Properties

Label 177.9.c.a.58.2
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 58.2
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.79

$q$-expansion

\(f(q)\) \(=\) \(q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} -1187.60i q^{10} +6339.18i q^{11} +34274.3 q^{12} +24786.9i q^{13} -40438.6i q^{14} -1766.12 q^{15} +283984. q^{16} +136845. q^{17} -68774.1i q^{18} -233393. q^{19} -27678.3 q^{20} -60137.4 q^{21} +199347. q^{22} -120422. i q^{23} -701338. i q^{24} -389199. q^{25} +779467. q^{26} -102276. q^{27} -942464. q^{28} +111206. q^{29} +55538.7i q^{30} -20065.6i q^{31} -5.09115e6i q^{32} -296454. i q^{33} -4.30332e6i q^{34} +48564.1 q^{35} -1.60285e6 q^{36} -3.36126e6i q^{37} +7.33945e6i q^{38} -1.15917e6i q^{39} +566367. i q^{40} +2.62741e6 q^{41} +1.89113e6i q^{42} +554113. i q^{43} -4.64598e6i q^{44} +82593.1 q^{45} -3.78688e6 q^{46} +3.60410e6i q^{47} -1.32806e7 q^{48} -4.11116e6 q^{49} +1.22390e7i q^{50} -6.39959e6 q^{51} -1.81663e7i q^{52} +4.83376e6 q^{53} +3.21625e6i q^{54} +239402. i q^{55} +1.92852e7i q^{56} +1.09147e7 q^{57} -3.49706e6i q^{58} +(-6.00418e6 - 1.05252e7i) q^{59} +1.29439e6 q^{60} +1.18994e7i q^{61} -630998. q^{62} +2.81235e6 q^{63} -8.74005e7 q^{64} +936087. i q^{65} -9.32252e6 q^{66} +3.03490e7i q^{67} -1.00293e8 q^{68} +5.63158e6i q^{69} -1.52718e6i q^{70} +8.90765e6 q^{71} +3.27984e7i q^{72} -2.96955e7i q^{73} -1.05701e8 q^{74} +1.82010e7 q^{75} +1.71053e8 q^{76} +8.15179e6i q^{77} -3.64521e7 q^{78} +4.37537e7 q^{79} +1.07248e7 q^{80} +4.78297e6 q^{81} -8.26235e7i q^{82} -4.96491e7i q^{83} +4.40747e7 q^{84} +5.16800e6 q^{85} +1.74251e7 q^{86} -5.20058e6 q^{87} -9.50684e7 q^{88} -4.18561e7i q^{89} -2.59729e6i q^{90} +3.18744e7i q^{91} +8.82573e7i q^{92} +938375. i q^{93} +1.13337e8 q^{94} -8.81418e6 q^{95} +2.38090e8i q^{96} -1.47054e8i q^{97} +1.29283e8i q^{98} +1.38638e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.4468i 1.96542i −0.185142 0.982712i \(-0.559274\pi\)
0.185142 0.982712i \(-0.440726\pi\)
\(3\) −46.7654 −0.577350
\(4\) −732.900 −2.86289
\(5\) 37.7655 0.0604248 0.0302124 0.999544i \(-0.490382\pi\)
0.0302124 + 0.999544i \(0.490382\pi\)
\(6\) 1470.62i 1.13474i
\(7\) 1285.94 0.535585 0.267792 0.963477i \(-0.413706\pi\)
0.267792 + 0.963477i \(0.413706\pi\)
\(8\) 14997.0i 3.66137i
\(9\) 2187.00 0.333333
\(10\) 1187.60i 0.118760i
\(11\) 6339.18i 0.432974i 0.976285 + 0.216487i \(0.0694600\pi\)
−0.976285 + 0.216487i \(0.930540\pi\)
\(12\) 34274.3 1.65289
\(13\) 24786.9i 0.867857i 0.900947 + 0.433928i \(0.142873\pi\)
−0.900947 + 0.433928i \(0.857127\pi\)
\(14\) 40438.6i 1.05265i
\(15\) −1766.12 −0.0348863
\(16\) 283984. 4.33325
\(17\) 136845. 1.63845 0.819223 0.573476i \(-0.194405\pi\)
0.819223 + 0.573476i \(0.194405\pi\)
\(18\) 68774.1i 0.655141i
\(19\) −233393. −1.79091 −0.895453 0.445156i \(-0.853148\pi\)
−0.895453 + 0.445156i \(0.853148\pi\)
\(20\) −27678.3 −0.172989
\(21\) −60137.4 −0.309220
\(22\) 199347. 0.850978
\(23\) 120422.i 0.430323i −0.976578 0.215161i \(-0.930972\pi\)
0.976578 0.215161i \(-0.0690278\pi\)
\(24\) 701338.i 2.11389i
\(25\) −389199. −0.996349
\(26\) 779467. 1.70571
\(27\) −102276. −0.192450
\(28\) −942464. −1.53332
\(29\) 111206. 0.157230 0.0786150 0.996905i \(-0.474950\pi\)
0.0786150 + 0.996905i \(0.474950\pi\)
\(30\) 55538.7i 0.0685663i
\(31\) 20065.6i 0.0217273i −0.999941 0.0108636i \(-0.996542\pi\)
0.999941 0.0108636i \(-0.00345807\pi\)
\(32\) 5.09115e6i 4.85530i
\(33\) 296454.i 0.249978i
\(34\) 4.30332e6i 3.22024i
\(35\) 48564.1 0.0323626
\(36\) −1.60285e6 −0.954297
\(37\) 3.36126e6i 1.79347i −0.442566 0.896736i \(-0.645932\pi\)
0.442566 0.896736i \(-0.354068\pi\)
\(38\) 7.33945e6i 3.51989i
\(39\) 1.15917e6i 0.501057i
\(40\) 566367.i 0.221237i
\(41\) 2.62741e6 0.929806 0.464903 0.885362i \(-0.346089\pi\)
0.464903 + 0.885362i \(0.346089\pi\)
\(42\) 1.89113e6i 0.607748i
\(43\) 554113.i 0.162078i 0.996711 + 0.0810391i \(0.0258239\pi\)
−0.996711 + 0.0810391i \(0.974176\pi\)
\(44\) 4.64598e6i 1.23956i
\(45\) 82593.1 0.0201416
\(46\) −3.78688e6 −0.845767
\(47\) 3.60410e6i 0.738593i 0.929312 + 0.369297i \(0.120401\pi\)
−0.929312 + 0.369297i \(0.879599\pi\)
\(48\) −1.32806e7 −2.50180
\(49\) −4.11116e6 −0.713149
\(50\) 1.22390e7i 1.95825i
\(51\) −6.39959e6 −0.945957
\(52\) 1.81663e7i 2.48458i
\(53\) 4.83376e6 0.612606 0.306303 0.951934i \(-0.400908\pi\)
0.306303 + 0.951934i \(0.400908\pi\)
\(54\) 3.21625e6i 0.378246i
\(55\) 239402.i 0.0261624i
\(56\) 1.92852e7i 1.96097i
\(57\) 1.09147e7 1.03398
\(58\) 3.49706e6i 0.309024i
\(59\) −6.00418e6 1.05252e7i −0.495502 0.868607i
\(60\) 1.29439e6 0.0998755
\(61\) 1.18994e7i 0.859418i 0.902967 + 0.429709i \(0.141384\pi\)
−0.902967 + 0.429709i \(0.858616\pi\)
\(62\) −630998. −0.0427033
\(63\) 2.81235e6 0.178528
\(64\) −8.74005e7 −5.20947
\(65\) 936087.i 0.0524400i
\(66\) −9.32252e6 −0.491312
\(67\) 3.03490e7i 1.50607i 0.657981 + 0.753034i \(0.271411\pi\)
−0.657981 + 0.753034i \(0.728589\pi\)
\(68\) −1.00293e8 −4.69069
\(69\) 5.63158e6i 0.248447i
\(70\) 1.52718e6i 0.0636062i
\(71\) 8.90765e6 0.350534 0.175267 0.984521i \(-0.443921\pi\)
0.175267 + 0.984521i \(0.443921\pi\)
\(72\) 3.27984e7i 1.22046i
\(73\) 2.96955e7i 1.04568i −0.852430 0.522841i \(-0.824872\pi\)
0.852430 0.522841i \(-0.175128\pi\)
\(74\) −1.05701e8 −3.52493
\(75\) 1.82010e7 0.575242
\(76\) 1.71053e8 5.12717
\(77\) 8.15179e6i 0.231894i
\(78\) −3.64521e7 −0.984790
\(79\) 4.37537e7 1.12333 0.561663 0.827366i \(-0.310162\pi\)
0.561663 + 0.827366i \(0.310162\pi\)
\(80\) 1.07248e7 0.261835
\(81\) 4.78297e6 0.111111
\(82\) 8.26235e7i 1.82746i
\(83\) 4.96491e7i 1.04616i −0.852283 0.523081i \(-0.824782\pi\)
0.852283 0.523081i \(-0.175218\pi\)
\(84\) 4.40747e7 0.885263
\(85\) 5.16800e6 0.0990027
\(86\) 1.74251e7 0.318552
\(87\) −5.20058e6 −0.0907768
\(88\) −9.50684e7 −1.58528
\(89\) 4.18561e7i 0.667112i −0.942730 0.333556i \(-0.891751\pi\)
0.942730 0.333556i \(-0.108249\pi\)
\(90\) 2.59729e6i 0.0395867i
\(91\) 3.18744e7i 0.464811i
\(92\) 8.82573e7i 1.23197i
\(93\) 938375.i 0.0125442i
\(94\) 1.13337e8 1.45165
\(95\) −8.81418e6 −0.108215
\(96\) 2.38090e8i 2.80321i
\(97\) 1.47054e8i 1.66107i −0.556965 0.830536i \(-0.688034\pi\)
0.556965 0.830536i \(-0.311966\pi\)
\(98\) 1.29283e8i 1.40164i
\(99\) 1.38638e7i 0.144325i
\(100\) 2.85244e8 2.85244
\(101\) 3.69158e7i 0.354753i −0.984143 0.177377i \(-0.943239\pi\)
0.984143 0.177377i \(-0.0567610\pi\)
\(102\) 2.01246e8i 1.85921i
\(103\) 1.29093e8i 1.14697i 0.819214 + 0.573487i \(0.194410\pi\)
−0.819214 + 0.573487i \(0.805590\pi\)
\(104\) −3.71728e8 −3.17754
\(105\) −2.27112e6 −0.0186845
\(106\) 1.52006e8i 1.20403i
\(107\) −1.28854e8 −0.983018 −0.491509 0.870872i \(-0.663555\pi\)
−0.491509 + 0.870872i \(0.663555\pi\)
\(108\) 7.49580e7 0.550963
\(109\) 1.07097e8i 0.758700i −0.925253 0.379350i \(-0.876148\pi\)
0.925253 0.379350i \(-0.123852\pi\)
\(110\) 7.52842e6 0.0514201
\(111\) 1.57190e8i 1.03546i
\(112\) 3.65186e8 2.32082
\(113\) 5.80716e7i 0.356164i −0.984016 0.178082i \(-0.943011\pi\)
0.984016 0.178082i \(-0.0569892\pi\)
\(114\) 3.43232e8i 2.03221i
\(115\) 4.54779e6i 0.0260022i
\(116\) −8.15027e7 −0.450132
\(117\) 5.42089e7i 0.289286i
\(118\) −3.30984e8 + 1.88812e8i −1.70718 + 0.973872i
\(119\) 1.75974e8 0.877526
\(120\) 2.64864e7i 0.127731i
\(121\) 1.74174e8 0.812533
\(122\) 3.74197e8 1.68912
\(123\) −1.22872e8 −0.536824
\(124\) 1.47061e7i 0.0622028i
\(125\) −2.94504e7 −0.120629
\(126\) 8.84393e7i 0.350884i
\(127\) −2.65214e8 −1.01949 −0.509743 0.860327i \(-0.670260\pi\)
−0.509743 + 0.860327i \(0.670260\pi\)
\(128\) 1.44513e9i 5.38352i
\(129\) 2.59133e7i 0.0935759i
\(130\) 2.94369e7 0.103067
\(131\) 2.83603e8i 0.962999i 0.876446 + 0.481500i \(0.159908\pi\)
−0.876446 + 0.481500i \(0.840092\pi\)
\(132\) 2.17271e8i 0.715659i
\(133\) −3.00129e8 −0.959182
\(134\) 9.54377e8 2.96006
\(135\) −3.86250e6 −0.0116288
\(136\) 2.05225e9i 5.99895i
\(137\) −3.73666e8 −1.06072 −0.530361 0.847772i \(-0.677944\pi\)
−0.530361 + 0.847772i \(0.677944\pi\)
\(138\) 1.77095e8 0.488304
\(139\) −3.45656e8 −0.925945 −0.462972 0.886373i \(-0.653217\pi\)
−0.462972 + 0.886373i \(0.653217\pi\)
\(140\) −3.55926e7 −0.0926505
\(141\) 1.68547e8i 0.426427i
\(142\) 2.80117e8i 0.688947i
\(143\) −1.57128e8 −0.375760
\(144\) 6.21072e8 1.44442
\(145\) 4.19974e6 0.00950058
\(146\) −9.33828e8 −2.05521
\(147\) 1.92260e8 0.411737
\(148\) 2.46346e9i 5.13451i
\(149\) 2.68970e8i 0.545706i 0.962056 + 0.272853i \(0.0879672\pi\)
−0.962056 + 0.272853i \(0.912033\pi\)
\(150\) 5.72364e8i 1.13059i
\(151\) 7.64144e8i 1.46983i −0.678159 0.734915i \(-0.737222\pi\)
0.678159 0.734915i \(-0.262778\pi\)
\(152\) 3.50018e9i 6.55716i
\(153\) 2.99279e8 0.546148
\(154\) 2.56348e8 0.455771
\(155\) 757786.i 0.00131286i
\(156\) 8.49553e8i 1.43447i
\(157\) 6.96606e8i 1.14654i −0.819367 0.573269i \(-0.805675\pi\)
0.819367 0.573269i \(-0.194325\pi\)
\(158\) 1.37591e9i 2.20781i
\(159\) −2.26053e8 −0.353689
\(160\) 1.92270e8i 0.293380i
\(161\) 1.54855e8i 0.230474i
\(162\) 1.50409e8i 0.218380i
\(163\) 1.03636e9 1.46811 0.734055 0.679090i \(-0.237625\pi\)
0.734055 + 0.679090i \(0.237625\pi\)
\(164\) −1.92563e9 −2.66193
\(165\) 1.11957e7i 0.0151049i
\(166\) −1.56130e9 −2.05615
\(167\) −1.15681e9 −1.48729 −0.743645 0.668575i \(-0.766905\pi\)
−0.743645 + 0.668575i \(0.766905\pi\)
\(168\) 9.01878e8i 1.13217i
\(169\) 2.01342e8 0.246825
\(170\) 1.62517e8i 0.194582i
\(171\) −5.10430e8 −0.596969
\(172\) 4.06109e8i 0.464012i
\(173\) 5.23234e8i 0.584133i 0.956398 + 0.292066i \(0.0943429\pi\)
−0.956398 + 0.292066i \(0.905657\pi\)
\(174\) 1.63541e8i 0.178415i
\(175\) −5.00486e8 −0.533629
\(176\) 1.80022e9i 1.87619i
\(177\) 2.80788e8 + 4.92216e8i 0.286078 + 0.501490i
\(178\) −1.31624e9 −1.31116
\(179\) 1.17775e9i 1.14720i −0.819135 0.573601i \(-0.805546\pi\)
0.819135 0.573601i \(-0.194454\pi\)
\(180\) −6.05325e7 −0.0576631
\(181\) −2.07305e8 −0.193150 −0.0965752 0.995326i \(-0.530789\pi\)
−0.0965752 + 0.995326i \(0.530789\pi\)
\(182\) 1.00235e9 0.913550
\(183\) 5.56478e8i 0.496185i
\(184\) 1.80596e9 1.57557
\(185\) 1.26939e8i 0.108370i
\(186\) 2.95089e7 0.0246548
\(187\) 8.67482e8i 0.709405i
\(188\) 2.64144e9i 2.11451i
\(189\) −1.31521e8 −0.103073
\(190\) 2.77178e8i 0.212688i
\(191\) 9.75780e8i 0.733193i −0.930380 0.366597i \(-0.880523\pi\)
0.930380 0.366597i \(-0.119477\pi\)
\(192\) 4.08732e9 3.00769
\(193\) −1.78978e9 −1.28994 −0.644971 0.764207i \(-0.723131\pi\)
−0.644971 + 0.764207i \(0.723131\pi\)
\(194\) −4.62436e9 −3.26471
\(195\) 4.37765e7i 0.0302763i
\(196\) 3.01307e9 2.04167
\(197\) −2.59972e9 −1.72608 −0.863041 0.505134i \(-0.831443\pi\)
−0.863041 + 0.505134i \(0.831443\pi\)
\(198\) 4.35971e8 0.283659
\(199\) 5.03763e8 0.321229 0.160614 0.987017i \(-0.448652\pi\)
0.160614 + 0.987017i \(0.448652\pi\)
\(200\) 5.83680e9i 3.64800i
\(201\) 1.41928e9i 0.869529i
\(202\) −1.16088e9 −0.697240
\(203\) 1.43004e8 0.0842100
\(204\) 4.69026e9 2.70817
\(205\) 9.92253e7 0.0561833
\(206\) 4.05956e9 2.25429
\(207\) 2.63363e8i 0.143441i
\(208\) 7.03907e9i 3.76064i
\(209\) 1.47952e9i 0.775416i
\(210\) 7.14193e7i 0.0367230i
\(211\) 5.13610e8i 0.259122i −0.991571 0.129561i \(-0.958643\pi\)
0.991571 0.129561i \(-0.0413568\pi\)
\(212\) −3.54266e9 −1.75382
\(213\) −4.16569e8 −0.202381
\(214\) 4.05203e9i 1.93205i
\(215\) 2.09263e7i 0.00979354i
\(216\) 1.53383e9i 0.704631i
\(217\) 2.58031e7i 0.0116368i
\(218\) −3.36784e9 −1.49117
\(219\) 1.38872e9i 0.603724i
\(220\) 1.75458e8i 0.0749000i
\(221\) 3.39195e9i 1.42194i
\(222\) 4.94313e9 2.03512
\(223\) −1.39299e9 −0.563286 −0.281643 0.959519i \(-0.590879\pi\)
−0.281643 + 0.959519i \(0.590879\pi\)
\(224\) 6.54691e9i 2.60042i
\(225\) −8.51178e8 −0.332116
\(226\) −1.82616e9 −0.700013
\(227\) 2.01523e9i 0.758966i −0.925199 0.379483i \(-0.876102\pi\)
0.925199 0.379483i \(-0.123898\pi\)
\(228\) −7.99938e9 −2.96017
\(229\) 2.76680e9i 1.00609i 0.864260 + 0.503045i \(0.167787\pi\)
−0.864260 + 0.503045i \(0.832213\pi\)
\(230\) −1.43013e8 −0.0511053
\(231\) 3.81222e8i 0.133884i
\(232\) 1.66775e9i 0.575677i
\(233\) 2.29527e9i 0.778771i 0.921075 + 0.389385i \(0.127313\pi\)
−0.921075 + 0.389385i \(0.872687\pi\)
\(234\) 1.70469e9 0.568569
\(235\) 1.36111e8i 0.0446293i
\(236\) 4.40046e9 + 7.71393e9i 1.41857 + 2.48672i
\(237\) −2.04616e9 −0.648553
\(238\) 5.53381e9i 1.72471i
\(239\) 2.38655e9 0.731442 0.365721 0.930725i \(-0.380823\pi\)
0.365721 + 0.930725i \(0.380823\pi\)
\(240\) −5.01548e8 −0.151171
\(241\) −4.37727e9 −1.29758 −0.648791 0.760967i \(-0.724725\pi\)
−0.648791 + 0.760967i \(0.724725\pi\)
\(242\) 5.47720e9i 1.59697i
\(243\) −2.23677e8 −0.0641500
\(244\) 8.72105e9i 2.46042i
\(245\) −1.55260e8 −0.0430919
\(246\) 3.86392e9i 1.05509i
\(247\) 5.78507e9i 1.55425i
\(248\) 3.00923e8 0.0795515
\(249\) 2.32186e9i 0.604002i
\(250\) 9.26121e8i 0.237087i
\(251\) −3.87770e8 −0.0976967 −0.0488483 0.998806i \(-0.515555\pi\)
−0.0488483 + 0.998806i \(0.515555\pi\)
\(252\) −2.06117e9 −0.511107
\(253\) 7.63376e8 0.186319
\(254\) 8.34012e9i 2.00372i
\(255\) −2.41683e8 −0.0571592
\(256\) 2.30701e10 5.37143
\(257\) 3.53688e9 0.810751 0.405375 0.914150i \(-0.367141\pi\)
0.405375 + 0.914150i \(0.367141\pi\)
\(258\) −8.14890e8 −0.183916
\(259\) 4.32237e9i 0.960556i
\(260\) 6.86058e8i 0.150130i
\(261\) 2.43207e8 0.0524100
\(262\) 8.91841e9 1.89270
\(263\) −7.41461e9 −1.54976 −0.774881 0.632107i \(-0.782190\pi\)
−0.774881 + 0.632107i \(0.782190\pi\)
\(264\) 4.44591e9 0.915261
\(265\) 1.82549e8 0.0370166
\(266\) 9.43808e9i 1.88520i
\(267\) 1.95742e9i 0.385157i
\(268\) 2.22428e10i 4.31171i
\(269\) 9.97114e9i 1.90430i −0.305628 0.952151i \(-0.598866\pi\)
0.305628 0.952151i \(-0.401134\pi\)
\(270\) 1.21463e8i 0.0228554i
\(271\) −1.49482e9 −0.277147 −0.138574 0.990352i \(-0.544252\pi\)
−0.138574 + 0.990352i \(0.544252\pi\)
\(272\) 3.88616e10 7.09979
\(273\) 1.49062e9i 0.268359i
\(274\) 1.17506e10i 2.08477i
\(275\) 2.46720e9i 0.431393i
\(276\) 4.12738e9i 0.711277i
\(277\) 2.03151e9 0.345063 0.172532 0.985004i \(-0.444805\pi\)
0.172532 + 0.985004i \(0.444805\pi\)
\(278\) 1.08698e10i 1.81987i
\(279\) 4.38834e7i 0.00724242i
\(280\) 7.28314e8i 0.118491i
\(281\) −3.16483e9 −0.507604 −0.253802 0.967256i \(-0.581681\pi\)
−0.253802 + 0.967256i \(0.581681\pi\)
\(282\) −5.30026e9 −0.838110
\(283\) 3.37837e9i 0.526698i −0.964701 0.263349i \(-0.915173\pi\)
0.964701 0.263349i \(-0.0848270\pi\)
\(284\) −6.52841e9 −1.00354
\(285\) 4.12199e8 0.0624780
\(286\) 4.94118e9i 0.738527i
\(287\) 3.37869e9 0.497990
\(288\) 1.11343e10i 1.61843i
\(289\) 1.17507e10 1.68450
\(290\) 1.32068e8i 0.0186727i
\(291\) 6.87701e9i 0.959020i
\(292\) 2.17638e10i 2.99367i
\(293\) −7.85832e8 −0.106625 −0.0533125 0.998578i \(-0.516978\pi\)
−0.0533125 + 0.998578i \(0.516978\pi\)
\(294\) 6.04596e9i 0.809237i
\(295\) −2.26751e8 3.97490e8i −0.0299406 0.0524853i
\(296\) 5.04086e10 6.56656
\(297\) 6.48345e8i 0.0833260i
\(298\) 8.45823e9 1.07254
\(299\) 2.98488e9 0.373459
\(300\) −1.33395e10 −1.64686
\(301\) 7.12555e8i 0.0868066i
\(302\) −2.40299e10 −2.88884
\(303\) 1.72638e9i 0.204817i
\(304\) −6.62797e10 −7.76044
\(305\) 4.49385e8i 0.0519301i
\(306\) 9.41136e9i 1.07341i
\(307\) 5.01321e9 0.564368 0.282184 0.959360i \(-0.408941\pi\)
0.282184 + 0.959360i \(0.408941\pi\)
\(308\) 5.97445e9i 0.663888i
\(309\) 6.03708e9i 0.662206i
\(310\) −2.38299e7 −0.00258034
\(311\) 1.21298e10 1.29661 0.648306 0.761380i \(-0.275478\pi\)
0.648306 + 0.761380i \(0.275478\pi\)
\(312\) 1.73840e10 1.83456
\(313\) 1.81441e10i 1.89042i −0.326457 0.945212i \(-0.605855\pi\)
0.326457 0.945212i \(-0.394145\pi\)
\(314\) −2.19060e10 −2.25343
\(315\) 1.06210e8 0.0107875
\(316\) −3.20671e10 −3.21596
\(317\) −1.64494e10 −1.62897 −0.814485 0.580184i \(-0.802981\pi\)
−0.814485 + 0.580184i \(0.802981\pi\)
\(318\) 7.10862e9i 0.695148i
\(319\) 7.04953e8i 0.0680766i
\(320\) −3.30072e9 −0.314781
\(321\) 6.02589e9 0.567546
\(322\) −4.86970e9 −0.452980
\(323\) −3.19385e10 −2.93430
\(324\) −3.50544e9 −0.318099
\(325\) 9.64701e9i 0.864688i
\(326\) 3.25901e10i 2.88546i
\(327\) 5.00841e9i 0.438035i
\(328\) 3.94031e10i 3.40436i
\(329\) 4.63465e9i 0.395579i
\(330\) −3.52069e8 −0.0296874
\(331\) −8.69871e9 −0.724674 −0.362337 0.932047i \(-0.618021\pi\)
−0.362337 + 0.932047i \(0.618021\pi\)
\(332\) 3.63878e10i 2.99505i
\(333\) 7.35106e9i 0.597824i
\(334\) 3.63779e10i 2.92315i
\(335\) 1.14614e9i 0.0910038i
\(336\) −1.70780e10 −1.33993
\(337\) 1.15654e10i 0.896688i −0.893861 0.448344i \(-0.852014\pi\)
0.893861 0.448344i \(-0.147986\pi\)
\(338\) 6.33157e9i 0.485115i
\(339\) 2.71574e9i 0.205631i
\(340\) −3.78763e9 −0.283434
\(341\) 1.27199e8 0.00940735
\(342\) 1.60514e10i 1.17330i
\(343\) −1.26999e10 −0.917536
\(344\) −8.31001e9 −0.593428
\(345\) 2.12679e8i 0.0150124i
\(346\) 1.64540e10 1.14807
\(347\) 8.66659e9i 0.597765i −0.954290 0.298882i \(-0.903386\pi\)
0.954290 0.298882i \(-0.0966138\pi\)
\(348\) 3.81150e9 0.259884
\(349\) 2.55465e10i 1.72199i 0.508617 + 0.860993i \(0.330157\pi\)
−0.508617 + 0.860993i \(0.669843\pi\)
\(350\) 1.57387e10i 1.04881i
\(351\) 2.53510e9i 0.167019i
\(352\) 3.22737e10 2.10222
\(353\) 1.53693e10i 0.989819i −0.868945 0.494909i \(-0.835201\pi\)
0.868945 0.494909i \(-0.164799\pi\)
\(354\) 1.54786e10 8.82987e9i 0.985641 0.562265i
\(355\) 3.36401e8 0.0211809
\(356\) 3.06763e10i 1.90987i
\(357\) −8.22948e9 −0.506640
\(358\) −3.70364e10 −2.25474
\(359\) 9.62493e8 0.0579455 0.0289728 0.999580i \(-0.490776\pi\)
0.0289728 + 0.999580i \(0.490776\pi\)
\(360\) 1.23865e9i 0.0737458i
\(361\) 3.74886e10 2.20734
\(362\) 6.51908e9i 0.379622i
\(363\) −8.14530e9 −0.469116
\(364\) 2.33607e10i 1.33070i
\(365\) 1.12147e9i 0.0631850i
\(366\) −1.74995e10 −0.975215
\(367\) 1.39474e10i 0.768825i −0.923161 0.384413i \(-0.874404\pi\)
0.923161 0.384413i \(-0.125596\pi\)
\(368\) 3.41979e10i 1.86470i
\(369\) 5.74614e9 0.309935
\(370\) −3.99183e9 −0.212993
\(371\) 6.21592e9 0.328103
\(372\) 6.87735e8i 0.0359128i
\(373\) −3.78415e9 −0.195494 −0.0977469 0.995211i \(-0.531164\pi\)
−0.0977469 + 0.995211i \(0.531164\pi\)
\(374\) 2.72795e10 1.39428
\(375\) 1.37726e9 0.0696451
\(376\) −5.40505e10 −2.70426
\(377\) 2.75644e9i 0.136453i
\(378\) 4.13590e9i 0.202583i
\(379\) 5.94715e9 0.288238 0.144119 0.989560i \(-0.453965\pi\)
0.144119 + 0.989560i \(0.453965\pi\)
\(380\) 6.45991e9 0.309808
\(381\) 1.24028e10 0.588601
\(382\) −3.06851e10 −1.44104
\(383\) 4.08122e10 1.89668 0.948341 0.317254i \(-0.102761\pi\)
0.948341 + 0.317254i \(0.102761\pi\)
\(384\) 6.75820e10i 3.10818i
\(385\) 3.07856e8i 0.0140122i
\(386\) 5.62828e10i 2.53528i
\(387\) 1.21185e9i 0.0540261i
\(388\) 1.07775e11i 4.75547i
\(389\) 2.01704e10 0.880878 0.440439 0.897782i \(-0.354823\pi\)
0.440439 + 0.897782i \(0.354823\pi\)
\(390\) −1.37663e9 −0.0595057
\(391\) 1.64791e10i 0.705061i
\(392\) 6.16549e10i 2.61110i
\(393\) 1.32628e10i 0.555988i
\(394\) 8.17528e10i 3.39248i
\(395\) 1.65238e9 0.0678767
\(396\) 1.01608e10i 0.413186i
\(397\) 1.20249e10i 0.484082i −0.970266 0.242041i \(-0.922183\pi\)
0.970266 0.242041i \(-0.0778169\pi\)
\(398\) 1.58417e10i 0.631350i
\(399\) 1.40356e10 0.553784
\(400\) −1.10526e11 −4.31743
\(401\) 2.78698e10i 1.07785i −0.842355 0.538923i \(-0.818831\pi\)
0.842355 0.538923i \(-0.181169\pi\)
\(402\) −4.46318e10 −1.70899
\(403\) 4.97363e8 0.0188562
\(404\) 2.70555e10i 1.01562i
\(405\) 1.80631e8 0.00671386
\(406\) 4.49701e9i 0.165508i
\(407\) 2.13076e10 0.776527
\(408\) 9.59744e10i 3.46350i
\(409\) 1.72521e10i 0.616521i −0.951302 0.308261i \(-0.900253\pi\)
0.951302 0.308261i \(-0.0997469\pi\)
\(410\) 3.12032e9i 0.110424i
\(411\) 1.74746e10 0.612408
\(412\) 9.46122e10i 3.28366i
\(413\) −7.72101e9 1.35348e10i −0.265384 0.465212i
\(414\) −8.28191e9 −0.281922
\(415\) 1.87502e9i 0.0632141i
\(416\) 1.26194e11 4.21371
\(417\) 1.61647e10 0.534594
\(418\) −4.65260e10 −1.52402
\(419\) 1.82949e10i 0.593573i 0.954944 + 0.296786i \(0.0959149\pi\)
−0.954944 + 0.296786i \(0.904085\pi\)
\(420\) 1.66450e9 0.0534918
\(421\) 2.14261e10i 0.682046i 0.940055 + 0.341023i \(0.110773\pi\)
−0.940055 + 0.341023i \(0.889227\pi\)
\(422\) −1.61514e10 −0.509284
\(423\) 7.88217e9i 0.246198i
\(424\) 7.24917e10i 2.24298i
\(425\) −5.32597e10 −1.63246
\(426\) 1.30998e10i 0.397764i
\(427\) 1.53019e10i 0.460291i
\(428\) 9.44368e10 2.81427
\(429\) 7.34816e9 0.216945
\(430\) 6.58066e8 0.0192484
\(431\) 4.23508e9i 0.122730i −0.998115 0.0613652i \(-0.980455\pi\)
0.998115 0.0613652i \(-0.0195454\pi\)
\(432\) −2.90447e10 −0.833934
\(433\) −2.36362e9 −0.0672397 −0.0336199 0.999435i \(-0.510704\pi\)
−0.0336199 + 0.999435i \(0.510704\pi\)
\(434\) −8.11425e8 −0.0228712
\(435\) −1.96402e8 −0.00548516
\(436\) 7.84911e10i 2.17207i
\(437\) 2.81056e10i 0.770668i
\(438\) 4.36708e10 1.18657
\(439\) 4.85762e10 1.30787 0.653937 0.756549i \(-0.273116\pi\)
0.653937 + 0.756549i \(0.273116\pi\)
\(440\) −3.59030e9 −0.0957901
\(441\) −8.99111e9 −0.237716
\(442\) 1.06666e11 2.79471
\(443\) 5.86159e10i 1.52195i −0.648781 0.760975i \(-0.724721\pi\)
0.648781 0.760975i \(-0.275279\pi\)
\(444\) 1.15205e11i 2.96441i
\(445\) 1.58072e9i 0.0403101i
\(446\) 4.38051e10i 1.10710i
\(447\) 1.25785e10i 0.315063i
\(448\) −1.12392e11 −2.79011
\(449\) 5.15270e10 1.26780 0.633898 0.773417i \(-0.281454\pi\)
0.633898 + 0.773417i \(0.281454\pi\)
\(450\) 2.67668e10i 0.652749i
\(451\) 1.66556e10i 0.402582i
\(452\) 4.25606e10i 1.01966i
\(453\) 3.57355e10i 0.848607i
\(454\) −6.33726e10 −1.49169
\(455\) 1.20375e9i 0.0280861i
\(456\) 1.63687e11i 3.78578i
\(457\) 9.53474e9i 0.218597i 0.994009 + 0.109299i \(0.0348604\pi\)
−0.994009 + 0.109299i \(0.965140\pi\)
\(458\) 8.70071e10 1.97739
\(459\) −1.39959e10 −0.315319
\(460\) 3.33308e9i 0.0744413i
\(461\) −2.27246e10 −0.503144 −0.251572 0.967839i \(-0.580948\pi\)
−0.251572 + 0.967839i \(0.580948\pi\)
\(462\) −1.19882e10 −0.263139
\(463\) 3.40934e10i 0.741902i 0.928652 + 0.370951i \(0.120968\pi\)
−0.928652 + 0.370951i \(0.879032\pi\)
\(464\) 3.15806e10 0.681317
\(465\) 3.54382e7i 0.000757983i
\(466\) 7.21788e10 1.53061
\(467\) 5.25875e10i 1.10564i 0.833299 + 0.552822i \(0.186449\pi\)
−0.833299 + 0.552822i \(0.813551\pi\)
\(468\) 3.97297e10i 0.828193i
\(469\) 3.90269e10i 0.806627i
\(470\) 4.28024e9 0.0877155
\(471\) 3.25770e10i 0.661954i
\(472\) 1.57846e11 9.00445e10i 3.18029 1.81422i
\(473\) −3.51262e9 −0.0701757
\(474\) 6.43450e10i 1.27468i
\(475\) 9.08361e10 1.78437
\(476\) −1.28971e11 −2.51226
\(477\) 1.05714e10 0.204202
\(478\) 7.50494e10i 1.43759i
\(479\) 5.04232e10 0.957830 0.478915 0.877861i \(-0.341030\pi\)
0.478915 + 0.877861i \(0.341030\pi\)
\(480\) 8.99157e9i 0.169383i
\(481\) 8.33150e10 1.55648
\(482\) 1.37651e11i 2.55030i
\(483\) 7.24187e9i 0.133064i
\(484\) −1.27652e11 −2.32619
\(485\) 5.55355e9i 0.100370i
\(486\) 7.03393e9i 0.126082i
\(487\) 5.41279e10 0.962289 0.481145 0.876641i \(-0.340221\pi\)
0.481145 + 0.876641i \(0.340221\pi\)
\(488\) −1.78454e11 −3.14665
\(489\) −4.84656e10 −0.847614
\(490\) 4.88243e9i 0.0846938i
\(491\) −7.11541e10 −1.22426 −0.612131 0.790757i \(-0.709687\pi\)
−0.612131 + 0.790757i \(0.709687\pi\)
\(492\) 9.00527e10 1.53687
\(493\) 1.52179e10 0.257613
\(494\) −1.81922e11 −3.05476
\(495\) 5.23572e8i 0.00872079i
\(496\) 5.69830e9i 0.0941496i
\(497\) 1.14547e10 0.187740
\(498\) 7.30150e10 1.18712
\(499\) −6.70056e10 −1.08071 −0.540355 0.841437i \(-0.681710\pi\)
−0.540355 + 0.841437i \(0.681710\pi\)
\(500\) 2.15842e10 0.345347
\(501\) 5.40986e10 0.858687
\(502\) 1.21941e10i 0.192015i
\(503\) 7.59711e10i 1.18680i −0.804909 0.593398i \(-0.797786\pi\)
0.804909 0.593398i \(-0.202214\pi\)
\(504\) 4.21767e10i 0.653657i
\(505\) 1.39414e9i 0.0214359i
\(506\) 2.40057e10i 0.366195i
\(507\) −9.41585e9 −0.142504
\(508\) 1.94375e11 2.91868
\(509\) 1.73280e10i 0.258152i −0.991635 0.129076i \(-0.958799\pi\)
0.991635 0.129076i \(-0.0412012\pi\)
\(510\) 7.60017e9i 0.112342i
\(511\) 3.81866e10i 0.560051i
\(512\) 3.55528e11i 5.17361i
\(513\) 2.38704e10 0.344660
\(514\) 1.11223e11i 1.59347i
\(515\) 4.87526e9i 0.0693057i
\(516\) 1.89919e10i 0.267897i
\(517\) −2.28470e10 −0.319792
\(518\) −1.35925e11 −1.88790
\(519\) 2.44692e10i 0.337249i
\(520\) −1.40385e10 −0.192002
\(521\) −2.24043e10 −0.304075 −0.152037 0.988375i \(-0.548583\pi\)
−0.152037 + 0.988375i \(0.548583\pi\)
\(522\) 7.64808e9i 0.103008i
\(523\) 1.85587e10 0.248050 0.124025 0.992279i \(-0.460420\pi\)
0.124025 + 0.992279i \(0.460420\pi\)
\(524\) 2.07853e11i 2.75696i
\(525\) 2.34054e10 0.308091
\(526\) 2.33166e11i 3.04594i
\(527\) 2.74587e9i 0.0355989i
\(528\) 8.41881e10i 1.08322i
\(529\) 6.38095e10 0.814822
\(530\) 5.74058e9i 0.0727533i
\(531\) −1.31311e10 2.30187e10i −0.165167 0.289536i
\(532\) 2.19964e11 2.74603
\(533\) 6.51252e10i 0.806938i
\(534\) 6.15545e10 0.756998
\(535\) −4.86622e9 −0.0593986
\(536\) −4.55142e11 −5.51427
\(537\) 5.50778e10i 0.662337i
\(538\) −3.13560e11 −3.74276
\(539\) 2.60614e10i 0.308775i
\(540\) 2.83082e9 0.0332918
\(541\) 1.21915e11i 1.42320i −0.702583 0.711602i \(-0.747970\pi\)
0.702583 0.711602i \(-0.252030\pi\)
\(542\) 4.70071e10i 0.544711i
\(543\) 9.69470e9 0.111515
\(544\) 6.96697e11i 7.95515i
\(545\) 4.04456e9i 0.0458442i
\(546\) −4.68751e10 −0.527438
\(547\) −2.86927e10 −0.320496 −0.160248 0.987077i \(-0.551229\pi\)
−0.160248 + 0.987077i \(0.551229\pi\)
\(548\) 2.73860e11 3.03673
\(549\) 2.60239e10i 0.286473i
\(550\) −7.75855e10 −0.847871
\(551\) −2.59546e10 −0.281584
\(552\) −8.44566e10 −0.909656
\(553\) 5.62645e10 0.601636
\(554\) 6.38843e10i 0.678196i
\(555\) 5.93637e9i 0.0625675i
\(556\) 2.53331e11 2.65088
\(557\) −6.01837e9 −0.0625256 −0.0312628 0.999511i \(-0.509953\pi\)
−0.0312628 + 0.999511i \(0.509953\pi\)
\(558\) −1.37999e9 −0.0142344
\(559\) −1.37347e10 −0.140661
\(560\) 1.37914e10 0.140235
\(561\) 4.05681e10i 0.409575i
\(562\) 9.95236e10i 0.997656i
\(563\) 1.35572e11i 1.34939i 0.738097 + 0.674695i \(0.235725\pi\)
−0.738097 + 0.674695i \(0.764275\pi\)
\(564\) 1.23528e11i 1.22081i
\(565\) 2.19310e9i 0.0215211i
\(566\) −1.06239e11 −1.03518
\(567\) 6.15061e9 0.0595094
\(568\) 1.33588e11i 1.28343i
\(569\) 1.49267e11i 1.42402i −0.702171 0.712008i \(-0.747786\pi\)
0.702171 0.712008i \(-0.252214\pi\)
\(570\) 1.29623e10i 0.122796i
\(571\) 1.48625e11i 1.39813i 0.715058 + 0.699065i \(0.246400\pi\)
−0.715058 + 0.699065i \(0.753600\pi\)
\(572\) 1.15159e11 1.07576
\(573\) 4.56327e10i 0.423309i
\(574\) 1.06249e11i 0.978761i
\(575\) 4.68681e10i 0.428752i
\(576\) −1.91145e11 −1.73649
\(577\) 9.53737e10 0.860449 0.430225 0.902722i \(-0.358434\pi\)
0.430225 + 0.902722i \(0.358434\pi\)
\(578\) 3.69521e11i 3.31076i
\(579\) 8.36997e10 0.744749
\(580\) −3.07799e9 −0.0271991
\(581\) 6.38457e10i 0.560309i
\(582\) 2.16260e11 1.88488
\(583\) 3.06421e10i 0.265243i
\(584\) 4.45342e11 3.82862
\(585\) 2.04722e9i 0.0174800i
\(586\) 2.47119e10i 0.209563i
\(587\) 5.24214e10i 0.441526i 0.975327 + 0.220763i \(0.0708548\pi\)
−0.975327 + 0.220763i \(0.929145\pi\)
\(588\) −1.40907e11 −1.17876
\(589\) 4.68316e9i 0.0389115i
\(590\) −1.24998e10 + 7.13058e9i −0.103156 + 0.0588460i
\(591\) 1.21577e11 0.996554
\(592\) 9.54542e11i 7.77156i
\(593\) 9.14118e8 0.00739237 0.00369618 0.999993i \(-0.498823\pi\)
0.00369618 + 0.999993i \(0.498823\pi\)
\(594\) −2.03884e10 −0.163771
\(595\) 6.64573e9 0.0530243
\(596\) 1.97128e11i 1.56229i
\(597\) −2.35587e10 −0.185461
\(598\) 9.38649e10i 0.734004i
\(599\) −2.33750e11 −1.81570 −0.907851 0.419292i \(-0.862278\pi\)
−0.907851 + 0.419292i \(0.862278\pi\)
\(600\) 2.72960e11i 2.10617i
\(601\) 1.03825e11i 0.795799i −0.917429 0.397900i \(-0.869739\pi\)
0.917429 0.397900i \(-0.130261\pi\)
\(602\) 2.24076e10 0.170612
\(603\) 6.63732e10i 0.502023i
\(604\) 5.60041e11i 4.20796i
\(605\) 6.57775e9 0.0490971
\(606\) 5.42891e10 0.402552
\(607\) 1.68867e11 1.24391 0.621956 0.783052i \(-0.286338\pi\)
0.621956 + 0.783052i \(0.286338\pi\)
\(608\) 1.18824e12i 8.69539i
\(609\) −6.68763e9 −0.0486186
\(610\) 1.41317e10 0.102065
\(611\) −8.93343e10 −0.640993
\(612\) −2.19342e11 −1.56356
\(613\) 6.54092e10i 0.463230i −0.972807 0.231615i \(-0.925599\pi\)
0.972807 0.231615i \(-0.0744010\pi\)
\(614\) 1.57649e11i 1.10922i
\(615\) −4.64031e9 −0.0324374
\(616\) −1.22252e11 −0.849051
\(617\) −1.26499e11 −0.872861 −0.436431 0.899738i \(-0.643758\pi\)
−0.436431 + 0.899738i \(0.643758\pi\)
\(618\) −1.89847e11 −1.30152
\(619\) −2.43799e11 −1.66062 −0.830308 0.557305i \(-0.811835\pi\)
−0.830308 + 0.557305i \(0.811835\pi\)
\(620\) 5.55381e8i 0.00375859i
\(621\) 1.23163e10i 0.0828157i
\(622\) 3.81442e11i 2.54839i
\(623\) 5.38244e10i 0.357295i
\(624\) 3.29184e11i 2.17121i
\(625\) 1.50919e11 0.989060
\(626\) −5.70575e11 −3.71548
\(627\) 6.91902e10i 0.447687i
\(628\) 5.10542e11i 3.28241i
\(629\) 4.59970e11i 2.93851i
\(630\) 3.33995e9i 0.0212021i
\(631\) −2.22925e11 −1.40618 −0.703089 0.711102i \(-0.748197\pi\)
−0.703089 + 0.711102i \(0.748197\pi\)
\(632\) 6.56172e11i 4.11291i
\(633\) 2.40192e10i 0.149604i
\(634\) 5.17281e11i 3.20162i
\(635\) −1.00159e10 −0.0616022
\(636\) 1.65674e11 1.01257
\(637\) 1.01903e11i 0.618911i
\(638\) 2.21685e10 0.133799
\(639\) 1.94810e10 0.116845
\(640\) 5.45760e10i 0.325298i
\(641\) −1.03535e11 −0.613273 −0.306637 0.951827i \(-0.599204\pi\)
−0.306637 + 0.951827i \(0.599204\pi\)
\(642\) 1.89495e11i 1.11547i
\(643\) −2.49767e11 −1.46114 −0.730569 0.682839i \(-0.760745\pi\)
−0.730569 + 0.682839i \(0.760745\pi\)
\(644\) 1.13493e11i 0.659823i
\(645\) 9.78628e8i 0.00565430i
\(646\) 1.00436e12i 5.76714i
\(647\) −1.61624e10 −0.0922333 −0.0461167 0.998936i \(-0.514685\pi\)
−0.0461167 + 0.998936i \(0.514685\pi\)
\(648\) 7.17300e10i 0.406819i
\(649\) 6.67212e10 3.80616e10i 0.376084 0.214540i
\(650\) −3.03368e11 −1.69948
\(651\) 1.20669e9i 0.00671850i
\(652\) −7.59546e11 −4.20304
\(653\) 4.42350e10 0.243284 0.121642 0.992574i \(-0.461184\pi\)
0.121642 + 0.992574i \(0.461184\pi\)
\(654\) 1.57498e11 0.860925
\(655\) 1.07104e10i 0.0581890i
\(656\) 7.46141e11 4.02908
\(657\) 6.49441e10i 0.348560i
\(658\) 1.45745e11 0.777481
\(659\) 5.50304e10i 0.291784i −0.989301 0.145892i \(-0.953395\pi\)
0.989301 0.145892i \(-0.0466052\pi\)
\(660\) 8.20535e9i 0.0432435i
\(661\) 1.96165e11 1.02758 0.513790 0.857916i \(-0.328241\pi\)
0.513790 + 0.857916i \(0.328241\pi\)
\(662\) 2.73546e11i 1.42429i
\(663\) 1.58626e11i 0.820955i
\(664\) 7.44586e11 3.83039
\(665\) −1.13345e10 −0.0579583
\(666\) −2.31167e11 −1.17498
\(667\) 1.33916e10i 0.0676597i
\(668\) 8.47825e11 4.25795
\(669\) 6.51438e10 0.325214
\(670\) 3.60425e10 0.178861
\(671\) −7.54322e10 −0.372106
\(672\) 3.06169e11i 1.50136i
\(673\) 2.22802e11i 1.08607i −0.839710 0.543036i \(-0.817275\pi\)
0.839710 0.543036i \(-0.182725\pi\)
\(674\) −3.63695e11 −1.76237
\(675\) 3.98056e10 0.191747
\(676\) −1.47564e11 −0.706632
\(677\) 4.92757e10 0.234573 0.117287 0.993098i \(-0.462580\pi\)
0.117287 + 0.993098i \(0.462580\pi\)
\(678\) 8.54012e10 0.404153
\(679\) 1.89102e11i 0.889645i
\(680\) 7.75043e10i 0.362485i
\(681\) 9.42432e10i 0.438189i
\(682\) 4.00001e9i 0.0184894i
\(683\) 4.89565e10i 0.224971i −0.993653 0.112486i \(-0.964119\pi\)
0.993653 0.112486i \(-0.0358812\pi\)
\(684\) 3.74094e11 1.70906
\(685\) −1.41117e10 −0.0640939
\(686\) 3.99370e11i 1.80335i
\(687\) 1.29391e11i 0.580866i
\(688\) 1.57359e11i 0.702325i
\(689\) 1.19814e11i 0.531655i
\(690\) 6.68808e9 0.0295056
\(691\) 2.12401e11i 0.931633i 0.884881 + 0.465817i \(0.154239\pi\)
−0.884881 + 0.465817i \(0.845761\pi\)
\(692\) 3.83478e11i 1.67231i
\(693\) 1.78280e10i 0.0772981i
\(694\) −2.72536e11 −1.17486
\(695\) −1.30539e10 −0.0559500
\(696\) 7.79929e10i 0.332367i
\(697\) 3.59547e11 1.52344
\(698\) 8.03355e11 3.38443
\(699\) 1.07339e11i 0.449623i
\(700\) 3.66806e11 1.52772
\(701\) 3.64391e11i 1.50902i −0.656287 0.754512i \(-0.727874\pi\)
0.656287 0.754512i \(-0.272126\pi\)
\(702\) −7.97206e10 −0.328263
\(703\) 7.84492e11i 3.21194i
\(704\) 5.54047e11i 2.25557i
\(705\) 6.36526e9i 0.0257668i
\(706\) −4.83315e11 −1.94541
\(707\) 4.74714e10i 0.190000i
\(708\) −2.05789e11 3.60745e11i −0.819011 1.43571i
\(709\) 2.29697e10 0.0909015 0.0454508 0.998967i \(-0.485528\pi\)
0.0454508 + 0.998967i \(0.485528\pi\)
\(710\) 1.05787e10i 0.0416294i
\(711\) 9.56893e10 0.374442
\(712\) 6.27715e11 2.44254
\(713\) −2.41634e9 −0.00934974
\(714\) 2.58791e11i 0.995762i
\(715\) −5.93402e9 −0.0227052
\(716\) 8.63171e11i 3.28431i
\(717\) −1.11608e11 −0.422298
\(718\) 3.02673e10i 0.113888i
\(719\) 2.79967e11i 1.04759i −0.851844 0.523796i \(-0.824515\pi\)
0.851844 0.523796i \(-0.175485\pi\)
\(720\) 2.34551e10 0.0872785
\(721\) 1.66006e11i 0.614302i
\(722\) 1.17889e12i 4.33836i
\(723\) 2.04705e11 0.749159
\(724\) 1.51934e11 0.552968
\(725\) −4.32812e10 −0.156656
\(726\) 2.56143e11i 0.922012i
\(727\) 2.27790e11 0.815450 0.407725 0.913105i \(-0.366322\pi\)
0.407725 + 0.913105i \(0.366322\pi\)
\(728\) −4.78019e11 −1.70184
\(729\) 1.04604e10 0.0370370
\(730\) −3.52665e10 −0.124185
\(731\) 7.58274e10i 0.265556i
\(732\) 4.07843e11i 1.42052i
\(733\) −2.02311e11 −0.700815 −0.350408 0.936597i \(-0.613957\pi\)
−0.350408 + 0.936597i \(0.613957\pi\)
\(734\) −4.38599e11 −1.51107
\(735\) 7.26079e9 0.0248791
\(736\) −6.13087e11 −2.08935
\(737\) −1.92388e11 −0.652089
\(738\) 1.80698e11i 0.609154i
\(739\) 5.04605e11i 1.69190i −0.533264 0.845949i \(-0.679035\pi\)
0.533264 0.845949i \(-0.320965\pi\)
\(740\) 9.30339e10i 0.310252i
\(741\) 2.70541e11i 0.897346i
\(742\) 1.95471e11i 0.644861i
\(743\) −3.95146e11 −1.29659 −0.648294 0.761390i \(-0.724517\pi\)
−0.648294 + 0.761390i \(0.724517\pi\)
\(744\) −1.40728e10 −0.0459291
\(745\) 1.01578e10i 0.0329741i
\(746\) 1.18999e11i 0.384228i
\(747\) 1.08583e11i 0.348721i
\(748\) 6.35778e11i 2.03095i
\(749\) −1.65698e11 −0.526490
\(750\) 4.33104e10i 0.136882i
\(751\) 3.95840e11i 1.24440i −0.782859 0.622200i \(-0.786239\pi\)
0.782859 0.622200i \(-0.213761\pi\)
\(752\) 1.02351e12i 3.20051i
\(753\) 1.81342e10 0.0564052
\(754\) 8.66812e10 0.268188
\(755\) 2.88583e10i 0.0888142i
\(756\) 9.63913e10 0.295088
\(757\) −5.41866e11 −1.65009 −0.825047 0.565064i \(-0.808851\pi\)
−0.825047 + 0.565064i \(0.808851\pi\)
\(758\) 1.87019e11i 0.566511i
\(759\) −3.56996e10 −0.107571
\(760\) 1.32186e11i 0.396215i
\(761\) −2.60900e11 −0.777921 −0.388960 0.921255i \(-0.627166\pi\)
−0.388960 + 0.921255i \(0.627166\pi\)
\(762\) 3.90029e11i 1.15685i
\(763\) 1.37720e11i 0.406348i
\(764\) 7.15149e11i 2.09905i
\(765\) 1.13024e10 0.0330009
\(766\) 1.28341e12i 3.72778i
\(767\) 2.60887e11 1.48825e11i 0.753826 0.430025i
\(768\) −1.07888e12 −3.10120
\(769\) 6.34131e10i 0.181332i −0.995881 0.0906658i \(-0.971101\pi\)
0.995881 0.0906658i \(-0.0288995\pi\)
\(770\) 9.68109e9 0.0275398
\(771\) −1.65403e11 −0.468087
\(772\) 1.31173e12 3.69296
\(773\) 5.07360e11i 1.42101i 0.703691 + 0.710506i \(0.251534\pi\)
−0.703691 + 0.710506i \(0.748466\pi\)
\(774\) 3.81086e10 0.106184
\(775\) 7.80950e9i 0.0216479i
\(776\) 2.20536e12 6.08180
\(777\) 2.02137e11i 0.554577i
\(778\) 6.34294e11i 1.73130i
\(779\) −6.13218e11 −1.66519
\(780\) 3.20838e10i 0.0866776i
\(781\) 5.64671e10i 0.151772i
\(782\) −5.18215e11