Properties

Label 69.7.d.a.22.18
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.18
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.17

$q$-expansion

\(f(q)\) \(=\) \(q+6.36312 q^{2} +15.5885 q^{3} -23.5107 q^{4} +60.2242i q^{5} +99.1913 q^{6} +233.613i q^{7} -556.841 q^{8} +243.000 q^{9} +O(q^{10})\) \(q+6.36312 q^{2} +15.5885 q^{3} -23.5107 q^{4} +60.2242i q^{5} +99.1913 q^{6} +233.613i q^{7} -556.841 q^{8} +243.000 q^{9} +383.214i q^{10} +1397.49i q^{11} -366.495 q^{12} -1285.15 q^{13} +1486.51i q^{14} +938.802i q^{15} -2038.57 q^{16} +2821.93i q^{17} +1546.24 q^{18} +10185.1i q^{19} -1415.91i q^{20} +3641.66i q^{21} +8892.40i q^{22} +(-3980.90 - 11497.3i) q^{23} -8680.29 q^{24} +11998.1 q^{25} -8177.54 q^{26} +3788.00 q^{27} -5492.39i q^{28} +5523.92 q^{29} +5973.71i q^{30} -27306.5 q^{31} +22666.2 q^{32} +21784.7i q^{33} +17956.3i q^{34} -14069.1 q^{35} -5713.09 q^{36} +39765.7i q^{37} +64809.3i q^{38} -20033.4 q^{39} -33535.3i q^{40} -18455.9 q^{41} +23172.4i q^{42} -30920.7i q^{43} -32855.9i q^{44} +14634.5i q^{45} +(-25330.9 - 73158.9i) q^{46} +62793.6 q^{47} -31778.1 q^{48} +63074.0 q^{49} +76345.1 q^{50} +43989.5i q^{51} +30214.6 q^{52} -56165.6i q^{53} +24103.5 q^{54} -84162.6 q^{55} -130085. i q^{56} +158771. i q^{57} +35149.4 q^{58} -159966. q^{59} -22071.8i q^{60} -333535. i q^{61} -173755. q^{62} +56767.9i q^{63} +274696. q^{64} -77396.8i q^{65} +138619. i q^{66} -244298. i q^{67} -66345.4i q^{68} +(-62056.1 - 179225. i) q^{69} -89523.7 q^{70} +437275. q^{71} -135312. q^{72} +494935. q^{73} +253034. i q^{74} +187031. q^{75} -239459. i q^{76} -326471. q^{77} -127475. q^{78} -571913. i q^{79} -122771. i q^{80} +59049.0 q^{81} -117437. q^{82} +720923. i q^{83} -85617.9i q^{84} -169948. q^{85} -196752. i q^{86} +86109.4 q^{87} -778179. i q^{88} +785492. i q^{89} +93120.9i q^{90} -300226. i q^{91} +(93593.5 + 270310. i) q^{92} -425666. q^{93} +399563. q^{94} -613392. q^{95} +353331. q^{96} -274434. i q^{97} +401348. q^{98} +339590. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + O(q^{10}) \) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + 384q^{13} + 29544q^{16} - 4860q^{18} + 29336q^{23} - 39204q^{24} - 61272q^{25} + 10088q^{26} + 64672q^{29} + 9696q^{31} - 319620q^{32} - 225744q^{35} + 198288q^{36} - 11664q^{39} + 135280q^{41} + 233232q^{46} - 74336q^{47} + 552096q^{48} - 722136q^{49} + 619324q^{50} + 1059720q^{52} - 78732q^{54} - 1019328q^{55} - 694344q^{58} + 1057648q^{59} - 488776q^{62} - 273888q^{64} - 23328q^{69} + 2785512q^{70} - 255392q^{71} - 228420q^{72} - 322560q^{73} - 365472q^{75} - 1002960q^{77} - 171072q^{78} + 1417176q^{81} - 5732712q^{82} - 2704704q^{85} + 611712q^{87} - 1611444q^{92} + 2484432q^{93} - 147720q^{94} - 1672656q^{95} - 1818612q^{96} + 9104212q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.36312 0.795390 0.397695 0.917518i \(-0.369810\pi\)
0.397695 + 0.917518i \(0.369810\pi\)
\(3\) 15.5885 0.577350
\(4\) −23.5107 −0.367354
\(5\) 60.2242i 0.481793i 0.970551 + 0.240897i \(0.0774415\pi\)
−0.970551 + 0.240897i \(0.922559\pi\)
\(6\) 99.1913 0.459219
\(7\) 233.613i 0.681087i 0.940229 + 0.340544i \(0.110611\pi\)
−0.940229 + 0.340544i \(0.889389\pi\)
\(8\) −556.841 −1.08758
\(9\) 243.000 0.333333
\(10\) 383.214i 0.383214i
\(11\) 1397.49i 1.04995i 0.851116 + 0.524977i \(0.175926\pi\)
−0.851116 + 0.524977i \(0.824074\pi\)
\(12\) −366.495 −0.212092
\(13\) −1285.15 −0.584955 −0.292477 0.956272i \(-0.594480\pi\)
−0.292477 + 0.956272i \(0.594480\pi\)
\(14\) 1486.51i 0.541730i
\(15\) 938.802i 0.278163i
\(16\) −2038.57 −0.497697
\(17\) 2821.93i 0.574379i 0.957874 + 0.287190i \(0.0927210\pi\)
−0.957874 + 0.287190i \(0.907279\pi\)
\(18\) 1546.24 0.265130
\(19\) 10185.1i 1.48493i 0.669884 + 0.742466i \(0.266344\pi\)
−0.669884 + 0.742466i \(0.733656\pi\)
\(20\) 1415.91i 0.176989i
\(21\) 3641.66i 0.393226i
\(22\) 8892.40i 0.835123i
\(23\) −3980.90 11497.3i −0.327188 0.944959i
\(24\) −8680.29 −0.627915
\(25\) 11998.1 0.767875
\(26\) −8177.54 −0.465267
\(27\) 3788.00 0.192450
\(28\) 5492.39i 0.250200i
\(29\) 5523.92 0.226492 0.113246 0.993567i \(-0.463875\pi\)
0.113246 + 0.993567i \(0.463875\pi\)
\(30\) 5973.71i 0.221249i
\(31\) −27306.5 −0.916603 −0.458301 0.888797i \(-0.651542\pi\)
−0.458301 + 0.888797i \(0.651542\pi\)
\(32\) 22666.2 0.691717
\(33\) 21784.7i 0.606191i
\(34\) 17956.3i 0.456856i
\(35\) −14069.1 −0.328143
\(36\) −5713.09 −0.122451
\(37\) 39765.7i 0.785060i 0.919739 + 0.392530i \(0.128400\pi\)
−0.919739 + 0.392530i \(0.871600\pi\)
\(38\) 64809.3i 1.18110i
\(39\) −20033.4 −0.337724
\(40\) 33535.3i 0.523989i
\(41\) −18455.9 −0.267784 −0.133892 0.990996i \(-0.542748\pi\)
−0.133892 + 0.990996i \(0.542748\pi\)
\(42\) 23172.4i 0.312768i
\(43\) 30920.7i 0.388906i −0.980912 0.194453i \(-0.937707\pi\)
0.980912 0.194453i \(-0.0622931\pi\)
\(44\) 32855.9i 0.385705i
\(45\) 14634.5i 0.160598i
\(46\) −25330.9 73158.9i −0.260242 0.751612i
\(47\) 62793.6 0.604814 0.302407 0.953179i \(-0.402210\pi\)
0.302407 + 0.953179i \(0.402210\pi\)
\(48\) −31778.1 −0.287345
\(49\) 63074.0 0.536120
\(50\) 76345.1 0.610761
\(51\) 43989.5i 0.331618i
\(52\) 30214.6 0.214885
\(53\) 56165.6i 0.377262i −0.982048 0.188631i \(-0.939595\pi\)
0.982048 0.188631i \(-0.0604050\pi\)
\(54\) 24103.5 0.153073
\(55\) −84162.6 −0.505861
\(56\) 130085.i 0.740737i
\(57\) 158771.i 0.857326i
\(58\) 35149.4 0.180150
\(59\) −159966. −0.778880 −0.389440 0.921052i \(-0.627331\pi\)
−0.389440 + 0.921052i \(0.627331\pi\)
\(60\) 22071.8i 0.102184i
\(61\) 333535.i 1.46944i −0.678372 0.734719i \(-0.737314\pi\)
0.678372 0.734719i \(-0.262686\pi\)
\(62\) −173755. −0.729057
\(63\) 56767.9i 0.227029i
\(64\) 274696. 1.04788
\(65\) 77396.8i 0.281827i
\(66\) 138619.i 0.482159i
\(67\) 244298.i 0.812260i −0.913815 0.406130i \(-0.866878\pi\)
0.913815 0.406130i \(-0.133122\pi\)
\(68\) 66345.4i 0.211001i
\(69\) −62056.1 179225.i −0.188902 0.545572i
\(70\) −89523.7 −0.261002
\(71\) 437275. 1.22174 0.610871 0.791731i \(-0.290820\pi\)
0.610871 + 0.791731i \(0.290820\pi\)
\(72\) −135312. −0.362527
\(73\) 494935. 1.27227 0.636135 0.771578i \(-0.280532\pi\)
0.636135 + 0.771578i \(0.280532\pi\)
\(74\) 253034.i 0.624429i
\(75\) 187031. 0.443333
\(76\) 239459.i 0.545496i
\(77\) −326471. −0.715110
\(78\) −127475. −0.268622
\(79\) 571913.i 1.15998i −0.814625 0.579988i \(-0.803057\pi\)
0.814625 0.579988i \(-0.196943\pi\)
\(80\) 122771.i 0.239787i
\(81\) 59049.0 0.111111
\(82\) −117437. −0.212993
\(83\) 720923.i 1.26082i 0.776261 + 0.630412i \(0.217114\pi\)
−0.776261 + 0.630412i \(0.782886\pi\)
\(84\) 85617.9i 0.144453i
\(85\) −169948. −0.276732
\(86\) 196752.i 0.309332i
\(87\) 86109.4 0.130765
\(88\) 778179.i 1.14191i
\(89\) 785492.i 1.11422i 0.830438 + 0.557111i \(0.188090\pi\)
−0.830438 + 0.557111i \(0.811910\pi\)
\(90\) 93120.9i 0.127738i
\(91\) 300226.i 0.398405i
\(92\) 93593.5 + 270310.i 0.120194 + 0.347135i
\(93\) −425666. −0.529201
\(94\) 399563. 0.481063
\(95\) −613392. −0.715430
\(96\) 353331. 0.399363
\(97\) 274434.i 0.300692i −0.988633 0.150346i \(-0.951961\pi\)
0.988633 0.150346i \(-0.0480388\pi\)
\(98\) 401348. 0.426425
\(99\) 339590.i 0.349985i
\(100\) −282082. −0.282082
\(101\) −999436. −0.970043 −0.485021 0.874502i \(-0.661188\pi\)
−0.485021 + 0.874502i \(0.661188\pi\)
\(102\) 279910.i 0.263766i
\(103\) 359691.i 0.329168i 0.986363 + 0.164584i \(0.0526282\pi\)
−0.986363 + 0.164584i \(0.947372\pi\)
\(104\) 715622. 0.636185
\(105\) −219316. −0.189454
\(106\) 357389.i 0.300070i
\(107\) 2.15412e6i 1.75841i 0.476447 + 0.879203i \(0.341924\pi\)
−0.476447 + 0.879203i \(0.658076\pi\)
\(108\) −89058.3 −0.0706973
\(109\) 1.90465e6i 1.47074i 0.677668 + 0.735368i \(0.262991\pi\)
−0.677668 + 0.735368i \(0.737009\pi\)
\(110\) −535537. −0.402357
\(111\) 619885.i 0.453255i
\(112\) 476235.i 0.338975i
\(113\) 2.60669e6i 1.80657i 0.429041 + 0.903285i \(0.358851\pi\)
−0.429041 + 0.903285i \(0.641149\pi\)
\(114\) 1.01028e6i 0.681909i
\(115\) 692416. 239746.i 0.455275 0.157637i
\(116\) −129871. −0.0832028
\(117\) −312290. −0.194985
\(118\) −1.01788e6 −0.619514
\(119\) −659238. −0.391202
\(120\) 522763.i 0.302525i
\(121\) −181415. −0.102404
\(122\) 2.12232e6i 1.16878i
\(123\) −287700. −0.154605
\(124\) 641994. 0.336718
\(125\) 1.66357e6i 0.851750i
\(126\) 361221.i 0.180577i
\(127\) 1.00672e6 0.491473 0.245736 0.969337i \(-0.420970\pi\)
0.245736 + 0.969337i \(0.420970\pi\)
\(128\) 297289. 0.141758
\(129\) 482007.i 0.224535i
\(130\) 492485.i 0.224163i
\(131\) −1.48663e6 −0.661284 −0.330642 0.943756i \(-0.607265\pi\)
−0.330642 + 0.943756i \(0.607265\pi\)
\(132\) 512173.i 0.222687i
\(133\) −2.37938e6 −1.01137
\(134\) 1.55450e6i 0.646064i
\(135\) 228129.i 0.0927212i
\(136\) 1.57136e6i 0.624684i
\(137\) 933505.i 0.363041i −0.983387 0.181520i \(-0.941898\pi\)
0.983387 0.181520i \(-0.0581018\pi\)
\(138\) −394870. 1.14043e6i −0.150251 0.433943i
\(139\) 2.57479e6 0.958734 0.479367 0.877615i \(-0.340866\pi\)
0.479367 + 0.877615i \(0.340866\pi\)
\(140\) 330775. 0.120545
\(141\) 978855. 0.349189
\(142\) 2.78243e6 0.971761
\(143\) 1.79598e6i 0.614176i
\(144\) −495372. −0.165899
\(145\) 332673.i 0.109122i
\(146\) 3.14933e6 1.01195
\(147\) 983227. 0.309529
\(148\) 934917.i 0.288395i
\(149\) 665234.i 0.201102i −0.994932 0.100551i \(-0.967940\pi\)
0.994932 0.100551i \(-0.0320605\pi\)
\(150\) 1.19010e6 0.352623
\(151\) −385234. −0.111891 −0.0559453 0.998434i \(-0.517817\pi\)
−0.0559453 + 0.998434i \(0.517817\pi\)
\(152\) 5.67151e6i 1.61498i
\(153\) 685728.i 0.191460i
\(154\) −2.07738e6 −0.568792
\(155\) 1.64451e6i 0.441613i
\(156\) 470999. 0.124064
\(157\) 2.55515e6i 0.660263i −0.943935 0.330132i \(-0.892907\pi\)
0.943935 0.330132i \(-0.107093\pi\)
\(158\) 3.63916e6i 0.922634i
\(159\) 875535.i 0.217812i
\(160\) 1.36505e6i 0.333265i
\(161\) 2.68592e6 929989.i 0.643599 0.222844i
\(162\) 375736. 0.0883767
\(163\) −4.76008e6 −1.09914 −0.549568 0.835449i \(-0.685208\pi\)
−0.549568 + 0.835449i \(0.685208\pi\)
\(164\) 433911. 0.0983715
\(165\) −1.31197e6 −0.292059
\(166\) 4.58732e6i 1.00285i
\(167\) 3.47396e6 0.745892 0.372946 0.927853i \(-0.378348\pi\)
0.372946 + 0.927853i \(0.378348\pi\)
\(168\) 2.02783e6i 0.427665i
\(169\) −3.17521e6 −0.657828
\(170\) −1.08140e6 −0.220110
\(171\) 2.47499e6i 0.494977i
\(172\) 726967.i 0.142866i
\(173\) 3.58125e6 0.691666 0.345833 0.938296i \(-0.387596\pi\)
0.345833 + 0.938296i \(0.387596\pi\)
\(174\) 547925. 0.104009
\(175\) 2.80290e6i 0.522990i
\(176\) 2.84887e6i 0.522559i
\(177\) −2.49362e6 −0.449687
\(178\) 4.99818e6i 0.886242i
\(179\) −1.81514e6 −0.316483 −0.158241 0.987400i \(-0.550582\pi\)
−0.158241 + 0.987400i \(0.550582\pi\)
\(180\) 344066.i 0.0589962i
\(181\) 5.36160e6i 0.904188i 0.891970 + 0.452094i \(0.149323\pi\)
−0.891970 + 0.452094i \(0.850677\pi\)
\(182\) 1.91038e6i 0.316888i
\(183\) 5.19929e6i 0.848380i
\(184\) 2.21673e6 + 6.40218e6i 0.355843 + 1.02772i
\(185\) −2.39485e6 −0.378237
\(186\) −2.70857e6 −0.420921
\(187\) −3.94361e6 −0.603072
\(188\) −1.47632e6 −0.222181
\(189\) 884924.i 0.131075i
\(190\) −3.90309e6 −0.569046
\(191\) 6.26268e6i 0.898794i 0.893332 + 0.449397i \(0.148361\pi\)
−0.893332 + 0.449397i \(0.851639\pi\)
\(192\) 4.28209e6 0.604995
\(193\) 1.28599e7 1.78882 0.894408 0.447252i \(-0.147597\pi\)
0.894408 + 0.447252i \(0.147597\pi\)
\(194\) 1.74626e6i 0.239168i
\(195\) 1.20650e6i 0.162713i
\(196\) −1.48291e6 −0.196946
\(197\) 9.53336e6 1.24694 0.623472 0.781845i \(-0.285721\pi\)
0.623472 + 0.781845i \(0.285721\pi\)
\(198\) 2.16085e6i 0.278374i
\(199\) 1.75998e6i 0.223331i −0.993746 0.111665i \(-0.964382\pi\)
0.993746 0.111665i \(-0.0356185\pi\)
\(200\) −6.68101e6 −0.835126
\(201\) 3.80823e6i 0.468959i
\(202\) −6.35954e6 −0.771563
\(203\) 1.29046e6i 0.154261i
\(204\) 1.03422e6i 0.121821i
\(205\) 1.11149e6i 0.129017i
\(206\) 2.28876e6i 0.261817i
\(207\) −967358. 2.79385e6i −0.109063 0.314986i
\(208\) 2.61985e6 0.291130
\(209\) −1.42336e7 −1.55911
\(210\) −1.39554e6 −0.150690
\(211\) −1.02042e6 −0.108626 −0.0543128 0.998524i \(-0.517297\pi\)
−0.0543128 + 0.998524i \(0.517297\pi\)
\(212\) 1.32049e6i 0.138589i
\(213\) 6.81644e6 0.705372
\(214\) 1.37069e7i 1.39862i
\(215\) 1.86218e6 0.187372
\(216\) −2.10931e6 −0.209305
\(217\) 6.37915e6i 0.624286i
\(218\) 1.21195e7i 1.16981i
\(219\) 7.71527e6 0.734545
\(220\) 1.97872e6 0.185830
\(221\) 3.62659e6i 0.335986i
\(222\) 3.94441e6i 0.360515i
\(223\) −5.16861e6 −0.466078 −0.233039 0.972467i \(-0.574867\pi\)
−0.233039 + 0.972467i \(0.574867\pi\)
\(224\) 5.29511e6i 0.471119i
\(225\) 2.91553e6 0.255958
\(226\) 1.65867e7i 1.43693i
\(227\) 7.01786e6i 0.599967i −0.953944 0.299983i \(-0.903019\pi\)
0.953944 0.299983i \(-0.0969812\pi\)
\(228\) 3.73280e6i 0.314942i
\(229\) 1.15614e7i 0.962731i −0.876520 0.481366i \(-0.840141\pi\)
0.876520 0.481366i \(-0.159859\pi\)
\(230\) 4.40593e6 1.52553e6i 0.362121 0.125383i
\(231\) −5.08919e6 −0.412869
\(232\) −3.07594e6 −0.246328
\(233\) −1.34263e7 −1.06143 −0.530713 0.847552i \(-0.678076\pi\)
−0.530713 + 0.847552i \(0.678076\pi\)
\(234\) −1.98714e6 −0.155089
\(235\) 3.78169e6i 0.291395i
\(236\) 3.76090e6 0.286125
\(237\) 8.91525e6i 0.669712i
\(238\) −4.19481e6 −0.311159
\(239\) 7.65228e6 0.560528 0.280264 0.959923i \(-0.409578\pi\)
0.280264 + 0.959923i \(0.409578\pi\)
\(240\) 1.91381e6i 0.138441i
\(241\) 9.36770e6i 0.669240i −0.942353 0.334620i \(-0.891392\pi\)
0.942353 0.334620i \(-0.108608\pi\)
\(242\) −1.15436e6 −0.0814510
\(243\) 920483. 0.0641500
\(244\) 7.84162e6i 0.539804i
\(245\) 3.79858e6i 0.258299i
\(246\) −1.83067e6 −0.122971
\(247\) 1.30894e7i 0.868618i
\(248\) 1.52054e7 0.996879
\(249\) 1.12381e7i 0.727937i
\(250\) 1.05855e7i 0.677474i
\(251\) 109973.i 0.00695448i −0.999994 0.00347724i \(-0.998893\pi\)
0.999994 0.00347724i \(-0.00110684\pi\)
\(252\) 1.33465e6i 0.0834000i
\(253\) 1.60674e7 5.56326e6i 0.992164 0.343533i
\(254\) 6.40591e6 0.390913
\(255\) −2.64923e6 −0.159771
\(256\) −1.56889e7 −0.935129
\(257\) 5.24170e6 0.308797 0.154398 0.988009i \(-0.450656\pi\)
0.154398 + 0.988009i \(0.450656\pi\)
\(258\) 3.06707e6i 0.178593i
\(259\) −9.28977e6 −0.534694
\(260\) 1.81965e6i 0.103530i
\(261\) 1.34231e6 0.0754974
\(262\) −9.45959e6 −0.525979
\(263\) 2.01529e7i 1.10782i 0.832576 + 0.553911i \(0.186865\pi\)
−0.832576 + 0.553911i \(0.813135\pi\)
\(264\) 1.21306e7i 0.659282i
\(265\) 3.38253e6 0.181762
\(266\) −1.51403e7 −0.804432
\(267\) 1.22446e7i 0.643297i
\(268\) 5.74360e6i 0.298387i
\(269\) −3.23774e7 −1.66336 −0.831678 0.555258i \(-0.812620\pi\)
−0.831678 + 0.555258i \(0.812620\pi\)
\(270\) 1.45161e6i 0.0737495i
\(271\) 1.93637e7 0.972929 0.486465 0.873700i \(-0.338286\pi\)
0.486465 + 0.873700i \(0.338286\pi\)
\(272\) 5.75268e6i 0.285867i
\(273\) 4.68007e6i 0.230019i
\(274\) 5.94001e6i 0.288759i
\(275\) 1.67671e7i 0.806234i
\(276\) 1.45898e6 + 4.21371e6i 0.0693940 + 0.200418i
\(277\) 3.05629e7 1.43799 0.718994 0.695016i \(-0.244603\pi\)
0.718994 + 0.695016i \(0.244603\pi\)
\(278\) 1.63837e7 0.762568
\(279\) −6.63548e6 −0.305534
\(280\) 7.83427e6 0.356882
\(281\) 1.20980e7i 0.545249i −0.962120 0.272625i \(-0.912108\pi\)
0.962120 0.272625i \(-0.0878917\pi\)
\(282\) 6.22857e6 0.277742
\(283\) 3.45135e7i 1.52275i −0.648310 0.761377i \(-0.724524\pi\)
0.648310 0.761377i \(-0.275476\pi\)
\(284\) −1.02806e7 −0.448812
\(285\) −9.56183e6 −0.413054
\(286\) 1.14280e7i 0.488509i
\(287\) 4.31154e6i 0.182384i
\(288\) 5.50788e6 0.230572
\(289\) 1.61743e7 0.670088
\(290\) 2.11684e6i 0.0867949i
\(291\) 4.27800e6i 0.173605i
\(292\) −1.16362e7 −0.467373
\(293\) 3.33872e7i 1.32733i −0.748032 0.663663i \(-0.769001\pi\)
0.748032 0.663663i \(-0.230999\pi\)
\(294\) 6.25639e6 0.246197
\(295\) 9.63379e6i 0.375259i
\(296\) 2.21432e7i 0.853816i
\(297\) 5.29368e6i 0.202064i
\(298\) 4.23296e6i 0.159954i
\(299\) 5.11603e6 + 1.47757e7i 0.191390 + 0.552758i
\(300\) −4.39722e6 −0.162860
\(301\) 7.22348e6 0.264879
\(302\) −2.45129e6 −0.0889968
\(303\) −1.55797e7 −0.560055
\(304\) 2.07631e7i 0.739046i
\(305\) 2.00868e7 0.707965
\(306\) 4.36337e6i 0.152285i
\(307\) −5.47778e7 −1.89317 −0.946585 0.322455i \(-0.895492\pi\)
−0.946585 + 0.322455i \(0.895492\pi\)
\(308\) 7.67556e6 0.262699
\(309\) 5.60703e6i 0.190045i
\(310\) 1.04642e7i 0.351255i
\(311\) 2.86189e7 0.951418 0.475709 0.879603i \(-0.342192\pi\)
0.475709 + 0.879603i \(0.342192\pi\)
\(312\) 1.11554e7 0.367302
\(313\) 3.59059e7i 1.17094i −0.810695 0.585468i \(-0.800911\pi\)
0.810695 0.585468i \(-0.199089\pi\)
\(314\) 1.62587e7i 0.525167i
\(315\) −3.41880e6 −0.109381
\(316\) 1.34461e7i 0.426122i
\(317\) 3.22286e7 1.01173 0.505865 0.862613i \(-0.331174\pi\)
0.505865 + 0.862613i \(0.331174\pi\)
\(318\) 5.57114e6i 0.173246i
\(319\) 7.71962e6i 0.237806i
\(320\) 1.65433e7i 0.504862i
\(321\) 3.35795e7i 1.01522i
\(322\) 1.70908e7 5.91763e6i 0.511913 0.177248i
\(323\) −2.87417e7 −0.852914
\(324\) −1.38828e6 −0.0408171
\(325\) −1.54192e7 −0.449172
\(326\) −3.02890e7 −0.874242
\(327\) 2.96905e7i 0.849130i
\(328\) 1.02770e7 0.291237
\(329\) 1.46694e7i 0.411931i
\(330\) −8.34820e6 −0.232301
\(331\) 3.35391e7 0.924842 0.462421 0.886661i \(-0.346981\pi\)
0.462421 + 0.886661i \(0.346981\pi\)
\(332\) 1.69494e7i 0.463169i
\(333\) 9.66306e6i 0.261687i
\(334\) 2.21053e7 0.593275
\(335\) 1.47126e7 0.391341
\(336\) 7.42377e6i 0.195707i
\(337\) 5.76754e7i 1.50696i −0.657472 0.753479i \(-0.728374\pi\)
0.657472 0.753479i \(-0.271626\pi\)
\(338\) −2.02043e7 −0.523230
\(339\) 4.06343e7i 1.04302i
\(340\) 3.99559e6 0.101659
\(341\) 3.81606e7i 0.962391i
\(342\) 1.57487e7i 0.393700i
\(343\) 4.22192e7i 1.04623i
\(344\) 1.72179e7i 0.422966i
\(345\) 1.07937e7 3.73727e6i 0.262853 0.0910118i
\(346\) 2.27879e7 0.550144
\(347\) −2.70139e7 −0.646545 −0.323272 0.946306i \(-0.604783\pi\)
−0.323272 + 0.946306i \(0.604783\pi\)
\(348\) −2.02449e6 −0.0480372
\(349\) 3.28000e6 0.0771609 0.0385804 0.999255i \(-0.487716\pi\)
0.0385804 + 0.999255i \(0.487716\pi\)
\(350\) 1.78352e7i 0.415981i
\(351\) −4.86812e6 −0.112575
\(352\) 3.16757e7i 0.726271i
\(353\) −4.41288e7 −1.00323 −0.501613 0.865092i \(-0.667260\pi\)
−0.501613 + 0.865092i \(0.667260\pi\)
\(354\) −1.58672e7 −0.357676
\(355\) 2.63345e7i 0.588627i
\(356\) 1.84674e7i 0.409314i
\(357\) −1.02765e7 −0.225861
\(358\) −1.15499e7 −0.251728
\(359\) 3.84523e7i 0.831073i 0.909576 + 0.415537i \(0.136406\pi\)
−0.909576 + 0.415537i \(0.863594\pi\)
\(360\) 8.14907e6i 0.174663i
\(361\) −5.66913e7 −1.20502
\(362\) 3.41165e7i 0.719182i
\(363\) −2.82797e6 −0.0591229
\(364\) 7.05852e6i 0.146356i
\(365\) 2.98070e7i 0.612971i
\(366\) 3.30837e7i 0.674794i
\(367\) 1.90097e7i 0.384571i 0.981339 + 0.192286i \(0.0615900\pi\)
−0.981339 + 0.192286i \(0.938410\pi\)
\(368\) 8.11533e6 + 2.34380e7i 0.162841 + 0.470303i
\(369\) −4.48479e6 −0.0892613
\(370\) −1.52387e7 −0.300846
\(371\) 1.31210e7 0.256948
\(372\) 1.00077e7 0.194404
\(373\) 6.82339e7i 1.31484i −0.753523 0.657421i \(-0.771647\pi\)
0.753523 0.657421i \(-0.228353\pi\)
\(374\) −2.50937e7 −0.479678
\(375\) 2.59326e7i 0.491758i
\(376\) −3.49660e7 −0.657783
\(377\) −7.09904e6 −0.132488
\(378\) 5.63088e6i 0.104256i
\(379\) 5.18792e7i 0.952961i 0.879185 + 0.476481i \(0.158088\pi\)
−0.879185 + 0.476481i \(0.841912\pi\)
\(380\) 1.44212e7 0.262816
\(381\) 1.56933e7 0.283752
\(382\) 3.98502e7i 0.714892i
\(383\) 1.02080e8i 1.81696i 0.417931 + 0.908479i \(0.362755\pi\)
−0.417931 + 0.908479i \(0.637245\pi\)
\(384\) 4.63427e6 0.0818442
\(385\) 1.96615e7i 0.344535i
\(386\) 8.18291e7 1.42281
\(387\) 7.51374e6i 0.129635i
\(388\) 6.45212e6i 0.110461i
\(389\) 2.97488e7i 0.505383i 0.967547 + 0.252691i \(0.0813157\pi\)
−0.967547 + 0.252691i \(0.918684\pi\)
\(390\) 7.67709e6i 0.129420i
\(391\) 3.24446e7 1.12338e7i 0.542765 0.187930i
\(392\) −3.51222e7 −0.583074
\(393\) −2.31742e7 −0.381793
\(394\) 6.06619e7 0.991808
\(395\) 3.44430e7 0.558869
\(396\) 7.98398e6i 0.128568i
\(397\) −5.08435e6 −0.0812576 −0.0406288 0.999174i \(-0.512936\pi\)
−0.0406288 + 0.999174i \(0.512936\pi\)
\(398\) 1.11990e7i 0.177635i
\(399\) −3.70909e7 −0.583913
\(400\) −2.44588e7 −0.382169
\(401\) 8.46941e7i 1.31347i −0.754122 0.656735i \(-0.771937\pi\)
0.754122 0.656735i \(-0.228063\pi\)
\(402\) 2.42322e7i 0.373005i
\(403\) 3.50928e7 0.536171
\(404\) 2.34974e7 0.356349
\(405\) 3.55618e6i 0.0535326i
\(406\) 8.21134e6i 0.122698i
\(407\) −5.55721e7 −0.824277
\(408\) 2.44952e7i 0.360661i
\(409\) 1.01530e7 0.148397 0.0741985 0.997243i \(-0.476360\pi\)
0.0741985 + 0.997243i \(0.476360\pi\)
\(410\) 7.07257e6i 0.102618i
\(411\) 1.45519e7i 0.209602i
\(412\) 8.45657e6i 0.120921i
\(413\) 3.73700e7i 0.530485i
\(414\) −6.15542e6 1.77776e7i −0.0867474 0.250537i
\(415\) −4.34170e7 −0.607456
\(416\) −2.91293e7 −0.404623
\(417\) 4.01371e7 0.553525
\(418\) −9.05703e7 −1.24010
\(419\) 2.98259e7i 0.405464i 0.979234 + 0.202732i \(0.0649820\pi\)
−0.979234 + 0.202732i \(0.935018\pi\)
\(420\) 5.15627e6 0.0695965
\(421\) 8.63872e7i 1.15772i −0.815427 0.578860i \(-0.803498\pi\)
0.815427 0.578860i \(-0.196502\pi\)
\(422\) −6.49306e6 −0.0863997
\(423\) 1.52588e7 0.201605
\(424\) 3.12753e7i 0.410303i
\(425\) 3.38576e7i 0.441052i
\(426\) 4.33738e7 0.561047
\(427\) 7.79179e7 1.00082
\(428\) 5.06449e7i 0.645958i
\(429\) 2.79965e7i 0.354594i
\(430\) 1.18492e7 0.149034
\(431\) 4.07286e7i 0.508707i −0.967111 0.254353i \(-0.918137\pi\)
0.967111 0.254353i \(-0.0818626\pi\)
\(432\) −7.72208e6 −0.0957818
\(433\) 1.05183e8i 1.29563i 0.761798 + 0.647814i \(0.224317\pi\)
−0.761798 + 0.647814i \(0.775683\pi\)
\(434\) 4.05913e7i 0.496551i
\(435\) 5.18586e6i 0.0630019i
\(436\) 4.47795e7i 0.540281i
\(437\) 1.17102e8 4.05460e7i 1.40320 0.485852i
\(438\) 4.90932e7 0.584250
\(439\) −5.25897e7 −0.621594 −0.310797 0.950476i \(-0.600596\pi\)
−0.310797 + 0.950476i \(0.600596\pi\)
\(440\) 4.68652e7 0.550164
\(441\) 1.53270e7 0.178707
\(442\) 2.30764e7i 0.267240i
\(443\) −1.46092e8 −1.68041 −0.840207 0.542266i \(-0.817566\pi\)
−0.840207 + 0.542266i \(0.817566\pi\)
\(444\) 1.45739e7i 0.166505i
\(445\) −4.73056e7 −0.536825
\(446\) −3.28885e7 −0.370714
\(447\) 1.03700e7i 0.116106i
\(448\) 6.41725e7i 0.713699i
\(449\) 3.09669e7 0.342104 0.171052 0.985262i \(-0.445283\pi\)
0.171052 + 0.985262i \(0.445283\pi\)
\(450\) 1.85519e7 0.203587
\(451\) 2.57920e7i 0.281161i
\(452\) 6.12851e7i 0.663651i
\(453\) −6.00520e6 −0.0646001
\(454\) 4.46555e7i 0.477208i
\(455\) 1.80809e7 0.191949
\(456\) 8.84101e7i 0.932410i
\(457\) 3.64508e7i 0.381908i −0.981599 0.190954i \(-0.938842\pi\)
0.981599 0.190954i \(-0.0611581\pi\)
\(458\) 7.35668e7i 0.765747i
\(459\) 1.06894e7i 0.110539i
\(460\) −1.62792e7 + 5.63659e6i −0.167247 + 0.0579086i
\(461\) 3.26518e7 0.333276 0.166638 0.986018i \(-0.446709\pi\)
0.166638 + 0.986018i \(0.446709\pi\)
\(462\) −3.23831e7 −0.328392
\(463\) 1.67599e8 1.68860 0.844302 0.535868i \(-0.180016\pi\)
0.844302 + 0.535868i \(0.180016\pi\)
\(464\) −1.12609e7 −0.112724
\(465\) 2.56354e7i 0.254965i
\(466\) −8.54334e7 −0.844248
\(467\) 3.58074e7i 0.351578i −0.984428 0.175789i \(-0.943752\pi\)
0.984428 0.175789i \(-0.0562477\pi\)
\(468\) 7.34215e6 0.0716285
\(469\) 5.70711e7 0.553220
\(470\) 2.40634e7i 0.231773i
\(471\) 3.98308e7i 0.381203i
\(472\) 8.90754e7 0.847094
\(473\) 4.32114e7 0.408333
\(474\) 5.67288e7i 0.532683i
\(475\) 1.22202e8i 1.14024i
\(476\) 1.54991e7 0.143710
\(477\) 1.36482e7i 0.125754i
\(478\) 4.86924e7 0.445838
\(479\) 4.01741e7i 0.365544i 0.983155 + 0.182772i \(0.0585070\pi\)
−0.983155 + 0.182772i \(0.941493\pi\)
\(480\) 2.12791e7i 0.192410i
\(481\) 5.11047e7i 0.459225i
\(482\) 5.96078e7i 0.532307i
\(483\) 4.18694e7 1.44971e7i 0.371582 0.128659i
\(484\) 4.26518e6 0.0376185
\(485\) 1.65275e7 0.144872
\(486\) 5.85715e6 0.0510243
\(487\) −1.60417e8 −1.38888 −0.694439 0.719552i \(-0.744347\pi\)
−0.694439 + 0.719552i \(0.744347\pi\)
\(488\) 1.85726e8i 1.59813i
\(489\) −7.42023e7 −0.634586
\(490\) 2.41708e7i 0.205449i
\(491\) −7.40765e7 −0.625800 −0.312900 0.949786i \(-0.601301\pi\)
−0.312900 + 0.949786i \(0.601301\pi\)
\(492\) 6.76401e6 0.0567948
\(493\) 1.55881e7i 0.130092i
\(494\) 8.32894e7i 0.690890i
\(495\) −2.04515e7 −0.168620
\(496\) 5.56661e7 0.456190
\(497\) 1.02153e8i 0.832112i
\(498\) 7.15092e7i 0.578994i
\(499\) −1.97181e8 −1.58695 −0.793474 0.608604i \(-0.791730\pi\)
−0.793474 + 0.608604i \(0.791730\pi\)
\(500\) 3.91117e7i 0.312894i
\(501\) 5.41537e7 0.430641
\(502\) 699772.i 0.00553153i
\(503\) 6.73802e6i 0.0529454i −0.999650 0.0264727i \(-0.991572\pi\)
0.999650 0.0264727i \(-0.00842750\pi\)
\(504\) 3.16107e7i 0.246912i
\(505\) 6.01902e7i 0.467360i
\(506\) 1.02239e8 3.53997e7i 0.789158 0.273242i
\(507\) −4.94966e7 −0.379797
\(508\) −2.36688e7 −0.180544
\(509\) 2.39743e7 0.181799 0.0908997 0.995860i \(-0.471026\pi\)
0.0908997 + 0.995860i \(0.471026\pi\)
\(510\) −1.68574e7 −0.127081
\(511\) 1.15623e8i 0.866526i
\(512\) −1.18857e8 −0.885551
\(513\) 3.85813e7i 0.285775i
\(514\) 3.33536e7 0.245614
\(515\) −2.16621e7 −0.158591
\(516\) 1.13323e7i 0.0824838i
\(517\) 8.77533e7i 0.635027i
\(518\) −5.91119e7 −0.425291
\(519\) 5.58262e7 0.399334
\(520\) 4.30977e7i 0.306510i
\(521\) 1.14966e8i 0.812933i −0.913666 0.406467i \(-0.866761\pi\)
0.913666 0.406467i \(-0.133239\pi\)
\(522\) 8.54130e6 0.0600499
\(523\) 2.70926e8i 1.89385i 0.321456 + 0.946925i \(0.395828\pi\)
−0.321456 + 0.946925i \(0.604172\pi\)
\(524\) 3.49516e7 0.242926
\(525\) 4.36929e7i 0.301948i
\(526\) 1.28235e8i 0.881152i
\(527\) 7.70570e7i 0.526478i
\(528\) 4.44096e7i 0.301700i
\(529\) −1.16341e8 + 9.15393e7i −0.785896 + 0.618359i
\(530\) 2.15234e7 0.144572
\(531\) −3.88716e7 −0.259627
\(532\) 5.59408e7 0.371530
\(533\) 2.37186e7 0.156641
\(534\) 7.79140e7i 0.511672i
\(535\) −1.29730e8 −0.847188
\(536\) 1.36035e8i 0.883398i
\(537\) −2.82952e7 −0.182722
\(538\) −2.06021e8 −1.32302
\(539\) 8.81453e7i 0.562902i
\(540\) 5.36346e6i 0.0340615i
\(541\) 1.43573e8 0.906739 0.453370 0.891323i \(-0.350222\pi\)
0.453370 + 0.891323i \(0.350222\pi\)
\(542\) 1.23214e8 0.773859
\(543\) 8.35790e7i 0.522033i
\(544\) 6.39623e7i 0.397308i
\(545\) −1.14706e8 −0.708591
\(546\) 2.97798e7i 0.182955i
\(547\) 2.07872e8 1.27009 0.635045 0.772475i \(-0.280982\pi\)
0.635045 + 0.772475i \(0.280982\pi\)
\(548\) 2.19473e7i 0.133364i
\(549\) 8.10489e7i 0.489813i
\(550\) 1.06691e8i 0.641271i
\(551\) 5.62619e7i 0.336325i
\(552\) 3.45554e7 + 9.98001e7i 0.205446 + 0.593354i
\(553\) 1.33606e8 0.790044
\(554\) 1.94475e8 1.14376
\(555\) −3.73321e7 −0.218375
\(556\) −6.05351e7 −0.352195
\(557\) 2.03427e8i 1.17718i −0.808431 0.588591i \(-0.799683\pi\)
0.808431 0.588591i \(-0.200317\pi\)
\(558\) −4.22224e7 −0.243019
\(559\) 3.97376e7i 0.227492i
\(560\) 2.86809e7 0.163316
\(561\) −6.14748e7 −0.348184
\(562\) 7.69812e7i 0.433686i
\(563\) 4.02092e7i 0.225320i −0.993634 0.112660i \(-0.964063\pi\)
0.993634 0.112660i \(-0.0359371\pi\)
\(564\) −2.30135e7 −0.128276
\(565\) −1.56986e8 −0.870393
\(566\) 2.19614e8i 1.21118i
\(567\) 1.37946e7i 0.0756763i
\(568\) −2.43492e8 −1.32874
\(569\) 2.17982e8i 1.18327i 0.806205 + 0.591636i \(0.201518\pi\)
−0.806205 + 0.591636i \(0.798482\pi\)
\(570\) −6.08431e7 −0.328539
\(571\) 1.53635e8i 0.825243i −0.910903 0.412621i \(-0.864613\pi\)
0.910903 0.412621i \(-0.135387\pi\)
\(572\) 4.22246e7i 0.225620i
\(573\) 9.76256e7i 0.518919i
\(574\) 2.74349e7i 0.145067i
\(575\) −4.77630e7 1.37945e8i −0.251240 0.725611i
\(576\) 6.67511e7 0.349294
\(577\) 4.00536e7 0.208504 0.104252 0.994551i \(-0.466755\pi\)
0.104252 + 0.994551i \(0.466755\pi\)
\(578\) 1.02919e8 0.532982
\(579\) 2.00466e8 1.03277
\(580\) 7.82137e6i 0.0400866i
\(581\) −1.68417e8 −0.858731
\(582\) 2.72214e7i 0.138084i
\(583\) 7.84908e7 0.396108
\(584\) −2.75600e8 −1.38370
\(585\) 1.88074e7i 0.0939424i
\(586\) 2.12447e8i 1.05574i
\(587\) −1.79154e8 −0.885750 −0.442875 0.896583i \(-0.646042\pi\)
−0.442875 + 0.896583i \(0.646042\pi\)
\(588\) −2.31163e7 −0.113707
\(589\) 2.78121e8i 1.36109i
\(590\) 6.13010e7i 0.298477i
\(591\) 1.48610e8 0.719924
\(592\) 8.10649e7i 0.390722i
\(593\) 3.94002e8 1.88944 0.944722 0.327872i \(-0.106331\pi\)
0.944722 + 0.327872i \(0.106331\pi\)
\(594\) 3.36843e7i 0.160720i
\(595\) 3.97021e7i 0.188479i
\(596\) 1.56401e7i 0.0738755i
\(597\) 2.74354e7i 0.128940i
\(598\) 3.25539e7 + 9.40198e7i 0.152230 + 0.439659i
\(599\) 3.26132e8 1.51745 0.758723 0.651413i \(-0.225823\pi\)
0.758723 + 0.651413i \(0.225823\pi\)
\(600\) −1.04147e8 −0.482160
\(601\) 3.34444e8 1.54064 0.770318 0.637659i \(-0.220097\pi\)
0.770318 + 0.637659i \(0.220097\pi\)
\(602\) 4.59639e7 0.210682
\(603\) 5.93644e7i 0.270753i
\(604\) 9.05711e6 0.0411035
\(605\) 1.09255e7i 0.0493375i
\(606\) −9.91353e7 −0.445462
\(607\) −2.70163e8 −1.20798 −0.603991 0.796991i \(-0.706424\pi\)
−0.603991 + 0.796991i \(0.706424\pi\)
\(608\) 2.30858e8i 1.02715i
\(609\) 2.01163e7i 0.0890626i
\(610\) 1.27815e8 0.563109
\(611\) −8.06989e7 −0.353789
\(612\) 1.61219e7i 0.0703335i
\(613\) 1.66910e8i 0.724606i −0.932060 0.362303i \(-0.881991\pi\)
0.932060 0.362303i \(-0.118009\pi\)
\(614\) −3.48558e8 −1.50581
\(615\) 1.73265e7i 0.0744877i
\(616\) 1.81793e8 0.777740
\(617\) 3.40980e6i 0.0145169i −0.999974 0.00725843i \(-0.997690\pi\)
0.999974 0.00725843i \(-0.00231045\pi\)
\(618\) 3.56782e7i 0.151160i
\(619\) 7.78890e7i 0.328401i −0.986427 0.164200i \(-0.947496\pi\)
0.986427 0.164200i \(-0.0525043\pi\)
\(620\) 3.86636e7i 0.162228i
\(621\) −1.50796e7 4.35518e7i −0.0629674 0.181857i
\(622\) 1.82105e8 0.756748
\(623\) −1.83501e8 −0.758882
\(624\) 4.08395e7 0.168084
\(625\) 8.72821e7 0.357508
\(626\) 2.28474e8i 0.931352i
\(627\) −2.21880e8 −0.900153
\(628\) 6.00732e7i 0.242550i
\(629\) −1.12216e8 −0.450923
\(630\) −2.17542e7 −0.0870006
\(631\) 2.97365e8i 1.18359i −0.806089 0.591795i \(-0.798420\pi\)
0.806089 0.591795i \(-0.201580\pi\)
\(632\) 3.18465e8i 1.26157i
\(633\) −1.59068e7 −0.0627150
\(634\) 2.05075e8 0.804720
\(635\) 6.06291e7i 0.236788i
\(636\) 2.05844e7i 0.0800142i
\(637\) −8.10593e7 −0.313606
\(638\) 4.91209e7i 0.189149i
\(639\) 1.06258e8 0.407247
\(640\) 1.79040e7i 0.0682982i
\(641\) 1.39938e8i 0.531328i 0.964066 + 0.265664i \(0.0855912\pi\)
−0.964066 + 0.265664i \(0.914409\pi\)
\(642\) 2.13670e8i 0.807493i
\(643\) 3.06153e8i 1.15161i 0.817587 + 0.575805i \(0.195311\pi\)
−0.817587 + 0.575805i \(0.804689\pi\)
\(644\) −6.31478e7 + 2.18647e7i −0.236429 + 0.0818625i
\(645\) 2.90284e7 0.108179
\(646\) −1.82887e8 −0.678400
\(647\) 2.49111e8 0.919771 0.459885 0.887978i \(-0.347890\pi\)
0.459885 + 0.887978i \(0.347890\pi\)
\(648\) −3.28809e7 −0.120842
\(649\) 2.23550e8i 0.817788i
\(650\) −9.81145e7 −0.357267
\(651\) 9.94412e7i 0.360432i
\(652\) 1.11913e8 0.403772
\(653\) −4.16924e8 −1.49733 −0.748665 0.662948i \(-0.769305\pi\)
−0.748665 + 0.662948i \(0.769305\pi\)
\(654\) 1.88924e8i 0.675390i
\(655\) 8.95309e7i 0.318602i
\(656\) 3.76237e7 0.133275
\(657\) 1.20269e8 0.424090
\(658\) 9.33431e7i 0.327646i
\(659\) 2.42010e8i 0.845622i 0.906218 + 0.422811i \(0.138957\pi\)
−0.906218 + 0.422811i \(0.861043\pi\)
\(660\) 3.08452e7 0.107289
\(661\) 4.85278e8i 1.68030i −0.542356 0.840149i \(-0.682468\pi\)
0.542356 0.840149i \(-0.317532\pi\)
\(662\) 2.13413e8 0.735610
\(663\) 5.65329e7i 0.193982i
\(664\) 4.01439e8i 1.37125i
\(665\) 1.43296e8i 0.487270i
\(666\) 6.14872e7i 0.208143i
\(667\) −2.19902e7 6.35102e7i −0.0741056 0.214026i
\(668\) −8.16752e7 −0.274006
\(669\) −8.05706e7 −0.269090
\(670\) 9.36183e7 0.311269
\(671\) 4.66111e8 1.54284
\(672\) 8.25426e7i 0.272001i
\(673\) −3.54234e8 −1.16211 −0.581053 0.813866i \(-0.697359\pi\)
−0.581053 + 0.813866i \(0.697359\pi\)
\(674\) 3.66996e8i 1.19862i
\(675\) 4.54486e7 0.147778
\(676\) 7.46513e7 0.241656
\(677\) 1.26295e8i 0.407023i 0.979073 + 0.203512i \(0.0652354\pi\)
−0.979073 + 0.203512i \(0.934765\pi\)
\(678\) 2.58561e8i 0.829611i
\(679\) 6.41113e7 0.204798
\(680\) 9.46341e7 0.300968
\(681\) 1.09398e8i 0.346391i
\(682\) 2.42820e8i 0.765477i
\(683\) 2.78165e7 0.0873054 0.0436527 0.999047i \(-0.486101\pi\)
0.0436527 + 0.999047i \(0.486101\pi\)
\(684\) 5.81887e7i 0.181832i
\(685\) 5.62196e7 0.174910
\(686\) 2.68646e8i 0.832163i
\(687\) 1.80225e8i 0.555833i
\(688\) 6.30340e7i 0.193557i
\(689\) 7.21810e7i 0.220681i
\(690\) 6.86817e7 2.37807e7i 0.209071 0.0723899i
\(691\) 6.07780e8 1.84210 0.921048 0.389449i \(-0.127335\pi\)
0.921048 + 0.389449i \(0.127335\pi\)
\(692\) −8.41976e7 −0.254086
\(693\) −7.93325e7 −0.238370
\(694\) −1.71893e8 −0.514256
\(695\) 1.55065e8i 0.461912i
\(696\) −4.79492e7 −0.142218
\(697\) 5.20813e7i 0.153810i
\(698\) 2.08710e7 0.0613730
\(699\) −2.09296e8 −0.612814
\(700\) 6.58980e7i 0.192122i
\(701\) 3.75291e8i 1.08947i −0.838609 0.544733i \(-0.816631\pi\)
0.838609 0.544733i \(-0.183369\pi\)
\(702\) −3.09765e7 −0.0895407
\(703\) −4.05019e8 −1.16576
\(704\) 3.83885e8i 1.10023i
\(705\) 5.89507e7i 0.168237i
\(706\) −2.80797e8 −0.797956
\(707\) 2.33481e8i 0.660684i
\(708\) 5.86266e7 0.165194
\(709\) 4.32348e8i 1.21309i −0.795048 0.606547i \(-0.792554\pi\)
0.795048 0.606547i \(-0.207446\pi\)
\(710\) 1.67570e8i 0.468188i
\(711\) 1.38975e8i 0.386659i
\(712\) 4.37394e8i 1.21181i
\(713\) 1.08704e8 + 3.13952e8i 0.299902 + 0.866152i
\(714\) −6.53907e7 −0.179648
\(715\) 1.08161e8 0.295906
\(716\) 4.26751e7 0.116261
\(717\) 1.19287e8 0.323621
\(718\) 2.44677e8i 0.661028i
\(719\) −1.83199e8 −0.492875 −0.246437 0.969159i \(-0.579260\pi\)
−0.246437 + 0.969159i \(0.579260\pi\)
\(720\) 2.98333e7i 0.0799290i
\(721\) −8.40284e7 −0.224192
\(722\) −3.60734e8 −0.958462
\(723\) 1.46028e8i 0.386386i
\(724\) 1.26055e8i 0.332157i
\(725\) 6.62763e7 0.173918
\(726\) −1.79947e7 −0.0470258
\(727\) 3.32462e8i 0.865244i 0.901575 + 0.432622i \(0.142412\pi\)
−0.901575 + 0.432622i \(0.857588\pi\)
\(728\) 1.67178e8i 0.433297i
\(729\) 1.43489e7 0.0370370
\(730\) 1.89666e8i 0.487551i
\(731\) 8.72560e7 0.223380
\(732\) 1.22239e8i 0.311656i
\(733\) 5.89347e8i 1.49644i 0.663450 + 0.748220i \(0.269091\pi\)
−0.663450 + 0.748220i \(0.730909\pi\)
\(734\) 1.20961e8i 0.305884i
\(735\) 5.92140e7i 0.149129i
\(736\) −9.02318e7 2.60600e8i −0.226322 0.653644i
\(737\) 3.41403e8 0.852836
\(738\) −2.85373e7 −0.0709976
\(739\) 5.99727e8 1.48601 0.743003 0.669288i \(-0.233401\pi\)
0.743003 + 0.669288i \(0.233401\pi\)
\(740\) 5.63046e7 0.138947
\(741\) 2.04043e8i 0.501497i
\(742\) 8.34906e7 0.204374
\(743\) 6.45667e7i 0.157414i −0.996898 0.0787068i \(-0.974921\pi\)
0.996898 0.0787068i \(-0.0250791\pi\)
\(744\) 2.37029e8 0.575549
\(745\) 4.00631e7 0.0968894
\(746\) 4.34181e8i 1.04581i
\(747\) 1.75184e8i 0.420275i
\(748\) 9.27169e7 0.221541
\(749\) −5.03231e8 −1.19763
\(750\) 1.65012e8i 0.391140i
\(751\) 8.08683e7i 0.190923i 0.995433 + 0.0954616i \(0.0304327\pi\)
−0.995433 + 0.0954616i \(0.969567\pi\)
\(752\) −1.28009e8 −0.301014
\(753\) 1.71431e6i 0.00401517i
\(754\) −4.51721e7 −0.105379
\(755\) 2.32004e7i 0.0539082i
\(756\) 2.08052e7i 0.0481510i
\(757\) 6.29360e7i 0.145081i 0.997365 + 0.0725406i \(0.0231107\pi\)
−0.997365 + 0.0725406i \(0.976889\pi\)
\(758\) 3.30113e8i 0.757976i
\(759\) 2.50466e8 8.67227e7i 0.572826 0.198339i
\(760\) 3.41562e8 0.778088
\(761\) −5.45904e8 −1.23869 −0.619344 0.785119i \(-0.712602\pi\)
−0.619344 + 0.785119i \(0.712602\pi\)
\(762\) 9.98583e7 0.225694
\(763\) −4.44950e8 −1.00170
\(764\) 1.47240e8i 0.330176i
\(765\) −4.12974e7 −0.0922441
\(766\) 6.49548e8i 1.44519i
\(767\) 2.05579e8 0.455609
\(768\) −2.44565e8 −0.539897
\(769\) 1.19089e8i 0.261874i 0.991391 + 0.130937i \(0.0417985\pi\)
−0.991391 + 0.130937i \(0.958201\pi\)
\(770\) 1.25108e8i 0.274040i
\(771\) 8.17100e7 0.178284
\(772\) −3.02345e8 −0.657129
\(773\) 3.69267e8i 0.799470i 0.916631 + 0.399735i \(0.130898\pi\)
−0.916631 + 0.399735i \(0.869102\pi\)
\(774\) 4.78108e7i 0.103111i
\(775\) −3.27625e8 −0.703837
\(776\) 1.52816e8i 0.327027i
\(777\) −1.44813e8 −0.308706
\(778\) 1.89295e8i 0.401977i
\(779\) 1.87976e8i 0.397641i
\(780\) 2.83655e7i 0.0597733i
\(781\) 6.11086e8i 1.28277i
\(782\) 2.06449e8 7.14821e7i 0.431710 0.149478i
\(783\) 2.09246e7 0.0435884
\(784\) −1.28581e8