Properties

Label 69.7.d.a.22.9
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 22.9
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.10

$q$-expansion

\(f(q)\) \(=\) \(q-4.73591 q^{2} -15.5885 q^{3} -41.5712 q^{4} -38.4146i q^{5} +73.8255 q^{6} +655.803i q^{7} +499.975 q^{8} +243.000 q^{9} +O(q^{10})\) \(q-4.73591 q^{2} -15.5885 q^{3} -41.5712 q^{4} -38.4146i q^{5} +73.8255 q^{6} +655.803i q^{7} +499.975 q^{8} +243.000 q^{9} +181.928i q^{10} +589.638i q^{11} +648.031 q^{12} -3173.89 q^{13} -3105.82i q^{14} +598.825i q^{15} +292.721 q^{16} +909.300i q^{17} -1150.83 q^{18} -3910.57i q^{19} +1596.94i q^{20} -10223.0i q^{21} -2792.47i q^{22} +(2677.23 - 11868.8i) q^{23} -7793.84 q^{24} +14149.3 q^{25} +15031.3 q^{26} -3788.00 q^{27} -27262.5i q^{28} -38085.2 q^{29} -2835.98i q^{30} -12573.1 q^{31} -33384.7 q^{32} -9191.55i q^{33} -4306.36i q^{34} +25192.4 q^{35} -10101.8 q^{36} -80835.5i q^{37} +18520.1i q^{38} +49476.1 q^{39} -19206.4i q^{40} +35231.0 q^{41} +48414.9i q^{42} -46800.8i q^{43} -24512.0i q^{44} -9334.76i q^{45} +(-12679.1 + 56209.5i) q^{46} +147162. q^{47} -4563.06 q^{48} -312428. q^{49} -67009.8 q^{50} -14174.6i q^{51} +131943. q^{52} +254361. i q^{53} +17939.6 q^{54} +22650.7 q^{55} +327885. i q^{56} +60959.8i q^{57} +180368. q^{58} -98850.5 q^{59} -24893.9i q^{60} -149261. i q^{61} +59545.0 q^{62} +159360. i q^{63} +139373. q^{64} +121924. i q^{65} +43530.3i q^{66} -331116. i q^{67} -37800.7i q^{68} +(-41733.8 + 185016. i) q^{69} -119309. q^{70} +371128. q^{71} +121494. q^{72} +31506.8 q^{73} +382829. i q^{74} -220566. q^{75} +162567. i q^{76} -386686. q^{77} -234314. q^{78} +242806. i q^{79} -11244.8i q^{80} +59049.0 q^{81} -166851. q^{82} -827839. i q^{83} +424980. i q^{84} +34930.4 q^{85} +221644. i q^{86} +593689. q^{87} +294804. i q^{88} -1.03994e6i q^{89} +44208.5i q^{90} -2.08145e6i q^{91} +(-111295. + 493400. i) q^{92} +195995. q^{93} -696944. q^{94} -150223. q^{95} +520416. q^{96} +833514. i q^{97} +1.47963e6 q^{98} +143282. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + O(q^{10}) \) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + 384q^{13} + 29544q^{16} - 4860q^{18} + 29336q^{23} - 39204q^{24} - 61272q^{25} + 10088q^{26} + 64672q^{29} + 9696q^{31} - 319620q^{32} - 225744q^{35} + 198288q^{36} - 11664q^{39} + 135280q^{41} + 233232q^{46} - 74336q^{47} + 552096q^{48} - 722136q^{49} + 619324q^{50} + 1059720q^{52} - 78732q^{54} - 1019328q^{55} - 694344q^{58} + 1057648q^{59} - 488776q^{62} - 273888q^{64} - 23328q^{69} + 2785512q^{70} - 255392q^{71} - 228420q^{72} - 322560q^{73} - 365472q^{75} - 1002960q^{77} - 171072q^{78} + 1417176q^{81} - 5732712q^{82} - 2704704q^{85} + 611712q^{87} - 1611444q^{92} + 2484432q^{93} - 147720q^{94} - 1672656q^{95} - 1818612q^{96} + 9104212q^{98} + O(q^{100}) \)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.73591 −0.591988 −0.295994 0.955190i \(-0.595651\pi\)
−0.295994 + 0.955190i \(0.595651\pi\)
\(3\) −15.5885 −0.577350
\(4\) −41.5712 −0.649550
\(5\) 38.4146i 0.307317i −0.988124 0.153659i \(-0.950894\pi\)
0.988124 0.153659i \(-0.0491056\pi\)
\(6\) 73.8255 0.341785
\(7\) 655.803i 1.91196i 0.293429 + 0.955981i \(0.405203\pi\)
−0.293429 + 0.955981i \(0.594797\pi\)
\(8\) 499.975 0.976514
\(9\) 243.000 0.333333
\(10\) 181.928i 0.181928i
\(11\) 589.638i 0.443004i 0.975160 + 0.221502i \(0.0710959\pi\)
−0.975160 + 0.221502i \(0.928904\pi\)
\(12\) 648.031 0.375018
\(13\) −3173.89 −1.44465 −0.722325 0.691554i \(-0.756926\pi\)
−0.722325 + 0.691554i \(0.756926\pi\)
\(14\) 3105.82i 1.13186i
\(15\) 598.825i 0.177430i
\(16\) 292.721 0.0714650
\(17\) 909.300i 0.185080i 0.995709 + 0.0925402i \(0.0294987\pi\)
−0.995709 + 0.0925402i \(0.970501\pi\)
\(18\) −1150.83 −0.197329
\(19\) 3910.57i 0.570138i −0.958507 0.285069i \(-0.907984\pi\)
0.958507 0.285069i \(-0.0920165\pi\)
\(20\) 1596.94i 0.199618i
\(21\) 10223.0i 1.10387i
\(22\) 2792.47i 0.262253i
\(23\) 2677.23 11868.8i 0.220040 0.975491i
\(24\) −7793.84 −0.563791
\(25\) 14149.3 0.905556
\(26\) 15031.3 0.855216
\(27\) −3788.00 −0.192450
\(28\) 27262.5i 1.24191i
\(29\) −38085.2 −1.56157 −0.780786 0.624799i \(-0.785181\pi\)
−0.780786 + 0.624799i \(0.785181\pi\)
\(30\) 2835.98i 0.105036i
\(31\) −12573.1 −0.422044 −0.211022 0.977481i \(-0.567679\pi\)
−0.211022 + 0.977481i \(0.567679\pi\)
\(32\) −33384.7 −1.01882
\(33\) 9191.55i 0.255768i
\(34\) 4306.36i 0.109565i
\(35\) 25192.4 0.587579
\(36\) −10101.8 −0.216517
\(37\) 80835.5i 1.59587i −0.602745 0.797934i \(-0.705927\pi\)
0.602745 0.797934i \(-0.294073\pi\)
\(38\) 18520.1i 0.337515i
\(39\) 49476.1 0.834069
\(40\) 19206.4i 0.300100i
\(41\) 35231.0 0.511179 0.255589 0.966785i \(-0.417730\pi\)
0.255589 + 0.966785i \(0.417730\pi\)
\(42\) 48414.9i 0.653479i
\(43\) 46800.8i 0.588637i −0.955707 0.294318i \(-0.904907\pi\)
0.955707 0.294318i \(-0.0950926\pi\)
\(44\) 24512.0i 0.287753i
\(45\) 9334.76i 0.102439i
\(46\) −12679.1 + 56209.5i −0.130261 + 0.577479i
\(47\) 147162. 1.41743 0.708714 0.705495i \(-0.249275\pi\)
0.708714 + 0.705495i \(0.249275\pi\)
\(48\) −4563.06 −0.0412603
\(49\) −312428. −2.65560
\(50\) −67009.8 −0.536079
\(51\) 14174.6i 0.106856i
\(52\) 131943. 0.938372
\(53\) 254361.i 1.70853i 0.519836 + 0.854266i \(0.325993\pi\)
−0.519836 + 0.854266i \(0.674007\pi\)
\(54\) 17939.6 0.113928
\(55\) 22650.7 0.136143
\(56\) 327885.i 1.86706i
\(57\) 60959.8i 0.329169i
\(58\) 180368. 0.924432
\(59\) −98850.5 −0.481308 −0.240654 0.970611i \(-0.577362\pi\)
−0.240654 + 0.970611i \(0.577362\pi\)
\(60\) 24893.9i 0.115249i
\(61\) 149261.i 0.657591i −0.944401 0.328796i \(-0.893357\pi\)
0.944401 0.328796i \(-0.106643\pi\)
\(62\) 59545.0 0.249845
\(63\) 159360.i 0.637321i
\(64\) 139373. 0.531665
\(65\) 121924.i 0.443966i
\(66\) 43530.3i 0.151412i
\(67\) 331116.i 1.10092i −0.834861 0.550460i \(-0.814452\pi\)
0.834861 0.550460i \(-0.185548\pi\)
\(68\) 37800.7i 0.120219i
\(69\) −41733.8 + 185016.i −0.127040 + 0.563200i
\(70\) −119309. −0.347840
\(71\) 371128. 1.03693 0.518464 0.855100i \(-0.326504\pi\)
0.518464 + 0.855100i \(0.326504\pi\)
\(72\) 121494. 0.325505
\(73\) 31506.8 0.0809907 0.0404954 0.999180i \(-0.487106\pi\)
0.0404954 + 0.999180i \(0.487106\pi\)
\(74\) 382829.i 0.944735i
\(75\) −220566. −0.522823
\(76\) 162567.i 0.370333i
\(77\) −386686. −0.847006
\(78\) −234314. −0.493759
\(79\) 242806.i 0.492469i 0.969210 + 0.246234i \(0.0791933\pi\)
−0.969210 + 0.246234i \(0.920807\pi\)
\(80\) 11244.8i 0.0219624i
\(81\) 59049.0 0.111111
\(82\) −166851. −0.302612
\(83\) 827839.i 1.44781i −0.689900 0.723905i \(-0.742345\pi\)
0.689900 0.723905i \(-0.257655\pi\)
\(84\) 424980.i 0.717020i
\(85\) 34930.4 0.0568784
\(86\) 221644.i 0.348466i
\(87\) 593689. 0.901574
\(88\) 294804.i 0.432599i
\(89\) 1.03994e6i 1.47515i −0.675265 0.737576i \(-0.735971\pi\)
0.675265 0.737576i \(-0.264029\pi\)
\(90\) 44208.5i 0.0606427i
\(91\) 2.08145e6i 2.76211i
\(92\) −111295. + 493400.i −0.142927 + 0.633630i
\(93\) 195995. 0.243667
\(94\) −696944. −0.839101
\(95\) −150223. −0.175213
\(96\) 520416. 0.588216
\(97\) 833514.i 0.913267i 0.889655 + 0.456633i \(0.150945\pi\)
−0.889655 + 0.456633i \(0.849055\pi\)
\(98\) 1.47963e6 1.57208
\(99\) 143282.i 0.147668i
\(100\) −588204. −0.588204
\(101\) −365591. −0.354839 −0.177420 0.984135i \(-0.556775\pi\)
−0.177420 + 0.984135i \(0.556775\pi\)
\(102\) 67129.5i 0.0632576i
\(103\) 1.37353e6i 1.25698i −0.777819 0.628489i \(-0.783674\pi\)
0.777819 0.628489i \(-0.216326\pi\)
\(104\) −1.58687e6 −1.41072
\(105\) −392711. −0.339239
\(106\) 1.20463e6i 1.01143i
\(107\) 1.26985e6i 1.03657i 0.855207 + 0.518287i \(0.173430\pi\)
−0.855207 + 0.518287i \(0.826570\pi\)
\(108\) 157471. 0.125006
\(109\) 1.06233e6i 0.820315i −0.912015 0.410157i \(-0.865474\pi\)
0.912015 0.410157i \(-0.134526\pi\)
\(110\) −107272. −0.0805949
\(111\) 1.26010e6i 0.921374i
\(112\) 191967.i 0.136638i
\(113\) 1.24438e6i 0.862415i −0.902253 0.431207i \(-0.858088\pi\)
0.902253 0.431207i \(-0.141912\pi\)
\(114\) 288700.i 0.194864i
\(115\) −455936. 102845.i −0.299785 0.0676220i
\(116\) 1.58325e6 1.01432
\(117\) −771256. −0.481550
\(118\) 468147. 0.284928
\(119\) −596321. −0.353867
\(120\) 299398.i 0.173263i
\(121\) 1.42389e6 0.803748
\(122\) 706885.i 0.389286i
\(123\) −549196. −0.295129
\(124\) 522679. 0.274138
\(125\) 1.14377e6i 0.585610i
\(126\) 754714.i 0.377286i
\(127\) −874087. −0.426721 −0.213360 0.976974i \(-0.568441\pi\)
−0.213360 + 0.976974i \(0.568441\pi\)
\(128\) 1.47657e6 0.704081
\(129\) 729552.i 0.339850i
\(130\) 577421.i 0.262822i
\(131\) −1.81535e6 −0.807509 −0.403754 0.914867i \(-0.632295\pi\)
−0.403754 + 0.914867i \(0.632295\pi\)
\(132\) 382104.i 0.166134i
\(133\) 2.56457e6 1.09008
\(134\) 1.56814e6i 0.651732i
\(135\) 145514.i 0.0591432i
\(136\) 454627.i 0.180734i
\(137\) 269246.i 0.104710i −0.998629 0.0523549i \(-0.983327\pi\)
0.998629 0.0523549i \(-0.0166727\pi\)
\(138\) 197647. 876220.i 0.0752062 0.333408i
\(139\) −1.01592e6 −0.378282 −0.189141 0.981950i \(-0.560570\pi\)
−0.189141 + 0.981950i \(0.560570\pi\)
\(140\) −1.04728e6 −0.381662
\(141\) −2.29402e6 −0.818353
\(142\) −1.75763e6 −0.613849
\(143\) 1.87145e6i 0.639985i
\(144\) 71131.1 0.0238217
\(145\) 1.46303e6i 0.479898i
\(146\) −149213. −0.0479456
\(147\) 4.87028e6 1.53321
\(148\) 3.36043e6i 1.03660i
\(149\) 5.31546e6i 1.60688i 0.595388 + 0.803438i \(0.296998\pi\)
−0.595388 + 0.803438i \(0.703002\pi\)
\(150\) 1.04458e6 0.309505
\(151\) −4.02808e6 −1.16995 −0.584975 0.811051i \(-0.698896\pi\)
−0.584975 + 0.811051i \(0.698896\pi\)
\(152\) 1.95519e6i 0.556748i
\(153\) 220960.i 0.0616935i
\(154\) 1.83131e6 0.501418
\(155\) 482991.i 0.129701i
\(156\) −2.05678e6 −0.541769
\(157\) 2.80608e6i 0.725107i −0.931963 0.362553i \(-0.881905\pi\)
0.931963 0.362553i \(-0.118095\pi\)
\(158\) 1.14991e6i 0.291536i
\(159\) 3.96510e6i 0.986421i
\(160\) 1.28246e6i 0.313101i
\(161\) 7.78359e6 + 1.75573e6i 1.86510 + 0.420708i
\(162\) −279651. −0.0657765
\(163\) −1.69615e6 −0.391652 −0.195826 0.980639i \(-0.562739\pi\)
−0.195826 + 0.980639i \(0.562739\pi\)
\(164\) −1.46459e6 −0.332036
\(165\) −353090. −0.0786020
\(166\) 3.92057e6i 0.857087i
\(167\) 4.14358e6 0.889665 0.444832 0.895614i \(-0.353263\pi\)
0.444832 + 0.895614i \(0.353263\pi\)
\(168\) 5.11122e6i 1.07795i
\(169\) 5.24680e6 1.08701
\(170\) −165427. −0.0336713
\(171\) 950270.i 0.190046i
\(172\) 1.94556e6i 0.382349i
\(173\) −3.49007e6 −0.674056 −0.337028 0.941495i \(-0.609422\pi\)
−0.337028 + 0.941495i \(0.609422\pi\)
\(174\) −2.81166e6 −0.533721
\(175\) 9.27916e6i 1.73139i
\(176\) 172599.i 0.0316593i
\(177\) 1.54093e6 0.277883
\(178\) 4.92504e6i 0.873272i
\(179\) −4.02563e6 −0.701899 −0.350949 0.936394i \(-0.614141\pi\)
−0.350949 + 0.936394i \(0.614141\pi\)
\(180\) 388057.i 0.0665393i
\(181\) 9.09130e6i 1.53317i 0.642143 + 0.766585i \(0.278046\pi\)
−0.642143 + 0.766585i \(0.721954\pi\)
\(182\) 9.85755e6i 1.63514i
\(183\) 2.32674e6i 0.379660i
\(184\) 1.33855e6 5.93411e6i 0.214872 0.952581i
\(185\) −3.10527e6 −0.490437
\(186\) −928215. −0.144248
\(187\) −536158. −0.0819913
\(188\) −6.11769e6 −0.920691
\(189\) 2.48418e6i 0.367957i
\(190\) 711444. 0.103724
\(191\) 91981.9i 0.0132009i −0.999978 0.00660043i \(-0.997899\pi\)
0.999978 0.00660043i \(-0.00210100\pi\)
\(192\) −2.17261e6 −0.306957
\(193\) 1.89895e6 0.264145 0.132073 0.991240i \(-0.457837\pi\)
0.132073 + 0.991240i \(0.457837\pi\)
\(194\) 3.94744e6i 0.540643i
\(195\) 1.90061e6i 0.256324i
\(196\) 1.29880e7 1.72494
\(197\) −2.32424e6 −0.304006 −0.152003 0.988380i \(-0.548572\pi\)
−0.152003 + 0.988380i \(0.548572\pi\)
\(198\) 678570.i 0.0874177i
\(199\) 6.58139e6i 0.835138i −0.908645 0.417569i \(-0.862882\pi\)
0.908645 0.417569i \(-0.137118\pi\)
\(200\) 7.07431e6 0.884288
\(201\) 5.16159e6i 0.635617i
\(202\) 1.73141e6 0.210061
\(203\) 2.49764e7i 2.98566i
\(204\) 589254.i 0.0694084i
\(205\) 1.35339e6i 0.157094i
\(206\) 6.50492e6i 0.744116i
\(207\) 650566. 2.88412e6i 0.0733466 0.325164i
\(208\) −929065. −0.103242
\(209\) 2.30582e6 0.252573
\(210\) 1.85984e6 0.200825
\(211\) −9.49872e6 −1.01115 −0.505577 0.862781i \(-0.668720\pi\)
−0.505577 + 0.862781i \(0.668720\pi\)
\(212\) 1.05741e7i 1.10978i
\(213\) −5.78531e6 −0.598670
\(214\) 6.01388e6i 0.613639i
\(215\) −1.79783e6 −0.180898
\(216\) −1.89390e6 −0.187930
\(217\) 8.24547e6i 0.806931i
\(218\) 5.03110e6i 0.485617i
\(219\) −491142. −0.0467600
\(220\) −941618. −0.0884315
\(221\) 2.88602e6i 0.267376i
\(222\) 5.96772e6i 0.545443i
\(223\) −1.00094e7 −0.902596 −0.451298 0.892373i \(-0.649039\pi\)
−0.451298 + 0.892373i \(0.649039\pi\)
\(224\) 2.18938e7i 1.94795i
\(225\) 3.43828e6 0.301852
\(226\) 5.89324e6i 0.510539i
\(227\) 1.06382e7i 0.909479i −0.890625 0.454739i \(-0.849732\pi\)
0.890625 0.454739i \(-0.150268\pi\)
\(228\) 2.53417e6i 0.213812i
\(229\) 1.56747e7i 1.30525i 0.757682 + 0.652624i \(0.226332\pi\)
−0.757682 + 0.652624i \(0.773668\pi\)
\(230\) 2.15927e6 + 487063.i 0.177469 + 0.0400314i
\(231\) 6.02784e6 0.489019
\(232\) −1.90416e7 −1.52490
\(233\) −1.75407e7 −1.38669 −0.693345 0.720605i \(-0.743864\pi\)
−0.693345 + 0.720605i \(0.743864\pi\)
\(234\) 3.65260e6 0.285072
\(235\) 5.65317e6i 0.435600i
\(236\) 4.10933e6 0.312633
\(237\) 3.78498e6i 0.284327i
\(238\) 2.82412e6 0.209485
\(239\) 1.76748e7 1.29468 0.647339 0.762202i \(-0.275882\pi\)
0.647339 + 0.762202i \(0.275882\pi\)
\(240\) 175288.i 0.0126800i
\(241\) 1.74693e7i 1.24803i −0.781413 0.624015i \(-0.785501\pi\)
0.781413 0.624015i \(-0.214499\pi\)
\(242\) −6.74340e6 −0.475809
\(243\) −920483. −0.0641500
\(244\) 6.20495e6i 0.427138i
\(245\) 1.20018e7i 0.816110i
\(246\) 2.60094e6 0.174713
\(247\) 1.24118e7i 0.823649i
\(248\) −6.28624e6 −0.412132
\(249\) 1.29047e7i 0.835894i
\(250\) 5.41679e6i 0.346674i
\(251\) 2.77630e7i 1.75568i 0.478957 + 0.877839i \(0.341015\pi\)
−0.478957 + 0.877839i \(0.658985\pi\)
\(252\) 6.62479e6i 0.413971i
\(253\) 6.99829e6 + 1.57859e6i 0.432146 + 0.0974785i
\(254\) 4.13960e6 0.252614
\(255\) −544512. −0.0328387
\(256\) −1.59127e7 −0.948473
\(257\) 2.30184e7 1.35605 0.678026 0.735038i \(-0.262836\pi\)
0.678026 + 0.735038i \(0.262836\pi\)
\(258\) 3.45509e6i 0.201187i
\(259\) 5.30121e7 3.05124
\(260\) 5.06853e6i 0.288378i
\(261\) −9.25470e6 −0.520524
\(262\) 8.59734e6 0.478036
\(263\) 1.22401e7i 0.672849i −0.941710 0.336424i \(-0.890782\pi\)
0.941710 0.336424i \(-0.109218\pi\)
\(264\) 4.59555e6i 0.249761i
\(265\) 9.77119e6 0.525061
\(266\) −1.21455e7 −0.645315
\(267\) 1.62110e7i 0.851679i
\(268\) 1.37649e7i 0.715103i
\(269\) −2.04992e7 −1.05312 −0.526562 0.850136i \(-0.676519\pi\)
−0.526562 + 0.850136i \(0.676519\pi\)
\(270\) 689143.i 0.0350121i
\(271\) −1.50443e7 −0.755898 −0.377949 0.925826i \(-0.623371\pi\)
−0.377949 + 0.925826i \(0.623371\pi\)
\(272\) 266171.i 0.0132268i
\(273\) 3.24466e7i 1.59471i
\(274\) 1.27512e6i 0.0619870i
\(275\) 8.34297e6i 0.401165i
\(276\) 1.73492e6 7.69135e6i 0.0825189 0.365826i
\(277\) −3.89399e7 −1.83213 −0.916063 0.401034i \(-0.868651\pi\)
−0.916063 + 0.401034i \(0.868651\pi\)
\(278\) 4.81131e6 0.223939
\(279\) −3.05526e6 −0.140681
\(280\) 1.25956e7 0.573779
\(281\) 2.98207e7i 1.34400i 0.740553 + 0.671998i \(0.234564\pi\)
−0.740553 + 0.671998i \(0.765436\pi\)
\(282\) 1.08643e7 0.484455
\(283\) 8.12480e6i 0.358470i −0.983806 0.179235i \(-0.942638\pi\)
0.983806 0.179235i \(-0.0573623\pi\)
\(284\) −1.54282e7 −0.673536
\(285\) 2.34175e6 0.101159
\(286\) 8.86301e6i 0.378864i
\(287\) 2.31046e7i 0.977355i
\(288\) −8.11249e6 −0.339607
\(289\) 2.33107e7 0.965745
\(290\) 6.92876e6i 0.284094i
\(291\) 1.29932e7i 0.527275i
\(292\) −1.30977e6 −0.0526075
\(293\) 3.59566e6i 0.142947i −0.997442 0.0714736i \(-0.977230\pi\)
0.997442 0.0714736i \(-0.0227702\pi\)
\(294\) −2.30652e7 −0.907642
\(295\) 3.79731e6i 0.147914i
\(296\) 4.04157e7i 1.55839i
\(297\) 2.23355e6i 0.0852561i
\(298\) 2.51735e7i 0.951252i
\(299\) −8.49723e6 + 3.76703e7i −0.317881 + 1.40924i
\(300\) 9.16919e6 0.339600
\(301\) 3.06921e7 1.12545
\(302\) 1.90766e7 0.692597
\(303\) 5.69900e6 0.204866
\(304\) 1.14471e6i 0.0407449i
\(305\) −5.73380e6 −0.202089
\(306\) 1.04645e6i 0.0365218i
\(307\) −3.56413e7 −1.23179 −0.615897 0.787826i \(-0.711206\pi\)
−0.615897 + 0.787826i \(0.711206\pi\)
\(308\) 1.60750e7 0.550173
\(309\) 2.14113e7i 0.725716i
\(310\) 2.28740e6i 0.0767816i
\(311\) 2.80618e7 0.932899 0.466450 0.884548i \(-0.345533\pi\)
0.466450 + 0.884548i \(0.345533\pi\)
\(312\) 2.47368e7 0.814480
\(313\) 1.51413e7i 0.493777i −0.969044 0.246889i \(-0.920592\pi\)
0.969044 0.246889i \(-0.0794082\pi\)
\(314\) 1.32894e7i 0.429255i
\(315\) 6.12176e6 0.195860
\(316\) 1.00938e7i 0.319883i
\(317\) 2.13859e7 0.671351 0.335676 0.941978i \(-0.391035\pi\)
0.335676 + 0.941978i \(0.391035\pi\)
\(318\) 1.87783e7i 0.583950i
\(319\) 2.24565e7i 0.691782i
\(320\) 5.35395e6i 0.163390i
\(321\) 1.97950e7i 0.598466i
\(322\) −3.68624e7 8.31498e6i −1.10412 0.249054i
\(323\) 3.55589e6 0.105521
\(324\) −2.45474e6 −0.0721722
\(325\) −4.49084e7 −1.30821
\(326\) 8.03279e6 0.231853
\(327\) 1.65601e7i 0.473609i
\(328\) 1.76146e7 0.499174
\(329\) 9.65091e7i 2.71007i
\(330\) 1.67220e6 0.0465315
\(331\) −2.67122e7 −0.736591 −0.368295 0.929709i \(-0.620059\pi\)
−0.368295 + 0.929709i \(0.620059\pi\)
\(332\) 3.44143e7i 0.940425i
\(333\) 1.96430e7i 0.531956i
\(334\) −1.96236e7 −0.526671
\(335\) −1.27197e7 −0.338332
\(336\) 2.99247e6i 0.0788882i
\(337\) 4.34797e7i 1.13605i −0.823011 0.568025i \(-0.807708\pi\)
0.823011 0.568025i \(-0.192292\pi\)
\(338\) −2.48484e7 −0.643498
\(339\) 1.93979e7i 0.497915i
\(340\) −1.45210e6 −0.0369453
\(341\) 7.41358e6i 0.186967i
\(342\) 4.50039e6i 0.112505i
\(343\) 1.27737e8i 3.16544i
\(344\) 2.33992e7i 0.574812i
\(345\) 7.10733e6 + 1.60319e6i 0.173081 + 0.0390416i
\(346\) 1.65286e7 0.399033
\(347\) 1.79683e7 0.430049 0.215024 0.976609i \(-0.431017\pi\)
0.215024 + 0.976609i \(0.431017\pi\)
\(348\) −2.46804e7 −0.585617
\(349\) −1.98878e7 −0.467855 −0.233927 0.972254i \(-0.575158\pi\)
−0.233927 + 0.972254i \(0.575158\pi\)
\(350\) 4.39452e7i 1.02496i
\(351\) 1.20227e7 0.278023
\(352\) 1.96849e7i 0.451341i
\(353\) 2.64567e7 0.601467 0.300733 0.953708i \(-0.402769\pi\)
0.300733 + 0.953708i \(0.402769\pi\)
\(354\) −7.29768e6 −0.164504
\(355\) 1.42567e7i 0.318665i
\(356\) 4.32314e7i 0.958184i
\(357\) 9.29573e6 0.204305
\(358\) 1.90650e7 0.415516
\(359\) 5.31179e7i 1.14804i −0.818841 0.574020i \(-0.805383\pi\)
0.818841 0.574020i \(-0.194617\pi\)
\(360\) 4.66715e6i 0.100033i
\(361\) 3.17533e7 0.674943
\(362\) 4.30555e7i 0.907618i
\(363\) −2.21962e7 −0.464044
\(364\) 8.65283e7i 1.79413i
\(365\) 1.21032e6i 0.0248898i
\(366\) 1.10192e7i 0.224754i
\(367\) 1.02909e7i 0.208188i 0.994567 + 0.104094i \(0.0331942\pi\)
−0.994567 + 0.104094i \(0.966806\pi\)
\(368\) 783679. 3.47424e6i 0.0157252 0.0697135i
\(369\) 8.56112e6 0.170393
\(370\) 1.47062e7 0.290333
\(371\) −1.66811e8 −3.26665
\(372\) −8.14776e6 −0.158274
\(373\) 2.28746e7i 0.440785i 0.975411 + 0.220392i \(0.0707338\pi\)
−0.975411 + 0.220392i \(0.929266\pi\)
\(374\) 2.53919e6 0.0485379
\(375\) 1.78296e7i 0.338102i
\(376\) 7.35772e7 1.38414
\(377\) 1.20878e8 2.25592
\(378\) 1.17648e7i 0.217826i
\(379\) 8.53493e7i 1.56777i −0.620906 0.783885i \(-0.713235\pi\)
0.620906 0.783885i \(-0.286765\pi\)
\(380\) 6.24496e6 0.113810
\(381\) 1.36257e7 0.246367
\(382\) 435618.i 0.00781475i
\(383\) 5.06708e7i 0.901906i −0.892548 0.450953i \(-0.851084\pi\)
0.892548 0.450953i \(-0.148916\pi\)
\(384\) −2.30174e7 −0.406502
\(385\) 1.48544e7i 0.260300i
\(386\) −8.99327e6 −0.156371
\(387\) 1.13726e7i 0.196212i
\(388\) 3.46502e7i 0.593212i
\(389\) 4.61864e7i 0.784630i 0.919831 + 0.392315i \(0.128326\pi\)
−0.919831 + 0.392315i \(0.871674\pi\)
\(390\) 9.00110e6i 0.151741i
\(391\) 1.07923e7 + 2.43440e6i 0.180544 + 0.0407251i
\(392\) −1.56206e8 −2.59323
\(393\) 2.82986e7 0.466215
\(394\) 1.10074e7 0.179968
\(395\) 9.32732e6 0.151344
\(396\) 5.95641e6i 0.0959177i
\(397\) −6.30551e7 −1.00774 −0.503870 0.863779i \(-0.668091\pi\)
−0.503870 + 0.863779i \(0.668091\pi\)
\(398\) 3.11688e7i 0.494392i
\(399\) −3.99776e7 −0.629359
\(400\) 4.14180e6 0.0647156
\(401\) 6.06571e7i 0.940695i −0.882481 0.470347i \(-0.844129\pi\)
0.882481 0.470347i \(-0.155871\pi\)
\(402\) 2.44448e7i 0.376278i
\(403\) 3.99057e7 0.609705
\(404\) 1.51981e7 0.230486
\(405\) 2.26835e6i 0.0341463i
\(406\) 1.18286e8i 1.76748i
\(407\) 4.76637e7 0.706975
\(408\) 7.08694e6i 0.104347i
\(409\) −8.56293e7 −1.25156 −0.625781 0.779998i \(-0.715220\pi\)
−0.625781 + 0.779998i \(0.715220\pi\)
\(410\) 6.40950e6i 0.0929978i
\(411\) 4.19713e6i 0.0604542i
\(412\) 5.70994e7i 0.816470i
\(413\) 6.48264e7i 0.920242i
\(414\) −3.08102e6 + 1.36589e7i −0.0434203 + 0.192493i
\(415\) −3.18011e7 −0.444937
\(416\) 1.05960e8 1.47184
\(417\) 1.58367e7 0.218401
\(418\) −1.09202e7 −0.149520
\(419\) 4.27680e7i 0.581403i 0.956814 + 0.290701i \(0.0938886\pi\)
−0.956814 + 0.290701i \(0.906111\pi\)
\(420\) 1.63255e7 0.220352
\(421\) 1.37696e7i 0.184534i 0.995734 + 0.0922668i \(0.0294113\pi\)
−0.995734 + 0.0922668i \(0.970589\pi\)
\(422\) 4.49850e7 0.598592
\(423\) 3.57603e7 0.472476
\(424\) 1.27174e8i 1.66841i
\(425\) 1.28660e7i 0.167601i
\(426\) 2.73987e7 0.354406
\(427\) 9.78856e7 1.25729
\(428\) 5.27891e7i 0.673306i
\(429\) 2.91730e7i 0.369496i
\(430\) 8.51437e6 0.107090
\(431\) 1.76722e7i 0.220729i 0.993891 + 0.110365i \(0.0352018\pi\)
−0.993891 + 0.110365i \(0.964798\pi\)
\(432\) −1.10882e6 −0.0137534
\(433\) 6.14430e7i 0.756848i −0.925632 0.378424i \(-0.876466\pi\)
0.925632 0.378424i \(-0.123534\pi\)
\(434\) 3.90498e7i 0.477694i
\(435\) 2.28063e7i 0.277069i
\(436\) 4.41624e7i 0.532835i
\(437\) −4.64138e7 1.04695e7i −0.556164 0.125453i
\(438\) 2.32600e6 0.0276814
\(439\) −4.41260e7 −0.521556 −0.260778 0.965399i \(-0.583979\pi\)
−0.260778 + 0.965399i \(0.583979\pi\)
\(440\) 1.13248e7 0.132945
\(441\) −7.59201e7 −0.885199
\(442\) 1.36679e7i 0.158284i
\(443\) 3.93587e7 0.452719 0.226360 0.974044i \(-0.427318\pi\)
0.226360 + 0.974044i \(0.427318\pi\)
\(444\) 5.23839e7i 0.598479i
\(445\) −3.99488e7 −0.453339
\(446\) 4.74036e7 0.534326
\(447\) 8.28599e7i 0.927730i
\(448\) 9.14010e7i 1.01652i
\(449\) −9.04011e7 −0.998699 −0.499349 0.866401i \(-0.666428\pi\)
−0.499349 + 0.866401i \(0.666428\pi\)
\(450\) −1.62834e7 −0.178693
\(451\) 2.07735e7i 0.226454i
\(452\) 5.17302e7i 0.560181i
\(453\) 6.27916e7 0.675471
\(454\) 5.03817e7i 0.538401i
\(455\) −7.99581e7 −0.848845
\(456\) 3.04784e7i 0.321438i
\(457\) 4.88645e7i 0.511970i 0.966681 + 0.255985i \(0.0823998\pi\)
−0.966681 + 0.255985i \(0.917600\pi\)
\(458\) 7.42340e7i 0.772692i
\(459\) 3.44442e6i 0.0356187i
\(460\) 1.89538e7 + 4.27538e6i 0.194725 + 0.0439239i
\(461\) −5.13497e7 −0.524125 −0.262063 0.965051i \(-0.584403\pi\)
−0.262063 + 0.965051i \(0.584403\pi\)
\(462\) −2.85473e7 −0.289494
\(463\) −9.15812e7 −0.922706 −0.461353 0.887217i \(-0.652636\pi\)
−0.461353 + 0.887217i \(0.652636\pi\)
\(464\) −1.11483e7 −0.111598
\(465\) 7.52909e6i 0.0748830i
\(466\) 8.30712e7 0.820905
\(467\) 1.65064e8i 1.62070i −0.585948 0.810349i \(-0.699278\pi\)
0.585948 0.810349i \(-0.300722\pi\)
\(468\) 3.20621e7 0.312791
\(469\) 2.17147e8 2.10492
\(470\) 2.67729e7i 0.257870i
\(471\) 4.37425e7i 0.418640i
\(472\) −4.94228e7 −0.470004
\(473\) 2.75955e7 0.260768
\(474\) 1.79253e7i 0.168318i
\(475\) 5.53320e7i 0.516292i
\(476\) 2.47898e7 0.229854
\(477\) 6.18098e7i 0.569511i
\(478\) −8.37064e7 −0.766434
\(479\) 5.12647e7i 0.466457i −0.972422 0.233228i \(-0.925071\pi\)
0.972422 0.233228i \(-0.0749290\pi\)
\(480\) 1.99916e7i 0.180769i
\(481\) 2.56563e8i 2.30547i
\(482\) 8.27330e7i 0.738819i
\(483\) −1.21334e8 2.73692e7i −1.07682 0.242896i
\(484\) −5.91927e7 −0.522074
\(485\) 3.20191e7 0.280663
\(486\) 4.35932e6 0.0379761
\(487\) 1.00852e8 0.873168 0.436584 0.899664i \(-0.356188\pi\)
0.436584 + 0.899664i \(0.356188\pi\)
\(488\) 7.46266e7i 0.642147i
\(489\) 2.64403e7 0.226120
\(490\) 5.68395e7i 0.483128i
\(491\) 4.28499e7 0.361998 0.180999 0.983483i \(-0.442067\pi\)
0.180999 + 0.983483i \(0.442067\pi\)
\(492\) 2.28308e7 0.191701
\(493\) 3.46308e7i 0.289016i
\(494\) 5.87809e7i 0.487591i
\(495\) 5.50413e6 0.0453809
\(496\) −3.68041e6 −0.0301613
\(497\) 2.43387e8i 1.98256i
\(498\) 6.11156e7i 0.494839i
\(499\) 2.43539e8 1.96005 0.980024 0.198877i \(-0.0637295\pi\)
0.980024 + 0.198877i \(0.0637295\pi\)
\(500\) 4.75479e7i 0.380383i
\(501\) −6.45920e7 −0.513648
\(502\) 1.31483e8i 1.03934i
\(503\) 2.71475e7i 0.213317i 0.994296 + 0.106659i \(0.0340152\pi\)
−0.994296 + 0.106659i \(0.965985\pi\)
\(504\) 7.96761e7i 0.622352i
\(505\) 1.40441e7i 0.109048i
\(506\) −3.31433e7 7.47607e6i −0.255825 0.0577061i
\(507\) −8.17895e7 −0.627587
\(508\) 3.63369e7 0.277176
\(509\) 1.63613e8 1.24069 0.620347 0.784327i \(-0.286992\pi\)
0.620347 + 0.784327i \(0.286992\pi\)
\(510\) 2.57876e6 0.0194401
\(511\) 2.06622e7i 0.154851i
\(512\) −1.91390e7 −0.142597
\(513\) 1.48132e7i 0.109723i
\(514\) −1.09013e8 −0.802766
\(515\) −5.27638e7 −0.386291
\(516\) 3.03283e7i 0.220749i
\(517\) 8.67722e7i 0.627926i
\(518\) −2.51060e8 −1.80630
\(519\) 5.44048e7 0.389166
\(520\) 6.09590e7i 0.433539i
\(521\) 3.82670e7i 0.270590i −0.990805 0.135295i \(-0.956802\pi\)
0.990805 0.135295i \(-0.0431982\pi\)
\(522\) 4.38294e7 0.308144
\(523\) 1.69427e8i 1.18434i −0.805812 0.592172i \(-0.798271\pi\)
0.805812 0.592172i \(-0.201729\pi\)
\(524\) 7.54664e7 0.524517
\(525\) 1.44648e8i 0.999618i
\(526\) 5.79679e7i 0.398319i
\(527\) 1.14327e7i 0.0781120i
\(528\) 2.69056e6i 0.0182785i
\(529\) −1.33701e8 6.35509e7i −0.903165 0.429294i
\(530\) −4.62754e7 −0.310830
\(531\) −2.40207e7 −0.160436
\(532\) −1.06612e8 −0.708062
\(533\) −1.11819e8 −0.738474
\(534\) 7.67737e7i 0.504184i
\(535\) 4.87807e7 0.318557
\(536\) 1.65550e8i 1.07506i
\(537\) 6.27533e7 0.405241
\(538\) 9.70822e7 0.623438
\(539\) 1.84220e8i 1.17644i
\(540\) 6.04921e6i 0.0384165i
\(541\) −1.41458e8 −0.893378 −0.446689 0.894689i \(-0.647397\pi\)
−0.446689 + 0.894689i \(0.647397\pi\)
\(542\) 7.12483e7 0.447483
\(543\) 1.41719e8i 0.885176i
\(544\) 3.03567e7i 0.188564i
\(545\) −4.08091e7 −0.252097
\(546\) 1.53664e8i 0.944048i
\(547\) −5.97977e7 −0.365361 −0.182681 0.983172i \(-0.558477\pi\)
−0.182681 + 0.983172i \(0.558477\pi\)
\(548\) 1.11929e7i 0.0680142i
\(549\) 3.62703e7i 0.219197i
\(550\) 3.95115e7i 0.237485i
\(551\) 1.48935e8i 0.890311i
\(552\) −2.08659e7 + 9.25035e7i −0.124056 + 0.549973i
\(553\) −1.59233e8 −0.941582
\(554\) 1.84416e8 1.08460
\(555\) 4.84063e7 0.283154
\(556\) 4.22331e7 0.245713
\(557\) 3.31067e7i 0.191580i 0.995402 + 0.0957900i \(0.0305377\pi\)
−0.995402 + 0.0957900i \(0.969462\pi\)
\(558\) 1.44694e7 0.0832816
\(559\) 1.48541e8i 0.850374i
\(560\) 7.37435e6 0.0419913
\(561\) 8.35787e6 0.0473377
\(562\) 1.41228e8i 0.795630i
\(563\) 2.07541e8i 1.16299i −0.813548 0.581497i \(-0.802467\pi\)
0.813548 0.581497i \(-0.197533\pi\)
\(564\) 9.53653e7 0.531561
\(565\) −4.78022e7 −0.265035
\(566\) 3.84783e7i 0.212210i
\(567\) 3.87245e7i 0.212440i
\(568\) 1.85555e8 1.01257
\(569\) 2.45063e8i 1.33027i 0.746723 + 0.665136i \(0.231626\pi\)
−0.746723 + 0.665136i \(0.768374\pi\)
\(570\) −1.10903e7 −0.0598851
\(571\) 1.57184e8i 0.844307i −0.906524 0.422153i \(-0.861274\pi\)
0.906524 0.422153i \(-0.138726\pi\)
\(572\) 7.77984e7i 0.415702i
\(573\) 1.43386e6i 0.00762152i
\(574\) 1.09421e8i 0.578582i
\(575\) 3.78809e7 1.67935e8i 0.199258 0.883362i
\(576\) 3.38676e7 0.177222
\(577\) 7.78829e7 0.405429 0.202715 0.979238i \(-0.435024\pi\)
0.202715 + 0.979238i \(0.435024\pi\)
\(578\) −1.10397e8 −0.571710
\(579\) −2.96018e7 −0.152504
\(580\) 6.08198e7i 0.311717i
\(581\) 5.42899e8 2.76816
\(582\) 6.15346e7i 0.312141i
\(583\) −1.49981e8 −0.756886
\(584\) 1.57526e7 0.0790886
\(585\) 2.96275e7i 0.147989i
\(586\) 1.70287e7i 0.0846231i
\(587\) −1.75136e7 −0.0865888 −0.0432944 0.999062i \(-0.513785\pi\)
−0.0432944 + 0.999062i \(0.513785\pi\)
\(588\) −2.02463e8 −0.995896
\(589\) 4.91680e7i 0.240623i
\(590\) 1.79837e7i 0.0875634i
\(591\) 3.62313e7 0.175518
\(592\) 2.36622e7i 0.114049i
\(593\) −3.78225e8 −1.81379 −0.906893 0.421361i \(-0.861553\pi\)
−0.906893 + 0.421361i \(0.861553\pi\)
\(594\) 1.05779e7i 0.0504706i
\(595\) 2.29075e7i 0.108749i
\(596\) 2.20970e8i 1.04375i
\(597\) 1.02594e8i 0.482167i
\(598\) 4.02421e7 1.78403e8i 0.188182 0.834255i
\(599\) −6.74384e7 −0.313781 −0.156891 0.987616i \(-0.550147\pi\)
−0.156891 + 0.987616i \(0.550147\pi\)
\(600\) −1.10278e8 −0.510544
\(601\) −1.98091e8 −0.912516 −0.456258 0.889847i \(-0.650811\pi\)
−0.456258 + 0.889847i \(0.650811\pi\)
\(602\) −1.45355e8 −0.666254
\(603\) 8.04612e7i 0.366974i
\(604\) 1.67452e8 0.759941
\(605\) 5.46981e7i 0.247005i
\(606\) −2.69899e7 −0.121279
\(607\) −3.35592e7 −0.150053 −0.0750267 0.997182i \(-0.523904\pi\)
−0.0750267 + 0.997182i \(0.523904\pi\)
\(608\) 1.30553e8i 0.580868i
\(609\) 3.89343e8i 1.72377i
\(610\) 2.71547e7 0.119634
\(611\) −4.67076e8 −2.04769
\(612\) 9.18557e6i 0.0400730i
\(613\) 6.44452e7i 0.279775i −0.990167 0.139888i \(-0.955326\pi\)
0.990167 0.139888i \(-0.0446741\pi\)
\(614\) 1.68794e8 0.729208
\(615\) 2.10972e7i 0.0906983i
\(616\) −1.93334e8 −0.827114
\(617\) 3.01733e8i 1.28460i 0.766453 + 0.642300i \(0.222020\pi\)
−0.766453 + 0.642300i \(0.777980\pi\)
\(618\) 1.01402e8i 0.429616i
\(619\) 6.36803e7i 0.268493i −0.990948 0.134246i \(-0.957139\pi\)
0.990948 0.134246i \(-0.0428614\pi\)
\(620\) 2.00785e7i 0.0842474i
\(621\) −1.01413e7 + 4.49589e7i −0.0423467 + 0.187733i
\(622\) −1.32898e8 −0.552265
\(623\) 6.81993e8 2.82043
\(624\) 1.44827e7 0.0596067
\(625\) 1.77146e8 0.725588
\(626\) 7.17080e7i 0.292310i
\(627\) −3.59442e7 −0.145823
\(628\) 1.16652e8i 0.470993i
\(629\) 7.35037e7 0.295364
\(630\) −2.89921e7 −0.115947
\(631\) 1.83010e8i 0.728427i 0.931315 + 0.364214i \(0.118662\pi\)
−0.931315 + 0.364214i \(0.881338\pi\)
\(632\) 1.21397e8i 0.480903i
\(633\) 1.48070e8 0.583790
\(634\) −1.01282e8 −0.397432
\(635\) 3.35778e7i 0.131139i
\(636\) 1.64834e8i 0.640730i
\(637\) 9.91615e8 3.83641
\(638\) 1.06352e8i 0.409527i
\(639\) 9.01840e7 0.345642
\(640\) 5.67217e7i 0.216376i
\(641\) 3.89706e8i 1.47967i 0.672791 + 0.739833i \(0.265095\pi\)
−0.672791 + 0.739833i \(0.734905\pi\)
\(642\) 9.37470e7i 0.354285i
\(643\) 2.85643e8i 1.07446i 0.843436 + 0.537230i \(0.180529\pi\)
−0.843436 + 0.537230i \(0.819471\pi\)
\(644\) −3.23573e8 7.29879e7i −1.21148 0.273271i
\(645\) 2.80255e7 0.104442
\(646\) −1.68403e7 −0.0624674
\(647\) −4.43292e8 −1.63673 −0.818365 0.574699i \(-0.805119\pi\)
−0.818365 + 0.574699i \(0.805119\pi\)
\(648\) 2.95230e7 0.108502
\(649\) 5.82860e7i 0.213221i
\(650\) 2.12682e8 0.774446
\(651\) 1.28534e8i 0.465882i
\(652\) 7.05108e7 0.254398
\(653\) 1.53784e8 0.552294 0.276147 0.961115i \(-0.410942\pi\)
0.276147 + 0.961115i \(0.410942\pi\)
\(654\) 7.84271e7i 0.280371i
\(655\) 6.97361e7i 0.248161i
\(656\) 1.03128e7 0.0365314
\(657\) 7.65614e6 0.0269969
\(658\) 4.57058e8i 1.60433i
\(659\) 1.40657e8i 0.491481i 0.969336 + 0.245740i \(0.0790311\pi\)
−0.969336 + 0.245740i \(0.920969\pi\)
\(660\) 1.46784e7 0.0510559
\(661\) 1.20638e8i 0.417713i −0.977946 0.208857i \(-0.933026\pi\)
0.977946 0.208857i \(-0.0669742\pi\)
\(662\) 1.26507e8 0.436053
\(663\) 4.49886e7i 0.154370i
\(664\) 4.13899e8i 1.41381i
\(665\) 9.85169e7i 0.335001i
\(666\) 9.30275e7i 0.314912i
\(667\) −1.01963e8 + 4.52025e8i −0.343608 + 1.52330i
\(668\) −1.72254e8 −0.577882
\(669\) 1.56031e8 0.521114
\(670\) 6.02393e7 0.200288
\(671\) 8.80098e7 0.291315
\(672\) 3.41290e8i 1.12465i
\(673\) −4.99233e8 −1.63779 −0.818895 0.573943i \(-0.805413\pi\)
−0.818895 + 0.573943i \(0.805413\pi\)
\(674\) 2.05916e8i 0.672528i
\(675\) −5.35975e7 −0.174274
\(676\) −2.18116e8 −0.706069
\(677\) 5.75205e8i 1.85377i 0.375342 + 0.926886i \(0.377525\pi\)
−0.375342 + 0.926886i \(0.622475\pi\)
\(678\) 9.18666e7i 0.294760i
\(679\) −5.46621e8 −1.74613
\(680\) 1.74644e7 0.0555425
\(681\) 1.65834e8i 0.525088i
\(682\) 3.51100e7i 0.110682i
\(683\) 3.10528e8 0.974626 0.487313 0.873227i \(-0.337977\pi\)
0.487313 + 0.873227i \(0.337977\pi\)
\(684\) 3.95038e7i 0.123444i
\(685\) −1.03430e7 −0.0321791
\(686\) 6.04950e8i 1.87390i
\(687\) 2.44345e8i 0.753585i
\(688\) 1.36995e7i 0.0420669i
\(689\) 8.07315e8i 2.46823i
\(690\) −3.36597e7 7.59255e6i −0.102462 0.0231122i
\(691\) 3.16160e7 0.0958237 0.0479119 0.998852i \(-0.484743\pi\)
0.0479119 + 0.998852i \(0.484743\pi\)
\(692\) 1.45086e8 0.437833
\(693\) −9.39648e7 −0.282335
\(694\) −8.50960e7 −0.254584
\(695\) 3.90263e7i 0.116253i
\(696\) 2.96830e8 0.880399
\(697\) 3.20355e7i 0.0946092i
\(698\) 9.41869e7 0.276964
\(699\) 2.73433e8 0.800606
\(700\) 3.85746e8i 1.12462i
\(701\) 6.49293e8i 1.88489i −0.334355 0.942447i \(-0.608519\pi\)
0.334355 0.942447i \(-0.391481\pi\)
\(702\) −5.69384e7 −0.164586
\(703\) −3.16113e8 −0.909864
\(704\) 8.21795e7i 0.235530i
\(705\) 8.81241e7i 0.251494i
\(706\) −1.25296e8 −0.356061
\(707\) 2.39756e8i 0.678439i
\(708\) −6.40582e7 −0.180499
\(709\) 2.76124e8i 0.774757i 0.921921 + 0.387379i \(0.126619\pi\)
−0.921921 + 0.387379i \(0.873381\pi\)
\(710\) 6.75186e7i 0.188646i
\(711\) 5.90020e7i 0.164156i
\(712\) 5.19942e8i 1.44051i
\(713\) −3.36610e7 + 1.49228e8i −0.0928664 + 0.411700i
\(714\) −4.40237e7 −0.120946
\(715\) −7.18911e7 −0.196678
\(716\) 1.67350e8 0.455918
\(717\) −2.75524e8 −0.747483
\(718\) 2.51561e8i 0.679627i
\(719\) −1.67972e7 −0.0451907 −0.0225953 0.999745i \(-0.507193\pi\)
−0.0225953 + 0.999745i \(0.507193\pi\)
\(720\) 2.73248e6i 0.00732081i
\(721\) 9.00767e8 2.40329
\(722\) −1.50381e8 −0.399558
\(723\) 2.72320e8i 0.720550i
\(724\) 3.77936e8i 0.995870i
\(725\) −5.38879e8 −1.41409
\(726\) 1.05119e8 0.274709
\(727\) 1.40934e8i 0.366786i −0.983040 0.183393i \(-0.941292\pi\)
0.983040 0.183393i \(-0.0587082\pi\)
\(728\) 1.04067e9i 2.69724i
\(729\) 1.43489e7 0.0370370
\(730\) 5.73197e6i 0.0147345i
\(731\) 4.25559e7 0.108945
\(732\) 9.67255e7i 0.246608i
\(733\) 4.60922e8i 1.17035i −0.810907 0.585175i \(-0.801026\pi\)
0.810907 0.585175i \(-0.198974\pi\)
\(734\) 4.87367e7i 0.123245i
\(735\) 1.87090e8i 0.471182i
\(736\) −8.93784e7 + 3.96236e8i −0.224181 + 0.993850i
\(737\) 1.95239e8 0.487712
\(738\) −4.05447e7 −0.100871
\(739\) −2.18814e8 −0.542177 −0.271088 0.962554i \(-0.587384\pi\)
−0.271088 + 0.962554i \(0.587384\pi\)
\(740\) 1.29090e8 0.318564
\(741\) 1.93480e8i 0.475534i
\(742\) 7.90000e8 1.93382
\(743\) 6.03913e8i 1.47234i −0.676797 0.736170i \(-0.736632\pi\)
0.676797 0.736170i \(-0.263368\pi\)
\(744\) 9.79928e7 0.237944
\(745\) 2.04192e8 0.493821
\(746\) 1.08332e8i 0.260939i
\(747\) 2.01165e8i 0.482603i
\(748\) 2.22887e7 0.0532574
\(749\) −8.32769e8 −1.98189
\(750\) 8.44393e7i 0.200152i
\(751\) 3.51109e8i 0.828938i 0.910063 + 0.414469i \(0.136033\pi\)
−0.910063 + 0.414469i \(0.863967\pi\)
\(752\) 4.30773e7 0.101297
\(753\) 4.32782e8i 1.01364i
\(754\) −5.72468e8 −1.33548
\(755\) 1.54737e8i 0.359546i
\(756\) 1.03270e8i 0.239007i
\(757\) 3.44892e8i 0.795051i −0.917591 0.397526i \(-0.869869\pi\)
0.917591 0.397526i \(-0.130131\pi\)
\(758\) 4.04206e8i 0.928101i
\(759\) −1.09093e8 2.46078e7i −0.249500 0.0562792i
\(760\) −7.51079e7 −0.171098
\(761\) −6.29042e8 −1.42733 −0.713667 0.700485i \(-0.752967\pi\)
−0.713667 + 0.700485i \(0.752967\pi\)
\(762\) −6.45299e7 −0.145847
\(763\) 6.96680e8 1.56841
\(764\) 3.82380e6i 0.00857462i
\(765\) 8.48809e6 0.0189595
\(766\) 2.39972e8i 0.533918i
\(767\) 3.13741e8 0.695321
\(768\) 2.48055e8 0.547601
\(769\) 7.77114e6i 0.0170886i −0.999963 0.00854428i \(-0.997280\pi\)
0.999963 0.00854428i \(-0.00271976\pi\)
\(770\) 7.03491e7i 0.154094i
\(771\) −3.58822e8 −0.782916
\(772\) −7.89418e7 −0.171575
\(773\) 3.82987e8i 0.829174i −0.910010 0.414587i \(-0.863926\pi\)
0.910010 0.414587i \(-0.136074\pi\)
\(774\) 5.38595e7i 0.116155i
\(775\) −1.77901e8 −0.382184
\(776\) 4.16736e8i 0.891818i
\(777\) −8.26377e8 −1.76163
\(778\) 2.18734e8i 0.464492i
\(779\) 1.37773e8i 0.291442i
\(780\) 7.90105e7i 0.166495i
\(781\) 2.18831e8i 0.459363i
\(782\) −5.11113e7 1.15291e7i −0.106880 0.0241088i
\(783\) 1.44266e8 0.300525
\(784\) −9.14542e7