Properties

Label 177.11.c.a.58.15
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 58.15
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.86

$q$-expansion

\(f(q)\) \(=\) \(q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +58292.2i q^{10} -33949.7i q^{11} +180483. q^{12} -413622. i q^{13} +203835. i q^{14} +170141. q^{15} -710959. q^{16} -2.03662e6 q^{17} -946104. i q^{18} +946849. q^{19} +1.56010e6 q^{20} +594944. q^{21} -1.63186e6 q^{22} +2.44743e6i q^{23} -1.76981e6i q^{24} -8.29492e6 q^{25} -1.98816e7 q^{26} -2.76145e6 q^{27} +5.45533e6 q^{28} -1.24602e7 q^{29} -8.17817e6i q^{30} +3.60531e7i q^{31} +4.70913e7i q^{32} +4.76302e6i q^{33} +9.78945e7i q^{34} +5.14273e6 q^{35} -2.53210e7 q^{36} -1.04163e8i q^{37} -4.55123e7i q^{38} +5.80296e7i q^{39} -1.52984e7i q^{40} +2.63018e7 q^{41} -2.85972e7i q^{42} +1.45679e8i q^{43} +4.36744e7i q^{44} -2.38701e7 q^{45} +1.17641e8 q^{46} +2.23833e8i q^{47} +9.97448e7 q^{48} -2.64492e8 q^{49} +3.98712e8i q^{50} +2.85730e8 q^{51} +5.32101e8i q^{52} -3.03978e8 q^{53} +1.32735e8i q^{54} +4.11717e7i q^{55} -5.34949e7i q^{56} -1.32839e8 q^{57} +5.98926e8i q^{58} +(-3.68406e8 - 6.12694e8i) q^{59} -2.18876e8 q^{60} -1.36135e9i q^{61} +1.73296e9 q^{62} -8.34684e7 q^{63} +1.53552e9 q^{64} +5.01610e8i q^{65} +2.28944e8 q^{66} +2.43057e9i q^{67} +2.62000e9 q^{68} -3.43365e8i q^{69} -2.47196e8i q^{70} +2.64328e9 q^{71} +2.48298e8i q^{72} -8.53440e8i q^{73} -5.00680e9 q^{74} +1.16374e9 q^{75} -1.21807e9 q^{76} +1.43968e8i q^{77} +2.78931e9 q^{78} +4.49737e7 q^{79} +8.62199e8 q^{80} +3.87420e8 q^{81} -1.26425e9i q^{82} +1.00500e9i q^{83} -7.65362e8 q^{84} +2.46987e9 q^{85} +7.00236e9 q^{86} +1.74812e9 q^{87} +4.28271e8 q^{88} -3.83266e9i q^{89} +1.14737e9i q^{90} +1.75402e9i q^{91} -3.14848e9i q^{92} -5.05810e9i q^{93} +1.07590e10 q^{94} -1.14827e9 q^{95} -6.60673e9i q^{96} +2.35025e9i q^{97} +1.27134e10i q^{98} -6.68233e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 48.0671i 1.50210i −0.660248 0.751048i \(-0.729549\pi\)
0.660248 0.751048i \(-0.270451\pi\)
\(3\) −140.296 −0.577350
\(4\) −1286.44 −1.25629
\(5\) −1212.73 −0.388073 −0.194036 0.980994i \(-0.562158\pi\)
−0.194036 + 0.980994i \(0.562158\pi\)
\(6\) 6743.62i 0.867235i
\(7\) −4240.63 −0.252313 −0.126157 0.992010i \(-0.540264\pi\)
−0.126157 + 0.992010i \(0.540264\pi\)
\(8\) 12614.8i 0.384974i
\(9\) 19683.0 0.333333
\(10\) 58292.2i 0.582922i
\(11\) 33949.7i 0.210801i −0.994430 0.105401i \(-0.966388\pi\)
0.994430 0.105401i \(-0.0336125\pi\)
\(12\) 180483. 0.725320
\(13\) 413622.i 1.11400i −0.830511 0.557002i \(-0.811952\pi\)
0.830511 0.557002i \(-0.188048\pi\)
\(14\) 203835.i 0.378999i
\(15\) 170141. 0.224054
\(16\) −710959. −0.678023
\(17\) −2.03662e6 −1.43439 −0.717193 0.696874i \(-0.754573\pi\)
−0.717193 + 0.696874i \(0.754573\pi\)
\(18\) 946104.i 0.500699i
\(19\) 946849. 0.382396 0.191198 0.981552i \(-0.438763\pi\)
0.191198 + 0.981552i \(0.438763\pi\)
\(20\) 1.56010e6 0.487532
\(21\) 594944. 0.145673
\(22\) −1.63186e6 −0.316643
\(23\) 2.44743e6i 0.380251i 0.981760 + 0.190126i \(0.0608895\pi\)
−0.981760 + 0.190126i \(0.939110\pi\)
\(24\) 1.76981e6i 0.222265i
\(25\) −8.29492e6 −0.849400
\(26\) −1.98816e7 −1.67334
\(27\) −2.76145e6 −0.192450
\(28\) 5.45533e6 0.316979
\(29\) −1.24602e7 −0.607485 −0.303743 0.952754i \(-0.598236\pi\)
−0.303743 + 0.952754i \(0.598236\pi\)
\(30\) 8.17817e6i 0.336550i
\(31\) 3.60531e7i 1.25931i 0.776874 + 0.629657i \(0.216804\pi\)
−0.776874 + 0.629657i \(0.783196\pi\)
\(32\) 4.70913e7i 1.40343i
\(33\) 4.76302e6i 0.121706i
\(34\) 9.78945e7i 2.15459i
\(35\) 5.14273e6 0.0979159
\(36\) −2.53210e7 −0.418764
\(37\) 1.04163e8i 1.50212i −0.660236 0.751058i \(-0.729544\pi\)
0.660236 0.751058i \(-0.270456\pi\)
\(38\) 4.55123e7i 0.574395i
\(39\) 5.80296e7i 0.643171i
\(40\) 1.52984e7i 0.149398i
\(41\) 2.63018e7 0.227021 0.113510 0.993537i \(-0.463790\pi\)
0.113510 + 0.993537i \(0.463790\pi\)
\(42\) 2.85972e7i 0.218815i
\(43\) 1.45679e8i 0.990957i 0.868620 + 0.495478i \(0.165007\pi\)
−0.868620 + 0.495478i \(0.834993\pi\)
\(44\) 4.36744e7i 0.264828i
\(45\) −2.38701e7 −0.129358
\(46\) 1.17641e8 0.571174
\(47\) 2.23833e8i 0.975968i 0.872853 + 0.487984i \(0.162268\pi\)
−0.872853 + 0.487984i \(0.837732\pi\)
\(48\) 9.97448e7 0.391457
\(49\) −2.64492e8 −0.936338
\(50\) 3.98712e8i 1.27588i
\(51\) 2.85730e8 0.828143
\(52\) 5.32101e8i 1.39951i
\(53\) −3.03978e8 −0.726880 −0.363440 0.931618i \(-0.618398\pi\)
−0.363440 + 0.931618i \(0.618398\pi\)
\(54\) 1.32735e8i 0.289078i
\(55\) 4.11717e7i 0.0818061i
\(56\) 5.34949e7i 0.0971342i
\(57\) −1.32839e8 −0.220776
\(58\) 5.98926e8i 0.912501i
\(59\) −3.68406e8 6.12694e8i −0.515308 0.857005i
\(60\) −2.18876e8 −0.281477
\(61\) 1.36135e9i 1.61183i −0.592029 0.805917i \(-0.701673\pi\)
0.592029 0.805917i \(-0.298327\pi\)
\(62\) 1.73296e9 1.89161
\(63\) −8.34684e7 −0.0841045
\(64\) 1.53552e9 1.43006
\(65\) 5.01610e8i 0.432314i
\(66\) 2.28944e8 0.182814
\(67\) 2.43057e9i 1.80025i 0.435628 + 0.900127i \(0.356526\pi\)
−0.435628 + 0.900127i \(0.643474\pi\)
\(68\) 2.62000e9 1.80201
\(69\) 3.43365e8i 0.219538i
\(70\) 2.47196e8i 0.147079i
\(71\) 2.64328e9 1.46504 0.732522 0.680743i \(-0.238343\pi\)
0.732522 + 0.680743i \(0.238343\pi\)
\(72\) 2.48298e8i 0.128325i
\(73\) 8.53440e8i 0.411679i −0.978586 0.205839i \(-0.934008\pi\)
0.978586 0.205839i \(-0.0659925\pi\)
\(74\) −5.00680e9 −2.25632
\(75\) 1.16374e9 0.490401
\(76\) −1.21807e9 −0.480400
\(77\) 1.43968e8i 0.0531880i
\(78\) 2.78931e9 0.966104
\(79\) 4.49737e7 0.0146158 0.00730792 0.999973i \(-0.497674\pi\)
0.00730792 + 0.999973i \(0.497674\pi\)
\(80\) 8.62199e8 0.263122
\(81\) 3.87420e8 0.111111
\(82\) 1.26425e9i 0.341007i
\(83\) 1.00500e9i 0.255138i 0.991830 + 0.127569i \(0.0407175\pi\)
−0.991830 + 0.127569i \(0.959283\pi\)
\(84\) −7.65362e8 −0.183008
\(85\) 2.46987e9 0.556646
\(86\) 7.00236e9 1.48851
\(87\) 1.74812e9 0.350732
\(88\) 4.28271e8 0.0811531
\(89\) 3.83266e9i 0.686358i −0.939270 0.343179i \(-0.888496\pi\)
0.939270 0.343179i \(-0.111504\pi\)
\(90\) 1.14737e9i 0.194307i
\(91\) 1.75402e9i 0.281078i
\(92\) 3.14848e9i 0.477707i
\(93\) 5.05810e9i 0.727065i
\(94\) 1.07590e10 1.46600
\(95\) −1.14827e9 −0.148397
\(96\) 6.60673e9i 0.810271i
\(97\) 2.35025e9i 0.273687i 0.990593 + 0.136844i \(0.0436958\pi\)
−0.990593 + 0.136844i \(0.956304\pi\)
\(98\) 1.27134e10i 1.40647i
\(99\) 6.68233e8i 0.0702670i
\(100\) 1.06709e10 1.06709
\(101\) 1.81712e9i 0.172893i 0.996256 + 0.0864466i \(0.0275512\pi\)
−0.996256 + 0.0864466i \(0.972449\pi\)
\(102\) 1.37342e10i 1.24395i
\(103\) 1.59866e9i 0.137901i −0.997620 0.0689507i \(-0.978035\pi\)
0.997620 0.0689507i \(-0.0219651\pi\)
\(104\) 5.21778e9 0.428863
\(105\) −7.21505e8 −0.0565318
\(106\) 1.46113e10i 1.09184i
\(107\) 2.24233e10 1.59875 0.799376 0.600832i \(-0.205164\pi\)
0.799376 + 0.600832i \(0.205164\pi\)
\(108\) 3.55244e9 0.241773
\(109\) 2.20040e10i 1.43011i 0.699069 + 0.715054i \(0.253598\pi\)
−0.699069 + 0.715054i \(0.746402\pi\)
\(110\) 1.97900e9 0.122881
\(111\) 1.46136e10i 0.867248i
\(112\) 3.01491e9 0.171074
\(113\) 3.36947e10i 1.82881i −0.404796 0.914407i \(-0.632658\pi\)
0.404796 0.914407i \(-0.367342\pi\)
\(114\) 6.38519e9i 0.331627i
\(115\) 2.96806e9i 0.147565i
\(116\) 1.60294e10 0.763178
\(117\) 8.14132e9i 0.371335i
\(118\) −2.94504e10 + 1.77082e10i −1.28730 + 0.774041i
\(119\) 8.63657e9 0.361915
\(120\) 2.14630e9i 0.0862550i
\(121\) 2.47848e10 0.955563
\(122\) −6.54360e10 −2.42113
\(123\) −3.69004e9 −0.131071
\(124\) 4.63802e10i 1.58206i
\(125\) 2.19025e10 0.717701
\(126\) 4.01208e9i 0.126333i
\(127\) −5.61401e10 −1.69924 −0.849619 0.527396i \(-0.823168\pi\)
−0.849619 + 0.527396i \(0.823168\pi\)
\(128\) 2.55864e10i 0.744662i
\(129\) 2.04382e10i 0.572129i
\(130\) 2.41109e10 0.649378
\(131\) 2.34480e10i 0.607785i 0.952706 + 0.303892i \(0.0982863\pi\)
−0.952706 + 0.303892i \(0.901714\pi\)
\(132\) 6.12735e9i 0.152898i
\(133\) −4.01524e9 −0.0964835
\(134\) 1.16830e11 2.70415
\(135\) 3.34888e9 0.0746846
\(136\) 2.56917e10i 0.552202i
\(137\) −1.20211e10 −0.249082 −0.124541 0.992214i \(-0.539746\pi\)
−0.124541 + 0.992214i \(0.539746\pi\)
\(138\) −1.65045e10 −0.329767
\(139\) −9.25758e10 −1.78412 −0.892059 0.451920i \(-0.850739\pi\)
−0.892059 + 0.451920i \(0.850739\pi\)
\(140\) −6.61582e9 −0.123011
\(141\) 3.14030e10i 0.563475i
\(142\) 1.27054e11i 2.20064i
\(143\) −1.40424e10 −0.234833
\(144\) −1.39938e10 −0.226008
\(145\) 1.51108e10 0.235748
\(146\) −4.10224e10 −0.618381
\(147\) 3.71072e10 0.540595
\(148\) 1.33999e11i 1.88710i
\(149\) 6.09103e10i 0.829391i −0.909960 0.414696i \(-0.863888\pi\)
0.909960 0.414696i \(-0.136112\pi\)
\(150\) 5.59378e10i 0.736629i
\(151\) 8.17973e10i 1.04197i −0.853567 0.520984i \(-0.825565\pi\)
0.853567 0.520984i \(-0.174435\pi\)
\(152\) 1.19444e10i 0.147213i
\(153\) −4.00869e10 −0.478129
\(154\) 6.92014e9 0.0798934
\(155\) 4.37225e10i 0.488705i
\(156\) 7.46517e10i 0.808010i
\(157\) 6.19935e10i 0.649902i −0.945731 0.324951i \(-0.894652\pi\)
0.945731 0.324951i \(-0.105348\pi\)
\(158\) 2.16176e9i 0.0219544i
\(159\) 4.26469e10 0.419664
\(160\) 5.71089e10i 0.544633i
\(161\) 1.03786e10i 0.0959425i
\(162\) 1.86222e10i 0.166900i
\(163\) −1.91119e11 −1.66099 −0.830493 0.557029i \(-0.811941\pi\)
−0.830493 + 0.557029i \(0.811941\pi\)
\(164\) −3.38357e10 −0.285204
\(165\) 5.77624e9i 0.0472308i
\(166\) 4.83074e10 0.383242
\(167\) 2.21143e11 1.70251 0.851257 0.524749i \(-0.175841\pi\)
0.851257 + 0.524749i \(0.175841\pi\)
\(168\) 7.50513e9i 0.0560805i
\(169\) −3.32246e10 −0.241005
\(170\) 1.18719e11i 0.836135i
\(171\) 1.86368e10 0.127465
\(172\) 1.87408e11i 1.24493i
\(173\) 2.47462e11i 1.59690i −0.602062 0.798450i \(-0.705654\pi\)
0.602062 0.798450i \(-0.294346\pi\)
\(174\) 8.40270e10i 0.526833i
\(175\) 3.51757e10 0.214315
\(176\) 2.41369e10i 0.142928i
\(177\) 5.16859e10 + 8.59586e10i 0.297513 + 0.494792i
\(178\) −1.84225e11 −1.03098
\(179\) 1.41480e11i 0.769893i −0.922939 0.384947i \(-0.874220\pi\)
0.922939 0.384947i \(-0.125780\pi\)
\(180\) 3.07075e10 0.162511
\(181\) 4.38883e10 0.225920 0.112960 0.993600i \(-0.463967\pi\)
0.112960 + 0.993600i \(0.463967\pi\)
\(182\) 8.43105e10 0.422206
\(183\) 1.90992e11i 0.930592i
\(184\) −3.08739e10 −0.146387
\(185\) 1.26321e11i 0.582930i
\(186\) −2.43128e11 −1.09212
\(187\) 6.91428e10i 0.302370i
\(188\) 2.87949e11i 1.22610i
\(189\) 1.17103e10 0.0485577
\(190\) 5.51939e10i 0.222907i
\(191\) 4.46656e11i 1.75714i 0.477612 + 0.878571i \(0.341502\pi\)
−0.477612 + 0.878571i \(0.658498\pi\)
\(192\) −2.15427e11 −0.825647
\(193\) 2.57216e10 0.0960529 0.0480265 0.998846i \(-0.484707\pi\)
0.0480265 + 0.998846i \(0.484707\pi\)
\(194\) 1.12969e11 0.411105
\(195\) 7.03740e10i 0.249597i
\(196\) 3.40254e11 1.17631
\(197\) 1.77712e11 0.598943 0.299471 0.954105i \(-0.403190\pi\)
0.299471 + 0.954105i \(0.403190\pi\)
\(198\) −3.21200e10 −0.105548
\(199\) 5.37426e11 1.72208 0.861039 0.508539i \(-0.169814\pi\)
0.861039 + 0.508539i \(0.169814\pi\)
\(200\) 1.04639e11i 0.326997i
\(201\) 3.40999e11i 1.03938i
\(202\) 8.73439e10 0.259702
\(203\) 5.28392e10 0.153277
\(204\) −3.67576e11 −1.04039
\(205\) −3.18969e10 −0.0881006
\(206\) −7.68427e10 −0.207141
\(207\) 4.81727e10i 0.126750i
\(208\) 2.94068e11i 0.755321i
\(209\) 3.21453e10i 0.0806094i
\(210\) 3.46806e10i 0.0849161i
\(211\) 5.80157e11i 1.38718i −0.720370 0.693590i \(-0.756028\pi\)
0.720370 0.693590i \(-0.243972\pi\)
\(212\) 3.91050e11 0.913173
\(213\) −3.70841e11 −0.845844
\(214\) 1.07782e12i 2.40148i
\(215\) 1.76669e11i 0.384563i
\(216\) 3.48352e10i 0.0740884i
\(217\) 1.52888e11i 0.317742i
\(218\) 1.05767e12 2.14816
\(219\) 1.19734e11i 0.237683i
\(220\) 5.29651e10i 0.102772i
\(221\) 8.42392e11i 1.59791i
\(222\) 7.02434e11 1.30269
\(223\) 6.90723e11 1.25250 0.626252 0.779620i \(-0.284588\pi\)
0.626252 + 0.779620i \(0.284588\pi\)
\(224\) 1.99697e11i 0.354104i
\(225\) −1.63269e11 −0.283133
\(226\) −1.61961e12 −2.74705
\(227\) 9.05355e11i 1.50207i 0.660263 + 0.751034i \(0.270445\pi\)
−0.660263 + 0.751034i \(0.729555\pi\)
\(228\) 1.70890e11 0.277359
\(229\) 2.08438e10i 0.0330978i −0.999863 0.0165489i \(-0.994732\pi\)
0.999863 0.0165489i \(-0.00526792\pi\)
\(230\) −1.42666e11 −0.221657
\(231\) 2.01982e10i 0.0307081i
\(232\) 1.57184e11i 0.233866i
\(233\) 1.06421e12i 1.54970i 0.632144 + 0.774851i \(0.282175\pi\)
−0.632144 + 0.774851i \(0.717825\pi\)
\(234\) −3.91329e11 −0.557780
\(235\) 2.71449e11i 0.378746i
\(236\) 4.73933e11 + 7.88195e11i 0.647377 + 1.07665i
\(237\) −6.30964e9 −0.00843846
\(238\) 4.15135e11i 0.543631i
\(239\) 5.41434e11 0.694314 0.347157 0.937807i \(-0.387147\pi\)
0.347157 + 0.937807i \(0.387147\pi\)
\(240\) −1.20963e11 −0.151914
\(241\) 6.09091e11 0.749199 0.374599 0.927187i \(-0.377780\pi\)
0.374599 + 0.927187i \(0.377780\pi\)
\(242\) 1.19133e12i 1.43535i
\(243\) −5.43536e10 −0.0641500
\(244\) 1.75130e12i 2.02493i
\(245\) 3.20757e11 0.363367
\(246\) 1.77369e11i 0.196881i
\(247\) 3.91638e11i 0.425990i
\(248\) −4.54804e11 −0.484803
\(249\) 1.40998e11i 0.147304i
\(250\) 1.05279e12i 1.07806i
\(251\) 1.61926e12 1.62536 0.812678 0.582713i \(-0.198009\pi\)
0.812678 + 0.582713i \(0.198009\pi\)
\(252\) 1.07377e11 0.105660
\(253\) 8.30895e10 0.0801574
\(254\) 2.69849e12i 2.55242i
\(255\) −3.46513e11 −0.321380
\(256\) 3.42509e11 0.311510
\(257\) 1.41412e12 1.26130 0.630652 0.776066i \(-0.282787\pi\)
0.630652 + 0.776066i \(0.282787\pi\)
\(258\) −9.82404e11 −0.859393
\(259\) 4.41716e11i 0.379004i
\(260\) 6.45293e11i 0.543113i
\(261\) −2.45254e11 −0.202495
\(262\) 1.12708e12 0.912951
\(263\) 1.67899e11 0.133434 0.0667172 0.997772i \(-0.478747\pi\)
0.0667172 + 0.997772i \(0.478747\pi\)
\(264\) −6.00847e10 −0.0468537
\(265\) 3.68642e11 0.282082
\(266\) 1.93001e11i 0.144928i
\(267\) 5.37708e11i 0.396269i
\(268\) 3.12679e12i 2.26164i
\(269\) 5.89368e10i 0.0418432i 0.999781 + 0.0209216i \(0.00666004\pi\)
−0.999781 + 0.0209216i \(0.993340\pi\)
\(270\) 1.60971e11i 0.112183i
\(271\) −1.49409e12 −1.02219 −0.511093 0.859525i \(-0.670759\pi\)
−0.511093 + 0.859525i \(0.670759\pi\)
\(272\) 1.44796e12 0.972547
\(273\) 2.46082e11i 0.162281i
\(274\) 5.77819e11i 0.374144i
\(275\) 2.81610e11i 0.179054i
\(276\) 4.41719e11i 0.275804i
\(277\) −1.48765e12 −0.912224 −0.456112 0.889922i \(-0.650758\pi\)
−0.456112 + 0.889922i \(0.650758\pi\)
\(278\) 4.44985e12i 2.67992i
\(279\) 7.09632e11i 0.419771i
\(280\) 6.48747e10i 0.0376951i
\(281\) 2.32124e12 1.32492 0.662458 0.749099i \(-0.269513\pi\)
0.662458 + 0.749099i \(0.269513\pi\)
\(282\) −1.50945e12 −0.846394
\(283\) 1.72438e12i 0.949948i −0.880000 0.474974i \(-0.842458\pi\)
0.880000 0.474974i \(-0.157542\pi\)
\(284\) −3.40042e12 −1.84052
\(285\) 1.61098e11 0.0856772
\(286\) 6.74975e11i 0.352742i
\(287\) −1.11536e11 −0.0572804
\(288\) 9.26898e11i 0.467810i
\(289\) 2.13184e12 1.05746
\(290\) 7.26334e11i 0.354117i
\(291\) 3.29730e11i 0.158013i
\(292\) 1.09790e12i 0.517189i
\(293\) −2.39530e12 −1.10923 −0.554615 0.832107i \(-0.687134\pi\)
−0.554615 + 0.832107i \(0.687134\pi\)
\(294\) 1.78364e12i 0.812025i
\(295\) 4.46776e11 + 7.43030e11i 0.199977 + 0.332580i
\(296\) 1.31400e12 0.578277
\(297\) 9.37504e10i 0.0405687i
\(298\) −2.92778e12 −1.24582
\(299\) 1.01231e12 0.423602
\(300\) −1.49709e12 −0.616087
\(301\) 6.17771e11i 0.250032i
\(302\) −3.93176e12 −1.56514
\(303\) 2.54936e11i 0.0998199i
\(304\) −6.73171e11 −0.259273
\(305\) 1.65094e12i 0.625508i
\(306\) 1.92686e12i 0.718195i
\(307\) −2.92215e12 −1.07154 −0.535772 0.844363i \(-0.679979\pi\)
−0.535772 + 0.844363i \(0.679979\pi\)
\(308\) 1.85207e11i 0.0668196i
\(309\) 2.24285e11i 0.0796174i
\(310\) −2.10161e12 −0.734081
\(311\) 3.22319e12 1.10786 0.553928 0.832565i \(-0.313128\pi\)
0.553928 + 0.832565i \(0.313128\pi\)
\(312\) −7.32034e11 −0.247604
\(313\) 1.49286e12i 0.496931i 0.968641 + 0.248465i \(0.0799262\pi\)
−0.968641 + 0.248465i \(0.920074\pi\)
\(314\) −2.97985e12 −0.976215
\(315\) 1.01224e11 0.0326386
\(316\) −5.78561e10 −0.0183617
\(317\) −4.43107e12 −1.38424 −0.692122 0.721781i \(-0.743324\pi\)
−0.692122 + 0.721781i \(0.743324\pi\)
\(318\) 2.04991e12i 0.630376i
\(319\) 4.23021e11i 0.128059i
\(320\) −1.86216e12 −0.554968
\(321\) −3.14590e12 −0.923039
\(322\) −4.98871e11 −0.144115
\(323\) −1.92838e12 −0.548503
\(324\) −4.98394e11 −0.139588
\(325\) 3.43096e12i 0.946235i
\(326\) 9.18654e12i 2.49496i
\(327\) 3.08707e12i 0.825673i
\(328\) 3.31793e11i 0.0873972i
\(329\) 9.49195e11i 0.246250i
\(330\) −2.77647e11 −0.0709452
\(331\) 4.35658e12 1.09649 0.548246 0.836317i \(-0.315296\pi\)
0.548246 + 0.836317i \(0.315296\pi\)
\(332\) 1.29288e12i 0.320528i
\(333\) 2.05024e12i 0.500706i
\(334\) 1.06297e13i 2.55734i
\(335\) 2.94761e12i 0.698629i
\(336\) −4.22981e11 −0.0987698
\(337\) 4.08576e12i 0.939989i 0.882669 + 0.469995i \(0.155744\pi\)
−0.882669 + 0.469995i \(0.844256\pi\)
\(338\) 1.59701e12i 0.362013i
\(339\) 4.72724e12i 1.05587i
\(340\) −3.17734e12 −0.699310
\(341\) 1.22399e12 0.265465
\(342\) 8.95818e11i 0.191465i
\(343\) 2.31949e12 0.488564
\(344\) −1.83772e12 −0.381493
\(345\) 4.16407e11i 0.0851967i
\(346\) −1.18948e13 −2.39870
\(347\) 4.87568e12i 0.969144i −0.874751 0.484572i \(-0.838975\pi\)
0.874751 0.484572i \(-0.161025\pi\)
\(348\) −2.24886e12 −0.440621
\(349\) 4.70800e12i 0.909305i 0.890669 + 0.454652i \(0.150237\pi\)
−0.890669 + 0.454652i \(0.849763\pi\)
\(350\) 1.69079e12i 0.321922i
\(351\) 1.14220e12i 0.214390i
\(352\) 1.59874e12 0.295845
\(353\) 4.05744e12i 0.740250i 0.928982 + 0.370125i \(0.120685\pi\)
−0.928982 + 0.370125i \(0.879315\pi\)
\(354\) 4.13178e12 2.48439e12i 0.743225 0.446893i
\(355\) −3.20557e12 −0.568543
\(356\) 4.93050e12i 0.862266i
\(357\) −1.21168e12 −0.208952
\(358\) −6.80054e12 −1.15645
\(359\) 8.17182e12 1.37040 0.685199 0.728356i \(-0.259715\pi\)
0.685199 + 0.728356i \(0.259715\pi\)
\(360\) 3.01118e11i 0.0497993i
\(361\) −5.23454e12 −0.853774
\(362\) 2.10958e12i 0.339354i
\(363\) −3.47722e12 −0.551694
\(364\) 2.25644e12i 0.353116i
\(365\) 1.03499e12i 0.159761i
\(366\) 9.18042e12 1.39784
\(367\) 6.99731e12i 1.05100i 0.850795 + 0.525498i \(0.176121\pi\)
−0.850795 + 0.525498i \(0.823879\pi\)
\(368\) 1.74002e12i 0.257819i
\(369\) 5.17698e11 0.0756736
\(370\) 6.07188e12 0.875617
\(371\) 1.28906e12 0.183402
\(372\) 6.50696e12i 0.913405i
\(373\) 1.07780e13 1.49278 0.746388 0.665511i \(-0.231786\pi\)
0.746388 + 0.665511i \(0.231786\pi\)
\(374\) 3.32349e12 0.454189
\(375\) −3.07284e12 −0.414365
\(376\) −2.82362e12 −0.375723
\(377\) 5.15382e12i 0.676741i
\(378\) 5.62879e11i 0.0729384i
\(379\) −1.18081e13 −1.51003 −0.755015 0.655708i \(-0.772370\pi\)
−0.755015 + 0.655708i \(0.772370\pi\)
\(380\) 1.47718e12 0.186430
\(381\) 7.87624e12 0.981056
\(382\) 2.14695e13 2.63939
\(383\) −4.15695e12 −0.504407 −0.252204 0.967674i \(-0.581155\pi\)
−0.252204 + 0.967674i \(0.581155\pi\)
\(384\) 3.58967e12i 0.429931i
\(385\) 1.74594e11i 0.0206408i
\(386\) 1.23636e12i 0.144281i
\(387\) 2.86740e12i 0.330319i
\(388\) 3.02346e12i 0.343831i
\(389\) 9.22414e11 0.103557 0.0517783 0.998659i \(-0.483511\pi\)
0.0517783 + 0.998659i \(0.483511\pi\)
\(390\) −3.38267e12 −0.374918
\(391\) 4.98449e12i 0.545427i
\(392\) 3.33653e12i 0.360466i
\(393\) 3.28967e12i 0.350905i
\(394\) 8.54209e12i 0.899669i
\(395\) −5.45409e10 −0.00567200
\(396\) 8.59643e11i 0.0882759i
\(397\) 6.05681e11i 0.0614174i 0.999528 + 0.0307087i \(0.00977641\pi\)
−0.999528 + 0.0307087i \(0.990224\pi\)
\(398\) 2.58325e13i 2.58673i
\(399\) 5.63322e11 0.0557048
\(400\) 5.89735e12 0.575913
\(401\) 9.92611e11i 0.0957321i 0.998854 + 0.0478660i \(0.0152421\pi\)
−0.998854 + 0.0478660i \(0.984758\pi\)
\(402\) −1.63908e13 −1.56124
\(403\) 1.49123e13 1.40288
\(404\) 2.33763e12i 0.217204i
\(405\) −4.69835e11 −0.0431192
\(406\) 2.53983e12i 0.230236i
\(407\) −3.53630e12 −0.316648
\(408\) 3.60444e12i 0.318814i
\(409\) 5.50739e12i 0.481204i 0.970624 + 0.240602i \(0.0773449\pi\)
−0.970624 + 0.240602i \(0.922655\pi\)
\(410\) 1.53319e12i 0.132335i
\(411\) 1.68651e12 0.143807
\(412\) 2.05658e12i 0.173244i
\(413\) 1.56227e12 + 2.59821e12i 0.130019 + 0.216234i
\(414\) 2.31552e12 0.190391
\(415\) 1.21879e12i 0.0990122i
\(416\) 1.94780e13 1.56343
\(417\) 1.29880e13 1.03006
\(418\) −1.54513e12 −0.121083
\(419\) 1.35032e13i 1.04560i 0.852454 + 0.522802i \(0.175113\pi\)
−0.852454 + 0.522802i \(0.824887\pi\)
\(420\) 9.28174e11 0.0710204
\(421\) 1.71630e13i 1.29772i −0.760906 0.648862i \(-0.775245\pi\)
0.760906 0.648862i \(-0.224755\pi\)
\(422\) −2.78864e13 −2.08368
\(423\) 4.40571e12i 0.325323i
\(424\) 3.83463e12i 0.279830i
\(425\) 1.68936e13 1.21837
\(426\) 1.78253e13i 1.27054i
\(427\) 5.77298e12i 0.406687i
\(428\) −2.88463e13 −2.00850
\(429\) 1.97009e12 0.135581
\(430\) −8.49195e12 −0.577650
\(431\) 6.74475e11i 0.0453502i 0.999743 + 0.0226751i \(0.00721833\pi\)
−0.999743 + 0.0226751i \(0.992782\pi\)
\(432\) 1.96328e12 0.130486
\(433\) 1.25185e13 0.822454 0.411227 0.911533i \(-0.365100\pi\)
0.411227 + 0.911533i \(0.365100\pi\)
\(434\) −7.34887e12 −0.477278
\(435\) −2.11999e12 −0.136109
\(436\) 2.83069e13i 1.79663i
\(437\) 2.31735e12i 0.145406i
\(438\) 5.75528e12 0.357023
\(439\) 2.48488e13 1.52399 0.761997 0.647581i \(-0.224219\pi\)
0.761997 + 0.647581i \(0.224219\pi\)
\(440\) −5.19375e11 −0.0314933
\(441\) −5.20600e12 −0.312113
\(442\) 4.04913e13 2.40022
\(443\) 1.48108e13i 0.868079i 0.900894 + 0.434040i \(0.142912\pi\)
−0.900894 + 0.434040i \(0.857088\pi\)
\(444\) 1.87996e13i 1.08952i
\(445\) 4.64797e12i 0.266357i
\(446\) 3.32010e13i 1.88138i
\(447\) 8.54548e12i 0.478849i
\(448\) −6.51157e12 −0.360824
\(449\) 2.59038e12 0.141949 0.0709744 0.997478i \(-0.477389\pi\)
0.0709744 + 0.997478i \(0.477389\pi\)
\(450\) 7.84786e12i 0.425293i
\(451\) 8.92938e11i 0.0478563i
\(452\) 4.33463e13i 2.29752i
\(453\) 1.14758e13i 0.601580i
\(454\) 4.35178e13 2.25625
\(455\) 2.12714e12i 0.109079i
\(456\) 1.67575e12i 0.0849932i
\(457\) 2.99458e12i 0.150230i 0.997175 + 0.0751148i \(0.0239323\pi\)
−0.997175 + 0.0751148i \(0.976068\pi\)
\(458\) −1.00190e12 −0.0497161
\(459\) 5.62403e12 0.276048
\(460\) 3.81824e12i 0.185385i
\(461\) −1.22054e13 −0.586201 −0.293101 0.956082i \(-0.594687\pi\)
−0.293101 + 0.956082i \(0.594687\pi\)
\(462\) −9.70868e11 −0.0461265
\(463\) 1.22561e13i 0.576031i 0.957626 + 0.288016i \(0.0929955\pi\)
−0.957626 + 0.288016i \(0.907004\pi\)
\(464\) 8.85870e12 0.411889
\(465\) 6.13410e12i 0.282154i
\(466\) 5.11535e13 2.32780
\(467\) 1.45069e13i 0.653118i 0.945177 + 0.326559i \(0.105889\pi\)
−0.945177 + 0.326559i \(0.894111\pi\)
\(468\) 1.04733e13i 0.466505i
\(469\) 1.03071e13i 0.454228i
\(470\) −1.30477e13 −0.568913
\(471\) 8.69745e12i 0.375221i
\(472\) 7.72904e12 4.64738e12i 0.329925 0.198380i
\(473\) 4.94576e12 0.208895
\(474\) 3.03286e11i 0.0126754i
\(475\) −7.85404e12 −0.324807
\(476\) −1.11105e13 −0.454671
\(477\) −5.98320e12 −0.242293
\(478\) 2.60251e13i 1.04293i
\(479\) −2.73650e13 −1.08522 −0.542610 0.839985i \(-0.682564\pi\)
−0.542610 + 0.839985i \(0.682564\pi\)
\(480\) 8.01215e12i 0.314444i
\(481\) −4.30840e13 −1.67336
\(482\) 2.92772e13i 1.12537i
\(483\) 1.45608e12i 0.0553924i
\(484\) −3.18843e13 −1.20047
\(485\) 2.85021e12i 0.106211i
\(486\) 2.61262e12i 0.0963595i
\(487\) 2.31886e13 0.846504 0.423252 0.906012i \(-0.360889\pi\)
0.423252 + 0.906012i \(0.360889\pi\)
\(488\) 1.71732e13 0.620515
\(489\) 2.68133e13 0.958971
\(490\) 1.54178e13i 0.545812i
\(491\) −2.44864e13 −0.858058 −0.429029 0.903291i \(-0.641144\pi\)
−0.429029 + 0.903291i \(0.641144\pi\)
\(492\) 4.74702e12 0.164663
\(493\) 2.53768e13 0.871368
\(494\) −1.88249e13 −0.639878
\(495\) 8.10384e11i 0.0272687i
\(496\) 2.56322e13i 0.853843i
\(497\) −1.12092e13 −0.369650
\(498\) −6.77734e12 −0.221265
\(499\) −1.95409e13 −0.631601 −0.315800 0.948826i \(-0.602273\pi\)
−0.315800 + 0.948826i \(0.602273\pi\)
\(500\) −2.81763e13 −0.901642
\(501\) −3.10255e13 −0.982947
\(502\) 7.78332e13i 2.44144i
\(503\) 4.04475e13i 1.25618i −0.778141 0.628090i \(-0.783837\pi\)
0.778141 0.628090i \(-0.216163\pi\)
\(504\) 1.05294e12i 0.0323781i
\(505\) 2.20368e12i 0.0670951i
\(506\) 3.99387e12i 0.120404i
\(507\) 4.66129e12 0.139144
\(508\) 7.22210e13 2.13474
\(509\) 4.75133e13i 1.39068i 0.718682 + 0.695339i \(0.244746\pi\)
−0.718682 + 0.695339i \(0.755254\pi\)
\(510\) 1.66559e13i 0.482743i
\(511\) 3.61912e12i 0.103872i
\(512\) 4.26638e13i 1.21258i
\(513\) −2.61468e12 −0.0735921
\(514\) 6.79725e13i 1.89460i
\(515\) 1.93873e12i 0.0535157i
\(516\) 2.62926e13i 0.718761i
\(517\) 7.59909e12 0.205735
\(518\) 2.12320e13 0.569301
\(519\) 3.47179e13i 0.921970i
\(520\) −6.32774e12 −0.166430
\(521\) −4.64189e13 −1.20922 −0.604611 0.796521i \(-0.706671\pi\)
−0.604611 + 0.796521i \(0.706671\pi\)
\(522\) 1.17887e13i 0.304167i
\(523\) −1.77026e13 −0.452407 −0.226204 0.974080i \(-0.572631\pi\)
−0.226204 + 0.974080i \(0.572631\pi\)
\(524\) 3.01645e13i 0.763555i
\(525\) −4.93501e12 −0.123735
\(526\) 8.07039e12i 0.200431i
\(527\) 7.34265e13i 1.80634i
\(528\) 3.38631e12i 0.0825195i
\(529\) 3.54366e13 0.855409
\(530\) 1.77195e13i 0.423714i
\(531\) −7.25133e12 1.20597e13i −0.171769 0.285668i
\(532\) 5.16537e12 0.121211
\(533\) 1.08790e13i 0.252902i
\(534\) 2.58460e13 0.595234
\(535\) −2.71933e13 −0.620431
\(536\) −3.06612e13 −0.693052
\(537\) 1.98491e13i 0.444498i
\(538\) 2.83292e12 0.0628525
\(539\) 8.97944e12i 0.197381i
\(540\) −4.30814e12 −0.0938256
\(541\) 7.67384e13i 1.65587i −0.560824 0.827935i \(-0.689516\pi\)
0.560824 0.827935i \(-0.310484\pi\)
\(542\) 7.18165e13i 1.53542i
\(543\) −6.15735e12 −0.130435
\(544\) 9.59072e13i 2.01306i
\(545\) 2.66848e13i 0.554986i
\(546\) −1.18284e13 −0.243761
\(547\) −5.33433e13 −1.08929 −0.544644 0.838667i \(-0.683335\pi\)
−0.544644 + 0.838667i \(0.683335\pi\)
\(548\) 1.54645e13 0.312919
\(549\) 2.67954e13i 0.537278i
\(550\) 1.35362e13 0.268957
\(551\) −1.17979e13 −0.232300
\(552\) 4.33149e12 0.0845166
\(553\) −1.90717e11 −0.00368777
\(554\) 7.15069e13i 1.37025i
\(555\) 1.77223e13i 0.336555i
\(556\) 1.19093e14 2.24137
\(557\) −8.38263e13 −1.56352 −0.781761 0.623578i \(-0.785679\pi\)
−0.781761 + 0.623578i \(0.785679\pi\)
\(558\) 3.41099e13 0.630536
\(559\) 6.02560e13 1.10393
\(560\) −3.65627e12 −0.0663893
\(561\) 9.70047e12i 0.174574i
\(562\) 1.11575e14i 1.99015i
\(563\) 8.01858e13i 1.41761i 0.705407 + 0.708803i \(0.250764\pi\)
−0.705407 + 0.708803i \(0.749236\pi\)
\(564\) 4.03981e13i 0.707889i
\(565\) 4.08625e13i 0.709712i
\(566\) −8.28857e13 −1.42691
\(567\) −1.64291e12 −0.0280348
\(568\) 3.33445e13i 0.564004i
\(569\) 4.44464e13i 0.745203i −0.927991 0.372602i \(-0.878466\pi\)
0.927991 0.372602i \(-0.121534\pi\)
\(570\) 7.74349e12i 0.128695i
\(571\) 5.25658e12i 0.0866009i −0.999062 0.0433005i \(-0.986213\pi\)
0.999062 0.0433005i \(-0.0137873\pi\)
\(572\) 1.80647e13 0.295019
\(573\) 6.26642e13i 1.01449i
\(574\) 5.36121e12i 0.0860407i
\(575\) 2.03012e13i 0.322985i
\(576\) 3.02236e13 0.476688
\(577\) −1.09977e14 −1.71958 −0.859790 0.510648i \(-0.829405\pi\)
−0.859790 + 0.510648i \(0.829405\pi\)
\(578\) 1.02471e14i 1.58841i
\(579\) −3.60863e12 −0.0554562
\(580\) −1.94392e13 −0.296169
\(581\) 4.26184e12i 0.0643748i
\(582\) −1.58492e13 −0.237351
\(583\) 1.03200e13i 0.153227i
\(584\) 1.07660e13 0.158486
\(585\) 9.87320e12i 0.144105i
\(586\) 1.15135e14i 1.66617i
\(587\) 3.08123e13i 0.442113i 0.975261 + 0.221056i \(0.0709505\pi\)
−0.975261 + 0.221056i \(0.929050\pi\)
\(588\) −4.77363e13 −0.679145
\(589\) 3.41368e13i 0.481556i
\(590\) 3.57153e13 2.14752e13i 0.499567 0.300384i
\(591\) −2.49323e13 −0.345800
\(592\) 7.40554e13i 1.01847i
\(593\) 1.74470e13 0.237929 0.118964 0.992899i \(-0.462043\pi\)
0.118964 + 0.992899i \(0.462043\pi\)
\(594\) 4.50631e12 0.0609381
\(595\) −1.04738e13 −0.140449
\(596\) 7.83576e13i 1.04196i
\(597\) −7.53987e13 −0.994242
\(598\) 4.86588e13i 0.636290i
\(599\) 2.40542e13 0.311929 0.155965 0.987763i \(-0.450151\pi\)
0.155965 + 0.987763i \(0.450151\pi\)
\(600\) 1.46805e13i 0.188792i
\(601\) 3.18260e13i 0.405891i −0.979190 0.202945i \(-0.934949\pi\)
0.979190 0.202945i \(-0.0650514\pi\)
\(602\) −2.96944e13 −0.375571
\(603\) 4.78409e13i 0.600085i
\(604\) 1.05228e14i 1.30902i
\(605\) −3.00572e13 −0.370828
\(606\) −1.22540e13 −0.149939
\(607\) −7.13963e13 −0.866427 −0.433214 0.901291i \(-0.642620\pi\)
−0.433214 + 0.901291i \(0.642620\pi\)
\(608\) 4.45884e13i 0.536665i
\(609\) −7.41314e12 −0.0884943
\(610\) 7.93560e13 0.939573
\(611\) 9.25824e13 1.08723
\(612\) 5.15694e13 0.600669
\(613\) 2.52653e13i 0.291892i 0.989293 + 0.145946i \(0.0466226\pi\)
−0.989293 + 0.145946i \(0.953377\pi\)
\(614\) 1.40459e14i 1.60956i
\(615\) 4.47501e12 0.0508649
\(616\) −1.81614e12 −0.0204760
\(617\) 4.37750e13 0.489554 0.244777 0.969579i \(-0.421285\pi\)
0.244777 + 0.969579i \(0.421285\pi\)
\(618\) 1.07807e13 0.119593
\(619\) −1.60155e14 −1.76233 −0.881165 0.472809i \(-0.843240\pi\)
−0.881165 + 0.472809i \(0.843240\pi\)
\(620\) 5.62465e13i 0.613956i
\(621\) 6.75845e12i 0.0731794i
\(622\) 1.54929e14i 1.66411i
\(623\) 1.62529e13i 0.173177i
\(624\) 4.12566e13i 0.436085i
\(625\) 5.44433e13 0.570880
\(626\) 7.17572e13 0.746438
\(627\) 4.50986e12i 0.0465399i
\(628\) 7.97511e13i 0.816467i
\(629\) 2.12140e14i 2.15462i
\(630\) 4.86556e12i 0.0490264i
\(631\) −3.60007e13 −0.359886 −0.179943 0.983677i \(-0.557591\pi\)
−0.179943 + 0.983677i \(0.557591\pi\)
\(632\) 5.67337e11i 0.00562672i
\(633\) 8.13937e13i 0.800889i
\(634\) 2.12989e14i 2.07927i
\(635\) 6.80826e13 0.659428
\(636\) −5.48628e13 −0.527221
\(637\) 1.09400e14i 1.04308i
\(638\) 2.03334e13 0.192356
\(639\) 5.20276e13 0.488348
\(640\) 3.10293e13i 0.288983i
\(641\) −1.24923e14 −1.15439 −0.577193 0.816608i \(-0.695852\pi\)
−0.577193 + 0.816608i \(0.695852\pi\)
\(642\) 1.51214e14i 1.38649i
\(643\) −1.32175e14 −1.20253 −0.601264 0.799050i \(-0.705336\pi\)
−0.601264 + 0.799050i \(0.705336\pi\)
\(644\) 1.33515e13i 0.120532i
\(645\) 2.47859e13i 0.222028i
\(646\) 9.26913e13i 0.823904i
\(647\) 2.26232e14 1.99541 0.997706 0.0676954i \(-0.0215646\pi\)
0.997706 + 0.0676954i \(0.0215646\pi\)
\(648\) 4.88725e12i 0.0427749i
\(649\) −2.08008e13 + 1.25073e13i −0.180658 + 0.108627i
\(650\) 1.64916e14 1.42134
\(651\) 2.14496e13i 0.183448i
\(652\) 2.45864e14 2.08668
\(653\) −1.61068e14 −1.35657 −0.678287 0.734797i \(-0.737277\pi\)
−0.678287 + 0.734797i \(0.737277\pi\)
\(654\) −1.48387e14 −1.24024
\(655\) 2.84360e13i 0.235865i
\(656\) −1.86995e13 −0.153925
\(657\) 1.67983e13i 0.137226i
\(658\) −4.56250e13 −0.369891
\(659\) 9.82649e13i 0.790627i 0.918546 + 0.395313i \(0.129364\pi\)
−0.918546 + 0.395313i \(0.870636\pi\)
\(660\) 7.43080e12i 0.0593356i
\(661\) 1.24089e14 0.983393 0.491696 0.870767i \(-0.336377\pi\)
0.491696 + 0.870767i \(0.336377\pi\)
\(662\) 2.09408e14i 1.64704i
\(663\) 1.18184e14i 0.922555i
\(664\) −1.26779e13 −0.0982217
\(665\) 4.86939e12 0.0374426
\(666\) −9.85488e13 −0.752108
\(667\) 3.04955e13i 0.230997i
\(668\) −2.84488e14 −2.13885
\(669\) −9.69057e13 −0.723134
\(670\) −1.41683e14 −1.04941
\(671\) −4.62174e13 −0.339776
\(672\) 2.80167e13i 0.204442i
\(673\) 1.05709e14i 0.765662i 0.923818 + 0.382831i \(0.125051\pi\)
−0.923818 + 0.382831i \(0.874949\pi\)
\(674\) 1.96390e14 1.41195
\(675\) 2.29060e13 0.163467
\(676\) 4.27416e13 0.302773
\(677\) 1.17787e14 0.828238 0.414119 0.910223i \(-0.364090\pi\)
0.414119 + 0.910223i \(0.364090\pi\)
\(678\) 2.27224e14 1.58601
\(679\) 9.96653e12i 0.0690550i
\(680\) 3.11570e13i 0.214294i
\(681\) 1.27018e14i 0.867219i
\(682\) 5.88337e13i 0.398753i
\(683\) 1.82949e14i 1.23091i 0.788172 + 0.615455i \(0.211028\pi\)
−0.788172 + 0.615455i \(0.788972\pi\)
\(684\) −2.39752e13 −0.160133
\(685\) 1.45783e13 0.0966617
\(686\) 1.11491e14i 0.733870i
\(687\) 2.92430e12i 0.0191090i
\(688\) 1.03572e14i 0.671891i
\(689\) 1.25732e14i 0.809747i
\(690\) 2.00155e13 0.127974
\(691\) 8.14976e13i 0.517314i −0.965969 0.258657i \(-0.916720\pi\)
0.965969 0.258657i \(-0.0832800\pi\)
\(692\) 3.18345e14i 2.00617i
\(693\) 2.83373e12i 0.0177293i
\(694\) −2.34360e14 −1.45575
\(695\) 1.12269e14 0.692367
\(696\) 2.20523e13i 0.135023i
\(697\) −5.35668e13 −0.325636
\(698\) 2.26300e14 1.36586
\(699\) 1.49305e14i 0.894721i
\(700\) −4.52515e13 −0.269242
\(701\) 2.29407e14i 1.35524i −0.735412 0.677620i \(-0.763012\pi\)
0.735412 0.677620i \(-0.236988\pi\)
\(702\) 5.49020e13 0.322035
\(703\) 9.86264e13i 0.574403i
\(704\) 5.21304e13i 0.301459i
\(705\) 3.80832e13i 0.218669i
\(706\) 1.95029e14 1.11193
\(707\) 7.70576e12i 0.0436233i
\(708\) −6.64910e13 1.10581e14i −0.373763 0.621603i
\(709\) 9.37167e13 0.523101 0.261551 0.965190i \(-0.415766\pi\)
0.261551 + 0.965190i \(0.415766\pi\)
\(710\) 1.54082e14i 0.854006i
\(711\) 8.85218e11 0.00487194
\(712\) 4.83485e13 0.264230
\(713\) −8.82373e13 −0.478855
\(714\) 5.82418e13i 0.313865i
\(715\) 1.70295e13 0.0911324
\(716\) 1.82006e14i 0.967211i
\(717\) −7.59610e13 −0.400862
\(718\) 3.92795e14i 2.05847i
\(719\) 6.45439e13i 0.335900i 0.985795 + 0.167950i \(0.0537148\pi\)
−0.985795 + 0.167950i \(0.946285\pi\)
\(720\) 1.69707e13 0.0877074
\(721\) 6.77931e12i 0.0347944i
\(722\) 2.51609e14i 1.28245i
\(723\) −8.54531e13 −0.432550
\(724\) −5.64597e13 −0.283822
\(725\) 1.03357e14 0.515998
\(726\) 1.67140e14i 0.828698i
\(727\) −2.81569e14 −1.38648 −0.693239 0.720708i \(-0.743817\pi\)
−0.693239 + 0.720708i \(0.743817\pi\)
\(728\) −2.21267e13 −0.108208
\(729\) 7.62560e12 0.0370370
\(730\) 4.97489e13 0.239977
\(731\) 2.96693e14i 1.42141i
\(732\) 2.45700e14i 1.16910i
\(733\) −1.25097e13 −0.0591188 −0.0295594 0.999563i \(-0.509410\pi\)
−0.0295594 + 0.999563i \(0.509410\pi\)
\(734\) 3.36340e14 1.57870
\(735\) −4.50009e13 −0.209790
\(736\) −1.15253e14 −0.533656
\(737\) 8.25171e13 0.379496
\(738\) 2.48842e13i 0.113669i
\(739\) 3.10630e14i 1.40936i 0.709526 + 0.704679i \(0.248909\pi\)
−0.709526 + 0.704679i \(0.751091\pi\)
\(740\) 1.62505e14i 0.732330i
\(741\) 5.49452e13i 0.245946i
\(742\) 6.19613e13i 0.275487i
\(743\) 1.22114e13 0.0539290 0.0269645 0.999636i \(-0.491416\pi\)
0.0269645 + 0.999636i \(0.491416\pi\)
\(744\) 6.38072e13 0.279901
\(745\) 7.38675e13i 0.321864i
\(746\) 5.18068e14i 2.24229i
\(747\) 1.97814e13i 0.0850461i
\(748\) 8.89483e13i 0.379865i
\(749\) −9.50890e13 −0.403386
\(750\) 1.47702e14i 0.622416i
\(751\) 2.02817e14i 0.848994i 0.905429 + 0.424497i \(0.139549\pi\)
−0.905429 + 0.424497i \(0.860451\pi\)
\(752\) 1.59136e14i 0.661729i
\(753\) −2.27176e14 −0.938400
\(754\) 2.47729e14 1.01653
\(755\) 9.91978e13i 0.404359i
\(756\) −1.50646e13 −0.0610027
\(757\) 1.52549e14 0.613663 0.306832 0.951764i \(-0.400731\pi\)
0.306832 + 0.951764i \(0.400731\pi\)
\(758\) 5.67583e14i 2.26821i
\(759\) −1.16571e13 −0.0462789
\(760\) 1.44852e13i 0.0571291i
\(761\) 2.28700e14 0.896072 0.448036 0.894016i \(-0.352124\pi\)
0.448036 + 0.894016i \(0.352124\pi\)
\(762\) 3.78587e14i 1.47364i
\(763\) 9.33108e13i 0.360836i
\(764\) 5.74598e14i 2.20748i
\(765\) 4.86144e13 0.185549
\(766\) 1.99813e14i 0.757668i
\(767\) −2.53424e14 + 1.52381e14i −0.954707 + 0.574055i
\(768\) −4.80527e13 −0.179850
\(769\) 4.33481e14i 1.61190i −0.591982 0.805951i \(-0.701654\pi\)
0.591982 0.805951i \(-0.298346\pi\)
\(770\) −8.39223e12 −0.0310044
\(771\) −1.98395e14 −0.728214
\(772\) −3.30893e13 −0.120670
\(773\) 1.19916e14i 0.434492i 0.976117 + 0.217246i \(0.0697073\pi\)
−0.976117 + 0.217246i \(0.930293\pi\)
\(774\) 1.37827e14 0.496171
\(775\) 2.99057e14i 1.06966i
\(776\) −2.96480e13 −0.105363
\(777\) 6.19710e13i 0.218818i
\(778\) 4.43377e13i 0.155552i
\(779\) 2.49038e13 0.0868118