Properties

Label 177.3.c.a.58.7
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.7
Root \(-1.61360i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.61360i q^{2} +1.73205 q^{3} +1.39629 q^{4} -6.36659 q^{5} -2.79484i q^{6} +6.66564 q^{7} -8.70746i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.61360i q^{2} +1.73205 q^{3} +1.39629 q^{4} -6.36659 q^{5} -2.79484i q^{6} +6.66564 q^{7} -8.70746i q^{8} +3.00000 q^{9} +10.2731i q^{10} -16.0509i q^{11} +2.41844 q^{12} -7.84026i q^{13} -10.7557i q^{14} -11.0272 q^{15} -8.46523 q^{16} +18.9063 q^{17} -4.84081i q^{18} +7.10898 q^{19} -8.88958 q^{20} +11.5452 q^{21} -25.8997 q^{22} +33.6730i q^{23} -15.0818i q^{24} +15.5334 q^{25} -12.6511 q^{26} +5.19615 q^{27} +9.30714 q^{28} -46.2052 q^{29} +17.7936i q^{30} +29.5207i q^{31} -21.1703i q^{32} -27.8009i q^{33} -30.5072i q^{34} -42.4373 q^{35} +4.18886 q^{36} +1.91983i q^{37} -11.4711i q^{38} -13.5797i q^{39} +55.4368i q^{40} +46.4596 q^{41} -18.6294i q^{42} -21.6675i q^{43} -22.4116i q^{44} -19.0998 q^{45} +54.3348 q^{46} +75.3742i q^{47} -14.6622 q^{48} -4.56931 q^{49} -25.0647i q^{50} +32.7466 q^{51} -10.9473i q^{52} +19.5526 q^{53} -8.38452i q^{54} +102.189i q^{55} -58.0408i q^{56} +12.3131 q^{57} +74.5569i q^{58} +(-4.68014 + 58.8141i) q^{59} -15.3972 q^{60} +41.0613i q^{61} +47.6346 q^{62} +19.9969 q^{63} -68.0214 q^{64} +49.9157i q^{65} -44.8597 q^{66} +90.1839i q^{67} +26.3986 q^{68} +58.3233i q^{69} +68.4770i q^{70} +57.1922 q^{71} -26.1224i q^{72} -69.6739i q^{73} +3.09784 q^{74} +26.9047 q^{75} +9.92617 q^{76} -106.989i q^{77} -21.9123 q^{78} +118.749 q^{79} +53.8946 q^{80} +9.00000 q^{81} -74.9673i q^{82} -86.3181i q^{83} +16.1204 q^{84} -120.368 q^{85} -34.9627 q^{86} -80.0298 q^{87} -139.762 q^{88} -38.4935i q^{89} +30.8194i q^{90} -52.2603i q^{91} +47.0172i q^{92} +51.1313i q^{93} +121.624 q^{94} -45.2599 q^{95} -36.6681i q^{96} +24.0445i q^{97} +7.37305i q^{98} -48.1526i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61360i 0.806801i −0.915023 0.403401i \(-0.867828\pi\)
0.915023 0.403401i \(-0.132172\pi\)
\(3\) 1.73205 0.577350
\(4\) 1.39629 0.349072
\(5\) −6.36659 −1.27332 −0.636659 0.771146i \(-0.719684\pi\)
−0.636659 + 0.771146i \(0.719684\pi\)
\(6\) 2.79484i 0.465807i
\(7\) 6.66564 0.952234 0.476117 0.879382i \(-0.342044\pi\)
0.476117 + 0.879382i \(0.342044\pi\)
\(8\) 8.70746i 1.08843i
\(9\) 3.00000 0.333333
\(10\) 10.2731i 1.02731i
\(11\) 16.0509i 1.45917i −0.683890 0.729586i \(-0.739713\pi\)
0.683890 0.729586i \(-0.260287\pi\)
\(12\) 2.41844 0.201537
\(13\) 7.84026i 0.603097i −0.953451 0.301548i \(-0.902497\pi\)
0.953451 0.301548i \(-0.0975035\pi\)
\(14\) 10.7557i 0.768263i
\(15\) −11.0272 −0.735150
\(16\) −8.46523 −0.529077
\(17\) 18.9063 1.11213 0.556067 0.831137i \(-0.312310\pi\)
0.556067 + 0.831137i \(0.312310\pi\)
\(18\) 4.84081i 0.268934i
\(19\) 7.10898 0.374157 0.187078 0.982345i \(-0.440098\pi\)
0.187078 + 0.982345i \(0.440098\pi\)
\(20\) −8.88958 −0.444479
\(21\) 11.5452 0.549772
\(22\) −25.8997 −1.17726
\(23\) 33.6730i 1.46404i 0.681282 + 0.732021i \(0.261423\pi\)
−0.681282 + 0.732021i \(0.738577\pi\)
\(24\) 15.0818i 0.628407i
\(25\) 15.5334 0.621336
\(26\) −12.6511 −0.486579
\(27\) 5.19615 0.192450
\(28\) 9.30714 0.332398
\(29\) −46.2052 −1.59328 −0.796642 0.604451i \(-0.793392\pi\)
−0.796642 + 0.604451i \(0.793392\pi\)
\(30\) 17.7936i 0.593120i
\(31\) 29.5207i 0.952280i 0.879369 + 0.476140i \(0.157964\pi\)
−0.879369 + 0.476140i \(0.842036\pi\)
\(32\) 21.1703i 0.661573i
\(33\) 27.8009i 0.842453i
\(34\) 30.5072i 0.897271i
\(35\) −42.4373 −1.21250
\(36\) 4.18886 0.116357
\(37\) 1.91983i 0.0518873i 0.999663 + 0.0259437i \(0.00825905\pi\)
−0.999663 + 0.0259437i \(0.991741\pi\)
\(38\) 11.4711i 0.301870i
\(39\) 13.5797i 0.348198i
\(40\) 55.4368i 1.38592i
\(41\) 46.4596 1.13316 0.566580 0.824007i \(-0.308266\pi\)
0.566580 + 0.824007i \(0.308266\pi\)
\(42\) 18.6294i 0.443557i
\(43\) 21.6675i 0.503895i −0.967741 0.251947i \(-0.918929\pi\)
0.967741 0.251947i \(-0.0810710\pi\)
\(44\) 22.4116i 0.509355i
\(45\) −19.0998 −0.424439
\(46\) 54.3348 1.18119
\(47\) 75.3742i 1.60371i 0.597521 + 0.801853i \(0.296152\pi\)
−0.597521 + 0.801853i \(0.703848\pi\)
\(48\) −14.6622 −0.305463
\(49\) −4.56931 −0.0932512
\(50\) 25.0647i 0.501295i
\(51\) 32.7466 0.642091
\(52\) 10.9473i 0.210524i
\(53\) 19.5526 0.368916 0.184458 0.982840i \(-0.440947\pi\)
0.184458 + 0.982840i \(0.440947\pi\)
\(54\) 8.38452i 0.155269i
\(55\) 102.189i 1.85799i
\(56\) 58.0408i 1.03644i
\(57\) 12.3131 0.216019
\(58\) 74.5569i 1.28546i
\(59\) −4.68014 + 58.8141i −0.0793243 + 0.996849i
\(60\) −15.3972 −0.256620
\(61\) 41.0613i 0.673136i 0.941659 + 0.336568i \(0.109266\pi\)
−0.941659 + 0.336568i \(0.890734\pi\)
\(62\) 47.6346 0.768301
\(63\) 19.9969 0.317411
\(64\) −68.0214 −1.06283
\(65\) 49.9157i 0.767934i
\(66\) −44.8597 −0.679692
\(67\) 90.1839i 1.34603i 0.739630 + 0.673014i \(0.235001\pi\)
−0.739630 + 0.673014i \(0.764999\pi\)
\(68\) 26.3986 0.388215
\(69\) 58.3233i 0.845266i
\(70\) 68.4770i 0.978243i
\(71\) 57.1922 0.805523 0.402762 0.915305i \(-0.368050\pi\)
0.402762 + 0.915305i \(0.368050\pi\)
\(72\) 26.1224i 0.362811i
\(73\) 69.6739i 0.954436i −0.878785 0.477218i \(-0.841645\pi\)
0.878785 0.477218i \(-0.158355\pi\)
\(74\) 3.09784 0.0418628
\(75\) 26.9047 0.358729
\(76\) 9.92617 0.130608
\(77\) 106.989i 1.38947i
\(78\) −21.9123 −0.280927
\(79\) 118.749 1.50315 0.751575 0.659647i \(-0.229294\pi\)
0.751575 + 0.659647i \(0.229294\pi\)
\(80\) 53.8946 0.673683
\(81\) 9.00000 0.111111
\(82\) 74.9673i 0.914235i
\(83\) 86.3181i 1.03998i −0.854173 0.519988i \(-0.825936\pi\)
0.854173 0.519988i \(-0.174064\pi\)
\(84\) 16.1204 0.191910
\(85\) −120.368 −1.41610
\(86\) −34.9627 −0.406543
\(87\) −80.0298 −0.919883
\(88\) −139.762 −1.58821
\(89\) 38.4935i 0.432512i −0.976337 0.216256i \(-0.930615\pi\)
0.976337 0.216256i \(-0.0693845\pi\)
\(90\) 30.8194i 0.342438i
\(91\) 52.2603i 0.574289i
\(92\) 47.0172i 0.511056i
\(93\) 51.1313i 0.549799i
\(94\) 121.624 1.29387
\(95\) −45.2599 −0.476420
\(96\) 36.6681i 0.381959i
\(97\) 24.0445i 0.247881i 0.992290 + 0.123941i \(0.0395532\pi\)
−0.992290 + 0.123941i \(0.960447\pi\)
\(98\) 7.37305i 0.0752352i
\(99\) 48.1526i 0.486390i
\(100\) 21.6891 0.216891
\(101\) 56.4784i 0.559192i −0.960118 0.279596i \(-0.909799\pi\)
0.960118 0.279596i \(-0.0902006\pi\)
\(102\) 52.8401i 0.518040i
\(103\) 99.6967i 0.967929i −0.875088 0.483964i \(-0.839196\pi\)
0.875088 0.483964i \(-0.160804\pi\)
\(104\) −68.2688 −0.656430
\(105\) −73.5036 −0.700034
\(106\) 31.5500i 0.297642i
\(107\) −193.034 −1.80406 −0.902030 0.431673i \(-0.857924\pi\)
−0.902030 + 0.431673i \(0.857924\pi\)
\(108\) 7.25532 0.0671789
\(109\) 65.4956i 0.600877i 0.953801 + 0.300439i \(0.0971330\pi\)
−0.953801 + 0.300439i \(0.902867\pi\)
\(110\) 164.893 1.49903
\(111\) 3.32524i 0.0299572i
\(112\) −56.4262 −0.503805
\(113\) 169.975i 1.50420i 0.659048 + 0.752101i \(0.270959\pi\)
−0.659048 + 0.752101i \(0.729041\pi\)
\(114\) 19.8685i 0.174285i
\(115\) 214.382i 1.86419i
\(116\) −64.5158 −0.556171
\(117\) 23.5208i 0.201032i
\(118\) 94.9025 + 7.55188i 0.804259 + 0.0639990i
\(119\) 126.022 1.05901
\(120\) 96.0194i 0.800161i
\(121\) −136.631 −1.12918
\(122\) 66.2566 0.543087
\(123\) 80.4704 0.654231
\(124\) 41.2194i 0.332414i
\(125\) 60.2699 0.482159
\(126\) 32.2671i 0.256088i
\(127\) −166.750 −1.31299 −0.656495 0.754331i \(-0.727962\pi\)
−0.656495 + 0.754331i \(0.727962\pi\)
\(128\) 25.0782i 0.195924i
\(129\) 37.5292i 0.290924i
\(130\) 80.5441 0.619570
\(131\) 45.5267i 0.347532i −0.984787 0.173766i \(-0.944406\pi\)
0.984787 0.173766i \(-0.0555936\pi\)
\(132\) 38.8181i 0.294077i
\(133\) 47.3859 0.356285
\(134\) 145.521 1.08598
\(135\) −33.0817 −0.245050
\(136\) 164.626i 1.21048i
\(137\) −106.697 −0.778807 −0.389404 0.921067i \(-0.627319\pi\)
−0.389404 + 0.921067i \(0.627319\pi\)
\(138\) 94.1107 0.681961
\(139\) −133.637 −0.961414 −0.480707 0.876881i \(-0.659620\pi\)
−0.480707 + 0.876881i \(0.659620\pi\)
\(140\) −59.2547 −0.423248
\(141\) 130.552i 0.925900i
\(142\) 92.2854i 0.649897i
\(143\) −125.843 −0.880022
\(144\) −25.3957 −0.176359
\(145\) 294.170 2.02876
\(146\) −112.426 −0.770040
\(147\) −7.91428 −0.0538386
\(148\) 2.68064i 0.0181124i
\(149\) 118.228i 0.793478i 0.917931 + 0.396739i \(0.129858\pi\)
−0.917931 + 0.396739i \(0.870142\pi\)
\(150\) 43.4134i 0.289423i
\(151\) 221.371i 1.46603i −0.680212 0.733015i \(-0.738112\pi\)
0.680212 0.733015i \(-0.261888\pi\)
\(152\) 61.9012i 0.407244i
\(153\) 56.7189 0.370711
\(154\) −172.638 −1.12103
\(155\) 187.946i 1.21255i
\(156\) 18.9612i 0.121546i
\(157\) 13.3063i 0.0847535i −0.999102 0.0423768i \(-0.986507\pi\)
0.999102 0.0423768i \(-0.0134930\pi\)
\(158\) 191.614i 1.21274i
\(159\) 33.8660 0.212994
\(160\) 134.783i 0.842392i
\(161\) 224.452i 1.39411i
\(162\) 14.5224i 0.0896446i
\(163\) 227.187 1.39378 0.696891 0.717177i \(-0.254566\pi\)
0.696891 + 0.717177i \(0.254566\pi\)
\(164\) 64.8709 0.395554
\(165\) 176.997i 1.07271i
\(166\) −139.283 −0.839055
\(167\) 176.740 1.05832 0.529162 0.848521i \(-0.322506\pi\)
0.529162 + 0.848521i \(0.322506\pi\)
\(168\) 100.530i 0.598390i
\(169\) 107.530 0.636274
\(170\) 194.227i 1.14251i
\(171\) 21.3269 0.124719
\(172\) 30.2540i 0.175895i
\(173\) 184.896i 1.06876i −0.845244 0.534381i \(-0.820545\pi\)
0.845244 0.534381i \(-0.179455\pi\)
\(174\) 129.136i 0.742163i
\(175\) 103.540 0.591657
\(176\) 135.874i 0.772014i
\(177\) −8.10623 + 101.869i −0.0457979 + 0.575531i
\(178\) −62.1133 −0.348951
\(179\) 290.925i 1.62528i 0.582765 + 0.812641i \(0.301971\pi\)
−0.582765 + 0.812641i \(0.698029\pi\)
\(180\) −26.6687 −0.148160
\(181\) 71.9948 0.397761 0.198881 0.980024i \(-0.436269\pi\)
0.198881 + 0.980024i \(0.436269\pi\)
\(182\) −84.3274 −0.463337
\(183\) 71.1203i 0.388635i
\(184\) 293.206 1.59351
\(185\) 12.2228i 0.0660690i
\(186\) 82.5056 0.443579
\(187\) 303.463i 1.62279i
\(188\) 105.244i 0.559809i
\(189\) 34.6357 0.183257
\(190\) 73.0315i 0.384376i
\(191\) 169.923i 0.889651i 0.895617 + 0.444825i \(0.146734\pi\)
−0.895617 + 0.444825i \(0.853266\pi\)
\(192\) −117.817 −0.613628
\(193\) −15.6413 −0.0810432 −0.0405216 0.999179i \(-0.512902\pi\)
−0.0405216 + 0.999179i \(0.512902\pi\)
\(194\) 38.7982 0.199991
\(195\) 86.4565i 0.443367i
\(196\) −6.38007 −0.0325514
\(197\) −100.597 −0.510645 −0.255323 0.966856i \(-0.582182\pi\)
−0.255323 + 0.966856i \(0.582182\pi\)
\(198\) −77.6992 −0.392420
\(199\) −84.4909 −0.424577 −0.212289 0.977207i \(-0.568092\pi\)
−0.212289 + 0.977207i \(0.568092\pi\)
\(200\) 135.257i 0.676283i
\(201\) 156.203i 0.777129i
\(202\) −91.1337 −0.451157
\(203\) −307.987 −1.51718
\(204\) 45.7237 0.224136
\(205\) −295.789 −1.44287
\(206\) −160.871 −0.780926
\(207\) 101.019i 0.488014i
\(208\) 66.3696i 0.319085i
\(209\) 114.105i 0.545959i
\(210\) 118.606i 0.564789i
\(211\) 307.104i 1.45547i −0.685859 0.727735i \(-0.740573\pi\)
0.685859 0.727735i \(-0.259427\pi\)
\(212\) 27.3010 0.128778
\(213\) 99.0597 0.465069
\(214\) 311.481i 1.45552i
\(215\) 137.948i 0.641618i
\(216\) 45.2453i 0.209469i
\(217\) 196.774i 0.906793i
\(218\) 105.684 0.484788
\(219\) 120.679i 0.551044i
\(220\) 142.686i 0.648571i
\(221\) 148.230i 0.670725i
\(222\) 5.36562 0.0241695
\(223\) −334.093 −1.49818 −0.749088 0.662471i \(-0.769508\pi\)
−0.749088 + 0.662471i \(0.769508\pi\)
\(224\) 141.114i 0.629972i
\(225\) 46.6002 0.207112
\(226\) 274.272 1.21359
\(227\) 194.419i 0.856471i −0.903667 0.428236i \(-0.859135\pi\)
0.903667 0.428236i \(-0.140865\pi\)
\(228\) 17.1926 0.0754063
\(229\) 198.825i 0.868230i 0.900857 + 0.434115i \(0.142939\pi\)
−0.900857 + 0.434115i \(0.857061\pi\)
\(230\) −345.927 −1.50403
\(231\) 185.311i 0.802212i
\(232\) 402.330i 1.73418i
\(233\) 268.492i 1.15233i 0.817335 + 0.576163i \(0.195450\pi\)
−0.817335 + 0.576163i \(0.804550\pi\)
\(234\) −37.9532 −0.162193
\(235\) 479.876i 2.04203i
\(236\) −6.53481 + 82.1213i −0.0276899 + 0.347972i
\(237\) 205.679 0.867844
\(238\) 203.350i 0.854412i
\(239\) 321.465 1.34504 0.672522 0.740077i \(-0.265211\pi\)
0.672522 + 0.740077i \(0.265211\pi\)
\(240\) 93.3482 0.388951
\(241\) −44.9975 −0.186712 −0.0933559 0.995633i \(-0.529759\pi\)
−0.0933559 + 0.995633i \(0.529759\pi\)
\(242\) 220.468i 0.911024i
\(243\) 15.5885 0.0641500
\(244\) 57.3334i 0.234973i
\(245\) 29.0909 0.118738
\(246\) 129.847i 0.527834i
\(247\) 55.7362i 0.225653i
\(248\) 257.050 1.03649
\(249\) 149.507i 0.600431i
\(250\) 97.2516i 0.389006i
\(251\) 307.277 1.22421 0.612105 0.790776i \(-0.290323\pi\)
0.612105 + 0.790776i \(0.290323\pi\)
\(252\) 27.9214 0.110799
\(253\) 540.481 2.13629
\(254\) 269.068i 1.05932i
\(255\) −208.484 −0.817586
\(256\) −231.619 −0.904763
\(257\) −269.259 −1.04770 −0.523850 0.851811i \(-0.675505\pi\)
−0.523850 + 0.851811i \(0.675505\pi\)
\(258\) −60.5572 −0.234718
\(259\) 12.7969i 0.0494089i
\(260\) 69.6966i 0.268064i
\(261\) −138.616 −0.531095
\(262\) −73.4619 −0.280389
\(263\) −294.101 −1.11825 −0.559127 0.829082i \(-0.688864\pi\)
−0.559127 + 0.829082i \(0.688864\pi\)
\(264\) −242.076 −0.916953
\(265\) −124.483 −0.469747
\(266\) 76.4619i 0.287451i
\(267\) 66.6728i 0.249711i
\(268\) 125.923i 0.469860i
\(269\) 52.5633i 0.195403i 0.995216 + 0.0977013i \(0.0311490\pi\)
−0.995216 + 0.0977013i \(0.968851\pi\)
\(270\) 53.3808i 0.197707i
\(271\) −63.5650 −0.234557 −0.117279 0.993099i \(-0.537417\pi\)
−0.117279 + 0.993099i \(0.537417\pi\)
\(272\) −160.046 −0.588405
\(273\) 90.5175i 0.331566i
\(274\) 172.166i 0.628343i
\(275\) 249.325i 0.906636i
\(276\) 81.4361i 0.295058i
\(277\) −76.0155 −0.274424 −0.137212 0.990542i \(-0.543814\pi\)
−0.137212 + 0.990542i \(0.543814\pi\)
\(278\) 215.636i 0.775670i
\(279\) 88.5620i 0.317427i
\(280\) 369.521i 1.31972i
\(281\) 146.718 0.522127 0.261063 0.965322i \(-0.415927\pi\)
0.261063 + 0.965322i \(0.415927\pi\)
\(282\) 210.659 0.747017
\(283\) 497.505i 1.75797i −0.476850 0.878985i \(-0.658221\pi\)
0.476850 0.878985i \(-0.341779\pi\)
\(284\) 79.8567 0.281185
\(285\) −78.3925 −0.275061
\(286\) 203.061i 0.710002i
\(287\) 309.683 1.07903
\(288\) 63.5110i 0.220524i
\(289\) 68.4476 0.236843
\(290\) 474.673i 1.63680i
\(291\) 41.6462i 0.143114i
\(292\) 97.2847i 0.333167i
\(293\) 158.624 0.541378 0.270689 0.962667i \(-0.412749\pi\)
0.270689 + 0.962667i \(0.412749\pi\)
\(294\) 12.7705i 0.0434371i
\(295\) 29.7965 374.445i 0.101005 1.26930i
\(296\) 16.7169 0.0564759
\(297\) 83.4028i 0.280818i
\(298\) 190.773 0.640179
\(299\) 264.005 0.882960
\(300\) 37.5666 0.125222
\(301\) 144.428i 0.479826i
\(302\) −357.204 −1.18280
\(303\) 97.8235i 0.322850i
\(304\) −60.1792 −0.197958
\(305\) 261.420i 0.857116i
\(306\) 91.5217i 0.299090i
\(307\) 302.624 0.985747 0.492873 0.870101i \(-0.335947\pi\)
0.492873 + 0.870101i \(0.335947\pi\)
\(308\) 149.388i 0.485025i
\(309\) 172.680i 0.558834i
\(310\) −303.270 −0.978290
\(311\) 545.048 1.75257 0.876283 0.481798i \(-0.160016\pi\)
0.876283 + 0.481798i \(0.160016\pi\)
\(312\) −118.245 −0.378990
\(313\) 378.973i 1.21078i 0.795931 + 0.605388i \(0.206982\pi\)
−0.795931 + 0.605388i \(0.793018\pi\)
\(314\) −21.4711 −0.0683792
\(315\) −127.312 −0.404165
\(316\) 165.808 0.524708
\(317\) −400.912 −1.26471 −0.632354 0.774680i \(-0.717911\pi\)
−0.632354 + 0.774680i \(0.717911\pi\)
\(318\) 54.6463i 0.171844i
\(319\) 741.635i 2.32487i
\(320\) 433.064 1.35333
\(321\) −334.346 −1.04157
\(322\) 362.176 1.12477
\(323\) 134.404 0.416113
\(324\) 12.5666 0.0387858
\(325\) 121.786i 0.374726i
\(326\) 366.589i 1.12451i
\(327\) 113.442i 0.346917i
\(328\) 404.545i 1.23337i
\(329\) 502.417i 1.52710i
\(330\) 285.603 0.865463
\(331\) −256.922 −0.776199 −0.388099 0.921618i \(-0.626868\pi\)
−0.388099 + 0.921618i \(0.626868\pi\)
\(332\) 120.525i 0.363027i
\(333\) 5.75949i 0.0172958i
\(334\) 285.188i 0.853857i
\(335\) 574.163i 1.71392i
\(336\) −97.7330 −0.290872
\(337\) 519.832i 1.54253i −0.636516 0.771264i \(-0.719625\pi\)
0.636516 0.771264i \(-0.280375\pi\)
\(338\) 173.511i 0.513347i
\(339\) 294.405i 0.868451i
\(340\) −168.069 −0.494320
\(341\) 473.833 1.38954
\(342\) 34.4132i 0.100623i
\(343\) −357.073 −1.04103
\(344\) −188.669 −0.548456
\(345\) 371.320i 1.07629i
\(346\) −298.349 −0.862279
\(347\) 144.710i 0.417032i 0.978019 + 0.208516i \(0.0668633\pi\)
−0.978019 + 0.208516i \(0.933137\pi\)
\(348\) −111.745 −0.321105
\(349\) 444.542i 1.27376i 0.770963 + 0.636880i \(0.219775\pi\)
−0.770963 + 0.636880i \(0.780225\pi\)
\(350\) 167.072i 0.477350i
\(351\) 40.7392i 0.116066i
\(352\) −339.802 −0.965348
\(353\) 625.820i 1.77286i −0.462863 0.886430i \(-0.653178\pi\)
0.462863 0.886430i \(-0.346822\pi\)
\(354\) 164.376 + 13.0802i 0.464339 + 0.0369498i
\(355\) −364.119 −1.02569
\(356\) 53.7480i 0.150978i
\(357\) 218.277 0.611421
\(358\) 469.438 1.31128
\(359\) −351.287 −0.978517 −0.489258 0.872139i \(-0.662732\pi\)
−0.489258 + 0.872139i \(0.662732\pi\)
\(360\) 166.310i 0.461973i
\(361\) −310.462 −0.860007
\(362\) 116.171i 0.320914i
\(363\) −236.652 −0.651933
\(364\) 72.9704i 0.200468i
\(365\) 443.585i 1.21530i
\(366\) 114.760 0.313551
\(367\) 221.302i 0.603002i −0.953466 0.301501i \(-0.902512\pi\)
0.953466 0.301501i \(-0.0974877\pi\)
\(368\) 285.050i 0.774592i
\(369\) 139.379 0.377720
\(370\) −19.7227 −0.0533046
\(371\) 130.330 0.351294
\(372\) 71.3940i 0.191919i
\(373\) −159.549 −0.427745 −0.213873 0.976862i \(-0.568608\pi\)
−0.213873 + 0.976862i \(0.568608\pi\)
\(374\) −489.668 −1.30927
\(375\) 104.390 0.278375
\(376\) 656.318 1.74553
\(377\) 362.261i 0.960905i
\(378\) 55.8882i 0.147852i
\(379\) 264.069 0.696752 0.348376 0.937355i \(-0.386733\pi\)
0.348376 + 0.937355i \(0.386733\pi\)
\(380\) −63.1958 −0.166305
\(381\) −288.819 −0.758055
\(382\) 274.189 0.717771
\(383\) −89.2279 −0.232971 −0.116486 0.993192i \(-0.537163\pi\)
−0.116486 + 0.993192i \(0.537163\pi\)
\(384\) 43.4368i 0.113117i
\(385\) 681.157i 1.76924i
\(386\) 25.2389i 0.0653857i
\(387\) 65.0024i 0.167965i
\(388\) 33.5730i 0.0865283i
\(389\) −161.318 −0.414699 −0.207350 0.978267i \(-0.566484\pi\)
−0.207350 + 0.978267i \(0.566484\pi\)
\(390\) 139.506 0.357709
\(391\) 636.631i 1.62821i
\(392\) 39.7871i 0.101498i
\(393\) 78.8545i 0.200648i
\(394\) 162.324i 0.411989i
\(395\) −756.025 −1.91399
\(396\) 67.2349i 0.169785i
\(397\) 519.713i 1.30910i 0.756018 + 0.654551i \(0.227142\pi\)
−0.756018 + 0.654551i \(0.772858\pi\)
\(398\) 136.335i 0.342549i
\(399\) 82.0747 0.205701
\(400\) −131.494 −0.328735
\(401\) 550.540i 1.37292i −0.727169 0.686459i \(-0.759164\pi\)
0.727169 0.686459i \(-0.240836\pi\)
\(402\) 252.050 0.626989
\(403\) 231.450 0.574317
\(404\) 78.8601i 0.195198i
\(405\) −57.2993 −0.141480
\(406\) 496.969i 1.22406i
\(407\) 30.8150 0.0757125
\(408\) 285.140i 0.698873i
\(409\) 17.8723i 0.0436976i 0.999761 + 0.0218488i \(0.00695524\pi\)
−0.999761 + 0.0218488i \(0.993045\pi\)
\(410\) 477.286i 1.16411i
\(411\) −184.804 −0.449645
\(412\) 139.205i 0.337877i
\(413\) −31.1961 + 392.033i −0.0755353 + 0.949233i
\(414\) 163.004 0.393731
\(415\) 549.551i 1.32422i
\(416\) −165.981 −0.398992
\(417\) −231.465 −0.555072
\(418\) −184.121 −0.440480
\(419\) 18.7816i 0.0448248i 0.999749 + 0.0224124i \(0.00713469\pi\)
−0.999749 + 0.0224124i \(0.992865\pi\)
\(420\) −102.632 −0.244362
\(421\) 561.743i 1.33431i 0.744920 + 0.667153i \(0.232487\pi\)
−0.744920 + 0.667153i \(0.767513\pi\)
\(422\) −495.544 −1.17427
\(423\) 226.123i 0.534569i
\(424\) 170.253i 0.401540i
\(425\) 293.679 0.691010
\(426\) 159.843i 0.375218i
\(427\) 273.700i 0.640983i
\(428\) −269.532 −0.629747
\(429\) −217.967 −0.508081
\(430\) 222.593 0.517658
\(431\) 43.8318i 0.101698i −0.998706 0.0508490i \(-0.983807\pi\)
0.998706 0.0508490i \(-0.0161927\pi\)
\(432\) −43.9866 −0.101821
\(433\) 100.552 0.232221 0.116111 0.993236i \(-0.462957\pi\)
0.116111 + 0.993236i \(0.462957\pi\)
\(434\) 317.515 0.731602
\(435\) 509.517 1.17130
\(436\) 91.4507i 0.209749i
\(437\) 239.381i 0.547781i
\(438\) −194.727 −0.444583
\(439\) 580.171 1.32157 0.660787 0.750573i \(-0.270223\pi\)
0.660787 + 0.750573i \(0.270223\pi\)
\(440\) 889.810 2.02229
\(441\) −13.7079 −0.0310837
\(442\) −239.185 −0.541142
\(443\) 763.409i 1.72327i −0.507528 0.861635i \(-0.669441\pi\)
0.507528 0.861635i \(-0.330559\pi\)
\(444\) 4.64300i 0.0104572i
\(445\) 245.072i 0.550724i
\(446\) 539.093i 1.20873i
\(447\) 204.777i 0.458115i
\(448\) −453.406 −1.01207
\(449\) 350.584 0.780810 0.390405 0.920643i \(-0.372335\pi\)
0.390405 + 0.920643i \(0.372335\pi\)
\(450\) 75.1942i 0.167098i
\(451\) 745.717i 1.65348i
\(452\) 237.334i 0.525074i
\(453\) 383.425i 0.846413i
\(454\) −313.715 −0.691002
\(455\) 332.720i 0.731252i
\(456\) 107.216i 0.235123i
\(457\) 627.986i 1.37415i −0.726587 0.687075i \(-0.758894\pi\)
0.726587 0.687075i \(-0.241106\pi\)
\(458\) 320.824 0.700489
\(459\) 98.2399 0.214030
\(460\) 299.339i 0.650736i
\(461\) 602.743 1.30747 0.653735 0.756724i \(-0.273201\pi\)
0.653735 + 0.756724i \(0.273201\pi\)
\(462\) −299.018 −0.647226
\(463\) 340.754i 0.735969i −0.929832 0.367985i \(-0.880048\pi\)
0.929832 0.367985i \(-0.119952\pi\)
\(464\) 391.138 0.842970
\(465\) 325.532i 0.700069i
\(466\) 433.239 0.929697
\(467\) 682.672i 1.46182i 0.682471 + 0.730912i \(0.260905\pi\)
−0.682471 + 0.730912i \(0.739095\pi\)
\(468\) 32.8418i 0.0701747i
\(469\) 601.133i 1.28173i
\(470\) −774.329 −1.64751
\(471\) 23.0472i 0.0489325i
\(472\) 512.121 + 40.7521i 1.08500 + 0.0863392i
\(473\) −347.782 −0.735269
\(474\) 331.884i 0.700178i
\(475\) 110.427 0.232477
\(476\) 175.963 0.369671
\(477\) 58.6577 0.122972
\(478\) 518.717i 1.08518i
\(479\) −757.928 −1.58231 −0.791156 0.611614i \(-0.790520\pi\)
−0.791156 + 0.611614i \(0.790520\pi\)
\(480\) 233.450i 0.486355i
\(481\) 15.0520 0.0312931
\(482\) 72.6081i 0.150639i
\(483\) 388.762i 0.804890i
\(484\) −190.776 −0.394165
\(485\) 153.081i 0.315631i
\(486\) 25.1536i 0.0517563i
\(487\) −105.431 −0.216491 −0.108246 0.994124i \(-0.534523\pi\)
−0.108246 + 0.994124i \(0.534523\pi\)
\(488\) 357.540 0.732663
\(489\) 393.499 0.804701
\(490\) 46.9411i 0.0957983i
\(491\) −603.562 −1.22925 −0.614625 0.788820i \(-0.710693\pi\)
−0.614625 + 0.788820i \(0.710693\pi\)
\(492\) 112.360 0.228373
\(493\) −873.570 −1.77195
\(494\) −89.9361 −0.182057
\(495\) 306.568i 0.619329i
\(496\) 249.899i 0.503830i
\(497\) 381.222 0.767046
\(498\) −241.245 −0.484428
\(499\) 308.346 0.617928 0.308964 0.951074i \(-0.400018\pi\)
0.308964 + 0.951074i \(0.400018\pi\)
\(500\) 84.1540 0.168308
\(501\) 306.123 0.611023
\(502\) 495.823i 0.987695i
\(503\) 6.39623i 0.0127162i 0.999980 + 0.00635809i \(0.00202386\pi\)
−0.999980 + 0.00635809i \(0.997976\pi\)
\(504\) 174.122i 0.345481i
\(505\) 359.575i 0.712029i
\(506\) 872.122i 1.72356i
\(507\) 186.248 0.367353
\(508\) −232.830 −0.458328
\(509\) 243.213i 0.477826i −0.971041 0.238913i \(-0.923209\pi\)
0.971041 0.238913i \(-0.0767911\pi\)
\(510\) 336.411i 0.659629i
\(511\) 464.420i 0.908846i
\(512\) 474.055i 0.925888i
\(513\) 36.9393 0.0720065
\(514\) 434.477i 0.845285i
\(515\) 634.727i 1.23248i
\(516\) 52.4015i 0.101553i
\(517\) 1209.82 2.34008
\(518\) 20.6491 0.0398631
\(519\) 320.249i 0.617050i
\(520\) 434.639 0.835844
\(521\) −903.968 −1.73506 −0.867532 0.497382i \(-0.834295\pi\)
−0.867532 + 0.497382i \(0.834295\pi\)
\(522\) 223.671i 0.428488i
\(523\) −860.311 −1.64495 −0.822477 0.568798i \(-0.807408\pi\)
−0.822477 + 0.568798i \(0.807408\pi\)
\(524\) 63.5683i 0.121314i
\(525\) 179.337 0.341594
\(526\) 474.562i 0.902209i
\(527\) 558.126i 1.05906i
\(528\) 235.341i 0.445722i
\(529\) −604.870 −1.14342
\(530\) 200.866i 0.378993i
\(531\) −14.0404 + 176.442i −0.0264414 + 0.332283i
\(532\) 66.1643 0.124369
\(533\) 364.255i 0.683406i
\(534\) −107.583 −0.201467
\(535\) 1228.97 2.29714
\(536\) 785.272 1.46506
\(537\) 503.898i 0.938357i
\(538\) 84.8163 0.157651
\(539\) 73.3414i 0.136069i
\(540\) −46.1916 −0.0855400
\(541\) 562.764i 1.04023i 0.854097 + 0.520115i \(0.174111\pi\)
−0.854097 + 0.520115i \(0.825889\pi\)
\(542\) 102.569i 0.189241i
\(543\) 124.699 0.229648
\(544\) 400.252i 0.735758i
\(545\) 416.983i 0.765107i
\(546\) −146.059 −0.267508
\(547\) −186.037 −0.340104 −0.170052 0.985435i \(-0.554394\pi\)
−0.170052 + 0.985435i \(0.554394\pi\)
\(548\) −148.979 −0.271860
\(549\) 123.184i 0.224379i
\(550\) −402.311 −0.731475
\(551\) −328.472 −0.596138
\(552\) 507.848 0.920015
\(553\) 791.537 1.43135
\(554\) 122.659i 0.221406i
\(555\) 21.1705i 0.0381450i
\(556\) −186.595 −0.335602
\(557\) −206.473 −0.370687 −0.185343 0.982674i \(-0.559340\pi\)
−0.185343 + 0.982674i \(0.559340\pi\)
\(558\) 142.904 0.256100
\(559\) −169.879 −0.303897
\(560\) 359.242 0.641503
\(561\) 525.613i 0.936921i
\(562\) 236.744i 0.421252i
\(563\) 560.271i 0.995152i −0.867420 0.497576i \(-0.834224\pi\)
0.867420 0.497576i \(-0.165776\pi\)
\(564\) 182.288i 0.323206i
\(565\) 1082.16i 1.91533i
\(566\) −802.776 −1.41833
\(567\) 59.9907 0.105804
\(568\) 497.999i 0.876758i
\(569\) 694.519i 1.22060i 0.792172 + 0.610298i \(0.208950\pi\)
−0.792172 + 0.610298i \(0.791050\pi\)
\(570\) 126.494i 0.221920i
\(571\) 344.549i 0.603414i −0.953401 0.301707i \(-0.902444\pi\)
0.953401 0.301707i \(-0.0975564\pi\)
\(572\) −175.713 −0.307191
\(573\) 294.316i 0.513640i
\(574\) 499.705i 0.870566i
\(575\) 523.056i 0.909663i
\(576\) −204.064 −0.354278
\(577\) −543.385 −0.941742 −0.470871 0.882202i \(-0.656060\pi\)
−0.470871 + 0.882202i \(0.656060\pi\)
\(578\) 110.447i 0.191085i
\(579\) −27.0916 −0.0467903
\(580\) 410.745 0.708182
\(581\) 575.365i 0.990301i
\(582\) 67.2005 0.115465
\(583\) 313.836i 0.538312i
\(584\) −606.682 −1.03884
\(585\) 149.747i 0.255978i
\(586\) 255.956i 0.436784i
\(587\) 995.683i 1.69622i −0.529818 0.848111i \(-0.677740\pi\)
0.529818 0.848111i \(-0.322260\pi\)
\(588\) −11.0506 −0.0187935
\(589\) 209.862i 0.356302i
\(590\) −604.205 48.0797i −1.02408 0.0814910i
\(591\) −174.239 −0.294821
\(592\) 16.2518i 0.0274524i
\(593\) 503.068 0.848345 0.424172 0.905581i \(-0.360565\pi\)
0.424172 + 0.905581i \(0.360565\pi\)
\(594\) −134.579 −0.226564
\(595\) −802.332 −1.34846
\(596\) 165.081i 0.276981i
\(597\) −146.342 −0.245130
\(598\) 425.999i 0.712373i
\(599\) −475.339 −0.793554 −0.396777 0.917915i \(-0.629871\pi\)
−0.396777 + 0.917915i \(0.629871\pi\)
\(600\) 234.271i 0.390452i
\(601\) 288.933i 0.480754i 0.970680 + 0.240377i \(0.0772710\pi\)
−0.970680 + 0.240377i \(0.922729\pi\)
\(602\) −233.049 −0.387124
\(603\) 270.552i 0.448676i
\(604\) 309.097i 0.511750i
\(605\) 869.872 1.43780
\(606\) −157.848 −0.260476
\(607\) 76.8532 0.126612 0.0633058 0.997994i \(-0.479836\pi\)
0.0633058 + 0.997994i \(0.479836\pi\)
\(608\) 150.499i 0.247532i
\(609\) −533.450 −0.875944
\(610\) −421.828 −0.691522
\(611\) 590.953 0.967190
\(612\) 79.1958 0.129405
\(613\) 518.309i 0.845529i 0.906240 + 0.422765i \(0.138940\pi\)
−0.906240 + 0.422765i \(0.861060\pi\)
\(614\) 488.315i 0.795302i
\(615\) −512.321 −0.833043
\(616\) −931.605 −1.51235
\(617\) −440.167 −0.713399 −0.356699 0.934219i \(-0.616098\pi\)
−0.356699 + 0.934219i \(0.616098\pi\)
\(618\) −278.636 −0.450868
\(619\) 624.254 1.00849 0.504244 0.863561i \(-0.331771\pi\)
0.504244 + 0.863561i \(0.331771\pi\)
\(620\) 262.427i 0.423269i
\(621\) 174.970i 0.281755i
\(622\) 879.490i 1.41397i
\(623\) 256.584i 0.411852i
\(624\) 114.956i 0.184224i
\(625\) −772.048 −1.23528
\(626\) 611.511 0.976855
\(627\) 197.636i 0.315209i
\(628\) 18.5794i 0.0295851i
\(629\) 36.2969i 0.0577057i
\(630\) 205.431i 0.326081i
\(631\) −647.088 −1.02550 −0.512748 0.858539i \(-0.671372\pi\)
−0.512748 + 0.858539i \(0.671372\pi\)
\(632\) 1034.00i 1.63608i
\(633\) 531.920i 0.840316i
\(634\) 646.913i 1.02037i
\(635\) 1061.63 1.67185
\(636\) 47.2867 0.0743501
\(637\) 35.8246i 0.0562395i
\(638\) 1196.70 1.87571
\(639\) 171.576 0.268508
\(640\) 159.663i 0.249473i
\(641\) 463.987 0.723848 0.361924 0.932208i \(-0.382120\pi\)
0.361924 + 0.932208i \(0.382120\pi\)
\(642\) 539.501i 0.840344i
\(643\) −12.4294 −0.0193304 −0.00966518 0.999953i \(-0.503077\pi\)
−0.00966518 + 0.999953i \(0.503077\pi\)
\(644\) 313.399i 0.486645i
\(645\) 238.933i 0.370438i
\(646\) 216.875i 0.335720i
\(647\) 879.244 1.35895 0.679477 0.733696i \(-0.262207\pi\)
0.679477 + 0.733696i \(0.262207\pi\)
\(648\) 78.3672i 0.120937i
\(649\) 944.018 + 75.1203i 1.45457 + 0.115748i
\(650\) −196.514 −0.302329
\(651\) 340.823i 0.523537i
\(652\) 317.218 0.486530
\(653\) 200.318 0.306766 0.153383 0.988167i \(-0.450983\pi\)
0.153383 + 0.988167i \(0.450983\pi\)
\(654\) 183.050 0.279893
\(655\) 289.849i 0.442518i
\(656\) −393.291 −0.599529
\(657\) 209.022i 0.318145i
\(658\) 810.701 1.23207
\(659\) 652.030i 0.989423i 0.869057 + 0.494712i \(0.164726\pi\)
−0.869057 + 0.494712i \(0.835274\pi\)
\(660\) 247.139i 0.374453i
\(661\) −440.130 −0.665855 −0.332928 0.942952i \(-0.608036\pi\)
−0.332928 + 0.942952i \(0.608036\pi\)
\(662\) 414.570i 0.626238i
\(663\) 256.742i 0.387243i
\(664\) −751.611 −1.13194
\(665\) −301.686 −0.453663
\(666\) 9.29353 0.0139543
\(667\) 1555.87i 2.33264i
\(668\) 246.780 0.369431
\(669\) −578.666 −0.864972
\(670\) −926.471 −1.38279
\(671\) 659.070 0.982221
\(672\) 244.416i 0.363714i
\(673\) 178.659i 0.265466i −0.991152 0.132733i \(-0.957625\pi\)
0.991152 0.132733i \(-0.0423754\pi\)
\(674\) −838.802 −1.24451
\(675\) 80.7140 0.119576
\(676\) 150.143 0.222105
\(677\) −890.544 −1.31543 −0.657713 0.753268i \(-0.728476\pi\)
−0.657713 + 0.753268i \(0.728476\pi\)
\(678\) 475.053 0.700667
\(679\) 160.272i 0.236041i
\(680\) 1048.10i 1.54133i
\(681\) 336.744i 0.494484i
\(682\) 764.578i 1.12108i
\(683\) 230.871i 0.338025i 0.985614 + 0.169013i \(0.0540578\pi\)
−0.985614 + 0.169013i \(0.945942\pi\)
\(684\) 29.7785 0.0435359
\(685\) 679.293 0.991669
\(686\) 576.175i 0.839905i
\(687\) 344.374i 0.501273i
\(688\) 183.420i 0.266599i
\(689\) 153.297i 0.222492i
\(690\) −599.164 −0.868353
\(691\) 305.505i 0.442120i 0.975260 + 0.221060i \(0.0709516\pi\)
−0.975260 + 0.221060i \(0.929048\pi\)
\(692\) 258.168i 0.373075i
\(693\) 320.968i 0.463157i
\(694\) 233.504 0.336462
\(695\) 850.808 1.22418
\(696\) 696.857i 1.00123i
\(697\) 878.378 1.26023
\(698\) 717.315 1.02767
\(699\) 465.041i 0.665295i
\(700\) 144.572 0.206531
\(701\) 309.337i 0.441280i −0.975355 0.220640i \(-0.929185\pi\)
0.975355 0.220640i \(-0.0708146\pi\)
\(702\) −65.7368 −0.0936422
\(703\) 13.6480i 0.0194140i
\(704\) 1091.80i 1.55086i
\(705\) 831.170i 1.17896i
\(706\) −1009.82 −1.43035
\(707\) 376.465i 0.532482i
\(708\) −11.3186 + 142.238i −0.0159868 + 0.200902i
\(709\) −1363.47 −1.92309 −0.961543 0.274655i \(-0.911436\pi\)
−0.961543 + 0.274655i \(0.911436\pi\)
\(710\) 587.543i 0.827525i
\(711\) 356.247 0.501050
\(712\) −335.181 −0.470760
\(713\) −994.049 −1.39418
\(714\) 352.213i 0.493295i
\(715\) 801.191 1.12055
\(716\) 406.215i 0.567340i
\(717\) 556.794 0.776561
\(718\) 566.838i 0.789468i
\(719\) 358.898i 0.499162i −0.968354 0.249581i \(-0.919707\pi\)
0.968354 0.249581i \(-0.0802929\pi\)
\(720\) 161.684 0.224561
\(721\) 664.542i 0.921694i
\(722\) 500.963i 0.693854i
\(723\) −77.9380 −0.107798
\(724\) 100.525 0.138847
\(725\) −717.725 −0.989966
\(726\) 381.861i 0.525980i
\(727\) 123.204 0.169469 0.0847345 0.996404i \(-0.472996\pi\)
0.0847345 + 0.996404i \(0.472996\pi\)
\(728\) −455.055 −0.625075
\(729\) 27.0000 0.0370370
\(730\) 715.769 0.980506
\(731\) 409.652i 0.560399i
\(732\) 99.3043i 0.135662i
\(733\) 505.875 0.690143 0.345071 0.938576i \(-0.387855\pi\)
0.345071 + 0.938576i \(0.387855\pi\)
\(734\) −357.093 −0.486503
\(735\) 50.3869 0.0685536
\(736\) 712.868 0.968571
\(737\) 1447.53 1.96408
\(738\) 224.902i 0.304745i
\(739\) 214.823i 0.290694i 0.989381 + 0.145347i \(0.0464298\pi\)
−0.989381 + 0.145347i \(0.953570\pi\)
\(740\) 17.0665i 0.0230628i
\(741\) 96.5380i 0.130281i
\(742\) 210.301i 0.283425i
\(743\) −919.142 −1.23707 −0.618534 0.785758i \(-0.712273\pi\)
−0.618534 + 0.785758i \(0.712273\pi\)
\(744\) 445.224 0.598419
\(745\) 752.710i 1.01035i
\(746\) 257.448i 0.345105i
\(747\) 258.954i 0.346659i
\(748\) 423.721i 0.566472i
\(749\) −1286.70 −1.71789
\(750\) 168.445i 0.224593i
\(751\) 448.537i 0.597254i 0.954370 + 0.298627i \(0.0965286\pi\)
−0.954370 + 0.298627i \(0.903471\pi\)
\(752\) 638.060i 0.848484i
\(753\) 532.219 0.706798
\(754\) 584.545 0.775259
\(755\) 1409.37i 1.86672i
\(756\) 48.3613 0.0639700
\(757\) −250.783 −0.331286 −0.165643 0.986186i \(-0.552970\pi\)
−0.165643 + 0.986186i \(0.552970\pi\)
\(758\) 426.102i 0.562140i
\(759\) 936.141 1.23339
\(760\) 394.099i 0.518551i
\(761\) 746.517 0.980968 0.490484 0.871450i \(-0.336820\pi\)
0.490484 + 0.871450i \(0.336820\pi\)
\(762\) 466.039i 0.611599i
\(763\) 436.570i 0.572175i
\(764\) 237.262i 0.310552i
\(765\) −361.105 −0.472033
\(766\) 143.978i 0.187961i
\(767\) 461.118 + 36.6935i 0.601196 + 0.0478403i
\(768\) −401.177 −0.522365
\(769\) 1189.01i 1.54618i 0.634296 + 0.773091i \(0.281290\pi\)
−0.634296 + 0.773091i \(0.718710\pi\)
\(770\) 1099.12 1.42742
\(771\) −466.370 −0.604889
\(772\) −21.8398 −0.0282899
\(773\) 900.789i 1.16532i 0.812717 + 0.582658i \(0.197987\pi\)
−0.812717 + 0.582658i \(0.802013\pi\)
\(774\) −104.888 −0.135514
\(775\) 458.557i 0.591686i
\(776\) 209.366 0.269802
\(777\) 22.1649i 0.0285262i
\(778\) 260.303i 0.334580i
\(779\) 330.280 0.423980
\(780\) 120.718i 0.154767i
\(781\) 917.985i 1.17540i
\(782\) 1027.27 1.31364
\(783\) −240.090 −0.306628
\(784\) 38.6803 0.0493371
\(785\) 84.7157i 0.107918i
\(786\) −127.240 −0.161883
\(787\) −212.704 −0.270272 −0.135136 0.990827i \(-0.543147\pi\)
−0.135136 + 0.990827i \(0.543147\pi\)
\(788\) −140.463 −0.178252
\(789\) −509.397 −0.645624
\(790\) 1219.92i 1.54421i
\(791\) 1132.99i 1.43235i