Properties

Label 1386.2.k.k.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
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 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.k.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +2.00000 q^{20} -1.00000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(0.500000 + 2.59808i) q^{28} +5.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(-5.00000 - 1.73205i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(3.50000 - 6.06218i) q^{38} +(1.00000 + 1.73205i) q^{40} -6.00000 q^{41} +11.0000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.50000 - 6.06218i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} +2.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(2.50000 + 4.33013i) q^{58} +(5.50000 - 9.52628i) q^{59} +(-5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-1.00000 - 5.19615i) q^{70} +5.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(1.50000 - 2.59808i) q^{74} +7.00000 q^{76} +(0.500000 + 2.59808i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-3.00000 - 5.19615i) q^{82} -14.0000 q^{83} +6.00000 q^{85} +(5.50000 + 9.52628i) q^{86} +(0.500000 - 0.866025i) q^{88} +(1.00000 + 1.73205i) q^{89} +(4.00000 - 3.46410i) q^{91} +7.00000 q^{92} +(3.50000 - 6.06218i) q^{94} +(-7.00000 + 12.1244i) q^{95} +15.0000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + 2q^{10} - q^{11} + 4q^{13} + 5q^{14} - q^{16} - 3q^{17} - 7q^{19} + 4q^{20} - 2q^{22} - 7q^{23} + q^{25} + 2q^{26} + q^{28} + 10q^{29} - 2q^{31} + q^{32} - 6q^{34} - 10q^{35} - 3q^{37} + 7q^{38} + 2q^{40} - 12q^{41} + 22q^{43} - q^{44} + 7q^{46} - 7q^{47} + 2q^{49} + 2q^{50} - 2q^{52} - 4q^{53} + 4q^{55} - 4q^{56} + 5q^{58} + 11q^{59} - 10q^{61} - 4q^{62} + 2q^{64} - 4q^{65} + 4q^{67} - 3q^{68} - 2q^{70} + 10q^{71} + 8q^{73} + 3q^{74} + 14q^{76} + q^{77} + 8q^{79} - 2q^{80} - 6q^{82} - 28q^{83} + 12q^{85} + 11q^{86} + q^{88} + 2q^{89} + 8q^{91} + 14q^{92} + 7q^{94} - 14q^{95} + 30q^{97} + 13q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 0 0
\(28\) 0.500000 + 2.59808i 0.0944911 + 0.490990i
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −5.00000 1.73205i −0.845154 0.292770i
\(36\) 0 0
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 3.50000 6.06218i 0.567775 0.983415i
\(39\) 0 0
\(40\) 1.00000 + 1.73205i 0.158114 + 0.273861i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) −3.50000 6.06218i −0.510527 0.884260i −0.999926 0.0121990i \(-0.996117\pi\)
0.489398 0.872060i \(-0.337217\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −2.00000 + 3.46410i −0.274721 + 0.475831i −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) 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
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) −1.00000 5.19615i −0.119523 0.621059i
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) 4.00000 6.92820i 0.468165 0.810885i −0.531174 0.847263i \(-0.678249\pi\)
0.999338 + 0.0363782i \(0.0115821\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 0.500000 + 2.59808i 0.0569803 + 0.296078i
\(78\) 0 0
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) 0 0
\(82\) −3.00000 5.19615i −0.331295 0.573819i
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 6.00000 0.650791
\(86\) 5.50000 + 9.52628i 0.593080 + 1.02725i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 7.00000 0.729800
\(93\) 0 0
\(94\) 3.50000 6.06218i 0.360997 0.625266i
\(95\) −7.00000 + 12.1244i −0.718185 + 1.24393i
\(96\) 0 0
\(97\) 15.0000 1.52302 0.761510 0.648154i \(-0.224459\pi\)
0.761510 + 0.648154i \(0.224459\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0 0
\(109\) −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i \(-0.894690\pi\)
0.754204 + 0.656640i \(0.228023\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 0 0
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −7.00000 + 12.1244i −0.652753 + 1.13060i
\(116\) −2.50000 + 4.33013i −0.232119 + 0.402042i
\(117\) 0 0
\(118\) 11.0000 1.01263
\(119\) 1.50000 + 7.79423i 0.137505 + 0.714496i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 0 0
\(133\) −17.5000 6.06218i −1.51744 0.525657i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) 17.0000 1.44192 0.720961 0.692976i \(-0.243701\pi\)
0.720961 + 0.692976i \(0.243701\pi\)
\(140\) 4.00000 3.46410i 0.338062 0.292770i
\(141\) 0 0
\(142\) 2.50000 + 4.33013i 0.209795 + 0.363376i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 0 0
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) 8.00000 0.662085
\(147\) 0 0
\(148\) 3.00000 0.246598
\(149\) 8.50000 + 14.7224i 0.696347 + 1.20611i 0.969724 + 0.244202i \(0.0785259\pi\)
−0.273377 + 0.961907i \(0.588141\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 0 0
\(154\) −2.00000 + 1.73205i −0.161165 + 0.139573i
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −0.500000 + 0.866025i −0.0399043 + 0.0691164i −0.885288 0.465044i \(-0.846039\pi\)
0.845383 + 0.534160i \(0.179372\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 0 0
\(160\) −2.00000 −0.158114
\(161\) −17.5000 6.06218i −1.37919 0.477767i
\(162\) 0 0
\(163\) −3.00000 5.19615i −0.234978 0.406994i 0.724288 0.689497i \(-0.242169\pi\)
−0.959266 + 0.282503i \(0.908835\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) −7.00000 12.1244i −0.543305 0.941033i
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 3.00000 + 5.19615i 0.230089 + 0.398527i
\(171\) 0 0
\(172\) −5.50000 + 9.52628i −0.419371 + 0.726372i
\(173\) 7.00000 + 12.1244i 0.532200 + 0.921798i 0.999293 + 0.0375896i \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −1.00000 + 1.73205i −0.0749532 + 0.129823i
\(179\) −4.50000 + 7.79423i −0.336346 + 0.582568i −0.983742 0.179585i \(-0.942524\pi\)
0.647397 + 0.762153i \(0.275858\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 5.00000 + 1.73205i 0.370625 + 0.128388i
\(183\) 0 0
\(184\) 3.50000 + 6.06218i 0.258023 + 0.446910i
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) −1.50000 2.59808i −0.109691 0.189990i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) −14.0000 −1.01567
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 0 0
\(193\) −12.0000 + 20.7846i −0.863779 + 1.49611i 0.00447566 + 0.999990i \(0.498575\pi\)
−0.868255 + 0.496119i \(0.834758\pi\)
\(194\) 7.50000 + 12.9904i 0.538469 + 0.932655i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 3.00000 0.211079
\(203\) 10.0000 8.66025i 0.701862 0.607831i
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) −5.00000 + 8.66025i −0.348367 + 0.603388i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 7.00000 0.484200
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −2.00000 3.46410i −0.137361 0.237915i
\(213\) 0 0
\(214\) −9.00000 + 15.5885i −0.615227 + 1.06561i
\(215\) −11.0000 19.0526i −0.750194 1.29937i
\(216\) 0 0
\(217\) 1.00000 + 5.19615i 0.0678844 + 0.352738i
\(218\) −4.00000 −0.270914
\(219\) 0 0
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −14.0000 −0.937509 −0.468755 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) −1.00000 1.73205i −0.0665190 0.115214i
\(227\) 5.00000 8.66025i 0.331862 0.574801i −0.651015 0.759065i \(-0.725657\pi\)
0.982877 + 0.184263i \(0.0589899\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −14.0000 −0.923133
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −4.50000 7.79423i −0.294805 0.510617i 0.680135 0.733087i \(-0.261921\pi\)
−0.974939 + 0.222470i \(0.928588\pi\)
\(234\) 0 0
\(235\) −7.00000 + 12.1244i −0.456630 + 0.790906i
\(236\) 5.50000 + 9.52628i 0.358020 + 0.620108i
\(237\) 0 0
\(238\) −6.00000 + 5.19615i −0.388922 + 0.336817i
\(239\) 10.0000 0.646846 0.323423 0.946254i \(-0.395166\pi\)
0.323423 + 0.946254i \(0.395166\pi\)
\(240\) 0 0
\(241\) 2.00000 3.46410i 0.128831 0.223142i −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) −13.0000 + 5.19615i −0.830540 + 0.331970i
\(246\) 0 0
\(247\) −7.00000 12.1244i −0.445399 0.771454i
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) 0 0
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −5.00000 −0.315597 −0.157799 0.987471i \(-0.550440\pi\)
−0.157799 + 0.987471i \(0.550440\pi\)
\(252\) 0 0
\(253\) 7.00000 0.440086
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 0 0
\(259\) −7.50000 2.59808i −0.466027 0.161437i
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) 4.00000 6.92820i 0.247121 0.428026i
\(263\) 15.0000 25.9808i 0.924940 1.60204i 0.133281 0.991078i \(-0.457449\pi\)
0.791658 0.610964i \(-0.209218\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) −3.50000 18.1865i −0.214599 1.11509i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −10.0000 + 17.3205i −0.609711 + 1.05605i 0.381577 + 0.924337i \(0.375381\pi\)
−0.991288 + 0.131713i \(0.957952\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) −12.0000 + 20.7846i −0.721010 + 1.24883i 0.239585 + 0.970875i \(0.422989\pi\)
−0.960595 + 0.277951i \(0.910345\pi\)
\(278\) 8.50000 + 14.7224i 0.509796 + 0.882993i
\(279\) 0 0
\(280\) 5.00000 + 1.73205i 0.298807 + 0.103510i
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 0 0
\(283\) −12.0000 + 20.7846i −0.713326 + 1.23552i 0.250276 + 0.968175i \(0.419479\pi\)
−0.963602 + 0.267342i \(0.913855\pi\)
\(284\) −2.50000 + 4.33013i −0.148348 + 0.256946i
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) −12.0000 + 10.3923i −0.708338 + 0.613438i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 5.00000 8.66025i 0.293610 0.508548i
\(291\) 0 0
\(292\) 4.00000 + 6.92820i 0.234082 + 0.405442i
\(293\) 3.00000 0.175262 0.0876309 0.996153i \(-0.472070\pi\)
0.0876309 + 0.996153i \(0.472070\pi\)
\(294\) 0 0
\(295\) −22.0000 −1.28089
\(296\) 1.50000 + 2.59808i 0.0871857 + 0.151010i
\(297\) 0 0
\(298\) −8.50000 + 14.7224i −0.492392 + 0.852848i
\(299\) −7.00000 12.1244i −0.404820 0.701170i
\(300\) 0 0
\(301\) 22.0000 19.0526i 1.26806 1.09817i
\(302\) 5.00000 0.287718
\(303\) 0 0
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) −10.0000 + 17.3205i −0.572598 + 0.991769i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) −2.50000 0.866025i −0.142451 0.0493464i
\(309\) 0 0
\(310\) 2.00000 + 3.46410i 0.113592 + 0.196748i
\(311\) 13.5000 23.3827i 0.765515 1.32591i −0.174459 0.984664i \(-0.555818\pi\)
0.939974 0.341246i \(-0.110849\pi\)
\(312\) 0 0
\(313\) −7.50000 12.9904i −0.423925 0.734260i 0.572394 0.819979i \(-0.306015\pi\)
−0.996319 + 0.0857188i \(0.972681\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i \(0.152241\pi\)
−0.0453045 + 0.998973i \(0.514426\pi\)
\(318\) 0 0
\(319\) −2.50000 + 4.33013i −0.139973 + 0.242441i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 0 0
\(322\) −3.50000 18.1865i −0.195047 1.01350i
\(323\) 21.0000 1.16847
\(324\) 0 0
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) 3.00000 5.19615i 0.166155 0.287788i
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) −17.5000 6.06218i −0.964806 0.334219i
\(330\) 0 0
\(331\) 7.00000 + 12.1244i 0.384755 + 0.666415i 0.991735 0.128302i \(-0.0409527\pi\)
−0.606980 + 0.794717i \(0.707619\pi\)
\(332\) 7.00000 12.1244i 0.384175 0.665410i
\(333\) 0 0
\(334\) 5.00000 + 8.66025i 0.273588 + 0.473868i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −1.00000 1.73205i −0.0541530 0.0937958i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −11.0000 −0.593080
\(345\) 0 0
\(346\) −7.00000 + 12.1244i −0.376322 + 0.651809i
\(347\) 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) 0 0
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 2.00000 1.73205i 0.106904 0.0925820i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 5.00000 8.66025i 0.266123 0.460939i −0.701734 0.712439i \(-0.747591\pi\)
0.967857 + 0.251500i \(0.0809239\pi\)
\(354\) 0 0
\(355\) −5.00000 8.66025i −0.265372 0.459639i
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) 0 0
\(364\) 1.00000 + 5.19615i 0.0524142 + 0.272352i
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) −3.50000 + 6.06218i −0.182450 + 0.316013i
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) 2.00000 + 10.3923i 0.103835 + 0.539542i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 1.50000 2.59808i 0.0775632 0.134343i
\(375\) 0 0
\(376\) 3.50000 + 6.06218i 0.180499 + 0.312633i
\(377\) 10.0000 0.515026
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −7.00000 12.1244i −0.359092 0.621966i
\(381\) 0 0
\(382\) 4.00000 6.92820i 0.204658 0.354478i
\(383\) 15.5000 + 26.8468i 0.792013 + 1.37181i 0.924719 + 0.380651i \(0.124300\pi\)
−0.132706 + 0.991155i \(0.542367\pi\)
\(384\) 0 0
\(385\) 4.00000 3.46410i 0.203859 0.176547i
\(386\) −24.0000 −1.22157
\(387\) 0 0
\(388\) −7.50000 + 12.9904i −0.380755 + 0.659487i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 21.0000 1.06202
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) −7.50000 12.9904i −0.377845 0.654446i
\(395\) 8.00000 13.8564i 0.402524 0.697191i
\(396\) 0 0
\(397\) 1.50000 + 2.59808i 0.0752828 + 0.130394i 0.901209 0.433384i \(-0.142681\pi\)
−0.825926 + 0.563778i \(0.809347\pi\)
\(398\) −10.0000 −0.501255
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 16.0000 + 27.7128i 0.799002 + 1.38391i 0.920267 + 0.391292i \(0.127972\pi\)
−0.121265 + 0.992620i \(0.538695\pi\)
\(402\) 0 0
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 1.50000 + 2.59808i 0.0746278 + 0.129259i
\(405\) 0 0
\(406\) 12.5000 + 4.33013i 0.620365 + 0.214901i
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) −16.0000 + 27.7128i −0.791149 + 1.37031i 0.134107 + 0.990967i \(0.457183\pi\)
−0.925256 + 0.379344i \(0.876150\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 0 0
\(412\) −10.0000 −0.492665
\(413\) −5.50000 28.5788i −0.270637 1.40627i
\(414\) 0 0
\(415\) 14.0000 + 24.2487i 0.687233 + 1.19032i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 0 0
\(418\) 3.50000 + 6.06218i 0.171191 + 0.296511i
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 0 0
\(421\) −17.0000 −0.828529 −0.414265 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(422\) 10.0000 + 17.3205i 0.486792 + 0.843149i
\(423\) 0 0
\(424\) 2.00000 3.46410i 0.0971286 0.168232i
\(425\) 1.50000 + 2.59808i 0.0727607 + 0.126025i
\(426\) 0 0
\(427\) −25.0000 8.66025i −1.20983 0.419099i
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 11.0000 19.0526i 0.530467 0.918796i
\(431\) 20.0000 34.6410i 0.963366 1.66860i 0.249424 0.968394i \(-0.419759\pi\)
0.713942 0.700205i \(-0.246908\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) −4.00000 + 3.46410i −0.192006 + 0.166282i
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) −24.5000 + 42.4352i −1.17199 + 2.02995i
\(438\) 0 0
\(439\) −2.50000 4.33013i −0.119318 0.206666i 0.800179 0.599761i \(-0.204738\pi\)
−0.919498 + 0.393095i \(0.871404\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 20.5000 + 35.5070i 0.973984 + 1.68699i 0.683247 + 0.730188i \(0.260567\pi\)
0.290738 + 0.956803i \(0.406099\pi\)
\(444\) 0 0
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) −7.00000 12.1244i −0.331460 0.574105i
\(447\) 0 0
\(448\) 2.00000 1.73205i 0.0944911 0.0818317i
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) 1.00000 1.73205i 0.0470360 0.0814688i
\(453\) 0 0
\(454\) 10.0000 0.469323
\(455\) −10.0000 3.46410i −0.468807 0.162400i
\(456\) 0 0
\(457\) −20.0000 34.6410i −0.935561 1.62044i −0.773631 0.633636i \(-0.781562\pi\)
−0.161929 0.986802i \(-0.551772\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 0 0
\(460\) −7.00000 12.1244i −0.326377 0.565301i
\(461\) −13.0000 −0.605470 −0.302735 0.953075i \(-0.597900\pi\)
−0.302735 + 0.953075i \(0.597900\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −2.50000 4.33013i −0.116060 0.201021i
\(465\) 0 0
\(466\) 4.50000 7.79423i 0.208458 0.361061i
\(467\) 6.50000 + 11.2583i 0.300784 + 0.520973i 0.976314 0.216359i \(-0.0694183\pi\)
−0.675530 + 0.737333i \(0.736085\pi\)
\(468\) 0 0
\(469\) −2.00000 10.3923i −0.0923514 0.479872i
\(470\) −14.0000 −0.645772
\(471\) 0 0
\(472\) −5.50000 + 9.52628i −0.253158 + 0.438483i
\(473\) −5.50000 + 9.52628i −0.252890 + 0.438019i
\(474\) 0 0
\(475\) −7.00000 −0.321182
\(476\) −7.50000 2.59808i −0.343762 0.119083i
\(477\) 0 0
\(478\) 5.00000 + 8.66025i 0.228695 + 0.396111i
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) −3.00000 5.19615i −0.136788 0.236924i
\(482\) 4.00000 0.182195
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −15.0000 25.9808i −0.681115 1.17973i
\(486\) 0 0
\(487\) −9.00000 + 15.5885i −0.407829 + 0.706380i −0.994646 0.103339i \(-0.967047\pi\)
0.586817 + 0.809719i \(0.300381\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 0 0
\(490\) −11.0000 8.66025i −0.496929 0.391230i
\(491\) 26.0000 1.17336 0.586682 0.809818i \(-0.300434\pi\)
0.586682 + 0.809818i \(0.300434\pi\)
\(492\) 0 0
\(493\) −7.50000 + 12.9904i −0.337783 + 0.585057i
\(494\) 7.00000 12.1244i 0.314945 0.545501i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 10.0000 8.66025i 0.448561 0.388465i
\(498\) 0 0
\(499\) 20.0000 + 34.6410i 0.895323 + 1.55074i 0.833404 + 0.552664i \(0.186389\pi\)
0.0619186 + 0.998081i \(0.480278\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) −2.50000 4.33013i −0.111580 0.193263i
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 3.50000 + 6.06218i 0.155594 + 0.269497i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) 2.00000 + 3.46410i 0.0886484 + 0.153544i 0.906940 0.421260i \(-0.138412\pi\)
−0.818292 + 0.574803i \(0.805079\pi\)
\(510\) 0 0
\(511\) −4.00000 20.7846i −0.176950 0.919457i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.00000 12.1244i 0.308757 0.534782i
\(515\) 10.0000 17.3205i 0.440653 0.763233i
\(516\) 0 0
\(517\) 7.00000 0.307860
\(518\) −1.50000 7.79423i −0.0659062 0.342459i
\(519\) 0 0
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 0 0
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 30.0000 1.30806
\(527\) −3.00000 5.19615i −0.130682 0.226348i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 4.00000 + 6.92820i 0.173749 + 0.300942i
\(531\) 0 0
\(532\) 14.0000 12.1244i 0.606977 0.525657i
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 18.0000 31.1769i 0.778208 1.34790i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −20.0000 −0.862261
\(539\) 5.50000 + 4.33013i 0.236902 + 0.186512i
\(540\) 0 0
\(541\) −8.00000 13.8564i −0.343947 0.595733i 0.641215 0.767361i \(-0.278431\pi\)
−0.985162 + 0.171628i \(0.945097\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 0 0
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 8.00000 0.342682
\(546\) 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
\(549\) 0 0
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) −17.5000 30.3109i −0.745525 1.29129i
\(552\) 0 0
\(553\) 20.0000 + 6.92820i 0.850487 + 0.294617i
\(554\) −24.0000 −1.01966
\(555\) 0 0
\(556\) −8.50000 + 14.7224i −0.360480 + 0.624370i
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) 0 0
\(559\) 22.0000 0.930501
\(560\) 1.00000 + 5.19615i 0.0422577 + 0.219578i
\(561\) 0 0
\(562\) −1.50000 2.59808i −0.0632737 0.109593i
\(563\) −21.0000 + 36.3731i −0.885044 + 1.53294i −0.0393818 + 0.999224i \(0.512539\pi\)
−0.845663 + 0.533718i \(0.820794\pi\)
\(564\) 0 0
\(565\) 2.00000 + 3.46410i 0.0841406 + 0.145736i
\(566\) −24.0000 −1.00880
\(567\) 0 0
\(568\) −5.00000 −0.209795
\(569\) 6.50000 + 11.2583i 0.272494 + 0.471974i 0.969500 0.245092i \(-0.0788181\pi\)
−0.697006 + 0.717066i \(0.745485\pi\)
\(570\) 0 0
\(571\) 21.5000 37.2391i 0.899747 1.55841i 0.0719297 0.997410i \(-0.477084\pi\)
0.827817 0.560998i \(-0.189582\pi\)
\(572\) −1.00000 1.73205i −0.0418121 0.0724207i
\(573\) 0 0
\(574\) −15.0000 5.19615i −0.626088 0.216883i
\(575\) −7.00000 −0.291920
\(576\) 0 0
\(577\) 9.00000 15.5885i 0.374675 0.648956i −0.615603 0.788056i \(-0.711088\pi\)
0.990278 + 0.139100i \(0.0444210\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) 10.0000 0.415227
\(581\) −28.0000 + 24.2487i −1.16164 + 1.00601i
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) −4.00000 + 6.92820i −0.165521 + 0.286691i
\(585\) 0 0
\(586\) 1.50000 + 2.59808i 0.0619644 + 0.107326i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 14.0000 0.576860
\(590\) −11.0000 19.0526i −0.452863 0.784381i
\(591\) 0 0
\(592\) −1.50000 + 2.59808i −0.0616496 + 0.106780i
\(593\) −10.5000 18.1865i −0.431183 0.746831i 0.565792 0.824548i \(-0.308570\pi\)
−0.996976 + 0.0777165i \(0.975237\pi\)
\(594\) 0 0
\(595\) 12.0000 10.3923i 0.491952 0.426043i
\(596\) −17.0000 −0.696347
\(597\) 0 0
\(598\) 7.00000 12.1244i 0.286251 0.495802i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 27.5000 + 9.52628i 1.12082 + 0.388262i
\(603\) 0 0
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −18.0000 31.1769i −0.730597 1.26543i −0.956628 0.291312i \(-0.905908\pi\)
0.226031 0.974120i \(-0.427425\pi\)
\(608\) −7.00000 −0.283887
\(609\) 0 0
\(610\) −20.0000 −0.809776
\(611\) −7.00000 12.1244i −0.283190 0.490499i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) −0.500000 2.59808i −0.0201456 0.104679i
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 0 0
\(619\) 13.0000 22.5167i 0.522514 0.905021i −0.477143 0.878826i \(-0.658328\pi\)
0.999657 0.0261952i \(-0.00833914\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) 0 0
\(622\) 27.0000 1.08260
\(623\) 5.00000 + 1.73205i 0.200321 + 0.0693932i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 7.50000 12.9904i 0.299760 0.519200i
\(627\) 0 0
\(628\) −0.500000 0.866025i −0.0199522 0.0345582i
\(629\) 9.00000 0.358854
\(630\) 0 0
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) 0 0
\(634\) −15.0000 + 25.9808i −0.595726 + 1.03183i
\(635\) 19.0000 + 32.9090i 0.753992 + 1.30595i
\(636\) 0 0
\(637\) 2.00000 13.8564i 0.0792429 0.549011i
\(638\) −5.00000 −0.197952
\(639\) 0 0
\(640\) 1.00000 1.73205i 0.0395285 0.0684653i
\(641\) −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 0 0
\(643\) 40.0000 1.57745 0.788723 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 14.0000 12.1244i 0.551677 0.477767i
\(645\) 0 0
\(646\) 10.5000 + 18.1865i 0.413117 + 0.715540i
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) 5.50000 + 9.52628i 0.215894 + 0.373939i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 6.00000 0.234978
\(653\) −5.00000 8.66025i −0.195665 0.338902i 0.751453 0.659786i \(-0.229353\pi\)
−0.947118 + 0.320884i \(0.896020\pi\)
\(654\) 0 0
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) 3.00000 + 5.19615i 0.117130 + 0.202876i
\(657\) 0 0
\(658\) −3.50000 18.1865i −0.136444 0.708985i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 5.50000 9.52628i 0.213925 0.370529i −0.739014 0.673690i \(-0.764708\pi\)
0.952940 + 0.303160i \(0.0980418\pi\)
\(662\) −7.00000 + 12.1244i −0.272063 + 0.471226i
\(663\) 0 0
\(664\) 14.0000 0.543305
\(665\) 7.00000 + 36.3731i 0.271448 + 1.41049i
\(666\) 0 0
\(667\) −17.5000 30.3109i −0.677603 1.17364i
\(668\) −5.00000 + 8.66025i −0.193456 + 0.335075i
\(669\) 0 0
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 4.00000 + 6.92820i 0.154074 + 0.266864i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −10.5000 18.1865i −0.403548 0.698965i 0.590603 0.806962i \(-0.298890\pi\)
−0.994151 + 0.107997i \(0.965556\pi\)
\(678\) 0 0
\(679\) 30.0000 25.9808i 1.15129 0.997050i
\(680\) −6.00000 −0.230089
\(681\) 0 0
\(682\) 1.00000 1.73205i 0.0382920 0.0663237i
\(683\) 19.5000 33.7750i 0.746147 1.29236i −0.203510 0.979073i \(-0.565235\pi\)
0.949657 0.313291i \(-0.101432\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −5.50000 9.52628i −0.209686 0.363186i
\(689\) −4.00000 + 6.92820i −0.152388 + 0.263944i
\(690\) 0 0
\(691\) −9.00000 15.5885i −0.342376 0.593013i 0.642497 0.766288i \(-0.277898\pi\)
−0.984873 + 0.173275i \(0.944565\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) −17.0000 29.4449i −0.644847 1.11691i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 4.00000 + 6.92820i 0.151402 + 0.262236i
\(699\) 0 0
\(700\) 2.50000 + 0.866025i 0.0944911 + 0.0327327i
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 0 0
\(703\) −10.5000 + 18.1865i −0.396015 + 0.685918i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 10.0000 0.376355
\(707\) −1.50000 7.79423i −0.0564133 0.293132i
\(708\) 0 0
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 5.00000 8.66025i 0.187647 0.325014i
\(711\) 0 0
\(712\) −1.00000 1.73205i −0.0374766 0.0649113i
\(713\) 14.0000 0.524304
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) 0 0
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) 4.50000 + 7.79423i 0.167822 + 0.290676i 0.937654 0.347571i \(-0.112993\pi\)
−0.769832 + 0.638247i \(0.779660\pi\)
\(720\) 0 0
\(721\) 25.0000 + 8.66025i 0.931049 + 0.322525i
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) −4.00000 + 3.46410i −0.148250 + 0.128388i
\(729\) 0 0
\(730\) −8.00000 13.8564i −0.296093 0.512849i
\(731\) −16.5000 + 28.5788i −0.610275 + 1.05703i
\(732\) 0 0
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 2.00000 + 3.46410i 0.0736709 + 0.127602i
\(738\) 0 0
\(739\) −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) −3.00000 5.19615i −0.110282 0.191014i
\(741\) 0 0
\(742\) −8.00000 + 6.92820i −0.293689 + 0.254342i
\(743\) 4.00000 0.146746 0.0733729 0.997305i \(-0.476624\pi\)
0.0733729 + 0.997305i \(0.476624\pi\)
\(744\) 0 0
\(745\) 17.0000 29.4449i 0.622832 1.07878i
\(746\) −11.0000 + 19.0526i −0.402739 + 0.697564i
\(747\) 0 0
\(748\) 3.00000 0.109691
\(749\) 45.0000 + 15.5885i 1.64426 + 0.569590i
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) 0 0
\(754\) 5.00000 + 8.66025i 0.182089 + 0.315388i
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) 15.0000 0.545184 0.272592 0.962130i \(-0.412119\pi\)
0.272592 + 0.962130i \(0.412119\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) 0 0
\(760\) 7.00000 12.1244i 0.253917 0.439797i
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) 0 0
\(763\) 2.00000 + 10.3923i 0.0724049 + 0.376227i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −15.5000 + 26.8468i −0.560038 + 0.970014i
\(767\) 11.0000 19.0526i 0.397187 0.687948i
\(768\) 0 0
\(769\) 28.0000 1.00971 0.504853 0.863205i \(-0.331547\pi\)
0.504853 + 0.863205i \(0.331547\pi\)
\(770\) 5.00000 + 1.73205i 0.180187 + 0.0624188i
\(771\) 0 0
\(772\) −12.0000 20.7846i −0.431889 0.748054i
\(773\) 2.00000 3.46410i 0.0719350 0.124595i −0.827814 0.561002i \(-0.810416\pi\)
0.899749 + 0.436407i \(0.143749\pi\)
\(774\) 0 0
\(775\) 1.00000 + 1.73205i 0.0359211 + 0.0622171i
\(776\) −15.0000 −0.538469
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 21.0000 + 36.3731i 0.752403 + 1.30320i
\(780\) 0 0
\(781\) −2.50000 + 4.33013i −0.0894570 + 0.154944i
\(782\) 10.5000 + 18.1865i 0.375479 + 0.650349i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 18.5000 32.0429i 0.659454 1.14221i −0.321303 0.946976i \(-0.604121\pi\)
0.980757 0.195231i \(-0.0625457\pi\)
\(788\) 7.50000 12.9904i 0.267176 0.462763i
\(789\) 0 0
\(790\)