	378.000	+	218.238i	0.0824381	+	0.0475957i
$277$	−2717.00	−	4705.98i	−0.589346	−	1.02078i	−0.994318	−	0.106448i	$-0.966052\pi$
$277$	−2717.00	−	4705.98i	−0.589346	−	1.02078i	0.404973	−	0.914329i	$-0.367281\pi$
$278$	−2175.00			−0.469237
$279$	−729.000	−	1262.67i	−0.156430	−	0.270945i
$280$	1470.00			0.313748
$281$	2909.00	+	5038.54i	0.617567	+	1.06966i	0.989928	+	0.141570i	$0.0452150\pi$
$281$	2909.00	+	5038.54i	0.617567	+	1.06966i	−0.372361	+	0.928088i	$0.621452\pi$
$282$			498.831i			0.105337i
$283$	1798.00	−	3114.23i	0.377668	−	0.654140i	−0.613055	−	0.790041i	$-0.710059\pi$
$283$	1798.00	−	3114.23i	0.377668	−	0.654140i	0.990722	+	0.135901i	$0.0433928\pi$
$284$	252.000	−	436.477i	0.0526530	−	0.0911977i
$285$		−	9529.74i		−	1.98068i
$286$	2021.00	+	3500.47i	0.417847	+	0.723732i
$287$	−2681.00			−0.551409
$288$	−2173.50	−	3764.61i	−0.444704	−	0.770250i
$289$	−4832.00			−0.983513
$290$	1820.00	+	3152.33i	0.368531	+	0.638315i
$291$	−904.500	−	522.213i	−0.182209	−	0.105198i
$292$	409.500	−	709.275i	0.0820691	−	0.142148i
$293$	−2848.00	+	4932.88i	−0.567856	+	0.983556i	0.428921	+	0.903342i	$0.358894\pi$
$293$	−2848.00	+	4932.88i	−0.567856	+	0.983556i	−0.996778	+	0.0802143i	$0.974440\pi$
$294$	220.500	−	127.306i	0.0437409	−	0.0252538i
$295$	3003.00	+	5201.35i	0.592683	+	1.02656i
$296$	−3690.00			−0.724584
$297$	−5710.50	+	3296.96i	−1.11568	+	0.644138i
$298$	2280.00			0.443211
$299$	−516.000	−	893.738i	−0.0998028	−	0.172864i
$300$	2236.50	−	1291.24i	0.430415	−	0.248500i
$301$	−591.500	+	1024.51i	−0.113267	+	0.196185i
$302$	−335.000	+	580.237i	−0.0638314	+	0.110559i
$303$	630.000	+	363.731i	0.119447	+	0.0689630i
$304$	2685.50	+	4651.42i	0.506658	+	0.877557i
$305$	5320.00			0.998762
$306$	−243.000			−0.0453967
$307$	−5117.00			−0.951279			−0.475639	−	0.879640i	$-0.657783\pi$
$307$	−5117.00			−0.951279			−0.475639	+	0.879640i	$0.657783\pi$
$308$	1151.50	+	1994.46i	0.213029	+	0.368976i
$309$			6910.88i			1.27232i
$310$	378.000	−	654.715i	0.0692547	−	0.119953i
$311$	783.000	−	1356.20i	0.142765	−	0.247276i	−0.785772	−	0.618516i	$-0.787734\pi$
$311$	783.000	−	1356.20i	0.142765	−	0.247276i	0.928537	+	0.371240i	$0.121067\pi$
$312$			6703.04i			1.21630i
$313$	−1493.50	−	2586.82i	−0.269705	−	0.467142i	0.699081	−	0.715043i	$-0.253593\pi$
$313$	−1493.50	−	2586.82i	−0.269705	−	0.467142i	−0.968786	+	0.247900i	$0.920259\pi$
$314$	782.000			0.140544
$315$	1323.00	−	2291.50i	0.236643	−	0.409878i
$316$	3682.00			0.655471
$317$	−3825.00	−	6625.09i	−0.677708	−	1.17382i	−0.975669	−	0.219247i	$-0.929640\pi$
$317$	−3825.00	−	6625.09i	−0.677708	−	1.17382i	0.297962	−	0.954578i	$-0.403693\pi$
$318$	−1350.00	−	779.423i	−0.238064	−	0.137446i
$319$	−6110.00	+	10582.8i	−1.07240	+	1.85744i
$320$	−1169.00	+	2024.77i	−0.204216	+	0.353712i
$321$	6178.50	−	3567.16i	1.07430	−	0.620247i
$322$	42.0000	+	72.7461i	0.00726885	+	0.0125900i
$323$	1179.00			0.203100
$324$	−5103.00			−0.875000
$325$	−6106.00			−1.04215
$326$	−1054.00	−	1825.58i	−0.179066	−	0.310152i
$327$	2997.00	−	1730.32i	0.506833	−	0.292620i
$328$	−2872.50	+	4975.32i	−0.483559	+	0.837548i
$329$	336.000	−	581.969i	0.0563048	−	0.0975228i
$330$	−2961.00	−	1709.53i	−0.493932	−	0.285172i
$331$	−4336.00	−	7510.17i	−0.720025	−	1.24712i	−0.960989	−	0.276585i	$-0.910797\pi$
$331$	−4336.00	−	7510.17i	−0.720025	−	1.24712i	0.240965	−	0.970534i	$-0.422536\pi$
$332$	−4032.00			−0.666520
$333$	−3321.00	+	5752.14i	−0.546516	+	0.946593i
$334$	44.0000			0.00720830
$335$	−1085.00	−	1879.28i	−0.176955	−	0.306495i
$336$			1491.30i			0.242133i
$337$	3500.50	−	6063.04i	0.565829	−	0.980045i	−0.431143	−	0.902284i	$-0.641890\pi$
$337$	3500.50	−	6063.04i	0.565829	−	0.980045i	0.996972	−	0.0777610i	$-0.0247771\pi$
$338$	2599.50	−	4502.47i	0.418326	−	0.724562i
$339$		−	4104.96i		−	0.657672i
$340$	441.000	+	763.834i	0.0703429	+	0.121837i
$341$	2538.00			0.403051
$342$	−3537.00			−0.559237
$343$	−343.000			−0.0539949
$344$	1267.50	+	2195.37i	0.198660	+	0.344089i
$345$	756.000	+	436.477i	0.117976	+	0.0681134i
$346$	−2255.00	+	3905.77i	−0.350374	+	0.606866i
$347$	1617.50	−	2801.59i	0.250236	−	0.433422i	−0.713355	−	0.700803i	$-0.752825\pi$
$347$	1617.50	−	2801.59i	0.250236	−	0.433422i	0.963591	+	0.267382i	$0.0861584\pi$
$348$	−8190.00	+	4728.50i	−1.26158	+	0.728374i
$349$	895.000	+	1550.19i	0.137273	+	0.237764i	0.926463	−	0.376385i	$-0.122833\pi$
$349$	895.000	+	1550.19i	0.137273	+	0.237764i	−0.789191	+	0.614148i	$0.789500\pi$
$350$	497.000			0.0759022
$351$	10449.0	+	6032.73i	1.58896	+	0.917389i
$352$	7567.00			1.14580
$353$	−66.5000	−	115.181i	−0.0100267	−	0.0173668i	0.860969	−	0.508658i	$-0.169858\pi$
$353$	−66.5000	−	115.181i	−0.0100267	−	0.0173668i	−0.870995	+	0.491291i	$0.836525\pi$
$354$	1930.50	−	1114.57i	0.289844	−	0.167342i
$355$	504.000	−	872.954i	0.0753508	−	0.130511i
$356$	−973.000	+	1685.29i	−0.144856	+	0.250899i
$357$	283.500	+	163.679i	0.0420292	+	0.0242655i
$358$	−872.000	−	1510.35i	−0.128734	−	0.222973i
$359$	−9094.00			−1.33694			−0.668472	−	0.743737i	$-0.733051\pi$
$359$	−9094.00			−1.33694			−0.668472	+	0.743737i	$0.733051\pi$
$360$	−2835.00	−	4910.36i	−0.415049	−	0.718886i
$361$	10302.0			1.50197
$362$	−1120.00	−	1939.90i	−0.162613	−	0.281654i
$363$		−	4562.22i		−	0.659654i
$364$	2107.00	−	3649.43i	0.303398	−	0.525500i
$365$	819.000	−	1418.55i	0.117448	−	0.203425i
$366$		−	1974.54i		−	0.281997i
$367$	−5565.00	−	9638.86i	−0.791528	−	1.37097i	−0.925021	−	0.379916i	$-0.875953\pi$
$367$	−5565.00	−	9638.86i	−0.791528	−	1.37097i	0.133493	−	0.991050i	$-0.457381\pi$
$368$	−492.000			−0.0696937
$369$	5170.50	+	8955.57i	0.729446	+	1.26344i
$370$	−3444.00			−0.483905
$371$	1050.00	+	1818.65i	0.146936	+	0.254501i
$372$	1701.00	+	982.073i	0.237077	+	0.136877i
$373$	6425.00	−	11128.4i	0.891887	−	1.54479i	0.0542765	−	0.998526i	$-0.482715\pi$
$373$	6425.00	−	11128.4i	0.891887	−	1.54479i	0.837611	−	0.546268i	$-0.183952\pi$
$374$	211.500	−	366.329i	0.0292417	−	0.0506482i
$375$	−3402.00	+	1964.15i	−0.468476	+	0.270475i
$376$	−720.000	−	1247.08i	−0.0987531	−	0.171045i
$377$	22360.0			3.05464
$378$	−850.500	−	491.036i	−0.115728	−	0.0668153i
$379$	807.000			0.109374			0.0546871	−	0.998504i	$-0.482584\pi$
$379$	807.000			0.109374			0.0546871	+	0.998504i	$0.482584\pi$
$380$	6419.00	+	11118.0i	0.866547	+	1.50090i
$381$	−2970.00	+	1714.73i	−0.399364	+	0.230573i
$382$	206.000	−	356.802i	0.0275913	−	0.0477895i
$383$	3990.00	−	6910.88i	0.532322	−	0.922009i	−0.466965	−	0.884276i	$-0.654653\pi$
$383$	3990.00	−	6910.88i	0.532322	−	0.922009i	0.999288	−	0.0377339i	$-0.0120139\pi$
$384$	6547.50	+	3780.20i	0.870119	+	0.502363i
$385$	2303.00	+	3988.91i	0.304862	+	0.528036i
$386$	3487.00			0.459802
$387$	4563.00			0.599355
$388$	1407.00			0.184097
$389$	1308.00	+	2265.52i	0.170484	+	0.295287i	0.938589	−	0.345037i	$-0.112134\pi$
$389$	1308.00	+	2265.52i	0.170484	+	0.295287i	−0.768105	+	0.640324i	$0.778800\pi$
$390$			6256.17i			0.812291i
$391$	−54.0000	+	93.5307i	−0.00698439	+	0.0120973i
$392$	−367.500	+	636.529i	−0.0473509	+	0.0820142i
$393$			3346.32i			0.429516i
$394$	−727.000	−	1259.20i	−0.0929587	−	0.161009i
$395$	7364.00			0.938033
$396$	4441.50	−	7692.90i	0.563621	−	0.976220i
$397$	−5934.00			−0.750174			−0.375087	−	0.926990i	$-0.622387\pi$
$397$	−5934.00			−0.750174			−0.375087	+	0.926990i	$0.622387\pi$
$398$	1791.00	+	3102.10i	0.225565	+	0.390689i
$399$	4126.50	+	2382.44i	0.517753	+	0.298925i
$400$	−1455.50	+	2521.00i	−0.181938	+	0.315125i
$401$	−3952.50	+	6845.93i	−0.492216	+	0.852542i	−0.999960	−	0.00896552i	$-0.997146\pi$
$401$	−3952.50	+	6845.93i	−0.492216	+	0.852542i	0.507744	+	0.861508i	$0.330479\pi$
$402$	−697.500	+	402.702i	−0.0865377	+	0.0499625i
$403$	−2322.00	−	4021.82i	−0.287015	−	0.497125i
$404$	−980.000			−0.120685
$405$	−10206.0			−1.25220
$406$	−1820.00			−0.222476
$407$	−5781.00	−	10013.0i	−0.704063	−	1.21947i
$408$	607.500	−	350.740i	0.0737150	−	0.0425594i
$409$	5196.50	−	9000.60i	0.628241	−	1.08814i	−0.359664	−	0.933082i	$-0.617109\pi$
$409$	5196.50	−	9000.60i	0.628241	−	1.08814i	0.987905	−	0.155063i	$-0.0495580\pi$
$410$	−2681.00	+	4643.63i	−0.322939	+	0.559347i
$411$	−2605.50	−	1504.29i	−0.312700	−	0.180538i
$412$	−4655.00	−	8062.70i	−0.556639	−	0.964128i
$413$	−3003.00			−0.357792
$414$	162.000	−	280.592i	0.0192316	−	0.0333100i
$415$	−8064.00			−0.953846
$416$	−6923.00	−	11991.0i	−0.815933	−	1.41324i
$417$		−	11301.6i		−	1.32720i
$418$	3078.50	−	5332.12i	0.360226	−	0.623929i
$419$	−4290.00	+	7430.50i	−0.500191	+	0.866357i	0.499809	+	0.866136i	$0.333404\pi$
$419$	−4290.00	+	7430.50i	−0.500191	+	0.866357i	−1.00000		0.000221073i	$0.999930\pi$
$420$			3564.56i			0.414126i
$421$	−2530.00	−	4382.09i	−0.292885	−	0.507292i	0.681606	−	0.731720i	$-0.261282\pi$
$421$	−2530.00	−	4382.09i	−0.292885	−	0.507292i	−0.974491	+	0.224428i	$0.927949\pi$
$422$	−1672.00			−0.192871
$423$	−2592.00			−0.297937
$424$	4500.00			0.515423
$425$	319.500	+	553.390i	0.0364659	+	0.0631609i
$426$	−324.000	−	187.061i	−0.0368494	−	0.0212750i
$427$	−1330.00	+	2303.63i	−0.150734	+	0.261078i
$428$	−4805.50	+	8323.37i	−0.542716	+	0.940012i
$429$	−18189.0	+	10501.4i	−2.04702	+	1.18185i
$430$	1183.00	+	2049.02i	0.132673	+	0.229796i
$431$	11136.0			1.24455			0.622276	−	0.782798i	$-0.286208\pi$
$431$	11136.0			1.24455			0.622276	+	0.782798i	$0.286208\pi$
$432$	4981.50	−	2876.07i	0.554798	−	0.320312i
$433$	8491.00			0.942382			0.471191	−	0.882031i	$-0.343824\pi$
$433$	8491.00			0.942382			0.471191	+	0.882031i	$0.343824\pi$
$434$	189.000	+	327.358i	0.0209039	+	0.0362066i
$435$	−16380.0	+	9457.00i	−1.80543	+	1.04236i
$436$	−2331.00	+	4037.41i	−0.256043	+	0.443479i
$437$	−786.000	+	1361.39i	−0.0860400	+	0.149026i
$438$	−526.500	−	303.975i	−0.0574364	−	0.0331609i
$439$	1380.00	+	2390.23i	0.150031	+	0.259862i	0.931239	−	0.364410i	$-0.118729\pi$
$439$	1380.00	+	2390.23i	0.150031	+	0.259862i	−0.781207	+	0.624272i	$0.785396\pi$
$440$	9870.00			1.06939
$441$	661.500	+	1145.75i	0.0714286	+	0.123718i
$442$	−774.000			−0.0832928
$443$	5068.50	+	8778.90i	0.543593	+	0.941531i	0.998694	+	0.0510909i	$0.0162698\pi$
$443$	5068.50	+	8778.90i	0.543593	+	0.941531i	−0.455101	+	0.890440i	$0.650397\pi$
$444$		−	8947.77i		−	0.956402i
$445$	−1946.00	+	3370.57i	−0.207302	+	0.359057i
$446$	−874.000	+	1513.81i	−0.0927917	+	0.160720i
$447$			11847.2i			1.25359i
$448$	−584.500	−	1012.38i	−0.0616407	−	0.106765i
$449$	13449.0			1.41358			0.706790	−	0.707423i	$-0.250143\pi$
$449$	13449.0			1.41358			0.706790	+	0.707423i	$0.250143\pi$
$450$	−958.500	−	1660.17i	−0.100409	−	0.173914i
$451$	−18001.0			−1.87945
$452$	2765.00	+	4789.12i	0.287732	+	0.498366i
$453$	−3015.00	−	1740.71i	−0.312709	−	0.180542i
$454$	−472.500	+	818.394i	−0.0488448	+	0.0846016i
$455$	4214.00	−	7298.86i	0.434188	−	0.752035i
$456$	8842.50	−	5105.22i	0.908088	−	0.524285i
$457$	7679.50	+	13301.3i	0.786065	+	1.36151i	0.928361	+	0.371681i	$0.121218\pi$
$457$	7679.50	+	13301.3i	0.786065	+	1.36151i	−0.142295	+	0.989824i	$0.545448\pi$
$458$	490.000			0.0499917
$459$		−	1262.67i		−	0.128401i
$460$	−1176.00			−0.119198
$461$	−7519.00	−	13023.3i	−0.759642	−	1.31574i	−0.943033	−	0.332698i	$-0.892041\pi$
$461$	−7519.00	−	13023.3i	−0.759642	−	1.31574i	0.183392	−	0.983040i	$-0.441292\pi$
$462$	1480.50	−	854.767i	0.149089	−	0.0860765i
$463$	844.000	−	1461.85i	0.0847171	−	0.146734i	−0.820554	−	0.571570i	$-0.806335\pi$
$463$	844.000	−	1461.85i	0.0847171	−	0.146734i	0.905271	+	0.424835i	$0.139668\pi$
$464$	5330.00	−	9231.83i	0.533274	−	0.923657i
$465$	3402.00	+	1964.15i	0.339277	+	0.195882i
$466$	181.500	+	314.367i	0.0180425	+	0.0312506i
$467$	−11121.0			−1.10197			−0.550983	−	0.834516i	$-0.685747\pi$
$467$	−11121.0			−1.10197			−0.550983	+	0.834516i	$0.685747\pi$
$468$	−16254.0			−1.60543
$469$	1085.00			0.106824
$470$	−672.000	−	1163.94i	−0.0659512	−	0.114231i
$471$			4063.39i			0.397518i
$472$	−3217.50	+	5572.87i	−0.313766	+	0.543458i
$473$	−3971.50	+	6878.84i	−0.386067	+	0.668688i
$474$		−	2733.18i		−	0.264850i
$475$	4650.50	+	8054.90i	0.449220	+	0.778072i
$476$	−441.000			−0.0424647
$477$	4050.00	−	7014.81i	0.388756	−	0.673346i
$478$	6546.00			0.626375
$479$	−8302.00	−	14379.5i	−0.791917	−	1.37164i	−0.924779	−	0.380505i	$-0.875750\pi$
$479$	−8302.00	−	14379.5i	−0.791917	−	1.37164i	0.132862	−	0.991135i	$-0.457583\pi$
$480$	10143.0	+	5856.06i	0.964505	+	0.556857i
$481$	−10578.0	+	18321.6i	−1.00273	+	1.73679i
$482$	−1830.50	+	3170.52i	−0.172981	+	0.299612i
$483$	−378.000	+	218.238i	−0.0356099	+	0.0205594i
$484$	3073.00	+	5322.59i	0.288599	+	0.499868i
$485$	2814.00			0.263458
$486$			3788.00i			0.353553i
$487$	−9794.00			−0.911311			−0.455656	−	0.890156i	$-0.650595\pi$
$487$	−9794.00			−0.911311			−0.455656	+	0.890156i	$0.650595\pi$
$488$	2850.00	+	4936.34i	0.264372	+	0.457905i
$489$	9486.00	−	5476.74i	0.877243	−	0.506476i
$490$	−343.000	+	594.093i	−0.0316228	+	0.0547723i
$491$	483.500	−	837.447i	0.0444400	−	0.0769724i	−0.842950	−	0.537992i	$-0.819183\pi$
$491$	483.500	−	837.447i	0.0444400	−	0.0769724i	0.887390	+	0.461020i	$0.152516\pi$
$492$	−12064.5	−	6965.44i	−1.10551	−	0.638265i
$493$	−1170.00	−	2026.50i	−0.106885	−	0.185130i
$494$	−11266.0			−1.02608
$495$	8883.00	−	15385.8i	0.806588	−	1.39705i
$496$	−2214.00			−0.200426
$497$	252.000	+	436.477i	0.0227440	+	0.0393937i
$498$			2992.98i			0.269315i
$499$	9494.50	−	16445.0i	0.851768	−	1.47531i	−0.0278434	−	0.999612i	$-0.508864\pi$
$499$	9494.50	−	16445.0i	0.851768	−	1.47531i	0.879611	−	0.475693i	$-0.157803\pi$
$500$	2646.00	−	4583.01i	0.236665	−	0.409917i
$501$			228.631i			0.0203882i
$502$	−1508.50	−	2612.80i	−0.134119	−	0.232301i
$503$	−9114.00			−0.807899			−0.403949	−	0.914781i	$-0.632363\pi$
$503$	−9114.00			−0.807899			−0.403949	+	0.914781i	$0.632363\pi$
$504$	2835.00			0.250557
$505$	−1960.00			−0.172711
$506$	282.000	+	488.438i	0.0247756	+	0.0429125i
$507$	23395.5	+	13507.4i	2.04937	+	1.18320i
$508$	2310.00	−	4001.04i	0.201751	−	0.349444i
$509$	−10591.0	+	18344.2i	−0.922275	+	1.59743i	−0.126388	+	0.991981i	$0.540338\pi$
$509$	−10591.0	+	18344.2i	−0.922275	+	1.59743i	−0.795887	+	0.605446i	$0.792995\pi$
$510$	567.000	−	327.358i	0.0492298	−	0.0284228i
$511$	409.500	+	709.275i	0.0354505	+	0.0614021i
$512$	−11521.0			−0.994455
$513$		−	18378.8i		−	1.58176i
$514$	91.0000			0.00780902
$515$	−9310.00	−	16125.4i	−0.796597	−	1.37975i
$516$	−5323.50	+	3073.52i	−0.454174	+	0.262218i
$517$	2256.00	−	3907.51i	0.191913	−	0.332402i
$518$	861.000	−	1491.30i	0.0730312	−	0.126494i
$519$	−20295.0	−	11717.3i	−1.71648	−	0.991009i
$520$	−9030.00	−	15640.4i	−0.761522	−	1.31900i
$521$	4107.00			0.345357			0.172678	−	0.984978i	$-0.444758\pi$
$521$	4107.00			0.345357			0.172678	+	0.984978i	$0.444758\pi$
$522$	3510.00	+	6079.50i	0.294308	+	0.509756i
$523$	16564.0			1.38488			0.692441	−	0.721475i	$-0.256535\pi$
$523$	16564.0			1.38488			0.692441	+	0.721475i	$0.256535\pi$
$524$	−2254.00	−	3904.04i	−0.187913	−	0.325475i
$525$			2582.49i			0.214684i
$526$	−475.000	+	822.724i	−0.0393745	+	0.0681986i
$527$	−243.000	+	420.888i	−0.0200859	+	0.0347897i
$528$			10013.0i			0.825302i
$529$	6011.50	+	10412.2i	0.494082	+	0.855776i
$530$	4200.00			0.344220
$531$	5791.50	+	10031.2i	0.473314	+	0.819804i
$532$	−6419.00			−0.523118
$533$	16469.0	+	28525.1i	1.33837	+	2.31813i
$534$	1251.00	+	722.265i	0.101378	+	0.0585308i
$535$	−9611.00	+	16646.7i	−0.776672	+	1.34524i
$536$	1162.50	−	2013.51i	0.0936798	−	0.162258i
$537$	7848.00	−	4531.04i	0.630663	−	0.364114i
$538$	−2598.00	−	4499.87i	−0.208193	−	0.360601i
$539$	−2303.00			−0.184039
$540$	11907.0	−	6874.51i	0.948881	−	0.547837i
$541$	12200.0			0.969536			0.484768	−	0.874643i	$-0.338904\pi$
$541$	12200.0			0.969536			0.484768	+	0.874643i	$0.338904\pi$
$542$	1373.00	+	2378.11i	0.108811	+	0.188466i
$543$	10080.0	−	5819.69i	0.796638	−	0.459939i
$544$	−724.500	+	1254.87i	−0.0571005	+	0.0989010i
$545$	−4662.00	+	8074.82i	−0.366419	+	0.634656i
$546$	−2709.00	−	1564.04i	−0.212334	−	0.122591i
$547$	−5025.50	−	8704.42i	−0.392824	−	0.680392i	0.599997	−	0.800003i	$-0.295169\pi$
$547$	−5025.50	−	8704.42i	−0.392824	−	0.680392i	−0.992821	+	0.119611i	$0.961835\pi$
$548$	4053.00			0.315941
$549$	10260.0			0.797607
$550$	3337.00			0.258709
$551$	−17030.0	−	29496.8i	−1.31670	−	2.28059i
$552$			935.307i			0.0721183i
$553$	−1841.00	+	3188.71i	−0.141568	+	0.245204i
$554$	2717.00	−	4705.98i	0.208365	−	0.360899i
$555$		−	17895.5i		−	1.36869i
$556$	7612.50	+	13185.2i	0.580651	+	1.00572i
$557$	−4796.00			−0.364835			−0.182417	−	0.983221i	$-0.558392\pi$
$557$	−4796.00			−0.364835			−0.182417	+	0.983221i	$0.558392\pi$
$558$	729.000	−	1262.67i	0.0553065	−	0.0957937i
$559$	14534.0			1.09968
$560$	−2009.00	−	3479.69i	−0.151600	−	0.262578i
$561$	1903.50	+	1098.99i	0.143255	+	0.0827081i
$562$	−2909.00	+	5038.54i	−0.218343	+	0.378181i
$563$	−7473.50	+	12944.5i	−0.559450	+	0.968996i	0.438092	+	0.898930i	$0.355654\pi$
$563$	−7473.50	+	12944.5i	−0.559450	+	0.968996i	−0.997542	+	0.0700661i	$0.977679\pi$
$564$	3024.00	−	1745.91i	0.225768	−	0.130347i
$565$	5530.00	+	9578.24i	0.411768	+	0.713203i
$566$	3596.00			0.267052
$567$	2551.50	−	4419.33i	0.188982	−	0.327327i
$568$	1080.00			0.0797813
$569$	13475.5	+	23340.3i	0.992834	+	1.71964i	0.599911	+	0.800067i	$0.295203\pi$
$569$	13475.5	+	23340.3i	0.992834	+	1.71964i	0.392923	+	0.919571i	$0.371464\pi$
$570$	8253.00	−	4764.87i	0.606456	−	0.350138i
$571$	252.500	−	437.343i	0.0185058	−	0.0320529i	−0.856624	−	0.515941i	$-0.827442\pi$
$571$	252.500	−	437.343i	0.0185058	−	0.0320529i	0.875130	+	0.483888i	$0.160776\pi$
$572$	14147.0	−	24503.3i	1.03412	−	1.79115i
$573$	1854.00	+	1070.41i	0.135169	+	0.0780400i
$574$	−1340.50	−	2321.81i	−0.0974763	−	0.168834i
$575$	−852.000			−0.0617928
$576$	−2254.50	+	3904.91i	−0.163086	+	0.282473i
$577$	17281.0			1.24682			0.623412	−	0.781894i	$-0.285746\pi$
$577$	17281.0			1.24682			0.623412	+	0.781894i	$0.285746\pi$
$578$	−2416.00	−	4184.63i	−0.173862	−	0.301138i
$579$			18119.0i			1.30052i
$580$	12740.0	−	22066.3i	0.912068	−	1.57975i
$581$	2016.00	−	3491.81i	0.143955	−	0.249337i
$582$		−	1044.43i		−	0.0743864i
$583$	7050.00	+	12211.0i	0.500825	+	0.867455i
$584$	1755.00			0.124353
$585$	−32508.0			−2.29750
$586$	−5696.00			−0.401535
$587$	−6318.50	−	10944.0i	−0.444280	−	0.769516i	0.553722	−	0.832702i	$-0.313207\pi$
$587$	−6318.50	−	10944.0i	−0.444280	−	0.769516i	−0.998002	+	0.0631861i	$0.979874\pi$
$588$	−1543.50	−	891.140i	−0.108253	−	0.0625000i
$589$	−3537.00	+	6126.26i	−0.247436	+	0.428571i
$590$	−3003.00	+	5201.35i	−0.209545	+	0.362943i
$591$	6543.00	−	3777.60i	0.455403	−	0.262927i
$592$	5043.00	+	8734.73i	0.350112	+	0.606411i
$593$	8346.00			0.577958			0.288979	−	0.957335i	$-0.406684\pi$
$593$	8346.00			0.577958			0.288979	+	0.957335i	$0.406684\pi$
$594$	−5710.50	−	3296.96i	−0.394452	−	0.227737i
$595$	−882.000			−0.0607705
$596$	−7980.00	−	13821.8i	−0.548446	−	0.949936i
$597$	−16119.0	+	9306.31i	−1.10504	+	0.637993i
$598$	516.000	−	893.738i	0.0352856	−	0.0611165i
$599$	−4980.00	+	8625.61i	−0.339695	+	0.588369i	−0.984375	−	0.176083i	$-0.943657\pi$
$599$	−4980.00	+	8625.61i	−0.339695	+	0.588369i	0.644680	+	0.764452i	$0.276991\pi$
$600$	4792.50	+	2766.95i	0.326088	+	0.188267i
$601$	−8488.50	−	14702.5i	−0.576128	−	0.997884i	−0.995918	−	0.0902622i	$-0.971230\pi$
$601$	−8488.50	−	14702.5i	−0.576128	−	0.997884i	0.419790	−	0.907621i	$-0.362104\pi$
$602$	−1183.00			−0.0800922
$603$	−2092.50	−	3624.32i	−0.141315	−	0.244765i
$604$	4690.00			0.315949
$605$	6146.00	+	10645.2i	0.413009	+	0.715353i
$606$			727.461i			0.0487642i
$607$	−4564.00	+	7905.08i	−0.305185	+	0.528595i	−0.977302	−	0.211849i	$-0.932051\pi$
$607$	−4564.00	+	7905.08i	−0.305185	+	0.528595i	0.672118	+	0.740444i	$0.265385\pi$
$608$	−10545.5	+	18265.3i	−0.703415	+	1.21835i
$609$		−	9457.00i		−	0.629256i
$610$	2660.00	+	4607.26i	0.176558	+	0.305807i
$611$	−8256.00			−0.546648
$612$	850.500	+	1473.11i	0.0561755	+	0.0972989i
$613$	−9374.00			−0.617638			−0.308819	−	0.951121i	$-0.599934\pi$
$613$	−9374.00			−0.617638			−0.308819	+	0.951121i	$0.599934\pi$
$614$	−2558.50	−	4431.45i	−0.168164	−	0.291268i
$615$	−24129.0	−	13930.9i	−1.58207	−	0.913411i
$616$	−2467.50	+	4273.84i	−0.161394	+	0.279542i
$617$	3640.50	−	6305.53i	0.237538	−	0.411428i	−0.722469	−	0.691403i	$-0.756993\pi$
$617$	3640.50	−	6305.53i	0.237538	−	0.411428i	0.960007	+	0.279975i	$0.0903262\pi$
$618$	−5985.00	+	3455.44i	−0.389566	+	0.224916i
$619$	5267.50	+	9123.58i	0.342033	+	0.592419i	0.984810	−	0.173634i	$-0.0555511\pi$
$619$	5267.50	+	9123.58i	0.342033	+	0.592419i	−0.642777	+	0.766054i	$0.722218\pi$
$620$	−5292.00			−0.342793
$621$	1458.00	+	841.777i	0.0942150	+	0.0543951i
$622$	1566.00			0.100950
$623$	−973.000	−	1685.29i	−0.0625721	−	0.108378i
$624$	15867.0	−	9160.82i	1.01793	−	0.587702i
$625$	9729.50	−	16852.0i	0.622688	−	1.07853i
$626$	1493.50	−	2586.82i	0.0953551	−	0.165160i
$627$	27706.5	+	15996.4i	1.76474	+	1.01887i
$628$	−2737.00	−	4740.62i	−0.173914	−	0.301228i
$629$	2214.00			0.140347
$630$	2646.00			0.167332
$631$	−13480.0			−0.850444			−0.425222	−	0.905089i	$-0.639804\pi$
$631$	−13480.0			−0.850444			−0.425222	+	0.905089i	$0.639804\pi$
$632$	3945.00	+	6832.94i	0.248297	+	0.430063i
$633$		−	8687.97i		−	0.545522i
$634$	3825.00	−	6625.09i	0.239606	−	0.415010i
$635$	4620.00	−	8002.07i	0.288723	−	0.500083i
$636$			10911.9i			0.680324i
$637$	2107.00	+	3649.43i	0.131056	+	0.226995i
$638$	−12220.0			−0.758298
$639$	972.000	−	1683.55i	0.0601748	−	0.104226i
$640$	−20370.0			−1.25812
$641$	−15124.5	−	26196.4i	−0.931953	−	1.61419i	−0.779979	−	0.625805i	$-0.784770\pi$
$641$	−15124.5	−	26196.4i	−0.931953	−	1.61419i	−0.151974	−	0.988385i	$-0.548563\pi$
$642$	6178.50	+	3567.16i	0.379822	+	0.219291i
$643$	−6722.50	+	11643.7i	−0.412301	+	0.714126i	−0.995141	−	0.0984607i	$-0.968608\pi$
$643$	−6722.50	+	11643.7i	−0.412301	+	0.714126i	0.582840	+	0.812587i	$0.301941\pi$
$644$	294.000	−	509.223i	0.0179895	−	0.0311587i
$645$	−10647.0	+	6147.05i	−0.649962	+	0.375255i
$646$	589.500	+	1021.04i	0.0359034	+	0.0621864i
$647$	−8164.00			−0.496074			−0.248037	−	0.968751i	$-0.579785\pi$
$647$	−8164.00			−0.496074			−0.248037	+	0.968751i	$0.579785\pi$
$648$	−5467.50	−	9469.99i	−0.331456	−	0.574099i
$649$	−20163.0			−1.21952
$650$	−3053.00	−	5287.95i	−0.184228	−	0.319093i
$651$	−1701.00	+	982.073i	−0.102408	+	0.0591251i
$652$	−7378.00	+	12779.1i	−0.443167	+	0.767587i
$653$	−6105.00	+	10574.2i	−0.365861	+	0.633690i	−0.988914	−	0.148490i	$-0.952559\pi$
$653$	−6105.00	+	10574.2i	−0.365861	+	0.633690i	0.623053	+	0.782180i	$0.285892\pi$
$654$	2997.00	+	1730.32i	0.179193	+	0.103457i
$655$	−4508.00	−	7808.09i	−0.268919	−	0.465782i
$656$	15703.0			0.934602
$657$	1579.50	−	2735.77i	0.0937932	−	0.162455i
$658$	672.000			0.0398135
$659$	13332.0	+	23091.7i	0.788074	+	1.36498i	0.927145	+	0.374702i	$0.122255\pi$
$659$	13332.0	+	23091.7i	0.788074	+	1.36498i	−0.139071	+	0.990282i	$0.544412\pi$
$660$			23933.5i			1.41153i
$661$	−1142.00	+	1978.00i	−0.0671992	+	0.116392i	−0.897667	−	0.440674i	$-0.854740\pi$
$661$	−1142.00	+	1978.00i	−0.0671992	+	0.116392i	0.830468	+	0.557066i	$0.188073\pi$
$662$	4336.00	−	7510.17i	0.254567	−	0.440923i
$663$		−	4021.82i		−	0.235588i
$664$	−4320.00	−	7482.46i	−0.252483	−	0.437313i
$665$	−12838.0			−0.748626
$666$	−6642.00			−0.386445
$667$	3120.00			0.181120
$668$	−154.000	−	266.736i	−0.00891982	−	0.0154496i
$669$	−7866.00	−	4541.44i	−0.454585	−	0.262455i
$670$	1085.00	−	1879.28i	0.0625630	−	0.108362i
$671$	−8930.00	+	15467.2i	−0.513769	+	0.889874i
$672$	−5071.50	+	2928.03i	−0.291127	+	0.168082i
$673$	−10727.0	−	18579.7i	−0.614406	−	1.06418i	−0.990488	−	0.137597i	$-0.956062\pi$
$673$	−10727.0	−	18579.7i	−0.614406	−	1.06418i	0.376082	−	0.926586i	$-0.377271\pi$
$674$	7001.00			0.400102
$675$	8626.50	−	4980.51i	0.491902	−	0.284000i
$676$	−36393.0			−2.07061
$677$	6777.00	+	11738.1i	0.384729	+	0.666369i	0.991732	−	0.128330i	$-0.0409617\pi$
$677$	6777.00	+	11738.1i	0.384729	+	0.666369i	−0.607003	+	0.794700i	$0.707628\pi$
$678$	3555.00	−	2052.48i	0.201370	−	0.116261i
$679$	−703.500	+	1218.50i	−0.0397612	+	0.0688684i
$680$	−945.000	+	1636.79i	−0.0532928	+	0.0923058i
$681$	−4252.50	−	2455.18i	−0.239290	−	0.138154i
$682$	1269.00	+	2197.97i	0.0712500	+	0.123409i
$683$	31527.0			1.76625			0.883124	−	0.469140i	$-0.155436\pi$
$683$	31527.0			1.76625			0.883124	+	0.469140i	$0.155436\pi$
$684$	12379.5	+	21441.9i	0.692020	+	1.19861i
$685$	8106.00			0.452138
$686$	−171.500	−	297.047i	−0.00954504	−	0.0165325i
$687$			2546.11i			0.141398i
$688$	3464.50	−	6000.69i	0.191981	−	0.332521i
$689$	12900.0	−	22343.5i	0.713281	−	1.23544i
$690$			872.954i			0.0481634i
$691$	7400.00	+	12817.2i	0.407394	+	0.705627i	0.994597	−	0.103813i	$-0.0331042\pi$
$691$	7400.00	+	12817.2i	0.407394	+	0.705627i	−0.587203	+	0.809440i	$0.699771\pi$
$692$	31570.0			1.73426
$693$	4441.50	+	7692.90i	0.243461	+	0.421687i
$694$	3235.00			0.176944
$695$	15225.0	+	26370.5i	0.830960	+	1.43926i
$696$	−17550.0	−	10132.5i	−0.955792	−	0.551827i
$697$	1723.50	−	2985.19i	0.0936617	−	0.162227i
$698$	−895.000	+	1550.19i	−0.0485333	+	0.0840622i
$699$	−1633.50	+	943.102i	−0.0883900	+	0.0510320i
$700$	−1739.50	−	3012.90i	−0.0939242	−	0.162681i
$701$	−22104.0			−1.19095			−0.595475	−	0.803374i	$-0.703036\pi$
$701$	−22104.0			−1.19095			−0.595475	+	0.803374i	$0.703036\pi$
$702$			12065.5i			0.648692i
$703$	32226.0			1.72891
$704$	−3924.50	−	6797.43i	−0.210100	−	0.363903i
$705$	6048.00	−	3491.81i	0.323093	−	0.186538i
$706$	66.5000	−	115.181i	0.00354499	−	0.00614010i
$707$	490.000	−	848.705i	0.0260656	−	0.0451469i
$708$	−13513.5	−	7802.02i	−0.717328	−	0.414150i
$709$	−6870.00	−	11899.2i	−0.363904	−	0.630301i	0.624695	−	0.780869i	$-0.285223\pi$
$709$	−6870.00	−	11899.2i	−0.363904	−	0.630301i	−0.988600	+	0.150568i	$0.951890\pi$
$710$	1008.00			0.0532811
$711$	14202.0			0.749109
$712$	−4170.00			−0.219491
$713$	−324.000	−	561.184i	−0.0170181	−	0.0294762i
$714$			327.358i			0.0171583i
$715$	28294.0	−	49006.6i	1.47991	−	2.56328i
$716$	−6104.00	+	10572.4i	−0.318599	+	0.551830i
$717$			34014.0i			1.77165i
$718$	−4547.00	−	7875.64i	−0.236341	−	0.409354i
$719$	−33402.0			−1.73252			−0.866262	−	0.499590i	$-0.833484\pi$
$719$	−33402.0			−1.73252			−0.866262	+	0.499590i	$0.833484\pi$
$720$	−7749.00	+	13421.7i	−0.401095	+	0.694716i
$721$	9310.00			0.480891
$722$	5151.00	+	8921.79i	0.265513	+	0.459882i
$723$	−16474.5	−	9511.56i	−0.847432	−	0.489265i
$724$	−7840.00	+	13579.3i	−0.402447	+	0.697058i
$725$	9230.00	−	15986.8i	0.472819	−	0.818946i
$726$	3951.00	−	2281.11i	0.201977	−	0.116612i
$727$	13943.0	+	24150.0i	0.711303	+	1.23201i	0.964368	+	0.264564i	$0.0852279\pi$
$727$	13943.0	+	24150.0i	0.711303	+	1.23201i	−0.253065	+	0.967449i	$0.581439\pi$
$728$	9030.00			0.459717
$729$	−19683.0			−1.00000
$730$	1638.00			0.0830481
$731$	−760.500	−	1317.22i	−0.0384789	−	0.0666475i
$732$	−11970.0	+	6910.88i	−0.604404	+	0.348953i
$733$	8169.00	−	14149.1i	0.411636	−	0.712974i	−0.583433	−	0.812161i	$-0.698291\pi$
$733$	8169.00	−	14149.1i	0.411636	−	0.712974i	0.995069	+	0.0991874i	$0.0316243\pi$
$734$	5565.00	−	9638.86i	0.279847	−	0.484710i
$735$	−3087.00	−	1782.28i	−0.154919	−	0.0894427i
$736$	−966.000	−	1673.16i	−0.0483794	−	0.0837956i
$737$	7285.00			0.364106
$738$	−5170.50	+	8955.57i	−0.257898	+	0.446692i
$739$	−23241.0			−1.15688			−0.578440	−	0.815725i	$-0.696338\pi$
$739$	−23241.0			−1.15688			−0.578440	+	0.815725i	$0.696338\pi$
$740$	12054.0	+	20878.1i	0.598803	+	1.03716i
$741$		−	58539.9i		−	2.90218i
$742$	−1050.00	+	1818.65i	−0.0519497	+	0.0899796i
$743$	11295.0	−	19563.5i	0.557703	−	0.965970i	−0.439985	−	0.898005i	$-0.645016\pi$
$743$	11295.0	−	19563.5i	0.557703	−	0.965970i	0.997688	−	0.0679647i	$-0.0216505\pi$
$744$			4208.88i			0.207399i
$745$	−15960.0	−	27643.5i	−0.784871	−	1.35944i
$746$	12850.0			0.630659
$747$	−15552.0			−0.761738
$748$	−2961.00			−0.144739
$749$	−4805.50	−	8323.37i	−0.234431	−	0.406047i
$750$	−3402.00	−	1964.15i	−0.165631	−	0.0956273i
$751$	685.000	−	1186.45i	0.0332836	−	0.0576489i	−0.848904	−	0.528547i	$-0.822737\pi$
$751$	685.000	−	1186.45i	0.0332836	−	0.0576489i	0.882187	+	0.470899i	$0.156070\pi$
$752$	−1968.00	+	3408.68i	−0.0954329	+	0.165295i
$753$	13576.5	−	7838.40i	0.657045	−	0.379345i
$754$	11180.0	+	19364.3i	0.539989	+	0.935288i
$755$	9380.00			0.452150
$756$			6874.51i			0.330719i
$757$	12560.0			0.603040			0.301520	−	0.953460i	$-0.402506\pi$
$757$	12560.0			0.603040			0.301520	+	0.953460i	$0.402506\pi$
$758$	403.500	+	698.883i	0.0193348	+	0.0334889i
$759$	−2538.00	+	1465.31i	−0.121375	+	0.0700758i
$760$	−13755.0	+	23824.4i	−0.656508	+	1.13711i
$761$	4683.00	−	8111.19i	0.223073	−	0.386374i	−0.732667	−	0.680588i	$-0.761724\pi$
$761$	4683.00	−	8111.19i	0.223073	−	0.386374i	0.955740	+	0.294214i	$0.0950578\pi$
$762$	−2970.00	−	1714.73i	−0.141197	−	0.0815198i
$763$	−2331.00	−	4037.41i	−0.110600	−	0.191565i
$764$	−2884.00			−0.136570
$765$	1701.00	+	2946.22i	0.0803919	+	0.139243i
$766$	7980.00			0.376409
$767$	18447.0	+	31951.1i	0.868426	+	1.50416i
$768$			618.342i			0.0290527i
$769$	5909.00	−	10234.7i	0.277092	−	0.479938i	−0.693569	−	0.720391i	$-0.743963\pi$
$769$	5909.00	−	10234.7i	0.277092	−	0.479938i	0.970661	+	0.240453i	$0.0772959\pi$
$770$	−2303.00	+	3988.91i	−0.107785	+	0.186689i
$771$			472.850i			0.0220873i
$772$	−12204.5	−	21138.8i	−0.568976	−	0.985496i
$773$	33164.0			1.54311			0.771556	−	0.636161i	$-0.219479\pi$
$773$	33164.0			1.54311			0.771556	+	0.636161i	$0.219479\pi$
$774$	2281.50	+	3951.67i	0.105952	+	0.183514i
$775$	−3834.00			−0.177705
$776$	1507.50	+	2611.07i	0.0697372	+	0.120788i
$777$	7749.00	+	4473.89i	0.357778	+	0.206563i
$778$	−1308.00	+	2265.52i	−0.0602752	+	0.104400i
$779$	25086.5	−	43451.1i	1.15381	−	1.99846i
$780$	37926.0	−	21896.6i	1.74099	−	1.00516i
$781$	1692.00	+	2930.63i	0.0775218	+	0.134272i
$782$	−108.000			−0.00493871
$783$	−31590.0	+	18238.5i	−1.44181	+	0.832427i
$784$	2009.00			0.0915179
$785$	−5474.00	−	9481.25i	−0.248886	−	0.431083i
$786$	−2898.00	+	1673.16i	−0.131512	+	0.0759283i
$787$	−12650.0	+	21910.4i	−0.572965	+	0.992405i	0.423294	+	0.905992i	$0.360874\pi$
$787$	−12650.0	+	21910.4i	−0.572965	+	0.992405i	−0.996259	+	0.0864129i	$0.972460\pi$
$788$	−5089.00	+	8814.41i	−0.230061	+	0.398477i
$789$	−4275.00	−	2468.17i	−0.192895	−	0.111368i
$790$	3682.00	+	6377.41i	0.165822	+	0.287213i
$791$	−5530.00			−0.248577
$792$	19035.0			0.854014
$793$	32680.0			1.46343
$794$	−2967.00	−	5138.99i	−0.132613	−	0.229693i
$795$			21823.8i			0.973600i
$796$	12537.0	−	21714.7i	0.558244	−	0.966907i
$797$	−8378.00	+	14511.1i	−0.372351	+	0.644931i	−0.989927	−	0.141580i	$-0.954782\pi$
$797$	−8378.00	+	14511.1i	−0.372351	+	0.644931i	0.617575	+	0.786512i	$0.288115\pi$
$798$			4764.87i			0.211372i
$799$	432.000	+	748.246i	0.0191277	+	0.0331302i
$800$	−11431.0			−0.505184
$801$	−3753.00	+	6500.39i	−0.165550	+	0.286741i
$802$	−7905.00			−0.348049
$803$	2749.50	+	4762.27i	0.120832	+	0.209286i
$804$	4882.50	+	2818.91i	0.214170	+	0.123651i
$805$	588.000	−	1018.45i	0.0257444	−	0.0445907i
$806$	2322.00	−	4021.82i	0.101475	−	0.175760i
$807$	23382.0	−	13499.6i	1.01993	−	0.588858i
$808$	−1050.00	−	1818.65i	−0.0457164	−	0.0791832i
$809$	−11355.0			−0.493474			−0.246737	−	0.969082i	$-0.579358\pi$
$809$	−11355.0			−0.493474			−0.246737	+	0.969082i	$0.579358\pi$
$810$	−5103.00	−	8838.66i	−0.221359	−	0.383406i
$811$	−19285.0			−0.835004			−0.417502	−	0.908676i	$-0.637094\pi$
$811$	−19285.0			−0.835004			−0.417502	+	0.908676i	$0.637094\pi$
$812$	6370.00	+	11033.2i	0.275299	+	0.476833i
$813$	−12357.0	+	7134.32i	−0.533061	+	0.307763i
$814$	5781.00	−	10013.0i	0.248924	−	0.431149i
$815$	−14756.0	+	25558.1i	−0.634209	+	1.09848i
$816$	−1660.50	−	958.690i	−0.0712367	−	0.0411285i
$817$	−11069.5	−	19172.9i	−0.474018	−	0.821023i
$818$	10393.0			0.444233
$819$	8127.00	−	14076.4i	0.346740	−	0.600572i
$820$	37534.0			1.59847
$821$	−14395.0	−	24932.9i	−0.611923	−	1.05988i	−0.990916	−	0.134482i	$-0.957063\pi$
$821$	−14395.0	−	24932.9i	−0.611923	−	1.05988i	0.378993	−	0.925400i	$-0.376271\pi$
$822$		−	3008.57i		−	0.127659i
$823$	17091.0	−	29602.5i	0.723882	−	1.25380i	−0.235551	−	0.971862i	$-0.575689\pi$
$823$	17091.0	−	29602.5i	0.723882	−	1.25380i	0.959433	−	0.281938i	$-0.0909773\pi$
$824$	9975.00	−	17277.2i	0.421718	−	0.730437i
$825$			17339.6i			0.731741i
$826$	−1501.50	−	2600.67i	−0.0632492	−	0.109551i
$827$	660.000			0.0277514			0.0138757	−	0.999904i	$-0.495583\pi$
$827$	660.000			0.0277514			0.0138757	+	0.999904i	$0.495583\pi$
$828$	−2268.00			−0.0951914
$829$	−21436.0			−0.898074			−0.449037	−	0.893513i	$-0.648233\pi$
$829$	−21436.0			−0.898074			−0.449037	+	0.893513i	$0.648233\pi$
$830$	−4032.00	−	6983.63i	−0.168618	−	0.292055i
$831$	24453.0	+	14117.9i	1.02078	+	0.589346i
$832$	−7181.00	+	12437.9i	−0.299226	+	0.518275i
$833$	220.500	−	381.917i	0.00917152	−	0.0158855i
$834$	9787.50	−	5650.82i	0.406371	−	0.234618i
$835$	−308.000	−	533.472i	−0.0127650	−	0.0221096i
$836$	−43099.0			−1.78303
$837$	6561.00	+	3788.00i	0.270945	+	0.156430i
$838$	−8580.00			−0.353689
$839$	21034.0	+	36432.0i	0.865524	+	1.49913i	0.866526	+	0.499131i	$0.166348\pi$
$839$	21034.0	+	36432.0i	0.865524	+	1.49913i	−0.00100268	+	0.999999i	$0.500319\pi$
$840$	−6615.00	+	3819.17i	−0.271713	+	0.156874i
$841$	−21605.5	+	37421.8i	−0.885871	+	1.53437i
$842$	2530.00	−	4382.09i	0.103551	−	0.179355i
$843$	−26181.0	−	15115.6i	−1.06966	−	0.617567i
$844$	5852.00	+	10136.0i	0.238666	+	0.413382i
$845$	−72786.0			−2.96321
$846$	−1296.00	−	2244.74i	−0.0526683	−	0.0912242i
$847$	−6146.00			−0.249326
$848$	−6150.00	−	10652.1i	−0.249047	−	0.431362i
$849$			18685.4i			0.755336i
$850$	−319.500	+	553.390i	−0.0128927	+	0.0223307i
$851$	−1476.00	+	2556.51i	−0.0594555	+	0.102980i
$852$			2618.86i			0.105306i
$853$	−4222.00	−	7312.72i	−0.169471	−	0.293532i	0.768763	−	0.639534i	$-0.220872\pi$
$853$	−4222.00	−	7312.72i	−0.169471	−	0.293532i	−0.938234	+	0.346002i	$0.887539\pi$
$854$	−2660.00			−0.106585
$855$	24759.0	+	42883.8i	0.990339	+	1.71532i
$856$	−20595.0			−0.822339
$857$	−14231.0	−	24648.8i	−0.567237	−	0.982482i	−0.996838	−	0.0794638i	$-0.974679\pi$
$857$	−14231.0	−	24648.8i	−0.567237	−	0.982482i	0.429601	−	0.903019i	$-0.358654\pi$
$858$	−18189.0	−	10501.4i	−0.723732	−	0.417847i
$859$	−20996.5	+	36367.0i	−0.833983	+	1.44450i	0.0608729	+	0.998146i	$0.480612\pi$
$859$	−20996.5	+	36367.0i	−0.833983	+	1.44450i	−0.894856	+	0.446355i	$0.852722\pi$
$860$	8281.00	−	14343.1i	0.328349	−	0.568716i
$861$	12064.5	−	6965.44i	0.477534	−	0.275705i
$862$	5568.00	+	9644.06i	0.220008	+	0.381065i
$863$	−35778.0			−1.41124			−0.705618	−	0.708592i	$-0.749331\pi$
$863$	−35778.0			−1.41124			−0.705618	+	0.708592i	$0.749331\pi$
$864$	19561.5	+	11293.8i	0.770250	+	0.444704i
$865$	63140.0			2.48188
$866$	4245.50	+	7353.42i	0.166591	+	0.288544i
$867$	21744.0	−	12553.9i	0.851747	−	0.491757i
$868$	1323.00	−	2291.50i	0.0517345	−	0.0896068i
$869$	−12361.0	+	21409.9i	−0.482530	+	0.835766i
$870$	−16380.0	−	9457.00i	−0.638315	−	0.368531i
$871$	−6665.00	−	11544.1i	−0.259282	−	0.449090i
$872$	−9990.00			−0.387963
$873$	5427.00			0.210396
$874$	−1572.00			−0.0608395
$875$	2646.00	+	4583.01i	0.102230	+	0.177067i
$876$			4255.65i			0.164138i
$877$	−18656.0	+	32313.1i	−0.718322	+	1.24417i	0.243342	+	0.969940i	$0.421756\pi$
$877$	−18656.0	+	32313.1i	−0.718322	+	1.24417i	−0.961664	+	0.274230i	$0.911577\pi$
$878$	−1380.00	+	2390.23i	−0.0530441	+	0.0918751i
$879$		−	29597.3i		−	1.13571i
$880$	−13489.0	−	23363.6i	−0.516721	−	0.894986i
$881$	−27510.0			−1.05203			−0.526013	−	0.850476i	$-0.676314\pi$
$881$	−27510.0			−1.05203			−0.526013	+	0.850476i	$0.676314\pi$
$882$	−661.500	+	1145.75i	−0.0252538	+	0.0437409i
$883$	−26899.0			−1.02517			−0.512584	−	0.858637i	$-0.671312\pi$
$883$	−26899.0			−1.02517			−0.512584	+	0.858637i	$0.671312\pi$
$884$	2709.00	+	4692.13i	0.103070	+	0.178522i
$885$	−27027.0	−	15604.0i	−1.02656	−	0.592683i
$886$	−5068.50	+	8778.90i	−0.192189	+	0.332881i
$887$	20531.0	−	35560.7i	0.777185	−	1.34612i	−0.156372	−	0.987698i	$-0.549980\pi$
$887$	20531.0	−	35560.7i	0.777185	−	1.34612i	0.933558	−	0.358427i	$-0.116687\pi$
$888$	16605.0	−	9586.90i	0.627508	−	0.362292i
$889$	2310.00	+	4001.04i	0.0871484	+	0.150945i
$890$	−3892.00			−0.146584
$891$	17131.5	−	29672.6i	0.644138	−	1.11568i
$892$	12236.0			0.459295
$893$	6288.00	+	10891.1i	0.235633	+	0.408128i
$894$	−10260.0	+	5923.61i	−0.383832	+	0.221605i
$895$	−12208.0	+	21144.9i	−0.455942	+	0.789715i
$896$	5092.50	−	8820.47i	0.189876	−	0.328874i
$897$	4644.00	+	2681.21i	0.172864	+	0.0998028i
$898$	6724.50	+	11647.2i	0.249888	+	0.432819i
$899$	14040.0			0.520868
$900$	−6709.50	+	11621.2i	−0.248500	+	0.430415i
$901$	−2700.00			−0.0998336
$902$	−9000.50	−	15589.3i	−0.332244	−	0.575463i
$903$		−	6147.05i		−	0.226535i
$904$	−5925.00	+	10262.4i	−0.217990	+	0.377569i
$905$	−15680.0	+	27158.6i	−0.575935	+	0.997548i
$906$		−	3481.42i		−	0.127663i
$907$	25881.5	+	44828.1i	0.947498	+	1.64112i	0.750670	+	0.660678i	$0.229731\pi$
$907$	25881.5	+	44828.1i	0.947498	+	1.64112i	0.196829	+	0.980438i	$0.436936\pi$
$908$	6615.00			0.241769
$909$	−3780.00			−0.137926
$910$	8428.00			0.307017
$911$	16776.0	+	29056.9i	0.610114	+	1.05675i	0.991221	+	0.132217i	$0.0422096\pi$
$911$	16776.0	+	29056.9i	0.610114	+	1.05675i	−0.381107	+	0.924531i	$0.624457\pi$
$912$	−24169.5	−	13954.3i	−0.877557	−	0.506658i
$913$	13536.0	−	23445.0i	0.490664	−	0.849855i
$914$	−7679.50	+	13301.3i	−0.277916	+	0.481365i
$915$	−23940.0	+	13821.8i	−0.864953	+	0.499381i
$916$	−1715.00	−	2970.47i	−0.0618616	−	0.107147i
$917$	4508.00			0.162342
$918$	1093.50	−	631.333i	0.0393147	−	0.0226983i
$919$	−8800.00			−0.315871			−0.157935	−	0.987449i	$-0.550484\pi$
$919$	−8800.00			−0.315871			−0.157935	+	0.987449i	$0.550484\pi$
$920$	−1260.00	−	2182.38i	−0.0451532	−	0.0782077i
$921$	23026.5	−	13294.4i	0.823832	−	0.475639i
$922$	7519.00	−	13023.3i	0.268574	−	0.465184i
$923$	3096.00	−	5362.43i	0.110407	−	0.191231i
$924$	−10363.5	−	5983.37i	−0.368976	−	0.213029i
$925$	8733.00	+	15126.0i	0.310421	+	0.537665i
$926$	1688.00			0.0599040
$927$	−17955.0	−	31099.0i	−0.636159	−	1.10186i
$928$	41860.0			1.48073
$929$	16073.0	+	27839.3i	0.567640	+	0.983182i	0.996799	+	0.0799528i	$0.0254770\pi$
$929$	16073.0	+	27839.3i	0.567640	+	0.983182i	−0.429158	+	0.903229i	$0.641190\pi$
$930$			3928.29i			0.138509i
$931$	3209.50	−	5559.02i	0.112983	−	0.195692i
$932$	1270.50	−	2200.57i	0.0446530	−	0.0773413i
$933$			8137.17i			0.285530i
$934$	−5560.50	−	9631.07i	−0.194802	−	0.337407i
$935$	−5922.00			−0.207134
$936$	−17415.0	−	30163.7i	−0.608149	−	1.05334i
$937$	−12558.0			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$937$	−12558.0			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$938$	542.500	+	939.638i	0.0188841	+	0.0327082i
$939$	13441.5	+	7760.45i	0.467142	+	0.269705i
$940$	−4704.00	+	8147.57i	−0.163221	+	0.282707i
$941$	17870.0	−	30951.7i	0.619071	−	1.07226i	−0.370585	−	0.928798i	$-0.620843\pi$
$941$	17870.0	−	30951.7i	0.619071	−	1.07226i	0.989656	−	0.143463i	$-0.0458238\pi$
$942$	−3519.00	+	2031.70i	−0.121715	+	0.0702720i
$943$	2298.00	+	3980.25i	0.0793565	+	0.137449i
$944$	17589.0			0.606433
$945$			13749.0i			0.473286i
$946$	−7943.00			−0.272991
$947$	−3233.50	−	5600.59i	−0.110955	−	0.192180i	0.805200	−	0.593003i	$-0.202058\pi$
$947$	−3233.50	−	5600.59i	−0.110955	−	0.192180i	−0.916156	+	0.400823i	$0.868724\pi$
$948$	−16569.0	+	9566.12i	−0.567654	+	0.327735i
$949$	5031.00	−	8713.95i	0.172090	−	0.298068i
$950$	−4650.50	+	8054.90i	−0.158823	+	0.275090i
$951$	34425.0	+	19875.3i	1.17382	+	0.677708i
$952$	−472.500	−	818.394i	−0.0160859	−	0.0278617i
$953$	26693.0			0.907315			0.453657	−	0.891176i	$-0.350119\pi$
$953$	26693.0			0.907315			0.453657	+	0.891176i	$0.350119\pi$
$954$	8100.00			0.274892
$955$	−5768.00			−0.195443
$956$	−22911.0	−	39683.0i	−0.775099	−	1.34251i
$957$		−	63497.0i		−	2.14479i
$958$	8302.00	−	14379.5i	0.279985	−	0.484948i
$959$	−2026.50	+	3510.00i	−0.0682368	+	0.118190i
$960$		−	12148.6i		−	0.408432i
$961$	13437.5	+	23274.4i	0.451059	+	0.781257i
$962$	−21156.0			−0.709040
$963$	−18535.5	+	32104.4i	−0.620247	+	1.07430i
$964$	25627.0			0.856214
$965$	−24409.0	−	42277.6i	−0.814252	−	1.41033i
$966$	−378.000	−	218.238i	−0.0125900	−	0.00726885i
$967$	14557.0	−	25213.5i	0.484097	−	0.838480i	−0.515736	−	0.856747i	$-0.672482\pi$
$967$	14557.0	−	25213.5i	0.484097	−	0.838480i	0.999833	+	0.0182672i	$0.00581494\pi$
$968$	−6585.00	+	11405.6i	−0.218647	+	0.378707i
$969$	−5305.50	+	3063.13i	−0.175890	+	0.101550i
$970$	1407.00	+	2437.00i	0.0465732	+	0.0806672i
$971$	22500.0			0.743624			0.371812	−	0.928308i	$-0.378737\pi$
$971$	22500.0			0.743624			0.371812	+	0.928308i	$0.378737\pi$
$972$	22963.5	−	13258.0i	0.757772	−	0.437500i
$973$	−15225.0			−0.501635
$974$	−4897.00	−	8481.85i	−0.161099	−	0.279031i
$975$	27477.0	−	15863.9i	0.902532	−	0.521077i
$976$	7790.00	−	13492.7i	0.255483	−	0.442510i
$977$	−10744.5	+	18610.0i	−0.351839	+	0.609404i	−0.986572	−	0.163328i	$-0.947777\pi$
$977$	−10744.5	+	18610.0i	−0.351839	+	0.609404i	0.634732	+	0.772732i	$0.281110\pi$
$978$	9486.00	+	5476.74i	0.310152	+	0.179066i
$979$	−6533.00	−	11315.5i	−0.213274	−	0.369402i
$980$	4802.00			0.156525
$981$	−8991.00	+	15572.9i	−0.292620	+	0.506833i
$982$	967.000			0.0314238
$983$	−2898.00	−	5019.48i	−0.0940304	−	0.162865i	0.815173	−	0.579217i	$-0.196642\pi$
$983$	−2898.00	−	5019.48i	−0.0940304	−	0.162865i	−0.909204	+	0.416352i	$0.863308\pi$
$984$		−	29851.9i		−	0.967118i
$985$	−10178.0	+	17628.8i	−0.329237	+	0.570255i
$986$	1170.00	−	2026.50i	0.0377894	−	0.0654532i
$987$			3491.81i			0.112610i
$988$	39431.0	+	68296.5i	1.26970	+	2.19919i
$989$	2028.00			0.0652039
$990$	17766.0			0.570344
$991$	−25180.0			−0.807133			−0.403567	−	0.914950i	$-0.632230\pi$
$991$	−25180.0			−0.807133			−0.403567	+	0.914950i	$0.632230\pi$
$992$	−4347.00	−	7529.22i	−0.139130	−	0.240981i
$993$	39024.0	+	22530.5i	1.24712	+	0.720025i
$994$	−252.000	+	436.477i	−0.00804120	+	0.0139278i
$995$	25074.0	−	43429.4i	0.798894	−	1.38372i
$996$	18144.0	−	10475.4i	0.577224	−	0.333260i
$997$	11935.0	+	20672.0i	0.379123	+	0.656660i	0.990935	−	0.134343i	$-0.0428925\pi$
$997$	11935.0	+	20672.0i	0.379123	+	0.656660i	−0.611812	+	0.791003i	$0.709559\pi$
$998$	18989.0			0.602291
$999$		−	34512.8i		−	1.09303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.a.22.1	✓	2
3.2	odd	2		189.4.f.a.64.1		2
9.2	odd	6		189.4.f.a.127.1		2
9.4	even	3		567.4.a.a.1.1		1
9.5	odd	6		567.4.a.b.1.1		1
9.7	even	3	inner	63.4.f.a.43.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.a.22.1	✓	2	1.1	even	1	trivial
63.4.f.a.43.1	yes	2	9.7	even	3	inner
189.4.f.a.64.1		2	3.2	odd	2
189.4.f.a.127.1		2	9.2	odd	6
567.4.a.a.1.1		1	9.4	even	3
567.4.a.b.1.1		1	9.5	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-4.50000 + 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +(7.00000 - 12.1244i) q^{5} +(-4.50000 - 2.59808i) q^{6} +(3.50000 + 6.06218i) q^{7} +15.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-4.50000 + 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +(7.00000 - 12.1244i) q^{5} +(-4.50000 - 2.59808i) q^{6} +(3.50000 + 6.06218i) q^{7} +15.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +14.0000 q^{10} +(23.5000 + 40.7032i) q^{11} +36.3731i q^{12} +(43.0000 - 74.4782i) q^{13} +(-3.50000 + 6.06218i) q^{14} +72.7461i q^{15} +(-20.5000 - 35.5070i) q^{16} -9.00000 q^{17} +27.0000 q^{18} -131.000 q^{19} +(-49.0000 - 84.8705i) q^{20} +(-31.5000 - 18.1865i) q^{21} +(-23.5000 + 40.7032i) q^{22} +(6.00000 - 10.3923i) q^{23} +(-67.5000 + 38.9711i) q^{24} +(-35.5000 - 61.4878i) q^{25} +86.0000 q^{26} +140.296i q^{27} +49.0000 q^{28} +(130.000 + 225.167i) q^{29} +(-63.0000 + 36.3731i) q^{30} +(27.0000 - 46.7654i) q^{31} +(80.5000 - 139.430i) q^{32} +(-211.500 - 122.110i) q^{33} +(-4.50000 - 7.79423i) q^{34} +98.0000 q^{35} +(-94.5000 - 163.679i) q^{36} -246.000 q^{37} +(-65.5000 - 113.449i) q^{38} +446.869i q^{39} +(105.000 - 181.865i) q^{40} +(-191.500 + 331.688i) q^{41} -36.3731i q^{42} +(84.5000 + 146.358i) q^{43} +329.000 q^{44} +(-189.000 - 327.358i) q^{45} +12.0000 q^{46} +(-48.0000 - 83.1384i) q^{47} +(184.500 + 106.521i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(35.5000 - 61.4878i) q^{50} +(40.5000 - 23.3827i) q^{51} +(-301.000 - 521.347i) q^{52} +300.000 q^{53} +(-121.500 + 70.1481i) q^{54} +658.000 q^{55} +(52.5000 + 90.9327i) q^{56} +(589.500 - 340.348i) q^{57} +(-130.000 + 225.167i) q^{58} +(-214.500 + 371.525i) q^{59} +(441.000 + 254.611i) q^{60} +(190.000 + 329.090i) q^{61} +54.0000 q^{62} +189.000 q^{63} -167.000 q^{64} +(-602.000 - 1042.69i) q^{65} -244.219i q^{66} +(77.5000 - 134.234i) q^{67} +(-31.5000 + 54.5596i) q^{68} +62.3538i q^{69} +(49.0000 + 84.8705i) q^{70} +72.0000 q^{71} +(202.500 - 350.740i) q^{72} +117.000 q^{73} +(-123.000 - 213.042i) q^{74} +(319.500 + 184.463i) q^{75} +(-458.500 + 794.145i) q^{76} +(-164.500 + 284.922i) q^{77} +(-387.000 + 223.435i) q^{78} +(263.000 + 455.529i) q^{79} -574.000 q^{80} +(-364.500 - 631.333i) q^{81} -383.000 q^{82} +(-288.000 - 498.831i) q^{83} +(-220.500 + 127.306i) q^{84} +(-63.0000 + 109.119i) q^{85} +(-84.5000 + 146.358i) q^{86} +(-1170.00 - 675.500i) q^{87} +(352.500 + 610.548i) q^{88} -278.000 q^{89} +(189.000 - 327.358i) q^{90} +602.000 q^{91} +(-42.0000 - 72.7461i) q^{92} +280.592i q^{93} +(48.0000 - 83.1384i) q^{94} +(-917.000 + 1588.29i) q^{95} +836.581i q^{96} +(100.500 + 174.071i) q^{97} -49.0000 q^{98} +1269.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 9 q^{3} + 7 q^{4} + 14 q^{5} - 9 q^{6} + 7 q^{7} + 30 q^{8} + 27 q^{9}+O(q^{10}) \) 2 * q + q^2 - 9 * q^3 + 7 * q^4 + 14 * q^5 - 9 * q^6 + 7 * q^7 + 30 * q^8 + 27 * q^9	\( 2 q + q^{2} - 9 q^{3} + 7 q^{4} + 14 q^{5} - 9 q^{6} + 7 q^{7} + 30 q^{8} + 27 q^{9} + 28 q^{10} + 47 q^{11} + 86 q^{13} - 7 q^{14} - 41 q^{16} - 18 q^{17} + 54 q^{18} - 262 q^{19} - 98 q^{20} - 63 q^{21} - 47 q^{22} + 12 q^{23} - 135 q^{24} - 71 q^{25} + 172 q^{26} + 98 q^{28} + 260 q^{29} - 126 q^{30} + 54 q^{31} + 161 q^{32} - 423 q^{33} - 9 q^{34} + 196 q^{35} - 189 q^{36} - 492 q^{37} - 131 q^{38} + 210 q^{40} - 383 q^{41} + 169 q^{43} + 658 q^{44} - 378 q^{45} + 24 q^{46} - 96 q^{47} + 369 q^{48} - 49 q^{49} + 71 q^{50} + 81 q^{51} - 602 q^{52} + 600 q^{53} - 243 q^{54} + 1316 q^{55} + 105 q^{56} + 1179 q^{57} - 260 q^{58} - 429 q^{59} + 882 q^{60} + 380 q^{61} + 108 q^{62} + 378 q^{63} - 334 q^{64} - 1204 q^{65} + 155 q^{67} - 63 q^{68} + 98 q^{70} + 144 q^{71} + 405 q^{72} + 234 q^{73} - 246 q^{74} + 639 q^{75} - 917 q^{76} - 329 q^{77} - 774 q^{78} + 526 q^{79} - 1148 q^{80} - 729 q^{81} - 766 q^{82} - 576 q^{83} - 441 q^{84} - 126 q^{85} - 169 q^{86} - 2340 q^{87} + 705 q^{88} - 556 q^{89} + 378 q^{90} + 1204 q^{91} - 84 q^{92} + 96 q^{94} - 1834 q^{95} + 201 q^{97} - 98 q^{98} + 2538 q^{99}+O(q^{100}) \) 2 * q + q^2 - 9 * q^3 + 7 * q^4 + 14 * q^5 - 9 * q^6 + 7 * q^7 + 30 * q^8 + 27 * q^9 + 28 * q^10 + 47 * q^11 + 86 * q^13 - 7 * q^14 - 41 * q^16 - 18 * q^17 + 54 * q^18 - 262 * q^19 - 98 * q^20 - 63 * q^21 - 47 * q^22 + 12 * q^23 - 135 * q^24 - 71 * q^25 + 172 * q^26 + 98 * q^28 + 260 * q^29 - 126 * q^30 + 54 * q^31 + 161 * q^32 - 423 * q^33 - 9 * q^34 + 196 * q^35 - 189 * q^36 - 492 * q^37 - 131 * q^38 + 210 * q^40 - 383 * q^41 + 169 * q^43 + 658 * q^44 - 378 * q^45 + 24 * q^46 - 96 * q^47 + 369 * q^48 - 49 * q^49 + 71 * q^50 + 81 * q^51 - 602 * q^52 + 600 * q^53 - 243 * q^54 + 1316 * q^55 + 105 * q^56 + 1179 * q^57 - 260 * q^58 - 429 * q^59 + 882 * q^60 + 380 * q^61 + 108 * q^62 + 378 * q^63 - 334 * q^64 - 1204 * q^65 + 155 * q^67 - 63 * q^68 + 98 * q^70 + 144 * q^71 + 405 * q^72 + 234 * q^73 - 246 * q^74 + 639 * q^75 - 917 * q^76 - 329 * q^77 - 774 * q^78 + 526 * q^79 - 1148 * q^80 - 729 * q^81 - 766 * q^82 - 576 * q^83 - 441 * q^84 - 126 * q^85 - 169 * q^86 - 2340 * q^87 + 705 * q^88 - 556 * q^89 + 378 * q^90 + 1204 * q^91 - 84 * q^92 + 96 * q^94 - 1834 * q^95 + 201 * q^97 - 98 * q^98 + 2538 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more