Properties

Label 177.7.c.a.58.9
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 58.9
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.52

$q$-expansion

\(f(q)\) \(=\) \(q-12.5406i q^{2} -15.5885 q^{3} -93.2673 q^{4} +48.4743 q^{5} +195.489i q^{6} -222.016 q^{7} +367.030i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-12.5406i q^{2} -15.5885 q^{3} -93.2673 q^{4} +48.4743 q^{5} +195.489i q^{6} -222.016 q^{7} +367.030i q^{8} +243.000 q^{9} -607.898i q^{10} -2577.25i q^{11} +1453.89 q^{12} -4161.02i q^{13} +2784.22i q^{14} -755.640 q^{15} -1366.32 q^{16} +5170.04 q^{17} -3047.37i q^{18} +1327.36 q^{19} -4521.07 q^{20} +3460.89 q^{21} -32320.3 q^{22} -3347.39i q^{23} -5721.43i q^{24} -13275.2 q^{25} -52181.7 q^{26} -3788.00 q^{27} +20706.8 q^{28} +16077.2 q^{29} +9476.20i q^{30} +28530.9i q^{31} +40624.4i q^{32} +40175.4i q^{33} -64835.5i q^{34} -10762.1 q^{35} -22663.9 q^{36} -52681.0i q^{37} -16646.0i q^{38} +64863.8i q^{39} +17791.5i q^{40} -4948.00 q^{41} -43401.7i q^{42} -21051.9i q^{43} +240373. i q^{44} +11779.3 q^{45} -41978.3 q^{46} +59914.8i q^{47} +21298.9 q^{48} -68357.8 q^{49} +166480. i q^{50} -80593.0 q^{51} +388087. i q^{52} -105642. q^{53} +47503.8i q^{54} -124931. i q^{55} -81486.5i q^{56} -20691.5 q^{57} -201618. i q^{58} +(-45352.4 + 200309. i) q^{59} +70476.5 q^{60} +152913. i q^{61} +357795. q^{62} -53949.9 q^{63} +422011. q^{64} -201703. i q^{65} +503824. q^{66} +115751. i q^{67} -482195. q^{68} +52180.6i q^{69} +134963. i q^{70} +181869. q^{71} +89188.2i q^{72} -648928. i q^{73} -660653. q^{74} +206940. q^{75} -123799. q^{76} +572192. i q^{77} +813433. q^{78} +576666. q^{79} -66231.6 q^{80} +59049.0 q^{81} +62051.0i q^{82} -316797. i q^{83} -322788. q^{84} +250614. q^{85} -264004. q^{86} -250618. q^{87} +945928. q^{88} +208482. i q^{89} -147719. i q^{90} +923813. i q^{91} +312201. i q^{92} -444753. i q^{93} +751369. q^{94} +64343.0 q^{95} -633272. i q^{96} -180262. i q^{97} +857250. i q^{98} -626272. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 12.5406i 1.56758i −0.621027 0.783789i \(-0.713284\pi\)
0.621027 0.783789i \(-0.286716\pi\)
\(3\) −15.5885 −0.577350
\(4\) −93.2673 −1.45730
\(5\) 48.4743 0.387795 0.193897 0.981022i \(-0.437887\pi\)
0.193897 + 0.981022i \(0.437887\pi\)
\(6\) 195.489i 0.905042i
\(7\) −222.016 −0.647278 −0.323639 0.946181i \(-0.604906\pi\)
−0.323639 + 0.946181i \(0.604906\pi\)
\(8\) 367.030i 0.716855i
\(9\) 243.000 0.333333
\(10\) 607.898i 0.607898i
\(11\) 2577.25i 1.93633i −0.250319 0.968163i \(-0.580535\pi\)
0.250319 0.968163i \(-0.419465\pi\)
\(12\) 1453.89 0.841373
\(13\) 4161.02i 1.89395i −0.321302 0.946977i \(-0.604120\pi\)
0.321302 0.946977i \(-0.395880\pi\)
\(14\) 2784.22i 1.01466i
\(15\) −755.640 −0.223893
\(16\) −1366.32 −0.333575
\(17\) 5170.04 1.05232 0.526159 0.850386i \(-0.323632\pi\)
0.526159 + 0.850386i \(0.323632\pi\)
\(18\) 3047.37i 0.522526i
\(19\) 1327.36 0.193521 0.0967606 0.995308i \(-0.469152\pi\)
0.0967606 + 0.995308i \(0.469152\pi\)
\(20\) −4521.07 −0.565134
\(21\) 3460.89 0.373706
\(22\) −32320.3 −3.03534
\(23\) 3347.39i 0.275120i −0.990493 0.137560i \(-0.956074\pi\)
0.990493 0.137560i \(-0.0439260\pi\)
\(24\) 5721.43i 0.413876i
\(25\) −13275.2 −0.849615
\(26\) −52181.7 −2.96892
\(27\) −3788.00 −0.192450
\(28\) 20706.8 0.943278
\(29\) 16077.2 0.659198 0.329599 0.944121i \(-0.393086\pi\)
0.329599 + 0.944121i \(0.393086\pi\)
\(30\) 9476.20i 0.350970i
\(31\) 28530.9i 0.957702i 0.877896 + 0.478851i \(0.158947\pi\)
−0.877896 + 0.478851i \(0.841053\pi\)
\(32\) 40624.4i 1.23976i
\(33\) 40175.4i 1.11794i
\(34\) 64835.5i 1.64959i
\(35\) −10762.1 −0.251011
\(36\) −22663.9 −0.485767
\(37\) 52681.0i 1.04004i −0.854155 0.520019i \(-0.825925\pi\)
0.854155 0.520019i \(-0.174075\pi\)
\(38\) 16646.0i 0.303360i
\(39\) 64863.8i 1.09347i
\(40\) 17791.5i 0.277992i
\(41\) −4948.00 −0.0717923 −0.0358961 0.999356i \(-0.511429\pi\)
−0.0358961 + 0.999356i \(0.511429\pi\)
\(42\) 43401.7i 0.585813i
\(43\) 21051.9i 0.264781i −0.991198 0.132390i \(-0.957735\pi\)
0.991198 0.132390i \(-0.0422653\pi\)
\(44\) 240373.i 2.82181i
\(45\) 11779.3 0.129265
\(46\) −41978.3 −0.431272
\(47\) 59914.8i 0.577086i 0.957467 + 0.288543i \(0.0931708\pi\)
−0.957467 + 0.288543i \(0.906829\pi\)
\(48\) 21298.9 0.192590
\(49\) −68357.8 −0.581032
\(50\) 166480.i 1.33184i
\(51\) −80593.0 −0.607556
\(52\) 388087.i 2.76006i
\(53\) −105642. −0.709594 −0.354797 0.934943i \(-0.615450\pi\)
−0.354797 + 0.934943i \(0.615450\pi\)
\(54\) 47503.8i 0.301681i
\(55\) 124931.i 0.750897i
\(56\) 81486.5i 0.464004i
\(57\) −20691.5 −0.111730
\(58\) 201618.i 1.03334i
\(59\) −45352.4 + 200309.i −0.220823 + 0.975314i
\(60\) 70476.5 0.326280
\(61\) 152913.i 0.673683i 0.941561 + 0.336841i \(0.109359\pi\)
−0.941561 + 0.336841i \(0.890641\pi\)
\(62\) 357795. 1.50127
\(63\) −53949.9 −0.215759
\(64\) 422011. 1.60985
\(65\) 201703.i 0.734465i
\(66\) 503824. 1.75246
\(67\) 115751.i 0.384859i 0.981311 + 0.192430i \(0.0616368\pi\)
−0.981311 + 0.192430i \(0.938363\pi\)
\(68\) −482195. −1.53354
\(69\) 52180.6i 0.158841i
\(70\) 134963.i 0.393479i
\(71\) 181869. 0.508141 0.254070 0.967186i \(-0.418231\pi\)
0.254070 + 0.967186i \(0.418231\pi\)
\(72\) 89188.2i 0.238952i
\(73\) 648928.i 1.66812i −0.551671 0.834062i \(-0.686010\pi\)
0.551671 0.834062i \(-0.313990\pi\)
\(74\) −660653. −1.63034
\(75\) 206940. 0.490526
\(76\) −123799. −0.282019
\(77\) 572192.i 1.25334i
\(78\) 813433. 1.71411
\(79\) 576666. 1.16962 0.584808 0.811172i \(-0.301170\pi\)
0.584808 + 0.811172i \(0.301170\pi\)
\(80\) −66231.6 −0.129359
\(81\) 59049.0 0.111111
\(82\) 62051.0i 0.112540i
\(83\) 316797.i 0.554047i −0.960863 0.277024i \(-0.910652\pi\)
0.960863 0.277024i \(-0.0893480\pi\)
\(84\) −322788. −0.544602
\(85\) 250614. 0.408083
\(86\) −264004. −0.415065
\(87\) −250618. −0.380588
\(88\) 945928. 1.38807
\(89\) 208482.i 0.295732i 0.989007 + 0.147866i \(0.0472405\pi\)
−0.989007 + 0.147866i \(0.952760\pi\)
\(90\) 147719.i 0.202633i
\(91\) 923813.i 1.22591i
\(92\) 312201.i 0.400933i
\(93\) 444753.i 0.552929i
\(94\) 751369. 0.904627
\(95\) 64343.0 0.0750465
\(96\) 633272.i 0.715776i
\(97\) 180262.i 0.197510i −0.995112 0.0987548i \(-0.968514\pi\)
0.995112 0.0987548i \(-0.0314860\pi\)
\(98\) 857250.i 0.910813i
\(99\) 626272.i 0.645442i
\(100\) 1.23815e6 1.23815
\(101\) 1.54557e6i 1.50012i −0.661371 0.750059i \(-0.730025\pi\)
0.661371 0.750059i \(-0.269975\pi\)
\(102\) 1.01069e6i 0.952392i
\(103\) 1.64324e6i 1.50379i 0.659281 + 0.751897i \(0.270861\pi\)
−0.659281 + 0.751897i \(0.729139\pi\)
\(104\) 1.52722e6 1.35769
\(105\) 167764. 0.144921
\(106\) 1.32482e6i 1.11234i
\(107\) −925802. −0.755730 −0.377865 0.925861i \(-0.623342\pi\)
−0.377865 + 0.925861i \(0.623342\pi\)
\(108\) 353296. 0.280458
\(109\) 1.70317e6i 1.31516i 0.753384 + 0.657581i \(0.228420\pi\)
−0.753384 + 0.657581i \(0.771580\pi\)
\(110\) −1.56671e6 −1.17709
\(111\) 821216.i 0.600466i
\(112\) 303346. 0.215916
\(113\) 1.24607e6i 0.863589i 0.901972 + 0.431794i \(0.142119\pi\)
−0.901972 + 0.431794i \(0.857881\pi\)
\(114\) 259485.i 0.175145i
\(115\) 162262.i 0.106690i
\(116\) −1.49947e6 −0.960650
\(117\) 1.01113e6i 0.631318i
\(118\) 2.51200e6 + 568747.i 1.52888 + 0.346157i
\(119\) −1.14783e6 −0.681142
\(120\) 277342.i 0.160499i
\(121\) −4.87066e6 −2.74936
\(122\) 1.91763e6 1.05605
\(123\) 77131.6 0.0414493
\(124\) 2.66100e6i 1.39566i
\(125\) −1.40092e6 −0.717271
\(126\) 676566.i 0.338219i
\(127\) −1.76313e6 −0.860741 −0.430371 0.902652i \(-0.641617\pi\)
−0.430371 + 0.902652i \(0.641617\pi\)
\(128\) 2.69232e6i 1.28380i
\(129\) 328167.i 0.152871i
\(130\) −2.52948e6 −1.15133
\(131\) 1.05099e6i 0.467505i −0.972296 0.233752i \(-0.924899\pi\)
0.972296 0.233752i \(-0.0751005\pi\)
\(132\) 3.74705e6i 1.62917i
\(133\) −294696. −0.125262
\(134\) 1.45160e6 0.603297
\(135\) −183621. −0.0746311
\(136\) 1.89756e6i 0.754359i
\(137\) −2.10794e6 −0.819778 −0.409889 0.912135i \(-0.634433\pi\)
−0.409889 + 0.912135i \(0.634433\pi\)
\(138\) 654377. 0.248995
\(139\) 3.12213e6 1.16253 0.581267 0.813713i \(-0.302557\pi\)
0.581267 + 0.813713i \(0.302557\pi\)
\(140\) 1.00375e6 0.365798
\(141\) 933979.i 0.333181i
\(142\) 2.28075e6i 0.796550i
\(143\) −1.07240e7 −3.66731
\(144\) −332017. −0.111192
\(145\) 779331. 0.255633
\(146\) −8.13797e6 −2.61491
\(147\) 1.06559e6 0.335459
\(148\) 4.91341e6i 1.51565i
\(149\) 4.06210e6i 1.22798i −0.789313 0.613990i \(-0.789563\pi\)
0.789313 0.613990i \(-0.210437\pi\)
\(150\) 2.59516e6i 0.768937i
\(151\) 3.77394e6i 1.09613i 0.836434 + 0.548067i \(0.184636\pi\)
−0.836434 + 0.548067i \(0.815364\pi\)
\(152\) 487181.i 0.138727i
\(153\) 1.25632e6 0.350773
\(154\) 7.17564e6 1.96471
\(155\) 1.38302e6i 0.371392i
\(156\) 6.04967e6i 1.59352i
\(157\) 4.32923e6i 1.11870i −0.828933 0.559348i \(-0.811052\pi\)
0.828933 0.559348i \(-0.188948\pi\)
\(158\) 7.23176e6i 1.83346i
\(159\) 1.64680e6 0.409684
\(160\) 1.96924e6i 0.480772i
\(161\) 743174.i 0.178079i
\(162\) 740511.i 0.174175i
\(163\) 8.17608e6 1.88791 0.943957 0.330068i \(-0.107072\pi\)
0.943957 + 0.330068i \(0.107072\pi\)
\(164\) 461486. 0.104623
\(165\) 1.94747e6i 0.433531i
\(166\) −3.97283e6 −0.868512
\(167\) 2.13038e6 0.457411 0.228706 0.973496i \(-0.426551\pi\)
0.228706 + 0.973496i \(0.426551\pi\)
\(168\) 1.27025e6i 0.267893i
\(169\) −1.24872e7 −2.58706
\(170\) 3.14286e6i 0.639703i
\(171\) 322549. 0.0645071
\(172\) 1.96346e6i 0.385866i
\(173\) 8.44401e6i 1.63084i 0.578872 + 0.815419i \(0.303493\pi\)
−0.578872 + 0.815419i \(0.696507\pi\)
\(174\) 3.14291e6i 0.596602i
\(175\) 2.94732e6 0.549937
\(176\) 3.52136e6i 0.645910i
\(177\) 706974. 3.12251e6i 0.127492 0.563098i
\(178\) 2.61449e6 0.463583
\(179\) 4.54211e6i 0.791952i −0.918261 0.395976i \(-0.870406\pi\)
0.918261 0.395976i \(-0.129594\pi\)
\(180\) −1.09862e6 −0.188378
\(181\) 3.26935e6 0.551349 0.275674 0.961251i \(-0.411099\pi\)
0.275674 + 0.961251i \(0.411099\pi\)
\(182\) 1.15852e7 1.92172
\(183\) 2.38368e6i 0.388951i
\(184\) 1.22859e6 0.197221
\(185\) 2.55368e6i 0.403321i
\(186\) −5.57748e6 −0.866760
\(187\) 1.33245e7i 2.03763i
\(188\) 5.58809e6i 0.840988i
\(189\) 840996. 0.124569
\(190\) 806902.i 0.117641i
\(191\) 5.28174e6i 0.758014i 0.925394 + 0.379007i \(0.123734\pi\)
−0.925394 + 0.379007i \(0.876266\pi\)
\(192\) −6.57850e6 −0.929444
\(193\) −2.45643e6 −0.341690 −0.170845 0.985298i \(-0.554650\pi\)
−0.170845 + 0.985298i \(0.554650\pi\)
\(194\) −2.26059e6 −0.309612
\(195\) 3.14423e6i 0.424044i
\(196\) 6.37554e6 0.846738
\(197\) 8.21269e6 1.07420 0.537102 0.843517i \(-0.319519\pi\)
0.537102 + 0.843517i \(0.319519\pi\)
\(198\) −7.85384e6 −1.01178
\(199\) 3.79081e6 0.481030 0.240515 0.970645i \(-0.422684\pi\)
0.240515 + 0.970645i \(0.422684\pi\)
\(200\) 4.87241e6i 0.609051i
\(201\) 1.80439e6i 0.222199i
\(202\) −1.93824e7 −2.35155
\(203\) −3.56939e6 −0.426684
\(204\) 7.51668e6 0.885392
\(205\) −239851. −0.0278407
\(206\) 2.06072e7 2.35731
\(207\) 813415.i 0.0917067i
\(208\) 5.68530e6i 0.631776i
\(209\) 3.42095e6i 0.374720i
\(210\) 2.10387e6i 0.227175i
\(211\) 1.02197e7i 1.08791i 0.839116 + 0.543953i \(0.183073\pi\)
−0.839116 + 0.543953i \(0.816927\pi\)
\(212\) 9.85296e6 1.03409
\(213\) −2.83506e6 −0.293375
\(214\) 1.16101e7i 1.18467i
\(215\) 1.02048e6i 0.102681i
\(216\) 1.39031e6i 0.137959i
\(217\) 6.33432e6i 0.619899i
\(218\) 2.13588e7 2.06162
\(219\) 1.01158e7i 0.963091i
\(220\) 1.16519e7i 1.09428i
\(221\) 2.15126e7i 1.99304i
\(222\) 1.02986e7 0.941277
\(223\) −1.74440e7 −1.57301 −0.786507 0.617582i \(-0.788112\pi\)
−0.786507 + 0.617582i \(0.788112\pi\)
\(224\) 9.01929e6i 0.802469i
\(225\) −3.22588e6 −0.283205
\(226\) 1.56265e7 1.35374
\(227\) 1.44622e7i 1.23640i −0.786022 0.618199i \(-0.787863\pi\)
0.786022 0.618199i \(-0.212137\pi\)
\(228\) 1.92984e6 0.162824
\(229\) 1.71115e7i 1.42489i −0.701727 0.712446i \(-0.747588\pi\)
0.701727 0.712446i \(-0.252412\pi\)
\(230\) −2.03487e6 −0.167245
\(231\) 8.91958e6i 0.723617i
\(232\) 5.90080e6i 0.472549i
\(233\) 2.25364e6i 0.178163i −0.996024 0.0890815i \(-0.971607\pi\)
0.996024 0.0890815i \(-0.0283932\pi\)
\(234\) −1.26802e7 −0.989640
\(235\) 2.90433e6i 0.223791i
\(236\) 4.22989e6 1.86823e7i 0.321805 1.42133i
\(237\) −8.98934e6 −0.675278
\(238\) 1.43945e7i 1.06774i
\(239\) 4.46792e6 0.327274 0.163637 0.986521i \(-0.447677\pi\)
0.163637 + 0.986521i \(0.447677\pi\)
\(240\) 1.03245e6 0.0746853
\(241\) 2.48112e7 1.77255 0.886273 0.463163i \(-0.153286\pi\)
0.886273 + 0.463163i \(0.153286\pi\)
\(242\) 6.10811e7i 4.30984i
\(243\) −920483. −0.0641500
\(244\) 1.42618e7i 0.981758i
\(245\) −3.31360e6 −0.225321
\(246\) 967279.i 0.0649750i
\(247\) 5.52318e6i 0.366520i
\(248\) −1.04717e7 −0.686533
\(249\) 4.93838e6i 0.319879i
\(250\) 1.75684e7i 1.12438i
\(251\) −1.31287e7 −0.830232 −0.415116 0.909769i \(-0.636259\pi\)
−0.415116 + 0.909769i \(0.636259\pi\)
\(252\) 5.03176e6 0.314426
\(253\) −8.62705e6 −0.532722
\(254\) 2.21107e7i 1.34928i
\(255\) −3.90669e6 −0.235607
\(256\) −6.75465e6 −0.402608
\(257\) −3.85412e6 −0.227052 −0.113526 0.993535i \(-0.536215\pi\)
−0.113526 + 0.993535i \(0.536215\pi\)
\(258\) 4.11542e6 0.239638
\(259\) 1.16960e7i 0.673193i
\(260\) 1.88122e7i 1.07034i
\(261\) 3.90675e6 0.219733
\(262\) −1.31801e7 −0.732850
\(263\) −1.01716e7 −0.559141 −0.279570 0.960125i \(-0.590192\pi\)
−0.279570 + 0.960125i \(0.590192\pi\)
\(264\) −1.47456e7 −0.801400
\(265\) −5.12094e6 −0.275177
\(266\) 3.69567e6i 0.196358i
\(267\) 3.24991e6i 0.170741i
\(268\) 1.07958e7i 0.560856i
\(269\) 2.34107e7i 1.20270i −0.798985 0.601350i \(-0.794630\pi\)
0.798985 0.601350i \(-0.205370\pi\)
\(270\) 2.30272e6i 0.116990i
\(271\) 2.23212e7 1.12152 0.560762 0.827977i \(-0.310508\pi\)
0.560762 + 0.827977i \(0.310508\pi\)
\(272\) −7.06395e6 −0.351027
\(273\) 1.44008e7i 0.707782i
\(274\) 2.64349e7i 1.28507i
\(275\) 3.42136e7i 1.64513i
\(276\) 4.86674e6i 0.231479i
\(277\) −2.40338e7 −1.13079 −0.565397 0.824819i \(-0.691277\pi\)
−0.565397 + 0.824819i \(0.691277\pi\)
\(278\) 3.91534e7i 1.82236i
\(279\) 6.93301e6i 0.319234i
\(280\) 3.95001e6i 0.179938i
\(281\) 7.96445e6 0.358953 0.179476 0.983762i \(-0.442560\pi\)
0.179476 + 0.983762i \(0.442560\pi\)
\(282\) −1.17127e7 −0.522287
\(283\) 1.63519e7i 0.721456i −0.932671 0.360728i \(-0.882528\pi\)
0.932671 0.360728i \(-0.117472\pi\)
\(284\) −1.69624e7 −0.740514
\(285\) −1.00301e6 −0.0433281
\(286\) 1.34485e8i 5.74880i
\(287\) 1.09854e6 0.0464695
\(288\) 9.87174e6i 0.413253i
\(289\) 2.59175e6 0.107374
\(290\) 9.77329e6i 0.400725i
\(291\) 2.81000e6i 0.114032i
\(292\) 6.05238e7i 2.43096i
\(293\) 2.31684e7 0.921071 0.460536 0.887641i \(-0.347657\pi\)
0.460536 + 0.887641i \(0.347657\pi\)
\(294\) 1.33632e7i 0.525858i
\(295\) −2.19843e6 + 9.70985e6i −0.0856339 + 0.378222i
\(296\) 1.93355e7 0.745556
\(297\) 9.76261e6i 0.372646i
\(298\) −5.09413e7 −1.92496
\(299\) −1.39285e7 −0.521065
\(300\) −1.93008e7 −0.714843
\(301\) 4.67387e6i 0.171387i
\(302\) 4.73275e7 1.71828
\(303\) 2.40931e7i 0.866093i
\(304\) −1.81361e6 −0.0645539
\(305\) 7.41236e6i 0.261251i
\(306\) 1.57550e7i 0.549864i
\(307\) 3.50205e7 1.21034 0.605170 0.796096i \(-0.293105\pi\)
0.605170 + 0.796096i \(0.293105\pi\)
\(308\) 5.33667e7i 1.82649i
\(309\) 2.56155e7i 0.868216i
\(310\) 1.73439e7 0.582185
\(311\) −2.49635e7 −0.829898 −0.414949 0.909845i \(-0.636201\pi\)
−0.414949 + 0.909845i \(0.636201\pi\)
\(312\) −2.38069e7 −0.783863
\(313\) 9.97787e6i 0.325390i 0.986676 + 0.162695i \(0.0520187\pi\)
−0.986676 + 0.162695i \(0.947981\pi\)
\(314\) −5.42913e7 −1.75364
\(315\) −2.61519e6 −0.0836703
\(316\) −5.37841e7 −1.70448
\(317\) 4.14321e7 1.30065 0.650324 0.759657i \(-0.274633\pi\)
0.650324 + 0.759657i \(0.274633\pi\)
\(318\) 2.06519e7i 0.642212i
\(319\) 4.14349e7i 1.27642i
\(320\) 2.04567e7 0.624289
\(321\) 1.44318e7 0.436321
\(322\) 9.31986e6 0.279153
\(323\) 6.86252e6 0.203646
\(324\) −5.50734e6 −0.161922
\(325\) 5.52385e7i 1.60913i
\(326\) 1.02533e8i 2.95945i
\(327\) 2.65498e7i 0.759309i
\(328\) 1.81606e6i 0.0514646i
\(329\) 1.33021e7i 0.373535i
\(330\) 2.44225e7 0.679593
\(331\) −1.94238e7 −0.535611 −0.267805 0.963473i \(-0.586298\pi\)
−0.267805 + 0.963473i \(0.586298\pi\)
\(332\) 2.95468e7i 0.807413i
\(333\) 1.28015e7i 0.346679i
\(334\) 2.67162e7i 0.717028i
\(335\) 5.61098e6i 0.149246i
\(336\) −4.72870e6 −0.124659
\(337\) 7.24837e7i 1.89387i −0.321422 0.946936i \(-0.604161\pi\)
0.321422 0.946936i \(-0.395839\pi\)
\(338\) 1.56598e8i 4.05542i
\(339\) 1.94243e7i 0.498593i
\(340\) −2.33741e7 −0.594700
\(341\) 7.35313e7 1.85442
\(342\) 4.04497e6i 0.101120i
\(343\) 4.12965e7 1.02337
\(344\) 7.72669e6 0.189809
\(345\) 2.52942e6i 0.0615976i
\(346\) 1.05893e8 2.55646
\(347\) 2.29379e7i 0.548991i 0.961588 + 0.274496i \(0.0885109\pi\)
−0.961588 + 0.274496i \(0.911489\pi\)
\(348\) 2.33745e7 0.554631
\(349\) 3.75880e7i 0.884247i −0.896954 0.442123i \(-0.854225\pi\)
0.896954 0.442123i \(-0.145775\pi\)
\(350\) 3.69612e7i 0.862069i
\(351\) 1.57619e7i 0.364492i
\(352\) 1.04699e8 2.40058
\(353\) 2.25945e7i 0.513663i 0.966456 + 0.256831i \(0.0826785\pi\)
−0.966456 + 0.256831i \(0.917321\pi\)
\(354\) −3.91582e7 8.86589e6i −0.882700 0.199854i
\(355\) 8.81598e6 0.197054
\(356\) 1.94445e7i 0.430971i
\(357\) 1.78929e7 0.393258
\(358\) −5.69609e7 −1.24145
\(359\) −6.84724e7 −1.47990 −0.739950 0.672662i \(-0.765151\pi\)
−0.739950 + 0.672662i \(0.765151\pi\)
\(360\) 4.32334e6i 0.0926642i
\(361\) −4.52840e7 −0.962550
\(362\) 4.09997e7i 0.864282i
\(363\) 7.59261e7 1.58734
\(364\) 8.61615e7i 1.78653i
\(365\) 3.14564e7i 0.646889i
\(366\) −2.98928e7 −0.609711
\(367\) 6.78171e7i 1.37196i −0.727621 0.685980i \(-0.759374\pi\)
0.727621 0.685980i \(-0.240626\pi\)
\(368\) 4.57361e6i 0.0917732i
\(369\) −1.20236e6 −0.0239308
\(370\) −3.20247e7 −0.632237
\(371\) 2.34543e7 0.459304
\(372\) 4.14809e7i 0.805784i
\(373\) 3.72116e6 0.0717053 0.0358527 0.999357i \(-0.488585\pi\)
0.0358527 + 0.999357i \(0.488585\pi\)
\(374\) −1.67097e8 −3.19415
\(375\) 2.18382e7 0.414117
\(376\) −2.19905e7 −0.413687
\(377\) 6.68974e7i 1.24849i
\(378\) 1.05466e7i 0.195271i
\(379\) 5.20364e7 0.955850 0.477925 0.878401i \(-0.341389\pi\)
0.477925 + 0.878401i \(0.341389\pi\)
\(380\) −6.00110e6 −0.109365
\(381\) 2.74844e7 0.496949
\(382\) 6.62363e7 1.18825
\(383\) −3.35438e7 −0.597058 −0.298529 0.954401i \(-0.596496\pi\)
−0.298529 + 0.954401i \(0.596496\pi\)
\(384\) 4.19691e7i 0.741201i
\(385\) 2.77366e7i 0.486039i
\(386\) 3.08052e7i 0.535626i
\(387\) 5.11562e6i 0.0882603i
\(388\) 1.68125e7i 0.287831i
\(389\) −7.19227e7 −1.22185 −0.610924 0.791690i \(-0.709202\pi\)
−0.610924 + 0.791690i \(0.709202\pi\)
\(390\) 3.94306e7 0.664722
\(391\) 1.73061e7i 0.289514i
\(392\) 2.50893e7i 0.416515i
\(393\) 1.63834e7i 0.269914i
\(394\) 1.02992e8i 1.68390i
\(395\) 2.79535e7 0.453571
\(396\) 5.84107e7i 0.940604i
\(397\) 2.23068e7i 0.356505i 0.983985 + 0.178252i \(0.0570443\pi\)
−0.983985 + 0.178252i \(0.942956\pi\)
\(398\) 4.75391e7i 0.754052i
\(399\) 4.59386e6 0.0723200
\(400\) 1.81383e7 0.283410
\(401\) 1.21946e8i 1.89118i 0.325357 + 0.945591i \(0.394516\pi\)
−0.325357 + 0.945591i \(0.605484\pi\)
\(402\) −2.26281e7 −0.348314
\(403\) 1.18718e8 1.81384
\(404\) 1.44151e8i 2.18612i
\(405\) 2.86236e6 0.0430883
\(406\) 4.47624e7i 0.668861i
\(407\) −1.35772e8 −2.01385
\(408\) 2.95800e7i 0.435530i
\(409\) 1.06170e8i 1.55178i 0.630867 + 0.775891i \(0.282699\pi\)
−0.630867 + 0.775891i \(0.717301\pi\)
\(410\) 3.00788e6i 0.0436424i
\(411\) 3.28595e7 0.473299
\(412\) 1.53260e8i 2.19148i
\(413\) 1.00690e7 4.44718e7i 0.142934 0.631299i
\(414\) −1.02007e7 −0.143757
\(415\) 1.53565e7i 0.214857i
\(416\) 1.69039e8 2.34805
\(417\) −4.86691e7 −0.671190
\(418\) −4.29008e7 −0.587404
\(419\) 1.13196e7i 0.153883i 0.997036 + 0.0769415i \(0.0245155\pi\)
−0.997036 + 0.0769415i \(0.975485\pi\)
\(420\) −1.56469e7 −0.211194
\(421\) 8.51436e7i 1.14105i −0.821279 0.570527i \(-0.806739\pi\)
0.821279 0.570527i \(-0.193261\pi\)
\(422\) 1.28161e8 1.70538
\(423\) 1.45593e7i 0.192362i
\(424\) 3.87738e7i 0.508676i
\(425\) −6.86335e7 −0.894066
\(426\) 3.55534e7i 0.459888i
\(427\) 3.39492e7i 0.436060i
\(428\) 8.63470e7 1.10133
\(429\) 1.67170e8 2.11732
\(430\) −1.27974e7 −0.160960
\(431\) 6.60582e7i 0.825078i −0.910940 0.412539i \(-0.864642\pi\)
0.910940 0.412539i \(-0.135358\pi\)
\(432\) 5.17563e6 0.0641966
\(433\) 5.92256e7 0.729534 0.364767 0.931099i \(-0.381149\pi\)
0.364767 + 0.931099i \(0.381149\pi\)
\(434\) −7.94363e7 −0.971740
\(435\) −1.21486e7 −0.147590
\(436\) 1.58850e8i 1.91659i
\(437\) 4.44319e6i 0.0532416i
\(438\) 1.26858e8 1.50972
\(439\) 1.45660e7 0.172165 0.0860826 0.996288i \(-0.472565\pi\)
0.0860826 + 0.996288i \(0.472565\pi\)
\(440\) 4.58532e7 0.538284
\(441\) −1.66109e7 −0.193677
\(442\) −2.69782e8 −3.12425
\(443\) 9.32610e7i 1.07273i 0.843987 + 0.536363i \(0.180202\pi\)
−0.843987 + 0.536363i \(0.819798\pi\)
\(444\) 7.65925e7i 0.875059i
\(445\) 1.01060e7i 0.114683i
\(446\) 2.18759e8i 2.46582i
\(447\) 6.33218e7i 0.708975i
\(448\) −9.36933e7 −1.04202
\(449\) −1.71584e8 −1.89556 −0.947778 0.318930i \(-0.896676\pi\)
−0.947778 + 0.318930i \(0.896676\pi\)
\(450\) 4.04546e7i 0.443946i
\(451\) 1.27522e7i 0.139013i
\(452\) 1.16217e8i 1.25851i
\(453\) 5.88299e7i 0.632854i
\(454\) −1.81366e8 −1.93815
\(455\) 4.47812e7i 0.475403i
\(456\) 7.59441e6i 0.0800939i
\(457\) 1.46508e8i 1.53502i −0.641037 0.767510i \(-0.721496\pi\)
0.641037 0.767510i \(-0.278504\pi\)
\(458\) −2.14589e8 −2.23363
\(459\) −1.95841e7 −0.202519
\(460\) 1.51338e7i 0.155480i
\(461\) −1.66731e8 −1.70182 −0.850912 0.525308i \(-0.823950\pi\)
−0.850912 + 0.525308i \(0.823950\pi\)
\(462\) −1.11857e8 −1.13433
\(463\) 1.07211e8i 1.08018i −0.841608 0.540089i \(-0.818391\pi\)
0.841608 0.540089i \(-0.181609\pi\)
\(464\) −2.19666e7 −0.219892
\(465\) 2.15591e7i 0.214423i
\(466\) −2.82621e7 −0.279285
\(467\) 1.05249e8i 1.03340i −0.856168 0.516698i \(-0.827161\pi\)
0.856168 0.516698i \(-0.172839\pi\)
\(468\) 9.43050e7i 0.920020i
\(469\) 2.56987e7i 0.249111i
\(470\) 3.64221e7 0.350810
\(471\) 6.74861e7i 0.645879i
\(472\) −7.35193e7 1.66457e7i −0.699158 0.158298i
\(473\) −5.42561e7 −0.512702
\(474\) 1.12732e8i 1.05855i
\(475\) −1.76211e7 −0.164419
\(476\) 1.07055e8 0.992629
\(477\) −2.56711e7 −0.236531
\(478\) 5.60305e7i 0.513028i
\(479\) 1.23350e8 1.12237 0.561183 0.827692i \(-0.310347\pi\)
0.561183 + 0.827692i \(0.310347\pi\)
\(480\) 3.06975e7i 0.277574i
\(481\) −2.19207e8 −1.96978
\(482\) 3.11149e8i 2.77860i
\(483\) 1.15849e7i 0.102814i
\(484\) 4.54273e8 4.00665
\(485\) 8.73807e6i 0.0765932i
\(486\) 1.15434e7i 0.100560i
\(487\) −1.98572e7 −0.171922 −0.0859611 0.996298i \(-0.527396\pi\)
−0.0859611 + 0.996298i \(0.527396\pi\)
\(488\) −5.61237e7 −0.482933
\(489\) −1.27452e8 −1.08999
\(490\) 4.15546e7i 0.353208i
\(491\) −1.31211e8 −1.10848 −0.554238 0.832358i \(-0.686990\pi\)
−0.554238 + 0.832358i \(0.686990\pi\)
\(492\) −7.19385e6 −0.0604041
\(493\) 8.31197e7 0.693686
\(494\) −6.92641e7 −0.574549
\(495\) 3.03581e7i 0.250299i
\(496\) 3.89824e7i 0.319465i
\(497\) −4.03779e7 −0.328908
\(498\) 6.19303e7 0.501436
\(499\) −1.87364e8 −1.50794 −0.753972 0.656907i \(-0.771865\pi\)
−0.753972 + 0.656907i \(0.771865\pi\)
\(500\) 1.30660e8 1.04528
\(501\) −3.32093e7 −0.264086
\(502\) 1.64642e8i 1.30145i
\(503\) 1.92336e8i 1.51132i 0.654964 + 0.755660i \(0.272684\pi\)
−0.654964 + 0.755660i \(0.727316\pi\)
\(504\) 1.98012e7i 0.154668i
\(505\) 7.49206e7i 0.581738i
\(506\) 1.08189e8i 0.835084i
\(507\) 1.94657e8 1.49364
\(508\) 1.64442e8 1.25436
\(509\) 9.10904e6i 0.0690748i −0.999403 0.0345374i \(-0.989004\pi\)
0.999403 0.0345374i \(-0.0109958\pi\)
\(510\) 4.89923e7i 0.369333i
\(511\) 1.44073e8i 1.07974i
\(512\) 8.76009e7i 0.652678i
\(513\) −5.02804e6 −0.0372432
\(514\) 4.83330e7i 0.355922i
\(515\) 7.96548e7i 0.583163i
\(516\) 3.06073e7i 0.222780i
\(517\) 1.54415e8 1.11743
\(518\) 1.46676e8 1.05528
\(519\) 1.31629e8i 0.941564i
\(520\) 7.40308e7 0.526505
\(521\) −4.65924e7 −0.329459 −0.164730 0.986339i \(-0.552675\pi\)
−0.164730 + 0.986339i \(0.552675\pi\)
\(522\) 4.89931e7i 0.344448i
\(523\) 1.13804e8 0.795522 0.397761 0.917489i \(-0.369787\pi\)
0.397761 + 0.917489i \(0.369787\pi\)
\(524\) 9.80233e7i 0.681295i
\(525\) −4.59441e7 −0.317506
\(526\) 1.27558e8i 0.876497i
\(527\) 1.47506e8i 1.00781i
\(528\) 5.48926e7i 0.372917i
\(529\) 1.36831e8 0.924309
\(530\) 6.42197e7i 0.431361i
\(531\) −1.10206e7 + 4.86751e7i −0.0736076 + 0.325105i
\(532\) 2.74855e7 0.182544
\(533\) 2.05887e7i 0.135971i
\(534\) −4.07559e7 −0.267650
\(535\) −4.48776e7 −0.293068
\(536\) −4.24842e7 −0.275888
\(537\) 7.08045e7i 0.457233i
\(538\) −2.93585e8 −1.88533
\(539\) 1.76175e8i 1.12507i
\(540\) 1.71258e7 0.108760
\(541\) 2.89674e7i 0.182944i −0.995808 0.0914718i \(-0.970843\pi\)
0.995808 0.0914718i \(-0.0291571\pi\)
\(542\) 2.79921e8i 1.75808i
\(543\) −5.09642e7 −0.318321
\(544\) 2.10030e8i 1.30462i
\(545\) 8.25602e7i 0.510013i
\(546\) −1.80595e8 −1.10950
\(547\) −2.65654e6 −0.0162313 −0.00811567 0.999967i \(-0.502583\pi\)
−0.00811567 + 0.999967i \(0.502583\pi\)
\(548\) 1.96602e8 1.19466
\(549\) 3.71579e7i 0.224561i
\(550\) 4.29060e8 2.57887
\(551\) 2.13402e7 0.127569
\(552\) −1.91518e7 −0.113866
\(553\) −1.28029e8 −0.757066
\(554\) 3.01399e8i 1.77261i
\(555\) 3.98079e7i 0.232857i
\(556\) −2.91192e8 −1.69416
\(557\) 2.85251e8 1.65068 0.825339 0.564638i \(-0.190984\pi\)
0.825339 + 0.564638i \(0.190984\pi\)
\(558\) 8.69442e7 0.500424
\(559\) −8.75975e7 −0.501483
\(560\) 1.47045e7 0.0837310
\(561\) 2.07708e8i 1.17643i
\(562\) 9.98792e7i 0.562686i
\(563\) 4.31220e7i 0.241643i 0.992674 + 0.120821i \(0.0385528\pi\)
−0.992674 + 0.120821i \(0.961447\pi\)
\(564\) 8.71097e7i 0.485544i
\(565\) 6.04024e7i 0.334895i
\(566\) −2.05063e8 −1.13094
\(567\) −1.31098e7 −0.0719197
\(568\) 6.67514e7i 0.364263i
\(569\) 5.01143e7i 0.272035i −0.990706 0.136017i \(-0.956570\pi\)
0.990706 0.136017i \(-0.0434303\pi\)
\(570\) 1.25784e7i 0.0679202i
\(571\) 1.37021e8i 0.736004i 0.929825 + 0.368002i \(0.119958\pi\)
−0.929825 + 0.368002i \(0.880042\pi\)
\(572\) 1.00020e9 5.34438
\(573\) 8.23342e7i 0.437639i
\(574\) 1.37763e7i 0.0728446i
\(575\) 4.44373e7i 0.233746i
\(576\) 1.02549e8 0.536615
\(577\) 1.66358e8 0.865996 0.432998 0.901395i \(-0.357456\pi\)
0.432998 + 0.901395i \(0.357456\pi\)
\(578\) 3.25021e7i 0.168317i
\(579\) 3.82919e7 0.197275
\(580\) −7.26860e7 −0.372535
\(581\) 7.03340e7i 0.358622i
\(582\) 3.52392e7 0.178754
\(583\) 2.72266e8i 1.37401i
\(584\) 2.38176e8 1.19580
\(585\) 4.90137e7i 0.244822i
\(586\) 2.90546e8i 1.44385i
\(587\) 2.97718e8i 1.47194i −0.677012 0.735972i \(-0.736725\pi\)
0.677012 0.735972i \(-0.263275\pi\)
\(588\) −9.93849e7 −0.488864
\(589\) 3.78708e7i 0.185336i
\(590\) 1.21768e8 + 2.75696e7i 0.592892 + 0.134238i
\(591\) −1.28023e8 −0.620192
\(592\) 7.19793e7i 0.346931i
\(593\) 2.48438e8 1.19139 0.595694 0.803211i \(-0.296877\pi\)
0.595694 + 0.803211i \(0.296877\pi\)
\(594\) 1.22429e8 0.584152
\(595\) −5.56404e7 −0.264143
\(596\) 3.78861e8i 1.78954i
\(597\) −5.90928e7 −0.277723
\(598\) 1.74672e8i 0.816810i
\(599\) −9.40947e7 −0.437809 −0.218904 0.975746i \(-0.570248\pi\)
−0.218904 + 0.975746i \(0.570248\pi\)
\(600\) 7.59533e7i 0.351636i
\(601\) 1.55857e8i 0.717965i −0.933344 0.358982i \(-0.883124\pi\)
0.933344 0.358982i \(-0.116876\pi\)
\(602\) 5.86133e7 0.268662
\(603\) 2.81276e7i 0.128286i
\(604\) 3.51985e8i 1.59740i
\(605\) −2.36102e8 −1.06619
\(606\) 3.02142e8 1.35767
\(607\) −4.24758e7 −0.189922 −0.0949611 0.995481i \(-0.530273\pi\)
−0.0949611 + 0.995481i \(0.530273\pi\)
\(608\) 5.39234e7i 0.239920i
\(609\) 5.56414e7 0.246346
\(610\) 9.29557e7 0.409531
\(611\) 2.49306e8 1.09297
\(612\) −1.17173e8 −0.511181
\(613\) 3.73187e8i 1.62011i −0.586353 0.810056i \(-0.699437\pi\)
0.586353 0.810056i \(-0.300563\pi\)
\(614\) 4.39179e8i 1.89730i
\(615\) 3.73890e6 0.0160738
\(616\) −2.10011e8 −0.898463
\(617\) −1.67464e8 −0.712961 −0.356480 0.934303i \(-0.616023\pi\)
−0.356480 + 0.934303i \(0.616023\pi\)
\(618\) −3.21235e8 −1.36100
\(619\) −2.22010e8 −0.936053 −0.468027 0.883714i \(-0.655035\pi\)
−0.468027 + 0.883714i \(0.655035\pi\)
\(620\) 1.28990e8i 0.541229i
\(621\) 1.26799e7i 0.0529469i
\(622\) 3.13058e8i 1.30093i
\(623\) 4.62864e7i 0.191421i
\(624\) 8.86250e7i 0.364756i
\(625\) 1.39517e8 0.571461
\(626\) 1.25129e8 0.510075
\(627\) 5.33273e7i 0.216345i
\(628\) 4.03776e8i 1.63028i
\(629\) 2.72363e8i 1.09445i
\(630\) 3.27961e7i 0.131160i
\(631\) −1.76655e8 −0.703132 −0.351566 0.936163i \(-0.614351\pi\)
−0.351566 + 0.936163i \(0.614351\pi\)
\(632\) 2.11654e8i 0.838445i
\(633\) 1.59309e8i 0.628102i
\(634\) 5.19585e8i 2.03887i
\(635\) −8.54664e7 −0.333791
\(636\) −1.53592e8 −0.597033
\(637\) 2.84438e8i 1.10045i
\(638\) −5.19620e8 −2.00089
\(639\) 4.41942e7 0.169380
\(640\) 1.30508e8i 0.497850i
\(641\) −3.17034e8 −1.20374 −0.601869 0.798595i \(-0.705577\pi\)
−0.601869 + 0.798595i \(0.705577\pi\)
\(642\) 1.80984e8i 0.683967i
\(643\) −2.99097e8 −1.12507 −0.562535 0.826773i \(-0.690174\pi\)
−0.562535 + 0.826773i \(0.690174\pi\)
\(644\) 6.93138e7i 0.259515i
\(645\) 1.59077e7i 0.0592827i
\(646\) 8.60603e7i 0.319231i
\(647\) 1.74573e7 0.0644561 0.0322281 0.999481i \(-0.489740\pi\)
0.0322281 + 0.999481i \(0.489740\pi\)
\(648\) 2.16727e7i 0.0796505i
\(649\) 5.16247e8 + 1.16884e8i 1.88853 + 0.427585i
\(650\) 6.92725e8 2.52244
\(651\) 9.87423e7i 0.357899i
\(652\) −7.62560e8 −2.75126
\(653\) 4.06062e8 1.45832 0.729160 0.684344i \(-0.239911\pi\)
0.729160 + 0.684344i \(0.239911\pi\)
\(654\) −3.32951e8 −1.19028
\(655\) 5.09462e7i 0.181296i
\(656\) 6.76056e6 0.0239481
\(657\) 1.57690e8i 0.556041i
\(658\) −1.66816e8 −0.585545
\(659\) 1.24543e8i 0.435174i −0.976041 0.217587i \(-0.930181\pi\)
0.976041 0.217587i \(-0.0698185\pi\)
\(660\) 1.81636e8i 0.631785i
\(661\) −2.93091e8 −1.01484 −0.507421 0.861698i \(-0.669401\pi\)
−0.507421 + 0.861698i \(0.669401\pi\)
\(662\) 2.43586e8i 0.839611i
\(663\) 3.35349e8i 1.15068i
\(664\) 1.16274e8 0.397171
\(665\) −1.42852e7 −0.0485759
\(666\) −1.60539e8 −0.543446
\(667\) 5.38165e7i 0.181359i
\(668\) −1.98694e8 −0.666586
\(669\) 2.71926e8 0.908180
\(670\) 7.03652e7 0.233955
\(671\) 3.94096e8 1.30447
\(672\) 1.40597e8i 0.463306i
\(673\) 5.89657e7i 0.193443i 0.995311 + 0.0967217i \(0.0308357\pi\)
−0.995311 + 0.0967217i \(0.969164\pi\)
\(674\) −9.08991e8 −2.96879
\(675\) 5.02865e7 0.163509
\(676\) 1.16465e9 3.77013
\(677\) −2.84900e8 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(678\) −2.43593e8 −0.781584
\(679\) 4.00210e7i 0.127844i
\(680\) 9.19829e7i 0.292537i
\(681\) 2.25444e8i 0.713835i
\(682\) 9.22128e8i 2.90695i
\(683\) 7.07388e7i 0.222022i 0.993819 + 0.111011i \(0.0354089\pi\)
−0.993819 + 0.111011i \(0.964591\pi\)
\(684\) −3.00833e7 −0.0940062
\(685\) −1.02181e8 −0.317905
\(686\) 5.17884e8i 1.60421i
\(687\) 2.66742e8i 0.822661i
\(688\) 2.87638e7i 0.0883243i
\(689\) 4.39579e8i 1.34394i
\(690\) 3.17205e7 0.0965590
\(691\) 1.82554e8i 0.553295i −0.960971 0.276648i \(-0.910776\pi\)
0.960971 0.276648i \(-0.0892235\pi\)
\(692\) 7.87550e8i 2.37662i
\(693\) 1.39043e8i 0.417780i
\(694\) 2.87656e8 0.860587
\(695\) 1.51343e8 0.450825
\(696\) 9.19844e7i 0.272826i
\(697\) −2.55813e7 −0.0755483
\(698\) −4.71377e8 −1.38613
\(699\) 3.51308e7i 0.102863i
\(700\) −2.74888e8 −0.801424
\(701\) 1.76642e8i 0.512790i 0.966572 + 0.256395i \(0.0825348\pi\)
−0.966572 + 0.256395i \(0.917465\pi\)
\(702\) 1.97664e8 0.571369
\(703\) 6.99268e7i 0.201269i
\(704\) 1.08763e9i 3.11719i
\(705\) 4.52740e7i 0.129206i
\(706\) 2.83349e8 0.805207
\(707\) 3.43142e8i 0.970993i
\(708\) −6.59375e7 + 2.91228e8i −0.185794 + 0.820603i
\(709\) 1.13091e8 0.317314 0.158657 0.987334i \(-0.449284\pi\)
0.158657 + 0.987334i \(0.449284\pi\)
\(710\) 1.10558e8i 0.308898i
\(711\) 1.40130e8 0.389872
\(712\) −7.65191e7 −0.211997
\(713\) 9.55039e7 0.263483
\(714\) 2.24389e8i 0.616462i
\(715\) −5.19838e8 −1.42216
\(716\) 4.23630e8i 1.15411i
\(717\) −6.96480e7 −0.188952
\(718\) 8.58687e8i 2.31986i
\(719\) 3.86770e8i 1.04056i 0.853997 + 0.520278i \(0.174172\pi\)
−0.853997 + 0.520278i \(0.825828\pi\)
\(720\) −1.60943e7 −0.0431196
\(721\) 3.64825e8i 0.973372i
\(722\) 5.67889e8i 1.50887i
\(723\) −3.86769e8 −1.02338
\(724\) −3.04924e8 −0.803481
\(725\) −2.13428e8 −0.560065
\(726\) 9.52161e8i 2.48829i
\(727\) −4.75413e7 −0.123728 −0.0618640 0.998085i \(-0.519705\pi\)
−0.0618640 + 0.998085i \(0.519705\pi\)
\(728\) −3.39067e8 −0.878802
\(729\) 1.43489e7 0.0370370
\(730\) −3.94483e8 −1.01405
\(731\) 1.08839e8i 0.278634i
\(732\) 2.22319e8i 0.566818i
\(733\) −4.83665e8 −1.22810 −0.614049 0.789268i \(-0.710460\pi\)
−0.614049 + 0.789268i \(0.710460\pi\)
\(734\) −8.50469e8 −2.15065
\(735\) 5.16539e7 0.130089
\(736\) 1.35986e8 0.341083
\(737\) 2.98321e8 0.745214
\(738\) 1.50784e7i 0.0375133i
\(739\) 1.08119e8i 0.267897i −0.990988 0.133949i \(-0.957234\pi\)
0.990988 0.133949i \(-0.0427657\pi\)
\(740\) 2.38174e8i 0.587760i
\(741\) 8.60978e7i 0.211611i
\(742\) 2.94131e8i 0.719995i
\(743\) 4.95229e8 1.20737 0.603684 0.797224i \(-0.293699\pi\)
0.603684 + 0.797224i \(0.293699\pi\)
\(744\) 1.63237e8 0.396370
\(745\) 1.96908e8i 0.476205i
\(746\) 4.66656e7i 0.112404i
\(747\) 7.69817e7i 0.184682i
\(748\) 1.24274e9i 2.96944i
\(749\) 2.05543e8 0.489167
\(750\) 2.73864e8i 0.649160i
\(751\) 6.79194e8i 1.60352i 0.597647 + 0.801759i \(0.296102\pi\)
−0.597647 + 0.801759i \(0.703898\pi\)
\(752\) 8.18630e7i 0.192501i
\(753\) 2.04656e8 0.479335
\(754\) −8.38935e8 −1.95711
\(755\) 1.82939e8i 0.425075i
\(756\) −7.84374e7 −0.181534
\(757\) 2.68360e8 0.618628 0.309314 0.950960i \(-0.399901\pi\)
0.309314 + 0.950960i \(0.399901\pi\)
\(758\) 6.52569e8i 1.49837i
\(759\) 1.34482e8 0.307567
\(760\) 2.36158e7i 0.0537975i
\(761\) −3.16771e8 −0.718772 −0.359386 0.933189i \(-0.617014\pi\)
−0.359386 + 0.933189i \(0.617014\pi\)
\(762\) 3.44672e8i 0.779007i
\(763\) 3.78132e8i 0.851275i
\(764\) 4.92614e8i 1.10465i
\(765\) 6.08993e7 0.136028
\(766\) 4.20661e8i 0.935935i
\(767\) 8.33489e8 + 1.88712e8i 1.84720 + 0.418228i
\(768\) 1.05295e8 0.232446
\(769\) 3.68040e8i 0.809311i −0.914469 0.404656i \(-0.867391\pi\)
0.914469 0.404656i \(-0.132609\pi\)
\(770\) 3.47834e8 0.761904
\(771\) 6.00797e7 0.131089
\(772\) 2.29104e8 0.497945
\(773\) 2.02647e8i 0.438734i −0.975642 0.219367i \(-0.929601\pi\)
0.975642 0.219367i \(-0.0703992\pi\)
\(774\) −6.41531e7 −0.138355
\(775\) 3.78754e8i 0.813678i
\(776\) 6.61614e7 0.141586
\(777\) 1.82323e8i 0.388668i
\(778\) 9.01955e8i 1.91534i
\(779\) −6.56778e6 −0.0138933
\(780\) 2.93254e8i 0.617959i
\(781\) 4.68722e8i 0.983926i
\(782\) −2.17030e8 −0.453836
\(783\) −6.09003e7 −0.126863
\(784\) 9.33989e7 0.193818
\(785\) 2.09857e8i 0.433824i