Properties

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

Related objects

Downloads

Learn more

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 72)
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.b.97.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{9} +(2.50000 + 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.50000 - 0.866025i) q^{15} -2.00000 q^{17} +4.00000 q^{19} +(-4.50000 + 2.59808i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.19615i q^{27} +(4.50000 + 7.79423i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(7.50000 - 4.33013i) q^{33} -3.00000 q^{35} -6.00000 q^{37} +(-7.50000 - 4.33013i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(-1.00000 + 1.73205i) q^{49} +3.46410i q^{51} +2.00000 q^{53} +5.00000 q^{55} -6.92820i q^{57} +(5.50000 - 9.52628i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-2.50000 - 4.33013i) q^{65} +(-0.500000 + 0.866025i) q^{67} +(1.50000 + 0.866025i) q^{69} -4.00000 q^{71} -2.00000 q^{73} +(6.00000 - 3.46410i) q^{75} +(7.50000 - 12.9904i) q^{77} +(0.500000 + 0.866025i) q^{79} +9.00000 q^{81} +(0.500000 + 0.866025i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(13.5000 - 7.79423i) q^{87} -18.0000 q^{89} -15.0000 q^{91} +(1.50000 + 0.866025i) q^{93} +(2.00000 - 3.46410i) q^{95} +(6.50000 + 11.2583i) q^{97} +(-7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{5} - 3q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + q^{5} - 3q^{7} - 6q^{9} + 5q^{11} + 5q^{13} - 3q^{15} - 4q^{17} + 8q^{19} - 9q^{21} - q^{23} + 4q^{25} + 9q^{29} - q^{31} + 15q^{33} - 6q^{35} - 12q^{37} - 15q^{39} - 3q^{41} + q^{43} - 3q^{45} - 3q^{47} - 2q^{49} + 4q^{53} + 10q^{55} + 11q^{59} - 7q^{61} + 9q^{63} - 5q^{65} - q^{67} + 3q^{69} - 8q^{71} - 4q^{73} + 12q^{75} + 15q^{77} + q^{79} + 18q^{81} + q^{83} - 2q^{85} + 27q^{87} - 36q^{89} - 30q^{91} + 3q^{93} + 4q^{95} + 13q^{97} - 15q^{99} + O(q^{100}) \)

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
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −4.50000 + 2.59808i −0.981981 + 0.566947i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i \(-0.861957\pi\)
0.817625 + 0.575751i \(0.195290\pi\)
\(32\) 0 0
\(33\) 7.50000 4.33013i 1.30558 0.753778i
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) −7.50000 4.33013i −1.20096 0.693375i
\(40\) 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 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 0 0
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 0 0
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) 3.46410i 0.485071i
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) 0 0
\(59\) 5.50000 9.52628i 0.716039 1.24022i −0.246518 0.969138i \(-0.579287\pi\)
0.962557 0.271078i \(-0.0873801\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) 4.50000 + 7.79423i 0.566947 + 0.981981i
\(64\) 0 0
\(65\) −2.50000 4.33013i −0.310087 0.537086i
\(66\) 0 0
\(67\) −0.500000 + 0.866025i −0.0610847 + 0.105802i −0.894951 0.446165i \(-0.852789\pi\)
0.833866 + 0.551967i \(0.186123\pi\)
\(68\) 0 0
\(69\) 1.50000 + 0.866025i 0.180579 + 0.104257i
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 6.00000 3.46410i 0.692820 0.400000i
\(76\) 0 0
\(77\) 7.50000 12.9904i 0.854704 1.48039i
\(78\) 0 0
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0.500000 + 0.866025i 0.0548821 + 0.0950586i 0.892161 0.451717i \(-0.149188\pi\)
−0.837279 + 0.546776i \(0.815855\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 0 0
\(87\) 13.5000 7.79423i 1.44735 0.835629i
\(88\) 0 0
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) −15.0000 −1.57243
\(92\) 0 0
\(93\) 1.50000 + 0.866025i 0.155543 + 0.0898027i
\(94\) 0 0
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) 0 0
\(97\) 6.50000 + 11.2583i 0.659975 + 1.14311i 0.980622 + 0.195911i \(0.0627665\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(98\) 0 0
\(99\) −7.50000 12.9904i −0.753778 1.30558i
\(100\) 0 0
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i \(-0.912559\pi\)
0.716173 + 0.697923i \(0.245892\pi\)
\(104\) 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
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 10.3923i 0.986394i
\(112\) 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
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) −7.50000 + 12.9904i −0.693375 + 1.20096i
\(118\) 0 0
\(119\) 3.00000 + 5.19615i 0.275010 + 0.476331i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) 4.50000 + 2.59808i 0.405751 + 0.234261i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) 0 0
\(131\) −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i \(-0.903426\pi\)
0.735901 + 0.677089i \(0.236759\pi\)
\(132\) 0 0
\(133\) −6.00000 10.3923i −0.520266 0.901127i
\(134\) 0 0
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) 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
\(139\) 1.50000 2.59808i 0.127228 0.220366i −0.795373 0.606120i \(-0.792725\pi\)
0.922602 + 0.385754i \(0.126059\pi\)
\(140\) 0 0
\(141\) −4.50000 + 2.59808i −0.378968 + 0.218797i
\(142\) 0 0
\(143\) 25.0000 2.09061
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) 3.00000 + 1.73205i 0.247436 + 0.142857i
\(148\) 0 0
\(149\) −9.50000 + 16.4545i −0.778270 + 1.34800i 0.154668 + 0.987967i \(0.450569\pi\)
−0.932938 + 0.360037i \(0.882764\pi\)
\(150\) 0 0
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0.500000 + 0.866025i 0.0401610 + 0.0695608i
\(156\) 0 0
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) 0 0
\(159\) 3.46410i 0.274721i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) 8.66025i 0.674200i
\(166\) 0 0
\(167\) −10.5000 + 18.1865i −0.812514 + 1.40732i 0.0985846 + 0.995129i \(0.468568\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −12.0000 −0.917663
\(172\) 0 0
\(173\) −1.50000 2.59808i −0.114043 0.197528i 0.803354 0.595502i \(-0.203047\pi\)
−0.917397 + 0.397974i \(0.869713\pi\)
\(174\) 0 0
\(175\) 6.00000 10.3923i 0.453557 0.785584i
\(176\) 0 0
\(177\) −16.5000 9.52628i −1.24022 0.716039i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) −10.5000 + 6.06218i −0.776182 + 0.448129i
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) −5.00000 8.66025i −0.365636 0.633300i
\(188\) 0 0
\(189\) 13.5000 7.79423i 0.981981 0.566947i
\(190\) 0 0
\(191\) −13.5000 23.3827i −0.976826 1.69191i −0.673774 0.738938i \(-0.735328\pi\)
−0.303052 0.952974i \(-0.598006\pi\)
\(192\) 0 0
\(193\) 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i \(-0.678351\pi\)
0.999326 + 0.0366998i \(0.0116845\pi\)
\(194\) 0 0
\(195\) −7.50000 + 4.33013i −0.537086 + 0.310087i
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 1.50000 + 0.866025i 0.105802 + 0.0610847i
\(202\) 0 0
\(203\) 13.5000 23.3827i 0.947514 1.64114i
\(204\) 0 0
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) 0 0
\(207\) 1.50000 2.59808i 0.104257 0.180579i
\(208\) 0 0
\(209\) 10.0000 + 17.3205i 0.691714 + 1.19808i
\(210\) 0 0
\(211\) 3.50000 6.06218i 0.240950 0.417338i −0.720035 0.693938i \(-0.755874\pi\)
0.960985 + 0.276600i \(0.0892077\pi\)
\(212\) 0 0
\(213\) 6.92820i 0.474713i
\(214\) 0 0
\(215\) 1.00000 0.0681994
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) 0 0
\(219\) 3.46410i 0.234082i
\(220\) 0 0
\(221\) −5.00000 + 8.66025i −0.336336 + 0.582552i
\(222\) 0 0
\(223\) −5.50000 9.52628i −0.368307 0.637927i 0.620994 0.783815i \(-0.286729\pi\)
−0.989301 + 0.145889i \(0.953396\pi\)
\(224\) 0 0
\(225\) −6.00000 10.3923i −0.400000 0.692820i
\(226\) 0 0
\(227\) 10.5000 + 18.1865i 0.696909 + 1.20708i 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) 0 0
\(229\) 8.50000 14.7224i 0.561696 0.972886i −0.435653 0.900115i \(-0.643482\pi\)
0.997349 0.0727709i \(-0.0231842\pi\)
\(230\) 0 0
\(231\) −22.5000 12.9904i −1.48039 0.854704i
\(232\) 0 0
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) 0 0
\(237\) 1.50000 0.866025i 0.0974355 0.0562544i
\(238\) 0 0
\(239\) −8.50000 + 14.7224i −0.549819 + 0.952315i 0.448467 + 0.893799i \(0.351970\pi\)
−0.998286 + 0.0585157i \(0.981363\pi\)
\(240\) 0 0
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 0 0
\(247\) 10.0000 17.3205i 0.636285 1.10208i
\(248\) 0 0
\(249\) 1.50000 0.866025i 0.0950586 0.0548821i
\(250\) 0 0
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) 0 0
\(255\) 3.00000 + 1.73205i 0.187867 + 0.108465i
\(256\) 0 0
\(257\) −3.50000 + 6.06218i −0.218324 + 0.378148i −0.954296 0.298864i \(-0.903392\pi\)
0.735972 + 0.677012i \(0.236726\pi\)
\(258\) 0 0
\(259\) 9.00000 + 15.5885i 0.559233 + 0.968620i
\(260\) 0 0
\(261\) −13.5000 23.3827i −0.835629 1.44735i
\(262\) 0 0
\(263\) −3.50000 6.06218i −0.215819 0.373810i 0.737706 0.675122i \(-0.235909\pi\)
−0.953526 + 0.301312i \(0.902576\pi\)
\(264\) 0 0
\(265\) 1.00000 1.73205i 0.0614295 0.106399i
\(266\) 0 0
\(267\) 31.1769i 1.90800i
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 25.9808i 1.57243i
\(274\) 0 0
\(275\) −10.0000 + 17.3205i −0.603023 + 1.04447i
\(276\) 0 0
\(277\) 14.5000 + 25.1147i 0.871221 + 1.50900i 0.860735 + 0.509053i \(0.170004\pi\)
0.0104855 + 0.999945i \(0.496662\pi\)
\(278\) 0 0
\(279\) 1.50000 2.59808i 0.0898027 0.155543i
\(280\) 0 0
\(281\) −9.50000 16.4545i −0.566722 0.981592i −0.996887 0.0788417i \(-0.974878\pi\)
0.430165 0.902750i \(-0.358455\pi\)
\(282\) 0 0
\(283\) −6.50000 + 11.2583i −0.386385 + 0.669238i −0.991960 0.126550i \(-0.959610\pi\)
0.605575 + 0.795788i \(0.292943\pi\)
\(284\) 0 0
\(285\) −6.00000 3.46410i −0.355409 0.205196i
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 19.5000 11.2583i 1.14311 0.659975i
\(292\) 0 0
\(293\) 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) 0 0
\(295\) −5.50000 9.52628i −0.320222 0.554641i
\(296\) 0 0
\(297\) −22.5000 + 12.9904i −1.30558 + 0.753778i
\(298\) 0 0
\(299\) 2.50000 + 4.33013i 0.144579 + 0.250418i
\(300\) 0 0
\(301\) 1.50000 2.59808i 0.0864586 0.149751i
\(302\) 0 0
\(303\) −4.50000 + 2.59808i −0.258518 + 0.149256i
\(304\) 0 0
\(305\) −7.00000 −0.400819
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 7.50000 + 4.33013i 0.426660 + 0.246332i
\(310\) 0 0
\(311\) −4.50000 + 7.79423i −0.255172 + 0.441970i −0.964942 0.262463i \(-0.915465\pi\)
0.709771 + 0.704433i \(0.248799\pi\)
\(312\) 0 0
\(313\) 4.50000 + 7.79423i 0.254355 + 0.440556i 0.964720 0.263278i \(-0.0848035\pi\)
−0.710365 + 0.703833i \(0.751470\pi\)
\(314\) 0 0
\(315\) 9.00000 0.507093
\(316\) 0 0
\(317\) −7.50000 12.9904i −0.421242 0.729612i 0.574819 0.818280i \(-0.305072\pi\)
−0.996061 + 0.0886679i \(0.971739\pi\)
\(318\) 0 0
\(319\) −22.5000 + 38.9711i −1.25976 + 2.18197i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 0 0
\(325\) 20.0000 1.10940
\(326\) 0 0
\(327\) 17.3205i 0.957826i
\(328\) 0 0
\(329\) −4.50000 + 7.79423i −0.248093 + 0.429710i
\(330\) 0 0
\(331\) −9.50000 16.4545i −0.522167 0.904420i −0.999667 0.0257885i \(-0.991790\pi\)
0.477500 0.878632i \(-0.341543\pi\)
\(332\) 0 0
\(333\) 18.0000 0.986394
\(334\) 0 0
\(335\) 0.500000 + 0.866025i 0.0273179 + 0.0473160i
\(336\) 0 0
\(337\) 4.50000 7.79423i 0.245131 0.424579i −0.717038 0.697034i \(-0.754502\pi\)
0.962168 + 0.272456i \(0.0878358\pi\)
\(338\) 0 0
\(339\) −13.5000 7.79423i −0.733219 0.423324i
\(340\) 0 0
\(341\) −5.00000 −0.270765
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 1.50000 0.866025i 0.0807573 0.0466252i
\(346\) 0 0
\(347\) −4.50000 + 7.79423i −0.241573 + 0.418416i −0.961162 0.275983i \(-0.910997\pi\)
0.719590 + 0.694399i \(0.244330\pi\)
\(348\) 0 0
\(349\) 10.5000 + 18.1865i 0.562052 + 0.973503i 0.997317 + 0.0732005i \(0.0233213\pi\)
−0.435265 + 0.900302i \(0.643345\pi\)
\(350\) 0 0
\(351\) 22.5000 + 12.9904i 1.20096 + 0.693375i
\(352\) 0 0
\(353\) 2.50000 + 4.33013i 0.133062 + 0.230469i 0.924855 0.380319i \(-0.124186\pi\)
−0.791794 + 0.610789i \(0.790853\pi\)
\(354\) 0 0
\(355\) −2.00000 + 3.46410i −0.106149 + 0.183855i
\(356\) 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
\(363\) 21.0000 + 12.1244i 1.10221 + 0.636364i
\(364\) 0 0
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i \(-0.961716\pi\)
0.392481 0.919760i \(-0.371617\pi\)
\(368\) 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
\(373\) −17.5000 + 30.3109i −0.906116 + 1.56944i −0.0867031 + 0.996234i \(0.527633\pi\)
−0.819413 + 0.573204i \(0.805700\pi\)
\(374\) 0 0
\(375\) 15.5885i 0.804984i
\(376\) 0 0
\(377\) 45.0000 2.31762
\(378\) 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
\(383\) 13.5000 23.3827i 0.689818 1.19480i −0.282079 0.959391i \(-0.591024\pi\)
0.971897 0.235408i \(-0.0756427\pi\)
\(384\) 0 0
\(385\) −7.50000 12.9904i −0.382235 0.662051i
\(386\) 0 0
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) 0 0
\(389\) −17.5000 30.3109i −0.887285 1.53682i −0.843072 0.537801i \(-0.819255\pi\)
−0.0442134 0.999022i \(-0.514078\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) 0 0
\(393\) 7.50000 + 4.33013i 0.378325 + 0.218426i
\(394\) 0 0
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −18.0000 + 10.3923i −0.901127 + 0.520266i
\(400\) 0 0
\(401\) 10.5000 18.1865i 0.524345 0.908192i −0.475253 0.879849i \(-0.657644\pi\)
0.999598 0.0283431i \(-0.00902310\pi\)
\(402\) 0 0
\(403\) 2.50000 + 4.33013i 0.124534 + 0.215699i
\(404\) 0 0
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 0 0
\(407\) −15.0000 25.9808i −0.743522 1.28782i
\(408\) 0 0
\(409\) 16.5000 28.5788i 0.815872 1.41313i −0.0928272 0.995682i \(-0.529590\pi\)
0.908700 0.417450i \(-0.137076\pi\)
\(410\) 0 0
\(411\) −4.50000 + 2.59808i −0.221969 + 0.128154i
\(412\) 0 0
\(413\) −33.0000 −1.62382
\(414\) 0 0
\(415\) 1.00000 0.0490881
\(416\) 0 0
\(417\) −4.50000 2.59808i −0.220366 0.127228i
\(418\) 0 0
\(419\) 7.50000 12.9904i 0.366399 0.634622i −0.622601 0.782540i \(-0.713924\pi\)
0.989000 + 0.147918i \(0.0472572\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) 0 0
\(423\) 4.50000 + 7.79423i 0.218797 + 0.378968i
\(424\) 0 0
\(425\) −4.00000 6.92820i −0.194029 0.336067i
\(426\) 0 0
\(427\) −10.5000 + 18.1865i −0.508131 + 0.880108i
\(428\) 0 0
\(429\) 43.3013i 2.09061i
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 15.5885i 0.747409i
\(436\) 0 0
\(437\) −2.00000 + 3.46410i −0.0956730 + 0.165710i
\(438\) 0 0
\(439\) 16.5000 + 28.5788i 0.787502 + 1.36399i 0.927493 + 0.373841i \(0.121959\pi\)
−0.139991 + 0.990153i \(0.544707\pi\)
\(440\) 0 0
\(441\) 3.00000 5.19615i 0.142857 0.247436i
\(442\) 0 0
\(443\) −11.5000 19.9186i −0.546381 0.946360i −0.998519 0.0544120i \(-0.982672\pi\)
0.452137 0.891948i \(-0.350662\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 0 0
\(447\) 28.5000 + 16.4545i 1.34800 + 0.778270i
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −15.0000 −0.706322
\(452\) 0 0
\(453\) 25.5000 14.7224i 1.19809 0.691720i
\(454\) 0 0
\(455\) −7.50000 + 12.9904i −0.351605 + 0.608998i
\(456\) 0 0
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 0 0
\(459\) 10.3923i 0.485071i
\(460\) 0 0
\(461\) 12.5000 + 21.6506i 0.582183 + 1.00837i 0.995220 + 0.0976564i \(0.0311346\pi\)
−0.413037 + 0.910714i \(0.635532\pi\)
\(462\) 0 0
\(463\) 11.5000 19.9186i 0.534450 0.925695i −0.464739 0.885448i \(-0.653852\pi\)
0.999190 0.0402476i \(-0.0128147\pi\)
\(464\) 0 0
\(465\) 1.50000 0.866025i 0.0695608 0.0401610i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 3.00000 0.138527
\(470\) 0 0
\(471\) 10.5000 + 6.06218i 0.483814 + 0.279330i
\(472\) 0 0
\(473\) −2.50000 + 4.33013i −0.114950 + 0.199099i
\(474\) 0 0
\(475\) 8.00000 + 13.8564i 0.367065 + 0.635776i
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 0.500000 + 0.866025i 0.0228456 + 0.0395697i 0.877222 0.480085i \(-0.159394\pi\)
−0.854377 + 0.519654i \(0.826061\pi\)
\(480\) 0 0
\(481\) −15.0000 + 25.9808i −0.683941 + 1.18462i
\(482\) 0 0
\(483\) 5.19615i 0.236433i
\(484\) 0 0
\(485\) 13.0000 0.590300
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 0 0
\(489\) 20.7846i 0.939913i
\(490\) 0 0
\(491\) 13.5000 23.3827i 0.609246 1.05525i −0.382118 0.924113i \(-0.624805\pi\)
0.991365 0.131132i \(-0.0418613\pi\)
\(492\) 0 0
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 0 0
\(495\) −15.0000 −0.674200
\(496\) 0 0
\(497\) 6.00000 + 10.3923i 0.269137 + 0.466159i
\(498\) 0 0
\(499\) 13.5000 23.3827i 0.604343 1.04675i −0.387812 0.921739i \(-0.626769\pi\)
0.992155 0.125014i \(-0.0398977\pi\)
\(500\) 0 0
\(501\) 31.5000 + 18.1865i 1.40732 + 0.812514i
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) −18.0000 + 10.3923i −0.799408 + 0.461538i
\(508\) 0 0
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) 3.00000 + 5.19615i 0.132712 + 0.229864i
\(512\) 0 0
\(513\) 20.7846i 0.917663i
\(514\) 0 0
\(515\) 2.50000 + 4.33013i 0.110163 + 0.190808i
\(516\) 0 0
\(517\) 7.50000 12.9904i 0.329850 0.571316i
\(518\) 0 0
\(519\) −4.50000 + 2.59808i −0.197528 + 0.114043i
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) −40.0000 −1.74908 −0.874539 0.484955i \(-0.838836\pi\)
−0.874539 + 0.484955i \(0.838836\pi\)
\(524\) 0 0
\(525\) −18.0000 10.3923i −0.785584 0.453557i
\(526\) 0 0
\(527\) 1.00000 1.73205i 0.0435607 0.0754493i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) −16.5000 + 28.5788i −0.716039 + 1.24022i
\(532\) 0 0
\(533\) 7.50000 + 12.9904i 0.324861 + 0.562676i
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 0 0
\(537\) 20.7846i 0.896922i
\(538\) 0 0
\(539\) −10.0000 −0.430730
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) 10.3923i 0.445976i
\(544\) 0 0
\(545\) 5.00000 8.66025i 0.214176 0.370965i
\(546\) 0 0
\(547\) −9.50000 16.4545i −0.406191 0.703543i 0.588269 0.808666i \(-0.299810\pi\)
−0.994459 + 0.105123i \(0.966476\pi\)
\(548\) 0 0
\(549\) 10.5000 + 18.1865i 0.448129 + 0.776182i
\(550\) 0 0
\(551\) 18.0000 + 31.1769i 0.766826 + 1.32818i
\(552\) 0 0
\(553\) 1.50000 2.59808i 0.0637865 0.110481i
\(554\) 0 0
\(555\) 9.00000 + 5.19615i 0.382029 + 0.220564i
\(556\) 0 0
\(557\) −22.0000 −0.932170 −0.466085 0.884740i \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) −15.0000 + 8.66025i −0.633300 + 0.365636i
\(562\) 0 0
\(563\) −0.500000 + 0.866025i −0.0210725 + 0.0364986i −0.876369 0.481640i \(-0.840041\pi\)
0.855297 + 0.518138i \(0.173375\pi\)
\(564\) 0 0
\(565\) −4.50000 7.79423i −0.189316 0.327906i
\(566\) 0 0
\(567\) −13.5000 23.3827i −0.566947 0.981981i
\(568\) 0 0
\(569\) 12.5000 + 21.6506i 0.524027 + 0.907642i 0.999609 + 0.0279702i \(0.00890434\pi\)
−0.475581 + 0.879672i \(0.657762\pi\)
\(570\) 0 0
\(571\) 7.50000 12.9904i 0.313865 0.543631i −0.665330 0.746549i \(-0.731709\pi\)
0.979196 + 0.202919i \(0.0650427\pi\)
\(572\) 0 0
\(573\) −40.5000 + 23.3827i −1.69191 + 0.976826i
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −19.5000 11.2583i −0.810392 0.467880i
\(580\) 0 0
\(581\) 1.50000 2.59808i 0.0622305 0.107786i
\(582\) 0 0
\(583\) 5.00000 + 8.66025i 0.207079 + 0.358671i
\(584\) 0 0
\(585\) 7.50000 + 12.9904i 0.310087 + 0.537086i
\(586\) 0 0
\(587\) 8.50000 + 14.7224i 0.350833 + 0.607660i 0.986396 0.164389i \(-0.0525653\pi\)
−0.635563 + 0.772049i \(0.719232\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) 10.3923i 0.427482i
\(592\) 0 0
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 0 0
\(597\) 34.6410i 1.41776i
\(598\) 0 0
\(599\) −10.5000 + 18.1865i −0.429018 + 0.743082i −0.996786 0.0801071i \(-0.974474\pi\)
0.567768 + 0.823189i \(0.307807\pi\)
\(600\) 0 0
\(601\) −9.50000 16.4545i −0.387513 0.671192i 0.604601 0.796528i \(-0.293332\pi\)
−0.992114 + 0.125336i \(0.959999\pi\)
\(602\) 0 0
\(603\) 1.50000 2.59808i 0.0610847 0.105802i
\(604\) 0 0
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i \(-0.918318\pi\)
0.703429 + 0.710766i \(0.251651\pi\)
\(608\) 0 0
\(609\) −40.5000 23.3827i −1.64114 0.947514i
\(610\) 0 0
\(611\) −15.0000 −0.606835
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) 4.50000 2.59808i 0.181458 0.104765i
\(616\) 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
\(619\) −5.50000 9.52628i −0.221064 0.382893i 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) 0 0
\(621\) −4.50000 2.59808i −0.180579 0.104257i
\(622\) 0 0
\(623\) 27.0000 + 46.7654i 1.08173 + 1.87362i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) 30.0000 17.3205i 1.19808 0.691714i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −10.5000 6.06218i −0.417338 0.240950i
\(634\) 0 0
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) 5.00000 + 8.66025i 0.198107 + 0.343132i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) 0.500000 + 0.866025i 0.0197488 + 0.0342059i 0.875731 0.482800i \(-0.160380\pi\)
−0.855982 + 0.517005i \(0.827047\pi\)
\(642\) 0 0
\(643\) 7.50000 12.9904i 0.295771 0.512291i −0.679393 0.733775i \(-0.737757\pi\)
0.975164 + 0.221484i \(0.0710901\pi\)
\(644\) 0 0
\(645\) 1.73205i 0.0681994i
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) 55.0000 2.15894
\(650\) 0 0
\(651\) 5.19615i 0.203653i
\(652\) 0 0
\(653\) 16.5000 28.5788i 0.645695 1.11838i −0.338446 0.940986i \(-0.609901\pi\)
0.984141 0.177390i \(-0.0567655\pi\)
\(654\) 0 0
\(655\) 2.50000 + 4.33013i 0.0976831 + 0.169192i
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 10.5000 + 18.1865i 0.409022 + 0.708447i 0.994780 0.102039i \(-0.0325366\pi\)
−0.585758 + 0.810486i \(0.699203\pi\)
\(660\) 0 0
\(661\) 12.5000 21.6506i 0.486194 0.842112i −0.513680 0.857982i \(-0.671718\pi\)
0.999874 + 0.0158695i \(0.00505163\pi\)
\(662\) 0 0
\(663\) 15.0000 + 8.66025i 0.582552 + 0.336336i
\(664\) 0 0
\(665\) −12.0000 −0.465340
\(666\) 0 0
\(667\) −9.00000 −0.348481
\(668\) 0 0
\(669\) −16.5000 + 9.52628i −0.637927 + 0.368307i
\(670\) 0 0
\(671\) 17.5000 30.3109i 0.675580 1.17014i
\(672\) 0 0
\(673\) −9.50000 16.4545i −0.366198 0.634274i 0.622770 0.782405i \(-0.286007\pi\)
−0.988968 + 0.148132i \(0.952674\pi\)
\(674\) 0 0
\(675\) −18.0000 + 10.3923i −0.692820 + 0.400000i
\(676\) 0 0
\(677\) −17.5000 30.3109i −0.672580 1.16494i −0.977170 0.212459i \(-0.931853\pi\)
0.304590 0.952483i \(-0.401480\pi\)
\(678\) 0 0
\(679\) 19.5000 33.7750i 0.748341 1.29617i
\(680\) 0 0
\(681\) 31.5000 18.1865i 1.20708 0.696909i
\(682\) 0 0
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) −25.5000 14.7224i −0.972886 0.561696i
\(688\) 0 0
\(689\) 5.00000 8.66025i 0.190485 0.329929i
\(690\) 0 0
\(691\) 20.5000 + 35.5070i 0.779857 + 1.35075i 0.932024 + 0.362397i \(0.118041\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 0 0
\(693\) −22.5000 + 38.9711i −0.854704 + 1.48039i
\(694\) 0 0
\(695\) −1.50000 2.59808i −0.0568982 0.0985506i
\(696\) 0 0
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) 0 0
\(699\) 45.0333i 1.70332i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 0 0
\(705\) 5.19615i 0.195698i
\(706\) 0 0
\(707\) −4.50000 + 7.79423i −0.169240 + 0.293132i
\(708\) 0 0
\(709\) −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 0 0
\(711\) −1.50000 2.59808i −0.0562544 0.0974355i
\(712\) 0 0
\(713\) −0.500000 0.866025i −0.0187251 0.0324329i
\(714\) 0 0
\(715\) 12.5000 21.6506i 0.467473 0.809688i
\(716\) 0 0
\(717\) 25.5000 + 14.7224i 0.952315 + 0.549819i
\(718\) 0 0
\(719\) −32.0000 −1.19340 −0.596699 0.802465i \(-0.703521\pi\)
−0.596699 + 0.802465i \(0.703521\pi\)
\(720\) 0 0
\(721\) 15.0000 0.558629
\(722\) 0 0
\(723\) −22.5000 + 12.9904i −0.836784 + 0.483117i
\(724\) 0 0
\(725\) −18.0000 + 31.1769i −0.668503 + 1.15788i
\(726\) 0 0
\(727\) −19.5000 33.7750i −0.723215 1.25265i −0.959705 0.281011i \(-0.909330\pi\)
0.236490 0.971634i \(-0.424003\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.00000 1.73205i −0.0369863 0.0640622i
\(732\) 0 0
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 0 0
\(735\) 3.00000 1.73205i 0.110657 0.0638877i
\(736\) 0 0
\(737\) −5.00000 −0.184177
\(738\) 0 0
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 0 0
\(741\) −30.0000 17.3205i −1.10208 0.636285i
\(742\) 0 0
\(743\) 5.50000 9.52628i 0.201775 0.349485i −0.747325 0.664459i \(-0.768662\pi\)
0.949101 + 0.314973i \(0.101996\pi\)
\(744\) 0 0
\(745\) 9.50000 + 16.4545i 0.348053 + 0.602846i
\(746\) 0 0
\(747\) −1.50000 2.59808i −0.0548821 0.0950586i
\(748\) 0 0
\(749\) 18.0000 + 31.1769i 0.657706 + 1.13918i
\(750\) 0 0
\(751\) 13.5000 23.3827i 0.492622 0.853246i −0.507342 0.861745i \(-0.669372\pi\)
0.999964 + 0.00849853i \(0.00270520\pi\)
\(752\) 0 0
\(753\) 34.6410i 1.26239i
\(754\) 0 0
\(755\) 17.0000 0.618693
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 8.66025i 0.314347i
\(760\) 0 0
\(761\) 2.50000 4.33013i 0.0906249 0.156967i −0.817149 0.576426i \(-0.804447\pi\)
0.907774 + 0.419459i \(0.137780\pi\)
\(762\) 0 0
\(763\) −15.0000 25.9808i −0.543036 0.940567i
\(764\) 0 0
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) 0 0
\(767\) −27.5000 47.6314i −0.992967 1.71987i
\(768\) 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
\(771\) 10.5000 + 6.06218i 0.378148 + 0.218324i
\(772\) 0 0
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 27.0000 15.5885i 0.968620 0.559233i
\(778\) 0 0
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) −10.0000 17.3205i −0.357828 0.619777i
\(782\) 0 0
\(783\) −40.5000 + 23.3827i −1.44735 + 0.835629i
\(784\) 0 0
\(785\) 3.50000 + 6.06218i 0.124920 + 0.216368i
\(786\) 0 0
\(787\) −26.5000 + 45.8993i −0.944623 + 1.63614i −0.188119 + 0.982146i \(0.560239\pi\)
−0.756504 + 0.653989i \(0.773094\pi\)
\(788\) 0 0
\(789\) −10.5000 + 6.06218i −0.373810 + 0.215819i
\(790\) 0 0
\(791\) −27.0000 −0.960009
\(792\) 0 0
\(793\) −35.0000 −1.24289
\(794\) 0 0
\(795\) −3.00000 1.73205i −0.106399 0.0614295i
\(796\) 0 0