Properties

Label 177.7.c.a.58.10
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 58.10
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.51

$q$-expansion

\(f(q)\) \(=\) \(q-11.8923i q^{2} +15.5885 q^{3} -77.4273 q^{4} +54.6144 q^{5} -185.383i q^{6} -559.219 q^{7} +159.682i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-11.8923i q^{2} +15.5885 q^{3} -77.4273 q^{4} +54.6144 q^{5} -185.383i q^{6} -559.219 q^{7} +159.682i q^{8} +243.000 q^{9} -649.492i q^{10} +2296.89i q^{11} -1206.97 q^{12} -2227.74i q^{13} +6650.41i q^{14} +851.354 q^{15} -3056.36 q^{16} -3185.15 q^{17} -2889.83i q^{18} +7584.09 q^{19} -4228.65 q^{20} -8717.36 q^{21} +27315.3 q^{22} +11089.9i q^{23} +2489.20i q^{24} -12642.3 q^{25} -26493.0 q^{26} +3788.00 q^{27} +43298.8 q^{28} +32846.9 q^{29} -10124.6i q^{30} +9813.00i q^{31} +46566.8i q^{32} +35804.9i q^{33} +37878.9i q^{34} -30541.4 q^{35} -18814.8 q^{36} +48671.8i q^{37} -90192.5i q^{38} -34727.0i q^{39} +8720.94i q^{40} +44741.9 q^{41} +103670. i q^{42} +140560. i q^{43} -177842. i q^{44} +13271.3 q^{45} +131885. q^{46} +138791. i q^{47} -47643.9 q^{48} +195077. q^{49} +150346. i q^{50} -49651.6 q^{51} +172488. i q^{52} -127534. q^{53} -45048.1i q^{54} +125443. i q^{55} -89297.2i q^{56} +118224. q^{57} -390626. i q^{58} +(204540. - 18540.2i) q^{59} -65918.1 q^{60} -29116.6i q^{61} +116699. q^{62} -135890. q^{63} +358181. q^{64} -121667. i q^{65} +425804. q^{66} -401180. i q^{67} +246618. q^{68} +172874. i q^{69} +363208. i q^{70} -697835. q^{71} +38802.8i q^{72} -209791. i q^{73} +578821. q^{74} -197073. q^{75} -587216. q^{76} -1.28446e6i q^{77} -412985. q^{78} -457805. q^{79} -166921. q^{80} +59049.0 q^{81} -532085. i q^{82} +267609. i q^{83} +674962. q^{84} -173955. q^{85} +1.67159e6 q^{86} +512033. q^{87} -366772. q^{88} +220394. i q^{89} -157827. i q^{90} +1.24579e6i q^{91} -858661. i q^{92} +152970. i q^{93} +1.65055e6 q^{94} +414201. q^{95} +725905. i q^{96} -955116. i q^{97} -2.31991e6i q^{98} +558144. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.8923i 1.48654i −0.668991 0.743270i \(-0.733274\pi\)
0.668991 0.743270i \(-0.266726\pi\)
\(3\) 15.5885 0.577350
\(4\) −77.4273 −1.20980
\(5\) 54.6144 0.436915 0.218458 0.975846i \(-0.429897\pi\)
0.218458 + 0.975846i \(0.429897\pi\)
\(6\) 185.383i 0.858254i
\(7\) −559.219 −1.63038 −0.815188 0.579197i \(-0.803366\pi\)
−0.815188 + 0.579197i \(0.803366\pi\)
\(8\) 159.682i 0.311879i
\(9\) 243.000 0.333333
\(10\) 649.492i 0.649492i
\(11\) 2296.89i 1.72569i 0.505472 + 0.862843i \(0.331318\pi\)
−0.505472 + 0.862843i \(0.668682\pi\)
\(12\) −1206.97 −0.698480
\(13\) 2227.74i 1.01399i −0.861949 0.506995i \(-0.830756\pi\)
0.861949 0.506995i \(-0.169244\pi\)
\(14\) 6650.41i 2.42362i
\(15\) 851.354 0.252253
\(16\) −3056.36 −0.746181
\(17\) −3185.15 −0.648311 −0.324156 0.946004i \(-0.605080\pi\)
−0.324156 + 0.946004i \(0.605080\pi\)
\(18\) 2889.83i 0.495513i
\(19\) 7584.09 1.10571 0.552857 0.833276i \(-0.313538\pi\)
0.552857 + 0.833276i \(0.313538\pi\)
\(20\) −4228.65 −0.528581
\(21\) −8717.36 −0.941298
\(22\) 27315.3 2.56530
\(23\) 11089.9i 0.911473i 0.890115 + 0.455737i \(0.150624\pi\)
−0.890115 + 0.455737i \(0.849376\pi\)
\(24\) 2489.20i 0.180064i
\(25\) −12642.3 −0.809105
\(26\) −26493.0 −1.50734
\(27\) 3788.00 0.192450
\(28\) 43298.8 1.97243
\(29\) 32846.9 1.34679 0.673396 0.739282i \(-0.264835\pi\)
0.673396 + 0.739282i \(0.264835\pi\)
\(30\) 10124.6i 0.374984i
\(31\) 9813.00i 0.329395i 0.986344 + 0.164697i \(0.0526648\pi\)
−0.986344 + 0.164697i \(0.947335\pi\)
\(32\) 46566.8i 1.42111i
\(33\) 35804.9i 0.996325i
\(34\) 37878.9i 0.963741i
\(35\) −30541.4 −0.712335
\(36\) −18814.8 −0.403267
\(37\) 48671.8i 0.960888i 0.877026 + 0.480444i \(0.159524\pi\)
−0.877026 + 0.480444i \(0.840476\pi\)
\(38\) 90192.5i 1.64369i
\(39\) 34727.0i 0.585428i
\(40\) 8720.94i 0.136265i
\(41\) 44741.9 0.649177 0.324588 0.945855i \(-0.394774\pi\)
0.324588 + 0.945855i \(0.394774\pi\)
\(42\) 103670.i 1.39928i
\(43\) 140560.i 1.76790i 0.467586 + 0.883948i \(0.345124\pi\)
−0.467586 + 0.883948i \(0.654876\pi\)
\(44\) 177842.i 2.08774i
\(45\) 13271.3 0.145638
\(46\) 131885. 1.35494
\(47\) 138791.i 1.33680i 0.743801 + 0.668401i \(0.233021\pi\)
−0.743801 + 0.668401i \(0.766979\pi\)
\(48\) −47643.9 −0.430808
\(49\) 195077. 1.65812
\(50\) 150346.i 1.20277i
\(51\) −49651.6 −0.374303
\(52\) 172488.i 1.22673i
\(53\) −127534. −0.856639 −0.428319 0.903627i \(-0.640894\pi\)
−0.428319 + 0.903627i \(0.640894\pi\)
\(54\) 45048.1i 0.286085i
\(55\) 125443.i 0.753978i
\(56\) 89297.2i 0.508480i
\(57\) 118224. 0.638384
\(58\) 390626.i 2.00206i
\(59\) 204540. 18540.2i 0.995917 0.0902731i
\(60\) −65918.1 −0.305176
\(61\) 29116.6i 0.128278i −0.997941 0.0641388i \(-0.979570\pi\)
0.997941 0.0641388i \(-0.0204300\pi\)
\(62\) 116699. 0.489659
\(63\) −135890. −0.543458
\(64\) 358181. 1.36635
\(65\) 121667.i 0.443028i
\(66\) 425804. 1.48108
\(67\) 401180.i 1.33387i −0.745115 0.666936i \(-0.767605\pi\)
0.745115 0.666936i \(-0.232395\pi\)
\(68\) 246618. 0.784328
\(69\) 172874.i 0.526239i
\(70\) 363208.i 1.05892i
\(71\) −697835. −1.94974 −0.974872 0.222765i \(-0.928492\pi\)
−0.974872 + 0.222765i \(0.928492\pi\)
\(72\) 38802.8i 0.103960i
\(73\) 209791.i 0.539285i −0.962961 0.269642i \(-0.913095\pi\)
0.962961 0.269642i \(-0.0869055\pi\)
\(74\) 578821. 1.42840
\(75\) −197073. −0.467137
\(76\) −587216. −1.33770
\(77\) 1.28446e6i 2.81352i
\(78\) −412985. −0.870262
\(79\) −457805. −0.928536 −0.464268 0.885695i \(-0.653683\pi\)
−0.464268 + 0.885695i \(0.653683\pi\)
\(80\) −166921. −0.326018
\(81\) 59049.0 0.111111
\(82\) 532085.i 0.965028i
\(83\) 267609.i 0.468022i 0.972234 + 0.234011i \(0.0751852\pi\)
−0.972234 + 0.234011i \(0.924815\pi\)
\(84\) 674962. 1.13878
\(85\) −173955. −0.283257
\(86\) 1.67159e6 2.62805
\(87\) 512033. 0.777571
\(88\) −366772. −0.538206
\(89\) 220394.i 0.312629i 0.987707 + 0.156315i \(0.0499614\pi\)
−0.987707 + 0.156315i \(0.950039\pi\)
\(90\) 157827.i 0.216497i
\(91\) 1.24579e6i 1.65318i
\(92\) 858661.i 1.10270i
\(93\) 152970.i 0.190176i
\(94\) 1.65055e6 1.98721
\(95\) 414201. 0.483103
\(96\) 725905.i 0.820477i
\(97\) 955116.i 1.04650i −0.852178 0.523252i \(-0.824719\pi\)
0.852178 0.523252i \(-0.175281\pi\)
\(98\) 2.31991e6i 2.46487i
\(99\) 558144.i 0.575229i
\(100\) 978857. 0.978857
\(101\) 805727.i 0.782031i −0.920384 0.391015i \(-0.872124\pi\)
0.920384 0.391015i \(-0.127876\pi\)
\(102\) 590473.i 0.556416i
\(103\) 1.08040e6i 0.988716i 0.869258 + 0.494358i \(0.164597\pi\)
−0.869258 + 0.494358i \(0.835403\pi\)
\(104\) 355730. 0.316243
\(105\) −476093. −0.411267
\(106\) 1.51667e6i 1.27343i
\(107\) 1.90839e6 1.55782 0.778908 0.627138i \(-0.215774\pi\)
0.778908 + 0.627138i \(0.215774\pi\)
\(108\) −293294. −0.232827
\(109\) 1.43192e6i 1.10570i 0.833280 + 0.552851i \(0.186460\pi\)
−0.833280 + 0.552851i \(0.813540\pi\)
\(110\) 1.49181e6 1.12082
\(111\) 758719.i 0.554769i
\(112\) 1.70917e6 1.21655
\(113\) 1.08804e6i 0.754063i 0.926200 + 0.377032i \(0.123055\pi\)
−0.926200 + 0.377032i \(0.876945\pi\)
\(114\) 1.40596e6i 0.948984i
\(115\) 605668.i 0.398237i
\(116\) −2.54325e6 −1.62935
\(117\) 541340.i 0.337997i
\(118\) −220486. 2.43246e6i −0.134195 1.48047i
\(119\) 1.78120e6 1.05699
\(120\) 135946.i 0.0786725i
\(121\) −3.50413e6 −1.97799
\(122\) −346264. −0.190690
\(123\) 697458. 0.374802
\(124\) 759795.i 0.398503i
\(125\) −1.54380e6 −0.790425
\(126\) 1.61605e6i 0.807873i
\(127\) −2.36792e6 −1.15600 −0.577998 0.816038i \(-0.696166\pi\)
−0.577998 + 0.816038i \(0.696166\pi\)
\(128\) 1.27933e6i 0.610030i
\(129\) 2.19111e6i 1.02070i
\(130\) −1.44690e6 −0.658579
\(131\) 275445.i 0.122524i 0.998122 + 0.0612619i \(0.0195125\pi\)
−0.998122 + 0.0612619i \(0.980488\pi\)
\(132\) 2.77228e6i 1.20536i
\(133\) −4.24117e6 −1.80273
\(134\) −4.77096e6 −1.98286
\(135\) 206879. 0.0840843
\(136\) 508612.i 0.202195i
\(137\) −3.89100e6 −1.51321 −0.756606 0.653871i \(-0.773144\pi\)
−0.756606 + 0.653871i \(0.773144\pi\)
\(138\) 2.05588e6 0.782276
\(139\) −2.75589e6 −1.02617 −0.513083 0.858339i \(-0.671497\pi\)
−0.513083 + 0.858339i \(0.671497\pi\)
\(140\) 2.36474e6 0.861785
\(141\) 2.16354e6i 0.771803i
\(142\) 8.29888e6i 2.89837i
\(143\) 5.11686e6 1.74983
\(144\) −742695. −0.248727
\(145\) 1.79391e6 0.588434
\(146\) −2.49490e6 −0.801668
\(147\) 3.04094e6 0.957318
\(148\) 3.76853e6i 1.16248i
\(149\) 136843.i 0.0413679i 0.999786 + 0.0206839i \(0.00658437\pi\)
−0.999786 + 0.0206839i \(0.993416\pi\)
\(150\) 2.34366e6i 0.694418i
\(151\) 1.92740e6i 0.559809i 0.960028 + 0.279905i \(0.0903028\pi\)
−0.960028 + 0.279905i \(0.909697\pi\)
\(152\) 1.21104e6i 0.344849i
\(153\) −773992. −0.216104
\(154\) −1.52752e7 −4.18240
\(155\) 535931.i 0.143918i
\(156\) 2.68882e6i 0.708252i
\(157\) 4.07228e6i 1.05230i 0.850392 + 0.526149i \(0.176365\pi\)
−0.850392 + 0.526149i \(0.823635\pi\)
\(158\) 5.44436e6i 1.38031i
\(159\) −1.98805e6 −0.494580
\(160\) 2.54322e6i 0.620903i
\(161\) 6.20168e6i 1.48604i
\(162\) 702230.i 0.165171i
\(163\) −2.90630e6 −0.671085 −0.335542 0.942025i \(-0.608920\pi\)
−0.335542 + 0.942025i \(0.608920\pi\)
\(164\) −3.46425e6 −0.785376
\(165\) 1.95546e6i 0.435310i
\(166\) 3.18249e6 0.695734
\(167\) 4.58396e6 0.984219 0.492110 0.870533i \(-0.336226\pi\)
0.492110 + 0.870533i \(0.336226\pi\)
\(168\) 1.39201e6i 0.293571i
\(169\) −136004. −0.0281769
\(170\) 2.06873e6i 0.421073i
\(171\) 1.84293e6 0.368571
\(172\) 1.08832e7i 2.13880i
\(173\) 6.14754e6i 1.18731i −0.804721 0.593653i \(-0.797685\pi\)
0.804721 0.593653i \(-0.202315\pi\)
\(174\) 6.08926e6i 1.15589i
\(175\) 7.06979e6 1.31914
\(176\) 7.02011e6i 1.28767i
\(177\) 3.18847e6 289013.i 0.574993 0.0521192i
\(178\) 2.62100e6 0.464736
\(179\) 4.13101e6i 0.720273i 0.932900 + 0.360137i \(0.117270\pi\)
−0.932900 + 0.360137i \(0.882730\pi\)
\(180\) −1.02756e6 −0.176194
\(181\) 4.09393e6 0.690406 0.345203 0.938528i \(-0.387810\pi\)
0.345203 + 0.938528i \(0.387810\pi\)
\(182\) 1.48154e7 2.45753
\(183\) 453882.i 0.0740611i
\(184\) −1.77086e6 −0.284270
\(185\) 2.65818e6i 0.419826i
\(186\) 1.81916e6 0.282705
\(187\) 7.31594e6i 1.11878i
\(188\) 1.07462e7i 1.61727i
\(189\) −2.11832e6 −0.313766
\(190\) 4.92581e6i 0.718152i
\(191\) 1.09834e7i 1.57630i 0.615485 + 0.788149i \(0.288960\pi\)
−0.615485 + 0.788149i \(0.711040\pi\)
\(192\) 5.58349e6 0.788864
\(193\) −9.97789e6 −1.38793 −0.693964 0.720010i \(-0.744137\pi\)
−0.693964 + 0.720010i \(0.744137\pi\)
\(194\) −1.13586e7 −1.55567
\(195\) 1.89659e6i 0.255782i
\(196\) −1.51043e7 −2.00600
\(197\) −8.47028e6 −1.10790 −0.553948 0.832551i \(-0.686879\pi\)
−0.553948 + 0.832551i \(0.686879\pi\)
\(198\) 6.63763e6 0.855101
\(199\) 5.05790e6 0.641816 0.320908 0.947110i \(-0.396012\pi\)
0.320908 + 0.947110i \(0.396012\pi\)
\(200\) 2.01874e6i 0.252343i
\(201\) 6.25377e6i 0.770112i
\(202\) −9.58196e6 −1.16252
\(203\) −1.83686e7 −2.19578
\(204\) 3.84439e6 0.452832
\(205\) 2.44355e6 0.283635
\(206\) 1.28484e7 1.46977
\(207\) 2.69485e6i 0.303824i
\(208\) 6.80876e6i 0.756621i
\(209\) 1.74198e7i 1.90812i
\(210\) 5.66185e6i 0.611365i
\(211\) 4.47808e6i 0.476700i 0.971179 + 0.238350i \(0.0766065\pi\)
−0.971179 + 0.238350i \(0.923394\pi\)
\(212\) 9.87460e6 1.03636
\(213\) −1.08782e7 −1.12569
\(214\) 2.26952e7i 2.31576i
\(215\) 7.67660e6i 0.772420i
\(216\) 604875.i 0.0600212i
\(217\) 5.48762e6i 0.537037i
\(218\) 1.70288e7 1.64367
\(219\) 3.27032e6i 0.311356i
\(220\) 9.71273e6i 0.912164i
\(221\) 7.09568e6i 0.657381i
\(222\) 9.02293e6 0.824686
\(223\) −6.43240e6 −0.580041 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(224\) 2.60410e7i 2.31694i
\(225\) −3.07207e6 −0.269702
\(226\) 1.29393e7 1.12095
\(227\) 1.97765e7i 1.69072i −0.534197 0.845360i \(-0.679386\pi\)
0.534197 0.845360i \(-0.320614\pi\)
\(228\) −9.15379e6 −0.772319
\(229\) 1.78077e7i 1.48286i 0.671028 + 0.741432i \(0.265853\pi\)
−0.671028 + 0.741432i \(0.734147\pi\)
\(230\) 7.20280e6 0.591995
\(231\) 2.00228e7i 1.62438i
\(232\) 5.24506e6i 0.420036i
\(233\) 1.83620e6i 0.145162i 0.997363 + 0.0725808i \(0.0231235\pi\)
−0.997363 + 0.0725808i \(0.976876\pi\)
\(234\) −6.43779e6 −0.502446
\(235\) 7.57998e6i 0.584069i
\(236\) −1.58370e7 + 1.43552e6i −1.20486 + 0.109213i
\(237\) −7.13647e6 −0.536091
\(238\) 2.11826e7i 1.57126i
\(239\) −1.30376e7 −0.955002 −0.477501 0.878631i \(-0.658457\pi\)
−0.477501 + 0.878631i \(0.658457\pi\)
\(240\) −2.60204e6 −0.188226
\(241\) 2.10381e7 1.50299 0.751495 0.659739i \(-0.229333\pi\)
0.751495 + 0.659739i \(0.229333\pi\)
\(242\) 4.16723e7i 2.94037i
\(243\) 920483. 0.0641500
\(244\) 2.25442e6i 0.155190i
\(245\) 1.06540e7 0.724459
\(246\) 8.29439e6i 0.557159i
\(247\) 1.68954e7i 1.12118i
\(248\) −1.56696e6 −0.102731
\(249\) 4.17161e6i 0.270213i
\(250\) 1.83594e7i 1.17500i
\(251\) −1.54860e7 −0.979308 −0.489654 0.871917i \(-0.662877\pi\)
−0.489654 + 0.871917i \(0.662877\pi\)
\(252\) 1.05216e7 0.657477
\(253\) −2.54723e7 −1.57292
\(254\) 2.81601e7i 1.71843i
\(255\) −2.71169e6 −0.163538
\(256\) 7.70942e6 0.459517
\(257\) 1.79898e7 1.05981 0.529904 0.848058i \(-0.322228\pi\)
0.529904 + 0.848058i \(0.322228\pi\)
\(258\) 2.60574e7 1.51730
\(259\) 2.72182e7i 1.56661i
\(260\) 9.42031e6i 0.535976i
\(261\) 7.98180e6 0.448931
\(262\) 3.27568e6 0.182137
\(263\) 1.18555e7 0.651707 0.325853 0.945420i \(-0.394348\pi\)
0.325853 + 0.945420i \(0.394348\pi\)
\(264\) −5.71741e6 −0.310733
\(265\) −6.96518e6 −0.374278
\(266\) 5.04373e7i 2.67983i
\(267\) 3.43560e6i 0.180497i
\(268\) 3.10623e7i 1.61372i
\(269\) 1.76151e7i 0.904957i −0.891775 0.452478i \(-0.850540\pi\)
0.891775 0.452478i \(-0.149460\pi\)
\(270\) 2.46027e6i 0.124995i
\(271\) 2.56878e6 0.129068 0.0645341 0.997916i \(-0.479444\pi\)
0.0645341 + 0.997916i \(0.479444\pi\)
\(272\) 9.73497e6 0.483757
\(273\) 1.94200e7i 0.954467i
\(274\) 4.62730e7i 2.24945i
\(275\) 2.90379e7i 1.39626i
\(276\) 1.33852e7i 0.636646i
\(277\) −3.26458e7 −1.53599 −0.767994 0.640457i \(-0.778745\pi\)
−0.767994 + 0.640457i \(0.778745\pi\)
\(278\) 3.27739e7i 1.52544i
\(279\) 2.38456e6i 0.109798i
\(280\) 4.87691e6i 0.222163i
\(281\) 2.87372e7 1.29516 0.647582 0.761996i \(-0.275780\pi\)
0.647582 + 0.761996i \(0.275780\pi\)
\(282\) 2.57295e7 1.14732
\(283\) 2.46553e7i 1.08781i 0.839148 + 0.543903i \(0.183054\pi\)
−0.839148 + 0.543903i \(0.816946\pi\)
\(284\) 5.40315e7 2.35880
\(285\) 6.45675e6 0.278920
\(286\) 6.08514e7i 2.60119i
\(287\) −2.50205e7 −1.05840
\(288\) 1.13157e7i 0.473702i
\(289\) −1.39924e7 −0.579693
\(290\) 2.13338e7i 0.874730i
\(291\) 1.48888e7i 0.604200i
\(292\) 1.62435e7i 0.652428i
\(293\) 6.34529e6 0.252260 0.126130 0.992014i \(-0.459744\pi\)
0.126130 + 0.992014i \(0.459744\pi\)
\(294\) 3.61639e7i 1.42309i
\(295\) 1.11709e7 1.01256e6i 0.435131 0.0394417i
\(296\) −7.77202e6 −0.299681
\(297\) 8.70060e6i 0.332108i
\(298\) 1.62738e6 0.0614950
\(299\) 2.47054e7 0.924225
\(300\) 1.52589e7 0.565143
\(301\) 7.86038e7i 2.88233i
\(302\) 2.29212e7 0.832179
\(303\) 1.25600e7i 0.451506i
\(304\) −2.31797e7 −0.825063
\(305\) 1.59018e6i 0.0560464i
\(306\) 9.20456e6i 0.321247i
\(307\) 2.12802e7 0.735464 0.367732 0.929932i \(-0.380134\pi\)
0.367732 + 0.929932i \(0.380134\pi\)
\(308\) 9.94525e7i 3.40380i
\(309\) 1.68417e7i 0.570835i
\(310\) 6.37347e6 0.213939
\(311\) 2.24785e6 0.0747284 0.0373642 0.999302i \(-0.488104\pi\)
0.0373642 + 0.999302i \(0.488104\pi\)
\(312\) 5.54528e6 0.182583
\(313\) 1.36818e7i 0.446179i −0.974798 0.223090i \(-0.928386\pi\)
0.974798 0.223090i \(-0.0716143\pi\)
\(314\) 4.84289e7 1.56428
\(315\) −7.42156e6 −0.237445
\(316\) 3.54466e7 1.12335
\(317\) −2.87039e7 −0.901079 −0.450539 0.892757i \(-0.648768\pi\)
−0.450539 + 0.892757i \(0.648768\pi\)
\(318\) 2.36426e7i 0.735214i
\(319\) 7.54457e7i 2.32414i
\(320\) 1.95618e7 0.596980
\(321\) 2.97489e7 0.899406
\(322\) −7.37524e7 −2.20906
\(323\) −2.41565e7 −0.716847
\(324\) −4.57201e6 −0.134422
\(325\) 2.81637e7i 0.820425i
\(326\) 3.45626e7i 0.997595i
\(327\) 2.23214e7i 0.638378i
\(328\) 7.14449e6i 0.202465i
\(329\) 7.76145e7i 2.17949i
\(330\) 2.32550e7 0.647105
\(331\) 3.54730e7 0.978169 0.489085 0.872236i \(-0.337331\pi\)
0.489085 + 0.872236i \(0.337331\pi\)
\(332\) 2.07202e7i 0.566214i
\(333\) 1.18273e7i 0.320296i
\(334\) 5.45140e7i 1.46308i
\(335\) 2.19102e7i 0.582789i
\(336\) 2.66434e7 0.702378
\(337\) 5.56747e7i 1.45468i 0.686276 + 0.727342i \(0.259244\pi\)
−0.686276 + 0.727342i \(0.740756\pi\)
\(338\) 1.61741e6i 0.0418860i
\(339\) 1.69608e7i 0.435359i
\(340\) 1.34689e7 0.342685
\(341\) −2.25394e7 −0.568432
\(342\) 2.19168e7i 0.547896i
\(343\) −4.32989e7 −1.07299
\(344\) −2.24449e7 −0.551370
\(345\) 9.44143e6i 0.229922i
\(346\) −7.31085e7 −1.76498
\(347\) 2.90745e7i 0.695862i 0.937520 + 0.347931i \(0.113116\pi\)
−0.937520 + 0.347931i \(0.886884\pi\)
\(348\) −3.96453e7 −0.940707
\(349\) 2.35075e7i 0.553007i 0.961013 + 0.276503i \(0.0891757\pi\)
−0.961013 + 0.276503i \(0.910824\pi\)
\(350\) 8.40763e7i 1.96096i
\(351\) 8.43866e6i 0.195143i
\(352\) −1.06959e8 −2.45239
\(353\) 6.92167e7i 1.57357i −0.617226 0.786786i \(-0.711743\pi\)
0.617226 0.786786i \(-0.288257\pi\)
\(354\) −3.43704e6 3.79183e7i −0.0774773 0.854750i
\(355\) −3.81118e7 −0.851873
\(356\) 1.70645e7i 0.378219i
\(357\) 2.77661e7 0.610254
\(358\) 4.91273e7 1.07071
\(359\) −9.18314e7 −1.98476 −0.992379 0.123220i \(-0.960678\pi\)
−0.992379 + 0.123220i \(0.960678\pi\)
\(360\) 2.11919e6i 0.0454216i
\(361\) 1.04726e7 0.222604
\(362\) 4.86863e7i 1.02632i
\(363\) −5.46240e7 −1.14199
\(364\) 9.64584e7i 2.00003i
\(365\) 1.14576e7i 0.235622i
\(366\) −5.39772e6 −0.110095
\(367\) 7.23105e7i 1.46286i −0.681916 0.731430i \(-0.738853\pi\)
0.681916 0.731430i \(-0.261147\pi\)
\(368\) 3.38947e7i 0.680124i
\(369\) 1.08723e7 0.216392
\(370\) 3.16120e7 0.624089
\(371\) 7.13193e7 1.39664
\(372\) 1.18440e7i 0.230076i
\(373\) 7.66390e7 1.47681 0.738403 0.674360i \(-0.235580\pi\)
0.738403 + 0.674360i \(0.235580\pi\)
\(374\) −8.70035e7 −1.66311
\(375\) −2.40655e7 −0.456352
\(376\) −2.21624e7 −0.416921
\(377\) 7.31743e7i 1.36563i
\(378\) 2.51917e7i 0.466426i
\(379\) −1.34455e7 −0.246978 −0.123489 0.992346i \(-0.539408\pi\)
−0.123489 + 0.992346i \(0.539408\pi\)
\(380\) −3.20705e7 −0.584459
\(381\) −3.69122e7 −0.667414
\(382\) 1.30619e8 2.34323
\(383\) −5.06181e6 −0.0900969 −0.0450484 0.998985i \(-0.514344\pi\)
−0.0450484 + 0.998985i \(0.514344\pi\)
\(384\) 1.99427e7i 0.352201i
\(385\) 7.01501e7i 1.22927i
\(386\) 1.18660e8i 2.06321i
\(387\) 3.41561e7i 0.589299i
\(388\) 7.39521e7i 1.26606i
\(389\) 1.04201e7 0.177020 0.0885098 0.996075i \(-0.471790\pi\)
0.0885098 + 0.996075i \(0.471790\pi\)
\(390\) −2.25549e7 −0.380231
\(391\) 3.53230e7i 0.590918i
\(392\) 3.11502e7i 0.517134i
\(393\) 4.29376e6i 0.0707392i
\(394\) 1.00731e8i 1.64693i
\(395\) −2.50027e7 −0.405692
\(396\) 4.32156e7i 0.695913i
\(397\) 3.94584e7i 0.630620i 0.948989 + 0.315310i \(0.102108\pi\)
−0.948989 + 0.315310i \(0.897892\pi\)
\(398\) 6.01501e7i 0.954086i
\(399\) −6.61132e7 −1.04081
\(400\) 3.86393e7 0.603739
\(401\) 7.49107e7i 1.16174i −0.813995 0.580872i \(-0.802712\pi\)
0.813995 0.580872i \(-0.197288\pi\)
\(402\) −7.43719e7 −1.14480
\(403\) 2.18608e7 0.334003
\(404\) 6.23853e7i 0.946102i
\(405\) 3.22492e6 0.0485461
\(406\) 2.18445e8i 3.26411i
\(407\) −1.11794e8 −1.65819
\(408\) 7.92848e6i 0.116737i
\(409\) 1.05414e8i 1.54073i −0.637600 0.770367i \(-0.720073\pi\)
0.637600 0.770367i \(-0.279927\pi\)
\(410\) 2.90595e7i 0.421635i
\(411\) −6.06547e7 −0.873653
\(412\) 8.36522e7i 1.19615i
\(413\) −1.14383e8 + 1.03680e7i −1.62372 + 0.147179i
\(414\) 3.20480e7 0.451647
\(415\) 1.46153e7i 0.204486i
\(416\) 1.03739e8 1.44099
\(417\) −4.29601e7 −0.592457
\(418\) 2.07162e8 2.83649
\(419\) 1.08862e8i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(420\) 3.68626e7 0.497552
\(421\) 5.53501e7i 0.741775i 0.928678 + 0.370887i \(0.120946\pi\)
−0.928678 + 0.370887i \(0.879054\pi\)
\(422\) 5.32548e7 0.708633
\(423\) 3.37262e7i 0.445601i
\(424\) 2.03649e7i 0.267168i
\(425\) 4.02676e7 0.524552
\(426\) 1.29367e8i 1.67338i
\(427\) 1.62825e7i 0.209141i
\(428\) −1.47762e8 −1.88465
\(429\) 7.97640e7 1.01026
\(430\) 9.12926e7 1.14823
\(431\) 6.15442e7i 0.768697i 0.923188 + 0.384348i \(0.125574\pi\)
−0.923188 + 0.384348i \(0.874426\pi\)
\(432\) −1.15775e7 −0.143603
\(433\) −7.93377e7 −0.977273 −0.488636 0.872488i \(-0.662505\pi\)
−0.488636 + 0.872488i \(0.662505\pi\)
\(434\) −6.52605e7 −0.798328
\(435\) 2.79643e7 0.339732
\(436\) 1.10870e8i 1.33768i
\(437\) 8.41068e7i 1.00783i
\(438\) −3.88917e7 −0.462843
\(439\) 6.40118e7 0.756600 0.378300 0.925683i \(-0.376509\pi\)
0.378300 + 0.925683i \(0.376509\pi\)
\(440\) −2.00310e7 −0.235150
\(441\) 4.74036e7 0.552708
\(442\) 8.43842e7 0.977224
\(443\) 8.42361e7i 0.968918i −0.874814 0.484459i \(-0.839016\pi\)
0.874814 0.484459i \(-0.160984\pi\)
\(444\) 5.87456e7i 0.671160i
\(445\) 1.20367e7i 0.136592i
\(446\) 7.64962e7i 0.862255i
\(447\) 2.13317e6i 0.0238838i
\(448\) −2.00302e8 −2.22767
\(449\) 1.28794e8 1.42285 0.711423 0.702764i \(-0.248051\pi\)
0.711423 + 0.702764i \(0.248051\pi\)
\(450\) 3.65341e7i 0.400923i
\(451\) 1.02767e8i 1.12028i
\(452\) 8.42437e7i 0.912267i
\(453\) 3.00451e7i 0.323206i
\(454\) −2.35188e8 −2.51332
\(455\) 6.80382e7i 0.722301i
\(456\) 1.88783e7i 0.199099i
\(457\) 3.91733e7i 0.410432i 0.978717 + 0.205216i \(0.0657897\pi\)
−0.978717 + 0.205216i \(0.934210\pi\)
\(458\) 2.11775e8 2.20434
\(459\) −1.20653e7 −0.124768
\(460\) 4.68953e7i 0.481787i
\(461\) 6.45172e7 0.658526 0.329263 0.944238i \(-0.393200\pi\)
0.329263 + 0.944238i \(0.393200\pi\)
\(462\) −2.38117e8 −2.41471
\(463\) 5.08703e7i 0.512533i 0.966606 + 0.256266i \(0.0824924\pi\)
−0.966606 + 0.256266i \(0.917508\pi\)
\(464\) −1.00392e8 −1.00495
\(465\) 8.35434e6i 0.0830909i
\(466\) 2.18367e7 0.215789
\(467\) 1.13345e8i 1.11289i −0.830885 0.556444i \(-0.812166\pi\)
0.830885 0.556444i \(-0.187834\pi\)
\(468\) 4.19145e7i 0.408909i
\(469\) 2.24347e8i 2.17471i
\(470\) 9.01435e7 0.868243
\(471\) 6.34806e7i 0.607545i
\(472\) 2.96054e6 + 3.26615e7i 0.0281543 + 0.310606i
\(473\) −3.22851e8 −3.05083
\(474\) 8.48692e7i 0.796921i
\(475\) −9.58802e7 −0.894639
\(476\) −1.37913e8 −1.27875
\(477\) −3.09907e7 −0.285546
\(478\) 1.55047e8i 1.41965i
\(479\) −6.43260e7 −0.585302 −0.292651 0.956219i \(-0.594537\pi\)
−0.292651 + 0.956219i \(0.594537\pi\)
\(480\) 3.96449e7i 0.358479i
\(481\) 1.08428e8 0.974331
\(482\) 2.50192e8i 2.23425i
\(483\) 9.66746e7i 0.857968i
\(484\) 2.71316e8 2.39298
\(485\) 5.21631e7i 0.457234i
\(486\) 1.09467e7i 0.0953616i
\(487\) 1.51710e8 1.31349 0.656745 0.754112i \(-0.271933\pi\)
0.656745 + 0.754112i \(0.271933\pi\)
\(488\) 4.64940e6 0.0400071
\(489\) −4.53047e7 −0.387451
\(490\) 1.26701e8i 1.07694i
\(491\) 4.86573e7 0.411059 0.205529 0.978651i \(-0.434108\pi\)
0.205529 + 0.978651i \(0.434108\pi\)
\(492\) −5.40023e7 −0.453437
\(493\) −1.04622e8 −0.873140
\(494\) −2.00925e8 −1.66668
\(495\) 3.04827e7i 0.251326i
\(496\) 2.99920e7i 0.245788i
\(497\) 3.90242e8 3.17881
\(498\) 4.96101e7 0.401682
\(499\) −7.52996e7 −0.606025 −0.303013 0.952987i \(-0.597992\pi\)
−0.303013 + 0.952987i \(0.597992\pi\)
\(500\) 1.19532e8 0.956258
\(501\) 7.14569e7 0.568239
\(502\) 1.84165e8i 1.45578i
\(503\) 7.64741e6i 0.0600911i −0.999549 0.0300456i \(-0.990435\pi\)
0.999549 0.0300456i \(-0.00956524\pi\)
\(504\) 2.16992e7i 0.169493i
\(505\) 4.40043e7i 0.341681i
\(506\) 3.02924e8i 2.33820i
\(507\) −2.12010e6 −0.0162679
\(508\) 1.83342e8 1.39853
\(509\) 1.63756e8i 1.24178i 0.783897 + 0.620891i \(0.213229\pi\)
−0.783897 + 0.620891i \(0.786771\pi\)
\(510\) 3.22483e7i 0.243107i
\(511\) 1.17319e8i 0.879236i
\(512\) 1.73560e8i 1.29312i
\(513\) 2.87285e7 0.212795
\(514\) 2.13940e8i 1.57545i
\(515\) 5.90052e7i 0.431985i
\(516\) 1.69652e8i 1.23484i
\(517\) −3.18787e8 −2.30690
\(518\) −3.23688e8 −2.32882
\(519\) 9.58306e7i 0.685492i
\(520\) 1.94280e7 0.138171
\(521\) 4.58496e7 0.324207 0.162104 0.986774i \(-0.448172\pi\)
0.162104 + 0.986774i \(0.448172\pi\)
\(522\) 9.49221e7i 0.667353i
\(523\) 1.15456e8 0.807074 0.403537 0.914963i \(-0.367781\pi\)
0.403537 + 0.914963i \(0.367781\pi\)
\(524\) 2.13269e7i 0.148230i
\(525\) 1.10207e8 0.761609
\(526\) 1.40989e8i 0.968789i
\(527\) 3.12559e7i 0.213550i
\(528\) 1.09433e8i 0.743439i
\(529\) 2.50501e7 0.169216
\(530\) 8.28321e7i 0.556380i
\(531\) 4.97033e7 4.50527e6i 0.331972 0.0300910i
\(532\) 3.28382e8 2.18095
\(533\) 9.96732e7i 0.658259i
\(534\) 4.08573e7 0.268315
\(535\) 1.04226e8 0.680634
\(536\) 6.40612e7 0.416007
\(537\) 6.43961e7i 0.415850i
\(538\) −2.09484e8 −1.34525
\(539\) 4.48069e8i 2.86140i
\(540\) −1.60181e7 −0.101725
\(541\) 8.19781e7i 0.517733i −0.965913 0.258867i \(-0.916651\pi\)
0.965913 0.258867i \(-0.0833490\pi\)
\(542\) 3.05488e7i 0.191865i
\(543\) 6.38180e7 0.398606
\(544\) 1.48323e8i 0.921320i
\(545\) 7.82033e7i 0.483098i
\(546\) 2.30949e8 1.41885
\(547\) −1.00028e8 −0.611166 −0.305583 0.952166i \(-0.598851\pi\)
−0.305583 + 0.952166i \(0.598851\pi\)
\(548\) 3.01270e8 1.83069
\(549\) 7.07533e6i 0.0427592i
\(550\) −3.45328e8 −2.07560
\(551\) 2.49114e8 1.48917
\(552\) −2.76050e7 −0.164123
\(553\) 2.56013e8 1.51386
\(554\) 3.88234e8i 2.28331i
\(555\) 4.14370e7i 0.242387i
\(556\) 2.13381e8 1.24146
\(557\) −1.27519e8 −0.737922 −0.368961 0.929445i \(-0.620286\pi\)
−0.368961 + 0.929445i \(0.620286\pi\)
\(558\) 2.83580e7 0.163220
\(559\) 3.13131e8 1.79263
\(560\) 9.33454e7 0.531531
\(561\) 1.14044e8i 0.645929i
\(562\) 3.41752e8i 1.92531i
\(563\) 2.14829e8i 1.20384i −0.798558 0.601918i \(-0.794403\pi\)
0.798558 0.601918i \(-0.205597\pi\)
\(564\) 1.67517e8i 0.933729i
\(565\) 5.94224e7i 0.329462i
\(566\) 2.93209e8 1.61707
\(567\) −3.30213e7 −0.181153
\(568\) 1.11432e8i 0.608085i
\(569\) 1.07673e8i 0.584478i 0.956345 + 0.292239i \(0.0944003\pi\)
−0.956345 + 0.292239i \(0.905600\pi\)
\(570\) 7.67857e7i 0.414626i
\(571\) 1.35569e8i 0.728200i −0.931360 0.364100i \(-0.881377\pi\)
0.931360 0.364100i \(-0.118623\pi\)
\(572\) −3.96185e8 −2.11695
\(573\) 1.71215e8i 0.910076i
\(574\) 2.97552e8i 1.57336i
\(575\) 1.40201e8i 0.737478i
\(576\) 8.70380e7 0.455451
\(577\) −615313. −0.00320308 −0.00160154 0.999999i \(-0.500510\pi\)
−0.00160154 + 0.999999i \(0.500510\pi\)
\(578\) 1.66402e8i 0.861736i
\(579\) −1.55540e8 −0.801320
\(580\) −1.38898e8 −0.711888
\(581\) 1.49652e8i 0.763052i
\(582\) −1.77062e8 −0.898167
\(583\) 2.92931e8i 1.47829i
\(584\) 3.34999e7 0.168192
\(585\) 2.95650e7i 0.147676i
\(586\) 7.54602e7i 0.374995i
\(587\) 1.76327e8i 0.871777i −0.900001 0.435888i \(-0.856434\pi\)
0.900001 0.435888i \(-0.143566\pi\)
\(588\) −2.35452e8 −1.15816
\(589\) 7.44227e7i 0.364217i
\(590\) −1.20417e7 1.32847e8i −0.0586316 0.646840i
\(591\) −1.32039e8 −0.639644
\(592\) 1.48759e8i 0.716996i
\(593\) 2.44819e8 1.17403 0.587017 0.809574i \(-0.300302\pi\)
0.587017 + 0.809574i \(0.300302\pi\)
\(594\) 1.03470e8 0.493693
\(595\) 9.72790e7 0.461815
\(596\) 1.05954e7i 0.0500470i
\(597\) 7.88448e7 0.370553
\(598\) 2.93804e8i 1.37390i
\(599\) 1.26127e8 0.586851 0.293425 0.955982i \(-0.405205\pi\)
0.293425 + 0.955982i \(0.405205\pi\)
\(600\) 3.14691e7i 0.145690i
\(601\) 3.93713e8i 1.81366i 0.421494 + 0.906831i \(0.361506\pi\)
−0.421494 + 0.906831i \(0.638494\pi\)
\(602\) −9.34782e8 −4.28470
\(603\) 9.74866e7i 0.444624i
\(604\) 1.49233e8i 0.677258i
\(605\) −1.91376e8 −0.864215
\(606\) −1.49368e8 −0.671181
\(607\) 3.80721e8 1.70232 0.851158 0.524909i \(-0.175901\pi\)
0.851158 + 0.524909i \(0.175901\pi\)
\(608\) 3.53167e8i 1.57134i
\(609\) −2.86338e8 −1.26773
\(610\) −1.89110e7 −0.0833152
\(611\) 3.09190e8 1.35551
\(612\) 5.99281e7 0.261443
\(613\) 2.52903e8i 1.09793i 0.835847 + 0.548963i \(0.184977\pi\)
−0.835847 + 0.548963i \(0.815023\pi\)
\(614\) 2.53071e8i 1.09330i
\(615\) 3.80912e7 0.163757
\(616\) 2.05106e8 0.877477
\(617\) −2.57534e8 −1.09642 −0.548212 0.836339i \(-0.684691\pi\)
−0.548212 + 0.836339i \(0.684691\pi\)
\(618\) 2.00287e8 0.848570
\(619\) 4.37180e8 1.84327 0.921635 0.388059i \(-0.126854\pi\)
0.921635 + 0.388059i \(0.126854\pi\)
\(620\) 4.14957e7i 0.174112i
\(621\) 4.20085e7i 0.175413i
\(622\) 2.67321e7i 0.111087i
\(623\) 1.23248e8i 0.509703i
\(624\) 1.06138e8i 0.436835i
\(625\) 1.13222e8 0.463756
\(626\) −1.62708e8 −0.663263
\(627\) 2.71548e8i 1.10165i
\(628\) 3.15306e8i 1.27307i
\(629\) 1.55027e8i 0.622954i
\(630\) 8.82595e7i 0.352972i
\(631\) −3.94167e7 −0.156889 −0.0784444 0.996918i \(-0.524995\pi\)
−0.0784444 + 0.996918i \(0.524995\pi\)
\(632\) 7.31032e7i 0.289591i
\(633\) 6.98064e7i 0.275223i
\(634\) 3.41356e8i 1.33949i
\(635\) −1.29323e8 −0.505072
\(636\) 1.53930e8 0.598344
\(637\) 4.34579e8i 1.68132i
\(638\) 8.97224e8 3.45493
\(639\) −1.69574e8 −0.649915
\(640\) 6.98696e7i 0.266532i
\(641\) −4.90871e7 −0.186377 −0.0931887 0.995648i \(-0.529706\pi\)
−0.0931887 + 0.995648i \(0.529706\pi\)
\(642\) 3.53783e8i 1.33700i
\(643\) −6.12735e7 −0.230484 −0.115242 0.993337i \(-0.536764\pi\)
−0.115242 + 0.993337i \(0.536764\pi\)
\(644\) 4.80179e8i 1.79782i
\(645\) 1.19666e8i 0.445957i
\(646\) 2.87277e8i 1.06562i
\(647\) −9.21937e7 −0.340399 −0.170199 0.985410i \(-0.554441\pi\)
−0.170199 + 0.985410i \(0.554441\pi\)
\(648\) 9.42907e6i 0.0346532i
\(649\) 4.25848e7 + 4.69807e8i 0.155783 + 1.71864i
\(650\) 3.34931e8 1.21959
\(651\) 8.55435e7i 0.310059i
\(652\) 2.25027e8 0.811880
\(653\) −8.97788e6 −0.0322429 −0.0161215 0.999870i \(-0.505132\pi\)
−0.0161215 + 0.999870i \(0.505132\pi\)
\(654\) 2.65453e8 0.948974
\(655\) 1.50432e7i 0.0535325i
\(656\) −1.36747e8 −0.484403
\(657\) 5.09792e7i 0.179762i
\(658\) −9.23016e8 −3.23990
\(659\) 1.22907e8i 0.429457i 0.976674 + 0.214728i \(0.0688866\pi\)
−0.976674 + 0.214728i \(0.931113\pi\)
\(660\) 1.51406e8i 0.526638i
\(661\) −8.72373e7 −0.302063 −0.151032 0.988529i \(-0.548260\pi\)
−0.151032 + 0.988529i \(0.548260\pi\)
\(662\) 4.21856e8i 1.45409i
\(663\) 1.10611e8i 0.379539i
\(664\) −4.27324e7 −0.145966
\(665\) −2.31629e8 −0.787639
\(666\) 1.40654e8 0.476133
\(667\) 3.64269e8i 1.22756i
\(668\) −3.54924e8 −1.19071
\(669\) −1.00271e8 −0.334887
\(670\) −2.60563e8 −0.866340
\(671\) 6.68775e7 0.221367
\(672\) 4.05940e8i 1.33768i
\(673\) 5.16451e8i 1.69428i −0.531373 0.847138i \(-0.678324\pi\)
0.531373 0.847138i \(-0.321676\pi\)
\(674\) 6.62102e8 2.16245
\(675\) −4.78889e7 −0.155712
\(676\) 1.05305e7 0.0340884
\(677\) −3.66895e8 −1.18243 −0.591216 0.806513i \(-0.701352\pi\)
−0.591216 + 0.806513i \(0.701352\pi\)
\(678\) 2.01703e8 0.647178
\(679\) 5.34119e8i 1.70619i
\(680\) 2.77775e7i 0.0883420i
\(681\) 3.08285e8i 0.976138i
\(682\) 2.68045e8i 0.844997i
\(683\) 3.14474e8i 0.987013i 0.869742 + 0.493507i \(0.164285\pi\)
−0.869742 + 0.493507i \(0.835715\pi\)
\(684\) −1.42694e8 −0.445898
\(685\) −2.12505e8 −0.661145
\(686\) 5.14925e8i 1.59504i
\(687\) 2.77594e8i 0.856131i
\(688\) 4.29602e8i 1.31917i
\(689\) 2.84112e8i 0.868623i
\(690\) 1.12281e8 0.341788
\(691\) 5.37088e8i 1.62784i −0.580978 0.813920i \(-0.697330\pi\)
0.580978 0.813920i \(-0.302670\pi\)
\(692\) 4.75987e8i 1.43641i
\(693\) 3.12124e8i 0.937838i
\(694\) 3.45763e8 1.03443
\(695\) −1.50511e8 −0.448347
\(696\) 8.17625e7i 0.242508i
\(697\) −1.42510e8 −0.420869
\(698\) 2.79559e8 0.822067
\(699\) 2.86235e7i 0.0838091i
\(700\) −5.47395e8 −1.59590
\(701\) 2.47147e8i 0.717466i 0.933440 + 0.358733i \(0.116791\pi\)
−0.933440 + 0.358733i \(0.883209\pi\)
\(702\) −1.00355e8 −0.290087
\(703\) 3.69132e8i 1.06247i
\(704\) 8.22702e8i 2.35790i
\(705\) 1.18160e8i 0.337213i
\(706\) −8.23147e8 −2.33918
\(707\) 4.50578e8i 1.27500i
\(708\) −2.46875e8 + 2.23775e7i −0.695628 + 0.0630539i
\(709\) 2.98391e8 0.837236 0.418618 0.908163i \(-0.362515\pi\)
0.418618 + 0.908163i \(0.362515\pi\)
\(710\) 4.53238e8i 1.26634i
\(711\) −1.11247e8 −0.309512
\(712\) −3.51930e7 −0.0975025
\(713\) −1.08825e8 −0.300235
\(714\) 3.30204e8i 0.907167i
\(715\) 2.79454e8 0.764527
\(716\) 3.19853e8i 0.871388i
\(717\) −2.03236e8 −0.551371
\(718\) 1.09209e9i 2.95042i
\(719\) 7.32429e7i 0.197051i −0.995135 0.0985255i \(-0.968587\pi\)
0.995135 0.0985255i \(-0.0314126\pi\)
\(720\) −4.05618e7 −0.108673
\(721\) 6.04178e8i 1.61198i
\(722\) 1.24544e8i 0.330910i
\(723\) 3.27952e8 0.867752
\(724\) −3.16982e8 −0.835255
\(725\) −4.15259e8 −1.08970
\(726\) 6.49607e8i 1.69762i
\(727\) 4.61548e8 1.20119 0.600597 0.799552i \(-0.294930\pi\)
0.600597 + 0.799552i \(0.294930\pi\)
\(728\) −1.98931e8 −0.515594
\(729\) 1.43489e7 0.0370370
\(730\) −1.36257e8 −0.350261
\(731\) 4.47705e8i 1.14615i
\(732\) 3.51429e7i 0.0895993i
\(733\) 2.07069e7 0.0525778 0.0262889 0.999654i \(-0.491631\pi\)
0.0262889 + 0.999654i \(0.491631\pi\)
\(734\) −8.59939e8 −2.17460
\(735\) 1.66079e8 0.418267
\(736\) −5.16422e8 −1.29530
\(737\) 9.21465e8 2.30185
\(738\) 1.29297e8i 0.321676i
\(739\) 1.68742e8i 0.418110i 0.977904 + 0.209055i \(0.0670388\pi\)
−0.977904 + 0.209055i \(0.932961\pi\)
\(740\) 2.05816e8i 0.507907i
\(741\) 2.63373e8i 0.647316i
\(742\) 8.48152e8i 2.07616i
\(743\) 4.95574e8 1.20821 0.604105 0.796905i \(-0.293531\pi\)
0.604105 + 0.796905i \(0.293531\pi\)
\(744\) −2.44265e7 −0.0593120
\(745\) 7.47359e6i 0.0180743i
\(746\) 9.11415e8i 2.19533i
\(747\) 6.50290e7i 0.156007i
\(748\) 5.66454e8i 1.35350i
\(749\) −1.06721e9 −2.53983
\(750\) 2.86194e8i 0.678386i
\(751\) 8.42475e7i 0.198901i 0.995042 + 0.0994506i \(0.0317085\pi\)
−0.995042 + 0.0994506i \(0.968291\pi\)
\(752\) 4.24195e8i 0.997497i
\(753\) −2.41404e8 −0.565404
\(754\) −8.70212e8 −2.03007
\(755\) 1.05264e8i 0.244589i
\(756\) 1.64016e8 0.379595
\(757\) 3.60531e8 0.831104 0.415552 0.909569i \(-0.363588\pi\)
0.415552 + 0.909569i \(0.363588\pi\)
\(758\) 1.59898e8i 0.367142i
\(759\) −3.97073e8 −0.908124
\(760\) 6.61405e7i 0.150670i
\(761\) 7.12021e8 1.61562 0.807810 0.589443i \(-0.200653\pi\)
0.807810 + 0.589443i \(0.200653\pi\)
\(762\) 4.38972e8i 0.992138i
\(763\) 8.00755e8i 1.80271i
\(764\) 8.50418e8i 1.90701i
\(765\) −4.22711e7 −0.0944190
\(766\) 6.01967e7i 0.133933i
\(767\) −4.13027e7 4.55662e8i −0.0915361 1.00985i
\(768\) 1.20178e8 0.265303
\(769\) 5.27498e8i 1.15996i 0.814632 + 0.579978i \(0.196939\pi\)
−0.814632 + 0.579978i \(0.803061\pi\)
\(770\) −8.34248e8 −1.82736
\(771\) 2.80433e8 0.611880
\(772\) 7.72562e8 1.67912
\(773\) 6.12907e8i 1.32696i 0.748196 + 0.663478i \(0.230920\pi\)
−0.748196 + 0.663478i \(0.769080\pi\)
\(774\) 4.06195e8 0.876016
\(775\) 1.24059e8i 0.266515i
\(776\) 1.52515e8 0.326383
\(777\) 4.24290e8i 0.904481i
\(778\) 1.23919e8i 0.263147i
\(779\) 3.39327e8 0.717804
\(780\) 1.46848e8i 0.309446i
\(781\) 1.60285e9i 3.36465i
\(782\) −4.20073e8 −0.878424
\(783\) 1.24424e8 0.259190
\(784\) −5.96224e8 −1.23726
\(785\) 2.22405e8i 0.459765i
\(786\) 5.10627e7