Properties

Label 324.3.o.a.5.15
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.15
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +O(q^{10})\) \(q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +(0.0259603 - 0.222104i) q^{11} +(-5.75523 - 19.2238i) q^{13} +(-1.04058 + 29.1612i) q^{15} +(-16.7302 - 2.94999i) q^{17} +(-3.63734 - 20.6284i) q^{19} +(1.99252 - 21.1694i) q^{21} +(12.0237 - 18.2812i) q^{23} +(19.9634 - 66.6825i) q^{25} +(-24.2403 - 11.8915i) q^{27} +(-9.72405 + 9.17417i) q^{29} +(-2.56933 + 44.1136i) q^{31} +(-0.471230 - 0.477473i) q^{33} +(-23.5785 + 64.7813i) q^{35} +(-46.1613 + 16.8013i) q^{37} +(-55.7997 - 22.5940i) q^{39} +(7.10244 - 29.9675i) q^{41} +(2.74269 + 6.35827i) q^{43} +(66.3128 + 57.1468i) q^{45} +(52.8732 - 3.07951i) q^{47} +(0.489143 - 1.13396i) q^{49} +(-38.2942 + 33.6301i) q^{51} +(-21.5125 - 12.4202i) q^{53} +(1.08751 + 1.88363i) q^{55} +(-55.1143 - 30.1871i) q^{57} +(-3.07094 - 26.2736i) q^{59} +(50.8973 + 25.5616i) q^{61} +(-45.8184 - 44.3814i) q^{63} +(156.560 + 116.555i) q^{65} +(47.8640 - 50.7328i) q^{67} +(-20.2370 - 62.4451i) q^{69} +(34.5875 - 41.2198i) q^{71} +(-59.4000 + 49.8425i) q^{73} +(-118.646 - 171.840i) q^{75} +(-0.711310 - 1.41633i) q^{77} +(73.2345 - 17.3569i) q^{79} +(-73.3158 + 34.4353i) q^{81} +(-25.7416 - 108.612i) q^{83} +(147.663 - 74.1590i) q^{85} +(3.23252 + 39.9757i) q^{87} +(69.0322 + 82.2694i) q^{89} +(-108.952 - 91.4217i) q^{91} +(98.4475 + 88.7785i) q^{93} +(148.195 + 139.815i) q^{95} +(38.6405 - 51.9032i) q^{97} +(-2.00184 + 0.207318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q+O(q^{10}) \) Copy content Toggle raw display \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.87615 2.34095i 0.625383 0.780318i
\(4\) 0 0
\(5\) −7.80193 + 5.80832i −1.56039 + 1.16166i −0.641513 + 0.767112i \(0.721693\pi\)
−0.918874 + 0.394552i \(0.870900\pi\)
\(6\) 0 0
\(7\) 5.92166 3.89473i 0.845951 0.556391i −0.0509101 0.998703i \(-0.516212\pi\)
0.896861 + 0.442313i \(0.145842\pi\)
\(8\) 0 0
\(9\) −1.96012 8.78396i −0.217791 0.975995i
\(10\) 0 0
\(11\) 0.0259603 0.222104i 0.00236003 0.0201913i −0.992007 0.126183i \(-0.959727\pi\)
0.994367 + 0.105991i \(0.0338016\pi\)
\(12\) 0 0
\(13\) −5.75523 19.2238i −0.442710 1.47876i −0.830506 0.557010i \(-0.811949\pi\)
0.387796 0.921745i \(-0.373237\pi\)
\(14\) 0 0
\(15\) −1.04058 + 29.1612i −0.0693722 + 1.94408i
\(16\) 0 0
\(17\) −16.7302 2.94999i −0.984131 0.173529i −0.341648 0.939828i \(-0.610985\pi\)
−0.642484 + 0.766299i \(0.722096\pi\)
\(18\) 0 0
\(19\) −3.63734 20.6284i −0.191439 1.08571i −0.917399 0.397969i \(-0.869715\pi\)
0.725960 0.687737i \(-0.241396\pi\)
\(20\) 0 0
\(21\) 1.99252 21.1694i 0.0948821 1.00807i
\(22\) 0 0
\(23\) 12.0237 18.2812i 0.522770 0.794833i −0.473530 0.880778i \(-0.657021\pi\)
0.996300 + 0.0859449i \(0.0273909\pi\)
\(24\) 0 0
\(25\) 19.9634 66.6825i 0.798538 2.66730i
\(26\) 0 0
\(27\) −24.2403 11.8915i −0.897789 0.440425i
\(28\) 0 0
\(29\) −9.72405 + 9.17417i −0.335312 + 0.316351i −0.835420 0.549613i \(-0.814775\pi\)
0.500107 + 0.865963i \(0.333294\pi\)
\(30\) 0 0
\(31\) −2.56933 + 44.1136i −0.0828815 + 1.42302i 0.658825 + 0.752296i \(0.271054\pi\)
−0.741707 + 0.670725i \(0.765983\pi\)
\(32\) 0 0
\(33\) −0.471230 0.477473i −0.0142797 0.0144689i
\(34\) 0 0
\(35\) −23.5785 + 64.7813i −0.673671 + 1.85090i
\(36\) 0 0
\(37\) −46.1613 + 16.8013i −1.24760 + 0.454090i −0.879591 0.475731i \(-0.842184\pi\)
−0.368012 + 0.929821i \(0.619961\pi\)
\(38\) 0 0
\(39\) −55.7997 22.5940i −1.43076 0.579334i
\(40\) 0 0
\(41\) 7.10244 29.9675i 0.173230 0.730916i −0.815192 0.579190i \(-0.803369\pi\)
0.988423 0.151725i \(-0.0484830\pi\)
\(42\) 0 0
\(43\) 2.74269 + 6.35827i 0.0637835 + 0.147867i 0.947127 0.320860i \(-0.103972\pi\)
−0.883343 + 0.468727i \(0.844713\pi\)
\(44\) 0 0
\(45\) 66.3128 + 57.1468i 1.47362 + 1.26993i
\(46\) 0 0
\(47\) 52.8732 3.07951i 1.12496 0.0655216i 0.514444 0.857524i \(-0.327998\pi\)
0.610518 + 0.792002i \(0.290961\pi\)
\(48\) 0 0
\(49\) 0.489143 1.13396i 0.00998251 0.0231421i
\(50\) 0 0
\(51\) −38.2942 + 33.6301i −0.750867 + 0.659413i
\(52\) 0 0
\(53\) −21.5125 12.4202i −0.405896 0.234344i 0.283129 0.959082i \(-0.408628\pi\)
−0.689025 + 0.724738i \(0.741961\pi\)
\(54\) 0 0
\(55\) 1.08751 + 1.88363i 0.0197730 + 0.0342478i
\(56\) 0 0
\(57\) −55.1143 30.1871i −0.966918 0.529599i
\(58\) 0 0
\(59\) −3.07094 26.2736i −0.0520498 0.445315i −0.993985 0.109519i \(-0.965069\pi\)
0.941935 0.335796i \(-0.109005\pi\)
\(60\) 0 0
\(61\) 50.8973 + 25.5616i 0.834381 + 0.419042i 0.814081 0.580752i \(-0.197241\pi\)
0.0203007 + 0.999794i \(0.493538\pi\)
\(62\) 0 0
\(63\) −45.8184 44.3814i −0.727275 0.704467i
\(64\) 0 0
\(65\) 156.560 + 116.555i 2.40862 + 1.79315i
\(66\) 0 0
\(67\) 47.8640 50.7328i 0.714388 0.757207i −0.263879 0.964556i \(-0.585002\pi\)
0.978267 + 0.207349i \(0.0664836\pi\)
\(68\) 0 0
\(69\) −20.2370 62.4451i −0.293291 0.905002i
\(70\) 0 0
\(71\) 34.5875 41.2198i 0.487148 0.580560i −0.465342 0.885131i \(-0.654069\pi\)
0.952490 + 0.304571i \(0.0985130\pi\)
\(72\) 0 0
\(73\) −59.4000 + 49.8425i −0.813699 + 0.682774i −0.951488 0.307687i \(-0.900445\pi\)
0.137789 + 0.990462i \(0.456001\pi\)
\(74\) 0 0
\(75\) −118.646 171.840i −1.58195 2.29120i
\(76\) 0 0
\(77\) −0.711310 1.41633i −0.00923779 0.0183939i
\(78\) 0 0
\(79\) 73.2345 17.3569i 0.927018 0.219707i 0.260739 0.965409i \(-0.416034\pi\)
0.666280 + 0.745702i \(0.267886\pi\)
\(80\) 0 0
\(81\) −73.3158 + 34.4353i −0.905134 + 0.425127i
\(82\) 0 0
\(83\) −25.7416 108.612i −0.310140 1.30858i −0.875291 0.483596i \(-0.839330\pi\)
0.565151 0.824987i \(-0.308818\pi\)
\(84\) 0 0
\(85\) 147.663 74.1590i 1.73721 0.872458i
\(86\) 0 0
\(87\) 3.23252 + 39.9757i 0.0371554 + 0.459491i
\(88\) 0 0
\(89\) 69.0322 + 82.2694i 0.775643 + 0.924375i 0.998728 0.0504239i \(-0.0160572\pi\)
−0.223085 + 0.974799i \(0.571613\pi\)
\(90\) 0 0
\(91\) −108.952 91.4217i −1.19728 1.00463i
\(92\) 0 0
\(93\) 98.4475 + 88.7785i 1.05858 + 0.954607i
\(94\) 0 0
\(95\) 148.195 + 139.815i 1.55994 + 1.47173i
\(96\) 0 0
\(97\) 38.6405 51.9032i 0.398356 0.535084i −0.557012 0.830505i \(-0.688052\pi\)
0.955367 + 0.295420i \(0.0954596\pi\)
\(98\) 0 0
\(99\) −2.00184 + 0.207318i −0.0202206 + 0.00209412i
\(100\) 0 0
\(101\) −64.7388 + 128.906i −0.640979 + 1.27629i 0.305089 + 0.952324i \(0.401314\pi\)
−0.946068 + 0.323970i \(0.894982\pi\)
\(102\) 0 0
\(103\) −72.2711 + 8.44728i −0.701661 + 0.0820124i −0.459440 0.888209i \(-0.651950\pi\)
−0.242221 + 0.970221i \(0.577876\pi\)
\(104\) 0 0
\(105\) 107.413 + 176.736i 1.02298 + 1.68320i
\(106\) 0 0
\(107\) −117.357 + 67.7563i −1.09680 + 0.633236i −0.935378 0.353650i \(-0.884940\pi\)
−0.161419 + 0.986886i \(0.551607\pi\)
\(108\) 0 0
\(109\) 73.2786 126.922i 0.672280 1.16442i −0.304975 0.952360i \(-0.598648\pi\)
0.977256 0.212064i \(-0.0680184\pi\)
\(110\) 0 0
\(111\) −47.2744 + 139.583i −0.425895 + 1.25751i
\(112\) 0 0
\(113\) 15.6022 + 6.73014i 0.138073 + 0.0595588i 0.463995 0.885838i \(-0.346416\pi\)
−0.325922 + 0.945397i \(0.605675\pi\)
\(114\) 0 0
\(115\) 12.3747 + 212.466i 0.107606 + 1.84753i
\(116\) 0 0
\(117\) −157.580 + 88.2348i −1.34684 + 0.754143i
\(118\) 0 0
\(119\) −110.560 + 47.6910i −0.929077 + 0.400765i
\(120\) 0 0
\(121\) 117.690 + 27.8930i 0.972643 + 0.230521i
\(122\) 0 0
\(123\) −56.8274 72.8501i −0.462011 0.592277i
\(124\) 0 0
\(125\) 148.393 + 407.706i 1.18714 + 3.26165i
\(126\) 0 0
\(127\) 185.745 + 67.6057i 1.46256 + 0.532328i 0.946069 0.323965i \(-0.105016\pi\)
0.516491 + 0.856293i \(0.327238\pi\)
\(128\) 0 0
\(129\) 20.0301 + 5.50856i 0.155272 + 0.0427020i
\(130\) 0 0
\(131\) −19.7774 1.15190i −0.150972 0.00879313i −0.0175078 0.999847i \(-0.505573\pi\)
−0.133465 + 0.991054i \(0.542610\pi\)
\(132\) 0 0
\(133\) −101.881 107.988i −0.766025 0.811939i
\(134\) 0 0
\(135\) 258.191 48.0191i 1.91252 0.355697i
\(136\) 0 0
\(137\) −223.265 66.8411i −1.62967 0.487891i −0.664015 0.747720i \(-0.731149\pi\)
−0.965655 + 0.259829i \(0.916334\pi\)
\(138\) 0 0
\(139\) 4.44861 + 2.92590i 0.0320044 + 0.0210496i 0.565410 0.824810i \(-0.308718\pi\)
−0.533406 + 0.845859i \(0.679088\pi\)
\(140\) 0 0
\(141\) 91.9891 129.551i 0.652405 0.918804i
\(142\) 0 0
\(143\) −4.41910 + 0.779207i −0.0309028 + 0.00544900i
\(144\) 0 0
\(145\) 22.5799 128.057i 0.155723 0.883150i
\(146\) 0 0
\(147\) −1.73684 3.27254i −0.0118153 0.0222622i
\(148\) 0 0
\(149\) 192.606 57.6624i 1.29266 0.386996i 0.434633 0.900608i \(-0.356878\pi\)
0.858023 + 0.513612i \(0.171693\pi\)
\(150\) 0 0
\(151\) 117.886 + 13.7789i 0.780703 + 0.0912511i 0.497103 0.867692i \(-0.334397\pi\)
0.283600 + 0.958943i \(0.408471\pi\)
\(152\) 0 0
\(153\) 6.88069 + 152.740i 0.0449719 + 0.998301i
\(154\) 0 0
\(155\) −236.181 359.095i −1.52375 2.31674i
\(156\) 0 0
\(157\) −63.5438 85.3542i −0.404738 0.543657i 0.552290 0.833652i \(-0.313754\pi\)
−0.957028 + 0.289994i \(0.906347\pi\)
\(158\) 0 0
\(159\) −69.4359 + 27.0575i −0.436704 + 0.170173i
\(160\) 0 0
\(161\) 155.084i 0.963254i
\(162\) 0 0
\(163\) −127.040 −0.779388 −0.389694 0.920944i \(-0.627419\pi\)
−0.389694 + 0.920944i \(0.627419\pi\)
\(164\) 0 0
\(165\) 6.44982 + 0.988152i 0.0390898 + 0.00598880i
\(166\) 0 0
\(167\) −100.508 + 74.8255i −0.601845 + 0.448057i −0.854465 0.519509i \(-0.826115\pi\)
0.252620 + 0.967565i \(0.418708\pi\)
\(168\) 0 0
\(169\) −195.235 + 128.408i −1.15524 + 0.759811i
\(170\) 0 0
\(171\) −174.069 + 72.3845i −1.01795 + 0.423301i
\(172\) 0 0
\(173\) −12.5925 + 107.736i −0.0727889 + 0.622749i 0.906775 + 0.421615i \(0.138537\pi\)
−0.979564 + 0.201134i \(0.935537\pi\)
\(174\) 0 0
\(175\) −141.494 472.623i −0.808538 2.70070i
\(176\) 0 0
\(177\) −67.2667 42.1042i −0.380038 0.237877i
\(178\) 0 0
\(179\) 174.081 + 30.6952i 0.972521 + 0.171482i 0.637264 0.770645i \(-0.280066\pi\)
0.335257 + 0.942127i \(0.391177\pi\)
\(180\) 0 0
\(181\) 15.6742 + 88.8926i 0.0865976 + 0.491120i 0.997000 + 0.0773965i \(0.0246607\pi\)
−0.910403 + 0.413723i \(0.864228\pi\)
\(182\) 0 0
\(183\) 155.329 71.1908i 0.848794 0.389021i
\(184\) 0 0
\(185\) 262.560 399.203i 1.41924 2.15785i
\(186\) 0 0
\(187\) −1.08953 + 3.63928i −0.00582635 + 0.0194614i
\(188\) 0 0
\(189\) −189.857 + 23.9924i −1.00453 + 0.126944i
\(190\) 0 0
\(191\) −9.65325 + 9.10737i −0.0505406 + 0.0476826i −0.711098 0.703093i \(-0.751802\pi\)
0.660557 + 0.750776i \(0.270320\pi\)
\(192\) 0 0
\(193\) 10.8605 186.468i 0.0562721 0.966155i −0.845509 0.533962i \(-0.820703\pi\)
0.901781 0.432194i \(-0.142260\pi\)
\(194\) 0 0
\(195\) 566.579 147.826i 2.90553 0.758081i
\(196\) 0 0
\(197\) 14.6800 40.3330i 0.0745179 0.204736i −0.896841 0.442353i \(-0.854144\pi\)
0.971359 + 0.237617i \(0.0763662\pi\)
\(198\) 0 0
\(199\) −189.630 + 69.0198i −0.952917 + 0.346833i −0.771254 0.636528i \(-0.780370\pi\)
−0.181663 + 0.983361i \(0.558148\pi\)
\(200\) 0 0
\(201\) −28.9632 207.230i −0.144096 1.03099i
\(202\) 0 0
\(203\) −21.8515 + 92.1989i −0.107643 + 0.454182i
\(204\) 0 0
\(205\) 118.648 + 275.058i 0.578773 + 1.34175i
\(206\) 0 0
\(207\) −184.149 69.7824i −0.889608 0.337113i
\(208\) 0 0
\(209\) −4.67609 + 0.272351i −0.0223736 + 0.00130311i
\(210\) 0 0
\(211\) −43.5439 + 100.946i −0.206369 + 0.478417i −0.989695 0.143195i \(-0.954263\pi\)
0.783326 + 0.621612i \(0.213522\pi\)
\(212\) 0 0
\(213\) −31.6022 158.302i −0.148367 0.743203i
\(214\) 0 0
\(215\) −58.3292 33.6764i −0.271298 0.156634i
\(216\) 0 0
\(217\) 156.596 + 271.233i 0.721642 + 1.24992i
\(218\) 0 0
\(219\) 5.23568 + 232.565i 0.0239072 + 1.06194i
\(220\) 0 0
\(221\) 39.5763 + 338.597i 0.179078 + 1.53211i
\(222\) 0 0
\(223\) 219.811 + 110.393i 0.985698 + 0.495036i 0.867222 0.497921i \(-0.165903\pi\)
0.118475 + 0.992957i \(0.462199\pi\)
\(224\) 0 0
\(225\) −624.867 44.6521i −2.77719 0.198454i
\(226\) 0 0
\(227\) −306.159 227.927i −1.34872 1.00408i −0.997705 0.0677147i \(-0.978429\pi\)
−0.351015 0.936370i \(-0.614163\pi\)
\(228\) 0 0
\(229\) 235.591 249.712i 1.02878 1.09045i 0.0329307 0.999458i \(-0.489516\pi\)
0.995852 0.0909882i \(-0.0290026\pi\)
\(230\) 0 0
\(231\) −4.65009 0.992113i −0.0201303 0.00429486i
\(232\) 0 0
\(233\) 252.865 301.353i 1.08526 1.29336i 0.131986 0.991252i \(-0.457865\pi\)
0.953273 0.302110i \(-0.0976909\pi\)
\(234\) 0 0
\(235\) −394.626 + 331.131i −1.67926 + 1.40907i
\(236\) 0 0
\(237\) 96.7672 204.003i 0.408300 0.860770i
\(238\) 0 0
\(239\) −46.1353 91.8629i −0.193035 0.384363i 0.776206 0.630480i \(-0.217142\pi\)
−0.969240 + 0.246116i \(0.920846\pi\)
\(240\) 0 0
\(241\) −218.503 + 51.7861i −0.906650 + 0.214880i −0.657385 0.753555i \(-0.728337\pi\)
−0.249265 + 0.968435i \(0.580189\pi\)
\(242\) 0 0
\(243\) −56.9402 + 236.235i −0.234322 + 0.972159i
\(244\) 0 0
\(245\) 2.77015 + 11.6882i 0.0113067 + 0.0477069i
\(246\) 0 0
\(247\) −375.623 + 188.645i −1.52074 + 0.763745i
\(248\) 0 0
\(249\) −302.552 143.513i −1.21507 0.576359i
\(250\) 0 0
\(251\) 62.0303 + 73.9248i 0.247133 + 0.294521i 0.875323 0.483538i \(-0.160649\pi\)
−0.628191 + 0.778059i \(0.716204\pi\)
\(252\) 0 0
\(253\) −3.74818 3.14510i −0.0148150 0.0124312i
\(254\) 0 0
\(255\) 103.435 484.805i 0.405626 1.90119i
\(256\) 0 0
\(257\) −116.548 109.957i −0.453495 0.427850i 0.425298 0.905053i \(-0.360169\pi\)
−0.878793 + 0.477203i \(0.841651\pi\)
\(258\) 0 0
\(259\) −207.915 + 279.278i −0.802759 + 1.07829i
\(260\) 0 0
\(261\) 99.6459 + 67.4332i 0.381785 + 0.258365i
\(262\) 0 0
\(263\) 196.054 390.375i 0.745452 1.48432i −0.125049 0.992151i \(-0.539909\pi\)
0.870501 0.492166i \(-0.163795\pi\)
\(264\) 0 0
\(265\) 239.980 28.0496i 0.905584 0.105848i
\(266\) 0 0
\(267\) 322.104 7.25145i 1.20638 0.0271590i
\(268\) 0 0
\(269\) −317.324 + 183.207i −1.17964 + 0.681068i −0.955932 0.293587i \(-0.905151\pi\)
−0.223712 + 0.974655i \(0.571817\pi\)
\(270\) 0 0
\(271\) 240.973 417.378i 0.889200 1.54014i 0.0483780 0.998829i \(-0.484595\pi\)
0.840822 0.541311i \(-0.182072\pi\)
\(272\) 0 0
\(273\) −418.425 + 83.5310i −1.53269 + 0.305974i
\(274\) 0 0
\(275\) −14.2922 6.16506i −0.0519717 0.0224184i
\(276\) 0 0
\(277\) 9.33521 + 160.279i 0.0337011 + 0.578626i 0.972318 + 0.233663i \(0.0750713\pi\)
−0.938616 + 0.344962i \(0.887892\pi\)
\(278\) 0 0
\(279\) 392.529 63.8993i 1.40691 0.229030i
\(280\) 0 0
\(281\) 180.072 77.6754i 0.640825 0.276425i −0.0507699 0.998710i \(-0.516168\pi\)
0.691595 + 0.722285i \(0.256908\pi\)
\(282\) 0 0
\(283\) −41.1308 9.74818i −0.145339 0.0344459i 0.157303 0.987550i \(-0.449720\pi\)
−0.302641 + 0.953105i \(0.597868\pi\)
\(284\) 0 0
\(285\) 605.335 84.6039i 2.12398 0.296856i
\(286\) 0 0
\(287\) −74.6574 205.120i −0.260130 0.714702i
\(288\) 0 0
\(289\) −0.372917 0.135731i −0.00129037 0.000469656i
\(290\) 0 0
\(291\) −49.0076 187.834i −0.168411 0.645477i
\(292\) 0 0
\(293\) 144.509 + 8.41666i 0.493203 + 0.0287258i 0.302945 0.953008i \(-0.402030\pi\)
0.190259 + 0.981734i \(0.439067\pi\)
\(294\) 0 0
\(295\) 176.565 + 187.148i 0.598524 + 0.634398i
\(296\) 0 0
\(297\) −3.27043 + 5.07517i −0.0110116 + 0.0170881i
\(298\) 0 0
\(299\) −420.633 125.929i −1.40680 0.421168i
\(300\) 0 0
\(301\) 41.0050 + 26.9694i 0.136229 + 0.0895995i
\(302\) 0 0
\(303\) 180.302 + 393.397i 0.595057 + 1.29834i
\(304\) 0 0
\(305\) −545.567 + 96.1981i −1.78874 + 0.315404i
\(306\) 0 0
\(307\) 19.9945 113.395i 0.0651288 0.369364i −0.934772 0.355249i \(-0.884396\pi\)
0.999900 0.0141144i \(-0.00449292\pi\)
\(308\) 0 0
\(309\) −115.817 + 185.032i −0.374811 + 0.598808i
\(310\) 0 0
\(311\) −185.156 + 55.4321i −0.595357 + 0.178238i −0.570284 0.821447i \(-0.693167\pi\)
−0.0250730 + 0.999686i \(0.507982\pi\)
\(312\) 0 0
\(313\) 260.741 + 30.4762i 0.833038 + 0.0973681i 0.521911 0.853000i \(-0.325219\pi\)
0.311127 + 0.950368i \(0.399294\pi\)
\(314\) 0 0
\(315\) 615.253 + 80.1331i 1.95318 + 0.254391i
\(316\) 0 0
\(317\) −66.9169 101.742i −0.211094 0.320953i 0.714384 0.699754i \(-0.246707\pi\)
−0.925478 + 0.378801i \(0.876337\pi\)
\(318\) 0 0
\(319\) 1.78518 + 2.39792i 0.00559619 + 0.00751699i
\(320\) 0 0
\(321\) −61.5657 + 401.849i −0.191793 + 1.25187i
\(322\) 0 0
\(323\) 355.848i 1.10170i
\(324\) 0 0
\(325\) −1396.79 −4.29781
\(326\) 0 0
\(327\) −159.637 409.667i −0.488188 1.25280i
\(328\) 0 0
\(329\) 301.103 224.163i 0.915207 0.681346i
\(330\) 0 0
\(331\) 245.574 161.516i 0.741914 0.487965i −0.121417 0.992602i \(-0.538744\pi\)
0.863332 + 0.504637i \(0.168374\pi\)
\(332\) 0 0
\(333\) 238.064 + 372.546i 0.714907 + 1.11876i
\(334\) 0 0
\(335\) −78.7587 + 673.824i −0.235101 + 2.01141i
\(336\) 0 0
\(337\) −21.2191 70.8766i −0.0629646 0.210316i 0.920718 0.390228i \(-0.127604\pi\)
−0.983683 + 0.179912i \(0.942419\pi\)
\(338\) 0 0
\(339\) 45.0270 23.8973i 0.132823 0.0704935i
\(340\) 0 0
\(341\) 9.73113 + 1.71586i 0.0285370 + 0.00503185i
\(342\) 0 0
\(343\) 58.7873 + 333.399i 0.171392 + 0.972009i
\(344\) 0 0
\(345\) 520.589 + 369.649i 1.50895 + 1.07145i
\(346\) 0 0
\(347\) −4.93395 + 7.50170i −0.0142189 + 0.0216187i −0.842527 0.538654i \(-0.818933\pi\)
0.828308 + 0.560272i \(0.189304\pi\)
\(348\) 0 0
\(349\) 71.6586 239.356i 0.205326 0.685835i −0.791849 0.610717i \(-0.790881\pi\)
0.997175 0.0751184i \(-0.0239335\pi\)
\(350\) 0 0
\(351\) −89.0908 + 534.430i −0.253820 + 1.52259i
\(352\) 0 0
\(353\) 433.435 408.925i 1.22786 1.15843i 0.245911 0.969292i \(-0.420913\pi\)
0.981951 0.189135i \(-0.0605685\pi\)
\(354\) 0 0
\(355\) −30.4315 + 522.489i −0.0857227 + 1.47180i
\(356\) 0 0
\(357\) −95.7850 + 348.291i −0.268305 + 0.975606i
\(358\) 0 0
\(359\) 67.8611 186.447i 0.189028 0.519351i −0.808587 0.588377i \(-0.799767\pi\)
0.997615 + 0.0690264i \(0.0219893\pi\)
\(360\) 0 0
\(361\) −73.0719 + 26.5960i −0.202415 + 0.0736731i
\(362\) 0 0
\(363\) 286.100 223.175i 0.788154 0.614807i
\(364\) 0 0
\(365\) 173.933 733.882i 0.476530 2.01064i
\(366\) 0 0
\(367\) −118.085 273.753i −0.321758 0.745920i −0.999939 0.0110248i \(-0.996491\pi\)
0.678181 0.734895i \(-0.262769\pi\)
\(368\) 0 0
\(369\) −277.155 3.64748i −0.751098 0.00988477i
\(370\) 0 0
\(371\) −175.763 + 10.2370i −0.473755 + 0.0275931i
\(372\) 0 0
\(373\) 116.880 270.958i 0.313351 0.726429i −0.686649 0.726989i \(-0.740919\pi\)
1.00000 0.000560420i \(0.000178387\pi\)
\(374\) 0 0
\(375\) 1232.83 + 417.537i 3.28754 + 1.11343i
\(376\) 0 0
\(377\) 232.327 + 134.134i 0.616251 + 0.355793i
\(378\) 0 0
\(379\) 33.9982 + 58.8866i 0.0897051 + 0.155374i 0.907386 0.420297i \(-0.138074\pi\)
−0.817681 + 0.575671i \(0.804741\pi\)
\(380\) 0 0
\(381\) 506.747 307.982i 1.33005 0.808352i
\(382\) 0 0
\(383\) −28.1065 240.466i −0.0733851 0.627850i −0.979016 0.203783i \(-0.934676\pi\)
0.905631 0.424067i \(-0.139398\pi\)
\(384\) 0 0
\(385\) 13.7761 + 6.91862i 0.0357821 + 0.0179705i
\(386\) 0 0
\(387\) 50.4748 36.5547i 0.130426 0.0944565i
\(388\) 0 0
\(389\) −281.915 209.878i −0.724718 0.539532i 0.170393 0.985376i \(-0.445496\pi\)
−0.895111 + 0.445844i \(0.852904\pi\)
\(390\) 0 0
\(391\) −255.089 + 270.378i −0.652400 + 0.691504i
\(392\) 0 0
\(393\) −39.8019 + 44.1368i −0.101277 + 0.112307i
\(394\) 0 0
\(395\) −470.556 + 560.787i −1.19128 + 1.41971i
\(396\) 0 0
\(397\) −497.642 + 417.571i −1.25351 + 1.05182i −0.257164 + 0.966368i \(0.582788\pi\)
−0.996343 + 0.0854486i \(0.972768\pi\)
\(398\) 0 0
\(399\) −443.939 + 35.8979i −1.11263 + 0.0899696i
\(400\) 0 0
\(401\) −1.55912 3.10446i −0.00388808 0.00774180i 0.891680 0.452666i \(-0.149527\pi\)
−0.895568 + 0.444924i \(0.853231\pi\)
\(402\) 0 0
\(403\) 862.820 204.492i 2.14099 0.507424i
\(404\) 0 0
\(405\) 371.994 694.504i 0.918504 1.71482i
\(406\) 0 0
\(407\) 2.53329 + 10.6888i 0.00622430 + 0.0262624i
\(408\) 0 0
\(409\) 290.223 145.755i 0.709591 0.356370i −0.0571155 0.998368i \(-0.518190\pi\)
0.766707 + 0.641997i \(0.221894\pi\)
\(410\) 0 0
\(411\) −575.350 + 397.248i −1.39988 + 0.966541i
\(412\) 0 0
\(413\) −120.514 143.623i −0.291800 0.347754i
\(414\) 0 0
\(415\) 831.690 + 697.871i 2.00407 + 1.68162i
\(416\) 0 0
\(417\) 15.1957 4.92457i 0.0364404 0.0118095i
\(418\) 0 0
\(419\) −469.091 442.564i −1.11955 1.05624i −0.997972 0.0636571i \(-0.979724\pi\)
−0.121576 0.992582i \(-0.538795\pi\)
\(420\) 0 0
\(421\) 10.0386 13.4842i 0.0238446 0.0320289i −0.790041 0.613054i \(-0.789941\pi\)
0.813886 + 0.581025i \(0.197348\pi\)
\(422\) 0 0
\(423\) −130.688 458.400i −0.308956 1.08369i
\(424\) 0 0
\(425\) −530.706 + 1056.72i −1.24872 + 2.48641i
\(426\) 0 0
\(427\) 400.952 46.8645i 0.938997 0.109753i
\(428\) 0 0
\(429\) −6.46681 + 11.8068i −0.0150741 + 0.0275217i
\(430\) 0 0
\(431\) −270.027 + 155.900i −0.626514 + 0.361718i −0.779401 0.626526i \(-0.784476\pi\)
0.152887 + 0.988244i \(0.451143\pi\)
\(432\) 0 0
\(433\) 67.0785 116.183i 0.154916 0.268322i −0.778113 0.628125i \(-0.783823\pi\)
0.933028 + 0.359803i \(0.117156\pi\)
\(434\) 0 0
\(435\) −257.412 293.112i −0.591751 0.673821i
\(436\) 0 0
\(437\) −420.845 181.535i −0.963033 0.415412i
\(438\) 0 0
\(439\) 22.8851 + 392.921i 0.0521300 + 0.895037i 0.918447 + 0.395543i \(0.129444\pi\)
−0.866317 + 0.499494i \(0.833519\pi\)
\(440\) 0 0
\(441\) −10.9194 2.07391i −0.0247607 0.00470275i
\(442\) 0 0
\(443\) 617.609 266.410i 1.39415 0.601378i 0.439266 0.898357i \(-0.355238\pi\)
0.954884 + 0.296979i \(0.0959791\pi\)
\(444\) 0 0
\(445\) −1016.43 240.899i −2.28412 0.541345i
\(446\) 0 0
\(447\) 226.372 559.064i 0.506426 1.25070i
\(448\) 0 0
\(449\) 204.853 + 562.829i 0.456243 + 1.25352i 0.928262 + 0.371928i \(0.121303\pi\)
−0.472019 + 0.881588i \(0.656475\pi\)
\(450\) 0 0
\(451\) −6.47154 2.35545i −0.0143493 0.00522272i
\(452\) 0 0
\(453\) 253.428 250.115i 0.559443 0.552129i
\(454\) 0 0
\(455\) 1381.04 + 80.4367i 3.03526 + 0.176784i
\(456\) 0 0
\(457\) 204.008 + 216.236i 0.446408 + 0.473165i 0.911027 0.412346i \(-0.135290\pi\)
−0.464620 + 0.885510i \(0.653809\pi\)
\(458\) 0 0
\(459\) 370.466 + 270.456i 0.807116 + 0.589228i
\(460\) 0 0
\(461\) 516.453 + 154.616i 1.12029 + 0.335392i 0.792811 0.609467i \(-0.208617\pi\)
0.327477 + 0.944859i \(0.393802\pi\)
\(462\) 0 0
\(463\) 434.060 + 285.485i 0.937494 + 0.616599i 0.923622 0.383304i \(-0.125214\pi\)
0.0138717 + 0.999904i \(0.495584\pi\)
\(464\) 0 0
\(465\) −1283.73 120.829i −2.76072 0.259847i
\(466\) 0 0
\(467\) 630.053 111.095i 1.34915 0.237891i 0.548061 0.836438i \(-0.315366\pi\)
0.801088 + 0.598547i \(0.204255\pi\)
\(468\) 0 0
\(469\) 85.8430 486.840i 0.183034 1.03804i
\(470\) 0 0
\(471\) −319.028 11.3841i −0.677342 0.0241701i
\(472\) 0 0
\(473\) 1.48340 0.444101i 0.00313615 0.000938903i
\(474\) 0 0
\(475\) −1448.17 169.267i −3.04878 0.356351i
\(476\) 0 0
\(477\) −66.9318 + 213.310i −0.140318 + 0.447191i
\(478\) 0 0
\(479\) −190.208 289.197i −0.397094 0.603752i 0.580498 0.814262i \(-0.302858\pi\)
−0.977592 + 0.210510i \(0.932488\pi\)
\(480\) 0 0
\(481\) 588.655 + 790.701i 1.22382 + 1.64387i
\(482\) 0 0
\(483\) −363.044 290.961i −0.751644 0.602403i
\(484\) 0 0
\(485\) 629.382i 1.29769i
\(486\) 0 0
\(487\) −918.147 −1.88531 −0.942656 0.333766i \(-0.891680\pi\)
−0.942656 + 0.333766i \(0.891680\pi\)
\(488\) 0 0
\(489\) −238.347 + 297.395i −0.487416 + 0.608170i
\(490\) 0 0
\(491\) 173.412 129.100i 0.353181 0.262934i −0.405917 0.913910i \(-0.633048\pi\)
0.759098 + 0.650976i \(0.225640\pi\)
\(492\) 0 0
\(493\) 189.749 124.800i 0.384887 0.253144i
\(494\) 0 0
\(495\) 14.4141 13.2448i 0.0291193 0.0267572i
\(496\) 0 0
\(497\) 44.2752 378.799i 0.0890849 0.762170i
\(498\) 0 0
\(499\) 249.130 + 832.151i 0.499258 + 1.66764i 0.721317 + 0.692605i \(0.243537\pi\)
−0.222059 + 0.975033i \(0.571278\pi\)
\(500\) 0 0
\(501\) −13.4053 + 375.669i −0.0267570 + 0.749838i
\(502\) 0 0
\(503\) −175.584 30.9602i −0.349073 0.0615510i −0.00363740 0.999993i \(-0.501158\pi\)
−0.345436 + 0.938442i \(0.612269\pi\)
\(504\) 0 0
\(505\) −243.638 1381.74i −0.482451 2.73611i
\(506\) 0 0
\(507\) −65.6929 + 697.949i −0.129572 + 1.37662i
\(508\) 0 0
\(509\) −72.3197 + 109.957i −0.142082 + 0.216025i −0.899517 0.436885i \(-0.856082\pi\)
0.757435 + 0.652910i \(0.226452\pi\)
\(510\) 0 0
\(511\) −157.623 + 526.498i −0.308460 + 1.03033i
\(512\) 0 0
\(513\) −157.132 + 543.292i −0.306300 + 1.05905i
\(514\) 0 0
\(515\) 514.790 485.679i 0.999591 0.943066i
\(516\) 0 0
\(517\) 0.688630 11.8233i 0.00133197 0.0228691i
\(518\) 0 0
\(519\) 228.578 + 231.606i 0.440421 + 0.446255i
\(520\) 0 0
\(521\) 5.11890 14.0641i 0.00982514 0.0269943i −0.934683 0.355482i \(-0.884317\pi\)
0.944508 + 0.328488i \(0.106539\pi\)
\(522\) 0 0
\(523\) −106.983 + 38.9386i −0.204556 + 0.0744524i −0.442266 0.896884i \(-0.645825\pi\)
0.237710 + 0.971336i \(0.423603\pi\)
\(524\) 0 0
\(525\) −1371.85 555.481i −2.61305 1.05806i
\(526\) 0 0
\(527\) 173.120 730.452i 0.328502 1.38606i
\(528\) 0 0
\(529\) 19.8951 + 46.1220i 0.0376089 + 0.0871872i
\(530\) 0 0
\(531\) −224.766 + 78.4744i −0.423289 + 0.147786i
\(532\) 0 0
\(533\) −616.967 + 35.9342i −1.15754 + 0.0674188i
\(534\) 0 0
\(535\) 522.063 1210.28i 0.975819 2.26220i
\(536\) 0 0
\(537\) 398.459 349.927i 0.742009 0.651634i
\(538\) 0 0
\(539\) −0.239159 0.138079i −0.000443710 0.000256176i
\(540\) 0 0
\(541\) 188.006 + 325.636i 0.347516 + 0.601915i 0.985808 0.167879i \(-0.0536919\pi\)
−0.638292 + 0.769795i \(0.720359\pi\)
\(542\) 0 0
\(543\) 237.501 + 130.083i 0.437386 + 0.239564i
\(544\) 0 0
\(545\) 165.491 + 1415.86i 0.303653 + 2.59792i
\(546\) 0 0
\(547\) 319.183 + 160.300i 0.583515 + 0.293052i 0.715964 0.698137i \(-0.245988\pi\)
−0.132448 + 0.991190i \(0.542284\pi\)
\(548\) 0 0
\(549\) 124.767 497.183i 0.227262 0.905616i
\(550\) 0 0
\(551\) 224.618 + 167.222i 0.407656 + 0.303488i
\(552\) 0 0
\(553\) 366.069 388.010i 0.661969 0.701646i
\(554\) 0 0
\(555\) −441.913 1363.60i −0.796240 2.45694i
\(556\) 0 0
\(557\) 11.5450 13.7588i 0.0207271 0.0247016i −0.755581 0.655055i \(-0.772646\pi\)
0.776308 + 0.630353i \(0.217090\pi\)
\(558\) 0 0
\(559\) 106.445 89.3183i 0.190421 0.159782i
\(560\) 0 0
\(561\) 6.47525 + 9.37836i 0.0115423 + 0.0167172i
\(562\) 0 0
\(563\) 354.677 + 706.219i 0.629976 + 1.25439i 0.951548 + 0.307501i \(0.0994927\pi\)
−0.321571 + 0.946885i \(0.604211\pi\)
\(564\) 0 0
\(565\) −160.818 + 38.1146i −0.284634 + 0.0674595i
\(566\) 0 0
\(567\) −300.035 + 489.459i −0.529162 + 0.863244i
\(568\) 0 0
\(569\) 21.8659 + 92.2596i 0.0384287 + 0.162143i 0.988876 0.148742i \(-0.0475225\pi\)
−0.950447 + 0.310886i \(0.899374\pi\)
\(570\) 0 0
\(571\) −894.561 + 449.265i −1.56666 + 0.786804i −0.999327 0.0366865i \(-0.988320\pi\)
−0.567330 + 0.823491i \(0.692023\pi\)
\(572\) 0 0
\(573\) 3.20898 + 39.6846i 0.00560032 + 0.0692576i
\(574\) 0 0
\(575\) −978.999 1166.73i −1.70261 2.02909i
\(576\) 0 0
\(577\) 278.455 + 233.651i 0.482590 + 0.404941i 0.851362 0.524579i \(-0.175777\pi\)
−0.368772 + 0.929520i \(0.620222\pi\)
\(578\) 0 0
\(579\) −416.137 375.266i −0.718716 0.648127i
\(580\) 0 0
\(581\) −575.450 542.909i −0.990447 0.934438i
\(582\) 0 0
\(583\) −3.31706 + 4.45559i −0.00568964 + 0.00764251i
\(584\) 0 0
\(585\) 716.934 1603.68i 1.22553 2.74133i
\(586\) 0 0
\(587\) −115.552 + 230.083i −0.196852 + 0.391965i −0.970303 0.241891i \(-0.922232\pi\)
0.773451 + 0.633856i \(0.218529\pi\)
\(588\) 0 0
\(589\) 919.340 107.455i 1.56085 0.182437i
\(590\) 0 0
\(591\) −66.8758 110.036i −0.113157 0.186186i
\(592\) 0 0
\(593\) 895.273 516.886i 1.50974 0.871646i 0.509800 0.860293i \(-0.329719\pi\)
0.999936 0.0113533i \(-0.00361395\pi\)
\(594\) 0 0
\(595\) 585.578 1014.25i 0.984164 1.70462i
\(596\) 0 0
\(597\) −194.203 + 573.407i −0.325298 + 0.960481i
\(598\) 0 0
\(599\) 277.319 + 119.624i 0.462970 + 0.199706i 0.614772 0.788705i \(-0.289248\pi\)
−0.151801 + 0.988411i \(0.548507\pi\)
\(600\) 0 0
\(601\) −32.1314 551.675i −0.0534632 0.917928i −0.913282 0.407328i \(-0.866460\pi\)
0.859819 0.510600i \(-0.170577\pi\)
\(602\) 0 0
\(603\) −539.454 320.993i −0.894618 0.532326i
\(604\) 0 0
\(605\) −1080.22 + 465.961i −1.78549 + 0.770183i
\(606\) 0 0
\(607\) 323.685 + 76.7148i 0.533254 + 0.126384i 0.488416 0.872611i \(-0.337575\pi\)
0.0448379 + 0.998994i \(0.485723\pi\)
\(608\) 0 0
\(609\) 174.837 + 224.132i 0.287088 + 0.368034i
\(610\) 0 0
\(611\) −363.498 998.702i −0.594922 1.63454i
\(612\) 0 0
\(613\) −13.7463 5.00323i −0.0224246 0.00816188i 0.330784 0.943707i \(-0.392687\pi\)
−0.353208 + 0.935545i \(0.614909\pi\)
\(614\) 0 0
\(615\) 866.500 + 238.300i 1.40894 + 0.387479i
\(616\) 0 0
\(617\) −414.972 24.1694i −0.672564 0.0391724i −0.281535 0.959551i \(-0.590844\pi\)
−0.391029 + 0.920378i \(0.627881\pi\)
\(618\) 0 0
\(619\) −287.903 305.159i −0.465109 0.492987i 0.451780 0.892130i \(-0.350789\pi\)
−0.916889 + 0.399143i \(0.869308\pi\)
\(620\) 0 0
\(621\) −508.848 + 300.161i −0.819401 + 0.483352i
\(622\) 0 0
\(623\) 729.202 + 218.309i 1.17047 + 0.350415i
\(624\) 0 0
\(625\) −2071.95 1362.74i −3.31512 2.18039i
\(626\) 0 0
\(627\) −8.13548 + 11.4575i −0.0129752 + 0.0182735i
\(628\) 0 0
\(629\) 821.853 144.915i 1.30660 0.230389i
\(630\) 0 0
\(631\) 27.6743 156.949i 0.0438578 0.248730i −0.954995 0.296623i \(-0.904140\pi\)
0.998852 + 0.0478930i \(0.0152506\pi\)
\(632\) 0 0
\(633\) 154.615 + 291.324i 0.244258 + 0.460228i
\(634\) 0 0
\(635\) −1841.85 + 551.413i −2.90055 + 0.868366i
\(636\) 0 0
\(637\) −24.6142 2.87699i −0.0386408 0.00451646i
\(638\) 0 0
\(639\) −429.869 223.019i −0.672721 0.349013i
\(640\) 0 0
\(641\) −265.484 403.649i −0.414172 0.629718i 0.566803 0.823853i \(-0.308180\pi\)
−0.980975 + 0.194136i \(0.937810\pi\)
\(642\) 0 0
\(643\) −259.780 348.945i −0.404012 0.542683i 0.552829 0.833295i \(-0.313548\pi\)
−0.956841 + 0.290612i \(0.906141\pi\)
\(644\) 0 0
\(645\) −188.269 + 73.3639i −0.291890 + 0.113743i
\(646\) 0 0
\(647\) 1108.99i 1.71405i 0.515275 + 0.857025i \(0.327690\pi\)
−0.515275 + 0.857025i \(0.672310\pi\)
\(648\) 0 0
\(649\) −5.91520 −0.00911432
\(650\) 0 0
\(651\) 928.741 + 142.289i 1.42664 + 0.218569i
\(652\) 0 0
\(653\) −376.255 + 280.112i −0.576195 + 0.428961i −0.845409 0.534119i \(-0.820643\pi\)
0.269214 + 0.963080i \(0.413236\pi\)
\(654\) 0 0
\(655\) 160.992 105.886i 0.245790 0.161658i
\(656\) 0 0
\(657\) 554.246 + 424.070i 0.843601 + 0.645464i
\(658\) 0 0
\(659\) −0.732907 + 6.27042i −0.00111215 + 0.00951506i −0.993783 0.111334i \(-0.964488\pi\)
0.992671 + 0.120849i \(0.0385617\pi\)
\(660\) 0 0
\(661\) −311.588 1040.78i −0.471388 1.57455i −0.781537 0.623859i \(-0.785564\pi\)
0.310149 0.950688i \(-0.399621\pi\)
\(662\) 0 0
\(663\) 866.890 + 542.612i 1.30753 + 0.818420i
\(664\) 0 0
\(665\) 1422.10 + 250.754i 2.13849 + 0.377074i
\(666\) 0 0
\(667\) 50.7953 + 288.074i 0.0761549 + 0.431896i
\(668\) 0 0
\(669\) 670.823 307.452i 1.00272 0.459570i
\(670\) 0 0
\(671\) 6.99864 10.6409i 0.0104302 0.0158583i
\(672\) 0 0
\(673\) 305.461 1020.31i 0.453879 1.51606i −0.358835 0.933401i \(-0.616826\pi\)
0.812715 0.582662i \(-0.197989\pi\)
\(674\) 0 0
\(675\) −1276.87 + 1379.01i −1.89166 + 2.04298i
\(676\) 0 0
\(677\) 54.6182 51.5296i 0.0806768 0.0761146i −0.644847 0.764312i \(-0.723079\pi\)
0.725524 + 0.688197i \(0.241598\pi\)
\(678\) 0 0
\(679\) 26.6666 457.847i 0.0392733 0.674296i
\(680\) 0 0
\(681\) −1107.97 + 289.079i −1.62697 + 0.424492i
\(682\) 0 0
\(683\) 244.956 673.012i 0.358648 0.985376i −0.620852 0.783928i \(-0.713213\pi\)
0.979499 0.201448i \(-0.0645647\pi\)
\(684\) 0 0
\(685\) 2130.13 775.304i 3.10968 1.13183i
\(686\) 0 0
\(687\) −142.560 1020.01i −0.207511 1.48472i
\(688\) 0 0
\(689\) −114.955 + 485.034i −0.166843 + 0.703967i
\(690\) 0 0
\(691\) −388.694 901.094i −0.562509 1.30404i −0.927775 0.373140i \(-0.878281\pi\)
0.365266 0.930903i \(-0.380978\pi\)
\(692\) 0 0
\(693\) −11.0468 + 9.02430i −0.0159405 + 0.0130221i
\(694\) 0 0
\(695\) −51.7024 + 3.01132i −0.0743919 + 0.00433283i
\(696\) 0 0
\(697\) −207.229 + 480.412i −0.297316 + 0.689257i
\(698\) 0 0
\(699\) −231.040 1157.33i −0.330530 1.65569i
\(700\) 0 0
\(701\) −298.741 172.478i −0.426163 0.246046i 0.271547 0.962425i \(-0.412465\pi\)
−0.697711 + 0.716379i \(0.745798\pi\)
\(702\) 0 0
\(703\) 514.490 + 891.122i 0.731849 + 1.26760i
\(704\) 0 0
\(705\) 34.7834 + 1545.05i 0.0493382 + 2.19156i
\(706\) 0 0
\(707\) 118.692 + 1015.48i 0.167881 + 1.43632i
\(708\) 0 0
\(709\) 1193.71 + 599.502i 1.68365 + 0.845559i 0.992416 + 0.122926i \(0.0392277\pi\)
0.691231 + 0.722634i \(0.257069\pi\)
\(710\) 0 0
\(711\) −296.011 609.267i −0.416330 0.856915i
\(712\) 0 0
\(713\) 775.555 + 577.380i 1.08774 + 0.809789i
\(714\) 0 0
\(715\) 29.9516 31.7469i 0.0418904 0.0444012i
\(716\) 0 0
\(717\) −301.603 64.3480i −0.420646 0.0897462i
\(718\) 0 0
\(719\) −211.094 + 251.572i −0.293594 + 0.349892i −0.892597 0.450855i \(-0.851119\pi\)
0.599003 + 0.800747i \(0.295564\pi\)
\(720\) 0 0
\(721\) −395.065 + 331.499i −0.547940 + 0.459776i
\(722\) 0 0
\(723\) −288.715 + 608.663i −0.399329 + 0.841857i
\(724\) 0 0
\(725\) 417.631 + 831.573i 0.576043 + 1.14700i
\(726\) 0 0
\(727\) −409.726 + 97.1068i −0.563584 + 0.133572i −0.502526 0.864562i \(-0.667596\pi\)
−0.0610585 + 0.998134i \(0.519448\pi\)
\(728\) 0 0
\(729\) 446.186 + 576.506i 0.612052 + 0.790818i
\(730\) 0 0
\(731\) −27.1290 114.466i −0.0371122 0.156589i
\(732\) 0 0
\(733\) −251.183 + 126.149i −0.342677 + 0.172099i −0.611811 0.791004i \(-0.709559\pi\)
0.269134 + 0.963103i \(0.413263\pi\)
\(734\) 0 0
\(735\) 32.5587 + 15.4440i 0.0442976 + 0.0210122i
\(736\) 0 0
\(737\) −10.0254 11.9478i −0.0136030 0.0162114i
\(738\) 0 0
\(739\) 255.809 + 214.649i 0.346155 + 0.290459i 0.799244 0.601007i \(-0.205233\pi\)
−0.453089 + 0.891465i \(0.649678\pi\)
\(740\) 0 0
\(741\) −263.116 + 1233.24i −0.355082 + 1.66429i
\(742\) 0 0
\(743\) 877.768 + 828.131i 1.18138 + 1.11458i 0.991137 + 0.132841i \(0.0424099\pi\)
0.190246 + 0.981737i \(0.439072\pi\)
\(744\) 0 0
\(745\) −1167.78 + 1568.59i −1.56748 + 2.10550i
\(746\) 0 0
\(747\) −903.590 + 439.007i −1.20963 + 0.587693i
\(748\) 0 0
\(749\) −431.057 + 858.305i −0.575510 + 1.14593i
\(750\) 0 0
\(751\) 63.6304 7.43733i 0.0847275 0.00990323i −0.0736235 0.997286i \(-0.523456\pi\)
0.158351 + 0.987383i \(0.449382\pi\)
\(752\) 0 0
\(753\) 289.433 6.51593i 0.384373 0.00865330i
\(754\) 0 0
\(755\) −999.772 + 577.219i −1.32420 + 0.764528i
\(756\) 0 0
\(757\) −77.6595 + 134.510i −0.102589 + 0.177689i −0.912750 0.408518i \(-0.866046\pi\)
0.810162 + 0.586206i \(0.199379\pi\)
\(758\) 0 0
\(759\) −14.3947 + 2.87364i −0.0189653 + 0.00378609i
\(760\) 0 0
\(761\) 30.1167 + 12.9911i 0.0395751 + 0.0170710i 0.415775 0.909467i \(-0.363510\pi\)
−0.376200 + 0.926538i \(0.622770\pi\)
\(762\) 0 0
\(763\) −60.3978 1036.99i −0.0791583 1.35910i
\(764\) 0 0
\(765\) −940.846 1151.70i −1.22986 1.50549i
\(766\) 0 0
\(767\) −487.404 + 210.246i −0.635468 + 0.274114i
\(768\) 0 0
\(769\) −44.2413 10.4854i −0.0575309 0.0136351i 0.201750 0.979437i \(-0.435337\pi\)
−0.259281 + 0.965802i \(0.583485\pi\)
\(770\) 0 0
\(771\) −476.067 + 66.5369i −0.617467 + 0.0862995i
\(772\) 0 0
\(773\) 272.957 + 749.942i 0.353113 + 0.970171i 0.981364 + 0.192159i \(0.0615491\pi\)
−0.628251 + 0.778011i \(0.716229\pi\)
\(774\) 0 0
\(775\) 2890.32 + 1051.99i 3.72944 + 1.35741i
\(776\) 0 0
\(777\) 263.697 + 1010.69i 0.339379 + 1.30075i
\(778\) 0 0
\(779\) −644.017 37.5097i −0.826722 0.0481511i
\(780\) 0 0
\(781\) −8.25719 8.75211i −0.0105726 0.0112063i
\(782\) 0 0
\(783\) 344.809 106.752i 0.440369 0.136337i
\(784\) 0 0
\(785\) 991.529 + 296.844i 1.26309 + 0.378146i
\(786\) 0 0
\(787\) 853.273 + 561.207i 1.08421 + 0.713096i 0.960236 0.279189i \(-0.0900657\pi\)
0.123974 + 0.992285i \(0.460436\pi\)
\(788\) 0 0
\(789\) −546.024 1191.36i −0.692045 1.50996i
\(790\) 0 0
\(791\) 118.603 20.9129i 0.149941 0.0264386i
\(792\) 0 0
\(793\) 198.465 1125.55i 0.250271 1.41936i
\(794\) 0 0