Properties

Label 76.5.j.a.33.2
Level $76$
Weight $5$
Character 76.33
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 33.2
Character \(\chi\) \(=\) 76.33
Dual form 76.5.j.a.53.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.79937 - 1.37524i) q^{3} +(0.638039 + 0.535378i) q^{5} +(23.1636 + 40.1206i) q^{7} +(-17.1762 - 6.25164i) q^{9} +O(q^{10})\) \(q+(-7.79937 - 1.37524i) q^{3} +(0.638039 + 0.535378i) q^{5} +(23.1636 + 40.1206i) q^{7} +(-17.1762 - 6.25164i) q^{9} +(95.5660 - 165.525i) q^{11} +(208.358 - 36.7391i) q^{13} +(-4.24003 - 5.05307i) q^{15} +(504.579 - 183.652i) q^{17} +(130.825 + 336.461i) q^{19} +(-125.486 - 344.771i) q^{21} +(-238.506 + 200.131i) q^{23} +(-108.410 - 614.822i) q^{25} +(680.917 + 393.128i) q^{27} +(67.5830 - 185.683i) q^{29} +(-677.986 + 391.435i) q^{31} +(-972.991 + 1159.57i) q^{33} +(-6.70040 + 37.9998i) q^{35} -1109.80i q^{37} -1675.58 q^{39} +(1014.78 + 178.934i) q^{41} +(867.530 + 727.944i) q^{43} +(-7.61212 - 13.1846i) q^{45} +(-1488.89 - 541.910i) q^{47} +(127.391 - 220.647i) q^{49} +(-4187.96 + 738.451i) q^{51} +(623.443 + 742.990i) q^{53} +(149.593 - 54.4476i) q^{55} +(-557.642 - 2804.10i) q^{57} +(1659.58 + 4559.66i) q^{59} +(-3868.03 + 3245.67i) q^{61} +(-147.045 - 833.932i) q^{63} +(152.610 + 88.1093i) q^{65} +(-70.2062 + 192.890i) q^{67} +(2135.43 - 1232.89i) q^{69} +(3442.94 - 4103.13i) q^{71} +(1418.98 - 8047.43i) q^{73} +4944.31i q^{75} +8854.63 q^{77} +(5647.18 + 995.751i) q^{79} +(-3635.90 - 3050.88i) q^{81} +(-2389.76 - 4139.18i) q^{83} +(420.264 + 152.964i) q^{85} +(-782.463 + 1355.27i) q^{87} +(11031.2 - 1945.10i) q^{89} +(6300.32 + 7508.43i) q^{91} +(5826.18 - 2120.56i) q^{93} +(-96.6620 + 284.716i) q^{95} +(613.294 + 1685.01i) q^{97} +(-2676.27 + 2245.66i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −7.79937 1.37524i −0.866597 0.152804i −0.277361 0.960766i \(-0.589460\pi\)
−0.589235 + 0.807961i \(0.700571\pi\)
\(4\) 0 0
\(5\) 0.638039 + 0.535378i 0.0255216 + 0.0214151i 0.655459 0.755231i \(-0.272475\pi\)
−0.629938 + 0.776646i \(0.716920\pi\)
\(6\) 0 0
\(7\) 23.1636 + 40.1206i 0.472728 + 0.818788i 0.999513 0.0312103i \(-0.00993616\pi\)
−0.526785 + 0.849998i \(0.676603\pi\)
\(8\) 0 0
\(9\) −17.1762 6.25164i −0.212052 0.0771807i
\(10\) 0 0
\(11\) 95.5660 165.525i 0.789802 1.36798i −0.136286 0.990669i \(-0.543517\pi\)
0.926088 0.377307i \(-0.123150\pi\)
\(12\) 0 0
\(13\) 208.358 36.7391i 1.23289 0.217391i 0.481021 0.876709i \(-0.340266\pi\)
0.751864 + 0.659318i \(0.229155\pi\)
\(14\) 0 0
\(15\) −4.24003 5.05307i −0.0188446 0.0224581i
\(16\) 0 0
\(17\) 504.579 183.652i 1.74595 0.635473i 0.746399 0.665499i \(-0.231781\pi\)
0.999549 + 0.0300258i \(0.00955895\pi\)
\(18\) 0 0
\(19\) 130.825 + 336.461i 0.362397 + 0.932024i
\(20\) 0 0
\(21\) −125.486 344.771i −0.284550 0.781794i
\(22\) 0 0
\(23\) −238.506 + 200.131i −0.450863 + 0.378319i −0.839756 0.542964i \(-0.817302\pi\)
0.388893 + 0.921283i \(0.372858\pi\)
\(24\) 0 0
\(25\) −108.410 614.822i −0.173455 0.983715i
\(26\) 0 0
\(27\) 680.917 + 393.128i 0.934042 + 0.539270i
\(28\) 0 0
\(29\) 67.5830 185.683i 0.0803603 0.220788i −0.893005 0.450046i \(-0.851408\pi\)
0.973366 + 0.229258i \(0.0736299\pi\)
\(30\) 0 0
\(31\) −677.986 + 391.435i −0.705500 + 0.407321i −0.809393 0.587268i \(-0.800204\pi\)
0.103892 + 0.994589i \(0.466870\pi\)
\(32\) 0 0
\(33\) −972.991 + 1159.57i −0.893472 + 1.06480i
\(34\) 0 0
\(35\) −6.70040 + 37.9998i −0.00546971 + 0.0310203i
\(36\) 0 0
\(37\) 1109.80i 0.810665i −0.914169 0.405332i \(-0.867156\pi\)
0.914169 0.405332i \(-0.132844\pi\)
\(38\) 0 0
\(39\) −1675.58 −1.10163
\(40\) 0 0
\(41\) 1014.78 + 178.934i 0.603679 + 0.106445i 0.467130 0.884188i \(-0.345288\pi\)
0.136549 + 0.990633i \(0.456399\pi\)
\(42\) 0 0
\(43\) 867.530 + 727.944i 0.469189 + 0.393696i 0.846498 0.532391i \(-0.178706\pi\)
−0.377310 + 0.926087i \(0.623151\pi\)
\(44\) 0 0
\(45\) −7.61212 13.1846i −0.00375907 0.00651090i
\(46\) 0 0
\(47\) −1488.89 541.910i −0.674009 0.245319i −0.0177359 0.999843i \(-0.505646\pi\)
−0.656273 + 0.754524i \(0.727868\pi\)
\(48\) 0 0
\(49\) 127.391 220.647i 0.0530574 0.0918981i
\(50\) 0 0
\(51\) −4187.96 + 738.451i −1.61014 + 0.283910i
\(52\) 0 0
\(53\) 623.443 + 742.990i 0.221945 + 0.264504i 0.865514 0.500884i \(-0.166992\pi\)
−0.643570 + 0.765388i \(0.722547\pi\)
\(54\) 0 0
\(55\) 149.593 54.4476i 0.0494524 0.0179992i
\(56\) 0 0
\(57\) −557.642 2804.10i −0.171635 0.863064i
\(58\) 0 0
\(59\) 1659.58 + 4559.66i 0.476754 + 1.30987i 0.912233 + 0.409671i \(0.134357\pi\)
−0.435480 + 0.900199i \(0.643421\pi\)
\(60\) 0 0
\(61\) −3868.03 + 3245.67i −1.03951 + 0.872257i −0.991952 0.126612i \(-0.959590\pi\)
−0.0475625 + 0.998868i \(0.515145\pi\)
\(62\) 0 0
\(63\) −147.045 833.932i −0.0370483 0.210111i
\(64\) 0 0
\(65\) 152.610 + 88.1093i 0.0361206 + 0.0208543i
\(66\) 0 0
\(67\) −70.2062 + 192.890i −0.0156396 + 0.0429695i −0.947267 0.320446i \(-0.896167\pi\)
0.931627 + 0.363415i \(0.118389\pi\)
\(68\) 0 0
\(69\) 2135.43 1232.89i 0.448525 0.258956i
\(70\) 0 0
\(71\) 3442.94 4103.13i 0.682987 0.813953i −0.307501 0.951548i \(-0.599493\pi\)
0.990489 + 0.137595i \(0.0439373\pi\)
\(72\) 0 0
\(73\) 1418.98 8047.43i 0.266275 1.51012i −0.499106 0.866541i \(-0.666338\pi\)
0.765380 0.643578i \(-0.222551\pi\)
\(74\) 0 0
\(75\) 4944.31i 0.878988i
\(76\) 0 0
\(77\) 8854.63 1.49344
\(78\) 0 0
\(79\) 5647.18 + 995.751i 0.904852 + 0.159550i 0.606665 0.794957i \(-0.292507\pi\)
0.298187 + 0.954507i \(0.403618\pi\)
\(80\) 0 0
\(81\) −3635.90 3050.88i −0.554169 0.465003i
\(82\) 0 0
\(83\) −2389.76 4139.18i −0.346894 0.600839i 0.638802 0.769371i \(-0.279430\pi\)
−0.985696 + 0.168533i \(0.946097\pi\)
\(84\) 0 0
\(85\) 420.264 + 152.964i 0.0581681 + 0.0211714i
\(86\) 0 0
\(87\) −782.463 + 1355.27i −0.103377 + 0.179055i
\(88\) 0 0
\(89\) 11031.2 1945.10i 1.39265 0.245562i 0.573532 0.819183i \(-0.305573\pi\)
0.819121 + 0.573621i \(0.194462\pi\)
\(90\) 0 0
\(91\) 6300.32 + 7508.43i 0.760816 + 0.906705i
\(92\) 0 0
\(93\) 5826.18 2120.56i 0.673624 0.245179i
\(94\) 0 0
\(95\) −96.6620 + 284.716i −0.0107105 + 0.0315475i
\(96\) 0 0
\(97\) 613.294 + 1685.01i 0.0651816 + 0.179085i 0.968007 0.250921i \(-0.0807335\pi\)
−0.902826 + 0.430006i \(0.858511\pi\)
\(98\) 0 0
\(99\) −2676.27 + 2245.66i −0.273061 + 0.229125i
\(100\) 0 0
\(101\) −2527.79 14335.8i −0.247798 1.40533i −0.813903 0.581000i \(-0.802661\pi\)
0.566105 0.824333i \(-0.308450\pi\)
\(102\) 0 0
\(103\) −16876.4 9743.57i −1.59076 0.918425i −0.993177 0.116618i \(-0.962795\pi\)
−0.597582 0.801808i \(-0.703872\pi\)
\(104\) 0 0
\(105\) 104.518 287.160i 0.00948007 0.0260463i
\(106\) 0 0
\(107\) −3946.18 + 2278.33i −0.344675 + 0.198998i −0.662337 0.749206i \(-0.730435\pi\)
0.317663 + 0.948204i \(0.397102\pi\)
\(108\) 0 0
\(109\) −8297.49 + 9888.56i −0.698383 + 0.832300i −0.992342 0.123517i \(-0.960582\pi\)
0.293959 + 0.955818i \(0.405027\pi\)
\(110\) 0 0
\(111\) −1526.24 + 8655.74i −0.123873 + 0.702519i
\(112\) 0 0
\(113\) 17919.3i 1.40334i 0.712500 + 0.701672i \(0.247563\pi\)
−0.712500 + 0.701672i \(0.752437\pi\)
\(114\) 0 0
\(115\) −259.322 −0.0196085
\(116\) 0 0
\(117\) −3808.48 671.538i −0.278215 0.0490567i
\(118\) 0 0
\(119\) 19056.1 + 15990.0i 1.34568 + 1.12916i
\(120\) 0 0
\(121\) −10945.2 18957.7i −0.747574 1.29484i
\(122\) 0 0
\(123\) −7668.60 2791.14i −0.506881 0.184490i
\(124\) 0 0
\(125\) 520.274 901.141i 0.0332976 0.0576731i
\(126\) 0 0
\(127\) −29312.4 + 5168.57i −1.81737 + 0.320452i −0.975629 0.219424i \(-0.929582\pi\)
−0.841744 + 0.539876i \(0.818471\pi\)
\(128\) 0 0
\(129\) −5765.09 6870.56i −0.346439 0.412870i
\(130\) 0 0
\(131\) 16507.9 6008.38i 0.961942 0.350118i 0.187148 0.982332i \(-0.440076\pi\)
0.774794 + 0.632213i \(0.217853\pi\)
\(132\) 0 0
\(133\) −10468.6 + 13042.5i −0.591815 + 0.737320i
\(134\) 0 0
\(135\) 223.980 + 615.379i 0.0122897 + 0.0337657i
\(136\) 0 0
\(137\) −5277.66 + 4428.48i −0.281190 + 0.235947i −0.772464 0.635059i \(-0.780976\pi\)
0.491274 + 0.871005i \(0.336531\pi\)
\(138\) 0 0
\(139\) −390.360 2213.84i −0.0202039 0.114582i 0.973038 0.230645i \(-0.0740836\pi\)
−0.993242 + 0.116063i \(0.962973\pi\)
\(140\) 0 0
\(141\) 10867.1 + 6274.13i 0.546608 + 0.315584i
\(142\) 0 0
\(143\) 13830.7 37999.5i 0.676349 1.85825i
\(144\) 0 0
\(145\) 142.531 82.2904i 0.00677913 0.00391393i
\(146\) 0 0
\(147\) −1297.01 + 1545.72i −0.0600218 + 0.0715312i
\(148\) 0 0
\(149\) −3144.64 + 17834.2i −0.141644 + 0.803304i 0.828356 + 0.560201i \(0.189276\pi\)
−0.970001 + 0.243103i \(0.921835\pi\)
\(150\) 0 0
\(151\) 12669.8i 0.555668i 0.960629 + 0.277834i \(0.0896166\pi\)
−0.960629 + 0.277834i \(0.910383\pi\)
\(152\) 0 0
\(153\) −9814.89 −0.419278
\(154\) 0 0
\(155\) −642.148 113.228i −0.0267283 0.00471292i
\(156\) 0 0
\(157\) 12674.1 + 10634.8i 0.514183 + 0.431451i 0.862598 0.505889i \(-0.168836\pi\)
−0.348415 + 0.937340i \(0.613280\pi\)
\(158\) 0 0
\(159\) −3840.67 6652.24i −0.151919 0.263132i
\(160\) 0 0
\(161\) −13554.0 4933.27i −0.522898 0.190319i
\(162\) 0 0
\(163\) −5938.09 + 10285.1i −0.223497 + 0.387108i −0.955867 0.293798i \(-0.905081\pi\)
0.732370 + 0.680906i \(0.238414\pi\)
\(164\) 0 0
\(165\) −1241.61 + 218.930i −0.0456056 + 0.00804150i
\(166\) 0 0
\(167\) −9815.28 11697.4i −0.351941 0.419427i 0.560809 0.827945i \(-0.310490\pi\)
−0.912750 + 0.408518i \(0.866046\pi\)
\(168\) 0 0
\(169\) 15224.6 5541.30i 0.533056 0.194016i
\(170\) 0 0
\(171\) −143.659 6597.00i −0.00491292 0.225608i
\(172\) 0 0
\(173\) 11914.5 + 32734.8i 0.398092 + 1.09375i 0.963212 + 0.268741i \(0.0866076\pi\)
−0.565120 + 0.825009i \(0.691170\pi\)
\(174\) 0 0
\(175\) 22155.9 18591.0i 0.723457 0.607052i
\(176\) 0 0
\(177\) −6673.05 37844.8i −0.212999 1.20798i
\(178\) 0 0
\(179\) 27682.7 + 15982.6i 0.863978 + 0.498818i 0.865342 0.501181i \(-0.167101\pi\)
−0.00136433 + 0.999999i \(0.500434\pi\)
\(180\) 0 0
\(181\) −19495.0 + 53562.1i −0.595068 + 1.63494i 0.165897 + 0.986143i \(0.446948\pi\)
−0.760965 + 0.648793i \(0.775274\pi\)
\(182\) 0 0
\(183\) 34631.8 19994.7i 1.03412 0.597052i
\(184\) 0 0
\(185\) 594.163 708.096i 0.0173605 0.0206894i
\(186\) 0 0
\(187\) 17821.6 101071.i 0.509640 2.89031i
\(188\) 0 0
\(189\) 36425.1i 1.01971i
\(190\) 0 0
\(191\) 50921.9 1.39585 0.697924 0.716172i \(-0.254107\pi\)
0.697924 + 0.716172i \(0.254107\pi\)
\(192\) 0 0
\(193\) 7155.09 + 1261.64i 0.192088 + 0.0338703i 0.268864 0.963178i \(-0.413352\pi\)
−0.0767763 + 0.997048i \(0.524463\pi\)
\(194\) 0 0
\(195\) −1069.09 897.071i −0.0281154 0.0235916i
\(196\) 0 0
\(197\) −6657.78 11531.6i −0.171552 0.297137i 0.767410 0.641156i \(-0.221545\pi\)
−0.938963 + 0.344019i \(0.888212\pi\)
\(198\) 0 0
\(199\) −27819.3 10125.4i −0.702491 0.255686i −0.0340168 0.999421i \(-0.510830\pi\)
−0.668474 + 0.743736i \(0.733052\pi\)
\(200\) 0 0
\(201\) 812.834 1407.87i 0.0201191 0.0348474i
\(202\) 0 0
\(203\) 9015.18 1589.62i 0.218767 0.0385746i
\(204\) 0 0
\(205\) 551.675 + 657.461i 0.0131273 + 0.0156445i
\(206\) 0 0
\(207\) 5347.78 1946.43i 0.124805 0.0454254i
\(208\) 0 0
\(209\) 68195.2 + 10499.3i 1.56121 + 0.240363i
\(210\) 0 0
\(211\) −16.0715 44.1560i −0.000360986 0.000991801i 0.939512 0.342516i \(-0.111279\pi\)
−0.939873 + 0.341524i \(0.889057\pi\)
\(212\) 0 0
\(213\) −32495.5 + 27267.0i −0.716250 + 0.601005i
\(214\) 0 0
\(215\) 163.792 + 928.913i 0.00354337 + 0.0200955i
\(216\) 0 0
\(217\) −31409.2 18134.1i −0.667019 0.385103i
\(218\) 0 0
\(219\) −22134.3 + 60813.4i −0.461506 + 1.26798i
\(220\) 0 0
\(221\) 98385.7 56803.0i 2.01441 1.16302i
\(222\) 0 0
\(223\) −15121.7 + 18021.4i −0.304082 + 0.362391i −0.896348 0.443352i \(-0.853789\pi\)
0.592265 + 0.805743i \(0.298234\pi\)
\(224\) 0 0
\(225\) −1981.57 + 11238.1i −0.0391422 + 0.221986i
\(226\) 0 0
\(227\) 9051.77i 0.175664i −0.996135 0.0878318i \(-0.972006\pi\)
0.996135 0.0878318i \(-0.0279938\pi\)
\(228\) 0 0
\(229\) −17379.0 −0.331401 −0.165700 0.986176i \(-0.552988\pi\)
−0.165700 + 0.986176i \(0.552988\pi\)
\(230\) 0 0
\(231\) −69060.5 12177.2i −1.29421 0.228205i
\(232\) 0 0
\(233\) −52913.9 44400.0i −0.974670 0.817845i 0.00860682 0.999963i \(-0.497260\pi\)
−0.983277 + 0.182118i \(0.941705\pi\)
\(234\) 0 0
\(235\) −659.840 1142.88i −0.0119482 0.0206949i
\(236\) 0 0
\(237\) −42675.1 15532.5i −0.759762 0.276531i
\(238\) 0 0
\(239\) −47309.5 + 81942.5i −0.828233 + 1.43454i 0.0711902 + 0.997463i \(0.477320\pi\)
−0.899423 + 0.437079i \(0.856013\pi\)
\(240\) 0 0
\(241\) −105764. + 18649.1i −1.82098 + 0.321088i −0.976667 0.214761i \(-0.931103\pi\)
−0.844314 + 0.535849i \(0.819992\pi\)
\(242\) 0 0
\(243\) −16775.0 19991.6i −0.284086 0.338560i
\(244\) 0 0
\(245\) 199.410 72.5793i 0.00332212 0.00120915i
\(246\) 0 0
\(247\) 39619.7 + 65297.7i 0.649408 + 1.07030i
\(248\) 0 0
\(249\) 12946.2 + 35569.5i 0.208807 + 0.573692i
\(250\) 0 0
\(251\) −4024.48 + 3376.94i −0.0638796 + 0.0536013i −0.674168 0.738578i \(-0.735498\pi\)
0.610289 + 0.792179i \(0.291053\pi\)
\(252\) 0 0
\(253\) 10333.6 + 58604.5i 0.161439 + 0.915566i
\(254\) 0 0
\(255\) −3067.44 1770.98i −0.0471732 0.0272354i
\(256\) 0 0
\(257\) 6106.37 16777.1i 0.0924521 0.254010i −0.884844 0.465887i \(-0.845735\pi\)
0.977296 + 0.211877i \(0.0679576\pi\)
\(258\) 0 0
\(259\) 44525.9 25707.0i 0.663763 0.383224i
\(260\) 0 0
\(261\) −2321.64 + 2766.83i −0.0340812 + 0.0406164i
\(262\) 0 0
\(263\) −817.509 + 4636.32i −0.0118190 + 0.0670289i −0.990147 0.140033i \(-0.955279\pi\)
0.978328 + 0.207062i \(0.0663902\pi\)
\(264\) 0 0
\(265\) 807.835i 0.0115035i
\(266\) 0 0
\(267\) −88711.4 −1.24439
\(268\) 0 0
\(269\) 7559.50 + 1332.94i 0.104469 + 0.0184208i 0.225638 0.974211i \(-0.427553\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(270\) 0 0
\(271\) 52245.4 + 43839.1i 0.711392 + 0.596929i 0.924989 0.379993i \(-0.124074\pi\)
−0.213597 + 0.976922i \(0.568518\pi\)
\(272\) 0 0
\(273\) −38812.6 67225.4i −0.520772 0.902004i
\(274\) 0 0
\(275\) −112129. 40811.5i −1.48269 0.539657i
\(276\) 0 0
\(277\) −31305.4 + 54222.6i −0.408000 + 0.706677i −0.994666 0.103153i \(-0.967107\pi\)
0.586665 + 0.809829i \(0.300440\pi\)
\(278\) 0 0
\(279\) 14092.4 2484.86i 0.181040 0.0319223i
\(280\) 0 0
\(281\) −67625.0 80592.3i −0.856435 1.02066i −0.999521 0.0309495i \(-0.990147\pi\)
0.143086 0.989710i \(-0.454298\pi\)
\(282\) 0 0
\(283\) 125903. 45824.9i 1.57204 0.572175i 0.598584 0.801060i \(-0.295730\pi\)
0.973453 + 0.228885i \(0.0735081\pi\)
\(284\) 0 0
\(285\) 1145.46 2087.67i 0.0141022 0.0257023i
\(286\) 0 0
\(287\) 16327.2 + 44858.6i 0.198220 + 0.544605i
\(288\) 0 0
\(289\) 156891. 131647.i 1.87846 1.57622i
\(290\) 0 0
\(291\) −2466.01 13985.5i −0.0291212 0.165155i
\(292\) 0 0
\(293\) 100485. + 58014.9i 1.17048 + 0.675779i 0.953794 0.300462i \(-0.0971409\pi\)
0.216689 + 0.976241i \(0.430474\pi\)
\(294\) 0 0
\(295\) −1382.27 + 3797.74i −0.0158835 + 0.0436397i
\(296\) 0 0
\(297\) 130145. 75139.3i 1.47542 0.851832i
\(298\) 0 0
\(299\) −42342.0 + 50461.3i −0.473619 + 0.564437i
\(300\) 0 0
\(301\) −9110.40 + 51667.7i −0.100555 + 0.570277i
\(302\) 0 0
\(303\) 115287.i 1.25572i
\(304\) 0 0
\(305\) −4205.62 −0.0452095
\(306\) 0 0
\(307\) −136092. 23996.7i −1.44396 0.254610i −0.603884 0.797072i \(-0.706381\pi\)
−0.840080 + 0.542462i \(0.817492\pi\)
\(308\) 0 0
\(309\) 118225. + 99202.8i 1.23821 + 1.03898i
\(310\) 0 0
\(311\) −57568.9 99712.2i −0.595205 1.03093i −0.993518 0.113676i \(-0.963737\pi\)
0.398313 0.917250i \(-0.369596\pi\)
\(312\) 0 0
\(313\) −49771.9 18115.5i −0.508037 0.184910i 0.0752683 0.997163i \(-0.476019\pi\)
−0.583305 + 0.812253i \(0.698241\pi\)
\(314\) 0 0
\(315\) 352.649 610.806i 0.00355403 0.00615576i
\(316\) 0 0
\(317\) −46437.0 + 8188.09i −0.462110 + 0.0814825i −0.399856 0.916578i \(-0.630940\pi\)
−0.0622538 + 0.998060i \(0.519829\pi\)
\(318\) 0 0
\(319\) −24276.5 28931.7i −0.238564 0.284310i
\(320\) 0 0
\(321\) 33911.0 12342.6i 0.329102 0.119783i
\(322\) 0 0
\(323\) 127803. + 145745.i 1.22500 + 1.39697i
\(324\) 0 0
\(325\) −45176.0 124120.i −0.427701 1.17510i
\(326\) 0 0
\(327\) 78314.3 65713.5i 0.732395 0.614553i
\(328\) 0 0
\(329\) −12746.3 72287.6i −0.117758 0.667840i
\(330\) 0 0
\(331\) 30281.9 + 17483.2i 0.276393 + 0.159575i 0.631789 0.775140i \(-0.282321\pi\)
−0.355396 + 0.934716i \(0.615654\pi\)
\(332\) 0 0
\(333\) −6938.07 + 19062.2i −0.0625677 + 0.171903i
\(334\) 0 0
\(335\) −148.063 + 85.4844i −0.00131934 + 0.000761724i
\(336\) 0 0
\(337\) 31733.6 37818.6i 0.279421 0.333001i −0.608020 0.793921i \(-0.708036\pi\)
0.887442 + 0.460920i \(0.152481\pi\)
\(338\) 0 0
\(339\) 24643.3 139759.i 0.214437 1.21613i
\(340\) 0 0
\(341\) 149632.i 1.28681i
\(342\) 0 0
\(343\) 123035. 1.04578
\(344\) 0 0
\(345\) 2022.55 + 356.630i 0.0169926 + 0.00299626i
\(346\) 0 0
\(347\) −33446.4 28064.9i −0.277774 0.233080i 0.493248 0.869889i \(-0.335810\pi\)
−0.771022 + 0.636809i \(0.780254\pi\)
\(348\) 0 0
\(349\) 28848.8 + 49967.6i 0.236852 + 0.410239i 0.959809 0.280653i \(-0.0905511\pi\)
−0.722957 + 0.690893i \(0.757218\pi\)
\(350\) 0 0
\(351\) 156317. + 56894.9i 1.26880 + 0.461805i
\(352\) 0 0
\(353\) 39122.8 67762.7i 0.313965 0.543803i −0.665252 0.746619i \(-0.731676\pi\)
0.979217 + 0.202816i \(0.0650093\pi\)
\(354\) 0 0
\(355\) 4393.46 774.686i 0.0348618 0.00614708i
\(356\) 0 0
\(357\) −126636. 150918.i −0.993618 1.18415i
\(358\) 0 0
\(359\) −136903. + 49828.5i −1.06224 + 0.386624i −0.813270 0.581887i \(-0.802315\pi\)
−0.248971 + 0.968511i \(0.580092\pi\)
\(360\) 0 0
\(361\) −96090.4 + 88035.2i −0.737336 + 0.675526i
\(362\) 0 0
\(363\) 59294.5 + 162910.i 0.449988 + 1.23633i
\(364\) 0 0
\(365\) 5213.78 4374.88i 0.0391352 0.0328383i
\(366\) 0 0
\(367\) −30340.5 172069.i −0.225263 1.27753i −0.862181 0.506600i \(-0.830902\pi\)
0.636918 0.770931i \(-0.280209\pi\)
\(368\) 0 0
\(369\) −16311.6 9417.48i −0.119796 0.0691643i
\(370\) 0 0
\(371\) −15368.0 + 42223.3i −0.111653 + 0.306764i
\(372\) 0 0
\(373\) 193882. 111938.i 1.39354 0.804561i 0.399836 0.916587i \(-0.369067\pi\)
0.993705 + 0.112025i \(0.0357337\pi\)
\(374\) 0 0
\(375\) −5297.10 + 6312.83i −0.0376682 + 0.0448913i
\(376\) 0 0
\(377\) 7259.62 41171.4i 0.0510777 0.289676i
\(378\) 0 0
\(379\) 194659.i 1.35518i 0.735440 + 0.677590i \(0.236976\pi\)
−0.735440 + 0.677590i \(0.763024\pi\)
\(380\) 0 0
\(381\) 235726. 1.62390
\(382\) 0 0
\(383\) −223241. 39363.5i −1.52187 0.268347i −0.650702 0.759333i \(-0.725525\pi\)
−0.871167 + 0.490987i \(0.836636\pi\)
\(384\) 0 0
\(385\) 5649.60 + 4740.58i 0.0381150 + 0.0319823i
\(386\) 0 0
\(387\) −10350.0 17926.8i −0.0691068 0.119696i
\(388\) 0 0
\(389\) −237179. 86325.9i −1.56739 0.570482i −0.594973 0.803745i \(-0.702837\pi\)
−0.972414 + 0.233263i \(0.925060\pi\)
\(390\) 0 0
\(391\) −83591.0 + 144784.i −0.546771 + 0.947036i
\(392\) 0 0
\(393\) −137014. + 24159.3i −0.887115 + 0.156422i
\(394\) 0 0
\(395\) 3070.02 + 3658.71i 0.0196765 + 0.0234495i
\(396\) 0 0
\(397\) 169678. 61757.6i 1.07657 0.391841i 0.257942 0.966160i \(-0.416956\pi\)
0.818631 + 0.574320i \(0.194733\pi\)
\(398\) 0 0
\(399\) 99585.0 87326.0i 0.625530 0.548527i
\(400\) 0 0
\(401\) 24795.4 + 68124.8i 0.154199 + 0.423659i 0.992605 0.121387i \(-0.0387343\pi\)
−0.838406 + 0.545046i \(0.816512\pi\)
\(402\) 0 0
\(403\) −126883. + 106467.i −0.781253 + 0.655549i
\(404\) 0 0
\(405\) −686.470 3893.17i −0.00418516 0.0237352i
\(406\) 0 0
\(407\) −183700. 106059.i −1.10897 0.640264i
\(408\) 0 0
\(409\) −50355.5 + 138351.i −0.301024 + 0.827056i 0.693299 + 0.720650i \(0.256157\pi\)
−0.994323 + 0.106406i \(0.966066\pi\)
\(410\) 0 0
\(411\) 47252.6 27281.3i 0.279732 0.161503i
\(412\) 0 0
\(413\) −144494. + 172202.i −0.847131 + 1.00957i
\(414\) 0 0
\(415\) 691.269 3920.38i 0.00401376 0.0227631i
\(416\) 0 0
\(417\) 17803.4i 0.102384i
\(418\) 0 0
\(419\) −118436. −0.674617 −0.337309 0.941394i \(-0.609517\pi\)
−0.337309 + 0.941394i \(0.609517\pi\)
\(420\) 0 0
\(421\) −3817.47 673.122i −0.0215383 0.00379778i 0.162869 0.986648i \(-0.447925\pi\)
−0.184407 + 0.982850i \(0.559036\pi\)
\(422\) 0 0
\(423\) 22185.6 + 18615.9i 0.123991 + 0.104041i
\(424\) 0 0
\(425\) −167614. 290316.i −0.927968 1.60729i
\(426\) 0 0
\(427\) −219816. 80006.5i −1.20560 0.438803i
\(428\) 0 0
\(429\) −160129. + 277351.i −0.870072 + 1.50701i
\(430\) 0 0
\(431\) −52442.0 + 9246.94i −0.282309 + 0.0497787i −0.313010 0.949750i \(-0.601337\pi\)
0.0307006 + 0.999529i \(0.490226\pi\)
\(432\) 0 0
\(433\) 168576. + 200901.i 0.899127 + 1.07154i 0.997081 + 0.0763465i \(0.0243255\pi\)
−0.0979547 + 0.995191i \(0.531230\pi\)
\(434\) 0 0
\(435\) −1224.82 + 445.799i −0.00647284 + 0.00235592i
\(436\) 0 0
\(437\) −98538.7 54065.8i −0.515993 0.283113i
\(438\) 0 0
\(439\) 47629.2 + 130860.i 0.247141 + 0.679014i 0.999788 + 0.0205899i \(0.00655444\pi\)
−0.752647 + 0.658424i \(0.771223\pi\)
\(440\) 0 0
\(441\) −3567.50 + 2993.49i −0.0183437 + 0.0153922i
\(442\) 0 0
\(443\) 51518.8 + 292178.i 0.262518 + 1.48881i 0.776012 + 0.630718i \(0.217240\pi\)
−0.513494 + 0.858093i \(0.671649\pi\)
\(444\) 0 0
\(445\) 8079.70 + 4664.82i 0.0408014 + 0.0235567i
\(446\) 0 0
\(447\) 49052.4 134770.i 0.245497 0.674497i
\(448\) 0 0
\(449\) 95659.2 55228.9i 0.474498 0.273951i −0.243623 0.969870i \(-0.578336\pi\)
0.718121 + 0.695919i \(0.245003\pi\)
\(450\) 0 0
\(451\) 126597. 150872.i 0.622401 0.741749i
\(452\) 0 0
\(453\) 17424.0 98816.4i 0.0849085 0.481540i
\(454\) 0 0
\(455\) 8163.73i 0.0394335i
\(456\) 0 0
\(457\) −197803. −0.947110 −0.473555 0.880764i \(-0.657030\pi\)
−0.473555 + 0.880764i \(0.657030\pi\)
\(458\) 0 0
\(459\) 415775. + 73312.3i 1.97348 + 0.347978i
\(460\) 0 0
\(461\) 29644.6 + 24874.8i 0.139490 + 0.117046i 0.709863 0.704340i \(-0.248757\pi\)
−0.570373 + 0.821386i \(0.693201\pi\)
\(462\) 0 0
\(463\) −60072.0 104048.i −0.280227 0.485368i 0.691213 0.722651i \(-0.257076\pi\)
−0.971441 + 0.237283i \(0.923743\pi\)
\(464\) 0 0
\(465\) 4852.63 + 1766.21i 0.0224425 + 0.00816840i
\(466\) 0 0
\(467\) 71703.3 124194.i 0.328780 0.569464i −0.653490 0.756935i \(-0.726696\pi\)
0.982270 + 0.187471i \(0.0600292\pi\)
\(468\) 0 0
\(469\) −9365.09 + 1651.32i −0.0425762 + 0.00750732i
\(470\) 0 0
\(471\) −84224.5 100375.i −0.379662 0.452463i
\(472\) 0 0
\(473\) 203399. 74031.3i 0.909133 0.330897i
\(474\) 0 0
\(475\) 192680. 116910.i 0.853986 0.518160i
\(476\) 0 0
\(477\) −6063.49 16659.3i −0.0266493 0.0732184i
\(478\) 0 0
\(479\) −120222. + 100878.i −0.523979 + 0.439671i −0.866016 0.500016i \(-0.833328\pi\)
0.342037 + 0.939686i \(0.388883\pi\)
\(480\) 0 0
\(481\) −40773.0 231235.i −0.176231 0.999457i
\(482\) 0 0
\(483\) 98928.5 + 57116.4i 0.424060 + 0.244831i
\(484\) 0 0
\(485\) −510.813 + 1403.45i −0.00217159 + 0.00596641i
\(486\) 0 0
\(487\) 134338. 77560.2i 0.566424 0.327025i −0.189296 0.981920i \(-0.560621\pi\)
0.755720 + 0.654895i \(0.227287\pi\)
\(488\) 0 0
\(489\) 60457.8 72050.8i 0.252833 0.301315i
\(490\) 0 0
\(491\) 27722.8 157224.i 0.114994 0.652163i −0.871759 0.489934i \(-0.837021\pi\)
0.986753 0.162228i \(-0.0518681\pi\)
\(492\) 0 0
\(493\) 106103.i 0.436551i
\(494\) 0 0
\(495\) −2909.84 −0.0118757
\(496\) 0 0
\(497\) 244371. + 43089.3i 0.989322 + 0.174444i
\(498\) 0 0
\(499\) 211495. + 177466.i 0.849375 + 0.712710i 0.959652 0.281190i \(-0.0907293\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(500\) 0 0
\(501\) 60466.2 + 104731.i 0.240900 + 0.417252i
\(502\) 0 0
\(503\) −58971.7 21463.9i −0.233081 0.0848347i 0.222839 0.974855i \(-0.428468\pi\)
−0.455920 + 0.890021i \(0.650690\pi\)
\(504\) 0 0
\(505\) 6062.25 10500.1i 0.0237712 0.0411729i
\(506\) 0 0
\(507\) −126363. + 22281.2i −0.491591 + 0.0866807i
\(508\) 0 0
\(509\) 266313. + 317380.i 1.02792 + 1.22502i 0.974017 + 0.226476i \(0.0727205\pi\)
0.0538991 + 0.998546i \(0.482835\pi\)
\(510\) 0 0
\(511\) 355736. 129477.i 1.36234 0.495852i
\(512\) 0 0
\(513\) −43190.7 + 280533.i −0.164118 + 1.06598i
\(514\) 0 0
\(515\) −5551.28 15252.0i −0.0209305 0.0575060i
\(516\) 0 0
\(517\) −231987. + 194660.i −0.867924 + 0.728275i
\(518\) 0 0
\(519\) −47907.4 271696.i −0.177856 1.00867i
\(520\) 0 0
\(521\) −126272. 72903.2i −0.465191 0.268578i 0.249033 0.968495i \(-0.419887\pi\)
−0.714225 + 0.699917i \(0.753221\pi\)
\(522\) 0 0
\(523\) 161926. 444889.i 0.591990 1.62648i −0.174818 0.984601i \(-0.555934\pi\)
0.766807 0.641877i \(-0.221844\pi\)
\(524\) 0 0
\(525\) −198369. + 114528.i −0.719705 + 0.415522i
\(526\) 0 0
\(527\) −270210. + 322023.i −0.972925 + 1.15949i
\(528\) 0 0
\(529\) −31760.9 + 180125.i −0.113496 + 0.643668i
\(530\) 0 0
\(531\) 88692.8i 0.314557i
\(532\) 0 0
\(533\) 218012. 0.767408
\(534\) 0 0
\(535\) −3737.59 659.037i −0.0130582 0.00230251i
\(536\) 0 0
\(537\) −193928. 162725.i −0.672499 0.564294i
\(538\) 0 0
\(539\) −24348.5 42172.8i −0.0838096 0.145163i
\(540\) 0 0
\(541\) 128104. + 46625.9i 0.437690 + 0.159306i 0.551461 0.834201i \(-0.314071\pi\)
−0.113771 + 0.993507i \(0.536293\pi\)
\(542\) 0 0
\(543\) 225710. 390940.i 0.765509 1.32590i
\(544\) 0 0
\(545\) −10588.2 + 1866.99i −0.0356477 + 0.00628564i
\(546\) 0 0
\(547\) −207771. 247611.i −0.694400 0.827554i 0.297481 0.954728i \(-0.403854\pi\)
−0.991880 + 0.127174i \(0.959409\pi\)
\(548\) 0 0
\(549\) 86729.0 31566.8i 0.287753 0.104733i
\(550\) 0 0
\(551\) 71316.5 1553.02i 0.234902 0.00511532i
\(552\) 0 0
\(553\) 90859.2 + 249634.i 0.297111 + 0.816306i
\(554\) 0 0
\(555\) −5607.90 + 4705.59i −0.0182060 + 0.0152766i
\(556\) 0 0
\(557\) −94444.8 535623.i −0.304416 1.72643i −0.626241 0.779630i \(-0.715407\pi\)
0.321825 0.946799i \(-0.395704\pi\)
\(558\) 0 0
\(559\) 207500. + 119800.i 0.664042 + 0.383385i
\(560\) 0 0
\(561\) −277995. + 763784.i −0.883305 + 2.42686i
\(562\) 0 0
\(563\) −364078. + 210201.i −1.14862 + 0.663158i −0.948552 0.316623i \(-0.897451\pi\)
−0.200072 + 0.979781i \(0.564118\pi\)
\(564\) 0 0
\(565\) −9593.61 + 11433.2i −0.0300528 + 0.0358155i
\(566\) 0 0
\(567\) 38182.6 216544.i 0.118768 0.673566i
\(568\) 0 0
\(569\) 311903.i 0.963374i 0.876343 + 0.481687i \(0.159976\pi\)
−0.876343 + 0.481687i \(0.840024\pi\)
\(570\) 0 0
\(571\) −4647.72 −0.0142550 −0.00712751 0.999975i \(-0.502269\pi\)
−0.00712751 + 0.999975i \(0.502269\pi\)
\(572\) 0 0
\(573\) −397159. 70029.8i −1.20964 0.213292i
\(574\) 0 0
\(575\) 148901. + 124943.i 0.450362 + 0.377899i
\(576\) 0 0
\(577\) 92600.9 + 160390.i 0.278140 + 0.481753i 0.970923 0.239394i \(-0.0769487\pi\)
−0.692782 + 0.721147i \(0.743615\pi\)
\(578\) 0 0
\(579\) −54070.1 19679.9i −0.161287 0.0587038i
\(580\) 0 0
\(581\) 110711. 191757.i 0.327973 0.568066i
\(582\) 0 0
\(583\) 182564. 32190.9i 0.537127 0.0947100i
\(584\) 0 0
\(585\) −2070.43 2467.45i −0.00604992 0.00721001i
\(586\) 0 0
\(587\) −177355. + 64551.9i −0.514715 + 0.187341i −0.586301 0.810094i \(-0.699416\pi\)
0.0715858 + 0.997434i \(0.477194\pi\)
\(588\) 0 0
\(589\) −220400. 176906.i −0.635304 0.509931i
\(590\) 0 0
\(591\) 36067.7 + 99095.3i 0.103263 + 0.283712i
\(592\) 0 0
\(593\) 131397. 110255.i 0.373659 0.313537i −0.436548 0.899681i \(-0.643799\pi\)
0.810207 + 0.586144i \(0.199355\pi\)
\(594\) 0 0
\(595\) 3597.86 + 20404.5i 0.0101627 + 0.0576357i
\(596\) 0 0
\(597\) 203048. + 117230.i 0.569706 + 0.328920i
\(598\) 0 0
\(599\) 136137. 374034.i 0.379423 1.04246i −0.592174 0.805810i \(-0.701730\pi\)
0.971596 0.236645i \(-0.0760477\pi\)
\(600\) 0 0
\(601\) −376812. + 217553.i −1.04322 + 0.602304i −0.920744 0.390168i \(-0.872417\pi\)
−0.122477 + 0.992471i \(0.539084\pi\)
\(602\) 0 0
\(603\) 2411.76 2874.22i 0.00663283 0.00790470i
\(604\) 0 0
\(605\) 3166.05 17955.6i 0.00864983 0.0490556i
\(606\) 0 0
\(607\) 48561.9i 0.131801i 0.997826 + 0.0659005i \(0.0209920\pi\)
−0.997826 + 0.0659005i \(0.979008\pi\)
\(608\) 0 0
\(609\) −72498.8 −0.195477
\(610\) 0 0
\(611\) −330130. 58210.8i −0.884306 0.155927i
\(612\) 0 0
\(613\) −265441. 222732.i −0.706395 0.592736i 0.217190 0.976129i \(-0.430311\pi\)
−0.923585 + 0.383394i \(0.874755\pi\)
\(614\) 0 0
\(615\) −3398.55 5886.47i −0.00898553 0.0155634i
\(616\) 0 0
\(617\) 380855. + 138620.i 1.00044 + 0.364129i 0.789753 0.613426i \(-0.210209\pi\)
0.210683 + 0.977554i \(0.432431\pi\)
\(618\) 0 0
\(619\) −163814. + 283734.i −0.427533 + 0.740508i −0.996653 0.0817457i \(-0.973950\pi\)
0.569120 + 0.822254i \(0.307284\pi\)
\(620\) 0 0
\(621\) −241080. + 42508.9i −0.625141 + 0.110229i
\(622\) 0 0
\(623\) 333561. + 397523.i 0.859409 + 1.02420i
\(624\) 0 0
\(625\) −365846. + 133157.i −0.936565 + 0.340882i
\(626\) 0 0
\(627\) −517440. 175672.i −1.31621 0.446857i
\(628\) 0 0
\(629\) −203817. 559982.i −0.515156 1.41538i
\(630\) 0 0
\(631\) −270104. + 226644.i −0.678379 + 0.569228i −0.915532 0.402244i \(-0.868230\pi\)
0.237153 + 0.971472i \(0.423786\pi\)
\(632\) 0 0
\(633\) 64.6222 + 366.491i 0.000161278 + 0.000914652i
\(634\) 0 0
\(635\) −21469.6 12395.5i −0.0532448 0.0307409i
\(636\) 0 0
\(637\) 18436.5 50653.8i 0.0454359 0.124834i
\(638\) 0 0
\(639\) −84788.0 + 48952.4i −0.207650 + 0.119887i
\(640\) 0 0
\(641\) 284607. 339181.i 0.692675 0.825498i −0.299002 0.954253i \(-0.596654\pi\)
0.991676 + 0.128755i \(0.0410981\pi\)
\(642\) 0 0
\(643\) −68762.6 + 389972.i −0.166315 + 0.943217i 0.781384 + 0.624050i \(0.214514\pi\)
−0.947699 + 0.319166i \(0.896597\pi\)
\(644\) 0 0
\(645\) 7470.19i 0.0179561i
\(646\) 0 0
\(647\) −129762. −0.309983 −0.154992 0.987916i \(-0.549535\pi\)
−0.154992 + 0.987916i \(0.549535\pi\)
\(648\) 0 0
\(649\) 913338. + 161046.i 2.16841 + 0.382350i
\(650\) 0 0
\(651\) 220034. + 184630.i 0.519191 + 0.435653i
\(652\) 0 0
\(653\) 126553. + 219197.i 0.296788 + 0.514052i 0.975399 0.220445i \(-0.0707511\pi\)
−0.678611 + 0.734498i \(0.737418\pi\)
\(654\) 0 0
\(655\) 13749.4 + 5004.39i 0.0320481 + 0.0116646i
\(656\) 0 0
\(657\) −74682.3 + 129354.i −0.173016 + 0.299673i
\(658\) 0 0
\(659\) 156021. 27510.7i 0.359263 0.0633477i 0.00889634 0.999960i \(-0.497168\pi\)
0.350366 + 0.936613i \(0.386057\pi\)
\(660\) 0 0
\(661\) −434961. 518366.i −0.995513 1.18641i −0.982456 0.186492i \(-0.940288\pi\)
−0.0130570 0.999915i \(-0.504156\pi\)
\(662\) 0 0
\(663\) −845464. + 307724.i −1.92339 + 0.700058i
\(664\) 0 0
\(665\) −13662.0 + 2716.93i −0.0308938 + 0.00614377i
\(666\) 0 0
\(667\) 21041.8 + 57812.0i 0.0472968 + 0.129947i
\(668\) 0 0
\(669\) 142723. 119759.i 0.318892 0.267582i
\(670\) 0 0
\(671\) 167587. + 950433.i 0.372216 + 2.11094i
\(672\) 0 0
\(673\) −706065. 407647.i −1.55889 0.900024i −0.997364 0.0725630i \(-0.976882\pi\)
−0.561523 0.827461i \(-0.689785\pi\)
\(674\) 0 0
\(675\) 167885. 461261.i 0.368473 1.01237i
\(676\) 0 0
\(677\) 316533. 182751.i 0.690624 0.398732i −0.113221 0.993570i \(-0.536117\pi\)
0.803846 + 0.594838i \(0.202784\pi\)
\(678\) 0 0
\(679\) −53397.6 + 63636.8i −0.115820 + 0.138028i
\(680\) 0 0
\(681\) −12448.3 + 70598.1i −0.0268422 + 0.152229i
\(682\) 0 0
\(683\) 125776.i 0.269623i −0.990871 0.134811i \(-0.956957\pi\)
0.990871 0.134811i \(-0.0430428\pi\)
\(684\) 0 0
\(685\) −5738.27 −0.0122292
\(686\) 0 0
\(687\) 135545. + 23900.3i 0.287191 + 0.0506395i
\(688\) 0 0
\(689\) 157196. + 131903.i 0.331133 + 0.277854i
\(690\) 0 0
\(691\) −289348. 501166.i −0.605989 1.04960i −0.991894 0.127065i \(-0.959444\pi\)
0.385905 0.922538i \(-0.373889\pi\)
\(692\) 0 0
\(693\) −152089. 55355.9i −0.316688 0.115265i
\(694\) 0 0
\(695\) 936.177 1621.51i 0.00193815 0.00335698i
\(696\) 0 0
\(697\) 544901. 96080.7i 1.12164 0.197775i
\(698\) 0 0
\(699\) 351634. + 419061.i 0.719675 + 0.857676i
\(700\) 0 0
\(701\) 733783. 267075.i 1.49325 0.543498i 0.538945 0.842341i \(-0.318823\pi\)
0.954302 + 0.298843i \(0.0966007\pi\)
\(702\) 0 0
\(703\) 373404. 145190.i 0.755559 0.293783i
\(704\) 0 0
\(705\) 3574.61 + 9821.16i 0.00719201 + 0.0197599i
\(706\) 0 0
\(707\) 516609. 433486.i 1.03353 0.867234i
\(708\) 0 0
\(709\) 157506. + 893259.i 0.313331 + 1.77699i 0.581427 + 0.813598i \(0.302494\pi\)
−0.268096 + 0.963392i \(0.586394\pi\)
\(710\) 0 0
\(711\) −90772.3 52407.4i −0.179562 0.103670i
\(712\) 0 0
\(713\) 83365.7 229045.i 0.163987 0.450550i
\(714\) 0 0
\(715\) 29168.6 16840.5i 0.0570563 0.0329415i
\(716\) 0 0
\(717\) 481675. 574038.i 0.936948 1.11661i
\(718\) 0 0
\(719\) −36072.2 + 204576.i −0.0697775 + 0.395728i 0.929837 + 0.367971i \(0.119947\pi\)
−0.999615 + 0.0277566i \(0.991164\pi\)
\(720\) 0 0
\(721\) 902787.i 1.73666i
\(722\) 0 0
\(723\) 850542. 1.62712
\(724\) 0 0
\(725\) −121488. 21421.7i −0.231131 0.0407547i
\(726\) 0 0
\(727\) −505469. 424139.i −0.956370 0.802489i 0.0239891 0.999712i \(-0.492363\pi\)
−0.980359 + 0.197223i \(0.936808\pi\)
\(728\) 0 0
\(729\) 295567. + 511938.i 0.556162 + 0.963301i
\(730\) 0 0
\(731\) 571425. + 207982.i 1.06936 + 0.389216i
\(732\) 0 0
\(733\) 235776. 408377.i 0.438826 0.760069i −0.558773 0.829321i \(-0.688728\pi\)
0.997599 + 0.0692514i \(0.0220611\pi\)
\(734\) 0 0
\(735\) −1655.09 + 291.836i −0.00306370 + 0.000540213i
\(736\) 0 0
\(737\) 25218.8 + 30054.6i 0.0464290 + 0.0553320i
\(738\) 0 0
\(739\) −559014. + 203465.i −1.02361 + 0.372563i −0.798644 0.601804i \(-0.794449\pi\)
−0.224965 + 0.974367i \(0.572227\pi\)
\(740\) 0 0
\(741\) −219209. 563768.i −0.399229 1.02675i
\(742\) 0 0
\(743\) −115197. 316500.i −0.208671 0.573319i 0.790566 0.612377i \(-0.209787\pi\)
−0.999237 + 0.0390578i \(0.987564\pi\)
\(744\) 0 0
\(745\) −11554.4 + 9695.31i −0.0208178 + 0.0174682i
\(746\) 0 0
\(747\) 15170.4 + 86035.4i 0.0271866 + 0.154183i
\(748\) 0 0
\(749\) −182816. 105549.i −0.325874 0.188144i
\(750\) 0 0
\(751\) −163368. + 448849.i −0.289659 + 0.795831i 0.706455 + 0.707758i \(0.250293\pi\)
−0.996114 + 0.0880731i \(0.971929\pi\)
\(752\) 0 0
\(753\) 36032.5 20803.4i 0.0635483 0.0366896i
\(754\) 0 0
\(755\) −6783.13 + 8083.82i −0.0118997 + 0.0141815i
\(756\) 0 0
\(757\) −126507. + 717459.i −0.220762 + 1.25200i 0.649861 + 0.760053i \(0.274827\pi\)
−0.870623 + 0.491950i \(0.836284\pi\)
\(758\) 0 0
\(759\) 471289.i 0.818095i
\(760\) 0 0
\(761\) −307163. −0.530396 −0.265198 0.964194i \(-0.585437\pi\)
−0.265198 + 0.964194i \(0.585437\pi\)
\(762\) 0 0
\(763\) −588935. 103845.i −1.01162 0.178376i
\(764\) 0 0
\(765\) −6262.28 5254.68i −0.0107006 0.00897891i
\(766\) 0 0
\(767\) 513304. + 889068.i 0.872537 + 1.51128i
\(768\) 0 0
\(769\) 968775. + 352605.i 1.63821 + 0.596261i 0.986725 0.162398i \(-0.0519229\pi\)
0.651488 + 0.758659i \(0.274145\pi\)
\(770\) 0 0
\(771\) −70698.3 + 122453.i −0.118932 + 0.205997i
\(772\) 0 0
\(773\) 1.03440e6 182393.i 1.73113 0.305245i 0.782740 0.622348i \(-0.213821\pi\)
0.948391 + 0.317103i \(0.102710\pi\)
\(774\) 0 0
\(775\) 314163. + 374405.i 0.523060 + 0.623359i
\(776\) 0 0
\(777\) −382627. + 139265.i −0.633773 + 0.230674i
\(778\) 0 0
\(779\) 72555.5 + 364844.i 0.119563 + 0.601219i
\(780\) 0 0
\(781\) −350144. 962013.i −0.574044 1.57717i
\(782\) 0 0
\(783\) 119015. 99865.8i 0.194124 0.162890i
\(784\) 0 0
\(785\) 2392.91 + 13570.9i 0.00388318 + 0.0220226i
\(786\) 0 0
\(787\) −152033. 87776.2i −0.245464 0.141719i 0.372221 0.928144i \(-0.378596\pi\)
−0.617686 + 0.786425i \(0.711930\pi\)
\(788\) 0 0
\(789\) 12752.1 35036.1i 0.0204846 0.0562810i
\(790\) 0 0
\(791\) −718933. + 415076.i −1.14904 + 0.663399i
\(792\)