Properties

Label 224.3.n.a.17.14
Level 224
Weight 3
Character 224.17
Analytic conductor 6.104
Analytic rank 0
Dimension 28
CM no
Inner twists 4

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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 17.14
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.14

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

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

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 0.137854 0.990453i \(-0.455980\pi\)
0.788830 0.614611i \(-0.210687\pi\)
\(4\) 0 0
\(5\) 1.52921 + 2.64866i 0.305841 + 0.529732i 0.977448 0.211175i \(-0.0677290\pi\)
−0.671607 + 0.740907i \(0.734396\pi\)
\(6\) 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 \(-0.331562\pi\)
−0.495172 + 0.868795i \(0.664895\pi\)
\(12\) 0 0
\(13\) −4.11412 −0.316471 −0.158235 0.987401i \(-0.550580\pi\)
−0.158235 + 0.987401i \(0.550580\pi\)
\(14\) 0 0
\(15\) 17.0051 1.13367
\(16\) 0 0
\(17\) 17.8551 + 10.3087i 1.05030 + 0.606392i 0.922734 0.385438i \(-0.125950\pi\)
0.127568 + 0.991830i \(0.459283\pi\)
\(18\) 0 0
\(19\) 4.46893 + 7.74042i 0.235207 + 0.407390i 0.959333 0.282277i \(-0.0910899\pi\)
−0.724126 + 0.689668i \(0.757757\pi\)
\(20\) 0 0
\(21\) −35.2698 16.4580i −1.67951 0.783712i
\(22\) 0 0
\(23\) −7.51940 13.0240i −0.326930 0.566260i 0.654971 0.755654i \(-0.272681\pi\)
−0.981901 + 0.189394i \(0.939348\pi\)
\(24\) 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 0.0801833 0.996780i \(-0.474449\pi\)
−0.823145 + 0.567831i \(0.807783\pi\)
\(32\) 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 \(-0.538348\pi\)
0.799657 + 0.600457i \(0.205015\pi\)
\(38\) 0 0
\(39\) −11.4375 + 19.8103i −0.293268 + 0.507956i
\(40\) 0 0
\(41\) 9.26915i 0.226077i 0.993591 + 0.113038i \(0.0360583\pi\)
−0.993591 + 0.113038i \(0.963942\pi\)
\(42\) 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 0.462472 0.886634i \(-0.346962\pi\)
0.999083 + 0.0428039i \(0.0136291\pi\)
\(48\) 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 \(-0.128624\pi\)
0.119229 + 0.992867i \(0.461958\pi\)
\(54\) 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 \(-0.911015\pi\)
0.719550 + 0.694441i \(0.244348\pi\)
\(60\) 0 0
\(61\) 12.6191 + 21.8569i 0.206871 + 0.358311i 0.950727 0.310029i \(-0.100339\pi\)
−0.743856 + 0.668339i \(0.767005\pi\)
\(62\) 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 \(-0.142498\pi\)
0.0758537 + 0.997119i \(0.475832\pi\)
\(68\) 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 0.574018 0.818843i \(-0.305384\pi\)
−0.422130 + 0.906535i \(0.638717\pi\)
\(74\) 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 0.998440 0.0558321i \(-0.0177812\pi\)
−0.547572 + 0.836758i \(0.684448\pi\)
\(80\) 0 0
\(81\) −101.012 + 174.958i −1.24706 + 2.15997i
\(82\) 0 0
\(83\) −30.0525 −0.362078 −0.181039 0.983476i \(-0.557946\pi\)
−0.181039 + 0.983476i \(0.557946\pi\)
\(84\) 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 −0.411558 0.911384i \(-0.635015\pi\)
0.583502 + 0.812112i \(0.301682\pi\)
\(90\) 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 \(0.0430765\pi\)
−0.990857 + 0.134916i \(0.956923\pi\)
\(98\) 0 0
\(99\) 2.68329i 0.0271039i
\(100\) 0 0
\(101\) 67.8445 117.510i 0.671727 1.16347i −0.305686 0.952132i \(-0.598886\pi\)
0.977414 0.211334i \(-0.0677807\pi\)
\(102\) 0 0
\(103\) −110.258 + 63.6577i −1.07047 + 0.618036i −0.928310 0.371807i \(-0.878738\pi\)
−0.142160 + 0.989844i \(0.545405\pi\)
\(104\) 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 \(-0.788287\pi\)
0.141047 + 0.990003i \(0.454953\pi\)
\(108\) 0 0
\(109\) 27.3608 + 15.7968i 0.251017 + 0.144925i 0.620230 0.784420i \(-0.287039\pi\)
−0.369213 + 0.929345i \(0.620373\pi\)
\(110\) 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 \(-0.307476\pi\)
−0.996702 + 0.0811427i \(0.974143\pi\)
\(132\) 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 −0.738845 0.673875i \(-0.764629\pi\)
0.953016 + 0.302921i \(0.0979619\pi\)
\(138\) 0 0
\(139\) 175.260 1.26086 0.630430 0.776246i \(-0.282879\pi\)
0.630430 + 0.776246i \(0.282879\pi\)
\(140\) 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 \(-0.743502\pi\)
0.278483 + 0.960441i \(0.410168\pi\)
\(150\) 0 0
\(151\) −86.3801 + 149.615i −0.572053 + 0.990825i 0.424302 + 0.905521i \(0.360520\pi\)
−0.996355 + 0.0853045i \(0.972814\pi\)
\(152\) 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 0.0131460 + 0.999914i \(0.495815\pi\)
−0.872524 + 0.488572i \(0.837518\pi\)
\(158\) 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 \(-0.982204\pi\)
−0.450826 + 0.892612i \(0.648871\pi\)
\(164\) 0 0
\(165\) 1.80318 + 1.04107i 0.0109284 + 0.00630950i
\(166\) 0 0
\(167\) 82.5676i 0.494417i −0.968962 0.247208i \(-0.920487\pi\)
0.968962 0.247208i \(-0.0795132\pi\)
\(168\) 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 −0.979153 0.203125i \(-0.934890\pi\)
0.313665 0.949534i \(1.60156\pi\)
\(174\) 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 \(-0.597345\pi\)
−0.976379 + 0.216063i \(0.930678\pi\)
\(180\) 0 0
\(181\) −183.991 −1.01653 −0.508263 0.861202i \(-0.669712\pi\)
−0.508263 + 0.861202i \(0.669712\pi\)
\(182\) 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 0.934310 + 0.356462i \(0.116017\pi\)
−0.158450 + 0.987367i \(0.550650\pi\)
\(192\) 0 0
\(193\) −47.8173 + 82.8220i −0.247758 + 0.429129i −0.962903 0.269846i \(-0.913027\pi\)
0.715145 + 0.698976i \(0.246360\pi\)
\(194\) 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 0.497583 0.867416i \(-0.334221\pi\)
−0.502413 + 0.864628i \(0.667554\pi\)
\(200\) 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 \(-0.774421\pi\)
0.759224 0.650829i \(-0.225579\pi\)
\(224\) 0 0
\(225\) −342.881 −1.52392
\(226\) 0 0
\(227\) −40.7118 + 70.5149i −0.179347 + 0.310638i −0.941657 0.336574i \(-0.890732\pi\)
0.762310 + 0.647212i \(0.224065\pi\)
\(228\) 0 0
\(229\) −117.111 202.842i −0.511400 0.885771i −0.999913 0.0132145i \(-0.995794\pi\)
0.488512 0.872557i \(1.66246\pi\)
\(230\) 0 0
\(231\) −2.73236 3.90442i −0.0118284 0.0169022i
\(232\) 0 0
\(233\) 30.9903 + 53.6768i 0.133006 + 0.230372i 0.924834 0.380371i \(-0.124204\pi\)
−0.791828 + 0.610744i \(0.790871\pi\)
\(234\) 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 0.00301303 0.999995i \(-0.499041\pi\)
−0.864515 + 0.502607i \(0.832374\pi\)
\(242\) 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 \(-0.412622\pi\)
0.271072 + 0.962559i \(0.412622\pi\)
\(252\) 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 −0.531662 0.846957i \(-0.678432\pi\)
0.467655 + 0.883911i \(0.345099\pi\)
\(258\) 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 −0.530596 0.847625i \(-0.678032\pi\)
0.999363 + 0.0356971i \(0.0113652\pi\)
\(264\) 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 −0.451565 0.892238i \(-0.649134\pi\)
0.998483 0.0550522i \(-0.0175325\pi\)
\(270\) 0 0
\(271\) −392.032 + 226.340i −1.44661 + 0.835202i −0.998278 0.0586635i \(-0.981316\pi\)
−0.448335 + 0.893866i \(0.647983\pi\)
\(272\) 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 \(-0.156977\pi\)
0.0304353 + 0.999537i \(0.490311\pi\)
\(278\) 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 \(-0.854008\pi\)
0.831746 + 0.555156i \(0.187341\pi\)
\(284\) 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 \(-0.857163\pi\)
−0.900996 + 0.433828i \(0.857163\pi\)
\(294\) 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 \(-0.591721\pi\)
−0.284179 + 0.958771i \(0.591721\pi\)
\(308\) 0 0
\(309\) 707.887i 2.29090i
\(310\) 0 0
\(311\) −11.9119 6.87736i −0.0383020 0.0221137i 0.480727 0.876870i \(-0.340373\pi\)
−0.519029 + 0.854757i \(0.673706\pi\)
\(312\) 0 0
\(313\) −365.368 + 210.945i −1.16731 + 0.673947i −0.953045 0.302829i \(-0.902069\pi\)
−0.214265 + 0.976776i \(0.568736\pi\)
\(314\) 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 \(-0.933612\pi\)
−0.309848 + 0.950786i \(0.600278\pi\)
\(318\) 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 \(-0.900066\pi\)
−0.208114 + 0.978105i \(0.566732\pi\)
\(332\) 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 \(-0.180385\pi\)
−0.0430845 + 0.999071i \(0.513718\pi\)
\(348\) 0 0
\(349\) 222.198 0.636670 0.318335 0.947978i \(-0.396876\pi\)
0.318335 + 0.947978i \(0.396876\pi\)
\(350\) 0 0
\(351\) 295.424 0.841664
\(352\) 0 0
\(353\) −118.142 68.2096i −0.334681 0.193228i 0.323236 0.946318i \(-0.395229\pi\)
−0.657918 + 0.753090i \(0.728562\pi\)
\(354\) 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 0.985649 0.168809i \(-0.0539920\pi\)
−0.639017 + 0.769193i \(0.720659\pi\)
\(360\) 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 0.775144 0.631785i \(-0.217677\pi\)
−0.159570 + 0.987187i \(0.551011\pi\)
\(368\) 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 \(-0.465616\pi\)
0.914883 + 0.403720i \(0.132283\pi\)
\(374\) 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 −0.669803 0.742539i \(-0.733621\pi\)
0.308156 + 0.951336i \(0.400288\pi\)
\(384\) 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 \(-0.112830\pi\)
0.168326 + 0.985731i \(0.446164\pi\)
\(390\) 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 \(-0.283259\pi\)
−0.987652 + 0.156665i \(0.949926\pi\)
\(398\) 0 0
\(399\) −30.2269 346.552i −0.0757566 0.868552i
\(400\) 0 0
\(401\) −70.8759 122.761i −0.176748 0.306136i 0.764017 0.645196i \(-0.223224\pi\)
−0.940765 + 0.339060i \(0.889891\pi\)
\(402\) 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 0.0496336 0.998767i \(-0.484195\pi\)
−0.840141 + 0.542368i \(0.817528\pi\)
\(410\) 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 \(-0.333393\pi\)
0.499838 + 0.866119i \(0.333393\pi\)
\(420\) 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 −0.706917 0.707296i \(-0.749915\pi\)
0.965995 + 0.258560i \(0.0832481\pi\)
\(432\) 0 0
\(433\) 591.725i 1.36657i −0.730151 0.683286i \(-0.760550\pi\)
0.730151 0.683286i \(-0.239450\pi\)
\(434\) 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 0.0992873 0.995059i \(-0.468344\pi\)
0.911390 + 0.411544i \(0.135010\pi\)
\(440\) 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 \(-0.610542\pi\)
0.644157 + 0.764894i \(0.277208\pi\)
\(444\) 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 0.999350 0.0360623i \(-0.0114815\pi\)
−0.530906 + 0.847431i \(0.678148\pi\)
\(458\) 0 0
\(459\) −1282.13 740.238i −2.79331 1.61272i
\(460\) 0 0
\(461\) 165.578 0.359171 0.179586 0.983742i \(-0.442524\pi\)
0.179586 + 0.983742i \(0.442524\pi\)
\(462\) 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 −0.990808 0.135275i \(-0.956808\pi\)
0.378253 0.925702i \(1.62348\pi\)
\(468\) 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 0.465954 0.884809i \(-0.345711\pi\)
−0.533290 + 0.845932i \(0.679045\pi\)
\(480\) 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 −0.690128 0.723688i \(-0.742446\pi\)
0.971796 + 0.235824i \(0.0757790\pi\)
\(488\) 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 \(-0.781756\pi\)
0.161327 + 0.986901i \(0.448423\pi\)
\(500\) 0 0
\(501\) −397.579 229.542i −0.793570 0.458168i
\(502\) 0 0
\(503\) 291.993i 0.580502i 0.956951 + 0.290251i \(0.0937388\pi\)
−0.956951 + 0.290251i \(0.906261\pi\)
\(504\) 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 \(-0.192686\pi\)
−0.903959 + 0.427618i \(0.859353\pi\)
\(510\) 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 0.903756 0.428048i \(-0.140799\pi\)
0.0811772 + 0.996700i \(0.474132\pi\)
\(522\) 0 0
\(523\) 151.233 + 261.943i 0.289164 + 0.500847i 0.973610 0.228217i \(-0.0732894\pi\)
−0.684446 + 0.729063i \(0.739956\pi\)
\(524\) 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 \(-0.901437\pi\)
−0.212327 + 0.977199i \(0.568104\pi\)
\(542\) 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 \(-0.108689\pi\)
0.181136 + 0.983458i \(0.442023\pi\)
\(558\) 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 \(-0.953116\pi\)
0.621683 + 0.783269i \(0.286449\pi\)
\(564\) 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 0.998658 0.0517822i \(-0.0164901\pi\)
−0.544174 + 0.838972i \(0.683157\pi\)
\(570\) 0 0
\(571\) 615.938 + 355.612i 1.07870 + 0.622788i 0.930545 0.366177i \(-0.119333\pi\)
0.148155 + 0.988964i \(0.452667\pi\)
\(572\) 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 0.881874 0.471486i \(-0.156282\pi\)
0.0326179 + 0.999468i \(0.489616\pi\)
\(578\) 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 \(-0.189126\pi\)
0.828621 + 0.559810i \(0.189126\pi\)
\(588\) 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 −0.718222 0.695814i \(-0.755044\pi\)
0.243482 + 0.969905i \(0.421710\pi\)
\(594\) 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 −0.605394 0.795926i \(-0.706985\pi\)
0.991989 + 0.126324i \(0.0403179\pi\)
\(600\) 0 0
\(601\) 325.247i 0.541176i −0.962695 0.270588i \(-0.912782\pi\)
0.962695 0.270588i \(-0.0872182\pi\)
\(602\) 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 −0.757452 0.652891i \(-0.773556\pi\)
0.186694 + 0.982418i \(0.440223\pi\)
\(608\) 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 \(-0.614878\pi\)
−0.986794 + 0.161982i \(0.948211\pi\)
\(614\) 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 −0.180251 0.983621i \(-0.557691\pi\)
0.941966 0.335708i \(-0.108976\pi\)
\(620\) 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 0.370447 + 0.928854i \(0.379204\pi\)
−0.989634 + 0.143610i \(0.954129\pi\)
\(642\) 0 0
\(643\) −841.343 −1.30847 −0.654233 0.756293i \(-0.727008\pi\)
−0.654233 + 0.756293i \(0.727008\pi\)
\(644\) 0 0
\(645\) 770.995i 1.19534i
\(646\) 0 0
\(647\) −476.604 275.167i −0.736637 0.425297i 0.0842084 0.996448i \(-0.473164\pi\)
−0.820845 + 0.571151i \(0.806497\pi\)
\(648\) 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 \(-0.883959\pi\)
−0.158375 + 0.987379i \(0.550626\pi\)
\(654\) 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 \(-0.874041\pi\)
0.795184 + 0.606369i \(0.207374\pi\)
\(662\) 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 \(-0.292468\pi\)
−0.991770 + 0.128030i \(0.959135\pi\)
\(678\) 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 \(-0.455102\pi\)
−0.787132 + 0.616785i \(0.788435\pi\)
\(684\) 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 −0.976053 0.217532i \(-0.930199\pi\)
0.299639 0.954053i \(1.59687\pi\)
\(692\) 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 \(-0.780308\pi\)
0.165815 + 0.986157i \(0.446975\pi\)
\(710\) 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 −0.0365511 0.999332i \(-0.511637\pi\)
0.847171 + 0.531320i \(0.178304\pi\)
\(720\) 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 \(0.0362954\pi\)
−0.993506 + 0.113778i \(0.963705\pi\)
\(728\) 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 −0.983719 0.179712i \(-0.942483\pi\)
0.336225 0.941782i \(1.60915\pi\)
\(734\) 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 \(-0.317795\pi\)
−0.457145 + 0.889392i \(0.651128\pi\)
\(740\) 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 0.999941 + 0.0108919i \(0.00346706\pi\)
−0.490538 + 0.871420i \(0.663200\pi\)
\(752\) 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 −0.109879 0.993945i \(-0.535046\pi\)
0.805842 + 0.592131i \(0.201713\pi\)
\(762\) 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 \(-0.780324\pi\)
0.771161 0.636640i \(-0.219676\pi\)
\(770\) 0 0
\(771\) 105.611i 0.136979i
\(772\) 0 0
\(773\) −228.660 + 396.051i −0.295809 + 0.512356i −0.975173 0.221445i \(-0.928923\pi\)
0.679364 + 0.733802i \(0.262256\pi\)
\(774\) 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 \(-0.870434\pi\)
0.802004 + 0.597318i \(0.203767\pi\)