Properties

Label 1520.2.q.o.961.4
Level $1520$
Weight $2$
Character 1520.961
Analytic conductor $12.137$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.4
Root \(-1.02359 + 1.77290i\) of defining polynomial
Character \(\chi\) \(=\) 1520.961
Dual form 1520.2.q.o.881.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.52359 - 2.63893i) q^{3} +(-0.500000 + 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 - 5.44319i) q^{9} +O(q^{10})\) \(q+(1.52359 - 2.63893i) q^{3} +(-0.500000 + 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 - 5.44319i) q^{9} -4.48517 q^{11} +(-2.21900 - 3.84342i) q^{13} +(1.52359 + 2.63893i) q^{15} +(-1.45172 + 2.51445i) q^{17} +(-3.60532 + 2.44983i) q^{19} +(0.928131 - 1.60757i) q^{21} +(-1.42363 - 2.46580i) q^{23} +(-0.500000 - 0.866025i) q^{25} -10.0107 q^{27} +(-0.558149 - 0.966742i) q^{29} +6.22908 q^{31} +(-6.83354 + 11.8360i) q^{33} +(-0.304588 + 0.527561i) q^{35} -3.77264 q^{37} -13.5233 q^{39} +(4.15184 - 7.19120i) q^{41} +(-4.99438 + 8.65053i) q^{43} +6.28525 q^{45} +(-2.94250 - 5.09656i) q^{47} -6.62891 q^{49} +(4.42363 + 7.66195i) q^{51} +(-4.22436 - 7.31681i) q^{53} +(2.24258 - 3.88427i) q^{55} +(0.971912 + 13.2467i) q^{57} +(5.11793 - 8.86451i) q^{59} +(2.49099 + 4.31453i) q^{61} +(-1.91441 - 3.31586i) q^{63} +4.43800 q^{65} +(4.23808 + 7.34057i) q^{67} -8.67608 q^{69} +(5.80995 - 10.0631i) q^{71} +(-1.86162 + 3.22443i) q^{73} -3.04717 q^{75} -2.73225 q^{77} +(4.51908 - 7.82728i) q^{79} +(-5.82432 + 10.0880i) q^{81} +2.12178 q^{83} +(-1.45172 - 2.51445i) q^{85} -3.40155 q^{87} +(-3.96608 - 6.86946i) q^{89} +(-1.35176 - 2.34131i) q^{91} +(9.49053 - 16.4381i) q^{93} +(-0.318955 - 4.34721i) q^{95} +(4.83628 - 8.37668i) q^{97} +(14.0952 + 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.52359 2.63893i 0.879643 1.52359i 0.0279089 0.999610i \(-0.491115\pi\)
0.851734 0.523975i \(-0.175552\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0.609175 0.230247 0.115123 0.993351i \(-0.463274\pi\)
0.115123 + 0.993351i \(0.463274\pi\)
\(8\) 0 0
\(9\) −3.14263 5.44319i −1.04754 1.81440i
\(10\) 0 0
\(11\) −4.48517 −1.35233 −0.676164 0.736751i \(-0.736359\pi\)
−0.676164 + 0.736751i \(0.736359\pi\)
\(12\) 0 0
\(13\) −2.21900 3.84342i −0.615439 1.06597i −0.990307 0.138894i \(-0.955645\pi\)
0.374868 0.927078i \(-0.377688\pi\)
\(14\) 0 0
\(15\) 1.52359 + 2.63893i 0.393388 + 0.681368i
\(16\) 0 0
\(17\) −1.45172 + 2.51445i −0.352093 + 0.609843i −0.986616 0.163061i \(-0.947863\pi\)
0.634523 + 0.772904i \(0.281197\pi\)
\(18\) 0 0
\(19\) −3.60532 + 2.44983i −0.827117 + 0.562030i
\(20\) 0 0
\(21\) 0.928131 1.60757i 0.202535 0.350800i
\(22\) 0 0
\(23\) −1.42363 2.46580i −0.296847 0.514154i 0.678566 0.734540i \(-0.262602\pi\)
−0.975413 + 0.220386i \(0.929268\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −10.0107 −1.92656
\(28\) 0 0
\(29\) −0.558149 0.966742i −0.103646 0.179519i 0.809538 0.587067i \(-0.199717\pi\)
−0.913184 + 0.407547i \(0.866384\pi\)
\(30\) 0 0
\(31\) 6.22908 1.11877 0.559387 0.828906i \(-0.311036\pi\)
0.559387 + 0.828906i \(0.311036\pi\)
\(32\) 0 0
\(33\) −6.83354 + 11.8360i −1.18957 + 2.06039i
\(34\) 0 0
\(35\) −0.304588 + 0.527561i −0.0514847 + 0.0891741i
\(36\) 0 0
\(37\) −3.77264 −0.620219 −0.310109 0.950701i \(-0.600366\pi\)
−0.310109 + 0.950701i \(0.600366\pi\)
\(38\) 0 0
\(39\) −13.5233 −2.16547
\(40\) 0 0
\(41\) 4.15184 7.19120i 0.648409 1.12308i −0.335094 0.942185i \(-0.608768\pi\)
0.983503 0.180893i \(-0.0578987\pi\)
\(42\) 0 0
\(43\) −4.99438 + 8.65053i −0.761637 + 1.31919i 0.180370 + 0.983599i \(0.442270\pi\)
−0.942007 + 0.335594i \(0.891063\pi\)
\(44\) 0 0
\(45\) 6.28525 0.936950
\(46\) 0 0
\(47\) −2.94250 5.09656i −0.429208 0.743409i 0.567595 0.823308i \(-0.307874\pi\)
−0.996803 + 0.0798983i \(0.974540\pi\)
\(48\) 0 0
\(49\) −6.62891 −0.946986
\(50\) 0 0
\(51\) 4.42363 + 7.66195i 0.619432 + 1.07289i
\(52\) 0 0
\(53\) −4.22436 7.31681i −0.580261 1.00504i −0.995448 0.0953049i \(-0.969617\pi\)
0.415188 0.909736i \(-0.363716\pi\)
\(54\) 0 0
\(55\) 2.24258 3.88427i 0.302390 0.523755i
\(56\) 0 0
\(57\) 0.971912 + 13.2467i 0.128733 + 1.75457i
\(58\) 0 0
\(59\) 5.11793 8.86451i 0.666297 1.15406i −0.312634 0.949874i \(-0.601211\pi\)
0.978932 0.204187i \(-0.0654552\pi\)
\(60\) 0 0
\(61\) 2.49099 + 4.31453i 0.318939 + 0.552419i 0.980267 0.197678i \(-0.0633401\pi\)
−0.661328 + 0.750097i \(0.730007\pi\)
\(62\) 0 0
\(63\) −1.91441 3.31586i −0.241193 0.417759i
\(64\) 0 0
\(65\) 4.43800 0.550466
\(66\) 0 0
\(67\) 4.23808 + 7.34057i 0.517764 + 0.896794i 0.999787 + 0.0206350i \(0.00656879\pi\)
−0.482023 + 0.876159i \(0.660098\pi\)
\(68\) 0 0
\(69\) −8.67608 −1.04448
\(70\) 0 0
\(71\) 5.80995 10.0631i 0.689514 1.19427i −0.282481 0.959273i \(-0.591157\pi\)
0.971995 0.235001i \(-0.0755093\pi\)
\(72\) 0 0
\(73\) −1.86162 + 3.22443i −0.217887 + 0.377391i −0.954162 0.299292i \(-0.903250\pi\)
0.736275 + 0.676682i \(0.236583\pi\)
\(74\) 0 0
\(75\) −3.04717 −0.351857
\(76\) 0 0
\(77\) −2.73225 −0.311369
\(78\) 0 0
\(79\) 4.51908 7.82728i 0.508437 0.880638i −0.491516 0.870869i \(-0.663557\pi\)
0.999952 0.00976923i \(-0.00310969\pi\)
\(80\) 0 0
\(81\) −5.82432 + 10.0880i −0.647146 + 1.12089i
\(82\) 0 0
\(83\) 2.12178 0.232896 0.116448 0.993197i \(-0.462849\pi\)
0.116448 + 0.993197i \(0.462849\pi\)
\(84\) 0 0
\(85\) −1.45172 2.51445i −0.157461 0.272730i
\(86\) 0 0
\(87\) −3.40155 −0.364684
\(88\) 0 0
\(89\) −3.96608 6.86946i −0.420404 0.728161i 0.575575 0.817749i \(-0.304778\pi\)
−0.995979 + 0.0895879i \(0.971445\pi\)
\(90\) 0 0
\(91\) −1.35176 2.34131i −0.141703 0.245436i
\(92\) 0 0
\(93\) 9.49053 16.4381i 0.984122 1.70455i
\(94\) 0 0
\(95\) −0.318955 4.34721i −0.0327241 0.446015i
\(96\) 0 0
\(97\) 4.83628 8.37668i 0.491050 0.850523i −0.508897 0.860827i \(-0.669947\pi\)
0.999947 + 0.0103043i \(0.00328001\pi\)
\(98\) 0 0
\(99\) 14.0952 + 24.4136i 1.41662 + 2.45366i
\(100\) 0 0
\(101\) 0.485632 + 0.841140i 0.0483222 + 0.0836965i 0.889175 0.457568i \(-0.151279\pi\)
−0.840853 + 0.541264i \(0.817946\pi\)
\(102\) 0 0
\(103\) 3.34143 0.329241 0.164620 0.986357i \(-0.447360\pi\)
0.164620 + 0.986357i \(0.447360\pi\)
\(104\) 0 0
\(105\) 0.928131 + 1.60757i 0.0905763 + 0.156883i
\(106\) 0 0
\(107\) −9.51655 −0.920000 −0.460000 0.887919i \(-0.652151\pi\)
−0.460000 + 0.887919i \(0.652151\pi\)
\(108\) 0 0
\(109\) −2.77178 + 4.80087i −0.265489 + 0.459840i −0.967692 0.252137i \(-0.918867\pi\)
0.702203 + 0.711977i \(0.252200\pi\)
\(110\) 0 0
\(111\) −5.74795 + 9.95573i −0.545571 + 0.944956i
\(112\) 0 0
\(113\) 1.54134 0.144997 0.0724987 0.997369i \(-0.476903\pi\)
0.0724987 + 0.997369i \(0.476903\pi\)
\(114\) 0 0
\(115\) 2.84726 0.265508
\(116\) 0 0
\(117\) −13.9470 + 24.1568i −1.28940 + 2.23330i
\(118\) 0 0
\(119\) −0.884350 + 1.53174i −0.0810682 + 0.140414i
\(120\) 0 0
\(121\) 9.11672 0.828793
\(122\) 0 0
\(123\) −12.6514 21.9128i −1.14074 1.97581i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 1.15274 + 1.99661i 0.102289 + 0.177171i 0.912628 0.408792i \(-0.134050\pi\)
−0.810338 + 0.585963i \(0.800717\pi\)
\(128\) 0 0
\(129\) 15.2187 + 26.3596i 1.33994 + 2.32084i
\(130\) 0 0
\(131\) −6.45905 + 11.1874i −0.564330 + 0.977448i 0.432782 + 0.901499i \(0.357532\pi\)
−0.997112 + 0.0759493i \(0.975801\pi\)
\(132\) 0 0
\(133\) −2.19627 + 1.49238i −0.190441 + 0.129405i
\(134\) 0 0
\(135\) 5.00536 8.66954i 0.430793 0.746155i
\(136\) 0 0
\(137\) 6.36677 + 11.0276i 0.543950 + 0.942149i 0.998672 + 0.0515159i \(0.0164053\pi\)
−0.454722 + 0.890633i \(0.650261\pi\)
\(138\) 0 0
\(139\) 5.30433 + 9.18738i 0.449908 + 0.779263i 0.998380 0.0569059i \(-0.0181235\pi\)
−0.548472 + 0.836169i \(0.684790\pi\)
\(140\) 0 0
\(141\) −17.9326 −1.51020
\(142\) 0 0
\(143\) 9.95258 + 17.2384i 0.832276 + 1.44154i
\(144\) 0 0
\(145\) 1.11630 0.0927035
\(146\) 0 0
\(147\) −10.0997 + 17.4932i −0.833010 + 1.44281i
\(148\) 0 0
\(149\) −1.88653 + 3.26757i −0.154551 + 0.267690i −0.932895 0.360147i \(-0.882726\pi\)
0.778344 + 0.627837i \(0.216060\pi\)
\(150\) 0 0
\(151\) 9.51562 0.774370 0.387185 0.922002i \(-0.373447\pi\)
0.387185 + 0.922002i \(0.373447\pi\)
\(152\) 0 0
\(153\) 18.2488 1.47533
\(154\) 0 0
\(155\) −3.11454 + 5.39454i −0.250166 + 0.433300i
\(156\) 0 0
\(157\) 1.72822 2.99336i 0.137927 0.238896i −0.788785 0.614669i \(-0.789290\pi\)
0.926712 + 0.375773i \(0.122623\pi\)
\(158\) 0 0
\(159\) −25.7447 −2.04169
\(160\) 0 0
\(161\) −0.867239 1.50210i −0.0683480 0.118382i
\(162\) 0 0
\(163\) −6.65283 −0.521090 −0.260545 0.965462i \(-0.583902\pi\)
−0.260545 + 0.965462i \(0.583902\pi\)
\(164\) 0 0
\(165\) −6.83354 11.8360i −0.531990 0.921434i
\(166\) 0 0
\(167\) −8.22775 14.2509i −0.636682 1.10277i −0.986156 0.165820i \(-0.946973\pi\)
0.349474 0.936946i \(-0.386360\pi\)
\(168\) 0 0
\(169\) −3.34790 + 5.79874i −0.257531 + 0.446057i
\(170\) 0 0
\(171\) 24.6651 + 11.9255i 1.88618 + 0.911968i
\(172\) 0 0
\(173\) 11.3912 19.7302i 0.866058 1.50006i 6.58713e−5 1.00000i \(-0.499979\pi\)
0.865992 0.500057i \(-0.166688\pi\)
\(174\) 0 0
\(175\) −0.304588 0.527561i −0.0230247 0.0398799i
\(176\) 0 0
\(177\) −15.5952 27.0117i −1.17221 2.03032i
\(178\) 0 0
\(179\) 2.32916 0.174090 0.0870449 0.996204i \(-0.472258\pi\)
0.0870449 + 0.996204i \(0.472258\pi\)
\(180\) 0 0
\(181\) 11.1696 + 19.3463i 0.830230 + 1.43800i 0.897856 + 0.440290i \(0.145124\pi\)
−0.0676258 + 0.997711i \(0.521542\pi\)
\(182\) 0 0
\(183\) 15.1810 1.12221
\(184\) 0 0
\(185\) 1.88632 3.26721i 0.138685 0.240210i
\(186\) 0 0
\(187\) 6.51119 11.2777i 0.476145 0.824708i
\(188\) 0 0
\(189\) −6.09829 −0.443585
\(190\) 0 0
\(191\) −2.23766 −0.161911 −0.0809556 0.996718i \(-0.525797\pi\)
−0.0809556 + 0.996718i \(0.525797\pi\)
\(192\) 0 0
\(193\) 2.27153 3.93441i 0.163508 0.283205i −0.772616 0.634873i \(-0.781052\pi\)
0.936125 + 0.351669i \(0.114386\pi\)
\(194\) 0 0
\(195\) 6.76167 11.7115i 0.484213 0.838681i
\(196\) 0 0
\(197\) −19.2236 −1.36962 −0.684812 0.728720i \(-0.740116\pi\)
−0.684812 + 0.728720i \(0.740116\pi\)
\(198\) 0 0
\(199\) −3.07547 5.32687i −0.218014 0.377612i 0.736186 0.676779i \(-0.236625\pi\)
−0.954201 + 0.299167i \(0.903291\pi\)
\(200\) 0 0
\(201\) 25.8283 1.82179
\(202\) 0 0
\(203\) −0.340010 0.588915i −0.0238641 0.0413338i
\(204\) 0 0
\(205\) 4.15184 + 7.19120i 0.289977 + 0.502255i
\(206\) 0 0
\(207\) −8.94786 + 15.4981i −0.621919 + 1.07720i
\(208\) 0 0
\(209\) 16.1705 10.9879i 1.11853 0.760049i
\(210\) 0 0
\(211\) 6.34661 10.9926i 0.436919 0.756765i −0.560531 0.828133i \(-0.689403\pi\)
0.997450 + 0.0713679i \(0.0227365\pi\)
\(212\) 0 0
\(213\) −17.7039 30.6641i −1.21305 2.10107i
\(214\) 0 0
\(215\) −4.99438 8.65053i −0.340614 0.589961i
\(216\) 0 0
\(217\) 3.79460 0.257594
\(218\) 0 0
\(219\) 5.67269 + 9.82538i 0.383325 + 0.663938i
\(220\) 0 0
\(221\) 12.8854 0.866767
\(222\) 0 0
\(223\) 11.2688 19.5181i 0.754614 1.30703i −0.190952 0.981599i \(-0.561158\pi\)
0.945566 0.325430i \(-0.105509\pi\)
\(224\) 0 0
\(225\) −3.14263 + 5.44319i −0.209508 + 0.362879i
\(226\) 0 0
\(227\) −18.1124 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(228\) 0 0
\(229\) −9.41604 −0.622229 −0.311115 0.950372i \(-0.600702\pi\)
−0.311115 + 0.950372i \(0.600702\pi\)
\(230\) 0 0
\(231\) −4.16282 + 7.21022i −0.273894 + 0.474398i
\(232\) 0 0
\(233\) −7.85000 + 13.5966i −0.514271 + 0.890743i 0.485592 + 0.874185i \(0.338604\pi\)
−0.999863 + 0.0165573i \(0.994729\pi\)
\(234\) 0 0
\(235\) 5.88500 0.383895
\(236\) 0 0
\(237\) −13.7704 23.8511i −0.894485 1.54929i
\(238\) 0 0
\(239\) 23.4610 1.51757 0.758783 0.651344i \(-0.225795\pi\)
0.758783 + 0.651344i \(0.225795\pi\)
\(240\) 0 0
\(241\) −6.58469 11.4050i −0.424157 0.734662i 0.572184 0.820125i \(-0.306096\pi\)
−0.996341 + 0.0854634i \(0.972763\pi\)
\(242\) 0 0
\(243\) 2.73161 + 4.73128i 0.175233 + 0.303512i
\(244\) 0 0
\(245\) 3.31445 5.74080i 0.211753 0.366766i
\(246\) 0 0
\(247\) 17.4159 + 8.42058i 1.10815 + 0.535789i
\(248\) 0 0
\(249\) 3.23272 5.59923i 0.204865 0.354837i
\(250\) 0 0
\(251\) −8.66257 15.0040i −0.546776 0.947045i −0.998493 0.0548830i \(-0.982521\pi\)
0.451716 0.892162i \(-0.350812\pi\)
\(252\) 0 0
\(253\) 6.38521 + 11.0595i 0.401435 + 0.695305i
\(254\) 0 0
\(255\) −8.84726 −0.554037
\(256\) 0 0
\(257\) 2.83980 + 4.91867i 0.177142 + 0.306818i 0.940900 0.338683i \(-0.109982\pi\)
−0.763759 + 0.645502i \(0.776648\pi\)
\(258\) 0 0
\(259\) −2.29820 −0.142803
\(260\) 0 0
\(261\) −3.50811 + 6.07622i −0.217146 + 0.376108i
\(262\) 0 0
\(263\) 2.82882 4.89966i 0.174433 0.302126i −0.765532 0.643398i \(-0.777524\pi\)
0.939965 + 0.341272i \(0.110858\pi\)
\(264\) 0 0
\(265\) 8.44872 0.519001
\(266\) 0 0
\(267\) −24.1707 −1.47922
\(268\) 0 0
\(269\) 11.9959 20.7775i 0.731402 1.26683i −0.224881 0.974386i \(-0.572199\pi\)
0.956284 0.292440i \(-0.0944672\pi\)
\(270\) 0 0
\(271\) −10.6497 + 18.4459i −0.646926 + 1.12051i 0.336927 + 0.941531i \(0.390612\pi\)
−0.983853 + 0.178978i \(0.942721\pi\)
\(272\) 0 0
\(273\) −8.23808 −0.498591
\(274\) 0 0
\(275\) 2.24258 + 3.88427i 0.135233 + 0.234230i
\(276\) 0 0
\(277\) −0.821109 −0.0493357 −0.0246678 0.999696i \(-0.507853\pi\)
−0.0246678 + 0.999696i \(0.507853\pi\)
\(278\) 0 0
\(279\) −19.5757 33.9060i −1.17196 2.02990i
\(280\) 0 0
\(281\) 0.293739 + 0.508772i 0.0175230 + 0.0303508i 0.874654 0.484748i \(-0.161089\pi\)
−0.857131 + 0.515099i \(0.827755\pi\)
\(282\) 0 0
\(283\) 15.4712 26.7969i 0.919667 1.59291i 0.119746 0.992805i \(-0.461792\pi\)
0.799921 0.600105i \(-0.204875\pi\)
\(284\) 0 0
\(285\) −11.9579 5.78165i −0.708327 0.342475i
\(286\) 0 0
\(287\) 2.52920 4.38070i 0.149294 0.258585i
\(288\) 0 0
\(289\) 4.28504 + 7.42191i 0.252061 + 0.436583i
\(290\) 0 0
\(291\) −14.7370 25.5252i −0.863896 1.49631i
\(292\) 0 0
\(293\) 3.76271 0.219820 0.109910 0.993942i \(-0.464944\pi\)
0.109910 + 0.993942i \(0.464944\pi\)
\(294\) 0 0
\(295\) 5.11793 + 8.86451i 0.297977 + 0.516112i
\(296\) 0 0
\(297\) 44.8998 2.60535
\(298\) 0 0
\(299\) −6.31806 + 10.9432i −0.365383 + 0.632861i
\(300\) 0 0
\(301\) −3.04246 + 5.26969i −0.175364 + 0.303740i
\(302\) 0 0
\(303\) 2.95961 0.170025
\(304\) 0 0
\(305\) −4.98199 −0.285268
\(306\) 0 0
\(307\) 10.1709 17.6166i 0.580485 1.00543i −0.414936 0.909850i \(-0.636196\pi\)
0.995422 0.0955798i \(-0.0304705\pi\)
\(308\) 0 0
\(309\) 5.09095 8.81779i 0.289614 0.501626i
\(310\) 0 0
\(311\) 7.67830 0.435397 0.217698 0.976016i \(-0.430145\pi\)
0.217698 + 0.976016i \(0.430145\pi\)
\(312\) 0 0
\(313\) −11.9964 20.7783i −0.678074 1.17446i −0.975560 0.219733i \(-0.929481\pi\)
0.297486 0.954726i \(-0.403852\pi\)
\(314\) 0 0
\(315\) 3.82882 0.215730
\(316\) 0 0
\(317\) −0.519518 0.899831i −0.0291790 0.0505395i 0.851067 0.525057i \(-0.175956\pi\)
−0.880246 + 0.474517i \(0.842623\pi\)
\(318\) 0 0
\(319\) 2.50339 + 4.33600i 0.140163 + 0.242769i
\(320\) 0 0
\(321\) −14.4993 + 25.1135i −0.809271 + 1.40170i
\(322\) 0 0
\(323\) −0.926066 12.6218i −0.0515277 0.702298i
\(324\) 0 0
\(325\) −2.21900 + 3.84342i −0.123088 + 0.213194i
\(326\) 0 0
\(327\) 8.44610 + 14.6291i 0.467070 + 0.808990i
\(328\) 0 0
\(329\) −1.79250 3.10470i −0.0988236 0.171167i
\(330\) 0 0
\(331\) −30.8316 −1.69466 −0.847328 0.531069i \(-0.821790\pi\)
−0.847328 + 0.531069i \(0.821790\pi\)
\(332\) 0 0
\(333\) 11.8560 + 20.5352i 0.649705 + 1.12532i
\(334\) 0 0
\(335\) −8.47616 −0.463102
\(336\) 0 0
\(337\) −10.3576 + 17.9400i −0.564217 + 0.977252i 0.432906 + 0.901439i \(0.357488\pi\)
−0.997122 + 0.0758124i \(0.975845\pi\)
\(338\) 0 0
\(339\) 2.34837 4.06749i 0.127546 0.220916i
\(340\) 0 0
\(341\) −27.9384 −1.51295
\(342\) 0 0
\(343\) −8.30239 −0.448287
\(344\) 0 0
\(345\) 4.33804 7.51370i 0.233552 0.404524i
\(346\) 0 0
\(347\) 4.11068 7.11991i 0.220673 0.382217i −0.734340 0.678782i \(-0.762508\pi\)
0.955013 + 0.296566i \(0.0958413\pi\)
\(348\) 0 0
\(349\) 11.9216 0.638150 0.319075 0.947730i \(-0.396628\pi\)
0.319075 + 0.947730i \(0.396628\pi\)
\(350\) 0 0
\(351\) 22.2138 + 38.4754i 1.18568 + 2.05366i
\(352\) 0 0
\(353\) −11.7983 −0.627959 −0.313980 0.949430i \(-0.601662\pi\)
−0.313980 + 0.949430i \(0.601662\pi\)
\(354\) 0 0
\(355\) 5.80995 + 10.0631i 0.308360 + 0.534095i
\(356\) 0 0
\(357\) 2.69477 + 4.66747i 0.142622 + 0.247029i
\(358\) 0 0
\(359\) 0.0554058 0.0959656i 0.00292420 0.00506487i −0.864560 0.502530i \(-0.832403\pi\)
0.867484 + 0.497465i \(0.165736\pi\)
\(360\) 0 0
\(361\) 6.99666 17.6648i 0.368245 0.929729i
\(362\) 0 0
\(363\) 13.8901 24.0584i 0.729042 1.26274i
\(364\) 0 0
\(365\) −1.86162 3.22443i −0.0974418 0.168774i
\(366\) 0 0
\(367\) 5.86986 + 10.1669i 0.306404 + 0.530708i 0.977573 0.210597i \(-0.0675408\pi\)
−0.671169 + 0.741305i \(0.734207\pi\)
\(368\) 0 0
\(369\) −52.1908 −2.71694
\(370\) 0 0
\(371\) −2.57338 4.45722i −0.133603 0.231407i
\(372\) 0 0
\(373\) 14.5190 0.751763 0.375882 0.926668i \(-0.377340\pi\)
0.375882 + 0.926668i \(0.377340\pi\)
\(374\) 0 0
\(375\) 1.52359 2.63893i 0.0786776 0.136274i
\(376\) 0 0
\(377\) −2.47706 + 4.29040i −0.127575 + 0.220967i
\(378\) 0 0
\(379\) 6.59023 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(380\) 0 0
\(381\) 7.02522 0.359913
\(382\) 0 0
\(383\) −1.43461 + 2.48481i −0.0733049 + 0.126968i −0.900348 0.435171i \(-0.856688\pi\)
0.827043 + 0.562139i \(0.190021\pi\)
\(384\) 0 0
\(385\) 1.36613 2.36620i 0.0696243 0.120593i
\(386\) 0 0
\(387\) 62.7819 3.19138
\(388\) 0 0
\(389\) 3.16575 + 5.48323i 0.160510 + 0.278011i 0.935052 0.354512i \(-0.115353\pi\)
−0.774542 + 0.632523i \(0.782020\pi\)
\(390\) 0 0
\(391\) 8.26682 0.418071
\(392\) 0 0
\(393\) 19.6818 + 34.0899i 0.992817 + 1.71961i
\(394\) 0 0
\(395\) 4.51908 + 7.82728i 0.227380 + 0.393833i
\(396\) 0 0
\(397\) 15.2749 26.4569i 0.766626 1.32784i −0.172756 0.984965i \(-0.555267\pi\)
0.939382 0.342871i \(-0.111399\pi\)
\(398\) 0 0
\(399\) 0.592065 + 8.06957i 0.0296403 + 0.403984i
\(400\) 0 0
\(401\) −15.1711 + 26.2771i −0.757609 + 1.31222i 0.186458 + 0.982463i \(0.440299\pi\)
−0.944067 + 0.329754i \(0.893034\pi\)
\(402\) 0 0
\(403\) −13.8223 23.9409i −0.688538 1.19258i
\(404\) 0 0
\(405\) −5.82432 10.0880i −0.289413 0.501277i
\(406\) 0 0
\(407\) 16.9209 0.838740
\(408\) 0 0
\(409\) 7.48628 + 12.9666i 0.370173 + 0.641158i 0.989592 0.143903i \(-0.0459652\pi\)
−0.619419 + 0.785060i \(0.712632\pi\)
\(410\) 0 0
\(411\) 38.8013 1.91393
\(412\) 0 0
\(413\) 3.11772 5.40004i 0.153413 0.265719i
\(414\) 0 0
\(415\) −1.06089 + 1.83752i −0.0520771 + 0.0902002i
\(416\) 0 0
\(417\) 32.3264 1.58303
\(418\) 0 0
\(419\) 6.17419 0.301629 0.150815 0.988562i \(-0.451810\pi\)
0.150815 + 0.988562i \(0.451810\pi\)
\(420\) 0 0
\(421\) 13.7714 23.8528i 0.671177 1.16251i −0.306394 0.951905i \(-0.599122\pi\)
0.977571 0.210608i \(-0.0675443\pi\)
\(422\) 0 0
\(423\) −18.4943 + 32.0331i −0.899226 + 1.55750i
\(424\) 0 0
\(425\) 2.90343 0.140837
\(426\) 0 0
\(427\) 1.51745 + 2.62830i 0.0734347 + 0.127193i
\(428\) 0 0
\(429\) 60.6544 2.92842
\(430\) 0 0
\(431\) −7.52941 13.0413i −0.362679 0.628179i 0.625722 0.780046i \(-0.284805\pi\)
−0.988401 + 0.151868i \(0.951471\pi\)
\(432\) 0 0
\(433\) 0.485420 + 0.840772i 0.0233278 + 0.0404049i 0.877454 0.479661i \(-0.159241\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(434\) 0 0
\(435\) 1.70077 2.94583i 0.0815459 0.141242i
\(436\) 0 0
\(437\) 11.1734 + 5.40234i 0.534497 + 0.258429i
\(438\) 0 0
\(439\) −13.7187 + 23.7616i −0.654760 + 1.13408i 0.327194 + 0.944957i \(0.393897\pi\)
−0.981954 + 0.189120i \(0.939436\pi\)
\(440\) 0 0
\(441\) 20.8322 + 36.0824i 0.992008 + 1.71821i
\(442\) 0 0
\(443\) −4.38272 7.59109i −0.208229 0.360664i 0.742928 0.669372i \(-0.233437\pi\)
−0.951157 + 0.308708i \(0.900103\pi\)
\(444\) 0 0
\(445\) 7.93217 0.376021
\(446\) 0 0
\(447\) 5.74859 + 9.95686i 0.271899 + 0.470943i
\(448\) 0 0
\(449\) −9.63397 −0.454655 −0.227327 0.973818i \(-0.572999\pi\)
−0.227327 + 0.973818i \(0.572999\pi\)
\(450\) 0 0
\(451\) −18.6217 + 32.2538i −0.876862 + 1.51877i
\(452\) 0 0
\(453\) 14.4979 25.1110i 0.681169 1.17982i
\(454\) 0 0
\(455\) 2.70352 0.126743
\(456\) 0 0
\(457\) −10.6708 −0.499161 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(458\) 0 0
\(459\) 14.5327 25.1714i 0.678330 1.17490i
\(460\) 0 0
\(461\) −2.84340 + 4.92491i −0.132430 + 0.229376i −0.924613 0.380908i \(-0.875611\pi\)
0.792183 + 0.610284i \(0.208945\pi\)
\(462\) 0 0
\(463\) −35.3550 −1.64309 −0.821543 0.570147i \(-0.806886\pi\)
−0.821543 + 0.570147i \(0.806886\pi\)
\(464\) 0 0
\(465\) 9.49053 + 16.4381i 0.440113 + 0.762298i
\(466\) 0 0
\(467\) 32.9071 1.52276 0.761380 0.648306i \(-0.224522\pi\)
0.761380 + 0.648306i \(0.224522\pi\)
\(468\) 0 0
\(469\) 2.58173 + 4.47169i 0.119213 + 0.206484i
\(470\) 0 0
\(471\) −5.26617 9.12127i −0.242652 0.420286i
\(472\) 0 0
\(473\) 22.4006 38.7991i 1.02998 1.78398i
\(474\) 0 0
\(475\) 3.92428 + 1.89738i 0.180058 + 0.0870579i
\(476\) 0 0
\(477\) −26.5512 + 45.9880i −1.21569 + 2.10564i
\(478\) 0 0
\(479\) −4.52861 7.84378i −0.206917 0.358391i 0.743825 0.668375i \(-0.233010\pi\)
−0.950742 + 0.309984i \(0.899676\pi\)
\(480\) 0 0
\(481\) 8.37149 + 14.4998i 0.381707 + 0.661136i
\(482\) 0 0
\(483\) −5.28525 −0.240487
\(484\) 0 0
\(485\) 4.83628 + 8.37668i 0.219604 + 0.380365i
\(486\) 0 0
\(487\) 16.5206 0.748620 0.374310 0.927304i \(-0.377880\pi\)
0.374310 + 0.927304i \(0.377880\pi\)
\(488\) 0 0
\(489\) −10.1362 + 17.5563i −0.458373 + 0.793925i
\(490\) 0 0
\(491\) −0.695625 + 1.20486i −0.0313931 + 0.0543745i −0.881295 0.472566i \(-0.843328\pi\)
0.849902 + 0.526941i \(0.176661\pi\)
\(492\) 0 0
\(493\) 3.24109 0.145972
\(494\) 0 0
\(495\) −28.1904 −1.26706
\(496\) 0 0
\(497\) 3.53928 6.13021i 0.158758 0.274977i
\(498\) 0 0
\(499\) −8.33255 + 14.4324i −0.373016 + 0.646083i −0.990028 0.140871i \(-0.955010\pi\)
0.617012 + 0.786954i \(0.288343\pi\)
\(500\) 0 0
\(501\) −50.1427 −2.24021
\(502\) 0 0
\(503\) 7.81956 + 13.5439i 0.348657 + 0.603892i 0.986011 0.166679i \(-0.0533045\pi\)
−0.637354 + 0.770571i \(0.719971\pi\)
\(504\) 0 0
\(505\) −0.971265 −0.0432207
\(506\) 0 0
\(507\) 10.2016 + 17.6697i 0.453070 + 0.784741i
\(508\) 0 0
\(509\) 9.57702 + 16.5879i 0.424494 + 0.735245i 0.996373 0.0850929i \(-0.0271187\pi\)
−0.571879 + 0.820338i \(0.693785\pi\)
\(510\) 0 0
\(511\) −1.13406 + 1.96424i −0.0501677 + 0.0868929i
\(512\) 0 0
\(513\) 36.0919 24.5246i 1.59349 1.08279i
\(514\) 0 0
\(515\) −1.67071 + 2.89376i −0.0736205 + 0.127514i
\(516\) 0 0
\(517\) 13.1976 + 22.8589i 0.580430 + 1.00533i
\(518\) 0 0
\(519\) −34.7110 60.1212i −1.52364 2.63903i
\(520\) 0 0
\(521\) −19.2394 −0.842892 −0.421446 0.906853i \(-0.638477\pi\)
−0.421446 + 0.906853i \(0.638477\pi\)
\(522\) 0 0
\(523\) 3.31973 + 5.74993i 0.145161 + 0.251427i 0.929433 0.368990i \(-0.120296\pi\)
−0.784272 + 0.620418i \(0.786963\pi\)
\(524\) 0 0
\(525\) −1.85626 −0.0810139
\(526\) 0 0
\(527\) −9.04285 + 15.6627i −0.393913 + 0.682277i
\(528\) 0 0
\(529\) 7.44657 12.8978i 0.323764 0.560775i
\(530\) 0 0
\(531\) −64.3349 −2.79190
\(532\) 0 0
\(533\) −36.8517 −1.59623
\(534\) 0 0
\(535\) 4.75828 8.24158i 0.205718 0.356314i
\(536\) 0 0
\(537\) 3.54868 6.14649i 0.153137 0.265241i
\(538\) 0 0
\(539\) 29.7317 1.28064
\(540\) 0 0
\(541\) −20.8756 36.1575i −0.897510 1.55453i −0.830667 0.556770i \(-0.812040\pi\)
−0.0668435 0.997763i \(-0.521293\pi\)
\(542\) 0 0
\(543\) 68.0714 2.92122
\(544\) 0 0
\(545\) −2.77178 4.80087i −0.118730 0.205647i
\(546\) 0 0
\(547\) 6.10258 + 10.5700i 0.260927 + 0.451939i 0.966489 0.256710i \(-0.0826384\pi\)
−0.705561 + 0.708649i \(0.749305\pi\)
\(548\) 0 0
\(549\) 15.6565 27.1179i 0.668204 1.15736i
\(550\) 0 0
\(551\) 4.38066 + 2.11804i 0.186622 + 0.0902317i
\(552\) 0 0
\(553\) 2.75291 4.76819i 0.117066 0.202764i
\(554\) 0 0
\(555\) −5.74795 9.95573i −0.243987 0.422597i
\(556\) 0 0
\(557\) −17.5774 30.4450i −0.744779 1.28999i −0.950298 0.311342i \(-0.899222\pi\)
0.205519 0.978653i \(-0.434112\pi\)
\(558\) 0 0
\(559\) 44.3301 1.87496
\(560\) 0 0
\(561\) −19.8407 34.3651i −0.837675 1.45090i
\(562\) 0 0
\(563\) −17.8406 −0.751891 −0.375945 0.926642i \(-0.622682\pi\)
−0.375945 + 0.926642i \(0.622682\pi\)
\(564\) 0 0
\(565\) −0.770672 + 1.33484i −0.0324224 + 0.0561572i
\(566\) 0 0
\(567\) −3.54803 + 6.14537i −0.149003 + 0.258081i
\(568\) 0 0
\(569\) 31.6042 1.32492 0.662459 0.749098i \(-0.269513\pi\)
0.662459 + 0.749098i \(0.269513\pi\)
\(570\) 0 0
\(571\) 4.73053 0.197967 0.0989833 0.995089i \(-0.468441\pi\)
0.0989833 + 0.995089i \(0.468441\pi\)
\(572\) 0 0
\(573\) −3.40926 + 5.90501i −0.142424 + 0.246685i
\(574\) 0 0
\(575\) −1.42363 + 2.46580i −0.0593694 + 0.102831i
\(576\) 0 0
\(577\) 24.4074 1.01609 0.508047 0.861330i \(-0.330368\pi\)
0.508047 + 0.861330i \(0.330368\pi\)
\(578\) 0 0
\(579\) −6.92174 11.9888i −0.287658 0.498238i
\(580\) 0 0
\(581\) 1.29254 0.0536235
\(582\) 0 0
\(583\) 18.9470 + 32.8171i 0.784703 + 1.35915i
\(584\) 0 0
\(585\) −13.9470 24.1568i −0.576636 0.998763i
\(586\) 0 0
\(587\) −14.3077 + 24.7817i −0.590543 + 1.02285i 0.403616 + 0.914928i \(0.367753\pi\)
−0.994159 + 0.107922i \(0.965580\pi\)
\(588\) 0 0
\(589\) −22.4578 + 15.2602i −0.925358 + 0.628785i
\(590\) 0 0
\(591\) −29.2888 + 50.7297i −1.20478 + 2.08674i
\(592\) 0 0
\(593\) −1.85756 3.21738i −0.0762807 0.132122i 0.825362 0.564604i \(-0.190971\pi\)
−0.901642 + 0.432482i \(0.857638\pi\)
\(594\) 0 0
\(595\) −0.884350 1.53174i −0.0362548 0.0627952i
\(596\) 0 0
\(597\) −18.7430 −0.767099
\(598\) 0 0
\(599\) 3.54970 + 6.14826i 0.145037 + 0.251211i 0.929387 0.369108i \(-0.120337\pi\)
−0.784350 + 0.620319i \(0.787003\pi\)
\(600\) 0 0
\(601\) −11.0596 −0.451131 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(602\) 0 0
\(603\) 26.6374 46.1373i 1.08476 1.87886i
\(604\) 0 0
\(605\) −4.55836 + 7.89531i −0.185324 + 0.320990i
\(606\) 0 0
\(607\) −27.1193 −1.10074 −0.550369 0.834921i \(-0.685513\pi\)
−0.550369 + 0.834921i \(0.685513\pi\)
\(608\) 0 0
\(609\) −2.07214 −0.0839673
\(610\) 0 0
\(611\) −13.0588 + 22.6185i −0.528302 + 0.915046i
\(612\) 0 0
\(613\) −20.9156 + 36.2268i −0.844772 + 1.46319i 0.0410468 + 0.999157i \(0.486931\pi\)
−0.885819 + 0.464031i \(0.846403\pi\)
\(614\) 0 0
\(615\) 25.3028 1.02031
\(616\) 0 0
\(617\) 8.85262 + 15.3332i 0.356393 + 0.617291i 0.987355 0.158523i \(-0.0506731\pi\)
−0.630962 + 0.775813i \(0.717340\pi\)
\(618\) 0 0
\(619\) 39.8064 1.59995 0.799976 0.600032i \(-0.204845\pi\)
0.799976 + 0.600032i \(0.204845\pi\)
\(620\) 0 0
\(621\) 14.2515 + 24.6844i 0.571895 + 0.990551i
\(622\) 0 0
\(623\) −2.41604 4.18471i −0.0967966 0.167657i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −4.35919 59.4137i −0.174089 2.37275i
\(628\) 0 0
\(629\) 5.47681 9.48611i 0.218375 0.378236i
\(630\) 0 0
\(631\) 23.0990 + 40.0087i 0.919557 + 1.59272i 0.800088 + 0.599882i \(0.204786\pi\)
0.119469 + 0.992838i \(0.461881\pi\)
\(632\) 0 0
\(633\) −19.3392 33.4965i −0.768664 1.33137i
\(634\) 0 0
\(635\) −2.30549 −0.0914905
\(636\) 0 0
\(637\) 14.7095 + 25.4776i 0.582813 + 1.00946i
\(638\) 0 0
\(639\) −73.0340 −2.88918
\(640\) 0 0
\(641\) −3.30674 + 5.72744i −0.130608 + 0.226220i −0.923911 0.382607i \(-0.875026\pi\)
0.793303 + 0.608827i \(0.208360\pi\)
\(642\) 0 0
\(643\) −15.3076 + 26.5135i −0.603673 + 1.04559i 0.388587 + 0.921412i \(0.372963\pi\)
−0.992260 + 0.124180i \(0.960370\pi\)
\(644\) 0 0
\(645\) −30.4375 −1.19847
\(646\) 0 0
\(647\) 11.8979 0.467753 0.233877 0.972266i \(-0.424859\pi\)
0.233877 + 0.972266i \(0.424859\pi\)
\(648\) 0 0
\(649\) −22.9548 + 39.7588i −0.901053 + 1.56067i
\(650\) 0 0
\(651\) 5.78140 10.0137i 0.226591 0.392467i
\(652\) 0 0
\(653\) −1.42899 −0.0559207 −0.0279604 0.999609i \(-0.508901\pi\)
−0.0279604 + 0.999609i \(0.508901\pi\)
\(654\) 0 0
\(655\) −6.45905 11.1874i −0.252376 0.437128i
\(656\) 0 0
\(657\) 23.4015 0.912981
\(658\) 0 0
\(659\) −12.2485 21.2150i −0.477134 0.826420i 0.522523 0.852625i \(-0.324991\pi\)
−0.999657 + 0.0262051i \(0.991658\pi\)
\(660\) 0 0
\(661\) 1.61303 + 2.79385i 0.0627396 + 0.108668i 0.895689 0.444681i \(-0.146683\pi\)
−0.832949 + 0.553349i \(0.813350\pi\)
\(662\) 0 0
\(663\) 19.6320 34.0037i 0.762445 1.32059i
\(664\) 0 0
\(665\) −0.194300 2.64822i −0.00753462 0.102693i
\(666\) 0 0
\(667\) −1.58919 + 2.75256i −0.0615338 + 0.106580i
\(668\) 0 0
\(669\) −34.3379 59.4750i −1.32758 2.29944i
\(670\) 0 0
\(671\) −11.1725 19.3514i −0.431311 0.747052i
\(672\) 0 0
\(673\) 37.1424 1.43173 0.715866 0.698237i \(-0.246032\pi\)
0.715866 + 0.698237i \(0.246032\pi\)
\(674\) 0 0
\(675\) 5.00536 + 8.66954i 0.192656 + 0.333691i
\(676\) 0 0
\(677\) −24.7550 −0.951412 −0.475706 0.879604i \(-0.657807\pi\)
−0.475706 + 0.879604i \(0.657807\pi\)
\(678\) 0 0
\(679\) 2.94614 5.10287i 0.113063 0.195830i
\(680\) 0 0
\(681\) −27.5957 + 47.7972i −1.05747 + 1.83159i
\(682\) 0 0
\(683\) −40.1153 −1.53497 −0.767484 0.641068i \(-0.778492\pi\)
−0.767484 + 0.641068i \(0.778492\pi\)
\(684\) 0 0
\(685\) −12.7335 −0.486524
\(686\) 0 0
\(687\) −14.3461 + 24.8482i −0.547340 + 0.948020i
\(688\) 0 0
\(689\) −18.7477 + 32.4720i −0.714230 + 1.23708i
\(690\) 0 0
\(691\) −39.4963 −1.50251 −0.751254 0.660013i \(-0.770551\pi\)
−0.751254 + 0.660013i \(0.770551\pi\)
\(692\) 0 0
\(693\) 8.58645 + 14.8722i 0.326172 + 0.564947i
\(694\) 0 0
\(695\) −10.6087 −0.402410
\(696\) 0 0
\(697\) 12.0546 + 20.8792i 0.456600 + 0.790855i
\(698\) 0 0
\(699\) 23.9203 + 41.4312i 0.904748 + 1.56707i
\(700\) 0 0
\(701\) −0.0109776 + 0.0190137i −0.000414618 + 0.000718139i −0.866233 0.499641i \(-0.833465\pi\)
0.865818 + 0.500359i \(0.166799\pi\)
\(702\) 0 0
\(703\) 13.6016 9.24234i 0.512994 0.348581i
\(704\) 0 0
\(705\) 8.96630 15.5301i 0.337690 0.584897i
\(706\) 0 0
\(707\) 0.295835 + 0.512402i 0.0111260 + 0.0192708i
\(708\) 0 0
\(709\) 8.90087 + 15.4168i 0.334279 + 0.578989i 0.983346 0.181743i \(-0.0581738\pi\)
−0.649067 + 0.760731i \(0.724840\pi\)
\(710\) 0 0
\(711\) −56.8071 −2.13043
\(712\) 0 0
\(713\) −8.86789 15.3596i −0.332105 0.575223i
\(714\) 0 0
\(715\) −19.9052 −0.744410
\(716\) 0 0
\(717\) 35.7448 61.9118i 1.33491 2.31214i
\(718\) 0 0
\(719\) 9.40515 16.2902i 0.350753 0.607522i −0.635629 0.771995i \(-0.719259\pi\)
0.986382 + 0.164473i \(0.0525923\pi\)
\(720\) 0 0
\(721\) 2.03552 0.0758066
\(722\) 0 0
\(723\) −40.1294 −1.49243
\(724\) 0 0
\(725\) −0.558149 + 0.966742i −0.0207291 + 0.0359039i
\(726\) 0 0
\(727\) 2.50151 4.33274i 0.0927758 0.160692i −0.815902 0.578190i \(-0.803759\pi\)
0.908678 + 0.417497i \(0.137093\pi\)
\(728\) 0 0
\(729\) −18.2986 −0.677725
\(730\) 0 0
\(731\) −14.5009 25.1162i −0.536334 0.928957i
\(732\) 0 0
\(733\) −23.5259 −0.868950 −0.434475 0.900684i \(-0.643066\pi\)
−0.434475 + 0.900684i \(0.643066\pi\)
\(734\) 0 0
\(735\) −10.0997 17.4932i −0.372533 0.645246i
\(736\) 0 0
\(737\) −19.0085 32.9237i −0.700187 1.21276i
\(738\) 0 0
\(739\) −18.6918 + 32.3752i −0.687590 + 1.19094i 0.285026 + 0.958520i \(0.407998\pi\)
−0.972615 + 0.232421i \(0.925335\pi\)
\(740\) 0 0
\(741\) 48.7559 33.1299i 1.79109 1.21706i
\(742\) 0 0
\(743\) 5.19430 8.99679i 0.190560 0.330060i −0.754876 0.655868i \(-0.772303\pi\)
0.945436 + 0.325808i \(0.105636\pi\)
\(744\) 0 0
\(745\) −1.88653 3.26757i −0.0691173 0.119715i
\(746\) 0 0
\(747\) −6.66797 11.5493i −0.243968 0.422566i
\(748\) 0 0
\(749\) −5.79725 −0.211827
\(750\) 0 0
\(751\) −15.6413 27.0915i −0.570758 0.988581i −0.996488 0.0837314i \(-0.973316\pi\)
0.425731 0.904850i \(-0.360017\pi\)
\(752\) 0 0
\(753\) −52.7927 −1.92387
\(754\) 0 0
\(755\) −4.75781 + 8.24077i −0.173154 + 0.299912i
\(756\) 0 0
\(757\) 6.31205 10.9328i 0.229415 0.397359i −0.728220 0.685344i \(-0.759652\pi\)
0.957635 + 0.287985i \(0.0929853\pi\)
\(758\) 0 0
\(759\) 38.9137 1.41248
\(760\) 0 0
\(761\) 11.5495 0.418668 0.209334 0.977844i \(-0.432870\pi\)
0.209334 + 0.977844i \(0.432870\pi\)
\(762\) 0 0
\(763\) −1.68850 + 2.92457i −0.0611279 + 0.105877i
\(764\) 0 0
\(765\) −9.12440 + 15.8039i −0.329893 + 0.571392i
\(766\) 0 0
\(767\) −45.4267 −1.64026
\(768\) 0 0
\(769\) 13.4603 + 23.3140i 0.485392 + 0.840724i 0.999859 0.0167864i \(-0.00534353\pi\)
−0.514467 + 0.857510i \(0.672010\pi\)
\(770\) 0 0
\(771\) 17.3067 0.623286
\(772\) 0 0
\(773\) −10.6666 18.4750i −0.383649 0.664500i 0.607932 0.793989i \(-0.291999\pi\)
−0.991581 + 0.129489i \(0.958666\pi\)
\(774\) 0 0
\(775\) −3.11454 5.39454i −0.111877 0.193778i
\(776\) 0 0
\(777\) −3.50151 + 6.06479i −0.125616 + 0.217573i
\(778\) 0 0
\(779\) 2.64851 + 36.0979i 0.0948926 + 1.29334i
\(780\) 0 0
\(781\) −26.0586 + 45.1348i −0.932450 + 1.61505i
\(782\) 0 0
\(783\) 5.58747 + 9.67779i 0.199680 + 0.345856i
\(784\) 0 0
\(785\) 1.72822 + 2.99336i 0.0616827 + 0.106838i
\(786\) 0 0
\(787\) −3.52489 −0.125649 −0.0628243 0.998025i \(-0.520011\pi\)
−0.0628243 + 0.998025i \(0.520011\pi\)
\(788\) 0 0
\(789\) −8.61990 14.9301i −0.306877 0.531526i
\(790\) 0 0
\(791\) 0.938948 0.0333852
\(792\) 0 0
\(793\) 11.0550 19.1479i 0.392575 0.679961i
\(794\) 0 0
\(795\) 12.8723 22.2956i 0.456535 0.790742i
\(796\) 0