Properties

Label 684.3.g.b.343.14
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 343.14
Root \(-1.92254 - 0.551226i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +O(q^{10})\) \(q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +(4.47404 + 1.28279i) q^{10} -19.2717i q^{11} +13.8067 q^{13} +(-4.75666 + 16.5900i) q^{14} +(7.01540 + 14.3800i) q^{16} +12.5180 q^{17} +4.35890i q^{19} +(7.89440 + 4.93241i) q^{20} +(10.6231 - 37.0506i) q^{22} +37.4981i q^{23} -19.5844 q^{25} +(26.5438 + 7.61058i) q^{26} +(-18.2897 + 29.2730i) q^{28} +6.36930 q^{29} -5.44851i q^{31} +(5.56075 + 31.5131i) q^{32} +(24.0663 + 6.90025i) q^{34} +20.0816i q^{35} +20.9250 q^{37} +(-2.40274 + 8.38015i) q^{38} +(12.4584 + 13.8343i) q^{40} -72.8337 q^{41} +10.1553i q^{43} +(40.8465 - 65.3755i) q^{44} +(-20.6699 + 72.0914i) q^{46} +32.4450i q^{47} -25.4638 q^{49} +(-37.6517 - 10.7954i) q^{50} +(46.8363 + 29.2633i) q^{52} +42.9339 q^{53} -44.8482i q^{55} +(-51.2987 + 46.1966i) q^{56} +(12.2452 + 3.51092i) q^{58} -38.9728i q^{59} +25.5611 q^{61} +(3.00336 - 10.4750i) q^{62} +(-6.68010 + 63.6504i) q^{64} +32.1302 q^{65} -65.3183i q^{67} +(42.4648 + 26.5320i) q^{68} +(-11.0695 + 38.6076i) q^{70} +18.7557i q^{71} +72.8251 q^{73} +(40.2292 + 11.5344i) q^{74} +(-9.23871 + 14.7867i) q^{76} +166.300 q^{77} -139.874i q^{79} +(16.3259 + 33.4644i) q^{80} +(-140.026 - 40.1478i) q^{82} -94.7116i q^{83} +29.1313 q^{85} +(-5.59789 + 19.5240i) q^{86} +(114.566 - 103.171i) q^{88} -33.3546 q^{89} +119.141i q^{91} +(-79.4773 + 127.205i) q^{92} +(-17.8845 + 62.3766i) q^{94} +10.1438i q^{95} -150.817 q^{97} +(-48.9551 - 14.0363i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92254 + 0.551226i 0.961269 + 0.275613i
\(3\) 0 0
\(4\) 3.39230 + 2.11950i 0.848075 + 0.529876i
\(5\) 2.32715 0.465431 0.232715 0.972545i \(-0.425239\pi\)
0.232715 + 0.972545i \(0.425239\pi\)
\(6\) 0 0
\(7\) 8.62924i 1.23275i 0.787453 + 0.616374i \(0.211399\pi\)
−0.787453 + 0.616374i \(0.788601\pi\)
\(8\) 5.35350 + 5.94475i 0.669187 + 0.743094i
\(9\) 0 0
\(10\) 4.47404 + 1.28279i 0.447404 + 0.128279i
\(11\) 19.2717i 1.75197i −0.482334 0.875987i \(-0.660211\pi\)
0.482334 0.875987i \(-0.339789\pi\)
\(12\) 0 0
\(13\) 13.8067 1.06205 0.531025 0.847356i \(-0.321807\pi\)
0.531025 + 0.847356i \(0.321807\pi\)
\(14\) −4.75666 + 16.5900i −0.339761 + 1.18500i
\(15\) 0 0
\(16\) 7.01540 + 14.3800i 0.438463 + 0.898749i
\(17\) 12.5180 0.736353 0.368177 0.929756i \(-0.379982\pi\)
0.368177 + 0.929756i \(0.379982\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) 7.89440 + 4.93241i 0.394720 + 0.246621i
\(21\) 0 0
\(22\) 10.6231 37.0506i 0.482867 1.68412i
\(23\) 37.4981i 1.63035i 0.579214 + 0.815175i \(0.303360\pi\)
−0.579214 + 0.815175i \(0.696640\pi\)
\(24\) 0 0
\(25\) −19.5844 −0.783374
\(26\) 26.5438 + 7.61058i 1.02092 + 0.292715i
\(27\) 0 0
\(28\) −18.2897 + 29.2730i −0.653204 + 1.04546i
\(29\) 6.36930 0.219631 0.109816 0.993952i \(-0.464974\pi\)
0.109816 + 0.993952i \(0.464974\pi\)
\(30\) 0 0
\(31\) 5.44851i 0.175758i −0.996131 0.0878791i \(-0.971991\pi\)
0.996131 0.0878791i \(-0.0280089\pi\)
\(32\) 5.56075 + 31.5131i 0.173774 + 0.984786i
\(33\) 0 0
\(34\) 24.0663 + 6.90025i 0.707833 + 0.202948i
\(35\) 20.0816i 0.573759i
\(36\) 0 0
\(37\) 20.9250 0.565542 0.282771 0.959187i \(-0.408746\pi\)
0.282771 + 0.959187i \(0.408746\pi\)
\(38\) −2.40274 + 8.38015i −0.0632299 + 0.220530i
\(39\) 0 0
\(40\) 12.4584 + 13.8343i 0.311460 + 0.345859i
\(41\) −72.8337 −1.77643 −0.888216 0.459425i \(-0.848055\pi\)
−0.888216 + 0.459425i \(0.848055\pi\)
\(42\) 0 0
\(43\) 10.1553i 0.236171i 0.993003 + 0.118085i \(0.0376757\pi\)
−0.993003 + 0.118085i \(0.962324\pi\)
\(44\) 40.8465 65.3755i 0.928329 1.48581i
\(45\) 0 0
\(46\) −20.6699 + 72.0914i −0.449346 + 1.56721i
\(47\) 32.4450i 0.690318i 0.938544 + 0.345159i \(0.112175\pi\)
−0.938544 + 0.345159i \(0.887825\pi\)
\(48\) 0 0
\(49\) −25.4638 −0.519669
\(50\) −37.6517 10.7954i −0.753033 0.215908i
\(51\) 0 0
\(52\) 46.8363 + 29.2633i 0.900698 + 0.562755i
\(53\) 42.9339 0.810074 0.405037 0.914300i \(-0.367259\pi\)
0.405037 + 0.914300i \(0.367259\pi\)
\(54\) 0 0
\(55\) 44.8482i 0.815423i
\(56\) −51.2987 + 46.1966i −0.916048 + 0.824940i
\(57\) 0 0
\(58\) 12.2452 + 3.51092i 0.211125 + 0.0605332i
\(59\) 38.9728i 0.660556i −0.943884 0.330278i \(-0.892858\pi\)
0.943884 0.330278i \(-0.107142\pi\)
\(60\) 0 0
\(61\) 25.5611 0.419034 0.209517 0.977805i \(-0.432811\pi\)
0.209517 + 0.977805i \(0.432811\pi\)
\(62\) 3.00336 10.4750i 0.0484412 0.168951i
\(63\) 0 0
\(64\) −6.68010 + 63.6504i −0.104377 + 0.994538i
\(65\) 32.1302 0.494311
\(66\) 0 0
\(67\) 65.3183i 0.974900i −0.873151 0.487450i \(-0.837927\pi\)
0.873151 0.487450i \(-0.162073\pi\)
\(68\) 42.4648 + 26.5320i 0.624483 + 0.390176i
\(69\) 0 0
\(70\) −11.0695 + 38.6076i −0.158135 + 0.551537i
\(71\) 18.7557i 0.264165i 0.991239 + 0.132083i \(0.0421665\pi\)
−0.991239 + 0.132083i \(0.957834\pi\)
\(72\) 0 0
\(73\) 72.8251 0.997604 0.498802 0.866716i \(-0.333773\pi\)
0.498802 + 0.866716i \(0.333773\pi\)
\(74\) 40.2292 + 11.5344i 0.543638 + 0.155871i
\(75\) 0 0
\(76\) −9.23871 + 14.7867i −0.121562 + 0.194562i
\(77\) 166.300 2.15974
\(78\) 0 0
\(79\) 139.874i 1.77056i −0.465060 0.885279i \(-0.653967\pi\)
0.465060 0.885279i \(-0.346033\pi\)
\(80\) 16.3259 + 33.4644i 0.204074 + 0.418306i
\(81\) 0 0
\(82\) −140.026 40.1478i −1.70763 0.489608i
\(83\) 94.7116i 1.14110i −0.821262 0.570552i \(-0.806729\pi\)
0.821262 0.570552i \(-0.193271\pi\)
\(84\) 0 0
\(85\) 29.1313 0.342721
\(86\) −5.59789 + 19.5240i −0.0650917 + 0.227024i
\(87\) 0 0
\(88\) 114.566 103.171i 1.30188 1.17240i
\(89\) −33.3546 −0.374770 −0.187385 0.982287i \(-0.560001\pi\)
−0.187385 + 0.982287i \(0.560001\pi\)
\(90\) 0 0
\(91\) 119.141i 1.30924i
\(92\) −79.4773 + 127.205i −0.863884 + 1.38266i
\(93\) 0 0
\(94\) −17.8845 + 62.3766i −0.190261 + 0.663581i
\(95\) 10.1438i 0.106777i
\(96\) 0 0
\(97\) −150.817 −1.55482 −0.777408 0.628996i \(-0.783466\pi\)
−0.777408 + 0.628996i \(0.783466\pi\)
\(98\) −48.9551 14.0363i −0.499542 0.143228i
\(99\) 0 0
\(100\) −66.4360 41.5091i −0.664360 0.415091i
\(101\) −77.7745 −0.770045 −0.385022 0.922907i \(-0.625806\pi\)
−0.385022 + 0.922907i \(0.625806\pi\)
\(102\) 0 0
\(103\) 14.9481i 0.145127i −0.997364 0.0725637i \(-0.976882\pi\)
0.997364 0.0725637i \(-0.0231180\pi\)
\(104\) 73.9139 + 82.0771i 0.710711 + 0.789203i
\(105\) 0 0
\(106\) 82.5420 + 23.6663i 0.778698 + 0.223267i
\(107\) 80.5205i 0.752528i 0.926512 + 0.376264i \(0.122792\pi\)
−0.926512 + 0.376264i \(0.877208\pi\)
\(108\) 0 0
\(109\) 53.8512 0.494048 0.247024 0.969009i \(-0.420547\pi\)
0.247024 + 0.969009i \(0.420547\pi\)
\(110\) 24.7215 86.2224i 0.224741 0.783840i
\(111\) 0 0
\(112\) −124.088 + 60.5376i −1.10793 + 0.540514i
\(113\) −105.921 −0.937355 −0.468677 0.883369i \(-0.655269\pi\)
−0.468677 + 0.883369i \(0.655269\pi\)
\(114\) 0 0
\(115\) 87.2638i 0.758815i
\(116\) 21.6066 + 13.4998i 0.186264 + 0.116377i
\(117\) 0 0
\(118\) 21.4828 74.9266i 0.182058 0.634972i
\(119\) 108.021i 0.907739i
\(120\) 0 0
\(121\) −250.399 −2.06941
\(122\) 49.1421 + 14.0899i 0.402804 + 0.115491i
\(123\) 0 0
\(124\) 11.5481 18.4830i 0.0931301 0.149056i
\(125\) −103.755 −0.830037
\(126\) 0 0
\(127\) 17.1409i 0.134968i 0.997720 + 0.0674839i \(0.0214971\pi\)
−0.997720 + 0.0674839i \(0.978503\pi\)
\(128\) −47.9285 + 118.688i −0.374441 + 0.927251i
\(129\) 0 0
\(130\) 61.7715 + 17.7110i 0.475166 + 0.136238i
\(131\) 229.336i 1.75066i −0.483526 0.875330i \(-0.660644\pi\)
0.483526 0.875330i \(-0.339356\pi\)
\(132\) 0 0
\(133\) −37.6140 −0.282812
\(134\) 36.0051 125.577i 0.268695 0.937141i
\(135\) 0 0
\(136\) 67.0151 + 74.4164i 0.492758 + 0.547179i
\(137\) 120.567 0.880054 0.440027 0.897985i \(-0.354969\pi\)
0.440027 + 0.897985i \(0.354969\pi\)
\(138\) 0 0
\(139\) 145.864i 1.04938i −0.851292 0.524692i \(-0.824181\pi\)
0.851292 0.524692i \(-0.175819\pi\)
\(140\) −42.5630 + 68.1227i −0.304021 + 0.486591i
\(141\) 0 0
\(142\) −10.3387 + 36.0586i −0.0728074 + 0.253934i
\(143\) 266.078i 1.86069i
\(144\) 0 0
\(145\) 14.8223 0.102223
\(146\) 140.009 + 40.1431i 0.958966 + 0.274953i
\(147\) 0 0
\(148\) 70.9840 + 44.3507i 0.479622 + 0.299667i
\(149\) −19.2547 −0.129226 −0.0646132 0.997910i \(-0.520581\pi\)
−0.0646132 + 0.997910i \(0.520581\pi\)
\(150\) 0 0
\(151\) 165.526i 1.09620i −0.836414 0.548099i \(-0.815352\pi\)
0.836414 0.548099i \(-0.184648\pi\)
\(152\) −25.9126 + 23.3354i −0.170477 + 0.153522i
\(153\) 0 0
\(154\) 319.719 + 91.6690i 2.07609 + 0.595253i
\(155\) 12.6795i 0.0818033i
\(156\) 0 0
\(157\) 149.449 0.951907 0.475954 0.879470i \(-0.342103\pi\)
0.475954 + 0.879470i \(0.342103\pi\)
\(158\) 77.1022 268.913i 0.487989 1.70198i
\(159\) 0 0
\(160\) 12.9407 + 73.3359i 0.0808795 + 0.458349i
\(161\) −323.580 −2.00981
\(162\) 0 0
\(163\) 146.763i 0.900384i −0.892932 0.450192i \(-0.851356\pi\)
0.892932 0.450192i \(-0.148644\pi\)
\(164\) −247.074 154.371i −1.50655 0.941289i
\(165\) 0 0
\(166\) 52.2075 182.087i 0.314503 1.09691i
\(167\) 213.493i 1.27840i 0.769040 + 0.639201i \(0.220735\pi\)
−0.769040 + 0.639201i \(0.779265\pi\)
\(168\) 0 0
\(169\) 21.6237 0.127951
\(170\) 56.0061 + 16.0579i 0.329447 + 0.0944584i
\(171\) 0 0
\(172\) −21.5243 + 34.4500i −0.125141 + 0.200291i
\(173\) 280.715 1.62263 0.811314 0.584610i \(-0.198753\pi\)
0.811314 + 0.584610i \(0.198753\pi\)
\(174\) 0 0
\(175\) 168.998i 0.965704i
\(176\) 277.127 135.199i 1.57459 0.768175i
\(177\) 0 0
\(178\) −64.1254 18.3859i −0.360255 0.103292i
\(179\) 35.1878i 0.196580i −0.995158 0.0982899i \(-0.968663\pi\)
0.995158 0.0982899i \(-0.0313372\pi\)
\(180\) 0 0
\(181\) −345.539 −1.90906 −0.954529 0.298120i \(-0.903641\pi\)
−0.954529 + 0.298120i \(0.903641\pi\)
\(182\) −65.6736 + 229.053i −0.360844 + 1.25853i
\(183\) 0 0
\(184\) −222.917 + 200.746i −1.21150 + 1.09101i
\(185\) 48.6958 0.263220
\(186\) 0 0
\(187\) 241.244i 1.29007i
\(188\) −68.7672 + 110.063i −0.365783 + 0.585442i
\(189\) 0 0
\(190\) −5.59154 + 19.5019i −0.0294292 + 0.102642i
\(191\) 100.233i 0.524782i −0.964962 0.262391i \(-0.915489\pi\)
0.964962 0.262391i \(-0.0845110\pi\)
\(192\) 0 0
\(193\) 168.119 0.871085 0.435543 0.900168i \(-0.356557\pi\)
0.435543 + 0.900168i \(0.356557\pi\)
\(194\) −289.952 83.1343i −1.49460 0.428528i
\(195\) 0 0
\(196\) −86.3808 53.9706i −0.440719 0.275360i
\(197\) −216.705 −1.10002 −0.550012 0.835157i \(-0.685377\pi\)
−0.550012 + 0.835157i \(0.685377\pi\)
\(198\) 0 0
\(199\) 82.2545i 0.413339i −0.978411 0.206670i \(-0.933738\pi\)
0.978411 0.206670i \(-0.0662625\pi\)
\(200\) −104.845 116.424i −0.524224 0.582121i
\(201\) 0 0
\(202\) −149.524 42.8713i −0.740220 0.212234i
\(203\) 54.9623i 0.270750i
\(204\) 0 0
\(205\) −169.495 −0.826806
\(206\) 8.23978 28.7383i 0.0399990 0.139506i
\(207\) 0 0
\(208\) 96.8592 + 198.540i 0.465669 + 0.954517i
\(209\) 84.0035 0.401931
\(210\) 0 0
\(211\) 16.4195i 0.0778173i −0.999243 0.0389087i \(-0.987612\pi\)
0.999243 0.0389087i \(-0.0123881\pi\)
\(212\) 145.645 + 90.9986i 0.687003 + 0.429239i
\(213\) 0 0
\(214\) −44.3850 + 154.804i −0.207407 + 0.723382i
\(215\) 23.6331i 0.109921i
\(216\) 0 0
\(217\) 47.0165 0.216666
\(218\) 103.531 + 29.6842i 0.474913 + 0.136166i
\(219\) 0 0
\(220\) 95.0561 152.139i 0.432073 0.691540i
\(221\) 172.832 0.782044
\(222\) 0 0
\(223\) 195.225i 0.875450i 0.899109 + 0.437725i \(0.144216\pi\)
−0.899109 + 0.437725i \(0.855784\pi\)
\(224\) −271.934 + 47.9851i −1.21399 + 0.214219i
\(225\) 0 0
\(226\) −203.637 58.3864i −0.901050 0.258347i
\(227\) 305.403i 1.34539i −0.739920 0.672695i \(-0.765137\pi\)
0.739920 0.672695i \(-0.234863\pi\)
\(228\) 0 0
\(229\) −229.686 −1.00300 −0.501499 0.865158i \(-0.667218\pi\)
−0.501499 + 0.865158i \(0.667218\pi\)
\(230\) −48.1020 + 167.768i −0.209139 + 0.729425i
\(231\) 0 0
\(232\) 34.0981 + 37.8639i 0.146974 + 0.163207i
\(233\) −187.667 −0.805436 −0.402718 0.915324i \(-0.631935\pi\)
−0.402718 + 0.915324i \(0.631935\pi\)
\(234\) 0 0
\(235\) 75.5044i 0.321295i
\(236\) 82.6030 132.207i 0.350013 0.560201i
\(237\) 0 0
\(238\) −59.5439 + 207.674i −0.250184 + 0.872581i
\(239\) 69.8504i 0.292261i −0.989265 0.146130i \(-0.953318\pi\)
0.989265 0.146130i \(-0.0466819\pi\)
\(240\) 0 0
\(241\) 297.561 1.23469 0.617346 0.786691i \(-0.288208\pi\)
0.617346 + 0.786691i \(0.288208\pi\)
\(242\) −481.402 138.026i −1.98926 0.570357i
\(243\) 0 0
\(244\) 86.7109 + 54.1768i 0.355372 + 0.222036i
\(245\) −59.2582 −0.241870
\(246\) 0 0
\(247\) 60.1818i 0.243651i
\(248\) 32.3900 29.1686i 0.130605 0.117615i
\(249\) 0 0
\(250\) −199.472 57.1922i −0.797889 0.228769i
\(251\) 36.4667i 0.145286i −0.997358 0.0726429i \(-0.976857\pi\)
0.997358 0.0726429i \(-0.0231433\pi\)
\(252\) 0 0
\(253\) 722.652 2.85633
\(254\) −9.44851 + 32.9540i −0.0371988 + 0.129740i
\(255\) 0 0
\(256\) −157.568 + 201.763i −0.615501 + 0.788136i
\(257\) 175.943 0.684604 0.342302 0.939590i \(-0.388793\pi\)
0.342302 + 0.939590i \(0.388793\pi\)
\(258\) 0 0
\(259\) 180.567i 0.697171i
\(260\) 108.995 + 68.1001i 0.419213 + 0.261924i
\(261\) 0 0
\(262\) 126.416 440.908i 0.482504 1.68285i
\(263\) 444.887i 1.69158i −0.533512 0.845792i \(-0.679128\pi\)
0.533512 0.845792i \(-0.320872\pi\)
\(264\) 0 0
\(265\) 99.9138 0.377033
\(266\) −72.3143 20.7338i −0.271858 0.0779466i
\(267\) 0 0
\(268\) 138.442 221.579i 0.516576 0.826788i
\(269\) −149.744 −0.556670 −0.278335 0.960484i \(-0.589783\pi\)
−0.278335 + 0.960484i \(0.589783\pi\)
\(270\) 0 0
\(271\) 439.685i 1.62245i 0.584731 + 0.811227i \(0.301200\pi\)
−0.584731 + 0.811227i \(0.698800\pi\)
\(272\) 87.8188 + 180.009i 0.322863 + 0.661797i
\(273\) 0 0
\(274\) 231.795 + 66.4598i 0.845968 + 0.242554i
\(275\) 377.424i 1.37245i
\(276\) 0 0
\(277\) 83.2452 0.300524 0.150262 0.988646i \(-0.451988\pi\)
0.150262 + 0.988646i \(0.451988\pi\)
\(278\) 80.4042 280.430i 0.289224 1.00874i
\(279\) 0 0
\(280\) −119.380 + 107.507i −0.426357 + 0.383952i
\(281\) 12.9851 0.0462105 0.0231052 0.999733i \(-0.492645\pi\)
0.0231052 + 0.999733i \(0.492645\pi\)
\(282\) 0 0
\(283\) 111.022i 0.392303i 0.980574 + 0.196152i \(0.0628445\pi\)
−0.980574 + 0.196152i \(0.937156\pi\)
\(284\) −39.7529 + 63.6251i −0.139975 + 0.224032i
\(285\) 0 0
\(286\) 146.669 511.545i 0.512829 1.78862i
\(287\) 628.500i 2.18990i
\(288\) 0 0
\(289\) −132.300 −0.457784
\(290\) 28.4965 + 8.17046i 0.0982639 + 0.0281740i
\(291\) 0 0
\(292\) 247.045 + 154.353i 0.846043 + 0.528607i
\(293\) 141.572 0.483179 0.241590 0.970378i \(-0.422331\pi\)
0.241590 + 0.970378i \(0.422331\pi\)
\(294\) 0 0
\(295\) 90.6956i 0.307443i
\(296\) 112.022 + 124.394i 0.378453 + 0.420251i
\(297\) 0 0
\(298\) −37.0179 10.6137i −0.124221 0.0356165i
\(299\) 517.723i 1.73151i
\(300\) 0 0
\(301\) −87.6329 −0.291139
\(302\) 91.2421 318.229i 0.302126 1.05374i
\(303\) 0 0
\(304\) −62.6809 + 30.5794i −0.206187 + 0.100590i
\(305\) 59.4846 0.195031
\(306\) 0 0
\(307\) 357.744i 1.16529i 0.812727 + 0.582645i \(0.197982\pi\)
−0.812727 + 0.582645i \(0.802018\pi\)
\(308\) 564.141 + 352.474i 1.83163 + 1.14440i
\(309\) 0 0
\(310\) 6.98927 24.3768i 0.0225460 0.0786349i
\(311\) 472.383i 1.51892i 0.650557 + 0.759458i \(0.274536\pi\)
−0.650557 + 0.759458i \(0.725464\pi\)
\(312\) 0 0
\(313\) 63.7596 0.203705 0.101852 0.994800i \(-0.467523\pi\)
0.101852 + 0.994800i \(0.467523\pi\)
\(314\) 287.322 + 82.3804i 0.915039 + 0.262358i
\(315\) 0 0
\(316\) 296.464 474.495i 0.938177 1.50157i
\(317\) −198.721 −0.626880 −0.313440 0.949608i \(-0.601481\pi\)
−0.313440 + 0.949608i \(0.601481\pi\)
\(318\) 0 0
\(319\) 122.747i 0.384788i
\(320\) −15.5456 + 148.124i −0.0485801 + 0.462888i
\(321\) 0 0
\(322\) −622.094 178.366i −1.93197 0.553930i
\(323\) 54.5647i 0.168931i
\(324\) 0 0
\(325\) −270.394 −0.831983
\(326\) 80.8993 282.156i 0.248157 0.865511i
\(327\) 0 0
\(328\) −389.915 432.978i −1.18877 1.32006i
\(329\) −279.975 −0.850989
\(330\) 0 0
\(331\) 438.736i 1.32549i −0.748846 0.662744i \(-0.769392\pi\)
0.748846 0.662744i \(-0.230608\pi\)
\(332\) 200.742 321.290i 0.604644 0.967742i
\(333\) 0 0
\(334\) −117.683 + 410.449i −0.352344 + 1.22889i
\(335\) 152.006i 0.453748i
\(336\) 0 0
\(337\) −538.699 −1.59851 −0.799257 0.600989i \(-0.794773\pi\)
−0.799257 + 0.600989i \(0.794773\pi\)
\(338\) 41.5724 + 11.9196i 0.122995 + 0.0352650i
\(339\) 0 0
\(340\) 98.8222 + 61.7440i 0.290653 + 0.181600i
\(341\) −105.002 −0.307924
\(342\) 0 0
\(343\) 203.100i 0.592127i
\(344\) −60.3710 + 54.3666i −0.175497 + 0.158043i
\(345\) 0 0
\(346\) 539.685 + 154.737i 1.55978 + 0.447217i
\(347\) 584.405i 1.68417i 0.539349 + 0.842083i \(0.318671\pi\)
−0.539349 + 0.842083i \(0.681329\pi\)
\(348\) 0 0
\(349\) −300.832 −0.861983 −0.430991 0.902356i \(-0.641836\pi\)
−0.430991 + 0.902356i \(0.641836\pi\)
\(350\) 93.1561 324.905i 0.266160 0.928301i
\(351\) 0 0
\(352\) 607.312 107.165i 1.72532 0.304447i
\(353\) 316.023 0.895250 0.447625 0.894221i \(-0.352270\pi\)
0.447625 + 0.894221i \(0.352270\pi\)
\(354\) 0 0
\(355\) 43.6475i 0.122951i
\(356\) −113.149 70.6951i −0.317833 0.198582i
\(357\) 0 0
\(358\) 19.3964 67.6498i 0.0541799 0.188966i
\(359\) 116.055i 0.323272i 0.986850 + 0.161636i \(0.0516770\pi\)
−0.986850 + 0.161636i \(0.948323\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) −664.312 190.470i −1.83512 0.526161i
\(363\) 0 0
\(364\) −252.520 + 404.162i −0.693736 + 1.11033i
\(365\) 169.475 0.464316
\(366\) 0 0
\(367\) 67.8773i 0.184952i −0.995715 0.0924759i \(-0.970522\pi\)
0.995715 0.0924759i \(-0.0294781\pi\)
\(368\) −539.222 + 263.064i −1.46528 + 0.714848i
\(369\) 0 0
\(370\) 93.6195 + 26.8424i 0.253026 + 0.0725470i
\(371\) 370.487i 0.998617i
\(372\) 0 0
\(373\) −267.337 −0.716721 −0.358361 0.933583i \(-0.616664\pi\)
−0.358361 + 0.933583i \(0.616664\pi\)
\(374\) 132.980 463.800i 0.355561 1.24011i
\(375\) 0 0
\(376\) −192.877 + 173.694i −0.512971 + 0.461952i
\(377\) 87.9388 0.233259
\(378\) 0 0
\(379\) 372.834i 0.983731i −0.870671 0.491866i \(-0.836315\pi\)
0.870671 0.491866i \(-0.163685\pi\)
\(380\) −21.4999 + 34.4109i −0.0565786 + 0.0905550i
\(381\) 0 0
\(382\) 55.2512 192.702i 0.144637 0.504457i
\(383\) 19.6246i 0.0512392i −0.999672 0.0256196i \(-0.991844\pi\)
0.999672 0.0256196i \(-0.00815587\pi\)
\(384\) 0 0
\(385\) 387.006 1.00521
\(386\) 323.216 + 92.6718i 0.837347 + 0.240082i
\(387\) 0 0
\(388\) −511.617 319.658i −1.31860 0.823860i
\(389\) −198.727 −0.510867 −0.255434 0.966827i \(-0.582218\pi\)
−0.255434 + 0.966827i \(0.582218\pi\)
\(390\) 0 0
\(391\) 469.401i 1.20051i
\(392\) −136.320 151.376i −0.347756 0.386163i
\(393\) 0 0
\(394\) −416.623 119.453i −1.05742 0.303181i
\(395\) 325.509i 0.824072i
\(396\) 0 0
\(397\) 295.448 0.744203 0.372101 0.928192i \(-0.378637\pi\)
0.372101 + 0.928192i \(0.378637\pi\)
\(398\) 45.3408 158.137i 0.113922 0.397330i
\(399\) 0 0
\(400\) −137.392 281.623i −0.343480 0.704057i
\(401\) 63.9986 0.159597 0.0797987 0.996811i \(-0.474572\pi\)
0.0797987 + 0.996811i \(0.474572\pi\)
\(402\) 0 0
\(403\) 75.2256i 0.186664i
\(404\) −263.835 164.843i −0.653056 0.408028i
\(405\) 0 0
\(406\) −30.2966 + 105.667i −0.0746222 + 0.260264i
\(407\) 403.262i 0.990815i
\(408\) 0 0
\(409\) 504.473 1.23343 0.616715 0.787186i \(-0.288463\pi\)
0.616715 + 0.787186i \(0.288463\pi\)
\(410\) −325.861 93.4302i −0.794783 0.227878i
\(411\) 0 0
\(412\) 31.6826 50.7085i 0.0768995 0.123079i
\(413\) 336.306 0.814299
\(414\) 0 0
\(415\) 220.408i 0.531105i
\(416\) 76.7754 + 435.091i 0.184556 + 1.04589i
\(417\) 0 0
\(418\) 161.500 + 46.3049i 0.386363 + 0.110777i
\(419\) 470.299i 1.12243i 0.827670 + 0.561215i \(0.189666\pi\)
−0.827670 + 0.561215i \(0.810334\pi\)
\(420\) 0 0
\(421\) −470.034 −1.11647 −0.558235 0.829683i \(-0.688521\pi\)
−0.558235 + 0.829683i \(0.688521\pi\)
\(422\) 9.05083 31.5670i 0.0214475 0.0748033i
\(423\) 0 0
\(424\) 229.847 + 255.231i 0.542091 + 0.601961i
\(425\) −245.157 −0.576840
\(426\) 0 0
\(427\) 220.573i 0.516564i
\(428\) −170.664 + 273.150i −0.398747 + 0.638201i
\(429\) 0 0
\(430\) −13.0271 + 45.4354i −0.0302957 + 0.105664i
\(431\) 224.005i 0.519733i 0.965645 + 0.259866i \(0.0836785\pi\)
−0.965645 + 0.259866i \(0.916321\pi\)
\(432\) 0 0
\(433\) 180.128 0.415999 0.207999 0.978129i \(-0.433305\pi\)
0.207999 + 0.978129i \(0.433305\pi\)
\(434\) 90.3909 + 25.9167i 0.208274 + 0.0597159i
\(435\) 0 0
\(436\) 182.680 + 114.138i 0.418990 + 0.261784i
\(437\) −163.450 −0.374028
\(438\) 0 0
\(439\) 590.004i 1.34397i −0.740563 0.671987i \(-0.765441\pi\)
0.740563 0.671987i \(-0.234559\pi\)
\(440\) 266.612 240.095i 0.605936 0.545671i
\(441\) 0 0
\(442\) 332.276 + 95.2693i 0.751755 + 0.215541i
\(443\) 157.459i 0.355439i 0.984081 + 0.177719i \(0.0568720\pi\)
−0.984081 + 0.177719i \(0.943128\pi\)
\(444\) 0 0
\(445\) −77.6212 −0.174430
\(446\) −107.613 + 375.328i −0.241285 + 0.841543i
\(447\) 0 0
\(448\) −549.255 57.6442i −1.22602 0.128670i
\(449\) 715.434 1.59339 0.796697 0.604379i \(-0.206579\pi\)
0.796697 + 0.604379i \(0.206579\pi\)
\(450\) 0 0
\(451\) 1403.63i 3.11226i
\(452\) −359.316 224.500i −0.794947 0.496682i
\(453\) 0 0
\(454\) 168.346 587.149i 0.370807 1.29328i
\(455\) 277.259i 0.609361i
\(456\) 0 0
\(457\) 31.3497 0.0685988 0.0342994 0.999412i \(-0.489080\pi\)
0.0342994 + 0.999412i \(0.489080\pi\)
\(458\) −441.581 126.609i −0.964150 0.276439i
\(459\) 0 0
\(460\) −184.956 + 296.025i −0.402078 + 0.643532i
\(461\) −368.719 −0.799824 −0.399912 0.916554i \(-0.630959\pi\)
−0.399912 + 0.916554i \(0.630959\pi\)
\(462\) 0 0
\(463\) 817.405i 1.76545i 0.469887 + 0.882726i \(0.344295\pi\)
−0.469887 + 0.882726i \(0.655705\pi\)
\(464\) 44.6832 + 91.5905i 0.0963001 + 0.197393i
\(465\) 0 0
\(466\) −360.796 103.447i −0.774241 0.221989i
\(467\) 86.9194i 0.186123i 0.995660 + 0.0930614i \(0.0296653\pi\)
−0.995660 + 0.0930614i \(0.970335\pi\)
\(468\) 0 0
\(469\) 563.647 1.20181
\(470\) −41.6200 + 145.160i −0.0885531 + 0.308851i
\(471\) 0 0
\(472\) 231.683 208.641i 0.490855 0.442036i
\(473\) 195.711 0.413765
\(474\) 0 0
\(475\) 85.3662i 0.179718i
\(476\) −228.951 + 366.439i −0.480989 + 0.769830i
\(477\) 0 0
\(478\) 38.5033 134.290i 0.0805509 0.280941i
\(479\) 333.107i 0.695421i −0.937602 0.347710i \(-0.886959\pi\)
0.937602 0.347710i \(-0.113041\pi\)
\(480\) 0 0
\(481\) 288.905 0.600634
\(482\) 572.072 + 164.023i 1.18687 + 0.340297i
\(483\) 0 0
\(484\) −849.429 530.722i −1.75502 1.09653i
\(485\) −350.975 −0.723659
\(486\) 0 0
\(487\) 264.690i 0.543511i 0.962366 + 0.271755i \(0.0876042\pi\)
−0.962366 + 0.271755i \(0.912396\pi\)
\(488\) 136.841 + 151.954i 0.280412 + 0.311382i
\(489\) 0 0
\(490\) −113.926 32.6646i −0.232502 0.0666625i
\(491\) 402.874i 0.820518i 0.911969 + 0.410259i \(0.134562\pi\)
−0.911969 + 0.410259i \(0.865438\pi\)
\(492\) 0 0
\(493\) 79.7310 0.161726
\(494\) −33.1738 + 115.702i −0.0671534 + 0.234214i
\(495\) 0 0
\(496\) 78.3495 38.2235i 0.157963 0.0770634i
\(497\) −161.848 −0.325650
\(498\) 0 0
\(499\) 350.536i 0.702477i −0.936286 0.351238i \(-0.885761\pi\)
0.936286 0.351238i \(-0.114239\pi\)
\(500\) −351.967 219.908i −0.703934 0.439817i
\(501\) 0 0
\(502\) 20.1014 70.1086i 0.0400426 0.139659i
\(503\) 339.615i 0.675179i −0.941293 0.337589i \(-0.890388\pi\)
0.941293 0.337589i \(-0.109612\pi\)
\(504\) 0 0
\(505\) −180.993 −0.358403
\(506\) 1389.33 + 398.345i 2.74570 + 0.787242i
\(507\) 0 0
\(508\) −36.3302 + 58.1471i −0.0715162 + 0.114463i
\(509\) 933.003 1.83301 0.916506 0.400020i \(-0.130997\pi\)
0.916506 + 0.400020i \(0.130997\pi\)
\(510\) 0 0
\(511\) 628.426i 1.22980i
\(512\) −414.148 + 301.041i −0.808882 + 0.587971i
\(513\) 0 0
\(514\) 338.257 + 96.9844i 0.658088 + 0.188686i
\(515\) 34.7866i 0.0675467i
\(516\) 0 0
\(517\) 625.270 1.20942
\(518\) −99.5333 + 347.147i −0.192149 + 0.670169i
\(519\) 0 0
\(520\) 172.009 + 191.006i 0.330787 + 0.367319i
\(521\) 415.284 0.797091 0.398545 0.917149i \(-0.369515\pi\)
0.398545 + 0.917149i \(0.369515\pi\)
\(522\) 0 0
\(523\) 241.598i 0.461947i 0.972960 + 0.230973i \(0.0741911\pi\)
−0.972960 + 0.230973i \(0.925809\pi\)
\(524\) 486.080 777.978i 0.927633 1.48469i
\(525\) 0 0
\(526\) 245.233 855.311i 0.466223 1.62607i
\(527\) 68.2044i 0.129420i
\(528\) 0 0
\(529\) −877.105 −1.65804
\(530\) 192.088 + 55.0750i 0.362430 + 0.103915i
\(531\) 0 0
\(532\) −127.598 79.7230i −0.239846 0.149855i
\(533\) −1005.59 −1.88666
\(534\) 0 0
\(535\) 187.384i 0.350250i
\(536\) 388.301 349.681i 0.724442 0.652391i
\(537\) 0 0
\(538\) −287.889 82.5428i −0.535109 0.153425i
\(539\) 490.731i 0.910447i
\(540\) 0 0
\(541\) −304.787 −0.563377 −0.281689 0.959506i \(-0.590894\pi\)
−0.281689 + 0.959506i \(0.590894\pi\)
\(542\) −242.366 + 845.311i −0.447169 + 1.55961i
\(543\) 0 0
\(544\) 69.6095 + 394.482i 0.127959 + 0.725150i
\(545\) 125.320 0.229945
\(546\) 0 0
\(547\) 555.915i 1.01630i −0.861269 0.508149i \(-0.830330\pi\)
0.861269 0.508149i \(-0.169670\pi\)
\(548\) 409.001 + 255.543i 0.746352 + 0.466319i
\(549\) 0 0
\(550\) −208.046 + 725.612i −0.378265 + 1.31930i
\(551\) 27.7632i 0.0503869i
\(552\) 0 0
\(553\) 1207.01 2.18265
\(554\) 160.042 + 45.8869i 0.288885 + 0.0828283i
\(555\) 0 0
\(556\) 309.160 494.816i 0.556043 0.889956i
\(557\) 192.055 0.344802 0.172401 0.985027i \(-0.444848\pi\)
0.172401 + 0.985027i \(0.444848\pi\)
\(558\) 0 0
\(559\) 140.211i 0.250825i
\(560\) −288.773 + 140.880i −0.515666 + 0.251572i
\(561\) 0 0
\(562\) 24.9644 + 7.15775i 0.0444207 + 0.0127362i
\(563\) 107.771i 0.191423i −0.995409 0.0957114i \(-0.969487\pi\)
0.995409 0.0957114i \(-0.0305126\pi\)
\(564\) 0 0
\(565\) −246.495 −0.436274
\(566\) −61.1981 + 213.444i −0.108124 + 0.377109i
\(567\) 0 0
\(568\) −111.498 + 100.409i −0.196300 + 0.176776i
\(569\) 647.934 1.13872 0.569362 0.822087i \(-0.307190\pi\)
0.569362 + 0.822087i \(0.307190\pi\)
\(570\) 0 0
\(571\) 285.402i 0.499828i 0.968268 + 0.249914i \(0.0804023\pi\)
−0.968268 + 0.249914i \(0.919598\pi\)
\(572\) 563.953 902.616i 0.985933 1.57800i
\(573\) 0 0
\(574\) 346.445 1208.31i 0.603563 2.10508i
\(575\) 734.376i 1.27717i
\(576\) 0 0
\(577\) −92.4624 −0.160247 −0.0801234 0.996785i \(-0.525531\pi\)
−0.0801234 + 0.996785i \(0.525531\pi\)
\(578\) −254.351 72.9269i −0.440053 0.126171i
\(579\) 0 0
\(580\) 50.2819 + 31.4160i 0.0866929 + 0.0541656i
\(581\) 817.289 1.40669
\(582\) 0 0
\(583\) 827.410i 1.41923i
\(584\) 389.869 + 432.927i 0.667584 + 0.741314i
\(585\) 0 0
\(586\) 272.177 + 78.0379i 0.464465 + 0.133170i
\(587\) 654.717i 1.11536i 0.830056 + 0.557681i \(0.188309\pi\)
−0.830056 + 0.557681i \(0.811691\pi\)
\(588\) 0 0
\(589\) 23.7495 0.0403217
\(590\) 49.9938 174.366i 0.0847352 0.295535i
\(591\) 0 0
\(592\) 146.798 + 300.902i 0.247969 + 0.508280i
\(593\) −106.297 −0.179253 −0.0896264 0.995975i \(-0.528567\pi\)
−0.0896264 + 0.995975i \(0.528567\pi\)
\(594\) 0 0
\(595\) 251.381i 0.422489i
\(596\) −65.3178 40.8105i −0.109594 0.0684740i
\(597\) 0 0
\(598\) −285.382 + 995.342i −0.477228 + 1.66445i
\(599\) 478.675i 0.799124i 0.916706 + 0.399562i \(0.130838\pi\)
−0.916706 + 0.399562i \(0.869162\pi\)
\(600\) 0 0
\(601\) 808.024 1.34447 0.672233 0.740340i \(-0.265335\pi\)
0.672233 + 0.740340i \(0.265335\pi\)
\(602\) −168.478 48.3055i −0.279863 0.0802418i
\(603\) 0 0
\(604\) 350.833 561.513i 0.580849 0.929657i
\(605\) −582.717 −0.963169
\(606\) 0 0
\(607\) 694.694i 1.14447i 0.820089 + 0.572236i \(0.193924\pi\)
−0.820089 + 0.572236i \(0.806076\pi\)
\(608\) −137.363 + 24.2388i −0.225925 + 0.0398664i
\(609\) 0 0
\(610\) 114.361 + 32.7894i 0.187478 + 0.0537531i
\(611\) 447.956i 0.733153i
\(612\) 0 0
\(613\) −496.830 −0.810489 −0.405245 0.914208i \(-0.632814\pi\)
−0.405245 + 0.914208i \(0.632814\pi\)
\(614\) −197.198 + 687.776i −0.321169 + 1.12016i
\(615\) 0 0
\(616\) 890.289 + 988.614i 1.44527 + 1.60489i
\(617\) −387.951 −0.628770 −0.314385 0.949296i \(-0.601798\pi\)
−0.314385 + 0.949296i \(0.601798\pi\)
\(618\) 0 0
\(619\) 882.105i 1.42505i 0.701647 + 0.712525i \(0.252448\pi\)
−0.701647 + 0.712525i \(0.747552\pi\)
\(620\) 26.8743 43.0127i 0.0433456 0.0693753i
\(621\) 0 0
\(622\) −260.389 + 908.173i −0.418633 + 1.46009i
\(623\) 287.824i 0.461998i
\(624\) 0 0
\(625\) 248.156 0.397050
\(626\) 122.580 + 35.1459i 0.195815 + 0.0561437i
\(627\) 0 0
\(628\) 506.977 + 316.759i 0.807289 + 0.504393i
\(629\) 261.940 0.416439
\(630\) 0 0
\(631\) 502.601i 0.796515i −0.917274 0.398258i \(-0.869615\pi\)
0.917274 0.398258i \(-0.130385\pi\)
\(632\) 831.517 748.816i 1.31569 1.18484i
\(633\) 0 0
\(634\) −382.048 109.540i −0.602600 0.172776i
\(635\) 39.8895i 0.0628181i
\(636\) 0 0
\(637\) −351.570 −0.551915
\(638\) 67.6616 235.987i 0.106053 0.369885i
\(639\) 0 0
\(640\) −111.537 + 276.205i −0.174277 + 0.431571i
\(641\) −385.625 −0.601600 −0.300800 0.953687i \(-0.597254\pi\)
−0.300800 + 0.953687i \(0.597254\pi\)
\(642\) 0 0
\(643\) 925.293i 1.43902i 0.694480 + 0.719512i \(0.255635\pi\)
−0.694480 + 0.719512i \(0.744365\pi\)
\(644\) −1097.68 685.829i −1.70447 1.06495i
\(645\) 0 0
\(646\) −30.0775 + 104.903i −0.0465596 + 0.162388i
\(647\) 656.956i 1.01539i 0.861538 + 0.507694i \(0.169502\pi\)
−0.861538 + 0.507694i \(0.830498\pi\)
\(648\) 0 0
\(649\) −751.073 −1.15728
\(650\) −519.843 149.048i −0.799759 0.229305i
\(651\) 0 0
\(652\) 311.064 497.863i 0.477092 0.763593i
\(653\) −392.897 −0.601680 −0.300840 0.953675i \(-0.597267\pi\)
−0.300840 + 0.953675i \(0.597267\pi\)
\(654\) 0 0
\(655\) 533.701i 0.814811i
\(656\) −510.958 1047.35i −0.778899 1.59657i
\(657\) 0 0
\(658\) −538.263 154.330i −0.818029 0.234543i
\(659\) 695.576i 1.05550i −0.849399 0.527751i \(-0.823035\pi\)
0.849399 0.527751i \(-0.176965\pi\)
\(660\) 0 0
\(661\) 1179.05 1.78373 0.891866 0.452299i \(-0.149396\pi\)
0.891866 + 0.452299i \(0.149396\pi\)
\(662\) 241.843 843.487i 0.365322 1.27415i
\(663\) 0 0
\(664\) 563.037 507.038i 0.847947 0.763612i
\(665\) −87.5335 −0.131629
\(666\) 0 0
\(667\) 238.837i 0.358076i
\(668\) −452.500 + 724.233i −0.677395 + 1.08418i
\(669\) 0 0
\(670\) 83.7894 292.237i 0.125059 0.436174i
\(671\) 492.606i 0.734137i
\(672\) 0 0
\(673\) −881.170 −1.30932 −0.654658 0.755925i \(-0.727187\pi\)
−0.654658 + 0.755925i \(0.727187\pi\)
\(674\) −1035.67 296.945i −1.53660 0.440571i
\(675\) 0 0
\(676\) 73.3542 + 45.8316i 0.108512 + 0.0677982i
\(677\) 126.536 0.186907 0.0934533 0.995624i \(-0.470209\pi\)
0.0934533 + 0.995624i \(0.470209\pi\)
\(678\) 0 0
\(679\) 1301.44i 1.91670i
\(680\) 155.954 + 173.178i 0.229345 + 0.254674i
\(681\) 0 0
\(682\) −201.870 57.8798i −0.295998 0.0848678i
\(683\) 873.042i 1.27825i 0.769105 + 0.639123i \(0.220702\pi\)
−0.769105 + 0.639123i \(0.779298\pi\)
\(684\) 0 0
\(685\) 280.579 0.409604
\(686\) −111.954 + 390.467i −0.163198 + 0.569193i
\(687\) 0 0
\(688\) −146.034 + 71.2439i −0.212258 + 0.103552i
\(689\) 592.774 0.860339
\(690\) 0 0
\(691\) 610.841i 0.883996i −0.897016 0.441998i \(-0.854270\pi\)
0.897016 0.441998i \(-0.145730\pi\)
\(692\) 952.269 + 594.976i 1.37611 + 0.859792i
\(693\) 0 0
\(694\) −322.139 + 1123.54i −0.464178 + 1.61894i
\(695\) 339.449i 0.488415i
\(696\) 0 0
\(697\) −911.733 −1.30808
\(698\) −578.361 165.826i −0.828597 0.237574i
\(699\) 0 0
\(700\) 358.192 573.292i 0.511703 0.818989i
\(701\) 506.393 0.722387 0.361193 0.932491i \(-0.382369\pi\)
0.361193 + 0.932491i \(0.382369\pi\)
\(702\) 0 0
\(703\) 91.2102i 0.129744i
\(704\) 1226.65 + 128.737i 1.74241 + 0.182865i
\(705\) 0 0
\(706\) 607.566 + 174.200i 0.860576 + 0.246742i
\(707\) 671.135i 0.949272i
\(708\) 0 0
\(709\) −1036.42 −1.46180 −0.730902 0.682483i \(-0.760900\pi\)
−0.730902 + 0.682483i \(0.760900\pi\)
\(710\) −24.0596 + 83.9140i −0.0338868 + 0.118189i
\(711\) 0 0
\(712\) −178.564 198.284i −0.250792 0.278489i
\(713\) 204.308 0.286548
\(714\) 0 0
\(715\) 619.204i 0.866020i
\(716\) 74.5806 119.367i 0.104163 0.166714i
\(717\) 0 0
\(718\) −63.9722 + 223.119i −0.0890978 + 0.310751i
\(719\) 834.943i 1.16126i 0.814169 + 0.580628i \(0.197193\pi\)
−0.814169 + 0.580628i \(0.802807\pi\)
\(720\) 0 0
\(721\) 128.991 0.178905
\(722\) −36.5282 10.4733i −0.0505931 0.0145059i
\(723\) 0 0
\(724\) −1172.17 732.372i −1.61902 1.01156i
\(725\) −124.739 −0.172053
\(726\) 0 0
\(727\) 225.252i 0.309838i −0.987927 0.154919i \(-0.950488\pi\)
0.987927 0.154919i \(-0.0495116\pi\)
\(728\) −708.263 + 637.821i −0.972889 + 0.876128i
\(729\) 0 0
\(730\) 325.822 + 93.4191i 0.446332 + 0.127971i
\(731\) 127.125i 0.173905i
\(732\) 0 0
\(733\) 697.401 0.951434 0.475717 0.879598i \(-0.342189\pi\)
0.475717 + 0.879598i \(0.342189\pi\)
\(734\) 37.4157 130.497i 0.0509751 0.177788i
\(735\) 0 0
\(736\) −1181.68 + 208.517i −1.60555 + 0.283312i
\(737\) −1258.80 −1.70800
\(738\) 0 0
\(739\) 1065.87i 1.44231i −0.692772 0.721157i \(-0.743611\pi\)
0.692772 0.721157i \(-0.256389\pi\)
\(740\) 165.191 + 103.211i 0.223231 + 0.139474i
\(741\) 0 0
\(742\) −204.222 + 712.275i −0.275232 + 0.959939i
\(743\) 1050.43i 1.41376i 0.707332 + 0.706881i \(0.249898\pi\)
−0.707332 + 0.706881i \(0.750102\pi\)
\(744\) 0 0
\(745\) −44.8087 −0.0601459
\(746\) −513.966 147.363i −0.688962 0.197538i
\(747\) 0 0
\(748\) 511.317 818.370i 0.683578 1.09408i
\(749\) −694.831 −0.927678
\(750\) 0 0
\(751\) 26.6606i 0.0355002i −0.999842 0.0177501i \(-0.994350\pi\)
0.999842 0.0177501i \(-0.00565033\pi\)
\(752\) −466.558 + 227.614i −0.620423 + 0.302679i
\(753\) 0 0
\(754\) 169.066 + 48.4741i 0.224225 + 0.0642893i
\(755\) 385.204i 0.510204i
\(756\) 0 0
\(757\) 445.989 0.589153 0.294577 0.955628i \(-0.404821\pi\)
0.294577 + 0.955628i \(0.404821\pi\)
\(758\) 205.516 716.788i 0.271129 0.945630i
\(759\) 0 0
\(760\) −60.3025 + 54.3050i −0.0793454 + 0.0714539i
\(761\) −294.799 −0.387384 −0.193692 0.981062i \(-0.562046\pi\)
−0.193692 + 0.981062i \(0.562046\pi\)
\(762\) 0 0
\(763\) 464.695i 0.609037i
\(764\) 212.445 340.022i 0.278070 0.445055i
\(765\) 0 0
\(766\) 10.8176 37.7291i 0.0141222 0.0492547i
\(767\) 538.084i 0.701543i
\(768\) 0 0
\(769\) −279.363 −0.363281 −0.181641 0.983365i \(-0.558141\pi\)
−0.181641 + 0.983365i \(0.558141\pi\)
\(770\) 744.034 + 213.328i 0.966278 + 0.277049i
\(771\) 0 0
\(772\) 570.312 + 356.330i 0.738746 + 0.461567i
\(773\) 1092.48 1.41329 0.706647 0.707566i \(-0.250207\pi\)
0.706647 + 0.707566i \(0.250207\pi\)
\(774\) 0 0
\(775\) 106.705i 0.137684i
\(776\) −807.400 896.571i −1.04046 1.15537i
\(777\) 0 0
\(778\) −382.061 109.544i −0.491081 0.140802i
\(779\) 317.475i 0.407542i
\(780\) 0 0
\(781\) 361.456 0.462811
\(782\) −258.746 + 902.441i −0.330877 + 1.15402i
\(783\) 0 0
\(784\) −178.639 366.169i −0.227856 0.467052i
\(785\) 347.792 0.443047
\(786\) 0 0
\(787\) 231.147i 0.293706i 0.989158 + 0.146853i \(0.0469145\pi\)
−0.989158 + 0.146853i \(0.953086\pi\)
\(788\) −735.127 459.306i −0.932903 0.582876i
\(789\) 0 0
\(790\) 179.429 625.802i 0.227125 0.792155i
\(791\) 914.019i 1.15552i