Properties

Label 1040.2.dh.a.289.3
Level $1040$
Weight $2$
Character 1040.289
Analytic conductor $8.304$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.dh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 8 x^{10} + 54 x^{8} - 78 x^{6} + 92 x^{4} - 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.3
Root \(-1.02826 - 0.593667i\) of defining polynomial
Character \(\chi\) \(=\) 1040.289
Dual form 1040.2.dh.a.529.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.298874 + 0.172555i) q^{3} +(1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} +(-1.44045 + 2.49493i) q^{9} +O(q^{10})\) \(q+(-0.298874 + 0.172555i) q^{3} +(1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} +(-1.44045 + 2.49493i) q^{9} +(1.94045 + 3.36096i) q^{11} +(2.96232 - 2.05540i) q^{13} +(-0.725633 - 0.262606i) q^{15} +(-4.71996 - 2.72507i) q^{17} +(-2.94045 + 5.09301i) q^{19} +0.700420 q^{21} +(0.298874 - 0.172555i) q^{23} +(-0.850210 + 4.92718i) q^{25} -2.02956i q^{27} +(1.50000 + 2.59808i) q^{29} -1.18048 q^{31} +(-1.15990 - 0.669668i) q^{33} +(-0.796234 - 4.46783i) q^{35} +(-4.71996 + 2.72507i) q^{37} +(-0.530689 + 1.12547i) q^{39} +(-0.0902394 - 0.156299i) q^{41} +(-1.15990 - 0.669668i) q^{43} +(-6.34196 + 1.13023i) q^{45} +12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +1.88090 q^{51} +2.42636i q^{53} +(-2.95310 + 8.16003i) q^{55} -2.02956i q^{57} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(5.06361 - 2.92347i) q^{63} +(7.78241 + 2.10573i) q^{65} +(-3.81417 + 2.20211i) q^{67} +(-0.0595504 + 0.103144i) q^{69} +(-0.940450 + 1.62891i) q^{71} +8.86014i q^{73} +(-0.596104 - 1.61932i) q^{75} -7.87651i q^{77} +11.1805 q^{79} +(-3.97114 - 6.87821i) q^{81} -7.83540i q^{83} +(-2.13820 - 11.9979i) q^{85} +(-0.896622 - 0.517665i) q^{87} +(6.12093 + 10.6018i) q^{89} +(-7.29249 + 0.606582i) q^{91} +(0.352814 - 0.203698i) q^{93} +(-12.9461 + 2.30719i) q^{95} +(-5.02801 - 2.90292i) q^{97} -11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{5} + 6 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −0.298874 + 0.172555i −0.172555 + 0.0996247i −0.583790 0.811905i \(-0.698431\pi\)
0.411235 + 0.911529i \(0.365098\pi\)
\(4\) 0 0
\(5\) 1.44045 + 1.71029i 0.644189 + 0.764867i
\(6\) 0 0
\(7\) −1.75765 1.01478i −0.664328 0.383550i 0.129596 0.991567i \(-0.458632\pi\)
−0.793924 + 0.608017i \(0.791965\pi\)
\(8\) 0 0
\(9\) −1.44045 + 2.49493i −0.480150 + 0.831644i
\(10\) 0 0
\(11\) 1.94045 + 3.36096i 0.585068 + 1.01337i 0.994867 + 0.101191i \(0.0322653\pi\)
−0.409799 + 0.912176i \(0.634401\pi\)
\(12\) 0 0
\(13\) 2.96232 2.05540i 0.821599 0.570066i
\(14\) 0 0
\(15\) −0.725633 0.262606i −0.187358 0.0678045i
\(16\) 0 0
\(17\) −4.71996 2.72507i −1.14476 0.660927i −0.197155 0.980372i \(-0.563170\pi\)
−0.947605 + 0.319445i \(0.896503\pi\)
\(18\) 0 0
\(19\) −2.94045 + 5.09301i −0.674585 + 1.16842i 0.302005 + 0.953306i \(0.402344\pi\)
−0.976590 + 0.215110i \(0.930989\pi\)
\(20\) 0 0
\(21\) 0.700420 0.152844
\(22\) 0 0
\(23\) 0.298874 0.172555i 0.0623195 0.0359802i −0.468516 0.883455i \(-0.655211\pi\)
0.530836 + 0.847475i \(0.321878\pi\)
\(24\) 0 0
\(25\) −0.850210 + 4.92718i −0.170042 + 0.985437i
\(26\) 0 0
\(27\) 2.02956i 0.390588i
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −1.18048 −0.212020 −0.106010 0.994365i \(-0.533808\pi\)
−0.106010 + 0.994365i \(0.533808\pi\)
\(32\) 0 0
\(33\) −1.15990 0.669668i −0.201913 0.116574i
\(34\) 0 0
\(35\) −0.796234 4.46783i −0.134588 0.755201i
\(36\) 0 0
\(37\) −4.71996 + 2.72507i −0.775957 + 0.447999i −0.834996 0.550257i \(-0.814530\pi\)
0.0590384 + 0.998256i \(0.481197\pi\)
\(38\) 0 0
\(39\) −0.530689 + 1.12547i −0.0849782 + 0.180219i
\(40\) 0 0
\(41\) −0.0902394 0.156299i −0.0140930 0.0244098i 0.858893 0.512155i \(-0.171153\pi\)
−0.872986 + 0.487745i \(0.837819\pi\)
\(42\) 0 0
\(43\) −1.15990 0.669668i −0.176883 0.102123i 0.408944 0.912559i \(-0.365897\pi\)
−0.585827 + 0.810436i \(0.699230\pi\)
\(44\) 0 0
\(45\) −6.34196 + 1.13023i −0.945404 + 0.168485i
\(46\) 0 0
\(47\) 12.2807i 1.79133i 0.444731 + 0.895664i \(0.353299\pi\)
−0.444731 + 0.895664i \(0.646701\pi\)
\(48\) 0 0
\(49\) −1.44045 2.49493i −0.205779 0.356419i
\(50\) 0 0
\(51\) 1.88090 0.263379
\(52\) 0 0
\(53\) 2.42636i 0.333286i 0.986017 + 0.166643i \(0.0532928\pi\)
−0.986017 + 0.166643i \(0.946707\pi\)
\(54\) 0 0
\(55\) −2.95310 + 8.16003i −0.398197 + 1.10030i
\(56\) 0 0
\(57\) 2.02956i 0.268821i
\(58\) 0 0
\(59\) 3.53069 6.11533i 0.459657 0.796149i −0.539286 0.842123i \(-0.681306\pi\)
0.998943 + 0.0459741i \(0.0146392\pi\)
\(60\) 0 0
\(61\) −3.38090 + 5.85589i −0.432880 + 0.749770i −0.997120 0.0758409i \(-0.975836\pi\)
0.564240 + 0.825611i \(0.309169\pi\)
\(62\) 0 0
\(63\) 5.06361 2.92347i 0.637954 0.368323i
\(64\) 0 0
\(65\) 7.78241 + 2.10573i 0.965289 + 0.261183i
\(66\) 0 0
\(67\) −3.81417 + 2.20211i −0.465975 + 0.269031i −0.714553 0.699581i \(-0.753370\pi\)
0.248578 + 0.968612i \(0.420037\pi\)
\(68\) 0 0
\(69\) −0.0595504 + 0.103144i −0.00716903 + 0.0124171i
\(70\) 0 0
\(71\) −0.940450 + 1.62891i −0.111611 + 0.193316i −0.916420 0.400218i \(-0.868934\pi\)
0.804809 + 0.593534i \(0.202268\pi\)
\(72\) 0 0
\(73\) 8.86014i 1.03700i 0.855077 + 0.518501i \(0.173510\pi\)
−0.855077 + 0.518501i \(0.826490\pi\)
\(74\) 0 0
\(75\) −0.596104 1.61932i −0.0688322 0.186982i
\(76\) 0 0
\(77\) 7.87651i 0.897611i
\(78\) 0 0
\(79\) 11.1805 1.25790 0.628951 0.777445i \(-0.283485\pi\)
0.628951 + 0.777445i \(0.283485\pi\)
\(80\) 0 0
\(81\) −3.97114 6.87821i −0.441238 0.764246i
\(82\) 0 0
\(83\) 7.83540i 0.860047i −0.902818 0.430024i \(-0.858505\pi\)
0.902818 0.430024i \(-0.141495\pi\)
\(84\) 0 0
\(85\) −2.13820 11.9979i −0.231920 1.30135i
\(86\) 0 0
\(87\) −0.896622 0.517665i −0.0961280 0.0554995i
\(88\) 0 0
\(89\) 6.12093 + 10.6018i 0.648817 + 1.12378i 0.983406 + 0.181420i \(0.0580693\pi\)
−0.334589 + 0.942364i \(0.608597\pi\)
\(90\) 0 0
\(91\) −7.29249 + 0.606582i −0.764460 + 0.0635870i
\(92\) 0 0
\(93\) 0.352814 0.203698i 0.0365852 0.0211224i
\(94\) 0 0
\(95\) −12.9461 + 2.30719i −1.32824 + 0.236713i
\(96\) 0 0
\(97\) −5.02801 2.90292i −0.510517 0.294747i 0.222529 0.974926i \(-0.428569\pi\)
−0.733046 + 0.680179i \(0.761902\pi\)
\(98\) 0 0
\(99\) −11.1805 −1.12368
\(100\) 0 0
\(101\) 2.97114 + 5.14616i 0.295639 + 0.512062i 0.975133 0.221619i \(-0.0711340\pi\)
−0.679494 + 0.733681i \(0.737801\pi\)
\(102\) 0 0
\(103\) 6.43378i 0.633939i 0.948436 + 0.316970i \(0.102665\pi\)
−0.948436 + 0.316970i \(0.897335\pi\)
\(104\) 0 0
\(105\) 1.00892 + 1.19792i 0.0984605 + 0.116905i
\(106\) 0 0
\(107\) 15.3106 8.83959i 1.48013 0.854555i 0.480387 0.877057i \(-0.340496\pi\)
0.999747 + 0.0225015i \(0.00716305\pi\)
\(108\) 0 0
\(109\) −5.76180 −0.551880 −0.275940 0.961175i \(-0.588989\pi\)
−0.275940 + 0.961175i \(0.588989\pi\)
\(110\) 0 0
\(111\) 0.940450 1.62891i 0.0892635 0.154609i
\(112\) 0 0
\(113\) 4.12222 + 2.37996i 0.387785 + 0.223888i 0.681200 0.732097i \(-0.261458\pi\)
−0.293415 + 0.955985i \(0.594792\pi\)
\(114\) 0 0
\(115\) 0.725633 + 0.262606i 0.0676656 + 0.0244881i
\(116\) 0 0
\(117\) 0.861026 + 10.3515i 0.0796019 + 0.956995i
\(118\) 0 0
\(119\) 5.53069 + 9.57943i 0.506997 + 0.878145i
\(120\) 0 0
\(121\) −2.03069 + 3.51726i −0.184608 + 0.319751i
\(122\) 0 0
\(123\) 0.0539404 + 0.0311425i 0.00486365 + 0.00280803i
\(124\) 0 0
\(125\) −9.65162 + 5.64325i −0.863267 + 0.504748i
\(126\) 0 0
\(127\) −14.4679 + 8.35307i −1.28382 + 0.741215i −0.977545 0.210728i \(-0.932417\pi\)
−0.306277 + 0.951942i \(0.599083\pi\)
\(128\) 0 0
\(129\) 0.462218 0.0406961
\(130\) 0 0
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) 10.3365 5.96781i 0.896292 0.517475i
\(134\) 0 0
\(135\) 3.47114 2.92347i 0.298748 0.251613i
\(136\) 0 0
\(137\) 1.71288 + 0.988931i 0.146341 + 0.0844901i 0.571383 0.820684i \(-0.306407\pi\)
−0.425042 + 0.905174i \(0.639741\pi\)
\(138\) 0 0
\(139\) −4.35021 + 7.53478i −0.368980 + 0.639092i −0.989406 0.145173i \(-0.953626\pi\)
0.620426 + 0.784265i \(0.286960\pi\)
\(140\) 0 0
\(141\) −2.11910 3.67039i −0.178460 0.309103i
\(142\) 0 0
\(143\) 12.6563 + 5.96781i 1.05838 + 0.499053i
\(144\) 0 0
\(145\) −2.28280 + 6.30784i −0.189576 + 0.523837i
\(146\) 0 0
\(147\) 0.861026 + 0.497113i 0.0710162 + 0.0410012i
\(148\) 0 0
\(149\) 11.1516 19.3152i 0.913576 1.58236i 0.104603 0.994514i \(-0.466643\pi\)
0.808973 0.587846i \(-0.200024\pi\)
\(150\) 0 0
\(151\) 19.1626 1.55943 0.779717 0.626132i \(-0.215363\pi\)
0.779717 + 0.626132i \(0.215363\pi\)
\(152\) 0 0
\(153\) 13.5977 7.85066i 1.09931 0.634688i
\(154\) 0 0
\(155\) −1.70042 2.01897i −0.136581 0.162167i
\(156\) 0 0
\(157\) 6.20265i 0.495025i 0.968885 + 0.247513i \(0.0796132\pi\)
−0.968885 + 0.247513i \(0.920387\pi\)
\(158\) 0 0
\(159\) −0.418681 0.725176i −0.0332035 0.0575102i
\(160\) 0 0
\(161\) −0.700420 −0.0552008
\(162\) 0 0
\(163\) 10.3365 + 5.96781i 0.809621 + 0.467435i 0.846824 0.531873i \(-0.178512\pi\)
−0.0372032 + 0.999308i \(0.511845\pi\)
\(164\) 0 0
\(165\) −0.525447 2.94839i −0.0409060 0.229532i
\(166\) 0 0
\(167\) −1.75765 + 1.01478i −0.136011 + 0.0785259i −0.566461 0.824088i \(-0.691688\pi\)
0.430451 + 0.902614i \(0.358355\pi\)
\(168\) 0 0
\(169\) 4.55063 12.1775i 0.350048 0.936732i
\(170\) 0 0
\(171\) −8.47114 14.6724i −0.647804 1.12203i
\(172\) 0 0
\(173\) −1.15990 0.669668i −0.0881855 0.0509139i 0.455259 0.890359i \(-0.349547\pi\)
−0.543444 + 0.839445i \(0.682880\pi\)
\(174\) 0 0
\(175\) 6.49437 7.79748i 0.490928 0.589434i
\(176\) 0 0
\(177\) 2.43695i 0.183173i
\(178\) 0 0
\(179\) −10.1120 17.5145i −0.755807 1.30910i −0.944972 0.327151i \(-0.893911\pi\)
0.189165 0.981945i \(-0.439422\pi\)
\(180\) 0 0
\(181\) 19.8232 1.47345 0.736723 0.676195i \(-0.236372\pi\)
0.736723 + 0.676195i \(0.236372\pi\)
\(182\) 0 0
\(183\) 2.33356i 0.172502i
\(184\) 0 0
\(185\) −11.4595 4.14720i −0.842522 0.304908i
\(186\) 0 0
\(187\) 21.1515i 1.54675i
\(188\) 0 0
\(189\) −2.05955 + 3.56725i −0.149810 + 0.259479i
\(190\) 0 0
\(191\) 0.768891 1.33176i 0.0556350 0.0963626i −0.836867 0.547407i \(-0.815615\pi\)
0.892502 + 0.451044i \(0.148948\pi\)
\(192\) 0 0
\(193\) 18.3625 10.6016i 1.32176 0.763118i 0.337750 0.941236i \(-0.390334\pi\)
0.984009 + 0.178117i \(0.0570007\pi\)
\(194\) 0 0
\(195\) −2.68931 + 0.713547i −0.192586 + 0.0510982i
\(196\) 0 0
\(197\) 8.01675 4.62847i 0.571170 0.329765i −0.186447 0.982465i \(-0.559697\pi\)
0.757616 + 0.652700i \(0.226364\pi\)
\(198\) 0 0
\(199\) 8.70225 15.0727i 0.616886 1.06848i −0.373164 0.927765i \(-0.621727\pi\)
0.990050 0.140713i \(-0.0449394\pi\)
\(200\) 0 0
\(201\) 0.759971 1.31631i 0.0536042 0.0928452i
\(202\) 0 0
\(203\) 6.08867i 0.427341i
\(204\) 0 0
\(205\) 0.137332 0.379477i 0.00959171 0.0265038i
\(206\) 0 0
\(207\) 0.994227i 0.0691036i
\(208\) 0 0
\(209\) −22.8232 −1.57871
\(210\) 0 0
\(211\) −3.64087 6.30617i −0.250648 0.434135i 0.713057 0.701107i \(-0.247310\pi\)
−0.963704 + 0.266972i \(0.913977\pi\)
\(212\) 0 0
\(213\) 0.649117i 0.0444768i
\(214\) 0 0
\(215\) −0.525447 2.94839i −0.0358352 0.201079i
\(216\) 0 0
\(217\) 2.07487 + 1.19792i 0.140851 + 0.0813204i
\(218\) 0 0
\(219\) −1.52886 2.64807i −0.103311 0.178940i
\(220\) 0 0
\(221\) −19.5831 + 1.62891i −1.31731 + 0.109572i
\(222\) 0 0
\(223\) 16.8589 9.73351i 1.12896 0.651804i 0.185285 0.982685i \(-0.440679\pi\)
0.943672 + 0.330881i \(0.107346\pi\)
\(224\) 0 0
\(225\) −11.0683 9.21858i −0.737887 0.614572i
\(226\) 0 0
\(227\) −4.16698 2.40581i −0.276572 0.159679i 0.355298 0.934753i \(-0.384379\pi\)
−0.631871 + 0.775074i \(0.717713\pi\)
\(228\) 0 0
\(229\) −1.52360 −0.100682 −0.0503410 0.998732i \(-0.516031\pi\)
−0.0503410 + 0.998732i \(0.516031\pi\)
\(230\) 0 0
\(231\) 1.35913 + 2.35408i 0.0894242 + 0.154887i
\(232\) 0 0
\(233\) 13.9652i 0.914889i −0.889238 0.457445i \(-0.848765\pi\)
0.889238 0.457445i \(-0.151235\pi\)
\(234\) 0 0
\(235\) −21.0037 + 17.6898i −1.37013 + 1.15395i
\(236\) 0 0
\(237\) −3.34155 + 1.92925i −0.217057 + 0.125318i
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 8.73294 15.1259i 0.562538 0.974344i −0.434736 0.900558i \(-0.643158\pi\)
0.997274 0.0737864i \(-0.0235083\pi\)
\(242\) 0 0
\(243\) 7.64668 + 4.41481i 0.490535 + 0.283210i
\(244\) 0 0
\(245\) 2.19217 6.05742i 0.140053 0.386994i
\(246\) 0 0
\(247\) 1.75765 + 21.1309i 0.111836 + 1.34453i
\(248\) 0 0
\(249\) 1.35204 + 2.34180i 0.0856819 + 0.148405i
\(250\) 0 0
\(251\) 4.64979 8.05367i 0.293492 0.508343i −0.681141 0.732152i \(-0.738516\pi\)
0.974633 + 0.223809i \(0.0718492\pi\)
\(252\) 0 0
\(253\) 1.15990 + 0.669668i 0.0729223 + 0.0421017i
\(254\) 0 0
\(255\) 2.70934 + 3.21689i 0.169665 + 0.201449i
\(256\) 0 0
\(257\) −9.43076 + 5.44485i −0.588274 + 0.339640i −0.764415 0.644725i \(-0.776972\pi\)
0.176141 + 0.984365i \(0.443639\pi\)
\(258\) 0 0
\(259\) 11.0614 0.687321
\(260\) 0 0
\(261\) −8.64270 −0.534970
\(262\) 0 0
\(263\) 11.6399 6.72031i 0.717749 0.414392i −0.0961749 0.995364i \(-0.530661\pi\)
0.813923 + 0.580972i \(0.197327\pi\)
\(264\) 0 0
\(265\) −4.14979 + 3.49505i −0.254920 + 0.214699i
\(266\) 0 0
\(267\) −3.65877 2.11239i −0.223913 0.129276i
\(268\) 0 0
\(269\) 1.83027 3.17012i 0.111593 0.193286i −0.804819 0.593520i \(-0.797738\pi\)
0.916413 + 0.400234i \(0.131071\pi\)
\(270\) 0 0
\(271\) 11.0018 + 19.0557i 0.668313 + 1.15755i 0.978376 + 0.206837i \(0.0663168\pi\)
−0.310062 + 0.950716i \(0.600350\pi\)
\(272\) 0 0
\(273\) 2.07487 1.43965i 0.125577 0.0871314i
\(274\) 0 0
\(275\) −18.2098 + 6.70343i −1.09809 + 0.404232i
\(276\) 0 0
\(277\) 8.56973 + 4.94774i 0.514905 + 0.297281i 0.734848 0.678232i \(-0.237254\pi\)
−0.219943 + 0.975513i \(0.570587\pi\)
\(278\) 0 0
\(279\) 1.70042 2.94521i 0.101801 0.176325i
\(280\) 0 0
\(281\) 4.06138 0.242281 0.121141 0.992635i \(-0.461345\pi\)
0.121141 + 0.992635i \(0.461345\pi\)
\(282\) 0 0
\(283\) 5.27294 3.04434i 0.313444 0.180967i −0.335023 0.942210i \(-0.608744\pi\)
0.648467 + 0.761243i \(0.275411\pi\)
\(284\) 0 0
\(285\) 3.47114 2.92347i 0.205613 0.173172i
\(286\) 0 0
\(287\) 0.366292i 0.0216215i
\(288\) 0 0
\(289\) 6.35204 + 11.0021i 0.373649 + 0.647180i
\(290\) 0 0
\(291\) 2.00366 0.117456
\(292\) 0 0
\(293\) 8.48019 + 4.89604i 0.495418 + 0.286030i 0.726819 0.686829i \(-0.240998\pi\)
−0.231401 + 0.972858i \(0.574331\pi\)
\(294\) 0 0
\(295\) 15.5448 2.77031i 0.905053 0.161294i
\(296\) 0 0
\(297\) 6.82125 3.93825i 0.395809 0.228521i
\(298\) 0 0
\(299\) 0.530689 1.12547i 0.0306905 0.0650876i
\(300\) 0 0
\(301\) 1.35913 + 2.35408i 0.0783390 + 0.135687i
\(302\) 0 0
\(303\) −1.77599 1.02537i −0.102028 0.0589059i
\(304\) 0 0
\(305\) −14.8853 + 2.65278i −0.852330 + 0.151898i
\(306\) 0 0
\(307\) 22.1046i 1.26158i −0.775955 0.630788i \(-0.782732\pi\)
0.775955 0.630788i \(-0.217268\pi\)
\(308\) 0 0
\(309\) −1.11018 1.92289i −0.0631560 0.109389i
\(310\) 0 0
\(311\) −7.63904 −0.433170 −0.216585 0.976264i \(-0.569492\pi\)
−0.216585 + 0.976264i \(0.569492\pi\)
\(312\) 0 0
\(313\) 26.1425i 1.47766i 0.673891 + 0.738831i \(0.264622\pi\)
−0.673891 + 0.738831i \(0.735378\pi\)
\(314\) 0 0
\(315\) 12.2939 + 4.44914i 0.692681 + 0.250680i
\(316\) 0 0
\(317\) 11.8428i 0.665159i −0.943075 0.332580i \(-0.892081\pi\)
0.943075 0.332580i \(-0.107919\pi\)
\(318\) 0 0
\(319\) −5.82135 + 10.0829i −0.325933 + 0.564532i
\(320\) 0 0
\(321\) −3.05063 + 5.28385i −0.170270 + 0.294916i
\(322\) 0 0
\(323\) 27.7576 16.0259i 1.54448 0.891704i
\(324\) 0 0
\(325\) 7.60876 + 16.3434i 0.422058 + 0.906569i
\(326\) 0 0
\(327\) 1.72205 0.994227i 0.0952297 0.0549809i
\(328\) 0 0
\(329\) 12.4622 21.5852i 0.687064 1.19003i
\(330\) 0 0
\(331\) −6.35021 + 10.9989i −0.349039 + 0.604553i −0.986079 0.166277i \(-0.946825\pi\)
0.637040 + 0.770831i \(0.280159\pi\)
\(332\) 0 0
\(333\) 15.7013i 0.860427i
\(334\) 0 0
\(335\) −9.26038 3.35132i −0.505948 0.183102i
\(336\) 0 0
\(337\) 15.2939i 0.833113i 0.909110 + 0.416556i \(0.136763\pi\)
−0.909110 + 0.416556i \(0.863237\pi\)
\(338\) 0 0
\(339\) −1.64270 −0.0892191
\(340\) 0 0
\(341\) −2.29066 3.96754i −0.124046 0.214854i
\(342\) 0 0
\(343\) 20.0538i 1.08281i
\(344\) 0 0
\(345\) −0.262187 + 0.0467255i −0.0141157 + 0.00251562i
\(346\) 0 0
\(347\) −10.5998 6.11981i −0.569029 0.328529i 0.187733 0.982220i \(-0.439886\pi\)
−0.756761 + 0.653691i \(0.773219\pi\)
\(348\) 0 0
\(349\) 9.35021 + 16.1950i 0.500505 + 0.866901i 1.00000 0.000583538i \(0.000185746\pi\)
−0.499495 + 0.866317i \(0.666481\pi\)
\(350\) 0 0
\(351\) −4.17156 6.01219i −0.222661 0.320907i
\(352\) 0 0
\(353\) 1.13348 0.654413i 0.0603288 0.0348309i −0.469532 0.882915i \(-0.655577\pi\)
0.529861 + 0.848084i \(0.322244\pi\)
\(354\) 0 0
\(355\) −4.14058 + 0.737912i −0.219759 + 0.0391643i
\(356\) 0 0
\(357\) −3.30596 1.90870i −0.174970 0.101019i
\(358\) 0 0
\(359\) −29.4082 −1.55210 −0.776051 0.630670i \(-0.782780\pi\)
−0.776051 + 0.630670i \(0.782780\pi\)
\(360\) 0 0
\(361\) −7.79249 13.4970i −0.410131 0.710368i
\(362\) 0 0
\(363\) 1.40162i 0.0735661i
\(364\) 0 0
\(365\) −15.1534 + 12.7626i −0.793168 + 0.668024i
\(366\) 0 0
\(367\) −28.9531 + 16.7161i −1.51134 + 0.872573i −0.511429 + 0.859326i \(0.670884\pi\)
−0.999912 + 0.0132473i \(0.995783\pi\)
\(368\) 0 0
\(369\) 0.519941 0.0270671
\(370\) 0 0
\(371\) 2.46222 4.26469i 0.127832 0.221412i
\(372\) 0 0
\(373\) 29.8589 + 17.2391i 1.54604 + 0.892604i 0.998438 + 0.0558628i \(0.0177909\pi\)
0.547598 + 0.836742i \(0.315542\pi\)
\(374\) 0 0
\(375\) 1.91085 3.35206i 0.0986757 0.173099i
\(376\) 0 0
\(377\) 9.78357 + 4.61322i 0.503879 + 0.237593i
\(378\) 0 0
\(379\) 8.70225 + 15.0727i 0.447004 + 0.774234i 0.998189 0.0601487i \(-0.0191575\pi\)
−0.551185 + 0.834383i \(0.685824\pi\)
\(380\) 0 0
\(381\) 2.88273 4.99303i 0.147687 0.255801i
\(382\) 0 0
\(383\) 1.51271 + 0.873366i 0.0772961 + 0.0446269i 0.538150 0.842849i \(-0.319123\pi\)
−0.460854 + 0.887476i \(0.652457\pi\)
\(384\) 0 0
\(385\) 13.4711 11.3457i 0.686553 0.578231i
\(386\) 0 0
\(387\) 3.34155 1.92925i 0.169861 0.0980692i
\(388\) 0 0
\(389\) −22.0435 −1.11765 −0.558826 0.829285i \(-0.688748\pi\)
−0.558826 + 0.829285i \(0.688748\pi\)
\(390\) 0 0
\(391\) −1.88090 −0.0951212
\(392\) 0 0
\(393\) 2.98874 1.72555i 0.150762 0.0870425i
\(394\) 0 0
\(395\) 16.1049 + 19.1219i 0.810326 + 0.962127i
\(396\) 0 0
\(397\) −19.5132 11.2660i −0.979339 0.565422i −0.0772687 0.997010i \(-0.524620\pi\)
−0.902071 + 0.431588i \(0.857953\pi\)
\(398\) 0 0
\(399\) −2.05955 + 3.56725i −0.103106 + 0.178586i
\(400\) 0 0
\(401\) 1.85204 + 3.20782i 0.0924863 + 0.160191i 0.908557 0.417761i \(-0.137185\pi\)
−0.816070 + 0.577953i \(0.803852\pi\)
\(402\) 0 0
\(403\) −3.49695 + 2.42636i −0.174196 + 0.120866i
\(404\) 0 0
\(405\) 6.04354 16.6995i 0.300306 0.829807i
\(406\) 0 0
\(407\) −18.3177 10.5757i −0.907975 0.524220i
\(408\) 0 0
\(409\) −6.74186 + 11.6772i −0.333363 + 0.577402i −0.983169 0.182698i \(-0.941517\pi\)
0.649806 + 0.760100i \(0.274850\pi\)
\(410\) 0 0
\(411\) −0.682580 −0.0336692
\(412\) 0 0
\(413\) −12.4114 + 7.16573i −0.610726 + 0.352603i
\(414\) 0 0
\(415\) 13.4008 11.2865i 0.657821 0.554033i
\(416\) 0 0
\(417\) 3.00260i 0.147038i
\(418\) 0 0
\(419\) −8.41159 14.5693i −0.410933 0.711757i 0.584059 0.811711i \(-0.301464\pi\)
−0.994992 + 0.0999544i \(0.968130\pi\)
\(420\) 0 0
\(421\) 17.1013 0.833464 0.416732 0.909029i \(-0.363175\pi\)
0.416732 + 0.909029i \(0.363175\pi\)
\(422\) 0 0
\(423\) −30.6396 17.6898i −1.48975 0.860106i
\(424\) 0 0
\(425\) 17.4399 20.9392i 0.845959 1.01570i
\(426\) 0 0
\(427\) 11.8849 6.86173i 0.575149 0.332062i
\(428\) 0 0
\(429\) −4.81243 + 0.400293i −0.232346 + 0.0193263i
\(430\) 0 0
\(431\) 4.83027 + 8.36627i 0.232666 + 0.402989i 0.958592 0.284784i \(-0.0919218\pi\)
−0.725926 + 0.687773i \(0.758588\pi\)
\(432\) 0 0
\(433\) −21.4538 12.3863i −1.03100 0.595249i −0.113730 0.993512i \(-0.536280\pi\)
−0.917272 + 0.398262i \(0.869613\pi\)
\(434\) 0 0
\(435\) −0.406180 2.27916i −0.0194748 0.109277i
\(436\) 0 0
\(437\) 2.02956i 0.0970869i
\(438\) 0 0
\(439\) −3.53069 6.11533i −0.168511 0.291869i 0.769386 0.638784i \(-0.220562\pi\)
−0.937896 + 0.346915i \(0.887229\pi\)
\(440\) 0 0
\(441\) 8.29958 0.395218
\(442\) 0 0
\(443\) 38.2438i 1.81702i 0.417865 + 0.908509i \(0.362778\pi\)
−0.417865 + 0.908509i \(0.637222\pi\)
\(444\) 0 0
\(445\) −9.31523 + 25.7399i −0.441584 + 1.22019i
\(446\) 0 0
\(447\) 7.69707i 0.364059i
\(448\) 0 0
\(449\) −6.24003 + 10.8080i −0.294485 + 0.510063i −0.974865 0.222796i \(-0.928481\pi\)
0.680380 + 0.732860i \(0.261815\pi\)
\(450\) 0 0
\(451\) 0.350210 0.606582i 0.0164908 0.0285628i
\(452\) 0 0
\(453\) −5.72721 + 3.30661i −0.269088 + 0.155358i
\(454\) 0 0
\(455\) −11.5419 11.5985i −0.541092 0.543748i
\(456\) 0 0
\(457\) −7.12930 + 4.11610i −0.333495 + 0.192543i −0.657392 0.753549i \(-0.728340\pi\)
0.323897 + 0.946092i \(0.395007\pi\)
\(458\) 0 0
\(459\) −5.53069 + 9.57943i −0.258150 + 0.447130i
\(460\) 0 0
\(461\) 2.27072 3.93300i 0.105758 0.183178i −0.808290 0.588785i \(-0.799606\pi\)
0.914048 + 0.405607i \(0.132940\pi\)
\(462\) 0 0
\(463\) 1.98845i 0.0924113i 0.998932 + 0.0462056i \(0.0147130\pi\)
−0.998932 + 0.0462056i \(0.985287\pi\)
\(464\) 0 0
\(465\) 0.856594 + 0.310000i 0.0397236 + 0.0143759i
\(466\) 0 0
\(467\) 32.8043i 1.51800i −0.651091 0.759000i \(-0.725688\pi\)
0.651091 0.759000i \(-0.274312\pi\)
\(468\) 0 0
\(469\) 8.93862 0.412747
\(470\) 0 0
\(471\) −1.07030 1.85381i −0.0493167 0.0854191i
\(472\) 0 0
\(473\) 5.19783i 0.238997i
\(474\) 0 0
\(475\) −22.5942 18.8183i −1.03669 0.863441i
\(476\) 0 0
\(477\) −6.05360 3.49505i −0.277176 0.160027i
\(478\) 0 0
\(479\) 15.4027 + 26.6782i 0.703766 + 1.21896i 0.967135 + 0.254263i \(0.0818329\pi\)
−0.263369 + 0.964695i \(0.584834\pi\)
\(480\) 0 0
\(481\) −8.38090 + 17.7740i −0.382136 + 0.810423i
\(482\) 0 0
\(483\) 0.209337 0.120861i 0.00952518 0.00549937i
\(484\) 0 0
\(485\) −2.27774 12.7809i −0.103427 0.580350i
\(486\) 0 0
\(487\) 19.3341 + 11.1626i 0.876113 + 0.505824i 0.869375 0.494153i \(-0.164522\pi\)
0.00673807 + 0.999977i \(0.497855\pi\)
\(488\) 0 0
\(489\) −4.11910 −0.186272
\(490\) 0 0
\(491\) 5.34129 + 9.25139i 0.241049 + 0.417509i 0.961013 0.276502i \(-0.0891752\pi\)
−0.719964 + 0.694011i \(0.755842\pi\)
\(492\) 0 0
\(493\) 16.3504i 0.736386i
\(494\) 0 0
\(495\) −16.1049 19.1219i −0.723862 0.859466i
\(496\) 0 0
\(497\) 3.30596 1.90870i 0.148292 0.0856167i
\(498\) 0 0
\(499\) 18.8195 0.842477 0.421239 0.906950i \(-0.361595\pi\)
0.421239 + 0.906950i \(0.361595\pi\)
\(500\) 0 0
\(501\) 0.350210 0.606582i 0.0156462 0.0271001i
\(502\) 0 0
\(503\) −4.92013 2.84064i −0.219378 0.126658i 0.386284 0.922380i \(-0.373758\pi\)
−0.605662 + 0.795722i \(0.707092\pi\)
\(504\) 0 0
\(505\) −4.52168 + 12.4943i −0.201212 + 0.555989i
\(506\) 0 0
\(507\) 0.741225 + 4.42478i 0.0329190 + 0.196511i
\(508\) 0 0
\(509\) 13.9622 + 24.1833i 0.618864 + 1.07190i 0.989693 + 0.143203i \(0.0457403\pi\)
−0.370829 + 0.928701i \(0.620926\pi\)
\(510\) 0 0
\(511\) 8.99108 15.5730i 0.397742 0.688909i
\(512\) 0 0
\(513\) 10.3365 + 5.96781i 0.456370 + 0.263485i
\(514\) 0 0
\(515\) −11.0037 + 9.26754i −0.484879 + 0.408376i
\(516\) 0 0
\(517\) −41.2750 + 23.8301i −1.81527 + 1.04805i
\(518\) 0 0
\(519\) 0.462218 0.0202891
\(520\) 0 0
\(521\) 6.29958 0.275990 0.137995 0.990433i \(-0.455934\pi\)
0.137995 + 0.990433i \(0.455934\pi\)
\(522\) 0 0
\(523\) −19.7948 + 11.4285i −0.865567 + 0.499735i −0.865873 0.500265i \(-0.833236\pi\)
0.000305526 1.00000i \(0.499903\pi\)
\(524\) 0 0
\(525\) −0.595504 + 3.45110i −0.0259899 + 0.150618i
\(526\) 0 0
\(527\) 5.57182 + 3.21689i 0.242712 + 0.140130i
\(528\) 0 0
\(529\) −11.4404 + 19.8154i −0.497411 + 0.861541i
\(530\) 0 0
\(531\) 10.1716 + 17.6177i 0.441408 + 0.764541i
\(532\) 0 0
\(533\) −0.588576 0.277529i −0.0254940 0.0120211i
\(534\) 0 0
\(535\) 37.1725 + 13.4527i 1.60711 + 0.581610i
\(536\) 0 0
\(537\) 6.04443 + 3.48975i 0.260837 + 0.150594i
\(538\) 0 0
\(539\) 5.59024 9.68258i 0.240789 0.417058i
\(540\) 0 0
\(541\) −9.48006 −0.407580 −0.203790 0.979015i \(-0.565326\pi\)
−0.203790 + 0.979015i \(0.565326\pi\)
\(542\) 0 0
\(543\) −5.92463 + 3.42059i −0.254250 + 0.146791i
\(544\) 0 0
\(545\) −8.29958 9.85437i −0.355515 0.422115i
\(546\) 0 0
\(547\) 33.3911i 1.42770i 0.700299 + 0.713850i \(0.253050\pi\)
−0.700299 + 0.713850i \(0.746950\pi\)
\(548\) 0 0
\(549\) −9.74003 16.8702i −0.415694 0.720004i
\(550\) 0 0
\(551\) −17.6427 −0.751604
\(552\) 0 0
\(553\) −19.6513 11.3457i −0.835660 0.482469i
\(554\) 0 0
\(555\) 4.14058 0.737912i 0.175758 0.0313226i
\(556\) 0 0
\(557\) 32.7053 18.8824i 1.38577 0.800073i 0.392932 0.919567i \(-0.371461\pi\)
0.992835 + 0.119495i \(0.0381274\pi\)
\(558\) 0 0
\(559\) −4.81243 + 0.400293i −0.203544 + 0.0169306i
\(560\) 0 0
\(561\) 3.64979 + 6.32162i 0.154094 + 0.266899i
\(562\) 0 0
\(563\) 22.4307 + 12.9504i 0.945343 + 0.545794i 0.891631 0.452762i \(-0.149561\pi\)
0.0537120 + 0.998556i \(0.482895\pi\)
\(564\) 0 0
\(565\) 1.86741 + 10.4784i 0.0785625 + 0.440830i
\(566\) 0 0
\(567\) 16.1193i 0.676947i
\(568\) 0 0
\(569\) −10.7725 18.6586i −0.451609 0.782209i 0.546878 0.837213i \(-0.315816\pi\)
−0.998486 + 0.0550035i \(0.982483\pi\)
\(570\) 0 0
\(571\) 2.22036 0.0929192 0.0464596 0.998920i \(-0.485206\pi\)
0.0464596 + 0.998920i \(0.485206\pi\)
\(572\) 0 0
\(573\) 0.530704i 0.0221705i
\(574\) 0 0
\(575\) 0.596104 + 1.61932i 0.0248593 + 0.0675301i
\(576\) 0 0
\(577\) 6.20265i 0.258220i −0.991630 0.129110i \(-0.958788\pi\)
0.991630 0.129110i \(-0.0412120\pi\)
\(578\) 0 0
\(579\) −3.65871 + 6.33707i −0.152051 + 0.263360i
\(580\) 0 0
\(581\) −7.95120 + 13.7719i −0.329871 + 0.571354i
\(582\) 0 0
\(583\) −8.15489 + 4.70823i −0.337741 + 0.194995i
\(584\) 0 0
\(585\) −16.4638 + 16.3834i −0.680695 + 0.677370i
\(586\) 0 0
\(587\) 1.58391 0.914469i 0.0653748 0.0377442i −0.466956 0.884280i \(-0.654649\pi\)
0.532331 + 0.846536i \(0.321316\pi\)
\(588\) 0 0
\(589\) 3.47114 6.01219i 0.143026 0.247728i
\(590\) 0 0
\(591\) −1.59733 + 2.76666i −0.0657055 + 0.113805i
\(592\) 0 0
\(593\) 0.0728761i 0.00299266i 0.999999 + 0.00149633i \(0.000476297\pi\)
−0.999999 + 0.00149633i \(0.999524\pi\)
\(594\) 0 0
\(595\) −8.41697 + 23.2578i −0.345062 + 0.953477i
\(596\) 0 0
\(597\) 6.00646i 0.245828i
\(598\) 0 0
\(599\) −14.5813 −0.595777 −0.297888 0.954601i \(-0.596282\pi\)
−0.297888 + 0.954601i \(0.596282\pi\)
\(600\) 0 0
\(601\) 22.2041 + 38.4586i 0.905723 + 1.56876i 0.819944 + 0.572444i \(0.194005\pi\)
0.0857795 + 0.996314i \(0.472662\pi\)
\(602\) 0 0
\(603\) 12.6881i 0.516700i
\(604\) 0 0
\(605\) −8.94065 + 1.59336i −0.363489 + 0.0647791i
\(606\) 0 0
\(607\) 31.3808 + 18.1177i 1.27371 + 0.735375i 0.975684 0.219183i \(-0.0703392\pi\)
0.298024 + 0.954558i \(0.403672\pi\)
\(608\) 0 0
\(609\) 1.05063 + 1.81975i 0.0425737 + 0.0737398i
\(610\) 0 0
\(611\) 25.2419 + 36.3794i 1.02118 + 1.47175i
\(612\) 0 0
\(613\) −2.90838 + 1.67915i −0.117468 + 0.0678203i −0.557583 0.830121i \(-0.688271\pi\)
0.440115 + 0.897942i \(0.354938\pi\)
\(614\) 0 0
\(615\) 0.0244356 + 0.137113i 0.000985339 + 0.00552894i
\(616\) 0 0
\(617\) 18.3441 + 10.5910i 0.738507 + 0.426377i 0.821526 0.570171i \(-0.193123\pi\)
−0.0830194 + 0.996548i \(0.526456\pi\)
\(618\) 0 0
\(619\) 25.4082 1.02124 0.510620 0.859807i \(-0.329416\pi\)
0.510620 + 0.859807i \(0.329416\pi\)
\(620\) 0 0
\(621\) −0.350210 0.606582i −0.0140534 0.0243413i
\(622\) 0 0
\(623\) 24.8455i 0.995416i
\(624\) 0 0
\(625\) −23.5543 8.37828i −0.942171 0.335131i
\(626\) 0 0
\(627\) 6.82125 3.93825i 0.272415 0.157279i
\(628\) 0 0
\(629\) 29.7041 1.18438
\(630\) 0 0
\(631\) 21.7725 37.7112i 0.866751 1.50126i 0.00145375 0.999999i \(-0.499537\pi\)
0.865298 0.501258i \(-0.167129\pi\)
\(632\) 0 0
\(633\) 2.17632 + 1.25650i 0.0865011 + 0.0499414i
\(634\) 0 0
\(635\) −35.1265 12.7123i −1.39395 0.504470i
\(636\) 0 0
\(637\) −9.39516 4.43007i −0.372250 0.175526i
\(638\) 0 0
\(639\) −2.70934 4.69272i −0.107180 0.185641i
\(640\) 0 0
\(641\) −24.1427 + 41.8164i −0.953579 + 1.65165i −0.215993 + 0.976395i \(0.569299\pi\)
−0.737586 + 0.675253i \(0.764035\pi\)
\(642\) 0 0
\(643\) −36.6710 21.1720i −1.44616 0.834943i −0.447913 0.894077i \(-0.647833\pi\)
−0.998250 + 0.0591344i \(0.981166\pi\)
\(644\) 0 0
\(645\) 0.665802 + 0.790529i 0.0262159 + 0.0311271i
\(646\) 0 0
\(647\) −29.7958 + 17.2026i −1.17139 + 0.676305i −0.954008 0.299781i \(-0.903086\pi\)
−0.217386 + 0.976086i \(0.569753\pi\)
\(648\) 0 0
\(649\) 27.4045 1.07572
\(650\) 0 0
\(651\) −0.826831 −0.0324061
\(652\) 0 0
\(653\) −12.4114 + 7.16573i −0.485696 + 0.280417i −0.722787 0.691071i \(-0.757139\pi\)
0.237091 + 0.971487i \(0.423806\pi\)
\(654\) 0 0
\(655\) −14.4045 17.1029i −0.562830 0.668267i
\(656\) 0 0
\(657\) −22.1054 12.7626i −0.862416 0.497916i
\(658\) 0 0
\(659\) −11.4116 + 19.7655i −0.444532 + 0.769953i −0.998020 0.0629051i \(-0.979963\pi\)
0.553487 + 0.832858i \(0.313297\pi\)
\(660\) 0 0
\(661\) −7.20934 12.4869i −0.280411 0.485686i 0.691075 0.722783i \(-0.257137\pi\)
−0.971486 + 0.237097i \(0.923804\pi\)
\(662\) 0 0
\(663\) 5.57182 3.86601i 0.216391 0.150143i
\(664\) 0 0
\(665\) 25.0960 + 9.08221i 0.973181 + 0.352193i
\(666\) 0 0
\(667\) 0.896622 + 0.517665i 0.0347173 + 0.0200441i
\(668\) 0 0
\(669\) −3.35913 + 5.81818i −0.129871 + 0.224944i
\(670\) 0 0
\(671\) −26.2419 −1.01306
\(672\) 0 0
\(673\) −29.5956 + 17.0871i −1.14083 + 0.658657i −0.946636 0.322306i \(-0.895542\pi\)
−0.194193 + 0.980963i \(0.562209\pi\)
\(674\) 0 0
\(675\) 10.0000 + 1.72555i 0.384900 + 0.0664164i
\(676\) 0 0
\(677\) 5.84695i 0.224716i −0.993668 0.112358i \(-0.964160\pi\)
0.993668 0.112358i \(-0.0358404\pi\)
\(678\) 0 0
\(679\) 5.89165 + 10.2046i 0.226101 + 0.391618i
\(680\) 0 0
\(681\) 1.66054 0.0636319
\(682\) 0 0
\(683\) −9.82834 5.67439i −0.376071 0.217125i 0.300036 0.953928i \(-0.403001\pi\)
−0.676107 + 0.736803i \(0.736334\pi\)
\(684\) 0 0
\(685\) 0.775953 + 4.35403i 0.0296476 + 0.166359i
\(686\) 0 0
\(687\) 0.455363 0.262904i 0.0173732 0.0100304i
\(688\) 0 0
\(689\) 4.98715 + 7.18765i 0.189995 + 0.273828i
\(690\) 0 0
\(691\) −9.41159 16.3013i −0.358034 0.620133i 0.629599 0.776921i \(-0.283219\pi\)
−0.987632 + 0.156788i \(0.949886\pi\)
\(692\) 0 0
\(693\) 19.6513 + 11.3457i 0.746493 + 0.430988i
\(694\) 0 0
\(695\) −19.1530 + 3.41334i −0.726513 + 0.129475i
\(696\) 0 0
\(697\) 0.983636i 0.0372579i
\(698\) 0 0
\(699\) 2.40976 + 4.17383i 0.0911455 + 0.157869i
\(700\) 0 0
\(701\) 19.1626 0.723763 0.361881 0.932224i \(-0.382135\pi\)
0.361881 + 0.932224i \(0.382135\pi\)
\(702\) 0 0
\(703\) 32.0518i 1.20885i
\(704\) 0 0
\(705\) 3.22499 8.91130i 0.121460 0.335619i
\(706\) 0 0
\(707\) 12.0602i 0.453570i
\(708\) 0 0
\(709\) 11.7419 20.3375i 0.440975 0.763791i −0.556787 0.830655i \(-0.687966\pi\)
0.997762 + 0.0668645i \(0.0212995\pi\)
\(710\) 0 0
\(711\) −16.1049 + 27.8945i −0.603982 + 1.04613i
\(712\) 0 0
\(713\) −0.352814 + 0.203698i −0.0132130 + 0.00762853i
\(714\) 0 0
\(715\) 8.02412 + 30.2424i 0.300085 + 1.13100i
\(716\) 0 0
\(717\) −1.19550 + 0.690220i −0.0446466 + 0.0257767i
\(718\) 0 0
\(719\) 7.05429 12.2184i 0.263080 0.455669i −0.703978 0.710221i \(-0.748595\pi\)
0.967059 + 0.254553i \(0.0819282\pi\)
\(720\) 0 0
\(721\) 6.52886 11.3083i 0.243148 0.421144i
\(722\) 0 0
\(723\) 6.02765i 0.224171i
\(724\) 0 0
\(725\) −14.0765 + 5.18187i −0.522789 + 0.192450i
\(726\) 0 0
\(727\) 25.3762i 0.941153i 0.882359 + 0.470576i \(0.155954\pi\)
−0.882359 + 0.470576i \(0.844046\pi\)
\(728\) 0 0
\(729\) 20.7796 0.769616
\(730\) 0 0
\(731\) 3.64979 + 6.32162i 0.134992 + 0.233814i
\(732\) 0 0
\(733\) 10.6692i 0.394074i −0.980396 0.197037i \(-0.936868\pi\)
0.980396 0.197037i \(-0.0631320\pi\)
\(734\) 0 0
\(735\) 0.390054 + 2.18867i 0.0143874 + 0.0807305i
\(736\) 0 0
\(737\) −14.8024 8.54617i −0.545254 0.314802i
\(738\) 0 0
\(739\) 0.707513 + 1.22545i 0.0260263 + 0.0450788i 0.878745 0.477291i \(-0.158381\pi\)
−0.852719 + 0.522370i \(0.825048\pi\)
\(740\) 0 0
\(741\) −4.17156 6.01219i −0.153246 0.220863i
\(742\) 0 0
\(743\) 25.8748 14.9389i 0.949256 0.548053i 0.0564064 0.998408i \(-0.482036\pi\)
0.892850 + 0.450355i \(0.148702\pi\)
\(744\) 0 0
\(745\) 49.0980 8.74998i 1.79881 0.320575i
\(746\) 0 0
\(747\) 19.5488 + 11.2865i 0.715253 + 0.412952i
\(748\) 0 0
\(749\) −35.8809 −1.31106
\(750\) 0 0
\(751\) −9.99291 17.3082i −0.364646 0.631586i 0.624073 0.781366i \(-0.285477\pi\)
−0.988719 + 0.149780i \(0.952143\pi\)
\(752\) 0 0
\(753\) 3.20938i 0.116956i
\(754\) 0 0
\(755\) 27.6028 + 32.7737i 1.00457 + 1.19276i
\(756\) 0 0
\(757\) 14.8024 8.54617i 0.538003 0.310616i −0.206266 0.978496i \(-0.566131\pi\)
0.744269 + 0.667880i \(0.232798\pi\)
\(758\) 0 0
\(759\) −0.462218 −0.0167775
\(760\) 0 0
\(761\) 21.1120 36.5671i 0.765310 1.32556i −0.174773 0.984609i \(-0.555919\pi\)
0.940083 0.340947i \(-0.110748\pi\)
\(762\) 0 0
\(763\) 10.1272 + 5.84695i 0.366630 + 0.211674i
\(764\) 0 0
\(765\) 33.0138 + 11.9477i 1.19362 + 0.431968i
\(766\) 0 0
\(767\) −2.11046 25.3725i −0.0762044 0.916149i
\(768\) 0 0
\(769\) −11.8827 20.5815i −0.428502 0.742187i 0.568238 0.822864i \(-0.307625\pi\)
−0.996740 + 0.0806767i \(0.974292\pi\)
\(770\) 0 0
\(771\) 1.87907 3.25465i 0.0676731 0.117213i
\(772\) 0 0
\(773\) 0.246026 + 0.142043i 0.00884894 + 0.00510894i 0.504418 0.863460i \(-0.331707\pi\)
−0.495569 + 0.868569i \(0.665040\pi\)
\(774\) 0 0
\(775\) 1.00366 5.81644i 0.0360524 0.208933i
\(776\) 0 0
\(777\) −3.30596 + 1.90870i −0.118601 + 0.0684741i
\(778\) 0 0
\(779\) 1.06138 0.0380278
\(780\) 0 0
\(781\) −7.29958 −0.261199
\(782\) 0 0
\(783\) 5.27294 3.04434i 0.188440 0.108796i
\(784\) 0 0
\(785\) −10.6084 + 8.93460i −0.378628 + 0.318890i
\(786\) 0 0
\(787\) −20.9008 12.0671i −0.745032 0.430145i 0.0788638 0.996885i \(-0.474871\pi\)
−0.823896 + 0.566741i \(0.808204\pi\)
\(788\) 0 0
\(789\) −2.31925 + 4.01705i −0.0825674 + 0.143011i
\(790\) 0 0
\(791\) −4.83027 8.36627i −0.171745 0.297470i
\(792\) 0 0
\(793\) 2.02093 + 24.2961i 0.0717652 + 0.862780i
\(794\) 0 0
\(795\) 0.637176 1.76065i 0.0225983 0.0624437i
\(796\) 0