Properties

Label 177.6.d.b.176.7
Level $177$
Weight $6$
Character 177.176
Analytic conductor $28.388$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.7
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.8

$q$-expansion

\(f(q)\) \(=\) \(q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +O(q^{10})\) \(q-9.95283 q^{2} +(-15.5523 - 1.06177i) q^{3} +67.0588 q^{4} -97.9414i q^{5} +(154.789 + 10.5677i) q^{6} -155.750 q^{7} -348.934 q^{8} +(240.745 + 33.0259i) q^{9} +974.794i q^{10} +637.985 q^{11} +(-1042.92 - 71.2012i) q^{12} -651.416i q^{13} +1550.16 q^{14} +(-103.992 + 1523.21i) q^{15} +1327.00 q^{16} +1943.14i q^{17} +(-2396.10 - 328.702i) q^{18} -604.694 q^{19} -6567.83i q^{20} +(2422.27 + 165.372i) q^{21} -6349.76 q^{22} -1689.09 q^{23} +(5426.71 + 370.489i) q^{24} -6467.52 q^{25} +6483.43i q^{26} +(-3709.07 - 769.245i) q^{27} -10444.4 q^{28} -6482.75i q^{29} +(1035.01 - 15160.2i) q^{30} +8950.46i q^{31} -2041.50 q^{32} +(-9922.11 - 677.396i) q^{33} -19339.7i q^{34} +15254.4i q^{35} +(16144.1 + 2214.68i) q^{36} +3363.48i q^{37} +6018.41 q^{38} +(-691.656 + 10131.0i) q^{39} +34175.1i q^{40} +2841.20i q^{41} +(-24108.4 - 1645.92i) q^{42} +8732.70i q^{43} +42782.5 q^{44} +(3234.61 - 23578.9i) q^{45} +16811.2 q^{46} +3956.62 q^{47} +(-20637.8 - 1408.97i) q^{48} +7451.21 q^{49} +64370.1 q^{50} +(2063.17 - 30220.2i) q^{51} -43683.1i q^{52} +14672.5i q^{53} +(36915.7 + 7656.16i) q^{54} -62485.2i q^{55} +54346.6 q^{56} +(9404.35 + 642.048i) q^{57} +64521.7i q^{58} +(26703.5 - 1358.34i) q^{59} +(-6973.55 + 102145. i) q^{60} +28285.7i q^{61} -89082.4i q^{62} +(-37496.2 - 5143.81i) q^{63} -22145.2 q^{64} -63800.6 q^{65} +(98753.0 + 6742.01i) q^{66} +47631.3i q^{67} +130304. i q^{68} +(26269.1 + 1793.43i) q^{69} -151825. i q^{70} -7395.45i q^{71} +(-84004.2 - 11523.9i) q^{72} +16012.4i q^{73} -33476.1i q^{74} +(100584. + 6867.04i) q^{75} -40550.0 q^{76} -99366.5 q^{77} +(6883.93 - 100832. i) q^{78} +20478.8 q^{79} -129968. i q^{80} +(56867.6 + 15901.7i) q^{81} -28278.0i q^{82} +58853.4 q^{83} +(162435. + 11089.6i) q^{84} +190314. q^{85} -86915.0i q^{86} +(-6883.22 + 100821. i) q^{87} -222615. q^{88} +75358.4 q^{89} +(-32193.5 + 234677. i) q^{90} +101458. i q^{91} -113268. q^{92} +(9503.36 - 139200. i) q^{93} -39379.5 q^{94} +59224.6i q^{95} +(31750.0 + 2167.61i) q^{96} -100295. i q^{97} -74160.6 q^{98} +(153592. + 21070.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.95283 −1.75943 −0.879714 0.475503i \(-0.842266\pi\)
−0.879714 + 0.475503i \(0.842266\pi\)
\(3\) −15.5523 1.06177i −0.997678 0.0681128i
\(4\) 67.0588 2.09559
\(5\) 97.9414i 1.75203i −0.482285 0.876014i \(-0.660193\pi\)
0.482285 0.876014i \(-0.339807\pi\)
\(6\) 154.789 + 10.5677i 1.75534 + 0.119840i
\(7\) −155.750 −1.20139 −0.600695 0.799478i \(-0.705110\pi\)
−0.600695 + 0.799478i \(0.705110\pi\)
\(8\) −348.934 −1.92761
\(9\) 240.745 + 33.0259i 0.990721 + 0.135909i
\(10\) 974.794i 3.08257i
\(11\) 637.985 1.58975 0.794875 0.606773i \(-0.207536\pi\)
0.794875 + 0.606773i \(0.207536\pi\)
\(12\) −1042.92 71.2012i −2.09072 0.142736i
\(13\) 651.416i 1.06905i −0.845151 0.534527i \(-0.820490\pi\)
0.845151 0.534527i \(-0.179510\pi\)
\(14\) 1550.16 2.11376
\(15\) −103.992 + 1523.21i −0.119336 + 1.74796i
\(16\) 1327.00 1.29590
\(17\) 1943.14i 1.63073i 0.578949 + 0.815364i \(0.303463\pi\)
−0.578949 + 0.815364i \(0.696537\pi\)
\(18\) −2396.10 328.702i −1.74310 0.239123i
\(19\) −604.694 −0.384283 −0.192142 0.981367i \(-0.561543\pi\)
−0.192142 + 0.981367i \(0.561543\pi\)
\(20\) 6567.83i 3.67153i
\(21\) 2422.27 + 165.372i 1.19860 + 0.0818301i
\(22\) −6349.76 −2.79705
\(23\) −1689.09 −0.665783 −0.332892 0.942965i \(-0.608024\pi\)
−0.332892 + 0.942965i \(0.608024\pi\)
\(24\) 5426.71 + 370.489i 1.92313 + 0.131295i
\(25\) −6467.52 −2.06961
\(26\) 6483.43i 1.88092i
\(27\) −3709.07 769.245i −0.979163 0.203074i
\(28\) −10444.4 −2.51762
\(29\) 6482.75i 1.43141i −0.698402 0.715706i \(-0.746105\pi\)
0.698402 0.715706i \(-0.253895\pi\)
\(30\) 1035.01 15160.2i 0.209962 3.07541i
\(31\) 8950.46i 1.67279i 0.548128 + 0.836394i \(0.315341\pi\)
−0.548128 + 0.836394i \(0.684659\pi\)
\(32\) −2041.50 −0.352432
\(33\) −9922.11 677.396i −1.58606 0.108282i
\(34\) 19339.7i 2.86915i
\(35\) 15254.4i 2.10487i
\(36\) 16144.1 + 2214.68i 2.07614 + 0.284810i
\(37\) 3363.48i 0.403910i 0.979395 + 0.201955i \(0.0647294\pi\)
−0.979395 + 0.201955i \(0.935271\pi\)
\(38\) 6018.41 0.676119
\(39\) −691.656 + 10131.0i −0.0728163 + 1.06657i
\(40\) 34175.1i 3.37722i
\(41\) 2841.20i 0.263963i 0.991252 + 0.131981i \(0.0421339\pi\)
−0.991252 + 0.131981i \(0.957866\pi\)
\(42\) −24108.4 1645.92i −2.10885 0.143974i
\(43\) 8732.70i 0.720240i 0.932906 + 0.360120i \(0.117264\pi\)
−0.932906 + 0.360120i \(0.882736\pi\)
\(44\) 42782.5 3.33146
\(45\) 3234.61 23578.9i 0.238117 1.73577i
\(46\) 16811.2 1.17140
\(47\) 3956.62 0.261264 0.130632 0.991431i \(-0.458299\pi\)
0.130632 + 0.991431i \(0.458299\pi\)
\(48\) −20637.8 1408.97i −1.29289 0.0882672i
\(49\) 7451.21 0.443340
\(50\) 64370.1 3.64132
\(51\) 2063.17 30220.2i 0.111073 1.62694i
\(52\) 43683.1i 2.24030i
\(53\) 14672.5i 0.717490i 0.933436 + 0.358745i \(0.116795\pi\)
−0.933436 + 0.358745i \(0.883205\pi\)
\(54\) 36915.7 + 7656.16i 1.72277 + 0.357295i
\(55\) 62485.2i 2.78529i
\(56\) 54346.6 2.31581
\(57\) 9404.35 + 642.048i 0.383391 + 0.0261746i
\(58\) 64521.7i 2.51847i
\(59\) 26703.5 1358.34i 0.998709 0.0508018i
\(60\) −6973.55 + 102145.i −0.250078 + 3.66300i
\(61\) 28285.7i 0.973290i 0.873600 + 0.486645i \(0.161779\pi\)
−0.873600 + 0.486645i \(0.838221\pi\)
\(62\) 89082.4i 2.94315i
\(63\) −37496.2 5143.81i −1.19024 0.163280i
\(64\) −22145.2 −0.675819
\(65\) −63800.6 −1.87301
\(66\) 98753.0 + 6742.01i 2.79056 + 0.190515i
\(67\) 47631.3i 1.29630i 0.761513 + 0.648150i \(0.224457\pi\)
−0.761513 + 0.648150i \(0.775543\pi\)
\(68\) 130304.i 3.41733i
\(69\) 26269.1 + 1793.43i 0.664237 + 0.0453484i
\(70\) 151825.i 3.70337i
\(71\) 7395.45i 0.174108i −0.996204 0.0870540i \(-0.972255\pi\)
0.996204 0.0870540i \(-0.0277453\pi\)
\(72\) −84004.2 11523.9i −1.90972 0.261980i
\(73\) 16012.4i 0.351681i 0.984419 + 0.175841i \(0.0562643\pi\)
−0.984419 + 0.175841i \(0.943736\pi\)
\(74\) 33476.1i 0.710650i
\(75\) 100584. + 6867.04i 2.06480 + 0.140967i
\(76\) −40550.0 −0.805299
\(77\) −99366.5 −1.90991
\(78\) 6883.93 100832.i 0.128115 1.87656i
\(79\) 20478.8 0.369179 0.184589 0.982816i \(-0.440905\pi\)
0.184589 + 0.982816i \(0.440905\pi\)
\(80\) 129968.i 2.27045i
\(81\) 56867.6 + 15901.7i 0.963057 + 0.269296i
\(82\) 28278.0i 0.464423i
\(83\) 58853.4 0.937727 0.468864 0.883271i \(-0.344664\pi\)
0.468864 + 0.883271i \(0.344664\pi\)
\(84\) 162435. + 11089.6i 2.51177 + 0.171482i
\(85\) 190314. 2.85708
\(86\) 86915.0i 1.26721i
\(87\) −6883.22 + 100821.i −0.0974975 + 1.42809i
\(88\) −222615. −3.06441
\(89\) 75358.4 1.00846 0.504228 0.863571i \(-0.331777\pi\)
0.504228 + 0.863571i \(0.331777\pi\)
\(90\) −32193.5 + 234677.i −0.418950 + 3.05397i
\(91\) 101458.i 1.28435i
\(92\) −113268. −1.39521
\(93\) 9503.36 139200.i 0.113938 1.66890i
\(94\) −39379.5 −0.459675
\(95\) 59224.6i 0.673275i
\(96\) 31750.0 + 2167.61i 0.351613 + 0.0240051i
\(97\) 100295.i 1.08230i −0.840926 0.541150i \(-0.817989\pi\)
0.840926 0.541150i \(-0.182011\pi\)
\(98\) −74160.6 −0.780024
\(99\) 153592. + 21070.1i 1.57500 + 0.216062i
\(100\) −433704. −4.33704
\(101\) −141030. −1.37565 −0.687826 0.725875i \(-0.741435\pi\)
−0.687826 + 0.725875i \(0.741435\pi\)
\(102\) −20534.4 + 300776.i −0.195426 + 2.86248i
\(103\) 53647.1i 0.498257i −0.968470 0.249128i \(-0.919856\pi\)
0.968470 0.249128i \(-0.0801441\pi\)
\(104\) 227301.i 2.06072i
\(105\) 16196.7 237241.i 0.143369 2.09998i
\(106\) 146033.i 1.26237i
\(107\) 107650.i 0.908978i 0.890752 + 0.454489i \(0.150178\pi\)
−0.890752 + 0.454489i \(0.849822\pi\)
\(108\) −248725. 51584.6i −2.05192 0.425560i
\(109\) 18877.0i 0.152183i 0.997101 + 0.0760917i \(0.0242442\pi\)
−0.997101 + 0.0760917i \(0.975756\pi\)
\(110\) 621904.i 4.90051i
\(111\) 3571.25 52309.7i 0.0275114 0.402972i
\(112\) −206681. −1.55688
\(113\) −15698.1 −0.115651 −0.0578256 0.998327i \(-0.518417\pi\)
−0.0578256 + 0.998327i \(0.518417\pi\)
\(114\) −93599.9 6390.19i −0.674549 0.0460524i
\(115\) 165432.i 1.16647i
\(116\) 434726.i 2.99965i
\(117\) 21513.6 156825.i 0.145294 1.05914i
\(118\) −265776. + 13519.3i −1.75716 + 0.0893821i
\(119\) 302645.i 1.95914i
\(120\) 36286.2 531500.i 0.230032 3.36938i
\(121\) 245974. 1.52731
\(122\) 281523.i 1.71243i
\(123\) 3016.71 44187.1i 0.0179792 0.263350i
\(124\) 600207.i 3.50547i
\(125\) 327371.i 1.87398i
\(126\) 373193. + 51195.4i 2.09415 + 0.287280i
\(127\) −44909.1 −0.247073 −0.123536 0.992340i \(-0.539424\pi\)
−0.123536 + 0.992340i \(0.539424\pi\)
\(128\) 285736. 1.54149
\(129\) 9272.15 135813.i 0.0490576 0.718567i
\(130\) 634996. 3.29543
\(131\) 151394. 0.770782 0.385391 0.922753i \(-0.374067\pi\)
0.385391 + 0.922753i \(0.374067\pi\)
\(132\) −665365. 45425.3i −3.32372 0.226915i
\(133\) 94181.3 0.461674
\(134\) 474066.i 2.28075i
\(135\) −75340.9 + 363271.i −0.355792 + 1.71552i
\(136\) 678027.i 3.14340i
\(137\) 345873.i 1.57440i −0.616697 0.787201i \(-0.711529\pi\)
0.616697 0.787201i \(-0.288471\pi\)
\(138\) −261452. 17849.7i −1.16868 0.0797872i
\(139\) −22047.5 −0.0967882 −0.0483941 0.998828i \(-0.515410\pi\)
−0.0483941 + 0.998828i \(0.515410\pi\)
\(140\) 1.02294e6i 4.41094i
\(141\) −61534.3 4201.03i −0.260657 0.0177954i
\(142\) 73605.6i 0.306330i
\(143\) 415594.i 1.69953i
\(144\) 319469. + 43825.4i 1.28387 + 0.176124i
\(145\) −634930. −2.50787
\(146\) 159369.i 0.618758i
\(147\) −115883. 7911.50i −0.442310 0.0301971i
\(148\) 225551.i 0.846428i
\(149\) −424520. −1.56651 −0.783254 0.621702i \(-0.786442\pi\)
−0.783254 + 0.621702i \(0.786442\pi\)
\(150\) −1.00110e6 68346.5i −3.63286 0.248021i
\(151\) 95892.3i 0.342248i 0.985249 + 0.171124i \(0.0547399\pi\)
−0.985249 + 0.171124i \(0.945260\pi\)
\(152\) 210998. 0.740747
\(153\) −64174.0 + 467801.i −0.221631 + 1.61560i
\(154\) 988978. 3.36035
\(155\) 876620. 2.93077
\(156\) −46381.6 + 679371.i −0.152593 + 2.23509i
\(157\) 385672.i 1.24873i −0.781132 0.624366i \(-0.785357\pi\)
0.781132 0.624366i \(-0.214643\pi\)
\(158\) −203822. −0.649543
\(159\) 15578.9 228191.i 0.0488703 0.715824i
\(160\) 199948.i 0.617471i
\(161\) 263076. 0.799866
\(162\) −565993. 158267.i −1.69443 0.473808i
\(163\) 487203. 1.43628 0.718142 0.695896i \(-0.244993\pi\)
0.718142 + 0.695896i \(0.244993\pi\)
\(164\) 190528.i 0.553157i
\(165\) −66345.1 + 971785.i −0.189714 + 2.77882i
\(166\) −585758. −1.64986
\(167\) 256.470i 0.000711615i −1.00000 0.000355808i \(-0.999887\pi\)
1.00000 0.000355808i \(-0.000113257\pi\)
\(168\) −845213. 57703.8i −2.31043 0.157736i
\(169\) −53049.4 −0.142878
\(170\) −1.89416e6 −5.02683
\(171\) −145577. 19970.6i −0.380718 0.0522277i
\(172\) 585604.i 1.50933i
\(173\) 442665. 1.12450 0.562250 0.826967i \(-0.309936\pi\)
0.562250 + 0.826967i \(0.309936\pi\)
\(174\) 68507.5 1.00346e6i 0.171540 2.51262i
\(175\) 1.00732e6 2.48640
\(176\) 846606. 2.06015
\(177\) −416743. 7227.84i −0.999850 0.0173411i
\(178\) −750029. −1.77430
\(179\) −8484.97 −0.0197933 −0.00989664 0.999951i \(-0.503150\pi\)
−0.00989664 + 0.999951i \(0.503150\pi\)
\(180\) 216909. 1.58117e6i 0.498995 3.63746i
\(181\) −178227. −0.404369 −0.202184 0.979347i \(-0.564804\pi\)
−0.202184 + 0.979347i \(0.564804\pi\)
\(182\) 1.00980e6i 2.25973i
\(183\) 30033.0 439906.i 0.0662935 0.971029i
\(184\) 589380. 1.28337
\(185\) 329424. 0.707662
\(186\) −94585.3 + 1.38543e6i −0.200466 + 2.93632i
\(187\) 1.23969e6i 2.59245i
\(188\) 265326. 0.547501
\(189\) 577689. + 119810.i 1.17636 + 0.243972i
\(190\) 589452.i 1.18458i
\(191\) −161763. −0.320845 −0.160423 0.987048i \(-0.551286\pi\)
−0.160423 + 0.987048i \(0.551286\pi\)
\(192\) 344408. + 23513.2i 0.674249 + 0.0460319i
\(193\) −29421.5 −0.0568554 −0.0284277 0.999596i \(-0.509050\pi\)
−0.0284277 + 0.999596i \(0.509050\pi\)
\(194\) 998214.i 1.90423i
\(195\) 992243. + 67741.8i 1.86866 + 0.127576i
\(196\) 499669. 0.929056
\(197\) 102771.i 0.188671i 0.995540 + 0.0943356i \(0.0300727\pi\)
−0.995540 + 0.0943356i \(0.969927\pi\)
\(198\) −1.52867e6 209707.i −2.77110 0.380145i
\(199\) −14462.2 −0.0258883 −0.0129441 0.999916i \(-0.504120\pi\)
−0.0129441 + 0.999916i \(0.504120\pi\)
\(200\) 2.25674e6 3.98938
\(201\) 50573.6 740774.i 0.0882946 1.29329i
\(202\) 1.40365e6 2.42036
\(203\) 1.00969e6i 1.71968i
\(204\) 138354. 2.02653e6i 0.232764 3.40939i
\(205\) 278271. 0.462470
\(206\) 533940.i 0.876647i
\(207\) −406640. 55783.7i −0.659605 0.0904861i
\(208\) 864428.i 1.38538i
\(209\) −385786. −0.610915
\(210\) −161203. + 2.36121e6i −0.252247 + 3.69477i
\(211\) 569457.i 0.880552i 0.897862 + 0.440276i \(0.145119\pi\)
−0.897862 + 0.440276i \(0.854881\pi\)
\(212\) 983923.i 1.50356i
\(213\) −7852.29 + 115016.i −0.0118590 + 0.173704i
\(214\) 1.07142e6i 1.59928i
\(215\) 855293. 1.26188
\(216\) 1.29422e6 + 268416.i 1.88744 + 0.391448i
\(217\) 1.39404e6i 2.00967i
\(218\) 187880.i 0.267756i
\(219\) 17001.5 249029.i 0.0239540 0.350864i
\(220\) 4.19018e6i 5.83681i
\(221\) 1.26579e6 1.74334
\(222\) −35544.1 + 520629.i −0.0484044 + 0.709000i
\(223\) −604508. −0.814030 −0.407015 0.913422i \(-0.633430\pi\)
−0.407015 + 0.913422i \(0.633430\pi\)
\(224\) 317965. 0.423408
\(225\) −1.55702e6 213596.i −2.05040 0.281279i
\(226\) 156240. 0.203480
\(227\) 864660. 1.11373 0.556866 0.830602i \(-0.312004\pi\)
0.556866 + 0.830602i \(0.312004\pi\)
\(228\) 630644. + 43055.0i 0.803429 + 0.0548512i
\(229\) 505214.i 0.636629i 0.947985 + 0.318315i \(0.103117\pi\)
−0.947985 + 0.318315i \(0.896883\pi\)
\(230\) 1.64651e6i 2.05232i
\(231\) 1.54537e6 + 105505.i 1.90548 + 0.130089i
\(232\) 2.26205e6i 2.75920i
\(233\) −181647. −0.219199 −0.109600 0.993976i \(-0.534957\pi\)
−0.109600 + 0.993976i \(0.534957\pi\)
\(234\) −214121. + 1.56085e6i −0.255635 + 1.86347i
\(235\) 387517.i 0.457742i
\(236\) 1.79071e6 91088.7i 2.09288 0.106460i
\(237\) −318491. 21743.8i −0.368321 0.0251458i
\(238\) 3.01217e6i 3.44697i
\(239\) 773579.i 0.876012i −0.898972 0.438006i \(-0.855685\pi\)
0.898972 0.438006i \(-0.144315\pi\)
\(240\) −137997. + 2.02130e6i −0.154647 + 2.26518i
\(241\) −264955. −0.293852 −0.146926 0.989147i \(-0.546938\pi\)
−0.146926 + 0.989147i \(0.546938\pi\)
\(242\) −2.44814e6 −2.68719
\(243\) −867535. 307688.i −0.942478 0.334268i
\(244\) 1.89680e6i 2.03961i
\(245\) 729782.i 0.776744i
\(246\) −30024.8 + 439787.i −0.0316332 + 0.463345i
\(247\) 393907.i 0.410820i
\(248\) 3.12312e6i 3.22448i
\(249\) −915303. 62489.0i −0.935549 0.0638712i
\(250\) 3.25826e6i 3.29713i
\(251\) 331435.i 0.332058i −0.986121 0.166029i \(-0.946905\pi\)
0.986121 0.166029i \(-0.0530946\pi\)
\(252\) −2.51445e6 344937.i −2.49426 0.342168i
\(253\) −1.07761e6 −1.05843
\(254\) 446973. 0.434707
\(255\) −2.95981e6 202070.i −2.85045 0.194604i
\(256\) −2.13523e6 −2.03632
\(257\) 1.61393e6i 1.52423i 0.647441 + 0.762116i \(0.275839\pi\)
−0.647441 + 0.762116i \(0.724161\pi\)
\(258\) −92284.1 + 1.35172e6i −0.0863133 + 1.26427i
\(259\) 523863.i 0.485253i
\(260\) −4.27839e6 −3.92506
\(261\) 214099. 1.56069e6i 0.194542 1.41813i
\(262\) −1.50680e6 −1.35614
\(263\) 1.10742e6i 0.987240i 0.869678 + 0.493620i \(0.164327\pi\)
−0.869678 + 0.493620i \(0.835673\pi\)
\(264\) 3.46216e6 + 236366.i 3.05730 + 0.208726i
\(265\) 1.43705e6 1.25706
\(266\) −937371. −0.812283
\(267\) −1.17199e6 80013.6i −1.00611 0.0686887i
\(268\) 3.19410e6i 2.71651i
\(269\) 412175. 0.347297 0.173649 0.984808i \(-0.444444\pi\)
0.173649 + 0.984808i \(0.444444\pi\)
\(270\) 749855. 3.61557e6i 0.625991 3.01834i
\(271\) 2.07215e6 1.71395 0.856975 0.515358i \(-0.172341\pi\)
0.856975 + 0.515358i \(0.172341\pi\)
\(272\) 2.57854e6i 2.11325i
\(273\) 107726. 1.57791e6i 0.0874808 1.28137i
\(274\) 3.44242e6i 2.77005i
\(275\) −4.12618e6 −3.29016
\(276\) 1.76158e6 + 120265.i 1.39197 + 0.0950314i
\(277\) 1.66702e6 1.30539 0.652696 0.757620i \(-0.273638\pi\)
0.652696 + 0.757620i \(0.273638\pi\)
\(278\) 219435. 0.170292
\(279\) −295597. + 2.15478e6i −0.227347 + 1.65727i
\(280\) 5.32278e6i 4.05736i
\(281\) 1.61261e6i 1.21833i 0.793044 + 0.609164i \(0.208495\pi\)
−0.793044 + 0.609164i \(0.791505\pi\)
\(282\) 612441. + 41812.2i 0.458608 + 0.0313098i
\(283\) 806837.i 0.598853i 0.954119 + 0.299426i \(0.0967953\pi\)
−0.954119 + 0.299426i \(0.903205\pi\)
\(284\) 495930.i 0.364858i
\(285\) 62883.1 921075.i 0.0458587 0.671712i
\(286\) 4.13633e6i 2.99020i
\(287\) 442519.i 0.317122i
\(288\) −491482. 67422.6i −0.349162 0.0478987i
\(289\) −2.35593e6 −1.65927
\(290\) 6.31935e6 4.41243
\(291\) −106490. + 1.55981e6i −0.0737185 + 1.07979i
\(292\) 1.07377e6i 0.736978i
\(293\) 1.83767e6i 1.25054i −0.780407 0.625271i \(-0.784988\pi\)
0.780407 0.625271i \(-0.215012\pi\)
\(294\) 1.15336e6 + 78741.8i 0.778212 + 0.0531296i
\(295\) −133038. 2.61538e6i −0.0890062 1.74977i
\(296\) 1.17363e6i 0.778579i
\(297\) −2.36633e6 490767.i −1.55663 0.322838i
\(298\) 4.22518e6 2.75616
\(299\) 1.10030e6i 0.711758i
\(300\) 6.74507e6 + 460495.i 4.32697 + 0.295408i
\(301\) 1.36012e6i 0.865290i
\(302\) 954400.i 0.602161i
\(303\) 2.19334e6 + 149742.i 1.37246 + 0.0936996i
\(304\) −802428. −0.497992
\(305\) 2.77034e6 1.70523
\(306\) 638713. 4.65595e6i 0.389944 2.84253i
\(307\) −571711. −0.346203 −0.173102 0.984904i \(-0.555379\pi\)
−0.173102 + 0.984904i \(0.555379\pi\)
\(308\) −6.66340e6 −4.00238
\(309\) −56961.1 + 834333.i −0.0339377 + 0.497100i
\(310\) −8.72485e6 −5.15649
\(311\) 361031.i 0.211662i −0.994384 0.105831i \(-0.966250\pi\)
0.994384 0.105831i \(-0.0337503\pi\)
\(312\) 241342. 3.53504e6i 0.140361 2.05593i
\(313\) 2.52393e6i 1.45618i −0.685479 0.728092i \(-0.740407\pi\)
0.685479 0.728092i \(-0.259593\pi\)
\(314\) 3.83853e6i 2.19706i
\(315\) −503792. + 3.67243e6i −0.286071 + 2.08534i
\(316\) 1.37328e6 0.773646
\(317\) 2.52519e6i 1.41138i −0.708518 0.705692i \(-0.750636\pi\)
0.708518 0.705692i \(-0.249364\pi\)
\(318\) −155054. + 2.27115e6i −0.0859837 + 1.25944i
\(319\) 4.13590e6i 2.27559i
\(320\) 2.16894e6i 1.18405i
\(321\) 114300. 1.67419e6i 0.0619130 0.906867i
\(322\) −2.61835e6 −1.40731
\(323\) 1.17500e6i 0.626661i
\(324\) 3.81347e6 + 1.06635e6i 2.01817 + 0.564334i
\(325\) 4.21304e6i 2.21252i
\(326\) −4.84904e6 −2.52704
\(327\) 20043.1 293580.i 0.0103656 0.151830i
\(328\) 991392.i 0.508816i
\(329\) −616245. −0.313880
\(330\) 660321. 9.67201e6i 0.333788 4.88913i
\(331\) −40207.5 −0.0201715 −0.0100857 0.999949i \(-0.503210\pi\)
−0.0100857 + 0.999949i \(0.503210\pi\)
\(332\) 3.94664e6 1.96509
\(333\) −111082. + 809742.i −0.0548951 + 0.400162i
\(334\) 2552.60i 0.00125204i
\(335\) 4.66507e6 2.27115
\(336\) 3.21435e6 + 219448.i 1.55326 + 0.106043i
\(337\) 3.28467e6i 1.57550i 0.615997 + 0.787748i \(0.288753\pi\)
−0.615997 + 0.787748i \(0.711247\pi\)
\(338\) 527992. 0.251383
\(339\) 244141. + 16667.8i 0.115383 + 0.00787733i
\(340\) 1.27622e7 5.98726
\(341\) 5.71026e6i 2.65932i
\(342\) 1.44890e6 + 198764.i 0.669845 + 0.0918908i
\(343\) 1.45717e6 0.668767
\(344\) 3.04713e6i 1.38834i
\(345\) 175651. 2.57284e6i 0.0794516 1.16376i
\(346\) −4.40577e6 −1.97848
\(347\) 282772. 0.126070 0.0630351 0.998011i \(-0.479922\pi\)
0.0630351 + 0.998011i \(0.479922\pi\)
\(348\) −461580. + 6.76096e6i −0.204314 + 2.99268i
\(349\) 854662.i 0.375605i −0.982207 0.187802i \(-0.939864\pi\)
0.982207 0.187802i \(-0.0601364\pi\)
\(350\) −1.00257e7 −4.37465
\(351\) −501098. + 2.41614e6i −0.217098 + 1.04678i
\(352\) −1.30245e6 −0.560279
\(353\) −1.83697e6 −0.784631 −0.392316 0.919831i \(-0.628326\pi\)
−0.392316 + 0.919831i \(0.628326\pi\)
\(354\) 4.14777e6 + 71937.5i 1.75916 + 0.0305103i
\(355\) −724321. −0.305042
\(356\) 5.05344e6 2.11331
\(357\) −321340. + 4.70681e6i −0.133443 + 1.95459i
\(358\) 84449.5 0.0348249
\(359\) 2.53506e6i 1.03813i 0.854734 + 0.519066i \(0.173720\pi\)
−0.854734 + 0.519066i \(0.826280\pi\)
\(360\) −1.12866e6 + 8.22749e6i −0.458996 + 3.34589i
\(361\) −2.11044e6 −0.852326
\(362\) 1.77386e6 0.711458
\(363\) −3.82545e6 261169.i −1.52376 0.104029i
\(364\) 6.80367e6i 2.69147i
\(365\) 1.56828e6 0.616155
\(366\) −298913. + 4.37831e6i −0.116639 + 1.70846i
\(367\) 3.58351e6i 1.38881i −0.719583 0.694406i \(-0.755667\pi\)
0.719583 0.694406i \(-0.244333\pi\)
\(368\) −2.24142e6 −0.862786
\(369\) −93833.4 + 684006.i −0.0358750 + 0.261513i
\(370\) −3.27870e6 −1.24508
\(371\) 2.28526e6i 0.861986i
\(372\) 637284. 9.33457e6i 0.238768 3.49733i
\(373\) 3.01455e6 1.12189 0.560945 0.827853i \(-0.310438\pi\)
0.560945 + 0.827853i \(0.310438\pi\)
\(374\) 1.23385e7i 4.56123i
\(375\) 347594. 5.09135e6i 0.127642 1.86963i
\(376\) −1.38060e6 −0.503614
\(377\) −4.22297e6 −1.53026
\(378\) −5.74964e6 1.19245e6i −2.06972 0.429251i
\(379\) −3.59767e6 −1.28654 −0.643270 0.765639i \(-0.722423\pi\)
−0.643270 + 0.765639i \(0.722423\pi\)
\(380\) 3.97153e6i 1.41091i
\(381\) 698438. + 47683.3i 0.246499 + 0.0168288i
\(382\) 1.61000e6 0.564504
\(383\) 1.70800e6i 0.594965i −0.954727 0.297482i \(-0.903853\pi\)
0.954727 0.297482i \(-0.0961470\pi\)
\(384\) −4.44384e6 303387.i −1.53791 0.104995i
\(385\) 9.73209e6i 3.34622i
\(386\) 292827. 0.100033
\(387\) −288406. + 2.10236e6i −0.0978873 + 0.713557i
\(388\) 6.72563e6i 2.26805i
\(389\) 178222.i 0.0597156i 0.999554 + 0.0298578i \(0.00950545\pi\)
−0.999554 + 0.0298578i \(0.990495\pi\)
\(390\) −9.87562e6 674222.i −3.28778 0.224461i
\(391\) 3.28213e6i 1.08571i
\(392\) −2.59998e6 −0.854584
\(393\) −2.35452e6 160747.i −0.768992 0.0525001i
\(394\) 1.02286e6i 0.331953i
\(395\) 2.00572e6i 0.646812i
\(396\) 1.02997e7 + 1.41293e6i 3.30055 + 0.452776i
\(397\) 1.69943e6i 0.541160i 0.962697 + 0.270580i \(0.0872155\pi\)
−0.962697 + 0.270580i \(0.912784\pi\)
\(398\) 143940. 0.0455485
\(399\) −1.46473e6 99999.3i −0.460602 0.0314459i
\(400\) −8.58239e6 −2.68200
\(401\) −182580. −0.0567011 −0.0283505 0.999598i \(-0.509025\pi\)
−0.0283505 + 0.999598i \(0.509025\pi\)
\(402\) −503351. + 7.37280e6i −0.155348 + 2.27545i
\(403\) 5.83047e6 1.78830
\(404\) −9.45732e6 −2.88280
\(405\) 1.55743e6 5.56969e6i 0.471815 1.68730i
\(406\) 1.00493e7i 3.02566i
\(407\) 2.14585e6i 0.642116i
\(408\) −719911. + 1.05448e7i −0.214106 + 3.13610i
\(409\) 4.30716e6i 1.27316i 0.771211 + 0.636580i \(0.219651\pi\)
−0.771211 + 0.636580i \(0.780349\pi\)
\(410\) −2.76959e6 −0.813683
\(411\) −367239. + 5.37911e6i −0.107237 + 1.57075i
\(412\) 3.59751e6i 1.04414i
\(413\) −4.15909e6 + 211562.i −1.19984 + 0.0610328i
\(414\) 4.04722e6 + 555206.i 1.16053 + 0.159204i
\(415\) 5.76419e6i 1.64292i
\(416\) 1.32987e6i 0.376769i
\(417\) 342888. + 23409.5i 0.0965634 + 0.00659252i
\(418\) 3.83966e6 1.07486
\(419\) 3.01036e6 0.837689 0.418844 0.908058i \(-0.362435\pi\)
0.418844 + 0.908058i \(0.362435\pi\)
\(420\) 1.08613e6 1.59091e7i 0.300442 4.40070i
\(421\) 5.34313e6i 1.46923i 0.678483 + 0.734616i \(0.262638\pi\)
−0.678483 + 0.734616i \(0.737362\pi\)
\(422\) 5.66771e6i 1.54927i
\(423\) 952537. + 130671.i 0.258840 + 0.0355082i
\(424\) 5.11975e6i 1.38304i
\(425\) 1.25673e7i 3.37496i
\(426\) 78152.5 1.14473e6i 0.0208650 0.305619i
\(427\) 4.40551e6i 1.16930i
\(428\) 7.21885e6i 1.90484i
\(429\) −441266. + 6.46342e6i −0.115760 + 1.69558i
\(430\) −8.51258e6 −2.22019
\(431\) 6.35167e6 1.64700 0.823502 0.567313i \(-0.192017\pi\)
0.823502 + 0.567313i \(0.192017\pi\)
\(432\) −4.92193e6 1.02079e6i −1.26889 0.263164i
\(433\) 4.41731e6 1.13224 0.566120 0.824323i \(-0.308444\pi\)
0.566120 + 0.824323i \(0.308444\pi\)
\(434\) 1.38746e7i 3.53587i
\(435\) 9.87459e6 + 674152.i 2.50205 + 0.170818i
\(436\) 1.26587e6i 0.318914i
\(437\) 1.02138e6 0.255849
\(438\) −169213. + 2.47854e6i −0.0421453 + 0.617321i
\(439\) 1.48299e6 0.367263 0.183632 0.982995i \(-0.441215\pi\)
0.183632 + 0.982995i \(0.441215\pi\)
\(440\) 2.18032e7i 5.36894i
\(441\) 1.79384e6 + 246083.i 0.439226 + 0.0602539i
\(442\) −1.25982e7 −3.06727
\(443\) 393210. 0.0951952 0.0475976 0.998867i \(-0.484843\pi\)
0.0475976 + 0.998867i \(0.484843\pi\)
\(444\) 239484. 3.50782e6i 0.0576526 0.844462i
\(445\) 7.38071e6i 1.76684i
\(446\) 6.01657e6 1.43223
\(447\) 6.60225e6 + 450744.i 1.56287 + 0.106699i
\(448\) 3.44913e6 0.811923
\(449\) 465305.i 0.108924i −0.998516 0.0544618i \(-0.982656\pi\)
0.998516 0.0544618i \(-0.0173443\pi\)
\(450\) 1.54968e7 + 2.12588e6i 3.60753 + 0.494889i
\(451\) 1.81265e6i 0.419635i
\(452\) −1.05269e6 −0.242357
\(453\) 101816. 1.49134e6i 0.0233115 0.341454i
\(454\) −8.60581e6 −1.95953
\(455\) 9.93697e6 2.25022
\(456\) −3.28150e6 224032.i −0.739027 0.0504544i
\(457\) 7.22237e6i 1.61767i 0.588037 + 0.808834i \(0.299901\pi\)
−0.588037 + 0.808834i \(0.700099\pi\)
\(458\) 5.02831e6i 1.12010i
\(459\) 1.49475e6 7.20723e6i 0.331159 1.59675i
\(460\) 1.10936e7i 2.44444i
\(461\) 2.52097e6i 0.552479i −0.961089 0.276240i \(-0.910912\pi\)
0.961089 0.276240i \(-0.0890883\pi\)
\(462\) −1.53808e7 1.05007e6i −3.35255 0.228883i
\(463\) 1.40533e6i 0.304666i 0.988329 + 0.152333i \(0.0486787\pi\)
−0.988329 + 0.152333i \(0.951321\pi\)
\(464\) 8.60261e6i 1.85496i
\(465\) −1.36334e7 930772.i −2.92397 0.199623i
\(466\) 1.80790e6 0.385665
\(467\) −5.91272e6 −1.25457 −0.627286 0.778789i \(-0.715834\pi\)
−0.627286 + 0.778789i \(0.715834\pi\)
\(468\) 1.44268e6 1.05165e7i 0.304477 2.21951i
\(469\) 7.41860e6i 1.55736i
\(470\) 3.85689e6i 0.805364i
\(471\) −409497. + 5.99808e6i −0.0850547 + 1.24583i
\(472\) −9.31777e6 + 473972.i −1.92512 + 0.0979258i
\(473\) 5.57133e6i 1.14500i
\(474\) 3.16989e6 + 216413.i 0.648035 + 0.0442422i
\(475\) 3.91087e6 0.795315
\(476\) 2.02950e7i 4.10555i
\(477\) −484575. + 3.53235e6i −0.0975135 + 0.710833i
\(478\) 7.69930e6i 1.54128i
\(479\) 5.22977e6i 1.04146i 0.853721 + 0.520731i \(0.174341\pi\)
−0.853721 + 0.520731i \(0.825659\pi\)
\(480\) 212299. 3.10964e6i 0.0420577 0.616037i
\(481\) 2.19102e6 0.431802
\(482\) 2.63705e6 0.517012
\(483\) −4.09143e6 279327.i −0.798008 0.0544811i
\(484\) 1.64947e7 3.20060
\(485\) −9.82298e6 −1.89622
\(486\) 8.63443e6 + 3.06236e6i 1.65822 + 0.588120i
\(487\) −5.95709e6 −1.13818 −0.569091 0.822274i \(-0.692705\pi\)
−0.569091 + 0.822274i \(0.692705\pi\)
\(488\) 9.86984e6i 1.87612i
\(489\) −7.57710e6 517299.i −1.43295 0.0978294i
\(490\) 7.26339e6i 1.36662i
\(491\) 2.21607e6i 0.414839i −0.978252 0.207419i \(-0.933494\pi\)
0.978252 0.207419i \(-0.0665065\pi\)
\(492\) 202297. 2.96313e6i 0.0376771 0.551872i
\(493\) 1.25969e7 2.33424
\(494\) 3.92049e6i 0.722808i
\(495\) 2.06363e6 1.50430e7i 0.378547 2.75944i
\(496\) 1.18772e7i 2.16776i
\(497\) 1.15184e6i 0.209172i
\(498\) 9.10986e6 + 621942.i 1.64603 + 0.112377i
\(499\) −1.44204e6 −0.259254 −0.129627 0.991563i \(-0.541378\pi\)
−0.129627 + 0.991563i \(0.541378\pi\)
\(500\) 2.19531e7i 3.92709i
\(501\) −272.313 + 3988.69i −4.84701e−5 + 0.000709963i
\(502\) 3.29872e6i 0.584233i
\(503\) −2.73709e6 −0.482358 −0.241179 0.970481i \(-0.577534\pi\)
−0.241179 + 0.970481i \(0.577534\pi\)
\(504\) 1.30837e7 + 1.79485e6i 2.29432 + 0.314740i
\(505\) 1.38127e7i 2.41018i
\(506\) 1.07253e7 1.86223
\(507\) 825038. + 56326.5i 0.142546 + 0.00973179i
\(508\) −3.01155e6 −0.517763
\(509\) 2.70098e6 0.462091 0.231046 0.972943i \(-0.425785\pi\)
0.231046 + 0.972943i \(0.425785\pi\)
\(510\) 2.94584e7 + 2.01117e6i 5.01515 + 0.342391i
\(511\) 2.49394e6i 0.422506i
\(512\) 1.21080e7 2.04126
\(513\) 2.24285e6 + 465158.i 0.376276 + 0.0780381i
\(514\) 1.60631e7i 2.68178i
\(515\) −5.25427e6 −0.872960
\(516\) 621779. 9.10746e6i 0.102804 1.50582i
\(517\) 2.52426e6 0.415345
\(518\) 5.21392e6i 0.853768i
\(519\) −6.88444e6 470010.i −1.12189 0.0765929i
\(520\) 2.22622e7 3.61043
\(521\) 4.10602e6i 0.662715i 0.943505 + 0.331357i \(0.107507\pi\)
−0.943505 + 0.331357i \(0.892493\pi\)
\(522\) −2.13089e6 + 1.55333e7i −0.342283 + 2.49510i
\(523\) 8.87108e6 1.41815 0.709075 0.705133i \(-0.249113\pi\)
0.709075 + 0.705133i \(0.249113\pi\)
\(524\) 1.01523e7 1.61524
\(525\) −1.56661e7 1.06954e6i −2.48063 0.169356i
\(526\) 1.10220e7i 1.73698i
\(527\) −1.73920e7 −2.72786
\(528\) −1.31666e7 898904.i −2.05537 0.140323i
\(529\) −3.58332e6 −0.556733
\(530\) −1.43027e7 −2.21171
\(531\) 6.47361e6 + 554896.i 0.996346 + 0.0854034i
\(532\) 6.31569e6 0.967479
\(533\) 1.85080e6 0.282191
\(534\) 1.16646e7 + 796361.i 1.77018 + 0.120853i
\(535\) 1.05434e7 1.59256
\(536\) 1.66202e7i 2.49875i
\(537\) 131960. + 9009.12i 0.0197473 + 0.00134818i
\(538\) −4.10231e6 −0.611045
\(539\) 4.75376e6 0.704799
\(540\) −5.05227e6 + 2.43605e7i −0.745594 + 3.59503i
\(541\) 9.21589e6i 1.35377i −0.736090 0.676883i \(-0.763330\pi\)
0.736090 0.676883i \(-0.236670\pi\)
\(542\) −2.06238e7 −3.01557
\(543\) 2.77184e6 + 189237.i 0.403430 + 0.0275427i
\(544\) 3.96692e6i 0.574720i
\(545\) 1.84884e6 0.266630
\(546\) −1.07218e6 + 1.57046e7i −0.153916 + 2.25448i
\(547\) 4.40437e6 0.629384 0.314692 0.949194i \(-0.398099\pi\)
0.314692 + 0.949194i \(0.398099\pi\)
\(548\) 2.31938e7i 3.29930i
\(549\) −934162. + 6.80965e6i −0.132279 + 0.964259i
\(550\) 4.10672e7 5.78879
\(551\) 3.92008e6i 0.550068i
\(552\) −9.16619e6 625788.i −1.28039 0.0874138i
\(553\) −3.18958e6 −0.443528
\(554\) −1.65915e7 −2.29674
\(555\) −5.12328e6 349774.i −0.706018 0.0482008i
\(556\) −1.47848e6 −0.202828
\(557\) 4.28592e6i 0.585337i 0.956214 + 0.292669i \(0.0945433\pi\)
−0.956214 + 0.292669i \(0.905457\pi\)
\(558\) 2.94203e6 2.14462e7i 0.400001 2.91584i
\(559\) 5.68862e6 0.769976
\(560\) 2.02426e7i 2.72770i
\(561\) 1.31627e6 1.92800e7i 0.176579 2.58643i
\(562\) 1.60501e7i 2.14356i
\(563\) 5.76513e6 0.766546 0.383273 0.923635i \(-0.374797\pi\)
0.383273 + 0.923635i \(0.374797\pi\)
\(564\) −4.12642e6 281716.i −0.546230 0.0372919i
\(565\) 1.53749e6i 0.202624i
\(566\) 8.03031e6i 1.05364i
\(567\) −8.85715e6 2.47669e6i −1.15701 0.323530i
\(568\) 2.58052e6i 0.335612i
\(569\) 1.15448e7 1.49487 0.747437 0.664333i \(-0.231284\pi\)
0.747437 + 0.664333i \(0.231284\pi\)
\(570\) −625864. + 9.16730e6i −0.0806851 + 1.18183i
\(571\) 2.93196e6i 0.376330i 0.982137 + 0.188165i \(0.0602539\pi\)
−0.982137 + 0.188165i \(0.939746\pi\)
\(572\) 2.78692e7i 3.56151i
\(573\) 2.51578e6 + 171756.i 0.320100 + 0.0218537i
\(574\) 4.40431e6i 0.557954i
\(575\) 1.09242e7 1.37791
\(576\) −5.33136e6 731367.i −0.669548 0.0918500i
\(577\) −1.26665e7 −1.58386 −0.791930 0.610612i \(-0.790924\pi\)
−0.791930 + 0.610612i \(0.790924\pi\)
\(578\) 2.34481e7 2.91937
\(579\) 457571. + 31239.0i 0.0567234 + 0.00387258i
\(580\) −4.25776e7 −5.25547
\(581\) −9.16645e6 −1.12658
\(582\) 1.05988e6 1.55245e7i 0.129702 1.89981i
\(583\) 9.36087e6i 1.14063i
\(584\) 5.58727e6i 0.677903i
\(585\) −1.53597e7 2.10707e6i −1.85564 0.254560i
\(586\) 1.82900e7i 2.20024i
\(587\) 1.61149e7 1.93033 0.965165 0.261644i \(-0.0842646\pi\)
0.965165 + 0.261644i \(0.0842646\pi\)
\(588\) −7.77098e6 530535.i −0.926899 0.0632806i
\(589\) 5.41229e6i 0.642825i
\(590\) 1.32410e6 + 2.60304e7i 0.156600 + 3.07859i
\(591\) 109120. 1.59832e6i 0.0128509 0.188233i
\(592\) 4.46333e6i 0.523426i
\(593\) 9.11826e6i 1.06482i 0.846487 + 0.532409i \(0.178713\pi\)
−0.846487 + 0.532409i \(0.821287\pi\)
\(594\) 2.35517e7 + 4.88452e6i 2.73877 + 0.568010i
\(595\) −2.96414e7 −3.43247
\(596\) −2.84678e7 −3.28275
\(597\) 224920. + 15355.6i 0.0258281 + 0.00176332i
\(598\) 1.09511e7i 1.25229i
\(599\) 7.55326e6i 0.860136i 0.902796 + 0.430068i \(0.141510\pi\)
−0.902796 + 0.430068i \(0.858490\pi\)
\(600\) −3.50973e7 2.39614e6i −3.98012 0.271728i
\(601\) 8.62609e6i 0.974155i −0.873359 0.487077i \(-0.838063\pi\)
0.873359 0.487077i \(-0.161937\pi\)
\(602\) 1.35371e7i 1.52241i
\(603\) −1.57307e6 + 1.14670e7i −0.176179 + 1.28427i
\(604\) 6.43042e6i 0.717211i
\(605\) 2.40911e7i 2.67589i
\(606\) −2.18299e7 1.49036e6i −2.41474 0.164858i
\(607\) 7.24442e6 0.798053 0.399027 0.916939i \(-0.369348\pi\)
0.399027 + 0.916939i \(0.369348\pi\)
\(608\) 1.23448e6 0.135434
\(609\) 1.07206e6 1.57030e7i 0.117133 1.71569i
\(610\) −2.75727e7 −3.00023
\(611\) 2.57740e6i 0.279305i
\(612\) −4.30343e6 + 3.13702e7i −0.464447 + 3.38562i
\(613\) 1.75286e7i 1.88406i 0.335522 + 0.942032i \(0.391087\pi\)
−0.335522 + 0.942032i \(0.608913\pi\)
\(614\) 5.69015e6 0.609119
\(615\) −4.32775e6 295461.i −0.461396 0.0315002i
\(616\) 3.46723e7 3.68156
\(617\) 3.56163e6i 0.376648i 0.982107 + 0.188324i \(0.0603056\pi\)
−0.982107 + 0.188324i \(0.939694\pi\)
\(618\) 566924. 8.30398e6i 0.0597109 0.874611i
\(619\) −3.47580e6 −0.364609 −0.182305 0.983242i \(-0.558356\pi\)
−0.182305 + 0.983242i \(0.558356\pi\)
\(620\) 5.87851e7 6.14169
\(621\) 6.26494e6 + 1.29932e6i 0.651910 + 0.135204i
\(622\) 3.59328e6i 0.372405i
\(623\) −1.17371e7 −1.21155
\(624\) −917827. + 1.34438e7i −0.0943625 + 1.38217i
\(625\) 1.18522e7 1.21366
\(626\) 2.51202e7i 2.56205i
\(627\) 5.99984e6 + 409617.i 0.609496 + 0.0416111i
\(628\) 2.58627e7i 2.61683i
\(629\) −6.53570e6 −0.658667
\(630\) 5.01415e6 3.65511e7i 0.503322 3.66901i
\(631\) −5.29472e6 −0.529382 −0.264691 0.964333i \(-0.585270\pi\)
−0.264691 + 0.964333i \(0.585270\pi\)
\(632\) −7.14575e6 −0.711631
\(633\) 604635. 8.85634e6i 0.0599769 0.878507i
\(634\) 2.51328e7i 2.48323i
\(635\) 4.39846e6i 0.432879i
\(636\) 1.04470e6 1.53022e7i 0.102412 1.50007i
\(637\) 4.85383e6i 0.473954i
\(638\) 4.11639e7i 4.00373i
\(639\) 244242. 1.78042e6i 0.0236629 0.172492i
\(640\) 2.79854e7i 2.70073i
\(641\) 1.09862e7i 1.05610i 0.849215 + 0.528048i \(0.177076\pi\)
−0.849215 + 0.528048i \(0.822924\pi\)
\(642\) −1.13760e6 + 1.66630e7i −0.108932 + 1.59557i
\(643\) −1.70326e7 −1.62463 −0.812314 0.583220i \(-0.801793\pi\)
−0.812314 + 0.583220i \(0.801793\pi\)
\(644\) 1.76416e7 1.67619
\(645\) −1.33017e7 908127.i −1.25895 0.0859503i
\(646\) 1.16946e7i 1.10257i
\(647\) 1.53045e7i 1.43733i −0.695355 0.718666i \(-0.744753\pi\)
0.695355 0.718666i \(-0.255247\pi\)
\(648\) −1.98430e7 5.54864e6i −1.85640 0.519097i
\(649\) 1.70365e7 866602.i 1.58770 0.0807622i
\(650\) 4.19317e7i 3.89277i
\(651\) −1.48015e6 + 2.16804e7i −0.136884 + 2.00501i
\(652\) 3.26712e7 3.00986
\(653\) 7.50437e6i 0.688702i −0.938841 0.344351i \(-0.888099\pi\)
0.938841 0.344351i \(-0.111901\pi\)
\(654\) −199486. + 2.92195e6i −0.0182376 + 0.267134i
\(655\) 1.48278e7i 1.35043i
\(656\) 3.77027e6i 0.342069i
\(657\) −528824. + 3.85491e6i −0.0477967 + 0.348418i
\(658\) 6.13338e6 0.552249
\(659\) 190355. 0.0170746 0.00853730 0.999964i \(-0.497282\pi\)
0.00853730 + 0.999964i \(0.497282\pi\)
\(660\) −4.44902e6 + 6.51667e7i −0.397562 + 5.82326i
\(661\) −2.13768e6 −0.190300 −0.0951500 0.995463i \(-0.530333\pi\)
−0.0951500 + 0.995463i \(0.530333\pi\)
\(662\) 400179. 0.0354902
\(663\) −1.96859e7 1.34398e6i −1.73929 0.118744i
\(664\) −2.05360e7 −1.80757
\(665\) 9.22425e6i 0.808867i
\(666\) 1.10558e6 8.05922e6i 0.0965839 0.704056i
\(667\) 1.09499e7i 0.953010i
\(668\) 17198.6i 0.00149125i
\(669\) 9.40147e6 + 641851.i 0.812139 + 0.0554458i
\(670\) −4.64307e7 −3.99593
\(671\) 1.80459e7i 1.54729i
\(672\) −4.94507e6 337607.i −0.422425 0.0288395i
\(673\) 8.41942e6i 0.716546i −0.933617 0.358273i \(-0.883366\pi\)
0.933617 0.358273i \(-0.116634\pi\)
\(674\) 3.26918e7i 2.77197i
\(675\) 2.39884e7 + 4.97510e6i 2.02648 + 0.420284i
\(676\) −3.55743e6 −0.299412
\(677\) 8.35803e6i 0.700862i −0.936589 0.350431i \(-0.886035\pi\)
0.936589 0.350431i \(-0.113965\pi\)
\(678\) −2.42989e6 165892.i −0.203008 0.0138596i
\(679\) 1.56209e7i 1.30027i
\(680\) −6.64069e7 −5.50733
\(681\) −1.34474e7 918073.i −1.11115 0.0758594i
\(682\) 5.68332e7i 4.67888i
\(683\) −1.62697e7 −1.33453 −0.667263 0.744823i \(-0.732534\pi\)
−0.667263 + 0.744823i \(0.732534\pi\)
\(684\) −9.76223e6 1.33920e6i −0.797827 0.109448i
\(685\) −3.38753e7 −2.75840
\(686\) −1.45030e7 −1.17665
\(687\) 536423. 7.85722e6i 0.0433626 0.635151i
\(688\) 1.15883e7i 0.933357i
\(689\) 9.55793e6 0.767036
\(690\) −1.74822e6 + 2.56070e7i −0.139789 + 2.04756i
\(691\) 5.24552e6i 0.417920i 0.977924 + 0.208960i \(0.0670079\pi\)
−0.977924 + 0.208960i \(0.932992\pi\)
\(692\) 2.96846e7 2.35649
\(693\) −2.39220e7 3.28167e6i −1.89219 0.259575i
\(694\) −2.81438e6 −0.221812
\(695\) 2.15936e6i 0.169576i
\(696\) 2.40179e6 3.51800e7i 0.187937 2.75279i
\(697\) −5.52085e6 −0.430451
\(698\) 8.50630e6i 0.660849i
\(699\) 2.82502e6 + 192868.i 0.218690 + 0.0149303i
\(700\) 6.75496e7 5.21048
\(701\) 1.25718e7 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(702\) 4.98734e6 2.40475e7i 0.381968 1.84173i
\(703\) 2.03387e6i 0.155216i
\(704\) −1.41283e7 −1.07438
\(705\) −411455. + 6.02676e6i −0.0311781 + 0.456679i
\(706\) 1.82831e7 1.38050
\(707\) 2.19655e7 1.65270
\(708\) −2.79462e7 484690.i −2.09527 0.0363397i
\(709\) 2.31592e6 0.173024 0.0865122 0.996251i \(-0.472428\pi\)
0.0865122 + 0.996251i \(0.472428\pi\)
\(710\) 7.20904e6 0.536700
\(711\) 4.93017e6 + 676331.i 0.365753 + 0.0501748i
\(712\) −2.62951e7 −1.94390
\(713\) 1.51181e7i 1.11371i
\(714\) 3.19824e6 4.68460e7i 0.234783 3.43896i
\(715\) −4.07038e7 −2.97763
\(716\) −568992. −0.0414785
\(717\) −821366. + 1.20309e7i −0.0596676 + 0.873977i
\(718\) 2.52310e7i 1.82652i
\(719\) 5.70070e6 0.411250 0.205625 0.978631i \(-0.434077\pi\)
0.205625 + 0.978631i \(0.434077\pi\)
\(720\) 4.29232e6 3.12892e7i 0.308575 2.24938i
\(721\) 8.35556e6i 0.598601i
\(722\) 2.10049e7 1.49961
\(723\) 4.12065e6 + 281322.i 0.293170 + 0.0200151i
\(724\) −1.19517e7 −0.847390
\(725\) 4.19273e7i 2.96246i
\(726\) 3.80741e7 + 2.59937e6i 2.68095 + 0.183032i
\(727\) −7.61455e6 −0.534329 −0.267164 0.963651i \(-0.586087\pi\)
−0.267164 + 0.963651i \(0.586087\pi\)
\(728\) 3.54022e7i 2.47572i
\(729\) 1.31654e7 + 5.70636e6i 0.917522 + 0.397686i
\(730\) −1.56088e7 −1.08408
\(731\) −1.69688e7 −1.17452
\(732\) 2.01398e6 2.94996e7i 0.138924 2.03488i
\(733\) −1.25719e7 −0.864256 −0.432128 0.901812i \(-0.642237\pi\)
−0.432128 + 0.901812i \(0.642237\pi\)
\(734\) 3.56661e7i 2.44352i
\(735\) −774863. + 1.13498e7i −0.0529062 + 0.774940i
\(736\) 3.44828e6 0.234643
\(737\) 3.03881e7i 2.06079i
\(738\) 933908. 6.80780e6i 0.0631194 0.460114i
\(739\) 1.65513e7i 1.11486i 0.830224 + 0.557431i \(0.188213\pi\)
−0.830224 + 0.557431i \(0.811787\pi\)
\(740\) 2.20908e7 1.48297
\(741\) 418240. 6.12614e6i 0.0279821 0.409866i
\(742\) 2.27448e7i 1.51660i
\(743\) 542980.i 0.0360838i 0.999837 + 0.0180419i \(0.00574323\pi\)
−0.999837 + 0.0180419i \(0.994257\pi\)
\(744\) −3.31605e6 + 4.85715e7i −0.219628 + 3.21699i
\(745\) 4.15781e7i 2.74457i
\(746\) −3.00033e7 −1.97388
\(747\) 1.41687e7 + 1.94369e6i 0.929026 + 0.127446i
\(748\) 8.31323e7i 5.43270i
\(749\) 1.67665e7i 1.09204i
\(750\) −3.45954e6 + 5.06734e7i −0.224577 + 3.28947i
\(751\) 1.90255e7i 1.23094i −0.788161 0.615470i \(-0.788966\pi\)
0.788161 0.615470i \(-0.211034\pi\)
\(752\) 5.25043e6 0.338571
\(753\) −351909. + 5.15457e6i −0.0226174 + 0.331287i
\(754\) 4.20305e7 2.69238
\(755\) 9.39183e6 0.599629
\(756\) 3.87391e7 + 8.03433e6i 2.46516 + 0.511264i
\(757\) −2.10511e7 −1.33516 −0.667582 0.744536i \(-0.732671\pi\)
−0.667582 + 0.744536i \(0.732671\pi\)
\(758\) 3.58070e7 2.26358
\(759\) 1.67593e7 + 1.14418e6i 1.05597 + 0.0720926i
\(760\) 2.06655e7i 1.29781i
\(761\) 2.35573e7i 1.47457i −0.675583 0.737284i \(-0.736108\pi\)
0.675583 0.737284i \(-0.263892\pi\)
\(762\) −6.95143e6 474584.i −0.433697 0.0296091i
\(763\) 2.94011e6i 0.182832i
\(764\) −1.08476e7 −0.672359
\(765\) 4.58171e7 + 6.28529e6i 2.83057 + 0.388304i
\(766\) 1.69994e7i 1.04680i
\(767\) −884845. 1.73951e7i −0.0543099 1.06767i
\(768\) 3.32077e7 + 2.26713e6i 2.03159 + 0.138699i
\(769\) 2.62066e7i 1.59807i −0.601285 0.799034i \(-0.705345\pi\)
0.601285 0.799034i \(-0.294655\pi\)
\(770\) 9.68619e7i 5.88743i
\(771\) 1.71362e6 2.51002e7i 0.103820 1.52069i
\(772\) −1.97297e6 −0.119145
\(773\) 1.37293e7 0.826420 0.413210 0.910636i \(-0.364408\pi\)
0.413210 + 0.910636i \(0.364408\pi\)
\(774\) 2.87045e6 2.09244e7i 0.172226 1.25545i
\(775\) 5.78872e7i 3.46201i
\(776\) 3.49962e7i 2.08625i
\(777\) −556224. + 8.14726e6i −0.0330520 + 0.484127i
\(778\) 1.77382e6i 0.105065i
\(779\) 1.71806e6i 0.101436i