Properties

Label 177.9.c.a.58.12
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 58.12
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.69

$q$-expansion

\(f(q)\) \(=\) \(q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-24.0665i q^{2} -46.7654 q^{3} -323.199 q^{4} -984.641 q^{5} +1125.48i q^{6} -1144.76 q^{7} +1617.24i q^{8} +2187.00 q^{9} +23696.9i q^{10} +25177.1i q^{11} +15114.5 q^{12} +6696.40i q^{13} +27550.5i q^{14} +46047.1 q^{15} -43817.4 q^{16} -891.553 q^{17} -52633.5i q^{18} -26924.9 q^{19} +318235. q^{20} +53535.4 q^{21} +605925. q^{22} -140383. i q^{23} -75630.9i q^{24} +578893. q^{25} +161159. q^{26} -102276. q^{27} +369987. q^{28} -177979. q^{29} -1.10820e6i q^{30} +1.04049e6i q^{31} +1.46855e6i q^{32} -1.17741e6i q^{33} +21456.6i q^{34} +1.12718e6 q^{35} -706836. q^{36} +116970. i q^{37} +647990. i q^{38} -313159. i q^{39} -1.59240e6i q^{40} +4.52564e6 q^{41} -1.28841e6i q^{42} -193497. i q^{43} -8.13719e6i q^{44} -2.15341e6 q^{45} -3.37854e6 q^{46} +2.11222e6i q^{47} +2.04914e6 q^{48} -4.45431e6 q^{49} -1.39320e7i q^{50} +41693.8 q^{51} -2.16427e6i q^{52} -1.23069e7 q^{53} +2.46143e6i q^{54} -2.47904e7i q^{55} -1.85136e6i q^{56} +1.25915e6 q^{57} +4.28334e6i q^{58} +(-1.18858e7 + 2.35778e6i) q^{59} -1.48824e7 q^{60} +1.29680e7i q^{61} +2.50410e7 q^{62} -2.50360e6 q^{63} +2.41256e7 q^{64} -6.59355e6i q^{65} -2.83363e7 q^{66} -1.51173e7i q^{67} +288149. q^{68} +6.56508e6i q^{69} -2.71274e7i q^{70} -1.88975e7 q^{71} +3.53691e6i q^{72} +4.52527e7i q^{73} +2.81506e6 q^{74} -2.70722e7 q^{75} +8.70210e6 q^{76} -2.88218e7i q^{77} -7.53667e6 q^{78} -3.05238e7 q^{79} +4.31445e7 q^{80} +4.78297e6 q^{81} -1.08917e8i q^{82} -6.98084e6i q^{83} -1.73026e7 q^{84} +877860. q^{85} -4.65680e6 q^{86} +8.32326e6 q^{87} -4.07174e7 q^{88} -7.29088e7i q^{89} +5.18252e7i q^{90} -7.66580e6i q^{91} +4.53718e7i q^{92} -4.86589e7i q^{93} +5.08339e7 q^{94} +2.65114e7 q^{95} -6.86772e7i q^{96} +5.68527e7i q^{97} +1.07200e8i q^{98} +5.50622e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.0665i 1.50416i −0.659072 0.752080i \(-0.729051\pi\)
0.659072 0.752080i \(-0.270949\pi\)
\(3\) −46.7654 −0.577350
\(4\) −323.199 −1.26250
\(5\) −984.641 −1.57543 −0.787713 0.616042i \(-0.788735\pi\)
−0.787713 + 0.616042i \(0.788735\pi\)
\(6\) 1125.48i 0.868427i
\(7\) −1144.76 −0.476787 −0.238393 0.971169i \(-0.576621\pi\)
−0.238393 + 0.971169i \(0.576621\pi\)
\(8\) 1617.24i 0.394835i
\(9\) 2187.00 0.333333
\(10\) 23696.9i 2.36969i
\(11\) 25177.1i 1.71963i 0.510608 + 0.859814i \(0.329420\pi\)
−0.510608 + 0.859814i \(0.670580\pi\)
\(12\) 15114.5 0.728902
\(13\) 6696.40i 0.234459i 0.993105 + 0.117230i \(0.0374014\pi\)
−0.993105 + 0.117230i \(0.962599\pi\)
\(14\) 27550.5i 0.717163i
\(15\) 46047.1 0.909573
\(16\) −43817.4 −0.668601
\(17\) −891.553 −0.0106746 −0.00533730 0.999986i \(-0.501699\pi\)
−0.00533730 + 0.999986i \(0.501699\pi\)
\(18\) 52633.5i 0.501386i
\(19\) −26924.9 −0.206605 −0.103302 0.994650i \(-0.532941\pi\)
−0.103302 + 0.994650i \(0.532941\pi\)
\(20\) 318235. 1.98897
\(21\) 53535.4 0.275273
\(22\) 605925. 2.58659
\(23\) 140383.i 0.501654i −0.968032 0.250827i \(-0.919297\pi\)
0.968032 0.250827i \(-0.0807026\pi\)
\(24\) 75630.9i 0.227958i
\(25\) 578893. 1.48197
\(26\) 161159. 0.352664
\(27\) −102276. −0.192450
\(28\) 369987. 0.601941
\(29\) −177979. −0.251639 −0.125819 0.992053i \(-0.540156\pi\)
−0.125819 + 0.992053i \(0.540156\pi\)
\(30\) 1.10820e6i 1.36814i
\(31\) 1.04049e6i 1.12666i 0.826234 + 0.563328i \(0.190479\pi\)
−0.826234 + 0.563328i \(0.809521\pi\)
\(32\) 1.46855e6i 1.40052i
\(33\) 1.17741e6i 0.992827i
\(34\) 21456.6i 0.0160563i
\(35\) 1.12718e6 0.751142
\(36\) −706836. −0.420832
\(37\) 116970.i 0.0624119i 0.999513 + 0.0312059i \(0.00993477\pi\)
−0.999513 + 0.0312059i \(0.990065\pi\)
\(38\) 647990.i 0.310766i
\(39\) 313159.i 0.135365i
\(40\) 1.59240e6i 0.622033i
\(41\) 4.52564e6 1.60157 0.800783 0.598954i \(-0.204417\pi\)
0.800783 + 0.598954i \(0.204417\pi\)
\(42\) 1.28841e6i 0.414054i
\(43\) 193497.i 0.0565979i −0.999600 0.0282989i \(-0.990991\pi\)
0.999600 0.0282989i \(-0.00900903\pi\)
\(44\) 8.13719e6i 2.17102i
\(45\) −2.15341e6 −0.525142
\(46\) −3.37854e6 −0.754568
\(47\) 2.11222e6i 0.432861i 0.976298 + 0.216431i \(0.0694415\pi\)
−0.976298 + 0.216431i \(0.930559\pi\)
\(48\) 2.04914e6 0.386017
\(49\) −4.45431e6 −0.772674
\(50\) 1.39320e7i 2.22911i
\(51\) 41693.8 0.00616298
\(52\) 2.16427e6i 0.296004i
\(53\) −1.23069e7 −1.55971 −0.779855 0.625960i \(-0.784707\pi\)
−0.779855 + 0.625960i \(0.784707\pi\)
\(54\) 2.46143e6i 0.289476i
\(55\) 2.47904e7i 2.70915i
\(56\) 1.85136e6i 0.188252i
\(57\) 1.25915e6 0.119283
\(58\) 4.28334e6i 0.378505i
\(59\) −1.18858e7 + 2.35778e6i −0.980887 + 0.194579i
\(60\) −1.48824e7 −1.14833
\(61\) 1.29680e7i 0.936603i 0.883569 + 0.468301i \(0.155134\pi\)
−0.883569 + 0.468301i \(0.844866\pi\)
\(62\) 2.50410e7 1.69467
\(63\) −2.50360e6 −0.158929
\(64\) 2.41256e7 1.43800
\(65\) 6.59355e6i 0.369373i
\(66\) −2.83363e7 −1.49337
\(67\) 1.51173e7i 0.750197i −0.926985 0.375098i \(-0.877609\pi\)
0.926985 0.375098i \(-0.122391\pi\)
\(68\) 288149. 0.0134766
\(69\) 6.56508e6i 0.289630i
\(70\) 2.71274e7i 1.12984i
\(71\) −1.88975e7 −0.743655 −0.371828 0.928302i \(-0.621269\pi\)
−0.371828 + 0.928302i \(0.621269\pi\)
\(72\) 3.53691e6i 0.131612i
\(73\) 4.52527e7i 1.59350i 0.604306 + 0.796752i \(0.293451\pi\)
−0.604306 + 0.796752i \(0.706549\pi\)
\(74\) 2.81506e6 0.0938774
\(75\) −2.70722e7 −0.855614
\(76\) 8.70210e6 0.260837
\(77\) 2.88218e7i 0.819895i
\(78\) −7.53667e6 −0.203611
\(79\) −3.05238e7 −0.783666 −0.391833 0.920036i \(-0.628159\pi\)
−0.391833 + 0.920036i \(0.628159\pi\)
\(80\) 4.31445e7 1.05333
\(81\) 4.78297e6 0.111111
\(82\) 1.08917e8i 2.40901i
\(83\) 6.98084e6i 0.147094i −0.997292 0.0735470i \(-0.976568\pi\)
0.997292 0.0735470i \(-0.0234319\pi\)
\(84\) −1.73026e7 −0.347531
\(85\) 877860. 0.0168170
\(86\) −4.65680e6 −0.0851322
\(87\) 8.32326e6 0.145284
\(88\) −4.07174e7 −0.678968
\(89\) 7.29088e7i 1.16204i −0.813890 0.581018i \(-0.802654\pi\)
0.813890 0.581018i \(-0.197346\pi\)
\(90\) 5.18252e7i 0.789897i
\(91\) 7.66580e6i 0.111787i
\(92\) 4.53718e7i 0.633336i
\(93\) 4.86589e7i 0.650475i
\(94\) 5.08339e7 0.651092
\(95\) 2.65114e7 0.325490
\(96\) 6.86772e7i 0.808589i
\(97\) 5.68527e7i 0.642191i 0.947047 + 0.321095i \(0.104051\pi\)
−0.947047 + 0.321095i \(0.895949\pi\)
\(98\) 1.07200e8i 1.16223i
\(99\) 5.50622e7i 0.573209i
\(100\) −1.87098e8 −1.87098
\(101\) 1.36115e8i 1.30804i −0.756478 0.654019i \(-0.773082\pi\)
0.756478 0.654019i \(-0.226918\pi\)
\(102\) 1.00343e6i 0.00927011i
\(103\) 4.47854e7i 0.397912i 0.980008 + 0.198956i \(0.0637551\pi\)
−0.980008 + 0.198956i \(0.936245\pi\)
\(104\) −1.08297e7 −0.0925727
\(105\) −5.27131e7 −0.433672
\(106\) 2.96184e8i 2.34605i
\(107\) −8.95949e7 −0.683516 −0.341758 0.939788i \(-0.611022\pi\)
−0.341758 + 0.939788i \(0.611022\pi\)
\(108\) 3.30554e7 0.242967
\(109\) 1.48038e8i 1.04874i 0.851492 + 0.524368i \(0.175698\pi\)
−0.851492 + 0.524368i \(0.824302\pi\)
\(110\) −5.96619e8 −4.07499
\(111\) 5.47014e6i 0.0360335i
\(112\) 5.01607e7 0.318780
\(113\) 9.73838e7i 0.597273i 0.954367 + 0.298637i \(0.0965319\pi\)
−0.954367 + 0.298637i \(0.903468\pi\)
\(114\) 3.03035e7i 0.179421i
\(115\) 1.38227e8i 0.790319i
\(116\) 5.75227e7 0.317692
\(117\) 1.46450e7i 0.0781531i
\(118\) 5.67437e7 + 2.86049e8i 0.292678 + 1.47541i
\(119\) 1.02062e6 0.00508951
\(120\) 7.44693e7i 0.359131i
\(121\) −4.19525e8 −1.95712
\(122\) 3.12096e8 1.40880
\(123\) −2.11643e8 −0.924665
\(124\) 3.36285e8i 1.42240i
\(125\) −1.85377e8 −0.759303
\(126\) 6.02530e7i 0.239054i
\(127\) 3.72172e8 1.43064 0.715318 0.698799i \(-0.246282\pi\)
0.715318 + 0.698799i \(0.246282\pi\)
\(128\) 2.04672e8i 0.762464i
\(129\) 9.04895e6i 0.0326768i
\(130\) −1.58684e8 −0.555597
\(131\) 5.81434e8i 1.97431i −0.159763 0.987155i \(-0.551073\pi\)
0.159763 0.987155i \(-0.448927\pi\)
\(132\) 3.80539e8i 1.25344i
\(133\) 3.08227e7 0.0985064
\(134\) −3.63821e8 −1.12842
\(135\) 1.00705e8 0.303191
\(136\) 1.44186e6i 0.00421470i
\(137\) −1.97317e8 −0.560121 −0.280061 0.959982i \(-0.590355\pi\)
−0.280061 + 0.959982i \(0.590355\pi\)
\(138\) 1.57999e8 0.435650
\(139\) −5.92003e8 −1.58586 −0.792930 0.609313i \(-0.791445\pi\)
−0.792930 + 0.609313i \(0.791445\pi\)
\(140\) −3.64304e8 −0.948313
\(141\) 9.87789e7i 0.249912i
\(142\) 4.54798e8i 1.11858i
\(143\) −1.68596e8 −0.403183
\(144\) −9.58287e7 −0.222867
\(145\) 1.75246e8 0.396438
\(146\) 1.08908e9 2.39689
\(147\) 2.08308e8 0.446104
\(148\) 3.78045e7i 0.0787947i
\(149\) 3.17764e8i 0.644703i −0.946620 0.322352i \(-0.895527\pi\)
0.946620 0.322352i \(-0.104473\pi\)
\(150\) 6.51534e8i 1.28698i
\(151\) 2.09697e8i 0.403352i 0.979452 + 0.201676i \(0.0646388\pi\)
−0.979452 + 0.201676i \(0.935361\pi\)
\(152\) 4.35441e7i 0.0815747i
\(153\) −1.94983e6 −0.00355820
\(154\) −6.93642e8 −1.23325
\(155\) 1.02451e9i 1.77496i
\(156\) 1.01213e8i 0.170898i
\(157\) 1.88420e7i 0.0310119i −0.999880 0.0155059i \(-0.995064\pi\)
0.999880 0.0155059i \(-0.00493589\pi\)
\(158\) 7.34604e8i 1.17876i
\(159\) 5.75535e8 0.900499
\(160\) 1.44599e9i 2.20641i
\(161\) 1.60706e8i 0.239182i
\(162\) 1.15110e8i 0.167129i
\(163\) 5.12195e8 0.725580 0.362790 0.931871i \(-0.381824\pi\)
0.362790 + 0.931871i \(0.381824\pi\)
\(164\) −1.46268e9 −2.02197
\(165\) 1.15933e9i 1.56413i
\(166\) −1.68005e8 −0.221253
\(167\) 1.16176e9 1.49365 0.746827 0.665018i \(-0.231576\pi\)
0.746827 + 0.665018i \(0.231576\pi\)
\(168\) 8.65796e7i 0.108687i
\(169\) 7.70889e8 0.945029
\(170\) 2.11271e7i 0.0252955i
\(171\) −5.88848e7 −0.0688682
\(172\) 6.25379e7i 0.0714545i
\(173\) 6.91440e8i 0.771916i −0.922516 0.385958i \(-0.873871\pi\)
0.922516 0.385958i \(-0.126129\pi\)
\(174\) 2.00312e8i 0.218530i
\(175\) −6.62697e8 −0.706582
\(176\) 1.10319e9i 1.14974i
\(177\) 5.55842e8 1.10263e8i 0.566315 0.112340i
\(178\) −1.75466e9 −1.74789
\(179\) 1.64428e9i 1.60163i −0.598911 0.800816i \(-0.704400\pi\)
0.598911 0.800816i \(-0.295600\pi\)
\(180\) 6.95980e8 0.662989
\(181\) −4.32961e8 −0.403399 −0.201699 0.979447i \(-0.564646\pi\)
−0.201699 + 0.979447i \(0.564646\pi\)
\(182\) −1.84489e8 −0.168146
\(183\) 6.06456e8i 0.540748i
\(184\) 2.27034e8 0.198070
\(185\) 1.15173e8i 0.0983253i
\(186\) −1.17105e9 −0.978418
\(187\) 2.24467e7i 0.0183563i
\(188\) 6.82668e8i 0.546485i
\(189\) 1.17082e8 0.0917576
\(190\) 6.38038e8i 0.489589i
\(191\) 1.24938e9i 0.938773i −0.882993 0.469386i \(-0.844475\pi\)
0.882993 0.469386i \(-0.155525\pi\)
\(192\) −1.12824e9 −0.830230
\(193\) −7.21573e8 −0.520057 −0.260028 0.965601i \(-0.583732\pi\)
−0.260028 + 0.965601i \(0.583732\pi\)
\(194\) 1.36825e9 0.965957
\(195\) 3.08350e8i 0.213258i
\(196\) 1.43963e9 0.975498
\(197\) 2.59760e9 1.72467 0.862336 0.506336i \(-0.169000\pi\)
0.862336 + 0.506336i \(0.169000\pi\)
\(198\) 1.32516e9 0.862198
\(199\) 2.46017e9 1.56875 0.784375 0.620288i \(-0.212984\pi\)
0.784375 + 0.620288i \(0.212984\pi\)
\(200\) 9.36211e8i 0.585132i
\(201\) 7.06966e8i 0.433126i
\(202\) −3.27582e9 −1.96750
\(203\) 2.03744e8 0.119978
\(204\) −1.34754e7 −0.00778074
\(205\) −4.45614e9 −2.52315
\(206\) 1.07783e9 0.598524
\(207\) 3.07019e8i 0.167218i
\(208\) 2.93419e8i 0.156760i
\(209\) 6.77891e8i 0.355283i
\(210\) 1.26862e9i 0.652312i
\(211\) 1.09561e9i 0.552747i 0.961050 + 0.276374i \(0.0891327\pi\)
−0.961050 + 0.276374i \(0.910867\pi\)
\(212\) 3.97756e9 1.96913
\(213\) 8.83750e8 0.429349
\(214\) 2.15624e9i 1.02812i
\(215\) 1.90525e8i 0.0891658i
\(216\) 1.65405e8i 0.0759859i
\(217\) 1.19112e9i 0.537174i
\(218\) 3.56275e9 1.57747
\(219\) 2.11626e9i 0.920010i
\(220\) 8.01222e9i 3.42028i
\(221\) 5.97019e6i 0.00250276i
\(222\) −1.31647e8 −0.0542001
\(223\) −1.24794e8 −0.0504630 −0.0252315 0.999682i \(-0.508032\pi\)
−0.0252315 + 0.999682i \(0.508032\pi\)
\(224\) 1.68114e9i 0.667748i
\(225\) 1.26604e9 0.493989
\(226\) 2.34369e9 0.898394
\(227\) 3.38194e9i 1.27369i −0.770993 0.636844i \(-0.780240\pi\)
0.770993 0.636844i \(-0.219760\pi\)
\(228\) −4.06957e8 −0.150595
\(229\) 2.52655e9i 0.918725i −0.888249 0.459362i \(-0.848078\pi\)
0.888249 0.459362i \(-0.151922\pi\)
\(230\) 3.32665e9 1.18877
\(231\) 1.34786e9i 0.473367i
\(232\) 2.87835e8i 0.0993556i
\(233\) 4.38522e8i 0.148788i −0.997229 0.0743940i \(-0.976298\pi\)
0.997229 0.0743940i \(-0.0237022\pi\)
\(234\) 3.52455e8 0.117555
\(235\) 2.07978e9i 0.681941i
\(236\) 3.84146e9 7.62033e8i 1.23836 0.245655i
\(237\) 1.42746e9 0.452450
\(238\) 2.45628e7i 0.00765543i
\(239\) −1.05004e9 −0.321821 −0.160910 0.986969i \(-0.551443\pi\)
−0.160910 + 0.986969i \(0.551443\pi\)
\(240\) −2.01767e9 −0.608141
\(241\) −7.95562e8 −0.235834 −0.117917 0.993023i \(-0.537622\pi\)
−0.117917 + 0.993023i \(0.537622\pi\)
\(242\) 1.00965e10i 2.94382i
\(243\) −2.23677e8 −0.0641500
\(244\) 4.19126e9i 1.18246i
\(245\) 4.38590e9 1.21729
\(246\) 5.09353e9i 1.39084i
\(247\) 1.80300e8i 0.0484404i
\(248\) −1.68272e9 −0.444842
\(249\) 3.26461e8i 0.0849248i
\(250\) 4.46138e9i 1.14211i
\(251\) −5.88382e9 −1.48240 −0.741199 0.671286i \(-0.765742\pi\)
−0.741199 + 0.671286i \(0.765742\pi\)
\(252\) 8.09161e8 0.200647
\(253\) 3.53444e9 0.862658
\(254\) 8.95690e9i 2.15190i
\(255\) −4.10535e7 −0.00970932
\(256\) 1.25041e9 0.291133
\(257\) −3.93418e9 −0.901823 −0.450912 0.892569i \(-0.648901\pi\)
−0.450912 + 0.892569i \(0.648901\pi\)
\(258\) 2.17777e8 0.0491511
\(259\) 1.33903e8i 0.0297572i
\(260\) 2.13103e9i 0.466332i
\(261\) −3.89240e8 −0.0838795
\(262\) −1.39931e10 −2.96968
\(263\) 3.00620e9 0.628340 0.314170 0.949367i \(-0.398274\pi\)
0.314170 + 0.949367i \(0.398274\pi\)
\(264\) 1.90416e9 0.392002
\(265\) 1.21179e10 2.45721
\(266\) 7.41796e8i 0.148169i
\(267\) 3.40961e9i 0.670902i
\(268\) 4.88589e9i 0.947119i
\(269\) 6.80415e9i 1.29947i 0.760162 + 0.649733i \(0.225119\pi\)
−0.760162 + 0.649733i \(0.774881\pi\)
\(270\) 2.42362e9i 0.456047i
\(271\) 2.05562e9 0.381124 0.190562 0.981675i \(-0.438969\pi\)
0.190562 + 0.981675i \(0.438969\pi\)
\(272\) 3.90656e7 0.00713705
\(273\) 3.58494e8i 0.0645403i
\(274\) 4.74874e9i 0.842512i
\(275\) 1.45748e10i 2.54843i
\(276\) 2.12183e9i 0.365657i
\(277\) 1.20555e9 0.204771 0.102385 0.994745i \(-0.467353\pi\)
0.102385 + 0.994745i \(0.467353\pi\)
\(278\) 1.42475e10i 2.38539i
\(279\) 2.27555e9i 0.375552i
\(280\) 1.82293e9i 0.296577i
\(281\) 9.91847e8 0.159081 0.0795407 0.996832i \(-0.474655\pi\)
0.0795407 + 0.996832i \(0.474655\pi\)
\(282\) −2.37727e9 −0.375908
\(283\) 5.20924e9i 0.812135i −0.913843 0.406068i \(-0.866900\pi\)
0.913843 0.406068i \(-0.133100\pi\)
\(284\) 6.10766e9 0.938861
\(285\) −1.23982e9 −0.187922
\(286\) 4.05751e9i 0.606451i
\(287\) −5.18080e9 −0.763606
\(288\) 3.21172e9i 0.466839i
\(289\) −6.97496e9 −0.999886
\(290\) 4.21756e9i 0.596306i
\(291\) 2.65874e9i 0.370769i
\(292\) 1.46256e10i 2.01179i
\(293\) −7.36969e9 −0.999952 −0.499976 0.866039i \(-0.666658\pi\)
−0.499976 + 0.866039i \(0.666658\pi\)
\(294\) 5.01325e9i 0.671011i
\(295\) 1.17032e10 2.32157e9i 1.54531 0.306545i
\(296\) −1.89169e8 −0.0246424
\(297\) 2.57501e9i 0.330942i
\(298\) −7.64749e9 −0.969736
\(299\) 9.40063e8 0.117618
\(300\) 8.74969e9 1.08021
\(301\) 2.21508e8i 0.0269851i
\(302\) 5.04668e9 0.606706
\(303\) 6.36546e9i 0.755196i
\(304\) 1.17978e9 0.138136
\(305\) 1.27689e10i 1.47555i
\(306\) 4.69256e7i 0.00535210i
\(307\) 1.38584e9 0.156012 0.0780061 0.996953i \(-0.475145\pi\)
0.0780061 + 0.996953i \(0.475145\pi\)
\(308\) 9.31517e9i 1.03511i
\(309\) 2.09441e9i 0.229735i
\(310\) −2.46564e10 −2.66983
\(311\) −7.57040e9 −0.809240 −0.404620 0.914485i \(-0.632596\pi\)
−0.404620 + 0.914485i \(0.632596\pi\)
\(312\) 5.06455e8 0.0534469
\(313\) 7.93693e9i 0.826942i −0.910517 0.413471i \(-0.864316\pi\)
0.910517 0.413471i \(-0.135684\pi\)
\(314\) −4.53462e8 −0.0466468
\(315\) 2.46515e9 0.250381
\(316\) 9.86527e9 0.989374
\(317\) 1.02666e10 1.01669 0.508347 0.861152i \(-0.330257\pi\)
0.508347 + 0.861152i \(0.330257\pi\)
\(318\) 1.38511e10i 1.35449i
\(319\) 4.48099e9i 0.432725i
\(320\) −2.37551e10 −2.26546
\(321\) 4.18994e9 0.394628
\(322\) 3.86764e9 0.359768
\(323\) 2.40050e7 0.00220542
\(324\) −1.54585e9 −0.140277
\(325\) 3.87650e9i 0.347461i
\(326\) 1.23268e10i 1.09139i
\(327\) 6.92303e9i 0.605488i
\(328\) 7.31906e9i 0.632354i
\(329\) 2.41800e9i 0.206382i
\(330\) 2.79011e10 2.35269
\(331\) 6.68667e9 0.557055 0.278527 0.960428i \(-0.410154\pi\)
0.278527 + 0.960428i \(0.410154\pi\)
\(332\) 2.25620e9i 0.185706i
\(333\) 2.55813e8i 0.0208040i
\(334\) 2.79595e10i 2.24669i
\(335\) 1.48851e10i 1.18188i
\(336\) −2.34578e9 −0.184048
\(337\) 8.59323e9i 0.666249i 0.942883 + 0.333125i \(0.108103\pi\)
−0.942883 + 0.333125i \(0.891897\pi\)
\(338\) 1.85526e10i 1.42147i
\(339\) 4.55419e9i 0.344836i
\(340\) −2.83723e8 −0.0212314
\(341\) −2.61965e10 −1.93743
\(342\) 1.41715e9i 0.103589i
\(343\) 1.16985e10 0.845188
\(344\) 3.12931e8 0.0223468
\(345\) 6.46425e9i 0.456291i
\(346\) −1.66406e10 −1.16108
\(347\) 1.27463e9i 0.0879160i −0.999033 0.0439580i \(-0.986003\pi\)
0.999033 0.0439580i \(-0.0139968\pi\)
\(348\) −2.69007e9 −0.183420
\(349\) 1.23114e10i 0.829860i −0.909853 0.414930i \(-0.863806\pi\)
0.909853 0.414930i \(-0.136194\pi\)
\(350\) 1.59488e10i 1.06281i
\(351\) 6.84880e8i 0.0451217i
\(352\) −3.69737e10 −2.40837
\(353\) 1.49416e9i 0.0962273i 0.998842 + 0.0481137i \(0.0153210\pi\)
−0.998842 + 0.0481137i \(0.984679\pi\)
\(354\) −2.65364e9 1.33772e10i −0.168978 0.851828i
\(355\) 1.86073e10 1.17157
\(356\) 2.35640e10i 1.46707i
\(357\) −4.77296e7 −0.00293843
\(358\) −3.95721e10 −2.40911
\(359\) 1.96126e10 1.18075 0.590374 0.807130i \(-0.298980\pi\)
0.590374 + 0.807130i \(0.298980\pi\)
\(360\) 3.48259e9i 0.207344i
\(361\) −1.62586e10 −0.957315
\(362\) 1.04199e10i 0.606776i
\(363\) 1.96193e10 1.12994
\(364\) 2.47758e9i 0.141131i
\(365\) 4.45577e10i 2.51045i
\(366\) −1.45953e10 −0.813371
\(367\) 1.35978e10i 0.749559i −0.927114 0.374779i \(-0.877718\pi\)
0.927114 0.374779i \(-0.122282\pi\)
\(368\) 6.15124e9i 0.335407i
\(369\) 9.89758e9 0.533856
\(370\) −2.77183e9 −0.147897
\(371\) 1.40885e10 0.743649
\(372\) 1.57265e10i 0.821221i
\(373\) −3.17309e10 −1.63926 −0.819628 0.572895i \(-0.805820\pi\)
−0.819628 + 0.572895i \(0.805820\pi\)
\(374\) −5.40214e8 −0.0276108
\(375\) 8.66921e9 0.438384
\(376\) −3.41598e9 −0.170908
\(377\) 1.19182e9i 0.0589990i
\(378\) 2.81776e9i 0.138018i
\(379\) −2.76387e10 −1.33955 −0.669777 0.742563i \(-0.733610\pi\)
−0.669777 + 0.742563i \(0.733610\pi\)
\(380\) −8.56845e9 −0.410930
\(381\) −1.74048e10 −0.825978
\(382\) −3.00682e10 −1.41206
\(383\) 8.72327e9 0.405400 0.202700 0.979241i \(-0.435028\pi\)
0.202700 + 0.979241i \(0.435028\pi\)
\(384\) 9.57157e9i 0.440209i
\(385\) 2.83791e10i 1.29168i
\(386\) 1.73658e10i 0.782249i
\(387\) 4.23178e8i 0.0188660i
\(388\) 1.83747e10i 0.810763i
\(389\) 2.74653e10 1.19946 0.599730 0.800203i \(-0.295275\pi\)
0.599730 + 0.800203i \(0.295275\pi\)
\(390\) 7.42091e9 0.320774
\(391\) 1.25159e8i 0.00535496i
\(392\) 7.20371e9i 0.305079i
\(393\) 2.71910e10i 1.13987i
\(394\) 6.25152e10i 2.59418i
\(395\) 3.00550e10 1.23461
\(396\) 1.77960e10i 0.723674i
\(397\) 2.85069e10i 1.14759i −0.818997 0.573797i \(-0.805470\pi\)
0.818997 0.573797i \(-0.194530\pi\)
\(398\) 5.92079e10i 2.35965i
\(399\) −1.44144e9 −0.0568727
\(400\) −2.53656e10 −0.990845
\(401\) 1.91705e10i 0.741404i 0.928752 + 0.370702i \(0.120883\pi\)
−0.928752 + 0.370702i \(0.879117\pi\)
\(402\) 1.70142e10 0.651491
\(403\) −6.96753e9 −0.264155
\(404\) 4.39922e10i 1.65139i
\(405\) −4.70951e9 −0.175047
\(406\) 4.90342e9i 0.180466i
\(407\) −2.94496e9 −0.107325
\(408\) 6.74290e7i 0.00243336i
\(409\) 1.83125e10i 0.654415i 0.944952 + 0.327208i \(0.106108\pi\)
−0.944952 + 0.327208i \(0.893892\pi\)
\(410\) 1.07244e11i 3.79522i
\(411\) 9.22760e9 0.323386
\(412\) 1.44746e10i 0.502362i
\(413\) 1.36064e10 2.69911e9i 0.467674 0.0927727i
\(414\) −7.38888e9 −0.251523
\(415\) 6.87362e9i 0.231736i
\(416\) −9.83398e9 −0.328364
\(417\) 2.76853e10 0.915597
\(418\) −1.63145e10 −0.534402
\(419\) 5.56865e9i 0.180673i 0.995911 + 0.0903367i \(0.0287943\pi\)
−0.995911 + 0.0903367i \(0.971206\pi\)
\(420\) 1.70368e10 0.547509
\(421\) 2.41135e10i 0.767595i −0.923417 0.383797i \(-0.874616\pi\)
0.923417 0.383797i \(-0.125384\pi\)
\(422\) 2.63676e10 0.831420
\(423\) 4.61943e9i 0.144287i
\(424\) 1.99032e10i 0.615828i
\(425\) −5.16114e8 −0.0158194
\(426\) 2.12688e10i 0.645810i
\(427\) 1.48454e10i 0.446560i
\(428\) 2.89570e10 0.862935
\(429\) 7.88443e9 0.232778
\(430\) 4.58528e9 0.134119
\(431\) 5.54031e10i 1.60556i 0.596279 + 0.802778i \(0.296645\pi\)
−0.596279 + 0.802778i \(0.703355\pi\)
\(432\) 4.48147e9 0.128672
\(433\) 5.43575e10 1.54635 0.773175 0.634193i \(-0.218668\pi\)
0.773175 + 0.634193i \(0.218668\pi\)
\(434\) −2.86661e10 −0.807996
\(435\) −8.19543e9 −0.228884
\(436\) 4.78456e10i 1.32402i
\(437\) 3.77981e9i 0.103644i
\(438\) −5.09311e10 −1.38384
\(439\) 1.48202e9 0.0399021 0.0199511 0.999801i \(-0.493649\pi\)
0.0199511 + 0.999801i \(0.493649\pi\)
\(440\) 4.00920e10 1.06966
\(441\) −9.74159e9 −0.257558
\(442\) −1.43682e8 −0.00376455
\(443\) 4.92945e9i 0.127992i −0.997950 0.0639961i \(-0.979615\pi\)
0.997950 0.0639961i \(-0.0203845\pi\)
\(444\) 1.76794e9i 0.0454921i
\(445\) 7.17890e10i 1.83070i
\(446\) 3.00335e9i 0.0759044i
\(447\) 1.48604e10i 0.372219i
\(448\) −2.76182e10 −0.685619
\(449\) −2.96211e10 −0.728812 −0.364406 0.931240i \(-0.618728\pi\)
−0.364406 + 0.931240i \(0.618728\pi\)
\(450\) 3.04692e10i 0.743038i
\(451\) 1.13942e11i 2.75410i
\(452\) 3.14743e10i 0.754055i
\(453\) 9.80656e9i 0.232875i
\(454\) −8.13917e10 −1.91583
\(455\) 7.54806e9i 0.176112i
\(456\) 2.03636e9i 0.0470972i
\(457\) 4.73775e10i 1.08619i 0.839670 + 0.543097i \(0.182748\pi\)
−0.839670 + 0.543097i \(0.817252\pi\)
\(458\) −6.08053e10 −1.38191
\(459\) 9.11844e7 0.00205433
\(460\) 4.46749e10i 0.997774i
\(461\) 3.64855e10 0.807823 0.403911 0.914798i \(-0.367650\pi\)
0.403911 + 0.914798i \(0.367650\pi\)
\(462\) 3.24384e10 0.712019
\(463\) 8.10218e10i 1.76310i 0.472086 + 0.881552i \(0.343501\pi\)
−0.472086 + 0.881552i \(0.656499\pi\)
\(464\) 7.79859e9 0.168246
\(465\) 4.79116e10i 1.02477i
\(466\) −1.05537e10 −0.223801
\(467\) 5.32338e10i 1.11923i 0.828752 + 0.559616i \(0.189051\pi\)
−0.828752 + 0.559616i \(0.810949\pi\)
\(468\) 4.73325e9i 0.0986680i
\(469\) 1.73058e10i 0.357684i
\(470\) −5.00532e10 −1.02575
\(471\) 8.81153e8i 0.0179047i
\(472\) −3.81311e9 1.92222e10i −0.0768265 0.387288i
\(473\) 4.87168e9 0.0973272
\(474\) 3.43540e10i 0.680556i
\(475\) −1.55867e10 −0.306181
\(476\) −3.29863e8 −0.00642548
\(477\) −2.69151e10 −0.519904
\(478\) 2.52708e10i 0.484070i
\(479\) 7.39499e10 1.40474 0.702370 0.711812i \(-0.252125\pi\)
0.702370 + 0.711812i \(0.252125\pi\)
\(480\) 6.76224e10i 1.27387i
\(481\) −7.83277e8 −0.0146331
\(482\) 1.91464e10i 0.354731i
\(483\) 7.51548e9i 0.138092i
\(484\) 1.35590e11 2.47085
\(485\) 5.59795e10i 1.01172i
\(486\) 5.38314e9i 0.0964919i
\(487\) −2.15971e10 −0.383954 −0.191977 0.981399i \(-0.561490\pi\)
−0.191977 + 0.981399i \(0.561490\pi\)
\(488\) −2.09725e10 −0.369803
\(489\) −2.39530e10 −0.418914
\(490\) 1.05554e11i 1.83100i
\(491\) −3.36314e10 −0.578653 −0.289327 0.957230i \(-0.593431\pi\)
−0.289327 + 0.957230i \(0.593431\pi\)
\(492\) 6.84029e10 1.16739
\(493\) 1.58678e8 0.00268614
\(494\) −4.33920e9 −0.0728621
\(495\) 5.42165e10i 0.903048i
\(496\) 4.55916e10i 0.753283i
\(497\) 2.16332e10 0.354565
\(498\) 7.85680e9 0.127740
\(499\) 2.60087e10 0.419485 0.209743 0.977757i \(-0.432737\pi\)
0.209743 + 0.977757i \(0.432737\pi\)
\(500\) 5.99135e10 0.958617
\(501\) −5.43301e10 −0.862361
\(502\) 1.41603e11i 2.22976i
\(503\) 4.32581e10i 0.675765i −0.941188 0.337883i \(-0.890289\pi\)
0.941188 0.337883i \(-0.109711\pi\)
\(504\) 4.04893e9i 0.0627506i
\(505\) 1.34024e11i 2.06072i
\(506\) 8.50618e10i 1.29758i
\(507\) −3.60509e10 −0.545613
\(508\) −1.20286e11 −1.80617
\(509\) 1.16070e11i 1.72921i −0.502454 0.864604i \(-0.667570\pi\)
0.502454 0.864604i \(-0.332430\pi\)
\(510\) 9.88015e8i 0.0146044i
\(511\) 5.18037e10i 0.759762i
\(512\) 8.24891e10i 1.20037i
\(513\) 2.75377e9 0.0397611
\(514\) 9.46821e10i 1.35649i
\(515\) 4.40975e10i 0.626881i
\(516\) 2.92461e9i 0.0412543i
\(517\) −5.31796e10 −0.744360
\(518\) −3.22258e9 −0.0447595
\(519\) 3.23354e10i 0.445666i
\(520\) 1.06634e10 0.145841
\(521\) −5.76566e10 −0.782525 −0.391263 0.920279i \(-0.627962\pi\)
−0.391263 + 0.920279i \(0.627962\pi\)
\(522\) 9.36768e9i 0.126168i
\(523\) 6.75826e10 0.903291 0.451646 0.892197i \(-0.350837\pi\)
0.451646 + 0.892197i \(0.350837\pi\)
\(524\) 1.87919e11i 2.49256i
\(525\) 3.09913e10 0.407945
\(526\) 7.23489e10i 0.945124i
\(527\) 9.27652e8i 0.0120266i
\(528\) 5.15913e10i 0.663805i
\(529\) 5.86035e10 0.748343
\(530\) 2.91635e11i 3.69603i
\(531\) −2.59942e10 + 5.15647e9i −0.326962 + 0.0648597i
\(532\) −9.96186e9 −0.124364
\(533\) 3.03055e10i 0.375502i
\(534\) 8.20575e10 1.00914
\(535\) 8.82189e10 1.07683
\(536\) 2.44483e10 0.296204
\(537\) 7.68952e10i 0.924702i
\(538\) 1.63752e11 1.95460
\(539\) 1.12147e11i 1.32871i
\(540\) −3.25477e10 −0.382777
\(541\) 7.24724e10i 0.846026i 0.906124 + 0.423013i \(0.139028\pi\)
−0.906124 + 0.423013i \(0.860972\pi\)
\(542\) 4.94718e10i 0.573272i
\(543\) 2.02476e10 0.232902
\(544\) 1.30929e9i 0.0149500i
\(545\) 1.45764e11i 1.65221i
\(546\) 8.62771e9 0.0970789
\(547\) 8.38360e10 0.936443 0.468221 0.883611i \(-0.344895\pi\)
0.468221 + 0.883611i \(0.344895\pi\)
\(548\) 6.37726e10 0.707151
\(549\) 2.83611e10i 0.312201i
\(550\) 3.50766e11 3.83325
\(551\) 4.79208e9 0.0519897
\(552\) −1.06173e10 −0.114356
\(553\) 3.49426e10 0.373641
\(554\) 2.90135e10i 0.308008i
\(555\) 5.38613e9i 0.0567681i
\(556\) 1.91335e11 2.00214
\(557\) 6.90382e10 0.717247 0.358624 0.933482i \(-0.383246\pi\)
0.358624 + 0.933482i \(0.383246\pi\)
\(558\) 5.47647e10 0.564890
\(559\) 1.29573e9 0.0132699
\(560\) −4.93903e10 −0.502214
\(561\) 1.04973e9i 0.0105980i
\(562\) 2.38703e10i 0.239284i
\(563\) 1.10659e11i 1.10142i 0.834696 + 0.550712i \(0.185644\pi\)
−0.834696 + 0.550712i \(0.814356\pi\)
\(564\) 3.19252e10i 0.315513i
\(565\) 9.58881e10i 0.940960i
\(566\) −1.25368e11 −1.22158
\(567\) −5.47537e9 −0.0529763
\(568\) 3.05619e10i 0.293621i
\(569\) 1.65136e11i 1.57541i 0.616054 + 0.787704i \(0.288730\pi\)
−0.616054 + 0.787704i \(0.711270\pi\)
\(570\) 2.98381e10i 0.282665i
\(571\) 1.33371e11i 1.25463i −0.778764 0.627317i \(-0.784153\pi\)
0.778764 0.627317i \(-0.215847\pi\)
\(572\) 5.44899e10 0.509016
\(573\) 5.84276e10i 0.542001i
\(574\) 1.24684e11i 1.14858i
\(575\) 8.12670e10i 0.743435i
\(576\) 5.27628e10 0.479333
\(577\) −1.27540e10 −0.115065 −0.0575323 0.998344i \(-0.518323\pi\)
−0.0575323 + 0.998344i \(0.518323\pi\)
\(578\) 1.67863e11i 1.50399i
\(579\) 3.37446e10 0.300255
\(580\) −5.66392e10 −0.500501
\(581\) 7.99142e9i 0.0701325i
\(582\) −6.39866e10 −0.557696
\(583\) 3.09851e11i 2.68212i
\(584\) −7.31846e10 −0.629171
\(585\) 1.44201e10i 0.123124i
\(586\) 1.77363e11i 1.50409i
\(587\) 1.33729e11i 1.12635i −0.826337 0.563175i \(-0.809580\pi\)
0.826337 0.563175i \(-0.190420\pi\)
\(588\) −6.73248e10 −0.563204
\(589\) 2.80151e10i 0.232772i
\(590\) −5.58722e10 2.81656e11i −0.461092 2.32440i
\(591\) −1.21478e11 −0.995740
\(592\) 5.12532e9i 0.0417287i
\(593\) 1.74593e11 1.41192 0.705959 0.708253i \(-0.250516\pi\)
0.705959 + 0.708253i \(0.250516\pi\)
\(594\) −6.19715e10 −0.497790
\(595\) −1.00494e9 −0.00801814
\(596\) 1.02701e11i 0.813935i
\(597\) −1.15051e11 −0.905718
\(598\) 2.26241e10i 0.176916i
\(599\) −7.88184e10 −0.612238 −0.306119 0.951993i \(-0.599031\pi\)
−0.306119 + 0.951993i \(0.599031\pi\)
\(600\) 4.37822e10i 0.337826i
\(601\) 4.56479e10i 0.349883i −0.984579 0.174942i \(-0.944026\pi\)
0.984579 0.174942i \(-0.0559737\pi\)
\(602\) 5.33094e9 0.0405899
\(603\) 3.30615e10i 0.250066i
\(604\) 6.77738e10i 0.509230i
\(605\) 4.13082e11 3.08329
\(606\) 1.53195e11 1.13593
\(607\) −6.77809e10 −0.499290 −0.249645 0.968337i \(-0.580314\pi\)
−0.249645 + 0.968337i \(0.580314\pi\)
\(608\) 3.95406e10i 0.289353i
\(609\) −9.52818e9 −0.0692693
\(610\) −3.07303e11 −2.21946
\(611\) −1.41443e10 −0.101488
\(612\) 6.30182e8 0.00449221
\(613\) 1.55090e11i 1.09835i 0.835707 + 0.549175i \(0.185058\pi\)
−0.835707 + 0.549175i \(0.814942\pi\)
\(614\) 3.33523e10i 0.234667i
\(615\) 2.08393e11 1.45674
\(616\) 4.66119e10 0.323723
\(617\) −3.07611e10 −0.212257 −0.106128 0.994352i \(-0.533845\pi\)
−0.106128 + 0.994352i \(0.533845\pi\)
\(618\) −5.04051e10 −0.345558
\(619\) 9.76912e10 0.665415 0.332708 0.943030i \(-0.392038\pi\)
0.332708 + 0.943030i \(0.392038\pi\)
\(620\) 3.31120e11i 2.24088i
\(621\) 1.43578e10i 0.0965434i
\(622\) 1.82193e11i 1.21723i
\(623\) 8.34634e10i 0.554044i
\(624\) 1.37218e10i 0.0905053i
\(625\) −4.36006e10 −0.285741
\(626\) −1.91014e11 −1.24385
\(627\) 3.17018e10i 0.205123i
\(628\) 6.08971e9i 0.0391524i
\(629\) 1.04285e8i 0.000666222i
\(630\) 5.93276e10i 0.376612i
\(631\) −2.20612e11 −1.39159 −0.695794 0.718241i \(-0.744947\pi\)
−0.695794 + 0.718241i \(0.744947\pi\)
\(632\) 4.93645e10i 0.309418i
\(633\) 5.12367e10i 0.319129i
\(634\) 2.47082e11i 1.52927i
\(635\) −3.66456e11 −2.25386
\(636\) −1.86012e11 −1.13688
\(637\) 2.98279e10i 0.181161i
\(638\) −1.07842e11 −0.650887
\(639\) −4.13289e10 −0.247885
\(640\) 2.01529e11i 1.20120i
\(641\) 1.03091e11 0.610646 0.305323 0.952249i \(-0.401236\pi\)
0.305323 + 0.952249i \(0.401236\pi\)
\(642\) 1.00837e11i 0.593583i
\(643\) −2.79059e11 −1.63249 −0.816247 0.577702i \(-0.803949\pi\)
−0.816247 + 0.577702i \(0.803949\pi\)
\(644\) 5.19400e10i 0.301966i
\(645\) 8.90997e9i 0.0514799i
\(646\) 5.77718e8i 0.00331731i
\(647\) −7.83016e10 −0.446842 −0.223421 0.974722i \(-0.571722\pi\)
−0.223421 + 0.974722i \(0.571722\pi\)
\(648\) 7.73522e9i 0.0438705i
\(649\) −5.93621e10 2.99248e11i −0.334603 1.68676i
\(650\) 9.32940e10 0.522637
\(651\) 5.57030e10i 0.310138i
\(652\) −1.65541e11 −0.916041
\(653\) 1.77534e11 0.976402 0.488201 0.872731i \(-0.337653\pi\)
0.488201 + 0.872731i \(0.337653\pi\)
\(654\) −1.66614e11 −0.910750
\(655\) 5.72504e11i 3.11038i
\(656\) −1.98302e11 −1.07081
\(657\) 9.89677e10i 0.531168i
\(658\) −5.81929e10 −0.310432
\(659\) 2.17806e11i 1.15486i 0.816440 + 0.577430i \(0.195944\pi\)
−0.816440 + 0.577430i \(0.804056\pi\)
\(660\) 3.74694e11i 1.97470i
\(661\) −2.68055e11 −1.40416 −0.702081 0.712097i \(-0.747746\pi\)
−0.702081 + 0.712097i \(0.747746\pi\)
\(662\) 1.60925e11i 0.837899i
\(663\) 2.79198e8i 0.00144497i
\(664\) 1.12897e10 0.0580778
\(665\) −3.03493e10 −0.155189
\(666\) 6.15654e9 0.0312925
\(667\) 2.49853e10i 0.126236i
\(668\) −3.75479e11 −1.88573
\(669\) 5.83602e9 0.0291348
\(670\) 3.58233e11 1.77773
\(671\) −3.26497e11 −1.61061
\(672\) 7.86193e10i 0.385524i
\(673\) 2.50768e11i 1.22239i 0.791478 + 0.611197i \(0.209312\pi\)
−0.791478 + 0.611197i \(0.790688\pi\)
\(674\) 2.06809e11 1.00215
\(675\) −5.92068e10 −0.285205
\(676\) −2.49150e11 −1.19309
\(677\) 8.82165e10 0.419948 0.209974 0.977707i \(-0.432662\pi\)
0.209974 + 0.977707i \(0.432662\pi\)
\(678\) −1.09604e11 −0.518688
\(679\) 6.50830e10i 0.306188i
\(680\) 1.41971e9i 0.00663995i
\(681\) 1.58158e11i 0.735364i
\(682\) 6.30459e11i 2.91420i
\(683\) 2.38268e11i 1.09492i −0.836832 0.547460i \(-0.815595\pi\)
0.836832 0.547460i \(-0.184405\pi\)
\(684\) 1.90315e10 0.0869458
\(685\) 1.94286e11 0.882430
\(686\) 2.81542e11i 1.27130i
\(687\) 1.18155e11i 0.530426i
\(688\) 8.47854e9i 0.0378414i
\(689\) 8.24117e10i 0.365689i
\(690\) −1.55572e11 −0.686334
\(691\) 5.08258e10i 0.222932i −0.993768 0.111466i \(-0.964445\pi\)
0.993768 0.111466i \(-0.0355546\pi\)
\(692\) 2.23472e11i 0.974540i
\(693\) 6.30333e10i 0.273298i
\(694\) −3.06760e10 −0.132240
\(695\) 5.82911e11 2.49841
\(696\) 1.34607e10i 0.0573630i
\(697\) −4.03485e9 −0.0170961
\(698\) −2.96292e11 −1.24824
\(699\) 2.05077e10i 0.0859028i
\(700\) 2.14183e11 0.892056
\(701\) 3.96206e11i 1.64077i −0.571810 0.820386i \(-0.693758\pi\)
0.571810 0.820386i \(-0.306242\pi\)
\(702\) −1.64827e10 −0.0678703
\(703\) 3.14941e9i 0.0128946i
\(704\) 6.07412e11i 2.47282i
\(705\) 9.72618e10i 0.393719i
\(706\) 3.59593e10 0.144741
\(707\) 1.55820e11i 0.623655i
\(708\) −1.79647e11 + 3.56367e10i −0.714970 + 0.141829i
\(709\) 3.38316e11 1.33887 0.669433 0.742872i \(-0.266537\pi\)
0.669433 + 0.742872i \(0.266537\pi\)
\(710\) 4.47813e11i 1.76223i
\(711\) −6.67556e10 −0.261222
\(712\) 1.17911e11 0.458812
\(713\) 1.46068e11 0.565191
\(714\) 1.14869e9i 0.00441986i
\(715\) 1.66006e11 0.635185
\(716\) 5.31428e11i 2.02205i
\(717\) 4.91055e10 0.185803
\(718\) 4.72007e11i 1.77603i
\(719\) 4.17322e11i 1.56155i −0.624812 0.780775i \(-0.714824\pi\)
0.624812 0.780775i \(-0.285176\pi\)
\(720\) 9.43569e10 0.351111
\(721\) 5.12687e10i 0.189719i
\(722\) 3.91289e11i 1.43995i
\(723\) 3.72047e10 0.136159
\(724\) 1.39932e11 0.509289
\(725\) −1.03031e11 −0.372920
\(726\) 4.72168e11i 1.69961i
\(727\) 3.81006e11 1.36394 0.681969 0.731381i \(-0.261124\pi\)
0.681969 + 0.731381i \(0.261124\pi\)
\(728\) 1.23975e10 0.0441374
\(729\) 1.04604e10 0.0370370
\(730\) −1.07235e12 −3.77612
\(731\) 1.72513e8i 0.000604160i
\(732\) 1.96006e11i 0.682691i
\(733\) 1.16004e11 0.401842 0.200921 0.979607i \(-0.435606\pi\)
0.200921 + 0.979607i \(0.435606\pi\)
\(734\) −3.27253e11 −1.12746
\(735\) −2.05108e11 −0.702804
\(736\) 2.06160e11 0.702575
\(737\) 3.80609e11 1.29006
\(738\) 2.38201e11i 0.803004i
\(739\) 2.35296e11i 0.788926i −0.918912 0.394463i \(-0.870931\pi\)
0.918912 0.394463i \(-0.129069\pi\)
\(740\) 3.72239e10i 0.124135i
\(741\) 8.43180e9i 0.0279671i
\(742\) 3.39061e11i 1.11857i
\(743\) −3.67325e11 −1.20530 −0.602650 0.798006i \(-0.705888\pi\)
−0.602650 + 0.798006i \(0.705888\pi\)
\(744\) 7.86932e10 0.256830
\(745\) 3.12884e11i 1.01568i
\(746\) 7.63653e11i 2.46570i
\(747\) 1.52671e10i 0.0490314i
\(748\) 7.25474e9i 0.0231748i
\(749\) 1.02565e11 0.325891
\(750\) 2.08638e11i 0.659399i
\(751\) 6.38730e10i 0.200797i 0.994947 + 0.100399i \(0.0320118\pi\)
−0.994947 + 0.100399i \(0.967988\pi\)
\(752\) 9.25522e10i 0.289411i
\(753\) 2.75159e11 0.855862
\(754\) −2.86830e10 −0.0887440
\(755\) 2.06476e11i 0.635451i
\(756\) −3.78407e10 −0.115844
\(757\) 4.64224e11 1.41366 0.706828 0.707385i \(-0.250125\pi\)
0.706828 + 0.707385i \(0.250125\pi\)
\(758\) 6.65167e11i 2.01490i
\(759\) −1.65289e11 −0.498056
\(760\) 4.28754e10i 0.128515i
\(761\) 1.03271e10 0.0307923 0.0153961 0.999881i \(-0.495099\pi\)
0.0153961 + 0.999881i \(0.495099\pi\)
\(762\) 4.18873e11i 1.24240i
\(763\) 1.69468e11i 0.500023i
\(764\) 4.03798e11i 1.18520i
\(765\) 1.91988e9 0.00560568
\(766\) 2.09939e11i 0.609787i
\(767\) −1.57887e10 7.95918e10i −0.0456209 0.229978i
\(768\) −5.84758e10 −0.168086
\(769\) 1.94833e11i 0.557131i −0.960417 0.278565i \(-0.910141\pi\)
0.960417 0.278565i \(-0.0898589\pi\)
\(770\) 6.82988e11 1.94290
\(771\) 1.83983e11 0.520668
\(772\) 2.33211e11 0.656569
\(773\) 1.43747e11i 0.402606i −0.979529 0.201303i \(-0.935482\pi\)
0.979529 0.201303i \(-0.0645177\pi\)
\(774\) −1.01844e10 −0.0283774
\(775\) 6.02333e11i 1.66967i
\(776\) −9.19446e10 −0.253559
\(777\) 6.26203e9i 0.0171803i
\(778\) 6.60994e11i 1.80418i
\(779\) −1.21853e11 −0.330891
\(780\) 9.96582e10i 0.269237i
\(781\) 4.75784e11i 1.27881i
\(782\) 3.01215e9 0.0