Properties

Label 108.5.k.a.29.7
Level 108
Weight 5
Character 108.29
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.7
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.21143 - 8.91810i) q^{3} +(1.79646 + 2.14093i) q^{5} +(-63.3056 + 23.0413i) q^{7} +(-78.0649 - 21.6073i) q^{9} +O(q^{10})\) \(q+(1.21143 - 8.91810i) q^{3} +(1.79646 + 2.14093i) q^{5} +(-63.3056 + 23.0413i) q^{7} +(-78.0649 - 21.6073i) q^{9} +(-23.1554 + 27.5956i) q^{11} +(8.29634 + 47.0509i) q^{13} +(21.2693 - 13.4274i) q^{15} +(0.309929 - 0.178937i) q^{17} +(-163.845 + 283.789i) q^{19} +(128.795 + 592.478i) q^{21} +(-242.445 + 666.113i) q^{23} +(107.174 - 607.813i) q^{25} +(-287.266 + 670.014i) q^{27} +(-1510.88 - 266.409i) q^{29} +(547.514 + 199.279i) q^{31} +(218.049 + 239.933i) q^{33} +(-163.056 - 94.1403i) q^{35} +(-343.789 - 595.460i) q^{37} +(429.655 - 16.9887i) q^{39} +(-498.566 + 87.9106i) q^{41} +(-1251.43 - 1050.07i) q^{43} +(-93.9804 - 205.948i) q^{45} +(453.321 + 1245.49i) q^{47} +(1637.42 - 1373.96i) q^{49} +(-1.22032 - 2.98074i) q^{51} -1435.60i q^{53} -100.678 q^{55} +(2332.37 + 1804.98i) q^{57} +(-989.454 - 1179.18i) q^{59} +(4824.54 - 1755.99i) q^{61} +(5439.80 - 430.858i) q^{63} +(-85.8289 + 102.287i) q^{65} +(-474.440 - 2690.68i) q^{67} +(5646.75 + 2969.10i) q^{69} +(-4492.65 + 2593.83i) q^{71} +(4367.67 - 7565.02i) q^{73} +(-5290.70 - 1692.11i) q^{75} +(830.030 - 2280.49i) q^{77} +(814.469 - 4619.08i) q^{79} +(5627.25 + 3373.54i) q^{81} +(-9403.81 - 1658.15i) q^{83} +(0.939867 + 0.342084i) q^{85} +(-4206.18 + 13151.4i) q^{87} +(-9672.46 - 5584.40i) q^{89} +(-1609.32 - 2787.43i) q^{91} +(2440.46 - 4641.37i) q^{93} +(-901.914 + 159.032i) q^{95} +(1339.14 + 1123.67i) q^{97} +(2403.89 - 1653.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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
\(3\) 1.21143 8.91810i 0.134603 0.990900i
\(4\) 0 0
\(5\) 1.79646 + 2.14093i 0.0718583 + 0.0856374i 0.800776 0.598964i \(-0.204421\pi\)
−0.728918 + 0.684601i \(0.759976\pi\)
\(6\) 0 0
\(7\) −63.3056 + 23.0413i −1.29195 + 0.470232i −0.894367 0.447334i \(-0.852373\pi\)
−0.397584 + 0.917566i \(0.630151\pi\)
\(8\) 0 0
\(9\) −78.0649 21.6073i −0.963764 0.266757i
\(10\) 0 0
\(11\) −23.1554 + 27.5956i −0.191367 + 0.228063i −0.853193 0.521595i \(-0.825337\pi\)
0.661826 + 0.749657i \(0.269782\pi\)
\(12\) 0 0
\(13\) 8.29634 + 47.0509i 0.0490908 + 0.278408i 0.999465 0.0327008i \(-0.0104108\pi\)
−0.950374 + 0.311109i \(0.899300\pi\)
\(14\) 0 0
\(15\) 21.2693 13.4274i 0.0945304 0.0596773i
\(16\) 0 0
\(17\) 0.309929 0.178937i 0.00107242 0.000619161i −0.499464 0.866335i \(-0.666470\pi\)
0.500536 + 0.865716i \(0.333136\pi\)
\(18\) 0 0
\(19\) −163.845 + 283.789i −0.453865 + 0.786118i −0.998622 0.0524761i \(-0.983289\pi\)
0.544757 + 0.838594i \(0.316622\pi\)
\(20\) 0 0
\(21\) 128.795 + 592.478i 0.292051 + 1.34349i
\(22\) 0 0
\(23\) −242.445 + 666.113i −0.458309 + 1.25919i 0.468435 + 0.883498i \(0.344818\pi\)
−0.926743 + 0.375695i \(0.877404\pi\)
\(24\) 0 0
\(25\) 107.174 607.813i 0.171478 0.972500i
\(26\) 0 0
\(27\) −287.266 + 670.014i −0.394055 + 0.919087i
\(28\) 0 0
\(29\) −1510.88 266.409i −1.79653 0.316776i −0.827081 0.562082i \(-0.810000\pi\)
−0.969446 + 0.245306i \(0.921112\pi\)
\(30\) 0 0
\(31\) 547.514 + 199.279i 0.569734 + 0.207366i 0.610793 0.791791i \(-0.290851\pi\)
−0.0410588 + 0.999157i \(0.513073\pi\)
\(32\) 0 0
\(33\) 218.049 + 239.933i 0.200229 + 0.220324i
\(34\) 0 0
\(35\) −163.056 94.1403i −0.133107 0.0768492i
\(36\) 0 0
\(37\) −343.789 595.460i −0.251124 0.434960i 0.712711 0.701457i \(-0.247467\pi\)
−0.963836 + 0.266498i \(0.914134\pi\)
\(38\) 0 0
\(39\) 429.655 16.9887i 0.282482 0.0111695i
\(40\) 0 0
\(41\) −498.566 + 87.9106i −0.296589 + 0.0522966i −0.319963 0.947430i \(-0.603670\pi\)
0.0233738 + 0.999727i \(0.492559\pi\)
\(42\) 0 0
\(43\) −1251.43 1050.07i −0.676812 0.567913i 0.238261 0.971201i \(-0.423423\pi\)
−0.915073 + 0.403289i \(0.867867\pi\)
\(44\) 0 0
\(45\) −93.9804 205.948i −0.0464101 0.101703i
\(46\) 0 0
\(47\) 453.321 + 1245.49i 0.205215 + 0.563824i 0.999016 0.0443538i \(-0.0141229\pi\)
−0.793801 + 0.608178i \(0.791901\pi\)
\(48\) 0 0
\(49\) 1637.42 1373.96i 0.681974 0.572244i
\(50\) 0 0
\(51\) −1.22032 2.98074i −0.000469175 0.00114600i
\(52\) 0 0
\(53\) 1435.60i 0.511072i −0.966800 0.255536i \(-0.917748\pi\)
0.966800 0.255536i \(-0.0822519\pi\)
\(54\) 0 0
\(55\) −100.678 −0.0332820
\(56\) 0 0
\(57\) 2332.37 + 1804.98i 0.717872 + 0.555549i
\(58\) 0 0
\(59\) −989.454 1179.18i −0.284244 0.338749i 0.604963 0.796253i \(-0.293188\pi\)
−0.889207 + 0.457505i \(0.848743\pi\)
\(60\) 0 0
\(61\) 4824.54 1755.99i 1.29657 0.471913i 0.400692 0.916213i \(-0.368770\pi\)
0.895878 + 0.444300i \(0.146547\pi\)
\(62\) 0 0
\(63\) 5439.80 430.858i 1.37057 0.108556i
\(64\) 0 0
\(65\) −85.8289 + 102.287i −0.0203145 + 0.0242099i
\(66\) 0 0
\(67\) −474.440 2690.68i −0.105689 0.599394i −0.990943 0.134285i \(-0.957126\pi\)
0.885253 0.465109i \(-0.153985\pi\)
\(68\) 0 0
\(69\) 5646.75 + 2969.10i 1.18604 + 0.623629i
\(70\) 0 0
\(71\) −4492.65 + 2593.83i −0.891222 + 0.514548i −0.874342 0.485310i \(-0.838707\pi\)
−0.0168803 + 0.999858i \(0.505373\pi\)
\(72\) 0 0
\(73\) 4367.67 7565.02i 0.819604 1.41960i −0.0863709 0.996263i \(-0.527527\pi\)
0.905975 0.423332i \(-0.139140\pi\)
\(74\) 0 0
\(75\) −5290.70 1692.11i −0.940569 0.300819i
\(76\) 0 0
\(77\) 830.030 2280.49i 0.139995 0.384633i
\(78\) 0 0
\(79\) 814.469 4619.08i 0.130503 0.740119i −0.847383 0.530982i \(-0.821823\pi\)
0.977886 0.209138i \(-0.0670656\pi\)
\(80\) 0 0
\(81\) 5627.25 + 3373.54i 0.857682 + 0.514181i
\(82\) 0 0
\(83\) −9403.81 1658.15i −1.36505 0.240695i −0.557343 0.830282i \(-0.688179\pi\)
−0.807704 + 0.589588i \(0.799290\pi\)
\(84\) 0 0
\(85\) 0.939867 + 0.342084i 0.000130085 + 4.73472e-5i
\(86\) 0 0
\(87\) −4206.18 + 13151.4i −0.555712 + 1.73754i
\(88\) 0 0
\(89\) −9672.46 5584.40i −1.22112 0.705012i −0.255960 0.966687i \(-0.582392\pi\)
−0.965156 + 0.261676i \(0.915725\pi\)
\(90\) 0 0
\(91\) −1609.32 2787.43i −0.194339 0.336605i
\(92\) 0 0
\(93\) 2440.46 4641.37i 0.282167 0.536637i
\(94\) 0 0
\(95\) −901.914 + 159.032i −0.0999351 + 0.0176213i
\(96\) 0 0
\(97\) 1339.14 + 1123.67i 0.142325 + 0.119425i 0.711171 0.703019i \(-0.248165\pi\)
−0.568845 + 0.822444i \(0.692610\pi\)
\(98\) 0 0
\(99\) 2403.89 1653.92i 0.245270 0.168750i
\(100\) 0 0
\(101\) 5798.66 + 15931.7i 0.568440 + 1.56178i 0.806940 + 0.590633i \(0.201122\pi\)
−0.238500 + 0.971142i \(0.576656\pi\)
\(102\) 0 0
\(103\) −614.976 + 516.026i −0.0579674 + 0.0486404i −0.671311 0.741176i \(-0.734269\pi\)
0.613344 + 0.789816i \(0.289824\pi\)
\(104\) 0 0
\(105\) −1037.08 + 1340.10i −0.0940665 + 0.121551i
\(106\) 0 0
\(107\) 110.997i 0.00969492i −0.999988 0.00484746i \(-0.998457\pi\)
0.999988 0.00484746i \(-0.00154300\pi\)
\(108\) 0 0
\(109\) −8515.84 −0.716761 −0.358381 0.933576i \(-0.616671\pi\)
−0.358381 + 0.933576i \(0.616671\pi\)
\(110\) 0 0
\(111\) −5726.84 + 2344.58i −0.464803 + 0.190292i
\(112\) 0 0
\(113\) 5198.29 + 6195.08i 0.407102 + 0.485165i 0.930172 0.367124i \(-0.119658\pi\)
−0.523070 + 0.852290i \(0.675213\pi\)
\(114\) 0 0
\(115\) −1861.65 + 677.584i −0.140767 + 0.0512351i
\(116\) 0 0
\(117\) 368.989 3852.28i 0.0269552 0.281415i
\(118\) 0 0
\(119\) −15.4973 + 18.4689i −0.00109436 + 0.00130421i
\(120\) 0 0
\(121\) 2317.04 + 13140.6i 0.158257 + 0.897520i
\(122\) 0 0
\(123\) 180.018 + 4552.75i 0.0118989 + 0.300929i
\(124\) 0 0
\(125\) 3006.55 1735.83i 0.192419 0.111093i
\(126\) 0 0
\(127\) −15006.6 + 25992.2i −0.930410 + 1.61152i −0.147789 + 0.989019i \(0.547216\pi\)
−0.782621 + 0.622498i \(0.786118\pi\)
\(128\) 0 0
\(129\) −10880.6 + 9888.24i −0.653845 + 0.594210i
\(130\) 0 0
\(131\) −3367.32 + 9251.64i −0.196219 + 0.539108i −0.998311 0.0580924i \(-0.981498\pi\)
0.802092 + 0.597201i \(0.203720\pi\)
\(132\) 0 0
\(133\) 3833.46 21740.6i 0.216714 1.22905i
\(134\) 0 0
\(135\) −1950.52 + 588.635i −0.107024 + 0.0322982i
\(136\) 0 0
\(137\) −27173.2 4791.37i −1.44777 0.255281i −0.606150 0.795351i \(-0.707287\pi\)
−0.841620 + 0.540070i \(0.818398\pi\)
\(138\) 0 0
\(139\) 23150.6 + 8426.12i 1.19821 + 0.436112i 0.862598 0.505889i \(-0.168836\pi\)
0.335609 + 0.942001i \(0.391058\pi\)
\(140\) 0 0
\(141\) 11656.5 2533.94i 0.586316 0.127455i
\(142\) 0 0
\(143\) −1490.50 860.542i −0.0728888 0.0420824i
\(144\) 0 0
\(145\) −2143.87 3713.29i −0.101967 0.176613i
\(146\) 0 0
\(147\) −10269.5 16267.1i −0.475241 0.752794i
\(148\) 0 0
\(149\) 37247.5 6567.74i 1.67774 0.295831i 0.747904 0.663807i \(-0.231060\pi\)
0.929835 + 0.367976i \(0.119949\pi\)
\(150\) 0 0
\(151\) −12653.1 10617.2i −0.554936 0.465646i 0.321673 0.946851i \(-0.395755\pi\)
−0.876608 + 0.481205i \(0.840199\pi\)
\(152\) 0 0
\(153\) −28.0609 + 7.27201i −0.00119872 + 0.000310650i
\(154\) 0 0
\(155\) 556.943 + 1530.19i 0.0231818 + 0.0636915i
\(156\) 0 0
\(157\) 3919.19 3288.59i 0.159000 0.133417i −0.559817 0.828616i \(-0.689129\pi\)
0.718817 + 0.695200i \(0.244684\pi\)
\(158\) 0 0
\(159\) −12802.8 1739.13i −0.506421 0.0687920i
\(160\) 0 0
\(161\) 47754.9i 1.84233i
\(162\) 0 0
\(163\) −36016.6 −1.35559 −0.677794 0.735252i \(-0.737064\pi\)
−0.677794 + 0.735252i \(0.737064\pi\)
\(164\) 0 0
\(165\) −121.964 + 897.857i −0.00447987 + 0.0329791i
\(166\) 0 0
\(167\) 12971.2 + 15458.5i 0.465102 + 0.554287i 0.946705 0.322102i \(-0.104390\pi\)
−0.481602 + 0.876390i \(0.659945\pi\)
\(168\) 0 0
\(169\) 24693.6 8987.74i 0.864592 0.314686i
\(170\) 0 0
\(171\) 18922.5 18613.7i 0.647121 0.636561i
\(172\) 0 0
\(173\) −20392.5 + 24302.9i −0.681363 + 0.812017i −0.990282 0.139071i \(-0.955588\pi\)
0.308919 + 0.951088i \(0.400033\pi\)
\(174\) 0 0
\(175\) 7220.12 + 40947.4i 0.235759 + 1.33706i
\(176\) 0 0
\(177\) −11714.7 + 7395.54i −0.373926 + 0.236061i
\(178\) 0 0
\(179\) 47563.9 27461.1i 1.48447 0.857060i 0.484627 0.874721i \(-0.338955\pi\)
0.999844 + 0.0176610i \(0.00562197\pi\)
\(180\) 0 0
\(181\) −10313.7 + 17863.9i −0.314817 + 0.545279i −0.979399 0.201937i \(-0.935276\pi\)
0.664582 + 0.747216i \(0.268610\pi\)
\(182\) 0 0
\(183\) −9815.48 45152.9i −0.293096 1.34829i
\(184\) 0 0
\(185\) 657.238 1805.75i 0.0192035 0.0527611i
\(186\) 0 0
\(187\) −2.23865 + 12.6960i −6.40183e−5 + 0.000363066i
\(188\) 0 0
\(189\) 2747.51 49034.6i 0.0769157 1.37271i
\(190\) 0 0
\(191\) 63011.6 + 11110.6i 1.72724 + 0.304560i 0.947076 0.321009i \(-0.104022\pi\)
0.780169 + 0.625569i \(0.215133\pi\)
\(192\) 0 0
\(193\) 31715.8 + 11543.6i 0.851454 + 0.309904i 0.730633 0.682770i \(-0.239225\pi\)
0.120821 + 0.992674i \(0.461447\pi\)
\(194\) 0 0
\(195\) 808.229 + 889.344i 0.0212552 + 0.0233884i
\(196\) 0 0
\(197\) −7886.51 4553.28i −0.203213 0.117325i 0.394940 0.918707i \(-0.370765\pi\)
−0.598153 + 0.801382i \(0.704099\pi\)
\(198\) 0 0
\(199\) 9023.29 + 15628.8i 0.227855 + 0.394656i 0.957172 0.289519i \(-0.0934954\pi\)
−0.729317 + 0.684176i \(0.760162\pi\)
\(200\) 0 0
\(201\) −24570.5 + 971.528i −0.608166 + 0.0240471i
\(202\) 0 0
\(203\) 101786. 17947.5i 2.46998 0.435525i
\(204\) 0 0
\(205\) −1083.86 909.469i −0.0257909 0.0216411i
\(206\) 0 0
\(207\) 33319.4 46761.4i 0.777599 1.09131i
\(208\) 0 0
\(209\) −4037.40 11092.7i −0.0924292 0.253947i
\(210\) 0 0
\(211\) −32956.5 + 27653.8i −0.740247 + 0.621141i −0.932904 0.360125i \(-0.882734\pi\)
0.192657 + 0.981266i \(0.438290\pi\)
\(212\) 0 0
\(213\) 17689.5 + 43208.2i 0.389903 + 0.952372i
\(214\) 0 0
\(215\) 4565.63i 0.0987696i
\(216\) 0 0
\(217\) −39252.4 −0.833578
\(218\) 0 0
\(219\) −62174.5 48115.8i −1.29635 1.00323i
\(220\) 0 0
\(221\) 10.9904 + 13.0979i 0.000225025 + 0.000268174i
\(222\) 0 0
\(223\) −13939.3 + 5073.49i −0.280305 + 0.102023i −0.478347 0.878171i \(-0.658764\pi\)
0.198042 + 0.980194i \(0.436542\pi\)
\(224\) 0 0
\(225\) −21499.7 + 45133.1i −0.424685 + 0.891518i
\(226\) 0 0
\(227\) −37883.9 + 45148.2i −0.735195 + 0.876171i −0.996012 0.0892169i \(-0.971564\pi\)
0.260817 + 0.965388i \(0.416008\pi\)
\(228\) 0 0
\(229\) 6889.02 + 39069.6i 0.131367 + 0.745019i 0.977321 + 0.211763i \(0.0679206\pi\)
−0.845954 + 0.533256i \(0.820968\pi\)
\(230\) 0 0
\(231\) −19332.1 10164.9i −0.362289 0.190494i
\(232\) 0 0
\(233\) −56676.4 + 32722.1i −1.04398 + 0.602740i −0.920957 0.389665i \(-0.872591\pi\)
−0.123019 + 0.992404i \(0.539258\pi\)
\(234\) 0 0
\(235\) −1852.14 + 3208.00i −0.0335380 + 0.0580896i
\(236\) 0 0
\(237\) −40206.8 12859.2i −0.715818 0.228938i
\(238\) 0 0
\(239\) 14949.7 41074.0i 0.261720 0.719069i −0.737332 0.675531i \(-0.763915\pi\)
0.999052 0.0435386i \(-0.0138632\pi\)
\(240\) 0 0
\(241\) 8549.32 48485.6i 0.147197 0.834793i −0.818381 0.574677i \(-0.805128\pi\)
0.965577 0.260117i \(-0.0837610\pi\)
\(242\) 0 0
\(243\) 36902.6 46097.6i 0.624948 0.780666i
\(244\) 0 0
\(245\) 5883.11 + 1037.35i 0.0980110 + 0.0172820i
\(246\) 0 0
\(247\) −14711.8 5354.67i −0.241142 0.0877685i
\(248\) 0 0
\(249\) −26179.6 + 81855.4i −0.422244 + 1.32023i
\(250\) 0 0
\(251\) −55699.9 32158.3i −0.884111 0.510442i −0.0120994 0.999927i \(-0.503851\pi\)
−0.872012 + 0.489485i \(0.837185\pi\)
\(252\) 0 0
\(253\) −12767.8 22114.6i −0.199470 0.345491i
\(254\) 0 0
\(255\) 4.18932 7.96742i 6.44263e−5 0.000122528i
\(256\) 0 0
\(257\) −20894.2 + 3684.22i −0.316344 + 0.0557800i −0.329566 0.944133i \(-0.606902\pi\)
0.0132216 + 0.999913i \(0.495791\pi\)
\(258\) 0 0
\(259\) 35483.9 + 29774.6i 0.528972 + 0.443860i
\(260\) 0 0
\(261\) 112190. + 53443.2i 1.64693 + 0.784533i
\(262\) 0 0
\(263\) 18444.1 + 50674.9i 0.266653 + 0.732624i 0.998681 + 0.0513488i \(0.0163520\pi\)
−0.732027 + 0.681275i \(0.761426\pi\)
\(264\) 0 0
\(265\) 3073.53 2579.00i 0.0437669 0.0367248i
\(266\) 0 0
\(267\) −61519.7 + 79494.8i −0.862962 + 1.11511i
\(268\) 0 0
\(269\) 68360.6i 0.944717i −0.881407 0.472358i \(-0.843403\pi\)
0.881407 0.472358i \(-0.156597\pi\)
\(270\) 0 0
\(271\) −46387.1 −0.631624 −0.315812 0.948822i \(-0.602277\pi\)
−0.315812 + 0.948822i \(0.602277\pi\)
\(272\) 0 0
\(273\) −26808.1 + 10975.3i −0.359700 + 0.147262i
\(274\) 0 0
\(275\) 14291.3 + 17031.7i 0.188976 + 0.225213i
\(276\) 0 0
\(277\) 29407.5 10703.4i 0.383264 0.139497i −0.143201 0.989694i \(-0.545739\pi\)
0.526465 + 0.850197i \(0.323517\pi\)
\(278\) 0 0
\(279\) −38435.8 27387.0i −0.493773 0.351832i
\(280\) 0 0
\(281\) −82866.8 + 98756.8i −1.04947 + 1.25070i −0.0822858 + 0.996609i \(0.526222\pi\)
−0.967179 + 0.254095i \(0.918222\pi\)
\(282\) 0 0
\(283\) 8633.45 + 48962.7i 0.107798 + 0.611354i 0.990066 + 0.140605i \(0.0449049\pi\)
−0.882268 + 0.470748i \(0.843984\pi\)
\(284\) 0 0
\(285\) 325.656 + 8236.01i 0.00400930 + 0.101398i
\(286\) 0 0
\(287\) 29536.4 17052.9i 0.358586 0.207030i
\(288\) 0 0
\(289\) −41760.4 + 72331.2i −0.499999 + 0.866024i
\(290\) 0 0
\(291\) 11643.3 10581.3i 0.137496 0.124955i
\(292\) 0 0
\(293\) −41261.9 + 113366.i −0.480633 + 1.32053i 0.428319 + 0.903628i \(0.359106\pi\)
−0.908952 + 0.416901i \(0.863116\pi\)
\(294\) 0 0
\(295\) 747.046 4236.71i 0.00858427 0.0486838i
\(296\) 0 0
\(297\) −11837.7 23441.8i −0.134200 0.265752i
\(298\) 0 0
\(299\) −33352.6 5880.97i −0.373068 0.0657819i
\(300\) 0 0
\(301\) 103417. + 37640.8i 1.14146 + 0.415457i
\(302\) 0 0
\(303\) 149105. 32412.9i 1.62408 0.353047i
\(304\) 0 0
\(305\) 12426.5 + 7174.46i 0.133583 + 0.0771240i
\(306\) 0 0
\(307\) −42628.5 73834.8i −0.452297 0.783401i 0.546231 0.837634i \(-0.316062\pi\)
−0.998528 + 0.0542330i \(0.982729\pi\)
\(308\) 0 0
\(309\) 3856.97 + 6109.54i 0.0403952 + 0.0639870i
\(310\) 0 0
\(311\) 128622. 22679.6i 1.32983 0.234484i 0.536820 0.843697i \(-0.319625\pi\)
0.793007 + 0.609212i \(0.208514\pi\)
\(312\) 0 0
\(313\) −131429. 110282.i −1.34153 1.12568i −0.981229 0.192844i \(-0.938229\pi\)
−0.360303 0.932835i \(-0.617327\pi\)
\(314\) 0 0
\(315\) 10694.8 + 10872.2i 0.107783 + 0.109572i
\(316\) 0 0
\(317\) −44695.5 122800.i −0.444780 1.22202i −0.936314 0.351165i \(-0.885786\pi\)
0.491534 0.870859i \(-0.336437\pi\)
\(318\) 0 0
\(319\) 42336.8 35524.8i 0.416041 0.349100i
\(320\) 0 0
\(321\) −989.883 134.465i −0.00960669 0.00130497i
\(322\) 0 0
\(323\) 117.272i 0.00112406i
\(324\) 0 0
\(325\) 29487.3 0.279170
\(326\) 0 0
\(327\) −10316.3 + 75945.1i −0.0964784 + 0.710239i
\(328\) 0 0
\(329\) −57395.4 68401.2i −0.530256 0.631934i
\(330\) 0 0
\(331\) 146219. 53219.2i 1.33459 0.485750i 0.426483 0.904496i \(-0.359752\pi\)
0.908104 + 0.418746i \(0.137530\pi\)
\(332\) 0 0
\(333\) 13971.6 + 53912.8i 0.125996 + 0.486187i
\(334\) 0 0
\(335\) 4908.26 5849.44i 0.0437359 0.0521224i
\(336\) 0 0
\(337\) −19651.5 111449.i −0.173036 0.981335i −0.940387 0.340107i \(-0.889537\pi\)
0.767351 0.641228i \(-0.221575\pi\)
\(338\) 0 0
\(339\) 61545.7 38853.9i 0.535547 0.338092i
\(340\) 0 0
\(341\) −18177.2 + 10494.6i −0.156321 + 0.0902519i
\(342\) 0 0
\(343\) 8875.78 15373.3i 0.0754429 0.130671i
\(344\) 0 0
\(345\) 3787.51 + 17423.2i 0.0318211 + 0.146383i
\(346\) 0 0
\(347\) −43939.9 + 120724.i −0.364922 + 1.00262i 0.612342 + 0.790593i \(0.290227\pi\)
−0.977265 + 0.212023i \(0.931995\pi\)
\(348\) 0 0
\(349\) 30410.3 172466.i 0.249672 1.41596i −0.559714 0.828686i \(-0.689089\pi\)
0.809386 0.587276i \(-0.199800\pi\)
\(350\) 0 0
\(351\) −33908.0 7957.45i −0.275225 0.0645892i
\(352\) 0 0
\(353\) −162310. 28619.6i −1.30255 0.229675i −0.521023 0.853542i \(-0.674450\pi\)
−0.781531 + 0.623867i \(0.785561\pi\)
\(354\) 0 0
\(355\) −13624.1 4958.76i −0.108106 0.0393475i
\(356\) 0 0
\(357\) 145.934 + 160.580i 0.00114504 + 0.00125995i
\(358\) 0 0
\(359\) −114576. 66150.4i −0.889005 0.513267i −0.0153883 0.999882i \(-0.504898\pi\)
−0.873617 + 0.486614i \(0.838232\pi\)
\(360\) 0 0
\(361\) 11469.8 + 19866.4i 0.0880123 + 0.152442i
\(362\) 0 0
\(363\) 119996. 4744.69i 0.910654 0.0360077i
\(364\) 0 0
\(365\) 24042.5 4239.35i 0.180466 0.0318210i
\(366\) 0 0
\(367\) −9070.65 7611.18i −0.0673452 0.0565093i 0.608494 0.793559i \(-0.291774\pi\)
−0.675839 + 0.737049i \(0.736219\pi\)
\(368\) 0 0
\(369\) 40820.0 + 3909.92i 0.299792 + 0.0287154i
\(370\) 0 0
\(371\) 33078.2 + 90881.6i 0.240322 + 0.660280i
\(372\) 0 0
\(373\) 174210. 146180.i 1.25215 1.05068i 0.255676 0.966762i \(-0.417702\pi\)
0.996473 0.0839156i \(-0.0267426\pi\)
\(374\) 0 0
\(375\) −11838.1 28915.5i −0.0841819 0.205621i
\(376\) 0 0
\(377\) 73298.5i 0.515718i
\(378\) 0 0
\(379\) 55108.6 0.383655 0.191828 0.981429i \(-0.438559\pi\)
0.191828 + 0.981429i \(0.438559\pi\)
\(380\) 0 0
\(381\) 213621. + 165318.i 1.47162 + 1.13886i
\(382\) 0 0
\(383\) −115966. 138203.i −0.790559 0.942152i 0.208800 0.977958i \(-0.433044\pi\)
−0.999359 + 0.0358069i \(0.988600\pi\)
\(384\) 0 0
\(385\) 6373.49 2319.76i 0.0429987 0.0156503i
\(386\) 0 0
\(387\) 75003.2 + 109014.i 0.500792 + 0.727878i
\(388\) 0 0
\(389\) 42524.9 50679.2i 0.281024 0.334912i −0.607005 0.794698i \(-0.707629\pi\)
0.888030 + 0.459786i \(0.152074\pi\)
\(390\) 0 0
\(391\) 44.0518 + 249.830i 0.000288144 + 0.00163415i
\(392\) 0 0
\(393\) 78427.7 + 41237.8i 0.507790 + 0.266999i
\(394\) 0 0
\(395\) 11352.3 6554.26i 0.0727596 0.0420078i
\(396\) 0 0
\(397\) 101672. 176102.i 0.645092 1.11733i −0.339188 0.940719i \(-0.610152\pi\)
0.984280 0.176614i \(-0.0565145\pi\)
\(398\) 0 0
\(399\) −189241. 60524.4i −1.18869 0.380176i
\(400\) 0 0
\(401\) −66530.2 + 182790.i −0.413743 + 1.13675i 0.541442 + 0.840738i \(0.317879\pi\)
−0.955185 + 0.296010i \(0.904344\pi\)
\(402\) 0 0
\(403\) −4833.89 + 27414.3i −0.0297637 + 0.168798i
\(404\) 0 0
\(405\) 2886.59 + 18108.0i 0.0175984 + 0.110398i
\(406\) 0 0
\(407\) 24392.6 + 4301.08i 0.147255 + 0.0259650i
\(408\) 0 0
\(409\) 22329.3 + 8127.22i 0.133484 + 0.0485842i 0.407898 0.913027i \(-0.366262\pi\)
−0.274414 + 0.961612i \(0.588484\pi\)
\(410\) 0 0
\(411\) −75648.3 + 236529.i −0.447832 + 1.40023i
\(412\) 0 0
\(413\) 89807.9 + 51850.6i 0.526520 + 0.303986i
\(414\) 0 0
\(415\) −13343.6 23111.7i −0.0774775 0.134195i
\(416\) 0 0
\(417\) 103190. 196251.i 0.593426 1.12860i
\(418\) 0 0
\(419\) 85498.0 15075.6i 0.486999 0.0858710i 0.0752430 0.997165i \(-0.476027\pi\)
0.411756 + 0.911294i \(0.364916\pi\)
\(420\) 0 0
\(421\) 151352. + 126999.i 0.853934 + 0.716536i 0.960652 0.277754i \(-0.0895899\pi\)
−0.106718 + 0.994289i \(0.534034\pi\)
\(422\) 0 0
\(423\) −8476.79 107024.i −0.0473752 0.598136i
\(424\) 0 0
\(425\) −75.5442 207.556i −0.000418238 0.00114910i
\(426\) 0 0
\(427\) −264960. + 222328.i −1.45320 + 1.21938i
\(428\) 0 0
\(429\) −9480.04 + 12250.0i −0.0515105 + 0.0665610i
\(430\) 0 0
\(431\) 328870.i 1.77039i 0.465219 + 0.885196i \(0.345976\pi\)
−0.465219 + 0.885196i \(0.654024\pi\)
\(432\) 0 0
\(433\) −72397.6 −0.386143 −0.193072 0.981185i \(-0.561845\pi\)
−0.193072 + 0.981185i \(0.561845\pi\)
\(434\) 0 0
\(435\) −35712.6 + 14620.8i −0.188731 + 0.0772669i
\(436\) 0 0
\(437\) −149312. 177943.i −0.781864 0.931789i
\(438\) 0 0
\(439\) −337287. + 122762.i −1.75013 + 0.636995i −0.999713 0.0239702i \(-0.992369\pi\)
−0.750417 + 0.660965i \(0.770147\pi\)
\(440\) 0 0
\(441\) −157513. + 71877.7i −0.809912 + 0.369587i
\(442\) 0 0
\(443\) 110730. 131963.i 0.564232 0.672425i −0.406205 0.913782i \(-0.633148\pi\)
0.970436 + 0.241357i \(0.0775925\pi\)
\(444\) 0 0
\(445\) −5420.33 30740.2i −0.0273720 0.155234i
\(446\) 0 0
\(447\) −13449.0 340133.i −0.0673093 1.70229i
\(448\) 0 0
\(449\) −118104. + 68187.2i −0.585829 + 0.338228i −0.763446 0.645871i \(-0.776494\pi\)
0.177618 + 0.984100i \(0.443161\pi\)
\(450\) 0 0
\(451\) 9118.57 15793.8i 0.0448305 0.0776487i
\(452\) 0 0
\(453\) −110014. + 99979.5i −0.536105 + 0.487208i
\(454\) 0 0
\(455\) 3076.62 8452.94i 0.0148611 0.0408305i
\(456\) 0 0
\(457\) −27641.6 + 156763.i −0.132352 + 0.750605i 0.844315 + 0.535847i \(0.180007\pi\)
−0.976667 + 0.214758i \(0.931104\pi\)
\(458\) 0 0
\(459\) 30.8587 + 259.059i 0.000146471 + 0.00122963i
\(460\) 0 0
\(461\) 26862.1 + 4736.51i 0.126397 + 0.0222872i 0.236489 0.971634i \(-0.424003\pi\)
−0.110092 + 0.993921i \(0.535114\pi\)
\(462\) 0 0
\(463\) −376701. 137108.i −1.75726 0.639589i −0.757347 0.653013i \(-0.773505\pi\)
−0.999910 + 0.0134236i \(0.995727\pi\)
\(464\) 0 0
\(465\) 14321.1 3113.16i 0.0662322 0.0143978i
\(466\) 0 0
\(467\) −10596.7 6117.99i −0.0485887 0.0280527i 0.475509 0.879711i \(-0.342264\pi\)
−0.524098 + 0.851658i \(0.675597\pi\)
\(468\) 0 0
\(469\) 92031.6 + 159403.i 0.418400 + 0.724689i
\(470\) 0 0
\(471\) −24580.1 38935.6i −0.110801 0.175511i
\(472\) 0 0
\(473\) 57954.6 10219.0i 0.259039 0.0456756i
\(474\) 0 0
\(475\) 154930. + 130002.i 0.686672 + 0.576186i
\(476\) 0 0
\(477\) −31019.5 + 112070.i −0.136332 + 0.492553i
\(478\) 0 0
\(479\) 113858. + 312822.i 0.496241 + 1.36341i 0.894882 + 0.446304i \(0.147260\pi\)
−0.398641 + 0.917107i \(0.630518\pi\)
\(480\) 0 0
\(481\) 25164.7 21115.7i 0.108768 0.0912674i
\(482\) 0 0
\(483\) −425883. 57851.7i −1.82556 0.247983i
\(484\) 0 0
\(485\) 4885.63i 0.0207700i
\(486\) 0 0
\(487\) 308646. 1.30137 0.650687 0.759346i \(-0.274481\pi\)
0.650687 + 0.759346i \(0.274481\pi\)
\(488\) 0 0
\(489\) −43631.6 + 321199.i −0.182466 + 1.34325i
\(490\) 0 0
\(491\) −232265. 276803.i −0.963433 1.14817i −0.988913 0.148499i \(-0.952556\pi\)
0.0254796 0.999675i \(-0.491889\pi\)
\(492\) 0 0
\(493\) −515.935 + 187.785i −0.00212276 + 0.000772623i
\(494\) 0 0
\(495\) 7859.43 + 2175.38i 0.0320760 + 0.00887820i
\(496\) 0 0
\(497\) 224645. 267721.i 0.909459 1.08385i
\(498\) 0 0
\(499\) −43062.5 244220.i −0.172941 0.980797i −0.940494 0.339811i \(-0.889637\pi\)
0.767553 0.640986i \(-0.221474\pi\)
\(500\) 0 0
\(501\) 153574. 96951.9i 0.611847 0.386261i
\(502\) 0 0
\(503\) −92432.5 + 53365.9i −0.365333 + 0.210925i −0.671417 0.741079i \(-0.734314\pi\)
0.306085 + 0.952004i \(0.400981\pi\)
\(504\) 0 0
\(505\) −23691.6 + 41035.1i −0.0928993 + 0.160906i
\(506\) 0 0
\(507\) −50238.9 231108.i −0.195445 0.899081i
\(508\) 0 0
\(509\) −62475.8 + 171651.i −0.241144 + 0.662537i 0.758793 + 0.651331i \(0.225789\pi\)
−0.999937 + 0.0112058i \(0.996433\pi\)
\(510\) 0 0
\(511\) −102189. + 579545.i −0.391349 + 2.21945i
\(512\) 0 0
\(513\) −143075. 191302.i −0.543663 0.726915i
\(514\) 0 0
\(515\) −2209.56 389.604i −0.00833087 0.00146896i
\(516\) 0 0
\(517\) −44866.8 16330.2i −0.167859 0.0610956i
\(518\) 0 0
\(519\) 192031. + 211304.i 0.712913 + 0.784462i
\(520\) 0 0
\(521\) 346945. + 200309.i 1.27816 + 0.737945i 0.976510 0.215474i \(-0.0691297\pi\)
0.301649 + 0.953419i \(0.402463\pi\)
\(522\) 0 0
\(523\) −1640.33 2841.14i −0.00599692 0.0103870i 0.863011 0.505184i \(-0.168576\pi\)
−0.869008 + 0.494798i \(0.835242\pi\)
\(524\) 0 0
\(525\) 373919. 14784.9i 1.35662 0.0536414i
\(526\) 0 0
\(527\) 205.349 36.2085i 0.000739386 0.000130374i
\(528\) 0 0
\(529\) −170556. 143114.i −0.609475 0.511410i
\(530\) 0 0
\(531\) 51762.6 + 113432.i 0.183581 + 0.402298i
\(532\) 0 0
\(533\) −8272.54 22728.6i −0.0291195 0.0800053i
\(534\) 0 0
\(535\) 237.638 199.402i 0.000830247 0.000696660i
\(536\) 0 0
\(537\) −187280. 457447.i −0.649446 1.58632i
\(538\) 0 0
\(539\) 77000.2i 0.265042i
\(540\) 0 0
\(541\) 197783. 0.675764 0.337882 0.941189i \(-0.390290\pi\)
0.337882 + 0.941189i \(0.390290\pi\)
\(542\) 0 0
\(543\) 146817. + 113619.i 0.497941 + 0.385348i
\(544\) 0 0
\(545\) −15298.3 18231.9i −0.0515053 0.0613816i
\(546\) 0 0
\(547\) −17508.9 + 6372.72i −0.0585173 + 0.0212986i −0.371113 0.928588i \(-0.621024\pi\)
0.312596 + 0.949886i \(0.398802\pi\)
\(548\) 0 0
\(549\) −414569. + 32835.8i −1.37547 + 0.108944i
\(550\) 0 0
\(551\) 323154. 385120.i 1.06441 1.26851i
\(552\) 0 0
\(553\) 54869.5 + 311180.i 0.179424 + 1.01756i
\(554\) 0 0
\(555\) −15307.6 8048.85i −0.0496961 0.0261305i
\(556\) 0 0
\(557\) 464794. 268349.i 1.49813 0.864948i 0.498135 0.867099i \(-0.334018\pi\)
0.999998 + 0.00215163i \(0.000684886\pi\)
\(558\) 0 0
\(559\) 39024.5 67592.4i 0.124886 0.216309i
\(560\) 0 0
\(561\) 110.513 + 35.3449i 0.000351144 + 0.000112305i
\(562\) 0 0
\(563\) −105660. + 290297.i −0.333343 + 0.915853i 0.653892 + 0.756588i \(0.273135\pi\)
−0.987236 + 0.159266i \(0.949087\pi\)
\(564\) 0 0
\(565\) −3924.75 + 22258.4i −0.0122946 + 0.0697263i
\(566\) 0 0
\(567\) −433967. 83904.5i −1.34987 0.260987i
\(568\) 0 0
\(569\) 111616. + 19680.9i 0.344748 + 0.0607884i 0.343342 0.939211i \(-0.388441\pi\)
0.00140673 + 0.999999i \(0.499552\pi\)
\(570\) 0 0
\(571\) 167605. + 61003.4i 0.514063 + 0.187103i 0.586008 0.810305i \(-0.300699\pi\)
−0.0719457 + 0.997409i \(0.522921\pi\)
\(572\) 0 0
\(573\) 175420. 548484.i 0.534281 1.67053i
\(574\) 0 0
\(575\) 378888. + 218751.i 1.14598 + 0.661629i
\(576\) 0 0
\(577\) −33755.5 58466.2i −0.101389 0.175612i 0.810868 0.585229i \(-0.198995\pi\)
−0.912257 + 0.409618i \(0.865662\pi\)
\(578\) 0 0
\(579\) 141369. 268860.i 0.421692 0.801992i
\(580\) 0 0
\(581\) 633520. 111707.i 1.87676 0.330923i
\(582\) 0 0
\(583\) 39616.3 + 33242.0i 0.116556 + 0.0978025i
\(584\) 0 0
\(585\) 8910.36 6130.48i 0.0260366 0.0179136i
\(586\) 0 0
\(587\) −225369. 619195.i −0.654059 1.79701i −0.602180 0.798360i \(-0.705701\pi\)
−0.0518795 0.998653i \(-0.516521\pi\)
\(588\) 0 0
\(589\) −146261. + 122727.i −0.421597 + 0.353762i
\(590\) 0 0
\(591\) −50160.5 + 64816.7i −0.143611 + 0.185572i
\(592\) 0 0
\(593\) 27873.9i 0.0792664i −0.999214 0.0396332i \(-0.987381\pi\)
0.999214 0.0396332i \(-0.0126189\pi\)
\(594\) 0 0
\(595\) −67.3809 −0.000190328
\(596\) 0 0
\(597\) 150310. 61537.4i 0.421735 0.172659i
\(598\) 0 0
\(599\) −354548. 422534.i −0.988147 1.17763i −0.984096 0.177636i \(-0.943155\pi\)
−0.00405057 0.999992i \(-0.501289\pi\)
\(600\) 0 0
\(601\) −251293. + 91463.1i −0.695715 + 0.253219i −0.665580 0.746326i \(-0.731816\pi\)
−0.0301346 + 0.999546i \(0.509594\pi\)
\(602\) 0 0
\(603\) −21101.3 + 220299.i −0.0580328 + 0.605868i
\(604\) 0 0
\(605\) −23970.7 + 28567.2i −0.0654892 + 0.0780470i
\(606\) 0 0
\(607\) −74129.4 420409.i −0.201193 1.14102i −0.903319 0.428970i \(-0.858877\pi\)
0.702125 0.712053i \(-0.252235\pi\)
\(608\) 0 0
\(609\) −36751.8 929475.i −0.0990934 2.50613i
\(610\) 0 0
\(611\) −54840.4 + 31662.1i −0.146899 + 0.0848121i
\(612\) 0 0
\(613\) −269887. + 467458.i −0.718226 + 1.24400i 0.243476 + 0.969907i \(0.421712\pi\)
−0.961702 + 0.274097i \(0.911621\pi\)
\(614\) 0 0
\(615\) −9423.75 + 8564.23i −0.0249157 + 0.0226432i
\(616\) 0 0
\(617\) −184549. + 507044.i −0.484776 + 1.33191i 0.420579 + 0.907256i \(0.361827\pi\)
−0.905355 + 0.424655i \(0.860395\pi\)
\(618\) 0 0
\(619\) 12734.3 72219.7i 0.0332348 0.188484i −0.963671 0.267093i \(-0.913937\pi\)
0.996906 + 0.0786093i \(0.0250480\pi\)
\(620\) 0 0
\(621\) −376659. 353793.i −0.976709 0.917417i
\(622\) 0 0
\(623\) 740993. + 130657.i 1.90914 + 0.336633i
\(624\) 0 0
\(625\) −353363. 128613.i −0.904608 0.329250i
\(626\) 0 0
\(627\) −103816. + 22567.9i −0.264077 + 0.0574059i
\(628\) 0 0
\(629\) −213.100 123.033i −0.000538620 0.000310972i
\(630\) 0 0
\(631\) 331505. + 574184.i 0.832591 + 1.44209i 0.895977 + 0.444101i \(0.146477\pi\)
−0.0633861 + 0.997989i \(0.520190\pi\)
\(632\) 0 0
\(633\) 206695. + 327410.i 0.515849 + 0.817118i
\(634\) 0 0
\(635\) −82606.2 + 14565.7i −0.204864 + 0.0361230i
\(636\) 0 0
\(637\) 78230.6 + 65643.3i 0.192796 + 0.161775i
\(638\) 0 0
\(639\) 406764. 105413.i 0.996187 0.258163i
\(640\) 0 0
\(641\) −148039. 406733.i −0.360296 0.989904i −0.978925 0.204221i \(-0.934534\pi\)
0.618629 0.785683i \(-0.287688\pi\)
\(642\) 0 0
\(643\) 240171. 201528.i 0.580897 0.487431i −0.304344 0.952562i \(-0.598437\pi\)
0.885242 + 0.465131i \(0.153993\pi\)
\(644\) 0 0
\(645\) −40716.7 5530.93i −0.0978708 0.0132947i
\(646\) 0 0
\(647\) 417006.i 0.996170i 0.867128 + 0.498085i \(0.165963\pi\)
−0.867128 + 0.498085i \(0.834037\pi\)
\(648\) 0 0
\(649\) 55451.5 0.131651
\(650\) 0 0
\(651\) −47551.5 + 350056.i −0.112202 + 0.825992i
\(652\) 0 0
\(653\) −165991. 197820.i −0.389276 0.463921i 0.535443 0.844571i \(-0.320145\pi\)
−0.924719 + 0.380650i \(0.875700\pi\)
\(654\) 0 0
\(655\) −25856.4 + 9410.96i −0.0602678 + 0.0219357i
\(656\) 0 0
\(657\) −504421. + 496189.i −1.16859 + 1.14952i
\(658\) 0 0
\(659\) −187100. + 222978.i −0.430828 + 0.513441i −0.937161 0.348897i \(-0.886556\pi\)
0.506333 + 0.862338i \(0.331001\pi\)
\(660\) 0 0
\(661\) −31474.8 178503.i −0.0720378 0.408547i −0.999408 0.0344018i \(-0.989047\pi\)
0.927370 0.374145i \(-0.122064\pi\)
\(662\) 0 0
\(663\) 130.122 82.1466i 0.000296023 0.000186880i
\(664\) 0 0
\(665\) 53431.9 30848.9i 0.120825 0.0697584i
\(666\) 0 0
\(667\) 543764. 941827.i 1.22225 2.11699i
\(668\) 0 0
\(669\) 28359.4 + 130458.i 0.0633644 + 0.291487i
\(670\) 0 0
\(671\) −63256.8 + 173797.i −0.140495 + 0.386008i
\(672\) 0 0
\(673\) −77824.8 + 441366.i −0.171826 + 0.974472i 0.769919 + 0.638142i \(0.220297\pi\)
−0.941744 + 0.336330i \(0.890814\pi\)
\(674\) 0 0
\(675\) 376456. + 246412.i 0.826241 + 0.540822i
\(676\) 0 0
\(677\) −27774.3 4897.36i −0.0605991 0.0106853i 0.143266 0.989684i \(-0.454239\pi\)
−0.203866 + 0.978999i \(0.565351\pi\)
\(678\) 0 0
\(679\) −110666. 40279.1i −0.240035 0.0873654i
\(680\) 0 0
\(681\) 356743. + 392546.i 0.769238 + 0.846440i
\(682\) 0 0
\(683\) −202638. 116993.i −0.434390 0.250795i 0.266825 0.963745i \(-0.414025\pi\)
−0.701215 + 0.712950i \(0.747359\pi\)
\(684\) 0 0
\(685\) −38557.5 66783.5i −0.0821727 0.142327i
\(686\) 0 0
\(687\) 356772. 14106.9i 0.755922 0.0298895i
\(688\) 0 0
\(689\) 67546.3 11910.2i 0.142286 0.0250889i
\(690\) 0 0
\(691\) 156806. + 131576.i 0.328403 + 0.275563i 0.792049 0.610458i \(-0.209014\pi\)
−0.463646 + 0.886021i \(0.653459\pi\)
\(692\) 0 0
\(693\) −114071. + 160091.i −0.237525 + 0.333351i
\(694\) 0 0
\(695\) 23549.2 + 64701.0i 0.0487537 + 0.133950i
\(696\) 0 0
\(697\) −138.789 + 116.458i −0.000285687 + 0.000239720i
\(698\) 0 0
\(699\) 223160. + 545086.i 0.456732 + 1.11561i
\(700\) 0 0
\(701\) 299004.i 0.608473i 0.952597 + 0.304237i \(0.0984013\pi\)
−0.952597 + 0.304237i \(0.901599\pi\)
\(702\) 0 0
\(703\) 225313. 0.455906
\(704\) 0 0
\(705\) 26365.5 + 20403.8i 0.0530466 + 0.0410519i
\(706\) 0 0
\(707\) −734174. 874955.i −1.46879 1.75044i
\(708\) 0 0
\(709\) −374736. + 136393.i −0.745474 + 0.271330i −0.686700 0.726941i \(-0.740941\pi\)
−0.0587740 + 0.998271i \(0.518719\pi\)
\(710\) 0 0
\(711\) −163387. + 342990.i −0.323206 + 0.678488i
\(712\) 0 0
\(713\) −265485. + 316392.i −0.522228 + 0.622367i
\(714\) 0 0
\(715\) −835.260 4737.00i −0.00163384 0.00926597i
\(716\) 0 0
\(717\) −348191. 183081.i −0.677297 0.356127i
\(718\) 0 0
\(719\) −664619. + 383718.i −1.28563 + 0.742257i −0.977871 0.209208i \(-0.932911\pi\)
−0.307756 + 0.951465i \(0.599578\pi\)
\(720\) 0 0
\(721\) 27041.5 46837.2i 0.0520187 0.0900991i
\(722\) 0 0
\(723\) −422043. 134981.i −0.807383 0.258223i
\(724\) 0 0
\(725\) −323853. + 889780.i −0.616130 + 1.69280i
\(726\) 0 0
\(727\) −2474.26 + 14032.3i −0.00468142 + 0.0265496i −0.987059 0.160358i \(-0.948735\pi\)
0.982378 + 0.186907i \(0.0598464\pi\)
\(728\) 0 0
\(729\) −366398. 384945.i −0.689442 0.724341i
\(730\) 0 0
\(731\) −575.750 101.520i −0.00107745 0.000189984i
\(732\) 0 0
\(733\) −100373. 36532.6i −0.186813 0.0679944i 0.246920 0.969036i \(-0.420582\pi\)
−0.433733 + 0.901042i \(0.642804\pi\)
\(734\) 0 0
\(735\) 16378.2 51209.5i 0.0303173 0.0947929i
\(736\) 0 0
\(737\) 85236.8 + 49211.5i 0.156925 + 0.0906007i
\(738\) 0 0
\(739\) −276629. 479136.i −0.506535 0.877344i −0.999971 0.00756237i \(-0.997593\pi\)
0.493436 0.869782i \(-0.335741\pi\)
\(740\) 0 0
\(741\) −65575.8 + 124715.i −0.119428 + 0.227134i
\(742\) 0 0
\(743\) 192790. 33994.1i 0.349227 0.0615781i 0.00371646 0.999993i \(-0.498817\pi\)
0.345510 + 0.938415i \(0.387706\pi\)
\(744\) 0 0
\(745\) 80974.6 + 67945.8i 0.145894 + 0.122419i
\(746\) 0 0
\(747\) 698279. + 332634.i 1.25138 + 0.596108i
\(748\) 0 0
\(749\) 2557.52 + 7026.74i 0.00455886 + 0.0125254i
\(750\) 0 0
\(751\) −284195. + 238468.i −0.503891 + 0.422815i −0.858974 0.512020i \(-0.828897\pi\)
0.355082 + 0.934835i \(0.384453\pi\)
\(752\) 0 0
\(753\) −354268. + 457779.i −0.624801 + 0.807358i
\(754\) 0 0
\(755\) 46162.8i 0.0809838i
\(756\) 0 0
\(757\) −467363. −0.815572 −0.407786 0.913078i \(-0.633699\pi\)
−0.407786 + 0.913078i \(0.633699\pi\)
\(758\) 0 0
\(759\) −212687. + 87074.7i −0.369197 + 0.151150i
\(760\) 0 0
\(761\) −193920. 231105.i −0.334852 0.399061i 0.572176 0.820131i \(-0.306099\pi\)
−0.907028 + 0.421069i \(0.861655\pi\)
\(762\) 0 0
\(763\) 539100. 196216.i 0.926020 0.337044i
\(764\) 0 0
\(765\) −65.9791 47.0127i −0.000112741 8.03327e-5i
\(766\) 0 0
\(767\) 47272.9 56337.6i 0.0803565 0.0957652i
\(768\) 0 0
\(769\) −43909.6 249024.i −0.0742518 0.421103i −0.999162 0.0409186i \(-0.986972\pi\)
0.924911 0.380185i \(-0.124140\pi\)
\(770\) 0 0
\(771\) 7544.31 + 190800.i 0.0126914 + 0.320974i
\(772\) 0 0
\(773\) −84150.9 + 48584.5i −0.140831 + 0.0813091i −0.568760 0.822503i \(-0.692577\pi\)
0.427929 + 0.903812i \(0.359243\pi\)
\(774\) 0 0
\(775\) 179803. 311429.i 0.299361 0.518508i
\(776\) 0 0
\(777\) 308519. 280379.i 0.511022 0.464413i
\(778\) 0 0
\(779\) 56739.7 155891.i 0.0935001 0.256889i
\(780\) 0