Properties

Label 690.3.k.b.277.1
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.1
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.24826 - 3.31048i) q^{10} +5.33526 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.44105 - 9.44105i) q^{13} -17.1508i q^{14} +(-4.05449 + 7.65252i) q^{15} -4.00000 q^{16} +(15.8456 + 15.8456i) q^{17} +(-3.00000 + 3.00000i) q^{18} -27.9154i q^{19} +(2.93778 + 9.55874i) q^{20} -21.0053 q^{21} +(-5.33526 - 5.33526i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(20.6847 - 14.0407i) q^{25} -18.8821 q^{26} +(3.67423 + 3.67423i) q^{27} +(-17.1508 + 17.1508i) q^{28} +43.2329i q^{29} +(11.7070 - 3.59803i) q^{30} -45.6018 q^{31} +(4.00000 + 4.00000i) q^{32} +(-6.53434 + 6.53434i) q^{33} -31.6913i q^{34} +(53.5812 + 28.3886i) q^{35} +6.00000 q^{36} +(-22.6647 - 22.6647i) q^{37} +(-27.9154 + 27.9154i) q^{38} +23.1258i q^{39} +(6.62095 - 12.4965i) q^{40} +27.4529 q^{41} +(21.0053 + 21.0053i) q^{42} +(-2.61316 + 2.61316i) q^{43} +10.6705i q^{44} +(-4.40667 - 14.3381i) q^{45} -6.78233 q^{46} +(-60.8180 - 60.8180i) q^{47} +(4.89898 - 4.89898i) q^{48} +98.0746i q^{49} +(-34.7255 - 6.64397i) q^{50} -38.8137 q^{51} +(18.8821 + 18.8821i) q^{52} +(9.28016 - 9.28016i) q^{53} -7.34847i q^{54} +(25.4992 - 7.83692i) q^{55} +34.3016 q^{56} +(34.1893 + 34.1893i) q^{57} +(43.2329 - 43.2329i) q^{58} +62.7885i q^{59} +(-15.3050 - 8.10898i) q^{60} +100.410 q^{61} +(45.6018 + 45.6018i) q^{62} +(25.7262 - 25.7262i) q^{63} -8.00000i q^{64} +(31.2544 - 58.9901i) q^{65} +13.0687 q^{66} +(-23.2724 - 23.2724i) q^{67} +(-31.6913 + 31.6913i) q^{68} +8.30662i q^{69} +(-25.1926 - 81.9699i) q^{70} +73.4573 q^{71} +(-6.00000 - 6.00000i) q^{72} +(74.1463 - 74.1463i) q^{73} +45.3294i q^{74} +(-8.13717 + 42.5298i) q^{75} +55.8309 q^{76} +(45.7519 + 45.7519i) q^{77} +(23.1258 - 23.1258i) q^{78} -42.9315i q^{79} +(-19.1175 + 5.87557i) q^{80} -9.00000 q^{81} +(-27.4529 - 27.4529i) q^{82} +(30.3118 - 30.3118i) q^{83} -42.0106i q^{84} +(99.0077 + 52.4566i) q^{85} +5.22632 q^{86} +(-52.9493 - 52.9493i) q^{87} +(10.6705 - 10.6705i) q^{88} +115.921i q^{89} +(-9.93143 + 18.7448i) q^{90} +161.921 q^{91} +(6.78233 + 6.78233i) q^{92} +(55.8506 - 55.8506i) q^{93} +121.636i q^{94} +(-41.0047 - 133.418i) q^{95} -9.79796 q^{96} +(131.149 + 131.149i) q^{97} +(98.0746 - 98.0746i) q^{98} -16.0058i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 4.77937 1.46889i 0.955874 0.293778i
\(6\) 2.44949 0.408248
\(7\) 8.57539 + 8.57539i 1.22506 + 1.22506i 0.965812 + 0.259243i \(0.0834732\pi\)
0.259243 + 0.965812i \(0.416527\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.24826 3.31048i −0.624826 0.331048i
\(11\) 5.33526 0.485024 0.242512 0.970148i \(-0.422029\pi\)
0.242512 + 0.970148i \(0.422029\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 9.44105 9.44105i 0.726235 0.726235i −0.243633 0.969868i \(-0.578339\pi\)
0.969868 + 0.243633i \(0.0783391\pi\)
\(14\) 17.1508i 1.22506i
\(15\) −4.05449 + 7.65252i −0.270299 + 0.510168i
\(16\) −4.00000 −0.250000
\(17\) 15.8456 + 15.8456i 0.932097 + 0.932097i 0.997837 0.0657401i \(-0.0209408\pi\)
−0.0657401 + 0.997837i \(0.520941\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 27.9154i 1.46923i −0.678482 0.734617i \(-0.737362\pi\)
0.678482 0.734617i \(-0.262638\pi\)
\(20\) 2.93778 + 9.55874i 0.146889 + 0.477937i
\(21\) −21.0053 −1.00025
\(22\) −5.33526 5.33526i −0.242512 0.242512i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 20.6847 14.0407i 0.827389 0.561630i
\(26\) −18.8821 −0.726235
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −17.1508 + 17.1508i −0.612528 + 0.612528i
\(29\) 43.2329i 1.49079i 0.666623 + 0.745395i \(0.267739\pi\)
−0.666623 + 0.745395i \(0.732261\pi\)
\(30\) 11.7070 3.59803i 0.390234 0.119934i
\(31\) −45.6018 −1.47103 −0.735513 0.677511i \(-0.763059\pi\)
−0.735513 + 0.677511i \(0.763059\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −6.53434 + 6.53434i −0.198010 + 0.198010i
\(34\) 31.6913i 0.932097i
\(35\) 53.5812 + 28.3886i 1.53089 + 0.811103i
\(36\) 6.00000 0.166667
\(37\) −22.6647 22.6647i −0.612559 0.612559i 0.331053 0.943612i \(-0.392596\pi\)
−0.943612 + 0.331053i \(0.892596\pi\)
\(38\) −27.9154 + 27.9154i −0.734617 + 0.734617i
\(39\) 23.1258i 0.592968i
\(40\) 6.62095 12.4965i 0.165524 0.312413i
\(41\) 27.4529 0.669584 0.334792 0.942292i \(-0.391334\pi\)
0.334792 + 0.942292i \(0.391334\pi\)
\(42\) 21.0053 + 21.0053i 0.500127 + 0.500127i
\(43\) −2.61316 + 2.61316i −0.0607711 + 0.0607711i −0.736839 0.676068i \(-0.763683\pi\)
0.676068 + 0.736839i \(0.263683\pi\)
\(44\) 10.6705i 0.242512i
\(45\) −4.40667 14.3381i −0.0979261 0.318625i
\(46\) −6.78233 −0.147442
\(47\) −60.8180 60.8180i −1.29400 1.29400i −0.932291 0.361709i \(-0.882194\pi\)
−0.361709 0.932291i \(-0.617806\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 98.0746i 2.00152i
\(50\) −34.7255 6.64397i −0.694509 0.132879i
\(51\) −38.8137 −0.761054
\(52\) 18.8821 + 18.8821i 0.363117 + 0.363117i
\(53\) 9.28016 9.28016i 0.175097 0.175097i −0.614117 0.789215i \(-0.710488\pi\)
0.789215 + 0.614117i \(0.210488\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 25.4992 7.83692i 0.463621 0.142489i
\(56\) 34.3016 0.612528
\(57\) 34.1893 + 34.1893i 0.599812 + 0.599812i
\(58\) 43.2329 43.2329i 0.745395 0.745395i
\(59\) 62.7885i 1.06421i 0.846678 + 0.532106i \(0.178599\pi\)
−0.846678 + 0.532106i \(0.821401\pi\)
\(60\) −15.3050 8.10898i −0.255084 0.135150i
\(61\) 100.410 1.64607 0.823036 0.567990i \(-0.192279\pi\)
0.823036 + 0.567990i \(0.192279\pi\)
\(62\) 45.6018 + 45.6018i 0.735513 + 0.735513i
\(63\) 25.7262 25.7262i 0.408352 0.408352i
\(64\) 8.00000i 0.125000i
\(65\) 31.2544 58.9901i 0.480837 0.907541i
\(66\) 13.0687 0.198010
\(67\) −23.2724 23.2724i −0.347349 0.347349i 0.511772 0.859121i \(-0.328989\pi\)
−0.859121 + 0.511772i \(0.828989\pi\)
\(68\) −31.6913 + 31.6913i −0.466048 + 0.466048i
\(69\) 8.30662i 0.120386i
\(70\) −25.1926 81.9699i −0.359895 1.17100i
\(71\) 73.4573 1.03461 0.517305 0.855801i \(-0.326935\pi\)
0.517305 + 0.855801i \(0.326935\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 74.1463 74.1463i 1.01570 1.01570i 0.0158275 0.999875i \(-0.494962\pi\)
0.999875 0.0158275i \(-0.00503825\pi\)
\(74\) 45.3294i 0.612559i
\(75\) −8.13717 + 42.5298i −0.108496 + 0.567064i
\(76\) 55.8309 0.734617
\(77\) 45.7519 + 45.7519i 0.594181 + 0.594181i
\(78\) 23.1258 23.1258i 0.296484 0.296484i
\(79\) 42.9315i 0.543437i −0.962377 0.271718i \(-0.912408\pi\)
0.962377 0.271718i \(-0.0875920\pi\)
\(80\) −19.1175 + 5.87557i −0.238968 + 0.0734446i
\(81\) −9.00000 −0.111111
\(82\) −27.4529 27.4529i −0.334792 0.334792i
\(83\) 30.3118 30.3118i 0.365202 0.365202i −0.500522 0.865724i \(-0.666858\pi\)
0.865724 + 0.500522i \(0.166858\pi\)
\(84\) 42.0106i 0.500127i
\(85\) 99.0077 + 52.4566i 1.16480 + 0.617137i
\(86\) 5.22632 0.0607711
\(87\) −52.9493 52.9493i −0.608613 0.608613i
\(88\) 10.6705 10.6705i 0.121256 0.121256i
\(89\) 115.921i 1.30249i 0.758868 + 0.651244i \(0.225753\pi\)
−0.758868 + 0.651244i \(0.774247\pi\)
\(90\) −9.93143 + 18.7448i −0.110349 + 0.208275i
\(91\) 161.921 1.77936
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 55.8506 55.8506i 0.600544 0.600544i
\(94\) 121.636i 1.29400i
\(95\) −41.0047 133.418i −0.431629 1.40440i
\(96\) −9.79796 −0.102062
\(97\) 131.149 + 131.149i 1.35205 + 1.35205i 0.883367 + 0.468682i \(0.155271\pi\)
0.468682 + 0.883367i \(0.344729\pi\)
\(98\) 98.0746 98.0746i 1.00076 1.00076i
\(99\) 16.0058i 0.161675i
\(100\) 28.0815 + 41.3694i 0.280815 + 0.413694i
\(101\) 23.7421 0.235071 0.117535 0.993069i \(-0.462501\pi\)
0.117535 + 0.993069i \(0.462501\pi\)
\(102\) 38.8137 + 38.8137i 0.380527 + 0.380527i
\(103\) −114.195 + 114.195i −1.10869 + 1.10869i −0.115368 + 0.993323i \(0.536805\pi\)
−0.993323 + 0.115368i \(0.963195\pi\)
\(104\) 37.7642i 0.363117i
\(105\) −100.392 + 30.8545i −0.956116 + 0.293853i
\(106\) −18.5603 −0.175097
\(107\) 24.2252 + 24.2252i 0.226404 + 0.226404i 0.811189 0.584785i \(-0.198821\pi\)
−0.584785 + 0.811189i \(0.698821\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 33.7671i 0.309790i −0.987931 0.154895i \(-0.950496\pi\)
0.987931 0.154895i \(-0.0495039\pi\)
\(110\) −33.3361 17.6623i −0.303055 0.160566i
\(111\) 55.5169 0.500153
\(112\) −34.3016 34.3016i −0.306264 0.306264i
\(113\) −109.556 + 109.556i −0.969518 + 0.969518i −0.999549 0.0300307i \(-0.990439\pi\)
0.0300307 + 0.999549i \(0.490439\pi\)
\(114\) 68.3786i 0.599812i
\(115\) 11.2264 21.1889i 0.0976206 0.184251i
\(116\) −86.4659 −0.745395
\(117\) −28.3232 28.3232i −0.242078 0.242078i
\(118\) 62.7885 62.7885i 0.532106 0.532106i
\(119\) 271.765i 2.28374i
\(120\) 7.19607 + 23.4140i 0.0599672 + 0.195117i
\(121\) −92.5350 −0.764752
\(122\) −100.410 100.410i −0.823036 0.823036i
\(123\) −33.6228 + 33.6228i −0.273356 + 0.273356i
\(124\) 91.2036i 0.735513i
\(125\) 78.2355 97.4895i 0.625884 0.779916i
\(126\) −51.4523 −0.408352
\(127\) −55.5449 55.5449i −0.437362 0.437362i 0.453762 0.891123i \(-0.350082\pi\)
−0.891123 + 0.453762i \(0.850082\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 6.40091i 0.0496194i
\(130\) −90.2445 + 27.7358i −0.694189 + 0.213352i
\(131\) 20.3671 0.155474 0.0777370 0.996974i \(-0.475231\pi\)
0.0777370 + 0.996974i \(0.475231\pi\)
\(132\) −13.0687 13.0687i −0.0990051 0.0990051i
\(133\) 239.386 239.386i 1.79989 1.79989i
\(134\) 46.5448i 0.347349i
\(135\) 22.9576 + 12.1635i 0.170056 + 0.0900998i
\(136\) 63.3826 0.466048
\(137\) −109.723 109.723i −0.800894 0.800894i 0.182341 0.983235i \(-0.441633\pi\)
−0.983235 + 0.182341i \(0.941633\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 239.354i 1.72197i −0.508627 0.860987i \(-0.669847\pi\)
0.508627 0.860987i \(-0.330153\pi\)
\(140\) −56.7772 + 107.162i −0.405552 + 0.765446i
\(141\) 148.973 1.05655
\(142\) −73.4573 73.4573i −0.517305 0.517305i
\(143\) 50.3705 50.3705i 0.352241 0.352241i
\(144\) 12.0000i 0.0833333i
\(145\) 63.5045 + 206.626i 0.437962 + 1.42501i
\(146\) −148.293 −1.01570
\(147\) −120.116 120.116i −0.817118 0.817118i
\(148\) 45.3294 45.3294i 0.306280 0.306280i
\(149\) 187.064i 1.25546i 0.778430 + 0.627731i \(0.216016\pi\)
−0.778430 + 0.627731i \(0.783984\pi\)
\(150\) 50.6670 34.3927i 0.337780 0.229284i
\(151\) −156.167 −1.03422 −0.517109 0.855919i \(-0.672992\pi\)
−0.517109 + 0.855919i \(0.672992\pi\)
\(152\) −55.8309 55.8309i −0.367308 0.367308i
\(153\) 47.5369 47.5369i 0.310699 0.310699i
\(154\) 91.5039i 0.594181i
\(155\) −217.948 + 66.9841i −1.40612 + 0.432156i
\(156\) −46.2515 −0.296484
\(157\) −60.0337 60.0337i −0.382380 0.382380i 0.489579 0.871959i \(-0.337151\pi\)
−0.871959 + 0.489579i \(0.837151\pi\)
\(158\) −42.9315 + 42.9315i −0.271718 + 0.271718i
\(159\) 22.7317i 0.142966i
\(160\) 24.9930 + 13.2419i 0.156206 + 0.0827619i
\(161\) 58.1611 0.361249
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 59.5443 59.5443i 0.365303 0.365303i −0.500458 0.865761i \(-0.666835\pi\)
0.865761 + 0.500458i \(0.166835\pi\)
\(164\) 54.9059i 0.334792i
\(165\) −21.6318 + 40.8282i −0.131102 + 0.247444i
\(166\) −60.6236 −0.365202
\(167\) 153.528 + 153.528i 0.919327 + 0.919327i 0.996980 0.0776536i \(-0.0247428\pi\)
−0.0776536 + 0.996980i \(0.524743\pi\)
\(168\) −42.0106 + 42.0106i −0.250063 + 0.250063i
\(169\) 9.26698i 0.0548342i
\(170\) −46.5511 151.464i −0.273830 0.890967i
\(171\) −83.7463 −0.489744
\(172\) −5.22632 5.22632i −0.0303856 0.0303856i
\(173\) 89.1455 89.1455i 0.515292 0.515292i −0.400851 0.916143i \(-0.631286\pi\)
0.916143 + 0.400851i \(0.131286\pi\)
\(174\) 105.899i 0.608613i
\(175\) 297.784 + 56.9746i 1.70162 + 0.325569i
\(176\) −21.3410 −0.121256
\(177\) −76.8998 76.8998i −0.434462 0.434462i
\(178\) 115.921 115.921i 0.651244 0.651244i
\(179\) 297.612i 1.66264i 0.555797 + 0.831318i \(0.312413\pi\)
−0.555797 + 0.831318i \(0.687587\pi\)
\(180\) 28.6762 8.81335i 0.159312 0.0489630i
\(181\) −147.512 −0.814981 −0.407490 0.913209i \(-0.633596\pi\)
−0.407490 + 0.913209i \(0.633596\pi\)
\(182\) −161.921 161.921i −0.889678 0.889678i
\(183\) −122.977 + 122.977i −0.672006 + 0.672006i
\(184\) 13.5647i 0.0737210i
\(185\) −141.615 75.0310i −0.765486 0.405573i
\(186\) −111.701 −0.600544
\(187\) 84.5407 + 84.5407i 0.452089 + 0.452089i
\(188\) 121.636 121.636i 0.647000 0.647000i
\(189\) 63.0160i 0.333418i
\(190\) −92.4134 + 174.423i −0.486386 + 0.918015i
\(191\) −131.722 −0.689643 −0.344821 0.938668i \(-0.612061\pi\)
−0.344821 + 0.938668i \(0.612061\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 207.885 207.885i 1.07713 1.07713i 0.0803601 0.996766i \(-0.474393\pi\)
0.996766 0.0803601i \(-0.0256070\pi\)
\(194\) 262.298i 1.35205i
\(195\) 33.9692 + 110.527i 0.174201 + 0.566803i
\(196\) −196.149 −1.00076
\(197\) −241.609 241.609i −1.22644 1.22644i −0.965300 0.261142i \(-0.915901\pi\)
−0.261142 0.965300i \(-0.584099\pi\)
\(198\) −16.0058 + 16.0058i −0.0808373 + 0.0808373i
\(199\) 217.535i 1.09314i 0.837413 + 0.546570i \(0.184067\pi\)
−0.837413 + 0.546570i \(0.815933\pi\)
\(200\) 13.2879 69.4509i 0.0664397 0.347255i
\(201\) 57.0055 0.283610
\(202\) −23.7421 23.7421i −0.117535 0.117535i
\(203\) −370.739 + 370.739i −1.82630 + 1.82630i
\(204\) 77.6275i 0.380527i
\(205\) 131.208 40.3254i 0.640037 0.196709i
\(206\) 228.390 1.10869
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −37.7642 + 37.7642i −0.181559 + 0.181559i
\(209\) 148.936i 0.712613i
\(210\) 131.247 + 69.5376i 0.624984 + 0.331132i
\(211\) 190.204 0.901440 0.450720 0.892665i \(-0.351167\pi\)
0.450720 + 0.892665i \(0.351167\pi\)
\(212\) 18.5603 + 18.5603i 0.0875487 + 0.0875487i
\(213\) −89.9664 + 89.9664i −0.422378 + 0.422378i
\(214\) 48.4505i 0.226404i
\(215\) −8.65080 + 16.3277i −0.0402363 + 0.0759428i
\(216\) 14.6969 0.0680414
\(217\) −391.053 391.053i −1.80209 1.80209i
\(218\) −33.7671 + 33.7671i −0.154895 + 0.154895i
\(219\) 181.621i 0.829317i
\(220\) 15.6738 + 50.9984i 0.0712447 + 0.231811i
\(221\) 299.199 1.35384
\(222\) −55.5169 55.5169i −0.250076 0.250076i
\(223\) −148.820 + 148.820i −0.667356 + 0.667356i −0.957103 0.289747i \(-0.906429\pi\)
0.289747 + 0.957103i \(0.406429\pi\)
\(224\) 68.6031i 0.306264i
\(225\) −42.1222 62.0542i −0.187210 0.275796i
\(226\) 219.111 0.969518
\(227\) 92.8831 + 92.8831i 0.409177 + 0.409177i 0.881451 0.472275i \(-0.156567\pi\)
−0.472275 + 0.881451i \(0.656567\pi\)
\(228\) −68.3786 + 68.3786i −0.299906 + 0.299906i
\(229\) 292.034i 1.27526i 0.770344 + 0.637629i \(0.220085\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(230\) −32.4153 + 9.96251i −0.140936 + 0.0433152i
\(231\) −112.069 −0.485147
\(232\) 86.4659 + 86.4659i 0.372698 + 0.372698i
\(233\) −41.9538 + 41.9538i −0.180059 + 0.180059i −0.791382 0.611323i \(-0.790638\pi\)
0.611323 + 0.791382i \(0.290638\pi\)
\(234\) 56.6463i 0.242078i
\(235\) −380.007 201.337i −1.61705 0.856751i
\(236\) −125.577 −0.532106
\(237\) 52.5802 + 52.5802i 0.221857 + 0.221857i
\(238\) 271.765 271.765i 1.14187 1.14187i
\(239\) 165.558i 0.692713i 0.938103 + 0.346357i \(0.112581\pi\)
−0.938103 + 0.346357i \(0.887419\pi\)
\(240\) 16.2180 30.6101i 0.0675748 0.127542i
\(241\) −376.816 −1.56355 −0.781777 0.623559i \(-0.785686\pi\)
−0.781777 + 0.623559i \(0.785686\pi\)
\(242\) 92.5350 + 92.5350i 0.382376 + 0.382376i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 200.821i 0.823036i
\(245\) 144.061 + 468.734i 0.588004 + 1.91320i
\(246\) 67.2457 0.273356
\(247\) −263.551 263.551i −1.06701 1.06701i
\(248\) −91.2036 + 91.2036i −0.367757 + 0.367757i
\(249\) 74.2484i 0.298186i
\(250\) −175.725 + 19.2539i −0.702900 + 0.0770157i
\(251\) −149.704 −0.596431 −0.298216 0.954499i \(-0.596391\pi\)
−0.298216 + 0.954499i \(0.596391\pi\)
\(252\) 51.4523 + 51.4523i 0.204176 + 0.204176i
\(253\) 18.0928 18.0928i 0.0715129 0.0715129i
\(254\) 111.090i 0.437362i
\(255\) −185.505 + 57.0132i −0.727471 + 0.223581i
\(256\) 16.0000 0.0625000
\(257\) −268.353 268.353i −1.04418 1.04418i −0.998978 0.0451978i \(-0.985608\pi\)
−0.0451978 0.998978i \(-0.514392\pi\)
\(258\) −6.40091 + 6.40091i −0.0248097 + 0.0248097i
\(259\) 388.717i 1.50084i
\(260\) 117.980 + 62.5088i 0.453770 + 0.240418i
\(261\) 129.699 0.496930
\(262\) −20.3671 20.3671i −0.0777370 0.0777370i
\(263\) −80.7650 + 80.7650i −0.307091 + 0.307091i −0.843780 0.536689i \(-0.819675\pi\)
0.536689 + 0.843780i \(0.319675\pi\)
\(264\) 26.1373i 0.0990051i
\(265\) 30.7218 57.9849i 0.115931 0.218811i
\(266\) −478.771 −1.79989
\(267\) −141.974 141.974i −0.531739 0.531739i
\(268\) 46.5448 46.5448i 0.173675 0.173675i
\(269\) 51.5840i 0.191762i −0.995393 0.0958811i \(-0.969433\pi\)
0.995393 0.0958811i \(-0.0305669\pi\)
\(270\) −10.7941 35.1210i −0.0399782 0.130078i
\(271\) 35.9992 0.132839 0.0664193 0.997792i \(-0.478843\pi\)
0.0664193 + 0.997792i \(0.478843\pi\)
\(272\) −63.3826 63.3826i −0.233024 0.233024i
\(273\) −198.312 + 198.312i −0.726419 + 0.726419i
\(274\) 219.445i 0.800894i
\(275\) 110.358 74.9111i 0.401303 0.272404i
\(276\) −16.6132 −0.0601929
\(277\) 262.283 + 262.283i 0.946870 + 0.946870i 0.998658 0.0517881i \(-0.0164920\pi\)
−0.0517881 + 0.998658i \(0.516492\pi\)
\(278\) −239.354 + 239.354i −0.860987 + 0.860987i
\(279\) 136.805i 0.490342i
\(280\) 163.940 50.3852i 0.585499 0.179947i
\(281\) −79.4049 −0.282580 −0.141290 0.989968i \(-0.545125\pi\)
−0.141290 + 0.989968i \(0.545125\pi\)
\(282\) −148.973 148.973i −0.528273 0.528273i
\(283\) −77.4320 + 77.4320i −0.273611 + 0.273611i −0.830552 0.556941i \(-0.811975\pi\)
0.556941 + 0.830552i \(0.311975\pi\)
\(284\) 146.915i 0.517305i
\(285\) 213.624 + 113.183i 0.749556 + 0.397133i
\(286\) −100.741 −0.352241
\(287\) 235.420 + 235.420i 0.820277 + 0.820277i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 213.169i 0.737609i
\(290\) 143.122 270.131i 0.493523 0.931485i
\(291\) −321.248 −1.10394
\(292\) 148.293 + 148.293i 0.507851 + 0.507851i
\(293\) 175.421 175.421i 0.598707 0.598707i −0.341262 0.939968i \(-0.610854\pi\)
0.939968 + 0.341262i \(0.110854\pi\)
\(294\) 240.233i 0.817118i
\(295\) 92.2294 + 300.089i 0.312642 + 1.01725i
\(296\) −90.6588 −0.306280
\(297\) 19.6030 + 19.6030i 0.0660034 + 0.0660034i
\(298\) 187.064 187.064i 0.627731 0.627731i
\(299\) 64.0323i 0.214155i
\(300\) −85.0597 16.2743i −0.283532 0.0542478i
\(301\) −44.8177 −0.148896
\(302\) 156.167 + 156.167i 0.517109 + 0.517109i
\(303\) −29.0781 + 29.0781i −0.0959672 + 0.0959672i
\(304\) 111.662i 0.367308i
\(305\) 479.898 147.492i 1.57344 0.483580i
\(306\) −95.0739 −0.310699
\(307\) −230.973 230.973i −0.752354 0.752354i 0.222564 0.974918i \(-0.428557\pi\)
−0.974918 + 0.222564i \(0.928557\pi\)
\(308\) −91.5039 + 91.5039i −0.297091 + 0.297091i
\(309\) 279.720i 0.905242i
\(310\) 284.932 + 150.964i 0.919135 + 0.486980i
\(311\) 202.569 0.651347 0.325674 0.945482i \(-0.394409\pi\)
0.325674 + 0.945482i \(0.394409\pi\)
\(312\) 46.2515 + 46.2515i 0.148242 + 0.148242i
\(313\) 288.074 288.074i 0.920366 0.920366i −0.0766893 0.997055i \(-0.524435\pi\)
0.997055 + 0.0766893i \(0.0244349\pi\)
\(314\) 120.067i 0.382380i
\(315\) 85.1659 160.744i 0.270368 0.510298i
\(316\) 85.8630 0.271718
\(317\) −17.6959 17.6959i −0.0558232 0.0558232i 0.678644 0.734467i \(-0.262568\pi\)
−0.734467 + 0.678644i \(0.762568\pi\)
\(318\) 22.7317 22.7317i 0.0714832 0.0714832i
\(319\) 230.659i 0.723069i
\(320\) −11.7511 38.2349i −0.0367223 0.119484i
\(321\) −59.3394 −0.184858
\(322\) −58.1611 58.1611i −0.180625 0.180625i
\(323\) 442.338 442.338i 1.36947 1.36947i
\(324\) 18.0000i 0.0555556i
\(325\) 62.7261 327.845i 0.193003 1.00875i
\(326\) −119.089 −0.365303
\(327\) 41.3561 + 41.3561i 0.126471 + 0.126471i
\(328\) 54.9059 54.9059i 0.167396 0.167396i
\(329\) 1043.08i 3.17044i
\(330\) 62.4600 19.1965i 0.189273 0.0581711i
\(331\) −318.113 −0.961067 −0.480533 0.876976i \(-0.659557\pi\)
−0.480533 + 0.876976i \(0.659557\pi\)
\(332\) 60.6236 + 60.6236i 0.182601 + 0.182601i
\(333\) −67.9941 + 67.9941i −0.204186 + 0.204186i
\(334\) 307.055i 0.919327i
\(335\) −145.412 77.0428i −0.434066 0.229978i
\(336\) 84.0213 0.250063
\(337\) 183.892 + 183.892i 0.545675 + 0.545675i 0.925187 0.379512i \(-0.123908\pi\)
−0.379512 + 0.925187i \(0.623908\pi\)
\(338\) −9.26698 + 9.26698i −0.0274171 + 0.0274171i
\(339\) 268.355i 0.791608i
\(340\) −104.913 + 198.015i −0.308568 + 0.582398i
\(341\) −243.298 −0.713483
\(342\) 83.7463 + 83.7463i 0.244872 + 0.244872i
\(343\) −420.833 + 420.833i −1.22692 + 1.22692i
\(344\) 10.4526i 0.0303856i
\(345\) 12.2015 + 39.7004i 0.0353667 + 0.115074i
\(346\) −178.291 −0.515292
\(347\) −27.3732 27.3732i −0.0788854 0.0788854i 0.666563 0.745449i \(-0.267765\pi\)
−0.745449 + 0.666563i \(0.767765\pi\)
\(348\) 105.899 105.899i 0.304306 0.304306i
\(349\) 285.470i 0.817965i −0.912542 0.408982i \(-0.865884\pi\)
0.912542 0.408982i \(-0.134116\pi\)
\(350\) −240.810 354.759i −0.688028 1.01360i
\(351\) 69.3773 0.197656
\(352\) 21.3410 + 21.3410i 0.0606280 + 0.0606280i
\(353\) 65.7593 65.7593i 0.186287 0.186287i −0.607802 0.794089i \(-0.707948\pi\)
0.794089 + 0.607802i \(0.207948\pi\)
\(354\) 153.800i 0.434462i
\(355\) 351.079 107.901i 0.988956 0.303946i
\(356\) −231.843 −0.651244
\(357\) −332.843 332.843i −0.932333 0.932333i
\(358\) 297.612 297.612i 0.831318 0.831318i
\(359\) 685.981i 1.91081i −0.295298 0.955405i \(-0.595419\pi\)
0.295298 0.955405i \(-0.404581\pi\)
\(360\) −37.4896 19.8629i −0.104138 0.0551746i
\(361\) −418.272 −1.15865
\(362\) 147.512 + 147.512i 0.407490 + 0.407490i
\(363\) 113.332 113.332i 0.312209 0.312209i
\(364\) 323.843i 0.889678i
\(365\) 245.459 463.285i 0.672492 1.26927i
\(366\) 245.954 0.672006
\(367\) −286.652 286.652i −0.781069 0.781069i 0.198943 0.980011i \(-0.436249\pi\)
−0.980011 + 0.198943i \(0.936249\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 82.3588i 0.223195i
\(370\) 66.5840 + 216.646i 0.179957 + 0.585529i
\(371\) 159.162 0.429008
\(372\) 111.701 + 111.701i 0.300272 + 0.300272i
\(373\) −307.918 + 307.918i −0.825516 + 0.825516i −0.986893 0.161376i \(-0.948407\pi\)
0.161376 + 0.986893i \(0.448407\pi\)
\(374\) 169.081i 0.452089i
\(375\) 23.5812 + 215.218i 0.0628831 + 0.573916i
\(376\) −243.272 −0.647000
\(377\) 408.164 + 408.164i 1.08266 + 1.08266i
\(378\) 63.0160 63.0160i 0.166709 0.166709i
\(379\) 86.8843i 0.229246i 0.993409 + 0.114623i \(0.0365660\pi\)
−0.993409 + 0.114623i \(0.963434\pi\)
\(380\) 266.836 82.0095i 0.702201 0.215814i
\(381\) 136.057 0.357104
\(382\) 131.722 + 131.722i 0.344821 + 0.344821i
\(383\) 159.134 159.134i 0.415492 0.415492i −0.468154 0.883647i \(-0.655081\pi\)
0.883647 + 0.468154i \(0.155081\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 285.870 + 151.461i 0.742519 + 0.393405i
\(386\) −415.771 −1.07713
\(387\) 7.83948 + 7.83948i 0.0202570 + 0.0202570i
\(388\) −262.298 + 262.298i −0.676025 + 0.676025i
\(389\) 70.6535i 0.181628i −0.995868 0.0908142i \(-0.971053\pi\)
0.995868 0.0908142i \(-0.0289469\pi\)
\(390\) 76.5573 144.496i 0.196301 0.370502i
\(391\) 107.470 0.274860
\(392\) 196.149 + 196.149i 0.500380 + 0.500380i
\(393\) −24.9445 + 24.9445i −0.0634720 + 0.0634720i
\(394\) 483.218i 1.22644i
\(395\) −63.0617 205.186i −0.159650 0.519457i
\(396\) 32.0116 0.0808373
\(397\) −7.66108 7.66108i −0.0192974 0.0192974i 0.697392 0.716690i \(-0.254344\pi\)
−0.716690 + 0.697392i \(0.754344\pi\)
\(398\) 217.535 217.535i 0.546570 0.546570i
\(399\) 586.373i 1.46961i
\(400\) −82.7389 + 56.1630i −0.206847 + 0.140407i
\(401\) −436.861 −1.08943 −0.544715 0.838621i \(-0.683362\pi\)
−0.544715 + 0.838621i \(0.683362\pi\)
\(402\) −57.0055 57.0055i −0.141805 0.141805i
\(403\) −430.529 + 430.529i −1.06831 + 1.06831i
\(404\) 47.4843i 0.117535i
\(405\) −43.0143 + 13.2200i −0.106208 + 0.0326420i
\(406\) 741.478 1.82630
\(407\) −120.922 120.922i −0.297106 0.297106i
\(408\) −77.6275 + 77.6275i −0.190263 + 0.190263i
\(409\) 397.297i 0.971385i −0.874130 0.485693i \(-0.838567\pi\)
0.874130 0.485693i \(-0.161433\pi\)
\(410\) −171.533 90.8823i −0.418373 0.221664i
\(411\) 268.764 0.653928
\(412\) −228.390 228.390i −0.554346 0.554346i
\(413\) −538.435 + 538.435i −1.30372 + 1.30372i
\(414\) 20.3470i 0.0491473i
\(415\) 100.346 189.396i 0.241799 0.456376i
\(416\) 75.5284 0.181559
\(417\) 293.148 + 293.148i 0.702993 + 0.702993i
\(418\) −148.936 + 148.936i −0.356307 + 0.356307i
\(419\) 188.910i 0.450859i 0.974260 + 0.225429i \(0.0723785\pi\)
−0.974260 + 0.225429i \(0.927622\pi\)
\(420\) −61.7091 200.784i −0.146926 0.478058i
\(421\) 92.6040 0.219962 0.109981 0.993934i \(-0.464921\pi\)
0.109981 + 0.993934i \(0.464921\pi\)
\(422\) −190.204 190.204i −0.450720 0.450720i
\(423\) −182.454 + 182.454i −0.431333 + 0.431333i
\(424\) 37.1207i 0.0875487i
\(425\) 550.247 + 105.278i 1.29470 + 0.247713i
\(426\) 179.933 0.422378
\(427\) 861.058 + 861.058i 2.01653 + 2.01653i
\(428\) −48.4505 + 48.4505i −0.113202 + 0.113202i
\(429\) 123.382i 0.287604i
\(430\) 24.9785 7.67689i 0.0580895 0.0178532i
\(431\) 111.346 0.258344 0.129172 0.991622i \(-0.458768\pi\)
0.129172 + 0.991622i \(0.458768\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 157.449 157.449i 0.363623 0.363623i −0.501522 0.865145i \(-0.667226\pi\)
0.865145 + 0.501522i \(0.167226\pi\)
\(434\) 782.106i 1.80209i
\(435\) −330.841 175.287i −0.760554 0.402960i
\(436\) 67.5342 0.154895
\(437\) −94.6658 94.6658i −0.216627 0.216627i
\(438\) 181.621 181.621i 0.414659 0.414659i
\(439\) 108.313i 0.246726i 0.992362 + 0.123363i \(0.0393680\pi\)
−0.992362 + 0.123363i \(0.960632\pi\)
\(440\) 35.3245 66.6722i 0.0802830 0.151528i
\(441\) 294.224 0.667174
\(442\) −299.199 299.199i −0.676921 0.676921i
\(443\) 179.232 179.232i 0.404586 0.404586i −0.475260 0.879846i \(-0.657646\pi\)
0.879846 + 0.475260i \(0.157646\pi\)
\(444\) 111.034i 0.250076i
\(445\) 170.276 + 554.031i 0.382643 + 1.24501i
\(446\) 297.641 0.667356
\(447\) −229.106 229.106i −0.512540 0.512540i
\(448\) 68.6031 68.6031i 0.153132 0.153132i
\(449\) 672.236i 1.49719i 0.663030 + 0.748593i \(0.269270\pi\)
−0.663030 + 0.748593i \(0.730730\pi\)
\(450\) −19.9319 + 104.176i −0.0442932 + 0.231503i
\(451\) 146.469 0.324764
\(452\) −219.111 219.111i −0.484759 0.484759i
\(453\) 191.265 191.265i 0.422218 0.422218i
\(454\) 185.766i 0.409177i
\(455\) 773.882 237.845i 1.70084 0.522736i
\(456\) 136.757 0.299906
\(457\) −353.101 353.101i −0.772649 0.772649i 0.205920 0.978569i \(-0.433981\pi\)
−0.978569 + 0.205920i \(0.933981\pi\)
\(458\) 292.034 292.034i 0.637629 0.637629i
\(459\) 116.441i 0.253685i
\(460\) 42.3778 + 22.4527i 0.0921256 + 0.0488103i
\(461\) 61.4442 0.133285 0.0666423 0.997777i \(-0.478771\pi\)
0.0666423 + 0.997777i \(0.478771\pi\)
\(462\) 112.069 + 112.069i 0.242573 + 0.242573i
\(463\) 593.423 593.423i 1.28169 1.28169i 0.341987 0.939705i \(-0.388900\pi\)
0.939705 0.341987i \(-0.111100\pi\)
\(464\) 172.932i 0.372698i
\(465\) 184.892 348.969i 0.397617 0.750471i
\(466\) 83.9075 0.180059
\(467\) −62.1024 62.1024i −0.132982 0.132982i 0.637483 0.770464i \(-0.279976\pi\)
−0.770464 + 0.637483i \(0.779976\pi\)
\(468\) 56.6463 56.6463i 0.121039 0.121039i
\(469\) 399.140i 0.851044i
\(470\) 178.670 + 581.343i 0.380149 + 1.23690i
\(471\) 147.052 0.312212
\(472\) 125.577 + 125.577i 0.266053 + 0.266053i
\(473\) −13.9419 + 13.9419i −0.0294754 + 0.0294754i
\(474\) 105.160i 0.221857i
\(475\) −391.953 577.423i −0.825165 1.21563i
\(476\) −543.530 −1.14187
\(477\) −27.8405 27.8405i −0.0583658 0.0583658i
\(478\) 165.558 165.558i 0.346357 0.346357i
\(479\) 188.974i 0.394518i −0.980351 0.197259i \(-0.936796\pi\)
0.980351 0.197259i \(-0.0632040\pi\)
\(480\) −46.8281 + 14.3921i −0.0975584 + 0.0299836i
\(481\) −427.957 −0.889724
\(482\) 376.816 + 376.816i 0.781777 + 0.781777i
\(483\) −71.2325 + 71.2325i −0.147479 + 0.147479i
\(484\) 185.070i 0.382376i
\(485\) 819.451 + 434.165i 1.68959 + 0.895185i
\(486\) −22.0454 −0.0453609
\(487\) −406.039 406.039i −0.833756 0.833756i 0.154272 0.988028i \(-0.450697\pi\)
−0.988028 + 0.154272i \(0.950697\pi\)
\(488\) 200.821 200.821i 0.411518 0.411518i
\(489\) 145.853i 0.298268i
\(490\) 324.674 612.795i 0.662599 1.25060i
\(491\) −388.154 −0.790538 −0.395269 0.918565i \(-0.629349\pi\)
−0.395269 + 0.918565i \(0.629349\pi\)
\(492\) −67.2457 67.2457i −0.136678 0.136678i
\(493\) −685.054 + 685.054i −1.38956 + 1.38956i
\(494\) 527.102i 1.06701i
\(495\) −23.5108 76.4975i −0.0474965 0.154540i
\(496\) 182.407 0.367757
\(497\) 629.925 + 629.925i 1.26745 + 1.26745i
\(498\) 74.2484 74.2484i 0.149093 0.149093i
\(499\) 536.161i 1.07447i −0.843433 0.537235i \(-0.819469\pi\)
0.843433 0.537235i \(-0.180531\pi\)
\(500\) 194.979 + 156.471i 0.389958 + 0.312942i
\(501\) −376.064 −0.750627
\(502\) 149.704 + 149.704i 0.298216 + 0.298216i
\(503\) 135.474 135.474i 0.269333 0.269333i −0.559499 0.828831i \(-0.689006\pi\)
0.828831 + 0.559499i \(0.189006\pi\)
\(504\) 102.905i 0.204176i
\(505\) 113.472 34.8746i 0.224698 0.0690587i
\(506\) −36.1855 −0.0715129
\(507\) 11.3497 + 11.3497i 0.0223860 + 0.0223860i
\(508\) 111.090 111.090i 0.218681 0.218681i
\(509\) 544.024i 1.06881i −0.845229 0.534405i \(-0.820536\pi\)
0.845229 0.534405i \(-0.179464\pi\)
\(510\) 242.518 + 128.492i 0.475526 + 0.251945i
\(511\) 1271.67 2.48858
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 102.568 102.568i 0.199937 0.199937i
\(514\) 536.706i 1.04418i
\(515\) −378.040 + 713.521i −0.734059 + 1.38548i
\(516\) 12.8018 0.0248097
\(517\) −324.480 324.480i −0.627621 0.627621i
\(518\) −388.717 + 388.717i −0.750419 + 0.750419i
\(519\) 218.361i 0.420734i
\(520\) −55.4715 180.489i −0.106676 0.347094i
\(521\) −537.878 −1.03240 −0.516198 0.856469i \(-0.672653\pi\)
−0.516198 + 0.856469i \(0.672653\pi\)
\(522\) −129.699 129.699i −0.248465 0.248465i
\(523\) −417.463 + 417.463i −0.798209 + 0.798209i −0.982813 0.184604i \(-0.940900\pi\)
0.184604 + 0.982813i \(0.440900\pi\)
\(524\) 40.7342i 0.0777370i
\(525\) −434.489 + 294.930i −0.827598 + 0.561772i
\(526\) 161.530 0.307091
\(527\) −722.590 722.590i −1.37114 1.37114i
\(528\) 26.1373 26.1373i 0.0495025 0.0495025i
\(529\) 23.0000i 0.0434783i
\(530\) −88.7066 + 27.2631i −0.167371 + 0.0514398i
\(531\) 188.365 0.354737
\(532\) 478.771 + 478.771i 0.899946 + 0.899946i
\(533\) 259.185 259.185i 0.486275 0.486275i
\(534\) 283.949i 0.531739i
\(535\) 151.365 + 80.1970i 0.282926 + 0.149901i
\(536\) −93.0896 −0.173675
\(537\) −364.499 364.499i −0.678768 0.678768i
\(538\) −51.5840 + 51.5840i −0.0958811 + 0.0958811i
\(539\) 523.253i 0.970786i
\(540\) −24.3269 + 45.9151i −0.0450499 + 0.0850280i
\(541\) 659.210 1.21850 0.609252 0.792977i \(-0.291470\pi\)
0.609252 + 0.792977i \(0.291470\pi\)
\(542\) −35.9992 35.9992i −0.0664193 0.0664193i
\(543\) 180.664 180.664i 0.332715 0.332715i
\(544\) 126.765i 0.233024i
\(545\) −49.6002 161.385i −0.0910095 0.296120i
\(546\) 396.625 0.726419
\(547\) −181.796 181.796i −0.332350 0.332350i 0.521128 0.853479i \(-0.325511\pi\)
−0.853479 + 0.521128i \(0.825511\pi\)
\(548\) 219.445 219.445i 0.400447 0.400447i
\(549\) 301.231i 0.548690i
\(550\) −185.269 35.4473i −0.336854 0.0644497i
\(551\) 1206.87 2.19032
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 368.154 368.154i 0.665740 0.665740i
\(554\) 524.566i 0.946870i
\(555\) 265.336 81.5484i 0.478083 0.146934i
\(556\) 478.709 0.860987
\(557\) 114.798 + 114.798i 0.206100 + 0.206100i 0.802607 0.596508i \(-0.203445\pi\)
−0.596508 + 0.802607i \(0.703445\pi\)
\(558\) 136.805 136.805i 0.245171 0.245171i
\(559\) 49.3419i 0.0882682i
\(560\) −214.325 113.554i −0.382723 0.202776i
\(561\) −207.081 −0.369129
\(562\) 79.4049 + 79.4049i 0.141290 + 0.141290i
\(563\) −271.045 + 271.045i −0.481430 + 0.481430i −0.905588 0.424158i \(-0.860570\pi\)
0.424158 + 0.905588i \(0.360570\pi\)
\(564\) 297.946i 0.528273i
\(565\) −362.681 + 684.532i −0.641914 + 1.21156i
\(566\) 154.864 0.273611
\(567\) −77.1785 77.1785i −0.136117 0.136117i
\(568\) 146.915 146.915i 0.258652 0.258652i
\(569\) 215.559i 0.378837i 0.981896 + 0.189419i \(0.0606604\pi\)
−0.981896 + 0.189419i \(0.939340\pi\)
\(570\) −100.441 326.806i −0.176212 0.573344i
\(571\) −622.372 −1.08997 −0.544984 0.838446i \(-0.683464\pi\)
−0.544984 + 0.838446i \(0.683464\pi\)
\(572\) 100.741 + 100.741i 0.176121 + 0.176121i
\(573\) 161.326 161.326i 0.281546 0.281546i
\(574\) 470.839i 0.820277i
\(575\) 22.5308 117.760i 0.0391840 0.204800i
\(576\) −24.0000 −0.0416667
\(577\) −454.606 454.606i −0.787879 0.787879i 0.193268 0.981146i \(-0.438091\pi\)
−0.981146 + 0.193268i \(0.938091\pi\)
\(578\) 213.169 213.169i 0.368804 0.368804i
\(579\) 509.213i 0.879470i
\(580\) −413.252 + 127.009i −0.712504 + 0.218981i
\(581\) 519.871 0.894786
\(582\) 321.248 + 321.248i 0.551972 + 0.551972i
\(583\) 49.5121 49.5121i 0.0849264 0.0849264i
\(584\) 296.585i 0.507851i
\(585\) −176.970 93.7632i −0.302514 0.160279i
\(586\) −350.842 −0.598707
\(587\) 246.656 + 246.656i 0.420197 + 0.420197i 0.885272 0.465074i \(-0.153972\pi\)
−0.465074 + 0.885272i \(0.653972\pi\)
\(588\) 240.233 240.233i 0.408559 0.408559i
\(589\) 1272.99i 2.16128i
\(590\) 207.860 392.319i 0.352305 0.664947i
\(591\) 591.819 1.00139
\(592\) 90.6588 + 90.6588i 0.153140 + 0.153140i
\(593\) −188.339 + 188.339i −0.317603 + 0.317603i −0.847846 0.530243i \(-0.822101\pi\)
0.530243 + 0.847846i \(0.322101\pi\)
\(594\) 39.2060i 0.0660034i
\(595\) 399.193 + 1298.87i 0.670913 + 2.18297i
\(596\) −374.128 −0.627731
\(597\) −266.425 266.425i −0.446273 0.446273i
\(598\) −64.0323 + 64.0323i −0.107077 + 0.107077i
\(599\) 353.101i 0.589485i 0.955577 + 0.294742i \(0.0952338\pi\)
−0.955577 + 0.294742i \(0.904766\pi\)
\(600\) 68.7853 + 101.334i 0.114642 + 0.168890i
\(601\) −285.740 −0.475441 −0.237721 0.971334i \(-0.576400\pi\)
−0.237721 + 0.971334i \(0.576400\pi\)
\(602\) 44.8177 + 44.8177i 0.0744480 + 0.0744480i
\(603\) −69.8172 + 69.8172i −0.115783 + 0.115783i
\(604\) 312.334i 0.517109i
\(605\) −442.259 + 135.924i −0.731006 + 0.224667i
\(606\) 58.1561 0.0959672
\(607\) −416.723 416.723i −0.686529 0.686529i 0.274934 0.961463i \(-0.411344\pi\)
−0.961463 + 0.274934i \(0.911344\pi\)
\(608\) 111.662 111.662i 0.183654 0.183654i
\(609\) 908.122i 1.49117i
\(610\) −627.390 332.406i −1.02851 0.544928i
\(611\) −1148.37 −1.87950
\(612\) 95.0739 + 95.0739i 0.155349 + 0.155349i
\(613\) 362.012 362.012i 0.590559 0.590559i −0.347224 0.937782i \(-0.612876\pi\)
0.937782 + 0.347224i \(0.112876\pi\)
\(614\) 461.945i 0.752354i
\(615\) −111.308 + 210.084i −0.180988 + 0.341600i
\(616\) 183.008 0.297091
\(617\) 163.519 + 163.519i 0.265023 + 0.265023i 0.827091 0.562068i \(-0.189994\pi\)
−0.562068 + 0.827091i \(0.689994\pi\)
\(618\) −279.720 + 279.720i −0.452621 + 0.452621i
\(619\) 46.8175i 0.0756341i −0.999285 0.0378171i \(-0.987960\pi\)
0.999285 0.0378171i \(-0.0120404\pi\)
\(620\) −133.968 435.896i −0.216078 0.703058i
\(621\) 24.9199 0.0401286
\(622\) −202.569 202.569i −0.325674 0.325674i
\(623\) −994.072 + 994.072i −1.59562 + 1.59562i
\(624\) 92.5031i 0.148242i
\(625\) 230.715 580.858i 0.369144 0.929372i
\(626\) −576.149 −0.920366
\(627\) 182.409 + 182.409i 0.290923 + 0.290923i
\(628\) 120.067 120.067i 0.191190 0.191190i
\(629\) 718.273i 1.14193i
\(630\) −245.910 + 75.5779i −0.390333 + 0.119965i
\(631\) −984.554 −1.56031 −0.780154 0.625588i \(-0.784859\pi\)
−0.780154 + 0.625588i \(0.784859\pi\)
\(632\) −85.8630 85.8630i −0.135859 0.135859i
\(633\) −232.951 + 232.951i −0.368011 + 0.368011i
\(634\) 35.3919i 0.0558232i
\(635\) −347.059 183.880i −0.546550 0.289575i
\(636\) −45.4633 −0.0714832
\(637\) 925.927 + 925.927i 1.45357 + 1.45357i
\(638\) 230.659 230.659i 0.361534 0.361534i
\(639\) 220.372i 0.344870i
\(640\) −26.4838 + 49.9861i −0.0413810 + 0.0781032i
\(641\) −83.9542 −0.130974 −0.0654869 0.997853i \(-0.520860\pi\)
−0.0654869 + 0.997853i \(0.520860\pi\)
\(642\) 59.3394 + 59.3394i 0.0924290 + 0.0924290i
\(643\) 87.3495 87.3495i 0.135847 0.135847i −0.635914 0.771760i \(-0.719377\pi\)
0.771760 + 0.635914i \(0.219377\pi\)
\(644\) 116.322i 0.180625i
\(645\) −9.40223 30.5923i −0.0145771 0.0474299i
\(646\) −884.676 −1.36947
\(647\) −447.854 447.854i −0.692202 0.692202i 0.270514 0.962716i \(-0.412806\pi\)
−0.962716 + 0.270514i \(0.912806\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 334.993i 0.516168i
\(650\) −390.571 + 265.119i −0.600879 + 0.407875i
\(651\) 957.881 1.47140
\(652\) 119.089 + 119.089i 0.182651 + 0.182651i
\(653\) 525.679 525.679i 0.805022 0.805022i −0.178854 0.983876i \(-0.557239\pi\)
0.983876 + 0.178854i \(0.0572388\pi\)
\(654\) 82.7121i 0.126471i
\(655\) 97.3418 29.9170i 0.148613 0.0456749i
\(656\) −109.812 −0.167396
\(657\) −222.439 222.439i −0.338567 0.338567i
\(658\) −1043.08 + 1043.08i −1.58522 + 1.58522i
\(659\) 279.050i 0.423445i 0.977330 + 0.211723i \(0.0679073\pi\)
−0.977330 + 0.211723i \(0.932093\pi\)
\(660\) −81.6564 43.2635i −0.123722 0.0655508i
\(661\) 210.642 0.318672 0.159336 0.987224i \(-0.449065\pi\)
0.159336 + 0.987224i \(0.449065\pi\)
\(662\) 318.113 + 318.113i 0.480533 + 0.480533i
\(663\) −366.443 + 366.443i −0.552704 + 0.552704i
\(664\) 121.247i 0.182601i
\(665\) 792.481 1495.74i 1.19170 2.24924i
\(666\) 135.988 0.204186
\(667\) 146.610 + 146.610i 0.219805 + 0.219805i
\(668\) −307.055 + 307.055i −0.459663 + 0.459663i
\(669\) 364.534i 0.544894i
\(670\) 68.3693 + 222.455i 0.102044 + 0.332022i
\(671\) 535.715 0.798384
\(672\) −84.0213 84.0213i −0.125032 0.125032i
\(673\) 440.741 440.741i 0.654890 0.654890i −0.299276 0.954166i \(-0.596745\pi\)
0.954166 + 0.299276i \(0.0967453\pi\)
\(674\) 367.785i 0.545675i
\(675\) 127.589 + 24.4115i 0.189021 + 0.0361652i
\(676\) 18.5340 0.0274171
\(677\) 707.522 + 707.522i 1.04508 + 1.04508i 0.998935 + 0.0461495i \(0.0146951\pi\)
0.0461495 + 0.998935i \(0.485305\pi\)
\(678\) −268.355 + 268.355i −0.395804 + 0.395804i
\(679\) 2249.30i 3.31267i
\(680\) 302.929 93.1021i 0.445483 0.136915i
\(681\) −227.516 −0.334091
\(682\) 243.298 + 243.298i 0.356741 + 0.356741i
\(683\) −346.952 + 346.952i −0.507982 + 0.507982i −0.913906 0.405925i \(-0.866949\pi\)
0.405925 + 0.913906i \(0.366949\pi\)
\(684\) 167.493i 0.244872i
\(685\) −685.575 363.234i −1.00084 0.530268i
\(686\) 841.667 1.22692
\(687\) −357.667 357.667i −0.520622 0.520622i
\(688\) 10.4526 10.4526i 0.0151928 0.0151928i
\(689\) 175.229i 0.254324i
\(690\) 27.4989 51.9019i 0.0398535 0.0752202i
\(691\) −438.734 −0.634926 −0.317463 0.948271i \(-0.602831\pi\)
−0.317463 + 0.948271i \(0.602831\pi\)
\(692\) 178.291 + 178.291i 0.257646 + 0.257646i
\(693\) 137.256 137.256i 0.198060 0.198060i
\(694\) 54.7465i 0.0788854i
\(695\) −351.586 1143.96i −0.505879 1.64599i
\(696\) −211.797 −0.304306
\(697\) 435.009 + 435.009i 0.624117 + 0.624117i
\(698\) −285.470 + 285.470i −0.408982 + 0.408982i
\(699\) 102.765i 0.147018i
\(700\) −113.949 + 595.569i −0.162785 + 0.850812i
\(701\) −405.008 −0.577758 −0.288879 0.957366i \(-0.593283\pi\)
−0.288879 + 0.957366i \(0.593283\pi\)
\(702\) −69.3773 69.3773i −0.0988280 0.0988280i
\(703\) −632.695 + 632.695i −0.899993 + 0.899993i
\(704\) 42.6821i 0.0606280i
\(705\) 711.997 218.825i 1.00992 0.310390i
\(706\) −131.519 −0.186287
\(707\) 203.598 + 203.598i 0.287975 + 0.287975i
\(708\) 153.800 153.800i 0.217231 0.217231i
\(709\) 216.541i 0.305417i −0.988271 0.152708i \(-0.951200\pi\)
0.988271 0.152708i \(-0.0487996\pi\)
\(710\) −458.980 243.179i −0.646451 0.342505i
\(711\) −128.795 −0.181146
\(712\) 231.843 + 231.843i 0.325622 + 0.325622i
\(713\) −154.643 + 154.643i −0.216891 + 0.216891i
\(714\) 665.686i 0.932333i
\(715\) 166.750 314.728i 0.233217 0.440179i
\(716\) −595.224 −0.831318
\(717\) −202.767 202.767i −0.282799 0.282799i
\(718\) −685.981 + 685.981i −0.955405 + 0.955405i
\(719\) 715.794i 0.995541i −0.867309 0.497771i \(-0.834152\pi\)
0.867309 0.497771i \(-0.165848\pi\)
\(720\) 17.6267 + 57.3524i 0.0244815 + 0.0796561i
\(721\) −1958.54 −2.71642
\(722\) 418.272 + 418.272i 0.579323 + 0.579323i
\(723\) 461.504 461.504i 0.638318 0.638318i
\(724\) 295.023i 0.407490i
\(725\) 607.022 + 894.261i 0.837272 + 1.23346i
\(726\) −226.663 −0.312209
\(727\) −518.797 518.797i −0.713614 0.713614i 0.253675 0.967289i \(-0.418361\pi\)
−0.967289 + 0.253675i \(0.918361\pi\)
\(728\) 323.843 323.843i 0.444839 0.444839i
\(729\) 27.0000i 0.0370370i
\(730\) −708.745 + 217.826i −0.970883 + 0.298391i
\(731\) −82.8144 −0.113289
\(732\) −245.954 245.954i −0.336003 0.336003i
\(733\) 229.564 229.564i 0.313184 0.313184i −0.532958 0.846142i \(-0.678920\pi\)
0.846142 + 0.532958i \(0.178920\pi\)
\(734\) 573.304i 0.781069i
\(735\) −750.518 397.642i −1.02111 0.541010i
\(736\) 27.1293 0.0368605
\(737\) −124.164 124.164i −0.168473 0.168473i
\(738\) −82.3588 + 82.3588i −0.111597 + 0.111597i
\(739\) 585.332i 0.792060i 0.918238 + 0.396030i \(0.129612\pi\)
−0.918238 + 0.396030i \(0.870388\pi\)
\(740\) 150.062 283.230i 0.202786 0.382743i
\(741\) 645.566 0.871209
\(742\) −159.162 159.162i −0.214504 0.214504i
\(743\) 660.093 660.093i 0.888416 0.888416i −0.105955 0.994371i \(-0.533790\pi\)
0.994371 + 0.105955i \(0.0337898\pi\)
\(744\) 223.402i 0.300272i
\(745\) 274.777 + 894.047i 0.368828 + 1.20006i
\(746\) 615.835 0.825516
\(747\) −90.9353 90.9353i −0.121734 0.121734i
\(748\) −169.081 + 169.081i −0.226045 + 0.226045i
\(749\) 415.481i 0.554715i
\(750\) 191.637 238.799i 0.255516 0.318399i
\(751\) −778.164 −1.03617 −0.518085 0.855329i \(-0.673355\pi\)
−0.518085 + 0.855329i \(0.673355\pi\)
\(752\) 243.272 + 243.272i 0.323500 + 0.323500i
\(753\) 183.350 183.350i 0.243492 0.243492i
\(754\) 816.329i 1.08266i
\(755\) −746.380 + 229.392i −0.988582 + 0.303831i
\(756\) −126.032 −0.166709
\(757\) −788.525 788.525i −1.04165 1.04165i −0.999094 0.0425507i \(-0.986452\pi\)
−0.0425507 0.999094i \(-0.513548\pi\)
\(758\) 86.8843 86.8843i 0.114623 0.114623i
\(759\) 44.3180i 0.0583900i
\(760\) −348.846 184.827i −0.459008 0.243193i
\(761\) 1511.09 1.98566 0.992830 0.119531i \(-0.0381390\pi\)
0.992830 + 0.119531i \(0.0381390\pi\)
\(762\) −136.057 136.057i −0.178552 0.178552i
\(763\) 289.566 289.566i 0.379510 0.379510i
\(764\) 263.444i 0.344821i
\(765\) 157.370 297.023i 0.205712 0.388265i
\(766\) −318.267 −0.415492
\(767\) 592.789 + 592.789i 0.772867 + 0.772867i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 359.692i 0.467740i 0.972268 + 0.233870i \(0.0751391\pi\)
−0.972268 + 0.233870i \(0.924861\pi\)
\(770\) −134.409 437.331i −0.174557 0.567962i
\(771\) 657.328 0.852566
\(772\) 415.771 + 415.771i 0.538563 + 0.538563i
\(773\) −872.985 + 872.985i −1.12935 + 1.12935i −0.139063 + 0.990284i \(0.544409\pi\)
−0.990284 + 0.139063i \(0.955591\pi\)
\(774\) 15.6790i 0.0202570i
\(775\) −943.261 + 640.283i −1.21711 + 0.826172i
\(776\) 524.595 0.676025
\(777\) 476.079 + 476.079i 0.612715 + 0.612715i
\(778\) −70.6535 + 70.6535i −0.0908142 + 0.0908142i
\(779\)