Properties

Label 390.2.i.d.211.1
Level $390$
Weight $2$
Character 390.211
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 390.211
Dual form 390.2.i.d.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +5.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.00000 - 6.92820i) q^{17} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} -5.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-0.500000 + 0.866025i) q^{30} -2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +8.00000 q^{34} +(-2.50000 + 4.33013i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-3.00000 + 5.19615i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(-2.00000 + 3.46410i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(0.500000 + 0.866025i) q^{50} -8.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.50000 + 4.33013i) q^{56} -5.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-1.00000 - 1.73205i) q^{62} +(2.50000 + 4.33013i) q^{63} +1.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.00000 + 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} -5.00000 q^{70} +(-1.00000 + 1.73205i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} +15.0000 q^{77} +(-3.50000 + 0.866025i) q^{78} -2.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} +(-4.00000 + 6.92820i) q^{85} -6.00000 q^{86} +(2.00000 - 3.46410i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +1.00000 q^{90} +(-17.5000 + 4.33013i) q^{91} -4.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} -1.00000 q^{96} +(9.00000 - 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} + 5q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} + 5q^{7} - 2q^{8} - q^{9} - q^{10} + 3q^{11} + 2q^{12} - 5q^{13} + 10q^{14} + q^{15} - q^{16} + 8q^{17} - 2q^{18} + 5q^{19} + q^{20} - 10q^{21} - 3q^{22} + 4q^{23} + q^{24} + 2q^{25} + 2q^{26} + 2q^{27} + 5q^{28} + 4q^{29} - q^{30} - 4q^{31} + q^{32} + 3q^{33} + 16q^{34} - 5q^{35} - q^{36} + 7q^{37} + 10q^{38} - 2q^{39} + 2q^{40} - 6q^{41} - 5q^{42} - 6q^{43} - 6q^{44} + q^{45} - 4q^{46} - 6q^{47} - q^{48} - 18q^{49} + q^{50} - 16q^{51} + 7q^{52} + 2q^{53} + q^{54} - 3q^{55} - 5q^{56} - 10q^{57} - 4q^{58} - 12q^{59} - 2q^{60} - 2q^{61} - 2q^{62} + 5q^{63} + 2q^{64} + 5q^{65} + 6q^{66} - 8q^{67} + 8q^{68} + 4q^{69} - 10q^{70} - 2q^{71} + q^{72} - 7q^{74} - q^{75} + 5q^{76} + 30q^{77} - 7q^{78} - 4q^{79} + q^{80} - q^{81} + 6q^{82} + 16q^{83} + 5q^{84} - 8q^{85} - 12q^{86} + 4q^{87} - 3q^{88} + 11q^{89} + 2q^{90} - 35q^{91} - 8q^{92} + 2q^{93} - 3q^{94} - 5q^{95} - 2q^{96} + 18q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 2.50000 4.33013i 0.944911 1.63663i 0.188982 0.981981i \(-0.439481\pi\)
0.755929 0.654654i \(-0.227186\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) 5.00000 1.33631
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.00000 6.92820i 0.970143 1.68034i 0.275029 0.961436i \(-0.411312\pi\)
0.695113 0.718900i \(-0.255354\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) −5.00000 −1.09109
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 1.00000 0.200000
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 1.00000 0.192450
\(28\) 2.50000 + 4.33013i 0.472456 + 0.818317i
\(29\) 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i \(-0.0455477\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 8.00000 1.37199
\(35\) −2.50000 + 4.33013i −0.422577 + 0.731925i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 5.00000 0.811107
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) 1.00000 0.158114
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) −2.50000 4.33013i −0.385758 0.668153i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) −2.00000 + 3.46410i −0.294884 + 0.510754i
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −9.00000 15.5885i −1.28571 2.22692i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −8.00000 −1.12022
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) −2.50000 + 4.33013i −0.334077 + 0.578638i
\(57\) −5.00000 −0.662266
\(58\) −2.00000 + 3.46410i −0.262613 + 0.454859i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) −1.00000 −0.129099
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −1.00000 1.73205i −0.127000 0.219971i
\(63\) 2.50000 + 4.33013i 0.314970 + 0.545545i
\(64\) 1.00000 0.125000
\(65\) 2.50000 + 2.59808i 0.310087 + 0.322252i
\(66\) 3.00000 0.369274
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 4.00000 + 6.92820i 0.485071 + 0.840168i
\(69\) 2.00000 3.46410i 0.240772 0.417029i
\(70\) −5.00000 −0.597614
\(71\) −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i \(-0.871199\pi\)
0.800566 + 0.599245i \(0.204532\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 15.0000 1.70941
\(78\) −3.50000 + 0.866025i −0.396297 + 0.0980581i
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 2.50000 4.33013i 0.272772 0.472456i
\(85\) −4.00000 + 6.92820i −0.433861 + 0.751469i
\(86\) −6.00000 −0.646997
\(87\) 2.00000 3.46410i 0.214423 0.371391i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 1.00000 0.105409
\(91\) −17.5000 + 4.33013i −1.83450 + 0.453921i
\(92\) −4.00000 −0.417029
\(93\) 1.00000 + 1.73205i 0.103695 + 0.179605i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −2.50000 + 4.33013i −0.256495 + 0.444262i
\(96\) −1.00000 −0.102062
\(97\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(98\) 9.00000 15.5885i 0.909137 1.57467i
\(99\) −3.00000 −0.301511
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i \(-0.0363659\pi\)
−0.595466 + 0.803380i \(0.703033\pi\)
\(102\) −4.00000 6.92820i −0.396059 0.685994i
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 5.00000 0.487950
\(106\) 0.500000 + 0.866025i 0.0485643 + 0.0841158i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) −5.00000 −0.472456
\(113\) −4.00000 + 6.92820i −0.376288 + 0.651751i −0.990519 0.137376i \(-0.956133\pi\)
0.614231 + 0.789127i \(0.289466\pi\)
\(114\) −2.50000 4.33013i −0.234146 0.405554i
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) −4.00000 −0.371391
\(117\) 3.50000 0.866025i 0.323575 0.0800641i
\(118\) −12.0000 −1.10469
\(119\) −20.0000 34.6410i −1.83340 3.17554i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −2.00000 −0.181071
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −1.00000 −0.0894427
\(126\) −2.50000 + 4.33013i −0.222718 + 0.385758i
\(127\) 10.5000 + 18.1865i 0.931724 + 1.61379i 0.780373 + 0.625314i \(0.215029\pi\)
0.151351 + 0.988480i \(0.451638\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 6.00000 0.528271
\(130\) −1.00000 + 3.46410i −0.0877058 + 0.303822i
\(131\) −19.0000 −1.66004 −0.830019 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(132\) 1.50000 + 2.59808i 0.130558 + 0.226134i
\(133\) −12.5000 21.6506i −1.08389 1.87735i
\(134\) 4.00000 6.92820i 0.345547 0.598506i
\(135\) −1.00000 −0.0860663
\(136\) −4.00000 + 6.92820i −0.342997 + 0.594089i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 4.00000 0.340503
\(139\) −3.50000 + 6.06218i −0.296866 + 0.514187i −0.975417 0.220366i \(-0.929275\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) −2.50000 4.33013i −0.211289 0.365963i
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) −2.00000 −0.167836
\(143\) 3.00000 10.3923i 0.250873 0.869048i
\(144\) 1.00000 0.0833333
\(145\) −2.00000 3.46410i −0.166091 0.287678i
\(146\) 0 0
\(147\) −9.00000 + 15.5885i −0.742307 + 1.28571i
\(148\) −7.00000 −0.575396
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 22.0000 1.79033 0.895167 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) 4.00000 + 6.92820i 0.323381 + 0.560112i
\(154\) 7.50000 + 12.9904i 0.604367 + 1.04679i
\(155\) 2.00000 0.160644
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) 15.0000 1.19713 0.598565 0.801074i \(-0.295738\pi\)
0.598565 + 0.801074i \(0.295738\pi\)
\(158\) −1.00000 1.73205i −0.0795557 0.137795i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 20.0000 1.57622
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i \(-0.546888\pi\)
0.930033 0.367477i \(-0.119778\pi\)
\(164\) 6.00000 0.468521
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 4.00000 + 6.92820i 0.310460 + 0.537733i
\(167\) 11.5000 + 19.9186i 0.889897 + 1.54135i 0.839996 + 0.542592i \(0.182557\pi\)
0.0499004 + 0.998754i \(0.484110\pi\)
\(168\) 5.00000 0.385758
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) −8.00000 −0.613572
\(171\) 2.50000 + 4.33013i 0.191180 + 0.331133i
\(172\) −3.00000 5.19615i −0.228748 0.396203i
\(173\) −2.50000 + 4.33013i −0.190071 + 0.329213i −0.945274 0.326278i \(-0.894205\pi\)
0.755202 + 0.655492i \(0.227539\pi\)
\(174\) 4.00000 0.303239
\(175\) 2.50000 4.33013i 0.188982 0.327327i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) 12.0000 0.901975
\(178\) −5.50000 + 9.52628i −0.412242 + 0.714025i
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −12.5000 12.9904i −0.926562 0.962911i
\(183\) 2.00000 0.147844
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) −1.00000 + 1.73205i −0.0733236 + 0.127000i
\(187\) 24.0000 1.75505
\(188\) 1.50000 2.59808i 0.109399 0.189484i
\(189\) 2.50000 4.33013i 0.181848 0.314970i
\(190\) −5.00000 −0.362738
\(191\) −1.00000 + 1.73205i −0.0723575 + 0.125327i −0.899934 0.436026i \(-0.856386\pi\)
0.827577 + 0.561353i \(0.189719\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −12.0000 20.7846i −0.863779 1.49611i −0.868255 0.496119i \(-0.834758\pi\)
0.00447566 0.999990i \(-0.498575\pi\)
\(194\) 0 0
\(195\) 1.00000 3.46410i 0.0716115 0.248069i
\(196\) 18.0000 1.28571
\(197\) −1.50000 2.59808i −0.106871 0.185105i 0.807630 0.589689i \(-0.200750\pi\)
−0.914501 + 0.404584i \(0.867416\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) −11.0000 + 19.0526i −0.779769 + 1.35060i 0.152305 + 0.988334i \(0.451330\pi\)
−0.932075 + 0.362267i \(0.882003\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) −4.00000 + 6.92820i −0.281439 + 0.487467i
\(203\) 20.0000 1.40372
\(204\) 4.00000 6.92820i 0.280056 0.485071i
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) −3.50000 6.06218i −0.243857 0.422372i
\(207\) −4.00000 −0.278019
\(208\) −1.00000 + 3.46410i −0.0693375 + 0.240192i
\(209\) 15.0000 1.03757
\(210\) 2.50000 + 4.33013i 0.172516 + 0.298807i
\(211\) 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i \(0.00603229\pi\)
−0.483499 + 0.875345i \(0.660634\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 2.00000 0.137038
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) −1.00000 −0.0680414
\(217\) −5.00000 + 8.66025i −0.339422 + 0.587896i
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 0 0
\(220\) 3.00000 0.202260
\(221\) −28.0000 + 6.92820i −1.88348 + 0.466041i
\(222\) 7.00000 0.469809
\(223\) 1.50000 + 2.59808i 0.100447 + 0.173980i 0.911869 0.410481i \(-0.134639\pi\)
−0.811422 + 0.584461i \(0.801306\pi\)
\(224\) −2.50000 4.33013i −0.167038 0.289319i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −8.00000 −0.532152
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 2.50000 4.33013i 0.165567 0.286770i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 2.00000 3.46410i 0.131876 0.228416i
\(231\) −7.50000 12.9904i −0.493464 0.854704i
\(232\) −2.00000 3.46410i −0.131306 0.227429i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 2.50000 + 2.59808i 0.163430 + 0.169842i
\(235\) 3.00000 0.195698
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 1.00000 + 1.73205i 0.0649570 + 0.112509i
\(238\) 20.0000 34.6410i 1.29641 2.24544i
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) 2.00000 0.128565
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) −6.00000 −0.382546
\(247\) −17.5000 + 4.33013i −1.11350 + 0.275519i
\(248\) 2.00000 0.127000
\(249\) −4.00000 6.92820i −0.253490 0.439057i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i \(-0.990305\pi\)
0.526140 + 0.850398i \(0.323639\pi\)
\(252\) −5.00000 −0.314970
\(253\) −6.00000 + 10.3923i −0.377217 + 0.653359i
\(254\) −10.5000 + 18.1865i −0.658829 + 1.14112i
\(255\) 8.00000 0.500979
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.0000 24.2487i −0.873296 1.51259i −0.858567 0.512702i \(-0.828645\pi\)
−0.0147291 0.999892i \(-0.504689\pi\)
\(258\) 3.00000 + 5.19615i 0.186772 + 0.323498i
\(259\) 35.0000 2.17479
\(260\) −3.50000 + 0.866025i −0.217061 + 0.0537086i
\(261\) −4.00000 −0.247594
\(262\) −9.50000 16.4545i −0.586912 1.01656i
\(263\) 7.50000 + 12.9904i 0.462470 + 0.801021i 0.999083 0.0428069i \(-0.0136300\pi\)
−0.536614 + 0.843828i \(0.680297\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) −1.00000 −0.0614295
\(266\) 12.5000 21.6506i 0.766424 1.32749i
\(267\) 5.50000 9.52628i 0.336595 0.582999i
\(268\) 8.00000 0.488678
\(269\) −2.00000 + 3.46410i −0.121942 + 0.211210i −0.920534 0.390664i \(-0.872246\pi\)
0.798591 + 0.601874i \(0.205579\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i \(-0.205434\pi\)
−0.920356 + 0.391082i \(0.872101\pi\)
\(272\) −8.00000 −0.485071
\(273\) 12.5000 + 12.9904i 0.756534 + 0.786214i
\(274\) 12.0000 0.724947
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) 7.50000 12.9904i 0.450631 0.780516i −0.547794 0.836613i \(-0.684532\pi\)
0.998425 + 0.0560969i \(0.0178656\pi\)
\(278\) −7.00000 −0.419832
\(279\) 1.00000 1.73205i 0.0598684 0.103695i
\(280\) 2.50000 4.33013i 0.149404 0.258775i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 5.00000 0.296174
\(286\) 10.5000 2.59808i 0.620878 0.153627i
\(287\) −30.0000 −1.77084
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −23.5000 40.7032i −1.38235 2.39431i
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) 0 0
\(293\) 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) −18.0000 −1.04978
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) 2.00000 0.115857
\(299\) 4.00000 13.8564i 0.231326 0.801337i
\(300\) 1.00000 0.0577350
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) 11.0000 + 19.0526i 0.632979 + 1.09635i
\(303\) 4.00000 6.92820i 0.229794 0.398015i
\(304\) −5.00000 −0.286770
\(305\) 1.00000 1.73205i 0.0572598 0.0991769i
\(306\) −4.00000 + 6.92820i −0.228665 + 0.396059i
\(307\) −6.00000 −0.342438 −0.171219 0.985233i \(-0.554771\pi\)
−0.171219 + 0.985233i \(0.554771\pi\)
\(308\) −7.50000 + 12.9904i −0.427352 + 0.740196i
\(309\) 3.50000 + 6.06218i 0.199108 + 0.344865i
\(310\) 1.00000 + 1.73205i 0.0567962 + 0.0983739i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 1.00000 3.46410i 0.0566139 0.196116i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 7.50000 + 12.9904i 0.423249 + 0.733090i
\(315\) −2.50000 4.33013i −0.140859 0.243975i
\(316\) 1.00000 1.73205i 0.0562544 0.0974355i
\(317\) −23.0000 −1.29181 −0.645904 0.763418i \(-0.723520\pi\)
−0.645904 + 0.763418i \(0.723520\pi\)
\(318\) 0.500000 0.866025i 0.0280386 0.0485643i
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) −1.00000 −0.0559017
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) 10.0000 + 17.3205i 0.557278 + 0.965234i
\(323\) −20.0000 34.6410i −1.11283 1.92748i
\(324\) 1.00000 0.0555556
\(325\) −2.50000 2.59808i −0.138675 0.144115i
\(326\) 20.0000 1.10770
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) −7.50000 + 12.9904i −0.413488 + 0.716183i
\(330\) −3.00000 −0.165145
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) −4.00000 + 6.92820i −0.219529 + 0.380235i
\(333\) −7.00000 −0.383598
\(334\) −11.5000 + 19.9186i −0.629252 + 1.08990i
\(335\) 4.00000 + 6.92820i 0.218543 + 0.378528i
\(336\) 2.50000 + 4.33013i 0.136386 + 0.236228i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −11.5000 + 6.06218i −0.625518 + 0.329739i
\(339\) 8.00000 0.434500
\(340\) −4.00000 6.92820i −0.216930 0.375735i
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) −2.50000 + 4.33013i −0.135185 + 0.234146i
\(343\) −55.0000 −2.96972
\(344\) 3.00000 5.19615i 0.161749 0.280158i
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) −5.00000 −0.268802
\(347\) 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i \(-0.692036\pi\)
0.996826 + 0.0796169i \(0.0253697\pi\)
\(348\) 2.00000 + 3.46410i 0.107211 + 0.185695i
\(349\) −4.00000 6.92820i −0.214115 0.370858i 0.738883 0.673833i \(-0.235353\pi\)
−0.952998 + 0.302975i \(0.902020\pi\)
\(350\) 5.00000 0.267261
\(351\) −2.50000 2.59808i −0.133440 0.138675i
\(352\) 3.00000 0.159901
\(353\) −8.00000 13.8564i −0.425797 0.737502i 0.570697 0.821160i \(-0.306673\pi\)
−0.996495 + 0.0836583i \(0.973340\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) −11.0000 −0.582999
\(357\) −20.0000 + 34.6410i −1.05851 + 1.83340i
\(358\) 2.00000 3.46410i 0.105703 0.183083i
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) −2.00000 −0.104973
\(364\) 5.00000 17.3205i 0.262071 0.907841i
\(365\) 0 0
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) 2.00000 3.46410i 0.104257 0.180579i
\(369\) 6.00000 0.312348
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) 2.50000 4.33013i 0.129794 0.224809i
\(372\) −2.00000 −0.103695
\(373\) −19.0000 + 32.9090i −0.983783 + 1.70396i −0.336557 + 0.941663i \(0.609263\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 12.0000 + 20.7846i 0.620505 + 1.07475i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 3.00000 0.154713
\(377\) 4.00000 13.8564i 0.206010 0.713641i
\(378\) 5.00000 0.257172
\(379\) 12.5000 + 21.6506i 0.642082 + 1.11212i 0.984967 + 0.172741i \(0.0552624\pi\)
−0.342885 + 0.939377i \(0.611404\pi\)
\(380\) −2.50000 4.33013i −0.128247 0.222131i
\(381\) 10.5000 18.1865i 0.537931 0.931724i
\(382\) −2.00000 −0.102329
\(383\) 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i \(-0.579593\pi\)
0.962818 0.270151i \(-0.0870736\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −15.0000 −0.764471
\(386\) 12.0000 20.7846i 0.610784 1.05791i
\(387\) −3.00000 5.19615i −0.152499 0.264135i
\(388\) 0 0
\(389\) −32.0000 −1.62246 −0.811232 0.584724i \(-0.801203\pi\)
−0.811232 + 0.584724i \(0.801203\pi\)
\(390\) 3.50000 0.866025i 0.177229 0.0438529i
\(391\) 32.0000 1.61831
\(392\) 9.00000 + 15.5885i 0.454569 + 0.787336i
\(393\) 9.50000 + 16.4545i 0.479212 + 0.830019i
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 2.00000 0.100631
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) −12.5000 + 21.6506i −0.627357 + 1.08661i 0.360723 + 0.932673i \(0.382530\pi\)
−0.988080 + 0.153941i \(0.950803\pi\)
\(398\) −22.0000 −1.10276
\(399\) −12.5000 + 21.6506i −0.625783 + 1.08389i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 9.50000 + 16.4545i 0.474407 + 0.821698i 0.999571 0.0293039i \(-0.00932905\pi\)
−0.525163 + 0.851002i \(0.675996\pi\)
\(402\) −8.00000 −0.399004
\(403\) 5.00000 + 5.19615i 0.249068 + 0.258839i
\(404\) −8.00000 −0.398015
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 10.0000 + 17.3205i 0.496292 + 0.859602i
\(407\) −10.5000 + 18.1865i −0.520466 + 0.901473i
\(408\) 8.00000 0.396059
\(409\) −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) −3.00000 + 5.19615i −0.148159 + 0.256620i
\(411\) −12.0000 −0.591916
\(412\) 3.50000 6.06218i 0.172433 0.298662i
\(413\) 30.0000 + 51.9615i 1.47620 + 2.55686i
\(414\) −2.00000 3.46410i −0.0982946 0.170251i
\(415\) −8.00000 −0.392705
\(416\) −3.50000 + 0.866025i −0.171602 + 0.0424604i
\(417\) 7.00000 0.342791
\(418\) 7.50000 + 12.9904i 0.366837 + 0.635380i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) −2.50000 + 4.33013i −0.121988 + 0.211289i
\(421\) 12.0000 0.584844 0.292422 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) −7.50000 + 12.9904i −0.365094 + 0.632362i
\(423\) 1.50000 2.59808i 0.0729325 0.126323i
\(424\) −1.00000 −0.0485643
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 1.00000 + 1.73205i 0.0484502 + 0.0839181i
\(427\) 5.00000 + 8.66025i 0.241967 + 0.419099i
\(428\) −6.00000 −0.290021
\(429\) −10.5000 + 2.59808i −0.506945 + 0.125436i
\(430\) 6.00000 0.289346
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −8.00000 + 13.8564i −0.384455 + 0.665896i −0.991693 0.128624i \(-0.958944\pi\)
0.607238 + 0.794520i \(0.292277\pi\)
\(434\) −10.0000 −0.480015
\(435\) −2.00000 + 3.46410i −0.0958927 + 0.166091i
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 20.0000 0.956730
\(438\) 0 0
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) 18.0000 0.857143
\(442\) −20.0000 20.7846i −0.951303 0.988623i
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) −5.50000 9.52628i −0.260725 0.451589i
\(446\) −1.50000 + 2.59808i −0.0710271 + 0.123022i
\(447\) −2.00000 −0.0945968
\(448\) 2.50000 4.33013i 0.118114 0.204579i
\(449\) 13.5000 23.3827i 0.637104 1.10350i −0.348961 0.937137i \(-0.613465\pi\)
0.986065 0.166360i \(-0.0532013\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −4.00000 6.92820i −0.188144 0.325875i
\(453\) −11.0000 19.0526i −0.516825 0.895167i
\(454\) 0 0
\(455\) 17.5000 4.33013i 0.820413 0.202999i
\(456\) 5.00000 0.234146
\(457\) −15.0000 25.9808i −0.701670 1.21533i −0.967880 0.251414i \(-0.919105\pi\)
0.266209 0.963915i \(-0.414229\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 4.00000 0.186501
\(461\) −4.00000 + 6.92820i −0.186299 + 0.322679i −0.944013 0.329907i \(-0.892983\pi\)
0.757715 + 0.652586i \(0.226316\pi\)
\(462\) 7.50000 12.9904i 0.348932 0.604367i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 2.00000 3.46410i 0.0928477 0.160817i
\(465\) −1.00000 1.73205i −0.0463739 0.0803219i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) −1.00000 + 3.46410i −0.0462250 + 0.160128i
\(469\) −40.0000 −1.84703
\(470\) 1.50000 + 2.59808i 0.0691898 + 0.119840i
\(471\) −7.50000 12.9904i −0.345582 0.598565i
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) −18.0000 −0.827641
\(474\) −1.00000 + 1.73205i −0.0459315 + 0.0795557i
\(475\) 2.50000 4.33013i 0.114708 0.198680i
\(476\) 40.0000 1.83340
\(477\) −0.500000 + 0.866025i −0.0228934 + 0.0396526i
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 1.00000 0.0456435
\(481\) 7.00000 24.2487i 0.319173 1.10565i
\(482\) 25.0000 1.13872
\(483\) −10.0000 17.3205i −0.455016 0.788110i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −18.5000 + 32.0429i −0.838315 + 1.45200i 0.0529875 + 0.998595i \(0.483126\pi\)
−0.891303 + 0.453409i \(0.850208\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) −20.0000 −0.904431
\(490\) −9.00000 + 15.5885i −0.406579 + 0.704215i
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) 32.0000 1.44121
\(494\) −12.5000 12.9904i −0.562402 0.584465i
\(495\) 3.00000 0.134840
\(496\) 1.00000 + 1.73205i 0.0449013 + 0.0777714i
\(497\) 5.00000 + 8.66025i 0.224281 + 0.388465i
\(498\) 4.00000 6.92820i 0.179244 0.310460i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 11.5000 19.9186i 0.513782 0.889897i
\(502\) −15.0000 −0.669483
\(503\) 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i \(-0.754469\pi\)
0.962197 + 0.272354i \(0.0878022\pi\)
\(504\) −2.50000 4.33013i −0.111359 0.192879i
\(505\) −4.00000 6.92820i −0.177998 0.308301i
\(506\) −12.0000 −0.533465
\(507\) 11.5000 6.06218i 0.510733 0.269231i
\(508\) −21.0000 −0.931724
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 4.00000 + 6.92820i 0.177123 + 0.306786i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.50000 4.33013i 0.110378 0.191180i
\(514\) 14.0000 24.2487i 0.617514 1.06956i
\(515\) 7.00000 0.308457
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) 17.5000 + 30.3109i 0.768906 + 1.33178i
\(519\) 5.00000 0.219476
\(520\) −2.50000 2.59808i −0.109632 0.113933i
\(521\) 5.00000 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(522\) −2.00000 3.46410i −0.0875376 0.151620i
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) 9.50000 16.4545i 0.415009 0.718817i
\(525\) −5.00000 −0.218218
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) −8.00000 + 13.8564i −0.348485 + 0.603595i
\(528\) −3.00000 −0.130558
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −0.500000 0.866025i −0.0217186 0.0376177i
\(531\) −6.00000 10.3923i −0.260378 0.450988i
\(532\) 25.0000 1.08389
\(533\) −6.00000 + 20.7846i −0.259889 + 0.900281i
\(534\) 11.0000 0.476017
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) −2.00000 + 3.46410i −0.0863064 + 0.149487i
\(538\) −4.00000 −0.172452
\(539\) 27.0000 46.7654i 1.16297 2.01433i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 2.00000 3.46410i 0.0859074 0.148796i
\(543\) 1.00000 + 1.73205i 0.0429141 + 0.0743294i
\(544\) −4.00000 6.92820i −0.171499 0.297044i
\(545\) −14.0000 −0.599694
\(546\) −5.00000 + 17.3205i −0.213980 + 0.741249i
\(547\) 6.00000 0.256541 0.128271 0.991739i \(-0.459057\pi\)
0.128271 + 0.991739i \(0.459057\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) 20.0000 0.852029
\(552\) −2.00000 + 3.46410i −0.0851257 + 0.147442i
\(553\) −5.00000 + 8.66025i −0.212622 + 0.368271i
\(554\) 15.0000 0.637289
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) −3.50000 6.06218i −0.148433 0.257094i
\(557\) −7.50000 12.9904i −0.317785 0.550420i 0.662240 0.749291i \(-0.269606\pi\)
−0.980026 + 0.198871i \(0.936272\pi\)
\(558\) 2.00000 0.0846668
\(559\) 21.0000 5.19615i 0.888205 0.219774i
\(560\) 5.00000 0.211289
\(561\) −12.0000 20.7846i −0.506640 0.877527i
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −18.0000 + 31.1769i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331202i \(0.892546\pi\)
\(564\) −3.00000 −0.126323
\(565\) 4.00000 6.92820i 0.168281 0.291472i
\(566\) −5.00000 + 8.66025i −0.210166 + 0.364018i
\(567\) −5.00000 −0.209980
\(568\) 1.00000 1.73205i 0.0419591 0.0726752i
\(569\) 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i \(-0.0648579\pi\)
−0.664897 + 0.746935i \(0.731525\pi\)
\(570\) 2.50000 + 4.33013i 0.104713 + 0.181369i
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) 7.50000 + 7.79423i 0.313591 + 0.325893i
\(573\) 2.00000 0.0835512
\(574\) −15.0000 25.9808i −0.626088 1.08442i
\(575\) 2.00000 + 3.46410i 0.0834058 + 0.144463i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 23.5000 40.7032i 0.977471 1.69303i
\(579\) −12.0000 + 20.7846i −0.498703 + 0.863779i
\(580\) 4.00000 0.166091
\(581\) 20.0000 34.6410i 0.829740 1.43715i
\(582\) 0 0
\(583\) 1.50000 + 2.59808i 0.0621237 + 0.107601i
\(584\) 0 0
\(585\) −3.50000 + 0.866025i −0.144707 + 0.0358057i
\(586\) 9.00000 0.371787
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) −9.00000 15.5885i −0.371154 0.642857i
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 12.0000 0.494032
\(591\) −1.50000 + 2.59808i −0.0617018 + 0.106871i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 20.0000 0.821302 0.410651 0.911793i \(-0.365302\pi\)
0.410651 + 0.911793i \(0.365302\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 20.0000 + 34.6410i 0.819920 + 1.42014i
\(596\) 1.00000 + 1.73205i 0.0409616 + 0.0709476i
\(597\) 22.0000 0.900400
\(598\) 14.0000 3.46410i 0.572503 0.141658i
\(599\) 34.0000 1.38920 0.694601 0.719395i \(-0.255581\pi\)
0.694601 + 0.719395i \(0.255581\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i \(-0.894483\pi\)
0.190927 0.981604i \(-0.438851\pi\)
\(602\) −15.0000 + 25.9808i −0.611354 + 1.05890i
\(603\) 8.00000 0.325785
\(604\) −11.0000 + 19.0526i −0.447584 + 0.775238i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 8.00000 0.324978
\(607\) 14.5000 25.1147i 0.588537 1.01938i −0.405887 0.913923i \(-0.633038\pi\)
0.994424 0.105453i \(-0.0336291\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) −10.0000 17.3205i −0.405220 0.701862i
\(610\) 2.00000 0.0809776
\(611\) 7.50000 + 7.79423i 0.303418 + 0.315321i
\(612\) −8.00000 −0.323381
\(613\) −12.5000 21.6506i −0.504870 0.874461i −0.999984 0.00563283i \(-0.998207\pi\)
0.495114 0.868828i \(-0.335126\pi\)
\(614\) −3.00000 5.19615i −0.121070 0.209700i
\(615\) 3.00000 5.19615i 0.120972 0.209529i
\(616\) −15.0000 −0.604367
\(617\) 7.00000 12.1244i 0.281809 0.488108i −0.690021 0.723789i \(-0.742399\pi\)
0.971830 + 0.235681i \(0.0757321\pi\)
\(618\) −3.50000 + 6.06218i −0.140791 + 0.243857i
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) −1.00000 + 1.73205i −0.0401610 + 0.0695608i
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) −6.00000 10.3923i −0.240578 0.416693i
\(623\) 55.0000 2.20353
\(624\) 3.50000 0.866025i 0.140112 0.0346688i
\(625\) 1.00000 0.0400000
\(626\) −3.00000 5.19615i −0.119904 0.207680i
\(627\) −7.50000 12.9904i −0.299521 0.518786i
\(628\) −7.50000 + 12.9904i −0.299283 + 0.518373i
\(629\) 56.0000 2.23287
\(630\) 2.50000 4.33013i 0.0996024 0.172516i
\(631\) −6.00000 + 10.3923i −0.238856 + 0.413711i −0.960386 0.278672i \(-0.910106\pi\)
0.721530 + 0.692383i \(0.243439\pi\)
\(632\) 2.00000 0.0795557
\(633\) 7.50000 12.9904i 0.298098 0.516321i
\(634\) −11.5000 19.9186i −0.456723 0.791068i
\(635\) −10.5000 18.1865i −0.416680 0.721711i
\(636\) 1.00000 0.0396526
\(637\) −18.0000 + 62.3538i −0.713186 + 2.47055i
\(638\) −12.0000 −0.475085
\(639\) −1.00000 1.73205i −0.0395594 0.0685189i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 6.00000 0.236801
\(643\) 22.0000 38.1051i 0.867595 1.50272i 0.00314839 0.999995i \(-0.498998\pi\)
0.864447 0.502724i \(-0.167669\pi\)
\(644\) −10.0000 + 17.3205i −0.394055 + 0.682524i
\(645\) −6.00000 −0.236250
\(646\) 20.0000 34.6410i 0.786889 1.36293i
\(647\) −1.50000 2.59808i −0.0589711 0.102141i 0.835033 0.550200i \(-0.185449\pi\)
−0.894004 + 0.448059i \(0.852115\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −36.0000 −1.41312
\(650\) 1.00000 3.46410i 0.0392232 0.135873i
\(651\) 10.0000 0.391931
\(652\) 10.0000 + 17.3205i 0.391630 + 0.678323i
\(653\) −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) 19.0000 0.742391
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) −15.0000 −0.584761
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) −4.00000 −0.155464
\(663\) 20.0000 + 20.7846i 0.776736 + 0.807207i
\(664\) −8.00000 −0.310460
\(665\) 12.5000 + 21.6506i 0.484729 + 0.839576i
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) −8.00000 + 13.8564i −0.309761 + 0.536522i
\(668\) −23.0000 −0.889897
\(669\) 1.50000 2.59808i 0.0579934 0.100447i
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) −6.00000 −0.231627
\(672\) −2.50000 + 4.33013i −0.0964396 + 0.167038i
\(673\) 16.0000 + 27.7128i 0.616755 + 1.06825i 0.990074 + 0.140548i \(0.0448863\pi\)
−0.373319 + 0.927703i \(0.621780\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) 1.00000 0.0384900
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 4.00000 + 6.92820i 0.153619 + 0.266076i
\(679\) 0 0
\(680\) 4.00000 6.92820i 0.153393 0.265684i
\(681\) 0 0
\(682\) 3.00000 5.19615i 0.114876 0.198971i
\(683\) −15.0000 + 25.9808i −0.573959 + 0.994126i 0.422195 + 0.906505i \(0.361260\pi\)
−0.996154 + 0.0876211i \(0.972074\pi\)
\(684\) −5.00000 −0.191180
\(685\) −6.00000 + 10.3923i −0.229248 + 0.397070i
\(686\) −27.5000 47.6314i −1.04995 1.81858i
\(687\) −7.00000 12.1244i −0.267067 0.462573i
\(688\) 6.00000 0.228748
\(689\) −2.50000 2.59808i −0.0952424 0.0989788i
\(690\) −4.00000 −0.152277
\(691\) −8.50000 14.7224i −0.323355 0.560068i 0.657823 0.753173i \(-0.271478\pi\)
−0.981178 + 0.193105i \(0.938144\pi\)
\(692\) −2.50000 4.33013i −0.0950357 0.164607i
\(693\) −7.50000 + 12.9904i −0.284901 + 0.493464i
\(694\) 16.0000 0.607352
\(695\) 3.50000 6.06218i 0.132763 0.229952i
\(696\) −2.00000 + 3.46410i −0.0758098 + 0.131306i
\(697\) −48.0000 −1.81813
\(698\) 4.00000 6.92820i 0.151402 0.262236i
\(699\) 7.00000 + 12.1244i 0.264764 + 0.458585i
\(700\) 2.50000 + 4.33013i 0.0944911 + 0.163663i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) 35.0000 1.32005
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) −1.50000 2.59808i −0.0564933 0.0978492i
\(706\) 8.00000 13.8564i 0.301084 0.521493i
\(707\) 40.0000 1.50435
\(708\) −6.00000 + 10.3923i −0.225494 + 0.390567i
\(709\) −16.0000 + 27.7128i −0.600893 + 1.04078i 0.391794 + 0.920053i \(0.371855\pi\)
−0.992686 + 0.120723i \(0.961479\pi\)
\(710\) 2.00000 0.0750587
\(711\) 1.00000 1.73205i 0.0375029 0.0649570i
\(712\) −5.50000 9.52628i −0.206121 0.357012i
\(713\) −4.00000 6.92820i −0.149801 0.259463i
\(714\) −40.0000 −1.49696
\(715\) −3.00000 + 10.3923i −0.112194 + 0.388650i
\(716\) 4.00000 0.149487
\(717\) 9.00000 + 15.5885i 0.336111 + 0.582162i
\(718\) −9.00000 15.5885i −0.335877 0.581756i
\(719\) 10.0000 17.3205i 0.372937 0.645946i −0.617079 0.786901i \(-0.711684\pi\)
0.990016 + 0.140955i \(0.0450174\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −17.5000 + 30.3109i −0.651734 + 1.12884i
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) −25.0000 −0.929760
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 2.00000 + 3.46410i 0.0742781 + 0.128654i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −11.0000 −0.407967 −0.203984 0.978974i \(-0.565389\pi\)
−0.203984 + 0.978974i \(0.565389\pi\)
\(728\) 17.5000 4.33013i 0.648593 0.160485i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) −43.0000 −1.58824 −0.794121 0.607760i \(-0.792068\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) −4.00000 + 6.92820i −0.147643 + 0.255725i
\(735\) 9.00000 15.5885i 0.331970 0.574989i
\(736\) 4.00000 0.147442
\(737\) 12.0000 20.7846i 0.442026 0.765611i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165831i \(0.946969\pi\)
\(740\) 7.00000 0.257325
\(741\) 12.5000 + 12.9904i 0.459199 + 0.477214i
\(742\) 5.00000 0.183556
\(743\) 8.00000 + 13.8564i 0.293492 + 0.508342i 0.974633 0.223810i \(-0.0718494\pi\)
−0.681141 + 0.732152i \(0.738516\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) −1.00000 + 1.73205i −0.0366372 + 0.0634574i
\(746\) −38.0000 −1.39128
\(747\) −4.00000 + 6.92820i −0.146352 + 0.253490i
\(748\) −12.0000 + 20.7846i −0.438763 + 0.759961i
\(749\) 30.0000 1.09618
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 4.00000 + 6.92820i 0.145962 + 0.252814i 0.929731 0.368238i \(-0.120039\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 15.0000 0.546630
\(754\) 14.0000 3.46410i 0.509850 0.126155i
\(755\) −22.0000 −0.800662
\(756\) 2.50000 + 4.33013i 0.0909241 + 0.157485i
\(757\) −8.50000 14.7224i −0.308938 0.535096i 0.669193 0.743089i \(-0.266640\pi\)
−0.978130 + 0.207993i \(0.933307\pi\)
\(758\) −12.5000 + 21.6506i −0.454020 + 0.786386i
\(759\) 12.0000 0.435572
\(760\) 2.50000 4.33013i 0.0906845 0.157070i
\(761\) −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i \(-0.885491\pi\)
0.772863 + 0.634573i \(0.218824\pi\)
\(762\) 21.0000 0.760750
\(763\) 35.0000 60.6218i 1.26709 2.19466i
\(764\) −1.00000 1.73205i −0.0361787 0.0626634i
\(765\) −4.00000 6.92820i −0.144620 0.250490i
\(766\) 28.0000 1.01168
\(767\) 42.0000 10.3923i 1.51653 0.375244i
\(768\) 1.00000 0.0360844
\(769\) 17.0000 + 29.4449i 0.613036 + 1.06181i 0.990726 + 0.135877i \(0.0433852\pi\)
−0.377690 + 0.925932i \(0.623282\pi\)
\(770\) −7.50000 12.9904i −0.270281 0.468141i
\(771\) −14.0000 + 24.2487i −0.504198 + 0.873296i
\(772\) 24.0000 0.863779
\(773\) −0.500000 + 0.866025i −0.0179838 + 0.0311488i −0.874877 0.484345i \(-0.839058\pi\)
0.856893 + 0.515494i \(0.172391\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) −17.5000 30.3109i −0.627809 1.08740i