Properties

Label 76.5.j.a.29.7
Level $76$
Weight $5$
Character 76.29
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 29.7
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.7

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 0.848696 + 0.528881i \(0.177388\pi\)
0.373472 + 0.927642i \(0.378167\pi\)
\(4\) 0 0
\(5\) −41.8937 15.2481i −1.67575 0.609922i −0.683030 0.730390i \(-0.739338\pi\)
−0.992717 + 0.120468i \(0.961561\pi\)
\(6\) 0 0
\(7\) −26.2709 + 45.5025i −0.536141 + 0.928623i 0.462966 + 0.886376i \(0.346785\pi\)
−0.999107 + 0.0422474i \(0.986548\pi\)
\(8\) 0 0
\(9\) −36.7834 + 208.609i −0.454116 + 2.57542i
\(10\) 0 0
\(11\) −55.1598 95.5395i −0.455866 0.789583i 0.542872 0.839816i \(-0.317337\pi\)
−0.998738 + 0.0502329i \(0.984004\pi\)
\(12\) 0 0
\(13\) 31.8438 37.9500i 0.188425 0.224556i −0.663559 0.748124i \(-0.730955\pi\)
0.851984 + 0.523568i \(0.175399\pi\)
\(14\) 0 0
\(15\) −260.928 716.893i −1.15968 3.18619i
\(16\) 0 0
\(17\) 62.4554 + 354.202i 0.216109 + 1.22561i 0.878972 + 0.476873i \(0.158230\pi\)
−0.662863 + 0.748740i \(0.730659\pi\)
\(18\) 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 −0.570356 0.821398i \(-0.693195\pi\)
0.0910666 + 0.995845i \(0.470972\pi\)
\(24\) 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 −0.171785 0.985134i \(-0.554953\pi\)
−0.498361 + 0.866970i \(0.666065\pi\)
\(30\) 0 0
\(31\) 910.085 + 525.438i 0.947019 + 0.546762i 0.892154 0.451732i \(-0.149194\pi\)
0.0548653 + 0.998494i \(0.482527\pi\)
\(32\) 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 \(0.0617180\pi\)
−0.981262 + 0.192680i \(0.938282\pi\)
\(38\) 0 0
\(39\) 847.742 0.557358
\(40\) 0 0
\(41\) 407.245 + 485.336i 0.242264 + 0.288719i 0.873451 0.486912i \(-0.161877\pi\)
−0.631188 + 0.775630i \(0.717432\pi\)
\(42\) 0 0
\(43\) −910.710 331.471i −0.492542 0.179271i 0.0837945 0.996483i \(-0.473296\pi\)
−0.576337 + 0.817212i \(0.695518\pi\)
\(44\) 0 0
\(45\) 4721.88 8178.53i 2.33179 4.03878i
\(46\) 0 0
\(47\) −22.9255 + 130.017i −0.0103782 + 0.0588578i −0.989557 0.144142i \(-0.953958\pi\)
0.979179 + 0.203000i \(0.0650690\pi\)
\(48\) 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 0.898211 0.439565i \(-0.144867\pi\)
−0.970616 + 0.240632i \(0.922645\pi\)
\(54\) 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 0.393687 0.919245i \(-0.371199\pi\)
0.684345 + 0.729159i \(0.260088\pi\)
\(60\) 0 0
\(61\) 1592.89 579.765i 0.428081 0.155809i −0.118989 0.992896i \(-0.537965\pi\)
0.547070 + 0.837087i \(0.315743\pi\)
\(62\) 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 0.444413 0.895822i \(-0.353412\pi\)
0.111222 + 0.993796i \(0.464524\pi\)
\(68\) 0 0
\(69\) −3998.56 2308.57i −0.839858 0.484892i
\(70\) 0 0
\(71\) 1828.11 5022.70i 0.362649 0.996371i −0.615440 0.788184i \(-0.711022\pi\)
0.978089 0.208187i \(-0.0667562\pi\)
\(72\) 0 0
\(73\) 500.371 419.861i 0.0938959 0.0787880i −0.594631 0.803998i \(-0.702702\pi\)
0.688527 + 0.725210i \(0.258258\pi\)
\(74\) 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 0.761763 0.647855i \(-0.224334\pi\)
−0.770292 + 0.637691i \(0.779889\pi\)
\(80\) 0 0
\(81\) −19876.2 7234.34i −3.02945 1.10263i
\(82\) 0 0
\(83\) −3329.40 + 5766.69i −0.483292 + 0.837086i −0.999816 0.0191865i \(-0.993892\pi\)
0.516524 + 0.856273i \(0.327226\pi\)
\(84\) 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 −0.475084 0.879940i \(-0.657582\pi\)
0.949070 + 0.315066i \(0.102027\pi\)
\(90\) 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 −0.866506 0.499166i \(-0.833640\pi\)
−0.643525 + 0.765425i \(0.722529\pi\)
\(98\) 0 0
\(99\) 21959.4 7992.56i 2.24052 0.815484i
\(100\) 0 0
\(101\) 8269.68 + 6939.09i 0.810674 + 0.680236i 0.950768 0.309902i \(-0.100296\pi\)
−0.140095 + 0.990138i \(0.544741\pi\)
\(102\) 0 0
\(103\) −17589.1 + 10155.0i −1.65794 + 0.957211i −0.684273 + 0.729226i \(0.739880\pi\)
−0.973665 + 0.227984i \(0.926787\pi\)
\(104\) 0 0
\(105\) 39475.3 + 6960.55i 3.58052 + 0.631343i
\(106\) 0 0
\(107\) −12395.5 7156.56i −1.08267 0.625082i −0.151057 0.988525i \(-0.548268\pi\)
−0.931616 + 0.363443i \(0.881601\pi\)
\(108\) 0 0
\(109\) −1122.64 + 3084.44i −0.0944906 + 0.259611i −0.977929 0.208936i \(-0.933000\pi\)
0.883439 + 0.468547i \(0.155222\pi\)
\(110\) 0 0
\(111\) −6915.61 + 5802.88i −0.561286 + 0.470975i
\(112\) 0 0
\(113\) 14029.8i 1.09874i 0.835578 + 0.549371i \(0.185133\pi\)
−0.835578 + 0.549371i \(0.814867\pi\)
\(114\) 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 −0.428833 0.903384i \(-0.641075\pi\)
0.964125 + 0.265447i \(0.0855197\pi\)
\(128\) 0 0
\(129\) −5672.21 15584.3i −0.340857 0.936498i
\(130\) 0 0
\(131\) −4716.15 26746.6i −0.274818 1.55857i −0.739539 0.673113i \(-0.764957\pi\)
0.464722 0.885457i \(-0.346154\pi\)
\(132\) 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 −0.191187 0.981554i \(-0.561234\pi\)
0.484473 + 0.874806i \(0.339011\pi\)
\(138\) 0 0
\(139\) 12225.2 + 10258.2i 0.632742 + 0.530934i 0.901780 0.432196i \(-0.142261\pi\)
−0.269038 + 0.963130i \(0.586706\pi\)
\(140\) 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 0.325625 0.945499i \(-0.394425\pi\)
0.987679 0.156494i \(-0.0500192\pi\)
\(150\) 0 0
\(151\) 9506.58i 0.416937i 0.978029 + 0.208468i \(0.0668479\pi\)
−0.978029 + 0.208468i \(0.933152\pi\)
\(152\) 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 0.419906 0.907567i \(-0.362063\pi\)
−0.261706 + 0.965148i \(0.584285\pi\)
\(158\) 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 0.992120 + 0.125288i \(0.0399855\pi\)
−0.387558 + 0.921846i \(0.626681\pi\)
\(164\) 0 0
\(165\) −54098.9 + 64472.6i −1.98710 + 2.36814i
\(166\) 0 0
\(167\) 2073.67 + 5697.35i 0.0743543 + 0.204287i 0.971302 0.237850i \(-0.0764427\pi\)
−0.896948 + 0.442137i \(0.854221\pi\)
\(168\) 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 −0.670610 0.741810i \(-0.733968\pi\)
−0.376454 + 0.926435i \(0.622857\pi\)
\(174\) 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 −0.0967384 0.995310i \(-0.530841\pi\)
0.813594 + 0.581433i \(0.197508\pi\)
\(180\) 0 0
\(181\) 10942.8 + 1929.51i 0.334018 + 0.0588965i 0.338142 0.941095i \(-0.390202\pi\)
−0.00412374 + 0.999991i \(0.501313\pi\)
\(182\) 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 −0.968561 0.248777i \(-0.919972\pi\)
−0.0768082 0.997046i \(-0.524473\pi\)
\(194\) 0 0
\(195\) −35515.0 12926.4i −0.933992 0.339945i
\(196\) 0 0
\(197\) −20192.4 + 34974.2i −0.520302 + 0.901189i 0.479420 + 0.877586i \(0.340847\pi\)
−0.999721 + 0.0236031i \(0.992486\pi\)
\(198\) 0 0
\(199\) −4759.75 + 26993.9i −0.120193 + 0.681647i 0.863855 + 0.503741i \(0.168043\pi\)
−0.984048 + 0.177906i \(0.943068\pi\)
\(200\) 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 −0.145572 0.989348i \(-0.546502\pi\)
0.201584 + 0.979471i \(0.435391\pi\)
\(212\) 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 −0.735414 0.677618i \(-0.763012\pi\)
0.998924 0.0463706i \(-0.0147655\pi\)
\(224\) 0 0
\(225\) −221105. + 185529.i −4.36751 + 3.66478i
\(226\) 0 0
\(227\) 15193.9i 0.294861i −0.989072 0.147430i \(-0.952900\pi\)
0.989072 0.147430i \(-0.0471002\pi\)
\(228\) 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 0.848546 0.529122i \(-0.177479\pi\)
0.309910 + 0.950766i \(0.399701\pi\)
\(234\) 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 0.999505 0.0314597i \(-0.0100156\pi\)
−0.526997 + 0.849867i \(0.676682\pi\)
\(240\) 0 0
\(241\) 29546.6 35212.3i 0.508714 0.606261i −0.449160 0.893451i \(-0.648277\pi\)
0.957874 + 0.287190i \(0.0927211\pi\)
\(242\) 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 −0.915259 0.402867i \(-0.868014\pi\)
−0.442171 + 0.896931i \(0.645792\pi\)
\(252\) 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 0.993026 0.117893i \(-0.0376139\pi\)
0.892818 + 0.450418i \(0.148725\pi\)
\(258\) 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 −0.999076 0.0429718i \(-0.986317\pi\)
−0.131169 + 0.991360i \(0.541873\pi\)
\(264\) 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 0.675368 0.737481i \(-0.263985\pi\)
−0.843554 + 0.537045i \(0.819541\pi\)
\(270\) 0 0
\(271\) 39181.9 + 14261.1i 0.533516 + 0.194184i 0.594707 0.803942i \(-0.297268\pi\)
−0.0611917 + 0.998126i \(0.519490\pi\)
\(272\) 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 0.818283 + 0.574816i \(0.194926\pi\)
0.0886635 + 0.996062i \(0.471740\pi\)
\(278\) 0 0
\(279\) −143087. + 170525.i −1.83820 + 2.19068i
\(280\) 0 0
\(281\) 37180.7 + 102153.i 0.470875 + 1.29372i 0.917050 + 0.398772i \(0.130563\pi\)
−0.446176 + 0.894945i \(0.647214\pi\)
\(282\) 0 0
\(283\) −21903.0 124218.i −0.273484 1.55100i −0.743738 0.668471i \(-0.766949\pi\)
0.470254 0.882531i \(-0.344162\pi\)
\(284\) 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 0.250133 0.968212i \(-0.419526\pi\)
0.963562 + 0.267485i \(0.0861924\pi\)
\(294\) 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 0.974782 0.223160i \(-0.0716371\pi\)
−0.389038 + 0.921222i \(0.627193\pi\)
\(308\) 0 0
\(309\) −326591. 118869.i −3.42048 1.24495i
\(310\) 0 0
\(311\) 25459.7 44097.5i 0.263229 0.455925i −0.703869 0.710329i \(-0.748546\pi\)
0.967098 + 0.254404i \(0.0818793\pi\)
\(312\) 0 0
\(313\) −5380.77 + 30515.9i −0.0549232 + 0.311485i −0.999876 0.0157205i \(-0.994996\pi\)
0.944953 + 0.327205i \(0.106107\pi\)
\(314\) 0 0
\(315\) 248096. + 429715.i 2.50034 + 4.33071i
\(316\) 0 0
\(317\) −48597.9 + 57916.7i −0.483614 + 0.576348i −0.951581 0.307397i \(-0.900542\pi\)
0.467968 + 0.883746i \(0.344986\pi\)
\(318\) 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 −0.753979 0.656899i \(-0.771868\pi\)
0.191902 + 0.981414i \(0.438534\pi\)
\(332\) 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 −0.458355 0.888769i \(-0.651561\pi\)
0.922410 0.386212i \(-0.126217\pi\)
\(338\) 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 0.856171 0.516692i \(-0.172837\pi\)
0.323742 + 0.946145i \(0.395059\pi\)
\(348\) 0 0
\(349\) 11647.2 20173.6i 0.0956250 0.165627i −0.814244 0.580522i \(-0.802848\pi\)
0.909869 + 0.414895i \(0.136182\pi\)
\(350\) 0 0
\(351\) −19258.9 + 109223.i −0.156321 + 0.886542i
\(352\) 0 0
\(353\) −28616.5 49565.3i −0.229650 0.397766i 0.728054 0.685520i \(-0.240425\pi\)
−0.957705 + 0.287753i \(0.907092\pi\)
\(354\) 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 0.995755 0.0920479i \(-0.0293413\pi\)
−0.967185 + 0.254071i \(0.918230\pi\)
\(360\) 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 0.677861 0.735190i \(-0.262907\pi\)
−0.606311 + 0.795227i \(0.707351\pi\)
\(368\) 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 0.999992 0.00393908i \(-0.00125385\pi\)
0.496585 + 0.867988i \(0.334587\pi\)
\(374\) 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 \(-0.725280\pi\)
0.650116 0.759835i \(-0.274720\pi\)
\(380\) 0 0
\(381\) 229846. 1.58339
\(382\) 0 0
\(383\) 9812.87 + 11694.5i 0.0668958 + 0.0797233i 0.798455 0.602055i \(-0.205651\pi\)
−0.731559 + 0.681778i \(0.761207\pi\)
\(384\) 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 0.310749 + 0.950492i \(0.399420\pi\)
−0.617096 + 0.786888i \(0.711691\pi\)
\(390\) 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 −0.954722 0.297498i \(-0.903848\pi\)
0.795395 0.606091i \(-0.207263\pi\)
\(398\) 0 0
\(399\) −322694. 34915.1i −2.02696 0.219315i
\(400\) 0 0
\(401\) 59433.0 10479.6i 0.369606 0.0651715i 0.0142397 0.999899i \(-0.495467\pi\)
0.355366 + 0.934727i \(0.384356\pi\)
\(402\) 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 −0.543632 0.839323i \(-0.682951\pi\)
−0.797913 + 0.602773i \(0.794062\pi\)
\(410\) 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 −0.968409 0.249368i \(-0.919777\pi\)
−0.0774170 0.996999i \(-0.524667\pi\)
\(422\) 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 −0.981100 0.193501i \(-0.938016\pi\)
0.360927 + 0.932594i \(0.382460\pi\)
\(432\) 0 0
\(433\) −95452.7 262254.i −0.509111 1.39877i −0.882156 0.470958i \(-0.843908\pi\)
0.373045 0.927813i \(-0.378314\pi\)
\(434\) 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 −0.168256 0.985743i \(-0.553814\pi\)
0.179035 + 0.983843i \(0.442703\pi\)
\(440\) 0 0
\(441\) 71587.5 26055.7i 0.368095 0.133976i
\(442\) 0 0
\(443\) −150418. 126215.i −0.766463 0.643139i 0.173337 0.984863i \(-0.444545\pi\)
−0.939801 + 0.341723i \(0.888989\pi\)
\(444\) 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 0.785020 0.619471i \(-0.212653\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(450\) 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 0.00432977 0.999991i \(-0.498622\pi\)
−0.639465 + 0.768820i \(0.720844\pi\)
\(462\) 0 0
\(463\) 185533. 321352.i 0.865483 1.49906i −0.00108317 0.999999i \(-0.500345\pi\)
0.866566 0.499062i \(-0.166322\pi\)
\(464\) 0 0
\(465\) 139216. 789535.i 0.643849 3.65145i
\(466\) 0 0
\(467\) −59097.8 102360.i −0.270980 0.469351i 0.698133 0.715968i \(-0.254014\pi\)
−0.969113 + 0.246617i \(0.920681\pi\)
\(468\) 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 −0.0214724 0.999769i \(-0.506835\pi\)
0.626191 + 0.779670i \(0.284613\pi\)
\(480\) 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 0.508096 0.861301i \(-0.330350\pi\)
−0.491860 + 0.870674i \(0.663683\pi\)
\(488\) 0 0
\(489\) −188020. + 516581.i −0.786297 + 2.16033i
\(490\) 0 0
\(491\) −216765. + 181887.i −0.899138 + 0.754466i −0.970022 0.243018i \(-0.921862\pi\)
0.0708839 + 0.997485i \(0.477418\pi\)
\(492\) 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 0.00485227 0.999988i \(-0.498455\pi\)
−0.639063 + 0.769154i \(0.720678\pi\)
\(500\) 0 0
\(501\) −51875.6 + 89851.2i −0.206675 + 0.357971i
\(502\) 0 0
\(503\) 38236.5 216850.i 0.151127 0.857085i −0.811114 0.584888i \(-0.801139\pi\)
0.962241 0.272197i \(-0.0877503\pi\)
\(504\) 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 0.987112 + 0.160030i \(0.0511591\pi\)
−0.653307 + 0.757094i \(0.726619\pi\)
\(510\) 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 −0.371810 0.928309i \(-0.621263\pi\)
0.618034 + 0.786151i \(0.287929\pi\)
\(522\) 0 0
\(523\) 35806.7 + 6313.68i 0.130906 + 0.0230823i 0.238717 0.971089i \(-0.423273\pi\)
−0.107811 + 0.994171i \(0.534384\pi\)
\(524\) 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 0.420806 + 0.907151i \(0.361747\pi\)
−0.705692 + 0.708519i \(0.749364\pi\)
\(542\) 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 0.987540 + 0.157369i \(0.0503011\pi\)
−0.655345 + 0.755330i \(0.727477\pi\)
\(548\) 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 0.337850 0.941200i \(-0.390300\pi\)
−0.868234 + 0.496155i \(0.834745\pi\)
\(558\) 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 −0.00696069 0.999976i \(-0.502216\pi\)
−0.869485 + 0.493960i \(0.835549\pi\)
\(564\) 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 \(0.00559613\pi\)
−0.999845 + 0.0175798i \(0.994404\pi\)
\(570\) 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 −0.918645 0.395084i \(-0.870716\pi\)
0.801475 + 0.598028i \(0.204049\pi\)
\(578\) 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 −0.617432 0.786624i \(-0.711827\pi\)
0.311155 0.950359i \(-0.399284\pi\)
\(588\) 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 −0.331060 0.943610i \(-0.607406\pi\)
0.352934 + 0.935648i \(0.385184\pi\)
\(594\) 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 0.539706 0.841854i \(-0.318536\pi\)
0.219227 + 0.975674i \(0.429647\pi\)
\(600\) 0 0
\(601\) 172114. + 99370.1i 0.476505 + 0.275110i 0.718959 0.695053i \(-0.244619\pi\)
−0.242454 + 0.970163i \(0.577952\pi\)
\(602\) 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 \(-0.936594\pi\)
0.980226 0.197881i \(-0.0634061\pi\)
\(608\) 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 0.723083 0.690761i \(-0.242724\pi\)
0.109902 + 0.993942i \(0.464946\pi\)
\(614\) 0 0
\(615\) 241672. 418589.i 0.638965 1.10672i
\(616\) 0 0
\(617\) −22609.1 + 128223.i −0.0593900 + 0.336818i −0.999996 0.00268147i \(-0.999146\pi\)
0.940606 + 0.339499i \(0.110258\pi\)
\(618\) 0 0
\(619\) −215279. 372875.i −0.561851 0.973155i −0.997335 0.0729581i \(-0.976756\pi\)
0.435484 0.900196i \(-0.356577\pi\)
\(620\) 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 −0.682293 0.731079i \(-0.739017\pi\)
−0.0527384 + 0.998608i \(0.516795\pi\)
\(632\) 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 −0.748930 0.662649i \(-0.769432\pi\)
0.999656 0.0262160i \(-0.00834577\pi\)
\(642\) 0 0
\(643\) 138701. 116384.i 0.335473 0.281496i −0.459452 0.888202i \(-0.651954\pi\)
0.794926 + 0.606707i \(0.207510\pi\)
\(644\) 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 0.194880 + 0.980827i \(0.437568\pi\)
−0.946861 + 0.321643i \(0.895765\pi\)
\(654\) 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 0.227631 0.973748i \(-0.426902\pi\)
0.919427 0.393262i \(-0.128653\pi\)
\(660\) 0 0
\(661\) −275464. 756832.i −0.630468 1.73220i −0.679784 0.733412i \(-0.737927\pi\)
0.0493168 0.998783i \(-0.484296\pi\)
\(662\) 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 −0.745823 0.666144i \(-0.767944\pi\)
0.203986 + 0.978974i \(0.434610\pi\)
\(674\) 0 0
\(675\) −3.00413e6 529710.i −6.59343 1.16260i
\(676\) 0 0
\(677\) 411346. + 237491.i 0.897491 + 0.518167i 0.876385 0.481611i \(-0.159948\pi\)
0.0211057 + 0.999777i \(0.493281\pi\)
\(678\) 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 \(-0.905091\pi\)
0.955877 0.293768i \(-0.0949092\pi\)
\(684\) 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 −0.690131 0.723685i \(-0.742447\pi\)
0.971795 + 0.235828i \(0.0757803\pi\)
\(692\) 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 0.966531 0.256549i \(-0.0825854\pi\)
−0.995987 + 0.0894963i \(0.971474\pi\)
\(702\) 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 0.148176 0.988961i \(-0.452660\pi\)
−0.948206 + 0.317657i \(0.897104\pi\)
\(710\) 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 −0.862043 0.506835i \(-0.830815\pi\)
0.349443 + 0.936958i \(0.386371\pi\)
\(720\) 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 0.0453112 0.998973i \(-0.485572\pi\)
−0.607417 + 0.794383i \(0.707794\pi\)
\(728\) 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 0.998997 + 0.0447870i \(0.0142609\pi\)
−0.460712 + 0.887550i \(0.652406\pi\)
\(734\) 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 −0.999861 0.0166650i \(-0.994695\pi\)
0.933862 0.357633i \(-0.116416\pi\)
\(740\) 0 0
\(741\) 293920. + 85254.4i 0.535295 + 0.155267i
\(742\) 0 0
\(743\) −817496. + 144147.i −1.48084 + 0.261112i −0.854914 0.518770i \(-0.826390\pi\)
−0.625926 + 0.779882i \(0.715279\pi\)
\(744\) 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 −0.402522 0.915410i \(-0.631866\pi\)
−0.691336 + 0.722534i \(0.742977\pi\)
\(752\) 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 0.486982 0.873412i \(-0.338098\pi\)
0.944706 0.327918i \(-0.106347\pi\)
\(758\) 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 −0.986330 0.164783i \(-0.947308\pi\)
0.983206 + 0.182499i \(0.0584187\pi\)
\(770\) 0 0
\(771\) 1.08217e6 + 1.87438e6i 1.82049 + 3.15318i
\(772\) 0 0
\(773\) −530184. + 631849.i −0.887294 + 1.05744i 0.110682 + 0.993856i \(0.464696\pi\)
−0.997977 + 0.0635803i \(0.979748\pi\)
\(774\) 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 −0.872533 0.488554i \(-0.837524\pi\)
−0.0131663 + 0.999913i \(0.504191\pi\)
\(788\) 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