Properties

Label 126.2.f.b.43.1
Level $126$
Weight $2$
Character 126.43
Analytic conductor $1.006$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 43.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.43
Dual form 126.2.f.b.85.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} -1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{14} -3.46410i q^{15} +(-0.500000 + 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{18} -7.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(1.50000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{26} +5.19615i q^{27} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 1.73205i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-2.50000 + 4.33013i) q^{34} -2.00000 q^{35} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +10.3923i q^{39} +(1.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} -1.73205i q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(3.00000 - 5.19615i) q^{45} -4.00000 q^{46} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-7.50000 - 4.33013i) q^{51} +(3.00000 - 5.19615i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 1.73205i) q^{60} +(6.00000 - 10.3923i) q^{61} +6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +1.73205i q^{66} +(-6.50000 - 11.2583i) q^{67} +(2.50000 + 4.33013i) q^{68} -6.92820i q^{69} +(-1.00000 + 1.73205i) q^{70} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +1.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} +(3.50000 + 6.06218i) q^{76} +(0.500000 + 0.866025i) q^{77} +(9.00000 + 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} +2.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.00000 q^{82} +(-8.00000 + 13.8564i) q^{83} +(-1.50000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(6.00000 - 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} -6.00000 q^{89} +(-3.00000 - 5.19615i) q^{90} +6.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +10.3923i q^{93} +(7.00000 + 12.1244i) q^{95} +1.73205i q^{96} +(2.50000 - 4.33013i) q^{97} -1.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9} - 4 q^{10} - q^{11} + 6 q^{13} - q^{14} - q^{16} - 10 q^{17} + 6 q^{18} - 14 q^{19} - 2 q^{20} + 3 q^{21} + q^{22} - 4 q^{23} - 3 q^{24} + q^{25} + 12 q^{26} - 2 q^{28} + 4 q^{29} - 6 q^{30} + 6 q^{31} + q^{32} - 3 q^{33} - 5 q^{34} - 4 q^{35} + 3 q^{36} + 4 q^{37} - 7 q^{38} + 2 q^{40} - 3 q^{41} + q^{43} + 2 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} - q^{49} - q^{50} - 15 q^{51} + 6 q^{52} + 24 q^{53} + 9 q^{54} + 4 q^{55} - q^{56} - 21 q^{57} - 4 q^{58} + 7 q^{59} - 6 q^{60} + 12 q^{61} + 12 q^{62} + 6 q^{63} + 2 q^{64} + 12 q^{65} - 13 q^{67} + 5 q^{68} - 2 q^{70} - 16 q^{71} - 3 q^{72} + 2 q^{73} + 2 q^{74} + 3 q^{75} + 7 q^{76} + q^{77} + 18 q^{78} + 6 q^{79} + 4 q^{80} - 9 q^{81} - 6 q^{82} - 16 q^{83} - 3 q^{84} + 10 q^{85} - q^{86} + 12 q^{87} + q^{88} - 12 q^{89} - 6 q^{90} + 12 q^{91} - 4 q^{92} + 14 q^{95} + 5 q^{97} - 2 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −2.00000 −0.632456
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 3.46410i 0.894427i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 3.00000 0.707107
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 1.50000 0.866025i 0.327327 0.188982i
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 6.00000 1.17670
\(27\) 5.19615i 1.00000i
\(28\) −1.00000 −0.188982
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) −3.00000 1.73205i −0.547723 0.316228i
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.50000 + 0.866025i −0.261116 + 0.150756i
\(34\) −2.50000 + 4.33013i −0.428746 + 0.742611i
\(35\) −2.00000 −0.338062
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −3.50000 + 6.06218i −0.567775 + 0.983415i
\(39\) 10.3923i 1.66410i
\(40\) 1.00000 + 1.73205i 0.158114 + 0.273861i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 1.73205i 0.267261i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 1.00000 0.150756
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) −4.00000 −0.589768
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −1.50000 + 0.866025i −0.216506 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) −7.50000 4.33013i −1.05021 0.606339i
\(52\) 3.00000 5.19615i 0.416025 0.720577i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 2.00000 0.269680
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) −10.5000 6.06218i −1.39076 0.802955i
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) −3.00000 + 1.73205i −0.387298 + 0.223607i
\(61\) 6.00000 10.3923i 0.768221 1.33060i −0.170305 0.985391i \(-0.554475\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(62\) 6.00000 0.762001
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 1.73205i 0.213201i
\(67\) −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i \(-0.874609\pi\)
0.129307 0.991605i \(-0.458725\pi\)
\(68\) 2.50000 + 4.33013i 0.303170 + 0.525105i
\(69\) 6.92820i 0.834058i
\(70\) −1.00000 + 1.73205i −0.119523 + 0.207020i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 1.50000 0.866025i 0.173205 0.100000i
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 0.500000 + 0.866025i 0.0569803 + 0.0986928i
\(78\) 9.00000 + 5.19615i 1.01905 + 0.588348i
\(79\) 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) 2.00000 0.223607
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −3.00000 −0.331295
\(83\) −8.00000 + 13.8564i −0.878114 + 1.52094i −0.0247060 + 0.999695i \(0.507865\pi\)
−0.853408 + 0.521243i \(0.825468\pi\)
\(84\) −1.50000 0.866025i −0.163663 0.0944911i
\(85\) 5.00000 + 8.66025i 0.542326 + 0.939336i
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 6.00000 3.46410i 0.643268 0.371391i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −3.00000 5.19615i −0.316228 0.547723i
\(91\) 6.00000 0.628971
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 10.3923i 1.07763i
\(94\) 0 0
\(95\) 7.00000 + 12.1244i 0.718185 + 1.24393i
\(96\) 1.73205i 0.176777i
\(97\) 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i \(-0.751641\pi\)
0.964579 + 0.263795i \(0.0849741\pi\)
\(98\) −1.00000 −0.101015
\(99\) −3.00000 −0.301511
\(100\) −1.00000 −0.100000
\(101\) 2.00000 3.46410i 0.199007 0.344691i −0.749199 0.662344i \(-0.769562\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(102\) −7.50000 + 4.33013i −0.742611 + 0.428746i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) −3.00000 1.73205i −0.292770 0.169031i
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 1.00000 1.73205i 0.0953463 0.165145i
\(111\) 3.00000 + 1.73205i 0.284747 + 0.164399i
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) 5.00000 + 8.66025i 0.470360 + 0.814688i 0.999425 0.0338931i \(-0.0107906\pi\)
−0.529065 + 0.848581i \(0.677457\pi\)
\(114\) −10.5000 + 6.06218i −0.983415 + 0.567775i
\(115\) −4.00000 + 6.92820i −0.373002 + 0.646058i
\(116\) −4.00000 −0.371391
\(117\) −9.00000 + 15.5885i −0.832050 + 1.44115i
\(118\) 7.00000 0.644402
\(119\) −2.50000 + 4.33013i −0.229175 + 0.396942i
\(120\) 3.46410i 0.316228i
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) −6.00000 10.3923i −0.543214 0.940875i
\(123\) 5.19615i 0.468521i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) −12.0000 −1.07331
\(126\) 1.50000 2.59808i 0.133631 0.231455i
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 1.50000 + 0.866025i 0.130558 + 0.0753778i
\(133\) −3.50000 + 6.06218i −0.303488 + 0.525657i
\(134\) −13.0000 −1.12303
\(135\) 9.00000 5.19615i 0.774597 0.447214i
\(136\) 5.00000 0.428746
\(137\) 9.50000 16.4545i 0.811640 1.40580i −0.100076 0.994980i \(-0.531909\pi\)
0.911716 0.410822i \(-0.134758\pi\)
\(138\) −6.00000 3.46410i −0.510754 0.294884i
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) −6.00000 −0.501745
\(144\) −3.00000 −0.250000
\(145\) −8.00000 −0.664364
\(146\) 0.500000 0.866025i 0.0413803 0.0716728i
\(147\) 1.73205i 0.142857i
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 12.0000 + 20.7846i 0.983078 + 1.70274i 0.650183 + 0.759778i \(0.274692\pi\)
0.332896 + 0.942964i \(0.391974\pi\)
\(150\) 1.73205i 0.141421i
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) 7.00000 0.567775
\(153\) −7.50000 12.9904i −0.606339 1.05021i
\(154\) 1.00000 0.0805823
\(155\) 6.00000 10.3923i 0.481932 0.834730i
\(156\) 9.00000 5.19615i 0.720577 0.416025i
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) −3.00000 5.19615i −0.238667 0.413384i
\(159\) 18.0000 + 10.3923i 1.42749 + 0.824163i
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) −4.00000 −0.315244
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 3.00000 + 1.73205i 0.233550 + 0.134840i
\(166\) 8.00000 + 13.8564i 0.620920 + 1.07547i
\(167\) −10.0000 17.3205i −0.773823 1.34030i −0.935454 0.353450i \(-0.885009\pi\)
0.161630 0.986851i \(-0.448325\pi\)
\(168\) −1.50000 + 0.866025i −0.115728 + 0.0668153i
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 10.0000 0.766965
\(171\) −10.5000 18.1865i −0.802955 1.39076i
\(172\) −1.00000 −0.0762493
\(173\) −1.00000 + 1.73205i −0.0760286 + 0.131685i −0.901533 0.432710i \(-0.857557\pi\)
0.825505 + 0.564396i \(0.190891\pi\)
\(174\) 6.92820i 0.525226i
\(175\) −0.500000 0.866025i −0.0377964 0.0654654i
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 12.1244i 0.911322i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) −6.00000 −0.447214
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 3.00000 5.19615i 0.222375 0.385164i
\(183\) 18.0000 10.3923i 1.33060 0.768221i
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 9.00000 + 5.19615i 0.659912 + 0.381000i
\(187\) 2.50000 4.33013i 0.182818 0.316650i
\(188\) 0 0
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) 14.0000 1.01567
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 1.50000 + 0.866025i 0.108253 + 0.0625000i
\(193\) −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i \(-0.957095\pi\)
0.379086 0.925361i \(-0.376238\pi\)
\(194\) −2.50000 4.33013i −0.179490 0.310885i
\(195\) 18.0000 10.3923i 1.28901 0.744208i
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 22.5167i 1.58820i
\(202\) −2.00000 3.46410i −0.140720 0.243733i
\(203\) −2.00000 3.46410i −0.140372 0.243132i
\(204\) 8.66025i 0.606339i
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) −14.0000 −0.975426
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) −6.00000 −0.416025
\(209\) 3.50000 6.06218i 0.242100 0.419330i
\(210\) −3.00000 + 1.73205i −0.207020 + 0.119523i
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) −12.0000 6.92820i −0.822226 0.474713i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) −2.00000 −0.136399
\(216\) 5.19615i 0.353553i
\(217\) 6.00000 0.407307
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 1.50000 + 0.866025i 0.101361 + 0.0585206i
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 3.00000 1.73205i 0.201347 0.116248i
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 1.00000 0.0668153
\(225\) 3.00000 0.200000
\(226\) 10.0000 0.665190
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 12.1244i 0.802955i
\(229\) 13.0000 + 22.5167i 0.859064 + 1.48794i 0.872823 + 0.488037i \(0.162287\pi\)
−0.0137585 + 0.999905i \(0.504380\pi\)
\(230\) 4.00000 + 6.92820i 0.263752 + 0.456832i
\(231\) 1.73205i 0.113961i
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) −29.0000 −1.89985 −0.949927 0.312473i \(-0.898843\pi\)
−0.949927 + 0.312473i \(0.898843\pi\)
\(234\) 9.00000 + 15.5885i 0.588348 + 1.01905i
\(235\) 0 0
\(236\) 3.50000 6.06218i 0.227831 0.394614i
\(237\) 9.00000 5.19615i 0.584613 0.337526i
\(238\) 2.50000 + 4.33013i 0.162051 + 0.280680i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 3.00000 + 1.73205i 0.193649 + 0.111803i
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 10.0000 0.642824
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −12.0000 −0.768221
\(245\) −1.00000 + 1.73205i −0.0638877 + 0.110657i
\(246\) −4.50000 2.59808i −0.286910 0.165647i
\(247\) −21.0000 36.3731i −1.33620 2.31436i
\(248\) −3.00000 5.19615i −0.190500 0.329956i
\(249\) −24.0000 + 13.8564i −1.52094 + 0.878114i
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) −1.50000 2.59808i −0.0944911 0.163663i
\(253\) 4.00000 0.251478
\(254\) −6.00000 + 10.3923i −0.376473 + 0.652071i
\(255\) 17.3205i 1.08465i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 1.73205i 0.107833i
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) −12.0000 −0.744208
\(261\) 12.0000 0.742781
\(262\) 4.00000 0.247121
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 1.50000 0.866025i 0.0923186 0.0533002i
\(265\) −12.0000 20.7846i −0.737154 1.27679i
\(266\) 3.50000 + 6.06218i 0.214599 + 0.371696i
\(267\) −9.00000 5.19615i −0.550791 0.317999i
\(268\) −6.50000 + 11.2583i −0.397051 + 0.687712i
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 10.3923i 0.632456i
\(271\) −6.00000 −0.364474 −0.182237 0.983255i \(-0.558334\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(272\) 2.50000 4.33013i 0.151585 0.262553i
\(273\) 9.00000 + 5.19615i 0.544705 + 0.314485i
\(274\) −9.50000 16.4545i −0.573916 0.994052i
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) −6.00000 + 3.46410i −0.361158 + 0.208514i
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 5.00000 0.299880
\(279\) −9.00000 + 15.5885i −0.538816 + 0.933257i
\(280\) 2.00000 0.119523
\(281\) −11.0000 + 19.0526i −0.656205 + 1.13658i 0.325385 + 0.945582i \(0.394506\pi\)
−0.981590 + 0.190999i \(0.938827\pi\)
\(282\) 0 0
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 24.2487i 1.43637i
\(286\) −3.00000 + 5.19615i −0.177394 + 0.307255i
\(287\) −3.00000 −0.177084
\(288\) −1.50000 + 2.59808i −0.0883883 + 0.153093i
\(289\) 8.00000 0.470588
\(290\) −4.00000 + 6.92820i −0.234888 + 0.406838i
\(291\) 7.50000 4.33013i 0.439658 0.253837i
\(292\) −0.500000 0.866025i −0.0292603 0.0506803i
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) −1.50000 0.866025i −0.0874818 0.0505076i
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) −2.00000 −0.116248
\(297\) −4.50000 2.59808i −0.261116 0.150756i
\(298\) 24.0000 1.39028
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) −1.50000 0.866025i −0.0866025 0.0500000i
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 6.00000 3.46410i 0.344691 0.199007i
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) −24.0000 −1.37424
\(306\) −15.0000 −0.857493
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0.500000 0.866025i 0.0284901 0.0493464i
\(309\) 24.2487i 1.37946i
\(310\) −6.00000 10.3923i −0.340777 0.590243i
\(311\) −1.00000 1.73205i −0.0567048 0.0982156i 0.836280 0.548303i \(-0.184726\pi\)
−0.892984 + 0.450088i \(0.851393\pi\)
\(312\) 10.3923i 0.588348i
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) −2.00000 −0.112867
\(315\) −3.00000 5.19615i −0.169031 0.292770i
\(316\) −6.00000 −0.337526
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 18.0000 10.3923i 1.00939 0.582772i
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 4.50000 + 2.59808i 0.251166 + 0.145010i
\(322\) −2.00000 + 3.46410i −0.111456 + 0.193047i
\(323\) 35.0000 1.94745
\(324\) 9.00000 0.500000
\(325\) 6.00000 0.332820
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) −3.00000 1.73205i −0.165900 0.0957826i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 0 0
\(330\) 3.00000 1.73205i 0.165145 0.0953463i
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 16.0000 0.878114
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) −20.0000 −1.09435
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 1.73205i 0.0944911i
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 11.5000 + 19.9186i 0.625518 + 1.08343i
\(339\) 17.3205i 0.940721i
\(340\) 5.00000 8.66025i 0.271163 0.469668i
\(341\) −6.00000 −0.324918
\(342\) −21.0000 −1.13555
\(343\) −1.00000 −0.0539949
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) −12.0000 + 6.92820i −0.646058 + 0.373002i
\(346\) 1.00000 + 1.73205i 0.0537603 + 0.0931156i
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) −6.00000 3.46410i −0.321634 0.185695i
\(349\) 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i \(-0.711079\pi\)
0.990282 + 0.139072i \(0.0444119\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −27.0000 + 15.5885i −1.44115 + 0.832050i
\(352\) −1.00000 −0.0533002
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 10.5000 + 6.06218i 0.558069 + 0.322201i
\(355\) 8.00000 + 13.8564i 0.424596 + 0.735422i
\(356\) 3.00000 + 5.19615i 0.159000 + 0.275396i
\(357\) −7.50000 + 4.33013i −0.396942 + 0.229175i
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 2.00000 0.105556 0.0527780 0.998606i \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) −3.00000 + 5.19615i −0.158114 + 0.273861i
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 17.3205i 0.909091i
\(364\) −3.00000 5.19615i −0.157243 0.272352i
\(365\) −1.00000 1.73205i −0.0523424 0.0906597i
\(366\) 20.7846i 1.08643i
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) 4.00000 0.208514
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) −4.00000 −0.207950
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 9.00000 5.19615i 0.466628 0.269408i
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) −2.50000 4.33013i −0.129272 0.223906i
\(375\) −18.0000 10.3923i −0.929516 0.536656i
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 4.50000 2.59808i 0.231455 0.133631i
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) 7.00000 12.1244i 0.359092 0.621966i
\(381\) −18.0000 10.3923i −0.922168 0.532414i
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) −2.00000 3.46410i −0.102195 0.177007i 0.810394 0.585886i \(-0.199253\pi\)
−0.912589 + 0.408879i \(0.865920\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) 1.00000 1.73205i 0.0509647 0.0882735i
\(386\) −17.0000 −0.865277
\(387\) 3.00000 0.152499
\(388\) −5.00000 −0.253837
\(389\) −4.00000 + 6.92820i −0.202808 + 0.351274i −0.949432 0.313972i \(-0.898340\pi\)
0.746624 + 0.665246i \(0.231673\pi\)
\(390\) 20.7846i 1.05247i
\(391\) 10.0000 + 17.3205i 0.505722 + 0.875936i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 6.92820i 0.349482i
\(394\) 5.00000 8.66025i 0.251896 0.436297i
\(395\) −12.0000 −0.603786
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 7.00000 12.1244i 0.350878 0.607739i
\(399\) −10.5000 + 6.06218i −0.525657 + 0.303488i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −4.50000 7.79423i −0.224719 0.389225i 0.731516 0.681824i \(-0.238813\pi\)
−0.956235 + 0.292599i \(0.905480\pi\)
\(402\) −19.5000 11.2583i −0.972572 0.561514i
\(403\) −18.0000 + 31.1769i −0.896644 + 1.55303i
\(404\) −4.00000 −0.199007
\(405\) 18.0000 0.894427
\(406\) −4.00000 −0.198517
\(407\) −1.00000 + 1.73205i −0.0495682 + 0.0858546i
\(408\) 7.50000 + 4.33013i 0.371305 + 0.214373i
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 3.00000 + 5.19615i 0.148159 + 0.256620i
\(411\) 28.5000 16.4545i 1.40580 0.811640i
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 7.00000 0.344447
\(414\) −6.00000 10.3923i −0.294884 0.510754i
\(415\) 32.0000 1.57082
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) 8.66025i 0.424094i
\(418\) −3.50000 6.06218i −0.171191 0.296511i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 3.46410i 0.169031i
\(421\) 6.00000 10.3923i 0.292422 0.506490i −0.681960 0.731390i \(-0.738872\pi\)
0.974382 + 0.224900i \(0.0722054\pi\)
\(422\) 16.0000 0.778868
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) −2.50000 + 4.33013i −0.121268 + 0.210042i
\(426\) −12.0000 + 6.92820i −0.581402 + 0.335673i
\(427\) −6.00000 10.3923i −0.290360 0.502919i
\(428\) −1.50000 2.59808i −0.0725052 0.125583i
\(429\) −9.00000 5.19615i −0.434524 0.250873i
\(430\) −1.00000 + 1.73205i −0.0482243 + 0.0835269i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 3.00000 5.19615i 0.144005 0.249423i
\(435\) −12.0000 6.92820i −0.575356 0.332182i
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 14.0000 + 24.2487i 0.669711 + 1.15997i
\(438\) 1.50000 0.866025i 0.0716728 0.0413803i
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) −30.0000 −1.42695
\(443\) −3.50000 + 6.06218i −0.166290 + 0.288023i −0.937113 0.349027i \(-0.886512\pi\)
0.770823 + 0.637050i \(0.219845\pi\)
\(444\) 3.46410i 0.164399i
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) 41.5692i 1.96616i
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) 1.50000 2.59808i 0.0707107 0.122474i
\(451\) 3.00000 0.141264
\(452\) 5.00000 8.66025i 0.235180 0.407344i
\(453\) −15.0000 + 8.66025i −0.704761 + 0.406894i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) −6.00000 10.3923i −0.281284 0.487199i
\(456\) 10.5000 + 6.06218i 0.491708 + 0.283887i
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) 26.0000 1.21490
\(459\) 25.9808i 1.21268i
\(460\) 8.00000 0.373002
\(461\) −7.00000 + 12.1244i −0.326023 + 0.564688i −0.981719 0.190337i \(-0.939042\pi\)
0.655696 + 0.755025i \(0.272375\pi\)
\(462\) 1.50000 + 0.866025i 0.0697863 + 0.0402911i
\(463\) 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i \(-0.107148\pi\)
−0.757982 + 0.652275i \(0.773815\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 18.0000 10.3923i 0.834730 0.481932i
\(466\) −14.5000 + 25.1147i −0.671700 + 1.16342i
\(467\) −13.0000 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 18.0000 0.832050
\(469\) −13.0000 −0.600284
\(470\) 0 0
\(471\) 3.46410i 0.159617i
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 0.500000 + 0.866025i 0.0229900 + 0.0398199i
\(474\) 10.3923i 0.477334i
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 5.00000 0.229175
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) −6.00000 −0.274434
\(479\) 10.0000 17.3205i 0.456912 0.791394i −0.541884 0.840453i \(-0.682289\pi\)
0.998796 + 0.0490589i \(0.0156222\pi\)
\(480\) 3.00000 1.73205i 0.136931 0.0790569i
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 11.5000 + 19.9186i 0.523811 + 0.907267i
\(483\) −6.00000 3.46410i −0.273009 0.157622i
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) −10.0000 −0.454077
\(486\) 15.5885i 0.707107i
\(487\) −10.0000 −0.453143 −0.226572 0.973995i \(-0.572752\pi\)
−0.226572 + 0.973995i \(0.572752\pi\)
\(488\) −6.00000 + 10.3923i −0.271607 + 0.470438i
\(489\) −6.00000 3.46410i −0.271329 0.156652i
\(490\) 1.00000 + 1.73205i 0.0451754 + 0.0782461i
\(491\) −16.5000 28.5788i −0.744635 1.28974i −0.950365 0.311136i \(-0.899290\pi\)
0.205731 0.978609i \(-0.434043\pi\)
\(492\) −4.50000 + 2.59808i −0.202876 + 0.117130i
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) −42.0000 −1.88967
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) −6.00000 −0.269408
\(497\) −4.00000 + 6.92820i −0.179425 + 0.310772i
\(498\) 27.7128i 1.24184i
\(499\) 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i \(0.0581915\pi\)
−0.334227 + 0.942493i \(0.608475\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) 34.6410i 1.54765i
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) −3.00000 −0.133631
\(505\) −8.00000 −0.355995
\(506\) 2.00000 3.46410i 0.0889108 0.153998i
\(507\) −34.5000 + 19.9186i −1.53220 + 0.884615i
\(508\) 6.00000 + 10.3923i 0.266207 + 0.461084i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 15.0000 + 8.66025i 0.664211 + 0.383482i
\(511\) 0.500000 0.866025i 0.0221187 0.0383107i
\(512\) −1.00000 −0.0441942
\(513\) 36.3731i 1.60591i
\(514\) 15.0000 0.661622
\(515\) −14.0000 + 24.2487i −0.616914 + 1.06853i
\(516\) −1.50000 0.866025i −0.0660338 0.0381246i
\(517\) 0 0
\(518\) −1.00000 1.73205i −0.0439375 0.0761019i
\(519\) −3.00000 + 1.73205i −0.131685 + 0.0760286i
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) −9.00000 −0.394297 −0.197149 0.980374i \(-0.563168\pi\)
−0.197149 + 0.980374i \(0.563168\pi\)
\(522\) 6.00000 10.3923i 0.262613 0.454859i
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 2.00000 3.46410i 0.0873704 0.151330i
\(525\) 1.73205i 0.0755929i
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −15.0000 25.9808i −0.653410 1.13174i
\(528\) 1.73205i 0.0753778i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −24.0000 −1.04249
\(531\) −10.5000 + 18.1865i −0.455661 + 0.789228i
\(532\) 7.00000 0.303488
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) −9.00000 + 5.19615i −0.389468 + 0.224860i
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 6.50000 + 11.2583i 0.280757 + 0.486286i
\(537\) 36.0000 + 20.7846i 1.55351 + 0.896922i
\(538\) 10.0000 17.3205i 0.431131 0.746740i
\(539\) 1.00000 0.0430730
\(540\) −9.00000 5.19615i −0.387298 0.223607i
\(541\) −24.0000 −1.03184 −0.515920 0.856637i \(-0.672550\pi\)
−0.515920 + 0.856637i \(0.672550\pi\)
\(542\) −3.00000 + 5.19615i −0.128861 + 0.223194i
\(543\) 0 0
\(544\) −2.50000 4.33013i −0.107187 0.185653i
\(545\) 2.00000 + 3.46410i 0.0856706 + 0.148386i
\(546\) 9.00000 5.19615i 0.385164 0.222375i
\(547\) 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i \(-0.685132\pi\)
0.998318 + 0.0579790i \(0.0184657\pi\)
\(548\) −19.0000 −0.811640
\(549\) 36.0000 1.53644
\(550\) 1.00000 0.0426401
\(551\) −14.0000 + 24.2487i −0.596420 + 1.03303i
\(552\) 6.92820i 0.294884i
\(553\) −3.00000 5.19615i −0.127573 0.220963i
\(554\) 1.00000 + 1.73205i 0.0424859 + 0.0735878i
\(555\) 6.92820i 0.294086i
\(556\) 2.50000 4.33013i 0.106024 0.183638i
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 9.00000 + 15.5885i 0.381000 + 0.659912i
\(559\) 6.00000 0.253773
\(560\) 1.00000 1.73205i 0.0422577 0.0731925i
\(561\) 7.50000 4.33013i 0.316650 0.182818i
\(562\) 11.0000 + 19.0526i 0.464007 + 0.803684i
\(563\) −15.5000 26.8468i −0.653247 1.13146i −0.982330 0.187156i \(-0.940073\pi\)
0.329083 0.944301i \(-0.393260\pi\)
\(564\) 0 0
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) −4.00000 −0.168133
\(567\) 4.50000 + 7.79423i 0.188982 + 0.327327i
\(568\) 8.00000 0.335673
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) 21.0000 + 12.1244i 0.879593 + 0.507833i
\(571\) 16.5000 + 28.5788i 0.690504 + 1.19599i 0.971673 + 0.236329i \(0.0759443\pi\)
−0.281170 + 0.959658i \(0.590722\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −18.0000 + 10.3923i −0.751961 + 0.434145i
\(574\) −1.50000 + 2.59808i −0.0626088 + 0.108442i
\(575\) −4.00000 −0.166812
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −35.0000 −1.45707 −0.728535 0.685009i \(-0.759798\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 29.4449i 1.22369i
\(580\) 4.00000 + 6.92820i 0.166091 + 0.287678i
\(581\) 8.00000 + 13.8564i 0.331896 + 0.574861i
\(582\) 8.66025i 0.358979i
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) −1.00000 −0.0413803
\(585\) 36.0000 1.48842
\(586\) 0 0
\(587\) 23.5000 40.7032i 0.969949 1.68000i 0.274263 0.961655i \(-0.411566\pi\)
0.695686 0.718346i \(-0.255100\pi\)
\(588\) −1.50000 + 0.866025i −0.0618590 + 0.0357143i
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) −7.00000 12.1244i −0.288185 0.499152i
\(591\) 15.0000 + 8.66025i 0.617018 + 0.356235i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) −4.50000 + 2.59808i −0.184637 + 0.106600i
\(595\) 10.0000 0.409960
\(596\) 12.0000 20.7846i 0.491539 0.851371i
\(597\) 21.0000 + 12.1244i 0.859473 + 0.496217i
\(598\) −12.0000 20.7846i −0.490716 0.849946i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) −1.50000 + 0.866025i −0.0612372 + 0.0353553i
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) −1.00000 −0.0407570
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) 10.0000 0.406894
\(605\) 10.0000 17.3205i 0.406558 0.704179i
\(606\) 6.92820i 0.281439i
\(607\) 12.0000 + 20.7846i 0.487065 + 0.843621i 0.999889 0.0148722i \(-0.00473415\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 6.92820i 0.280745i
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) 0 0
\(612\) −7.50000 + 12.9904i −0.303170 + 0.525105i
\(613\) 42.0000 1.69636 0.848182 0.529705i \(-0.177697\pi\)
0.848182 + 0.529705i \(0.177697\pi\)
\(614\) 3.50000 6.06218i 0.141249 0.244650i
\(615\) −9.00000 + 5.19615i −0.362915 + 0.209529i
\(616\) −0.500000 0.866025i −0.0201456 0.0348932i
\(617\) 8.50000 + 14.7224i 0.342197 + 0.592703i 0.984840 0.173463i \(-0.0554956\pi\)
−0.642643 + 0.766165i \(0.722162\pi\)
\(618\) −21.0000 12.1244i −0.844744 0.487713i
\(619\) −18.5000 + 32.0429i −0.743578 + 1.28791i 0.207279 + 0.978282i \(0.433539\pi\)
−0.950856 + 0.309633i \(0.899794\pi\)
\(620\) −12.0000 −0.481932
\(621\) 18.0000 10.3923i 0.722315 0.417029i
\(622\) −2.00000 −0.0801927
\(623\) −3.00000 + 5.19615i −0.120192 + 0.208179i
\(624\) −9.00000 5.19615i −0.360288 0.208013i
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −8.50000 14.7224i −0.339728 0.588427i
\(627\) 10.5000 6.06218i 0.419330 0.242100i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −10.0000 −0.398726
\(630\) −6.00000 −0.239046
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −3.00000 + 5.19615i −0.119334 + 0.206692i
\(633\) 27.7128i 1.10149i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 12.0000 + 20.7846i 0.476205 + 0.824812i
\(636\) 20.7846i 0.824163i
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) 4.00000 0.158362
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) −2.00000 −0.0790569
\(641\) −0.500000 + 0.866025i −0.0197488 + 0.0342059i −0.875731 0.482800i \(-0.839620\pi\)
0.855982 + 0.517005i \(0.172953\pi\)
\(642\) 4.50000 2.59808i 0.177601 0.102538i
\(643\) 3.50000 + 6.06218i 0.138027 + 0.239069i 0.926750 0.375680i \(-0.122591\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 2.00000 + 3.46410i 0.0788110 + 0.136505i
\(645\) −3.00000 1.73205i −0.118125 0.0681994i
\(646\) 17.5000 30.3109i 0.688528 1.19257i
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) −7.00000 −0.274774
\(650\) 3.00000 5.19615i 0.117670 0.203810i
\(651\) 9.00000 + 5.19615i 0.352738 + 0.203653i
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) −3.00000 + 1.73205i −0.117309 + 0.0677285i
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 3.00000 0.117130
\(657\) 1.50000 + 2.59808i 0.0585206 + 0.101361i
\(658\) 0 0
\(659\) −8.00000 + 13.8564i −0.311636 + 0.539769i −0.978717 0.205216i \(-0.934210\pi\)
0.667081 + 0.744985i \(0.267544\pi\)
\(660\) 3.46410i 0.134840i
\(661\) −14.0000 24.2487i −0.544537 0.943166i −0.998636 0.0522143i \(-0.983372\pi\)
0.454099 0.890951i \(-0.349961\pi\)
\(662\) 4.00000 + 6.92820i 0.155464 + 0.269272i
\(663\) 51.9615i 2.01802i
\(664\) 8.00000 13.8564i 0.310460 0.537733i
\(665\) 14.0000 0.542897
\(666\) 6.00000 0.232495
\(667\) −16.0000 −0.619522
\(668\) −10.0000 + 17.3205i −0.386912 + 0.670151i
\(669\) 6.00000 3.46410i 0.231973 0.133930i
\(670\) 13.0000 + 22.5167i 0.502234 + 0.869894i
\(671\) 6.00000 + 10.3923i 0.231627 + 0.401190i
\(672\) 1.50000 + 0.866025i 0.0578638 + 0.0334077i
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 9.00000 0.346667
\(675\) 4.50000 + 2.59808i 0.173205 + 0.100000i
\(676\) 23.0000 0.884615
\(677\) −15.0000 + 25.9808i −0.576497 + 0.998522i 0.419380 + 0.907811i \(0.362247\pi\)
−0.995877 + 0.0907112i \(0.971086\pi\)
\(678\) 15.0000 + 8.66025i 0.576072 + 0.332595i
\(679\) −2.50000 4.33013i −0.0959412 0.166175i
\(680\) −5.00000 8.66025i −0.191741 0.332106i
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) 39.0000 1.49229 0.746147 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) −10.5000 + 18.1865i −0.401478 + 0.695379i
\(685\) −38.0000 −1.45191
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 45.0333i 1.71813i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) 36.0000 + 62.3538i 1.37149 + 2.37549i
\(690\) 13.8564i 0.527504i
\(691\) −16.0000 + 27.7128i −0.608669 + 1.05425i 0.382791 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(692\) 2.00000 0.0760286
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) 3.00000 0.113878
\(695\) 5.00000 8.66025i 0.189661 0.328502i
\(696\) −6.00000 + 3.46410i −0.227429 + 0.131306i
\(697\) 7.50000 + 12.9904i 0.284083 + 0.492046i
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) −43.5000 25.1147i −1.64532 0.949927i
\(700\) −0.500000 + 0.866025i −0.0188982 + 0.0327327i
\(701\) 8.00000 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 31.1769i 1.17670i
\(703\) −14.0000 −0.528020
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −7.50000 12.9904i −0.282266 0.488899i
\(707\) −2.00000 3.46410i −0.0752177 0.130281i
\(708\) 10.5000 6.06218i 0.394614 0.227831i
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 16.0000 0.600469
\(711\) 18.0000 0.675053
\(712\) 6.00000 0.224860
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 8.66025i 0.324102i
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −12.0000 20.7846i −0.448461 0.776757i
\(717\) 10.3923i 0.388108i
\(718\) 1.00000 1.73205i 0.0373197 0.0646396i
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 3.00000 + 5.19615i 0.111803 + 0.193649i
\(721\) −14.0000 −0.521387
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) −34.5000 + 19.9186i −1.28307 + 0.740780i
\(724\) 0 0
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 15.0000 + 8.66025i 0.556702 + 0.321412i
\(727\) 7.00000 12.1244i 0.259616 0.449667i −0.706523 0.707690i \(-0.749737\pi\)
0.966139 + 0.258022i \(0.0830708\pi\)
\(728\) −6.00000 −0.222375
\(729\) −27.0000 −1.00000
\(730\) −2.00000 −0.0740233
\(731\) −2.50000 + 4.33013i −0.0924658 + 0.160156i
\(732\) −18.0000 10.3923i −0.665299 0.384111i
\(733\) 9.00000 + 15.5885i 0.332423 + 0.575773i 0.982986 0.183679i \(-0.0588007\pi\)
−0.650564 + 0.759452i \(0.725467\pi\)
\(734\) −11.0000 19.0526i −0.406017 0.703243i
\(735\) −3.00000 + 1.73205i −0.110657 + 0.0638877i
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) 13.0000 0.478861
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) −33.0000 −1.21392 −0.606962 0.794731i \(-0.707612\pi\)
−0.606962 + 0.794731i \(0.707612\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) 72.7461i 2.67240i
\(742\) −6.00000 10.3923i −0.220267 0.381514i
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 10.3923i 0.381000i
\(745\) 24.0000 41.5692i 0.879292 1.52298i
\(746\) −22.0000 −0.805477
\(747\) −48.0000 −1.75623
\(748\) −5.00000 −0.182818
\(749\) 1.50000 2.59808i 0.0548088 0.0949316i
\(750\) −18.0000 + 10.3923i −0.657267 + 0.379473i
\(751\) 9.00000 + 15.5885i 0.328415 + 0.568831i 0.982197 0.187851i \(-0.0601523\pi\)
−0.653783 + 0.756682i \(0.726819\pi\)
\(752\) 0 0
\(753\) 4.50000 + 2.59808i 0.163989 + 0.0946792i
\(754\) 12.0000 20.7846i 0.437014 0.756931i
\(755\) 20.0000 0.727875
\(756\) 5.19615i 0.188982i
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) −8.50000 + 14.7224i −0.308734 + 0.534743i
\(759\) 6.00000 + 3.46410i 0.217786 + 0.125739i
\(760\) −7.00000 12.1244i −0.253917 0.439797i
\(761\) −5.00000 8.66025i −0.181250 0.313934i 0.761057 0.648686i \(-0.224681\pi\)
−0.942306 + 0.334752i \(0.891348\pi\)
\(762\) −18.0000 + 10.3923i −0.652071 + 0.376473i
\(763\) −1.00000 + 1.73205i −0.0362024 + 0.0627044i
\(764\) 12.0000 0.434145
\(765\) −15.0000 + 25.9808i −0.542326 + 0.939336i
\(766\) −4.00000 −0.144526
\(767\) −21.0000 + 36.3731i −0.758266 + 1.31336i
\(768\) 1.73205i 0.0625000i
\(769\) −11.0000 19.0526i −0.396670 0.687053i 0.596643 0.802507i \(-0.296501\pi\)
−0.993313 + 0.115454i \(0.963168\pi\)
\(770\) −1.00000 1.73205i −0.0360375 0.0624188i
\(771\) 25.9808i 0.935674i
\(772\) −8.50000 + 14.7224i −0.305922 + 0.529872i
\(773\) −52.0000 −1.87031 −0.935155 0.354239i \(-0.884740\pi\)
−0.935155 + 0.354239i \(0.884740\pi\)
\(774\) 1.50000 2.59808i 0.0539164 0.0933859i
\(775\) 6.00000 0.215526
\(776\) −2.50000 +