Properties

Label 336.3.bh.e.241.2
Level $336$
Weight $3$
Character 336.241
Analytic conductor $9.155$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.15533688251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.3.bh.e.145.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(7.24264 - 4.18154i) q^{5} +(6.74264 + 1.88064i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(7.24264 - 4.18154i) q^{5} +(6.74264 + 1.88064i) q^{7} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} +17.8639i q^{13} -14.4853 q^{15} +(-16.2426 - 9.37769i) q^{17} +(14.7426 - 8.51167i) q^{19} +(-8.48528 - 8.66025i) q^{21} +(6.72792 + 11.6531i) q^{23} +(22.4706 - 38.9202i) q^{25} -5.19615i q^{27} +33.9411 q^{29} +(-12.7721 - 7.37396i) q^{31} +(-9.00000 + 5.19615i) q^{33} +(56.6985 - 14.5738i) q^{35} +(-2.98528 - 5.17066i) q^{37} +(15.4706 - 26.7958i) q^{39} -35.2354i q^{41} -15.4853 q^{43} +(21.7279 + 12.5446i) q^{45} +(28.7574 - 16.6031i) q^{47} +(41.9264 + 25.3609i) q^{49} +(16.2426 + 28.1331i) q^{51} +(17.2721 - 29.9161i) q^{53} -50.1785i q^{55} -29.4853 q^{57} +(-23.6985 - 13.6823i) q^{59} +(-34.9706 + 20.1903i) q^{61} +(5.22792 + 20.3389i) q^{63} +(74.6985 + 129.382i) q^{65} +(-57.1985 + 99.0707i) q^{67} -23.3062i q^{69} -18.6030 q^{71} +(-101.353 - 58.5161i) q^{73} +(-67.4117 + 38.9202i) q^{75} +(30.0000 - 29.3939i) q^{77} +(-44.1690 - 76.5030i) q^{79} +(-4.50000 + 7.79423i) q^{81} +75.7601i q^{83} -156.853 q^{85} +(-50.9117 - 29.3939i) q^{87} +(-18.0000 + 10.3923i) q^{89} +(-33.5955 + 120.450i) q^{91} +(12.7721 + 22.1219i) q^{93} +(71.1838 - 123.294i) q^{95} -30.5826i q^{97} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9} + O(q^{10}) \) \( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9} + 12 q^{11} - 24 q^{15} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} - 102 q^{31} - 36 q^{33} + 108 q^{35} + 22 q^{37} - 6 q^{39} - 28 q^{43} + 36 q^{45} + 132 q^{47} - 2 q^{49} + 48 q^{51} + 120 q^{53} - 84 q^{57} + 24 q^{59} - 72 q^{61} - 30 q^{63} + 180 q^{65} - 110 q^{67} - 312 q^{71} - 66 q^{73} - 66 q^{75} + 120 q^{77} + 10 q^{79} - 18 q^{81} - 288 q^{85} - 72 q^{89} + 222 q^{91} + 102 q^{93} + 132 q^{95} + 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) 0 0
\(5\) 7.24264 4.18154i 1.44853 0.836308i 0.450134 0.892961i \(-0.351376\pi\)
0.998394 + 0.0566528i \(0.0180428\pi\)
\(6\) 0 0
\(7\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.00000 5.19615i 0.272727 0.472377i −0.696832 0.717234i \(-0.745408\pi\)
0.969559 + 0.244857i \(0.0787410\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i 0.726590 + 0.687072i \(0.241104\pi\)
−0.726590 + 0.687072i \(0.758896\pi\)
\(14\) 0 0
\(15\) −14.4853 −0.965685
\(16\) 0 0
\(17\) −16.2426 9.37769i −0.955449 0.551629i −0.0606799 0.998157i \(-0.519327\pi\)
−0.894770 + 0.446528i \(0.852660\pi\)
\(18\) 0 0
\(19\) 14.7426 8.51167i 0.775928 0.447983i −0.0590569 0.998255i \(-0.518809\pi\)
0.834985 + 0.550272i \(0.185476\pi\)
\(20\) 0 0
\(21\) −8.48528 8.66025i −0.404061 0.412393i
\(22\) 0 0
\(23\) 6.72792 + 11.6531i 0.292518 + 0.506657i 0.974405 0.224802i \(-0.0721734\pi\)
−0.681886 + 0.731458i \(0.738840\pi\)
\(24\) 0 0
\(25\) 22.4706 38.9202i 0.898823 1.55681i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) 33.9411 1.17038 0.585192 0.810895i \(-0.301019\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(30\) 0 0
\(31\) −12.7721 7.37396i −0.412003 0.237870i 0.279647 0.960103i \(-0.409782\pi\)
−0.691650 + 0.722233i \(0.743116\pi\)
\(32\) 0 0
\(33\) −9.00000 + 5.19615i −0.272727 + 0.157459i
\(34\) 0 0
\(35\) 56.6985 14.5738i 1.61996 0.416396i
\(36\) 0 0
\(37\) −2.98528 5.17066i −0.0806833 0.139748i 0.822860 0.568244i \(-0.192377\pi\)
−0.903544 + 0.428496i \(0.859044\pi\)
\(38\) 0 0
\(39\) 15.4706 26.7958i 0.396681 0.687072i
\(40\) 0 0
\(41\) 35.2354i 0.859399i −0.902972 0.429700i \(-0.858619\pi\)
0.902972 0.429700i \(-0.141381\pi\)
\(42\) 0 0
\(43\) −15.4853 −0.360123 −0.180061 0.983655i \(-0.557630\pi\)
−0.180061 + 0.983655i \(0.557630\pi\)
\(44\) 0 0
\(45\) 21.7279 + 12.5446i 0.482843 + 0.278769i
\(46\) 0 0
\(47\) 28.7574 16.6031i 0.611859 0.353257i −0.161834 0.986818i \(-0.551741\pi\)
0.773693 + 0.633561i \(0.218408\pi\)
\(48\) 0 0
\(49\) 41.9264 + 25.3609i 0.855641 + 0.517570i
\(50\) 0 0
\(51\) 16.2426 + 28.1331i 0.318483 + 0.551629i
\(52\) 0 0
\(53\) 17.2721 29.9161i 0.325888 0.564455i −0.655803 0.754932i \(-0.727670\pi\)
0.981692 + 0.190477i \(0.0610033\pi\)
\(54\) 0 0
\(55\) 50.1785i 0.912336i
\(56\) 0 0
\(57\) −29.4853 −0.517286
\(58\) 0 0
\(59\) −23.6985 13.6823i −0.401669 0.231904i 0.285535 0.958368i \(-0.407829\pi\)
−0.687204 + 0.726465i \(0.741162\pi\)
\(60\) 0 0
\(61\) −34.9706 + 20.1903i −0.573288 + 0.330988i −0.758461 0.651718i \(-0.774049\pi\)
0.185174 + 0.982706i \(0.440715\pi\)
\(62\) 0 0
\(63\) 5.22792 + 20.3389i 0.0829829 + 0.322839i
\(64\) 0 0
\(65\) 74.6985 + 129.382i 1.14921 + 1.99049i
\(66\) 0 0
\(67\) −57.1985 + 99.0707i −0.853709 + 1.47867i 0.0241291 + 0.999709i \(0.492319\pi\)
−0.877838 + 0.478958i \(0.841015\pi\)
\(68\) 0 0
\(69\) 23.3062i 0.337771i
\(70\) 0 0
\(71\) −18.6030 −0.262015 −0.131007 0.991381i \(-0.541821\pi\)
−0.131007 + 0.991381i \(0.541821\pi\)
\(72\) 0 0
\(73\) −101.353 58.5161i −1.38839 0.801590i −0.395260 0.918569i \(-0.629346\pi\)
−0.993134 + 0.116979i \(0.962679\pi\)
\(74\) 0 0
\(75\) −67.4117 + 38.9202i −0.898823 + 0.518935i
\(76\) 0 0
\(77\) 30.0000 29.3939i 0.389610 0.381739i
\(78\) 0 0
\(79\) −44.1690 76.5030i −0.559102 0.968393i −0.997572 0.0696469i \(-0.977813\pi\)
0.438470 0.898746i \(-0.355521\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 75.7601i 0.912772i 0.889782 + 0.456386i \(0.150856\pi\)
−0.889782 + 0.456386i \(0.849144\pi\)
\(84\) 0 0
\(85\) −156.853 −1.84533
\(86\) 0 0
\(87\) −50.9117 29.3939i −0.585192 0.337861i
\(88\) 0 0
\(89\) −18.0000 + 10.3923i −0.202247 + 0.116767i −0.597703 0.801717i \(-0.703920\pi\)
0.395456 + 0.918485i \(0.370587\pi\)
\(90\) 0 0
\(91\) −33.5955 + 120.450i −0.369181 + 1.32362i
\(92\) 0 0
\(93\) 12.7721 + 22.1219i 0.137334 + 0.237870i
\(94\) 0 0
\(95\) 71.1838 123.294i 0.749303 1.29783i
\(96\) 0 0
\(97\) 30.5826i 0.315284i −0.987496 0.157642i \(-0.949611\pi\)
0.987496 0.157642i \(-0.0503892\pi\)
\(98\) 0 0
\(99\) 18.0000 0.181818
\(100\) 0 0
\(101\) 110.823 + 63.9839i 1.09726 + 0.633504i 0.935500 0.353326i \(-0.114949\pi\)
0.161761 + 0.986830i \(0.448283\pi\)
\(102\) 0 0
\(103\) 70.1102 40.4781i 0.680681 0.392992i −0.119430 0.992843i \(-0.538107\pi\)
0.800112 + 0.599851i \(0.204774\pi\)
\(104\) 0 0
\(105\) −97.6690 27.2416i −0.930181 0.259443i
\(106\) 0 0
\(107\) 84.7279 + 146.753i 0.791850 + 1.37152i 0.924820 + 0.380404i \(0.124215\pi\)
−0.132971 + 0.991120i \(0.542452\pi\)
\(108\) 0 0
\(109\) −89.4706 + 154.968i −0.820831 + 1.42172i 0.0842335 + 0.996446i \(0.473156\pi\)
−0.905064 + 0.425275i \(0.860177\pi\)
\(110\) 0 0
\(111\) 10.3413i 0.0931650i
\(112\) 0 0
\(113\) −17.3970 −0.153955 −0.0769777 0.997033i \(-0.524527\pi\)
−0.0769777 + 0.997033i \(0.524527\pi\)
\(114\) 0 0
\(115\) 97.4558 + 56.2662i 0.847442 + 0.489271i
\(116\) 0 0
\(117\) −46.4117 + 26.7958i −0.396681 + 0.229024i
\(118\) 0 0
\(119\) −91.8823 93.7769i −0.772120 0.788041i
\(120\) 0 0
\(121\) 42.5000 + 73.6122i 0.351240 + 0.608365i
\(122\) 0 0
\(123\) −30.5147 + 52.8530i −0.248087 + 0.429700i
\(124\) 0 0
\(125\) 166.769i 1.33415i
\(126\) 0 0
\(127\) −167.426 −1.31832 −0.659159 0.752004i \(-0.729088\pi\)
−0.659159 + 0.752004i \(0.729088\pi\)
\(128\) 0 0
\(129\) 23.2279 + 13.4106i 0.180061 + 0.103959i
\(130\) 0 0
\(131\) 1.54416 0.891519i 0.0117874 0.00680549i −0.494095 0.869408i \(-0.664500\pi\)
0.505882 + 0.862603i \(0.331167\pi\)
\(132\) 0 0
\(133\) 115.412 29.6656i 0.867757 0.223049i
\(134\) 0 0
\(135\) −21.7279 37.6339i −0.160948 0.278769i
\(136\) 0 0
\(137\) −50.4853 + 87.4431i −0.368506 + 0.638271i −0.989332 0.145677i \(-0.953464\pi\)
0.620826 + 0.783948i \(0.286797\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i −0.862799 0.505548i \(-0.831290\pi\)
0.862799 0.505548i \(-0.168710\pi\)
\(140\) 0 0
\(141\) −57.5147 −0.407906
\(142\) 0 0
\(143\) 92.8234 + 53.5916i 0.649115 + 0.374766i
\(144\) 0 0
\(145\) 245.823 141.926i 1.69533 0.978801i
\(146\) 0 0
\(147\) −40.9264 74.3507i −0.278411 0.505787i
\(148\) 0 0
\(149\) −91.4558 158.406i −0.613798 1.06313i −0.990594 0.136833i \(-0.956308\pi\)
0.376797 0.926296i \(-0.377026\pi\)
\(150\) 0 0
\(151\) −144.397 + 250.103i −0.956271 + 1.65631i −0.224840 + 0.974396i \(0.572186\pi\)
−0.731432 + 0.681915i \(0.761148\pi\)
\(152\) 0 0
\(153\) 56.2662i 0.367753i
\(154\) 0 0
\(155\) −123.338 −0.795730
\(156\) 0 0
\(157\) 162.000 + 93.5307i 1.03185 + 0.595737i 0.917513 0.397705i \(-0.130193\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(158\) 0 0
\(159\) −51.8162 + 29.9161i −0.325888 + 0.188152i
\(160\) 0 0
\(161\) 23.4487 + 91.2255i 0.145644 + 0.566618i
\(162\) 0 0
\(163\) 8.02944 + 13.9074i 0.0492604 + 0.0853214i 0.889604 0.456732i \(-0.150980\pi\)
−0.840344 + 0.542054i \(0.817647\pi\)
\(164\) 0 0
\(165\) −43.4558 + 75.2677i −0.263369 + 0.456168i
\(166\) 0 0
\(167\) 176.117i 1.05459i −0.849681 0.527297i \(-0.823206\pi\)
0.849681 0.527297i \(-0.176794\pi\)
\(168\) 0 0
\(169\) −150.118 −0.888271
\(170\) 0 0
\(171\) 44.2279 + 25.5350i 0.258643 + 0.149328i
\(172\) 0 0
\(173\) −200.184 + 115.576i −1.15713 + 0.668070i −0.950615 0.310373i \(-0.899546\pi\)
−0.206517 + 0.978443i \(0.566213\pi\)
\(174\) 0 0
\(175\) 224.706 220.166i 1.28403 1.25809i
\(176\) 0 0
\(177\) 23.6985 + 41.0470i 0.133890 + 0.231904i
\(178\) 0 0
\(179\) −42.6396 + 73.8540i −0.238210 + 0.412592i −0.960201 0.279311i \(-0.909894\pi\)
0.721991 + 0.691903i \(0.243227\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i 0.999881 + 0.0154325i \(0.00491250\pi\)
−0.999881 + 0.0154325i \(0.995087\pi\)
\(182\) 0 0
\(183\) 69.9411 0.382192
\(184\) 0 0
\(185\) −43.2426 24.9662i −0.233744 0.134952i
\(186\) 0 0
\(187\) −97.4558 + 56.2662i −0.521154 + 0.300889i
\(188\) 0 0
\(189\) 9.77208 35.0358i 0.0517041 0.185375i
\(190\) 0 0
\(191\) 92.6985 + 160.558i 0.485332 + 0.840620i 0.999858 0.0168547i \(-0.00536527\pi\)
−0.514526 + 0.857475i \(0.672032\pi\)
\(192\) 0 0
\(193\) −113.897 + 197.275i −0.590140 + 1.02215i 0.404073 + 0.914727i \(0.367594\pi\)
−0.994213 + 0.107425i \(0.965739\pi\)
\(194\) 0 0
\(195\) 258.763i 1.32699i
\(196\) 0 0
\(197\) 123.161 0.625185 0.312593 0.949887i \(-0.398803\pi\)
0.312593 + 0.949887i \(0.398803\pi\)
\(198\) 0 0
\(199\) −5.39697 3.11594i −0.0271205 0.0156580i 0.486378 0.873748i \(-0.338318\pi\)
−0.513499 + 0.858090i \(0.671651\pi\)
\(200\) 0 0
\(201\) 171.595 99.0707i 0.853709 0.492889i
\(202\) 0 0
\(203\) 228.853 + 63.8309i 1.12735 + 0.314438i
\(204\) 0 0
\(205\) −147.338 255.197i −0.718722 1.24486i
\(206\) 0 0
\(207\) −20.1838 + 34.9593i −0.0975061 + 0.168886i
\(208\) 0 0
\(209\) 102.140i 0.488708i
\(210\) 0 0
\(211\) 124.912 0.591999 0.295999 0.955188i \(-0.404347\pi\)
0.295999 + 0.955188i \(0.404347\pi\)
\(212\) 0 0
\(213\) 27.9045 + 16.1107i 0.131007 + 0.0756371i
\(214\) 0 0
\(215\) −112.154 + 64.7523i −0.521648 + 0.301174i
\(216\) 0 0
\(217\) −72.2498 73.7396i −0.332948 0.339814i
\(218\) 0 0
\(219\) 101.353 + 175.548i 0.462798 + 0.801590i
\(220\) 0 0
\(221\) 167.522 290.156i 0.758017 1.31292i
\(222\) 0 0
\(223\) 228.631i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) 0 0
\(225\) 134.823 0.599215
\(226\) 0 0
\(227\) 146.823 + 84.7685i 0.646799 + 0.373430i 0.787229 0.616661i \(-0.211515\pi\)
−0.140430 + 0.990091i \(0.544848\pi\)
\(228\) 0 0
\(229\) 30.0442 17.3460i 0.131197 0.0757467i −0.432965 0.901411i \(-0.642533\pi\)
0.564162 + 0.825664i \(0.309199\pi\)
\(230\) 0 0
\(231\) −70.4558 + 18.1101i −0.305004 + 0.0783985i
\(232\) 0 0
\(233\) 127.243 + 220.391i 0.546106 + 0.945883i 0.998536 + 0.0540833i \(0.0172237\pi\)
−0.452431 + 0.891800i \(0.649443\pi\)
\(234\) 0 0
\(235\) 138.853 240.500i 0.590863 1.02340i
\(236\) 0 0
\(237\) 153.006i 0.645595i
\(238\) 0 0
\(239\) −197.147 −0.824884 −0.412442 0.910984i \(-0.635324\pi\)
−0.412442 + 0.910984i \(0.635324\pi\)
\(240\) 0 0
\(241\) 76.6173 + 44.2350i 0.317914 + 0.183548i 0.650462 0.759538i \(-0.274575\pi\)
−0.332548 + 0.943086i \(0.607908\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 0 0
\(245\) 409.706 + 8.36308i 1.67227 + 0.0341350i
\(246\) 0 0
\(247\) 152.051 + 263.361i 0.615592 + 1.06624i
\(248\) 0 0
\(249\) 65.6102 113.640i 0.263495 0.456386i
\(250\) 0 0
\(251\) 215.903i 0.860172i −0.902788 0.430086i \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(252\) 0 0
\(253\) 80.7351 0.319111
\(254\) 0 0
\(255\) 235.279 + 135.839i 0.922664 + 0.532700i
\(256\) 0 0
\(257\) −3.72792 + 2.15232i −0.0145055 + 0.00837477i −0.507235 0.861808i \(-0.669332\pi\)
0.492730 + 0.870182i \(0.335999\pi\)
\(258\) 0 0
\(259\) −10.4045 40.4781i −0.0401720 0.156286i
\(260\) 0 0
\(261\) 50.9117 + 88.1816i 0.195064 + 0.337861i
\(262\) 0 0
\(263\) 141.338 244.805i 0.537407 0.930817i −0.461635 0.887070i \(-0.652737\pi\)
0.999043 0.0437468i \(-0.0139295\pi\)
\(264\) 0 0
\(265\) 288.896i 1.09017i
\(266\) 0 0
\(267\) 36.0000 0.134831
\(268\) 0 0
\(269\) −330.765 190.967i −1.22961 0.709914i −0.262660 0.964888i \(-0.584600\pi\)
−0.966948 + 0.254974i \(0.917933\pi\)
\(270\) 0 0
\(271\) 73.0294 42.1636i 0.269481 0.155585i −0.359171 0.933272i \(-0.616940\pi\)
0.628652 + 0.777687i \(0.283607\pi\)
\(272\) 0 0
\(273\) 154.706 151.580i 0.566687 0.555238i
\(274\) 0 0
\(275\) −134.823 233.521i −0.490267 0.849167i
\(276\) 0 0
\(277\) 68.5589 118.747i 0.247505 0.428691i −0.715328 0.698789i \(-0.753723\pi\)
0.962833 + 0.270098i \(0.0870560\pi\)
\(278\) 0 0
\(279\) 44.2438i 0.158580i
\(280\) 0 0
\(281\) −325.103 −1.15695 −0.578474 0.815701i \(-0.696352\pi\)
−0.578474 + 0.815701i \(0.696352\pi\)
\(282\) 0 0
\(283\) −168.507 97.2876i −0.595432 0.343773i 0.171811 0.985130i \(-0.445038\pi\)
−0.767242 + 0.641357i \(0.778372\pi\)
\(284\) 0 0
\(285\) −213.551 + 123.294i −0.749303 + 0.432610i
\(286\) 0 0
\(287\) 66.2649 237.579i 0.230888 0.827803i
\(288\) 0 0
\(289\) 31.3823 + 54.3557i 0.108589 + 0.188082i
\(290\) 0 0
\(291\) −26.4853 + 45.8739i −0.0910147 + 0.157642i
\(292\) 0 0
\(293\) 239.702i 0.818095i 0.912513 + 0.409048i \(0.134139\pi\)
−0.912513 + 0.409048i \(0.865861\pi\)
\(294\) 0 0
\(295\) −228.853 −0.775772
\(296\) 0 0
\(297\) −27.0000 15.5885i −0.0909091 0.0524864i
\(298\) 0 0
\(299\) −208.169 + 120.187i −0.696219 + 0.401962i
\(300\) 0 0
\(301\) −104.412 29.1222i −0.346883 0.0967515i
\(302\) 0 0
\(303\) −110.823 191.952i −0.365754 0.633504i
\(304\) 0 0
\(305\) −168.853 + 292.462i −0.553616 + 0.958891i
\(306\) 0 0
\(307\) 540.272i 1.75984i 0.475120 + 0.879921i \(0.342405\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(308\) 0 0
\(309\) −140.220 −0.453788
\(310\) 0 0
\(311\) −350.044 202.098i −1.12554 0.649832i −0.182732 0.983163i \(-0.558494\pi\)
−0.942810 + 0.333330i \(0.891828\pi\)
\(312\) 0 0
\(313\) −113.706 + 65.6482i −0.363278 + 0.209739i −0.670518 0.741893i \(-0.733928\pi\)
0.307240 + 0.951632i \(0.400595\pi\)
\(314\) 0 0
\(315\) 122.912 + 125.446i 0.390196 + 0.398242i
\(316\) 0 0
\(317\) 46.9706 + 81.3554i 0.148172 + 0.256642i 0.930552 0.366160i \(-0.119328\pi\)
−0.782380 + 0.622802i \(0.785994\pi\)
\(318\) 0 0
\(319\) 101.823 176.363i 0.319196 0.552863i
\(320\) 0 0
\(321\) 293.506i 0.914349i
\(322\) 0 0
\(323\) −319.279 −0.988481
\(324\) 0 0
\(325\) 695.265 + 401.411i 2.13928 + 1.23511i
\(326\) 0 0
\(327\) 268.412 154.968i 0.820831 0.473907i
\(328\) 0 0
\(329\) 225.125 57.8664i 0.684270 0.175886i
\(330\) 0 0
\(331\) −130.684 226.351i −0.394815 0.683840i 0.598263 0.801300i \(-0.295858\pi\)
−0.993078 + 0.117460i \(0.962525\pi\)
\(332\) 0 0
\(333\) 8.95584 15.5120i 0.0268944 0.0465825i
\(334\) 0 0
\(335\) 956.711i 2.85585i
\(336\) 0 0
\(337\) 136.265 0.404347 0.202173 0.979350i \(-0.435200\pi\)
0.202173 + 0.979350i \(0.435200\pi\)
\(338\) 0 0
\(339\) 26.0955 + 15.0662i 0.0769777 + 0.0444431i
\(340\) 0 0
\(341\) −76.6325 + 44.2438i −0.224729 + 0.129747i
\(342\) 0 0
\(343\) 235.000 + 249.848i 0.685131 + 0.728420i
\(344\) 0 0
\(345\) −97.4558 168.798i −0.282481 0.489271i
\(346\) 0 0
\(347\) −161.095 + 279.026i −0.464252 + 0.804108i −0.999167 0.0407975i \(-0.987010\pi\)
0.534915 + 0.844906i \(0.320343\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i −0.868088 0.496411i \(-0.834651\pi\)
0.868088 0.496411i \(-0.165349\pi\)
\(350\) 0 0
\(351\) 92.8234 0.264454
\(352\) 0 0
\(353\) −537.448 310.296i −1.52252 0.879025i −0.999646 0.0266116i \(-0.991528\pi\)
−0.522869 0.852413i \(-0.675138\pi\)
\(354\) 0 0
\(355\) −134.735 + 77.7893i −0.379535 + 0.219125i
\(356\) 0 0
\(357\) 56.6102 + 220.238i 0.158572 + 0.616912i
\(358\) 0 0
\(359\) 10.1177 + 17.5245i 0.0281831 + 0.0488146i 0.879773 0.475394i \(-0.157695\pi\)
−0.851590 + 0.524209i \(0.824361\pi\)
\(360\) 0 0
\(361\) −35.6030 + 61.6663i −0.0986234 + 0.170821i
\(362\) 0 0
\(363\) 147.224i 0.405577i
\(364\) 0 0
\(365\) −978.749 −2.68151
\(366\) 0 0
\(367\) 269.831 + 155.787i 0.735234 + 0.424488i 0.820334 0.571885i \(-0.193788\pi\)
−0.0850998 + 0.996372i \(0.527121\pi\)
\(368\) 0 0
\(369\) 91.5442 52.8530i 0.248087 0.143233i
\(370\) 0 0
\(371\) 172.721 169.231i 0.465555 0.456149i
\(372\) 0 0
\(373\) 340.691 + 590.094i 0.913380 + 1.58202i 0.809255 + 0.587457i \(0.199871\pi\)
0.104125 + 0.994564i \(0.466796\pi\)
\(374\) 0 0
\(375\) −144.426 + 250.154i −0.385137 + 0.667077i
\(376\) 0 0
\(377\) 606.320i 1.60828i
\(378\) 0 0
\(379\) 624.779 1.64849 0.824246 0.566231i \(-0.191599\pi\)
0.824246 + 0.566231i \(0.191599\pi\)
\(380\) 0 0
\(381\) 251.140 + 144.996i 0.659159 + 0.380566i
\(382\) 0 0
\(383\) −119.772 + 69.1502i −0.312720 + 0.180549i −0.648143 0.761519i \(-0.724454\pi\)
0.335423 + 0.942068i \(0.391121\pi\)
\(384\) 0 0
\(385\) 94.3675 338.336i 0.245110 0.878794i
\(386\) 0 0
\(387\) −23.2279 40.2319i −0.0600205 0.103959i
\(388\) 0 0
\(389\) 281.787 488.069i 0.724388 1.25468i −0.234838 0.972035i \(-0.575456\pi\)
0.959226 0.282642i \(-0.0912107\pi\)
\(390\) 0 0
\(391\) 252.370i 0.645446i
\(392\) 0 0
\(393\) −3.08831 −0.00785830
\(394\) 0 0
\(395\) −639.801 369.389i −1.61975 0.935163i
\(396\) 0 0
\(397\) −392.603 + 226.669i −0.988923 + 0.570955i −0.904952 0.425513i \(-0.860094\pi\)
−0.0839711 + 0.996468i \(0.526760\pi\)
\(398\) 0 0
\(399\) −198.809 55.4511i −0.498267 0.138975i
\(400\) 0 0
\(401\) 137.875 + 238.807i 0.343828 + 0.595528i 0.985140 0.171752i \(-0.0549429\pi\)
−0.641312 + 0.767280i \(0.721610\pi\)
\(402\) 0 0
\(403\) 131.727 228.159i 0.326867 0.566151i
\(404\) 0 0
\(405\) 75.2677i 0.185846i
\(406\) 0 0
\(407\) −35.8234 −0.0880181
\(408\) 0 0
\(409\) −377.441 217.916i −0.922839 0.532801i −0.0382993 0.999266i \(-0.512194\pi\)
−0.884540 + 0.466465i \(0.845527\pi\)
\(410\) 0 0
\(411\) 151.456 87.4431i 0.368506 0.212757i
\(412\) 0 0
\(413\) −134.059 136.823i −0.324598 0.331291i
\(414\) 0 0
\(415\) 316.794 + 548.703i 0.763359 + 1.32218i
\(416\) 0 0
\(417\) −121.713 + 210.813i −0.291878 + 0.505548i
\(418\) 0 0
\(419\) 301.257i 0.718991i −0.933147 0.359496i \(-0.882949\pi\)
0.933147 0.359496i \(-0.117051\pi\)
\(420\) 0 0
\(421\) −203.794 −0.484071 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(422\) 0 0
\(423\) 86.2721 + 49.8092i 0.203953 + 0.117752i
\(424\) 0 0
\(425\) −729.963 + 421.444i −1.71756 + 0.991633i
\(426\) 0 0
\(427\) −273.765 + 70.3688i −0.641135 + 0.164798i
\(428\) 0 0
\(429\) −92.8234 160.775i −0.216372 0.374766i
\(430\) 0 0
\(431\) −197.860 + 342.703i −0.459072 + 0.795136i −0.998912 0.0466317i \(-0.985151\pi\)
0.539840 + 0.841767i \(0.318485\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i 0.998693 + 0.0511184i \(0.0162786\pi\)
−0.998693 + 0.0511184i \(0.983721\pi\)
\(434\) 0 0
\(435\) −491.647 −1.13022
\(436\) 0 0
\(437\) 198.375 + 114.532i 0.453947 + 0.262086i
\(438\) 0 0
\(439\) −344.558 + 198.931i −0.784871 + 0.453146i −0.838154 0.545434i \(-0.816365\pi\)
0.0532827 + 0.998579i \(0.483032\pi\)
\(440\) 0 0
\(441\) −3.00000 + 146.969i −0.00680272 + 0.333264i
\(442\) 0 0
\(443\) −59.2721 102.662i −0.133797 0.231743i 0.791340 0.611376i \(-0.209384\pi\)
−0.925137 + 0.379633i \(0.876050\pi\)
\(444\) 0 0
\(445\) −86.9117 + 150.535i −0.195307 + 0.338282i
\(446\) 0 0
\(447\) 316.812i 0.708752i
\(448\) 0 0
\(449\) 713.897 1.58997 0.794985 0.606629i \(-0.207479\pi\)
0.794985 + 0.606629i \(0.207479\pi\)
\(450\) 0 0
\(451\) −183.088 105.706i −0.405961 0.234382i
\(452\) 0 0
\(453\) 433.191 250.103i 0.956271 0.552104i
\(454\) 0 0
\(455\) 260.345 + 1012.85i 0.572187 + 2.22605i
\(456\) 0 0
\(457\) 62.5883 + 108.406i 0.136955 + 0.237213i 0.926342 0.376682i \(-0.122935\pi\)
−0.789388 + 0.613895i \(0.789602\pi\)
\(458\) 0 0
\(459\) −48.7279 + 84.3992i −0.106161 + 0.183876i
\(460\) 0 0
\(461\) 655.767i 1.42249i −0.702945 0.711244i \(-0.748132\pi\)
0.702945 0.711244i \(-0.251868\pi\)
\(462\) 0 0
\(463\) −869.396 −1.87775 −0.938873 0.344265i \(-0.888128\pi\)
−0.938873 + 0.344265i \(0.888128\pi\)
\(464\) 0 0
\(465\) 185.007 + 106.814i 0.397865 + 0.229707i
\(466\) 0 0
\(467\) 231.551 133.686i 0.495827 0.286266i −0.231162 0.972915i \(-0.574253\pi\)
0.726989 + 0.686649i \(0.240919\pi\)
\(468\) 0 0
\(469\) −571.985 + 560.428i −1.21958 + 1.19494i
\(470\) 0 0
\(471\) −162.000 280.592i −0.343949 0.595737i
\(472\) 0 0
\(473\) −46.4558 + 80.4639i −0.0982153 + 0.170114i
\(474\) 0 0
\(475\) 765.048i 1.61063i
\(476\) 0 0
\(477\) 103.632 0.217259
\(478\) 0 0
\(479\) −235.331 135.868i −0.491296 0.283650i 0.233816 0.972281i \(-0.424879\pi\)
−0.725112 + 0.688631i \(0.758212\pi\)
\(480\) 0 0
\(481\) 92.3680 53.3287i 0.192033 0.110870i
\(482\) 0 0
\(483\) 43.8305 157.145i 0.0907464 0.325353i
\(484\) 0 0
\(485\) −127.882 221.499i −0.263675 0.456698i
\(486\) 0 0
\(487\) −280.757 + 486.285i −0.576503 + 0.998532i 0.419374 + 0.907814i \(0.362250\pi\)
−0.995877 + 0.0907186i \(0.971084\pi\)
\(488\) 0 0
\(489\) 27.8148i 0.0568810i
\(490\) 0 0
\(491\) 406.441 0.827781 0.413891 0.910327i \(-0.364170\pi\)
0.413891 + 0.910327i \(0.364170\pi\)
\(492\) 0 0
\(493\) −551.294 318.289i −1.11824 0.645618i
\(494\) 0 0
\(495\) 130.368 75.2677i 0.263369 0.152056i
\(496\) 0 0
\(497\) −125.434 34.9856i −0.252381 0.0703935i
\(498\) 0 0
\(499\) −185.713 321.665i −0.372171 0.644619i 0.617728 0.786391i \(-0.288053\pi\)
−0.989899 + 0.141773i \(0.954720\pi\)
\(500\) 0 0
\(501\) −152.522 + 264.176i −0.304435 + 0.527297i
\(502\) 0 0
\(503\) 64.6292i 0.128488i 0.997934 + 0.0642438i \(0.0204635\pi\)
−0.997934 + 0.0642438i \(0.979536\pi\)
\(504\) 0 0
\(505\) 1070.21 2.11922
\(506\) 0 0
\(507\) 225.177 + 130.006i 0.444135 + 0.256422i
\(508\) 0 0
\(509\) 871.889 503.385i 1.71294 0.988969i 0.782410 0.622764i \(-0.213990\pi\)
0.930534 0.366205i \(-0.119343\pi\)
\(510\) 0 0
\(511\) −573.338 585.161i −1.12199 1.14513i
\(512\) 0 0
\(513\) −44.2279 76.6050i −0.0862143 0.149328i
\(514\) 0 0
\(515\) 338.522 586.337i 0.657324 1.13852i
\(516\) 0 0
\(517\) 199.237i 0.385371i
\(518\) 0 0
\(519\) 400.368 0.771421
\(520\) 0 0
\(521\) −322.294 186.077i −0.618607 0.357153i 0.157719 0.987484i \(-0.449586\pi\)
−0.776327 + 0.630331i \(0.782919\pi\)
\(522\) 0 0
\(523\) 551.904 318.642i 1.05527 0.609258i 0.131147 0.991363i \(-0.458134\pi\)
0.924119 + 0.382105i \(0.124801\pi\)
\(524\) 0 0
\(525\) −527.727 + 135.648i −1.00520 + 0.258377i
\(526\) 0 0
\(527\) 138.302 + 239.545i 0.262432 + 0.454545i
\(528\) 0 0
\(529\) 173.970 301.325i 0.328866 0.569613i
\(530\) 0 0
\(531\) 82.0940i 0.154603i
\(532\) 0 0
\(533\) 629.440 1.18094
\(534\) 0 0
\(535\) 1227.31 + 708.586i 2.29403 + 1.32446i
\(536\) 0 0
\(537\) 127.919 73.8540i 0.238210 0.137531i
\(538\) 0 0
\(539\) 257.558 141.773i 0.477845 0.263030i
\(540\) 0 0
\(541\) −110.412 191.239i −0.204088 0.353491i 0.745754 0.666222i \(-0.232090\pi\)
−0.949842 + 0.312731i \(0.898756\pi\)
\(542\) 0 0
\(543\) 4.83810 8.37983i 0.00890994 0.0154325i
\(544\) 0 0
\(545\) 1496.50i 2.74587i
\(546\) 0 0
\(547\) 160.676 0.293741 0.146870 0.989156i \(-0.453080\pi\)
0.146870 + 0.989156i \(0.453080\pi\)
\(548\) 0 0
\(549\) −104.912 60.5708i −0.191096 0.110329i
\(550\) 0 0
\(551\) 500.382 288.896i 0.908134 0.524311i
\(552\) 0 0
\(553\) −153.942 598.898i −0.278375 1.08300i
\(554\) 0 0
\(555\) 43.2426 + 74.8985i 0.0779147 + 0.134952i
\(556\) 0 0
\(557\) 237.177 410.802i 0.425811 0.737526i −0.570685 0.821169i \(-0.693322\pi\)
0.996496 + 0.0836431i \(0.0266556\pi\)
\(558\) 0 0
\(559\) 276.627i 0.494860i
\(560\) 0 0
\(561\) 194.912 0.347436
\(562\) 0 0
\(563\) 430.301 + 248.434i 0.764300 + 0.441269i 0.830837 0.556515i \(-0.187862\pi\)
−0.0665378 + 0.997784i \(0.521195\pi\)
\(564\) 0 0
\(565\) −126.000 + 72.7461i −0.223009 + 0.128754i
\(566\) 0 0
\(567\) −45.0000 + 44.0908i −0.0793651 + 0.0777616i
\(568\) 0 0
\(569\) −392.647 680.084i −0.690065 1.19523i −0.971816 0.235740i \(-0.924249\pi\)
0.281752 0.959487i \(-0.409085\pi\)
\(570\) 0 0
\(571\) −357.521 + 619.245i −0.626132 + 1.08449i 0.362189 + 0.932105i \(0.382030\pi\)
−0.988321 + 0.152388i \(0.951304\pi\)
\(572\) 0 0
\(573\) 321.117i 0.560414i
\(574\) 0 0
\(575\) 604.721 1.05169
\(576\) 0 0
\(577\) 669.117 + 386.315i 1.15965 + 0.669524i 0.951220 0.308514i \(-0.0998317\pi\)
0.208429 + 0.978038i \(0.433165\pi\)
\(578\) 0 0
\(579\) 341.691 197.275i 0.590140 0.340717i
\(580\) 0 0
\(581\) −142.477 + 510.823i −0.245228 + 0.879214i
\(582\) 0 0
\(583\) −103.632 179.497i −0.177757 0.307885i
\(584\) 0 0
\(585\) −224.095 + 388.145i −0.383069 + 0.663495i
\(586\) 0 0
\(587\) 436.477i 0.743572i −0.928318 0.371786i \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 0 0
\(589\) −251.059 −0.426246
\(590\) 0 0
\(591\) −184.742 106.661i −0.312593 0.180475i
\(592\) 0 0
\(593\) 722.397 417.076i 1.21821 0.703332i 0.253673 0.967290i \(-0.418361\pi\)
0.964534 + 0.263958i \(0.0850279\pi\)
\(594\) 0 0
\(595\) −1057.60 294.983i −1.77748 0.495770i
\(596\) 0 0
\(597\) 5.39697 + 9.34783i 0.00904015 + 0.0156580i
\(598\) 0 0
\(599\) 436.794 756.549i 0.729205 1.26302i −0.228014 0.973658i \(-0.573223\pi\)
0.957220 0.289363i \(-0.0934434\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i −0.986203 0.165542i \(-0.947063\pi\)
0.986203 0.165542i \(-0.0529375\pi\)
\(602\) 0 0
\(603\) −343.191 −0.569139
\(604\) 0 0
\(605\) 615.624 + 355.431i 1.01756 + 0.587489i
\(606\) 0 0
\(607\) −137.654 + 79.4748i −0.226778 + 0.130930i −0.609085 0.793105i \(-0.708463\pi\)
0.382307 + 0.924035i \(0.375130\pi\)
\(608\) 0 0
\(609\) −288.000 293.939i −0.472906 0.482658i
\(610\) 0 0
\(611\) 296.595 + 513.718i 0.485426 + 0.840782i
\(612\) 0 0
\(613\) 357.368 618.979i 0.582981 1.00975i −0.412143 0.911119i \(-0.635219\pi\)
0.995124 0.0986338i \(-0.0314473\pi\)
\(614\) 0 0
\(615\) 510.394i 0.829909i
\(616\) 0 0
\(617\) −639.381 −1.03627 −0.518137 0.855298i \(-0.673374\pi\)
−0.518137 + 0.855298i \(0.673374\pi\)
\(618\) 0 0
\(619\) −148.978 86.0126i −0.240676 0.138954i 0.374812 0.927101i \(-0.377707\pi\)
−0.615487 + 0.788147i \(0.711041\pi\)
\(620\) 0 0
\(621\) 60.5513 34.9593i 0.0975061 0.0562952i
\(622\) 0 0
\(623\) −140.912 + 36.2201i −0.226182 + 0.0581382i
\(624\) 0 0
\(625\) −135.588 234.846i −0.216941 0.375753i
\(626\) 0 0
\(627\) −88.4558 + 153.210i −0.141078 + 0.244354i
\(628\) 0 0
\(629\) 111.980i 0.178029i
\(630\) 0 0
\(631\) 1141.06 1.80833 0.904166 0.427180i \(-0.140493\pi\)
0.904166 + 0.427180i \(0.140493\pi\)
\(632\) 0 0
\(633\) −187.368 108.177i −0.295999 0.170895i
\(634\) 0 0
\(635\) −1212.61 + 700.100i −1.90962 + 1.10252i
\(636\) 0 0
\(637\) −453.044 + 748.968i −0.711215 + 1.17577i
\(638\) 0 0
\(639\) −27.9045 48.3321i −0.0436691 0.0756371i
\(640\) 0 0
\(641\) −114.551 + 198.409i −0.178707 + 0.309530i −0.941438 0.337186i \(-0.890525\pi\)
0.762731 + 0.646716i \(0.223858\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i 0.834975 + 0.550288i \(0.185482\pi\)
−0.834975 + 0.550288i \(0.814518\pi\)
\(644\) 0 0
\(645\) 224.309 0.347765
\(646\) 0 0
\(647\) −1021.37 589.687i −1.57862 0.911417i −0.995052 0.0993530i \(-0.968323\pi\)
−0.583568 0.812064i \(-0.698344\pi\)
\(648\) 0 0
\(649\) −142.191 + 82.0940i −0.219092 + 0.126493i
\(650\) 0 0
\(651\) 44.5143 + 173.180i 0.0683783 + 0.266021i
\(652\) 0 0
\(653\) 77.3818 + 134.029i 0.118502 + 0.205252i 0.919174 0.393851i \(-0.128857\pi\)
−0.800672 + 0.599103i \(0.795524\pi\)
\(654\) 0 0
\(655\) 7.45584 12.9139i 0.0113830 0.0197159i
\(656\) 0 0
\(657\) 351.096i 0.534393i
\(658\) 0 0
\(659\) −591.308 −0.897280 −0.448640 0.893712i \(-0.648092\pi\)
−0.448640 + 0.893712i \(0.648092\pi\)
\(660\) 0 0
\(661\) 140.441 + 81.0837i 0.212468 + 0.122668i 0.602458 0.798151i \(-0.294188\pi\)
−0.389990 + 0.920819i \(0.627522\pi\)
\(662\) 0 0
\(663\) −502.566 + 290.156i −0.758017 + 0.437642i
\(664\) 0 0
\(665\) 711.838 697.456i 1.07043 1.04881i
\(666\) 0 0
\(667\) 228.353 + 395.519i 0.342359 + 0.592983i
\(668\) 0 0
\(669\) −198.000 + 342.946i −0.295964 + 0.512625i
\(670\) 0 0
\(671\) 242.283i 0.361078i
\(672\) 0 0
\(673\) 42.3238 0.0628883 0.0314441 0.999506i \(-0.489989\pi\)
0.0314441 + 0.999506i \(0.489989\pi\)
\(674\) 0 0
\(675\) −202.235 116.760i −0.299608 0.172978i
\(676\) 0 0
\(677\) 430.721 248.677i 0.636220 0.367322i −0.146937 0.989146i \(-0.546941\pi\)
0.783157 + 0.621824i \(0.213608\pi\)
\(678\) 0 0
\(679\) 57.5147 206.207i 0.0847050 0.303693i
\(680\) 0 0
\(681\) −146.823 254.306i −0.215600 0.373430i
\(682\) 0 0
\(683\) 608.080 1053.23i 0.890308 1.54206i 0.0508015 0.998709i \(-0.483822\pi\)
0.839506 0.543350i \(-0.182844\pi\)
\(684\) 0 0
\(685\) 844.425i 1.23274i
\(686\) 0 0
\(687\) −60.0883 −0.0874648
\(688\) 0 0
\(689\) 534.418 + 308.546i 0.775642 + 0.447817i
\(690\) 0 0
\(691\) 932.182 538.196i 1.34903 0.778865i 0.360921 0.932596i \(-0.382462\pi\)
0.988113 + 0.153731i \(0.0491290\pi\)
\(692\) 0 0
\(693\) 121.368 + 33.8515i 0.175134 + 0.0488477i
\(694\) 0 0
\(695\) −587.683 1017.90i −0.845588 1.46460i
\(696\) 0 0
\(697\) −330.426 + 572.315i −0.474069 + 0.821112i
\(698\) 0 0
\(699\) 440.781i 0.630589i
\(700\) 0 0
\(701\) −695.897 −0.992720 −0.496360 0.868117i \(-0.665330\pi\)
−0.496360 + 0.868117i \(0.665330\pi\)
\(702\) 0 0
\(703\) −88.0219 50.8194i −0.125209 0.0722894i
\(704\) 0 0
\(705\) −416.558 + 240.500i −0.590863 + 0.341135i
\(706\) 0 0
\(707\) 626.912 + 639.839i 0.886721 + 0.905006i
\(708\) 0 0
\(709\) −127.412 220.684i −0.179707 0.311261i 0.762073 0.647491i \(-0.224182\pi\)
−0.941780 + 0.336229i \(0.890848\pi\)
\(710\) 0 0
\(711\) 132.507 229.509i 0.186367 0.322798i
\(712\) 0 0
\(713\) 198.446i 0.278325i
\(714\) 0 0
\(715\) 896.382 1.25368
\(716\) 0 0
\(717\) 295.721 + 170.734i 0.412442 + 0.238123i
\(718\) 0 0
\(719\) 964.925 557.100i 1.34204 0.774826i 0.354931 0.934892i \(-0.384504\pi\)
0.987106 + 0.160066i \(0.0511709\pi\)
\(720\) 0 0
\(721\) 548.852 141.078i 0.761238 0.195669i
\(722\) 0 0
\(723\) −76.6173 132.705i −0.105971 0.183548i
\(724\) 0 0
\(725\) 762.676 1320.99i 1.05197 1.82206i
\(726\) 0 0
\(727\) 398.345i 0.547930i −0.961740 0.273965i \(-0.911665\pi\)
0.961740 0.273965i \(-0.0883353\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 251.522 + 145.216i 0.344079 + 0.198654i
\(732\) 0 0
\(733\) 818.514 472.569i 1.11666 0.644706i 0.176116 0.984369i \(-0.443646\pi\)
0.940547 + 0.339663i \(0.110313\pi\)
\(734\) 0 0
\(735\) −607.316 367.360i −0.826280 0.499810i
\(736\) 0 0
\(737\) 343.191 + 594.424i 0.465659 + 0.806546i
\(738\) 0 0
\(739\) 96.3162 166.825i 0.130333 0.225744i −0.793472 0.608607i \(-0.791729\pi\)
0.923805 + 0.382863i \(0.125062\pi\)
\(740\) 0 0
\(741\) 526.721i 0.710825i
\(742\) 0 0
\(743\) 911.616 1.22694 0.613470 0.789718i \(-0.289773\pi\)
0.613470 + 0.789718i \(0.289773\pi\)
\(744\) 0 0
\(745\) −1324.76 764.853i −1.77821 1.02665i
\(746\) 0 0
\(747\) −196.831 + 113.640i −0.263495 + 0.152129i
\(748\) 0 0
\(749\) 295.301 + 1148.85i 0.394260 + 1.53384i
\(750\) 0 0
\(751\) −195.831 339.189i −0.260760 0.451650i 0.705684 0.708527i \(-0.250640\pi\)
−0.966444 + 0.256877i \(0.917307\pi\)
\(752\) 0 0
\(753\) −186.978 + 323.855i −0.248310 + 0.430086i
\(754\) 0 0
\(755\) 2415.21i 3.19895i
\(756\) 0 0
\(757\) −152.823 −0.201879 −0.100940 0.994893i \(-0.532185\pi\)
−0.100940 + 0.994893i \(0.532185\pi\)
\(758\) 0 0
\(759\) −121.103 69.9186i −0.159555 0.0921194i
\(760\) 0 0
\(761\) −109.331 + 63.1223i −0.143667 + 0.0829465i −0.570111 0.821568i \(-0.693100\pi\)
0.426443 + 0.904514i \(0.359766\pi\)
\(762\) 0 0
\(763\) −894.706 + 876.629i −1.17262 + 1.14892i
\(764\) 0 0
\(765\) −235.279 407.516i −0.307555 0.532700i
\(766\) 0 0
\(767\) 244.419 423.347i 0.318669 0.551951i
\(768\) 0 0
\(769\) 369.148i 0.480037i 0.970768 + 0.240018i \(0.0771535\pi\)
−0.970768 + 0.240018i \(0.922847\pi\)
\(770\) 0 0
\(771\) 7.45584 0.00967036
\(772\) 0 0
\(773\) −1215.65 701.853i −1.57263 0.907961i −0.995845 0.0910674i \(-0.970972\pi\)
−0.576789 0.816893i \(-0.695695\pi\)
\(774\) 0 0
\(775\) −573.992 + 331.394i −0.740634 + 0.427605i
\(776\) 0 0
\(777\) −19.4483 + 69.7278i −0.0250299 + 0.0897398i
\(778\) 0 0
\(779\) −299.912 519.462i −0.384996 0.666832i
\(780\) 0 0
\(781\) −55.8091 + 96.6642i −0.0714585 + 0.123770i
\(782\) 0 0
\(783\) 176.363i 0.225240i
\(784\) 0 0
\(785\) 1564.41 1.99288
\(786\) 0 0
\(787\) −196.161 113.253i −0.249251 0.143905i 0.370170 0.928964i \(-0.379299\pi\)
−0.619421 + 0.785059i \(0.712633\pi\)
\(788\) 0 0
\(789\) −424.014 + 244.805i −0.537407 + 0.310272i
\(790\) 0 0
\(791\) −117.302 32.7174i −0.148295 0.0413621i
\(792\) 0 0