Properties

Label 144.3.m.c.91.2
Level $144$
Weight $3$
Character 144.91
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.2
Root \(-1.87459 + 0.697079i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.c.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.87459 - 0.697079i) q^{2} +(3.02816 + 2.61347i) q^{4} +(5.24354 + 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 - 7.01005i) q^{8} +O(q^{10})\) \(q+(-1.87459 - 0.697079i) q^{2} +(3.02816 + 2.61347i) q^{4} +(5.24354 + 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 - 7.01005i) q^{8} +(-6.17431 - 13.4846i) q^{10} +(-12.2863 + 12.2863i) q^{11} +(-5.73657 + 5.73657i) q^{13} +(9.98774 + 3.71401i) q^{14} +(2.33953 + 15.8280i) q^{16} +23.3997 q^{17} +(11.7492 + 11.7492i) q^{19} +(2.17444 + 29.5821i) q^{20} +(31.5962 - 14.4672i) q^{22} -5.80841 q^{23} +29.9894i q^{25} +(14.7526 - 6.75487i) q^{26} +(-16.1339 - 13.9245i) q^{28} +(-18.3914 + 18.3914i) q^{29} +16.9053i q^{31} +(6.64774 - 31.3019i) q^{32} +(-43.8648 - 16.3114i) q^{34} +(-27.9374 - 27.9374i) q^{35} +(15.3391 + 15.3391i) q^{37} +(-13.8348 - 30.2151i) q^{38} +(16.5449 - 56.9701i) q^{40} -29.2351i q^{41} +(33.4099 - 33.4099i) q^{43} +(-69.3146 + 5.09498i) q^{44} +(10.8884 + 4.04892i) q^{46} -18.2125i q^{47} -20.6128 q^{49} +(20.9050 - 56.2178i) q^{50} +(-32.3637 + 2.37890i) q^{52} +(66.9856 + 66.9856i) q^{53} -128.847 q^{55} +(20.5380 + 37.3493i) q^{56} +(47.2965 - 21.6560i) q^{58} +(27.1523 - 27.1523i) q^{59} +(65.2399 - 65.2399i) q^{61} +(11.7843 - 31.6904i) q^{62} +(-34.2817 + 54.0441i) q^{64} -60.1599 q^{65} +(-37.6951 - 37.6951i) q^{67} +(70.8580 + 61.1544i) q^{68} +(32.8965 + 71.8456i) q^{70} -42.6559 q^{71} -106.391i q^{73} +(-18.0620 - 39.4471i) q^{74} +(4.87228 + 66.2847i) q^{76} +(65.4607 - 65.4607i) q^{77} +21.2821i q^{79} +(-70.7275 + 95.2623i) q^{80} +(-20.3792 + 54.8038i) q^{82} +(-24.1638 - 24.1638i) q^{83} +(122.697 + 122.697i) q^{85} +(-85.9192 + 39.3405i) q^{86} +(133.488 + 38.7667i) q^{88} +52.8029i q^{89} +(30.5643 - 30.5643i) q^{91} +(-17.5888 - 15.1801i) q^{92} +(-12.6955 + 34.1409i) q^{94} +123.215i q^{95} -21.0222 q^{97} +(38.6405 + 14.3688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87459 0.697079i −0.937294 0.348540i
\(3\) 0 0
\(4\) 3.02816 + 2.61347i 0.757040 + 0.653368i
\(5\) 5.24354 + 5.24354i 1.04871 + 1.04871i 0.998751 + 0.0499563i \(0.0159082\pi\)
0.0499563 + 0.998751i \(0.484092\pi\)
\(6\) 0 0
\(7\) −5.32796 −0.761138 −0.380569 0.924753i \(-0.624272\pi\)
−0.380569 + 0.924753i \(0.624272\pi\)
\(8\) −3.85476 7.01005i −0.481845 0.876256i
\(9\) 0 0
\(10\) −6.17431 13.4846i −0.617431 1.34846i
\(11\) −12.2863 + 12.2863i −1.11693 + 1.11693i −0.124743 + 0.992189i \(0.539811\pi\)
−0.992189 + 0.124743i \(0.960189\pi\)
\(12\) 0 0
\(13\) −5.73657 + 5.73657i −0.441275 + 0.441275i −0.892440 0.451165i \(-0.851008\pi\)
0.451165 + 0.892440i \(0.351008\pi\)
\(14\) 9.98774 + 3.71401i 0.713410 + 0.265287i
\(15\) 0 0
\(16\) 2.33953 + 15.8280i 0.146220 + 0.989252i
\(17\) 23.3997 1.37645 0.688226 0.725496i \(-0.258390\pi\)
0.688226 + 0.725496i \(0.258390\pi\)
\(18\) 0 0
\(19\) 11.7492 + 11.7492i 0.618380 + 0.618380i 0.945116 0.326736i \(-0.105949\pi\)
−0.326736 + 0.945116i \(0.605949\pi\)
\(20\) 2.17444 + 29.5821i 0.108722 + 1.47911i
\(21\) 0 0
\(22\) 31.5962 14.4672i 1.43619 0.657599i
\(23\) −5.80841 −0.252540 −0.126270 0.991996i \(-0.540301\pi\)
−0.126270 + 0.991996i \(0.540301\pi\)
\(24\) 0 0
\(25\) 29.9894i 1.19958i
\(26\) 14.7526 6.75487i 0.567406 0.259803i
\(27\) 0 0
\(28\) −16.1339 13.9245i −0.576212 0.497303i
\(29\) −18.3914 + 18.3914i −0.634185 + 0.634185i −0.949115 0.314930i \(-0.898019\pi\)
0.314930 + 0.949115i \(0.398019\pi\)
\(30\) 0 0
\(31\) 16.9053i 0.545332i 0.962109 + 0.272666i \(0.0879053\pi\)
−0.962109 + 0.272666i \(0.912095\pi\)
\(32\) 6.64774 31.3019i 0.207742 0.978184i
\(33\) 0 0
\(34\) −43.8648 16.3114i −1.29014 0.479748i
\(35\) −27.9374 27.9374i −0.798211 0.798211i
\(36\) 0 0
\(37\) 15.3391 + 15.3391i 0.414571 + 0.414571i 0.883327 0.468756i \(-0.155298\pi\)
−0.468756 + 0.883327i \(0.655298\pi\)
\(38\) −13.8348 30.2151i −0.364074 0.795133i
\(39\) 0 0
\(40\) 16.5449 56.9701i 0.413622 1.42425i
\(41\) 29.2351i 0.713051i −0.934286 0.356526i \(-0.883961\pi\)
0.934286 0.356526i \(-0.116039\pi\)
\(42\) 0 0
\(43\) 33.4099 33.4099i 0.776975 0.776975i −0.202340 0.979315i \(-0.564855\pi\)
0.979315 + 0.202340i \(0.0648546\pi\)
\(44\) −69.3146 + 5.09498i −1.57533 + 0.115795i
\(45\) 0 0
\(46\) 10.8884 + 4.04892i 0.236704 + 0.0880201i
\(47\) 18.2125i 0.387500i −0.981051 0.193750i \(-0.937935\pi\)
0.981051 0.193750i \(-0.0620650\pi\)
\(48\) 0 0
\(49\) −20.6128 −0.420670
\(50\) 20.9050 56.2178i 0.418100 1.12436i
\(51\) 0 0
\(52\) −32.3637 + 2.37890i −0.622378 + 0.0457480i
\(53\) 66.9856 + 66.9856i 1.26388 + 1.26388i 0.949197 + 0.314681i \(0.101898\pi\)
0.314681 + 0.949197i \(0.398102\pi\)
\(54\) 0 0
\(55\) −128.847 −2.34267
\(56\) 20.5380 + 37.3493i 0.366750 + 0.666952i
\(57\) 0 0
\(58\) 47.2965 21.6560i 0.815457 0.373380i
\(59\) 27.1523 27.1523i 0.460209 0.460209i −0.438515 0.898724i \(-0.644495\pi\)
0.898724 + 0.438515i \(0.144495\pi\)
\(60\) 0 0
\(61\) 65.2399 65.2399i 1.06951 1.06951i 0.0721103 0.997397i \(-0.477027\pi\)
0.997397 0.0721103i \(-0.0229733\pi\)
\(62\) 11.7843 31.6904i 0.190070 0.511136i
\(63\) 0 0
\(64\) −34.2817 + 54.0441i −0.535651 + 0.844440i
\(65\) −60.1599 −0.925537
\(66\) 0 0
\(67\) −37.6951 37.6951i −0.562614 0.562614i 0.367435 0.930049i \(-0.380236\pi\)
−0.930049 + 0.367435i \(0.880236\pi\)
\(68\) 70.8580 + 61.1544i 1.04203 + 0.899330i
\(69\) 0 0
\(70\) 32.8965 + 71.8456i 0.469950 + 1.02637i
\(71\) −42.6559 −0.600788 −0.300394 0.953815i \(-0.597118\pi\)
−0.300394 + 0.953815i \(0.597118\pi\)
\(72\) 0 0
\(73\) 106.391i 1.45742i −0.684825 0.728708i \(-0.740121\pi\)
0.684825 0.728708i \(-0.259879\pi\)
\(74\) −18.0620 39.4471i −0.244081 0.533069i
\(75\) 0 0
\(76\) 4.87228 + 66.2847i 0.0641089 + 0.872168i
\(77\) 65.4607 65.4607i 0.850139 0.850139i
\(78\) 0 0
\(79\) 21.2821i 0.269394i 0.990887 + 0.134697i \(0.0430061\pi\)
−0.990887 + 0.134697i \(0.956994\pi\)
\(80\) −70.7275 + 95.2623i −0.884094 + 1.19078i
\(81\) 0 0
\(82\) −20.3792 + 54.8038i −0.248527 + 0.668339i
\(83\) −24.1638 24.1638i −0.291130 0.291130i 0.546396 0.837527i \(-0.315999\pi\)
−0.837527 + 0.546396i \(0.815999\pi\)
\(84\) 0 0
\(85\) 122.697 + 122.697i 1.44350 + 1.44350i
\(86\) −85.9192 + 39.3405i −0.999061 + 0.457448i
\(87\) 0 0
\(88\) 133.488 + 38.7667i 1.51691 + 0.440531i
\(89\) 52.8029i 0.593291i 0.954988 + 0.296645i \(0.0958679\pi\)
−0.954988 + 0.296645i \(0.904132\pi\)
\(90\) 0 0
\(91\) 30.5643 30.5643i 0.335871 0.335871i
\(92\) −17.5888 15.1801i −0.191183 0.165001i
\(93\) 0 0
\(94\) −12.6955 + 34.1409i −0.135059 + 0.363201i
\(95\) 123.215i 1.29700i
\(96\) 0 0
\(97\) −21.0222 −0.216724 −0.108362 0.994112i \(-0.534560\pi\)
−0.108362 + 0.994112i \(0.534560\pi\)
\(98\) 38.6405 + 14.3688i 0.394291 + 0.146620i
\(99\) 0 0
\(100\) −78.3764 + 90.8127i −0.783764 + 0.908127i
\(101\) 3.24960 + 3.24960i 0.0321743 + 0.0321743i 0.723011 0.690837i \(-0.242758\pi\)
−0.690837 + 0.723011i \(0.742758\pi\)
\(102\) 0 0
\(103\) 105.112 1.02050 0.510252 0.860025i \(-0.329552\pi\)
0.510252 + 0.860025i \(0.329552\pi\)
\(104\) 62.3268 + 18.1006i 0.599296 + 0.174044i
\(105\) 0 0
\(106\) −78.8761 172.265i −0.744114 1.62514i
\(107\) 99.6160 99.6160i 0.930991 0.930991i −0.0667770 0.997768i \(-0.521272\pi\)
0.997768 + 0.0667770i \(0.0212716\pi\)
\(108\) 0 0
\(109\) −108.050 + 108.050i −0.991282 + 0.991282i −0.999962 0.00868078i \(-0.997237\pi\)
0.00868078 + 0.999962i \(0.497237\pi\)
\(110\) 241.535 + 89.8165i 2.19577 + 0.816513i
\(111\) 0 0
\(112\) −12.4649 84.3312i −0.111294 0.752957i
\(113\) 23.2835 0.206048 0.103024 0.994679i \(-0.467148\pi\)
0.103024 + 0.994679i \(0.467148\pi\)
\(114\) 0 0
\(115\) −30.4566 30.4566i −0.264840 0.264840i
\(116\) −103.757 + 7.62671i −0.894460 + 0.0657475i
\(117\) 0 0
\(118\) −69.8268 + 31.9721i −0.591752 + 0.270950i
\(119\) −124.673 −1.04767
\(120\) 0 0
\(121\) 180.904i 1.49508i
\(122\) −167.775 + 76.8206i −1.37521 + 0.629677i
\(123\) 0 0
\(124\) −44.1815 + 51.1919i −0.356302 + 0.412838i
\(125\) −26.1621 + 26.1621i −0.209297 + 0.209297i
\(126\) 0 0
\(127\) 118.180i 0.930550i 0.885166 + 0.465275i \(0.154045\pi\)
−0.885166 + 0.465275i \(0.845955\pi\)
\(128\) 101.937 77.4135i 0.796383 0.604793i
\(129\) 0 0
\(130\) 112.775 + 41.9362i 0.867500 + 0.322586i
\(131\) 69.2067 + 69.2067i 0.528296 + 0.528296i 0.920064 0.391768i \(-0.128137\pi\)
−0.391768 + 0.920064i \(0.628137\pi\)
\(132\) 0 0
\(133\) −62.5994 62.5994i −0.470672 0.470672i
\(134\) 44.3864 + 96.9393i 0.331241 + 0.723428i
\(135\) 0 0
\(136\) −90.2002 164.033i −0.663237 1.20613i
\(137\) 124.474i 0.908572i −0.890856 0.454286i \(-0.849894\pi\)
0.890856 0.454286i \(-0.150106\pi\)
\(138\) 0 0
\(139\) 169.014 169.014i 1.21593 1.21593i 0.246881 0.969046i \(-0.420594\pi\)
0.969046 0.246881i \(-0.0794057\pi\)
\(140\) −11.5853 157.612i −0.0827524 1.12580i
\(141\) 0 0
\(142\) 79.9623 + 29.7346i 0.563115 + 0.209398i
\(143\) 140.962i 0.985749i
\(144\) 0 0
\(145\) −192.872 −1.33015
\(146\) −74.1632 + 199.440i −0.507967 + 1.36603i
\(147\) 0 0
\(148\) 6.36098 + 86.5377i 0.0429796 + 0.584714i
\(149\) −146.988 146.988i −0.986495 0.986495i 0.0134145 0.999910i \(-0.495730\pi\)
−0.999910 + 0.0134145i \(0.995730\pi\)
\(150\) 0 0
\(151\) 75.5456 0.500302 0.250151 0.968207i \(-0.419520\pi\)
0.250151 + 0.968207i \(0.419520\pi\)
\(152\) 37.0722 127.653i 0.243896 0.839822i
\(153\) 0 0
\(154\) −168.343 + 77.0806i −1.09314 + 0.500523i
\(155\) −88.6435 + 88.6435i −0.571893 + 0.571893i
\(156\) 0 0
\(157\) −81.5356 + 81.5356i −0.519335 + 0.519335i −0.917370 0.398035i \(-0.869692\pi\)
0.398035 + 0.917370i \(0.369692\pi\)
\(158\) 14.8353 39.8952i 0.0938943 0.252501i
\(159\) 0 0
\(160\) 198.990 129.275i 1.24369 0.807968i
\(161\) 30.9470 0.192217
\(162\) 0 0
\(163\) 55.8065 + 55.8065i 0.342371 + 0.342371i 0.857258 0.514887i \(-0.172166\pi\)
−0.514887 + 0.857258i \(0.672166\pi\)
\(164\) 76.4051 88.5286i 0.465885 0.539809i
\(165\) 0 0
\(166\) 28.4531 + 62.1413i 0.171404 + 0.374345i
\(167\) 24.6339 0.147508 0.0737540 0.997276i \(-0.476502\pi\)
0.0737540 + 0.997276i \(0.476502\pi\)
\(168\) 0 0
\(169\) 103.183i 0.610553i
\(170\) −144.477 315.536i −0.849865 1.85610i
\(171\) 0 0
\(172\) 188.487 13.8548i 1.09585 0.0805509i
\(173\) −4.88551 + 4.88551i −0.0282399 + 0.0282399i −0.721086 0.692846i \(-0.756357\pi\)
0.692846 + 0.721086i \(0.256357\pi\)
\(174\) 0 0
\(175\) 159.782i 0.913042i
\(176\) −223.211 165.723i −1.26825 0.941609i
\(177\) 0 0
\(178\) 36.8078 98.9836i 0.206785 0.556088i
\(179\) 229.504 + 229.504i 1.28215 + 1.28215i 0.939444 + 0.342702i \(0.111342\pi\)
0.342702 + 0.939444i \(0.388658\pi\)
\(180\) 0 0
\(181\) 116.607 + 116.607i 0.644238 + 0.644238i 0.951595 0.307356i \(-0.0994443\pi\)
−0.307356 + 0.951595i \(0.599444\pi\)
\(182\) −78.6011 + 35.9897i −0.431874 + 0.197746i
\(183\) 0 0
\(184\) 22.3900 + 40.7173i 0.121685 + 0.221290i
\(185\) 160.863i 0.869528i
\(186\) 0 0
\(187\) −287.495 + 287.495i −1.53740 + 1.53740i
\(188\) 47.5978 55.1504i 0.253180 0.293353i
\(189\) 0 0
\(190\) 85.8905 230.977i 0.452055 1.21567i
\(191\) 94.2316i 0.493359i 0.969097 + 0.246680i \(0.0793395\pi\)
−0.969097 + 0.246680i \(0.920660\pi\)
\(192\) 0 0
\(193\) 84.2667 0.436615 0.218308 0.975880i \(-0.429946\pi\)
0.218308 + 0.975880i \(0.429946\pi\)
\(194\) 39.4079 + 14.6541i 0.203134 + 0.0755367i
\(195\) 0 0
\(196\) −62.4189 53.8710i −0.318464 0.274852i
\(197\) 56.9578 + 56.9578i 0.289126 + 0.289126i 0.836734 0.547609i \(-0.184462\pi\)
−0.547609 + 0.836734i \(0.684462\pi\)
\(198\) 0 0
\(199\) −196.179 −0.985827 −0.492913 0.870078i \(-0.664068\pi\)
−0.492913 + 0.870078i \(0.664068\pi\)
\(200\) 210.227 115.602i 1.05114 0.578009i
\(201\) 0 0
\(202\) −3.82644 8.35690i −0.0189428 0.0413708i
\(203\) 97.9886 97.9886i 0.482702 0.482702i
\(204\) 0 0
\(205\) 153.295 153.295i 0.747782 0.747782i
\(206\) −197.042 73.2714i −0.956513 0.355686i
\(207\) 0 0
\(208\) −104.220 77.3778i −0.501056 0.372009i
\(209\) −288.708 −1.38138
\(210\) 0 0
\(211\) 177.340 + 177.340i 0.840475 + 0.840475i 0.988921 0.148445i \(-0.0474269\pi\)
−0.148445 + 0.988921i \(0.547427\pi\)
\(212\) 27.7782 + 377.908i 0.131029 + 1.78259i
\(213\) 0 0
\(214\) −256.179 + 117.299i −1.19710 + 0.548125i
\(215\) 350.373 1.62964
\(216\) 0 0
\(217\) 90.0707i 0.415072i
\(218\) 277.868 127.229i 1.27462 0.583622i
\(219\) 0 0
\(220\) −390.169 336.738i −1.77350 1.53063i
\(221\) −134.234 + 134.234i −0.607394 + 0.607394i
\(222\) 0 0
\(223\) 377.924i 1.69473i 0.531012 + 0.847364i \(0.321812\pi\)
−0.531012 + 0.847364i \(0.678188\pi\)
\(224\) −35.4189 + 166.775i −0.158120 + 0.744532i
\(225\) 0 0
\(226\) −43.6469 16.2304i −0.193128 0.0718160i
\(227\) −103.909 103.909i −0.457750 0.457750i 0.440166 0.897916i \(-0.354920\pi\)
−0.897916 + 0.440166i \(0.854920\pi\)
\(228\) 0 0
\(229\) −101.055 101.055i −0.441290 0.441290i 0.451156 0.892445i \(-0.351012\pi\)
−0.892445 + 0.451156i \(0.851012\pi\)
\(230\) 35.8630 + 78.3243i 0.155926 + 0.340541i
\(231\) 0 0
\(232\) 199.819 + 58.0302i 0.861288 + 0.250130i
\(233\) 287.259i 1.23287i −0.787405 0.616436i \(-0.788576\pi\)
0.787405 0.616436i \(-0.211424\pi\)
\(234\) 0 0
\(235\) 95.4979 95.4979i 0.406374 0.406374i
\(236\) 153.184 11.2598i 0.649083 0.0477110i
\(237\) 0 0
\(238\) 233.710 + 86.9067i 0.981974 + 0.365154i
\(239\) 150.941i 0.631554i 0.948833 + 0.315777i \(0.102265\pi\)
−0.948833 + 0.315777i \(0.897735\pi\)
\(240\) 0 0
\(241\) 37.7817 0.156771 0.0783853 0.996923i \(-0.475024\pi\)
0.0783853 + 0.996923i \(0.475024\pi\)
\(242\) −126.105 + 339.121i −0.521093 + 1.40133i
\(243\) 0 0
\(244\) 368.060 27.0543i 1.50844 0.110878i
\(245\) −108.084 108.084i −0.441159 0.441159i
\(246\) 0 0
\(247\) −134.800 −0.545751
\(248\) 118.507 65.1658i 0.477850 0.262765i
\(249\) 0 0
\(250\) 67.2801 30.8061i 0.269121 0.123224i
\(251\) −100.915 + 100.915i −0.402050 + 0.402050i −0.878955 0.476905i \(-0.841759\pi\)
0.476905 + 0.878955i \(0.341759\pi\)
\(252\) 0 0
\(253\) 71.3637 71.3637i 0.282070 0.282070i
\(254\) 82.3807 221.539i 0.324333 0.872199i
\(255\) 0 0
\(256\) −245.053 + 74.0602i −0.957239 + 0.289298i
\(257\) −241.295 −0.938891 −0.469446 0.882961i \(-0.655546\pi\)
−0.469446 + 0.882961i \(0.655546\pi\)
\(258\) 0 0
\(259\) −81.7263 81.7263i −0.315546 0.315546i
\(260\) −182.174 157.226i −0.700669 0.604716i
\(261\) 0 0
\(262\) −81.4916 177.977i −0.311037 0.679300i
\(263\) 118.747 0.451509 0.225754 0.974184i \(-0.427515\pi\)
0.225754 + 0.974184i \(0.427515\pi\)
\(264\) 0 0
\(265\) 702.483i 2.65088i
\(266\) 73.7113 + 160.985i 0.277110 + 0.605206i
\(267\) 0 0
\(268\) −15.6318 212.662i −0.0583275 0.793515i
\(269\) −7.74853 + 7.74853i −0.0288050 + 0.0288050i −0.721363 0.692558i \(-0.756484\pi\)
0.692558 + 0.721363i \(0.256484\pi\)
\(270\) 0 0
\(271\) 131.899i 0.486712i −0.969937 0.243356i \(-0.921752\pi\)
0.969937 0.243356i \(-0.0782484\pi\)
\(272\) 54.7442 + 370.371i 0.201265 + 1.36166i
\(273\) 0 0
\(274\) −86.7685 + 233.338i −0.316673 + 0.851599i
\(275\) −368.457 368.457i −1.33984 1.33984i
\(276\) 0 0
\(277\) −202.352 202.352i −0.730513 0.730513i 0.240208 0.970721i \(-0.422784\pi\)
−0.970721 + 0.240208i \(0.922784\pi\)
\(278\) −434.647 + 199.015i −1.56348 + 0.715883i
\(279\) 0 0
\(280\) −88.1506 + 303.534i −0.314824 + 1.08405i
\(281\) 68.8493i 0.245015i 0.992468 + 0.122508i \(0.0390936\pi\)
−0.992468 + 0.122508i \(0.960906\pi\)
\(282\) 0 0
\(283\) 206.773 206.773i 0.730646 0.730646i −0.240102 0.970748i \(-0.577181\pi\)
0.970748 + 0.240102i \(0.0771808\pi\)
\(284\) −129.169 111.480i −0.454821 0.392535i
\(285\) 0 0
\(286\) −98.2617 + 264.246i −0.343572 + 0.923936i
\(287\) 155.764i 0.542730i
\(288\) 0 0
\(289\) 258.545 0.894620
\(290\) 361.555 + 134.447i 1.24674 + 0.463610i
\(291\) 0 0
\(292\) 278.051 322.170i 0.952229 1.10332i
\(293\) 361.237 + 361.237i 1.23289 + 1.23289i 0.962848 + 0.270043i \(0.0870379\pi\)
0.270043 + 0.962848i \(0.412962\pi\)
\(294\) 0 0
\(295\) 284.749 0.965250
\(296\) 48.3994 166.657i 0.163512 0.563029i
\(297\) 0 0
\(298\) 173.080 + 378.004i 0.580804 + 1.26847i
\(299\) 33.3204 33.3204i 0.111439 0.111439i
\(300\) 0 0
\(301\) −178.007 + 178.007i −0.591385 + 0.591385i
\(302\) −141.617 52.6613i −0.468930 0.174375i
\(303\) 0 0
\(304\) −158.479 + 213.454i −0.521314 + 0.702153i
\(305\) 684.176 2.24320
\(306\) 0 0
\(307\) −10.9073 10.9073i −0.0355286 0.0355286i 0.689119 0.724648i \(-0.257998\pi\)
−0.724648 + 0.689119i \(0.757998\pi\)
\(308\) 369.305 27.1459i 1.19904 0.0881360i
\(309\) 0 0
\(310\) 227.962 104.379i 0.735360 0.336705i
\(311\) 160.251 0.515278 0.257639 0.966241i \(-0.417055\pi\)
0.257639 + 0.966241i \(0.417055\pi\)
\(312\) 0 0
\(313\) 355.500i 1.13578i −0.823103 0.567892i \(-0.807759\pi\)
0.823103 0.567892i \(-0.192241\pi\)
\(314\) 209.682 96.0089i 0.667778 0.305761i
\(315\) 0 0
\(316\) −55.6202 + 64.4456i −0.176013 + 0.203942i
\(317\) −72.5192 + 72.5192i −0.228767 + 0.228767i −0.812178 0.583410i \(-0.801718\pi\)
0.583410 + 0.812178i \(0.301718\pi\)
\(318\) 0 0
\(319\) 451.922i 1.41668i
\(320\) −463.140 + 103.625i −1.44731 + 0.323829i
\(321\) 0 0
\(322\) −58.0129 21.5725i −0.180164 0.0669954i
\(323\) 274.928 + 274.928i 0.851170 + 0.851170i
\(324\) 0 0
\(325\) −172.036 172.036i −0.529343 0.529343i
\(326\) −65.7127 143.516i −0.201573 0.440233i
\(327\) 0 0
\(328\) −204.940 + 112.694i −0.624816 + 0.343580i
\(329\) 97.0355i 0.294941i
\(330\) 0 0
\(331\) −248.096 + 248.096i −0.749536 + 0.749536i −0.974392 0.224856i \(-0.927809\pi\)
0.224856 + 0.974392i \(0.427809\pi\)
\(332\) −10.0205 136.323i −0.0301822 0.410613i
\(333\) 0 0
\(334\) −46.1783 17.1717i −0.138258 0.0514124i
\(335\) 395.312i 1.18003i
\(336\) 0 0
\(337\) −467.271 −1.38656 −0.693280 0.720668i \(-0.743835\pi\)
−0.693280 + 0.720668i \(0.743835\pi\)
\(338\) 71.9270 193.426i 0.212802 0.572268i
\(339\) 0 0
\(340\) 50.8812 + 692.212i 0.149651 + 2.03592i
\(341\) −207.703 207.703i −0.609098 0.609098i
\(342\) 0 0
\(343\) 370.894 1.08133
\(344\) −362.993 105.418i −1.05521 0.306448i
\(345\) 0 0
\(346\) 12.5639 5.75273i 0.0363118 0.0166264i
\(347\) −292.821 + 292.821i −0.843863 + 0.843863i −0.989359 0.145496i \(-0.953522\pi\)
0.145496 + 0.989359i \(0.453522\pi\)
\(348\) 0 0
\(349\) 346.260 346.260i 0.992150 0.992150i −0.00781941 0.999969i \(-0.502489\pi\)
0.999969 + 0.00781941i \(0.00248902\pi\)
\(350\) −111.381 + 299.526i −0.318231 + 0.855789i
\(351\) 0 0
\(352\) 302.907 + 466.259i 0.860531 + 1.32460i
\(353\) −8.01816 −0.0227143 −0.0113572 0.999936i \(-0.503615\pi\)
−0.0113572 + 0.999936i \(0.503615\pi\)
\(354\) 0 0
\(355\) −223.668 223.668i −0.630051 0.630051i
\(356\) −137.999 + 159.896i −0.387637 + 0.449145i
\(357\) 0 0
\(358\) −270.243 590.208i −0.754869 1.64863i
\(359\) −590.403 −1.64458 −0.822289 0.569071i \(-0.807303\pi\)
−0.822289 + 0.569071i \(0.807303\pi\)
\(360\) 0 0
\(361\) 84.9121i 0.235213i
\(362\) −137.306 299.875i −0.379298 0.828383i
\(363\) 0 0
\(364\) 172.432 12.6747i 0.473715 0.0348205i
\(365\) 557.867 557.867i 1.52840 1.52840i
\(366\) 0 0
\(367\) 397.100i 1.08202i −0.841017 0.541008i \(-0.818043\pi\)
0.841017 0.541008i \(-0.181957\pi\)
\(368\) −13.5889 91.9358i −0.0369265 0.249825i
\(369\) 0 0
\(370\) 112.134 301.551i 0.303065 0.815003i
\(371\) −356.897 356.897i −0.961986 0.961986i
\(372\) 0 0
\(373\) −165.010 165.010i −0.442387 0.442387i 0.450427 0.892814i \(-0.351272\pi\)
−0.892814 + 0.450427i \(0.851272\pi\)
\(374\) 739.340 338.527i 1.97685 0.905154i
\(375\) 0 0
\(376\) −127.671 + 70.2048i −0.339549 + 0.186715i
\(377\) 211.007i 0.559700i
\(378\) 0 0
\(379\) −206.669 + 206.669i −0.545300 + 0.545300i −0.925078 0.379778i \(-0.876000\pi\)
0.379778 + 0.925078i \(0.376000\pi\)
\(380\) −322.019 + 373.115i −0.847418 + 0.981881i
\(381\) 0 0
\(382\) 65.6869 176.645i 0.171955 0.462423i
\(383\) 598.414i 1.56244i −0.624257 0.781219i \(-0.714598\pi\)
0.624257 0.781219i \(-0.285402\pi\)
\(384\) 0 0
\(385\) 686.492 1.78310
\(386\) −157.965 58.7405i −0.409237 0.152178i
\(387\) 0 0
\(388\) −63.6586 54.9409i −0.164069 0.141600i
\(389\) −186.696 186.696i −0.479939 0.479939i 0.425173 0.905112i \(-0.360213\pi\)
−0.905112 + 0.425173i \(0.860213\pi\)
\(390\) 0 0
\(391\) −135.915 −0.347609
\(392\) 79.4574 + 144.497i 0.202697 + 0.368614i
\(393\) 0 0
\(394\) −67.0683 146.476i −0.170224 0.371768i
\(395\) −111.594 + 111.594i −0.282515 + 0.282515i
\(396\) 0 0
\(397\) −57.3727 + 57.3727i −0.144516 + 0.144516i −0.775663 0.631147i \(-0.782584\pi\)
0.631147 + 0.775663i \(0.282584\pi\)
\(398\) 367.756 + 136.753i 0.924009 + 0.343600i
\(399\) 0 0
\(400\) −474.673 + 70.1610i −1.18668 + 0.175402i
\(401\) 466.082 1.16230 0.581149 0.813797i \(-0.302603\pi\)
0.581149 + 0.813797i \(0.302603\pi\)
\(402\) 0 0
\(403\) −96.9784 96.9784i −0.240641 0.240641i
\(404\) 1.34758 + 18.3331i 0.00333559 + 0.0453789i
\(405\) 0 0
\(406\) −251.994 + 115.382i −0.620675 + 0.284193i
\(407\) −376.921 −0.926096
\(408\) 0 0
\(409\) 597.952i 1.46198i 0.682386 + 0.730992i \(0.260942\pi\)
−0.682386 + 0.730992i \(0.739058\pi\)
\(410\) −394.225 + 180.507i −0.961524 + 0.440260i
\(411\) 0 0
\(412\) 318.296 + 274.707i 0.772563 + 0.666765i
\(413\) −144.667 + 144.667i −0.350282 + 0.350282i
\(414\) 0 0
\(415\) 253.408i 0.610621i
\(416\) 141.430 + 217.701i 0.339977 + 0.523319i
\(417\) 0 0
\(418\) 541.208 + 201.252i 1.29476 + 0.481464i
\(419\) 4.65301 + 4.65301i 0.0111050 + 0.0111050i 0.712638 0.701532i \(-0.247500\pi\)
−0.701532 + 0.712638i \(0.747500\pi\)
\(420\) 0 0
\(421\) 34.3754 + 34.3754i 0.0816519 + 0.0816519i 0.746753 0.665101i \(-0.231612\pi\)
−0.665101 + 0.746753i \(0.731612\pi\)
\(422\) −208.820 456.060i −0.494834 1.08071i
\(423\) 0 0
\(424\) 211.359 727.786i 0.498488 1.71648i
\(425\) 701.742i 1.65116i
\(426\) 0 0
\(427\) −347.596 + 347.596i −0.814042 + 0.814042i
\(428\) 561.997 41.3097i 1.31308 0.0965181i
\(429\) 0 0
\(430\) −656.804 244.237i −1.52745 0.567994i
\(431\) 423.823i 0.983347i −0.870780 0.491674i \(-0.836385\pi\)
0.870780 0.491674i \(-0.163615\pi\)
\(432\) 0 0
\(433\) 833.377 1.92466 0.962330 0.271885i \(-0.0876472\pi\)
0.962330 + 0.271885i \(0.0876472\pi\)
\(434\) −62.7864 + 168.845i −0.144669 + 0.389045i
\(435\) 0 0
\(436\) −609.577 + 44.8071i −1.39811 + 0.102769i
\(437\) −68.2443 68.2443i −0.156165 0.156165i
\(438\) 0 0
\(439\) 32.3193 0.0736203 0.0368102 0.999322i \(-0.488280\pi\)
0.0368102 + 0.999322i \(0.488280\pi\)
\(440\) 496.674 + 903.224i 1.12880 + 2.05278i
\(441\) 0 0
\(442\) 345.205 158.062i 0.781007 0.357606i
\(443\) −119.527 + 119.527i −0.269813 + 0.269813i −0.829025 0.559212i \(-0.811104\pi\)
0.559212 + 0.829025i \(0.311104\pi\)
\(444\) 0 0
\(445\) −276.874 + 276.874i −0.622189 + 0.622189i
\(446\) 263.443 708.453i 0.590680 1.58846i
\(447\) 0 0
\(448\) 182.651 287.945i 0.407704 0.642735i
\(449\) 182.359 0.406146 0.203073 0.979164i \(-0.434907\pi\)
0.203073 + 0.979164i \(0.434907\pi\)
\(450\) 0 0
\(451\) 359.190 + 359.190i 0.796430 + 0.796430i
\(452\) 70.5061 + 60.8507i 0.155987 + 0.134625i
\(453\) 0 0
\(454\) 122.354 + 267.220i 0.269502 + 0.588591i
\(455\) 320.530 0.704461
\(456\) 0 0
\(457\) 272.942i 0.597246i −0.954371 0.298623i \(-0.903473\pi\)
0.954371 0.298623i \(-0.0965274\pi\)
\(458\) 118.994 + 259.881i 0.259811 + 0.567425i
\(459\) 0 0
\(460\) −12.6301 171.825i −0.0274566 0.373533i
\(461\) −188.323 + 188.323i −0.408510 + 0.408510i −0.881219 0.472709i \(-0.843276\pi\)
0.472709 + 0.881219i \(0.343276\pi\)
\(462\) 0 0
\(463\) 116.023i 0.250590i 0.992120 + 0.125295i \(0.0399877\pi\)
−0.992120 + 0.125295i \(0.960012\pi\)
\(464\) −334.126 248.072i −0.720100 0.534638i
\(465\) 0 0
\(466\) −200.242 + 538.492i −0.429704 + 1.15556i
\(467\) 271.914 + 271.914i 0.582257 + 0.582257i 0.935523 0.353266i \(-0.114929\pi\)
−0.353266 + 0.935523i \(0.614929\pi\)
\(468\) 0 0
\(469\) 200.838 + 200.838i 0.428227 + 0.428227i
\(470\) −245.589 + 112.450i −0.522530 + 0.239255i
\(471\) 0 0
\(472\) −295.005 85.6736i −0.625011 0.181512i
\(473\) 820.966i 1.73566i
\(474\) 0 0
\(475\) −352.352 + 352.352i −0.741793 + 0.741793i
\(476\) −377.529 325.829i −0.793128 0.684514i
\(477\) 0 0
\(478\) 105.218 282.953i 0.220121 0.591952i
\(479\) 775.808i 1.61964i 0.586678 + 0.809820i \(0.300435\pi\)
−0.586678 + 0.809820i \(0.699565\pi\)
\(480\) 0 0
\(481\) −175.988 −0.365880
\(482\) −70.8252 26.3369i −0.146940 0.0546408i
\(483\) 0 0
\(484\) 472.788 547.807i 0.976835 1.13183i
\(485\) −110.231 110.231i −0.227280 0.227280i
\(486\) 0 0
\(487\) 174.891 0.359118 0.179559 0.983747i \(-0.442533\pi\)
0.179559 + 0.983747i \(0.442533\pi\)
\(488\) −708.819 205.851i −1.45250 0.421826i
\(489\) 0 0
\(490\) 127.270 + 277.956i 0.259735 + 0.567258i
\(491\) 348.578 348.578i 0.709934 0.709934i −0.256587 0.966521i \(-0.582598\pi\)
0.966521 + 0.256587i \(0.0825980\pi\)
\(492\) 0 0
\(493\) −430.352 + 430.352i −0.872926 + 0.872926i
\(494\) 252.695 + 93.9666i 0.511529 + 0.190216i
\(495\) 0 0
\(496\) −267.577 + 39.5503i −0.539470 + 0.0797386i
\(497\) 227.269 0.457282
\(498\) 0 0
\(499\) −607.544 607.544i −1.21752 1.21752i −0.968496 0.249027i \(-0.919889\pi\)
−0.249027 0.968496i \(-0.580111\pi\)
\(500\) −147.597 + 10.8491i −0.295194 + 0.0216983i
\(501\) 0 0
\(502\) 259.519 118.828i 0.516969 0.236709i
\(503\) 130.935 0.260309 0.130154 0.991494i \(-0.458453\pi\)
0.130154 + 0.991494i \(0.458453\pi\)
\(504\) 0 0
\(505\) 34.0789i 0.0674829i
\(506\) −183.524 + 84.0314i −0.362695 + 0.166070i
\(507\) 0 0
\(508\) −308.860 + 357.868i −0.607992 + 0.704464i
\(509\) 61.5539 61.5539i 0.120931 0.120931i −0.644051 0.764982i \(-0.722748\pi\)
0.764982 + 0.644051i \(0.222748\pi\)
\(510\) 0 0
\(511\) 566.849i 1.10929i
\(512\) 511.000 + 31.9891i 0.998046 + 0.0624786i
\(513\) 0 0
\(514\) 452.329 + 168.202i 0.880017 + 0.327241i
\(515\) 551.159 + 551.159i 1.07021 + 1.07021i
\(516\) 0 0
\(517\) 223.763 + 223.763i 0.432811 + 0.432811i
\(518\) 96.2335 + 210.173i 0.185779 + 0.405739i
\(519\) 0 0
\(520\) 231.902 + 421.724i 0.445965 + 0.811008i
\(521\) 32.5929i 0.0625584i 0.999511 + 0.0312792i \(0.00995810\pi\)
−0.999511 + 0.0312792i \(0.990042\pi\)
\(522\) 0 0
\(523\) −226.407 + 226.407i −0.432900 + 0.432900i −0.889614 0.456713i \(-0.849026\pi\)
0.456713 + 0.889614i \(0.349026\pi\)
\(524\) 28.6993 + 390.439i 0.0547697 + 0.745113i
\(525\) 0 0
\(526\) −222.601 82.7759i −0.423196 0.157369i
\(527\) 395.578i 0.750623i
\(528\) 0 0
\(529\) −495.262 −0.936224
\(530\) 489.686 1316.87i 0.923936 2.48465i
\(531\) 0 0
\(532\) −25.9593 353.163i −0.0487957 0.663840i
\(533\) 167.709 + 167.709i 0.314652 + 0.314652i
\(534\) 0 0
\(535\) 1044.68 1.95267
\(536\) −118.939 + 409.550i −0.221901 + 0.764087i
\(537\) 0 0
\(538\) 19.9266 9.12397i 0.0370384 0.0169590i
\(539\) 253.254 253.254i 0.469859 0.469859i
\(540\) 0 0
\(541\) 510.912 510.912i 0.944385 0.944385i −0.0541480 0.998533i \(-0.517244\pi\)
0.998533 + 0.0541480i \(0.0172443\pi\)
\(542\) −91.9440 + 247.256i −0.169638 + 0.456192i
\(543\) 0 0
\(544\) 155.555 732.454i 0.285947 1.34642i
\(545\) −1133.13 −2.07913
\(546\) 0 0
\(547\) 512.889 + 512.889i 0.937639 + 0.937639i 0.998167 0.0605271i \(-0.0192782\pi\)
−0.0605271 + 0.998167i \(0.519278\pi\)
\(548\) 325.310 376.929i 0.593632 0.687826i
\(549\) 0 0
\(550\) 433.862 + 947.550i 0.788840 + 1.72282i
\(551\) −432.168 −0.784334
\(552\) 0 0
\(553\) 113.390i 0.205046i
\(554\) 238.272 + 520.382i 0.430093 + 0.939318i
\(555\) 0 0
\(556\) 953.514 70.0883i 1.71495 0.126058i
\(557\) −566.691 + 566.691i −1.01740 + 1.01740i −0.0175529 + 0.999846i \(0.505588\pi\)
−0.999846 + 0.0175529i \(0.994412\pi\)
\(558\) 0 0
\(559\) 383.317i 0.685720i
\(560\) 376.834 507.554i 0.672917 0.906346i
\(561\) 0 0
\(562\) 47.9934 129.064i 0.0853975 0.229651i
\(563\) −548.653 548.653i −0.974517 0.974517i 0.0251665 0.999683i \(-0.491988\pi\)
−0.999683 + 0.0251665i \(0.991988\pi\)
\(564\) 0 0
\(565\) 122.088 + 122.088i 0.216085 + 0.216085i
\(566\) −531.751 + 243.477i −0.939489 + 0.430171i
\(567\) 0 0
\(568\) 164.428 + 299.020i 0.289487 + 0.526444i
\(569\) 551.224i 0.968760i −0.874858 0.484380i \(-0.839045\pi\)
0.874858 0.484380i \(-0.160955\pi\)
\(570\) 0 0
\(571\) 458.387 458.387i 0.802780 0.802780i −0.180749 0.983529i \(-0.557852\pi\)
0.983529 + 0.180749i \(0.0578522\pi\)
\(572\) 368.400 426.856i 0.644057 0.746251i
\(573\) 0 0
\(574\) 108.580 291.993i 0.189163 0.508698i
\(575\) 174.191i 0.302941i
\(576\) 0 0
\(577\) −718.488 −1.24521 −0.622607 0.782535i \(-0.713926\pi\)
−0.622607 + 0.782535i \(0.713926\pi\)
\(578\) −484.666 180.227i −0.838522 0.311811i
\(579\) 0 0
\(580\) −584.047 504.065i −1.00698 0.869078i
\(581\) 128.744 + 128.744i 0.221590 + 0.221590i
\(582\) 0 0
\(583\) −1646.00 −2.82333
\(584\) −745.809 + 410.113i −1.27707 + 0.702248i
\(585\) 0 0
\(586\) −425.360 928.982i −0.725870 1.58529i
\(587\) −3.02450 + 3.02450i −0.00515247 + 0.00515247i −0.709678 0.704526i \(-0.751160\pi\)
0.704526 + 0.709678i \(0.251160\pi\)
\(588\) 0 0
\(589\) −198.624 + 198.624i −0.337222 + 0.337222i
\(590\) −533.786 198.492i −0.904723 0.336428i
\(591\) 0 0
\(592\) −206.902 + 278.674i −0.349496 + 0.470734i
\(593\) −576.193 −0.971657 −0.485829 0.874054i \(-0.661482\pi\)
−0.485829 + 0.874054i \(0.661482\pi\)
\(594\) 0 0
\(595\) −653.726 653.726i −1.09870 1.09870i
\(596\) −60.9543 829.252i −0.102272 1.39136i
\(597\) 0 0
\(598\) −85.6890 + 39.2351i −0.143293 + 0.0656105i
\(599\) 1101.40 1.83873 0.919365 0.393406i \(-0.128703\pi\)
0.919365 + 0.393406i \(0.128703\pi\)
\(600\) 0 0
\(601\) 7.11053i 0.0118312i 0.999983 + 0.00591558i \(0.00188300\pi\)
−0.999983 + 0.00591558i \(0.998117\pi\)
\(602\) 457.775 209.605i 0.760423 0.348181i
\(603\) 0 0
\(604\) 228.764 + 197.436i 0.378749 + 0.326882i
\(605\) 948.578 948.578i 1.56790 1.56790i
\(606\) 0 0
\(607\) 528.384i 0.870485i −0.900313 0.435242i \(-0.856663\pi\)
0.900313 0.435242i \(-0.143337\pi\)
\(608\) 445.878 289.667i 0.733352 0.476425i
\(609\) 0 0
\(610\) −1282.55 476.925i −2.10254 0.781844i
\(611\) 104.477 + 104.477i 0.170994 + 0.170994i
\(612\) 0 0
\(613\) −642.364 642.364i −1.04790 1.04790i −0.998793 0.0491093i \(-0.984362\pi\)
−0.0491093 0.998793i \(-0.515638\pi\)
\(614\) 12.8434 + 28.0499i 0.0209176 + 0.0456838i
\(615\) 0 0
\(616\) −711.218 206.548i −1.15458 0.335305i
\(617\) 1068.16i 1.73122i −0.500717 0.865611i \(-0.666930\pi\)
0.500717 0.865611i \(-0.333070\pi\)
\(618\) 0 0
\(619\) 691.136 691.136i 1.11654 1.11654i 0.124290 0.992246i \(-0.460335\pi\)
0.992246 0.124290i \(-0.0396653\pi\)
\(620\) −500.094 + 36.7595i −0.806603 + 0.0592896i
\(621\) 0 0
\(622\) −300.405 111.708i −0.482967 0.179595i
\(623\) 281.332i 0.451576i
\(624\) 0 0
\(625\) 475.371 0.760594
\(626\) −247.812 + 666.417i −0.395866 + 1.06456i
\(627\) 0 0
\(628\) −459.994 + 33.8120i −0.732474 + 0.0538407i
\(629\) 358.931 + 358.931i 0.570637 + 0.570637i
\(630\) 0 0
\(631\) 486.622 0.771191 0.385596 0.922668i \(-0.373996\pi\)
0.385596 + 0.922668i \(0.373996\pi\)
\(632\) 149.189 82.0374i 0.236058 0.129806i
\(633\) 0 0
\(634\) 186.495 85.3920i 0.294156 0.134688i
\(635\) −619.681 + 619.681i −0.975875 + 0.975875i
\(636\) 0 0
\(637\) 118.247 118.247i 0.185631 0.185631i
\(638\) −315.026 + 847.168i −0.493770 + 1.32785i
\(639\) 0 0
\(640\) 940.431 + 128.590i 1.46942 + 0.200922i
\(641\) 691.017 1.07803 0.539015 0.842296i \(-0.318797\pi\)
0.539015 + 0.842296i \(0.318797\pi\)
\(642\) 0 0
\(643\) 652.605 + 652.605i 1.01494 + 1.01494i 0.999887 + 0.0150512i \(0.00479113\pi\)
0.0150512 + 0.999887i \(0.495209\pi\)
\(644\) 93.7126 + 80.8792i 0.145516 + 0.125589i
\(645\) 0 0
\(646\) −323.730 707.023i −0.501130 1.09446i
\(647\) −1156.72 −1.78782 −0.893911 0.448245i \(-0.852049\pi\)
−0.893911 + 0.448245i \(0.852049\pi\)
\(648\) 0 0
\(649\) 667.201i 1.02804i
\(650\) 202.574 + 442.420i 0.311653 + 0.680647i
\(651\) 0 0
\(652\) 23.1424 + 314.840i 0.0354945 + 0.482883i
\(653\) 209.105 209.105i 0.320222 0.320222i −0.528630 0.848852i \(-0.677294\pi\)
0.848852 + 0.528630i \(0.177294\pi\)
\(654\) 0 0
\(655\) 725.776i 1.10806i
\(656\) 462.734 68.3963i 0.705388 0.104263i
\(657\) 0 0
\(658\) 67.6414 181.902i 0.102799 0.276446i
\(659\) −533.902 533.902i −0.810170 0.810170i 0.174489 0.984659i \(-0.444173\pi\)
−0.984659 + 0.174489i \(0.944173\pi\)
\(660\) 0 0
\(661\) 283.120 + 283.120i 0.428320 + 0.428320i 0.888056 0.459736i \(-0.152056\pi\)
−0.459736 + 0.888056i \(0.652056\pi\)
\(662\) 638.021 292.136i 0.963779 0.441293i
\(663\) 0 0
\(664\) −76.2439 + 262.535i −0.114825 + 0.395384i
\(665\) 656.484i 0.987195i
\(666\) 0 0
\(667\) 106.825 106.825i 0.160157 0.160157i
\(668\) 74.5953 + 64.3799i 0.111670 + 0.0963771i
\(669\) 0 0
\(670\) −275.563 + 741.047i −0.411289 + 1.10604i
\(671\) 1603.11i 2.38913i
\(672\) 0 0
\(673\) −397.854 −0.591164 −0.295582 0.955317i \(-0.595514\pi\)
−0.295582 + 0.955317i \(0.595514\pi\)
\(674\) 875.941 + 325.725i 1.29962 + 0.483271i
\(675\) 0 0
\(676\) −269.667 + 312.456i −0.398916 + 0.462213i
\(677\) −289.959 289.959i −0.428299 0.428299i 0.459749 0.888049i \(-0.347939\pi\)
−0.888049 + 0.459749i \(0.847939\pi\)
\(678\) 0 0
\(679\) 112.005 0.164956
\(680\) 387.145 1333.08i 0.569331 1.96041i
\(681\) 0 0
\(682\) 244.572 + 534.142i 0.358609 + 0.783199i
\(683\) 150.197 150.197i 0.219908 0.219908i −0.588551 0.808460i \(-0.700302\pi\)
0.808460 + 0.588551i \(0.200302\pi\)
\(684\) 0 0
\(685\) 652.686 652.686i 0.952826 0.952826i
\(686\) −695.274 258.543i −1.01352 0.376884i
\(687\) 0 0
\(688\) 606.977 + 450.650i 0.882234 + 0.655015i
\(689\) −768.535 −1.11544
\(690\) 0 0
\(691\) 791.212 + 791.212i 1.14502 + 1.14502i 0.987518 + 0.157506i \(0.0503453\pi\)
0.157506 + 0.987518i \(0.449655\pi\)
\(692\) −27.5622 + 2.02597i −0.0398298 + 0.00292770i
\(693\) 0 0
\(694\) 753.037 344.799i 1.08507 0.496828i
\(695\) 1772.46 2.55030
\(696\) 0 0
\(697\) 684.092i 0.981481i
\(698\) −890.466 + 407.725i −1.27574 + 0.584133i
\(699\) 0 0
\(700\) 417.587 483.847i 0.596553 0.691210i
\(701\) −900.201 + 900.201i −1.28417 + 1.28417i −0.345893 + 0.938274i \(0.612424\pi\)
−0.938274 + 0.345893i \(0.887576\pi\)
\(702\) 0 0
\(703\) 360.445i 0.512724i
\(704\) −242.807 1085.19i −0.344896 1.54147i
\(705\) 0 0
\(706\) 15.0308 + 5.58929i 0.0212900 + 0.00791685i
\(707\) −17.3138 17.3138i −0.0244891 0.0244891i
\(708\) 0 0
\(709\) 128.490 + 128.490i 0.181227 + 0.181227i 0.791891 0.610663i \(-0.209097\pi\)
−0.610663 + 0.791891i \(0.709097\pi\)
\(710\) 263.371 + 575.200i 0.370945 + 0.810140i
\(711\) 0 0
\(712\) 370.151 203.542i 0.519875 0.285874i
\(713\) 98.1928i 0.137718i
\(714\) 0 0
\(715\) 739.140 739.140i 1.03376 1.03376i
\(716\) 95.1730 + 1294.78i 0.132923 + 1.80835i
\(717\) 0 0
\(718\) 1106.76 + 411.558i 1.54145 + 0.573200i
\(719\) 1246.14i 1.73315i −0.499045 0.866576i \(-0.666316\pi\)
0.499045 0.866576i \(-0.333684\pi\)
\(720\) 0 0
\(721\) −560.033 −0.776745
\(722\) −59.1904 + 159.175i −0.0819812 + 0.220464i
\(723\) 0 0
\(724\) 48.3558 + 657.855i 0.0667897 + 0.908639i
\(725\) −551.546 551.546i −0.760753 0.760753i
\(726\) 0 0
\(727\) −1130.07 −1.55443 −0.777216 0.629234i \(-0.783369\pi\)
−0.777216 + 0.629234i \(0.783369\pi\)
\(728\) −332.075 96.4392i −0.456147 0.132471i
\(729\) 0 0
\(730\) −1434.65 + 656.893i −1.96527 + 0.899854i
\(731\) 781.782 781.782i 1.06947 1.06947i
\(732\) 0 0
\(733\) −708.087 + 708.087i −0.966012 + 0.966012i −0.999441 0.0334292i \(-0.989357\pi\)
0.0334292 + 0.999441i \(0.489357\pi\)
\(734\) −276.810 + 744.399i −0.377126 + 1.01417i
\(735\) 0 0
\(736\) −38.6128 + 181.814i −0.0524631 + 0.247030i
\(737\) 926.264 1.25680
\(738\) 0 0
\(739\) −32.7516 32.7516i −0.0443188 0.0443188i 0.684600 0.728919i \(-0.259977\pi\)
−0.728919 + 0.684600i \(0.759977\pi\)
\(740\) −420.410 + 487.118i −0.568122 + 0.658268i
\(741\) 0 0
\(742\) 420.249 + 917.819i 0.566373 + 1.23695i
\(743\) −708.128 −0.953066 −0.476533 0.879157i \(-0.658107\pi\)
−0.476533 + 0.879157i \(0.658107\pi\)
\(744\) 0 0
\(745\) 1541.47i 2.06909i
\(746\) 194.301 + 424.352i 0.260457 + 0.568836i
\(747\) 0 0
\(748\) −1621.94 + 119.221i −2.16837 + 0.159386i
\(749\) −530.751 + 530.751i −0.708612 + 0.708612i
\(750\) 0 0
\(751\) 1242.37i 1.65429i −0.561990 0.827144i \(-0.689964\pi\)
0.561990 0.827144i \(-0.310036\pi\)
\(752\) 288.268 42.6086i 0.383335 0.0566604i
\(753\) 0 0
\(754\) −147.089 + 395.551i −0.195078 + 0.524604i
\(755\) 396.127 + 396.127i 0.524671 + 0.524671i
\(756\) 0 0
\(757\) −311.304 311.304i −0.411233 0.411233i 0.470935 0.882168i \(-0.343917\pi\)
−0.882168 + 0.470935i \(0.843917\pi\)
\(758\) 531.483 243.354i 0.701165 0.321048i
\(759\) 0 0
\(760\) 863.743 474.964i 1.13650 0.624952i
\(761\) 179.137i 0.235397i 0.993049 + 0.117699i \(0.0375517\pi\)
−0.993049 + 0.117699i \(0.962448\pi\)
\(762\) 0 0
\(763\) 575.685 575.685i 0.754502 0.754502i
\(764\) −246.272 + 285.348i −0.322345 + 0.373493i
\(765\) 0 0
\(766\) −417.142 + 1121.78i −0.544572 + 1.46446i
\(767\) 311.523i 0.406158i
\(768\) 0 0
\(769\) −967.409 −1.25801 −0.629005 0.777402i \(-0.716537\pi\)
−0.629005 + 0.777402i \(0.716537\pi\)
\(770\) −1286.89 478.539i −1.67128 0.621479i
\(771\) 0 0
\(772\) 255.173 + 220.229i 0.330535 + 0.285270i
\(773\) 96.7342 + 96.7342i 0.125141 + 0.125141i 0.766904 0.641762i \(-0.221796\pi\)
−0.641762 + 0.766904i \(0.721796\pi\)
\(774\) 0 0
\(775\) −506.979 −0.654166
\(776\) 81.0355 + 147.367i 0.104427 + 0.189905i
\(777\) 0 0
\(778\) 219.836 + 480.120i 0.282566 + 0.617121i
\(779\) 343.489 343.489i 0.440936 0.440936i
\(780\) 0 0
\(781\) 524.082 524.082i 0.671039 0.671039i
\(782\) 254.785 + 94.7435i 0.325812 + 0.121155i
\(783\) 0 0
\(784\) −48.2242 326.260i −0.0615105 0.416148i
\(785\) −855.070 −1.08926
\(786\) 0 0
\(787\) −381.038 381.038i −0.484166 0.484166i 0.422293 0.906459i \(-0.361225\pi\)