Properties

Label 147.6.e.m.79.2
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(3.72311 - 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.m.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(4.22311 - 7.31464i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-19.6693 - 34.0683i) q^{4} +(18.0000 - 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(4.22311 - 7.31464i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-19.6693 - 34.0683i) q^{4} +(18.0000 - 31.1769i) q^{5} -76.0160 q^{6} -61.9840 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-152.032 - 263.327i) q^{10} +(-147.785 - 255.971i) q^{11} +(-177.024 + 306.615i) q^{12} -1148.13 q^{13} -324.000 q^{15} +(367.653 - 636.794i) q^{16} +(-516.192 - 894.071i) q^{17} +(342.072 + 592.486i) q^{18} +(-1054.26 + 1826.02i) q^{19} -1416.19 q^{20} -2496.45 q^{22} +(320.494 - 555.112i) q^{23} +(278.928 + 483.117i) q^{24} +(914.500 + 1583.96i) q^{25} +(-4848.67 + 8398.15i) q^{26} +729.000 q^{27} +7631.58 q^{29} +(-1368.29 + 2369.94i) q^{30} +(483.488 + 837.426i) q^{31} +(-4097.03 - 7096.26i) q^{32} +(-1330.06 + 2303.74i) q^{33} -8719.74 q^{34} +3186.43 q^{36} +(886.605 - 1535.65i) q^{37} +(8904.48 + 15423.0i) q^{38} +(5166.58 + 8948.77i) q^{39} +(-1115.71 + 1932.47i) q^{40} -11976.4 q^{41} -19802.9 q^{43} +(-5813.66 + 10069.6i) q^{44} +(1458.00 + 2525.33i) q^{45} +(-2706.97 - 4688.60i) q^{46} +(13983.1 - 24219.4i) q^{47} -6617.76 q^{48} +15448.1 q^{50} +(-4645.73 + 8046.64i) q^{51} +(22582.9 + 39114.8i) q^{52} +(3557.16 + 6161.19i) q^{53} +(3078.65 - 5332.37i) q^{54} -10640.5 q^{55} +18976.6 q^{57} +(32229.0 - 55822.3i) q^{58} +(10434.8 + 18073.5i) q^{59} +(6372.86 + 11038.1i) q^{60} +(11934.2 - 20670.6i) q^{61} +8167.30 q^{62} -45679.0 q^{64} +(-20666.3 + 35795.1i) q^{65} +(11234.0 + 19457.9i) q^{66} +(-17335.8 - 30026.4i) q^{67} +(-20306.3 + 35171.5i) q^{68} -5768.90 q^{69} -28413.2 q^{71} +(2510.35 - 4348.06i) q^{72} +(7646.34 + 13243.8i) q^{73} +(-7488.46 - 12970.4i) q^{74} +(8230.50 - 14255.6i) q^{75} +82946.0 q^{76} +87276.1 q^{78} +(36529.8 - 63271.4i) q^{79} +(-13235.5 - 22924.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-50577.6 + 87603.0i) q^{82} -30340.9 q^{83} -37165.8 q^{85} +(-83630.0 + 144851. i) q^{86} +(-34342.1 - 59482.3i) q^{87} +(9160.30 + 15866.1i) q^{88} +(18044.7 - 31254.4i) q^{89} +24629.2 q^{90} -25215.6 q^{92} +(4351.39 - 7536.83i) q^{93} +(-118104. - 204562. i) q^{94} +(37953.2 + 65736.9i) q^{95} +(-36873.2 + 63866.3i) q^{96} -153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.22311 7.31464i 0.746548 1.29306i −0.202921 0.979195i \(-0.565043\pi\)
0.949468 0.313863i \(-0.101623\pi\)
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) −19.6693 34.0683i −0.614667 1.06463i
\(5\) 18.0000 31.1769i 0.321994 0.557710i −0.658906 0.752226i \(-0.728980\pi\)
0.980899 + 0.194516i \(0.0623136\pi\)
\(6\) −76.0160 −0.862039
\(7\) 0 0
\(8\) −61.9840 −0.342416
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) −152.032 263.327i −0.480767 0.832714i
\(11\) −147.785 255.971i −0.368255 0.637836i 0.621038 0.783780i \(-0.286711\pi\)
−0.989293 + 0.145945i \(0.953378\pi\)
\(12\) −177.024 + 306.615i −0.354878 + 0.614667i
\(13\) −1148.13 −1.88422 −0.942111 0.335302i \(-0.891162\pi\)
−0.942111 + 0.335302i \(0.891162\pi\)
\(14\) 0 0
\(15\) −324.000 −0.371806
\(16\) 367.653 636.794i 0.359036 0.621869i
\(17\) −516.192 894.071i −0.433200 0.750325i 0.563946 0.825811i \(-0.309282\pi\)
−0.997147 + 0.0754862i \(0.975949\pi\)
\(18\) 342.072 + 592.486i 0.248849 + 0.431019i
\(19\) −1054.26 + 1826.02i −0.669980 + 1.16044i 0.307929 + 0.951409i \(0.400364\pi\)
−0.977909 + 0.209031i \(0.932969\pi\)
\(20\) −1416.19 −0.791675
\(21\) 0 0
\(22\) −2496.45 −1.09968
\(23\) 320.494 555.112i 0.126328 0.218807i −0.795923 0.605398i \(-0.793014\pi\)
0.922251 + 0.386591i \(0.126347\pi\)
\(24\) 278.928 + 483.117i 0.0988471 + 0.171208i
\(25\) 914.500 + 1583.96i 0.292640 + 0.506867i
\(26\) −4848.67 + 8398.15i −1.40666 + 2.43641i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 7631.58 1.68508 0.842538 0.538637i \(-0.181060\pi\)
0.842538 + 0.538637i \(0.181060\pi\)
\(30\) −1368.29 + 2369.94i −0.277571 + 0.480767i
\(31\) 483.488 + 837.426i 0.0903611 + 0.156510i 0.907663 0.419700i \(-0.137865\pi\)
−0.817302 + 0.576210i \(0.804531\pi\)
\(32\) −4097.03 7096.26i −0.707284 1.22505i
\(33\) −1330.06 + 2303.74i −0.212612 + 0.368255i
\(34\) −8719.74 −1.29362
\(35\) 0 0
\(36\) 3186.43 0.409778
\(37\) 886.605 1535.65i 0.106470 0.184411i −0.807868 0.589363i \(-0.799379\pi\)
0.914338 + 0.404953i \(0.132712\pi\)
\(38\) 8904.48 + 15423.0i 1.00034 + 1.73265i
\(39\) 5166.58 + 8948.77i 0.543928 + 0.942111i
\(40\) −1115.71 + 1932.47i −0.110256 + 0.190969i
\(41\) −11976.4 −1.11267 −0.556335 0.830958i \(-0.687793\pi\)
−0.556335 + 0.830958i \(0.687793\pi\)
\(42\) 0 0
\(43\) −19802.9 −1.63327 −0.816636 0.577153i \(-0.804163\pi\)
−0.816636 + 0.577153i \(0.804163\pi\)
\(44\) −5813.66 + 10069.6i −0.452708 + 0.784113i
\(45\) 1458.00 + 2525.33i 0.107331 + 0.185903i
\(46\) −2706.97 4688.60i −0.188620 0.326700i
\(47\) 13983.1 24219.4i 0.923332 1.59926i 0.129110 0.991630i \(-0.458788\pi\)
0.794222 0.607628i \(-0.207879\pi\)
\(48\) −6617.76 −0.414580
\(49\) 0 0
\(50\) 15448.1 0.873879
\(51\) −4645.73 + 8046.64i −0.250108 + 0.433200i
\(52\) 22582.9 + 39114.8i 1.15817 + 2.00601i
\(53\) 3557.16 + 6161.19i 0.173946 + 0.301283i 0.939796 0.341736i \(-0.111015\pi\)
−0.765850 + 0.643019i \(0.777682\pi\)
\(54\) 3078.65 5332.37i 0.143673 0.248849i
\(55\) −10640.5 −0.474303
\(56\) 0 0
\(57\) 18976.6 0.773627
\(58\) 32229.0 55822.3i 1.25799 2.17890i
\(59\) 10434.8 + 18073.5i 0.390259 + 0.675948i 0.992484 0.122379i \(-0.0390522\pi\)
−0.602225 + 0.798327i \(0.705719\pi\)
\(60\) 6372.86 + 11038.1i 0.228537 + 0.395838i
\(61\) 11934.2 20670.6i 0.410646 0.711259i −0.584315 0.811527i \(-0.698637\pi\)
0.994960 + 0.100268i \(0.0319700\pi\)
\(62\) 8167.30 0.269835
\(63\) 0 0
\(64\) −45679.0 −1.39401
\(65\) −20666.3 + 35795.1i −0.606708 + 1.05085i
\(66\) 11234.0 + 19457.9i 0.317450 + 0.549839i
\(67\) −17335.8 30026.4i −0.471798 0.817178i 0.527682 0.849442i \(-0.323061\pi\)
−0.999479 + 0.0322646i \(0.989728\pi\)
\(68\) −20306.3 + 35171.5i −0.532548 + 0.922400i
\(69\) −5768.90 −0.145871
\(70\) 0 0
\(71\) −28413.2 −0.668921 −0.334461 0.942410i \(-0.608554\pi\)
−0.334461 + 0.942410i \(0.608554\pi\)
\(72\) 2510.35 4348.06i 0.0570694 0.0988471i
\(73\) 7646.34 + 13243.8i 0.167937 + 0.290875i 0.937694 0.347461i \(-0.112956\pi\)
−0.769757 + 0.638337i \(0.779623\pi\)
\(74\) −7488.46 12970.4i −0.158969 0.275343i
\(75\) 8230.50 14255.6i 0.168956 0.292640i
\(76\) 82946.0 1.64726
\(77\) 0 0
\(78\) 87276.1 1.62427
\(79\) 36529.8 63271.4i 0.658535 1.14062i −0.322460 0.946583i \(-0.604510\pi\)
0.980995 0.194033i \(-0.0621570\pi\)
\(80\) −13235.5 22924.6i −0.231215 0.400476i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −50577.6 + 87603.0i −0.830661 + 1.43875i
\(83\) −30340.9 −0.483429 −0.241715 0.970347i \(-0.577710\pi\)
−0.241715 + 0.970347i \(0.577710\pi\)
\(84\) 0 0
\(85\) −37165.8 −0.557951
\(86\) −83630.0 + 144851.i −1.21931 + 2.11192i
\(87\) −34342.1 59482.3i −0.486440 0.842538i
\(88\) 9160.30 + 15866.1i 0.126096 + 0.218406i
\(89\) 18044.7 31254.4i 0.241477 0.418250i −0.719658 0.694328i \(-0.755702\pi\)
0.961135 + 0.276078i \(0.0890349\pi\)
\(90\) 24629.2 0.320512
\(91\) 0 0
\(92\) −25215.6 −0.310599
\(93\) 4351.39 7536.83i 0.0521700 0.0903611i
\(94\) −118104. 204562.i −1.37862 2.38784i
\(95\) 37953.2 + 65736.9i 0.431459 + 0.747309i
\(96\) −36873.2 + 63866.3i −0.408351 + 0.707284i
\(97\) −153963. −1.66145 −0.830724 0.556685i \(-0.812073\pi\)
−0.830724 + 0.556685i \(0.812073\pi\)
\(98\) 0 0
\(99\) 23941.2 0.245503
\(100\) 35975.2 62310.9i 0.359752 0.623109i
\(101\) −69904.4 121078.i −0.681869 1.18103i −0.974410 0.224779i \(-0.927834\pi\)
0.292541 0.956253i \(-0.405499\pi\)
\(102\) 39238.8 + 67963.7i 0.373436 + 0.646810i
\(103\) 57962.7 100394.i 0.538339 0.932430i −0.460655 0.887579i \(-0.652385\pi\)
0.998994 0.0448508i \(-0.0142813\pi\)
\(104\) 71165.6 0.645188
\(105\) 0 0
\(106\) 60089.2 0.519436
\(107\) −41530.9 + 71933.6i −0.350681 + 0.607397i −0.986369 0.164549i \(-0.947383\pi\)
0.635688 + 0.771946i \(0.280716\pi\)
\(108\) −14338.9 24835.8i −0.118293 0.204889i
\(109\) −22678.1 39279.7i −0.182827 0.316666i 0.760015 0.649906i \(-0.225192\pi\)
−0.942842 + 0.333240i \(0.891858\pi\)
\(110\) −44936.1 + 77831.5i −0.354090 + 0.613301i
\(111\) −15958.9 −0.122941
\(112\) 0 0
\(113\) −355.533 −0.00261929 −0.00130965 0.999999i \(-0.500417\pi\)
−0.00130965 + 0.999999i \(0.500417\pi\)
\(114\) 80140.3 138807.i 0.577549 1.00034i
\(115\) −11537.8 19984.0i −0.0813538 0.140909i
\(116\) −150108. 259995.i −1.03576 1.79399i
\(117\) 46499.2 80538.9i 0.314037 0.543928i
\(118\) 176269. 1.16539
\(119\) 0 0
\(120\) 20082.8 0.127313
\(121\) 36844.8 63817.0i 0.228777 0.396253i
\(122\) −100799. 174588.i −0.613133 1.06198i
\(123\) 53893.7 + 93346.7i 0.321200 + 0.556335i
\(124\) 19019.8 32943.2i 0.111084 0.192403i
\(125\) 178344. 1.02090
\(126\) 0 0
\(127\) 168967. 0.929593 0.464797 0.885417i \(-0.346127\pi\)
0.464797 + 0.885417i \(0.346127\pi\)
\(128\) −61802.5 + 107045.i −0.333412 + 0.577486i
\(129\) 89113.2 + 154349.i 0.471485 + 0.816636i
\(130\) 174552. + 302333.i 0.905872 + 1.56902i
\(131\) 86984.6 150662.i 0.442858 0.767052i −0.555043 0.831822i \(-0.687298\pi\)
0.997900 + 0.0647701i \(0.0206314\pi\)
\(132\) 104646. 0.522742
\(133\) 0 0
\(134\) −292843. −1.40888
\(135\) 13122.0 22728.0i 0.0619677 0.107331i
\(136\) 31995.6 + 55418.1i 0.148335 + 0.256924i
\(137\) −183862. 318458.i −0.836931 1.44961i −0.892448 0.451150i \(-0.851014\pi\)
0.0555168 0.998458i \(-0.482319\pi\)
\(138\) −24362.7 + 42197.4i −0.108900 + 0.188620i
\(139\) 217967. 0.956870 0.478435 0.878123i \(-0.341204\pi\)
0.478435 + 0.878123i \(0.341204\pi\)
\(140\) 0 0
\(141\) −251695. −1.06617
\(142\) −119992. + 207833.i −0.499381 + 0.864954i
\(143\) 169676. + 293887.i 0.693873 + 1.20182i
\(144\) 29779.9 + 51580.3i 0.119679 + 0.207290i
\(145\) 137368. 237929.i 0.542584 0.939783i
\(146\) 129165. 0.501492
\(147\) 0 0
\(148\) −69755.7 −0.261773
\(149\) 32453.0 56210.3i 0.119754 0.207420i −0.799916 0.600112i \(-0.795123\pi\)
0.919670 + 0.392692i \(0.128456\pi\)
\(150\) −69516.6 120406.i −0.252267 0.436939i
\(151\) 111889. + 193797.i 0.399341 + 0.691678i 0.993645 0.112562i \(-0.0359057\pi\)
−0.594304 + 0.804240i \(0.702572\pi\)
\(152\) 65347.0 113184.i 0.229412 0.397354i
\(153\) 83623.1 0.288800
\(154\) 0 0
\(155\) 34811.1 0.116383
\(156\) 203246. 352033.i 0.668669 1.15817i
\(157\) 229986. + 398348.i 0.744652 + 1.28977i 0.950357 + 0.311161i \(0.100718\pi\)
−0.205706 + 0.978614i \(0.565949\pi\)
\(158\) −308538. 534404.i −0.983256 1.70305i
\(159\) 32014.5 55450.7i 0.100428 0.173946i
\(160\) −294986. −0.910964
\(161\) 0 0
\(162\) −55415.7 −0.165899
\(163\) −45534.3 + 78867.7i −0.134236 + 0.232504i −0.925305 0.379223i \(-0.876191\pi\)
0.791069 + 0.611727i \(0.209525\pi\)
\(164\) 235567. + 408015.i 0.683921 + 1.18459i
\(165\) 47882.3 + 82934.6i 0.136919 + 0.237151i
\(166\) −128133. + 221933.i −0.360903 + 0.625103i
\(167\) −314772. −0.873384 −0.436692 0.899611i \(-0.643850\pi\)
−0.436692 + 0.899611i \(0.643850\pi\)
\(168\) 0 0
\(169\) 946905. 2.55029
\(170\) −156955. + 271855.i −0.416537 + 0.721464i
\(171\) −85394.7 147908.i −0.223327 0.386813i
\(172\) 389510. + 674652.i 1.00392 + 1.73884i
\(173\) 181071. 313625.i 0.459975 0.796701i −0.538984 0.842316i \(-0.681192\pi\)
0.998959 + 0.0456154i \(0.0145249\pi\)
\(174\) −580122. −1.45260
\(175\) 0 0
\(176\) −217334. −0.528867
\(177\) 93912.9 162662.i 0.225316 0.390259i
\(178\) −152410. 263982.i −0.360548 0.624487i
\(179\) 86948.1 + 150599.i 0.202828 + 0.351308i 0.949438 0.313953i \(-0.101653\pi\)
−0.746611 + 0.665261i \(0.768320\pi\)
\(180\) 57355.8 99343.1i 0.131946 0.228537i
\(181\) 134973. 0.306233 0.153116 0.988208i \(-0.451069\pi\)
0.153116 + 0.988208i \(0.451069\pi\)
\(182\) 0 0
\(183\) −214815. −0.474173
\(184\) −19865.5 + 34408.1i −0.0432569 + 0.0749231i
\(185\) −31917.8 55283.2i −0.0685652 0.118758i
\(186\) −36752.8 63657.8i −0.0778948 0.134918i
\(187\) −152571. + 264260.i −0.319056 + 0.552622i
\(188\) −1.10015e6 −2.27017
\(189\) 0 0
\(190\) 641123. 1.28842
\(191\) −90706.7 + 157109.i −0.179910 + 0.311614i −0.941850 0.336035i \(-0.890914\pi\)
0.761939 + 0.647648i \(0.224247\pi\)
\(192\) 205555. + 356032.i 0.402416 + 0.697006i
\(193\) −482999. 836579.i −0.933369 1.61664i −0.777517 0.628861i \(-0.783521\pi\)
−0.155851 0.987781i \(-0.549812\pi\)
\(194\) −650202. + 1.12618e6i −1.24035 + 2.14835i
\(195\) 371993. 0.700566
\(196\) 0 0
\(197\) −699058. −1.28336 −0.641679 0.766974i \(-0.721762\pi\)
−0.641679 + 0.766974i \(0.721762\pi\)
\(198\) 101106. 175121.i 0.183280 0.317450i
\(199\) 208095. + 360432.i 0.372503 + 0.645194i 0.989950 0.141419i \(-0.0451664\pi\)
−0.617447 + 0.786612i \(0.711833\pi\)
\(200\) −56684.4 98180.2i −0.100205 0.173560i
\(201\) −156022. + 270238.i −0.272393 + 0.471798i
\(202\) −1.18086e6 −2.03619
\(203\) 0 0
\(204\) 365513. 0.614933
\(205\) −215575. + 373387.i −0.358273 + 0.620546i
\(206\) −489566. 847953.i −0.803791 1.39221i
\(207\) 25960.0 + 44964.1i 0.0421094 + 0.0729357i
\(208\) −422113. + 731121.i −0.676504 + 1.17174i
\(209\) 623212. 0.986894
\(210\) 0 0
\(211\) −407152. −0.629580 −0.314790 0.949161i \(-0.601934\pi\)
−0.314790 + 0.949161i \(0.601934\pi\)
\(212\) 139934. 242373.i 0.213837 0.370377i
\(213\) 127860. + 221459.i 0.193101 + 0.334461i
\(214\) 350779. + 607567.i 0.523600 + 0.906901i
\(215\) −356453. + 617394.i −0.525903 + 0.910891i
\(216\) −45186.3 −0.0658981
\(217\) 0 0
\(218\) −383089. −0.545957
\(219\) 68817.0 119195.i 0.0969584 0.167937i
\(220\) 209292. + 362504.i 0.291538 + 0.504959i
\(221\) 592654. + 1.02651e6i 0.816246 + 1.41378i
\(222\) −67396.2 + 116734.i −0.0917810 + 0.158969i
\(223\) 882022. 1.18773 0.593865 0.804565i \(-0.297602\pi\)
0.593865 + 0.804565i \(0.297602\pi\)
\(224\) 0 0
\(225\) −148149. −0.195093
\(226\) −1501.45 + 2600.60i −0.00195542 + 0.00338690i
\(227\) 563251. + 975579.i 0.725499 + 1.25660i 0.958768 + 0.284189i \(0.0917244\pi\)
−0.233269 + 0.972412i \(0.574942\pi\)
\(228\) −373257. 646500.i −0.475523 0.823629i
\(229\) −155042. + 268541.i −0.195371 + 0.338393i −0.947022 0.321168i \(-0.895925\pi\)
0.751651 + 0.659561i \(0.229258\pi\)
\(230\) −194902. −0.242938
\(231\) 0 0
\(232\) −473036. −0.576998
\(233\) −568268. + 984268.i −0.685746 + 1.18775i 0.287456 + 0.957794i \(0.407190\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(234\) −392742. 680250.i −0.468887 0.812136i
\(235\) −503391. 871898.i −0.594614 1.02990i
\(236\) 410490. 710989.i 0.479758 0.830966i
\(237\) −657536. −0.760411
\(238\) 0 0
\(239\) 87506.8 0.0990940 0.0495470 0.998772i \(-0.484222\pi\)
0.0495470 + 0.998772i \(0.484222\pi\)
\(240\) −119120. + 206321.i −0.133492 + 0.231215i
\(241\) −268884. 465721.i −0.298210 0.516515i 0.677516 0.735508i \(-0.263056\pi\)
−0.975727 + 0.218992i \(0.929723\pi\)
\(242\) −311199. 539012.i −0.341586 0.591644i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) −938948. −1.00964
\(245\) 0 0
\(246\) 910397. 0.959164
\(247\) 1.21042e6 2.09651e6i 1.26239 2.18653i
\(248\) −29968.5 51907.0i −0.0309411 0.0535916i
\(249\) 136534. + 236484.i 0.139554 + 0.241715i
\(250\) 753167. 1.30452e6i 0.762151 1.32008i
\(251\) 1.35353e6 1.35607 0.678036 0.735028i \(-0.262831\pi\)
0.678036 + 0.735028i \(0.262831\pi\)
\(252\) 0 0
\(253\) −189457. −0.186084
\(254\) 713567. 1.23593e6i 0.693986 1.20202i
\(255\) 167246. + 289679.i 0.161067 + 0.278976i
\(256\) −208866. 361766.i −0.199190 0.345007i
\(257\) 488450. 846020.i 0.461304 0.799002i −0.537722 0.843122i \(-0.680715\pi\)
0.999026 + 0.0441199i \(0.0140484\pi\)
\(258\) 1.50534e6 1.40794
\(259\) 0 0
\(260\) 1.62597e6 1.49169
\(261\) −309079. + 535341.i −0.280846 + 0.486440i
\(262\) −734691. 1.27252e6i −0.661229 1.14528i
\(263\) 621874. + 1.07712e6i 0.554387 + 0.960227i 0.997951 + 0.0639842i \(0.0203807\pi\)
−0.443564 + 0.896243i \(0.646286\pi\)
\(264\) 82442.7 142795.i 0.0728018 0.126096i
\(265\) 256116. 0.224038
\(266\) 0 0
\(267\) −324805. −0.278833
\(268\) −681966. + 1.18120e6i −0.579997 + 1.00458i
\(269\) 542042. + 938844.i 0.456722 + 0.791066i 0.998785 0.0492716i \(-0.0156900\pi\)
−0.542063 + 0.840338i \(0.682357\pi\)
\(270\) −110831. 191965.i −0.0925237 0.160256i
\(271\) 1.08314e6 1.87605e6i 0.895900 1.55174i 0.0632128 0.998000i \(-0.479865\pi\)
0.832687 0.553744i \(-0.186801\pi\)
\(272\) −759119. −0.622139
\(273\) 0 0
\(274\) −3.10587e6 −2.49924
\(275\) 270299. 468171.i 0.215532 0.373313i
\(276\) 113470. + 196536.i 0.0896622 + 0.155300i
\(277\) −126929. 219848.i −0.0993946 0.172157i 0.812040 0.583602i \(-0.198357\pi\)
−0.911434 + 0.411446i \(0.865024\pi\)
\(278\) 920497. 1.59435e6i 0.714349 1.23729i
\(279\) −78325.1 −0.0602407
\(280\) 0 0
\(281\) 1.14116e6 0.862143 0.431072 0.902318i \(-0.358136\pi\)
0.431072 + 0.902318i \(0.358136\pi\)
\(282\) −1.06294e6 + 1.84106e6i −0.795948 + 1.37862i
\(283\) 304959. + 528204.i 0.226347 + 0.392045i 0.956723 0.291001i \(-0.0939883\pi\)
−0.730376 + 0.683046i \(0.760655\pi\)
\(284\) 558870. + 967990.i 0.411164 + 0.712156i
\(285\) 341579. 591632.i 0.249103 0.431459i
\(286\) 2.86624e6 2.07204
\(287\) 0 0
\(288\) 663718. 0.471523
\(289\) 177020. 306608.i 0.124675 0.215943i
\(290\) −1.16024e6 2.00960e6i −0.810130 1.40319i
\(291\) 692833. + 1.20002e6i 0.479618 + 0.830724i
\(292\) 300797. 520995.i 0.206450 0.357583i
\(293\) 156438. 0.106457 0.0532283 0.998582i \(-0.483049\pi\)
0.0532283 + 0.998582i \(0.483049\pi\)
\(294\) 0 0
\(295\) 751303. 0.502644
\(296\) −54955.3 + 95185.4i −0.0364570 + 0.0631453i
\(297\) −107735. 186603.i −0.0708707 0.122752i
\(298\) −274106. 474765.i −0.178804 0.309698i
\(299\) −367968. + 637340.i −0.238030 + 0.412281i
\(300\) −647554. −0.415406
\(301\) 0 0
\(302\) 1.89007e6 1.19251
\(303\) −629139. + 1.08970e6i −0.393677 + 0.681869i
\(304\) 775201. + 1.34269e6i 0.481095 + 0.833281i
\(305\) −429630. 744141.i −0.264451 0.458042i
\(306\) 353150. 611673.i 0.215603 0.373436i
\(307\) 293229. 0.177566 0.0887831 0.996051i \(-0.471702\pi\)
0.0887831 + 0.996051i \(0.471702\pi\)
\(308\) 0 0
\(309\) −1.04333e6 −0.621620
\(310\) 147011. 254631.i 0.0868853 0.150490i
\(311\) −1.22608e6 2.12363e6i −0.718816 1.24503i −0.961469 0.274913i \(-0.911351\pi\)
0.242653 0.970113i \(-0.421982\pi\)
\(312\) −320245. 554681.i −0.186250 0.322594i
\(313\) −917705. + 1.58951e6i −0.529471 + 0.917071i 0.469938 + 0.882700i \(0.344276\pi\)
−0.999409 + 0.0343716i \(0.989057\pi\)
\(314\) 3.88503e6 2.22367
\(315\) 0 0
\(316\) −2.87406e6 −1.61912
\(317\) −294980. + 510920.i −0.164871 + 0.285565i −0.936609 0.350375i \(-0.886054\pi\)
0.771738 + 0.635940i \(0.219387\pi\)
\(318\) −270401. 468349.i −0.149948 0.259718i
\(319\) −1.12783e6 1.95346e6i −0.620537 1.07480i
\(320\) −822221. + 1.42413e6i −0.448863 + 0.777454i
\(321\) 747556. 0.404931
\(322\) 0 0
\(323\) 2.17679e6 1.16094
\(324\) −129050. + 223522.i −0.0682963 + 0.118293i
\(325\) −1.04996e6 1.81859e6i −0.551399 0.955050i
\(326\) 384593. + 666134.i 0.200427 + 0.347151i
\(327\) −204103. + 353517.i −0.105555 + 0.182827i
\(328\) 742344. 0.380996
\(329\) 0 0
\(330\) 808849. 0.408868
\(331\) −88659.2 + 153562.i −0.0444789 + 0.0770396i −0.887408 0.460985i \(-0.847496\pi\)
0.842929 + 0.538025i \(0.180829\pi\)
\(332\) 596785. + 1.03366e6i 0.297148 + 0.514675i
\(333\) 71815.0 + 124387.i 0.0354899 + 0.0614703i
\(334\) −1.32932e6 + 2.30245e6i −0.652023 + 1.12934i
\(335\) −1.24817e6 −0.607664
\(336\) 0 0
\(337\) −3.04781e6 −1.46189 −0.730943 0.682438i \(-0.760920\pi\)
−0.730943 + 0.682438i \(0.760920\pi\)
\(338\) 3.99888e6 6.92627e6i 1.90391 3.29767i
\(339\) 1599.90 + 2771.10i 0.000756124 + 0.00130965i
\(340\) 731027. + 1.26618e6i 0.342954 + 0.594014i
\(341\) 142904. 247518.i 0.0665518 0.115271i
\(342\) −1.44253e6 −0.666896
\(343\) 0 0
\(344\) 1.22747e6 0.559259
\(345\) −103840. + 179856.i −0.0469697 + 0.0813538i
\(346\) −1.52937e6 2.64895e6i −0.686787 1.18955i
\(347\) 1.21180e6 + 2.09891e6i 0.540268 + 0.935771i 0.998888 + 0.0471388i \(0.0150103\pi\)
−0.458621 + 0.888632i \(0.651656\pi\)
\(348\) −1.35097e6 + 2.33995e6i −0.597996 + 1.03576i
\(349\) −2.67690e6 −1.17644 −0.588218 0.808702i \(-0.700170\pi\)
−0.588218 + 0.808702i \(0.700170\pi\)
\(350\) 0 0
\(351\) −836985. −0.362619
\(352\) −1.21096e6 + 2.09744e6i −0.520921 + 0.902262i
\(353\) −475206. 823081.i −0.202976 0.351565i 0.746510 0.665374i \(-0.231728\pi\)
−0.949486 + 0.313809i \(0.898395\pi\)
\(354\) −793209. 1.37388e6i −0.336418 0.582694i
\(355\) −511438. + 885837.i −0.215388 + 0.373064i
\(356\) −1.41971e6 −0.593711
\(357\) 0 0
\(358\) 1.46877e6 0.605683
\(359\) −1.39441e6 + 2.41518e6i −0.571022 + 0.989039i 0.425439 + 0.904987i \(0.360120\pi\)
−0.996461 + 0.0840524i \(0.973214\pi\)
\(360\) −90372.7 156530.i −0.0367520 0.0636563i
\(361\) −984862. 1.70583e6i −0.397747 0.688919i
\(362\) 570007. 987282.i 0.228617 0.395977i
\(363\) −663206. −0.264169
\(364\) 0 0
\(365\) 550536. 0.216299
\(366\) −907187. + 1.57129e6i −0.353993 + 0.613133i
\(367\) −76940.7 133265.i −0.0298189 0.0516478i 0.850731 0.525602i \(-0.176160\pi\)
−0.880550 + 0.473954i \(0.842826\pi\)
\(368\) −235662. 408178.i −0.0907129 0.157119i
\(369\) 485044. 840120.i 0.185445 0.321200i
\(370\) −539169. −0.204749
\(371\) 0 0
\(372\) −342356. −0.128269
\(373\) 1.19191e6 2.06444e6i 0.443578 0.768299i −0.554374 0.832268i \(-0.687042\pi\)
0.997952 + 0.0639683i \(0.0203757\pi\)
\(374\) 1.28865e6 + 2.23200e6i 0.476381 + 0.825117i
\(375\) −802548. 1.39005e6i −0.294709 0.510450i
\(376\) −866727. + 1.50121e6i −0.316164 + 0.547612i
\(377\) −8.76203e6 −3.17506
\(378\) 0 0
\(379\) 3.65191e6 1.30594 0.652969 0.757385i \(-0.273523\pi\)
0.652969 + 0.757385i \(0.273523\pi\)
\(380\) 1.49303e6 2.58600e6i 0.530407 0.918692i
\(381\) −760352. 1.31697e6i −0.268350 0.464797i
\(382\) 766129. + 1.32697e6i 0.268623 + 0.465269i
\(383\) −1.07865e6 + 1.86827e6i −0.375736 + 0.650794i −0.990437 0.137967i \(-0.955943\pi\)
0.614701 + 0.788760i \(0.289277\pi\)
\(384\) 1.11245e6 0.384991
\(385\) 0 0
\(386\) −8.15904e6 −2.78722
\(387\) 802019. 1.38914e6i 0.272212 0.471485i
\(388\) 3.02835e6 + 5.24525e6i 1.02124 + 1.76883i
\(389\) 1.83236e6 + 3.17373e6i 0.613954 + 1.06340i 0.990567 + 0.137029i \(0.0437553\pi\)
−0.376613 + 0.926371i \(0.622911\pi\)
\(390\) 1.57097e6 2.72100e6i 0.523006 0.905872i
\(391\) −661746. −0.218902
\(392\) 0 0
\(393\) −1.56572e6 −0.511368
\(394\) −2.95220e6 + 5.11336e6i −0.958087 + 1.65946i
\(395\) −1.31507e6 2.27777e6i −0.424089 0.734543i
\(396\) −470906. 815634.i −0.150903 0.261371i
\(397\) 1.97324e6 3.41775e6i 0.628353 1.08834i −0.359529 0.933134i \(-0.617063\pi\)
0.987882 0.155205i \(-0.0496039\pi\)
\(398\) 3.51524e6 1.11236
\(399\) 0 0
\(400\) 1.34488e6 0.420274
\(401\) −12508.0 + 21664.5i −0.00388444 + 0.00672804i −0.867961 0.496632i \(-0.834570\pi\)
0.864077 + 0.503360i \(0.167903\pi\)
\(402\) 1.31780e6 + 2.28249e6i 0.406708 + 0.704439i
\(403\) −555106. 961472.i −0.170260 0.294900i
\(404\) −2.74994e6 + 4.76304e6i −0.838244 + 1.45188i
\(405\) −236196. −0.0715542
\(406\) 0 0
\(407\) −524107. −0.156832
\(408\) 287961. 498763.i 0.0856412 0.148335i
\(409\) −416350. 721139.i −0.123069 0.213163i 0.797907 0.602780i \(-0.205940\pi\)
−0.920977 + 0.389618i \(0.872607\pi\)
\(410\) 1.82079e6 + 3.15371e6i 0.534935 + 0.926535i
\(411\) −1.65476e6 + 2.86612e6i −0.483203 + 0.836931i
\(412\) −4.56035e6 −1.32360
\(413\) 0 0
\(414\) 438528. 0.125747
\(415\) −546136. + 945935.i −0.155661 + 0.269613i
\(416\) 4.70391e6 + 8.14741e6i 1.33268 + 2.30827i
\(417\) −980850. 1.69888e6i −0.276225 0.478435i
\(418\) 2.63190e6 4.55858e6i 0.736763 1.27611i
\(419\) 3.95178e6 1.09966 0.549828 0.835278i \(-0.314693\pi\)
0.549828 + 0.835278i \(0.314693\pi\)
\(420\) 0 0
\(421\) 4.72285e6 1.29867 0.649336 0.760502i \(-0.275047\pi\)
0.649336 + 0.760502i \(0.275047\pi\)
\(422\) −1.71945e6 + 2.97817e6i −0.470011 + 0.814084i
\(423\) 1.13263e6 + 1.96177e6i 0.307777 + 0.533086i
\(424\) −220487. 381895.i −0.0595619 0.103164i
\(425\) 944115. 1.63526e6i 0.253544 0.439150i
\(426\) 2.15986e6 0.576636
\(427\) 0 0
\(428\) 3.26754e6 0.862207
\(429\) 1.52708e6 2.64499e6i 0.400608 0.693873i
\(430\) 3.01068e6 + 5.21465e6i 0.785224 + 1.36005i
\(431\) −2.03905e6 3.53174e6i −0.528731 0.915789i −0.999439 0.0334995i \(-0.989335\pi\)
0.470708 0.882289i \(-0.343999\pi\)
\(432\) 268019. 464223.i 0.0690966 0.119679i
\(433\) −1.79927e6 −0.461186 −0.230593 0.973050i \(-0.574067\pi\)
−0.230593 + 0.973050i \(0.574067\pi\)
\(434\) 0 0
\(435\) −2.47263e6 −0.626522
\(436\) −892127. + 1.54521e6i −0.224756 + 0.389288i
\(437\) 675766. + 1.17046e6i 0.169275 + 0.293193i
\(438\) −581244. 1.00674e6i −0.144768 0.250746i
\(439\) −2.25913e6 + 3.91293e6i −0.559475 + 0.969039i 0.438065 + 0.898943i \(0.355664\pi\)
−0.997540 + 0.0700959i \(0.977669\pi\)
\(440\) 659542. 0.162409
\(441\) 0 0
\(442\) 1.00114e7 2.43746
\(443\) 1.42628e6 2.47039e6i 0.345299 0.598075i −0.640109 0.768284i \(-0.721111\pi\)
0.985408 + 0.170209i \(0.0544443\pi\)
\(444\) 313901. + 543692.i 0.0755675 + 0.130887i
\(445\) −649611. 1.12516e6i −0.155508 0.269348i
\(446\) 3.72488e6 6.45168e6i 0.886696 1.53580i
\(447\) −584155. −0.138280
\(448\) 0 0
\(449\) −1.90246e6 −0.445348 −0.222674 0.974893i \(-0.571478\pi\)
−0.222674 + 0.974893i \(0.571478\pi\)
\(450\) −625650. + 1.08366e6i −0.145646 + 0.252267i
\(451\) 1.76993e6 + 3.06561e6i 0.409746 + 0.709700i
\(452\) 6993.09 + 12112.4i 0.00160999 + 0.00278859i
\(453\) 1.00700e6 1.74417e6i 0.230559 0.399341i
\(454\) 9.51468e6 2.16648
\(455\) 0 0
\(456\) −1.17625e6 −0.264903
\(457\) −1.32417e6 + 2.29353e6i −0.296588 + 0.513705i −0.975353 0.220650i \(-0.929182\pi\)
0.678765 + 0.734355i \(0.262515\pi\)
\(458\) 1.30952e6 + 2.26815e6i 0.291708 + 0.505253i
\(459\) −376304. 651778.i −0.0833695 0.144400i
\(460\) −453881. + 786146.i −0.100011 + 0.173224i
\(461\) 1.09031e6 0.238944 0.119472 0.992838i \(-0.461880\pi\)
0.119472 + 0.992838i \(0.461880\pi\)
\(462\) 0 0
\(463\) −2.50851e6 −0.543831 −0.271916 0.962321i \(-0.587657\pi\)
−0.271916 + 0.962321i \(0.587657\pi\)
\(464\) 2.80578e6 4.85975e6i 0.605004 1.04790i
\(465\) −156650. 271326.i −0.0335968 0.0581914i
\(466\) 4.79971e6 + 8.31335e6i 1.02388 + 1.77342i
\(467\) 1.60468e6 2.77938e6i 0.340483 0.589734i −0.644040 0.764992i \(-0.722743\pi\)
0.984522 + 0.175259i \(0.0560762\pi\)
\(468\) −3.65843e6 −0.772112
\(469\) 0 0
\(470\) −8.50350e6 −1.77563
\(471\) 2.06988e6 3.58513e6i 0.429925 0.744652i
\(472\) −646789. 1.12027e6i −0.133631 0.231456i
\(473\) 2.92657e6 + 5.06898e6i 0.601460 + 1.04176i
\(474\) −2.77685e6 + 4.80964e6i −0.567683 + 0.983256i
\(475\) −3.85647e6 −0.784252
\(476\) 0 0
\(477\) −576260. −0.115964
\(478\) 369551. 640081.i 0.0739784 0.128134i
\(479\) −1.15731e6 2.00452e6i −0.230468 0.399182i 0.727478 0.686131i \(-0.240692\pi\)
−0.957946 + 0.286949i \(0.907359\pi\)
\(480\) 1.32744e6 + 2.29919e6i 0.262973 + 0.455482i
\(481\) −1.01794e6 + 1.76312e6i −0.200612 + 0.347471i
\(482\) −4.54211e6 −0.890513
\(483\) 0 0
\(484\) −2.89885e6 −0.562486
\(485\) −2.77133e6 + 4.80009e6i −0.534976 + 0.926605i
\(486\) 249370. + 431922.i 0.0478911 + 0.0829497i
\(487\) 2.31867e6 + 4.01606e6i 0.443014 + 0.767322i 0.997911 0.0645962i \(-0.0205759\pi\)
−0.554898 + 0.831919i \(0.687243\pi\)
\(488\) −739727. + 1.28124e6i −0.140612 + 0.243547i
\(489\) 819618. 0.155003
\(490\) 0 0
\(491\) 5.02151e6 0.940007 0.470003 0.882665i \(-0.344253\pi\)
0.470003 + 0.882665i \(0.344253\pi\)
\(492\) 2.12011e6 3.67213e6i 0.394862 0.683921i
\(493\) −3.93936e6 6.82317e6i −0.729976 1.26436i
\(494\) −1.02235e7 1.77076e7i −1.88487 3.26469i
\(495\) 430941. 746411.i 0.0790505 0.136919i
\(496\) 711024. 0.129772
\(497\) 0 0
\(498\) 2.30639e6 0.416735
\(499\) −1.68911e6 + 2.92562e6i −0.303673 + 0.525978i −0.976965 0.213399i \(-0.931546\pi\)
0.673292 + 0.739377i \(0.264880\pi\)
\(500\) −3.50791e6 6.07587e6i −0.627514 1.08689i
\(501\) 1.41648e6 + 2.45341e6i 0.252124 + 0.436692i
\(502\) 5.71610e6 9.90057e6i 1.01237 1.75348i
\(503\) 5.03743e6 0.887747 0.443873 0.896090i \(-0.353604\pi\)
0.443873 + 0.896090i \(0.353604\pi\)
\(504\) 0 0
\(505\) −5.03311e6 −0.878230
\(506\) −800097. + 1.38581e6i −0.138921 + 0.240617i
\(507\) −4.26107e6 7.38039e6i −0.736205 1.27515i
\(508\) −3.32347e6 5.75642e6i −0.571390 0.989677i
\(509\) −3.36233e6 + 5.82373e6i −0.575236 + 0.996338i 0.420780 + 0.907163i \(0.361756\pi\)
−0.996016 + 0.0891752i \(0.971577\pi\)
\(510\) 2.82520e6 0.480976
\(511\) 0 0
\(512\) −7.48361e6 −1.26164
\(513\) −768553. + 1.33117e6i −0.128938 + 0.223327i
\(514\) −4.12556e6 7.14568e6i −0.688771 1.19299i
\(515\) −2.08666e6 3.61420e6i −0.346684 0.600473i
\(516\) 3.50559e6 6.07187e6i 0.579612 1.00392i
\(517\) −8.26595e6 −1.36009
\(518\) 0 0
\(519\) −3.25929e6 −0.531134
\(520\) 1.28098e6 2.21872e6i 0.207747 0.359828i
\(521\) −2.21385e6 3.83450e6i −0.357317 0.618892i 0.630194 0.776437i \(-0.282975\pi\)
−0.987512 + 0.157546i \(0.949642\pi\)
\(522\) 2.61055e6 + 4.52161e6i 0.419330 + 0.726301i
\(523\) −4.47955e6 + 7.75882e6i −0.716111 + 1.24034i 0.246418 + 0.969164i \(0.420746\pi\)
−0.962529 + 0.271178i \(0.912587\pi\)
\(524\) −6.84372e6 −1.08884
\(525\) 0 0
\(526\) 1.05050e7 1.65551
\(527\) 499145. 864545.i 0.0782889 0.135600i
\(528\) 978005. + 1.69395e6i 0.152671 + 0.264434i
\(529\) 3.01274e6 + 5.21822e6i 0.468082 + 0.810742i
\(530\) 1.08161e6 1.87340e6i 0.167255 0.289694i
\(531\) −1.69043e6 −0.260173
\(532\) 0 0
\(533\) 1.37504e7 2.09652
\(534\) −1.37169e6 + 2.37583e6i −0.208162 + 0.360548i
\(535\) 1.49511e6 + 2.58961e6i 0.225834 + 0.391156i
\(536\) 1.07454e6 + 1.86116e6i 0.161551 + 0.279815i
\(537\) 782533. 1.35539e6i 0.117103 0.202828i
\(538\) 9.15641e6 1.36386
\(539\) 0 0
\(540\) −1.03240e6 −0.152358
\(541\) 5.02337e6 8.70073e6i 0.737907 1.27809i −0.215529 0.976498i \(-0.569147\pi\)
0.953436 0.301595i \(-0.0975192\pi\)
\(542\) −9.14840e6 1.58455e7i −1.33766 2.31690i
\(543\) −607380. 1.05201e6i −0.0884018 0.153116i
\(544\) −4.22970e6 + 7.32606e6i −0.612791 + 1.06139i
\(545\) −1.63282e6 −0.235477
\(546\) 0 0
\(547\) −1.31426e7 −1.87808 −0.939039 0.343811i \(-0.888282\pi\)
−0.939039 + 0.343811i \(0.888282\pi\)
\(548\) −7.23287e6 + 1.25277e7i −1.02887 + 1.78205i
\(549\) 966667. + 1.67432e6i 0.136882 + 0.237086i
\(550\) −2.28300e6 3.95427e6i −0.321810 0.557391i
\(551\) −8.04564e6 + 1.39355e7i −1.12897 + 1.95543i
\(552\) 357579. 0.0499487
\(553\) 0 0
\(554\) −2.14415e6 −0.296811
\(555\) −287260. + 497549.i −0.0395861 + 0.0685652i
\(556\) −4.28726e6 7.42575e6i −0.588156 1.01872i
\(557\) −4.53376e6 7.85270e6i −0.619185 1.07246i −0.989635 0.143607i \(-0.954130\pi\)
0.370450 0.928853i \(-0.379204\pi\)
\(558\) −330775. + 572920.i −0.0449726 + 0.0778948i
\(559\) 2.27363e7 3.07744
\(560\) 0 0
\(561\) 2.74627e6 0.368414
\(562\) 4.81923e6 8.34715e6i 0.643631 1.11480i
\(563\) 5.25898e6 + 9.10882e6i 0.699247 + 1.21113i 0.968728 + 0.248126i \(0.0798145\pi\)
−0.269481 + 0.963006i \(0.586852\pi\)
\(564\) 4.95068e6 + 8.57483e6i 0.655340 + 1.13508i
\(565\) −6399.59 + 11084.4i −0.000843395 + 0.00146080i
\(566\) 5.15150e6 0.675916
\(567\) 0 0
\(568\) 1.76117e6 0.229050
\(569\) −3.66153e6 + 6.34196e6i −0.474114 + 0.821189i −0.999561 0.0296373i \(-0.990565\pi\)
0.525447 + 0.850826i \(0.323898\pi\)
\(570\) −2.88505e6 4.99706e6i −0.371934 0.644209i
\(571\) 3.48990e6 + 6.04469e6i 0.447943 + 0.775861i 0.998252 0.0591007i \(-0.0188233\pi\)
−0.550309 + 0.834961i \(0.685490\pi\)
\(572\) 6.67483e6 1.15611e7i 0.853002 1.47744i
\(573\) 1.63272e6 0.207743
\(574\) 0 0
\(575\) 1.17237e6 0.147875
\(576\) 1.85000e6 3.20429e6i 0.232335 0.402416i
\(577\) −2.90605e6 5.03343e6i −0.363382 0.629397i 0.625133 0.780518i \(-0.285045\pi\)
−0.988515 + 0.151122i \(0.951711\pi\)
\(578\) −1.49515e6 2.58968e6i −0.186151 0.322423i
\(579\) −4.34699e6 + 7.52921e6i −0.538881 + 0.933369i
\(580\) −1.08078e7 −1.33403
\(581\) 0 0
\(582\) 1.17036e7 1.43223
\(583\) 1.05139e6 1.82106e6i 0.128113 0.221898i
\(584\) −473951. 820906.i −0.0575044 0.0996005i
\(585\) −1.67397e6 2.89940e6i −0.202236 0.350283i
\(586\) 660654. 1.14429e6i 0.0794750 0.137655i
\(587\) 7.37446e6 0.883355 0.441677 0.897174i \(-0.354384\pi\)
0.441677 + 0.897174i \(0.354384\pi\)
\(588\) 0 0
\(589\) −2.03888e6 −0.242161
\(590\) 3.17284e6 5.49552e6i 0.375247 0.649948i
\(591\) 3.14576e6 + 5.44862e6i 0.370473 + 0.641679i
\(592\) −651927. 1.12917e6i −0.0764530 0.132420i
\(593\) 4.73264e6 8.19717e6i 0.552671 0.957254i −0.445410 0.895327i \(-0.646942\pi\)
0.998081 0.0619274i \(-0.0197247\pi\)
\(594\) −1.81991e6 −0.211633
\(595\) 0 0
\(596\) −2.55332e6 −0.294435
\(597\) 1.87286e6 3.24388e6i 0.215065 0.372503i
\(598\) 3.10794e6 + 5.38311e6i 0.355402 + 0.615575i
\(599\) 4.26098e6 + 7.38023e6i 0.485224 + 0.840432i 0.999856 0.0169788i \(-0.00540478\pi\)
−0.514632 + 0.857411i \(0.672071\pi\)
\(600\) −510159. + 883622.i −0.0578532 + 0.100205i
\(601\) 657065. 0.0742031 0.0371016 0.999311i \(-0.488187\pi\)
0.0371016 + 0.999311i \(0.488187\pi\)
\(602\) 0 0
\(603\) 2.80839e6 0.314532
\(604\) 4.40155e6 7.62371e6i 0.490923 0.850303i
\(605\) −1.32641e6 2.29741e6i −0.147330 0.255182i
\(606\) 5.31385e6 + 9.20386e6i 0.587798 + 1.01810i
\(607\) 2.93443e6 5.08257e6i 0.323260 0.559902i −0.657899 0.753106i \(-0.728555\pi\)
0.981159 + 0.193204i \(0.0618880\pi\)
\(608\) 1.72773e7 1.89547
\(609\) 0 0
\(610\) −7.25750e6 −0.789700
\(611\) −1.60544e7 + 2.78070e7i −1.73976 + 3.01336i
\(612\) −1.64481e6 2.84890e6i −0.177516 0.307467i
\(613\) −1.92201e6 3.32902e6i −0.206588 0.357820i 0.744050 0.668124i \(-0.232902\pi\)
−0.950637 + 0.310304i \(0.899569\pi\)
\(614\) 1.23834e6 2.14486e6i 0.132562 0.229603i
\(615\) 3.88035e6 0.413698
\(616\) 0 0
\(617\) 6.44660e6 0.681739 0.340869 0.940111i \(-0.389279\pi\)
0.340869 + 0.940111i \(0.389279\pi\)
\(618\) −4.40609e6 + 7.63158e6i −0.464069 + 0.803791i
\(619\) 3.36870e6 + 5.83476e6i 0.353375 + 0.612063i 0.986838 0.161709i \(-0.0517007\pi\)
−0.633464 + 0.773772i \(0.718367\pi\)
\(620\) −684712. 1.18596e6i −0.0715367 0.123905i
\(621\) 233640. 404677.i 0.0243119 0.0421094i
\(622\) −2.07115e7 −2.14652
\(623\) 0 0
\(624\) 7.59804e6 0.781160
\(625\) 352380. 610339.i 0.0360837 0.0624987i
\(626\) 7.75114e6 + 1.34254e7i 0.790551 + 1.36927i
\(627\) −2.80446e6 4.85746e6i −0.284892 0.493447i
\(628\) 9.04736e6 1.56705e7i 0.915425 1.58556i
\(629\) −1.83063e6 −0.184491
\(630\) 0 0
\(631\) −9.14514e6 −0.914360 −0.457180 0.889374i \(-0.651140\pi\)
−0.457180 + 0.889374i \(0.651140\pi\)
\(632\) −2.26426e6 + 3.92181e6i −0.225493 + 0.390566i
\(633\) 1.83219e6 + 3.17344e6i 0.181744 + 0.314790i
\(634\) 2.49147e6 + 4.31534e6i 0.246168 + 0.426376i
\(635\) 3.04141e6 5.26787e6i 0.299323 0.518443i
\(636\) −2.51881e6 −0.246918
\(637\) 0 0
\(638\) −1.90518e7 −1.85304
\(639\) 1.15074e6 1.99313e6i 0.111487 0.193101i
\(640\) 2.22489e6 + 3.85362e6i 0.214713 + 0.371894i
\(641\) 520442. + 901432.i 0.0500296 + 0.0866538i 0.889956 0.456047i \(-0.150735\pi\)
−0.839926 + 0.542701i \(0.817402\pi\)
\(642\) 3.15701e6 5.46811e6i 0.302300 0.523600i
\(643\) 9.08713e6 0.866761 0.433381 0.901211i \(-0.357321\pi\)
0.433381 + 0.901211i \(0.357321\pi\)
\(644\) 0 0
\(645\) 6.41615e6 0.607261
\(646\) 9.19284e6 1.59225e7i 0.866699 1.50117i
\(647\) 1.10356e6 + 1.91141e6i 0.103641 + 0.179512i 0.913182 0.407551i \(-0.133617\pi\)
−0.809541 + 0.587064i \(0.800284\pi\)
\(648\) 203339. + 352193.i 0.0190231 + 0.0329490i
\(649\) 3.08420e6 5.34199e6i 0.287429 0.497842i
\(650\) −1.77364e7 −1.64658
\(651\) 0 0
\(652\) 3.58252e6 0.330042
\(653\) 9.18048e6 1.59011e7i 0.842524 1.45929i −0.0452296 0.998977i \(-0.514402\pi\)
0.887754 0.460318i \(-0.152265\pi\)
\(654\) 1.72390e6 + 2.98588e6i 0.157604 + 0.272978i
\(655\) −3.13145e6 5.42382e6i −0.285195 0.493972i
\(656\) −4.40316e6 + 7.62649e6i −0.399489 + 0.691935i
\(657\) −1.23871e6 −0.111958
\(658\) 0 0
\(659\) 6.21208e6 0.557216 0.278608 0.960405i \(-0.410127\pi\)
0.278608 + 0.960405i \(0.410127\pi\)
\(660\) 1.88363e6 3.26254e6i 0.168320 0.291538i
\(661\) 7.71149e6 + 1.33567e7i 0.686491 + 1.18904i 0.972966 + 0.230950i \(0.0741833\pi\)
−0.286475 + 0.958088i \(0.592483\pi\)
\(662\) 748835. + 1.29702e6i 0.0664112 + 0.115028i
\(663\) 5.33389e6 9.23857e6i 0.471260 0.816246i
\(664\) 1.88065e6 0.165534
\(665\) 0 0
\(666\) 1.21313e6 0.105980
\(667\) 2.44588e6 4.23638e6i 0.212873 0.368707i
\(668\) 6.19136e6 + 1.07238e7i 0.536840 + 0.929834i
\(669\) −3.96910e6 6.87468e6i −0.342868 0.593865i
\(670\) −5.27118e6 + 9.12995e6i −0.453650 + 0.785745i
\(671\) −7.05475e6 −0.604889
\(672\) 0 0
\(673\) −2.27201e7 −1.93362 −0.966811 0.255491i \(-0.917763\pi\)
−0.966811 + 0.255491i \(0.917763\pi\)
\(674\) −1.28713e7 + 2.22937e7i −1.09137 + 1.89030i
\(675\) 666670. + 1.15471e6i 0.0563186 + 0.0975467i
\(676\) −1.86250e7 3.22594e7i −1.56758 2.71513i
\(677\) 6.80867e6 1.17930e7i 0.570940 0.988897i −0.425530 0.904944i \(-0.639912\pi\)
0.996470 0.0839525i \(-0.0267544\pi\)
\(678\) 27026.2 0.00225793
\(679\) 0 0
\(680\) 2.30369e6 0.191052
\(681\) 5.06926e6 8.78021e6i 0.418867 0.725499i
\(682\) −1.20700e6 2.09059e6i −0.0993682 0.172111i
\(683\) −1.19993e6 2.07833e6i −0.0984245 0.170476i 0.812608 0.582810i \(-0.198047\pi\)
−0.911033 + 0.412334i \(0.864714\pi\)
\(684\) −3.35931e6 + 5.81850e6i −0.274543 + 0.475523i
\(685\) −1.32380e7 −1.07795
\(686\) 0 0
\(687\) 2.79076e6 0.225595
\(688\) −7.28061e6 + 1.26104e7i −0.586404 + 1.01568i
\(689\) −4.08408e6 7.07383e6i −0.327753 0.567684i
\(690\) 877057. + 1.51911e6i 0.0701302 + 0.121469i
\(691\) −701824. + 1.21560e6i −0.0559156 + 0.0968487i −0.892628 0.450793i \(-0.851141\pi\)
0.836713 + 0.547642i \(0.184474\pi\)
\(692\) −1.42462e7 −1.13093
\(693\) 0 0
\(694\) 2.04703e7 1.61334
\(695\) 3.92340e6 6.79553e6i 0.308106 0.533656i
\(696\) 2.12866e6 + 3.68695e6i 0.166565 + 0.288499i
\(697\) 6.18211e6 + 1.07077e7i 0.482009 + 0.834864i
\(698\) −1.13048e7 + 1.95806e7i −0.878266 + 1.52120i
\(699\) 1.02288e7 0.791831
\(700\) 0 0
\(701\) −5.78991e6 −0.445017 −0.222509 0.974931i \(-0.571425\pi\)
−0.222509 + 0.974931i \(0.571425\pi\)
\(702\) −3.53468e6 + 6.12225e6i −0.270712 + 0.468887i
\(703\) 1.86942e6 + 3.23793e6i 0.142665 + 0.247103i
\(704\) 6.75066e6 + 1.16925e7i 0.513351 + 0.889150i
\(705\) −4.53052e6 + 7.84708e6i −0.343301 + 0.594614i
\(706\) −8.02739e6 −0.606126
\(707\) 0 0
\(708\) −7.38882e6 −0.553977
\(709\) 5.65716e6 9.79849e6i 0.422652 0.732055i −0.573546 0.819173i \(-0.694433\pi\)
0.996198 + 0.0871187i \(0.0277659\pi\)
\(710\) 4.31972e6 + 7.48198e6i 0.321595 + 0.557020i
\(711\) 2.95891e6 + 5.12498e6i 0.219512 + 0.380206i
\(712\) −1.11848e6 + 1.93727e6i −0.0826857 + 0.143216i
\(713\) 619821. 0.0456607
\(714\) 0 0
\(715\) 1.22167e7 0.893692
\(716\) 3.42042e6 5.92435e6i 0.249343 0.431875i
\(717\) −393781. 682048.i −0.0286060 0.0495470i
\(718\) 1.17775e7 + 2.03992e7i 0.852591 + 1.47673i
\(719\) −1.36890e7 + 2.37101e7i −0.987529 + 1.71045i −0.357420 + 0.933944i \(0.616344\pi\)
−0.630109 + 0.776507i \(0.716990\pi\)
\(720\) 2.14415e6 0.154143
\(721\) 0 0
\(722\) −1.66367e7 −1.18775
\(723\) −2.41996e6 + 4.19149e6i −0.172172 + 0.298210i
\(724\) −2.65484e6 4.59831e6i −0.188231 0.326026i
\(725\) 6.97908e6 + 1.20881e7i 0.493121 + 0.854110i
\(726\) −2.80079e6 + 4.85111e6i −0.197215 + 0.341586i
\(727\) 9.86471e6 0.692226 0.346113 0.938193i \(-0.387501\pi\)
0.346113 + 0.938193i \(0.387501\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 2.32498e6 4.02698e6i 0.161477 0.279687i
\(731\) 1.02221e7 + 1.77052e7i 0.707534 + 1.22548i
\(732\) 4.22527e6 + 7.31837e6i 0.291458 + 0.504820i
\(733\) 1.93938e6 3.35911e6i 0.133322 0.230921i −0.791633 0.610997i \(-0.790769\pi\)
0.924955 + 0.380076i \(0.124102\pi\)
\(734\) −1.29972e6 −0.0890448
\(735\) 0 0
\(736\) −5.25229e6 −0.357400
\(737\) −5.12393e6 + 8.87490e6i −0.347483 + 0.601859i
\(738\) −4.09679e6 7.09584e6i −0.276887 0.479582i
\(739\) 3.97749e6 + 6.88922e6i 0.267916 + 0.464044i 0.968323 0.249699i \(-0.0803318\pi\)
−0.700408 + 0.713743i \(0.746998\pi\)
\(740\) −1.25560e6 + 2.17477e6i −0.0842894 + 0.145994i
\(741\) −2.17876e7 −1.45768
\(742\) 0 0
\(743\) 1.65977e7 1.10300 0.551500 0.834175i \(-0.314056\pi\)
0.551500 + 0.834175i \(0.314056\pi\)
\(744\) −269717. + 467163.i −0.0178639 + 0.0309411i
\(745\) −1.16831e6 2.02357e6i −0.0771200 0.133576i
\(746\) −1.00671e7 1.74367e7i −0.662304 1.14714i
\(747\) 1.22881e6 2.12835e6i 0.0805716 0.139554i
\(748\) 1.20039e7 0.784453
\(749\) 0 0
\(750\) −1.35570e7 −0.880056
\(751\) −7.55359e6 + 1.30832e7i −0.488713 + 0.846475i −0.999916 0.0129846i \(-0.995867\pi\)
0.511203 + 0.859460i \(0.329200\pi\)
\(752\) −1.02818e7 1.78087e7i −0.663020 1.14838i
\(753\) −6.09088e6 1.05497e7i −0.391464 0.678036i
\(754\) −3.70030e7 + 6.40911e7i −2.37033 + 4.10553i
\(755\) 8.05598e6 0.514341
\(756\) 0 0
\(757\) 5.80923e6 0.368450 0.184225 0.982884i \(-0.441022\pi\)
0.184225 + 0.982884i \(0.441022\pi\)
\(758\) 1.54224e7 2.67124e7i 0.974944 1.68865i
\(759\) 852556. + 1.47667e6i 0.0537178 + 0.0930420i
\(760\) −2.35249e6 4.07464e6i −0.147739 0.255891i
\(761\) 1.27135e7 2.20204e7i 0.795799 1.37836i −0.126531 0.991963i \(-0.540384\pi\)
0.922331 0.386402i \(-0.126282\pi\)
\(762\) −1.28442e7 −0.801346
\(763\) 0 0
\(764\) 7.13656e6 0.442340
\(765\) 1.50522e6 2.60711e6i 0.0929919 0.161067i
\(766\) 9.11050e6 + 1.57798e7i 0.561010 + 0.971697i
\(767\) −1.19804e7 2.07507e7i −0.735334 1.27364i
\(768\) −1.87979e6 + 3.25589e6i −0.115002 + 0.199190i
\(769\) −1.53909e7 −0.938532 −0.469266 0.883057i \(-0.655481\pi\)
−0.469266 + 0.883057i \(0.655481\pi\)
\(770\) 0 0
\(771\) −8.79210e6 −0.532668
\(772\) −1.90005e7 + 3.29099e7i −1.14742 + 1.98739i
\(773\) 452696. + 784093.i 0.0272495 + 0.0471975i