Properties

Label 36.6.e.a.13.1
Level $36$
Weight $6$
Character 36.13
Analytic conductor $5.774$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 36.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.77381751327\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 13.1
Root \(2.13639i\) of defining polynomial
Character \(\chi\) \(=\) 36.13
Dual form 36.6.e.a.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +O(q^{10})\) \(q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +(138.873 + 240.536i) q^{11} +(-291.929 + 505.636i) q^{13} +(407.098 - 163.533i) q^{15} -1612.01 q^{17} +1368.76 q^{19} +(333.149 - 2336.58i) q^{21} +(-428.014 + 741.342i) q^{23} +(1166.47 + 2020.38i) q^{25} +(1561.44 - 3451.21i) q^{27} +(-4267.49 - 7391.50i) q^{29} +(-1469.19 + 2544.71i) q^{31} +(611.138 - 4286.30i) q^{33} -4261.17 q^{35} +4036.80 q^{37} +(8445.52 - 3392.59i) q^{39} +(-9449.81 + 16367.5i) q^{41} +(10158.6 + 17595.1i) q^{43} +(-6566.39 - 1911.32i) q^{45} +(147.890 + 256.152i) q^{47} +(-3058.67 + 5297.78i) q^{49} +(19770.7 + 15510.3i) q^{51} +3039.13 q^{53} -7816.81 q^{55} +(-16787.4 - 13169.9i) q^{57} +(8618.31 - 14927.4i) q^{59} +(-12826.2 - 22215.7i) q^{61} +(-26568.0 + 25452.0i) q^{63} +(-8215.95 - 14230.4i) q^{65} +(13140.1 - 22759.4i) q^{67} +(12382.5 - 4974.07i) q^{69} +76665.7 q^{71} +1496.33 q^{73} +(5133.25 - 36002.8i) q^{75} +(-21026.5 + 36419.0i) q^{77} +(-49637.1 - 85974.0i) q^{79} +(-52357.1 + 27304.1i) q^{81} +(-25025.7 - 43345.7i) q^{83} +(22683.8 - 39289.6i) q^{85} +(-18779.8 + 131715. i) q^{87} +136635. q^{89} -88400.8 q^{91} +(42503.6 - 17073.9i) q^{93} +(-19261.0 + 33361.0i) q^{95} +(33325.0 + 57720.5i) q^{97} +(-48737.1 + 46689.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + O(q^{10}) \) \( 10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + 177q^{11} - 181q^{13} + 117q^{15} + 2280q^{17} - 832q^{19} - 207q^{21} + 399q^{23} - 4778q^{25} - 7128q^{27} - 6033q^{29} + 2759q^{31} + 9603q^{33} + 37146q^{35} - 15172q^{37} + 5529q^{39} - 18435q^{41} + 1469q^{43} - 64089q^{45} - 25155q^{47} - 4056q^{49} + 90612q^{51} + 116844q^{53} + 14778q^{55} + 26934q^{57} - 90537q^{59} + 1403q^{61} - 198255q^{63} - 148407q^{65} + 13907q^{67} + 214425q^{69} + 229368q^{71} + 15200q^{73} + 44640q^{75} - 211983q^{77} + 29993q^{79} - 404172q^{81} - 228951q^{83} - 49662q^{85} + 397323q^{87} + 598332q^{89} + 124930q^{91} + 250041q^{93} - 394764q^{95} + 40541q^{97} - 697239q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −12.2647 9.62174i −0.786779 0.617235i
\(4\) 0 0
\(5\) −14.0718 + 24.3731i −0.251724 + 0.435999i −0.964001 0.265900i \(-0.914331\pi\)
0.712276 + 0.701899i \(0.247664\pi\)
\(6\) 0 0
\(7\) 75.7039 + 131.123i 0.583947 + 1.01143i 0.995006 + 0.0998170i \(0.0318257\pi\)
−0.411059 + 0.911609i \(0.634841\pi\)
\(8\) 0 0
\(9\) 57.8441 + 236.015i 0.238042 + 0.971255i
\(10\) 0 0
\(11\) 138.873 + 240.536i 0.346049 + 0.599374i 0.985544 0.169421i \(-0.0541898\pi\)
−0.639495 + 0.768795i \(0.720856\pi\)
\(12\) 0 0
\(13\) −291.929 + 505.636i −0.479092 + 0.829812i −0.999713 0.0239762i \(-0.992367\pi\)
0.520620 + 0.853788i \(0.325701\pi\)
\(14\) 0 0
\(15\) 407.098 163.533i 0.467165 0.187662i
\(16\) 0 0
\(17\) −1612.01 −1.35283 −0.676417 0.736519i \(-0.736468\pi\)
−0.676417 + 0.736519i \(0.736468\pi\)
\(18\) 0 0
\(19\) 1368.76 0.869851 0.434925 0.900467i \(-0.356775\pi\)
0.434925 + 0.900467i \(0.356775\pi\)
\(20\) 0 0
\(21\) 333.149 2336.58i 0.164850 1.15620i
\(22\) 0 0
\(23\) −428.014 + 741.342i −0.168709 + 0.292213i −0.937966 0.346727i \(-0.887293\pi\)
0.769257 + 0.638939i \(0.220627\pi\)
\(24\) 0 0
\(25\) 1166.47 + 2020.38i 0.373270 + 0.646522i
\(26\) 0 0
\(27\) 1561.44 3451.21i 0.412207 0.911090i
\(28\) 0 0
\(29\) −4267.49 7391.50i −0.942274 1.63207i −0.761120 0.648611i \(-0.775350\pi\)
−0.181154 0.983455i \(-0.557983\pi\)
\(30\) 0 0
\(31\) −1469.19 + 2544.71i −0.274583 + 0.475591i −0.970030 0.242986i \(-0.921873\pi\)
0.695447 + 0.718577i \(0.255206\pi\)
\(32\) 0 0
\(33\) 611.138 4286.30i 0.0976910 0.685169i
\(34\) 0 0
\(35\) −4261.17 −0.587975
\(36\) 0 0
\(37\) 4036.80 0.484767 0.242383 0.970181i \(-0.422071\pi\)
0.242383 + 0.970181i \(0.422071\pi\)
\(38\) 0 0
\(39\) 8445.52 3392.59i 0.889129 0.357166i
\(40\) 0 0
\(41\) −9449.81 + 16367.5i −0.877937 + 1.52063i −0.0243361 + 0.999704i \(0.507747\pi\)
−0.853601 + 0.520928i \(0.825586\pi\)
\(42\) 0 0
\(43\) 10158.6 + 17595.1i 0.837840 + 1.45118i 0.891697 + 0.452632i \(0.149515\pi\)
−0.0538576 + 0.998549i \(0.517152\pi\)
\(44\) 0 0
\(45\) −6566.39 1911.32i −0.483387 0.140703i
\(46\) 0 0
\(47\) 147.890 + 256.152i 0.00976546 + 0.0169143i 0.870867 0.491519i \(-0.163558\pi\)
−0.861101 + 0.508433i \(0.830225\pi\)
\(48\) 0 0
\(49\) −3058.67 + 5297.78i −0.181988 + 0.315213i
\(50\) 0 0
\(51\) 19770.7 + 15510.3i 1.06438 + 0.835016i
\(52\) 0 0
\(53\) 3039.13 0.148614 0.0743069 0.997235i \(-0.476326\pi\)
0.0743069 + 0.997235i \(0.476326\pi\)
\(54\) 0 0
\(55\) −7816.81 −0.348436
\(56\) 0 0
\(57\) −16787.4 13169.9i −0.684380 0.536902i
\(58\) 0 0
\(59\) 8618.31 14927.4i 0.322324 0.558281i −0.658643 0.752455i \(-0.728869\pi\)
0.980967 + 0.194174i \(0.0622027\pi\)
\(60\) 0 0
\(61\) −12826.2 22215.7i −0.441342 0.764426i 0.556448 0.830883i \(-0.312164\pi\)
−0.997789 + 0.0664565i \(0.978831\pi\)
\(62\) 0 0
\(63\) −26568.0 + 25452.0i −0.843349 + 0.807923i
\(64\) 0 0
\(65\) −8215.95 14230.4i −0.241198 0.417768i
\(66\) 0 0
\(67\) 13140.1 22759.4i 0.357613 0.619403i −0.629949 0.776637i \(-0.716924\pi\)
0.987561 + 0.157233i \(0.0502575\pi\)
\(68\) 0 0
\(69\) 12382.5 4974.07i 0.313101 0.125774i
\(70\) 0 0
\(71\) 76665.7 1.80491 0.902454 0.430786i \(-0.141764\pi\)
0.902454 + 0.430786i \(0.141764\pi\)
\(72\) 0 0
\(73\) 1496.33 0.0328640 0.0164320 0.999865i \(-0.494769\pi\)
0.0164320 + 0.999865i \(0.494769\pi\)
\(74\) 0 0
\(75\) 5133.25 36002.8i 0.105375 0.739065i
\(76\) 0 0
\(77\) −21026.5 + 36419.0i −0.404148 + 0.700006i
\(78\) 0 0
\(79\) −49637.1 85974.0i −0.894826 1.54988i −0.834019 0.551735i \(-0.813966\pi\)
−0.0608070 0.998150i \(-0.519367\pi\)
\(80\) 0 0
\(81\) −52357.1 + 27304.1i −0.886672 + 0.462398i
\(82\) 0 0
\(83\) −25025.7 43345.7i −0.398740 0.690639i 0.594830 0.803851i \(-0.297219\pi\)
−0.993571 + 0.113213i \(0.963886\pi\)
\(84\) 0 0
\(85\) 22683.8 39289.6i 0.340541 0.589834i
\(86\) 0 0
\(87\) −18779.8 + 131715.i −0.266008 + 1.86568i
\(88\) 0 0
\(89\) 136635. 1.82847 0.914235 0.405185i \(-0.132793\pi\)
0.914235 + 0.405185i \(0.132793\pi\)
\(90\) 0 0
\(91\) −88400.8 −1.11906
\(92\) 0 0
\(93\) 42503.6 17073.9i 0.509588 0.204703i
\(94\) 0 0
\(95\) −19261.0 + 33361.0i −0.218963 + 0.379254i
\(96\) 0 0
\(97\) 33325.0 + 57720.5i 0.359617 + 0.622875i 0.987897 0.155113i \(-0.0495740\pi\)
−0.628280 + 0.777987i \(0.716241\pi\)
\(98\) 0 0
\(99\) −48737.1 + 46689.8i −0.499771 + 0.478778i
\(100\) 0 0
\(101\) 12338.7 + 21371.2i 0.120355 + 0.208462i 0.919908 0.392135i \(-0.128263\pi\)
−0.799552 + 0.600596i \(0.794930\pi\)
\(102\) 0 0
\(103\) −57883.5 + 100257.i −0.537603 + 0.931155i 0.461430 + 0.887177i \(0.347337\pi\)
−0.999032 + 0.0439785i \(0.985997\pi\)
\(104\) 0 0
\(105\) 52261.8 + 40999.9i 0.462606 + 0.362919i
\(106\) 0 0
\(107\) 84364.3 0.712360 0.356180 0.934417i \(-0.384079\pi\)
0.356180 + 0.934417i \(0.384079\pi\)
\(108\) 0 0
\(109\) 198400. 1.59947 0.799735 0.600354i \(-0.204973\pi\)
0.799735 + 0.600354i \(0.204973\pi\)
\(110\) 0 0
\(111\) −49510.0 38841.1i −0.381404 0.299215i
\(112\) 0 0
\(113\) −114453. + 198238.i −0.843199 + 1.46046i 0.0439777 + 0.999033i \(0.485997\pi\)
−0.887176 + 0.461430i \(0.847336\pi\)
\(114\) 0 0
\(115\) −12045.9 20864.1i −0.0849364 0.147114i
\(116\) 0 0
\(117\) −136224. 39651.6i −0.920003 0.267791i
\(118\) 0 0
\(119\) −122035. 211371.i −0.789983 1.36829i
\(120\) 0 0
\(121\) 41953.8 72666.2i 0.260500 0.451200i
\(122\) 0 0
\(123\) 273383. 109819.i 1.62933 0.654507i
\(124\) 0 0
\(125\) −153606. −0.879293
\(126\) 0 0
\(127\) −246629. −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(128\) 0 0
\(129\) 44704.6 313542.i 0.236525 1.65890i
\(130\) 0 0
\(131\) 84612.6 146553.i 0.430781 0.746135i −0.566159 0.824296i \(-0.691571\pi\)
0.996941 + 0.0781606i \(0.0249047\pi\)
\(132\) 0 0
\(133\) 103621. + 179477.i 0.507947 + 0.879789i
\(134\) 0 0
\(135\) 62144.3 + 86621.8i 0.293472 + 0.409065i
\(136\) 0 0
\(137\) −49985.3 86577.0i −0.227531 0.394095i 0.729545 0.683933i \(-0.239732\pi\)
−0.957076 + 0.289838i \(0.906399\pi\)
\(138\) 0 0
\(139\) 18699.4 32388.2i 0.0820899 0.142184i −0.822058 0.569404i \(-0.807174\pi\)
0.904147 + 0.427221i \(0.140507\pi\)
\(140\) 0 0
\(141\) 650.815 4564.58i 0.00275683 0.0193354i
\(142\) 0 0
\(143\) −162165. −0.663158
\(144\) 0 0
\(145\) 240205. 0.948773
\(146\) 0 0
\(147\) 88487.5 35545.7i 0.337745 0.135673i
\(148\) 0 0
\(149\) −127267. + 220433.i −0.469623 + 0.813411i −0.999397 0.0347281i \(-0.988943\pi\)
0.529774 + 0.848139i \(0.322277\pi\)
\(150\) 0 0
\(151\) 118363. + 205010.i 0.422448 + 0.731701i 0.996178 0.0873434i \(-0.0278377\pi\)
−0.573731 + 0.819044i \(0.694504\pi\)
\(152\) 0 0
\(153\) −93245.0 380457.i −0.322031 1.31395i
\(154\) 0 0
\(155\) −41348.3 71617.4i −0.138238 0.239436i
\(156\) 0 0
\(157\) −127406. + 220673.i −0.412515 + 0.714497i −0.995164 0.0982266i \(-0.968683\pi\)
0.582649 + 0.812724i \(0.302016\pi\)
\(158\) 0 0
\(159\) −37273.9 29241.7i −0.116926 0.0917297i
\(160\) 0 0
\(161\) −129609. −0.394069
\(162\) 0 0
\(163\) 215050. 0.633973 0.316987 0.948430i \(-0.397329\pi\)
0.316987 + 0.948430i \(0.397329\pi\)
\(164\) 0 0
\(165\) 95870.5 + 75211.3i 0.274142 + 0.215067i
\(166\) 0 0
\(167\) −96168.5 + 166569.i −0.266834 + 0.462171i −0.968043 0.250786i \(-0.919311\pi\)
0.701208 + 0.712956i \(0.252644\pi\)
\(168\) 0 0
\(169\) 15201.2 + 26329.2i 0.0409411 + 0.0709121i
\(170\) 0 0
\(171\) 79174.9 + 323049.i 0.207061 + 0.844847i
\(172\) 0 0
\(173\) 4150.57 + 7189.00i 0.0105437 + 0.0182622i 0.871249 0.490841i \(-0.163310\pi\)
−0.860705 + 0.509103i \(0.829977\pi\)
\(174\) 0 0
\(175\) −176612. + 305902.i −0.435939 + 0.755069i
\(176\) 0 0
\(177\) −249328. + 100156.i −0.598188 + 0.240294i
\(178\) 0 0
\(179\) 574496. 1.34015 0.670077 0.742292i \(-0.266261\pi\)
0.670077 + 0.742292i \(0.266261\pi\)
\(180\) 0 0
\(181\) −224707. −0.509823 −0.254912 0.966964i \(-0.582046\pi\)
−0.254912 + 0.966964i \(0.582046\pi\)
\(182\) 0 0
\(183\) −56444.2 + 395879.i −0.124592 + 0.873846i
\(184\) 0 0
\(185\) −56805.1 + 98389.3i −0.122028 + 0.211358i
\(186\) 0 0
\(187\) −223865. 387745.i −0.468147 0.810854i
\(188\) 0 0
\(189\) 570740. 56529.5i 1.16221 0.115112i
\(190\) 0 0
\(191\) 239041. + 414031.i 0.474121 + 0.821201i 0.999561 0.0296294i \(-0.00943271\pi\)
−0.525440 + 0.850830i \(0.676099\pi\)
\(192\) 0 0
\(193\) 263025. 455572.i 0.508281 0.880368i −0.491673 0.870780i \(-0.663615\pi\)
0.999954 0.00958824i \(-0.00305208\pi\)
\(194\) 0 0
\(195\) −36155.8 + 253583.i −0.0680912 + 0.477567i
\(196\) 0 0
\(197\) −222278. −0.408067 −0.204034 0.978964i \(-0.565405\pi\)
−0.204034 + 0.978964i \(0.565405\pi\)
\(198\) 0 0
\(199\) −109696. −0.196363 −0.0981813 0.995169i \(-0.531303\pi\)
−0.0981813 + 0.995169i \(0.531303\pi\)
\(200\) 0 0
\(201\) −380144. + 152705.i −0.663679 + 0.266602i
\(202\) 0 0
\(203\) 646131. 1.11913e6i 1.10048 1.90608i
\(204\) 0 0
\(205\) −265952. 460642.i −0.441996 0.765560i
\(206\) 0 0
\(207\) −199726. 58135.5i −0.323973 0.0943008i
\(208\) 0 0
\(209\) 190085. + 329237.i 0.301011 + 0.521366i
\(210\) 0 0
\(211\) 309436. 535959.i 0.478482 0.828754i −0.521214 0.853426i \(-0.674521\pi\)
0.999696 + 0.0246717i \(0.00785404\pi\)
\(212\) 0 0
\(213\) −940279. 737657.i −1.42006 1.11405i
\(214\) 0 0
\(215\) −571797. −0.843618
\(216\) 0 0
\(217\) −444893. −0.641367
\(218\) 0 0
\(219\) −18352.0 14397.3i −0.0258567 0.0202848i
\(220\) 0 0
\(221\) 470592. 815089.i 0.648132 1.12260i
\(222\) 0 0
\(223\) −231653. 401234.i −0.311943 0.540301i 0.666840 0.745201i \(-0.267646\pi\)
−0.978783 + 0.204900i \(0.934313\pi\)
\(224\) 0 0
\(225\) −409367. + 392171.i −0.539084 + 0.516439i
\(226\) 0 0
\(227\) 573326. + 993029.i 0.738477 + 1.27908i 0.953181 + 0.302400i \(0.0977878\pi\)
−0.214704 + 0.976679i \(0.568879\pi\)
\(228\) 0 0
\(229\) 175527. 304022.i 0.221185 0.383104i −0.733983 0.679168i \(-0.762341\pi\)
0.955168 + 0.296064i \(0.0956741\pi\)
\(230\) 0 0
\(231\) 608298. 244355.i 0.750043 0.301295i
\(232\) 0 0
\(233\) 814275. 0.982610 0.491305 0.870988i \(-0.336520\pi\)
0.491305 + 0.870988i \(0.336520\pi\)
\(234\) 0 0
\(235\) −8324.30 −0.00983281
\(236\) 0 0
\(237\) −218437. + 1.53204e6i −0.252613 + 1.77173i
\(238\) 0 0
\(239\) 357452. 619124.i 0.404783 0.701105i −0.589513 0.807759i \(-0.700680\pi\)
0.994296 + 0.106654i \(0.0340137\pi\)
\(240\) 0 0
\(241\) −22648.5 39228.3i −0.0251186 0.0435068i 0.853193 0.521596i \(-0.174663\pi\)
−0.878311 + 0.478089i \(0.841330\pi\)
\(242\) 0 0
\(243\) 904856. + 168891.i 0.983023 + 0.183480i
\(244\) 0 0
\(245\) −86082.2 149099.i −0.0916216 0.158693i
\(246\) 0 0
\(247\) −399582. + 692097.i −0.416739 + 0.721813i
\(248\) 0 0
\(249\) −110130. + 772411.i −0.112566 + 0.789496i
\(250\) 0 0
\(251\) −1.35110e6 −1.35364 −0.676822 0.736147i \(-0.736643\pi\)
−0.676822 + 0.736147i \(0.736643\pi\)
\(252\) 0 0
\(253\) −237759. −0.233526
\(254\) 0 0
\(255\) −656244. + 263615.i −0.631997 + 0.253875i
\(256\) 0 0
\(257\) −600097. + 1.03940e6i −0.566747 + 0.981634i 0.430138 + 0.902763i \(0.358465\pi\)
−0.996885 + 0.0788708i \(0.974869\pi\)
\(258\) 0 0
\(259\) 305602. + 529318.i 0.283078 + 0.490306i
\(260\) 0 0
\(261\) 1.49766e6 1.43475e6i 1.36085 1.30369i
\(262\) 0 0
\(263\) 656802. + 1.13761e6i 0.585525 + 1.01416i 0.994810 + 0.101752i \(0.0324449\pi\)
−0.409285 + 0.912407i \(0.634222\pi\)
\(264\) 0 0
\(265\) −42766.1 + 74073.0i −0.0374097 + 0.0647956i
\(266\) 0 0
\(267\) −1.67579e6 1.31467e6i −1.43860 1.12860i
\(268\) 0 0
\(269\) 321363. 0.270779 0.135389 0.990792i \(-0.456771\pi\)
0.135389 + 0.990792i \(0.456771\pi\)
\(270\) 0 0
\(271\) 384928. 0.318388 0.159194 0.987247i \(-0.449110\pi\)
0.159194 + 0.987247i \(0.449110\pi\)
\(272\) 0 0
\(273\) 1.08421e6 + 850570.i 0.880451 + 0.690722i
\(274\) 0 0
\(275\) −323983. + 561155.i −0.258339 + 0.447457i
\(276\) 0 0
\(277\) 847964. + 1.46872e6i 0.664015 + 1.15011i 0.979551 + 0.201194i \(0.0644822\pi\)
−0.315536 + 0.948913i \(0.602184\pi\)
\(278\) 0 0
\(279\) −685573. 199554.i −0.527283 0.153479i
\(280\) 0 0
\(281\) −530669. 919146.i −0.400920 0.694415i 0.592917 0.805264i \(-0.297976\pi\)
−0.993837 + 0.110849i \(0.964643\pi\)
\(282\) 0 0
\(283\) 192313. 333096.i 0.142739 0.247231i −0.785788 0.618496i \(-0.787742\pi\)
0.928527 + 0.371265i \(0.121076\pi\)
\(284\) 0 0
\(285\) 557221. 223838.i 0.406364 0.163238i
\(286\) 0 0
\(287\) −2.86155e6 −2.05067
\(288\) 0 0
\(289\) 1.17871e6 0.830158
\(290\) 0 0
\(291\) 146653. 1.02857e6i 0.101521 0.712033i
\(292\) 0 0
\(293\) 667643. 1.15639e6i 0.454334 0.786929i −0.544316 0.838880i \(-0.683211\pi\)
0.998650 + 0.0519513i \(0.0165441\pi\)
\(294\) 0 0
\(295\) 242551. + 420110.i 0.162273 + 0.281066i
\(296\) 0 0
\(297\) 1.04698e6 103699.i 0.688728 0.0682158i
\(298\) 0 0
\(299\) −249900. 432839.i −0.161655 0.279994i
\(300\) 0 0
\(301\) −1.53809e6 + 2.66404e6i −0.978508 + 1.69483i
\(302\) 0 0
\(303\) 54298.7 380831.i 0.0339768 0.238301i
\(304\) 0 0
\(305\) 721954. 0.444386
\(306\) 0 0
\(307\) 636269. 0.385296 0.192648 0.981268i \(-0.438292\pi\)
0.192648 + 0.981268i \(0.438292\pi\)
\(308\) 0 0
\(309\) 1.67457e6 672680.i 0.997716 0.400786i
\(310\) 0 0
\(311\) 269890. 467464.i 0.158229 0.274061i −0.776001 0.630732i \(-0.782755\pi\)
0.934230 + 0.356671i \(0.116088\pi\)
\(312\) 0 0
\(313\) −976605. 1.69153e6i −0.563454 0.975931i −0.997192 0.0748915i \(-0.976139\pi\)
0.433738 0.901039i \(-0.357194\pi\)
\(314\) 0 0
\(315\) −246483. 1.00570e6i −0.139962 0.571073i
\(316\) 0 0
\(317\) −781983. 1.35443e6i −0.437068 0.757024i 0.560394 0.828226i \(-0.310650\pi\)
−0.997462 + 0.0712021i \(0.977316\pi\)
\(318\) 0 0
\(319\) 1.18528e6 2.05297e6i 0.652146 1.12955i
\(320\) 0 0
\(321\) −1.03470e6 811732.i −0.560469 0.439693i
\(322\) 0 0
\(323\) −2.20646e6 −1.17676
\(324\) 0 0
\(325\) −1.36210e6 −0.715323
\(326\) 0 0
\(327\) −2.43331e6 1.90896e6i −1.25843 0.987249i
\(328\) 0 0
\(329\) −22391.6 + 38783.5i −0.0114050 + 0.0197541i
\(330\) 0 0
\(331\) 1.28000e6 + 2.21702e6i 0.642154 + 1.11224i 0.984951 + 0.172834i \(0.0552925\pi\)
−0.342796 + 0.939410i \(0.611374\pi\)
\(332\) 0 0
\(333\) 233505. + 952745.i 0.115395 + 0.470832i
\(334\) 0 0
\(335\) 369811. + 640532.i 0.180040 + 0.311838i
\(336\) 0 0
\(337\) 299646. 519002.i 0.143725 0.248940i −0.785171 0.619279i \(-0.787425\pi\)
0.928897 + 0.370339i \(0.120758\pi\)
\(338\) 0 0
\(339\) 3.31112e6 1.33009e6i 1.56486 0.628609i
\(340\) 0 0
\(341\) −816125. −0.380076
\(342\) 0 0
\(343\) 1.61850e6 0.742808
\(344\) 0 0
\(345\) −53010.1 + 371793.i −0.0239779 + 0.168172i
\(346\) 0 0
\(347\) −1.34386e6 + 2.32764e6i −0.599144 + 1.03775i 0.393804 + 0.919195i \(0.371159\pi\)
−0.992948 + 0.118553i \(0.962174\pi\)
\(348\) 0 0
\(349\) −335807. 581635.i −0.147580 0.255615i 0.782753 0.622333i \(-0.213815\pi\)
−0.930332 + 0.366717i \(0.880482\pi\)
\(350\) 0 0
\(351\) 1.28923e6 + 1.79703e6i 0.558549 + 0.778550i
\(352\) 0 0
\(353\) 764881. + 1.32481e6i 0.326706 + 0.565871i 0.981856 0.189627i \(-0.0607280\pi\)
−0.655150 + 0.755499i \(0.727395\pi\)
\(354\) 0 0
\(355\) −1.07883e6 + 1.86858e6i −0.454339 + 0.786939i
\(356\) 0 0
\(357\) −537038. + 3.76659e6i −0.223015 + 1.56415i
\(358\) 0 0
\(359\) 3.27210e6 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(360\) 0 0
\(361\) −602583. −0.243360
\(362\) 0 0
\(363\) −1.21372e6 + 487557.i −0.483452 + 0.194204i
\(364\) 0 0
\(365\) −21056.1 + 36470.2i −0.00827267 + 0.0143287i
\(366\) 0 0
\(367\) −313571. 543121.i −0.121526 0.210490i 0.798843 0.601539i \(-0.205446\pi\)
−0.920370 + 0.391049i \(0.872112\pi\)
\(368\) 0 0
\(369\) −4.40960e6 1.28353e6i −1.68591 0.490727i
\(370\) 0 0
\(371\) 230074. + 398500.i 0.0867826 + 0.150312i
\(372\) 0 0
\(373\) −66186.8 + 114639.i −0.0246320 + 0.0426638i −0.878079 0.478516i \(-0.841175\pi\)
0.853447 + 0.521180i \(0.174508\pi\)
\(374\) 0 0
\(375\) 1.88393e6 + 1.47796e6i 0.691809 + 0.542730i
\(376\) 0 0
\(377\) 4.98322e6 1.80574
\(378\) 0 0
\(379\) −163225. −0.0583700 −0.0291850 0.999574i \(-0.509291\pi\)
−0.0291850 + 0.999574i \(0.509291\pi\)
\(380\) 0 0
\(381\) 3.02482e6 + 2.37300e6i 1.06755 + 0.837501i
\(382\) 0 0
\(383\) 398301. 689877.i 0.138744 0.240312i −0.788277 0.615320i \(-0.789027\pi\)
0.927021 + 0.375008i \(0.122360\pi\)
\(384\) 0 0
\(385\) −591763. 1.02496e6i −0.203468 0.352417i
\(386\) 0 0
\(387\) −3.56510e6 + 3.41535e6i −1.21003 + 1.15920i
\(388\) 0 0
\(389\) −2.04745e6 3.54629e6i −0.686024 1.18823i −0.973114 0.230325i \(-0.926021\pi\)
0.287089 0.957904i \(-0.407312\pi\)
\(390\) 0 0
\(391\) 689961. 1.19505e6i 0.228235 0.395315i
\(392\) 0 0
\(393\) −2.44784e6 + 983307.i −0.799470 + 0.321150i
\(394\) 0 0
\(395\) 2.79394e6 0.900998
\(396\) 0 0
\(397\) −5.58867e6 −1.77964 −0.889820 0.456312i \(-0.849170\pi\)
−0.889820 + 0.456312i \(0.849170\pi\)
\(398\) 0 0
\(399\) 456002. 3.19823e6i 0.143395 1.00572i
\(400\) 0 0
\(401\) −1.11676e6 + 1.93429e6i −0.346817 + 0.600705i −0.985682 0.168614i \(-0.946071\pi\)
0.638865 + 0.769319i \(0.279404\pi\)
\(402\) 0 0
\(403\) −857798. 1.48575e6i −0.263101 0.455704i
\(404\) 0 0
\(405\) 71273.1 1.66032e6i 0.0215918 0.502985i
\(406\) 0 0
\(407\) 560604. + 970995.i 0.167753 + 0.290557i
\(408\) 0 0
\(409\) 2.30256e6 3.98815e6i 0.680617 1.17886i −0.294176 0.955751i \(-0.595045\pi\)
0.974793 0.223111i \(-0.0716214\pi\)
\(410\) 0 0
\(411\) −219969. + 1.54278e6i −0.0642329 + 0.450506i
\(412\) 0 0
\(413\) 2.60976e6 0.752880
\(414\) 0 0
\(415\) 1.40863e6 0.401491
\(416\) 0 0
\(417\) −540973. + 217310.i −0.152347 + 0.0611985i
\(418\) 0 0
\(419\) −571064. + 989112.i −0.158909 + 0.275239i −0.934476 0.356027i \(-0.884131\pi\)
0.775566 + 0.631266i \(0.217464\pi\)
\(420\) 0 0
\(421\) −962383. 1.66690e6i −0.264632 0.458356i 0.702835 0.711353i \(-0.251917\pi\)
−0.967467 + 0.252996i \(0.918584\pi\)
\(422\) 0 0
\(423\) −51901.2 + 49721.0i −0.0141035 + 0.0135111i
\(424\) 0 0
\(425\) −1.88035e6 3.25687e6i −0.504972 0.874637i
\(426\) 0 0
\(427\) 1.94199e6 3.36363e6i 0.515440 0.892769i
\(428\) 0 0
\(429\) 1.98890e6 + 1.56031e6i 0.521758 + 0.409324i
\(430\) 0 0
\(431\) 2.21303e6 0.573843 0.286922 0.957954i \(-0.407368\pi\)
0.286922 + 0.957954i \(0.407368\pi\)
\(432\) 0 0
\(433\) 3.00235e6 0.769558 0.384779 0.923009i \(-0.374278\pi\)
0.384779 + 0.923009i \(0.374278\pi\)
\(434\) 0 0
\(435\) −2.94604e6 2.31119e6i −0.746474 0.585616i
\(436\) 0 0
\(437\) −585851. + 1.01472e6i −0.146752 + 0.254181i
\(438\) 0 0
\(439\) −960857. 1.66425e6i −0.237956 0.412153i 0.722171 0.691714i \(-0.243144\pi\)
−0.960128 + 0.279562i \(0.909811\pi\)
\(440\) 0 0
\(441\) −1.42728e6 415447.i −0.349472 0.101723i
\(442\) 0 0
\(443\) 924258. + 1.60086e6i 0.223761 + 0.387565i 0.955947 0.293540i \(-0.0948332\pi\)
−0.732186 + 0.681105i \(0.761500\pi\)
\(444\) 0 0
\(445\) −1.92271e6 + 3.33022e6i −0.460270 + 0.797211i
\(446\) 0 0
\(447\) 3.68183e6 1.47900e6i 0.871555 0.350107i
\(448\) 0 0
\(449\) 3.45640e6 0.809110 0.404555 0.914514i \(-0.367426\pi\)
0.404555 + 0.914514i \(0.367426\pi\)
\(450\) 0 0
\(451\) −5.24931e6 −1.21524
\(452\) 0 0
\(453\) 520877. 3.65324e6i 0.119259 0.836436i
\(454\) 0 0
\(455\) 1.24396e6 2.15460e6i 0.281694 0.487908i
\(456\) 0 0
\(457\) −1.79319e6 3.10589e6i −0.401638 0.695658i 0.592286 0.805728i \(-0.298226\pi\)
−0.993924 + 0.110070i \(0.964892\pi\)
\(458\) 0 0
\(459\) −2.51704e6 + 5.56336e6i −0.557647 + 1.23255i
\(460\) 0 0
\(461\) −4.21775e6 7.30536e6i −0.924333 1.60099i −0.792630 0.609703i \(-0.791289\pi\)
−0.131703 0.991289i \(-0.542045\pi\)
\(462\) 0 0
\(463\) −2.47237e6 + 4.28227e6i −0.535995 + 0.928370i 0.463120 + 0.886296i \(0.346730\pi\)
−0.999114 + 0.0420745i \(0.986603\pi\)
\(464\) 0 0
\(465\) −181961. + 1.27621e6i −0.0390252 + 0.273709i
\(466\) 0 0
\(467\) −4.12589e6 −0.875438 −0.437719 0.899112i \(-0.644213\pi\)
−0.437719 + 0.899112i \(0.644213\pi\)
\(468\) 0 0
\(469\) 3.97904e6 0.835307
\(470\) 0 0
\(471\) 3.68585e6 1.48062e6i 0.765571 0.307532i
\(472\) 0 0
\(473\) −2.82151e6 + 4.88700e6i −0.579867 + 1.00436i
\(474\) 0 0
\(475\) 1.59662e6 + 2.76543e6i 0.324689 + 0.562378i
\(476\) 0 0
\(477\) 175796. + 717280.i 0.0353763 + 0.144342i
\(478\) 0 0
\(479\) 561301. + 972203.i 0.111778 + 0.193606i 0.916487 0.400064i \(-0.131012\pi\)
−0.804709 + 0.593669i \(0.797679\pi\)
\(480\) 0 0
\(481\) −1.17846e6 + 2.04115e6i −0.232248 + 0.402265i
\(482\) 0 0
\(483\) 1.58962e6 + 1.24707e6i 0.310045 + 0.243233i
\(484\) 0 0
\(485\) −1.87577e6 −0.362097
\(486\) 0 0
\(487\) 8.11380e6 1.55025 0.775126 0.631807i \(-0.217687\pi\)
0.775126 + 0.631807i \(0.217687\pi\)
\(488\) 0 0
\(489\) −2.63752e6 2.06916e6i −0.498797 0.391310i
\(490\) 0 0
\(491\) 1.66481e6 2.88353e6i 0.311645 0.539786i −0.667073 0.744992i \(-0.732453\pi\)
0.978719 + 0.205207i \(0.0657866\pi\)
\(492\) 0 0
\(493\) 6.87921e6 + 1.19151e7i 1.27474 + 2.20791i
\(494\) 0 0
\(495\) −452156. 1.84488e6i −0.0829422 0.338420i
\(496\) 0 0
\(497\) 5.80389e6 + 1.00526e7i 1.05397 + 1.82553i
\(498\) 0 0
\(499\) −940630. + 1.62922e6i −0.169109 + 0.292906i −0.938107 0.346346i \(-0.887422\pi\)
0.768998 + 0.639252i \(0.220756\pi\)
\(500\) 0 0
\(501\) 2.78216e6 1.11760e6i 0.495207 0.198926i
\(502\) 0 0
\(503\) −7.96749e6 −1.40411 −0.702056 0.712122i \(-0.747734\pi\)
−0.702056 + 0.712122i \(0.747734\pi\)
\(504\) 0 0
\(505\) −694511. −0.121186
\(506\) 0 0
\(507\) 66895.5 469180.i 0.0115578 0.0810625i
\(508\) 0 0
\(509\) −5.40561e6 + 9.36279e6i −0.924805 + 1.60181i −0.132931 + 0.991125i \(0.542439\pi\)
−0.791874 + 0.610684i \(0.790894\pi\)
\(510\) 0 0
\(511\) 113278. + 196204.i 0.0191908 + 0.0332395i
\(512\) 0 0
\(513\) 2.13724e6 4.72389e6i 0.358558 0.792512i
\(514\) 0 0
\(515\) −1.62905e6 2.82160e6i −0.270655 0.468789i
\(516\) 0 0
\(517\) −41075.9 + 71145.5i −0.00675865 + 0.0117063i
\(518\) 0 0
\(519\) 18265.4 128106.i 0.00297653 0.0208763i
\(520\) 0 0
\(521\) −1.19670e6 −0.193148 −0.0965740 0.995326i \(-0.530788\pi\)
−0.0965740 + 0.995326i \(0.530788\pi\)
\(522\) 0 0
\(523\) −6.43371e6 −1.02851 −0.514254 0.857638i \(-0.671931\pi\)
−0.514254 + 0.857638i \(0.671931\pi\)
\(524\) 0 0
\(525\) 5.10940e6 2.05246e6i 0.809043 0.324995i
\(526\) 0 0
\(527\) 2.36834e6 4.10209e6i 0.371465 0.643396i
\(528\) 0 0
\(529\) 2.85178e6 + 4.93943e6i 0.443074 + 0.767427i
\(530\) 0 0
\(531\) 4.02160e6 + 1.17059e6i 0.618960 + 0.180164i
\(532\) 0 0
\(533\) −5.51735e6 9.55633e6i −0.841226 1.45705i
\(534\) 0 0
\(535\) −1.18716e6 + 2.05622e6i −0.179318 + 0.310588i
\(536\) 0 0
\(537\) −7.04600e6 5.52765e6i −1.05440 0.827190i
\(538\) 0 0
\(539\) −1.69907e6 −0.251907
\(540\) 0 0
\(541\) 5.85989e6 0.860788 0.430394 0.902641i \(-0.358375\pi\)
0.430394 + 0.902641i \(0.358375\pi\)
\(542\) 0 0
\(543\) 2.75595e6 + 2.16207e6i 0.401118 + 0.314681i
\(544\) 0 0
\(545\) −2.79185e6 + 4.83563e6i −0.402625 + 0.697368i
\(546\) 0 0
\(547\) −2.59436e6 4.49357e6i −0.370734 0.642130i 0.618945 0.785434i \(-0.287560\pi\)
−0.989679 + 0.143305i \(0.954227\pi\)
\(548\) 0 0
\(549\) 4.50132e6 4.31223e6i 0.637395 0.610621i
\(550\) 0 0
\(551\) −5.84118e6 1.01172e7i −0.819637 1.41965i
\(552\) 0 0
\(553\) 7.51545e6 1.30171e7i 1.04506 1.81010i
\(554\) 0 0
\(555\) 1.64337e6 660148.i 0.226466 0.0909723i
\(556\) 0 0
\(557\) 5.07405e6 0.692973 0.346487 0.938055i \(-0.387375\pi\)
0.346487 + 0.938055i \(0.387375\pi\)
\(558\) 0 0
\(559\) −1.18623e7 −1.60561
\(560\) 0 0
\(561\) −985158. + 6.90954e6i −0.132160 + 0.926919i
\(562\) 0 0
\(563\) 3.05439e6 5.29036e6i 0.406119 0.703419i −0.588332 0.808620i \(-0.700215\pi\)
0.994451 + 0.105200i \(0.0335484\pi\)
\(564\) 0 0
\(565\) −3.22111e6 5.57913e6i −0.424507 0.735268i
\(566\) 0 0
\(567\) −7.54384e6 4.79819e6i −0.985451 0.626787i
\(568\) 0 0
\(569\) 5.40483e6 + 9.36143e6i 0.699844 + 1.21216i 0.968520 + 0.248934i \(0.0800803\pi\)
−0.268677 + 0.963230i \(0.586586\pi\)
\(570\) 0 0
\(571\) −6.02796e6 + 1.04407e7i −0.773714 + 1.34011i 0.161801 + 0.986823i \(0.448270\pi\)
−0.935515 + 0.353288i \(0.885063\pi\)
\(572\) 0 0
\(573\) 1.05194e6 7.37794e6i 0.133846 0.938747i
\(574\) 0 0
\(575\) −1.99706e6 −0.251896
\(576\) 0 0
\(577\) 1.22323e7 1.52957 0.764786 0.644285i \(-0.222845\pi\)
0.764786 + 0.644285i \(0.222845\pi\)
\(578\) 0 0
\(579\) −7.60931e6 + 3.05669e6i −0.943298 + 0.378926i
\(580\) 0 0
\(581\) 3.78908e6 6.56288e6i 0.465686 0.806593i
\(582\) 0 0
\(583\) 422054. + 731019.i 0.0514277 + 0.0890754i
\(584\) 0 0
\(585\) 2.88335e6 2.76223e6i 0.348344 0.333711i
\(586\) 0 0
\(587\) 4.29817e6 + 7.44465e6i 0.514859 + 0.891762i 0.999851 + 0.0172439i \(0.00548917\pi\)
−0.484992 + 0.874519i \(0.661177\pi\)
\(588\) 0 0
\(589\) −2.01097e6 + 3.48311e6i −0.238846 + 0.413693i
\(590\) 0 0
\(591\) 2.72617e6 + 2.13871e6i 0.321059 + 0.251874i
\(592\) 0 0
\(593\) −5.78455e6 −0.675511 −0.337756 0.941234i \(-0.609668\pi\)
−0.337756 + 0.941234i \(0.609668\pi\)
\(594\) 0 0
\(595\) 6.86903e6 0.795432
\(596\) 0 0
\(597\) 1.34539e6 + 1.05547e6i 0.154494 + 0.121202i
\(598\) 0 0
\(599\) 2.62557e6 4.54761e6i 0.298989 0.517865i −0.676916 0.736061i \(-0.736684\pi\)
0.975905 + 0.218196i \(0.0700172\pi\)
\(600\) 0 0
\(601\) 3.11169e6 + 5.38960e6i 0.351407 + 0.608654i 0.986496 0.163784i \(-0.0523701\pi\)
−0.635090 + 0.772439i \(0.719037\pi\)
\(602\) 0 0
\(603\) 6.13163e6 + 1.78477e6i 0.686725 + 0.199889i
\(604\) 0 0
\(605\) 1.18073e6 + 2.04509e6i 0.131148 + 0.227156i
\(606\) 0 0
\(607\) 7.94049e6 1.37533e7i 0.874733 1.51508i 0.0176871 0.999844i \(-0.494370\pi\)
0.857046 0.515239i \(-0.172297\pi\)
\(608\) 0 0
\(609\) −1.86926e7 + 7.50887e6i −2.04233 + 0.820411i
\(610\) 0 0
\(611\) −172693. −0.0187142
\(612\) 0 0
\(613\) −1.28661e7 −1.38292 −0.691458 0.722417i \(-0.743031\pi\)
−0.691458 + 0.722417i \(0.743031\pi\)
\(614\) 0 0
\(615\) −1.17037e6 + 8.20854e6i −0.124777 + 0.875142i
\(616\) 0 0
\(617\) 3.43797e6 5.95473e6i 0.363571 0.629723i −0.624975 0.780645i \(-0.714891\pi\)
0.988546 + 0.150922i \(0.0482242\pi\)
\(618\) 0 0
\(619\) −6.52408e6 1.13000e7i −0.684373 1.18537i −0.973633 0.228118i \(-0.926743\pi\)
0.289261 0.957250i \(-0.406591\pi\)
\(620\) 0 0
\(621\) 1.89021e6 + 2.63472e6i 0.196689 + 0.274161i
\(622\) 0 0
\(623\) 1.03438e7 + 1.79160e7i 1.06773 + 1.84936i
\(624\) 0 0
\(625\) −1.48369e6 + 2.56983e6i −0.151930 + 0.263151i
\(626\) 0 0
\(627\) 836504. 5.86693e6i 0.0849765 0.595994i
\(628\) 0 0
\(629\) −6.50734e6 −0.655809
\(630\) 0 0
\(631\) −1.52784e7 −1.52758 −0.763790 0.645464i \(-0.776664\pi\)
−0.763790 + 0.645464i \(0.776664\pi\)
\(632\) 0 0
\(633\) −8.95200e6 + 3.59605e6i −0.887995 + 0.356711i
\(634\) 0 0
\(635\) 3.47052e6 6.01111e6i 0.341554 0.591590i
\(636\) 0 0
\(637\) −1.78583e6 3.09315e6i −0.174378 0.302032i
\(638\) 0 0
\(639\) 4.43466e6 + 1.80942e7i 0.429643 + 1.75303i
\(640\) 0 0
\(641\) 5.96157e6 + 1.03257e7i 0.573080 + 0.992604i 0.996247 + 0.0865524i \(0.0275850\pi\)
−0.423167 + 0.906052i \(0.639082\pi\)
\(642\) 0 0
\(643\) 3.00302e6 5.20137e6i 0.286438 0.496125i −0.686519 0.727112i \(-0.740862\pi\)
0.972957 + 0.230987i \(0.0741955\pi\)
\(644\) 0 0
\(645\) 7.01291e6 + 5.50169e6i 0.663741 + 0.520711i
\(646\) 0 0
\(647\) 1.19440e7 1.12173 0.560864 0.827908i \(-0.310469\pi\)
0.560864 + 0.827908i \(0.310469\pi\)
\(648\) 0 0
\(649\) 4.78742e6 0.446159
\(650\) 0 0
\(651\) 5.45647e6 + 4.28065e6i 0.504614 + 0.395874i
\(652\) 0 0
\(653\) 1.53297e6 2.65518e6i 0.140686 0.243675i −0.787069 0.616864i \(-0.788403\pi\)
0.927755 + 0.373190i \(0.121736\pi\)
\(654\) 0 0
\(655\) 2.38131e6 + 4.12454e6i 0.216876 + 0.375641i
\(656\) 0 0
\(657\) 86553.9 + 353157.i 0.00782300 + 0.0319193i
\(658\) 0 0
\(659\) 1.55065e6 + 2.68581e6i 0.139092 + 0.240914i 0.927153 0.374683i \(-0.122248\pi\)
−0.788061 + 0.615597i \(0.788915\pi\)
\(660\) 0 0
\(661\) −6.48853e6 + 1.12385e7i −0.577621 + 1.00047i 0.418130 + 0.908387i \(0.362685\pi\)
−0.995751 + 0.0920819i \(0.970648\pi\)
\(662\) 0 0
\(663\) −1.36142e7 + 5.46888e6i −1.20284 + 0.483186i
\(664\) 0 0
\(665\) −5.83253e6 −0.511450
\(666\) 0 0
\(667\) 7.30618e6 0.635881
\(668\) 0 0
\(669\) −1.01943e6 + 7.14991e6i −0.0880627 + 0.617640i
\(670\) 0 0
\(671\) 3.56245e6 6.17034e6i 0.305452 0.529058i
\(672\) 0 0
\(673\) −1.10703e7 1.91743e7i −0.942154 1.63186i −0.761352 0.648338i \(-0.775464\pi\)
−0.180801 0.983520i \(-0.557869\pi\)
\(674\) 0 0
\(675\) 8.79412e6 871023.i 0.742904 0.0735817i
\(676\) 0 0
\(677\) −799850. 1.38538e6i −0.0670713 0.116171i 0.830540 0.556960i \(-0.188032\pi\)
−0.897611 + 0.440789i \(0.854699\pi\)
\(678\) 0 0
\(679\) −5.04566e6 + 8.73934e6i −0.419994 + 0.727452i
\(680\) 0 0
\(681\) 2.52302e6 1.76956e7i 0.208475 1.46217i
\(682\) 0 0
\(683\) 1.36986e7 1.12363 0.561816 0.827262i \(-0.310103\pi\)
0.561816 + 0.827262i \(0.310103\pi\)
\(684\) 0 0
\(685\) 2.81353e6 0.229100
\(686\) 0 0
\(687\) −5.07801e6 + 2.03985e6i −0.410489 + 0.164895i
\(688\) 0 0
\(689\) −887210. + 1.53669e6i −0.0711998 + 0.123322i
\(690\) 0 0
\(691\) 2.09107e6 + 3.62183e6i 0.166599 + 0.288558i 0.937222 0.348733i \(-0.113388\pi\)
−0.770623 + 0.637291i \(0.780055\pi\)
\(692\) 0 0
\(693\) −9.81170e6 2.85595e6i −0.776088 0.225901i
\(694\) 0 0
\(695\) 526268. + 911522.i 0.0413280 + 0.0715822i
\(696\) 0 0
\(697\) 1.52331e7 2.63846e7i 1.18770 2.05716i
\(698\) 0 0
\(699\) −9.98681e6 7.83474e6i −0.773097 0.606501i
\(700\) 0 0
\(701\) −1.47134e7 −1.13089 −0.565443 0.824788i \(-0.691295\pi\)
−0.565443 + 0.824788i \(0.691295\pi\)
\(702\) 0 0
\(703\) 5.52543e6 0.421675
\(704\) 0 0
\(705\) 102095. + 80094.2i 0.00773625 + 0.00606916i
\(706\) 0 0
\(707\) −1.86818e6 + 3.23577e6i −0.140562 + 0.243461i
\(708\) 0 0
\(709\) 4.25908e6 + 7.37694e6i 0.318200 + 0.551139i 0.980113 0.198442i \(-0.0635883\pi\)
−0.661913 + 0.749581i \(0.730255\pi\)
\(710\) 0 0
\(711\) 1.74199e7 1.66882e7i 1.29233 1.23804i
\(712\) 0 0
\(713\) −1.25767e6 2.17834e6i −0.0926493 0.160473i
\(714\) 0 0
\(715\) 2.28195e6 3.95246e6i 0.166933 0.289136i
\(716\) 0 0
\(717\) −1.03411e7 + 4.15404e6i −0.751221 + 0.301768i
\(718\) 0 0
\(719\) −1.20183e7 −0.867003 −0.433502 0.901153i \(-0.642722\pi\)
−0.433502 + 0.901153i \(0.642722\pi\)
\(720\) 0 0
\(721\) −1.75280e7 −1.25573
\(722\) 0 0
\(723\) −99668.7 + 699040.i −0.00709109 + 0.0497343i
\(724\) 0 0
\(725\) 9.95577e6 1.72439e7i 0.703445 1.21840i
\(726\) 0 0
\(727\) −1.49257e6 2.58521e6i −0.104737 0.181409i 0.808894 0.587955i \(-0.200067\pi\)
−0.913631 + 0.406545i \(0.866733\pi\)
\(728\) 0 0
\(729\) −9.47274e6 1.07777e7i −0.660171 0.751115i
\(730\) 0 0
\(731\) −1.63757e7 2.83635e7i −1.13346 1.96321i
\(732\) 0 0
\(733\) −1.05675e7 + 1.83035e7i −0.726464 + 1.25827i 0.231905 + 0.972739i \(0.425504\pi\)
−0.958369 + 0.285534i \(0.907829\pi\)
\(734\) 0 0
\(735\) −378820. + 2.65691e6i −0.0258651 + 0.181409i
\(736\) 0 0
\(737\) 7.29926e6 0.495006
\(738\) 0 0
\(739\) 1.33961e7 0.902337 0.451168 0.892439i \(-0.351007\pi\)
0.451168 + 0.892439i \(0.351007\pi\)
\(740\) 0 0
\(741\) 1.15599e7 4.64366e6i 0.773409 0.310681i
\(742\) 0 0
\(743\) −5.95418e6 + 1.03129e7i −0.395685 + 0.685347i −0.993188 0.116519i \(-0.962826\pi\)
0.597503 + 0.801867i \(0.296160\pi\)
\(744\) 0 0
\(745\) −3.58175e6 6.20377e6i −0.236431 0.409511i
\(746\) 0 0
\(747\) 8.78265e6 8.41372e6i 0.575869 0.551679i
\(748\) 0 0
\(749\) 6.38671e6 + 1.10621e7i 0.415980 + 0.720499i
\(750\) 0 0
\(751\) −2.33184e6 + 4.03886e6i −0.150868 + 0.261312i −0.931547 0.363621i \(-0.881540\pi\)
0.780679 + 0.624933i \(0.214874\pi\)
\(752\) 0 0
\(753\) 1.65708e7 + 1.30000e7i 1.06502 + 0.835517i
\(754\) 0 0
\(755\) −6.66232e6 −0.425361
\(756\) 0 0
\(757\) 138599. 0.00879065 0.00439532 0.999990i \(-0.498601\pi\)
0.00439532 + 0.999990i \(0.498601\pi\)
\(758\) 0 0
\(759\) 2.91604e6 + 2.28766e6i 0.183734 + 0.144141i
\(760\) 0 0
\(761\) −1.19856e6 + 2.07597e6i −0.0750237 + 0.129945i −0.901097 0.433618i \(-0.857237\pi\)
0.826073 + 0.563563i \(0.190570\pi\)
\(762\) 0 0
\(763\) 1.50197e7 + 2.60148e7i 0.934005 + 1.61774i
\(764\) 0 0
\(765\) 1.05851e7 + 3.08106e6i 0.653942 + 0.190347i
\(766\) 0 0
\(767\) 5.03188e6 + 8.71546e6i 0.308846 + 0.534936i
\(768\) 0 0
\(769\) −399739. + 692369.i −0.0243759 + 0.0422203i −0.877956 0.478741i \(-0.841093\pi\)
0.853580 + 0.520962i \(0.174427\pi\)
\(770\) 0 0
\(771\) 1.73608e7 6.97390e6i 1.05180 0.422513i
\(772\) 0 0
\(773\) 1.07743e6 0.0648546 0.0324273 0.999474i \(-0.489676\pi\)
0.0324273 + 0.999474i \(0.489676\pi\)
\(774\) 0 0
\(775\) −6.85505e6 −0.409974
\(776\) 0 0
\(777\) 1.34486e6 9.43232e6i 0.0799140 0.560488i
\(778\) 0 0
\(779\) −1.29346e7 + 2.24033e7i −0.763674 + 1.32272i
\(780\) 0 0
\(781\) 1.06468e7 + 1.84408e7i 0.624586 + 1.08182i
\(782\) 0 0
\(783\) −3.21730e7 + 3.18661e6i −1.87537 + 0.185748i
\(784\) 0 0
\(785\) −3.58566e6 6.21055e6i −0.207680 0.359713i
\(786\) 0 0
\(787\) −1.53546e6 + 2.65949e6i −0.0883692 + 0.153060i −0.906822 0.421514i \(-0.861499\pi\)
0.818453 + 0.574574i \(0.194832\pi\)
\(788\) 0 0
\(789\) 2.89038e6 2.02721e7i 0.165296 1.15932i
\(790\) 0 0
\(791\) −3.46581e7 −1.96953
\(792\) 0 0
\(793\) 1.49774e7 0.845774
\(794\) 0 0
\(795\) 1.23722e6