Properties

Label 1134.2.f.k.757.1
Level $1134$
Weight $2$
Character 1134.757
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: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 757.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.k.379.1

$q$-expansion

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

Character values

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

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

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
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 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 \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 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 −0.169701 + 0.985496i \(0.554280\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) 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 \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 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 \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −9.00000 −1.32698
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 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 \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 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 \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) −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 −0.129307 0.991605i \(-0.541275\pi\)
0.923408 0.383819i \(-0.125391\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 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 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 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 \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 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 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 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 \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 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 −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 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 \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 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 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) −7.00000 + 12.1244i −0.593732 + 1.02837i 0.399992 + 0.916519i \(0.369013\pi\)
−0.993724 + 0.111856i \(0.964321\pi\)
\(140\) 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 \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) −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 −0.115050 + 0.993360i \(0.536703\pi\)
−0.802749 + 0.596316i \(0.796630\pi\)
\(158\) −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 \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 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 −0.810745 0.585399i \(-0.800938\pi\)
−0.101598 0.994826i \(-0.532395\pi\)
\(174\) 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 \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 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 \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 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 \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 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 −0.550743 0.834675i \(-0.685655\pi\)
0.998221 + 0.0596196i \(0.0189888\pi\)
\(212\) 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 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) −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 \(-0.0701218\pi\)
−0.677158 + 0.735838i \(0.736789\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 12.0000 0.786146 0.393073 0.919507i \(-0.371412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(234\) 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 \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 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 −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 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 \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 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 \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 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 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −14.0000 −0.839664
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 + 5.19615i 0.178965 + 0.309976i 0.941526 0.336939i \(-0.109392\pi\)
−0.762561 + 0.646916i \(0.776058\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 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 \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 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 −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) −23.0000 −1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i \(0.152241\pi\)
−0.0453045 + 0.998973i \(0.514426\pi\)
\(318\) 0 0
\(319\) 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 0.999667 + 0.0257885i \(0.00820965\pi\)
−0.477500 + 0.878632i \(0.658457\pi\)
\(332\) 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 −0.632882 0.774248i \(-0.718128\pi\)
0.986960 + 0.160968i \(0.0514616\pi\)
\(338\) 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 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 0.500000 + 0.866025i 0.0267644 + 0.0463573i 0.879097 0.476642i \(-0.158146\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(350\) 5.00000 0.267261
\(351\) 0 0
\(352\) 0 0
\(353\) −13.5000 23.3827i −0.718532 1.24453i −0.961581 0.274521i \(-0.911481\pi\)
0.243049 0.970014i \(-0.421853\pi\)
\(354\) 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 \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 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 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 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 −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 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 \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 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 \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 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 −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 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 \(-0.952743\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) 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 \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 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 −0.893843 0.448379i \(-0.852001\pi\)
0.0586141 0.998281i \(-0.481332\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 15.0000 0.713477
\(443\) −3.00000 5.19615i −0.142534 0.246877i 0.785916 0.618333i \(-0.212192\pi\)
−0.928450 + 0.371457i \(0.878858\pi\)
\(444\) 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 −0.906702 0.421771i \(-0.861409\pi\)
0.0880870 0.996113i \(-0.471925\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) 11.0000 19.0526i 0.511213 0.885448i −0.488702 0.872451i \(-0.662530\pi\)
0.999916 0.0129968i \(-0.00413714\pi\)
\(464\) −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 \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) 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 0.903859 + 0.427830i \(0.140722\pi\)
−0.0814184 + 0.996680i \(0.525945\pi\)
\(480\) 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 \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 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 −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 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 \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 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 \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 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 −0.764231 0.644942i \(-0.776881\pi\)
−0.176421 0.984315i \(-0.556452\pi\)
\(548\) −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 \(-0.646761\pi\)
−0.444899 + 0.895581i \(0.646761\pi\)
\(558\) 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 \(-0.853470\pi\)
0.832684 + 0.553748i \(0.186803\pi\)
\(564\) 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 −0.999994 0.00354413i \(-0.998872\pi\)
0.496928 0.867792i \(-0.334461\pi\)
\(570\) 0 0
\(571\) −2.50000 + 4.33013i −0.104622 + 0.181210i −0.913584 0.406651i \(-0.866697\pi\)
0.808962 + 0.587861i \(0.200030\pi\)
\(572\) 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 0.974668 + 0.223659i \(0.0718001\pi\)
−0.293640 + 0.955916i \(0.594867\pi\)
\(588\) 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 \(-0.831019\pi\)
−0.862367 + 0.506284i \(0.831019\pi\)
\(594\) 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 \(-0.852854\pi\)
0.833753 + 0.552137i \(0.186188\pi\)
\(600\) 0 0
\(601\) −4.00000 6.92820i −0.163163 0.282607i 0.772838 0.634603i \(-0.218836\pi\)
−0.936002 + 0.351996i \(0.885503\pi\)
\(602\) 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 −0.912291 0.409542i \(-0.865689\pi\)
0.810819 + 0.585296i \(0.199022\pi\)
\(608\) 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 0.0398207 + 0.999207i \(0.487321\pi\)
−0.885249 + 0.465118i \(0.846012\pi\)
\(618\) 0 0
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 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 0.964498 + 0.264089i \(0.0850714\pi\)
−0.253541 + 0.967325i \(0.581595\pi\)
\(642\) 0 0
\(643\) 20.0000 34.6410i 0.788723 1.36611i −0.138027 0.990429i \(-0.544076\pi\)
0.926750 0.375680i \(-0.122591\pi\)
\(644\) −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 \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 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 \(-0.889681\pi\)
0.764442 + 0.644692i \(0.223014\pi\)
\(654\) 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 \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −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 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 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 \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) 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 \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 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 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 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 \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 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 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 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 \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 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 0.664243 0.747517i \(-0.268754\pi\)
−0.979490 + 0.201492i \(0.935421\pi\)
\(728\) −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 −0.996398 0.0847976i \(-0.972976\pi\)
0.571636 + 0.820507i \(0.306309\pi\)
\(734\) −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 \(-0.815808\pi\)
0.892228 + 0.451585i \(0.149141\pi\)
\(744\) 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 −0.965013 0.262201i \(-0.915552\pi\)
0.709580 + 0.704625i \(0.248885\pi\)
\(752\) −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 \(-0.781176\pi\)
0.935988 + 0.352032i \(0.114509\pi\)
\(762\) 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 −0.239293 0.970947i \(-0.576916\pi\)
0.960512 0.278240i \(-0.0897509\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 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 −0.963394 0.268091i \(-0.913607\pi\)
0.713871 + 0.700278i \(0.246941\pi\)
\(788\) 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