Properties

Label 177.11.c.a.58.2
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.2
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.99

$q$-expansion

\(f(q)\) \(=\) \(q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} -224473. i q^{10} -271175. i q^{11} +421345. q^{12} -568274. i q^{13} +969335. i q^{14} -496254. q^{15} +4.89563e6 q^{16} -787841. q^{17} -1.24910e6i q^{18} -2.77833e6 q^{19} -1.06231e7 q^{20} +2.14297e6 q^{21} -1.72089e7 q^{22} +8.00619e6i q^{23} -1.76219e7i q^{24} +2.74610e6 q^{25} -3.60631e7 q^{26} -2.76145e6 q^{27} +4.58735e7 q^{28} -3.11900e7 q^{29} +3.14926e7i q^{30} -4.29591e7i q^{31} -1.82061e8i q^{32} +3.80447e7i q^{33} +4.99969e7i q^{34} -5.40291e7 q^{35} -5.91131e7 q^{36} +6.24534e7i q^{37} +1.76315e8i q^{38} +7.97267e7i q^{39} +4.44288e8i q^{40} +6.93263e7 q^{41} -1.35994e8i q^{42} -9.52345e7i q^{43} +8.14406e8i q^{44} +6.96226e7 q^{45} +5.08078e8 q^{46} -3.13127e8i q^{47} -6.86838e8 q^{48} -4.91622e7 q^{49} -1.74269e8i q^{50} +1.10531e8 q^{51} +1.70667e9i q^{52} -1.32764e8 q^{53} +1.75243e8i q^{54} -9.59197e8i q^{55} -1.91856e9i q^{56} +3.89789e8 q^{57} +1.97934e9i q^{58} +(-5.75728e8 - 4.23855e8i) q^{59} +1.49038e9 q^{60} +8.26364e8i q^{61} -2.72621e9 q^{62} -3.00650e8 q^{63} -6.54056e9 q^{64} -2.01010e9i q^{65} +2.41434e9 q^{66} -1.28334e8i q^{67} +2.36609e9 q^{68} -1.12324e9i q^{69} +3.42873e9i q^{70} +1.24650e9 q^{71} +2.47228e9i q^{72} +2.30278e9i q^{73} +3.96333e9 q^{74} -3.85268e8 q^{75} +8.34403e9 q^{76} +4.14208e9i q^{77} +5.05951e9 q^{78} -1.18761e9 q^{79} +1.73168e10 q^{80} +3.87420e8 q^{81} -4.39949e9i q^{82} +2.67136e9i q^{83} -6.43587e9 q^{84} -2.78674e9 q^{85} -6.04364e9 q^{86} +4.37583e9 q^{87} +3.40608e10 q^{88} +4.15156e9i q^{89} -4.41829e9i q^{90} +8.68016e9i q^{91} -2.40446e10i q^{92} +6.02700e9i q^{93} -1.98712e10 q^{94} -9.82749e9 q^{95} +2.55424e10i q^{96} -6.37540e9i q^{97} +3.11987e9i q^{98} -5.33753e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 63.4607i 1.98315i −0.129551 0.991573i \(-0.541354\pi\)
0.129551 0.991573i \(-0.458646\pi\)
\(3\) −140.296 −0.577350
\(4\) −3003.25 −2.93287
\(5\) 3537.19 1.13190 0.565951 0.824439i \(-0.308509\pi\)
0.565951 + 0.824439i \(0.308509\pi\)
\(6\) 8903.28i 1.14497i
\(7\) −15274.6 −0.908823 −0.454411 0.890792i \(-0.650150\pi\)
−0.454411 + 0.890792i \(0.650150\pi\)
\(8\) 125605.i 3.83315i
\(9\) 19683.0 0.333333
\(10\) 224473.i 2.24473i
\(11\) 271175.i 1.68378i −0.539648 0.841891i \(-0.681443\pi\)
0.539648 0.841891i \(-0.318557\pi\)
\(12\) 421345. 1.69329
\(13\) 568274.i 1.53053i −0.643717 0.765264i \(-0.722608\pi\)
0.643717 0.765264i \(-0.277392\pi\)
\(14\) 969335.i 1.80233i
\(15\) −496254. −0.653504
\(16\) 4.89563e6 4.66884
\(17\) −787841. −0.554873 −0.277437 0.960744i \(-0.589485\pi\)
−0.277437 + 0.960744i \(0.589485\pi\)
\(18\) 1.24910e6i 0.661048i
\(19\) −2.77833e6 −1.12206 −0.561030 0.827796i \(-0.689595\pi\)
−0.561030 + 0.827796i \(0.689595\pi\)
\(20\) −1.06231e7 −3.31972
\(21\) 2.14297e6 0.524709
\(22\) −1.72089e7 −3.33918
\(23\) 8.00619e6i 1.24390i 0.783055 + 0.621952i \(0.213660\pi\)
−0.783055 + 0.621952i \(0.786340\pi\)
\(24\) 1.76219e7i 2.21307i
\(25\) 2.74610e6 0.281201
\(26\) −3.60631e7 −3.03526
\(27\) −2.76145e6 −0.192450
\(28\) 4.58735e7 2.66546
\(29\) −3.11900e7 −1.52063 −0.760317 0.649552i \(-0.774957\pi\)
−0.760317 + 0.649552i \(0.774957\pi\)
\(30\) 3.14926e7i 1.29599i
\(31\) 4.29591e7i 1.50054i −0.661133 0.750269i \(-0.729924\pi\)
0.661133 0.750269i \(-0.270076\pi\)
\(32\) 1.82061e8i 5.42583i
\(33\) 3.80447e7i 0.972131i
\(34\) 4.99969e7i 1.10039i
\(35\) −5.40291e7 −1.02870
\(36\) −5.91131e7 −0.977622
\(37\) 6.24534e7i 0.900632i 0.892869 + 0.450316i \(0.148689\pi\)
−0.892869 + 0.450316i \(0.851311\pi\)
\(38\) 1.76315e8i 2.22521i
\(39\) 7.97267e7i 0.883651i
\(40\) 4.44288e8i 4.33875i
\(41\) 6.93263e7 0.598382 0.299191 0.954193i \(-0.403283\pi\)
0.299191 + 0.954193i \(0.403283\pi\)
\(42\) 1.35994e8i 1.04057i
\(43\) 9.52345e7i 0.647816i −0.946089 0.323908i \(-0.895003\pi\)
0.946089 0.323908i \(-0.104997\pi\)
\(44\) 8.14406e8i 4.93830i
\(45\) 6.96226e7 0.377300
\(46\) 5.08078e8 2.46684
\(47\) 3.13127e8i 1.36531i −0.730741 0.682654i \(-0.760825\pi\)
0.730741 0.682654i \(-0.239175\pi\)
\(48\) −6.86838e8 −2.69555
\(49\) −4.91622e7 −0.174041
\(50\) 1.74269e8i 0.557662i
\(51\) 1.10531e8 0.320356
\(52\) 1.70667e9i 4.48883i
\(53\) −1.32764e8 −0.317469 −0.158734 0.987321i \(-0.550741\pi\)
−0.158734 + 0.987321i \(0.550741\pi\)
\(54\) 1.75243e8i 0.381657i
\(55\) 9.59197e8i 1.90587i
\(56\) 1.91856e9i 3.48366i
\(57\) 3.89789e8 0.647821
\(58\) 1.97934e9i 3.01564i
\(59\) −5.75728e8 4.23855e8i −0.805300 0.592868i
\(60\) 1.49038e9 1.91664
\(61\) 8.26364e8i 0.978413i 0.872168 + 0.489206i \(0.162713\pi\)
−0.872168 + 0.489206i \(0.837287\pi\)
\(62\) −2.72621e9 −2.97578
\(63\) −3.00650e8 −0.302941
\(64\) −6.54056e9 −6.09137
\(65\) 2.01010e9i 1.73241i
\(66\) 2.41434e9 1.92788
\(67\) 1.28334e8i 0.0950533i −0.998870 0.0475266i \(-0.984866\pi\)
0.998870 0.0475266i \(-0.0151339\pi\)
\(68\) 2.36609e9 1.62737
\(69\) 1.12324e9i 0.718168i
\(70\) 3.42873e9i 2.04006i
\(71\) 1.24650e9 0.690878 0.345439 0.938441i \(-0.387730\pi\)
0.345439 + 0.938441i \(0.387730\pi\)
\(72\) 2.47228e9i 1.27772i
\(73\) 2.30278e9i 1.11081i 0.831581 + 0.555404i \(0.187436\pi\)
−0.831581 + 0.555404i \(0.812564\pi\)
\(74\) 3.96333e9 1.78608
\(75\) −3.85268e8 −0.162351
\(76\) 8.34403e9 3.29085
\(77\) 4.14208e9i 1.53026i
\(78\) 5.05951e9 1.75241
\(79\) −1.18761e9 −0.385957 −0.192979 0.981203i \(-0.561815\pi\)
−0.192979 + 0.981203i \(0.561815\pi\)
\(80\) 1.73168e10 5.28466
\(81\) 3.87420e8 0.111111
\(82\) 4.39949e9i 1.18668i
\(83\) 2.67136e9i 0.678177i 0.940755 + 0.339088i \(0.110119\pi\)
−0.940755 + 0.339088i \(0.889881\pi\)
\(84\) −6.43587e9 −1.53890
\(85\) −2.78674e9 −0.628062
\(86\) −6.04364e9 −1.28471
\(87\) 4.37583e9 0.877939
\(88\) 3.40608e10 6.45419
\(89\) 4.15156e9i 0.743466i 0.928340 + 0.371733i \(0.121236\pi\)
−0.928340 + 0.371733i \(0.878764\pi\)
\(90\) 4.41829e9i 0.748242i
\(91\) 8.68016e9i 1.39098i
\(92\) 2.40446e10i 3.64820i
\(93\) 6.02700e9i 0.866336i
\(94\) −1.98712e10 −2.70761
\(95\) −9.82749e9 −1.27006
\(96\) 2.55424e10i 3.13260i
\(97\) 6.37540e9i 0.742418i −0.928549 0.371209i \(-0.878943\pi\)
0.928549 0.371209i \(-0.121057\pi\)
\(98\) 3.11987e9i 0.345148i
\(99\) 5.33753e9i 0.561260i
\(100\) −8.24725e9 −0.824725
\(101\) 5.60220e9i 0.533030i 0.963831 + 0.266515i \(0.0858722\pi\)
−0.963831 + 0.266515i \(0.914128\pi\)
\(102\) 7.01437e9i 0.635313i
\(103\) 8.39383e9i 0.724060i −0.932167 0.362030i \(-0.882084\pi\)
0.932167 0.362030i \(-0.117916\pi\)
\(104\) 7.13780e10 5.86675
\(105\) 7.58008e9 0.593919
\(106\) 8.42529e9i 0.629587i
\(107\) 1.66010e10 1.18363 0.591814 0.806075i \(-0.298412\pi\)
0.591814 + 0.806075i \(0.298412\pi\)
\(108\) 8.29333e9 0.564430
\(109\) 1.14611e10i 0.744892i −0.928054 0.372446i \(-0.878519\pi\)
0.928054 0.372446i \(-0.121481\pi\)
\(110\) −6.08713e10 −3.77963
\(111\) 8.76196e9i 0.519980i
\(112\) −7.47787e10 −4.24314
\(113\) 2.70084e10i 1.46591i −0.680279 0.732953i \(-0.738141\pi\)
0.680279 0.732953i \(-0.261859\pi\)
\(114\) 2.47363e10i 1.28472i
\(115\) 2.83194e10i 1.40798i
\(116\) 9.36714e10 4.45982
\(117\) 1.11853e10i 0.510176i
\(118\) −2.68981e10 + 3.65361e10i −1.17574 + 1.59703i
\(119\) 1.20339e10 0.504282
\(120\) 6.23319e10i 2.50498i
\(121\) −4.75983e10 −1.83512
\(122\) 5.24416e10 1.94033
\(123\) −9.72621e9 −0.345476
\(124\) 1.29017e11i 4.40088i
\(125\) −2.48294e10 −0.813610
\(126\) 1.90794e10i 0.600776i
\(127\) 5.99776e9 0.181539 0.0907696 0.995872i \(-0.471067\pi\)
0.0907696 + 0.995872i \(0.471067\pi\)
\(128\) 2.28638e11i 6.65424i
\(129\) 1.33610e10i 0.374017i
\(130\) −1.27562e11 −3.43561
\(131\) 3.52715e10i 0.914256i −0.889401 0.457128i \(-0.848878\pi\)
0.889401 0.457128i \(-0.151122\pi\)
\(132\) 1.14258e11i 2.85113i
\(133\) 4.24378e10 1.01975
\(134\) −8.14415e9 −0.188504
\(135\) −9.76777e9 −0.217835
\(136\) 9.89566e10i 2.12692i
\(137\) −4.49614e10 −0.931617 −0.465808 0.884886i \(-0.654236\pi\)
−0.465808 + 0.884886i \(0.654236\pi\)
\(138\) −7.12814e10 −1.42423
\(139\) 6.54168e10 1.26071 0.630355 0.776307i \(-0.282909\pi\)
0.630355 + 0.776307i \(0.282909\pi\)
\(140\) 1.62263e11 3.01703
\(141\) 4.39305e10i 0.788261i
\(142\) 7.91038e10i 1.37011i
\(143\) −1.54102e11 −2.57707
\(144\) 9.63607e10 1.55628
\(145\) −1.10325e11 −1.72121
\(146\) 1.46136e11 2.20289
\(147\) 6.89727e9 0.100483
\(148\) 1.87563e11i 2.64143i
\(149\) 1.17694e10i 0.160259i 0.996784 + 0.0801296i \(0.0255334\pi\)
−0.996784 + 0.0801296i \(0.974467\pi\)
\(150\) 2.44493e10i 0.321967i
\(151\) 1.26674e11i 1.61363i 0.590806 + 0.806814i \(0.298810\pi\)
−0.590806 + 0.806814i \(0.701190\pi\)
\(152\) 3.48972e11i 4.30103i
\(153\) −1.55071e10 −0.184958
\(154\) 2.62859e11 3.03473
\(155\) 1.51955e11i 1.69846i
\(156\) 2.39440e11i 2.59163i
\(157\) 7.42949e9i 0.0778862i −0.999241 0.0389431i \(-0.987601\pi\)
0.999241 0.0389431i \(-0.0123991\pi\)
\(158\) 7.53667e10i 0.765410i
\(159\) 1.86263e10 0.183291
\(160\) 6.43983e11i 6.14150i
\(161\) 1.22291e11i 1.13049i
\(162\) 2.45860e10i 0.220349i
\(163\) 1.39455e11 1.21198 0.605992 0.795471i \(-0.292776\pi\)
0.605992 + 0.795471i \(0.292776\pi\)
\(164\) −2.08205e11 −1.75498
\(165\) 1.34572e11i 1.10036i
\(166\) 1.69527e11 1.34492
\(167\) 5.22512e10 0.402266 0.201133 0.979564i \(-0.435538\pi\)
0.201133 + 0.979564i \(0.435538\pi\)
\(168\) 2.69167e11i 2.01129i
\(169\) −1.85077e11 −1.34252
\(170\) 1.76849e11i 1.24554i
\(171\) −5.46859e10 −0.374020
\(172\) 2.86013e11i 1.89996i
\(173\) 7.25153e10i 0.467950i −0.972243 0.233975i \(-0.924827\pi\)
0.972243 0.233975i \(-0.0751733\pi\)
\(174\) 2.77693e11i 1.74108i
\(175\) −4.19456e10 −0.255562
\(176\) 1.32757e12i 7.86130i
\(177\) 8.07725e10 + 5.94653e10i 0.464940 + 0.342292i
\(178\) 2.63461e11 1.47440
\(179\) 1.80016e11i 0.979592i 0.871837 + 0.489796i \(0.162929\pi\)
−0.871837 + 0.489796i \(0.837071\pi\)
\(180\) −2.09094e11 −1.10657
\(181\) 3.56609e10 0.183569 0.0917844 0.995779i \(-0.470743\pi\)
0.0917844 + 0.995779i \(0.470743\pi\)
\(182\) 5.50848e11 2.75851
\(183\) 1.15936e11i 0.564887i
\(184\) −1.00562e12 −4.76808
\(185\) 2.20910e11i 1.01943i
\(186\) 3.82477e11 1.71807
\(187\) 2.13642e11i 0.934285i
\(188\) 9.40399e11i 4.00427i
\(189\) 4.21800e10 0.174903
\(190\) 6.23659e11i 2.51871i
\(191\) 3.85490e10i 0.151651i −0.997121 0.0758257i \(-0.975841\pi\)
0.997121 0.0758257i \(-0.0241593\pi\)
\(192\) 9.17614e11 3.51685
\(193\) 2.29585e11 0.857349 0.428674 0.903459i \(-0.358981\pi\)
0.428674 + 0.903459i \(0.358981\pi\)
\(194\) −4.04587e11 −1.47232
\(195\) 2.82009e11i 1.00021i
\(196\) 1.47647e11 0.510438
\(197\) −2.59798e11 −0.875599 −0.437799 0.899073i \(-0.644242\pi\)
−0.437799 + 0.899073i \(0.644242\pi\)
\(198\) −3.38723e11 −1.11306
\(199\) 6.07744e11 1.94740 0.973700 0.227832i \(-0.0731639\pi\)
0.973700 + 0.227832i \(0.0731639\pi\)
\(200\) 3.44924e11i 1.07789i
\(201\) 1.80047e10i 0.0548790i
\(202\) 3.55519e11 1.05708
\(203\) 4.76414e11 1.38199
\(204\) −3.31953e11 −0.939562
\(205\) 2.45221e11 0.677310
\(206\) −5.32678e11 −1.43592
\(207\) 1.57586e11i 0.414635i
\(208\) 2.78206e12i 7.14578i
\(209\) 7.53413e11i 1.88930i
\(210\) 4.81037e11i 1.17783i
\(211\) 3.48490e11i 0.833255i 0.909077 + 0.416628i \(0.136788\pi\)
−0.909077 + 0.416628i \(0.863212\pi\)
\(212\) 3.98724e11 0.931093
\(213\) −1.74879e11 −0.398879
\(214\) 1.05351e12i 2.34730i
\(215\) 3.36863e11i 0.733264i
\(216\) 3.46851e11i 0.737691i
\(217\) 6.56183e11i 1.36372i
\(218\) −7.27328e11 −1.47723
\(219\) 3.23072e11i 0.641325i
\(220\) 2.88071e12i 5.58967i
\(221\) 4.47710e11i 0.849249i
\(222\) −5.56040e11 −1.03120
\(223\) −9.61110e10 −0.174281 −0.0871403 0.996196i \(-0.527773\pi\)
−0.0871403 + 0.996196i \(0.527773\pi\)
\(224\) 2.78090e12i 4.93112i
\(225\) 5.40515e10 0.0937336
\(226\) −1.71397e12 −2.90711
\(227\) 1.97002e11i 0.326845i 0.986556 + 0.163423i \(0.0522534\pi\)
−0.986556 + 0.163423i \(0.947747\pi\)
\(228\) −1.17064e12 −1.89997
\(229\) 1.93983e11i 0.308026i 0.988069 + 0.154013i \(0.0492197\pi\)
−0.988069 + 0.154013i \(0.950780\pi\)
\(230\) 1.79717e12 2.79222
\(231\) 5.81118e11i 0.883495i
\(232\) 3.91761e12i 5.82883i
\(233\) 4.62830e11i 0.673972i −0.941510 0.336986i \(-0.890592\pi\)
0.941510 0.336986i \(-0.109408\pi\)
\(234\) −7.09829e11 −1.01175
\(235\) 1.10759e12i 1.54540i
\(236\) 1.72906e12 + 1.27295e12i 2.36184 + 1.73880i
\(237\) 1.66617e11 0.222833
\(238\) 7.63682e11i 1.00006i
\(239\) −1.34407e12 −1.72358 −0.861789 0.507267i \(-0.830656\pi\)
−0.861789 + 0.507267i \(0.830656\pi\)
\(240\) −2.42948e12 −3.05110
\(241\) 3.68238e11 0.452943 0.226471 0.974018i \(-0.427281\pi\)
0.226471 + 0.974018i \(0.427281\pi\)
\(242\) 3.02062e12i 3.63931i
\(243\) −5.43536e10 −0.0641500
\(244\) 2.48178e12i 2.86955i
\(245\) −1.73896e11 −0.196997
\(246\) 6.17232e11i 0.685130i
\(247\) 1.57885e12i 1.71734i
\(248\) 5.39587e12 5.75179
\(249\) 3.74782e11i 0.391545i
\(250\) 1.57569e12i 1.61351i
\(251\) −4.16900e11 −0.418469 −0.209234 0.977866i \(-0.567097\pi\)
−0.209234 + 0.977866i \(0.567097\pi\)
\(252\) 9.02928e11 0.888485
\(253\) 2.17108e12 2.09446
\(254\) 3.80622e11i 0.360019i
\(255\) 3.90969e11 0.362612
\(256\) 7.81198e12 7.10496
\(257\) 1.65267e12 1.47407 0.737037 0.675852i \(-0.236224\pi\)
0.737037 + 0.675852i \(0.236224\pi\)
\(258\) 8.47899e11 0.741730
\(259\) 9.53949e11i 0.818515i
\(260\) 6.03683e12i 5.08092i
\(261\) −6.13912e11 −0.506878
\(262\) −2.23835e12 −1.81310
\(263\) 8.88346e11 0.705998 0.352999 0.935624i \(-0.385162\pi\)
0.352999 + 0.935624i \(0.385162\pi\)
\(264\) −4.77860e12 −3.72633
\(265\) −4.69612e11 −0.359343
\(266\) 2.69313e12i 2.02232i
\(267\) 5.82448e11i 0.429240i
\(268\) 3.85419e11i 0.278778i
\(269\) 8.05656e11i 0.571990i 0.958231 + 0.285995i \(0.0923240\pi\)
−0.958231 + 0.285995i \(0.907676\pi\)
\(270\) 6.19869e11i 0.431998i
\(271\) 1.43475e12 0.981587 0.490794 0.871276i \(-0.336707\pi\)
0.490794 + 0.871276i \(0.336707\pi\)
\(272\) −3.85698e12 −2.59061
\(273\) 1.21779e12i 0.803082i
\(274\) 2.85328e12i 1.84753i
\(275\) 7.44673e11i 0.473481i
\(276\) 3.37337e12i 2.10629i
\(277\) 1.40442e12 0.861191 0.430596 0.902545i \(-0.358304\pi\)
0.430596 + 0.902545i \(0.358304\pi\)
\(278\) 4.15139e12i 2.50017i
\(279\) 8.45564e11i 0.500179i
\(280\) 6.78632e12i 3.94316i
\(281\) −1.17796e12 −0.672355 −0.336177 0.941799i \(-0.609134\pi\)
−0.336177 + 0.941799i \(0.609134\pi\)
\(282\) 2.78786e12 1.56324
\(283\) 7.49696e11i 0.413003i −0.978446 0.206501i \(-0.933792\pi\)
0.978446 0.206501i \(-0.0662078\pi\)
\(284\) −3.74356e12 −2.02625
\(285\) 1.37876e12 0.733270
\(286\) 9.77939e12i 5.11071i
\(287\) −1.05893e12 −0.543824
\(288\) 3.58350e12i 1.80861i
\(289\) −1.39530e12 −0.692115
\(290\) 7.00129e12i 3.41341i
\(291\) 8.94444e11i 0.428635i
\(292\) 6.91585e12i 3.25785i
\(293\) 3.53806e12 1.63843 0.819213 0.573490i \(-0.194411\pi\)
0.819213 + 0.573490i \(0.194411\pi\)
\(294\) 4.37705e11i 0.199271i
\(295\) −2.03646e12 1.49926e12i −0.911520 0.671068i
\(296\) −7.84444e12 −3.45226
\(297\) 7.48835e11i 0.324044i
\(298\) 7.46894e11 0.317817
\(299\) 4.54972e12 1.90383
\(300\) 1.15706e12 0.476155
\(301\) 1.45467e12i 0.588750i
\(302\) 8.03883e12 3.20006
\(303\) 7.85967e11i 0.307745i
\(304\) −1.36017e13 −5.23871
\(305\) 2.92301e12i 1.10747i
\(306\) 9.84089e11i 0.366798i
\(307\) −2.20403e11 −0.0808211 −0.0404106 0.999183i \(-0.512867\pi\)
−0.0404106 + 0.999183i \(0.512867\pi\)
\(308\) 1.24397e13i 4.48804i
\(309\) 1.17762e12i 0.418036i
\(310\) −9.64314e12 −3.36830
\(311\) 4.06893e12 1.39855 0.699276 0.714852i \(-0.253506\pi\)
0.699276 + 0.714852i \(0.253506\pi\)
\(312\) −1.00141e13 −3.38717
\(313\) 3.98362e12i 1.32604i −0.748602 0.663020i \(-0.769275\pi\)
0.748602 0.663020i \(-0.230725\pi\)
\(314\) −4.71480e11 −0.154460
\(315\) −1.06346e12 −0.342899
\(316\) 3.56670e12 1.13196
\(317\) −1.46358e12 −0.457216 −0.228608 0.973519i \(-0.573417\pi\)
−0.228608 + 0.973519i \(0.573417\pi\)
\(318\) 1.18204e12i 0.363492i
\(319\) 8.45793e12i 2.56042i
\(320\) −2.31352e13 −6.89483
\(321\) −2.32905e12 −0.683367
\(322\) −7.76069e12 −2.24192
\(323\) 2.18888e12 0.622601
\(324\) −1.16352e12 −0.325874
\(325\) 1.56054e12i 0.430386i
\(326\) 8.84993e12i 2.40354i
\(327\) 1.60794e12i 0.430063i
\(328\) 8.70772e12i 2.29369i
\(329\) 4.78288e12i 1.24082i
\(330\) 8.54000e12 2.18217
\(331\) 3.84998e12 0.968989 0.484495 0.874794i \(-0.339003\pi\)
0.484495 + 0.874794i \(0.339003\pi\)
\(332\) 8.02279e12i 1.98900i
\(333\) 1.22927e12i 0.300211i
\(334\) 3.31589e12i 0.797753i
\(335\) 4.53941e11i 0.107591i
\(336\) 1.04912e13 2.44978
\(337\) 2.99149e12i 0.688236i 0.938926 + 0.344118i \(0.111822\pi\)
−0.938926 + 0.344118i \(0.888178\pi\)
\(338\) 1.17451e13i 2.66240i
\(339\) 3.78917e12i 0.846342i
\(340\) 8.36930e12 1.84202
\(341\) −1.16494e13 −2.52658
\(342\) 3.47040e12i 0.741736i
\(343\) 5.06563e12 1.06700
\(344\) 1.19619e13 2.48318
\(345\) 3.97311e12i 0.812896i
\(346\) −4.60187e12 −0.928012
\(347\) 3.80325e12i 0.755974i −0.925811 0.377987i \(-0.876616\pi\)
0.925811 0.377987i \(-0.123384\pi\)
\(348\) −1.31417e13 −2.57488
\(349\) 4.05477e12i 0.783139i −0.920148 0.391570i \(-0.871932\pi\)
0.920148 0.391570i \(-0.128068\pi\)
\(350\) 2.66189e12i 0.506816i
\(351\) 1.56926e12i 0.294550i
\(352\) −4.93702e13 −9.13590
\(353\) 8.59729e12i 1.56851i 0.620437 + 0.784257i \(0.286955\pi\)
−0.620437 + 0.784257i \(0.713045\pi\)
\(354\) 3.77371e12 5.12587e12i 0.678815 0.922044i
\(355\) 4.40912e12 0.782006
\(356\) 1.24682e13i 2.18049i
\(357\) −1.68832e12 −0.291147
\(358\) 1.14239e13 1.94267
\(359\) −4.33032e12 −0.726186 −0.363093 0.931753i \(-0.618279\pi\)
−0.363093 + 0.931753i \(0.618279\pi\)
\(360\) 8.74493e12i 1.44625i
\(361\) 1.58805e12 0.259017
\(362\) 2.26306e12i 0.364044i
\(363\) 6.67785e12 1.05951
\(364\) 2.60687e13i 4.07955i
\(365\) 8.14539e12i 1.25733i
\(366\) −7.35735e12 −1.12025
\(367\) 3.71511e12i 0.558009i −0.960290 0.279004i \(-0.909996\pi\)
0.960290 0.279004i \(-0.0900044\pi\)
\(368\) 3.91954e13i 5.80758i
\(369\) 1.36455e12 0.199461
\(370\) 1.40191e13 2.02167
\(371\) 2.02792e12 0.288523
\(372\) 1.81006e13i 2.54085i
\(373\) −5.40807e12 −0.749028 −0.374514 0.927221i \(-0.622190\pi\)
−0.374514 + 0.927221i \(0.622190\pi\)
\(374\) 1.35579e13 1.85282
\(375\) 3.48347e12 0.469738
\(376\) 3.93302e13 5.23344
\(377\) 1.77245e13i 2.32737i
\(378\) 2.67677e12i 0.346858i
\(379\) −5.39111e12 −0.689418 −0.344709 0.938710i \(-0.612022\pi\)
−0.344709 + 0.938710i \(0.612022\pi\)
\(380\) 2.95144e13 3.72492
\(381\) −8.41462e11 −0.104812
\(382\) −2.44635e12 −0.300747
\(383\) 2.79998e12 0.339752 0.169876 0.985465i \(-0.445663\pi\)
0.169876 + 0.985465i \(0.445663\pi\)
\(384\) 3.20770e13i 3.84183i
\(385\) 1.46513e13i 1.73210i
\(386\) 1.45696e13i 1.70025i
\(387\) 1.87450e12i 0.215939i
\(388\) 1.91469e13i 2.17741i
\(389\) −6.90292e12 −0.774970 −0.387485 0.921876i \(-0.626656\pi\)
−0.387485 + 0.921876i \(0.626656\pi\)
\(390\) 1.78964e13 1.98355
\(391\) 6.30761e12i 0.690209i
\(392\) 6.17501e12i 0.667125i
\(393\) 4.94846e12i 0.527846i
\(394\) 1.64870e13i 1.73644i
\(395\) −4.20081e12 −0.436866
\(396\) 1.60300e13i 1.64610i
\(397\) 5.45035e12i 0.552678i 0.961060 + 0.276339i \(0.0891212\pi\)
−0.961060 + 0.276339i \(0.910879\pi\)
\(398\) 3.85678e13i 3.86198i
\(399\) −5.95386e12 −0.588755
\(400\) 1.34439e13 1.31288
\(401\) 1.49009e12i 0.143711i 0.997415 + 0.0718557i \(0.0228921\pi\)
−0.997415 + 0.0718557i \(0.977108\pi\)
\(402\) 1.14259e12 0.108833
\(403\) −2.44126e13 −2.29662
\(404\) 1.68248e13i 1.56331i
\(405\) 1.37038e12 0.125767
\(406\) 3.02335e13i 2.74068i
\(407\) 1.69358e13 1.51647
\(408\) 1.38832e13i 1.22798i
\(409\) 8.65719e12i 0.756415i −0.925721 0.378208i \(-0.876541\pi\)
0.925721 0.378208i \(-0.123459\pi\)
\(410\) 1.55619e13i 1.34320i
\(411\) 6.30792e12 0.537869
\(412\) 2.52088e13i 2.12357i
\(413\) 8.79401e12 + 6.47422e12i 0.731875 + 0.538812i
\(414\) 1.00005e13 0.822281
\(415\) 9.44913e12i 0.767629i
\(416\) −1.03460e14 −8.30438
\(417\) −9.17773e12 −0.727872
\(418\) 4.78121e13 3.74676
\(419\) 1.38750e13i 1.07439i −0.843458 0.537196i \(-0.819484\pi\)
0.843458 0.537196i \(-0.180516\pi\)
\(420\) −2.27649e13 −1.74188
\(421\) 1.17891e13i 0.891397i 0.895183 + 0.445699i \(0.147045\pi\)
−0.895183 + 0.445699i \(0.852955\pi\)
\(422\) 2.21154e13 1.65247
\(423\) 6.16327e12i 0.455103i
\(424\) 1.66758e13i 1.21691i
\(425\) −2.16349e12 −0.156031
\(426\) 1.10980e13i 0.791034i
\(427\) 1.26224e13i 0.889204i
\(428\) −4.98570e13 −3.47142
\(429\) 2.16199e13 1.48787
\(430\) −2.13775e13 −1.45417
\(431\) 8.12118e12i 0.546051i 0.962007 + 0.273025i \(0.0880243\pi\)
−0.962007 + 0.273025i \(0.911976\pi\)
\(432\) −1.35190e13 −0.898518
\(433\) −1.62737e13 −1.06917 −0.534585 0.845114i \(-0.679532\pi\)
−0.534585 + 0.845114i \(0.679532\pi\)
\(434\) 4.16418e13 2.70446
\(435\) 1.54782e13 0.993740
\(436\) 3.44205e13i 2.18467i
\(437\) 2.22438e13i 1.39573i
\(438\) −2.05023e13 −1.27184
\(439\) 2.87183e11 0.0176131 0.00880655 0.999961i \(-0.497197\pi\)
0.00880655 + 0.999961i \(0.497197\pi\)
\(440\) 1.20480e14 7.30551
\(441\) −9.67660e11 −0.0580136
\(442\) 2.84120e13 1.68418
\(443\) 2.13237e13i 1.24981i 0.780700 + 0.624906i \(0.214863\pi\)
−0.780700 + 0.624906i \(0.785137\pi\)
\(444\) 2.63144e13i 1.52503i
\(445\) 1.46849e13i 0.841530i
\(446\) 6.09927e12i 0.345624i
\(447\) 1.65120e12i 0.0925257i
\(448\) 9.99043e13 5.53597
\(449\) −6.85125e12 −0.375438 −0.187719 0.982223i \(-0.560109\pi\)
−0.187719 + 0.982223i \(0.560109\pi\)
\(450\) 3.43015e12i 0.185887i
\(451\) 1.87995e13i 1.00755i
\(452\) 8.11130e13i 4.29931i
\(453\) 1.77719e13i 0.931629i
\(454\) 1.25019e13 0.648181
\(455\) 3.07034e13i 1.57445i
\(456\) 4.89593e13i 2.48320i
\(457\) 2.16366e13i 1.08544i 0.839912 + 0.542722i \(0.182606\pi\)
−0.839912 + 0.542722i \(0.817394\pi\)
\(458\) 1.23103e13 0.610860
\(459\) 2.17558e12 0.106785
\(460\) 8.50505e13i 4.12941i
\(461\) −2.85231e13 −1.36991 −0.684954 0.728586i \(-0.740178\pi\)
−0.684954 + 0.728586i \(0.740178\pi\)
\(462\) −3.68781e13 −1.75210
\(463\) 2.28437e13i 1.07365i 0.843695 + 0.536823i \(0.180376\pi\)
−0.843695 + 0.536823i \(0.819624\pi\)
\(464\) −1.52695e14 −7.09959
\(465\) 2.13187e13i 0.980607i
\(466\) −2.93715e13 −1.33658
\(467\) 2.57417e13i 1.15892i 0.815001 + 0.579460i \(0.196736\pi\)
−0.815001 + 0.579460i \(0.803264\pi\)
\(468\) 3.35924e13i 1.49628i
\(469\) 1.96025e12i 0.0863866i
\(470\) −7.02884e13 −3.06474
\(471\) 1.04233e12i 0.0449676i
\(472\) 5.32383e13 7.23143e13i 2.27255 3.08684i
\(473\) −2.58252e13 −1.09078
\(474\) 1.05737e13i 0.441910i
\(475\) −7.62958e12 −0.315524
\(476\) −3.61410e13 −1.47899
\(477\) −2.61319e12 −0.105823
\(478\) 8.52953e13i 3.41811i
\(479\) 2.39832e13 0.951109 0.475554 0.879686i \(-0.342247\pi\)
0.475554 + 0.879686i \(0.342247\pi\)
\(480\) 9.03483e13i 3.54580i
\(481\) 3.54906e13 1.37844
\(482\) 2.33686e13i 0.898252i
\(483\) 1.71570e13i 0.652688i
\(484\) 1.42950e14 5.38216
\(485\) 2.25510e13i 0.840344i
\(486\) 3.44931e12i 0.127219i
\(487\) −4.35984e13 −1.59157 −0.795785 0.605579i \(-0.792942\pi\)
−0.795785 + 0.605579i \(0.792942\pi\)
\(488\) −1.03795e14 −3.75041
\(489\) −1.95650e13 −0.699740
\(490\) 1.10356e13i 0.390674i
\(491\) 1.82138e13 0.638253 0.319126 0.947712i \(-0.396611\pi\)
0.319126 + 0.947712i \(0.396611\pi\)
\(492\) 2.92103e13 1.01324
\(493\) 2.45727e13 0.843760
\(494\) 1.00195e14 3.40574
\(495\) 1.88799e13i 0.635291i
\(496\) 2.10312e14i 7.00576i
\(497\) −1.90398e13 −0.627886
\(498\) −2.37839e13 −0.776491
\(499\) −1.37633e13 −0.444858 −0.222429 0.974949i \(-0.571399\pi\)
−0.222429 + 0.974949i \(0.571399\pi\)
\(500\) 7.45690e13 2.38621
\(501\) −7.33064e12 −0.232249
\(502\) 2.64567e13i 0.829884i
\(503\) 5.90065e13i 1.83257i −0.400529 0.916284i \(-0.631173\pi\)
0.400529 0.916284i \(-0.368827\pi\)
\(504\) 3.77630e13i 1.16122i
\(505\) 1.98161e13i 0.603337i
\(506\) 1.37778e14i 4.15362i
\(507\) 2.59656e13 0.775102
\(508\) −1.80128e13 −0.532430
\(509\) 2.78998e13i 0.816606i 0.912846 + 0.408303i \(0.133879\pi\)
−0.912846 + 0.408303i \(0.866121\pi\)
\(510\) 2.48112e13i 0.719112i
\(511\) 3.51741e13i 1.00953i
\(512\) 2.61628e14i 7.43593i
\(513\) 7.67221e12 0.215940
\(514\) 1.04879e14i 2.92330i
\(515\) 2.96906e13i 0.819564i
\(516\) 4.01266e13i 1.09694i
\(517\) −8.49120e13 −2.29888
\(518\) −6.05382e13 −1.62323
\(519\) 1.01736e13i 0.270171i
\(520\) 2.52478e14 6.64058
\(521\) −2.12484e12 −0.0553526 −0.0276763 0.999617i \(-0.508811\pi\)
−0.0276763 + 0.999617i \(0.508811\pi\)
\(522\) 3.89593e13i 1.00521i
\(523\) 6.37536e12 0.162928 0.0814641 0.996676i \(-0.474040\pi\)
0.0814641 + 0.996676i \(0.474040\pi\)
\(524\) 1.05929e14i 2.68139i
\(525\) 5.88480e12 0.147549
\(526\) 5.63750e13i 1.40010i
\(527\) 3.38450e13i 0.832609i
\(528\) 1.86253e14i 4.53872i
\(529\) −2.26726e13 −0.547298
\(530\) 2.98019e13i 0.712630i
\(531\) −1.13321e13 8.34275e12i −0.268433 0.197623i
\(532\) −1.27452e14 −2.99080
\(533\) 3.93964e13i 0.915841i
\(534\) −3.69625e13 −0.851246
\(535\) 5.87209e13 1.33975
\(536\) 1.61193e13 0.364354
\(537\) 2.52555e13i 0.565567i
\(538\) 5.11274e13 1.13434
\(539\) 1.33315e13i 0.293047i
\(540\) 2.93351e13 0.638879
\(541\) 2.78098e13i 0.600084i 0.953926 + 0.300042i \(0.0970007\pi\)
−0.953926 + 0.300042i \(0.902999\pi\)
\(542\) 9.10500e13i 1.94663i
\(543\) −5.00308e12 −0.105984
\(544\) 1.43435e14i 3.01065i
\(545\) 4.05400e13i 0.843144i
\(546\) −7.72819e13 −1.59263
\(547\) 2.91420e13 0.595090 0.297545 0.954708i \(-0.403832\pi\)
0.297545 + 0.954708i \(0.403832\pi\)
\(548\) 1.35031e14 2.73231
\(549\) 1.62653e13i 0.326138i
\(550\) −4.72575e13 −0.938981
\(551\) 8.66560e13 1.70624
\(552\) 1.41084e14 2.75285
\(553\) 1.81403e13 0.350767
\(554\) 8.91257e13i 1.70787i
\(555\) 3.09927e13i 0.588566i
\(556\) −1.96463e14 −3.69750
\(557\) −1.00678e14 −1.87784 −0.938918 0.344141i \(-0.888170\pi\)
−0.938918 + 0.344141i \(0.888170\pi\)
\(558\) −5.36601e13 −0.991928
\(559\) −5.41193e13 −0.991501
\(560\) −2.64507e14 −4.80282
\(561\) 2.99732e13i 0.539410i
\(562\) 7.47540e13i 1.33338i
\(563\) 8.71239e13i 1.54027i 0.637884 + 0.770133i \(0.279810\pi\)
−0.637884 + 0.770133i \(0.720190\pi\)
\(564\) 1.31934e14i 2.31186i
\(565\) 9.55338e13i 1.65926i
\(566\) −4.75762e13 −0.819044
\(567\) −5.91769e12 −0.100980
\(568\) 1.56567e14i 2.64824i
\(569\) 3.85604e13i 0.646517i −0.946311 0.323258i \(-0.895222\pi\)
0.946311 0.323258i \(-0.104778\pi\)
\(570\) 8.74969e13i 1.45418i
\(571\) 2.61452e13i 0.430736i −0.976533 0.215368i \(-0.930905\pi\)
0.976533 0.215368i \(-0.0690952\pi\)
\(572\) 4.62806e14 7.55821
\(573\) 5.40828e12i 0.0875560i
\(574\) 6.72004e13i 1.07848i
\(575\) 2.19858e13i 0.349787i
\(576\) −1.28738e14 −2.03046
\(577\) 3.06953e13 0.479947 0.239973 0.970779i \(-0.422861\pi\)
0.239973 + 0.970779i \(0.422861\pi\)
\(578\) 8.85467e13i 1.37257i
\(579\) −3.22099e13 −0.494991
\(580\) 3.31334e14 5.04807
\(581\) 4.08040e13i 0.616342i
\(582\) 5.67620e13 0.850046
\(583\) 3.60022e13i 0.534548i
\(584\) −2.89241e14 −4.25790
\(585\) 3.95647e13i 0.577469i
\(586\) 2.24527e14i 3.24924i
\(587\) 2.54401e13i 0.365029i 0.983203 + 0.182515i \(0.0584237\pi\)
−0.983203 + 0.182515i \(0.941576\pi\)
\(588\) −2.07143e13 −0.294702
\(589\) 1.19355e14i 1.68369i
\(590\) −9.51439e13 + 1.29235e14i −1.33082 + 1.80768i
\(591\) 3.64487e13 0.505527
\(592\) 3.05748e14i 4.20490i
\(593\) 1.36225e13 0.185773 0.0928864 0.995677i \(-0.470391\pi\)
0.0928864 + 0.995677i \(0.470391\pi\)
\(594\) 4.75215e13 0.642626
\(595\) 4.25664e13 0.570797
\(596\) 3.53465e13i 0.470019i
\(597\) −8.52641e13 −1.12433
\(598\) 2.88728e14i 3.77557i
\(599\) 1.16474e14 1.51041 0.755205 0.655489i \(-0.227537\pi\)
0.755205 + 0.655489i \(0.227537\pi\)
\(600\) 4.83915e13i 0.622318i
\(601\) 1.07353e14i 1.36912i 0.728956 + 0.684560i \(0.240006\pi\)
−0.728956 + 0.684560i \(0.759994\pi\)
\(602\) 9.23141e13 1.16758
\(603\) 2.52599e12i 0.0316844i
\(604\) 3.80435e14i 4.73255i
\(605\) −1.68364e14 −2.07717
\(606\) −4.98780e13 −0.610303
\(607\) −8.44133e13 −1.02440 −0.512198 0.858868i \(-0.671168\pi\)
−0.512198 + 0.858868i \(0.671168\pi\)
\(608\) 5.05824e14i 6.08810i
\(609\) −6.68390e13 −0.797891
\(610\) 1.85496e14 2.19627
\(611\) −1.77942e14 −2.08964
\(612\) 4.65717e13 0.542456
\(613\) 9.06076e13i 1.04680i −0.852088 0.523398i \(-0.824664\pi\)
0.852088 0.523398i \(-0.175336\pi\)
\(614\) 1.39869e13i 0.160280i
\(615\) −3.44035e13 −0.391045
\(616\) −5.20265e14 −5.86572
\(617\) −1.24220e14 −1.38920 −0.694599 0.719397i \(-0.744418\pi\)
−0.694599 + 0.719397i \(0.744418\pi\)
\(618\) 7.47327e13 0.829026
\(619\) −2.99465e13 −0.329528 −0.164764 0.986333i \(-0.552686\pi\)
−0.164764 + 0.986333i \(0.552686\pi\)
\(620\) 4.56359e14i 4.98136i
\(621\) 2.21087e13i 0.239389i
\(622\) 2.58217e14i 2.77353i
\(623\) 6.34133e13i 0.675679i
\(624\) 3.90312e14i 4.12562i
\(625\) −1.14644e14 −1.20213
\(626\) −2.52803e14 −2.62973
\(627\) 1.05701e14i 1.09079i
\(628\) 2.23126e13i 0.228430i
\(629\) 4.92033e13i 0.499737i
\(630\) 6.74876e13i 0.680019i
\(631\) 7.50471e13 0.750218 0.375109 0.926981i \(-0.377605\pi\)
0.375109 + 0.926981i \(0.377605\pi\)
\(632\) 1.49170e14i 1.47943i
\(633\) 4.88918e13i 0.481080i
\(634\) 9.28800e13i 0.906726i
\(635\) 2.12152e13 0.205484
\(636\) −5.59394e13 −0.537567
\(637\) 2.79376e13i 0.266374i
\(638\) 5.36746e14 5.07768
\(639\) 2.45349e13 0.230293
\(640\) 8.08736e14i 7.53194i
\(641\) 1.27671e14 1.17978 0.589890 0.807484i \(-0.299171\pi\)
0.589890 + 0.807484i \(0.299171\pi\)
\(642\) 1.47803e14i 1.35522i
\(643\) −1.71159e14 −1.55720 −0.778599 0.627522i \(-0.784069\pi\)
−0.778599 + 0.627522i \(0.784069\pi\)
\(644\) 3.67272e14i 3.31557i
\(645\) 4.72605e13i 0.423350i
\(646\) 1.38908e14i 1.23471i
\(647\) −2.06196e14 −1.81869 −0.909346 0.416041i \(-0.863417\pi\)
−0.909346 + 0.416041i \(0.863417\pi\)
\(648\) 4.86619e13i 0.425906i
\(649\) −1.14939e14 + 1.56123e14i −0.998259 + 1.35595i
\(650\) −9.90329e13 −0.853518
\(651\) 9.20599e13i 0.787346i
\(652\) −4.18820e14 −3.55459
\(653\) 6.59315e13 0.555299 0.277650 0.960682i \(-0.410445\pi\)
0.277650 + 0.960682i \(0.410445\pi\)
\(654\) 1.02041e14 0.852878
\(655\) 1.24762e14i 1.03485i
\(656\) 3.39396e14 2.79375
\(657\) 4.53257e13i 0.370269i
\(658\) 3.03525e14 2.46073
\(659\) 4.23653e13i 0.340866i 0.985369 + 0.170433i \(0.0545166\pi\)
−0.985369 + 0.170433i \(0.945483\pi\)
\(660\) 4.04153e14i 3.22720i
\(661\) 5.82687e13 0.461772 0.230886 0.972981i \(-0.425837\pi\)
0.230886 + 0.972981i \(0.425837\pi\)
\(662\) 2.44323e14i 1.92165i
\(663\) 6.28119e13i 0.490314i
\(664\) −3.35536e14 −2.59955
\(665\) 1.50111e14 1.15426
\(666\) 7.80102e13 0.595361
\(667\) 2.49713e14i 1.89152i
\(668\) −1.56924e14 −1.17979
\(669\) 1.34840e13 0.100621
\(670\) −2.88074e13 −0.213368
\(671\) 2.24089e14 1.64743
\(672\) 3.90149e14i 2.84698i
\(673\) 2.60802e13i 0.188901i −0.995530 0.0944507i \(-0.969891\pi\)
0.995530 0.0944507i \(-0.0301095\pi\)
\(674\) 1.89842e14 1.36487
\(675\) −7.58322e12 −0.0541171
\(676\) 5.55834e14 3.93742
\(677\) 3.97353e13 0.279405 0.139702 0.990194i \(-0.455385\pi\)
0.139702 + 0.990194i \(0.455385\pi\)
\(678\) 2.40463e14 1.67842
\(679\) 9.73816e13i 0.674727i
\(680\) 3.50028e14i 2.40746i
\(681\) 2.76387e13i 0.188704i
\(682\) 7.39280e14i 5.01057i
\(683\) 9.13519e13i 0.614630i −0.951608 0.307315i \(-0.900569\pi\)
0.951608 0.307315i \(-0.0994306\pi\)
\(684\) 1.64236e14 1.09695
\(685\) −1.59037e14 −1.05450
\(686\) 3.21468e14i 2.11601i
\(687\) 2.72151e13i 0.177839i
\(688\) 4.66233e14i 3.02455i
\(689\) 7.54464e13i 0.485895i
\(690\) −2.52136e14 −1.61209
\(691\) 1.66013e13i 0.105378i 0.998611 + 0.0526892i \(0.0167793\pi\)
−0.998611 + 0.0526892i \(0.983221\pi\)
\(692\) 2.17782e14i 1.37243i
\(693\) 8.15286e13i 0.510086i
\(694\) −2.41356e14 −1.49921
\(695\) 2.31392e14 1.42700
\(696\) 5.49625e14i 3.36528i
\(697\) −5.46181e13 −0.332027
\(698\) −2.57318e14 −1.55308
\(699\) 6.49333e13i 0.389118i
\(700\) 1.25973e14 0.749529
\(701\) 7.36214e13i 0.434924i 0.976069 + 0.217462i \(0.0697779\pi\)
−0.976069 + 0.217462i \(0.930222\pi\)
\(702\) 9.95863e13 0.584136
\(703\) 1.73516e14i 1.01056i
\(704\) 1.77363e15i 10.2565i
\(705\) 1.55391e14i 0.892234i
\(706\) 5.45590e14 3.11059
\(707\) 8.55713e13i 0.484430i
\(708\) −2.42580e14 1.78589e14i −1.36361 1.00390i
\(709\) −7.87948e13 −0.439811 −0.219906 0.975521i \(-0.570575\pi\)
−0.219906 + 0.975521i \(0.570575\pi\)
\(710\) 2.79806e14i 1.55083i
\(711\) −2.33758e13 −0.128652
\(712\) −5.21456e14 −2.84982
\(713\) 3.43939e14 1.86653
\(714\) 1.07142e14i 0.577387i
\(715\) −5.45087e14 −2.91699
\(716\) 5.40633e14i 2.87301i
\(717\) 1.88567e14 0.995108
\(718\) 2.74805e14i 1.44013i
\(719\) 7.23964e12i 0.0376767i −0.999823 0.0188383i \(-0.994003\pi\)
0.999823 0.0188383i \(-0.00599678\pi\)
\(720\) 3.40846e14 1.76155
\(721\) 1.28212e14i 0.658042i
\(722\) 1.00779e14i 0.513669i
\(723\) −5.16624e13 −0.261507
\(724\) −1.07099e14 −0.538383
\(725\) −8.56509e13 −0.427604
\(726\) 4.23781e14i 2.10116i
\(727\) −1.20450e14 −0.593111 −0.296555 0.955016i \(-0.595838\pi\)
−0.296555 + 0.955016i \(0.595838\pi\)
\(728\) −1.09027e15 −5.33184
\(729\) 7.62560e12 0.0370370
\(730\) 5.16912e14 2.49346
\(731\) 7.50296e13i 0.359456i
\(732\) 3.48184e14i 1.65674i
\(733\) 2.09581e14 0.990449 0.495224 0.868765i \(-0.335086\pi\)
0.495224 + 0.868765i \(0.335086\pi\)
\(734\) −2.35763e14 −1.10661
\(735\) 2.43970e13 0.113736
\(736\) 1.45761e15 6.74921
\(737\) −3.48009e13 −0.160049
\(738\) 8.65952e13i 0.395560i
\(739\) 1.83607e14i 0.833041i −0.909126 0.416521i \(-0.863249\pi\)
0.909126 0.416521i \(-0.136751\pi\)
\(740\) 6.63448e14i 2.98984i
\(741\) 2.21507e14i 0.991509i
\(742\) 1.28693e14i 0.572183i
\(743\) 1.11239e14 0.491261 0.245631 0.969364i \(-0.421005\pi\)
0.245631 + 0.969364i \(0.421005\pi\)
\(744\) −7.57020e14 −3.32080
\(745\) 4.16306e13i 0.181398i
\(746\) 3.43200e14i 1.48543i
\(747\) 5.25805e13i 0.226059i
\(748\) 6.41623e14i 2.74013i
\(749\) −2.53573e14 −1.07571
\(750\) 2.21063e14i 0.931558i
\(751\) 2.25353e12i 0.00943331i 0.999989 + 0.00471665i \(0.00150136\pi\)
−0.999989 + 0.00471665i \(0.998499\pi\)
\(752\) 1.53295e15i 6.37440i
\(753\) 5.84894e13 0.241603
\(754\) 1.12481e15 4.61552
\(755\) 4.48071e14i 1.82647i
\(756\) −1.26677e14 −0.512967
\(757\) −2.44932e14 −0.985294 −0.492647 0.870229i \(-0.663971\pi\)
−0.492647 + 0.870229i \(0.663971\pi\)
\(758\) 3.42124e14i 1.36722i
\(759\) −3.04594e14 −1.20924
\(760\) 1.23438e15i 4.86834i
\(761\) −1.44245e14 −0.565167 −0.282584 0.959243i \(-0.591191\pi\)
−0.282584 + 0.959243i \(0.591191\pi\)
\(762\) 5.33997e13i 0.207857i
\(763\) 1.75063e14i 0.676975i
\(764\) 1.15773e14i 0.444773i
\(765\) −5.48515e13 −0.209354
\(766\) 1.77689e14i 0.673777i
\(767\) −2.40866e14 + 3.27172e14i −0.907401 + 1.23253i
\(768\) −1.09599e15 −4.10205
\(769\) 3.66398e14i 1.36245i 0.732073 + 0.681227i \(0.238553\pi\)
−0.732073 + 0.681227i \(0.761447\pi\)
\(770\) 9.29783e14 3.43501
\(771\) −2.31863e14 −0.851057
\(772\) −6.89503e14 −2.51449
\(773\) 8.64869e13i 0.313367i −0.987649 0.156683i \(-0.949920\pi\)
0.987649 0.156683i \(-0.0500802\pi\)
\(774\) −1.18957e14 −0.428238
\(775\) 1.17970e14i 0.421953i
\(776\) 8.00780e14 2.84580
\(777\) 1.33835e14i 0.472570i
\(778\) 4.38064e14i 1.53688i
\(779\) −1.92611e14 −0.671421