Properties

Label 76.3.b.b.39.11
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.11
Root \(1.57398 + 1.23393i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57398 - 1.23393i) q^{2} +2.90118i q^{3} +(0.954817 - 3.88437i) q^{4} +3.66290 q^{5} +(3.57986 + 4.56639i) q^{6} +1.93414i q^{7} +(-3.29019 - 7.29209i) q^{8} +0.583162 q^{9} +O(q^{10})\) \(q+(1.57398 - 1.23393i) q^{2} +2.90118i q^{3} +(0.954817 - 3.88437i) q^{4} +3.66290 q^{5} +(3.57986 + 4.56639i) q^{6} +1.93414i q^{7} +(-3.29019 - 7.29209i) q^{8} +0.583162 q^{9} +(5.76533 - 4.51977i) q^{10} +0.752428i q^{11} +(11.2692 + 2.77009i) q^{12} -13.0118 q^{13} +(2.38660 + 3.04430i) q^{14} +10.6267i q^{15} +(-14.1766 - 7.41772i) q^{16} -23.9304 q^{17} +(0.917885 - 0.719584i) q^{18} -4.35890i q^{19} +(3.49740 - 14.2281i) q^{20} -5.61130 q^{21} +(0.928446 + 1.18431i) q^{22} -6.26712i q^{23} +(21.1557 - 9.54543i) q^{24} -11.5832 q^{25} +(-20.4803 + 16.0557i) q^{26} +27.8025i q^{27} +(7.51293 + 1.84675i) q^{28} +33.1165 q^{29} +(13.1127 + 16.7262i) q^{30} +17.5328i q^{31} +(-31.4667 + 5.81771i) q^{32} -2.18293 q^{33} +(-37.6660 + 29.5285i) q^{34} +7.08457i q^{35} +(0.556813 - 2.26522i) q^{36} +41.5073 q^{37} +(-5.37859 - 6.86081i) q^{38} -37.7495i q^{39} +(-12.0516 - 26.7102i) q^{40} -5.51661 q^{41} +(-8.83206 + 6.92396i) q^{42} -84.5402i q^{43} +(2.92271 + 0.718431i) q^{44} +2.13607 q^{45} +(-7.73320 - 9.86431i) q^{46} +18.3582i q^{47} +(21.5201 - 41.1290i) q^{48} +45.2591 q^{49} +(-18.2316 + 14.2929i) q^{50} -69.4264i q^{51} +(-12.4239 + 50.5426i) q^{52} -41.2010 q^{53} +(34.3064 + 43.7605i) q^{54} +2.75607i q^{55} +(14.1040 - 6.36370i) q^{56} +12.6459 q^{57} +(52.1246 - 40.8635i) q^{58} +69.5279i q^{59} +(41.2781 + 10.1466i) q^{60} +87.6461 q^{61} +(21.6343 + 27.5962i) q^{62} +1.12792i q^{63} +(-42.3493 + 47.9848i) q^{64} -47.6609 q^{65} +(-3.43588 + 2.69359i) q^{66} -105.121i q^{67} +(-22.8492 + 92.9546i) q^{68} +18.1820 q^{69} +(8.74189 + 11.1510i) q^{70} +74.9540i q^{71} +(-1.91872 - 4.25248i) q^{72} +48.7353 q^{73} +(65.3316 - 51.2173i) q^{74} -33.6048i q^{75} +(-16.9316 - 4.16195i) q^{76} -1.45530 q^{77} +(-46.5804 - 59.4169i) q^{78} +95.9473i q^{79} +(-51.9277 - 27.1704i) q^{80} -75.4115 q^{81} +(-8.68302 + 6.80713i) q^{82} -65.8722i q^{83} +(-5.35776 + 21.7963i) q^{84} -87.6548 q^{85} +(-104.317 - 133.064i) q^{86} +96.0768i q^{87} +(5.48677 - 2.47563i) q^{88} +3.38934 q^{89} +(3.36212 - 2.63576i) q^{90} -25.1667i q^{91} +(-24.3438 - 5.98395i) q^{92} -50.8657 q^{93} +(22.6528 + 28.8954i) q^{94} -15.9662i q^{95} +(-16.8782 - 91.2906i) q^{96} -23.5177 q^{97} +(71.2368 - 55.8467i) q^{98} +0.438788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57398 1.23393i 0.786989 0.616967i
\(3\) 2.90118i 0.967060i 0.875328 + 0.483530i \(0.160646\pi\)
−0.875328 + 0.483530i \(0.839354\pi\)
\(4\) 0.954817 3.88437i 0.238704 0.971092i
\(5\) 3.66290 0.732580 0.366290 0.930501i \(-0.380628\pi\)
0.366290 + 0.930501i \(0.380628\pi\)
\(6\) 3.57986 + 4.56639i 0.596644 + 0.761065i
\(7\) 1.93414i 0.276306i 0.990411 + 0.138153i \(0.0441166\pi\)
−0.990411 + 0.138153i \(0.955883\pi\)
\(8\) −3.29019 7.29209i −0.411274 0.911512i
\(9\) 0.583162 0.0647958
\(10\) 5.76533 4.51977i 0.576533 0.451977i
\(11\) 0.752428i 0.0684025i 0.999415 + 0.0342013i \(0.0108887\pi\)
−0.999415 + 0.0342013i \(0.989111\pi\)
\(12\) 11.2692 + 2.77009i 0.939104 + 0.230841i
\(13\) −13.0118 −1.00091 −0.500453 0.865763i \(-0.666833\pi\)
−0.500453 + 0.865763i \(0.666833\pi\)
\(14\) 2.38660 + 3.04430i 0.170472 + 0.217450i
\(15\) 10.6267i 0.708449i
\(16\) −14.1766 7.41772i −0.886041 0.463608i
\(17\) −23.9304 −1.40767 −0.703836 0.710363i \(-0.748531\pi\)
−0.703836 + 0.710363i \(0.748531\pi\)
\(18\) 0.917885 0.719584i 0.0509936 0.0399769i
\(19\) 4.35890i 0.229416i
\(20\) 3.49740 14.2281i 0.174870 0.711403i
\(21\) −5.61130 −0.267205
\(22\) 0.928446 + 1.18431i 0.0422021 + 0.0538321i
\(23\) 6.26712i 0.272483i −0.990676 0.136242i \(-0.956498\pi\)
0.990676 0.136242i \(-0.0435024\pi\)
\(24\) 21.1557 9.54543i 0.881486 0.397726i
\(25\) −11.5832 −0.463326
\(26\) −20.4803 + 16.0557i −0.787703 + 0.617526i
\(27\) 27.8025i 1.02972i
\(28\) 7.51293 + 1.84675i 0.268319 + 0.0659554i
\(29\) 33.1165 1.14195 0.570974 0.820968i \(-0.306566\pi\)
0.570974 + 0.820968i \(0.306566\pi\)
\(30\) 13.1127 + 16.7262i 0.437089 + 0.557541i
\(31\) 17.5328i 0.565574i 0.959183 + 0.282787i \(0.0912589\pi\)
−0.959183 + 0.282787i \(0.908741\pi\)
\(32\) −31.4667 + 5.81771i −0.983335 + 0.181803i
\(33\) −2.18293 −0.0661493
\(34\) −37.6660 + 29.5285i −1.10782 + 0.868487i
\(35\) 7.08457i 0.202416i
\(36\) 0.556813 2.26522i 0.0154670 0.0629227i
\(37\) 41.5073 1.12182 0.560910 0.827877i \(-0.310451\pi\)
0.560910 + 0.827877i \(0.310451\pi\)
\(38\) −5.37859 6.86081i −0.141542 0.180548i
\(39\) 37.7495i 0.967937i
\(40\) −12.0516 26.7102i −0.301291 0.667755i
\(41\) −5.51661 −0.134551 −0.0672757 0.997734i \(-0.521431\pi\)
−0.0672757 + 0.997734i \(0.521431\pi\)
\(42\) −8.83206 + 6.92396i −0.210287 + 0.164856i
\(43\) 84.5402i 1.96605i −0.183468 0.983026i \(-0.558733\pi\)
0.183468 0.983026i \(-0.441267\pi\)
\(44\) 2.92271 + 0.718431i 0.0664252 + 0.0163280i
\(45\) 2.13607 0.0474681
\(46\) −7.73320 9.86431i −0.168113 0.214441i
\(47\) 18.3582i 0.390599i 0.980744 + 0.195300i \(0.0625679\pi\)
−0.980744 + 0.195300i \(0.937432\pi\)
\(48\) 21.5201 41.1290i 0.448336 0.856854i
\(49\) 45.2591 0.923655
\(50\) −18.2316 + 14.2929i −0.364633 + 0.285857i
\(51\) 69.4264i 1.36130i
\(52\) −12.4239 + 50.5426i −0.238921 + 0.971973i
\(53\) −41.2010 −0.777377 −0.388688 0.921369i \(-0.627072\pi\)
−0.388688 + 0.921369i \(0.627072\pi\)
\(54\) 34.3064 + 43.7605i 0.635304 + 0.810379i
\(55\) 2.75607i 0.0501103i
\(56\) 14.1040 6.36370i 0.251856 0.113638i
\(57\) 12.6459 0.221859
\(58\) 52.1246 40.8635i 0.898701 0.704544i
\(59\) 69.5279i 1.17844i 0.807973 + 0.589219i \(0.200565\pi\)
−0.807973 + 0.589219i \(0.799435\pi\)
\(60\) 41.2781 + 10.1466i 0.687969 + 0.169110i
\(61\) 87.6461 1.43682 0.718411 0.695619i \(-0.244870\pi\)
0.718411 + 0.695619i \(0.244870\pi\)
\(62\) 21.6343 + 27.5962i 0.348940 + 0.445100i
\(63\) 1.12792i 0.0179035i
\(64\) −42.3493 + 47.9848i −0.661707 + 0.749762i
\(65\) −47.6609 −0.733244
\(66\) −3.43588 + 2.69359i −0.0520588 + 0.0408119i
\(67\) 105.121i 1.56897i −0.620145 0.784487i \(-0.712926\pi\)
0.620145 0.784487i \(-0.287074\pi\)
\(68\) −22.8492 + 92.9546i −0.336017 + 1.36698i
\(69\) 18.1820 0.263508
\(70\) 8.74189 + 11.1510i 0.124884 + 0.159300i
\(71\) 74.9540i 1.05569i 0.849341 + 0.527845i \(0.177000\pi\)
−0.849341 + 0.527845i \(0.823000\pi\)
\(72\) −1.91872 4.25248i −0.0266488 0.0590622i
\(73\) 48.7353 0.667607 0.333803 0.942643i \(-0.391668\pi\)
0.333803 + 0.942643i \(0.391668\pi\)
\(74\) 65.3316 51.2173i 0.882860 0.692125i
\(75\) 33.6048i 0.448064i
\(76\) −16.9316 4.16195i −0.222784 0.0547625i
\(77\) −1.45530 −0.0189000
\(78\) −46.5804 59.4169i −0.597185 0.761756i
\(79\) 95.9473i 1.21452i 0.794502 + 0.607261i \(0.207732\pi\)
−0.794502 + 0.607261i \(0.792268\pi\)
\(80\) −51.9277 27.1704i −0.649096 0.339630i
\(81\) −75.4115 −0.931006
\(82\) −8.68302 + 6.80713i −0.105890 + 0.0830137i
\(83\) 65.8722i 0.793641i −0.917896 0.396821i \(-0.870114\pi\)
0.917896 0.396821i \(-0.129886\pi\)
\(84\) −5.35776 + 21.7963i −0.0637828 + 0.259480i
\(85\) −87.6548 −1.03123
\(86\) −104.317 133.064i −1.21299 1.54726i
\(87\) 96.0768i 1.10433i
\(88\) 5.48677 2.47563i 0.0623497 0.0281322i
\(89\) 3.38934 0.0380825 0.0190412 0.999819i \(-0.493939\pi\)
0.0190412 + 0.999819i \(0.493939\pi\)
\(90\) 3.36212 2.63576i 0.0373569 0.0292863i
\(91\) 25.1667i 0.276557i
\(92\) −24.3438 5.98395i −0.264606 0.0650429i
\(93\) −50.8657 −0.546943
\(94\) 22.6528 + 28.8954i 0.240987 + 0.307397i
\(95\) 15.9662i 0.168065i
\(96\) −16.8782 91.2906i −0.175815 0.950943i
\(97\) −23.5177 −0.242451 −0.121225 0.992625i \(-0.538682\pi\)
−0.121225 + 0.992625i \(0.538682\pi\)
\(98\) 71.2368 55.8467i 0.726906 0.569864i
\(99\) 0.438788i 0.00443220i
\(100\) −11.0598 + 44.9933i −0.110598 + 0.449933i
\(101\) −153.325 −1.51807 −0.759035 0.651050i \(-0.774329\pi\)
−0.759035 + 0.651050i \(0.774329\pi\)
\(102\) −85.6676 109.276i −0.839878 1.07133i
\(103\) 114.566i 1.11229i 0.831084 + 0.556147i \(0.187721\pi\)
−0.831084 + 0.556147i \(0.812279\pi\)
\(104\) 42.8113 + 94.8832i 0.411647 + 0.912338i
\(105\) −20.5536 −0.195749
\(106\) −64.8494 + 50.8392i −0.611787 + 0.479616i
\(107\) 161.991i 1.51393i 0.653454 + 0.756966i \(0.273319\pi\)
−0.653454 + 0.756966i \(0.726681\pi\)
\(108\) 107.995 + 26.5463i 0.999954 + 0.245799i
\(109\) 120.924 1.10939 0.554696 0.832053i \(-0.312834\pi\)
0.554696 + 0.832053i \(0.312834\pi\)
\(110\) 3.40080 + 4.33799i 0.0309164 + 0.0394363i
\(111\) 120.420i 1.08487i
\(112\) 14.3469 27.4197i 0.128098 0.244818i
\(113\) −91.1817 −0.806918 −0.403459 0.914998i \(-0.632192\pi\)
−0.403459 + 0.914998i \(0.632192\pi\)
\(114\) 19.9044 15.6043i 0.174600 0.136879i
\(115\) 22.9558i 0.199616i
\(116\) 31.6202 128.637i 0.272588 1.10894i
\(117\) −7.58799 −0.0648546
\(118\) 85.7928 + 109.435i 0.727057 + 0.927418i
\(119\) 46.2849i 0.388948i
\(120\) 77.4911 34.9640i 0.645759 0.291366i
\(121\) 120.434 0.995321
\(122\) 137.953 108.149i 1.13076 0.886471i
\(123\) 16.0047i 0.130119i
\(124\) 68.1038 + 16.7406i 0.549224 + 0.135005i
\(125\) −134.000 −1.07200
\(126\) 1.39178 + 1.77532i 0.0110459 + 0.0140899i
\(127\) 191.974i 1.51160i −0.654800 0.755802i \(-0.727247\pi\)
0.654800 0.755802i \(-0.272753\pi\)
\(128\) −7.44683 + 127.783i −0.0581783 + 0.998306i
\(129\) 245.266 1.90129
\(130\) −75.0172 + 58.8104i −0.577055 + 0.452387i
\(131\) 92.3292i 0.704803i −0.935849 0.352401i \(-0.885365\pi\)
0.935849 0.352401i \(-0.114635\pi\)
\(132\) −2.08430 + 8.47930i −0.0157901 + 0.0642371i
\(133\) 8.43073 0.0633890
\(134\) −129.713 165.459i −0.968005 1.23477i
\(135\) 101.838i 0.754353i
\(136\) 78.7357 + 174.503i 0.578939 + 1.28311i
\(137\) −2.46732 −0.0180097 −0.00900483 0.999959i \(-0.502866\pi\)
−0.00900483 + 0.999959i \(0.502866\pi\)
\(138\) 28.6181 22.4354i 0.207378 0.162575i
\(139\) 245.321i 1.76490i −0.470409 0.882448i \(-0.655894\pi\)
0.470409 0.882448i \(-0.344106\pi\)
\(140\) 27.5191 + 6.76447i 0.196565 + 0.0483176i
\(141\) −53.2603 −0.377733
\(142\) 92.4883 + 117.976i 0.651326 + 0.830817i
\(143\) 9.79043i 0.0684646i
\(144\) −8.26729 4.32574i −0.0574117 0.0300398i
\(145\) 121.302 0.836568
\(146\) 76.7083 60.1361i 0.525399 0.411891i
\(147\) 131.305i 0.893229i
\(148\) 39.6319 161.230i 0.267783 1.08939i
\(149\) 52.3645 0.351439 0.175720 0.984440i \(-0.443775\pi\)
0.175720 + 0.984440i \(0.443775\pi\)
\(150\) −41.4661 52.8933i −0.276441 0.352622i
\(151\) 25.3459i 0.167853i 0.996472 + 0.0839267i \(0.0267461\pi\)
−0.996472 + 0.0839267i \(0.973254\pi\)
\(152\) −31.7855 + 14.3416i −0.209115 + 0.0943527i
\(153\) −13.9553 −0.0912113
\(154\) −2.29062 + 1.79575i −0.0148741 + 0.0116607i
\(155\) 64.2208i 0.414328i
\(156\) −146.633 36.0439i −0.939956 0.231051i
\(157\) −54.8571 −0.349408 −0.174704 0.984621i \(-0.555897\pi\)
−0.174704 + 0.984621i \(0.555897\pi\)
\(158\) 118.393 + 151.019i 0.749320 + 0.955816i
\(159\) 119.531i 0.751770i
\(160\) −115.259 + 21.3097i −0.720372 + 0.133185i
\(161\) 12.1215 0.0752888
\(162\) −118.696 + 93.0527i −0.732691 + 0.574399i
\(163\) 26.8048i 0.164446i 0.996614 + 0.0822232i \(0.0262020\pi\)
−0.996614 + 0.0822232i \(0.973798\pi\)
\(164\) −5.26735 + 21.4285i −0.0321180 + 0.130662i
\(165\) −7.99585 −0.0484597
\(166\) −81.2819 103.681i −0.489650 0.624587i
\(167\) 62.7282i 0.375618i 0.982206 + 0.187809i \(0.0601386\pi\)
−0.982206 + 0.187809i \(0.939861\pi\)
\(168\) 18.4622 + 40.9181i 0.109894 + 0.243560i
\(169\) 0.306683 0.00181469
\(170\) −137.967 + 108.160i −0.811569 + 0.636236i
\(171\) 2.54195i 0.0148652i
\(172\) −328.385 80.7204i −1.90922 0.469305i
\(173\) 328.974 1.90159 0.950793 0.309827i \(-0.100271\pi\)
0.950793 + 0.309827i \(0.100271\pi\)
\(174\) 118.552 + 151.223i 0.681336 + 0.869097i
\(175\) 22.4035i 0.128020i
\(176\) 5.58130 10.6669i 0.0317119 0.0606074i
\(177\) −201.713 −1.13962
\(178\) 5.33475 4.18222i 0.0299705 0.0234956i
\(179\) 335.845i 1.87623i −0.346327 0.938114i \(-0.612571\pi\)
0.346327 0.938114i \(-0.387429\pi\)
\(180\) 2.03955 8.29727i 0.0113308 0.0460959i
\(181\) −58.9250 −0.325552 −0.162776 0.986663i \(-0.552045\pi\)
−0.162776 + 0.986663i \(0.552045\pi\)
\(182\) −31.0540 39.6118i −0.170626 0.217647i
\(183\) 254.277i 1.38949i
\(184\) −45.7004 + 20.6200i −0.248372 + 0.112065i
\(185\) 152.037 0.821823
\(186\) −80.0616 + 62.7649i −0.430439 + 0.337446i
\(187\) 18.0059i 0.0962883i
\(188\) 71.3099 + 17.5287i 0.379308 + 0.0932377i
\(189\) −53.7740 −0.284518
\(190\) −19.7012 25.1305i −0.103691 0.132266i
\(191\) 98.6857i 0.516679i 0.966054 + 0.258339i \(0.0831753\pi\)
−0.966054 + 0.258339i \(0.916825\pi\)
\(192\) −139.212 122.863i −0.725065 0.639910i
\(193\) −278.391 −1.44244 −0.721220 0.692706i \(-0.756418\pi\)
−0.721220 + 0.692706i \(0.756418\pi\)
\(194\) −37.0164 + 29.0193i −0.190806 + 0.149584i
\(195\) 138.273i 0.709091i
\(196\) 43.2141 175.803i 0.220480 0.896954i
\(197\) −47.3378 −0.240293 −0.120147 0.992756i \(-0.538336\pi\)
−0.120147 + 0.992756i \(0.538336\pi\)
\(198\) 0.541435 + 0.690642i 0.00273452 + 0.00348809i
\(199\) 251.355i 1.26309i −0.775340 0.631545i \(-0.782421\pi\)
0.775340 0.631545i \(-0.217579\pi\)
\(200\) 38.1108 + 84.4655i 0.190554 + 0.422328i
\(201\) 304.975 1.51729
\(202\) −241.330 + 189.193i −1.19470 + 0.936598i
\(203\) 64.0520i 0.315527i
\(204\) −269.678 66.2895i −1.32195 0.324949i
\(205\) −20.2068 −0.0985697
\(206\) 141.367 + 180.325i 0.686249 + 0.875364i
\(207\) 3.65475i 0.0176558i
\(208\) 184.464 + 96.5178i 0.886844 + 0.464028i
\(209\) 3.27976 0.0156926
\(210\) −32.3509 + 25.3618i −0.154052 + 0.120770i
\(211\) 38.9936i 0.184804i −0.995722 0.0924019i \(-0.970546\pi\)
0.995722 0.0924019i \(-0.0294544\pi\)
\(212\) −39.3394 + 160.040i −0.185563 + 0.754905i
\(213\) −217.455 −1.02092
\(214\) 199.886 + 254.970i 0.934046 + 1.19145i
\(215\) 309.662i 1.44029i
\(216\) 202.738 91.4754i 0.938603 0.423497i
\(217\) −33.9109 −0.156272
\(218\) 190.331 149.212i 0.873080 0.684458i
\(219\) 141.390i 0.645615i
\(220\) 10.7056 + 2.63154i 0.0486618 + 0.0119615i
\(221\) 311.378 1.40895
\(222\) 148.590 + 189.539i 0.669326 + 0.853778i
\(223\) 189.466i 0.849622i 0.905282 + 0.424811i \(0.139660\pi\)
−0.905282 + 0.424811i \(0.860340\pi\)
\(224\) −11.2523 60.8611i −0.0502334 0.271702i
\(225\) −6.75486 −0.0300216
\(226\) −143.518 + 112.512i −0.635035 + 0.497841i
\(227\) 167.625i 0.738438i 0.929342 + 0.369219i \(0.120375\pi\)
−0.929342 + 0.369219i \(0.879625\pi\)
\(228\) 12.0746 49.1215i 0.0529586 0.215445i
\(229\) 203.355 0.888013 0.444006 0.896024i \(-0.353557\pi\)
0.444006 + 0.896024i \(0.353557\pi\)
\(230\) −28.3260 36.1320i −0.123156 0.157096i
\(231\) 4.22209i 0.0182775i
\(232\) −108.960 241.489i −0.469653 1.04090i
\(233\) −200.769 −0.861671 −0.430836 0.902430i \(-0.641781\pi\)
−0.430836 + 0.902430i \(0.641781\pi\)
\(234\) −11.9433 + 9.36307i −0.0510399 + 0.0400131i
\(235\) 67.2441i 0.286145i
\(236\) 270.072 + 66.3864i 1.14437 + 0.281298i
\(237\) −278.360 −1.17452
\(238\) −57.1124 72.8514i −0.239968 0.306098i
\(239\) 165.710i 0.693349i −0.937986 0.346674i \(-0.887311\pi\)
0.937986 0.346674i \(-0.112689\pi\)
\(240\) 78.8261 150.651i 0.328442 0.627714i
\(241\) −396.818 −1.64655 −0.823273 0.567646i \(-0.807854\pi\)
−0.823273 + 0.567646i \(0.807854\pi\)
\(242\) 189.560 148.607i 0.783307 0.614080i
\(243\) 31.4401i 0.129383i
\(244\) 83.6860 340.450i 0.342975 1.39529i
\(245\) 165.780 0.676651
\(246\) −19.7487 25.1910i −0.0802792 0.102402i
\(247\) 56.7171i 0.229624i
\(248\) 127.851 57.6862i 0.515527 0.232606i
\(249\) 191.107 0.767498
\(250\) −210.914 + 165.348i −0.843655 + 0.661391i
\(251\) 249.643i 0.994592i 0.867581 + 0.497296i \(0.165674\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(252\) 4.38126 + 1.07696i 0.0173859 + 0.00427364i
\(253\) 4.71555 0.0186385
\(254\) −236.883 302.163i −0.932610 1.18962i
\(255\) 254.302i 0.997263i
\(256\) 145.955 + 210.317i 0.570136 + 0.821550i
\(257\) 24.5770 0.0956302 0.0478151 0.998856i \(-0.484774\pi\)
0.0478151 + 0.998856i \(0.484774\pi\)
\(258\) 386.044 302.642i 1.49629 1.17303i
\(259\) 80.2811i 0.309966i
\(260\) −45.5074 + 185.132i −0.175029 + 0.712048i
\(261\) 19.3123 0.0739934
\(262\) −113.928 145.324i −0.434840 0.554672i
\(263\) 343.809i 1.30726i 0.756816 + 0.653628i \(0.226754\pi\)
−0.756816 + 0.653628i \(0.773246\pi\)
\(264\) 7.18225 + 15.9181i 0.0272055 + 0.0602959i
\(265\) −150.915 −0.569491
\(266\) 13.2698 10.4030i 0.0498864 0.0391089i
\(267\) 9.83308i 0.0368280i
\(268\) −408.330 100.372i −1.52362 0.374521i
\(269\) 64.7826 0.240828 0.120414 0.992724i \(-0.461578\pi\)
0.120414 + 0.992724i \(0.461578\pi\)
\(270\) 125.661 + 160.290i 0.465411 + 0.593668i
\(271\) 113.329i 0.418189i 0.977895 + 0.209095i \(0.0670517\pi\)
−0.977895 + 0.209095i \(0.932948\pi\)
\(272\) 339.253 + 177.509i 1.24725 + 0.652607i
\(273\) 73.0130 0.267447
\(274\) −3.88352 + 3.04451i −0.0141734 + 0.0111114i
\(275\) 8.71549i 0.0316927i
\(276\) 17.3605 70.6257i 0.0629004 0.255890i
\(277\) −42.8037 −0.154526 −0.0772629 0.997011i \(-0.524618\pi\)
−0.0772629 + 0.997011i \(0.524618\pi\)
\(278\) −302.709 386.129i −1.08888 1.38895i
\(279\) 10.2245i 0.0366468i
\(280\) 51.6614 23.3096i 0.184505 0.0832486i
\(281\) −202.018 −0.718924 −0.359462 0.933160i \(-0.617040\pi\)
−0.359462 + 0.933160i \(0.617040\pi\)
\(282\) −83.8306 + 65.7197i −0.297272 + 0.233049i
\(283\) 77.5872i 0.274160i 0.990560 + 0.137080i \(0.0437717\pi\)
−0.990560 + 0.137080i \(0.956228\pi\)
\(284\) 291.149 + 71.5674i 1.02517 + 0.251998i
\(285\) 46.3208 0.162529
\(286\) −12.0807 15.4099i −0.0422404 0.0538809i
\(287\) 10.6699i 0.0371774i
\(288\) −18.3502 + 3.39267i −0.0637160 + 0.0117801i
\(289\) 283.665 0.981540
\(290\) 190.927 149.679i 0.658370 0.516135i
\(291\) 68.2291i 0.234464i
\(292\) 46.5333 189.306i 0.159360 0.648308i
\(293\) 327.131 1.11649 0.558243 0.829677i \(-0.311476\pi\)
0.558243 + 0.829677i \(0.311476\pi\)
\(294\) 162.021 + 206.671i 0.551093 + 0.702962i
\(295\) 254.674i 0.863300i
\(296\) −136.567 302.675i −0.461375 1.02255i
\(297\) −20.9193 −0.0704355
\(298\) 82.4206 64.6143i 0.276579 0.216826i
\(299\) 81.5464i 0.272730i
\(300\) −130.534 32.0864i −0.435112 0.106955i
\(301\) 163.513 0.543232
\(302\) 31.2751 + 39.8938i 0.103560 + 0.132099i
\(303\) 444.823i 1.46806i
\(304\) −32.3331 + 61.7946i −0.106359 + 0.203272i
\(305\) 321.039 1.05259
\(306\) −21.9654 + 17.2199i −0.0717823 + 0.0562743i
\(307\) 268.290i 0.873910i −0.899483 0.436955i \(-0.856057\pi\)
0.899483 0.436955i \(-0.143943\pi\)
\(308\) −1.38955 + 5.65294i −0.00451152 + 0.0183537i
\(309\) −332.377 −1.07566
\(310\) 79.2442 + 101.082i 0.255627 + 0.326072i
\(311\) 449.497i 1.44533i 0.691199 + 0.722664i \(0.257083\pi\)
−0.691199 + 0.722664i \(0.742917\pi\)
\(312\) −275.273 + 124.203i −0.882286 + 0.398087i
\(313\) −283.901 −0.907032 −0.453516 0.891248i \(-0.649830\pi\)
−0.453516 + 0.891248i \(0.649830\pi\)
\(314\) −86.3439 + 67.6900i −0.274981 + 0.215573i
\(315\) 4.13146i 0.0131157i
\(316\) 372.695 + 91.6121i 1.17941 + 0.289912i
\(317\) −553.100 −1.74480 −0.872398 0.488797i \(-0.837436\pi\)
−0.872398 + 0.488797i \(0.837436\pi\)
\(318\) −147.494 188.140i −0.463817 0.591635i
\(319\) 24.9178i 0.0781121i
\(320\) −155.121 + 175.763i −0.484754 + 0.549261i
\(321\) −469.964 −1.46406
\(322\) 19.0790 14.9571i 0.0592515 0.0464507i
\(323\) 104.310i 0.322942i
\(324\) −72.0041 + 292.926i −0.222235 + 0.904092i
\(325\) 150.718 0.463747
\(326\) 33.0753 + 42.1901i 0.101458 + 0.129418i
\(327\) 350.822i 1.07285i
\(328\) 18.1507 + 40.2276i 0.0553375 + 0.122645i
\(329\) −35.5073 −0.107925
\(330\) −12.5853 + 9.86634i −0.0381372 + 0.0298980i
\(331\) 280.828i 0.848422i 0.905563 + 0.424211i \(0.139448\pi\)
−0.905563 + 0.424211i \(0.860552\pi\)
\(332\) −255.872 62.8959i −0.770699 0.189445i
\(333\) 24.2055 0.0726892
\(334\) 77.4024 + 98.7328i 0.231744 + 0.295607i
\(335\) 385.049i 1.14940i
\(336\) 79.5494 + 41.6230i 0.236754 + 0.123878i
\(337\) 93.1413 0.276384 0.138192 0.990405i \(-0.455871\pi\)
0.138192 + 0.990405i \(0.455871\pi\)
\(338\) 0.482713 0.378427i 0.00142814 0.00111961i
\(339\) 264.534i 0.780337i
\(340\) −83.6942 + 340.483i −0.246159 + 1.00142i
\(341\) −13.1922 −0.0386867
\(342\) −3.13659 4.00097i −0.00917132 0.0116987i
\(343\) 182.311i 0.531518i
\(344\) −616.475 + 278.153i −1.79208 + 0.808586i
\(345\) 66.5989 0.193040
\(346\) 517.799 405.932i 1.49653 1.17322i
\(347\) 221.251i 0.637612i −0.947820 0.318806i \(-0.896718\pi\)
0.947820 0.318806i \(-0.103282\pi\)
\(348\) 373.198 + 91.7358i 1.07241 + 0.263609i
\(349\) −227.761 −0.652611 −0.326306 0.945264i \(-0.605804\pi\)
−0.326306 + 0.945264i \(0.605804\pi\)
\(350\) −27.6444 35.2626i −0.0789841 0.100750i
\(351\) 361.760i 1.03065i
\(352\) −4.37740 23.6764i −0.0124358 0.0672626i
\(353\) −169.824 −0.481089 −0.240545 0.970638i \(-0.577326\pi\)
−0.240545 + 0.970638i \(0.577326\pi\)
\(354\) −317.492 + 248.900i −0.896869 + 0.703108i
\(355\) 274.549i 0.773378i
\(356\) 3.23620 13.1654i 0.00909045 0.0369816i
\(357\) 134.281 0.376136
\(358\) −414.410 528.612i −1.15757 1.47657i
\(359\) 585.928i 1.63211i −0.577972 0.816056i \(-0.696156\pi\)
0.577972 0.816056i \(-0.303844\pi\)
\(360\) −7.02807 15.5764i −0.0195224 0.0432678i
\(361\) −19.0000 −0.0526316
\(362\) −92.7466 + 72.7095i −0.256206 + 0.200855i
\(363\) 349.400i 0.962535i
\(364\) −97.7566 24.0296i −0.268562 0.0660153i
\(365\) 178.512 0.489075
\(366\) 313.761 + 400.227i 0.857270 + 1.09352i
\(367\) 428.832i 1.16848i −0.811581 0.584239i \(-0.801393\pi\)
0.811581 0.584239i \(-0.198607\pi\)
\(368\) −46.4877 + 88.8467i −0.126325 + 0.241431i
\(369\) −3.21708 −0.00871837
\(370\) 239.303 187.604i 0.646766 0.507037i
\(371\) 79.6886i 0.214794i
\(372\) −48.5675 + 197.581i −0.130558 + 0.531133i
\(373\) −127.502 −0.341830 −0.170915 0.985286i \(-0.554672\pi\)
−0.170915 + 0.985286i \(0.554672\pi\)
\(374\) −22.2181 28.3409i −0.0594067 0.0757779i
\(375\) 388.759i 1.03669i
\(376\) 133.869 60.4019i 0.356036 0.160643i
\(377\) −430.905 −1.14298
\(378\) −84.6390 + 66.3535i −0.223913 + 0.175538i
\(379\) 244.665i 0.645555i 0.946475 + 0.322777i \(0.104616\pi\)
−0.946475 + 0.322777i \(0.895384\pi\)
\(380\) −62.0187 15.2448i −0.163207 0.0401179i
\(381\) 556.950 1.46181
\(382\) 121.772 + 155.329i 0.318774 + 0.406621i
\(383\) 685.025i 1.78858i −0.447491 0.894288i \(-0.647682\pi\)
0.447491 0.894288i \(-0.352318\pi\)
\(384\) −370.722 21.6046i −0.965422 0.0562619i
\(385\) −5.33063 −0.0138458
\(386\) −438.181 + 343.516i −1.13518 + 0.889937i
\(387\) 49.3007i 0.127392i
\(388\) −22.4551 + 91.3515i −0.0578740 + 0.235442i
\(389\) 290.167 0.745931 0.372966 0.927845i \(-0.378341\pi\)
0.372966 + 0.927845i \(0.378341\pi\)
\(390\) −170.619 217.638i −0.437486 0.558047i
\(391\) 149.975i 0.383567i
\(392\) −148.911 330.034i −0.379875 0.841922i
\(393\) 267.863 0.681586
\(394\) −74.5086 + 58.4117i −0.189108 + 0.148253i
\(395\) 351.445i 0.889735i
\(396\) 1.70441 + 0.418962i 0.00430407 + 0.00105798i
\(397\) 317.752 0.800384 0.400192 0.916431i \(-0.368943\pi\)
0.400192 + 0.916431i \(0.368943\pi\)
\(398\) −310.155 395.627i −0.779284 0.994038i
\(399\) 24.4591i 0.0613009i
\(400\) 164.210 + 85.9207i 0.410526 + 0.214802i
\(401\) 445.424 1.11078 0.555392 0.831589i \(-0.312568\pi\)
0.555392 + 0.831589i \(0.312568\pi\)
\(402\) 480.025 376.319i 1.19409 0.936118i
\(403\) 228.133i 0.566087i
\(404\) −146.397 + 595.571i −0.362369 + 1.47419i
\(405\) −276.225 −0.682036
\(406\) 79.0359 + 100.817i 0.194670 + 0.248317i
\(407\) 31.2313i 0.0767353i
\(408\) −506.264 + 228.426i −1.24084 + 0.559868i
\(409\) 571.233 1.39666 0.698328 0.715778i \(-0.253928\pi\)
0.698328 + 0.715778i \(0.253928\pi\)
\(410\) −31.8050 + 24.9338i −0.0775733 + 0.0608142i
\(411\) 7.15815i 0.0174164i
\(412\) 445.018 + 109.390i 1.08014 + 0.265509i
\(413\) −134.477 −0.325610
\(414\) −4.50971 5.75249i −0.0108930 0.0138949i
\(415\) 241.283i 0.581406i
\(416\) 409.438 75.6988i 0.984227 0.181968i
\(417\) 711.719 1.70676
\(418\) 5.16227 4.04700i 0.0123499 0.00968182i
\(419\) 308.595i 0.736502i 0.929726 + 0.368251i \(0.120043\pi\)
−0.929726 + 0.368251i \(0.879957\pi\)
\(420\) −19.6249 + 79.8378i −0.0467260 + 0.190090i
\(421\) 38.8298 0.0922324 0.0461162 0.998936i \(-0.485316\pi\)
0.0461162 + 0.998936i \(0.485316\pi\)
\(422\) −48.1155 61.3751i −0.114018 0.145439i
\(423\) 10.7058i 0.0253092i
\(424\) 135.559 + 300.441i 0.319715 + 0.708588i
\(425\) 277.190 0.652212
\(426\) −342.270 + 268.325i −0.803450 + 0.629871i
\(427\) 169.520i 0.397003i
\(428\) 629.232 + 154.672i 1.47017 + 0.361382i
\(429\) 28.4038 0.0662093
\(430\) −382.103 487.402i −0.888611 1.13349i
\(431\) 479.659i 1.11290i −0.830881 0.556450i \(-0.812163\pi\)
0.830881 0.556450i \(-0.187837\pi\)
\(432\) 206.231 394.146i 0.477386 0.912375i
\(433\) 434.901 1.00439 0.502195 0.864754i \(-0.332526\pi\)
0.502195 + 0.864754i \(0.332526\pi\)
\(434\) −53.3751 + 41.8438i −0.122984 + 0.0964143i
\(435\) 351.920i 0.809011i
\(436\) 115.460 469.713i 0.264817 1.07732i
\(437\) −27.3177 −0.0625120
\(438\) 174.466 + 222.544i 0.398323 + 0.508092i
\(439\) 25.4779i 0.0580363i 0.999579 + 0.0290182i \(0.00923807\pi\)
−0.999579 + 0.0290182i \(0.990762\pi\)
\(440\) 20.0975 9.06799i 0.0456762 0.0206091i
\(441\) 26.3934 0.0598490
\(442\) 490.102 384.219i 1.10883 0.869274i
\(443\) 805.631i 1.81858i 0.416164 + 0.909290i \(0.363374\pi\)
−0.416164 + 0.909290i \(0.636626\pi\)
\(444\) 467.756 + 114.979i 1.05351 + 0.258962i
\(445\) 12.4148 0.0278985
\(446\) 233.788 + 298.215i 0.524189 + 0.668644i
\(447\) 151.919i 0.339863i
\(448\) −92.8094 81.9096i −0.207164 0.182834i
\(449\) −106.288 −0.236721 −0.118360 0.992971i \(-0.537764\pi\)
−0.118360 + 0.992971i \(0.537764\pi\)
\(450\) −10.6320 + 8.33505i −0.0236267 + 0.0185223i
\(451\) 4.15085i 0.00920366i
\(452\) −87.0618 + 354.183i −0.192615 + 0.783591i
\(453\) −73.5328 −0.162324
\(454\) 206.839 + 263.839i 0.455592 + 0.581143i
\(455\) 92.1830i 0.202600i
\(456\) −41.6076 92.2154i −0.0912447 0.202227i
\(457\) −730.620 −1.59873 −0.799365 0.600846i \(-0.794831\pi\)
−0.799365 + 0.600846i \(0.794831\pi\)
\(458\) 320.076 250.926i 0.698856 0.547874i
\(459\) 665.325i 1.44951i
\(460\) −89.1689 21.9186i −0.193845 0.0476491i
\(461\) −854.696 −1.85401 −0.927003 0.375055i \(-0.877624\pi\)
−0.927003 + 0.375055i \(0.877624\pi\)
\(462\) −5.20978 6.64549i −0.0112766 0.0143842i
\(463\) 769.128i 1.66118i 0.556882 + 0.830591i \(0.311997\pi\)
−0.556882 + 0.830591i \(0.688003\pi\)
\(464\) −469.481 245.649i −1.01181 0.529416i
\(465\) −186.316 −0.400680
\(466\) −316.007 + 247.736i −0.678126 + 0.531622i
\(467\) 54.2556i 0.116179i 0.998311 + 0.0580895i \(0.0185009\pi\)
−0.998311 + 0.0580895i \(0.981499\pi\)
\(468\) −7.24514 + 29.4745i −0.0154811 + 0.0629798i
\(469\) 203.320 0.433517
\(470\) 82.9748 + 105.841i 0.176542 + 0.225193i
\(471\) 159.150i 0.337899i
\(472\) 507.004 228.760i 1.07416 0.484661i
\(473\) 63.6104 0.134483
\(474\) −438.133 + 343.478i −0.924331 + 0.724637i
\(475\) 50.4898i 0.106294i
\(476\) −179.788 44.1936i −0.377705 0.0928436i
\(477\) −24.0269 −0.0503708
\(478\) −204.475 260.824i −0.427773 0.545658i
\(479\) 512.359i 1.06964i −0.844965 0.534821i \(-0.820379\pi\)
0.844965 0.534821i \(-0.179621\pi\)
\(480\) −61.8232 334.388i −0.128798 0.696642i
\(481\) −540.085 −1.12284
\(482\) −624.582 + 489.646i −1.29581 + 1.01586i
\(483\) 35.1666i 0.0728088i
\(484\) 114.992 467.810i 0.237587 0.966549i
\(485\) −86.1431 −0.177615
\(486\) 38.7950 + 49.4860i 0.0798250 + 0.101823i
\(487\) 445.189i 0.914146i −0.889429 0.457073i \(-0.848898\pi\)
0.889429 0.457073i \(-0.151102\pi\)
\(488\) −288.373 639.124i −0.590927 1.30968i
\(489\) −77.7654 −0.159030
\(490\) 260.933 204.561i 0.532517 0.417471i
\(491\) 219.288i 0.446615i −0.974748 0.223308i \(-0.928315\pi\)
0.974748 0.223308i \(-0.0716855\pi\)
\(492\) −62.1680 15.2815i −0.126358 0.0310600i
\(493\) −792.492 −1.60749
\(494\) 69.9851 + 89.2715i 0.141670 + 0.180711i
\(495\) 1.60724i 0.00324694i
\(496\) 130.053 248.556i 0.262204 0.501121i
\(497\) −144.972 −0.291694
\(498\) 300.798 235.813i 0.604013 0.473521i
\(499\) 277.168i 0.555446i −0.960661 0.277723i \(-0.910420\pi\)
0.960661 0.277723i \(-0.0895798\pi\)
\(500\) −127.946 + 520.507i −0.255892 + 1.04101i
\(501\) −181.986 −0.363245
\(502\) 308.042 + 392.932i 0.613630 + 0.782733i
\(503\) 328.913i 0.653903i 0.945041 + 0.326951i \(0.106021\pi\)
−0.945041 + 0.326951i \(0.893979\pi\)
\(504\) 8.22490 3.71107i 0.0163192 0.00736324i
\(505\) −561.614 −1.11211
\(506\) 7.42218 5.81868i 0.0146683 0.0114994i
\(507\) 0.889743i 0.00175492i
\(508\) −745.697 183.300i −1.46791 0.360826i
\(509\) −371.573 −0.730006 −0.365003 0.931006i \(-0.618932\pi\)
−0.365003 + 0.931006i \(0.618932\pi\)
\(510\) −313.792 400.266i −0.615278 0.784835i
\(511\) 94.2610i 0.184464i
\(512\) 489.247 + 150.936i 0.955560 + 0.294796i
\(513\) 121.188 0.236234
\(514\) 38.6836 30.3263i 0.0752599 0.0590006i
\(515\) 419.645i 0.814845i
\(516\) 234.184 952.705i 0.453846 1.84633i
\(517\) −13.8132 −0.0267180
\(518\) 99.0616 + 126.361i 0.191239 + 0.243940i
\(519\) 954.413i 1.83895i
\(520\) 156.813 + 347.548i 0.301564 + 0.668361i
\(521\) −607.799 −1.16660 −0.583300 0.812256i \(-0.698239\pi\)
−0.583300 + 0.812256i \(0.698239\pi\)
\(522\) 30.3971 23.8301i 0.0582320 0.0456515i
\(523\) 384.474i 0.735131i 0.929998 + 0.367566i \(0.119809\pi\)
−0.929998 + 0.367566i \(0.880191\pi\)
\(524\) −358.641 88.1574i −0.684429 0.168239i
\(525\) 64.9965 0.123803
\(526\) 424.237 + 541.147i 0.806534 + 1.02880i
\(527\) 419.567i 0.796142i
\(528\) 30.9466 + 16.1924i 0.0586110 + 0.0306673i
\(529\) 489.723 0.925753
\(530\) −237.537 + 186.219i −0.448183 + 0.351357i
\(531\) 40.5460i 0.0763579i
\(532\) 8.04981 32.7481i 0.0151312 0.0615566i
\(533\) 71.7809 0.134673
\(534\) 12.1334 + 15.4771i 0.0227217 + 0.0289833i
\(535\) 593.356i 1.10908i
\(536\) −766.554 + 345.869i −1.43014 + 0.645278i
\(537\) 974.346 1.81442
\(538\) 101.966 79.9375i 0.189529 0.148583i
\(539\) 34.0542i 0.0631803i
\(540\) 395.575 + 97.2363i 0.732546 + 0.180067i
\(541\) −382.676 −0.707350 −0.353675 0.935368i \(-0.615068\pi\)
−0.353675 + 0.935368i \(0.615068\pi\)
\(542\) 139.841 + 178.378i 0.258009 + 0.329111i
\(543\) 170.952i 0.314828i
\(544\) 753.012 139.220i 1.38421 0.255919i
\(545\) 442.932 0.812719
\(546\) 114.921 90.0932i 0.210478 0.165006i
\(547\) 179.104i 0.327430i 0.986508 + 0.163715i \(0.0523477\pi\)
−0.986508 + 0.163715i \(0.947652\pi\)
\(548\) −2.35584 + 9.58400i −0.00429898 + 0.0174891i
\(549\) 51.1119 0.0931000
\(550\) −10.7543 13.7180i −0.0195533 0.0249418i
\(551\) 144.351i 0.261981i
\(552\) −59.8223 132.585i −0.108374 0.240190i
\(553\) −185.576 −0.335580
\(554\) −67.3720 + 52.8169i −0.121610 + 0.0953373i
\(555\) 441.087i 0.794752i
\(556\) −952.916 234.236i −1.71388 0.421288i
\(557\) 720.325 1.29322 0.646612 0.762819i \(-0.276185\pi\)
0.646612 + 0.762819i \(0.276185\pi\)
\(558\) 12.6163 + 16.0931i 0.0226099 + 0.0288407i
\(559\) 1100.02i 1.96783i
\(560\) 52.5514 100.436i 0.0938418 0.179349i
\(561\) 52.2384 0.0931165
\(562\) −317.971 + 249.276i −0.565785 + 0.443552i
\(563\) 175.948i 0.312519i −0.987716 0.156260i \(-0.950056\pi\)
0.987716 0.156260i \(-0.0499436\pi\)
\(564\) −50.8538 + 206.883i −0.0901664 + 0.366813i
\(565\) −333.989 −0.591132
\(566\) 95.7374 + 122.121i 0.169147 + 0.215761i
\(567\) 145.857i 0.257243i
\(568\) 546.572 246.613i 0.962274 0.434178i
\(569\) −547.930 −0.962971 −0.481485 0.876454i \(-0.659903\pi\)
−0.481485 + 0.876454i \(0.659903\pi\)
\(570\) 72.9080 57.1568i 0.127909 0.100275i
\(571\) 376.007i 0.658507i 0.944242 + 0.329253i \(0.106797\pi\)
−0.944242 + 0.329253i \(0.893203\pi\)
\(572\) −38.0297 9.34807i −0.0664854 0.0163428i
\(573\) −286.305 −0.499659
\(574\) −13.1660 16.7942i −0.0229372 0.0292582i
\(575\) 72.5930i 0.126249i
\(576\) −24.6965 + 27.9829i −0.0428759 + 0.0485815i
\(577\) 458.453 0.794546 0.397273 0.917700i \(-0.369957\pi\)
0.397273 + 0.917700i \(0.369957\pi\)
\(578\) 446.483 350.024i 0.772462 0.605578i
\(579\) 807.662i 1.39493i
\(580\) 115.822 471.183i 0.199692 0.812385i
\(581\) 127.406 0.219288
\(582\) −84.1902 107.391i −0.144657 0.184521i
\(583\) 31.0008i 0.0531745i
\(584\) −160.348 355.382i −0.274569 0.608531i
\(585\) −27.7940 −0.0475112
\(586\) 514.896 403.657i 0.878663 0.688835i
\(587\) 335.174i 0.570995i 0.958379 + 0.285497i \(0.0921588\pi\)
−0.958379 + 0.285497i \(0.907841\pi\)
\(588\) 510.036 + 125.372i 0.867408 + 0.213218i
\(589\) 76.4236 0.129752
\(590\) 314.250 + 400.851i 0.532628 + 0.679408i
\(591\) 137.335i 0.232378i
\(592\) −588.435 307.890i −0.993978 0.520084i
\(593\) −280.543 −0.473092 −0.236546 0.971620i \(-0.576015\pi\)
−0.236546 + 0.971620i \(0.576015\pi\)
\(594\) −32.9266 + 25.8131i −0.0554320 + 0.0434564i
\(595\) 169.537i 0.284936i
\(596\) 49.9985 203.403i 0.0838901 0.341280i
\(597\) 729.225 1.22148
\(598\) 100.623 + 128.352i 0.168266 + 0.214636i
\(599\) 677.612i 1.13124i −0.824667 0.565619i \(-0.808637\pi\)
0.824667 0.565619i \(-0.191363\pi\)
\(600\) −245.050 + 110.566i −0.408416 + 0.184277i
\(601\) 177.699 0.295672 0.147836 0.989012i \(-0.452769\pi\)
0.147836 + 0.989012i \(0.452769\pi\)
\(602\) 257.366 201.764i 0.427518 0.335156i
\(603\) 61.3028i 0.101663i
\(604\) 98.4527 + 24.2006i 0.163001 + 0.0400673i
\(605\) 441.137 0.729152
\(606\) −548.882 700.142i −0.905746 1.15535i
\(607\) 826.068i 1.36090i −0.732793 0.680451i \(-0.761784\pi\)
0.732793 0.680451i \(-0.238216\pi\)
\(608\) 25.3588 + 137.160i 0.0417085 + 0.225593i
\(609\) −185.826 −0.305134
\(610\) 505.308 396.141i 0.828374 0.649411i
\(611\) 238.873i 0.390954i
\(612\) −13.3248 + 54.2076i −0.0217725 + 0.0885746i
\(613\) 839.090 1.36883 0.684413 0.729095i \(-0.260059\pi\)
0.684413 + 0.729095i \(0.260059\pi\)
\(614\) −331.052 422.283i −0.539173 0.687758i
\(615\) 58.6235i 0.0953227i
\(616\) 4.78823 + 10.6122i 0.00777310 + 0.0172276i
\(617\) 615.452 0.997491 0.498746 0.866748i \(-0.333794\pi\)
0.498746 + 0.866748i \(0.333794\pi\)
\(618\) −523.155 + 410.132i −0.846529 + 0.663643i
\(619\) 118.351i 0.191197i 0.995420 + 0.0955984i \(0.0304765\pi\)
−0.995420 + 0.0955984i \(0.969524\pi\)
\(620\) 249.457 + 61.3191i 0.402351 + 0.0989018i
\(621\) 174.241 0.280582
\(622\) 554.650 + 707.499i 0.891720 + 1.13746i
\(623\) 6.55547i 0.0105224i
\(624\) −280.016 + 535.162i −0.448743 + 0.857631i
\(625\) −201.251 −0.322002
\(626\) −446.854 + 350.315i −0.713824 + 0.559608i
\(627\) 9.51516i 0.0151757i
\(628\) −52.3785 + 213.085i −0.0834053 + 0.339308i
\(629\) −993.288 −1.57915
\(630\) 5.09794 + 6.50282i 0.00809197 + 0.0103219i
\(631\) 665.915i 1.05533i −0.849452 0.527667i \(-0.823067\pi\)
0.849452 0.527667i \(-0.176933\pi\)
\(632\) 699.657 315.685i 1.10705 0.499501i
\(633\) 113.127 0.178716
\(634\) −870.568 + 682.489i −1.37313 + 1.07648i
\(635\) 703.181i 1.10737i
\(636\) −464.304 114.131i −0.730038 0.179451i
\(637\) −588.902 −0.924493
\(638\) 30.7469 + 39.2200i 0.0481926 + 0.0614734i
\(639\) 43.7104i 0.0684043i
\(640\) −27.2770 + 468.057i −0.0426203 + 0.731339i
\(641\) 396.009 0.617798 0.308899 0.951095i \(-0.400039\pi\)
0.308899 + 0.951095i \(0.400039\pi\)
\(642\) −739.714 + 579.905i −1.15220 + 0.903278i
\(643\) 890.406i 1.38477i −0.721529 0.692384i \(-0.756560\pi\)
0.721529 0.692384i \(-0.243440\pi\)
\(644\) 11.5738 47.0844i 0.0179718 0.0731124i
\(645\) 898.386 1.39285
\(646\) 128.712 + 164.182i 0.199245 + 0.254152i
\(647\) 1022.42i 1.58025i 0.612945 + 0.790126i \(0.289985\pi\)
−0.612945 + 0.790126i \(0.710015\pi\)
\(648\) 248.118 + 549.907i 0.382898 + 0.848623i
\(649\) −52.3147 −0.0806082
\(650\) 237.226 185.976i 0.364964 0.286116i
\(651\) 98.3816i 0.151124i
\(652\) 104.120 + 25.5936i 0.159693 + 0.0392541i
\(653\) 298.828 0.457623 0.228811 0.973471i \(-0.426516\pi\)
0.228811 + 0.973471i \(0.426516\pi\)
\(654\) 432.890 + 552.186i 0.661912 + 0.844320i
\(655\) 338.193i 0.516324i
\(656\) 78.2070 + 40.9207i 0.119218 + 0.0623790i
\(657\) 28.4206 0.0432581
\(658\) −55.8878 + 43.8137i −0.0849358 + 0.0665861i
\(659\) 76.0870i 0.115458i −0.998332 0.0577292i \(-0.981614\pi\)
0.998332 0.0577292i \(-0.0183860\pi\)
\(660\) −7.63457 + 31.0588i −0.0115675 + 0.0470588i
\(661\) −63.4958 −0.0960602 −0.0480301 0.998846i \(-0.515294\pi\)
−0.0480301 + 0.998846i \(0.515294\pi\)
\(662\) 346.523 + 442.017i 0.523448 + 0.667699i
\(663\) 903.362i 1.36254i
\(664\) −480.346 + 216.732i −0.723413 + 0.326404i
\(665\) 30.8809 0.0464375
\(666\) 38.0990 29.8680i 0.0572056 0.0448468i
\(667\) 207.545i 0.311162i
\(668\) 243.659 + 59.8939i 0.364760 + 0.0896616i
\(669\) −549.674 −0.821636
\(670\) −475.124 606.058i −0.709141 0.904565i
\(671\) 65.9474i 0.0982822i
\(672\) 176.569 32.6449i 0.262752 0.0485787i
\(673\) −814.516 −1.21028 −0.605138 0.796120i \(-0.706882\pi\)
−0.605138 + 0.796120i \(0.706882\pi\)
\(674\) 146.602 114.930i 0.217511 0.170520i
\(675\) 322.040i 0.477097i
\(676\) 0.292826 1.19127i 0.000433175 0.00176224i
\(677\) 127.732 0.188673 0.0943365 0.995540i \(-0.469927\pi\)
0.0943365 + 0.995540i \(0.469927\pi\)
\(678\) −326.418 416.371i −0.481442 0.614117i
\(679\) 45.4866i 0.0669906i
\(680\) 288.401 + 639.187i 0.424119 + 0.939980i
\(681\) −486.311 −0.714113
\(682\) −20.7642 + 16.2782i −0.0304460 + 0.0238684i
\(683\) 518.648i 0.759367i 0.925116 + 0.379684i \(0.123967\pi\)
−0.925116 + 0.379684i \(0.876033\pi\)
\(684\) −9.87386 2.42709i −0.0144355 0.00354838i
\(685\) −9.03756 −0.0131935
\(686\) 224.959 + 286.953i 0.327929 + 0.418299i
\(687\) 589.969i 0.858761i
\(688\) −627.096 + 1198.50i −0.911476 + 1.74200i
\(689\) 536.098 0.778082
\(690\) 104.825 82.1787i 0.151921 0.119100i
\(691\) 1279.00i 1.85094i −0.378823 0.925469i \(-0.623671\pi\)
0.378823 0.925469i \(-0.376329\pi\)
\(692\) 314.110 1277.86i 0.453916 1.84662i
\(693\) −0.848678 −0.00122464
\(694\) −273.009 348.245i −0.393385 0.501793i
\(695\) 898.585i 1.29293i
\(696\) 700.601 316.111i 1.00661 0.454183i
\(697\) 132.015 0.189404
\(698\) −358.491 + 281.042i −0.513598 + 0.402639i
\(699\) 582.468i 0.833287i
\(700\) −87.0234 21.3912i −0.124319 0.0305589i
\(701\) 189.067 0.269710 0.134855 0.990865i \(-0.456943\pi\)
0.134855 + 0.990865i \(0.456943\pi\)
\(702\) −446.388 569.402i −0.635880 0.811114i
\(703\) 180.926i 0.257363i
\(704\) −36.1051 31.8648i −0.0512856 0.0452625i
\(705\) −195.087 −0.276719
\(706\) −267.300 + 209.552i −0.378612 + 0.296816i
\(707\) 296.552i 0.419452i
\(708\) −192.599 + 783.527i −0.272032 + 1.10668i
\(709\) 722.894 1.01960 0.509798 0.860294i \(-0.329720\pi\)
0.509798 + 0.860294i \(0.329720\pi\)
\(710\) 338.775 + 432.134i 0.477148 + 0.608640i
\(711\) 55.9528i 0.0786960i
\(712\) −11.1516 24.7154i −0.0156623 0.0347126i
\(713\) 109.880 0.154109
\(714\) 211.355 165.693i 0.296015 0.232064i
\(715\) 35.8614i 0.0501558i
\(716\) −1304.55 320.670i −1.82199 0.447863i
\(717\) 480.755 0.670509
\(718\) −722.997 922.239i −1.00696 1.28446i
\(719\) 768.781i 1.06924i 0.845094 + 0.534618i \(0.179545\pi\)
−0.845094 + 0.534618i \(0.820455\pi\)
\(720\) −30.2823 15.8447i −0.0420587 0.0220066i
\(721\) −221.588 −0.307334
\(722\) −29.9056 + 23.4447i −0.0414205 + 0.0324719i
\(723\) 1151.24i 1.59231i
\(724\) −56.2625 + 228.886i −0.0777107 + 0.316141i
\(725\) −383.594 −0.529095
\(726\) 431.136 + 549.948i 0.593852 + 0.757505i
\(727\) 1092.23i 1.50238i 0.660085 + 0.751191i \(0.270520\pi\)
−0.660085 + 0.751191i \(0.729480\pi\)
\(728\) −183.518 + 82.8032i −0.252085 + 0.113741i
\(729\) −769.916 −1.05613
\(730\) 280.975 220.273i 0.384897 0.301743i
\(731\) 2023.08i 2.76756i
\(732\) 987.706 + 242.788i 1.34932 + 0.331678i
\(733\) 571.768 0.780038 0.390019 0.920807i \(-0.372468\pi\)
0.390019 + 0.920807i \(0.372468\pi\)
\(734\) −529.150 674.972i −0.720912 0.919580i
\(735\) 480.956i 0.654362i
\(736\) 36.4602 + 197.206i 0.0495384 + 0.267942i
\(737\) 79.0961 0.107322
\(738\) −5.06361 + 3.96966i −0.00686126 + 0.00537894i
\(739\) 299.431i 0.405184i −0.979263 0.202592i \(-0.935063\pi\)
0.979263 0.202592i \(-0.0649365\pi\)
\(740\) 145.168 590.569i 0.196173 0.798066i
\(741\) −164.546 −0.222060
\(742\) −98.3304 125.428i −0.132521 0.169041i
\(743\) 16.0943i 0.0216612i −0.999941 0.0108306i \(-0.996552\pi\)
0.999941 0.0108306i \(-0.00344755\pi\)
\(744\) 167.358 + 370.918i 0.224944 + 0.498545i
\(745\) 191.806 0.257458
\(746\) −200.686 + 157.330i −0.269016 + 0.210898i
\(747\) 38.4142i 0.0514246i
\(748\) −69.9416 17.1924i −0.0935049 0.0229844i
\(749\) −313.313 −0.418309
\(750\) −479.703 611.899i −0.639604 0.815865i
\(751\) 699.482i 0.931401i 0.884942 + 0.465701i \(0.154198\pi\)
−0.884942 + 0.465701i \(0.845802\pi\)
\(752\) 136.176 260.257i 0.181085 0.346087i
\(753\) −724.258 −0.961830
\(754\) −678.235 + 531.708i −0.899516 + 0.705183i
\(755\) 92.8393i 0.122966i
\(756\) −51.3443 + 208.878i −0.0679157 + 0.276294i
\(757\) 11.5679 0.0152812 0.00764062 0.999971i \(-0.497568\pi\)
0.00764062 + 0.999971i \(0.497568\pi\)
\(758\) 301.901 + 385.098i 0.398286 + 0.508045i
\(759\) 13.6807i 0.0180246i
\(760\) −116.427 + 52.5319i −0.153194 + 0.0691209i
\(761\) −354.338 −0.465622 −0.232811 0.972522i \(-0.574792\pi\)
−0.232811 + 0.972522i \(0.574792\pi\)
\(762\) 876.628 687.239i 1.15043 0.901889i
\(763\) 233.884i 0.306532i
\(764\) 383.332 + 94.2267i 0.501743 + 0.123333i
\(765\) −51.1170 −0.0668195
\(766\) −845.275 1078.21i −1.10349 1.40759i
\(767\) 904.682i 1.17951i
\(768\) −610.167 + 423.441i −0.794488 + 0.551355i
\(769\) 847.602 1.10221 0.551106 0.834435i \(-0.314206\pi\)
0.551106 + 0.834435i \(0.314206\pi\)
\(770\) −8.39030 + 6.57764i −0.0108965 + 0.00854239i
\(771\) 71.3021i 0.0924801i
\(772\) −265.812 + 1081.37i −0.344316 + 1.40074i
\(773\) 712.408 0.921615 0.460807 0.887500i \(-0.347560\pi\)
0.460807 + 0.887500i \(0.347560\pi\)
\(774\) −60.8337 77.5982i −0.0785966 0.100256i
\(775\) 203.085i 0.262045i
\(776\) 77.3778 + 171.493i 0.0997137 + 0.220997i
\(777\) −232.910 −0.299755
\(778\) 456.717 358.047i 0.587040 0.460215i
\(779\) 24.0463i 0.0308682i