Properties

Label 1134.2.f.e.379.1
Level $1134$
Weight $2$
Character 1134.379
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
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 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.e.757.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +2.00000 q^{19} +(4.50000 + 7.79423i) q^{23} +(2.50000 - 4.33013i) q^{25} +5.00000 q^{26} +1.00000 q^{28} +(1.50000 - 2.59808i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +2.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(3.00000 + 5.19615i) q^{41} +(0.500000 - 0.866025i) q^{43} -9.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.50000 + 4.33013i) q^{50} +(-2.50000 + 4.33013i) q^{52} +3.00000 q^{53} +(-0.500000 + 0.866025i) q^{56} +(1.50000 + 2.59808i) q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(6.50000 + 11.2583i) q^{67} +(-1.50000 - 2.59808i) q^{68} +9.00000 q^{71} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(5.00000 - 8.66025i) q^{79} -6.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(0.500000 + 0.866025i) q^{86} +15.0000 q^{89} +5.00000 q^{91} +(4.50000 - 7.79423i) q^{92} +(3.00000 + 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8} - 5 q^{13} - q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 9 q^{23} + 5 q^{25} + 10 q^{26} + 2 q^{28} + 3 q^{29} - 5 q^{31} - q^{32} - 3 q^{34} + 4 q^{37} - 2 q^{38} + 6 q^{41} + q^{43} - 18 q^{46} + 6 q^{47} - q^{49} + 5 q^{50} - 5 q^{52} + 6 q^{53} - q^{56} + 3 q^{58} + 3 q^{59} + 10 q^{61} + 10 q^{62} + 2 q^{64} + 13 q^{67} - 3 q^{68} + 18 q^{71} + 4 q^{73} - 2 q^{74} - 2 q^{76} + 10 q^{79} - 12 q^{82} + 12 q^{83} + q^{86} + 30 q^{89} + 10 q^{91} + 9 q^{92} + 6 q^{94} - 8 q^{97} + 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) −2.50000 4.33013i −0.693375 1.20096i −0.970725 0.240192i \(-0.922790\pi\)
0.277350 0.960769i \(-0.410544\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 5.00000 0.980581
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −9.00000 −1.32698
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 2.50000 + 4.33013i 0.353553 + 0.612372i
\(51\) 0 0
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 5.00000 0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 5.00000 0.524142
\(92\) 4.50000 7.79423i 0.469157 0.812605i
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −2.50000 4.33013i −0.245145 0.424604i
\(105\) 0 0
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −6.00000 10.3923i −0.564433 0.977626i −0.997102 0.0760733i \(-0.975762\pi\)
0.432670 0.901553i \(-0.357572\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 5.00000 + 8.66025i 0.452679 + 0.784063i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 0 0
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 0 0
\(133\) −1.00000 + 1.73205i −0.0867110 + 0.150188i
\(134\) −13.0000 −1.12303
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 0 0
\(139\) −7.00000 12.1244i −0.593732 1.02837i −0.993724 0.111856i \(-0.964321\pi\)
0.399992 0.916519i \(-0.369013\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.50000 + 7.79423i −0.377632 + 0.654077i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 0 0
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 12.0000 20.7846i 0.912343 1.58022i 0.101598 0.994826i \(-0.467605\pi\)
0.810745 0.585399i \(-0.199062\pi\)
\(174\) 0 0
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) 0 0
\(177\) 0 0
\(178\) −7.50000 + 12.9904i −0.562149 + 0.973670i
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −2.50000 + 4.33013i −0.185312 + 0.320970i
\(183\) 0 0
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 0 0
\(202\) −9.00000 15.5885i −0.633238 1.09680i
\(203\) 1.50000 + 2.59808i 0.105279 + 0.182349i
\(204\) 0 0
\(205\) 0 0
\(206\) −13.0000 −0.905753
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) 0 0
\(216\) 0 0
\(217\) 5.00000 0.339422
\(218\) 8.00000 13.8564i 0.541828 0.938474i
\(219\) 0 0
\(220\) 0 0
\(221\) −7.50000 12.9904i −0.504505 0.873828i
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 12.0000 0.798228
\(227\) −4.50000 + 7.79423i −0.298675 + 0.517321i −0.975833 0.218517i \(-0.929878\pi\)
0.677158 + 0.735838i \(0.263211\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) 0 0
\(238\) −1.50000 2.59808i −0.0972306 0.168408i
\(239\) −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i \(-0.293538\pi\)
−0.992195 + 0.124696i \(0.960204\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) −2.50000 4.33013i −0.158750 0.274963i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −10.0000 + 17.3205i −0.627456 + 1.08679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.00000 −0.556022
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 1.73205i −0.0613139 0.106199i
\(267\) 0 0
\(268\) 6.50000 11.2583i 0.397051 0.687712i
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) −9.00000 15.5885i −0.543710 0.941733i
\(275\) 0 0
\(276\) 0 0
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 14.0000 0.839664
\(279\) 0 0
\(280\) 0 0
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −4.50000 7.79423i −0.267026 0.462502i
\(285\) 0 0
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) 9.00000 0.521356
\(299\) 22.5000 38.9711i 1.30121 2.25376i
\(300\) 0 0
\(301\) 0.500000 + 0.866025i 0.0288195 + 0.0499169i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 23.0000 1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −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
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 4.50000 7.79423i 0.250775 0.434355i
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −25.0000 −1.38675
\(326\) −5.50000 + 9.52628i −0.304617 + 0.527612i
\(327\) 0 0
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i \(-0.658457\pi\)
0.999667 0.0257885i \(-0.00820965\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) 12.0000 + 20.7846i 0.645124 + 1.11739i
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) 0 0
\(349\) 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i \(-0.824813\pi\)
0.879097 + 0.476642i \(0.158146\pi\)
\(350\) −5.00000 −0.267261
\(351\) 0 0
\(352\) 0 0
\(353\) 13.5000 23.3827i 0.718532 1.24453i −0.243049 0.970014i \(-0.578147\pi\)
0.961581 0.274521i \(-0.0885192\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.50000 12.9904i −0.397499 0.688489i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 3.50000 6.06218i 0.183956 0.318621i
\(363\) 0 0
\(364\) −2.50000 4.33013i −0.131036 0.226960i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) −9.00000 −0.469157
\(369\) 0 0
\(370\) 0 0
\(371\) −1.50000 + 2.59808i −0.0778761 + 0.134885i
\(372\) 0 0
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) 13.5000 + 23.3827i 0.682724 + 1.18251i
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 0 0
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −5.50000 + 9.52628i −0.275690 + 0.477509i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) −12.5000 + 21.6506i −0.622669 + 1.07849i
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) 0 0
\(408\) 0 0
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) −3.00000 −0.147620
\(414\) 0 0
\(415\) 0 0
\(416\) −2.50000 + 4.33013i −0.122573 + 0.212302i
\(417\) 0 0
\(418\) 0 0
\(419\) 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i \(-0.0472572\pi\)
−0.622601 + 0.782540i \(0.713924\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −13.0000 −0.632830
\(423\) 0 0
\(424\) 3.00000 0.145693
\(425\) 7.50000 12.9904i 0.363803 0.630126i
\(426\) 0 0
\(427\) 5.00000 + 8.66025i 0.241967 + 0.419099i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −2.50000 + 4.33013i −0.120004 + 0.207853i
\(435\) 0 0
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) 9.00000 + 15.5885i 0.430528 + 0.745697i
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 15.0000 0.713477
\(443\) 3.00000 5.19615i 0.142534 0.246877i −0.785916 0.618333i \(-0.787808\pi\)
0.928450 + 0.371457i \(0.121142\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 0 0
\(454\) −4.50000 7.79423i −0.211195 0.365801i
\(455\) 0 0
\(456\) 0 0
\(457\) −17.5000 + 30.3109i −0.818615 + 1.41788i 0.0880870 + 0.996113i \(0.471925\pi\)
−0.906702 + 0.421771i \(0.861409\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 0 0
\(463\) 11.0000 + 19.0526i 0.511213 + 0.885448i 0.999916 + 0.0129968i \(0.00413714\pi\)
−0.488702 + 0.872451i \(0.662530\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 6.00000 10.3923i 0.277945 0.481414i
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 0 0
\(469\) −13.0000 −0.600284
\(470\) 0 0
\(471\) 0 0
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) 0 0
\(474\) 0 0
\(475\) 5.00000 8.66025i 0.229416 0.397360i
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 0 0
\(481\) −5.00000 8.66025i −0.227980 0.394874i
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) 0 0
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 0 0
\(490\) 0 0
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 0 0
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) 10.0000 0.449921
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) −4.50000 + 7.79423i −0.201853 + 0.349619i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −10.0000 17.3205i −0.443678 0.768473i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −1.00000 1.73205i −0.0439375 0.0761019i
\(519\) 0 0
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 4.50000 7.79423i 0.196583 0.340492i
\(525\) 0 0
\(526\) −4.50000 7.79423i −0.196209 0.339845i
\(527\) −7.50000 12.9904i −0.326705 0.565870i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000 0.0867110
\(533\) 15.0000 25.9808i 0.649722 1.12535i
\(534\) 0 0
\(535\) 0 0
\(536\) 6.50000 + 11.2583i 0.280757 + 0.486286i
\(537\) 0 0
\(538\) 12.0000 20.7846i 0.517357 0.896088i
\(539\) 0 0
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 3.50000 6.06218i 0.150338 0.260393i
\(543\) 0 0
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) 0 0
\(547\) −22.0000 + 38.1051i −0.940652 + 1.62926i −0.176421 + 0.984315i \(0.556452\pi\)
−0.764231 + 0.644942i \(0.776881\pi\)
\(548\) 18.0000 0.768922
\(549\) 0 0
\(550\) 0 0
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) 5.00000 + 8.66025i 0.212622 + 0.368271i
\(554\) −4.00000 6.92820i −0.169944 0.294351i
\(555\) 0 0
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) 21.0000 0.889799 0.444899 0.895581i \(-0.353239\pi\)
0.444899 + 0.895581i \(0.353239\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) 1.50000 + 2.59808i 0.0632175 + 0.109496i 0.895902 0.444252i \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 9.00000 0.377632
\(569\) 12.0000 20.7846i 0.503066 0.871336i −0.496928 0.867792i \(-0.665539\pi\)
0.999994 0.00354413i \(-0.00112814\pi\)
\(570\) 0 0
\(571\) −2.50000 4.33013i −0.104622 0.181210i 0.808962 0.587861i \(-0.200030\pi\)
−0.913584 + 0.406651i \(0.866697\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) 45.0000 1.87663
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −16.5000 + 28.5788i −0.681028 + 1.17957i 0.293640 + 0.955916i \(0.405133\pi\)
−0.974668 + 0.223659i \(0.928200\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) 0 0
\(598\) 22.5000 + 38.9711i 0.920093 + 1.59365i
\(599\) 1.50000 + 2.59808i 0.0612883 + 0.106155i 0.895042 0.445983i \(-0.147146\pi\)
−0.833753 + 0.552137i \(0.813812\pi\)
\(600\) 0 0
\(601\) −4.00000 + 6.92820i −0.163163 + 0.282607i −0.936002 0.351996i \(-0.885503\pi\)
0.772838 + 0.634603i \(0.218836\pi\)
\(602\) −1.00000 −0.0407570
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −2.50000 4.33013i −0.101472 0.175754i 0.810819 0.585296i \(-0.199022\pi\)
−0.912291 + 0.409542i \(0.865689\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 0 0
\(610\) 0 0
\(611\) −30.0000 −1.21367
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i \(0.153988\pi\)
−0.0398207 + 0.999207i \(0.512679\pi\)
\(618\) 0 0
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −7.50000 + 12.9904i −0.300481 + 0.520449i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) −11.5000 + 19.9186i −0.458900 + 0.794838i
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 0 0
\(634\) −15.0000 25.9808i −0.595726 1.03183i
\(635\) 0 0
\(636\) 0 0
\(637\) −2.50000 + 4.33013i −0.0990536 + 0.171566i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 + 31.1769i −0.710957 + 1.23141i 0.253541 + 0.967325i \(0.418405\pi\)
−0.964498 + 0.264089i \(0.914929\pi\)
\(642\) 0 0
\(643\) 20.0000 + 34.6410i 0.788723 + 1.36611i 0.926750 + 0.375680i \(0.122591\pi\)
−0.138027 + 0.990429i \(0.544076\pi\)
\(644\) 4.50000 + 7.79423i 0.177325 + 0.307136i
\(645\) 0 0
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 30.0000 1.17942 0.589711 0.807614i \(-0.299242\pi\)
0.589711 + 0.807614i \(0.299242\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 12.5000 21.6506i 0.490290 0.849208i
\(651\) 0 0
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 9.50000 + 16.4545i 0.369228 + 0.639522i
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 27.0000 1.04544
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) −13.0000 −0.500741
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) −7.50000 12.9904i −0.285727 0.494894i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) −24.0000 −0.912343
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 0 0
\(697\) 9.00000 + 15.5885i 0.340899 + 0.590455i
\(698\) 0.500000 + 0.866025i 0.0189253 + 0.0327795i
\(699\) 0 0
\(700\) 2.50000 4.33013i 0.0944911 0.163663i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 13.5000 + 23.3827i 0.508079 + 0.880019i
\(707\) −9.00000 15.5885i −0.338480 0.586264i
\(708\) 0 0
\(709\) 14.0000 24.2487i 0.525781 0.910679i −0.473768 0.880650i \(-0.657106\pi\)
0.999549 0.0300298i \(-0.00956021\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 15.0000 0.562149
\(713\) 22.5000 38.9711i 0.842632 1.45948i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 + 20.7846i 0.448461 + 0.776757i
\(717\) 0 0
\(718\) 1.50000 2.59808i 0.0559795 0.0969593i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −13.0000 −0.484145
\(722\) 7.50000 12.9904i 0.279121 0.483452i
\(723\) 0 0
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) −7.50000 12.9904i −0.278543 0.482451i
\(726\) 0 0
\(727\) −8.50000 + 14.7224i −0.315248 + 0.546025i −0.979490 0.201492i \(-0.935421\pi\)
0.664243 + 0.747517i \(0.268754\pi\)
\(728\) 5.00000 0.185312
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) −11.5000 19.9186i −0.424762 0.735710i 0.571636 0.820507i \(-0.306309\pi\)
−0.996398 + 0.0847976i \(0.972976\pi\)
\(734\) 9.50000 + 16.4545i 0.350651 + 0.607346i
\(735\) 0 0
\(736\) 4.50000 7.79423i 0.165872 0.287299i
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.50000 2.59808i −0.0550667 0.0953784i
\(743\) −1.50000 2.59808i −0.0550297 0.0953142i 0.837198 0.546899i \(-0.184192\pi\)
−0.892228 + 0.451585i \(0.850859\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 14.0000 0.512576
\(747\) 0 0
\(748\) 0 0
\(749\) 6.00000 10.3923i 0.219235 0.379727i
\(750\) 0 0
\(751\) −7.00000 12.1244i −0.255434 0.442424i 0.709580 0.704625i \(-0.248885\pi\)
−0.965013 + 0.262201i \(0.915552\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) 7.50000 12.9904i 0.273134 0.473082i
\(755\) 0 0
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 8.00000 13.8564i 0.290573 0.503287i
\(759\) 0 0
\(760\) 0 0
\(761\) −4.50000 7.79423i −0.163125 0.282541i 0.772863 0.634573i \(-0.218824\pi\)
−0.935988 + 0.352032i \(0.885491\pi\)
\(762\) 0 0
\(763\) 8.00000 13.8564i 0.289619 0.501636i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 0 0
\(767\) 7.50000 12.9904i 0.270809 0.469055i
\(768\) 0 0
\(769\) 20.0000 + 34.6410i 0.721218 + 1.24919i 0.960512 + 0.278240i \(0.0897509\pi\)
−0.239293 + 0.970947i \(0.576916\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −25.0000 −0.898027
\(776\) −4.00000 + 6.92820i −0.143592 + 0.248708i
\(777\) 0 0
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) −27.0000 −0.965518
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 12.1244i −0.249523 0.432187i 0.713871 0.700278i \(-0.246941\pi\)
−0.963394 + 0.268091i \(0.913607\pi\)
\(788\) −9.00000 15.5885i −0.320612 0.555316i
\(789\) 0 0
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) −50.0000 −1.77555
\(794\) −1.00000 + 1.73205i −0.0354887 + 0.0614682i
\(795\) 0 0
\(796\) −5.50000 9.52628i −0.194942 0.337650i
\(797\) 3.00000 + 5.19615i 0.106265 + 0.184057i