Properties

Label 370.2.e.c.211.1
Level $370$
Weight $2$
Character 370.211
Analytic conductor $2.954$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
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 \(\chi\) \(=\) 370.211
Dual form 370.2.e.c.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -6.00000 q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} -9.00000 q^{27} +6.00000 q^{29} +(1.50000 - 2.59808i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +(-1.00000 + 1.73205i) q^{34} +6.00000 q^{36} +(-5.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(-1.50000 - 2.59808i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +7.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -6.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} -8.00000 q^{47} -3.00000 q^{48} +(3.50000 + 6.06218i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(1.00000 - 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 + 1.73205i) q^{59} +3.00000 q^{60} +(-5.00000 + 8.66025i) q^{61} +(2.50000 + 4.33013i) q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +6.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} -2.00000 q^{68} +(-9.00000 + 15.5885i) q^{69} +(3.00000 + 5.19615i) q^{72} -2.00000 q^{73} +(-5.00000 - 3.46410i) q^{74} -3.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(1.50000 - 2.59808i) q^{78} +(2.00000 - 3.46410i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +2.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(9.00000 - 15.5885i) q^{87} -2.00000 q^{88} +(-1.00000 - 1.73205i) q^{89} +(-3.00000 - 5.19615i) q^{90} +(3.00000 - 5.19615i) q^{92} +(7.50000 - 12.9904i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-1.50000 - 2.59808i) q^{96} +18.0000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(-6.00000 - 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 3q^{3} - q^{4} + q^{5} + 6q^{6} - 2q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + q^{2} + 3q^{3} - q^{4} + q^{5} + 6q^{6} - 2q^{8} - 6q^{9} + 2q^{10} + 4q^{11} + 3q^{12} + q^{13} - 3q^{15} - q^{16} + 2q^{17} + 6q^{18} - 2q^{19} + q^{20} + 2q^{22} - 12q^{23} - 3q^{24} - q^{25} + 2q^{26} - 18q^{27} + 12q^{29} + 3q^{30} + 10q^{31} + q^{32} + 6q^{33} - 2q^{34} + 12q^{36} - 11q^{37} - 4q^{38} - 3q^{39} - q^{40} - 3q^{41} + 14q^{43} - 2q^{44} - 12q^{45} - 6q^{46} - 16q^{47} - 6q^{48} + 7q^{49} + q^{50} + 12q^{51} + q^{52} + 11q^{53} - 9q^{54} + 2q^{55} + 6q^{57} + 6q^{58} + 2q^{59} + 6q^{60} - 10q^{61} + 5q^{62} + 2q^{64} - q^{65} + 12q^{66} - 4q^{67} - 4q^{68} - 18q^{69} + 6q^{72} - 4q^{73} - 10q^{74} - 6q^{75} - 2q^{76} + 3q^{78} + 4q^{79} - 2q^{80} - 9q^{81} - 6q^{82} - 12q^{83} + 4q^{85} + 7q^{86} + 18q^{87} - 4q^{88} - 2q^{89} - 6q^{90} + 6q^{92} + 15q^{93} - 8q^{94} + 2q^{95} - 3q^{96} + 36q^{97} - 7q^{98} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 3.00000 1.22474
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 1.00000 0.316228
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.50000 + 2.59808i 0.433013 + 0.750000i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) −1.50000 2.59808i −0.387298 0.670820i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 3.00000 5.19615i 0.707107 1.22474i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 1.00000 + 1.73205i 0.213201 + 0.369274i
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 0.196116
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) −5.50000 + 2.59808i −0.904194 + 0.427121i
\(38\) −2.00000 −0.324443
\(39\) −1.50000 2.59808i −0.240192 0.416025i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) −6.00000 −0.894427
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −3.00000 −0.433013
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 6.00000 0.840168
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i \(0.105931\pi\)
−0.189651 + 0.981852i \(0.560736\pi\)
\(54\) −4.50000 7.79423i −0.612372 1.06066i
\(55\) 1.00000 1.73205i 0.134840 0.233550i
\(56\) 0 0
\(57\) 3.00000 + 5.19615i 0.397360 + 0.688247i
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 1.00000 + 1.73205i 0.130189 + 0.225494i 0.923749 0.382998i \(-0.125108\pi\)
−0.793560 + 0.608492i \(0.791775\pi\)
\(60\) 3.00000 0.387298
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 2.50000 + 4.33013i 0.317500 + 0.549927i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.500000 0.866025i −0.0620174 0.107417i
\(66\) 6.00000 0.738549
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) −2.00000 −0.242536
\(69\) −9.00000 + 15.5885i −1.08347 + 1.87663i
\(70\) 0 0
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 3.00000 + 5.19615i 0.353553 + 0.612372i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −5.00000 3.46410i −0.581238 0.402694i
\(75\) −3.00000 −0.346410
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 0 0
\(78\) 1.50000 2.59808i 0.169842 0.294174i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.00000 −0.111803
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −3.00000 −0.331295
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 3.50000 + 6.06218i 0.377415 + 0.653701i
\(87\) 9.00000 15.5885i 0.964901 1.67126i
\(88\) −2.00000 −0.213201
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) −3.00000 5.19615i −0.316228 0.547723i
\(91\) 0 0
\(92\) 3.00000 5.19615i 0.312772 0.541736i
\(93\) 7.50000 12.9904i 0.777714 1.34704i
\(94\) −4.00000 6.92820i −0.412568 0.714590i
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) −3.50000 + 6.06218i −0.353553 + 0.612372i
\(99\) −6.00000 10.3923i −0.603023 1.04447i
\(100\) 1.00000 0.100000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 3.00000 + 5.19615i 0.297044 + 0.514496i
\(103\) −18.0000 −1.77359 −0.886796 0.462160i \(-0.847074\pi\)
−0.886796 + 0.462160i \(0.847074\pi\)
\(104\) −0.500000 + 0.866025i −0.0490290 + 0.0849208i
\(105\) 0 0
\(106\) −5.50000 + 9.52628i −0.534207 + 0.925274i
\(107\) 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i \(-0.526345\pi\)
0.904396 0.426694i \(-0.140322\pi\)
\(108\) 4.50000 7.79423i 0.433013 0.750000i
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) 2.00000 0.190693
\(111\) −1.50000 + 18.1865i −0.142374 + 1.72619i
\(112\) 0 0
\(113\) −10.0000 17.3205i −0.940721 1.62938i −0.764100 0.645097i \(-0.776817\pi\)
−0.176620 0.984279i \(-0.556517\pi\)
\(114\) −3.00000 + 5.19615i −0.280976 + 0.486664i
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −6.00000 −0.554700
\(118\) −1.00000 + 1.73205i −0.0920575 + 0.159448i
\(119\) 0 0
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) −7.00000 −0.636364
\(122\) −10.0000 −0.905357
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.00000 + 3.46410i 0.177471 + 0.307389i 0.941014 0.338368i \(-0.109875\pi\)
−0.763542 + 0.645758i \(0.776542\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 10.5000 18.1865i 0.924473 1.60123i
\(130\) 0.500000 0.866025i 0.0438529 0.0759555i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 3.00000 + 5.19615i 0.261116 + 0.452267i
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) −4.50000 + 7.79423i −0.387298 + 0.670820i
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −18.0000 −1.53226
\(139\) −7.00000 12.1244i −0.593732 1.02837i −0.993724 0.111856i \(-0.964321\pi\)
0.399992 0.916519i \(-0.369013\pi\)
\(140\) 0 0
\(141\) −12.0000 + 20.7846i −1.01058 + 1.75038i
\(142\) 0 0
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) −3.00000 + 5.19615i −0.250000 + 0.433013i
\(145\) 3.00000 5.19615i 0.249136 0.431517i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 21.0000 1.73205
\(148\) 0.500000 6.06218i 0.0410997 0.498308i
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) −1.50000 2.59808i −0.122474 0.212132i
\(151\) 4.50000 7.79423i 0.366205 0.634285i −0.622764 0.782410i \(-0.713990\pi\)
0.988969 + 0.148124i \(0.0473236\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) 0 0
\(155\) 2.50000 4.33013i 0.200805 0.347804i
\(156\) 3.00000 0.240192
\(157\) −1.50000 2.59808i −0.119713 0.207349i 0.799941 0.600079i \(-0.204864\pi\)
−0.919654 + 0.392730i \(0.871531\pi\)
\(158\) 4.00000 0.318223
\(159\) 33.0000 2.61707
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 5.00000 8.66025i 0.386912 0.670151i −0.605121 0.796134i \(-0.706875\pi\)
0.992032 + 0.125983i \(0.0402085\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 1.00000 + 1.73205i 0.0766965 + 0.132842i
\(171\) 12.0000 0.917663
\(172\) −3.50000 + 6.06218i −0.266872 + 0.462237i
\(173\) −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i \(-0.851372\pi\)
0.0566411 0.998395i \(-0.481961\pi\)
\(174\) 18.0000 1.36458
\(175\) 0 0
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) 6.00000 0.450988
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 3.00000 5.19615i 0.223607 0.387298i
\(181\) −8.00000 + 13.8564i −0.594635 + 1.02994i 0.398963 + 0.916967i \(0.369370\pi\)
−0.993598 + 0.112972i \(0.963963\pi\)
\(182\) 0 0
\(183\) 15.0000 + 25.9808i 1.10883 + 1.92055i
\(184\) 6.00000 0.442326
\(185\) −0.500000 + 6.06218i −0.0367607 + 0.445700i
\(186\) 15.0000 1.09985
\(187\) 2.00000 + 3.46410i 0.146254 + 0.253320i
\(188\) 4.00000 6.92820i 0.291730 0.505291i
\(189\) 0 0
\(190\) −1.00000 + 1.73205i −0.0725476 + 0.125656i
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 1.50000 2.59808i 0.108253 0.187500i
\(193\) 26.0000 1.87152 0.935760 0.352636i \(-0.114715\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) 9.00000 + 15.5885i 0.646162 + 1.11919i
\(195\) −3.00000 −0.214834
\(196\) −7.00000 −0.500000
\(197\) −5.50000 9.52628i −0.391859 0.678719i 0.600836 0.799372i \(-0.294834\pi\)
−0.992695 + 0.120653i \(0.961501\pi\)
\(198\) 6.00000 10.3923i 0.426401 0.738549i
\(199\) 25.0000 1.77220 0.886102 0.463491i \(-0.153403\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 6.00000 + 10.3923i 0.423207 + 0.733017i
\(202\) −9.00000 15.5885i −0.633238 1.09680i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) −9.00000 15.5885i −0.627060 1.08610i
\(207\) 18.0000 + 31.1769i 1.25109 + 2.16695i
\(208\) −1.00000 −0.0693375
\(209\) −2.00000 + 3.46410i −0.138343 + 0.239617i
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) −11.0000 −0.755483
\(213\) 0 0
\(214\) 17.0000 1.16210
\(215\) 3.50000 6.06218i 0.238698 0.413437i
\(216\) 9.00000 0.612372
\(217\) 0 0
\(218\) −9.00000 + 15.5885i −0.609557 + 1.05578i
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 1.00000 + 1.73205i 0.0674200 + 0.116775i
\(221\) 2.00000 0.134535
\(222\) −16.5000 + 7.79423i −1.10741 + 0.523114i
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) −3.00000 + 5.19615i −0.200000 + 0.346410i
\(226\) 10.0000 17.3205i 0.665190 1.15214i
\(227\) 12.5000 21.6506i 0.829654 1.43700i −0.0686556 0.997640i \(-0.521871\pi\)
0.898310 0.439363i \(-0.144796\pi\)
\(228\) −6.00000 −0.397360
\(229\) 6.00000 10.3923i 0.396491 0.686743i −0.596799 0.802391i \(-0.703561\pi\)
0.993290 + 0.115648i \(0.0368944\pi\)
\(230\) −6.00000 −0.395628
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) −2.00000 −0.130189
\(237\) −6.00000 10.3923i −0.389742 0.675053i
\(238\) 0 0
\(239\) −12.0000 20.7846i −0.776215 1.34444i −0.934109 0.356988i \(-0.883804\pi\)
0.157893 0.987456i \(-0.449530\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0 0
\(244\) −5.00000 8.66025i −0.320092 0.554416i
\(245\) 7.00000 0.447214
\(246\) −4.50000 + 7.79423i −0.286910 + 0.496942i
\(247\) 1.00000 + 1.73205i 0.0636285 + 0.110208i
\(248\) −5.00000 −0.317500
\(249\) −36.0000 −2.28141
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) 3.00000 5.19615i 0.187867 0.325396i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.00000 + 13.8564i 0.499026 + 0.864339i 0.999999 0.00112398i \(-0.000357774\pi\)
−0.500973 + 0.865463i \(0.667024\pi\)
\(258\) 21.0000 1.30740
\(259\) 0 0
\(260\) 1.00000 0.0620174
\(261\) −18.0000 31.1769i −1.11417 1.92980i
\(262\) −3.00000 + 5.19615i −0.185341 + 0.321019i
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 11.0000 0.675725
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) −9.00000 −0.547723
\(271\) −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i \(-0.176336\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 0 0
\(274\) −3.00000 5.19615i −0.181237 0.313911i
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) −9.00000 15.5885i −0.541736 0.938315i
\(277\) −14.5000 + 25.1147i −0.871221 + 1.50900i −0.0104855 + 0.999945i \(0.503338\pi\)
−0.860735 + 0.509053i \(0.829996\pi\)
\(278\) 7.00000 12.1244i 0.419832 0.727171i
\(279\) −15.0000 25.9808i −0.898027 1.55543i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) −24.0000 −1.42918
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) 0 0
\(285\) 6.00000 0.355409
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) −6.00000 −0.353553
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 6.00000 0.352332
\(291\) 27.0000 46.7654i 1.58277 2.74143i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) −13.5000 + 23.3827i −0.788678 + 1.36603i 0.138098 + 0.990419i \(0.455901\pi\)
−0.926777 + 0.375613i \(0.877432\pi\)
\(294\) 10.5000 + 18.1865i 0.612372 + 1.06066i
\(295\) 2.00000 0.116445
\(296\) 5.50000 2.59808i 0.319681 0.151010i
\(297\) −18.0000 −1.04447
\(298\) −2.00000 3.46410i −0.115857 0.200670i
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 1.50000 2.59808i 0.0866025 0.150000i
\(301\) 0 0
\(302\) 9.00000 0.517892
\(303\) −27.0000 + 46.7654i −1.55111 + 2.68660i
\(304\) 2.00000 0.114708
\(305\) 5.00000 + 8.66025i 0.286299 + 0.495885i
\(306\) 12.0000 0.685994
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) −27.0000 + 46.7654i −1.53598 + 2.66039i
\(310\) 5.00000 0.283981
\(311\) −1.50000 2.59808i −0.0850572 0.147323i 0.820358 0.571850i \(-0.193774\pi\)
−0.905416 + 0.424526i \(0.860441\pi\)
\(312\) 1.50000 + 2.59808i 0.0849208 + 0.147087i
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 1.50000 2.59808i 0.0846499 0.146618i
\(315\) 0 0
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) −8.50000 14.7224i −0.477408 0.826894i 0.522257 0.852788i \(-0.325090\pi\)
−0.999665 + 0.0258939i \(0.991757\pi\)
\(318\) 16.5000 + 28.5788i 0.925274 + 1.60262i
\(319\) 12.0000 0.671871
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −25.5000 44.1673i −1.42327 2.46518i
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −1.00000 −0.0554700
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 54.0000 2.98621
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 0 0
\(330\) 3.00000 5.19615i 0.165145 0.286039i
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 12.0000 0.658586
\(333\) 30.0000 + 20.7846i 1.64399 + 1.13899i
\(334\) 10.0000 0.547176
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0 0
\(337\) −5.00000 + 8.66025i −0.272367 + 0.471754i −0.969468 0.245220i \(-0.921140\pi\)
0.697100 + 0.716974i \(0.254473\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) −60.0000 −3.25875
\(340\) −1.00000 + 1.73205i −0.0542326 + 0.0939336i
\(341\) 10.0000 0.541530
\(342\) 6.00000 + 10.3923i 0.324443 + 0.561951i
\(343\) 0 0
\(344\) −7.00000 −0.377415
\(345\) 9.00000 + 15.5885i 0.484544 + 0.839254i
\(346\) 11.0000 19.0526i 0.591364 1.02427i
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 9.00000 + 15.5885i 0.482451 + 0.835629i
\(349\) 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i \(-0.115328\pi\)
−0.774493 + 0.632583i \(0.781995\pi\)
\(350\) 0 0
\(351\) −4.50000 + 7.79423i −0.240192 + 0.416025i
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 2.00000 + 3.46410i 0.105703 + 0.183083i
\(359\) 21.0000 1.10834 0.554169 0.832404i \(-0.313036\pi\)
0.554169 + 0.832404i \(0.313036\pi\)
\(360\) 6.00000 0.316228
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −16.0000 −0.840941
\(363\) −10.5000 + 18.1865i −0.551107 + 0.954545i
\(364\) 0 0
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) −15.0000 + 25.9808i −0.784063 + 1.35804i
\(367\) −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i \(0.404077\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 18.0000 0.937043
\(370\) −5.50000 + 2.59808i −0.285931 + 0.135068i
\(371\) 0 0
\(372\) 7.50000 + 12.9904i 0.388857 + 0.673520i
\(373\) 8.50000 14.7224i 0.440113 0.762299i −0.557584 0.830120i \(-0.688272\pi\)
0.997697 + 0.0678218i \(0.0216049\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) 8.00000 0.412568
\(377\) 3.00000 5.19615i 0.154508 0.267615i
\(378\) 0 0
\(379\) 5.00000 + 8.66025i 0.256833 + 0.444847i 0.965392 0.260804i \(-0.0839877\pi\)
−0.708559 + 0.705652i \(0.750654\pi\)
\(380\) −2.00000 −0.102598
\(381\) 12.0000 0.614779
\(382\) −1.50000 2.59808i −0.0767467 0.132929i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) 13.0000 + 22.5167i 0.661683 + 1.14607i
\(387\) −21.0000 36.3731i −1.06749 1.84895i
\(388\) −9.00000 + 15.5885i −0.456906 + 0.791384i
\(389\) −8.00000 + 13.8564i −0.405616 + 0.702548i −0.994393 0.105748i \(-0.966276\pi\)
0.588777 + 0.808296i \(0.299610\pi\)
\(390\) −1.50000 2.59808i −0.0759555 0.131559i
\(391\) −6.00000 10.3923i −0.303433 0.525561i
\(392\) −3.50000 6.06218i −0.176777 0.306186i
\(393\) 18.0000 0.907980
\(394\) 5.50000 9.52628i 0.277086 0.479927i
\(395\) −2.00000 3.46410i −0.100631 0.174298i
\(396\) 12.0000 0.603023
\(397\) 25.0000 1.25471 0.627357 0.778732i \(-0.284137\pi\)
0.627357 + 0.778732i \(0.284137\pi\)
\(398\) 12.5000 + 21.6506i 0.626568 + 1.08525i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −6.00000 + 10.3923i −0.299253 + 0.518321i
\(403\) 2.50000 4.33013i 0.124534 0.215699i
\(404\) 9.00000 15.5885i 0.447767 0.775555i
\(405\) 4.50000 + 7.79423i 0.223607 + 0.387298i
\(406\) 0 0
\(407\) −11.0000 + 5.19615i −0.545250 + 0.257564i
\(408\) −6.00000 −0.297044
\(409\) −14.5000 25.1147i −0.716979 1.24184i −0.962191 0.272374i \(-0.912191\pi\)
0.245212 0.969469i \(-0.421142\pi\)
\(410\) −1.50000 + 2.59808i −0.0740797 + 0.128310i
\(411\) −9.00000 + 15.5885i −0.443937 + 0.768922i
\(412\) 9.00000 15.5885i 0.443398 0.767988i
\(413\) 0 0
\(414\) −18.0000 + 31.1769i −0.884652 + 1.53226i
\(415\) −12.0000 −0.589057
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) −42.0000 −2.05675
\(418\) −4.00000 −0.195646
\(419\) 7.00000 + 12.1244i 0.341972 + 0.592314i 0.984799 0.173698i \(-0.0555717\pi\)
−0.642827 + 0.766012i \(0.722238\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −1.00000 1.73205i −0.0486792 0.0843149i
\(423\) 24.0000 + 41.5692i 1.16692 + 2.02116i
\(424\) −5.50000 9.52628i −0.267104 0.462637i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) 0 0
\(428\) 8.50000 + 14.7224i 0.410863 + 0.711636i
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 7.00000 0.337570
\(431\) −6.50000 + 11.2583i −0.313094 + 0.542295i −0.979030 0.203714i \(-0.934699\pi\)
0.665937 + 0.746008i \(0.268032\pi\)
\(432\) 4.50000 + 7.79423i 0.216506 + 0.375000i
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) −9.00000 15.5885i −0.431517 0.747409i
\(436\) −18.0000 −0.862044
\(437\) 6.00000 10.3923i 0.287019 0.497131i
\(438\) −6.00000 −0.286691
\(439\) −3.50000 + 6.06218i −0.167046 + 0.289332i −0.937380 0.348309i \(-0.886756\pi\)
0.770334 + 0.637641i \(0.220089\pi\)
\(440\) −1.00000 + 1.73205i −0.0476731 + 0.0825723i
\(441\) 21.0000 36.3731i 1.00000 1.73205i
\(442\) 1.00000 + 1.73205i 0.0475651 + 0.0823853i
\(443\) −21.0000 −0.997740 −0.498870 0.866677i \(-0.666252\pi\)
−0.498870 + 0.866677i \(0.666252\pi\)
\(444\) −15.0000 10.3923i −0.711868 0.493197i
\(445\) −2.00000 −0.0948091
\(446\) 1.00000 + 1.73205i 0.0473514 + 0.0820150i
\(447\) −6.00000 + 10.3923i −0.283790 + 0.491539i
\(448\) 0 0
\(449\) −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i \(-0.998358\pi\)
0.504461 + 0.863434i \(0.331691\pi\)
\(450\) −6.00000 −0.282843
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) 20.0000 0.940721
\(453\) −13.5000 23.3827i −0.634285 1.09861i
\(454\) 25.0000 1.17331
\(455\) 0 0
\(456\) −3.00000 5.19615i −0.140488 0.243332i
\(457\) −6.00000 + 10.3923i −0.280668 + 0.486132i −0.971549 0.236837i \(-0.923889\pi\)
0.690881 + 0.722968i \(0.257223\pi\)
\(458\) 12.0000 0.560723
\(459\) −9.00000 15.5885i −0.420084 0.727607i
\(460\) −3.00000 5.19615i −0.139876 0.242272i
\(461\) 7.00000 + 12.1244i 0.326023 + 0.564688i 0.981719 0.190337i \(-0.0609581\pi\)
−0.655696 + 0.755025i \(0.727625\pi\)
\(462\) 0 0
\(463\) −10.0000 + 17.3205i −0.464739 + 0.804952i −0.999190 0.0402476i \(-0.987185\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) −7.50000 12.9904i −0.347804 0.602414i
\(466\) −8.00000 13.8564i −0.370593 0.641886i
\(467\) −23.0000 −1.06431 −0.532157 0.846646i \(-0.678618\pi\)
−0.532157 + 0.846646i \(0.678618\pi\)
\(468\) 3.00000 5.19615i 0.138675 0.240192i
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) −9.00000 −0.414698
\(472\) −1.00000 1.73205i −0.0460287 0.0797241i
\(473\) 14.0000 0.643721
\(474\) 6.00000 10.3923i 0.275589 0.477334i
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 33.0000 57.1577i 1.51097 2.61707i
\(478\) 12.0000 20.7846i 0.548867 0.950666i
\(479\) −3.50000 6.06218i −0.159919 0.276988i 0.774920 0.632059i \(-0.217790\pi\)
−0.934839 + 0.355071i \(0.884457\pi\)
\(480\) −3.00000 −0.136931
\(481\) −0.500000 + 6.06218i −0.0227980 + 0.276412i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 9.00000 15.5885i 0.408669 0.707835i
\(486\) 0 0
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 3.00000 0.135665
\(490\) 3.50000 + 6.06218i 0.158114 + 0.273861i
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −9.00000 −0.405751
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) −1.00000 + 1.73205i −0.0449921 + 0.0779287i
\(495\) −12.0000 −0.539360
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) 0 0
\(498\) −18.0000 31.1769i −0.806599 1.39707i
\(499\) 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −15.0000 25.9808i −0.670151 1.16073i
\(502\) −5.00000 8.66025i −0.223161 0.386526i
\(503\) −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i \(-0.986958\pi\)
0.464107 0.885779i \(-0.346375\pi\)
\(504\) 0 0
\(505\) −9.00000 + 15.5885i −0.400495 + 0.693677i
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) 36.0000 1.59882
\(508\) −4.00000 −0.177471
\(509\) 12.0000 + 20.7846i 0.531891 + 0.921262i 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 6.00000 0.265684
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 9.00000 15.5885i 0.397360 0.688247i
\(514\) −8.00000 + 13.8564i −0.352865 + 0.611180i
\(515\) −9.00000 + 15.5885i −0.396587 + 0.686909i
\(516\) 10.5000 + 18.1865i 0.462237 + 0.800617i
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) −66.0000 −2.89708
\(520\) 0.500000 + 0.866025i 0.0219265 + 0.0379777i
\(521\) −12.5000 + 21.6506i −0.547635 + 0.948532i 0.450801 + 0.892624i \(0.351138\pi\)
−0.998436 + 0.0559071i \(0.982195\pi\)
\(522\) 18.0000 31.1769i 0.787839 1.36458i
\(523\) 4.50000 7.79423i 0.196771 0.340818i −0.750708 0.660634i \(-0.770288\pi\)
0.947480 + 0.319816i \(0.103621\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 5.00000 + 8.66025i 0.217803 + 0.377247i
\(528\) −6.00000 −0.261116
\(529\) 13.0000 0.565217
\(530\) 5.50000 + 9.52628i 0.238905 + 0.413795i
\(531\) 6.00000 10.3923i 0.260378 0.450988i
\(532\) 0 0
\(533\) 1.50000 + 2.59808i 0.0649722 + 0.112535i
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) −8.50000 14.7224i −0.367487 0.636506i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 6.00000 10.3923i 0.258919 0.448461i
\(538\) 1.00000 + 1.73205i 0.0431131 + 0.0746740i
\(539\) 7.00000 + 12.1244i 0.301511 + 0.522233i
\(540\) −4.50000 7.79423i −0.193649 0.335410i
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 0.500000 0.866025i 0.0214768 0.0371990i
\(543\) 24.0000 + 41.5692i 1.02994 + 1.78391i
\(544\) 2.00000 0.0857493
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) −11.0000 −0.470326 −0.235163 0.971956i \(-0.575562\pi\)
−0.235163 + 0.971956i \(0.575562\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) 60.0000 2.56074
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 9.00000 15.5885i 0.383065 0.663489i
\(553\) 0 0
\(554\) −29.0000 −1.23209
\(555\) 15.0000 + 10.3923i 0.636715 + 0.441129i
\(556\) 14.0000 0.593732
\(557\) 12.5000 + 21.6506i 0.529642 + 0.917367i 0.999402 + 0.0345728i \(0.0110071\pi\)
−0.469760 + 0.882794i \(0.655660\pi\)
\(558\) 15.0000 25.9808i 0.635001 1.09985i
\(559\) 3.50000 6.06218i 0.148034 0.256403i
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −9.50000 + 16.4545i −0.400733 + 0.694090i
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) −20.0000 −0.841406
\(566\) 11.0000 0.462364
\(567\) 0 0
\(568\) 0 0
\(569\) 21.0000 0.880366 0.440183 0.897908i \(-0.354914\pi\)
0.440183 + 0.897908i \(0.354914\pi\)
\(570\) 3.00000 + 5.19615i 0.125656 + 0.217643i
\(571\) 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i \(-0.0858769\pi\)
−0.712735 + 0.701434i \(0.752544\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) −4.50000 + 7.79423i −0.187990 + 0.325609i
\(574\) 0 0
\(575\) 3.00000 + 5.19615i 0.125109 + 0.216695i
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) 16.0000 + 27.7128i 0.666089 + 1.15370i 0.978989 + 0.203913i \(0.0653661\pi\)
−0.312900 + 0.949786i \(0.601301\pi\)
\(578\) 13.0000 0.540729
\(579\) 39.0000 67.5500i 1.62078 2.80728i
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) 0 0
\(582\) 54.0000 2.23837
\(583\) 11.0000 + 19.0526i 0.455573 + 0.789076i
\(584\) 2.00000 0.0827606
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) −27.0000 −1.11536
\(587\) 7.50000 12.9904i 0.309558 0.536170i −0.668708 0.743525i \(-0.733152\pi\)
0.978266 + 0.207355i \(0.0664855\pi\)
\(588\) −10.5000 + 18.1865i −0.433013 + 0.750000i
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 1.00000 + 1.73205i 0.0411693 + 0.0713074i
\(591\) −33.0000 −1.35744
\(592\) 5.00000 + 3.46410i 0.205499 + 0.142374i
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) −9.00000 15.5885i −0.369274 0.639602i
\(595\) 0 0
\(596\) 2.00000 3.46410i 0.0819232 0.141895i
\(597\) 37.5000 64.9519i 1.53477 2.65830i
\(598\) −6.00000 −0.245358
\(599\) 7.50000 12.9904i 0.306442 0.530773i −0.671140 0.741331i \(-0.734195\pi\)
0.977581 + 0.210558i \(0.0675282\pi\)
\(600\) 3.00000 0.122474
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) 0 0
\(603\) 24.0000 0.977356
\(604\) 4.50000 + 7.79423i 0.183102 + 0.317143i
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) −54.0000 −2.19360
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) 0 0
\(610\) −5.00000 + 8.66025i −0.202444 + 0.350643i
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) −3.00000 5.19615i −0.121169 0.209871i 0.799060 0.601251i \(-0.205331\pi\)
−0.920229 + 0.391381i \(0.871998\pi\)
\(614\) −11.5000 19.9186i −0.464102 0.803849i
\(615\) 9.00000 0.362915
\(616\) 0 0
\(617\) 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) −54.0000 −2.17220
\(619\) −26.0000 −1.04503 −0.522514 0.852631i \(-0.675006\pi\)
−0.522514 + 0.852631i \(0.675006\pi\)
\(620\) 2.50000 + 4.33013i 0.100402 + 0.173902i
\(621\) 54.0000 2.16695
\(622\) 1.50000 2.59808i 0.0601445 0.104173i
\(623\) 0 0
\(624\) −1.50000 + 2.59808i −0.0600481 + 0.104006i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) 3.00000 0.119713
\(629\) −10.0000 6.92820i −0.398726 0.276246i
\(630\) 0 0
\(631\) −7.50000 12.9904i −0.298570 0.517139i 0.677239 0.735763i \(-0.263176\pi\)
−0.975809 + 0.218624i \(0.929843\pi\)
\(632\) −2.00000 + 3.46410i −0.0795557 + 0.137795i
\(633\) −3.00000 + 5.19615i −0.119239 + 0.206529i
\(634\) 8.50000 14.7224i 0.337578 0.584702i
\(635\) 4.00000 0.158735
\(636\) −16.5000 + 28.5788i −0.654268 + 1.13322i
\(637\) 7.00000 0.277350
\(638\) 6.00000 + 10.3923i 0.237542 + 0.411435i
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 0.500000 + 0.866025i 0.0197488 + 0.0342059i 0.875731 0.482800i \(-0.160380\pi\)
−0.855982 + 0.517005i \(0.827047\pi\)
\(642\) 25.5000 44.1673i 1.00640 1.74314i
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 0 0
\(645\) −10.5000 18.1865i −0.413437 0.716094i
\(646\) −2.00000 3.46410i −0.0786889 0.136293i
\(647\) 8.00000 13.8564i 0.314512 0.544752i −0.664821 0.747002i \(-0.731492\pi\)
0.979334 + 0.202251i \(0.0648256\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) −0.500000 0.866025i −0.0196116 0.0339683i
\(651\) 0 0
\(652\) −1.00000 −0.0391630
\(653\) 2.50000 4.33013i 0.0978326 0.169451i −0.812955 0.582327i \(-0.802142\pi\)
0.910787 + 0.412876i \(0.135476\pi\)
\(654\) 27.0000 + 46.7654i 1.05578 + 1.82867i
\(655\) 6.00000 0.234439
\(656\) 3.00000 0.117130
\(657\) 6.00000 + 10.3923i 0.234082 + 0.405442i
\(658\) 0 0
\(659\) 20.0000 34.6410i 0.779089 1.34942i −0.153378 0.988168i \(-0.549015\pi\)
0.932467 0.361255i \(-0.117652\pi\)
\(660\) 6.00000 0.233550
\(661\) 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i \(-0.650039\pi\)
0.998636 0.0522143i \(-0.0166279\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 3.00000 5.19615i 0.116510 0.201802i
\(664\) 6.00000 + 10.3923i 0.232845 + 0.403300i
\(665\) 0 0
\(666\) −3.00000 + 36.3731i −0.116248 + 1.40943i
\(667\) −36.0000 −1.39393
\(668\) 5.00000 + 8.66025i 0.193456 + 0.335075i
\(669\) 3.00000 5.19615i 0.115987 0.200895i
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) −10.0000 + 17.3205i −0.386046 + 0.668651i
\(672\) 0 0
\(673\) −14.0000 + 24.2487i −0.539660 + 0.934719i 0.459262 + 0.888301i \(0.348114\pi\)
−0.998922 + 0.0464181i \(0.985219\pi\)
\(674\) −10.0000 −0.385186
\(675\) 4.50000 + 7.79423i 0.173205 + 0.300000i
\(676\) −12.0000 −0.461538
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) −30.0000 51.9615i −1.15214 1.99557i
\(679\) 0 0
\(680\) −2.00000 −0.0766965
\(681\) −37.5000 64.9519i −1.43700 2.48896i
\(682\) 5.00000 + 8.66025i 0.191460 + 0.331618i
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) −6.00000 + 10.3923i −0.229416 + 0.397360i
\(685\) −3.00000 + 5.19615i −0.114624 + 0.198535i
\(686\) 0 0
\(687\) −18.0000 31.1769i −0.686743 1.18947i
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) 11.0000 0.419067
\(690\) −9.00000 + 15.5885i −0.342624 + 0.593442i
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 2.00000 + 3.46410i 0.0759190 + 0.131495i
\(695\) −14.0000 −0.531050
\(696\) −9.00000 + 15.5885i −0.341144 + 0.590879i
\(697\) −6.00000 −0.227266
\(698\) −3.00000 + 5.19615i −0.113552 + 0.196677i
\(699\) −24.0000 + 41.5692i −0.907763 + 1.57229i
\(700\) 0 0
\(701\) 11.0000 + 19.0526i 0.415464 + 0.719605i 0.995477 0.0950021i \(-0.0302858\pi\)
−0.580013 + 0.814607i \(0.696952\pi\)
\(702\) −9.00000 −0.339683
\(703\) 1.00000 12.1244i 0.0377157 0.457279i
\(704\) 2.00000 0.0753778
\(705\) 12.0000 + 20.7846i 0.451946 + 0.782794i
\(706\) 12.0000 20.7846i 0.451626 0.782239i
\(707\) 0 0
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) 24.0000 0.901339 0.450669 0.892691i \(-0.351185\pi\)
0.450669 + 0.892691i \(0.351185\pi\)
\(710\) 0 0
\(711\) −24.0000 −0.900070
\(712\) 1.00000 + 1.73205i 0.0374766 + 0.0649113i
\(713\) −30.0000 −1.12351
\(714\) 0 0
\(715\) −1.00000 1.73205i −0.0373979 0.0647750i
\(716\) −2.00000 + 3.46410i −0.0747435 + 0.129460i
\(717\) −72.0000 −2.68889
\(718\) 10.5000 + 18.1865i 0.391857 + 0.678715i
\(719\) 18.5000 + 32.0429i 0.689934 + 1.19500i 0.971859 + 0.235564i \(0.0756936\pi\)
−0.281925 + 0.959436i \(0.590973\pi\)
\(720\) 3.00000 + 5.19615i 0.111803 + 0.193649i
\(721\) 0 0
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) −15.0000 25.9808i −0.557856 0.966235i
\(724\) −8.00000 13.8564i −0.297318 0.514969i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) −21.0000 −0.779383
\(727\) −26.0000 + 45.0333i −0.964287 + 1.67019i −0.252767 + 0.967527i \(0.581341\pi\)
−0.711520 + 0.702666i \(0.751993\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −2.00000 −0.0740233
\(731\) 7.00000 + 12.1244i 0.258904 + 0.448435i
\(732\) −30.0000 −1.10883
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) −26.0000 −0.959678
\(735\) 10.5000 18.1865i 0.387298 0.670820i
\(736\) −3.00000 + 5.19615i −0.110581 + 0.191533i
\(737\) −4.00000 + 6.92820i −0.147342 + 0.255204i
\(738\) 9.00000 + 15.5885i 0.331295 + 0.573819i
\(739\) −6.00000 −0.220714 −0.110357 0.993892i \(-0.535199\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(740\) −5.00000 3.46410i −0.183804 0.127343i
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) 21.0000 36.3731i 0.770415 1.33440i −0.166920 0.985970i \(-0.553382\pi\)
0.937336 0.348428i \(-0.113284\pi\)
\(744\) −7.50000 + 12.9904i −0.274963 + 0.476250i
\(745\) −2.00000 + 3.46410i −0.0732743 + 0.126915i
\(746\) 17.0000 0.622414
\(747\) −36.0000 + 62.3538i −1.31717 + 2.28141i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) −3.00000 −0.109545
\(751\) 11.0000 0.401396 0.200698 0.979653i \(-0.435679\pi\)
0.200698 + 0.979653i \(0.435679\pi\)
\(752\) 4.00000 + 6.92820i 0.145865 + 0.252646i
\(753\) −15.0000 + 25.9808i −0.546630 + 0.946792i
\(754\) 6.00000 0.218507
\(755\) −4.50000 7.79423i −0.163772 0.283661i
\(756\) 0 0
\(757\) 23.5000 + 40.7032i 0.854122 + 1.47938i 0.877457 + 0.479655i \(0.159238\pi\)
−0.0233351 + 0.999728i \(0.507428\pi\)
\(758\) −5.00000 + 8.66025i −0.181608 + 0.314555i
\(759\) −18.0000 + 31.1769i −0.653359 + 1.13165i
\(760\) −1.00000 1.73205i −0.0362738 0.0628281i
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 6.00000 + 10.3923i 0.217357 + 0.376473i
\(763\) 0 0
\(764\) 1.50000 2.59808i 0.0542681 0.0939951i
\(765\) −6.00000 10.3923i −0.216930 0.375735i
\(766\) 12.0000 0.433578
\(767\) 2.00000 0.0722158
\(768\) 1.50000 + 2.59808i 0.0541266 + 0.0937500i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 48.0000 1.72868
\(772\) −13.0000 + 22.5167i −0.467880 + 0.810392i
\(773\) 3.50000 6.06218i 0.125886 0.218041i −0.796193 0.605043i \(-0.793156\pi\)
0.922079 + 0.387002i \(0.126489\pi\)
\(774\) 21.0000 36.3731i 0.754829 1.30740i
\(775\) −2.50000 4.33013i −0.0898027 0.155543i
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) −16.0000 −0.573628
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 1.50000 2.59808i 0.0537086 0.0930261i
\(781\) 0 0
\(782\) 6.00000 10.3923i 0.214560 0.371628i
\(783\) −54.0000 −1.92980