Properties

Label 76.5.j.a.21.7
Level $76$
Weight $5$
Character 76.21
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 21.7
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.7

$q$-expansion

\(f(q)\) \(=\) \(q+(10.9995 - 13.1087i) q^{3} +(-41.8937 + 15.2481i) q^{5} +(-26.2709 - 45.5025i) q^{7} +(-36.7834 - 208.609i) q^{9} +O(q^{10})\) \(q+(10.9995 - 13.1087i) q^{3} +(-41.8937 + 15.2481i) q^{5} +(-26.2709 - 45.5025i) q^{7} +(-36.7834 - 208.609i) q^{9} +(-55.1598 + 95.5395i) q^{11} +(31.8438 + 37.9500i) q^{13} +(-260.928 + 716.893i) q^{15} +(62.4554 - 354.202i) q^{17} +(346.709 - 100.566i) q^{19} +(-885.446 - 156.128i) q^{21} +(-253.544 - 92.2824i) q^{23} +(1043.80 - 875.852i) q^{25} +(-1938.81 - 1119.37i) q^{27} +(-563.593 + 99.3766i) q^{29} +(910.085 - 525.438i) q^{31} +(645.669 + 1773.96i) q^{33} +(1794.41 + 1505.69i) q^{35} -527.558i q^{37} +847.742 q^{39} +(407.245 - 485.336i) q^{41} +(-910.710 + 331.471i) q^{43} +(4721.88 + 8178.53i) q^{45} +(-22.9255 - 130.017i) q^{47} +(-179.821 + 311.459i) q^{49} +(-3956.15 - 4714.76i) q^{51} +(-203.387 + 558.802i) q^{53} +(854.054 - 4843.58i) q^{55} +(2495.34 - 5651.09i) q^{57} +(3752.63 + 661.690i) q^{59} +(1592.89 + 579.765i) q^{61} +(-8525.91 + 7154.09i) q^{63} +(-1912.72 - 1104.31i) q^{65} +(2494.24 - 439.803i) q^{67} +(-3998.56 + 2308.57i) q^{69} +(1828.11 + 5022.70i) q^{71} +(500.371 + 419.861i) q^{73} -23316.8i q^{75} +5796.39 q^{77} +(-53.2273 + 63.4339i) q^{79} +(-19876.2 + 7234.34i) q^{81} +(-3329.40 - 5766.69i) q^{83} +(2784.41 + 15791.2i) q^{85} +(-4896.54 + 8481.06i) q^{87} +(3754.44 + 4474.37i) q^{89} +(890.255 - 2445.96i) q^{91} +(3122.68 - 17709.6i) q^{93} +(-12991.5 + 9499.74i) q^{95} +(-14207.9 - 2505.23i) q^{97} +(21959.4 + 7992.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 10.9995 13.1087i 1.22217 1.45652i 0.373472 0.927642i \(-0.378167\pi\)
0.848696 0.528881i \(-0.177388\pi\)
\(4\) 0 0
\(5\) −41.8937 + 15.2481i −1.67575 + 0.609922i −0.992717 0.120468i \(-0.961561\pi\)
−0.683030 + 0.730390i \(0.739338\pi\)
\(6\) 0 0
\(7\) −26.2709 45.5025i −0.536141 0.928623i −0.999107 0.0422474i \(-0.986548\pi\)
0.462966 0.886376i \(-0.346785\pi\)
\(8\) 0 0
\(9\) −36.7834 208.609i −0.454116 2.57542i
\(10\) 0 0
\(11\) −55.1598 + 95.5395i −0.455866 + 0.789583i −0.998738 0.0502329i \(-0.984004\pi\)
0.542872 + 0.839816i \(0.317337\pi\)
\(12\) 0 0
\(13\) 31.8438 + 37.9500i 0.188425 + 0.224556i 0.851984 0.523568i \(-0.175399\pi\)
−0.663559 + 0.748124i \(0.730955\pi\)
\(14\) 0 0
\(15\) −260.928 + 716.893i −1.15968 + 3.18619i
\(16\) 0 0
\(17\) 62.4554 354.202i 0.216109 1.22561i −0.662863 0.748740i \(-0.730659\pi\)
0.878972 0.476873i \(-0.158230\pi\)
\(18\) 0 0
\(19\) 346.709 100.566i 0.960414 0.278577i
\(20\) 0 0
\(21\) −885.446 156.128i −2.00781 0.354032i
\(22\) 0 0
\(23\) −253.544 92.2824i −0.479289 0.174447i 0.0910666 0.995845i \(-0.470972\pi\)
−0.570356 + 0.821398i \(0.693195\pi\)
\(24\) 0 0
\(25\) 1043.80 875.852i 1.67008 1.40136i
\(26\) 0 0
\(27\) −1938.81 1119.37i −2.65955 1.53549i
\(28\) 0 0
\(29\) −563.593 + 99.3766i −0.670146 + 0.118165i −0.498361 0.866970i \(-0.666065\pi\)
−0.171785 + 0.985134i \(0.554953\pi\)
\(30\) 0 0
\(31\) 910.085 525.438i 0.947019 0.546762i 0.0548653 0.998494i \(-0.482527\pi\)
0.892154 + 0.451732i \(0.149194\pi\)
\(32\) 0 0
\(33\) 645.669 + 1773.96i 0.592901 + 1.62898i
\(34\) 0 0
\(35\) 1794.41 + 1505.69i 1.46482 + 1.22913i
\(36\) 0 0
\(37\) 527.558i 0.385360i −0.981262 0.192680i \(-0.938282\pi\)
0.981262 0.192680i \(-0.0617180\pi\)
\(38\) 0 0
\(39\) 847.742 0.557358
\(40\) 0 0
\(41\) 407.245 485.336i 0.242264 0.288719i −0.631188 0.775630i \(-0.717432\pi\)
0.873451 + 0.486912i \(0.161877\pi\)
\(42\) 0 0
\(43\) −910.710 + 331.471i −0.492542 + 0.179271i −0.576337 0.817212i \(-0.695518\pi\)
0.0837945 + 0.996483i \(0.473296\pi\)
\(44\) 0 0
\(45\) 4721.88 + 8178.53i 2.33179 + 4.03878i
\(46\) 0 0
\(47\) −22.9255 130.017i −0.0103782 0.0588578i 0.979179 0.203000i \(-0.0650690\pi\)
−0.989557 + 0.144142i \(0.953958\pi\)
\(48\) 0 0
\(49\) −179.821 + 311.459i −0.0748941 + 0.129720i
\(50\) 0 0
\(51\) −3956.15 4714.76i −1.52101 1.81267i
\(52\) 0 0
\(53\) −203.387 + 558.802i −0.0724056 + 0.198933i −0.970616 0.240632i \(-0.922645\pi\)
0.898211 + 0.439565i \(0.144867\pi\)
\(54\) 0 0
\(55\) 854.054 4843.58i 0.282332 1.60118i
\(56\) 0 0
\(57\) 2495.34 5651.09i 0.768032 1.73933i
\(58\) 0 0
\(59\) 3752.63 + 661.690i 1.07803 + 0.190086i 0.684345 0.729159i \(-0.260088\pi\)
0.393687 + 0.919245i \(0.371199\pi\)
\(60\) 0 0
\(61\) 1592.89 + 579.765i 0.428081 + 0.155809i 0.547070 0.837087i \(-0.315743\pi\)
−0.118989 + 0.992896i \(0.537965\pi\)
\(62\) 0 0
\(63\) −8525.91 + 7154.09i −2.14813 + 1.80249i
\(64\) 0 0
\(65\) −1912.72 1104.31i −0.452715 0.261375i
\(66\) 0 0
\(67\) 2494.24 439.803i 0.555635 0.0979734i 0.111222 0.993796i \(-0.464524\pi\)
0.444413 + 0.895822i \(0.353412\pi\)
\(68\) 0 0
\(69\) −3998.56 + 2308.57i −0.839858 + 0.484892i
\(70\) 0 0
\(71\) 1828.11 + 5022.70i 0.362649 + 0.996371i 0.978089 + 0.208187i \(0.0667562\pi\)
−0.615440 + 0.788184i \(0.711022\pi\)
\(72\) 0 0
\(73\) 500.371 + 419.861i 0.0938959 + 0.0787880i 0.688527 0.725210i \(-0.258258\pi\)
−0.594631 + 0.803998i \(0.702702\pi\)
\(74\) 0 0
\(75\) 23316.8i 4.14521i
\(76\) 0 0
\(77\) 5796.39 0.977633
\(78\) 0 0
\(79\) −53.2273 + 63.4339i −0.00852866 + 0.0101641i −0.770292 0.637691i \(-0.779889\pi\)
0.761763 + 0.647855i \(0.224334\pi\)
\(80\) 0 0
\(81\) −19876.2 + 7234.34i −3.02945 + 1.10263i
\(82\) 0 0
\(83\) −3329.40 5766.69i −0.483292 0.837086i 0.516524 0.856273i \(-0.327226\pi\)
−0.999816 + 0.0191865i \(0.993892\pi\)
\(84\) 0 0
\(85\) 2784.41 + 15791.2i 0.385385 + 2.18563i
\(86\) 0 0
\(87\) −4896.54 + 8481.06i −0.646921 + 1.12050i
\(88\) 0 0
\(89\) 3754.44 + 4474.37i 0.473986 + 0.564874i 0.949070 0.315066i \(-0.102027\pi\)
−0.475084 + 0.879940i \(0.657582\pi\)
\(90\) 0 0
\(91\) 890.255 2445.96i 0.107506 0.295370i
\(92\) 0 0
\(93\) 3122.68 17709.6i 0.361045 2.04759i
\(94\) 0 0
\(95\) −12991.5 + 9499.74i −1.43950 + 1.05260i
\(96\) 0 0
\(97\) −14207.9 2505.23i −1.51003 0.266259i −0.643525 0.765425i \(-0.722529\pi\)
−0.866506 + 0.499166i \(0.833640\pi\)
\(98\) 0 0
\(99\) 21959.4 + 7992.56i 2.24052 + 0.815484i
\(100\) 0 0
\(101\) 8269.68 6939.09i 0.810674 0.680236i −0.140095 0.990138i \(-0.544741\pi\)
0.950768 + 0.309902i \(0.100296\pi\)
\(102\) 0 0
\(103\) −17589.1 10155.0i −1.65794 0.957211i −0.973665 0.227984i \(-0.926787\pi\)
−0.684273 0.729226i \(-0.739880\pi\)
\(104\) 0 0
\(105\) 39475.3 6960.55i 3.58052 0.631343i
\(106\) 0 0
\(107\) −12395.5 + 7156.56i −1.08267 + 0.625082i −0.931616 0.363443i \(-0.881601\pi\)
−0.151057 + 0.988525i \(0.548268\pi\)
\(108\) 0 0
\(109\) −1122.64 3084.44i −0.0944906 0.259611i 0.883439 0.468547i \(-0.155222\pi\)
−0.977929 + 0.208936i \(0.933000\pi\)
\(110\) 0 0
\(111\) −6915.61 5802.88i −0.561286 0.470975i
\(112\) 0 0
\(113\) 14029.8i 1.09874i −0.835578 0.549371i \(-0.814867\pi\)
0.835578 0.549371i \(-0.185133\pi\)
\(114\) 0 0
\(115\) 12029.0 0.909567
\(116\) 0 0
\(117\) 6745.39 8038.85i 0.492760 0.587249i
\(118\) 0 0
\(119\) −17757.9 + 6463.33i −1.25400 + 0.456418i
\(120\) 0 0
\(121\) 1235.30 + 2139.61i 0.0843728 + 0.146138i
\(122\) 0 0
\(123\) −1882.63 10676.9i −0.124438 0.705725i
\(124\) 0 0
\(125\) −16441.6 + 28477.7i −1.05226 + 1.82257i
\(126\) 0 0
\(127\) 8633.73 + 10289.3i 0.535292 + 0.637936i 0.964125 0.265447i \(-0.0855197\pi\)
−0.428833 + 0.903384i \(0.641075\pi\)
\(128\) 0 0
\(129\) −5672.21 + 15584.3i −0.340857 + 0.936498i
\(130\) 0 0
\(131\) −4716.15 + 26746.6i −0.274818 + 1.55857i 0.464722 + 0.885457i \(0.346154\pi\)
−0.739539 + 0.673113i \(0.764957\pi\)
\(132\) 0 0
\(133\) −13684.4 13134.2i −0.773611 0.742506i
\(134\) 0 0
\(135\) 98292.1 + 17331.5i 5.39326 + 0.950976i
\(136\) 0 0
\(137\) 5504.69 + 2003.54i 0.293286 + 0.106747i 0.484473 0.874806i \(-0.339011\pi\)
−0.191187 + 0.981554i \(0.561234\pi\)
\(138\) 0 0
\(139\) 12225.2 10258.2i 0.632742 0.530934i −0.269038 0.963130i \(-0.586706\pi\)
0.901780 + 0.432196i \(0.142261\pi\)
\(140\) 0 0
\(141\) −1956.52 1129.60i −0.0984116 0.0568180i
\(142\) 0 0
\(143\) −5382.22 + 949.031i −0.263202 + 0.0464097i
\(144\) 0 0
\(145\) 22095.7 12756.9i 1.05092 0.606751i
\(146\) 0 0
\(147\) 2104.88 + 5783.11i 0.0974075 + 0.267625i
\(148\) 0 0
\(149\) 29156.7 + 24465.3i 1.31330 + 1.10199i 0.987679 + 0.156494i \(0.0500192\pi\)
0.325625 + 0.945499i \(0.394425\pi\)
\(150\) 0 0
\(151\) 9506.58i 0.416937i −0.978029 0.208468i \(-0.933152\pi\)
0.978029 0.208468i \(-0.0668479\pi\)
\(152\) 0 0
\(153\) −76187.2 −3.25461
\(154\) 0 0
\(155\) −30114.9 + 35889.6i −1.25348 + 1.49384i
\(156\) 0 0
\(157\) 3899.48 1419.29i 0.158200 0.0575802i −0.261706 0.965148i \(-0.584285\pi\)
0.419906 + 0.907567i \(0.362063\pi\)
\(158\) 0 0
\(159\) 5088.01 + 8812.69i 0.201258 + 0.348589i
\(160\) 0 0
\(161\) 2461.74 + 13961.2i 0.0949710 + 0.538607i
\(162\) 0 0
\(163\) 16062.6 27821.3i 0.604563 1.04713i −0.387558 0.921846i \(-0.626681\pi\)
0.992120 0.125288i \(-0.0399855\pi\)
\(164\) 0 0
\(165\) −54098.9 64472.6i −1.98710 2.36814i
\(166\) 0 0
\(167\) 2073.67 5697.35i 0.0743543 0.204287i −0.896948 0.442137i \(-0.854221\pi\)
0.971302 + 0.237850i \(0.0764427\pi\)
\(168\) 0 0
\(169\) 4533.39 25710.1i 0.158727 0.900184i
\(170\) 0 0
\(171\) −33732.2 68627.6i −1.15359 2.34696i
\(172\) 0 0
\(173\) −31337.6 5525.66i −1.04706 0.184626i −0.376454 0.926435i \(-0.622857\pi\)
−0.670610 + 0.741810i \(0.733968\pi\)
\(174\) 0 0
\(175\) −67275.1 24486.1i −2.19674 0.799547i
\(176\) 0 0
\(177\) 49951.0 41913.8i 1.59440 1.33786i
\(178\) 0 0
\(179\) 22968.8 + 13261.0i 0.716856 + 0.413877i 0.813594 0.581433i \(-0.197508\pi\)
−0.0967384 + 0.995310i \(0.530841\pi\)
\(180\) 0 0
\(181\) 10942.8 1929.51i 0.334018 0.0588965i −0.00412374 0.999991i \(-0.501313\pi\)
0.338142 + 0.941095i \(0.390202\pi\)
\(182\) 0 0
\(183\) 25121.0 14503.6i 0.750127 0.433086i
\(184\) 0 0
\(185\) 8044.24 + 22101.4i 0.235040 + 0.645767i
\(186\) 0 0
\(187\) 30395.3 + 25504.7i 0.869207 + 0.729351i
\(188\) 0 0
\(189\) 117628.i 3.29295i
\(190\) 0 0
\(191\) −29302.4 −0.803223 −0.401612 0.915810i \(-0.631550\pi\)
−0.401612 + 0.915810i \(0.631550\pi\)
\(192\) 0 0
\(193\) −38939.0 + 46405.6i −1.04537 + 1.24582i −0.0768082 + 0.997046i \(0.524473\pi\)
−0.968561 + 0.248777i \(0.919972\pi\)
\(194\) 0 0
\(195\) −35515.0 + 12926.4i −0.933992 + 0.339945i
\(196\) 0 0
\(197\) −20192.4 34974.2i −0.520302 0.901189i −0.999721 0.0236031i \(-0.992486\pi\)
0.479420 0.877586i \(-0.340847\pi\)
\(198\) 0 0
\(199\) −4759.75 26993.9i −0.120193 0.681647i −0.984048 0.177906i \(-0.943068\pi\)
0.863855 0.503741i \(-0.168043\pi\)
\(200\) 0 0
\(201\) 21670.2 37533.9i 0.536378 0.929034i
\(202\) 0 0
\(203\) 19328.0 + 23034.2i 0.469023 + 0.558960i
\(204\) 0 0
\(205\) −9660.58 + 26542.2i −0.229877 + 0.631582i
\(206\) 0 0
\(207\) −9924.75 + 56286.1i −0.231622 + 1.31359i
\(208\) 0 0
\(209\) −9516.34 + 38671.7i −0.217860 + 0.885320i
\(210\) 0 0
\(211\) 2493.73 + 439.712i 0.0560124 + 0.00987650i 0.201584 0.979471i \(-0.435391\pi\)
−0.145572 + 0.989348i \(0.546502\pi\)
\(212\) 0 0
\(213\) 85949.5 + 31283.1i 1.89445 + 0.689525i
\(214\) 0 0
\(215\) 33098.7 27773.1i 0.716035 0.600825i
\(216\) 0 0
\(217\) −47817.5 27607.5i −1.01547 0.586283i
\(218\) 0 0
\(219\) 11007.7 1940.95i 0.229513 0.0404693i
\(220\) 0 0
\(221\) 15430.8 8908.98i 0.315939 0.182408i
\(222\) 0 0
\(223\) 13104.1 + 36003.2i 0.263510 + 0.723989i 0.998924 + 0.0463706i \(0.0147655\pi\)
−0.735414 + 0.677618i \(0.763012\pi\)
\(224\) 0 0
\(225\) −221105. 185529.i −4.36751 3.66478i
\(226\) 0 0
\(227\) 15193.9i 0.294861i 0.989072 + 0.147430i \(0.0471002\pi\)
−0.989072 + 0.147430i \(0.952900\pi\)
\(228\) 0 0
\(229\) 102554. 1.95560 0.977801 0.209538i \(-0.0671959\pi\)
0.977801 + 0.209538i \(0.0671959\pi\)
\(230\) 0 0
\(231\) 63757.4 75983.1i 1.19483 1.42394i
\(232\) 0 0
\(233\) 62891.4 22890.6i 1.15846 0.421643i 0.309910 0.950766i \(-0.399701\pi\)
0.848546 + 0.529122i \(0.177479\pi\)
\(234\) 0 0
\(235\) 2942.94 + 5097.32i 0.0532899 + 0.0923009i
\(236\) 0 0
\(237\) 246.061 + 1395.48i 0.00438073 + 0.0248444i
\(238\) 0 0
\(239\) 26990.1 46748.2i 0.472508 0.818407i −0.526997 0.849867i \(-0.676682\pi\)
0.999505 + 0.0314597i \(0.0100156\pi\)
\(240\) 0 0
\(241\) 29546.6 + 35212.3i 0.508714 + 0.606261i 0.957874 0.287190i \(-0.0927211\pi\)
−0.449160 + 0.893451i \(0.648277\pi\)
\(242\) 0 0
\(243\) −61774.2 + 169723.i −1.04615 + 2.87428i
\(244\) 0 0
\(245\) 2784.21 15790.1i 0.0463842 0.263058i
\(246\) 0 0
\(247\) 14857.1 + 9955.20i 0.243522 + 0.163176i
\(248\) 0 0
\(249\) −112216. 19786.6i −1.80990 0.319134i
\(250\) 0 0
\(251\) −85519.4 31126.5i −1.35743 0.494064i −0.442171 0.896931i \(-0.645792\pi\)
−0.915259 + 0.402867i \(0.868014\pi\)
\(252\) 0 0
\(253\) 22802.0 19133.2i 0.356232 0.298914i
\(254\) 0 0
\(255\) 237629. + 137195.i 3.65442 + 2.10988i
\(256\) 0 0
\(257\) 124558. 21963.0i 1.88584 0.332525i 0.892818 0.450418i \(-0.148725\pi\)
0.993026 + 0.117893i \(0.0376139\pi\)
\(258\) 0 0
\(259\) −24005.2 + 13859.4i −0.357855 + 0.206607i
\(260\) 0 0
\(261\) 41461.7 + 113915.i 0.608648 + 1.67225i
\(262\) 0 0
\(263\) −78177.9 65599.1i −1.13025 0.948388i −0.131169 0.991360i \(-0.541873\pi\)
−0.999076 + 0.0429718i \(0.986317\pi\)
\(264\) 0 0
\(265\) 26511.5i 0.377523i
\(266\) 0 0
\(267\) 99950.1 1.40204
\(268\) 0 0
\(269\) −12170.1 + 14503.8i −0.168186 + 0.200436i −0.843554 0.537045i \(-0.819541\pi\)
0.675368 + 0.737481i \(0.263985\pi\)
\(270\) 0 0
\(271\) 39181.9 14261.1i 0.533516 0.194184i −0.0611917 0.998126i \(-0.519490\pi\)
0.594707 + 0.803942i \(0.297268\pi\)
\(272\) 0 0
\(273\) −22270.9 38574.4i −0.298823 0.517576i
\(274\) 0 0
\(275\) 26102.7 + 148036.i 0.345160 + 1.95750i
\(276\) 0 0
\(277\) 69589.1 120532.i 0.906946 1.57088i 0.0886635 0.996062i \(-0.471740\pi\)
0.818283 0.574816i \(-0.194926\pi\)
\(278\) 0 0
\(279\) −143087. 170525.i −1.83820 2.19068i
\(280\) 0 0
\(281\) 37180.7 102153.i 0.470875 1.29372i −0.446176 0.894945i \(-0.647214\pi\)
0.917050 0.398772i \(-0.130563\pi\)
\(282\) 0 0
\(283\) −21903.0 + 124218.i −0.273484 + 1.55100i 0.470254 + 0.882531i \(0.344162\pi\)
−0.743738 + 0.668471i \(0.766949\pi\)
\(284\) 0 0
\(285\) −18370.7 + 274794.i −0.226171 + 3.38312i
\(286\) 0 0
\(287\) −32782.7 5780.48i −0.397998 0.0701778i
\(288\) 0 0
\(289\) −43074.5 15677.8i −0.515733 0.187711i
\(290\) 0 0
\(291\) −189120. + 158691.i −2.23332 + 1.87398i
\(292\) 0 0
\(293\) 104194. + 60156.7i 1.21369 + 0.700727i 0.963562 0.267485i \(-0.0861924\pi\)
0.250133 + 0.968212i \(0.419526\pi\)
\(294\) 0 0
\(295\) −167301. + 29499.7i −1.92245 + 0.338979i
\(296\) 0 0
\(297\) 213888. 123489.i 2.42479 1.39995i
\(298\) 0 0
\(299\) −4571.69 12560.6i −0.0511369 0.140498i
\(300\) 0 0
\(301\) 39008.0 + 32731.6i 0.430547 + 0.361272i
\(302\) 0 0
\(303\) 184731.i 2.01213i
\(304\) 0 0
\(305\) −75572.4 −0.812388
\(306\) 0 0
\(307\) 55205.7 65791.6i 0.585743 0.698062i −0.389038 0.921222i \(-0.627193\pi\)
0.974782 + 0.223160i \(0.0716371\pi\)
\(308\) 0 0
\(309\) −326591. + 118869.i −3.42048 + 1.24495i
\(310\) 0 0
\(311\) 25459.7 + 44097.5i 0.263229 + 0.455925i 0.967098 0.254404i \(-0.0818793\pi\)
−0.703869 + 0.710329i \(0.748546\pi\)
\(312\) 0 0
\(313\) −5380.77 30515.9i −0.0549232 0.311485i 0.944953 0.327205i \(-0.106107\pi\)
−0.999876 + 0.0157205i \(0.994996\pi\)
\(314\) 0 0
\(315\) 248096. 429715.i 2.50034 4.33071i
\(316\) 0 0
\(317\) −48597.9 57916.7i −0.483614 0.576348i 0.467968 0.883746i \(-0.344986\pi\)
−0.951581 + 0.307397i \(0.900542\pi\)
\(318\) 0 0
\(319\) 21593.2 59327.0i 0.212196 0.583003i
\(320\) 0 0
\(321\) −42531.5 + 241208.i −0.412763 + 2.34089i
\(322\) 0 0
\(323\) −13967.0 129086.i −0.133874 1.23730i
\(324\) 0 0
\(325\) 66477.2 + 11721.7i 0.629370 + 0.110975i
\(326\) 0 0
\(327\) −52781.5 19210.9i −0.493612 0.179660i
\(328\) 0 0
\(329\) −5313.82 + 4458.83i −0.0490925 + 0.0411935i
\(330\) 0 0
\(331\) −61581.7 35554.2i −0.562077 0.324515i 0.191902 0.981414i \(-0.438534\pi\)
−0.753979 + 0.656899i \(0.771868\pi\)
\(332\) 0 0
\(333\) −110054. + 19405.4i −0.992466 + 0.174998i
\(334\) 0 0
\(335\) −97787.0 + 56457.3i −0.871347 + 0.503073i
\(336\) 0 0
\(337\) 52702.3 + 144798.i 0.464055 + 1.27498i 0.922410 + 0.386212i \(0.126217\pi\)
−0.458355 + 0.888769i \(0.651561\pi\)
\(338\) 0 0
\(339\) −183913. 154321.i −1.60034 1.34285i
\(340\) 0 0
\(341\) 115932.i 0.997000i
\(342\) 0 0
\(343\) −107257. −0.911667
\(344\) 0 0
\(345\) 132313. 157685.i 1.11164 1.32480i
\(346\) 0 0
\(347\) 142072. 51710.0i 1.17991 0.429453i 0.323742 0.946145i \(-0.395059\pi\)
0.856171 + 0.516692i \(0.172837\pi\)
\(348\) 0 0
\(349\) 11647.2 + 20173.6i 0.0956250 + 0.165627i 0.909869 0.414895i \(-0.136182\pi\)
−0.814244 + 0.580522i \(0.802848\pi\)
\(350\) 0 0
\(351\) −19258.9 109223.i −0.156321 0.886542i
\(352\) 0 0
\(353\) −28616.5 + 49565.3i −0.229650 + 0.397766i −0.957705 0.287753i \(-0.907092\pi\)
0.728054 + 0.685520i \(0.240425\pi\)
\(354\) 0 0
\(355\) −153173. 182544.i −1.21542 1.44848i
\(356\) 0 0
\(357\) −110602. + 303876.i −0.867813 + 2.38430i
\(358\) 0 0
\(359\) 3682.01 20881.7i 0.0285691 0.162023i −0.967185 0.254071i \(-0.918230\pi\)
0.995755 + 0.0920479i \(0.0293413\pi\)
\(360\) 0 0
\(361\) 110094. 69734.7i 0.844789 0.535099i
\(362\) 0 0
\(363\) 41635.2 + 7341.40i 0.315971 + 0.0557142i
\(364\) 0 0
\(365\) −27364.5 9959.85i −0.205400 0.0747596i
\(366\) 0 0
\(367\) 9637.00 8086.40i 0.0715500 0.0600376i −0.606311 0.795227i \(-0.707351\pi\)
0.677861 + 0.735190i \(0.262907\pi\)
\(368\) 0 0
\(369\) −116225. 67102.8i −0.853588 0.492819i
\(370\) 0 0
\(371\) 30770.1 5425.59i 0.223553 0.0394184i
\(372\) 0 0
\(373\) 208217. 120214.i 1.49658 0.864049i 0.496585 0.867988i \(-0.334587\pi\)
0.999992 + 0.00393908i \(0.00125385\pi\)
\(374\) 0 0
\(375\) 192456. + 528769.i 1.36858 + 3.76014i
\(376\) 0 0
\(377\) −21718.3 18223.8i −0.152807 0.128220i
\(378\) 0 0
\(379\) 218287.i 1.51967i 0.650116 + 0.759835i \(0.274720\pi\)
−0.650116 + 0.759835i \(0.725280\pi\)
\(380\) 0 0
\(381\) 229846. 1.58339
\(382\) 0 0
\(383\) 9812.87 11694.5i 0.0668958 0.0797233i −0.731559 0.681778i \(-0.761207\pi\)
0.798455 + 0.602055i \(0.205651\pi\)
\(384\) 0 0
\(385\) −242832. + 88383.6i −1.63827 + 0.596280i
\(386\) 0 0
\(387\) 102647. + 177790.i 0.685369 + 1.18709i
\(388\) 0 0
\(389\) −46356.7 262902.i −0.306347 1.73738i −0.617096 0.786888i \(-0.711691\pi\)
0.310749 0.950492i \(-0.399420\pi\)
\(390\) 0 0
\(391\) −48521.8 + 84042.3i −0.317383 + 0.549724i
\(392\) 0 0
\(393\) 298738. + 356022.i 1.93422 + 2.30511i
\(394\) 0 0
\(395\) 1262.65 3469.09i 0.00809259 0.0222342i
\(396\) 0 0
\(397\) −25111.4 + 142414.i −0.159327 + 0.903589i 0.795395 + 0.606091i \(0.207263\pi\)
−0.954722 + 0.297498i \(0.903848\pi\)
\(398\) 0 0
\(399\) −322694. + 34915.1i −2.02696 + 0.219315i
\(400\) 0 0
\(401\) 59433.0 + 10479.6i 0.369606 + 0.0651715i 0.355366 0.934727i \(-0.384356\pi\)
0.0142397 + 0.999899i \(0.495467\pi\)
\(402\) 0 0
\(403\) 48921.0 + 17805.8i 0.301221 + 0.109635i
\(404\) 0 0
\(405\) 722377. 606147.i 4.40407 3.69545i
\(406\) 0 0
\(407\) 50402.7 + 29100.0i 0.304274 + 0.175673i
\(408\) 0 0
\(409\) −224415. + 39570.4i −1.34155 + 0.236551i −0.797913 0.602773i \(-0.794062\pi\)
−0.543632 + 0.839323i \(0.682951\pi\)
\(410\) 0 0
\(411\) 86812.7 50121.3i 0.513925 0.296715i
\(412\) 0 0
\(413\) −68476.4 188137.i −0.401459 1.10300i
\(414\) 0 0
\(415\) 227412. + 190821.i 1.32043 + 1.10797i
\(416\) 0 0
\(417\) 273092.i 1.57049i
\(418\) 0 0
\(419\) 103744. 0.590930 0.295465 0.955354i \(-0.404525\pi\)
0.295465 + 0.955354i \(0.404525\pi\)
\(420\) 0 0
\(421\) −185363. + 220907.i −1.04583 + 1.24637i −0.0774170 + 0.996999i \(0.524667\pi\)
−0.968409 + 0.249368i \(0.919777\pi\)
\(422\) 0 0
\(423\) −26279.4 + 9564.93i −0.146871 + 0.0534566i
\(424\) 0 0
\(425\) −245038. 424418.i −1.35661 2.34972i
\(426\) 0 0
\(427\) −15465.9 87711.5i −0.0848242 0.481062i
\(428\) 0 0
\(429\) −46761.2 + 80992.8i −0.254081 + 0.440080i
\(430\) 0 0
\(431\) −115204. 137295.i −0.620173 0.739093i 0.360927 0.932594i \(-0.382460\pi\)
−0.981100 + 0.193501i \(0.938016\pi\)
\(432\) 0 0
\(433\) −95452.7 + 262254.i −0.509111 + 1.39877i 0.373045 + 0.927813i \(0.378314\pi\)
−0.882156 + 0.470958i \(0.843908\pi\)
\(434\) 0 0
\(435\) 75814.6 429966.i 0.400658 2.27225i
\(436\) 0 0
\(437\) −97186.6 6497.18i −0.508913 0.0340221i
\(438\) 0 0
\(439\) 2077.19 + 366.264i 0.0107782 + 0.00190049i 0.179035 0.983843i \(-0.442703\pi\)
−0.168256 + 0.985743i \(0.553814\pi\)
\(440\) 0 0
\(441\) 71587.5 + 26055.7i 0.368095 + 0.133976i
\(442\) 0 0
\(443\) −150418. + 126215.i −0.766463 + 0.643139i −0.939801 0.341723i \(-0.888989\pi\)
0.173337 + 0.984863i \(0.444545\pi\)
\(444\) 0 0
\(445\) −225513. 130200.i −1.13881 0.657492i
\(446\) 0 0
\(447\) 641418. 113099.i 3.21016 0.566037i
\(448\) 0 0
\(449\) 129237. 74614.8i 0.641052 0.370111i −0.143968 0.989582i \(-0.545986\pi\)
0.785020 + 0.619471i \(0.212653\pi\)
\(450\) 0 0
\(451\) 23905.2 + 65679.0i 0.117528 + 0.322904i
\(452\) 0 0
\(453\) −124619. 104568.i −0.607278 0.509567i
\(454\) 0 0
\(455\) 116045.i 0.560535i
\(456\) 0 0
\(457\) −48048.6 −0.230064 −0.115032 0.993362i \(-0.536697\pi\)
−0.115032 + 0.993362i \(0.536697\pi\)
\(458\) 0 0
\(459\) −517573. + 616820.i −2.45667 + 2.92774i
\(460\) 0 0
\(461\) −134980. + 49128.5i −0.635135 + 0.231170i −0.639465 0.768820i \(-0.720844\pi\)
0.00432977 + 0.999991i \(0.498622\pi\)
\(462\) 0 0
\(463\) 185533. + 321352.i 0.865483 + 1.49906i 0.866566 + 0.499062i \(0.166322\pi\)
−0.00108317 + 0.999999i \(0.500345\pi\)
\(464\) 0 0
\(465\) 139216. + 789535.i 0.643849 + 3.65145i
\(466\) 0 0
\(467\) −59097.8 + 102360.i −0.270980 + 0.469351i −0.969113 0.246617i \(-0.920681\pi\)
0.698133 + 0.715968i \(0.254014\pi\)
\(468\) 0 0
\(469\) −85538.2 101940.i −0.388879 0.463448i
\(470\) 0 0
\(471\) 24287.2 66728.7i 0.109480 0.300795i
\(472\) 0 0
\(473\) 18565.9 105293.i 0.0829841 0.470626i
\(474\) 0 0
\(475\) 273814. 408638.i 1.21358 1.81114i
\(476\) 0 0
\(477\) 124052. + 21873.8i 0.545216 + 0.0961363i
\(478\) 0 0
\(479\) 138747. + 50499.8i 0.604718 + 0.220099i 0.626191 0.779670i \(-0.284613\pi\)
−0.0214724 + 0.999769i \(0.506835\pi\)
\(480\) 0 0
\(481\) 20020.8 16799.5i 0.0865351 0.0726116i
\(482\) 0 0
\(483\) 210092. + 121296.i 0.900564 + 0.519941i
\(484\) 0 0
\(485\) 633421. 111689.i 2.69283 0.474818i
\(486\) 0 0
\(487\) 3850.49 2223.08i 0.0162352 0.00937341i −0.491860 0.870674i \(-0.663683\pi\)
0.508096 + 0.861301i \(0.330350\pi\)
\(488\) 0 0
\(489\) −188020. 516581.i −0.786297 2.16033i
\(490\) 0 0
\(491\) −216765. 181887.i −0.899138 0.754466i 0.0708839 0.997485i \(-0.477418\pi\)
−0.970022 + 0.243018i \(0.921862\pi\)
\(492\) 0 0
\(493\) 205832.i 0.846876i
\(494\) 0 0
\(495\) −1.04183e6 −4.25194
\(496\) 0 0
\(497\) 180520. 215135.i 0.730822 0.870960i
\(498\) 0 0
\(499\) −157919. + 57477.9i −0.634211 + 0.230834i −0.639063 0.769154i \(-0.720678\pi\)
0.00485227 + 0.999988i \(0.498455\pi\)
\(500\) 0 0
\(501\) −51875.6 89851.2i −0.206675 0.357971i
\(502\) 0 0
\(503\) 38236.5 + 216850.i 0.151127 + 0.857085i 0.962241 + 0.272197i \(0.0877503\pi\)
−0.811114 + 0.584888i \(0.801139\pi\)
\(504\) 0 0
\(505\) −240640. + 416801.i −0.943593 + 1.63435i
\(506\) 0 0
\(507\) −287162. 342226.i −1.11715 1.33136i
\(508\) 0 0
\(509\) 86482.7 237609.i 0.333806 0.917123i −0.653307 0.757094i \(-0.726619\pi\)
0.987112 0.160030i \(-0.0511591\pi\)
\(510\) 0 0
\(511\) 5959.55 33798.3i 0.0228229 0.129435i
\(512\) 0 0
\(513\) −784774. 193118.i −2.98202 0.733816i
\(514\) 0 0
\(515\) 891715. + 157233.i 3.36211 + 0.592830i
\(516\) 0 0
\(517\) 13686.3 + 4981.41i 0.0512042 + 0.0186368i
\(518\) 0 0
\(519\) −417132. + 350016.i −1.54860 + 1.29943i
\(520\) 0 0
\(521\) 66835.3 + 38587.4i 0.246224 + 0.142158i 0.618034 0.786151i \(-0.287929\pi\)
−0.371810 + 0.928309i \(0.621263\pi\)
\(522\) 0 0
\(523\) 35806.7 6313.68i 0.130906 0.0230823i −0.107811 0.994171i \(-0.534384\pi\)
0.238717 + 0.971089i \(0.423273\pi\)
\(524\) 0 0
\(525\) −1.06097e6 + 612554.i −3.84934 + 2.22242i
\(526\) 0 0
\(527\) −129272. 355171.i −0.465459 1.27884i
\(528\) 0 0
\(529\) −158602. 133083.i −0.566758 0.475567i
\(530\) 0 0
\(531\) 807172.i 2.86271i
\(532\) 0 0
\(533\) 31386.8 0.110482
\(534\) 0 0
\(535\) 410171. 488823.i 1.43304 1.70783i
\(536\) 0 0
\(537\) 426480. 155226.i 1.47894 0.538290i
\(538\) 0 0
\(539\) −19837.7 34360.0i −0.0682833 0.118270i
\(540\) 0 0
\(541\) −83380.7 472876.i −0.284886 1.61567i −0.705692 0.708519i \(-0.749364\pi\)
0.420806 0.907151i \(-0.361747\pi\)
\(542\) 0 0
\(543\) 95071.8 164669.i 0.322442 0.558487i
\(544\) 0 0
\(545\) 94063.3 + 112100.i 0.316685 + 0.377410i
\(546\) 0 0
\(547\) 99395.7 273088.i 0.332195 0.912698i −0.655345 0.755330i \(-0.727477\pi\)
0.987540 0.157369i \(-0.0503011\pi\)
\(548\) 0 0
\(549\) 62352.3 353617.i 0.206875 1.17325i
\(550\) 0 0
\(551\) −185409. + 91133.3i −0.610699 + 0.300175i
\(552\) 0 0
\(553\) 4284.73 + 755.514i 0.0140111 + 0.00247054i
\(554\) 0 0
\(555\) 378203. + 137655.i 1.22783 + 0.446894i
\(556\) 0 0
\(557\) −164551. + 138075.i −0.530384 + 0.445045i −0.868234 0.496155i \(-0.834745\pi\)
0.337850 + 0.941200i \(0.390300\pi\)
\(558\) 0 0
\(559\) −41579.9 24006.1i −0.133064 0.0768243i
\(560\) 0 0
\(561\) 668666. 117904.i 2.12463 0.374630i
\(562\) 0 0
\(563\) −277806. + 160391.i −0.876445 + 0.506016i −0.869485 0.493960i \(-0.835549\pi\)
−0.00696069 + 0.999976i \(0.502216\pi\)
\(564\) 0 0
\(565\) 213928. + 587762.i 0.670148 + 1.84122i
\(566\) 0 0
\(567\) 851347. + 714365.i 2.64814 + 2.22205i
\(568\) 0 0
\(569\) 11383.3i 0.0351597i −0.999845 0.0175798i \(-0.994404\pi\)
0.999845 0.0175798i \(-0.00559613\pi\)
\(570\) 0 0
\(571\) 386192. 1.18449 0.592244 0.805759i \(-0.298242\pi\)
0.592244 + 0.805759i \(0.298242\pi\)
\(572\) 0 0
\(573\) −322312. + 384116.i −0.981673 + 1.16991i
\(574\) 0 0
\(575\) −345475. + 125743.i −1.04491 + 0.380318i
\(576\) 0 0
\(577\) −39009.3 67566.1i −0.117170 0.202945i 0.801475 0.598028i \(-0.204049\pi\)
−0.918645 + 0.395084i \(0.870716\pi\)
\(578\) 0 0
\(579\) 180008. + 1.02088e6i 0.536952 + 3.04521i
\(580\) 0 0
\(581\) −174933. + 302992.i −0.518225 + 0.897592i
\(582\) 0 0
\(583\) −42168.9 50254.9i −0.124067 0.147857i
\(584\) 0 0
\(585\) −160013. + 439631.i −0.467566 + 1.28463i
\(586\) 0 0
\(587\) −105534. + 598511.i −0.306277 + 1.73698i 0.311155 + 0.950359i \(0.399284\pi\)
−0.617432 + 0.786624i \(0.711827\pi\)
\(588\) 0 0
\(589\) 262694. 273698.i 0.757215 0.788936i
\(590\) 0 0
\(591\) −680573. 120003.i −1.94850 0.343573i
\(592\) 0 0
\(593\) 7691.86 + 2799.61i 0.0218737 + 0.00796137i 0.352934 0.935648i \(-0.385184\pi\)
−0.331060 + 0.943610i \(0.607406\pi\)
\(594\) 0 0
\(595\) 645389. 541546.i 1.82300 1.52968i
\(596\) 0 0
\(597\) −406210. 234525.i −1.13973 0.658023i
\(598\) 0 0
\(599\) 272306. 48014.8i 0.758932 0.133820i 0.219227 0.975674i \(-0.429647\pi\)
0.539706 + 0.841854i \(0.318536\pi\)
\(600\) 0 0
\(601\) 172114. 99370.1i 0.476505 0.275110i −0.242454 0.970163i \(-0.577952\pi\)
0.718959 + 0.695053i \(0.244619\pi\)
\(602\) 0 0
\(603\) −183494. 504145.i −0.504646 1.38650i
\(604\) 0 0
\(605\) −84376.2 70800.0i −0.230520 0.193429i
\(606\) 0 0
\(607\) 145818.i 0.395763i 0.980226 + 0.197881i \(0.0634061\pi\)
−0.980226 + 0.197881i \(0.936594\pi\)
\(608\) 0 0
\(609\) 514547. 1.38736
\(610\) 0 0
\(611\) 4204.10 5010.26i 0.0112614 0.0134208i
\(612\) 0 0
\(613\) 313010. 113926.i 0.832985 0.303182i 0.109902 0.993942i \(-0.464946\pi\)
0.723083 + 0.690761i \(0.242724\pi\)
\(614\) 0 0
\(615\) 241672. + 418589.i 0.638965 + 1.10672i
\(616\) 0 0
\(617\) −22609.1 128223.i −0.0593900 0.336818i 0.940606 0.339499i \(-0.110258\pi\)
−0.999996 + 0.00268147i \(0.999146\pi\)
\(618\) 0 0
\(619\) −215279. + 372875.i −0.561851 + 0.973155i 0.435484 + 0.900196i \(0.356577\pi\)
−0.997335 + 0.0729581i \(0.976756\pi\)
\(620\) 0 0
\(621\) 388275. + 462728.i 1.00683 + 1.19989i
\(622\) 0 0
\(623\) 104963. 288382.i 0.270432 0.743006i
\(624\) 0 0
\(625\) 106689. 605062.i 0.273123 1.54896i
\(626\) 0 0
\(627\) 402260. + 550116.i 1.02323 + 1.39933i
\(628\) 0 0
\(629\) −186862. 32948.9i −0.472303 0.0832797i
\(630\) 0 0
\(631\) −292661. 106520.i −0.735031 0.267530i −0.0527384 0.998608i \(-0.516795\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(632\) 0 0
\(633\) 33193.8 27852.9i 0.0828419 0.0695126i
\(634\) 0 0
\(635\) −518590. 299408.i −1.28611 0.742534i
\(636\) 0 0
\(637\) −17546.0 + 3093.84i −0.0432414 + 0.00762463i
\(638\) 0 0
\(639\) 980538. 566114.i 2.40139 1.38644i
\(640\) 0 0
\(641\) 103019. + 283042.i 0.250726 + 0.688865i 0.999656 + 0.0262160i \(0.00834577\pi\)
−0.748930 + 0.662649i \(0.769432\pi\)
\(642\) 0 0
\(643\) 138701. + 116384.i 0.335473 + 0.281496i 0.794926 0.606707i \(-0.207510\pi\)
−0.459452 + 0.888202i \(0.651954\pi\)
\(644\) 0 0
\(645\) 739372.i 1.77723i
\(646\) 0 0
\(647\) 67772.6 0.161900 0.0809498 0.996718i \(-0.474205\pi\)
0.0809498 + 0.996718i \(0.474205\pi\)
\(648\) 0 0
\(649\) −270212. + 322026.i −0.641526 + 0.764541i
\(650\) 0 0
\(651\) −887867. + 323157.i −2.09501 + 0.762521i
\(652\) 0 0
\(653\) −320652. 555385.i −0.751981 1.30247i −0.946861 0.321643i \(-0.895765\pi\)
0.194880 0.980827i \(-0.437568\pi\)
\(654\) 0 0
\(655\) −210257. 1.19243e6i −0.490081 2.77939i
\(656\) 0 0
\(657\) 69181.5 119826.i 0.160273 0.277600i
\(658\) 0 0
\(659\) 498145. + 593666.i 1.14706 + 1.36701i 0.919427 + 0.393262i \(0.128653\pi\)
0.227631 + 0.973748i \(0.426902\pi\)
\(660\) 0 0
\(661\) −275464. + 756832.i −0.630468 + 1.73220i 0.0493168 + 0.998783i \(0.484296\pi\)
−0.679784 + 0.733412i \(0.737927\pi\)
\(662\) 0 0
\(663\) 52946.1 300272.i 0.120450 0.683106i
\(664\) 0 0
\(665\) 773561. + 341579.i 1.74925 + 0.772410i
\(666\) 0 0
\(667\) 152066. + 26813.4i 0.341807 + 0.0602698i
\(668\) 0 0
\(669\) 616094. + 224240.i 1.37656 + 0.501027i
\(670\) 0 0
\(671\) −143254. + 120204.i −0.318172 + 0.266978i
\(672\) 0 0
\(673\) −245414. 141690.i −0.541838 0.312830i 0.203986 0.978974i \(-0.434610\pi\)
−0.745823 + 0.666144i \(0.767944\pi\)
\(674\) 0 0
\(675\) −3.00413e6 + 529710.i −6.59343 + 1.16260i
\(676\) 0 0
\(677\) 411346. 237491.i 0.897491 0.518167i 0.0211057 0.999777i \(-0.493281\pi\)
0.876385 + 0.481611i \(0.159948\pi\)
\(678\) 0 0
\(679\) 259259. + 712310.i 0.562335 + 1.54500i
\(680\) 0 0
\(681\) 199172. + 167125.i 0.429471 + 0.360369i
\(682\) 0 0
\(683\) 274079.i 0.587535i 0.955877 + 0.293768i \(0.0949092\pi\)
−0.955877 + 0.293768i \(0.905091\pi\)
\(684\) 0 0
\(685\) −261162. −0.556581
\(686\) 0 0
\(687\) 1.12804e6 1.34435e6i 2.39007 2.84838i
\(688\) 0 0
\(689\) −27683.2 + 10075.8i −0.0583146 + 0.0212248i
\(690\) 0 0
\(691\) 134489. + 232942.i 0.281664 + 0.487856i 0.971795 0.235828i \(-0.0757803\pi\)
−0.690131 + 0.723685i \(0.742447\pi\)
\(692\) 0 0
\(693\) −213211. 1.20918e6i −0.443959 2.51782i
\(694\) 0 0
\(695\) −355742. + 616163.i −0.736488 + 1.27563i
\(696\) 0 0
\(697\) −146472. 174559.i −0.301502 0.359316i
\(698\) 0 0
\(699\) 391708. 1.07621e6i 0.801694 2.20264i
\(700\) 0 0
\(701\) −14474.6 + 82089.7i −0.0294558 + 0.167052i −0.995987 0.0894963i \(-0.971474\pi\)
0.966531 + 0.256549i \(0.0825854\pi\)
\(702\) 0 0
\(703\) −53054.7 182909.i −0.107353 0.370105i
\(704\) 0 0
\(705\) 99190.1 + 17489.9i 0.199568 + 0.0351891i
\(706\) 0 0
\(707\) −532998. 193995.i −1.06632 0.388108i
\(708\) 0 0
\(709\) −402160. + 337452.i −0.800029 + 0.671304i −0.948206 0.317657i \(-0.897104\pi\)
0.148176 + 0.988961i \(0.452660\pi\)
\(710\) 0 0
\(711\) 15190.8 + 8770.40i 0.0300497 + 0.0173492i
\(712\) 0 0
\(713\) −279235. + 49236.7i −0.549277 + 0.0968523i
\(714\) 0 0
\(715\) 211010. 121827.i 0.412754 0.238304i
\(716\) 0 0
\(717\) −315931. 868013.i −0.614545 1.68845i
\(718\) 0 0
\(719\) −264994. 222356.i −0.512600 0.430122i 0.349443 0.936958i \(-0.386371\pi\)
−0.862043 + 0.506835i \(0.830815\pi\)
\(720\) 0 0
\(721\) 1.06713e6i 2.05280i
\(722\) 0 0
\(723\) 786585. 1.50477
\(724\) 0 0
\(725\) −501239. + 597353.i −0.953606 + 1.13646i
\(726\) 0 0
\(727\) −297089. + 108132.i −0.562106 + 0.204590i −0.607417 0.794383i \(-0.707794\pi\)
0.0453112 + 0.998973i \(0.485572\pi\)
\(728\) 0 0
\(729\) 688717. + 1.19289e6i 1.29594 + 2.24464i
\(730\) 0 0
\(731\) 60529.2 + 343278.i 0.113274 + 0.642408i
\(732\) 0 0
\(733\) 289215. 500934.i 0.538285 0.932337i −0.460712 0.887550i \(-0.652406\pi\)
0.998997 0.0447870i \(-0.0142609\pi\)
\(734\) 0 0
\(735\) −176362. 210180.i −0.326461 0.389061i
\(736\) 0 0
\(737\) −95563.4 + 262558.i −0.175937 + 0.483382i
\(738\) 0 0
\(739\) −36043.3 + 204412.i −0.0659988 + 0.374298i 0.933862 + 0.357633i \(0.116416\pi\)
−0.999861 + 0.0166650i \(0.994695\pi\)
\(740\) 0 0
\(741\) 293920. 85254.4i 0.535295 0.155267i
\(742\) 0 0
\(743\) −817496. 144147.i −1.48084 0.261112i −0.625926 0.779882i \(-0.715279\pi\)
−0.854914 + 0.518770i \(0.826390\pi\)
\(744\) 0 0
\(745\) −1.59453e6 580361.i −2.87290 1.04565i
\(746\) 0 0
\(747\) −1.08052e6 + 906662.i −1.93638 + 1.62482i
\(748\) 0 0
\(749\) 651283. + 376019.i 1.16093 + 0.670264i
\(750\) 0 0
\(751\) −616937. + 108783.i −1.09386 + 0.192877i −0.691336 0.722534i \(-0.742977\pi\)
−0.402522 + 0.915410i \(0.631866\pi\)
\(752\) 0 0
\(753\) −1.34870e6 + 778673.i −2.37862 + 1.37330i
\(754\) 0 0
\(755\) 144957. + 398266.i 0.254299 + 0.698681i
\(756\) 0 0
\(757\) 820428. + 688421.i 1.43169 + 1.20133i 0.944706 + 0.327918i \(0.106347\pi\)
0.486982 + 0.873412i \(0.338098\pi\)
\(758\) 0 0
\(759\) 509361.i 0.884183i
\(760\) 0 0
\(761\) 499722. 0.862898 0.431449 0.902137i \(-0.358002\pi\)
0.431449 + 0.902137i \(0.358002\pi\)
\(762\) 0 0
\(763\) −110857. + 132114.i −0.190420 + 0.226934i
\(764\) 0 0
\(765\) 3.19176e6 1.16171e6i 5.45391 1.98506i
\(766\) 0 0
\(767\) 94387.0 + 163483.i 0.160443 + 0.277896i
\(768\) 0 0
\(769\) −1847.28 10476.5i −0.00312378 0.0177158i 0.983206 0.182499i \(-0.0584187\pi\)
−0.986330 + 0.164783i \(0.947308\pi\)
\(770\) 0 0
\(771\) 1.08217e6 1.87438e6i 1.82049 3.15318i
\(772\) 0 0
\(773\) −530184. 631849.i −0.887294 1.05744i −0.997977 0.0635803i \(-0.979748\pi\)
0.110682 0.993856i \(-0.464696\pi\)
\(774\) 0 0
\(775\) 489741. 1.34555e6i 0.815386 2.24025i
\(776\) 0 0
\(777\) −82366.7 + 467125.i −0.136430 + 0.773732i
\(778\) 0 0
\(779\) 92387.2 209226.i 0.152243 0.344779i
\(780\) 0 0
\(781\) −580705. 102394.i −0.952036 0.167870i
\(782\) 0 0
\(783\) 1.20394e6 + 438197.i 1.96372 + 0.714737i
\(784\) 0 0
\(785\) −141722. + 118919.i −0.229984 + 0.192980i
\(786\) 0 0
\(787\) −548575. 316720.i −0.885700 0.511359i −0.0131663 0.999913i \(-0.504191\pi\)
−0.872533 + 0.488554i \(0.837524\pi\)
\(788\) 0 0
\(789\) −1.71984e6 + 303254.i −2.76270 + 0.487138i
\(790\) 0 0
\(791\) −638394. + 368577.i −1.02032 + 0.589081i
\(792\) 0 0