Properties

Label 324.3.o.a.65.15
Level $324$
Weight $3$
Character 324.65
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 65.15
Character \(\chi\) \(=\) 324.65
Dual form 324.3.o.a.5.15

$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{31}{54}\right)\)

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 −0.918874 0.394552i \(-0.870900\pi\)
−0.641513 0.767112i \(-0.721693\pi\)
\(6\) 0 0
\(7\) 5.92166 + 3.89473i 0.845951 + 0.556391i 0.896861 0.442313i \(-0.145842\pi\)
−0.0509101 + 0.998703i \(0.516212\pi\)
\(8\) 0 0
\(9\) −1.96012 + 8.78396i −0.217791 + 0.975995i
\(10\) 0 0
\(11\) 0.0259603 + 0.222104i 0.00236003 + 0.0201913i 0.994367 0.105991i \(-0.0338016\pi\)
−0.992007 + 0.126183i \(0.959727\pi\)
\(12\) 0 0
\(13\) −5.75523 + 19.2238i −0.442710 + 1.47876i 0.387796 + 0.921745i \(0.373237\pi\)
−0.830506 + 0.557010i \(0.811949\pi\)
\(14\) 0 0
\(15\) −1.04058 29.1612i −0.0693722 1.94408i
\(16\) 0 0
\(17\) −16.7302 + 2.94999i −0.984131 + 0.173529i −0.642484 0.766299i \(-0.722096\pi\)
−0.341648 + 0.939828i \(0.610985\pi\)
\(18\) 0 0
\(19\) −3.63734 + 20.6284i −0.191439 + 1.08571i 0.725960 + 0.687737i \(0.241396\pi\)
−0.917399 + 0.397969i \(0.869715\pi\)
\(20\) 0 0
\(21\) 1.99252 + 21.1694i 0.0948821 + 1.00807i
\(22\) 0 0
\(23\) 12.0237 + 18.2812i 0.522770 + 0.794833i 0.996300 0.0859449i \(-0.0273909\pi\)
−0.473530 + 0.880778i \(0.657021\pi\)
\(24\) 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 0.500107 0.865963i \(-0.333294\pi\)
−0.835420 + 0.549613i \(0.814775\pi\)
\(30\) 0 0
\(31\) −2.56933 44.1136i −0.0828815 1.42302i −0.741707 0.670725i \(-0.765983\pi\)
0.658825 0.752296i \(-0.271054\pi\)
\(32\) 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 −0.368012 0.929821i \(-0.619961\pi\)
−0.879591 + 0.475731i \(0.842184\pi\)
\(38\) 0 0
\(39\) −55.7997 + 22.5940i −1.43076 + 0.579334i
\(40\) 0 0
\(41\) 7.10244 + 29.9675i 0.173230 + 0.730916i 0.988423 + 0.151725i \(0.0484830\pi\)
−0.815192 + 0.579190i \(0.803369\pi\)
\(42\) 0 0
\(43\) 2.74269 6.35827i 0.0637835 0.147867i −0.883343 0.468727i \(-0.844713\pi\)
0.947127 + 0.320860i \(0.103972\pi\)
\(44\) 0 0
\(45\) 66.3128 57.1468i 1.47362 1.26993i
\(46\) 0 0
\(47\) 52.8732 + 3.07951i 1.12496 + 0.0655216i 0.610518 0.792002i \(-0.290961\pi\)
0.514444 + 0.857524i \(0.327998\pi\)
\(48\) 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 −0.689025 0.724738i \(-0.741961\pi\)
0.283129 + 0.959082i \(0.408628\pi\)
\(54\) 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 0.941935 + 0.335796i \(0.109005\pi\)
−0.993985 + 0.109519i \(0.965069\pi\)
\(60\) 0 0
\(61\) 50.8973 25.5616i 0.834381 0.419042i 0.0203007 0.999794i \(-0.493538\pi\)
0.814081 + 0.580752i \(0.197241\pi\)
\(62\) 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 0.978267 0.207349i \(-0.0664836\pi\)
−0.263879 + 0.964556i \(0.585002\pi\)
\(68\) 0 0
\(69\) −20.2370 + 62.4451i −0.293291 + 0.905002i
\(70\) 0 0
\(71\) 34.5875 + 41.2198i 0.487148 + 0.580560i 0.952490 0.304571i \(-0.0985130\pi\)
−0.465342 + 0.885131i \(0.654069\pi\)
\(72\) 0 0
\(73\) −59.4000 49.8425i −0.813699 0.682774i 0.137789 0.990462i \(-0.456001\pi\)
−0.951488 + 0.307687i \(0.900445\pi\)
\(74\) 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 0.666280 0.745702i \(-0.267886\pi\)
0.260739 + 0.965409i \(0.416034\pi\)
\(80\) 0 0
\(81\) −73.3158 34.4353i −0.905134 0.425127i
\(82\) 0 0
\(83\) −25.7416 + 108.612i −0.310140 + 1.30858i 0.565151 + 0.824987i \(0.308818\pi\)
−0.875291 + 0.483596i \(0.839330\pi\)
\(84\) 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 −0.223085 0.974799i \(-0.571613\pi\)
0.998728 + 0.0504239i \(0.0160572\pi\)
\(90\) 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 0.955367 0.295420i \(-0.0954596\pi\)
−0.557012 + 0.830505i \(0.688052\pi\)
\(98\) 0 0
\(99\) −2.00184 0.207318i −0.0202206 0.00209412i
\(100\) 0 0
\(101\) −64.7388 128.906i −0.640979 1.27629i −0.946068 0.323970i \(-0.894982\pi\)
0.305089 0.952324i \(-0.401314\pi\)
\(102\) 0 0
\(103\) −72.2711 8.44728i −0.701661 0.0820124i −0.242221 0.970221i \(-0.577876\pi\)
−0.459440 + 0.888209i \(0.651950\pi\)
\(104\) 0 0
\(105\) 107.413 176.736i 1.02298 1.68320i
\(106\) 0 0
\(107\) −117.357 67.7563i −1.09680 0.633236i −0.161419 0.986886i \(-0.551607\pi\)
−0.935378 + 0.353650i \(0.884940\pi\)
\(108\) 0 0
\(109\) 73.2786 + 126.922i 0.672280 + 1.16442i 0.977256 + 0.212064i \(0.0680184\pi\)
−0.304975 + 0.952360i \(0.598648\pi\)
\(110\) 0 0
\(111\) −47.2744 139.583i −0.425895 1.25751i
\(112\) 0 0
\(113\) 15.6022 6.73014i 0.138073 0.0595588i −0.325922 0.945397i \(-0.605675\pi\)
0.463995 + 0.885838i \(0.346416\pi\)
\(114\) 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 0.516491 0.856293i \(-0.327238\pi\)
0.946069 + 0.323965i \(0.105016\pi\)
\(128\) 0 0
\(129\) 20.0301 5.50856i 0.155272 0.0427020i
\(130\) 0 0
\(131\) −19.7774 + 1.15190i −0.150972 + 0.00879313i −0.133465 0.991054i \(-0.542610\pi\)
−0.0175078 + 0.999847i \(0.505573\pi\)
\(132\) 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 −0.965655 0.259829i \(-0.916334\pi\)
−0.664015 + 0.747720i \(0.731149\pi\)
\(138\) 0 0
\(139\) 4.44861 2.92590i 0.0320044 0.0210496i −0.533406 0.845859i \(-0.679088\pi\)
0.565410 + 0.824810i \(0.308718\pi\)
\(140\) 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 0.858023 0.513612i \(-0.171693\pi\)
0.434633 + 0.900608i \(0.356878\pi\)
\(150\) 0 0
\(151\) 117.886 13.7789i 0.780703 0.0912511i 0.283600 0.958943i \(-0.408471\pi\)
0.497103 + 0.867692i \(0.334397\pi\)
\(152\) 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 −0.957028 0.289994i \(-0.906347\pi\)
0.552290 + 0.833652i \(0.313754\pi\)
\(158\) 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 0.252620 0.967565i \(-0.418708\pi\)
−0.854465 + 0.519509i \(0.826115\pi\)
\(168\) 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 −0.979564 0.201134i \(-0.935537\pi\)
0.906775 0.421615i \(-0.138537\pi\)
\(174\) 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 0.335257 0.942127i \(-0.391177\pi\)
0.637264 + 0.770645i \(0.280066\pi\)
\(180\) 0 0
\(181\) 15.6742 88.8926i 0.0865976 0.491120i −0.910403 0.413723i \(-0.864228\pi\)
0.997000 0.0773965i \(-0.0246607\pi\)
\(182\) 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 0.660557 0.750776i \(-0.270320\pi\)
−0.711098 + 0.703093i \(0.751802\pi\)
\(192\) 0 0
\(193\) 10.8605 + 186.468i 0.0562721 + 0.966155i 0.901781 + 0.432194i \(0.142260\pi\)
−0.845509 + 0.533962i \(0.820703\pi\)
\(194\) 0 0
\(195\) 566.579 + 147.826i 2.90553 + 0.758081i
\(196\) 0 0
\(197\) 14.6800 + 40.3330i 0.0745179 + 0.204736i 0.971359 0.237617i \(-0.0763662\pi\)
−0.896841 + 0.442353i \(0.854144\pi\)
\(198\) 0 0
\(199\) −189.630 69.0198i −0.952917 0.346833i −0.181663 0.983361i \(-0.558148\pi\)
−0.771254 + 0.636528i \(0.780370\pi\)
\(200\) 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 0.783326 0.621612i \(-0.213522\pi\)
−0.989695 + 0.143195i \(0.954263\pi\)
\(212\) 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 0.118475 0.992957i \(-0.462199\pi\)
0.867222 + 0.497921i \(0.165903\pi\)
\(224\) 0 0
\(225\) −624.867 + 44.6521i −2.77719 + 0.198454i
\(226\) 0 0
\(227\) −306.159 + 227.927i −1.34872 + 1.00408i −0.351015 + 0.936370i \(0.614163\pi\)
−0.997705 + 0.0677147i \(0.978429\pi\)
\(228\) 0 0
\(229\) 235.591 + 249.712i 1.02878 + 1.09045i 0.995852 + 0.0909882i \(0.0290026\pi\)
0.0329307 + 0.999458i \(0.489516\pi\)
\(230\) 0 0
\(231\) −4.65009 + 0.992113i −0.0201303 + 0.00429486i
\(232\) 0 0
\(233\) 252.865 + 301.353i 1.08526 + 1.29336i 0.953273 + 0.302110i \(0.0976909\pi\)
0.131986 + 0.991252i \(0.457865\pi\)
\(234\) 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 −0.969240 0.246116i \(-0.920846\pi\)
0.776206 + 0.630480i \(0.217142\pi\)
\(240\) 0 0
\(241\) −218.503 51.7861i −0.906650 0.214880i −0.249265 0.968435i \(-0.580189\pi\)
−0.657385 + 0.753555i \(0.728337\pi\)
\(242\) 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 −0.628191 0.778059i \(-0.716204\pi\)
0.875323 + 0.483538i \(0.160649\pi\)
\(252\) 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 −0.878793 0.477203i \(-0.841651\pi\)
0.425298 + 0.905053i \(0.360169\pi\)
\(258\) 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 0.870501 + 0.492166i \(0.163795\pi\)
−0.125049 + 0.992151i \(0.539909\pi\)
\(264\) 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 −0.223712 0.974655i \(-0.571817\pi\)
−0.955932 + 0.293587i \(0.905151\pi\)
\(270\) 0 0
\(271\) 240.973 + 417.378i 0.889200 + 1.54014i 0.840822 + 0.541311i \(0.182072\pi\)
0.0483780 + 0.998829i \(0.484595\pi\)
\(272\) 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 −0.938616 0.344962i \(-0.887892\pi\)
0.972318 0.233663i \(-0.0750713\pi\)
\(278\) 0 0
\(279\) 392.529 + 63.8993i 1.40691 + 0.229030i
\(280\) 0 0
\(281\) 180.072 + 77.6754i 0.640825 + 0.276425i 0.691595 0.722285i \(-0.256908\pi\)
−0.0507699 + 0.998710i \(0.516168\pi\)
\(282\) 0 0
\(283\) −41.1308 + 9.74818i −0.145339 + 0.0344459i −0.302641 0.953105i \(-0.597868\pi\)
0.157303 + 0.987550i \(0.449720\pi\)
\(284\) 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 0.190259 0.981734i \(-0.439067\pi\)
0.302945 + 0.953008i \(0.402030\pi\)
\(294\) 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 0.999900 + 0.0141144i \(0.00449292\pi\)
−0.934772 + 0.355249i \(0.884396\pi\)
\(308\) 0 0
\(309\) −115.817 185.032i −0.374811 0.598808i
\(310\) 0 0
\(311\) −185.156 55.4321i −0.595357 0.178238i −0.0250730 0.999686i \(-0.507982\pi\)
−0.570284 + 0.821447i \(0.693167\pi\)
\(312\) 0 0
\(313\) 260.741 30.4762i 0.833038 0.0973681i 0.311127 0.950368i \(-0.399294\pi\)
0.521911 + 0.853000i \(0.325219\pi\)
\(314\) 0 0
\(315\) 615.253 80.1331i 1.95318 0.254391i
\(316\) 0 0
\(317\) −66.9169 + 101.742i −0.211094 + 0.320953i −0.925478 0.378801i \(-0.876337\pi\)
0.714384 + 0.699754i \(0.246707\pi\)
\(318\) 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 0.863332 0.504637i \(-0.168374\pi\)
−0.121417 + 0.992602i \(0.538744\pi\)
\(332\) 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 −0.983683 0.179912i \(-0.942419\pi\)
0.920718 + 0.390228i \(0.127604\pi\)
\(338\) 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 0.828308 0.560272i \(-0.189304\pi\)
−0.842527 + 0.538654i \(0.818933\pi\)
\(348\) 0 0
\(349\) 71.6586 + 239.356i 0.205326 + 0.685835i 0.997175 + 0.0751184i \(0.0239335\pi\)
−0.791849 + 0.610717i \(0.790881\pi\)
\(350\) 0 0
\(351\) −89.0908 534.430i −0.253820 1.52259i
\(352\) 0 0
\(353\) 433.435 + 408.925i 1.22786 + 1.15843i 0.981951 + 0.189135i \(0.0605685\pi\)
0.245911 + 0.969292i \(0.420913\pi\)
\(354\) 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 0.997615 0.0690264i \(-0.0219893\pi\)
−0.808587 + 0.588377i \(0.799767\pi\)
\(360\) 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 0.678181 + 0.734895i \(0.262769\pi\)
−0.999939 + 0.0110248i \(0.996491\pi\)
\(368\) 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 1.00000 0.000560420i \(-0.000178387\pi\)
−0.686649 + 0.726989i \(0.740919\pi\)
\(374\) 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 −0.817681 0.575671i \(-0.804741\pi\)
0.907386 + 0.420297i \(0.138074\pi\)
\(380\) 0 0
\(381\) 506.747 + 307.982i 1.33005 + 0.808352i
\(382\) 0 0
\(383\) −28.1065 + 240.466i −0.0733851 + 0.627850i 0.905631 + 0.424067i \(0.139398\pi\)
−0.979016 + 0.203783i \(0.934676\pi\)
\(384\) 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 −0.895111 0.445844i \(-0.852904\pi\)
0.170393 + 0.985376i \(0.445496\pi\)
\(390\) 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 −0.996343 0.0854486i \(-0.972768\pi\)
−0.257164 0.966368i \(-0.582788\pi\)
\(398\) 0 0
\(399\) −443.939 35.8979i −1.11263 0.0899696i
\(400\) 0 0
\(401\) −1.55912 + 3.10446i −0.00388808 + 0.00774180i −0.895568 0.444924i \(-0.853231\pi\)
0.891680 + 0.452666i \(0.149527\pi\)
\(402\) 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 0.766707 0.641997i \(-0.221894\pi\)
−0.0571155 + 0.998368i \(0.518190\pi\)
\(410\) 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 −0.121576 + 0.992582i \(0.538795\pi\)
−0.997972 + 0.0636571i \(0.979724\pi\)
\(420\) 0 0
\(421\) 10.0386 + 13.4842i 0.0238446 + 0.0320289i 0.813886 0.581025i \(-0.197348\pi\)
−0.790041 + 0.613054i \(0.789941\pi\)
\(422\) 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 0.152887 0.988244i \(-0.451143\pi\)
−0.779401 + 0.626526i \(0.784476\pi\)
\(432\) 0 0
\(433\) 67.0785 + 116.183i 0.154916 + 0.268322i 0.933028 0.359803i \(-0.117156\pi\)
−0.778113 + 0.628125i \(0.783823\pi\)
\(434\) 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 −0.866317 0.499494i \(-0.833519\pi\)
0.918447 0.395543i \(-0.129444\pi\)
\(440\) 0 0
\(441\) −10.9194 + 2.07391i −0.0247607 + 0.00470275i
\(442\) 0 0
\(443\) 617.609 + 266.410i 1.39415 + 0.601378i 0.954884 0.296979i \(-0.0959791\pi\)
0.439266 + 0.898357i \(0.355238\pi\)
\(444\) 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 −0.472019 0.881588i \(-0.656475\pi\)
0.928262 0.371928i \(-0.121303\pi\)
\(450\) 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 −0.464620 0.885510i \(-0.653809\pi\)
0.911027 + 0.412346i \(0.135290\pi\)
\(458\) 0 0
\(459\) 370.466 270.456i 0.807116 0.589228i
\(460\) 0 0
\(461\) 516.453 154.616i 1.12029 0.335392i 0.327477 0.944859i \(-0.393802\pi\)
0.792811 + 0.609467i \(0.208617\pi\)
\(462\) 0 0
\(463\) 434.060 285.485i 0.937494 0.616599i 0.0138717 0.999904i \(-0.495584\pi\)
0.923622 + 0.383304i \(0.125214\pi\)
\(464\) 0 0
\(465\) −1283.73 + 120.829i −2.76072 + 0.259847i
\(466\) 0 0
\(467\) 630.053 + 111.095i 1.34915 + 0.237891i 0.801088 0.598547i \(-0.204255\pi\)
0.548061 + 0.836438i \(0.315366\pi\)
\(468\) 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 −0.977592 0.210510i \(-0.932488\pi\)
0.580498 + 0.814262i \(0.302858\pi\)
\(480\) 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 0.759098 0.650976i \(-0.225640\pi\)
−0.405917 + 0.913910i \(0.633048\pi\)
\(492\) 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 −0.222059 0.975033i \(-0.571278\pi\)
0.721317 0.692605i \(-0.243537\pi\)
\(500\) 0 0
\(501\) −13.4053 375.669i −0.0267570 0.749838i
\(502\) 0 0
\(503\) −175.584 + 30.9602i −0.349073 + 0.0615510i −0.345436 0.938442i \(-0.612269\pi\)
−0.00363740 + 0.999993i \(0.501158\pi\)
\(504\) 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 0.757435 0.652910i \(-0.226452\pi\)
−0.899517 + 0.436885i \(0.856082\pi\)
\(510\) 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 0.944508 0.328488i \(-0.106539\pi\)
−0.934683 + 0.355482i \(0.884317\pi\)
\(522\) 0 0
\(523\) −106.983 38.9386i −0.204556 0.0744524i 0.237710 0.971336i \(-0.423603\pi\)
−0.442266 + 0.896884i \(0.645825\pi\)
\(524\) 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 −0.638292 0.769795i \(-0.720359\pi\)
0.985808 + 0.167879i \(0.0536919\pi\)
\(542\) 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 −0.132448 0.991190i \(-0.542284\pi\)
0.715964 + 0.698137i \(0.245988\pi\)
\(548\) 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 0.776308 0.630353i \(-0.217090\pi\)
−0.755581 + 0.655055i \(0.772646\pi\)
\(558\) 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 −0.321571 0.946885i \(-0.604211\pi\)
0.951548 0.307501i \(-0.0994927\pi\)
\(564\) 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 −0.950447 0.310886i \(-0.899374\pi\)
0.988876 + 0.148742i \(0.0475225\pi\)
\(570\) 0 0
\(571\) −894.561 449.265i −1.56666 0.786804i −0.567330 0.823491i \(-0.692023\pi\)
−0.999327 + 0.0366865i \(0.988320\pi\)
\(572\) 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 −0.368772 0.929520i \(-0.620222\pi\)
0.851362 + 0.524579i \(0.175777\pi\)
\(578\) 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 0.773451 0.633856i \(-0.218529\pi\)
−0.970303 + 0.241891i \(0.922232\pi\)
\(588\) 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 0.999936 + 0.0113533i \(0.00361395\pi\)
0.509800 + 0.860293i \(0.329719\pi\)
\(594\) 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 −0.151801 0.988411i \(-0.548507\pi\)
0.614772 + 0.788705i \(0.289248\pi\)
\(600\) 0 0
\(601\) −32.1314 + 551.675i −0.0534632 + 0.917928i 0.859819 + 0.510600i \(0.170577\pi\)
−0.913282 + 0.407328i \(0.866460\pi\)
\(602\) 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 0.0448379 0.998994i \(-0.485723\pi\)
0.488416 + 0.872611i \(0.337575\pi\)
\(608\) 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 −0.353208 0.935545i \(-0.614909\pi\)
0.330784 + 0.943707i \(0.392687\pi\)
\(614\) 0 0
\(615\) 866.500 238.300i 1.40894 0.387479i
\(616\) 0 0
\(617\) −414.972 + 24.1694i −0.672564 + 0.0391724i −0.391029 0.920378i \(-0.627881\pi\)
−0.281535 + 0.959551i \(0.590844\pi\)
\(618\) 0 0
\(619\) −287.903 + 305.159i −0.465109 + 0.492987i −0.916889 0.399143i \(-0.869308\pi\)
0.451780 + 0.892130i \(0.350789\pi\)
\(620\) 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 0.998852 0.0478930i \(-0.0152506\pi\)
−0.954995 + 0.296623i \(0.904140\pi\)
\(632\) 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 −0.980975 0.194136i \(-0.937810\pi\)
0.566803 + 0.823853i \(0.308180\pi\)
\(642\) 0 0
\(643\) −259.780 + 348.945i −0.404012 + 0.542683i −0.956841 0.290612i \(-0.906141\pi\)
0.552829 + 0.833295i \(0.313548\pi\)
\(644\) 0 0
\(645\) −188.269 73.3639i −0.291890 0.113743i
\(646\) 0 0
\(647\) 1108.99i 1.71405i −0.515275 0.857025i \(-0.672310\pi\)
0.515275 0.857025i \(-0.327690\pi\)
\(648\) 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 0.269214 0.963080i \(-0.413236\pi\)
−0.845409 + 0.534119i \(0.820643\pi\)
\(654\) 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 0.992671 0.120849i \(-0.0385617\pi\)
−0.993783 + 0.111334i \(0.964488\pi\)
\(660\) 0 0
\(661\) −311.588 + 1040.78i −0.471388 + 1.57455i 0.310149 + 0.950688i \(0.399621\pi\)
−0.781537 + 0.623859i \(0.785564\pi\)
\(662\) 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 0.812715 + 0.582662i \(0.197989\pi\)
−0.358835 + 0.933401i \(0.616826\pi\)
\(674\) 0 0
\(675\) −1276.87 1379.01i −1.89166 2.04298i
\(676\) 0 0
\(677\) 54.6182 + 51.5296i 0.0806768 + 0.0761146i 0.725524 0.688197i \(-0.241598\pi\)
−0.644847 + 0.764312i \(0.723079\pi\)
\(678\) 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 0.979499 + 0.201448i \(0.0645647\pi\)
−0.620852 + 0.783928i \(0.713213\pi\)
\(684\) 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 0.365266 + 0.930903i \(0.380978\pi\)
−0.927775 + 0.373140i \(0.878281\pi\)
\(692\) 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 −0.697711 0.716379i \(-0.745798\pi\)
0.271547 + 0.962425i \(0.412465\pi\)
\(702\) 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 0.691231 0.722634i \(-0.257069\pi\)
0.992416 0.122926i \(-0.0392277\pi\)
\(710\) 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 0.599003 0.800747i \(-0.295564\pi\)
−0.892597 + 0.450855i \(0.851119\pi\)
\(720\) 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 −0.0610585 0.998134i \(-0.519448\pi\)
−0.502526 + 0.864562i \(0.667596\pi\)
\(728\) 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 0.269134 0.963103i \(-0.413263\pi\)
−0.611811 + 0.791004i \(0.709559\pi\)
\(734\) 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 −0.453089 0.891465i \(-0.649678\pi\)
0.799244 + 0.601007i \(0.205233\pi\)
\(740\) 0 0
\(741\) −263.116 1233.24i −0.355082 1.66429i
\(742\) 0 0
\(743\) 877.768 828.131i 1.18138 1.11458i 0.190246 0.981737i \(-0.439072\pi\)
0.991137 0.132841i \(-0.0424099\pi\)
\(744\) 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 0.158351 0.987383i \(-0.449382\pi\)
−0.0736235 + 0.997286i \(0.523456\pi\)
\(752\) 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 0.810162 0.586206i \(-0.199379\pi\)
−0.912750 + 0.408518i \(0.866046\pi\)
\(758\) 0 0
\(759\) −14.3947 2.87364i −0.0189653 0.00378609i
\(760\) 0 0
\(761\) 30.1167 12.9911i 0.0395751 0.0170710i −0.376200 0.926538i \(-0.622770\pi\)
0.415775 + 0.909467i \(0.363510\pi\)
\(762\) 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 −0.259281 0.965802i \(-0.583485\pi\)
0.201750 + 0.979437i \(0.435337\pi\)
\(770\) 0 0
\(771\) −476.067 66.5369i −0.617467 0.0862995i
\(772\) 0 0
\(773\) 272.957 749.942i 0.353113 0.970171i −0.628251 0.778011i \(-0.716229\pi\)
0.981364 0.192159i \(-0.0615491\pi\)
\(774\) 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 0.123974 0.992285i \(-0.460436\pi\)
0.960236 + 0.279189i \(0.0900657\pi\)
\(788\) 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