Properties

Label 177.9.c.a.58.6
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.6
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.75

$q$-expansion

\(f(q)\) \(=\) \(q-28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} +1334.70i q^{6} +1132.75 q^{7} +8634.97i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} +1334.70i q^{6} +1132.75 q^{7} +8634.97i q^{8} +2187.00 q^{9} -29093.1i q^{10} +4608.39i q^{11} +26120.9 q^{12} -8985.26i q^{13} -32329.1i q^{14} -47671.0 q^{15} +103456. q^{16} -141765. q^{17} -62417.8i q^{18} +37622.4 q^{19} -569370. q^{20} -52973.4 q^{21} +131525. q^{22} +368411. i q^{23} -403817. i q^{24} +648482. q^{25} -256443. q^{26} -102276. q^{27} -632700. q^{28} +1.07625e6 q^{29} +1.36055e6i q^{30} +1.36196e6i q^{31} -742110. i q^{32} -215513. i q^{33} +4.04601e6i q^{34} +1.15468e6 q^{35} -1.22155e6 q^{36} +454793. i q^{37} -1.07376e6i q^{38} +420199. i q^{39} +8.80219e6i q^{40} -2.19561e6 q^{41} +1.51188e6i q^{42} -155344. i q^{43} -2.57403e6i q^{44} +2.22935e6 q^{45} +1.05146e7 q^{46} +4.12397e6i q^{47} -4.83814e6 q^{48} -4.48168e6 q^{49} -1.85079e7i q^{50} +6.62967e6 q^{51} +5.01874e6i q^{52} -8.47567e6 q^{53} +2.91899e6i q^{54} +4.69764e6i q^{55} +9.78124e6i q^{56} -1.75943e6 q^{57} -3.07167e7i q^{58} +(8.59574e6 + 8.54071e6i) q^{59} +2.66268e7 q^{60} +1.90458e7i q^{61} +3.88709e7 q^{62} +2.47732e6 q^{63} +5.30453e6 q^{64} -9.15927e6i q^{65} -6.15083e6 q^{66} +1.59131e6i q^{67} +7.91830e7 q^{68} -1.72289e7i q^{69} -3.29551e7i q^{70} +2.82229e7 q^{71} +1.88847e7i q^{72} +3.05689e7i q^{73} +1.29800e7 q^{74} -3.03265e7 q^{75} -2.10141e7 q^{76} +5.22015e6i q^{77} +1.19926e7 q^{78} -4.78817e6 q^{79} +1.05459e8 q^{80} +4.78297e6 q^{81} +6.26636e7i q^{82} -6.63663e7i q^{83} +2.95884e7 q^{84} -1.44510e8 q^{85} -4.43357e6 q^{86} -5.03314e7 q^{87} -3.97933e7 q^{88} +8.43518e7i q^{89} -6.36266e7i q^{90} -1.01780e7i q^{91} -2.05777e8i q^{92} -6.36926e7i q^{93} +1.17700e8 q^{94} +3.83510e7 q^{95} +3.47051e7i q^{96} -1.27671e8i q^{97} +1.27909e8i q^{98} +1.00786e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 28.5404i 1.78377i −0.452259 0.891887i \(-0.649382\pi\)
0.452259 0.891887i \(-0.350618\pi\)
\(3\) −46.7654 −0.577350
\(4\) −558.553 −2.18185
\(5\) 1019.37 1.63099 0.815493 0.578767i \(-0.196466\pi\)
0.815493 + 0.578767i \(0.196466\pi\)
\(6\) 1334.70i 1.02986i
\(7\) 1132.75 0.471782 0.235891 0.971780i \(-0.424199\pi\)
0.235891 + 0.971780i \(0.424199\pi\)
\(8\) 8634.97i 2.10815i
\(9\) 2187.00 0.333333
\(10\) 29093.1i 2.90931i
\(11\) 4608.39i 0.314760i 0.987538 + 0.157380i \(0.0503047\pi\)
−0.987538 + 0.157380i \(0.949695\pi\)
\(12\) 26120.9 1.25969
\(13\) 8985.26i 0.314599i −0.987551 0.157299i \(-0.949721\pi\)
0.987551 0.157299i \(-0.0502788\pi\)
\(14\) 32329.1i 0.841552i
\(15\) −47671.0 −0.941650
\(16\) 103456. 1.57861
\(17\) −141765. −1.69735 −0.848676 0.528913i \(-0.822600\pi\)
−0.848676 + 0.528913i \(0.822600\pi\)
\(18\) 62417.8i 0.594591i
\(19\) 37622.4 0.288690 0.144345 0.989527i \(-0.453892\pi\)
0.144345 + 0.989527i \(0.453892\pi\)
\(20\) −569370. −3.55856
\(21\) −52973.4 −0.272383
\(22\) 131525. 0.561460
\(23\) 368411.i 1.31650i 0.752800 + 0.658250i \(0.228703\pi\)
−0.752800 + 0.658250i \(0.771297\pi\)
\(24\) 403817.i 1.21714i
\(25\) 648482. 1.66011
\(26\) −256443. −0.561173
\(27\) −102276. −0.192450
\(28\) −632700. −1.02936
\(29\) 1.07625e6 1.52168 0.760839 0.648940i \(-0.224788\pi\)
0.760839 + 0.648940i \(0.224788\pi\)
\(30\) 1.36055e6i 1.67969i
\(31\) 1.36196e6i 1.47475i 0.675485 + 0.737374i \(0.263934\pi\)
−0.675485 + 0.737374i \(0.736066\pi\)
\(32\) 742110.i 0.707732i
\(33\) 215513.i 0.181727i
\(34\) 4.04601e6i 3.02769i
\(35\) 1.15468e6 0.769469
\(36\) −1.22155e6 −0.727282
\(37\) 454793.i 0.242665i 0.992612 + 0.121332i \(0.0387167\pi\)
−0.992612 + 0.121332i \(0.961283\pi\)
\(38\) 1.07376e6i 0.514958i
\(39\) 420199.i 0.181634i
\(40\) 8.80219e6i 3.43835i
\(41\) −2.19561e6 −0.776999 −0.388500 0.921449i \(-0.627006\pi\)
−0.388500 + 0.921449i \(0.627006\pi\)
\(42\) 1.51188e6i 0.485870i
\(43\) 155344.i 0.0454381i −0.999742 0.0227190i \(-0.992768\pi\)
0.999742 0.0227190i \(-0.00723232\pi\)
\(44\) 2.57403e6i 0.686757i
\(45\) 2.22935e6 0.543662
\(46\) 1.05146e7 2.34834
\(47\) 4.12397e6i 0.845131i 0.906332 + 0.422566i \(0.138870\pi\)
−0.906332 + 0.422566i \(0.861130\pi\)
\(48\) −4.83814e6 −0.911409
\(49\) −4.48168e6 −0.777422
\(50\) 1.85079e7i 2.96126i
\(51\) 6.62967e6 0.979967
\(52\) 5.01874e6i 0.686407i
\(53\) −8.47567e6 −1.07416 −0.537082 0.843530i \(-0.680474\pi\)
−0.537082 + 0.843530i \(0.680474\pi\)
\(54\) 2.91899e6i 0.343287i
\(55\) 4.69764e6i 0.513368i
\(56\) 9.78124e6i 0.994585i
\(57\) −1.75943e6 −0.166675
\(58\) 3.07167e7i 2.71433i
\(59\) 8.59574e6 + 8.54071e6i 0.709374 + 0.704833i
\(60\) 2.66268e7 2.05454
\(61\) 1.90458e7i 1.37556i 0.725918 + 0.687781i \(0.241415\pi\)
−0.725918 + 0.687781i \(0.758585\pi\)
\(62\) 3.88709e7 2.63062
\(63\) 2.47732e6 0.157261
\(64\) 5.30453e6 0.316175
\(65\) 9.15927e6i 0.513106i
\(66\) −6.15083e6 −0.324159
\(67\) 1.59131e6i 0.0789686i 0.999220 + 0.0394843i \(0.0125715\pi\)
−0.999220 + 0.0394843i \(0.987428\pi\)
\(68\) 7.91830e7 3.70336
\(69\) 1.72289e7i 0.760081i
\(70\) 3.29551e7i 1.37256i
\(71\) 2.82229e7 1.11063 0.555314 0.831641i \(-0.312598\pi\)
0.555314 + 0.831641i \(0.312598\pi\)
\(72\) 1.88847e7i 0.702715i
\(73\) 3.05689e7i 1.07644i 0.842806 + 0.538218i \(0.180902\pi\)
−0.842806 + 0.538218i \(0.819098\pi\)
\(74\) 1.29800e7 0.432859
\(75\) −3.03265e7 −0.958467
\(76\) −2.10141e7 −0.629878
\(77\) 5.22015e6i 0.148498i
\(78\) 1.19926e7 0.323993
\(79\) −4.78817e6 −0.122931 −0.0614655 0.998109i \(-0.519577\pi\)
−0.0614655 + 0.998109i \(0.519577\pi\)
\(80\) 1.05459e8 2.57469
\(81\) 4.78297e6 0.111111
\(82\) 6.26636e7i 1.38599i
\(83\) 6.63663e7i 1.39841i −0.714920 0.699206i \(-0.753537\pi\)
0.714920 0.699206i \(-0.246463\pi\)
\(84\) 2.95884e7 0.594299
\(85\) −1.44510e8 −2.76836
\(86\) −4.43357e6 −0.0810512
\(87\) −5.03314e7 −0.878542
\(88\) −3.97933e7 −0.663559
\(89\) 8.43518e7i 1.34442i 0.740361 + 0.672209i \(0.234654\pi\)
−0.740361 + 0.672209i \(0.765346\pi\)
\(90\) 6.36266e7i 0.969769i
\(91\) 1.01780e7i 0.148422i
\(92\) 2.05777e8i 2.87240i
\(93\) 6.36926e7i 0.851446i
\(94\) 1.17700e8 1.50752
\(95\) 3.83510e7 0.470850
\(96\) 3.47051e7i 0.408609i
\(97\) 1.27671e8i 1.44214i −0.692864 0.721068i \(-0.743651\pi\)
0.692864 0.721068i \(-0.256349\pi\)
\(98\) 1.27909e8i 1.38674i
\(99\) 1.00786e7i 0.104920i
\(100\) −3.62211e8 −3.62211
\(101\) 3.20910e7i 0.308388i −0.988041 0.154194i \(-0.950722\pi\)
0.988041 0.154194i \(-0.0492781\pi\)
\(102\) 1.89213e8i 1.74804i
\(103\) 1.23245e8i 1.09502i 0.836800 + 0.547509i \(0.184424\pi\)
−0.836800 + 0.547509i \(0.815576\pi\)
\(104\) 7.75874e7 0.663221
\(105\) −5.39993e7 −0.444253
\(106\) 2.41899e8i 1.91607i
\(107\) −5.92387e7 −0.451929 −0.225965 0.974136i \(-0.572553\pi\)
−0.225965 + 0.974136i \(0.572553\pi\)
\(108\) 5.71265e7 0.419897
\(109\) 6.91512e7i 0.489885i −0.969538 0.244942i \(-0.921231\pi\)
0.969538 0.244942i \(-0.0787690\pi\)
\(110\) 1.34072e8 0.915732
\(111\) 2.12686e7i 0.140103i
\(112\) 1.17189e8 0.744758
\(113\) 7.29000e7i 0.447109i 0.974691 + 0.223555i \(0.0717661\pi\)
−0.974691 + 0.223555i \(0.928234\pi\)
\(114\) 5.02147e7i 0.297311i
\(115\) 3.75545e8i 2.14719i
\(116\) −6.01145e8 −3.32007
\(117\) 1.96508e7i 0.104866i
\(118\) 2.43755e8 2.45325e8i 1.25726 1.26536i
\(119\) −1.60584e8 −0.800780
\(120\) 4.11638e8i 1.98514i
\(121\) 1.93122e8 0.900926
\(122\) 5.43575e8 2.45369
\(123\) 1.02679e8 0.448601
\(124\) 7.60727e8i 3.21767i
\(125\) 2.62850e8 1.07663
\(126\) 7.07036e7i 0.280517i
\(127\) −5.75493e7 −0.221221 −0.110610 0.993864i \(-0.535281\pi\)
−0.110610 + 0.993864i \(0.535281\pi\)
\(128\) 3.41374e8i 1.27172i
\(129\) 7.26471e6i 0.0262337i
\(130\) −2.61409e8 −0.915265
\(131\) 4.64228e8i 1.57633i −0.615466 0.788164i \(-0.711032\pi\)
0.615466 0.788164i \(-0.288968\pi\)
\(132\) 1.20376e8i 0.396499i
\(133\) 4.26167e7 0.136199
\(134\) 4.54165e7 0.140862
\(135\) −1.04257e8 −0.313883
\(136\) 1.22413e9i 3.57827i
\(137\) −1.42176e8 −0.403595 −0.201797 0.979427i \(-0.564678\pi\)
−0.201797 + 0.979427i \(0.564678\pi\)
\(138\) −4.91718e8 −1.35581
\(139\) −5.03971e6 −0.0135004 −0.00675020 0.999977i \(-0.502149\pi\)
−0.00675020 + 0.999977i \(0.502149\pi\)
\(140\) −6.44952e8 −1.67886
\(141\) 1.92859e8i 0.487937i
\(142\) 8.05493e8i 1.98111i
\(143\) 4.14076e7 0.0990230
\(144\) 2.26257e8 0.526202
\(145\) 1.09710e9 2.48184
\(146\) 8.72448e8 1.92012
\(147\) 2.09588e8 0.448845
\(148\) 2.54026e8i 0.529458i
\(149\) 9.48159e7i 0.192369i 0.995364 + 0.0961847i \(0.0306639\pi\)
−0.995364 + 0.0961847i \(0.969336\pi\)
\(150\) 8.65529e8i 1.70969i
\(151\) 3.28428e8i 0.631732i −0.948804 0.315866i \(-0.897705\pi\)
0.948804 0.315866i \(-0.102295\pi\)
\(152\) 3.24868e8i 0.608601i
\(153\) −3.10039e8 −0.565784
\(154\) 1.48985e8 0.264886
\(155\) 1.38834e9i 2.40529i
\(156\) 2.34703e8i 0.396297i
\(157\) 1.00364e9i 1.65188i 0.563760 + 0.825939i \(0.309354\pi\)
−0.563760 + 0.825939i \(0.690646\pi\)
\(158\) 1.36656e8i 0.219281i
\(159\) 3.96368e8 0.620169
\(160\) 7.56482e8i 1.15430i
\(161\) 4.17316e8i 0.621101i
\(162\) 1.36508e8i 0.198197i
\(163\) 2.53012e8 0.358419 0.179209 0.983811i \(-0.442646\pi\)
0.179209 + 0.983811i \(0.442646\pi\)
\(164\) 1.22637e9 1.69529
\(165\) 2.19687e8i 0.296393i
\(166\) −1.89412e9 −2.49445
\(167\) 1.03285e9 1.32792 0.663959 0.747769i \(-0.268875\pi\)
0.663959 + 0.747769i \(0.268875\pi\)
\(168\) 4.57423e8i 0.574224i
\(169\) 7.34996e8 0.901027
\(170\) 4.12437e9i 4.93812i
\(171\) 8.22802e7 0.0962301
\(172\) 8.67677e7i 0.0991389i
\(173\) 3.04295e8i 0.339711i 0.985469 + 0.169856i \(0.0543301\pi\)
−0.985469 + 0.169856i \(0.945670\pi\)
\(174\) 1.43648e9i 1.56712i
\(175\) 7.34566e8 0.783211
\(176\) 4.76764e8i 0.496882i
\(177\) −4.01983e8 3.99410e8i −0.409557 0.406935i
\(178\) 2.40743e9 2.39814
\(179\) 1.71863e9i 1.67406i 0.547157 + 0.837030i \(0.315710\pi\)
−0.547157 + 0.837030i \(0.684290\pi\)
\(180\) −1.24521e9 −1.18619
\(181\) −9.08307e8 −0.846288 −0.423144 0.906062i \(-0.639074\pi\)
−0.423144 + 0.906062i \(0.639074\pi\)
\(182\) −2.90485e8 −0.264751
\(183\) 8.90685e8i 0.794181i
\(184\) −3.18121e9 −2.77537
\(185\) 4.63601e8i 0.395783i
\(186\) −1.81781e9 −1.51879
\(187\) 6.53307e8i 0.534258i
\(188\) 2.30345e9i 1.84395i
\(189\) −1.15853e8 −0.0907945
\(190\) 1.09455e9i 0.839889i
\(191\) 1.61997e9i 1.21723i −0.793464 0.608617i \(-0.791725\pi\)
0.793464 0.608617i \(-0.208275\pi\)
\(192\) −2.48068e8 −0.182544
\(193\) 2.18095e9 1.57187 0.785934 0.618311i \(-0.212183\pi\)
0.785934 + 0.618311i \(0.212183\pi\)
\(194\) −3.64379e9 −2.57244
\(195\) 4.28337e8i 0.296242i
\(196\) 2.50326e9 1.69622
\(197\) −2.14024e8 −0.142101 −0.0710505 0.997473i \(-0.522635\pi\)
−0.0710505 + 0.997473i \(0.522635\pi\)
\(198\) 2.87646e8 0.187153
\(199\) 1.13469e9 0.723543 0.361772 0.932267i \(-0.382172\pi\)
0.361772 + 0.932267i \(0.382172\pi\)
\(200\) 5.59962e9i 3.49976i
\(201\) 7.44180e7i 0.0455925i
\(202\) −9.15888e8 −0.550094
\(203\) 1.21913e9 0.717900
\(204\) −3.70302e9 −2.13814
\(205\) −2.23813e9 −1.26727
\(206\) 3.51747e9 1.95326
\(207\) 8.05714e8i 0.438833i
\(208\) 9.29576e8i 0.496628i
\(209\) 1.73379e8i 0.0908680i
\(210\) 1.54116e9i 0.792447i
\(211\) 1.95172e9i 0.984663i −0.870408 0.492332i \(-0.836145\pi\)
0.870408 0.492332i \(-0.163855\pi\)
\(212\) 4.73411e9 2.34366
\(213\) −1.31986e9 −0.641222
\(214\) 1.69069e9i 0.806139i
\(215\) 1.58352e8i 0.0741088i
\(216\) 8.83149e8i 0.405713i
\(217\) 1.54276e9i 0.695759i
\(218\) −1.97360e9 −0.873843
\(219\) 1.42957e9i 0.621481i
\(220\) 2.62388e9i 1.12009i
\(221\) 1.27379e9i 0.533985i
\(222\) −6.07013e8 −0.249911
\(223\) 1.32438e9 0.535543 0.267772 0.963482i \(-0.413713\pi\)
0.267772 + 0.963482i \(0.413713\pi\)
\(224\) 8.40624e8i 0.333895i
\(225\) 1.41823e9 0.553371
\(226\) 2.08059e9 0.797542
\(227\) 1.82424e9i 0.687036i −0.939146 0.343518i \(-0.888381\pi\)
0.939146 0.343518i \(-0.111619\pi\)
\(228\) 9.82732e8 0.363660
\(229\) 1.80199e9i 0.655255i −0.944807 0.327628i \(-0.893751\pi\)
0.944807 0.327628i \(-0.106249\pi\)
\(230\) 1.07182e10 3.83010
\(231\) 2.44122e8i 0.0857353i
\(232\) 9.29342e9i 3.20792i
\(233\) 3.16225e9i 1.07293i 0.843921 + 0.536467i \(0.180241\pi\)
−0.843921 + 0.536467i \(0.819759\pi\)
\(234\) −5.60840e8 −0.187058
\(235\) 4.20383e9i 1.37840i
\(236\) −4.80117e9 4.77044e9i −1.54774 1.53784i
\(237\) 2.23921e8 0.0709743
\(238\) 4.58311e9i 1.42841i
\(239\) 5.10702e9 1.56522 0.782612 0.622510i \(-0.213887\pi\)
0.782612 + 0.622510i \(0.213887\pi\)
\(240\) −4.93183e9 −1.48650
\(241\) −2.02026e8 −0.0598880 −0.0299440 0.999552i \(-0.509533\pi\)
−0.0299440 + 0.999552i \(0.509533\pi\)
\(242\) 5.51176e9i 1.60705i
\(243\) −2.23677e8 −0.0641500
\(244\) 1.06381e10i 3.00127i
\(245\) −4.56847e9 −1.26796
\(246\) 2.93049e9i 0.800202i
\(247\) 3.38047e8i 0.0908217i
\(248\) −1.17605e10 −3.10898
\(249\) 3.10364e9i 0.807373i
\(250\) 7.50184e9i 1.92047i
\(251\) 2.06222e9 0.519565 0.259782 0.965667i \(-0.416349\pi\)
0.259782 + 0.965667i \(0.416349\pi\)
\(252\) −1.38371e9 −0.343119
\(253\) −1.69778e9 −0.414381
\(254\) 1.64248e9i 0.394607i
\(255\) 6.75806e9 1.59831
\(256\) −8.38497e9 −1.95228
\(257\) −1.00844e9 −0.231163 −0.115581 0.993298i \(-0.536873\pi\)
−0.115581 + 0.993298i \(0.536873\pi\)
\(258\) 2.07337e8 0.0467949
\(259\) 5.15166e8i 0.114485i
\(260\) 5.11593e9i 1.11952i
\(261\) 2.35377e9 0.507226
\(262\) −1.32492e10 −2.81181
\(263\) −7.21830e9 −1.50873 −0.754366 0.656454i \(-0.772055\pi\)
−0.754366 + 0.656454i \(0.772055\pi\)
\(264\) 1.86095e9 0.383106
\(265\) −8.63981e9 −1.75195
\(266\) 1.21630e9i 0.242948i
\(267\) 3.94474e9i 0.776200i
\(268\) 8.88828e8i 0.172297i
\(269\) 6.48688e9i 1.23887i 0.785047 + 0.619437i \(0.212639\pi\)
−0.785047 + 0.619437i \(0.787361\pi\)
\(270\) 2.97552e9i 0.559897i
\(271\) −8.97992e9 −1.66493 −0.832464 0.554079i \(-0.813070\pi\)
−0.832464 + 0.554079i \(0.813070\pi\)
\(272\) −1.46663e10 −2.67945
\(273\) 4.75980e8i 0.0856915i
\(274\) 4.05777e9i 0.719921i
\(275\) 2.98846e9i 0.522536i
\(276\) 9.62323e9i 1.65838i
\(277\) −1.27542e9 −0.216638 −0.108319 0.994116i \(-0.534547\pi\)
−0.108319 + 0.994116i \(0.534547\pi\)
\(278\) 1.43835e8i 0.0240816i
\(279\) 2.97861e9i 0.491583i
\(280\) 9.97066e9i 1.62215i
\(281\) 3.69474e9 0.592595 0.296298 0.955096i \(-0.404248\pi\)
0.296298 + 0.955096i \(0.404248\pi\)
\(282\) −5.50427e9 −0.870368
\(283\) 1.45323e9i 0.226562i −0.993563 0.113281i \(-0.963864\pi\)
0.993563 0.113281i \(-0.0361361\pi\)
\(284\) −1.57640e10 −2.42322
\(285\) −1.79350e9 −0.271845
\(286\) 1.18179e9i 0.176635i
\(287\) −2.48708e9 −0.366574
\(288\) 1.62300e9i 0.235911i
\(289\) 1.31214e10 1.88100
\(290\) 3.13116e10i 4.42703i
\(291\) 5.97060e9i 0.832618i
\(292\) 1.70743e10i 2.34862i
\(293\) 8.50585e9 1.15411 0.577055 0.816705i \(-0.304202\pi\)
0.577055 + 0.816705i \(0.304202\pi\)
\(294\) 5.98171e9i 0.800637i
\(295\) 8.76220e9 + 8.70611e9i 1.15698 + 1.14957i
\(296\) −3.92712e9 −0.511573
\(297\) 4.71328e8i 0.0605755i
\(298\) 2.70608e9 0.343143
\(299\) 3.31027e9 0.414169
\(300\) 1.69389e10 2.09123
\(301\) 1.75965e8i 0.0214369i
\(302\) −9.37347e9 −1.12687
\(303\) 1.50075e9i 0.178048i
\(304\) 3.89225e9 0.455729
\(305\) 1.94147e10i 2.24352i
\(306\) 8.84863e9i 1.00923i
\(307\) −5.58937e9 −0.629230 −0.314615 0.949219i \(-0.601875\pi\)
−0.314615 + 0.949219i \(0.601875\pi\)
\(308\) 2.91573e9i 0.324000i
\(309\) 5.76361e9i 0.632209i
\(310\) 3.96236e10 4.29050
\(311\) −3.30025e9 −0.352781 −0.176391 0.984320i \(-0.556442\pi\)
−0.176391 + 0.984320i \(0.556442\pi\)
\(312\) −3.62840e9 −0.382911
\(313\) 1.37415e10i 1.43171i 0.698247 + 0.715857i \(0.253964\pi\)
−0.698247 + 0.715857i \(0.746036\pi\)
\(314\) 2.86442e10 2.94658
\(315\) 2.52530e9 0.256490
\(316\) 2.67445e9 0.268217
\(317\) −8.87944e9 −0.879323 −0.439661 0.898164i \(-0.644902\pi\)
−0.439661 + 0.898164i \(0.644902\pi\)
\(318\) 1.13125e10i 1.10624i
\(319\) 4.95981e9i 0.478963i
\(320\) 5.40726e9 0.515676
\(321\) 2.77032e9 0.260921
\(322\) 1.19104e10 1.10790
\(323\) −5.33352e9 −0.490009
\(324\) −2.67154e9 −0.242427
\(325\) 5.82678e9i 0.522270i
\(326\) 7.22106e9i 0.639338i
\(327\) 3.23388e9i 0.282835i
\(328\) 1.89590e10i 1.63803i
\(329\) 4.67142e9i 0.398718i
\(330\) −6.26995e9 −0.528698
\(331\) −2.05246e10 −1.70987 −0.854934 0.518736i \(-0.826403\pi\)
−0.854934 + 0.518736i \(0.826403\pi\)
\(332\) 3.70691e10i 3.05112i
\(333\) 9.94633e8i 0.0808883i
\(334\) 2.94779e10i 2.36870i
\(335\) 1.62212e9i 0.128797i
\(336\) −5.48039e9 −0.429986
\(337\) 9.56605e9i 0.741674i −0.928698 0.370837i \(-0.879071\pi\)
0.928698 0.370837i \(-0.120929\pi\)
\(338\) 2.09771e10i 1.60723i
\(339\) 3.40920e9i 0.258139i
\(340\) 8.07164e10 6.04013
\(341\) −6.27645e9 −0.464191
\(342\) 2.34831e9i 0.171653i
\(343\) −1.16067e10 −0.838555
\(344\) 1.34139e9 0.0957901
\(345\) 1.75625e10i 1.23968i
\(346\) 8.68468e9 0.605968
\(347\) 2.43628e9i 0.168039i −0.996464 0.0840194i \(-0.973224\pi\)
0.996464 0.0840194i \(-0.0267758\pi\)
\(348\) 2.81128e10 1.91684
\(349\) 9.35066e8i 0.0630290i 0.999503 + 0.0315145i \(0.0100330\pi\)
−0.999503 + 0.0315145i \(0.989967\pi\)
\(350\) 2.09648e10i 1.39707i
\(351\) 9.18975e8i 0.0605446i
\(352\) 3.41994e9 0.222765
\(353\) 3.18010e9i 0.204806i 0.994743 + 0.102403i \(0.0326531\pi\)
−0.994743 + 0.102403i \(0.967347\pi\)
\(354\) −1.13993e10 + 1.14727e10i −0.725880 + 0.730557i
\(355\) 2.87695e10 1.81142
\(356\) 4.71149e10i 2.93331i
\(357\) 7.50975e9 0.462330
\(358\) 4.90504e10 2.98614
\(359\) 5.00991e9 0.301615 0.150807 0.988563i \(-0.451813\pi\)
0.150807 + 0.988563i \(0.451813\pi\)
\(360\) 1.92504e10i 1.14612i
\(361\) −1.55681e10 −0.916658
\(362\) 2.59234e10i 1.50959i
\(363\) −9.03140e9 −0.520150
\(364\) 5.68497e9i 0.323834i
\(365\) 3.11609e10i 1.75565i
\(366\) −2.54205e10 −1.41664
\(367\) 4.69877e9i 0.259012i 0.991579 + 0.129506i \(0.0413391\pi\)
−0.991579 + 0.129506i \(0.958661\pi\)
\(368\) 3.81141e10i 2.07824i
\(369\) −4.80181e9 −0.259000
\(370\) 1.32313e10 0.705987
\(371\) −9.60080e9 −0.506771
\(372\) 3.55757e10i 1.85772i
\(373\) −2.30261e10 −1.18955 −0.594777 0.803890i \(-0.702760\pi\)
−0.594777 + 0.803890i \(0.702760\pi\)
\(374\) −1.86456e10 −0.952995
\(375\) −1.22923e10 −0.621595
\(376\) −3.56103e10 −1.78166
\(377\) 9.67043e9i 0.478719i
\(378\) 3.30648e9i 0.161957i
\(379\) 2.29516e10 1.11239 0.556194 0.831052i \(-0.312261\pi\)
0.556194 + 0.831052i \(0.312261\pi\)
\(380\) −2.14211e10 −1.02732
\(381\) 2.69132e9 0.127722
\(382\) −4.62346e10 −2.17127
\(383\) 3.54785e10 1.64881 0.824403 0.566003i \(-0.191511\pi\)
0.824403 + 0.566003i \(0.191511\pi\)
\(384\) 1.59645e10i 0.734225i
\(385\) 5.32124e9i 0.242198i
\(386\) 6.22450e10i 2.80385i
\(387\) 3.39737e8i 0.0151460i
\(388\) 7.13111e10i 3.14652i
\(389\) −3.93579e10 −1.71883 −0.859415 0.511278i \(-0.829172\pi\)
−0.859415 + 0.511278i \(0.829172\pi\)
\(390\) 1.22249e10 0.528429
\(391\) 5.22276e10i 2.23456i
\(392\) 3.86992e10i 1.63892i
\(393\) 2.17098e10i 0.910093i
\(394\) 6.10832e9i 0.253476i
\(395\) −4.88090e9 −0.200499
\(396\) 5.62941e9i 0.228919i
\(397\) 3.54396e10i 1.42668i 0.700818 + 0.713340i \(0.252818\pi\)
−0.700818 + 0.713340i \(0.747182\pi\)
\(398\) 3.23844e10i 1.29064i
\(399\) −1.99299e9 −0.0786344
\(400\) 6.70891e10 2.62067
\(401\) 9.00839e9i 0.348393i 0.984711 + 0.174197i \(0.0557328\pi\)
−0.984711 + 0.174197i \(0.944267\pi\)
\(402\) −2.12392e9 −0.0813268
\(403\) 1.22376e10 0.463954
\(404\) 1.79245e10i 0.672855i
\(405\) 4.87560e9 0.181221
\(406\) 3.47943e10i 1.28057i
\(407\) −2.09587e9 −0.0763811
\(408\) 5.72470e10i 2.06591i
\(409\) 1.89660e10i 0.677772i −0.940827 0.338886i \(-0.889950\pi\)
0.940827 0.338886i \(-0.110050\pi\)
\(410\) 6.38772e10i 2.26053i
\(411\) 6.64893e9 0.233015
\(412\) 6.88390e10i 2.38916i
\(413\) 9.73681e9 + 9.67448e9i 0.334670 + 0.332527i
\(414\) 2.29954e10 0.782779
\(415\) 6.76515e10i 2.28079i
\(416\) −6.66806e9 −0.222652
\(417\) 2.35684e8 0.00779445
\(418\) 4.94830e9 0.162088
\(419\) 3.49441e9i 0.113375i −0.998392 0.0566876i \(-0.981946\pi\)
0.998392 0.0566876i \(-0.0180539\pi\)
\(420\) 3.01614e10 0.969292
\(421\) 2.84577e10i 0.905881i −0.891541 0.452941i \(-0.850375\pi\)
0.891541 0.452941i \(-0.149625\pi\)
\(422\) −5.57028e10 −1.75642
\(423\) 9.01912e9i 0.281710i
\(424\) 7.31872e10i 2.26450i
\(425\) −9.19317e10 −2.81780
\(426\) 3.76692e10i 1.14379i
\(427\) 2.15741e10i 0.648965i
\(428\) 3.30879e10 0.986040
\(429\) −1.93644e9 −0.0571710
\(430\) −4.51943e9 −0.132193
\(431\) 5.38709e9i 0.156115i −0.996949 0.0780575i \(-0.975128\pi\)
0.996949 0.0780575i \(-0.0248718\pi\)
\(432\) −1.05810e10 −0.303803
\(433\) −1.33819e10 −0.380686 −0.190343 0.981718i \(-0.560960\pi\)
−0.190343 + 0.981718i \(0.560960\pi\)
\(434\) 4.40309e10 1.24108
\(435\) −5.13061e10 −1.43289
\(436\) 3.86246e10i 1.06885i
\(437\) 1.38605e10i 0.380061i
\(438\) −4.08003e10 −1.10858
\(439\) 4.83699e10 1.30232 0.651159 0.758941i \(-0.274283\pi\)
0.651159 + 0.758941i \(0.274283\pi\)
\(440\) −4.05640e10 −1.08226
\(441\) −9.80144e9 −0.259141
\(442\) 3.63545e10 0.952508
\(443\) 4.24323e10i 1.10175i −0.834589 0.550873i \(-0.814295\pi\)
0.834589 0.550873i \(-0.185705\pi\)
\(444\) 1.18796e10i 0.305682i
\(445\) 8.59854e10i 2.19273i
\(446\) 3.77984e10i 0.955288i
\(447\) 4.43410e9i 0.111065i
\(448\) 6.00870e9 0.149166
\(449\) 6.76235e9 0.166384 0.0831921 0.996534i \(-0.473488\pi\)
0.0831921 + 0.996534i \(0.473488\pi\)
\(450\) 4.04768e10i 0.987088i
\(451\) 1.01183e10i 0.244568i
\(452\) 4.07185e10i 0.975524i
\(453\) 1.53591e10i 0.364731i
\(454\) −5.20646e10 −1.22552
\(455\) 1.03751e10i 0.242074i
\(456\) 1.51926e10i 0.351376i
\(457\) 6.09387e10i 1.39710i 0.715560 + 0.698551i \(0.246172\pi\)
−0.715560 + 0.698551i \(0.753828\pi\)
\(458\) −5.14295e10 −1.16883
\(459\) 1.44991e10 0.326656
\(460\) 2.09762e11i 4.68484i
\(461\) −2.44762e10 −0.541927 −0.270964 0.962590i \(-0.587342\pi\)
−0.270964 + 0.962590i \(0.587342\pi\)
\(462\) −6.96734e9 −0.152932
\(463\) 3.15779e10i 0.687163i 0.939123 + 0.343581i \(0.111640\pi\)
−0.939123 + 0.343581i \(0.888360\pi\)
\(464\) 1.11345e11 2.40213
\(465\) 6.49261e10i 1.38870i
\(466\) 9.02519e10 1.91387
\(467\) 7.82070e10i 1.64429i −0.569280 0.822144i \(-0.692778\pi\)
0.569280 0.822144i \(-0.307222\pi\)
\(468\) 1.09760e10i 0.228802i
\(469\) 1.80255e9i 0.0372560i
\(470\) 1.19979e11 2.45875
\(471\) 4.69354e10i 0.953712i
\(472\) −7.37487e10 + 7.42239e10i −1.48589 + 1.49546i
\(473\) 7.15885e8 0.0143021
\(474\) 6.39078e9i 0.126602i
\(475\) 2.43974e10 0.479258
\(476\) 8.96944e10 1.74718
\(477\) −1.85363e10 −0.358055
\(478\) 1.45756e11i 2.79200i
\(479\) 9.23414e8 0.0175410 0.00877050 0.999962i \(-0.497208\pi\)
0.00877050 + 0.999962i \(0.497208\pi\)
\(480\) 3.53772e10i 0.666435i
\(481\) 4.08643e9 0.0763421
\(482\) 5.76591e9i 0.106827i
\(483\) 1.95160e10i 0.358593i
\(484\) −1.07869e11 −1.96568
\(485\) 1.30144e11i 2.35210i
\(486\) 6.38383e9i 0.114429i
\(487\) −1.08429e10 −0.192766 −0.0963829 0.995344i \(-0.530727\pi\)
−0.0963829 + 0.995344i \(0.530727\pi\)
\(488\) −1.64460e11 −2.89989
\(489\) −1.18322e10 −0.206933
\(490\) 1.30386e11i 2.26176i
\(491\) 8.23576e10 1.41703 0.708513 0.705698i \(-0.249366\pi\)
0.708513 + 0.705698i \(0.249366\pi\)
\(492\) −5.73515e10 −0.978778
\(493\) −1.52575e11 −2.58282
\(494\) −9.64799e9 −0.162005
\(495\) 1.02737e10i 0.171123i
\(496\) 1.40902e11i 2.32805i
\(497\) 3.19695e10 0.523974
\(498\) 8.85791e10 1.44017
\(499\) −5.20239e10 −0.839075 −0.419538 0.907738i \(-0.637808\pi\)
−0.419538 + 0.907738i \(0.637808\pi\)
\(500\) −1.46816e11 −2.34905
\(501\) −4.83016e10 −0.766674
\(502\) 5.88564e10i 0.926785i
\(503\) 9.39091e10i 1.46702i 0.679680 + 0.733509i \(0.262119\pi\)
−0.679680 + 0.733509i \(0.737881\pi\)
\(504\) 2.13916e10i 0.331528i
\(505\) 3.27124e10i 0.502976i
\(506\) 4.84553e10i 0.739161i
\(507\) −3.43724e10 −0.520208
\(508\) 3.21443e10 0.482669
\(509\) 1.17018e11i 1.74334i 0.490095 + 0.871669i \(0.336962\pi\)
−0.490095 + 0.871669i \(0.663038\pi\)
\(510\) 1.92878e11i 2.85102i
\(511\) 3.46269e10i 0.507843i
\(512\) 1.51918e11i 2.21070i
\(513\) −3.84786e9 −0.0555585
\(514\) 2.87813e10i 0.412342i
\(515\) 1.25632e11i 1.78596i
\(516\) 4.05772e9i 0.0572379i
\(517\) −1.90049e10 −0.266013
\(518\) 1.47030e10 0.204215
\(519\) 1.42304e10i 0.196132i
\(520\) 7.90900e10 1.08170
\(521\) 9.93682e10 1.34864 0.674321 0.738438i \(-0.264436\pi\)
0.674321 + 0.738438i \(0.264436\pi\)
\(522\) 6.71774e10i 0.904776i
\(523\) −5.39431e10 −0.720990 −0.360495 0.932761i \(-0.617392\pi\)
−0.360495 + 0.932761i \(0.617392\pi\)
\(524\) 2.59296e11i 3.43930i
\(525\) −3.43523e10 −0.452187
\(526\) 2.06013e11i 2.69123i
\(527\) 1.93078e11i 2.50317i
\(528\) 2.22961e10i 0.286875i
\(529\) −5.74154e10 −0.733172
\(530\) 2.46583e11i 3.12507i
\(531\) 1.87989e10 + 1.86785e10i 0.236458 + 0.234944i
\(532\) −2.38037e10 −0.297165
\(533\) 1.97282e10i 0.244443i
\(534\) −1.12584e11 −1.38457
\(535\) −6.03859e10 −0.737090
\(536\) −1.37409e10 −0.166477
\(537\) 8.03725e10i 0.966519i
\(538\) 1.85138e11 2.20987
\(539\) 2.06534e10i 0.244701i
\(540\) 5.82328e10 0.684845
\(541\) 1.11202e11i 1.29815i −0.760725 0.649075i \(-0.775156\pi\)
0.760725 0.649075i \(-0.224844\pi\)
\(542\) 2.56290e11i 2.96985i
\(543\) 4.24773e10 0.488605
\(544\) 1.05205e11i 1.20127i
\(545\) 7.04904e10i 0.798995i
\(546\) 1.35846e10 0.152854
\(547\) −1.12537e11 −1.25703 −0.628516 0.777797i \(-0.716337\pi\)
−0.628516 + 0.777797i \(0.716337\pi\)
\(548\) 7.94130e10 0.880581
\(549\) 4.16532e10i 0.458521i
\(550\) 8.52917e10 0.932086
\(551\) 4.04913e10 0.439294
\(552\) 1.48771e11 1.60236
\(553\) −5.42380e9 −0.0579966
\(554\) 3.64009e10i 0.386432i
\(555\) 2.16805e10i 0.228505i
\(556\) 2.81494e9 0.0294558
\(557\) 4.45807e10 0.463155 0.231578 0.972816i \(-0.425611\pi\)
0.231578 + 0.972816i \(0.425611\pi\)
\(558\) 8.50106e10 0.876872
\(559\) −1.39580e9 −0.0142948
\(560\) 1.19459e11 1.21469
\(561\) 3.05521e10i 0.308454i
\(562\) 1.05449e11i 1.05706i
\(563\) 3.41893e10i 0.340296i 0.985419 + 0.170148i \(0.0544246\pi\)
−0.985419 + 0.170148i \(0.945575\pi\)
\(564\) 1.07722e11i 1.06460i
\(565\) 7.43118e10i 0.729229i
\(566\) −4.14756e10 −0.404136
\(567\) 5.41790e9 0.0524202
\(568\) 2.43704e11i 2.34137i
\(569\) 1.30593e11i 1.24586i 0.782277 + 0.622930i \(0.214058\pi\)
−0.782277 + 0.622930i \(0.785942\pi\)
\(570\) 5.11871e10i 0.484910i
\(571\) 1.69505e11i 1.59455i −0.603616 0.797275i \(-0.706274\pi\)
0.603616 0.797275i \(-0.293726\pi\)
\(572\) −2.31283e10 −0.216053
\(573\) 7.57586e10i 0.702770i
\(574\) 7.09821e10i 0.653885i
\(575\) 2.38908e11i 2.18554i
\(576\) 1.16010e10 0.105392
\(577\) −2.04372e11 −1.84382 −0.921909 0.387407i \(-0.873371\pi\)
−0.921909 + 0.387407i \(0.873371\pi\)
\(578\) 3.74490e11i 3.35528i
\(579\) −1.01993e11 −0.907518
\(580\) −6.12786e11 −5.41498
\(581\) 7.51763e10i 0.659745i
\(582\) 1.70403e11 1.48520
\(583\) 3.90593e10i 0.338104i
\(584\) −2.63961e11 −2.26928
\(585\) 2.00313e10i 0.171035i
\(586\) 2.42760e11i 2.05867i
\(587\) 2.15948e11i 1.81885i 0.415868 + 0.909425i \(0.363478\pi\)
−0.415868 + 0.909425i \(0.636522\pi\)
\(588\) −1.17066e11 −0.979310
\(589\) 5.12402e10i 0.425745i
\(590\) 2.48476e11 2.50076e11i 2.05057 2.06379i
\(591\) 1.00089e10 0.0820421
\(592\) 4.70509e10i 0.383073i
\(593\) −8.98244e10 −0.726400 −0.363200 0.931711i \(-0.618316\pi\)
−0.363200 + 0.931711i \(0.618316\pi\)
\(594\) −1.34519e10 −0.108053
\(595\) −1.63693e11 −1.30606
\(596\) 5.29597e10i 0.419720i
\(597\) −5.30641e10 −0.417738
\(598\) 9.44762e10i 0.738784i
\(599\) 1.85353e11 1.43977 0.719885 0.694094i \(-0.244195\pi\)
0.719885 + 0.694094i \(0.244195\pi\)
\(600\) 2.61868e11i 2.02059i
\(601\) 6.21320e10i 0.476231i 0.971237 + 0.238116i \(0.0765297\pi\)
−0.971237 + 0.238116i \(0.923470\pi\)
\(602\) −5.02212e9 −0.0382385
\(603\) 3.48019e9i 0.0263229i
\(604\) 1.83445e11i 1.37834i
\(605\) 1.96862e11 1.46940
\(606\) 4.28318e10 0.317597
\(607\) 1.27832e10 0.0941638 0.0470819 0.998891i \(-0.485008\pi\)
0.0470819 + 0.998891i \(0.485008\pi\)
\(608\) 2.79200e10i 0.204315i
\(609\) −5.70128e10 −0.414480
\(610\) 5.54101e11 4.00193
\(611\) 3.70550e10 0.265877
\(612\) 1.73173e11 1.23445
\(613\) 2.61394e11i 1.85120i 0.378501 + 0.925601i \(0.376440\pi\)
−0.378501 + 0.925601i \(0.623560\pi\)
\(614\) 1.59523e11i 1.12240i
\(615\) 1.04667e11 0.731661
\(616\) −4.50758e10 −0.313055
\(617\) −6.95322e10 −0.479783 −0.239892 0.970800i \(-0.577112\pi\)
−0.239892 + 0.970800i \(0.577112\pi\)
\(618\) −1.64496e11 −1.12772
\(619\) 1.25236e11 0.853034 0.426517 0.904480i \(-0.359740\pi\)
0.426517 + 0.904480i \(0.359740\pi\)
\(620\) 7.75459e11i 5.24798i
\(621\) 3.76795e10i 0.253360i
\(622\) 9.41904e10i 0.629282i
\(623\) 9.55494e10i 0.634272i
\(624\) 4.34720e10i 0.286728i
\(625\) 1.46274e10 0.0958622
\(626\) 3.92187e11 2.55385
\(627\) 8.10813e9i 0.0524627i
\(628\) 5.60584e11i 3.60414i
\(629\) 6.44735e10i 0.411888i
\(630\) 7.20729e10i 0.457520i
\(631\) 2.29719e11 1.44904 0.724519 0.689255i \(-0.242062\pi\)
0.724519 + 0.689255i \(0.242062\pi\)
\(632\) 4.13457e10i 0.259157i
\(633\) 9.12729e10i 0.568496i
\(634\) 2.53422e11i 1.56851i
\(635\) −5.86638e10 −0.360807
\(636\) −2.21392e11 −1.35311
\(637\) 4.02691e10i 0.244576i
\(638\) 1.41555e11 0.854361
\(639\) 6.17236e10 0.370209
\(640\) 3.47985e11i 2.07415i
\(641\) 2.02783e11 1.20115 0.600577 0.799567i \(-0.294938\pi\)
0.600577 + 0.799567i \(0.294938\pi\)
\(642\) 7.90659e10i 0.465425i
\(643\) −5.69766e10 −0.333313 −0.166657 0.986015i \(-0.553297\pi\)
−0.166657 + 0.986015i \(0.553297\pi\)
\(644\) 2.33093e11i 1.35515i
\(645\) 7.40540e9i 0.0427868i
\(646\) 1.52221e11i 0.874065i
\(647\) −3.14802e11 −1.79647 −0.898237 0.439512i \(-0.855151\pi\)
−0.898237 + 0.439512i \(0.855151\pi\)
\(648\) 4.13008e10i 0.234238i
\(649\) −3.93590e10 + 3.96125e10i −0.221853 + 0.223282i
\(650\) −1.66298e11 −0.931611
\(651\) 7.21477e10i 0.401697i
\(652\) −1.41321e11 −0.782015
\(653\) 3.29760e11 1.81361 0.906807 0.421546i \(-0.138512\pi\)
0.906807 + 0.421546i \(0.138512\pi\)
\(654\) 9.22962e10 0.504513
\(655\) 4.73218e11i 2.57097i
\(656\) −2.27149e11 −1.22658
\(657\) 6.68542e10i 0.358812i
\(658\) 1.33324e11 0.711222
\(659\) 1.81204e11i 0.960785i 0.877053 + 0.480393i \(0.159506\pi\)
−0.877053 + 0.480393i \(0.840494\pi\)
\(660\) 1.22707e11i 0.646685i
\(661\) 2.36523e11 1.23899 0.619494 0.785001i \(-0.287338\pi\)
0.619494 + 0.785001i \(0.287338\pi\)
\(662\) 5.85780e11i 3.05002i
\(663\) 5.95693e10i 0.308297i
\(664\) 5.73070e11 2.94806
\(665\) 4.34420e10 0.222138
\(666\) 2.83872e10 0.144286
\(667\) 3.96504e11i 2.00329i
\(668\) −5.76901e11 −2.89731
\(669\) −6.19353e10 −0.309196
\(670\) 4.62960e10 0.229744
\(671\) −8.77706e10 −0.432971
\(672\) 3.93121e10i 0.192774i
\(673\) 3.76786e11i 1.83668i −0.395790 0.918341i \(-0.629529\pi\)
0.395790 0.918341i \(-0.370471\pi\)
\(674\) −2.73019e11 −1.32298
\(675\) −6.63240e10 −0.319489
\(676\) −4.10534e11 −1.96590
\(677\) 3.19535e11 1.52112 0.760559 0.649268i \(-0.224925\pi\)
0.760559 + 0.649268i \(0.224925\pi\)
\(678\) −9.72997e10 −0.460461
\(679\) 1.44619e11i 0.680374i
\(680\) 1.24784e12i 5.83610i
\(681\) 8.53114e10i 0.396660i
\(682\) 1.79132e11i 0.828011i
\(683\) 1.91834e11i 0.881540i 0.897620 + 0.440770i \(0.145295\pi\)
−0.897620 + 0.440770i \(0.854705\pi\)
\(684\) −4.59578e10 −0.209959
\(685\) −1.44930e11 −0.658257
\(686\) 3.31259e11i 1.49579i
\(687\) 8.42707e10i 0.378312i
\(688\) 1.60712e10i 0.0717289i
\(689\) 7.61561e10i 0.337931i
\(690\) −5.01241e11 −2.21131
\(691\) 4.73092e10i 0.207508i −0.994603 0.103754i \(-0.966915\pi\)
0.994603 0.103754i \(-0.0330854\pi\)
\(692\) 1.69965e11i 0.741198i
\(693\) 1.14165e10i 0.0494993i
\(694\) −6.95324e10 −0.299743
\(695\) −5.13731e9 −0.0220189
\(696\) 4.34610e11i 1.85209i
\(697\) 3.11260e11 1.31884
\(698\) 2.66871e10 0.112430
\(699\) 1.47884e11i 0.619459i
\(700\) −4.10294e11 −1.70885
\(701\) 1.75140e11i 0.725292i 0.931927 + 0.362646i \(0.118127\pi\)
−0.931927 + 0.362646i \(0.881873\pi\)
\(702\) 2.62279e10 0.107998
\(703\) 1.71104e10i 0.0700550i
\(704\) 2.44454e10i 0.0995191i
\(705\) 1.96594e11i 0.795818i
\(706\) 9.07613e10 0.365327
\(707\) 3.63510e10i 0.145492i
\(708\) 2.24529e11 + 2.23091e11i 0.893591 + 0.887870i
\(709\) −4.53463e11 −1.79456 −0.897278 0.441467i \(-0.854458\pi\)
−0.897278 + 0.441467i \(0.854458\pi\)
\(710\) 8.21092e11i 3.23116i
\(711\) −1.04717e10 −0.0409770
\(712\) −7.28375e11 −2.83423
\(713\) −5.01761e11 −1.94151
\(714\) 2.14331e11i 0.824693i
\(715\) 4.22095e10 0.161505
\(716\) 9.59947e11i 3.65254i
\(717\) −2.38832e11 −0.903682
\(718\) 1.42985e11i 0.538012i
\(719\) 1.80912e11i 0.676942i 0.940977 + 0.338471i \(0.109910\pi\)
−0.940977 + 0.338471i \(0.890090\pi\)
\(720\) 2.30639e11 0.858229
\(721\) 1.39606e11i 0.516610i
\(722\) 4.44320e11i 1.63511i
\(723\) 9.44784e9 0.0345764
\(724\) 5.07337e11 1.84647
\(725\) 6.97931e11 2.52616
\(726\) 2.57760e11i 0.927830i
\(727\) −2.99841e11 −1.07338 −0.536691 0.843779i \(-0.680326\pi\)
−0.536691 + 0.843779i \(0.680326\pi\)
\(728\) 8.78870e10 0.312895
\(729\) 1.04604e10 0.0370370
\(730\) 8.89343e11 3.13168
\(731\) 2.20222e10i 0.0771244i
\(732\) 4.97494e11i 1.73278i
\(733\) −2.19804e11 −0.761410 −0.380705 0.924696i \(-0.624319\pi\)
−0.380705 + 0.924696i \(0.624319\pi\)
\(734\) 1.34105e11 0.462018
\(735\) 2.13646e11 0.732059
\(736\) 2.73401e11 0.931729
\(737\) −7.33337e9 −0.0248561
\(738\) 1.37045e11i 0.461997i
\(739\) 7.66573e10i 0.257025i 0.991708 + 0.128513i \(0.0410203\pi\)
−0.991708 + 0.128513i \(0.958980\pi\)
\(740\) 2.58945e11i 0.863537i
\(741\) 1.58089e10i 0.0524359i
\(742\) 2.74011e11i 0.903965i
\(743\) 1.01874e10 0.0334280 0.0167140 0.999860i \(-0.494680\pi\)
0.0167140 + 0.999860i \(0.494680\pi\)
\(744\) 5.49983e11 1.79497
\(745\) 9.66521e10i 0.313752i
\(746\) 6.57172e11i 2.12190i
\(747\) 1.45143e11i 0.466137i
\(748\) 3.64906e11i 1.16567i
\(749\) −6.71025e10 −0.213212
\(750\) 3.50826e11i 1.10878i
\(751\) 2.54136e11i 0.798925i −0.916750 0.399462i \(-0.869197\pi\)
0.916750 0.399462i \(-0.130803\pi\)
\(752\) 4.26648e11i 1.33413i
\(753\) −9.64403e10 −0.299971
\(754\) −2.75998e11 −0.853925
\(755\) 3.34789e11i 1.03035i
\(756\) 6.47099e10 0.198100
\(757\) 8.96205e10 0.272913 0.136456 0.990646i \(-0.456429\pi\)
0.136456 + 0.990646i \(0.456429\pi\)
\(758\) 6.55047e11i 1.98425i
\(759\) 7.93974e10 0.239243
\(760\) 3.31160e11i 0.992620i
\(761\) 1.56648e11 0.467075 0.233537 0.972348i \(-0.424970\pi\)
0.233537 + 0.972348i \(0.424970\pi\)
\(762\) 7.68111e10i 0.227827i
\(763\) 7.83309e10i 0.231119i
\(764\) 9.04840e11i 2.65582i
\(765\) −3.16043e11 −0.922785
\(766\) 1.01257e12i 2.94110i
\(767\) 7.67405e10 7.72349e10i 0.221740 0.223168i
\(768\) 3.92126e11 1.12715
\(769\) 6.55610e11i 1.87474i −0.348339 0.937369i \(-0.613254\pi\)
0.348339 0.937369i \(-0.386746\pi\)
\(770\) 1.51870e11 0.432026
\(771\) 4.71601e10 0.133462
\(772\) −1.21817e12 −3.42957
\(773\) 4.84858e11i 1.35799i −0.734143 0.678995i \(-0.762416\pi\)
0.734143 0.678995i \(-0.237584\pi\)
\(774\) −9.69621e9 −0.0270171
\(775\) 8.83206e11i 2.44825i
\(776\) 1.10244e12 3.04023
\(777\) 2.40919e10i 0.0660979i
\(778\) 1.12329e12i 3.06600i
\(779\) −8.26043e10 −0.224312
\(780\) 2.39249e11i 0.646355i
\(781\) 1.30062e11i 0.349581i
\(782\) −1.49059e12 −3.98595