Properties

Label 1386.2.k.i.793.1
Level $1386$
Weight $2$
Character 1386.793
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 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.i.991.1

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 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 \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 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 \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) −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 −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −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 \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 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 −0.489398 0.872060i \(-0.662783\pi\)
0.999926 0.0121990i \(-0.00388317\pi\)
\(48\) 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 \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 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 −0.962557 0.271078i \(-0.912620\pi\)
0.246518 0.969138i \(-0.420713\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 2.00000 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 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 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 \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i \(-0.0115821\pi\)
−0.531174 + 0.847263i \(0.678249\pi\)
\(74\) −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 −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 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 \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 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 \(-0.867138\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(90\) 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 \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0 0
\(109\) −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i \(-0.228023\pi\)
−0.945769 + 0.324840i \(0.894690\pi\)
\(110\) −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 \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 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 \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 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 \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 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 0.273377 + 0.961907i \(0.411859\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(150\) 0 0
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) −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 0.845383 0.534160i \(-0.179372\pi\)
−0.885288 + 0.465044i \(0.846039\pi\)
\(158\) 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 −0.959266 0.282503i \(-0.908835\pi\)
0.724288 + 0.689497i \(0.242169\pi\)
\(164\) −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 \(-0.626458\pi\)
−0.386912 + 0.922117i \(0.626458\pi\)
\(168\) 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 0.467093 + 0.884208i \(0.345301\pi\)
−0.999293 + 0.0375896i \(0.988032\pi\)
\(174\) 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 \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 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 \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0 0
\(193\) −12.0000 20.7846i −0.863779 1.49611i −0.868255 0.496119i \(-0.834758\pi\)
0.00447566 0.999990i \(-0.498575\pi\)
\(194\) −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 \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 0 0
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) 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 \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 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 \(-0.738079\pi\)
0.974939 + 0.222470i \(0.0714120\pi\)
\(234\) 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 \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) 0 0
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) −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 \(-0.449560\pi\)
0.157799 + 0.987471i \(0.449560\pi\)
\(252\) 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 \(-0.689499\pi\)
0.997429 + 0.0716680i \(0.0228322\pi\)
\(258\) 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 −0.791658 0.610964i \(-0.790782\pi\)
−0.133281 0.991078i \(-0.542551\pi\)
\(264\) 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 0.991288 + 0.131713i \(0.0420477\pi\)
−0.381577 + 0.924337i \(0.624619\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) −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 −0.960595 0.277951i \(-0.910345\pi\)
0.239585 0.970875i \(-0.422989\pi\)
\(278\) −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 \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) −12.0000 20.7846i −0.713326 1.23552i −0.963602 0.267342i \(-0.913855\pi\)
0.250276 0.968175i \(-0.419479\pi\)
\(284\) 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 \(-0.527930\pi\)
−0.0876309 + 0.996153i \(0.527930\pi\)
\(294\) 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 −0.939974 0.341246i \(-0.889151\pi\)
0.174459 0.984664i \(-0.444182\pi\)
\(312\) 0 0
\(313\) −7.50000 + 12.9904i −0.423925 + 0.734260i −0.996319 0.0857188i \(-0.972681\pi\)
0.572394 + 0.819979i \(0.306015\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −15.0000 + 25.9808i −0.842484 + 1.45922i 0.0453045 + 0.998973i \(0.485574\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(318\) 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 −0.606980 0.794717i \(-0.707619\pi\)
0.991735 + 0.128302i \(0.0409527\pi\)
\(332\) −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 −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 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 \(-0.252409\pi\)
−0.967857 + 0.251500i \(0.919076\pi\)
\(354\) 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 \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 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 −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) −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 0.132706 + 0.991155i \(0.457633\pi\)
−0.924719 + 0.380651i \(0.875700\pi\)
\(384\) 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 \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 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 −0.825926 0.563778i \(-0.809347\pi\)
0.901209 + 0.433384i \(0.142681\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −16.0000 + 27.7128i −0.799002 + 1.38391i 0.121265 + 0.992620i \(0.461305\pi\)
−0.920267 + 0.391292i \(0.872028\pi\)
\(402\) 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 −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 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 \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 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 −0.713942 0.700205i \(-0.753092\pi\)
−0.249424 0.968394i \(-0.580241\pi\)
\(432\) 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 −0.919498 0.393095i \(-0.871404\pi\)
0.800179 + 0.599761i \(0.204738\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −20.5000 + 35.5070i −0.973984 + 1.68699i −0.290738 + 0.956803i \(0.593901\pi\)
−0.683247 + 0.730188i \(0.739433\pi\)
\(444\) 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 \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) 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 −0.161929 + 0.986802i \(0.551772\pi\)
−0.773631 + 0.633636i \(0.781562\pi\)
\(458\) 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 \(-0.402100\pi\)
0.302735 + 0.953075i \(0.402100\pi\)
\(462\) 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 \(-0.930582\pi\)
0.675530 + 0.737333i \(0.263915\pi\)
\(468\) 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 \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 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 0.586817 0.809719i \(-0.300381\pi\)
−0.994646 + 0.103339i \(0.967047\pi\)
\(488\) −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 \(-0.699566\pi\)
−0.586682 + 0.809818i \(0.699566\pi\)
\(492\) 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 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) −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 \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 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 \(-0.861588\pi\)
0.818292 + 0.574803i \(0.194921\pi\)
\(510\) 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 \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i \(-0.689279\pi\)
0.997478 + 0.0709788i \(0.0226123\pi\)
\(524\) −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 −0.985162 0.171628i \(-0.945097\pi\)
0.641215 + 0.767361i \(0.278431\pi\)
\(542\) −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 \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 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 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 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 \(-0.921182\pi\)
0.697006 + 0.717066i \(0.254515\pi\)
\(570\) 0 0
\(571\) 21.5000 + 37.2391i 0.899747 + 1.55841i 0.827817 + 0.560998i \(0.189582\pi\)
0.0719297 + 0.997410i \(0.477084\pi\)
\(572\) 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 0.990278 0.139100i \(-0.0444210\pi\)
−0.615603 + 0.788056i \(0.711088\pi\)
\(578\) 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 \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 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 \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 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 0.226031 + 0.974120i \(0.427425\pi\)
−0.956628 + 0.291312i \(0.905908\pi\)
\(608\) 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 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −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 \(-0.631888\pi\)
−0.402585 + 0.915383i \(0.631888\pi\)
\(618\) 0 0
\(619\) 13.0000 + 22.5167i 0.522514 + 0.905021i 0.999657 + 0.0261952i \(0.00833914\pi\)
−0.477143 + 0.878826i \(0.658328\pi\)
\(620\) 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 \(-0.0905072\pi\)
−0.722862 + 0.690992i \(0.757174\pi\)
\(642\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 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 \(-0.770647\pi\)
0.947118 + 0.320884i \(0.103980\pi\)
\(654\) 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 \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i \(-0.0980418\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 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 \(-0.701110\pi\)
0.994151 + 0.107997i \(0.0344436\pi\)
\(678\) 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 −0.949657 0.313291i \(-0.898568\pi\)
0.203510 0.979073i \(-0.434765\pi\)
\(684\) 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 −0.984873 0.173275i \(-0.944565\pi\)
0.642497 + 0.766288i \(0.277898\pi\)
\(692\) 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 \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 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 −0.413114 0.910679i \(-0.635559\pi\)
0.995228 0.0975728i \(-0.0311079\pi\)
\(710\) −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 \(-0.887007\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(720\) 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 −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) 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 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) 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 \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) 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 −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) 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 −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) 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 \(-0.189584\pi\)
−0.899749 + 0.436407i \(0.856251\pi\)
\(774\) 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 0.980757 + 0.195231i \(0.0625457\pi\)
−0.321303 + 0.946976i \(0.604121\pi\)
\(788\) −7.50000 12.9904i −0.267176 0.462763i
\(789\) 0 0