Properties

Label 684.3.g.b.343.3
Level $684$
Weight $3$
Character 684.343
Analytic conductor $18.638$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
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: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 343.3
Root \(1.57398 + 1.23393i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +O(q^{10})\) \(q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +(5.76533 + 4.51977i) q^{10} +0.752428i q^{11} -13.0118 q^{13} +(-2.38660 + 3.04430i) q^{14} +(-14.1766 + 7.41772i) q^{16} +23.9304 q^{17} +4.35890i q^{19} +(-3.49740 - 14.2281i) q^{20} +(0.928446 - 1.18431i) q^{22} -6.26712i q^{23} -11.5832 q^{25} +(20.4803 + 16.0557i) q^{26} +(7.51293 - 1.84675i) q^{28} -33.1165 q^{29} -17.5328i q^{31} +(31.4667 + 5.81771i) q^{32} +(-37.6660 - 29.5285i) q^{34} +7.08457i q^{35} +41.5073 q^{37} +(5.37859 - 6.86081i) q^{38} +(-12.0516 + 26.7102i) q^{40} +5.51661 q^{41} +84.5402i q^{43} +(-2.92271 + 0.718431i) q^{44} +(-7.73320 + 9.86431i) q^{46} +18.3582i q^{47} +45.2591 q^{49} +(18.2316 + 14.2929i) q^{50} +(-12.4239 - 50.5426i) q^{52} +41.2010 q^{53} -2.75607i q^{55} +(-14.1040 - 6.36370i) q^{56} +(52.1246 + 40.8635i) q^{58} +69.5279i q^{59} +87.6461 q^{61} +(-21.6343 + 27.5962i) q^{62} +(-42.3493 - 47.9848i) q^{64} +47.6609 q^{65} +105.121i q^{67} +(22.8492 + 92.9546i) q^{68} +(8.74189 - 11.1510i) q^{70} +74.9540i q^{71} +48.7353 q^{73} +(-65.3316 - 51.2173i) q^{74} +(-16.9316 + 4.16195i) q^{76} +1.45530 q^{77} -95.9473i q^{79} +(51.9277 - 27.1704i) q^{80} +(-8.68302 - 6.80713i) q^{82} -65.8722i q^{83} -87.6548 q^{85} +(104.317 - 133.064i) q^{86} +(5.48677 + 2.47563i) q^{88} -3.38934 q^{89} +25.1667i q^{91} +(24.3438 - 5.98395i) q^{92} +(22.6528 - 28.8954i) q^{94} -15.9662i q^{95} -23.5177 q^{97} +(-71.2368 - 55.8467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 0 0
\(4\) 0.954817 + 3.88437i 0.238704 + 0.971092i
\(5\) −3.66290 −0.732580 −0.366290 0.930501i \(-0.619372\pi\)
−0.366290 + 0.930501i \(0.619372\pi\)
\(6\) 0 0
\(7\) 1.93414i 0.276306i −0.990411 0.138153i \(-0.955883\pi\)
0.990411 0.138153i \(-0.0441166\pi\)
\(8\) 3.29019 7.29209i 0.411274 0.911512i
\(9\) 0 0
\(10\) 5.76533 + 4.51977i 0.576533 + 0.451977i
\(11\) 0.752428i 0.0684025i 0.999415 + 0.0342013i \(0.0108887\pi\)
−0.999415 + 0.0342013i \(0.989111\pi\)
\(12\) 0 0
\(13\) −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
\(15\) 0 0
\(16\) −14.1766 + 7.41772i −0.886041 + 0.463608i
\(17\) 23.9304 1.40767 0.703836 0.710363i \(-0.251469\pi\)
0.703836 + 0.710363i \(0.251469\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) −3.49740 14.2281i −0.174870 0.711403i
\(21\) 0 0
\(22\) 0.928446 1.18431i 0.0422021 0.0538321i
\(23\) 6.26712i 0.272483i −0.990676 0.136242i \(-0.956498\pi\)
0.990676 0.136242i \(-0.0435024\pi\)
\(24\) 0 0
\(25\) −11.5832 −0.463326
\(26\) 20.4803 + 16.0557i 0.787703 + 0.617526i
\(27\) 0 0
\(28\) 7.51293 1.84675i 0.268319 0.0659554i
\(29\) −33.1165 −1.14195 −0.570974 0.820968i \(-0.693434\pi\)
−0.570974 + 0.820968i \(0.693434\pi\)
\(30\) 0 0
\(31\) 17.5328i 0.565574i −0.959183 0.282787i \(-0.908741\pi\)
0.959183 0.282787i \(-0.0912589\pi\)
\(32\) 31.4667 + 5.81771i 0.983335 + 0.181803i
\(33\) 0 0
\(34\) −37.6660 29.5285i −1.10782 0.868487i
\(35\) 7.08457i 0.202416i
\(36\) 0 0
\(37\) 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
\(39\) 0 0
\(40\) −12.0516 + 26.7102i −0.301291 + 0.667755i
\(41\) 5.51661 0.134551 0.0672757 0.997734i \(-0.478569\pi\)
0.0672757 + 0.997734i \(0.478569\pi\)
\(42\) 0 0
\(43\) 84.5402i 1.96605i 0.183468 + 0.983026i \(0.441267\pi\)
−0.183468 + 0.983026i \(0.558733\pi\)
\(44\) −2.92271 + 0.718431i −0.0664252 + 0.0163280i
\(45\) 0 0
\(46\) −7.73320 + 9.86431i −0.168113 + 0.214441i
\(47\) 18.3582i 0.390599i 0.980744 + 0.195300i \(0.0625679\pi\)
−0.980744 + 0.195300i \(0.937432\pi\)
\(48\) 0 0
\(49\) 45.2591 0.923655
\(50\) 18.2316 + 14.2929i 0.364633 + 0.285857i
\(51\) 0 0
\(52\) −12.4239 50.5426i −0.238921 0.971973i
\(53\) 41.2010 0.777377 0.388688 0.921369i \(-0.372928\pi\)
0.388688 + 0.921369i \(0.372928\pi\)
\(54\) 0 0
\(55\) 2.75607i 0.0501103i
\(56\) −14.1040 6.36370i −0.251856 0.113638i
\(57\) 0 0
\(58\) 52.1246 + 40.8635i 0.898701 + 0.704544i
\(59\) 69.5279i 1.17844i 0.807973 + 0.589219i \(0.200565\pi\)
−0.807973 + 0.589219i \(0.799435\pi\)
\(60\) 0 0
\(61\) 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
\(63\) 0 0
\(64\) −42.3493 47.9848i −0.661707 0.749762i
\(65\) 47.6609 0.733244
\(66\) 0 0
\(67\) 105.121i 1.56897i 0.620145 + 0.784487i \(0.287074\pi\)
−0.620145 + 0.784487i \(0.712926\pi\)
\(68\) 22.8492 + 92.9546i 0.336017 + 1.36698i
\(69\) 0 0
\(70\) 8.74189 11.1510i 0.124884 0.159300i
\(71\) 74.9540i 1.05569i 0.849341 + 0.527845i \(0.177000\pi\)
−0.849341 + 0.527845i \(0.823000\pi\)
\(72\) 0 0
\(73\) 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
\(75\) 0 0
\(76\) −16.9316 + 4.16195i −0.222784 + 0.0547625i
\(77\) 1.45530 0.0189000
\(78\) 0 0
\(79\) 95.9473i 1.21452i −0.794502 0.607261i \(-0.792268\pi\)
0.794502 0.607261i \(-0.207732\pi\)
\(80\) 51.9277 27.1704i 0.649096 0.339630i
\(81\) 0 0
\(82\) −8.68302 6.80713i −0.105890 0.0830137i
\(83\) 65.8722i 0.793641i −0.917896 0.396821i \(-0.870114\pi\)
0.917896 0.396821i \(-0.129886\pi\)
\(84\) 0 0
\(85\) −87.6548 −1.03123
\(86\) 104.317 133.064i 1.21299 1.54726i
\(87\) 0 0
\(88\) 5.48677 + 2.47563i 0.0623497 + 0.0281322i
\(89\) −3.38934 −0.0380825 −0.0190412 0.999819i \(-0.506061\pi\)
−0.0190412 + 0.999819i \(0.506061\pi\)
\(90\) 0 0
\(91\) 25.1667i 0.276557i
\(92\) 24.3438 5.98395i 0.264606 0.0650429i
\(93\) 0 0
\(94\) 22.6528 28.8954i 0.240987 0.307397i
\(95\) 15.9662i 0.168065i
\(96\) 0 0
\(97\) −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 0
\(100\) −11.0598 44.9933i −0.110598 0.449933i
\(101\) 153.325 1.51807 0.759035 0.651050i \(-0.225671\pi\)
0.759035 + 0.651050i \(0.225671\pi\)
\(102\) 0 0
\(103\) 114.566i 1.11229i −0.831084 0.556147i \(-0.812279\pi\)
0.831084 0.556147i \(-0.187721\pi\)
\(104\) −42.8113 + 94.8832i −0.411647 + 0.912338i
\(105\) 0 0
\(106\) −64.8494 50.8392i −0.611787 0.479616i
\(107\) 161.991i 1.51393i 0.653454 + 0.756966i \(0.273319\pi\)
−0.653454 + 0.756966i \(0.726681\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) 14.3469 + 27.4197i 0.128098 + 0.244818i
\(113\) 91.1817 0.806918 0.403459 0.914998i \(-0.367808\pi\)
0.403459 + 0.914998i \(0.367808\pi\)
\(114\) 0 0
\(115\) 22.9558i 0.199616i
\(116\) −31.6202 128.637i −0.272588 1.10894i
\(117\) 0 0
\(118\) 85.7928 109.435i 0.727057 0.927418i
\(119\) 46.2849i 0.388948i
\(120\) 0 0
\(121\) 120.434 0.995321
\(122\) −137.953 108.149i −1.13076 0.886471i
\(123\) 0 0
\(124\) 68.1038 16.7406i 0.549224 0.135005i
\(125\) 134.000 1.07200
\(126\) 0 0
\(127\) 191.974i 1.51160i 0.654800 + 0.755802i \(0.272753\pi\)
−0.654800 + 0.755802i \(0.727247\pi\)
\(128\) 7.44683 + 127.783i 0.0581783 + 0.998306i
\(129\) 0 0
\(130\) −75.0172 58.8104i −0.577055 0.452387i
\(131\) 92.3292i 0.704803i −0.935849 0.352401i \(-0.885365\pi\)
0.935849 0.352401i \(-0.114635\pi\)
\(132\) 0 0
\(133\) 8.43073 0.0633890
\(134\) 129.713 165.459i 0.968005 1.23477i
\(135\) 0 0
\(136\) 78.7357 174.503i 0.578939 1.28311i
\(137\) 2.46732 0.0180097 0.00900483 0.999959i \(-0.497134\pi\)
0.00900483 + 0.999959i \(0.497134\pi\)
\(138\) 0 0
\(139\) 245.321i 1.76490i 0.470409 + 0.882448i \(0.344106\pi\)
−0.470409 + 0.882448i \(0.655894\pi\)
\(140\) −27.5191 + 6.76447i −0.196565 + 0.0483176i
\(141\) 0 0
\(142\) 92.4883 117.976i 0.651326 0.830817i
\(143\) 9.79043i 0.0684646i
\(144\) 0 0
\(145\) 121.302 0.836568
\(146\) −76.7083 60.1361i −0.525399 0.411891i
\(147\) 0 0
\(148\) 39.6319 + 161.230i 0.267783 + 1.08939i
\(149\) −52.3645 −0.351439 −0.175720 0.984440i \(-0.556225\pi\)
−0.175720 + 0.984440i \(0.556225\pi\)
\(150\) 0 0
\(151\) 25.3459i 0.167853i −0.996472 0.0839267i \(-0.973254\pi\)
0.996472 0.0839267i \(-0.0267461\pi\)
\(152\) 31.7855 + 14.3416i 0.209115 + 0.0943527i
\(153\) 0 0
\(154\) −2.29062 1.79575i −0.0148741 0.0116607i
\(155\) 64.2208i 0.414328i
\(156\) 0 0
\(157\) −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
\(159\) 0 0
\(160\) −115.259 21.3097i −0.720372 0.133185i
\(161\) −12.1215 −0.0752888
\(162\) 0 0
\(163\) 26.8048i 0.164446i −0.996614 0.0822232i \(-0.973798\pi\)
0.996614 0.0822232i \(-0.0262020\pi\)
\(164\) 5.26735 + 21.4285i 0.0321180 + 0.130662i
\(165\) 0 0
\(166\) −81.2819 + 103.681i −0.489650 + 0.624587i
\(167\) 62.7282i 0.375618i 0.982206 + 0.187809i \(0.0601386\pi\)
−0.982206 + 0.187809i \(0.939861\pi\)
\(168\) 0 0
\(169\) 0.306683 0.00181469
\(170\) 137.967 + 108.160i 0.811569 + 0.636236i
\(171\) 0 0
\(172\) −328.385 + 80.7204i −1.90922 + 0.469305i
\(173\) −328.974 −1.90159 −0.950793 0.309827i \(-0.899729\pi\)
−0.950793 + 0.309827i \(0.899729\pi\)
\(174\) 0 0
\(175\) 22.4035i 0.128020i
\(176\) −5.58130 10.6669i −0.0317119 0.0606074i
\(177\) 0 0
\(178\) 5.33475 + 4.18222i 0.0299705 + 0.0234956i
\(179\) 335.845i 1.87623i −0.346327 0.938114i \(-0.612571\pi\)
0.346327 0.938114i \(-0.387429\pi\)
\(180\) 0 0
\(181\) −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
\(183\) 0 0
\(184\) −45.7004 20.6200i −0.248372 0.112065i
\(185\) −152.037 −0.821823
\(186\) 0 0
\(187\) 18.0059i 0.0962883i
\(188\) −71.3099 + 17.5287i −0.379308 + 0.0932377i
\(189\) 0 0
\(190\) −19.7012 + 25.1305i −0.103691 + 0.132266i
\(191\) 98.6857i 0.516679i 0.966054 + 0.258339i \(0.0831753\pi\)
−0.966054 + 0.258339i \(0.916825\pi\)
\(192\) 0 0
\(193\) −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
\(195\) 0 0
\(196\) 43.2141 + 175.803i 0.220480 + 0.896954i
\(197\) 47.3378 0.240293 0.120147 0.992756i \(-0.461664\pi\)
0.120147 + 0.992756i \(0.461664\pi\)
\(198\) 0 0
\(199\) 251.355i 1.26309i 0.775340 + 0.631545i \(0.217579\pi\)
−0.775340 + 0.631545i \(0.782421\pi\)
\(200\) −38.1108 + 84.4655i −0.190554 + 0.422328i
\(201\) 0 0
\(202\) −241.330 189.193i −1.19470 0.936598i
\(203\) 64.0520i 0.315527i
\(204\) 0 0
\(205\) −20.2068 −0.0985697
\(206\) −141.367 + 180.325i −0.686249 + 0.875364i
\(207\) 0 0
\(208\) 184.464 96.5178i 0.886844 0.464028i
\(209\) −3.27976 −0.0156926
\(210\) 0 0
\(211\) 38.9936i 0.184804i 0.995722 + 0.0924019i \(0.0294544\pi\)
−0.995722 + 0.0924019i \(0.970546\pi\)
\(212\) 39.3394 + 160.040i 0.185563 + 0.754905i
\(213\) 0 0
\(214\) 199.886 254.970i 0.934046 1.19145i
\(215\) 309.662i 1.44029i
\(216\) 0 0
\(217\) −33.9109 −0.156272
\(218\) −190.331 149.212i −0.873080 0.684458i
\(219\) 0 0
\(220\) 10.7056 2.63154i 0.0486618 0.0119615i
\(221\) −311.378 −1.40895
\(222\) 0 0
\(223\) 189.466i 0.849622i −0.905282 0.424811i \(-0.860340\pi\)
0.905282 0.424811i \(-0.139660\pi\)
\(224\) 11.2523 60.8611i 0.0502334 0.271702i
\(225\) 0 0
\(226\) −143.518 112.512i −0.635035 0.497841i
\(227\) 167.625i 0.738438i 0.929342 + 0.369219i \(0.120375\pi\)
−0.929342 + 0.369219i \(0.879625\pi\)
\(228\) 0 0
\(229\) 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
\(231\) 0 0
\(232\) −108.960 + 241.489i −0.469653 + 1.04090i
\(233\) 200.769 0.861671 0.430836 0.902430i \(-0.358219\pi\)
0.430836 + 0.902430i \(0.358219\pi\)
\(234\) 0 0
\(235\) 67.2441i 0.286145i
\(236\) −270.072 + 66.3864i −1.14437 + 0.281298i
\(237\) 0 0
\(238\) −57.1124 + 72.8514i −0.239968 + 0.306098i
\(239\) 165.710i 0.693349i −0.937986 0.346674i \(-0.887311\pi\)
0.937986 0.346674i \(-0.112689\pi\)
\(240\) 0 0
\(241\) −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
\(243\) 0 0
\(244\) 83.6860 + 340.450i 0.342975 + 1.39529i
\(245\) −165.780 −0.676651
\(246\) 0 0
\(247\) 56.7171i 0.229624i
\(248\) −127.851 57.6862i −0.515527 0.232606i
\(249\) 0 0
\(250\) −210.914 165.348i −0.843655 0.661391i
\(251\) 249.643i 0.994592i 0.867581 + 0.497296i \(0.165674\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(252\) 0 0
\(253\) 4.71555 0.0186385
\(254\) 236.883 302.163i 0.932610 1.18962i
\(255\) 0 0
\(256\) 145.955 210.317i 0.570136 0.821550i
\(257\) −24.5770 −0.0956302 −0.0478151 0.998856i \(-0.515226\pi\)
−0.0478151 + 0.998856i \(0.515226\pi\)
\(258\) 0 0
\(259\) 80.2811i 0.309966i
\(260\) 45.5074 + 185.132i 0.175029 + 0.712048i
\(261\) 0 0
\(262\) −113.928 + 145.324i −0.434840 + 0.554672i
\(263\) 343.809i 1.30726i 0.756816 + 0.653628i \(0.226754\pi\)
−0.756816 + 0.653628i \(0.773246\pi\)
\(264\) 0 0
\(265\) −150.915 −0.569491
\(266\) −13.2698 10.4030i −0.0498864 0.0391089i
\(267\) 0 0
\(268\) −408.330 + 100.372i −1.52362 + 0.374521i
\(269\) −64.7826 −0.240828 −0.120414 0.992724i \(-0.538422\pi\)
−0.120414 + 0.992724i \(0.538422\pi\)
\(270\) 0 0
\(271\) 113.329i 0.418189i −0.977895 0.209095i \(-0.932948\pi\)
0.977895 0.209095i \(-0.0670517\pi\)
\(272\) −339.253 + 177.509i −1.24725 + 0.652607i
\(273\) 0 0
\(274\) −3.88352 3.04451i −0.0141734 0.0111114i
\(275\) 8.71549i 0.0316927i
\(276\) 0 0
\(277\) −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
\(279\) 0 0
\(280\) 51.6614 + 23.3096i 0.184505 + 0.0832486i
\(281\) 202.018 0.718924 0.359462 0.933160i \(-0.382960\pi\)
0.359462 + 0.933160i \(0.382960\pi\)
\(282\) 0 0
\(283\) 77.5872i 0.274160i −0.990560 0.137080i \(-0.956228\pi\)
0.990560 0.137080i \(-0.0437717\pi\)
\(284\) −291.149 + 71.5674i −1.02517 + 0.251998i
\(285\) 0 0
\(286\) −12.0807 + 15.4099i −0.0422404 + 0.0538809i
\(287\) 10.6699i 0.0371774i
\(288\) 0 0
\(289\) 283.665 0.981540
\(290\) −190.927 149.679i −0.658370 0.516135i
\(291\) 0 0
\(292\) 46.5333 + 189.306i 0.159360 + 0.648308i
\(293\) −327.131 −1.11649 −0.558243 0.829677i \(-0.688524\pi\)
−0.558243 + 0.829677i \(0.688524\pi\)
\(294\) 0 0
\(295\) 254.674i 0.863300i
\(296\) 136.567 302.675i 0.461375 1.02255i
\(297\) 0 0
\(298\) 82.4206 + 64.6143i 0.276579 + 0.216826i
\(299\) 81.5464i 0.272730i
\(300\) 0 0
\(301\) 163.513 0.543232
\(302\) −31.2751 + 39.8938i −0.103560 + 0.132099i
\(303\) 0 0
\(304\) −32.3331 61.7946i −0.106359 0.203272i
\(305\) −321.039 −1.05259
\(306\) 0 0
\(307\) 268.290i 0.873910i 0.899483 + 0.436955i \(0.143943\pi\)
−0.899483 + 0.436955i \(0.856057\pi\)
\(308\) 1.38955 + 5.65294i 0.00451152 + 0.0183537i
\(309\) 0 0
\(310\) 79.2442 101.082i 0.255627 0.326072i
\(311\) 449.497i 1.44533i 0.691199 + 0.722664i \(0.257083\pi\)
−0.691199 + 0.722664i \(0.742917\pi\)
\(312\) 0 0
\(313\) −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
\(315\) 0 0
\(316\) 372.695 91.6121i 1.17941 0.289912i
\(317\) 553.100 1.74480 0.872398 0.488797i \(-0.162564\pi\)
0.872398 + 0.488797i \(0.162564\pi\)
\(318\) 0 0
\(319\) 24.9178i 0.0781121i
\(320\) 155.121 + 175.763i 0.484754 + 0.549261i
\(321\) 0 0
\(322\) 19.0790 + 14.9571i 0.0592515 + 0.0464507i
\(323\) 104.310i 0.322942i
\(324\) 0 0
\(325\) 150.718 0.463747
\(326\) −33.0753 + 42.1901i −0.101458 + 0.129418i
\(327\) 0 0
\(328\) 18.1507 40.2276i 0.0553375 0.122645i
\(329\) 35.5073 0.107925
\(330\) 0 0
\(331\) 280.828i 0.848422i −0.905563 0.424211i \(-0.860552\pi\)
0.905563 0.424211i \(-0.139448\pi\)
\(332\) 255.872 62.8959i 0.770699 0.189445i
\(333\) 0 0
\(334\) 77.4024 98.7328i 0.231744 0.295607i
\(335\) 385.049i 1.14940i
\(336\) 0 0
\(337\) 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
\(339\) 0 0
\(340\) −83.6942 340.483i −0.246159 1.00142i
\(341\) 13.1922 0.0386867
\(342\) 0 0
\(343\) 182.311i 0.531518i
\(344\) 616.475 + 278.153i 1.79208 + 0.808586i
\(345\) 0 0
\(346\) 517.799 + 405.932i 1.49653 + 1.17322i
\(347\) 221.251i 0.637612i −0.947820 0.318806i \(-0.896718\pi\)
0.947820 0.318806i \(-0.103282\pi\)
\(348\) 0 0
\(349\) −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
\(351\) 0 0
\(352\) −4.37740 + 23.6764i −0.0124358 + 0.0672626i
\(353\) 169.824 0.481089 0.240545 0.970638i \(-0.422674\pi\)
0.240545 + 0.970638i \(0.422674\pi\)
\(354\) 0 0
\(355\) 274.549i 0.773378i
\(356\) −3.23620 13.1654i −0.00909045 0.0369816i
\(357\) 0 0
\(358\) −414.410 + 528.612i −1.15757 + 1.47657i
\(359\) 585.928i 1.63211i −0.577972 0.816056i \(-0.696156\pi\)
0.577972 0.816056i \(-0.303844\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) 92.7466 + 72.7095i 0.256206 + 0.200855i
\(363\) 0 0
\(364\) −97.7566 + 24.0296i −0.268562 + 0.0660153i
\(365\) −178.512 −0.489075
\(366\) 0 0
\(367\) 428.832i 1.16848i 0.811581 + 0.584239i \(0.198607\pi\)
−0.811581 + 0.584239i \(0.801393\pi\)
\(368\) 46.4877 + 88.8467i 0.126325 + 0.241431i
\(369\) 0 0
\(370\) 239.303 + 187.604i 0.646766 + 0.507037i
\(371\) 79.6886i 0.214794i
\(372\) 0 0
\(373\) −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
\(375\) 0 0
\(376\) 133.869 + 60.4019i 0.356036 + 0.160643i
\(377\) 430.905 1.14298
\(378\) 0 0
\(379\) 244.665i 0.645555i −0.946475 0.322777i \(-0.895384\pi\)
0.946475 0.322777i \(-0.104616\pi\)
\(380\) 62.0187 15.2448i 0.163207 0.0401179i
\(381\) 0 0
\(382\) 121.772 155.329i 0.318774 0.406621i
\(383\) 685.025i 1.78858i −0.447491 0.894288i \(-0.647682\pi\)
0.447491 0.894288i \(-0.352318\pi\)
\(384\) 0 0
\(385\) −5.33063 −0.0138458
\(386\) 438.181 + 343.516i 1.13518 + 0.889937i
\(387\) 0 0
\(388\) −22.4551 91.3515i −0.0578740 0.235442i
\(389\) −290.167 −0.745931 −0.372966 0.927845i \(-0.621659\pi\)
−0.372966 + 0.927845i \(0.621659\pi\)
\(390\) 0 0
\(391\) 149.975i 0.383567i
\(392\) 148.911 330.034i 0.379875 0.841922i
\(393\) 0 0
\(394\) −74.5086 58.4117i −0.189108 0.148253i
\(395\) 351.445i 0.889735i
\(396\) 0 0
\(397\) 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
\(399\) 0 0
\(400\) 164.210 85.9207i 0.410526 0.214802i
\(401\) −445.424 −1.11078 −0.555392 0.831589i \(-0.687432\pi\)
−0.555392 + 0.831589i \(0.687432\pi\)
\(402\) 0 0
\(403\) 228.133i 0.566087i
\(404\) 146.397 + 595.571i 0.362369 + 1.47419i
\(405\) 0 0
\(406\) 79.0359 100.817i 0.194670 0.248317i
\(407\) 31.2313i 0.0767353i
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) 445.018 109.390i 1.08014 0.265509i
\(413\) 134.477 0.325610
\(414\) 0 0
\(415\) 241.283i 0.581406i
\(416\) −409.438 75.6988i −0.984227 0.181968i
\(417\) 0 0
\(418\) 5.16227 + 4.04700i 0.0123499 + 0.00968182i
\(419\) 308.595i 0.736502i 0.929726 + 0.368251i \(0.120043\pi\)
−0.929726 + 0.368251i \(0.879957\pi\)
\(420\) 0 0
\(421\) 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
\(423\) 0 0
\(424\) 135.559 300.441i 0.319715 0.708588i
\(425\) −277.190 −0.652212
\(426\) 0 0
\(427\) 169.520i 0.397003i
\(428\) −629.232 + 154.672i −1.47017 + 0.361382i
\(429\) 0 0
\(430\) −382.103 + 487.402i −0.888611 + 1.13349i
\(431\) 479.659i 1.11290i −0.830881 0.556450i \(-0.812163\pi\)
0.830881 0.556450i \(-0.187837\pi\)
\(432\) 0 0
\(433\) 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
\(435\) 0 0
\(436\) 115.460 + 469.713i 0.264817 + 1.07732i
\(437\) 27.3177 0.0625120
\(438\) 0 0
\(439\) 25.4779i 0.0580363i −0.999579 0.0290182i \(-0.990762\pi\)
0.999579 0.0290182i \(-0.00923807\pi\)
\(440\) −20.0975 9.06799i −0.0456762 0.0206091i
\(441\) 0 0
\(442\) 490.102 + 384.219i 1.10883 + 0.869274i
\(443\) 805.631i 1.81858i 0.416164 + 0.909290i \(0.363374\pi\)
−0.416164 + 0.909290i \(0.636626\pi\)
\(444\) 0 0
\(445\) 12.4148 0.0278985
\(446\) −233.788 + 298.215i −0.524189 + 0.668644i
\(447\) 0 0
\(448\) −92.8094 + 81.9096i −0.207164 + 0.182834i
\(449\) 106.288 0.236721 0.118360 0.992971i \(-0.462236\pi\)
0.118360 + 0.992971i \(0.462236\pi\)
\(450\) 0 0
\(451\) 4.15085i 0.00920366i
\(452\) 87.0618 + 354.183i 0.192615 + 0.783591i
\(453\) 0 0
\(454\) 206.839 263.839i 0.455592 0.581143i
\(455\) 92.1830i 0.202600i
\(456\) 0 0
\(457\) −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
\(459\) 0 0
\(460\) −89.1689 + 21.9186i −0.193845 + 0.0476491i
\(461\) 854.696 1.85401 0.927003 0.375055i \(-0.122376\pi\)
0.927003 + 0.375055i \(0.122376\pi\)
\(462\) 0 0
\(463\) 769.128i 1.66118i −0.556882 0.830591i \(-0.688003\pi\)
0.556882 0.830591i \(-0.311997\pi\)
\(464\) 469.481 245.649i 1.01181 0.529416i
\(465\) 0 0
\(466\) −316.007 247.736i −0.678126 0.531622i
\(467\) 54.2556i 0.116179i 0.998311 + 0.0580895i \(0.0185009\pi\)
−0.998311 + 0.0580895i \(0.981499\pi\)
\(468\) 0 0
\(469\) 203.320 0.433517
\(470\) −82.9748 + 105.841i −0.176542 + 0.225193i
\(471\) 0 0
\(472\) 507.004 + 228.760i 1.07416 + 0.484661i
\(473\) −63.6104 −0.134483
\(474\) 0 0
\(475\) 50.4898i 0.106294i
\(476\) 179.788 44.1936i 0.377705 0.0928436i
\(477\) 0 0
\(478\) −204.475 + 260.824i −0.427773 + 0.545658i
\(479\) 512.359i 1.06964i −0.844965 0.534821i \(-0.820379\pi\)
0.844965 0.534821i \(-0.179621\pi\)
\(480\) 0 0
\(481\) −540.085 −1.12284
\(482\) 624.582 + 489.646i 1.29581 + 1.01586i
\(483\) 0 0
\(484\) 114.992 + 467.810i 0.237587 + 0.966549i
\(485\) 86.1431 0.177615
\(486\) 0 0
\(487\) 445.189i 0.914146i 0.889429 + 0.457073i \(0.151102\pi\)
−0.889429 + 0.457073i \(0.848898\pi\)
\(488\) 288.373 639.124i 0.590927 1.30968i
\(489\) 0 0
\(490\) 260.933 + 204.561i 0.532517 + 0.417471i
\(491\) 219.288i 0.446615i −0.974748 0.223308i \(-0.928315\pi\)
0.974748 0.223308i \(-0.0716855\pi\)
\(492\) 0 0
\(493\) −792.492 −1.60749
\(494\) −69.9851 + 89.2715i −0.141670 + 0.180711i
\(495\) 0 0
\(496\) 130.053 + 248.556i 0.262204 + 0.501121i
\(497\) 144.972 0.291694
\(498\) 0 0
\(499\) 277.168i 0.555446i 0.960661 + 0.277723i \(0.0895798\pi\)
−0.960661 + 0.277723i \(0.910420\pi\)
\(500\) 127.946 + 520.507i 0.255892 + 1.04101i
\(501\) 0 0
\(502\) 308.042 392.932i 0.613630 0.782733i
\(503\) 328.913i 0.653903i 0.945041 + 0.326951i \(0.106021\pi\)
−0.945041 + 0.326951i \(0.893979\pi\)
\(504\) 0 0
\(505\) −561.614 −1.11211
\(506\) −7.42218 5.81868i −0.0146683 0.0114994i
\(507\) 0 0
\(508\) −745.697 + 183.300i −1.46791 + 0.360826i
\(509\) 371.573 0.730006 0.365003 0.931006i \(-0.381068\pi\)
0.365003 + 0.931006i \(0.381068\pi\)
\(510\) 0 0
\(511\) 94.2610i 0.184464i
\(512\) −489.247 + 150.936i −0.955560 + 0.294796i
\(513\) 0 0
\(514\) 38.6836 + 30.3263i 0.0752599 + 0.0590006i
\(515\) 419.645i 0.814845i
\(516\) 0 0
\(517\) −13.8132 −0.0267180
\(518\) −99.0616 + 126.361i −0.191239 + 0.243940i
\(519\) 0 0
\(520\) 156.813 347.548i 0.301564 0.668361i
\(521\) 607.799 1.16660 0.583300 0.812256i \(-0.301761\pi\)
0.583300 + 0.812256i \(0.301761\pi\)
\(522\) 0 0
\(523\) 384.474i 0.735131i −0.929998 0.367566i \(-0.880191\pi\)
0.929998 0.367566i \(-0.119809\pi\)
\(524\) 358.641 88.1574i 0.684429 0.168239i
\(525\) 0 0
\(526\) 424.237 541.147i 0.806534 1.02880i
\(527\) 419.567i 0.796142i
\(528\) 0 0
\(529\) 489.723 0.925753
\(530\) 237.537 + 186.219i 0.448183 + 0.351357i
\(531\) 0 0
\(532\) 8.04981 + 32.7481i 0.0151312 + 0.0615566i
\(533\) −71.7809 −0.134673
\(534\) 0 0
\(535\) 593.356i 1.10908i
\(536\) 766.554 + 345.869i 1.43014 + 0.645278i
\(537\) 0 0
\(538\) 101.966 + 79.9375i 0.189529 + 0.148583i
\(539\) 34.0542i 0.0631803i
\(540\) 0 0
\(541\) −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
\(543\) 0 0
\(544\) 753.012 + 139.220i 1.38421 + 0.255919i
\(545\) −442.932 −0.812719
\(546\) 0 0
\(547\) 179.104i 0.327430i −0.986508 0.163715i \(-0.947652\pi\)
0.986508 0.163715i \(-0.0523477\pi\)
\(548\) 2.35584 + 9.58400i 0.00429898 + 0.0174891i
\(549\) 0 0
\(550\) −10.7543 + 13.7180i −0.0195533 + 0.0249418i
\(551\) 144.351i 0.261981i
\(552\) 0 0
\(553\) −185.576 −0.335580
\(554\) 67.3720 + 52.8169i 0.121610 + 0.0953373i
\(555\) 0 0
\(556\) −952.916 + 234.236i −1.71388 + 0.421288i
\(557\) −720.325 −1.29322 −0.646612 0.762819i \(-0.723815\pi\)
−0.646612 + 0.762819i \(0.723815\pi\)
\(558\) 0 0
\(559\) 1100.02i 1.96783i
\(560\) −52.5514 100.436i −0.0938418 0.179349i
\(561\) 0 0
\(562\) −317.971 249.276i −0.565785 0.443552i
\(563\) 175.948i 0.312519i −0.987716 0.156260i \(-0.950056\pi\)
0.987716 0.156260i \(-0.0499436\pi\)
\(564\) 0 0
\(565\) −333.989 −0.591132
\(566\) −95.7374 + 122.121i −0.169147 + 0.215761i
\(567\) 0 0
\(568\) 546.572 + 246.613i 0.962274 + 0.434178i
\(569\) 547.930 0.962971 0.481485 0.876454i \(-0.340097\pi\)
0.481485 + 0.876454i \(0.340097\pi\)
\(570\) 0 0
\(571\) 376.007i 0.658507i −0.944242 0.329253i \(-0.893203\pi\)
0.944242 0.329253i \(-0.106797\pi\)
\(572\) 38.0297 9.34807i 0.0664854 0.0163428i
\(573\) 0 0
\(574\) −13.1660 + 16.7942i −0.0229372 + 0.0292582i
\(575\) 72.5930i 0.126249i
\(576\) 0 0
\(577\) 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
\(579\) 0 0
\(580\) 115.822 + 471.183i 0.199692 + 0.812385i
\(581\) −127.406 −0.219288
\(582\) 0 0
\(583\) 31.0008i 0.0531745i
\(584\) 160.348 355.382i 0.274569 0.608531i
\(585\) 0 0
\(586\) 514.896 + 403.657i 0.878663 + 0.688835i
\(587\) 335.174i 0.570995i 0.958379 + 0.285497i \(0.0921588\pi\)
−0.958379 + 0.285497i \(0.907841\pi\)
\(588\) 0 0
\(589\) 76.4236 0.129752
\(590\) −314.250 + 400.851i −0.532628 + 0.679408i
\(591\) 0 0
\(592\) −588.435 + 307.890i −0.993978 + 0.520084i
\(593\) 280.543 0.473092 0.236546 0.971620i \(-0.423985\pi\)
0.236546 + 0.971620i \(0.423985\pi\)
\(594\) 0 0
\(595\) 169.537i 0.284936i
\(596\) −49.9985 203.403i −0.0838901 0.341280i
\(597\) 0 0
\(598\) 100.623 128.352i 0.168266 0.214636i
\(599\) 677.612i 1.13124i −0.824667 0.565619i \(-0.808637\pi\)
0.824667 0.565619i \(-0.191363\pi\)
\(600\) 0 0
\(601\) 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
\(603\) 0 0
\(604\) 98.4527 24.2006i 0.163001 0.0400673i
\(605\) −441.137 −0.729152
\(606\) 0 0
\(607\) 826.068i 1.36090i 0.732793 + 0.680451i \(0.238216\pi\)
−0.732793 + 0.680451i \(0.761784\pi\)
\(608\) −25.3588 + 137.160i −0.0417085 + 0.225593i
\(609\) 0 0
\(610\) 505.308 + 396.141i 0.828374 + 0.649411i
\(611\) 238.873i 0.390954i
\(612\) 0 0
\(613\) 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
\(615\) 0 0
\(616\) 4.78823 10.6122i 0.00777310 0.0172276i
\(617\) −615.452 −0.997491 −0.498746 0.866748i \(-0.666206\pi\)
−0.498746 + 0.866748i \(0.666206\pi\)
\(618\) 0 0
\(619\) 118.351i 0.191197i −0.995420 0.0955984i \(-0.969524\pi\)
0.995420 0.0955984i \(-0.0304765\pi\)
\(620\) −249.457 + 61.3191i −0.402351 + 0.0989018i
\(621\) 0 0
\(622\) 554.650 707.499i 0.891720 1.13746i
\(623\) 6.55547i 0.0105224i
\(624\) 0 0
\(625\) −201.251 −0.322002
\(626\) 446.854 + 350.315i 0.713824 + 0.559608i
\(627\) 0 0
\(628\) −52.3785 213.085i −0.0834053 0.339308i
\(629\) 993.288 1.57915
\(630\) 0 0
\(631\) 665.915i 1.05533i 0.849452 + 0.527667i \(0.176933\pi\)
−0.849452 + 0.527667i \(0.823067\pi\)
\(632\) −699.657 315.685i −1.10705 0.499501i
\(633\) 0 0
\(634\) −870.568 682.489i −1.37313 1.07648i
\(635\) 703.181i 1.10737i
\(636\) 0 0
\(637\) −588.902 −0.924493
\(638\) −30.7469 + 39.2200i −0.0481926 + 0.0614734i
\(639\) 0 0
\(640\) −27.2770 468.057i −0.0426203 0.731339i
\(641\) −396.009 −0.617798 −0.308899 0.951095i \(-0.599961\pi\)
−0.308899 + 0.951095i \(0.599961\pi\)
\(642\) 0 0
\(643\) 890.406i 1.38477i 0.721529 + 0.692384i \(0.243440\pi\)
−0.721529 + 0.692384i \(0.756560\pi\)
\(644\) −11.5738 47.0844i −0.0179718 0.0731124i
\(645\) 0 0
\(646\) 128.712 164.182i 0.199245 0.254152i
\(647\) 1022.42i 1.58025i 0.612945 + 0.790126i \(0.289985\pi\)
−0.612945 + 0.790126i \(0.710015\pi\)
\(648\) 0 0
\(649\) −52.3147 −0.0806082
\(650\) −237.226 185.976i −0.364964 0.286116i
\(651\) 0 0
\(652\) 104.120 25.5936i 0.159693 0.0392541i
\(653\) −298.828 −0.457623 −0.228811 0.973471i \(-0.573484\pi\)
−0.228811 + 0.973471i \(0.573484\pi\)
\(654\) 0 0
\(655\) 338.193i 0.516324i
\(656\) −78.2070 + 40.9207i −0.119218 + 0.0623790i
\(657\) 0 0
\(658\) −55.8878 43.8137i −0.0849358 0.0665861i
\(659\) 76.0870i 0.115458i −0.998332 0.0577292i \(-0.981614\pi\)
0.998332 0.0577292i \(-0.0183860\pi\)
\(660\) 0 0
\(661\) −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
\(663\) 0 0
\(664\) −480.346 216.732i −0.723413 0.326404i
\(665\) −30.8809 −0.0464375
\(666\) 0 0
\(667\) 207.545i 0.311162i
\(668\) −243.659 + 59.8939i −0.364760 + 0.0896616i
\(669\) 0 0
\(670\) −475.124 + 606.058i −0.709141 + 0.904565i
\(671\) 65.9474i 0.0982822i
\(672\) 0 0
\(673\) −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
\(675\) 0 0
\(676\) 0.292826 + 1.19127i 0.000433175 + 0.00176224i
\(677\) −127.732 −0.188673 −0.0943365 0.995540i \(-0.530073\pi\)
−0.0943365 + 0.995540i \(0.530073\pi\)
\(678\) 0 0
\(679\) 45.4866i 0.0669906i
\(680\) −288.401 + 639.187i −0.424119 + 0.939980i
\(681\) 0 0
\(682\) −20.7642 16.2782i −0.0304460 0.0238684i
\(683\) 518.648i 0.759367i 0.925116 + 0.379684i \(0.123967\pi\)
−0.925116 + 0.379684i \(0.876033\pi\)
\(684\) 0 0
\(685\) −9.03756 −0.0131935
\(686\) −224.959 + 286.953i −0.327929 + 0.418299i
\(687\) 0 0
\(688\) −627.096 1198.50i −0.911476 1.74200i
\(689\) −536.098 −0.778082
\(690\) 0 0
\(691\) 1279.00i 1.85094i 0.378823 + 0.925469i \(0.376329\pi\)
−0.378823 + 0.925469i \(0.623671\pi\)
\(692\) −314.110 1277.86i −0.453916 1.84662i
\(693\) 0 0
\(694\) −273.009 + 348.245i −0.393385 + 0.501793i
\(695\) 898.585i 1.29293i
\(696\) 0 0
\(697\) 132.015 0.189404
\(698\) 358.491 + 281.042i 0.513598 + 0.402639i
\(699\) 0 0
\(700\) −87.0234 + 21.3912i −0.124319 + 0.0305589i
\(701\) −189.067 −0.269710 −0.134855 0.990865i \(-0.543057\pi\)
−0.134855 + 0.990865i \(0.543057\pi\)
\(702\) 0 0
\(703\) 180.926i 0.257363i
\(704\) 36.1051 31.8648i 0.0512856 0.0452625i
\(705\) 0 0
\(706\) −267.300 209.552i −0.378612 0.296816i
\(707\) 296.552i 0.419452i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) −11.1516 + 24.7154i −0.0156623 + 0.0347126i
\(713\) −109.880 −0.154109
\(714\) 0 0
\(715\) 35.8614i 0.0501558i
\(716\) 1304.55 320.670i 1.82199 0.447863i
\(717\) 0 0
\(718\) −722.997 + 922.239i −1.00696 + 1.28446i
\(719\) 768.781i 1.06924i 0.845094 + 0.534618i \(0.179545\pi\)
−0.845094 + 0.534618i \(0.820455\pi\)
\(720\) 0 0
\(721\) −221.588 −0.307334
\(722\) 29.9056 + 23.4447i 0.0414205 + 0.0324719i
\(723\) 0 0
\(724\) −56.2625 228.886i −0.0777107 0.316141i
\(725\) 383.594 0.529095
\(726\) 0 0
\(727\) 1092.23i 1.50238i −0.660085 0.751191i \(-0.729480\pi\)
0.660085 0.751191i \(-0.270520\pi\)
\(728\) 183.518 + 82.8032i 0.252085 + 0.113741i
\(729\) 0 0
\(730\) 280.975 + 220.273i 0.384897 + 0.301743i
\(731\) 2023.08i 2.76756i
\(732\) 0 0
\(733\) 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
\(735\) 0 0
\(736\) 36.4602 197.206i 0.0495384 0.267942i
\(737\) −79.0961 −0.107322
\(738\) 0 0
\(739\) 299.431i 0.405184i 0.979263 + 0.202592i \(0.0649365\pi\)
−0.979263 + 0.202592i \(0.935063\pi\)
\(740\) −145.168 590.569i −0.196173 0.798066i
\(741\) 0 0
\(742\) −98.3304 + 125.428i −0.132521 + 0.169041i
\(743\) 16.0943i 0.0216612i −0.999941 0.0108306i \(-0.996552\pi\)
0.999941 0.0108306i \(-0.00344755\pi\)
\(744\) 0 0
\(745\) 191.806 0.257458
\(746\) 200.686 + 157.330i 0.269016 + 0.210898i
\(747\) 0 0
\(748\) −69.9416 + 17.1924i −0.0935049 + 0.0229844i
\(749\) 313.313 0.418309
\(750\) 0 0
\(751\) 699.482i 0.931401i −0.884942 0.465701i \(-0.845802\pi\)
0.884942 0.465701i \(-0.154198\pi\)
\(752\) −136.176 260.257i −0.181085 0.346087i
\(753\) 0 0
\(754\) −678.235 531.708i −0.899516 0.705183i
\(755\) 92.8393i 0.122966i
\(756\) 0 0
\(757\) 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
\(759\) 0 0
\(760\) −116.427 52.5319i −0.153194 0.0691209i
\(761\) 354.338 0.465622 0.232811 0.972522i \(-0.425208\pi\)
0.232811 + 0.972522i \(0.425208\pi\)
\(762\) 0 0
\(763\) 233.884i 0.306532i
\(764\) −383.332 + 94.2267i −0.501743 + 0.123333i
\(765\) 0 0
\(766\) −845.275 + 1078.21i −1.10349 + 1.40759i
\(767\) 904.682i 1.17951i
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) −265.812 1081.37i −0.344316 1.40074i
\(773\) −712.408 −0.921615 −0.460807 0.887500i \(-0.652440\pi\)
−0.460807 + 0.887500i \(0.652440\pi\)
\(774\) 0 0
\(775\) 203.085i 0.262045i
\(776\) −77.3778 + 171.493i −0.0997137 + 0.220997i
\(777\) 0 0
\(778\) 456.717 + 358.047i 0.587040 + 0.460215i
\(779\) 24.0463i 0.0308682i
\(780\) 0 0
\(781\) −56.3975 −0.0722119
\(782\) −185.059 + 236.057i −0.236648 + 0.301863i
\(783\) 0 0
\(784\) −641.622 + 335.719i −0.818396 + 0.428213i
\(785\) 200.936 0.255970
\(786\) 0 0
\(787\) 514.229i 0.653404i −0.945127 0.326702i \(-0.894063\pi\)
0.945127 0.326702i \(-0.105937\pi\)
\(788\) 45.1989 + 183.877i 0.0573590 + 0.233347i
\(789\) 0 0
\(790\) 433.660 553.167i 0.548937 0.700212i
\(791\)