Properties

Label 177.7.c.a.58.18
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.18
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.43

$q$-expansion

\(f(q)\) \(=\) \(q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +37.5501i q^{10} +24.8744i q^{11} -209.691 q^{12} -177.466i q^{13} +657.394i q^{14} +82.3307 q^{15} -3054.14 q^{16} -715.296 q^{17} -1727.66i q^{18} +11687.5 q^{19} -71.0454 q^{20} +1441.37 q^{21} +176.850 q^{22} -13557.4i q^{23} +8583.95i q^{24} -15597.1 q^{25} -1261.74 q^{26} -3788.00 q^{27} -1243.80 q^{28} -31537.4 q^{29} -585.349i q^{30} -37264.3i q^{31} -13528.2i q^{32} -387.753i q^{33} +5085.56i q^{34} +488.350 q^{35} +3268.76 q^{36} +17556.2i q^{37} -83094.9i q^{38} +2766.42i q^{39} +2908.32i q^{40} -64099.4 q^{41} -10247.8i q^{42} +76044.2i q^{43} +334.603i q^{44} -1283.41 q^{45} -96389.3 q^{46} +32613.7i q^{47} +47609.4 q^{48} -109099. q^{49} +110891. i q^{50} +11150.4 q^{51} -2387.22i q^{52} -56531.8 q^{53} +26931.6i q^{54} -131.374i q^{55} +50916.3i q^{56} -182190. q^{57} +224223. i q^{58} +(168147. + 117928. i) q^{59} +1107.49 q^{60} -290251. i q^{61} -264939. q^{62} -22468.7 q^{63} -291647. q^{64} +937.290i q^{65} -2756.82 q^{66} +149412. i q^{67} -9621.95 q^{68} +211339. i q^{69} -3472.03i q^{70} -683880. q^{71} -133811. i q^{72} +714312. i q^{73} +124820. q^{74} +243135. q^{75} +157217. q^{76} -2299.98i q^{77} +19668.5 q^{78} -489011. q^{79} +16130.5 q^{80} +59049.0 q^{81} +455730. i q^{82} -559911. i q^{83} +19388.9 q^{84} +3777.84 q^{85} +540654. q^{86} +491620. q^{87} +13697.3 q^{88} +783652. i q^{89} +9124.69i q^{90} +16409.2i q^{91} -182370. i q^{92} +580892. i q^{93} +231874. q^{94} -61727.6 q^{95} +210883. i q^{96} +1.32625e6i q^{97} +775668. i q^{98} +6044.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.10973i 0.888717i −0.895849 0.444358i \(-0.853432\pi\)
0.895849 0.444358i \(-0.146568\pi\)
\(3\) −15.5885 −0.577350
\(4\) 13.4517 0.210183
\(5\) −5.28151 −0.0422521 −0.0211261 0.999777i \(-0.506725\pi\)
−0.0211261 + 0.999777i \(0.506725\pi\)
\(6\) 110.830i 0.513101i
\(7\) −92.4639 −0.269574 −0.134787 0.990875i \(-0.543035\pi\)
−0.134787 + 0.990875i \(0.543035\pi\)
\(8\) 550.661i 1.07551i
\(9\) 243.000 0.333333
\(10\) 37.5501i 0.0375501i
\(11\) 24.8744i 0.0186885i 0.999956 + 0.00934424i \(0.00297441\pi\)
−0.999956 + 0.00934424i \(0.997026\pi\)
\(12\) −209.691 −0.121349
\(13\) 177.466i 0.0807766i −0.999184 0.0403883i \(-0.987141\pi\)
0.999184 0.0403883i \(-0.0128595\pi\)
\(14\) 657.394i 0.239575i
\(15\) 82.3307 0.0243943
\(16\) −3054.14 −0.745640
\(17\) −715.296 −0.145592 −0.0727962 0.997347i \(-0.523192\pi\)
−0.0727962 + 0.997347i \(0.523192\pi\)
\(18\) 1727.66i 0.296239i
\(19\) 11687.5 1.70396 0.851981 0.523572i \(-0.175401\pi\)
0.851981 + 0.523572i \(0.175401\pi\)
\(20\) −71.0454 −0.00888067
\(21\) 1441.37 0.155639
\(22\) 176.850 0.0166088
\(23\) 13557.4i 1.11427i −0.830421 0.557137i \(-0.811900\pi\)
0.830421 0.557137i \(-0.188100\pi\)
\(24\) 8583.95i 0.620946i
\(25\) −15597.1 −0.998215
\(26\) −1261.74 −0.0717875
\(27\) −3788.00 −0.192450
\(28\) −1243.80 −0.0566599
\(29\) −31537.4 −1.29310 −0.646551 0.762871i \(-0.723789\pi\)
−0.646551 + 0.762871i \(0.723789\pi\)
\(30\) 585.349i 0.0216796i
\(31\) 37264.3i 1.25086i −0.780282 0.625428i \(-0.784924\pi\)
0.780282 0.625428i \(-0.215076\pi\)
\(32\) 13528.2i 0.412847i
\(33\) 387.753i 0.0107898i
\(34\) 5085.56i 0.129390i
\(35\) 488.350 0.0113901
\(36\) 3268.76 0.0700610
\(37\) 17556.2i 0.346598i 0.984869 + 0.173299i \(0.0554426\pi\)
−0.984869 + 0.173299i \(0.944557\pi\)
\(38\) 83094.9i 1.51434i
\(39\) 2766.42i 0.0466364i
\(40\) 2908.32i 0.0454425i
\(41\) −64099.4 −0.930042 −0.465021 0.885300i \(-0.653953\pi\)
−0.465021 + 0.885300i \(0.653953\pi\)
\(42\) 10247.8i 0.138319i
\(43\) 76044.2i 0.956447i 0.878238 + 0.478224i \(0.158719\pi\)
−0.878238 + 0.478224i \(0.841281\pi\)
\(44\) 334.603i 0.00392800i
\(45\) −1283.41 −0.0140840
\(46\) −96389.3 −0.990274
\(47\) 32613.7i 0.314127i 0.987588 + 0.157064i \(0.0502028\pi\)
−0.987588 + 0.157064i \(0.949797\pi\)
\(48\) 47609.4 0.430496
\(49\) −109099. −0.927330
\(50\) 110891.i 0.887130i
\(51\) 11150.4 0.0840579
\(52\) 2387.22i 0.0169779i
\(53\) −56531.8 −0.379721 −0.189861 0.981811i \(-0.560804\pi\)
−0.189861 + 0.981811i \(0.560804\pi\)
\(54\) 26931.6i 0.171034i
\(55\) 131.374i 0.000789627i
\(56\) 50916.3i 0.289930i
\(57\) −182190. −0.983783
\(58\) 224223.i 1.14920i
\(59\) 168147. + 117928.i 0.818717 + 0.574197i
\(60\) 1107.49 0.00512726
\(61\) 290251.i 1.27875i −0.768896 0.639373i \(-0.779194\pi\)
0.768896 0.639373i \(-0.220806\pi\)
\(62\) −264939. −1.11166
\(63\) −22468.7 −0.0898581
\(64\) −291647. −1.11254
\(65\) 937.290i 0.00341298i
\(66\) −2756.82 −0.00958907
\(67\) 149412.i 0.496778i 0.968660 + 0.248389i \(0.0799011\pi\)
−0.968660 + 0.248389i \(0.920099\pi\)
\(68\) −9621.95 −0.0306010
\(69\) 211339.i 0.643326i
\(70\) 3472.03i 0.0101225i
\(71\) −683880. −1.91076 −0.955378 0.295388i \(-0.904551\pi\)
−0.955378 + 0.295388i \(0.904551\pi\)
\(72\) 133811.i 0.358503i
\(73\) 714312.i 1.83620i 0.396353 + 0.918098i \(0.370276\pi\)
−0.396353 + 0.918098i \(0.629724\pi\)
\(74\) 124820. 0.308027
\(75\) 243135. 0.576320
\(76\) 157217. 0.358144
\(77\) 2299.98i 0.00503793i
\(78\) 19668.5 0.0414465
\(79\) −489011. −0.991830 −0.495915 0.868371i \(-0.665167\pi\)
−0.495915 + 0.868371i \(0.665167\pi\)
\(80\) 16130.5 0.0315049
\(81\) 59049.0 0.111111
\(82\) 455730.i 0.826544i
\(83\) 559911.i 0.979231i −0.871939 0.489615i \(-0.837137\pi\)
0.871939 0.489615i \(-0.162863\pi\)
\(84\) 19388.9 0.0327126
\(85\) 3777.84 0.00615159
\(86\) 540654. 0.850010
\(87\) 491620. 0.746572
\(88\) 13697.3 0.0200996
\(89\) 783652.i 1.11161i 0.831312 + 0.555806i \(0.187590\pi\)
−0.831312 + 0.555806i \(0.812410\pi\)
\(90\) 9124.69i 0.0125167i
\(91\) 16409.2i 0.0217753i
\(92\) 182370.i 0.234201i
\(93\) 580892.i 0.722182i
\(94\) 231874. 0.279170
\(95\) −61727.6 −0.0719960
\(96\) 210883.i 0.238357i
\(97\) 1.32625e6i 1.45315i 0.687089 + 0.726573i \(0.258888\pi\)
−0.687089 + 0.726573i \(0.741112\pi\)
\(98\) 775668.i 0.824133i
\(99\) 6044.47i 0.00622949i
\(100\) −209808. −0.209808
\(101\) 1.69524e6i 1.64539i −0.568486 0.822693i \(-0.692470\pi\)
0.568486 0.822693i \(-0.307530\pi\)
\(102\) 79276.1i 0.0747036i
\(103\) 1.22743e6i 1.12327i 0.827385 + 0.561635i \(0.189827\pi\)
−0.827385 + 0.561635i \(0.810173\pi\)
\(104\) −97723.7 −0.0868760
\(105\) −7612.62 −0.00657606
\(106\) 401926.i 0.337465i
\(107\) −1.85505e6 −1.51427 −0.757137 0.653256i \(-0.773402\pi\)
−0.757137 + 0.653256i \(0.773402\pi\)
\(108\) −50955.0 −0.0404497
\(109\) 1.82202e6i 1.40694i −0.710727 0.703468i \(-0.751634\pi\)
0.710727 0.703468i \(-0.248366\pi\)
\(110\) −934.036 −0.000701755
\(111\) 273674.i 0.200108i
\(112\) 282398. 0.201005
\(113\) 2.47615e6i 1.71609i −0.513571 0.858047i \(-0.671678\pi\)
0.513571 0.858047i \(-0.328322\pi\)
\(114\) 1.29532e6i 0.874305i
\(115\) 71603.5i 0.0470804i
\(116\) −424232. −0.271788
\(117\) 43124.3i 0.0269255i
\(118\) 838437. 1.19548e6i 0.510298 0.727608i
\(119\) 66139.1 0.0392480
\(120\) 45336.3i 0.0262363i
\(121\) 1.77094e6 0.999651
\(122\) −2.06361e6 −1.13644
\(123\) 999211. 0.536960
\(124\) 501268.i 0.262909i
\(125\) 164900. 0.0844288
\(126\) 159747.i 0.0798583i
\(127\) −2.30876e6 −1.12711 −0.563557 0.826077i \(-0.690568\pi\)
−0.563557 + 0.826077i \(0.690568\pi\)
\(128\) 1.20773e6i 0.575889i
\(129\) 1.18541e6i 0.552205i
\(130\) 6663.88 0.00303317
\(131\) 3.34462e6i 1.48776i −0.668313 0.743880i \(-0.732983\pi\)
0.668313 0.743880i \(-0.267017\pi\)
\(132\) 5215.94i 0.00226783i
\(133\) −1.08067e6 −0.459344
\(134\) 1.06228e6 0.441495
\(135\) 20006.3 0.00813142
\(136\) 393885.i 0.156586i
\(137\) 1.22052e6 0.474660 0.237330 0.971429i \(-0.423728\pi\)
0.237330 + 0.971429i \(0.423728\pi\)
\(138\) 1.50256e6 0.571735
\(139\) −4.97156e6 −1.85118 −0.925590 0.378529i \(-0.876430\pi\)
−0.925590 + 0.378529i \(0.876430\pi\)
\(140\) 6569.13 0.00239400
\(141\) 508397.i 0.181362i
\(142\) 4.86221e6i 1.69812i
\(143\) 4414.36 0.00150959
\(144\) −742157. −0.248547
\(145\) 166565. 0.0546362
\(146\) 5.07856e6 1.63186
\(147\) 1.70069e6 0.535394
\(148\) 236161.i 0.0728489i
\(149\) 74289.4i 0.0224578i −0.999937 0.0112289i \(-0.996426\pi\)
0.999937 0.0112289i \(-0.00357435\pi\)
\(150\) 1.72862e6i 0.512185i
\(151\) 628940.i 0.182675i −0.995820 0.0913373i \(-0.970886\pi\)
0.995820 0.0913373i \(-0.0291141\pi\)
\(152\) 6.43584e6i 1.83263i
\(153\) −173817. −0.0485308
\(154\) −16352.2 −0.00447729
\(155\) 196812.i 0.0528513i
\(156\) 37213.1i 0.00980217i
\(157\) 4.07664e6i 1.05343i −0.850043 0.526713i \(-0.823424\pi\)
0.850043 0.526713i \(-0.176576\pi\)
\(158\) 3.47673e6i 0.881455i
\(159\) 881243. 0.219232
\(160\) 71449.2i 0.0174436i
\(161\) 1.25357e6i 0.300380i
\(162\) 419823.i 0.0987463i
\(163\) 2.85092e6 0.658298 0.329149 0.944278i \(-0.393238\pi\)
0.329149 + 0.944278i \(0.393238\pi\)
\(164\) −862247. −0.195479
\(165\) 2047.92i 0.000455892i
\(166\) −3.98082e6 −0.870259
\(167\) 5.22737e6 1.12236 0.561182 0.827693i \(-0.310347\pi\)
0.561182 + 0.827693i \(0.310347\pi\)
\(168\) 793706.i 0.167391i
\(169\) 4.79531e6 0.993475
\(170\) 26859.5i 0.00546702i
\(171\) 2.84006e6 0.567988
\(172\) 1.02292e6i 0.201029i
\(173\) 4.18140e6i 0.807576i −0.914853 0.403788i \(-0.867693\pi\)
0.914853 0.403788i \(-0.132307\pi\)
\(174\) 3.49529e6i 0.663491i
\(175\) 1.44217e6 0.269093
\(176\) 75969.8i 0.0139349i
\(177\) −2.62116e6 1.83832e6i −0.472687 0.331513i
\(178\) 5.57155e6 0.987907
\(179\) 1.83198e6i 0.319419i −0.987164 0.159709i \(-0.948944\pi\)
0.987164 0.159709i \(-0.0510557\pi\)
\(180\) −17264.0 −0.00296022
\(181\) −4.22034e6 −0.711725 −0.355862 0.934538i \(-0.615813\pi\)
−0.355862 + 0.934538i \(0.615813\pi\)
\(182\) 116665. 0.0193521
\(183\) 4.52457e6i 0.738285i
\(184\) −7.46552e6 −1.19841
\(185\) 92723.3i 0.0146445i
\(186\) 4.12999e6 0.641815
\(187\) 17792.5i 0.00272090i
\(188\) 438709.i 0.0660242i
\(189\) 350253. 0.0518796
\(190\) 438867.i 0.0639841i
\(191\) 9.72301e6i 1.39541i −0.716387 0.697703i \(-0.754206\pi\)
0.716387 0.697703i \(-0.245794\pi\)
\(192\) 4.54632e6 0.642328
\(193\) 8.09351e6 1.12581 0.562905 0.826522i \(-0.309684\pi\)
0.562905 + 0.826522i \(0.309684\pi\)
\(194\) 9.42926e6 1.29143
\(195\) 14610.9i 0.00197049i
\(196\) −1.46757e6 −0.194909
\(197\) 1.05142e7 1.37523 0.687615 0.726075i \(-0.258658\pi\)
0.687615 + 0.726075i \(0.258658\pi\)
\(198\) 42974.6 0.00553625
\(199\) 1.83582e6 0.232955 0.116477 0.993193i \(-0.462840\pi\)
0.116477 + 0.993193i \(0.462840\pi\)
\(200\) 8.58872e6i 1.07359i
\(201\) 2.32911e6i 0.286815i
\(202\) −1.20527e7 −1.46228
\(203\) 2.91608e6 0.348587
\(204\) 149991. 0.0176675
\(205\) 338542. 0.0392962
\(206\) 8.72668e6 0.998268
\(207\) 3.29444e6i 0.371425i
\(208\) 542007.i 0.0602303i
\(209\) 290719.i 0.0318445i
\(210\) 54123.7i 0.00584426i
\(211\) 1.44513e7i 1.53837i 0.639026 + 0.769185i \(0.279337\pi\)
−0.639026 + 0.769185i \(0.720663\pi\)
\(212\) −760449. −0.0798110
\(213\) 1.06606e7 1.10317
\(214\) 1.31889e7i 1.34576i
\(215\) 401629.i 0.0404119i
\(216\) 2.08590e6i 0.206982i
\(217\) 3.44560e6i 0.337199i
\(218\) −1.29541e7 −1.25037
\(219\) 1.11350e7i 1.06013i
\(220\) 1767.21i 0.000165966i
\(221\) 126941.i 0.0117605i
\(222\) −1.94575e6 −0.177839
\(223\) −1.05264e7 −0.949214 −0.474607 0.880198i \(-0.657410\pi\)
−0.474607 + 0.880198i \(0.657410\pi\)
\(224\) 1.25087e6i 0.111293i
\(225\) −3.79010e6 −0.332738
\(226\) −1.76047e7 −1.52512
\(227\) 8.08343e6i 0.691064i 0.938407 + 0.345532i \(0.112301\pi\)
−0.938407 + 0.345532i \(0.887699\pi\)
\(228\) −2.45076e6 −0.206774
\(229\) 1.41787e7i 1.18067i −0.807157 0.590336i \(-0.798995\pi\)
0.807157 0.590336i \(-0.201005\pi\)
\(230\) 509081. 0.0418412
\(231\) 35853.2i 0.00290865i
\(232\) 1.73664e7i 1.39074i
\(233\) 1.32063e7i 1.04403i 0.852935 + 0.522016i \(0.174820\pi\)
−0.852935 + 0.522016i \(0.825180\pi\)
\(234\) −306602. −0.0239292
\(235\) 172249.i 0.0132725i
\(236\) 2.26187e6 + 1.58633e6i 0.172080 + 0.120686i
\(237\) 7.62292e6 0.572633
\(238\) 470231.i 0.0348803i
\(239\) 1.69314e7 1.24022 0.620111 0.784514i \(-0.287088\pi\)
0.620111 + 0.784514i \(0.287088\pi\)
\(240\) −251450. −0.0181893
\(241\) −1.23242e7 −0.880455 −0.440227 0.897886i \(-0.645102\pi\)
−0.440227 + 0.897886i \(0.645102\pi\)
\(242\) 1.25909e7i 0.888406i
\(243\) −920483. −0.0641500
\(244\) 3.90437e6i 0.268771i
\(245\) 576210. 0.0391816
\(246\) 7.10412e6i 0.477205i
\(247\) 2.07413e6i 0.137640i
\(248\) −2.05200e7 −1.34531
\(249\) 8.72815e6i 0.565359i
\(250\) 1.17239e6i 0.0750333i
\(251\) −404077. −0.0255530 −0.0127765 0.999918i \(-0.504067\pi\)
−0.0127765 + 0.999918i \(0.504067\pi\)
\(252\) −302243. −0.0188866
\(253\) 337231. 0.0208241
\(254\) 1.64147e7i 1.00169i
\(255\) −58890.8 −0.00355162
\(256\) −1.00788e7 −0.600741
\(257\) −8.33624e6 −0.491101 −0.245551 0.969384i \(-0.578969\pi\)
−0.245551 + 0.969384i \(0.578969\pi\)
\(258\) −8.42797e6 −0.490754
\(259\) 1.62332e6i 0.0934337i
\(260\) 12608.2i 0.000717350i
\(261\) −7.66360e6 −0.431034
\(262\) −2.37794e7 −1.32220
\(263\) −2.75857e6 −0.151641 −0.0758205 0.997121i \(-0.524158\pi\)
−0.0758205 + 0.997121i \(0.524158\pi\)
\(264\) −213520. −0.0116045
\(265\) 298573. 0.0160440
\(266\) 7.68328e6i 0.408227i
\(267\) 1.22159e7i 0.641789i
\(268\) 2.00985e6i 0.104414i
\(269\) 2.04406e7i 1.05012i −0.851066 0.525058i \(-0.824043\pi\)
0.851066 0.525058i \(-0.175957\pi\)
\(270\) 142240.i 0.00722653i
\(271\) −1.41673e7 −0.711835 −0.355918 0.934517i \(-0.615832\pi\)
−0.355918 + 0.934517i \(0.615832\pi\)
\(272\) 2.18462e6 0.108560
\(273\) 255794.i 0.0125720i
\(274\) 8.67757e6i 0.421839i
\(275\) 387968.i 0.0186551i
\(276\) 2.84286e6i 0.135216i
\(277\) 5.15145e6 0.242376 0.121188 0.992630i \(-0.461330\pi\)
0.121188 + 0.992630i \(0.461330\pi\)
\(278\) 3.53465e7i 1.64517i
\(279\) 9.05522e6i 0.416952i
\(280\) 268915.i 0.0122501i
\(281\) −672904. −0.0303273 −0.0151637 0.999885i \(-0.504827\pi\)
−0.0151637 + 0.999885i \(0.504827\pi\)
\(282\) −3.61456e6 −0.161179
\(283\) 1.23913e7i 0.546711i 0.961913 + 0.273356i \(0.0881336\pi\)
−0.961913 + 0.273356i \(0.911866\pi\)
\(284\) −9.19936e6 −0.401608
\(285\) 962238. 0.0415669
\(286\) 31384.9i 0.00134160i
\(287\) 5.92689e6 0.250715
\(288\) 3.28734e6i 0.137616i
\(289\) −2.36259e7 −0.978803
\(290\) 1.18424e6i 0.0485561i
\(291\) 2.06741e7i 0.838974i
\(292\) 9.60871e6i 0.385937i
\(293\) 4.23495e7 1.68363 0.841813 0.539769i \(-0.181488\pi\)
0.841813 + 0.539769i \(0.181488\pi\)
\(294\) 1.20915e7i 0.475814i
\(295\) −888072. 622838.i −0.0345925 0.0242610i
\(296\) 9.66752e6 0.372769
\(297\) 94223.9i 0.00359660i
\(298\) −528178. −0.0199587
\(299\) −2.40598e6 −0.0900073
\(300\) 3.27058e6 0.121133
\(301\) 7.03135e6i 0.257833i
\(302\) −4.47159e6 −0.162346
\(303\) 2.64262e7i 0.949964i
\(304\) −3.56952e7 −1.27054
\(305\) 1.53297e6i 0.0540298i
\(306\) 1.23579e6i 0.0431301i
\(307\) −1.52601e7 −0.527402 −0.263701 0.964604i \(-0.584943\pi\)
−0.263701 + 0.964604i \(0.584943\pi\)
\(308\) 30938.7i 0.00105889i
\(309\) 1.91337e7i 0.648520i
\(310\) 1.39928e6 0.0469699
\(311\) −6.21630e6 −0.206657 −0.103329 0.994647i \(-0.532949\pi\)
−0.103329 + 0.994647i \(0.532949\pi\)
\(312\) 1.52336e6 0.0501579
\(313\) 9.26899e6i 0.302273i −0.988513 0.151137i \(-0.951707\pi\)
0.988513 0.151137i \(-0.0482933\pi\)
\(314\) −2.89838e7 −0.936196
\(315\) 118669. 0.00379669
\(316\) −6.57803e6 −0.208466
\(317\) −5.63002e6 −0.176739 −0.0883694 0.996088i \(-0.528166\pi\)
−0.0883694 + 0.996088i \(0.528166\pi\)
\(318\) 6.26540e6i 0.194835i
\(319\) 784473.i 0.0241661i
\(320\) 1.54034e6 0.0470073
\(321\) 2.89174e7 0.874266
\(322\) 8.91253e6 0.266952
\(323\) −8.36001e6 −0.248084
\(324\) 794310. 0.0233537
\(325\) 2.76796e6i 0.0806324i
\(326\) 2.02693e7i 0.585040i
\(327\) 2.84025e7i 0.812295i
\(328\) 3.52970e7i 1.00027i
\(329\) 3.01559e6i 0.0846807i
\(330\) 14560.2 0.000405158
\(331\) 5.30847e7 1.46381 0.731906 0.681405i \(-0.238631\pi\)
0.731906 + 0.681405i \(0.238631\pi\)
\(332\) 7.53176e6i 0.205818i
\(333\) 4.26616e6i 0.115533i
\(334\) 3.71652e7i 0.997463i
\(335\) 789123.i 0.0209899i
\(336\) −4.40215e6 −0.116050
\(337\) 1.54982e7i 0.404940i 0.979288 + 0.202470i \(0.0648969\pi\)
−0.979288 + 0.202470i \(0.935103\pi\)
\(338\) 3.40934e7i 0.882918i
\(339\) 3.85993e7i 0.990787i
\(340\) 50818.5 0.00129296
\(341\) 926925. 0.0233766
\(342\) 2.01921e7i 0.504780i
\(343\) 2.09661e7 0.519558
\(344\) 4.18746e7 1.02867
\(345\) 1.11619e6i 0.0271819i
\(346\) −2.97286e7 −0.717706
\(347\) 2.85902e6i 0.0684272i 0.999415 + 0.0342136i \(0.0108927\pi\)
−0.999415 + 0.0342136i \(0.989107\pi\)
\(348\) 6.61313e6 0.156917
\(349\) 8.13353e7i 1.91339i 0.291097 + 0.956694i \(0.405980\pi\)
−0.291097 + 0.956694i \(0.594020\pi\)
\(350\) 1.02534e7i 0.239147i
\(351\) 672241.i 0.0155455i
\(352\) 336504. 0.00771547
\(353\) 2.35290e7i 0.534909i −0.963570 0.267455i \(-0.913817\pi\)
0.963570 0.267455i \(-0.0861825\pi\)
\(354\) −1.30699e7 + 1.86357e7i −0.294621 + 0.420084i
\(355\) 3.61192e6 0.0807334
\(356\) 1.05415e7i 0.233642i
\(357\) −1.03101e6 −0.0226598
\(358\) −1.30249e7 −0.283873
\(359\) −4.68770e7 −1.01316 −0.506579 0.862194i \(-0.669090\pi\)
−0.506579 + 0.862194i \(0.669090\pi\)
\(360\) 706723.i 0.0151475i
\(361\) 8.95514e7 1.90349
\(362\) 3.00055e7i 0.632522i
\(363\) −2.76063e7 −0.577149
\(364\) 220732.i 0.00457679i
\(365\) 3.77265e6i 0.0775832i
\(366\) 3.21685e7 0.656126
\(367\) 5.44819e7i 1.10218i −0.834445 0.551092i \(-0.814211\pi\)
0.834445 0.551092i \(-0.185789\pi\)
\(368\) 4.14061e7i 0.830848i
\(369\) −1.55762e7 −0.310014
\(370\) −659238. −0.0130148
\(371\) 5.22715e6 0.102363
\(372\) 7.81399e6i 0.151790i
\(373\) 5.54160e7 1.06785 0.533923 0.845533i \(-0.320717\pi\)
0.533923 + 0.845533i \(0.320717\pi\)
\(374\) −126500. −0.00241811
\(375\) −2.57054e6 −0.0487450
\(376\) 1.79591e7 0.337847
\(377\) 5.59683e6i 0.104452i
\(378\) 2.49020e6i 0.0461062i
\(379\) 8.30586e7 1.52569 0.762846 0.646580i \(-0.223801\pi\)
0.762846 + 0.646580i \(0.223801\pi\)
\(380\) −830341. −0.0151323
\(381\) 3.59900e7 0.650740
\(382\) −6.91280e7 −1.24012
\(383\) −1.23695e7 −0.220168 −0.110084 0.993922i \(-0.535112\pi\)
−0.110084 + 0.993922i \(0.535112\pi\)
\(384\) 1.88266e7i 0.332490i
\(385\) 12147.4i 0.000212863i
\(386\) 5.75427e7i 1.00053i
\(387\) 1.84788e7i 0.318816i
\(388\) 1.78403e7i 0.305426i
\(389\) 8.65306e6 0.147001 0.0735006 0.997295i \(-0.476583\pi\)
0.0735006 + 0.997295i \(0.476583\pi\)
\(390\) −103880. −0.00175120
\(391\) 9.69753e6i 0.162230i
\(392\) 6.00768e7i 0.997352i
\(393\) 5.21375e7i 0.858959i
\(394\) 7.47528e7i 1.22219i
\(395\) 2.58272e6 0.0419069
\(396\) 81308.4i 0.00130933i
\(397\) 5.99639e7i 0.958338i 0.877723 + 0.479169i \(0.159062\pi\)
−0.877723 + 0.479169i \(0.840938\pi\)
\(398\) 1.30522e7i 0.207031i
\(399\) 1.68460e7 0.265203
\(400\) 4.76358e7 0.744309
\(401\) 1.08704e8i 1.68582i −0.538053 0.842911i \(-0.680840\pi\)
0.538053 0.842911i \(-0.319160\pi\)
\(402\) −1.65593e7 −0.254897
\(403\) −6.61315e6 −0.101040
\(404\) 2.28039e7i 0.345832i
\(405\) −311868. −0.00469468
\(406\) 2.07325e7i 0.309795i
\(407\) −436699. −0.00647738
\(408\) 6.14007e6i 0.0904050i
\(409\) 1.07716e8i 1.57439i −0.616706 0.787193i \(-0.711533\pi\)
0.616706 0.787193i \(-0.288467\pi\)
\(410\) 2.40694e6i 0.0349232i
\(411\) −1.90260e7 −0.274045
\(412\) 1.65110e7i 0.236092i
\(413\) −1.55476e7 1.09041e7i −0.220705 0.154789i
\(414\) −2.34226e7 −0.330091
\(415\) 2.95718e6i 0.0413746i
\(416\) −2.40079e6 −0.0333484
\(417\) 7.74990e7 1.06878
\(418\) 2.06693e6 0.0283007
\(419\) 4.18212e6i 0.0568531i 0.999596 + 0.0284265i \(0.00904967\pi\)
−0.999596 + 0.0284265i \(0.990950\pi\)
\(420\) −102403. −0.00138218
\(421\) 2.52986e7i 0.339040i −0.985527 0.169520i \(-0.945778\pi\)
0.985527 0.169520i \(-0.0542217\pi\)
\(422\) 1.02745e8 1.36717
\(423\) 7.92512e6i 0.104709i
\(424\) 3.11298e7i 0.408394i
\(425\) 1.11565e7 0.145333
\(426\) 7.57943e7i 0.980410i
\(427\) 2.68378e7i 0.344717i
\(428\) −2.49536e7 −0.318274
\(429\) −68813.0 −0.000871563
\(430\) −2.85547e6 −0.0359147
\(431\) 1.36407e8i 1.70374i 0.523752 + 0.851871i \(0.324532\pi\)
−0.523752 + 0.851871i \(0.675468\pi\)
\(432\) 1.15691e7 0.143499
\(433\) 3.58849e7 0.442027 0.221013 0.975271i \(-0.429064\pi\)
0.221013 + 0.975271i \(0.429064\pi\)
\(434\) 2.44973e7 0.299674
\(435\) −2.59650e6 −0.0315443
\(436\) 2.45093e7i 0.295714i
\(437\) 1.58452e8i 1.89868i
\(438\) −7.91670e7 −0.942154
\(439\) 9.35625e7 1.10588 0.552940 0.833221i \(-0.313506\pi\)
0.552940 + 0.833221i \(0.313506\pi\)
\(440\) −72342.7 −0.000849252
\(441\) −2.65112e7 −0.309110
\(442\) 902515. 0.0104517
\(443\) 9.40911e7i 1.08227i −0.840934 0.541137i \(-0.817994\pi\)
0.840934 0.541137i \(-0.182006\pi\)
\(444\) 3.68138e6i 0.0420593i
\(445\) 4.13887e6i 0.0469679i
\(446\) 7.48397e7i 0.843582i
\(447\) 1.15806e6i 0.0129660i
\(448\) 2.69668e7 0.299913
\(449\) −1.35505e8 −1.49698 −0.748490 0.663146i \(-0.769221\pi\)
−0.748490 + 0.663146i \(0.769221\pi\)
\(450\) 2.69466e7i 0.295710i
\(451\) 1.59443e6i 0.0173811i
\(452\) 3.33084e7i 0.360694i
\(453\) 9.80420e6i 0.105467i
\(454\) 5.74710e7 0.614160
\(455\) 86665.5i 0.000920052i
\(456\) 1.00325e8i 1.05807i
\(457\) 3.81923e7i 0.400154i −0.979780 0.200077i \(-0.935881\pi\)
0.979780 0.200077i \(-0.0641192\pi\)
\(458\) −1.00807e8 −1.04928
\(459\) 2.70954e6 0.0280193
\(460\) 963189.i 0.00989550i
\(461\) 1.08095e8 1.10333 0.551663 0.834067i \(-0.313994\pi\)
0.551663 + 0.834067i \(0.313994\pi\)
\(462\) 254906. 0.00258496
\(463\) 1.29566e8i 1.30542i −0.757610 0.652708i \(-0.773633\pi\)
0.757610 0.652708i \(-0.226367\pi\)
\(464\) 9.63198e7 0.964188
\(465\) 3.06799e6i 0.0305137i
\(466\) 9.38934e7 0.927849
\(467\) 2.80116e6i 0.0275035i 0.999905 + 0.0137517i \(0.00437745\pi\)
−0.999905 + 0.0137517i \(0.995623\pi\)
\(468\) 580095.i 0.00565929i
\(469\) 1.38153e7i 0.133918i
\(470\) −1.22465e6 −0.0117955
\(471\) 6.35486e7i 0.608195i
\(472\) 6.49383e7 9.25922e7i 0.617554 0.880538i
\(473\) −1.89155e6 −0.0178745
\(474\) 5.41969e7i 0.508908i
\(475\) −1.82291e8 −1.70092
\(476\) 889683. 0.00824925
\(477\) −1.37372e7 −0.126574
\(478\) 1.20378e8i 1.10220i
\(479\) −1.46808e8 −1.33581 −0.667905 0.744247i \(-0.732809\pi\)
−0.667905 + 0.744247i \(0.732809\pi\)
\(480\) 1.11378e6i 0.0100711i
\(481\) 3.11563e6 0.0279970
\(482\) 8.76216e7i 0.782475i
\(483\) 1.95412e7i 0.173424i
\(484\) 2.38222e7 0.210110
\(485\) 7.00459e6i 0.0613985i
\(486\) 6.54439e6i 0.0570112i
\(487\) 2.04812e8 1.77324 0.886622 0.462495i \(-0.153046\pi\)
0.886622 + 0.462495i \(0.153046\pi\)
\(488\) −1.59830e8 −1.37530
\(489\) −4.44414e7 −0.380068
\(490\) 4.09670e6i 0.0348214i
\(491\) −1.51228e8 −1.27758 −0.638791 0.769381i \(-0.720565\pi\)
−0.638791 + 0.769381i \(0.720565\pi\)
\(492\) 1.34411e7 0.112860
\(493\) 2.25586e7 0.188266
\(494\) −1.47465e7 −0.122323
\(495\) 31923.9i 0.000263209i
\(496\) 1.13810e8i 0.932689i
\(497\) 6.32343e7 0.515090
\(498\) 6.20548e7 0.502444
\(499\) −4.19145e7 −0.337336 −0.168668 0.985673i \(-0.553947\pi\)
−0.168668 + 0.985673i \(0.553947\pi\)
\(500\) 2.21819e6 0.0177455
\(501\) −8.14866e7 −0.647997
\(502\) 2.87288e6i 0.0227094i
\(503\) 2.33489e8i 1.83469i −0.398094 0.917345i \(-0.630328\pi\)
0.398094 0.917345i \(-0.369672\pi\)
\(504\) 1.23727e7i 0.0966432i
\(505\) 8.95345e6i 0.0695211i
\(506\) 2.39762e6i 0.0185067i
\(507\) −7.47516e7 −0.573583
\(508\) −3.10568e7 −0.236900
\(509\) 9.20786e7i 0.698241i 0.937078 + 0.349121i \(0.113520\pi\)
−0.937078 + 0.349121i \(0.886480\pi\)
\(510\) 418698.i 0.00315638i
\(511\) 6.60481e7i 0.494991i
\(512\) 1.48952e8i 1.10978i
\(513\) −4.42721e7 −0.327928
\(514\) 5.92685e7i 0.436450i
\(515\) 6.48267e6i 0.0474605i
\(516\) 1.59458e7i 0.116064i
\(517\) −811244. −0.00587056
\(518\) −1.15413e7 −0.0830361
\(519\) 6.51816e7i 0.466254i
\(520\) 516129. 0.00367069
\(521\) 5.17563e7 0.365974 0.182987 0.983115i \(-0.441423\pi\)
0.182987 + 0.983115i \(0.441423\pi\)
\(522\) 5.44861e7i 0.383067i
\(523\) −1.64753e8 −1.15167 −0.575834 0.817566i \(-0.695323\pi\)
−0.575834 + 0.817566i \(0.695323\pi\)
\(524\) 4.49909e7i 0.312702i
\(525\) −2.24812e7 −0.155361
\(526\) 1.96127e7i 0.134766i
\(527\) 2.66550e7i 0.182115i
\(528\) 1.18425e6i 0.00804530i
\(529\) −3.57665e7 −0.241607
\(530\) 2.12278e6i 0.0142586i
\(531\) 4.08598e7 + 2.86565e7i 0.272906 + 0.191399i
\(532\) −1.45369e7 −0.0965463
\(533\) 1.13755e7i 0.0751256i
\(534\) −8.68519e7 −0.570369
\(535\) 9.79747e6 0.0639813
\(536\) 8.22755e7 0.534289
\(537\) 2.85577e7i 0.184417i
\(538\) −1.45327e8 −0.933256
\(539\) 2.71378e6i 0.0173304i
\(540\) 269120. 0.00170909
\(541\) 9.80167e7i 0.619025i 0.950895 + 0.309513i \(0.100166\pi\)
−0.950895 + 0.309513i \(0.899834\pi\)
\(542\) 1.00726e8i 0.632620i
\(543\) 6.57887e7 0.410915
\(544\) 9.67664e6i 0.0601074i
\(545\) 9.62304e6i 0.0594460i
\(546\) −1.81863e6 −0.0111729
\(547\) 2.45510e8 1.50005 0.750027 0.661407i \(-0.230040\pi\)
0.750027 + 0.661407i \(0.230040\pi\)
\(548\) 1.64181e7 0.0997655
\(549\) 7.05311e7i 0.426249i
\(550\) −2.75835e6 −0.0165791
\(551\) −3.68593e8 −2.20340
\(552\) 1.16376e8 0.691904
\(553\) 4.52158e7 0.267372
\(554\) 3.66255e7i 0.215404i
\(555\) 1.44541e6i 0.00845499i
\(556\) −6.68760e7 −0.389086
\(557\) −2.60073e8 −1.50497 −0.752487 0.658607i \(-0.771146\pi\)
−0.752487 + 0.658607i \(0.771146\pi\)
\(558\) −6.43802e7 −0.370552
\(559\) 1.34953e7 0.0772586
\(560\) −1.49149e6 −0.00849290
\(561\) 277358.i 0.00157091i
\(562\) 4.78416e6i 0.0269524i
\(563\) 2.31232e8i 1.29575i 0.761745 + 0.647877i \(0.224343\pi\)
−0.761745 + 0.647877i \(0.775657\pi\)
\(564\) 6.83880e6i 0.0381191i
\(565\) 1.30778e7i 0.0725086i
\(566\) 8.80989e7 0.485871
\(567\) −5.45990e6 −0.0299527
\(568\) 3.76586e8i 2.05504i
\(569\) 2.95772e8i 1.60554i 0.596289 + 0.802770i \(0.296641\pi\)
−0.596289 + 0.802770i \(0.703359\pi\)
\(570\) 6.84125e6i 0.0369412i
\(571\) 2.55594e8i 1.37291i 0.727171 + 0.686456i \(0.240835\pi\)
−0.727171 + 0.686456i \(0.759165\pi\)
\(572\) 59380.6 0.000317290
\(573\) 1.51567e8i 0.805638i
\(574\) 4.21386e7i 0.222815i
\(575\) 2.11456e8i 1.11228i
\(576\) −7.08702e7 −0.370848
\(577\) 2.32931e8 1.21255 0.606276 0.795255i \(-0.292663\pi\)
0.606276 + 0.795255i \(0.292663\pi\)
\(578\) 1.67974e8i 0.869878i
\(579\) −1.26165e8 −0.649986
\(580\) 2.24059e6 0.0114836
\(581\) 5.17716e7i 0.263975i
\(582\) −1.46988e8 −0.745610
\(583\) 1.40619e6i 0.00709641i
\(584\) 3.93343e8 1.97485
\(585\) 227762.i 0.00113766i
\(586\) 3.01094e8i 1.49627i
\(587\) 1.57150e8i 0.776964i 0.921456 + 0.388482i \(0.127000\pi\)
−0.921456 + 0.388482i \(0.873000\pi\)
\(588\) 2.28772e7 0.112531
\(589\) 4.35525e8i 2.13141i
\(590\) −4.42821e6 + 6.31396e6i −0.0215612 + 0.0307430i
\(591\) −1.63899e8 −0.793990
\(592\) 5.36192e7i 0.258437i
\(593\) −6.64478e7 −0.318652 −0.159326 0.987226i \(-0.550932\pi\)
−0.159326 + 0.987226i \(0.550932\pi\)
\(594\) −669907. −0.00319636
\(595\) −349314. −0.00165831
\(596\) 999319.i 0.00472026i
\(597\) −2.86177e7 −0.134497
\(598\) 1.71058e7i 0.0799910i
\(599\) 1.81573e8 0.844835 0.422417 0.906401i \(-0.361182\pi\)
0.422417 + 0.906401i \(0.361182\pi\)
\(600\) 1.33885e8i 0.619837i
\(601\) 3.47824e8i 1.60227i −0.598483 0.801136i \(-0.704229\pi\)
0.598483 0.801136i \(-0.295771\pi\)
\(602\) −4.99910e7 −0.229141
\(603\) 3.63072e7i 0.165593i
\(604\) 8.46031e6i 0.0383951i
\(605\) −9.35326e6 −0.0422374
\(606\) 1.87883e8 0.844249
\(607\) −1.91587e8 −0.856644 −0.428322 0.903626i \(-0.640895\pi\)
−0.428322 + 0.903626i \(0.640895\pi\)
\(608\) 1.58110e8i 0.703476i
\(609\) −4.54571e7 −0.201257
\(610\) 1.08990e7 0.0480171
\(611\) 5.78782e6 0.0253742
\(612\) −2.33813e6 −0.0102003
\(613\) 1.35949e8i 0.590193i 0.955468 + 0.295096i \(0.0953517\pi\)
−0.955468 + 0.295096i \(0.904648\pi\)
\(614\) 1.08495e8i 0.468711i
\(615\) −5.27735e6 −0.0226877
\(616\) −1.26651e6 −0.00541834
\(617\) 4.51298e7 0.192136 0.0960678 0.995375i \(-0.469373\pi\)
0.0960678 + 0.995375i \(0.469373\pi\)
\(618\) −1.36035e8 −0.576351
\(619\) −2.39592e8 −1.01018 −0.505092 0.863066i \(-0.668541\pi\)
−0.505092 + 0.863066i \(0.668541\pi\)
\(620\) 2.64745e6i 0.0111084i
\(621\) 5.13553e7i 0.214442i
\(622\) 4.41963e7i 0.183660i
\(623\) 7.24595e7i 0.299662i
\(624\) 8.44905e6i 0.0347740i
\(625\) 2.42834e8 0.994647
\(626\) −6.59001e7 −0.268635
\(627\) 4.53185e6i 0.0183854i
\(628\) 5.48378e7i 0.221412i
\(629\) 1.25579e7i 0.0504620i
\(630\) 843704.i 0.00337418i
\(631\) 2.71459e8 1.08048 0.540240 0.841511i \(-0.318333\pi\)
0.540240 + 0.841511i \(0.318333\pi\)
\(632\) 2.69279e8i 1.06672i
\(633\) 2.25274e8i 0.888178i
\(634\) 4.00279e7i 0.157071i
\(635\) 1.21938e7 0.0476230
\(636\) 1.18542e7 0.0460789
\(637\) 1.93615e7i 0.0749065i
\(638\) −5.57740e6 −0.0214768
\(639\) −1.66183e8 −0.636918
\(640\) 6.37863e6i 0.0243325i
\(641\) 3.22726e8 1.22535 0.612675 0.790335i \(-0.290093\pi\)
0.612675 + 0.790335i \(0.290093\pi\)
\(642\) 2.05595e8i 0.776975i
\(643\) −4.58458e8 −1.72451 −0.862256 0.506472i \(-0.830949\pi\)
−0.862256 + 0.506472i \(0.830949\pi\)
\(644\) 1.68626e7i 0.0631346i
\(645\) 6.26077e6i 0.0233318i
\(646\) 5.94374e7i 0.220477i
\(647\) −1.30910e8 −0.483349 −0.241675 0.970357i \(-0.577697\pi\)
−0.241675 + 0.970357i \(0.577697\pi\)
\(648\) 3.25160e7i 0.119501i
\(649\) −2.93338e6 + 4.18256e6i −0.0107309 + 0.0153006i
\(650\) 1.96794e7 0.0716593
\(651\) 5.37116e7i 0.194682i
\(652\) 3.83497e7 0.138363
\(653\) −5.20303e8 −1.86860 −0.934300 0.356487i \(-0.883974\pi\)
−0.934300 + 0.356487i \(0.883974\pi\)
\(654\) 2.01934e8 0.721900
\(655\) 1.76647e7i 0.0628610i
\(656\) 1.95769e8 0.693477
\(657\) 1.73578e8i 0.612065i
\(658\) −2.14400e7 −0.0752571
\(659\) 3.84699e8i 1.34420i −0.740459 0.672102i \(-0.765392\pi\)
0.740459 0.672102i \(-0.234608\pi\)
\(660\) 27548.0i 9.58206e-5i
\(661\) −3.53367e6 −0.0122355 −0.00611775 0.999981i \(-0.501947\pi\)
−0.00611775 + 0.999981i \(0.501947\pi\)
\(662\) 3.77418e8i 1.30091i
\(663\) 1.97881e6i 0.00678991i
\(664\) −3.08321e8 −1.05317
\(665\) 5.70758e6 0.0194083
\(666\) 3.03312e7 0.102676
\(667\) 4.27565e8i 1.44087i
\(668\) 7.03170e7 0.235902
\(669\) 1.64090e8 0.548029
\(670\) −5.61046e6 −0.0186541
\(671\) 7.21981e6 0.0238978
\(672\) 1.94991e7i 0.0642549i
\(673\) 2.92865e8i 0.960776i −0.877056 0.480388i \(-0.840496\pi\)
0.877056 0.480388i \(-0.159504\pi\)
\(674\) 1.10188e8 0.359877
\(675\) 5.90818e7 0.192107
\(676\) 6.45052e7 0.208811
\(677\) 4.31519e8 1.39070 0.695351 0.718670i \(-0.255249\pi\)
0.695351 + 0.718670i \(0.255249\pi\)
\(678\) 2.74431e8 0.880529
\(679\) 1.22630e8i 0.391731i
\(680\) 2.08031e6i 0.00661609i
\(681\) 1.26008e8i 0.398986i
\(682\) 6.59019e6i 0.0207752i
\(683\) 3.46467e8i 1.08742i 0.839272 + 0.543712i \(0.182982\pi\)
−0.839272 + 0.543712i \(0.817018\pi\)
\(684\) 3.82036e7 0.119381
\(685\) −6.44619e6 −0.0200554
\(686\) 1.49063e8i 0.461740i
\(687\) 2.21024e8i 0.681662i
\(688\) 2.32250e8i 0.713166i
\(689\) 1.00325e7i 0.0306726i
\(690\) −7.93579e6 −0.0241570
\(691\) 2.41016e8i 0.730485i −0.930912 0.365243i \(-0.880986\pi\)
0.930912 0.365243i \(-0.119014\pi\)
\(692\) 5.62470e7i 0.169739i
\(693\) 558895.i 0.00167931i
\(694\) 2.03269e7 0.0608124
\(695\) 2.62574e7 0.0782162
\(696\) 2.70716e8i 0.802946i
\(697\) 4.58501e7 0.135407
\(698\) 5.78272e8 1.70046
\(699\) 2.05866e8i 0.602773i
\(700\) 1.93996e7 0.0565587
\(701\) 3.94108e7i 0.114409i −0.998362 0.0572046i \(-0.981781\pi\)
0.998362 0.0572046i \(-0.0182187\pi\)
\(702\) 4.77945e6 0.0138155
\(703\) 2.05188e8i 0.590589i
\(704\) 7.25452e6i 0.0207917i
\(705\) 2.68510e6i 0.00766291i
\(706\) −1.67285e8 −0.475383
\(707\) 1.56749e8i 0.443554i
\(708\) −3.52590e7 2.47285e7i −0.0993506 0.0696783i
\(709\) 6.41700e7 0.180050 0.0900250 0.995940i \(-0.471305\pi\)
0.0900250 + 0.995940i \(0.471305\pi\)
\(710\) 2.56798e7i 0.0717491i
\(711\) −1.18830e8 −0.330610
\(712\) 4.31526e8 1.19555
\(713\) −5.05206e8 −1.39380
\(714\) 7.33018e6i 0.0201382i
\(715\) −23314.5 −6.37834e−5
\(716\) 2.46432e7i 0.0671364i
\(717\) −2.63934e8 −0.716042
\(718\) 3.33283e8i 0.900409i
\(719\) 7.86926e7i 0.211713i −0.994381 0.105856i \(-0.966242\pi\)
0.994381 0.105856i \(-0.0337584\pi\)
\(720\) 3.91971e6 0.0105016
\(721\) 1.13493e8i 0.302805i
\(722\) 6.36686e8i 1.69166i
\(723\) 1.92115e8 0.508331
\(724\) −5.67708e7 −0.149592
\(725\) 4.91893e8 1.29079
\(726\) 1.96273e8i 0.512922i
\(727\) 1.84082e8 0.479080 0.239540 0.970886i \(-0.423003\pi\)
0.239540 + 0.970886i \(0.423003\pi\)
\(728\) 9.03592e6 0.0234195
\(729\) 1.43489e7 0.0370370
\(730\) −2.68225e7 −0.0689495
\(731\) 5.43941e7i 0.139252i
\(732\) 6.08632e7i 0.155175i
\(733\) −4.12617e8 −1.04770 −0.523848 0.851812i \(-0.675504\pi\)
−0.523848 + 0.851812i \(0.675504\pi\)
\(734\) −3.87351e8 −0.979528
\(735\) −8.98223e6 −0.0226215
\(736\) −1.83406e8 −0.460024
\(737\) −3.71654e6 −0.00928402
\(738\) 1.10742e8i 0.275515i
\(739\) 4.38567e8i 1.08668i −0.839512 0.543342i \(-0.817159\pi\)
0.839512 0.543342i \(-0.182841\pi\)
\(740\) 1.24729e6i 0.00307802i
\(741\) 3.23325e7i 0.0794667i
\(742\) 3.71637e7i 0.0909718i
\(743\) −1.55606e8 −0.379367 −0.189683 0.981845i \(-0.560746\pi\)
−0.189683 + 0.981845i \(0.560746\pi\)
\(744\) 3.19875e8 0.776714
\(745\) 392361.i 0.000948891i
\(746\) 3.93993e8i 0.949013i
\(747\) 1.36058e8i 0.326410i
\(748\) 239340.i 0.000571887i
\(749\) 1.71525e8 0.408209
\(750\) 1.82758e7i 0.0433205i
\(751\) 1.66999e8i 0.394270i −0.980376 0.197135i \(-0.936836\pi\)
0.980376 0.197135i \(-0.0631637\pi\)
\(752\) 9.96068e7i 0.234226i
\(753\) 6.29893e6 0.0147531
\(754\) 3.97920e7 0.0928285
\(755\) 3.32175e6i 0.00771839i
\(756\) 4.71150e6 0.0109042
\(757\) −1.60340e8 −0.369619 −0.184810 0.982774i \(-0.559167\pi\)
−0.184810 + 0.982774i \(0.559167\pi\)
\(758\) 5.90524e8i 1.35591i
\(759\) −5.25691e6 −0.0120228
\(760\) 3.39910e7i 0.0774324i
\(761\) −2.04852e8 −0.464821 −0.232410 0.972618i \(-0.574661\pi\)
−0.232410 + 0.972618i \(0.574661\pi\)
\(762\) 2.55880e8i 0.578323i
\(763\) 1.68471e8i 0.379273i
\(764\) 1.30791e8i 0.293290i
\(765\) 918016. 0.00205053
\(766\) 8.79436e7i 0.195667i
\(767\) 2.09282e7 2.98405e7i 0.0463817 0.0661332i
\(768\) 1.57112e8 0.346838
\(769\) 6.58830e8i 1.44875i 0.689405 + 0.724377i \(0.257872\pi\)
−0.689405 + 0.724377i \(0.742128\pi\)
\(770\) 86364.6 0.000189175
\(771\) 1.29949e8 0.283537
\(772\) 1.08871e8 0.236626
\(773\) 6.88094e8i 1.48974i −0.667211 0.744868i \(-0.732512\pi\)
0.667211 0.744868i \(-0.267488\pi\)
\(774\) 1.31379e8 0.283337
\(775\) 5.81215e8i 1.24862i
\(776\) 7.30312e8 1.56287
\(777\) 2.53050e7i 0.0539440i
\(778\) 6.15209e7i 0.130642i
\(779\) −7.49161e8 −1.58476
\(780\) 196542.i 0.000414162i
\(781\) 1.70111e7i 0.0357091i
\(782\) 6.89469e7 0.144176
\(783\) 1.19464e8 0.248857
\(784\) 3.33205e8 0.691454
\(785\) 2.15308e7i