Properties

Label 684.3.b.a.683.6
Level $684$
Weight $3$
Character 684.683
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 683.6
Character \(\chi\) \(=\) 684.683
Dual form 684.3.b.a.683.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +O(q^{10})\) \(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +(4.07438 - 12.6443i) q^{10} -10.1736 q^{11} -3.45114i q^{13} +(0.288815 - 0.896300i) q^{14} +(5.09220 + 15.1680i) q^{16} +14.2737i q^{17} +(-13.6293 - 13.2379i) q^{19} +(-15.5121 + 21.5706i) q^{20} +(19.3666 + 6.24052i) q^{22} -25.5501 q^{23} -19.1197 q^{25} +(-2.11694 + 6.56963i) q^{26} +(-1.09958 + 1.52905i) q^{28} -14.1589 q^{29} +19.3243 q^{31} +(-0.389466 - 31.9976i) q^{32} +(8.75551 - 27.1716i) q^{34} -3.12746 q^{35} -30.0832i q^{37} +(17.8248 + 33.5601i) q^{38} +(42.7604 - 31.5469i) q^{40} +25.6549 q^{41} -38.5869i q^{43} +(-33.0386 - 23.7591i) q^{44} +(48.6375 + 15.6725i) q^{46} +16.5047 q^{47} +48.7783 q^{49} +(36.3964 + 11.7280i) q^{50} +(8.05965 - 11.2075i) q^{52} -41.6477 q^{53} -67.5759i q^{55} +(3.03110 - 2.23623i) q^{56} +(26.9530 + 8.68510i) q^{58} -31.3349i q^{59} -3.53469 q^{61} +(-36.7859 - 11.8535i) q^{62} +(-18.8860 + 61.1500i) q^{64} +22.9234 q^{65} +13.9620 q^{67} +(-33.3342 + 46.3535i) q^{68} +(5.95346 + 1.91839i) q^{70} -128.352i q^{71} -71.6376 q^{73} +(-18.4531 + 57.2667i) q^{74} +(-13.3456 - 74.8191i) q^{76} -4.79017i q^{77} -100.177 q^{79} +(-100.750 + 33.8237i) q^{80} +(-48.8369 - 15.7367i) q^{82} +58.6257 q^{83} -94.8096 q^{85} +(-23.6693 + 73.4545i) q^{86} +(48.3188 + 65.4940i) q^{88} -108.060 q^{89} +1.62494 q^{91} +(-82.9734 - 59.6687i) q^{92} +(-31.4186 - 10.1240i) q^{94} +(87.9296 - 90.5295i) q^{95} +124.227i q^{97} +(-92.8550 - 29.9207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 8 q^{4} + O(q^{10}) \) \( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90361 0.613402i −0.951806 0.306701i
\(3\) 0 0
\(4\) 3.24748 + 2.33536i 0.811869 + 0.583840i
\(5\) 6.64226i 1.32845i 0.747531 + 0.664226i \(0.231239\pi\)
−0.747531 + 0.664226i \(0.768761\pi\)
\(6\) 0 0
\(7\) 0.470842i 0.0672631i 0.999434 + 0.0336316i \(0.0107073\pi\)
−0.999434 + 0.0336316i \(0.989293\pi\)
\(8\) −4.74942 6.43762i −0.593678 0.804703i
\(9\) 0 0
\(10\) 4.07438 12.6443i 0.407438 1.26443i
\(11\) −10.1736 −0.924875 −0.462437 0.886652i \(-0.653025\pi\)
−0.462437 + 0.886652i \(0.653025\pi\)
\(12\) 0 0
\(13\) 3.45114i 0.265472i −0.991151 0.132736i \(-0.957624\pi\)
0.991151 0.132736i \(-0.0423763\pi\)
\(14\) 0.288815 0.896300i 0.0206297 0.0640214i
\(15\) 0 0
\(16\) 5.09220 + 15.1680i 0.318263 + 0.948003i
\(17\) 14.2737i 0.839629i 0.907610 + 0.419814i \(0.137905\pi\)
−0.907610 + 0.419814i \(0.862095\pi\)
\(18\) 0 0
\(19\) −13.6293 13.2379i −0.717332 0.696731i
\(20\) −15.5121 + 21.5706i −0.775603 + 1.07853i
\(21\) 0 0
\(22\) 19.3666 + 6.24052i 0.880301 + 0.283660i
\(23\) −25.5501 −1.11087 −0.555437 0.831558i \(-0.687449\pi\)
−0.555437 + 0.831558i \(0.687449\pi\)
\(24\) 0 0
\(25\) −19.1197 −0.764787
\(26\) −2.11694 + 6.56963i −0.0814206 + 0.252678i
\(27\) 0 0
\(28\) −1.09958 + 1.52905i −0.0392709 + 0.0546088i
\(29\) −14.1589 −0.488238 −0.244119 0.969745i \(-0.578499\pi\)
−0.244119 + 0.969745i \(0.578499\pi\)
\(30\) 0 0
\(31\) 19.3243 0.623364 0.311682 0.950187i \(-0.399108\pi\)
0.311682 + 0.950187i \(0.399108\pi\)
\(32\) −0.389466 31.9976i −0.0121708 0.999926i
\(33\) 0 0
\(34\) 8.75551 27.1716i 0.257515 0.799164i
\(35\) −3.12746 −0.0893559
\(36\) 0 0
\(37\) 30.0832i 0.813059i −0.913638 0.406529i \(-0.866739\pi\)
0.913638 0.406529i \(-0.133261\pi\)
\(38\) 17.8248 + 33.5601i 0.469073 + 0.883160i
\(39\) 0 0
\(40\) 42.7604 31.5469i 1.06901 0.788673i
\(41\) 25.6549 0.625728 0.312864 0.949798i \(-0.398712\pi\)
0.312864 + 0.949798i \(0.398712\pi\)
\(42\) 0 0
\(43\) 38.5869i 0.897370i −0.893690 0.448685i \(-0.851893\pi\)
0.893690 0.448685i \(-0.148107\pi\)
\(44\) −33.0386 23.7591i −0.750877 0.539979i
\(45\) 0 0
\(46\) 48.6375 + 15.6725i 1.05734 + 0.340706i
\(47\) 16.5047 0.351164 0.175582 0.984465i \(-0.443819\pi\)
0.175582 + 0.984465i \(0.443819\pi\)
\(48\) 0 0
\(49\) 48.7783 0.995476
\(50\) 36.3964 + 11.7280i 0.727929 + 0.234561i
\(51\) 0 0
\(52\) 8.05965 11.2075i 0.154993 0.215529i
\(53\) −41.6477 −0.785805 −0.392903 0.919580i \(-0.628529\pi\)
−0.392903 + 0.919580i \(0.628529\pi\)
\(54\) 0 0
\(55\) 67.5759i 1.22865i
\(56\) 3.03110 2.23623i 0.0541268 0.0399326i
\(57\) 0 0
\(58\) 26.9530 + 8.68510i 0.464708 + 0.149743i
\(59\) 31.3349i 0.531099i −0.964097 0.265550i \(-0.914447\pi\)
0.964097 0.265550i \(-0.0855534\pi\)
\(60\) 0 0
\(61\) −3.53469 −0.0579457 −0.0289728 0.999580i \(-0.509224\pi\)
−0.0289728 + 0.999580i \(0.509224\pi\)
\(62\) −36.7859 11.8535i −0.593321 0.191186i
\(63\) 0 0
\(64\) −18.8860 + 61.1500i −0.295094 + 0.955468i
\(65\) 22.9234 0.352667
\(66\) 0 0
\(67\) 13.9620 0.208388 0.104194 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(68\) −33.3342 + 46.3535i −0.490209 + 0.681669i
\(69\) 0 0
\(70\) 5.95346 + 1.91839i 0.0850494 + 0.0274055i
\(71\) 128.352i 1.80777i −0.427773 0.903886i \(-0.640702\pi\)
0.427773 0.903886i \(-0.359298\pi\)
\(72\) 0 0
\(73\) −71.6376 −0.981337 −0.490668 0.871346i \(-0.663247\pi\)
−0.490668 + 0.871346i \(0.663247\pi\)
\(74\) −18.4531 + 57.2667i −0.249366 + 0.773874i
\(75\) 0 0
\(76\) −13.3456 74.8191i −0.175600 0.984462i
\(77\) 4.79017i 0.0622100i
\(78\) 0 0
\(79\) −100.177 −1.26807 −0.634034 0.773305i \(-0.718602\pi\)
−0.634034 + 0.773305i \(0.718602\pi\)
\(80\) −100.750 + 33.8237i −1.25938 + 0.422797i
\(81\) 0 0
\(82\) −48.8369 15.7367i −0.595572 0.191912i
\(83\) 58.6257 0.706333 0.353167 0.935560i \(-0.385105\pi\)
0.353167 + 0.935560i \(0.385105\pi\)
\(84\) 0 0
\(85\) −94.8096 −1.11541
\(86\) −23.6693 + 73.4545i −0.275224 + 0.854122i
\(87\) 0 0
\(88\) 48.3188 + 65.4940i 0.549077 + 0.744250i
\(89\) −108.060 −1.21415 −0.607077 0.794643i \(-0.707658\pi\)
−0.607077 + 0.794643i \(0.707658\pi\)
\(90\) 0 0
\(91\) 1.62494 0.0178565
\(92\) −82.9734 59.6687i −0.901885 0.648573i
\(93\) 0 0
\(94\) −31.4186 10.1240i −0.334240 0.107702i
\(95\) 87.9296 90.5295i 0.925575 0.952942i
\(96\) 0 0
\(97\) 124.227i 1.28069i 0.768087 + 0.640346i \(0.221209\pi\)
−0.768087 + 0.640346i \(0.778791\pi\)
\(98\) −92.8550 29.9207i −0.947500 0.305313i
\(99\) 0 0
\(100\) −62.0907 44.6513i −0.620907 0.446513i
\(101\) 16.1661i 0.160060i −0.996792 0.0800301i \(-0.974498\pi\)
0.996792 0.0800301i \(-0.0255016\pi\)
\(102\) 0 0
\(103\) 8.61325 0.0836238 0.0418119 0.999126i \(-0.486687\pi\)
0.0418119 + 0.999126i \(0.486687\pi\)
\(104\) −22.2171 + 16.3909i −0.213626 + 0.157605i
\(105\) 0 0
\(106\) 79.2810 + 25.5468i 0.747934 + 0.241007i
\(107\) 192.384i 1.79798i −0.437972 0.898989i \(-0.644303\pi\)
0.437972 0.898989i \(-0.355697\pi\)
\(108\) 0 0
\(109\) 31.7667i 0.291438i 0.989326 + 0.145719i \(0.0465495\pi\)
−0.989326 + 0.145719i \(0.953450\pi\)
\(110\) −41.4512 + 128.638i −0.376829 + 1.16944i
\(111\) 0 0
\(112\) −7.14175 + 2.39762i −0.0637656 + 0.0214073i
\(113\) −157.215 −1.39128 −0.695640 0.718391i \(-0.744879\pi\)
−0.695640 + 0.718391i \(0.744879\pi\)
\(114\) 0 0
\(115\) 169.711i 1.47574i
\(116\) −45.9807 33.0661i −0.396385 0.285053i
\(117\) 0 0
\(118\) −19.2209 + 59.6494i −0.162889 + 0.505504i
\(119\) −6.72065 −0.0564761
\(120\) 0 0
\(121\) −17.4974 −0.144607
\(122\) 6.72867 + 2.16818i 0.0551530 + 0.0177720i
\(123\) 0 0
\(124\) 62.7551 + 45.1291i 0.506090 + 0.363944i
\(125\) 39.0587i 0.312470i
\(126\) 0 0
\(127\) −118.218 −0.930851 −0.465425 0.885087i \(-0.654099\pi\)
−0.465425 + 0.885087i \(0.654099\pi\)
\(128\) 73.4612 104.821i 0.573915 0.818915i
\(129\) 0 0
\(130\) −43.6372 14.0612i −0.335671 0.108163i
\(131\) 126.719 0.967322 0.483661 0.875255i \(-0.339307\pi\)
0.483661 + 0.875255i \(0.339307\pi\)
\(132\) 0 0
\(133\) 6.23295 6.41725i 0.0468643 0.0482500i
\(134\) −26.5783 8.56433i −0.198345 0.0639129i
\(135\) 0 0
\(136\) 91.8887 67.7918i 0.675652 0.498469i
\(137\) 20.4018i 0.148918i −0.997224 0.0744590i \(-0.976277\pi\)
0.997224 0.0744590i \(-0.0237230\pi\)
\(138\) 0 0
\(139\) 106.578i 0.766746i −0.923594 0.383373i \(-0.874762\pi\)
0.923594 0.383373i \(-0.125238\pi\)
\(140\) −10.1563 7.30373i −0.0725453 0.0521695i
\(141\) 0 0
\(142\) −78.7313 + 244.332i −0.554446 + 1.72065i
\(143\) 35.1106i 0.245529i
\(144\) 0 0
\(145\) 94.0471i 0.648601i
\(146\) 136.370 + 43.9426i 0.934042 + 0.300977i
\(147\) 0 0
\(148\) 70.2550 97.6944i 0.474696 0.660097i
\(149\) 187.048i 1.25535i −0.778474 0.627677i \(-0.784006\pi\)
0.778474 0.627677i \(-0.215994\pi\)
\(150\) 0 0
\(151\) −280.997 −1.86091 −0.930454 0.366409i \(-0.880587\pi\)
−0.930454 + 0.366409i \(0.880587\pi\)
\(152\) −20.4893 + 150.613i −0.134798 + 0.990873i
\(153\) 0 0
\(154\) −2.93830 + 9.11862i −0.0190799 + 0.0592118i
\(155\) 128.357i 0.828109i
\(156\) 0 0
\(157\) −191.202 −1.21785 −0.608923 0.793230i \(-0.708398\pi\)
−0.608923 + 0.793230i \(0.708398\pi\)
\(158\) 190.699 + 61.4490i 1.20695 + 0.388918i
\(159\) 0 0
\(160\) 212.537 2.58693i 1.32835 0.0161683i
\(161\) 12.0301i 0.0747209i
\(162\) 0 0
\(163\) 177.569i 1.08938i −0.838637 0.544691i \(-0.816647\pi\)
0.838637 0.544691i \(-0.183353\pi\)
\(164\) 83.3136 + 59.9133i 0.508009 + 0.365325i
\(165\) 0 0
\(166\) −111.601 35.9611i −0.672292 0.216633i
\(167\) 101.127i 0.605550i 0.953062 + 0.302775i \(0.0979131\pi\)
−0.953062 + 0.302775i \(0.902087\pi\)
\(168\) 0 0
\(169\) 157.090 0.929525
\(170\) 180.481 + 58.1564i 1.06165 + 0.342097i
\(171\) 0 0
\(172\) 90.1143 125.310i 0.523920 0.728547i
\(173\) 178.731 1.03313 0.516565 0.856248i \(-0.327211\pi\)
0.516565 + 0.856248i \(0.327211\pi\)
\(174\) 0 0
\(175\) 9.00234i 0.0514419i
\(176\) −51.8061 154.314i −0.294353 0.876784i
\(177\) 0 0
\(178\) 205.704 + 66.2840i 1.15564 + 0.372382i
\(179\) 149.034i 0.832591i 0.909229 + 0.416296i \(0.136672\pi\)
−0.909229 + 0.416296i \(0.863328\pi\)
\(180\) 0 0
\(181\) 40.0902i 0.221493i −0.993849 0.110746i \(-0.964676\pi\)
0.993849 0.110746i \(-0.0353242\pi\)
\(182\) −3.09326 0.996742i −0.0169959 0.00547660i
\(183\) 0 0
\(184\) 121.348 + 164.482i 0.659501 + 0.893924i
\(185\) 199.820 1.08011
\(186\) 0 0
\(187\) 145.215i 0.776552i
\(188\) 53.5987 + 38.5444i 0.285099 + 0.205024i
\(189\) 0 0
\(190\) −222.915 + 118.397i −1.17324 + 0.623141i
\(191\) −12.1725 −0.0637301 −0.0318651 0.999492i \(-0.510145\pi\)
−0.0318651 + 0.999492i \(0.510145\pi\)
\(192\) 0 0
\(193\) 268.517i 1.39128i 0.718390 + 0.695641i \(0.244879\pi\)
−0.718390 + 0.695641i \(0.755121\pi\)
\(194\) 76.2012 236.480i 0.392790 1.21897i
\(195\) 0 0
\(196\) 158.406 + 113.915i 0.808196 + 0.581198i
\(197\) 67.3589i 0.341923i −0.985278 0.170962i \(-0.945313\pi\)
0.985278 0.170962i \(-0.0546874\pi\)
\(198\) 0 0
\(199\) 347.506i 1.74626i 0.487485 + 0.873131i \(0.337914\pi\)
−0.487485 + 0.873131i \(0.662086\pi\)
\(200\) 90.8073 + 123.085i 0.454037 + 0.615426i
\(201\) 0 0
\(202\) −9.91630 + 30.7739i −0.0490906 + 0.152346i
\(203\) 6.66660i 0.0328404i
\(204\) 0 0
\(205\) 170.406i 0.831251i
\(206\) −16.3963 5.28338i −0.0795936 0.0256475i
\(207\) 0 0
\(208\) 52.3470 17.5739i 0.251668 0.0844899i
\(209\) 138.659 + 134.677i 0.663442 + 0.644389i
\(210\) 0 0
\(211\) 130.187 0.616998 0.308499 0.951225i \(-0.400173\pi\)
0.308499 + 0.951225i \(0.400173\pi\)
\(212\) −135.250 97.2623i −0.637971 0.458784i
\(213\) 0 0
\(214\) −118.008 + 366.224i −0.551442 + 1.71133i
\(215\) 256.304 1.19211
\(216\) 0 0
\(217\) 9.09867i 0.0419294i
\(218\) 19.4858 60.4715i 0.0893843 0.277392i
\(219\) 0 0
\(220\) 157.814 219.451i 0.717336 0.997505i
\(221\) 49.2605 0.222898
\(222\) 0 0
\(223\) −375.296 −1.68294 −0.841470 0.540303i \(-0.818309\pi\)
−0.841470 + 0.540303i \(0.818309\pi\)
\(224\) 15.0658 0.183377i 0.0672581 0.000818646i
\(225\) 0 0
\(226\) 299.275 + 96.4357i 1.32423 + 0.426707i
\(227\) 151.029i 0.665326i 0.943046 + 0.332663i \(0.107947\pi\)
−0.943046 + 0.332663i \(0.892053\pi\)
\(228\) 0 0
\(229\) 239.645 1.04649 0.523243 0.852183i \(-0.324722\pi\)
0.523243 + 0.852183i \(0.324722\pi\)
\(230\) −104.101 + 323.063i −0.452612 + 1.40462i
\(231\) 0 0
\(232\) 67.2466 + 91.1497i 0.289856 + 0.392887i
\(233\) 285.201i 1.22404i −0.790844 0.612018i \(-0.790358\pi\)
0.790844 0.612018i \(-0.209642\pi\)
\(234\) 0 0
\(235\) 109.629i 0.466505i
\(236\) 73.1781 101.759i 0.310077 0.431183i
\(237\) 0 0
\(238\) 12.7935 + 4.12246i 0.0537542 + 0.0173213i
\(239\) −30.9287 −0.129409 −0.0647045 0.997904i \(-0.520610\pi\)
−0.0647045 + 0.997904i \(0.520610\pi\)
\(240\) 0 0
\(241\) 81.9792i 0.340162i −0.985430 0.170081i \(-0.945597\pi\)
0.985430 0.170081i \(-0.0544030\pi\)
\(242\) 33.3082 + 10.7329i 0.137637 + 0.0443510i
\(243\) 0 0
\(244\) −11.4788 8.25476i −0.0470443 0.0338310i
\(245\) 323.998i 1.32244i
\(246\) 0 0
\(247\) −45.6858 + 47.0366i −0.184963 + 0.190432i
\(248\) −91.7791 124.402i −0.370077 0.501623i
\(249\) 0 0
\(250\) 23.9587 74.3526i 0.0958347 0.297410i
\(251\) 68.9014 0.274508 0.137254 0.990536i \(-0.456172\pi\)
0.137254 + 0.990536i \(0.456172\pi\)
\(252\) 0 0
\(253\) 259.937 1.02742
\(254\) 225.041 + 72.5152i 0.885989 + 0.285493i
\(255\) 0 0
\(256\) −204.139 + 154.477i −0.797418 + 0.603427i
\(257\) −432.173 −1.68161 −0.840803 0.541342i \(-0.817917\pi\)
−0.840803 + 0.541342i \(0.817917\pi\)
\(258\) 0 0
\(259\) 14.1644 0.0546889
\(260\) 74.4431 + 53.5343i 0.286320 + 0.205901i
\(261\) 0 0
\(262\) −241.224 77.7298i −0.920703 0.296679i
\(263\) −440.010 −1.67304 −0.836522 0.547934i \(-0.815415\pi\)
−0.836522 + 0.547934i \(0.815415\pi\)
\(264\) 0 0
\(265\) 276.635i 1.04391i
\(266\) −15.8015 + 8.39264i −0.0594041 + 0.0315513i
\(267\) 0 0
\(268\) 45.3413 + 32.6063i 0.169184 + 0.121665i
\(269\) 217.732 0.809413 0.404706 0.914447i \(-0.367374\pi\)
0.404706 + 0.914447i \(0.367374\pi\)
\(270\) 0 0
\(271\) 301.510i 1.11258i 0.830987 + 0.556291i \(0.187776\pi\)
−0.830987 + 0.556291i \(0.812224\pi\)
\(272\) −216.504 + 72.6845i −0.795970 + 0.267222i
\(273\) 0 0
\(274\) −12.5145 + 38.8370i −0.0456733 + 0.141741i
\(275\) 194.516 0.707332
\(276\) 0 0
\(277\) 99.8731 0.360553 0.180276 0.983616i \(-0.442301\pi\)
0.180276 + 0.983616i \(0.442301\pi\)
\(278\) −65.3750 + 202.883i −0.235162 + 0.729794i
\(279\) 0 0
\(280\) 14.8536 + 20.1334i 0.0530486 + 0.0719049i
\(281\) 530.591 1.88822 0.944112 0.329625i \(-0.106922\pi\)
0.944112 + 0.329625i \(0.106922\pi\)
\(282\) 0 0
\(283\) 135.855i 0.480052i 0.970766 + 0.240026i \(0.0771560\pi\)
−0.970766 + 0.240026i \(0.922844\pi\)
\(284\) 299.748 416.819i 1.05545 1.46767i
\(285\) 0 0
\(286\) 21.5369 66.8369i 0.0753039 0.233696i
\(287\) 12.0794i 0.0420884i
\(288\) 0 0
\(289\) 85.2617 0.295023
\(290\) −57.6887 + 179.029i −0.198927 + 0.617342i
\(291\) 0 0
\(292\) −232.641 167.299i −0.796717 0.572943i
\(293\) −96.2009 −0.328331 −0.164165 0.986433i \(-0.552493\pi\)
−0.164165 + 0.986433i \(0.552493\pi\)
\(294\) 0 0
\(295\) 208.134 0.705540
\(296\) −193.664 + 142.878i −0.654271 + 0.482695i
\(297\) 0 0
\(298\) −114.735 + 356.066i −0.385018 + 1.19485i
\(299\) 88.1770i 0.294906i
\(300\) 0 0
\(301\) 18.1683 0.0603599
\(302\) 534.909 + 172.364i 1.77122 + 0.570742i
\(303\) 0 0
\(304\) 131.390 274.140i 0.432203 0.901776i
\(305\) 23.4783i 0.0769781i
\(306\) 0 0
\(307\) 368.613 1.20070 0.600348 0.799739i \(-0.295029\pi\)
0.600348 + 0.799739i \(0.295029\pi\)
\(308\) 11.1868 15.5560i 0.0363206 0.0505063i
\(309\) 0 0
\(310\) 78.7344 244.342i 0.253982 0.788199i
\(311\) 69.9477 0.224912 0.112456 0.993657i \(-0.464128\pi\)
0.112456 + 0.993657i \(0.464128\pi\)
\(312\) 0 0
\(313\) −465.161 −1.48614 −0.743068 0.669216i \(-0.766630\pi\)
−0.743068 + 0.669216i \(0.766630\pi\)
\(314\) 363.974 + 117.284i 1.15915 + 0.373514i
\(315\) 0 0
\(316\) −325.323 233.950i −1.02950 0.740348i
\(317\) −477.532 −1.50641 −0.753205 0.657786i \(-0.771493\pi\)
−0.753205 + 0.657786i \(0.771493\pi\)
\(318\) 0 0
\(319\) 144.047 0.451559
\(320\) −406.174 125.446i −1.26929 0.392019i
\(321\) 0 0
\(322\) −7.37927 + 22.9006i −0.0229170 + 0.0711198i
\(323\) 188.954 194.541i 0.584996 0.602293i
\(324\) 0 0
\(325\) 65.9846i 0.203030i
\(326\) −108.921 + 338.023i −0.334115 + 1.03688i
\(327\) 0 0
\(328\) −121.846 165.156i −0.371481 0.503526i
\(329\) 7.77111i 0.0236204i
\(330\) 0 0
\(331\) −158.883 −0.480009 −0.240004 0.970772i \(-0.577149\pi\)
−0.240004 + 0.970772i \(0.577149\pi\)
\(332\) 190.385 + 136.912i 0.573450 + 0.412385i
\(333\) 0 0
\(334\) 62.0315 192.506i 0.185723 0.576366i
\(335\) 92.7395i 0.276834i
\(336\) 0 0
\(337\) 611.695i 1.81512i −0.419922 0.907560i \(-0.637943\pi\)
0.419922 0.907560i \(-0.362057\pi\)
\(338\) −299.038 96.3591i −0.884727 0.285086i
\(339\) 0 0
\(340\) −307.892 221.414i −0.905565 0.651219i
\(341\) −196.598 −0.576533
\(342\) 0 0
\(343\) 46.0381i 0.134222i
\(344\) −248.408 + 183.265i −0.722116 + 0.532748i
\(345\) 0 0
\(346\) −340.235 109.634i −0.983339 0.316862i
\(347\) −332.664 −0.958685 −0.479343 0.877628i \(-0.659125\pi\)
−0.479343 + 0.877628i \(0.659125\pi\)
\(348\) 0 0
\(349\) −34.3612 −0.0984562 −0.0492281 0.998788i \(-0.515676\pi\)
−0.0492281 + 0.998788i \(0.515676\pi\)
\(350\) −5.52205 + 17.1370i −0.0157773 + 0.0489627i
\(351\) 0 0
\(352\) 3.96228 + 325.532i 0.0112565 + 0.924806i
\(353\) 66.4096i 0.188129i 0.995566 + 0.0940646i \(0.0299860\pi\)
−0.995566 + 0.0940646i \(0.970014\pi\)
\(354\) 0 0
\(355\) 852.547 2.40154
\(356\) −350.921 252.358i −0.985733 0.708871i
\(357\) 0 0
\(358\) 91.4177 283.703i 0.255357 0.792465i
\(359\) 423.674 1.18015 0.590076 0.807348i \(-0.299098\pi\)
0.590076 + 0.807348i \(0.299098\pi\)
\(360\) 0 0
\(361\) 10.5162 + 360.847i 0.0291308 + 0.999576i
\(362\) −24.5914 + 76.3162i −0.0679321 + 0.210818i
\(363\) 0 0
\(364\) 5.27695 + 3.79482i 0.0144971 + 0.0104253i
\(365\) 475.836i 1.30366i
\(366\) 0 0
\(367\) 280.945i 0.765517i 0.923848 + 0.382759i \(0.125026\pi\)
−0.923848 + 0.382759i \(0.874974\pi\)
\(368\) −130.106 387.545i −0.353550 1.05311i
\(369\) 0 0
\(370\) −380.380 122.570i −1.02806 0.331271i
\(371\) 19.6095i 0.0528557i
\(372\) 0 0
\(373\) 72.2157i 0.193608i −0.995303 0.0968038i \(-0.969138\pi\)
0.995303 0.0968038i \(-0.0308619\pi\)
\(374\) −89.0753 + 276.433i −0.238169 + 0.739126i
\(375\) 0 0
\(376\) −78.3878 106.251i −0.208478 0.282583i
\(377\) 48.8643i 0.129614i
\(378\) 0 0
\(379\) −84.5932 −0.223201 −0.111601 0.993753i \(-0.535598\pi\)
−0.111601 + 0.993753i \(0.535598\pi\)
\(380\) 496.968 88.6452i 1.30781 0.233277i
\(381\) 0 0
\(382\) 23.1716 + 7.46661i 0.0606587 + 0.0195461i
\(383\) 60.9941i 0.159254i 0.996825 + 0.0796268i \(0.0253729\pi\)
−0.996825 + 0.0796268i \(0.974627\pi\)
\(384\) 0 0
\(385\) 31.8176 0.0826430
\(386\) 164.709 511.153i 0.426707 1.32423i
\(387\) 0 0
\(388\) −290.115 + 403.425i −0.747719 + 1.03975i
\(389\) 147.820i 0.380001i 0.981784 + 0.190001i \(0.0608490\pi\)
−0.981784 + 0.190001i \(0.939151\pi\)
\(390\) 0 0
\(391\) 364.695i 0.932723i
\(392\) −231.669 314.016i −0.590992 0.801062i
\(393\) 0 0
\(394\) −41.3181 + 128.225i −0.104868 + 0.325445i
\(395\) 665.404i 1.68457i
\(396\) 0 0
\(397\) −116.017 −0.292234 −0.146117 0.989267i \(-0.546678\pi\)
−0.146117 + 0.989267i \(0.546678\pi\)
\(398\) 213.161 661.517i 0.535580 1.66210i
\(399\) 0 0
\(400\) −97.3612 290.008i −0.243403 0.725020i
\(401\) −145.033 −0.361678 −0.180839 0.983513i \(-0.557881\pi\)
−0.180839 + 0.983513i \(0.557881\pi\)
\(402\) 0 0
\(403\) 66.6907i 0.165486i
\(404\) 37.7536 52.4989i 0.0934495 0.129948i
\(405\) 0 0
\(406\) −4.08931 + 12.6906i −0.0100722 + 0.0312577i
\(407\) 306.055i 0.751978i
\(408\) 0 0
\(409\) 197.143i 0.482012i −0.970524 0.241006i \(-0.922523\pi\)
0.970524 0.241006i \(-0.0774773\pi\)
\(410\) 104.528 324.388i 0.254945 0.791189i
\(411\) 0 0
\(412\) 27.9713 + 20.1150i 0.0678915 + 0.0488229i
\(413\) 14.7538 0.0357234
\(414\) 0 0
\(415\) 389.407i 0.938331i
\(416\) −110.428 + 1.34410i −0.265453 + 0.00323101i
\(417\) 0 0
\(418\) −181.342 341.427i −0.433834 0.816812i
\(419\) −659.596 −1.57421 −0.787107 0.616816i \(-0.788422\pi\)
−0.787107 + 0.616816i \(0.788422\pi\)
\(420\) 0 0
\(421\) 714.982i 1.69830i 0.528155 + 0.849148i \(0.322884\pi\)
−0.528155 + 0.849148i \(0.677116\pi\)
\(422\) −247.825 79.8568i −0.587263 0.189234i
\(423\) 0 0
\(424\) 197.802 + 268.112i 0.466515 + 0.632340i
\(425\) 272.908i 0.642137i
\(426\) 0 0
\(427\) 1.66428i 0.00389761i
\(428\) 449.285 624.761i 1.04973 1.45972i
\(429\) 0 0
\(430\) −487.904 157.218i −1.13466 0.365622i
\(431\) 534.659i 1.24051i 0.784401 + 0.620255i \(0.212971\pi\)
−0.784401 + 0.620255i \(0.787029\pi\)
\(432\) 0 0
\(433\) 482.402i 1.11409i 0.830482 + 0.557046i \(0.188065\pi\)
−0.830482 + 0.557046i \(0.811935\pi\)
\(434\) 5.58115 17.3203i 0.0128598 0.0399086i
\(435\) 0 0
\(436\) −74.1867 + 103.162i −0.170153 + 0.236609i
\(437\) 348.231 + 338.230i 0.796866 + 0.773981i
\(438\) 0 0
\(439\) 376.488 0.857603 0.428802 0.903399i \(-0.358936\pi\)
0.428802 + 0.903399i \(0.358936\pi\)
\(440\) −435.028 + 320.946i −0.988701 + 0.729423i
\(441\) 0 0
\(442\) −93.7729 30.2165i −0.212156 0.0683631i
\(443\) −828.172 −1.86946 −0.934731 0.355356i \(-0.884360\pi\)
−0.934731 + 0.355356i \(0.884360\pi\)
\(444\) 0 0
\(445\) 717.761i 1.61295i
\(446\) 714.417 + 230.207i 1.60183 + 0.516160i
\(447\) 0 0
\(448\) −28.7920 8.89233i −0.0642678 0.0198489i
\(449\) 484.547 1.07917 0.539585 0.841931i \(-0.318581\pi\)
0.539585 + 0.841931i \(0.318581\pi\)
\(450\) 0 0
\(451\) −261.003 −0.578720
\(452\) −510.551 367.152i −1.12954 0.812284i
\(453\) 0 0
\(454\) 92.6415 287.501i 0.204056 0.633261i
\(455\) 10.7933i 0.0237215i
\(456\) 0 0
\(457\) 14.5377 0.0318113 0.0159056 0.999873i \(-0.494937\pi\)
0.0159056 + 0.999873i \(0.494937\pi\)
\(458\) −456.192 146.999i −0.996052 0.320958i
\(459\) 0 0
\(460\) 396.335 551.131i 0.861598 1.19811i
\(461\) 822.917i 1.78507i 0.450979 + 0.892534i \(0.351075\pi\)
−0.450979 + 0.892534i \(0.648925\pi\)
\(462\) 0 0
\(463\) 13.5543i 0.0292750i 0.999893 + 0.0146375i \(0.00465943\pi\)
−0.999893 + 0.0146375i \(0.995341\pi\)
\(464\) −72.1000 214.763i −0.155388 0.462851i
\(465\) 0 0
\(466\) −174.943 + 542.911i −0.375413 + 1.16505i
\(467\) −335.258 −0.717897 −0.358948 0.933357i \(-0.616865\pi\)
−0.358948 + 0.933357i \(0.616865\pi\)
\(468\) 0 0
\(469\) 6.57390i 0.0140169i
\(470\) 67.2465 208.690i 0.143078 0.444022i
\(471\) 0 0
\(472\) −201.722 + 148.822i −0.427377 + 0.315302i
\(473\) 392.569i 0.829955i
\(474\) 0 0
\(475\) 260.588 + 253.104i 0.548606 + 0.532851i
\(476\) −21.8252 15.6951i −0.0458512 0.0329730i
\(477\) 0 0
\(478\) 58.8763 + 18.9717i 0.123172 + 0.0396899i
\(479\) −760.782 −1.58827 −0.794136 0.607740i \(-0.792076\pi\)
−0.794136 + 0.607740i \(0.792076\pi\)
\(480\) 0 0
\(481\) −103.821 −0.215845
\(482\) −50.2862 + 156.057i −0.104328 + 0.323769i
\(483\) 0 0
\(484\) −56.8223 40.8627i −0.117402 0.0844270i
\(485\) −825.149 −1.70134
\(486\) 0 0
\(487\) −687.736 −1.41219 −0.706095 0.708117i \(-0.749545\pi\)
−0.706095 + 0.708117i \(0.749545\pi\)
\(488\) 16.7877 + 22.7550i 0.0344010 + 0.0466291i
\(489\) 0 0
\(490\) 198.741 616.767i 0.405594 1.25871i
\(491\) −276.744 −0.563634 −0.281817 0.959468i \(-0.590937\pi\)
−0.281817 + 0.959468i \(0.590937\pi\)
\(492\) 0 0
\(493\) 202.100i 0.409939i
\(494\) 115.820 61.5157i 0.234454 0.124526i
\(495\) 0 0
\(496\) 98.4031 + 293.111i 0.198393 + 0.590950i
\(497\) 60.4334 0.121596
\(498\) 0 0
\(499\) 75.2973i 0.150896i −0.997150 0.0754482i \(-0.975961\pi\)
0.997150 0.0754482i \(-0.0240388\pi\)
\(500\) −91.2161 + 126.842i −0.182432 + 0.253684i
\(501\) 0 0
\(502\) −131.162 42.2643i −0.261278 0.0841917i
\(503\) 379.172 0.753820 0.376910 0.926250i \(-0.376987\pi\)
0.376910 + 0.926250i \(0.376987\pi\)
\(504\) 0 0
\(505\) 107.379 0.212632
\(506\) −494.820 159.446i −0.977905 0.315111i
\(507\) 0 0
\(508\) −383.910 276.081i −0.755729 0.543467i
\(509\) 565.844 1.11168 0.555839 0.831290i \(-0.312397\pi\)
0.555839 + 0.831290i \(0.312397\pi\)
\(510\) 0 0
\(511\) 33.7300i 0.0660078i
\(512\) 483.358 168.846i 0.944059 0.329777i
\(513\) 0 0
\(514\) 822.689 + 265.096i 1.60056 + 0.515750i
\(515\) 57.2115i 0.111090i
\(516\) 0 0
\(517\) −167.913 −0.324783
\(518\) −26.9636 8.68848i −0.0520532 0.0167731i
\(519\) 0 0
\(520\) −108.873 147.572i −0.209371 0.283792i
\(521\) −324.637 −0.623103 −0.311552 0.950229i \(-0.600849\pi\)
−0.311552 + 0.950229i \(0.600849\pi\)
\(522\) 0 0
\(523\) 271.054 0.518268 0.259134 0.965841i \(-0.416563\pi\)
0.259134 + 0.965841i \(0.416563\pi\)
\(524\) 411.518 + 295.935i 0.785339 + 0.564761i
\(525\) 0 0
\(526\) 837.609 + 269.903i 1.59241 + 0.513124i
\(527\) 275.829i 0.523394i
\(528\) 0 0
\(529\) 123.809 0.234043
\(530\) −169.688 + 526.605i −0.320167 + 0.993595i
\(531\) 0 0
\(532\) 35.2279 6.28368i 0.0662179 0.0118114i
\(533\) 88.5385i 0.166113i
\(534\) 0 0
\(535\) 1277.86 2.38853
\(536\) −66.3115 89.8823i −0.123716 0.167691i
\(537\) 0 0
\(538\) −414.477 133.557i −0.770404 0.248248i
\(539\) −496.252 −0.920690
\(540\) 0 0
\(541\) 4.97150 0.00918947 0.00459473 0.999989i \(-0.498537\pi\)
0.00459473 + 0.999989i \(0.498537\pi\)
\(542\) 184.947 573.958i 0.341230 1.05896i
\(543\) 0 0
\(544\) 456.724 5.55911i 0.839567 0.0102190i
\(545\) −211.003 −0.387161
\(546\) 0 0
\(547\) 148.968 0.272337 0.136168 0.990686i \(-0.456521\pi\)
0.136168 + 0.990686i \(0.456521\pi\)
\(548\) 47.6454 66.2542i 0.0869442 0.120902i
\(549\) 0 0
\(550\) −370.284 119.317i −0.673243 0.216939i
\(551\) 192.976 + 187.434i 0.350229 + 0.340171i
\(552\) 0 0
\(553\) 47.1677i 0.0852942i
\(554\) −190.120 61.2624i −0.343176 0.110582i
\(555\) 0 0
\(556\) 248.897 346.109i 0.447657 0.622498i
\(557\) 507.393i 0.910940i −0.890251 0.455470i \(-0.849471\pi\)
0.890251 0.455470i \(-0.150529\pi\)
\(558\) 0 0
\(559\) −133.169 −0.238227
\(560\) −15.9256 47.4374i −0.0284386 0.0847096i
\(561\) 0 0
\(562\) −1010.04 325.466i −1.79722 0.579120i
\(563\) 430.982i 0.765510i −0.923850 0.382755i \(-0.874975\pi\)
0.923850 0.382755i \(-0.125025\pi\)
\(564\) 0 0
\(565\) 1044.26i 1.84825i
\(566\) 83.3336 258.615i 0.147232 0.456917i
\(567\) 0 0
\(568\) −826.281 + 609.597i −1.45472 + 1.07323i
\(569\) −607.193 −1.06712 −0.533561 0.845761i \(-0.679147\pi\)
−0.533561 + 0.845761i \(0.679147\pi\)
\(570\) 0 0
\(571\) 248.126i 0.434547i −0.976111 0.217274i \(-0.930284\pi\)
0.976111 0.217274i \(-0.0697164\pi\)
\(572\) −81.9958 + 114.021i −0.143349 + 0.199337i
\(573\) 0 0
\(574\) 7.40952 22.9945i 0.0129086 0.0400600i
\(575\) 488.510 0.849582
\(576\) 0 0
\(577\) 958.765 1.66164 0.830818 0.556543i \(-0.187873\pi\)
0.830818 + 0.556543i \(0.187873\pi\)
\(578\) −162.305 52.2997i −0.280805 0.0904839i
\(579\) 0 0
\(580\) 219.634 305.416i 0.378679 0.526579i
\(581\) 27.6034i 0.0475102i
\(582\) 0 0
\(583\) 423.708 0.726772
\(584\) 340.237 + 461.176i 0.582597 + 0.789685i
\(585\) 0 0
\(586\) 183.129 + 59.0098i 0.312507 + 0.100699i
\(587\) −702.884 −1.19742 −0.598708 0.800967i \(-0.704319\pi\)
−0.598708 + 0.800967i \(0.704319\pi\)
\(588\) 0 0
\(589\) −263.377 255.813i −0.447159 0.434317i
\(590\) −396.207 127.670i −0.671538 0.216390i
\(591\) 0 0
\(592\) 456.303 153.190i 0.770782 0.258766i
\(593\) 266.340i 0.449141i 0.974458 + 0.224570i \(0.0720979\pi\)
−0.974458 + 0.224570i \(0.927902\pi\)
\(594\) 0 0
\(595\) 44.6403i 0.0750258i
\(596\) 436.824 607.433i 0.732926 1.01918i
\(597\) 0 0
\(598\) 54.0880 167.855i 0.0904481 0.280694i
\(599\) 929.881i 1.55239i 0.630493 + 0.776195i \(0.282853\pi\)
−0.630493 + 0.776195i \(0.717147\pi\)
\(600\) 0 0
\(601\) 666.868i 1.10960i −0.831985 0.554798i \(-0.812795\pi\)
0.831985 0.554798i \(-0.187205\pi\)
\(602\) −34.5854 11.1445i −0.0574509 0.0185124i
\(603\) 0 0
\(604\) −912.531 656.229i −1.51081 1.08647i
\(605\) 116.222i 0.192103i
\(606\) 0 0
\(607\) 146.368 0.241134 0.120567 0.992705i \(-0.461529\pi\)
0.120567 + 0.992705i \(0.461529\pi\)
\(608\) −418.273 + 441.261i −0.687949 + 0.725759i
\(609\) 0 0
\(610\) −14.4016 + 44.6936i −0.0236093 + 0.0732682i
\(611\) 56.9601i 0.0932243i
\(612\) 0 0
\(613\) 8.51007 0.0138827 0.00694133 0.999976i \(-0.497790\pi\)
0.00694133 + 0.999976i \(0.497790\pi\)
\(614\) −701.697 226.108i −1.14283 0.368254i
\(615\) 0 0
\(616\) −30.8373 + 22.7505i −0.0500605 + 0.0369327i
\(617\) 1036.99i 1.68069i 0.542052 + 0.840345i \(0.317648\pi\)
−0.542052 + 0.840345i \(0.682352\pi\)
\(618\) 0 0
\(619\) 1128.03i 1.82234i 0.412035 + 0.911168i \(0.364818\pi\)
−0.412035 + 0.911168i \(0.635182\pi\)
\(620\) −299.759 + 416.836i −0.483483 + 0.672316i
\(621\) 0 0
\(622\) −133.153 42.9061i −0.214073 0.0689808i
\(623\) 50.8790i 0.0816677i
\(624\) 0 0
\(625\) −737.430 −1.17989
\(626\) 885.485 + 285.330i 1.41451 + 0.455799i
\(627\) 0 0
\(628\) −620.923 446.525i −0.988731 0.711026i
\(629\) 429.398 0.682668
\(630\) 0 0
\(631\) 73.3862i 0.116301i −0.998308 0.0581507i \(-0.981480\pi\)
0.998308 0.0581507i \(-0.0185204\pi\)
\(632\) 475.784 + 644.904i 0.752823 + 1.02042i
\(633\) 0 0
\(634\) 909.036 + 292.919i 1.43381 + 0.462017i
\(635\) 785.235i 1.23659i
\(636\) 0 0
\(637\) 168.341i 0.264271i
\(638\) −274.210 88.3589i −0.429796 0.138494i
\(639\) 0 0
\(640\) 696.249 + 487.948i 1.08789 + 0.762419i
\(641\) 458.489 0.715271 0.357635 0.933861i \(-0.383583\pi\)
0.357635 + 0.933861i \(0.383583\pi\)
\(642\) 0 0
\(643\) 691.411i 1.07529i −0.843172 0.537645i \(-0.819314\pi\)
0.843172 0.537645i \(-0.180686\pi\)
\(644\) 28.0945 39.0673i 0.0436250 0.0606636i
\(645\) 0 0
\(646\) −479.026 + 254.425i −0.741526 + 0.393847i
\(647\) 504.684 0.780037 0.390018 0.920807i \(-0.372469\pi\)
0.390018 + 0.920807i \(0.372469\pi\)
\(648\) 0 0
\(649\) 318.789i 0.491200i
\(650\) 40.4751 125.609i 0.0622694 0.193245i
\(651\) 0 0
\(652\) 414.688 576.652i 0.636025 0.884436i
\(653\) 251.132i 0.384581i −0.981338 0.192291i \(-0.938408\pi\)
0.981338 0.192291i \(-0.0615916\pi\)
\(654\) 0 0
\(655\) 841.702i 1.28504i
\(656\) 130.640 + 389.134i 0.199146 + 0.593192i
\(657\) 0 0
\(658\) 4.76682 14.7932i 0.00724440 0.0224820i
\(659\) 785.619i 1.19214i 0.802933 + 0.596069i \(0.203271\pi\)
−0.802933 + 0.596069i \(0.796729\pi\)
\(660\) 0 0
\(661\) 1136.79i 1.71981i 0.510455 + 0.859905i \(0.329477\pi\)
−0.510455 + 0.859905i \(0.670523\pi\)
\(662\) 302.451 + 97.4591i 0.456875 + 0.147219i
\(663\) 0 0
\(664\) −278.438 377.410i −0.419334 0.568389i
\(665\) 42.6251 + 41.4009i 0.0640978 + 0.0622570i
\(666\) 0 0
\(667\) 361.762 0.542371
\(668\) −236.168 + 328.407i −0.353544 + 0.491628i
\(669\) 0 0
\(670\) 56.8866 176.540i 0.0849053 0.263492i
\(671\) 35.9606 0.0535925
\(672\) 0 0
\(673\) 196.852i 0.292499i −0.989248 0.146250i \(-0.953280\pi\)
0.989248 0.146250i \(-0.0467202\pi\)
\(674\) −375.215 + 1164.43i −0.556699 + 1.72764i
\(675\) 0 0
\(676\) 510.145 + 366.861i 0.754652 + 0.542693i
\(677\) 1186.26 1.75223 0.876117 0.482099i \(-0.160125\pi\)
0.876117 + 0.482099i \(0.160125\pi\)
\(678\) 0 0
\(679\) −58.4913 −0.0861433
\(680\) 450.291 + 610.349i 0.662192 + 0.897572i
\(681\) 0 0
\(682\) 374.246 + 120.594i 0.548748 + 0.176823i
\(683\) 777.354i 1.13815i −0.822287 0.569073i \(-0.807302\pi\)
0.822287 0.569073i \(-0.192698\pi\)
\(684\) 0 0
\(685\) 135.514 0.197831
\(686\) 28.2399 87.6387i 0.0411660 0.127753i
\(687\) 0 0
\(688\) 585.288 196.492i 0.850709 0.285599i
\(689\) 143.732i 0.208609i
\(690\) 0 0
\(691\) 531.659i 0.769405i −0.923041 0.384702i \(-0.874304\pi\)
0.923041 0.384702i \(-0.125696\pi\)
\(692\) 580.426 + 417.402i 0.838766 + 0.603182i
\(693\) 0 0
\(694\) 633.263 + 204.057i 0.912482 + 0.294030i
\(695\) 707.918 1.01859
\(696\) 0 0
\(697\) 366.190i 0.525380i
\(698\) 65.4104 + 21.0772i 0.0937112 + 0.0301966i
\(699\) 0 0
\(700\) 21.0237 29.2349i 0.0300338 0.0417641i
\(701\) 609.856i 0.869980i −0.900435 0.434990i \(-0.856752\pi\)
0.900435 0.434990i \(-0.143248\pi\)
\(702\) 0 0
\(703\) −398.238 + 410.013i −0.566484 + 0.583233i
\(704\) 192.139 622.117i 0.272925 0.883689i
\(705\) 0 0
\(706\) 40.7358 126.418i 0.0576994 0.179063i
\(707\) 7.61166 0.0107661
\(708\) 0 0
\(709\) 963.066 1.35834 0.679172 0.733979i \(-0.262339\pi\)
0.679172 + 0.733979i \(0.262339\pi\)
\(710\) −1622.92 522.954i −2.28580 0.736555i
\(711\) 0 0
\(712\) 513.221 + 695.647i 0.720816 + 0.977033i
\(713\) −493.737 −0.692479
\(714\) 0 0
\(715\) −233.214 −0.326173
\(716\) −348.048 + 483.984i −0.486100 + 0.675955i
\(717\) 0 0
\(718\) −806.511 259.883i −1.12327 0.361954i
\(719\) 1180.47 1.64182 0.820910 0.571057i \(-0.193466\pi\)
0.820910 + 0.571057i \(0.193466\pi\)
\(720\) 0 0
\(721\) 4.05548i 0.00562479i
\(722\) 201.325 693.363i 0.278844 0.960336i
\(723\) 0 0
\(724\) 93.6250 130.192i 0.129316 0.179823i
\(725\) 270.713 0.373398
\(726\) 0 0
\(727\) 86.0390i 0.118348i −0.998248 0.0591740i \(-0.981153\pi\)
0.998248 0.0591740i \(-0.0188467\pi\)
\(728\) −7.71752 10.4608i −0.0106010 0.0143692i
\(729\) 0 0
\(730\) −291.879 + 905.806i −0.399834 + 1.24083i
\(731\) 550.778 0.753458
\(732\) 0 0
\(733\) −824.526 −1.12486 −0.562432 0.826843i \(-0.690134\pi\)
−0.562432 + 0.826843i \(0.690134\pi\)
\(734\) 172.332 534.810i 0.234785 0.728624i
\(735\) 0 0
\(736\) 9.95089 + 817.543i 0.0135202 + 1.11079i
\(737\) −142.044 −0.192733
\(738\) 0 0
\(739\) 1108.68i 1.50024i 0.661300 + 0.750121i \(0.270005\pi\)
−0.661300 + 0.750121i \(0.729995\pi\)
\(740\) 648.912 + 466.652i 0.876908 + 0.630611i
\(741\) 0 0
\(742\) −12.0285 + 37.3288i −0.0162109 + 0.0503084i
\(743\) 1014.11i 1.36488i 0.730941 + 0.682441i \(0.239081\pi\)
−0.730941 + 0.682441i \(0.760919\pi\)
\(744\) 0 0
\(745\) 1242.42 1.66768
\(746\) −44.2972 + 137.471i −0.0593797 + 0.184277i
\(747\) 0 0
\(748\) 339.129 471.583i 0.453382 0.630458i
\(749\) 90.5822 0.120938
\(750\) 0 0
\(751\) −1425.08 −1.89758 −0.948788 0.315915i \(-0.897689\pi\)
−0.948788 + 0.315915i \(0.897689\pi\)
\(752\) 84.0453 + 250.344i 0.111762 + 0.332905i
\(753\) 0 0
\(754\) 29.9735 93.0187i 0.0397526 0.123367i
\(755\) 1866.46i 2.47213i
\(756\) 0 0
\(757\) 354.171 0.467861 0.233931 0.972253i \(-0.424841\pi\)
0.233931 + 0.972253i \(0.424841\pi\)
\(758\) 161.033 + 51.8896i 0.212444 + 0.0684560i
\(759\) 0 0
\(760\) −1000.41 136.095i −1.31633 0.179073i
\(761\) 1284.03i 1.68729i −0.536899 0.843647i \(-0.680404\pi\)
0.536899 0.843647i \(-0.319596\pi\)
\(762\) 0 0
\(763\) −14.9571 −0.0196030
\(764\) −39.5298 28.4270i −0.0517405 0.0372082i
\(765\) 0 0
\(766\) 37.4139 116.109i 0.0488432 0.151578i
\(767\) −108.141 −0.140992
\(768\) 0 0
\(769\) 203.965 0.265233 0.132617 0.991167i \(-0.457662\pi\)
0.132617 + 0.991167i \(0.457662\pi\)
\(770\) −60.5683 19.5170i −0.0786601 0.0253467i
\(771\) 0 0
\(772\) −627.084 + 872.004i −0.812285 + 1.12954i
\(773\) −528.359 −0.683518 −0.341759 0.939788i \(-0.611023\pi\)
−0.341759 + 0.939788i \(0.611023\pi\)
\(774\) 0 0
\(775\) −369.474 −0.476740
\(776\) 799.728 590.007i 1.03058 0.760318i
\(777\) 0 0
\(778\) 90.6734 281.393i 0.116547 0.361687i
\(779\) −349.658 339.616i −0.448855 0.435965i
\(780\) 0 0
\(781\) 1305.80i 1.67196i
\(782\) −223.704 + 694.237i −0.286067 + 0.887771i
\(783\) 0 0
\(784\) 248.389 + 739.871i 0.316823 + 0.943714i
\(785\) 1270.01i 1.61785i
\(786\) 0 0
\(787\) −9.60697 −0.0122071 −0.00610354 0.999981i \(-0.501943\pi\)
−0.00610354 + 0.999981i \(0.501943\pi\)
\(788\) 157.307 218.746i 0.199628 0.277597i
\(789\) 0 0
\(790\) −408.160 + 1266.67i −0.516659 + 1.60338i
\(791\) 74.0232i 0.0935818i
\(792\) 0 0
\(793\) 12.1987i 0.0153830i
\(794\) 220.852 + 71.1651i 0.278151 + 0.0