Properties

Label 847.2.f.h.729.1
Level $847$
Weight $2$
Character 847.729
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 729.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 847.729
Dual form 847.2.f.h.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +O(q^{10})\) \(q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +6.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(1.61803 + 1.17557i) q^{17} +(1.85410 + 5.70634i) q^{19} +(-1.61803 + 1.17557i) q^{20} -3.00000 q^{21} -5.00000 q^{23} +(-1.23607 - 3.80423i) q^{25} +(7.28115 + 5.29007i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-3.09017 + 9.51057i) q^{29} +(-0.809017 + 0.587785i) q^{31} +(0.809017 - 0.587785i) q^{35} +(-3.70820 - 11.4127i) q^{36} +(-1.54508 + 4.75528i) q^{37} +(9.70820 + 7.05342i) q^{39} +(0.618034 + 1.90211i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(2.47214 + 7.60845i) q^{47} +(-3.70820 + 11.4127i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.85410 - 5.70634i) q^{51} +(-2.47214 - 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +(14.5623 - 10.5801i) q^{57} +(0.927051 - 2.85317i) q^{59} +(4.85410 + 3.52671i) q^{60} +(-1.61803 - 1.17557i) q^{61} +(1.85410 + 5.70634i) q^{63} +(6.47214 - 4.70228i) q^{64} -4.00000 q^{65} -3.00000 q^{67} +(-3.23607 + 2.35114i) q^{68} +(4.63525 + 14.2658i) q^{69} +(-0.809017 - 0.587785i) q^{71} +(-3.09017 + 9.51057i) q^{73} +(-9.70820 + 7.05342i) q^{75} -12.0000 q^{76} +(4.85410 - 3.52671i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(2.78115 - 8.55951i) q^{81} +(9.70820 + 7.05342i) q^{83} +(1.85410 - 5.70634i) q^{84} +(0.618034 + 1.90211i) q^{85} +30.0000 q^{87} -15.0000 q^{89} +(1.23607 + 3.80423i) q^{91} +(3.09017 - 9.51057i) q^{92} +(2.42705 + 1.76336i) q^{93} +(-1.85410 + 5.70634i) q^{95} +(4.04508 - 2.93893i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9} + 24 q^{12} - 4 q^{13} - 3 q^{15} - 4 q^{16} + 2 q^{17} - 6 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{23} + 4 q^{25} + 9 q^{27} + 2 q^{28} + 10 q^{29} - q^{31} + q^{35} + 12 q^{36} + 5 q^{37} + 12 q^{39} - 2 q^{41} + 32 q^{43} - 24 q^{45} - 8 q^{47} + 12 q^{48} - q^{49} - 6 q^{51} + 8 q^{52} + 6 q^{53} + 18 q^{57} - 3 q^{59} + 6 q^{60} - 2 q^{61} - 6 q^{63} + 8 q^{64} - 16 q^{65} - 12 q^{67} - 4 q^{68} - 15 q^{69} - q^{71} + 10 q^{73} - 12 q^{75} - 48 q^{76} + 6 q^{79} + 4 q^{80} - 9 q^{81} + 12 q^{83} - 6 q^{84} - 2 q^{85} + 120 q^{87} - 60 q^{89} - 4 q^{91} - 10 q^{92} + 3 q^{93} + 6 q^{95} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(3\) −0.927051 2.85317i −0.535233 1.64728i −0.743145 0.669131i \(-0.766667\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(4\) −0.618034 + 1.90211i −0.309017 + 0.951057i
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i 0.753804 0.657099i \(-0.228217\pi\)
−0.392000 + 0.919965i \(0.628217\pi\)
\(6\) 0 0
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) 0 0
\(9\) −4.85410 + 3.52671i −1.61803 + 1.17557i
\(10\) 0 0
\(11\) 0 0
\(12\) 6.00000 1.73205
\(13\) −3.23607 + 2.35114i −0.897524 + 0.652089i −0.937829 0.347098i \(-0.887167\pi\)
0.0403050 + 0.999187i \(0.487167\pi\)
\(14\) 0 0
\(15\) 0.927051 2.85317i 0.239364 0.736685i
\(16\) −3.23607 2.35114i −0.809017 0.587785i
\(17\) 1.61803 + 1.17557i 0.392431 + 0.285118i 0.766451 0.642303i \(-0.222021\pi\)
−0.374020 + 0.927421i \(0.622021\pi\)
\(18\) 0 0
\(19\) 1.85410 + 5.70634i 0.425360 + 1.30912i 0.902649 + 0.430377i \(0.141620\pi\)
−0.477289 + 0.878746i \(0.658380\pi\)
\(20\) −1.61803 + 1.17557i −0.361803 + 0.262866i
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) −1.23607 3.80423i −0.247214 0.760845i
\(26\) 0 0
\(27\) 7.28115 + 5.29007i 1.40126 + 1.01807i
\(28\) 1.61803 + 1.17557i 0.305780 + 0.222162i
\(29\) −3.09017 + 9.51057i −0.573830 + 1.76607i 0.0662984 + 0.997800i \(0.478881\pi\)
−0.640129 + 0.768268i \(0.721119\pi\)
\(30\) 0 0
\(31\) −0.809017 + 0.587785i −0.145304 + 0.105569i −0.658062 0.752964i \(-0.728624\pi\)
0.512758 + 0.858533i \(0.328624\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.809017 0.587785i 0.136749 0.0993538i
\(36\) −3.70820 11.4127i −0.618034 1.90211i
\(37\) −1.54508 + 4.75528i −0.254010 + 0.781764i 0.740013 + 0.672593i \(0.234819\pi\)
−0.994023 + 0.109171i \(0.965181\pi\)
\(38\) 0 0
\(39\) 9.70820 + 7.05342i 1.55456 + 1.12945i
\(40\) 0 0
\(41\) 0.618034 + 1.90211i 0.0965207 + 0.297060i 0.987647 0.156695i \(-0.0500840\pi\)
−0.891126 + 0.453755i \(0.850084\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 0 0
\(47\) 2.47214 + 7.60845i 0.360598 + 1.10981i 0.952692 + 0.303938i \(0.0983015\pi\)
−0.592094 + 0.805869i \(0.701699\pi\)
\(48\) −3.70820 + 11.4127i −0.535233 + 1.64728i
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 0 0
\(51\) 1.85410 5.70634i 0.259626 0.799047i
\(52\) −2.47214 7.60845i −0.342824 1.05510i
\(53\) 4.85410 3.52671i 0.666762 0.484431i −0.202178 0.979349i \(-0.564802\pi\)
0.868940 + 0.494918i \(0.164802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 14.5623 10.5801i 1.92882 1.40137i
\(58\) 0 0
\(59\) 0.927051 2.85317i 0.120692 0.371451i −0.872400 0.488793i \(-0.837437\pi\)
0.993092 + 0.117342i \(0.0374373\pi\)
\(60\) 4.85410 + 3.52671i 0.626662 + 0.455296i
\(61\) −1.61803 1.17557i −0.207168 0.150516i 0.479363 0.877616i \(-0.340868\pi\)
−0.686531 + 0.727100i \(0.740868\pi\)
\(62\) 0 0
\(63\) 1.85410 + 5.70634i 0.233595 + 0.718931i
\(64\) 6.47214 4.70228i 0.809017 0.587785i
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) −3.23607 + 2.35114i −0.392431 + 0.285118i
\(69\) 4.63525 + 14.2658i 0.558019 + 1.71741i
\(70\) 0 0
\(71\) −0.809017 0.587785i −0.0960127 0.0697573i 0.538743 0.842470i \(-0.318899\pi\)
−0.634756 + 0.772713i \(0.718899\pi\)
\(72\) 0 0
\(73\) −3.09017 + 9.51057i −0.361677 + 1.11313i 0.590359 + 0.807141i \(0.298986\pi\)
−0.952036 + 0.305987i \(0.901014\pi\)
\(74\) 0 0
\(75\) −9.70820 + 7.05342i −1.12101 + 0.814459i
\(76\) −12.0000 −1.37649
\(77\) 0 0
\(78\) 0 0
\(79\) 4.85410 3.52671i 0.546129 0.396786i −0.280227 0.959934i \(-0.590410\pi\)
0.826356 + 0.563148i \(0.190410\pi\)
\(80\) −1.23607 3.80423i −0.138197 0.425325i
\(81\) 2.78115 8.55951i 0.309017 0.951057i
\(82\) 0 0
\(83\) 9.70820 + 7.05342i 1.06561 + 0.774214i 0.975119 0.221683i \(-0.0711551\pi\)
0.0904951 + 0.995897i \(0.471155\pi\)
\(84\) 1.85410 5.70634i 0.202299 0.622613i
\(85\) 0.618034 + 1.90211i 0.0670352 + 0.206313i
\(86\) 0 0
\(87\) 30.0000 3.21634
\(88\) 0 0
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) 1.23607 + 3.80423i 0.129575 + 0.398791i
\(92\) 3.09017 9.51057i 0.322172 0.991545i
\(93\) 2.42705 + 1.76336i 0.251673 + 0.182851i
\(94\) 0 0
\(95\) −1.85410 + 5.70634i −0.190227 + 0.585458i
\(96\) 0 0
\(97\) 4.04508 2.93893i 0.410716 0.298403i −0.363176 0.931721i \(-0.618307\pi\)
0.773892 + 0.633318i \(0.218307\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.00000 0.800000
\(101\) −9.70820 + 7.05342i −0.966002 + 0.701842i −0.954537 0.298092i \(-0.903650\pi\)
−0.0114654 + 0.999934i \(0.503650\pi\)
\(102\) 0 0
\(103\) −3.70820 + 11.4127i −0.365380 + 1.12452i 0.584362 + 0.811493i \(0.301345\pi\)
−0.949743 + 0.313032i \(0.898655\pi\)
\(104\) 0 0
\(105\) −2.42705 1.76336i −0.236856 0.172086i
\(106\) 0 0
\(107\) 3.09017 + 9.51057i 0.298738 + 0.919421i 0.981940 + 0.189192i \(0.0605868\pi\)
−0.683202 + 0.730229i \(0.739413\pi\)
\(108\) −14.5623 + 10.5801i −1.40126 + 1.01807i
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) 15.0000 1.42374
\(112\) −3.23607 + 2.35114i −0.305780 + 0.222162i
\(113\) −5.87132 18.0701i −0.552328 1.69989i −0.702898 0.711290i \(-0.748111\pi\)
0.150571 0.988599i \(-0.451889\pi\)
\(114\) 0 0
\(115\) −4.04508 2.93893i −0.377206 0.274056i
\(116\) −16.1803 11.7557i −1.50231 1.09149i
\(117\) 7.41641 22.8254i 0.685647 2.11020i
\(118\) 0 0
\(119\) 1.61803 1.17557i 0.148325 0.107764i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 4.85410 3.52671i 0.437680 0.317993i
\(124\) −0.618034 1.90211i −0.0555011 0.170815i
\(125\) 2.78115 8.55951i 0.248754 0.765586i
\(126\) 0 0
\(127\) 1.61803 + 1.17557i 0.143577 + 0.104315i 0.657255 0.753668i \(-0.271717\pi\)
−0.513678 + 0.857983i \(0.671717\pi\)
\(128\) 0 0
\(129\) −7.41641 22.8254i −0.652978 2.00966i
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) 0 0
\(135\) 2.78115 + 8.55951i 0.239364 + 0.736685i
\(136\) 0 0
\(137\) 2.42705 + 1.76336i 0.207357 + 0.150654i 0.686617 0.727019i \(-0.259095\pi\)
−0.479260 + 0.877673i \(0.659095\pi\)
\(138\) 0 0
\(139\) 3.09017 9.51057i 0.262105 0.806676i −0.730241 0.683189i \(-0.760592\pi\)
0.992346 0.123486i \(-0.0394076\pi\)
\(140\) 0.618034 + 1.90211i 0.0522334 + 0.160758i
\(141\) 19.4164 14.1068i 1.63516 1.18801i
\(142\) 0 0
\(143\) 0 0
\(144\) 24.0000 2.00000
\(145\) −8.09017 + 5.87785i −0.671852 + 0.488129i
\(146\) 0 0
\(147\) −0.927051 + 2.85317i −0.0764619 + 0.235325i
\(148\) −8.09017 5.87785i −0.665008 0.483157i
\(149\) −17.7984 12.9313i −1.45810 1.05937i −0.983853 0.178979i \(-0.942720\pi\)
−0.474247 0.880392i \(-0.657280\pi\)
\(150\) 0 0
\(151\) −1.85410 5.70634i −0.150885 0.464375i 0.846836 0.531854i \(-0.178505\pi\)
−0.997721 + 0.0674788i \(0.978505\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) −19.4164 + 14.1068i −1.55456 + 1.12945i
\(157\) 2.16312 + 6.65740i 0.172636 + 0.531318i 0.999518 0.0310576i \(-0.00988752\pi\)
−0.826882 + 0.562376i \(0.809888\pi\)
\(158\) 0 0
\(159\) −14.5623 10.5801i −1.15487 0.839059i
\(160\) 0 0
\(161\) −1.54508 + 4.75528i −0.121770 + 0.374769i
\(162\) 0 0
\(163\) −3.23607 + 2.35114i −0.253468 + 0.184156i −0.707263 0.706951i \(-0.750070\pi\)
0.453794 + 0.891107i \(0.350070\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 0 0
\(167\) −1.61803 + 1.17557i −0.125207 + 0.0909684i −0.648626 0.761107i \(-0.724656\pi\)
0.523419 + 0.852075i \(0.324656\pi\)
\(168\) 0 0
\(169\) 0.927051 2.85317i 0.0713116 0.219475i
\(170\) 0 0
\(171\) −29.1246 21.1603i −2.22721 1.61817i
\(172\) −4.94427 + 15.2169i −0.376997 + 1.16028i
\(173\) −4.94427 15.2169i −0.375906 1.15692i −0.942865 0.333174i \(-0.891880\pi\)
0.566959 0.823746i \(-0.308120\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −9.00000 −0.676481
\(178\) 0 0
\(179\) 0.309017 + 0.951057i 0.0230970 + 0.0710853i 0.961941 0.273258i \(-0.0881014\pi\)
−0.938844 + 0.344344i \(0.888101\pi\)
\(180\) 3.70820 11.4127i 0.276393 0.850651i
\(181\) −4.04508 2.93893i −0.300669 0.218449i 0.427213 0.904151i \(-0.359495\pi\)
−0.727882 + 0.685702i \(0.759495\pi\)
\(182\) 0 0
\(183\) −1.85410 + 5.70634i −0.137059 + 0.421825i
\(184\) 0 0
\(185\) −4.04508 + 2.93893i −0.297401 + 0.216074i
\(186\) 0 0
\(187\) 0 0
\(188\) −16.0000 −1.16692
\(189\) 7.28115 5.29007i 0.529626 0.384796i
\(190\) 0 0
\(191\) 1.54508 4.75528i 0.111798 0.344080i −0.879467 0.475959i \(-0.842101\pi\)
0.991266 + 0.131879i \(0.0421010\pi\)
\(192\) −19.4164 14.1068i −1.40126 1.01807i
\(193\) 11.3262 + 8.22899i 0.815280 + 0.592336i 0.915357 0.402644i \(-0.131909\pi\)
−0.100076 + 0.994980i \(0.531909\pi\)
\(194\) 0 0
\(195\) 3.70820 + 11.4127i 0.265550 + 0.817279i
\(196\) 1.61803 1.17557i 0.115574 0.0839693i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 2.78115 + 8.55951i 0.196167 + 0.603741i
\(202\) 0 0
\(203\) 8.09017 + 5.87785i 0.567819 + 0.412544i
\(204\) 9.70820 + 7.05342i 0.679710 + 0.493838i
\(205\) −0.618034 + 1.90211i −0.0431654 + 0.132849i
\(206\) 0 0
\(207\) 24.2705 17.6336i 1.68692 1.22562i
\(208\) 16.0000 1.10940
\(209\) 0 0
\(210\) 0 0
\(211\) −1.61803 + 1.17557i −0.111390 + 0.0809296i −0.642086 0.766633i \(-0.721931\pi\)
0.530696 + 0.847562i \(0.321931\pi\)
\(212\) 3.70820 + 11.4127i 0.254680 + 0.783826i
\(213\) −0.927051 + 2.85317i −0.0635205 + 0.195496i
\(214\) 0 0
\(215\) 6.47214 + 4.70228i 0.441396 + 0.320693i
\(216\) 0 0
\(217\) 0.309017 + 0.951057i 0.0209774 + 0.0645619i
\(218\) 0 0
\(219\) 30.0000 2.02721
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 0.309017 + 0.951057i 0.0206933 + 0.0636875i 0.960870 0.277000i \(-0.0893402\pi\)
−0.940177 + 0.340687i \(0.889340\pi\)
\(224\) 0 0
\(225\) 19.4164 + 14.1068i 1.29443 + 0.940456i
\(226\) 0 0
\(227\) −1.23607 + 3.80423i −0.0820407 + 0.252495i −0.983660 0.180035i \(-0.942379\pi\)
0.901620 + 0.432530i \(0.142379\pi\)
\(228\) 11.1246 + 34.2380i 0.736745 + 2.26747i
\(229\) 5.66312 4.11450i 0.374229 0.271894i −0.384733 0.923028i \(-0.625707\pi\)
0.758963 + 0.651134i \(0.225707\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.85410 3.52671i 0.318003 0.231043i −0.417320 0.908760i \(-0.637031\pi\)
0.735323 + 0.677717i \(0.237031\pi\)
\(234\) 0 0
\(235\) −2.47214 + 7.60845i −0.161264 + 0.496321i
\(236\) 4.85410 + 3.52671i 0.315975 + 0.229569i
\(237\) −14.5623 10.5801i −0.945923 0.687254i
\(238\) 0 0
\(239\) −1.23607 3.80423i −0.0799546 0.246075i 0.903087 0.429458i \(-0.141295\pi\)
−0.983042 + 0.183383i \(0.941295\pi\)
\(240\) −9.70820 + 7.05342i −0.626662 + 0.455296i
\(241\) 12.0000 0.772988 0.386494 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 3.23607 2.35114i 0.207168 0.150516i
\(245\) −0.309017 0.951057i −0.0197424 0.0607608i
\(246\) 0 0
\(247\) −19.4164 14.1068i −1.23544 0.897597i
\(248\) 0 0
\(249\) 11.1246 34.2380i 0.704994 2.16975i
\(250\) 0 0
\(251\) 16.9894 12.3435i 1.07236 0.779114i 0.0960240 0.995379i \(-0.469387\pi\)
0.976335 + 0.216265i \(0.0693875\pi\)
\(252\) −12.0000 −0.755929
\(253\) 0 0
\(254\) 0 0
\(255\) 4.85410 3.52671i 0.303976 0.220851i
\(256\) 4.94427 + 15.2169i 0.309017 + 0.951057i
\(257\) −1.85410 + 5.70634i −0.115656 + 0.355952i −0.992083 0.125582i \(-0.959920\pi\)
0.876428 + 0.481534i \(0.159920\pi\)
\(258\) 0 0
\(259\) 4.04508 + 2.93893i 0.251349 + 0.182616i
\(260\) 2.47214 7.60845i 0.153315 0.471856i
\(261\) −18.5410 57.0634i −1.14766 3.53214i
\(262\) 0 0
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 13.9058 + 42.7975i 0.851019 + 2.61917i
\(268\) 1.85410 5.70634i 0.113257 0.348570i
\(269\) 14.5623 + 10.5801i 0.887879 + 0.645082i 0.935324 0.353792i \(-0.115108\pi\)
−0.0474448 + 0.998874i \(0.515108\pi\)
\(270\) 0 0
\(271\) −4.94427 + 15.2169i −0.300343 + 0.924361i 0.681031 + 0.732255i \(0.261532\pi\)
−0.981374 + 0.192106i \(0.938468\pi\)
\(272\) −2.47214 7.60845i −0.149895 0.461330i
\(273\) 9.70820 7.05342i 0.587567 0.426893i
\(274\) 0 0
\(275\) 0 0
\(276\) −30.0000 −1.80579
\(277\) 19.4164 14.1068i 1.16662 0.847598i 0.176019 0.984387i \(-0.443678\pi\)
0.990600 + 0.136789i \(0.0436781\pi\)
\(278\) 0 0
\(279\) 1.85410 5.70634i 0.111002 0.341630i
\(280\) 0 0
\(281\) −3.23607 2.35114i −0.193048 0.140257i 0.487063 0.873367i \(-0.338068\pi\)
−0.680111 + 0.733110i \(0.738068\pi\)
\(282\) 0 0
\(283\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(284\) 1.61803 1.17557i 0.0960127 0.0697573i
\(285\) 18.0000 1.06623
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) −4.01722 12.3637i −0.236307 0.727279i
\(290\) 0 0
\(291\) −12.1353 8.81678i −0.711381 0.516849i
\(292\) −16.1803 11.7557i −0.946883 0.687951i
\(293\) 1.85410 5.70634i 0.108318 0.333368i −0.882177 0.470918i \(-0.843923\pi\)
0.990495 + 0.137550i \(0.0439228\pi\)
\(294\) 0 0
\(295\) 2.42705 1.76336i 0.141308 0.102667i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 16.1803 11.7557i 0.935733 0.679850i
\(300\) −7.41641 22.8254i −0.428187 1.31782i
\(301\) 2.47214 7.60845i 0.142492 0.438544i
\(302\) 0 0
\(303\) 29.1246 + 21.1603i 1.67317 + 1.21563i
\(304\) 7.41641 22.8254i 0.425360 1.30912i
\(305\) −0.618034 1.90211i −0.0353885 0.108915i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 36.0000 2.04797
\(310\) 0 0
\(311\) 2.47214 + 7.60845i 0.140182 + 0.431436i 0.996360 0.0852452i \(-0.0271674\pi\)
−0.856178 + 0.516681i \(0.827167\pi\)
\(312\) 0 0
\(313\) 18.6074 + 13.5191i 1.05175 + 0.764142i 0.972545 0.232716i \(-0.0747612\pi\)
0.0792071 + 0.996858i \(0.474761\pi\)
\(314\) 0 0
\(315\) −1.85410 + 5.70634i −0.104467 + 0.321516i
\(316\) 3.70820 + 11.4127i 0.208603 + 0.642013i
\(317\) −7.28115 + 5.29007i −0.408950 + 0.297120i −0.773177 0.634191i \(-0.781333\pi\)
0.364226 + 0.931310i \(0.381333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 8.00000 0.447214
\(321\) 24.2705 17.6336i 1.35465 0.984209i
\(322\) 0 0
\(323\) −3.70820 + 11.4127i −0.206330 + 0.635018i
\(324\) 14.5623 + 10.5801i 0.809017 + 0.587785i
\(325\) 12.9443 + 9.40456i 0.718019 + 0.521671i
\(326\) 0 0
\(327\) 3.70820 + 11.4127i 0.205064 + 0.631123i
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −19.4164 + 14.1068i −1.06561 + 0.774214i
\(333\) −9.27051 28.5317i −0.508021 1.56353i
\(334\) 0 0
\(335\) −2.42705 1.76336i −0.132604 0.0963424i
\(336\) 9.70820 + 7.05342i 0.529626 + 0.384796i
\(337\) 5.56231 17.1190i 0.302998 0.932532i −0.677419 0.735598i \(-0.736901\pi\)
0.980417 0.196934i \(-0.0630986\pi\)
\(338\) 0 0
\(339\) −46.1140 + 33.5038i −2.50457 + 1.81967i
\(340\) −4.00000 −0.216930
\(341\) 0 0
\(342\) 0 0
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) 0 0
\(345\) −4.63525 + 14.2658i −0.249554 + 0.768047i
\(346\) 0 0
\(347\) 11.3262 + 8.22899i 0.608024 + 0.441756i 0.848718 0.528846i \(-0.177375\pi\)
−0.240694 + 0.970601i \(0.577375\pi\)
\(348\) −18.5410 + 57.0634i −0.993903 + 3.05892i
\(349\) 10.5066 + 32.3359i 0.562404 + 1.73090i 0.675541 + 0.737323i \(0.263910\pi\)
−0.113136 + 0.993579i \(0.536090\pi\)
\(350\) 0 0
\(351\) −36.0000 −1.92154
\(352\) 0 0
\(353\) 9.00000 0.479022 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(354\) 0 0
\(355\) −0.309017 0.951057i −0.0164009 0.0504768i
\(356\) 9.27051 28.5317i 0.491336 1.51218i
\(357\) −4.85410 3.52671i −0.256906 0.186653i
\(358\) 0 0
\(359\) −2.47214 + 7.60845i −0.130474 + 0.401559i −0.994859 0.101273i \(-0.967708\pi\)
0.864384 + 0.502832i \(0.167708\pi\)
\(360\) 0 0
\(361\) −13.7533 + 9.99235i −0.723857 + 0.525913i
\(362\) 0 0
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) −8.09017 + 5.87785i −0.423459 + 0.307661i
\(366\) 0 0
\(367\) −3.39919 + 10.4616i −0.177436 + 0.546092i −0.999736 0.0229617i \(-0.992690\pi\)
0.822300 + 0.569054i \(0.192690\pi\)
\(368\) 16.1803 + 11.7557i 0.843459 + 0.612808i
\(369\) −9.70820 7.05342i −0.505389 0.367187i
\(370\) 0 0
\(371\) −1.85410 5.70634i −0.0962602 0.296258i
\(372\) −4.85410 + 3.52671i −0.251673 + 0.182851i
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) −27.0000 −1.39427
\(376\) 0 0
\(377\) −12.3607 38.0423i −0.636607 1.95928i
\(378\) 0 0
\(379\) 23.4615 + 17.0458i 1.20514 + 0.875583i 0.994780 0.102042i \(-0.0325377\pi\)
0.210356 + 0.977625i \(0.432538\pi\)
\(380\) −9.70820 7.05342i −0.498020 0.361833i
\(381\) 1.85410 5.70634i 0.0949885 0.292345i
\(382\) 0 0
\(383\) −13.7533 + 9.99235i −0.702760 + 0.510585i −0.880830 0.473433i \(-0.843015\pi\)
0.178070 + 0.984018i \(0.443015\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −38.8328 + 28.2137i −1.97398 + 1.43418i
\(388\) 3.09017 + 9.51057i 0.156880 + 0.482826i
\(389\) 2.78115 8.55951i 0.141010 0.433984i −0.855466 0.517858i \(-0.826729\pi\)
0.996476 + 0.0838742i \(0.0267294\pi\)
\(390\) 0 0
\(391\) −8.09017 5.87785i −0.409137 0.297256i
\(392\) 0 0
\(393\) 16.6869 + 51.3571i 0.841744 + 2.59062i
\(394\) 0 0
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) −5.56231 17.1190i −0.278464 0.857023i
\(400\) −4.94427 + 15.2169i −0.247214 + 0.760845i
\(401\) 4.85410 + 3.52671i 0.242402 + 0.176116i 0.702353 0.711829i \(-0.252133\pi\)
−0.459951 + 0.887945i \(0.652133\pi\)
\(402\) 0 0
\(403\) 1.23607 3.80423i 0.0615729 0.189502i
\(404\) −7.41641 22.8254i −0.368980 1.13560i
\(405\) 7.28115 5.29007i 0.361803 0.262866i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −21.0344 + 15.2824i −1.04009 + 0.755667i −0.970302 0.241895i \(-0.922231\pi\)
−0.0697838 + 0.997562i \(0.522231\pi\)
\(410\) 0 0
\(411\) 2.78115 8.55951i 0.137184 0.422209i
\(412\) −19.4164 14.1068i −0.956578 0.694994i
\(413\) −2.42705 1.76336i −0.119427 0.0867691i
\(414\) 0 0
\(415\) 3.70820 + 11.4127i 0.182029 + 0.560226i
\(416\) 0 0
\(417\) −30.0000 −1.46911
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 4.85410 3.52671i 0.236856 0.172086i
\(421\) 6.79837 + 20.9232i 0.331332 + 1.01974i 0.968501 + 0.249012i \(0.0801057\pi\)
−0.637168 + 0.770725i \(0.719894\pi\)
\(422\) 0 0
\(423\) −38.8328 28.2137i −1.88812 1.37180i
\(424\) 0 0
\(425\) 2.47214 7.60845i 0.119916 0.369064i
\(426\) 0 0
\(427\) −1.61803 + 1.17557i −0.0783022 + 0.0568898i
\(428\) −20.0000 −0.966736
\(429\) 0 0
\(430\) 0 0
\(431\) −16.1803 + 11.7557i −0.779380 + 0.566252i −0.904793 0.425852i \(-0.859974\pi\)
0.125413 + 0.992105i \(0.459974\pi\)
\(432\) −11.1246 34.2380i −0.535233 1.64728i
\(433\) −7.72542 + 23.7764i −0.371260 + 1.14262i 0.574707 + 0.818359i \(0.305116\pi\)
−0.945967 + 0.324262i \(0.894884\pi\)
\(434\) 0 0
\(435\) 24.2705 + 17.6336i 1.16368 + 0.845464i
\(436\) 2.47214 7.60845i 0.118394 0.364379i
\(437\) −9.27051 28.5317i −0.443469 1.36486i
\(438\) 0 0
\(439\) 14.0000 0.668184 0.334092 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) −12.0517 37.0912i −0.572592 1.76226i −0.644237 0.764826i \(-0.722825\pi\)
0.0716450 0.997430i \(-0.477175\pi\)
\(444\) −9.27051 + 28.5317i −0.439959 + 1.35405i
\(445\) −12.1353 8.81678i −0.575266 0.417955i
\(446\) 0 0
\(447\) −20.3951 + 62.7697i −0.964656 + 2.96891i
\(448\) −2.47214 7.60845i −0.116797 0.359466i
\(449\) −12.1353 + 8.81678i −0.572698 + 0.416090i −0.836084 0.548601i \(-0.815161\pi\)
0.263386 + 0.964690i \(0.415161\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 38.0000 1.78737
\(453\) −14.5623 + 10.5801i −0.684197 + 0.497098i
\(454\) 0 0
\(455\) −1.23607 + 3.80423i −0.0579478 + 0.178345i
\(456\) 0 0
\(457\) 6.47214 + 4.70228i 0.302754 + 0.219963i 0.728781 0.684747i \(-0.240087\pi\)
−0.426027 + 0.904710i \(0.640087\pi\)
\(458\) 0 0
\(459\) 5.56231 + 17.1190i 0.259626 + 0.799047i
\(460\) 8.09017 5.87785i 0.377206 0.274056i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 32.3607 23.5114i 1.50231 1.09149i
\(465\) 0.927051 + 2.85317i 0.0429910 + 0.132313i
\(466\) 0 0
\(467\) −2.42705 1.76336i −0.112311 0.0815984i 0.530212 0.847865i \(-0.322112\pi\)
−0.642523 + 0.766267i \(0.722112\pi\)
\(468\) 38.8328 + 28.2137i 1.79505 + 1.30418i
\(469\) −0.927051 + 2.85317i −0.0428072 + 0.131747i
\(470\) 0 0
\(471\) 16.9894 12.3435i 0.782828 0.568758i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 19.4164 14.1068i 0.890886 0.647266i
\(476\) 1.23607 + 3.80423i 0.0566551 + 0.174366i
\(477\) −11.1246 + 34.2380i −0.509361 + 1.56765i
\(478\) 0 0
\(479\) −22.6525 16.4580i −1.03502 0.751985i −0.0657112 0.997839i \(-0.520932\pi\)
−0.969307 + 0.245854i \(0.920932\pi\)
\(480\) 0 0
\(481\) −6.18034 19.0211i −0.281799 0.867289i
\(482\) 0 0
\(483\) 15.0000 0.682524
\(484\) 0 0
\(485\) 5.00000 0.227038
\(486\) 0 0
\(487\) −4.01722 12.3637i −0.182038 0.560254i 0.817847 0.575436i \(-0.195167\pi\)
−0.999885 + 0.0151813i \(0.995167\pi\)
\(488\) 0 0
\(489\) 9.70820 + 7.05342i 0.439020 + 0.318967i
\(490\) 0 0
\(491\) 9.27051 28.5317i 0.418372 1.28762i −0.490827 0.871257i \(-0.663305\pi\)
0.909200 0.416361i \(-0.136695\pi\)
\(492\) 3.70820 + 11.4127i 0.167179 + 0.514523i
\(493\) −16.1803 + 11.7557i −0.728726 + 0.529450i
\(494\) 0 0
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) −0.809017 + 0.587785i −0.0362894 + 0.0263658i
\(498\) 0 0
\(499\) 13.5967 41.8465i 0.608674 1.87331i 0.139444 0.990230i \(-0.455468\pi\)
0.469230 0.883076i \(-0.344532\pi\)
\(500\) 14.5623 + 10.5801i 0.651246 + 0.473158i
\(501\) 4.85410 + 3.52671i 0.216865 + 0.157562i
\(502\) 0 0
\(503\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −3.23607 + 2.35114i −0.143577 + 0.104315i
\(509\) −9.57953 29.4828i −0.424605 1.30680i −0.903372 0.428858i \(-0.858916\pi\)
0.478767 0.877942i \(-0.341084\pi\)
\(510\) 0 0
\(511\) 8.09017 + 5.87785i 0.357888 + 0.260021i
\(512\) 0 0
\(513\) −16.6869 + 51.3571i −0.736745 + 2.26747i
\(514\) 0 0
\(515\) −9.70820 + 7.05342i −0.427795 + 0.310811i
\(516\) 48.0000 2.11308
\(517\) 0 0
\(518\) 0 0
\(519\) −38.8328 + 28.2137i −1.70457 + 1.23844i
\(520\) 0 0
\(521\) 2.16312 6.65740i 0.0947680 0.291666i −0.892425 0.451195i \(-0.850998\pi\)
0.987193 + 0.159530i \(0.0509977\pi\)
\(522\) 0 0
\(523\) 25.8885 + 18.8091i 1.13203 + 0.822466i 0.985989 0.166813i \(-0.0533477\pi\)
0.146038 + 0.989279i \(0.453348\pi\)
\(524\) 11.1246 34.2380i 0.485981 1.49570i
\(525\) 3.70820 + 11.4127i 0.161839 + 0.498090i
\(526\) 0 0
\(527\) −2.00000 −0.0871214
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 5.56231 + 17.1190i 0.241384 + 0.742902i
\(532\) −3.70820 + 11.4127i −0.160771 + 0.494802i
\(533\) −6.47214 4.70228i −0.280339 0.203678i
\(534\) 0 0
\(535\) −3.09017 + 9.51057i −0.133600 + 0.411178i
\(536\) 0 0
\(537\) 2.42705 1.76336i 0.104735 0.0760944i
\(538\) 0 0
\(539\) 0 0
\(540\) −18.0000 −0.774597
\(541\) 25.8885 18.8091i 1.11304 0.808668i 0.129896 0.991528i \(-0.458536\pi\)
0.983139 + 0.182860i \(0.0585355\pi\)
\(542\) 0 0
\(543\) −4.63525 + 14.2658i −0.198918 + 0.612206i
\(544\) 0 0
\(545\) −3.23607 2.35114i −0.138618 0.100712i
\(546\) 0 0
\(547\) 7.41641 + 22.8254i 0.317103 + 0.975942i 0.974880 + 0.222730i \(0.0714967\pi\)
−0.657778 + 0.753212i \(0.728503\pi\)
\(548\) −4.85410 + 3.52671i −0.207357 + 0.150654i
\(549\) 12.0000 0.512148
\(550\) 0 0
\(551\) −60.0000 −2.55609
\(552\) 0 0
\(553\) −1.85410 5.70634i −0.0788444 0.242658i
\(554\) 0 0
\(555\) 12.1353 + 8.81678i 0.515113 + 0.374251i
\(556\) 16.1803 + 11.7557i 0.686199 + 0.498553i
\(557\) −4.32624 + 13.3148i −0.183309 + 0.564166i −0.999915 0.0130289i \(-0.995853\pi\)
0.816607 + 0.577195i \(0.195853\pi\)
\(558\) 0 0
\(559\) −25.8885 + 18.8091i −1.09497 + 0.795541i
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 0 0
\(563\) 16.1803 11.7557i 0.681920 0.495444i −0.192074 0.981380i \(-0.561521\pi\)
0.873994 + 0.485937i \(0.161521\pi\)
\(564\) 14.8328 + 45.6507i 0.624574 + 1.92224i
\(565\) 5.87132 18.0701i 0.247008 0.760214i
\(566\) 0 0
\(567\) −7.28115 5.29007i −0.305780 0.222162i
\(568\) 0 0
\(569\) 5.56231 + 17.1190i 0.233184 + 0.717667i 0.997357 + 0.0726553i \(0.0231473\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 6.18034 + 19.0211i 0.257738 + 0.793236i
\(576\) −14.8328 + 45.6507i −0.618034 + 1.90211i
\(577\) 20.2254 + 14.6946i 0.841995 + 0.611746i 0.922927 0.384974i \(-0.125790\pi\)
−0.0809319 + 0.996720i \(0.525790\pi\)
\(578\) 0 0
\(579\) 12.9787 39.9444i 0.539377 1.66003i
\(580\) −6.18034 19.0211i −0.256625 0.789809i
\(581\) 9.70820 7.05342i 0.402764 0.292625i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 19.4164 14.1068i 0.802770 0.583246i
\(586\) 0 0
\(587\) 11.1246 34.2380i 0.459162 1.41315i −0.407017 0.913421i \(-0.633431\pi\)
0.866179 0.499734i \(-0.166569\pi\)
\(588\) −4.85410 3.52671i −0.200180 0.145439i
\(589\) −4.85410 3.52671i −0.200010 0.145316i
\(590\) 0 0
\(591\) 16.6869 + 51.3571i 0.686408 + 2.11255i
\(592\) 16.1803 11.7557i 0.665008 0.483157i
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 2.00000 0.0819920
\(596\) 35.5967 25.8626i 1.45810 1.05937i
\(597\) 7.41641 + 22.8254i 0.303533 + 0.934180i
\(598\) 0 0
\(599\) 38.8328 + 28.2137i 1.58667 + 1.15278i 0.908511 + 0.417861i \(0.137220\pi\)
0.678155 + 0.734919i \(0.262780\pi\)
\(600\) 0 0
\(601\) −2.47214 + 7.60845i −0.100841 + 0.310355i −0.988732 0.149698i \(-0.952170\pi\)
0.887891 + 0.460053i \(0.152170\pi\)
\(602\) 0 0
\(603\) 14.5623 10.5801i 0.593023 0.430856i
\(604\) 12.0000 0.488273
\(605\) 0 0
\(606\) 0 0
\(607\) −8.09017 + 5.87785i −0.328370 + 0.238575i −0.739739 0.672894i \(-0.765051\pi\)
0.411369 + 0.911469i \(0.365051\pi\)
\(608\) 0 0
\(609\) 9.27051 28.5317i 0.375660 1.15616i
\(610\) 0 0
\(611\) −25.8885 18.8091i −1.04734 0.760936i
\(612\) 7.41641 22.8254i 0.299791 0.922660i
\(613\) −4.94427 15.2169i −0.199697 0.614605i −0.999890 0.0148615i \(-0.995269\pi\)
0.800192 0.599744i \(-0.204731\pi\)
\(614\) 0 0
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) 5.25329 + 16.1680i 0.211148 + 0.649845i 0.999405 + 0.0344993i \(0.0109837\pi\)
−0.788257 + 0.615346i \(0.789016\pi\)
\(620\) 0.618034 1.90211i 0.0248208 0.0763907i
\(621\) −36.4058 26.4503i −1.46091 1.06142i
\(622\) 0 0
\(623\) −4.63525 + 14.2658i −0.185708 + 0.571549i
\(624\) −14.8328 45.6507i −0.593788 1.82749i
\(625\) −8.89919 + 6.46564i −0.355967 + 0.258626i
\(626\) 0 0
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −8.09017 + 5.87785i −0.322576 + 0.234365i
\(630\) 0 0
\(631\) 8.34346 25.6785i 0.332148 1.02225i −0.635962 0.771720i \(-0.719397\pi\)
0.968110 0.250526i \(-0.0806035\pi\)
\(632\) 0 0
\(633\) 4.85410 + 3.52671i 0.192933 + 0.140174i
\(634\) 0 0
\(635\) 0.618034 + 1.90211i 0.0245259 + 0.0754831i
\(636\) 29.1246 21.1603i 1.15487 0.839059i
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 4.63525 + 14.2658i 0.183082 + 0.563467i 0.999910 0.0134135i \(-0.00426978\pi\)
−0.816828 + 0.576881i \(0.804270\pi\)
\(642\) 0 0
\(643\) 23.4615 + 17.0458i 0.925231 + 0.672220i 0.944821 0.327588i \(-0.106236\pi\)
−0.0195896 + 0.999808i \(0.506236\pi\)
\(644\) −8.09017 5.87785i −0.318797 0.231620i
\(645\) 7.41641 22.8254i 0.292021 0.898748i
\(646\) 0 0
\(647\) 16.9894 12.3435i 0.667921 0.485273i −0.201408 0.979507i \(-0.564552\pi\)
0.869328 + 0.494235i \(0.164552\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 2.42705 1.76336i 0.0951236 0.0691114i
\(652\) −2.47214 7.60845i −0.0968163 0.297970i
\(653\) −5.25329 + 16.1680i −0.205577 + 0.632701i 0.794112 + 0.607771i \(0.207936\pi\)
−0.999689 + 0.0249299i \(0.992064\pi\)
\(654\) 0 0
\(655\) −14.5623 10.5801i −0.568996 0.413400i
\(656\) 2.47214 7.60845i 0.0965207 0.297060i
\(657\) −18.5410 57.0634i −0.723354 2.22625i
\(658\) 0 0
\(659\) 2.00000 0.0779089 0.0389545 0.999241i \(-0.487597\pi\)
0.0389545 + 0.999241i \(0.487597\pi\)
\(660\) 0 0
\(661\) 35.0000 1.36134 0.680671 0.732589i \(-0.261688\pi\)
0.680671 + 0.732589i \(0.261688\pi\)
\(662\) 0 0
\(663\) 7.41641 + 22.8254i 0.288029 + 0.886463i
\(664\) 0 0
\(665\) 4.85410 + 3.52671i 0.188234 + 0.136760i
\(666\) 0 0
\(667\) 15.4508 47.5528i 0.598259 1.84125i
\(668\) −1.23607 3.80423i −0.0478249 0.147190i
\(669\) 2.42705 1.76336i 0.0938352 0.0681753i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.23607 2.35114i 0.124741 0.0906298i −0.523665 0.851924i \(-0.675436\pi\)
0.648407 + 0.761294i \(0.275436\pi\)
\(674\) 0 0
\(675\) 11.1246 34.2380i 0.428187 1.31782i
\(676\) 4.85410 + 3.52671i 0.186696 + 0.135643i
\(677\) 30.7426 + 22.3358i 1.18154 + 0.858436i 0.992344 0.123504i \(-0.0394132\pi\)
0.189192 + 0.981940i \(0.439413\pi\)
\(678\) 0 0
\(679\) −1.54508 4.75528i −0.0592949 0.182491i
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 58.2492 42.3205i 2.22721 1.61817i
\(685\) 0.927051 + 2.85317i 0.0354208 + 0.109014i
\(686\) 0 0
\(687\) −16.9894 12.3435i −0.648184 0.470934i
\(688\) −25.8885 18.8091i −0.986991 0.717091i
\(689\) −7.41641 + 22.8254i −0.282543 + 0.869577i
\(690\) 0 0
\(691\) −12.1353 + 8.81678i −0.461647 + 0.335406i −0.794177 0.607687i \(-0.792098\pi\)
0.332530 + 0.943093i \(0.392098\pi\)
\(692\) 32.0000 1.21646
\(693\) 0 0
\(694\) 0 0
\(695\) 8.09017 5.87785i 0.306878 0.222960i
\(696\) 0 0
\(697\) −1.23607 + 3.80423i −0.0468194 + 0.144095i
\(698\) 0 0
\(699\) −14.5623 10.5801i −0.550797 0.400177i
\(700\) 2.47214 7.60845i 0.0934380 0.287572i
\(701\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(702\) 0 0
\(703\) −30.0000 −1.13147
\(704\) 0 0
\(705\) 24.0000 0.903892
\(706\) 0 0
\(707\) 3.70820 + 11.4127i 0.139461 + 0.429218i
\(708\) 5.56231 17.1190i 0.209044 0.643372i
\(709\) −31.5517 22.9236i −1.18495 0.860915i −0.192226 0.981351i \(-0.561571\pi\)
−0.992721 + 0.120436i \(0.961571\pi\)
\(710\) 0 0
\(711\) −11.1246 + 34.2380i −0.417206 + 1.28403i
\(712\) 0 0
\(713\) 4.04508 2.93893i 0.151490 0.110064i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.00000 −0.0747435
\(717\) −9.70820 + 7.05342i −0.362560 + 0.263415i
\(718\) 0 0
\(719\) −3.39919 + 10.4616i −0.126768 + 0.390153i −0.994219 0.107370i \(-0.965757\pi\)
0.867451 + 0.497523i \(0.165757\pi\)
\(720\) 19.4164 + 14.1068i 0.723607 + 0.525731i
\(721\) 9.70820 + 7.05342i 0.361552 + 0.262683i
\(722\) 0 0
\(723\) −11.1246 34.2380i −0.413729 1.27333i
\(724\) 8.09017 5.87785i 0.300669 0.218449i
\(725\) 40.0000 1.48556
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) −8.34346 25.6785i −0.309017 0.951057i
\(730\) 0 0
\(731\) 12.9443 + 9.40456i 0.478761 + 0.347840i
\(732\) −9.70820 7.05342i −0.358826 0.260702i
\(733\) 1.23607 3.80423i 0.0456552 0.140512i −0.925630 0.378429i \(-0.876464\pi\)
0.971286 + 0.237917i \(0.0764645\pi\)
\(734\) 0 0
\(735\) −2.42705 + 1.76336i −0.0895231 + 0.0650424i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −14.5623 + 10.5801i −0.535683 + 0.389197i −0.822479 0.568795i \(-0.807410\pi\)
0.286796 + 0.957992i \(0.407410\pi\)
\(740\) −3.09017 9.51057i −0.113597 0.349615i
\(741\) −22.2492 + 68.4761i −0.817346 + 2.51553i
\(742\) 0 0
\(743\) −19.4164 14.1068i −0.712319 0.517530i 0.171602 0.985166i \(-0.445106\pi\)
−0.883921 + 0.467636i \(0.845106\pi\)
\(744\) 0 0
\(745\) −6.79837 20.9232i −0.249073 0.766568i
\(746\) 0 0
\(747\) −72.0000 −2.63434
\(748\) 0 0
\(749\) 10.0000 0.365392
\(750\) 0 0
\(751\) −7.10739 21.8743i −0.259352 0.798205i −0.992941 0.118611i \(-0.962156\pi\)
0.733588 0.679594i \(-0.237844\pi\)
\(752\) 9.88854 30.4338i 0.360598 1.10981i
\(753\) −50.9681 37.0305i −1.85738 1.34947i
\(754\) 0 0
\(755\) 1.85410 5.70634i 0.0674777 0.207675i
\(756\) 5.56231 + 17.1190i 0.202299 + 0.622613i
\(757\) −30.7426 + 22.3358i −1.11736 + 0.811810i −0.983807 0.179232i \(-0.942639\pi\)
−0.133554 + 0.991042i \(0.542639\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.8328 + 28.2137i −1.40769 + 1.02275i −0.414035 + 0.910261i \(0.635881\pi\)
−0.993653 + 0.112485i \(0.964119\pi\)
\(762\) 0 0
\(763\) −1.23607 + 3.80423i −0.0447487 + 0.137722i
\(764\) 8.09017 + 5.87785i 0.292692 + 0.212653i
\(765\) −9.70820 7.05342i −0.351001 0.255017i
\(766\) 0 0
\(767\) 3.70820 + 11.4127i 0.133895 + 0.412088i
\(768\) 38.8328 28.2137i 1.40126 1.01807i
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −22.6525 + 16.4580i −0.815280 + 0.592336i
\(773\) −1.85410 5.70634i −0.0666874 0.205243i 0.912160 0.409834i \(-0.134413\pi\)
−0.978847 + 0.204591i \(0.934413\pi\)
\(774\) 0 0
\(775\) 3.23607 + 2.35114i 0.116243 + 0.0844555i
\(776\) 0 0
\(777\) 4.63525 14.2658i 0.166289 0.511784i
\(778\) 0 0
\(779\) −9.70820 + 7.05342i −0.347833 + 0.252715i
\(780\) −24.0000 −0.859338
\(781\) 0 0
\(782\) 0 0
\(783\) −72.8115 + 52.9007i −2.60207 + 1.89052i
\(784\) 1.23607 + 3.80423i 0.0441453 + 0.135865i
\(785\) −2.16312 + 6.65740i −0.0772050 + 0.237613i
\(786\) 0 0
\(787\) −17.7984 12.9313i −0.634444 0.460950i 0.223493 0.974705i \(-0.428254\pi\)
−0.857937 + 0.513755i \(0.828254\pi\)
\(788\) 11.1246 34.2380i 0.396298 1.21968i