Properties

Label 1386.2.k.l.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.l.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(1.50000 + 2.59808i) q^{19} +2.00000 q^{20} +1.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(-2.50000 + 0.866025i) q^{28} +1.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(1.00000 - 5.19615i) q^{35} +(2.50000 + 4.33013i) q^{37} +(-1.50000 + 2.59808i) q^{38} +(1.00000 + 1.73205i) q^{40} +10.0000 q^{41} +1.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} +(3.50000 + 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} -2.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} +(0.500000 + 0.866025i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(7.00000 + 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(0.500000 + 0.866025i) q^{68} +(5.00000 - 1.73205i) q^{70} -5.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(-2.50000 + 4.33013i) q^{74} -3.00000 q^{76} +(2.50000 - 0.866025i) q^{77} +(-1.00000 + 1.73205i) q^{80} +(5.00000 + 8.66025i) q^{82} +6.00000 q^{83} -2.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(4.00000 + 3.46410i) q^{91} +1.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +(3.00000 - 5.19615i) q^{95} +7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + 2q^{10} + q^{11} + 4q^{13} - q^{14} - q^{16} + q^{17} + 3q^{19} + 4q^{20} + 2q^{22} - q^{23} + q^{25} + 2q^{26} - 5q^{28} + 2q^{29} + 2q^{31} + q^{32} + 2q^{34} + 2q^{35} + 5q^{37} - 3q^{38} + 2q^{40} + 20q^{41} + 2q^{43} + q^{44} + q^{46} + 7q^{47} + 2q^{49} + 2q^{50} - 2q^{52} + 12q^{53} - 4q^{55} - 4q^{56} + q^{58} - 3q^{59} + 14q^{61} + 4q^{62} + 2q^{64} - 4q^{65} - 12q^{67} + q^{68} + 10q^{70} - 10q^{71} + 8q^{73} - 5q^{74} - 6q^{76} + 5q^{77} - 2q^{80} + 10q^{82} + 12q^{83} - 4q^{85} + q^{86} - q^{88} - 6q^{89} + 8q^{91} + 2q^{92} - 7q^{94} + 6q^{95} + 14q^{97} - 11q^{98} + O(q^{100}) \)

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 \(0.410544\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) 0 0
\(19\) 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i \(-0.0548427\pi\)
−0.641071 + 0.767482i \(0.721509\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 0 0
\(28\) −2.50000 + 0.866025i −0.472456 + 0.163663i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 1.00000 5.19615i 0.169031 0.878310i
\(36\) 0 0
\(37\) 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) −1.50000 + 2.59808i −0.243332 + 0.421464i
\(39\) 0 0
\(40\) 1.00000 + 1.73205i 0.158114 + 0.273861i
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 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
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 0 0
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) 0.500000 + 0.866025i 0.0606339 + 0.105021i
\(69\) 0 0
\(70\) 5.00000 1.73205i 0.597614 0.207020i
\(71\) −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 −0.531174 0.847263i \(-0.678249\pi\)
0.999338 + 0.0363782i \(0.0115821\pi\)
\(74\) −2.50000 + 4.33013i −0.290619 + 0.503367i
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) 2.50000 0.866025i 0.284901 0.0986928i
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) 0 0
\(82\) 5.00000 + 8.66025i 0.552158 + 0.956365i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) 4.00000 + 3.46410i 0.419314 + 0.363137i
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) 3.00000 + 5.19615i 0.295599 + 0.511992i 0.975124 0.221660i \(-0.0711475\pi\)
−0.679525 + 0.733652i \(0.737814\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) 0 0
\(109\) 10.0000 17.3205i 0.957826 1.65900i 0.230063 0.973176i \(-0.426107\pi\)
0.727764 0.685828i \(-0.240560\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.00000 + 1.73205i −0.0932505 + 0.161515i
\(116\) −0.500000 + 0.866025i −0.0464238 + 0.0804084i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) 2.50000 0.866025i 0.229175 0.0793884i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −7.00000 + 12.1244i −0.633750 + 1.09769i
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) −1.50000 + 7.79423i −0.130066 + 0.675845i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) 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
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 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
\(145\) −1.00000 1.73205i −0.0830455 0.143839i
\(146\) 8.00000 0.662085
\(147\) 0 0
\(148\) −5.00000 −0.410997
\(149\) −5.50000 9.52628i −0.450578 0.780423i 0.547844 0.836580i \(-0.315449\pi\)
−0.998422 + 0.0561570i \(0.982115\pi\)
\(150\) 0 0
\(151\) 7.50000 12.9904i 0.610341 1.05714i −0.380841 0.924640i \(-0.624366\pi\)
0.991183 0.132502i \(-0.0423010\pi\)
\(152\) −1.50000 2.59808i −0.121666 0.210732i
\(153\) 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 \(0.179372\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −2.00000 −0.158114
\(161\) 0.500000 2.59808i 0.0394055 0.204757i
\(162\) 0 0
\(163\) −5.00000 8.66025i −0.391630 0.678323i 0.601035 0.799223i \(-0.294755\pi\)
−0.992665 + 0.120900i \(0.961422\pi\)
\(164\) −5.00000 + 8.66025i −0.390434 + 0.676252i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −1.00000 1.73205i −0.0766965 0.132842i
\(171\) 0 0
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) 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
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −3.50000 + 6.06218i −0.261602 + 0.453108i −0.966668 0.256034i \(-0.917584\pi\)
0.705066 + 0.709142i \(0.250918\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −1.00000 + 5.19615i −0.0741249 + 0.385164i
\(183\) 0 0
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 5.00000 8.66025i 0.367607 0.636715i
\(186\) 0 0
\(187\) −0.500000 0.866025i −0.0365636 0.0633300i
\(188\) −7.00000 −0.510527
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) −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
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) −27.0000 −1.92367 −0.961835 0.273629i \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) 0 0
\(199\) 1.00000 1.73205i 0.0708881 0.122782i −0.828403 0.560133i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −9.00000 −0.633238
\(203\) 2.00000 + 1.73205i 0.140372 + 0.121566i
\(204\) 0 0
\(205\) −10.0000 17.3205i −0.698430 1.20972i
\(206\) −3.00000 + 5.19615i −0.209020 + 0.362033i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) 1.00000 1.73205i 0.0683586 0.118401i
\(215\) −1.00000 1.73205i −0.0681994 0.118125i
\(216\) 0 0
\(217\) 5.00000 1.73205i 0.339422 0.117579i
\(218\) 20.0000 1.35457
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 2.50000 0.866025i 0.167038 0.0578638i
\(225\) 0 0
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) −5.00000 + 8.66025i −0.331862 + 0.574801i −0.982877 0.184263i \(-0.941010\pi\)
0.651015 + 0.759065i \(0.274343\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) −10.5000 18.1865i −0.687878 1.19144i −0.972523 0.232806i \(-0.925209\pi\)
0.284645 0.958633i \(-0.408124\pi\)
\(234\) 0 0
\(235\) 7.00000 12.1244i 0.456630 0.790906i
\(236\) −1.50000 2.59808i −0.0976417 0.169120i
\(237\) 0 0
\(238\) 2.00000 + 1.73205i 0.129641 + 0.112272i
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0 0
\(241\) 6.00000 10.3923i 0.386494 0.669427i −0.605481 0.795860i \(-0.707019\pi\)
0.991975 + 0.126432i \(0.0403527\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) −14.0000 −0.896258
\(245\) 11.0000 8.66025i 0.702764 0.553283i
\(246\) 0 0
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 0 0
\(259\) −2.50000 + 12.9904i −0.155342 + 0.807183i
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) 0 0
\(263\) −3.00000 + 5.19615i −0.184988 + 0.320408i −0.943572 0.331166i \(-0.892558\pi\)
0.758585 + 0.651575i \(0.225891\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) −7.50000 + 2.59808i −0.459855 + 0.159298i
\(267\) 0 0
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 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 \(-0.577011\pi\)
0.960595 0.277951i \(-0.0896552\pi\)
\(278\) −6.50000 11.2583i −0.389844 0.675230i
\(279\) 0 0
\(280\) −1.00000 + 5.19615i −0.0597614 + 0.310530i
\(281\) −7.00000 −0.417585 −0.208792 0.977960i \(-0.566953\pi\)
−0.208792 + 0.977960i \(0.566953\pi\)
\(282\) 0 0
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 2.50000 4.33013i 0.148348 0.256946i
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 20.0000 + 17.3205i 1.18056 + 1.02240i
\(288\) 0 0
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 1.00000 1.73205i 0.0587220 0.101710i
\(291\) 0 0
\(292\) 4.00000 + 6.92820i 0.234082 + 0.405442i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) −2.50000 4.33013i −0.145310 0.251684i
\(297\) 0 0
\(298\) 5.50000 9.52628i 0.318606 0.551843i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0 0
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 15.0000 0.863153
\(303\) 0 0
\(304\) 1.50000 2.59808i 0.0860309 0.149010i
\(305\) 14.0000 24.2487i 0.801638 1.38848i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) −0.500000 + 2.59808i −0.0284901 + 0.148039i
\(309\) 0 0
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) 6.50000 11.2583i 0.368581 0.638401i −0.620763 0.783998i \(-0.713177\pi\)
0.989344 + 0.145597i \(0.0465103\pi\)
\(312\) 0 0
\(313\) −3.50000 6.06218i −0.197832 0.342655i 0.749993 0.661445i \(-0.230057\pi\)
−0.947825 + 0.318791i \(0.896723\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) 0.500000 0.866025i 0.0279946 0.0484881i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 0 0
\(322\) 2.50000 0.866025i 0.139320 0.0482617i
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) 5.00000 8.66025i 0.276924 0.479647i
\(327\) 0 0
\(328\) −10.0000 −0.552158
\(329\) −3.50000 + 18.1865i −0.192961 + 1.00266i
\(330\) 0 0
\(331\) 1.00000 + 1.73205i 0.0549650 + 0.0952021i 0.892199 0.451643i \(-0.149162\pi\)
−0.837234 + 0.546845i \(0.815829\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 0 0
\(334\) −1.00000 1.73205i −0.0547176 0.0947736i
\(335\) 24.0000 1.31126
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) −1.00000 1.73205i −0.0541530 0.0937958i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) −7.00000 + 12.1244i −0.376322 + 0.651809i
\(347\) −16.0000 + 27.7128i −0.858925 + 1.48770i 0.0140303 + 0.999902i \(0.495534\pi\)
−0.872955 + 0.487800i \(0.837799\pi\)
\(348\) 0 0
\(349\) −16.0000 −0.856460 −0.428230 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(350\) 2.00000 + 1.73205i 0.106904 + 0.0925820i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) 5.00000 + 8.66025i 0.265372 + 0.459639i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −7.00000 −0.369961
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) 0 0
\(364\) −5.00000 + 1.73205i −0.262071 + 0.0907841i
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) 16.0000 27.7128i 0.835193 1.44660i −0.0586798 0.998277i \(-0.518689\pi\)
0.893873 0.448320i \(-0.147978\pi\)
\(368\) −0.500000 + 0.866025i −0.0260643 + 0.0451447i
\(369\) 0 0
\(370\) 10.0000 0.519875
\(371\) 30.0000 10.3923i 1.55752 0.539542i
\(372\) 0 0
\(373\) −13.0000 22.5167i −0.673114 1.16587i −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) 0.500000 0.866025i 0.0258544 0.0447811i
\(375\) 0 0
\(376\) −3.50000 6.06218i −0.180499 0.312633i
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 3.00000 + 5.19615i 0.153897 + 0.266557i
\(381\) 0 0
\(382\) 4.00000 6.92820i 0.204658 0.354478i
\(383\) 12.5000 + 21.6506i 0.638720 + 1.10630i 0.985714 + 0.168428i \(0.0538692\pi\)
−0.346994 + 0.937867i \(0.612797\pi\)
\(384\) 0 0
\(385\) −4.00000 3.46410i −0.203859 0.176547i
\(386\) −8.00000 −0.407189
\(387\) 0 0
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) −15.0000 + 25.9808i −0.760530 + 1.31728i 0.182047 + 0.983290i \(0.441728\pi\)
−0.942578 + 0.333987i \(0.891606\pi\)
\(390\) 0 0
\(391\) −1.00000 −0.0505722
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 0 0
\(394\) −13.5000 23.3827i −0.680120 1.17800i
\(395\) 0 0
\(396\) 0 0
\(397\) 13.5000 + 23.3827i 0.677546 + 1.17354i 0.975718 + 0.219031i \(0.0702897\pi\)
−0.298172 + 0.954512i \(0.596377\pi\)
\(398\) 2.00000 0.100251
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) −4.50000 7.79423i −0.223883 0.387777i
\(405\) 0 0
\(406\) −0.500000 + 2.59808i −0.0248146 + 0.128940i
\(407\) 5.00000 0.247841
\(408\) 0 0
\(409\) −8.00000 + 13.8564i −0.395575 + 0.685155i −0.993174 0.116639i \(-0.962788\pi\)
0.597600 + 0.801795i \(0.296121\pi\)
\(410\) 10.0000 17.3205i 0.493865 0.855399i
\(411\) 0 0
\(412\) −6.00000 −0.295599
\(413\) −7.50000 + 2.59808i −0.369051 + 0.127843i
\(414\) 0 0
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 0 0
\(418\) 1.50000 + 2.59808i 0.0733674 + 0.127076i
\(419\) −29.0000 −1.41674 −0.708371 0.705840i \(-0.750570\pi\)
−0.708371 + 0.705840i \(0.750570\pi\)
\(420\) 0 0
\(421\) −17.0000 −0.828529 −0.414265 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 0 0
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) −0.500000 0.866025i −0.0242536 0.0420084i
\(426\) 0 0
\(427\) −7.00000 + 36.3731i −0.338754 + 1.76022i
\(428\) 2.00000 0.0966736
\(429\) 0 0
\(430\) 1.00000 1.73205i 0.0482243 0.0835269i
\(431\) −8.00000 + 13.8564i −0.385346 + 0.667440i −0.991817 0.127666i \(-0.959251\pi\)
0.606471 + 0.795106i \(0.292585\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 4.00000 + 3.46410i 0.192006 + 0.166282i
\(435\) 0 0
\(436\) 10.0000 + 17.3205i 0.478913 + 0.829502i
\(437\) 1.50000 2.59808i 0.0717547 0.124283i
\(438\) 0 0
\(439\) −15.5000 26.8468i −0.739775 1.28133i −0.952597 0.304236i \(-0.901599\pi\)
0.212822 0.977091i \(-0.431735\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) 7.50000 + 12.9904i 0.356336 + 0.617192i 0.987346 0.158583i \(-0.0506926\pi\)
−0.631010 + 0.775775i \(0.717359\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 0 0
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) 5.00000 8.66025i 0.235180 0.407344i
\(453\) 0 0
\(454\) −10.0000 −0.469323
\(455\) 2.00000 10.3923i 0.0937614 0.487199i
\(456\) 0 0
\(457\) −16.0000 27.7128i −0.748448 1.29635i −0.948566 0.316579i \(-0.897466\pi\)
0.200118 0.979772i \(-0.435868\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 0 0
\(460\) −1.00000 1.73205i −0.0466252 0.0807573i
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) 0 0
\(466\) 10.5000 18.1865i 0.486403 0.842475i
\(467\) 13.5000 + 23.3827i 0.624705 + 1.08202i 0.988598 + 0.150581i \(0.0481143\pi\)
−0.363892 + 0.931441i \(0.618552\pi\)
\(468\) 0 0
\(469\) −30.0000 + 10.3923i −1.38527 + 0.479872i
\(470\) 14.0000 0.645772
\(471\) 0 0
\(472\) 1.50000 2.59808i 0.0690431 0.119586i
\(473\) 0.500000 0.866025i 0.0229900 0.0398199i
\(474\) 0 0
\(475\) 3.00000 0.137649
\(476\) −0.500000 + 2.59808i −0.0229175 + 0.119083i
\(477\) 0 0
\(478\) 11.0000 + 19.0526i 0.503128 + 0.871444i
\(479\) −13.0000 + 22.5167i −0.593985 + 1.02881i 0.399704 + 0.916644i \(0.369113\pi\)
−0.993689 + 0.112168i \(0.964220\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 12.0000 0.546585
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −7.00000 12.1244i −0.317854 0.550539i
\(486\) 0 0
\(487\) 17.0000 29.4449i 0.770344 1.33427i −0.167031 0.985952i \(-0.553418\pi\)
0.937375 0.348323i \(-0.113249\pi\)
\(488\) −7.00000 12.1244i −0.316875 0.548844i
\(489\) 0 0
\(490\) 13.0000 + 5.19615i 0.587280 + 0.234738i
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) 0.500000 0.866025i 0.0225189 0.0390038i
\(494\) −3.00000 + 5.19615i −0.134976 + 0.233786i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −10.0000 8.66025i −0.448561 0.388465i
\(498\) 0 0
\(499\) −4.00000 6.92820i −0.179065 0.310149i 0.762496 0.646993i \(-0.223974\pi\)
−0.941560 + 0.336844i \(0.890640\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) 10.5000 + 18.1865i 0.468638 + 0.811705i
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) −0.500000 0.866025i −0.0222277 0.0384995i
\(507\) 0 0
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) −10.0000 17.3205i −0.443242 0.767718i 0.554686 0.832060i \(-0.312839\pi\)
−0.997928 + 0.0643419i \(0.979505\pi\)
\(510\) 0 0
\(511\) 20.0000 6.92820i 0.884748 0.306486i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) 6.00000 10.3923i 0.264392 0.457940i
\(516\) 0 0
\(517\) 7.00000 0.307860
\(518\) −12.5000 + 4.33013i −0.549218 + 0.190255i
\(519\) 0 0
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) 7.00000 12.1244i 0.306676 0.531178i −0.670957 0.741496i \(-0.734117\pi\)
0.977633 + 0.210318i \(0.0674500\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) −1.00000 1.73205i −0.0435607 0.0754493i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) −12.0000 20.7846i −0.521247 0.902826i
\(531\) 0 0
\(532\) −6.00000 5.19615i −0.260133 0.225282i
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) −2.00000 + 3.46410i −0.0864675 + 0.149766i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) 12.0000 0.517357
\(539\) 6.50000 + 2.59808i 0.279975 + 0.111907i
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) −0.500000 0.866025i −0.0214373 0.0371305i
\(545\) −40.0000 −1.71341
\(546\) 0 0
\(547\) 39.0000 1.66752 0.833760 0.552127i \(-0.186184\pi\)
0.833760 + 0.552127i \(0.186184\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 0 0
\(550\) 0.500000 0.866025i 0.0213201 0.0369274i
\(551\) 1.50000 + 2.59808i 0.0639021 + 0.110682i
\(552\) 0 0
\(553\) 0 0
\(554\) 24.0000 1.01966
\(555\) 0 0
\(556\) 6.50000 11.2583i 0.275661 0.477460i
\(557\) −17.5000 + 30.3109i −0.741499 + 1.28431i 0.210314 + 0.977634i \(0.432551\pi\)
−0.951813 + 0.306680i \(0.900782\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) −5.00000 + 1.73205i −0.211289 + 0.0731925i
\(561\) 0 0
\(562\) −3.50000 6.06218i −0.147639 0.255718i
\(563\) −19.0000 + 32.9090i −0.800755 + 1.38695i 0.118366 + 0.992970i \(0.462235\pi\)
−0.919120 + 0.393977i \(0.871099\pi\)
\(564\) 0 0
\(565\) 10.0000 + 17.3205i 0.420703 + 0.728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 5.00000 0.209795
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) −3.50000 + 6.06218i −0.146470 + 0.253694i −0.929921 0.367760i \(-0.880125\pi\)
0.783450 + 0.621455i \(0.213458\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 0 0
\(574\) −5.00000 + 25.9808i −0.208696 + 1.08442i
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −7.00000 + 12.1244i −0.291414 + 0.504744i −0.974144 0.225927i \(-0.927459\pi\)
0.682730 + 0.730670i \(0.260792\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) 0 0
\(580\) 2.00000 0.0830455
\(581\) 12.0000 + 10.3923i 0.497844 + 0.431145i
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −4.00000 + 6.92820i −0.165521 + 0.286691i
\(585\) 0 0
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 3.00000 + 5.19615i 0.123508 + 0.213922i
\(591\) 0 0
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) 7.50000 + 12.9904i 0.307988 + 0.533451i 0.977922 0.208970i \(-0.0670110\pi\)
−0.669934 + 0.742421i \(0.733678\pi\)
\(594\) 0 0
\(595\) −4.00000 3.46410i −0.163984 0.142014i
\(596\) 11.0000 0.450578
\(597\) 0 0
\(598\) 1.00000 1.73205i 0.0408930 0.0708288i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) −0.500000 + 2.59808i −0.0203785 + 0.105890i
\(603\) 0 0
\(604\) 7.50000 + 12.9904i 0.305171 + 0.528571i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 14.0000 + 24.2487i 0.568242 + 0.984225i 0.996740 + 0.0806818i \(0.0257098\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(608\) 3.00000 0.121666
\(609\) 0 0
\(610\) 28.0000 1.13369
\(611\) 7.00000 + 12.1244i 0.283190 + 0.490499i
\(612\) 0 0
\(613\) 7.00000 12.1244i 0.282727 0.489698i −0.689328 0.724449i \(-0.742094\pi\)
0.972056 + 0.234751i \(0.0754275\pi\)
\(614\) −2.00000 3.46410i −0.0807134 0.139800i
\(615\) 0 0
\(616\) −2.50000 + 0.866025i −0.100728 + 0.0348932i
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) −13.0000 + 22.5167i −0.522514 + 0.905021i 0.477143 + 0.878826i \(0.341672\pi\)
−0.999657 + 0.0261952i \(0.991661\pi\)
\(620\) 2.00000 3.46410i 0.0803219 0.139122i
\(621\) 0 0
\(622\) 13.0000 0.521253
\(623\) 3.00000 15.5885i 0.120192 0.624538i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 3.50000 6.06218i 0.139888 0.242293i
\(627\) 0 0
\(628\) −0.500000 0.866025i −0.0199522 0.0345582i
\(629\) 5.00000 0.199363
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) 1.00000 + 1.73205i 0.0396838 + 0.0687343i
\(636\) 0 0
\(637\) 2.00000 + 13.8564i 0.0792429 + 0.549011i
\(638\) 1.00000 0.0395904
\(639\) 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
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 2.00000 + 1.73205i 0.0788110 + 0.0682524i
\(645\) 0 0
\(646\) 1.50000 + 2.59808i 0.0590167 + 0.102220i
\(647\) 24.0000 41.5692i 0.943537 1.63425i 0.184884 0.982760i \(-0.440809\pi\)
0.758654 0.651494i \(-0.225858\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) 7.00000 + 12.1244i 0.273931 + 0.474463i 0.969865 0.243643i \(-0.0783426\pi\)
−0.695934 + 0.718106i \(0.745009\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −5.00000 8.66025i −0.195217 0.338126i
\(657\) 0 0
\(658\) −17.5000 + 6.06218i −0.682221 + 0.236328i
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) −2.50000 + 4.33013i −0.0972387 + 0.168422i −0.910541 0.413419i \(-0.864334\pi\)
0.813302 + 0.581842i \(0.197668\pi\)
\(662\) −1.00000 + 1.73205i −0.0388661 + 0.0673181i
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 15.0000 5.19615i 0.581675 0.201498i
\(666\) 0 0
\(667\) −0.500000 0.866025i −0.0193601 0.0335326i
\(668\) 1.00000 1.73205i 0.0386912 0.0670151i
\(669\) 0 0
\(670\) 12.0000 + 20.7846i 0.463600 + 0.802980i
\(671\) 14.0000 0.540464
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 3.50000 + 6.06218i 0.134516 + 0.232988i 0.925412 0.378962i \(-0.123719\pi\)
−0.790897 + 0.611950i \(0.790385\pi\)
\(678\) 0 0
\(679\) 14.0000 + 12.1244i 0.537271 + 0.465290i
\(680\) 2.00000 0.0766965
\(681\) 0 0
\(682\) 1.00000 1.73205i 0.0382920 0.0663237i
\(683\) −19.5000 + 33.7750i −0.746147 + 1.29236i 0.203510 + 0.979073i \(0.434765\pi\)
−0.949657 + 0.313291i \(0.898568\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) 0 0
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) 12.0000 20.7846i 0.457164 0.791831i
\(690\) 0 0
\(691\) 9.00000 + 15.5885i 0.342376 + 0.593013i 0.984873 0.173275i \(-0.0554350\pi\)
−0.642497 + 0.766288i \(0.722102\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 13.0000 + 22.5167i 0.493118 + 0.854106i
\(696\) 0 0
\(697\) 5.00000 8.66025i 0.189389 0.328031i
\(698\) −8.00000 13.8564i −0.302804 0.524473i
\(699\) 0 0
\(700\) −0.500000 + 2.59808i −0.0188982 + 0.0981981i
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) −7.50000 + 12.9904i −0.282868 + 0.489942i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) −22.5000 + 7.79423i −0.846200 + 0.293132i
\(708\) 0 0
\(709\) −4.50000 7.79423i −0.169001 0.292718i 0.769068 0.639167i \(-0.220721\pi\)
−0.938069 + 0.346449i \(0.887387\pi\)
\(710\) −5.00000 + 8.66025i −0.187647 + 0.325014i
\(711\) 0 0
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −3.50000 6.06218i −0.130801 0.226554i
\(717\) 0 0
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) 11.5000 + 19.9186i 0.428878 + 0.742838i 0.996774 0.0802624i \(-0.0255758\pi\)
−0.567896 + 0.823100i \(0.692242\pi\)
\(720\) 0 0
\(721\) −3.00000 + 15.5885i −0.111726 + 0.580544i
\(722\) 10.0000 0.372161
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 0.500000 0.866025i 0.0185695 0.0321634i
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) −4.00000 3.46410i −0.148250 0.128388i
\(729\) 0 0
\(730\) −8.00000 13.8564i −0.296093 0.512849i
\(731\) 0.500000 0.866025i 0.0184932 0.0320311i
\(732\) 0 0
\(733\) 5.00000 + 8.66025i 0.184679 + 0.319874i 0.943468 0.331463i \(-0.107542\pi\)
−0.758789 + 0.651336i \(0.774209\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 6.00000 + 10.3923i 0.221013 + 0.382805i
\(738\) 0 0
\(739\) −18.0000 + 31.1769i −0.662141 + 1.14686i 0.317911 + 0.948120i \(0.397019\pi\)
−0.980052 + 0.198741i \(0.936315\pi\)
\(740\) 5.00000 + 8.66025i 0.183804 + 0.318357i
\(741\) 0 0
\(742\) 24.0000 + 20.7846i 0.881068 + 0.763027i
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) −11.0000 + 19.0526i −0.403009 + 0.698032i
\(746\) 13.0000 22.5167i 0.475964 0.824394i
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) 1.00000 5.19615i 0.0365392 0.189863i
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 3.50000 6.06218i 0.127632 0.221065i
\(753\) 0 0
\(754\) 1.00000 + 1.73205i 0.0364179 + 0.0630776i
\(755\) −30.0000 −1.09181
\(756\) 0 0
\(757\) 47.0000 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(758\) −4.00000 6.92820i −0.145287 0.251644i
\(759\) 0 0
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 9.00000 + 15.5885i 0.326250 + 0.565081i 0.981764 0.190101i \(-0.0608816\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(762\) 0 0
\(763\) 50.0000 17.3205i 1.81012 0.627044i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −12.5000 + 21.6506i −0.451643 + 0.782269i
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 0 0
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 1.00000 5.19615i 0.0360375 0.187256i
\(771\) 0 0
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) 18.0000 31.1769i 0.647415 1.12136i −0.336323 0.941747i \(-0.609183\pi\)
0.983738 0.179609i \(-0.0574833\pi\)
\(774\) 0 0
\(775\) −1.00000 1.73205i −0.0359211 0.0622171i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 15.0000 + 25.9808i 0.537431 + 0.930857i
\(780\) 0 0
\(781\) −2.50000 + 4.33013i −0.0894570 + 0.154944i
\(782\) −0.500000 0.866025i −0.0178800 0.0309690i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 15.5000 26.8468i 0.552515 0.956985i −0.445577 0.895244i \(-0.647001\pi\)
0.998092 0.0617409i \(-0.0196653\pi\)
\(788\) 13.5000 23.3827i 0.480918 0.832974i
\(789\) 0 0
\(790\) 0