Properties

Label 2646.2.h.j.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
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: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.j.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -3.00000 q^{23} -4.00000 q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.00000 + 6.92820i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{37} -7.00000 q^{38} -1.00000 q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{52} +(2.00000 + 3.46410i) q^{53} +2.00000 q^{55} -8.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +5.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +6.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.00000 + 10.3923i) q^{82} +(-6.00000 + 10.3923i) q^{83} +8.00000 q^{86} -2.00000 q^{88} +(-7.00000 + 12.1244i) q^{89} +(1.50000 - 2.59808i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-3.50000 + 6.06218i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} - q^{16} - 7 q^{19} - q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} - 2 q^{26} - 8 q^{29} + 4 q^{31} + q^{32} + 6 q^{37} - 14 q^{38} - 2 q^{40} + 12 q^{41} + 8 q^{43} - 2 q^{44} - 3 q^{46} + 8 q^{47} - 4 q^{50} - 4 q^{52} + 4 q^{53} + 4 q^{55} - 16 q^{58} - 4 q^{59} + 13 q^{61} + 8 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 10 q^{71} - 14 q^{73} + 12 q^{74} - 7 q^{76} + 11 q^{79} - q^{80} - 12 q^{82} - 12 q^{83} + 16 q^{86} - 4 q^{88} - 14 q^{89} + 3 q^{92} - 8 q^{94} - 7 q^{95} - 2 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 0 0
\(22\) 1.00000 + 1.73205i 0.213201 + 0.369274i
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 + 6.92820i −0.742781 + 1.28654i 0.208443 + 0.978035i \(0.433160\pi\)
−0.951224 + 0.308500i \(0.900173\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) −7.00000 −1.13555
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 6.00000 + 10.3923i 0.937043 + 1.62301i 0.770950 + 0.636895i \(0.219782\pi\)
0.166092 + 0.986110i \(0.446885\pi\)
\(42\) 0 0
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 0 0
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 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
\(56\) 0 0
\(57\) 0 0
\(58\) −8.00000 −1.05045
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 0 0
\(82\) −6.00000 + 10.3923i −0.662589 + 1.14764i
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) −7.00000 + 12.1244i −0.741999 + 1.28518i 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) −3.50000 + 6.06218i −0.359092 + 0.621966i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −11.0000 −1.09454 −0.547270 0.836956i \(-0.684333\pi\)
−0.547270 + 0.836956i \(0.684333\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 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
\(112\) 0 0
\(113\) −0.500000 0.866025i −0.0470360 0.0814688i 0.841549 0.540181i \(-0.181644\pi\)
−0.888585 + 0.458712i \(0.848311\pi\)
\(114\) 0 0
\(115\) −3.00000 −0.279751
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −6.50000 + 11.2583i −0.588482 + 1.01928i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −9.00000 −0.804984
\(126\) 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
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 4.50000 + 7.79423i 0.381685 + 0.661098i 0.991303 0.131597i \(-0.0420106\pi\)
−0.609618 + 0.792695i \(0.708677\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.50000 + 4.33013i 0.209795 + 0.363376i
\(143\) 2.00000 + 3.46410i 0.167248 + 0.289683i
\(144\) 0 0
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 7.00000 12.1244i 0.579324 1.00342i
\(147\) 0 0
\(148\) 3.00000 + 5.19615i 0.246598 + 0.427121i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 3.50000 6.06218i 0.283887 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 3.46410i 0.160644 0.278243i
\(156\) 0 0
\(157\) 5.50000 9.52628i 0.438948 0.760280i −0.558661 0.829396i \(-0.688685\pi\)
0.997609 + 0.0691164i \(0.0220180\pi\)
\(158\) −5.50000 + 9.52628i −0.437557 + 0.757870i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 3.00000 5.19615i 0.234978 0.406994i −0.724288 0.689497i \(-0.757831\pi\)
0.959266 + 0.282503i \(0.0911648\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −1.00000 1.73205i −0.0773823 0.134030i 0.824737 0.565516i \(-0.191323\pi\)
−0.902120 + 0.431486i \(0.857990\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 11.0000 + 19.0526i 0.836315 + 1.44854i 0.892956 + 0.450145i \(0.148628\pi\)
−0.0566411 + 0.998395i \(0.518039\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) 0 0
\(178\) −14.0000 −1.04934
\(179\) −12.0000 20.7846i −0.896922 1.55351i −0.831408 0.555663i \(-0.812464\pi\)
−0.0655145 0.997852i \(-0.520869\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) −7.00000 −0.507833
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) −5.50000 9.52628i −0.386979 0.670267i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) 0 0
\(208\) 1.00000 1.73205i 0.0693375 0.120096i
\(209\) −7.00000 + 12.1244i −0.484200 + 0.838659i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 3.46410i 0.135457 0.234619i
\(219\) 0 0
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.00000 + 1.73205i −0.0669650 + 0.115987i −0.897564 0.440884i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) 17.0000 1.12833 0.564165 0.825662i \(-0.309198\pi\)
0.564165 + 0.825662i \(0.309198\pi\)
\(228\) 0 0
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) −1.50000 2.59808i −0.0989071 0.171312i
\(231\) 0 0
\(232\) 4.00000 6.92820i 0.262613 0.454859i
\(233\) 0.500000 0.866025i 0.0327561 0.0567352i −0.849183 0.528099i \(-0.822905\pi\)
0.881939 + 0.471364i \(0.156238\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0 0
\(244\) −13.0000 −0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) −14.0000 −0.890799
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 0 0
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) 7.00000 0.441836 0.220918 0.975292i \(-0.429095\pi\)
0.220918 + 0.975292i \(0.429095\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.00000 0.499026 0.249513 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) −19.0000 −1.17159 −0.585795 0.810459i \(-0.699218\pi\)
−0.585795 + 0.810459i \(0.699218\pi\)
\(264\) 0 0
\(265\) 2.00000 + 3.46410i 0.122859 + 0.212798i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) −3.50000 6.06218i −0.213399 0.369618i 0.739377 0.673291i \(-0.235120\pi\)
−0.952776 + 0.303674i \(0.901787\pi\)
\(270\) 0 0
\(271\) 7.00000 12.1244i 0.425220 0.736502i −0.571221 0.820796i \(-0.693530\pi\)
0.996441 + 0.0842940i \(0.0268635\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.00000 + 1.73205i 0.0604122 + 0.104637i
\(275\) −8.00000 −0.482418
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −4.50000 + 7.79423i −0.269892 + 0.467467i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) 12.5000 21.6506i 0.743048 1.28700i −0.208053 0.978117i \(-0.566713\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) −2.50000 + 4.33013i −0.148348 + 0.256946i
\(285\) 0 0
\(286\) −2.00000 + 3.46410i −0.118262 + 0.204837i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −8.00000 −0.469776
\(291\) 0 0
\(292\) 14.0000 0.819288
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) −2.00000 + 3.46410i −0.116445 + 0.201688i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 9.50000 + 16.4545i 0.546664 + 0.946849i
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) 6.50000 + 11.2583i 0.372189 + 0.644650i
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 0.227185
\(311\) 5.00000 8.66025i 0.283524 0.491078i −0.688726 0.725022i \(-0.741830\pi\)
0.972250 + 0.233944i \(0.0751631\pi\)
\(312\) 0 0
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) 11.0000 0.620766
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) −8.00000 + 13.8564i −0.447914 + 0.775810i
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) 6.00000 0.332309
\(327\) 0 0
\(328\) −6.00000 10.3923i −0.331295 0.573819i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) 0 0
\(334\) 1.00000 1.73205i 0.0547176 0.0947736i
\(335\) 1.00000 1.73205i 0.0546358 0.0946320i
\(336\) 0 0
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 0 0
\(341\) 4.00000 6.92820i 0.216612 0.375183i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −15.0000 + 25.9808i −0.802932 + 1.39072i 0.114747 + 0.993395i \(0.463394\pi\)
−0.917679 + 0.397324i \(0.869939\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) 5.00000 0.265372
\(356\) −7.00000 12.1244i −0.370999 0.642590i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 14.5000 25.1147i 0.765281 1.32551i −0.174817 0.984601i \(-0.555933\pi\)
0.940098 0.340904i \(-0.110733\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 0 0
\(364\) 0 0
\(365\) −7.00000 12.1244i −0.366397 0.634618i
\(366\) 0 0
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) −16.0000 −0.824042
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −3.50000 6.06218i −0.179546 0.310983i
\(381\) 0 0
\(382\) −1.50000 + 2.59808i −0.0767467 + 0.132929i
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) −1.00000 1.73205i −0.0507673 0.0879316i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 5.50000 + 9.52628i 0.276735 + 0.479319i
\(396\) 0 0
\(397\) 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) 7.00000 12.1244i 0.350878 0.607739i
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 5.50000 9.52628i 0.273635 0.473950i
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 0 0
\(409\) −12.0000 + 20.7846i −0.593362 + 1.02773i 0.400414 + 0.916334i \(0.368866\pi\)
−0.993776 + 0.111398i \(0.964467\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 0 0
\(412\) 4.00000 6.92820i 0.197066 0.341328i
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) −14.0000 −0.684762
\(419\) 2.50000 + 4.33013i 0.122133 + 0.211541i 0.920609 0.390487i \(-0.127693\pi\)
−0.798476 + 0.602027i \(0.794360\pi\)
\(420\) 0 0
\(421\) 18.0000 31.1769i 0.877266 1.51947i 0.0229375 0.999737i \(-0.492698\pi\)
0.854329 0.519733i \(-0.173969\pi\)
\(422\) −11.0000 + 19.0526i −0.535472 + 0.927464i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 + 6.92820i 0.193347 + 0.334887i
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) 16.0000 + 27.7128i 0.770693 + 1.33488i 0.937184 + 0.348836i \(0.113423\pi\)
−0.166491 + 0.986043i \(0.553244\pi\)
\(432\) 0 0
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) 10.5000 18.1865i 0.502283 0.869980i
\(438\) 0 0
\(439\) −18.0000 31.1769i −0.859093 1.48799i −0.872795 0.488087i \(-0.837695\pi\)
0.0137020 0.999906i \(-0.495638\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) 0 0
\(445\) −7.00000 + 12.1244i −0.331832 + 0.574750i
\(446\) −2.00000 −0.0947027
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) 1.00000 0.0470360
\(453\) 0 0
\(454\) 8.50000 + 14.7224i 0.398925 + 0.690958i
\(455\) 0 0
\(456\) 0 0
\(457\) −8.50000 14.7224i −0.397613 0.688686i 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) 0 0
\(460\) 1.50000 2.59808i 0.0699379 0.121136i
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) 0.500000 + 0.866025i 0.0232370 + 0.0402476i 0.877410 0.479741i \(-0.159269\pi\)
−0.854173 + 0.519989i \(0.825936\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 1.00000 0.0463241
\(467\) 14.0000 24.2487i 0.647843 1.12210i −0.335794 0.941935i \(-0.609005\pi\)
0.983637 0.180161i \(-0.0576619\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −4.00000 + 6.92820i −0.184506 + 0.319574i
\(471\) 0 0
\(472\) 2.00000 3.46410i 0.0920575 0.159448i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) −5.00000 8.66025i −0.227744 0.394464i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) −12.5000 21.6506i −0.566429 0.981084i −0.996915 0.0784867i \(-0.974991\pi\)
0.430486 0.902597i \(-0.358342\pi\)
\(488\) −6.50000 11.2583i −0.294241 0.509641i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.00000 + 5.19615i 0.135388 + 0.234499i 0.925746 0.378147i \(-0.123439\pi\)
−0.790358 + 0.612646i \(0.790105\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −7.00000 12.1244i −0.314945 0.545501i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 24.0000 1.07439 0.537194 0.843459i \(-0.319484\pi\)
0.537194 + 0.843459i \(0.319484\pi\)
\(500\) 4.50000 7.79423i 0.201246 0.348569i
\(501\) 0 0
\(502\) 3.50000 + 6.06218i 0.156213 + 0.270568i
\(503\) 14.0000 0.624229 0.312115 0.950044i \(-0.398963\pi\)
0.312115 + 0.950044i \(0.398963\pi\)
\(504\) 0 0
\(505\) −11.0000 −0.489494
\(506\) −3.00000 5.19615i −0.133366 0.230997i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) −34.0000 −1.50702 −0.753512 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 4.00000 + 6.92820i 0.176432 + 0.305590i
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 8.00000 + 13.8564i 0.351840 + 0.609404i
\(518\) 0 0
\(519\) 0 0
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) −7.00000 12.1244i −0.306676 0.531178i 0.670957 0.741496i \(-0.265883\pi\)
−0.977633 + 0.210318i \(0.932550\pi\)
\(522\) 0 0
\(523\) 17.5000 30.3109i 0.765222 1.32540i −0.174908 0.984585i \(-0.555963\pi\)
0.940129 0.340818i \(-0.110704\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) −9.50000 16.4545i −0.414220 0.717450i
\(527\) 0 0
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −2.00000 + 3.46410i −0.0868744 + 0.150471i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 + 20.7846i −0.519778 + 0.900281i
\(534\) 0 0
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 3.50000 6.06218i 0.150896 0.261359i
\(539\) 0 0
\(540\) 0 0
\(541\) 10.0000 17.3205i 0.429934 0.744667i −0.566933 0.823764i \(-0.691870\pi\)
0.996867 + 0.0790969i \(0.0252036\pi\)
\(542\) 14.0000 0.601351
\(543\) 0 0
\(544\) 0 0
\(545\) −2.00000 3.46410i −0.0856706 0.148386i
\(546\) 0 0
\(547\) 4.00000 6.92820i 0.171028 0.296229i −0.767752 0.640747i \(-0.778625\pi\)
0.938779 + 0.344519i \(0.111958\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) −4.00000 6.92820i −0.170561 0.295420i
\(551\) −28.0000 48.4974i −1.19284 2.06606i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 1.73205i −0.0424859 0.0735878i
\(555\) 0 0
\(556\) −9.00000 −0.381685
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −15.0000 −0.632737
\(563\) −5.50000 + 9.52628i −0.231797 + 0.401485i −0.958337 0.285640i \(-0.907794\pi\)
0.726540 + 0.687124i \(0.241127\pi\)
\(564\) 0 0
\(565\) −0.500000 0.866025i −0.0210352 0.0364340i
\(566\) 25.0000 1.05083
\(567\) 0 0
\(568\) −5.00000 −0.209795
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 14.0000 + 24.2487i 0.582828 + 1.00949i 0.995142 + 0.0984456i \(0.0313871\pi\)
−0.412315 + 0.911041i \(0.635280\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) −4.00000 6.92820i −0.166091 0.287678i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) 0 0
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) 11.5000 19.9186i 0.474656 0.822128i −0.524923 0.851150i \(-0.675906\pi\)
0.999579 + 0.0290218i \(0.00923921\pi\)
\(588\) 0 0
\(589\) 14.0000 + 24.2487i 0.576860 + 0.999151i
\(590\) −4.00000 −0.164677
\(591\) 0 0
\(592\) −6.00000 −0.246598
\(593\) −21.0000 + 36.3731i −0.862367 + 1.49366i 0.00727173 + 0.999974i \(0.497685\pi\)
−0.869638 + 0.493689i \(0.835648\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.00000 8.66025i 0.204808 0.354738i
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) 13.0000 22.5167i 0.530281 0.918474i −0.469095 0.883148i \(-0.655420\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) 6.00000 0.243532 0.121766 0.992559i \(-0.461144\pi\)
0.121766 + 0.992559i \(0.461144\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) −6.50000 + 11.2583i −0.263177 + 0.455836i
\(611\) −8.00000 + 13.8564i −0.323645 + 0.560570i
\(612\) 0 0
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 0 0
\(616\) 0 0
\(617\) −11.0000 19.0526i −0.442843 0.767027i 0.555056 0.831813i \(-0.312697\pi\)
−0.997899 + 0.0647859i \(0.979364\pi\)
\(618\) 0 0
\(619\) 11.0000 0.442127 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) 2.00000 + 3.46410i 0.0803219 + 0.139122i
\(621\) 0 0
\(622\) 10.0000 0.400963
\(623\) 0 0
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 0 0
\(628\) 5.50000 + 9.52628i 0.219474 + 0.380140i
\(629\) 0 0
\(630\) 0 0
\(631\) 9.00000 0.358284 0.179142 0.983823i \(-0.442668\pi\)
0.179142 + 0.983823i \(0.442668\pi\)
\(632\) −5.50000 9.52628i −0.218778 0.378935i
\(633\) 0 0
\(634\) −12.0000 + 20.7846i −0.476581 + 0.825462i
\(635\) −19.0000 −0.753992
\(636\) 0 0
\(637\) 0 0
\(638\) −16.0000 −0.633446
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −47.0000 −1.85639 −0.928194 0.372096i \(-0.878639\pi\)
−0.928194 + 0.372096i \(0.878639\pi\)
\(642\) 0 0
\(643\) −6.00000 10.3923i −0.236617 0.409832i 0.723124 0.690718i \(-0.242705\pi\)
−0.959741 + 0.280885i \(0.909372\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.0000 + 36.3731i 0.825595 + 1.42997i 0.901464 + 0.432855i \(0.142494\pi\)
−0.0758684 + 0.997118i \(0.524173\pi\)
\(648\) 0 0
\(649\) −4.00000 + 6.92820i −0.157014 + 0.271956i
\(650\) 4.00000 6.92820i 0.156893 0.271746i
\(651\) 0 0
\(652\) 3.00000 + 5.19615i 0.117489 + 0.203497i
\(653\) 32.0000 1.25226 0.626128 0.779720i \(-0.284639\pi\)
0.626128 + 0.779720i \(0.284639\pi\)
\(654\) 0 0
\(655\) 15.0000 0.586098
\(656\) 6.00000 10.3923i 0.234261 0.405751i
\(657\) 0 0
\(658\) 0 0
\(659\) 10.0000 17.3205i 0.389545 0.674711i −0.602844 0.797859i \(-0.705966\pi\)
0.992388 + 0.123148i \(0.0392990\pi\)
\(660\) 0 0
\(661\) −15.5000 + 26.8468i −0.602880 + 1.04422i 0.389503 + 0.921025i \(0.372647\pi\)
−0.992383 + 0.123194i \(0.960686\pi\)
\(662\) −2.00000 + 3.46410i −0.0777322 + 0.134636i
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 20.7846i 0.464642 0.804783i
\(668\) 2.00000 0.0773823
\(669\) 0 0
\(670\) 2.00000 0.0772667
\(671\) 13.0000 + 22.5167i 0.501859 + 0.869246i
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 8.00000 0.306336
\(683\) −5.00000 8.66025i −0.191320 0.331375i 0.754368 0.656452i \(-0.227943\pi\)
−0.945688 + 0.325076i \(0.894610\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) −4.00000 + 6.92820i −0.152388 + 0.263944i
\(690\) 0 0
\(691\) −14.5000 25.1147i −0.551606 0.955410i −0.998159 0.0606524i \(-0.980682\pi\)
0.446553 0.894757i \(-0.352651\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 4.50000 + 7.79423i 0.170695 + 0.295652i
\(696\) 0 0
\(697\) 0 0
\(698\) −30.0000 −1.13552
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) 21.0000 + 36.3731i 0.792030 + 1.37184i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 12.0000 + 20.7846i 0.451626 + 0.782239i
\(707\) 0 0
\(708\) 0 0
\(709\) 16.0000 + 27.7128i 0.600893 + 1.04078i 0.992686 + 0.120723i \(0.0385214\pi\)
−0.391794 + 0.920053i \(0.628145\pi\)
\(710\) 2.50000 + 4.33013i 0.0938233 + 0.162507i
\(711\) 0 0
\(712\) 7.00000 12.1244i 0.262336 0.454379i
\(713\) −6.00000 + 10.3923i −0.224702 + 0.389195i
\(714\) 0 0
\(715\) 2.00000 + 3.46410i 0.0747958 + 0.129550i
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 29.0000 1.08227
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 0 0
\(724\) 3.50000 6.06218i 0.130076 0.225299i
\(725\) 16.0000 27.7128i 0.594225 1.02923i
\(726\) 0 0
\(727\) 13.0000 22.5167i 0.482143 0.835097i −0.517647 0.855595i \(-0.673192\pi\)
0.999790 + 0.0204978i \(0.00652512\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) 0 0
\(732\) 0 0
\(733\) −1.00000 −0.0369358 −0.0184679 0.999829i \(-0.505879\pi\)
−0.0184679 + 0.999829i \(0.505879\pi\)
\(734\) 16.0000 + 27.7128i 0.590571 + 1.02290i
\(735\) 0 0
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) 2.00000 3.46410i 0.0736709 0.127602i
\(738\) 0 0
\(739\) 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i \(0.0796718\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(740\) 3.00000 + 5.19615i 0.110282 + 0.191014i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 + 41.5692i 0.880475 + 1.52503i 0.850814 + 0.525467i \(0.176109\pi\)
0.0296605 + 0.999560i \(0.490557\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) −16.0000 27.7128i −0.585802 1.01464i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −39.0000 −1.42313 −0.711565 0.702620i \(-0.752013\pi\)
−0.711565 + 0.702620i \(0.752013\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) 0 0
\(754\) −8.00000 13.8564i −0.291343 0.504621i
\(755\) 19.0000 0.691481
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −6.00000 10.3923i −0.217930 0.377466i
\(759\) 0 0
\(760\) 3.50000 6.06218i 0.126958 0.219898i
\(761\) −20.0000 −0.724999 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.00000 −0.108536
\(765\) 0 0
\(766\) −3.00000 5.19615i −0.108394 0.187745i
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) 1.00000 + 1.73205i 0.0360609 + 0.0624593i 0.883493 0.468445i \(-0.155186\pi\)
−0.847432 + 0.530904i \(0.821852\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) 0 0
\(778\) 15.0000 + 25.9808i 0.537776 + 0.931455i
\(779\) −84.0000 −3.00961
\(780\) 0 0
\(781\) 10.0000 0.357828
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.50000 9.52628i 0.196303 0.340007i
\(786\) 0 0
\(787\) 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i \(-0.810621\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(788\) −6.00000 + 10.3923i −0.213741 + 0.370211i
\(789\) 0 0
\(790\) −5.50000 + 9.52628i −0.195681 + 0.338930i
\(791\) 0 0
\(792\) 0 0
\(793\) −13.0000 + 22.5167i −0.461644 + 0.799590i
\(794\) 14.0000 0.496841
\(795\) 0 0