Properties

Label 224.3.n.a.145.1
Level 224
Weight 3
Character 224.145
Analytic conductor 6.104
Analytic rank 0
Dimension 28
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.1
Character \(\chi\) \(=\) 224.145
Dual form 224.3.n.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.78005 - 4.81519i) q^{3} +(-1.52921 + 2.64866i) q^{5} +(-0.608243 + 6.97352i) q^{7} +(-10.9574 + 18.9787i) q^{9} +O(q^{10})\) \(q+(-2.78005 - 4.81519i) q^{3} +(-1.52921 + 2.64866i) q^{5} +(-0.608243 + 6.97352i) q^{7} +(-10.9574 + 18.9787i) q^{9} +(-0.106038 + 0.0612210i) q^{11} +4.11412 q^{13} +17.0051 q^{15} +(17.8551 - 10.3087i) q^{17} +(-4.46893 + 7.74042i) q^{19} +(35.2698 - 16.4580i) q^{21} +(-7.51940 + 13.0240i) q^{23} +(7.82306 + 13.5499i) q^{25} +71.8074 q^{27} +31.6239i q^{29} +(-23.0318 + 13.2974i) q^{31} +(0.589582 + 0.340395i) q^{33} +(-17.5404 - 12.2750i) q^{35} +(-25.1405 - 14.5149i) q^{37} +(-11.4375 - 19.8103i) q^{39} -9.26915i q^{41} +45.3391i q^{43} +(-33.5122 - 58.0448i) q^{45} +(68.6931 + 39.6600i) q^{47} +(-48.2601 - 8.48319i) q^{49} +(-99.2764 - 57.3172i) q^{51} +(-55.0507 + 31.7835i) q^{53} -0.374478i q^{55} +49.6955 q^{57} +(14.2561 + 24.6923i) q^{59} +(-12.6191 + 21.8569i) q^{61} +(-125.684 - 87.9552i) q^{63} +(-6.29133 + 10.8969i) q^{65} +(-65.4798 + 37.8048i) q^{67} +83.6173 q^{69} +2.81874 q^{71} +(11.0878 - 6.40155i) q^{73} +(43.4970 - 75.3391i) q^{75} +(-0.362429 - 0.776695i) q^{77} +(35.6186 - 61.6932i) q^{79} +(-101.012 - 174.958i) q^{81} +30.0525 q^{83} +63.0563i q^{85} +(152.275 - 87.9160i) q^{87} +(15.3030 + 8.83521i) q^{89} +(-2.50238 + 28.6899i) q^{91} +(128.059 + 73.9351i) q^{93} +(-13.6678 - 23.6734i) q^{95} -26.1737i q^{97} -2.68329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −2.78005 4.81519i −0.926684 1.60506i −0.788830 0.614611i \(-0.789313\pi\)
−0.137854 0.990453i \(1.45598\pi\)
\(4\) 0 0
\(5\) −1.52921 + 2.64866i −0.305841 + 0.529732i −0.977448 0.211175i \(-0.932271\pi\)
0.671607 + 0.740907i \(0.265604\pi\)
\(6\) 0 0
\(7\) −0.608243 + 6.97352i −0.0868918 + 0.996218i
\(8\) 0 0
\(9\) −10.9574 + 18.9787i −1.21749 + 2.10875i
\(10\) 0 0
\(11\) −0.106038 + 0.0612210i −0.00963981 + 0.00556554i −0.504812 0.863229i \(-0.668438\pi\)
0.495172 + 0.868795i \(0.335105\pi\)
\(12\) 0 0
\(13\) 4.11412 0.316471 0.158235 0.987401i \(-0.449420\pi\)
0.158235 + 0.987401i \(0.449420\pi\)
\(14\) 0 0
\(15\) 17.0051 1.13367
\(16\) 0 0
\(17\) 17.8551 10.3087i 1.05030 0.606392i 0.127568 0.991830i \(-0.459283\pi\)
0.922734 + 0.385438i \(0.125950\pi\)
\(18\) 0 0
\(19\) −4.46893 + 7.74042i −0.235207 + 0.407390i −0.959333 0.282277i \(-0.908910\pi\)
0.724126 + 0.689668i \(0.242243\pi\)
\(20\) 0 0
\(21\) 35.2698 16.4580i 1.67951 0.783712i
\(22\) 0 0
\(23\) −7.51940 + 13.0240i −0.326930 + 0.566260i −0.981901 0.189394i \(-0.939348\pi\)
0.654971 + 0.755654i \(0.272681\pi\)
\(24\) 0 0
\(25\) 7.82306 + 13.5499i 0.312922 + 0.541998i
\(26\) 0 0
\(27\) 71.8074 2.65953
\(28\) 0 0
\(29\) 31.6239i 1.09048i 0.838280 + 0.545239i \(0.183561\pi\)
−0.838280 + 0.545239i \(0.816439\pi\)
\(30\) 0 0
\(31\) −23.0318 + 13.2974i −0.742962 + 0.428949i −0.823145 0.567831i \(-0.807783\pi\)
0.0801833 + 0.996780i \(0.474449\pi\)
\(32\) 0 0
\(33\) 0.589582 + 0.340395i 0.0178661 + 0.0103150i
\(34\) 0 0
\(35\) −17.5404 12.2750i −0.501154 0.350714i
\(36\) 0 0
\(37\) −25.1405 14.5149i −0.679474 0.392295i 0.120183 0.992752i \(-0.461652\pi\)
−0.799657 + 0.600457i \(0.794985\pi\)
\(38\) 0 0
\(39\) −11.4375 19.8103i −0.293268 0.507956i
\(40\) 0 0
\(41\) 9.26915i 0.226077i −0.993591 0.113038i \(-0.963942\pi\)
0.993591 0.113038i \(-0.0360583\pi\)
\(42\) 0 0
\(43\) 45.3391i 1.05440i 0.849742 + 0.527199i \(0.176758\pi\)
−0.849742 + 0.527199i \(0.823242\pi\)
\(44\) 0 0
\(45\) −33.5122 58.0448i −0.744715 1.28988i
\(46\) 0 0
\(47\) 68.6931 + 39.6600i 1.46156 + 0.843830i 0.999083 0.0428039i \(-0.0136291\pi\)
0.462472 + 0.886634i \(0.346962\pi\)
\(48\) 0 0
\(49\) −48.2601 8.48319i −0.984900 0.173126i
\(50\) 0 0
\(51\) −99.2764 57.3172i −1.94660 1.12387i
\(52\) 0 0
\(53\) −55.0507 + 31.7835i −1.03869 + 0.599689i −0.919462 0.393178i \(-0.871376\pi\)
−0.119229 + 0.992867i \(0.538042\pi\)
\(54\) 0 0
\(55\) 0.374478i 0.00680869i
\(56\) 0 0
\(57\) 49.6955 0.871850
\(58\) 0 0
\(59\) 14.2561 + 24.6923i 0.241629 + 0.418514i 0.961178 0.275928i \(-0.0889850\pi\)
−0.719550 + 0.694441i \(0.755652\pi\)
\(60\) 0 0
\(61\) −12.6191 + 21.8569i −0.206871 + 0.358311i −0.950727 0.310029i \(-0.899661\pi\)
0.743856 + 0.668339i \(0.232995\pi\)
\(62\) 0 0
\(63\) −125.684 87.9552i −1.99498 1.39611i
\(64\) 0 0
\(65\) −6.29133 + 10.8969i −0.0967897 + 0.167645i
\(66\) 0 0
\(67\) −65.4798 + 37.8048i −0.977311 + 0.564251i −0.901457 0.432868i \(-0.857502\pi\)
−0.0758537 + 0.997119i \(0.524168\pi\)
\(68\) 0 0
\(69\) 83.6173 1.21184
\(70\) 0 0
\(71\) 2.81874 0.0397006 0.0198503 0.999803i \(-0.493681\pi\)
0.0198503 + 0.999803i \(0.493681\pi\)
\(72\) 0 0
\(73\) 11.0878 6.40155i 0.151888 0.0876925i −0.422130 0.906535i \(-0.638717\pi\)
0.574018 + 0.818843i \(0.305384\pi\)
\(74\) 0 0
\(75\) 43.4970 75.3391i 0.579960 1.00452i
\(76\) 0 0
\(77\) −0.362429 0.776695i −0.00470687 0.0100869i
\(78\) 0 0
\(79\) 35.6186 61.6932i 0.450868 0.780926i −0.547572 0.836758i \(-0.684448\pi\)
0.998440 + 0.0558321i \(0.0177812\pi\)
\(80\) 0 0
\(81\) −101.012 174.958i −1.24706 2.15997i
\(82\) 0 0
\(83\) 30.0525 0.362078 0.181039 0.983476i \(-0.442054\pi\)
0.181039 + 0.983476i \(0.442054\pi\)
\(84\) 0 0
\(85\) 63.0563i 0.741839i
\(86\) 0 0
\(87\) 152.275 87.9160i 1.75029 1.01053i
\(88\) 0 0
\(89\) 15.3030 + 8.83521i 0.171944 + 0.0992720i 0.583502 0.812112i \(-0.301682\pi\)
−0.411558 + 0.911384i \(0.635015\pi\)
\(90\) 0 0
\(91\) −2.50238 + 28.6899i −0.0274987 + 0.315274i
\(92\) 0 0
\(93\) 128.059 + 73.9351i 1.37698 + 0.795001i
\(94\) 0 0
\(95\) −13.6678 23.6734i −0.143872 0.249193i
\(96\) 0 0
\(97\) 26.1737i 0.269832i −0.990857 0.134916i \(-0.956923\pi\)
0.990857 0.134916i \(-0.0430765\pi\)
\(98\) 0 0
\(99\) 2.68329i 0.0271039i
\(100\) 0 0
\(101\) −67.8445 117.510i −0.671727 1.16347i −0.977414 0.211334i \(-0.932219\pi\)
0.305686 0.952132i \(1.59889\pi\)
\(102\) 0 0
\(103\) −110.258 63.6577i −1.07047 0.618036i −0.142160 0.989844i \(-0.545405\pi\)
−0.928310 + 0.371807i \(0.878738\pi\)
\(104\) 0 0
\(105\) −10.3432 + 118.585i −0.0985068 + 1.12938i
\(106\) 0 0
\(107\) 69.1003 + 39.8951i 0.645797 + 0.372851i 0.786844 0.617152i \(-0.211713\pi\)
−0.141047 + 0.990003i \(0.545047\pi\)
\(108\) 0 0
\(109\) −27.3608 + 15.7968i −0.251017 + 0.144925i −0.620230 0.784420i \(-0.712961\pi\)
0.369213 + 0.929345i \(0.379627\pi\)
\(110\) 0 0
\(111\) 161.409i 1.45413i
\(112\) 0 0
\(113\) 57.7985 0.511491 0.255745 0.966744i \(-0.417679\pi\)
0.255745 + 0.966744i \(0.417679\pi\)
\(114\) 0 0
\(115\) −22.9974 39.8327i −0.199978 0.346371i
\(116\) 0 0
\(117\) −45.0799 + 78.0808i −0.385299 + 0.667357i
\(118\) 0 0
\(119\) 61.0275 + 130.783i 0.512836 + 1.09902i
\(120\) 0 0
\(121\) −60.4925 + 104.776i −0.499938 + 0.865918i
\(122\) 0 0
\(123\) −44.6327 + 25.7687i −0.362868 + 0.209502i
\(124\) 0 0
\(125\) −124.313 −0.994500
\(126\) 0 0
\(127\) −67.8062 −0.533907 −0.266954 0.963709i \(-0.586017\pi\)
−0.266954 + 0.963709i \(0.586017\pi\)
\(128\) 0 0
\(129\) 218.316 126.045i 1.69238 0.977093i
\(130\) 0 0
\(131\) 56.0784 97.1307i 0.428080 0.741456i −0.568623 0.822598i \(-0.692524\pi\)
0.996702 + 0.0811427i \(0.0258569\pi\)
\(132\) 0 0
\(133\) −51.2598 35.8723i −0.385412 0.269716i
\(134\) 0 0
\(135\) −109.808 + 190.193i −0.813394 + 1.40884i
\(136\) 0 0
\(137\) 29.3413 + 50.8207i 0.214170 + 0.370954i 0.953016 0.302921i \(-0.0979619\pi\)
−0.738845 + 0.673875i \(0.764629\pi\)
\(138\) 0 0
\(139\) −175.260 −1.26086 −0.630430 0.776246i \(-0.717121\pi\)
−0.630430 + 0.776246i \(0.717121\pi\)
\(140\) 0 0
\(141\) 441.027i 3.12785i
\(142\) 0 0
\(143\) −0.436252 + 0.251870i −0.00305072 + 0.00176133i
\(144\) 0 0
\(145\) −83.7610 48.3594i −0.577662 0.333513i
\(146\) 0 0
\(147\) 93.3174 + 255.965i 0.634812 + 1.74126i
\(148\) 0 0
\(149\) 61.6922 + 35.6180i 0.414041 + 0.239047i 0.692525 0.721394i \(-0.256498\pi\)
−0.278483 + 0.960441i \(0.589832\pi\)
\(150\) 0 0
\(151\) −86.3801 149.615i −0.572053 0.990825i −0.996355 0.0853045i \(-0.972814\pi\)
0.424302 0.905521i \(-0.360520\pi\)
\(152\) 0 0
\(153\) 451.824i 2.95310i
\(154\) 0 0
\(155\) 81.3380i 0.524761i
\(156\) 0 0
\(157\) 134.922 + 233.692i 0.859378 + 1.48849i 0.872524 + 0.488572i \(0.162482\pi\)
−0.0131460 + 0.999914i \(0.504185\pi\)
\(158\) 0 0
\(159\) 306.087 + 176.720i 1.92508 + 1.11144i
\(160\) 0 0
\(161\) −86.2494 60.3584i −0.535711 0.374897i
\(162\) 0 0
\(163\) 236.230 + 136.387i 1.44926 + 0.836733i 0.998438 0.0558788i \(-0.0177960\pi\)
0.450826 + 0.892612i \(0.351129\pi\)
\(164\) 0 0
\(165\) −1.80318 + 1.04107i −0.0109284 + 0.00630950i
\(166\) 0 0
\(167\) 82.5676i 0.494417i 0.968962 + 0.247208i \(0.0795132\pi\)
−0.968962 + 0.247208i \(0.920487\pi\)
\(168\) 0 0
\(169\) −152.074 −0.899846
\(170\) 0 0
\(171\) −97.9355 169.629i −0.572722 0.991984i
\(172\) 0 0
\(173\) 115.129 199.410i 0.665488 1.15266i −0.313665 0.949534i \(-0.601557\pi\)
0.979153 0.203125i \(-0.0651097\pi\)
\(174\) 0 0
\(175\) −99.2491 + 46.3127i −0.567138 + 0.264644i
\(176\) 0 0
\(177\) 79.2654 137.292i 0.447827 0.775660i
\(178\) 0 0
\(179\) 228.664 132.019i 1.27745 0.737538i 0.301074 0.953601i \(-0.402655\pi\)
0.976379 + 0.216063i \(0.0693216\pi\)
\(180\) 0 0
\(181\) 183.991 1.01653 0.508263 0.861202i \(-0.330288\pi\)
0.508263 + 0.861202i \(0.330288\pi\)
\(182\) 0 0
\(183\) 140.327 0.766815
\(184\) 0 0
\(185\) 76.8901 44.3925i 0.415622 0.239960i
\(186\) 0 0
\(187\) −1.26221 + 2.18622i −0.00674980 + 0.0116910i
\(188\) 0 0
\(189\) −43.6763 + 500.751i −0.231092 + 2.64947i
\(190\) 0 0
\(191\) 148.189 256.671i 0.775860 1.34383i −0.158450 0.987367i \(-0.550650\pi\)
0.934310 0.356462i \(-0.116017\pi\)
\(192\) 0 0
\(193\) −47.8173 82.8220i −0.247758 0.429129i 0.715145 0.698976i \(-0.246360\pi\)
−0.962903 + 0.269846i \(0.913027\pi\)
\(194\) 0 0
\(195\) 69.9609 0.358774
\(196\) 0 0
\(197\) 161.104i 0.817786i 0.912582 + 0.408893i \(0.134085\pi\)
−0.912582 + 0.408893i \(0.865915\pi\)
\(198\) 0 0
\(199\) −0.961074 + 0.554877i −0.00482952 + 0.00278832i −0.502413 0.864628i \(-0.667554\pi\)
0.497583 + 0.867416i \(0.334221\pi\)
\(200\) 0 0
\(201\) 364.075 + 210.199i 1.81132 + 1.04576i
\(202\) 0 0
\(203\) −220.530 19.2350i −1.08635 0.0947536i
\(204\) 0 0
\(205\) 24.5508 + 14.1744i 0.119760 + 0.0691436i
\(206\) 0 0
\(207\) −164.786 285.417i −0.796067 1.37883i
\(208\) 0 0
\(209\) 1.09437i 0.00523622i
\(210\) 0 0
\(211\) 214.045i 1.01443i −0.861819 0.507216i \(-0.830675\pi\)
0.861819 0.507216i \(-0.169325\pi\)
\(212\) 0 0
\(213\) −7.83624 13.5728i −0.0367899 0.0637219i
\(214\) 0 0
\(215\) −120.088 69.3328i −0.558549 0.322478i
\(216\) 0 0
\(217\) −78.7210 168.701i −0.362770 0.777424i
\(218\) 0 0
\(219\) −61.6494 35.5933i −0.281504 0.162526i
\(220\) 0 0
\(221\) 73.4581 42.4111i 0.332390 0.191905i
\(222\) 0 0
\(223\) 290.270i 1.30166i 0.759224 + 0.650829i \(0.225579\pi\)
−0.759224 + 0.650829i \(0.774421\pi\)
\(224\) 0 0
\(225\) −342.881 −1.52392
\(226\) 0 0
\(227\) 40.7118 + 70.5149i 0.179347 + 0.310638i 0.941657 0.336574i \(-0.109268\pi\)
−0.762310 + 0.647212i \(0.775935\pi\)
\(228\) 0 0
\(229\) 117.111 202.842i 0.511400 0.885771i −0.488512 0.872557i \(-0.662460\pi\)
0.999913 0.0132145i \(-0.00420642\pi\)
\(230\) 0 0
\(231\) −2.73236 + 3.90442i −0.0118284 + 0.0169022i
\(232\) 0 0
\(233\) 30.9903 53.6768i 0.133006 0.230372i −0.791828 0.610744i \(-0.790871\pi\)
0.924834 + 0.380371i \(0.124204\pi\)
\(234\) 0 0
\(235\) −210.092 + 121.297i −0.894008 + 0.516156i
\(236\) 0 0
\(237\) −396.086 −1.67125
\(238\) 0 0
\(239\) −97.0822 −0.406202 −0.203101 0.979158i \(-0.565102\pi\)
−0.203101 + 0.979158i \(0.565102\pi\)
\(240\) 0 0
\(241\) −207.622 + 119.871i −0.861502 + 0.497388i −0.864515 0.502607i \(-0.832374\pi\)
0.00301303 + 0.999995i \(0.499041\pi\)
\(242\) 0 0
\(243\) −238.503 + 413.100i −0.981494 + 1.70000i
\(244\) 0 0
\(245\) 96.2687 114.852i 0.392933 0.468784i
\(246\) 0 0
\(247\) −18.3857 + 31.8450i −0.0744361 + 0.128927i
\(248\) 0 0
\(249\) −83.5475 144.709i −0.335532 0.581159i
\(250\) 0 0
\(251\) −136.078 −0.542144 −0.271072 0.962559i \(-0.587378\pi\)
−0.271072 + 0.962559i \(0.587378\pi\)
\(252\) 0 0
\(253\) 1.84138i 0.00727818i
\(254\) 0 0
\(255\) 303.628 175.300i 1.19070 0.687450i
\(256\) 0 0
\(257\) −16.4497 9.49721i −0.0640064 0.0369541i 0.467655 0.883911i \(-0.345099\pi\)
−0.531662 + 0.846957i \(0.678432\pi\)
\(258\) 0 0
\(259\) 116.512 166.490i 0.449852 0.642817i
\(260\) 0 0
\(261\) −600.181 346.515i −2.29954 1.32764i
\(262\) 0 0
\(263\) 123.286 + 213.537i 0.468767 + 0.811928i 0.999363 0.0356971i \(-0.0113652\pi\)
−0.530596 + 0.847625i \(0.678032\pi\)
\(264\) 0 0
\(265\) 194.414i 0.733638i
\(266\) 0 0
\(267\) 98.2494i 0.367975i
\(268\) 0 0
\(269\) −147.121 254.821i −0.546918 0.947290i −0.998483 0.0550522i \(-0.982467\pi\)
0.451565 0.892238i \(1.64913\pi\)
\(270\) 0 0
\(271\) −392.032 226.340i −1.44661 0.835202i −0.448335 0.893866i \(-0.647983\pi\)
−0.998278 + 0.0586635i \(0.981316\pi\)
\(272\) 0 0
\(273\) 145.104 67.7100i 0.531517 0.248022i
\(274\) 0 0
\(275\) −1.65908 0.957871i −0.00603302 0.00348317i
\(276\) 0 0
\(277\) −252.424 + 145.737i −0.911277 + 0.526126i −0.880842 0.473411i \(-0.843023\pi\)
−0.0304353 + 0.999537i \(0.509689\pi\)
\(278\) 0 0
\(279\) 582.820i 2.08896i
\(280\) 0 0
\(281\) 495.433 1.76311 0.881553 0.472086i \(-0.156499\pi\)
0.881553 + 0.472086i \(0.156499\pi\)
\(282\) 0 0
\(283\) 18.3685 + 31.8151i 0.0649062 + 0.112421i 0.896652 0.442735i \(-0.145992\pi\)
−0.831746 + 0.555156i \(0.812659\pi\)
\(284\) 0 0
\(285\) −75.9946 + 131.626i −0.266648 + 0.461847i
\(286\) 0 0
\(287\) 64.6386 + 5.63789i 0.225222 + 0.0196442i
\(288\) 0 0
\(289\) 68.0371 117.844i 0.235423 0.407764i
\(290\) 0 0
\(291\) −126.032 + 72.7644i −0.433098 + 0.250049i
\(292\) 0 0
\(293\) 527.984 1.80199 0.900996 0.433828i \(-0.142837\pi\)
0.900996 + 0.433828i \(0.142837\pi\)
\(294\) 0 0
\(295\) −87.2021 −0.295600
\(296\) 0 0
\(297\) −7.61430 + 4.39612i −0.0256374 + 0.0148017i
\(298\) 0 0
\(299\) −30.9357 + 53.5822i −0.103464 + 0.179205i
\(300\) 0 0
\(301\) −316.173 27.5772i −1.05041 0.0916185i
\(302\) 0 0
\(303\) −377.222 + 653.368i −1.24496 + 2.15633i
\(304\) 0 0
\(305\) −38.5944 66.8475i −0.126539 0.219172i
\(306\) 0 0
\(307\) 174.486 0.568359 0.284179 0.958771i \(-0.408279\pi\)
0.284179 + 0.958771i \(0.408279\pi\)
\(308\) 0 0
\(309\) 707.887i 2.29090i
\(310\) 0 0
\(311\) −11.9119 + 6.87736i −0.0383020 + 0.0221137i −0.519029 0.854757i \(-0.673706\pi\)
0.480727 + 0.876870i \(0.340373\pi\)
\(312\) 0 0
\(313\) −365.368 210.945i −1.16731 0.673947i −0.214265 0.976776i \(-0.568736\pi\)
−0.953045 + 0.302829i \(0.902069\pi\)
\(314\) 0 0
\(315\) 425.160 198.393i 1.34971 0.629818i
\(316\) 0 0
\(317\) 408.352 + 235.762i 1.28818 + 0.743730i 0.978329 0.207056i \(-0.0663883\pi\)
0.309848 + 0.950786i \(0.399722\pi\)
\(318\) 0 0
\(319\) −1.93605 3.35333i −0.00606911 0.0105120i
\(320\) 0 0
\(321\) 443.642i 1.38206i
\(322\) 0 0
\(323\) 184.275i 0.570510i
\(324\) 0 0
\(325\) 32.1850 + 55.7460i 0.0990308 + 0.171526i
\(326\) 0 0
\(327\) 152.129 + 87.8317i 0.465226 + 0.268598i
\(328\) 0 0
\(329\) −318.352 + 454.910i −0.967635 + 1.38271i
\(330\) 0 0
\(331\) 383.707 + 221.533i 1.15923 + 0.669284i 0.951120 0.308820i \(-0.0999342\pi\)
0.208114 + 0.978105i \(0.433268\pi\)
\(332\) 0 0
\(333\) 550.949 318.090i 1.65450 0.955227i
\(334\) 0 0
\(335\) 231.245i 0.690284i
\(336\) 0 0
\(337\) 556.978 1.65276 0.826378 0.563117i \(-0.190398\pi\)
0.826378 + 0.563117i \(0.190398\pi\)
\(338\) 0 0
\(339\) −160.683 278.311i −0.473990 0.820975i
\(340\) 0 0
\(341\) 1.62816 2.82006i 0.00477467 0.00826998i
\(342\) 0 0
\(343\) 88.5116 331.383i 0.258051 0.966131i
\(344\) 0 0
\(345\) −127.868 + 221.474i −0.370632 + 0.641953i
\(346\) 0 0
\(347\) −277.806 + 160.392i −0.800595 + 0.462223i −0.843679 0.536848i \(-0.819615\pi\)
0.0430845 + 0.999071i \(0.486282\pi\)
\(348\) 0 0
\(349\) −222.198 −0.636670 −0.318335 0.947978i \(-0.603124\pi\)
−0.318335 + 0.947978i \(0.603124\pi\)
\(350\) 0 0
\(351\) 295.424 0.841664
\(352\) 0 0
\(353\) −118.142 + 68.2096i −0.334681 + 0.193228i −0.657918 0.753090i \(-0.728562\pi\)
0.323236 + 0.946318i \(0.395229\pi\)
\(354\) 0 0
\(355\) −4.31043 + 7.46589i −0.0121421 + 0.0210307i
\(356\) 0 0
\(357\) 460.087 657.443i 1.28876 1.84158i
\(358\) 0 0
\(359\) 124.441 215.538i 0.346632 0.600384i −0.639017 0.769193i \(-0.720659\pi\)
0.985649 + 0.168809i \(0.0539920\pi\)
\(360\) 0 0
\(361\) 140.557 + 243.452i 0.389355 + 0.674383i
\(362\) 0 0
\(363\) 672.689 1.85314
\(364\) 0 0
\(365\) 39.1572i 0.107280i
\(366\) 0 0
\(367\) 225.916 130.432i 0.615574 0.355402i −0.159570 0.987187i \(-0.551011\pi\)
0.775144 + 0.631785i \(0.217677\pi\)
\(368\) 0 0
\(369\) 175.917 + 101.566i 0.476739 + 0.275245i
\(370\) 0 0
\(371\) −188.159 403.229i −0.507167 1.08687i
\(372\) 0 0
\(373\) −381.464 220.239i −1.02269 0.590452i −0.107810 0.994172i \(-0.534384\pi\)
−0.914883 + 0.403720i \(0.867717\pi\)
\(374\) 0 0
\(375\) 345.595 + 598.589i 0.921588 + 1.59624i
\(376\) 0 0
\(377\) 130.104i 0.345104i
\(378\) 0 0
\(379\) 283.715i 0.748587i 0.927310 + 0.374294i \(0.122115\pi\)
−0.927310 + 0.374294i \(0.877885\pi\)
\(380\) 0 0
\(381\) 188.505 + 326.500i 0.494763 + 0.856955i
\(382\) 0 0
\(383\) −138.511 79.9691i −0.361646 0.208797i 0.308156 0.951336i \(-0.400288\pi\)
−0.669803 + 0.742539i \(0.733621\pi\)
\(384\) 0 0
\(385\) 2.61143 + 0.227773i 0.00678294 + 0.000591619i
\(386\) 0 0
\(387\) −860.479 496.798i −2.22346 1.28371i
\(388\) 0 0
\(389\) −430.295 + 248.431i −1.10616 + 0.638640i −0.937831 0.347091i \(-0.887170\pi\)
−0.168326 + 0.985731i \(0.553836\pi\)
\(390\) 0 0
\(391\) 310.060i 0.792992i
\(392\) 0 0
\(393\) −623.604 −1.58678
\(394\) 0 0
\(395\) 108.936 + 188.683i 0.275788 + 0.477679i
\(396\) 0 0
\(397\) 142.186 246.273i 0.358150 0.620334i −0.629502 0.776999i \(-0.716741\pi\)
0.987652 + 0.156665i \(0.0500743\pi\)
\(398\) 0 0
\(399\) −30.2269 + 346.552i −0.0757566 + 0.868552i
\(400\) 0 0
\(401\) −70.8759 + 122.761i −0.176748 + 0.306136i −0.940765 0.339060i \(-0.889891\pi\)
0.764017 + 0.645196i \(0.223224\pi\)
\(402\) 0 0
\(403\) −94.7556 + 54.7072i −0.235126 + 0.135750i
\(404\) 0 0
\(405\) 617.872 1.52561
\(406\) 0 0
\(407\) 3.55447 0.00873333
\(408\) 0 0
\(409\) −323.318 + 186.668i −0.790508 + 0.456400i −0.840141 0.542368i \(-0.817528\pi\)
0.0496336 + 0.998767i \(0.484195\pi\)
\(410\) 0 0
\(411\) 163.141 282.568i 0.396937 0.687514i
\(412\) 0 0
\(413\) −180.864 + 84.3964i −0.437926 + 0.204350i
\(414\) 0 0
\(415\) −45.9565 + 79.5989i −0.110738 + 0.191805i
\(416\) 0 0
\(417\) 487.231 + 843.908i 1.16842 + 2.02376i
\(418\) 0 0
\(419\) −418.864 −0.999676 −0.499838 0.866119i \(-0.666607\pi\)
−0.499838 + 0.866119i \(0.666607\pi\)
\(420\) 0 0
\(421\) 315.112i 0.748485i 0.927331 + 0.374243i \(0.122097\pi\)
−0.927331 + 0.374243i \(0.877903\pi\)
\(422\) 0 0
\(423\) −1505.39 + 869.139i −3.55885 + 2.05470i
\(424\) 0 0
\(425\) 279.364 + 161.291i 0.657326 + 0.379507i
\(426\) 0 0
\(427\) −144.744 101.294i −0.338980 0.237222i
\(428\) 0 0
\(429\) 2.42561 + 1.40043i 0.00565410 + 0.00326440i
\(430\) 0 0
\(431\) 111.663 + 193.405i 0.259078 + 0.448736i 0.965995 0.258560i \(-0.0832481\pi\)
−0.706917 + 0.707296i \(0.749915\pi\)
\(432\) 0 0
\(433\) 591.725i 1.36657i 0.730151 + 0.683286i \(0.239450\pi\)
−0.730151 + 0.683286i \(0.760550\pi\)
\(434\) 0 0
\(435\) 537.767i 1.23625i
\(436\) 0 0
\(437\) −67.2074 116.407i −0.153793 0.266377i
\(438\) 0 0
\(439\) 443.687 + 256.163i 1.01068 + 0.583515i 0.911390 0.411544i \(-0.135010\pi\)
0.0992873 + 0.995059i \(0.468344\pi\)
\(440\) 0 0
\(441\) 689.804 822.962i 1.56418 1.86613i
\(442\) 0 0
\(443\) −134.591 77.7063i −0.303818 0.175409i 0.340339 0.940303i \(-0.389458\pi\)
−0.644157 + 0.764894i \(0.722792\pi\)
\(444\) 0 0
\(445\) −46.8030 + 27.0217i −0.105175 + 0.0607229i
\(446\) 0 0
\(447\) 396.079i 0.886084i
\(448\) 0 0
\(449\) −369.139 −0.822136 −0.411068 0.911605i \(-0.634844\pi\)
−0.411068 + 0.911605i \(0.634844\pi\)
\(450\) 0 0
\(451\) 0.567467 + 0.982881i 0.00125824 + 0.00217934i
\(452\) 0 0
\(453\) −480.282 + 831.873i −1.06023 + 1.83636i
\(454\) 0 0
\(455\) −72.1632 50.5007i −0.158600 0.110991i
\(456\) 0 0
\(457\) 214.079 370.795i 0.468444 0.811369i −0.530906 0.847431i \(-0.678148\pi\)
0.999350 + 0.0360623i \(0.0114815\pi\)
\(458\) 0 0
\(459\) 1282.13 740.238i 2.79331 1.61272i
\(460\) 0 0
\(461\) −165.578 −0.359171 −0.179586 0.983742i \(-0.557476\pi\)
−0.179586 + 0.983742i \(0.557476\pi\)
\(462\) 0 0
\(463\) 605.376 1.30751 0.653754 0.756708i \(-0.273193\pi\)
0.653754 + 0.756708i \(0.273193\pi\)
\(464\) 0 0
\(465\) −391.658 + 226.124i −0.842275 + 0.486288i
\(466\) 0 0
\(467\) 286.063 495.476i 0.612555 1.06098i −0.378253 0.925702i \(-0.623475\pi\)
0.990808 0.135275i \(-0.0431916\pi\)
\(468\) 0 0
\(469\) −223.805 479.620i −0.477196 1.02264i
\(470\) 0 0
\(471\) 750.182 1299.35i 1.59274 2.75871i
\(472\) 0 0
\(473\) −2.77570 4.80766i −0.00586830 0.0101642i
\(474\) 0 0
\(475\) −139.843 −0.294406
\(476\) 0 0
\(477\) 1393.06i 2.92045i
\(478\) 0 0
\(479\) −32.2540 + 18.6218i −0.0673361 + 0.0388765i −0.533290 0.845932i \(-0.679045\pi\)
0.465954 + 0.884809i \(0.345711\pi\)
\(480\) 0 0
\(481\) −103.431 59.7160i −0.215034 0.124150i
\(482\) 0 0
\(483\) −50.8596 + 583.107i −0.105299 + 1.20726i
\(484\) 0 0
\(485\) 69.3254 + 40.0250i 0.142939 + 0.0825259i
\(486\) 0 0
\(487\) 137.172 + 237.589i 0.281668 + 0.487863i 0.971796 0.235824i \(-0.0757790\pi\)
−0.690128 + 0.723688i \(0.742446\pi\)
\(488\) 0 0
\(489\) 1516.66i 3.10155i
\(490\) 0 0
\(491\) 881.994i 1.79632i 0.439667 + 0.898161i \(0.355097\pi\)
−0.439667 + 0.898161i \(0.644903\pi\)
\(492\) 0 0
\(493\) 326.000 + 564.648i 0.661257 + 1.14533i
\(494\) 0 0
\(495\) 7.10712 + 4.10330i 0.0143578 + 0.00828949i
\(496\) 0 0
\(497\) −1.71448 + 19.6566i −0.00344965 + 0.0395504i
\(498\) 0 0
\(499\) 305.733 + 176.515i 0.612692 + 0.353738i 0.774018 0.633163i \(-0.218244\pi\)
−0.161327 + 0.986901i \(0.551577\pi\)
\(500\) 0 0
\(501\) 397.579 229.542i 0.793570 0.458168i
\(502\) 0 0
\(503\) 291.993i 0.580502i −0.956951 0.290251i \(-0.906261\pi\)
0.956951 0.290251i \(-0.0937388\pi\)
\(504\) 0 0
\(505\) 414.993 0.821768
\(506\) 0 0
\(507\) 422.774 + 732.266i 0.833873 + 1.44431i
\(508\) 0 0
\(509\) 41.5606 71.9851i 0.0816515 0.141425i −0.822308 0.569043i \(-0.807314\pi\)
0.903959 + 0.427618i \(0.140647\pi\)
\(510\) 0 0
\(511\) 37.8973 + 81.2148i 0.0741630 + 0.158933i
\(512\) 0 0
\(513\) −320.902 + 555.819i −0.625541 + 1.08347i
\(514\) 0 0
\(515\) 337.216 194.692i 0.654788 0.378042i
\(516\) 0 0
\(517\) −9.71210 −0.0187855
\(518\) 0 0
\(519\) −1280.26 −2.46679
\(520\) 0 0
\(521\) 513.150 296.267i 0.984933 0.568651i 0.0811772 0.996700i \(-0.474132\pi\)
0.903756 + 0.428048i \(0.140799\pi\)
\(522\) 0 0
\(523\) −151.233 + 261.943i −0.289164 + 0.500847i −0.973610 0.228217i \(-0.926711\pi\)
0.684446 + 0.729063i \(0.260044\pi\)
\(524\) 0 0
\(525\) 498.922 + 349.152i 0.950328 + 0.665051i
\(526\) 0 0
\(527\) −274.157 + 474.855i −0.520223 + 0.901052i
\(528\) 0 0
\(529\) 151.417 + 262.262i 0.286233 + 0.495770i
\(530\) 0 0
\(531\) −624.838 −1.17672
\(532\) 0 0
\(533\) 38.1344i 0.0715467i
\(534\) 0 0
\(535\) −211.337 + 122.016i −0.395023 + 0.228067i
\(536\) 0 0
\(537\) −1271.40 734.041i −2.36759 1.36693i
\(538\) 0 0
\(539\) 5.63675 2.05499i 0.0104578 0.00381260i
\(540\) 0 0
\(541\) 630.140 + 363.811i 1.16477 + 0.672480i 0.952442 0.304719i \(-0.0985626\pi\)
0.212327 + 0.977199i \(0.431896\pi\)
\(542\) 0 0
\(543\) −511.505 885.952i −0.941997 1.63159i
\(544\) 0 0
\(545\) 96.6260i 0.177296i
\(546\) 0 0
\(547\) 1033.51i 1.88941i −0.327921 0.944705i \(-0.606348\pi\)
0.327921 0.944705i \(-0.393652\pi\)
\(548\) 0 0
\(549\) −276.545 478.990i −0.503724 0.872476i
\(550\) 0 0
\(551\) −244.782 141.325i −0.444250 0.256488i
\(552\) 0 0
\(553\) 408.554 + 285.911i 0.738796 + 0.517019i
\(554\) 0 0
\(555\) −427.517 246.827i −0.770301 0.444734i
\(556\) 0 0
\(557\) −625.736 + 361.269i −1.12340 + 0.648597i −0.942268 0.334861i \(-0.891311\pi\)
−0.181136 + 0.983458i \(0.557977\pi\)
\(558\) 0 0
\(559\) 186.530i 0.333686i
\(560\) 0 0
\(561\) 14.0361 0.0250197
\(562\) 0 0
\(563\) 206.897 + 358.355i 0.367489 + 0.636510i 0.989172 0.146759i \(-0.0468841\pi\)
−0.621683 + 0.783269i \(0.713551\pi\)
\(564\) 0 0
\(565\) −88.3857 + 153.089i −0.156435 + 0.270953i
\(566\) 0 0
\(567\) 1281.51 597.992i 2.26016 1.05466i
\(568\) 0 0
\(569\) 258.602 447.911i 0.454485 0.787190i −0.544174 0.838972i \(-0.683157\pi\)
0.998658 + 0.0517822i \(0.0164901\pi\)
\(570\) 0 0
\(571\) −615.938 + 355.612i −1.07870 + 0.622788i −0.930545 0.366177i \(-0.880667\pi\)
−0.148155 + 0.988964i \(0.547333\pi\)
\(572\) 0 0
\(573\) −1647.89 −2.87591
\(574\) 0 0
\(575\) −235.299 −0.409215
\(576\) 0 0
\(577\) 527.662 304.646i 0.914491 0.527982i 0.0326179 0.999468i \(-0.489616\pi\)
0.881874 + 0.471486i \(0.156282\pi\)
\(578\) 0 0
\(579\) −265.869 + 460.499i −0.459187 + 0.795335i
\(580\) 0 0
\(581\) −18.2792 + 209.572i −0.0314616 + 0.360709i
\(582\) 0 0
\(583\) 3.89164 6.74051i 0.00667519 0.0115618i
\(584\) 0 0
\(585\) −137.873 238.803i −0.235680 0.408210i
\(586\) 0 0
\(587\) −972.801 −1.65724 −0.828621 0.559810i \(-0.810874\pi\)
−0.828621 + 0.559810i \(0.810874\pi\)
\(588\) 0 0
\(589\) 237.701i 0.403567i
\(590\) 0 0
\(591\) 775.745 447.877i 1.31260 0.757829i
\(592\) 0 0
\(593\) −281.520 162.536i −0.474739 0.274091i 0.243482 0.969905i \(-0.421710\pi\)
−0.718222 + 0.695814i \(0.755044\pi\)
\(594\) 0 0
\(595\) −439.724 38.3535i −0.739033 0.0644597i
\(596\) 0 0
\(597\) 5.34367 + 3.08517i 0.00895088 + 0.00516779i
\(598\) 0 0
\(599\) 231.570 + 401.091i 0.386595 + 0.669602i 0.991989 0.126324i \(-0.0403179\pi\)
−0.605394 + 0.795926i \(0.706985\pi\)
\(600\) 0 0
\(601\) 325.247i 0.541176i 0.962695 + 0.270588i \(0.0872182\pi\)
−0.962695 + 0.270588i \(0.912782\pi\)
\(602\) 0 0
\(603\) 1656.97i 2.74787i
\(604\) 0 0
\(605\) −185.011 320.448i −0.305803 0.529667i
\(606\) 0 0
\(607\) −346.450 200.023i −0.570758 0.329527i 0.186694 0.982418i \(-0.440223\pi\)
−0.757452 + 0.652891i \(0.773556\pi\)
\(608\) 0 0
\(609\) 520.464 + 1115.37i 0.854621 + 1.83147i
\(610\) 0 0
\(611\) 282.612 + 163.166i 0.462540 + 0.267047i
\(612\) 0 0
\(613\) 821.365 474.215i 1.33991 0.773597i 0.353116 0.935579i \(-0.385122\pi\)
0.986794 + 0.161982i \(0.0517886\pi\)
\(614\) 0 0
\(615\) 157.623i 0.256297i
\(616\) 0 0
\(617\) −1066.14 −1.72793 −0.863967 0.503548i \(-0.832028\pi\)
−0.863967 + 0.503548i \(0.832028\pi\)
\(618\) 0 0
\(619\) −471.501 816.664i −0.761715 1.31933i −0.941966 0.335708i \(-0.891024\pi\)
0.180251 0.983621i \(1.55769\pi\)
\(620\) 0 0
\(621\) −539.948 + 935.218i −0.869482 + 1.50599i
\(622\) 0 0
\(623\) −70.9205 + 101.342i −0.113837 + 0.162668i
\(624\) 0 0
\(625\) −5.47705 + 9.48652i −0.00876328 + 0.0151784i
\(626\) 0 0
\(627\) −5.26960 + 3.04240i −0.00840446 + 0.00485232i
\(628\) 0 0
\(629\) −598.517 −0.951537
\(630\) 0 0
\(631\) 575.646 0.912276 0.456138 0.889909i \(-0.349232\pi\)
0.456138 + 0.889909i \(0.349232\pi\)
\(632\) 0 0
\(633\) −1030.67 + 595.056i −1.62823 + 0.940057i
\(634\) 0 0
\(635\) 103.690 179.596i 0.163291 0.282828i
\(636\) 0 0
\(637\) −198.548 34.9008i −0.311692 0.0547894i
\(638\) 0 0
\(639\) −30.8860 + 53.4961i −0.0483349 + 0.0837185i
\(640\) 0 0
\(641\) −396.899 687.449i −0.619187 1.07246i −0.989634 0.143610i \(-0.954129\pi\)
0.370447 0.928854i \(-0.379204\pi\)
\(642\) 0 0
\(643\) 841.343 1.30847 0.654233 0.756293i \(-0.272992\pi\)
0.654233 + 0.756293i \(0.272992\pi\)
\(644\) 0 0
\(645\) 770.995i 1.19534i
\(646\) 0 0
\(647\) −476.604 + 275.167i −0.736637 + 0.425297i −0.820845 0.571151i \(-0.806497\pi\)
0.0842084 + 0.996448i \(0.473164\pi\)
\(648\) 0 0
\(649\) −3.02337 1.74555i −0.00465851 0.00268959i
\(650\) 0 0
\(651\) −593.479 + 848.054i −0.911642 + 1.30269i
\(652\) 0 0
\(653\) 713.506 + 411.943i 1.09266 + 0.630847i 0.934283 0.356532i \(-0.116041\pi\)
0.158375 + 0.987379i \(0.449374\pi\)
\(654\) 0 0
\(655\) 171.511 + 297.066i 0.261849 + 0.453535i
\(656\) 0 0
\(657\) 280.577i 0.427058i
\(658\) 0 0
\(659\) 354.257i 0.537567i 0.963201 + 0.268784i \(0.0866217\pi\)
−0.963201 + 0.268784i \(0.913378\pi\)
\(660\) 0 0
\(661\) 84.3031 + 146.017i 0.127539 + 0.220904i 0.922722 0.385465i \(-0.125959\pi\)
−0.795184 + 0.606369i \(0.792626\pi\)
\(662\) 0 0
\(663\) −408.435 235.810i −0.616040 0.355671i
\(664\) 0 0
\(665\) 173.400 80.9138i 0.260752 0.121675i
\(666\) 0 0
\(667\) −411.869 237.793i −0.617494 0.356511i
\(668\) 0 0
\(669\) 1397.70 806.965i 2.08924 1.20623i
\(670\) 0 0
\(671\) 3.09022i 0.00460539i
\(672\) 0 0
\(673\) 514.054 0.763824 0.381912 0.924199i \(-0.375266\pi\)
0.381912 + 0.924199i \(0.375266\pi\)
\(674\) 0 0
\(675\) 561.753 + 972.986i 0.832227 + 1.44146i
\(676\) 0 0
\(677\) 260.650 451.460i 0.385008 0.666853i −0.606762 0.794883i \(-0.707532\pi\)
0.991770 + 0.128030i \(0.0408654\pi\)
\(678\) 0 0
\(679\) 182.523 + 15.9200i 0.268812 + 0.0234462i
\(680\) 0 0
\(681\) 226.362 392.070i 0.332396 0.575727i
\(682\) 0 0
\(683\) 441.591 254.953i 0.646547 0.373284i −0.140585 0.990069i \(-0.544898\pi\)
0.787132 + 0.616785i \(0.211565\pi\)
\(684\) 0 0
\(685\) −179.476 −0.262009
\(686\) 0 0
\(687\) −1302.30 −1.89563
\(688\) 0 0
\(689\) −226.485 + 130.761i −0.328715 + 0.189784i
\(690\) 0 0
\(691\) 467.402 809.565i 0.676415 1.17158i −0.299639 0.954053i \(-0.596866\pi\)
0.976053 0.217532i \(-0.0698005\pi\)
\(692\) 0 0
\(693\) 18.7120 + 1.63209i 0.0270014 + 0.00235511i
\(694\) 0 0
\(695\) 268.008 464.203i 0.385623 0.667919i
\(696\) 0 0
\(697\) −95.5526 165.502i −0.137091 0.237449i
\(698\) 0 0
\(699\) −344.619 −0.493017
\(700\) 0 0
\(701\) 364.276i 0.519651i −0.965656 0.259826i \(-0.916335\pi\)
0.965656 0.259826i \(-0.0836651\pi\)
\(702\) 0 0
\(703\) 224.703 129.732i 0.319634 0.184541i
\(704\) 0 0
\(705\) 1168.13 + 674.422i 1.65693 + 0.956626i
\(706\) 0 0
\(707\) 860.725 401.640i 1.21743 0.568091i
\(708\) 0 0
\(709\) 429.168 + 247.780i 0.605315 + 0.349479i 0.771130 0.636678i \(-0.219692\pi\)
−0.165815 + 0.986157i \(0.553025\pi\)
\(710\) 0 0
\(711\) 780.572 + 1351.99i 1.09785 + 1.90153i
\(712\) 0 0
\(713\) 399.955i 0.560946i
\(714\) 0 0
\(715\) 1.54065i 0.00215475i
\(716\) 0 0
\(717\) 269.894 + 467.470i 0.376421 + 0.651980i
\(718\) 0 0
\(719\) 582.836 + 336.500i 0.810620 + 0.468012i 0.847171 0.531320i \(-0.178304\pi\)
−0.0365511 + 0.999332i \(0.511637\pi\)
\(720\) 0 0
\(721\) 510.983 730.171i 0.708714 1.01272i
\(722\) 0 0
\(723\) 1154.40 + 666.493i 1.59668 + 0.921844i
\(724\) 0 0
\(725\) −428.502 + 247.395i −0.591037 + 0.341235i
\(726\) 0 0
\(727\) 165.434i 0.227557i −0.993506 0.113778i \(-0.963705\pi\)
0.993506 0.113778i \(-0.0362954\pi\)
\(728\) 0 0
\(729\) 833.991 1.14402
\(730\) 0 0
\(731\) 467.386 + 809.536i 0.639378 + 1.10744i
\(732\) 0 0
\(733\) 474.614 822.055i 0.647495 1.12149i −0.336225 0.941782i \(-0.609150\pi\)
0.983719 0.179712i \(-0.0575165\pi\)
\(734\) 0 0
\(735\) −820.667 144.257i −1.11655 0.196268i
\(736\) 0 0
\(737\) 4.62889 8.01748i 0.00628073 0.0108785i
\(738\) 0 0
\(739\) −62.4587 + 36.0605i −0.0845178 + 0.0487964i −0.541663 0.840596i \(-0.682205\pi\)
0.457145 + 0.889392i \(0.348872\pi\)
\(740\) 0 0
\(741\) 204.453 0.275915
\(742\) 0 0
\(743\) −159.310 −0.214415 −0.107208 0.994237i \(-0.534191\pi\)
−0.107208 + 0.994237i \(0.534191\pi\)
\(744\) 0 0
\(745\) −188.680 + 108.934i −0.253262 + 0.146221i
\(746\) 0 0
\(747\) −329.297 + 570.358i −0.440825 + 0.763532i
\(748\) 0 0
\(749\) −320.239 + 457.607i −0.427556 + 0.610957i
\(750\) 0 0
\(751\) 382.562 662.616i 0.509403 0.882312i −0.490538 0.871420i \(-0.663200\pi\)
0.999941 0.0108919i \(-0.00346706\pi\)
\(752\) 0 0
\(753\) 378.305 + 655.243i 0.502397 + 0.870176i
\(754\) 0 0
\(755\) 528.371 0.699830
\(756\) 0 0
\(757\) 950.822i 1.25604i −0.778197 0.628020i \(-0.783866\pi\)
0.778197 0.628020i \(-0.216134\pi\)
\(758\) 0 0
\(759\) −8.86660 + 5.11913i −0.0116819 + 0.00674457i
\(760\) 0 0
\(761\) 529.627 + 305.781i 0.695962 + 0.401814i 0.805842 0.592131i \(-0.201713\pi\)
−0.109879 + 0.993945i \(0.535046\pi\)
\(762\) 0 0
\(763\) −93.5172 200.410i −0.122565 0.262660i
\(764\) 0 0
\(765\) −1196.73 690.931i −1.56435 0.903178i
\(766\) 0 0
\(767\) 58.6513 + 101.587i 0.0764685 + 0.132447i
\(768\) 0 0
\(769\) 979.152i 1.27328i 0.771161 + 0.636640i \(0.219676\pi\)
−0.771161 + 0.636640i \(0.780324\pi\)
\(770\) 0 0
\(771\) 105.611i 0.136979i
\(772\) 0 0
\(773\) 228.660 + 396.051i 0.295809 + 0.512356i 0.975173 0.221445i \(-0.0710774\pi\)
−0.679364 + 0.733802i \(0.737744\pi\)
\(774\) 0 0
\(775\) −360.359 208.053i −0.464979 0.268456i
\(776\) 0 0
\(777\) −1125.59 98.1756i −1.44863 0.126352i
\(778\) 0 0
\(779\) 71.7471 + 41.4232i 0.0921015 + 0.0531748i
\(780\) 0 0
\(781\) −0.298893 + 0.172566i −0.000382706 + 0.000220955i
\(782\) 0 0
\(783\) 2270.83i 2.90016i
\(784\) 0 0
\(785\) −825.296 −1.05133
\(786\) 0 0
\(787\) 91.5206 + 158.518i 0.116290 + 0.201421i 0.918295 0.395897i \(-0.129566\pi\)
−0.802004 +