Properties

Label 147.6.c.c.146.14
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.14
Root \(5.89199 - 3.40174i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.c.146.4

$q$-expansion

\(f(q)\) \(=\) \(q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +O(q^{10})\) \(q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +101.468i q^{10} +96.0737i q^{11} +(-177.622 - 134.366i) q^{12} -416.854i q^{13} +(185.413 + 140.259i) q^{15} -1277.07 q^{16} +208.498 q^{17} +(-1590.89 + 449.790i) q^{18} +2651.38i q^{19} -213.085 q^{20} -653.636 q^{22} +2617.73i q^{23} +(-1133.31 + 1498.15i) q^{24} -2902.57 q^{25} +2836.06 q^{26} +(-1377.18 + 3528.78i) q^{27} -7220.50i q^{29} +(-954.253 + 1261.45i) q^{30} +4297.41i q^{31} -4832.28i q^{32} +(-903.523 + 1194.39i) q^{33} +1418.52i q^{34} +(-944.567 - 3340.89i) q^{36} +3679.00 q^{37} -18038.6 q^{38} +(3920.29 - 5182.35i) q^{39} +1797.26i q^{40} +15452.3 q^{41} -6011.11 q^{43} -1372.65i q^{44} +(985.997 + 3487.42i) q^{45} -17809.7 q^{46} -3907.44 q^{47} +(-15876.6 - 12010.1i) q^{48} -19747.6i q^{50} +(2592.06 + 1960.82i) q^{51} +5955.77i q^{52} -36297.2i q^{53} +(-24008.0 - 9369.63i) q^{54} +1432.85i q^{55} +(-24934.8 + 32962.1i) q^{57} +49124.6 q^{58} -7827.45 q^{59} +(-2649.08 - 2003.95i) q^{60} -20193.7i q^{61} -29237.3 q^{62} -7989.78 q^{64} -6217.00i q^{65} +(-8126.04 - 6147.10i) q^{66} +43937.9 q^{67} -2978.91 q^{68} +(-24618.3 + 32543.7i) q^{69} -26028.0i q^{71} +(-28178.6 + 7966.93i) q^{72} +50911.3i q^{73} +25030.0i q^{74} +(-36084.9 - 27297.1i) q^{75} -37881.4i q^{76} +(35258.0 + 26671.6i) q^{78} -50114.3 q^{79} -19046.3 q^{80} +(-50307.5 + 30918.3i) q^{81} +105129. i q^{82} +107835. q^{83} +3109.57 q^{85} -40896.5i q^{86} +(67905.0 - 89765.6i) q^{87} -11577.6 q^{88} +136779. q^{89} +(-23726.6 + 6708.22i) q^{90} -37400.6i q^{92} +(-40414.8 + 53425.6i) q^{93} -26584.2i q^{94} +39543.0i q^{95} +(45445.1 - 60075.2i) q^{96} +25183.4i q^{97} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.80349i 1.20270i 0.798986 + 0.601349i \(0.205370\pi\)
−0.798986 + 0.601349i \(0.794630\pi\)
\(3\) 12.4320 + 9.40448i 0.797516 + 0.603297i
\(4\) −14.2874 −0.446483
\(5\) 14.9141 0.266792 0.133396 0.991063i \(-0.457412\pi\)
0.133396 + 0.991063i \(0.457412\pi\)
\(6\) −63.9832 + 84.5813i −0.725585 + 0.959171i
\(7\) 0 0
\(8\) 120.507i 0.665714i
\(9\) 66.1117 + 233.834i 0.272065 + 0.962279i
\(10\) 101.468i 0.320870i
\(11\) 96.0737i 0.239399i 0.992810 + 0.119700i \(0.0381931\pi\)
−0.992810 + 0.119700i \(0.961807\pi\)
\(12\) −177.622 134.366i −0.356077 0.269362i
\(13\) 416.854i 0.684109i −0.939680 0.342055i \(-0.888877\pi\)
0.939680 0.342055i \(-0.111123\pi\)
\(14\) 0 0
\(15\) 185.413 + 140.259i 0.212771 + 0.160955i
\(16\) −1277.07 −1.24714
\(17\) 208.498 0.174977 0.0874884 0.996166i \(-0.472116\pi\)
0.0874884 + 0.996166i \(0.472116\pi\)
\(18\) −1590.89 + 449.790i −1.15733 + 0.327211i
\(19\) 2651.38i 1.68495i 0.538733 + 0.842476i \(0.318903\pi\)
−0.538733 + 0.842476i \(0.681097\pi\)
\(20\) −213.085 −0.119118
\(21\) 0 0
\(22\) −653.636 −0.287925
\(23\) 2617.73i 1.03182i 0.856642 + 0.515911i \(0.172546\pi\)
−0.856642 + 0.515911i \(0.827454\pi\)
\(24\) −1133.31 + 1498.15i −0.401624 + 0.530918i
\(25\) −2902.57 −0.928822
\(26\) 2836.06 0.822777
\(27\) −1377.18 + 3528.78i −0.363564 + 0.931569i
\(28\) 0 0
\(29\) 7220.50i 1.59431i −0.603776 0.797154i \(-0.706338\pi\)
0.603776 0.797154i \(-0.293662\pi\)
\(30\) −954.253 + 1261.45i −0.193580 + 0.255899i
\(31\) 4297.41i 0.803160i 0.915824 + 0.401580i \(0.131539\pi\)
−0.915824 + 0.401580i \(0.868461\pi\)
\(32\) 4832.28i 0.834214i
\(33\) −903.523 + 1194.39i −0.144429 + 0.190925i
\(34\) 1418.52i 0.210444i
\(35\) 0 0
\(36\) −944.567 3340.89i −0.121472 0.429641i
\(37\) 3679.00 0.441799 0.220900 0.975297i \(-0.429101\pi\)
0.220900 + 0.975297i \(0.429101\pi\)
\(38\) −18038.6 −2.02649
\(39\) 3920.29 5182.35i 0.412721 0.545588i
\(40\) 1797.26i 0.177607i
\(41\) 15452.3 1.43560 0.717798 0.696251i \(-0.245150\pi\)
0.717798 + 0.696251i \(0.245150\pi\)
\(42\) 0 0
\(43\) −6011.11 −0.495774 −0.247887 0.968789i \(-0.579736\pi\)
−0.247887 + 0.968789i \(0.579736\pi\)
\(44\) 1372.65i 0.106888i
\(45\) 985.997 + 3487.42i 0.0725846 + 0.256728i
\(46\) −17809.7 −1.24097
\(47\) −3907.44 −0.258016 −0.129008 0.991644i \(-0.541179\pi\)
−0.129008 + 0.991644i \(0.541179\pi\)
\(48\) −15876.6 12010.1i −0.994611 0.752394i
\(49\) 0 0
\(50\) 19747.6i 1.11709i
\(51\) 2592.06 + 1960.82i 0.139547 + 0.105563i
\(52\) 5955.77i 0.305443i
\(53\) 36297.2i 1.77494i −0.460868 0.887469i \(-0.652462\pi\)
0.460868 0.887469i \(-0.347538\pi\)
\(54\) −24008.0 9369.63i −1.12040 0.437258i
\(55\) 1432.85i 0.0638697i
\(56\) 0 0
\(57\) −24934.8 + 32962.1i −1.01653 + 1.34378i
\(58\) 49124.6 1.91747
\(59\) −7827.45 −0.292746 −0.146373 0.989230i \(-0.546760\pi\)
−0.146373 + 0.989230i \(0.546760\pi\)
\(60\) −2649.08 2003.95i −0.0949984 0.0718635i
\(61\) 20193.7i 0.694850i −0.937708 0.347425i \(-0.887056\pi\)
0.937708 0.347425i \(-0.112944\pi\)
\(62\) −29237.3 −0.965959
\(63\) 0 0
\(64\) −7989.78 −0.243829
\(65\) 6217.00i 0.182515i
\(66\) −8126.04 6147.10i −0.229625 0.173704i
\(67\) 43937.9 1.19578 0.597892 0.801577i \(-0.296005\pi\)
0.597892 + 0.801577i \(0.296005\pi\)
\(68\) −2978.91 −0.0781241
\(69\) −24618.3 + 32543.7i −0.622495 + 0.822894i
\(70\) 0 0
\(71\) 26028.0i 0.612765i −0.951908 0.306383i \(-0.900881\pi\)
0.951908 0.306383i \(-0.0991187\pi\)
\(72\) −28178.6 + 7966.93i −0.640603 + 0.181117i
\(73\) 50911.3i 1.11817i 0.829111 + 0.559084i \(0.188847\pi\)
−0.829111 + 0.559084i \(0.811153\pi\)
\(74\) 25030.0i 0.531351i
\(75\) −36084.9 27297.1i −0.740751 0.560356i
\(76\) 37881.4i 0.752302i
\(77\) 0 0
\(78\) 35258.0 + 26671.6i 0.656178 + 0.496379i
\(79\) −50114.3 −0.903429 −0.451715 0.892163i \(-0.649187\pi\)
−0.451715 + 0.892163i \(0.649187\pi\)
\(80\) −19046.3 −0.332726
\(81\) −50307.5 + 30918.3i −0.851962 + 0.523604i
\(82\) 105129.i 1.72659i
\(83\) 107835. 1.71817 0.859086 0.511832i \(-0.171033\pi\)
0.859086 + 0.511832i \(0.171033\pi\)
\(84\) 0 0
\(85\) 3109.57 0.0466824
\(86\) 40896.5i 0.596266i
\(87\) 67905.0 89765.6i 0.961842 1.27149i
\(88\) −11577.6 −0.159371
\(89\) 136779. 1.83039 0.915194 0.403013i \(-0.132037\pi\)
0.915194 + 0.403013i \(0.132037\pi\)
\(90\) −23726.6 + 6708.22i −0.308766 + 0.0872973i
\(91\) 0 0
\(92\) 37400.6i 0.460690i
\(93\) −40414.8 + 53425.6i −0.484544 + 0.640533i
\(94\) 26584.2i 0.310316i
\(95\) 39543.0i 0.449531i
\(96\) 45445.1 60075.2i 0.503279 0.665299i
\(97\) 25183.4i 0.271759i 0.990725 + 0.135880i \(0.0433861\pi\)
−0.990725 + 0.135880i \(0.956614\pi\)
\(98\) 0 0
\(99\) −22465.3 + 6351.59i −0.230369 + 0.0651320i
\(100\) 41470.3 0.414703
\(101\) 78062.7 0.761448 0.380724 0.924689i \(-0.375675\pi\)
0.380724 + 0.924689i \(0.375675\pi\)
\(102\) −13340.4 + 17635.1i −0.126960 + 0.167833i
\(103\) 97991.9i 0.910117i 0.890462 + 0.455059i \(0.150382\pi\)
−0.890462 + 0.455059i \(0.849618\pi\)
\(104\) 50233.9 0.455421
\(105\) 0 0
\(106\) 246947. 2.13471
\(107\) 135095.i 1.14072i 0.821395 + 0.570360i \(0.193196\pi\)
−0.821395 + 0.570360i \(0.806804\pi\)
\(108\) 19676.4 50417.2i 0.162325 0.415929i
\(109\) 75132.0 0.605702 0.302851 0.953038i \(-0.402062\pi\)
0.302851 + 0.953038i \(0.402062\pi\)
\(110\) −9748.40 −0.0768160
\(111\) 45737.5 + 34599.0i 0.352342 + 0.266536i
\(112\) 0 0
\(113\) 88078.7i 0.648895i 0.945904 + 0.324448i \(0.105178\pi\)
−0.945904 + 0.324448i \(0.894822\pi\)
\(114\) −224257. 169644.i −1.61616 1.22258i
\(115\) 39041.0i 0.275281i
\(116\) 103163.i 0.711831i
\(117\) 97474.5 27558.9i 0.658304 0.186122i
\(118\) 53254.0i 0.352085i
\(119\) 0 0
\(120\) −16902.3 + 22343.6i −0.107150 + 0.141645i
\(121\) 151821. 0.942688
\(122\) 137388. 0.835695
\(123\) 192103. + 145320.i 1.14491 + 0.866091i
\(124\) 61398.9i 0.358597i
\(125\) −89895.8 −0.514594
\(126\) 0 0
\(127\) −141581. −0.778923 −0.389462 0.921043i \(-0.627339\pi\)
−0.389462 + 0.921043i \(0.627339\pi\)
\(128\) 208991.i 1.12747i
\(129\) −74730.4 56531.3i −0.395388 0.299099i
\(130\) 42297.3 0.219510
\(131\) −153197. −0.779959 −0.389979 0.920824i \(-0.627518\pi\)
−0.389979 + 0.920824i \(0.627518\pi\)
\(132\) 12909.0 17064.8i 0.0644850 0.0852446i
\(133\) 0 0
\(134\) 298931.i 1.43817i
\(135\) −20539.4 + 52628.6i −0.0969960 + 0.248535i
\(136\) 25125.6i 0.116485i
\(137\) 90239.8i 0.410768i 0.978681 + 0.205384i \(0.0658444\pi\)
−0.978681 + 0.205384i \(0.934156\pi\)
\(138\) −221411. 167491.i −0.989694 0.748674i
\(139\) 133215.i 0.584814i −0.956294 0.292407i \(-0.905544\pi\)
0.956294 0.292407i \(-0.0944562\pi\)
\(140\) 0 0
\(141\) −48577.5 36747.4i −0.205772 0.155661i
\(142\) 177081. 0.736972
\(143\) 40048.7 0.163775
\(144\) −84429.1 298621.i −0.339301 1.20009i
\(145\) 107687.i 0.425348i
\(146\) −346374. −1.34482
\(147\) 0 0
\(148\) −52563.5 −0.197256
\(149\) 28153.3i 0.103888i −0.998650 0.0519439i \(-0.983458\pi\)
0.998650 0.0519439i \(-0.0165417\pi\)
\(150\) 185716. 245503.i 0.673939 0.890900i
\(151\) −6546.74 −0.0233659 −0.0116830 0.999932i \(-0.503719\pi\)
−0.0116830 + 0.999932i \(0.503719\pi\)
\(152\) −319510. −1.12170
\(153\) 13784.2 + 48754.0i 0.0476050 + 0.168377i
\(154\) 0 0
\(155\) 64092.0i 0.214276i
\(156\) −56010.9 + 74042.5i −0.184273 + 0.243596i
\(157\) 68166.3i 0.220709i −0.993892 0.110355i \(-0.964801\pi\)
0.993892 0.110355i \(-0.0351986\pi\)
\(158\) 340952.i 1.08655i
\(159\) 341356. 451248.i 1.07081 1.41554i
\(160\) 72069.2i 0.222561i
\(161\) 0 0
\(162\) −210352. 342266.i −0.629738 1.02465i
\(163\) 423816. 1.24942 0.624709 0.780857i \(-0.285217\pi\)
0.624709 + 0.780857i \(0.285217\pi\)
\(164\) −220773. −0.640969
\(165\) −13475.2 + 17813.3i −0.0385324 + 0.0509371i
\(166\) 733657.i 2.06644i
\(167\) −30916.2 −0.0857818 −0.0428909 0.999080i \(-0.513657\pi\)
−0.0428909 + 0.999080i \(0.513657\pi\)
\(168\) 0 0
\(169\) 197526. 0.531995
\(170\) 21155.9i 0.0561448i
\(171\) −619982. + 175287.i −1.62139 + 0.458416i
\(172\) 85883.4 0.221354
\(173\) 179220. 0.455272 0.227636 0.973746i \(-0.426900\pi\)
0.227636 + 0.973746i \(0.426900\pi\)
\(174\) 610719. + 461991.i 1.52921 + 1.15681i
\(175\) 0 0
\(176\) 122693.i 0.298563i
\(177\) −97311.3 73613.1i −0.233469 0.176613i
\(178\) 930572.i 2.20140i
\(179\) 142179.i 0.331667i 0.986154 + 0.165834i \(0.0530315\pi\)
−0.986154 + 0.165834i \(0.946969\pi\)
\(180\) −14087.4 49826.4i −0.0324077 0.114625i
\(181\) 321437.i 0.729288i −0.931147 0.364644i \(-0.881191\pi\)
0.931147 0.364644i \(-0.118809\pi\)
\(182\) 0 0
\(183\) 189911. 251049.i 0.419201 0.554154i
\(184\) −315455. −0.686898
\(185\) 54869.0 0.117868
\(186\) −363480. 274962.i −0.770368 0.582761i
\(187\) 20031.2i 0.0418893i
\(188\) 55827.3 0.115200
\(189\) 0 0
\(190\) −269030. −0.540651
\(191\) 528819.i 1.04887i 0.851449 + 0.524437i \(0.175724\pi\)
−0.851449 + 0.524437i \(0.824276\pi\)
\(192\) −99329.4 75139.7i −0.194457 0.147101i
\(193\) −95232.1 −0.184031 −0.0920153 0.995758i \(-0.529331\pi\)
−0.0920153 + 0.995758i \(0.529331\pi\)
\(194\) −171335. −0.326844
\(195\) 58467.6 77290.1i 0.110111 0.145558i
\(196\) 0 0
\(197\) 705756.i 1.29565i −0.761787 0.647827i \(-0.775678\pi\)
0.761787 0.647827i \(-0.224322\pi\)
\(198\) −43213.0 152842.i −0.0783342 0.277064i
\(199\) 87307.3i 0.156285i −0.996942 0.0781426i \(-0.975101\pi\)
0.996942 0.0781426i \(-0.0248990\pi\)
\(200\) 349780.i 0.618330i
\(201\) 546239. + 413213.i 0.953657 + 0.721413i
\(202\) 531099.i 0.915792i
\(203\) 0 0
\(204\) −37034.0 28015.1i −0.0623053 0.0471321i
\(205\) 230457. 0.383005
\(206\) −666687. −1.09460
\(207\) −612113. + 173062.i −0.992900 + 0.280722i
\(208\) 532350.i 0.853177i
\(209\) −254728. −0.403376
\(210\) 0 0
\(211\) −330657. −0.511294 −0.255647 0.966770i \(-0.582289\pi\)
−0.255647 + 0.966770i \(0.582289\pi\)
\(212\) 518594.i 0.792479i
\(213\) 244779. 323581.i 0.369680 0.488690i
\(214\) −919115. −1.37194
\(215\) −89650.4 −0.132268
\(216\) −425243. 165960.i −0.620159 0.242030i
\(217\) 0 0
\(218\) 511160.i 0.728476i
\(219\) −478794. + 632931.i −0.674587 + 0.891757i
\(220\) 20471.8i 0.0285167i
\(221\) 86913.4i 0.119703i
\(222\) −235394. + 311174.i −0.320563 + 0.423761i
\(223\) 232532.i 0.313128i 0.987668 + 0.156564i \(0.0500417\pi\)
−0.987668 + 0.156564i \(0.949958\pi\)
\(224\) 0 0
\(225\) −191894. 678719.i −0.252700 0.893786i
\(226\) −599242. −0.780425
\(227\) 448252. 0.577375 0.288687 0.957423i \(-0.406781\pi\)
0.288687 + 0.957423i \(0.406781\pi\)
\(228\) 356255. 470944.i 0.453862 0.599973i
\(229\) 576156.i 0.726025i −0.931784 0.363012i \(-0.881748\pi\)
0.931784 0.363012i \(-0.118252\pi\)
\(230\) −265615. −0.331080
\(231\) 0 0
\(232\) 870122. 1.06135
\(233\) 406966.i 0.491098i −0.969384 0.245549i \(-0.921032\pi\)
0.969384 0.245549i \(-0.0789682\pi\)
\(234\) 187497. + 663167.i 0.223848 + 0.791741i
\(235\) −58276.0 −0.0688367
\(236\) 111834. 0.130706
\(237\) −623024. 471299.i −0.720499 0.545036i
\(238\) 0 0
\(239\) 266151.i 0.301393i 0.988580 + 0.150696i \(0.0481516\pi\)
−0.988580 + 0.150696i \(0.951848\pi\)
\(240\) −236785. 179121.i −0.265354 0.200732i
\(241\) 388486.i 0.430857i 0.976520 + 0.215428i \(0.0691148\pi\)
−0.976520 + 0.215428i \(0.930885\pi\)
\(242\) 1.03291e6i 1.13377i
\(243\) −916196. 88737.8i −0.995342 0.0964036i
\(244\) 288516.i 0.310238i
\(245\) 0 0
\(246\) −988685. + 1.30697e6i −1.04165 + 1.37698i
\(247\) 1.10524e6 1.15269
\(248\) −517868. −0.534675
\(249\) 1.34062e6 + 1.01414e6i 1.37027 + 1.03657i
\(250\) 611605.i 0.618901i
\(251\) 1.09673e6 1.09879 0.549397 0.835561i \(-0.314857\pi\)
0.549397 + 0.835561i \(0.314857\pi\)
\(252\) 0 0
\(253\) −251495. −0.247017
\(254\) 963242.i 0.936810i
\(255\) 38658.3 + 29243.9i 0.0372300 + 0.0281634i
\(256\) 1.16620e6 1.11217
\(257\) 100324. 0.0947482 0.0473741 0.998877i \(-0.484915\pi\)
0.0473741 + 0.998877i \(0.484915\pi\)
\(258\) 384610. 508427.i 0.359726 0.475532i
\(259\) 0 0
\(260\) 88825.1i 0.0814896i
\(261\) 1.68840e6 477359.i 1.53417 0.433755i
\(262\) 1.04227e6i 0.938055i
\(263\) 1.30495e6i 1.16333i −0.813427 0.581667i \(-0.802401\pi\)
0.813427 0.581667i \(-0.197599\pi\)
\(264\) −143933. 108881.i −0.127101 0.0961484i
\(265\) 541340.i 0.473539i
\(266\) 0 0
\(267\) 1.70044e6 + 1.28633e6i 1.45976 + 1.10427i
\(268\) −627761. −0.533897
\(269\) 1.26072e6 1.06228 0.531139 0.847285i \(-0.321764\pi\)
0.531139 + 0.847285i \(0.321764\pi\)
\(270\) −358058. 139740.i −0.298912 0.116657i
\(271\) 1.24738e6i 1.03176i −0.856662 0.515878i \(-0.827466\pi\)
0.856662 0.515878i \(-0.172534\pi\)
\(272\) −266267. −0.218220
\(273\) 0 0
\(274\) −613945. −0.494030
\(275\) 278861.i 0.222359i
\(276\) 351733. 464966.i 0.277933 0.367408i
\(277\) 658899. 0.515964 0.257982 0.966150i \(-0.416942\pi\)
0.257982 + 0.966150i \(0.416942\pi\)
\(278\) 906330. 0.703354
\(279\) −1.00488e6 + 284109.i −0.772864 + 0.218511i
\(280\) 0 0
\(281\) 1.28896e6i 0.973809i −0.873455 0.486904i \(-0.838126\pi\)
0.873455 0.486904i \(-0.161874\pi\)
\(282\) 250011. 330496.i 0.187213 0.247482i
\(283\) 1.00909e6i 0.748966i −0.927234 0.374483i \(-0.877820\pi\)
0.927234 0.374483i \(-0.122180\pi\)
\(284\) 371873.i 0.273589i
\(285\) −371881. + 491600.i −0.271201 + 0.358509i
\(286\) 272471.i 0.196972i
\(287\) 0 0
\(288\) 1.12995e6 319470.i 0.802746 0.226960i
\(289\) −1.37639e6 −0.969383
\(290\) 732650. 0.511566
\(291\) −236836. + 313081.i −0.163952 + 0.216733i
\(292\) 727392.i 0.499242i
\(293\) 1.94711e6 1.32502 0.662508 0.749055i \(-0.269492\pi\)
0.662508 + 0.749055i \(0.269492\pi\)
\(294\) 0 0
\(295\) −116739. −0.0781021
\(296\) 443345.i 0.294112i
\(297\) −339023. 132311.i −0.223017 0.0870371i
\(298\) 191541. 0.124946
\(299\) 1.09121e6 0.705878
\(300\) 515561. + 390006.i 0.330732 + 0.250189i
\(301\) 0 0
\(302\) 44540.7i 0.0281022i
\(303\) 970480. + 734139.i 0.607267 + 0.459380i
\(304\) 3.38599e6i 2.10137i
\(305\) 301171.i 0.185380i
\(306\) −331697. + 93780.5i −0.202506 + 0.0572544i
\(307\) 1.97804e6i 1.19782i −0.800818 0.598908i \(-0.795602\pi\)
0.800818 0.598908i \(-0.204398\pi\)
\(308\) 0 0
\(309\) −921563. + 1.21824e6i −0.549071 + 0.725833i
\(310\) −436049. −0.257710
\(311\) −1.07146e6 −0.628169 −0.314084 0.949395i \(-0.601697\pi\)
−0.314084 + 0.949395i \(0.601697\pi\)
\(312\) 624510. + 472423.i 0.363206 + 0.274754i
\(313\) 416279.i 0.240173i 0.992763 + 0.120086i \(0.0383172\pi\)
−0.992763 + 0.120086i \(0.961683\pi\)
\(314\) 463768. 0.265446
\(315\) 0 0
\(316\) 716005. 0.403365
\(317\) 2.89214e6i 1.61648i −0.588851 0.808242i \(-0.700420\pi\)
0.588851 0.808242i \(-0.299580\pi\)
\(318\) 3.07006e6 + 2.32241e6i 1.70247 + 1.28787i
\(319\) 693700. 0.381676
\(320\) −119160. −0.0650515
\(321\) −1.27049e6 + 1.67950e6i −0.688193 + 0.909743i
\(322\) 0 0
\(323\) 552808.i 0.294828i
\(324\) 718765. 441743.i 0.380386 0.233780i
\(325\) 1.20995e6i 0.635416i
\(326\) 2.88342e6i 1.50267i
\(327\) 934045. + 706577.i 0.483057 + 0.365418i
\(328\) 1.86211e6i 0.955697i
\(329\) 0 0
\(330\) −121193. 91678.6i −0.0612620 0.0463429i
\(331\) −3.47755e6 −1.74463 −0.872315 0.488944i \(-0.837382\pi\)
−0.872315 + 0.488944i \(0.837382\pi\)
\(332\) −1.54069e6 −0.767134
\(333\) 243225. + 860274.i 0.120198 + 0.425134i
\(334\) 210338.i 0.103170i
\(335\) 655295. 0.319025
\(336\) 0 0
\(337\) 916887. 0.439786 0.219893 0.975524i \(-0.429429\pi\)
0.219893 + 0.975524i \(0.429429\pi\)
\(338\) 1.34387e6i 0.639829i
\(339\) −828334. + 1.09500e6i −0.391477 + 0.517504i
\(340\) −44427.8 −0.0208429
\(341\) −412868. −0.192276
\(342\) −1.19256e6 4.21804e6i −0.551336 1.95005i
\(343\) 0 0
\(344\) 724382.i 0.330044i
\(345\) −367161. + 485360.i −0.166077 + 0.219541i
\(346\) 1.21932e6i 0.547555i
\(347\) 1.23792e6i 0.551912i 0.961170 + 0.275956i \(0.0889945\pi\)
−0.961170 + 0.275956i \(0.911006\pi\)
\(348\) −970189. + 1.28252e6i −0.429446 + 0.567697i
\(349\) 2.19902e6i 0.966419i 0.875505 + 0.483210i \(0.160529\pi\)
−0.875505 + 0.483210i \(0.839471\pi\)
\(350\) 0 0
\(351\) 1.47098e6 + 574083.i 0.637295 + 0.248718i
\(352\) 464255. 0.199710
\(353\) 2.66911e6 1.14006 0.570032 0.821622i \(-0.306931\pi\)
0.570032 + 0.821622i \(0.306931\pi\)
\(354\) 500826. 662056.i 0.212412 0.280793i
\(355\) 388184.i 0.163481i
\(356\) −1.95422e6 −0.817237
\(357\) 0 0
\(358\) −967312. −0.398896
\(359\) 4.54793e6i 1.86242i 0.364484 + 0.931210i \(0.381245\pi\)
−0.364484 + 0.931210i \(0.618755\pi\)
\(360\) −420259. + 118820.i −0.170908 + 0.0483206i
\(361\) −4.55371e6 −1.83907
\(362\) 2.18689e6 0.877113
\(363\) 1.88744e6 + 1.42780e6i 0.751809 + 0.568721i
\(364\) 0 0
\(365\) 759296.i 0.298318i
\(366\) 1.70801e6 + 1.29206e6i 0.666480 + 0.504173i
\(367\) 2.13509e6i 0.827469i −0.910398 0.413735i \(-0.864224\pi\)
0.910398 0.413735i \(-0.135776\pi\)
\(368\) 3.34301e6i 1.28682i
\(369\) 1.02157e6 + 3.61326e6i 0.390575 + 1.38144i
\(370\) 373300.i 0.141760i
\(371\) 0 0
\(372\) 577425. 763315.i 0.216341 0.285987i
\(373\) −3.25854e6 −1.21269 −0.606346 0.795201i \(-0.707365\pi\)
−0.606346 + 0.795201i \(0.707365\pi\)
\(374\) −136282. −0.0503802
\(375\) −1.11759e6 845423.i −0.410397 0.310453i
\(376\) 470874.i 0.171765i
\(377\) −3.00989e6 −1.09068
\(378\) 0 0
\(379\) −3.32017e6 −1.18730 −0.593652 0.804722i \(-0.702314\pi\)
−0.593652 + 0.804722i \(0.702314\pi\)
\(380\) 564968.i 0.200708i
\(381\) −1.76014e6 1.33149e6i −0.621204 0.469922i
\(382\) −3.59781e6 −1.26148
\(383\) −3.46201e6 −1.20596 −0.602978 0.797758i \(-0.706019\pi\)
−0.602978 + 0.797758i \(0.706019\pi\)
\(384\) 1.96545e6 2.59819e6i 0.680197 0.899173i
\(385\) 0 0
\(386\) 647910.i 0.221333i
\(387\) −397405. 1.40560e6i −0.134882 0.477073i
\(388\) 359806.i 0.121336i
\(389\) 2.49213e6i 0.835018i −0.908673 0.417509i \(-0.862903\pi\)
0.908673 0.417509i \(-0.137097\pi\)
\(390\) 525842. + 397784.i 0.175063 + 0.132430i
\(391\) 545792.i 0.180545i
\(392\) 0 0
\(393\) −1.90455e6 1.44074e6i −0.622030 0.470547i
\(394\) 4.80161e6 1.55828
\(395\) −747410. −0.241027
\(396\) 320971. 90748.0i 0.102856 0.0290803i
\(397\) 3.04840e6i 0.970722i −0.874314 0.485361i \(-0.838688\pi\)
0.874314 0.485361i \(-0.161312\pi\)
\(398\) 593994. 0.187964
\(399\) 0 0
\(400\) 3.70678e6 1.15837
\(401\) 51572.9i 0.0160162i −0.999968 0.00800812i \(-0.997451\pi\)
0.999968 0.00800812i \(-0.00254909\pi\)
\(402\) −2.81129e6 + 3.71633e6i −0.867642 + 1.14696i
\(403\) 1.79139e6 0.549449
\(404\) −1.11532e6 −0.339973
\(405\) −750291. + 461119.i −0.227296 + 0.139693i
\(406\) 0 0
\(407\) 353455.i 0.105766i
\(408\) −236293. + 312362.i −0.0702748 + 0.0928983i
\(409\) 4.53920e6i 1.34175i 0.741571 + 0.670875i \(0.234081\pi\)
−0.741571 + 0.670875i \(0.765919\pi\)
\(410\) 1.56791e6i 0.460639i
\(411\) −848658. + 1.12187e6i −0.247815 + 0.327594i
\(412\) 1.40005e6i 0.406351i
\(413\) 0 0
\(414\) −1.17743e6 4.16450e6i −0.337624 1.19416i
\(415\) 1.60827e6 0.458394
\(416\) −2.01435e6 −0.570693
\(417\) 1.25282e6 1.65614e6i 0.352817 0.466399i
\(418\) 1.73304e6i 0.485140i
\(419\) 1.89078e6 0.526145 0.263072 0.964776i \(-0.415264\pi\)
0.263072 + 0.964776i \(0.415264\pi\)
\(420\) 0 0
\(421\) −5.04901e6 −1.38836 −0.694178 0.719803i \(-0.744232\pi\)
−0.694178 + 0.719803i \(0.744232\pi\)
\(422\) 2.24962e6i 0.614933i
\(423\) −258327. 913691.i −0.0701971 0.248284i
\(424\) 4.37407e6 1.18160
\(425\) −605181. −0.162522
\(426\) 2.20148e6 + 1.66535e6i 0.587747 + 0.444613i
\(427\) 0 0
\(428\) 1.93016e6i 0.509312i
\(429\) 497887. + 376637.i 0.130613 + 0.0988051i
\(430\) 609935.i 0.159079i
\(431\) 3.26850e6i 0.847530i −0.905772 0.423765i \(-0.860708\pi\)
0.905772 0.423765i \(-0.139292\pi\)
\(432\) 1.75875e6 4.50649e6i 0.453414 1.16179i
\(433\) 1.69788e6i 0.435198i 0.976038 + 0.217599i \(0.0698226\pi\)
−0.976038 + 0.217599i \(0.930177\pi\)
\(434\) 0 0
\(435\) 1.01274e6 1.33877e6i 0.256612 0.339222i
\(436\) −1.07344e6 −0.270435
\(437\) −6.94058e6 −1.73857
\(438\) −4.30614e6 3.25747e6i −1.07251 0.811325i
\(439\) 4.42320e6i 1.09541i 0.836673 + 0.547703i \(0.184498\pi\)
−0.836673 + 0.547703i \(0.815502\pi\)
\(440\) −172669. −0.0425190
\(441\) 0 0
\(442\) 591314. 0.143967
\(443\) 5.22017e6i 1.26379i −0.775054 0.631895i \(-0.782277\pi\)
0.775054 0.631895i \(-0.217723\pi\)
\(444\) −653471. 494332.i −0.157315 0.119004i
\(445\) 2.03993e6 0.488332
\(446\) −1.58203e6 −0.376598
\(447\) 264767. 350004.i 0.0626752 0.0828522i
\(448\) 0 0
\(449\) 3.80274e6i 0.890186i 0.895484 + 0.445093i \(0.146829\pi\)
−0.895484 + 0.445093i \(0.853171\pi\)
\(450\) 4.61765e6 1.30555e6i 1.07495 0.303921i
\(451\) 1.48456e6i 0.343681i
\(452\) 1.25842e6i 0.289720i
\(453\) −81389.4 61568.7i −0.0186347 0.0140966i
\(454\) 3.04968e6i 0.694407i
\(455\) 0 0
\(456\) −3.97217e6 3.00482e6i −0.894572 0.676717i
\(457\) 1.83749e6 0.411561 0.205781 0.978598i \(-0.434027\pi\)
0.205781 + 0.978598i \(0.434027\pi\)
\(458\) 3.91987e6 0.873188
\(459\) −287140. + 735745.i −0.0636154 + 0.163003i
\(460\) 557797.i 0.122908i
\(461\) −7.79775e6 −1.70890 −0.854450 0.519533i \(-0.826106\pi\)
−0.854450 + 0.519533i \(0.826106\pi\)
\(462\) 0 0
\(463\) 254809. 0.0552410 0.0276205 0.999618i \(-0.491207\pi\)
0.0276205 + 0.999618i \(0.491207\pi\)
\(464\) 9.22106e6i 1.98832i
\(465\) −602751. + 796795.i −0.129272 + 0.170889i
\(466\) 2.76878e6 0.590642
\(467\) −4.98525e6 −1.05778 −0.528889 0.848691i \(-0.677391\pi\)
−0.528889 + 0.848691i \(0.677391\pi\)
\(468\) −1.39266e6 + 393746.i −0.293921 + 0.0831002i
\(469\) 0 0
\(470\) 396480.i 0.0827897i
\(471\) 641068. 847446.i 0.133153 0.176019i
\(472\) 943264.i 0.194885i
\(473\) 577509.i 0.118688i
\(474\) 3.20648e6 4.23873e6i 0.655514 0.866543i
\(475\) 7.69581e6i 1.56502i
\(476\) 0 0
\(477\) 8.48750e6 2.39967e6i 1.70798 0.482897i
\(478\) −1.81075e6 −0.362485
\(479\) 7.71216e6 1.53581 0.767904 0.640564i \(-0.221300\pi\)
0.767904 + 0.640564i \(0.221300\pi\)
\(480\) 677773. 895968.i 0.134271 0.177496i
\(481\) 1.53360e6i 0.302239i
\(482\) −2.64306e6 −0.518191
\(483\) 0 0
\(484\) −2.16913e6 −0.420894
\(485\) 375588.i 0.0725031i
\(486\) 603727. 6.23332e6i 0.115944 1.19710i
\(487\) −8.12051e6 −1.55153 −0.775767 0.631020i \(-0.782637\pi\)
−0.775767 + 0.631020i \(0.782637\pi\)
\(488\) 2.43348e6 0.462572
\(489\) 5.26890e6 + 3.98576e6i 0.996432 + 0.753771i
\(490\) 0 0
\(491\) 7.72726e6i 1.44651i 0.690581 + 0.723255i \(0.257355\pi\)
−0.690581 + 0.723255i \(0.742645\pi\)
\(492\) −2.74466e6 2.07626e6i −0.511183 0.386695i
\(493\) 1.50546e6i 0.278967i
\(494\) 7.51947e6i 1.38634i
\(495\) −335050. + 94728.4i −0.0614605 + 0.0173767i
\(496\) 5.48808e6i 1.00165i
\(497\) 0 0
\(498\) −6.89966e6 + 9.12086e6i −1.24668 + 1.64802i
\(499\) 2.33074e6 0.419028 0.209514 0.977806i \(-0.432812\pi\)
0.209514 + 0.977806i \(0.432812\pi\)
\(500\) 1.28438e6 0.229757
\(501\) −384352. 290751.i −0.0684124 0.0517519i
\(502\) 7.46161e6i 1.32152i
\(503\) 3.86914e6 0.681859 0.340930 0.940089i \(-0.389258\pi\)
0.340930 + 0.940089i \(0.389258\pi\)
\(504\) 0 0
\(505\) 1.16424e6 0.203148
\(506\) 1.71104e6i 0.297087i
\(507\) 2.45565e6 + 1.85763e6i 0.424275 + 0.320951i
\(508\) 2.02283e6 0.347776
\(509\) −4.29903e6 −0.735489 −0.367744 0.929927i \(-0.619870\pi\)
−0.367744 + 0.929927i \(0.619870\pi\)
\(510\) −198960. + 263011.i −0.0338720 + 0.0447764i
\(511\) 0 0
\(512\) 1.24648e6i 0.210142i
\(513\) −9.35613e6 3.65143e6i −1.56965 0.612589i
\(514\) 682552.i 0.113953i
\(515\) 1.46146e6i 0.242812i
\(516\) 1.06771e6 + 807688.i 0.176534 + 0.133543i
\(517\) 375402.i 0.0617689i
\(518\) 0 0
\(519\) 2.22807e6 + 1.68547e6i 0.363087 + 0.274664i
\(520\) 749193. 0.121503
\(521\) −4.57032e6 −0.737653 −0.368827 0.929498i \(-0.620240\pi\)
−0.368827 + 0.929498i \(0.620240\pi\)
\(522\) 3.24771e6 + 1.14870e7i 0.521676 + 1.84514i
\(523\) 2.15375e6i 0.344304i 0.985070 + 0.172152i \(0.0550720\pi\)
−0.985070 + 0.172152i \(0.944928\pi\)
\(524\) 2.18879e6 0.348238
\(525\) 0 0
\(526\) 8.87821e6 1.39914
\(527\) 896002.i 0.140534i
\(528\) 1.15386e6 1.52532e6i 0.180122 0.238109i
\(529\) −416145. −0.0646555
\(530\) 3.68300e6 0.569524
\(531\) −517486. 1.83032e6i −0.0796457 0.281703i
\(532\) 0 0
\(533\) 6.44133e6i 0.982104i
\(534\) −8.75154e6 + 1.15689e7i −1.32810 + 1.75566i
\(535\) 2.01482e6i 0.304335i
\(536\) 5.29484e6i 0.796051i
\(537\) −1.33712e6 + 1.76757e6i −0.200094 + 0.264510i
\(538\) 8.57730e6i 1.27760i
\(539\) 0 0
\(540\) 293456. 751928.i 0.0433070 0.110967i
\(541\) −5.46624e6 −0.802963 −0.401481 0.915867i \(-0.631505\pi\)
−0.401481 + 0.915867i \(0.631505\pi\)
\(542\) 8.48656e6 1.24089
\(543\) 3.02294e6 3.99612e6i 0.439978 0.581619i
\(544\) 1.00752e6i 0.145968i
\(545\) 1.12053e6 0.161596
\(546\) 0 0
\(547\) 7.32611e6 1.04690 0.523450 0.852056i \(-0.324645\pi\)
0.523450 + 0.852056i \(0.324645\pi\)
\(548\) 1.28930e6i 0.183401i
\(549\) 4.72197e6 1.33504e6i 0.668640 0.189044i
\(550\) 1.89722e6 0.267431
\(551\) 1.91443e7 2.68633
\(552\) −3.92175e6 2.96669e6i −0.547813 0.414404i
\(553\) 0 0
\(554\) 4.48281e6i 0.620549i
\(555\) 682134. + 516014.i 0.0940020 + 0.0711097i
\(556\) 1.90331e6i 0.261109i
\(557\) 7.63525e6i 1.04276i 0.853324 + 0.521381i \(0.174583\pi\)
−0.853324 + 0.521381i \(0.825417\pi\)
\(558\) −1.93293e6 6.83668e6i −0.262803 0.929522i
\(559\) 2.50575e6i 0.339163i
\(560\) 0 0
\(561\) −188383. + 249029.i −0.0252717 + 0.0334074i
\(562\) 8.76942e6 1.17120
\(563\) 2.17576e6 0.289295 0.144648 0.989483i \(-0.453795\pi\)
0.144648 + 0.989483i \(0.453795\pi\)
\(564\) 694048. + 525026.i 0.0918738 + 0.0694998i
\(565\) 1.31361e6i 0.173120i
\(566\) 6.86531e6 0.900780
\(567\) 0 0
\(568\) 3.13656e6 0.407927
\(569\) 8.38705e6i 1.08600i −0.839734 0.542998i \(-0.817289\pi\)
0.839734 0.542998i \(-0.182711\pi\)
\(570\) −3.34459e6 2.53009e6i −0.431178 0.326173i
\(571\) 2.54473e6 0.326626 0.163313 0.986574i \(-0.447782\pi\)
0.163313 + 0.986574i \(0.447782\pi\)
\(572\) −572193. −0.0731228
\(573\) −4.97326e6 + 6.57430e6i −0.632783 + 0.836494i
\(574\) 0 0
\(575\) 7.59813e6i 0.958379i
\(576\) −528218. 1.86828e6i −0.0663372 0.234631i
\(577\) 1.02039e7i 1.27592i −0.770068 0.637962i \(-0.779778\pi\)
0.770068 0.637962i \(-0.220222\pi\)
\(578\) 9.36422e6i 1.16588i
\(579\) −1.18393e6 895608.i −0.146767 0.111025i
\(580\) 1.53858e6i 0.189911i
\(581\) 0 0
\(582\) −2.13004e6 1.61131e6i −0.260664 0.197184i
\(583\) 3.48720e6 0.424919
\(584\) −6.13517e6 −0.744380
\(585\) 1.45375e6 411017.i 0.175630 0.0496558i
\(586\) 1.32471e7i 1.59359i
\(587\) −1.90974e6 −0.228760 −0.114380 0.993437i \(-0.536488\pi\)
−0.114380 + 0.993437i \(0.536488\pi\)
\(588\) 0 0
\(589\) −1.13940e7 −1.35329
\(590\) 794235.i 0.0939332i
\(591\) 6.63727e6 8.77400e6i 0.781665 1.03331i
\(592\) −4.69833e6 −0.550984
\(593\) −9.68502e6 −1.13100 −0.565502 0.824747i \(-0.691317\pi\)
−0.565502 + 0.824747i \(0.691317\pi\)
\(594\) 900175. 2.30654e6i 0.104679 0.268222i
\(595\) 0 0
\(596\) 402239.i 0.0463841i
\(597\) 821080. 1.08541e6i 0.0942865 0.124640i
\(598\) 7.42403e6i 0.848959i
\(599\) 4.03346e6i 0.459315i −0.973271 0.229658i \(-0.926239\pi\)
0.973271 0.229658i \(-0.0737606\pi\)
\(600\) 3.28950e6 4.34849e6i 0.373037 0.493128i
\(601\) 1.16260e7i 1.31293i −0.754356 0.656466i \(-0.772051\pi\)
0.754356 0.656466i \(-0.227949\pi\)
\(602\) 0 0
\(603\) 2.90481e6 + 1.02742e7i 0.325330 + 1.15068i
\(604\) 93536.2 0.0104325
\(605\) 2.26427e6 0.251501
\(606\) −4.99471e6 + 6.60265e6i −0.552495 + 0.730359i
\(607\) 7.51421e6i 0.827774i −0.910328 0.413887i \(-0.864171\pi\)
0.910328 0.413887i \(-0.135829\pi\)
\(608\) 1.28122e7 1.40561
\(609\) 0 0
\(610\) 2.04901e6 0.222956
\(611\) 1.62883e6i 0.176511i
\(612\) −196941. 696570.i −0.0212548 0.0751772i
\(613\) 3.74103e6 0.402105 0.201053 0.979580i \(-0.435564\pi\)
0.201053 + 0.979580i \(0.435564\pi\)
\(614\) 1.34576e7 1.44061
\(615\) 2.86505e6 + 2.16732e6i 0.305453 + 0.231066i
\(616\) 0 0
\(617\) 1.48513e7i 1.57055i −0.619146 0.785276i \(-0.712521\pi\)
0.619146 0.785276i \(-0.287479\pi\)
\(618\) −8.28828e6 6.26984e6i −0.872958 0.660367i
\(619\) 8.36596e6i 0.877585i 0.898588 + 0.438793i \(0.144594\pi\)
−0.898588 + 0.438793i \(0.855406\pi\)
\(620\) 915711.i 0.0956707i
\(621\) −9.23738e6 3.60508e6i −0.961213 0.375134i
\(622\) 7.28969e6i 0.755497i
\(623\) 0 0
\(624\) −5.00647e6 + 6.61820e6i −0.514719 + 0.680423i
\(625\) 7.72981e6 0.791533
\(626\) −2.83215e6 −0.288855
\(627\) −3.16679e6 2.39558e6i −0.321699 0.243356i
\(628\) 973922.i 0.0985428i
\(629\) 767065. 0.0773047
\(630\) 0 0
\(631\) 8.21939e6 0.821800 0.410900 0.911680i \(-0.365215\pi\)
0.410900 + 0.911680i \(0.365215\pi\)
\(632\) 6.03913e6i 0.601426i
\(633\) −4.11074e6 3.10965e6i −0.407766 0.308463i
\(634\) 1.96766e7 1.94414
\(635\) −2.11155e6 −0.207810
\(636\) −4.87710e6 + 6.44718e6i −0.478100 + 0.632015i
\(637\) 0 0
\(638\) 4.71958e6i 0.459041i
\(639\) 6.08622e6 1.72075e6i 0.589651 0.166712i
\(640\) 3.11692e6i 0.300799i
\(641\) 4.93371e6i 0.474273i 0.971476 + 0.237137i \(0.0762089\pi\)
−0.971476 + 0.237137i \(0.923791\pi\)
\(642\) −1.14265e7 8.64380e6i −1.09415 0.827689i
\(643\) 1.06965e7i 1.02027i −0.860094 0.510135i \(-0.829595\pi\)
0.860094 0.510135i \(-0.170405\pi\)
\(644\) 0 0
\(645\) −1.11454e6 843115.i −0.105486 0.0797971i
\(646\) −3.76102e6 −0.354589
\(647\) −8.71767e6 −0.818728 −0.409364 0.912371i \(-0.634249\pi\)
−0.409364 + 0.912371i \(0.634249\pi\)
\(648\) −3.72588e6 6.06241e6i −0.348571 0.567163i
\(649\) 752012.i 0.0700831i
\(650\) −8.23186e6 −0.764213
\(651\) 0 0
\(652\) −6.05524e6 −0.557844
\(653\) 9.86209e6i 0.905078i 0.891745 + 0.452539i \(0.149482\pi\)
−0.891745 + 0.452539i \(0.850518\pi\)
\(654\) −4.80719e6 + 6.35476e6i −0.439488 + 0.580972i
\(655\) −2.28479e6 −0.208087
\(656\) −1.97336e7 −1.79038
\(657\) −1.19048e7 + 3.36583e6i −1.07599 + 0.304214i
\(658\) 0 0
\(659\) 7.63431e6i 0.684788i 0.939556 + 0.342394i \(0.111238\pi\)
−0.939556 + 0.342394i \(0.888762\pi\)
\(660\) 192527. 254507.i 0.0172041 0.0227426i
\(661\) 1.40247e7i 1.24850i 0.781223 + 0.624252i \(0.214596\pi\)
−0.781223 + 0.624252i \(0.785404\pi\)
\(662\) 2.36595e7i 2.09826i
\(663\) 817375. 1.08051e6i 0.0722166 0.0954653i
\(664\) 1.29949e7i 1.14381i
\(665\) 0 0
\(666\) −5.85286e6 + 1.65478e6i −0.511308 + 0.144562i
\(667\) 1.89013e7 1.64504
\(668\) 441714. 0.0383001
\(669\) −2.18684e6 + 2.89085e6i −0.188909 + 0.249724i
\(670\) 4.45829e6i 0.383691i
\(671\) 1.94008e6 0.166347
\(672\) 0 0
\(673\) −1.03156e7 −0.877920 −0.438960 0.898507i \(-0.644653\pi\)
−0.438960 + 0.898507i \(0.644653\pi\)
\(674\) 6.23803e6i 0.528930i
\(675\) 3.99736e6 1.02425e7i 0.337687 0.865262i
\(676\) −2.82214e6 −0.237526
\(677\) 4.53726e6 0.380472 0.190236 0.981738i \(-0.439075\pi\)
0.190236 + 0.981738i \(0.439075\pi\)
\(678\) −7.44981e6 5.63556e6i −0.622402 0.470828i
\(679\) 0 0
\(680\) 374725.i 0.0310771i
\(681\) 5.57269e6 + 4.21558e6i 0.460466 + 0.348329i
\(682\) 2.80894e6i 0.231250i
\(683\) 901559.i 0.0739507i −0.999316 0.0369754i \(-0.988228\pi\)
0.999316 0.0369754i \(-0.0117723\pi\)
\(684\) 8.85796e6 2.50440e6i 0.723925 0.204675i
\(685\) 1.34585e6i 0.109590i
\(686\) 0 0
\(687\) 5.41844e6 7.16280e6i 0.438009 0.579016i
\(688\) 7.67659e6 0.618297
\(689\) −1.51306e7 −1.21425
\(690\) −3.30214e6 2.49797e6i −0.264042 0.199740i
\(691\) 1.71097e7i 1.36316i −0.731742 0.681582i \(-0.761292\pi\)
0.731742 0.681582i \(-0.238708\pi\)
\(692\) −2.56059e6 −0.203271
\(693\) 0 0
\(694\) −8.42220e6 −0.663784
\(695\) 1.98679e6i 0.156023i
\(696\) 1.08174e7 + 8.18304e6i 0.846447 + 0.640312i
\(697\) 3.22177e6 0.251196
\(698\) −1.49610e7 −1.16231
\(699\) 3.82730e6 5.05942e6i 0.296278 0.391658i
\(700\) 0 0
\(701\) 2.02857e6i 0.155917i 0.996957 + 0.0779587i \(0.0248402\pi\)
−0.996957 + 0.0779587i \(0.975160\pi\)
\(702\) −3.90577e6 + 1.00078e7i −0.299132 + 0.766473i
\(703\) 9.75441e6i 0.744411i
\(704\) 767608.i 0.0583724i
\(705\) −724490. 548055.i −0.0548984 0.0415290i
\(706\) 1.81592e7i 1.37115i
\(707\) 0 0
\(708\) 1.39033e6 + 1.05174e6i 0.104240 + 0.0788545i
\(709\) −1.67894e7 −1.25435 −0.627176 0.778878i \(-0.715789\pi\)
−0.627176 + 0.778878i \(0.715789\pi\)
\(710\) 2.64100e6 0.196618
\(711\) −3.31314e6 1.17184e7i −0.245791 0.869351i
\(712\) 1.64828e7i 1.21852i
\(713\) −1.12494e7 −0.828718
\(714\) 0 0
\(715\) 597290. 0.0436939
\(716\) 2.03137e6i 0.148084i
\(717\) −2.50301e6 + 3.30880e6i −0.181829 + 0.240366i
\(718\) −3.09418e7 −2.23993
\(719\) 2.63704e7 1.90237 0.951183 0.308627i \(-0.0998696\pi\)
0.951183 + 0.308627i \(0.0998696\pi\)
\(720\) −1.25918e6 4.45367e6i −0.0905228 0.320175i
\(721\) 0 0
\(722\) 3.09811e7i 2.21184i
\(723\) −3.65351e6 + 4.82968e6i −0.259935 + 0.343615i
\(724\) 4.59251e6i 0.325614i
\(725\) 2.09580e7i 1.48083i
\(726\) −9.71399e6 + 1.28412e7i −0.684000 + 0.904199i
\(727\) 1.63660e7i 1.14844i −0.818702 0.574218i \(-0.805306\pi\)
0.818702 0.574218i \(-0.194694\pi\)
\(728\) 0 0
\(729\) −1.05557e7 9.71953e6i −0.735642 0.677371i
\(730\) −5.16586e6 −0.358786
\(731\) −1.25331e6 −0.0867489
\(732\) −2.71334e6 + 3.58685e6i −0.187166 + 0.247420i
\(733\) 2.65023e7i 1.82189i 0.412525 + 0.910946i \(0.364647\pi\)
−0.412525 + 0.910946i \(0.635353\pi\)
\(734\) 1.45261e7 0.995196
\(735\) 0 0
\(736\) 1.26496e7 0.860759
\(737\) 4.22128e6i 0.286270i
\(738\) −2.45828e7 + 6.95027e6i −1.66146 + 0.469743i
\(739\) −1.36791e7 −0.921397 −0.460698 0.887557i \(-0.652401\pi\)
−0.460698 + 0.887557i \(0.652401\pi\)
\(740\) −783937. −0.0526262
\(741\) 1.37404e7 + 1.03942e7i 0.919290 + 0.695416i
\(742\) 0 0
\(743\) 9.39766e6i 0.624522i 0.949996 + 0.312261i \(0.101086\pi\)
−0.949996 + 0.312261i \(0.898914\pi\)
\(744\) −6.43816e6 4.87028e6i −0.426412 0.322568i
\(745\) 419882.i 0.0277164i
\(746\) 2.21694e7i 1.45850i
\(747\) 7.12918e6 + 2.52156e7i 0.467453 + 1.65336i
\(748\) 286195.i 0.0187029i
\(749\) 0 0
\(750\) 5.75183e6 7.60351e6i 0.373381 0.493584i
\(751\) −1.35043e7 −0.873723 −0.436862 0.899529i \(-0.643910\pi\)
−0.436862 + 0.899529i \(0.643910\pi\)
\(752\) 4.99006e6 0.321782
\(753\) 1.36346e7 + 1.03142e7i 0.876307 + 0.662900i
\(754\) 2.04778e7i 1.31176i
\(755\) −97638.9 −0.00623383
\(756\) 0 0
\(757\) −7.36283e6 −0.466987 −0.233494 0.972358i \(-0.575016\pi\)
−0.233494 + 0.972358i \(0.575016\pi\)
\(758\) 2.25887e7i 1.42797i
\(759\) −3.12659e6 2.36517e6i −0.197000 0.149025i
\(760\) −4.76521e6 −0.299259
\(761\) 2.48311e6 0.155430 0.0777150 0.996976i \(-0.475238\pi\)
0.0777150 + 0.996976i \(0.475238\pi\)
\(762\) 9.05879e6 1.19751e7i 0.565175 0.747121i
\(763\) 0 0
\(764\) 7.55547e6i 0.468304i
\(765\) 205579. + 727122.i 0.0127006 + 0.0449215i
\(766\) 2.35538e7i 1.45040i
\(767\) 3.26290e6i 0.200270i
\(768\) 1.44982e7 + 1.09675e7i 0.886976 + 0.670971i
\(769\) 2.15050e7i 1.31136i 0.755038 + 0.655681i \(0.227618\pi\)
−0.755038 + 0.655681i \(0.772382\pi\)
\(770\) 0 0
\(771\) 1.24723e6 + 943492.i 0.0755632 + 0.0571614i
\(772\) 1.36062e6 0.0821664
\(773\) −9.92550e6 −0.597453 −0.298726 0.954339i \(-0.596562\pi\)
−0.298726 + 0.954339i \(0.596562\pi\)
\(774\) 9.56299e6 2.70374e6i 0.573774 0.162223i
\(775\) 1.24735e7i 0.745993i
\(776\) −3.03478e6 −0.180914
\(777\) 0 0
\(778\) 1.69551e7 1.00427
\(779\) 4.09698e7i 2.41891i