Properties

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

$q$-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 \(-0.788601\pi\)
0.787453 0.616374i \(-0.211399\pi\)
\(8\) 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 \(0.339789\pi\)
−0.482334 + 0.875987i \(0.660211\pi\)
\(12\) 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 \(-0.696640\pi\)
0.579214 0.815175i \(-0.303360\pi\)
\(24\) 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 \(0.0280089\pi\)
−0.996131 + 0.0878791i \(0.971991\pi\)
\(32\) 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 \(-0.962324\pi\)
0.993003 0.118085i \(-0.0376757\pi\)
\(44\) 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 \(-0.887825\pi\)
0.938544 0.345159i \(-0.112175\pi\)
\(48\) 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 \(0.107142\pi\)
−0.943884 + 0.330278i \(0.892858\pi\)
\(60\) 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 \(0.162073\pi\)
−0.873151 + 0.487450i \(0.837927\pi\)
\(68\) 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 \(-0.957834\pi\)
0.991239 0.132083i \(-0.0421665\pi\)
\(72\) 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 \(0.346033\pi\)
−0.465060 + 0.885279i \(0.653967\pi\)
\(80\) 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 \(0.193271\pi\)
−0.821262 + 0.570552i \(0.806729\pi\)
\(84\) 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 \(0.0231180\pi\)
−0.997364 + 0.0725637i \(0.976882\pi\)
\(104\) 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 \(-0.877208\pi\)
0.926512 0.376264i \(-0.122792\pi\)
\(108\) 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 \(-0.978503\pi\)
0.997720 0.0674839i \(-0.0214971\pi\)
\(128\) −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 \(0.339356\pi\)
−0.483526 + 0.875330i \(0.660644\pi\)
\(132\) 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 \(0.175819\pi\)
−0.851292 + 0.524692i \(0.824181\pi\)
\(140\) −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 \(0.184648\pi\)
−0.836414 + 0.548099i \(0.815352\pi\)
\(152\) −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 \(0.148644\pi\)
−0.892932 + 0.450192i \(0.851356\pi\)
\(164\) −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 \(-0.779265\pi\)
0.769040 0.639201i \(-0.220735\pi\)
\(168\) 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 \(0.0313372\pi\)
−0.995158 + 0.0982899i \(0.968663\pi\)
\(180\) 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 \(0.0845110\pi\)
−0.964962 + 0.262391i \(0.915489\pi\)
\(192\) 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 \(0.0662625\pi\)
−0.978411 + 0.206670i \(0.933738\pi\)
\(200\) −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 \(0.0123881\pi\)
−0.999243 + 0.0389087i \(0.987612\pi\)
\(212\) 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 \(-0.855784\pi\)
0.899109 0.437725i \(-0.144216\pi\)
\(224\) −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 \(0.234863\pi\)
−0.739920 + 0.672695i \(0.765137\pi\)
\(228\) 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 \(0.0466819\pi\)
−0.989265 + 0.146130i \(0.953318\pi\)
\(240\) 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 \(0.0231433\pi\)
−0.997358 + 0.0726429i \(0.976857\pi\)
\(252\) 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 \(0.320872\pi\)
−0.533512 + 0.845792i \(0.679128\pi\)
\(264\) 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 \(-0.698800\pi\)
0.584731 0.811227i \(-0.301200\pi\)
\(272\) 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 \(-0.937156\pi\)
0.980574 0.196152i \(-0.0628445\pi\)
\(284\) −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 \(-0.802018\pi\)
0.812727 0.582645i \(-0.197982\pi\)
\(308\) 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 \(-0.725464\pi\)
0.650557 0.759458i \(-0.274536\pi\)
\(312\) 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 \(0.230608\pi\)
−0.748846 + 0.662744i \(0.769392\pi\)
\(332\) 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 \(-0.681329\pi\)
0.539349 0.842083i \(-0.318671\pi\)
\(348\) 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 \(-0.948323\pi\)
0.986850 0.161636i \(-0.0516770\pi\)
\(360\) 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 \(0.0294781\pi\)
−0.995715 + 0.0924759i \(0.970522\pi\)
\(368\) −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 \(0.163685\pi\)
−0.870671 + 0.491866i \(0.836315\pi\)
\(380\) −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 \(0.00815587\pi\)
−0.999672 + 0.0256196i \(0.991844\pi\)
\(384\) 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 \(-0.810334\pi\)
0.827670 0.561215i \(-0.189666\pi\)
\(420\) 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 \(-0.916321\pi\)
0.965645 0.259866i \(-0.0836785\pi\)
\(432\) 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 \(0.234559\pi\)
−0.740563 + 0.671987i \(0.765441\pi\)
\(440\) 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 \(-0.943128\pi\)
0.984081 0.177719i \(-0.0568720\pi\)
\(444\) 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 \(-0.655705\pi\)
0.469887 0.882726i \(-0.344295\pi\)
\(464\) 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 \(-0.970335\pi\)
0.995660 0.0930614i \(-0.0296653\pi\)
\(468\) 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 \(0.113041\pi\)
−0.937602 + 0.347710i \(0.886959\pi\)
\(480\) 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 \(-0.912396\pi\)
0.962366 0.271755i \(-0.0876042\pi\)
\(488\) 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 \(-0.865438\pi\)
0.911969 0.410259i \(-0.134562\pi\)
\(492\) 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 \(0.114239\pi\)
−0.936286 + 0.351238i \(0.885761\pi\)
\(500\) −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 \(0.109612\pi\)
−0.941293 + 0.337589i \(0.890388\pi\)
\(504\) 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 \(-0.925809\pi\)
0.972960 0.230973i \(-0.0741911\pi\)
\(524\) 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 \(0.169670\pi\)
−0.861269 + 0.508149i \(0.830330\pi\)
\(548\) 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 \(0.0305126\pi\)
−0.995409 + 0.0957114i \(0.969487\pi\)
\(564\) 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 \(-0.919598\pi\)
0.968268 0.249914i \(-0.0804023\pi\)
\(572\) 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 \(-0.811691\pi\)
0.830056 0.557681i \(-0.188309\pi\)
\(588\) 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 \(-0.869162\pi\)
0.916706 0.399562i \(-0.130838\pi\)
\(600\) 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 \(-0.806076\pi\)
0.820089 0.572236i \(-0.193924\pi\)
\(608\) −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 \(-0.747552\pi\)
0.701647 0.712525i \(-0.252448\pi\)
\(620\) 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 \(0.130385\pi\)
−0.917274 + 0.398258i \(0.869615\pi\)
\(632\) 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 \(-0.744365\pi\)
0.694480 0.719512i \(-0.255635\pi\)
\(644\) −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 \(-0.830498\pi\)
0.861538 0.507694i \(-0.169502\pi\)
\(648\) 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 \(0.176965\pi\)
−0.849399 + 0.527751i \(0.823035\pi\)
\(660\) 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 \(-0.779298\pi\)
0.769105 0.639123i \(-0.220702\pi\)
\(684\) 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 \(0.145730\pi\)
−0.897016 + 0.441998i \(0.854270\pi\)
\(692\) 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 \(-0.802807\pi\)
0.814169 0.580628i \(-0.197193\pi\)
\(720\) 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 \(0.0495116\pi\)
−0.987927 + 0.154919i \(0.950488\pi\)
\(728\) −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 \(0.256389\pi\)
−0.692772 + 0.721157i \(0.743611\pi\)
\(740\) 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 \(-0.750102\pi\)
0.707332 0.706881i \(-0.249898\pi\)
\(744\) 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 \(0.00565033\pi\)
−0.999842 + 0.0177501i \(0.994350\pi\)
\(752\) −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 \(-0.953086\pi\)
0.989158 0.146853i \(-0.0469145\pi\)
\(788\) −735.127 + 459.306i −0.932903 + 0.582876i
\(789\) 0 0
\(790\) 179.429 + 625.802i 0.227125 + 0.792155i
\(791\)