Properties

Label 1152.2.i.h.769.4
Level $1152$
Weight $2$
Character 1152.769
Analytic conductor $9.199$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.8528759163648.1
Defining polynomial: \(x^{10} - 2 x^{9} + x^{8} + 9 x^{6} - 36 x^{5} + 27 x^{4} + 27 x^{2} - 162 x + 243\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 769.4
Root \(1.72806 - 0.117480i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.h.385.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.762291 + 1.55529i) q^{3} +(0.705463 - 1.22190i) q^{5} +(-1.17123 - 2.02864i) q^{7} +(-1.83783 + 2.37116i) q^{9} +O(q^{10})\) \(q+(0.762291 + 1.55529i) q^{3} +(0.705463 - 1.22190i) q^{5} +(-1.17123 - 2.02864i) q^{7} +(-1.83783 + 2.37116i) q^{9} +(-1.30116 - 2.25368i) q^{11} +(1.26229 - 2.18635i) q^{13} +(2.43817 + 0.165755i) q^{15} +4.94479 q^{17} -1.00929 q^{19} +(2.26229 - 3.36802i) q^{21} +(1.50663 - 2.60955i) q^{23} +(1.50464 + 2.60612i) q^{25} +(-5.08879 - 1.05083i) q^{27} +(-0.0708926 - 0.122790i) q^{29} +(4.77135 - 8.26422i) q^{31} +(2.51325 - 3.74164i) q^{33} -3.30505 q^{35} +9.00324 q^{37} +(4.36263 + 0.296587i) q^{39} +(4.33084 - 7.50123i) q^{41} +(-3.15717 - 5.46838i) q^{43} +(1.60080 + 3.91840i) q^{45} +(3.24898 + 5.62740i) q^{47} +(0.756418 - 1.31015i) q^{49} +(3.76937 + 7.69057i) q^{51} -6.02590 q^{53} -3.67169 q^{55} +(-0.769369 - 1.56973i) q^{57} +(-5.64142 + 9.77123i) q^{59} +(-3.45856 - 5.99040i) q^{61} +(6.96275 + 0.951101i) q^{63} +(-1.78100 - 3.08478i) q^{65} +(0.154962 - 0.268402i) q^{67} +(5.20708 + 0.353996i) q^{69} -8.24940 q^{71} -6.78931 q^{73} +(-2.90628 + 4.32677i) q^{75} +(-3.04793 + 5.27917i) q^{77} +(4.99530 + 8.65211i) q^{79} +(-2.24479 - 8.71556i) q^{81} +(3.47041 + 6.01093i) q^{83} +(3.48837 - 6.04203i) q^{85} +(0.136932 - 0.203860i) q^{87} +15.8969 q^{89} -5.91375 q^{91} +(16.4904 + 1.12108i) q^{93} +(-0.712014 + 1.23325i) q^{95} +(7.44449 + 12.8942i) q^{97} +(7.73514 + 1.05661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + q^{3} + 4q^{7} - q^{9} + O(q^{10}) \) \( 10q + q^{3} + 4q^{7} - q^{9} - q^{11} + 6q^{13} - 12q^{15} - 6q^{17} + 18q^{19} + 16q^{21} - 4q^{23} + q^{25} - 2q^{27} - 4q^{29} + 8q^{31} - 13q^{33} - 24q^{35} - 20q^{37} + 18q^{39} - 5q^{41} - 13q^{43} - 12q^{45} + 6q^{47} + 3q^{49} + 3q^{51} - 12q^{55} + 27q^{57} - 13q^{59} + 10q^{61} + 20q^{63} - 17q^{67} - 10q^{69} - 8q^{71} - 34q^{73} - 29q^{75} + 8q^{77} + 6q^{79} - q^{81} + 12q^{83} + 18q^{85} - 10q^{87} + 44q^{89} + 36q^{91} + 26q^{93} + 6q^{95} + 27q^{97} + 34q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.762291 + 1.55529i 0.440109 + 0.897945i
\(4\) 0 0
\(5\) 0.705463 1.22190i 0.315493 0.546449i −0.664049 0.747689i \(-0.731164\pi\)
0.979542 + 0.201239i \(0.0644969\pi\)
\(6\) 0 0
\(7\) −1.17123 2.02864i −0.442685 0.766753i 0.555203 0.831715i \(-0.312641\pi\)
−0.997888 + 0.0649620i \(0.979307\pi\)
\(8\) 0 0
\(9\) −1.83783 + 2.37116i −0.612609 + 0.790386i
\(10\) 0 0
\(11\) −1.30116 2.25368i −0.392315 0.679510i 0.600439 0.799670i \(-0.294992\pi\)
−0.992754 + 0.120161i \(0.961659\pi\)
\(12\) 0 0
\(13\) 1.26229 2.18635i 0.350096 0.606385i −0.636170 0.771549i \(-0.719482\pi\)
0.986266 + 0.165164i \(0.0528155\pi\)
\(14\) 0 0
\(15\) 2.43817 + 0.165755i 0.629532 + 0.0427979i
\(16\) 0 0
\(17\) 4.94479 1.19929 0.599644 0.800267i \(-0.295309\pi\)
0.599644 + 0.800267i \(0.295309\pi\)
\(18\) 0 0
\(19\) −1.00929 −0.231546 −0.115773 0.993276i \(-0.536935\pi\)
−0.115773 + 0.993276i \(0.536935\pi\)
\(20\) 0 0
\(21\) 2.26229 3.36802i 0.493672 0.734961i
\(22\) 0 0
\(23\) 1.50663 2.60955i 0.314153 0.544129i −0.665104 0.746751i \(-0.731613\pi\)
0.979257 + 0.202622i \(0.0649461\pi\)
\(24\) 0 0
\(25\) 1.50464 + 2.60612i 0.300929 + 0.521224i
\(26\) 0 0
\(27\) −5.08879 1.05083i −0.979337 0.202233i
\(28\) 0 0
\(29\) −0.0708926 0.122790i −0.0131644 0.0228015i 0.859368 0.511357i \(-0.170857\pi\)
−0.872533 + 0.488556i \(0.837524\pi\)
\(30\) 0 0
\(31\) 4.77135 8.26422i 0.856960 1.48430i −0.0178546 0.999841i \(-0.505684\pi\)
0.874815 0.484458i \(-0.160983\pi\)
\(32\) 0 0
\(33\) 2.51325 3.74164i 0.437501 0.651335i
\(34\) 0 0
\(35\) −3.30505 −0.558656
\(36\) 0 0
\(37\) 9.00324 1.48012 0.740062 0.672539i \(-0.234796\pi\)
0.740062 + 0.672539i \(0.234796\pi\)
\(38\) 0 0
\(39\) 4.36263 + 0.296587i 0.698580 + 0.0474920i
\(40\) 0 0
\(41\) 4.33084 7.50123i 0.676364 1.17150i −0.299705 0.954032i \(-0.596888\pi\)
0.976068 0.217464i \(-0.0697785\pi\)
\(42\) 0 0
\(43\) −3.15717 5.46838i −0.481464 0.833920i 0.518310 0.855193i \(-0.326561\pi\)
−0.999774 + 0.0212731i \(0.993228\pi\)
\(44\) 0 0
\(45\) 1.60080 + 3.91840i 0.238633 + 0.584121i
\(46\) 0 0
\(47\) 3.24898 + 5.62740i 0.473912 + 0.820840i 0.999554 0.0298661i \(-0.00950808\pi\)
−0.525642 + 0.850706i \(0.676175\pi\)
\(48\) 0 0
\(49\) 0.756418 1.31015i 0.108060 0.187165i
\(50\) 0 0
\(51\) 3.76937 + 7.69057i 0.527817 + 1.07689i
\(52\) 0 0
\(53\) −6.02590 −0.827721 −0.413861 0.910340i \(-0.635820\pi\)
−0.413861 + 0.910340i \(0.635820\pi\)
\(54\) 0 0
\(55\) −3.67169 −0.495090
\(56\) 0 0
\(57\) −0.769369 1.56973i −0.101905 0.207916i
\(58\) 0 0
\(59\) −5.64142 + 9.77123i −0.734451 + 1.27211i 0.220513 + 0.975384i \(0.429227\pi\)
−0.954964 + 0.296722i \(0.904106\pi\)
\(60\) 0 0
\(61\) −3.45856 5.99040i −0.442823 0.766992i 0.555075 0.831801i \(-0.312690\pi\)
−0.997898 + 0.0648083i \(0.979356\pi\)
\(62\) 0 0
\(63\) 6.96275 + 0.951101i 0.877224 + 0.119827i
\(64\) 0 0
\(65\) −1.78100 3.08478i −0.220906 0.382620i
\(66\) 0 0
\(67\) 0.154962 0.268402i 0.0189316 0.0327905i −0.856404 0.516306i \(-0.827307\pi\)
0.875336 + 0.483515i \(0.160640\pi\)
\(68\) 0 0
\(69\) 5.20708 + 0.353996i 0.626859 + 0.0426161i
\(70\) 0 0
\(71\) −8.24940 −0.979023 −0.489512 0.871997i \(-0.662825\pi\)
−0.489512 + 0.871997i \(0.662825\pi\)
\(72\) 0 0
\(73\) −6.78931 −0.794628 −0.397314 0.917683i \(-0.630058\pi\)
−0.397314 + 0.917683i \(0.630058\pi\)
\(74\) 0 0
\(75\) −2.90628 + 4.32677i −0.335589 + 0.499612i
\(76\) 0 0
\(77\) −3.04793 + 5.27917i −0.347344 + 0.601618i
\(78\) 0 0
\(79\) 4.99530 + 8.65211i 0.562015 + 0.973438i 0.997321 + 0.0731553i \(0.0233069\pi\)
−0.435306 + 0.900283i \(0.643360\pi\)
\(80\) 0 0
\(81\) −2.24479 8.71556i −0.249421 0.968395i
\(82\) 0 0
\(83\) 3.47041 + 6.01093i 0.380928 + 0.659786i 0.991195 0.132410i \(-0.0422714\pi\)
−0.610268 + 0.792195i \(0.708938\pi\)
\(84\) 0 0
\(85\) 3.48837 6.04203i 0.378367 0.655351i
\(86\) 0 0
\(87\) 0.136932 0.203860i 0.0146807 0.0218561i
\(88\) 0 0
\(89\) 15.8969 1.68507 0.842535 0.538642i \(-0.181062\pi\)
0.842535 + 0.538642i \(0.181062\pi\)
\(90\) 0 0
\(91\) −5.91375 −0.619930
\(92\) 0 0
\(93\) 16.4904 + 1.12108i 1.70997 + 0.116250i
\(94\) 0 0
\(95\) −0.712014 + 1.23325i −0.0730511 + 0.126528i
\(96\) 0 0
\(97\) 7.44449 + 12.8942i 0.755874 + 1.30921i 0.944939 + 0.327247i \(0.106121\pi\)
−0.189065 + 0.981965i \(0.560546\pi\)
\(98\) 0 0
\(99\) 7.73514 + 1.05661i 0.777411 + 0.106193i
\(100\) 0 0
\(101\) −0.823082 1.42562i −0.0818997 0.141855i 0.822166 0.569248i \(-0.192765\pi\)
−0.904066 + 0.427393i \(0.859432\pi\)
\(102\) 0 0
\(103\) 6.40783 11.0987i 0.631382 1.09359i −0.355887 0.934529i \(-0.615821\pi\)
0.987269 0.159057i \(-0.0508454\pi\)
\(104\) 0 0
\(105\) −2.51941 5.14030i −0.245869 0.501642i
\(106\) 0 0
\(107\) −13.6556 −1.32014 −0.660070 0.751204i \(-0.729473\pi\)
−0.660070 + 0.751204i \(0.729473\pi\)
\(108\) 0 0
\(109\) −12.9953 −1.24473 −0.622363 0.782729i \(-0.713827\pi\)
−0.622363 + 0.782729i \(0.713827\pi\)
\(110\) 0 0
\(111\) 6.86309 + 14.0026i 0.651415 + 1.32907i
\(112\) 0 0
\(113\) −3.75804 + 6.50912i −0.353527 + 0.612326i −0.986865 0.161549i \(-0.948351\pi\)
0.633338 + 0.773875i \(0.281684\pi\)
\(114\) 0 0
\(115\) −2.12574 3.68189i −0.198226 0.343338i
\(116\) 0 0
\(117\) 2.86432 + 7.01123i 0.264806 + 0.648188i
\(118\) 0 0
\(119\) −5.79151 10.0312i −0.530907 0.919558i
\(120\) 0 0
\(121\) 2.11395 3.66148i 0.192178 0.332861i
\(122\) 0 0
\(123\) 14.9679 + 1.01757i 1.34961 + 0.0917514i
\(124\) 0 0
\(125\) 11.3005 1.01075
\(126\) 0 0
\(127\) 2.09832 0.186196 0.0930981 0.995657i \(-0.470323\pi\)
0.0930981 + 0.995657i \(0.470323\pi\)
\(128\) 0 0
\(129\) 6.09821 9.07879i 0.536917 0.799343i
\(130\) 0 0
\(131\) −4.00428 + 6.93562i −0.349856 + 0.605968i −0.986224 0.165418i \(-0.947103\pi\)
0.636368 + 0.771386i \(0.280436\pi\)
\(132\) 0 0
\(133\) 1.18211 + 2.04748i 0.102502 + 0.177539i
\(134\) 0 0
\(135\) −4.87396 + 5.47666i −0.419484 + 0.471355i
\(136\) 0 0
\(137\) 1.17445 + 2.03420i 0.100340 + 0.173793i 0.911825 0.410580i \(-0.134674\pi\)
−0.811485 + 0.584373i \(0.801340\pi\)
\(138\) 0 0
\(139\) 5.62654 9.74546i 0.477237 0.826599i −0.522422 0.852687i \(-0.674972\pi\)
0.999660 + 0.0260876i \(0.00830490\pi\)
\(140\) 0 0
\(141\) −6.27554 + 9.34280i −0.528496 + 0.786806i
\(142\) 0 0
\(143\) −6.56978 −0.549392
\(144\) 0 0
\(145\) −0.200049 −0.0166131
\(146\) 0 0
\(147\) 2.61427 + 0.177728i 0.215622 + 0.0146587i
\(148\) 0 0
\(149\) −11.9924 + 20.7715i −0.982458 + 1.70167i −0.329729 + 0.944076i \(0.606957\pi\)
−0.652729 + 0.757591i \(0.726376\pi\)
\(150\) 0 0
\(151\) −6.56507 11.3710i −0.534258 0.925362i −0.999199 0.0400204i \(-0.987258\pi\)
0.464941 0.885342i \(-0.346076\pi\)
\(152\) 0 0
\(153\) −9.08767 + 11.7249i −0.734695 + 0.947901i
\(154\) 0 0
\(155\) −6.73203 11.6602i −0.540729 0.936571i
\(156\) 0 0
\(157\) 11.6217 20.1293i 0.927511 1.60650i 0.140038 0.990146i \(-0.455278\pi\)
0.787473 0.616350i \(-0.211389\pi\)
\(158\) 0 0
\(159\) −4.59349 9.37200i −0.364287 0.743248i
\(160\) 0 0
\(161\) −7.05845 −0.556284
\(162\) 0 0
\(163\) 22.5825 1.76879 0.884397 0.466735i \(-0.154570\pi\)
0.884397 + 0.466735i \(0.154570\pi\)
\(164\) 0 0
\(165\) −2.79889 5.71052i −0.217894 0.444564i
\(166\) 0 0
\(167\) −12.4260 + 21.5224i −0.961549 + 1.66545i −0.242935 + 0.970043i \(0.578110\pi\)
−0.718614 + 0.695409i \(0.755223\pi\)
\(168\) 0 0
\(169\) 3.31325 + 5.73871i 0.254865 + 0.441439i
\(170\) 0 0
\(171\) 1.85489 2.39318i 0.141847 0.183011i
\(172\) 0 0
\(173\) −3.98389 6.90030i −0.302890 0.524620i 0.673900 0.738823i \(-0.264618\pi\)
−0.976789 + 0.214203i \(0.931285\pi\)
\(174\) 0 0
\(175\) 3.52458 6.10475i 0.266433 0.461476i
\(176\) 0 0
\(177\) −19.4975 1.32551i −1.46552 0.0996312i
\(178\) 0 0
\(179\) −3.70760 −0.277119 −0.138560 0.990354i \(-0.544247\pi\)
−0.138560 + 0.990354i \(0.544247\pi\)
\(180\) 0 0
\(181\) −13.0683 −0.971362 −0.485681 0.874136i \(-0.661428\pi\)
−0.485681 + 0.874136i \(0.661428\pi\)
\(182\) 0 0
\(183\) 6.68036 9.94547i 0.493826 0.735191i
\(184\) 0 0
\(185\) 6.35146 11.0010i 0.466968 0.808813i
\(186\) 0 0
\(187\) −6.43398 11.1440i −0.470499 0.814928i
\(188\) 0 0
\(189\) 3.82840 + 11.5541i 0.278475 + 0.840436i
\(190\) 0 0
\(191\) 0.157984 + 0.273636i 0.0114313 + 0.0197996i 0.871684 0.490068i \(-0.163028\pi\)
−0.860253 + 0.509867i \(0.829695\pi\)
\(192\) 0 0
\(193\) −10.0237 + 17.3616i −0.721522 + 1.24971i 0.238867 + 0.971052i \(0.423224\pi\)
−0.960390 + 0.278661i \(0.910109\pi\)
\(194\) 0 0
\(195\) 3.44008 5.12146i 0.246349 0.366755i
\(196\) 0 0
\(197\) −23.5586 −1.67848 −0.839240 0.543761i \(-0.817000\pi\)
−0.839240 + 0.543761i \(0.817000\pi\)
\(198\) 0 0
\(199\) 0.249396 0.0176792 0.00883960 0.999961i \(-0.497186\pi\)
0.00883960 + 0.999961i \(0.497186\pi\)
\(200\) 0 0
\(201\) 0.535568 + 0.0364098i 0.0377760 + 0.00256815i
\(202\) 0 0
\(203\) −0.166064 + 0.287631i −0.0116554 + 0.0201877i
\(204\) 0 0
\(205\) −6.11050 10.5837i −0.426776 0.739197i
\(206\) 0 0
\(207\) 3.41875 + 8.36835i 0.237619 + 0.581641i
\(208\) 0 0
\(209\) 1.31325 + 2.27461i 0.0908391 + 0.157338i
\(210\) 0 0
\(211\) 1.17490 2.03499i 0.0808834 0.140094i −0.822746 0.568409i \(-0.807559\pi\)
0.903630 + 0.428315i \(0.140893\pi\)
\(212\) 0 0
\(213\) −6.28844 12.8302i −0.430877 0.879108i
\(214\) 0 0
\(215\) −8.90907 −0.607593
\(216\) 0 0
\(217\) −22.3535 −1.51745
\(218\) 0 0
\(219\) −5.17542 10.5593i −0.349723 0.713532i
\(220\) 0 0
\(221\) 6.24177 10.8111i 0.419867 0.727230i
\(222\) 0 0
\(223\) −4.71439 8.16556i −0.315699 0.546806i 0.663887 0.747833i \(-0.268906\pi\)
−0.979586 + 0.201027i \(0.935572\pi\)
\(224\) 0 0
\(225\) −8.94479 1.22185i −0.596320 0.0814563i
\(226\) 0 0
\(227\) 0.0231851 + 0.0401577i 0.00153885 + 0.00266536i 0.866794 0.498667i \(-0.166177\pi\)
−0.865255 + 0.501332i \(0.832844\pi\)
\(228\) 0 0
\(229\) 4.03468 6.98827i 0.266619 0.461798i −0.701367 0.712800i \(-0.747427\pi\)
0.967987 + 0.251002i \(0.0807600\pi\)
\(230\) 0 0
\(231\) −10.5340 0.716141i −0.693089 0.0471186i
\(232\) 0 0
\(233\) 3.99336 0.261614 0.130807 0.991408i \(-0.458243\pi\)
0.130807 + 0.991408i \(0.458243\pi\)
\(234\) 0 0
\(235\) 9.16814 0.598063
\(236\) 0 0
\(237\) −9.64863 + 14.3645i −0.626746 + 0.933076i
\(238\) 0 0
\(239\) −1.84910 + 3.20273i −0.119608 + 0.207167i −0.919612 0.392827i \(-0.871497\pi\)
0.800004 + 0.599994i \(0.204830\pi\)
\(240\) 0 0
\(241\) 13.0879 + 22.6689i 0.843066 + 1.46023i 0.887290 + 0.461211i \(0.152585\pi\)
−0.0442246 + 0.999022i \(0.514082\pi\)
\(242\) 0 0
\(243\) 11.8440 10.1351i 0.759793 0.650165i
\(244\) 0 0
\(245\) −1.06725 1.84853i −0.0681841 0.118098i
\(246\) 0 0
\(247\) −1.27401 + 2.20665i −0.0810635 + 0.140406i
\(248\) 0 0
\(249\) −6.70326 + 9.97956i −0.424802 + 0.632429i
\(250\) 0 0
\(251\) 19.7393 1.24593 0.622967 0.782248i \(-0.285927\pi\)
0.622967 + 0.782248i \(0.285927\pi\)
\(252\) 0 0
\(253\) −7.84146 −0.492988
\(254\) 0 0
\(255\) 12.0562 + 0.819626i 0.754991 + 0.0513270i
\(256\) 0 0
\(257\) −3.53591 + 6.12438i −0.220564 + 0.382028i −0.954979 0.296672i \(-0.904123\pi\)
0.734415 + 0.678700i \(0.237456\pi\)
\(258\) 0 0
\(259\) −10.5449 18.2643i −0.655229 1.13489i
\(260\) 0 0
\(261\) 0.421442 + 0.0575684i 0.0260866 + 0.00356339i
\(262\) 0 0
\(263\) 4.03211 + 6.98383i 0.248631 + 0.430641i 0.963146 0.268979i \(-0.0866861\pi\)
−0.714515 + 0.699620i \(0.753353\pi\)
\(264\) 0 0
\(265\) −4.25105 + 7.36304i −0.261140 + 0.452308i
\(266\) 0 0
\(267\) 12.1181 + 24.7242i 0.741614 + 1.51310i
\(268\) 0 0
\(269\) −8.76619 −0.534484 −0.267242 0.963629i \(-0.586112\pi\)
−0.267242 + 0.963629i \(0.586112\pi\)
\(270\) 0 0
\(271\) −27.7606 −1.68634 −0.843168 0.537650i \(-0.819312\pi\)
−0.843168 + 0.537650i \(0.819312\pi\)
\(272\) 0 0
\(273\) −4.50800 9.19758i −0.272836 0.556663i
\(274\) 0 0
\(275\) 3.91557 6.78197i 0.236118 0.408968i
\(276\) 0 0
\(277\) 13.7727 + 23.8551i 0.827524 + 1.43331i 0.899975 + 0.435942i \(0.143585\pi\)
−0.0724506 + 0.997372i \(0.523082\pi\)
\(278\) 0 0
\(279\) 10.8269 + 26.5018i 0.648188 + 1.58662i
\(280\) 0 0
\(281\) 3.24109 + 5.61373i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(282\) 0 0
\(283\) −3.32863 + 5.76536i −0.197866 + 0.342715i −0.947836 0.318757i \(-0.896735\pi\)
0.749970 + 0.661472i \(0.230068\pi\)
\(284\) 0 0
\(285\) −2.46081 0.167295i −0.145766 0.00990968i
\(286\) 0 0
\(287\) −20.2897 −1.19766
\(288\) 0 0
\(289\) 7.45099 0.438293
\(290\) 0 0
\(291\) −14.3794 + 21.4075i −0.842933 + 1.25493i
\(292\) 0 0
\(293\) −2.61375 + 4.52714i −0.152697 + 0.264479i −0.932218 0.361897i \(-0.882129\pi\)
0.779521 + 0.626376i \(0.215462\pi\)
\(294\) 0 0
\(295\) 7.95963 + 13.7865i 0.463428 + 0.802681i
\(296\) 0 0
\(297\) 4.25310 + 12.8358i 0.246790 + 0.744808i
\(298\) 0 0
\(299\) −3.80360 6.58802i −0.219968 0.380995i
\(300\) 0 0
\(301\) −7.39557 + 12.8095i −0.426274 + 0.738328i
\(302\) 0 0
\(303\) 1.58982 2.36686i 0.0913327 0.135973i
\(304\) 0 0
\(305\) −9.75955 −0.558830
\(306\) 0 0
\(307\) 15.8311 0.903531 0.451765 0.892137i \(-0.350794\pi\)
0.451765 + 0.892137i \(0.350794\pi\)
\(308\) 0 0
\(309\) 22.1463 + 1.50558i 1.25986 + 0.0856496i
\(310\) 0 0
\(311\) −1.40298 + 2.43003i −0.0795557 + 0.137794i −0.903058 0.429518i \(-0.858683\pi\)
0.823503 + 0.567312i \(0.192017\pi\)
\(312\) 0 0
\(313\) −7.35704 12.7428i −0.415845 0.720264i 0.579672 0.814850i \(-0.303181\pi\)
−0.995517 + 0.0945858i \(0.969847\pi\)
\(314\) 0 0
\(315\) 6.07411 7.83680i 0.342237 0.441554i
\(316\) 0 0
\(317\) 0.668345 + 1.15761i 0.0375380 + 0.0650178i 0.884184 0.467139i \(-0.154715\pi\)
−0.846646 + 0.532156i \(0.821382\pi\)
\(318\) 0 0
\(319\) −0.184486 + 0.319538i −0.0103292 + 0.0178907i
\(320\) 0 0
\(321\) −10.4096 21.2384i −0.581005 1.18541i
\(322\) 0 0
\(323\) −4.99071 −0.277691
\(324\) 0 0
\(325\) 7.59719 0.421416
\(326\) 0 0
\(327\) −9.90620 20.2114i −0.547814 1.11769i
\(328\) 0 0
\(329\) 7.61063 13.1820i 0.419588 0.726747i
\(330\) 0 0
\(331\) 2.69612 + 4.66981i 0.148192 + 0.256676i 0.930559 0.366141i \(-0.119321\pi\)
−0.782367 + 0.622817i \(0.785988\pi\)
\(332\) 0 0
\(333\) −16.5464 + 21.3481i −0.906737 + 1.16987i
\(334\) 0 0
\(335\) −0.218640 0.378695i −0.0119456 0.0206903i
\(336\) 0 0
\(337\) 11.8198 20.4725i 0.643866 1.11521i −0.340696 0.940173i \(-0.610663\pi\)
0.984562 0.175035i \(-0.0560039\pi\)
\(338\) 0 0
\(339\) −12.9883 0.882988i −0.705425 0.0479573i
\(340\) 0 0
\(341\) −24.8332 −1.34479
\(342\) 0 0
\(343\) −19.9411 −1.07672
\(344\) 0 0
\(345\) 4.10595 6.11280i 0.221057 0.329102i
\(346\) 0 0
\(347\) −0.649676 + 1.12527i −0.0348764 + 0.0604077i −0.882937 0.469492i \(-0.844437\pi\)
0.848060 + 0.529900i \(0.177770\pi\)
\(348\) 0 0
\(349\) 6.27720 + 10.8724i 0.336011 + 0.581988i 0.983678 0.179935i \(-0.0575888\pi\)
−0.647668 + 0.761923i \(0.724255\pi\)
\(350\) 0 0
\(351\) −8.72102 + 9.79942i −0.465493 + 0.523054i
\(352\) 0 0
\(353\) −7.71760 13.3673i −0.410766 0.711468i 0.584207 0.811604i \(-0.301405\pi\)
−0.994974 + 0.100136i \(0.968072\pi\)
\(354\) 0 0
\(355\) −5.81965 + 10.0799i −0.308875 + 0.534987i
\(356\) 0 0
\(357\) 11.1866 16.6541i 0.592056 0.881431i
\(358\) 0 0
\(359\) 28.8687 1.52363 0.761817 0.647792i \(-0.224308\pi\)
0.761817 + 0.647792i \(0.224308\pi\)
\(360\) 0 0
\(361\) −17.9813 −0.946386
\(362\) 0 0
\(363\) 7.30609 + 0.496694i 0.383470 + 0.0260697i
\(364\) 0 0
\(365\) −4.78961 + 8.29584i −0.250699 + 0.434224i
\(366\) 0 0
\(367\) 0.959507 + 1.66192i 0.0500859 + 0.0867513i 0.889981 0.455997i \(-0.150717\pi\)
−0.839896 + 0.542748i \(0.817384\pi\)
\(368\) 0 0
\(369\) 9.82729 + 24.0551i 0.511588 + 1.25226i
\(370\) 0 0
\(371\) 7.05775 + 12.2244i 0.366420 + 0.634658i
\(372\) 0 0
\(373\) 4.71108 8.15984i 0.243931 0.422500i −0.717900 0.696147i \(-0.754896\pi\)
0.961830 + 0.273646i \(0.0882297\pi\)
\(374\) 0 0
\(375\) 8.61427 + 17.5755i 0.444839 + 0.907596i
\(376\) 0 0
\(377\) −0.357948 −0.0184353
\(378\) 0 0
\(379\) 16.1191 0.827984 0.413992 0.910281i \(-0.364134\pi\)
0.413992 + 0.910281i \(0.364134\pi\)
\(380\) 0 0
\(381\) 1.59953 + 3.26349i 0.0819465 + 0.167194i
\(382\) 0 0
\(383\) 4.35380 7.54100i 0.222469 0.385327i −0.733088 0.680133i \(-0.761922\pi\)
0.955557 + 0.294806i \(0.0952552\pi\)
\(384\) 0 0
\(385\) 4.30041 + 7.44853i 0.219169 + 0.379612i
\(386\) 0 0
\(387\) 18.7687 + 2.56378i 0.954068 + 0.130324i
\(388\) 0 0
\(389\) 10.1015 + 17.4963i 0.512167 + 0.887099i 0.999900 + 0.0141065i \(0.00449040\pi\)
−0.487734 + 0.872993i \(0.662176\pi\)
\(390\) 0 0
\(391\) 7.44995 12.9037i 0.376760 0.652568i
\(392\) 0 0
\(393\) −13.8393 0.940845i −0.698100 0.0474593i
\(394\) 0 0
\(395\) 14.0960 0.709246
\(396\) 0 0
\(397\) −35.3319 −1.77326 −0.886628 0.462483i \(-0.846959\pi\)
−0.886628 + 0.462483i \(0.846959\pi\)
\(398\) 0 0
\(399\) −2.28330 + 3.39929i −0.114308 + 0.170178i
\(400\) 0 0
\(401\) 5.03813 8.72630i 0.251592 0.435771i −0.712372 0.701802i \(-0.752379\pi\)
0.963964 + 0.266031i \(0.0857125\pi\)
\(402\) 0 0
\(403\) −12.0457 20.8637i −0.600037 1.03930i
\(404\) 0 0
\(405\) −12.2331 3.40560i −0.607870 0.169226i
\(406\) 0 0
\(407\) −11.7147 20.2904i −0.580675 1.00576i
\(408\) 0 0
\(409\) 2.08466 3.61073i 0.103080 0.178539i −0.809872 0.586606i \(-0.800464\pi\)
0.912952 + 0.408067i \(0.133797\pi\)
\(410\) 0 0
\(411\) −2.26849 + 3.37725i −0.111897 + 0.166588i
\(412\) 0 0
\(413\) 26.4297 1.30052
\(414\) 0 0
\(415\) 9.79300 0.480719
\(416\) 0 0
\(417\) 19.4460 + 1.32201i 0.952276 + 0.0647392i
\(418\) 0 0
\(419\) 8.13944 14.0979i 0.397638 0.688729i −0.595796 0.803136i \(-0.703163\pi\)
0.993434 + 0.114407i \(0.0364968\pi\)
\(420\) 0 0
\(421\) 6.90585 + 11.9613i 0.336570 + 0.582957i 0.983785 0.179351i \(-0.0573996\pi\)
−0.647215 + 0.762308i \(0.724066\pi\)
\(422\) 0 0
\(423\) −19.3145 2.63833i −0.939103 0.128280i
\(424\) 0 0
\(425\) 7.44015 + 12.8867i 0.360900 + 0.625098i
\(426\) 0 0
\(427\) −8.10157 + 14.0323i −0.392063 + 0.679072i
\(428\) 0 0
\(429\) −5.00808 10.2179i −0.241792 0.493324i
\(430\) 0 0
\(431\) −13.2716 −0.639268 −0.319634 0.947541i \(-0.603560\pi\)
−0.319634 + 0.947541i \(0.603560\pi\)
\(432\) 0 0
\(433\) −4.32495 −0.207844 −0.103922 0.994585i \(-0.533139\pi\)
−0.103922 + 0.994585i \(0.533139\pi\)
\(434\) 0 0
\(435\) −0.152495 0.311133i −0.00731158 0.0149177i
\(436\) 0 0
\(437\) −1.52062 + 2.63379i −0.0727410 + 0.125991i
\(438\) 0 0
\(439\) 9.69938 + 16.7998i 0.462926 + 0.801812i 0.999105 0.0422926i \(-0.0134662\pi\)
−0.536179 + 0.844104i \(0.680133\pi\)
\(440\) 0 0
\(441\) 1.71642 + 4.20142i 0.0817343 + 0.200068i
\(442\) 0 0
\(443\) 15.1280 + 26.2025i 0.718754 + 1.24492i 0.961494 + 0.274827i \(0.0886204\pi\)
−0.242740 + 0.970091i \(0.578046\pi\)
\(444\) 0 0
\(445\) 11.2147 19.4244i 0.531627 0.920806i
\(446\) 0 0
\(447\) −41.4473 2.81774i −1.96039 0.133274i
\(448\) 0 0
\(449\) −8.49691 −0.400994 −0.200497 0.979694i \(-0.564256\pi\)
−0.200497 + 0.979694i \(0.564256\pi\)
\(450\) 0 0
\(451\) −22.5405 −1.06139
\(452\) 0 0
\(453\) 12.6807 18.8786i 0.595792 0.886994i
\(454\) 0 0
\(455\) −4.17194 + 7.22601i −0.195583 + 0.338760i
\(456\) 0 0
\(457\) −15.8223 27.4050i −0.740136 1.28195i −0.952433 0.304748i \(-0.901428\pi\)
0.212297 0.977205i \(-0.431906\pi\)
\(458\) 0 0
\(459\) −25.1630 5.19615i −1.17451 0.242536i
\(460\) 0 0
\(461\) 9.62685 + 16.6742i 0.448367 + 0.776594i 0.998280 0.0586276i \(-0.0186725\pi\)
−0.549913 + 0.835222i \(0.685339\pi\)
\(462\) 0 0
\(463\) 7.46981 12.9381i 0.347151 0.601284i −0.638591 0.769546i \(-0.720482\pi\)
0.985742 + 0.168263i \(0.0538157\pi\)
\(464\) 0 0
\(465\) 13.0032 19.3587i 0.603009 0.897738i
\(466\) 0 0
\(467\) −39.9590 −1.84908 −0.924540 0.381084i \(-0.875551\pi\)
−0.924540 + 0.381084i \(0.875551\pi\)
\(468\) 0 0
\(469\) −0.725987 −0.0335230
\(470\) 0 0
\(471\) 40.1660 + 2.73063i 1.85075 + 0.125821i
\(472\) 0 0
\(473\) −8.21598 + 14.2305i −0.377771 + 0.654319i
\(474\) 0 0
\(475\) −1.51862 2.63032i −0.0696789 0.120687i
\(476\) 0 0
\(477\) 11.0746 14.2884i 0.507069 0.654220i
\(478\) 0 0
\(479\) 16.1993 + 28.0581i 0.740167 + 1.28201i 0.952419 + 0.304792i \(0.0985869\pi\)
−0.212252 + 0.977215i \(0.568080\pi\)
\(480\) 0 0
\(481\) 11.3647 19.6843i 0.518186 0.897525i
\(482\) 0 0
\(483\) −5.38059 10.9779i −0.244825 0.499512i
\(484\) 0 0
\(485\) 21.0073 0.953891
\(486\) 0 0
\(487\) 27.8763 1.26320 0.631598 0.775296i \(-0.282399\pi\)
0.631598 + 0.775296i \(0.282399\pi\)
\(488\) 0 0
\(489\) 17.2144 + 35.1222i 0.778462 + 1.58828i
\(490\) 0 0
\(491\) −8.12126 + 14.0664i −0.366507 + 0.634809i −0.989017 0.147803i \(-0.952780\pi\)
0.622510 + 0.782612i \(0.286113\pi\)
\(492\) 0 0
\(493\) −0.350549 0.607170i −0.0157880 0.0273455i
\(494\) 0 0
\(495\) 6.74793 8.70616i 0.303297 0.391313i
\(496\) 0 0
\(497\) 9.66198 + 16.7350i 0.433399 + 0.750669i
\(498\) 0 0
\(499\) −18.1826 + 31.4932i −0.813966 + 1.40983i 0.0961021 + 0.995371i \(0.469362\pi\)
−0.910068 + 0.414459i \(0.863971\pi\)
\(500\) 0 0
\(501\) −42.9456 2.91960i −1.91867 0.130438i
\(502\) 0 0
\(503\) 43.2509 1.92846 0.964231 0.265063i \(-0.0853929\pi\)
0.964231 + 0.265063i \(0.0853929\pi\)
\(504\) 0 0
\(505\) −2.32262 −0.103355
\(506\) 0 0
\(507\) −6.39968 + 9.52761i −0.284220 + 0.423136i
\(508\) 0 0
\(509\) 21.2885 36.8728i 0.943597 1.63436i 0.185062 0.982727i \(-0.440751\pi\)
0.758536 0.651632i \(-0.225915\pi\)
\(510\) 0 0
\(511\) 7.95187 + 13.7730i 0.351770 + 0.609284i
\(512\) 0 0
\(513\) 5.13604 + 1.06059i 0.226762 + 0.0468263i
\(514\) 0 0
\(515\) −9.04098 15.6594i −0.398393 0.690037i
\(516\) 0 0
\(517\) 8.45489 14.6443i 0.371846 0.644056i
\(518\) 0 0
\(519\) 7.69506 11.4561i 0.337776 0.502868i
\(520\) 0 0
\(521\) 21.0544 0.922408 0.461204 0.887294i \(-0.347418\pi\)
0.461204 + 0.887294i \(0.347418\pi\)
\(522\) 0 0
\(523\) 21.0092 0.918667 0.459333 0.888264i \(-0.348088\pi\)
0.459333 + 0.888264i \(0.348088\pi\)
\(524\) 0 0
\(525\) 12.1814 + 0.828134i 0.531639 + 0.0361427i
\(526\) 0 0
\(527\) 23.5934 40.8649i 1.02774 1.78010i
\(528\) 0 0
\(529\) 6.96016 + 12.0554i 0.302616 + 0.524146i
\(530\) 0 0
\(531\) −12.8012 31.3345i −0.555524 1.35980i
\(532\) 0 0
\(533\) −10.9336 18.9375i −0.473585 0.820273i
\(534\) 0 0
\(535\) −9.63355 + 16.6858i −0.416495 + 0.721390i
\(536\) 0 0
\(537\) −2.82627 5.76638i −0.121962 0.248837i
\(538\) 0 0
\(539\) −3.93689 −0.169574
\(540\) 0 0
\(541\) 12.3375 0.530429 0.265215 0.964189i \(-0.414557\pi\)
0.265215 + 0.964189i \(0.414557\pi\)
\(542\) 0 0
\(543\) −9.96187 20.3250i −0.427505 0.872229i
\(544\) 0 0
\(545\) −9.16772 + 15.8790i −0.392702 + 0.680179i
\(546\) 0 0
\(547\) 0.461070 + 0.798596i 0.0197139 + 0.0341455i 0.875714 0.482830i \(-0.160391\pi\)
−0.856000 + 0.516976i \(0.827058\pi\)
\(548\) 0 0
\(549\) 20.5604 + 2.80852i 0.877498 + 0.119865i
\(550\) 0 0
\(551\) 0.0715510 + 0.123930i 0.00304817 + 0.00527959i
\(552\) 0 0
\(553\) 11.7013 20.2673i 0.497591 0.861853i
\(554\) 0 0
\(555\) 21.9514 + 1.49234i 0.931786 + 0.0633461i
\(556\) 0 0
\(557\) −19.1352 −0.810786 −0.405393 0.914142i \(-0.632865\pi\)
−0.405393 + 0.914142i \(0.632865\pi\)
\(558\) 0 0
\(559\) −15.9411 −0.674235
\(560\) 0 0
\(561\) 12.4275 18.5016i 0.524690 0.781139i
\(562\) 0 0
\(563\) 16.9309 29.3252i 0.713552 1.23591i −0.249963 0.968255i \(-0.580419\pi\)
0.963515 0.267653i \(-0.0862482\pi\)
\(564\) 0 0
\(565\) 5.30232 + 9.18388i 0.223070 + 0.386369i
\(566\) 0 0
\(567\) −15.0515 + 14.7618i −0.632105 + 0.619938i
\(568\) 0 0
\(569\) −14.1745 24.5509i −0.594225 1.02923i −0.993656 0.112465i \(-0.964125\pi\)
0.399431 0.916763i \(-0.369208\pi\)
\(570\) 0 0
\(571\) −11.9901 + 20.7674i −0.501769 + 0.869089i 0.498229 + 0.867045i \(0.333984\pi\)
−0.999998 + 0.00204345i \(0.999350\pi\)
\(572\) 0 0
\(573\) −0.305153 + 0.454300i −0.0127479 + 0.0189787i
\(574\) 0 0
\(575\) 9.06773 0.378151
\(576\) 0 0
\(577\) 10.2508 0.426746 0.213373 0.976971i \(-0.431555\pi\)
0.213373 + 0.976971i \(0.431555\pi\)
\(578\) 0 0
\(579\) −34.6432 2.35517i −1.43972 0.0978774i
\(580\) 0 0
\(581\) 8.12934 14.0804i 0.337262 0.584155i
\(582\) 0 0
\(583\) 7.84068 + 13.5805i 0.324728 + 0.562445i
\(584\) 0 0
\(585\) 10.5877 + 1.44626i 0.437746 + 0.0597955i
\(586\) 0 0
\(587\) −2.15393 3.73071i −0.0889021 0.153983i 0.818145 0.575012i \(-0.195002\pi\)
−0.907047 + 0.421029i \(0.861669\pi\)
\(588\) 0 0
\(589\) −4.81566 + 8.34097i −0.198426 + 0.343684i
\(590\) 0 0
\(591\) −17.9585 36.6403i −0.738714 1.50718i
\(592\) 0 0
\(593\) −27.4046 −1.12537 −0.562686 0.826670i \(-0.690232\pi\)
−0.562686 + 0.826670i \(0.690232\pi\)
\(594\) 0 0
\(595\) −16.3428 −0.669990
\(596\) 0 0
\(597\) 0.190112 + 0.387882i 0.00778077 + 0.0158749i
\(598\) 0 0
\(599\) 13.5711 23.5058i 0.554500 0.960423i −0.443442 0.896303i \(-0.646243\pi\)
0.997942 0.0641195i \(-0.0204239\pi\)
\(600\) 0 0
\(601\) 11.7512 + 20.3537i 0.479341 + 0.830244i 0.999719 0.0236923i \(-0.00754221\pi\)
−0.520378 + 0.853936i \(0.674209\pi\)
\(602\) 0 0
\(603\) 0.351631 + 0.860716i 0.0143195 + 0.0350510i
\(604\) 0 0
\(605\) −2.98263 5.16607i −0.121261 0.210031i
\(606\) 0 0
\(607\) 2.69717 4.67164i 0.109475 0.189616i −0.806083 0.591803i \(-0.798416\pi\)
0.915558 + 0.402187i \(0.131750\pi\)
\(608\) 0 0
\(609\) −0.573937 0.0390183i −0.0232571 0.00158110i
\(610\) 0 0
\(611\) 16.4046 0.663660
\(612\) 0 0
\(613\) −5.92486 −0.239303 −0.119651 0.992816i \(-0.538178\pi\)
−0.119651 + 0.992816i \(0.538178\pi\)
\(614\) 0 0
\(615\) 11.8027 17.5714i 0.475930 0.708548i
\(616\) 0 0
\(617\) −6.12456 + 10.6081i −0.246566 + 0.427064i −0.962571 0.271031i \(-0.912635\pi\)
0.716005 + 0.698095i \(0.245969\pi\)
\(618\) 0 0
\(619\) −0.656697 1.13743i −0.0263949 0.0457173i 0.852526 0.522684i \(-0.175069\pi\)
−0.878921 + 0.476967i \(0.841736\pi\)
\(620\) 0 0
\(621\) −10.4091 + 11.6962i −0.417703 + 0.469354i
\(622\) 0 0
\(623\) −18.6190 32.2491i −0.745955 1.29203i
\(624\) 0 0
\(625\) 0.448881 0.777485i 0.0179553 0.0310994i
\(626\) 0 0
\(627\) −2.53659 + 3.77638i −0.101302 + 0.150814i
\(628\) 0 0
\(629\) 44.5192 1.77510
\(630\) 0 0
\(631\) −28.7173 −1.14322 −0.571608 0.820527i \(-0.693680\pi\)
−0.571608 + 0.820527i \(0.693680\pi\)
\(632\) 0 0
\(633\) 4.06060 + 0.276054i 0.161394 + 0.0109722i
\(634\) 0 0
\(635\) 1.48029 2.56394i 0.0587435 0.101747i
\(636\) 0 0
\(637\) −1.90964 3.30759i −0.0756626 0.131052i
\(638\) 0 0
\(639\) 15.1610 19.5606i 0.599758 0.773806i
\(640\) 0 0
\(641\) 9.67893 + 16.7644i 0.382295 + 0.662154i 0.991390 0.130943i \(-0.0418006\pi\)
−0.609095 + 0.793097i \(0.708467\pi\)
\(642\) 0 0
\(643\) 0.415416 0.719521i 0.0163824 0.0283751i −0.857718 0.514120i \(-0.828118\pi\)
0.874100 + 0.485745i \(0.161452\pi\)
\(644\) 0 0
\(645\) −6.79130 13.8561i −0.267407 0.545585i
\(646\) 0 0
\(647\) 10.1290 0.398211 0.199106 0.979978i \(-0.436196\pi\)
0.199106 + 0.979978i \(0.436196\pi\)
\(648\) 0 0
\(649\) 29.3616 1.15254
\(650\) 0 0
\(651\) −17.0399 34.7661i −0.667845 1.36259i
\(652\) 0 0
\(653\) 21.0565 36.4709i 0.824004 1.42722i −0.0786734 0.996900i \(-0.525068\pi\)
0.902678 0.430317i \(-0.141598\pi\)
\(654\) 0 0
\(655\) 5.64975 + 9.78565i 0.220754 + 0.382357i
\(656\) 0 0
\(657\) 12.4776 16.0985i 0.486796 0.628063i
\(658\) 0 0
\(659\) 13.0094 + 22.5329i 0.506774 + 0.877759i 0.999969 + 0.00784021i \(0.00249564\pi\)
−0.493195 + 0.869919i \(0.664171\pi\)
\(660\) 0 0
\(661\) −14.6544 + 25.3822i −0.569990 + 0.987252i 0.426576 + 0.904452i \(0.359720\pi\)
−0.996566 + 0.0828004i \(0.973614\pi\)
\(662\) 0 0
\(663\) 21.5723 + 1.46656i 0.837799 + 0.0569566i
\(664\) 0 0
\(665\) 3.33574 0.129355
\(666\) 0 0
\(667\) −0.427235 −0.0165426
\(668\) 0 0
\(669\) 9.10605 13.5568i 0.352060 0.524134i
\(670\) 0 0
\(671\) −9.00029 + 15.5890i −0.347453 + 0.601805i
\(672\) 0 0
\(673\) −7.72976 13.3883i −0.297960 0.516082i 0.677709 0.735330i \(-0.262973\pi\)
−0.975669 + 0.219248i \(0.929640\pi\)
\(674\) 0 0
\(675\) −4.91821 14.8431i −0.189302 0.571312i
\(676\) 0 0
\(677\) −3.02467 5.23889i −0.116248 0.201347i 0.802030 0.597284i \(-0.203753\pi\)
−0.918278 + 0.395937i \(0.870420\pi\)
\(678\) 0 0
\(679\) 17.4385 30.2044i 0.669228 1.15914i
\(680\) 0 0
\(681\) −0.0447830 + 0.0666713i −0.00171609 + 0.00255485i
\(682\) 0 0
\(683\) 25.1518 0.962406 0.481203 0.876609i \(-0.340200\pi\)
0.481203 + 0.876609i \(0.340200\pi\)
\(684\) 0 0
\(685\) 3.31411 0.126626
\(686\) 0 0
\(687\) 13.9444 + 0.947988i 0.532011 + 0.0361680i
\(688\) 0 0
\(689\) −7.60644 + 13.1747i −0.289782 + 0.501918i
\(690\) 0 0
\(691\) 21.8943 + 37.9221i 0.832899 + 1.44262i 0.895729 + 0.444600i \(0.146654\pi\)
−0.0628298 + 0.998024i \(0.520013\pi\)
\(692\) 0 0
\(693\) −6.91619 16.9293i −0.262724 0.643092i
\(694\) 0 0
\(695\) −7.93864 13.7501i −0.301130 0.521572i
\(696\) 0 0
\(697\) 21.4151 37.0921i 0.811155 1.40496i
\(698\) 0 0
\(699\) 3.04410 + 6.21081i 0.115138 + 0.234914i
\(700\) 0 0
\(701\) 37.4594 1.41482 0.707412 0.706802i \(-0.249863\pi\)
0.707412 + 0.706802i \(0.249863\pi\)
\(702\) 0 0
\(703\) −9.08685 −0.342717
\(704\) 0 0
\(705\) 6.98879 + 14.2591i 0.263213 + 0.537028i
\(706\) 0 0
\(707\) −1.92804 + 3.33947i −0.0725116 + 0.125594i
\(708\) 0 0
\(709\) 16.4907 + 28.5627i 0.619321 + 1.07269i 0.989610 + 0.143778i \(0.0459252\pi\)
−0.370289 + 0.928916i \(0.620741\pi\)
\(710\) 0 0
\(711\) −29.6960 4.05643i −1.11369 0.152128i
\(712\) 0 0
\(713\) −14.3773 24.9022i −0.538433 0.932594i
\(714\) 0 0
\(715\) −4.63474 + 8.02760i −0.173329 + 0.300215i
\(716\) 0 0
\(717\) −6.39070 0.434463i −0.238665 0.0162253i
\(718\) 0 0
\(719\) 12.0397 0.449006 0.224503 0.974473i \(-0.427924\pi\)
0.224503 + 0.974473i \(0.427924\pi\)
\(720\) 0 0
\(721\) −30.0203 −1.11801
\(722\) 0 0
\(723\) −25.2798 + 37.6357i −0.940168 + 1.39969i
\(724\) 0 0
\(725\) 0.213336 0.369509i 0.00792311 0.0137232i
\(726\) 0 0
\(727\) 15.6359 + 27.0822i 0.579905 + 1.00443i 0.995490 + 0.0948705i \(0.0302437\pi\)
−0.415585 + 0.909555i \(0.636423\pi\)
\(728\) 0 0
\(729\) 24.7915 + 10.6949i 0.918204 + 0.396109i
\(730\) 0 0
\(731\) −15.6116 27.0400i −0.577414 1.00011i
\(732\) 0 0
\(733\) −2.40335 + 4.16273i −0.0887699 + 0.153754i −0.906991 0.421149i \(-0.861627\pi\)
0.818222 + 0.574903i \(0.194960\pi\)
\(734\) 0 0
\(735\) 2.06144 3.06900i 0.0760374 0.113202i
\(736\) 0 0
\(737\) −0.806522 −0.0297086
\(738\) 0 0
\(739\) −7.79606 −0.286783 −0.143391 0.989666i \(-0.545801\pi\)
−0.143391 + 0.989666i \(0.545801\pi\)
\(740\) 0 0
\(741\) −4.40315 0.299342i −0.161754 0.0109966i
\(742\) 0 0
\(743\) −23.5475 + 40.7855i −0.863875 + 1.49628i 0.00428429 + 0.999991i \(0.498636\pi\)
−0.868160 + 0.496285i \(0.834697\pi\)
\(744\) 0 0
\(745\) 16.9204 + 29.3071i 0.619917 + 1.07373i
\(746\) 0 0
\(747\) −20.6309 2.81815i −0.754845 0.103111i
\(748\) 0 0
\(749\) 15.9940 + 27.7023i 0.584406 + 1.01222i
\(750\) 0 0
\(751\) −6.25631 + 10.8362i −0.228296 + 0.395420i −0.957303 0.289086i \(-0.906649\pi\)
0.729007 + 0.684506i \(0.239982\pi\)
\(752\) 0 0
\(753\) 15.0471 + 30.7002i 0.548346 + 1.11878i
\(754\) 0 0
\(755\) −18.5257 −0.674218
\(756\) 0 0
\(757\) 13.0507 0.474337 0.237168 0.971469i \(-0.423781\pi\)
0.237168 + 0.971469i \(0.423781\pi\)
\(758\) 0 0
\(759\) −5.97747 12.1957i −0.216968 0.442676i
\(760\) 0 0
\(761\) 11.5379 19.9842i 0.418249 0.724428i −0.577515 0.816380i \(-0.695977\pi\)
0.995763 + 0.0919523i \(0.0293107\pi\)
\(762\) 0 0
\(763\) 15.2206 + 26.3628i 0.551021 + 0.954397i
\(764\) 0 0
\(765\) 7.91560 + 19.3757i 0.286189 + 0.700530i
\(766\) 0 0
\(767\) 14.2422 + 24.6683i 0.514257 + 0.890720i
\(768\) 0 0
\(769\) 16.7111 28.9444i 0.602617 1.04376i −0.389807 0.920897i \(-0.627458\pi\)
0.992423 0.122866i \(-0.0392085\pi\)
\(770\) 0 0
\(771\) −12.2205 0.830797i −0.440112 0.0299204i
\(772\) 0 0
\(773\) −9.28916 −0.334108 −0.167054 0.985948i \(-0.553425\pi\)
−0.167054 + 0.985948i \(0.553425\pi\)
\(774\) 0 0
\(775\) 28.7167 1.03154
\(776\) 0 0
\(777\) 20.3679 30.3231i 0.730696 1.08783i
\(778\) 0 0
\(779\) −4.37106 + 7.57089i −0.156609 + 0.271255i
\(780\) 0 0
\(781\) 10.7338 + 18.5915i 0.384086 + 0.665256i
\(782\) 0 0
\(783\) 0.231726 + 0.699347i 0.00828122 + 0.0249926i
\(784\) 0 0
\(785\) −16.3973 28.4010i −0.585246 1.01368i
\(786\) 0 0
\(787\) 4.77105 8.26370i 0.170070 0.294569i −0.768374 0.640001i \(-0.778934\pi\)
0.938444 + 0.345431i \(0.112267\pi\)
\(788\) 0 0
\(789\) −7.78820 + 11.5948i −0.277267 + 0.412786i
\(790\) 0 0
\(791\) 17.6062 0.626004
\(792\) 0 0
\(793\) −17.4628 −0.620123
\(794\) 0 0
\(795\) −14.6922 0.998826i −0.521077 0.0354247i
\(796\) 0 0
\(797\)