Properties

Label 144.2.i.a.49.1
Level $144$
Weight $2$
Character 144.49
Analytic conductor $1.150$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 144.49
Dual form 144.2.i.a.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{3} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +4.00000 q^{19} +(1.50000 - 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} +(2.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(1.50000 + 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(4.50000 - 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(3.00000 - 5.19615i) q^{49} +10.3923i q^{51} -6.00000 q^{53} -9.00000 q^{55} +6.92820i q^{57} +(-1.50000 + 2.59808i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{63} +(1.50000 + 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-4.50000 - 2.59808i) q^{69} +12.0000 q^{71} -10.0000 q^{73} +(6.00000 - 3.46410i) q^{75} +(1.50000 - 2.59808i) q^{77} +(5.50000 + 9.52628i) q^{79} +9.00000 q^{81} +(-4.50000 - 7.79423i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(4.50000 - 2.59808i) q^{87} +6.00000 q^{89} -1.00000 q^{91} +(7.50000 + 4.33013i) q^{93} +(-6.00000 + 10.3923i) q^{95} +(-5.50000 - 9.52628i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{5} - q^{7} - 6q^{9} + O(q^{10}) \) \( 2q - 3q^{5} - q^{7} - 6q^{9} + 3q^{11} + q^{13} - 9q^{15} + 12q^{17} + 8q^{19} + 3q^{21} - 3q^{23} - 4q^{25} - 3q^{29} + 5q^{31} - 9q^{33} + 6q^{35} + 4q^{37} + 3q^{39} - 3q^{41} - q^{43} + 9q^{45} - 9q^{47} + 6q^{49} - 12q^{53} - 18q^{55} - 3q^{59} + 13q^{61} + 3q^{63} + 3q^{65} - 7q^{67} - 9q^{69} + 24q^{71} - 20q^{73} + 12q^{75} + 3q^{77} + 11q^{79} + 18q^{81} - 9q^{83} - 18q^{85} + 9q^{87} + 12q^{89} - 2q^{91} + 15q^{93} - 12q^{95} - 11q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 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
\(15\) −4.50000 2.59808i −1.16190 0.670820i
\(16\) 0 0
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 1.50000 0.866025i 0.327327 0.188982i
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 0 0
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 1.50000 + 0.866025i 0.240192 + 0.138675i
\(40\) 0 0
\(41\) −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
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 4.50000 7.79423i 0.670820 1.16190i
\(46\) 0 0
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0 0
\(51\) 10.3923i 1.45521i
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) 0 0
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 0 0
\(63\) 1.50000 + 2.59808i 0.188982 + 0.327327i
\(64\) 0 0
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) 0 0
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 0 0
\(69\) −4.50000 2.59808i −0.541736 0.312772i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 6.00000 3.46410i 0.692820 0.400000i
\(76\) 0 0
\(77\) 1.50000 2.59808i 0.170941 0.296078i
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0 0
\(85\) −9.00000 + 15.5885i −0.976187 + 1.69081i
\(86\) 0 0
\(87\) 4.50000 2.59808i 0.482451 0.278543i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 7.50000 + 4.33013i 0.777714 + 0.449013i
\(94\) 0 0
\(95\) −6.00000 + 10.3923i −0.615587 + 1.06623i
\(96\) 0 0
\(97\) −5.50000 9.52628i −0.558440 0.967247i −0.997627 0.0688512i \(-0.978067\pi\)
0.439187 0.898396i \(-0.355267\pi\)
\(98\) 0 0
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) 0 0
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) −3.50000 + 6.06218i −0.344865 + 0.597324i −0.985329 0.170664i \(-0.945409\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 5.19615i 0.507093i
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 3.46410i 0.328798i
\(112\) 0 0
\(113\) 4.50000 7.79423i 0.423324 0.733219i −0.572938 0.819599i \(-0.694196\pi\)
0.996262 + 0.0863794i \(0.0275297\pi\)
\(114\) 0 0
\(115\) −4.50000 7.79423i −0.419627 0.726816i
\(116\) 0 0
\(117\) −1.50000 + 2.59808i −0.138675 + 0.240192i
\(118\) 0 0
\(119\) −3.00000 5.19615i −0.275010 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −4.50000 2.59808i −0.405751 0.234261i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) 0 0
\(131\) 10.5000 18.1865i 0.917389 1.58896i 0.114024 0.993478i \(-0.463626\pi\)
0.803365 0.595487i \(-0.203041\pi\)
\(132\) 0 0
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 0 0
\(135\) 13.5000 + 7.79423i 1.16190 + 0.670820i
\(136\) 0 0
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 0 0
\(139\) 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i \(-0.765320\pi\)
0.952355 + 0.304991i \(0.0986536\pi\)
\(140\) 0 0
\(141\) 13.5000 7.79423i 1.13691 0.656392i
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) 9.00000 + 5.19615i 0.742307 + 0.428571i
\(148\) 0 0
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 0 0
\(151\) −6.50000 11.2583i −0.528962 0.916190i −0.999430 0.0337724i \(-0.989248\pi\)
0.470467 0.882418i \(-0.344085\pi\)
\(152\) 0 0
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) 7.50000 + 12.9904i 0.602414 + 1.04341i
\(156\) 0 0
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 0 0
\(159\) 10.3923i 0.824163i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) 0 0
\(165\) 15.5885i 1.21356i
\(166\) 0 0
\(167\) 4.50000 7.79423i 0.348220 0.603136i −0.637713 0.770274i \(-0.720119\pi\)
0.985933 + 0.167139i \(0.0534527\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) −12.0000 −0.917663
\(172\) 0 0
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) 0 0
\(177\) −4.50000 2.59808i −0.338241 0.195283i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −19.5000 + 11.2583i −1.44148 + 0.832240i
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) −4.50000 + 2.59808i −0.327327 + 0.188982i
\(190\) 0 0
\(191\) 7.50000 + 12.9904i 0.542681 + 0.939951i 0.998749 + 0.0500060i \(0.0159241\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 0 0
\(195\) −4.50000 + 2.59808i −0.322252 + 0.186052i
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) −10.5000 6.06218i −0.740613 0.427593i
\(202\) 0 0
\(203\) −1.50000 + 2.59808i −0.105279 + 0.182349i
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 0 0
\(207\) 4.50000 7.79423i 0.312772 0.541736i
\(208\) 0 0
\(209\) 6.00000 + 10.3923i 0.415029 + 0.718851i
\(210\) 0 0
\(211\) 8.50000 14.7224i 0.585164 1.01353i −0.409691 0.912224i \(-0.634363\pi\)
0.994855 0.101310i \(-0.0323033\pi\)
\(212\) 0 0
\(213\) 20.7846i 1.42414i
\(214\) 0 0
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) 0 0
\(219\) 17.3205i 1.17041i
\(220\) 0 0
\(221\) 3.00000 5.19615i 0.201802 0.349531i
\(222\) 0 0
\(223\) −0.500000 0.866025i −0.0334825 0.0579934i 0.848799 0.528716i \(-0.177326\pi\)
−0.882281 + 0.470723i \(0.843993\pi\)
\(224\) 0 0
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) 0 0
\(227\) 13.5000 + 23.3827i 0.896026 + 1.55196i 0.832529 + 0.553981i \(0.186892\pi\)
0.0634974 + 0.997982i \(0.479775\pi\)
\(228\) 0 0
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 0 0
\(231\) 4.50000 + 2.59808i 0.296078 + 0.170941i
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 27.0000 1.76129
\(236\) 0 0
\(237\) −16.5000 + 9.52628i −1.07179 + 0.618798i
\(238\) 0 0
\(239\) −13.5000 + 23.3827i −0.873242 + 1.51250i −0.0146191 + 0.999893i \(0.504654\pi\)
−0.858623 + 0.512607i \(0.828680\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) 0 0
\(247\) 2.00000 3.46410i 0.127257 0.220416i
\(248\) 0 0
\(249\) 13.5000 7.79423i 0.855528 0.493939i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) −27.0000 15.5885i −1.69081 0.976187i
\(256\) 0 0
\(257\) 4.50000 7.79423i 0.280702 0.486191i −0.690856 0.722993i \(-0.742766\pi\)
0.971558 + 0.236802i \(0.0760993\pi\)
\(258\) 0 0
\(259\) −1.00000 1.73205i −0.0621370 0.107624i
\(260\) 0 0
\(261\) 4.50000 + 7.79423i 0.278543 + 0.482451i
\(262\) 0 0
\(263\) −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i \(-0.942499\pi\)
0.336270 0.941766i \(-0.390834\pi\)
\(264\) 0 0
\(265\) 9.00000 15.5885i 0.552866 0.957591i
\(266\) 0 0
\(267\) 10.3923i 0.635999i
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 1.73205i 0.104828i
\(274\) 0 0
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 0 0
\(279\) −7.50000 + 12.9904i −0.449013 + 0.777714i
\(280\) 0 0
\(281\) −1.50000 2.59808i −0.0894825 0.154988i 0.817810 0.575488i \(-0.195188\pi\)
−0.907293 + 0.420500i \(0.861855\pi\)
\(282\) 0 0
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) 0 0
\(285\) −18.0000 10.3923i −1.06623 0.615587i
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 16.5000 9.52628i 0.967247 0.558440i
\(292\) 0 0
\(293\) 10.5000 18.1865i 0.613417 1.06247i −0.377244 0.926114i \(-0.623128\pi\)
0.990660 0.136355i \(-0.0435386\pi\)
\(294\) 0 0
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) 0 0
\(297\) 13.5000 7.79423i 0.783349 0.452267i
\(298\) 0 0
\(299\) 1.50000 + 2.59808i 0.0867472 + 0.150251i
\(300\) 0 0
\(301\) −0.500000 + 0.866025i −0.0288195 + 0.0499169i
\(302\) 0 0
\(303\) 22.5000 12.9904i 1.29259 0.746278i
\(304\) 0 0
\(305\) −39.0000 −2.23313
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −10.5000 6.06218i −0.597324 0.344865i
\(310\) 0 0
\(311\) 10.5000 18.1865i 0.595400 1.03126i −0.398090 0.917346i \(-0.630327\pi\)
0.993490 0.113917i \(-0.0363399\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 0 0
\(315\) −9.00000 −0.507093
\(316\) 0 0
\(317\) 10.5000 + 18.1865i 0.589739 + 1.02146i 0.994266 + 0.106932i \(0.0341026\pi\)
−0.404528 + 0.914526i \(0.632564\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) 0 0
\(327\) 3.46410i 0.191565i
\(328\) 0 0
\(329\) −4.50000 + 7.79423i −0.248093 + 0.429710i
\(330\) 0 0
\(331\) 5.50000 + 9.52628i 0.302307 + 0.523612i 0.976658 0.214799i \(-0.0689098\pi\)
−0.674351 + 0.738411i \(0.735576\pi\)
\(332\) 0 0
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) −10.5000 18.1865i −0.573676 0.993636i
\(336\) 0 0
\(337\) −11.5000 + 19.9186i −0.626445 + 1.08503i 0.361815 + 0.932250i \(0.382157\pi\)
−0.988260 + 0.152784i \(0.951176\pi\)
\(338\) 0 0
\(339\) 13.5000 + 7.79423i 0.733219 + 0.423324i
\(340\) 0 0
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 13.5000 7.79423i 0.726816 0.419627i
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) 0.500000 + 0.866025i 0.0267644 + 0.0463573i 0.879097 0.476642i \(-0.158146\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(350\) 0 0
\(351\) −4.50000 2.59808i −0.240192 0.138675i
\(352\) 0 0
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) −18.0000 + 31.1769i −0.955341 + 1.65470i
\(356\) 0 0
\(357\) 9.00000 5.19615i 0.476331 0.275010i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 3.00000 + 1.73205i 0.157459 + 0.0909091i
\(364\) 0 0
\(365\) 15.0000 25.9808i 0.785136 1.35990i
\(366\) 0 0
\(367\) −6.50000 11.2583i −0.339297 0.587680i 0.645003 0.764180i \(-0.276856\pi\)
−0.984301 + 0.176500i \(0.943523\pi\)
\(368\) 0 0
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) 3.00000 + 5.19615i 0.155752 + 0.269771i
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) 0 0
\(375\) 5.19615i 0.268328i
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 27.7128i 1.41977i
\(382\) 0 0
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) 0 0
\(385\) 4.50000 + 7.79423i 0.229341 + 0.397231i
\(386\) 0 0
\(387\) 1.50000 + 2.59808i 0.0762493 + 0.132068i
\(388\) 0 0
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) 0 0
\(393\) 31.5000 + 18.1865i 1.58896 + 0.917389i
\(394\) 0 0
\(395\) −33.0000 −1.66041
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 6.00000 3.46410i 0.300376 0.173422i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −2.50000 4.33013i −0.124534 0.215699i
\(404\) 0 0
\(405\) −13.5000 + 23.3827i −0.670820 + 1.16190i
\(406\) 0 0
\(407\) 3.00000 + 5.19615i 0.148704 + 0.257564i
\(408\) 0 0
\(409\) −11.5000 + 19.9186i −0.568638 + 0.984911i 0.428063 + 0.903749i \(0.359196\pi\)
−0.996701 + 0.0811615i \(0.974137\pi\)
\(410\) 0 0
\(411\) 4.50000 2.59808i 0.221969 0.128154i
\(412\) 0 0
\(413\) 3.00000 0.147620
\(414\) 0 0
\(415\) 27.0000 1.32538
\(416\) 0 0
\(417\) 7.50000 + 4.33013i 0.367277 + 0.212047i
\(418\) 0 0
\(419\) 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i \(-0.762780\pi\)
0.954759 + 0.297382i \(0.0961133\pi\)
\(420\) 0 0
\(421\) −17.5000 30.3109i −0.852898 1.47726i −0.878582 0.477592i \(-0.841510\pi\)
0.0256838 0.999670i \(-0.491824\pi\)
\(422\) 0 0
\(423\) 13.5000 + 23.3827i 0.656392 + 1.13691i
\(424\) 0 0
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) 0 0
\(427\) 6.50000 11.2583i 0.314557 0.544829i
\(428\) 0 0
\(429\) 5.19615i 0.250873i
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 15.5885i 0.747409i
\(436\) 0 0
\(437\) −6.00000 + 10.3923i −0.287019 + 0.497131i
\(438\) 0 0
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0 0
\(441\) −9.00000 + 15.5885i −0.428571 + 0.742307i
\(442\) 0 0
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 0 0
\(447\) −22.5000 12.9904i −1.06421 0.614424i
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −9.00000 −0.423793
\(452\) 0 0
\(453\) 19.5000 11.2583i 0.916190 0.528962i
\(454\) 0 0
\(455\) 1.50000 2.59808i 0.0703211 0.121800i
\(456\) 0 0
\(457\) 18.5000 + 32.0429i 0.865393 + 1.49891i 0.866656 + 0.498906i \(0.166265\pi\)
−0.00126243 + 0.999999i \(0.500402\pi\)
\(458\) 0 0
\(459\) 31.1769i 1.45521i
\(460\) 0 0
\(461\) −1.50000 2.59808i −0.0698620 0.121004i 0.828978 0.559281i \(-0.188923\pi\)
−0.898840 + 0.438276i \(0.855589\pi\)
\(462\) 0 0
\(463\) −9.50000 + 16.4545i −0.441502 + 0.764705i −0.997801 0.0662777i \(-0.978888\pi\)
0.556299 + 0.830982i \(0.312221\pi\)
\(464\) 0 0
\(465\) −22.5000 + 12.9904i −1.04341 + 0.602414i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) 0 0
\(471\) 19.5000 + 11.2583i 0.898513 + 0.518756i
\(472\) 0 0
\(473\) 1.50000 2.59808i 0.0689701 0.119460i
\(474\) 0 0
\(475\) −8.00000 13.8564i −0.367065 0.635776i
\(476\) 0 0
\(477\) 18.0000 0.824163
\(478\) 0 0
\(479\) 13.5000 + 23.3827i 0.616831 + 1.06838i 0.990060 + 0.140643i \(0.0449170\pi\)
−0.373230 + 0.927739i \(0.621750\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) 0 0
\(483\) 5.19615i 0.236433i
\(484\) 0 0
\(485\) 33.0000 1.49845
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 0 0
\(489\) 34.6410i 1.56652i
\(490\) 0 0
\(491\) −1.50000 + 2.59808i −0.0676941 + 0.117250i −0.897886 0.440228i \(-0.854898\pi\)
0.830192 + 0.557478i \(0.188231\pi\)
\(492\) 0 0
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 0 0
\(495\) 27.0000 1.21356
\(496\) 0 0
\(497\) −6.00000 10.3923i −0.269137 0.466159i
\(498\) 0 0
\(499\) 2.50000 4.33013i 0.111915 0.193843i −0.804627 0.593780i \(-0.797635\pi\)
0.916542 + 0.399937i \(0.130968\pi\)
\(500\) 0 0
\(501\) 13.5000 + 7.79423i 0.603136 + 0.348220i
\(502\) 0 0
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) −18.0000 + 10.3923i −0.799408 + 0.461538i
\(508\) 0 0
\(509\) −19.5000 + 33.7750i −0.864322 + 1.49705i 0.00339621 + 0.999994i \(0.498919\pi\)
−0.867719 + 0.497056i \(0.834414\pi\)
\(510\) 0 0
\(511\) 5.00000 + 8.66025i 0.221187 + 0.383107i
\(512\) 0 0
\(513\) 20.7846i 0.917663i
\(514\) 0 0
\(515\) −10.5000 18.1865i −0.462685 0.801394i
\(516\) 0 0
\(517\) 13.5000 23.3827i 0.593729 1.02837i
\(518\) 0 0
\(519\) −13.5000 + 7.79423i −0.592584 + 0.342129i
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 0 0
\(525\) −6.00000 3.46410i −0.261861 0.151186i
\(526\) 0 0
\(527\) 15.0000 25.9808i 0.653410 1.13174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 4.50000 7.79423i 0.195283 0.338241i
\(532\) 0 0
\(533\) 1.50000 + 2.59808i 0.0649722 + 0.112535i
\(534\) 0 0
\(535\) 18.0000 31.1769i 0.778208 1.34790i
\(536\) 0 0
\(537\) 20.7846i 0.896922i
\(538\) 0 0
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 0 0
\(543\) 3.46410i 0.148659i
\(544\) 0 0
\(545\) −3.00000 + 5.19615i −0.128506 + 0.222579i
\(546\) 0 0
\(547\) −6.50000 11.2583i −0.277920 0.481371i 0.692948 0.720988i \(-0.256312\pi\)
−0.970868 + 0.239616i \(0.922978\pi\)
\(548\) 0 0
\(549\) −19.5000 33.7750i −0.832240 1.44148i
\(550\) 0 0
\(551\) −6.00000 10.3923i −0.255609 0.442727i
\(552\) 0 0
\(553\) 5.50000 9.52628i 0.233884 0.405099i
\(554\) 0 0
\(555\) −9.00000 5.19615i −0.382029 0.220564i
\(556\) 0 0
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) −27.0000 + 15.5885i −1.13994 + 0.658145i
\(562\) 0 0
\(563\) 4.50000 7.79423i 0.189652 0.328488i −0.755482 0.655169i \(-0.772597\pi\)
0.945134 + 0.326682i \(0.105931\pi\)
\(564\) 0 0
\(565\) 13.5000 + 23.3827i 0.567949 + 0.983717i
\(566\) 0 0
\(567\) −4.50000 7.79423i −0.188982 0.327327i
\(568\) 0 0
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) −15.5000 + 26.8468i −0.648655 + 1.12350i 0.334790 + 0.942293i \(0.391335\pi\)
−0.983444 + 0.181210i \(0.941999\pi\)
\(572\) 0 0
\(573\) −22.5000 + 12.9904i −0.939951 + 0.542681i
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) −16.5000 9.52628i −0.685717 0.395899i
\(580\) 0 0
\(581\) −4.50000 + 7.79423i −0.186691 + 0.323359i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 0 0
\(585\) −4.50000 7.79423i −0.186052 0.322252i
\(586\) 0 0
\(587\) 7.50000 + 12.9904i 0.309558 + 0.536170i 0.978266 0.207355i \(-0.0664855\pi\)
−0.668708 + 0.743525i \(0.733152\pi\)
\(588\) 0 0
\(589\) 10.0000 17.3205i 0.412043 0.713679i
\(590\) 0 0
\(591\) 10.3923i 0.427482i
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 18.0000 0.737928
\(596\) 0 0
\(597\) 6.92820i 0.283552i
\(598\) 0 0
\(599\) −19.5000 + 33.7750i −0.796748 + 1.38001i 0.124975 + 0.992160i \(0.460115\pi\)
−0.921723 + 0.387849i \(0.873218\pi\)
\(600\) 0 0
\(601\) −17.5000 30.3109i −0.713840 1.23641i −0.963405 0.268049i \(-0.913621\pi\)
0.249565 0.968358i \(-0.419712\pi\)
\(602\) 0 0
\(603\) 10.5000 18.1865i 0.427593 0.740613i
\(604\) 0 0
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) 0 0
\(607\) 20.5000 35.5070i 0.832069 1.44119i −0.0643251 0.997929i \(-0.520489\pi\)
0.896394 0.443257i \(-0.146177\pi\)
\(608\) 0 0
\(609\) −4.50000 2.59808i −0.182349 0.105279i
\(610\) 0 0
\(611\) −9.00000 −0.364101
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 13.5000 7.79423i 0.544373 0.314294i
\(616\) 0 0
\(617\) −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(618\) 0 0
\(619\) −6.50000 11.2583i −0.261257 0.452510i 0.705319 0.708890i \(-0.250804\pi\)
−0.966576 + 0.256379i \(0.917470\pi\)
\(620\) 0 0
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 0 0
\(623\) −3.00000 5.19615i −0.120192 0.208179i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) −18.0000 + 10.3923i −0.718851 + 0.415029i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 25.5000 + 14.7224i 1.01353 + 0.585164i
\(634\) 0 0
\(635\) −24.0000 + 41.5692i −0.952411 + 1.64962i
\(636\) 0 0
\(637\) −3.00000 5.19615i −0.118864 0.205879i
\(638\) 0 0
\(639\) −36.0000 −1.42414
\(640\) 0 0
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 0 0
\(643\) 20.5000 35.5070i 0.808441 1.40026i −0.105502 0.994419i \(-0.533645\pi\)
0.913943 0.405842i \(-0.133022\pi\)
\(644\) 0 0
\(645\) 5.19615i 0.204598i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 8.66025i 0.339422i
\(652\) 0 0
\(653\) 10.5000 18.1865i 0.410897 0.711694i −0.584091 0.811688i \(-0.698549\pi\)
0.994988 + 0.0999939i \(0.0318823\pi\)
\(654\) 0 0
\(655\) 31.5000 + 54.5596i 1.23081 + 2.13182i
\(656\) 0 0
\(657\) 30.0000 1.17041
\(658\) 0 0
\(659\) −10.5000 18.1865i −0.409022 0.708447i 0.585758 0.810486i \(-0.300797\pi\)
−0.994780 + 0.102039i \(0.967463\pi\)
\(660\) 0 0
\(661\) −5.50000 + 9.52628i −0.213925 + 0.370529i −0.952940 0.303160i \(-0.901958\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 0 0
\(663\) 9.00000 + 5.19615i 0.349531 + 0.201802i
\(664\) 0 0
\(665\) 12.0000 0.465340
\(666\) 0 0
\(667\) 9.00000 0.348481
\(668\) 0 0
\(669\) 1.50000 0.866025i 0.0579934 0.0334825i
\(670\) 0 0
\(671\) −19.5000 + 33.7750i −0.752789 + 1.30387i
\(672\) 0 0
\(673\) −5.50000 9.52628i −0.212009 0.367211i 0.740334 0.672239i \(-0.234667\pi\)
−0.952343 + 0.305028i \(0.901334\pi\)
\(674\) 0 0
\(675\) −18.0000 + 10.3923i −0.692820 + 0.400000i
\(676\) 0 0
\(677\) −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i \(-0.259740\pi\)
−0.973392 + 0.229147i \(0.926406\pi\)
\(678\) 0 0
\(679\) −5.50000 + 9.52628i −0.211071 + 0.365585i
\(680\) 0 0
\(681\) −40.5000 + 23.3827i −1.55196 + 0.896026i
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) 19.5000 + 11.2583i 0.743971 + 0.429532i
\(688\) 0 0
\(689\) −3.00000 + 5.19615i −0.114291 + 0.197958i
\(690\) 0 0
\(691\) −0.500000 0.866025i −0.0190209 0.0329452i 0.856358 0.516382i \(-0.172722\pi\)
−0.875379 + 0.483437i \(0.839388\pi\)
\(692\) 0 0
\(693\) −4.50000 + 7.79423i −0.170941 + 0.296078i
\(694\) 0 0
\(695\) 7.50000 + 12.9904i 0.284491 + 0.492753i
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) 0 0
\(699\) 10.3923i 0.393073i
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 46.7654i 1.76129i
\(706\) 0 0
\(707\) −7.50000 + 12.9904i −0.282067 + 0.488554i
\(708\) 0 0
\(709\) 12.5000 + 21.6506i 0.469447 + 0.813107i 0.999390 0.0349269i \(-0.0111198\pi\)
−0.529943 + 0.848034i \(0.677787\pi\)
\(710\) 0 0
\(711\) −16.5000 28.5788i −0.618798 1.07179i
\(712\) 0 0
\(713\) 7.50000 + 12.9904i 0.280877 + 0.486494i
\(714\) 0 0
\(715\) −4.50000 + 7.79423i −0.168290 + 0.291488i
\(716\) 0 0
\(717\) −40.5000 23.3827i −1.51250 0.873242i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 7.00000 0.260694
\(722\) 0 0
\(723\) −1.50000 + 0.866025i −0.0557856 + 0.0322078i
\(724\) 0 0
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 0 0
\(727\) −18.5000 32.0429i −0.686127 1.18841i −0.973081 0.230463i \(-0.925976\pi\)
0.286954 0.957944i \(-0.407357\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −3.00000 5.19615i −0.110959 0.192187i
\(732\) 0 0
\(733\) −11.5000 + 19.9186i −0.424762 + 0.735710i −0.996398 0.0847976i \(-0.972976\pi\)
0.571636 + 0.820507i \(0.306309\pi\)
\(734\) 0 0
\(735\) −27.0000 + 15.5885i −0.995910 + 0.574989i
\(736\) 0 0
\(737\) −21.0000 −0.773545
\(738\) 0 0
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 0 0
\(741\) 6.00000 + 3.46410i 0.220416 + 0.127257i
\(742\) 0 0
\(743\) 4.50000 7.79423i 0.165089 0.285943i −0.771598 0.636111i \(-0.780542\pi\)
0.936687 + 0.350168i \(0.113876\pi\)
\(744\) 0 0
\(745\) −22.5000 38.9711i −0.824336 1.42779i
\(746\) 0 0
\(747\) 13.5000 + 23.3827i 0.493939 + 0.855528i
\(748\) 0 0
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 0 0
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) 0 0
\(753\) 20.7846i 0.757433i
\(754\) 0 0
\(755\) 39.0000 1.41936
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 15.5885i 0.565825i
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) −1.00000 1.73205i −0.0362024 0.0627044i
\(764\) 0 0
\(765\) 27.0000 46.7654i 0.976187 1.69081i
\(766\) 0 0
\(767\) 1.50000 + 2.59808i 0.0541619 + 0.0938111i
\(768\) 0 0
\(769\) 0.500000 0.866025i 0.0180305 0.0312297i −0.856869 0.515534i \(-0.827594\pi\)
0.874900 + 0.484304i \(0.160927\pi\)
\(770\) 0 0
\(771\) 13.5000 + 7.79423i 0.486191 + 0.280702i
\(772\) 0 0
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) −20.0000 −0.718421
\(776\) 0 0
\(777\) 3.00000 1.73205i 0.107624 0.0621370i
\(778\) 0 0
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 18.0000 + 31.1769i 0.644091 + 1.11560i
\(782\) 0 0
\(783\) −13.5000 + 7.79423i −0.482451 + 0.278543i
\(784\) 0 0
\(785\) 19.5000 + 33.7750i 0.695985 + 1.20548i
\(786\) 0 0
\(787\) −21.5000 + 37.2391i −0.766392 + 1.32743i 0.173115 + 0.984902i \(0.444617\pi\)
−0.939507 + 0.342529i \(0.888717\pi\)
\(788\) 0 0
\(789\) 31.5000 18.1865i 1.12143 0.647458i
\(790\) 0 0
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 13.0000 0.461644
\(794\) 0 0
\(795\) 27.0000 + 15.5885i 0.957591 + 0.552866i
\(796\)