Properties

Label 177.7.c.a.58.13
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.13
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.48

$q$-expansion

\(f(q)\) \(=\) \(q-10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} +158.263i q^{6} -654.718 q^{7} -253.057i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} +158.263i q^{6} -654.718 q^{7} -253.057i q^{8} +243.000 q^{9} +1058.93i q^{10} -442.991i q^{11} +609.112 q^{12} +3003.02i q^{13} +6647.07i q^{14} +1625.90 q^{15} -5069.95 q^{16} -6614.72 q^{17} -2467.07i q^{18} -2022.49 q^{19} +4075.53 q^{20} +10206.1 q^{21} -4497.50 q^{22} -7860.31i q^{23} +3944.78i q^{24} -4746.22 q^{25} +30488.4 q^{26} -3788.00 q^{27} +25582.8 q^{28} +24340.1 q^{29} -16507.0i q^{30} +13844.9i q^{31} +35277.3i q^{32} +6905.55i q^{33} +67156.4i q^{34} +68288.0 q^{35} -9495.11 q^{36} -73303.9i q^{37} +20533.5i q^{38} -46812.5i q^{39} +26394.2i q^{40} -5255.31 q^{41} -103618. i q^{42} +72295.0i q^{43} +17309.7i q^{44} -25345.2 q^{45} -79802.3 q^{46} -175954. i q^{47} +79032.7 q^{48} +311007. q^{49} +48186.3i q^{50} +103113. q^{51} -117342. i q^{52} -23803.5 q^{53} +38457.9i q^{54} +46204.6i q^{55} +165681. i q^{56} +31527.5 q^{57} -247114. i q^{58} +(-114946. - 170200. i) q^{59} -63531.2 q^{60} +28156.5i q^{61} +140561. q^{62} -159097. q^{63} +33678.3 q^{64} -313219. i q^{65} +70109.0 q^{66} -320803. i q^{67} +258467. q^{68} +122530. i q^{69} -693299. i q^{70} +554734. q^{71} -61493.0i q^{72} +125135. i q^{73} -744223. q^{74} +73986.2 q^{75} +79027.9 q^{76} +290035. i q^{77} -475266. q^{78} -858752. q^{79} +528803. q^{80} +59049.0 q^{81} +53354.8i q^{82} +520126. i q^{83} -398797. q^{84} +689925. q^{85} +733979. q^{86} -379424. q^{87} -112102. q^{88} +300665. i q^{89} +257319. i q^{90} -1.96613e6i q^{91} +307138. i q^{92} -215820. i q^{93} -1.78639e6 q^{94} +210949. q^{95} -549919. i q^{96} -1.22552e6i q^{97} -3.15752e6i q^{98} -107647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.1526i 1.26907i −0.772894 0.634535i \(-0.781192\pi\)
0.772894 0.634535i \(-0.218808\pi\)
\(3\) −15.5885 −0.577350
\(4\) −39.0745 −0.610539
\(5\) −104.301 −0.834411 −0.417206 0.908812i \(-0.636990\pi\)
−0.417206 + 0.908812i \(0.636990\pi\)
\(6\) 158.263i 0.732698i
\(7\) −654.718 −1.90880 −0.954400 0.298531i \(-0.903503\pi\)
−0.954400 + 0.298531i \(0.903503\pi\)
\(8\) 253.057i 0.494253i
\(9\) 243.000 0.333333
\(10\) 1058.93i 1.05893i
\(11\) 442.991i 0.332826i −0.986056 0.166413i \(-0.946782\pi\)
0.986056 0.166413i \(-0.0532185\pi\)
\(12\) 609.112 0.352495
\(13\) 3003.02i 1.36687i 0.730010 + 0.683437i \(0.239515\pi\)
−0.730010 + 0.683437i \(0.760485\pi\)
\(14\) 6647.07i 2.42240i
\(15\) 1625.90 0.481747
\(16\) −5069.95 −1.23778
\(17\) −6614.72 −1.34637 −0.673186 0.739474i \(-0.735074\pi\)
−0.673186 + 0.739474i \(0.735074\pi\)
\(18\) 2467.07i 0.423023i
\(19\) −2022.49 −0.294867 −0.147433 0.989072i \(-0.547101\pi\)
−0.147433 + 0.989072i \(0.547101\pi\)
\(20\) 4075.53 0.509441
\(21\) 10206.1 1.10205
\(22\) −4497.50 −0.422379
\(23\) 7860.31i 0.646035i −0.946393 0.323018i \(-0.895303\pi\)
0.946393 0.323018i \(-0.104697\pi\)
\(24\) 3944.78i 0.285357i
\(25\) −4746.22 −0.303758
\(26\) 30488.4 1.73466
\(27\) −3788.00 −0.192450
\(28\) 25582.8 1.16540
\(29\) 24340.1 0.997993 0.498997 0.866604i \(-0.333702\pi\)
0.498997 + 0.866604i \(0.333702\pi\)
\(30\) 16507.0i 0.611371i
\(31\) 13844.9i 0.464733i 0.972628 + 0.232367i \(0.0746469\pi\)
−0.972628 + 0.232367i \(0.925353\pi\)
\(32\) 35277.3i 1.07658i
\(33\) 6905.55i 0.192157i
\(34\) 67156.4i 1.70864i
\(35\) 68288.0 1.59272
\(36\) −9495.11 −0.203513
\(37\) 73303.9i 1.44718i −0.690231 0.723589i \(-0.742491\pi\)
0.690231 0.723589i \(-0.257509\pi\)
\(38\) 20533.5i 0.374207i
\(39\) 46812.5i 0.789165i
\(40\) 26394.2i 0.412410i
\(41\) −5255.31 −0.0762512 −0.0381256 0.999273i \(-0.512139\pi\)
−0.0381256 + 0.999273i \(0.512139\pi\)
\(42\) 103618.i 1.39857i
\(43\) 72295.0i 0.909291i 0.890673 + 0.454645i \(0.150234\pi\)
−0.890673 + 0.454645i \(0.849766\pi\)
\(44\) 17309.7i 0.203203i
\(45\) −25345.2 −0.278137
\(46\) −79802.3 −0.819864
\(47\) 175954.i 1.69475i −0.530993 0.847376i \(-0.678181\pi\)
0.530993 0.847376i \(-0.321819\pi\)
\(48\) 79032.7 0.714633
\(49\) 311007. 2.64352
\(50\) 48186.3i 0.385490i
\(51\) 103113. 0.777328
\(52\) 117342.i 0.834530i
\(53\) −23803.5 −0.159887 −0.0799435 0.996799i \(-0.525474\pi\)
−0.0799435 + 0.996799i \(0.525474\pi\)
\(54\) 38457.9i 0.244233i
\(55\) 46204.6i 0.277714i
\(56\) 165681.i 0.943430i
\(57\) 31527.5 0.170242
\(58\) 247114.i 1.26652i
\(59\) −114946. 170200.i −0.559676 0.828711i
\(60\) −63531.2 −0.294126
\(61\) 28156.5i 0.124048i 0.998075 + 0.0620240i \(0.0197555\pi\)
−0.998075 + 0.0620240i \(0.980244\pi\)
\(62\) 140561. 0.589779
\(63\) −159097. −0.636267
\(64\) 33678.3 0.128473
\(65\) 313219.i 1.14053i
\(66\) 70109.0 0.243861
\(67\) 320803.i 1.06663i −0.845917 0.533315i \(-0.820946\pi\)
0.845917 0.533315i \(-0.179054\pi\)
\(68\) 258467. 0.822013
\(69\) 122530.i 0.372989i
\(70\) 693299.i 2.02128i
\(71\) 554734. 1.54992 0.774961 0.632009i \(-0.217769\pi\)
0.774961 + 0.632009i \(0.217769\pi\)
\(72\) 61493.0i 0.164751i
\(73\) 125135.i 0.321671i 0.986981 + 0.160835i \(0.0514188\pi\)
−0.986981 + 0.160835i \(0.948581\pi\)
\(74\) −744223. −1.83657
\(75\) 73986.2 0.175375
\(76\) 79027.9 0.180028
\(77\) 290035.i 0.635298i
\(78\) −475266. −1.00151
\(79\) −858752. −1.74175 −0.870877 0.491501i \(-0.836448\pi\)
−0.870877 + 0.491501i \(0.836448\pi\)
\(80\) 528803. 1.03282
\(81\) 59049.0 0.111111
\(82\) 53354.8i 0.0967681i
\(83\) 520126.i 0.909650i 0.890581 + 0.454825i \(0.150298\pi\)
−0.890581 + 0.454825i \(0.849702\pi\)
\(84\) −398797. −0.672843
\(85\) 689925. 1.12343
\(86\) 733979. 1.15395
\(87\) −379424. −0.576192
\(88\) −112102. −0.164500
\(89\) 300665.i 0.426495i 0.976998 + 0.213247i \(0.0684040\pi\)
−0.976998 + 0.213247i \(0.931596\pi\)
\(90\) 257319.i 0.352975i
\(91\) 1.96613e6i 2.60909i
\(92\) 307138.i 0.394430i
\(93\) 215820.i 0.268314i
\(94\) −1.78639e6 −2.15076
\(95\) 210949. 0.246040
\(96\) 549919.i 0.621563i
\(97\) 1.22552e6i 1.34278i −0.741103 0.671391i \(-0.765697\pi\)
0.741103 0.671391i \(-0.234303\pi\)
\(98\) 3.15752e6i 3.35481i
\(99\) 107647.i 0.110942i
\(100\) 185456. 0.185456
\(101\) 927913.i 0.900624i 0.892871 + 0.450312i \(0.148687\pi\)
−0.892871 + 0.450312i \(0.851313\pi\)
\(102\) 1.04686e6i 0.986484i
\(103\) 412082.i 0.377114i 0.982062 + 0.188557i \(0.0603809\pi\)
−0.982062 + 0.188557i \(0.939619\pi\)
\(104\) 759937. 0.675581
\(105\) −1.06451e6 −0.919560
\(106\) 241666.i 0.202908i
\(107\) −879511. −0.717943 −0.358971 0.933349i \(-0.616872\pi\)
−0.358971 + 0.933349i \(0.616872\pi\)
\(108\) 148014. 0.117498
\(109\) 1.22209e6i 0.943676i 0.881685 + 0.471838i \(0.156409\pi\)
−0.881685 + 0.471838i \(0.843591\pi\)
\(110\) 469095. 0.352438
\(111\) 1.14270e6i 0.835529i
\(112\) 3.31939e6 2.36268
\(113\) 1.16448e6i 0.807040i 0.914971 + 0.403520i \(0.132213\pi\)
−0.914971 + 0.403520i \(0.867787\pi\)
\(114\) 320085.i 0.216048i
\(115\) 819841.i 0.539059i
\(116\) −951076. −0.609314
\(117\) 729734.i 0.455624i
\(118\) −1.72796e6 + 1.16699e6i −1.05169 + 0.710269i
\(119\) 4.33078e6 2.56995
\(120\) 411446.i 0.238105i
\(121\) 1.57532e6 0.889227
\(122\) 285861. 0.157426
\(123\) 81922.1 0.0440236
\(124\) 540982.i 0.283738i
\(125\) 2.12475e6 1.08787
\(126\) 1.61524e6i 0.807467i
\(127\) −1.36949e6 −0.668571 −0.334285 0.942472i \(-0.608495\pi\)
−0.334285 + 0.942472i \(0.608495\pi\)
\(128\) 1.91583e6i 0.913538i
\(129\) 1.12697e6i 0.524979i
\(130\) −3.17998e6 −1.44742
\(131\) 3.89962e6i 1.73464i 0.497754 + 0.867318i \(0.334158\pi\)
−0.497754 + 0.867318i \(0.665842\pi\)
\(132\) 269831.i 0.117319i
\(133\) 1.32416e6 0.562842
\(134\) −3.25697e6 −1.35363
\(135\) 395093. 0.160582
\(136\) 1.67390e6i 0.665448i
\(137\) −538204. −0.209308 −0.104654 0.994509i \(-0.533373\pi\)
−0.104654 + 0.994509i \(0.533373\pi\)
\(138\) 1.24399e6 0.473349
\(139\) 3.79961e6 1.41480 0.707400 0.706813i \(-0.249868\pi\)
0.707400 + 0.706813i \(0.249868\pi\)
\(140\) −2.66832e6 −0.972421
\(141\) 2.74286e6i 0.978466i
\(142\) 5.63198e6i 1.96696i
\(143\) 1.33031e6 0.454931
\(144\) −1.23200e6 −0.412594
\(145\) −2.53870e6 −0.832737
\(146\) 1.27044e6 0.408223
\(147\) −4.84812e6 −1.52624
\(148\) 2.86432e6i 0.883560i
\(149\) 2.19953e6i 0.664921i 0.943117 + 0.332461i \(0.107879\pi\)
−0.943117 + 0.332461i \(0.892121\pi\)
\(150\) 751150.i 0.222563i
\(151\) 5.72520e6i 1.66288i −0.555617 0.831438i \(-0.687518\pi\)
0.555617 0.831438i \(-0.312482\pi\)
\(152\) 511807.i 0.145739i
\(153\) −1.60738e6 −0.448790
\(154\) 2.94459e6 0.806238
\(155\) 1.44404e6i 0.387779i
\(156\) 1.82917e6i 0.481816i
\(157\) 332770.i 0.0859893i 0.999075 + 0.0429947i \(0.0136898\pi\)
−0.999075 + 0.0429947i \(0.986310\pi\)
\(158\) 8.71854e6i 2.21041i
\(159\) 371060. 0.0923108
\(160\) 3.67947e6i 0.898309i
\(161\) 5.14629e6i 1.23315i
\(162\) 599499.i 0.141008i
\(163\) 3.50429e6 0.809165 0.404582 0.914502i \(-0.367417\pi\)
0.404582 + 0.914502i \(0.367417\pi\)
\(164\) 205349. 0.0465544
\(165\) 720258.i 0.160338i
\(166\) 5.28061e6 1.15441
\(167\) 4.97745e6 1.06870 0.534352 0.845262i \(-0.320556\pi\)
0.534352 + 0.845262i \(0.320556\pi\)
\(168\) 2.58272e6i 0.544690i
\(169\) −4.19132e6 −0.868343
\(170\) 7.00450e6i 1.42571i
\(171\) −491466. −0.0982890
\(172\) 2.82489e6i 0.555158i
\(173\) 7.61411e6i 1.47055i 0.677767 + 0.735276i \(0.262948\pi\)
−0.677767 + 0.735276i \(0.737052\pi\)
\(174\) 3.85213e6i 0.731228i
\(175\) 3.10744e6 0.579813
\(176\) 2.24594e6i 0.411966i
\(177\) 1.79183e6 + 2.65315e6i 0.323129 + 0.478457i
\(178\) 3.05252e6 0.541252
\(179\) 1.59663e6i 0.278384i −0.990265 0.139192i \(-0.955549\pi\)
0.990265 0.139192i \(-0.0444505\pi\)
\(180\) 990353. 0.169814
\(181\) −1.02310e7 −1.72537 −0.862686 0.505741i \(-0.831219\pi\)
−0.862686 + 0.505741i \(0.831219\pi\)
\(182\) −1.99613e7 −3.31112
\(183\) 438917.i 0.0716191i
\(184\) −1.98911e6 −0.319305
\(185\) 7.64570e6i 1.20754i
\(186\) −2.19113e6 −0.340509
\(187\) 2.93026e6i 0.448107i
\(188\) 6.87533e6i 1.03471i
\(189\) 2.48007e6 0.367349
\(190\) 2.14167e6i 0.312242i
\(191\) 1.13201e7i 1.62462i −0.583227 0.812309i \(-0.698210\pi\)
0.583227 0.812309i \(-0.301790\pi\)
\(192\) −524993. −0.0741736
\(193\) 1.96778e6 0.273719 0.136860 0.990590i \(-0.456299\pi\)
0.136860 + 0.990590i \(0.456299\pi\)
\(194\) −1.24422e7 −1.70409
\(195\) 4.88260e6i 0.658488i
\(196\) −1.21525e7 −1.61397
\(197\) −6.29328e6 −0.823149 −0.411574 0.911376i \(-0.635021\pi\)
−0.411574 + 0.911376i \(0.635021\pi\)
\(198\) −1.09289e6 −0.140793
\(199\) 8.10498e6 1.02847 0.514236 0.857649i \(-0.328076\pi\)
0.514236 + 0.857649i \(0.328076\pi\)
\(200\) 1.20107e6i 0.150133i
\(201\) 5.00082e6i 0.615819i
\(202\) 9.42070e6 1.14295
\(203\) −1.59359e7 −1.90497
\(204\) −4.02910e6 −0.474589
\(205\) 548136. 0.0636248
\(206\) 4.18369e6 0.478584
\(207\) 1.91006e6i 0.215345i
\(208\) 1.52252e7i 1.69189i
\(209\) 895947.i 0.0981394i
\(210\) 1.08075e7i 1.16699i
\(211\) 1.19788e7i 1.27516i 0.770382 + 0.637582i \(0.220065\pi\)
−0.770382 + 0.637582i \(0.779935\pi\)
\(212\) 930110. 0.0976173
\(213\) −8.64745e6 −0.894848
\(214\) 8.92929e6i 0.911120i
\(215\) 7.54047e6i 0.758722i
\(216\) 958580.i 0.0951190i
\(217\) 9.06449e6i 0.887083i
\(218\) 1.24073e7 1.19759
\(219\) 1.95067e6i 0.185717i
\(220\) 1.80542e6i 0.169555i
\(221\) 1.98641e7i 1.84032i
\(222\) 1.16013e7 1.06035
\(223\) −6.83511e6 −0.616355 −0.308178 0.951329i \(-0.599719\pi\)
−0.308178 + 0.951329i \(0.599719\pi\)
\(224\) 2.30967e7i 2.05497i
\(225\) −1.15333e6 −0.101253
\(226\) 1.18224e7 1.02419
\(227\) 9.63771e6i 0.823941i 0.911197 + 0.411971i \(0.135159\pi\)
−0.911197 + 0.411971i \(0.864841\pi\)
\(228\) −1.23192e6 −0.103939
\(229\) 1.02822e7i 0.856212i 0.903728 + 0.428106i \(0.140819\pi\)
−0.903728 + 0.428106i \(0.859181\pi\)
\(230\) 8.32349e6 0.684104
\(231\) 4.52119e6i 0.366790i
\(232\) 6.15943e6i 0.493261i
\(233\) 195801.i 0.0154791i −0.999970 0.00773956i \(-0.997536\pi\)
0.999970 0.00773956i \(-0.00246360\pi\)
\(234\) 7.40867e6 0.578219
\(235\) 1.83523e7i 1.41412i
\(236\) 4.49145e6 + 6.65048e6i 0.341705 + 0.505961i
\(237\) 1.33866e7 1.00560
\(238\) 4.39685e7i 3.26145i
\(239\) 3.73985e6 0.273943 0.136972 0.990575i \(-0.456263\pi\)
0.136972 + 0.990575i \(0.456263\pi\)
\(240\) −8.24322e6 −0.596298
\(241\) −3.69307e6 −0.263837 −0.131919 0.991261i \(-0.542114\pi\)
−0.131919 + 0.991261i \(0.542114\pi\)
\(242\) 1.59935e7i 1.12849i
\(243\) −920483. −0.0641500
\(244\) 1.10020e6i 0.0757362i
\(245\) −3.24385e7 −2.20578
\(246\) 831720.i 0.0558691i
\(247\) 6.07359e6i 0.403046i
\(248\) 3.50355e6 0.229696
\(249\) 8.10797e6i 0.525187i
\(250\) 2.15716e7i 1.38058i
\(251\) 1.05621e7 0.667928 0.333964 0.942586i \(-0.391614\pi\)
0.333964 + 0.942586i \(0.391614\pi\)
\(252\) 6.21662e6 0.388466
\(253\) −3.48205e6 −0.215017
\(254\) 1.39038e7i 0.848463i
\(255\) −1.07549e7 −0.648611
\(256\) 2.16060e7 1.28782
\(257\) 1.61502e6 0.0951432 0.0475716 0.998868i \(-0.484852\pi\)
0.0475716 + 0.998868i \(0.484852\pi\)
\(258\) −1.14416e7 −0.666236
\(259\) 4.79934e7i 2.76237i
\(260\) 1.22389e7i 0.696341i
\(261\) 5.91463e6 0.332664
\(262\) 3.95911e7 2.20138
\(263\) −3.39349e6 −0.186543 −0.0932715 0.995641i \(-0.529732\pi\)
−0.0932715 + 0.995641i \(0.529732\pi\)
\(264\) 1.74750e6 0.0949742
\(265\) 2.48274e6 0.133411
\(266\) 1.34437e7i 0.714286i
\(267\) 4.68691e6i 0.246237i
\(268\) 1.25352e7i 0.651219i
\(269\) 669790.i 0.0344098i −0.999852 0.0172049i \(-0.994523\pi\)
0.999852 0.0172049i \(-0.00547676\pi\)
\(270\) 4.01121e6i 0.203790i
\(271\) −9.11749e6 −0.458107 −0.229054 0.973414i \(-0.573563\pi\)
−0.229054 + 0.973414i \(0.573563\pi\)
\(272\) 3.35363e7 1.66651
\(273\) 3.06490e7i 1.50636i
\(274\) 5.46415e6i 0.265626i
\(275\) 2.10253e6i 0.101099i
\(276\) 4.78781e6i 0.227724i
\(277\) 2.33110e7 1.09679 0.548393 0.836221i \(-0.315240\pi\)
0.548393 + 0.836221i \(0.315240\pi\)
\(278\) 3.85758e7i 1.79548i
\(279\) 3.36430e6i 0.154911i
\(280\) 1.72808e7i 0.787208i
\(281\) −1.64403e7 −0.740954 −0.370477 0.928842i \(-0.620806\pi\)
−0.370477 + 0.928842i \(0.620806\pi\)
\(282\) 2.78470e7 1.24174
\(283\) 2.24174e7i 0.989066i −0.869159 0.494533i \(-0.835339\pi\)
0.869159 0.494533i \(-0.164661\pi\)
\(284\) −2.16760e7 −0.946289
\(285\) −3.28837e6 −0.142051
\(286\) 1.35061e7i 0.577339i
\(287\) 3.44075e6 0.145548
\(288\) 8.57239e6i 0.358859i
\(289\) 1.96170e7 0.812715
\(290\) 2.57743e7i 1.05680i
\(291\) 1.91040e7i 0.775256i
\(292\) 4.88960e6i 0.196393i
\(293\) 3.78032e7 1.50289 0.751443 0.659798i \(-0.229358\pi\)
0.751443 + 0.659798i \(0.229358\pi\)
\(294\) 4.92209e7i 1.93690i
\(295\) 1.19890e7 + 1.77521e7i 0.467000 + 0.691486i
\(296\) −1.85501e7 −0.715272
\(297\) 1.67805e6i 0.0640524i
\(298\) 2.23308e7 0.843832
\(299\) 2.36047e7 0.883048
\(300\) −2.89098e6 −0.107073
\(301\) 4.73329e7i 1.73565i
\(302\) −5.81255e7 −2.11031
\(303\) 1.44647e7i 0.519975i
\(304\) 1.02539e7 0.364981
\(305\) 2.93677e6i 0.103507i
\(306\) 1.63190e7i 0.569547i
\(307\) −1.78309e7 −0.616252 −0.308126 0.951345i \(-0.599702\pi\)
−0.308126 + 0.951345i \(0.599702\pi\)
\(308\) 1.13330e7i 0.387875i
\(309\) 6.42372e6i 0.217727i
\(310\) −1.46607e7 −0.492118
\(311\) −4.32981e7 −1.43942 −0.719710 0.694274i \(-0.755725\pi\)
−0.719710 + 0.694274i \(0.755725\pi\)
\(312\) −1.18462e7 −0.390047
\(313\) 3.12259e7i 1.01831i −0.860674 0.509157i \(-0.829957\pi\)
0.860674 0.509157i \(-0.170043\pi\)
\(314\) 3.37846e6 0.109127
\(315\) 1.65940e7 0.530908
\(316\) 3.35553e7 1.06341
\(317\) 344531. 0.0108156 0.00540780 0.999985i \(-0.498279\pi\)
0.00540780 + 0.999985i \(0.498279\pi\)
\(318\) 3.76721e6i 0.117149i
\(319\) 1.07824e7i 0.332158i
\(320\) −3.51269e6 −0.107199
\(321\) 1.37102e7 0.414505
\(322\) 5.22480e7 1.56496
\(323\) 1.33782e7 0.397000
\(324\) −2.30731e6 −0.0678377
\(325\) 1.42530e7i 0.415199i
\(326\) 3.55775e7i 1.02689i
\(327\) 1.90505e7i 0.544831i
\(328\) 1.32989e6i 0.0376874i
\(329\) 1.15201e8i 3.23494i
\(330\) −7.31247e6 −0.203480
\(331\) 1.63978e7 0.452171 0.226086 0.974107i \(-0.427407\pi\)
0.226086 + 0.974107i \(0.427407\pi\)
\(332\) 2.03237e7i 0.555377i
\(333\) 1.78129e7i 0.482393i
\(334\) 5.05339e7i 1.35626i
\(335\) 3.34602e7i 0.890007i
\(336\) −5.17442e7 −1.36409
\(337\) 7.51217e7i 1.96280i −0.191976 0.981400i \(-0.561490\pi\)
0.191976 0.981400i \(-0.438510\pi\)
\(338\) 4.25527e7i 1.10199i
\(339\) 1.81524e7i 0.465945i
\(340\) −2.69585e7 −0.685896
\(341\) 6.13315e6 0.154675
\(342\) 4.98964e6i 0.124736i
\(343\) −1.26595e8 −3.13715
\(344\) 1.82948e7 0.449420
\(345\) 1.27801e7i 0.311226i
\(346\) 7.73027e7 1.86623
\(347\) 5.29666e7i 1.26769i −0.773459 0.633846i \(-0.781475\pi\)
0.773459 0.633846i \(-0.218525\pi\)
\(348\) 1.48258e7 0.351788
\(349\) 7.42339e7i 1.74633i 0.487426 + 0.873164i \(0.337936\pi\)
−0.487426 + 0.873164i \(0.662064\pi\)
\(350\) 3.15485e7i 0.735824i
\(351\) 1.13754e7i 0.263055i
\(352\) 1.56275e7 0.358313
\(353\) 6.31527e6i 0.143571i 0.997420 + 0.0717857i \(0.0228698\pi\)
−0.997420 + 0.0717857i \(0.977130\pi\)
\(354\) 2.69363e7 1.81916e7i 0.607195 0.410074i
\(355\) −5.78596e7 −1.29327
\(356\) 1.17484e7i 0.260392i
\(357\) −6.75102e7 −1.48376
\(358\) −1.62099e7 −0.353289
\(359\) −3.59250e7 −0.776450 −0.388225 0.921565i \(-0.626912\pi\)
−0.388225 + 0.921565i \(0.626912\pi\)
\(360\) 6.41380e6i 0.137470i
\(361\) −4.29554e7 −0.913053
\(362\) 1.03871e8i 2.18962i
\(363\) −2.45568e7 −0.513395
\(364\) 7.68257e7i 1.59295i
\(365\) 1.30518e7i 0.268405i
\(366\) −4.45613e6 −0.0908897
\(367\) 1.84700e7i 0.373653i 0.982393 + 0.186827i \(0.0598203\pi\)
−0.982393 + 0.186827i \(0.940180\pi\)
\(368\) 3.98514e7i 0.799650i
\(369\) −1.27704e6 −0.0254171
\(370\) 7.76235e7 1.53246
\(371\) 1.55846e7 0.305192
\(372\) 8.43307e6i 0.163816i
\(373\) −7.31675e7 −1.40991 −0.704955 0.709252i \(-0.749033\pi\)
−0.704955 + 0.709252i \(0.749033\pi\)
\(374\) 2.97497e7 0.568679
\(375\) −3.31215e7 −0.628082
\(376\) −4.45266e7 −0.837636
\(377\) 7.30937e7i 1.36413i
\(378\) 2.51791e7i 0.466191i
\(379\) −2.43432e7 −0.447157 −0.223579 0.974686i \(-0.571774\pi\)
−0.223579 + 0.974686i \(0.571774\pi\)
\(380\) −8.24272e6 −0.150217
\(381\) 2.13482e7 0.386000
\(382\) −1.14928e8 −2.06176
\(383\) 3.71024e7 0.660399 0.330199 0.943911i \(-0.392884\pi\)
0.330199 + 0.943911i \(0.392884\pi\)
\(384\) 2.98648e7i 0.527431i
\(385\) 3.02510e7i 0.530100i
\(386\) 1.99781e7i 0.347369i
\(387\) 1.75677e7i 0.303097i
\(388\) 4.78867e7i 0.819822i
\(389\) −3.94013e7 −0.669362 −0.334681 0.942331i \(-0.608629\pi\)
−0.334681 + 0.942331i \(0.608629\pi\)
\(390\) 4.95709e7 0.835667
\(391\) 5.19938e7i 0.869803i
\(392\) 7.87027e7i 1.30657i
\(393\) 6.07891e7i 1.00149i
\(394\) 6.38929e7i 1.04463i
\(395\) 8.95691e7 1.45334
\(396\) 4.20625e6i 0.0677344i
\(397\) 8.86748e7i 1.41719i 0.705614 + 0.708596i \(0.250671\pi\)
−0.705614 + 0.708596i \(0.749329\pi\)
\(398\) 8.22863e7i 1.30520i
\(399\) −2.06417e7 −0.324957
\(400\) 2.40631e7 0.375986
\(401\) 1.10931e8i 1.72036i −0.509990 0.860181i \(-0.670351\pi\)
0.509990 0.860181i \(-0.329649\pi\)
\(402\) 5.07711e7 0.781517
\(403\) −4.15764e7 −0.635231
\(404\) 3.62578e7i 0.549866i
\(405\) −6.15889e6 −0.0927123
\(406\) 1.61790e8i 2.41754i
\(407\) −3.24730e7 −0.481658
\(408\) 2.60936e7i 0.384196i
\(409\) 4.60916e7i 0.673677i −0.941562 0.336839i \(-0.890642\pi\)
0.941562 0.336839i \(-0.109358\pi\)
\(410\) 5.56498e6i 0.0807444i
\(411\) 8.38977e6 0.120844
\(412\) 1.61019e7i 0.230243i
\(413\) 7.52571e7 + 1.11433e8i 1.06831 + 1.58184i
\(414\) −1.93920e7 −0.273288
\(415\) 5.42499e7i 0.759022i
\(416\) −1.05939e8 −1.47155
\(417\) −5.92301e7 −0.816835
\(418\) 9.09615e6 0.124546
\(419\) 6.43202e7i 0.874390i −0.899367 0.437195i \(-0.855972\pi\)
0.899367 0.437195i \(-0.144028\pi\)
\(420\) 4.15950e7 0.561427
\(421\) 1.80783e7i 0.242276i −0.992636 0.121138i \(-0.961346\pi\)
0.992636 0.121138i \(-0.0386543\pi\)
\(422\) 1.21616e8 1.61827
\(423\) 4.27569e7i 0.564918i
\(424\) 6.02365e6i 0.0790246i
\(425\) 3.13949e7 0.408971
\(426\) 8.77938e7i 1.13563i
\(427\) 1.84346e7i 0.236783i
\(428\) 3.43665e7 0.438333
\(429\) −2.07375e7 −0.262654
\(430\) −7.65551e7 −0.962872
\(431\) 1.40777e7i 0.175833i 0.996128 + 0.0879166i \(0.0280209\pi\)
−0.996128 + 0.0879166i \(0.971979\pi\)
\(432\) 1.92050e7 0.238211
\(433\) −9.56225e7 −1.17787 −0.588934 0.808181i \(-0.700452\pi\)
−0.588934 + 0.808181i \(0.700452\pi\)
\(434\) −9.20278e7 −1.12577
\(435\) 3.95744e7 0.480781
\(436\) 4.77525e7i 0.576151i
\(437\) 1.58974e7i 0.190494i
\(438\) −1.98043e7 −0.235687
\(439\) 8.07733e7 0.954716 0.477358 0.878709i \(-0.341595\pi\)
0.477358 + 0.878709i \(0.341595\pi\)
\(440\) 1.16924e7 0.137261
\(441\) 7.55748e7 0.881173
\(442\) −2.01672e8 −2.33549
\(443\) 8.66157e7i 0.996290i 0.867094 + 0.498145i \(0.165985\pi\)
−0.867094 + 0.498145i \(0.834015\pi\)
\(444\) 4.46503e7i 0.510123i
\(445\) 3.13598e7i 0.355872i
\(446\) 6.93939e7i 0.782198i
\(447\) 3.42872e7i 0.383892i
\(448\) −2.20498e7 −0.245228
\(449\) 1.10404e8 1.21968 0.609841 0.792524i \(-0.291233\pi\)
0.609841 + 0.792524i \(0.291233\pi\)
\(450\) 1.17093e7i 0.128497i
\(451\) 2.32806e6i 0.0253784i
\(452\) 4.55013e7i 0.492730i
\(453\) 8.92471e7i 0.960062i
\(454\) 9.78474e7 1.04564
\(455\) 2.05070e8i 2.17705i
\(456\) 7.97828e6i 0.0841424i
\(457\) 1.11206e8i 1.16514i 0.812779 + 0.582572i \(0.197953\pi\)
−0.812779 + 0.582572i \(0.802047\pi\)
\(458\) 1.04391e8 1.08659
\(459\) 2.50565e7 0.259109
\(460\) 3.20349e7i 0.329117i
\(461\) 8.07065e7 0.823770 0.411885 0.911236i \(-0.364871\pi\)
0.411885 + 0.911236i \(0.364871\pi\)
\(462\) −4.59017e7 −0.465482
\(463\) 1.13852e8i 1.14709i 0.819173 + 0.573547i \(0.194433\pi\)
−0.819173 + 0.573547i \(0.805567\pi\)
\(464\) −1.23403e8 −1.23530
\(465\) 2.25103e7i 0.223884i
\(466\) −1.98788e6 −0.0196441
\(467\) 1.34224e8i 1.31789i −0.752192 0.658944i \(-0.771003\pi\)
0.752192 0.658944i \(-0.228997\pi\)
\(468\) 2.85140e7i 0.278177i
\(469\) 2.10035e8i 2.03598i
\(470\) 1.86323e8 1.79462
\(471\) 5.18736e6i 0.0496460i
\(472\) −4.30704e7 + 2.90879e7i −0.409593 + 0.276622i
\(473\) 3.20260e7 0.302635
\(474\) 1.35909e8i 1.27618i
\(475\) 9.59920e6 0.0895682
\(476\) −1.69223e8 −1.56906
\(477\) −5.78425e6 −0.0532957
\(478\) 3.79691e7i 0.347653i
\(479\) 1.89590e8 1.72508 0.862538 0.505992i \(-0.168874\pi\)
0.862538 + 0.505992i \(0.168874\pi\)
\(480\) 5.73573e7i 0.518639i
\(481\) 2.20133e8 1.97811
\(482\) 3.74941e7i 0.334828i
\(483\) 8.02227e7i 0.711961i
\(484\) −6.15549e7 −0.542908
\(485\) 1.27824e8i 1.12043i
\(486\) 9.34526e6i 0.0814109i
\(487\) −1.40587e7 −0.121719 −0.0608595 0.998146i \(-0.519384\pi\)
−0.0608595 + 0.998146i \(0.519384\pi\)
\(488\) 7.12522e6 0.0613111
\(489\) −5.46264e7 −0.467171
\(490\) 3.29334e8i 2.79929i
\(491\) 1.36388e8 1.15221 0.576104 0.817377i \(-0.304572\pi\)
0.576104 + 0.817377i \(0.304572\pi\)
\(492\) −3.20107e6 −0.0268782
\(493\) −1.61003e8 −1.34367
\(494\) −6.16625e7 −0.511493
\(495\) 1.12277e7i 0.0925712i
\(496\) 7.01928e7i 0.575238i
\(497\) −3.63195e8 −2.95849
\(498\) −8.23166e7 −0.666499
\(499\) 1.80444e8 1.45225 0.726123 0.687565i \(-0.241320\pi\)
0.726123 + 0.687565i \(0.241320\pi\)
\(500\) −8.30235e7 −0.664188
\(501\) −7.75907e7 −0.617016
\(502\) 1.07232e8i 0.847647i
\(503\) 4.39678e7i 0.345486i −0.984967 0.172743i \(-0.944737\pi\)
0.984967 0.172743i \(-0.0552631\pi\)
\(504\) 4.02606e7i 0.314477i
\(505\) 9.67827e7i 0.751490i
\(506\) 3.53517e7i 0.272872i
\(507\) 6.53363e7 0.501338
\(508\) 5.35121e7 0.408189
\(509\) 4.22630e7i 0.320484i 0.987078 + 0.160242i \(0.0512275\pi\)
−0.987078 + 0.160242i \(0.948773\pi\)
\(510\) 1.09189e8i 0.823133i
\(511\) 8.19284e7i 0.614005i
\(512\) 9.67430e7i 0.720791i
\(513\) 7.66119e6 0.0567472
\(514\) 1.63966e7i 0.120743i
\(515\) 4.29807e7i 0.314668i
\(516\) 4.40357e7i 0.320521i
\(517\) −7.79462e7 −0.564058
\(518\) 4.87256e8 3.50565
\(519\) 1.18692e8i 0.849024i
\(520\) −7.92625e7 −0.563712
\(521\) 2.74322e7 0.193976 0.0969880 0.995286i \(-0.469079\pi\)
0.0969880 + 0.995286i \(0.469079\pi\)
\(522\) 6.00487e7i 0.422175i
\(523\) 7.55469e7 0.528095 0.264047 0.964510i \(-0.414943\pi\)
0.264047 + 0.964510i \(0.414943\pi\)
\(524\) 1.52376e8i 1.05906i
\(525\) −4.84402e7 −0.334755
\(526\) 3.44526e7i 0.236736i
\(527\) 9.15799e7i 0.625703i
\(528\) 3.50108e7i 0.237848i
\(529\) 8.62514e7 0.582638
\(530\) 2.52061e7i 0.169309i
\(531\) −2.79318e7 4.13586e7i −0.186559 0.276237i
\(532\) −5.17410e7 −0.343637
\(533\) 1.57818e7i 0.104226i
\(534\) −4.75842e7 −0.312492
\(535\) 9.17342e7 0.599060
\(536\) −8.11815e7 −0.527185
\(537\) 2.48890e7i 0.160725i
\(538\) −6.80009e6 −0.0436684
\(539\) 1.37773e8i 0.879831i
\(540\) −1.54381e7 −0.0980419
\(541\) 2.82600e8i 1.78476i −0.451285 0.892380i \(-0.649034\pi\)
0.451285 0.892380i \(-0.350966\pi\)
\(542\) 9.25659e7i 0.581371i
\(543\) 1.59486e8 0.996143
\(544\) 2.33350e8i 1.44947i
\(545\) 1.27465e8i 0.787414i
\(546\) 3.11166e8 1.91167
\(547\) 7.30113e7 0.446095 0.223048 0.974808i \(-0.428399\pi\)
0.223048 + 0.974808i \(0.428399\pi\)
\(548\) 2.10301e7 0.127791
\(549\) 6.84204e6i 0.0413493i
\(550\) 2.13461e7 0.128301
\(551\) −4.92276e7 −0.294275
\(552\) 3.10072e7 0.184351
\(553\) 5.62241e8 3.32466
\(554\) 2.36667e8i 1.39190i
\(555\) 1.19185e8i 0.697175i
\(556\) −1.48468e8 −0.863791
\(557\) −3.01043e8 −1.74206 −0.871031 0.491229i \(-0.836548\pi\)
−0.871031 + 0.491229i \(0.836548\pi\)
\(558\) 3.41563e7 0.196593
\(559\) −2.17103e8 −1.24289
\(560\) −3.46217e8 −1.97144
\(561\) 4.56783e7i 0.258715i
\(562\) 1.66911e8i 0.940323i
\(563\) 1.26927e7i 0.0711262i 0.999367 + 0.0355631i \(0.0113225\pi\)
−0.999367 + 0.0355631i \(0.988678\pi\)
\(564\) 1.07176e8i 0.597392i
\(565\) 1.21456e8i 0.673403i
\(566\) −2.27594e8 −1.25519
\(567\) −3.86605e7 −0.212089
\(568\) 1.40380e8i 0.766054i
\(569\) 2.72018e8i 1.47659i 0.674476 + 0.738297i \(0.264370\pi\)
−0.674476 + 0.738297i \(0.735630\pi\)
\(570\) 3.33853e7i 0.180273i
\(571\) 2.66755e8i 1.43286i 0.697658 + 0.716431i \(0.254226\pi\)
−0.697658 + 0.716431i \(0.745774\pi\)
\(572\) −5.19813e7 −0.277753
\(573\) 1.76463e8i 0.937974i
\(574\) 3.49324e7i 0.184711i
\(575\) 3.73068e7i 0.196238i
\(576\) 8.18383e6 0.0428242
\(577\) −2.29588e8 −1.19515 −0.597575 0.801813i \(-0.703869\pi\)
−0.597575 + 0.801813i \(0.703869\pi\)
\(578\) 1.99162e8i 1.03139i
\(579\) −3.06747e7 −0.158032
\(580\) 9.91986e7 0.508419
\(581\) 3.40536e8i 1.73634i
\(582\) 1.93954e8 0.983854
\(583\) 1.05447e7i 0.0532145i
\(584\) 3.16664e7 0.158987
\(585\) 7.61123e7i 0.380178i
\(586\) 3.83800e8i 1.90727i
\(587\) 3.03353e8i 1.49980i −0.661550 0.749901i \(-0.730101\pi\)
0.661550 0.749901i \(-0.269899\pi\)
\(588\) 1.89438e8 0.931827
\(589\) 2.80011e7i 0.137034i
\(590\) 1.80229e8 1.21719e8i 0.877544 0.592656i
\(591\) 9.81025e7 0.475245
\(592\) 3.71647e8i 1.79129i
\(593\) 3.40728e7 0.163397 0.0816985 0.996657i \(-0.473966\pi\)
0.0816985 + 0.996657i \(0.473966\pi\)
\(594\) 1.70365e7 0.0812870
\(595\) −4.51706e8 −2.14440
\(596\) 8.59454e7i 0.405961i
\(597\) −1.26344e8 −0.593789
\(598\) 2.39648e8i 1.12065i
\(599\) 2.96815e8 1.38104 0.690520 0.723314i \(-0.257382\pi\)
0.690520 + 0.723314i \(0.257382\pi\)
\(600\) 1.87228e7i 0.0866795i
\(601\) 1.19578e8i 0.550845i 0.961323 + 0.275423i \(0.0888178\pi\)
−0.961323 + 0.275423i \(0.911182\pi\)
\(602\) −4.80550e8 −2.20267
\(603\) 7.79550e7i 0.355543i
\(604\) 2.23710e8i 1.01525i
\(605\) −1.64308e8 −0.741981
\(606\) −1.46854e8 −0.659885
\(607\) −4.34360e8 −1.94216 −0.971078 0.238763i \(-0.923258\pi\)
−0.971078 + 0.238763i \(0.923258\pi\)
\(608\) 7.13481e7i 0.317447i
\(609\) 2.48416e8 1.09983
\(610\) −2.98157e7 −0.131358
\(611\) 5.28394e8 2.31651
\(612\) 6.28075e7 0.274004
\(613\) 1.91315e8i 0.830552i −0.909696 0.415276i \(-0.863685\pi\)
0.909696 0.415276i \(-0.136315\pi\)
\(614\) 1.81030e8i 0.782068i
\(615\) −8.54459e6 −0.0367338
\(616\) 7.33954e7 0.313998
\(617\) 1.22851e8 0.523027 0.261513 0.965200i \(-0.415778\pi\)
0.261513 + 0.965200i \(0.415778\pi\)
\(618\) −6.52173e7 −0.276310
\(619\) 2.76299e8 1.16495 0.582474 0.812849i \(-0.302085\pi\)
0.582474 + 0.812849i \(0.302085\pi\)
\(620\) 5.64251e7i 0.236754i
\(621\) 2.97748e7i 0.124330i
\(622\) 4.39587e8i 1.82673i
\(623\) 1.96851e8i 0.814093i
\(624\) 2.37337e8i 0.976813i
\(625\) −1.47454e8 −0.603973
\(626\) −3.17022e8 −1.29231
\(627\) 1.39664e7i 0.0566608i
\(628\) 1.30028e7i 0.0524999i
\(629\) 4.84885e8i 1.94844i
\(630\) 1.68472e8i 0.673760i
\(631\) −4.17250e7 −0.166077 −0.0830383 0.996546i \(-0.526462\pi\)
−0.0830383 + 0.996546i \(0.526462\pi\)
\(632\) 2.17314e8i 0.860867i
\(633\) 1.86731e8i 0.736217i
\(634\) 3.49787e6i 0.0137258i
\(635\) 1.42840e8 0.557863
\(636\) −1.44990e7 −0.0563594
\(637\) 9.33961e8i 3.61335i
\(638\) −1.09469e8 −0.421532
\(639\) 1.34800e8 0.516641
\(640\) 1.99823e8i 0.762266i
\(641\) 4.30270e8 1.63368 0.816840 0.576864i \(-0.195724\pi\)
0.816840 + 0.576864i \(0.195724\pi\)
\(642\) 1.39194e8i 0.526035i
\(643\) 5.22591e7 0.196575 0.0982877 0.995158i \(-0.468663\pi\)
0.0982877 + 0.995158i \(0.468663\pi\)
\(644\) 2.01089e8i 0.752888i
\(645\) 1.17544e8i 0.438048i
\(646\) 1.35823e8i 0.503821i
\(647\) 1.95145e8 0.720516 0.360258 0.932853i \(-0.382689\pi\)
0.360258 + 0.932853i \(0.382689\pi\)
\(648\) 1.49428e7i 0.0549170i
\(649\) −7.53971e7 + 5.09200e7i −0.275817 + 0.186275i
\(650\) −1.44704e8 −0.526916
\(651\) 1.41301e8i 0.512157i
\(652\) −1.36928e8 −0.494027
\(653\) −2.87811e8 −1.03364 −0.516818 0.856095i \(-0.672884\pi\)
−0.516818 + 0.856095i \(0.672884\pi\)
\(654\) −1.93411e8 −0.691429
\(655\) 4.06736e8i 1.44740i
\(656\) 2.66442e7 0.0943823
\(657\) 3.04079e7i 0.107224i
\(658\) 1.16958e9 4.10537
\(659\) 4.19404e8i 1.46547i −0.680516 0.732734i \(-0.738244\pi\)
0.680516 0.732734i \(-0.261756\pi\)
\(660\) 2.81438e7i 0.0978927i
\(661\) −1.64917e8 −0.571032 −0.285516 0.958374i \(-0.592165\pi\)
−0.285516 + 0.958374i \(0.592165\pi\)
\(662\) 1.66480e8i 0.573837i
\(663\) 3.09651e8i 1.06251i
\(664\) 1.31622e8 0.449597
\(665\) −1.38112e8 −0.469642
\(666\) −1.80846e8 −0.612190
\(667\) 1.91320e8i 0.644739i
\(668\) −1.94491e8 −0.652486
\(669\) 1.06549e8 0.355853
\(670\) 3.39706e8 1.12948
\(671\) 1.24731e7 0.0412864
\(672\) 3.60042e8i 1.18644i
\(673\) 4.61298e8i 1.51334i 0.653796 + 0.756671i \(0.273175\pi\)
−0.653796 + 0.756671i \(0.726825\pi\)
\(674\) −7.62678e8 −2.49093
\(675\) 1.79787e7 0.0584583
\(676\) 1.63774e8 0.530157
\(677\) 4.24564e7 0.136829 0.0684143 0.997657i \(-0.478206\pi\)
0.0684143 + 0.997657i \(0.478206\pi\)
\(678\) −1.84293e8 −0.591317
\(679\) 8.02371e8i 2.56310i
\(680\) 1.74591e8i 0.555257i
\(681\) 1.50237e8i 0.475703i
\(682\) 6.22672e7i 0.196294i
\(683\) 6.61697e7i 0.207681i −0.994594 0.103841i \(-0.966887\pi\)
0.994594 0.103841i \(-0.0331132\pi\)
\(684\) 1.92038e7 0.0600093
\(685\) 5.61355e7 0.174649
\(686\) 1.28527e9i 3.98126i
\(687\) 1.60284e8i 0.494334i
\(688\) 3.66532e8i 1.12550i
\(689\) 7.14824e7i 0.218545i
\(690\) −1.29750e8 −0.394968
\(691\) 9.68980e7i 0.293684i −0.989160 0.146842i \(-0.953089\pi\)
0.989160 0.146842i \(-0.0469109\pi\)
\(692\) 2.97518e8i 0.897830i
\(693\) 7.04784e7i 0.211766i
\(694\) −5.37747e8 −1.60879
\(695\) −3.96305e8 −1.18053
\(696\) 9.60161e7i 0.284784i
\(697\) 3.47624e7 0.102662
\(698\) 7.53664e8 2.21621
\(699\) 3.05223e6i 0.00893688i
\(700\) −1.21422e8 −0.353999
\(701\) 5.03940e8i 1.46294i 0.681876 + 0.731468i \(0.261164\pi\)
−0.681876 + 0.731468i \(0.738836\pi\)
\(702\) −1.15490e8 −0.333835
\(703\) 1.48257e8i 0.426725i
\(704\) 1.49192e7i 0.0427590i
\(705\) 2.86084e8i 0.816443i
\(706\) 6.41162e7 0.182202
\(707\) 6.07522e8i 1.71911i
\(708\) −7.00148e7 1.03671e8i −0.197283 0.292117i
\(709\) 1.17112e8 0.328596 0.164298 0.986411i \(-0.447464\pi\)
0.164298 + 0.986411i \(0.447464\pi\)
\(710\) 5.87423e8i 1.64125i
\(711\) −2.08677e8 −0.580585
\(712\) 7.60856e7 0.210796
\(713\) 1.08825e8 0.300234
\(714\) 6.85401e8i 1.88300i
\(715\) −1.38753e8 −0.379599
\(716\) 6.23874e7i 0.169964i
\(717\) −5.82985e7 −0.158161
\(718\) 3.64731e8i 0.985369i
\(719\) 5.86668e8i 1.57836i −0.614162 0.789180i \(-0.710506\pi\)
0.614162 0.789180i \(-0.289494\pi\)
\(720\) 1.28499e8 0.344273
\(721\) 2.69798e8i 0.719834i
\(722\) 4.36107e8i 1.15873i
\(723\) 5.75693e7 0.152327
\(724\) 3.99772e8 1.05341
\(725\) −1.15523e8 −0.303149
\(726\) 2.49314e8i 0.651535i
\(727\) −1.83589e8 −0.477797 −0.238898 0.971045i \(-0.576786\pi\)
−0.238898 + 0.971045i \(0.576786\pi\)
\(728\) −4.97545e8 −1.28955
\(729\) 1.43489e7 0.0370370
\(730\) −1.32509e8 −0.340625
\(731\) 4.78211e8i 1.22424i
\(732\) 1.71505e7i 0.0437263i
\(733\) −1.27061e8 −0.322626 −0.161313 0.986903i \(-0.551573\pi\)
−0.161313 + 0.986903i \(0.551573\pi\)
\(734\) 1.87518e8 0.474192
\(735\) 5.05666e8 1.27351
\(736\) 2.77291e8 0.695508
\(737\) −1.42113e8 −0.355002
\(738\) 1.29652e7i 0.0322560i
\(739\) 6.00659e8i 1.48831i −0.668005 0.744157i \(-0.732851\pi\)
0.668005 0.744157i \(-0.267149\pi\)
\(740\) 2.98752e8i 0.737252i
\(741\) 9.46779e7i 0.232699i
\(742\) 1.58223e8i 0.387310i
\(743\) 3.85539e8 0.939944 0.469972 0.882681i \(-0.344264\pi\)
0.469972 + 0.882681i \(0.344264\pi\)
\(744\) −5.46149e7 −0.132615
\(745\) 2.29414e8i 0.554818i
\(746\) 7.42838e8i 1.78928i
\(747\) 1.26391e8i 0.303217i
\(748\) 1.14499e8i 0.273587i
\(749\) 5.75832e8 1.37041
\(750\) 3.36268e8i 0.797080i
\(751\) 1.49633e8i 0.353270i 0.984276 + 0.176635i \(0.0565213\pi\)
−0.984276 + 0.176635i \(0.943479\pi\)
\(752\) 8.92080e8i 2.09773i
\(753\) −1.64647e8 −0.385628
\(754\) 7.42088e8 1.73118
\(755\) 5.97147e8i 1.38752i
\(756\) −9.69076e7 −0.224281
\(757\) 3.76913e7 0.0868868 0.0434434 0.999056i \(-0.486167\pi\)
0.0434434 + 0.999056i \(0.486167\pi\)
\(758\) 2.47146e8i 0.567474i
\(759\) 5.42798e7 0.124140
\(760\) 5.33822e7i 0.121606i
\(761\) −3.09488e8 −0.702248 −0.351124 0.936329i \(-0.614200\pi\)
−0.351124 + 0.936329i \(0.614200\pi\)
\(762\) 2.16739e8i 0.489861i
\(763\) 8.00123e8i 1.80129i
\(764\) 4.42329e8i 0.991894i
\(765\) 1.67652e8 0.374476
\(766\) 3.76685e8i 0.838092i
\(767\) 5.11114e8 3.45185e8i 1.13274 0.765007i
\(768\) −3.36804e8 −0.743521
\(769\) 1.14414e8i 0.251594i 0.992056 + 0.125797i \(0.0401488\pi\)
−0.992056 + 0.125797i \(0.959851\pi\)
\(770\) −3.07125e8 −0.672734
\(771\) −2.51756e7 −0.0549310
\(772\) −7.68902e7 −0.167116
\(773\) 3.74267e8i 0.810294i 0.914252 + 0.405147i \(0.132780\pi\)
−0.914252 + 0.405147i \(0.867220\pi\)
\(774\) 1.78357e8 0.384651
\(775\) 6.57108e7i 0.141166i
\(776\) −3.10127e8 −0.663674
\(777\) 7.48144e8i 1.59486i
\(778\) 4.00024e8i 0.849468i
\(779\) 1.06288e7 0.0224840
\(780\) 1.90785e8i 0.402033i
\(781\) 2.45742e8i 0.515854i
\(782\) 5.27870e8 1.10384
\(783\) −9.22000e7 −0.192064
\(784\) −1.57679e9 −3.27210
\(785\) 3.47083e7i 0.0717505i