Properties

Label 177.9.c.a.58.15
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 58.15
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.66

$q$-expansion

\(f(q)\) \(=\) \(q-20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} -972.254i q^{6} +1280.77 q^{7} -1658.51i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} -972.254i q^{6} +1280.77 q^{7} -1658.51i q^{8} +2187.00 q^{9} +12521.6i q^{10} -19456.6i q^{11} -8241.26 q^{12} +31433.4i q^{13} -26627.3i q^{14} -28166.2 q^{15} -79594.3 q^{16} +137031. q^{17} -45467.8i q^{18} -149188. q^{19} +106139. q^{20} +59895.7 q^{21} -404503. q^{22} -411676. i q^{23} -77561.0i q^{24} -27873.9 q^{25} +653501. q^{26} +102276. q^{27} -225705. q^{28} -288373. q^{29} +585577. i q^{30} -1.63017e6i q^{31} +1.23019e6i q^{32} -909895. i q^{33} -2.84888e6i q^{34} -771393. q^{35} -385405. q^{36} +2.14787e6i q^{37} +3.10163e6i q^{38} +1.46999e6i q^{39} +998903. i q^{40} +960198. q^{41} -1.24523e6i q^{42} +21546.2i q^{43} +3.42875e6i q^{44} -1.31720e6 q^{45} -8.55876e6 q^{46} -106905. i q^{47} -3.72226e6 q^{48} -4.12443e6 q^{49} +579499. i q^{50} +6.40830e6 q^{51} -5.53937e6i q^{52} -1.48206e7 q^{53} -2.12632e6i q^{54} +1.17185e7i q^{55} -2.12417e6i q^{56} -6.97686e6 q^{57} +5.99529e6i q^{58} +(4.18654e6 + 1.13712e7i) q^{59} +4.96361e6 q^{60} -1.74260e6i q^{61} -3.38914e7 q^{62} +2.80104e6 q^{63} +5.19953e6 q^{64} -1.89320e7i q^{65} -1.89168e7 q^{66} +5.44049e6i q^{67} -2.41483e7 q^{68} -1.92522e7i q^{69} +1.60373e7i q^{70} -2.69743e7 q^{71} -3.62717e6i q^{72} -2.23392e7i q^{73} +4.46544e7 q^{74} -1.30353e6 q^{75} +2.62908e7 q^{76} -2.49194e7i q^{77} +3.05612e7 q^{78} -1.27758e7 q^{79} +4.79387e7 q^{80} +4.78297e6 q^{81} -1.99625e7i q^{82} +6.43241e7i q^{83} -1.05552e7 q^{84} -8.25321e7 q^{85} +447946. q^{86} -1.34859e7 q^{87} -3.22690e7 q^{88} +3.11328e7i q^{89} +2.73847e7i q^{90} +4.02589e7i q^{91} +7.25479e7i q^{92} -7.62357e7i q^{93} -2.22255e6 q^{94} +8.98545e7 q^{95} +5.75302e7i q^{96} -3.65832e7i q^{97} +8.57470e7i q^{98} -4.25516e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.7900i 1.29938i −0.760200 0.649689i \(-0.774899\pi\)
0.760200 0.649689i \(-0.225101\pi\)
\(3\) 46.7654 0.577350
\(4\) −176.226 −0.688381
\(5\) −602.288 −0.963661 −0.481831 0.876264i \(-0.660028\pi\)
−0.481831 + 0.876264i \(0.660028\pi\)
\(6\) 972.254i 0.750196i
\(7\) 1280.77 0.533432 0.266716 0.963775i \(-0.414061\pi\)
0.266716 + 0.963775i \(0.414061\pi\)
\(8\) 1658.51i 0.404910i
\(9\) 2187.00 0.333333
\(10\) 12521.6i 1.25216i
\(11\) 19456.6i 1.32891i −0.747327 0.664456i \(-0.768663\pi\)
0.747327 0.664456i \(-0.231337\pi\)
\(12\) −8241.26 −0.397437
\(13\) 31433.4i 1.10057i 0.834977 + 0.550285i \(0.185481\pi\)
−0.834977 + 0.550285i \(0.814519\pi\)
\(14\) 26627.3i 0.693130i
\(15\) −28166.2 −0.556370
\(16\) −79594.3 −1.21451
\(17\) 137031. 1.64068 0.820338 0.571879i \(-0.193785\pi\)
0.820338 + 0.571879i \(0.193785\pi\)
\(18\) 45467.8i 0.433126i
\(19\) −149188. −1.14478 −0.572389 0.819983i \(-0.693983\pi\)
−0.572389 + 0.819983i \(0.693983\pi\)
\(20\) 106139. 0.663366
\(21\) 59895.7 0.307977
\(22\) −404503. −1.72676
\(23\) 411676.i 1.47111i −0.677466 0.735554i \(-0.736922\pi\)
0.677466 0.735554i \(-0.263078\pi\)
\(24\) 77561.0i 0.233775i
\(25\) −27873.9 −0.0713572
\(26\) 653501. 1.43006
\(27\) 102276. 0.192450
\(28\) −225705. −0.367205
\(29\) −288373. −0.407721 −0.203861 0.979000i \(-0.565349\pi\)
−0.203861 + 0.979000i \(0.565349\pi\)
\(30\) 585577.i 0.722935i
\(31\) 1.63017e6i 1.76517i −0.470150 0.882587i \(-0.655800\pi\)
0.470150 0.882587i \(-0.344200\pi\)
\(32\) 1.23019e6i 1.17320i
\(33\) 909895.i 0.767248i
\(34\) 2.84888e6i 2.13186i
\(35\) −771393. −0.514048
\(36\) −385405. −0.229460
\(37\) 2.14787e6i 1.14605i 0.819540 + 0.573023i \(0.194229\pi\)
−0.819540 + 0.573023i \(0.805771\pi\)
\(38\) 3.10163e6i 1.48750i
\(39\) 1.46999e6i 0.635414i
\(40\) 998903.i 0.390196i
\(41\) 960198. 0.339801 0.169901 0.985461i \(-0.445655\pi\)
0.169901 + 0.985461i \(0.445655\pi\)
\(42\) 1.24523e6i 0.400179i
\(43\) 21546.2i 0.00630227i 0.999995 + 0.00315113i \(0.00100304\pi\)
−0.999995 + 0.00315113i \(0.998997\pi\)
\(44\) 3.42875e6i 0.914798i
\(45\) −1.31720e6 −0.321220
\(46\) −8.55876e6 −1.91152
\(47\) 106905.i 0.0219081i −0.999940 0.0109541i \(-0.996513\pi\)
0.999940 0.0109541i \(-0.00348686\pi\)
\(48\) −3.72226e6 −0.701199
\(49\) −4.12443e6 −0.715450
\(50\) 579499.i 0.0927199i
\(51\) 6.40830e6 0.947244
\(52\) 5.53937e6i 0.757612i
\(53\) −1.48206e7 −1.87828 −0.939142 0.343528i \(-0.888378\pi\)
−0.939142 + 0.343528i \(0.888378\pi\)
\(54\) 2.12632e6i 0.250065i
\(55\) 1.17185e7i 1.28062i
\(56\) 2.12417e6i 0.215992i
\(57\) −6.97686e6 −0.660937
\(58\) 5.99529e6i 0.529784i
\(59\) 4.18654e6 + 1.13712e7i 0.345500 + 0.938419i
\(60\) 4.96361e6 0.382995
\(61\) 1.74260e6i 0.125857i −0.998018 0.0629285i \(-0.979956\pi\)
0.998018 0.0629285i \(-0.0200440\pi\)
\(62\) −3.38914e7 −2.29363
\(63\) 2.80104e6 0.177811
\(64\) 5.19953e6 0.309916
\(65\) 1.89320e7i 1.06058i
\(66\) −1.89168e7 −0.996944
\(67\) 5.44049e6i 0.269984i 0.990847 + 0.134992i \(0.0431009\pi\)
−0.990847 + 0.134992i \(0.956899\pi\)
\(68\) −2.41483e7 −1.12941
\(69\) 1.92522e7i 0.849344i
\(70\) 1.60373e7i 0.667942i
\(71\) −2.69743e7 −1.06149 −0.530746 0.847531i \(-0.678088\pi\)
−0.530746 + 0.847531i \(0.678088\pi\)
\(72\) 3.62717e6i 0.134970i
\(73\) 2.23392e7i 0.786639i −0.919402 0.393319i \(-0.871327\pi\)
0.919402 0.393319i \(-0.128673\pi\)
\(74\) 4.46544e7 1.48915
\(75\) −1.30353e6 −0.0411981
\(76\) 2.62908e7 0.788043
\(77\) 2.49194e7i 0.708884i
\(78\) 3.05612e7 0.825643
\(79\) −1.27758e7 −0.328005 −0.164003 0.986460i \(-0.552441\pi\)
−0.164003 + 0.986460i \(0.552441\pi\)
\(80\) 4.79387e7 1.17038
\(81\) 4.78297e6 0.111111
\(82\) 1.99625e7i 0.441530i
\(83\) 6.43241e7i 1.35538i 0.735347 + 0.677691i \(0.237019\pi\)
−0.735347 + 0.677691i \(0.762981\pi\)
\(84\) −1.05552e7 −0.212006
\(85\) −8.25321e7 −1.58106
\(86\) 447946. 0.00818902
\(87\) −1.34859e7 −0.235398
\(88\) −3.22690e7 −0.538090
\(89\) 3.11328e7i 0.496202i 0.968734 + 0.248101i \(0.0798064\pi\)
−0.968734 + 0.248101i \(0.920194\pi\)
\(90\) 2.73847e7i 0.417386i
\(91\) 4.02589e7i 0.587079i
\(92\) 7.25479e7i 1.01268i
\(93\) 7.62357e7i 1.01912i
\(94\) −2.22255e6 −0.0284669
\(95\) 8.98545e7 1.10318
\(96\) 5.75302e7i 0.677347i
\(97\) 3.65832e7i 0.413233i −0.978422 0.206617i \(-0.933755\pi\)
0.978422 0.206617i \(-0.0662453\pi\)
\(98\) 8.57470e7i 0.929640i
\(99\) 4.25516e7i 0.442971i
\(100\) 4.91209e6 0.0491209
\(101\) 7.05978e6i 0.0678431i −0.999424 0.0339216i \(-0.989200\pi\)
0.999424 0.0339216i \(-0.0107996\pi\)
\(102\) 1.33229e8i 1.23083i
\(103\) 6.68911e7i 0.594319i 0.954828 + 0.297159i \(0.0960393\pi\)
−0.954828 + 0.297159i \(0.903961\pi\)
\(104\) 5.21327e7 0.445632
\(105\) −3.60745e7 −0.296786
\(106\) 3.08120e8i 2.44060i
\(107\) −2.26559e8 −1.72841 −0.864206 0.503139i \(-0.832178\pi\)
−0.864206 + 0.503139i \(0.832178\pi\)
\(108\) −1.80236e7 −0.132479
\(109\) 6.94363e6i 0.0491904i −0.999697 0.0245952i \(-0.992170\pi\)
0.999697 0.0245952i \(-0.00782969\pi\)
\(110\) 2.43628e8 1.66401
\(111\) 1.00446e8i 0.661670i
\(112\) −1.01942e8 −0.647860
\(113\) 1.80429e8i 1.10661i 0.832980 + 0.553304i \(0.186633\pi\)
−0.832980 + 0.553304i \(0.813367\pi\)
\(114\) 1.45049e8i 0.858807i
\(115\) 2.47948e8i 1.41765i
\(116\) 5.08188e7 0.280668
\(117\) 6.87448e7i 0.366857i
\(118\) 2.36407e8 8.70384e7i 1.21936 0.448934i
\(119\) 1.75505e8 0.875189
\(120\) 4.67141e7i 0.225280i
\(121\) −1.64201e8 −0.766007
\(122\) −3.62287e7 −0.163536
\(123\) 4.49040e7 0.196184
\(124\) 2.87278e8i 1.21511i
\(125\) 2.52057e8 1.03243
\(126\) 5.82338e7i 0.231043i
\(127\) 1.91244e7 0.0735144 0.0367572 0.999324i \(-0.488297\pi\)
0.0367572 + 0.999324i \(0.488297\pi\)
\(128\) 2.06830e8i 0.770501i
\(129\) 1.00762e6i 0.00363862i
\(130\) −3.93596e8 −1.37809
\(131\) 1.24907e8i 0.424133i 0.977255 + 0.212066i \(0.0680193\pi\)
−0.977255 + 0.212066i \(0.931981\pi\)
\(132\) 1.60347e8i 0.528159i
\(133\) −1.91076e8 −0.610661
\(134\) 1.13108e8 0.350811
\(135\) −6.15996e7 −0.185457
\(136\) 2.27267e8i 0.664326i
\(137\) −1.18066e8 −0.335153 −0.167577 0.985859i \(-0.553594\pi\)
−0.167577 + 0.985859i \(0.553594\pi\)
\(138\) −4.00254e8 −1.10362
\(139\) 5.31707e8 1.42434 0.712170 0.702007i \(-0.247713\pi\)
0.712170 + 0.702007i \(0.247713\pi\)
\(140\) 1.35939e8 0.353861
\(141\) 4.99944e6i 0.0126487i
\(142\) 5.60797e8i 1.37928i
\(143\) 6.11587e8 1.46256
\(144\) −1.74073e8 −0.404838
\(145\) 1.73684e8 0.392905
\(146\) −4.64432e8 −1.02214
\(147\) −1.92880e8 −0.413065
\(148\) 3.78510e8i 0.788916i
\(149\) 5.45532e8i 1.10681i −0.832911 0.553407i \(-0.813327\pi\)
0.832911 0.553407i \(-0.186673\pi\)
\(150\) 2.71005e7i 0.0535319i
\(151\) 2.12379e8i 0.408511i 0.978918 + 0.204255i \(0.0654773\pi\)
−0.978918 + 0.204255i \(0.934523\pi\)
\(152\) 2.47431e8i 0.463532i
\(153\) 2.99686e8 0.546892
\(154\) −5.18076e8 −0.921108
\(155\) 9.81835e8i 1.70103i
\(156\) 2.59051e8i 0.437407i
\(157\) 8.76380e8i 1.44243i −0.692713 0.721213i \(-0.743585\pi\)
0.692713 0.721213i \(-0.256415\pi\)
\(158\) 2.65610e8i 0.426203i
\(159\) −6.93089e8 −1.08443
\(160\) 7.40928e8i 1.13057i
\(161\) 5.27263e8i 0.784736i
\(162\) 9.94381e7i 0.144375i
\(163\) −8.37355e8 −1.18620 −0.593101 0.805128i \(-0.702097\pi\)
−0.593101 + 0.805128i \(0.702097\pi\)
\(164\) −1.69211e8 −0.233913
\(165\) 5.48019e8i 0.739367i
\(166\) 1.33730e9 1.76115
\(167\) 1.08575e9 1.39593 0.697963 0.716133i \(-0.254090\pi\)
0.697963 + 0.716133i \(0.254090\pi\)
\(168\) 9.93378e7i 0.124703i
\(169\) −1.72327e8 −0.211254
\(170\) 1.71584e9i 2.05439i
\(171\) −3.26275e8 −0.381592
\(172\) 3.79699e6i 0.00433836i
\(173\) 4.68803e8i 0.523367i −0.965154 0.261683i \(-0.915722\pi\)
0.965154 0.261683i \(-0.0842776\pi\)
\(174\) 2.80372e8i 0.305871i
\(175\) −3.57001e7 −0.0380642
\(176\) 1.54863e9i 1.61398i
\(177\) 1.95785e8 + 5.31777e8i 0.199474 + 0.541796i
\(178\) 6.47252e8 0.644753
\(179\) 1.14428e9i 1.11460i −0.830310 0.557302i \(-0.811836\pi\)
0.830310 0.557302i \(-0.188164\pi\)
\(180\) 2.32125e8 0.221122
\(181\) −1.96453e9 −1.83039 −0.915197 0.403006i \(-0.867965\pi\)
−0.915197 + 0.403006i \(0.867965\pi\)
\(182\) 8.36985e8 0.762838
\(183\) 8.14932e7i 0.0726636i
\(184\) −6.82770e8 −0.595667
\(185\) 1.29364e9i 1.10440i
\(186\) −1.58494e9 −1.32423
\(187\) 2.66615e9i 2.18031i
\(188\) 1.88393e7i 0.0150812i
\(189\) 1.30992e8 0.102659
\(190\) 1.86808e9i 1.43344i
\(191\) 2.38546e9i 1.79241i −0.443638 0.896206i \(-0.646312\pi\)
0.443638 0.896206i \(-0.353688\pi\)
\(192\) 2.43158e8 0.178930
\(193\) −2.68938e9 −1.93831 −0.969155 0.246451i \(-0.920735\pi\)
−0.969155 + 0.246451i \(0.920735\pi\)
\(194\) −7.60567e8 −0.536946
\(195\) 8.85360e8i 0.612324i
\(196\) 7.26830e8 0.492502
\(197\) −1.73442e9 −1.15157 −0.575784 0.817602i \(-0.695303\pi\)
−0.575784 + 0.817602i \(0.695303\pi\)
\(198\) −8.84649e8 −0.575586
\(199\) 1.06579e9 0.679610 0.339805 0.940496i \(-0.389639\pi\)
0.339805 + 0.940496i \(0.389639\pi\)
\(200\) 4.62292e7i 0.0288933i
\(201\) 2.54426e8i 0.155875i
\(202\) −1.46773e8 −0.0881538
\(203\) −3.69340e8 −0.217492
\(204\) −1.12931e9 −0.652065
\(205\) −5.78316e8 −0.327453
\(206\) 1.39067e9 0.772244
\(207\) 9.00336e8i 0.490369i
\(208\) 2.50192e9i 1.33666i
\(209\) 2.90270e9i 1.52131i
\(210\) 7.49990e8i 0.385636i
\(211\) 1.55428e9i 0.784149i −0.919933 0.392075i \(-0.871757\pi\)
0.919933 0.392075i \(-0.128243\pi\)
\(212\) 2.61176e9 1.29298
\(213\) −1.26146e9 −0.612853
\(214\) 4.71018e9i 2.24586i
\(215\) 1.29770e7i 0.00607325i
\(216\) 1.69626e8i 0.0779250i
\(217\) 2.08788e9i 0.941600i
\(218\) −1.44358e8 −0.0639169
\(219\) 1.04470e9i 0.454166i
\(220\) 2.06510e9i 0.881555i
\(221\) 4.30734e9i 1.80568i
\(222\) 2.08828e9 0.859758
\(223\) 8.02134e8 0.324360 0.162180 0.986761i \(-0.448147\pi\)
0.162180 + 0.986761i \(0.448147\pi\)
\(224\) 1.57559e9i 0.625822i
\(225\) −6.09602e7 −0.0237857
\(226\) 3.75113e9 1.43790
\(227\) 7.27978e7i 0.0274167i −0.999906 0.0137083i \(-0.995636\pi\)
0.999906 0.0137083i \(-0.00436364\pi\)
\(228\) 1.22950e9 0.454977
\(229\) 2.46205e9i 0.895271i 0.894216 + 0.447635i \(0.147734\pi\)
−0.894216 + 0.447635i \(0.852266\pi\)
\(230\) 5.15484e9 1.84206
\(231\) 1.16537e9i 0.409275i
\(232\) 4.78271e8i 0.165090i
\(233\) 4.04138e9i 1.37122i −0.727971 0.685608i \(-0.759536\pi\)
0.727971 0.685608i \(-0.240464\pi\)
\(234\) 1.42921e9 0.476685
\(235\) 6.43875e7i 0.0211120i
\(236\) −7.37776e8 2.00389e9i −0.237835 0.645990i
\(237\) −5.97467e8 −0.189374
\(238\) 3.64876e9i 1.13720i
\(239\) 2.73887e9 0.839421 0.419711 0.907658i \(-0.362132\pi\)
0.419711 + 0.907658i \(0.362132\pi\)
\(240\) 2.24187e9 0.675718
\(241\) 1.16077e9 0.344094 0.172047 0.985089i \(-0.444962\pi\)
0.172047 + 0.985089i \(0.444962\pi\)
\(242\) 3.41373e9i 0.995333i
\(243\) 2.23677e8 0.0641500
\(244\) 3.07090e8i 0.0866376i
\(245\) 2.48409e9 0.689452
\(246\) 9.33556e8i 0.254918i
\(247\) 4.68950e9i 1.25991i
\(248\) −2.70366e9 −0.714737
\(249\) 3.00814e9i 0.782530i
\(250\) 5.24027e9i 1.34151i
\(251\) −2.40560e9 −0.606077 −0.303039 0.952978i \(-0.598001\pi\)
−0.303039 + 0.952978i \(0.598001\pi\)
\(252\) −4.93616e8 −0.122402
\(253\) −8.00982e9 −1.95497
\(254\) 3.97597e8i 0.0955230i
\(255\) −3.85964e9 −0.912823
\(256\) 5.63108e9 1.31109
\(257\) −4.85521e9 −1.11295 −0.556475 0.830864i \(-0.687846\pi\)
−0.556475 + 0.830864i \(0.687846\pi\)
\(258\) 2.09484e7 0.00472793
\(259\) 2.75093e9i 0.611337i
\(260\) 3.33630e9i 0.730081i
\(261\) −6.30673e8 −0.135907
\(262\) 2.59682e9 0.551108
\(263\) 3.33459e9 0.696978 0.348489 0.937313i \(-0.386695\pi\)
0.348489 + 0.937313i \(0.386695\pi\)
\(264\) −1.50907e9 −0.310667
\(265\) 8.92625e9 1.81003
\(266\) 3.97248e9i 0.793479i
\(267\) 1.45594e9i 0.286482i
\(268\) 9.58753e8i 0.185852i
\(269\) 4.70921e9i 0.899370i −0.893187 0.449685i \(-0.851536\pi\)
0.893187 0.449685i \(-0.148464\pi\)
\(270\) 1.28066e9i 0.240978i
\(271\) 2.40442e9 0.445793 0.222896 0.974842i \(-0.428449\pi\)
0.222896 + 0.974842i \(0.428449\pi\)
\(272\) −1.09069e10 −1.99262
\(273\) 1.88272e9i 0.338950i
\(274\) 2.45460e9i 0.435490i
\(275\) 5.42331e8i 0.0948274i
\(276\) 3.39273e9i 0.584673i
\(277\) −4.90773e8 −0.0833608 −0.0416804 0.999131i \(-0.513271\pi\)
−0.0416804 + 0.999131i \(0.513271\pi\)
\(278\) 1.10542e10i 1.85075i
\(279\) 3.56519e9i 0.588391i
\(280\) 1.27937e9i 0.208143i
\(281\) 1.05372e10 1.69006 0.845028 0.534723i \(-0.179584\pi\)
0.845028 + 0.534723i \(0.179584\pi\)
\(282\) −1.03939e8 −0.0164354
\(283\) 3.49969e8i 0.0545611i −0.999628 0.0272806i \(-0.991315\pi\)
0.999628 0.0272806i \(-0.00868475\pi\)
\(284\) 4.75357e9 0.730712
\(285\) 4.20208e9 0.636920
\(286\) 1.27149e10i 1.90042i
\(287\) 1.22979e9 0.181261
\(288\) 2.69042e9i 0.391067i
\(289\) 1.18017e10 1.69182
\(290\) 3.61089e9i 0.510532i
\(291\) 1.71083e9i 0.238580i
\(292\) 3.93673e9i 0.541507i
\(293\) −3.02477e9 −0.410414 −0.205207 0.978719i \(-0.565787\pi\)
−0.205207 + 0.978719i \(0.565787\pi\)
\(294\) 4.00999e9i 0.536728i
\(295\) −2.52151e9 6.84872e9i −0.332944 0.904318i
\(296\) 3.56228e9 0.464046
\(297\) 1.98994e9i 0.255749i
\(298\) −1.13416e10 −1.43817
\(299\) 1.29404e10 1.61906
\(300\) 2.29716e8 0.0283600
\(301\) 2.75957e7i 0.00336183i
\(302\) 4.41536e9 0.530810
\(303\) 3.30153e8i 0.0391692i
\(304\) 1.18746e10 1.39035
\(305\) 1.04955e9i 0.121284i
\(306\) 6.23049e9i 0.710619i
\(307\) −1.28019e10 −1.44118 −0.720592 0.693359i \(-0.756130\pi\)
−0.720592 + 0.693359i \(0.756130\pi\)
\(308\) 4.39144e9i 0.487983i
\(309\) 3.12819e9i 0.343130i
\(310\) 2.04124e10 2.21028
\(311\) −5.47848e9 −0.585623 −0.292812 0.956170i \(-0.594591\pi\)
−0.292812 + 0.956170i \(0.594591\pi\)
\(312\) 2.43800e9 0.257286
\(313\) 3.97064e9i 0.413698i 0.978373 + 0.206849i \(0.0663209\pi\)
−0.978373 + 0.206849i \(0.933679\pi\)
\(314\) −1.82200e10 −1.87426
\(315\) −1.68704e9 −0.171349
\(316\) 2.25143e9 0.225793
\(317\) −5.72571e9 −0.567012 −0.283506 0.958970i \(-0.591498\pi\)
−0.283506 + 0.958970i \(0.591498\pi\)
\(318\) 1.44094e10i 1.40908i
\(319\) 5.61077e9i 0.541826i
\(320\) −3.13162e9 −0.298654
\(321\) −1.05951e10 −0.997899
\(322\) −1.09618e10 −1.01967
\(323\) −2.04434e10 −1.87821
\(324\) −8.42882e8 −0.0764868
\(325\) 8.76171e8i 0.0785336i
\(326\) 1.74086e10i 1.54133i
\(327\) 3.24721e8i 0.0284001i
\(328\) 1.59250e9i 0.137589i
\(329\) 1.36920e8i 0.0116865i
\(330\) 1.13933e10 0.960717
\(331\) −1.50335e10 −1.25241 −0.626207 0.779657i \(-0.715393\pi\)
−0.626207 + 0.779657i \(0.715393\pi\)
\(332\) 1.13356e10i 0.933019i
\(333\) 4.69740e9i 0.382015i
\(334\) 2.25727e10i 1.81384i
\(335\) 3.27674e9i 0.260173i
\(336\) −4.76736e9 −0.374042
\(337\) 1.42090e10i 1.10165i 0.834622 + 0.550824i \(0.185686\pi\)
−0.834622 + 0.550824i \(0.814314\pi\)
\(338\) 3.58268e9i 0.274499i
\(339\) 8.43785e9i 0.638900i
\(340\) 1.45443e10 1.08837
\(341\) −3.17177e10 −2.34576
\(342\) 6.78327e9i 0.495832i
\(343\) −1.26658e10 −0.915076
\(344\) 3.57346e7 0.00255185
\(345\) 1.15954e10i 0.818480i
\(346\) −9.74643e9 −0.680051
\(347\) 2.07944e10i 1.43426i −0.696938 0.717131i \(-0.745455\pi\)
0.696938 0.717131i \(-0.254545\pi\)
\(348\) 2.37656e9 0.162043
\(349\) 2.15161e10i 1.45032i −0.688582 0.725158i \(-0.741767\pi\)
0.688582 0.725158i \(-0.258233\pi\)
\(350\) 7.42206e8i 0.0494598i
\(351\) 3.21488e9i 0.211805i
\(352\) 2.39353e10 1.55908
\(353\) 1.48394e9i 0.0955693i −0.998858 0.0477847i \(-0.984784\pi\)
0.998858 0.0477847i \(-0.0152161\pi\)
\(354\) 1.10557e10 4.07038e9i 0.703998 0.259192i
\(355\) 1.62463e10 1.02292
\(356\) 5.48640e9i 0.341576i
\(357\) 8.20756e9 0.505291
\(358\) −2.37897e10 −1.44829
\(359\) 4.06704e9 0.244851 0.122425 0.992478i \(-0.460933\pi\)
0.122425 + 0.992478i \(0.460933\pi\)
\(360\) 2.18460e9i 0.130065i
\(361\) 5.27364e9 0.310515
\(362\) 4.08427e10i 2.37837i
\(363\) −7.67890e9 −0.442255
\(364\) 7.09466e9i 0.404134i
\(365\) 1.34546e10i 0.758053i
\(366\) −1.69425e9 −0.0944174
\(367\) 5.50301e9i 0.303345i 0.988431 + 0.151672i \(0.0484658\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(368\) 3.27671e10i 1.78668i
\(369\) 2.09995e9 0.113267
\(370\) −2.68948e10 −1.43503
\(371\) −1.89817e10 −1.00194
\(372\) 1.34347e10i 0.701545i
\(373\) 3.30749e10 1.70869 0.854346 0.519705i \(-0.173958\pi\)
0.854346 + 0.519705i \(0.173958\pi\)
\(374\) −5.54295e10 −2.83305
\(375\) 1.17875e10 0.596071
\(376\) −1.77303e8 −0.00887083
\(377\) 9.06455e9i 0.448726i
\(378\) 2.72333e9i 0.133393i
\(379\) 1.41681e10 0.686679 0.343339 0.939211i \(-0.388442\pi\)
0.343339 + 0.939211i \(0.388442\pi\)
\(380\) −1.58347e10 −0.759407
\(381\) 8.94359e8 0.0424436
\(382\) −4.95937e10 −2.32902
\(383\) −8.97160e9 −0.416941 −0.208471 0.978029i \(-0.566849\pi\)
−0.208471 + 0.978029i \(0.566849\pi\)
\(384\) 9.67248e9i 0.444849i
\(385\) 1.50087e10i 0.683124i
\(386\) 5.59124e10i 2.51860i
\(387\) 4.71215e7i 0.00210076i
\(388\) 6.44690e9i 0.284462i
\(389\) 3.52009e9 0.153729 0.0768644 0.997042i \(-0.475509\pi\)
0.0768644 + 0.997042i \(0.475509\pi\)
\(390\) −1.84067e10 −0.795640
\(391\) 5.64123e10i 2.41361i
\(392\) 6.84042e9i 0.289693i
\(393\) 5.84132e9i 0.244873i
\(394\) 3.60587e10i 1.49632i
\(395\) 7.69474e9 0.316086
\(396\) 7.49868e9i 0.304933i
\(397\) 1.68100e10i 0.676716i 0.941017 + 0.338358i \(0.109872\pi\)
−0.941017 + 0.338358i \(0.890128\pi\)
\(398\) 2.21578e10i 0.883070i
\(399\) −8.93575e9 −0.352565
\(400\) 2.21860e9 0.0866642
\(401\) 4.92452e10i 1.90452i −0.305281 0.952262i \(-0.598751\pi\)
0.305281 0.952262i \(-0.401249\pi\)
\(402\) 5.28953e9 0.202541
\(403\) 5.12419e10 1.94270
\(404\) 1.24411e9i 0.0467019i
\(405\) −2.88073e9 −0.107073
\(406\) 7.67859e9i 0.282604i
\(407\) 4.17903e10 1.52299
\(408\) 1.06282e10i 0.383549i
\(409\) 1.58367e9i 0.0565941i −0.999600 0.0282970i \(-0.990992\pi\)
0.999600 0.0282970i \(-0.00900843\pi\)
\(410\) 1.20232e10i 0.425486i
\(411\) −5.52141e9 −0.193501
\(412\) 1.17879e10i 0.409118i
\(413\) 5.36200e9 + 1.45638e10i 0.184301 + 0.500583i
\(414\) −1.87180e10 −0.637174
\(415\) 3.87417e10i 1.30613i
\(416\) −3.86690e10 −1.29119
\(417\) 2.48655e10 0.822343
\(418\) 6.03473e10 1.97675
\(419\) 5.04742e10i 1.63762i −0.574064 0.818811i \(-0.694634\pi\)
0.574064 0.818811i \(-0.305366\pi\)
\(420\) 6.35725e9 0.204302
\(421\) 6.73644e9i 0.214438i −0.994235 0.107219i \(-0.965805\pi\)
0.994235 0.107219i \(-0.0341946\pi\)
\(422\) −3.23135e10 −1.01891
\(423\) 2.33801e8i 0.00730271i
\(424\) 2.45801e10i 0.760537i
\(425\) −3.81958e9 −0.117074
\(426\) 2.62259e10i 0.796328i
\(427\) 2.23187e9i 0.0671362i
\(428\) 3.99256e10 1.18981
\(429\) 2.86011e10 0.844410
\(430\) −2.69793e8 −0.00789144
\(431\) 6.35021e10i 1.84026i 0.391615 + 0.920129i \(0.371917\pi\)
−0.391615 + 0.920129i \(0.628083\pi\)
\(432\) −8.14058e9 −0.233733
\(433\) −4.18521e10 −1.19060 −0.595300 0.803503i \(-0.702967\pi\)
−0.595300 + 0.803503i \(0.702967\pi\)
\(434\) −4.34071e10 −1.22349
\(435\) 8.12239e9 0.226844
\(436\) 1.22364e9i 0.0338618i
\(437\) 6.14173e10i 1.68409i
\(438\) −2.17193e10 −0.590133
\(439\) 7.14779e10 1.92448 0.962241 0.272200i \(-0.0877513\pi\)
0.962241 + 0.272200i \(0.0877513\pi\)
\(440\) 1.94353e10 0.518537
\(441\) −9.02012e9 −0.238483
\(442\) 8.95498e10 2.34626
\(443\) 5.53832e10i 1.43801i 0.695003 + 0.719007i \(0.255403\pi\)
−0.695003 + 0.719007i \(0.744597\pi\)
\(444\) 1.77012e10i 0.455481i
\(445\) 1.87509e10i 0.478170i
\(446\) 1.66764e10i 0.421466i
\(447\) 2.55120e10i 0.639020i
\(448\) 6.65941e9 0.165319
\(449\) 4.87436e10 1.19931 0.599657 0.800257i \(-0.295304\pi\)
0.599657 + 0.800257i \(0.295304\pi\)
\(450\) 1.26737e9i 0.0309066i
\(451\) 1.86822e10i 0.451566i
\(452\) 3.17963e10i 0.761768i
\(453\) 9.93198e9i 0.235854i
\(454\) −1.51347e9 −0.0356246
\(455\) 2.42475e10i 0.565746i
\(456\) 1.15712e10i 0.267620i
\(457\) 4.73704e10i 1.08603i −0.839722 0.543016i \(-0.817282\pi\)
0.839722 0.543016i \(-0.182718\pi\)
\(458\) 5.11860e10 1.16329
\(459\) 1.40149e10 0.315748
\(460\) 4.36947e10i 0.975883i
\(461\) 6.58324e10 1.45759 0.728796 0.684731i \(-0.240080\pi\)
0.728796 + 0.684731i \(0.240080\pi\)
\(462\) −2.42280e10 −0.531802
\(463\) 6.41251e10i 1.39542i −0.716381 0.697709i \(-0.754203\pi\)
0.716381 0.697709i \(-0.245797\pi\)
\(464\) 2.29529e10 0.495182
\(465\) 4.59159e10i 0.982089i
\(466\) −8.40204e10 −1.78173
\(467\) 2.86597e10i 0.602566i 0.953535 + 0.301283i \(0.0974148\pi\)
−0.953535 + 0.301283i \(0.902585\pi\)
\(468\) 1.21146e10i 0.252537i
\(469\) 6.96801e9i 0.144018i
\(470\) 1.33862e9 0.0274325
\(471\) 4.09842e10i 0.832785i
\(472\) 1.88592e10 6.94343e9i 0.379976 0.139896i
\(473\) 4.19216e8 0.00837516
\(474\) 1.24214e10i 0.246068i
\(475\) 4.15846e9 0.0816881
\(476\) −3.09285e10 −0.602464
\(477\) −3.24126e10 −0.626095
\(478\) 5.69412e10i 1.09072i
\(479\) 7.46400e10 1.41785 0.708924 0.705285i \(-0.249181\pi\)
0.708924 + 0.705285i \(0.249181\pi\)
\(480\) 3.46498e10i 0.652733i
\(481\) −6.75149e10 −1.26130
\(482\) 2.41324e10i 0.447108i
\(483\) 2.46576e10i 0.453067i
\(484\) 2.89363e10 0.527305
\(485\) 2.20337e10i 0.398217i
\(486\) 4.65026e9i 0.0833551i
\(487\) −6.01198e9 −0.106881 −0.0534406 0.998571i \(-0.517019\pi\)
−0.0534406 + 0.998571i \(0.517019\pi\)
\(488\) −2.89012e9 −0.0509608
\(489\) −3.91592e10 −0.684855
\(490\) 5.16444e10i 0.895858i
\(491\) 1.02951e11 1.77136 0.885679 0.464299i \(-0.153694\pi\)
0.885679 + 0.464299i \(0.153694\pi\)
\(492\) −7.91323e9 −0.135050
\(493\) −3.95161e10 −0.668938
\(494\) −9.74948e10 −1.63709
\(495\) 2.56283e10i 0.426874i
\(496\) 1.29753e11i 2.14382i
\(497\) −3.45479e10 −0.566234
\(498\) 6.25394e10 1.01680
\(499\) −8.73352e10 −1.40860 −0.704299 0.709903i \(-0.748739\pi\)
−0.704299 + 0.709903i \(0.748739\pi\)
\(500\) −4.44189e10 −0.710702
\(501\) 5.07753e10 0.805939
\(502\) 5.00124e10i 0.787523i
\(503\) 9.91846e9i 0.154943i −0.996995 0.0774716i \(-0.975315\pi\)
0.996995 0.0774716i \(-0.0246847\pi\)
\(504\) 4.64557e9i 0.0719974i
\(505\) 4.25202e9i 0.0653778i
\(506\) 1.66524e11i 2.54025i
\(507\) −8.05892e9 −0.121968
\(508\) −3.37021e9 −0.0506059
\(509\) 8.51383e10i 1.26839i −0.773172 0.634197i \(-0.781331\pi\)
0.773172 0.634197i \(-0.218669\pi\)
\(510\) 8.02421e10i 1.18610i
\(511\) 2.86113e10i 0.419618i
\(512\) 6.41219e10i 0.933097i
\(513\) −1.52584e10 −0.220312
\(514\) 1.00940e11i 1.44614i
\(515\) 4.02877e10i 0.572722i
\(516\) 1.77568e8i 0.00250475i
\(517\) −2.08000e9 −0.0291140
\(518\) 5.71920e10 0.794358
\(519\) 2.19238e10i 0.302166i
\(520\) −3.13989e10 −0.429438
\(521\) −2.11893e10 −0.287585 −0.143792 0.989608i \(-0.545930\pi\)
−0.143792 + 0.989608i \(0.545930\pi\)
\(522\) 1.31117e10i 0.176595i
\(523\) 4.36038e10 0.582798 0.291399 0.956602i \(-0.405879\pi\)
0.291399 + 0.956602i \(0.405879\pi\)
\(524\) 2.20118e10i 0.291965i
\(525\) −1.66953e9 −0.0219764
\(526\) 6.93262e10i 0.905638i
\(527\) 2.23384e11i 2.89608i
\(528\) 7.24225e10i 0.931832i
\(529\) −9.11662e10 −1.16416
\(530\) 1.85577e11i 2.35191i
\(531\) 9.15597e9 + 2.48687e10i 0.115167 + 0.312806i
\(532\) 3.36725e10 0.420367
\(533\) 3.01823e10i 0.373975i
\(534\) 3.02690e10 0.372248
\(535\) 1.36454e11 1.66560
\(536\) 9.02311e9 0.109319
\(537\) 5.35128e10i 0.643517i
\(538\) −9.79045e10 −1.16862
\(539\) 8.02474e10i 0.950770i
\(540\) 1.08554e10 0.127665
\(541\) 4.90102e10i 0.572133i −0.958210 0.286067i \(-0.907652\pi\)
0.958210 0.286067i \(-0.0923479\pi\)
\(542\) 4.99880e10i 0.579253i
\(543\) −9.18721e10 −1.05678
\(544\) 1.68574e11i 1.92484i
\(545\) 4.18207e9i 0.0474029i
\(546\) 3.91419e10 0.440424
\(547\) 4.37934e10 0.489169 0.244585 0.969628i \(-0.421348\pi\)
0.244585 + 0.969628i \(0.421348\pi\)
\(548\) 2.08063e10 0.230713
\(549\) 3.81106e9i 0.0419524i
\(550\) 1.12751e10 0.123217
\(551\) 4.30220e10 0.466750
\(552\) −3.19300e10 −0.343908
\(553\) −1.63629e10 −0.174969
\(554\) 1.02032e10i 0.108317i
\(555\) 6.04975e10i 0.637625i
\(556\) −9.37005e10 −0.980489
\(557\) 1.51954e11 1.57867 0.789333 0.613965i \(-0.210427\pi\)
0.789333 + 0.613965i \(0.210427\pi\)
\(558\) −7.41205e10 −0.764542
\(559\) −6.77270e8 −0.00693609
\(560\) 6.13985e10 0.624317
\(561\) 1.24684e11i 1.25880i
\(562\) 2.19069e11i 2.19602i
\(563\) 1.75330e11i 1.74511i 0.488515 + 0.872555i \(0.337539\pi\)
−0.488515 + 0.872555i \(0.662461\pi\)
\(564\) 8.81029e8i 0.00870711i
\(565\) 1.08671e11i 1.06639i
\(566\) −7.27586e9 −0.0708955
\(567\) 6.12589e9 0.0592702
\(568\) 4.47373e10i 0.429809i
\(569\) 5.01500e10i 0.478434i −0.970966 0.239217i \(-0.923109\pi\)
0.970966 0.239217i \(-0.0768907\pi\)
\(570\) 8.73614e10i 0.827599i
\(571\) 5.51474e10i 0.518777i −0.965773 0.259389i \(-0.916479\pi\)
0.965773 0.259389i \(-0.0835210\pi\)
\(572\) −1.07777e11 −1.00680
\(573\) 1.11557e11i 1.03485i
\(574\) 2.55674e10i 0.235526i
\(575\) 1.14750e10i 0.104974i
\(576\) 1.13714e10 0.103305
\(577\) −4.02122e10 −0.362789 −0.181395 0.983410i \(-0.558061\pi\)
−0.181395 + 0.983410i \(0.558061\pi\)
\(578\) 2.45358e11i 2.19831i
\(579\) −1.25770e11 −1.11908
\(580\) −3.06076e10 −0.270468
\(581\) 8.23844e10i 0.723004i
\(582\) −3.55682e10 −0.310006
\(583\) 2.88358e11i 2.49608i
\(584\) −3.70498e10 −0.318518
\(585\) 4.14042e10i 0.353526i
\(586\) 6.28852e10i 0.533283i
\(587\) 1.68429e11i 1.41862i −0.704898 0.709309i \(-0.749007\pi\)
0.704898 0.709309i \(-0.250993\pi\)
\(588\) 3.39905e10 0.284346
\(589\) 2.43203e11i 2.02073i
\(590\) −1.42385e11 + 5.24222e10i −1.17505 + 0.432620i
\(591\) −8.11109e10 −0.664858
\(592\) 1.70958e11i 1.39189i
\(593\) 2.68170e10 0.216866 0.108433 0.994104i \(-0.465417\pi\)
0.108433 + 0.994104i \(0.465417\pi\)
\(594\) −4.13709e10 −0.332315
\(595\) −1.05705e11 −0.843386
\(596\) 9.61366e10i 0.761910i
\(597\) 4.98421e10 0.392373
\(598\) 2.69031e11i 2.10377i
\(599\) 2.26978e11 1.76310 0.881549 0.472092i \(-0.156501\pi\)
0.881549 + 0.472092i \(0.156501\pi\)
\(600\) 2.16193e9i 0.0166815i
\(601\) 1.68922e11i 1.29475i 0.762170 + 0.647377i \(0.224134\pi\)
−0.762170 + 0.647377i \(0.775866\pi\)
\(602\) 5.73716e8 0.00436829
\(603\) 1.18983e10i 0.0899948i
\(604\) 3.74266e10i 0.281211i
\(605\) 9.88960e10 0.738172
\(606\) −6.86390e9 −0.0508956
\(607\) 1.62456e11 1.19669 0.598344 0.801239i \(-0.295826\pi\)
0.598344 + 0.801239i \(0.295826\pi\)
\(608\) 1.83530e11i 1.34305i
\(609\) −1.72723e10 −0.125569
\(610\) 2.18201e10 0.157593
\(611\) 3.36038e9 0.0241114
\(612\) −5.28124e10 −0.376470
\(613\) 1.28216e11i 0.908027i −0.890995 0.454013i \(-0.849992\pi\)
0.890995 0.454013i \(-0.150008\pi\)
\(614\) 2.66151e11i 1.87264i
\(615\) −2.70451e10 −0.189055
\(616\) −4.13292e10 −0.287035
\(617\) 3.11451e10 0.214906 0.107453 0.994210i \(-0.465730\pi\)
0.107453 + 0.994210i \(0.465730\pi\)
\(618\) 6.50351e10 0.445856
\(619\) −2.72037e11 −1.85296 −0.926480 0.376344i \(-0.877181\pi\)
−0.926480 + 0.376344i \(0.877181\pi\)
\(620\) 1.73024e11i 1.17096i
\(621\) 4.21045e10i 0.283115i
\(622\) 1.13898e11i 0.760945i
\(623\) 3.98740e10i 0.264690i
\(624\) 1.17003e11i 0.771719i
\(625\) −1.40923e11 −0.923551
\(626\) 8.25498e10 0.537550
\(627\) 1.35746e11i 0.878328i
\(628\) 1.54441e11i 0.992939i
\(629\) 2.94325e11i 1.88029i
\(630\) 3.50735e10i 0.222647i
\(631\) −1.70619e11 −1.07624 −0.538121 0.842867i \(-0.680866\pi\)
−0.538121 + 0.842867i \(0.680866\pi\)
\(632\) 2.11889e10i 0.132813i
\(633\) 7.26864e10i 0.452729i
\(634\) 1.19038e11i 0.736763i
\(635\) −1.15184e10 −0.0708430
\(636\) 1.22140e11 0.746500
\(637\) 1.29645e11i 0.787403i
\(638\) 1.16648e11 0.704036
\(639\) −5.89928e10 −0.353831
\(640\) 1.24571e11i 0.742502i
\(641\) −9.03740e10 −0.535317 −0.267659 0.963514i \(-0.586250\pi\)
−0.267659 + 0.963514i \(0.586250\pi\)
\(642\) 2.20273e11i 1.29665i
\(643\) −9.94208e10 −0.581612 −0.290806 0.956782i \(-0.593923\pi\)
−0.290806 + 0.956782i \(0.593923\pi\)
\(644\) 9.29172e10i 0.540197i
\(645\) 6.06875e8i 0.00350639i
\(646\) 4.25020e11i 2.44050i
\(647\) 2.16018e11 1.23274 0.616372 0.787455i \(-0.288602\pi\)
0.616372 + 0.787455i \(0.288602\pi\)
\(648\) 7.93261e9i 0.0449900i
\(649\) 2.21244e11 8.14559e10i 1.24708 0.459139i
\(650\) −1.82156e10 −0.102045
\(651\) 9.76404e10i 0.543633i
\(652\) 1.47563e11 0.816560
\(653\) −1.67238e10 −0.0919777 −0.0459888 0.998942i \(-0.514644\pi\)
−0.0459888 + 0.998942i \(0.514644\pi\)
\(654\) −6.75097e9 −0.0369024
\(655\) 7.52300e10i 0.408720i
\(656\) −7.64262e10 −0.412693
\(657\) 4.88557e10i 0.262213i
\(658\) −2.84658e9 −0.0151852
\(659\) 1.66939e11i 0.885147i −0.896732 0.442574i \(-0.854066\pi\)
0.896732 0.442574i \(-0.145934\pi\)
\(660\) 9.65750e10i 0.508966i
\(661\) 2.82067e11 1.47756 0.738782 0.673944i \(-0.235401\pi\)
0.738782 + 0.673944i \(0.235401\pi\)
\(662\) 3.12547e11i 1.62736i
\(663\) 2.01434e11i 1.04251i
\(664\) 1.06682e11 0.548808
\(665\) 1.15083e11 0.588470
\(666\) 9.76591e10 0.496382
\(667\) 1.18716e11i 0.599802i
\(668\) −1.91336e11 −0.960930
\(669\) 3.75121e10 0.187269
\(670\) −6.81235e10 −0.338063
\(671\) −3.39050e10 −0.167253
\(672\) 7.36830e10i 0.361319i
\(673\) 7.75508e10i 0.378030i 0.981974 + 0.189015i \(0.0605295\pi\)
−0.981974 + 0.189015i \(0.939471\pi\)
\(674\) 2.95405e11 1.43146
\(675\) −2.85083e9 −0.0137327
\(676\) 3.03684e10 0.145424
\(677\) 1.51021e11 0.718921 0.359461 0.933160i \(-0.382961\pi\)
0.359461 + 0.933160i \(0.382961\pi\)
\(678\) 1.75423e11 0.830172
\(679\) 4.68547e10i 0.220432i
\(680\) 1.36880e11i 0.640186i
\(681\) 3.40442e9i 0.0158290i
\(682\) 6.59411e11i 3.04803i
\(683\) 2.89247e11i 1.32919i 0.747206 + 0.664593i \(0.231395\pi\)
−0.747206 + 0.664593i \(0.768605\pi\)
\(684\) 5.74980e10 0.262681
\(685\) 7.11099e10 0.322974
\(686\) 2.63323e11i 1.18903i
\(687\) 1.15139e11i 0.516885i
\(688\) 1.71495e9i 0.00765418i
\(689\) 4.65861e11i 2.06718i
\(690\) 2.41068e11 1.06351
\(691\) 1.18108e10i 0.0518046i 0.999664 + 0.0259023i \(0.00824587\pi\)
−0.999664 + 0.0259023i \(0.991754\pi\)
\(692\) 8.26151e10i 0.360276i
\(693\) 5.44988e10i 0.236295i
\(694\) −4.32317e11 −1.86365
\(695\) −3.20241e11 −1.37258
\(696\) 2.23665e10i 0.0953150i
\(697\) 1.31577e11 0.557504
\(698\) −4.47322e11 −1.88451
\(699\) 1.88997e11i 0.791672i
\(700\) 6.29127e9 0.0262027
\(701\) 3.43372e11i 1.42198i 0.703203 + 0.710989i \(0.251752\pi\)
−0.703203 + 0.710989i \(0.748248\pi\)
\(702\) 6.68374e10 0.275214
\(703\) 3.20438e11i 1.31197i
\(704\) 1.01165e11i 0.411852i
\(705\) 3.01110e9i 0.0121890i
\(706\) −3.08512e10 −0.124181
\(707\) 9.04196e9i 0.0361897i
\(708\) −3.45024e10 9.37126e10i −0.137314 0.372962i
\(709\) −4.25429e10 −0.168361 −0.0841806 0.996451i \(-0.526827\pi\)
−0.0841806 + 0.996451i \(0.526827\pi\)
\(710\) 3.37761e11i 1.32916i
\(711\) −2.79408e10 −0.109335
\(712\) 5.16341e10 0.200917
\(713\) −6.71104e11 −2.59676
\(714\) 1.70635e11i 0.656563i
\(715\) −3.68352e11 −1.40941
\(716\) 2.01652e11i 0.767273i
\(717\) 1.28084e11 0.484640
\(718\) 8.45540e10i 0.318153i
\(719\) 2.07734e11i 0.777308i −0.921384 0.388654i \(-0.872940\pi\)
0.921384 0.388654i \(-0.127060\pi\)
\(720\) 1.04842e11 0.390126
\(721\) 8.56722e10i 0.317029i
\(722\) 1.09639e11i 0.403476i
\(723\) 5.42837e10 0.198663
\(724\) 3.46201e11 1.26001
\(725\) 8.03809e9 0.0290938
\(726\) 1.59645e11i 0.574656i
\(727\) 4.48539e10 0.160569 0.0802847 0.996772i \(-0.474417\pi\)
0.0802847 + 0.996772i \(0.474417\pi\)
\(728\) 6.67700e10 0.237714
\(729\) 1.04604e10 0.0370370
\(730\) 2.79722e11 0.984997
\(731\) 2.95249e9i 0.0103400i
\(732\) 1.43612e10i 0.0500203i
\(733\) −1.81016e11 −0.627047 −0.313523 0.949580i \(-0.601509\pi\)
−0.313523 + 0.949580i \(0.601509\pi\)
\(734\) 1.14408e11 0.394159
\(735\) 1.16170e11 0.398055
\(736\) 5.06439e11 1.72590
\(737\) 1.05853e11 0.358785
\(738\) 4.36581e10i 0.147177i
\(739\) 7.57291e10i 0.253913i −0.991908 0.126957i \(-0.959479\pi\)
0.991908 0.126957i \(-0.0405209\pi\)
\(740\) 2.27972e11i 0.760248i
\(741\) 2.19306e11i 0.727408i
\(742\) 3.94631e11i 1.30189i
\(743\) 4.21136e11 1.38187 0.690934 0.722918i \(-0.257199\pi\)
0.690934 + 0.722918i \(0.257199\pi\)
\(744\) −1.26438e11 −0.412653
\(745\) 3.28567e11i 1.06659i
\(746\) 6.87629e11i 2.22024i
\(747\) 1.40677e11i 0.451794i
\(748\) 4.69845e11i 1.50089i
\(749\) −2.90171e11 −0.921990
\(750\) 2.45063e11i 0.774521i
\(751\) 5.28692e11i 1.66205i 0.556237 + 0.831023i \(0.312244\pi\)
−0.556237 + 0.831023i \(0.687756\pi\)
\(752\) 8.50901e9i 0.0266077i
\(753\) −1.12499e11 −0.349919
\(754\) −1.88452e11 −0.583064
\(755\) 1.27913e11i 0.393666i
\(756\) −2.30841e10 −0.0706686
\(757\) 2.75157e10 0.0837910 0.0418955 0.999122i \(-0.486660\pi\)
0.0418955 + 0.999122i \(0.486660\pi\)
\(758\) 2.94555e11i 0.892255i
\(759\) −3.74582e11 −1.12870
\(760\) 1.49025e11i 0.446688i
\(761\) −2.00208e11 −0.596957 −0.298479 0.954416i \(-0.596479\pi\)
−0.298479 + 0.954416i \(0.596479\pi\)
\(762\) 1.85938e10i 0.0551502i
\(763\) 8.89319e9i 0.0262397i
\(764\) 4.20378e11i 1.23386i
\(765\) −1.80498e11 −0.527018
\(766\) 1.86520e11i 0.541764i
\(767\) −3.57434e11 + 1.31597e11i −1.03280 + 0.380246i
\(768\) 2.63340e11 0.756957
\(769\) 3.28397e11i 0.939060i −0.882917 0.469530i \(-0.844423\pi\)
0.882917 0.469530i \(-0.155577\pi\)
\(770\) 3.12031e11 0.887636
\(771\) −2.27056e11 −0.642562
\(772\) 4.73938e11 1.33430
\(773\) 3.06586e11i 0.858685i −0.903142 0.429343i \(-0.858745\pi\)
0.903142 0.429343i \(-0.141255\pi\)
\(774\) 9.79658e8 0.00272967
\(775\) 4.54393e10i 0.125958i
\(776\) −6.06738e10 −0.167322
\(777\) 1.28648e11i 0.352956i
\(778\) 7.31828e10i 0.199752i
\(779\) −1.43250e11 −0.388997
\(780\) 1.56023e11i 0.421512i
\(781\) 5.24829e11i 1.41063i
\(782\) −1.17281e12