Properties

Label 640.2.j.d.607.8
Level $640$
Weight $2$
Character 640.607
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 607.8
Root \(1.41303 + 0.0578659i\) of defining polynomial
Character \(\chi\) \(=\) 640.607
Dual form 640.2.j.d.543.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.96251i q^{3} +(1.72581 - 1.42182i) q^{5} +(-1.60205 - 1.60205i) q^{7} -0.851447 q^{9} +O(q^{10})\) \(q+1.96251i q^{3} +(1.72581 - 1.42182i) q^{5} +(-1.60205 - 1.60205i) q^{7} -0.851447 q^{9} +(-0.754587 - 0.754587i) q^{11} +5.94580 q^{13} +(2.79034 + 3.38692i) q^{15} +(1.95574 + 1.95574i) q^{17} +(0.780680 + 0.780680i) q^{19} +(3.14404 - 3.14404i) q^{21} +(4.93121 - 4.93121i) q^{23} +(0.956833 - 4.90759i) q^{25} +4.21656i q^{27} +(-1.44802 + 1.44802i) q^{29} +3.60859i q^{31} +(1.48089 - 1.48089i) q^{33} +(-5.04266 - 0.486998i) q^{35} -10.2364 q^{37} +11.6687i q^{39} +6.93334i q^{41} +9.91344 q^{43} +(-1.46944 + 1.21061i) q^{45} +(-0.104270 + 0.104270i) q^{47} -1.86688i q^{49} +(-3.83816 + 3.83816i) q^{51} -4.03213i q^{53} +(-2.37516 - 0.229383i) q^{55} +(-1.53209 + 1.53209i) q^{57} +(-3.46736 + 3.46736i) q^{59} +(-0.680578 - 0.680578i) q^{61} +(1.36406 + 1.36406i) q^{63} +(10.2613 - 8.45388i) q^{65} +9.04721 q^{67} +(9.67754 + 9.67754i) q^{69} -3.64007 q^{71} +(2.94030 + 2.94030i) q^{73} +(9.63120 + 1.87779i) q^{75} +2.41777i q^{77} -10.7140 q^{79} -10.8294 q^{81} -4.23845i q^{83} +(6.15595 + 0.594515i) q^{85} +(-2.84176 - 2.84176i) q^{87} -0.0426256 q^{89} +(-9.52546 - 9.52546i) q^{91} -7.08189 q^{93} +(2.45730 + 0.237315i) q^{95} +(-1.91173 - 1.91173i) q^{97} +(0.642491 + 0.642491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} - 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} + 6 q^{35} - 8 q^{37} + 44 q^{43} + 4 q^{45} - 38 q^{47} - 8 q^{51} - 6 q^{55} + 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} - 12 q^{67} - 32 q^{69} + 24 q^{71} + 14 q^{73} - 64 q^{75} + 16 q^{79} + 2 q^{81} + 10 q^{85} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 34 q^{95} + 18 q^{97} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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
\(3\) 1.96251i 1.13306i 0.824043 + 0.566528i \(0.191714\pi\)
−0.824043 + 0.566528i \(0.808286\pi\)
\(4\) 0 0
\(5\) 1.72581 1.42182i 0.771805 0.635859i
\(6\) 0 0
\(7\) −1.60205 1.60205i −0.605517 0.605517i 0.336254 0.941771i \(-0.390840\pi\)
−0.941771 + 0.336254i \(0.890840\pi\)
\(8\) 0 0
\(9\) −0.851447 −0.283816
\(10\) 0 0
\(11\) −0.754587 0.754587i −0.227517 0.227517i 0.584138 0.811654i \(-0.301433\pi\)
−0.811654 + 0.584138i \(0.801433\pi\)
\(12\) 0 0
\(13\) 5.94580 1.64907 0.824534 0.565812i \(-0.191437\pi\)
0.824534 + 0.565812i \(0.191437\pi\)
\(14\) 0 0
\(15\) 2.79034 + 3.38692i 0.720464 + 0.874498i
\(16\) 0 0
\(17\) 1.95574 + 1.95574i 0.474336 + 0.474336i 0.903315 0.428978i \(-0.141126\pi\)
−0.428978 + 0.903315i \(0.641126\pi\)
\(18\) 0 0
\(19\) 0.780680 + 0.780680i 0.179100 + 0.179100i 0.790964 0.611863i \(-0.209580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(20\) 0 0
\(21\) 3.14404 3.14404i 0.686085 0.686085i
\(22\) 0 0
\(23\) 4.93121 4.93121i 1.02823 1.02823i 0.0286378 0.999590i \(-0.490883\pi\)
0.999590 0.0286378i \(-0.00911693\pi\)
\(24\) 0 0
\(25\) 0.956833 4.90759i 0.191367 0.981519i
\(26\) 0 0
\(27\) 4.21656i 0.811477i
\(28\) 0 0
\(29\) −1.44802 + 1.44802i −0.268891 + 0.268891i −0.828653 0.559762i \(-0.810892\pi\)
0.559762 + 0.828653i \(0.310892\pi\)
\(30\) 0 0
\(31\) 3.60859i 0.648121i 0.946036 + 0.324061i \(0.105048\pi\)
−0.946036 + 0.324061i \(0.894952\pi\)
\(32\) 0 0
\(33\) 1.48089 1.48089i 0.257789 0.257789i
\(34\) 0 0
\(35\) −5.04266 0.486998i −0.852365 0.0823177i
\(36\) 0 0
\(37\) −10.2364 −1.68285 −0.841427 0.540371i \(-0.818284\pi\)
−0.841427 + 0.540371i \(0.818284\pi\)
\(38\) 0 0
\(39\) 11.6687i 1.86849i
\(40\) 0 0
\(41\) 6.93334i 1.08281i 0.840763 + 0.541403i \(0.182107\pi\)
−0.840763 + 0.541403i \(0.817893\pi\)
\(42\) 0 0
\(43\) 9.91344 1.51179 0.755893 0.654695i \(-0.227203\pi\)
0.755893 + 0.654695i \(0.227203\pi\)
\(44\) 0 0
\(45\) −1.46944 + 1.21061i −0.219050 + 0.180467i
\(46\) 0 0
\(47\) −0.104270 + 0.104270i −0.0152093 + 0.0152093i −0.714671 0.699461i \(-0.753423\pi\)
0.699461 + 0.714671i \(0.253423\pi\)
\(48\) 0 0
\(49\) 1.86688i 0.266698i
\(50\) 0 0
\(51\) −3.83816 + 3.83816i −0.537450 + 0.537450i
\(52\) 0 0
\(53\) 4.03213i 0.553856i −0.960891 0.276928i \(-0.910684\pi\)
0.960891 0.276928i \(-0.0893164\pi\)
\(54\) 0 0
\(55\) −2.37516 0.229383i −0.320267 0.0309300i
\(56\) 0 0
\(57\) −1.53209 + 1.53209i −0.202931 + 0.202931i
\(58\) 0 0
\(59\) −3.46736 + 3.46736i −0.451412 + 0.451412i −0.895823 0.444411i \(-0.853413\pi\)
0.444411 + 0.895823i \(0.353413\pi\)
\(60\) 0 0
\(61\) −0.680578 0.680578i −0.0871391 0.0871391i 0.662194 0.749333i \(-0.269626\pi\)
−0.749333 + 0.662194i \(0.769626\pi\)
\(62\) 0 0
\(63\) 1.36406 + 1.36406i 0.171855 + 0.171855i
\(64\) 0 0
\(65\) 10.2613 8.45388i 1.27276 1.04857i
\(66\) 0 0
\(67\) 9.04721 1.10529 0.552646 0.833416i \(-0.313618\pi\)
0.552646 + 0.833416i \(0.313618\pi\)
\(68\) 0 0
\(69\) 9.67754 + 9.67754i 1.16504 + 1.16504i
\(70\) 0 0
\(71\) −3.64007 −0.431997 −0.215998 0.976394i \(-0.569301\pi\)
−0.215998 + 0.976394i \(0.569301\pi\)
\(72\) 0 0
\(73\) 2.94030 + 2.94030i 0.344136 + 0.344136i 0.857920 0.513784i \(-0.171757\pi\)
−0.513784 + 0.857920i \(0.671757\pi\)
\(74\) 0 0
\(75\) 9.63120 + 1.87779i 1.11212 + 0.216829i
\(76\) 0 0
\(77\) 2.41777i 0.275530i
\(78\) 0 0
\(79\) −10.7140 −1.20542 −0.602711 0.797960i \(-0.705913\pi\)
−0.602711 + 0.797960i \(0.705913\pi\)
\(80\) 0 0
\(81\) −10.8294 −1.20326
\(82\) 0 0
\(83\) 4.23845i 0.465230i −0.972569 0.232615i \(-0.925272\pi\)
0.972569 0.232615i \(-0.0747282\pi\)
\(84\) 0 0
\(85\) 6.15595 + 0.594515i 0.667707 + 0.0644842i
\(86\) 0 0
\(87\) −2.84176 2.84176i −0.304668 0.304668i
\(88\) 0 0
\(89\) −0.0426256 −0.00451831 −0.00225915 0.999997i \(-0.500719\pi\)
−0.00225915 + 0.999997i \(0.500719\pi\)
\(90\) 0 0
\(91\) −9.52546 9.52546i −0.998539 0.998539i
\(92\) 0 0
\(93\) −7.08189 −0.734358
\(94\) 0 0
\(95\) 2.45730 + 0.237315i 0.252113 + 0.0243480i
\(96\) 0 0
\(97\) −1.91173 1.91173i −0.194106 0.194106i 0.603362 0.797468i \(-0.293828\pi\)
−0.797468 + 0.603362i \(0.793828\pi\)
\(98\) 0 0
\(99\) 0.642491 + 0.642491i 0.0645728 + 0.0645728i
\(100\) 0 0
\(101\) −4.96537 + 4.96537i −0.494073 + 0.494073i −0.909587 0.415514i \(-0.863602\pi\)
0.415514 + 0.909587i \(0.363602\pi\)
\(102\) 0 0
\(103\) 0.442220 0.442220i 0.0435733 0.0435733i −0.684984 0.728558i \(-0.740191\pi\)
0.728558 + 0.684984i \(0.240191\pi\)
\(104\) 0 0
\(105\) 0.955739 9.89627i 0.0932706 0.965777i
\(106\) 0 0
\(107\) 17.5924i 1.70072i −0.526204 0.850359i \(-0.676385\pi\)
0.526204 0.850359i \(-0.323615\pi\)
\(108\) 0 0
\(109\) 0.345161 0.345161i 0.0330605 0.0330605i −0.690383 0.723444i \(-0.742558\pi\)
0.723444 + 0.690383i \(0.242558\pi\)
\(110\) 0 0
\(111\) 20.0890i 1.90677i
\(112\) 0 0
\(113\) −5.43662 + 5.43662i −0.511435 + 0.511435i −0.914966 0.403531i \(-0.867783\pi\)
0.403531 + 0.914966i \(0.367783\pi\)
\(114\) 0 0
\(115\) 1.49901 15.5216i 0.139784 1.44740i
\(116\) 0 0
\(117\) −5.06253 −0.468031
\(118\) 0 0
\(119\) 6.26638i 0.574438i
\(120\) 0 0
\(121\) 9.86120i 0.896472i
\(122\) 0 0
\(123\) −13.6067 −1.22688
\(124\) 0 0
\(125\) −5.32642 9.83002i −0.476410 0.879223i
\(126\) 0 0
\(127\) 6.27150 6.27150i 0.556505 0.556505i −0.371805 0.928311i \(-0.621261\pi\)
0.928311 + 0.371805i \(0.121261\pi\)
\(128\) 0 0
\(129\) 19.4552i 1.71294i
\(130\) 0 0
\(131\) −1.61521 + 1.61521i −0.141122 + 0.141122i −0.774138 0.633017i \(-0.781816\pi\)
0.633017 + 0.774138i \(0.281816\pi\)
\(132\) 0 0
\(133\) 2.50138i 0.216897i
\(134\) 0 0
\(135\) 5.99520 + 7.27697i 0.515985 + 0.626302i
\(136\) 0 0
\(137\) −6.83585 + 6.83585i −0.584026 + 0.584026i −0.936007 0.351981i \(-0.885508\pi\)
0.351981 + 0.936007i \(0.385508\pi\)
\(138\) 0 0
\(139\) −13.7427 + 13.7427i −1.16564 + 1.16564i −0.182423 + 0.983220i \(0.558394\pi\)
−0.983220 + 0.182423i \(0.941606\pi\)
\(140\) 0 0
\(141\) −0.204631 0.204631i −0.0172330 0.0172330i
\(142\) 0 0
\(143\) −4.48662 4.48662i −0.375190 0.375190i
\(144\) 0 0
\(145\) −0.440176 + 4.55784i −0.0365547 + 0.378508i
\(146\) 0 0
\(147\) 3.66378 0.302184
\(148\) 0 0
\(149\) −1.73811 1.73811i −0.142391 0.142391i 0.632318 0.774709i \(-0.282104\pi\)
−0.774709 + 0.632318i \(0.782104\pi\)
\(150\) 0 0
\(151\) 5.83522 0.474864 0.237432 0.971404i \(-0.423694\pi\)
0.237432 + 0.971404i \(0.423694\pi\)
\(152\) 0 0
\(153\) −1.66521 1.66521i −0.134624 0.134624i
\(154\) 0 0
\(155\) 5.13078 + 6.22773i 0.412114 + 0.500223i
\(156\) 0 0
\(157\) 3.14732i 0.251183i −0.992082 0.125592i \(-0.959917\pi\)
0.992082 0.125592i \(-0.0400829\pi\)
\(158\) 0 0
\(159\) 7.91310 0.627550
\(160\) 0 0
\(161\) −15.8001 −1.24522
\(162\) 0 0
\(163\) 7.82117i 0.612601i 0.951935 + 0.306301i \(0.0990913\pi\)
−0.951935 + 0.306301i \(0.900909\pi\)
\(164\) 0 0
\(165\) 0.450167 4.66128i 0.0350454 0.362880i
\(166\) 0 0
\(167\) −9.88460 9.88460i −0.764893 0.764893i 0.212309 0.977203i \(-0.431902\pi\)
−0.977203 + 0.212309i \(0.931902\pi\)
\(168\) 0 0
\(169\) 22.3525 1.71942
\(170\) 0 0
\(171\) −0.664708 0.664708i −0.0508315 0.0508315i
\(172\) 0 0
\(173\) −3.49245 −0.265526 −0.132763 0.991148i \(-0.542385\pi\)
−0.132763 + 0.991148i \(0.542385\pi\)
\(174\) 0 0
\(175\) −9.39509 + 6.32931i −0.710202 + 0.478451i
\(176\) 0 0
\(177\) −6.80473 6.80473i −0.511475 0.511475i
\(178\) 0 0
\(179\) −13.0809 13.0809i −0.977713 0.977713i 0.0220444 0.999757i \(-0.492982\pi\)
−0.999757 + 0.0220444i \(0.992982\pi\)
\(180\) 0 0
\(181\) −13.6393 + 13.6393i −1.01380 + 1.01380i −0.0138952 + 0.999903i \(0.504423\pi\)
−0.999903 + 0.0138952i \(0.995577\pi\)
\(182\) 0 0
\(183\) 1.33564 1.33564i 0.0987335 0.0987335i
\(184\) 0 0
\(185\) −17.6661 + 14.5544i −1.29884 + 1.07006i
\(186\) 0 0
\(187\) 2.95155i 0.215839i
\(188\) 0 0
\(189\) 6.75513 6.75513i 0.491363 0.491363i
\(190\) 0 0
\(191\) 2.92523i 0.211662i −0.994384 0.105831i \(-0.966250\pi\)
0.994384 0.105831i \(-0.0337503\pi\)
\(192\) 0 0
\(193\) 0.0830702 0.0830702i 0.00597953 0.00597953i −0.704111 0.710090i \(-0.748654\pi\)
0.710090 + 0.704111i \(0.248654\pi\)
\(194\) 0 0
\(195\) 16.5908 + 20.1379i 1.18809 + 1.44211i
\(196\) 0 0
\(197\) −7.80487 −0.556074 −0.278037 0.960570i \(-0.589684\pi\)
−0.278037 + 0.960570i \(0.589684\pi\)
\(198\) 0 0
\(199\) 10.9740i 0.777924i 0.921254 + 0.388962i \(0.127166\pi\)
−0.921254 + 0.388962i \(0.872834\pi\)
\(200\) 0 0
\(201\) 17.7552i 1.25236i
\(202\) 0 0
\(203\) 4.63960 0.325636
\(204\) 0 0
\(205\) 9.85799 + 11.9656i 0.688512 + 0.835715i
\(206\) 0 0
\(207\) −4.19866 + 4.19866i −0.291827 + 0.291827i
\(208\) 0 0
\(209\) 1.17818i 0.0814966i
\(210\) 0 0
\(211\) 8.92204 8.92204i 0.614218 0.614218i −0.329824 0.944042i \(-0.606989\pi\)
0.944042 + 0.329824i \(0.106989\pi\)
\(212\) 0 0
\(213\) 7.14367i 0.489477i
\(214\) 0 0
\(215\) 17.1087 14.0952i 1.16680 0.961283i
\(216\) 0 0
\(217\) 5.78113 5.78113i 0.392449 0.392449i
\(218\) 0 0
\(219\) −5.77037 + 5.77037i −0.389926 + 0.389926i
\(220\) 0 0
\(221\) 11.6284 + 11.6284i 0.782213 + 0.782213i
\(222\) 0 0
\(223\) 13.1678 + 13.1678i 0.881784 + 0.881784i 0.993716 0.111931i \(-0.0357037\pi\)
−0.111931 + 0.993716i \(0.535704\pi\)
\(224\) 0 0
\(225\) −0.814693 + 4.17856i −0.0543129 + 0.278570i
\(226\) 0 0
\(227\) −19.3432 −1.28385 −0.641927 0.766766i \(-0.721865\pi\)
−0.641927 + 0.766766i \(0.721865\pi\)
\(228\) 0 0
\(229\) 13.2143 + 13.2143i 0.873223 + 0.873223i 0.992822 0.119599i \(-0.0381610\pi\)
−0.119599 + 0.992822i \(0.538161\pi\)
\(230\) 0 0
\(231\) −4.74490 −0.312191
\(232\) 0 0
\(233\) −20.6884 20.6884i −1.35534 1.35534i −0.879570 0.475769i \(-0.842170\pi\)
−0.475769 0.879570i \(-0.657830\pi\)
\(234\) 0 0
\(235\) −0.0316965 + 0.328204i −0.00206765 + 0.0214096i
\(236\) 0 0
\(237\) 21.0264i 1.36581i
\(238\) 0 0
\(239\) −14.1053 −0.912395 −0.456198 0.889878i \(-0.650789\pi\)
−0.456198 + 0.889878i \(0.650789\pi\)
\(240\) 0 0
\(241\) 12.8011 0.824592 0.412296 0.911050i \(-0.364727\pi\)
0.412296 + 0.911050i \(0.364727\pi\)
\(242\) 0 0
\(243\) 8.60310i 0.551889i
\(244\) 0 0
\(245\) −2.65438 3.22189i −0.169582 0.205839i
\(246\) 0 0
\(247\) 4.64177 + 4.64177i 0.295349 + 0.295349i
\(248\) 0 0
\(249\) 8.31800 0.527132
\(250\) 0 0
\(251\) 6.84118 + 6.84118i 0.431812 + 0.431812i 0.889244 0.457433i \(-0.151231\pi\)
−0.457433 + 0.889244i \(0.651231\pi\)
\(252\) 0 0
\(253\) −7.44205 −0.467878
\(254\) 0 0
\(255\) −1.16674 + 12.0811i −0.0730642 + 0.756549i
\(256\) 0 0
\(257\) −6.66524 6.66524i −0.415766 0.415766i 0.467975 0.883742i \(-0.344984\pi\)
−0.883742 + 0.467975i \(0.844984\pi\)
\(258\) 0 0
\(259\) 16.3992 + 16.3992i 1.01900 + 1.01900i
\(260\) 0 0
\(261\) 1.23291 1.23291i 0.0763154 0.0763154i
\(262\) 0 0
\(263\) −7.32015 + 7.32015i −0.451380 + 0.451380i −0.895812 0.444432i \(-0.853405\pi\)
0.444432 + 0.895812i \(0.353405\pi\)
\(264\) 0 0
\(265\) −5.73298 6.95869i −0.352174 0.427469i
\(266\) 0 0
\(267\) 0.0836533i 0.00511950i
\(268\) 0 0
\(269\) −15.9801 + 15.9801i −0.974321 + 0.974321i −0.999678 0.0253576i \(-0.991928\pi\)
0.0253576 + 0.999678i \(0.491928\pi\)
\(270\) 0 0
\(271\) 3.59684i 0.218492i 0.994015 + 0.109246i \(0.0348437\pi\)
−0.994015 + 0.109246i \(0.965156\pi\)
\(272\) 0 0
\(273\) 18.6938 18.6938i 1.13140 1.13140i
\(274\) 0 0
\(275\) −4.42522 + 2.98119i −0.266851 + 0.179773i
\(276\) 0 0
\(277\) 20.9416 1.25826 0.629131 0.777300i \(-0.283411\pi\)
0.629131 + 0.777300i \(0.283411\pi\)
\(278\) 0 0
\(279\) 3.07252i 0.183947i
\(280\) 0 0
\(281\) 3.26699i 0.194892i 0.995241 + 0.0974462i \(0.0310674\pi\)
−0.995241 + 0.0974462i \(0.968933\pi\)
\(282\) 0 0
\(283\) −0.000151619 0 −9.01279e−6 0 −4.50640e−6 1.00000i \(-0.500001\pi\)
−4.50640e−6 1.00000i \(0.500001\pi\)
\(284\) 0 0
\(285\) −0.465733 + 4.82247i −0.0275877 + 0.285658i
\(286\) 0 0
\(287\) 11.1075 11.1075i 0.655657 0.655657i
\(288\) 0 0
\(289\) 9.35017i 0.550010i
\(290\) 0 0
\(291\) 3.75178 3.75178i 0.219933 0.219933i
\(292\) 0 0
\(293\) 11.0593i 0.646091i −0.946384 0.323045i \(-0.895293\pi\)
0.946384 0.323045i \(-0.104707\pi\)
\(294\) 0 0
\(295\) −1.05402 + 10.9140i −0.0613677 + 0.635436i
\(296\) 0 0
\(297\) 3.18176 3.18176i 0.184624 0.184624i
\(298\) 0 0
\(299\) 29.3200 29.3200i 1.69562 1.69562i
\(300\) 0 0
\(301\) −15.8818 15.8818i −0.915413 0.915413i
\(302\) 0 0
\(303\) −9.74459 9.74459i −0.559812 0.559812i
\(304\) 0 0
\(305\) −2.14221 0.206885i −0.122663 0.0118462i
\(306\) 0 0
\(307\) −15.1317 −0.863613 −0.431806 0.901966i \(-0.642124\pi\)
−0.431806 + 0.901966i \(0.642124\pi\)
\(308\) 0 0
\(309\) 0.867862 + 0.867862i 0.0493709 + 0.0493709i
\(310\) 0 0
\(311\) −27.1556 −1.53985 −0.769925 0.638134i \(-0.779707\pi\)
−0.769925 + 0.638134i \(0.779707\pi\)
\(312\) 0 0
\(313\) 13.6695 + 13.6695i 0.772646 + 0.772646i 0.978568 0.205922i \(-0.0660194\pi\)
−0.205922 + 0.978568i \(0.566019\pi\)
\(314\) 0 0
\(315\) 4.29356 + 0.414653i 0.241915 + 0.0233631i
\(316\) 0 0
\(317\) 25.8314i 1.45084i 0.688307 + 0.725419i \(0.258354\pi\)
−0.688307 + 0.725419i \(0.741646\pi\)
\(318\) 0 0
\(319\) 2.18532 0.122354
\(320\) 0 0
\(321\) 34.5252 1.92701
\(322\) 0 0
\(323\) 3.05361i 0.169908i
\(324\) 0 0
\(325\) 5.68914 29.1796i 0.315576 1.61859i
\(326\) 0 0
\(327\) 0.677383 + 0.677383i 0.0374594 + 0.0374594i
\(328\) 0 0
\(329\) 0.334091 0.0184190
\(330\) 0 0
\(331\) 13.6207 + 13.6207i 0.748659 + 0.748659i 0.974227 0.225568i \(-0.0724239\pi\)
−0.225568 + 0.974227i \(0.572424\pi\)
\(332\) 0 0
\(333\) 8.71576 0.477621
\(334\) 0 0
\(335\) 15.6138 12.8635i 0.853071 0.702810i
\(336\) 0 0
\(337\) 16.0911 + 16.0911i 0.876536 + 0.876536i 0.993174 0.116638i \(-0.0372119\pi\)
−0.116638 + 0.993174i \(0.537212\pi\)
\(338\) 0 0
\(339\) −10.6694 10.6694i −0.579484 0.579484i
\(340\) 0 0
\(341\) 2.72299 2.72299i 0.147458 0.147458i
\(342\) 0 0
\(343\) −14.2052 + 14.2052i −0.767007 + 0.767007i
\(344\) 0 0
\(345\) 30.4614 + 2.94183i 1.63998 + 0.158383i
\(346\) 0 0
\(347\) 5.57562i 0.299315i −0.988738 0.149658i \(-0.952183\pi\)
0.988738 0.149658i \(-0.0478171\pi\)
\(348\) 0 0
\(349\) 15.0811 15.0811i 0.807273 0.807273i −0.176947 0.984220i \(-0.556622\pi\)
0.984220 + 0.176947i \(0.0566222\pi\)
\(350\) 0 0
\(351\) 25.0708i 1.33818i
\(352\) 0 0
\(353\) 2.57880 2.57880i 0.137256 0.137256i −0.635141 0.772397i \(-0.719058\pi\)
0.772397 + 0.635141i \(0.219058\pi\)
\(354\) 0 0
\(355\) −6.28206 + 5.17554i −0.333417 + 0.274689i
\(356\) 0 0
\(357\) 12.2978 0.650870
\(358\) 0 0
\(359\) 5.77227i 0.304649i −0.988331 0.152324i \(-0.951324\pi\)
0.988331 0.152324i \(-0.0486758\pi\)
\(360\) 0 0
\(361\) 17.7811i 0.935846i
\(362\) 0 0
\(363\) 19.3527 1.01575
\(364\) 0 0
\(365\) 9.25499 + 0.893807i 0.484428 + 0.0467840i
\(366\) 0 0
\(367\) −8.30496 + 8.30496i −0.433516 + 0.433516i −0.889822 0.456307i \(-0.849172\pi\)
0.456307 + 0.889822i \(0.349172\pi\)
\(368\) 0 0
\(369\) 5.90337i 0.307317i
\(370\) 0 0
\(371\) −6.45967 + 6.45967i −0.335369 + 0.335369i
\(372\) 0 0
\(373\) 16.0484i 0.830953i 0.909604 + 0.415477i \(0.136385\pi\)
−0.909604 + 0.415477i \(0.863615\pi\)
\(374\) 0 0
\(375\) 19.2915 10.4532i 0.996209 0.539799i
\(376\) 0 0
\(377\) −8.60964 + 8.60964i −0.443419 + 0.443419i
\(378\) 0 0
\(379\) −8.91367 + 8.91367i −0.457865 + 0.457865i −0.897954 0.440089i \(-0.854947\pi\)
0.440089 + 0.897954i \(0.354947\pi\)
\(380\) 0 0
\(381\) 12.3079 + 12.3079i 0.630552 + 0.630552i
\(382\) 0 0
\(383\) 24.8928 + 24.8928i 1.27196 + 1.27196i 0.945057 + 0.326904i \(0.106005\pi\)
0.326904 + 0.945057i \(0.393995\pi\)
\(384\) 0 0
\(385\) 3.43764 + 4.17261i 0.175199 + 0.212656i
\(386\) 0 0
\(387\) −8.44078 −0.429069
\(388\) 0 0
\(389\) −16.5819 16.5819i −0.840738 0.840738i 0.148217 0.988955i \(-0.452647\pi\)
−0.988955 + 0.148217i \(0.952647\pi\)
\(390\) 0 0
\(391\) 19.2883 0.975452
\(392\) 0 0
\(393\) −3.16987 3.16987i −0.159899 0.159899i
\(394\) 0 0
\(395\) −18.4904 + 15.2335i −0.930351 + 0.766478i
\(396\) 0 0
\(397\) 8.62531i 0.432892i 0.976295 + 0.216446i \(0.0694465\pi\)
−0.976295 + 0.216446i \(0.930553\pi\)
\(398\) 0 0
\(399\) 4.90897 0.245756
\(400\) 0 0
\(401\) 19.7107 0.984307 0.492153 0.870508i \(-0.336210\pi\)
0.492153 + 0.870508i \(0.336210\pi\)
\(402\) 0 0
\(403\) 21.4559i 1.06880i
\(404\) 0 0
\(405\) −18.6894 + 15.3975i −0.928686 + 0.765107i
\(406\) 0 0
\(407\) 7.72426 + 7.72426i 0.382877 + 0.382877i
\(408\) 0 0
\(409\) −26.7930 −1.32483 −0.662414 0.749138i \(-0.730468\pi\)
−0.662414 + 0.749138i \(0.730468\pi\)
\(410\) 0 0
\(411\) −13.4154 13.4154i −0.661734 0.661734i
\(412\) 0 0
\(413\) 11.1098 0.546675
\(414\) 0 0
\(415\) −6.02633 7.31475i −0.295821 0.359067i
\(416\) 0 0
\(417\) −26.9702 26.9702i −1.32074 1.32074i
\(418\) 0 0
\(419\) 11.0752 + 11.0752i 0.541061 + 0.541061i 0.923840 0.382779i \(-0.125033\pi\)
−0.382779 + 0.923840i \(0.625033\pi\)
\(420\) 0 0
\(421\) 0.243092 0.243092i 0.0118476 0.0118476i −0.701158 0.713006i \(-0.747333\pi\)
0.713006 + 0.701158i \(0.247333\pi\)
\(422\) 0 0
\(423\) 0.0887804 0.0887804i 0.00431665 0.00431665i
\(424\) 0 0
\(425\) 11.4693 7.72666i 0.556342 0.374798i
\(426\) 0 0
\(427\) 2.18064i 0.105528i
\(428\) 0 0
\(429\) 8.80505 8.80505i 0.425112 0.425112i
\(430\) 0 0
\(431\) 20.7024i 0.997200i 0.866832 + 0.498600i \(0.166152\pi\)
−0.866832 + 0.498600i \(0.833848\pi\)
\(432\) 0 0
\(433\) −5.68221 + 5.68221i −0.273069 + 0.273069i −0.830335 0.557265i \(-0.811851\pi\)
0.557265 + 0.830335i \(0.311851\pi\)
\(434\) 0 0
\(435\) −8.94480 0.863851i −0.428871 0.0414185i
\(436\) 0 0
\(437\) 7.69939 0.368312
\(438\) 0 0
\(439\) 18.7902i 0.896808i −0.893831 0.448404i \(-0.851993\pi\)
0.893831 0.448404i \(-0.148007\pi\)
\(440\) 0 0
\(441\) 1.58955i 0.0756930i
\(442\) 0 0
\(443\) −12.1641 −0.577934 −0.288967 0.957339i \(-0.593312\pi\)
−0.288967 + 0.957339i \(0.593312\pi\)
\(444\) 0 0
\(445\) −0.0735637 + 0.0606062i −0.00348725 + 0.00287301i
\(446\) 0 0
\(447\) 3.41105 3.41105i 0.161337 0.161337i
\(448\) 0 0
\(449\) 27.2708i 1.28699i 0.765452 + 0.643493i \(0.222516\pi\)
−0.765452 + 0.643493i \(0.777484\pi\)
\(450\) 0 0
\(451\) 5.23181 5.23181i 0.246356 0.246356i
\(452\) 0 0
\(453\) 11.4517i 0.538047i
\(454\) 0 0
\(455\) −29.9826 2.89559i −1.40561 0.135748i
\(456\) 0 0
\(457\) −19.7514 + 19.7514i −0.923933 + 0.923933i −0.997305 0.0733714i \(-0.976624\pi\)
0.0733714 + 0.997305i \(0.476624\pi\)
\(458\) 0 0
\(459\) −8.24649 + 8.24649i −0.384913 + 0.384913i
\(460\) 0 0
\(461\) −12.9262 12.9262i −0.602035 0.602035i 0.338818 0.940852i \(-0.389973\pi\)
−0.940852 + 0.338818i \(0.889973\pi\)
\(462\) 0 0
\(463\) −14.5647 14.5647i −0.676879 0.676879i 0.282414 0.959293i \(-0.408865\pi\)
−0.959293 + 0.282414i \(0.908865\pi\)
\(464\) 0 0
\(465\) −12.2220 + 10.0692i −0.566781 + 0.466948i
\(466\) 0 0
\(467\) 42.3556 1.95998 0.979991 0.199040i \(-0.0637825\pi\)
0.979991 + 0.199040i \(0.0637825\pi\)
\(468\) 0 0
\(469\) −14.4941 14.4941i −0.669274 0.669274i
\(470\) 0 0
\(471\) 6.17665 0.284605
\(472\) 0 0
\(473\) −7.48056 7.48056i −0.343956 0.343956i
\(474\) 0 0
\(475\) 4.57824 3.08428i 0.210064 0.141517i
\(476\) 0 0
\(477\) 3.43315i 0.157193i
\(478\) 0 0
\(479\) −27.0905 −1.23780 −0.618899 0.785470i \(-0.712421\pi\)
−0.618899 + 0.785470i \(0.712421\pi\)
\(480\) 0 0
\(481\) −60.8636 −2.77514
\(482\) 0 0
\(483\) 31.0078i 1.41090i
\(484\) 0 0
\(485\) −6.01741 0.581136i −0.273236 0.0263880i
\(486\) 0 0
\(487\) 21.9674 + 21.9674i 0.995436 + 0.995436i 0.999990 0.00455390i \(-0.00144956\pi\)
−0.00455390 + 0.999990i \(0.501450\pi\)
\(488\) 0 0
\(489\) −15.3491 −0.694111
\(490\) 0 0
\(491\) 6.11955 + 6.11955i 0.276171 + 0.276171i 0.831579 0.555407i \(-0.187438\pi\)
−0.555407 + 0.831579i \(0.687438\pi\)
\(492\) 0 0
\(493\) −5.66390 −0.255089
\(494\) 0 0
\(495\) 2.02233 + 0.195308i 0.0908968 + 0.00877842i
\(496\) 0 0
\(497\) 5.83157 + 5.83157i 0.261581 + 0.261581i
\(498\) 0 0
\(499\) 15.4115 + 15.4115i 0.689914 + 0.689914i 0.962213 0.272298i \(-0.0877838\pi\)
−0.272298 + 0.962213i \(0.587784\pi\)
\(500\) 0 0
\(501\) 19.3986 19.3986i 0.866667 0.866667i
\(502\) 0 0
\(503\) 26.4312 26.4312i 1.17851 1.17851i 0.198387 0.980124i \(-0.436430\pi\)
0.980124 0.198387i \(-0.0635704\pi\)
\(504\) 0 0
\(505\) −1.50940 + 15.6292i −0.0671673 + 0.695488i
\(506\) 0 0
\(507\) 43.8671i 1.94820i
\(508\) 0 0
\(509\) −0.233714 + 0.233714i −0.0103592 + 0.0103592i −0.712267 0.701908i \(-0.752332\pi\)
0.701908 + 0.712267i \(0.252332\pi\)
\(510\) 0 0
\(511\) 9.42101i 0.416761i
\(512\) 0 0
\(513\) −3.29178 + 3.29178i −0.145336 + 0.145336i
\(514\) 0 0
\(515\) 0.134428 1.39195i 0.00592362 0.0613365i
\(516\) 0 0
\(517\) 0.157362 0.00692075
\(518\) 0 0
\(519\) 6.85397i 0.300856i
\(520\) 0 0
\(521\) 4.50147i 0.197213i 0.995127 + 0.0986064i \(0.0314385\pi\)
−0.995127 + 0.0986064i \(0.968562\pi\)
\(522\) 0 0
\(523\) 12.6042 0.551141 0.275571 0.961281i \(-0.411133\pi\)
0.275571 + 0.961281i \(0.411133\pi\)
\(524\) 0 0
\(525\) −12.4213 18.4380i −0.542111 0.804699i
\(526\) 0 0
\(527\) −7.05746 + 7.05746i −0.307428 + 0.307428i
\(528\) 0 0
\(529\) 25.6336i 1.11450i
\(530\) 0 0
\(531\) 2.95227 2.95227i 0.128118 0.128118i
\(532\) 0 0
\(533\) 41.2242i 1.78562i
\(534\) 0 0
\(535\) −25.0132 30.3610i −1.08142 1.31262i
\(536\) 0 0
\(537\) 25.6714 25.6714i 1.10780 1.10780i
\(538\) 0 0
\(539\) −1.40873 + 1.40873i −0.0606782 + 0.0606782i
\(540\) 0 0
\(541\) −14.5013 14.5013i −0.623459 0.623459i 0.322955 0.946414i \(-0.395324\pi\)
−0.946414 + 0.322955i \(0.895324\pi\)
\(542\) 0 0
\(543\) −26.7672 26.7672i −1.14869 1.14869i
\(544\) 0 0
\(545\) 0.104924 1.08644i 0.00449444 0.0465380i
\(546\) 0 0
\(547\) −30.2936 −1.29526 −0.647630 0.761955i \(-0.724240\pi\)
−0.647630 + 0.761955i \(0.724240\pi\)
\(548\) 0 0
\(549\) 0.579476 + 0.579476i 0.0247314 + 0.0247314i
\(550\) 0 0
\(551\) −2.26088 −0.0963169
\(552\) 0 0
\(553\) 17.1644 + 17.1644i 0.729904 + 0.729904i
\(554\) 0 0
\(555\) −28.5631 34.6699i −1.21244 1.47165i
\(556\) 0 0
\(557\) 9.72758i 0.412171i 0.978534 + 0.206085i \(0.0660725\pi\)
−0.978534 + 0.206085i \(0.933928\pi\)
\(558\) 0 0
\(559\) 58.9433 2.49304
\(560\) 0 0
\(561\) 5.79245 0.244557
\(562\) 0 0
\(563\) 17.7853i 0.749562i −0.927113 0.374781i \(-0.877718\pi\)
0.927113 0.374781i \(-0.122282\pi\)
\(564\) 0 0
\(565\) −1.65265 + 17.1125i −0.0695276 + 0.719928i
\(566\) 0 0
\(567\) 17.3492 + 17.3492i 0.728597 + 0.728597i
\(568\) 0 0
\(569\) −15.7897 −0.661938 −0.330969 0.943642i \(-0.607376\pi\)
−0.330969 + 0.943642i \(0.607376\pi\)
\(570\) 0 0
\(571\) −23.3108 23.3108i −0.975528 0.975528i 0.0241793 0.999708i \(-0.492303\pi\)
−0.999708 + 0.0241793i \(0.992303\pi\)
\(572\) 0 0
\(573\) 5.74079 0.239825
\(574\) 0 0
\(575\) −19.4820 28.9187i −0.812456 1.20599i
\(576\) 0 0
\(577\) 25.7383 + 25.7383i 1.07150 + 1.07150i 0.997239 + 0.0742597i \(0.0236594\pi\)
0.0742597 + 0.997239i \(0.476341\pi\)
\(578\) 0 0
\(579\) 0.163026 + 0.163026i 0.00677514 + 0.00677514i
\(580\) 0 0
\(581\) −6.79020 + 6.79020i −0.281705 + 0.281705i
\(582\) 0 0
\(583\) −3.04260 + 3.04260i −0.126011 + 0.126011i
\(584\) 0 0
\(585\) −8.73697 + 7.19803i −0.361229 + 0.297602i
\(586\) 0 0
\(587\) 23.1327i 0.954790i −0.878689 0.477395i \(-0.841581\pi\)
0.878689 0.477395i \(-0.158419\pi\)
\(588\) 0 0
\(589\) −2.81715 + 2.81715i −0.116079 + 0.116079i
\(590\) 0 0
\(591\) 15.3171i 0.630063i
\(592\) 0 0
\(593\) −25.5047 + 25.5047i −1.04735 + 1.04735i −0.0485322 + 0.998822i \(0.515454\pi\)
−0.998822 + 0.0485322i \(0.984546\pi\)
\(594\) 0 0
\(595\) −8.90969 10.8146i −0.365261 0.443354i
\(596\) 0 0
\(597\) −21.5365 −0.881432
\(598\) 0 0
\(599\) 11.0699i 0.452304i 0.974092 + 0.226152i \(0.0726146\pi\)
−0.974092 + 0.226152i \(0.927385\pi\)
\(600\) 0 0
\(601\) 13.7579i 0.561197i −0.959825 0.280599i \(-0.909467\pi\)
0.959825 0.280599i \(-0.0905330\pi\)
\(602\) 0 0
\(603\) −7.70322 −0.313700
\(604\) 0 0
\(605\) −14.0209 17.0185i −0.570030 0.691902i
\(606\) 0 0
\(607\) 18.4675 18.4675i 0.749573 0.749573i −0.224826 0.974399i \(-0.572181\pi\)
0.974399 + 0.224826i \(0.0721813\pi\)
\(608\) 0 0
\(609\) 9.10526i 0.368964i
\(610\) 0 0
\(611\) −0.619968 + 0.619968i −0.0250812 + 0.0250812i
\(612\) 0 0
\(613\) 11.6810i 0.471790i −0.971779 0.235895i \(-0.924198\pi\)
0.971779 0.235895i \(-0.0758021\pi\)
\(614\) 0 0
\(615\) −23.4826 + 19.3464i −0.946912 + 0.780122i
\(616\) 0 0
\(617\) 29.1000 29.1000i 1.17152 1.17152i 0.189677 0.981847i \(-0.439256\pi\)
0.981847 0.189677i \(-0.0607441\pi\)
\(618\) 0 0
\(619\) 4.23279 4.23279i 0.170130 0.170130i −0.616906 0.787036i \(-0.711614\pi\)
0.787036 + 0.616906i \(0.211614\pi\)
\(620\) 0 0
\(621\) 20.7927 + 20.7927i 0.834383 + 0.834383i
\(622\) 0 0
\(623\) 0.0682883 + 0.0682883i 0.00273591 + 0.00273591i
\(624\) 0 0
\(625\) −23.1689 9.39149i −0.926758 0.375660i
\(626\) 0 0
\(627\) 2.31220 0.0923402
\(628\) 0 0
\(629\) −20.0197 20.0197i −0.798239 0.798239i
\(630\) 0 0
\(631\) −1.33886 −0.0532991 −0.0266496 0.999645i \(-0.508484\pi\)
−0.0266496 + 0.999645i \(0.508484\pi\)
\(632\) 0 0
\(633\) 17.5096 + 17.5096i 0.695944 + 0.695944i
\(634\) 0 0
\(635\) 1.90644 19.7404i 0.0756548 0.783373i
\(636\) 0 0
\(637\) 11.1001i 0.439803i
\(638\) 0 0
\(639\) 3.09933 0.122608
\(640\) 0 0
\(641\) 24.5069 0.967965 0.483982 0.875078i \(-0.339190\pi\)
0.483982 + 0.875078i \(0.339190\pi\)
\(642\) 0 0
\(643\) 10.8979i 0.429771i −0.976639 0.214885i \(-0.931062\pi\)
0.976639 0.214885i \(-0.0689378\pi\)
\(644\) 0 0
\(645\) 27.6619 + 33.5760i 1.08919 + 1.32205i
\(646\) 0 0
\(647\) −11.6612 11.6612i −0.458448 0.458448i 0.439698 0.898146i \(-0.355085\pi\)
−0.898146 + 0.439698i \(0.855085\pi\)
\(648\) 0 0
\(649\) 5.23285 0.205407
\(650\) 0 0
\(651\) 11.3455 + 11.3455i 0.444666 + 0.444666i
\(652\) 0 0
\(653\) −5.28393 −0.206776 −0.103388 0.994641i \(-0.532968\pi\)
−0.103388 + 0.994641i \(0.532968\pi\)
\(654\) 0 0
\(655\) −0.491000 + 5.08409i −0.0191849 + 0.198652i
\(656\) 0 0
\(657\) −2.50351 2.50351i −0.0976713 0.0976713i
\(658\) 0 0
\(659\) −16.2902 16.2902i −0.634578 0.634578i 0.314635 0.949213i \(-0.398118\pi\)
−0.949213 + 0.314635i \(0.898118\pi\)
\(660\) 0 0
\(661\) 12.7924 12.7924i 0.497566 0.497566i −0.413114 0.910679i \(-0.635559\pi\)
0.910679 + 0.413114i \(0.135559\pi\)
\(662\) 0 0
\(663\) −22.8209 + 22.8209i −0.886291 + 0.886291i
\(664\) 0 0
\(665\) −3.55652 4.31690i −0.137916 0.167402i
\(666\) 0 0
\(667\) 14.2810i 0.552962i
\(668\) 0 0
\(669\) −25.8420 + 25.8420i −0.999111 + 0.999111i
\(670\) 0 0
\(671\) 1.02711i 0.0396512i
\(672\) 0 0
\(673\) 11.9553 11.9553i 0.460841 0.460841i −0.438090 0.898931i \(-0.644345\pi\)
0.898931 + 0.438090i \(0.144345\pi\)
\(674\) 0 0
\(675\) 20.6931 + 4.03454i 0.796480 + 0.155290i
\(676\) 0 0
\(677\) 3.18699 0.122486 0.0612430 0.998123i \(-0.480494\pi\)
0.0612430 + 0.998123i \(0.480494\pi\)
\(678\) 0 0
\(679\) 6.12535i 0.235069i
\(680\) 0 0
\(681\) 37.9613i 1.45468i
\(682\) 0 0
\(683\) −35.1661 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(684\) 0 0
\(685\) −2.07799 + 21.5167i −0.0793961 + 0.822112i
\(686\) 0 0
\(687\) −25.9331 + 25.9331i −0.989410 + 0.989410i
\(688\) 0 0
\(689\) 23.9743i 0.913346i
\(690\) 0 0
\(691\) −2.90121 + 2.90121i −0.110367 + 0.110367i −0.760134 0.649767i \(-0.774867\pi\)
0.649767 + 0.760134i \(0.274867\pi\)
\(692\) 0 0
\(693\) 2.05860i 0.0781999i
\(694\) 0 0
\(695\) −4.17758 + 43.2571i −0.158465 + 1.64083i
\(696\) 0 0
\(697\) −13.5598 + 13.5598i −0.513614 + 0.513614i
\(698\) 0 0
\(699\) 40.6011 40.6011i 1.53568 1.53568i
\(700\) 0 0
\(701\) −15.7397 15.7397i −0.594481 0.594481i 0.344358 0.938839i \(-0.388097\pi\)
−0.938839 + 0.344358i \(0.888097\pi\)
\(702\) 0 0
\(703\) −7.99136 7.99136i −0.301400 0.301400i
\(704\) 0 0
\(705\) −0.644103 0.0622047i −0.0242583 0.00234276i
\(706\) 0 0
\(707\) 15.9095 0.598339
\(708\) 0 0
\(709\) 1.95755 + 1.95755i 0.0735172 + 0.0735172i 0.742909 0.669392i \(-0.233445\pi\)
−0.669392 + 0.742909i \(0.733445\pi\)
\(710\) 0 0
\(711\) 9.12243 0.342118
\(712\) 0 0
\(713\) 17.7947 + 17.7947i 0.666416 + 0.666416i
\(714\) 0 0
\(715\) −14.1222 1.36387i −0.528142 0.0510057i
\(716\) 0 0
\(717\) 27.6818i 1.03379i
\(718\) 0 0
\(719\) −0.0658604 −0.00245618 −0.00122809 0.999999i \(-0.500391\pi\)
−0.00122809 + 0.999999i \(0.500391\pi\)
\(720\) 0 0
\(721\) −1.41692 −0.0527687
\(722\) 0 0
\(723\) 25.1223i 0.934309i
\(724\) 0 0
\(725\) 5.72078 + 8.49181i 0.212465 + 0.315378i
\(726\) 0 0
\(727\) −16.2286 16.2286i −0.601885 0.601885i 0.338927 0.940813i \(-0.389936\pi\)
−0.940813 + 0.338927i \(0.889936\pi\)
\(728\) 0 0
\(729\) −15.6045 −0.577943
\(730\) 0 0
\(731\) 19.3881 + 19.3881i 0.717095 + 0.717095i
\(732\) 0 0
\(733\) 0.669106 0.0247140 0.0123570 0.999924i \(-0.496067\pi\)
0.0123570 + 0.999924i \(0.496067\pi\)
\(734\) 0 0
\(735\) 6.32298 5.20925i 0.233227 0.192146i
\(736\) 0 0
\(737\) −6.82691 6.82691i −0.251472 0.251472i
\(738\) 0 0
\(739\) −23.4183 23.4183i −0.861454 0.861454i 0.130053 0.991507i \(-0.458485\pi\)
−0.991507 + 0.130053i \(0.958485\pi\)
\(740\) 0 0
\(741\) −9.10952 + 9.10952i −0.334647 + 0.334647i
\(742\) 0 0
\(743\) 30.0968 30.0968i 1.10414 1.10414i 0.110238 0.993905i \(-0.464839\pi\)
0.993905 0.110238i \(-0.0351614\pi\)
\(744\) 0 0
\(745\) −5.47092 0.528358i −0.200439 0.0193575i
\(746\) 0 0
\(747\) 3.60882i 0.132040i
\(748\) 0 0
\(749\) −28.1838 + 28.1838i −1.02981 + 1.02981i
\(750\) 0 0
\(751\) 53.2724i 1.94394i −0.235107 0.971970i \(-0.575544\pi\)
0.235107 0.971970i \(-0.424456\pi\)
\(752\) 0 0
\(753\) −13.4259 + 13.4259i −0.489267 + 0.489267i
\(754\) 0 0
\(755\) 10.0705 8.29666i 0.366502 0.301946i
\(756\) 0 0
\(757\) 27.1717 0.987574 0.493787 0.869583i \(-0.335612\pi\)
0.493787 + 0.869583i \(0.335612\pi\)
\(758\) 0 0
\(759\) 14.6051i 0.530132i
\(760\) 0 0
\(761\) 12.9068i 0.467870i 0.972252 + 0.233935i \(0.0751604\pi\)
−0.972252 + 0.233935i \(0.924840\pi\)
\(762\) 0 0
\(763\) −1.10593 −0.0400374
\(764\) 0 0
\(765\) −5.24147 0.506198i −0.189506 0.0183016i
\(766\) 0 0
\(767\) −20.6162 + 20.6162i −0.744409 + 0.744409i
\(768\) 0 0
\(769\) 34.4858i 1.24359i −0.783180 0.621795i \(-0.786404\pi\)
0.783180 0.621795i \(-0.213596\pi\)
\(770\) 0 0
\(771\) 13.0806 13.0806i 0.471087 0.471087i
\(772\) 0 0
\(773\) 26.6789i 0.959574i 0.877385 + 0.479787i \(0.159286\pi\)
−0.877385 + 0.479787i \(0.840714\pi\)
\(774\) 0 0
\(775\) 17.7095 + 3.45281i 0.636143 + 0.124029i
\(776\) 0 0
\(777\) −32.1836 + 32.1836i −1.15458 + 1.15458i
\(778\) 0 0
\(779\) −5.41272 + 5.41272i −0.193931 + 0.193931i
\(780\) 0 0
\(781\) 2.74675 + 2.74675i 0.0982864 + 0.0982864i
\(782\) 0 0
\(783\) −6.10566 6.10566i −0.218199 0.218199i
\(784\) 0 0
\(785\) −4.47493 5.43167i −0.159717 0.193865i
\(786\) 0 0
\(787\) 33.2611 1.18563 0.592815 0.805338i \(-0.298016\pi\)
0.592815 + 0.805338i \(0.298016\pi\)
\(788\) 0 0
\(789\) −14.3659 14.3659i −0.511439 0.511439i
\(790\) 0 0
\(791\) 17.4195 0.619365
\(792\) 0 0
\(793\) −4.04658 4.04658i −0.143698 0.143698i
\(794\) 0 0
\(795\) 13.6565 11.2510i 0.484346 0.399033i
\(796\) 0 0
\(797\) 15.9072i 0.563461i −0.959494 0.281730i \(-0.909092\pi\)